LMFDB - Embedded newform 280.2.w.a.43.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [280,2,Mod(43,280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(280, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("280.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 280 = 2^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	280.w (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:	$2.23581125660$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.8
Character	$\chi$	$=$	280.43
Dual form			280.2.w.a.267.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.15591 + 0.814786i) q^{2} +(-0.824980 - 0.824980i) q^{3} +(0.672247 - 1.88364i) q^{4} +(1.57833 - 1.58394i) q^{5} +(1.62578 + 0.281419i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(0.757704 + 2.72505i) q^{8} -1.63882i q^{9} +O(q^{10})$	\(q+(-1.15591 + 0.814786i) q^{2} +(-0.824980 - 0.824980i) q^{3} +(0.672247 - 1.88364i) q^{4} +(1.57833 - 1.58394i) q^{5} +(1.62578 + 0.281419i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(0.757704 + 2.72505i) q^{8} -1.63882i q^{9} +(-0.533826 + 3.11689i) q^{10} -3.75635 q^{11} +(-2.10855 + 0.999371i) q^{12} +(-4.02663 + 4.02663i) q^{13} +(1.39349 + 0.241210i) q^{14} +(-2.60881 + 0.00463396i) q^{15} +(-3.09617 - 2.53254i) q^{16} +(3.23613 - 3.23613i) q^{17} +(1.33529 + 1.89432i) q^{18} -7.11626i q^{19} +(-1.92255 - 4.03780i) q^{20} +1.16670i q^{21} +(4.34199 - 3.06062i) q^{22} +(-2.28956 + 2.28956i) q^{23} +(1.62302 - 2.87320i) q^{24} +(-0.0177627 - 4.99997i) q^{25} +(1.37357 - 7.93526i) q^{26} +(-3.82693 + 3.82693i) q^{27} +(-1.80728 + 0.856581i) q^{28} +3.96189 q^{29} +(3.01177 - 2.13098i) q^{30} -1.00933i q^{31} +(5.64236 + 0.404668i) q^{32} +(3.09891 + 3.09891i) q^{33} +(-1.10391 + 6.37741i) q^{34} +(-2.23606 + 0.00397187i) q^{35} +(-3.08693 - 1.10169i) q^{36} +(-7.48107 - 7.48107i) q^{37} +(5.79823 + 8.22574i) q^{38} +6.64377 q^{39} +(5.51223 + 3.10086i) q^{40} +4.39471 q^{41} +(-0.950609 - 1.34860i) q^{42} +(-4.93667 - 4.93667i) q^{43} +(-2.52519 + 7.07559i) q^{44} +(-2.59580 - 2.58659i) q^{45} +(0.781021 - 4.51203i) q^{46} +(4.78656 + 4.78656i) q^{47} +(0.464982 + 4.64357i) q^{48} +1.00000i q^{49} +(4.09444 + 5.76503i) q^{50} -5.33947 q^{51} +(4.87781 + 10.2916i) q^{52} +(6.78875 - 6.78875i) q^{53} +(1.30545 - 7.54171i) q^{54} +(-5.92875 + 5.94985i) q^{55} +(1.39112 - 2.46268i) q^{56} +(-5.87077 + 5.87077i) q^{57} +(-4.57959 + 3.22810i) q^{58} -0.808549i q^{59} +(-1.74504 + 4.91716i) q^{60} +12.9452i q^{61} +(0.822392 + 1.16670i) q^{62} +(-1.15882 + 1.15882i) q^{63} +(-6.85177 + 4.12956i) q^{64} +(0.0226178 + 12.7333i) q^{65} +(-6.10700 - 1.05711i) q^{66} +(-1.01005 + 1.01005i) q^{67} +(-3.92020 - 8.27116i) q^{68} +3.77769 q^{69} +(2.58145 - 1.82651i) q^{70} -4.28172i q^{71} +(4.46586 - 1.24174i) q^{72} +(2.38810 + 2.38810i) q^{73} +(14.7429 + 2.55196i) q^{74} +(-4.11022 + 4.13953i) q^{75} +(-13.4044 - 4.78389i) q^{76} +(2.65614 + 2.65614i) q^{77} +(-7.67959 + 5.41326i) q^{78} +11.6388 q^{79} +(-8.89817 + 0.906982i) q^{80} +1.39783 q^{81} +(-5.07988 + 3.58074i) q^{82} +(5.74036 + 5.74036i) q^{83} +(2.19763 + 0.784309i) q^{84} +(-0.0181775 - 10.2335i) q^{85} +(9.72866 + 1.68401i) q^{86} +(-3.26848 - 3.26848i) q^{87} +(-2.84620 - 10.2362i) q^{88} -4.29776i q^{89} +(5.10802 + 0.874843i) q^{90} +5.69451 q^{91} +(2.77355 + 5.85186i) q^{92} +(-0.832681 + 0.832681i) q^{93} +(-9.43285 - 1.63280i) q^{94} +(-11.2718 - 11.2318i) q^{95} +(-4.32099 - 4.98868i) q^{96} +(5.24195 - 5.24195i) q^{97} +(-0.814786 - 1.15591i) q^{98} +6.15597i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 8 q^{6}+O(q^{10}) $ 72 * q + 8 * q^6	$ 72 q + 8 q^{6} + 16 q^{10} - 16 q^{12} - 8 q^{16} + 8 q^{17} - 28 q^{18} - 20 q^{20} - 36 q^{22} - 8 q^{25} - 32 q^{26} - 4 q^{30} + 40 q^{32} + 64 q^{36} - 4 q^{40} + 20 q^{42} - 64 q^{43} + 48 q^{46} - 80 q^{48} - 32 q^{51} + 16 q^{52} - 24 q^{56} + 4 q^{58} - 80 q^{60} - 40 q^{62} - 8 q^{65} + 32 q^{66} - 24 q^{68} + 40 q^{72} - 40 q^{73} + 112 q^{75} - 8 q^{76} + 28 q^{78} - 20 q^{80} - 72 q^{81} + 24 q^{82} + 80 q^{83} + 8 q^{86} - 88 q^{88} + 136 q^{90} - 96 q^{92} - 56 q^{96} - 8 q^{97}+O(q^{100}) $ 72 * q + 8 * q^6 + 16 * q^10 - 16 * q^12 - 8 * q^16 + 8 * q^17 - 28 * q^18 - 20 * q^20 - 36 * q^22 - 8 * q^25 - 32 * q^26 - 4 * q^30 + 40 * q^32 + 64 * q^36 - 4 * q^40 + 20 * q^42 - 64 * q^43 + 48 * q^46 - 80 * q^48 - 32 * q^51 + 16 * q^52 - 24 * q^56 + 4 * q^58 - 80 * q^60 - 40 * q^62 - 8 * q^65 + 32 * q^66 - 24 * q^68 + 40 * q^72 - 40 * q^73 + 112 * q^75 - 8 * q^76 + 28 * q^78 - 20 * q^80 - 72 * q^81 + 24 * q^82 + 80 * q^83 + 8 * q^86 - 88 * q^88 + 136 * q^90 - 96 * q^92 - 56 * q^96 - 8 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/280\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$141$	$241$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.15591	+	0.814786i	−0.817351	+	0.576141i
$2$	−1.15591	+	0.814786i	−0.817351	+	0.576141i
$3$	−0.824980	−	0.824980i	−0.476302	−	0.476302i	0.427645	−	0.903947i	$-0.359343\pi$
$3$	−0.824980	−	0.824980i	−0.476302	−	0.476302i	−0.903947	+	0.427645i	$0.859343\pi$
$4$	0.672247	−	1.88364i	0.336124	−	0.941818i
$5$	1.57833	−	1.58394i	0.705850	−	0.708362i
$5$	1.57833	−	1.58394i	0.705850	−	0.708362i
$6$	1.62578	+	0.281419i	0.663723	+	0.114889i
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$8$	0.757704	+	2.72505i	0.267889	+	0.963450i
$9$		−	1.63882i		−	0.546272i
$10$	−0.533826	+	3.11689i	−0.168811	+	0.985649i
$11$	−3.75635			−1.13258			−0.566291	−	0.824206i	$-0.691622\pi$
$11$	−3.75635			−1.13258			−0.566291	+	0.824206i	$0.691622\pi$
$12$	−2.10855	+	0.999371i	−0.608686	+	0.288493i
$13$	−4.02663	+	4.02663i	−1.11679	+	1.11679i	−0.124576	+	0.992210i	$0.539757\pi$
$13$	−4.02663	+	4.02663i	−1.11679	+	1.11679i	−0.992210	+	0.124576i	$0.960243\pi$
$14$	1.39349	+	0.241210i	0.372426	+	0.0644660i
$15$	−2.60881	+	0.00463396i	−0.673592	+	0.00119648i
$16$	−3.09617	−	2.53254i	−0.774042	−	0.633135i
$17$	3.23613	−	3.23613i	0.784876	−	0.784876i	−0.195773	−	0.980649i	$-0.562722\pi$
$17$	3.23613	−	3.23613i	0.784876	−	0.784876i	0.980649	+	0.195773i	$0.0627217\pi$
$18$	1.33529	+	1.89432i	0.314730	+	0.446496i
$19$		−	7.11626i		−	1.63258i	−0.577641	−	0.816291i	$-0.696027\pi$
$19$		−	7.11626i		−	1.63258i	0.577641	−	0.816291i	$-0.303973\pi$
$20$	−1.92255	−	4.03780i	−0.429895	−	0.902879i
$21$			1.16670i			0.254594i
$22$	4.34199	−	3.06062i	0.925716	−	0.652526i
$23$	−2.28956	+	2.28956i	−0.477407	+	0.477407i	−0.904302	−	0.426894i	$-0.859608\pi$
$23$	−2.28956	+	2.28956i	−0.477407	+	0.477407i	0.426894	+	0.904302i	$0.359608\pi$
$24$	1.62302	−	2.87320i	0.331297	−	0.586489i
$25$	−0.0177627	−	4.99997i	−0.00355254	−	0.999994i
$26$	1.37357	−	7.93526i	0.269380	−	1.55623i
$27$	−3.82693	+	3.82693i	−0.736493	+	0.736493i
$28$	−1.80728	+	0.856581i	−0.341544	+	0.161879i
$29$	3.96189			0.735705			0.367853	−	0.929884i	$-0.380093\pi$
$29$	3.96189			0.735705			0.367853	+	0.929884i	$0.380093\pi$
$30$	3.01177	−	2.13098i	0.549871	−	0.389062i
$31$		−	1.00933i		−	0.181282i	−0.995884	−	0.0906409i	$-0.971108\pi$
$31$		−	1.00933i		−	0.181282i	0.995884	−	0.0906409i	$-0.0288916\pi$
$32$	5.64236	+	0.404668i	0.997438	+	0.0715359i
$33$	3.09891	+	3.09891i	0.539451	+	0.539451i
$34$	−1.10391	+	6.37741i	−0.189320	+	1.09372i
$35$	−2.23606	+	0.00397187i	−0.377964	+	0.000671368i
$36$	−3.08693	−	1.10169i	−0.514489	−	0.183615i
$37$	−7.48107	−	7.48107i	−1.22988	−	1.22988i	−0.964009	−	0.265871i	$-0.914340\pi$
$37$	−7.48107	−	7.48107i	−1.22988	−	1.22988i	−0.265871	−	0.964009i	$-0.585660\pi$
$38$	5.79823	+	8.22574i	0.940597	+	1.33439i
$39$	6.64377			1.06386
$40$	5.51223	+	3.10086i	0.871560	+	0.490289i
$41$	4.39471			0.686338			0.343169	−	0.939274i	$-0.388500\pi$
$41$	4.39471			0.686338			0.343169	+	0.939274i	$0.388500\pi$
$42$	−0.950609	−	1.34860i	−0.146682	−	0.208093i
$43$	−4.93667	−	4.93667i	−0.752835	−	0.752835i	0.222173	−	0.975007i	$-0.428685\pi$
$43$	−4.93667	−	4.93667i	−0.752835	−	0.752835i	−0.975007	+	0.222173i	$0.928685\pi$
$44$	−2.52519	+	7.07559i	−0.380687	+	1.06669i
$45$	−2.59580	−	2.58659i	−0.386958	−	0.385586i
$46$	0.781021	−	4.51203i	0.115155	−	0.665263i
$47$	4.78656	+	4.78656i	0.698192	+	0.698192i	0.964020	−	0.265829i	$-0.0856455\pi$
$47$	4.78656	+	4.78656i	0.698192	+	0.698192i	−0.265829	+	0.964020i	$0.585646\pi$
$48$	0.464982	+	4.64357i	0.0671144	+	0.670241i
$49$			1.00000i			0.142857i
$50$	4.09444	+	5.76503i	0.579041	+	0.815299i
$51$	−5.33947			−0.747676
$52$	4.87781	+	10.2916i	0.676431	+	1.42719i
$53$	6.78875	−	6.78875i	0.932506	−	0.932506i	−0.0653560	−	0.997862i	$-0.520818\pi$
$53$	6.78875	−	6.78875i	0.932506	−	0.932506i	0.997862	+	0.0653560i	$0.0208183\pi$
$54$	1.30545	−	7.54171i	0.177649	−	1.02630i
$55$	−5.92875	+	5.94985i	−0.799432	+	0.802277i
$56$	1.39112	−	2.46268i	0.185897	−	0.329089i
$57$	−5.87077	+	5.87077i	−0.777602	+	0.777602i
$58$	−4.57959	+	3.22810i	−0.601329	+	0.423870i
$59$		−	0.808549i		−	0.105264i	−0.998614	−	0.0526320i	$-0.983239\pi$
$59$		−	0.808549i		−	0.105264i	0.998614	−	0.0526320i	$-0.0167610\pi$
