LMFDB - Embedded newform 770.2.bi.a.27.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(27,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([5, 10, 8]))

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

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

chi := DirichletCharacter("770.27");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.bi (of order $20$, degree $8$, 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:	$384$
Relative dimension:	$48$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			27.1
Character	$\chi$	$=$	770.27
Dual form			770.2.bi.a.713.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.453990 + 0.891007i) q^{2} +(-0.454148 - 2.86738i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(-1.32097 + 1.80417i) q^{5} +(2.76103 + 0.897114i) q^{6} +(-2.60332 - 0.471965i) q^{7} +(0.987688 - 0.156434i) q^{8} +(-5.16244 + 1.67738i) q^{9} +O(q^{10})$	\(q+(-0.453990 + 0.891007i) q^{2} +(-0.454148 - 2.86738i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(-1.32097 + 1.80417i) q^{5} +(2.76103 + 0.897114i) q^{6} +(-2.60332 - 0.471965i) q^{7} +(0.987688 - 0.156434i) q^{8} +(-5.16244 + 1.67738i) q^{9} +(-1.00782 - 1.99607i) q^{10} +(0.743793 + 3.23215i) q^{11} +(-2.05282 + 2.05282i) q^{12} +(1.44601 - 2.83796i) q^{13} +(1.60240 - 2.10530i) q^{14} +(5.77316 + 2.96837i) q^{15} +(-0.309017 + 0.951057i) q^{16} +(-0.440831 - 0.865180i) q^{17} +(0.849143 - 5.36128i) q^{18} +(6.43026 + 4.67186i) q^{19} +(2.23605 + 0.00822499i) q^{20} +(-0.171011 + 7.67903i) q^{21} +(-3.21754 - 0.804640i) q^{22} +(-5.57198 + 5.57198i) q^{23} +(-0.897114 - 2.76103i) q^{24} +(-1.51006 - 4.76652i) q^{25} +(1.87217 + 2.57682i) q^{26} +(3.20022 + 6.28079i) q^{27} +(1.14836 + 2.38354i) q^{28} +(-0.279474 - 0.384662i) q^{29} +(-5.26579 + 3.79631i) q^{30} +(8.22487 - 2.67242i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(8.93000 - 3.60061i) q^{33} +0.971014 q^{34} +(4.29041 - 4.07337i) q^{35} +(4.39143 + 3.19056i) q^{36} +(6.63983 + 1.05165i) q^{37} +(-7.08193 + 3.60842i) q^{38} +(-8.79422 - 2.85742i) q^{39} +(-1.02248 + 1.98860i) q^{40} +(-2.19971 + 3.02764i) q^{41} +(-6.76443 - 3.63858i) q^{42} +(0.220919 - 0.220919i) q^{43} +(2.17767 - 2.50155i) q^{44} +(3.79317 - 11.5297i) q^{45} +(-2.43504 - 7.49429i) q^{46} +(1.26300 - 0.200039i) q^{47} +(2.86738 + 0.454148i) q^{48} +(6.55450 + 2.45735i) q^{49} +(4.93255 + 0.818481i) q^{50} +(-2.28060 + 1.65695i) q^{51} +(-3.14591 + 0.498263i) q^{52} +(6.76938 + 3.44917i) q^{53} -7.04909 q^{54} +(-6.81387 - 2.92765i) q^{55} +(-2.64510 - 0.0589060i) q^{56} +(10.4757 - 20.5597i) q^{57} +(0.469615 - 0.0743797i) q^{58} +(-0.799298 + 0.580724i) q^{59} +(-0.991915 - 6.41534i) q^{60} +(0.440018 + 0.142970i) q^{61} +(-1.35287 + 8.54166i) q^{62} +(14.2311 - 1.93025i) q^{63} +(0.951057 - 0.309017i) q^{64} +(3.21002 + 6.35773i) q^{65} +(-0.845968 + 9.59133i) q^{66} +(5.38544 + 5.38544i) q^{67} +(-0.440831 + 0.865180i) q^{68} +(18.5075 + 13.4465i) q^{69} +(1.68159 + 5.67206i) q^{70} +(-3.29348 + 10.1363i) q^{71} +(-4.83648 + 2.46431i) q^{72} +(8.59605 + 1.36148i) q^{73} +(-3.95144 + 5.43869i) q^{74} +(-12.9816 + 6.49462i) q^{75} -7.94824i q^{76} +(-0.410867 - 8.76534i) q^{77} +(6.53847 - 6.53847i) q^{78} +(-0.177146 + 0.0575582i) q^{79} +(-1.30766 - 1.81384i) q^{80} +(3.38172 - 2.45696i) q^{81} +(-1.69900 - 3.33448i) q^{82} +(-5.63712 + 2.87225i) q^{83} +(6.31298 - 4.37527i) q^{84} +(2.14326 + 0.347545i) q^{85} +(0.0965451 + 0.297135i) q^{86} +(-0.976050 + 0.976050i) q^{87} +(1.24025 + 3.07600i) q^{88} +8.03454 q^{89} +(8.55097 + 8.61410i) q^{90} +(-5.10385 + 6.70565i) q^{91} +(7.78295 + 1.23270i) q^{92} +(-11.3981 - 22.3701i) q^{93} +(-0.395153 + 1.21616i) q^{94} +(-16.9230 + 5.42989i) q^{95} +(-1.70641 + 2.34867i) q^{96} +(-5.63752 - 2.87246i) q^{97} +(-5.16519 + 4.72449i) q^{98} +(-9.26131 - 15.4381i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 384 q - 4 q^{7}+O(q^{10}) $ 384 * q - 4 * q^7	$ 384 q - 4 q^{7} + 24 q^{15} + 96 q^{16} + 16 q^{22} + 16 q^{23} - 40 q^{25} + 4 q^{28} + 16 q^{30} - 32 q^{35} + 80 q^{36} - 64 q^{37} + 44 q^{42} - 80 q^{43} - 16 q^{46} - 64 q^{50} - 136 q^{51} + 80 q^{53} + 8 q^{56} - 112 q^{57} - 96 q^{58} + 68 q^{63} - 272 q^{65} + 160 q^{67} - 8 q^{70} + 16 q^{71} + 96 q^{77} + 24 q^{81} - 80 q^{85} - 16 q^{88} - 84 q^{91} + 16 q^{92} + 88 q^{93} - 184 q^{95} - 32 q^{98}+O(q^{100}) $ 384 * q - 4 * q^7 + 24 * q^15 + 96 * q^16 + 16 * q^22 + 16 * q^23 - 40 * q^25 + 4 * q^28 + 16 * q^30 - 32 * q^35 + 80 * q^36 - 64 * q^37 + 44 * q^42 - 80 * q^43 - 16 * q^46 - 64 * q^50 - 136 * q^51 + 80 * q^53 + 8 * q^56 - 112 * q^57 - 96 * q^58 + 68 * q^63 - 272 * q^65 + 160 * q^67 - 8 * q^70 + 16 * q^71 + 96 * q^77 + 24 * q^81 - 80 * q^85 - 16 * q^88 - 84 * q^91 + 16 * q^92 + 88 * q^93 - 184 * q^95 - 32 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$211$	$617$	$661$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	−0.453990	+	0.891007i	−0.321020	+	0.630037i
$2$	−0.453990	+	0.891007i	−0.321020	+	0.630037i
$3$	−0.454148	−	2.86738i	−0.262203	−	1.65548i	−0.669964	−	0.742393i	$-0.733691\pi$
$3$	−0.454148	−	2.86738i	−0.262203	−	1.65548i	0.407762	−	0.913088i	$-0.366309\pi$
$4$	−0.587785	−	0.809017i	−0.293893	−	0.404508i
$5$	−1.32097	+	1.80417i	−0.590757	+	0.806849i
$5$	−1.32097	+	1.80417i	−0.590757	+	0.806849i
$6$	2.76103	+	0.897114i	1.12719	+	0.366245i
$7$	−2.60332	−	0.471965i	−0.983961	−	0.178386i
$7$	−2.60332	−	0.471965i	−0.983961	−	0.178386i
$8$	0.987688	−	0.156434i	0.349201	−	0.0553079i
$9$	−5.16244	+	1.67738i	−1.72081	+	0.559126i
$10$	−1.00782	−	1.99607i	−0.318700	−	0.631213i
$11$	0.743793	+	3.23215i	0.224262	+	0.974529i
$11$	0.743793	+	3.23215i	0.224262	+	0.974529i
$12$	−2.05282	+	2.05282i	−0.592597	+	0.592597i
$13$	1.44601	−	2.83796i	0.401052	−	0.787110i	−0.598853	−	0.800859i	$-0.704377\pi$
$13$	1.44601	−	2.83796i	0.401052	−	0.787110i	0.999905	+	0.0137493i	$0.00437669\pi$
$14$	1.60240	−	2.10530i	0.428261	−	0.562666i
$15$	5.77316	+	2.96837i	1.49062	+	0.766430i
$16$	−0.309017	+	0.951057i	−0.0772542	+	0.237764i
$17$	−0.440831	−	0.865180i	−0.106917	−	0.209837i	0.831349	−	0.555751i	$-0.187569\pi$
$17$	−0.440831	−	0.865180i	−0.106917	−	0.209837i	−0.938266	+	0.345914i	$0.887569\pi$
$18$	0.849143	−	5.36128i	0.200145	−	1.26367i
$19$	6.43026	+	4.67186i	1.47520	+	1.07180i	0.979064	+	0.203555i	$0.0652495\pi$
$19$	6.43026	+	4.67186i	1.47520	+	1.07180i	0.496139	+	0.868243i	$0.334751\pi$
$20$	2.23605	+	0.00822499i	0.499997	+	0.00183916i
$21$	−0.171011	+	7.67903i	−0.0373177	+	1.67570i
$22$	−3.21754	−	0.804640i	−0.685982	−	0.171550i
$23$	−5.57198	+	5.57198i	−1.16184	+	1.16184i	−0.177765	+	0.984073i	$0.556887\pi$
$23$	−5.57198	+	5.57198i	−1.16184	+	1.16184i	−0.984073	+	0.177765i	$0.943113\pi$
$24$	−0.897114	−	2.76103i	−0.183123	−	0.563593i
$25$	−1.51006	−	4.76652i	−0.302012	−	0.953304i
$26$	1.87217	+	2.57682i	0.367162	+	0.505355i
$27$	3.20022	+	6.28079i	0.615883	+	1.20874i
$28$	1.14836	+	2.38354i	0.217020	+	0.450447i
$29$	−0.279474	−	0.384662i	−0.0518969	−	0.0714300i	0.782280	−	0.622927i	$-0.214057\pi$
$29$	−0.279474	−	0.384662i	−0.0518969	−	0.0714300i	−0.834177	+	0.551497i	$0.814057\pi$
$30$	−5.26579	+	3.79631i	−0.961398	+	0.693108i
$31$	8.22487	−	2.67242i	1.47723	−	0.479981i	0.543946	−	0.839120i	$-0.316930\pi$
$31$	8.22487	−	2.67242i	1.47723	−	0.479981i	0.933284	+	0.359139i	$0.116930\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	8.93000	−	3.60061i	1.55451	−	0.626785i
$34$	0.971014			0.166528
$35$	4.29041	−	4.07337i	0.725212	−	0.688525i
$36$	4.39143	+	3.19056i	0.731905	+	0.531760i
$37$	6.63983	+	1.05165i	1.09158	+	0.172889i	0.676171	−	0.736745i	$-0.263638\pi$
$37$	6.63983	+	1.05165i	1.09158	+	0.172889i	0.415410	+	0.909634i	$0.363638\pi$
$38$	−7.08193	+	3.60842i	−1.14884	+	0.585364i
$39$	−8.79422	−	2.85742i	−1.40820	−	0.457553i
$40$	−1.02248	+	1.98860i	−0.161668	+	0.314426i
$41$	−2.19971	+	3.02764i	−0.343537	+	0.472839i	−0.945470	−	0.325708i	$-0.894397\pi$
$41$	−2.19971	+	3.02764i	−0.343537	+	0.472839i	0.601933	+	0.798547i	$0.294397\pi$
$42$	−6.76443	−	3.63858i	−1.04377	−	0.561445i
$43$	0.220919	−	0.220919i	0.0336898	−	0.0336898i	−0.690061	−	0.723751i	$-0.742416\pi$
$43$	0.220919	−	0.220919i	0.0336898	−	0.0336898i	0.723751	+	0.690061i	$0.242416\pi$
$44$	2.17767	−	2.50155i	0.328296	−	0.377123i
$45$	3.79317	−	11.5297i	0.565452	−	1.71874i
$46$	−2.43504	−	7.49429i	−0.359028	−	1.10497i
$47$	1.26300	−	0.200039i	0.184227	−	0.0291787i	−0.0636390	−	0.997973i	$-0.520271\pi$
$47$	1.26300	−	0.200039i	0.184227	−	0.0291787i	0.247866	+	0.968794i	$0.420271\pi$
$48$	2.86738	+	0.454148i	0.413870	+	0.0655506i
$49$	6.55450	+	2.45735i	0.936357	+	0.351050i
$50$	4.93255	+	0.818481i	0.697568	+	0.115751i
$51$	−2.28060	+	1.65695i	−0.319347	+	0.232019i
$52$	−3.14591	+	0.498263i	−0.436259	+	0.0690966i
$53$	6.76938	+	3.44917i	0.929845	+	0.473780i	0.852209	−	0.523202i	$-0.175263\pi$
$53$	6.76938	+	3.44917i	0.929845	+	0.473780i	0.0776365	+	0.996982i	$0.475263\pi$
$54$	−7.04909			−0.959260
$55$	−6.81387	−	2.92765i	−0.918782	−	0.394764i
$56$	−2.64510	−	0.0589060i	−0.353466	−	0.00787165i
$57$	10.4757	−	20.5597i	1.38754	−	2.72320i
$58$	0.469615	−	0.0743797i	0.0616635	−	0.00976654i
$59$	−0.799298	+	0.580724i	−0.104060	+	0.0756039i	−0.638598	−	0.769540i	$-0.720485\pi$
$59$	−0.799298	+	0.580724i	−0.104060	+	0.0756039i	0.534539	+	0.845144i	$0.320485\pi$
$60$	−0.991915	−	6.41534i	−0.128056	−	0.828217i
$61$	0.440018	+	0.142970i	0.0563385	+	0.0183055i	0.337051	−	0.941487i	$-0.390571\pi$
$61$	0.440018	+	0.142970i	0.0563385	+	0.0183055i	−0.280712	+	0.959792i	$0.590571\pi$
