LMFDB - Embedded newform 560.2.t.a.43.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [560,2,Mod(43,560)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(560, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 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("560.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.t (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:	$4.47162251319$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$72$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.15
Character	$\chi$	$=$	560.43
Dual form			560.2.t.a.547.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.11562 + 0.869134i) q^{2} -2.40982i q^{3} +(0.489211 - 1.93925i) q^{4} +(-2.07668 + 0.829085i) q^{5} +(2.09446 + 2.68844i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(1.13969 + 2.58865i) q^{8} -2.80723 q^{9} +O(q^{10})$	\(q+(-1.11562 + 0.869134i) q^{2} -2.40982i q^{3} +(0.489211 - 1.93925i) q^{4} +(-2.07668 + 0.829085i) q^{5} +(2.09446 + 2.68844i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(1.13969 + 2.58865i) q^{8} -2.80723 q^{9} +(1.59620 - 2.72986i) q^{10} +(-2.34682 + 2.34682i) q^{11} +(-4.67323 - 1.17891i) q^{12} +4.48941 q^{13} +(0.174291 - 1.40343i) q^{14} +(1.99794 + 5.00443i) q^{15} +(-3.52135 - 1.89740i) q^{16} +(-2.44324 + 2.44324i) q^{17} +(3.13179 - 2.43986i) q^{18} +(-2.49650 + 2.49650i) q^{19} +(0.591861 + 4.43280i) q^{20} +(1.70400 + 1.70400i) q^{21} +(0.578455 - 4.65786i) q^{22} +(-2.43246 - 2.43246i) q^{23} +(6.23817 - 2.74645i) q^{24} +(3.62524 - 3.44349i) q^{25} +(-5.00847 + 3.90190i) q^{26} -0.464550i q^{27} +(1.02533 + 1.71718i) q^{28} +(3.09156 + 3.09156i) q^{29} +(-6.57847 - 3.84656i) q^{30} +10.1502i q^{31} +(5.57758 - 0.943746i) q^{32} +(5.65541 + 5.65541i) q^{33} +(0.602222 - 4.84924i) q^{34} +(0.882186 - 2.05469i) q^{35} +(-1.37333 + 5.44390i) q^{36} +11.7133 q^{37} +(0.615349 - 4.95494i) q^{38} -10.8187i q^{39} +(-4.51299 - 4.43091i) q^{40} +12.2006i q^{41} +(-3.38202 - 0.420010i) q^{42} +1.81456 q^{43} +(3.40297 + 5.69915i) q^{44} +(5.82972 - 2.32743i) q^{45} +(4.82784 + 0.599565i) q^{46} +(2.14045 + 2.14045i) q^{47} +(-4.57239 + 8.48580i) q^{48} -1.00000i q^{49} +(-1.05152 + 6.99245i) q^{50} +(5.88778 + 5.88778i) q^{51} +(2.19627 - 8.70607i) q^{52} -4.30788i q^{53} +(0.403756 + 0.518260i) q^{54} +(2.92789 - 6.81932i) q^{55} +(-2.63633 - 1.02457i) q^{56} +(6.01611 + 6.01611i) q^{57} +(-6.13599 - 0.762022i) q^{58} +(4.71152 + 4.71152i) q^{59} +(10.6822 - 1.42628i) q^{60} +(2.97080 - 2.97080i) q^{61} +(-8.82190 - 11.3238i) q^{62} +(1.98501 - 1.98501i) q^{63} +(-5.40221 + 5.90052i) q^{64} +(-9.32309 + 3.72210i) q^{65} +(-11.2246 - 1.39397i) q^{66} -8.05320 q^{67} +(3.54279 + 5.93331i) q^{68} +(-5.86180 + 5.86180i) q^{69} +(0.801617 + 3.05899i) q^{70} -11.9106 q^{71} +(-3.19937 - 7.26692i) q^{72} +(-8.55814 + 8.55814i) q^{73} +(-13.0675 + 10.1804i) q^{74} +(-8.29820 - 8.73617i) q^{75} +(3.62001 + 6.06264i) q^{76} -3.31891i q^{77} +(9.40288 + 12.0695i) q^{78} +1.48361 q^{79} +(8.88583 + 1.02081i) q^{80} -9.54116 q^{81} +(-10.6040 - 13.6112i) q^{82} -9.70769i q^{83} +(4.13809 - 2.47086i) q^{84} +(3.04819 - 7.09950i) q^{85} +(-2.02436 + 1.57710i) q^{86} +(7.45010 - 7.45010i) q^{87} +(-8.74975 - 3.40044i) q^{88} -4.91472 q^{89} +(-4.48090 + 7.66334i) q^{90} +(-3.17449 + 3.17449i) q^{91} +(-5.90713 + 3.52715i) q^{92} +24.4602 q^{93} +(-4.24826 - 0.527587i) q^{94} +(3.11463 - 7.25425i) q^{95} +(-2.27426 - 13.4409i) q^{96} +(-9.69326 + 9.69326i) q^{97} +(0.869134 + 1.11562i) q^{98} +(6.58806 - 6.58806i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 8 q^{4} - 144 q^{9}+O(q^{10}) $ 144 * q + 8 * q^4 - 144 * q^9	$ 144 q + 8 q^{4} - 144 q^{9} - 16 q^{12} + 8 q^{16} - 28 q^{18} - 16 q^{19} + 4 q^{22} + 32 q^{26} - 36 q^{30} + 32 q^{34} - 32 q^{36} - 56 q^{38} + 8 q^{40} - 20 q^{42} + 64 q^{43} - 56 q^{44} - 32 q^{46} - 80 q^{48} - 48 q^{50} - 16 q^{51} - 16 q^{52} + 32 q^{54} - 24 q^{56} + 52 q^{58} + 72 q^{60} - 32 q^{61} - 40 q^{62} + 32 q^{64} + 32 q^{66} - 24 q^{68} - 32 q^{69} + 80 q^{72} - 16 q^{73} - 32 q^{74} - 88 q^{75} + 76 q^{78} + 128 q^{80} + 144 q^{81} + 56 q^{82} + 32 q^{86} - 112 q^{87} + 88 q^{88} + 88 q^{90} - 136 q^{92} - 8 q^{94} + 80 q^{95} + 32 q^{96} + 64 q^{99}+O(q^{100}) $ 144 * q + 8 * q^4 - 144 * q^9 - 16 * q^12 + 8 * q^16 - 28 * q^18 - 16 * q^19 + 4 * q^22 + 32 * q^26 - 36 * q^30 + 32 * q^34 - 32 * q^36 - 56 * q^38 + 8 * q^40 - 20 * q^42 + 64 * q^43 - 56 * q^44 - 32 * q^46 - 80 * q^48 - 48 * q^50 - 16 * q^51 - 16 * q^52 + 32 * q^54 - 24 * q^56 + 52 * q^58 + 72 * q^60 - 32 * q^61 - 40 * q^62 + 32 * q^64 + 32 * q^66 - 24 * q^68 - 32 * q^69 + 80 * q^72 - 16 * q^73 - 32 * q^74 - 88 * q^75 + 76 * q^78 + 128 * q^80 + 144 * q^81 + 56 * q^82 + 32 * q^86 - 112 * q^87 + 88 * q^88 + 88 * q^90 - 136 * q^92 - 8 * q^94 + 80 * q^95 + 32 * q^96 + 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−1.11562	+	0.869134i	−0.788862	+	0.614571i
$2$	−1.11562	+	0.869134i	−0.788862	+	0.614571i
$3$		−	2.40982i		−	1.39131i	−0.718376	−	0.695655i	$-0.755114\pi$
$3$		−	2.40982i		−	1.39131i	0.718376	−	0.695655i	$-0.244886\pi$
$4$	0.489211	−	1.93925i	0.244606	−	0.969623i
$5$	−2.07668	+	0.829085i	−0.928722	+	0.370778i
$5$	−2.07668	+	0.829085i	−0.928722	+	0.370778i
$6$	2.09446	+	2.68844i	0.855058	+	1.09755i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$8$	1.13969	+	2.58865i	0.402942	+	0.915226i
$9$	−2.80723			−0.935742
$10$	1.59620	−	2.72986i	0.504764	−	0.863258i
$11$	−2.34682	+	2.34682i	−0.707593	+	0.707593i	−0.966029	−	0.258435i	$-0.916793\pi$
$11$	−2.34682	+	2.34682i	−0.707593	+	0.707593i	0.258435	+	0.966029i	$0.416793\pi$
$12$	−4.67323	−	1.17891i	−1.34905	−	0.340322i
$13$	4.48941			1.24514			0.622570	−	0.782564i	$-0.286089\pi$
$13$	4.48941			1.24514			0.622570	+	0.782564i	$0.286089\pi$
$14$	0.174291	−	1.40343i	0.0465812	−	0.375083i
$15$	1.99794	+	5.00443i	0.515867	+	1.29214i
$16$	−3.52135	−	1.89740i	−0.880336	−	0.474350i
$17$	−2.44324	+	2.44324i	−0.592574	+	0.592574i	−0.938326	−	0.345752i	$-0.887624\pi$
$17$	−2.44324	+	2.44324i	−0.592574	+	0.592574i	0.345752	+	0.938326i	$0.387624\pi$
$18$	3.13179	−	2.43986i	0.738171	−	0.575080i
$19$	−2.49650	+	2.49650i	−0.572736	+	0.572736i	−0.932892	−	0.360156i	$-0.882724\pi$
$19$	−2.49650	+	2.49650i	−0.572736	+	0.572736i	0.360156	+	0.932892i	$0.382724\pi$
$20$	0.591861	+	4.43280i	0.132344	+	0.991204i
$21$	1.70400	+	1.70400i	0.371843	+	0.371843i
$22$	0.578455	−	4.65786i	0.123327	−	0.993059i
$23$	−2.43246	−	2.43246i	−0.507204	−	0.507204i	0.406463	−	0.913667i	$-0.366762\pi$
$23$	−2.43246	−	2.43246i	−0.507204	−	0.507204i	−0.913667	+	0.406463i	$0.866762\pi$
$24$	6.23817	−	2.74645i	1.27336	−	0.560617i
$25$	3.62524	−	3.44349i	0.725048	−	0.688699i
$26$	−5.00847	+	3.90190i	−0.982243	+	0.765226i
$27$		−	0.464550i		−	0.0894026i
$28$	1.02533	+	1.71718i	0.193769	+	0.324516i
$29$	3.09156	+	3.09156i	0.574089	+	0.574089i	0.933268	−	0.359180i	$-0.116944\pi$
$29$	3.09156	+	3.09156i	0.574089	+	0.574089i	−0.359180	+	0.933268i	$0.616944\pi$
$30$	−6.57847	−	3.84656i	−1.20106	−	0.702282i
$31$			10.1502i			1.82303i	0.411265	+	0.911516i	$0.365087\pi$
$31$			10.1502i			1.82303i	−0.411265	+	0.911516i	$0.634913\pi$
$32$	5.57758	−	0.943746i	0.985985	−	0.166832i
$33$	5.65541	+	5.65541i	0.984481	+	0.984481i
$34$	0.602222	−	4.84924i	0.103280	−	0.831637i
$35$	0.882186	−	2.05469i	0.149117	−	0.347306i
$36$	−1.37333	+	5.44390i	−0.228888	+	0.907317i
$37$	11.7133			1.92565			0.962824	−	0.270128i	$-0.0870661\pi$
$37$	11.7133			1.92565			0.962824	+	0.270128i	$0.0870661\pi$
$38$	0.615349	−	4.95494i	0.0998228	−	0.803797i
$39$		−	10.8187i		−	1.73237i
$40$	−4.51299	−	4.43091i	−0.713566	−	0.700588i
$41$			12.2006i			1.90542i	0.303886	+	0.952708i	$0.401716\pi$
$41$			12.2006i			1.90542i	−0.303886	+	0.952708i	$0.598284\pi$
$42$	−3.38202	−	0.420010i	−0.521857	−	0.0648089i
$43$	1.81456			0.276718			0.138359	−	0.990382i	$-0.455817\pi$
$43$	1.81456			0.276718			0.138359	+	0.990382i	$0.455817\pi$
$44$	3.40297	+	5.69915i	0.513017	+	0.859179i
$45$	5.82972	−	2.32743i	0.869044	−	0.346952i
$46$	4.82784	+	0.599565i	0.711826	+	0.0884010i
$47$	2.14045	+	2.14045i	0.312216	+	0.312216i	0.845768	−	0.533551i	$-0.179143\pi$
$47$	2.14045	+	2.14045i	0.312216	+	0.312216i	−0.533551	+	0.845768i	$0.679143\pi$
$48$	−4.57239	+	8.48580i	−0.659968	+	1.22482i
$49$		−	1.00000i		−	0.142857i
$50$	−1.05152	+	6.99245i	−0.148708	+	0.988881i
$51$	5.88778	+	5.88778i	0.824454	+	0.824454i
$52$	2.19627	−	8.70607i	0.304568	−	1.20732i
$53$		−	4.30788i		−	0.591732i	−0.955229	−	0.295866i	$-0.904392\pi$
$53$		−	4.30788i		−	0.591732i	0.955229	−	0.295866i	$-0.0956082\pi$
$54$	0.403756	+	0.518260i	0.0549442	+	0.0705263i
$55$	2.92789	−	6.81932i	0.394797	−	0.919517i
$56$	−2.63633	−	1.02457i	−0.352295	−	0.136914i
$57$	6.01611	+	6.01611i	0.796854	+	0.796854i
$58$	−6.13599	−	0.762022i	−0.805695	−	0.100058i
$59$	4.71152	+	4.71152i	0.613388	+	0.613388i	0.943827	−	0.330439i	$-0.107197\pi$