$60$	−1.74504	+	4.91716i	−0.225283	+	0.634803i
$61$			12.9452i			1.65746i	0.559648	+	0.828731i	$0.310936\pi$
$61$			12.9452i			1.65746i	−0.559648	+	0.828731i	$0.689064\pi$
$62$	0.822392	+	1.16670i	0.104444	+	0.148171i
$63$	−1.15882	+	1.15882i	−0.145997	+	0.145997i
$64$	−6.85177	+	4.12956i	−0.856471	+	0.516195i
$65$	0.0226178	+	12.7333i	0.00280540	+	1.57937i
$66$	−6.10700	−	1.05711i	−0.751720	−	0.130121i
$67$	−1.01005	+	1.01005i	−0.123397	+	0.123397i	−0.766108	−	0.642711i	$-0.777809\pi$
$67$	−1.01005	+	1.01005i	−0.123397	+	0.123397i	0.642711	+	0.766108i	$0.277809\pi$
$68$	−3.92020	−	8.27116i	−0.475395	−	1.00303i
$69$	3.77769			0.454780
$70$	2.58145	−	1.82651i	0.308542	−	0.218309i
$71$		−	4.28172i		−	0.508147i	−0.967185	−	0.254073i	$-0.918230\pi$
$71$		−	4.28172i		−	0.508147i	0.967185	−	0.254073i	$-0.0817705\pi$
$72$	4.46586	−	1.24174i	0.526306	−	0.146340i
$73$	2.38810	+	2.38810i	0.279506	+	0.279506i	0.832912	−	0.553406i	$-0.186672\pi$
$73$	2.38810	+	2.38810i	0.279506	+	0.279506i	−0.553406	+	0.832912i	$0.686672\pi$
$74$	14.7429	+	2.55196i	1.71383	+	0.296659i
$75$	−4.11022	+	4.13953i	−0.474607	+	0.477991i
$76$	−13.4044	−	4.78389i	−1.53759	−	0.548750i
$77$	2.65614	+	2.65614i	0.302695	+	0.302695i
$78$	−7.67959	+	5.41326i	−0.869543	+	0.612930i
$79$	11.6388			1.30947			0.654735	−	0.755858i	$-0.272780\pi$
$79$	11.6388			1.30947			0.654735	+	0.755858i	$0.272780\pi$
$80$	−8.89817	+	0.906982i	−0.994845	+	0.101404i
$81$	1.39783			0.155314
$82$	−5.07988	+	3.58074i	−0.560978	+	0.395427i
$83$	5.74036	+	5.74036i	0.630086	+	0.630086i	0.948090	−	0.318003i	$-0.103012\pi$
$83$	5.74036	+	5.74036i	0.630086	+	0.630086i	−0.318003	+	0.948090i	$0.603012\pi$
$84$	2.19763	+	0.784309i	0.239781	+	0.0855752i
$85$	−0.0181775	−	10.2335i	−0.00197163	−	1.10998i
$86$	9.72866	+	1.68401i	1.04907	+	0.181591i
$87$	−3.26848	−	3.26848i	−0.350418	−	0.350418i
$88$	−2.84620	−	10.2362i	−0.303406	−	1.09119i
$89$		−	4.29776i		−	0.455562i	−0.973712	−	0.227781i	$-0.926853\pi$
$89$		−	4.29776i		−	0.455562i	0.973712	−	0.227781i	$-0.0731470\pi$
$90$	5.10802	+	0.874843i	0.538433	+	0.0922165i
$91$	5.69451			0.596947
$92$	2.77355	+	5.85186i	0.289163	+	0.610099i
$93$	−0.832681	+	0.832681i	−0.0863450	+	0.0863450i
$94$	−9.43285	−	1.63280i	−0.972924	−	0.168411i
$95$	−11.2718	−	11.2318i	−1.15646	−	1.15236i
$96$	−4.32099	−	4.98868i	−0.441009	−	0.509155i
$97$	5.24195	−	5.24195i	0.532240	−	0.532240i	−0.388999	−	0.921238i	$-0.627179\pi$
$97$	5.24195	−	5.24195i	0.532240	−	0.532240i	0.921238	+	0.388999i	$0.127179\pi$
$98$	−0.814786	−	1.15591i	−0.0823058	−	0.116764i
$99$			6.15597i			0.618698i
$100$	−9.43006	−	3.32776i	−0.943006	−	0.332776i
$101$			8.34945i			0.830802i	0.909638	+	0.415401i	$0.136359\pi$
$101$			8.34945i			0.830802i	−0.909638	+	0.415401i	$0.863641\pi$
$102$	6.17194	−	4.35053i	0.611113	−	0.430767i
$103$	2.91602	−	2.91602i	0.287324	−	0.287324i	−0.548697	−	0.836021i	$-0.684876\pi$
$103$	2.91602	−	2.91602i	0.287324	−	0.287324i	0.836021	+	0.548697i	$0.184876\pi$
$104$	−14.0238	−	7.92177i	−1.37514	−	0.776793i
$105$	1.84798	+	1.84143i	0.180345	+	0.179705i
$106$	−2.31579	+	13.3785i	−0.224930	+	1.29944i
$107$	11.2885	−	11.2885i	1.09130	−	1.09130i	0.0959101	−	0.995390i	$-0.469424\pi$
$107$	11.2885	−	11.2885i	1.09130	−	1.09130i	0.995390	−	0.0959101i	$-0.0305761\pi$
$108$	4.63590	+	9.78119i	0.446089	+	0.941195i
$109$	6.90449			0.661330			0.330665	−	0.943748i	$-0.392727\pi$
$109$	6.90449			0.661330			0.330665	+	0.943748i	$0.392727\pi$
$110$	2.00524	−	11.7081i	0.191192	−	1.11633i
$111$			12.3435i			1.17159i
$112$	0.398546	+	3.98010i	0.0376590	+	0.376084i
$113$	5.32400	+	5.32400i	0.500840	+	0.500840i	0.911699	−	0.410859i	$-0.134771\pi$
$113$	5.32400	+	5.32400i	0.500840	+	0.500840i	−0.410859	+	0.911699i	$0.634771\pi$
$114$	2.00265	−	11.5695i	0.187565	−	1.08358i
$115$	0.0128606	+	7.24023i	0.00119926	+	0.675155i
$116$	2.66337	−	7.46277i	0.247288	−	0.692900i
$117$	6.59891	+	6.59891i	0.610069	+	0.610069i
$118$	0.658794	+	0.934608i	0.0606469	+	0.0860377i
$119$	−4.57657			−0.419534
$120$	−1.98933	−	7.10562i	−0.181600	−	0.648652i
$121$	3.11015			0.282741
$122$	−10.5476	−	14.9634i	−0.954931	−	1.35473i
$123$	−3.62554	−	3.62554i	−0.326904	−	0.326904i
$124$	−1.90122	−	0.678523i	−0.170734	−	0.0609331i
$125$	−7.94771	−	7.86345i	−0.710865	−	0.703329i
$126$	0.395299	−	2.28368i	0.0352160	−	0.203446i
$127$	−3.01644	−	3.01644i	−0.267666	−	0.267666i	0.560493	−	0.828159i	$-0.310612\pi$
$127$	−3.01644	−	3.01644i	−0.267666	−	0.267666i	−0.828159	+	0.560493i	$0.810612\pi$
$128$	4.55531	−	10.3561i	0.402636	−	0.915360i
$129$			8.14530i			0.717154i
$130$	−10.4011	−	14.7001i	−0.912233	−	1.28928i
$131$	12.7308			1.11230			0.556149	−	0.831082i	$-0.312278\pi$
$131$	12.7308			1.11230			0.556149	+	0.831082i	$0.312278\pi$
$132$	7.92045	−	3.75398i	0.689387	−	0.326742i
$133$	−5.03196	+	5.03196i	−0.436326	+	0.436326i
$134$	0.344550	−	1.99050i	0.0297646	−	0.171953i
$135$	0.0214961	+	12.1018i	0.00185009	+	1.04156i
$136$	11.2706	+	6.36657i	0.966448	+	0.545929i
$137$	−2.41432	+	2.41432i	−0.206269	+	0.206269i	−0.802680	−	0.596410i	$-0.796593\pi$
$137$	−2.41432	+	2.41432i	−0.206269	+	0.206269i	0.596410	+	0.802680i	$0.296593\pi$
$138$	−4.36666	+	3.07801i	−0.371715	+	0.262017i
$139$			5.10599i			0.433085i	0.976273	+	0.216542i	$0.0694780\pi$
$139$			5.10599i			0.433085i	−0.976273	+	0.216542i	$0.930522\pi$
$140$	−1.49571	+	4.21460i	−0.126410	+	0.356199i
$141$		−	7.89763i		−	0.665101i
$142$	3.48869	+	4.94927i	0.292764	+	0.415334i
$143$	15.1254	−	15.1254i	1.26485	−	1.26485i
$144$	−4.15037	+	5.07405i	−0.345864	+	0.422838i
$145$	6.25317	−	6.27542i	0.519297	−	0.521145i
$146$	−4.70621	−	0.814633i	−0.389489	−	0.0674195i
$147$	0.824980	−	0.824980i	0.0680432	−	0.0680432i
$148$	−19.1207	+	9.06248i	−1.57171	+	0.744931i
$149$	−6.93629			−0.568243			−0.284121	−	0.958788i	$-0.591702\pi$
$149$	−6.93629			−0.568243			−0.284121	+	0.958788i	$0.591702\pi$
$150$	1.37821	−	8.13386i	0.112530	−	0.664127i
$151$		−	18.1459i		−	1.47669i	−0.674423	−	0.738345i	$-0.735607\pi$
$151$		−	18.1459i		−	1.47669i	0.674423	−	0.738345i	$-0.264393\pi$
$152$	19.3921	−	5.39202i	1.57291	−	0.437350i
$153$	−5.30342	−	5.30342i	−0.428756	−	0.428756i
$154$	−5.23444	−	0.906068i	−0.421803	−	0.0730130i
$155$	−1.59873	−	1.59306i	−0.128413	−	0.127958i
$156$	4.46626	−	12.5145i	0.357587	−	1.00196i
$157$	−8.76090	−	8.76090i	−0.699196	−	0.699196i	0.265041	−	0.964237i	$-0.414614\pi$
$157$	−8.76090	−	8.76090i	−0.699196	−	0.699196i	−0.964237	+	0.265041i	$0.914614\pi$
$158$	−13.4534	+	9.48315i	−1.07030	+	0.754439i
$159$	−11.2012			−0.888309
$160$	9.54647	−	8.29849i	0.754715	−	0.656053i
$161$	3.23793			0.255185
$162$	−1.61576	+	1.13893i	−0.126946	+	0.0894828i
$163$	2.05771	+	2.05771i	0.161172	+	0.161172i	0.783086	−	0.621914i	$-0.213645\pi$
$163$	2.05771	+	2.05771i	0.161172	+	0.161172i	−0.621914	+	0.783086i	$0.713645\pi$
$164$	2.95433	−	8.27802i	0.230694	−	0.646405i
$165$	9.79960	−	0.0174068i	0.762898	−	0.00135512i
$166$	−11.3125	−	1.95816i	−0.878019	−	0.151983i
$167$	7.20461	+	7.20461i	0.557509	+	0.557509i	0.928598	−	0.371088i	$-0.121015\pi$
$167$	7.20461	+	7.20461i	0.557509	+	0.557509i	−0.371088	+	0.928598i	$0.621015\pi$
$168$	−3.17931	+	0.884011i	−0.245289	+	0.0682029i
$169$		−	19.4275i		−	1.49442i
$170$	8.35913	+	11.8142i	0.641116	+	0.906107i
$171$	−11.6622			−0.891835
$172$	−12.6175	+	5.98022i	−0.962079	+	0.455988i
$173$	0.680198	−	0.680198i	0.0517145	−	0.0517145i	−0.680777	−	0.732491i	$-0.738358\pi$
$173$	0.680198	−	0.680198i	0.0517145	−	0.0517145i	0.732491	+	0.680777i	$0.238358\pi$
$174$	6.44118	+	1.11495i	0.488304	+	0.0845243i
$175$	−3.52295	+	3.54807i	−0.266310	+	0.268209i
$176$	11.6303	+	9.51309i	0.876665	+	0.717076i
$177$	−0.667036	+	0.667036i	−0.0501375	+	0.0501375i
$178$	3.50176	+	4.96782i	0.262468	+	0.372354i
$179$			2.08267i			0.155666i	0.996966	+	0.0778329i	$0.0248001\pi$
$179$			2.08267i			0.155666i	−0.996966	+	0.0778329i	$0.975200\pi$
$180$	−6.61721	+	3.15071i	−0.493218	+	0.234840i
$181$			11.8888i			0.883685i	0.897093	+	0.441842i	$0.145675\pi$
$181$			11.8888i			0.883685i	−0.897093	+	0.441842i	$0.854325\pi$
$182$	−6.58234	+	4.63981i	−0.487915	+	0.343926i
$183$	10.6795	−	10.6795i	0.789452	−	0.789452i
$184$	−7.97399	−	4.50436i	−0.587850	−	0.332066i
$185$	−23.6572	+	0.0420216i	−1.73931	+	0.00308949i
$186$	0.284046	−	1.64096i	0.0208272	−	0.120321i
$187$	−12.1560	+	12.1560i	−0.888936	+	0.888936i
$188$	12.2339	−	5.79838i	0.892248	−	0.422891i
$189$	5.41210			0.393672
$190$	22.1806	+	3.79884i	1.60915	+	0.275597i
$191$			20.0132i			1.44811i	0.689744	+	0.724053i	$0.257723\pi$
$191$			20.0132i			1.44811i	−0.689744	+	0.724053i	$0.742277\pi$
$192$	9.05937	+	2.24577i	0.653804	+	0.162074i
$193$	−5.50637	−	5.50637i	−0.396357	−	0.396357i	0.480589	−	0.876946i	$-0.340423\pi$
$193$	−5.50637	−	5.50637i	−0.396357	−	0.396357i	−0.876946	+	0.480589i	$0.840423\pi$
$194$	−1.78815	+	10.3303i	−0.128381	+	0.741671i
$195$	10.4861	−	10.5234i	0.750922	−	0.753594i
$196$	1.88364	+	0.672247i	0.134545	+	0.0480177i
$197$	−6.09476	−	6.09476i	−0.434233	−	0.434233i	0.455832	−	0.890066i	$-0.349342\pi$
