LMFDB - Embedded newform 770.2.l.c.573.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(573,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3, 2, 0]))

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

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

chi := DirichletCharacter("770.573");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.l (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.14848095564$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			573.4
Character	$\chi$	$=$	770.573
Dual form			770.2.l.c.727.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(-0.839228 + 0.839228i) q^{3} -1.00000i q^{4} +(0.690407 - 2.12681i) q^{5} -1.18685i q^{6} +(-2.60331 + 0.472008i) q^{7} +(0.707107 + 0.707107i) q^{8} +1.59139i q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.839228 + 0.839228i) q^{3} -1.00000i q^{4} +(0.690407 - 2.12681i) q^{5} -1.18685i q^{6} +(-2.60331 + 0.472008i) q^{7} +(0.707107 + 0.707107i) q^{8} +1.59139i q^{9} +(1.01569 + 1.99208i) q^{10} -1.00000 q^{11} +(0.839228 + 0.839228i) q^{12} +(0.602492 - 0.602492i) q^{13} +(1.50706 - 2.17458i) q^{14} +(1.20547 + 2.36429i) q^{15} -1.00000 q^{16} +(2.58133 + 2.58133i) q^{17} +(-1.12529 - 1.12529i) q^{18} +2.70548 q^{19} +(-2.12681 - 0.690407i) q^{20} +(1.78865 - 2.58089i) q^{21} +(0.707107 - 0.707107i) q^{22} +(-4.92628 - 4.92628i) q^{23} -1.18685 q^{24} +(-4.04668 - 2.93673i) q^{25} +0.852052i q^{26} +(-3.85322 - 3.85322i) q^{27} +(0.472008 + 2.60331i) q^{28} -6.57017i q^{29} +(-2.52420 - 0.819407i) q^{30} -5.10532i q^{31} +(0.707107 - 0.707107i) q^{32} +(0.839228 - 0.839228i) q^{33} -3.65055 q^{34} +(-0.793468 + 5.86263i) q^{35} +1.59139 q^{36} +(-5.69415 + 5.69415i) q^{37} +(-1.91306 + 1.91306i) q^{38} +1.01126i q^{39} +(1.99208 - 1.01569i) q^{40} -8.40875i q^{41} +(0.560201 + 3.08973i) q^{42} +(-6.41724 - 6.41724i) q^{43} +1.00000i q^{44} +(3.38460 + 1.09871i) q^{45} +6.96682 q^{46} +(-3.53754 - 3.53754i) q^{47} +(0.839228 - 0.839228i) q^{48} +(6.55442 - 2.45756i) q^{49} +(4.93802 - 0.784849i) q^{50} -4.33265 q^{51} +(-0.602492 - 0.602492i) q^{52} +(6.49916 + 6.49916i) q^{53} +5.44928 q^{54} +(-0.690407 + 2.12681i) q^{55} +(-2.17458 - 1.50706i) q^{56} +(-2.27051 + 2.27051i) q^{57} +(4.64581 + 4.64581i) q^{58} -13.5142 q^{59} +(2.36429 - 1.20547i) q^{60} -15.5309i q^{61} +(3.61001 + 3.61001i) q^{62} +(-0.751150 - 4.14289i) q^{63} +1.00000i q^{64} +(-0.865424 - 1.69735i) q^{65} +1.18685i q^{66} +(-6.87331 + 6.87331i) q^{67} +(2.58133 - 2.58133i) q^{68} +8.26855 q^{69} +(-3.58444 - 4.70657i) q^{70} +14.3845 q^{71} +(-1.12529 + 1.12529i) q^{72} +(3.43395 - 3.43395i) q^{73} -8.05275i q^{74} +(5.86067 - 0.931495i) q^{75} -2.70548i q^{76} +(2.60331 - 0.472008i) q^{77} +(-0.715066 - 0.715066i) q^{78} -1.87664i q^{79} +(-0.690407 + 2.12681i) q^{80} +1.69328 q^{81} +(5.94589 + 5.94589i) q^{82} +(3.37187 - 3.37187i) q^{83} +(-2.58089 - 1.78865i) q^{84} +(7.27218 - 3.70784i) q^{85} +9.07535 q^{86} +(5.51387 + 5.51387i) q^{87} +(-0.707107 - 0.707107i) q^{88} +5.67839 q^{89} +(-3.17018 + 1.61637i) q^{90} +(-1.28409 + 1.85285i) q^{91} +(-4.92628 + 4.92628i) q^{92} +(4.28453 + 4.28453i) q^{93} +5.00284 q^{94} +(1.86788 - 5.75405i) q^{95} +1.18685i q^{96} +(-2.87612 - 2.87612i) q^{97} +(-2.89691 + 6.37243i) q^{98} -1.59139i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q+O(q^{10}) $ 40 * q	$ 40 q - 40 q^{11} + 56 q^{15} - 40 q^{16} - 8 q^{18} - 4 q^{21} - 32 q^{25} - 24 q^{30} + 48 q^{35} - 48 q^{36} - 8 q^{37} - 40 q^{42} - 8 q^{43} + 32 q^{46} + 16 q^{50} - 8 q^{51} + 56 q^{53} + 4 q^{56} + 32 q^{57} - 8 q^{58} + 8 q^{60} - 16 q^{63} + 8 q^{65} - 24 q^{67} - 4 q^{70} - 24 q^{71} - 8 q^{72} - 16 q^{78} - 24 q^{81} + 96 q^{85} - 96 q^{86} + 64 q^{91} + 24 q^{93} - 112 q^{95} + 16 q^{98}+O(q^{100}) $ 40 * q - 40 * q^11 + 56 * q^15 - 40 * q^16 - 8 * q^18 - 4 * q^21 - 32 * q^25 - 24 * q^30 + 48 * q^35 - 48 * q^36 - 8 * q^37 - 40 * q^42 - 8 * q^43 + 32 * q^46 + 16 * q^50 - 8 * q^51 + 56 * q^53 + 4 * q^56 + 32 * q^57 - 8 * q^58 + 8 * q^60 - 16 * q^63 + 8 * q^65 - 24 * q^67 - 4 * q^70 - 24 * q^71 - 8 * q^72 - 16 * q^78 - 24 * q^81 + 96 * q^85 - 96 * q^86 + 64 * q^91 + 24 * q^93 - 112 * q^95 + 16 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	−0.839228	+	0.839228i	−0.484528	+	0.484528i	−0.906574	−	0.422046i	$-0.861312\pi$
$3$	−0.839228	+	0.839228i	−0.484528	+	0.484528i	0.422046	+	0.906574i	$0.361312\pi$
$4$		−	1.00000i		−	0.500000i
$5$	0.690407	−	2.12681i	0.308759	−	0.951140i
$5$	0.690407	−	2.12681i	0.308759	−	0.951140i
$6$		−	1.18685i		−	0.484528i
$7$	−2.60331	+	0.472008i	−0.983958	+	0.178402i
$7$	−2.60331	+	0.472008i	−0.983958	+	0.178402i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$			1.59139i			0.530465i
$10$	1.01569	+	1.99208i	0.321190	+	0.629950i
$11$	−1.00000			−0.301511
$11$	−1.00000			−0.301511
$12$	0.839228	+	0.839228i	0.242264	+	0.242264i
$13$	0.602492	−	0.602492i	0.167101	−	0.167101i	−0.618603	−	0.785704i	$-0.712301\pi$
$13$	0.602492	−	0.602492i	0.167101	−	0.167101i	0.785704	+	0.618603i	$0.212301\pi$
$14$	1.50706	−	2.17458i	0.402778	−	0.581180i
$15$	1.20547	+	2.36429i	0.311252	+	0.610457i
$16$	−1.00000			−0.250000
$17$	2.58133	+	2.58133i	0.626065	+	0.626065i	0.947075	−	0.321011i	$-0.104023\pi$
$17$	2.58133	+	2.58133i	0.626065	+	0.626065i	−0.321011	+	0.947075i	$0.604023\pi$
$18$	−1.12529	−	1.12529i	−0.265232	−	0.265232i
$19$	2.70548			0.620679			0.310339	−	0.950626i	$-0.399557\pi$
$19$	2.70548			0.620679			0.310339	+	0.950626i	$0.399557\pi$
$20$	−2.12681	−	0.690407i	−0.475570	−	0.154380i
$21$	1.78865	−	2.58089i	0.390314	−	0.563196i
$22$	0.707107	−	0.707107i	0.150756	−	0.150756i
$23$	−4.92628	−	4.92628i	−1.02720	−	1.02720i	−0.999620	−	0.0275814i	$-0.991219\pi$
$23$	−4.92628	−	4.92628i	−1.02720	−	1.02720i	−0.0275814	−	0.999620i	$-0.508781\pi$
$24$	−1.18685			−0.242264
$25$	−4.04668	−	2.93673i	−0.809335	−	0.587347i
$26$			0.852052i			0.167101i
$27$	−3.85322	−	3.85322i	−0.741553	−	0.741553i
$28$	0.472008	+	2.60331i	0.0892011	+	0.491979i
$29$		−	6.57017i		−	1.22005i	−0.792382	−	0.610025i	$-0.791159\pi$
$29$		−	6.57017i		−	1.22005i	0.792382	−	0.610025i	$-0.208841\pi$
$30$	−2.52420	−	0.819407i	−0.460854	−	0.149603i
$31$		−	5.10532i		−	0.916943i	−0.888709	−	0.458471i	$-0.848397\pi$
$31$		−	5.10532i		−	0.916943i	0.888709	−	0.458471i	$-0.151603\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	0.839228	−	0.839228i	0.146091	−	0.146091i
$34$	−3.65055			−0.626065
$35$	−0.793468	+	5.86263i	−0.134121	+	0.990965i
$36$	1.59139			0.265232
$37$	−5.69415	+	5.69415i	−0.936113	+	0.936113i	−0.998078	−	0.0619654i	$-0.980263\pi$
$37$	−5.69415	+	5.69415i	−0.936113	+	0.936113i	0.0619654	+	0.998078i	$0.480263\pi$
$38$	−1.91306	+	1.91306i	−0.310339	+	0.310339i
$39$			1.01126i			0.161931i
$40$	1.99208	−	1.01569i	0.314975	−	0.160595i
$41$		−	8.40875i		−	1.31323i	−0.754227	−	0.656613i	$-0.771988\pi$
$41$		−	8.40875i		−	1.31323i	0.754227	−	0.656613i	$-0.228012\pi$
$42$	0.560201	+	3.08973i	0.0864409	+	0.476755i
$43$	−6.41724	−	6.41724i	−0.978620	−	0.978620i	0.0211559	−	0.999776i	$-0.493265\pi$
$43$	−6.41724	−	6.41724i	−0.978620	−	0.978620i	−0.999776	+	0.0211559i	$0.993265\pi$
$44$			1.00000i			0.150756i
$45$	3.38460	+	1.09871i	0.504546	+	0.163786i
$46$	6.96682			1.02720
$47$	−3.53754	−	3.53754i	−0.516003	−	0.516003i	0.400356	−	0.916359i	$-0.368886\pi$
$47$	−3.53754	−	3.53754i	−0.516003	−	0.516003i	−0.916359	+	0.400356i	$0.868886\pi$
$48$	0.839228	−	0.839228i	0.121132	−	0.121132i
$49$	6.55442	−	2.45756i	0.936345	−	0.351080i
$50$	4.93802	−	0.784849i	0.698341	−	0.110994i
$51$	−4.33265			−0.606692
$52$	−0.602492	−	0.602492i	−0.0835506	−	0.0835506i
$53$	6.49916	+	6.49916i	0.892728	+	0.892728i	0.994779	−	0.102051i	$-0.0325406\pi$
$53$	6.49916	+	6.49916i	0.892728	+	0.892728i	−0.102051	+	0.994779i	$0.532541\pi$
$54$	5.44928			0.741553
$55$	−0.690407	+	2.12681i	−0.0930944	+	0.286780i
$56$	−2.17458	−	1.50706i	−0.290590	−	0.201389i
$57$	−2.27051	+	2.27051i	−0.300737	+	0.300737i
$58$	4.64581	+	4.64581i	0.610025	+	0.610025i
$59$	−13.5142			−1.75940			−0.879701	−	0.475527i	$-0.842258\pi$
$59$	−13.5142			−1.75940			−0.879701	+	0.475527i	$0.842258\pi$
$60$	2.36429	−	1.20547i	0.305228	−	0.155626i
$61$		−	15.5309i		−	1.98853i	−0.106929	−	0.994267i	$-0.534102\pi$
$61$		−	15.5309i		−	1.98853i	0.106929	−	0.994267i	$-0.465898\pi$
$62$	3.61001	+	3.61001i	0.458471	+	0.458471i
$63$	−0.751150	−	4.14289i	−0.0946360	−	0.521955i
$64$			1.00000i			0.125000i
$65$	−0.865424	−	1.69735i	−0.107343	−	0.210531i