$59$	4.71152	+	4.71152i	0.613388	+	0.613388i	−0.330439	+	0.943827i	$0.607197\pi$
$60$	10.6822	−	1.42628i	1.37907	−	0.184132i
$61$	2.97080	−	2.97080i	0.380372	−	0.380372i	−0.490864	−	0.871236i	$-0.663319\pi$
$61$	2.97080	−	2.97080i	0.380372	−	0.380372i	0.871236	+	0.490864i	$0.163319\pi$
$62$	−8.82190	−	11.3238i	−1.12038	−	1.43812i
$63$	1.98501	−	1.98501i	0.250088	−	0.250088i
$64$	−5.40221	+	5.90052i	−0.675276	+	0.737565i
$65$	−9.32309	+	3.72210i	−1.15639	+	0.461670i
$66$	−11.2246	−	1.39397i	−1.38165	−	0.171586i
$67$	−8.05320			−0.983855			−0.491928	−	0.870636i	$-0.663708\pi$
$67$	−8.05320			−0.983855			−0.491928	+	0.870636i	$0.663708\pi$
$68$	3.54279	+	5.93331i	0.429626	+	0.719520i
$69$	−5.86180	+	5.86180i	−0.705677	+	0.705677i
$70$	0.801617	+	3.05899i	0.0958115	+	0.365619i
$71$	−11.9106			−1.41353			−0.706765	−	0.707449i	$-0.749846\pi$
$71$	−11.9106			−1.41353			−0.706765	+	0.707449i	$0.749846\pi$
$72$	−3.19937	−	7.26692i	−0.377050	−	0.856415i
$73$	−8.55814	+	8.55814i	−1.00165	+	1.00165i	−0.00165608	+	0.999999i	$0.500527\pi$
$73$	−8.55814	+	8.55814i	−1.00165	+	1.00165i	−0.999999	+	0.00165608i	$0.999473\pi$
$74$	−13.0675	+	10.1804i	−1.51907	+	1.18345i
$75$	−8.29820	−	8.73617i	−0.958193	−	1.00877i
$76$	3.62001	+	6.06264i	0.415244	+	0.695433i
$77$		−	3.31891i		−	0.378224i
$78$	9.40288	+	12.0695i	1.06467	+	1.36660i
$79$	1.48361			0.166919			0.0834593	−	0.996511i	$-0.473403\pi$
$79$	1.48361			0.166919			0.0834593	+	0.996511i	$0.473403\pi$
$80$	8.88583	+	1.02081i	0.993466	+	0.114130i
$81$	−9.54116			−1.06013
$82$	−10.6040	−	13.6112i	−1.17101	−	1.50311i
$83$		−	9.70769i		−	1.06556i	−0.846254	−	0.532779i	$-0.821148\pi$
$83$		−	9.70769i		−	1.06556i	0.846254	−	0.532779i	$-0.178852\pi$
$84$	4.13809	−	2.47086i	0.451502	−	0.269593i
$85$	3.04819	−	7.09950i	0.330623	−	0.770049i
$86$	−2.02436	+	1.57710i	−0.218292	+	0.170063i
$87$	7.45010	−	7.45010i	0.798735	−	0.798735i
$88$	−8.74975	−	3.40044i	−0.932726	−	0.362488i
$89$	−4.91472			−0.520959			−0.260479	−	0.965479i	$-0.583881\pi$
$89$	−4.91472			−0.520959			−0.260479	+	0.965479i	$0.583881\pi$
$90$	−4.48090	+	7.66334i	−0.472329	+	0.807786i
$91$	−3.17449	+	3.17449i	−0.332777	+	0.332777i
$92$	−5.90713	+	3.52715i	−0.615861	+	0.367731i
$93$	24.4602			2.53640
$94$	−4.24826	−	0.527587i	−0.438174	−	0.0544164i
$95$	3.11463	−	7.25425i	0.319555	−	0.744271i
$96$	−2.27426	−	13.4409i	−0.232115	−	1.37181i
$97$	−9.69326	+	9.69326i	−0.984201	+	0.984201i	−0.999877	−	0.0156756i	$-0.995010\pi$
$97$	−9.69326	+	9.69326i	−0.984201	+	0.984201i	0.0156756	+	0.999877i	$0.495010\pi$
$98$	0.869134	+	1.11562i	0.0877958	+	0.112695i
$99$	6.58806	−	6.58806i	0.662125	−	0.662125i
$100$	−4.90427	−	8.71482i	−0.490427	−	0.871482i
$101$	2.76235	+	2.76235i	0.274864	+	0.274864i	0.831055	−	0.556191i	$-0.187738\pi$
$101$	2.76235	+	2.76235i	0.274864	+	0.274864i	−0.556191	+	0.831055i	$0.687738\pi$
$102$	−11.6858	−	1.45125i	−1.15706	−	0.143695i
$103$	−2.54232	−	2.54232i	−0.250503	−	0.250503i	0.570674	−	0.821177i	$-0.306682\pi$
$103$	−2.54232	−	2.54232i	−0.250503	−	0.250503i	−0.821177	+	0.570674i	$0.806682\pi$
$104$	5.11655	+	11.6215i	0.501719	+	1.13958i
$105$	−4.95143	−	2.12591i	−0.483210	−	0.207468i
$106$	3.74412	+	4.80595i	0.363661	+	0.466795i
$107$			5.98004i			0.578112i	0.957312	+	0.289056i	$0.0933415\pi$
$107$			5.98004i			0.578112i	−0.957312	+	0.289056i	$0.906659\pi$
$108$	−0.900876	−	0.227263i	−0.0866868	−	0.0218684i
$109$	−7.04035	−	7.04035i	−0.674344	−	0.674344i	0.284371	−	0.958714i	$-0.408215\pi$
$109$	−7.04035	−	7.04035i	−0.674344	−	0.674344i	−0.958714	+	0.284371i	$0.908215\pi$
$110$	2.66049	+	10.1525i	0.253668	+	0.968002i
$111$		−	28.2268i		−	2.67917i
$112$	3.83163	−	1.14830i	0.362055	−	0.108504i
$113$	6.03615	+	6.03615i	0.567833	+	0.567833i	0.931521	−	0.363688i	$-0.118483\pi$
$113$	6.03615	+	6.03615i	0.567833	+	0.567833i	−0.363688	+	0.931521i	$0.618483\pi$
$114$	−11.9405	−	1.48288i	−1.11833	−	0.138884i
$115$	7.06818	+	3.03474i	0.659111	+	0.282991i
$116$	7.50772	−	4.48287i	0.697075	−	0.416224i
$117$	−12.6028			−1.16513
$118$	−9.35120	−	1.16132i	−0.860848	−	0.106908i
$119$		−	3.45527i		−	0.316744i
$120$	−10.6777	+	10.8755i	−0.974735	+	0.992791i
$121$		−	0.0151342i		−	0.00137584i
$122$	−0.732257	+	5.89631i	−0.0662955	+	0.533827i
$123$	29.4013			2.65102
$124$	19.6838	+	4.96560i	1.76765	+	0.445924i
$125$	−4.67353	+	10.1567i	−0.418013	+	0.908441i
$126$	−0.489274	+	3.93975i	−0.0435880	+	0.350981i
$127$	8.74399	+	8.74399i	0.775904	+	0.775904i	0.979131	−	0.203228i	$-0.0651432\pi$
$127$	8.74399	+	8.74399i	0.775904	+	0.775904i	−0.203228	+	0.979131i	$0.565143\pi$
$128$	0.898457	−	11.2780i	0.0794131	−	0.996842i
$129$		−	4.37276i		−	0.385000i
$130$	7.16601	−	12.2555i	0.628501	−	1.07488i
$131$	1.34402	+	1.34402i	0.117428	+	0.117428i	0.763379	−	0.645951i	$-0.223539\pi$
$131$	1.34402	+	1.34402i	0.117428	+	0.117428i	−0.645951	+	0.763379i	$0.723539\pi$
$132$	13.7339	−	8.20054i	1.19538	−	0.713766i
$133$		−	3.53058i		−	0.306141i
$134$	8.98430	−	6.99931i	0.776126	−	0.604649i
$135$	0.385151	+	0.964723i	0.0331485	+	0.0830302i
$136$	−9.10925	−	3.54016i	−0.781111	−	0.303566i
$137$	0.585584	+	0.585584i	0.0500299	+	0.0500299i	0.731679	−	0.681649i	$-0.238737\pi$
$137$	0.585584	+	0.585584i	0.0500299	+	0.0500299i	−0.681649	+	0.731679i	$0.738737\pi$
$138$	1.44484	−	11.6342i	0.122993	−	0.990370i
$139$	−6.23701	−	6.23701i	−0.529016	−	0.529016i	0.391263	−	0.920279i	$-0.372038\pi$
$139$	−6.23701	−	6.23701i	−0.529016	−	0.529016i	−0.920279	+	0.391263i	$0.872038\pi$
$140$	−3.55297	−	2.71595i	−0.300281	−	0.229540i
$141$	5.15809	−	5.15809i	0.434389	−	0.434389i
$142$	13.2877	−	10.3519i	1.11508	−	0.868714i
$143$	−10.5358	+	10.5358i	−0.881052	+	0.881052i
$144$	9.88521	+	5.32643i	0.823768	+	0.443869i
$145$	−8.98336	−	3.85703i	−0.746028	−	0.320309i
$146$	2.10945	−	16.9858i	0.174579	−	1.40575i
$147$	−2.40982			−0.198758
$148$	5.73026	−	22.7149i	0.471024	−	1.86715i
$149$	−1.92918	+	1.92918i	−0.158044	+	0.158044i	−0.781700	−	0.623655i	$-0.785647\pi$
$149$	−1.92918	+	1.92918i	−0.158044	+	0.158044i	0.623655	+	0.781700i	$0.285647\pi$
$150$	16.8505	+	2.53398i	1.37584	+	0.206899i
$151$	8.05786			0.655739			0.327870	−	0.944723i	$-0.393669\pi$
$151$	8.05786			0.655739			0.327870	+	0.944723i	$0.393669\pi$
$152$	−9.30780	−	3.61732i	−0.754963	−	0.293404i
$153$	6.85874	−	6.85874i	0.554496	−	0.554496i
$154$	2.88457	+	3.70263i	0.232446	+	0.298367i
$155$	−8.41538	−	21.0788i	−0.675940	−	1.69309i
$156$	−20.9801	−	5.29261i	−1.67975	−	0.423748i
$157$			10.1484i			0.809928i	0.914333	+	0.404964i	$0.132716\pi$
$157$			10.1484i			0.809928i	−0.914333	+	0.404964i	$0.867284\pi$
$158$	−1.65514	+	1.28945i	−0.131676	+	0.102583i
$159$	−10.3812			−0.823283
$160$	−10.8004	+	6.58414i	−0.853848	+	0.520522i
$161$	3.44002			0.271112
$162$	10.6443	−	8.29255i	0.836295	−	0.651524i
$163$		−	15.4065i		−	1.20673i	−0.797464	−	0.603367i	$-0.793825\pi$
$163$		−	15.4065i		−	1.20673i	0.797464	−	0.603367i	$-0.206175\pi$
$164$	23.6600	+	5.96868i	1.84754	+	0.466075i
$165$	−16.4333	−	7.05569i	−1.27933	−	0.549285i
$166$	8.43729	+	10.8301i	0.654861	+	0.840578i
$167$	−8.60232	+	8.60232i	−0.665667	+	0.665667i	−0.956710	−	0.291043i	$-0.905998\pi$
$167$	−8.60232	+	8.60232i	−0.665667	+	0.665667i	0.291043	+	0.956710i	$0.405998\pi$
$168$	−2.46902	+	6.35309i	−0.190489	+	0.490151i
$169$	7.15483			0.550371
$170$	2.76980	+	10.5696i	0.212434	+	0.810654i
$171$	7.00824	−	7.00824i	0.535934	−	0.535934i
$172$	0.887703	−	3.51888i	0.0676867	−	0.268312i
$173$	8.07360			0.613825			0.306912	−	0.951738i	$-0.400704\pi$
$173$	8.07360			0.613825			0.306912	+	0.951738i	$0.400704\pi$
$174$	−1.83634	+	14.7866i	−0.139212	+	1.12097i
$175$	−0.128512	+	4.99835i	−0.00971461	+	0.377840i
$176$	12.7168	−	3.81111i	0.958567	−	0.287273i
$177$	11.3539	−	11.3539i	0.853412	−	0.853412i
$178$	5.48295	−	4.27155i	0.410964	−	0.320166i
$179$	−10.8927	+	10.8927i	−0.814158	+	0.814158i	−0.985254	−	0.171096i	$-0.945269\pi$
$179$	−10.8927	+	10.8927i	−0.814158	+	0.814158i	0.171096	+	0.985254i	$0.445269\pi$
$180$	−1.66149	−	12.4439i	−0.123840	−	0.927511i
$181$	−12.5519	−	12.5519i	−0.932974	−	0.932974i	0.0649164	−	0.997891i	$-0.479322\pi$
$181$	−12.5519	−	12.5519i	−0.932974	−	0.932974i	−0.997891	+	0.0649164i	$0.979322\pi$
$182$	0.782464	−	6.30059i	0.0580001	−	0.467031i
$183$	−7.15910	−	7.15910i	−0.529216	−	0.529216i
$184$	3.52454	−	9.06905i	0.259832	−	0.668579i
$185$	−24.3248	+	9.71129i	−1.78839	+	0.713988i
$186$	−27.2882	+	21.2592i	−2.00087	+	1.55880i
$187$		−	11.4677i		−	0.838602i
$188$	5.19798	−	3.10372i	0.379102	−	0.226362i
$189$	0.328486	+	0.328486i	0.0238939	+	0.0238939i
$190$	2.83018	+	10.8000i	0.205323	+	0.783516i
$191$		−	9.83980i		−	0.711983i	−0.934489	−	0.355991i	$-0.884143\pi$
$191$		−	9.83980i		−	0.711983i	0.934489	−	0.355991i	$-0.115857\pi$
$192$	14.2192	+	13.0183i	1.02618	+	0.939518i
$193$	−6.74831	−	6.74831i	−0.485754	−	0.485754i	0.421210	−	0.906963i	$-0.361606\pi$
$193$	−6.74831	−	6.74831i	−0.485754	−	0.485754i	−0.906963	+	0.421210i	$0.861606\pi$
