LMFDB - Embedded newform 784.2.m.k.589.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [784,2,Mod(197,784)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(784, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 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("784.197");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 784 = 2^{4} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	784.m (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:	$6.26027151847$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 112)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			589.4
Character	$\chi$	$=$	784.589
Dual form			784.2.m.k.197.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.669670 + 1.24561i) q^{2} +(0.608827 + 0.608827i) q^{3} +(-1.10308 - 1.66829i) q^{4} +(-1.48423 + 1.48423i) q^{5} +(-1.16607 + 0.350647i) q^{6} +(2.81674 - 0.256804i) q^{8} -2.25866i q^{9} +O(q^{10})$	\(q+(-0.669670 + 1.24561i) q^{2} +(0.608827 + 0.608827i) q^{3} +(-1.10308 - 1.66829i) q^{4} +(-1.48423 + 1.48423i) q^{5} +(-1.16607 + 0.350647i) q^{6} +(2.81674 - 0.256804i) q^{8} -2.25866i q^{9} +(-0.854824 - 2.84271i) q^{10} +(2.82452 - 2.82452i) q^{11} +(0.344116 - 1.68729i) q^{12} +(0.990473 + 0.990473i) q^{13} -1.80728 q^{15} +(-1.56641 + 3.68054i) q^{16} +6.15656 q^{17} +(2.81341 + 1.51256i) q^{18} +(2.77648 + 2.77648i) q^{19} +(4.11335 + 0.838901i) q^{20} +(1.62675 + 5.40975i) q^{22} +6.82961i q^{23} +(1.87126 + 1.55856i) q^{24} +0.594143i q^{25} +(-1.89703 + 0.570452i) q^{26} +(3.20161 - 3.20161i) q^{27} +(-3.83574 - 3.83574i) q^{29} +(1.21028 - 2.25116i) q^{30} -4.10261 q^{31} +(-3.53553 - 4.41588i) q^{32} +3.43929 q^{33} +(-4.12286 + 7.66866i) q^{34} +(-3.76811 + 2.49149i) q^{36} +(-0.0542444 + 0.0542444i) q^{37} +(-5.31773 + 1.59908i) q^{38} +1.20605i q^{39} +(-3.79953 + 4.56184i) q^{40} +8.68707i q^{41} +(0.713530 - 0.713530i) q^{43} +(-7.82782 - 1.59645i) q^{44} +(3.35236 + 3.35236i) q^{45} +(-8.50703 - 4.57359i) q^{46} +3.90675 q^{47} +(-3.19449 + 1.28714i) q^{48} +(-0.740070 - 0.397880i) q^{50} +(3.74828 + 3.74828i) q^{51} +(0.559826 - 2.74498i) q^{52} +(5.17243 - 5.17243i) q^{53} +(1.84393 + 6.13199i) q^{54} +8.38446i q^{55} +3.38079i q^{57} +(7.34652 - 2.20915i) q^{58} +(2.32669 - 2.32669i) q^{59} +(1.99358 + 3.01507i) q^{60} +(6.47617 + 6.47617i) q^{61} +(2.74740 - 5.11025i) q^{62} +(7.86810 - 1.44670i) q^{64} -2.94017 q^{65} +(-2.30319 + 4.28401i) q^{66} +(1.09616 + 1.09616i) q^{67} +(-6.79120 - 10.2710i) q^{68} +(-4.15805 + 4.15805i) q^{69} -2.86486i q^{71} +(-0.580033 - 6.36207i) q^{72} +10.3418i q^{73} +(-0.0312415 - 0.103893i) q^{74} +(-0.361731 + 0.361731i) q^{75} +(1.56929 - 7.69467i) q^{76} +(-1.50227 - 0.807659i) q^{78} +6.67261 q^{79} +(-3.13784 - 7.78766i) q^{80} -2.87752 q^{81} +(-10.8207 - 5.81747i) q^{82} +(-10.2078 - 10.2078i) q^{83} +(-9.13773 + 9.13773i) q^{85} +(0.410950 + 1.36661i) q^{86} -4.67061i q^{87} +(7.23061 - 8.68131i) q^{88} +1.34347i q^{89} +(-6.42071 + 1.93076i) q^{90} +(11.3938 - 7.53363i) q^{92} +(-2.49778 - 2.49778i) q^{93} +(-2.61623 + 4.86628i) q^{94} -8.24184 q^{95} +(0.535983 - 4.84104i) q^{96} +18.7539 q^{97} +(-6.37963 - 6.37963i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{2} + 4 q^{4} + 4 q^{5} + 2 q^{6} - 2 q^{8}+O(q^{10}) $ 24 * q + 4 * q^2 + 4 * q^4 + 4 * q^5 + 2 * q^6 - 2 * q^8	$ 24 q + 4 q^{2} + 4 q^{4} + 4 q^{5} + 2 q^{6} - 2 q^{8} - 2 q^{10} + 4 q^{11} + 2 q^{12} + 12 q^{13} - 20 q^{15} - 16 q^{16} + 8 q^{17} - 18 q^{18} - 4 q^{19} + 8 q^{20} + 18 q^{24} - 10 q^{26} + 12 q^{27} + 12 q^{29} + 4 q^{30} + 28 q^{31} - 16 q^{32} + 16 q^{33} + 22 q^{34} - 36 q^{36} + 24 q^{37} + 20 q^{38} + 26 q^{40} - 20 q^{43} - 6 q^{44} - 28 q^{45} + 14 q^{46} - 20 q^{47} - 28 q^{48} + 28 q^{50} - 24 q^{51} - 16 q^{52} + 16 q^{53} + 64 q^{54} + 6 q^{58} - 20 q^{59} - 46 q^{60} + 8 q^{61} - 12 q^{62} + 40 q^{64} - 8 q^{65} - 20 q^{66} - 48 q^{67} + 20 q^{69} + 32 q^{72} + 8 q^{74} - 4 q^{75} + 18 q^{76} + 58 q^{78} + 36 q^{79} - 28 q^{80} + 2 q^{82} + 4 q^{83} + 20 q^{86} + 42 q^{88} + 10 q^{90} + 38 q^{92} - 8 q^{93} - 72 q^{94} + 4 q^{95} - 120 q^{96} + 24 q^{97} - 12 q^{99}+O(q^{100}) $ 24 * q + 4 * q^2 + 4 * q^4 + 4 * q^5 + 2 * q^6 - 2 * q^8 - 2 * q^10 + 4 * q^11 + 2 * q^12 + 12 * q^13 - 20 * q^15 - 16 * q^16 + 8 * q^17 - 18 * q^18 - 4 * q^19 + 8 * q^20 + 18 * q^24 - 10 * q^26 + 12 * q^27 + 12 * q^29 + 4 * q^30 + 28 * q^31 - 16 * q^32 + 16 * q^33 + 22 * q^34 - 36 * q^36 + 24 * q^37 + 20 * q^38 + 26 * q^40 - 20 * q^43 - 6 * q^44 - 28 * q^45 + 14 * q^46 - 20 * q^47 - 28 * q^48 + 28 * q^50 - 24 * q^51 - 16 * q^52 + 16 * q^53 + 64 * q^54 + 6 * q^58 - 20 * q^59 - 46 * q^60 + 8 * q^61 - 12 * q^62 + 40 * q^64 - 8 * q^65 - 20 * q^66 - 48 * q^67 + 20 * q^69 + 32 * q^72 + 8 * q^74 - 4 * q^75 + 18 * q^76 + 58 * q^78 + 36 * q^79 - 28 * q^80 + 2 * q^82 + 4 * q^83 + 20 * q^86 + 42 * q^88 + 10 * q^90 + 38 * q^92 - 8 * q^93 - 72 * q^94 + 4 * q^95 - 120 * q^96 + 24 * q^97 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$.

$n$	$197$	$687$	$689$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$

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 $

$2$	−0.669670	+	1.24561i	−0.473528	+	0.880779i
$2$	−0.669670	+	1.24561i	−0.473528	+	0.880779i
$3$	0.608827	+	0.608827i	0.351507	+	0.351507i	0.860670	−	0.509163i	$-0.170045\pi$
$3$	0.608827	+	0.608827i	0.351507	+	0.351507i	−0.509163	+	0.860670i	$0.670045\pi$
$4$	−1.10308	−	1.66829i	−0.551542	−	0.834147i
$5$	−1.48423	+	1.48423i	−0.663766	+	0.663766i	−0.956266	−	0.292499i	$-0.905513\pi$
$5$	−1.48423	+	1.48423i	−0.663766	+	0.663766i	0.292499	+	0.956266i	$0.405513\pi$
$6$	−1.16607	+	0.350647i	−0.476048	+	0.143151i
$7$		0			0
$7$		0			0
$8$	2.81674	−	0.256804i	0.995870	−	0.0907940i
$9$		−	2.25866i		−	0.752886i
$10$	−0.854824	−	2.84271i	−0.270319	−	0.898943i
$11$	2.82452	−	2.82452i	0.851625	−	0.851625i	−0.138708	−	0.990333i	$-0.544295\pi$
$11$	2.82452	−	2.82452i	0.851625	−	0.851625i	0.990333	+	0.138708i	$0.0442950\pi$
$12$	0.344116	−	1.68729i	0.0993376	−	0.487079i
$13$	0.990473	+	0.990473i	0.274708	+	0.274708i	0.830992	−	0.556284i	$-0.187773\pi$
$13$	0.990473	+	0.990473i	0.274708	+	0.274708i	−0.556284	+	0.830992i	$0.687773\pi$
$14$		0			0
$15$	−1.80728			−0.466636
$16$	−1.56641	+	3.68054i	−0.391603	+	0.920134i
$17$	6.15656			1.49318			0.746592	−	0.665282i	$-0.231689\pi$
$17$	6.15656			1.49318			0.746592	+	0.665282i	$0.231689\pi$
$18$	2.81341	+	1.51256i	0.663126	+	0.356513i
$19$	2.77648	+	2.77648i	0.636968	+	0.636968i	0.949806	−	0.312839i	$-0.101280\pi$
$19$	2.77648	+	2.77648i	0.636968	+	0.636968i	−0.312839	+	0.949806i	$0.601280\pi$
$20$	4.11335	+	0.838901i	0.919774	+	0.187584i
$21$		0			0
$22$	1.62675	+	5.40975i	0.346825	+	1.15336i
$23$			6.82961i			1.42407i	0.702143	+	0.712036i	$0.252227\pi$
$23$			6.82961i			1.42407i	−0.702143	+	0.712036i	$0.747773\pi$
$24$	1.87126	+	1.55856i	0.381969	+	0.318140i
$25$			0.594143i			0.118829i
$26$	−1.89703	+	0.570452i	−0.372039	+	0.111875i
$27$	3.20161	−	3.20161i	0.616151	−	0.616151i
$28$		0			0
$29$	−3.83574	−	3.83574i	−0.712279	−	0.712279i	0.254732	−	0.967012i	$-0.418013\pi$
$29$	−3.83574	−	3.83574i	−0.712279	−	0.712279i	−0.967012	+	0.254732i	$0.918013\pi$
$30$	1.21028	−	2.25116i	0.220966	−	0.411003i
$31$	−4.10261			−0.736851			−0.368425	−	0.929657i	$-0.620103\pi$
$31$	−4.10261			−0.736851			−0.368425	+	0.929657i	$0.620103\pi$
$32$	−3.53553	−	4.41588i	−0.624999	−	0.780625i
$33$	3.43929			0.598704
$34$	−4.12286	+	7.66866i	−0.707065	+	1.31516i
$35$		0			0
$36$	−3.76811	+	2.49149i	−0.628018	+	0.415248i
$37$	−0.0542444	+	0.0542444i	−0.00891773	+	0.00891773i	−0.711552	−	0.702634i	$-0.752007\pi$
$37$	−0.0542444	+	0.0542444i	−0.00891773	+	0.00891773i	0.702634	+	0.711552i	$0.252007\pi$
$38$	−5.31773	+	1.59908i	−0.862650	+	0.259405i
$39$			1.20605i			0.193123i
$40$	−3.79953	+	4.56184i	−0.600759	+	0.721291i
$41$			8.68707i			1.35669i	0.734742	+	0.678346i	$0.237303\pi$
$41$			8.68707i			1.35669i	−0.734742	+	0.678346i	$0.762697\pi$
$42$		0			0
$43$	0.713530	−	0.713530i	0.108812	−	0.108812i	−0.650604	−	0.759417i	$-0.725484\pi$
$43$	0.713530	−	0.713530i	0.108812	−	0.108812i	0.759417	+	0.650604i	$0.225484\pi$
$44$	−7.82782	−	1.59645i	−1.18009	−	0.240674i
$45$	3.35236	+	3.35236i	0.499740	+	0.499740i
$46$	−8.50703	−	4.57359i	−1.25429	−	0.674339i
$47$	3.90675			0.569858			0.284929	−	0.958549i	$-0.408030\pi$
$47$	3.90675			0.569858			0.284929	+	0.958549i	$0.408030\pi$
$48$	−3.19449	+	1.28714i	−0.461084	+	0.185782i
$49$		0			0
$50$	−0.740070	−	0.397880i	−0.104662	−	0.0562687i
$51$	3.74828	+	3.74828i	0.524864	+	0.524864i