$62$	−1.35287	+	8.54166i	−0.171814	+	1.08479i
$63$	14.2311	−	1.93025i	1.79295	−	0.243189i
$64$	0.951057	−	0.309017i	0.118882	−	0.0386271i
$65$	3.21002	+	6.35773i	0.398154	+	0.788579i
$66$	−0.845968	+	9.59133i	−0.104131	+	1.18061i
$67$	5.38544	+	5.38544i	0.657936	+	0.657936i	0.954891	−	0.296955i	$-0.0959712\pi$
$67$	5.38544	+	5.38544i	0.657936	+	0.657936i	−0.296955	+	0.954891i	$0.595971\pi$
$68$	−0.440831	+	0.865180i	−0.0534586	+	0.104918i
$69$	18.5075	+	13.4465i	2.22804	+	1.61876i
$70$	1.68159	+	5.67206i	0.200989	+	0.677941i
$71$	−3.29348	+	10.1363i	−0.390864	+	1.20296i	0.541272	+	0.840847i	$0.317943\pi$
$71$	−3.29348	+	10.1363i	−0.390864	+	1.20296i	−0.932136	+	0.362108i	$0.882057\pi$
$72$	−4.83648	+	2.46431i	−0.569985	+	0.290422i
$73$	8.59605	+	1.36148i	1.00609	+	0.159349i	0.637670	−	0.770310i	$-0.279898\pi$
$73$	8.59605	+	1.36148i	1.00609	+	0.159349i	0.368422	+	0.929659i	$0.379898\pi$
$74$	−3.95144	+	5.43869i	−0.459346	+	0.632235i
$75$	−12.9816	+	6.49462i	−1.49899	+	0.749934i
$76$		−	7.94824i		−	0.911725i
$77$	−0.410867	−	8.76534i	−0.0468226	−	0.998903i
$78$	6.53847	−	6.53847i	0.740336	−	0.740336i
$79$	−0.177146	+	0.0575582i	−0.0199305	+	0.00647581i	−0.318965	−	0.947766i	$-0.603335\pi$
$79$	−0.177146	+	0.0575582i	−0.0199305	+	0.00647581i	0.299035	+	0.954242i	$0.403335\pi$
$80$	−1.30766	−	1.81384i	−0.146201	−	0.202793i
$81$	3.38172	−	2.45696i	0.375747	−	0.272996i
$82$	−1.69900	−	3.33448i	−0.187623	−	0.368232i
$83$	−5.63712	+	2.87225i	−0.618754	+	0.315271i	−0.735121	−	0.677935i	$-0.762875\pi$
$83$	−5.63712	+	2.87225i	−0.618754	+	0.315271i	0.116368	+	0.993206i	$0.462875\pi$
$84$	6.31298	−	4.37527i	0.688803	−	0.477381i
$85$	2.14326	+	0.347545i	0.232469	+	0.0376965i
$86$	0.0965451	+	0.297135i	0.0104107	+	0.0320409i
$87$	−0.976050	+	0.976050i	−0.104644	+	0.104644i
$88$	1.24025	+	3.07600i	0.132212	+	0.327903i
$89$	8.03454			0.851660			0.425830	−	0.904803i	$-0.359982\pi$
$89$	8.03454			0.851660			0.425830	+	0.904803i	$0.359982\pi$
$90$	8.55097	+	8.61410i	0.901351	+	0.908006i
$91$	−5.10385	+	6.70565i	−0.535029	+	0.702943i
$92$	7.78295	+	1.23270i	0.811429	+	0.128518i
$93$	−11.3981	−	22.3701i	−1.18193	−	2.31967i
$94$	−0.395153	+	1.21616i	−0.0407569	+	0.125437i
$95$	−16.9230	+	5.42989i	−1.73627	+	0.557095i
$96$	−1.70641	+	2.34867i	−0.174160	+	0.239711i
$97$	−5.63752	−	2.87246i	−0.572403	−	0.291654i	0.143731	−	0.989617i	$-0.454090\pi$
$97$	−5.63752	−	2.87246i	−0.572403	−	0.291654i	−0.716134	+	0.697963i	$0.754090\pi$
$98$	−5.16519	+	4.72449i	−0.521763	+	0.477245i
$99$	−9.26131	−	15.4381i	−0.930797	−	1.55159i
$100$	−2.96860	+	4.02336i	−0.296860	+	0.402336i
$101$	−7.48627	+	2.43244i	−0.744912	+	0.242037i	−0.656790	−	0.754073i	$-0.728086\pi$
$101$	−7.48627	+	2.43244i	−0.744912	+	0.242037i	−0.0881215	+	0.996110i	$0.528086\pi$
$102$	−0.440984	−	2.78427i	−0.0436640	−	0.275683i
$103$	−17.2391	−	2.73040i	−1.69862	−	0.269035i	−0.769454	−	0.638703i	$-0.779471\pi$
$103$	−17.2391	−	2.73040i	−1.69862	−	0.269035i	−0.929164	+	0.369668i	$0.879471\pi$
$104$	0.984257	−	3.02923i	0.0965143	−	0.297040i
$105$	−13.6284	−	10.4523i	−1.32999	−	1.02004i
$106$	−6.14646	+	4.46567i	−0.596997	+	0.433744i
$107$	0.930419	+	5.87443i	0.0899470	+	0.567903i	0.990965	+	0.134121i	$0.0428211\pi$
$107$	0.930419	+	5.87443i	0.0899470	+	0.567903i	−0.901018	+	0.433782i	$0.857179\pi$
$108$	3.20022	−	6.28079i	0.307941	−	0.604369i
$109$			11.4539i			1.09709i	0.836122	+	0.548543i	$0.184817\pi$
$109$			11.4539i			1.09709i	−0.836122	+	0.548543i	$0.815183\pi$
$110$	5.70199	−	4.74208i	0.543663	−	0.452140i
$111$		−	19.5165i		−	1.85242i
$112$	1.25333	−	2.33005i	0.118429	−	0.220169i
$113$	15.1961	−	2.40683i	1.42953	−	0.226416i	0.606804	−	0.794851i	$-0.292451\pi$
$113$	15.1961	−	2.40683i	1.42953	−	0.226416i	0.822728	+	0.568436i	$0.192451\pi$
$114$	13.5630	+	18.6678i	1.27029	+	1.74840i
$115$	−2.69236	−	17.4132i	−0.251064	−	1.62379i
$116$	−0.146928	+	0.452198i	−0.0136419	+	0.0419855i
$117$	−2.70462	+	17.0763i	−0.250043	+	1.57871i
$118$	−0.154555	−	0.975823i	−0.0142280	−	0.0898318i
$119$	0.739288	+	2.46039i	0.0677704	+	0.225544i
$120$	6.16643	+	2.02870i	0.562916	+	0.185194i
$121$	−9.89355	+	4.80809i	−0.899413	+	0.437099i
$122$	−0.327151	+	0.327151i	−0.0296189	+	0.0296189i
$123$	9.68040	+	4.93241i	0.872852	+	0.444740i
$124$	−6.99649	−	5.08325i	−0.628303	−	0.456489i
$125$	10.5944	+	3.57204i	0.947589	+	0.319493i
$126$	−4.74092	+	13.5563i	−0.422355	+	1.20769i
$127$	−16.0366	+	8.17107i	−1.42302	+	0.725065i	−0.984782	−	0.173794i	$-0.944397\pi$
$127$	−16.0366	+	8.17107i	−1.42302	+	0.725065i	−0.438238	+	0.898859i	$0.644397\pi$
$128$	−0.156434	+	0.987688i	−0.0138270	+	0.0873001i
$129$	−0.733788	−	0.533128i	−0.0646064	−	0.0469393i
$130$	−7.12210	−	0.0261976i	−0.624649	−	0.00229768i
$131$			9.38136i			0.819654i	0.912163	+	0.409827i	$0.134411\pi$
$131$			9.38136i			0.819654i	−0.912163	+	0.409827i	$0.865589\pi$
$132$	−8.16187	−	5.10813i	−0.710400	−	0.444606i
$133$	−14.5350	−	15.1972i	−1.26035	−	1.31776i
$134$	−7.24340	+	2.35352i	−0.625734	+	0.203313i
$135$	−15.5590	−	2.52301i	−1.33911	−	0.217146i
$136$	−0.570748	−	0.785567i	−0.0489412	−	0.0673618i
$137$	−0.743673	+	0.378920i	−0.0635363	+	0.0323734i	−0.485470	−	0.874253i	$-0.661351\pi$
$137$	−0.743673	+	0.378920i	−0.0635363	+	0.0323734i	0.421934	+	0.906627i	$0.361351\pi$
$138$	−20.3831	+	10.3857i	−1.73513	+	0.884090i
$139$	−5.38096	+	3.90949i	−0.456407	+	0.331599i	−0.792120	−	0.610365i	$-0.791023\pi$
$139$	−5.38096	+	3.90949i	−0.456407	+	0.331599i	0.335713	+	0.941964i	$0.391023\pi$
$140$	−5.81727	−	1.07675i	−0.491649	−	0.0910020i
$141$	−1.14718	−	3.53065i	−0.0966097	−	0.297334i
$142$	−7.53629	−	7.53629i	−0.632431	−	0.632431i
$143$	10.2483	+	2.56288i	0.857002	+	0.214318i
$144$		−	5.42811i		−	0.452342i
$145$	1.06317	+	0.00391072i	0.0882918	+	0.000324768i
$146$	−5.11561	+	7.04104i	−0.423371	+	0.582720i
$147$	4.06943	−	19.9102i	0.335641	−	1.64217i
$148$	−3.05199	−	5.98988i	−0.250872	−	0.492365i
$149$	−15.6300	−	5.07849i	−1.28046	−	0.416046i	−0.411716	−	0.911312i	$-0.635070\pi$
$149$	−15.6300	−	5.07849i	−1.28046	−	0.416046i	−0.868741	+	0.495266i	$0.835070\pi$
$150$	0.106785	−	14.5152i	0.00871900	−	1.18516i
$151$	4.55015	+	3.30588i	0.370286	+	0.269029i	0.757330	−	0.653033i	$-0.226504\pi$
$151$	4.55015	+	3.30588i	0.370286	+	0.269029i	−0.387044	+	0.922061i	$0.626504\pi$
$152$	7.08193	+	3.60842i	0.574421	+	0.292682i
$153$	3.72700	+	3.72700i	0.301310	+	0.301310i
$154$	7.99650	+	3.61330i	0.644377	+	0.291168i
$155$	−6.04332	+	18.3693i	−0.485411	+	1.47545i
$156$	2.85742	+	8.79422i	0.228776	+	0.704101i
$157$	10.6559	−	1.68774i	0.850437	−	0.134696i	0.284023	−	0.958817i	$-0.408331\pi$
$157$	10.6559	−	1.68774i	0.850437	−	0.134696i	0.566413	+	0.824121i	$0.308331\pi$
$158$	0.0291379	−	0.183969i	0.00231808	−	0.0146358i
$159$	6.81577	−	20.9768i	0.540526	−	1.66357i
$160$	2.20981	−	0.341672i	0.174701	−	0.0270115i
$161$	17.1354	−	11.8758i	1.35046	−	0.935947i
$162$	0.653902	+	4.12857i	0.0513754	+	0.324371i
$163$	−2.05762	−	1.04841i	−0.161165	−	0.0821179i	0.371547	−	0.928414i	$-0.378827\pi$
$163$	−2.05762	−	1.04841i	−0.161165	−	0.0821179i	−0.532713	+	0.846296i	$0.678827\pi$
$164$	3.74237			0.292230
$165$	−5.30017	+	20.8675i	−0.412618	+	1.62454i
$166$		−	6.32668i		−	0.491046i
$167$	18.6553	+	9.50535i	1.44359	+	0.735546i	0.987973	−	0.154629i	$-0.0494183\pi$
$167$	18.6553	+	9.50535i	1.44359	+	0.735546i	0.455618	+	0.890175i	$0.349418\pi$
$168$	1.03236	+	7.61124i	0.0796482	+	0.587220i
$169$	1.67813	+	2.30975i	0.129087	+	0.177673i
$170$	−1.28268	+	1.75188i	−0.0983773	+	0.134363i
$171$	−41.0323	−	13.3322i	−3.13782	−	1.01954i
$172$	−0.308580	−	0.0488743i	−0.0235290	−	0.00372663i
$173$	−0.311798	−	1.96862i	−0.0237056	−	0.149671i	0.972996	−	0.230820i	$-0.0741410\pi$
$173$	−0.311798	−	1.96862i	−0.0237056	−	0.149671i	−0.996702	+	0.0811492i	$0.974141\pi$
$174$	−0.426550	−	1.31278i	−0.0323366	−	0.0995220i
$175$	1.68153	+	13.1214i	0.127112	+	0.991888i
$176$	−3.30380	−	0.291400i	−0.249033	−	0.0219651i
$177$	2.02816	+	2.02816i	0.152446	+	0.152446i
$178$	−3.64761	+	7.15883i	−0.273400	+	0.536577i
$179$	2.83245	−	3.89853i	0.211707	−	0.291390i	−0.689936	−	0.723870i	$-0.742362\pi$
$179$	2.83245	−	3.89853i	0.211707	−	0.291390i	0.901643	+	0.432480i	$0.142362\pi$
$180$	−11.5573	+	3.70824i	−0.861429	+	0.276396i
$181$	7.47999	+	2.43040i	0.555984	+	0.180650i	0.573513	−	0.819196i	$-0.305580\pi$
$181$	7.47999	+	2.43040i	0.555984	+	0.180650i	−0.0175296	+	0.999846i	$0.505580\pi$
$182$	−3.65767	−	7.59186i	−0.271125	−	0.562746i
$183$	0.210117	−	1.32663i	0.0155323	−	0.0980671i
$184$	−4.63173	+	6.37503i	−0.341456	+	0.469973i
$185$	−10.6684	+	10.5902i	−0.784355	+	0.778606i
$186$	25.1066			1.84090
$187$	2.46850	−	2.06835i	0.180515	−	0.151252i
$188$	−0.904207	−	0.904207i	−0.0659461	−	0.0659461i
$189$	−5.36687	−	17.8613i	−0.390382	−	1.29922i
$190$	2.84483	−	17.5436i	0.206386	−	1.27275i
$191$	14.8752	−	10.8075i	1.07633	−	0.782000i	0.0992915	−	0.995058i	$-0.468342\pi$
$191$	14.8752	−	10.8075i	1.07633	−	0.782000i	0.977040	+	0.213058i	$0.0683424\pi$
$192$	−1.31799	−	2.58670i	−0.0951177	−	0.186679i
$193$	9.12411	+	17.9071i	0.656768	+	1.28898i	0.943628	+	0.331007i	$0.107388\pi$
$193$	9.12411	+	17.9071i	0.656768	+	1.28898i	−0.286860	+	0.957972i	$0.592612\pi$
$194$	5.11876	−	3.71900i	0.367506	−	0.267008i
$195$	16.7722	−	12.0917i	1.20108	−	0.865905i
$196$	−1.86460	−	6.74709i	−0.133186	−	0.481935i
$197$	−13.3058	−	13.3058i	−0.947997	−	0.947997i	0.0507164	−	0.998713i	$-0.483850\pi$
$197$	−13.3058	−	13.3058i	−0.947997	−	0.947997i	−0.998713	+	0.0507164i	$0.983850\pi$
