LMFDB - Embedded newform 115.2.e.a.68.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [115,2,Mod(22,115)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(115, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("115.22");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	115.e (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:	$0.918279623245$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 6 x^{18} + 3 x^{16} + 80 x^{14} - 600 x^{12} + 3500 x^{10} - 15000 x^{8} + 50000 x^{6} + \cdots + 9765625 $ x^20 - 6x^18 + 3x^16 + 80x^14 - 600x^12 + 3500x^10 - 15000x^8 + 50000x^6 + 46875x^4 - 2343750*x^2 + 9765625
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			68.8
Root			$2.22384 - 0.233538i$ of defining polynomial
Character	$\chi$	$=$	115.68
Dual form			115.2.e.a.22.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.562704 - 0.562704i) q^{2} +(0.534388 + 0.534388i) q^{3} +1.36673i q^{4} +(0.233538 - 2.22384i) q^{5} +0.601404 q^{6} +(0.567230 + 0.567230i) q^{7} +(1.89447 + 1.89447i) q^{8} -2.42886i q^{9} +O(q^{10})$	\(q+(0.562704 - 0.562704i) q^{2} +(0.534388 + 0.534388i) q^{3} +1.36673i q^{4} +(0.233538 - 2.22384i) q^{5} +0.601404 q^{6} +(0.567230 + 0.567230i) q^{7} +(1.89447 + 1.89447i) q^{8} -2.42886i q^{9} +(-1.11995 - 1.38278i) q^{10} +4.83416i q^{11} +(-0.730363 + 0.730363i) q^{12} +(-3.26120 - 3.26120i) q^{13} +0.638365 q^{14} +(1.31319 - 1.06359i) q^{15} -0.601404 q^{16} +(-1.54673 - 1.54673i) q^{17} +(-1.36673 - 1.36673i) q^{18} -7.21323 q^{19} +(3.03938 + 0.319183i) q^{20} +0.606242i q^{21} +(2.72020 + 2.72020i) q^{22} +(4.11977 - 2.45509i) q^{23} +2.02477i q^{24} +(-4.89092 - 1.03870i) q^{25} -3.67018 q^{26} +(2.90112 - 2.90112i) q^{27} +(-0.775250 + 0.775250i) q^{28} +5.91435i q^{29} +(0.140451 - 1.33743i) q^{30} -1.58613 q^{31} +(-4.12736 + 4.12736i) q^{32} +(-2.58332 + 2.58332i) q^{33} -1.74070 q^{34} +(1.39390 - 1.12896i) q^{35} +3.31959 q^{36} +(6.03976 + 6.03976i) q^{37} +(-4.05891 + 4.05891i) q^{38} -3.48549i q^{39} +(4.65543 - 3.77057i) q^{40} +1.73346 q^{41} +(0.341135 + 0.341135i) q^{42} +(4.49303 - 4.49303i) q^{43} -6.60699 q^{44} +(-5.40139 - 0.567230i) q^{45} +(0.936723 - 3.69970i) q^{46} +(0.427100 - 0.427100i) q^{47} +(-0.321383 - 0.321383i) q^{48} -6.35650i q^{49} +(-3.33662 + 2.16766i) q^{50} -1.65311i q^{51} +(4.45718 - 4.45718i) q^{52} +(6.85025 - 6.85025i) q^{53} -3.26494i q^{54} +(10.7504 + 1.12896i) q^{55} +2.14920i q^{56} +(-3.85466 - 3.85466i) q^{57} +(3.32803 + 3.32803i) q^{58} +7.76922i q^{59} +(1.45364 + 1.79478i) q^{60} +7.62173i q^{61} +(-0.892524 + 0.892524i) q^{62} +(1.37772 - 1.37772i) q^{63} +3.44215i q^{64} +(-8.01400 + 6.49077i) q^{65} +2.90729i q^{66} +(-1.20560 - 1.20560i) q^{67} +(2.11396 - 2.11396i) q^{68} +(3.51353 + 0.889586i) q^{69} +(0.149082 - 1.41962i) q^{70} +10.2992 q^{71} +(4.60140 - 4.60140i) q^{72} +(0.559153 + 0.559153i) q^{73} +6.79719 q^{74} +(-2.05858 - 3.16872i) q^{75} -9.85853i q^{76} +(-2.74208 + 2.74208i) q^{77} +(-1.96130 - 1.96130i) q^{78} -5.66273 q^{79} +(-0.140451 + 1.33743i) q^{80} -4.18593 q^{81} +(0.975423 - 0.975423i) q^{82} +(2.15297 - 2.15297i) q^{83} -0.828568 q^{84} +(-3.80090 + 3.07846i) q^{85} -5.05649i q^{86} +(-3.16056 + 3.16056i) q^{87} +(-9.15818 + 9.15818i) q^{88} +9.48215 q^{89} +(-3.35857 + 2.72020i) q^{90} -3.69970i q^{91} +(3.35544 + 5.63061i) q^{92} +(-0.847611 - 0.847611i) q^{93} -0.480662i q^{94} +(-1.68456 + 16.0411i) q^{95} -4.41122 q^{96} +(-5.03841 - 5.03841i) q^{97} +(-3.57683 - 3.57683i) q^{98} +11.7415 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 4 q^{2} - 8 q^{3} - 8 q^{6} + 4 q^{8}+O(q^{10}) $ 20 * q - 4 * q^2 - 8 * q^3 - 8 * q^6 + 4 * q^8	$ 20 q - 4 q^{2} - 8 q^{3} - 8 q^{6} + 4 q^{8} - 16 q^{12} + 4 q^{13} + 8 q^{16} + 8 q^{18} - 12 q^{25} - 16 q^{26} + 4 q^{27} - 4 q^{31} + 24 q^{32} - 8 q^{35} - 32 q^{36} - 36 q^{41} + 32 q^{46} - 8 q^{47} + 4 q^{48} + 60 q^{50} + 40 q^{52} - 12 q^{55} + 36 q^{58} - 60 q^{62} - 76 q^{70} + 44 q^{71} + 72 q^{72} - 56 q^{73} + 28 q^{75} - 12 q^{77} - 44 q^{78} + 92 q^{81} + 28 q^{82} - 4 q^{85} + 24 q^{87} - 72 q^{92} - 8 q^{93} + 64 q^{95} - 104 q^{96} - 60 q^{98}+O(q^{100}) $ 20 * q - 4 * q^2 - 8 * q^3 - 8 * q^6 + 4 * q^8 - 16 * q^12 + 4 * q^13 + 8 * q^16 + 8 * q^18 - 12 * q^25 - 16 * q^26 + 4 * q^27 - 4 * q^31 + 24 * q^32 - 8 * q^35 - 32 * q^36 - 36 * q^41 + 32 * q^46 - 8 * q^47 + 4 * q^48 + 60 * q^50 + 40 * q^52 - 12 * q^55 + 36 * q^58 - 60 * q^62 - 76 * q^70 + 44 * q^71 + 72 * q^72 - 56 * q^73 + 28 * q^75 - 12 * q^77 - 44 * q^78 + 92 * q^81 + 28 * q^82 - 4 * q^85 + 24 * q^87 - 72 * q^92 - 8 * q^93 + 64 * q^95 - 104 * q^96 - 60 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	0.562704	−	0.562704i	0.397892	−	0.397892i	−0.479597	−	0.877489i	$-0.659217\pi$
$2$	0.562704	−	0.562704i	0.397892	−	0.397892i	0.877489	+	0.479597i	$0.159217\pi$
$3$	0.534388	+	0.534388i	0.308529	+	0.308529i	0.844339	−	0.535810i	$-0.179994\pi$
$3$	0.534388	+	0.534388i	0.308529	+	0.308529i	−0.535810	+	0.844339i	$0.679994\pi$
$4$			1.36673i			0.683364i
$5$	0.233538	−	2.22384i	0.104441	−	0.994531i
$5$	0.233538	−	2.22384i	0.104441	−	0.994531i
$6$	0.601404			0.245522
$7$	0.567230	+	0.567230i	0.214393	+	0.214393i	0.806131	−	0.591738i	$-0.201558\pi$
$7$	0.567230	+	0.567230i	0.214393	+	0.214393i	−0.591738	+	0.806131i	$0.701558\pi$
$8$	1.89447	+	1.89447i	0.669797	+	0.669797i
$9$		−	2.42886i		−	0.809620i
$10$	−1.11995	−	1.38278i	−0.354159	−	0.437272i
$11$			4.83416i			1.45755i	0.684751	+	0.728777i	$0.259911\pi$
$11$			4.83416i			1.45755i	−0.684751	+	0.728777i	$0.740089\pi$
$12$	−0.730363	+	0.730363i	−0.210838	+	0.210838i
$13$	−3.26120	−	3.26120i	−0.904494	−	0.904494i	0.0913268	−	0.995821i	$-0.470889\pi$
$13$	−3.26120	−	3.26120i	−0.904494	−	0.904494i	−0.995821	+	0.0913268i	$0.970889\pi$
$14$	0.638365			0.170610
$15$	1.31319	−	1.06359i	0.339065	−	0.274619i
$16$	−0.601404			−0.150351
$17$	−1.54673	−	1.54673i	−0.375137	−	0.375137i	0.494207	−	0.869344i	$-0.335458\pi$
$17$	−1.54673	−	1.54673i	−0.375137	−	0.375137i	−0.869344	+	0.494207i	$0.835458\pi$
$18$	−1.36673	−	1.36673i	−0.322141	−	0.322141i
$19$	−7.21323			−1.65483			−0.827414	−	0.561592i	$-0.810189\pi$
$19$	−7.21323			−1.65483			−0.827414	+	0.561592i	$0.810189\pi$
$20$	3.03938	+	0.319183i	0.679627	+	0.0713714i
$21$			0.606242i			0.132293i
$22$	2.72020	+	2.72020i	0.579949	+	0.579949i
$23$	4.11977	−	2.45509i	0.859032	−	0.511922i
$23$	4.11977	−	2.45509i	0.859032	−	0.511922i
$24$			2.02477i			0.413303i
$25$	−4.89092	−	1.03870i	−0.978184	−	0.207740i
$26$	−3.67018			−0.719782
$27$	2.90112	−	2.90112i	0.558320	−	0.558320i
$28$	−0.775250	+	0.775250i	−0.146508	+	0.146508i
$29$			5.91435i			1.09827i	0.835735	+	0.549134i	$0.185042\pi$
$29$			5.91435i			1.09827i	−0.835735	+	0.549134i	$0.814958\pi$
$30$	0.140451	−	1.33743i	0.0256426	−	0.244180i
$31$	−1.58613			−0.284878			−0.142439	−	0.989804i	$-0.545494\pi$
$31$	−1.58613			−0.284878			−0.142439	+	0.989804i	$0.545494\pi$
$32$	−4.12736	+	4.12736i	−0.729620	+	0.729620i
$33$	−2.58332	+	2.58332i	−0.449698	+	0.449698i
$34$	−1.74070			−0.298528
$35$	1.39390	−	1.12896i	0.235612	−	0.190829i
$36$	3.31959			0.553265
$37$	6.03976	+	6.03976i	0.992930	+	0.992930i	0.999975	−	0.00704521i	$-0.00224258\pi$
$37$	6.03976	+	6.03976i	0.992930	+	0.992930i	−0.00704521	+	0.999975i	$0.502243\pi$
$38$	−4.05891	+	4.05891i	−0.658443	+	0.658443i
$39$		−	3.48549i		−	0.558125i
$40$	4.65543	−	3.77057i	0.736088	−	0.596179i
$41$	1.73346			0.270721			0.135360	−	0.990796i	$-0.456781\pi$
$41$	1.73346			0.270721			0.135360	+	0.990796i	$0.456781\pi$
$42$	0.341135	+	0.341135i	0.0526382	+	0.0526382i
$43$	4.49303	−	4.49303i	0.685180	−	0.685180i	−0.275982	−	0.961163i	$-0.589003\pi$
$43$	4.49303	−	4.49303i	0.685180	−	0.685180i	0.961163	+	0.275982i	$0.0890032\pi$
$44$	−6.60699			−0.996041
$45$	−5.40139	−	0.567230i	−0.805192	−	0.0845577i
$46$	0.936723	−	3.69970i	0.138112	−	0.545491i
$47$	0.427100	−	0.427100i	0.0622989	−	0.0622989i	−0.675271	−	0.737570i	$-0.735973\pi$
$47$	0.427100	−	0.427100i	0.0622989	−	0.0622989i	0.737570	+	0.675271i	$0.235973\pi$
$48$	−0.321383	−	0.321383i	−0.0463877	−	0.0463877i
$49$		−	6.35650i		−	0.908071i
$50$	−3.33662	+	2.16766i	−0.471869	+	0.306553i
$51$		−	1.65311i		−	0.231481i
$52$	4.45718	−	4.45718i	0.618099	−	0.618099i
$53$	6.85025	−	6.85025i	0.940954	−	0.940954i	−0.0573973	−	0.998351i	$-0.518280\pi$
$53$	6.85025	−	6.85025i	0.940954	−	0.940954i	0.998351	+	0.0573973i	$0.0182802\pi$
$54$		−	3.26494i		−	0.444302i
$55$	10.7504	+	1.12896i	1.44958	+	0.152229i
$56$			2.14920i			0.287199i