$52$	0.559826	−	2.74498i	0.0776339	−	0.380660i
$53$	5.17243	−	5.17243i	0.710488	−	0.710488i	−0.256149	−	0.966637i	$-0.582454\pi$
$53$	5.17243	−	5.17243i	0.710488	−	0.710488i	0.966637	+	0.256149i	$0.0824537\pi$
$54$	1.84393	+	6.13199i	0.250928	+	0.834458i
$55$			8.38446i			1.13056i
$56$		0			0
$57$			3.38079i			0.447797i
$58$	7.34652	−	2.20915i	0.964645	−	0.290076i
$59$	2.32669	−	2.32669i	0.302909	−	0.302909i	−0.539242	−	0.842151i	$-0.681289\pi$
$59$	2.32669	−	2.32669i	0.302909	−	0.302909i	0.842151	+	0.539242i	$0.181289\pi$
$60$	1.99358	+	3.01507i	0.257370	+	0.389243i
$61$	6.47617	+	6.47617i	0.829189	+	0.829189i	0.987405	−	0.158216i	$-0.0505741\pi$
$61$	6.47617	+	6.47617i	0.829189	+	0.829189i	−0.158216	+	0.987405i	$0.550574\pi$
$62$	2.74740	−	5.11025i	0.348920	−	0.649002i
$63$		0			0
$64$	7.86810	−	1.44670i	0.983513	−	0.180838i
$65$	−2.94017			−0.364684
$66$	−2.30319	+	4.28401i	−0.283503	+	0.527325i
$67$	1.09616	+	1.09616i	0.133918	+	0.133918i	0.770888	−	0.636971i	$-0.219813\pi$
$67$	1.09616	+	1.09616i	0.133918	+	0.133918i	−0.636971	+	0.770888i	$0.719813\pi$
$68$	−6.79120	−	10.2710i	−0.823554	−	1.24554i
$69$	−4.15805	+	4.15805i	−0.500571	+	0.500571i
$70$		0			0
$71$		−	2.86486i		−	0.339997i	−0.985444	−	0.169998i	$-0.945624\pi$
$71$		−	2.86486i		−	0.339997i	0.985444	−	0.169998i	$-0.0543762\pi$
$72$	−0.580033	−	6.36207i	−0.0683576	−	0.749777i
$73$			10.3418i			1.21041i	0.796068	+	0.605207i	$0.206910\pi$
$73$			10.3418i			1.21041i	−0.796068	+	0.605207i	$0.793090\pi$
$74$	−0.0312415	−	0.103893i	−0.00363175	−	0.0120773i
$75$	−0.361731	+	0.361731i	−0.0417691	+	0.0417691i
$76$	1.56929	−	7.69467i	0.180010	−	0.882639i
$77$		0			0
$78$	−1.50227	−	0.807659i	−0.170099	−	0.0914493i
$79$	6.67261			0.750727			0.375364	−	0.926878i	$-0.377518\pi$
$79$	6.67261			0.750727			0.375364	+	0.926878i	$0.377518\pi$
$80$	−3.13784	−	7.78766i	−0.350821	−	0.870687i
$81$	−2.87752			−0.319724
$82$	−10.8207	−	5.81747i	−1.19495	−	0.642432i
$83$	−10.2078	−	10.2078i	−1.12045	−	1.12045i	−0.991674	−	0.128776i	$-0.958895\pi$
$83$	−10.2078	−	10.2078i	−1.12045	−	1.12045i	−0.128776	−	0.991674i	$-0.541105\pi$
$84$		0			0
$85$	−9.13773	+	9.13773i	−0.991126	+	0.991126i
$86$	0.410950	+	1.36661i	0.0443139	+	0.147365i
$87$		−	4.67061i		−	0.500742i
$88$	7.23061	−	8.68131i	0.770785	−	0.925430i
$89$			1.34347i			0.142407i	0.997462	+	0.0712036i	$0.0226840\pi$
$89$			1.34347i			0.142407i	−0.997462	+	0.0712036i	$0.977316\pi$
$90$	−6.42071	+	1.93076i	−0.676802	+	0.203519i
$91$		0			0
$92$	11.3938	−	7.53363i	1.18789	−	0.785436i
$93$	−2.49778	−	2.49778i	−0.259008	−	0.259008i
$94$	−2.61623	+	4.86628i	−0.269844	+	0.501919i
$95$	−8.24184			−0.845595
$96$	0.535983	−	4.84104i	0.0547035	−	0.494086i
$97$	18.7539			1.90417			0.952086	−	0.305831i	$-0.0989343\pi$
$97$	18.7539			1.90417			0.952086	+	0.305831i	$0.0989343\pi$
$98$		0			0
$99$	−6.37963	−	6.37963i	−0.641177	−	0.641177i
$100$	0.991206	−	0.655390i	0.0991206	−	0.0655390i
$101$	−3.14576	+	3.14576i	−0.313015	+	0.313015i	−0.846077	−	0.533061i	$-0.821041\pi$
$101$	−3.14576	+	3.14576i	−0.313015	+	0.313015i	0.533061	+	0.846077i	$0.321041\pi$
$102$	−7.17900	+	2.15878i	−0.710827	+	0.213751i
$103$			8.96231i			0.883083i	0.897241	+	0.441541i	$0.145568\pi$
$103$			8.96231i			0.883083i	−0.897241	+	0.441541i	$0.854432\pi$
$104$	3.04427	+	2.53555i	0.298515	+	0.248631i
$105$		0			0
$106$	2.97901	+	9.90665i	0.289347	+	0.962219i
$107$	8.98268	−	8.98268i	0.868388	−	0.868388i	−0.123906	−	0.992294i	$-0.539542\pi$
$107$	8.98268	−	8.98268i	0.868388	−	0.868388i	0.992294	+	0.123906i	$0.0395420\pi$
$108$	−8.87289	−	1.80959i	−0.853794	−	0.174128i
$109$	10.2344	+	10.2344i	0.980278	+	0.980278i	0.999809	−	0.0195308i	$-0.00621725\pi$
$109$	10.2344	+	10.2344i	0.980278	+	0.980278i	−0.0195308	+	0.999809i	$0.506217\pi$
$110$	−10.4438	−	5.61482i	−0.995773	−	0.535352i
$111$	−0.0660510			−0.00626928
$112$		0			0
$113$	2.61081			0.245605			0.122802	−	0.992431i	$-0.460812\pi$
$113$	2.61081			0.245605			0.122802	+	0.992431i	$0.460812\pi$
$114$	−4.21114	−	2.26401i	−0.394410	−	0.212044i
$115$	−10.1367	−	10.1367i	−0.945251	−	0.945251i
$116$	−2.16800	+	10.6303i	−0.201294	+	0.986998i
$117$	2.23714	−	2.23714i	0.206824	−	0.206824i
$118$	1.34003	+	4.45625i	0.123360	+	0.410231i
$119$		0			0
$120$	−5.09063	+	0.464116i	−0.464709	+	0.0423678i
$121$		−	4.95584i		−	0.450531i
$122$	−12.4037	+	3.72988i	−1.12298	+	0.337687i
$123$	−5.28893	+	5.28893i	−0.476886	+	0.476886i
$124$	4.52552	+	6.84436i	0.406404	+	0.614642i
$125$	−8.30298	−	8.30298i	−0.742641	−	0.742641i
$126$		0			0
$127$	−9.68594			−0.859488			−0.429744	−	0.902951i	$-0.641396\pi$
$127$	−9.68594			−0.859488			−0.429744	+	0.902951i	$0.641396\pi$
$128$	−3.46701	+	10.7694i	−0.306443	+	0.951889i
$129$	0.868833			0.0764965
$130$	1.96895	−	3.66231i	0.172688	−	0.321206i
$131$	−9.78833	−	9.78833i	−0.855210	−	0.855210i	0.135559	−	0.990769i	$-0.456717\pi$
$131$	−9.78833	−	9.78833i	−0.855210	−	0.855210i	−0.990769	+	0.135559i	$0.956717\pi$
$132$	−3.79383	−	5.73775i	−0.330210	−	0.499407i
$133$		0			0
$134$	−2.09946	+	0.631323i	−0.181366	+	0.0545380i
$135$			9.50384i			0.817961i
$136$	17.3415	−	1.58103i	1.48702	−	0.135572i
$137$			11.3214i			0.967252i	0.875275	+	0.483626i	$0.160681\pi$
$137$			11.3214i			0.967252i	−0.875275	+	0.483626i	$0.839319\pi$
$138$	−2.39479	−	7.96383i	−0.203858	−	0.677927i
$139$	−2.29276	+	2.29276i	−0.194469	+	0.194469i	−0.797624	−	0.603155i	$-0.793910\pi$
$139$	−2.29276	+	2.29276i	−0.194469	+	0.194469i	0.603155	+	0.797624i	$0.293910\pi$
$140$		0			0
$141$	2.37854	+	2.37854i	0.200309	+	0.200309i
$142$	3.56850	+	1.91851i	0.299462	+	0.160998i
$143$	5.59523			0.467896
$144$	8.31308	+	3.53799i	0.692756	+	0.294833i
$145$	11.3862			0.945574
$146$	−12.8818	−	6.92558i	−1.06611	−	0.573165i
$147$		0			0
$148$	0.150332	+	0.0306595i	0.0123572	+	0.00252020i
$149$	−1.33453	+	1.33453i	−0.109329	+	0.109329i	−0.759655	−	0.650326i	$-0.774632\pi$
$149$	−1.33453	+	1.33453i	−0.109329	+	0.109329i	0.650326	+	0.759655i	$0.274632\pi$
$150$	−0.208335	−	0.692815i	−0.0170105	−	0.0565681i
$151$		−	14.2301i		−	1.15803i	−0.815319	−	0.579013i	$-0.803438\pi$
$151$		−	14.2301i		−	1.15803i	0.815319	−	0.579013i	$-0.196562\pi$
$152$	8.53364	+	7.10762i	0.692170	+	0.576504i
$153$		−	13.9056i		−	1.12420i
$154$		0			0
$155$	6.08920	−	6.08920i	0.489097	−	0.489097i
$156$	2.01205	−	1.33038i	0.161093	−	0.106516i
$157$	13.7127	+	13.7127i	1.09440	+	1.09440i	0.995053	+	0.0993429i	$0.0316741\pi$
$157$	13.7127	+	13.7127i	1.09440	+	1.09440i	0.0993429	+	0.995053i	$0.468326\pi$
$158$	−4.46845	+	8.31147i	−0.355491	+	0.661225i
$159$	6.29824			0.499483
$160$	11.8017	+	1.30664i	0.933006	+	0.103299i
$161$		0			0
$162$	1.92699	−	3.58426i	0.151398	−	0.281606i
$163$	−3.00462	−	3.00462i	−0.235340	−	0.235340i	0.579577	−	0.814917i	$-0.303218\pi$
$163$	−3.00462	−	3.00462i	−0.235340	−	0.235340i	−0.814917	+	0.579577i	$0.803218\pi$
$164$	14.4926	−	9.58257i	1.13168	−	0.748273i
$165$	−5.10469	+	5.10469i	−0.397399	+	0.397399i
$166$	19.5508	−	5.87906i	1.51743	−	0.456303i
$167$		−	12.2720i		−	0.949638i	−0.880084	−	0.474819i	$-0.842514\pi$
$167$		−	12.2720i		−	0.949638i	0.880084	−	0.474819i	$-0.157486\pi$
$168$		0			0
$169$		−	11.0379i		−	0.849071i
$170$	−5.26277	−	17.5013i	−0.403636	−	1.34229i
$171$	6.27111	−	6.27111i	0.479564	−	0.479564i
$172$	−1.97746	−	0.403295i	−0.150780	−	0.0307509i
$173$	−10.5567	−	10.5567i	−0.802610	−	0.802610i	0.180893	−	0.983503i	$-0.442101\pi$
$173$	−10.5567	−	10.5567i	−0.802610	−	0.802610i	−0.983503	+	0.180893i	$0.942101\pi$
$174$	5.81775	+	3.12777i	0.441043	+	0.237115i
$175$		0			0
$176$	5.97139	+	14.8201i	0.450110	+	1.11711i
$177$	2.83310			0.212949
$178$	−1.67343	−	0.899679i	−0.125429	−	0.0674338i
$179$	4.83087	+	4.83087i	0.361076	+	0.361076i	0.864209	−	0.503133i	$-0.167819\pi$
$179$	4.83087	+	4.83087i	0.361076	+	0.361076i	−0.503133	+	0.864209i	$0.667819\pi$
$180$	1.89479	−	9.29066i	0.141229	−	0.692485i
$181$	−5.61848	+	5.61848i	−0.417618	+	0.417618i	−0.884382	−	0.466764i	$-0.845420\pi$
$181$	−5.61848	+	5.61848i	−0.417618	+	0.417618i	0.466764	+	0.884382i	$0.345420\pi$
$182$		0			0
$183$			7.88574i			0.582931i
$184$	1.75387	+	19.2373i	0.129297	+	1.41819i
$185$		−	0.161022i		−	0.0118386i
$186$	4.78395	−	1.43857i	0.350776	−	0.105481i
$187$	17.3893	−	17.3893i	1.27163	−	1.27163i
$188$	−4.30947	−	6.51761i	−0.314301	−	0.475345i
$189$		0			0
$190$	5.51932	−	10.2661i	0.400413	−	0.744782i
$191$	−6.39882			−0.463002			−0.231501	−	0.972835i	$-0.574364\pi$
$191$	−6.39882			−0.463002			−0.231501	+	0.972835i	$0.574364\pi$
$192$	5.67111	+	3.90952i	0.409277	+	0.282146i
