LMFDB - Embedded newform 560.2.bd.b.141.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [560,2,Mod(141,560)]

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([0, 3, 0, 0]))

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

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

chi := DirichletCharacter("560.141");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.bd (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:	$52$
Relative dimension:	$26$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			141.19
Character	$\chi$	$=$	560.141
Dual form			560.2.bd.b.421.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.865210 + 1.11867i) q^{2} +(-1.52217 - 1.52217i) q^{3} +(-0.502824 + 1.93576i) q^{4} +(0.707107 - 0.707107i) q^{5} +(0.385801 - 3.01979i) q^{6} +1.00000i q^{7} +(-2.60052 + 1.11235i) q^{8} +1.63398i q^{9} +O(q^{10})$	\(q+(0.865210 + 1.11867i) q^{2} +(-1.52217 - 1.52217i) q^{3} +(-0.502824 + 1.93576i) q^{4} +(0.707107 - 0.707107i) q^{5} +(0.385801 - 3.01979i) q^{6} +1.00000i q^{7} +(-2.60052 + 1.11235i) q^{8} +1.63398i q^{9} +(1.40281 + 0.179220i) q^{10} +(1.21085 - 1.21085i) q^{11} +(3.71193 - 2.18117i) q^{12} +(3.41133 + 3.41133i) q^{13} +(-1.11867 + 0.865210i) q^{14} -2.15267 q^{15} +(-3.49434 - 1.94669i) q^{16} +5.56719 q^{17} +(-1.82787 + 1.41373i) q^{18} +(3.53383 + 3.53383i) q^{19} +(1.01324 + 1.72434i) q^{20} +(1.52217 - 1.52217i) q^{21} +(2.40217 + 0.306895i) q^{22} -7.63813i q^{23} +(5.65159 + 2.26524i) q^{24} -1.00000i q^{25} +(-0.864619 + 6.76765i) q^{26} +(-2.07931 + 2.07931i) q^{27} +(-1.93576 - 0.502824i) q^{28} +(4.70836 + 4.70836i) q^{29} +(-1.86251 - 2.40811i) q^{30} +7.02180 q^{31} +(-0.845639 - 5.59329i) q^{32} -3.68622 q^{33} +(4.81679 + 6.22782i) q^{34} +(0.707107 + 0.707107i) q^{35} +(-3.16299 - 0.821602i) q^{36} +(2.30892 - 2.30892i) q^{37} +(-0.895667 + 7.01067i) q^{38} -10.3852i q^{39} +(-1.05229 + 2.62539i) q^{40} -1.46358i q^{41} +(3.01979 + 0.385801i) q^{42} +(-7.93729 + 7.93729i) q^{43} +(1.73507 + 2.95275i) q^{44} +(1.15540 + 1.15540i) q^{45} +(8.54451 - 6.60859i) q^{46} -3.39840 q^{47} +(2.35577 + 8.28215i) q^{48} -1.00000 q^{49} +(1.11867 - 0.865210i) q^{50} +(-8.47418 - 8.47418i) q^{51} +(-8.31881 + 4.88822i) q^{52} +(-3.98920 + 3.98920i) q^{53} +(-4.12510 - 0.527013i) q^{54} -1.71240i q^{55} +(-1.11235 - 2.60052i) q^{56} -10.7581i q^{57} +(-1.19336 + 9.34080i) q^{58} +(4.12507 - 4.12507i) q^{59} +(1.08241 - 4.16705i) q^{60} +(5.67988 + 5.67988i) q^{61} +(6.07533 + 7.85504i) q^{62} -1.63398 q^{63} +(5.52536 - 5.78536i) q^{64} +4.82435 q^{65} +(-3.18935 - 4.12364i) q^{66} +(-5.68559 - 5.68559i) q^{67} +(-2.79931 + 10.7767i) q^{68} +(-11.6265 + 11.6265i) q^{69} +(-0.179220 + 1.40281i) q^{70} +0.786312i q^{71} +(-1.81755 - 4.24918i) q^{72} +2.82170i q^{73} +(4.58062 + 0.585209i) q^{74} +(-1.52217 + 1.52217i) q^{75} +(-8.61753 + 5.06375i) q^{76} +(1.21085 + 1.21085i) q^{77} +(11.6176 - 8.98539i) q^{78} -6.07238 q^{79} +(-3.84739 + 1.09435i) q^{80} +11.2321 q^{81} +(1.63725 - 1.26630i) q^{82} +(-9.61118 - 9.61118i) q^{83} +(2.18117 + 3.71193i) q^{84} +(3.93660 - 3.93660i) q^{85} +(-15.7466 - 2.01175i) q^{86} -14.3338i q^{87} +(-1.80194 + 4.49571i) q^{88} -7.88825i q^{89} +(-0.292841 + 2.29216i) q^{90} +(-3.41133 + 3.41133i) q^{91} +(14.7856 + 3.84063i) q^{92} +(-10.6883 - 10.6883i) q^{93} +(-2.94033 - 3.80167i) q^{94} +4.99759 q^{95} +(-7.22671 + 9.80112i) q^{96} -2.80418 q^{97} +(-0.865210 - 1.11867i) q^{98} +(1.97849 + 1.97849i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q - 8 q^{4} + 