$194$	2.38924	−	19.2387i	0.171537	−	1.38126i
$195$	8.96959	+	22.4670i	0.642326	+	1.60889i
$196$	−1.93925	−	0.489211i	−0.138518	−	0.0349436i
$197$	11.8523			0.844443			0.422221	−	0.906493i	$-0.361251\pi$
$197$	11.8523			0.844443			0.422221	+	0.906493i	$0.361251\pi$
$198$	−1.62385	+	13.0757i	−0.115402	+	0.929247i
$199$			10.3205i			0.731602i	0.930693	+	0.365801i	$0.119205\pi$
$199$			10.3205i			0.731602i	−0.930693	+	0.365801i	$0.880795\pi$
$200$	13.0456	+	5.45995i	0.922467	+	0.386077i
$201$			19.4068i			1.36885i
$202$	−5.48258	−	0.680877i	−0.385753	−	0.0479063i
$203$	−4.37213			−0.306863
$204$	14.2982	−	8.53748i	1.00107	−	0.597743i
$205$	−10.1153	−	25.3368i	−0.706486	−	1.76960i
$206$	5.04589	+	0.626644i	0.351564	+	0.0436603i
$207$	6.82847	+	6.82847i	0.474612	+	0.474612i
$208$	−15.8088	−	8.51821i	−1.09614	−	0.590632i
$209$		−	11.7177i		−	0.810529i
$210$	7.37161	−	1.93175i	0.508689	−	0.133304i
$211$	4.12123	+	4.12123i	0.283717	+	0.283717i	0.834590	−	0.550872i	$-0.185705\pi$
$211$	4.12123	+	4.12123i	0.283717	+	0.283717i	−0.550872	+	0.834590i	$0.685705\pi$
$212$	−8.35403	−	2.10746i	−0.573757	−	0.144741i
$213$			28.7024i			1.96666i
$214$	−5.19746	−	6.67145i	−0.355291	−	0.456051i
$215$	−3.76827	+	1.50442i	−0.256994	+	0.102601i
$216$	1.20256	−	0.529443i	0.0818236	−	0.0360241i
$217$	−7.17728	−	7.17728i	−0.487226	−	0.487226i
$218$	13.9734	+	1.73534i	0.946396	+	0.117532i
$219$	20.6236	+	20.6236i	1.39361	+	1.39361i
$220$	−11.7920	−	9.01399i	−0.795015	−	0.607723i
$221$	−10.9687	+	10.9687i	−0.737837	+	0.737837i
$222$	24.5329	+	31.4904i	1.64654	+	2.11350i
$223$	−2.97066	+	2.97066i	−0.198930	+	0.198930i	−0.799541	−	0.600611i	$-0.794924\pi$
$223$	−2.97066	+	2.97066i	−0.198930	+	0.198930i	0.600611	+	0.799541i	$0.294924\pi$
$224$	−3.27661	+	4.61127i	−0.218928	+	0.308103i
$225$	−10.1769	+	9.66667i	−0.678458	+	0.644444i
$226$	−11.9803	−	1.48782i	−0.796915	−	0.0989681i
$227$	−14.9111			−0.989682			−0.494841	−	0.868983i	$-0.664774\pi$
$227$	−14.9111			−0.989682			−0.494841	+	0.868983i	$0.664774\pi$
$228$	14.6099	−	8.72357i	0.967562	−	0.577733i
$229$	−17.6004	+	17.6004i	−1.16307	+	1.16307i	−0.179267	+	0.983800i	$0.557373\pi$
$229$	−17.6004	+	17.6004i	−1.16307	+	1.16307i	−0.983800	+	0.179267i	$0.942627\pi$
$230$	−10.5230	+	2.75758i	−0.693865	+	0.181829i
$231$	−7.99796			−0.526227
$232$	−4.47954	+	11.5264i	−0.294096	+	0.756745i
$233$	−2.93845	+	2.93845i	−0.192505	+	0.192505i	−0.796777	−	0.604273i	$-0.793464\pi$
$233$	−2.93845	+	2.93845i	−0.192505	+	0.192505i	0.604273	+	0.796777i	$0.293464\pi$
$234$	14.0599	−	10.9535i	0.919126	−	0.716054i
$235$	−6.21964	−	2.67042i	−0.405725	−	0.174199i
$236$	11.4417	−	6.83187i	0.744793	−	0.444717i
$237$		−	3.57522i		−	0.232236i
$238$	3.00309	+	3.85476i	0.194662	+	0.249867i
$239$	28.6850			1.85548			0.927741	−	0.373225i	$-0.121748\pi$
$239$	28.6850			1.85548			0.927741	+	0.373225i	$0.121748\pi$
$240$	2.45997	−	21.4132i	0.158790	−	1.38222i
$241$	23.0840			1.48697			0.743486	−	0.668752i	$-0.233171\pi$
$241$	23.0840			1.48697			0.743486	+	0.668752i	$0.233171\pi$
$242$	0.0131537	+	0.0168840i	0.000845550	+	0.00108535i
$243$			21.5988i			1.38556i
$244$	−4.30777	−	7.21447i	−0.275777	−	0.461859i
$245$	0.829085	+	2.07668i	0.0529683	+	0.132675i
$246$	−32.8006	+	25.5537i	−2.09129	+	1.62924i
$247$	−11.2078	+	11.2078i	−0.713137	+	0.713137i
$248$	−26.2753	+	11.5681i	−1.66849	+	0.734576i
$249$	−23.3938			−1.48252
$250$	−3.61364	−	15.3929i	−0.228547	−	0.973533i
$251$	12.7284	−	12.7284i	0.803411	−	0.803411i	−0.180216	−	0.983627i	$-0.557680\pi$
$251$	12.7284	−	12.7284i	0.803411	−	0.803411i	0.983627	+	0.180216i	$0.0576798\pi$
$252$	−2.87833	−	4.82051i	−0.181318	−	0.303663i
$253$	11.4171			0.717788
$254$	−17.3547	−	2.15526i	−1.08893	−	0.135233i
$255$	−17.1085	−	7.34559i	−1.07138	−	0.459999i
$256$	8.79974	+	13.3628i	0.549984	+	0.835175i
$257$	10.3240	−	10.3240i	0.643995	−	0.643995i	−0.307540	−	0.951535i	$-0.599506\pi$
$257$	10.3240	−	10.3240i	0.643995	−	0.643995i	0.951535	+	0.307540i	$0.0995057\pi$
$258$	3.80052	+	4.87834i	0.236610	+	0.303712i
$259$	−8.28253	+	8.28253i	−0.514651	+	0.514651i
$260$	2.65711	+	19.9007i	0.164787	+	1.23419i
$261$	−8.67871	−	8.67871i	−0.537199	−	0.537199i
$262$	−2.66755	−	0.331280i	−0.164802	−	0.0204665i
$263$	−3.99183	−	3.99183i	−0.246147	−	0.246147i	0.573240	−	0.819387i	$-0.305686\pi$
$263$	−3.99183	−	3.99183i	−0.246147	−	0.246147i	−0.819387	+	0.573240i	$0.805686\pi$
$264$	−8.19445	+	21.0853i	−0.504334	+	1.29771i
$265$	3.57159	+	8.94610i	0.219401	+	0.549554i
$266$	3.06855	+	3.93879i	0.188145	+	0.241503i
$267$			11.8436i			0.724815i
$268$	−3.93971	+	15.6171i	−0.240656	+	0.953968i
$269$	14.3428	+	14.3428i	0.874494	+	0.874494i	0.992958	−	0.118464i	$-0.0377971\pi$
$269$	14.3428	+	14.3428i	0.874494	+	0.874494i	−0.118464	+	0.992958i	$0.537797\pi$
$270$	−1.26816	−	0.741516i	−0.0771775	−	0.0451272i
$271$		−	15.2118i		−	0.924050i	−0.886867	−	0.462025i	$-0.847123\pi$
$271$		−	15.2118i		−	0.924050i	0.886867	−	0.462025i	$-0.152877\pi$
$272$	13.2393	−	3.96769i	0.802752	−	0.240577i
$273$	7.64996	+	7.64996i	0.462996	+	0.462996i
$274$	−1.16224	−	0.144338i	−0.0702135	−	0.00871975i
$275$	−0.426520	+	16.5890i	−0.0257201	+	1.00036i
$276$	8.49980	+	14.2351i	0.511628	+	0.856853i
$277$	23.7444			1.42666			0.713331	−	0.700827i	$-0.247186\pi$
$277$	23.7444			1.42666			0.713331	+	0.700827i	$0.247186\pi$
$278$	12.3789	+	1.53733i	0.742439	+	0.0922028i
$279$		−	28.4939i		−	1.70589i
$280$	6.32429	−	0.0580407i	0.377949	−	0.00346860i
$281$		−	7.83055i		−	0.467131i	−0.972341	−	0.233566i	$-0.924961\pi$
$281$		−	7.83055i		−	0.467131i	0.972341	−	0.233566i	$-0.0750394\pi$
$282$	−1.27139	+	10.2375i	−0.0757101	+	0.609636i
$283$	−16.5930			−0.986353			−0.493177	−	0.869929i	$-0.664164\pi$
$283$	−16.5930			−0.986353			−0.493177	+	0.869929i	$0.664164\pi$
$284$	−5.82680	+	23.0976i	−0.345757	+	1.37059i
$285$	−17.4814	−	7.50570i	−1.03551	−	0.444600i
$286$	2.59692	−	20.9111i	0.153559	−	1.23650i
$287$	−8.62714	−	8.62714i	−0.509244	−	0.509244i
$288$	−15.6575	+	2.64931i	−0.922628	+	0.156112i
$289$			5.06111i			0.297713i
$290$	13.3743	−	3.50477i	0.785365	−	0.205807i
$291$	23.3590	+	23.3590i	1.36933	+	1.36933i
$292$	12.4096	+	20.7831i	0.726217	+	1.21624i
$293$		−	6.83604i		−	0.399366i	−0.979861	−	0.199683i	$-0.936009\pi$
$293$		−	6.83604i		−	0.399366i	0.979861	−	0.199683i	$-0.0639912\pi$
$294$	2.68844	−	2.09446i	0.156793	−	0.122151i
$295$	−13.6906	−	5.87809i	−0.797097	−	0.342236i
$296$	13.3495	+	30.3215i	0.775924	+	1.76240i
$297$	1.09021	+	1.09021i	0.0632607	+	0.0632607i
$298$	0.475513	−	3.82894i	0.0275457	−	0.221805i
$299$	−10.9203	−	10.9203i	−0.631539	−	0.631539i
$300$	−21.0011	+	11.8184i	−1.21250	+	0.682336i
$301$	−1.28309	+	1.28309i	−0.0739560	+	0.0739560i
$302$	−8.98950	+	7.00336i	−0.517287	+	0.402998i
$303$	6.65676	−	6.65676i	0.382421	−	0.382421i
$304$	13.5279	−	4.05418i	0.775878	−	0.232523i
$305$	−3.70638	+	8.63247i	−0.212226	+	0.494294i
$306$	−1.69057	+	13.6129i	−0.0966437	+	0.778198i
$307$	0.277015			0.0158101			0.00790504	−	0.999969i	$-0.497484\pi$
$307$	0.277015			0.0158101			0.00790504	+	0.999969i	$0.497484\pi$
$308$	−6.43617	−	1.62365i	−0.366735	−	0.0925158i
$309$	−6.12654	+	6.12654i	−0.348527	+	0.348527i
$310$	27.7087	+	16.2018i	1.57375	+	0.920200i
$311$	−15.6551			−0.887718			−0.443859	−	0.896097i	$-0.646391\pi$
$311$	−15.6551			−0.887718			−0.443859	+	0.896097i	$0.646391\pi$
$312$	28.0057	−	12.3299i	1.58551	−	0.698046i
$313$	19.7759	−	19.7759i	1.11780	−	1.11780i	0.125734	−	0.992064i	$-0.459871\pi$
$313$	19.7759	−	19.7759i	1.11780	−	1.11780i	0.992064	−	0.125734i	$-0.0401287\pi$
$314$	−8.82029	−	11.3217i	−0.497758	−	0.638921i
$315$	−2.47650	+	5.76798i	−0.139535	+	0.324989i
$316$	0.725796	−	2.87708i	0.0408292	−	0.161848i
$317$			18.0255i			1.01241i	0.862412	+	0.506207i	$0.168953\pi$
$317$			18.0255i			1.01241i	−0.862412	+	0.506207i	$0.831047\pi$
$318$	11.5815	−	9.02266i	0.649456	−	0.505965i
$319$	−14.5107			−0.812442
$320$	6.32665	−	16.7324i	0.353670	−	0.935370i
$321$	14.4108			0.804333
$322$	−3.83775	+	2.98984i	−0.213870	+	0.166617i
$323$		−	12.1991i		−	0.678777i
$324$	−4.66764	+	18.5026i	−0.259313	+	1.02792i
$325$	16.2752	−	15.4593i	0.902785	−	0.857526i
$326$	13.3904	+	17.1878i	0.741623	+	0.951946i
$327$	−16.9660	+	16.9660i	−0.938221	+	0.938221i
$328$	−31.5831	+	13.9049i	−1.74389	+	0.767772i
$329$	−3.02705			−0.166887
$330$	24.4657	−	6.41130i	1.34679	−	0.352930i
$331$	−14.5382	+	14.5382i	−0.799093	+	0.799093i	−0.982953	−	0.183859i	$-0.941141\pi$
$331$	−14.5382	+	14.5382i	−0.799093	+	0.799093i	0.183859	+	0.982953i	$0.441141\pi$
$332$	−18.8256	−	4.74911i	−1.03319	−	0.260641i
$333$	−32.8818			−1.80191
$334$	2.12034	−	17.0735i	0.116020	−	0.934219i
$335$	16.7240	−	6.67678i	0.913727	−	0.364792i
$336$	−2.76720	−	9.23354i	−0.150963	−	0.503731i
$337$	10.1367	−	10.1367i	0.552183	−	0.552183i	−0.374887	−	0.927070i	$-0.622319\pi$
$337$	10.1367	−	10.1367i	0.552183	−	0.552183i	0.927070	+	0.374887i	$0.122319\pi$
$338$	−7.98206	+	6.21851i	−0.434167	+	0.338242i
