LMFDB - Embedded newform 112.2.m.d.29.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [112,2,Mod(29,112)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(112, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 0]))

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

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

chi := DirichletCharacter("112.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 112 = 2^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	112.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:	$0.894324502638$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	12.0.20138089353117696.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3x^{10} - 2x^{9} + 2x^{8} + 4x^{7} + 2x^{6} + 8x^{5} + 8x^{4} - 16x^{3} - 48x^{2} + 64 $ x^12 - 3x^10 - 2x^9 + 2x^8 + 4x^7 + 2x^6 + 8x^5 + 8x^4 - 16x^3 - 48*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			29.5
Root			$-1.12465 - 0.857418i$ of defining polynomial
Character	$\chi$	$=$	112.29
Dual form			112.2.m.d.85.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.857418 + 1.12465i) q^{2} +(0.416854 + 0.416854i) q^{3} +(-0.529667 + 1.92859i) q^{4} +(-1.13169 + 1.13169i) q^{5} +(-0.111396 + 0.826233i) q^{6} -1.00000i q^{7} +(-2.62313 + 1.05792i) q^{8} -2.65247i q^{9} +O(q^{10})$	\(q+(0.857418 + 1.12465i) q^{2} +(0.416854 + 0.416854i) q^{3} +(-0.529667 + 1.92859i) q^{4} +(-1.13169 + 1.13169i) q^{5} +(-0.111396 + 0.826233i) q^{6} -1.00000i q^{7} +(-2.62313 + 1.05792i) q^{8} -2.65247i q^{9} +(-2.24309 - 0.302422i) q^{10} +(3.85718 - 3.85718i) q^{11} +(-1.02473 + 0.583146i) q^{12} +(4.66311 + 4.66311i) q^{13} +(1.12465 - 0.857418i) q^{14} -0.943500 q^{15} +(-3.43890 - 2.04302i) q^{16} -5.33230 q^{17} +(2.98309 - 2.27427i) q^{18} +(-2.55919 - 2.55919i) q^{19} +(-1.58315 - 2.78199i) q^{20} +(0.416854 - 0.416854i) q^{21} +(7.64518 + 1.03075i) q^{22} -2.60484i q^{23} +(-1.53446 - 0.652465i) q^{24} +2.43855i q^{25} +(-1.24612 + 9.24260i) q^{26} +(2.35625 - 2.35625i) q^{27} +(1.92859 + 0.529667i) q^{28} +(-1.22279 - 1.22279i) q^{29} +(-0.808974 - 1.06111i) q^{30} -0.833708 q^{31} +(-0.650901 - 5.61928i) q^{32} +3.21576 q^{33} +(-4.57201 - 5.99696i) q^{34} +(1.13169 + 1.13169i) q^{35} +(5.11551 + 1.40492i) q^{36} +(-4.42967 + 4.42967i) q^{37} +(0.683893 - 5.07249i) q^{38} +3.88768i q^{39} +(1.77134 - 4.16581i) q^{40} -0.263382i q^{41} +(0.826233 + 0.111396i) q^{42} +(1.25233 - 1.25233i) q^{43} +(5.39588 + 9.48193i) q^{44} +(3.00177 + 3.00177i) q^{45} +(2.92953 - 2.23344i) q^{46} -10.7559 q^{47} +(-0.581880 - 2.28516i) q^{48} -1.00000 q^{49} +(-2.74251 + 2.09086i) q^{50} +(-2.22279 - 2.22279i) q^{51} +(-11.4631 + 6.52333i) q^{52} +(0.0476221 - 0.0476221i) q^{53} +(4.67025 + 0.629661i) q^{54} +8.73026i q^{55} +(1.05792 + 2.62313i) q^{56} -2.13362i q^{57} +(0.326766 - 2.42365i) q^{58} +(-3.60682 + 3.60682i) q^{59} +(0.499741 - 1.81962i) q^{60} +(4.46399 + 4.46399i) q^{61} +(-0.714837 - 0.937629i) q^{62} -2.65247 q^{63} +(5.76162 - 5.55011i) q^{64} -10.5544 q^{65} +(2.75725 + 3.61660i) q^{66} +(9.50964 + 9.50964i) q^{67} +(2.82435 - 10.2838i) q^{68} +(1.08584 - 1.08584i) q^{69} +(-0.302422 + 2.24309i) q^{70} +2.05301i q^{71} +(2.80609 + 6.95776i) q^{72} -5.48268i q^{73} +(-8.77991 - 1.18374i) q^{74} +(-1.01652 + 1.01652i) q^{75} +(6.29115 - 3.58011i) q^{76} +(-3.85718 - 3.85718i) q^{77} +(-4.37227 + 3.33337i) q^{78} +5.21576 q^{79} +(6.20385 - 1.57971i) q^{80} -5.99297 q^{81} +(0.296212 - 0.225828i) q^{82} +(5.84045 + 5.84045i) q^{83} +(0.583146 + 1.02473i) q^{84} +(6.03452 - 6.03452i) q^{85} +(2.48221 + 0.334661i) q^{86} -1.01945i q^{87} +(-6.03730 + 14.1984i) q^{88} -6.32651i q^{89} +(-0.802163 + 5.94971i) q^{90} +(4.66311 - 4.66311i) q^{91} +(5.02367 + 1.37970i) q^{92} +(-0.347535 - 0.347535i) q^{93} +(-9.22231 - 12.0966i) q^{94} +5.79243 q^{95} +(2.07109 - 2.61375i) q^{96} +18.8089 q^{97} +(-0.857418 - 1.12465i) q^{98} +(-10.2310 - 10.2310i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{2} + 4 q^{3} - 6 q^{4} + 4 q^{5} + 4 q^{6} - 4 q^{8}+O(q^{10}) $ 12 * q + 2 * q^2 + 4 * q^3 - 6 * q^4 + 4 * q^5 + 4 * q^6 - 4 * q^8	$ 12 q + 2 q^{2} + 4 q^{3} - 6 q^{4} + 4 q^{5} + 4 q^{6} - 4 q^{8} - 4 q^{10} + 8 q^{12} - 24 q^{15} + 10 q^{16} - 8 q^{17} - 20 q^{20} + 4 q^{21} + 14 q^{22} - 8 q^{24} - 20 q^{26} + 4 q^{27} - 4 q^{29} - 28 q^{30} - 8 q^{31} + 12 q^{32} + 8 q^{34} - 4 q^{35} - 16 q^{36} - 20 q^{37} + 16 q^{38} - 8 q^{40} - 12 q^{42} + 16 q^{43} + 14 q^{44} + 40 q^{45} - 28 q^{46} + 16 q^{47} + 16 q^{48} - 12 q^{49} + 44 q^{50} - 16 q^{51} - 16 q^{52} + 4 q^{53} + 64 q^{54} + 6 q^{56} + 14 q^{58} - 16 q^{59} + 60 q^{60} - 20 q^{61} + 8 q^{62} + 12 q^{63} - 18 q^{64} + 32 q^{65} + 12 q^{66} + 24 q^{67} - 28 q^{68} - 4 q^{69} + 20 q^{70} + 6 q^{72} - 38 q^{74} - 40 q^{75} + 48 q^{76} - 76 q^{78} + 24 q^{79} + 24 q^{80} - 44 q^{81} - 16 q^{82} - 20 q^{83} + 8 q^{84} - 8 q^{85} + 38 q^{86} - 14 q^{88} - 40 q^{90} + 32 q^{92} - 48 q^{93} - 24 q^{94} - 16 q^{96} + 48 q^{97} - 2 q^{98} + 32 q^{99}+O(q^{100}) $ 12 * q + 2 * q^2 + 4 * q^3 - 6 * q^4 + 4 * q^5 + 4 * q^6 - 4 * q^8 - 4 * q^10 + 8 * q^12 - 24 * q^15 + 10 * q^16 - 8 * q^17 - 20 * q^20 + 4 * q^21 + 14 * q^22 - 8 * q^24 - 20 * q^26 + 4 * q^27 - 4 * q^29 - 28 * q^30 - 8 * q^31 + 12 * q^32 + 8 * q^34 - 4 * q^35 - 16 * q^36 - 20 * q^37 + 16 * q^38 - 8 * q^40 - 12 * q^42 + 16 * q^43 + 14 * q^44 + 40 * q^45 - 28 * q^46 + 16 * q^47 + 16 * q^48 - 12 * q^49 + 44 * q^50 - 16 * q^51 - 16 * q^52 + 4 * q^53 + 64 * q^54 + 6 * q^56 + 14 * q^58 - 16 * q^59 + 60 * q^60 - 20 * q^61 + 8 * q^62 + 12 * q^63 - 18 * q^64 + 32 * q^65 + 12 * q^66 + 24 * q^67 - 28 * q^68 - 4 * q^69 + 20 * q^70 + 6 * q^72 - 38 * q^74 - 40 * q^75 + 48 * q^76 - 76 * q^78 + 24 * q^79 + 24 * q^80 - 44 * q^81 - 16 * q^82 - 20 * q^83 + 8 * q^84 - 8 * q^85 + 38 * q^86 - 14 * q^88 - 40 * q^90 + 32 * q^92 - 48 * q^93 - 24 * q^94 - 16 * q^96 + 48 * q^97 - 2 * q^98 + 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/112\mathbb{Z}\right)^\times$.

$n$	$15$	$17$	$85$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	0.857418	+	1.12465i	0.606286	+	0.795246i
$2$	0.857418	+	1.12465i	0.606286	+	0.795246i
$3$	0.416854	+	0.416854i	0.240671	+	0.240671i	0.817128	−	0.576457i	$-0.195565\pi$
$3$	0.416854	+	0.416854i	0.240671	+	0.240671i	−0.576457	+	0.817128i	$0.695565\pi$
$4$	−0.529667	+	1.92859i	−0.264834	+	0.964294i
$5$	−1.13169	+	1.13169i	−0.506108	+	0.506108i	−0.913329	−	0.407222i	$-0.866498\pi$
$5$	−1.13169	+	1.13169i	−0.506108	+	0.506108i	0.407222	+	0.913329i	$0.366498\pi$
$6$	−0.111396	+	0.826233i	−0.0454772	+	0.337308i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	−2.62313	+	1.05792i	−0.927416	+	0.374030i
$9$		−	2.65247i		−	0.884155i
$10$	−2.24309	−	0.302422i	−0.709326	−	0.0956341i
$11$	3.85718	−	3.85718i	1.16298	−	1.16298i	0.179163	−	0.983819i	$-0.442661\pi$
$11$	3.85718	−	3.85718i	1.16298	−	1.16298i	0.983819	−	0.179163i	$-0.0573390\pi$
$12$	−1.02473	+	0.583146i	−0.295815	+	0.168340i
$13$	4.66311	+	4.66311i	1.29332	+	1.29332i	0.932724	+	0.360591i	$0.117425\pi$
$13$	4.66311	+	4.66311i	1.29332	+	1.29332i	0.360591	+	0.932724i	$0.382575\pi$
$14$	1.12465	−	0.857418i	0.300575	−	0.229155i
$15$	−0.943500			−0.243611
$16$	−3.43890	−	2.04302i	−0.859726	−	0.510755i
$17$	−5.33230			−1.29327			−0.646637	−	0.762798i	$-0.723825\pi$
$17$	−5.33230			−1.29327			−0.646637	+	0.762798i	$0.723825\pi$
$18$	2.98309	−	2.27427i	0.703121	−	0.536051i
$19$	−2.55919	−	2.55919i	−0.587119	−	0.587119i	0.349731	−	0.936850i	$-0.386273\pi$
$19$	−2.55919	−	2.55919i	−0.587119	−	0.587119i	−0.936850	+	0.349731i	$0.886273\pi$
$20$	−1.58315	−	2.78199i	−0.354002	−	0.622071i
$21$	0.416854	−	0.416854i	0.0909650	−	0.0909650i
$22$	7.64518	+	1.03075i	1.62996	+	0.219757i
$23$		−	2.60484i		−	0.543147i	−0.962418	−	0.271574i	$-0.912456\pi$
$23$		−	2.60484i		−	0.543147i	0.962418	−	0.271574i	$-0.0875441\pi$
$24$	−1.53446	−	0.652465i	−0.313220	−	0.133184i
$25$			2.43855i			0.487710i
$26$	−1.24612	+	9.24260i	−0.244385	+	1.81262i
$27$	2.35625	−	2.35625i	0.453461	−	0.453461i
$28$	1.92859	+	0.529667i	0.364469	+	0.100098i
$29$	−1.22279	−	1.22279i	−0.227067	−	0.227067i	0.584399	−	0.811466i	$-0.301330\pi$
$29$	−1.22279	−	1.22279i	−0.227067	−	0.227067i	−0.811466	+	0.584399i	$0.801330\pi$
$30$	−0.808974	−	1.06111i	−0.147698	−	0.193731i
$31$	−0.833708			−0.149738			−0.0748692	−	0.997193i	$-0.523854\pi$
$31$	−0.833708			−0.149738			−0.0748692	+	0.997193i	$0.523854\pi$
$32$	−0.650901	−	5.61928i	−0.115064	−	0.993358i
$33$	3.21576			0.559792
$34$	−4.57201	−	5.99696i	−0.784094	−	1.02847i
$35$	1.13169	+	1.13169i	0.191291	+	0.191291i
$36$	5.11551	+	1.40492i	0.852586	+	0.234154i
$37$	−4.42967	+	4.42967i	−0.728234	+	0.728234i	−0.970268	−	0.242034i	$-0.922185\pi$
$37$	−4.42967	+	4.42967i	−0.728234	+	0.728234i	0.242034	+	0.970268i	$0.422185\pi$
$38$	0.683893	−	5.07249i	0.110942	−	0.822867i
$39$			3.88768i			0.622526i
$40$	1.77134	−	4.16581i	0.280073	−	0.658672i
$41$		−	0.263382i		−	0.0411333i	−0.999788	−	0.0205667i	$-0.993453\pi$
$41$		−	0.263382i		−	0.0411333i	0.999788	−	0.0205667i	$-0.00654703\pi$
$42$	0.826233	+	0.111396i	0.127490	+	0.0171888i
$43$	1.25233	−	1.25233i	0.190979	−	0.190979i	−0.605140	−	0.796119i	$-0.706883\pi$
$43$	1.25233	−	1.25233i	0.190979	−	0.190979i	0.796119	+	0.605140i	$0.206883\pi$