$57$	−3.85466	−	3.85466i	−0.510562	−	0.510562i
$58$	3.32803	+	3.32803i	0.436992	+	0.436992i
$59$			7.76922i			1.01147i	0.862690	+	0.505733i	$0.168778\pi$
$59$			7.76922i			1.01147i	−0.862690	+	0.505733i	$0.831222\pi$
$60$	1.45364	+	1.79478i	0.187664	+	0.231705i
$61$			7.62173i			0.975862i	0.872882	+	0.487931i	$0.162248\pi$
$61$			7.62173i			0.975862i	−0.872882	+	0.487931i	$0.837752\pi$
$62$	−0.892524	+	0.892524i	−0.113351	+	0.113351i
$63$	1.37772	−	1.37772i	0.173577	−	0.173577i
$64$			3.44215i			0.430269i
$65$	−8.01400	+	6.49077i	−0.994014	+	0.805081i
$66$			2.90729i			0.357862i
$67$	−1.20560	−	1.20560i	−0.147287	−	0.147287i	0.629618	−	0.776905i	$-0.283211\pi$
$67$	−1.20560	−	1.20560i	−0.147287	−	0.147287i	−0.776905	+	0.629618i	$0.783211\pi$
$68$	2.11396	−	2.11396i	0.256355	−	0.256355i
$69$	3.51353	+	0.889586i	0.422979	+	0.107094i
$70$	0.149082	−	1.41962i	0.0178187	−	0.169677i
$71$	10.2992			1.22229			0.611145	−	0.791519i	$-0.290709\pi$
$71$	10.2992			1.22229			0.611145	+	0.791519i	$0.290709\pi$
$72$	4.60140	−	4.60140i	0.542281	−	0.542281i
$73$	0.559153	+	0.559153i	0.0654439	+	0.0654439i	0.739071	−	0.673627i	$-0.235265\pi$
$73$	0.559153	+	0.559153i	0.0654439	+	0.0654439i	−0.673627	+	0.739071i	$0.735265\pi$
$74$	6.79719			0.790157
$75$	−2.05858	−	3.16872i	−0.237704	−	0.365892i
$76$		−	9.85853i		−	1.13085i
$77$	−2.74208	+	2.74208i	−0.312489	+	0.312489i
$78$	−1.96130	−	1.96130i	−0.222073	−	0.222073i
$79$	−5.66273			−0.637107			−0.318553	−	0.947905i	$-0.603197\pi$
$79$	−5.66273			−0.637107			−0.318553	+	0.947905i	$0.603197\pi$
$80$	−0.140451	+	1.33743i	−0.0157028	+	0.149529i
$81$	−4.18593			−0.465104
$82$	0.975423	−	0.975423i	0.107717	−	0.107717i
$83$	2.15297	−	2.15297i	0.236319	−	0.236319i	−0.579005	−	0.815324i	$-0.696559\pi$
$83$	2.15297	−	2.15297i	0.236319	−	0.236319i	0.815324	+	0.579005i	$0.196559\pi$
$84$	−0.828568			−0.0904042
$85$	−3.80090	+	3.07846i	−0.412265	+	0.333906i
$86$		−	5.05649i		−	0.545255i
$87$	−3.16056	+	3.16056i	−0.338847	+	0.338847i
$88$	−9.15818	+	9.15818i	−0.976265	+	0.976265i
$89$	9.48215			1.00511			0.502553	−	0.864546i	$-0.332394\pi$
$89$	9.48215			1.00511			0.502553	+	0.864546i	$0.332394\pi$
$90$	−3.35857	+	2.72020i	−0.354024	+	0.286734i
$91$		−	3.69970i		−	0.387834i
$92$	3.35544	+	5.63061i	0.349829	+	0.587032i
$93$	−0.847611	−	0.847611i	−0.0878932	−	0.0878932i
$94$		−	0.480662i		−	0.0495765i
$95$	−1.68456	+	16.0411i	−0.172832	+	1.64578i
$96$	−4.41122			−0.450218
$97$	−5.03841	−	5.03841i	−0.511573	−	0.511573i	0.403435	−	0.915008i	$-0.367816\pi$
$97$	−5.03841	−	5.03841i	−0.511573	−	0.511573i	−0.915008	+	0.403435i	$0.867816\pi$
$98$	−3.57683	−	3.57683i	−0.361314	−	0.361314i
$99$	11.7415			1.18007
$100$	1.41962	−	6.68456i	0.141962	−	0.668456i
$101$	−9.69182			−0.964372			−0.482186	−	0.876069i	$-0.660157\pi$
$101$	−9.69182			−0.964372			−0.482186	+	0.876069i	$0.660157\pi$
$102$	−0.930210	−	0.930210i	−0.0921045	−	0.0921045i
$103$	−10.1377	+	10.1377i	−0.998895	+	0.998895i	−0.999999	−	0.00110398i	$-0.999649\pi$
$103$	−10.1377	+	10.1377i	−0.998895	+	0.998895i	0.00110398	+	0.999999i	$0.499649\pi$
$104$		−	12.3565i		−	1.21165i
$105$	1.34818	+	0.141580i	0.131569	+	0.0138168i
$106$		−	7.70932i		−	0.748796i
$107$	−3.08318	−	3.08318i	−0.298062	−	0.298062i	0.542192	−	0.840255i	$-0.317594\pi$
$107$	−3.08318	−	3.08318i	−0.298062	−	0.298062i	−0.840255	+	0.542192i	$0.817594\pi$
$108$	3.96504	+	3.96504i	0.381536	+	0.381536i
$109$	9.96867			0.954826			0.477413	−	0.878679i	$-0.341575\pi$
$109$	9.96867			0.954826			0.477413	+	0.878679i	$0.341575\pi$
$110$	6.68456	−	5.41402i	0.637348	−	0.516207i
$111$			6.45515i			0.612695i
$112$	−0.341135	−	0.341135i	−0.0322342	−	0.0322342i
$113$	−7.78046	+	7.78046i	−0.731924	+	0.731924i	−0.971001	−	0.239077i	$-0.923155\pi$
$113$	−7.78046	+	7.78046i	−0.731924	+	0.731924i	0.239077	+	0.971001i	$0.423155\pi$
$114$	−4.33807			−0.406297
$115$	−4.49761	−	9.73507i	−0.419404	−	0.907800i
$116$	−8.08331			−0.750517
$117$	−7.92100	+	7.92100i	−0.732296	+	0.732296i
$118$	4.37177	+	4.37177i	0.402454	+	0.402454i
$119$		−	1.75470i		−	0.160853i
$120$	4.50275	+	0.472859i	0.411043	+	0.0431659i
$121$	−12.3691			−1.12447
$122$	4.28878	+	4.28878i	0.388288	+	0.388288i
$123$	0.926338	+	0.926338i	0.0835251	+	0.0835251i
$124$		−	2.16781i		−	0.194676i
$125$	−3.45212	+	10.6340i	−0.308767	+	0.951138i
$126$		−	1.55050i		−	0.138129i
$127$	−5.56625	+	5.56625i	−0.493925	+	0.493925i	−0.909541	−	0.415615i	$-0.863566\pi$
$127$	−5.56625	+	5.56625i	−0.493925	+	0.493925i	0.415615	+	0.909541i	$0.363566\pi$
$128$	−6.31780	−	6.31780i	−0.558420	−	0.558420i
$129$	4.80204			0.422796
$130$	−0.857125	+	8.16189i	−0.0751749	+	0.715845i
$131$	13.3479			1.16621			0.583105	−	0.812397i	$-0.301838\pi$
$131$	13.3479			1.16621			0.583105	+	0.812397i	$0.301838\pi$
$132$	−3.53069	−	3.53069i	−0.307307	−	0.307307i
$133$	−4.09156	−	4.09156i	−0.354783	−	0.354783i
$134$	−1.35679			−0.117208
$135$	−5.77410	−	7.12914i	−0.496955	−	0.613578i
$136$		−	5.86047i		−	0.502531i
$137$	−7.81947	−	7.81947i	−0.668062	−	0.668062i	0.289205	−	0.957267i	$-0.406609\pi$
$137$	−7.81947	−	7.81947i	−0.668062	−	0.668062i	−0.957267	+	0.289205i	$0.906609\pi$
$138$	2.47765	−	1.47650i	0.210911	−	0.125688i
$139$		−	1.41624i		−	0.120124i	−0.998195	−	0.0600619i	$-0.980870\pi$
$139$		−	1.41624i		−	0.120124i	0.998195	−	0.0600619i	$-0.0191298\pi$
$140$	1.54298	+	1.90508i	0.130406	+	0.161009i
$141$	0.456474			0.0384420
$142$	5.79540	−	5.79540i	0.486339	−	0.486339i
$143$	15.7652	−	15.7652i	1.31835	−	1.31835i
$144$			1.46073i			0.121727i
$145$	13.1526	+	1.38122i	1.09226	+	0.114704i
$146$	0.629275			0.0520792
$147$	3.39684	−	3.39684i	0.280166	−	0.280166i
$148$	−8.25471	+	8.25471i	−0.678533	+	0.678533i
$149$	−1.68523			−0.138059			−0.0690297	−	0.997615i	$-0.521990\pi$
$149$	−1.68523			−0.138059			−0.0690297	+	0.997615i	$0.521990\pi$
$150$	−2.94142	−	0.624679i	−0.240166	−	0.0510048i
$151$	11.9136			0.969516			0.484758	−	0.874648i	$-0.338908\pi$
$151$	11.9136			0.969516			0.484758	+	0.874648i	$0.338908\pi$
$152$	−13.6653	−	13.6653i	−1.10840	−	1.10840i
$153$	−3.75679	+	3.75679i	−0.303718	+	0.303718i
$154$			3.08596i			0.248674i
$155$	−0.370422	+	3.52731i	−0.0297530	+	0.283320i
$156$	4.76372			0.381403
$157$	−1.83857	−	1.83857i	−0.146734	−	0.146734i	0.629923	−	0.776657i	$-0.283086\pi$
$157$	−1.83857	−	1.83857i	−0.146734	−	0.146734i	−0.776657	+	0.629923i	$0.783086\pi$
$158$	−3.18644	+	3.18644i	−0.253500	+	0.253500i
$159$	7.32138			0.580623
$160$	8.21468	+	10.1425i	0.649428	+	0.801832i
$161$	3.72946	+	0.944257i	0.293923	+	0.0744179i
$162$	−2.35544	+	2.35544i	−0.185061	+	0.185061i
$163$	9.28861	+	9.28861i	0.727540	+	0.727540i	0.970129	−	0.242589i	$-0.0779966\pi$
$163$	9.28861	+	9.28861i	0.727540	+	0.727540i	−0.242589	+	0.970129i	$0.577997\pi$
$164$			2.36917i			0.185001i
$165$	5.14158	+	6.34818i	0.400271	+	0.494205i
$166$		−	2.42297i		−	0.188059i
$167$	8.51690	−	8.51690i	0.659058	−	0.659058i	−0.296099	−	0.955157i	$-0.595686\pi$
$167$	8.51690	−	8.51690i	0.659058	−	0.659058i	0.955157	+	0.296099i	$0.0956860\pi$
$168$	−1.14851	+	1.14851i	−0.0886093	+	0.0886093i
$169$			8.27085i			0.636219i
$170$	−0.406519	+	3.87104i	−0.0311786	+	0.296895i
$171$			17.5199i			1.33978i
$172$	6.14075	+	6.14075i	0.468228	+	0.468228i
$173$	8.16896	+	8.16896i	0.621075	+	0.621075i	0.945806	−	0.324732i	$-0.105274\pi$
$173$	8.16896	+	8.16896i	0.621075	+	0.621075i	−0.324732	+	0.945806i	$0.605274\pi$
$174$			3.55692i			0.269649i
$175$	−2.18510	−	3.36346i	−0.165178	−	0.254254i
$176$		−	2.90729i		−	0.219145i
$177$	−4.15178	+	4.15178i	−0.312067	+	0.312067i
$178$	5.33564	−	5.33564i	0.399923	−	0.399923i
$179$		−	0.886067i		−	0.0662278i	−0.999452	−	0.0331139i	$-0.989458\pi$
$179$		−	0.886067i		−	0.0662278i	0.999452	−	0.0331139i	$-0.0105424\pi$
$180$	0.775250	−	7.38224i	0.0577837	−	0.550239i
$181$		−	18.9869i		−	1.41128i	−0.708570	−	0.705641i	$-0.750659\pi$
$181$		−	18.9869i		−	1.41128i	0.708570	−	0.705641i	$-0.249341\pi$
$182$	−2.08184	−	2.08184i	−0.154316	−	0.154316i
$183$	−4.07296	+	4.07296i	−0.301082	+	0.301082i
$184$	12.4559	+	3.15369i	0.918261	+	0.232493i
$185$	14.8420	−	12.0209i	1.09120	−	0.883797i
$186$	−0.953908			−0.0699439
$187$	7.47714	−	7.47714i	0.546783	−	0.546783i
$188$	0.583730	+	0.583730i	0.0425729	+	0.0425729i
$189$	3.29120			0.239400
$190$	8.07846	+	9.97428i	0.586073	+	0.723610i
$191$		−	0.856663i		−	0.0619860i	−0.999520	−	0.0309930i	$-0.990133\pi$
$191$		−	0.856663i		−	0.0619860i	0.999520	−	0.0309930i	$-0.00986695\pi$
$192$	−1.83944	+	1.83944i	−0.132750	+	0.132750i
$193$	−2.20769	−	2.20769i	−0.158913	−	0.158913i	0.623172	−	0.782085i	$-0.285844\pi$