$339$	14.5460	−	14.5460i	0.790031	−	0.790031i
$340$	−12.2765	−	9.38435i	−0.665785	−	0.508938i
$341$	−23.8207	−	23.8207i	−1.28996	−	1.28996i
$342$	−1.72742	+	13.9096i	−0.0934084	+	0.752147i
$343$	0.707107	+	0.707107i	0.0381802	+	0.0381802i
$344$	2.06804	+	4.69726i	0.111501	+	0.253259i
$345$	7.31318	−	17.0330i	0.393728	−	0.917027i
$346$	−9.00706	+	7.01704i	−0.484223	+	0.377239i
$347$			8.11318i			0.435538i	0.976000	+	0.217769i	$0.0698780\pi$
$347$			8.11318i			0.435538i	−0.976000	+	0.217769i	$0.930122\pi$
$348$	−10.8029	−	18.0923i	−0.579097	−	0.969846i
$349$	14.5875	+	14.5875i	0.780851	+	0.780851i	0.979974	−	0.199123i	$-0.0638094\pi$
$349$	14.5875	+	14.5875i	0.780851	+	0.780851i	−0.199123	+	0.979974i	$0.563809\pi$
$350$	−4.20087	−	5.68795i	−0.224546	−	0.304034i
$351$		−	2.08556i		−	0.111319i
$352$	−10.8748	+	15.3044i	−0.579627	+	0.815726i
$353$	−17.1513	−	17.1513i	−0.912870	−	0.912870i	0.0836275	−	0.996497i	$-0.473349\pi$
$353$	−17.1513	−	17.1513i	−0.912870	−	0.912870i	−0.996497	+	0.0836275i	$0.973349\pi$
$354$	−2.79856	+	22.5347i	−0.148742	+	1.19771i
$355$	24.7346	−	9.87490i	1.31278	−	0.524106i
$356$	−2.40433	+	9.53084i	−0.127429	+	0.505133i
$357$	−8.32657			−0.440689
$358$	2.68488	−	21.6193i	0.141900	−	1.14262i
$359$		−	25.3205i		−	1.33637i	−0.743997	−	0.668183i	$-0.767073\pi$
$359$		−	25.3205i		−	1.33637i	0.743997	−	0.668183i	$-0.232927\pi$
$360$	12.6690	+	12.4386i	0.667714	+	0.655570i
$361$			6.53497i			0.343946i
$362$	24.9124	+	3.09385i	1.30937	+	0.162609i
$363$	−0.0364707			−0.00191422
$364$	4.60313	+	7.70912i	0.241269	+	0.404068i
$365$	10.6771	−	24.8680i	0.558867	−	1.30165i
$366$	14.2090	+	1.76461i	0.742719	+	0.0922375i
$367$	−12.5089	−	12.5089i	−0.652958	−	0.652958i	0.300746	−	0.953704i	$-0.402764\pi$
$367$	−12.5089	−	12.5089i	−0.652958	−	0.652958i	−0.953704	+	0.300746i	$0.902764\pi$
$368$	3.95019	+	13.1809i	0.205918	+	0.687102i
$369$		−	34.2499i		−	1.78298i
$370$	18.6967	−	31.9756i	0.971997	−	1.66233i
$371$	3.04613	+	3.04613i	0.158147	+	0.158147i
$372$	11.9662	−	47.4343i	0.620418	−	2.45935i
$373$		−	19.4218i		−	1.00562i	−0.864396	−	0.502811i	$-0.832299\pi$
$373$		−	19.4218i		−	1.00562i	0.864396	−	0.502811i	$-0.167701\pi$
$374$	9.96698	+	12.7936i	0.515380	+	0.661541i
$375$	24.4758	+	11.2624i	1.26392	+	0.581586i
$376$	−3.10141	+	7.98031i	−0.159943	+	0.411553i
$377$	13.8793	+	13.8793i	0.714820	+	0.714820i
$378$	−0.651964	−	0.0809668i	−0.0335334	−	0.00416448i
$379$	5.54332	+	5.54332i	0.284741	+	0.284741i	0.834997	−	0.550255i	$-0.185470\pi$
$379$	5.54332	+	5.54332i	0.284741	+	0.284741i	−0.550255	+	0.834997i	$0.685470\pi$
$380$	−12.5441	−	9.58890i	−0.643497	−	0.491900i
$381$	21.0714	−	21.0714i	1.07952	−	1.07952i
$382$	8.55211	+	10.9775i	0.437564	+	0.561656i
$383$	−8.84593	+	8.84593i	−0.452006	+	0.452006i	−0.896020	−	0.444014i	$-0.853554\pi$
$383$	−8.84593	+	8.84593i	−0.452006	+	0.452006i	0.444014	+	0.896020i	$0.353554\pi$
$384$	−27.1779	−	2.16512i	−1.38692	−	0.110488i
$385$	2.75165	+	6.89232i	0.140237	+	0.351265i
$386$	13.3937	+	1.66335i	0.681723	+	0.0846625i
$387$	−5.09388			−0.258937
$388$	14.0556	+	23.5397i	0.713563	+	1.19505i
$389$	19.8381	−	19.8381i	1.00583	−	1.00583i	0.00584880	−	0.999983i	$-0.498138\pi$
$389$	19.8381	−	19.8381i	1.00583	−	1.00583i	0.999983	−	0.00584880i	$-0.00186174\pi$
$390$	−29.5335	−	17.2688i	−1.49548	−	0.874439i
$391$	11.8862			0.601111
$392$	2.58865	−	1.13969i	0.130747	−	0.0575631i
$393$	3.23884	−	3.23884i	0.163378	−	0.163378i
$394$	−13.2227	+	10.3013i	−0.666148	+	0.518970i
$395$	−3.08098	+	1.23003i	−0.155021	+	0.0618897i
$396$	−9.55291	−	15.9988i	−0.480052	−	0.803970i
$397$			3.92255i			0.196867i	0.995144	+	0.0984336i	$0.0313832\pi$
$397$			3.92255i			0.196867i	−0.995144	+	0.0984336i	$0.968617\pi$
$398$	−8.96992	−	11.5138i	−0.449621	−	0.577133i
$399$	−8.50807			−0.425936
$400$	−19.2994	+	5.24720i	−0.964970	+	0.262360i
$401$	3.65238			0.182391			0.0911957	−	0.995833i	$-0.470931\pi$
$401$	3.65238			0.182391			0.0911957	+	0.995833i	$0.470931\pi$
$402$	−16.8671	−	21.6505i	−0.841253	−	1.07983i
$403$			45.5685i			2.26993i
$404$	6.70825	−	4.00550i	0.333748	−	0.199281i
$405$	19.8140	−	7.91043i	0.984565	−	0.393072i
$406$	4.87763	−	3.79997i	0.242073	−	0.188589i
$407$	−27.4889	+	27.4889i	−1.36258	+	1.36258i
$408$	−8.53114	+	21.9516i	−0.422354	+	1.08677i
$409$	−5.26435			−0.260305			−0.130153	−	0.991494i	$-0.541547\pi$
$409$	−5.26435			−0.260305			−0.130153	+	0.991494i	$0.541547\pi$
$410$	33.3060	+	19.4747i	1.64487	+	0.961785i
$411$	1.41115	−	1.41115i	0.0696070	−	0.0696070i
$412$	−6.17393	+	3.68646i	−0.304167	+	0.181619i
$413$	−6.66310			−0.327870
$414$	−13.5528	−	1.68311i	−0.666086	−	0.0827205i
$415$	8.04850	+	20.1598i	0.395085	+	0.989607i
$416$	25.0400	−	4.23686i	1.22769	−	0.207729i
$417$	−15.0301	+	15.0301i	−0.736026	+	0.736026i
$418$	10.1842	+	13.0725i	0.498127	+	0.639395i
$419$	16.3169	−	16.3169i	0.797135	−	0.797135i	−0.185508	−	0.982643i	$-0.559393\pi$
$419$	16.3169	−	16.3169i	0.797135	−	0.797135i	0.982643	+	0.185508i	$0.0593931\pi$
$420$	−6.54495	+	8.56202i	−0.319361	+	0.417784i
$421$	4.04552	+	4.04552i	0.197167	+	0.197167i	0.798784	−	0.601618i	$-0.205477\pi$
$421$	4.04552	+	4.04552i	0.197167	+	0.197167i	−0.601618	+	0.798784i	$0.705477\pi$
$422$	−8.17963	−	1.01582i	−0.398178	−	0.0494494i
$423$	−6.00872	−	6.00872i	−0.292154	−	0.292154i
$424$	11.1516	−	4.90965i	0.541568	−	0.238434i
$425$	−0.444044	+	17.2706i	−0.0215393	+	0.837749i
$426$	−24.9463	−	32.0210i	−1.20865	−	1.55142i
$427$			4.20135i			0.203318i
$428$	11.5968	+	2.92550i	0.560551	+	0.141410i
$429$	25.3895	+	25.3895i	1.22582	+	1.22582i
$430$	2.89641	−	4.95350i	0.139677	−	0.238879i
$431$		−	31.0821i		−	1.49717i	−0.663037	−	0.748587i	$-0.730733\pi$
$431$		−	31.0821i		−	1.49717i	0.663037	−	0.748587i	$-0.269267\pi$
$432$	−0.881437	+	1.63584i	−0.0424082	+	0.0787044i
$433$	19.1212	+	19.1212i	0.918905	+	0.918905i	0.996950	−	0.0780449i	$-0.0248677\pi$
$433$	19.1212	+	19.1212i	0.918905	+	0.918905i	−0.0780449	+	0.996950i	$0.524868\pi$
$434$	14.2451	+	1.76909i	0.683789	+	0.0849190i
$435$	−9.29475	+	21.6483i	−0.445649	+	1.03796i
$436$	−17.0972	+	10.2088i	−0.818807	+	0.488911i
$437$	12.1453			0.580988
$438$	−40.9327	−	5.08339i	−1.95584	−	0.242894i
$439$			29.7712i			1.42090i	0.703747	+	0.710451i	$0.251509\pi$
$439$			29.7712i			1.42090i	−0.703747	+	0.710451i	$0.748491\pi$
$440$	20.9897	−	0.192632i	1.00065	−	0.00918335i
$441$			2.80723i			0.133677i
$442$	2.70362	−	21.7702i	0.128598	−	1.03550i
$443$	4.41389			0.209710			0.104855	−	0.994487i	$-0.466562\pi$
$443$	4.41389			0.209710			0.104855	+	0.994487i	$0.466562\pi$
$444$	−54.7388	−	13.8089i	−2.59779	−	0.655341i
$445$	10.2063	−	4.07471i	0.483826	−	0.193160i
$446$	0.732223	−	5.89603i	0.0346718	−	0.279185i
$447$	4.64897	+	4.64897i	0.219889	+	0.219889i
$448$	−0.352363	−	7.99224i	−0.0166476	−	0.377598i
$449$		−	5.13263i		−	0.242224i	−0.992639	−	0.121112i	$-0.961354\pi$
$449$		−	5.13263i		−	0.242224i	0.992639	−	0.121112i	$-0.0386460\pi$
$450$	2.95187	−	19.6294i	0.139152	−	0.925338i
$451$	−28.6327	−	28.6327i	−1.34826	−	1.34826i
$452$	14.6585	−	8.75262i	0.689479	−	0.411689i
$453$		−	19.4180i		−	0.912336i
$454$	16.6351	−	12.9597i	0.780723	−	0.608230i
$455$	3.96050	−	9.22435i	0.185671	−	0.432444i
$456$	−8.71709	+	22.4301i	−0.408215	+	1.05039i
$457$	−22.9695	−	22.9695i	−1.07447	−	1.07447i	−0.996994	−	0.0774759i	$-0.975314\pi$
$457$	−22.9695	−	22.9695i	−1.07447	−	1.07447i	−0.0774759	−	0.996994i	$-0.524686\pi$
$458$	4.33823	−	34.9325i	0.202712	−	1.63229i
$459$	1.13501	+	1.13501i	0.0529777	+	0.0529777i
$460$	9.34294	−	12.2223i	0.435617	−	0.569868i
$461$	−4.69983	+	4.69983i	−0.218893	+	0.218893i	−0.808032	−	0.589139i	$-0.799467\pi$
$461$	−4.69983	+	4.69983i	−0.218893	+	0.218893i	0.589139	+	0.808032i	$0.299467\pi$
$462$	8.92268	−	6.95130i	0.415120	−	0.323404i
$463$	−14.0202	+	14.0202i	−0.651575	+	0.651575i	−0.953372	−	0.301797i	$-0.902413\pi$
$463$	−14.0202	+	14.0202i	−0.651575	+	0.651575i	0.301797	+	0.953372i	$0.402413\pi$
$464$	−5.02052	−	16.7524i	−0.233072	−	0.777710i
$465$	−50.7961	+	20.2796i	−2.35561	+	0.940442i
$466$	0.724284	−	5.83211i	0.0335518	−	0.270167i
$467$	−8.90065			−0.411873			−0.205937	−	0.978565i	$-0.566024\pi$
$467$	−8.90065			−0.411873			−0.205937	+	0.978565i	$0.566024\pi$
$468$	−6.16543	+	24.4399i	−0.284997	+	1.12974i
$469$	5.69447	−	5.69447i	0.262946	−	0.262946i
$470$	9.25970	−	2.42653i	0.427118	−	0.111928i
$471$	24.4557			1.12686
$472$	−6.82679	+	17.5662i	−0.314229	+	0.808548i
$473$	−4.25845	+	4.25845i	−0.195804	+	0.195804i
$474$	3.10735	+	3.98858i	0.142725	+	0.183202i
$475$	−0.453723	+	17.6471i	−0.0208183	+	0.809704i
$476$	−6.70062	−	1.69036i	−0.307122	−	0.0774773i
$477$			12.0932i			0.553709i
$478$	−32.0016	+	24.9312i	−1.46372	+	1.14032i
$479$	27.9791			1.27840			0.639198	−	0.769042i	$-0.279266\pi$
$479$	27.9791			1.27840			0.639198	+	0.769042i	$0.279266\pi$
$480$	15.8666	+	26.0271i	0.724208	+	1.18797i
$481$	52.5857			2.39770
$482$	−25.7530	+	20.0631i	−1.17301	+	0.913849i