$44$	5.39588	+	9.48193i	0.813460	+	1.42945i
$45$	3.00177	+	3.00177i	0.447478	+	0.447478i
$46$	2.92953	−	2.23344i	0.431936	−	0.329303i
$47$	−10.7559			−1.56891			−0.784455	−	0.620186i	$-0.787057\pi$
$47$	−10.7559			−1.56891			−0.784455	+	0.620186i	$0.787057\pi$
$48$	−0.581880	−	2.28516i	−0.0839872	−	0.329835i
$49$	−1.00000			−0.142857
$50$	−2.74251	+	2.09086i	−0.387850	+	0.295692i
$51$	−2.22279	−	2.22279i	−0.311253	−	0.311253i
$52$	−11.4631	+	6.52333i	−1.58965	+	0.904623i
$53$	0.0476221	−	0.0476221i	0.00654139	−	0.00654139i	−0.703829	−	0.710370i	$-0.748528\pi$
$53$	0.0476221	−	0.0476221i	0.00654139	−	0.00654139i	0.710370	+	0.703829i	$0.248528\pi$
$54$	4.67025	+	0.629661i	0.635541	+	0.0856861i
$55$			8.73026i			1.17719i
$56$	1.05792	+	2.62313i	0.141370	+	0.350530i
$57$		−	2.13362i		−	0.282605i
$58$	0.326766	−	2.42365i	0.0429065	−	0.318241i
$59$	−3.60682	+	3.60682i	−0.469567	+	0.469567i	−0.901774	−	0.432207i	$-0.857735\pi$
$59$	−3.60682	+	3.60682i	−0.469567	+	0.469567i	0.432207	+	0.901774i	$0.357735\pi$
$60$	0.499741	−	1.81962i	0.0645163	−	0.234912i
$61$	4.46399	+	4.46399i	0.571556	+	0.571556i	0.932563	−	0.361007i	$-0.117567\pi$
$61$	4.46399	+	4.46399i	0.571556	+	0.571556i	−0.361007	+	0.932563i	$0.617567\pi$
$62$	−0.714837	−	0.937629i	−0.0907844	−	0.119079i
$63$	−2.65247			−0.334179
$64$	5.76162	−	5.55011i	0.720203	−	0.693764i
$65$	−10.5544			−1.30911
$66$	2.75725	+	3.61660i	0.339394	+	0.445173i
$67$	9.50964	+	9.50964i	1.16179	+	1.16179i	0.984084	+	0.177704i	$0.0568668\pi$
$67$	9.50964	+	9.50964i	1.16179	+	1.16179i	0.177704	+	0.984084i	$0.443133\pi$
$68$	2.82435	−	10.2838i	0.342502	−	1.24710i
$69$	1.08584	−	1.08584i	0.130720	−	0.130720i
$70$	−0.302422	+	2.24309i	−0.0361463	+	0.268100i
$71$			2.05301i			0.243647i	0.992552	+	0.121824i	$0.0388743\pi$
$71$			2.05301i			0.243647i	−0.992552	+	0.121824i	$0.961126\pi$
$72$	2.80609	+	6.95776i	0.330701	+	0.819980i
$73$		−	5.48268i		−	0.641700i	−0.947130	−	0.320850i	$-0.896032\pi$
$73$		−	5.48268i		−	0.641700i	0.947130	−	0.320850i	$-0.103968\pi$
$74$	−8.77991	−	1.18374i	−1.02064	−	0.137607i
$75$	−1.01652	+	1.01652i	−0.117378	+	0.117378i
$76$	6.29115	−	3.58011i	0.721645	−	0.410667i
$77$	−3.85718	−	3.85718i	−0.439566	−	0.439566i
$78$	−4.37227	+	3.33337i	−0.495062	+	0.377429i
$79$	5.21576			0.586819			0.293409	−	0.955987i	$-0.405210\pi$
$79$	5.21576			0.586819			0.293409	+	0.955987i	$0.405210\pi$
$80$	6.20385	−	1.57971i	0.693611	−	0.176617i
$81$	−5.99297			−0.665885
$82$	0.296212	−	0.225828i	0.0327111	−	0.0249386i
$83$	5.84045	+	5.84045i	0.641073	+	0.641073i	0.950819	−	0.309746i	$-0.100244\pi$
$83$	5.84045	+	5.84045i	0.641073	+	0.641073i	−0.309746	+	0.950819i	$0.600244\pi$
$84$	0.583146	+	1.02473i	0.0636264	+	0.111808i
$85$	6.03452	−	6.03452i	0.654535	−	0.654535i
$86$	2.48221	+	0.334661i	0.267663	+	0.0360874i
$87$		−	1.01945i		−	0.109297i
$88$	−6.03730	+	14.1984i	−0.643578	+	1.51356i
$89$		−	6.32651i		−	0.670609i	−0.942110	−	0.335304i	$-0.891161\pi$
$89$		−	6.32651i		−	0.670609i	0.942110	−	0.335304i	$-0.108839\pi$
$90$	−0.802163	+	5.94971i	−0.0845554	+	0.627154i
$91$	4.66311	−	4.66311i	0.488827	−	0.488827i
$92$	5.02367	+	1.37970i	0.523754	+	0.143844i
$93$	−0.347535	−	0.347535i	−0.0360377	−	0.0360377i
$94$	−9.22231	−	12.0966i	−0.951208	−	1.24767i
$95$	5.79243			0.594291
$96$	2.07109	−	2.61375i	0.211380	−	0.266765i
$97$	18.8089			1.90976			0.954878	−	0.296999i	$-0.0959858\pi$
$97$	18.8089			1.90976			0.954878	+	0.296999i	$0.0959858\pi$
$98$	−0.857418	−	1.12465i	−0.0866123	−	0.113607i
$99$	−10.2310	−	10.2310i	−1.02826	−	1.02826i
$100$	−4.70296	−	1.29162i	−0.470296	−	0.129162i
$101$	−2.88523	+	2.88523i	−0.287091	+	0.287091i	−0.835929	−	0.548838i	$-0.815070\pi$
$101$	−2.88523	+	2.88523i	−0.287091	+	0.287091i	0.548838	+	0.835929i	$0.315070\pi$
$102$	0.593996	−	4.40572i	0.0588144	−	0.436231i
$103$		−	7.74040i		−	0.762684i	−0.924434	−	0.381342i	$-0.875462\pi$
$103$		−	7.74040i		−	0.762684i	0.924434	−	0.381342i	$-0.124538\pi$
$104$	−17.1651	−	7.29876i	−1.68318	−	0.715703i
$105$			0.943500i			0.0920762i
$106$	0.0943901	+	0.0127260i	0.00916798	+	0.00123606i
$107$	−2.33447	+	2.33447i	−0.225682	+	0.225682i	−0.810886	−	0.585204i	$-0.801014\pi$
$107$	−2.33447	+	2.33447i	−0.225682	+	0.225682i	0.585204	+	0.810886i	$0.301014\pi$
$108$	3.29621	+	5.79227i	0.317178	+	0.557362i
$109$	−4.92827	−	4.92827i	−0.472042	−	0.472042i	0.430533	−	0.902575i	$-0.358326\pi$
$109$	−4.92827	−	4.92827i	−0.472042	−	0.472042i	−0.902575	+	0.430533i	$0.858326\pi$
$110$	−9.81847	+	7.48549i	−0.936155	+	0.713713i
$111$	−3.69306			−0.350529
$112$	−2.04302	+	3.43890i	−0.193047	+	0.324946i
$113$	5.24381			0.493296			0.246648	−	0.969105i	$-0.420671\pi$
$113$	5.24381			0.493296			0.246648	+	0.969105i	$0.420671\pi$
$114$	2.39957	−	1.82941i	0.224741	−	0.171340i
$115$	2.94788	+	2.94788i	0.274891	+	0.274891i
$116$	3.00593	−	1.71059i	0.279094	−	0.158824i
$117$	12.3687	−	12.3687i	1.14349	−	1.14349i
$118$	−7.14895	−	0.963849i	−0.658114	−	0.0887295i
$119$			5.33230i			0.488811i
$120$	2.47492	−	0.998145i	0.225929	−	0.0911178i
$121$		−	18.7556i		−	1.70506i
$122$	−1.19291	+	8.84793i	−0.108001	+	0.801054i
$123$	0.109792	−	0.109792i	0.00989959	−	0.00989959i
$124$	0.441588	−	1.60788i	0.0396558	−	0.144392i
$125$	−8.41814	−	8.41814i	−0.752941	−	0.752941i
$126$	−2.27427	−	2.98309i	−0.202608	−	0.265755i
$127$	−17.6789			−1.56875			−0.784373	−	0.620290i	$-0.787015\pi$
$127$	−17.6789			−1.56875			−0.784373	+	0.620290i	$0.787015\pi$
$128$	11.1820	+	1.72103i	0.988362	+	0.152119i
$129$	1.04408			0.0919262
$130$	−9.04954	−	11.8700i	−0.793697	−	1.04107i
$131$	−2.17911	−	2.17911i	−0.190390	−	0.190390i	0.605475	−	0.795865i	$-0.292983\pi$
$131$	−2.17911	−	2.17911i	−0.190390	−	0.190390i	−0.795865	+	0.605475i	$0.792983\pi$
$132$	−1.70328	+	6.20188i	−0.148252	+	0.539804i
$133$	−2.55919	+	2.55919i	−0.221910	+	0.221910i
$134$	−2.54126	+	18.8487i	−0.219531	+	1.62828i
$135$			5.33310i			0.459000i
$136$	13.9873	−	5.64113i	1.19940	−	0.483723i
$137$			8.54650i			0.730177i	0.930973	+	0.365088i	$0.118961\pi$
$137$			8.54650i			0.730177i	−0.930973	+	0.365088i	$0.881039\pi$
$138$	2.15221	+	0.290169i	0.183208	+	0.0247008i
$139$	−5.72549	+	5.72549i	−0.485629	+	0.485629i	−0.906924	−	0.421295i	$-0.861576\pi$
$139$	−5.72549	+	5.72549i	−0.485629	+	0.485629i	0.421295	+	0.906924i	$0.361576\pi$
$140$	−2.78199	+	1.58315i	−0.235121	+	0.133800i
$141$	−4.48364	−	4.48364i	−0.377591	−	0.377591i
$142$	−2.30891	+	1.76029i	−0.193760	+	0.147720i
$143$	35.9729			3.00821
$144$	−5.41904	+	9.12158i	−0.451587	+	0.760131i
$145$	2.76764			0.229840
$146$	6.16609	−	4.70095i	0.510309	−	0.389054i
$147$	−0.416854	−	0.416854i	−0.0343815	−	0.0343815i
$148$	−6.19676	−	10.8893i	−0.509371	−	0.895092i
$149$	0.395157	−	0.395157i	0.0323725	−	0.0323725i	−0.690735	−	0.723108i	$-0.742713\pi$
$149$	0.395157	−	0.395157i	0.0323725	−	0.0323725i	0.723108	+	0.690735i	$0.242713\pi$
$150$	−2.01481	−	0.271645i	−0.164509	−	0.0221797i
$151$		−	3.71559i		−	0.302371i	−0.988505	−	0.151185i	$-0.951691\pi$
$151$		−	3.71559i		−	0.302371i	0.988505	−	0.151185i	$-0.0483090\pi$
$152$	9.42051	+	4.00568i	0.764105	+	0.324904i
$153$			14.1437i			1.14345i
$154$	1.03075	−	7.64518i	0.0830604	−	0.616066i
$155$	0.943500	−	0.943500i	0.0757837	−	0.0757837i
$156$	−7.49773	−	2.05918i	−0.600299	−	0.164866i
$157$	3.99542	+	3.99542i	0.318869	+	0.318869i	0.848333	−	0.529464i	$-0.177607\pi$
$157$	3.99542	+	3.99542i	0.318869	+	0.318869i	−0.529464	+	0.848333i	$0.677607\pi$
$158$	4.47209	+	5.86590i	0.355780	+	0.466666i
$159$	0.0397029			0.00314864
$160$	7.09591	+	5.62267i	0.560981	+	0.444511i
$161$	−2.60484			−0.205290
$162$	−5.13848	−	6.73998i	−0.403717	−	0.529543i
$163$	3.37168	+	3.37168i	0.264090	+	0.264090i	0.826713	−	0.562623i	$-0.190208\pi$
$163$	3.37168	+	3.37168i	0.264090	+	0.264090i	−0.562623	+	0.826713i	$0.690208\pi$
$164$	0.507955	+	0.139505i	0.0396646	+	0.0108935i
$165$	−3.63925	+	3.63925i	−0.283315	+	0.283315i
$166$	−1.56074	+	11.5762i	−0.121137	+	0.898485i
$167$		−	12.4233i		−	0.961345i	−0.876900	−	0.480673i	$-0.840393\pi$
$167$		−	12.4233i		−	0.961345i	0.876900	−	0.480673i	$-0.159607\pi$
$168$	−0.652465	+	1.53446i	−0.0503388	+	0.118386i
$169$			30.4893i			2.34533i
$170$	11.9608	+	1.61260i	0.917353	+	0.123681i
$171$	−6.78817	+	6.78817i	−0.519105	+	0.519105i
$172$	1.75191	+	3.07856i	0.133582	+	0.234738i
$173$	9.25908	+	9.25908i	0.703955	+	0.703955i	0.965257	−	0.261302i	$-0.0841519\pi$
$173$	9.25908	+	9.25908i	0.703955	+	0.703955i	−0.261302	+	0.965257i	$0.584152\pi$
$174$	1.14652	−	0.874097i	0.0869178	−	0.0662651i
$175$	2.43855			0.184337
$176$	−21.1448	+	5.38417i	−1.59385	+	0.405847i
$177$	−3.00703			−0.226022
$178$	7.11510	−	5.42447i	0.533299	−	0.406581i
$179$	−9.95523	−	9.95523i	−0.744088	−	0.744088i	0.229274	−	0.973362i	$-0.426365\pi$
$179$	−9.95523	−	9.95523i	−0.744088	−	0.744088i	−0.973362	+	0.229274i	$0.926365\pi$
$180$	−7.37912	+	4.19924i	−0.550007	+	0.312993i
$181$	−5.08125	+	5.08125i	−0.377687	+	0.377687i	−0.870267	−	0.492580i	$-0.836054\pi$
$181$	−5.08125	+	5.08125i	−0.377687	+	0.377687i	0.492580	+	0.870267i	$0.336054\pi$
$182$	9.24260	+	1.24612i	0.685107	+	0.0923688i
$183$			3.72167i			0.275114i
$184$	2.75571	+	6.83284i	0.203154	+	0.503724i
$185$		−	10.0260i		−	0.737129i
$186$	0.0928717	−	0.688837i	0.00680968	−	0.0505080i
$187$	−20.5676	+	20.5676i	−1.50405	+	1.50405i