$66$			1.18685i			0.146091i
$67$	−6.87331	+	6.87331i	−0.839708	+	0.839708i	−0.988820	−	0.149112i	$-0.952359\pi$
$67$	−6.87331	+	6.87331i	−0.839708	+	0.839708i	0.149112	+	0.988820i	$0.452359\pi$
$68$	2.58133	−	2.58133i	0.313032	−	0.313032i
$69$	8.26855			0.995416
$70$	−3.58444	−	4.70657i	−0.428422	−	0.562543i
$71$	14.3845			1.70713			0.853566	−	0.520985i	$-0.174435\pi$
$71$	14.3845			1.70713			0.853566	+	0.520985i	$0.174435\pi$
$72$	−1.12529	+	1.12529i	−0.132616	+	0.132616i
$73$	3.43395	−	3.43395i	0.401914	−	0.401914i	−0.476993	−	0.878907i	$-0.658273\pi$
$73$	3.43395	−	3.43395i	0.401914	−	0.401914i	0.878907	+	0.476993i	$0.158273\pi$
$74$		−	8.05275i		−	0.936113i
$75$	5.86067	−	0.931495i	0.676732	−	0.107560i
$76$		−	2.70548i		−	0.310339i
$77$	2.60331	−	0.472008i	0.296674	−	0.0537903i
$78$	−0.715066	−	0.715066i	−0.0809653	−	0.0809653i
$79$		−	1.87664i		−	0.211138i	−0.994412	−	0.105569i	$-0.966334\pi$
$79$		−	1.87664i		−	0.211138i	0.994412	−	0.105569i	$-0.0336664\pi$
$80$	−0.690407	+	2.12681i	−0.0771898	+	0.237785i
$81$	1.69328			0.188143
$82$	5.94589	+	5.94589i	0.656613	+	0.656613i
$83$	3.37187	−	3.37187i	0.370111	−	0.370111i	−0.497407	−	0.867518i	$-0.665714\pi$
$83$	3.37187	−	3.37187i	0.370111	−	0.370111i	0.867518	+	0.497407i	$0.165714\pi$
$84$	−2.58089	−	1.78865i	−0.281598	−	0.195157i
$85$	7.27218	−	3.70784i	0.788778	−	0.402172i
$86$	9.07535			0.978620
$87$	5.51387	+	5.51387i	0.591149	+	0.591149i
$88$	−0.707107	−	0.707107i	−0.0753778	−	0.0753778i
$89$	5.67839			0.601908			0.300954	−	0.953639i	$-0.402695\pi$
$89$	5.67839			0.601908			0.300954	+	0.953639i	$0.402695\pi$
$90$	−3.17018	+	1.61637i	−0.334166	+	0.170380i
$91$	−1.28409	+	1.85285i	−0.134609	+	0.194232i
$92$	−4.92628	+	4.92628i	−0.513600	+	0.513600i
$93$	4.28453	+	4.28453i	0.444285	+	0.444285i
$94$	5.00284			0.516003
$95$	1.86788	−	5.75405i	0.191640	−	0.590353i
$96$			1.18685i			0.121132i
$97$	−2.87612	−	2.87612i	−0.292026	−	0.292026i	0.545854	−	0.837880i	$-0.316205\pi$
$97$	−2.87612	−	2.87612i	−0.292026	−	0.292026i	−0.837880	+	0.545854i	$0.816205\pi$
$98$	−2.89691	+	6.37243i	−0.292632	+	0.643713i
$99$		−	1.59139i		−	0.159941i
$100$	−2.93673	+	4.04668i	−0.293673	+	0.404668i
$101$			19.0250i			1.89305i	0.322625	+	0.946527i	$0.395435\pi$
$101$			19.0250i			1.89305i	−0.322625	+	0.946527i	$0.604565\pi$
$102$	3.06364	−	3.06364i	0.303346	−	0.303346i
$103$	−1.52845	+	1.52845i	−0.150602	+	0.150602i	−0.778387	−	0.627785i	$-0.783962\pi$
$103$	−1.52845	+	1.52845i	−0.150602	+	0.150602i	0.627785	+	0.778387i	$0.283962\pi$
$104$	0.852052			0.0835506
$105$	−4.25418	−	5.58598i	−0.415165	−	0.545136i
$106$	−9.19120			−0.892728
$107$	2.89652	−	2.89652i	0.280017	−	0.280017i	−0.553099	−	0.833116i	$-0.686555\pi$
$107$	2.89652	−	2.89652i	0.280017	−	0.280017i	0.833116	+	0.553099i	$0.186555\pi$
$108$	−3.85322	+	3.85322i	−0.370777	+	0.370777i
$109$		−	3.43835i		−	0.329334i	−0.986349	−	0.164667i	$-0.947345\pi$
$109$		−	3.43835i		−	0.329334i	0.986349	−	0.164667i	$-0.0526549\pi$
$110$	−1.01569	−	1.99208i	−0.0968426	−	0.189937i
$111$		−	9.55738i		−	0.907146i
$112$	2.60331	−	0.472008i	0.245989	−	0.0446005i
$113$	−6.75021	−	6.75021i	−0.635006	−	0.635006i	0.314313	−	0.949319i	$-0.398226\pi$
$113$	−6.75021	−	6.75021i	−0.635006	−	0.635006i	−0.949319	+	0.314313i	$0.898226\pi$
$114$		−	3.21099i		−	0.300737i
$115$	−13.8784	+	7.07615i	−1.29417	+	0.659854i
$116$	−6.57017			−0.610025
$117$	0.958802	+	0.958802i	0.0886413	+	0.0886413i
$118$	9.55600	−	9.55600i	0.879701	−	0.879701i
$119$	−7.93840	−	5.50159i	−0.727712	−	0.504330i
$120$	−0.819407	+	2.52420i	−0.0748013	+	0.230427i
$121$	1.00000			0.0909091
$122$	10.9820	+	10.9820i	0.994267	+	0.994267i
$123$	7.05686	+	7.05686i	0.636296	+	0.636296i
$124$	−5.10532			−0.458471
$125$	−9.03974	+	6.57899i	−0.808539	+	0.588443i
$126$	3.46061	+	2.39832i	0.308295	+	0.213659i
$127$	−3.99971	+	3.99971i	−0.354917	+	0.354917i	−0.861935	−	0.507019i	$-0.830748\pi$
$127$	−3.99971	+	3.99971i	−0.354917	+	0.354917i	0.507019	+	0.861935i	$0.330748\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	10.7711			0.948338
$130$	1.81216	+	0.588263i	0.158937	+	0.0515940i
$131$			0.907531i			0.0792914i	0.999214	+	0.0396457i	$0.0126229\pi$
$131$			0.907531i			0.0792914i	−0.999214	+	0.0396457i	$0.987377\pi$
$132$	−0.839228	−	0.839228i	−0.0730454	−	0.0730454i
$133$	−7.04319	+	1.27701i	−0.610722	+	0.110730i
$134$		−	9.72033i		−	0.839708i
$135$	−10.8554	+	5.53480i	−0.934283	+	0.476360i
$136$			3.65055i			0.313032i
$137$	−6.13578	+	6.13578i	−0.524215	+	0.524215i	−0.918842	−	0.394626i	$-0.870874\pi$
$137$	−6.13578	+	6.13578i	−0.524215	+	0.524215i	0.394626	+	0.918842i	$0.370874\pi$
$138$	−5.84674	+	5.84674i	−0.497708	+	0.497708i
$139$	−13.4814			−1.14348			−0.571740	−	0.820435i	$-0.693731\pi$
$139$	−13.4814			−1.14348			−0.571740	+	0.820435i	$0.693731\pi$
$140$	5.86263	+	0.793468i	0.495483	+	0.0670603i
$141$	5.93760			0.500036
$142$	−10.1714	+	10.1714i	−0.853566	+	0.853566i
$143$	−0.602492	+	0.602492i	−0.0503829	+	0.0503829i
$144$		−	1.59139i		−	0.132616i
$145$	−13.9735	−	4.53609i	−1.16044	−	0.376702i
$146$			4.85635i			0.401914i
$147$	−3.43819	+	7.56310i	−0.283577	+	0.623794i
$148$	5.69415	+	5.69415i	0.468056	+	0.468056i
$149$			7.59752i			0.622413i	0.950342	+	0.311207i	$0.100733\pi$
$149$			7.59752i			0.622413i	−0.950342	+	0.311207i	$0.899267\pi$
$150$	−3.48545	+	4.80279i	−0.284586	+	0.392146i
$151$	2.04817			0.166678			0.0833388	−	0.996521i	$-0.473442\pi$
$151$	2.04817			0.166678			0.0833388	+	0.996521i	$0.473442\pi$
$152$	1.91306	+	1.91306i	0.155170	+	0.155170i
$153$	−4.10791	+	4.10791i	−0.332105	+	0.332105i
$154$	−1.50706	+	2.17458i	−0.121442	+	0.175232i
$155$	−10.8581	−	3.52475i	−0.872141	−	0.283115i
$156$	1.01126			0.0809653
$157$	−7.21485	−	7.21485i	−0.575808	−	0.575808i	0.357938	−	0.933745i	$-0.383480\pi$
$157$	−7.21485	−	7.21485i	−0.575808	−	0.575808i	−0.933745	+	0.357938i	$0.883480\pi$
$158$	1.32698	+	1.32698i	0.105569	+	0.105569i
$159$	−10.9085			−0.865104
$160$	−1.01569	−	1.99208i	−0.0802976	−	0.157487i
$161$	15.1499	+	10.4994i	1.19398	+	0.827467i
$162$	−1.19733	+	1.19733i	−0.0940713	+	0.0940713i
$163$	−2.70519	−	2.70519i	−0.211887	−	0.211887i	0.593182	−	0.805069i	$-0.297872\pi$
$163$	−2.70519	−	2.70519i	−0.211887	−	0.211887i	−0.805069	+	0.593182i	$0.797872\pi$
$164$	−8.40875			−0.656613
$165$	−1.20547	−	2.36429i	−0.0938459	−	0.184060i
$166$			4.76855i			0.370111i
$167$	5.94397	+	5.94397i	0.459958	+	0.459958i	0.898642	−	0.438684i	$-0.144555\pi$
$167$	5.94397	+	5.94397i	0.459958	+	0.459958i	−0.438684	+	0.898642i	$0.644555\pi$
$168$	3.08973	−	0.560201i	0.238378	−	0.0432205i
$169$			12.2740i			0.944154i
$170$	−2.52037	+	7.76405i	−0.193303	+	0.595475i
$171$			4.30548i			0.329248i
$172$	−6.41724	+	6.41724i	−0.489310	+	0.489310i
$173$	12.3766	−	12.3766i	0.940977	−	0.940977i	−0.0573758	−	0.998353i	$-0.518273\pi$
$173$	12.3766	−	12.3766i	0.940977	−	0.940977i	0.998353	+	0.0573758i	$0.0182733\pi$
$174$	−7.79779			−0.591149
$175$	11.9209	+	5.73516i	0.901136	+	0.433537i
$176$	1.00000			0.0753778
$177$	11.3415	−	11.3415i	0.852480	−	0.852480i
$178$	−4.01523	+	4.01523i	−0.300954	+	0.300954i
$179$			20.1567i			1.50658i	0.657687	+	0.753292i	$0.271535\pi$
$179$			20.1567i			1.50658i	−0.657687	+	0.753292i	$0.728465\pi$
$180$	1.09871	−	3.38460i	0.0818929	−	0.252273i
$181$		−	12.4841i		−	0.927934i	−0.885852	−	0.463967i	$-0.846426\pi$
$181$		−	12.4841i		−	0.927934i	0.885852	−	0.463967i	$-0.153574\pi$
$182$	−0.402175	−	2.21815i	−0.0298112	−	0.164421i
$183$	13.0340	+	13.0340i	0.963501	+	0.963501i
$184$		−	6.96682i		−	0.513600i
$185$	8.17912	+	16.0417i	0.601341	+	1.17941i
$186$	−6.05924			−0.444285
$187$	−2.58133	−	2.58133i	−0.188766	−	0.188766i
$188$	−3.53754	+	3.53754i	−0.258002	+	0.258002i
$189$	11.8499	+	8.21238i	0.861952	+	0.597362i
$190$	2.74793	+	5.38952i	0.199356	+	0.390997i
$191$	27.0812			1.95953			0.979764	−	0.200158i	$-0.0641455\pi$
$191$	27.0812			1.95953			0.979764	+	0.200158i	$0.0641455\pi$
$192$	−0.839228	−	0.839228i	−0.0605660	−	0.0605660i
$193$	−5.32712	−	5.32712i	−0.383455	−	0.383455i	0.488890	−	0.872345i	$-0.337402\pi$
$193$	−5.32712	−	5.32712i	−0.383455	−	0.383455i	−0.872345	+	0.488890i	$0.837402\pi$
$194$	4.06745			0.292026
$195$	2.15075	+	0.698178i	0.154019	+	0.0499976i
$196$	−2.45756	−	6.55442i	−0.175540	−	0.468173i
$197$	2.09900	−	2.09900i	0.149547	−	0.149547i	−0.628368	−	0.777916i	$-0.716277\pi$
$197$	2.09900	−	2.09900i	0.149547	−	0.149547i	0.777916	+	0.628368i	$0.216277\pi$