$193$	−2.20769	−	2.20769i	−0.158913	−	0.158913i	−0.782085	+	0.623172i	$0.785844\pi$
$194$	−5.67027			−0.407102
$195$	−7.75117	−	0.813994i	−0.555073	−	0.0582913i
$196$	8.68761			0.620544
$197$	−0.615785	+	0.615785i	−0.0438729	+	0.0438729i	−0.728703	−	0.684830i	$-0.759876\pi$
$197$	−0.615785	+	0.615785i	−0.0438729	+	0.0438729i	0.684830	+	0.728703i	$0.259876\pi$
$198$	6.60699	−	6.60699i	0.469538	−	0.469538i
$199$	−15.2284			−1.07952			−0.539758	−	0.841820i	$-0.681484\pi$
$199$	−15.2284			−1.07952			−0.539758	+	0.841820i	$0.681484\pi$
$200$	−7.29792	−	11.2335i	−0.516041	−	0.794328i
$201$		−	1.28851i		−	0.0908846i
$202$	−5.45362	+	5.45362i	−0.383716	+	0.383716i
$203$	−3.35480	+	3.35480i	−0.235461	+	0.235461i
$204$	2.25935			0.158186
$205$	0.404828	−	3.85493i	0.0282744	−	0.269240i
$206$			11.4090i			0.794904i
$207$	−5.96307	−	10.0063i	−0.414462	−	0.695489i
$208$	1.96130	+	1.96130i	0.135992	+	0.135992i
$209$		−	34.8699i		−	2.41200i
$210$	0.838296	−	0.678961i	0.0578479	−	0.0468527i
$211$	−23.0609			−1.58758			−0.793790	−	0.608192i	$-0.791895\pi$
$211$	−23.0609			−1.58758			−0.793790	+	0.608192i	$0.791895\pi$
$212$	9.36243	+	9.36243i	0.643014	+	0.643014i
$213$	5.50377	+	5.50377i	0.377112	+	0.377112i
$214$	−3.46984			−0.237193
$215$	−8.94248	−	11.0411i	−0.609872	−	0.752994i
$216$	10.9922			0.747922
$217$	−0.899703	−	0.899703i	−0.0610758	−	0.0610758i
$218$	5.60941	−	5.60941i	0.379917	−	0.379917i
$219$			0.597609i			0.0403827i
$220$	−1.54298	+	14.6929i	−0.104028	+	0.990594i
$221$			10.0884i			0.678619i
$222$	3.63234	+	3.63234i	0.243786	+	0.243786i
$223$	−10.8090	−	10.8090i	−0.723823	−	0.723823i	0.245559	−	0.969382i	$-0.421029\pi$
$223$	−10.8090	−	10.8090i	−0.723823	−	0.723823i	−0.969382	+	0.245559i	$0.921029\pi$
$224$	−4.68232			−0.312851
$225$	−2.52286	+	11.8794i	−0.168190	+	0.791957i
$226$			8.75619i			0.582453i
$227$	1.11638	+	1.11638i	0.0740970	+	0.0740970i	0.743184	−	0.669087i	$-0.233315\pi$
$227$	1.11638	+	1.11638i	0.0740970	+	0.0740970i	−0.669087	+	0.743184i	$0.733315\pi$
$228$	5.26828	−	5.26828i	0.348900	−	0.348900i
$229$	2.59736			0.171639			0.0858194	−	0.996311i	$-0.472649\pi$
$229$	2.59736			0.171639			0.0858194	+	0.996311i	$0.472649\pi$
$230$	−8.00878	−	2.94714i	−0.528083	−	0.194329i
$231$	−2.93067			−0.192824
$232$	−11.2046	+	11.2046i	−0.735616	+	0.735616i
$233$	−19.1532	−	19.1532i	−1.25477	−	1.25477i	−0.953558	−	0.301208i	$-0.902610\pi$
$233$	−19.1532	−	19.1532i	−1.25477	−	1.25477i	−0.301208	−	0.953558i	$-0.597390\pi$
$234$			8.91435i			0.582749i
$235$	−0.850058	−	1.04955i	−0.0554516	−	0.0684648i
$236$	−10.6184			−0.691200
$237$	−3.02609	−	3.02609i	−0.196566	−	0.196566i
$238$	−0.987379	−	0.987379i	−0.0640022	−	0.0640022i
$239$			10.3864i			0.671839i	0.941891	+	0.335919i	$0.109047\pi$
$239$			10.3864i			0.671839i	−0.941891	+	0.335919i	$0.890953\pi$
$240$	−0.789759	+	0.639649i	−0.0509788	+	0.0412892i
$241$		−	9.55818i		−	0.615696i	−0.951436	−	0.307848i	$-0.900391\pi$
$241$		−	9.55818i		−	0.615696i	0.951436	−	0.307848i	$-0.0996089\pi$
$242$	−6.96015	+	6.96015i	−0.447416	+	0.447416i
$243$	−10.9403	−	10.9403i	−0.701818	−	0.701818i
$244$	−10.4168			−0.666870
$245$	−14.1358	−	1.48448i	−0.903105	−	0.0948401i
$246$	1.04251			0.0664679
$247$	23.5238	+	23.5238i	1.49678	+	1.49678i
$248$	−3.00489	−	3.00489i	−0.190810	−	0.190810i
$249$	2.30104			0.145823
$250$	4.04130	+	7.92634i	0.255594	+	0.501306i
$251$			19.4829i			1.22975i	0.788624	+	0.614876i	$0.210794\pi$
$251$			19.4829i			1.22975i	−0.788624	+	0.614876i	$0.789206\pi$
$252$	1.88297	+	1.88297i	0.118616	+	0.118616i
$253$	11.8683	+	19.9156i	0.746154	+	1.25209i
$254$			6.26431i			0.393058i
$255$	−3.67624	−	0.386063i	−0.230215	−	0.0241762i
$256$	−13.9944			−0.874650
$257$	19.0057	−	19.0057i	1.18554	−	1.18554i	0.207253	−	0.978287i	$-0.433548\pi$
$257$	19.0057	−	19.0057i	1.18554	−	1.18554i	0.978287	−	0.207253i	$-0.0664522\pi$
$258$	2.70213	−	2.70213i	0.168227	−	0.168227i
$259$			6.85186i			0.425754i
$260$	−8.87112	−	10.9530i	−0.550164	−	0.679274i
$261$	14.3651			0.889179
$262$	7.51090	−	7.51090i	0.464025	−	0.464025i
$263$	2.88544	−	2.88544i	0.177924	−	0.177924i	−0.612526	−	0.790450i	$-0.709847\pi$
$263$	2.88544	−	2.88544i	0.177924	−	0.177924i	0.790450	+	0.612526i	$0.209847\pi$
$264$	−9.78804			−0.602412
$265$	−13.6341	−	16.8336i	−0.837534	−	1.03408i
$266$	−4.60467			−0.282331
$267$	5.06715	+	5.06715i	0.310104	+	0.310104i
$268$	1.64772	−	1.64772i	0.100651	−	0.100651i
$269$			3.34632i			0.204028i	0.994783	+	0.102014i	$0.0325287\pi$
$269$			3.34632i			0.204028i	−0.994783	+	0.102014i	$0.967471\pi$
$270$	−7.26070	−	0.762486i	−0.441872	−	0.0464034i
$271$	3.53702			0.214858			0.107429	−	0.994213i	$-0.465738\pi$
$271$	3.53702			0.214858			0.107429	+	0.994213i	$0.465738\pi$
$272$	0.930210	+	0.930210i	0.0564023	+	0.0564023i
$273$	1.97708	−	1.97708i	0.119658	−	0.119658i
$274$	−8.80009			−0.531633
$275$	5.02125	−	23.6435i	0.302793	−	1.42576i
$276$	−1.21582	+	4.80204i	−0.0731839	+	0.289049i
$277$	−16.2246	+	16.2246i	−0.974842	+	0.974842i	−0.999691	−	0.0248493i	$-0.992089\pi$
$277$	−16.2246	+	16.2246i	−0.974842	+	0.974842i	0.0248493	+	0.999691i	$0.492089\pi$
$278$	−0.796923	−	0.796923i	−0.0477962	−	0.0477962i
$279$			3.85250i			0.230643i
$280$	4.77948	+	0.501920i	0.285629	+	0.0299954i
$281$		−	13.4117i		−	0.800076i	−0.916499	−	0.400038i	$-0.868997\pi$
$281$		−	13.4117i		−	0.800076i	0.916499	−	0.400038i	$-0.131003\pi$
$282$	0.256860	−	0.256860i	0.0152958	−	0.0152958i
$283$	5.13628	−	5.13628i	0.305320	−	0.305320i	−0.537771	−	0.843091i	$-0.680733\pi$
$283$	5.13628	−	5.13628i	0.305320	−	0.305320i	0.843091	+	0.537771i	$0.180733\pi$
$284$			14.0762i			0.835269i
$285$	−9.47236	+	7.67194i	−0.561094	+	0.454446i
$286$		−	17.7422i		−	1.04912i
$287$	0.983269	+	0.983269i	0.0580405	+	0.0580405i
$288$	10.0248	+	10.0248i	0.590715	+	0.590715i
$289$		−	12.2153i		−	0.718544i
$290$	8.17822	−	6.62378i	0.480242	−	0.388962i
$291$		−	5.38493i		−	0.315670i
$292$	−0.764210	+	0.764210i	−0.0447220	+	0.0447220i
$293$	3.42432	−	3.42432i	0.200051	−	0.200051i	−0.599971	−	0.800022i	$-0.704821\pi$
$293$	3.42432	−	3.42432i	0.200051	−	0.200051i	0.800022	+	0.599971i	$0.204821\pi$
$294$		−	3.82283i		−	0.222952i
$295$	17.2775	+	1.81441i	1.00593	+	0.105639i
$296$			22.8843i			1.33012i
$297$	14.0245	+	14.0245i	0.813782	+	0.813782i
$298$	−0.948286	+	0.948286i	−0.0549327	+	0.0549327i
$299$	−21.4419	−	5.42886i	−1.24002	−	0.313959i
$300$	4.33078	−	2.81352i	0.250038	−	0.162439i
$301$	5.09716			0.293795
$302$	6.70384	−	6.70384i	0.385763	−	0.385763i
$303$	−5.17919	−	5.17919i	−0.297537	−	0.297537i
$304$	4.33807			0.248805
$305$	16.9495	+	1.77996i	0.970526	+	0.101920i
$306$			4.22792i			0.241694i
$307$	0.852220	−	0.852220i	0.0486388	−	0.0486388i	−0.682369	−	0.731008i	$-0.739050\pi$
$307$	0.852220	−	0.852220i	0.0486388	−	0.0486388i	0.731008	+	0.682369i	$0.239050\pi$
$308$	−3.74768	−	3.74768i	−0.213544	−	0.213544i
$309$	−10.8349			−0.616376
$310$	1.77639	+	2.19327i	0.100892	+	0.124569i
$311$	12.4265			0.704641			0.352321	−	0.935879i	$-0.385393\pi$
$311$	12.4265			0.704641			0.352321	+	0.935879i	$0.385393\pi$
$312$	6.60316	−	6.60316i	0.373831	−	0.373831i
$313$	−20.9442	+	20.9442i	−1.18384	+	1.18384i	−0.205096	+	0.978742i	$0.565751\pi$
$313$	−20.9442	+	20.9442i	−1.18384	+	1.18384i	−0.978742	+	0.205096i	$0.934249\pi$
$314$	−2.06915			−0.116769
$315$	−2.74208	−	3.38558i	−0.154499	−	0.190756i
$316$		−	7.73941i		−	0.435376i
$317$	11.3821	−	11.3821i	0.639282	−	0.639282i	−0.311096	−	0.950378i	$-0.600696\pi$
$317$	11.3821	−	11.3821i	0.639282	−	0.639282i	0.950378	+	0.311096i	$0.100696\pi$
$318$	4.11977	−	4.11977i	0.231025	−	0.231025i
$319$	−28.5909			−1.60078
$320$	7.65479	+	0.803872i	0.427916	+	0.0449378i
$321$		−	3.29523i		−	0.183922i
$322$	2.62992	−	1.56724i	0.146560	−	0.0873391i
$323$	11.1569	+	11.1569i	0.620787	+	0.620787i
$324$		−	5.72104i		−	0.317835i
$325$	12.5629	+	19.3377i	0.696862	+	1.07266i
$326$	10.4535			0.578965
$327$	5.32714	+	5.32714i	0.294591	+	0.294591i
$328$	3.28399	+	3.28399i	0.181328	+	0.181328i
$329$	0.484528			0.0267129
$330$	6.46534	+	0.678961i	0.355905	+	0.0373756i
$331$	−19.2375			−1.05739			−0.528693	−	0.848813i	$-0.677318\pi$
$331$	−19.2375			−1.05739			−0.528693	+	0.848813i	$0.677318\pi$
$332$	2.94253	+	2.94253i	0.161492	+	0.161492i
$333$	14.6697	−	14.6697i	0.803896	−	0.803896i
$334$		−	9.58499i		−	0.524467i
$335$	−2.96260	+	2.39950i	−0.161864	+	0.131099i
$336$		−	0.364596i		−	0.0198904i
$337$	7.74457	+	7.74457i	0.421873	+	0.421873i	0.885848	−	0.463975i	$-0.153577\pi$