$198$	17.9600	−	1.24312i	1.27636	−	0.0883450i
$199$	−23.2034			−1.64484			−0.822421	−	0.568879i	$-0.807377\pi$
$199$	−23.2034			−1.64484			−0.822421	+	0.568879i	$0.807377\pi$
$200$	−2.23712	−	4.47161i	−0.158188	−	0.316191i
$201$	12.9963	−	17.8879i	0.916689	−	1.26171i
$202$	1.23138	−	7.77462i	0.0866395	−	0.547020i
$203$	0.546011	+	1.13330i	0.0383224	+	0.0795420i
$204$	2.68100	+	0.871110i	0.187708	+	0.0609899i
$205$	−2.55662	−	7.96809i	−0.178562	−	0.556516i
$206$	10.2592	−	14.1206i	0.714791	−	0.983826i
$207$	19.4187	−	38.1113i	1.34969	−	2.64892i
$208$	2.25222	+	2.25222i	0.156163	+	0.156163i
$209$	−10.3173	+	24.2584i	−0.713666	+	1.67799i
$210$	15.5002	−	7.39772i	1.06962	−	0.510491i
$211$	2.72508	+	8.38695i	0.187603	+	0.577381i	0.999983	−	0.00574587i	$-0.00182898\pi$
$211$	2.72508	+	8.38695i	0.187603	+	0.577381i	−0.812381	+	0.583127i	$0.801829\pi$
$212$	−1.18850	−	7.50391i	−0.0816267	−	0.515371i
$213$	30.5603	+	4.84027i	2.09396	+	0.331650i
$214$	−5.65656	−	1.83793i	−0.386674	−	0.125638i
$215$	0.106747	+	0.690403i	0.00728011	+	0.0470851i
$216$	4.14335	+	5.70283i	0.281919	+	0.388029i
$217$	−22.6732	+	3.07531i	−1.53916	+	0.208765i
$218$	−10.2055	−	5.19997i	−0.691204	−	0.352186i
$219$		−	25.2664i		−	1.70735i
$220$	1.63658	+	7.23337i	0.110338	+	0.487674i
$221$	−3.09280			−0.208044
$222$	17.3893	+	8.86031i	1.16710	+	0.594665i
$223$	−0.532848	−	3.36427i	−0.0356821	−	0.225288i	0.963403	−	0.268058i	$-0.0863818\pi$
$223$	−0.532848	−	3.36427i	−0.0356821	−	0.225288i	−0.999085	+	0.0427697i	$0.986382\pi$
$224$	1.50709	+	2.17455i	0.100697	+	0.145293i
$225$	15.7908	+	22.0739i	1.05272	+	1.47159i
$226$	−4.75440	+	14.6325i	−0.316258	+	0.973342i
$227$	0.983840	−	6.21172i	0.0652997	−	0.412286i	−0.933287	−	0.359132i	$-0.883073\pi$
$227$	0.983840	−	6.21172i	0.0652997	−	0.412286i	0.998586	−	0.0531538i	$-0.0169274\pi$
$228$	−22.7906	+	3.60968i	−1.50934	+	0.239057i
$229$	−6.17310	−	18.9988i	−0.407930	−	1.25548i	−0.918424	−	0.395597i	$-0.870538\pi$
$229$	−6.17310	−	18.9988i	−0.407930	−	1.25548i	0.510494	−	0.859881i	$-0.329462\pi$
$230$	16.7376	+	5.50653i	1.10365	+	0.363090i
$231$	−24.9470	+	5.15887i	−1.64139	+	0.339429i
$232$	−0.336207	−	0.336207i	−0.0220731	−	0.0220731i
$233$	14.7425	+	7.51167i	0.965813	+	0.492106i	0.864436	−	0.502742i	$-0.167675\pi$
$233$	14.7425	+	7.51167i	0.965813	+	0.492106i	0.101376	+	0.994848i	$0.467675\pi$
$234$	−13.9872	−	10.1623i	−0.914375	−	0.664332i
$235$	−1.30748	+	2.54291i	−0.0852908	+	0.165881i
$236$	0.939632	+	0.305305i	0.0611648	+	0.0198736i
$237$	0.245492	+	0.481805i	0.0159464	+	0.0312966i
$238$	−2.52786	−	0.458285i	−0.163857	−	0.0297062i
$239$	−4.76757	+	6.56199i	−0.308388	+	0.424460i	−0.934878	−	0.354970i	$-0.884491\pi$
$239$	−4.76757	+	6.56199i	−0.308388	+	0.424460i	0.626489	+	0.779430i	$0.284491\pi$
$240$	−4.60709	+	4.57332i	−0.297386	+	0.295207i
$241$		−	24.6982i		−	1.59095i	−0.605984	−	0.795477i	$-0.707221\pi$
$241$		−	24.6982i		−	1.59095i	0.605984	−	0.795477i	$-0.292779\pi$
$242$	0.207533	−	10.9980i	0.0133407	−	0.706981i
$243$	6.37254	+	6.37254i	0.408798	+	0.408798i
$244$	−0.142970	−	0.440018i	−0.00915274	−	0.0281692i
$245$	−13.0918	+	8.57934i	−0.836404	+	0.548114i
$246$	−8.78962	+	6.38603i	−0.560405	+	0.407158i
$247$	22.5568	−	11.4933i	1.43526	−	0.731299i
$248$	7.70555	−	3.92617i	0.489303	−	0.249312i
$249$	10.7959	+	14.8593i	0.684164	+	0.941671i
$250$	−7.99245	+	7.81798i	−0.505487	+	0.494452i
$251$	7.99072	−	2.59634i	0.504370	−	0.163880i	−0.0457706	−	0.998952i	$-0.514574\pi$
$251$	7.99072	−	2.59634i	0.504370	−	0.163880i	0.550140	+	0.835072i	$0.314574\pi$
$252$	−9.92645	−	10.3786i	−0.625307	−	0.653793i
$253$	−22.1538	−	13.8651i	−1.39280	−	0.871689i
$254$		−	17.9983i		−	1.12932i
$255$	0.0231860	−	6.30337i	0.00145196	−	0.394732i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	4.72230	−	29.8154i	0.294569	−	1.85983i	−0.185556	−	0.982634i	$-0.559409\pi$
$257$	4.72230	−	29.8154i	0.294569	−	1.85983i	0.480125	−	0.877200i	$-0.340591\pi$
$258$	0.808153	−	0.411775i	0.0503134	−	0.0256360i
$259$	−16.7892	−	5.87153i	−1.04323	−	0.364839i
$260$	3.25671	−	6.33394i	0.201972	−	0.392814i
$261$	2.08799	+	1.51701i	0.129243	+	0.0939008i
$262$	−8.35886	−	4.25905i	−0.516412	−	0.263125i
$263$	−17.6983	+	17.6983i	−1.09133	+	1.09133i	−0.0959380	+	0.995387i	$0.530585\pi$
$263$	−17.6983	+	17.6983i	−1.09133	+	1.09133i	−0.995387	+	0.0959380i	$0.969415\pi$
$264$	8.25679	−	4.95324i	0.508170	−	0.304851i
$265$	−15.1650	+	7.65685i	−0.931582	+	0.470356i
$266$	20.1396	−	6.05144i	1.23484	−	0.371038i
$267$	−3.64887	−	23.0381i	−0.223307	−	1.40991i
$268$	1.19143	−	7.52239i	0.0727782	−	0.459503i
$269$	−2.09923	+	6.46078i	−0.127993	+	0.393921i	−0.994434	−	0.105357i	$-0.966401\pi$
$269$	−2.09923	+	6.46078i	−0.127993	+	0.393921i	0.866442	+	0.499278i	$0.166401\pi$
$270$	9.31166	−	12.7178i	0.566690	−	0.773978i
$271$	17.0943	+	23.5283i	1.03841	+	1.42925i	0.898444	+	0.439089i	$0.144699\pi$
$271$	17.0943	+	23.5283i	1.03841	+	1.42925i	0.139964	+	0.990157i	$0.455301\pi$
$272$	0.959059	−	0.151900i	0.0581515	−	0.00921030i
$273$	21.5455	+	11.5893i	1.30399	+	0.701417i
$274$		−	0.834644i		−	0.0504227i
$275$	14.2829	−	8.42604i	0.861293	−	0.508109i
$276$		−	22.8765i		−	1.37700i
$277$	−1.83622	+	3.60379i	−0.110328	+	0.216531i	−0.939568	−	0.342361i	$-0.888773\pi$
$277$	−1.83622	+	3.60379i	−0.110328	+	0.216531i	0.829240	+	0.558892i	$0.188773\pi$
$278$	−1.04048	−	6.56934i	−0.0624039	−	0.394003i
$279$	−37.9777	+	27.5924i	−2.27367	+	1.65191i
$280$	3.60038	−	4.69439i	0.215164	−	0.280543i
$281$	4.39312	−	13.5206i	0.262071	−	0.806573i	−0.730282	−	0.683146i	$-0.760611\pi$
$281$	4.39312	−	13.5206i	0.262071	−	0.806573i	0.992354	−	0.123427i	$-0.0393885\pi$
$282$	3.66664	+	0.580738i	0.218345	+	0.0345825i
$283$	−3.05279	−	19.2746i	−0.181470	−	1.14575i	−0.895309	−	0.445445i	$-0.853045\pi$
$283$	−3.05279	−	19.2746i	−0.181470	−	1.14575i	0.713840	−	0.700309i	$-0.246955\pi$
$284$	10.1363	−	3.29348i	0.601478	−	0.195432i
$285$	23.2551	+	46.0587i	1.37751	+	2.72828i
$286$	−6.93615	+	7.96774i	−0.410143	+	0.471142i
$287$	7.15549	−	6.84372i	0.422375	−	0.403972i
$288$	4.83648	+	2.46431i	0.284992	+	0.145211i
$289$	9.43814	−	12.9905i	0.555185	−	0.764147i
$290$	−0.486155	+	0.945519i	−0.0285480	+	0.0555228i
$291$	−5.67616	+	17.4694i	−0.332742	+	1.02408i
$292$	−3.95117	−	7.75461i	−0.231225	−	0.453804i
$293$	−22.6600	−	3.58899i	−1.32381	−	0.209671i	−0.545797	−	0.837918i	$-0.683773\pi$
$293$	−22.6600	−	3.58899i	−1.32381	−	0.209671i	−0.778014	+	0.628247i	$0.783773\pi$
$294$	15.8927	+	12.6649i	0.926879	+	0.738634i
$295$	0.00812618	−	2.20919i	0.000473124	−	0.128624i
$296$	6.72260			0.390743
$297$	−17.9201	+	15.0152i	−1.03983	+	0.871269i
$298$	11.6208	−	11.6208i	0.673176	−	0.673176i
$299$	7.75591	+	23.8702i	0.448536	+	1.38045i
$300$	12.8847	+	6.68491i	0.743897	+	0.385954i
$301$	−0.679387	+	0.470855i	−0.0391592	+	0.0271397i
$302$	−5.01128	+	2.55338i	−0.288367	+	0.146930i
$303$	10.3746	+	20.3613i	0.596005	+	1.16973i
$304$	−6.43026	+	4.67186i	−0.368801	+	0.267949i
$305$	−0.839194	+	0.605007i	−0.0480521	+	0.0346426i
$306$	−5.01280	+	1.62876i	−0.286563	+	0.0931099i
$307$	−6.90727	+	6.90727i	−0.394219	+	0.394219i	−0.876188	−	0.481969i	$-0.839922\pi$
$307$	−6.90727	+	6.90727i	−0.394219	+	0.394219i	0.481969	+	0.876188i	$0.339922\pi$
$308$	−6.84981	+	5.48454i	−0.390304	+	0.312510i
$309$			50.6710i			2.88257i
$310$	−13.6235	−	13.7241i	−0.773764	−	0.779477i
$311$	7.22891	−	9.94974i	0.409914	−	0.564198i	−0.553284	−	0.832993i	$-0.686625\pi$
$311$	7.22891	−	9.94974i	0.409914	−	0.564198i	0.963197	+	0.268795i	$0.0866254\pi$
$312$	−9.13295	−	1.44652i	−0.517051	−	0.0818929i
$313$	−11.2139	+	5.71375i	−0.633845	+	0.322960i	−0.741224	−	0.671258i	$-0.765754\pi$
$313$	−11.2139	+	5.71375i	−0.633845	+	0.322960i	0.107379	+	0.994218i	$0.465754\pi$
$314$	−3.33391	+	10.2607i	−0.188144	+	0.579046i
$315$	−15.3164	+	28.2252i	−0.862982	+	1.59031i
$316$	0.150689	+	0.109482i	0.00847694	+	0.00615886i
$317$	−10.8989	+	21.3903i	−0.612144	+	1.20140i	0.351994	+	0.936002i	$0.385504\pi$
$317$	−10.8989	+	21.3903i	−0.612144	+	1.20140i	−0.964139	+	0.265399i	$0.914496\pi$
$318$	15.5962	+	15.5962i	0.874589	+	0.874589i
$319$	1.03542	−	1.18941i	0.0579721	−	0.0665941i
$320$	−0.698801	+	2.12407i	−0.0390641	+	0.118739i
$321$	16.4217	−	5.33572i	0.916568	−	0.297811i
$322$	2.80214	+	20.6593i	0.156157	+	1.15130i
$323$	1.20734	−	7.62283i	0.0671781	−	0.424146i
$324$	−3.97545	−	1.29170i	−0.220858	−	0.0717612i
$325$	−15.7108	−	2.60696i	−0.871477	−	0.144608i
$326$	1.86828	−	1.35739i	0.103475	−	0.0751787i
$327$	32.8427	−	5.20177i	1.81621	−	0.287659i
$328$	−1.69900	+	3.33448i	−0.0938117	+	0.184116i
$329$	−3.38240	−	0.0753256i	−0.186478	−	0.00415284i
$330$	−16.1869	−	14.1962i	−0.891059	−	0.781472i
$331$	23.6245			1.29852			0.649259	−	0.760567i	$-0.275079\pi$
$331$	23.6245			1.29852			0.649259	+	0.760567i	$0.275079\pi$
$332$	5.63712	+	2.87225i	0.309377	+	0.157635i
$333$	−36.0417	+	5.70845i	−1.97507	+	0.312821i
$334$	−16.9387	+	12.3067i	−0.926842	+	0.673390i
$335$	−16.8303	+	2.60223i	−0.919536	+	0.142175i
$336$	−7.25035	−	2.53559i	−0.395539	−	0.138328i
$337$	6.31306	+	0.999890i	0.343894	+	0.0544675i	0.325993	−	0.945372i	$-0.394302\pi$
$337$	6.31306	+	0.999890i	0.343894	+	0.0544675i	0.0179014	+	0.999840i	$0.494302\pi$
$338$	−2.81985	+	0.446621i	−0.153380	+	0.0242930i
$339$	−13.8026	−	42.4800i	−0.749654	−	2.30720i
$340$	−0.978606	−	1.93821i	−0.0530724	−	0.105114i
$341$	14.7553	+	24.5962i	0.799042	+	1.33196i
$342$	30.5073	−	30.5073i	1.64965	−	1.64965i
$343$	−15.9036	−	9.49074i	−0.858716	−	0.512452i