$197$	−6.09476	−	6.09476i	−0.434233	−	0.434233i	−0.890066	+	0.455832i	$0.849342\pi$
$198$	−5.01580	−	7.11573i	−0.356457	−	0.505693i
$199$	−7.64819			−0.542166			−0.271083	−	0.962556i	$-0.587382\pi$
$199$	−7.64819			−0.542166			−0.271083	+	0.962556i	$0.587382\pi$
$200$	13.6117	−	3.83690i	0.962492	−	0.271310i
$201$	1.66654			0.117549
$202$	−6.80302	−	9.65120i	−0.478659	−	0.679056i
$203$	−2.80148	−	2.80148i	−0.196626	−	0.196626i
$204$	−3.58945	+	10.0576i	−0.251312	+	0.704175i
$205$	6.93629	−	6.96097i	0.484451	−	0.486175i
$206$	−0.994719	+	5.74658i	−0.0693054	+	0.400383i
$207$	3.75218	+	3.75218i	0.260794	+	0.260794i
$208$	22.6647	−	2.26952i	1.57151	−	0.157363i
$209$			26.7311i			1.84903i
$210$	−3.63647	−	0.622813i	−0.250940	−	0.0429782i
$211$	17.4660			1.20241			0.601205	−	0.799095i	$-0.294687\pi$
$211$	17.4660			1.20241			0.601205	+	0.799095i	$0.294687\pi$
$212$	−8.22381	−	17.3512i	−0.564813	−	1.19169i
$213$	−3.53233	+	3.53233i	−0.242031	+	0.242031i
$214$	−3.85076	+	22.2462i	−0.263232	+	1.52072i
$215$	−15.6111	+	0.0277296i	−1.06467	+	0.00189114i
$216$	−13.3282	−	7.52889i	−0.906872	−	0.512276i
$217$	−0.713707	+	0.713707i	−0.0484496	+	0.0484496i
$218$	−7.98095	+	5.62568i	−0.540538	+	0.381019i
$219$		−	3.94027i		−	0.266259i
$220$	7.22176	+	15.1674i	0.486891	+	1.02258i
$221$			26.0614i			1.75308i
$222$	−10.0573	−	14.2679i	−0.675000	−	0.957599i
$223$	2.68984	−	2.68984i	0.180125	−	0.180125i	−0.611285	−	0.791410i	$-0.709347\pi$
$223$	2.68984	−	2.68984i	0.180125	−	0.180125i	0.791410	+	0.611285i	$0.209347\pi$
$224$	−3.70361	−	4.27590i	−0.247458	−	0.285695i
$225$	−8.19403	+	0.0291098i	−0.546269	+	0.00194065i
$226$	−10.4920	−	1.81613i	−0.697916	−	0.120807i
$227$	2.69124	−	2.69124i	0.178624	−	0.178624i	−0.612132	−	0.790756i	$-0.709688\pi$
$227$	2.69124	−	2.69124i	0.178624	−	0.178624i	0.790756	+	0.612132i	$0.209688\pi$
$228$	7.11178	+	15.0050i	0.470989	+	0.993730i
$229$	−6.60720			−0.436616			−0.218308	−	0.975880i	$-0.570054\pi$
$229$	−6.60720			−0.436616			−0.218308	+	0.975880i	$0.570054\pi$
$230$	−5.91410	−	8.35856i	−0.389964	−	0.551147i
$231$		−	4.38252i		−	0.288349i
$232$	3.00194	+	10.7964i	0.197087	+	0.708815i
$233$	−18.3917	−	18.3917i	−1.20488	−	1.20488i	−0.972665	−	0.232215i	$-0.925403\pi$
$233$	−18.3917	−	18.3917i	−1.20488	−	1.20488i	−0.232215	−	0.972665i	$-0.574597\pi$
$234$	−13.0044	−	2.25103i	−0.850126	−	0.147155i
$235$	15.1364	−	0.0268864i	0.987391	−	0.00175388i
$236$	−1.52301	−	0.543545i	−0.0991396	−	0.0353818i
$237$	−9.60179	−	9.60179i	−0.623703	−	0.623703i
$238$	5.29010	−	3.72893i	0.342906	−	0.241710i
$239$	2.86773			0.185498			0.0927492	−	0.995690i	$-0.470435\pi$
$239$	2.86773			0.185498			0.0927492	+	0.995690i	$0.470435\pi$
$240$	8.08905	+	6.59257i	0.522146	+	0.425548i
$241$	2.10549			0.135626			0.0678131	−	0.997698i	$-0.478398\pi$
$241$	2.10549			0.135626			0.0678131	+	0.997698i	$0.478398\pi$
$242$	−3.59505	+	2.53411i	−0.231098	+	0.162898i
$243$	10.3276	+	10.3276i	0.662517	+	0.662517i
$244$	24.3840	+	8.70237i	1.56103	+	0.557112i
$245$	1.58394	+	1.57833i	0.101195	+	0.100836i
$246$	7.14484	+	1.23675i	0.455538	+	0.0788525i
$247$	28.6545	+	28.6545i	1.82324	+	1.82324i
$248$	2.75049	−	0.764777i	0.174656	−	0.0485634i
$249$		−	9.47136i		−	0.600223i
$250$	15.5939	+	2.61375i	0.986242	+	0.165308i
$251$	−8.29723			−0.523716			−0.261858	−	0.965106i	$-0.584335\pi$
$251$	−8.29723			−0.523716			−0.261858	+	0.965106i	$0.584335\pi$
$252$	1.40378	+	2.96181i	0.0884298	+	0.186576i
$253$	8.60040	−	8.60040i	0.540703	−	0.540703i
$254$	5.94448	+	1.02897i	0.372990	+	0.0645635i
$255$	−8.42744	+	8.45743i	−0.527747	+	0.529625i
$256$	3.17250	+	15.6823i	0.198281	+	0.980145i
$257$	−18.4254	+	18.4254i	−1.14934	+	1.14934i	−0.162660	+	0.986682i	$0.552007\pi$
$257$	−18.4254	+	18.4254i	−1.14934	+	1.14934i	−0.986682	+	0.162660i	$0.947993\pi$
$258$	−6.63668	−	9.41522i	−0.413182	−	0.586166i
$259$			10.5798i			0.657398i
$260$	24.0001	+	8.51732i	1.48842	+	0.528222i
$261$		−	6.49282i		−	0.401895i
$262$	−14.7157	+	10.3729i	−0.909138	+	0.640841i
$263$	−0.441018	+	0.441018i	−0.0271944	+	0.0271944i	−0.720573	−	0.693379i	$-0.756121\pi$
$263$	−0.441018	+	0.441018i	−0.0271944	+	0.0271944i	0.693379	+	0.720573i	$0.256121\pi$
$264$	−6.09662	+	10.7927i	−0.375221	+	0.664247i
$265$	−0.0381328	−	21.4679i	−0.00234248	−	1.31876i
$266$	1.71651	−	9.91645i	0.105246	−	0.608016i
$267$	−3.54556	+	3.54556i	−0.216985	+	0.216985i
$268$	1.22356	+	2.58157i	0.0747410	+	0.157694i
$269$	15.7733			0.961718			0.480859	−	0.876798i	$-0.340325\pi$
$269$	15.7733			0.961718			0.480859	+	0.876798i	$0.340325\pi$
$270$	−9.88522	−	13.9710i	−0.601595	−	0.850251i
$271$		−	14.3087i		−	0.869192i	−0.900625	−	0.434596i	$-0.856891\pi$
$271$		−	14.3087i		−	0.869192i	0.900625	−	0.434596i	$-0.143109\pi$
$272$	−18.2152	+	1.82397i	−1.10446	+	0.110595i
$273$	−4.69786	−	4.69786i	−0.284327	−	0.284327i
$274$	0.823577	−	4.75788i	0.0497541	−	0.287434i
$275$	0.0667229	+	18.7816i	0.00402354	+	1.13257i
$276$	2.53954	−	7.11579i	0.152862	−	0.428320i
$277$	−9.68344	−	9.68344i	−0.581822	−	0.581822i	0.353582	−	0.935404i	$-0.384964\pi$
$277$	−9.68344	−	9.68344i	−0.581822	−	0.581822i	−0.935404	+	0.353582i	$0.884964\pi$
$278$	−4.16029	−	5.90206i	−0.249518	−	0.353982i
$279$	−1.65412			−0.0990293
$280$	−1.70510	−	6.09037i	−0.101899	−	0.363969i
$281$	−8.54275			−0.509618			−0.254809	−	0.966991i	$-0.582013\pi$
$281$	−8.54275			−0.509618			−0.254809	+	0.966991i	$0.582013\pi$
$282$	6.43488	+	9.12894i	0.383192	+	0.543620i
$283$	7.21294	+	7.21294i	0.428765	+	0.428765i	0.888207	−	0.459443i	$-0.151951\pi$
$283$	7.21294	+	7.21294i	0.428765	+	0.428765i	−0.459443	+	0.888207i	$0.651951\pi$
$284$	−8.06520	−	2.87837i	−0.478582	−	0.170800i
$285$	0.0329765	+	18.5650i	0.00195336	+	1.09969i
$286$	−5.15962	+	29.8076i	−0.305094	+	1.76256i
$287$	−3.10753	−	3.10753i	−0.183431	−	0.183431i
$288$	0.663177	−	9.24680i	0.0390781	−	0.544873i
$289$		−	3.94501i		−	0.232060i
$290$	−2.11496	+	12.3488i	−0.124195	+	0.725147i
$291$	−8.64901			−0.507014
$292$	6.10370	−	2.89292i	0.357192	−	0.169295i
$293$	−0.0229166	+	0.0229166i	−0.00133880	+	0.00133880i	−0.707776	−	0.706437i	$-0.750301\pi$
$293$	−0.0229166	+	0.0229166i	−0.00133880	+	0.00133880i	0.706437	+	0.707776i	$0.250301\pi$
$294$	−0.281419	+	1.62578i	−0.0164127	+	0.0948176i
$295$	−1.28070	−	1.27616i	−0.0745650	−	0.0743006i
$296$	14.7178	−	26.0547i	0.855457	−	1.51440i
$297$	14.3753	−	14.3753i	0.834138	−	0.834138i
$298$	8.01771	−	5.65159i	0.464453	−	0.327388i
$299$		−	18.4385i		−	1.06632i
$300$	5.03428	+	10.5249i	0.290654	+	0.607658i
$301$			6.98150i			0.402407i
$302$	14.7850	+	20.9750i	0.850782	+	1.20697i
$303$	6.88813	−	6.88813i	0.395713	−	0.395713i
$304$	−18.0222	+	22.0331i	−1.03364	+	1.26369i
$305$	20.5045	+	20.4317i	1.17408	+	1.16992i
$306$	10.4514	+	1.80911i	0.597468	+	0.103420i
$307$	23.8818	−	23.8818i	1.36301	−	1.36301i	0.492950	−	0.870058i	$-0.335918\pi$
$307$	23.8818	−	23.8818i	1.36301	−	1.36301i	0.870058	−	0.492950i	$-0.164082\pi$
$308$	6.78878	−	3.21762i	0.386827	−	0.183341i
$309$	−4.81131			−0.273706
$310$	3.14599	+	0.538809i	0.178680	+	0.0306023i
$311$		−	20.8836i		−	1.18420i	−0.805863	−	0.592102i	$-0.798298\pi$
$311$		−	20.8836i		−	1.18420i	0.805863	−	0.592102i	$-0.201702\pi$
$312$	5.03401	+	18.1046i	0.284995	+	1.02497i
$313$	2.17730	+	2.17730i	0.123068	+	0.123068i	0.765958	−	0.642890i	$-0.222265\pi$
$313$	2.17730	+	2.17730i	0.123068	+	0.123068i	−0.642890	+	0.765958i	$0.722265\pi$
$314$	17.2651	+	2.98854i	0.974323	+	0.168653i
$315$	0.00650916	+	3.66450i	0.000366750	+	0.206471i
$316$	7.82417	−	21.9233i	0.440144	−	1.23328i
$317$	−21.9203	−	21.9203i	−1.23116	−	1.23116i	−0.963517	−	0.267648i	$-0.913754\pi$
$317$	−21.9203	−	21.9203i	−1.23116	−	1.23116i	−0.267648	−	0.963517i	$-0.586246\pi$
$318$	12.9475	−	9.12654i	0.726060	−	0.511791i
$319$	−14.8823			−0.833246
$320$	−4.27335	+	17.3706i	−0.238887	+	0.971047i
$321$	−18.6256			−1.03958
$322$	−3.74275	+	2.63822i	−0.208576	+	0.147022i
$323$	−23.0291	−	23.0291i	−1.28137	−	1.28137i
$324$	0.939685	−	2.63300i	0.0522047	−	0.146278i
$325$	20.2045	+	20.0615i	1.12075	+	1.11281i
$326$	−4.05511	−	0.701930i	−0.224592	−	0.0388763i
$327$	−5.69606	−	5.69606i	−0.314993	−	0.314993i
$328$	3.32989	+	11.9758i	0.183862	+	0.661252i
$329$		−	6.76922i		−	0.373199i
$330$	−11.3133	+	8.00470i	−0.622774	+	0.440644i
$331$	19.6466			1.07988			0.539938	−	0.841705i	$-0.318448\pi$
$331$	19.6466			1.07988			0.539938	+	0.841705i	$0.318448\pi$
$332$	14.6717	−	6.95380i	0.805213	−	0.381639i
$333$	−12.2601	+	12.2601i	−0.671849	+	0.671849i
$334$	−14.1981	−	2.45765i	−0.776884	−	0.134477i
$335$	0.00567351	+	3.19405i	0.000309977	+	0.174510i
$336$	2.95471	−	3.61229i	0.161192	−	0.197067i
$337$	−6.08144	+	6.08144i	−0.331277	+	0.331277i	−0.853071	−	0.521794i	$-0.825263\pi$
$337$	−6.08144	+	6.08144i	−0.331277	+	0.331277i	0.521794	+	0.853071i	$0.325263\pi$
$338$	15.8292	+	22.4564i	0.860998	+	1.22147i
$339$		−	8.78438i		−	0.477102i
$340$	−19.2884	−	6.84521i	−1.04606	−	0.371234i
$341$			3.79141i			0.205316i