$198$	1.12529	+	1.12529i	0.0799705	+	0.0799705i
$199$	−18.3552			−1.30117			−0.650583	−	0.759435i	$-0.725475\pi$
$199$	−18.3552			−1.30117			−0.650583	+	0.759435i	$0.725475\pi$
$200$	−0.784849	−	4.93802i	−0.0554972	−	0.349171i
$201$		−	11.5365i		−	0.813725i
$202$	−13.4527	−	13.4527i	−0.946527	−	0.946527i
$203$	3.10117	+	17.1042i	0.217660	+	1.20048i
$204$			4.33265i			0.303346i
$205$	−17.8839	−	5.80546i	−1.24906	−	0.405471i
$206$		−	2.16155i		−	0.150602i
$207$	7.83966	−	7.83966i	0.544894	−	0.544894i
$208$	−0.602492	+	0.602492i	−0.0417753	+	0.0417753i
$209$	−2.70548			−0.187142
$210$	6.95804	+	0.941725i	0.480151	+	0.0649852i
$211$	−8.49845			−0.585058			−0.292529	−	0.956257i	$-0.594497\pi$
$211$	−8.49845			−0.585058			−0.292529	+	0.956257i	$0.594497\pi$
$212$	6.49916	−	6.49916i	0.446364	−	0.446364i
$213$	−12.0719	+	12.0719i	−0.827154	+	0.827154i
$214$			4.09629i			0.280017i
$215$	−18.0788	+	9.21777i	−1.23296	+	0.628647i
$216$		−	5.44928i		−	0.370777i
$217$	2.40975	+	13.2907i	0.163585	+	0.902233i
$218$	2.43128	+	2.43128i	0.164667	+	0.164667i
$219$			5.76374i			0.389477i
$220$	2.12681	+	0.690407i	0.143390	+	0.0465472i
$221$	3.11046			0.209232
$222$	6.75809	+	6.75809i	0.453573	+	0.453573i
$223$	8.37825	−	8.37825i	0.561049	−	0.561049i	−0.368556	−	0.929605i	$-0.620148\pi$
$223$	8.37825	−	8.37825i	0.561049	−	0.561049i	0.929605	+	0.368556i	$0.120148\pi$
$224$	−1.50706	+	2.17458i	−0.100694	+	0.145295i
$225$	4.67350	−	6.43986i	0.311567	−	0.429324i
$226$	9.54624			0.635006
$227$	0.767232	+	0.767232i	0.0509230	+	0.0509230i	0.732110	−	0.681187i	$-0.238536\pi$
$227$	0.767232	+	0.767232i	0.0509230	+	0.0509230i	−0.681187	+	0.732110i	$0.738536\pi$
$228$	2.27051	+	2.27051i	0.150368	+	0.150368i
$229$	−21.9177			−1.44836			−0.724181	−	0.689610i	$-0.757782\pi$
$229$	−21.9177			−1.44836			−0.724181	+	0.689610i	$0.757782\pi$
$230$	4.80994	−	14.8171i	0.317158	−	0.977012i
$231$	−1.78865	+	2.58089i	−0.117684	+	0.169810i
$232$	4.64581	−	4.64581i	0.305012	−	0.305012i
$233$	2.57170	+	2.57170i	0.168477	+	0.168477i	0.786310	−	0.617832i	$-0.211989\pi$
$233$	2.57170	+	2.57170i	0.168477	+	0.168477i	−0.617832	+	0.786310i	$0.711989\pi$
$234$	−1.35595			−0.0886413
$235$	−9.96603	+	5.08135i	−0.650112	+	0.331471i
$236$			13.5142i			0.879701i
$237$	1.57493	+	1.57493i	0.102302	+	0.102302i
$238$	9.50351	−	1.72309i	0.616021	−	0.111691i
$239$		−	19.0352i		−	1.23128i	−0.788026	−	0.615642i	$-0.788897\pi$
$239$		−	19.0352i		−	1.23128i	0.788026	−	0.615642i	$-0.211103\pi$
$240$	−1.20547	−	2.36429i	−0.0778129	−	0.152614i
$241$			6.34448i			0.408684i	0.978900	+	0.204342i	$0.0655054\pi$
$241$			6.34448i			0.408684i	−0.978900	+	0.204342i	$0.934495\pi$
$242$	−0.707107	+	0.707107i	−0.0454545	+	0.0454545i
$243$	10.1386	−	10.1386i	0.650393	−	0.650393i
$244$	−15.5309			−0.994267
$245$	−0.701566	−	15.6367i	−0.0448214	−	0.998995i
$246$	−9.97991			−0.636296
$247$	1.63003	−	1.63003i	0.103716	−	0.103716i
$248$	3.61001	−	3.61001i	0.229236	−	0.229236i
$249$			5.65954i			0.358658i
$250$	1.74001	−	11.0441i	0.110048	−	0.698491i
$251$		−	7.89047i		−	0.498042i	−0.968498	−	0.249021i	$-0.919891\pi$
$251$		−	7.89047i		−	0.498042i	0.968498	−	0.249021i	$-0.0801089\pi$
$252$	−4.14289	+	0.751150i	−0.260977	+	0.0473180i
$253$	4.92628	+	4.92628i	0.309713	+	0.309713i
$254$		−	5.65644i		−	0.354917i
$255$	−2.99129	+	9.21474i	−0.187322	+	0.577049i
$256$	1.00000			0.0625000
$257$	13.2231	+	13.2231i	0.824836	+	0.824836i	0.986797	−	0.161961i	$-0.0517820\pi$
$257$	13.2231	+	13.2231i	0.824836	+	0.824836i	−0.161961	+	0.986797i	$0.551782\pi$
$258$	−7.61629	+	7.61629i	−0.474169	+	0.474169i
$259$	12.1359	−	17.5113i	0.754091	−	1.08810i
$260$	−1.69735	+	0.865424i	−0.105265	+	0.0536713i
$261$	10.4557			0.647193
$262$	−0.641722	−	0.641722i	−0.0396457	−	0.0396457i
$263$	18.6917	+	18.6917i	1.15258	+	1.15258i	0.986034	+	0.166544i	$0.0532607\pi$
$263$	18.6917	+	18.6917i	1.15258	+	1.15258i	0.166544	+	0.986034i	$0.446739\pi$
$264$	1.18685			0.0730454
$265$	18.3096	−	9.33544i	1.12475	−	0.573471i
$266$	4.07731	−	5.88326i	0.249996	−	0.360726i
$267$	−4.76546	+	4.76546i	−0.291642	+	0.291642i
$268$	6.87331	+	6.87331i	0.419854	+	0.419854i
$269$	−11.4919			−0.700671			−0.350335	−	0.936624i	$-0.613932\pi$
$269$	−11.4919			−0.700671			−0.350335	+	0.936624i	$0.613932\pi$
$270$	3.76222	−	11.5896i	0.228961	−	0.705321i
$271$		−	18.1748i		−	1.10404i	−0.833831	−	0.552020i	$-0.813857\pi$
$271$		−	18.1748i		−	1.10404i	0.833831	−	0.552020i	$-0.186143\pi$
$272$	−2.58133	−	2.58133i	−0.156516	−	0.156516i
$273$	−0.477321	−	2.63261i	−0.0288888	−	0.159333i
$274$		−	8.67731i		−	0.524215i
$275$	4.04668	+	2.93673i	0.244024	+	0.177092i
$276$		−	8.26855i		−	0.497708i
$277$	−2.69426	+	2.69426i	−0.161883	+	0.161883i	−0.783400	−	0.621518i	$-0.786516\pi$
$277$	−2.69426	+	2.69426i	−0.161883	+	0.161883i	0.621518	+	0.783400i	$0.286516\pi$
$278$	9.53280	−	9.53280i	0.571740	−	0.571740i
$279$	8.12458			0.486406
$280$	−4.70657	+	3.58444i	−0.281271	+	0.214211i
$281$	−21.5350			−1.28467			−0.642334	−	0.766424i	$-0.722034\pi$
$281$	−21.5350			−1.28467			−0.642334	+	0.766424i	$0.722034\pi$
$282$	−4.19852	+	4.19852i	−0.250018	+	0.250018i
$283$	3.53867	−	3.53867i	0.210352	−	0.210352i	−0.594065	−	0.804417i	$-0.702478\pi$
$283$	3.53867	−	3.53867i	0.210352	−	0.210352i	0.804417	+	0.594065i	$0.202478\pi$
$284$		−	14.3845i		−	0.853566i
$285$	3.26138	+	6.39653i	0.193187	+	0.378898i
$286$		−	0.852052i		−	0.0503829i
$287$	3.96900	+	21.8906i	0.234283	+	1.29216i
$288$	1.12529	+	1.12529i	0.0663081	+	0.0663081i
$289$		−	3.67347i		−	0.216086i
$290$	13.0883	−	6.67328i	0.768570	−	0.391868i
$291$	4.82745			0.282990
$292$	−3.43395	−	3.43395i	−0.200957	−	0.200957i
$293$	16.5284	−	16.5284i	0.965597	−	0.965597i	−0.0338308	−	0.999428i	$-0.510771\pi$
$293$	16.5284	−	16.5284i	0.965597	−	0.965597i	0.999428	+	0.0338308i	$0.0107707\pi$
$294$	−2.91675	−	7.77909i	−0.170108	−	0.453686i
$295$	−9.33031	+	28.7423i	−0.543232	+	1.67344i
$296$	−8.05275			−0.468056
$297$	3.85322	+	3.85322i	0.223587	+	0.223587i
$298$	−5.37226	−	5.37226i	−0.311207	−	0.311207i
$299$	−5.93609			−0.343293
$300$	−0.931495	−	5.86067i	−0.0537799	−	0.338366i
$301$	19.7350	+	13.6771i	1.13751	+	0.788333i
$302$	−1.44827	+	1.44827i	−0.0833388	+	0.0833388i
$303$	−15.9663	−	15.9663i	−0.917238	−	0.917238i
$304$	−2.70548			−0.155170
$305$	−33.0314	−	10.7227i	−1.89137	−	0.613978i
$306$		−	5.80947i		−	0.332105i
$307$	−11.8810	−	11.8810i	−0.678083	−	0.678083i	0.281483	−	0.959566i	$-0.409174\pi$
$307$	−11.8810	−	11.8810i	−0.678083	−	0.678083i	−0.959566	+	0.281483i	$0.909174\pi$
$308$	−0.472008	−	2.60331i	−0.0268951	−	0.148337i
$309$		−	2.56543i		−	0.145942i
$310$	10.1702	−	5.18544i	0.577628	−	0.294513i
$311$			28.0760i			1.59205i	0.605266	+	0.796023i	$0.293067\pi$
$311$			28.0760i			1.59205i	−0.605266	+	0.796023i	$0.706933\pi$
$312$	−0.715066	+	0.715066i	−0.0404826	+	0.0404826i
$313$	−21.5824	+	21.5824i	−1.21991	+	1.21991i	−0.252243	+	0.967664i	$0.581168\pi$
$313$	−21.5824	+	21.5824i	−1.21991	+	1.21991i	−0.967664	+	0.252243i	$0.918832\pi$
$314$	10.2033			0.575808
$315$	−9.32975	−	1.26272i	−0.525672	−	0.0711462i
$316$	−1.87664			−0.105569
$317$	8.89647	−	8.89647i	0.499675	−	0.499675i	−0.411661	−	0.911337i	$-0.635051\pi$
$317$	8.89647	−	8.89647i	0.499675	−	0.499675i	0.911337	+	0.411661i	$0.135051\pi$
$318$	7.71351	−	7.71351i	0.432552	−	0.432552i
$319$			6.57017i			0.367859i
$320$	2.12681	+	0.690407i	0.118893	+	0.0385949i
$321$			4.86167i			0.271352i
$322$	−18.1368	+	3.28839i	−1.01072	+	0.183255i
$323$	6.98373	+	6.98373i	0.388585	+	0.388585i
$324$		−	1.69328i		−	0.0940713i
$325$	−4.20745	+	0.668732i	−0.233387	+	0.0370946i
$326$	3.82572			0.211887
$327$	2.88556	+	2.88556i	0.159572	+	0.159572i
$328$	5.94589	−	5.94589i	0.328307	−	0.328307i
$329$	10.8790	+	7.53955i	0.599781	+	0.415669i
$330$	2.52420	+	0.819407i	0.138953	+	0.0451069i
$331$	22.6812			1.24667			0.623336	−	0.781954i	$-0.285777\pi$
$331$	22.6812			1.24667			0.623336	+	0.781954i	$0.285777\pi$
$332$	−3.37187	−	3.37187i	−0.185055	−	0.185055i
$333$	−9.06164	−	9.06164i	−0.496575	−	0.496575i
$334$	−8.40604			−0.459958
$335$	9.87287	+	19.3636i	0.539413	+	1.05795i
$336$	−1.78865	+	2.58089i	−0.0975786	+	0.140799i
$337$	10.7811	−	10.7811i	0.587286	−	0.587286i	−0.349610	−	0.936895i	$-0.613686\pi$
$337$	10.7811	−	10.7811i	0.587286	−	0.587286i	0.936895	+	0.349610i	$0.113686\pi$
$338$	−8.67903	−	8.67903i	−0.472077	−	0.472077i
$339$	11.3299			0.615357
$340$	−3.70784	−	7.27218i	−0.201086	−	0.394389i
$341$			5.10532i			0.276469i