$188$	5.69705	−	20.7437i	0.415500	−	1.51289i
$189$	−2.35625	−	2.35625i	−0.171392	−	0.171392i
$190$	4.96654	+	6.51445i	0.360311	+	0.472608i
$191$	20.7927			1.50451			0.752254	−	0.658873i	$-0.228967\pi$
$191$	20.7927			1.50451			0.752254	+	0.658873i	$0.228967\pi$
$192$	4.71534	+	0.0881695i	0.340300	+	0.00636309i
$193$	13.3447			0.960574			0.480287	−	0.877111i	$-0.340533\pi$
$193$	13.3447			0.960574			0.480287	+	0.877111i	$0.340533\pi$
$194$	16.1271	+	21.1534i	1.15786	+	1.51873i
$195$	−4.39965	−	4.39965i	−0.315065	−	0.315065i
$196$	0.529667	−	1.92859i	0.0378334	−	0.137756i
$197$	0.194462	−	0.194462i	0.0138549	−	0.0138549i	−0.700145	−	0.714000i	$-0.746882\pi$
$197$	0.194462	−	0.194462i	0.0138549	−	0.0138549i	0.714000	+	0.700145i	$0.246882\pi$
$198$	2.73404	−	20.2786i	0.194299	−	1.44114i
$199$		−	14.4003i		−	1.02081i	−0.859935	−	0.510403i	$-0.829496\pi$
$199$		−	14.4003i		−	1.02081i	0.859935	−	0.510403i	$-0.170504\pi$
$200$	−2.57979	−	6.39664i	−0.182418	−	0.452311i
$201$			7.92827i			0.559217i
$202$	−5.71872	−	0.771019i	−0.402367	−	0.0542487i
$203$	−1.22279	+	1.22279i	−0.0858232	+	0.0858232i
$204$	5.46419	−	3.10951i	0.382570	−	0.217709i
$205$	0.298067	+	0.298067i	0.0208179	+	0.0208179i
$206$	8.70522	−	6.63676i	0.606522	−	0.462405i
$207$	−6.90926			−0.480227
$208$	−6.50917	−	25.5628i	−0.451330	−	1.77246i
$209$	−19.7425			−1.36562
$210$	−1.06111	+	0.808974i	−0.0732232	+	0.0558245i
$211$	7.72356	+	7.72356i	0.531711	+	0.531711i	0.921081	−	0.389370i	$-0.127307\pi$
$211$	7.72356	+	7.72356i	0.531711	+	0.531711i	−0.389370	+	0.921081i	$0.627307\pi$
$212$	0.0666195	+	0.117067i	0.00457544	+	0.00804021i
$213$	−0.855805	+	0.855805i	−0.0586388	+	0.0586388i
$214$	−4.62708	−	0.623841i	−0.316301	−	0.0426449i
$215$			2.83451i			0.193312i
$216$	−3.68804	+	8.67348i	−0.250939	+	0.590156i
$217$			0.833708i			0.0565958i
$218$	1.31698	−	9.76815i	0.0891971	−	0.661583i
$219$	2.28548	−	2.28548i	0.154438	−	0.154438i
$220$	−16.8371	−	4.62414i	−1.13516	−	0.311759i
$221$	−24.8651	−	24.8651i	−1.67261	−	1.67261i
$222$	−3.16649	−	4.15339i	−0.212521	−	0.278757i
$223$	−7.06285			−0.472963			−0.236482	−	0.971636i	$-0.575994\pi$
$223$	−7.06285			−0.472963			−0.236482	+	0.971636i	$0.575994\pi$
$224$	−5.61928	+	0.650901i	−0.375454	+	0.0434901i
$225$	6.46817			0.431212
$226$	4.49614	+	5.89744i	0.299079	+	0.392292i
$227$	−11.8229	−	11.8229i	−0.784711	−	0.784711i	0.195911	−	0.980622i	$-0.437234\pi$
$227$	−11.8229	−	11.8229i	−0.784711	−	0.784711i	−0.980622	+	0.195911i	$0.937234\pi$
$228$	4.11488	+	1.13011i	0.272514	+	0.0748433i
$229$	−9.37815	+	9.37815i	−0.619726	+	0.619726i	−0.945461	−	0.325735i	$-0.894388\pi$
$229$	−9.37815	+	9.37815i	−0.619726	+	0.619726i	0.325735	+	0.945461i	$0.394388\pi$
$230$	−0.787761	+	5.84289i	−0.0519434	+	0.385269i
$231$		−	3.21576i		−	0.211581i
$232$	4.50115	+	1.91393i	0.295515	+	0.125656i
$233$			24.4385i			1.60102i	0.599318	+	0.800511i	$0.295439\pi$
$233$			24.4385i			1.60102i	−0.599318	+	0.800511i	$0.704561\pi$
$234$	24.5157	+	3.30530i	1.60264	+	0.216074i
$235$	12.1724	−	12.1724i	0.794037	−	0.794037i
$236$	−5.04565	−	8.86648i	−0.328444	−	0.577158i
$237$	2.17421	+	2.17421i	0.141230	+	0.141230i
$238$	−5.99696	+	4.57201i	−0.388725	+	0.296360i
$239$	−6.27660			−0.406000			−0.203000	−	0.979179i	$-0.565069\pi$
$239$	−6.27660			−0.406000			−0.203000	+	0.979179i	$0.565069\pi$
$240$	3.24461	+	1.92759i	0.209438	+	0.124425i
$241$	−15.0124			−0.967034			−0.483517	−	0.875335i	$-0.660641\pi$
$241$	−15.0124			−0.967034			−0.483517	+	0.875335i	$0.660641\pi$
$242$	21.0935	−	16.0814i	1.35594	−	1.03375i
$243$	−9.56695	−	9.56695i	−0.613720	−	0.613720i
$244$	−10.9736	+	6.24477i	−0.702515	+	0.399781i
$245$	1.13169	−	1.13169i	0.0723011	−	0.0723011i
$246$	0.217615	+	0.0293396i	0.0138746	+	0.00187063i
$247$		−	23.8676i		−	1.51866i
$248$	2.18693	−	0.881994i	0.138870	−	0.0560067i
$249$			4.86923i			0.308575i
$250$	2.24958	−	16.6853i	0.142276	−	1.05527i
$251$	11.7926	−	11.7926i	0.744339	−	0.744339i	−0.229071	−	0.973410i	$-0.573569\pi$
$251$	11.7926	−	11.7926i	0.744339	−	0.744339i	0.973410	+	0.229071i	$0.0735687\pi$
$252$	1.40492	−	5.11551i	0.0885019	−	0.322247i
$253$	−10.0473	−	10.0473i	−0.631671	−	0.631671i
$254$	−15.1582	−	19.8825i	−0.951109	−	1.24754i
$255$	5.03103			0.315055
$256$	7.65213	+	14.0515i	0.478258	+	0.878219i
$257$	20.3977			1.27237			0.636186	−	0.771536i	$-0.280511\pi$
$257$	20.3977			1.27237			0.636186	+	0.771536i	$0.280511\pi$
$258$	0.895214	+	1.17422i	0.0557336	+	0.0731039i
$259$	4.42967	+	4.42967i	0.275247	+	0.275247i
$260$	5.59033	−	20.3551i	0.346697	−	1.26237i
$261$	−3.24341	+	3.24341i	−0.200762	+	0.200762i
$262$	0.582324	−	4.31914i	0.0359761	−	0.266838i
$263$			23.3452i			1.43953i	0.694219	+	0.719764i	$0.255750\pi$
$263$			23.3452i			1.43953i	−0.694219	+	0.719764i	$0.744250\pi$
$264$	−8.43536	+	3.40201i	−0.519160	+	0.209379i
$265$			0.107787i			0.00662130i
$266$	−5.07249	−	0.683893i	−0.311014	−	0.0419322i
$267$	2.63723	−	2.63723i	0.161396	−	0.161396i
$268$	−23.3771	+	13.3032i	−1.42799	+	0.812624i
$269$	22.0705	+	22.0705i	1.34566	+	1.34566i	0.890312	+	0.455352i	$0.150487\pi$
$269$	22.0705	+	22.0705i	1.34566	+	1.34566i	0.455352	+	0.890312i	$0.349513\pi$
$270$	−5.99786	+	4.57270i	−0.365018	+	0.278286i
$271$	1.46392			0.0889266			0.0444633	−	0.999011i	$-0.485842\pi$
$271$	1.46392			0.0889266			0.0444633	+	0.999011i	$0.485842\pi$
$272$	18.3373	+	10.8940i	1.11186	+	0.660546i
$273$	3.88768			0.235293
$274$	−9.61180	+	7.32792i	−0.580670	+	0.442696i
$275$	9.40592	+	9.40592i	0.567199	+	0.567199i
$276$	1.51900	+	2.66927i	0.0914333	+	0.160671i
$277$	−1.39234	+	1.39234i	−0.0836578	+	0.0836578i	−0.747697	−	0.664040i	$-0.768841\pi$
$277$	−1.39234	+	1.39234i	−0.0836578	+	0.0836578i	0.664040	+	0.747697i	$0.268841\pi$
$278$	−11.3483	−	1.53002i	−0.680625	−	0.0917645i
$279$			2.21138i			0.132392i
$280$	−4.16581	−	1.77134i	−0.248955	−	0.105858i
$281$		−	5.66742i		−	0.338090i	−0.985608	−	0.169045i	$-0.945932\pi$
$281$		−	5.66742i		−	0.338090i	0.985608	−	0.169045i	$-0.0540683\pi$
$282$	1.19816	−	8.88688i	0.0713496	−	0.529206i
$283$	−16.6615	+	16.6615i	−0.990424	+	0.990424i	−0.999955	−	0.00953050i	$-0.996966\pi$
$283$	−16.6615	+	16.6615i	−0.990424	+	0.990424i	0.00953050	+	0.999955i	$0.496966\pi$
$284$	−3.95941	−	1.08741i	−0.234948	−	0.0645260i
$285$	2.41460	+	2.41460i	0.143029	+	0.143029i
$286$	30.8438	+	40.4569i	1.82383	+	2.39226i
$287$	−0.263382			−0.0155469
$288$	−14.9050	+	1.72649i	−0.878283	+	0.101734i
$289$	11.4334			0.672555
$290$	2.37303	+	3.11263i	0.139349	+	0.182780i
$291$	7.84057	+	7.84057i	0.459622	+	0.459622i
$292$	10.5738	+	2.90400i	0.618787	+	0.169944i
$293$	17.1121	−	17.1121i	0.999698	−	0.999698i	−0.000302098	−	1.00000i	$-0.500096\pi$
$293$	17.1121	−	17.1121i	0.999698	−	0.999698i	1.00000		0.000302098i	$9.61608e-5\pi$
$294$	0.111396	−	0.826233i	0.00649674	−	0.0481869i
$295$		−	8.16360i		−	0.475303i
$296$	6.93338	−	16.3058i	0.402995	−	0.947758i
$297$		−	18.1770i		−	1.05473i
$298$	0.783227	+	0.105598i	0.0453711	+	0.00611711i
$299$	12.1467	−	12.1467i	0.702461	−	0.702461i
$300$	−1.42203	−	2.49887i	−0.0821010	−	0.144272i
$301$	−1.25233	−	1.25233i	−0.0721833	−	0.0721833i
$302$	4.17874	−	3.18582i	0.240459	−	0.183323i
$303$	−2.40544			−0.138189
$304$	3.57234	+	14.0293i	0.204888	+	0.804636i
$305$	−10.1037			−0.578537
$306$	−15.9067	+	12.1271i	−0.909328	+	0.693261i
$307$	−9.59837	−	9.59837i	−0.547808	−	0.547808i	0.377998	−	0.925806i	$-0.376612\pi$
$307$	−9.59837	−	9.59837i	−0.547808	−	0.547808i	−0.925806	+	0.377998i	$0.876612\pi$
$308$	9.48193	−	5.39588i	0.540283	−	0.307459i
$309$	3.22662	−	3.22662i	0.183556	−	0.183556i
$310$	1.87008	+	0.252131i	0.106213	+	0.0143201i
$311$		−	19.1866i		−	1.08797i	−0.839094	−	0.543987i	$-0.816914\pi$
$311$		−	19.1866i		−	1.08797i	0.839094	−	0.543987i	$-0.183086\pi$
$312$	−4.11284	−	10.1979i	−0.232844	−	0.577341i
$313$		−	5.03963i		−	0.284857i	−0.989805	−	0.142428i	$-0.954509\pi$
$313$		−	5.03963i		−	0.284857i	0.989805	−	0.142428i	$-0.0454911\pi$
$314$	−1.06769	+	7.91918i	−0.0602535	+	0.446905i
$315$	3.00177	−	3.00177i	0.169131	−	0.169131i
$316$	−2.76262	+	10.0591i	−0.155409	+	0.565866i
$317$	5.52596	+	5.52596i	0.310369	+	0.310369i	0.845052	−	0.534683i	$-0.179569\pi$
$317$	5.52596	+	5.52596i	0.310369	+	0.310369i	−0.534683	+	0.845052i	$0.679569\pi$
$318$	0.0340420	+	0.0446518i	0.00190898	+	0.00250395i
$319$	−9.43305			−0.528149
$320$	−0.239366	+	12.8014i	−0.0133810	+	0.715619i
$321$	−1.94627			−0.108630
$322$	−2.23344	−	2.92953i	−0.124465	−	0.163256i
$323$	13.6464	+	13.6464i	0.759306	+	0.759306i
$324$	3.17428	−	11.5580i	0.176349	−	0.642109i
$325$	−11.3712	+	11.3712i	−0.630763	+	0.630763i
$326$	−0.901013	+	6.68289i	−0.0499025	+	0.370131i
$327$		−	4.10874i		−	0.227214i
$328$	0.278636	+	0.690885i	0.0153851	+	0.0381477i
$329$			10.7559i			0.592992i
$330$	−7.21323	−	0.972515i	−0.397075	−	0.0535352i
$331$	−14.7514	+	14.7514i	−0.810813	+	0.810813i	−0.984756	−	0.173943i	$-0.944349\pi$
$331$	−14.7514	+	14.7514i	−0.810813	+	0.810813i	0.173943	+	0.984756i	$0.444349\pi$
$332$	−14.3573	+	8.17033i	−0.787961	+	0.448405i
$333$	11.7496	+	11.7496i	0.643872	+	0.643872i
$334$	13.9719	−	10.6520i	0.764506	−	0.582850i
$335$	−21.5239			−1.17598
$336$	−2.28516	+	0.581880i	−0.124666	+	0.0317442i
$337$	16.7111			0.910311			0.455156	−	0.890412i	$-0.349584\pi$