$344$	0.183640	−	0.252758i	0.00990119	−	0.0136278i
$345$	−48.7076	+	15.6282i	−2.62233	+	0.841395i
$346$	1.89560	+	0.615919i	0.101908	+	0.0331120i
$347$	5.06536	−	2.58093i	0.271923	−	0.138552i	−0.312712	−	0.949848i	$-0.601238\pi$
$347$	5.06536	−	2.58093i	0.271923	−	0.138552i	0.584635	+	0.811296i	$0.301238\pi$
$348$	1.36335	+	0.215933i	0.0730832	+	0.0115752i
$349$	8.88921	+	6.45839i	0.475828	+	0.345709i	0.799708	−	0.600389i	$-0.204987\pi$
$349$	8.88921	+	6.45839i	0.475828	+	0.345709i	−0.323880	+	0.946098i	$0.604987\pi$
$350$	−12.4547	−	4.45876i	−0.665732	−	0.238331i
$351$	22.4522			1.19841
$352$	1.75953	−	2.81141i	0.0937834	−	0.149849i
$353$	17.2364	+	17.2364i	0.917401	+	0.917401i	0.996840	−	0.0794389i	$-0.0253129\pi$
$353$	17.2364	+	17.2364i	0.917401	+	0.917401i	−0.0794389	+	0.996840i	$0.525313\pi$
$354$	−2.72786	+	0.886337i	−0.144984	+	0.0471083i
$355$	−13.9370	−	19.3318i	−0.739698	−	1.02602i
$356$	−4.72259	−	6.50008i	−0.250297	−	0.344504i
$357$	6.71913	−	3.23720i	0.355614	−	0.171331i
$358$	2.18771	+	4.29362i	0.115624	+	0.226925i
$359$	9.38618	+	12.9190i	0.495384	+	0.681837i	0.981370	−	0.192130i	$-0.0615394\pi$
$359$	9.38618	+	12.9190i	0.495384	+	0.681837i	−0.485986	+	0.873967i	$0.661539\pi$
$360$	1.94283	−	11.9811i	0.102396	−	0.631460i
$361$	13.6507	+	42.0124i	0.718456	+	2.21118i
$362$	−5.56135	+	5.56135i	−0.292298	+	0.292298i
$363$	18.2798	+	26.1849i	0.959438	+	1.37435i
$364$	8.42495	+	0.187623i	0.441587	+	0.00983411i
$365$	−13.8115	+	13.7103i	−0.722927	+	0.717628i
$366$	1.08664	+	0.789492i	0.0567997	+	0.0412674i
$367$	−1.16891	+	7.38022i	−0.0610167	+	0.385244i	0.938215	+	0.346053i	$0.112478\pi$
$367$	−1.16891	+	7.38022i	−0.0610167	+	0.385244i	−0.999232	+	0.0391914i	$0.987522\pi$
$368$	−3.57743	−	7.02110i	−0.186486	−	0.366000i
$369$	6.27737	−	19.3198i	0.326787	−	1.00575i
$370$	−4.59258	−	14.3134i	−0.238757	−	0.744120i
$371$	−15.9949	−	12.1742i	−0.830415	−	0.632052i
$372$	−11.3981	+	22.3701i	−0.590967	+	1.15984i
$373$	14.8147	−	14.8147i	0.767074	−	0.767074i	−0.210516	−	0.977590i	$-0.567514\pi$
$373$	14.8147	−	14.8147i	0.767074	−	0.767074i	0.977590	+	0.210516i	$0.0675144\pi$
$374$	0.722233	+	3.13846i	0.0373458	+	0.162286i
$375$	5.43098	−	32.0003i	0.280454	−	1.65249i
$376$	1.21616	−	0.395153i	0.0627185	−	0.0203785i
$377$	−1.49578	+	0.236908i	−0.0770366	+	0.0122014i
$378$	18.3510	+	3.32692i	0.943874	+	0.171118i
$379$	−8.04664	−	2.61451i	−0.413328	−	0.134298i	0.0949689	−	0.995480i	$-0.469725\pi$
$379$	−8.04664	−	2.61451i	−0.413328	−	0.134298i	−0.508297	+	0.861182i	$0.669725\pi$
$380$	14.3400	+	10.4994i	0.735625	+	0.538608i
$381$	30.7126	+	42.2722i	1.57345	+	2.16567i
$382$	2.87632	+	18.1604i	0.147165	+	0.929166i
$383$	−7.96259	+	15.6275i	−0.406869	+	0.798526i	−0.999978	−	0.00659644i	$-0.997900\pi$
$383$	−7.96259	+	15.6275i	−0.406869	+	0.798526i	0.593109	+	0.805122i	$0.297900\pi$
$384$	2.90312			0.148149
$385$	16.3569	+	10.8375i	0.833625	+	0.552330i
$386$	−20.0976			−1.02294
$387$	−0.769915	+	1.51104i	−0.0391370	+	0.0768107i
$388$	0.989782	+	6.24924i	0.0502486	+	0.317257i
$389$	−18.7291	−	25.7784i	−0.949603	−	1.30702i	−0.951703	−	0.307019i	$-0.900668\pi$
$389$	−18.7291	−	25.7784i	−0.949603	−	1.30702i	0.00210005	−	0.999998i	$-0.499332\pi$
$390$	3.15937	+	20.4336i	0.159981	+	1.03470i
$391$	7.27707	+	2.36446i	0.368017	+	0.119576i
$392$	6.85822	+	1.40174i	0.346392	+	0.0707987i
$393$	26.8999	−	4.26053i	1.35692	−	0.214915i
$394$	17.8962	−	5.81483i	0.901598	−	0.292947i
$395$	0.130160	−	0.395635i	0.00654907	−	0.0199065i
$396$	−7.04605	+	16.5669i	−0.354077	+	0.832516i
$397$	12.5798	−	12.5798i	0.631364	−	0.631364i	−0.317046	−	0.948410i	$-0.602691\pi$
$397$	12.5798	−	12.5798i	0.631364	−	0.631364i	0.948410	+	0.317046i	$0.102691\pi$
$398$	10.5341	−	20.6743i	0.528027	−	1.03631i
$399$	−36.9750	+	48.5792i	−1.85106	+	2.43200i
$400$	4.99986	+	0.0367830i	0.249993	+	0.00183915i
$401$	6.12629	−	18.8548i	0.305932	−	0.941563i	−0.673395	−	0.739283i	$-0.735165\pi$
$401$	6.12629	−	18.8548i	0.305932	−	0.941563i	0.979328	−	0.202281i	$-0.0648353\pi$
$402$	10.0380	+	19.7007i	0.500651	+	0.982583i
$403$	4.30904	−	27.2062i	0.214649	−	1.35524i
$404$	6.36820	+	4.62677i	0.316830	+	0.230190i
$405$	−0.0343807	+	9.34678i	−0.00170839	+	0.464445i
$406$	−1.25766	−	0.0280080i	−0.0624167	−	0.00139001i
$407$	1.53958	+	22.2431i	0.0763143	+	1.10255i
$408$	−1.99331	+	1.99331i	−0.0986837	+	0.0986837i
$409$	−1.78310	−	5.48781i	−0.0881685	−	0.271355i	0.897245	−	0.441534i	$-0.145565\pi$
$409$	−1.78310	−	5.48781i	−0.0881685	−	0.271355i	−0.985413	+	0.170179i	$0.945565\pi$
$410$	8.26030	+	1.33947i	0.407947	+	0.0661516i
$411$	1.42425	+	1.96031i	0.0702529	+	0.0966948i
$412$	7.92394	+	15.5516i	0.390384	+	0.766173i
$413$	2.35491	−	1.13457i	0.115877	−	0.0558284i
$414$	25.1415	+	34.6043i	1.23564	+	1.70071i
$415$	2.26444	−	13.9645i	0.111157	−	0.685490i
$416$	−3.02923	+	0.984257i	−0.148520	+	0.0482571i
$417$	13.6537	+	13.6537i	0.668627	+	0.668627i
$418$	−16.9304	−	20.2059i	−0.828095	−	0.988304i
$419$	2.80555			0.137060			0.0685301	−	0.997649i	$-0.478169\pi$
$419$	2.80555			0.137060			0.0685301	+	0.997649i	$0.478169\pi$
$420$	−0.445550	+	17.1693i	−0.0217406	+	0.837777i
$421$	−2.06569	−	1.50081i	−0.100676	−	0.0731451i	0.536309	−	0.844022i	$-0.319818\pi$
$421$	−2.06569	−	1.50081i	−0.100676	−	0.0731451i	−0.636984	+	0.770877i	$0.719818\pi$
$422$	−8.70999	−	1.37953i	−0.423995	−	0.0671543i
$423$	−6.18461	+	3.15122i	−0.300706	+	0.153217i
$424$	7.22560	+	2.34774i	0.350906	+	0.114016i
$425$	−3.45822	+	3.40771i	−0.167748	+	0.165298i
$426$	−18.1868	+	25.0320i	−0.881153	+	1.21280i
$427$	−1.07803	−	0.579870i	−0.0521694	−	0.0280619i
$428$	4.20563	−	4.20563i	0.203287	−	0.203287i
$429$	2.69451	−	30.5495i	0.130092	−	1.47495i
$430$	−0.663616	−	0.218324i	−0.0320024	−	0.0105285i
$431$	1.60044	+	4.92564i	0.0770903	+	0.237260i	0.982174	−	0.187974i	$-0.0601920\pi$
$431$	1.60044	+	4.92564i	0.0770903	+	0.237260i	−0.905084	+	0.425233i	$0.860192\pi$
$432$	−6.96231	+	1.10272i	−0.334974	+	0.0530547i
$433$	32.7051	+	5.17998i	1.57171	+	0.248934i	0.880614	−	0.473834i	$-0.157130\pi$
$433$	32.7051	+	5.17998i	1.57171	+	0.248934i	0.691091	+	0.722767i	$0.257130\pi$
$434$	7.55330	−	21.5981i	0.362570	−	1.03674i
$435$	−0.471625	−	3.05030i	−0.0226127	−	0.146251i
$436$	9.26641	−	6.73244i	0.443781	−	0.322425i
$437$	−61.8608	+	9.79778i	−2.95920	+	0.468691i
$438$	22.5126	+	11.4707i	1.07569	+	0.548092i
$439$	−18.3904			−0.877726			−0.438863	−	0.898554i	$-0.644619\pi$
$439$	−18.3904			−0.877726			−0.438863	+	0.898554i	$0.644619\pi$
$440$	−7.18797	−	1.82568i	−0.342673	−	0.0870360i
$441$	−37.9591	−	1.69153i	−1.80758	−	0.0805490i
$442$	1.40410	−	2.75570i	0.0667863	−	0.131075i
$443$	27.8595	−	4.41251i	1.32364	−	0.209645i	0.545701	−	0.837980i	$-0.316263\pi$
$443$	27.8595	−	4.41251i	1.32364	−	0.209645i	0.777943	+	0.628335i	$0.216263\pi$
$444$	−15.7892	+	11.4715i	−0.749321	+	0.544414i
$445$	−10.6134	+	14.4957i	−0.503124	+	0.687161i
$446$	3.23949	+	1.05258i	0.153394	+	0.0498409i
$447$	−7.46362	+	47.1234i	−0.353017	+	2.22886i
$448$	−2.62174	+	0.355603i	−0.123866	+	0.0168007i
$449$	−28.7048	+	9.32675i	−1.35466	+	0.440156i	−0.894257	−	0.447553i	$-0.852296\pi$
$449$	−28.7048	+	9.32675i	−1.35466	+	0.440156i	−0.460404	+	0.887709i	$0.652296\pi$
$450$	−26.8369	+	4.04840i	−1.26510	+	0.190843i
$451$	−11.4219	−	4.85785i	−0.537837	−	0.228747i
$452$	−10.8792	−	10.8792i	−0.511716	−	0.511716i
$453$	7.41276	−	14.5484i	0.348282	−	0.683542i
$454$	5.08803	+	3.69667i	0.238793	+	0.173493i
$455$	−5.35608	−	18.0662i	−0.251097	−	0.846956i
$456$	7.13047	−	21.9453i	0.333915	−	1.02768i
$457$	8.57559	−	4.36948i	0.401149	−	0.204396i	−0.241763	−	0.970335i	$-0.577726\pi$
$457$	8.57559	−	4.36948i	0.401149	−	0.204396i	0.642913	+	0.765939i	$0.277726\pi$
$458$	19.7306	+	3.12502i	0.921951	+	0.146023i
$459$	4.02325	−	5.53753i	0.187789	−	0.258470i
$460$	−12.5051	+	12.4134i	−0.583052	+	0.578778i
$461$		−	13.5655i		−	0.631810i	−0.948791	−	0.315905i	$-0.897692\pi$
$461$		−	13.5655i		−	0.631810i	0.948791	−	0.315905i	$-0.102308\pi$
$462$	6.72909	−	24.5700i	0.313066	−	1.14310i
$463$	−22.4562	+	22.4562i	−1.04363	+	1.04363i	−0.0446253	+	0.999004i	$0.514209\pi$
$463$	−22.4562	+	22.4562i	−1.04363	+	1.04363i	−0.999004	+	0.0446253i	$0.985791\pi$
$464$	0.452198	−	0.146928i	0.0209928	−	0.00682096i
$465$	55.4162	+	8.98613i	2.56986	+	0.416722i
$466$	−13.3859	+	9.72543i	−0.620090	+	0.450522i
$467$	0.307289	+	0.603088i	0.0142196	+	0.0279076i	0.898007	−	0.439981i	$-0.145015\pi$
$467$	0.307289	+	0.603088i	0.0142196	+	0.0279076i	−0.883787	+	0.467889i	$0.845015\pi$
$468$	15.4048	−	7.84912i	0.712086	−	0.362826i
$469$	−11.4783	−	16.5617i	−0.530017	−	0.764750i
$470$	−1.67217	−	2.31943i	−0.0771313	−	0.106987i
$471$	−9.67875	−	29.7881i	−0.445973	−	1.37256i
$472$	−0.698612	+	0.698612i	−0.0321562	+	0.0321562i
$473$	0.878360	+	0.549724i	0.0403870	+	0.0252764i
$474$	−0.540742			−0.0248371
$475$	12.5584	−	37.7048i	0.576220	−	1.73001i
$476$	1.55596	−	2.04428i	0.0713172	−	0.0936994i
$477$	−40.7320	−	6.45132i	−1.86499	−	0.295386i
$478$	−3.68235	−	7.22702i	−0.168427	−	0.330556i
$479$	0.0334818	−	0.103046i	0.00152982	−	0.00470831i	−0.950289	−	0.311370i	$-0.899212\pi$
$479$	0.0334818	−	0.103046i	0.00152982	−	0.00470831i	0.951819	+	0.306662i	$0.0992121\pi$
$480$	−1.98328	−	6.18119i	−0.0905241	−	0.282131i
$481$	12.5858	−	17.3229i	0.573864	−	0.789856i
$482$	22.0063	+	11.2128i	1.00236	+	0.510727i
$483$	−41.8345	−	43.7403i	−1.90354	−	1.99025i
$484$	9.70511	+	5.17792i	0.441141	+	0.235360i
$485$	12.6294	−	6.37660i	0.573472	−	0.289547i