$342$	13.4805	−	9.50224i	0.728941	−	0.513822i
$343$	0.707107	−	0.707107i	0.0381802	−	0.0381802i
$344$	9.71212	−	17.1932i	0.523643	−	0.926995i
$345$	5.96243	−	5.98365i	0.321007	−	0.322149i
$346$	−0.232031	+	1.34046i	−0.0124740	+	0.0720637i
$347$	5.49258	−	5.49258i	0.294857	−	0.294857i	−0.544138	−	0.838996i	$-0.683143\pi$
$347$	5.49258	−	5.49258i	0.294857	−	0.294857i	0.838996	+	0.544138i	$0.183143\pi$
$348$	−8.35386	+	3.95940i	−0.447814	+	0.212246i
$349$	17.0265			0.911407			0.455703	−	0.890132i	$-0.349388\pi$
$349$	17.0265			0.911407			0.455703	+	0.890132i	$0.349388\pi$
$350$	1.18129	−	6.97170i	0.0631426	−	0.372653i
$351$		−	30.8193i		−	1.64501i
$352$	−21.1947	−	1.52007i	−1.12968	−	0.0810203i
$353$	1.63669	+	1.63669i	0.0871120	+	0.0871120i	0.749320	−	0.662208i	$-0.230380\pi$
$353$	1.63669	+	1.63669i	0.0871120	+	0.0871120i	−0.662208	+	0.749320i	$0.730380\pi$
$354$	0.227541	−	1.31452i	0.0120937	−	0.0698662i
$355$	−6.78201	−	6.75796i	−0.359952	−	0.358675i
$356$	−8.09541	−	2.88916i	−0.429056	−	0.153125i
$357$	3.77558	+	3.77558i	0.199825	+	0.199825i
$358$	−1.69693	−	2.40737i	−0.0896855	−	0.127234i
$359$	−21.3341			−1.12597			−0.562984	−	0.826468i	$-0.690347\pi$
$359$	−21.3341			−1.12597			−0.562984	+	0.826468i	$0.690347\pi$
$360$	5.08174	−	9.03354i	0.267831	−	0.476109i
$361$	−31.6412			−1.66532
$362$	−9.68680	−	13.7423i	−0.509127	−	0.722280i
$363$	−2.56581	−	2.56581i	−0.134670	−	0.134670i
$364$	3.82812	−	10.7264i	0.200648	−	0.562216i
$365$	7.55182	−	0.0134141i	0.395280	−	0.000702127i
$366$	−3.64302	+	21.0461i	−0.190424	+	1.10009i
$367$	−17.3803	−	17.3803i	−0.907244	−	0.907244i	0.0888055	−	0.996049i	$-0.471695\pi$
$367$	−17.3803	−	17.3803i	−0.907244	−	0.907244i	−0.996049	+	0.0888055i	$0.971695\pi$
$368$	12.8873	−	1.29046i	0.671796	−	0.0672701i
$369$		−	7.20212i		−	0.374927i
$370$	27.3113	−	19.3241i	1.41985	−	1.00461i
$371$	−9.60074			−0.498445
$372$	1.00870	+	2.12823i	0.0522986	+	0.110344i
$373$	−4.97126	+	4.97126i	−0.257402	+	0.257402i	−0.823997	−	0.566595i	$-0.808261\pi$
$373$	−4.97126	+	4.97126i	−0.257402	+	0.257402i	0.566595	+	0.823997i	$0.308261\pi$
$374$	4.14668	−	23.9558i	0.214420	−	1.23872i
$375$	0.0695092	+	13.0439i	0.00358944	+	0.673583i
$376$	−9.41681	+	16.6704i	−0.485635	+	0.859710i
$377$	−15.9531	+	15.9531i	−0.821625	+	0.821625i
$378$	−6.25589	+	4.40970i	−0.321768	+	0.226811i
$379$			20.6605i			1.06126i	0.847604	+	0.530630i	$0.178044\pi$
$379$			20.6605i			1.06126i	−0.847604	+	0.530630i	$0.821956\pi$
$380$	−28.7340	+	13.6814i	−1.47402	+	0.701839i
$381$			4.97700i			0.254979i
$382$	−16.3065	−	23.1334i	−0.834313	−	1.18361i
$383$	−2.69655	+	2.69655i	−0.137787	+	0.137787i	−0.772636	−	0.634849i	$-0.781062\pi$
$383$	−2.69655	+	2.69655i	−0.137787	+	0.137787i	0.634849	+	0.772636i	$0.281062\pi$
$384$	−12.3016	+	4.78555i	−0.627765	+	0.244211i
$385$	8.39944	−	0.0149197i	0.428075	−	0.000760379i
$386$	10.8514	+	1.87834i	0.552320	+	0.0956052i
$387$	−8.09030	+	8.09030i	−0.411253	+	0.411253i
$388$	−6.35004	−	13.3978i	−0.322375	−	0.680171i
$389$	1.71820			0.0871164			0.0435582	−	0.999051i	$-0.486131\pi$
$389$	1.71820			0.0871164			0.0435582	+	0.999051i	$0.486131\pi$
$390$	−3.54662	+	20.7079i	−0.179590	+	1.04859i
$391$			14.8186i			0.749411i
$392$	−2.72505	+	0.757704i	−0.137636	+	0.0382698i
$393$	−10.5027	−	10.5027i	−0.529790	−	0.529790i
$394$	12.0109	+	2.07906i	0.605100	+	0.104741i
$395$	18.3699	−	18.4353i	0.924289	−	0.927578i
$396$	11.5956	+	4.13833i	0.582701	+	0.207959i
$397$	−4.86345	−	4.86345i	−0.244089	−	0.244089i	0.574450	−	0.818540i	$-0.305216\pi$
$397$	−4.86345	−	4.86345i	−0.244089	−	0.244089i	−0.818540	+	0.574450i	$0.805216\pi$
$398$	8.84060	−	6.23164i	0.443139	−	0.312364i
$399$	8.30252			0.415646
$400$	−12.6076	+	15.5257i	−0.630381	+	0.776286i
$401$	−0.297006			−0.0148318			−0.00741590	−	0.999973i	$-0.502361\pi$
$401$	−0.297006			−0.0148318			−0.00741590	+	0.999973i	$0.502361\pi$
$402$	−1.92637	+	1.35787i	−0.0960785	+	0.0677246i
$403$	4.06422	+	4.06422i	0.202453	+	0.202453i
$404$	15.7273	+	5.61290i	0.782464	+	0.279252i
$405$	2.20623	−	2.21408i	0.109628	−	0.110019i
$406$	5.52086	+	0.955648i	0.273996	+	0.0474280i
$407$	28.1015	+	28.1015i	1.39294	+	1.39294i
$408$	−4.04574	−	14.5503i	−0.200294	−	0.720348i
$409$		−	8.01971i		−	0.396549i	−0.980147	−	0.198274i	$-0.936466\pi$
$409$		−	8.01971i		−	0.396549i	0.980147	−	0.198274i	$-0.0635337\pi$
$410$	−2.34601	+	13.6978i	−0.115861	+	0.676488i
$411$	3.98353			0.196493
$412$	−3.53243	−	7.45301i	−0.174030	−	0.367183i
$413$	−0.571730	+	0.571730i	−0.0281330	+	0.0281330i
$414$	−7.39440	−	1.27995i	−0.363415	−	0.0629062i
$415$	18.1526	−	0.0322440i	0.891075	−	0.00158279i
$416$	−24.3491	+	21.0903i	−1.19382	+	1.03403i
$417$	4.21234	−	4.21234i	0.206279	−	0.206279i
$418$	−21.7802	−	30.8988i	−1.06530	−	1.51131i
$419$		−	0.259157i		−	0.0126607i	−0.999980	−	0.00633033i	$-0.997985\pi$
$419$		−	0.259157i		−	0.0126607i	0.999980	−	0.00633033i	$-0.00201502\pi$
$420$	4.71089	−	2.24303i	0.229868	−	0.109449i
$421$		−	19.9012i		−	0.969925i	−0.874535	−	0.484962i	$-0.838833\pi$
$421$		−	19.9012i		−	0.969925i	0.874535	−	0.484962i	$-0.161167\pi$
$422$	−20.1891	+	14.2311i	−0.982791	+	0.692758i
$423$	7.84430	−	7.84430i	0.381403	−	0.381403i
$424$	23.6435	+	13.3558i	1.14823	+	0.648615i
$425$	−16.2380	−	16.1230i	−0.787659	−	0.782082i
$426$	1.20496	−	6.96115i	0.0583803	−	0.337269i
$427$	9.15363	−	9.15363i	0.442975	−	0.442975i
$428$	−13.6748	−	28.8521i	−0.660994	−	1.39462i
$429$	−24.9563			−1.20490
$430$	18.0224	−	12.7518i	0.869117	−	0.614944i
$431$			32.3954i			1.56043i	0.625510	+	0.780216i	$0.284891\pi$
$431$			32.3954i			1.56043i	−0.625510	+	0.780216i	$0.715109\pi$
$432$	21.5407	−	2.15697i	1.03638	−	0.103777i
$433$	23.1936	+	23.1936i	1.11461	+	1.11461i	0.992518	+	0.122096i	$0.0389615\pi$
$433$	23.1936	+	23.1936i	1.11461	+	1.11461i	0.122096	+	0.992518i	$0.461039\pi$
$434$	0.243461	−	1.40650i	0.0116865	−	0.0675141i
$435$	−10.3358	+	0.0183593i	−0.495565	+	0.000880260i
$436$	4.64152	−	13.0055i	0.222289	−	0.622852i
$437$	16.2931	+	16.2931i	0.779407	+	0.779407i
$438$	3.21047	+	4.55459i	0.153402	+	0.217627i
$439$	−10.4136			−0.497014			−0.248507	−	0.968630i	$-0.579940\pi$
$439$	−10.4136			−0.497014			−0.248507	+	0.968630i	$0.579940\pi$
$440$	−20.7059	−	11.6479i	−0.987113	−	0.555292i
$441$	1.63882			0.0780389
$442$	−21.2344	−	30.1245i	−1.01002	−	1.43288i
$443$	−5.71427	−	5.71427i	−0.271493	−	0.271493i	0.558208	−	0.829701i	$-0.311489\pi$
$443$	−5.71427	−	5.71427i	−0.271493	−	0.271493i	−0.829701	+	0.558208i	$0.811489\pi$
$444$	23.2506	+	8.29786i	1.10342	+	0.393799i
$445$	−6.80742	−	6.78327i	−0.322702	−	0.321558i
$446$	−0.917564	+	5.30085i	−0.0434479	+	0.251003i
$447$	5.72230	+	5.72230i	0.270655	+	0.270655i
$448$	7.76497	+	1.92489i	0.366860	+	0.0909427i
$449$		−	1.71448i		−	0.0809112i	−0.999181	−	0.0404556i	$-0.987119\pi$
$449$		−	1.71448i		−	0.0809112i	0.999181	−	0.0404556i	$-0.0128809\pi$
$450$	9.44783	−	6.71003i	0.445375	−	0.316314i
$451$	−16.5080			−0.777333
$452$	13.6075	−	6.44943i	0.640044	−	0.303356i
$453$	−14.9700	+	14.9700i	−0.703351	+	0.703351i
$454$	−0.918043	+	5.30362i	−0.0430859	+	0.248911i
$455$	8.98781	−	9.01980i	0.421355	−	0.422855i
$456$	−20.4464	−	11.5498i	−0.957492	−	0.540870i
$457$	6.22202	−	6.22202i	0.291054	−	0.291054i	−0.546443	−	0.837496i	$-0.684018\pi$
$457$	6.22202	−	6.22202i	0.291054	−	0.291054i	0.837496	+	0.546443i	$0.184018\pi$
$458$	7.63732	−	5.38346i	0.356869	−	0.251552i
$459$			24.7688i			1.15611i
$460$	13.6466	+	4.84300i	0.636276	+	0.225806i
$461$		−	7.77638i		−	0.362182i	−0.983466	−	0.181091i	$-0.942037\pi$
$461$		−	7.77638i		−	0.362182i	0.983466	−	0.181091i	$-0.0579629\pi$
$462$	3.57082	+	5.06579i	0.166129	+	0.235682i
$463$	−19.9679	+	19.9679i	−0.927986	+	0.927986i	−0.997576	−	0.0695900i	$-0.977831\pi$
$463$	−19.9679	+	19.9679i	−0.927986	+	0.927986i	0.0695900	+	0.997576i	$0.477831\pi$
$464$	−12.2667	−	10.0336i	−0.569467	−	0.465800i
$465$	0.00467722	+	2.63316i	0.000216901	+	0.122110i
$466$	36.2444	+	6.27381i	1.67899	+	0.290629i
$467$	−10.9935	+	10.9935i	−0.508717	+	0.508717i	−0.914133	−	0.405415i	$-0.867127\pi$
$467$	−10.9935	+	10.9935i	−0.508717	+	0.508717i	0.405415	+	0.914133i	$0.367127\pi$
$468$	16.8660	−	7.99384i	0.779633	−	0.369515i
$469$	1.42843			0.0659586
$470$	−17.4744	+	12.3640i	−0.806034	+	0.570310i
$471$			14.4551i			0.666057i
$472$	2.20333	−	0.612641i	0.101417	−	0.0281991i
$473$	18.5438	+	18.5438i	0.852647	+	0.852647i
$474$	18.9222	+	3.27538i	0.869125	+	0.150443i
$475$	−35.5811	+	0.126404i	−1.63257	+	0.00579981i
$476$	−3.07659	+	8.62059i	−0.141015	+	0.395124i
$477$	−11.1255	−	11.1255i	−0.509402	−	0.509402i
$478$	−3.31484	+	2.33659i	−0.151617	+	0.106873i
$479$	−11.6242			−0.531125			−0.265562	−	0.964094i	$-0.585558\pi$
$479$	−11.6242			−0.531125			−0.265562	+	0.964094i	$0.585558\pi$
$480$	−14.7217	−	1.02956i	−0.671952	−	0.0469926i
$481$	60.2470			2.74703
$482$	−2.43375	+	1.71552i	−0.110854	+	0.0781398i
$483$	−2.67123	−	2.67123i	−0.121545	−	0.121545i
$484$	2.09079	−	5.85839i	0.0950359	−	0.266290i