$337$	16.7111			0.910311			0.455156	+	0.890412i	$0.349584\pi$
$338$	−34.2897	+	26.1421i	−1.86511	+	1.42194i
$339$	2.18590	+	2.18590i	0.118722	+	0.118722i
$340$	8.44181	+	14.8344i	0.457821	+	0.804507i
$341$	−3.21576	+	3.21576i	−0.174143	+	0.174143i
$342$	−13.4546	−	1.81400i	−0.727542	−	0.0980900i
$343$			1.00000i			0.0539949i
$344$	−1.96017	+	4.60990i	−0.105685	+	0.248549i
$345$			2.45767i			0.132316i
$346$	−2.47430	+	18.3521i	−0.133019	+	0.986616i
$347$	5.57925	−	5.57925i	0.299510	−	0.299510i	−0.541312	−	0.840822i	$-0.682072\pi$
$347$	5.57925	−	5.57925i	0.299510	−	0.299510i	0.840822	+	0.541312i	$0.182072\pi$
$348$	1.96610	+	0.539970i	0.105394	+	0.0289454i
$349$	−17.9789	−	17.9789i	−0.962388	−	0.962388i	0.0369299	−	0.999318i	$-0.488242\pi$
$349$	−17.9789	−	17.9789i	−0.962388	−	0.962388i	−0.999318	+	0.0369299i	$0.988242\pi$
$350$	2.09086	+	2.74251i	0.111761	+	0.146593i
$351$	21.9750			1.17294
$352$	−24.1852	−	19.1639i	−1.28908	−	1.02144i
$353$	−25.0318			−1.33231			−0.666155	−	0.745814i	$-0.732061\pi$
$353$	−25.0318			−1.33231			−0.666155	+	0.745814i	$0.732061\pi$
$354$	−2.57828	−	3.38185i	−0.137034	−	0.179743i
$355$	−2.32337	−	2.32337i	−0.123312	−	0.123312i
$356$	12.2012	+	3.35095i	0.646664	+	0.177600i
$357$	−2.22279	+	2.22279i	−0.117643	+	0.117643i
$358$	2.66033	−	19.7319i	0.140603	−	1.04286i
$359$			17.9910i			0.949526i	0.880114	+	0.474763i	$0.157466\pi$
$359$			17.9910i			0.949526i	−0.880114	+	0.474763i	$0.842534\pi$
$360$	−11.0497	−	4.69841i	−0.582368	−	0.247628i
$361$		−	5.90105i		−	0.310582i
$362$	−10.0714	−	1.35786i	−0.529340	−	0.0713677i
$363$	7.81836	−	7.81836i	0.410357	−	0.410357i
$364$	6.52333	+	11.4631i	0.341915	+	0.600831i
$365$	6.20470	+	6.20470i	0.324769	+	0.324769i
$366$	−4.18557	+	3.19103i	−0.218783	+	0.166798i
$367$	10.3077			0.538060			0.269030	−	0.963132i	$-0.413297\pi$
$367$	10.3077			0.538060			0.269030	+	0.963132i	$0.413297\pi$
$368$	−5.32175	+	8.95781i	−0.277415	+	0.466958i
$369$	−0.698611			−0.0363682
$370$	11.2758	−	8.59651i	0.586199	−	0.446911i
$371$	−0.0476221	−	0.0476221i	−0.00247241	−	0.00247241i
$372$	0.854329	−	0.486174i	0.0442949	−	0.0252069i
$373$	16.0555	−	16.0555i	0.831324	−	0.831324i	−0.156374	−	0.987698i	$-0.549981\pi$
$373$	16.0555	−	16.0555i	0.831324	−	0.831324i	0.987698	+	0.156374i	$0.0499805\pi$
$374$	−40.7664	−	5.49628i	−2.10798	−	0.284206i
$375$		−	7.01827i		−	0.362422i
$376$	28.2141	−	11.3789i	1.45503	−	0.586820i
$377$		−	11.4040i		−	0.587338i
$378$	0.629661	−	4.67025i	0.0323863	−	0.240212i
$379$	15.7922	−	15.7922i	0.811190	−	0.811190i	−0.173622	−	0.984812i	$-0.555547\pi$
$379$	15.7922	−	15.7922i	0.811190	−	0.811190i	0.984812	+	0.173622i	$0.0555471\pi$
$380$	−3.06806	+	11.1712i	−0.157388	+	0.573071i
$381$	−7.36951	−	7.36951i	−0.377551	−	0.377551i
$382$	17.8281	+	23.3845i	0.912163	+	1.19645i
$383$	18.3633			0.938319			0.469160	−	0.883113i	$-0.344557\pi$
$383$	18.3633			0.938319			0.469160	+	0.883113i	$0.344557\pi$
$384$	3.94386	+	5.37870i	0.201259	+	0.274481i
$385$	8.73026			0.444935
$386$	11.4420	+	15.0081i	0.582383	+	0.763893i
$387$	−3.32177	−	3.32177i	−0.168855	−	0.168855i
$388$	−9.96247	+	36.2746i	−0.505768	+	1.84157i
$389$	13.9554	−	13.9554i	0.707565	−	0.707565i	−0.258458	−	0.966023i	$-0.583214\pi$
$389$	13.9554	−	13.9554i	0.707565	−	0.707565i	0.966023	+	0.258458i	$0.0832143\pi$
$390$	1.17572	−	8.72040i	0.0595348	−	0.441574i
$391$			13.8898i			0.702438i
$392$	2.62313	−	1.05792i	0.132488	−	0.0534329i
$393$		−	1.81674i		−	0.0916426i
$394$	0.385437	+	0.0519661i	0.0194180	+	0.00261802i
$395$	−5.90263	+	5.90263i	−0.296993	+	0.296993i
$396$	25.1505	−	14.3124i	1.26386	−	0.719225i
$397$	−1.12815	−	1.12815i	−0.0566202	−	0.0566202i	0.678230	−	0.734850i	$-0.262747\pi$
$397$	−1.12815	−	1.12815i	−0.0566202	−	0.0566202i	−0.734850	+	0.678230i	$0.762747\pi$
$398$	16.1952	−	12.3470i	0.811793	−	0.618901i
$399$	−2.13362			−0.106815
$400$	4.98201	−	8.38595i	0.249101	−	0.419297i
$401$	−14.3470			−0.716454			−0.358227	−	0.933635i	$-0.616619\pi$
$401$	−14.3470			−0.716454			−0.358227	+	0.933635i	$0.616619\pi$
$402$	−8.91651	+	6.79784i	−0.444715	+	0.339046i
$403$	−3.88768	−	3.88768i	−0.193659	−	0.193659i
$404$	−4.03621	−	7.09263i	−0.200809	−	0.352872i
$405$	6.78219	−	6.78219i	0.337010	−	0.337010i
$406$	−2.42365	−	0.326766i	−0.120284	−	0.0162171i
$407$			34.1721i			1.69385i
$408$	8.18220	+	3.47914i	0.405079	+	0.172243i
$409$		−	39.2518i		−	1.94088i	−0.241350	−	0.970438i	$-0.577590\pi$
$409$		−	39.2518i		−	1.94088i	0.241350	−	0.970438i	$-0.422410\pi$
$410$	−0.0796523	+	0.590788i	−0.00393375	+	0.0291769i
$411$	−3.56264	+	3.56264i	−0.175732	+	0.175732i
$412$	14.9280	+	4.09984i	0.735451	+	0.201984i
$413$	3.60682	+	3.60682i	0.177480	+	0.177480i
$414$	−5.92412	−	7.77048i	−0.291155	−	0.381898i
$415$	−13.2192			−0.648904
$416$	23.1681	−	29.2386i	1.13591	−	1.43354i
$417$	−4.77338			−0.233754
$418$	−16.9276	−	22.2034i	−0.827956	−	1.08600i
$419$	−4.41473	−	4.41473i	−0.215673	−	0.215673i	0.590999	−	0.806672i	$-0.298734\pi$
$419$	−4.41473	−	4.41473i	−0.215673	−	0.215673i	−0.806672	+	0.590999i	$0.798734\pi$
$420$	−1.81962	−	0.499741i	−0.0887885	−	0.0243849i
$421$	−7.57494	+	7.57494i	−0.369180	+	0.369180i	−0.867178	−	0.497998i	$-0.834069\pi$
$421$	−7.57494	+	7.57494i	−0.369180	+	0.369180i	0.497998	+	0.867178i	$0.334069\pi$
$422$	−2.06396	+	15.3086i	−0.100472	+	0.745211i
$423$			28.5297i			1.38716i
$424$	−0.0745386	+	0.175299i	−0.00361992	+	0.00851327i
$425$		−	13.0031i		−	0.630743i
$426$	−1.69626	−	0.228697i	−0.0821842	−	0.0110804i
$427$	4.46399	−	4.46399i	0.216028	−	0.216028i
$428$	−3.26574	−	5.73873i	−0.157856	−	0.277392i
$429$	14.9955	+	14.9955i	0.723987	+	0.723987i
$430$	−3.18782	+	2.43036i	−0.153731	+	0.117202i
$431$	−18.5396			−0.893020			−0.446510	−	0.894779i	$-0.647333\pi$
$431$	−18.5396			−0.893020			−0.446510	+	0.894779i	$0.647333\pi$
$432$	−12.9168	+	3.28906i	−0.621460	+	0.158245i
$433$	7.21190			0.346582			0.173291	−	0.984871i	$-0.444560\pi$
$433$	7.21190			0.346582			0.173291	+	0.984871i	$0.444560\pi$
$434$	−0.937629	+	0.714837i	−0.0450076	+	0.0343133i
$435$	1.15370	+	1.15370i	0.0553159	+	0.0553159i
$436$	12.1149	−	6.89425i	0.580200	−	0.330175i
$437$	−6.66630	+	6.66630i	−0.318892	+	0.318892i
$438$	4.52997	+	0.610748i	0.216450	+	0.0291827i
$439$			15.1615i			0.723617i	0.932252	+	0.361809i	$0.117841\pi$
$439$			15.1615i			0.723617i	−0.932252	+	0.361809i	$0.882159\pi$
$440$	−9.23590	−	22.9006i	−0.440304	−	1.09174i
$441$			2.65247i			0.126308i
$442$	6.64471	−	49.2843i	0.316056	−	2.34422i
$443$	−2.11746	+	2.11746i	−0.100603	+	0.100603i	−0.755617	−	0.655014i	$-0.772663\pi$
$443$	−2.11746	+	2.11746i	−0.100603	+	0.100603i	0.655014	+	0.755617i	$0.272663\pi$
$444$	1.95609	−	7.12238i	0.0928320	−	0.338013i
$445$	7.15965	+	7.15965i	0.339400	+	0.339400i
$446$	−6.05581	−	7.94322i	−0.286751	−	0.376122i
$447$	0.329445			0.0155822
$448$	−5.55011	−	5.76162i	−0.262218	−	0.272211i
$449$	4.29509			0.202698			0.101349	−	0.994851i	$-0.467684\pi$
$449$	4.29509			0.202698			0.101349	+	0.994851i	$0.467684\pi$
$450$	5.54593	+	7.27442i	0.261438	+	0.342919i
$451$	−1.01591	−	1.01591i	−0.0478373	−	0.0478373i
$452$	−2.77747	+	10.1131i	−0.130641	+	0.475682i
$453$	1.54886	−	1.54886i	0.0727718	−	0.0727718i
$454$	3.15942	−	23.4337i	0.148279	−	1.09980i
$455$			10.5544i			0.494798i
$456$	2.25719	+	5.59676i	0.105703	+	0.262093i
$457$		−	27.7833i		−	1.29965i	−0.760085	−	0.649823i	$-0.774843\pi$
$457$		−	27.7833i		−	1.29965i	0.760085	−	0.649823i	$-0.225157\pi$
$458$	−18.5881	−	2.50612i	−0.868566	−	0.117103i
$459$	−12.5643	+	12.5643i	−0.586449	+	0.586449i
$460$	−7.24664	+	4.12385i	−0.337876	+	0.192275i
$461$	−6.50912	−	6.50912i	−0.303160	−	0.303160i	0.539089	−	0.842249i	$-0.318769\pi$
$461$	−6.50912	−	6.50912i	−0.303160	−	0.303160i	−0.842249	+	0.539089i	$0.818769\pi$
$462$	3.61660	−	2.75725i	0.168259	−	0.128279i
$463$	−39.1018			−1.81722			−0.908608	−	0.417650i	$-0.862854\pi$
$463$	−39.1018			−1.81722			−0.908608	+	0.417650i	$0.862854\pi$
$464$	1.70688	+	6.70325i	0.0792397	+	0.311191i
$465$	0.786604			0.0364779
$466$	−27.4848	+	20.9541i	−1.27321	+	0.970678i
$467$	16.4618	+	16.4618i	0.761762	+	0.761762i	0.976641	−	0.214879i	$-0.0689356\pi$
$467$	16.4618	+	16.4618i	0.761762	+	0.761762i	−0.214879	+	0.976641i	$0.568936\pi$
$468$	17.3029	+	30.4055i	0.799827	+	1.40550i
$469$	9.50964	−	9.50964i	0.439114	−	0.439114i
$470$	24.1264	+	3.25282i	1.11287	+	0.150041i
$471$			3.33101i			0.153485i
$472$	5.64543	−	13.2769i	0.259852	−	0.611117i
$473$		−	9.66094i		−	0.444210i
$474$	−0.581014	+	4.30943i	−0.0266869	+	0.197939i
$475$	6.24073	−	6.24073i	0.286344	−	0.286344i
$476$	−10.2838	−	2.82435i	−0.471358	−	0.129454i
$477$	−0.126316	−	0.126316i	−0.00578361	−	0.00578361i
$478$	−5.38167	−	7.05897i	−0.246152	−	0.322870i
$479$	−37.2565			−1.70229			−0.851145	−	0.524930i	$-0.824092\pi$
$479$	−37.2565			−1.70229			−0.851145	+	0.524930i	$0.824092\pi$
$480$	0.614125	+	5.30179i	0.0280308	+	0.241993i
$481$	−41.3121			−1.88367
$482$	−12.8719	−	16.8837i	−0.586300	−	0.769031i
$483$	−1.08584	−	1.08584i	−0.0494074	−	0.0494074i
$484$	36.1719	+	9.93424i	1.64418	+	0.451556i
$485$	−21.2859	+	21.2859i	−0.966542	+	0.966542i
$486$	2.55658	−	18.9623i	0.115969	−	0.860149i
$487$		−	38.4219i		−	1.74106i	−0.492113	−	0.870531i	$-0.663775\pi$
$487$		−	38.4219i		−	1.74106i	0.492113	−	0.870531i	$-0.336225\pi$