$193$	−9.81524			−0.706517			−0.353258	−	0.935526i	$-0.614926\pi$
$193$	−9.81524			−0.706517			−0.353258	+	0.935526i	$0.614926\pi$
$194$	−12.5589	+	23.3600i	−0.901679	+	1.67715i
$195$	−1.79006	−	1.79006i	−0.128189	−	0.128189i
$196$		0			0
$197$	14.8073	−	14.8073i	1.05498	−	1.05498i	0.0565783	−	0.998398i	$-0.481981\pi$
$197$	14.8073	−	14.8073i	1.05498	−	1.05498i	0.998398	−	0.0565783i	$-0.0180191\pi$
$198$	12.2188	−	3.67428i	0.868350	−	0.261119i
$199$			4.34547i			0.308042i	0.988068	+	0.154021i	$0.0492224\pi$
$199$			4.34547i			0.308042i	−0.988068	+	0.154021i	$0.950778\pi$
$200$	0.152578	+	1.67355i	0.0107889	+	0.118338i
$201$			1.33475i			0.0941458i
$202$	−1.81177	−	6.02501i	−0.127476	−	0.423919i
$203$		0			0
$204$	2.11857	−	10.3879i	0.148329	−	0.727299i
$205$	−12.8936	−	12.8936i	−0.900527	−	0.900527i
$206$	−11.1635	−	6.00179i	−0.777800	−	0.418165i
$207$	15.4258			1.07216
$208$	−5.19696	+	2.09398i	−0.360345	+	0.145192i
$209$	15.6844			1.08492
$210$		0			0
$211$	−14.5998	−	14.5998i	−1.00509	−	1.00509i	−0.999987	−	0.00510394i	$-0.998375\pi$
$211$	−14.5998	−	14.5998i	−1.00509	−	1.00509i	−0.00510394	−	0.999987i	$-0.501625\pi$
$212$	−14.3348	−	2.92351i	−0.984516	−	0.200788i
$213$	1.74421	−	1.74421i	0.119511	−	0.119511i
$214$	5.17347	+	17.2043i	0.353651	+	1.17606i
$215$			2.11808i			0.144452i
$216$	8.19594	−	9.84032i	0.557663	−	0.669549i
$217$		0			0
$218$	−19.6017	+	5.89439i	−1.32760	+	0.399219i
$219$	−6.29636	+	6.29636i	−0.425468	+	0.425468i
$220$	13.9877	−	9.24876i	0.943054	−	0.623551i
$221$	6.09791	+	6.09791i	0.410190	+	0.410190i
$222$	0.0442324	−	0.0822737i	0.00296868	−	0.00552185i
$223$	−0.272719			−0.0182626			−0.00913130	−	0.999958i	$-0.502907\pi$
$223$	−0.272719			−0.0182626			−0.00913130	+	0.999958i	$0.502907\pi$
$224$		0			0
$225$	1.34197			0.0894645
$226$	−1.74838	+	3.25205i	−0.116301	+	0.216323i
$227$	−8.06734	−	8.06734i	−0.535448	−	0.535448i	0.386741	−	0.922189i	$-0.373601\pi$
$227$	−8.06734	−	8.06734i	−0.535448	−	0.535448i	−0.922189	+	0.386741i	$0.873601\pi$
$228$	5.64015	−	3.72930i	0.373528	−	0.246979i
$229$	−11.1110	+	11.1110i	−0.734234	+	0.734234i	−0.971456	−	0.237222i	$-0.923763\pi$
$229$	−11.1110	+	11.1110i	−0.734234	+	0.734234i	0.237222	+	0.971456i	$0.423763\pi$
$230$	19.4146	−	5.83812i	1.28016	−	0.384954i
$231$		0			0
$232$	−11.7893	−	9.81927i	−0.774008	−	0.644667i
$233$		−	5.72415i		−	0.375001i	−0.982264	−	0.187501i	$-0.939961\pi$
$233$		−	5.72415i		−	0.375001i	0.982264	−	0.187501i	$-0.0600387\pi$
$234$	1.28846	+	4.28475i	0.0842291	+	0.280103i
$235$	−5.79850	+	5.79850i	−0.378252	+	0.378252i
$236$	−6.44813	−	1.31507i	−0.419737	−	0.0856036i
$237$	4.06247	+	4.06247i	0.263886	+	0.263886i
$238$		0			0
$239$	14.5430			0.940708			0.470354	−	0.882478i	$-0.344126\pi$
$239$	14.5430			0.940708			0.470354	+	0.882478i	$0.344126\pi$
$240$	2.83094	−	6.65174i	0.182736	−	0.429368i
$241$	3.01824			0.194422			0.0972111	−	0.995264i	$-0.469008\pi$
$241$	3.01824			0.194422			0.0972111	+	0.995264i	$0.469008\pi$
$242$	6.17304	+	3.31878i	0.396818	+	0.213339i
$243$	−11.3568	−	11.3568i	−0.728536	−	0.728536i
$244$	3.66040	−	17.9479i	0.234333	−	1.14900i
$245$		0			0
$246$	−3.04610	−	10.1298i	−0.194212	−	0.645851i
$247$			5.50005i			0.349960i
$248$	−11.5560	+	1.05357i	−0.733807	+	0.0669016i
$249$		−	12.4296i		−	0.787691i
$250$	15.9025	−	4.78201i	1.00576	−	0.302441i
$251$	13.5264	−	13.5264i	0.853777	−	0.853777i	−0.136819	−	0.990596i	$-0.543688\pi$
$251$	13.5264	−	13.5264i	0.853777	−	0.853777i	0.990596	+	0.136819i	$0.0436880\pi$
$252$		0			0
$253$	19.2904	+	19.2904i	1.21278	+	1.21278i
$254$	6.48638	−	12.0649i	0.406992	−	0.757018i
$255$	−11.1266			−0.696774
$256$	−11.0927	−	11.5305i	−0.693294	−	0.720655i
$257$	−3.04827			−0.190146			−0.0950728	−	0.995470i	$-0.530308\pi$
$257$	−3.04827			−0.190146			−0.0950728	+	0.995470i	$0.530308\pi$
$258$	−0.581832	+	1.08223i	−0.0362233	+	0.0673765i
$259$		0			0
$260$	3.24326	+	4.90508i	0.201138	+	0.304200i
$261$	−8.66363	+	8.66363i	−0.536265	+	0.536265i
$262$	18.7474	−	5.63748i	1.15822	−	0.348285i
$263$		−	26.9916i		−	1.66438i	−0.554494	−	0.832188i	$-0.687088\pi$
$263$		−	26.9916i		−	1.66438i	0.554494	−	0.832188i	$-0.312912\pi$
$264$	9.68761	−	0.883225i	0.596231	−	0.0543587i
$265$			15.3541i			0.943197i
$266$		0			0
$267$	−0.817939	+	0.817939i	−0.0500570	+	0.0500570i
$268$	0.619563	−	3.03788i	0.0378458	−	0.185568i
$269$	−12.8683	−	12.8683i	−0.784596	−	0.784596i	0.196007	−	0.980603i	$-0.437202\pi$
$269$	−12.8683	−	12.8683i	−0.784596	−	0.784596i	−0.980603	+	0.196007i	$0.937202\pi$
$270$	−11.8381	−	6.36444i	−0.720442	−	0.387327i
$271$	−31.3082			−1.90183			−0.950917	−	0.309445i	$-0.899857\pi$
$271$	−31.3082			−1.90183			−0.950917	+	0.309445i	$0.899857\pi$
$272$	−9.64371	+	22.6594i	−0.584736	+	1.37393i
$273$		0			0
$274$	−14.1020	−	7.58160i	−0.851935	−	0.458021i
$275$	1.67817	+	1.67817i	0.101197	+	0.101197i
$276$	11.5235	+	2.35018i	0.693636	+	0.141464i
$277$	11.6413	−	11.6413i	0.699457	−	0.699457i	−0.264837	−	0.964293i	$-0.585318\pi$
$277$	11.6413	−	11.6413i	0.699457	−	0.699457i	0.964293	+	0.264837i	$0.0853180\pi$
$278$	−1.32049	−	4.39127i	−0.0791977	−	0.263371i
$279$			9.26640i			0.554765i
$280$		0			0
$281$			25.4166i			1.51622i	0.652124	+	0.758112i	$0.273878\pi$
$281$			25.4166i			1.51622i	−0.652124	+	0.758112i	$0.726122\pi$
$282$	−4.55556	+	1.36989i	−0.271280	+	0.0815758i
$283$	−4.40095	+	4.40095i	−0.261609	+	0.261609i	−0.825708	−	0.564098i	$-0.809224\pi$
$283$	−4.40095	+	4.40095i	−0.261609	+	0.261609i	0.564098	+	0.825708i	$0.309224\pi$
$284$	−4.77943	+	3.16018i	−0.283607	+	0.187522i
$285$	−5.01786	−	5.01786i	−0.297232	−	0.297232i
$286$	−3.74696	+	6.96947i	−0.221562	+	0.412113i
$287$		0			0
$288$	−9.97397	+	7.98556i	−0.587722	+	0.470553i
$289$	20.9032			1.22960
$290$	−7.62501	+	14.1828i	−0.447756	+	0.832841i
$291$	11.4179	+	11.4179i	0.669329	+	0.669329i
$292$	17.2531	−	11.4078i	1.00966	−	0.667594i
$293$	−18.5820	+	18.5820i	−1.08557	+	1.08557i	−0.0895915	+	0.995979i	$0.528556\pi$
$293$	−18.5820	+	18.5820i	−1.08557	+	1.08557i	−0.995979	+	0.0895915i	$0.971444\pi$
$294$		0			0
$295$			6.90666i			0.402121i
$296$	−0.138863	+	0.166723i	−0.00807122	+	0.00969057i
$297$		−	18.0861i		−	1.04946i
$298$	−0.768609	−	2.55600i	−0.0445243	−	0.148065i
$299$	−6.76455	+	6.76455i	−0.391204	+	0.391204i
$300$	1.00249	+	0.204454i	0.0578789	+	0.0118042i
$301$		0			0
$302$	17.7251	+	9.52944i	1.01996	+	0.548358i
$303$	−3.83045			−0.220054
$304$	−14.5680	+	5.86982i	−0.835534	+	0.336657i
$305$	−19.2242			−1.10078
$306$	17.3209	+	9.31214i	0.990170	+	0.532340i
$307$	−19.0620	−	19.0620i	−1.08792	−	1.08792i	−0.995742	−	0.0921822i	$-0.970616\pi$
$307$	−19.0620	−	19.0620i	−1.08792	−	1.08792i	−0.0921822	−	0.995742i	$-0.529384\pi$
$308$		0			0
$309$	−5.45650	+	5.45650i	−0.310409	+	0.310409i
$310$	3.50701	+	11.6625i	0.199185	+	0.662387i
$311$		−	6.87255i		−	0.389707i	−0.980832	−	0.194853i	$-0.937577\pi$
$311$		−	6.87255i		−	0.389707i	0.980832	−	0.194853i	$-0.0624231\pi$
$312$	0.309720	+	3.39715i	0.0175344	+	0.192326i
$313$		−	8.02235i		−	0.453450i	−0.973959	−	0.226725i	$-0.927198\pi$
$313$		−	8.02235i		−	0.453450i	0.973959	−	0.226725i	$-0.0728019\pi$
$314$	−26.2637	+	7.89770i	−1.48215	+	0.445693i
$315$		0			0
$316$	−7.36045	−	11.1319i	−0.414058	−	0.626217i
$317$	1.96643	+	1.96643i	0.110446	+	0.110446i	0.760170	−	0.649724i	$-0.225116\pi$
$317$	1.96643	+	1.96643i	0.110446	+	0.110446i	−0.649724	+	0.760170i	$0.725116\pi$
$318$	−4.21774	+	7.84514i	−0.236519	+	0.439934i
$319$	−21.6683			−1.21319
$320$	−9.53081	+	13.8253i	−0.532789	+	0.772857i
$321$	10.9378			0.610488
$322$		0			0
$323$	17.0935	+	17.0935i	0.951110	+	0.951110i
$324$	3.17414	+	4.80054i	0.176341	+	0.266697i
$325$	−0.588483	+	0.588483i	−0.0326432	+	0.0326432i
$326$	5.75468	−	1.73048i	0.318722	−	0.0958422i
$327$			12.4620i			0.689149i
$328$	2.23088	+	24.4693i	0.123180	+	1.35109i
$329$		0			0
$330$	−2.93999	−	9.77690i	−0.161841	−	0.538201i
$331$	−7.59879	+	7.59879i	−0.417667	+	0.417667i	−0.884399	−	0.466732i	$-0.845431\pi$
$331$	−7.59879	+	7.59879i	−0.417667	+	0.417667i	0.466732	+	0.884399i	$0.345431\pi$
$332$	−5.76955	+	28.2896i	−0.316645	+	1.55259i
$333$	0.122520	+	0.122520i	0.00671404	+	0.00671404i
$334$	15.2861	+	8.21821i	0.836420	+	0.449680i
$335$	−3.25391			−0.177780
$336$		0			0
$337$	16.4062			0.893704			0.446852	−	0.894608i	$-0.352545\pi$
$337$	16.4062			0.893704			0.446852	+	0.894608i	$0.352545\pi$
$338$	13.7489	+	7.39177i	0.747844	+	0.402059i
$339$	1.58953	+	1.58953i	0.0863316	+	0.0863316i
$340$	25.3241	+	5.16474i	1.37339	+	0.280097i
$341$	−11.5879	+	11.5879i	−0.627521	+	0.627521i