$337$	7.74457	+	7.74457i	0.421873	+	0.421873i	−0.463975	+	0.885848i	$0.653577\pi$
$338$	4.65404	+	4.65404i	0.253146	+	0.253146i
$339$	−8.31557			−0.451640
$340$	−4.20742	−	5.19480i	−0.228179	−	0.281727i
$341$		−	7.66763i		−	0.415225i
$342$	9.85853	+	9.85853i	0.533088	+	0.533088i
$343$	7.57621	−	7.57621i	0.409077	−	0.409077i
$344$	17.0238			0.917863
$345$	2.79884	−	7.60577i	0.150684	−	0.409481i
$346$	9.19341			0.494241
$347$	−18.9895	+	18.9895i	−1.01941	+	1.01941i	−0.0196016	+	0.999808i	$0.506240\pi$
$347$	−18.9895	+	18.9895i	−1.01941	+	1.01941i	−0.999808	+	0.0196016i	$0.993760\pi$
$348$	−4.31962	−	4.31962i	−0.231556	−	0.231556i
$349$			35.4284i			1.89644i	0.317613	+	0.948220i	$0.397119\pi$
$349$			35.4284i			1.89644i	−0.317613	+	0.948220i	$0.602881\pi$
$350$	−3.12219	−	0.663070i	−0.166888	−	0.0354426i
$351$	−18.9222			−1.00999
$352$	−19.9523	−	19.9523i	−1.06346	−	1.06346i
$353$	5.00451	+	5.00451i	0.266363	+	0.266363i	0.827633	−	0.561270i	$-0.189687\pi$
$353$	5.00451	+	5.00451i	0.266363	+	0.266363i	−0.561270	+	0.827633i	$0.689687\pi$
$354$			4.67244i			0.248337i
$355$	2.40525	−	22.9038i	0.127657	−	1.21561i
$356$			12.9595i			0.686853i
$357$	0.937692	−	0.937692i	0.0496279	−	0.0496279i
$358$	−0.498593	−	0.498593i	−0.0263515	−	0.0263515i
$359$	5.35281			0.282510			0.141255	−	0.989973i	$-0.454886\pi$
$359$	5.35281			0.282510			0.141255	+	0.989973i	$0.454886\pi$
$360$	−9.15818	−	11.3074i	−0.482679	−	0.595951i
$361$	33.0307			1.73846
$362$	−10.6840	−	10.6840i	−0.561537	−	0.561537i
$363$	−6.60991	−	6.60991i	−0.346930	−	0.346930i
$364$	5.05649			0.265032
$365$	1.37405	−	1.11288i	0.0719210	−	0.0582509i
$366$			4.58374i			0.239596i
$367$	9.14790	+	9.14790i	0.477517	+	0.477517i	0.904337	−	0.426820i	$-0.140366\pi$
$367$	9.14790	+	9.14790i	0.477517	+	0.477517i	−0.426820	+	0.904337i	$0.640366\pi$
$368$	−2.47765	+	1.47650i	−0.129156	+	0.0769680i
$369$		−	4.21032i		−	0.219181i
$370$	1.58740	−	15.1159i	0.0825250	−	0.785836i
$371$	7.77134			0.403468
$372$	1.15845	−	1.15845i	0.0600630	−	0.0600630i
$373$	−22.5936	+	22.5936i	−1.16985	+	1.16985i	−0.187607	+	0.982244i	$0.560073\pi$
$373$	−22.5936	+	22.5936i	−1.16985	+	1.16985i	−0.982244	+	0.187607i	$0.939927\pi$
$374$		−	8.41484i		−	0.435121i
$375$	−7.52747	+	3.83793i	−0.388717	+	0.198190i
$376$	1.61826			0.0834552
$377$	19.2879	−	19.2879i	0.993376	−	0.993376i
$378$	1.85197	−	1.85197i	0.0952552	−	0.0952552i
$379$	3.15771			0.162201			0.0811003	−	0.996706i	$-0.474157\pi$
$379$	3.15771			0.162201			0.0811003	+	0.996706i	$0.474157\pi$
$380$	−21.9238	−	2.30234i	−1.12467	−	0.118107i
$381$	−5.94908			−0.304781
$382$	−0.482048	−	0.482048i	−0.0246637	−	0.0246637i
$383$	7.33768	−	7.33768i	0.374938	−	0.374938i	−0.494334	−	0.869272i	$-0.664588\pi$
$383$	7.33768	−	7.33768i	0.374938	−	0.374938i	0.869272	+	0.494334i	$0.164588\pi$
$384$		−	6.75231i		−	0.344577i
$385$	5.45757	+	6.73833i	0.278144	+	0.343417i
$386$	−2.48456			−0.126461
$387$	−10.9129	−	10.9129i	−0.554735	−	0.554735i
$388$	6.88614	−	6.88614i	0.349591	−	0.349591i
$389$	23.7568			1.20452			0.602258	−	0.798302i	$-0.294268\pi$
$389$	23.7568			1.20452			0.602258	+	0.798302i	$0.294268\pi$
$390$	−4.81965	+	3.90358i	−0.244053	+	0.197665i
$391$	−10.1695	−	2.57481i	−0.514296	−	0.130214i
$392$	12.0422	−	12.0422i	0.608223	−	0.608223i
$393$	7.13294	+	7.13294i	0.359809	+	0.359809i
$394$			0.693009i			0.0349133i
$395$	−1.32246	+	12.5930i	−0.0665402	+	0.633623i
$396$			16.0474i			0.806414i
$397$	14.7958	−	14.7958i	0.742582	−	0.742582i	−0.230492	−	0.973074i	$-0.574034\pi$
$397$	14.7958	−	14.7958i	0.742582	−	0.742582i	0.973074	+	0.230492i	$0.0740336\pi$
$398$	−8.56911	+	8.56911i	−0.429530	+	0.429530i
$399$		−	4.37296i		−	0.218922i
$400$	2.94142	+	0.624679i	0.147071	+	0.0312339i
$401$		−	14.0064i		−	0.699446i	−0.936853	−	0.349723i	$-0.886276\pi$
$401$		−	14.0064i		−	0.699446i	0.936853	−	0.349723i	$-0.113724\pi$
$402$	−0.725050	−	0.725050i	−0.0361622	−	0.0361622i
$403$	5.17270	+	5.17270i	0.257671	+	0.257671i
$404$		−	13.2461i		−	0.659017i
$405$	−0.977573	+	9.30885i	−0.0485760	+	0.462560i
$406$			3.77552i			0.187376i
$407$	−29.1972	+	29.1972i	−1.44725	+	1.44725i
$408$	3.13176	−	3.13176i	0.155045	−	0.155045i
$409$			13.3170i			0.658485i	0.944245	+	0.329243i	$0.106793\pi$
$409$			13.3170i			0.658485i	−0.944245	+	0.329243i	$0.893207\pi$
$410$	−1.94139	−	2.39698i	−0.0958782	−	0.118379i
$411$		−	8.35726i		−	0.412233i
$412$	−13.8555	−	13.8555i	−0.682609	−	0.682609i
$413$	−4.40694	+	4.40694i	−0.216851	+	0.216851i
$414$	−8.98605	−	2.27517i	−0.441640	−	0.111818i
$415$	−4.28506	−	5.29066i	−0.210345	−	0.259708i
$416$	26.9203			1.31987
$417$	0.756820	−	0.756820i	0.0370616	−	0.0370616i
$418$	−19.6214	−	19.6214i	−0.959716	−	0.959716i
$419$	−22.1797			−1.08355			−0.541774	−	0.840524i	$-0.682247\pi$
$419$	−22.1797			−1.08355			−0.541774	+	0.840524i	$0.682247\pi$
$420$	−0.193502	+	1.84260i	−0.00944192	+	0.0899098i
$421$			26.9905i			1.31544i	0.753264	+	0.657718i	$0.228478\pi$
$421$			26.9905i			1.31544i	−0.753264	+	0.657718i	$0.771522\pi$
$422$	−12.9765	+	12.9765i	−0.631685	+	0.631685i
$423$	−1.03737	−	1.03737i	−0.0504384	−	0.0504384i
$424$	25.9552			1.26050
$425$	5.95834	+	9.17152i	0.289022	+	0.444884i
$426$	6.19398			0.300099
$427$	−4.32327	+	4.32327i	−0.209218	+	0.209218i
$428$	4.21387	−	4.21387i	0.203685	−	0.203685i
$429$	16.8494			0.813498
$430$	−11.2448	−	1.18088i	−0.542273	−	0.0569471i
$431$			20.9137i			1.00738i	0.863885	+	0.503689i	$0.168024\pi$
$431$			20.9137i			1.00738i	−0.863885	+	0.503689i	$0.831976\pi$
$432$	−1.74474	+	1.74474i	−0.0839440	+	0.0839440i
$433$	19.1693	−	19.1693i	0.921216	−	0.921216i	−0.0758998	−	0.997115i	$-0.524183\pi$
$433$	19.1693	−	19.1693i	0.921216	−	0.921216i	0.997115	+	0.0758998i	$0.0241829\pi$
$434$	−1.01253			−0.0486031
$435$	6.29046	+	7.76668i	0.301605	+	0.372384i
$436$			13.6245i			0.652494i
$437$	−29.7169	+	17.7091i	−1.42155	+	0.847143i
$438$	0.336277	+	0.336277i	0.0160679	+	0.0160679i
$439$			2.00079i			0.0954925i	0.998859	+	0.0477462i	$0.0152039\pi$
$439$			2.00079i			0.0954925i	−0.998859	+	0.0477462i	$0.984796\pi$
$440$	18.2275	+	22.5051i	0.868964	+	1.07289i
$441$	−15.4390			−0.735193
$442$	5.67678	+	5.67678i	0.270017	+	0.270017i
$443$	−9.20286	−	9.20286i	−0.437241	−	0.437241i	0.453841	−	0.891083i	$-0.350053\pi$
$443$	−9.20286	−	9.20286i	−0.437241	−	0.437241i	−0.891083	+	0.453841i	$0.850053\pi$
$444$	−8.82243			−0.418694
$445$	2.21444	−	21.0868i	0.104974	−	0.999609i
$446$	−12.1645			−0.576006
$447$	−0.900567	−	0.900567i	−0.0425954	−	0.0425954i
$448$	−1.95249	+	1.95249i	−0.0922465	+	0.0922465i
$449$			5.65418i			0.266837i	0.991060	+	0.133419i	$0.0425955\pi$
$449$			5.65418i			0.266837i	−0.991060	+	0.133419i	$0.957405\pi$
$450$	5.26494	+	8.10418i	0.248192	+	0.382035i
$451$			8.37981i			0.394590i
$452$	−10.6338	−	10.6338i	−0.500171	−	0.500171i
$453$	6.36649	+	6.36649i	0.299124	+	0.299124i
$454$	1.25639			0.0589652
$455$	−8.22754	−	0.864020i	−0.385713	−	0.0405059i
$456$		−	14.6051i		−	0.683946i
$457$	−29.5314	−	29.5314i	−1.38142	−	1.38142i	−0.842100	−	0.539321i	$-0.818681\pi$
$457$	−29.5314	−	29.5314i	−1.38142	−	1.38142i	−0.539321	−	0.842100i	$-0.681319\pi$
$458$	1.46155	−	1.46155i	0.0682936	−	0.0682936i
$459$	−8.97449			−0.418893
$460$	13.3052	−	6.14701i	0.620358	−	0.286606i
$461$	−29.6945			−1.38301			−0.691506	−	0.722370i	$-0.743053\pi$
$461$	−29.6945			−1.38301			−0.691506	+	0.722370i	$0.743053\pi$
$462$	−1.64910	+	1.64910i	−0.0767231	+	0.0767231i
$463$	−14.0086	−	14.0086i	−0.651033	−	0.651033i	0.302209	−	0.953242i	$-0.402276\pi$
$463$	−14.0086	−	14.0086i	−0.651033	−	0.651033i	−0.953242	+	0.302209i	$0.902276\pi$
$464$		−	3.55692i		−	0.165126i
$465$	−2.08290	+	1.68700i	−0.0965921	+	0.0782328i
$466$	−21.5551			−0.998522
$467$	24.1082	+	24.1082i	1.11559	+	1.11559i	0.992380	+	0.123213i	$0.0393199\pi$
$467$	24.1082	+	24.1082i	1.11559	+	1.11559i	0.123213	+	0.992380i	$0.460680\pi$
$468$	−10.8259	−	10.8259i	−0.500425	−	0.500425i
$469$		−	1.36770i		−	0.0631545i
$470$	−1.06891	−	0.112253i	−0.0493053	−	0.00517783i
$471$		−	1.96502i		−	0.0905435i
$472$	−14.7186	+	14.7186i	−0.677477	+	0.677477i
$473$	21.7200	+	21.7200i	0.998688	+	0.998688i
$474$	−3.40559			−0.156424
$475$	35.2793	+	7.49238i	1.61873	+	0.343774i
$476$	2.39820			0.109921
$477$	−16.6383	−	16.6383i	−0.761815	−	0.761815i
$478$	5.84445	+	5.84445i	0.267319	+	0.267319i
$479$	9.03195			0.412681			0.206340	−	0.978480i	$-0.433845\pi$
$479$	9.03195			0.412681			0.206340	+	0.978480i	$0.433845\pi$
$480$	−1.03019	+	9.80984i	−0.0470213	+	0.447756i
$481$		−	39.3937i		−	1.79620i