$488$	−16.4322	−	6.98710i	−0.743849	−	0.316291i
$489$			2.81100i			0.127118i
$490$	2.24309	+	0.302422i	0.101332	+	0.0136620i
$491$	9.52330	−	9.52330i	0.429781	−	0.429781i	−0.458773	−	0.888554i	$-0.651711\pi$
$491$	9.52330	−	9.52330i	0.429781	−	0.429781i	0.888554	+	0.458773i	$0.151711\pi$
$492$	0.153590	+	0.269896i	0.00692437	+	0.0121679i
$493$	6.52029	+	6.52029i	0.293659	+	0.293659i
$494$	26.8427	−	20.4645i	1.20771	−	0.920743i
$495$	23.1567			1.04082
$496$	2.86704	+	1.70328i	0.128734	+	0.0764797i
$497$	2.05301			0.0920901
$498$	−5.47618	+	4.17497i	−0.245393	+	0.187085i
$499$	9.78190	+	9.78190i	0.437898	+	0.437898i	0.891304	−	0.453406i	$-0.149791\pi$
$499$	9.78190	+	9.78190i	0.437898	+	0.437898i	−0.453406	+	0.891304i	$0.649791\pi$
$500$	20.6939	−	11.7763i	0.925461	−	0.526653i
$501$	5.17871	−	5.17871i	0.231368	−	0.231368i
$502$	23.3736	+	3.15132i	1.04322	+	0.140650i
$503$		−	11.0554i		−	0.492938i	−0.969151	−	0.246469i	$-0.920730\pi$
$503$		−	11.0554i		−	0.492938i	0.969151	−	0.246469i	$-0.0792703\pi$
$504$	6.95776	−	2.80609i	0.309923	−	0.124993i
$505$		−	6.53038i		−	0.290598i
$506$	2.68495	−	19.9145i	0.119361	−	0.885307i
$507$	−12.7096	+	12.7096i	−0.564452	+	0.564452i
$508$	9.36392	−	34.0953i	0.415457	−	1.51273i
$509$	−0.173240	−	0.173240i	−0.00767871	−	0.00767871i	0.703257	−	0.710936i	$-0.251728\pi$
$509$	−0.173240	−	0.173240i	−0.00767871	−	0.00767871i	−0.710936	+	0.703257i	$0.751728\pi$
$510$	4.31369	+	5.65814i	0.191014	+	0.250546i
$511$	−5.48268			−0.242540
$512$	−9.24192	+	20.6540i	−0.408439	+	0.912786i
$513$	−12.0602			−0.532472
$514$	17.4893	+	22.9402i	0.771422	+	1.01185i
$515$	8.75973	+	8.75973i	0.386000	+	0.386000i
$516$	−0.553015	+	2.01360i	−0.0243451	+	0.0886439i
$517$	−41.4874	+	41.4874i	−1.82461	+	1.82461i
$518$	−1.18374	+	8.77991i	−0.0520106	+	0.385767i
$519$			7.71937i			0.338843i
$520$	27.6856	−	11.1657i	1.21409	−	0.489648i
$521$			29.9861i			1.31371i	0.754015	+	0.656857i	$0.228115\pi$
$521$			29.9861i			1.31371i	−0.754015	+	0.656857i	$0.771885\pi$
$522$	−6.42866	−	0.866737i	−0.281375	−	0.0379360i
$523$	1.48931	−	1.48931i	0.0651228	−	0.0651228i	−0.673795	−	0.738918i	$-0.735337\pi$
$523$	1.48931	−	1.48931i	0.0651228	−	0.0651228i	0.738918	+	0.673795i	$0.235337\pi$
$524$	5.35681	−	3.04840i	0.234013	−	0.133170i
$525$	1.01652	+	1.01652i	0.0443646	+	0.0443646i
$526$	−26.2552	+	20.0166i	−1.14478	+	0.872766i
$527$	4.44558			0.193653
$528$	−11.0587	−	6.56986i	−0.481268	−	0.285917i
$529$	16.2148			0.704991
$530$	−0.121222	+	0.0924185i	−0.00526556	+	0.00401440i
$531$	9.56695	+	9.56695i	0.415170	+	0.415170i
$532$	−3.58011	−	6.29115i	−0.155217	−	0.272756i
$533$	1.22818	−	1.22818i	0.0531983	−	0.0531983i
$534$	5.22717	+	0.704747i	0.226202	+	0.0304974i
$535$		−	5.28380i		−	0.228439i
$536$	−35.0054	−	14.8846i	−1.51200	−	0.642917i
$537$		−	8.29975i		−	0.358161i
$538$	−5.89790	+	43.7452i	−0.254277	+	1.88599i
$539$	−3.85718	+	3.85718i	−0.166140	+	0.166140i
$540$	−10.2854	−	2.82477i	−0.442611	−	0.121559i
$541$	12.0837	+	12.0837i	0.519519	+	0.519519i	0.917426	−	0.397907i	$-0.130263\pi$
$541$	12.0837	+	12.0837i	0.519519	+	0.519519i	−0.397907	+	0.917426i	$0.630263\pi$
$542$	1.25519	+	1.64639i	0.0539150	+	0.0707186i
$543$	−4.23628			−0.181796
$544$	3.47080	+	29.9637i	0.148809	+	1.28468i
$545$	11.1545			0.477808
$546$	3.33337	+	4.37227i	0.142655	+	0.187116i
$547$	12.2663	+	12.2663i	0.524468	+	0.524468i	0.918918	−	0.394449i	$-0.129065\pi$
$547$	12.2663	+	12.2663i	0.524468	+	0.524468i	−0.394449	+	0.918918i	$0.629065\pi$
$548$	−16.4827	−	4.52680i	−0.704105	−	0.193375i
$549$	11.8406	−	11.8406i	0.505344	−	0.505344i
$550$	−2.51354	+	18.6432i	−0.107178	+	0.794947i
$551$			6.25872i			0.266631i
$552$	−1.69957	+	3.99703i	−0.0723385	+	0.170125i
$553$		−	5.21576i		−	0.221797i
$554$	−2.75972	−	0.372076i	−0.117249	−	0.0158080i
$555$	4.17940	−	4.17940i	0.177406	−	0.177406i
$556$	−8.00950	−	14.0747i	−0.339678	−	0.596901i
$557$	−2.32720	−	2.32720i	−0.0986065	−	0.0986065i	0.656083	−	0.754689i	$-0.272212\pi$
$557$	−2.32720	−	2.32720i	−0.0986065	−	0.0986065i	−0.754689	+	0.656083i	$0.772212\pi$
$558$	−2.48703	+	1.89608i	−0.105284	+	0.0802675i
$559$	11.6795			0.493992
$560$	−1.57971	−	6.20385i	−0.0667549	−	0.262160i
$561$	−17.1474			−0.723964
$562$	6.37385	−	4.85935i	0.268865	−	0.204979i
$563$	−12.0571	−	12.0571i	−0.508146	−	0.508146i	0.405811	−	0.913957i	$-0.366989\pi$
$563$	−12.0571	−	12.0571i	−0.508146	−	0.508146i	−0.913957	+	0.405811i	$0.866989\pi$
$564$	11.0219	−	6.27226i	0.464107	−	0.264110i
$565$	−5.93437	+	5.93437i	−0.249661	+	0.249661i
$566$	−33.0242	−	4.45245i	−1.38811	−	0.187151i
$567$			5.99297i			0.251681i
$568$	−2.17191	−	5.38531i	−0.0911315	−	0.225963i
$569$		−	7.99770i		−	0.335281i	−0.985848	−	0.167641i	$-0.946385\pi$
$569$		−	7.99770i		−	0.335281i	0.985848	−	0.167641i	$-0.0536148\pi$
$570$	−0.645253	+	4.78590i	−0.0270267	+	0.200459i
$571$	22.0516	−	22.0516i	0.922832	−	0.922832i	−0.0743968	−	0.997229i	$-0.523703\pi$
$571$	22.0516	−	22.0516i	0.922832	−	0.922832i	0.997229	+	0.0743968i	$0.0237031\pi$
$572$	−19.0537	+	69.3769i	−0.796674	+	2.90079i
$573$	8.66753	+	8.66753i	0.362091	+	0.362091i
$574$	−0.225828	−	0.296212i	−0.00942589	−	0.0123636i
$575$	6.35204			0.264899
$576$	−14.7215	−	15.2825i	−0.613395	−	0.636771i
$577$	43.4199			1.80760			0.903798	−	0.427960i	$-0.140768\pi$
$577$	43.4199			1.80760			0.903798	+	0.427960i	$0.140768\pi$
$578$	9.80324	+	12.8586i	0.407761	+	0.534847i
$579$	5.56280	+	5.56280i	0.231182	+	0.231182i
$580$	−1.46593	+	5.33765i	−0.0608695	+	0.221634i
$581$	5.84045	−	5.84045i	0.242303	−	0.242303i
$582$	−2.09524	+	15.5405i	−0.0868503	+	0.644176i
$583$		−	0.367373i		−	0.0152150i
$584$	5.80023	+	14.3818i	0.240015	+	0.595123i
$585$			27.9952i			1.15746i
$586$	33.9173	+	4.57286i	1.40111	+	0.188903i
$587$	−18.2274	+	18.2274i	−0.752326	+	0.752326i	−0.974913	−	0.222587i	$-0.928550\pi$
$587$	−18.2274	+	18.2274i	−0.752326	+	0.752326i	0.222587	+	0.974913i	$0.428550\pi$
$588$	1.02473	−	0.583146i	0.0422593	−	0.0240485i
$589$	2.13362	+	2.13362i	0.0879143	+	0.0879143i
$590$	9.18118	−	6.99962i	0.377983	−	0.288170i
$591$	0.162125			0.00666892
$592$	24.2831	−	6.18331i	0.998031	−	0.254133i
$593$	−39.7514			−1.63239			−0.816197	−	0.577773i	$-0.803922\pi$
$593$	−39.7514			−1.63239			−0.816197	+	0.577773i	$0.803922\pi$
$594$	20.4427	−	15.5853i	0.838774	−	0.639471i
$595$	−6.03452	−	6.03452i	−0.247391	−	0.247391i
$596$	0.552793	+	0.971396i	0.0226433	+	0.0397899i
$597$	6.00280	−	6.00280i	0.245678	−	0.245678i
$598$	24.0755	+	3.24596i	0.984522	+	0.132737i
$599$			37.5296i			1.53342i	0.641996	+	0.766708i	$0.278107\pi$
$599$			37.5296i			1.53342i	−0.641996	+	0.766708i	$0.721893\pi$
$600$	1.59107	−	3.74186i	0.0649552	−	0.152761i
$601$			3.99899i			0.163122i	0.996668	+	0.0815611i	$0.0259906\pi$
$601$			3.99899i			0.163122i	−0.996668	+	0.0815611i	$0.974009\pi$
$602$	0.334661	−	2.48221i	0.0136398	−	0.101167i
$603$	25.2240	−	25.2240i	1.02720	−	1.02720i
$604$	7.16585	+	1.96803i	0.291574	+	0.0800780i
$605$	21.2256	+	21.2256i	0.862942	+	0.862942i
$606$	−2.06247	−	2.70527i	−0.0837820	−	0.109894i
$607$	−24.3672			−0.989035			−0.494517	−	0.869168i	$-0.664655\pi$
$607$	−24.3672			−0.989035			−0.494517	+	0.869168i	$0.664655\pi$
$608$	−12.7151	+	16.0466i	−0.515663	+	0.650776i
$609$	−1.01945			−0.0413103
$610$	−8.66311	−	11.3631i	−0.350759	−	0.460080i
$611$	−50.1560	−	50.1560i	−2.02909	−	2.02909i
$612$	−27.2775	−	7.49148i	−1.10263	−	0.302825i
$613$	−16.7167	+	16.7167i	−0.675179	+	0.675179i	−0.958905	−	0.283726i	$-0.908429\pi$
$613$	−16.7167	+	16.7167i	−0.675179	+	0.675179i	0.283726	+	0.958905i	$0.408429\pi$
$614$	2.56497	−	19.0246i	0.103514	−	0.767771i
$615$			0.248501i			0.0100205i
$616$	14.1984	+	6.03730i	0.572072	+	0.243250i
$617$			2.64202i			0.106364i	0.998585	+	0.0531819i	$0.0169363\pi$
$617$			2.64202i			0.106364i	−0.998585	+	0.0531819i	$0.983064\pi$
$618$	6.39537	+	0.862248i	0.257259	+	0.0346847i
$619$	26.9772	−	26.9772i	1.08431	−	1.08431i	0.0882048	−	0.996102i	$-0.471887\pi$
$619$	26.9772	−	26.9772i	1.08431	−	1.08431i	0.996102	−	0.0882048i	$-0.0281130\pi$
$620$	1.31988	+	2.31936i	0.0530077	+	0.0931479i
$621$	−6.13767	−	6.13767i	−0.246296	−	0.246296i
$622$	21.5782	−	16.4510i	0.865207	−	0.659623i
$623$	−6.32651			−0.253466
$624$	7.94260	−	13.3693i	0.317959	−	0.535202i
$625$	6.86071			0.274428
$626$	5.66781	−	4.32107i	0.226531	−	0.172705i
$627$	−8.22975	−	8.22975i	−0.328665	−	0.328665i
$628$	−9.82175	+	5.58927i	−0.391931	+	0.223036i
$629$	23.6204	−	23.6204i	0.941805	−	0.941805i
$630$	5.94971	+	0.802163i	0.237042	+	0.0319589i
$631$		−	18.9710i		−	0.755223i	−0.925964	−	0.377611i	$-0.876746\pi$
$631$		−	18.9710i		−	0.755223i	0.925964	−	0.377611i	$-0.123254\pi$
$632$	−13.6816	+	5.51784i	−0.544225	+	0.219488i
$633$			6.43919i			0.255935i
$634$	−1.47670	+	10.9528i	−0.0586474	+	0.434992i
$635$	20.0070	−	20.0070i	0.793954	−	0.793954i
$636$	−0.0210293	+	0.0765705i	−0.000833867	+	0.00303622i
$637$	−4.66311	−	4.66311i	−0.184759	−	0.184759i
$638$	−8.08807	−	10.6089i	−0.320210	−	0.420009i
$639$	5.44554			0.215422
$640$	−14.6023	+	10.7069i	−0.577206	+	0.423229i
$641$	31.3762			1.23929			0.619643	−	0.784884i	$-0.287277\pi$
$641$	31.3762			1.23929			0.619643	+	0.784884i	$0.287277\pi$
$642$	−1.66877	−	2.18887i	−0.0658610	−	0.0863877i