$342$	3.61178	+	12.0109i	0.195303	+	0.649477i
$343$		0			0
$344$	1.82660	−	2.19307i	0.0984834	−	0.118242i
$345$		−	12.3430i		−	0.664524i
$346$	20.2190	−	6.08000i	1.08698	−	0.326863i
$347$	−25.6609	+	25.6609i	−1.37755	+	1.37755i	−0.528812	+	0.848739i	$0.677362\pi$
$347$	−25.6609	+	25.6609i	−1.37755	+	1.37755i	−0.848739	+	0.528812i	$0.822638\pi$
$348$	−7.79195	+	5.15207i	−0.417692	+	0.276180i
$349$	−10.3424	−	10.3424i	−0.553614	−	0.553614i	0.373868	−	0.927482i	$-0.378031\pi$
$349$	−10.3424	−	10.3424i	−0.553614	−	0.553614i	−0.927482	+	0.373868i	$0.878031\pi$
$350$		0			0
$351$	6.34223			0.338523
$352$	−22.4589	−	2.48657i	−1.19707	−	0.132535i
$353$	−9.14998			−0.487005			−0.243502	−	0.969900i	$-0.578296\pi$
$353$	−9.14998			−0.487005			−0.243502	+	0.969900i	$0.578296\pi$
$354$	−1.89724	+	3.52893i	−0.100837	+	0.187561i
$355$	4.25210	+	4.25210i	0.225678	+	0.225678i
$356$	2.24130	−	1.48196i	0.118789	−	0.0785435i
$357$		0			0
$358$	−9.25247	+	2.78229i	−0.489008	+	0.147049i
$359$		−	8.42864i		−	0.444847i	−0.974950	−	0.222423i	$-0.928603\pi$
$359$		−	8.42864i		−	0.444847i	0.974950	−	0.222423i	$-0.0713967\pi$
$360$	10.3036	+	8.58185i	0.543050	+	0.452303i
$361$		−	3.58235i		−	0.188545i
$362$	−3.23590	−	10.7610i	−0.170075	−	0.565583i
$363$	3.01725	−	3.01725i	0.158365	−	0.158365i
$364$		0			0
$365$	−15.3495	−	15.3495i	−0.803432	−	0.803432i
$366$	−9.82255	−	5.28085i	−0.513433	−	0.276034i
$367$	−9.30363			−0.485646			−0.242823	−	0.970071i	$-0.578073\pi$
$367$	−9.30363			−0.485646			−0.242823	+	0.970071i	$0.578073\pi$
$368$	−25.1366	−	10.6980i	−1.31034	−	0.557671i
$369$	19.6211			1.02144
$370$	0.200571	+	0.107832i	0.0104272	+	0.00560590i
$371$		0			0
$372$	−1.41177	+	6.92230i	−0.0731970	+	0.358904i
$373$	14.5173	−	14.5173i	0.751677	−	0.751677i	−0.223115	−	0.974792i	$-0.571623\pi$
$373$	14.5173	−	14.5173i	0.751677	−	0.751677i	0.974792	+	0.223115i	$0.0716227\pi$
$374$	10.0152	+	33.3054i	0.517873	+	1.72218i
$375$		−	10.1102i		−	0.522086i
$376$	11.0043	−	1.00327i	0.567504	−	0.0517397i
$377$		−	7.59840i		−	0.391337i
$378$		0			0
$379$	−9.02290	+	9.02290i	−0.463475	+	0.463475i	−0.899793	−	0.436317i	$-0.856282\pi$
$379$	−9.02290	+	9.02290i	−0.463475	+	0.463475i	0.436317	+	0.899793i	$0.356282\pi$
$380$	9.09144	+	13.7498i	0.466381	+	0.705351i
$381$	−5.89706	−	5.89706i	−0.302116	−	0.302116i
$382$	4.28510	−	7.97042i	0.219245	−	0.407802i
$383$	1.12560			0.0575152			0.0287576	−	0.999586i	$-0.490845\pi$
$383$	1.12560			0.0575152			0.0287576	+	0.999586i	$0.490845\pi$
$384$	−8.66751	+	4.44589i	−0.442312	+	0.226879i
$385$		0			0
$386$	6.57298	−	12.2260i	0.334556	−	0.622285i
$387$	−1.61162	−	1.61162i	−0.0819233	−	0.0819233i
$388$	−20.6871	−	31.2871i	−1.05023	−	1.58836i
$389$	12.2214	−	12.2214i	0.619650	−	0.619650i	−0.325792	−	0.945441i	$-0.605631\pi$
$389$	12.2214	−	12.2214i	0.619650	−	0.619650i	0.945441	+	0.325792i	$0.105631\pi$
$390$	3.42846	−	1.03096i	0.173607	−	0.0522049i
$391$			42.0469i			2.12640i
$392$		0			0
$393$		−	11.9188i		−	0.601224i
$394$	8.52810	+	28.3601i	0.429639	+	1.42876i
$395$	−9.90367	+	9.90367i	−0.498308	+	0.498308i
$396$	−3.60583	+	17.6804i	−0.181200	+	0.888472i
$397$	−20.0508	−	20.0508i	−1.00632	−	1.00632i	−0.999980	−	0.00634293i	$-0.997981\pi$
$397$	−20.0508	−	20.0508i	−1.00632	−	1.00632i	−0.00634293	−	0.999980i	$-0.502019\pi$
$398$	−5.41276	−	2.91003i	−0.271317	−	0.145867i
$399$		0			0
$400$	−2.18677	−	0.930673i	−0.109338	−	0.0465337i
$401$	−22.5272			−1.12495			−0.562477	−	0.826813i	$-0.690151\pi$
$401$	−22.5272			−1.12495			−0.562477	+	0.826813i	$0.690151\pi$
$402$	−1.66257	−	0.893841i	−0.0829216	−	0.0445807i
$403$	−4.06353	−	4.06353i	−0.202419	−	0.202419i
$404$	8.71810	+	1.77802i	0.433742	+	0.0884597i
$405$	4.27088	−	4.27088i	0.212222	−	0.212222i
$406$		0			0
$407$			0.306429i			0.0151891i
$408$	11.5205	+	9.59537i	0.570351	+	0.475042i
$409$			30.8657i			1.52621i	0.646275	+	0.763105i	$0.276326\pi$
$409$			30.8657i			1.52621i	−0.646275	+	0.763105i	$0.723674\pi$
$410$	24.6948	−	7.42592i	1.21959	−	0.366740i
$411$	−6.89277	+	6.89277i	−0.339995	+	0.339995i
$412$	14.9518	−	9.88618i	0.736621	−	0.487057i
$413$		0			0
$414$	−10.3302	+	19.2145i	−0.507700	+	0.944340i
$415$	30.3013			1.48743
$416$	0.871966	−	7.87566i	0.0427516	−	0.386136i
$417$	−2.79179			−0.136714
$418$	−10.5034	+	19.5367i	−0.513738	+	0.955570i
$419$	7.74947	+	7.74947i	0.378586	+	0.378586i	0.870592	−	0.492006i	$-0.163736\pi$
$419$	7.74947	+	7.74947i	0.378586	+	0.378586i	−0.492006	+	0.870592i	$0.663736\pi$
$420$		0			0
$421$	−12.7552	+	12.7552i	−0.621651	+	0.621651i	−0.945953	−	0.324302i	$-0.894870\pi$
$421$	−12.7552	+	12.7552i	−0.621651	+	0.621651i	0.324302	+	0.945953i	$0.394870\pi$
$422$	27.9627	−	8.40859i	1.36120	−	0.409324i
$423$		−	8.82401i		−	0.429038i
$424$	13.2411	−	15.8977i	0.643046	−	0.772062i
$425$			3.65788i			0.177433i
$426$	1.00456	+	3.34064i	0.0486709	+	0.161855i
$427$		0			0
$428$	−24.8944	−	5.07710i	−1.20332	−	0.245411i
$429$	3.40653	+	3.40653i	0.164469	+	0.164469i
$430$	−2.63830	−	1.41842i	−0.127230	−	0.0684021i
$431$	9.85361			0.474632			0.237316	−	0.971433i	$-0.423732\pi$
$431$	9.85361			0.474632			0.237316	+	0.971433i	$0.423732\pi$
$432$	6.76861	+	16.7987i	0.325655	+	0.808228i
$433$	−14.9150			−0.716769			−0.358385	−	0.933574i	$-0.616672\pi$
$433$	−14.9150			−0.716769			−0.358385	+	0.933574i	$0.616672\pi$
$434$		0			0
$435$	6.93224	+	6.93224i	0.332375	+	0.332375i
$436$	5.78460	−	28.3634i	0.277032	−	1.35836i
$437$	−18.9623	+	18.9623i	−0.907088	+	0.907088i
$438$	−3.62632	−	12.0593i	−0.173272	−	0.576215i
$439$			9.29191i			0.443479i	0.975106	+	0.221739i	$0.0711734\pi$
$439$			9.29191i			0.443479i	−0.975106	+	0.221739i	$0.928827\pi$
$440$	2.15316	+	23.6169i	0.102648	+	1.12589i
$441$		0			0
$442$	−11.6792	+	3.51202i	−0.555523	+	0.167050i
$443$	7.19883	−	7.19883i	0.342027	−	0.342027i	−0.515102	−	0.857129i	$-0.672246\pi$
$443$	7.19883	−	7.19883i	0.342027	−	0.342027i	0.857129	+	0.515102i	$0.172246\pi$
$444$	0.0728598	+	0.110192i	0.00345777	+	0.00522950i
$445$	−1.99401	−	1.99401i	−0.0945251	−	0.0945251i
$446$	0.182632	−	0.339701i	0.00864786	−	0.0160853i
$447$	−1.62500			−0.0768598
$448$		0			0
$449$	3.82136			0.180341			0.0901705	−	0.995926i	$-0.471259\pi$
$449$	3.82136			0.180341			0.0901705	+	0.995926i	$0.471259\pi$
$450$	−0.898675	+	1.67157i	−0.0423639	+	0.0787984i
$451$	24.5368	+	24.5368i	1.15539	+	1.15539i
$452$	−2.87995	−	4.35560i	−0.135461	−	0.204870i
$453$	8.66364	−	8.66364i	0.407053	−	0.407053i
$454$	15.4512	−	4.64629i	0.725161	−	0.218061i
$455$		0			0
$456$	0.868201	+	9.52282i	0.0406572	+	0.445947i
$457$			25.0923i			1.17377i	0.809671	+	0.586885i	$0.199646\pi$
$457$			25.0923i			1.17377i	−0.809671	+	0.586885i	$0.800354\pi$
$458$	−6.39924	−	21.2806i	−0.299017	−	0.994378i
$459$	19.7109	−	19.7109i	0.920027	−	0.920027i
$460$	−5.72937	+	28.0926i	−0.267133	+	1.30982i
$461$	7.13847	+	7.13847i	0.332472	+	0.332472i	0.853524	−	0.521053i	$-0.174461\pi$
$461$	7.13847	+	7.13847i	0.332472	+	0.332472i	−0.521053	+	0.853524i	$0.674461\pi$
$462$		0			0
$463$	3.67655			0.170864			0.0854320	−	0.996344i	$-0.472773\pi$
$463$	3.67655			0.170864			0.0854320	+	0.996344i	$0.472773\pi$
$464$	20.1259	−	8.10923i	0.934323	−	0.376462i
$465$	7.41455			0.343841
$466$	7.13005	+	3.83329i	0.330293	+	0.177574i
$467$	−6.88062	−	6.88062i	−0.318397	−	0.318397i	0.529754	−	0.848151i	$-0.322284\pi$
$467$	−6.88062	−	6.88062i	−0.318397	−	0.318397i	−0.848151	+	0.529754i	$0.822284\pi$
$468$	−6.19996	−	1.26446i	−0.286593	−	0.0584495i
$469$		0			0
$470$	−3.33958	−	11.1057i	−0.154043	−	0.512270i
$471$			16.6974i			0.769375i
$472$	5.95618	−	7.15118i	0.274155	−	0.329160i
$473$		−	4.03076i		−	0.185335i
$474$	−7.78076	+	2.33973i	−0.357382	+	0.107468i
$475$	−1.64963	+	1.64963i	−0.0756900	+	0.0756900i
$476$		0			0
$477$	−11.6828	−	11.6828i	−0.534917	−	0.534917i
$478$	−9.73901	+	18.1149i	−0.445452	+	0.828555i
$479$	16.1336			0.737161			0.368581	−	0.929596i	$-0.379844\pi$
$479$	16.1336			0.737161			0.368581	+	0.929596i	$0.379844\pi$
$480$	6.38968	+	7.98072i	0.291648	+	0.364268i
$481$	−0.107455			−0.00489954
$482$	−2.02123	+	3.75955i	−0.0920644	+	0.171243i
$483$		0			0
$484$	−8.26780	+	5.46671i	−0.375809	+	0.248487i
$485$	−27.8351	+	27.8351i	−1.26392	+	1.26392i
$486$	21.7514	−	6.54080i	0.986662	−	0.296697i
$487$			13.0739i			0.592437i	0.955120	+	0.296218i	$0.0957256\pi$
$487$			13.0739i			0.592437i	−0.955120	+	0.296218i	$0.904274\pi$
$488$	19.9048	+	16.5786i	0.901050	+	0.750479i
$489$		−	3.65859i		−	0.165447i
$490$		0			0
$491$	10.1749	−	10.1749i	0.459188	−	0.459188i	−0.439201	−	0.898389i	$-0.644738\pi$