$482$	−5.37842	−	5.37842i	−0.244980	−	0.244980i
$483$	1.48838	+	2.49758i	0.0677236	+	0.113644i
$484$		−	16.9052i		−	0.768420i
$485$	−12.3813	+	10.0280i	−0.562205	+	0.455346i
$486$	−12.3123			−0.558495
$487$	24.1401	−	24.1401i	1.09389	−	1.09389i	0.0987834	−	0.995109i	$-0.468505\pi$
$487$	24.1401	−	24.1401i	1.09389	−	1.09389i	0.995109	−	0.0987834i	$-0.0314951\pi$
$488$	−14.4391	+	14.4391i	−0.653630	+	0.653630i
$489$			9.92744i			0.448935i
$490$	−8.78961	+	7.11896i	−0.397074	+	0.321602i
$491$	−18.9437			−0.854916			−0.427458	−	0.904035i	$-0.640591\pi$
$491$	−18.9437			−0.854916			−0.427458	+	0.904035i	$0.640591\pi$
$492$	−1.26605	+	1.26605i	−0.0570781	+	0.0570781i
$493$	9.14790	−	9.14790i	0.412001	−	0.412001i
$494$	26.4738			1.19111
$495$	2.74208	−	26.1112i	0.123247	−	1.17361i
$496$	0.953908			0.0428317
$497$	5.84202	+	5.84202i	0.262050	+	0.262050i
$498$	1.29481	−	1.29481i	0.0580217	−	0.0580217i
$499$		−	22.2256i		−	0.994956i	−0.867477	−	0.497478i	$-0.834260\pi$
$499$		−	22.2256i		−	0.994956i	0.867477	−	0.497478i	$-0.165740\pi$
$500$	−14.5339	−	4.71811i	−0.649974	−	0.211000i
$501$	9.10266			0.406677
$502$	10.9631	+	10.9631i	0.489308	+	0.489308i
$503$	−23.8440	+	23.8440i	−1.06315	+	1.06315i	−0.0652839	+	0.997867i	$0.520795\pi$
$503$	−23.8440	+	23.8440i	−1.06315	+	1.06315i	−0.997867	+	0.0652839i	$0.979205\pi$
$504$	5.22011			0.232522
$505$	−2.26340	+	21.5530i	−0.100720	+	0.959098i
$506$	17.8850	+	4.52827i	0.795083	+	0.201306i
$507$	−4.41984	+	4.41984i	−0.196292	+	0.196292i
$508$	−7.60756	−	7.60756i	−0.337531	−	0.337531i
$509$			8.10179i			0.359106i	0.983748	+	0.179553i	$0.0574651\pi$
$509$			8.10179i			0.359106i	−0.983748	+	0.179553i	$0.942535\pi$
$510$	−2.28588	+	1.85140i	−0.101220	+	0.0819813i
$511$			0.634337i			0.0280614i
$512$	4.76090	−	4.76090i	0.210404	−	0.210404i
$513$	−20.9264	+	20.9264i	−0.923924	+	0.923924i
$514$		−	21.3891i		−	0.943433i
$515$	20.1770	+	24.9121i	0.889107	+	1.09776i
$516$			6.56308i			0.288924i
$517$	2.06467	+	2.06467i	0.0908041	+	0.0908041i
$518$	3.85557	+	3.85557i	0.169404	+	0.169404i
$519$			8.73079i			0.383239i
$520$	−27.4789	−	2.88571i	−1.20503	−	0.126547i
$521$		−	30.6696i		−	1.34366i	−0.740705	−	0.671831i	$-0.765508\pi$
$521$		−	30.6696i		−	1.34366i	0.740705	−	0.671831i	$-0.234492\pi$
$522$	8.08331	−	8.08331i	0.353797	−	0.353797i
$523$	−22.7601	+	22.7601i	−0.995230	+	0.995230i	−0.999989	−	0.00475898i	$-0.998485\pi$
$523$	−22.7601	+	22.7601i	−0.995230	+	0.995230i	0.00475898	+	0.999989i	$0.498485\pi$
$524$			18.2429i			0.796946i
$525$	0.629704	−	2.96508i	0.0274825	−	0.129407i
$526$		−	3.24730i		−	0.141589i
$527$	2.45332	+	2.45332i	0.106868	+	0.106868i
$528$	1.55362	−	1.55362i	0.0676126	−	0.0676126i
$529$	10.9451	−	20.2288i	0.475872	−	0.879515i
$530$	−17.1443	−	1.80042i	−0.744701	−	0.0782051i
$531$	18.8703			0.818903
$532$	5.59205	−	5.59205i	0.242446	−	0.242446i
$533$	−5.65315	−	5.65315i	−0.244865	−	0.244865i
$534$	5.70261			0.246776
$535$	−7.57654	+	6.13646i	−0.327562	+	0.265302i
$536$		−	4.56793i		−	0.197305i
$537$	0.473503	−	0.473503i	0.0204332	−	0.0204332i
$538$	1.88298	+	1.88298i	0.0811812	+	0.0811812i
$539$	30.7284			1.32356
$540$	9.74359	−	7.89162i	0.419298	−	0.339601i
$541$	29.6451			1.27454			0.637271	−	0.770640i	$-0.280063\pi$
$541$	29.6451			1.27454			0.637271	+	0.770640i	$0.280063\pi$
$542$	1.99029	−	1.99029i	0.0854904	−	0.0854904i
$543$	10.1463	−	10.1463i	0.435421	−	0.435421i
$544$	12.7678			0.547415
$545$	2.32806	−	22.1687i	0.0997232	−	0.949604i
$546$		−	2.22502i		−	0.0952219i
$547$	20.8948	−	20.8948i	0.893397	−	0.893397i	−0.101444	−	0.994841i	$-0.532346\pi$
$547$	20.8948	−	20.8948i	0.893397	−	0.893397i	0.994841	+	0.101444i	$0.0323463\pi$
$548$	10.6871	−	10.6871i	0.456530	−	0.456530i
$549$	18.5121			0.790078
$550$	−10.4788	−	16.1298i	−0.446818	−	0.687775i
$551$		−	42.6616i		−	1.81744i
$552$	4.97098	+	8.34157i	0.211579	+	0.355041i
$553$	−3.21207	−	3.21207i	−0.136591	−	0.136591i
$554$			18.2593i			0.775763i
$555$	14.3552	+	1.50752i	0.609345	+	0.0639906i
$556$	1.93561			0.0820883
$557$	−26.3855	−	26.3855i	−1.11799	−	1.11799i	−0.992036	−	0.125956i	$-0.959800\pi$
$557$	−26.3855	−	26.3855i	−1.11799	−	1.11799i	−0.125956	−	0.992036i	$-0.540200\pi$
$558$	2.16781	+	2.16781i	0.0917709	+	0.0917709i
$559$	−29.3053			−1.23948
$560$	−0.838296	+	0.678961i	−0.0354245	+	0.0286913i
$561$	7.99139			0.337397
$562$	−7.54683	−	7.54683i	−0.318344	−	0.318344i
$563$	−11.8041	+	11.8041i	−0.497485	+	0.497485i	−0.910654	−	0.413169i	$-0.864422\pi$
$563$	−11.8041	+	11.8041i	−0.497485	+	0.497485i	0.413169	+	0.910654i	$0.364422\pi$
$564$			0.623876i			0.0262699i
$565$	15.4855	+	19.1195i	0.651478	+	0.804364i
$566$		−	5.78042i		−	0.242969i
$567$	−2.37439	−	2.37439i	−0.0997149	−	0.0997149i
$568$	19.5115	+	19.5115i	0.818686	+	0.818686i
$569$	9.00741			0.377610			0.188805	−	0.982015i	$-0.439539\pi$
$569$	9.00741			0.377610			0.188805	+	0.982015i	$0.439539\pi$
$570$	−1.01310	+	9.64716i	−0.0424342	+	0.404075i
$571$		−	6.93746i		−	0.290324i	−0.989408	−	0.145162i	$-0.953630\pi$
$571$		−	6.93746i		−	0.290324i	0.989408	−	0.145162i	$-0.0463703\pi$
$572$	21.5467	+	21.5467i	0.900913	+	0.900913i
$573$	0.457790	−	0.457790i	0.0191245	−	0.0191245i
$574$	1.10658			0.0461877
$575$	−22.6996	+	7.72845i	−0.946638	+	0.322298i
$576$	8.36050			0.348354
$577$	−1.29251	+	1.29251i	−0.0538079	+	0.0538079i	−0.733499	−	0.679691i	$-0.762114\pi$
$577$	−1.29251	+	1.29251i	−0.0538079	+	0.0538079i	0.679691	+	0.733499i	$0.262114\pi$
$578$	−6.87357	−	6.87357i	−0.285903	−	0.285903i
$579$		−	2.35953i		−	0.0980587i
$580$	−1.88776	+	17.9760i	−0.0783849	+	0.746412i
$581$	2.44246			0.101330
$582$	−3.03012	−	3.03012i	−0.125603	−	0.125603i
$583$	33.1152	+	33.1152i	1.37149	+	1.37149i
$584$			2.11860i			0.0876682i
$585$	15.7652	+	19.4649i	0.651810	+	0.804773i
$586$		−	3.85375i		−	0.159197i
$587$	−25.9490	+	25.9490i	−1.07103	+	1.07103i	−0.0737552	+	0.997276i	$0.523498\pi$
$587$	−25.9490	+	25.9490i	−1.07103	+	1.07103i	−0.997276	+	0.0737552i	$0.976502\pi$
$588$	4.64255	+	4.64255i	0.191456	+	0.191456i
$589$	11.4411			0.471424
$590$	10.7431	−	8.70114i	0.442286	−	0.358220i
$591$	−0.658136			−0.0270721
$592$	−3.63234	−	3.63234i	−0.149288	−	0.149288i
$593$	8.76326	+	8.76326i	0.359864	+	0.359864i	0.863763	−	0.503899i	$-0.168102\pi$
$593$	8.76326	+	8.76326i	0.359864	+	0.359864i	−0.503899	+	0.863763i	$0.668102\pi$
$594$	15.7832			0.647594
$595$	−3.90218	−	0.409789i	−0.159974	−	0.0167997i
$596$		−	2.30325i		−	0.0943449i
$597$	−8.13790	−	8.13790i	−0.333062	−	0.333062i
$598$	−15.1203	+	9.01063i	−0.618315	+	0.368472i
$599$			13.7566i			0.562079i	0.959696	+	0.281040i	$0.0906793\pi$
$599$			13.7566i			0.562079i	−0.959696	+	0.281040i	$0.909321\pi$
$600$	2.10312	−	9.90296i	0.0858597	−	0.404287i
$601$	−22.6973			−0.925844			−0.462922	−	0.886399i	$-0.653199\pi$
$601$	−22.6973			−0.925844			−0.462922	+	0.886399i	$0.653199\pi$
$602$	2.86819	−	2.86819i	0.116899	−	0.116899i
$603$	−2.92822	+	2.92822i	−0.119246	+	0.119246i
$604$			16.2827i			0.662533i
$605$	−2.88866	+	27.5069i	−0.117441	+	1.11832i
$606$	−5.82870			−0.236775
$607$	−5.93174	+	5.93174i	−0.240762	+	0.240762i	−0.817165	−	0.576403i	$-0.804456\pi$
$607$	−5.93174	+	5.93174i	−0.240762	+	0.240762i	0.576403	+	0.817165i	$0.304456\pi$
$608$	29.7716	−	29.7716i	1.20740	−	1.20740i
$609$	−3.58553			−0.145293
$610$	10.5391	−	8.53596i	0.426717	−	0.345611i
$611$	−2.78572			−0.112698
$612$	−5.13451	−	5.13451i	−0.207550	−	0.207550i
$613$	13.0088	−	13.0088i	0.525421	−	0.525421i	−0.393783	−	0.919204i	$-0.628834\pi$
$613$	13.0088	−	13.0088i	0.525421	−	0.525421i	0.919204	+	0.393783i	$0.128834\pi$
$614$		−	0.959095i		−	0.0387059i
$615$	2.27636	−	1.84369i	0.0917918	−	0.0743449i
$616$	−10.3896			−0.418609
$617$	22.0113	+	22.0113i	0.886143	+	0.886143i	0.994150	−	0.108007i	$-0.0344470\pi$
$617$	22.0113	+	22.0113i	0.886143	+	0.886143i	−0.108007	+	0.994150i	$0.534447\pi$
$618$	−6.09684	+	6.09684i	−0.245251	+	0.245251i
$619$	−35.8644			−1.44151			−0.720755	−	0.693189i	$-0.756205\pi$
$619$	−35.8644			−1.44151			−0.720755	+	0.693189i	$0.756205\pi$
$620$	−4.82087	−	0.506266i	−0.193611	−	0.0203321i
$621$	4.82943	−	19.0744i	0.193799	−	0.765431i
$622$	6.99243	−	6.99243i	0.280371	−	0.280371i
$623$	5.37856	+	5.37856i	0.215487	+	0.215487i
$624$			2.09619i			0.0839147i
$625$	22.8422	+	10.1604i	0.913688	+	0.406416i
$626$			23.5708i			0.942079i
$627$	18.6341	−	18.6341i	0.744173	−	0.744173i
$628$	2.51283	−	2.51283i	0.100273	−	0.100273i
$629$		−	18.6837i		−	0.744970i
$630$	−3.44806	−	0.362100i	−0.137374	−	0.0144264i
$631$		−	28.0113i		−	1.11511i	−0.830140	−	0.557555i	$-0.811739\pi$