$483$		−	8.28983i		−	0.377200i
$484$	−0.0293490	−	0.00740383i	−0.00133404	−	0.000336538i
$485$	12.0933	−	28.1664i	0.549129	−	1.27897i
$486$	−18.7723	−	24.0960i	−0.851528	−	1.09302i
$487$	27.6242	−	27.6242i	1.25177	−	1.25177i	0.296845	−	0.954926i	$-0.404066\pi$
$487$	27.6242	−	27.6242i	1.25177	−	1.25177i	0.954926	−	0.296845i	$-0.0959344\pi$
$488$	11.0762	+	4.30457i	0.501395	+	0.194859i
$489$	−37.1270			−1.67894
$490$	−2.72986	−	1.59620i	−0.123323	−	0.0721091i
$491$	2.27238	−	2.27238i	0.102551	−	0.102551i	−0.653970	−	0.756521i	$-0.726898\pi$
$491$	2.27238	−	2.27238i	0.102551	−	0.102551i	0.756521	+	0.653970i	$0.226898\pi$
$492$	14.3834	−	57.0163i	0.648455	−	2.57049i
$493$	−15.1069			−0.680380
$494$	2.76256	−	22.2448i	0.124293	−	1.00084i
$495$	−8.21926	+	19.1434i	−0.369428	+	0.860431i
$496$	19.2590	−	35.7424i	0.864756	−	1.60488i
$497$	8.42208	−	8.42208i	0.377782	−	0.377782i
$498$	26.0985	−	20.3323i	1.16950	−	0.911114i
$499$	5.32226	−	5.32226i	0.238257	−	0.238257i	−0.577871	−	0.816128i	$-0.696116\pi$
$499$	5.32226	−	5.32226i	0.238257	−	0.238257i	0.816128	+	0.577871i	$0.196116\pi$
$500$	17.4100	+	14.0319i	0.778597	+	0.627525i
$501$	20.7300	+	20.7300i	0.926149	+	0.926149i
$502$	−3.13736	+	25.2628i	−0.140027	+	1.12753i
$503$	18.3430	+	18.3430i	0.817873	+	0.817873i	0.985800	−	0.167927i	$-0.0537072\pi$
$503$	18.3430	+	18.3430i	0.817873	+	0.817873i	−0.167927	+	0.985800i	$0.553707\pi$
$504$	7.40079	+	2.87619i	0.329657	+	0.128116i
$505$	−8.02675	−	3.44631i	−0.357186	−	0.153359i
$506$	−12.7371	+	9.92300i	−0.566235	+	0.441131i
$507$		−	17.2418i		−	0.765737i
$508$	21.2344	−	12.6791i	0.942124	−	0.562543i
$509$	−17.9583	−	17.9583i	−0.795988	−	0.795988i	0.186472	−	0.982460i	$-0.440295\pi$
$509$	−17.9583	−	17.9583i	−0.795988	−	0.795988i	−0.982460	+	0.186472i	$0.940295\pi$
$510$	25.4709	−	6.67472i	1.12787	−	0.295562i
$511$		−	12.1030i		−	0.535407i
$512$	−21.4312	−	7.25964i	−0.947136	−	0.320834i
$513$	1.15975	+	1.15975i	0.0512042	+	0.0512042i
$514$	−2.54471	+	20.4907i	−0.112243	+	0.903804i
$515$	7.38741	+	3.17180i	0.325528	+	0.139766i
$516$	−8.47986	−	2.13920i	−0.373305	−	0.0941732i
$517$	−10.0465			−0.441844
$518$	2.04152	−	16.4388i	0.0896990	−	0.722278i
$519$		−	19.4559i		−	0.854020i
$520$	−20.2607	−	19.8922i	−0.888489	−	0.872329i
$521$		−	35.5533i		−	1.55762i	−0.627262	−	0.778809i	$-0.715824\pi$
$521$		−	35.5533i		−	1.55762i	0.627262	−	0.778809i	$-0.284176\pi$
$522$	17.2251	+	2.13917i	0.753922	+	0.0936289i
$523$	34.4599			1.50683			0.753414	−	0.657546i	$-0.228406\pi$
$523$	34.4599			1.50683			0.753414	+	0.657546i	$0.228406\pi$
$524$	3.26389	−	1.94887i	0.142584	−	0.0851370i
$525$	12.0451	+	0.309691i	0.525692	+	0.0135160i
$526$	7.92280	+	0.983925i	0.345450	+	0.0429012i
$527$	−24.7995	−	24.7995i	−1.08028	−	1.08028i
$528$	−9.18408	−	30.6452i	−0.399686	−	1.33366i
$529$		−	11.1662i		−	0.485489i
$530$	−11.7599	−	6.87624i	−0.510817	−	0.298685i
$531$	−13.2263	−	13.2263i	−0.573973	−	0.573973i
$532$	−6.84667	−	1.72720i	−0.296841	−	0.0748837i
$533$			54.7736i			2.37251i
$534$	−10.2937	−	13.2129i	−0.445450	−	0.571779i
$535$	−4.95796	−	12.4187i	−0.214351	−	0.536906i
$536$	−9.17816	−	20.8469i	−0.396436	−	0.900449i
$537$	26.2494	+	26.2494i	1.13275	+	1.13275i
$538$	−28.4669	−	3.53527i	−1.22729	−	0.152416i
$539$	2.34682	+	2.34682i	0.101085	+	0.101085i
$540$	2.05926	−	0.274949i	0.0886162	−	0.0118319i
$541$	−8.37193	+	8.37193i	−0.359938	+	0.359938i	−0.863790	−	0.503852i	$-0.831916\pi$
$541$	−8.37193	+	8.37193i	−0.359938	+	0.359938i	0.503852	+	0.863790i	$0.331916\pi$
$542$	13.2211	+	16.9706i	0.567894	+	0.728948i
$543$	−30.2478	+	30.2478i	−1.29806	+	1.29806i
$544$	−11.3216	+	15.9332i	−0.485409	+	0.683130i
$545$	20.4576	+	8.78355i	0.876309	+	0.376246i
$546$	−15.1833	−	1.88560i	−0.649784	−	0.0806961i
$547$	−26.3514			−1.12670			−0.563352	−	0.826217i	$-0.690488\pi$
$547$	−26.3514			−1.12670			−0.563352	+	0.826217i	$0.690488\pi$
$548$	1.42207	−	0.849118i	0.0607477	−	0.0362725i
$549$	−8.33972	+	8.33972i	−0.355931	+	0.355931i
$550$	−13.9423	−	18.8778i	−0.594501	−	0.804950i
$551$	−15.4362			−0.657603
$552$	−21.8548	−	8.49349i	−0.930201	−	0.361507i
$553$	−1.04907	+	1.04907i	−0.0446109	+	0.0446109i
$554$	−26.4897	+	20.6371i	−1.12544	+	0.876785i
$555$	23.4024	+	58.6182i	0.993378	+	2.48821i
$556$	−15.1463	+	9.04388i	−0.642347	+	0.383546i
$557$			31.2312i			1.32331i	0.749809	+	0.661655i	$0.230146\pi$
$557$			31.2312i			1.32331i	−0.749809	+	0.661655i	$0.769854\pi$
$558$	24.7651	+	31.7884i	1.04839	+	1.34571i
$559$	8.14631			0.344552
$560$	−7.00505	+	5.56141i	−0.296017	+	0.235012i
$561$	−27.6351			−1.16676
$562$	6.80580	+	8.73591i	0.287085	+	0.368502i
$563$			2.59760i			0.109476i	0.998501	+	0.0547380i	$0.0174324\pi$
$563$			2.59760i			0.109476i	−0.998501	+	0.0547380i	$0.982568\pi$
$564$	−7.47940	−	12.5262i	−0.314940	−	0.527448i
$565$	−17.5397	−	7.53070i	−0.737899	−	0.316819i
$566$	18.5115	−	14.4216i	0.778096	−	0.606184i
$567$	6.74662	−	6.74662i	0.283331	−	0.283331i
$568$	−13.5744	−	30.8324i	−0.569570	−	1.29370i
$569$	32.1881			1.34940			0.674698	−	0.738094i	$-0.264274\pi$
$569$	32.1881			1.34940			0.674698	+	0.738094i	$0.264274\pi$
$570$	26.0261	−	6.82021i	1.09011	−	0.285667i
$571$	−3.12862	+	3.12862i	−0.130929	+	0.130929i	−0.769534	−	0.638606i	$-0.779512\pi$
$571$	−3.12862	+	3.12862i	−0.130929	+	0.130929i	0.638606	+	0.769534i	$0.279512\pi$
$572$	15.2773	+	25.5858i	0.638778	+	1.06980i
$573$	−23.7121			−0.990588
$574$	17.1227	+	2.12646i	0.714690	+	0.0887566i
$575$	−17.1944	−	0.442085i	−0.717057	−	0.0184362i
$576$	15.1652	−	16.5641i	0.631884	−	0.690171i
$577$	−19.6591	+	19.6591i	−0.818419	+	0.818419i	−0.985879	−	0.167460i	$-0.946444\pi$
$577$	−19.6591	+	19.6591i	−0.818419	+	0.818419i	0.167460	+	0.985879i	$0.446444\pi$
$578$	−4.39879	−	5.64627i	−0.182965	−	0.234854i
$579$	−16.2622	+	16.2622i	−0.675834	+	0.675834i
$580$	−11.8745	+	15.5340i	−0.493062	+	0.645016i
$581$	6.86438	+	6.86438i	0.284782	+	0.284782i
$582$	−46.3619	−	5.75763i	−1.92176	−	0.238662i
$583$	10.1098	+	10.1098i	0.418706	+	0.418706i
$584$	−31.9077	−	12.4004i	−1.32035	−	0.513131i
$585$	26.1720	−	10.4488i	1.08208	−	0.432004i
$586$	5.94144	+	7.62642i	0.245439	+	0.315044i
$587$		−	23.2725i		−	0.960559i	−0.877115	−	0.480280i	$-0.840535\pi$
$587$		−	23.2725i		−	0.960559i	0.877115	−	0.480280i	$-0.159465\pi$
$588$	−1.17891	+	4.67323i	−0.0486174	+	0.192721i
$589$	−25.3400	−	25.3400i	−1.04412	−	1.04412i
$590$	20.3823	−	5.34125i	0.839127	−	0.219896i
$591$		−	28.5619i		−	1.17488i
$592$	−41.2464	−	22.2248i	−1.69522	−	0.913432i
$593$	−32.5472	−	32.5472i	−1.33655	−	1.33655i	−0.899376	−	0.437176i	$-0.855979\pi$
$593$	−32.5472	−	32.5472i	−1.33655	−	1.33655i	−0.437176	−	0.899376i	$-0.644021\pi$
$594$	−2.16381	−	0.268721i	−0.0887821	−	0.0110258i
$595$	2.86471	+	7.17550i	0.117442	+	0.294167i
$596$	2.79737	+	4.68493i	0.114585	+	0.191902i
$597$	24.8706			1.01789
$598$	21.6742	+	2.69169i	0.886322	+	0.110072i
$599$			40.6659i			1.66156i	0.556599	+	0.830781i	$0.312106\pi$
$599$			40.6659i			1.66156i	−0.556599	+	0.830781i	$0.687894\pi$
$600$	13.1575	−	31.4377i	0.537152	−	1.28344i
$601$		−	1.52717i		−	0.0622944i	−0.999515	−	0.0311472i	$-0.990084\pi$
$601$		−	1.52717i		−	0.0622944i	0.999515	−	0.0311472i	$-0.00991607\pi$
$602$	0.316261	−	2.54661i	0.0128899	−	0.103792i
$603$	22.6072			0.920635
$604$	3.94199	−	15.6262i	0.160397	−	0.635819i
$605$	0.0125475	+	0.0314290i	0.000510130	+	0.00127777i
$606$	−1.64079	+	13.2120i	−0.0666525	+	0.536702i
$607$	21.9476	+	21.9476i	0.890825	+	0.890825i	0.994601	−	0.103776i	$-0.0330924\pi$
$607$	21.9476	+	21.9476i	0.890825	+	0.890825i	−0.103776	+	0.994601i	$0.533092\pi$
$608$	−11.5684	+	16.2805i	−0.469159	+	0.660261i
$609$			10.5360i			0.426942i
$610$	−3.36787	−	12.8519i	−0.136361	−	0.520358i
$611$	9.60935	+	9.60935i	0.388753	+	0.388753i
$612$	−9.94541	−	16.6562i	−0.402019	−	0.673285i
$613$		−	42.3381i		−	1.71002i	−0.518612	−	0.855010i	$-0.673551\pi$
$613$		−	42.3381i		−	1.71002i	0.518612	−	0.855010i	$-0.326449\pi$
$614$	−0.309043	+	0.240763i	−0.0124720	+	0.00971642i
$615$	−61.0572	+	24.3761i	−2.46206	+	0.982941i
$616$	8.59148	−	3.78253i	0.346161	−	0.152402i
$617$	14.4092	+	14.4092i	0.580093	+	0.580093i	0.934929	−	0.354836i	$-0.115463\pi$
$617$	14.4092	+	14.4092i	0.580093	+	0.580093i	−0.354836	+	0.934929i	$0.615463\pi$
$618$	1.51010	−	12.1597i	0.0607451	−	0.489134i
$619$	14.6752	+	14.6752i	0.589846	+	0.589846i	0.937590	−	0.347744i	$-0.113052\pi$
$619$	14.6752	+	14.6752i	0.589846	+	0.589846i	−0.347744	+	0.937590i	$0.613052\pi$
$620$	−44.9938	+	6.00752i	−1.80700	+	0.241268i
$621$	−1.13000	+	1.13000i	−0.0453453	+	0.0453453i
$622$	17.4651	−	13.6064i	0.700287	−	0.545566i
$623$	3.47523	−	3.47523i	0.139232	−	0.139232i
$624$	−20.5274	+	38.0963i	−0.821752	+	1.52507i
$625$	1.28470	−	24.9670i	0.0513879	−	0.998679i
$626$	−4.87445	+	39.2502i	−0.194822	+	1.56875i
$627$	−28.2375			−1.12770
$628$	19.6802	+	4.96469i	0.785324	+	0.198113i
$629$	−28.6184	+	28.6184i	−1.14109	+	1.14109i
$630$	−2.25032	−	8.58727i	−0.0896549	−	0.342125i