$491$	10.1749	−	10.1749i	0.459188	−	0.459188i	0.898389	+	0.439201i	$0.144738\pi$
$492$	14.6576	+	2.98936i	0.660816	+	0.134771i
$493$	−23.6150	−	23.6150i	−1.06356	−	1.06356i
$494$	−6.85092	−	3.68322i	−0.308237	−	0.165716i
$495$	18.9376			0.851183
$496$	6.42638	−	15.0998i	0.288553	−	0.678001i
$497$		0			0
$498$	15.4824	+	8.32370i	0.693781	+	0.372994i
$499$	−29.4380	−	29.4380i	−1.31783	−	1.31783i	−0.915492	−	0.402336i	$-0.868198\pi$
$499$	−29.4380	−	29.4380i	−1.31783	−	1.31783i	−0.402336	−	0.915492i	$-0.631802\pi$
$500$	−4.69293	+	23.0107i	−0.209874	+	1.02907i
$501$	7.47154	−	7.47154i	0.333804	−	0.333804i
$502$	7.79036	+	25.9068i	0.347701	+	1.15628i
$503$			35.0535i			1.56296i	0.623930	+	0.781480i	$0.285535\pi$
$503$			35.0535i			1.56296i	−0.623930	+	0.781480i	$0.714465\pi$
$504$		0			0
$505$		−	9.33805i		−	0.415538i
$506$	−36.9465	+	11.1101i	−1.64247	+	0.493903i
$507$	6.72019	−	6.72019i	0.298454	−	0.298454i
$508$	10.6844	+	16.1590i	0.474044	+	0.716939i
$509$	−2.10306	−	2.10306i	−0.0932163	−	0.0932163i	0.658961	−	0.752177i	$-0.270996\pi$
$509$	−2.10306	−	2.10306i	−0.0932163	−	0.0932163i	−0.752177	+	0.658961i	$0.770996\pi$
$510$	7.45115	−	13.8594i	0.329942	−	0.613704i
$511$		0			0
$512$	21.7909	−	6.09556i	0.963032	−	0.269388i
$513$	17.7784			0.784937
$514$	2.04133	−	3.79695i	0.0900393	−	0.167476i
$515$	−13.3021	−	13.3021i	−0.586160	−	0.586160i
$516$	−0.958396	−	1.44947i	−0.0421910	−	0.0638093i
$517$	11.0347	−	11.0347i	0.485305	−	0.485305i
$518$		0			0
$519$		−	12.8544i		−	0.564245i
$520$	−8.28172	+	0.755049i	−0.363177	+	0.0331111i
$521$		−	25.2536i		−	1.10638i	−0.833054	−	0.553191i	$-0.813410\pi$
$521$		−	25.2536i		−	1.10638i	0.833054	−	0.553191i	$-0.186590\pi$
$522$	−4.98972	−	16.5933i	−0.218394	−	0.726268i
$523$	0.491294	−	0.491294i	0.0214828	−	0.0214828i	−0.696284	−	0.717767i	$-0.745164\pi$
$523$	0.491294	−	0.491294i	0.0214828	−	0.0214828i	0.717767	+	0.696284i	$0.245164\pi$
$524$	−5.53247	+	27.1272i	−0.241687	+	1.18506i
$525$		0			0
$526$	33.6210	+	18.0755i	1.46595	+	0.788129i
$527$	−25.2580			−1.10025
$528$	−5.38735	+	12.6584i	−0.234454	+	0.550888i
$529$	−23.6436			−1.02798
$530$	−19.1252	−	10.2822i	−0.830747	−	0.446630i
$531$	−5.25519	−	5.25519i	−0.228056	−	0.228056i
$532$		0			0
$533$	−8.60431	+	8.60431i	−0.372694	+	0.372694i
$534$	−0.471083	−	1.56658i	−0.0203857	−	0.0677926i
$535$			26.6647i			1.15281i
$536$	3.36911	+	2.80611i	0.145523	+	0.121206i
$537$			5.88234i			0.253842i
$538$	24.6464	−	7.41137i	1.06258	−	0.319527i
$539$		0			0
$540$	15.8552	−	10.4835i	0.682300	−	0.451140i
$541$	−8.20162	−	8.20162i	−0.352615	−	0.352615i	0.508467	−	0.861082i	$-0.330213\pi$
$541$	−8.20162	−	8.20162i	−0.352615	−	0.352615i	−0.861082	+	0.508467i	$0.830213\pi$
$542$	20.9661	−	38.9977i	0.900573	−	1.67510i
$543$	−6.84137			−0.293591
$544$	−21.7667	−	27.1866i	−0.933239	−	1.16562i
$545$	−30.3804			−1.30135
$546$		0			0
$547$	8.29783	+	8.29783i	0.354790	+	0.354790i	0.861888	−	0.507098i	$-0.169282\pi$
$547$	8.29783	+	8.29783i	0.354790	+	0.354790i	−0.507098	+	0.861888i	$0.669282\pi$
$548$	18.8874	−	12.4884i	0.806831	−	0.533480i
$549$	14.6275	−	14.6275i	0.624285	−	0.624285i
$550$	−3.21416	+	0.966524i	−0.137052	+	0.0412127i
$551$		−	21.2997i		−	0.907398i
$552$	−10.6444	+	12.7800i	−0.453055	+	0.543952i
$553$		0			0
$554$	6.70467	+	22.2963i	0.284854	+	0.947279i
$555$	0.0980346	−	0.0980346i	0.00416134	−	0.00416134i
$556$	6.35410	+	1.29589i	0.269474	+	0.0549580i
$557$	−14.2708	−	14.2708i	−0.604672	−	0.604672i	0.336877	−	0.941549i	$-0.390629\pi$
$557$	−14.2708	−	14.2708i	−0.604672	−	0.604672i	−0.941549	+	0.336877i	$0.890629\pi$
$558$	−11.5423	−	6.20543i	−0.488625	−	0.262697i
$559$	1.41347			0.0597832
$560$		0			0
$561$	21.1742			0.893975
$562$	−31.6591	−	17.0207i	−1.33546	−	0.717975i
$563$	−18.1116	−	18.1116i	−0.763311	−	0.763311i	0.213608	−	0.976919i	$-0.431478\pi$
$563$	−18.1116	−	18.1116i	−0.763311	−	0.763311i	−0.976919	+	0.213608i	$0.931478\pi$
$564$	1.34437	−	6.59182i	0.0566083	−	0.277566i
$565$	−3.87504	+	3.87504i	−0.163024	+	0.163024i
$566$	−2.53468	−	8.42904i	−0.106540	−	0.354299i
$567$		0			0
$568$	−0.735709	−	8.06959i	−0.0308697	−	0.338592i
$569$			33.0530i			1.38566i	0.721103	+	0.692828i	$0.243635\pi$
$569$			33.0530i			1.38566i	−0.721103	+	0.692828i	$0.756365\pi$
$570$	9.61060	−	2.88998i	0.402544	−	0.121048i
$571$	10.5610	−	10.5610i	0.441964	−	0.441964i	−0.450707	−	0.892672i	$-0.648828\pi$
$571$	10.5610	−	10.5610i	0.441964	−	0.441964i	0.892672	+	0.450707i	$0.148828\pi$
$572$	−6.17200	−	9.33449i	−0.258064	−	0.390294i
$573$	−3.89577	−	3.89577i	−0.162748	−	0.162748i
$574$		0			0
$575$	−4.05777			−0.169221
$576$	−3.26761	−	17.7714i	−0.136150	−	0.740473i
$577$	−1.33325			−0.0555038			−0.0277519	−	0.999615i	$-0.508835\pi$
$577$	−1.33325			−0.0555038			−0.0277519	+	0.999615i	$0.508835\pi$
$578$	−13.9982	+	26.0372i	−0.582250	+	1.08301i
$579$	−5.97579	−	5.97579i	−0.248345	−	0.248345i
$580$	−12.5600	−	18.9956i	−0.521524	−	0.788748i
$581$		0			0
$582$	−21.8685	+	6.57601i	−0.906477	+	0.272584i
$583$		−	29.2193i		−	1.21014i
$584$	2.65581	+	29.1302i	0.109898	+	1.20541i
$585$			6.64085i			0.274565i
$586$	−10.7021	−	35.5897i	−0.442099	−	1.47020i
$587$	19.7266	−	19.7266i	0.814203	−	0.814203i	−0.171058	−	0.985261i	$-0.554719\pi$
$587$	19.7266	−	19.7266i	0.814203	−	0.814203i	0.985261	+	0.171058i	$0.0547186\pi$
$588$		0			0
$589$	−11.3908	−	11.3908i	−0.469350	−	0.469350i
$590$	−8.60299	−	4.62518i	−0.354180	−	0.190416i
$591$	18.0302			0.741662
$592$	−0.114680	−	0.284618i	−0.00471330	−	0.0116977i
$593$	−18.8050			−0.772228			−0.386114	−	0.922451i	$-0.626183\pi$
$593$	−18.8050			−0.772228			−0.386114	+	0.922451i	$0.626183\pi$
$594$	22.5282	+	12.1117i	0.924342	+	0.496949i
$595$		0			0
$596$	3.69849	+	0.754292i	0.151496	+	0.0308970i
$597$	−2.64564	+	2.64564i	−0.108279	+	0.108279i
$598$	−3.89597	−	12.9560i	−0.159318	−	0.529810i
$599$			27.8049i			1.13608i	0.823001	+	0.568039i	$0.192298\pi$
$599$			27.8049i			1.13608i	−0.823001	+	0.568039i	$0.807702\pi$
$600$	−0.926009	+	1.11180i	−0.0378042	+	0.0453889i
$601$		−	13.6372i		−	0.556271i	−0.960542	−	0.278136i	$-0.910284\pi$
$601$		−	13.6372i		−	0.556271i	0.960542	−	0.278136i	$-0.0897165\pi$
$602$		0			0
$603$	2.47586	−	2.47586i	0.100825	−	0.100825i
$604$	−23.7399	+	15.6969i	−0.965963	+	0.638699i
$605$	7.35559	+	7.35559i	0.299047	+	0.299047i
$606$	2.56514	−	4.77125i	0.104202	−	0.193819i
$607$	29.0978			1.18104			0.590522	−	0.807022i	$-0.298922\pi$
$607$	29.0978			1.18104			0.590522	+	0.807022i	$0.298922\pi$
$608$	2.44428	−	22.0769i	0.0991286	−	0.895337i
$609$		0			0
$610$	12.8739	−	23.9459i	0.521248	−	0.969539i
$611$	3.86953	+	3.86953i	0.156544	+	0.156544i
$612$	−23.1986	+	15.3390i	−0.937747	+	0.620042i
$613$	−20.4886	+	20.4886i	−0.827526	+	0.827526i	−0.987174	−	0.159648i	$-0.948964\pi$
$613$	−20.4886	+	20.4886i	−0.827526	+	0.827526i	0.159648	+	0.987174i	$0.448964\pi$
$614$	36.5090	−	10.9785i	1.47338	−	0.443058i
$615$		−	15.6999i		−	0.633082i
$616$		0			0
$617$		−	5.44754i		−	0.219310i	−0.993970	−	0.109655i	$-0.965025\pi$
$617$		−	5.44754i		−	0.219310i	0.993970	−	0.109655i	$-0.0349745\pi$
$618$	−3.14261	−	10.4507i	−0.126414	−	0.420390i
$619$	−4.29604	+	4.29604i	−0.172672	+	0.172672i	−0.788152	−	0.615480i	$-0.788962\pi$
$619$	−4.29604	+	4.29604i	−0.172672	+	0.172672i	0.615480	+	0.788152i	$0.288962\pi$
$620$	−16.8755	−	3.44168i	−0.677736	−	0.138221i
$621$	21.8658	+	21.8658i	0.877444	+	0.877444i
$622$	8.56051	+	4.60234i	0.343245	+	0.184537i
$623$		0			0
$624$	−4.43893	−	1.88918i	−0.177699	−	0.0756277i
$625$	21.6763			0.867051
$626$	9.99272	+	5.37233i	0.399389	+	0.214722i
$627$	9.54912	+	9.54912i	0.381355	+	0.381355i
$628$	7.75059	−	38.0032i	0.309282	−	1.51649i
$629$	−0.333959	+	0.333959i	−0.0133158	+	0.0133158i
$630$		0			0
$631$			31.5326i			1.25529i	0.778499	+	0.627646i	$0.215982\pi$
$631$			31.5326i			1.25529i	−0.778499	+	0.627646i	$0.784018\pi$
$632$	18.7950	−	1.71355i	0.747627	−	0.0681615i
$633$		−	17.7775i		−	0.706592i
$634$	−3.76627	+	1.13254i	−0.149578	+	0.0449791i
$635$	14.3761	−	14.3761i	0.570499	−	0.570499i
$636$	−6.94748	−	10.5073i	−0.275486	−	0.416642i
$637$		0			0
$638$	14.5106	−	26.9902i	0.574480	−	1.06855i
$639$	−6.47075			−0.255979
$640$	−10.8384	−	21.1300i	−0.428425	−	0.835238i
$641$	27.2265			1.07538			0.537691	−	0.843142i	$-0.319297\pi$
$641$	27.2265			1.07538			0.537691	+	0.843142i	$0.319297\pi$
$642$	−7.32472	+	13.6242i	−0.289084	+	0.537705i
$643$	8.13921	+	8.13921i	0.320979	+	0.320979i	0.849143	−	0.528164i	$-0.177119\pi$
$643$	8.13921	+	8.13921i	0.320979	+	0.320979i	−0.528164	+	0.849143i	$0.677119\pi$
$644$		0			0