$342$	−3.04443	−	3.04443i	−0.164624	−	0.164624i
$343$	−15.9032	+	9.49153i	−0.858691	+	0.512494i
$344$		−	9.07535i		−	0.489310i
$345$	5.70866	−	17.5857i	0.307344	−	0.946780i
$346$			17.5032i			0.940977i
$347$	−4.59195	+	4.59195i	−0.246509	+	0.246509i	−0.819536	−	0.573027i	$-0.805769\pi$
$347$	−4.59195	+	4.59195i	−0.246509	+	0.246509i	0.573027	+	0.819536i	$0.305769\pi$
$348$	5.51387	−	5.51387i	0.295574	−	0.295574i
$349$	26.9050			1.44019			0.720097	−	0.693874i	$-0.244097\pi$
$349$	26.9050			1.44019			0.720097	+	0.693874i	$0.244097\pi$
$350$	−12.4847	+	4.37398i	−0.667336	+	0.233799i
$351$	−4.64307			−0.247829
$352$	−0.707107	+	0.707107i	−0.0376889	+	0.0376889i
$353$	17.6164	−	17.6164i	0.937625	−	0.937625i	−0.0605405	−	0.998166i	$-0.519282\pi$
$353$	17.6164	−	17.6164i	0.937625	−	0.937625i	0.998166	+	0.0605405i	$0.0192824\pi$
$354$			16.0393i			0.852480i
$355$	9.93119	−	30.5933i	0.527093	−	1.62372i
$356$		−	5.67839i		−	0.300954i
$357$	11.2792	−	2.04504i	0.596959	−	0.108235i
$358$	−14.2529	−	14.2529i	−0.753292	−	0.753292i
$359$			26.7161i			1.41002i	0.709197	+	0.705010i	$0.249058\pi$
$359$			26.7161i			1.41002i	−0.709197	+	0.705010i	$0.750942\pi$
$360$	1.61637	+	3.17018i	0.0851901	+	0.167083i
$361$	−11.6804			−0.614758
$362$	8.82757	+	8.82757i	0.463967	+	0.463967i
$363$	−0.839228	+	0.839228i	−0.0440480	+	0.0440480i
$364$	1.85285	+	1.28409i	0.0971159	+	0.0673046i
$365$	−4.93256	−	9.67421i	−0.258182	−	0.506371i
$366$	−18.4329			−0.963501
$367$	5.33580	+	5.33580i	0.278526	+	0.278526i	0.832521	−	0.553994i	$-0.186897\pi$
$367$	5.33580	+	5.33580i	0.278526	+	0.278526i	−0.553994	+	0.832521i	$0.686897\pi$
$368$	4.92628	+	4.92628i	0.256800	+	0.256800i
$369$	13.3816			0.696620
$370$	−17.1267	−	5.55967i	−0.890375	−	0.289034i
$371$	−19.9870	−	13.8516i	−1.03767	−	0.719142i
$372$	4.28453	−	4.28453i	0.222142	−	0.222142i
$373$	−13.7595	−	13.7595i	−0.712441	−	0.712441i	0.254605	−	0.967045i	$-0.418055\pi$
$373$	−13.7595	−	13.7595i	−0.712441	−	0.712441i	−0.967045	+	0.254605i	$0.918055\pi$
$374$	3.65055			0.188766
$375$	2.06513	−	13.1077i	0.106643	−	0.676877i
$376$		−	5.00284i		−	0.258002i
$377$	−3.95847	−	3.95847i	−0.203872	−	0.203872i
$378$	−14.1862	+	2.57210i	−0.729657	+	0.132295i
$379$			28.7305i			1.47578i	0.674919	+	0.737892i	$0.264179\pi$
$379$			28.7305i			1.47578i	−0.674919	+	0.737892i	$0.735821\pi$
$380$	−5.75405	−	1.86788i	−0.295176	−	0.0958202i
$381$		−	6.71333i		−	0.343934i
$382$	−19.1493	+	19.1493i	−0.979764	+	0.979764i
$383$	−16.5413	+	16.5413i	−0.845223	+	0.845223i	−0.989533	−	0.144309i	$-0.953904\pi$
$383$	−16.5413	+	16.5413i	−0.845223	+	0.845223i	0.144309	+	0.989533i	$0.453904\pi$
$384$	1.18685			0.0605660
$385$	0.793468	−	5.86263i	0.0404389	−	0.298787i
$386$	7.53369			0.383455
$387$	10.2124	−	10.2124i	0.519123	−	0.519123i
$388$	−2.87612	+	2.87612i	−0.146013	+	0.146013i
$389$		−	25.2618i		−	1.28082i	−0.768032	−	0.640411i	$-0.778764\pi$
$389$		−	25.2618i		−	1.28082i	0.768032	−	0.640411i	$-0.221236\pi$
$390$	−2.01450	+	1.02713i	−0.102008	+	0.0520105i
$391$		−	25.4327i		−	1.28619i
$392$	6.37243	+	2.89691i	0.321856	+	0.146316i
$393$	−0.761625	−	0.761625i	−0.0384189	−	0.0384189i
$394$			2.96843i			0.149547i
$395$	−3.99126	−	1.29564i	−0.200822	−	0.0651909i
$396$	−1.59139			−0.0799705
$397$	−1.26483	−	1.26483i	−0.0634801	−	0.0634801i	0.674654	−	0.738134i	$-0.264293\pi$
$397$	−1.26483	−	1.26483i	−0.0634801	−	0.0634801i	−0.738134	+	0.674654i	$0.764293\pi$
$398$	12.9791	−	12.9791i	0.650583	−	0.650583i
$399$	4.83914	−	6.98254i	0.242260	−	0.349564i
$400$	4.04668	+	2.93673i	0.202334	+	0.146837i
$401$	−25.8990			−1.29333			−0.646666	−	0.762773i	$-0.723837\pi$
$401$	−25.8990			−1.29333			−0.646666	+	0.762773i	$0.723837\pi$
$402$	8.15757	+	8.15757i	0.406863	+	0.406863i
$403$	−3.07592	−	3.07592i	−0.153222	−	0.153222i
$404$	19.0250			0.946527
$405$	1.16905	−	3.60130i	0.0580908	−	0.178950i
$406$	−14.2873	−	9.90162i	−0.709068	−	0.491409i
$407$	5.69415	−	5.69415i	0.282249	−	0.282249i
$408$	−3.06364	−	3.06364i	−0.151673	−	0.151673i
$409$	11.3056			0.559026			0.279513	−	0.960142i	$-0.409827\pi$
$409$	11.3056			0.559026			0.279513	+	0.960142i	$0.409827\pi$
$410$	16.7509	−	8.54072i	0.827267	−	0.421796i
$411$		−	10.2986i		−	0.507994i
$412$	1.52845	+	1.52845i	0.0753012	+	0.0753012i
$413$	35.1817	−	6.37882i	1.73118	−	0.313881i
$414$			11.0869i			0.544894i
$415$	−4.84338	−	9.49931i	−0.237752	−	0.466303i
$416$		−	0.852052i		−	0.0417753i
$417$	11.3140	−	11.3140i	0.554048	−	0.554048i
$418$	1.91306	−	1.91306i	0.0935709	−	0.0935709i
$419$	4.86907			0.237870			0.118935	−	0.992902i	$-0.462052\pi$
$419$	4.86907			0.237870			0.118935	+	0.992902i	$0.462052\pi$
$420$	−5.58598	+	4.25418i	−0.272568	+	0.207583i
$421$	−15.5536			−0.758038			−0.379019	−	0.925389i	$-0.623739\pi$
$421$	−15.5536			−0.758038			−0.379019	+	0.925389i	$0.623739\pi$
$422$	6.00932	−	6.00932i	0.292529	−	0.292529i
$423$	5.62962	−	5.62962i	0.273721	−	0.273721i
$424$			9.19120i			0.446364i
$425$	−2.86513	−	18.0265i	−0.138979	−	0.874413i
$426$		−	17.0723i		−	0.827154i
$427$	7.33073	+	40.4318i	0.354759	+	1.95663i
$428$	−2.89652	−	2.89652i	−0.140008	−	0.140008i
$429$		−	1.01126i		−	0.0488239i
$430$	6.26568	−	19.3016i	0.302158	−	0.930805i
$431$	31.2519			1.50535			0.752677	−	0.658390i	$-0.228762\pi$
$431$	31.2519			1.50535			0.752677	+	0.658390i	$0.228762\pi$
$432$	3.85322	+	3.85322i	0.185388	+	0.185388i
$433$	−8.83730	+	8.83730i	−0.424693	+	0.424693i	−0.886816	−	0.462123i	$-0.847088\pi$
$433$	−8.83730	+	8.83730i	−0.424693	+	0.424693i	0.462123	+	0.886816i	$0.347088\pi$
$434$	−11.1019	−	7.69401i	−0.532909	−	0.369324i
$435$	15.5338	−	7.92016i	0.744788	−	0.379743i
$436$	−3.43835			−0.164667
$437$	−13.3279	−	13.3279i	−0.637562	−	0.637562i
$438$	−4.07558	−	4.07558i	−0.194739	−	0.194739i
$439$	−10.3948			−0.496118			−0.248059	−	0.968745i	$-0.579793\pi$
$439$	−10.3948			−0.496118			−0.248059	+	0.968745i	$0.579793\pi$
$440$	−1.99208	+	1.01569i	−0.0949685	+	0.0484213i
$441$	3.91095	+	10.4307i	0.186236	+	0.496698i
$442$	−2.19943	+	2.19943i	−0.104616	+	0.104616i
$443$	1.50130	+	1.50130i	0.0713290	+	0.0713290i	0.741871	−	0.670542i	$-0.233939\pi$
$443$	1.50130	+	1.50130i	0.0713290	+	0.0713290i	−0.670542	+	0.741871i	$0.733939\pi$
$444$	−9.55738			−0.453573
$445$	3.92040	−	12.0769i	0.185845	−	0.572499i
$446$			11.8486i			0.561049i
$447$	−6.37605	−	6.37605i	−0.301577	−	0.301577i
$448$	−0.472008	−	2.60331i	−0.0223003	−	0.122995i
$449$		−	2.78803i		−	0.131575i	−0.997834	−	0.0657877i	$-0.979044\pi$
$449$		−	2.78803i		−	0.131575i	0.997834	−	0.0657877i	$-0.0209560\pi$
$450$	1.24900	+	7.85833i	0.0588786	+	0.370445i
$451$			8.40875i			0.395953i
$452$	−6.75021	+	6.75021i	−0.317503	+	0.317503i
$453$	−1.71888	+	1.71888i	−0.0807600	+	0.0807600i
$454$	−1.08503			−0.0509230
$455$	3.05413	+	4.01024i	0.143180	+	0.188003i
$456$	−3.21099			−0.150368
$457$	0.110937	−	0.110937i	0.00518941	−	0.00518941i	−0.704507	−	0.709697i	$-0.748832\pi$
$457$	0.110937	−	0.110937i	0.00518941	−	0.00518941i	0.709697	+	0.704507i	$0.248832\pi$
$458$	15.4982	−	15.4982i	0.724181	−	0.724181i
$459$		−	19.8929i		−	0.928521i
$460$	7.07615	+	13.8784i	0.329927	+	0.647085i
$461$			23.5061i			1.09479i	0.836875	+	0.547394i	$0.184380\pi$
$461$			23.5061i			1.09479i	−0.836875	+	0.547394i	$0.815620\pi$
$462$	−0.560201	−	3.08973i	−0.0260629	−	0.143747i
$463$	−8.95357	−	8.95357i	−0.416108	−	0.416108i	0.467752	−	0.883860i	$-0.345064\pi$
$463$	−8.95357	−	8.95357i	−0.416108	−	0.416108i	−0.883860	+	0.467752i	$0.845064\pi$
$464$			6.57017i			0.305012i
$465$	12.0705	−	6.15433i	0.559754	−	0.285400i
$466$	−3.63693			−0.168477
$467$	−25.9581	−	25.9581i	−1.20120	−	1.20120i	−0.973802	−	0.227396i	$-0.926979\pi$
$467$	−25.9581	−	25.9581i	−1.20120	−	1.20120i	−0.227396	−	0.973802i	$-0.573021\pi$
$468$	0.958802	−	0.958802i	0.0443206	−	0.0443206i
$469$	14.6491	−	21.1376i	0.676432	−	0.976043i
$470$	3.45399	−	10.6401i	0.159321	−	0.490791i
$471$	12.1098			0.557990
$472$	−9.55600	−	9.55600i	−0.439851	−	0.439851i
$473$	6.41724	+	6.41724i	0.295065	+	0.295065i
$474$	−2.22728			−0.102302
$475$	−10.9482	−	7.94526i	−0.502337	−	0.364554i
$476$	−5.50159	+	7.93840i	−0.252165	+	0.363856i
$477$	−10.3427	+	10.3427i	−0.473561	+	0.473561i
$478$	13.4599	+	13.4599i	0.615642	+	0.615642i
$479$	7.42756			0.339374			0.169687	−	0.985498i	$-0.445724\pi$
$479$	7.42756			0.339374			0.169687	+	0.985498i	$0.445724\pi$
$480$	2.52420	+	0.819407i	0.115214	+	0.0374007i
$481$			6.86136i			0.312851i
$482$	−4.48622	−	4.48622i	−0.204342	−	0.204342i