$485$	−0.0294444	−	16.5765i	−0.00133700	−	0.752700i
$486$	−20.3526	−	3.52298i	−0.923211	−	0.159805i
$487$	−19.1480	−	19.1480i	−0.867677	−	0.867677i	0.124538	−	0.992215i	$-0.460255\pi$
$487$	−19.1480	−	19.1480i	−0.867677	−	0.867677i	−0.992215	+	0.124538i	$0.960255\pi$
$488$	−35.2762	+	9.80862i	−1.59688	+	0.444015i
$489$		−	3.39513i		−	0.153533i
$490$	−3.11689	−	0.533826i	−0.140807	−	0.0241158i
$491$	34.4320			1.55389			0.776947	−	0.629566i	$-0.216767\pi$
$491$	34.4320			1.55389			0.776947	+	0.629566i	$0.216767\pi$
$492$	−9.26646	+	4.39194i	−0.417764	+	0.198004i
$493$	12.8212	−	12.8212i	0.577437	−	0.577437i
$494$	−56.4693	−	9.77470i	−2.54068	−	0.439784i
$495$	9.75071	+	9.71613i	0.438262	+	0.436708i
$496$	−2.55618	+	3.12507i	−0.114776	+	0.140320i
$497$	−3.02763	+	3.02763i	−0.135808	+	0.135808i
$498$	7.71713	+	10.9480i	0.345813	+	0.490592i
$499$		−	22.2619i		−	0.996578i	−0.867011	−	0.498289i	$-0.833962\pi$
$499$		−	22.2619i		−	0.996578i	0.867011	−	0.498289i	$-0.166038\pi$
$500$	−20.1547	+	9.68440i	−0.901346	+	0.433100i
$501$		−	11.8873i		−	0.531086i
$502$	9.59083	−	6.76046i	0.428060	−	0.301734i
$503$	9.59698	−	9.59698i	0.427908	−	0.427908i	−0.460007	−	0.887915i	$-0.652153\pi$
$503$	9.59698	−	9.59698i	0.427908	−	0.427908i	0.887915	+	0.460007i	$0.152153\pi$
$504$	−4.03588	−	2.27979i	−0.179772	−	0.101550i
$505$	13.2251	+	13.1782i	0.588508	+	0.586421i
$506$	−2.93379	+	16.9488i	−0.130423	+	0.753464i
$507$	−16.0273	+	16.0273i	−0.711797	+	0.711797i
$508$	−7.70966	+	3.65408i	−0.342061	+	0.162123i
$509$	27.0823			1.20040			0.600201	−	0.799849i	$-0.295087\pi$
$509$	27.0823			1.20040			0.600201	+	0.799849i	$0.295087\pi$
$510$	2.85035	−	16.6426i	0.126216	−	0.736946i
$511$		−	3.37728i		−	0.149402i
$512$	−16.4449	−	15.5424i	−0.726767	−	0.686884i
$513$	27.2334	+	27.2334i	1.20239	+	1.20239i
$514$	6.28530	−	36.3108i	0.277233	−	1.60160i
$515$	−0.0163795	−	9.22125i	−0.000721766	−	0.406337i
$516$	15.3428	+	5.47566i	0.675428	+	0.241052i
$517$	−17.9800	−	17.9800i	−0.790759	−	0.790759i
$518$	−8.62030	−	12.2293i	−0.378754	−	0.537325i
$519$	−1.12230			−0.0492635
$520$	−34.6817	+	9.70971i	−1.52089	+	0.425799i
$521$	12.5187			0.548454			0.274227	−	0.961665i	$-0.411578\pi$
$521$	12.5187			0.548454			0.274227	+	0.961665i	$0.411578\pi$
$522$	5.29026	+	7.50510i	0.231548	+	0.328489i
$523$	16.8541	+	16.8541i	0.736980	+	0.736980i	0.971992	−	0.235012i	$-0.0755130\pi$
$523$	16.8541	+	16.8541i	0.736980	+	0.736980i	−0.235012	+	0.971992i	$0.575513\pi$
$524$	8.55827	−	23.9803i	0.373870	−	1.04758i
$525$	5.83345	−	0.0207237i	0.254593	−	0.000904456i
$526$	0.150441	−	0.869112i	0.00655954	−	0.0378951i
$527$	−3.26633	−	3.26633i	−0.142284	−	0.142284i
$528$	−1.74663	−	17.4429i	−0.0760125	−	0.759103i
$529$			12.5158i			0.544165i
$530$	17.5358	+	24.7838i	0.761706	+	1.07654i
$531$	−1.32506			−0.0575029
$532$	6.09565	+	12.8611i	0.264280	+	0.557599i
$533$	−17.6959	+	17.6959i	−0.766492	+	0.766492i
$534$	1.20947	−	6.98722i	0.0523389	−	0.302367i
$535$	−0.0634082	−	35.6973i	−0.00274138	−	1.54333i
$536$	−3.51775	−	1.98711i	−0.151944	−	0.0858303i
$537$	1.71816	−	1.71816i	0.0741440	−	0.0741440i
$538$	−18.2325	+	12.8519i	−0.786061	+	0.554085i
$539$		−	3.75635i		−	0.161797i
$540$	22.8098	+	8.09491i	0.981579	+	0.348349i
$541$		−	22.1676i		−	0.953059i	−0.879159	−	0.476529i	$-0.841895\pi$
$541$		−	22.1676i		−	0.953059i	0.879159	−	0.476529i	$-0.158105\pi$
$542$	11.6585	+	16.5396i	0.500777	+	0.710435i
$543$	9.80799	−	9.80799i	0.420901	−	0.420901i
$544$	19.5689	−	16.9498i	0.839012	−	0.726718i
$545$	10.8975	−	10.9363i	0.466799	−	0.468461i
$546$	9.25804	+	1.60254i	0.396208	+	0.0685825i
$547$	−28.0003	+	28.0003i	−1.19720	+	1.19720i	−0.222204	+	0.975000i	$0.571325\pi$
$547$	−28.0003	+	28.0003i	−1.19720	+	1.19720i	−0.975000	+	0.222204i	$0.928675\pi$
$548$	2.92468	+	6.17072i	0.124936	+	0.263600i
$549$	21.2148			0.905425
$550$	−15.3801	−	21.6555i	−0.655811	−	0.923392i
$551$		−	28.1939i		−	1.20110i
$552$	2.86237	+	10.2944i	0.121831	+	0.438158i
$553$	−8.22989	−	8.22989i	−0.349971	−	0.349971i
$554$	19.0831	+	3.30324i	0.810764	+	0.140341i
$555$	19.5514	+	19.4820i	0.829909	+	0.826966i
$556$	9.61783	+	3.43249i	0.407887	+	0.145570i
$557$	20.9790	+	20.9790i	0.888909	+	0.888909i	0.994418	−	0.105509i	$-0.0336473\pi$
$557$	20.9790	+	20.9790i	0.888909	+	0.888909i	−0.105509	+	0.994418i	$0.533647\pi$
$558$	1.91201	−	1.34775i	0.0809416	−	0.0570548i
$559$	39.7563			1.68151
$560$	6.93329	+	5.65062i	0.292985	+	0.238782i
$561$	20.0569			0.846804
$562$	9.87464	−	6.96051i	0.416536	−	0.293612i
$563$	−5.62484	−	5.62484i	−0.237059	−	0.237059i	0.578572	−	0.815631i	$-0.303610\pi$
$563$	−5.62484	−	5.62484i	−0.237059	−	0.237059i	−0.815631	+	0.578572i	$0.803610\pi$
$564$	−14.8763	−	5.30916i	−0.626404	−	0.223556i
$565$	16.8359	−	0.0299053i	0.708293	−	0.00125812i
$566$	−14.2145	−	2.46049i	−0.597480	−	0.103422i
$567$	−0.988413	−	0.988413i	−0.0415094	−	0.0415094i
$568$	11.6679	−	3.24428i	0.489574	−	0.136127i
$569$			44.0354i			1.84606i	0.384727	+	0.923030i	$0.374295\pi$
$569$			44.0354i			1.84606i	−0.384727	+	0.923030i	$0.625705\pi$
$570$	−15.1646	−	21.4325i	−0.635175	−	0.897710i
$571$	−29.2525			−1.22418			−0.612090	−	0.790788i	$-0.709671\pi$
$571$	−29.2525			−1.22418			−0.612090	+	0.790788i	$0.709671\pi$
$572$	−18.3228	−	38.6588i	−0.766113	−	1.61641i
$573$	16.5105	−	16.5105i	0.689736	−	0.689736i
$574$	6.12398	+	1.06005i	0.255610	+	0.0442455i
$575$	11.4884	+	11.4071i	0.479100	+	0.475708i
$576$	6.76759	+	11.2288i	0.281983	+	0.467867i
$577$	17.3731	−	17.3731i	0.723254	−	0.723254i	−0.246013	−	0.969267i	$-0.579121\pi$
$577$	17.3731	−	17.3731i	0.723254	−	0.723254i	0.969267	+	0.246013i	$0.0791206\pi$
$578$	3.21434	+	4.56007i	0.133699	+	0.189674i
$579$			9.08529i			0.377572i
$580$	−7.61693	−	15.9973i	−0.316276	−	0.664253i
$581$		−	8.11809i		−	0.336795i
$582$	9.99746	−	7.04709i	0.414408	−	0.292111i
$583$	−25.5009	+	25.5009i	−1.05614	+	1.05614i
$584$	−4.69821	+	8.31716i	−0.194413	+	0.344166i
$585$	20.8676	−	0.0370665i	0.862767	−	0.00153251i
$586$	0.00781737	−	0.0451616i	0.000322932	−	0.00186561i
$587$	1.60705	−	1.60705i	0.0663300	−	0.0663300i	−0.673164	−	0.739494i	$-0.735065\pi$
$587$	1.60705	−	1.60705i	0.0663300	−	0.0663300i	0.739494	+	0.673164i	$0.235065\pi$
$588$	−0.999371	−	2.10855i	−0.0412134	−	0.0869552i
$589$	−7.18269			−0.295958
$590$	2.52016	+	0.431624i	0.103753	+	0.0177697i
$591$			10.0561i			0.413653i
$592$	4.21654	+	42.1087i	0.173299	+	1.73066i
$593$	−1.61385	−	1.61385i	−0.0662730	−	0.0662730i	0.673193	−	0.739466i	$-0.264922\pi$
$593$	−1.61385	−	1.61385i	−0.0662730	−	0.0662730i	−0.739466	+	0.673193i	$0.764922\pi$
$594$	−4.90373	+	28.3293i	−0.201202	+	1.16236i
$595$	−7.22333	+	7.24904i	−0.296128	+	0.297182i
$596$	−4.66290	+	13.0654i	−0.191000	+	0.535181i
$597$	6.30960	+	6.30960i	0.258235	+	0.258235i
$598$	15.0234	+	21.3132i	0.614352	+	0.871560i
$599$	−9.12169			−0.372702			−0.186351	−	0.982483i	$-0.559666\pi$
$599$	−9.12169			−0.372702			−0.186351	+	0.982483i	$0.559666\pi$
$600$	−14.3947	−	8.06401i	−0.587663	−	0.329212i
$601$	−5.60440			−0.228608			−0.114304	−	0.993446i	$-0.536464\pi$
$601$	−5.60440			−0.228608			−0.114304	+	0.993446i	$0.536464\pi$
$602$	−5.68843	−	8.06998i	−0.231843	−	0.328908i
$603$	1.65529	+	1.65529i	0.0674085	+	0.0674085i
$604$	−34.1802	−	12.1985i	−1.39077	−	0.496351i
$605$	4.90883	−	4.92630i	0.199572	−	0.200283i
$606$	−2.34969	+	13.5744i	−0.0954498	+	0.551422i
$607$	8.19524	+	8.19524i	0.332634	+	0.332634i	0.853586	−	0.520952i	$-0.174423\pi$
$607$	8.19524	+	8.19524i	0.332634	+	0.332634i	−0.520952	+	0.853586i	$0.674423\pi$
$608$	2.87972	−	40.1525i	0.116788	−	1.62840i
$609$			4.62233i			0.187306i
$610$	−40.3488	−	6.91047i	−1.63367	−	0.279797i
$611$	−38.5474			−1.55946
$612$	−13.5549	+	6.42450i	−0.547925	+	0.259695i
$613$	−28.3287	+	28.3287i	−1.14419	+	1.14419i	−0.156511	+	0.987676i	$0.550025\pi$
$613$	−28.3287	+	28.3287i	−1.14419	+	1.14419i	−0.987676	+	0.156511i	$0.949975\pi$
$614$	−8.14662	+	47.0638i	−0.328771	+	1.89934i
$615$	−11.4650	+	0.0203649i	−0.462312	+	0.000821192i
$616$	−5.22554	+	9.25067i	−0.210543	+	0.372720i
$617$	10.0649	−	10.0649i	0.405196	−	0.405196i	−0.474863	−	0.880060i	$-0.657503\pi$
$617$	10.0649	−	10.0649i	0.405196	−	0.405196i	0.880060	+	0.474863i	$0.157503\pi$
$618$	5.56144	−	3.92019i	0.223714	−	0.157693i
$619$		−	5.70055i		−	0.229124i	−0.993416	−	0.114562i	$-0.963453\pi$
$619$		−	5.70055i		−	0.229124i	0.993416	−	0.114562i	$-0.0365465\pi$
$620$	−4.07549	+	1.94049i	−0.163676	+	0.0779321i
$621$		−	17.5240i		−	0.703214i
$622$	17.0157	+	24.1396i	0.682268	+	0.967909i
$623$	−3.03898	+	3.03898i	−0.121754	+	0.121754i
$624$	−20.5702	−	16.8256i	−0.823468	−	0.673564i
$625$	−24.9994	+	0.177626i	−0.999975	+	0.00710503i
$626$	−4.29079	−	0.742724i	−0.171494	−	0.0296852i
$627$	22.0527	−	22.0527i	0.880698	−	0.880698i
$628$	−22.3918	+	10.6128i	−0.893531	+	0.423499i
$629$	−48.4193			−1.93061
$630$	−2.99331	−	4.23052i	−0.119256	−	0.168548i
$631$			27.0784i			1.07797i	0.842314	+	0.538987i	$0.181193\pi$
$631$			27.0784i			1.07797i	−0.842314	+	0.538987i	$0.818807\pi$