$645$	−1.28955	+	1.28955i	−0.0507758	+	0.0507758i
$646$	−32.7389	+	9.84484i	−1.28810	+	0.387340i
$647$			7.73922i			0.304260i	0.988360	+	0.152130i	$0.0486133\pi$
$647$			7.73922i			0.304260i	−0.988360	+	0.152130i	$0.951387\pi$
$648$	−8.10523	+	0.738958i	−0.318403	+	0.0290290i
$649$		−	13.1435i		−	0.515929i
$650$	−0.338930	−	1.12711i	−0.0132939	−	0.0442089i
$651$		0			0
$652$	−1.69824	+	8.32693i	−0.0665083	+	0.326108i
$653$	7.12570	+	7.12570i	0.278850	+	0.278850i	0.832650	−	0.553800i	$-0.186823\pi$
$653$	7.12570	+	7.12570i	0.278850	+	0.278850i	−0.553800	+	0.832650i	$0.686823\pi$
$654$	−15.5227	−	8.34541i	−0.606987	−	0.326331i
$655$	29.0562			1.13532
$656$	−31.9731	−	13.6075i	−1.24834	−	0.531285i
$657$	23.3585			0.911304
$658$		0			0
$659$	−4.61254	−	4.61254i	−0.179679	−	0.179679i	0.611537	−	0.791216i	$-0.290552\pi$
$659$	−4.61254	−	4.61254i	−0.179679	−	0.179679i	−0.791216	+	0.611537i	$0.790552\pi$
$660$	14.1470	+	2.88522i	0.550672	+	0.112307i
$661$	13.7655	−	13.7655i	0.535417	−	0.535417i	−0.386763	−	0.922179i	$-0.626407\pi$
$661$	13.7655	−	13.7655i	0.535417	−	0.535417i	0.922179	+	0.386763i	$0.126407\pi$
$662$	−4.37644	−	14.5538i	−0.170095	−	0.565649i
$663$			7.42514i			0.288369i
$664$	−31.3741	−	26.1313i	−1.21755	−	1.01409i
$665$		0			0
$666$	−0.234659	+	0.0705638i	−0.00909287	+	0.00273429i
$667$	26.1966	−	26.1966i	1.01434	−	1.01434i
$668$	−20.4733	+	13.5371i	−0.792137	+	0.523765i
$669$	−0.166039	−	0.166039i	−0.00641942	−	0.00641942i
$670$	2.17904	−	4.05310i	0.0841838	−	0.156585i
$671$	36.5842			1.41232
$672$		0			0
$673$	−28.4799			−1.09782			−0.548910	−	0.835881i	$-0.684957\pi$
$673$	−28.4799			−1.09782			−0.548910	+	0.835881i	$0.684957\pi$
$674$	−10.9868	+	20.4357i	−0.423194	+	0.787155i
$675$	1.90222	+	1.90222i	0.0732164	+	0.0732164i
$676$	−18.4145	+	12.1758i	−0.708250	+	0.468298i
$677$	−7.32134	+	7.32134i	−0.281382	+	0.281382i	−0.833660	−	0.552278i	$-0.813759\pi$
$677$	−7.32134	+	7.32134i	−0.281382	+	0.281382i	0.552278	+	0.833660i	$0.313759\pi$
$678$	−3.04440	+	0.915474i	−0.116920	+	0.0351586i
$679$		0			0
$680$	−23.3920	+	28.0852i	−0.897044	+	1.07702i
$681$		−	9.82323i		−	0.376427i
$682$	−6.67393	−	22.1941i	−0.255558	−	0.849855i
$683$	−6.59739	+	6.59739i	−0.252442	+	0.252442i	−0.821971	−	0.569529i	$-0.807126\pi$
$683$	−6.59739	+	6.59739i	−0.252442	+	0.252442i	0.569529	+	0.821971i	$0.307126\pi$
$684$	−17.3796	−	3.54450i	−0.664527	−	0.135527i
$685$	−16.8035	−	16.8035i	−0.642029	−	0.642029i
$686$		0			0
$687$	−13.5293			−0.516176
$688$	1.50849	+	3.74386i	0.0575107	+	0.142733i
$689$	10.2463			0.390354
$690$	15.3745	+	8.26573i	0.585299	+	0.314671i
$691$	18.2600	+	18.2600i	0.694645	+	0.694645i	0.963250	−	0.268606i	$-0.0865628\pi$
$691$	18.2600	+	18.2600i	0.694645	+	0.694645i	−0.268606	+	0.963250i	$0.586563\pi$
$692$	−5.96675	+	29.2566i	−0.226822	+	1.11217i
$693$		0			0
$694$	−14.7791	−	49.1479i	−0.561008	−	1.86563i
$695$		−	6.80595i		−	0.258164i
$696$	−1.19943	−	13.1559i	−0.0454643	−	0.498673i
$697$			53.4825i			2.02579i
$698$	19.8085	−	5.95657i	0.749763	−	0.225459i
$699$	3.48502	−	3.48502i	0.131815	−	0.131815i
$700$		0			0
$701$	3.43743	+	3.43743i	0.129830	+	0.129830i	0.769036	−	0.639206i	$-0.220737\pi$
$701$	3.43743	+	3.43743i	0.129830	+	0.129830i	−0.639206	+	0.769036i	$0.720737\pi$
$702$	−4.24720	+	7.89994i	−0.160300	+	0.298164i
$703$	−0.301217			−0.0113606
$704$	18.1374	−	26.3099i	0.683578	−	0.991591i
$705$	−7.06057			−0.265916
$706$	6.12747	−	11.3973i	0.230610	−	0.428943i
$707$		0			0
$708$	−3.12515	−	4.72644i	−0.117450	−	0.177631i
$709$	21.1582	−	21.1582i	0.794613	−	0.794613i	−0.187627	−	0.982240i	$-0.560080\pi$
$709$	21.1582	−	21.1582i	0.794613	−	0.794613i	0.982240	+	0.187627i	$0.0600797\pi$
$710$	−8.14397	+	2.44895i	−0.305638	+	0.0919076i
$711$		−	15.0712i		−	0.565212i
$712$	0.345008	+	3.78420i	0.0129297	+	0.141819i
$713$		−	28.0192i		−	1.04933i
$714$		0			0
$715$	−8.30458	+	8.30458i	−0.310574	+	0.310574i
$716$	2.73046	−	13.3882i	0.102042	−	0.500340i
$717$	8.85417	+	8.85417i	0.330665	+	0.330665i
$718$	10.4988	+	5.64441i	0.391811	+	0.210647i
$719$	−4.99542			−0.186298			−0.0931488	−	0.995652i	$-0.529693\pi$
$719$	−4.99542			−0.186298			−0.0931488	+	0.995652i	$0.529693\pi$
$720$	−17.5897	+	7.08731i	−0.655528	+	0.264128i
$721$		0			0
$722$	4.46220	+	2.39899i	0.166066	+	0.0892812i
$723$	1.83759	+	1.83759i	0.0683407	+	0.0683407i
$724$	15.5709	+	3.17562i	0.578689	+	0.118021i
$725$	2.27898	−	2.27898i	0.0846392	−	0.0846392i
$726$	1.73775	+	5.77888i	0.0644941	+	0.214474i
$727$		−	4.59798i		−	0.170530i	−0.996358	−	0.0852648i	$-0.972826\pi$
$727$		−	4.59798i		−	0.170530i	0.996358	−	0.0852648i	$-0.0271736\pi$
$728$		0			0
$729$		−	5.19606i		−	0.192447i
$730$	29.3987	−	8.84040i	1.08809	−	0.327198i
$731$	4.39289	−	4.39289i	0.162477	−	0.162477i
$732$	13.1557	−	8.69863i	0.486250	−	0.321511i
$733$	7.49156	+	7.49156i	0.276707	+	0.276707i	0.831793	−	0.555086i	$-0.187315\pi$
$733$	7.49156	+	7.49156i	0.276707	+	0.276707i	−0.555086	+	0.831793i	$0.687315\pi$
$734$	6.23037	−	11.5887i	0.229967	−	0.427746i
$735$		0			0
$736$	30.1588	−	24.1463i	1.11167	−	0.890045i
$737$	6.19227			0.228095
$738$	−13.1397	+	24.4403i	−0.483679	+	0.899658i
$739$	33.5809	+	33.5809i	1.23529	+	1.23529i	0.961903	+	0.273389i	$0.0881447\pi$
$739$	33.5809	+	33.5809i	1.23529	+	1.23529i	0.273389	+	0.961903i	$0.411855\pi$
$740$	−0.268632	+	0.177621i	−0.00987512	+	0.00652947i
$741$	−3.34858	+	3.34858i	−0.123013	+	0.123013i
$742$		0			0
$743$		−	17.5619i		−	0.644285i	−0.946691	−	0.322142i	$-0.895597\pi$
$743$		−	17.5619i		−	0.644285i	0.946691	−	0.322142i	$-0.104403\pi$
$744$	−7.67705	−	6.39417i	−0.281454	−	0.234422i
$745$		−	3.96150i		−	0.145138i
$746$	8.36107	+	27.8047i	0.306121	+	1.01800i
$747$	−23.0559	+	23.0559i	−0.843571	+	0.843571i
$748$	−48.1924	−	9.82863i	−1.76209	−	0.359370i
$749$		0			0
$750$	12.5933	+	6.77047i	0.459842	+	0.247223i
$751$	−18.0472			−0.658552			−0.329276	−	0.944234i	$-0.606805\pi$
$751$	−18.0472			−0.658552			−0.329276	+	0.944234i	$0.606805\pi$
$752$	−6.11958	+	14.3789i	−0.223158	+	0.524346i
$753$	16.4704			0.600216
$754$	9.46463	+	5.08842i	0.344682	+	0.185309i
$755$	21.1206	+	21.1206i	0.768658	+	0.768658i
$756$		0			0
$757$	18.4795	−	18.4795i	0.671647	−	0.671647i	−0.286448	−	0.958096i	$-0.592475\pi$
$757$	18.4795	−	18.4795i	0.671647	−	0.671647i	0.958096	+	0.286448i	$0.0924747\pi$
$758$	−5.19664	−	17.2814i	−0.188751	−	0.627688i
$759$			23.4890i			0.852598i
$760$	−23.2152	+	2.11654i	−0.842103	+	0.0767750i
$761$			6.48364i			0.235032i	0.993071	+	0.117516i	$0.0374931\pi$
$761$			6.48364i			0.235032i	−0.993071	+	0.117516i	$0.962507\pi$
$762$	11.2945	−	3.39635i	0.409157	−	0.123037i
$763$		0			0
$764$	7.05843	+	10.6751i	0.255365	+	0.386212i
$765$	20.6390	+	20.6390i	0.746205	+	0.746205i
$766$	−0.753778	+	1.40205i	−0.0272351	+	0.0506582i
$767$	4.60904			0.166423
$768$	0.266527	−	13.7736i	0.00961748	−	0.497012i
$769$	23.9598			0.864014			0.432007	−	0.901870i	$-0.357806\pi$
$769$	23.9598			0.864014			0.432007	+	0.901870i	$0.357806\pi$
$770$		0			0
$771$	−1.85587	−	1.85587i	−0.0668374	−	0.0668374i
$772$	10.8270	+	16.3747i	0.389674	+	0.589339i
$773$	1.94399	−	1.94399i	0.0699204	−	0.0699204i	−0.671282	−	0.741202i	$-0.734256\pi$
$773$	1.94399	−	1.94399i	0.0699204	−	0.0699204i	0.741202	+	0.671282i	$0.234256\pi$
$774$	3.08670	−	0.928195i	0.110949	−	0.0333633i
$775$		−	2.43754i		−	0.0875590i
$776$	52.8250	−	4.81608i	1.89631	−	0.172887i
$777$		0			0
$778$	7.03878	+	23.4074i	0.252352	+	0.839196i
$779$	−24.1195	+	24.1195i	−0.864169	+	0.864169i
$780$	−1.01176	+	4.96093i	−0.0362268	+	0.177630i
$781$	−8.09187	−	8.09187i	−0.289550	−	0.289550i
$782$	−52.3740	−	28.1576i	−1.87289	−	1.00691i
$783$	−24.5611			−0.877743
$784$		0			0
$785$	−40.7056			−1.45285
$786$	14.8462	+	7.98167i	0.529545	+	0.284697i
$787$	34.8373	+	34.8373i	1.24181	+	1.24181i	0.959247	+	0.282567i	$0.0911861\pi$
$787$	34.8373	+	34.8373i	1.24181	+	1.24181i	0.282567	+	0.959247i	$0.408814\pi$
$788$	−41.0366	−	8.36924i	−1.46187	−	0.298142i
$789$	16.4332	−	16.4332i	0.585039	−	0.585039i
$790$	−5.70391	−	18.9683i	−0.202936	−	0.674861i
$791$		0			0
$792$	−19.6081	−	16.3315i	−0.696744	−	0.580314i
$793$			12.8290i			0.455570i
$794$	38.4030	−	11.5481i	1.36287	−	0.409825i
$795$	−9.34801	+	9.34801i	−0.331540	+	0.331540i
$796$	7.24952	−	4.79342i	0.256953	−	0.169898i
$797$	−22.5200	−	22.5200i	−0.797699	−	0.797699i	0.185033	−	0.982732i	$-0.440761\pi$
$797$	−22.5200	−	22.5200i	−0.797699	−	0.797699i	−0.982732	+	0.185033i	$0.940761\pi$
$798$		0			0
$799$	24.0521			0.850903
$800$	2.62367	−	2.10061i	0.0927606	−	0.0742678i
$801$	3.03443			0.107216