$631$		−	28.0113i		−	1.11511i	0.830140	−	0.557555i	$-0.188261\pi$
$632$	−10.7279	−	10.7279i	−0.426732	−	0.426732i
$633$	−12.3235	−	12.3235i	−0.489815	−	0.489815i
$634$		−	12.8095i		−	0.508730i
$635$	11.0785	+	13.6784i	0.439638	+	0.542810i
$636$			10.0063i			0.396777i
$637$	−20.7298	+	20.7298i	−0.821345	+	0.821345i
$638$	−16.0882	+	16.0882i	−0.636939	+	0.636939i
$639$		−	25.0153i		−	0.989590i
$640$	−15.5252	+	12.5743i	−0.613688	+	0.497044i
$641$			12.7821i			0.504864i	0.967615	+	0.252432i	$0.0812303\pi$
$641$			12.7821i			0.504864i	−0.967615	+	0.252432i	$0.918770\pi$
$642$	−1.85424	−	1.85424i	−0.0731810	−	0.0731810i
$643$	24.7733	−	24.7733i	0.976963	−	0.976963i	−0.0227777	−	0.999741i	$-0.507251\pi$
$643$	24.7733	−	24.7733i	0.976963	−	0.976963i	0.999741	+	0.0227777i	$0.00725099\pi$
$644$	−1.29054	+	5.09716i	−0.0508545	+	0.200856i
$645$	1.12146	−	10.6790i	0.0441573	−	0.420484i
$646$	12.5561			0.494012
$647$	25.4047	−	25.4047i	0.998760	−	0.998760i	−0.00123888	−	0.999999i	$-0.500394\pi$
$647$	25.4047	−	25.4047i	0.998760	−	0.998760i	0.999999	+	0.00123888i	$0.000394348\pi$
$648$	−7.93013	−	7.93013i	−0.311525	−	0.311525i
$649$	−37.5577			−1.47427
$650$	17.9506	+	3.81222i	0.704079	+	0.149527i
$651$		−	0.961581i		−	0.0376873i
$652$	−12.6950	+	12.6950i	−0.497175	+	0.497175i
$653$	−16.1609	−	16.1609i	−0.632424	−	0.632424i	0.316252	−	0.948675i	$-0.397576\pi$
$653$	−16.1609	−	16.1609i	−0.632424	−	0.632424i	−0.948675	+	0.316252i	$0.897576\pi$
$654$	5.99520			0.234431
$655$	3.11723	−	29.6835i	0.121800	−	1.15983i
$656$	−1.04251			−0.0407031
$657$	1.35810	−	1.35810i	0.0529847	−	0.0529847i
$658$	0.272646	−	0.272646i	0.0106288	−	0.0106288i
$659$	41.1528			1.60308			0.801542	−	0.597938i	$-0.204013\pi$
$659$	41.1528			1.60308			0.801542	+	0.597938i	$0.204013\pi$
$660$	−8.67624	+	7.02714i	−0.337722	+	0.273531i
$661$			39.9719i			1.55473i	0.629053	+	0.777363i	$0.283443\pi$
$661$			39.9719i			1.55473i	−0.629053	+	0.777363i	$0.716557\pi$
$662$	−10.8250	+	10.8250i	−0.420725	+	0.420725i
$663$	−5.39111	+	5.39111i	−0.209374	+	0.209374i
$664$	8.15749			0.316572
$665$	−10.0545	+	8.14344i	−0.389897	+	0.315789i
$666$		−	16.5094i		−	0.639727i
$667$	14.5203	+	24.3658i	0.562227	+	0.943447i
$668$	11.6403	+	11.6403i	0.450376	+	0.450376i
$669$		−	11.5524i		−	0.446641i
$670$	−0.316861	+	3.01727i	−0.0122414	+	0.116567i
$671$	−36.8447			−1.42237
$672$	−2.50218	−	2.50218i	−0.0965235	−	0.0965235i
$673$	−30.3229	−	30.3229i	−1.16886	−	1.16886i	−0.982477	−	0.186386i	$-0.940323\pi$
$673$	−30.3229	−	30.3229i	−1.16886	−	1.16886i	−0.186386	−	0.982477i	$-0.559677\pi$
$674$	8.71580			0.335720
$675$	−17.2025	+	11.1757i	−0.662125	+	0.430154i
$676$	−11.3040			−0.434770
$677$	7.89711	+	7.89711i	0.303511	+	0.303511i	0.842386	−	0.538875i	$-0.181150\pi$
$677$	7.89711	+	7.89711i	0.303511	+	0.303511i	−0.538875	+	0.842386i	$0.681150\pi$
$678$	−4.67920	+	4.67920i	−0.179704	+	0.179704i
$679$		−	5.71588i		−	0.219355i
$680$	−13.0327	−	1.36864i	−0.499783	−	0.0524850i
$681$			1.19316i			0.0457222i
$682$	−4.31461	−	4.31461i	−0.165215	−	0.165215i
$683$	−2.82643	−	2.82643i	−0.108150	−	0.108150i	0.650961	−	0.759111i	$-0.274366\pi$
$683$	−2.82643	−	2.82643i	−0.108150	−	0.108150i	−0.759111	+	0.650961i	$0.774366\pi$
$684$	−23.9450			−0.915559
$685$	−19.2154	+	15.5631i	−0.734182	+	0.594636i
$686$		−	8.52633i		−	0.325537i
$687$	1.38800	+	1.38800i	0.0529555	+	0.0529555i
$688$	−2.70213	+	2.70213i	−0.103018	+	0.103018i
$689$	−44.6801			−1.70217
$690$	−2.70488	−	5.85471i	−0.102973	−	0.222885i
$691$	30.5842			1.16348			0.581738	−	0.813376i	$-0.302373\pi$
$691$	30.5842			1.16348			0.581738	+	0.813376i	$0.302373\pi$
$692$	−11.1648	+	11.1648i	−0.424420	+	0.424420i
$693$	6.66013	+	6.66013i	0.252997	+	0.252997i
$694$			21.3709i			0.811229i
$695$	−3.14949	−	0.330745i	−0.119467	−	0.0125459i
$696$	−11.9752			−0.453918
$697$	−2.68119	−	2.68119i	−0.101557	−	0.101557i
$698$	19.9357	+	19.9357i	0.754578	+	0.754578i
$699$		−	20.4705i		−	0.774264i
$700$	4.59694	−	2.98643i	0.173748	−	0.112877i
$701$		−	37.3772i		−	1.41172i	−0.708352	−	0.705860i	$-0.750561\pi$
$701$		−	37.3772i		−	1.41172i	0.708352	−	0.705860i	$-0.249439\pi$
$702$	−10.6476	+	10.6476i	−0.401869	+	0.401869i
$703$	−43.5662	−	43.5662i	−1.64313	−	1.64313i
$704$	−16.6399			−0.627140
$705$	0.106604	−	1.01512i	0.00401493	−	0.0382318i
$706$	5.63211			0.211967
$707$	−5.49749	−	5.49749i	−0.206754	−	0.206754i
$708$	−5.67435	−	5.67435i	−0.213255	−	0.213255i
$709$	25.9421			0.974277			0.487138	−	0.873325i	$-0.338041\pi$
$709$	25.9421			0.974277			0.487138	+	0.873325i	$0.338041\pi$
$710$	−11.5346	−	14.2415i	−0.432886	−	0.534473i
$711$			13.7540i			0.515814i
$712$	17.9637	+	17.9637i	0.673217	+	0.673217i
$713$	−6.53451	+	3.89410i	−0.244719	+	0.145835i
$714$		−	1.05529i		−	0.0394931i
$715$	−31.3774	−	38.7410i	−1.17345	−	1.44883i
$716$	1.21101			0.0452577
$717$	−5.55035	+	5.55035i	−0.207282	+	0.207282i
$718$	3.01205	−	3.01205i	0.112409	−	0.112409i
$719$			37.2807i			1.39034i	0.718847	+	0.695169i	$0.244670\pi$
$719$			37.2807i			1.39034i	−0.718847	+	0.695169i	$0.755330\pi$
$720$	3.24842	+	0.341135i	0.121061	+	0.0127133i
$721$	−11.5008			−0.428312
$722$	18.5865	−	18.5865i	0.691718	−	0.691718i
$723$	5.10777	−	5.10777i	0.189960	−	0.189960i
$724$	25.9499			0.964419
$725$	6.14324	−	28.9266i	0.228154	−	1.07431i
$726$	−7.43884			−0.276081
$727$	6.35280	+	6.35280i	0.235612	+	0.235612i	0.815030	−	0.579418i	$-0.196720\pi$
$727$	6.35280	+	6.35280i	0.235612	+	0.235612i	−0.579418	+	0.815030i	$0.696720\pi$
$728$	7.00898	−	7.00898i	0.259770	−	0.259770i
$729$			0.865118i			0.0320414i
$730$	0.146959	−	1.39941i	0.00543921	−	0.0517944i
$731$	−13.8990			−0.514073
$732$	−5.56663	−	5.56663i	−0.205749	−	0.205749i
$733$	11.9450	−	11.9450i	0.441200	−	0.441200i	−0.451215	−	0.892415i	$-0.649009\pi$
$733$	11.9450	−	11.9450i	0.441200	−	0.441200i	0.892415	+	0.451215i	$0.149009\pi$
$734$	10.2951			0.380000
$735$	−6.76073	−	8.34731i	−0.249373	−	0.307895i
$736$	−6.87073	+	27.1368i	−0.253259	+	1.00028i
$737$	5.82804	−	5.82804i	0.214679	−	0.214679i
$738$	−2.36917	−	2.36917i	−0.0872102	−	0.0872102i
$739$			34.9255i			1.28476i	0.766388	+	0.642378i	$0.222052\pi$
$739$			34.9255i			1.28476i	−0.766388	+	0.642378i	$0.777948\pi$
$740$	16.4294	+	20.2849i	0.603955	+	0.745689i
$741$			25.1416i			0.923602i
$742$	4.37296	−	4.37296i	0.160536	−	0.160536i
$743$	−10.8082	+	10.8082i	−0.396513	+	0.396513i	−0.877001	−	0.480488i	$-0.840460\pi$
$743$	−10.8082	+	10.8082i	−0.396513	+	0.396513i	0.480488	+	0.877001i	$0.340460\pi$
$744$		−	3.21155i		−	0.117741i
$745$	−0.393565	+	3.74768i	−0.0144191	+	0.137304i
$746$			25.4270i			0.930948i
$747$	−5.22927	−	5.22927i	−0.191329	−	0.191329i
$748$	10.2192	+	10.2192i	0.373652	+	0.373652i
$749$		−	3.49775i		−	0.127805i
$750$	−2.07612	+	6.39536i	−0.0758091	+	0.233526i
$751$			47.9254i			1.74882i	0.485186	+	0.874411i	$0.338752\pi$
$751$			47.9254i			1.74882i	−0.485186	+	0.874411i	$0.661248\pi$
$752$	−0.256860	+	0.256860i	−0.00936671	+	0.00936671i
$753$	−10.4115	+	10.4115i	−0.379414	+	0.379414i
$754$		−	21.7067i		−	0.790513i
$755$	2.78228	−	26.4940i	0.101257	−	0.964214i
$756$			4.49818i			0.163597i
$757$	−8.26698	−	8.26698i	−0.300469	−	0.300469i	0.540729	−	0.841197i	$-0.318149\pi$
$757$	−8.26698	−	8.26698i	−0.300469	−	0.300469i	−0.841197	+	0.540729i	$0.818149\pi$
$758$	1.77685	−	1.77685i	0.0645382	−	0.0645382i
$759$	−4.30040	+	16.9850i	−0.156095	+	0.616515i
$760$	−33.5807	+	27.1980i	−1.21810	+	0.986574i
$761$	−4.56566			−0.165505			−0.0827526	−	0.996570i	$-0.526371\pi$
$761$	−4.56566			−0.165505			−0.0827526	+	0.996570i	$0.526371\pi$
$762$	−3.34757	+	3.34757i	−0.121270	+	0.121270i
$763$	5.65453	+	5.65453i	0.204708	+	0.204708i
$764$	1.17083			0.0423590
$765$	7.47714	+	9.23185i	0.270337	+	0.333778i
$766$		−	8.25789i		−	0.298370i
$767$	25.3370	−	25.3370i	0.914865	−	0.914865i
$768$	−7.47844	−	7.47844i	−0.269855	−	0.269855i
$769$	−25.4099			−0.916303			−0.458152	−	0.888874i	$-0.651488\pi$
$769$	−25.4099			−0.916303			−0.458152	+	0.888874i	$0.651488\pi$
$770$	6.86268	+	0.720688i	0.247314	+	0.0259718i
$771$	20.3128			0.731547
$772$	3.01732	−	3.01732i	0.108596	−	0.108596i
$773$	9.02684	−	9.02684i	0.324673	−	0.324673i	−0.525884	−	0.850557i	$-0.676265\pi$
$773$	9.02684	−	9.02684i	0.324673	−	0.324673i	0.850557	+	0.525884i	$0.176265\pi$
$774$	−12.2815			−0.441449
$775$	7.75766	+	1.64752i	0.278663	+	0.0591806i
$776$		−	19.0903i		−	0.685300i
$777$	−3.66155	+	3.66155i	−0.131357	+	0.131357i
$778$	13.3680	−	13.3680i	0.479267	−	0.479267i
$779$	−12.5038			−0.447996