$486$	−8.57104	+	2.78490i	−0.388790	+	0.126326i
$487$	−1.81974	−	11.4894i	−0.0824603	−	0.520634i	−0.993996	−	0.109414i	$-0.965103\pi$
$487$	−1.81974	−	11.4894i	−0.0824603	−	0.520634i	0.911536	−	0.411220i	$-0.134897\pi$
$488$	0.456966	+	0.0723763i	0.0206859	+	0.00327632i
$489$	−2.07173	+	6.37612i	−0.0936867	+	0.288338i
$490$	−1.70070	−	15.5598i	−0.0768299	−	0.702920i
$491$	25.4152	−	18.4653i	1.14697	−	0.833325i	0.158898	−	0.987295i	$-0.449206\pi$
$491$	25.4152	−	18.4653i	1.14697	−	0.833325i	0.988076	+	0.153970i	$0.0492059\pi$
$492$	−1.69959	−	10.7308i	−0.0766235	−	0.483782i
$493$	−0.209602	+	0.411366i	−0.00943998	+	0.0185270i
$494$			25.3161i			1.13903i
$495$	40.0870	+	3.68437i	1.80178	+	0.165600i
$496$			8.64814i			0.388313i
$497$	13.3579	−	24.8335i	0.599185	−	1.11394i
$498$	−18.1410	+	2.87325i	−0.812917	+	0.128753i
$499$	8.18640	+	11.2676i	0.366474	+	0.504408i	0.951938	−	0.306290i	$-0.0990878\pi$
$499$	8.18640	+	11.2676i	0.366474	+	0.504408i	−0.585464	+	0.810698i	$0.699088\pi$
$500$	−3.33737	−	10.6706i	−0.149252	−	0.477204i
$501$	18.7832	−	57.8086i	0.839170	−	2.58270i
$502$	−1.31435	+	8.29849i	−0.0586624	+	0.370380i
$503$	5.61261	+	35.4366i	0.250254	+	1.58004i	0.717914	+	0.696132i	$0.245097\pi$
$503$	5.61261	+	35.4366i	0.250254	+	1.58004i	−0.467660	+	0.883909i	$0.654903\pi$
$504$	13.7539	−	4.13273i	0.612650	−	0.184086i
$505$	5.50063	−	16.7197i	0.244775	−	0.744017i
$506$	22.4115	−	13.4446i	0.996312	−	0.597686i
$507$	5.86080	−	5.86080i	0.260287	−	0.260287i
$508$	16.0366	+	8.17107i	0.711510	+	0.362533i
$509$	16.8747	+	12.2602i	0.747956	+	0.543422i	0.895193	−	0.445680i	$-0.147038\pi$
$509$	16.8747	+	12.2602i	0.747956	+	0.543422i	−0.147237	+	0.989101i	$0.547038\pi$
$510$	5.60582	+	2.88233i	0.248230	+	0.127632i
$511$	−21.7357	−	7.60140i	−0.961529	−	0.336266i
$512$	0.891007	−	0.453990i	0.0393773	−	0.0200637i
$513$	−8.76469	+	55.3381i	−0.386970	+	2.44324i
$514$	24.4218	+	17.7435i	1.07720	+	0.782633i
$515$	27.6985	−	27.4955i	1.22054	−	1.21159i
$516$			0.907012i			0.0399290i
$517$	1.58597	+	3.93341i	0.0697507	+	0.172991i
$518$	12.8537	−	12.2937i	0.564760	−	0.540154i
$519$	−5.50317	+	1.78809i	−0.241562	+	0.0784883i
$520$	4.16507	+	5.77730i	0.182650	+	0.253351i
$521$	1.06797	+	1.46994i	0.0467887	+	0.0643991i	0.831770	−	0.555120i	$-0.187328\pi$
$521$	1.06797	+	1.46994i	0.0467887	+	0.0643991i	−0.784982	+	0.619519i	$0.787328\pi$
$522$	−2.29960	+	1.17170i	−0.100651	+	0.0512840i
$523$	−23.0283	+	11.7335i	−1.00696	+	0.513070i	−0.878041	−	0.478586i	$-0.841149\pi$
$523$	−23.0283	+	11.7335i	−1.00696	+	0.513070i	−0.128915	+	0.991656i	$0.541149\pi$
$524$	7.58968	−	5.51423i	0.331557	−	0.240890i
$525$	36.8605	−	10.7807i	1.60872	−	0.470507i
$526$	−7.73445	−	23.8042i	−0.337238	−	1.03791i
$527$	−5.93790	−	5.93790i	−0.258659	−	0.258659i
$528$	0.664861	+	9.60558i	0.0289344	+	0.418029i
$529$		−	39.0939i		−	1.69973i
$530$	0.0624889	−	16.9883i	0.00271434	−	0.737924i
$531$	3.15223	−	4.33868i	0.136795	−	0.188283i
$532$	−3.75129	+	20.6918i	−0.162639	+	0.897102i
$533$	5.41153	+	10.6207i	0.234399	+	0.460035i
$534$	22.1836	+	7.20790i	0.959979	+	0.311916i
$535$	−11.8275	−	6.08133i	−0.511349	−	0.262919i
$536$	6.16160	+	4.47667i	0.266141	+	0.193363i
$537$	−12.4649	−	6.35118i	−0.537900	−	0.274074i
$538$	−4.80357	−	4.80357i	−0.207096	−	0.207096i
$539$	−3.06732	+	23.0129i	−0.132119	+	0.991234i
$540$	7.10420	+	14.0705i	0.305716	+	0.605498i
$541$	3.46581	+	10.6667i	0.149007	+	0.458596i	0.997504	−	0.0706030i	$-0.0224924\pi$
$541$	3.46581	+	10.6667i	0.149007	+	0.458596i	−0.848498	+	0.529199i	$0.822492\pi$
$542$	−28.7246	+	4.54953i	−1.23383	+	0.195419i
$543$	3.57184	−	22.5517i	0.153282	−	0.967787i
$544$	−0.300060	+	0.923489i	−0.0128650	+	0.0395943i
$545$	−20.6648	−	15.1303i	−0.885183	−	0.648111i
$546$	−20.1076	+	13.9358i	−0.860527	+	0.596396i
$547$	−1.81120	−	11.4355i	−0.0774413	−	0.488945i	−0.995675	−	0.0929060i	$-0.970384\pi$
$547$	−1.81120	−	11.4355i	−0.0774413	−	0.488945i	0.918234	−	0.396039i	$-0.129616\pi$
$548$	0.743673	+	0.378920i	0.0317681	+	0.0161867i
$549$	−2.51138			−0.107183
$550$	1.02335	+	16.5515i	0.0436356	+	0.705759i
$551$		−	3.77914i		−	0.160997i
$552$	20.3831	+	10.3857i	0.867563	+	0.442045i
$553$	0.488332	−	0.0662355i	0.0207660	−	0.00281662i
$554$	−2.37738	−	3.27218i	−0.101005	−	0.139021i
$555$	35.2111	+	25.7808i	1.49463	+	1.09433i
$556$	6.32569	+	2.05534i	0.268269	+	0.0871659i
$557$	−38.6423	−	6.12034i	−1.63733	−	0.259327i	−0.731147	−	0.682220i	$-0.761015\pi$
$557$	−38.6423	−	6.12034i	−1.63733	−	0.259327i	−0.906180	+	0.422893i	$0.861015\pi$
$558$	−7.34351	−	46.3651i	−0.310875	−	1.96279i
$559$	−0.307508	−	0.946412i	−0.0130062	−	0.0400289i
$560$	2.54819	+	5.33917i	0.107681	+	0.225621i
$561$	−7.05180	−	6.13879i	−0.297727	−	0.259180i
$562$	10.0525	+	10.0525i	0.424040	+	0.424040i
$563$	−3.70389	+	7.26929i	−0.156100	+	0.306364i	−0.955790	−	0.294049i	$-0.904997\pi$
$563$	−3.70389	+	7.26929i	−0.156100	+	0.306364i	0.799690	+	0.600413i	$0.204997\pi$
$564$	−2.18206	+	3.00335i	−0.0918813	+	0.126464i
$565$	−15.7314	+	30.5958i	−0.661823	+	1.28717i
$566$	18.5597	+	6.03041i	0.780123	+	0.253477i
$567$	−9.96328	+	4.80020i	−0.418419	+	0.201589i
$568$	−1.66727	+	10.5267i	−0.0699569	+	0.441691i
$569$	19.7957	−	27.2465i	0.829880	−	1.14223i	−0.158066	−	0.987429i	$-0.550526\pi$
$569$	19.7957	−	27.2465i	0.829880	−	1.14223i	0.987945	−	0.154803i	$-0.0494742\pi$
$570$	−51.5962	−	0.189789i	−2.16113	−	0.00794939i
$571$	−16.6280			−0.695861			−0.347930	−	0.937520i	$-0.613115\pi$
$571$	−16.6280			−0.695861			−0.347930	+	0.937520i	$0.613115\pi$
$572$	−3.95036	−	9.79743i	−0.165173	−	0.409651i
$573$	−37.7446	−	37.7446i	−1.57680	−	1.57680i
$574$	2.84928	+	9.48257i	0.118927	+	0.395795i
$575$	34.9730	+	18.1449i	1.45847	+	0.756696i
$576$	−4.39143	+	3.19056i	−0.182976	+	0.132940i
$577$	18.6331	+	36.5695i	0.775706	+	1.52241i	0.850952	+	0.525244i	$0.176026\pi$
$577$	18.6331	+	36.5695i	0.775706	+	1.52241i	−0.0752459	+	0.997165i	$0.523974\pi$
$578$	7.28979	+	14.3070i	0.303215	+	0.595093i
$579$	47.2027	−	34.2947i	1.96168	−	1.42524i
$580$	−0.621754	−	0.862424i	−0.0258169	−	0.0358102i
$581$	16.0308	−	4.81686i	0.665069	−	0.199837i
$582$	−12.9884	−	12.9884i	−0.538388	−	0.538388i
$583$	−6.11321	+	24.4451i	−0.253183	+	1.01241i
$584$	8.70320			0.360141
$585$	−27.2359	−	27.4370i	−1.12606	−	1.13438i
$586$	13.4852	−	18.5608i	0.557070	−	0.766741i
$587$	5.16977	−	32.6407i	0.213379	−	1.34722i	−0.615650	−	0.788020i	$-0.711107\pi$
$587$	5.16977	−	32.6407i	0.213379	−	1.34722i	0.829030	−	0.559205i	$-0.188893\pi$
$588$	−18.4997	+	8.41070i	−0.762913	+	0.346851i
$589$	65.3732	+	21.2410i	2.69366	+	0.875222i
$590$	1.96471	+	1.01019i	0.0808860	+	0.0415890i
$591$	−32.1099	+	44.1955i	−1.32082	+	1.81796i
$592$	−3.05199	+	5.98988i	−0.125436	+	0.246182i
$593$	−6.65757	−	6.65757i	−0.273394	−	0.273394i	0.557071	−	0.830465i	$-0.311925\pi$
$593$	−6.65757	−	6.65757i	−0.273394	−	0.273394i	−0.830465	+	0.557071i	$0.811925\pi$
$594$	−5.24306	−	22.7837i	−0.215125	−	0.934826i
$595$	−5.41555	−	1.91631i	−0.222016	−	0.0785611i
$596$	5.07849	+	15.6300i	0.208023	+	0.640229i
$597$	10.5378	+	66.5328i	0.431282	+	2.72301i
$598$	−24.7896	−	3.92629i	−1.01372	−	0.160558i
$599$	−2.50270	−	0.813178i	−0.102258	−	0.0332255i	0.257441	−	0.966294i	$-0.417121\pi$
$599$	−2.50270	−	0.813178i	−0.102258	−	0.0332255i	−0.359699	+	0.933068i	$0.617121\pi$
$600$	−11.8058	+	8.44543i	−0.481971	+	0.344783i
$601$	8.68478	+	11.9536i	0.354260	+	0.487596i	0.948538	−	0.316663i	$-0.102562\pi$
$601$	8.68478	+	11.9536i	0.354260	+	0.487596i	−0.594279	+	0.804259i	$0.702562\pi$
$602$	−0.111100	−	0.819102i	−0.00452809	−	0.0333841i
$603$	−36.8354	−	18.7686i	−1.50005	−	0.764316i
$604$		−	5.62430i		−	0.228849i
$605$	4.39449	−	24.2010i	0.178661	−	0.983911i
$606$	−22.8520			−0.928299
$607$	−27.7047	−	14.1163i	−1.12450	−	0.572961i	−0.210062	−	0.977688i	$-0.567367\pi$
$607$	−27.7047	−	14.1163i	−1.12450	−	0.572961i	−0.914438	+	0.404727i	$0.867367\pi$
$608$	−1.24338	−	7.85038i	−0.0504257	−	0.318375i
$609$	3.00163	−	2.08030i	0.121632	−	0.0842982i
$610$	−0.158079	−	1.02240i	−0.00640042	−	0.0413956i
$611$	1.25861	−	3.87361i	0.0509179	−	0.156709i
$612$	0.824530	−	5.20588i	0.0333297	−	0.210435i
$613$	−16.8188	+	2.66384i	−0.679305	+	0.107591i	−0.486546	−	0.873655i	$-0.661744\pi$
$613$	−16.8188	+	2.66384i	−0.679305	+	0.107591i	−0.192759	+	0.981246i	$0.561744\pi$
$614$	−3.01859	−	9.29026i	−0.121820	−	0.374924i
$615$	−21.6864	+	10.9495i	−0.874482	+	0.441527i
$616$	−1.77701	−	8.59315i	−0.0715978	−	0.346228i
$617$	18.0306	+	18.0306i	0.725886	+	0.725886i	0.969797	−	0.243912i	$-0.0784307\pi$
$617$	18.0306	+	18.0306i	0.725886	+	0.725886i	−0.243912	+	0.969797i	$0.578431\pi$
$618$	−45.1482	−	23.0041i	−1.81613	−	0.925362i
$619$	4.94679	+	3.59405i	0.198828	+	0.144457i	0.682745	−	0.730657i	$-0.260786\pi$
$619$	4.94679	+	3.59405i	0.198828	+	0.144457i	−0.483916	+	0.875114i	$0.660786\pi$
$620$	18.4132	−	5.90803i	0.739493	−	0.237272i
$621$	−52.8280	−	17.1648i	−2.11991	−	0.688802i
$622$	5.58343	+	10.9581i	0.223875	+	0.439380i
$623$	−20.9164	−	3.79202i	−0.838000	−	0.151924i
$624$	5.43513	−	7.48081i	0.217579	−	0.299472i
$625$	−20.4394	+	14.3955i	−0.817577	+	0.575819i
$626$		−	12.5856i		−	0.503022i
$627$	74.2437	+	18.5668i	2.96501	+	0.741487i
$628$	−7.62881	−	7.62881i	−0.304423	−	0.304423i
$629$	−2.01718	−	6.20825i	−0.0804303	−	0.247539i
$630$	−18.1953	−	26.4610i	−0.724918	−	1.05423i
$631$	37.4445	−	27.2050i	1.49064	−	1.08301i	0.516713	−	0.856159i	$-0.327155\pi$
$631$	37.4445	−	27.2050i	1.49064	−	1.08301i	0.973928	−	0.226856i	$-0.0728446\pi$