$483$	−21.5256	+	3.90282i	−0.979447	+	0.177584i
$484$		−	1.00000i		−	0.0454545i
$485$	−8.10268	+	4.13129i	−0.367924	+	0.187592i
$486$			14.3382i			0.650393i
$487$	21.4387	−	21.4387i	0.971479	−	0.971479i	−0.0281252	−	0.999604i	$-0.508954\pi$
$487$	21.4387	−	21.4387i	0.971479	−	0.971479i	0.999604	+	0.0281252i	$0.00895371\pi$
$488$	10.9820	−	10.9820i	0.497133	−	0.497133i
$489$	4.54054			0.205330
$490$	11.5529	+	10.5608i	0.521908	+	0.477087i
$491$	−16.0121			−0.722614			−0.361307	−	0.932447i	$-0.617669\pi$
$491$	−16.0121			−0.722614			−0.361307	+	0.932447i	$0.617669\pi$
$492$	7.05686	−	7.05686i	0.318148	−	0.318148i
$493$	16.9598	−	16.9598i	0.763830	−	0.763830i
$494$			2.30521i			0.103716i
$495$	−3.38460	−	1.09871i	−0.152126	−	0.0493833i
$496$			5.10532i			0.229236i
$497$	−37.4474	+	6.78962i	−1.67975	+	0.304556i
$498$	−4.00190	−	4.00190i	−0.179329	−	0.179329i
$499$			27.7010i			1.24007i	0.784576	+	0.620033i	$0.212881\pi$
$499$			27.7010i			1.24007i	−0.784576	+	0.620033i	$0.787119\pi$
$500$	6.57899	+	9.03974i	0.294221	+	0.404269i
$501$	−9.97668			−0.445725
$502$	5.57941	+	5.57941i	0.249021	+	0.249021i
$503$	6.73980	−	6.73980i	0.300513	−	0.300513i	−0.540702	−	0.841214i	$-0.681841\pi$
$503$	6.73980	−	6.73980i	0.300513	−	0.300513i	0.841214	+	0.540702i	$0.181841\pi$
$504$	2.39832	−	3.46061i	0.106830	−	0.154148i
$505$	40.4625	+	13.1350i	1.80056	+	0.584498i
$506$	−6.96682			−0.309713
$507$	−10.3007	−	10.3007i	−0.457470	−	0.457470i
$508$	3.99971	+	3.99971i	0.177458	+	0.177458i
$509$	10.3418			0.458392			0.229196	−	0.973380i	$-0.426390\pi$
$509$	10.3418			0.458392			0.229196	+	0.973380i	$0.426390\pi$
$510$	−4.40064	−	8.63096i	−0.194864	−	0.382186i
$511$	−7.31879	+	10.5605i	−0.323764	+	0.467169i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−10.4248	−	10.4248i	−0.460267	−	0.460267i
$514$	−18.7003			−0.824836
$515$	2.19547	+	4.30597i	0.0967441	+	0.189744i
$516$		−	10.7711i		−	0.474169i
$517$	3.53754	+	3.53754i	0.155581	+	0.155581i
$518$	3.80096	+	20.9638i	0.167005	+	0.921095i
$519$			20.7736i			0.911860i
$520$	0.588263	−	1.81216i	0.0257970	−	0.0794683i
$521$		−	10.5883i		−	0.463880i	−0.972730	−	0.231940i	$-0.925493\pi$
$521$		−	10.5883i		−	0.463880i	0.972730	−	0.231940i	$-0.0745073\pi$
$522$	−7.39332	+	7.39332i	−0.323597	+	0.323597i
$523$	−1.95434	+	1.95434i	−0.0854573	+	0.0854573i	−0.748543	−	0.663086i	$-0.769246\pi$
$523$	−1.95434	+	1.95434i	−0.0854573	+	0.0854573i	0.663086	+	0.748543i	$0.269246\pi$
$524$	0.907531			0.0396457
$525$	−14.8175	+	5.19125i	−0.646687	+	0.226565i
$526$	−26.4340			−1.15258
$527$	13.1785	−	13.1785i	0.574065	−	0.574065i
$528$	−0.839228	+	0.839228i	−0.0365227	+	0.0365227i
$529$			25.5365i			1.11028i
$530$	−6.34566	+	19.5480i	−0.275638	+	0.849109i
$531$		−	21.5065i		−	0.933301i
$532$	1.27701	+	7.04319i	0.0553652	+	0.305361i
$533$	−5.06621	−	5.06621i	−0.219442	−	0.219442i
$534$		−	6.73938i		−	0.291642i
$535$	−4.16058	−	8.16013i	−0.179878	−	0.352793i
$536$	−9.72033			−0.419854
$537$	−16.9161	−	16.9161i	−0.729982	−	0.729982i
$538$	8.12597	−	8.12597i	0.350335	−	0.350335i
$539$	−6.55442	+	2.45756i	−0.282319	+	0.105855i
$540$	5.53480	+	10.8554i	0.238180	+	0.467141i
$541$	28.0819			1.20734			0.603668	−	0.797236i	$-0.293705\pi$
$541$	28.0819			1.20734			0.603668	+	0.797236i	$0.293705\pi$
$542$	12.8515	+	12.8515i	0.552020	+	0.552020i
$543$	10.4770	+	10.4770i	0.449610	+	0.449610i
$544$	3.65055			0.156516
$545$	−7.31272	−	2.37386i	−0.313243	−	0.101685i
$546$	2.19905	+	1.52402i	0.0941108	+	0.0652220i
$547$	12.7129	−	12.7129i	0.543563	−	0.543563i	−0.381009	−	0.924571i	$-0.624423\pi$
$547$	12.7129	−	12.7129i	0.543563	−	0.543563i	0.924571	+	0.381009i	$0.124423\pi$
$548$	6.13578	+	6.13578i	0.262108	+	0.262108i
$549$	24.7158			1.05485
$550$	−4.93802	+	0.784849i	−0.210558	+	0.0334661i
$551$		−	17.7754i		−	0.757259i
$552$	5.84674	+	5.84674i	0.248854	+	0.248854i
$553$	0.885787	+	4.88546i	0.0376675	+	0.207751i
$554$		−	3.81026i		−	0.161883i
$555$	−20.3268	−	6.59848i	−0.862823	−	0.280090i
$556$			13.4814i			0.571740i
$557$	20.5740	−	20.5740i	0.871750	−	0.871750i	−0.120914	−	0.992663i	$-0.538582\pi$
$557$	20.5740	−	20.5740i	0.871750	−	0.871750i	0.992663	+	0.120914i	$0.0385824\pi$
$558$	−5.74494	+	5.74494i	−0.243203	+	0.243203i
$559$	−7.73267			−0.327057
$560$	0.793468	−	5.86263i	0.0335301	−	0.247741i
$561$	4.33265			0.182925
$562$	15.2275	−	15.2275i	0.642334	−	0.642334i
$563$	−15.5852	+	15.5852i	−0.656837	+	0.656837i	−0.954630	−	0.297793i	$-0.903749\pi$
$563$	−15.5852	+	15.5852i	−0.656837	+	0.656837i	0.297793	+	0.954630i	$0.403749\pi$
$564$		−	5.93760i		−	0.250018i
$565$	−19.0168	+	9.69605i	−0.800044	+	0.407916i
$566$			5.00443i			0.210352i
$567$	−4.40814	+	0.799243i	−0.185124	+	0.0335651i
$568$	10.1714	+	10.1714i	0.426783	+	0.426783i
$569$			21.1500i			0.886654i	0.896360	+	0.443327i	$0.146202\pi$
$569$			21.1500i			0.886654i	−0.896360	+	0.443327i	$0.853798\pi$
$570$	−6.82917	−	2.21689i	−0.286043	−	0.0928552i
$571$	−3.88295			−0.162496			−0.0812481	−	0.996694i	$-0.525891\pi$
$571$	−3.88295			−0.162496			−0.0812481	+	0.996694i	$0.525891\pi$
$572$	0.602492	+	0.602492i	0.0251915	+	0.0251915i
$573$	−22.7273	+	22.7273i	−0.949446	+	0.949446i
$574$	−18.2855	−	12.6725i	−0.763221	−	0.528939i
$575$	5.46790	+	34.4023i	0.228027	+	1.43467i
$576$	−1.59139			−0.0663081
$577$	−5.57092	−	5.57092i	−0.231921	−	0.231921i	0.581573	−	0.813494i	$-0.302437\pi$
$577$	−5.57092	−	5.57092i	−0.231921	−	0.231921i	−0.813494	+	0.581573i	$0.802437\pi$
$578$	2.59753	+	2.59753i	0.108043	+	0.108043i
$579$	8.94134			0.371589
$580$	−4.53609	+	13.9735i	−0.188351	+	0.580219i
$581$	−7.18647	+	10.3696i	−0.298145	+	0.430202i
$582$	−3.41352	+	3.41352i	−0.141495	+	0.141495i
$583$	−6.49916	−	6.49916i	−0.269168	−	0.269168i
$584$	4.85635			0.200957
$585$	2.70116	−	1.37723i	0.111679	−	0.0569415i
$586$			23.3746i			0.965597i
$587$	22.8657	+	22.8657i	0.943769	+	0.943769i	0.998501	−	0.0547317i	$-0.0174304\pi$
$587$	22.8657	+	22.8657i	0.943769	+	0.943769i	−0.0547317	+	0.998501i	$0.517430\pi$
$588$	7.56310	+	3.43819i	0.311897	+	0.141789i
$589$		−	13.8123i		−	0.569127i
$590$	−13.7263	−	26.9214i	−0.565103	−	1.10834i
$591$			3.52307i			0.144920i
$592$	5.69415	−	5.69415i	0.234028	−	0.234028i
$593$	−19.2900	+	19.2900i	−0.792145	+	0.792145i	−0.981843	−	0.189698i	$-0.939249\pi$
$593$	−19.2900	+	19.2900i	−0.792145	+	0.792145i	0.189698	+	0.981843i	$0.439249\pi$
$594$	−5.44928			−0.223587
$595$	−17.1816	+	13.0852i	−0.704376	+	0.536440i
$596$	7.59752			0.311207
$597$	15.4042	−	15.4042i	0.630452	−	0.630452i
$598$	4.19745	−	4.19745i	0.171647	−	0.171647i
$599$		−	3.12950i		−	0.127868i	−0.997954	−	0.0639339i	$-0.979635\pi$
$599$		−	3.12950i		−	0.127868i	0.997954	−	0.0639339i	$-0.0203647\pi$
$600$	4.80279	+	3.48545i	0.196073	+	0.142293i
$601$			26.5503i			1.08301i	0.840697	+	0.541506i	$0.182145\pi$
$601$			26.5503i			1.08301i	−0.840697	+	0.541506i	$0.817855\pi$
$602$	−23.6259	+	4.28364i	−0.962921	+	0.174588i
$603$	−10.9381	−	10.9381i	−0.445436	−	0.445436i
$604$		−	2.04817i		−	0.0833388i
$605$	0.690407	−	2.12681i	0.0280690	−	0.0864673i
$606$	22.5797			0.917238
$607$	−5.46747	−	5.46747i	−0.221918	−	0.221918i	0.587388	−	0.809306i	$-0.300156\pi$
$607$	−5.46747	−	5.46747i	−0.221918	−	0.221918i	−0.809306	+	0.587388i	$0.800156\pi$
$608$	1.91306	−	1.91306i	0.0775849	−	0.0775849i
$609$	−16.9569	−	11.7517i	−0.687128	−	0.476203i
$610$	30.9388	−	15.7747i	1.25268	−	0.638698i
$611$	−4.26268			−0.172449
$612$	4.10791	+	4.10791i	0.166053	+	0.166053i
$613$	15.9645	+	15.9645i	0.644802	+	0.644802i	0.951732	−	0.306930i	$-0.0993018\pi$
$613$	15.9645	+	15.9645i	0.644802	+	0.644802i	−0.306930	+	0.951732i	$0.599302\pi$
$614$	16.8022			0.678083
$615$	19.8807	−	10.1365i	0.801669	−	0.408744i
$616$	2.17458	+	1.50706i	0.0876162	+	0.0607210i
$617$	3.01598	−	3.01598i	0.121419	−	0.121419i	−0.643786	−	0.765205i	$-0.722637\pi$
$617$	3.01598	−	3.01598i	0.121419	−	0.121419i	0.765205	+	0.643786i	$0.222637\pi$
$618$	1.81403	+	1.81403i	0.0729711	+	0.0729711i
$619$	14.1100			0.567127			0.283564	−	0.958953i	$-0.408483\pi$
$619$	14.1100			0.567127			0.283564	+	0.958953i	$0.408483\pi$
$620$	−3.52475	+	10.8581i	−0.141557	+	0.436071i
$621$			37.9641i			1.52345i
$622$	−19.8528	−	19.8528i	−0.796023	−	0.796023i
$623$	−14.7826	+	2.68025i	−0.592252	+	0.107382i
$624$		−	1.01126i		−	0.0404826i
$625$	7.75119	+	23.7680i	0.310048	+	0.950721i
$626$		−	30.5221i		−	1.21991i
$627$	2.27051	−	2.27051i	0.0906755	−	0.0906755i
$628$	−7.21485	+	7.21485i	−0.287904	+	0.287904i