$780$	1.11251	−	10.5937i	0.0398342	−	0.379317i
$781$			49.7880i			1.78155i
$782$	−7.17130	+	4.27358i	−0.256445	+	0.152823i
$783$	17.1582	+	17.1582i	0.613185	+	0.613185i
$784$			3.82283i			0.136530i
$785$	−4.51807	+	3.65932i	−0.161257	+	0.130607i
$786$	8.02747			0.286330
$787$	−10.2762	−	10.2762i	−0.366306	−	0.366306i	0.499822	−	0.866128i	$-0.333399\pi$
$787$	−10.2762	−	10.2762i	−0.366306	−	0.366306i	−0.866128	+	0.499822i	$0.833399\pi$
$788$	−0.841611	−	0.841611i	−0.0299811	−	0.0299811i
$789$	3.08389			0.109789
$790$	6.34198	+	7.83028i	0.225637	+	0.278589i
$791$	−8.82662			−0.313839
$792$	22.2439	+	22.2439i	0.790404	+	0.790404i
$793$	24.8560	−	24.8560i	0.882662	−	0.882662i
$794$		−	16.6514i		−	0.590935i
$795$	1.70982	−	16.2816i	0.0606410	−	0.577448i
$796$		−	20.8132i		−	0.737703i
$797$	8.02749	+	8.02749i	0.284348	+	0.284348i	0.834840	−	0.550492i	$-0.185560\pi$
$797$	8.02749	+	8.02749i	0.284348	+	0.284348i	−0.550492	+	0.834840i	$0.685560\pi$
$798$	−2.46068	−	2.46068i	−0.0871072	−	0.0871072i
$799$	−1.32122			−0.0467413
$800$	24.4737	−	15.8995i	0.865274	−	0.562132i
$801$		−	23.0308i		−	0.813754i
$802$	−7.88145	−	7.88145i	−0.278304	−	0.278304i
$803$	−2.70304	+	2.70304i	−0.0953881	+	0.0953881i
$804$	1.76104			0.0621073
$805$	2.97085	−	8.07320i	0.104709	−	0.284543i
$806$	5.82140			0.205050
$807$	−1.78823	+	1.78823i	−0.0629487	+	0.0629487i
$808$	−18.3609	−	18.3609i	−0.645933	−	0.645933i
$809$		−	21.6165i		−	0.759997i	−0.924987	−	0.379998i	$-0.875925\pi$
$809$		−	21.6165i		−	0.759997i	0.924987	−	0.379998i	$-0.124075\pi$
$810$	4.68804	+	5.78821i	0.164721	+	0.203377i
$811$	43.0541			1.51183			0.755917	−	0.654668i	$-0.227192\pi$
$811$	43.0541			1.51183			0.755917	+	0.654668i	$0.227192\pi$
$812$	−4.58510	−	4.58510i	−0.160905	−	0.160905i
$813$	1.89014	+	1.89014i	0.0662901	+	0.0662901i
$814$			32.8587i			1.15170i
$815$	22.8256	−	18.4871i	0.799547	−	0.647576i
$816$			0.994186i			0.0348035i
$817$	−32.4092	+	32.4092i	−1.13386	+	1.13386i
$818$	7.49355	+	7.49355i	0.262006	+	0.262006i
$819$	−8.98605			−0.313998
$820$	5.26864	+	0.553289i	0.183989	+	0.0193217i
$821$	1.01813			0.0355331			0.0177665	−	0.999842i	$-0.494344\pi$
$821$	1.01813			0.0355331			0.0177665	+	0.999842i	$0.494344\pi$
$822$	−4.70266	−	4.70266i	−0.164024	−	0.164024i
$823$	18.8063	+	18.8063i	0.655548	+	0.655548i	0.954323	−	0.298775i	$-0.0965781\pi$
$823$	18.8063	+	18.8063i	0.655548	+	0.655548i	−0.298775	+	0.954323i	$0.596578\pi$
$824$	−38.4111			−1.33811
$825$	15.3181	−	9.95151i	0.533308	−	0.346467i
$826$			4.95960i			0.172567i
$827$	−6.01414	−	6.01414i	−0.209132	−	0.209132i	0.594766	−	0.803899i	$-0.297245\pi$
$827$	−6.01414	−	6.01414i	−0.209132	−	0.209132i	−0.803899	+	0.594766i	$0.797245\pi$
$828$	13.6760	−	8.14990i	0.475273	−	0.283229i
$829$		−	7.53915i		−	0.261845i	−0.991393	−	0.130923i	$-0.958206\pi$
$829$		−	7.53915i		−	0.261845i	0.991393	−	0.130923i	$-0.0417940\pi$
$830$	−5.38830	−	0.565855i	−0.187031	−	0.0196411i
$831$	−17.3405			−0.601534
$832$	11.2255	−	11.2255i	0.389175	−	0.389175i
$833$	−9.83179	+	9.83179i	−0.340651	+	0.340651i
$834$		−	0.851731i		−	0.0294930i
$835$	−16.9512	−	20.9292i	−0.586620	−	0.724286i
$836$	47.6577			1.64828
$837$	−4.60156	+	4.60156i	−0.159053	+	0.159053i
$838$	−12.4806	+	12.4806i	−0.431135	+	0.431135i
$839$	−21.4324			−0.739928			−0.369964	−	0.929046i	$-0.620630\pi$
$839$	−21.4324			−0.739928			−0.369964	+	0.929046i	$0.620630\pi$
$840$	2.28588	+	2.82232i	0.0788702	+	0.0973792i
$841$	−5.97954			−0.206191
$842$	15.1877	+	15.1877i	0.523401	+	0.523401i
$843$	7.16706	−	7.16706i	0.246847	−	0.246847i
$844$		−	31.5180i		−	1.08490i
$845$	18.3930	+	1.93156i	0.632740	+	0.0664475i
$846$	−1.16746			−0.0401381
$847$	−7.01614	−	7.01614i	−0.241077	−	0.241077i
$848$	−4.11977	+	4.11977i	−0.141473	+	0.141473i
$849$	5.48954			0.188400
$850$	8.51363	+	1.80807i	0.292015	+	0.0620162i
$851$	39.7106	+	10.0543i	1.36126	+	0.344656i
$852$	−7.52216	+	7.52216i	−0.257705	+	0.257705i
$853$	22.6024	+	22.6024i	0.773891	+	0.773891i	0.978784	−	0.204894i	$-0.0656849\pi$
$853$	22.6024	+	22.6024i	0.773891	+	0.773891i	−0.204894	+	0.978784i	$0.565685\pi$
$854$			4.86545i			0.166492i
$855$	38.9615	+	4.09156i	1.33245	+	0.139928i
$856$		−	11.6820i		−	0.399283i
$857$	−3.93538	+	3.93538i	−0.134430	+	0.134430i	−0.771120	−	0.636690i	$-0.780303\pi$
$857$	−3.93538	+	3.93538i	−0.134430	+	0.134430i	0.636690	+	0.771120i	$0.280303\pi$
$858$	9.48124	−	9.48124i	0.323684	−	0.323684i
$859$			8.61072i			0.293794i	0.989152	+	0.146897i	$0.0469286\pi$
$859$			8.61072i			0.293794i	−0.989152	+	0.146897i	$0.953071\pi$
$860$	15.0901	−	12.2219i	0.514569	−	0.416765i
$861$			1.05089i			0.0358144i
$862$	11.7682	+	11.7682i	0.400828	+	0.400828i
$863$	8.32218	+	8.32218i	0.283290	+	0.283290i	0.834420	−	0.551129i	$-0.185803\pi$
$863$	8.32218	+	8.32218i	0.283290	+	0.283290i	−0.551129	+	0.834420i	$0.685803\pi$
$864$			23.9479i			0.814723i
$865$	20.0742	−	16.2587i	0.682544	−	0.552812i
$866$		−	21.5732i		−	0.733088i
$867$	6.52768	−	6.52768i	0.221692	−	0.221692i
$868$	1.22965	−	1.22965i	0.0417370	−	0.0417370i
$869$		−	27.3746i		−	0.928618i
$870$	7.91001	+	0.830674i	0.268174	+	0.0281625i
$871$			7.86337i			0.266440i
$872$	18.8854	+	18.8854i	0.639539	+	0.639539i
$873$	−12.2376	+	12.2376i	−0.414180	+	0.414180i
$874$	−6.75680	+	26.6868i	−0.228552	+	0.902694i
$875$	−7.99009	+	4.07381i	−0.270114	+	0.137720i
$876$	−0.816769			−0.0275961
$877$	25.7069	−	25.7069i	0.868061	−	0.868061i	−0.124197	−	0.992258i	$-0.539635\pi$
$877$	25.7069	−	25.7069i	0.868061	−	0.868061i	0.992258	+	0.124197i	$0.0396354\pi$
$878$	1.12585	+	1.12585i	0.0379957	+	0.0379957i
$879$	3.65983			0.123443
$880$	−6.46534	−	0.678961i	−0.217946	−	0.0228878i
$881$			19.5891i			0.659972i	0.943986	+	0.329986i	$0.107044\pi$
$881$			19.5891i			0.659972i	−0.943986	+	0.329986i	$0.892956\pi$
$882$	−8.68761	+	8.68761i	−0.292527	+	0.292527i
$883$	8.21468	+	8.21468i	0.276446	+	0.276446i	0.831688	−	0.555243i	$-0.187375\pi$
$883$	8.21468	+	8.21468i	0.276446	+	0.276446i	−0.555243	+	0.831688i	$0.687375\pi$
$884$	−13.7881			−0.463744
$885$	8.26329	+	10.2025i	0.277767	+	0.342953i
$886$	−10.3570			−0.347949
$887$	28.1878	−	28.1878i	0.946454	−	0.946454i	−0.0521833	−	0.998638i	$-0.516618\pi$
$887$	28.1878	−	28.1878i	0.946454	−	0.946454i	0.998638	+	0.0521833i	$0.0166180\pi$
$888$	−12.2291	+	12.2291i	−0.410381	+	0.410381i
$889$	−6.31469			−0.211788
$890$	−10.6195	−	13.1117i	−0.355968	−	0.439505i
$891$		−	20.2355i		−	0.677914i
$892$	14.7729	−	14.7729i	0.494635	−	0.494635i
$893$	−3.08077	+	3.08077i	−0.103094	+	0.103094i
$894$	−1.01351			−0.0338967
$895$	−1.97047	−	0.206930i	−0.0658656	−	0.00691691i
$896$		−	7.16729i		−	0.239442i
$897$	−8.55720	−	14.3594i	−0.285717	−	0.479447i
$898$	3.18163	+	3.18163i	0.106172	+	0.106172i
$899$		−	9.38095i		−	0.312872i
$900$	−16.2359	−	3.44806i	−0.541195	−	0.114935i
$901$	−21.1910			−0.705974
$902$	4.71535	+	4.71535i	0.157004	+	0.157004i
$903$	2.72386	+	2.72386i	0.0906444	+	0.0906444i
$904$	−29.4797			−0.980481
$905$	−42.2237	−	4.43414i	−1.40356	−	0.147396i
$906$	7.16490			0.238038
$907$	−18.3725	−	18.3725i	−0.610050	−	0.610050i	0.332909	−	0.942959i	$-0.391970\pi$
$907$	−18.3725	−	18.3725i	−0.610050	−	0.610050i	−0.942959	+	0.332909i	$0.891970\pi$
$908$	−1.52579	+	1.52579i	−0.0506353	+	0.0506353i
$909$			23.5401i			0.780775i
$910$	−5.11586	+	4.14348i	−0.169589	+	0.137355i
$911$		−	0.00957127i		−	0.000317110i	−1.00000		0.000158555i	$-0.999950\pi$
$911$		−	0.00957127i		−	0.000317110i	1.00000		0.000158555i	$-5.04697e-5\pi$
$912$	2.31821	+	2.31821i	0.0767636	+	0.0767636i
$913$	10.4078	+	10.4078i	0.344448	+	0.344448i
$914$	−33.2349			−1.09931
$915$	8.10642	+	10.0088i	0.267990	+	0.330881i
$916$			3.54989i			0.117292i
$917$	7.57132	+	7.57132i	0.250027	+	0.250027i
$918$	−5.04998	+	5.04998i	−0.166674	+	0.166674i
$919$	51.2431			1.69036			0.845178	−	0.534485i	$-0.179495\pi$
$919$	51.2431			1.69036			0.845178	+	0.534485i	$0.179495\pi$
$920$	9.92222	−	26.9634i	0.327126	−	0.888957i
$921$	0.910832			0.0300129
$922$	−16.7092	+	16.7092i	−0.550289	+	0.550289i
$923$	−33.5877	−	33.5877i	−1.10555	−	1.10555i
$924$		−	4.00543i		−	0.131769i
$925$	−23.2665	−	35.8135i	−0.764997	−	1.17754i
$926$	−15.7653			−0.518081
$927$	24.6230	+	24.6230i	0.808725	+	0.808725i
$928$	−24.4106	−	24.4106i	−0.801318	−	0.801318i
$929$			27.0431i			0.887257i	0.896211	+	0.443628i	$0.146309\pi$
$929$			27.0431i			0.887257i	−0.896211	+	0.443628i	$0.853691\pi$
$930$	−0.222773	+	2.12134i	−0.00730503	+	0.0695614i
$931$			45.8509i			1.50270i
$932$	26.1772	−	26.1772i	0.857463	−	0.857463i