$631$	19.0148			0.756969			0.378485	−	0.925608i	$-0.376445\pi$
$631$	19.0148			0.756969			0.378485	+	0.925608i	$0.376445\pi$
$632$	1.69085	+	3.84053i	0.0672585	+	0.152768i
$633$	9.93142	−	9.93142i	0.394739	−	0.394739i
$634$	−15.6666	−	20.1096i	−0.622200	−	0.798655i
$635$	−25.4080	−	10.9090i	−1.00829	−	0.432911i
$636$	−5.07860	+	20.1317i	−0.201379	+	0.798273i
$637$		−	4.48941i		−	0.177877i
$638$	16.1884	−	12.6117i	0.640905	−	0.499303i
$639$	33.4358			1.32270
$640$	7.48459	+	24.1657i	0.295854	+	0.955233i
$641$	−34.9937			−1.38217			−0.691084	−	0.722774i	$-0.742867\pi$
$641$	−34.9937			−1.38217			−0.691084	+	0.722774i	$0.742867\pi$
$642$	−16.0770	+	12.5249i	−0.634508	+	0.494320i
$643$		−	7.16531i		−	0.282572i	−0.989969	−	0.141286i	$-0.954876\pi$
$643$		−	7.16531i		−	0.282572i	0.989969	−	0.141286i	$-0.0451237\pi$
$644$	1.68290	−	6.67105i	0.0663154	−	0.262876i
$645$	3.62539	+	9.08085i	0.142750	+	0.357558i
$646$	10.6027	+	13.6096i	0.417157	+	0.535461i
$647$	12.7344	−	12.7344i	0.500639	−	0.500639i	−0.410997	−	0.911637i	$-0.634819\pi$
$647$	12.7344	−	12.7344i	0.500639	−	0.500639i	0.911637	+	0.410997i	$0.134819\pi$
$648$	−10.8740	−	24.6987i	−0.427170	−	0.970257i
$649$	−22.1142			−0.868058
$650$	−4.72073	+	31.3920i	−0.185162	+	1.23129i
$651$	−17.2960	+	17.2960i	−0.677882	+	0.677882i
$652$	−29.8771	−	7.53705i	−1.17008	−	0.295174i
$653$	−24.1866			−0.946497			−0.473248	−	0.880929i	$-0.656919\pi$
$653$	−24.1866			−0.946497			−0.473248	+	0.880929i	$0.656919\pi$
$654$	4.18185	−	33.6733i	0.163523	−	1.31673i
$655$	−3.90541	−	1.67680i	−0.152597	−	0.0655179i
$656$	23.1495	−	42.9626i	0.903835	−	1.67741i
$657$	24.0246	−	24.0246i	0.937290	−	0.937290i
$658$	3.37703	−	2.63091i	0.131650	−	0.102564i
$659$	0.529989	−	0.529989i	0.0206454	−	0.0206454i	−0.696709	−	0.717354i	$-0.745353\pi$
$659$	0.529989	−	0.529989i	0.0206454	−	0.0206454i	0.717354	+	0.696709i	$0.245353\pi$
$660$	−21.7221	+	28.4165i	−0.845531	+	1.10611i
$661$	21.1546	+	21.1546i	0.822818	+	0.822818i	0.986511	−	0.163693i	$-0.0523408\pi$
$661$	21.1546	+	21.1546i	0.822818	+	0.822818i	−0.163693	+	0.986511i	$0.552341\pi$
$662$	3.58345	−	28.8548i	0.139275	−	1.12147i
$663$	26.4327	+	26.4327i	1.02656	+	1.02656i
$664$	25.1298	−	11.0638i	0.975226	−	0.429358i
$665$	2.92715	+	7.33191i	0.113510	+	0.284319i
$666$	36.6835	−	28.5787i	1.42146	−	1.10740i
$667$		−	15.0402i		−	0.582360i
$668$	12.4737	+	20.8904i	0.482620	+	0.808272i
$669$	7.15876	+	7.15876i	0.276774	+	0.276774i
$670$	−12.8545	+	21.9841i	−0.496614	+	0.849320i
$671$			13.9439i			0.538298i
$672$	11.1123	+	7.89604i	0.428667	+	0.304596i
$673$	2.40011	+	2.40011i	0.0925176	+	0.0925176i	0.751851	−	0.659333i	$-0.229161\pi$
$673$	2.40011	+	2.40011i	0.0925176	+	0.0925176i	−0.659333	+	0.751851i	$0.729161\pi$
$674$	−2.49855	+	20.1189i	−0.0962405	+	0.774952i
$675$	−1.59967	−	1.68410i	−0.0615715	−	0.0648212i
$676$	3.50022	−	13.8750i	0.134624	−	0.533653i
$677$	−31.1344			−1.19659			−0.598296	−	0.801275i	$-0.704155\pi$
$677$	−31.1344			−1.19659			−0.598296	+	0.801275i	$0.704155\pi$
$678$	−3.58537	+	28.8703i	−0.137695	+	1.10876i
$679$		−	13.7083i		−	0.526078i
$680$	21.8521	−	0.200546i	0.837991	−	0.00769060i
$681$			35.9330i			1.37695i
$682$	47.2783	+	5.87144i	1.81038	+	0.224829i
$683$	5.20104			0.199012			0.0995061	−	0.995037i	$-0.468274\pi$
$683$	5.20104			0.199012			0.0995061	+	0.995037i	$0.468274\pi$
$684$	−10.1622	−	17.0192i	−0.388561	−	0.650746i
$685$	−1.70157	−	0.730575i	−0.0650138	−	0.0279138i
$686$	−1.40343	−	0.174291i	−0.0535833	−	0.00665446i
$687$	42.4138	+	42.4138i	1.61819	+	1.61819i
$688$	−6.38969	−	3.44295i	−0.243605	−	0.131261i
$689$		−	19.3398i		−	0.736789i
$690$	6.64527	+	25.3585i	0.252981	+	0.965381i
$691$	29.4509	+	29.4509i	1.12036	+	1.12036i	0.991687	+	0.128677i	$0.0410730\pi$
$691$	29.4509	+	29.4509i	1.12036	+	1.12036i	0.128677	+	0.991687i	$0.458927\pi$
$692$	3.94970	−	15.6567i	0.150145	−	0.595178i
$693$			9.31692i			0.353920i
$694$	−7.05144	−	9.05122i	−0.267669	−	0.343580i
$695$	18.1233	+	7.78130i	0.687457	+	0.295161i
$696$	27.7765	+	10.7949i	1.05287	+	0.409179i
$697$	−29.8091	−	29.8091i	−1.12910	−	1.12910i
$698$	−28.9526	−	3.59559i	−1.09587	−	0.136095i
$699$	7.08114	+	7.08114i	0.267833	+	0.267833i
$700$	9.63015	+	2.69446i	0.363986	+	0.101841i
$701$	16.8941	−	16.8941i	0.638082	−	0.638082i	−0.312000	−	0.950082i	$-0.600999\pi$
$701$	16.8941	−	16.8941i	0.638082	−	0.638082i	0.950082	+	0.312000i	$0.100999\pi$
$702$	1.81263	+	2.32669i	0.0684132	+	0.0878151i
$703$	−29.2422	+	29.2422i	−1.10289	+	1.10289i
$704$	−1.16946	−	26.5255i	−0.0440757	−	0.999717i
$705$	−6.43523	+	14.9882i	−0.242365	+	0.564489i
$706$	34.0410	+	4.22752i	1.28115	+	0.159105i
$707$	−3.90655			−0.146921
$708$	−16.4636	−	27.5725i	−0.618738	−	1.03624i
$709$	5.13449	−	5.13449i	0.192830	−	0.192830i	−0.604088	−	0.796918i	$-0.706462\pi$
$709$	5.13449	−	5.13449i	0.192830	−	0.192830i	0.796918	+	0.604088i	$0.206462\pi$
$710$	−19.0118	+	32.5143i	−0.713498	+	1.22024i
$711$	−4.16482			−0.156193
$712$	−5.60126	−	12.7225i	−0.209916	−	0.476795i
$713$	24.6900	−	24.6900i	0.924648	−	0.924648i
$714$	9.28928	−	7.23691i	0.347643	−	0.270835i
$715$	13.1445	−	30.6147i	0.491577	−	1.14493i
$716$	15.7948	+	26.4524i	0.590278	+	0.988574i
$717$		−	69.1258i		−	2.58155i
$718$	22.0069	+	28.2480i	0.821291	+	1.05421i
$719$	21.5817			0.804860			0.402430	−	0.915451i	$-0.368166\pi$
$719$	21.5817			0.804860			0.402430	+	0.915451i	$0.368166\pi$
$720$	−24.9445	−	2.86564i	−0.929628	−	0.106796i
$721$	3.59539			0.133899
$722$	−5.67977	−	7.29054i	−0.211379	−	0.271326i
$723$		−	55.6283i		−	2.06884i
$724$	−30.4817	+	18.2007i	−1.13284	+	0.676422i
$725$	21.8534	+	0.561872i	0.811616	+	0.0208674i
$726$	0.0406874	−	0.0316980i	0.00151005	−	0.00117642i
$727$	−24.6504	+	24.6504i	−0.914233	+	0.914233i	−0.996602	−	0.0823689i	$-0.973751\pi$
$727$	−24.6504	+	24.6504i	−0.914233	+	0.914233i	0.0823689	+	0.996602i	$0.473751\pi$
$728$	−11.8356	−	4.59971i	−0.438656	−	0.170476i
$729$	23.4258			0.867620
$730$	9.70200	+	37.0231i	0.359087	+	1.37028i
$731$	−4.43341	+	4.43341i	−0.163976	+	0.163976i
$732$	−17.3856	+	10.3809i	−0.642589	+	0.383691i
$733$	−8.49140			−0.313637			−0.156819	−	0.987627i	$-0.550124\pi$
$733$	−8.49140			−0.313637			−0.156819	+	0.987627i	$0.550124\pi$
$734$	24.8270	+	3.08324i	0.916382	+	0.113805i
$735$	5.00443	−	1.99794i	0.184591	−	0.0736953i
$736$	−15.8629	−	11.2716i	−0.584713	−	0.415477i
$737$	18.8994	−	18.8994i	0.696169	−	0.696169i
$738$	29.7678	+	38.2098i	1.09577	+	1.40652i
$739$	20.8443	−	20.8443i	0.766770	−	0.766770i	−0.210766	−	0.977537i	$-0.567596\pi$
$739$	20.8443	−	20.8443i	0.766770	−	0.766770i	0.977537	+	0.210766i	$0.0675958\pi$
$740$	6.93263	+	51.9225i	0.254848	+	1.90871i
$741$	27.0088	+	27.0088i	0.992194	+	0.992194i
$742$	−6.04581	−	0.750824i	−0.221949	−	0.0275636i
$743$	29.0367	+	29.0367i	1.06525	+	1.06525i	0.997717	+	0.0675365i	$0.0215139\pi$
$743$	29.0367	+	29.0367i	1.06525	+	1.06525i	0.0675365	+	0.997717i	$0.478486\pi$
$744$	27.8771	+	63.3188i	1.02202	+	2.32138i
$745$	2.40684	−	5.60575i	0.0881799	−	0.205379i
$746$	16.8801	+	21.6673i	0.618026	+	0.793297i
$747$			27.2517i			0.997087i
$748$	−22.2387	−	5.61013i	−0.813128	−	0.205127i
$749$	−4.22853	−	4.22853i	−0.154507	−	0.154507i
$750$	−37.0941	+	8.70822i	−1.35449	+	0.317979i
$751$			25.2691i			0.922081i	0.887379	+	0.461041i	$0.152524\pi$
$751$			25.2691i			0.922081i	−0.887379	+	0.461041i	$0.847476\pi$
$752$	−3.47597	−	11.5985i	−0.126755	−	0.422955i
$753$	−30.6732	−	30.6732i	−1.11779	−	1.11779i
$754$	−27.5470	−	3.42103i	−1.00320	−	0.124587i
$755$	−16.7336	+	6.68064i	−0.608999	+	0.243134i
$756$	0.797715	−	0.476316i	0.0290126	−	0.0173235i
$757$	6.06652			0.220491			0.110246	−	0.993904i	$-0.464836\pi$
$757$	6.06652			0.220491			0.110246	+	0.993904i	$0.464836\pi$
$758$	−11.0021	−	1.36634i	−0.399615	−	0.0496278i
$759$		−	27.5132i		−	0.998665i
$760$	22.3284	−	0.204918i	0.809938	−	0.00743314i
$761$			42.5121i			1.54106i	0.637402	+	0.770532i	$0.280009\pi$
$761$			42.5121i			1.54106i	−0.637402	+	0.770532i	$0.719991\pi$
$762$	−5.19378	+	41.8216i	−0.188151	+	1.51504i
$763$	9.95656			0.360452
$764$	−19.0818	−	4.81374i	−0.690355	−	0.174155i
$765$	−8.55696	+	19.9299i	−0.309378	+	0.720568i
$766$	2.18039	−	17.5570i	0.0787806	−	0.634360i
$767$	21.1520	+	21.1520i	0.763753	+	0.763753i
$768$	32.2019	−	21.2058i	1.16199	−	0.765198i
$769$			14.1317i			0.509603i	0.966993	+	0.254802i	$0.0820102\pi$
$769$			14.1317i			0.509603i	−0.966993	+	0.254802i	$0.917990\pi$
$770$	−9.06015	−	5.29765i	−0.326505	−	0.190914i
$771$	−24.8790	−	24.8790i	−0.895997	−	0.895997i
$772$	−16.3880	+	9.78528i	−0.589816	+	0.352180i
$773$		−	35.8287i		−	1.28867i	−0.764744	−	0.644334i	$-0.777135\pi$
$773$		−	35.8287i		−	1.28867i	0.764744	−	0.644334i	$-0.222865\pi$
$774$	5.68283	−	4.42727i	0.204265	−	0.159135i
$775$	34.9522	+	36.7969i	1.25552	+	1.32178i
$776$	−36.1398	−	14.0451i	−1.29734	−	0.504190i
$777$	19.9594	+	19.9594i	0.716039	+	0.716039i
$778$	−4.88979	+	39.3737i	−0.175307	+	1.41162i