$629$	−29.3970			−1.17213
$630$	7.49001	−	5.70425i	0.298409	−	0.227263i
$631$	−17.8293			−0.709774			−0.354887	−	0.934909i	$-0.615481\pi$
$631$	−17.8293			−0.709774			−0.354887	+	0.934909i	$0.615481\pi$
$632$	1.32698	−	1.32698i	0.0527845	−	0.0527845i
$633$	7.13214	−	7.13214i	0.283477	−	0.283477i
$634$			12.5815i			0.499675i
$635$	5.74521	+	11.2681i	0.227992	+	0.447159i
$636$			10.9085i			0.432552i
$637$	2.46832	−	5.42965i	0.0977985	−	0.215130i
$638$	−4.64581	−	4.64581i	−0.183929	−	0.183929i
$639$			22.8915i			0.905573i
$640$	−1.99208	+	1.01569i	−0.0787437	+	0.0401488i
$641$	−25.8093			−1.01941			−0.509704	−	0.860350i	$-0.670245\pi$
$641$	−25.8093			−1.01941			−0.509704	+	0.860350i	$0.670245\pi$
$642$	−3.43772	−	3.43772i	−0.135676	−	0.135676i
$643$	21.5734	−	21.5734i	0.850771	−	0.850771i	−0.139457	−	0.990228i	$-0.544536\pi$
$643$	21.5734	−	21.5734i	0.850771	−	0.850771i	0.990228	+	0.139457i	$0.0445356\pi$
$644$	10.4994	−	15.1499i	0.413734	−	0.596989i
$645$	7.43641	−	22.9080i	0.292808	−	0.902003i
$646$	−9.87648			−0.388585
$647$	−21.3153	−	21.3153i	−0.837991	−	0.837991i	0.150603	−	0.988594i	$-0.451878\pi$
$647$	−21.3153	−	21.3153i	−0.837991	−	0.837991i	−0.988594	+	0.150603i	$0.951878\pi$
$648$	1.19733	+	1.19733i	0.0470357	+	0.0470357i
$649$	13.5142			0.530480
$650$	2.50225	−	3.44798i	0.0981463	−	0.135241i
$651$	−13.1763	−	9.13161i	−0.516419	−	0.357896i
$652$	−2.70519	+	2.70519i	−0.105943	+	0.105943i
$653$	−4.42972	−	4.42972i	−0.173348	−	0.173348i	0.615101	−	0.788449i	$-0.289115\pi$
$653$	−4.42972	−	4.42972i	−0.173348	−	0.173348i	−0.788449	+	0.615101i	$0.789115\pi$
$654$	−4.08079			−0.159572
$655$	1.93015	+	0.626566i	0.0754172	+	0.0244820i
$656$			8.40875i			0.328307i
$657$	5.46477	+	5.46477i	0.213201	+	0.213201i
$658$	−13.0239	+	2.36138i	−0.507725	+	0.0920561i
$659$		−	11.2248i		−	0.437256i	−0.975808	−	0.218628i	$-0.929842\pi$
$659$		−	11.2248i		−	0.437256i	0.975808	−	0.218628i	$-0.0701582\pi$
$660$	−2.36429	+	1.20547i	−0.0920299	+	0.0469230i
$661$		−	43.9884i		−	1.71095i	−0.517843	−	0.855476i	$-0.673265\pi$
$661$		−	43.9884i		−	1.71095i	0.517843	−	0.855476i	$-0.326735\pi$
$662$	−16.0380	+	16.0380i	−0.623336	+	0.623336i
$663$	−2.61039	+	2.61039i	−0.101379	+	0.101379i
$664$	4.76855			0.185055
$665$	−2.14671	+	15.8612i	−0.0832458	+	0.615071i
$666$	12.8151			0.496575
$667$	−32.3665	+	32.3665i	−1.25324	+	1.25324i
$668$	5.94397	−	5.94397i	0.229979	−	0.229979i
$669$			14.0625i			0.543688i
$670$	−20.6733	−	6.71098i	−0.798680	−	0.259268i
$671$			15.5309i			0.599565i
$672$	−0.560201	−	3.08973i	−0.0216102	−	0.119189i
$673$	25.9623	+	25.9623i	1.00077	+	1.00077i	1.00000		0.000773471i	$0.000246204\pi$
$673$	25.9623	+	25.9623i	1.00077	+	1.00077i	0.000773471		1.00000i	$0.499754\pi$
$674$			15.2468i			0.587286i
$675$	4.27686	+	26.9087i	0.164617	+	1.03571i
$676$	12.2740			0.472077
$677$	−13.7467	−	13.7467i	−0.528328	−	0.528328i	0.391745	−	0.920074i	$-0.371871\pi$
$677$	−13.7467	−	13.7467i	−0.528328	−	0.528328i	−0.920074	+	0.391745i	$0.871871\pi$
$678$	−8.01147	+	8.01147i	−0.307679	+	0.307679i
$679$	8.84499	+	6.12988i	0.339440	+	0.235243i
$680$	7.76405	+	2.52037i	0.297738	+	0.0966516i
$681$	−1.28777			−0.0493473
$682$	−3.61001	−	3.61001i	−0.138234	−	0.138234i
$683$	−16.1936	−	16.1936i	−0.619632	−	0.619632i	0.325805	−	0.945437i	$-0.394365\pi$
$683$	−16.1936	−	16.1936i	−0.619632	−	0.619632i	−0.945437	+	0.325805i	$0.894365\pi$
$684$	4.30548			0.164624
$685$	8.81349	+	17.2859i	0.336746	+	0.660459i
$686$	4.53372	−	17.9568i	0.173098	−	0.685592i
$687$	18.3939	−	18.3939i	0.701773	−	0.701773i
$688$	6.41724	+	6.41724i	0.244655	+	0.244655i
$689$	7.83138			0.298352
$690$	8.39831	+	16.4716i	0.319718	+	0.627062i
$691$			29.7561i			1.13198i	0.824414	+	0.565988i	$0.191505\pi$
$691$			29.7561i			1.13198i	−0.824414	+	0.565988i	$0.808495\pi$
$692$	−12.3766	−	12.3766i	−0.470488	−	0.470488i
$693$	0.751150	+	4.14289i	0.0285338	+	0.157375i
$694$		−	6.49399i		−	0.246509i
$695$	−9.30766	+	28.6725i	−0.353060	+	1.08761i
$696$			7.79779i			0.295574i
$697$	21.7058	−	21.7058i	0.822165	−	0.822165i
$698$	−19.0247	+	19.0247i	−0.720097	+	0.720097i
$699$	−4.31648			−0.163264
$700$	5.73516	−	11.9209i	0.216769	−	0.450568i
$701$	−25.6908			−0.970328			−0.485164	−	0.874423i	$-0.661240\pi$
$701$	−25.6908			−0.970328			−0.485164	+	0.874423i	$0.661240\pi$
$702$	3.28315	−	3.28315i	0.123914	−	0.123914i
$703$	−15.4054	+	15.4054i	−0.581026	+	0.581026i
$704$		−	1.00000i		−	0.0376889i
$705$	4.09936	−	12.6282i	0.154391	−	0.475605i
$706$			24.9133i			0.937625i
$707$	−8.97993	−	49.5278i	−0.337725	−	1.86268i
$708$	−11.3415	−	11.3415i	−0.426240	−	0.426240i
$709$			31.9539i			1.20005i	0.799979	+	0.600027i	$0.204844\pi$
$709$			31.9539i			1.20005i	−0.799979	+	0.600027i	$0.795156\pi$
$710$	14.6103	+	28.6551i	0.548314	+	1.07541i
$711$	2.98647			0.112001
$712$	4.01523	+	4.01523i	0.150477	+	0.150477i
$713$	−25.1503	+	25.1503i	−0.941885	+	0.941885i
$714$	−6.52954	+	9.42167i	−0.244362	+	0.352597i
$715$	0.865424	+	1.69735i	0.0323650	+	0.0634774i
$716$	20.1567			0.753292
$717$	15.9749	+	15.9749i	0.596592	+	0.596592i
$718$	−18.8911	−	18.8911i	−0.705010	−	0.705010i
$719$	11.2175			0.418342			0.209171	−	0.977879i	$-0.432923\pi$
$719$	11.2175			0.418342			0.209171	+	0.977879i	$0.432923\pi$
$720$	−3.38460	−	1.09871i	−0.126137	−	0.0409465i
$721$	3.25758	−	4.70046i	0.121319	−	0.175054i
$722$	8.25929	−	8.25929i	0.307379	−	0.307379i
$723$	−5.32446	−	5.32446i	−0.198019	−	0.198019i
$724$	−12.4841			−0.463967
$725$	−19.2948	+	26.5874i	−0.716592	+	0.987430i
$726$		−	1.18685i		−	0.0440480i
$727$	6.29700	+	6.29700i	0.233543	+	0.233543i	0.814170	−	0.580627i	$-0.197192\pi$
$727$	6.29700	+	6.29700i	0.233543	+	0.233543i	−0.580627	+	0.814170i	$0.697192\pi$
$728$	−2.21815	+	0.402175i	−0.0822103	+	0.0149056i
$729$			22.0971i			0.818410i
$730$	10.3285	+	3.35285i	0.382277	+	0.124095i
$731$		−	33.1300i		−	1.22536i
$732$	13.0340	−	13.0340i	0.481750	−	0.481750i
$733$	14.6461	−	14.6461i	0.540968	−	0.540968i	−0.382845	−	0.923813i	$-0.625056\pi$
$733$	14.6461	−	14.6461i	0.540968	−	0.540968i	0.923813	+	0.382845i	$0.125056\pi$
$734$	−7.54595			−0.278526
$735$	13.7116	+	12.5340i	0.505759	+	0.462324i
$736$	−6.96682			−0.256800
$737$	6.87331	−	6.87331i	0.253182	−	0.253182i
$738$	−9.46225	+	9.46225i	−0.348310	+	0.348310i
$739$		−	37.6439i		−	1.38475i	−0.721536	−	0.692377i	$-0.756563\pi$
$739$		−	37.6439i		−	1.38475i	0.721536	−	0.692377i	$-0.243437\pi$
$740$	16.0417	−	8.17912i	0.589704	−	0.300671i
$741$			2.73593i			0.100507i
$742$	23.9275	−	4.33832i	0.878406	−	0.159265i
$743$	−5.70607	−	5.70607i	−0.209336	−	0.209336i	0.594650	−	0.803985i	$-0.297291\pi$
$743$	−5.70607	−	5.70607i	−0.209336	−	0.209336i	−0.803985	+	0.594650i	$0.797291\pi$
$744$			6.05924i			0.222142i
$745$	16.1585	+	5.24538i	0.592002	+	0.192176i
$746$	19.4589			0.712441
$747$	5.36598	+	5.36598i	0.196331	+	0.196331i
$748$	−2.58133	+	2.58133i	−0.0943828	+	0.0943828i
$749$	−6.17335	+	8.90770i	−0.225569	+	0.325480i
$750$	7.80826	+	10.7288i	0.285117	+	0.391760i
$751$	4.03362			0.147189			0.0735945	−	0.997288i	$-0.476553\pi$
$751$	4.03362			0.147189			0.0735945	+	0.997288i	$0.476553\pi$
$752$	3.53754	+	3.53754i	0.129001	+	0.129001i
$753$	6.62190	+	6.62190i	0.241316	+	0.241316i
$754$	5.59813			0.203872
$755$	1.41407	−	4.35607i	0.0514633	−	0.158534i
$756$	8.21238	−	11.8499i	0.298681	−	0.430976i
$757$	−27.3083	+	27.3083i	−0.992538	+	0.992538i	−0.999972	−	0.00743433i	$-0.997634\pi$
$757$	−27.3083	+	27.3083i	−0.992538	+	0.992538i	0.00743433	+	0.999972i	$0.497634\pi$
$758$	−20.3155	−	20.3155i	−0.737892	−	0.737892i
$759$	−8.26855			−0.300129
$760$	5.38952	−	2.74793i	0.195498	−	0.0996781i
$761$		−	35.9673i		−	1.30381i	−0.758300	−	0.651906i	$-0.773970\pi$
$761$		−	35.9673i		−	1.30381i	0.758300	−	0.651906i	$-0.226030\pi$
$762$	4.74704	+	4.74704i	0.171967	+	0.171967i
$763$	1.62293	+	8.95107i	0.0587539	+	0.324051i
$764$		−	27.0812i		−	0.979764i
$765$	5.90064	+	11.5729i	0.213338	+	0.418419i
$766$		−	23.3930i		−	0.845223i
$767$	−8.14221	+	8.14221i	−0.293998	+	0.293998i
$768$	−0.839228	+	0.839228i	−0.0302830	+	0.0302830i
$769$	27.4810			0.990991			0.495496	−	0.868610i	$-0.334986\pi$
$769$	27.4810			0.990991			0.495496	+	0.868610i	$0.334986\pi$
$770$	3.58444	+	4.70657i	0.129174	+	0.169613i
$771$	−22.1944			−0.799312
$772$	−5.32712	+	5.32712i	−0.191727	+	0.191727i
$773$	−2.74375	+	2.74375i	−0.0986859	+	0.0986859i	−0.754726	−	0.656040i	$-0.772230\pi$
$773$	−2.74375	+	2.74375i	−0.0986859	+	0.0986859i	0.656040	+	0.754726i	$0.272230\pi$