$802$	15.0858	−	28.0601i	0.532697	−	0.990835i
$803$	29.2106	+	29.2106i	1.03082	+	1.03082i
$804$	2.22675	−	1.47234i	0.0785315	−	0.0519254i
$805$		0			0
$806$	7.78279	−	2.34034i	0.274137	−	0.0824351i
$807$		−	15.6692i		−	0.551581i
$808$	−8.05297	+	9.66866i	−0.283302	+	0.340142i
$809$		−	47.4650i		−	1.66878i	−0.551173	−	0.834391i	$-0.685820\pi$
$809$		−	47.4650i		−	1.66878i	0.551173	−	0.834391i	$-0.314180\pi$
$810$	2.45977	+	8.17994i	0.0864275	+	0.287414i
$811$	−39.0893	+	39.0893i	−1.37261	+	1.37261i	−0.516058	+	0.856554i	$0.672601\pi$
$811$	−39.0893	+	39.0893i	−1.37261	+	1.37261i	−0.856554	+	0.516058i	$0.827399\pi$
$812$		0			0
$813$	−19.0613	−	19.0613i	−0.668507	−	0.668507i
$814$	−0.381691	−	0.205206i	−0.0133783	−	0.00719248i
$815$	8.91906			0.312421
$816$	−19.6670	+	7.92433i	−0.688484	+	0.277407i
$817$	3.96220			0.138620
$818$	−38.4466	−	20.6698i	−1.34425	−	0.722703i
$819$		0			0
$820$	−7.28759	+	35.7330i	−0.254494	+	1.24785i
$821$	8.90329	−	8.90329i	0.310727	−	0.310727i	−0.534464	−	0.845191i	$-0.679487\pi$
$821$	8.90329	−	8.90329i	0.310727	−	0.310727i	0.845191	+	0.534464i	$0.179487\pi$
$822$	−3.96982	−	13.2016i	−0.138463	−	0.460458i
$823$			4.96474i			0.173060i	0.996249	+	0.0865300i	$0.0275779\pi$
$823$			4.96474i			0.173060i	−0.996249	+	0.0865300i	$0.972422\pi$
$824$	2.30156	+	25.2445i	0.0801786	+	0.879435i
$825$			2.04343i			0.0711432i
$826$		0			0
$827$	11.3168	−	11.3168i	0.393524	−	0.393524i	−0.482417	−	0.875942i	$-0.660241\pi$
$827$	11.3168	−	11.3168i	0.393524	−	0.393524i	0.875942	+	0.482417i	$0.160241\pi$
$828$	−17.0159	−	25.7347i	−0.591344	−	0.894343i
$829$	−25.0135	−	25.0135i	−0.868754	−	0.868754i	0.123581	−	0.992335i	$-0.460562\pi$
$829$	−25.0135	−	25.0135i	−0.868754	−	0.868754i	−0.992335	+	0.123581i	$0.960562\pi$
$830$	−20.2919	+	37.7436i	−0.704342	+	1.31010i
$831$	14.1751			0.491727
$832$	9.22607	+	6.36023i	0.319856	+	0.220501i
$833$		0			0
$834$	1.86958	−	3.47748i	0.0647382	−	0.120415i
$835$	18.2145	+	18.2145i	0.630337	+	0.630337i
$836$	−17.3013	−	26.1663i	−0.598376	−	0.904979i
$837$	−13.1350	+	13.1350i	−0.454011	+	0.454011i
$838$	−14.8424	+	4.46322i	−0.512722	+	0.154179i
$839$		−	47.7342i		−	1.64797i	−0.566614	−	0.823983i	$-0.691747\pi$
$839$		−	47.7342i		−	1.64797i	0.566614	−	0.823983i	$-0.308253\pi$
$840$		0			0
$841$			0.425820i			0.0146834i
$842$	−7.34622	−	24.4298i	−0.253168	−	0.841906i
$843$	−15.4743	+	15.4743i	−0.532963	+	0.532963i
$844$	−8.25196	+	40.4615i	−0.284044	+	1.39274i
$845$	16.3828	+	16.3828i	0.563585	+	0.563585i
$846$	10.9913	+	5.90918i	0.377888	+	0.203162i
$847$		0			0
$848$	10.9352	+	27.1395i	0.375515	+	0.931974i
$849$	−5.35883			−0.183915
$850$	−4.55628	−	2.44957i	−0.156279	−	0.0840196i
$851$	−0.370468	−	0.370468i	−0.0126995	−	0.0126995i
$852$	−4.83386	−	0.985844i	−0.165605	−	0.0337745i
$853$	−3.65043	+	3.65043i	−0.124988	+	0.124988i	−0.766834	−	0.641846i	$-0.778169\pi$
$853$	−3.65043	+	3.65043i	−0.124988	+	0.124988i	0.641846	+	0.766834i	$0.278169\pi$
$854$		0			0
$855$			18.6155i			0.636637i
$856$	22.9951	−	27.6087i	0.785957	−	0.943646i
$857$		−	21.9855i		−	0.751010i	−0.926820	−	0.375505i	$-0.877469\pi$
$857$		−	21.9855i		−	0.751010i	0.926820	−	0.375505i	$-0.122531\pi$
$858$	−6.52445	+	1.96195i	−0.222741	+	0.0669799i
$859$	8.76394	−	8.76394i	0.299022	−	0.299022i	−0.541609	−	0.840631i	$-0.682185\pi$
$859$	8.76394	−	8.76394i	0.299022	−	0.299022i	0.840631	+	0.541609i	$0.182185\pi$
$860$	3.53358	−	2.33642i	0.120494	−	0.0796713i
$861$		0			0
$862$	−6.59867	+	12.2737i	−0.224752	+	0.418045i
$863$	18.4657			0.628578			0.314289	−	0.949327i	$-0.398234\pi$
$863$	18.4657			0.628578			0.314289	+	0.949327i	$0.398234\pi$
$864$	−25.4574	−	2.81855i	−0.866077	−	0.0958890i
$865$	31.3370			1.06549
$866$	9.98813	−	18.5783i	0.339410	−	0.631315i
$867$	12.7264	+	12.7264i	0.432213	+	0.432213i
$868$		0			0
$869$	18.8469	−	18.8469i	0.639338	−	0.639338i
$870$	−13.2772	+	3.99255i	−0.450138	+	0.135360i
$871$			2.17144i			0.0735764i
$872$	31.4560	+	26.1995i	1.06523	+	0.887226i
$873$		−	42.3587i		−	1.43362i
$874$	−10.9211	−	36.3180i	−0.369412	−	1.22848i
$875$		0			0
$876$	17.4496	+	3.55877i	0.589567	+	0.120240i
$877$	13.7104	+	13.7104i	0.462968	+	0.462968i	0.899627	−	0.436659i	$-0.143838\pi$
$877$	13.7104	+	13.7104i	0.462968	+	0.462968i	−0.436659	+	0.899627i	$0.643838\pi$
$878$	−11.5741	−	6.22252i	−0.390607	−	0.210000i
$879$	−22.6264			−0.763170
$880$	−30.8593	−	13.1335i	−1.04027	−	0.442731i
$881$	−21.6393			−0.729046			−0.364523	−	0.931194i	$-0.618768\pi$
$881$	−21.6393			−0.729046			−0.364523	+	0.931194i	$0.618768\pi$
$882$		0			0
$883$	−34.6173	−	34.6173i	−1.16496	−	1.16496i	−0.983374	−	0.181589i	$-0.941876\pi$
$883$	−34.6173	−	34.6173i	−1.16496	−	1.16496i	−0.181589	−	0.983374i	$-0.558124\pi$
$884$	3.44660	−	16.8996i	0.115922	−	0.568395i
$885$	−4.20496	+	4.20496i	−0.141348	+	0.141348i
$886$	4.14609	+	13.7878i	0.139291	+	0.463209i
$887$		−	3.88332i		−	0.130389i	−0.997873	−	0.0651945i	$-0.979233\pi$
$887$		−	3.88332i		−	0.130389i	0.997873	−	0.0651945i	$-0.0207668\pi$
$888$	−0.186049	+	0.0169622i	−0.00624339	+	0.000569213i
$889$		0			0
$890$	3.81908	−	1.14843i	0.128016	−	0.0384954i
$891$	−8.12760	+	8.12760i	−0.272285	+	0.272285i
$892$	0.300832	+	0.454975i	0.0100726	+	0.0152337i
$893$	10.8470	+	10.8470i	0.362981	+	0.362981i
$894$	1.08821	−	2.02411i	0.0363953	−	0.0676965i
$895$	−14.3402			−0.479341
$896$		0			0
$897$	−8.23688			−0.275022
$898$	−2.55905	+	4.75992i	−0.0853966	+	0.158840i
$899$	15.7366	+	15.7366i	0.524843	+	0.524843i
$900$	−1.48030	−	2.23880i	−0.0493434	−	0.0746265i
$901$	31.8444	−	31.8444i	1.06089	−	1.06089i
$902$	−46.9949	+	14.1317i	−1.56476	+	0.470535i
$903$		0			0
$904$	7.35399	−	0.670468i	0.244590	−	0.0222994i
$905$		−	16.6782i		−	0.554402i
$906$	4.98973	+	16.5933i	0.165773	+	0.551275i
$907$	28.3184	−	28.3184i	0.940295	−	0.940295i	−0.0580200	−	0.998315i	$-0.518479\pi$
$907$	28.3184	−	28.3184i	0.940295	−	0.940295i	0.998315	+	0.0580200i	$0.0184787\pi$
$908$	−4.55975	+	22.3576i	−0.151320	+	0.741965i
$909$	7.10521	+	7.10521i	0.235665	+	0.235665i
$910$		0			0
$911$	−30.3771			−1.00644			−0.503218	−	0.864159i	$-0.667851\pi$
$911$	−30.3771			−1.00644			−0.503218	+	0.864159i	$0.667851\pi$
$912$	−12.4431	−	5.29571i	−0.412033	−	0.175359i
$913$	−57.6642			−1.90841
$914$	−31.2552	−	16.8036i	−1.03383	−	0.555813i
$915$	−11.7042	−	11.7042i	−0.386930	−	0.386930i
$916$	30.7927	+	6.28004i	1.01742	+	0.207498i
$917$		0			0
$918$	11.3523	+	37.7519i	0.374681	+	1.24600i
$919$		−	11.2581i		−	0.371370i	−0.982609	−	0.185685i	$-0.940550\pi$
$919$		−	11.2581i		−	0.371370i	0.982609	−	0.185685i	$-0.0594504\pi$
$920$	−31.1556	−	25.9493i	−1.02717	−	0.855524i
$921$		−	23.2109i		−	0.764825i
$922$	−13.6722	+	4.11132i	−0.450269	+	0.135399i
$923$	2.83757	−	2.83757i	0.0933998	−	0.0933998i
$924$		0			0
$925$	−0.0322290	−	0.0322290i	−0.00105968	−	0.00105968i
$926$	−2.46208	+	4.57955i	−0.0809089	+	0.150493i
$927$	20.2428			0.664861
$928$	−3.37680	+	30.4996i	−0.110849	+	1.00120i
$929$	25.6829			0.842629			0.421314	−	0.906915i	$-0.361569\pi$
$929$	25.6829			0.842629			0.421314	+	0.906915i	$0.361569\pi$
$930$	−4.96530	+	9.23562i	−0.162819	+	0.302848i
$931$		0			0
$932$	−9.54957	+	6.31422i	−0.312806	+	0.206829i
$933$	4.18420	−	4.18420i	0.136984	−	0.136984i
$934$	13.1783	−	3.96281i	0.431207	−	0.129667i
$935$			51.6194i			1.68814i
$936$	5.72695	−	6.87596i	0.187191	−	0.224748i
$937$			23.0570i			0.753238i	0.926368	+	0.376619i	$0.122913\pi$
$937$			23.0570i			0.753238i	−0.926368	+	0.376619i	$0.877087\pi$
$938$		0			0
$939$	4.88423	−	4.88423i	0.159391	−	0.159391i
$940$	16.0698	+	3.27737i	0.524140	+	0.106896i
$941$	22.6035	+	22.6035i	0.736852	+	0.736852i	0.971967	−	0.235116i	$-0.0755469\pi$
$941$	22.6035	+	22.6035i	0.736852	+	0.736852i	−0.235116	+	0.971967i	$0.575547\pi$
$942$	−20.7984	−	11.1817i	−0.677649	−	0.364321i
$943$	−59.3293			−1.93203
$944$	4.91890	+	12.2080i	0.160097	+	0.397337i
$945$		0			0
$946$	5.02075	+	2.69928i	0.163239	+	0.0877612i
$947$	−7.60485	−	7.60485i	−0.247125	−	0.247125i	0.572665	−	0.819790i	$-0.305910\pi$
$947$	−7.60485	−	7.60485i	−0.247125	−	0.247125i	−0.819790	+	0.572665i	$0.805910\pi$
$948$	2.29615	−	11.2586i	0.0745755	−	0.365663i
$949$	−10.2433	+	10.2433i	−0.332510	+	0.332510i
$950$	−0.950083	−	3.15949i	−0.0308248	−	0.102507i
$951$			2.39443i			0.0776449i
$952$		0			0
$953$			2.60332i			0.0843297i	0.999111	+	0.0421649i	$0.0134255\pi$
$953$			2.60332i			0.0843297i	−0.999111	+	0.0421649i	$0.986575\pi$
$954$	22.3758	−	6.72856i	0.724442	−	0.217845i
$955$	9.49729	−	9.49729i	0.307325	−	0.307325i
$956$	−16.0421	−	24.2620i	−0.518840	−	0.784689i