$632$	8.81878	+	31.7164i	0.350792	+	1.26161i
$633$	−14.4091	−	14.4091i	−0.572711	−	0.572711i
$634$	43.1981	+	7.47749i	1.71562	+	0.296969i
$635$	−9.53880	+	0.0169435i	−0.378536	+	0.000672383i
$636$	−7.52995	+	21.0989i	−0.298582	+	0.836626i
$637$	−4.02663	−	4.02663i	−0.159541	−	0.159541i
$638$	17.2025	−	12.1259i	0.681054	−	0.480067i
$639$	−7.01696			−0.277586
$640$	−9.21374	−	23.5607i	−0.364205	−	0.931319i
$641$	−12.7679			−0.504303			−0.252151	−	0.967688i	$-0.581138\pi$
$641$	−12.7679			−0.504303			−0.252151	+	0.967688i	$0.581138\pi$
$642$	21.5294	−	15.1758i	0.849699	−	0.598943i
$643$	15.1297	+	15.1297i	0.596657	+	0.596657i	0.939421	−	0.342765i	$-0.111363\pi$
$643$	15.1297	+	15.1297i	0.596657	+	0.596657i	−0.342765	+	0.939421i	$0.611363\pi$
$644$	2.17669	−	6.09909i	0.0857737	−	0.240338i
$645$	12.9017	+	12.8560i	0.508004	+	0.506203i
$646$	45.3833	+	7.85574i	1.78558	+	0.309080i
$647$	22.0668	+	22.0668i	0.867537	+	0.867537i	0.992199	−	0.124662i	$-0.0397848\pi$
$647$	22.0668	+	22.0668i	0.867537	+	0.867537i	−0.124662	+	0.992199i	$0.539785\pi$
$648$	1.05914	+	3.80914i	0.0416069	+	0.149637i
$649$			3.03719i			0.119220i
$650$	−39.7004	−	6.72687i	−1.55718	−	0.263849i
$651$	1.17759			0.0461533
$652$	5.25926	−	2.49268i	0.205969	−	0.0976210i
$653$	4.15264	−	4.15264i	0.162505	−	0.162505i	−0.621170	−	0.783676i	$-0.713342\pi$
$653$	4.15264	−	4.15264i	0.162505	−	0.162505i	0.783676	+	0.621170i	$0.213342\pi$
$654$	11.2252	+	1.94305i	0.438940	+	0.0759794i
$655$	20.0934	−	20.1649i	0.785116	−	0.787910i
$656$	−13.6067	−	11.1298i	−0.531254	−	0.434544i
$657$	3.91366	−	3.91366i	0.152686	−	0.152686i
$658$	5.51547	+	7.82460i	0.215015	+	0.305035i
$659$		−	7.33416i		−	0.285698i	−0.989744	−	0.142849i	$-0.954374\pi$
$659$		−	7.33416i		−	0.285698i	0.989744	−	0.142849i	$-0.0456264\pi$
$660$	6.55497	−	18.4706i	0.255152	−	0.718966i
$661$			14.1992i			0.552286i	0.961117	+	0.276143i	$0.0890563\pi$
$661$			14.1992i			0.552286i	−0.961117	+	0.276143i	$0.910944\pi$
$662$	−22.7097	+	16.0078i	−0.882637	+	0.622160i
$663$	21.5001	−	21.5001i	0.834994	−	0.834994i
$664$	−11.2933	+	19.9922i	−0.438263	+	0.775849i
$665$	0.0282648	+	15.9124i	0.00109606	+	0.617057i
$666$	4.18219	−	24.1609i	0.162057	−	0.936216i
$667$	−9.07101	+	9.07101i	−0.351231	+	0.351231i
$668$	18.4141	−	8.72758i	0.712464	−	0.337680i
$669$	−4.43813			−0.171588
$670$	−2.60903	−	3.68741i	−0.100796	−	0.142457i
$671$		−	48.6266i		−	1.87721i
$672$	−0.472125	+	6.58293i	−0.0182126	+	0.253942i
$673$	34.0222	+	34.0222i	1.31146	+	1.31146i	0.920340	+	0.391120i	$0.127912\pi$
$673$	34.0222	+	34.0222i	1.31146	+	1.31146i	0.391120	+	0.920340i	$0.372088\pi$
$674$	2.07451	−	11.9847i	0.0799073	−	0.461632i
$675$	19.2025	+	19.0666i	0.739105	+	0.733872i
$676$	−36.5943	−	13.0601i	−1.40747	−	0.502311i
$677$	31.2959	+	31.2959i	1.20280	+	1.20280i	0.973312	+	0.229487i	$0.0737049\pi$
$677$	31.2959	+	31.2959i	1.20280	+	1.20280i	0.229487	+	0.973312i	$0.426295\pi$
$678$	7.15739	+	10.1539i	0.274878	+	0.389960i
$679$	−7.41324			−0.284494
$680$	27.8730	−	7.80350i	1.06888	−	0.299251i
$681$	−4.44044			−0.170158
$682$	−3.08919	−	4.38252i	−0.118291	−	0.167816i
$683$	−15.2332	−	15.2332i	−0.582884	−	0.582884i	0.352811	−	0.935695i	$-0.385226\pi$
$683$	−15.2332	−	15.2332i	−0.582884	−	0.582884i	−0.935695	+	0.352811i	$0.885226\pi$
$684$	−7.83992	+	21.9674i	−0.299767	+	0.839946i
$685$	0.0135614	+	7.63473i	0.000518154	+	0.291708i
$686$	−0.241210	+	1.39349i	−0.00920943	+	0.0532037i
$687$	5.45081	+	5.45081i	0.207961	+	0.207961i
$688$	2.78245	+	27.7870i	0.106080	+	1.05937i
$689$			54.6715i			2.08282i
$690$	−2.01663	+	11.7747i	−0.0767717	+	0.448254i
$691$	−36.3852			−1.38416			−0.692078	−	0.721823i	$-0.743305\pi$
$691$	−36.3852			−1.38416			−0.692078	+	0.721823i	$0.743305\pi$
$692$	−0.823984	−	1.73851i	−0.0313232	−	0.0660881i
$693$	4.35293	−	4.35293i	0.165354	−	0.165354i
$694$	−1.87364	+	10.8242i	−0.0711225	+	0.410881i
$695$	8.08761	+	8.05893i	0.306781	+	0.305693i
$696$	6.43023	−	11.3833i	0.243737	−	0.431483i
$697$	14.2218	−	14.2218i	0.538690	−	0.538690i
$698$	−19.6810	+	13.8729i	−0.744939	+	0.525098i
$699$			30.3455i			1.14777i
$700$	4.31498	+	9.02114i	0.163091	+	0.340967i
$701$			32.6468i			1.23305i	0.787334	+	0.616526i	$0.211461\pi$
$701$			32.6468i			1.23305i	−0.787334	+	0.616526i	$0.788539\pi$
$702$	25.1111	+	35.6242i	0.947757	+	1.34455i
$703$	−53.2372	+	53.2372i	−2.00788	+	2.00788i
$704$	25.7376	−	15.5121i	0.970023	−	0.584633i
$705$	−12.5094	−	12.4651i	−0.471132	−	0.469461i
$706$	−3.22541	−	0.558310i	−0.121390	−	0.0210123i
$707$	5.90395	−	5.90395i	0.222041	−	0.222041i
$708$	0.808040	+	1.70487i	0.0303680	+	0.0640728i
$709$	33.6345			1.26317			0.631585	−	0.775307i	$-0.282405\pi$
$709$	33.6345			1.26317			0.631585	+	0.775307i	$0.282405\pi$
$710$	13.3457	+	2.28569i	0.500854	+	0.0857805i
$711$		−	19.0739i		−	0.715327i
$712$	11.7116	−	3.25643i	0.438911	−	0.122040i
$713$	2.31094	+	2.31094i	0.0865453	+	0.0865453i
$714$	−7.44051	−	1.28793i	−0.278454	−	0.0481997i
$715$	−0.0849605	−	47.8307i	−0.00317734	−	1.78877i
$716$	3.92299	+	1.40007i	0.146609	+	0.0523230i
$717$	−2.36582	−	2.36582i	−0.0883533	−	0.0883533i
$718$	24.6602	−	17.3827i	0.920311	−	0.648716i
$719$	−30.8821			−1.15171			−0.575854	−	0.817553i	$-0.695330\pi$
$719$	−30.8821			−1.15171			−0.575854	+	0.817553i	$0.695330\pi$
$720$	1.48638	+	14.5825i	0.0553940	+	0.543457i
$721$	−4.12388			−0.153581
$722$	36.5743	−	25.7808i	1.36115	−	0.959461i
$723$	−1.73698	−	1.73698i	−0.0645991	−	0.0645991i
$724$	22.3941	+	7.99219i	0.832270	+	0.297027i
$725$	−0.0703739	−	19.8093i	−0.00261362	−	0.735701i
$726$	5.05642	+	0.875254i	0.187662	+	0.0324837i
$727$	17.6567	+	17.6567i	0.654852	+	0.654852i	0.954157	−	0.299306i	$-0.0967550\pi$
$727$	17.6567	+	17.6567i	0.654852	+	0.654852i	−0.299306	+	0.954157i	$0.596755\pi$
$728$	4.31476	+	15.5178i	0.159915	+	0.575129i
$729$		−	21.2336i		−	0.786430i
$730$	−8.71828	+	6.16862i	−0.322678	+	0.228311i
$731$	−31.9514			−1.18176
$732$	−12.9370	−	27.2956i	−0.478167	−	1.00887i
$733$	−1.84381	+	1.84381i	−0.0681025	+	0.0681025i	−0.740338	−	0.672235i	$-0.765334\pi$
$733$	−1.84381	+	1.84381i	−0.0681025	+	0.0681025i	0.672235	+	0.740338i	$0.265334\pi$
$734$	34.2512	+	5.92880i	1.26424	+	0.218836i
$735$	−0.00463396	−	2.60881i	−0.000170926	−	0.0962274i
$736$	−13.8451	+	11.9920i	−0.510336	+	0.442032i
$737$	3.79410	−	3.79410i	0.139757	−	0.139757i
$738$	5.86819	+	8.32499i	0.216011	+	0.306447i
$739$			20.8282i			0.766176i	0.923712	+	0.383088i	$0.125139\pi$
$739$			20.8282i			0.766176i	−0.923712	+	0.383088i	$0.874861\pi$
$740$	−15.8243	+	44.5897i	−0.581714	+	1.63915i
$741$		−	47.2788i		−	1.73683i
$742$	11.0976	−	7.82255i	0.407405	−	0.287175i
$743$	−12.3584	+	12.3584i	−0.453384	+	0.453384i	−0.896476	−	0.443092i	$-0.853882\pi$
$743$	−12.3584	+	12.3584i	−0.453384	+	0.453384i	0.443092	+	0.896476i	$0.353882\pi$
$744$	−2.90002	−	1.63817i	−0.106320	−	0.0600582i
$745$	−10.9477	+	10.9867i	−0.401094	+	0.402521i
$746$	1.69581	−	9.79683i	0.0620879	−	0.358687i
$747$	9.40740	−	9.40740i	0.344199	−	0.344199i
$748$	14.7256	+	31.0693i	0.538423	+	1.13601i
$749$	−15.9643			−0.583324
$750$	−10.7083	−	15.0209i	−0.391013	−	0.548486i
$751$		−	42.8143i		−	1.56232i	−0.624333	−	0.781158i	$-0.714629\pi$
$751$		−	42.8143i		−	1.56232i	0.624333	−	0.781158i	$-0.285371\pi$
$752$	−2.69784	−	26.9421i	−0.0983802	−	0.982479i
$753$	6.84504	+	6.84504i	0.249447	+	0.249447i
$754$	5.44195	−	31.4386i	0.198184	−	1.14493i
$755$	−28.7421	−	28.6401i	−1.04603	−	1.04232i
$756$	3.63827	−	10.1944i	0.132323	−	0.370767i
$757$	14.9290	+	14.9290i	0.542605	+	0.542605i	0.924292	−	0.381687i	$-0.124657\pi$
$757$	14.9290	+	14.9290i	0.542605	+	0.542605i	−0.381687	+	0.924292i	$0.624657\pi$
$758$	−16.8339	−	23.8817i	−0.611435	−	0.867421i
$759$	−14.1903			−0.515076
$760$	22.0665	−	39.2265i	0.800436	−	1.42289i
$761$	1.00927			0.0365859			0.0182930	−	0.999833i	$-0.494177\pi$
$761$	1.00927			0.0365859			0.0182930	+	0.999833i	$0.494177\pi$
$762$	−4.05519	−	5.75295i	−0.146904	−	0.208408i
$763$	−4.88221	−	4.88221i	−0.176748	−	0.176748i
$764$	37.6976	+	13.4538i	1.36385	+	0.486743i
$765$	−16.7709	+	0.0297896i	−0.606351	+	0.00107705i
$766$	0.919851	−	5.31407i	0.0332356	−	0.192005i
$767$	3.25573	+	3.25573i	0.117557	+	0.117557i
$768$	10.3204	−	15.5548i	0.372404	−	0.561287i
$769$		−	50.3632i		−	1.81615i	−0.418813	−	0.908073i	$-0.637554\pi$
$769$		−	50.3632i		−	1.81615i	0.418813	−	0.908073i	$-0.362446\pi$
$770$	−9.69682	+	6.86099i	−0.349449	+	0.247253i
$771$	30.4011			1.09487
$772$	−14.0736	+	6.67035i	−0.506521	+	0.240071i
$773$	−21.2946	+	21.2946i	−0.765915	+	0.765915i	−0.977385	−	0.211470i	$-0.932175\pi$
$773$	−21.2946	+	21.2946i	−0.765915	+	0.765915i	0.211470	+	0.977385i	$0.432175\pi$
$774$	2.75978	−	15.9435i	0.0991982	−	0.573077i
$775$	−5.04664	+	0.0179285i	−0.181281	+	0.000644011i
$776$	18.2564	+	10.3127i	0.655367	+	0.370205i
$777$	8.72814	−	8.72814i	0.313120	−	0.313120i
$778$	−1.98609	+	1.39997i	−0.0712047	+	0.0501913i
$779$		−	31.2739i		−	1.12050i
$780$	−12.7730	−	26.8262i	−0.457346	−	0.960533i