$774$			14.4425i			0.519123i
$775$	−14.9930	+	20.6596i	−0.538563	+	0.742114i
$776$		−	4.06745i		−	0.146013i
$777$	4.51116	+	24.8808i	0.161837	+	0.892594i
$778$	17.8628	+	17.8628i	0.640411	+	0.640411i
$779$		−	22.7497i		−	0.815092i
$780$	0.698178	−	2.15075i	0.0249988	−	0.0770093i
$781$	−14.3845			−0.514720
$782$	17.9837	+	17.9837i	0.643094	+	0.643094i
$783$	−25.3163	+	25.3163i	−0.904732	+	0.904732i
$784$	−6.55442	+	2.45756i	−0.234086	+	0.0877701i
$785$	−20.3258	+	10.3635i	−0.725460	+	0.369888i
$786$	1.07710			0.0384189
$787$	−2.86262	−	2.86262i	−0.102041	−	0.102041i	0.654243	−	0.756284i	$-0.272987\pi$
$787$	−2.86262	−	2.86262i	−0.102041	−	0.102041i	−0.756284	+	0.654243i	$0.772987\pi$
$788$	−2.09900	−	2.09900i	−0.0747737	−	0.0747737i
$789$	−31.3731			−1.11691
$790$	3.73840	−	1.90609i	0.133006	−	0.0678156i
$791$	20.7590	+	14.3867i	0.738106	+	0.511533i
$792$	1.12529	−	1.12529i	0.0399853	−	0.0399853i
$793$	−9.35727	−	9.35727i	−0.332286	−	0.332286i
$794$	1.78874			0.0634801
$795$	−7.53133	+	23.2004i	−0.267109	+	0.822835i
$796$			18.3552i			0.650583i
$797$	−6.13956	−	6.13956i	−0.217474	−	0.217474i	0.589959	−	0.807433i	$-0.299144\pi$
$797$	−6.13956	−	6.13956i	−0.217474	−	0.217474i	−0.807433	+	0.589959i	$0.799144\pi$
$798$	1.51561	+	8.35919i	0.0536521	+	0.295912i
$799$		−	18.2631i		−	0.646102i
$800$	−4.93802	+	0.784849i	−0.174585	+	0.0277486i
$801$			9.03656i			0.319291i
$802$	18.3133	−	18.3133i	0.646666	−	0.646666i
$803$	−3.43395	+	3.43395i	−0.121182	+	0.121182i
$804$	−11.5365			−0.406863
$805$	32.7898	−	24.9721i	1.15569	−	0.880151i
$806$	4.35000			0.153222
$807$	9.64428	−	9.64428i	0.339495	−	0.339495i
$808$	−13.4527	+	13.4527i	−0.473263	+	0.473263i
$809$		−	6.37010i		−	0.223961i	−0.993710	−	0.111980i	$-0.964281\pi$
$809$		−	6.37010i		−	0.223961i	0.993710	−	0.111980i	$-0.0357194\pi$
$810$	1.71986	+	3.37315i	0.0604296	+	0.118520i
$811$		−	17.0496i		−	0.598694i	−0.954144	−	0.299347i	$-0.903231\pi$
$811$		−	17.0496i		−	0.598694i	0.954144	−	0.299347i	$-0.0967688\pi$
$812$	17.1042	−	3.10117i	0.600239	−	0.108830i
$813$	15.2528	+	15.2528i	0.534939	+	0.534939i
$814$			8.05275i			0.282249i
$815$	−7.62112	+	3.88576i	−0.266956	+	0.136112i
$816$	4.33265			0.151673
$817$	−17.3617	−	17.3617i	−0.607409	−	0.607409i
$818$	−7.99427	+	7.99427i	−0.279513	+	0.279513i
$819$	−2.94862	−	2.04349i	−0.103033	−	0.0714055i
$820$	−5.80546	+	17.8839i	−0.202735	+	0.624531i
$821$	−30.6153			−1.06848			−0.534240	−	0.845333i	$-0.679402\pi$
$821$	−30.6153			−1.06848			−0.534240	+	0.845333i	$0.679402\pi$
$822$	7.28224	+	7.28224i	0.253997	+	0.253997i
$823$	−14.3099	−	14.3099i	−0.498811	−	0.498811i	0.412257	−	0.911068i	$-0.364741\pi$
$823$	−14.3099	−	14.3099i	−0.498811	−	0.498811i	−0.911068	+	0.412257i	$0.864741\pi$
$824$	−2.16155			−0.0753012
$825$	−5.86067	+	0.931495i	−0.204042	+	0.0324305i
$826$	−20.3667	+	29.3877i	−0.708648	+	1.02253i
$827$	27.8178	−	27.8178i	0.967321	−	0.967321i	−0.0321621	−	0.999483i	$-0.510239\pi$
$827$	27.8178	−	27.8178i	0.967321	−	0.967321i	0.999483	+	0.0321621i	$0.0102393\pi$
$828$	−7.83966	−	7.83966i	−0.272447	−	0.272447i
$829$	6.35742			0.220802			0.110401	−	0.993887i	$-0.464786\pi$
$829$	6.35742			0.220802			0.110401	+	0.993887i	$0.464786\pi$
$830$	10.1418	+	3.29224i	0.352027	+	0.114275i
$831$		−	4.52220i		−	0.156873i
$832$	0.602492	+	0.602492i	0.0208877	+	0.0208877i
$833$	23.2629	+	10.5753i	0.806012	+	0.366414i
$834$			16.0004i			0.554048i
$835$	16.7455	−	8.53796i	0.579501	−	0.295468i
$836$			2.70548i			0.0935709i
$837$	−19.6720	+	19.6720i	−0.679962	+	0.679962i
$838$	−3.44296	+	3.44296i	−0.118935	+	0.118935i
$839$	21.2645			0.734133			0.367067	−	0.930195i	$-0.380362\pi$
$839$	21.2645			0.734133			0.367067	+	0.930195i	$0.380362\pi$
$840$	0.941725	−	6.95804i	0.0324926	−	0.240075i
$841$	−14.1671			−0.488522
$842$	10.9981	−	10.9981i	0.379019	−	0.379019i
$843$	18.0727	−	18.0727i	0.622458	−	0.622458i
$844$			8.49845i			0.292529i
$845$	26.1045	+	8.47406i	0.898023	+	0.291516i
$846$			7.96148i			0.273721i
$847$	−2.60331	+	0.472008i	−0.0894507	+	0.0162184i
$848$	−6.49916	−	6.49916i	−0.223182	−	0.223182i
$849$			5.93950i			0.203843i
$850$	14.7726	+	10.7207i	0.506696	+	0.367717i
$851$	56.1020			1.92315
$852$	12.0719	+	12.0719i	0.413577	+	0.413577i
$853$	6.78454	−	6.78454i	0.232298	−	0.232298i	−0.581353	−	0.813651i	$-0.697477\pi$
$853$	6.78454	−	6.78454i	0.232298	−	0.232298i	0.813651	+	0.581353i	$0.197477\pi$
$854$	−33.7732	−	23.4060i	−1.15570	−	0.800937i
$855$	9.15695	+	2.97253i	0.313161	+	0.101658i
$856$	4.09629			0.140008
$857$	−38.5410	−	38.5410i	−1.31654	−	1.31654i	−0.916499	−	0.400036i	$-0.868997\pi$
$857$	−38.5410	−	38.5410i	−1.31654	−	1.31654i	−0.400036	−	0.916499i	$-0.631003\pi$
$858$	0.715066	+	0.715066i	0.0244119	+	0.0244119i
$859$	−25.3562			−0.865142			−0.432571	−	0.901600i	$-0.642393\pi$
$859$	−25.3562			−0.865142			−0.432571	+	0.901600i	$0.642393\pi$
$860$	9.21777	+	18.0788i	0.314324	+	0.616482i
$861$	−21.7021	−	15.0403i	−0.739604	−	0.512571i
$862$	−22.0985	+	22.0985i	−0.752677	+	0.752677i
$863$	−3.41154	−	3.41154i	−0.116130	−	0.116130i	0.646654	−	0.762784i	$-0.276168\pi$
$863$	−3.41154	−	3.41154i	−0.116130	−	0.116130i	−0.762784	+	0.646654i	$0.776168\pi$
$864$	−5.44928			−0.185388
$865$	−17.7779	−	34.8677i	−0.604466	−	1.18554i
$866$		−	12.4978i		−	0.424693i
$867$	3.08287	+	3.08287i	0.104700	+	0.104700i
$868$	13.2907	−	2.40975i	0.451116	−	0.0817923i
$869$			1.87664i			0.0636605i
$870$	−5.38364	+	16.5844i	−0.182523	+	0.562265i
$871$			8.28223i			0.280633i
$872$	2.43128	−	2.43128i	0.0823335	−	0.0823335i
$873$	4.57705	−	4.57705i	0.154910	−	0.154910i
$874$	18.8486			0.637562
$875$	20.4279	−	21.3940i	0.690589	−	0.723248i
$876$	5.76374			0.194739
$877$	−21.6542	+	21.6542i	−0.731209	+	0.731209i	−0.970859	−	0.239650i	$-0.922967\pi$
$877$	−21.6542	+	21.6542i	−0.731209	+	0.731209i	0.239650	+	0.970859i	$0.422967\pi$
$878$	7.35025	−	7.35025i	0.248059	−	0.248059i
$879$			27.7421i			0.935718i
$880$	0.690407	−	2.12681i	0.0232736	−	0.0716949i
$881$			48.7274i			1.64167i	0.571168	+	0.820833i	$0.306490\pi$
$881$			48.7274i			1.64167i	−0.571168	+	0.820833i	$0.693510\pi$
$882$	−10.1410	−	4.61013i	−0.341467	−	0.155231i
$883$	−30.2256	−	30.2256i	−1.01717	−	1.01717i	−0.999850	−	0.0173237i	$-0.994485\pi$
$883$	−30.2256	−	30.2256i	−1.01717	−	1.01717i	−0.0173237	−	0.999850i	$-0.505515\pi$
$884$		−	3.11046i		−	0.104616i
$885$	−16.2910	−	31.9516i	−0.547617	−	1.07404i
$886$	−2.12316			−0.0713290
$887$	32.9145	+	32.9145i	1.10516	+	1.10516i	0.993778	+	0.111382i	$0.0355277\pi$
$887$	32.9145	+	32.9145i	1.10516	+	1.10516i	0.111382	+	0.993778i	$0.464472\pi$
$888$	6.75809	−	6.75809i	0.226787	−	0.226787i
$889$	8.52457	−	12.3004i	0.285905	−	0.412541i
$890$	5.76750	+	11.3118i	0.193327	+	0.379172i
$891$	−1.69328			−0.0567272
$892$	−8.37825	−	8.37825i	−0.280524	−	0.280524i
$893$	−9.57073	−	9.57073i	−0.320272	−	0.320272i
$894$	9.01710			0.301577
$895$	42.8696	+	13.9163i	1.43297	+	0.465171i
$896$	2.17458	+	1.50706i	0.0726475	+	0.0503472i
$897$	4.98173	−	4.98173i	0.166335	−	0.166335i
$898$	1.97144	+	1.97144i	0.0657877	+	0.0657877i
$899$	−33.5428			−1.11872
$900$	−6.43986	−	4.67350i	−0.214662	−	0.155783i
$901$			33.5529i			1.11781i
$902$	−5.94589	−	5.94589i	−0.197976	−	0.197976i
$903$	−28.0404	+	5.08402i	−0.933125	+	0.169186i
$904$		−	9.54624i		−	0.317503i
$905$	−26.5513	−	8.61909i	−0.882595	−	0.286508i
$906$		−	2.43086i		−	0.0807600i
$907$	−33.0122	+	33.0122i	−1.09615	+	1.09615i	−0.101295	+	0.994856i	$0.532299\pi$
$907$	−33.0122	+	33.0122i	−1.09615	+	1.09615i	−0.994856	+	0.101295i	$0.967701\pi$
$908$	0.767232	−	0.767232i	0.0254615	−	0.0254615i
$909$	−30.2762			−1.00420
$910$	−4.99527	−	0.676076i	−0.165591	−	0.0224117i
$911$	−11.1345			−0.368902			−0.184451	−	0.982842i	$-0.559051\pi$
$911$	−11.1345			−0.368902			−0.184451	+	0.982842i	$0.559051\pi$
$912$	2.27051	−	2.27051i	0.0751841	−	0.0751841i
$913$	−3.37187	+	3.37187i	−0.111593	+	0.111593i
$914$			0.156888i			0.00518941i
$915$	36.7196	−	18.7221i	1.21391	−	0.618935i
$916$			21.9177i			0.724181i
$917$	−0.428362	−	2.36258i	−0.0141458	−	0.0780194i
$918$	14.0664	+	14.0664i	0.464260	+	0.464260i
$919$		−	3.65223i		−	0.120476i	−0.998184	−	0.0602379i	$-0.980814\pi$
$919$		−	3.65223i		−	0.120476i	0.998184	−	0.0602379i	$-0.0191859\pi$
$920$	−14.8171	−	4.80994i	−0.488506	−	0.158579i
$921$	19.9417			0.657101
$922$	−16.6213	−	16.6213i	−0.547394	−	0.547394i
$923$	8.66657	−	8.66657i	0.285264	−	0.285264i