$933$	6.64056	+	6.64056i	0.217402	+	0.217402i
$934$	27.1315			0.887771
$935$	−14.8818	−	18.3742i	−0.486686	−	0.600899i
$936$	−30.0122			−0.980979
$937$	29.4335	+	29.4335i	0.961552	+	0.961552i	0.999288	−	0.0377358i	$-0.0120145\pi$
$937$	29.4335	+	29.4335i	0.961552	+	0.961552i	−0.0377358	+	0.999288i	$0.512015\pi$
$938$	−0.769610	−	0.769610i	−0.0251287	−	0.0251287i
$939$	−22.3847			−0.730497
$940$	1.43444	−	1.16180i	0.0467864	−	0.0378937i
$941$			24.9652i			0.813843i	0.913463	+	0.406921i	$0.133398\pi$
$941$			24.9652i			0.813843i	−0.913463	+	0.406921i	$0.866602\pi$
$942$	−1.10573	−	1.10573i	−0.0360265	−	0.0360265i
$943$	7.14145	−	4.25580i	0.232558	−	0.138588i
$944$		−	4.67244i		−	0.152075i
$945$	0.768619	−	7.31910i	0.0250032	−	0.238090i
$946$	24.4439			0.794739
$947$	−27.5348	+	27.5348i	−0.894759	+	0.894759i	−0.994967	−	0.100207i	$-0.968049\pi$
$947$	−27.5348	+	27.5348i	−0.894759	+	0.894759i	0.100207	+	0.994967i	$0.468049\pi$
$948$	4.13585	−	4.13585i	0.134326	−	0.134326i
$949$		−	3.64702i		−	0.118387i
$950$	24.0678	−	15.6358i	0.780863	−	0.507293i
$951$	12.1649			0.394474
$952$	3.32424	−	3.32424i	0.107739	−	0.107739i
$953$	−18.7803	+	18.7803i	−0.608355	+	0.608355i	−0.942516	−	0.334161i	$-0.891547\pi$
$953$	−18.7803	+	18.7803i	−0.608355	+	0.608355i	0.334161	+	0.942516i	$0.391547\pi$
$954$	−18.7249			−0.606240
$955$	−1.90508	−	0.200063i	−0.0616470	−	0.00647389i
$956$	−14.1954			−0.459110
$957$	−15.2786	−	15.2786i	−0.493888	−	0.493888i
$958$	5.08232	−	5.08232i	0.164202	−	0.164202i
$959$		−	8.87088i		−	0.286456i
$960$	3.66105	+	4.52020i	0.118160	+	0.145889i
$961$	−28.4842			−0.918844
$962$	−22.1670	−	22.1670i	−0.714693	−	0.714693i
$963$	−7.48861	+	7.48861i	−0.241317	+	0.241317i
$964$	13.0634			0.420745
$965$	−5.42514	+	4.39398i	−0.174641	+	0.141447i
$966$	2.24291	+	0.567880i	0.0721646	+	0.0182713i
$967$	11.5658	−	11.5658i	0.371931	−	0.371931i	−0.496249	−	0.868180i	$-0.665290\pi$
$967$	11.5658	−	11.5658i	0.371931	−	0.371931i	0.868180	+	0.496249i	$0.165290\pi$
$968$	−23.4329	−	23.4329i	−0.753163	−	0.753163i
$969$			11.9242i			0.383062i
$970$	−1.32422	+	12.6098i	−0.0425182	+	0.404875i
$971$		−	45.0087i		−	1.44440i	−0.691685	−	0.722199i	$-0.743131\pi$
$971$		−	45.0087i		−	1.44440i	0.691685	−	0.722199i	$-0.256869\pi$
$972$	14.9524	−	14.9524i	0.479597	−	0.479597i
$973$	0.803333	−	0.803333i	0.0257537	−	0.0257537i
$974$		−	27.1675i		−	0.870501i
$975$	−3.62038	+	17.0473i	−0.115945	+	0.545949i
$976$		−	4.58374i		−	0.146722i
$977$	2.16566	+	2.16566i	0.0692857	+	0.0692857i	0.740900	−	0.671615i	$-0.234399\pi$
$977$	2.16566	+	2.16566i	0.0692857	+	0.0692857i	−0.671615	+	0.740900i	$0.734399\pi$
$978$	5.58621	+	5.58621i	0.178627	+	0.178627i
$979$			45.8382i			1.46500i
$980$	2.02888	−	19.3198i	0.0648103	−	0.617150i
$981$		−	24.2125i		−	0.773046i
$982$	−10.6597	+	10.6597i	−0.340164	+	0.340164i
$983$	23.8741	−	23.8741i	0.761465	−	0.761465i	−0.215122	−	0.976587i	$-0.569015\pi$
$983$	23.8741	−	23.8741i	0.761465	−	0.761465i	0.976587	+	0.215122i	$0.0690151\pi$
$984$			3.50984i			0.111890i
$985$	1.22560	+	1.51322i	0.0390508	+	0.0482151i
$986$		−	10.2951i		−	0.327863i
$987$	0.258926	+	0.258926i	0.00824170	+	0.00824170i
$988$	−32.1506	+	32.1506i	−1.02285	+	1.02285i
$989$	7.47946	−	29.5410i	0.237833	−	0.939351i
$990$	−13.1499	−	16.2359i	−0.417931	−	0.516009i
$991$	24.8035			0.787909			0.393955	−	0.919130i	$-0.371107\pi$
$991$	24.8035			0.787909			0.393955	+	0.919130i	$0.371107\pi$
$992$	6.54654	−	6.54654i	0.207853	−	0.207853i
$993$	−10.2803	−	10.2803i	−0.326234	−	0.326234i
$994$	6.57465			0.208535
$995$	−3.55642	+	33.8656i	−0.112746	+	1.07361i
$996$			3.14490i			0.0996500i
$997$	−16.6526	+	16.6526i	−0.527394	+	0.527394i	−0.919795	−	0.392400i	$-0.871645\pi$
$997$	−16.6526	+	16.6526i	−0.527394	+	0.527394i	0.392400	+	0.919795i	$0.371645\pi$
$998$	−12.5064	−	12.5064i	−0.395885	−	0.395885i
$999$	35.0441			1.10875

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.2.e.a.68.8	yes	20
5.2	odd	4	inner	115.2.e.a.22.7	✓	20
5.3	odd	4		575.2.e.d.482.4		20
5.4	even	2		575.2.e.d.68.3		20
23.22	odd	2	inner	115.2.e.a.68.7	yes	20
115.22	even	4	inner	115.2.e.a.22.8	yes	20
115.68	even	4		575.2.e.d.482.3		20
115.114	odd	2		575.2.e.d.68.4		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.2.e.a.22.7	✓	20	5.2	odd	4	inner
115.2.e.a.22.8	yes	20	115.22	even	4	inner
115.2.e.a.68.7	yes	20	23.22	odd	2	inner
115.2.e.a.68.8	yes	20	1.1	even	1	trivial
575.2.e.d.68.3		20	5.4	even	2
575.2.e.d.68.4		20	115.114	odd	2
575.2.e.d.482.3		20	115.68	even	4
575.2.e.d.482.4		20	5.3	odd	4

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:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	115.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.562704 - 0.562704i) q^{2} +(0.534388 + 0.534388i) q^{3} +1.36673i q^{4} +(0.233538 - 2.22384i) q^{5} +0.601404 q^{6} +(0.567230 + 0.567230i) q^{7} +(1.89447 + 1.89447i) q^{8} -2.42886i q^{9} +O(q^{10})\)	\(q+(0.562704 - 0.562704i) q^{2} +(0.534388 + 0.534388i) q^{3} +1.36673i q^{4} +(0.233538 - 2.22384i) q^{5} +0.601404 q^{6} +(0.567230 + 0.567230i) q^{7} +(1.89447 + 1.89447i) q^{8} -2.42886i q^{9} +(-1.11995 - 1.38278i) q^{10} +4.83416i q^{11} +(-0.730363 + 0.730363i) q^{12} +(-3.26120 - 3.26120i) q^{13} +0.638365 q^{14} +(1.31319 - 1.06359i) q^{15} -0.601404 q^{16} +(-1.54673 - 1.54673i) q^{17} +(-1.36673 - 1.36673i) q^{18} -7.21323 q^{19} +(3.03938 + 0.319183i) q^{20} +0.606242i q^{21} +(2.72020 + 2.72020i) q^{22} +(4.11977 - 2.45509i) q^{23} +2.02477i q^{24} +(-4.89092 - 1.03870i) q^{25} -3.67018 q^{26} +(2.90112 - 2.90112i) q^{27} +(-0.775250 + 0.775250i) q^{28} +5.91435i q^{29} +(0.140451 - 1.33743i) q^{30} -1.58613 q^{31} +(-4.12736 + 4.12736i) q^{32} +(-2.58332 + 2.58332i) q^{33} -1.74070 q^{34} +(1.39390 - 1.12896i) q^{35} +3.31959 q^{36} +(6.03976 + 6.03976i) q^{37} +(-4.05891 + 4.05891i) q^{38} -3.48549i q^{39} +(4.65543 - 3.77057i) q^{40} +1.73346 q^{41} +(0.341135 + 0.341135i) q^{42} +(4.49303 - 4.49303i) q^{43} -6.60699 q^{44} +(-5.40139 - 0.567230i) q^{45} +(0.936723 - 3.69970i) q^{46} +(0.427100 - 0.427100i) q^{47} +(-0.321383 - 0.321383i) q^{48} -6.35650i q^{49} +(-3.33662 + 2.16766i) q^{50} -1.65311i q^{51} +(4.45718 - 4.45718i) q^{52} +(6.85025 - 6.85025i) q^{53} -3.26494i q^{54} +(10.7504 + 1.12896i) q^{55} +2.14920i q^{56} +(-3.85466 - 3.85466i) q^{57} +(3.32803 + 3.32803i) q^{58} +7.76922i q^{59} +(1.45364 + 1.79478i) q^{60} +7.62173i q^{61} +(-0.892524 + 0.892524i) q^{62} +(1.37772 - 1.37772i) q^{63} +3.44215i q^{64} +(-8.01400 + 6.49077i) q^{65} +2.90729i q^{66} +(-1.20560 - 1.20560i) q^{67} +(2.11396 - 2.11396i) q^{68} +(3.51353 + 0.889586i) q^{69} +(0.149082 - 1.41962i) q^{70} +10.2992 q^{71} +(4.60140 - 4.60140i) q^{72} +(0.559153 + 0.559153i) q^{73} +6.79719 q^{74} +(-2.05858 - 3.16872i) q^{75} -9.85853i q^{76} +(-2.74208 + 2.74208i) q^{77} +(-1.96130 - 1.96130i) q^{78} -5.66273 q^{79} +(-0.140451 + 1.33743i) q^{80} -4.18593 q^{81} +(0.975423 - 0.975423i) q^{82} +(2.15297 - 2.15297i) q^{83} -0.828568 q^{84} +(-3.80090 + 3.07846i) q^{85} -5.05649i q^{86} +(-3.16056 + 3.16056i) q^{87} +(-9.15818 + 9.15818i) q^{88} +9.48215 q^{89} +(-3.35857 + 2.72020i) q^{90} -3.69970i q^{91} +(3.35544 + 5.63061i) q^{92} +(-0.847611 - 0.847611i) q^{93} -0.480662i q^{94} +(-1.68456 + 16.0411i) q^{95} -4.41122 q^{96} +(-5.03841 - 5.03841i) q^{97} +(-3.57683 - 3.57683i) q^{98} +11.7415 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4 q^{2} - 8 q^{3} - 8 q^{6} + 4 q^{8}+O(q^{10}) \) 20 * q - 4 * q^2 - 8 * q^3 - 8 * q^6 + 4 * q^8	\( 20 q - 4 q^{2} - 8 q^{3} - 8 q^{6} + 4 q^{8} - 16 q^{12} + 4 q^{13} + 8 q^{16} + 8 q^{18} - 12 q^{25} - 16 q^{26} + 4 q^{27} - 4 q^{31} + 24 q^{32} - 8 q^{35} - 32 q^{36} - 36 q^{41} + 32 q^{46} - 8 q^{47} + 4 q^{48} + 60 q^{50} + 40 q^{52} - 12 q^{55} + 36 q^{58} - 60 q^{62} - 76 q^{70} + 44 q^{71} + 72 q^{72} - 56 q^{73} + 28 q^{75} - 12 q^{77} - 44 q^{78} + 92 q^{81} + 28 q^{82} - 4 q^{85} + 24 q^{87} - 72 q^{92} - 8 q^{93} + 64 q^{95} - 104 q^{96} - 60 q^{98}+O(q^{100}) \) 20 * q - 4 * q^2 - 8 * q^3 - 8 * q^6 + 4 * q^8 - 16 * q^12 + 4 * q^13 + 8 * q^16 + 8 * q^18 - 12 * q^25 - 16 * q^26 + 4 * q^27 - 4 * q^31 + 24 * q^32 - 8 * q^35 - 32 * q^36 - 36 * q^41 + 32 * q^46 - 8 * q^47 + 4 * q^48 + 60 * q^50 + 40 * q^52 - 12 * q^55 + 36 * q^58 - 60 * q^62 - 76 * q^70 + 44 * q^71 + 72 * q^72 - 56 * q^73 + 28 * q^75 - 12 * q^77 - 44 * q^78 + 92 * q^81 + 28 * q^82 - 4 * q^85 + 24 * q^87 - 72 * q^92 - 8 * q^93 + 64 * q^95 - 104 * q^96 - 60 * q^98

Introduction

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