$632$	−0.165961	+	0.0845614i	−0.00660157	+	0.00336367i
$633$	22.8110	−	11.6228i	0.906654	−	0.461963i
$634$	−14.1109	−	19.4220i	−0.560416	−	0.771347i
$635$	6.44195	−	39.7266i	0.255641	−	1.57650i
$636$	−20.9768	+	6.81577i	−0.831784	+	0.270263i
$637$	16.4518	−	15.0481i	0.651843	−	0.596226i
$638$	0.589702	+	1.46254i	0.0233465	+	0.0579026i
$639$		−	57.8523i		−	2.28860i
$640$	−1.57531	−	1.58694i	−0.0622697	−	0.0627295i
$641$	8.82302	+	6.41030i	0.348488	+	0.253192i	0.748235	−	0.663434i	$-0.230902\pi$
$641$	8.82302	+	6.41030i	0.348488	+	0.253192i	−0.399746	+	0.916626i	$0.630902\pi$
$642$	−2.70112	+	17.0542i	−0.106605	+	0.673075i
$643$	1.43007	−	0.728658i	0.0563965	−	0.0287354i	−0.425565	−	0.904928i	$-0.639925\pi$
$643$	1.43007	−	0.728658i	0.0563965	−	0.0287354i	0.481961	+	0.876192i	$0.339925\pi$
$644$	−19.6797	−	6.88238i	−0.775488	−	0.271204i
$645$	1.93117	−	0.619630i	0.0760396	−	0.0243979i
$646$	6.24387	+	4.53644i	0.245662	+	0.178484i
$647$	7.65785	+	3.90187i	0.301061	+	0.153398i	0.597995	−	0.801500i	$-0.295964\pi$
$647$	7.65785	+	3.90187i	0.301061	+	0.153398i	−0.296934	+	0.954898i	$0.595964\pi$
$648$	2.95573	−	2.95573i	0.116112	−	0.116112i
$649$	−2.47150	−	2.15151i	−0.0970148	−	0.0844542i
$650$	9.45537	−	12.8149i	0.370870	−	0.502641i
$651$	19.1151	+	63.6160i	0.749178	+	2.49331i
$652$	0.361258	+	2.28089i	0.0141479	+	0.0893266i
$653$	−6.44801	+	40.7111i	−0.252330	+	1.59315i	0.457784	+	0.889063i	$0.348643\pi$
$653$	−6.44801	+	40.7111i	−0.252330	+	1.59315i	−0.710114	+	0.704086i	$0.751357\pi$
$654$	−10.2755	+	31.6246i	−0.401802	+	1.23662i
$655$	−16.9256	−	12.3925i	−0.661337	−	0.484216i
$656$	−2.19971	−	3.02764i	−0.0858843	−	0.118210i
$657$	−46.6603	+	7.39026i	−1.82039	+	0.288322i
$658$	1.60269	−	2.97954i	0.0624794	−	0.116155i
$659$			0.878120i			0.0342067i	0.999854	+	0.0171034i	$0.00544443\pi$
$659$			0.878120i			0.0342067i	−0.999854	+	0.0171034i	$0.994556\pi$
$660$	19.9976	−	7.97770i	0.778404	−	0.310532i
$661$			5.64171i			0.219437i	0.993963	+	0.109719i	$0.0349950\pi$
$661$			5.64171i			0.219437i	−0.993963	+	0.109719i	$0.965005\pi$
$662$	−10.7253	+	21.0496i	−0.416850	+	0.818114i
$663$	1.40459	+	8.86822i	0.0545497	+	0.344413i
$664$	−5.11839	+	3.71873i	−0.198632	+	0.144315i
$665$	46.6187	−	6.14863i	1.80780	−	0.238434i
$666$	11.2763	−	34.7050i	0.436949	−	1.34479i
$667$	3.70055	+	0.586110i	0.143286	+	0.0226943i
$668$	−3.27532	−	20.6796i	−0.126726	−	0.800116i
$669$	−9.40464	+	3.05575i	−0.363604	+	0.118142i
$670$	5.32218	−	16.1773i	0.205614	−	0.624982i
$671$	−0.134819	+	1.52854i	−0.00520465	+	0.0590087i
$672$	5.55082	−	5.30897i	0.214127	−	0.204798i
$673$	−7.83647	−	3.99288i	−0.302074	−	0.153914i	0.296383	−	0.955069i	$-0.404219\pi$
$673$	−7.83647	−	3.99288i	−0.302074	−	0.153914i	−0.598457	+	0.801155i	$0.704219\pi$
$674$	−3.75698	+	5.17103i	−0.144713	+	0.199181i
$675$	25.1050	−	24.7383i	0.966291	−	0.952177i
$676$	0.882245	−	2.71527i	0.0339325	−	0.104433i
$677$	−15.9359	−	31.2760i	−0.612466	−	1.20203i	−0.964011	−	0.265861i	$-0.914344\pi$
$677$	−15.9359	−	31.2760i	−0.612466	−	1.20203i	0.351545	−	0.936171i	$-0.385656\pi$
$678$	44.1162	+	6.98732i	1.69427	+	0.268346i
$679$	13.3205	+	10.1386i	0.511195	+	0.389085i
$680$	2.17124	+	0.00798658i	0.0832632	+	0.000306271i
$681$	−18.2582			−0.699654
$682$	−28.6142	+	1.98056i	−1.09569	+	0.0758397i
$683$	19.5548	−	19.5548i	0.748242	−	0.748242i	−0.225907	−	0.974149i	$-0.572535\pi$
$683$	19.5548	−	19.5548i	0.748242	−	0.748242i	0.974149	+	0.225907i	$0.0725345\pi$
$684$	13.3322	+	41.0323i	0.509769	+	1.56891i
$685$	0.298735	−	1.84226i	0.0114141	−	0.0703890i
$686$	15.6764	−	9.86154i	0.598528	−	0.376515i
$687$	−51.6733	+	26.3289i	−1.97146	+	1.00451i
$688$	0.141839	+	0.278374i	0.00540755	+	0.0106129i
$689$	19.5772	−	14.2237i	0.745833	−	0.541880i
$690$	8.18794	−	50.4938i	0.311710	−	1.92227i
$691$	5.81521	−	1.88948i	0.221221	−	0.0718791i	−0.196309	−	0.980542i	$-0.562896\pi$
$691$	5.81521	−	1.88948i	0.221221	−	0.0718791i	0.417531	+	0.908663i	$0.362896\pi$
$692$	−1.40937	+	1.40937i	−0.0535763	+	0.0535763i
$693$	16.8239	+	44.5613i	0.639086	+	1.69275i
$694$			5.68499i			0.215799i
$695$	0.0547063	−	14.8725i	0.00207513	−	0.564146i
$696$	−0.811346	+	1.11672i	−0.0307540	+	0.0423292i
$697$	3.58916	+	0.568467i	0.135949	+	0.0215322i
$698$	−9.79008	+	4.98829i	−0.370560	+	0.188810i
$699$	14.8435	−	45.6837i	0.561434	−	1.72792i
$700$	9.62710	−	9.07298i	0.363870	−	0.342927i
$701$	−27.1611	−	19.7337i	−1.02586	−	0.745332i	−0.0583849	−	0.998294i	$-0.518595\pi$
$701$	−27.1611	−	19.7337i	−1.02586	−	0.745332i	−0.967476	+	0.252963i	$0.918595\pi$
$702$	−10.1931	+	20.0051i	−0.384713	+	0.755043i
$703$	37.7827	+	37.7827i	1.42500	+	1.42500i
$704$	1.70618	+	2.84411i	0.0643040	+	0.107191i
$705$	7.88528	+	2.59419i	0.296977	+	0.0977028i
$706$	−23.1829	+	7.53258i	−0.872500	+	0.283492i
$707$	20.6372	−	2.79914i	0.776140	−	0.105273i
$708$	0.448692	−	2.83293i	0.0168629	−	0.106468i
$709$	−6.27298	−	2.03821i	−0.235587	−	0.0765468i	0.188844	−	0.982007i	$-0.439526\pi$
$709$	−6.27298	−	2.03821i	−0.235587	−	0.0765468i	−0.424431	+	0.905460i	$0.639526\pi$
$710$	23.5520	−	3.64151i	0.883890	−	0.136664i
$711$	0.817959	−	0.594282i	0.0306758	−	0.0222873i
$712$	7.93562	−	1.25688i	0.297400	−	0.0471035i
$713$	−30.9381	+	60.7194i	−1.15864	+	2.27396i
$714$	−0.166054	+	7.45645i	−0.00621443	+	0.279051i
$715$	−18.1615	+	15.1041i	−0.679203	+	0.564861i
$716$	−4.81884			−0.180089
$717$	20.9809	+	10.6903i	0.783546	+	0.399237i
$718$	−15.7721	+	2.49806i	−0.588610	+	0.0932267i
$719$	34.8667	−	25.3321i	1.30031	−	0.944728i	0.300349	−	0.953830i	$-0.402897\pi$
$719$	34.8667	−	25.3321i	1.30031	−	0.944728i	0.999959	+	0.00910107i	$0.00289700\pi$
$720$	9.79323	+	7.17038i	0.364972	+	0.267224i
$721$	43.5901	+	15.2443i	1.62338	+	0.567729i
$722$	−43.6306	−	6.91041i	−1.62376	−	0.257179i
$723$	−70.8192	+	11.2167i	−2.63379	+	0.417152i
$724$	−2.43040	−	7.47999i	−0.0903250	−	0.277992i
$725$	−1.41148	+	1.91298i	−0.0524210	+	0.0710463i
$726$	−31.6298	+	4.39966i	−1.17389	+	0.163287i
$727$	4.68654	−	4.68654i	0.173814	−	0.173814i	−0.614839	−	0.788653i	$-0.710779\pi$
$727$	4.68654	−	4.68654i	0.173814	−	0.173814i	0.788653	+	0.614839i	$0.210779\pi$
$728$	−3.99202	+	7.42151i	−0.147954	+	0.275059i
$729$	22.7493	−	31.3117i	0.842566	−	1.15969i
$730$	−5.94564	−	18.5305i	−0.220058	−	0.685843i
$731$	−0.288523	−	0.0937466i	−0.0106714	−	0.00346734i
$732$	−1.19677	+	0.609783i	−0.0442338	+	0.0225382i
$733$	−30.7390	−	4.86858i	−1.13537	−	0.179825i	−0.439672	−	0.898158i	$-0.644905\pi$
$733$	−30.7390	−	4.86858i	−1.13537	−	0.179825i	−0.695699	+	0.718333i	$0.744905\pi$
$734$	−6.04515	−	4.39206i	−0.223130	−	0.162114i
$735$	30.5458	+	33.6428i	1.12670	+	1.24093i
$736$	7.87997			0.290459
$737$	−13.4009	+	21.4122i	−0.493628	+	0.788728i
$738$	14.3642	+	14.3642i	0.528753	+	0.528753i
$739$	4.84979	−	1.57579i	0.178403	−	0.0579665i	−0.218454	−	0.975847i	$-0.570101\pi$
$739$	4.84979	−	1.57579i	0.178403	−	0.0579665i	0.396856	+	0.917881i	$0.370101\pi$
$740$	14.8384	+	2.40615i	0.545469	+	0.0884517i
$741$	−43.1997	−	59.4593i	−1.58698	−	2.18429i
$742$	18.1088	−	8.72462i	0.664796	−	0.320291i
$743$	19.0552	+	37.3979i	0.699067	+	1.37200i	0.918127	+	0.396285i	$0.129701\pi$
$743$	19.0552	+	37.3979i	0.699067	+	1.37200i	−0.219060	+	0.975711i	$0.570299\pi$
$744$	−14.7573	−	20.3117i	−0.541028	−	0.744661i
$745$	29.8092	−	21.4906i	1.09213	−	0.787354i
$746$	6.47425	+	19.9257i	0.237039	+	0.729531i
$747$	24.2834	−	24.2834i	0.888483	−	0.888483i
$748$	−3.12428	−	0.781317i	−0.114235	−	0.0285678i
$749$	0.350353	−	15.7321i	0.0128016	−	0.574839i
$750$	26.0468	+	19.3669i	0.951096	+	0.707178i
$751$	14.6633	+	10.6535i	0.535070	+	0.388751i	0.822251	−	0.569125i	$-0.192718\pi$
$751$	14.6633	+	10.6535i	0.535070	+	0.388751i	−0.287181	+	0.957876i	$0.592718\pi$
$752$	−0.200039	+	1.26300i	−0.00729469	+	0.0460568i
$753$	−11.0737	−	21.7333i	−0.403547	−	0.792005i
$754$	0.467983	−	1.44030i	0.0170430	−	0.0524528i
$755$	−11.9750	+	3.84227i	−0.435815	+	0.139835i
$756$	−11.2955	+	14.8405i	−0.410813	+	0.539743i
$757$	−3.71447	+	7.29005i	−0.135005	+	0.264962i	−0.948605	−	0.316463i	$-0.897505\pi$
$757$	−3.71447	+	7.29005i	−0.135005	+	0.264962i	0.813600	+	0.581425i	$0.197505\pi$
$758$	5.98265	−	5.98265i	0.217300	−	0.217300i
$759$	−29.6952	+	69.8202i	−1.07787	+	2.53431i
$760$	−15.8653	+	8.01038i	−0.575493	+	0.290567i
$761$	−5.17605	+	1.68180i	−0.187632	+	0.0609653i	−0.401326	−	0.915935i	$-0.631450\pi$
$761$	−5.17605	+	1.68180i	−0.187632	+	0.0609653i	0.213694	+	0.976901i	$0.431450\pi$
$762$	−51.6080	+	8.17391i	−1.86956	+	0.296109i
$763$	5.40584	−	29.8181i	0.195705	−	1.07949i
$764$	−17.4868	−	5.68182i	−0.632651	−	0.205561i
$765$	−11.6474	+	1.80087i	−0.421113	+	0.0651108i
$766$	−10.3092	−	14.1894i	−0.372487	−	0.512685i
$767$	0.492277	+	3.10812i	0.0177751	+	0.112228i
$768$	−1.31799	+	2.58670i	−0.0475588	+	0.0933395i
$769$	17.6011			0.634712			0.317356	−	0.948306i	$-0.397205\pi$
$769$	17.6011			0.634712			0.317356	+	0.948306i	$0.397205\pi$
$770$	−17.0822	+	9.65399i	−0.615599	+	0.347906i
$771$	−87.6367			−3.15616
$772$	9.12411	−	17.9071i	0.328384	−	0.644490i
$773$	−5.05603	−	31.9225i	−0.181853	−	1.14817i	−0.894638	−	0.446791i	$-0.852567\pi$
$773$	−5.05603	−	31.9225i	−0.181853	−	1.14817i	0.712786	−	0.701382i	$-0.247433\pi$
$774$	−0.996816	−	1.37200i	−0.0358298	−	0.0493155i
$775$	−25.1582	−	35.1685i	−0.903709	−	1.26329i
$776$	−6.01746	−	1.95519i	−0.216014	−	0.0701873i
$777$	−9.21110	+	50.8076i	−0.330447	+	1.82271i
$778$	31.4716	−	4.98461i	1.12831	−	0.178707i
$779$	−28.2894	+	9.19180i	−1.01357	+	0.329330i
$780$	−19.6408	−	6.46166i	−0.703255	−	0.231365i