$924$	2.58089	+	1.78865i	0.0849050	+	0.0588421i
$925$	39.7646	−	6.32019i	1.30745	−	0.207807i
$926$	12.6623			0.416108
$927$	−2.43236	−	2.43236i	−0.0798892	−	0.0798892i
$928$	−4.64581	−	4.64581i	−0.152506	−	0.152506i
$929$	42.1410			1.38260			0.691301	−	0.722567i	$-0.257038\pi$
$929$	42.1410			1.38260			0.691301	+	0.722567i	$0.257038\pi$
$930$	−4.18334	+	12.8869i	−0.137177	+	0.422577i
$931$	17.7328	−	6.64888i	0.581170	−	0.217908i
$932$	2.57170	−	2.57170i	0.0842387	−	0.0842387i
$933$	−23.5622	−	23.5622i	−0.771391	−	0.771391i
$934$	36.7103			1.20120
$935$	−7.27218	+	3.70784i	−0.237826	+	0.121259i
$936$			1.35595i			0.0443206i
$937$	10.8290	+	10.8290i	0.353768	+	0.353768i	0.861509	−	0.507742i	$-0.169520\pi$
$937$	10.8290	+	10.8290i	0.353768	+	0.353768i	−0.507742	+	0.861509i	$0.669520\pi$
$938$	4.58807	+	25.3050i	0.149806	+	0.826238i
$939$		−	36.2250i		−	1.18216i
$940$	5.08135	+	9.96603i	0.165735	+	0.325056i
$941$		−	51.5601i		−	1.68081i	−0.541959	−	0.840405i	$-0.682317\pi$
$941$		−	51.5601i		−	1.68081i	0.541959	−	0.840405i	$-0.317683\pi$
$942$	−8.56293	+	8.56293i	−0.278995	+	0.278995i
$943$	−41.4239	+	41.4239i	−1.34895	+	1.34895i
$944$	13.5142			0.439851
$945$	25.6474	−	19.5326i	0.834311	−	0.635396i
$946$	−9.07535			−0.295065
$947$	16.7289	−	16.7289i	0.543617	−	0.543617i	−0.380971	−	0.924587i	$-0.624410\pi$
$947$	16.7289	−	16.7289i	0.543617	−	0.543617i	0.924587	+	0.380971i	$0.124410\pi$
$948$	1.57493	−	1.57493i	0.0511512	−	0.0511512i
$949$		−	4.13786i		−	0.134321i
$950$	13.3597	−	2.12339i	0.433446	−	0.0688919i
$951$			14.9323i			0.484214i
$952$	−1.72309	−	9.50351i	−0.0558456	−	0.308011i
$953$	17.0247	+	17.0247i	0.551485	+	0.551485i	0.926869	−	0.375385i	$-0.122489\pi$
$953$	17.0247	+	17.0247i	0.551485	+	0.551485i	−0.375385	+	0.926869i	$0.622489\pi$
$954$		−	14.6268i		−	0.473561i
$955$	18.6970	−	57.5967i	0.605022	−	1.86379i
$956$	−19.0352			−0.615642
$957$	−5.51387	−	5.51387i	−0.178238	−	0.178238i
$958$	−5.25208	+	5.25208i	−0.169687	+	0.169687i
$959$	13.0772	−	18.8695i	0.422285	−	0.609327i
$960$	−2.36429	+	1.20547i	−0.0763071	+	0.0389065i
$961$	4.93569			0.159216
$962$	−4.85172	−	4.85172i	−0.156426	−	0.156426i
$963$	4.60950	+	4.60950i	0.148539	+	0.148539i
$964$	6.34448			0.204342
$965$	−15.0077	+	7.65192i	−0.483114	+	0.246324i
$966$	12.4612	−	17.9806i	0.400931	−	0.578516i
$967$	20.6979	−	20.6979i	0.665600	−	0.665600i	−0.291094	−	0.956694i	$-0.594019\pi$
$967$	20.6979	−	20.6979i	0.665600	−	0.665600i	0.956694	+	0.291094i	$0.0940194\pi$
$968$	0.707107	+	0.707107i	0.0227273	+	0.0227273i
$969$	−11.7219			−0.376561
$970$	2.80820	−	8.65072i	0.0901658	−	0.277758i
$971$		−	48.8107i		−	1.56641i	−0.621763	−	0.783205i	$-0.713583\pi$
$971$		−	48.8107i		−	1.56641i	0.621763	−	0.783205i	$-0.286417\pi$
$972$	−10.1386	−	10.1386i	−0.325196	−	0.325196i
$973$	35.0963	−	6.36334i	1.12513	−	0.203999i
$974$			30.3189i			0.971479i
$975$	2.96979	−	4.09223i	0.0951094	−	0.131056i
$976$			15.5309i			0.497133i
$977$	19.3765	−	19.3765i	0.619909	−	0.619909i	−0.325599	−	0.945508i	$-0.605566\pi$
$977$	19.3765	−	19.3765i	0.619909	−	0.619909i	0.945508	+	0.325599i	$0.105566\pi$
$978$	−3.21065	+	3.21065i	−0.102665	+	0.102665i
$979$	−5.67839			−0.181482
$980$	−15.6367	+	0.701566i	−0.499498	+	0.0224107i
$981$	5.47176			0.174700
$982$	11.3222	−	11.3222i	0.361307	−	0.361307i
$983$	8.61503	−	8.61503i	0.274777	−	0.274777i	−0.556243	−	0.831020i	$-0.687758\pi$
$983$	8.61503	−	8.61503i	0.274777	−	0.274777i	0.831020	+	0.556243i	$0.187758\pi$
$984$			9.97991i			0.318148i
$985$	−3.01502	−	5.91334i	−0.0960664	−	0.188415i
$986$			23.9847i			0.763830i
$987$	−15.4574	+	2.80259i	−0.492014	+	0.0892075i
$988$	−1.63003	−	1.63003i	−0.0518581	−	0.0518581i
$989$			63.2263i			2.01048i
$990$	3.17018	−	1.61637i	0.100755	−	0.0513716i
$991$	−14.4679			−0.459588			−0.229794	−	0.973239i	$-0.573805\pi$
$991$	−14.4679			−0.459588			−0.229794	+	0.973239i	$0.573805\pi$
$992$	−3.61001	−	3.61001i	−0.114618	−	0.114618i
$993$	−19.0347	+	19.0347i	−0.604048	+	0.604048i
$994$	21.6783	−	31.2803i	0.687595	−	0.992151i
$995$	−12.6726	+	39.0381i	−0.401747	+	1.23759i
$996$	5.65954			0.179329
$997$	9.81981	+	9.81981i	0.310996	+	0.310996i	0.845296	−	0.534299i	$-0.179424\pi$
$997$	9.81981	+	9.81981i	0.310996	+	0.310996i	−0.534299	+	0.845296i	$0.679424\pi$
$998$	−19.5876	−	19.5876i	−0.620033	−	0.620033i
$999$	43.8817			1.38836

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.l.c.573.4	✓	40
5.2	odd	4	inner	770.2.l.c.727.7	yes	40
7.6	odd	2	inner	770.2.l.c.573.7	yes	40
35.27	even	4	inner	770.2.l.c.727.4	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.l.c.573.4	✓	40	1.1	even	1	trivial
770.2.l.c.573.7	yes	40	7.6	odd	2	inner
770.2.l.c.727.4	yes	40	35.27	even	4	inner
770.2.l.c.727.7	yes	40	5.2	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.839228 + 0.839228i) q^{3} -1.00000i q^{4} +(0.690407 - 2.12681i) q^{5} -1.18685i q^{6} +(-2.60331 + 0.472008i) q^{7} +(0.707107 + 0.707107i) q^{8} +1.59139i q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.839228 + 0.839228i) q^{3} -1.00000i q^{4} +(0.690407 - 2.12681i) q^{5} -1.18685i q^{6} +(-2.60331 + 0.472008i) q^{7} +(0.707107 + 0.707107i) q^{8} +1.59139i q^{9} +(1.01569 + 1.99208i) q^{10} -1.00000 q^{11} +(0.839228 + 0.839228i) q^{12} +(0.602492 - 0.602492i) q^{13} +(1.50706 - 2.17458i) q^{14} +(1.20547 + 2.36429i) q^{15} -1.00000 q^{16} +(2.58133 + 2.58133i) q^{17} +(-1.12529 - 1.12529i) q^{18} +2.70548 q^{19} +(-2.12681 - 0.690407i) q^{20} +(1.78865 - 2.58089i) q^{21} +(0.707107 - 0.707107i) q^{22} +(-4.92628 - 4.92628i) q^{23} -1.18685 q^{24} +(-4.04668 - 2.93673i) q^{25} +0.852052i q^{26} +(-3.85322 - 3.85322i) q^{27} +(0.472008 + 2.60331i) q^{28} -6.57017i q^{29} +(-2.52420 - 0.819407i) q^{30} -5.10532i q^{31} +(0.707107 - 0.707107i) q^{32} +(0.839228 - 0.839228i) q^{33} -3.65055 q^{34} +(-0.793468 + 5.86263i) q^{35} +1.59139 q^{36} +(-5.69415 + 5.69415i) q^{37} +(-1.91306 + 1.91306i) q^{38} +1.01126i q^{39} +(1.99208 - 1.01569i) q^{40} -8.40875i q^{41} +(0.560201 + 3.08973i) q^{42} +(-6.41724 - 6.41724i) q^{43} +1.00000i q^{44} +(3.38460 + 1.09871i) q^{45} +6.96682 q^{46} +(-3.53754 - 3.53754i) q^{47} +(0.839228 - 0.839228i) q^{48} +(6.55442 - 2.45756i) q^{49} +(4.93802 - 0.784849i) q^{50} -4.33265 q^{51} +(-0.602492 - 0.602492i) q^{52} +(6.49916 + 6.49916i) q^{53} +5.44928 q^{54} +(-0.690407 + 2.12681i) q^{55} +(-2.17458 - 1.50706i) q^{56} +(-2.27051 + 2.27051i) q^{57} +(4.64581 + 4.64581i) q^{58} -13.5142 q^{59} +(2.36429 - 1.20547i) q^{60} -15.5309i q^{61} +(3.61001 + 3.61001i) q^{62} +(-0.751150 - 4.14289i) q^{63} +1.00000i q^{64} +(-0.865424 - 1.69735i) q^{65} +1.18685i q^{66} +(-6.87331 + 6.87331i) q^{67} +(2.58133 - 2.58133i) q^{68} +8.26855 q^{69} +(-3.58444 - 4.70657i) q^{70} +14.3845 q^{71} +(-1.12529 + 1.12529i) q^{72} +(3.43395 - 3.43395i) q^{73} -8.05275i q^{74} +(5.86067 - 0.931495i) q^{75} -2.70548i q^{76} +(2.60331 - 0.472008i) q^{77} +(-0.715066 - 0.715066i) q^{78} -1.87664i q^{79} +(-0.690407 + 2.12681i) q^{80} +1.69328 q^{81} +(5.94589 + 5.94589i) q^{82} +(3.37187 - 3.37187i) q^{83} +(-2.58089 - 1.78865i) q^{84} +(7.27218 - 3.70784i) q^{85} +9.07535 q^{86} +(5.51387 + 5.51387i) q^{87} +(-0.707107 - 0.707107i) q^{88} +5.67839 q^{89} +(-3.17018 + 1.61637i) q^{90} +(-1.28409 + 1.85285i) q^{91} +(-4.92628 + 4.92628i) q^{92} +(4.28453 + 4.28453i) q^{93} +5.00284 q^{94} +(1.86788 - 5.75405i) q^{95} +1.18685i q^{96} +(-2.87612 - 2.87612i) q^{97} +(-2.89691 + 6.37243i) q^{98} -1.59139i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q+O(q^{10}) \) 40 * q	\( 40 q - 40 q^{11} + 56 q^{15} - 40 q^{16} - 8 q^{18} - 4 q^{21} - 32 q^{25} - 24 q^{30} + 48 q^{35} - 48 q^{36} - 8 q^{37} - 40 q^{42} - 8 q^{43} + 32 q^{46} + 16 q^{50} - 8 q^{51} + 56 q^{53} + 4 q^{56} + 32 q^{57} - 8 q^{58} + 8 q^{60} - 16 q^{63} + 8 q^{65} - 24 q^{67} - 4 q^{70} - 24 q^{71} - 8 q^{72} - 16 q^{78} - 24 q^{81} + 96 q^{85} - 96 q^{86} + 64 q^{91} + 24 q^{93} - 112 q^{95} + 16 q^{98}+O(q^{100}) \) 40 * q - 40 * q^11 + 56 * q^15 - 40 * q^16 - 8 * q^18 - 4 * q^21 - 32 * q^25 - 24 * q^30 + 48 * q^35 - 48 * q^36 - 8 * q^37 - 40 * q^42 - 8 * q^43 + 32 * q^46 + 16 * q^50 - 8 * q^51 + 56 * q^53 + 4 * q^56 + 32 * q^57 - 8 * q^58 + 8 * q^60 - 16 * q^63 + 8 * q^65 - 24 * q^67 - 4 * q^70 - 24 * q^71 - 8 * q^72 - 16 * q^78 - 24 * q^81 + 96 * q^85 - 96 * q^86 + 64 * q^91 + 24 * q^93 - 112 * q^95 + 16 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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