$643$	13.5690	+	13.5690i	0.535110	+	0.535110i	0.922089	−	0.386978i	$-0.126481\pi$
$643$	13.5690	+	13.5690i	0.535110	+	0.535110i	−0.386978	+	0.922089i	$0.626481\pi$
$644$	1.37970	−	5.02367i	0.0543678	−	0.197960i
$645$	−1.18158	+	1.18158i	−0.0465245	+	0.0465245i
$646$	−3.64672	+	27.0481i	−0.143478	+	1.06419i
$647$		−	39.6587i		−	1.55915i	−0.626312	−	0.779573i	$-0.715436\pi$
$647$		−	39.6587i		−	1.55915i	0.626312	−	0.779573i	$-0.284564\pi$
$648$	15.7203	−	6.34007i	0.617553	−	0.249061i
$649$			27.8242i			1.09220i
$650$	−22.5386	−	3.03874i	−0.884035	−	0.119189i
$651$	−0.347535	+	0.347535i	−0.0136210	+	0.0136210i
$652$	−8.28845	+	4.71671i	−0.324601	+	0.184721i
$653$	2.96664	+	2.96664i	0.116094	+	0.116094i	0.762767	−	0.646673i	$-0.223840\pi$
$653$	2.96664	+	2.96664i	0.116094	+	0.116094i	−0.646673	+	0.762767i	$0.723840\pi$
$654$	4.62088	−	3.52291i	0.180691	−	0.137757i
$655$	4.93216			0.192715
$656$	−0.538094	+	0.905745i	−0.0210091	+	0.0353634i
$657$	−14.5426			−0.567362
$658$	−12.0966	+	9.22231i	−0.471575	+	0.359523i
$659$	−19.5078	−	19.5078i	−0.759915	−	0.759915i	0.216391	−	0.976307i	$-0.430571\pi$
$659$	−19.5078	−	19.5078i	−0.759915	−	0.759915i	−0.976307	+	0.216391i	$0.930571\pi$
$660$	−5.09102	−	8.94620i	−0.198168	−	0.348230i
$661$	11.9741	−	11.9741i	0.465739	−	0.465739i	−0.434792	−	0.900531i	$-0.643178\pi$
$661$	11.9741	−	11.9741i	0.465739	−	0.465739i	0.900531	+	0.434792i	$0.143178\pi$
$662$	−29.2383	−	3.94203i	−1.13638	−	0.153211i
$663$		−	20.7303i		−	0.805097i
$664$	−21.4990	−	9.14155i	−0.834323	−	0.354761i
$665$		−	5.79243i		−	0.224621i
$666$	−3.13983	+	23.2884i	−0.121666	+	0.902407i
$667$	−3.18518	+	3.18518i	−0.123331	+	0.123331i
$668$	23.9595	+	6.58023i	0.927020	+	0.254597i
$669$	−2.94418	−	2.94418i	−0.113828	−	0.113828i
$670$	−18.4550	−	24.2069i	−0.712980	−	0.935193i
$671$	34.4368			1.32942
$672$	−2.61375	−	2.07109i	−0.100828	−	0.0798940i
$673$	−30.9400			−1.19265			−0.596324	−	0.802744i	$-0.703373\pi$
$673$	−30.9400			−1.19265			−0.596324	+	0.802744i	$0.703373\pi$
$674$	14.3284	+	18.7941i	0.551909	+	0.723922i
$675$	5.74585	+	5.74585i	0.221158	+	0.221158i
$676$	−58.8012	−	16.1492i	−2.26159	−	0.621122i
$677$	−0.0123354	+	0.0123354i	−0.000474089	+	0.000474089i	−0.707344	−	0.706870i	$-0.750107\pi$
$677$	−0.0123354	+	0.0123354i	−0.000474089	+	0.000474089i	0.706870	+	0.707344i	$0.250107\pi$
$678$	−0.584138	+	4.33260i	−0.0224337	+	0.166393i
$679$		−	18.8089i		−	0.721820i
$680$	−9.44530	+	22.2133i	−0.362211	+	0.851843i
$681$		−	9.85681i		−	0.377714i
$682$	−6.37385	−	0.859347i	−0.244067	−	0.0329061i
$683$	−14.1350	+	14.1350i	−0.540860	+	0.540860i	−0.923781	−	0.382921i	$-0.874918\pi$
$683$	−14.1350	+	14.1350i	−0.540860	+	0.540860i	0.382921	+	0.923781i	$0.374918\pi$
$684$	−9.49612	−	16.6871i	−0.363093	−	0.638046i
$685$	−9.67199	−	9.67199i	−0.369548	−	0.369548i
$686$	−1.12465	+	0.857418i	−0.0429393	+	0.0327364i
$687$	−7.81864			−0.298300
$688$	−6.86520	+	1.74811i	−0.261733	+	0.0666461i
$689$	0.444134			0.0169202
$690$	−2.76401	+	2.10725i	−0.105224	+	0.0802217i
$691$	31.5355	+	31.5355i	1.19967	+	1.19967i	0.974266	+	0.225402i	$0.0723695\pi$
$691$	31.5355	+	31.5355i	1.19967	+	1.19967i	0.225402	+	0.974266i	$0.427631\pi$
$692$	−22.7612	+	12.9527i	−0.865250	+	0.492388i
$693$	−10.2310	+	10.2310i	−0.388645	+	0.388645i
$694$	11.0584	+	1.49094i	0.419773	+	0.0565954i
$695$		−	12.9590i		−	0.491561i
$696$	1.07850	+	2.67415i	0.0408803	+	0.101364i
$697$			1.40443i			0.0531966i
$698$	4.80450	−	35.6354i	0.181853	−	1.34882i
$699$	−10.1873	+	10.1873i	−0.385319	+	0.385319i
$700$	−1.29162	+	4.70296i	−0.0488187	+	0.177755i
$701$	−16.8654	−	16.8654i	−0.636998	−	0.636998i	0.312816	−	0.949814i	$-0.398728\pi$
$701$	−16.8654	−	16.8654i	−0.636998	−	0.636998i	−0.949814	+	0.312816i	$0.898728\pi$
$702$	18.8417	+	24.7141i	0.711135	+	0.932773i
$703$	22.6728			0.855120
$704$	0.815838	−	43.6313i	0.0307481	−	1.64442i
$705$	10.1482			0.382203
$706$	−21.4627	−	28.1520i	−0.807761	−	1.05951i
$707$	2.88523	+	2.88523i	0.108510	+	0.108510i
$708$	1.59273	−	5.79933i	0.0598583	−	0.217952i
$709$	21.6343	−	21.6343i	0.812493	−	0.812493i	−0.172514	−	0.985007i	$-0.555189\pi$
$709$	21.6343	−	21.6343i	0.812493	−	0.812493i	0.985007	+	0.172514i	$0.0551890\pi$
$710$	0.620874	−	4.60508i	0.0233010	−	0.172826i
$711$		−	13.8346i		−	0.518839i
$712$	6.69293	+	16.5953i	0.250828	+	0.621934i
$713$			2.17168i			0.0813300i
$714$	−4.40572	−	0.593996i	−0.164880	−	0.0222298i
$715$	−40.7102	+	40.7102i	−1.52248	+	1.52248i
$716$	24.4725	−	13.9266i	0.914580	−	0.520460i
$717$	−2.61643	−	2.61643i	−0.0977123	−	0.0977123i
$718$	−20.2335	+	15.4258i	−0.755107	+	0.575685i
$719$	40.3698			1.50554			0.752769	−	0.658284i	$-0.228717\pi$
$719$	40.3698			1.50554			0.752769	+	0.658284i	$0.228717\pi$
$720$	−4.19012	−	16.4555i	−0.156157	−	0.613260i
$721$	−7.74040			−0.288267
$722$	6.63661	−	5.05967i	0.246989	−	0.188302i
$723$	−6.25799	−	6.25799i	−0.232737	−	0.232737i
$724$	−7.10827	−	12.4910i	−0.264177	−	0.464225i
$725$	2.98184	−	2.98184i	0.110743	−	0.110743i
$726$	15.4965	+	2.08930i	0.575129	+	0.0775411i
$727$		−	3.43634i		−	0.127447i	−0.997968	−	0.0637234i	$-0.979702\pi$
$727$		−	3.43634i		−	0.127447i	0.997968	−	0.0637234i	$-0.0202976\pi$
$728$	−7.29876	+	17.1651i	−0.270510	+	0.636183i
$729$			10.0029i			0.370476i
$730$	−1.65808	+	12.2981i	−0.0613684	+	0.455174i
$731$	−6.67782	+	6.67782i	−0.246988	+	0.246988i
$732$	−7.17756	−	1.97125i	−0.265290	−	0.0728593i
$733$	−27.3393	−	27.3393i	−1.00980	−	1.00980i	−0.999951	−	0.00984960i	$-0.996865\pi$
$733$	−27.3393	−	27.3393i	−1.00980	−	1.00980i	−0.00984960	−	0.999951i	$-0.503135\pi$
$734$	8.83805	+	11.5926i	0.326218	+	0.427890i
$735$	0.943500			0.0348015
$736$	−14.6373	+	1.69549i	−0.539540	+	0.0624967i
$737$	73.3607			2.70228
$738$	−0.599002	−	0.785692i	−0.0220496	−	0.0289217i
$739$	−28.3591	−	28.3591i	−1.04321	−	1.04321i	−0.999023	−	0.0441845i	$-0.985931\pi$
$739$	−28.3591	−	28.3591i	−1.04321	−	1.04321i	−0.0441845	−	0.999023i	$-0.514069\pi$
$740$	19.3361	+	5.31047i	0.710809	+	0.195217i
$741$	9.94932	−	9.94932i	0.365497	−	0.365497i
$742$	0.0127260	−	0.0943901i	0.000467187	−	0.00346517i
$743$		−	34.1733i		−	1.25370i	−0.779141	−	0.626848i	$-0.784344\pi$
$743$		−	34.1733i		−	1.25370i	0.779141	−	0.626848i	$-0.215656\pi$
$744$	1.27929	+	0.543966i	0.0469011	+	0.0199427i
$745$			0.894391i			0.0327679i
$746$	31.8231	+	4.29052i	1.16513	+	0.157087i
$747$	15.4916	−	15.4916i	0.566808	−	0.566808i
$748$	−28.7725	−	50.5605i	−1.05203	−	1.84867i
$749$	2.33447	+	2.33447i	0.0852997	+	0.0852997i
$750$	7.89309	−	6.01760i	0.288215	−	0.219732i
$751$	8.55791			0.312282			0.156141	−	0.987735i	$-0.450095\pi$
$751$	8.55791			0.312282			0.156141	+	0.987735i	$0.450095\pi$
$752$	36.9885	+	21.9745i	1.34883	+	0.801329i
$753$	9.83155			0.358281
$754$	12.8255	−	9.77803i	0.467078	−	0.356095i
$755$	4.20490	+	4.20490i	0.153032	+	0.153032i
$756$	5.79227	−	3.29621i	0.210663	−	0.119882i
$757$	−25.0492	+	25.0492i	−0.910428	+	0.910428i	−0.996306	−	0.0858779i	$-0.972631\pi$
$757$	−25.0492	+	25.0492i	−0.910428	+	0.910428i	0.0858779	+	0.996306i	$0.472631\pi$
$758$	31.3012	+	4.22015i	1.13691	+	0.153283i
$759$		−	8.37655i		−	0.304050i
$760$	−15.1943	+	6.12792i	−0.551155	+	0.222283i
$761$			28.4224i			1.03031i	0.857097	+	0.515155i	$0.172266\pi$
$761$			28.4224i			1.03031i	−0.857097	+	0.515155i	$0.827734\pi$
$762$	1.96935	−	14.6069i	0.0713421	−	0.529151i
$763$	−4.92827	+	4.92827i	−0.178415	+	0.178415i
$764$	−11.0132	+	40.1006i	−0.398445	+	1.45079i
$765$	−16.0063	−	16.0063i	−0.578711	−	0.578711i
$766$	15.7450	+	20.6522i	0.568890	+	0.746195i
$767$	−33.6380			−1.21460
$768$	−2.66761	+	9.04725i	−0.0962589	+	0.326465i
$769$	−12.0189			−0.433413			−0.216707	−	0.976237i	$-0.569531\pi$
$769$	−12.0189			−0.433413			−0.216707	+	0.976237i	$0.569531\pi$
$770$	7.48549	+	9.81847i	0.269758	+	0.353833i
$771$	8.50286	+	8.50286i	0.306223	+	0.306223i
$772$	−7.06826	+	25.7365i	−0.254392	+	0.926276i
$773$	5.06913	−	5.06913i	0.182324	−	0.182324i	−0.610044	−	0.792368i	$-0.708848\pi$
$773$	5.06913	−	5.06913i	0.182324	−	0.182324i	0.792368	+	0.610044i	$0.208848\pi$
$774$	0.887676	−	6.58397i	0.0319069	−	0.236656i
$775$		−	2.03304i		−	0.0730290i
$776$	−49.3382	+	19.8983i	−1.77114	+	0.714306i
$777$			3.69306i			0.132488i
$778$	27.6604	+	3.72929i	0.991675	+	0.133701i
$779$	−0.674045	+	0.674045i	−0.0241502	+	0.0241502i
$780$	10.8155	−	6.15476i	0.387256	−	0.220376i
$781$	7.91882	+	7.91882i	0.283358	+	0.283358i
$782$	−15.6211	+	11.9094i	−0.558611	+	0.425878i
$783$	−5.76241			−0.205932
$784$	3.43890	+	2.04302i	0.122818	+	0.0729650i
$785$	−9.04315			−0.322764
$786$	2.04320	−	1.55771i	0.0728784	−	0.0555616i
$787$	16.9635	+	16.9635i	0.604684	+	0.604684i	0.941552	−	0.336868i	$-0.109368\pi$
$787$	16.9635	+	16.9635i	0.604684	+	0.604684i	−0.336868	+	0.941552i	$0.609368\pi$
$788$	0.272037	+	0.478038i	0.00969093	+	0.0170294i
$789$	−9.73155	+	9.73155i	−0.346453	+	0.346453i
$790$	−11.6994	−	1.57736i	−0.416246	−	0.0561199i
$791$		−	5.24381i		−	0.186448i
$792$	37.6609	+	16.0137i	1.33822	+	0.569023i
$793$			41.6322i			1.47840i
$794$	0.301475	−	2.23607i	0.0106990	−	0.0793551i
$795$	−0.0449314	+	0.0449314i	−0.00159355	+	0.00159355i
$796$	27.7722	+	7.62734i	0.984358	+	0.270344i
$797$	35.5609	+	35.5609i	1.25963	+	1.25963i	0.951268	+	0.308366i	$0.0997820\pi$
$797$	35.5609	+	35.5609i	1.25963	+	1.25963i	0.308366	+	0.951268i	$0.400218\pi$