$957$	−13.1922	−	13.1922i	−0.426444	−	0.426444i
$958$	−10.8042	+	20.0961i	−0.349067	+	0.649276i
$959$		0			0
$960$	−14.2198	+	2.61459i	−0.458943	+	0.0843856i
$961$	−14.1686			−0.457051
$962$	0.0719596	−	0.133847i	0.00232007	−	0.00431541i
$963$	−20.2888	−	20.2888i	−0.653798	−	0.653798i
$964$	−3.32937	−	5.03532i	−0.107232	−	0.162177i
$965$	14.5680	−	14.5680i	0.468962	−	0.468962i
$966$		0			0
$967$			10.6383i			0.342106i	0.985262	+	0.171053i	$0.0547169\pi$
$967$			10.6383i			0.342106i	−0.985262	+	0.171053i	$0.945283\pi$
$968$	−1.27268	−	13.9593i	−0.0409055	−	0.448670i
$969$			20.8140i			0.668643i
$970$	−16.0313	−	53.3119i	−0.514734	−	1.71174i
$971$	1.31482	−	1.31482i	0.0421945	−	0.0421945i	−0.685695	−	0.727889i	$-0.740501\pi$
$971$	1.31482	−	1.31482i	0.0421945	−	0.0421945i	0.727889	+	0.685695i	$0.240501\pi$
$972$	−6.41896	+	31.4739i	−0.205888	+	1.00952i
$973$		0			0
$974$	−16.2850	−	8.75523i	−0.521806	−	0.280536i
$975$	−0.716569			−0.0229486
$976$	−33.9802	+	13.6914i	−1.08768	+	0.438252i
$977$	6.41094			0.205104			0.102552	−	0.994728i	$-0.467299\pi$
$977$	6.41094			0.205104			0.102552	+	0.994728i	$0.467299\pi$
$978$	4.55717	+	2.45005i	0.145722	+	0.0783438i
$979$	3.79465	+	3.79465i	0.121278	+	0.121278i
$980$		0			0
$981$	23.1160	−	23.1160i	0.738038	−	0.738038i
$982$	5.86014	+	19.4878i	0.187004	+	0.621881i
$983$			19.1693i			0.611405i	0.952127	+	0.305702i	$0.0988913\pi$
$983$			19.1693i			0.611405i	−0.952127	+	0.305702i	$0.901109\pi$
$984$	−13.5393	+	16.2558i	−0.431618	+	0.518215i
$985$			43.9548i			1.40052i
$986$	45.2292	−	13.6008i	1.44039	−	0.433137i
$987$		0			0
$988$	9.17571	−	6.06702i	0.291918	−	0.193018i
$989$	4.87313	+	4.87313i	0.154957	+	0.154957i
$990$	−12.6820	+	23.5889i	−0.403059	+	0.749704i
$991$	−16.1814			−0.514019			−0.257009	−	0.966409i	$-0.582737\pi$
$991$	−16.1814			−0.514019			−0.257009	+	0.966409i	$0.582737\pi$
$992$	14.5049	+	18.1166i	0.460531	+	0.575204i
$993$	−9.25270			−0.293626
$994$		0			0
$995$	−6.44966	−	6.44966i	−0.204468	−	0.204468i
$996$	−20.7362	+	13.7108i	−0.657050	+	0.434445i
$997$	−19.0081	+	19.0081i	−0.601992	+	0.601992i	−0.940841	−	0.338849i	$-0.889962\pi$
$997$	−19.0081	+	19.0081i	−0.601992	+	0.601992i	0.338849	+	0.940841i	$0.389962\pi$
$998$	56.3821	−	16.9545i	1.78474	−	0.536686i
$999$			0.347340i			0.0109893i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.2.m.k.589.4		24
7.2	even	3		784.2.x.o.557.12		48
7.3	odd	6		112.2.w.c.93.4	yes	48
7.4	even	3		784.2.x.o.765.4		48
7.5	odd	6		112.2.w.c.109.12	yes	48
7.6	odd	2		784.2.m.j.589.4		24
16.5	even	4	inner	784.2.m.k.197.4		24
28.3	even	6		448.2.ba.c.401.8		48
28.19	even	6		448.2.ba.c.81.5		48
56.3	even	6		896.2.ba.e.289.5		48
56.5	odd	6		896.2.ba.f.417.5		48
56.19	even	6		896.2.ba.e.417.8		48
56.45	odd	6		896.2.ba.f.289.8		48
112.3	even	12		896.2.ba.e.737.8		48
112.5	odd	12		112.2.w.c.53.4	yes	48
112.19	even	12		896.2.ba.e.865.5		48
112.37	even	12		784.2.x.o.165.4		48
112.45	odd	12		896.2.ba.f.737.5		48
112.53	even	12		784.2.x.o.373.12		48
112.59	even	12		448.2.ba.c.177.5		48
112.61	odd	12		896.2.ba.f.865.8		48
112.69	odd	4		784.2.m.j.197.4		24
112.75	even	12		448.2.ba.c.305.8		48
112.101	odd	12		112.2.w.c.37.12	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.w.c.37.12	✓	48	112.101	odd	12
112.2.w.c.53.4	yes	48	112.5	odd	12
112.2.w.c.93.4	yes	48	7.3	odd	6
112.2.w.c.109.12	yes	48	7.5	odd	6
448.2.ba.c.81.5		48	28.19	even	6
448.2.ba.c.177.5		48	112.59	even	12
448.2.ba.c.305.8		48	112.75	even	12
448.2.ba.c.401.8		48	28.3	even	6
784.2.m.j.197.4		24	112.69	odd	4
784.2.m.j.589.4		24	7.6	odd	2
784.2.m.k.197.4		24	16.5	even	4	inner
784.2.m.k.589.4		24	1.1	even	1	trivial
784.2.x.o.165.4		48	112.37	even	12
784.2.x.o.373.12		48	112.53	even	12
784.2.x.o.557.12		48	7.2	even	3
784.2.x.o.765.4		48	7.4	even	3
896.2.ba.e.289.5		48	56.3	even	6
896.2.ba.e.417.8		48	56.19	even	6
896.2.ba.e.737.8		48	112.3	even	12
896.2.ba.e.865.5		48	112.19	even	12
896.2.ba.f.289.8		48	56.45	odd	6
896.2.ba.f.417.5		48	56.5	odd	6
896.2.ba.f.737.5		48	112.45	odd	12
896.2.ba.f.865.8		48	112.61	odd	12

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:	\( N \)	\(=\)	\( 784 = 2^{4} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	784.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.669670 + 1.24561i) q^{2} +(0.608827 + 0.608827i) q^{3} +(-1.10308 - 1.66829i) q^{4} +(-1.48423 + 1.48423i) q^{5} +(-1.16607 + 0.350647i) q^{6} +(2.81674 - 0.256804i) q^{8} -2.25866i q^{9} +O(q^{10})\)	\(q+(-0.669670 + 1.24561i) q^{2} +(0.608827 + 0.608827i) q^{3} +(-1.10308 - 1.66829i) q^{4} +(-1.48423 + 1.48423i) q^{5} +(-1.16607 + 0.350647i) q^{6} +(2.81674 - 0.256804i) q^{8} -2.25866i q^{9} +(-0.854824 - 2.84271i) q^{10} +(2.82452 - 2.82452i) q^{11} +(0.344116 - 1.68729i) q^{12} +(0.990473 + 0.990473i) q^{13} -1.80728 q^{15} +(-1.56641 + 3.68054i) q^{16} +6.15656 q^{17} +(2.81341 + 1.51256i) q^{18} +(2.77648 + 2.77648i) q^{19} +(4.11335 + 0.838901i) q^{20} +(1.62675 + 5.40975i) q^{22} +6.82961i q^{23} +(1.87126 + 1.55856i) q^{24} +0.594143i q^{25} +(-1.89703 + 0.570452i) q^{26} +(3.20161 - 3.20161i) q^{27} +(-3.83574 - 3.83574i) q^{29} +(1.21028 - 2.25116i) q^{30} -4.10261 q^{31} +(-3.53553 - 4.41588i) q^{32} +3.43929 q^{33} +(-4.12286 + 7.66866i) q^{34} +(-3.76811 + 2.49149i) q^{36} +(-0.0542444 + 0.0542444i) q^{37} +(-5.31773 + 1.59908i) q^{38} +1.20605i q^{39} +(-3.79953 + 4.56184i) q^{40} +8.68707i q^{41} +(0.713530 - 0.713530i) q^{43} +(-7.82782 - 1.59645i) q^{44} +(3.35236 + 3.35236i) q^{45} +(-8.50703 - 4.57359i) q^{46} +3.90675 q^{47} +(-3.19449 + 1.28714i) q^{48} +(-0.740070 - 0.397880i) q^{50} +(3.74828 + 3.74828i) q^{51} +(0.559826 - 2.74498i) q^{52} +(5.17243 - 5.17243i) q^{53} +(1.84393 + 6.13199i) q^{54} +8.38446i q^{55} +3.38079i q^{57} +(7.34652 - 2.20915i) q^{58} +(2.32669 - 2.32669i) q^{59} +(1.99358 + 3.01507i) q^{60} +(6.47617 + 6.47617i) q^{61} +(2.74740 - 5.11025i) q^{62} +(7.86810 - 1.44670i) q^{64} -2.94017 q^{65} +(-2.30319 + 4.28401i) q^{66} +(1.09616 + 1.09616i) q^{67} +(-6.79120 - 10.2710i) q^{68} +(-4.15805 + 4.15805i) q^{69} -2.86486i q^{71} +(-0.580033 - 6.36207i) q^{72} +10.3418i q^{73} +(-0.0312415 - 0.103893i) q^{74} +(-0.361731 + 0.361731i) q^{75} +(1.56929 - 7.69467i) q^{76} +(-1.50227 - 0.807659i) q^{78} +6.67261 q^{79} +(-3.13784 - 7.78766i) q^{80} -2.87752 q^{81} +(-10.8207 - 5.81747i) q^{82} +(-10.2078 - 10.2078i) q^{83} +(-9.13773 + 9.13773i) q^{85} +(0.410950 + 1.36661i) q^{86} -4.67061i q^{87} +(7.23061 - 8.68131i) q^{88} +1.34347i q^{89} +(-6.42071 + 1.93076i) q^{90} +(11.3938 - 7.53363i) q^{92} +(-2.49778 - 2.49778i) q^{93} +(-2.61623 + 4.86628i) q^{94} -8.24184 q^{95} +(0.535983 - 4.84104i) q^{96} +18.7539 q^{97} +(-6.37963 - 6.37963i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{2} + 4 q^{4} + 4 q^{5} + 2 q^{6} - 2 q^{8}+O(q^{10}) \) 24 * q + 4 * q^2 + 4 * q^4 + 4 * q^5 + 2 * q^6 - 2 * q^8	\( 24 q + 4 q^{2} + 4 q^{4} + 4 q^{5} + 2 q^{6} - 2 q^{8} - 2 q^{10} + 4 q^{11} + 2 q^{12} + 12 q^{13} - 20 q^{15} - 16 q^{16} + 8 q^{17} - 18 q^{18} - 4 q^{19} + 8 q^{20} + 18 q^{24} - 10 q^{26} + 12 q^{27} + 12 q^{29} + 4 q^{30} + 28 q^{31} - 16 q^{32} + 16 q^{33} + 22 q^{34} - 36 q^{36} + 24 q^{37} + 20 q^{38} + 26 q^{40} - 20 q^{43} - 6 q^{44} - 28 q^{45} + 14 q^{46} - 20 q^{47} - 28 q^{48} + 28 q^{50} - 24 q^{51} - 16 q^{52} + 16 q^{53} + 64 q^{54} + 6 q^{58} - 20 q^{59} - 46 q^{60} + 8 q^{61} - 12 q^{62} + 40 q^{64} - 8 q^{65} - 20 q^{66} - 48 q^{67} + 20 q^{69} + 32 q^{72} + 8 q^{74} - 4 q^{75} + 18 q^{76} + 58 q^{78} + 36 q^{79} - 28 q^{80} + 2 q^{82} + 4 q^{83} + 20 q^{86} + 42 q^{88} + 10 q^{90} + 38 q^{92} - 8 q^{93} - 72 q^{94} + 4 q^{95} - 120 q^{96} + 24 q^{97} - 12 q^{99}+O(q^{100}) \) 24 * q + 4 * q^2 + 4 * q^4 + 4 * q^5 + 2 * q^6 - 2 * q^8 - 2 * q^10 + 4 * q^11 + 2 * q^12 + 12 * q^13 - 20 * q^15 - 16 * q^16 + 8 * q^17 - 18 * q^18 - 4 * q^19 + 8 * q^20 + 18 * q^24 - 10 * q^26 + 12 * q^27 + 12 * q^29 + 4 * q^30 + 28 * q^31 - 16 * q^32 + 16 * q^33 + 22 * q^34 - 36 * q^36 + 24 * q^37 + 20 * q^38 + 26 * q^40 - 20 * q^43 - 6 * q^44 - 28 * q^45 + 14 * q^46 - 20 * q^47 - 28 * q^48 + 28 * q^50 - 24 * q^51 - 16 * q^52 + 16 * q^53 + 64 * q^54 + 6 * q^58 - 20 * q^59 - 46 * q^60 + 8 * q^61 - 12 * q^62 + 40 * q^64 - 8 * q^65 - 20 * q^66 - 48 * q^67 + 20 * q^69 + 32 * q^72 + 8 * q^74 - 4 * q^75 + 18 * q^76 + 58 * q^78 + 36 * q^79 - 28 * q^80 + 2 * q^82 + 4 * q^83 + 20 * q^86 + 42 * q^88 + 10 * q^90 + 38 * q^92 - 8 * q^93 - 72 * q^94 + 4 * q^95 - 120 * q^96 + 24 * q^97 - 12 * q^99

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