$779$	−30.4589	−	30.4589i	−1.09130	−	1.09130i
$780$	47.9570	−	6.40315i	1.71714	−	0.229270i
$781$	27.9521	−	27.9521i	1.00020	−	1.00020i
$782$	−13.2605	+	10.3307i	−0.474194	+	0.369425i
$783$	1.43618	−	1.43618i	0.0513250	−	0.0513250i
$784$	−1.89740	+	3.52135i	−0.0677643	+	0.125762i
$785$	−8.41385	−	21.0749i	−0.300303	−	0.752197i
$786$	−0.798325	+	6.42830i	−0.0284753	+	0.229290i
$787$	16.0687			0.572789			0.286394	−	0.958112i	$-0.407543\pi$
$787$	16.0687			0.572789			0.286394	+	0.958112i	$0.407543\pi$
$788$	5.79828	−	22.9845i	0.206555	−	0.818791i
$789$	−9.61959	+	9.61959i	−0.342466	+	0.342466i
$790$	2.36814	−	4.05004i	0.0842545	−	0.144094i
$791$	−8.53640			−0.303520
$792$	24.5625	+	9.54581i	0.872791	+	0.339196i
$793$	13.3372	−	13.3372i	0.473617	−	0.473617i
$794$	−3.40922	−	4.37607i	−0.120989	−	0.155301i
$795$	21.5585	−	8.60689i	0.764600	−	0.305255i
$796$	20.0140	+	5.04891i	0.709378	+	0.178954i
$797$			0.960275i			0.0340147i	0.999855	+	0.0170073i	$0.00541387\pi$
$797$			0.960275i			0.0340147i	−0.999855	+	0.0170073i	$0.994586\pi$
$798$	9.49176	−	7.39465i	0.336005	−	0.261768i
$799$	−10.4593			−0.370022
$800$	16.9703	−	22.6276i	0.599989	−	0.800008i
$801$	13.7967			0.487483
$802$	−4.07467	+	3.17441i	−0.143882	+	0.112092i
$803$		−	40.1688i		−	1.41753i
$804$	37.6345	+	9.49400i	1.32726	+	0.334828i
$805$	−7.14384	+	2.85207i	−0.251787	+	0.100522i
$806$	−39.6051	−	50.8371i	−1.39503	−	1.79066i
$807$	34.5635	−	34.5635i	1.21669	−	1.21669i
$808$	−4.00253	+	10.2990i	−0.140808	+	0.362317i
$809$	−36.4907			−1.28295			−0.641473	−	0.767146i	$-0.721676\pi$
$809$	−36.4907			−1.28295			−0.641473	+	0.767146i	$0.721676\pi$
$810$	−15.2296	+	26.0460i	−0.535114	+	0.915164i
$811$	−38.9206	+	38.9206i	−1.36669	+	1.36669i	−0.501571	+	0.865117i	$0.667244\pi$
$811$	−38.9206	+	38.9206i	−1.36669	+	1.36669i	−0.865117	+	0.501571i	$0.832756\pi$
$812$	−2.13889	+	8.47863i	−0.0750605	+	0.297542i
$813$	−36.6577			−1.28564
$814$	6.77560	−	54.5587i	0.237485	−	1.91228i
$815$	12.7733	+	31.9945i	0.447430	+	1.12072i
$816$	−9.56142	−	31.9044i	−0.334717	−	1.11688i
$817$	−4.53005	+	4.53005i	−0.158486	+	0.158486i
$818$	5.87300	−	4.57542i	0.205345	−	0.159976i
$819$	8.91152	−	8.91152i	0.311394	−	0.311394i
$820$	−54.0829	+	7.22107i	−1.88866	+	0.252171i
$821$	−26.5392	−	26.5392i	−0.926224	−	0.926224i	0.0712358	−	0.997460i	$-0.477306\pi$
$821$	−26.5392	−	26.5392i	−0.926224	−	0.926224i	−0.997460	+	0.0712358i	$0.977306\pi$
$822$	−0.347827	+	2.80079i	−0.0121319	+	0.0976887i
$823$	33.6422	+	33.6422i	1.17269	+	1.17269i	0.981565	+	0.191129i	$0.0612149\pi$
$823$	33.6422	+	33.6422i	1.17269	+	1.17269i	0.191129	+	0.981565i	$0.438785\pi$
$824$	3.68372	−	9.47865i	0.128328	−	0.330205i
$825$	39.9766	+	1.02784i	1.39181	+	0.0357846i
$826$	7.43348	−	5.79113i	0.258644	−	0.201499i
$827$		−	55.9964i		−	1.94719i	−0.228291	−	0.973593i	$-0.573314\pi$
$827$		−	55.9964i		−	1.94719i	0.228291	−	0.973593i	$-0.426686\pi$
$828$	16.5827	−	9.90152i	0.576287	−	0.344102i
$829$	26.6012	+	26.6012i	0.923897	+	0.923897i	0.997302	−	0.0734049i	$-0.0233865\pi$
$829$	26.6012	+	26.6012i	0.923897	+	0.923897i	−0.0734049	+	0.997302i	$0.523387\pi$
$830$	−26.5006	−	15.4954i	−0.919851	−	0.537855i
$831$		−	57.2197i		−	1.98493i
$832$	−24.2527	+	26.4899i	−0.840812	+	0.918371i
$833$	2.44324	+	2.44324i	0.0846534	+	0.0846534i
$834$	3.70468	−	29.8310i	0.128283	−	1.03296i
$835$	10.7323	−	24.9964i	0.371405	−	0.865035i
$836$	−22.7235	−	5.73242i	−0.785907	−	0.198260i
$837$	4.71528			0.162984
$838$	−4.02187	+	32.3851i	−0.138933	+	1.11872i
$839$		−	39.9065i		−	1.37773i	−0.724892	−	0.688863i	$-0.758110\pi$
$839$		−	39.9065i		−	1.37773i	0.724892	−	0.688863i	$-0.241890\pi$
$840$	−0.139868	−	15.2404i	−0.00482589	−	0.525843i
$841$		−	9.88449i		−	0.340845i
$842$	−8.02937	−	0.997159i	−0.276710	−	0.0343644i
$843$	−18.8702			−0.649924
$844$	10.0082	−	5.97593i	0.344498	−	0.205700i
$845$	−14.8583	+	5.93196i	−0.511142	+	0.204066i
$846$	11.9258	+	1.48106i	0.410018	+	0.0509198i
$847$	0.0107015	+	0.0107015i	0.000367708	+	0.000367708i
$848$	−8.17377	+	15.1695i	−0.280688	+	0.520923i
$849$			39.9862i			1.37232i
$850$	−14.5151	−	19.6534i	−0.497865	−	0.674106i
$851$	−28.4921	−	28.4921i	−0.976696	−	0.976696i
$852$	55.6610	+	14.0415i	1.90692	+	0.481055i
$853$		−	27.3120i		−	0.935146i	−0.883954	−	0.467573i	$-0.845128\pi$
$853$		−	27.3120i		−	0.935146i	0.883954	−	0.467573i	$-0.154872\pi$
$854$	−3.65154	−	4.68711i	−0.124953	−	0.160389i
$855$	−8.74348	+	20.3643i	−0.299021	+	0.696445i
$856$	−15.4802	+	6.81540i	−0.529103	+	0.232946i
$857$	13.3155	+	13.3155i	0.454850	+	0.454850i	0.896960	−	0.442111i	$-0.145770\pi$
$857$	13.3155	+	13.3155i	0.454850	+	0.454850i	−0.442111	+	0.896960i	$0.645770\pi$
$858$	−50.3919	−	6.25812i	−1.72035	−	0.213649i
$859$	−0.152620	−	0.152620i	−0.00520732	−	0.00520732i	0.704498	−	0.709706i	$-0.251172\pi$
$859$	−0.152620	−	0.152620i	−0.00520732	−	0.00520732i	−0.709706	+	0.704498i	$0.751172\pi$
$860$	1.07397	+	8.04358i	0.0366220	+	0.274284i
$861$	−20.7898	+	20.7898i	−0.708516	+	0.708516i
$862$	27.0145	+	34.6758i	0.920119	+	1.18106i
$863$	−3.13243	+	3.13243i	−0.106629	+	0.106629i	−0.758409	−	0.651779i	$-0.774023\pi$
$863$	−3.13243	+	3.13243i	−0.106629	+	0.106629i	0.651779	+	0.758409i	$0.274023\pi$
$864$	−0.438417	−	2.59106i	−0.0149152	−	0.0881497i
$865$	−16.7663	+	6.69370i	−0.570072	+	0.227593i
$866$	−37.9508	−	4.71307i	−1.28962	−	0.160157i
$867$	12.1964			0.414210
$868$	−17.4297	+	10.4073i	−0.591603	+	0.353247i
$869$	−3.48176	+	3.48176i	−0.118110	+	0.118110i
$870$	−8.44586	−	32.2296i	−0.286342	−	1.09269i
$871$	−36.1541			−1.22504
$872$	10.2012	−	26.2488i	0.345455	−	0.888898i
$873$	27.2112	−	27.2112i	0.920959	−	0.920959i
$874$	−13.5495	+	10.5559i	−0.458319	+	0.357058i
$875$	−3.87717	−	10.4865i	−0.131072	−	0.354510i
$876$	50.0834	−	29.9049i	1.69216	−	1.01039i
$877$			26.9004i			0.908362i	0.890909	+	0.454181i	$0.150068\pi$
$877$			26.9004i			0.908362i	−0.890909	+	0.454181i	$0.849932\pi$
$878$	−25.8752	−	33.2133i	−0.873244	−	1.12089i
$879$	−16.4736			−0.555642
$880$	−23.2491	+	18.4578i	−0.783727	+	0.622212i
$881$	7.85863			0.264764			0.132382	−	0.991199i	$-0.457737\pi$
$881$	7.85863			0.264764			0.132382	+	0.991199i	$0.457737\pi$
$882$	−2.43986	−	3.13179i	−0.0821542	−	0.105453i
$883$		−	23.2291i		−	0.781721i	−0.920450	−	0.390860i	$-0.872178\pi$
$883$		−	23.2291i		−	0.781721i	0.920450	−	0.390860i	$-0.127822\pi$
$884$	15.9050	+	26.6371i	0.534944	+	0.895902i
$885$	−14.1651	+	32.9918i	−0.476156	+	1.10901i
$886$	−4.92422	+	3.83627i	−0.165433	+	0.128882i
$887$	20.2207	−	20.2207i	0.678945	−	0.678945i	−0.280816	−	0.959762i	$-0.590605\pi$
$887$	20.2207	−	20.2207i	0.678945	−	0.678945i	0.959762	+	0.280816i	$0.0906051\pi$
$888$	73.0694	−	32.1699i	2.45205	−	1.07955i
$889$	−12.3659			−0.414738
$890$	−7.84488	+	13.4165i	−0.262961	+	0.449722i
$891$	22.3914	−	22.3914i	0.750140	−	0.750140i
$892$	4.30756	+	7.21413i	0.144228	+	0.241547i
$893$	−10.6872			−0.357635
$894$	−9.22706	−	1.14590i	−0.308599	−	0.0383246i
$895$	13.5897	−	31.6516i	0.454254	−	1.05800i
$896$	7.33943	+	8.61004i	0.245193	+	0.287641i
$897$	−26.3160	+	26.3160i	−0.878666	+	0.878666i
$898$	4.46094	+	5.72606i	0.148864	+	0.191081i
$899$	−31.3800	+	31.3800i	−1.04658	+	1.04658i
$900$	13.7674	+	24.4645i	0.458914	+	0.815482i
$901$	10.5252	+	10.5252i	0.350645	+	0.350645i
$902$	56.8288	+	7.05751i	1.89219	+	0.234989i
$903$	3.09201	+	3.09201i	0.102896	+	0.102896i
$904$	−8.74612	+	22.5048i	−0.290892	+	0.748499i
$905$	36.4729	+	15.6597i	1.21240	+	0.520547i
$906$	16.8768	+	21.6631i	0.560695	+	0.719707i
$907$		−	1.14534i		−	0.0380305i	−0.999819	−	0.0190152i	$-0.993947\pi$
$907$		−	1.14534i		−	0.0380305i	0.999819	−	0.0190152i	$-0.00605310\pi$
$908$	−7.29466	+	28.9162i	−0.242082	+	0.959618i
$909$	−7.75454	−	7.75454i	−0.257202	−	0.257202i
$910$	3.59879	+	13.7331i	0.119299	+	0.455247i
$911$			11.9795i			0.396899i	0.980111	+	0.198449i	$0.0635905\pi$
$911$			11.9795i			0.396899i	−0.980111	+	0.198449i	$0.936409\pi$
$912$	−9.76983	−	32.5998i	−0.323512	−	1.07949i
$913$	22.7822	+	22.7822i	0.753981	+	0.753981i
$914$	45.5889	+	5.66164i	1.50795	+	0.187270i
$915$	20.8027	+	8.93169i	0.687716	+	0.295273i
$916$	25.5212	+	42.7418i	0.843244	+	1.41223i
$917$	−1.90073			−0.0627676
$918$	−2.25271	−	0.279762i	−0.0743506	−	0.00923353i
$919$			5.36067i			0.176832i	0.996084	+	0.0884160i	$0.0281805\pi$
$919$			5.36067i			0.176832i	−0.996084	+	0.0884160i	$0.971820\pi$
$920$	0.199661	+	21.7557i	0.00658264	+	0.717264i
$921$		−	0.667556i		−	0.0219967i
$922$	1.15843	−	9.32800i	0.0381510	−	0.307201i
$923$	−53.4717			−1.76004
$924$	−3.91269	+	15.5100i	−0.128718	+	0.510242i
$925$	42.4634	−	40.3346i	1.39619	−	1.32619i
$926$	3.45577	−	27.8267i	0.113564	−	0.914441i
$927$	7.13688	+	7.13688i	0.234406	+	0.234406i
$928$	20.1611	+	14.3258i	0.661819	+	0.470266i
$929$		−	20.1129i		−	0.659882i	−0.944002	−	0.329941i	$-0.892971\pi$
$929$		−	20.1129i		−	0.659882i	0.944002	−	0.329941i	$-0.107029\pi$
$930$	39.0434	−	66.7729i	1.28028	−	2.18957i