$781$	−35.2116	−	3.10571i	−1.25997	−	0.111131i
$782$	−5.41047	+	5.41047i	−0.193478	+	0.193478i
$783$	1.52161	−	2.98632i	0.0543777	−	0.106722i
$784$	−4.36253	+	5.47434i	−0.155805	+	0.195512i
$785$	−11.0312	+	21.4546i	−0.393722	+	0.765747i
$786$	−8.41615	+	25.9022i	−0.300194	+	0.923902i
$787$	−11.9545	−	23.4620i	−0.426131	−	0.836330i	−0.999851	−	0.0172781i	$-0.994500\pi$
$787$	−11.9545	−	23.4620i	−0.426131	−	0.836330i	0.573719	−	0.819052i	$-0.305500\pi$
$788$	−2.94366	+	18.5855i	−0.104863	+	0.662082i
$789$	58.7854	+	42.7101i	2.09282	+	1.52052i
$790$	0.293421	+	0.295588i	0.0104395	+	0.0105165i
$791$	−40.6963	−	0.906302i	−1.44699	−	0.0322244i
$792$	−11.5623	−	13.7993i	−0.410850	−	0.490336i
$793$	1.04202	−	1.04202i	0.0370031	−	0.0370031i
$794$	5.49759	+	16.9199i	0.195102	+	0.600463i
$795$	28.8423	+	40.0066i	1.02293	+	1.41889i
$796$	13.6386	+	18.7719i	0.483407	+	0.665353i
$797$	−11.6486	−	22.8616i	−0.412614	−	0.809800i	−1.00000		0.000492968i	$-0.999843\pi$
$797$	−11.6486	−	22.8616i	−0.412614	−	0.809800i	0.587386	−	0.809307i	$-0.300157\pi$
$798$	−26.4981	−	54.9995i	−0.938023	−	1.94696i
$799$	−0.729840	−	1.00454i	−0.0258199	−	0.0355380i
$800$	−2.30266	+	4.43821i	−0.0814115	+	0.156915i
$801$	−41.4778	+	13.4770i	−1.46555	+	0.476185i
$802$	14.0185	+	14.0185i	0.495009	+	0.495009i
$803$	1.99317	+	28.7964i	0.0703376	+	1.01620i
$804$	−22.1106			−0.779782
$805$	−1.20936	+	46.6028i	−0.0426244	+	1.64253i
$806$	22.2847	+	16.1908i	0.784944	+	0.570295i
$807$	19.4789	+	3.08515i	0.685689	+	0.108602i
$808$	−7.01359	+	3.57360i	−0.246737	+	0.125719i
$809$	−1.61103	−	0.523457i	−0.0566409	−	0.0184038i	0.280559	−	0.959837i	$-0.409480\pi$
$809$	−1.61103	−	0.523457i	−0.0566409	−	0.0184038i	−0.337200	+	0.941433i	$0.609480\pi$
$810$	−8.31243	−	4.27398i	−0.292069	−	0.150172i
$811$	7.46281	−	10.2717i	0.262055	−	0.360687i	−0.657633	−	0.753339i	$-0.728442\pi$
$811$	7.46281	−	10.2717i	0.262055	−	0.360687i	0.919687	+	0.392651i	$0.128442\pi$
$812$	0.595921	−	1.10787i	0.0209127	−	0.0388786i
$813$	59.7013	−	59.7013i	2.09382	−	2.09382i
$814$	−20.5177	−	8.72638i	−0.719145	−	0.305860i
$815$	4.60958	−	2.32738i	0.161466	−	0.0815245i
$816$	−0.871110	−	2.68100i	−0.0304950	−	0.0938538i
$817$	2.45267	−	0.388464i	0.0858080	−	0.0135906i
$818$	5.69919	+	0.902662i	0.199267	+	0.0315608i
$819$	15.1004	−	43.1786i	0.527651	−	1.50878i
$820$	−4.94357	+	6.75188i	−0.172637	+	0.235786i
$821$	9.46669	−	6.87795i	0.330390	−	0.240042i	−0.410206	−	0.911993i	$-0.634543\pi$
$821$	9.46669	−	6.87795i	0.330390	−	0.240042i	0.740596	+	0.671951i	$0.234543\pi$
$822$	−2.39324	+	0.379052i	−0.0834738	+	0.0132210i
$823$	−35.9076	−	18.2959i	−1.25166	−	0.637753i	−0.302682	−	0.953092i	$-0.597882\pi$
$823$	−35.9076	−	18.2959i	−1.25166	−	0.637753i	−0.948979	+	0.315338i	$0.897882\pi$
$824$	−17.4540			−0.608038
$825$	−30.6472	−	37.1279i	−1.06700	−	1.29263i
$826$	−0.0581984	+	2.61332i	−0.00202498	+	0.0909290i
$827$	−8.64409	+	16.9650i	−0.300585	+	0.589930i	−0.991059	−	0.133427i	$-0.957402\pi$
$827$	−8.64409	+	16.9650i	−0.300585	+	0.589930i	0.690474	+	0.723357i	$0.257402\pi$
$828$	−42.2467	+	6.69122i	−1.46817	+	0.232536i
$829$	−10.0656	+	7.31305i	−0.349591	+	0.253993i	−0.748697	−	0.662912i	$-0.769320\pi$
$829$	−10.0656	+	7.31305i	−0.349591	+	0.253993i	0.399106	+	0.916905i	$0.369320\pi$
$830$	11.4144	+	8.35738i	0.396200	+	0.290089i
$831$	11.1674	+	3.62849i	0.387391	+	0.125871i
$832$	0.498263	−	3.14591i	0.0172742	−	0.109065i
$833$	−0.763380	−	6.75410i	−0.0264496	−	0.234016i
$834$	−18.3643	+	5.96691i	−0.635902	+	0.206617i
$835$	−41.7924	+	21.1010i	−1.44629	+	0.730231i
$836$	25.6899	−	5.91184i	0.888503	−	0.204465i
$837$	43.1063	+	43.1063i	1.48997	+	1.48997i
$838$	−1.27369	+	2.49977i	−0.0439990	+	0.0863530i
$839$	4.33396	+	3.14880i	0.149625	+	0.108709i	0.660079	−	0.751196i	$-0.270523\pi$
$839$	4.33396	+	3.14880i	0.149625	+	0.108709i	−0.510454	+	0.859905i	$0.670523\pi$
$840$	−15.0957	−	8.19169i	−0.520851	−	0.282640i
$841$	8.89163	−	27.3656i	0.306608	−	0.943643i
$842$	2.27504	−	1.15919i	0.0784029	−	0.0399483i
$843$	−40.7639	−	6.45636i	−1.40398	−	0.222369i
$844$	5.18342	−	7.13436i	0.178421	−	0.245575i
$845$	−6.38394	−	0.0234824i	−0.219614	−	0.000807818i
$846$		−	6.94115i		−	0.238642i
$847$	28.0253	−	7.84758i	0.962960	−	0.269646i
$848$	−5.37221	+	5.37221i	−0.184482	+	0.184482i
$849$	−53.8811	+	17.5070i	−1.84919	+	0.600839i
$850$	−1.46629	−	4.62836i	−0.0502933	−	0.158751i
$851$	−42.8567	+	31.1372i	−1.46911	+	1.06737i
$852$	−14.0470	−	27.5688i	−0.481243	−	0.944493i
$853$	−6.35046	+	3.23572i	−0.217436	+	0.110789i	−0.559316	−	0.828954i	$-0.688936\pi$
$853$	−6.35046	+	3.23572i	−0.217436	+	0.110789i	0.341881	+	0.939743i	$0.388936\pi$
$854$	1.00608	−	0.697274i	0.0344274	−	0.0238602i
$855$	78.2561	−	56.4178i	2.67630	−	1.92945i
$856$	1.83793	+	5.65656i	0.0628191	+	0.193337i
$857$	−20.5398	+	20.5398i	−0.701627	+	0.701627i	−0.964760	−	0.263133i	$-0.915244\pi$
$857$	−20.5398	+	20.5398i	−0.701627	+	0.701627i	0.263133	+	0.964760i	$0.415244\pi$
$858$	25.9966	+	16.2700i	0.887508	+	0.555449i
$859$	−38.4267			−1.31110			−0.655551	−	0.755151i	$-0.727563\pi$
$859$	−38.4267			−1.31110			−0.655551	+	0.755151i	$0.727563\pi$
$860$	0.495803	−	0.492169i	0.0169068	−	0.0167828i
$861$	−22.8732	−	17.4094i	−0.779516	−	0.593311i
$862$	−5.11536	−	0.810193i	−0.174230	−	0.0275953i
$863$	−17.5976	−	34.5373i	−0.599030	−	1.17566i	−0.969102	−	0.246659i	$-0.920667\pi$
$863$	−17.5976	−	34.5373i	−0.599030	−	1.17566i	0.370072	−	0.929003i	$-0.379333\pi$
$864$	2.17829	−	6.70408i	0.0741069	−	0.228078i
$865$	3.96360	+	2.03795i	0.134766	+	0.0692924i
$866$	−19.4632	+	26.7888i	−0.661386	+	0.910320i
$867$	−41.5350	−	21.1631i	−1.41060	−	0.718737i
$868$	15.8150	+	16.5354i	0.536794	+	0.561248i
$869$	−0.317797	−	0.529751i	−0.0107805	−	0.0179706i
$870$	2.93195	+	0.964585i	0.0994023	+	0.0327025i
$871$	23.0711	−	7.49626i	0.781735	−	0.254001i
$872$	1.79179	+	11.3129i	0.0606775	+	0.383103i
$873$	33.9215	+	5.37264i	1.14807	+	0.181836i
$874$	19.3543	−	59.5664i	0.654669	−	2.01486i
$875$	−25.8946	−	14.2993i	−0.875397	−	0.483405i
$876$	−20.4410	+	14.8512i	−0.690637	+	0.501777i
$877$	4.81751	+	30.4166i	0.162676	+	1.02709i	0.925019	+	0.379922i	$0.124049\pi$
$877$	4.81751	+	30.4166i	0.162676	+	1.02709i	−0.762343	+	0.647173i	$0.775951\pi$
$878$	8.34907	−	16.3860i	0.281767	−	0.553000i
$879$			66.6047i			2.24652i
$880$	4.88996	−	5.57568i	0.164841	−	0.187956i
$881$		−	0.829157i		−	0.0279350i	−0.999902	−	0.0139675i	$-0.995554\pi$
$881$		−	0.829157i		−	0.0279350i	0.999902	−	0.0139675i	$-0.00444614\pi$
$882$	18.7402	−	33.0539i	0.631016	−	1.11298i
$883$	−23.3650	+	3.70065i	−0.786293	+	0.124537i	−0.536654	−	0.843802i	$-0.680312\pi$
$883$	−23.3650	+	3.70065i	−0.786293	+	0.124537i	−0.249639	+	0.968339i	$0.580312\pi$
$884$	1.81790	+	2.50213i	0.0611426	+	0.0841556i
$885$	−6.33828	+	0.979999i	−0.213059	+	0.0329423i
$886$	−8.71637	+	26.8262i	−0.292832	+	0.901245i
$887$	−5.59279	+	35.3115i	−0.187787	+	1.18564i	0.696100	+	0.717944i	$0.254917\pi$
$887$	−5.59279	+	35.3115i	−0.187787	+	1.18564i	−0.883888	+	0.467699i	$0.845083\pi$
$888$	−3.05305	−	19.2762i	−0.102454	−	0.646868i
$889$	45.6048	−	13.7031i	1.52954	−	0.459589i
$890$	−8.09736	−	16.0375i	−0.271424	−	0.537579i
$891$	10.4566	+	9.10274i	0.350308	+	0.304953i
$892$	−2.40855	+	2.40855i	−0.0806443	+	0.0806443i
$893$	9.05597	+	4.61425i	0.303046	+	0.154410i
$894$	−38.5989	−	28.0437i	−1.29094	−	0.937922i
$895$	3.29202	+	10.2601i	0.110040	+	0.342956i
$896$	0.873402	−	2.49743i	0.0291783	−	0.0834334i
$897$	64.9227	−	33.0797i	2.16770	−	1.10450i
$898$	4.72150	−	29.8104i	0.157559	−	0.994786i
$899$	−3.32661	−	2.41693i	−0.110949	−	0.0806090i
$900$	8.57655	−	25.7498i	0.285885	−	0.858326i
$901$		−	7.37723i		−	0.245771i
$902$	9.51382	−	7.97159i	0.316776	−	0.265425i
$903$	1.65866	+	1.73422i	0.0551968	+	0.0577113i
$904$	14.6325	−	4.75440i	0.486671	−	0.158129i
$905$	−14.2657	+	10.2847i	−0.474209	+	0.341875i
$906$	9.59736	+	13.2096i	0.318851	+	0.438861i
$907$	−28.1066	+	14.3210i	−0.933264	+	0.475522i	−0.853384	−	0.521283i	$-0.825454\pi$
$907$	−28.1066	+	14.3210i	−0.933264	+	0.475522i	−0.0798800	+	0.996804i	$0.525454\pi$
$908$	−5.60367	+	2.85521i	−0.185964	+	0.0947536i
$909$	34.5673	−	25.1146i	1.14652	−	0.832999i
$910$	18.5287	+	3.42958i	0.614221	+	0.113690i
$911$	8.44199	+	25.9818i	0.279696	+	0.860814i	0.987939	+	0.154846i	$0.0494880\pi$
$911$	8.44199	+	25.9818i	0.279696	+	0.860814i	−0.708243	+	0.705969i	$0.750512\pi$
$912$	16.3163	+	16.3163i	0.540286	+	0.540286i
$913$	−13.4764	−	16.0836i	−0.446003	−	0.532290i
$914$			9.62461i			0.318354i
$915$	2.11590	+	2.13153i	0.0699496	+	0.0704661i
$916$	−11.7419	+	16.1614i	−0.387964	+	0.533987i
$917$	4.42767	−	24.4226i	0.146215	−	0.806507i
$918$	3.10746	+	6.09873i	0.102561	+	0.201288i
$919$	39.3600	+	12.7888i	1.29837	+	0.421865i	0.875013	−	0.484100i	$-0.160853\pi$
$919$	39.3600	+	12.7888i	1.29837	+	0.421865i	0.423353	+	0.905965i	$0.360853\pi$
$920$	−5.38325	−	16.7777i	−0.177480	−	0.553143i
$921$	22.9427	+	16.6688i	0.755987	+	0.549257i
$922$	12.0870	+	6.15862i	0.398063	+	0.202823i
$923$	24.0040	+	24.0040i	0.790101	+	0.790101i
$924$	18.8371	+	17.1502i	0.619694	+	0.564200i
$925$	−5.01385	−	33.2369i	−0.164854	−	1.09282i
$926$	−9.81373	−	30.2036i	−0.322499	−	0.992550i
$927$	93.5756	−	14.8209i	3.07343	−	0.486783i
$928$	−0.0743797	+	0.469615i	−0.00244163	+	0.0154159i
$929$	−7.18647	+	22.1177i	−0.235780	+	0.725657i	0.761237	+	0.648474i	$0.224593\pi$
$929$	−7.18647	+	22.1177i	−0.235780	+	0.725657i	−0.997017	+	0.0771829i	$0.975407\pi$
$930$	−33.1651	+	45.2965i	−1.08753	+	1.48533i