$798$	−1.82941	−	2.39957i	−0.0647603	−	0.0849440i
$799$	57.3537			2.02903
$800$	13.7029	−	1.58725i	0.484471	−	0.0561179i
$801$	−16.7808			−0.592922
$802$	−12.3014	−	16.1353i	−0.434376	−	0.569757i
$803$	−21.1477	−	21.1477i	−0.746285	−	0.746285i
$804$	−15.2904	−	4.19934i	−0.539249	−	0.148099i
$805$	2.94788	−	2.94788i	0.103899	−	0.103899i
$806$	1.03890	−	7.70563i	0.0365938	−	0.271419i
$807$			18.4004i			0.647724i
$808$	4.51600	−	10.6207i	0.158872	−	0.373634i
$809$			11.8621i			0.417050i	0.978017	+	0.208525i	$0.0668663\pi$
$809$			11.8621i			0.417050i	−0.978017	+	0.208525i	$0.933134\pi$
$810$	13.4427	+	1.81240i	0.472330	+	0.0636814i
$811$	20.4859	−	20.4859i	0.719357	−	0.719357i	−0.249117	−	0.968473i	$-0.580140\pi$
$811$	20.4859	−	20.4859i	0.719357	−	0.719357i	0.968473	+	0.249117i	$0.0801403\pi$
$812$	−1.71059	−	3.00593i	−0.0600299	−	0.105488i
$813$	0.610240	+	0.610240i	0.0214020	+	0.0214020i
$814$	−38.4316	+	29.2998i	−1.34703	+	1.02696i
$815$	−7.63140			−0.267316
$816$	3.10276	+	12.1852i	0.108618	+	0.426567i
$817$	−6.40993			−0.224255
$818$	44.1445	−	33.6552i	1.54347	−	1.17673i
$819$	−12.3687	−	12.3687i	−0.432199	−	0.432199i
$820$	−0.732724	+	0.416972i	−0.0255878	+	0.0145613i
$821$	−29.0707	+	29.0707i	−1.01458	+	1.01458i	−0.0146829	+	0.999892i	$0.504674\pi$
$821$	−29.0707	+	29.0707i	−1.01458	+	1.01458i	−0.999892	+	0.0146829i	$0.995326\pi$
$822$	−7.06140	−	0.952045i	−0.246294	−	0.0332064i
$823$			51.3595i			1.79028i	0.445785	+	0.895140i	$0.352925\pi$
$823$			51.3595i			1.79028i	−0.445785	+	0.895140i	$0.647075\pi$
$824$	8.18870	+	20.3041i	0.285267	+	0.707326i
$825$			7.84180i			0.273016i
$826$	−0.963849	+	7.14895i	−0.0335366	+	0.248744i
$827$	−24.4414	+	24.4414i	−0.849912	+	0.849912i	−0.990122	−	0.140210i	$-0.955222\pi$
$827$	−24.4414	+	24.4414i	−0.849912	+	0.849912i	0.140210	+	0.990122i	$0.455222\pi$
$828$	3.65961	−	13.3251i	0.127180	−	0.463080i
$829$	−11.3861	−	11.3861i	−0.395455	−	0.395455i	0.481172	−	0.876626i	$-0.340211\pi$
$829$	−11.3861	−	11.3861i	−0.395455	−	0.395455i	−0.876626	+	0.481172i	$0.840211\pi$
$830$	−11.3344	−	14.8669i	−0.393422	−	0.516039i
$831$	−1.16081			−0.0402680
$832$	52.7479	+	0.986303i	1.82870	+	0.0341939i
$833$	5.33230			0.184753
$834$	−4.09279	−	5.36838i	−0.141722	−	0.185892i
$835$	14.0594	+	14.0594i	0.486544	+	0.486544i
$836$	10.4570	−	38.0752i	0.361662	−	1.31686i
$837$	−1.96443	+	1.96443i	−0.0679006	+	0.0679006i
$838$	1.17975	−	8.75028i	0.0407537	−	0.302273i
$839$			35.2906i			1.21837i	0.793029	+	0.609184i	$0.208503\pi$
$839$			35.2906i			1.21837i	−0.793029	+	0.609184i	$0.791497\pi$
$840$	−0.998145	−	2.47492i	−0.0344393	−	0.0853930i
$841$		−	26.0096i		−	0.896881i
$842$	−15.0140	−	2.02425i	−0.517418	−	0.0697603i
$843$	2.36249	−	2.36249i	0.0813683	−	0.0813683i
$844$	−18.9865	+	10.8046i	−0.653541	+	0.371911i
$845$	−34.5044	−	34.5044i	−1.18699	−	1.18699i
$846$	−32.0858	+	24.4619i	−1.10313	+	0.841016i
$847$	−18.7556			−0.644451
$848$	−0.261061	+	0.0664749i	−0.00896486	+	0.00228276i
$849$	−13.8908			−0.476732
$850$	14.6239	−	11.1491i	0.501596	−	0.382411i
$851$	11.5386	+	11.5386i	0.395538	+	0.395538i
$852$	−1.19720	−	2.10379i	−0.0410155	−	0.0720746i
$853$	−6.93449	+	6.93449i	−0.237432	+	0.237432i	−0.815786	−	0.578354i	$-0.803695\pi$
$853$	−6.93449	+	6.93449i	−0.237432	+	0.237432i	0.578354	+	0.815786i	$0.303695\pi$
$854$	8.84793	+	1.19291i	0.302770	+	0.0408206i
$855$		−	15.3642i		−	0.525445i
$856$	3.65394	−	8.59330i	0.124889	−	0.293713i
$857$			29.1791i			0.996737i	0.866965	+	0.498369i	$0.166067\pi$
$857$			29.1791i			0.996737i	−0.866965	+	0.498369i	$0.833933\pi$
$858$	−4.00723	+	29.7220i	−0.136805	+	1.01469i
$859$	−1.62614	+	1.62614i	−0.0554833	+	0.0554833i	−0.734304	−	0.678821i	$-0.762491\pi$
$859$	−1.62614	+	1.62614i	−0.0554833	+	0.0554833i	0.678821	+	0.734304i	$0.262491\pi$
$860$	−5.46660	−	1.50135i	−0.186409	−	0.0511955i
$861$	−0.109792	−	0.109792i	−0.00374169	−	0.00374169i
$862$	−15.8962	−	20.8505i	−0.541426	−	0.710171i
$863$	−33.7059			−1.14736			−0.573681	−	0.819079i	$-0.694485\pi$
$863$	−33.7059			−1.14736			−0.573681	+	0.819079i	$0.694485\pi$
$864$	−14.7741	−	11.7068i	−0.502626	−	0.398272i
$865$	−20.9568			−0.712554
$866$	6.18362	+	8.11085i	0.210128	+	0.275618i
$867$	4.76608	+	4.76608i	0.161864	+	0.161864i
$868$	−1.60788	−	0.441588i	−0.0545750	−	0.0149885i
$869$	20.1181	−	20.1181i	0.682460	−	0.682460i
$870$	−0.308304	+	2.28672i	−0.0104525	+	0.0775270i
$871$			88.6891i			3.00512i
$872$	18.1412	+	7.71378i	0.614338	+	0.261222i
$873$		−	49.8900i		−	1.68852i
$874$	−13.2130	−	1.78143i	−0.446938	−	0.0602579i
$875$	−8.41814	+	8.41814i	−0.284585	+	0.284585i
$876$	3.19720	+	5.61829i	0.108024	+	0.189824i
$877$	−25.3846	−	25.3846i	−0.857178	−	0.857178i	0.133827	−	0.991005i	$-0.457273\pi$
$877$	−25.3846	−	25.3846i	−0.857178	−	0.857178i	−0.991005	+	0.133827i	$0.957273\pi$
$878$	−17.0513	+	12.9997i	−0.575454	+	0.438719i
$879$	14.2665			0.481196
$880$	17.8361	−	30.0225i	0.601255	−	1.01206i
$881$	13.0482			0.439606			0.219803	−	0.975544i	$-0.429459\pi$
$881$	13.0482			0.439606			0.219803	+	0.975544i	$0.429459\pi$
$882$	−2.98309	+	2.27427i	−0.100446	+	0.0765787i
$883$	−24.2895	−	24.2895i	−0.817407	−	0.817407i	0.168325	−	0.985732i	$-0.446164\pi$
$883$	−24.2895	−	24.2895i	−0.817407	−	0.817407i	−0.985732	+	0.168325i	$0.946164\pi$
$884$	61.1248	−	34.7843i	2.05585	−	1.16992i
$885$	3.40303	−	3.40303i	0.114392	−	0.114392i
$886$	−4.19694	−	0.565848i	−0.140999	−	0.0190100i
$887$		−	19.8489i		−	0.666461i	−0.942845	−	0.333230i	$-0.891861\pi$
$887$		−	19.8489i		−	0.666461i	0.942845	−	0.333230i	$-0.108139\pi$
$888$	9.68736	−	3.90695i	0.325087	−	0.131109i
$889$			17.6789i			0.592930i
$890$	−1.91327	+	14.1909i	−0.0641331	+	0.475680i
$891$	−23.1159	+	23.1159i	−0.774413	+	0.774413i
$892$	3.74096	−	13.6213i	0.125257	−	0.456076i
$893$	27.5264	+	27.5264i	0.921137	+	0.921137i
$894$	0.282473	+	0.370510i	0.00944730	+	0.0123917i
$895$	22.5325			0.753178
$896$	1.72103	−	11.1820i	0.0574956	−	0.373566i
$897$	10.1268			0.338124
$898$	3.68269	+	4.83047i	0.122893	+	0.161195i
$899$	1.01945	+	1.01945i	0.0340006	+	0.0340006i
$900$	−3.42598	+	12.4744i	−0.114199	+	0.415815i
$901$	−0.253935	+	0.253935i	−0.00845981	+	0.00845981i
$902$	0.271481	−	2.01360i	0.00903935	−	0.0670456i
$903$		−	1.04408i		−	0.0347448i
$904$	−13.7552	+	5.54751i	−0.457491	+	0.184508i
$905$		−	11.5008i		−	0.382300i
$906$	3.06994	+	0.413902i	0.101992	+	0.0137510i
$907$	−39.6217	+	39.6217i	−1.31562	+	1.31562i	−0.398408	+	0.917208i	$0.630437\pi$
$907$	−39.6217	+	39.6217i	−1.31562	+	1.31562i	−0.917208	+	0.398408i	$0.869563\pi$
$908$	29.0636	−	16.5392i	0.964510	−	0.548874i
$909$	7.65297	+	7.65297i	0.253833	+	0.253833i
$910$	−11.8700	+	9.04954i	−0.393487	+	0.299989i
$911$	11.6260			0.385188			0.192594	−	0.981279i	$-0.438310\pi$
$911$	11.6260			0.385188			0.192594	+	0.981279i	$0.438310\pi$
$912$	−4.35903	+	7.33732i	−0.144342	+	0.242963i
$913$	45.0553			1.49111
$914$	31.2464	−	23.8219i	1.03354	−	0.787958i
$915$	−4.21178	−	4.21178i	−0.139237	−	0.139237i
$916$	−13.1193	−	23.0539i	−0.433474	−	0.761722i
$917$	−2.17911	+	2.17911i	−0.0719606	+	0.0719606i
$918$	−24.9032	−	3.35754i	−0.821928	−	0.110815i
$919$		−	42.1056i		−	1.38894i	−0.719523	−	0.694468i	$-0.755640\pi$
$919$		−	42.1056i		−	1.38894i	0.719523	−	0.694468i	$-0.244360\pi$
$920$	−10.8513	−	4.61405i	−0.357756	−	0.152121i
$921$		−	8.00224i		−	0.263683i
$922$	1.73943	−	12.9015i	0.0572851	−	0.424889i
$923$	−9.57342	+	9.57342i	−0.315113	+	0.315113i
$924$	6.20188	+	1.70328i	0.204027	+	0.0560339i
$925$	−10.8020	−	10.8020i	−0.355167	−	0.355167i
$926$	−33.5266	−	43.9758i	−1.10175	−	1.44513i
$927$	−20.5311			−0.674331
$928$	−6.07530	+	7.66713i	−0.199431	+	0.251686i
$929$	30.3239			0.994894			0.497447	−	0.867494i	$-0.334271\pi$
$929$	30.3239			0.994894			0.497447	+	0.867494i	$0.334271\pi$
$930$	0.674449	+	0.884653i	0.0221160	+	0.0290089i
$931$	2.55919	+	2.55919i	0.0838742	+	0.0838742i
$932$	−47.1319	−	12.9443i	−1.54386	−	0.424005i
$933$	7.99802	−	7.99802i	0.261843	−	0.261843i
$934$	−4.39909	+	32.6284i	−0.143943	+	1.06763i
$935$		−	46.5524i		−	1.52243i
$936$	−19.3597	+	45.5299i	−0.632792	+	1.48819i
$937$			17.7772i			0.580757i	0.956912	+	0.290378i	$0.0937812\pi$
$937$			17.7772i			0.580757i	−0.956912	+	0.290378i	$0.906219\pi$
$938$	18.8487	+	2.54126i	0.615433	+	0.0829751i
$939$	2.10079	−	2.10079i	0.0685567	−	0.0685567i
$940$	17.0282	+	29.9228i	0.555397	+	0.975973i
$941$	−21.1596	−	21.1596i	−0.689783	−	0.689783i	0.272401	−	0.962184i	$-0.412182\pi$
$941$	−21.1596	−	21.1596i	−0.689783	−	0.689783i	−0.962184	+	0.272401i	$0.912182\pi$
$942$	−3.74622	+	2.85607i	−0.122058	+	0.0930558i
$943$	−0.686068			−0.0223415
$944$	19.7723	−	5.03470i	0.643533	−	0.163865i
$945$	5.33310			0.173486
$946$	10.8652	−	8.28347i	0.353257	−	0.269319i
$947$	11.8498	+	11.8498i	0.385066	+	0.385066i	0.872923	−	0.487857i	$-0.162221\pi$
$947$	11.8498	+	11.8498i	0.385066	+	0.385066i	−0.487857	+	0.872923i	$0.662221\pi$
$948$	−5.34477	+	3.04155i	−0.173590	+	0.0987849i
$949$	25.5664	−	25.5664i	0.829920	−	0.829920i
$950$	12.3695	+	1.66771i	0.401321	+	0.0541076i
$951$			4.60704i			0.149394i
$952$	−5.64113	−	13.9873i	−0.182830	−	0.453332i
$953$		−	14.1855i		−	0.459513i	−0.973248	−	0.229757i	$-0.926207\pi$
$953$		−	14.1855i		−	0.459513i	0.973248	−	0.229757i	$-0.0737930\pi$