$931$	2.49650	+	2.49650i	0.0818195	+	0.0818195i
$932$	4.26086	+	7.13591i	0.139569	+	0.233744i
$933$			37.7259i			1.23509i
$934$	9.92974	−	7.73586i	0.324911	−	0.253125i
$935$	9.50770	+	23.8148i	0.310935	+	0.778828i
$936$	−14.3633	−	32.6242i	−0.469479	−	1.06636i
$937$	11.2798	+	11.2798i	0.368495	+	0.368495i	0.866928	−	0.498433i	$-0.166091\pi$
$937$	11.2798	+	11.2798i	0.368495	+	0.368495i	−0.498433	+	0.866928i	$0.666091\pi$
$938$	−1.40360	+	11.3021i	−0.0458292	+	0.369027i
$939$	−47.6563	−	47.6563i	−1.55520	−	1.55520i
$940$	−8.22132	+	10.7550i	−0.268150	+	0.350790i
$941$	−13.4391	+	13.4391i	−0.438102	+	0.438102i	−0.891373	−	0.453271i	$-0.850257\pi$
$941$	−13.4391	+	13.4391i	−0.438102	+	0.438102i	0.453271	+	0.891373i	$0.350257\pi$
$942$	−27.2833	+	21.2553i	−0.888937	+	0.692535i
$943$	29.6776	−	29.6776i	0.966434	−	0.966434i
$944$	−7.65125	−	25.5305i	−0.249027	−	0.830948i
$945$	−0.954505	−	0.409819i	−0.0310501	−	0.0133314i
$946$	1.04964	−	8.45197i	0.0341268	−	0.274797i
$947$	−16.7848			−0.545434			−0.272717	−	0.962094i	$-0.587922\pi$
$947$	−16.7848			−0.545434			−0.272717	+	0.962094i	$0.587922\pi$
$948$	−6.93323	−	1.74904i	−0.225181	−	0.0568061i
$949$	−38.4210	+	38.4210i	−1.24720	+	1.24720i
$950$	−14.8315	−	20.0818i	−0.481198	−	0.651539i
$951$	43.4382			1.40858
$952$	8.94448	−	3.93794i	0.289892	−	0.127629i
$953$	−14.6385	+	14.6385i	−0.474188	+	0.474188i	−0.903267	−	0.429079i	$-0.858838\pi$
$953$	−14.6385	+	14.6385i	−0.474188	+	0.474188i	0.429079	+	0.903267i	$0.358838\pi$
$954$	−10.5106	−	13.4914i	−0.340293	−	0.436800i
$955$	8.15802	+	20.4342i	0.263987	+	0.661234i
$956$	14.0330	−	55.6273i	0.453861	−	1.79912i
$957$			34.9681i			1.13036i
$958$	−31.2140	+	24.3176i	−1.00848	+	0.785665i
$959$	−0.828141			−0.0267421
$960$	−40.3221	−	15.2461i	−1.30139	−	0.492065i
$961$	−72.0268			−2.32345
$962$	−58.6656	+	45.7040i	−1.89145	+	1.47356i
$963$		−	16.7873i		−	0.540964i
$964$	11.2929	−	44.7655i	0.363721	−	1.44180i
$965$	19.6090	+	8.41919i	0.631237	+	0.271023i
$966$	7.20498	+	9.24829i	0.231816	+	0.297559i
$967$	−18.3696	+	18.3696i	−0.590727	+	0.590727i	−0.937828	−	0.347101i	$-0.887166\pi$
$967$	−18.3696	+	18.3696i	−0.590727	+	0.590727i	0.347101	+	0.937828i	$0.387166\pi$
$968$	0.0391772	−	0.0172483i	0.00125920	−	0.000554383i
$969$	−29.3977			−0.944389
$970$	10.9888	+	41.9337i	0.352830	+	1.34641i
$971$	−24.3279	+	24.3279i	−0.780718	+	0.780718i	−0.979952	−	0.199234i	$-0.936155\pi$
$971$	−24.3279	+	24.3279i	−0.780718	+	0.780718i	0.199234	+	0.979952i	$0.436155\pi$
$972$	41.8854	+	10.5664i	1.34347	+	0.338917i
$973$	8.82047			0.282771
$974$	−6.80893	+	54.8272i	−0.218172	+	1.75678i
$975$	−37.2540	−	39.2203i	−1.19308	−	1.25605i
$976$	−16.0980	+	4.82442i	−0.515285	+	0.154426i
$977$	14.1661	−	14.1661i	0.453213	−	0.453213i	−0.443207	−	0.896419i	$-0.646159\pi$
$977$	14.1661	−	14.1661i	0.453213	−	0.453213i	0.896419	+	0.443207i	$0.146159\pi$
$978$	41.4196	−	32.2683i	1.32445	−	1.03183i
$979$	11.5340	−	11.5340i	0.368627	−	0.368627i
$980$	4.43280	−	0.591861i	0.141601	−	0.0189063i
$981$	19.7639	+	19.7639i	0.631012	+	0.631012i
$982$	−0.560105	+	4.51010i	−0.0178737	+	0.143923i
$983$	22.5767	+	22.5767i	0.720086	+	0.720086i	0.968623	−	0.248536i	$-0.0799495\pi$
$983$	22.5767	+	22.5767i	0.720086	+	0.720086i	−0.248536	+	0.968623i	$0.579950\pi$
$984$	33.5084	+	76.1096i	1.06821	+	2.42629i
$985$	−24.6135	+	9.82657i	−0.784252	+	0.313101i
$986$	16.8535	−	13.1299i	0.536726	−	0.418142i
$987$			7.29464i			0.232191i
$988$	16.2517	+	27.2177i	0.517036	+	0.865911i
$989$	−4.41385	−	4.41385i	−0.140352	−	0.140352i
$990$	−7.46860	−	28.5003i	−0.237368	−	0.905801i
$991$			49.6002i			1.57560i	0.615930	+	0.787801i	$0.288781\pi$
$991$			49.6002i			1.57560i	−0.615930	+	0.787801i	$0.711219\pi$
$992$	9.57922	+	56.6136i	0.304141	+	1.79748i
$993$	35.0345	+	35.0345i	1.11179	+	1.11179i
$994$	−2.07591	+	16.7157i	−0.0658439	+	0.530191i
$995$	−8.55658	−	21.4325i	−0.271262	−	0.679455i
$996$	−11.4445	+	45.3663i	−0.362633	+	1.43749i
$997$	−0.659673			−0.0208920			−0.0104460	−	0.999945i	$-0.503325\pi$
$997$	−0.659673			−0.0208920			−0.0104460	+	0.999945i	$0.503325\pi$
$998$	−1.31185	+	10.5634i	−0.0415260	+	0.334378i
$999$		−	5.44139i		−	0.172158i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.t.a.43.15	✓	144
5.2	odd	4		560.2.bl.a.267.22	yes	144
16.3	odd	4		560.2.bl.a.323.22	yes	144
80.67	even	4	inner	560.2.t.a.547.15	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.t.a.43.15	✓	144	1.1	even	1	trivial
560.2.t.a.547.15	yes	144	80.67	even	4	inner
560.2.bl.a.267.22	yes	144	5.2	odd	4
560.2.bl.a.323.22	yes	144	16.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.t (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.11562 + 0.869134i) q^{2} -2.40982i q^{3} +(0.489211 - 1.93925i) q^{4} +(-2.07668 + 0.829085i) q^{5} +(2.09446 + 2.68844i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(1.13969 + 2.58865i) q^{8} -2.80723 q^{9} +O(q^{10})\)	\(q+(-1.11562 + 0.869134i) q^{2} -2.40982i q^{3} +(0.489211 - 1.93925i) q^{4} +(-2.07668 + 0.829085i) q^{5} +(2.09446 + 2.68844i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(1.13969 + 2.58865i) q^{8} -2.80723 q^{9} +(1.59620 - 2.72986i) q^{10} +(-2.34682 + 2.34682i) q^{11} +(-4.67323 - 1.17891i) q^{12} +4.48941 q^{13} +(0.174291 - 1.40343i) q^{14} +(1.99794 + 5.00443i) q^{15} +(-3.52135 - 1.89740i) q^{16} +(-2.44324 + 2.44324i) q^{17} +(3.13179 - 2.43986i) q^{18} +(-2.49650 + 2.49650i) q^{19} +(0.591861 + 4.43280i) q^{20} +(1.70400 + 1.70400i) q^{21} +(0.578455 - 4.65786i) q^{22} +(-2.43246 - 2.43246i) q^{23} +(6.23817 - 2.74645i) q^{24} +(3.62524 - 3.44349i) q^{25} +(-5.00847 + 3.90190i) q^{26} -0.464550i q^{27} +(1.02533 + 1.71718i) q^{28} +(3.09156 + 3.09156i) q^{29} +(-6.57847 - 3.84656i) q^{30} +10.1502i q^{31} +(5.57758 - 0.943746i) q^{32} +(5.65541 + 5.65541i) q^{33} +(0.602222 - 4.84924i) q^{34} +(0.882186 - 2.05469i) q^{35} +(-1.37333 + 5.44390i) q^{36} +11.7133 q^{37} +(0.615349 - 4.95494i) q^{38} -10.8187i q^{39} +(-4.51299 - 4.43091i) q^{40} +12.2006i q^{41} +(-3.38202 - 0.420010i) q^{42} +1.81456 q^{43} +(3.40297 + 5.69915i) q^{44} +(5.82972 - 2.32743i) q^{45} +(4.82784 + 0.599565i) q^{46} +(2.14045 + 2.14045i) q^{47} +(-4.57239 + 8.48580i) q^{48} -1.00000i q^{49} +(-1.05152 + 6.99245i) q^{50} +(5.88778 + 5.88778i) q^{51} +(2.19627 - 8.70607i) q^{52} -4.30788i q^{53} +(0.403756 + 0.518260i) q^{54} +(2.92789 - 6.81932i) q^{55} +(-2.63633 - 1.02457i) q^{56} +(6.01611 + 6.01611i) q^{57} +(-6.13599 - 0.762022i) q^{58} +(4.71152 + 4.71152i) q^{59} +(10.6822 - 1.42628i) q^{60} +(2.97080 - 2.97080i) q^{61} +(-8.82190 - 11.3238i) q^{62} +(1.98501 - 1.98501i) q^{63} +(-5.40221 + 5.90052i) q^{64} +(-9.32309 + 3.72210i) q^{65} +(-11.2246 - 1.39397i) q^{66} -8.05320 q^{67} +(3.54279 + 5.93331i) q^{68} +(-5.86180 + 5.86180i) q^{69} +(0.801617 + 3.05899i) q^{70} -11.9106 q^{71} +(-3.19937 - 7.26692i) q^{72} +(-8.55814 + 8.55814i) q^{73} +(-13.0675 + 10.1804i) q^{74} +(-8.29820 - 8.73617i) q^{75} +(3.62001 + 6.06264i) q^{76} -3.31891i q^{77} +(9.40288 + 12.0695i) q^{78} +1.48361 q^{79} +(8.88583 + 1.02081i) q^{80} -9.54116 q^{81} +(-10.6040 - 13.6112i) q^{82} -9.70769i q^{83} +(4.13809 - 2.47086i) q^{84} +(3.04819 - 7.09950i) q^{85} +(-2.02436 + 1.57710i) q^{86} +(7.45010 - 7.45010i) q^{87} +(-8.74975 - 3.40044i) q^{88} -4.91472 q^{89} +(-4.48090 + 7.66334i) q^{90} +(-3.17449 + 3.17449i) q^{91} +(-5.90713 + 3.52715i) q^{92} +24.4602 q^{93} +(-4.24826 - 0.527587i) q^{94} +(3.11463 - 7.25425i) q^{95} +(-2.27426 - 13.4409i) q^{96} +(-9.69326 + 9.69326i) q^{97} +(0.869134 + 1.11562i) q^{98} +(6.58806 - 6.58806i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 8 q^{4} - 144 q^{9}+O(q^{10}) \) 144 * q + 8 * q^4 - 144 * q^9	\( 144 q + 8 q^{4} - 144 q^{9} - 16 q^{12} + 8 q^{16} - 28 q^{18} - 16 q^{19} + 4 q^{22} + 32 q^{26} - 36 q^{30} + 32 q^{34} - 32 q^{36} - 56 q^{38} + 8 q^{40} - 20 q^{42} + 64 q^{43} - 56 q^{44} - 32 q^{46} - 80 q^{48} - 48 q^{50} - 16 q^{51} - 16 q^{52} + 32 q^{54} - 24 q^{56} + 52 q^{58} + 72 q^{60} - 32 q^{61} - 40 q^{62} + 32 q^{64} + 32 q^{66} - 24 q^{68} - 32 q^{69} + 80 q^{72} - 16 q^{73} - 32 q^{74} - 88 q^{75} + 76 q^{78} + 128 q^{80} + 144 q^{81} + 56 q^{82} + 32 q^{86} - 112 q^{87} + 88 q^{88} + 88 q^{90} - 136 q^{92} - 8 q^{94} + 80 q^{95} + 32 q^{96} + 64 q^{99}+O(q^{100}) \) 144 * q + 8 * q^4 - 144 * q^9 - 16 * q^12 + 8 * q^16 - 28 * q^18 - 16 * q^19 + 4 * q^22 + 32 * q^26 - 36 * q^30 + 32 * q^34 - 32 * q^36 - 56 * q^38 + 8 * q^40 - 20 * q^42 + 64 * q^43 - 56 * q^44 - 32 * q^46 - 80 * q^48 - 48 * q^50 - 16 * q^51 - 16 * q^52 + 32 * q^54 - 24 * q^56 + 52 * q^58 + 72 * q^60 - 32 * q^61 - 40 * q^62 + 32 * q^64 + 32 * q^66 - 24 * q^68 - 32 * q^69 + 80 * q^72 - 16 * q^73 - 32 * q^74 - 88 * q^75 + 76 * q^78 + 128 * q^80 + 144 * q^81 + 56 * q^82 + 32 * q^86 - 112 * q^87 + 88 * q^88 + 88 * q^90 - 136 * q^92 - 8 * q^94 + 80 * q^95 + 32 * q^96 + 64 * q^99

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