$931$	30.6668	+	46.4231i	1.00506	+	1.52145i
$932$	−2.58835	−	16.3422i	−0.0847841	−	0.535306i
$933$	−31.8127	−	16.2094i	−1.04150	−	0.530671i
$934$	−0.676862			−0.0221476
$935$	0.470823	+	7.18583i	0.0153976	+	0.235002i
$936$			17.2892i			0.565115i
$937$	−42.2742	−	21.5398i	−1.38104	−	0.703674i	−0.403607	−	0.914932i	$-0.632244\pi$
$937$	−42.2742	−	21.5398i	−1.38104	−	0.703674i	−0.977430	+	0.211259i	$0.932244\pi$
$938$	19.9676	−	2.70833i	0.651966	−	0.0884302i
$939$	21.4762	+	29.5595i	0.700850	+	0.964638i
$940$	2.82578	−	0.436910i	0.0921667	−	0.0142504i
$941$	−4.61689	−	1.50012i	−0.150506	−	0.0489025i	0.232795	−	0.972526i	$-0.425213\pi$
$941$	−4.61689	−	1.50012i	−0.150506	−	0.0489025i	−0.383301	+	0.923623i	$0.625213\pi$
$942$	30.9355	+	4.89970i	1.00793	+	0.159641i
$943$	−4.61322	−	29.1267i	−0.150227	−	0.948496i
$944$	−0.305305	−	0.939632i	−0.00993682	−	0.0305824i
$945$	39.3142	+	13.9115i	1.27889	+	0.452541i
$946$	−0.888575	+	0.533055i	−0.0288901	+	0.0173311i
$947$	5.86552	+	5.86552i	0.190604	+	0.190604i	0.795957	−	0.605353i	$-0.206968\pi$
$947$	5.86552	+	5.86552i	0.190604	+	0.190604i	−0.605353	+	0.795957i	$0.706968\pi$
$948$	0.245492	−	0.481805i	0.00797320	−	0.0156483i
$949$	16.2938	−	22.4266i	0.528921	−	0.727997i
$950$	27.8938	+	28.3072i	0.904994	+	0.918408i
$951$	66.2839	+	21.5369i	2.14940	+	0.698383i
$952$	1.11508	+	2.31445i	0.0361398	+	0.0750118i
$953$	2.25408	−	14.2317i	0.0730167	−	0.461009i	−0.923906	−	0.382619i	$-0.875022\pi$
$953$	2.25408	−	14.2317i	0.0730167	−	0.461009i	0.996923	−	0.0783898i	$-0.0249779\pi$
$954$	24.2401	−	33.3637i	0.784803	−	1.08019i
$955$	−0.151231	+	41.1137i	−0.00489371	+	1.33041i
$956$	8.11107			0.262331
$957$	−3.88072	−	2.42876i	−0.125446	−	0.0785106i
$958$	0.0766146	+	0.0766146i	0.00247531	+	0.00247531i
$959$	2.11485	−	0.635462i	0.0682922	−	0.0205201i
$960$	6.40787	+	1.03908i	0.206813	+	0.0335363i
$961$	35.4271	−	25.7393i	1.14281	−	0.830299i
$962$	9.72097	+	19.0785i	0.313417	+	0.615115i
$963$	−14.6569	−	28.7657i	−0.472311	−	0.926963i
$964$	−19.9813	+	14.5173i	−0.643554	+	0.467569i
$965$	−44.3601	−	7.19332i	−1.42800	−	0.231561i
$966$	57.9653	−	17.4172i	1.86500	−	0.560388i
$967$	−35.5571	−	35.5571i	−1.14344	−	1.14344i	−0.987816	−	0.155623i	$-0.950261\pi$
$967$	−35.5571	−	35.5571i	−1.14344	−	1.14344i	−0.155623	−	0.987816i	$-0.549739\pi$
$968$	−9.01959	+	6.29659i	−0.289901	+	0.202380i
$969$	−22.4059			−0.719780
$970$	−0.0520406	+	14.1478i	−0.00167092	+	0.454259i
$971$	−24.7869	+	34.1162i	−0.795448	+	1.09484i	0.197960	+	0.980210i	$0.436568\pi$
$971$	−24.7869	+	34.1162i	−0.795448	+	1.09484i	−0.993408	+	0.114630i	$0.963432\pi$
$972$	1.40981	−	8.90117i	0.0452196	−	0.285505i
$973$	15.8535	−	7.63802i	0.508239	−	0.244864i
$974$	11.0633	+	3.59467i	0.354490	+	0.115181i
$975$	−0.340125	+	46.2327i	−0.0108927	+	1.48063i
$976$	−0.271946	+	0.374301i	−0.00870478	+	0.0119811i
$977$	11.3615	−	22.2981i	0.363486	−	0.713381i	−0.634753	−	0.772715i	$-0.718898\pi$
$977$	11.3615	−	22.2981i	0.363486	−	0.713381i	0.998238	+	0.0593348i	$0.0188980\pi$
$978$	−4.74062	−	4.74062i	−0.151588	−	0.151588i
$979$	5.97603	+	25.9688i	0.190995	+	0.829967i
$980$	14.6360	+	5.54867i	0.467530	+	0.177246i
$981$	−19.2125	−	59.1301i	−0.613409	−	1.88788i
$982$	4.91438	+	31.0282i	0.156824	+	0.990149i
$983$	−10.9526	−	1.73472i	−0.349333	−	0.0553290i	−0.0206978	−	0.999786i	$-0.506589\pi$
$983$	−10.9526	−	1.73472i	−0.349333	−	0.0553290i	−0.328636	+	0.944457i	$0.606589\pi$
$984$	10.3328	+	3.35733i	0.329398	+	0.107028i
$985$	41.5824	−	6.42931i	1.32493	−	0.204855i
$986$	−0.271373	−	0.373513i	−0.00864227	−	0.0118951i
$987$	1.32012	+	9.73282i	0.0420199	+	0.309799i
$988$	−22.5568	−	11.4933i	−0.717628	−	0.365650i
$989$			2.46191i			0.0782842i
$990$	−21.4819	+	34.0451i	−0.682740	+	1.08202i
$991$	6.62327			0.210395			0.105198	−	0.994451i	$-0.466452\pi$
$991$	6.62327			0.210395			0.105198	+	0.994451i	$0.466452\pi$
$992$	−7.70555	−	3.92617i	−0.244651	−	0.124656i
$993$	−10.7290	−	67.7403i	−0.340475	−	2.14967i
$994$	16.0625	+	23.1762i	0.509470	+	0.735104i
$995$	30.6510	−	41.8628i	0.971703	−	1.32714i
$996$	5.67575	−	17.4682i	0.179843	−	0.553500i
$997$	7.19335	−	45.4170i	0.227816	−	1.43837i	−0.563071	−	0.826408i	$-0.690380\pi$
$997$	7.19335	−	45.4170i	0.227816	−	1.43837i	0.790887	−	0.611962i	$-0.209620\pi$
$998$	−13.7561	+	2.17875i	−0.435441	+	0.0689671i
$999$	14.6438	+	45.0688i	0.463308	+	1.42592i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.bi.a.27.1	✓	384
5.3	odd	4	inner	770.2.bi.a.643.48	yes	384
7.6	odd	2	inner	770.2.bi.a.27.24	yes	384
11.9	even	5	inner	770.2.bi.a.97.25	yes	384
35.13	even	4	inner	770.2.bi.a.643.25	yes	384
55.53	odd	20	inner	770.2.bi.a.713.24	yes	384
77.20	odd	10	inner	770.2.bi.a.97.48	yes	384
385.328	even	20	inner	770.2.bi.a.713.1	yes	384

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.bi.a.27.1	✓	384	1.1	even	1	trivial
770.2.bi.a.27.24	yes	384	7.6	odd	2	inner
770.2.bi.a.97.25	yes	384	11.9	even	5	inner
770.2.bi.a.97.48	yes	384	77.20	odd	10	inner
770.2.bi.a.643.25	yes	384	35.13	even	4	inner
770.2.bi.a.643.48	yes	384	5.3	odd	4	inner
770.2.bi.a.713.1	yes	384	385.328	even	20	inner
770.2.bi.a.713.24	yes	384	55.53	odd	20	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.bi (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.453990 + 0.891007i) q^{2} +(-0.454148 - 2.86738i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(-1.32097 + 1.80417i) q^{5} +(2.76103 + 0.897114i) q^{6} +(-2.60332 - 0.471965i) q^{7} +(0.987688 - 0.156434i) q^{8} +(-5.16244 + 1.67738i) q^{9} +O(q^{10})\)	\(q+(-0.453990 + 0.891007i) q^{2} +(-0.454148 - 2.86738i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(-1.32097 + 1.80417i) q^{5} +(2.76103 + 0.897114i) q^{6} +(-2.60332 - 0.471965i) q^{7} +(0.987688 - 0.156434i) q^{8} +(-5.16244 + 1.67738i) q^{9} +(-1.00782 - 1.99607i) q^{10} +(0.743793 + 3.23215i) q^{11} +(-2.05282 + 2.05282i) q^{12} +(1.44601 - 2.83796i) q^{13} +(1.60240 - 2.10530i) q^{14} +(5.77316 + 2.96837i) q^{15} +(-0.309017 + 0.951057i) q^{16} +(-0.440831 - 0.865180i) q^{17} +(0.849143 - 5.36128i) q^{18} +(6.43026 + 4.67186i) q^{19} +(2.23605 + 0.00822499i) q^{20} +(-0.171011 + 7.67903i) q^{21} +(-3.21754 - 0.804640i) q^{22} +(-5.57198 + 5.57198i) q^{23} +(-0.897114 - 2.76103i) q^{24} +(-1.51006 - 4.76652i) q^{25} +(1.87217 + 2.57682i) q^{26} +(3.20022 + 6.28079i) q^{27} +(1.14836 + 2.38354i) q^{28} +(-0.279474 - 0.384662i) q^{29} +(-5.26579 + 3.79631i) q^{30} +(8.22487 - 2.67242i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(8.93000 - 3.60061i) q^{33} +0.971014 q^{34} +(4.29041 - 4.07337i) q^{35} +(4.39143 + 3.19056i) q^{36} +(6.63983 + 1.05165i) q^{37} +(-7.08193 + 3.60842i) q^{38} +(-8.79422 - 2.85742i) q^{39} +(-1.02248 + 1.98860i) q^{40} +(-2.19971 + 3.02764i) q^{41} +(-6.76443 - 3.63858i) q^{42} +(0.220919 - 0.220919i) q^{43} +(2.17767 - 2.50155i) q^{44} +(3.79317 - 11.5297i) q^{45} +(-2.43504 - 7.49429i) q^{46} +(1.26300 - 0.200039i) q^{47} +(2.86738 + 0.454148i) q^{48} +(6.55450 + 2.45735i) q^{49} +(4.93255 + 0.818481i) q^{50} +(-2.28060 + 1.65695i) q^{51} +(-3.14591 + 0.498263i) q^{52} +(6.76938 + 3.44917i) q^{53} -7.04909 q^{54} +(-6.81387 - 2.92765i) q^{55} +(-2.64510 - 0.0589060i) q^{56} +(10.4757 - 20.5597i) q^{57} +(0.469615 - 0.0743797i) q^{58} +(-0.799298 + 0.580724i) q^{59} +(-0.991915 - 6.41534i) q^{60} +(0.440018 + 0.142970i) q^{61} +(-1.35287 + 8.54166i) q^{62} +(14.2311 - 1.93025i) q^{63} +(0.951057 - 0.309017i) q^{64} +(3.21002 + 6.35773i) q^{65} +(-0.845968 + 9.59133i) q^{66} +(5.38544 + 5.38544i) q^{67} +(-0.440831 + 0.865180i) q^{68} +(18.5075 + 13.4465i) q^{69} +(1.68159 + 5.67206i) q^{70} +(-3.29348 + 10.1363i) q^{71} +(-4.83648 + 2.46431i) q^{72} +(8.59605 + 1.36148i) q^{73} +(-3.95144 + 5.43869i) q^{74} +(-12.9816 + 6.49462i) q^{75} -7.94824i q^{76} +(-0.410867 - 8.76534i) q^{77} +(6.53847 - 6.53847i) q^{78} +(-0.177146 + 0.0575582i) q^{79} +(-1.30766 - 1.81384i) q^{80} +(3.38172 - 2.45696i) q^{81} +(-1.69900 - 3.33448i) q^{82} +(-5.63712 + 2.87225i) q^{83} +(6.31298 - 4.37527i) q^{84} +(2.14326 + 0.347545i) q^{85} +(0.0965451 + 0.297135i) q^{86} +(-0.976050 + 0.976050i) q^{87} +(1.24025 + 3.07600i) q^{88} +8.03454 q^{89} +(8.55097 + 8.61410i) q^{90} +(-5.10385 + 6.70565i) q^{91} +(7.78295 + 1.23270i) q^{92} +(-11.3981 - 22.3701i) q^{93} +(-0.395153 + 1.21616i) q^{94} +(-16.9230 + 5.42989i) q^{95} +(-1.70641 + 2.34867i) q^{96} +(-5.63752 - 2.87246i) q^{97} +(-5.16519 + 4.72449i) q^{98} +(-9.26131 - 15.4381i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 384 q - 4 q^{7}+O(q^{10}) \) 384 * q - 4 * q^7	\( 384 q - 4 q^{7} + 24 q^{15} + 96 q^{16} + 16 q^{22} + 16 q^{23} - 40 q^{25} + 4 q^{28} + 16 q^{30} - 32 q^{35} + 80 q^{36} - 64 q^{37} + 44 q^{42} - 80 q^{43} - 16 q^{46} - 64 q^{50} - 136 q^{51} + 80 q^{53} + 8 q^{56} - 112 q^{57} - 96 q^{58} + 68 q^{63} - 272 q^{65} + 160 q^{67} - 8 q^{70} + 16 q^{71} + 96 q^{77} + 24 q^{81} - 80 q^{85} - 16 q^{88} - 84 q^{91} + 16 q^{92} + 88 q^{93} - 184 q^{95} - 32 q^{98}+O(q^{100}) \) 384 * q - 4 * q^7 + 24 * q^15 + 96 * q^16 + 16 * q^22 + 16 * q^23 - 40 * q^25 + 4 * q^28 + 16 * q^30 - 32 * q^35 + 80 * q^36 - 64 * q^37 + 44 * q^42 - 80 * q^43 - 16 * q^46 - 64 * q^50 - 136 * q^51 + 80 * q^53 + 8 * q^56 - 112 * q^57 - 96 * q^58 + 68 * q^63 - 272 * q^65 + 160 * q^67 - 8 * q^70 + 16 * q^71 + 96 * q^77 + 24 * q^81 - 80 * q^85 - 16 * q^88 - 84 * q^91 + 16 * q^92 + 88 * q^93 - 184 * q^95 - 32 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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