$954$	0.0337554	−	0.250366i	0.00109287	−	0.00810591i
$955$	−23.5309	+	23.5309i	−0.761443	+	0.761443i
$956$	3.32451	−	12.1050i	0.107522	−	0.391503i
$957$	−3.93220	−	3.93220i	−0.127110	−	0.127110i
$958$	−31.9444	−	41.9004i	−1.03208	−	1.35374i
$959$	8.54650			0.275981
$960$	−5.43609	+	5.23653i	−0.175449	+	0.169008i
$961$	−30.3049			−0.977578
$962$	−35.4218	−	46.4616i	−1.14204	−	1.49798i
$963$	6.19211	+	6.19211i	0.199538	+	0.199538i
$964$	7.95158	−	28.9528i	0.256103	−	0.932506i
$965$	−15.1021	+	15.1021i	−0.486154	+	0.486154i
$966$	0.290169	−	2.15221i	0.00933603	−	0.0692461i
$967$			8.54873i			0.274909i	0.990508	+	0.137454i	$0.0438920\pi$
$967$			8.54873i			0.274909i	−0.990508	+	0.137454i	$0.956108\pi$
$968$	19.8419	+	49.1984i	0.637743	+	1.58130i
$969$			11.3771i			0.365485i
$970$	−42.1900	−	5.68822i	−1.35464	−	0.182638i
$971$	−25.5089	+	25.5089i	−0.818619	+	0.818619i	−0.985908	−	0.167289i	$-0.946499\pi$
$971$	−25.5089	+	25.5089i	−0.818619	+	0.818619i	0.167289	+	0.985908i	$0.446499\pi$
$972$	23.5180	−	13.3834i	0.754341	−	0.429273i
$973$	5.72549	+	5.72549i	0.183551	+	0.183551i
$974$	43.2111	−	32.9437i	1.38457	−	1.05558i
$975$	−9.48030			−0.303613
$976$	−6.23122	−	24.4713i	−0.199456	−	0.783306i
$977$	13.2375			0.423506			0.211753	−	0.977323i	$-0.432083\pi$
$977$	13.2375			0.423506			0.211753	+	0.977323i	$0.432083\pi$
$978$	−3.16138	+	2.41020i	−0.101090	+	0.0770697i
$979$	−24.4025	−	24.4025i	−0.779906	−	0.779906i
$980$	1.58315	+	2.78199i	0.0505717	+	0.0888673i
$981$	−13.0721	+	13.0721i	−0.417359	+	0.417359i
$982$	18.8758	+	2.54491i	0.602352	+	0.0812114i
$983$		−	19.9233i		−	0.635455i	−0.948182	−	0.317727i	$-0.897080\pi$
$983$		−	19.9233i		−	0.635455i	0.948182	−	0.317727i	$-0.102920\pi$
$984$	−0.171847	+	0.404149i	−0.00547830	+	0.0128838i
$985$			0.440142i			0.0140241i
$986$	−1.74242	+	12.9237i	−0.0554899	+	0.411573i
$987$	−4.48364	+	4.48364i	−0.142716	+	0.142716i
$988$	46.0308	+	12.6419i	1.46444	+	0.402193i
$989$	−3.26213	−	3.26213i	−0.103730	−	0.103730i
$990$	19.8550	+	26.0432i	0.631033	+	0.827706i
$991$	54.3594			1.72678			0.863392	−	0.504533i	$-0.168335\pi$
$991$	54.3594			1.72678			0.863392	+	0.504533i	$0.168335\pi$
$992$	0.542661	+	4.68484i	0.0172295	+	0.148744i
$993$	−12.2984			−0.390278
$994$	1.76029	+	2.30891i	0.0558329	+	0.0732343i
$995$	16.2966	+	16.2966i	0.516638	+	0.516638i
$996$	−9.39075	−	2.57908i	−0.297557	−	0.0817211i
$997$	14.4032	−	14.4032i	0.456153	−	0.456153i	−0.441237	−	0.897390i	$-0.645460\pi$
$997$	14.4032	−	14.4032i	0.456153	−	0.456153i	0.897390	+	0.441237i	$0.145460\pi$
$998$	−2.61402	+	19.3884i	−0.0827452	+	0.613728i
$999$			20.8749i			0.660452i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	112.2.m.d.29.5	✓	12
4.3	odd	2		448.2.m.d.337.4		12
7.2	even	3		784.2.x.l.557.4		24
7.3	odd	6		784.2.x.m.765.1		24
7.4	even	3		784.2.x.l.765.1		24
7.5	odd	6		784.2.x.m.557.4		24
7.6	odd	2		784.2.m.h.589.5		12
8.3	odd	2		896.2.m.h.673.3		12
8.5	even	2		896.2.m.g.673.4		12
16.3	odd	4		896.2.m.h.225.3		12
16.5	even	4	inner	112.2.m.d.85.5	yes	12
16.11	odd	4		448.2.m.d.113.4		12
16.13	even	4		896.2.m.g.225.4		12
32.5	even	8		7168.2.a.bj.1.6		12
32.11	odd	8		7168.2.a.bi.1.6		12
32.21	even	8		7168.2.a.bj.1.7		12
32.27	odd	8		7168.2.a.bi.1.7		12
112.5	odd	12		784.2.x.m.165.1		24
112.37	even	12		784.2.x.l.165.1		24
112.53	even	12		784.2.x.l.373.4		24
112.69	odd	4		784.2.m.h.197.5		12
112.101	odd	12		784.2.x.m.373.4		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.m.d.29.5	✓	12	1.1	even	1	trivial
112.2.m.d.85.5	yes	12	16.5	even	4	inner
448.2.m.d.113.4		12	16.11	odd	4
448.2.m.d.337.4		12	4.3	odd	2
784.2.m.h.197.5		12	112.69	odd	4
784.2.m.h.589.5		12	7.6	odd	2
784.2.x.l.165.1		24	112.37	even	12
784.2.x.l.373.4		24	112.53	even	12
784.2.x.l.557.4		24	7.2	even	3
784.2.x.l.765.1		24	7.4	even	3
784.2.x.m.165.1		24	112.5	odd	12
784.2.x.m.373.4		24	112.101	odd	12
784.2.x.m.557.4		24	7.5	odd	6
784.2.x.m.765.1		24	7.3	odd	6
896.2.m.g.225.4		12	16.13	even	4
896.2.m.g.673.4		12	8.5	even	2
896.2.m.h.225.3		12	16.3	odd	4
896.2.m.h.673.3		12	8.3	odd	2
7168.2.a.bi.1.6		12	32.11	odd	8
7168.2.a.bi.1.7		12	32.27	odd	8
7168.2.a.bj.1.6		12	32.5	even	8
7168.2.a.bj.1.7		12	32.21	even	8

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:	\( N \)	\(=\)	\( 112 = 2^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	112.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.857418 + 1.12465i) q^{2} +(0.416854 + 0.416854i) q^{3} +(-0.529667 + 1.92859i) q^{4} +(-1.13169 + 1.13169i) q^{5} +(-0.111396 + 0.826233i) q^{6} -1.00000i q^{7} +(-2.62313 + 1.05792i) q^{8} -2.65247i q^{9} +O(q^{10})\)	\(q+(0.857418 + 1.12465i) q^{2} +(0.416854 + 0.416854i) q^{3} +(-0.529667 + 1.92859i) q^{4} +(-1.13169 + 1.13169i) q^{5} +(-0.111396 + 0.826233i) q^{6} -1.00000i q^{7} +(-2.62313 + 1.05792i) q^{8} -2.65247i q^{9} +(-2.24309 - 0.302422i) q^{10} +(3.85718 - 3.85718i) q^{11} +(-1.02473 + 0.583146i) q^{12} +(4.66311 + 4.66311i) q^{13} +(1.12465 - 0.857418i) q^{14} -0.943500 q^{15} +(-3.43890 - 2.04302i) q^{16} -5.33230 q^{17} +(2.98309 - 2.27427i) q^{18} +(-2.55919 - 2.55919i) q^{19} +(-1.58315 - 2.78199i) q^{20} +(0.416854 - 0.416854i) q^{21} +(7.64518 + 1.03075i) q^{22} -2.60484i q^{23} +(-1.53446 - 0.652465i) q^{24} +2.43855i q^{25} +(-1.24612 + 9.24260i) q^{26} +(2.35625 - 2.35625i) q^{27} +(1.92859 + 0.529667i) q^{28} +(-1.22279 - 1.22279i) q^{29} +(-0.808974 - 1.06111i) q^{30} -0.833708 q^{31} +(-0.650901 - 5.61928i) q^{32} +3.21576 q^{33} +(-4.57201 - 5.99696i) q^{34} +(1.13169 + 1.13169i) q^{35} +(5.11551 + 1.40492i) q^{36} +(-4.42967 + 4.42967i) q^{37} +(0.683893 - 5.07249i) q^{38} +3.88768i q^{39} +(1.77134 - 4.16581i) q^{40} -0.263382i q^{41} +(0.826233 + 0.111396i) q^{42} +(1.25233 - 1.25233i) q^{43} +(5.39588 + 9.48193i) q^{44} +(3.00177 + 3.00177i) q^{45} +(2.92953 - 2.23344i) q^{46} -10.7559 q^{47} +(-0.581880 - 2.28516i) q^{48} -1.00000 q^{49} +(-2.74251 + 2.09086i) q^{50} +(-2.22279 - 2.22279i) q^{51} +(-11.4631 + 6.52333i) q^{52} +(0.0476221 - 0.0476221i) q^{53} +(4.67025 + 0.629661i) q^{54} +8.73026i q^{55} +(1.05792 + 2.62313i) q^{56} -2.13362i q^{57} +(0.326766 - 2.42365i) q^{58} +(-3.60682 + 3.60682i) q^{59} +(0.499741 - 1.81962i) q^{60} +(4.46399 + 4.46399i) q^{61} +(-0.714837 - 0.937629i) q^{62} -2.65247 q^{63} +(5.76162 - 5.55011i) q^{64} -10.5544 q^{65} +(2.75725 + 3.61660i) q^{66} +(9.50964 + 9.50964i) q^{67} +(2.82435 - 10.2838i) q^{68} +(1.08584 - 1.08584i) q^{69} +(-0.302422 + 2.24309i) q^{70} +2.05301i q^{71} +(2.80609 + 6.95776i) q^{72} -5.48268i q^{73} +(-8.77991 - 1.18374i) q^{74} +(-1.01652 + 1.01652i) q^{75} +(6.29115 - 3.58011i) q^{76} +(-3.85718 - 3.85718i) q^{77} +(-4.37227 + 3.33337i) q^{78} +5.21576 q^{79} +(6.20385 - 1.57971i) q^{80} -5.99297 q^{81} +(0.296212 - 0.225828i) q^{82} +(5.84045 + 5.84045i) q^{83} +(0.583146 + 1.02473i) q^{84} +(6.03452 - 6.03452i) q^{85} +(2.48221 + 0.334661i) q^{86} -1.01945i q^{87} +(-6.03730 + 14.1984i) q^{88} -6.32651i q^{89} +(-0.802163 + 5.94971i) q^{90} +(4.66311 - 4.66311i) q^{91} +(5.02367 + 1.37970i) q^{92} +(-0.347535 - 0.347535i) q^{93} +(-9.22231 - 12.0966i) q^{94} +5.79243 q^{95} +(2.07109 - 2.61375i) q^{96} +18.8089 q^{97} +(-0.857418 - 1.12465i) q^{98} +(-10.2310 - 10.2310i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{2} + 4 q^{3} - 6 q^{4} + 4 q^{5} + 4 q^{6} - 4 q^{8}+O(q^{10}) \) 12 * q + 2 * q^2 + 4 * q^3 - 6 * q^4 + 4 * q^5 + 4 * q^6 - 4 * q^8	\( 12 q + 2 q^{2} + 4 q^{3} - 6 q^{4} + 4 q^{5} + 4 q^{6} - 4 q^{8} - 4 q^{10} + 8 q^{12} - 24 q^{15} + 10 q^{16} - 8 q^{17} - 20 q^{20} + 4 q^{21} + 14 q^{22} - 8 q^{24} - 20 q^{26} + 4 q^{27} - 4 q^{29} - 28 q^{30} - 8 q^{31} + 12 q^{32} + 8 q^{34} - 4 q^{35} - 16 q^{36} - 20 q^{37} + 16 q^{38} - 8 q^{40} - 12 q^{42} + 16 q^{43} + 14 q^{44} + 40 q^{45} - 28 q^{46} + 16 q^{47} + 16 q^{48} - 12 q^{49} + 44 q^{50} - 16 q^{51} - 16 q^{52} + 4 q^{53} + 64 q^{54} + 6 q^{56} + 14 q^{58} - 16 q^{59} + 60 q^{60} - 20 q^{61} + 8 q^{62} + 12 q^{63} - 18 q^{64} + 32 q^{65} + 12 q^{66} + 24 q^{67} - 28 q^{68} - 4 q^{69} + 20 q^{70} + 6 q^{72} - 38 q^{74} - 40 q^{75} + 48 q^{76} - 76 q^{78} + 24 q^{79} + 24 q^{80} - 44 q^{81} - 16 q^{82} - 20 q^{83} + 8 q^{84} - 8 q^{85} + 38 q^{86} - 14 q^{88} - 40 q^{90} + 32 q^{92} - 48 q^{93} - 24 q^{94} - 16 q^{96} + 48 q^{97} - 2 q^{98} + 32 q^{99}+O(q^{100}) \) 12 * q + 2 * q^2 + 4 * q^3 - 6 * q^4 + 4 * q^5 + 4 * q^6 - 4 * q^8 - 4 * q^10 + 8 * q^12 - 24 * q^15 + 10 * q^16 - 8 * q^17 - 20 * q^20 + 4 * q^21 + 14 * q^22 - 8 * q^24 - 20 * q^26 + 4 * q^27 - 4 * q^29 - 28 * q^30 - 8 * q^31 + 12 * q^32 + 8 * q^34 - 4 * q^35 - 16 * q^36 - 20 * q^37 + 16 * q^38 - 8 * q^40 - 12 * q^42 + 16 * q^43 + 14 * q^44 + 40 * q^45 - 28 * q^46 + 16 * q^47 + 16 * q^48 - 12 * q^49 + 44 * q^50 - 16 * q^51 - 16 * q^52 + 4 * q^53 + 64 * q^54 + 6 * q^56 + 14 * q^58 - 16 * q^59 + 60 * q^60 - 20 * q^61 + 8 * q^62 + 12 * q^63 - 18 * q^64 + 32 * q^65 + 12 * q^66 + 24 * q^67 - 28 * q^68 - 4 * q^69 + 20 * q^70 + 6 * q^72 - 38 * q^74 - 40 * q^75 + 48 * q^76 - 76 * q^78 + 24 * q^79 + 24 * q^80 - 44 * q^81 - 16 * q^82 - 20 * q^83 + 8 * q^84 - 8 * q^85 + 38 * q^86 - 14 * q^88 - 40 * q^90 + 32 * q^92 - 48 * q^93 - 24 * q^94 - 16 * q^96 + 48 * q^97 - 2 * q^98 + 32 * q^99

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