$781$			16.0836i			0.575517i
$782$	−12.0740	−	17.1290i	−0.431766	−	0.612531i
$783$	−15.1619	+	15.1619i	−0.541842	+	0.541842i
$784$	2.53254	−	3.09617i	0.0904478	−	0.110577i
$785$	−27.7043	+	0.0492105i	−0.988811	+	0.00175640i
$786$	20.6976	+	3.58270i	0.738258	+	0.127791i
$787$	2.77580	−	2.77580i	0.0989464	−	0.0989464i	−0.655901	−	0.754847i	$-0.727711\pi$
$787$	2.77580	−	2.77580i	0.0989464	−	0.0989464i	0.754847	+	0.655901i	$0.227711\pi$
$788$	−15.5775	+	7.38311i	−0.554925	+	0.263013i
$789$	0.727662			0.0259055
$790$	−6.21310	+	36.2770i	−0.221052	+	1.29068i
$791$		−	7.52927i		−	0.267710i
$792$	−16.7753	+	4.66440i	−0.596084	+	0.165742i
$793$	−52.1255	−	52.1255i	−1.85103	−	1.85103i
$794$	9.58437	+	1.65903i	0.340136	+	0.0588768i
$795$	−17.6791	+	17.7420i	−0.627013	+	0.629244i
$796$	−5.14147	+	14.4064i	−0.182235	+	0.510621i
$797$	18.8315	+	18.8315i	0.667046	+	0.667046i	0.957031	−	0.289985i	$-0.0936505\pi$
$797$	18.8315	+	18.8315i	0.667046	+	0.667046i	−0.289985	+	0.957031i	$0.593650\pi$
$798$	−9.59695	+	6.76478i	−0.339728	+	0.239471i
$799$	30.9798			1.09599
$800$	1.92311	−	28.2188i	0.0679920	−	0.997686i
$801$	−7.04324			−0.248861
$802$	0.343312	−	0.241997i	0.0121228	−	0.00854520i
$803$	−8.97053	−	8.97053i	−0.316563	−	0.316563i
$804$	1.12033	−	3.13916i	0.0395109	−	0.110709i
$805$	5.11052	−	5.12871i	0.180122	−	0.180763i
$806$	−8.00933	−	1.38639i	−0.282117	−	0.0488337i
$807$	−13.0127	−	13.0127i	−0.458068	−	0.458068i
$808$	−22.7527	+	6.32641i	−0.800436	+	0.222562i
$809$		−	54.1390i		−	1.90343i	−0.306987	−	0.951714i	$-0.599321\pi$
$809$		−	54.1390i		−	1.90343i	0.306987	−	0.951714i	$-0.400679\pi$
$810$	−0.746196	+	4.35688i	−0.0262187	+	0.153085i
$811$	2.13578			0.0749974			0.0374987	−	0.999297i	$-0.488061\pi$
$811$	2.13578			0.0749974			0.0374987	+	0.999297i	$0.488061\pi$
$812$	−7.16026	+	3.39368i	−0.251276	+	0.119095i
$813$	−11.8044	+	11.8044i	−0.413998	+	0.413998i
$814$	−55.3794	−	9.58604i	−1.94105	−	0.335991i
$815$	6.50703	−	0.0115583i	0.227931	−	0.000404869i
$816$	16.5319	+	13.5224i	0.578732	+	0.473380i
$817$	−35.1306	+	35.1306i	−1.22906	+	1.22906i
$818$	6.53434	+	9.27004i	0.228468	+	0.324119i
$819$		−	9.33227i		−	0.326096i
$820$	−8.44903	−	17.7449i	−0.295053	−	0.619680i
$821$		−	44.2539i		−	1.54447i	−0.635335	−	0.772237i	$-0.719138\pi$
$821$		−	44.2539i		−	1.54447i	0.635335	−	0.772237i	$-0.280862\pi$
$822$	−4.60459	+	3.24572i	−0.160604	+	0.113208i
$823$	1.34042	−	1.34042i	0.0467239	−	0.0467239i	−0.683359	−	0.730083i	$-0.739482\pi$
$823$	1.34042	−	1.34042i	0.0467239	−	0.0467239i	0.730083	+	0.683359i	$0.239482\pi$
$824$	10.1558	+	5.73681i	0.353793	+	0.199851i
$825$	15.4394	−	15.5495i	0.537531	−	0.541364i
$826$	0.195030	−	1.12671i	0.00678596	−	0.0392031i
$827$	34.0770	−	34.0770i	1.18497	−	1.18497i	0.206535	−	0.978439i	$-0.433781\pi$
$827$	34.0770	−	34.0770i	1.18497	−	1.18497i	0.978439	−	0.206535i	$-0.0662189\pi$
$828$	9.59013	−	4.54534i	0.333280	−	0.157962i
$829$	−32.8425			−1.14067			−0.570333	−	0.821414i	$-0.693186\pi$
$829$	−32.8425			−1.14067			−0.570333	+	0.821414i	$0.693186\pi$
$830$	−20.9564	+	14.8277i	−0.727409	+	0.514678i
$831$			15.9773i			0.554246i
$832$	10.9613	−	44.2177i	0.380016	−	1.53297i
$833$	3.23613	+	3.23613i	0.112125	+	0.112125i
$834$	−1.43692	+	8.30124i	−0.0497566	+	0.287448i
$835$	22.7829	−	0.0404687i	0.788436	−	0.00140048i
$836$	50.3517	+	17.9699i	1.74145	+	0.621504i
$837$	3.86265	+	3.86265i	0.133513	+	0.133513i
$838$	0.211158	+	0.299562i	0.00729433	+	0.0103482i
$839$	−15.5393			−0.536478			−0.268239	−	0.963352i	$-0.586442\pi$
$839$	−15.5393			−0.536478			−0.268239	+	0.963352i	$0.586442\pi$
$840$	−3.61776	+	6.43110i	−0.124825	+	0.221894i
$841$	−13.3034			−0.458738
$842$	16.2152	+	23.0040i	0.558813	+	0.792769i
$843$	7.04760	+	7.04760i	0.242732	+	0.242732i
$844$	11.7415	−	32.8996i	0.404159	−	1.13245i
$845$	−30.7721	−	30.6630i	−1.05859	−	1.05484i
$846$	−2.67586	+	15.4587i	−0.0919981	+	0.531482i
$847$	−2.19921	−	2.19921i	−0.0755656	−	0.0755656i
$848$	−38.2119	+	3.82633i	−1.31220	+	0.131397i
$849$		−	11.9011i		−	0.408443i
$850$	31.9065	+	5.40625i	1.09438	+	0.185433i
$851$	34.2568			1.17431
$852$	4.27902	+	9.02823i	0.146597	+	0.309302i
$853$	16.5105	−	16.5105i	0.565309	−	0.565309i	−0.365502	−	0.930811i	$-0.619103\pi$
$853$	16.5105	−	16.5105i	0.565309	−	0.565309i	0.930811	+	0.365502i	$0.119103\pi$
$854$	−3.12251	+	18.0390i	−0.106850	+	0.617282i
$855$	−18.4069	+	18.4724i	−0.629501	+	0.631741i
$856$	39.3150	+	22.2084i	1.34376	+	0.759066i
$857$	33.2019	−	33.2019i	1.13415	−	1.13415i	0.144675	−	0.989479i	$-0.453786\pi$
$857$	33.2019	−	33.2019i	1.13415	−	1.13415i	0.989479	−	0.144675i	$-0.0462138\pi$
$858$	28.8472	−	20.3341i	0.984828	−	0.694194i
$859$		−	55.4620i		−	1.89234i	−0.323672	−	0.946169i	$-0.604917\pi$
$859$		−	55.4620i		−	1.89234i	0.323672	−	0.946169i	$-0.395083\pi$
$860$	−10.4423	+	29.4242i	−0.356079	+	1.00336i
$861$			5.12729i			0.174738i
$862$	−26.3953	−	37.4461i	−0.899029	−	1.27542i
$863$	14.1859	−	14.1859i	0.482895	−	0.482895i	−0.423160	−	0.906055i	$-0.639079\pi$
$863$	14.1859	−	14.1859i	0.482895	−	0.482895i	0.906055	+	0.423160i	$0.139079\pi$
$864$	−23.1416	+	20.0443i	−0.787292	+	0.681920i
$865$	−0.00382072	−	2.15097i	−0.000129908	−	0.0731352i
$866$	−45.7075	−	7.91186i	−1.55320	−	0.268856i
$867$	−3.25455	+	3.25455i	−0.110530	+	0.110530i
$868$	0.864577	+	1.82415i	0.0293456	+	0.0619158i
$869$	−43.7195			−1.48308
$870$	11.9323	−	8.44271i	0.404543	−	0.286235i
$871$		−	8.13419i		−	0.275617i
$872$	5.23156	+	18.8151i	0.177163	+	0.637158i
$873$	−8.59060	−	8.59060i	−0.290748	−	0.290748i
$874$	−32.1088	−	5.55795i	−1.08610	−	0.188000i
$875$	0.0595777	+	11.1802i	0.00201409	+	0.377959i
$876$	−7.42203	−	2.64883i	−0.250767	−	0.0894958i
$877$	3.73511	+	3.73511i	0.126126	+	0.126126i	0.767352	−	0.641226i	$-0.221574\pi$
$877$	3.73511	+	3.73511i	0.126126	+	0.126126i	−0.641226	+	0.767352i	$0.721574\pi$
$878$	12.0372	−	8.48485i	0.406234	−	0.286350i
$879$	0.0378115			0.00127535
$880$	33.4246	−	3.40694i	1.12674	−	0.114848i
$881$	−24.1243			−0.812770			−0.406385	−	0.913702i	$-0.633211\pi$
$881$	−24.1243			−0.812770			−0.406385	+	0.913702i	$0.633211\pi$
$882$	−1.89432	+	1.33529i	−0.0637851	+	0.0449614i
$883$	17.0009	+	17.0009i	0.572125	+	0.572125i	0.932722	−	0.360597i	$-0.117427\pi$
$883$	17.0009	+	17.0009i	0.572125	+	0.572125i	−0.360597	+	0.932722i	$0.617427\pi$
$884$	49.0901	+	17.5197i	1.65108	+	0.589251i
$885$	0.00374679	+	2.10935i	0.000125947	+	0.0709050i
$886$	11.2611	+	1.94927i	0.378324	+	0.0654868i
$887$	−19.5877	−	19.5877i	−0.657692	−	0.657692i	0.297141	−	0.954833i	$-0.403967\pi$
$887$	−19.5877	−	19.5877i	−0.657692	−	0.657692i	−0.954833	+	0.297141i	$0.903967\pi$
$888$	−33.6365	+	9.35268i	−1.12877	+	0.313856i
$889$			4.26589i			0.143073i
$890$	13.3957	+	2.29426i	0.449024	+	0.0769036i
$891$	−5.25072			−0.175906
$892$	−3.25844	−	6.87492i	−0.109101	−	0.230189i
$893$	34.0624	−	34.0624i	1.13986	−	1.13986i
$894$	−11.2769	−	1.95200i	−0.377156	−	0.0652847i
$895$	3.29883	+	3.28713i	0.110268	+	0.109877i
$896$	−10.5440	+	4.10179i	−0.352249	+	0.137031i
$897$	−15.2114	+	15.2114i	−0.507892	+	0.507892i
$898$	1.39693	+	1.98178i	0.0466162	+	0.0661328i
$899$		−	3.99888i		−	0.133370i
$900$	−5.45359	+	15.4541i	−0.181786	+	0.515138i
$901$		−	43.9385i		−	1.46380i
$902$	19.0818	−	13.4505i	0.635354	−	0.447853i
$903$	5.75960	−	5.75960i	0.191667	−	0.191667i
$904$	−10.4741	+	18.5422i	−0.348365	+	0.616703i
$905$	18.8311	+	18.7644i	0.625968	+	0.623749i
$906$	5.10659	−	29.5013i	0.169655	−	0.980113i
$907$	15.5500	−	15.5500i	0.516330	−	0.516330i	−0.400129	−	0.916459i	$-0.631035\pi$
$907$	15.5500	−	15.5500i	0.516330	−	0.516330i	0.916459	+	0.400129i	$0.131035\pi$
$908$	−3.26014	−	6.87850i	−0.108192	−	0.228271i
$909$	13.6832			0.453844
$910$	−3.03988	+	17.7492i	−0.100771	+	0.588380i
$911$			21.4974i			0.712239i	0.934440	+	0.356120i	$0.115900\pi$
$911$			21.4974i			0.712239i	−0.934440	+	0.356120i	$0.884100\pi$
$912$	33.0448	−	3.30893i	1.09422	−	0.109570i
$913$	−21.5628	−	21.5628i	−0.713624	−	0.713624i
$914$	−2.12247	+	12.2617i	−0.0702050	+	0.405581i
$915$	−0.0599875	−	33.7715i	−0.00198313	−	1.11645i
$916$	−4.44168	+	12.4456i	−0.146757	+	0.411213i
$917$	−9.00206	−	9.00206i	−0.297274	−	0.297274i
$918$	−20.1813	−	28.6305i	−0.666083	−	0.944948i
$919$	55.0840			1.81705			0.908526	−	0.417828i	$-0.137209\pi$
$919$	55.0840			1.81705			0.908526	+	0.417828i	$0.137209\pi$
$920$	−19.7202	+	5.52099i	−0.650157	+	0.182022i
$921$	−39.4040			−1.29841
$922$	6.33608	+	8.98878i	0.208668	+	0.296030i
$923$	17.2409	+	17.2409i	0.567491	+	0.567491i
$924$	−8.25507	−	2.94614i	−0.271572	−	0.0969208i
$925$	−37.2722	+	37.5380i	−1.22550	+	1.23424i
$926$	6.81148	−	39.3506i	0.223839	−	1.29314i
$927$	−4.77882	−	4.77882i	−0.156957	−	0.156957i
$928$	22.3544	+	1.60325i	0.733820	+	0.0526294i
$929$			27.3872i			0.898543i	0.893395	+	0.449272i	$0.148316\pi$
$929$			27.3872i			0.898543i	−0.893395	+	0.449272i	$0.851684\pi$
$930$	−2.15087	−	3.03988i	−0.0705298	−	0.0996817i
$931$	7.11626			0.233226
$932$	−47.0070	+	22.2795i	−1.53977	+	0.729788i
$933$	−17.2286	+	17.2286i	−0.564039	+	0.564039i
$934$	3.75012	−	21.6648i	0.122708	−	0.708893i
$935$	0.0682811	+	38.4406i	0.00223303	+	1.25714i
$936$	−12.9823	+	22.9824i	−0.424341	+	0.751202i
$937$	−28.9345	+	28.9345i	−0.945250	+	0.945250i	−0.998577	−	0.0533271i	$-0.983017\pi$
$937$	−28.9345	+	28.9345i	−0.945250	+	0.945250i	0.0533271	+	0.998577i	$0.483017\pi$
$938$	−1.65113	+	1.16386i	−0.0539113	+	0.0380014i
$939$		−	3.59245i		−	0.117235i
$940$	10.1248	−	28.5296i	0.330234	−	0.930532i
$941$			25.5839i			0.834010i	0.908904	+	0.417005i	$0.136920\pi$
$941$			25.5839i			0.834010i	−0.908904	+	0.417005i	$0.863080\pi$
$942$	−11.7778	−	16.7088i	−0.383743	−	0.544402i
$943$	−10.0620	+	10.0620i	−0.327663	+	0.327663i
$944$	−2.04768	+	2.50340i	−0.0666463	+	0.0814788i
$945$	8.54206	−	8.57246i	0.277873	−	0.278862i
$946$	−36.5442	−	6.32571i	−1.18816	−	0.205667i
$947$	14.0237	−	14.0237i	0.455708	−	0.455708i	−0.441536	−	0.897244i	$-0.645566\pi$
$947$	14.0237	−	14.0237i	0.455708	−	0.455708i	0.897244	+	0.441536i	$0.145566\pi$
$948$	−24.5411	+	11.6315i	−0.797057	+	0.377774i
$949$	−19.2320			−0.624297
$950$	41.0255	−	29.1371i	1.33104	−	0.945332i
$951$			36.1675i			1.17281i
$952$	−3.46769	−	12.4714i	−0.112388	−	0.404200i
$953$	36.3165	+	36.3165i	1.17641	+	1.17641i	0.980653	+	0.195753i	$0.0627151\pi$
$953$	36.3165	+	36.3165i	1.17641	+	1.17641i	0.195753	+	0.980653i	$0.437285\pi$
$954$	21.9250	+	3.79516i	0.709848	+	0.122873i
$955$	31.6998	+	31.5874i	1.02578	+	1.02215i
$956$	1.92783	−	5.40177i	0.0623504	−	0.174706i
$957$	12.2776	+	12.2776i	0.396877	+	0.396877i
$958$	13.4365	−	9.47126i	0.434115	−	0.306003i
$959$	3.41436			0.110255
$960$	17.8558	−	10.8050i	0.576295	−	0.348729i
$961$	29.9812			0.967137
$962$	−69.6400	+	49.0884i	−2.24528	+	1.58267i
$963$	−18.4998	−	18.4998i	−0.596147	−	0.596147i
$964$	1.41541	−	3.96597i	0.0455872	−	0.127735i
$965$	−17.4126	+	0.0309296i	−0.560533	+	0.000995660i
$966$	5.26418	+	0.911215i	0.169372	+	0.0293179i
$967$	−17.1902	−	17.1902i	−0.552799	−	0.552799i	0.374448	−	0.927248i	$-0.377832\pi$
$967$	−17.1902	−	17.1902i	−0.552799	−	0.552799i	−0.927248	+	0.374448i	$0.877832\pi$
$968$	2.35657	+	8.47530i	0.0757431	+	0.272407i
$969$			37.9971i			1.22064i
$970$	13.5403	+	19.1369i	0.434754	+	0.614449i
$971$	59.2449			1.90126			0.950630	−	0.310327i	$-0.100439\pi$
$971$	59.2449			1.90126			0.950630	+	0.310327i	$0.100439\pi$
$972$	26.3962	−	12.5107i	0.846657	−	0.401282i
$973$	3.61048	−	3.61048i	0.115747	−	0.115747i
$974$	37.7348	+	6.53179i	1.20910	+	0.209292i
$975$	−0.118011	−	33.2187i	−0.00377939	−	1.06385i
$976$	32.7842	−	40.0805i	1.04940	−	1.28294i
$977$	−0.836306	+	0.836306i	−0.0267558	+	0.0267558i	−0.720358	−	0.693602i	$-0.756023\pi$
$977$	−0.836306	+	0.836306i	−0.0267558	+	0.0267558i	0.693602	+	0.720358i	$0.256023\pi$
$978$	2.76631	+	3.92446i	0.0884568	+	0.125490i
$979$			16.1439i			0.515961i
$980$	4.03780	−	1.92255i	0.128983	−	0.0614136i
$981$		−	11.3152i		−	0.361266i
$982$	−39.8002	+	28.0547i	−1.27008	+	0.895262i
$983$	9.43467	−	9.43467i	0.300919	−	0.300919i	−0.540454	−	0.841373i	$-0.681748\pi$
$983$	9.43467	−	9.43467i	0.300919	−	0.300919i	0.841373	+	0.540454i	$0.181748\pi$
$984$	7.13269	−	12.6269i	0.227382	−	0.402530i
$985$	−19.2733	+	0.0342346i	−0.614098	+	0.00109081i
$986$	−4.37359	+	25.2666i	−0.139283	+	0.804654i
$987$	−5.58447	+	5.58447i	−0.177756	+	0.177756i
$988$	73.2377	−	34.7118i	2.33000	−	1.10433i
$989$	22.6056			0.718818
$990$	−19.1875	−	3.28621i	−0.609819	−	0.104443i
$991$			20.9319i			0.664923i	0.943117	+	0.332462i	$0.107879\pi$
$991$			20.9319i			0.664923i	−0.943117	+	0.332462i	$0.892121\pi$
$992$	0.408446	−	5.69503i	0.0129682	−	0.180817i
$993$	−16.2081	−	16.2081i	−0.514347	−	0.514347i
$994$	1.03279	−	5.96654i	0.0327582	−	0.189247i
$995$	−12.0713	+	12.1143i	−0.382687	+	0.384049i
$996$	−17.8406	−	6.36709i	−0.565301	−	0.201749i
$997$	0.257441	+	0.257441i	0.00815323	+	0.00815323i	0.711172	−	0.703018i	$-0.248165\pi$
$997$	0.257441	+	0.257441i	0.00815323	+	0.00815323i	−0.703018	+	0.711172i	$0.748165\pi$
$998$	18.1387	+	25.7327i	0.574169	+	0.814554i
$999$	57.2590			1.81160

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.w.a.43.8	✓	72
4.3	odd	2		1120.2.bi.a.463.24		72
5.2	odd	4	inner	280.2.w.a.267.11	yes	72
8.3	odd	2	inner	280.2.w.a.43.11	yes	72
8.5	even	2		1120.2.bi.a.463.23		72
20.7	even	4		1120.2.bi.a.687.23		72
40.27	even	4	inner	280.2.w.a.267.8	yes	72
40.37	odd	4		1120.2.bi.a.687.24		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.w.a.43.8	✓	72	1.1	even	1	trivial
280.2.w.a.43.11	yes	72	8.3	odd	2	inner
280.2.w.a.267.8	yes	72	40.27	even	4	inner
280.2.w.a.267.11	yes	72	5.2	odd	4	inner
1120.2.bi.a.463.23		72	8.5	even	2
1120.2.bi.a.463.24		72	4.3	odd	2
1120.2.bi.a.687.23		72	20.7	even	4
1120.2.bi.a.687.24		72	40.37	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	280.w (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.15591 + 0.814786i) q^{2} +(-0.824980 - 0.824980i) q^{3} +(0.672247 - 1.88364i) q^{4} +(1.57833 - 1.58394i) q^{5} +(1.62578 + 0.281419i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(0.757704 + 2.72505i) q^{8} -1.63882i q^{9} +O(q^{10})\)	\(q+(-1.15591 + 0.814786i) q^{2} +(-0.824980 - 0.824980i) q^{3} +(0.672247 - 1.88364i) q^{4} +(1.57833 - 1.58394i) q^{5} +(1.62578 + 0.281419i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(0.757704 + 2.72505i) q^{8} -1.63882i q^{9} +(-0.533826 + 3.11689i) q^{10} -3.75635 q^{11} +(-2.10855 + 0.999371i) q^{12} +(-4.02663 + 4.02663i) q^{13} +(1.39349 + 0.241210i) q^{14} +(-2.60881 + 0.00463396i) q^{15} +(-3.09617 - 2.53254i) q^{16} +(3.23613 - 3.23613i) q^{17} +(1.33529 + 1.89432i) q^{18} -7.11626i q^{19} +(-1.92255 - 4.03780i) q^{20} +1.16670i q^{21} +(4.34199 - 3.06062i) q^{22} +(-2.28956 + 2.28956i) q^{23} +(1.62302 - 2.87320i) q^{24} +(-0.0177627 - 4.99997i) q^{25} +(1.37357 - 7.93526i) q^{26} +(-3.82693 + 3.82693i) q^{27} +(-1.80728 + 0.856581i) q^{28} +3.96189 q^{29} +(3.01177 - 2.13098i) q^{30} -1.00933i q^{31} +(5.64236 + 0.404668i) q^{32} +(3.09891 + 3.09891i) q^{33} +(-1.10391 + 6.37741i) q^{34} +(-2.23606 + 0.00397187i) q^{35} +(-3.08693 - 1.10169i) q^{36} +(-7.48107 - 7.48107i) q^{37} +(5.79823 + 8.22574i) q^{38} +6.64377 q^{39} +(5.51223 + 3.10086i) q^{40} +4.39471 q^{41} +(-0.950609 - 1.34860i) q^{42} +(-4.93667 - 4.93667i) q^{43} +(-2.52519 + 7.07559i) q^{44} +(-2.59580 - 2.58659i) q^{45} +(0.781021 - 4.51203i) q^{46} +(4.78656 + 4.78656i) q^{47} +(0.464982 + 4.64357i) q^{48} +1.00000i q^{49} +(4.09444 + 5.76503i) q^{50} -5.33947 q^{51} +(4.87781 + 10.2916i) q^{52} +(6.78875 - 6.78875i) q^{53} +(1.30545 - 7.54171i) q^{54} +(-5.92875 + 5.94985i) q^{55} +(1.39112 - 2.46268i) q^{56} +(-5.87077 + 5.87077i) q^{57} +(-4.57959 + 3.22810i) q^{58} -0.808549i q^{59} +(-1.74504 + 4.91716i) q^{60} +12.9452i q^{61} +(0.822392 + 1.16670i) q^{62} +(-1.15882 + 1.15882i) q^{63} +(-6.85177 + 4.12956i) q^{64} +(0.0226178 + 12.7333i) q^{65} +(-6.10700 - 1.05711i) q^{66} +(-1.01005 + 1.01005i) q^{67} +(-3.92020 - 8.27116i) q^{68} +3.77769 q^{69} +(2.58145 - 1.82651i) q^{70} -4.28172i q^{71} +(4.46586 - 1.24174i) q^{72} +(2.38810 + 2.38810i) q^{73} +(14.7429 + 2.55196i) q^{74} +(-4.11022 + 4.13953i) q^{75} +(-13.4044 - 4.78389i) q^{76} +(2.65614 + 2.65614i) q^{77} +(-7.67959 + 5.41326i) q^{78} +11.6388 q^{79} +(-8.89817 + 0.906982i) q^{80} +1.39783 q^{81} +(-5.07988 + 3.58074i) q^{82} +(5.74036 + 5.74036i) q^{83} +(2.19763 + 0.784309i) q^{84} +(-0.0181775 - 10.2335i) q^{85} +(9.72866 + 1.68401i) q^{86} +(-3.26848 - 3.26848i) q^{87} +(-2.84620 - 10.2362i) q^{88} -4.29776i q^{89} +(5.10802 + 0.874843i) q^{90} +5.69451 q^{91} +(2.77355 + 5.85186i) q^{92} +(-0.832681 + 0.832681i) q^{93} +(-9.43285 - 1.63280i) q^{94} +(-11.2718 - 11.2318i) q^{95} +(-4.32099 - 4.98868i) q^{96} +(5.24195 - 5.24195i) q^{97} +(-0.814786 - 1.15591i) q^{98} +6.15597i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 8 q^{6}+O(q^{10}) \) 72 * q + 8 * q^6	\( 72 q + 8 q^{6} + 16 q^{10} - 16 q^{12} - 8 q^{16} + 8 q^{17} - 28 q^{18} - 20 q^{20} - 36 q^{22} - 8 q^{25} - 32 q^{26} - 4 q^{30} + 40 q^{32} + 64 q^{36} - 4 q^{40} + 20 q^{42} - 64 q^{43} + 48 q^{46} - 80 q^{48} - 32 q^{51} + 16 q^{52} - 24 q^{56} + 4 q^{58} - 80 q^{60} - 40 q^{62} - 8 q^{65} + 32 q^{66} - 24 q^{68} + 40 q^{72} - 40 q^{73} + 112 q^{75} - 8 q^{76} + 28 q^{78} - 20 q^{80} - 72 q^{81} + 24 q^{82} + 80 q^{83} + 8 q^{86} - 88 q^{88} + 136 q^{90} - 96 q^{92} - 56 q^{96} - 8 q^{97}+O(q^{100}) \) 72 * q + 8 * q^6 + 16 * q^10 - 16 * q^12 - 8 * q^16 + 8 * q^17 - 28 * q^18 - 20 * q^20 - 36 * q^22 - 8 * q^25 - 32 * q^26 - 4 * q^30 + 40 * q^32 + 64 * q^36 - 4 * q^40 + 20 * q^42 - 64 * q^43 + 48 * q^46 - 80 * q^48 - 32 * q^51 + 16 * q^52 - 24 * q^56 + 4 * q^58 - 80 * q^60 - 40 * q^62 - 8 * q^65 + 32 * q^66 - 24 * q^68 + 40 * q^72 - 40 * q^73 + 112 * q^75 - 8 * q^76 + 28 * q^78 - 20 * q^80 - 72 * q^81 + 24 * q^82 + 80 * q^83 + 8 * q^86 - 88 * q^88 + 136 * q^90 - 96 * q^92 - 56 * q^96 - 8 * q^97

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