12 q^{6}+O(q^{10}) $ 52 * q - 8 * q^4 + 12 * q^6	$ 52 q - 8 q^{4} + 12 q^{6} - 4 q^{10} - 4 q^{11} + 40 q^{12} + 8 q^{15} - 4 q^{16} + 8 q^{19} + 32 q^{22} + 12 q^{24} - 12 q^{26} - 24 q^{27} + 4 q^{28} + 4 q^{29} - 16 q^{34} + 4 q^{36} - 12 q^{37} + 16 q^{38} - 4 q^{42} + 36 q^{43} + 28 q^{44} - 16 q^{46} + 32 q^{48} - 52 q^{49} - 8 q^{51} - 80 q^{52} - 4 q^{53} + 48 q^{54} - 12 q^{56} - 56 q^{58} + 24 q^{59} - 16 q^{61} - 72 q^{62} - 68 q^{63} + 4 q^{64} + 40 q^{65} - 12 q^{66} - 12 q^{67} - 72 q^{69} - 8 q^{72} + 68 q^{74} - 4 q^{77} - 4 q^{78} - 16 q^{79} - 32 q^{80} - 116 q^{81} + 104 q^{82} + 16 q^{85} - 68 q^{86} - 48 q^{88} + 36 q^{90} + 64 q^{92} + 8 q^{93} - 72 q^{94} - 32 q^{95} - 52 q^{99}+O(q^{100}) $ 52 * q - 8 * q^4 + 12 * q^6 - 4 * q^10 - 4 * q^11 + 40 * q^12 + 8 * q^15 - 4 * q^16 + 8 * q^19 + 32 * q^22 + 12 * q^24 - 12 * q^26 - 24 * q^27 + 4 * q^28 + 4 * q^29 - 16 * q^34 + 4 * q^36 - 12 * q^37 + 16 * q^38 - 4 * q^42 + 36 * q^43 + 28 * q^44 - 16 * q^46 + 32 * q^48 - 52 * q^49 - 8 * q^51 - 80 * q^52 - 4 * q^53 + 48 * q^54 - 12 * q^56 - 56 * q^58 + 24 * q^59 - 16 * q^61 - 72 * q^62 - 68 * q^63 + 4 * q^64 + 40 * q^65 - 12 * q^66 - 12 * q^67 - 72 * q^69 - 8 * q^72 + 68 * q^74 - 4 * q^77 - 4 * q^78 - 16 * q^79 - 32 * q^80 - 116 * q^81 + 104 * q^82 + 16 * q^85 - 68 * q^86 - 48 * q^88 + 36 * q^90 + 64 * q^92 + 8 * q^93 - 72 * q^94 - 32 * q^95 - 52 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	0.865210	+	1.11867i	0.611796	+	0.791016i
$2$	0.865210	+	1.11867i	0.611796	+	0.791016i
$3$	−1.52217	−	1.52217i	−0.878823	−	0.878823i	0.114590	−	0.993413i	$-0.463445\pi$
$3$	−1.52217	−	1.52217i	−0.878823	−	0.878823i	−0.993413	+	0.114590i	$0.963445\pi$
$4$	−0.502824	+	1.93576i	−0.251412	+	0.967880i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$6$	0.385801	−	3.01979i	0.157503	−	1.23282i
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$	−2.60052	+	1.11235i	−0.919421	+	0.393274i
$9$			1.63398i			0.544659i
$10$	1.40281	+	0.179220i	0.443608	+	0.0566743i
$11$	1.21085	−	1.21085i	0.365084	−	0.365084i	−0.500597	−	0.865681i	$-0.666886\pi$
$11$	1.21085	−	1.21085i	0.365084	−	0.365084i	0.865681	+	0.500597i	$0.166886\pi$
$12$	3.71193	−	2.18117i	1.07154	−	0.629649i
$13$	3.41133	+	3.41133i	0.946133	+	0.946133i	0.998622	−	0.0524888i	$-0.0167154\pi$
$13$	3.41133	+	3.41133i	0.946133	+	0.946133i	−0.0524888	+	0.998622i	$0.516715\pi$
$14$	−1.11867	+	0.865210i	−0.298976	+	0.231237i
$15$	−2.15267			−0.555816
$16$	−3.49434	−	1.94669i	−0.873584	−	0.486673i
$17$	5.56719			1.35024			0.675121	−	0.737707i	$-0.264091\pi$
$17$	5.56719			1.35024			0.675121	+	0.737707i	$0.264091\pi$
$18$	−1.82787	+	1.41373i	−0.430834	+	0.333220i
$19$	3.53383	+	3.53383i	0.810716	+	0.810716i	0.984741	−	0.174026i	$-0.0556775\pi$
$19$	3.53383	+	3.53383i	0.810716	+	0.810716i	−0.174026	+	0.984741i	$0.555678\pi$
$20$	1.01324	+	1.72434i	0.226567	+	0.385574i
$21$	1.52217	−	1.52217i	0.332164	−	0.332164i
$22$	2.40217	+	0.306895i	0.512144	+	0.0654303i
$23$		−	7.63813i		−	1.59266i	−0.604862	−	0.796330i	$-0.706772\pi$
$23$		−	7.63813i		−	1.59266i	0.604862	−	0.796330i	$-0.293228\pi$
$24$	5.65159	+	2.26524i	1.15363	+	0.462390i
$25$		−	1.00000i		−	0.200000i
$26$	−0.864619	+	6.76765i	−0.169566	+	1.32725i
$27$	−2.07931	+	2.07931i	−0.400164	+	0.400164i
$28$	−1.93576	−	0.502824i	−0.365824	−	0.0950247i
$29$	4.70836	+	4.70836i	0.874321	+	0.874321i	0.992940	−	0.118619i	$-0.0378468\pi$
$29$	4.70836	+	4.70836i	0.874321	+	0.874321i	−0.118619	+	0.992940i	$0.537847\pi$
$30$	−1.86251	−	2.40811i	−0.340046	−	0.439659i
$31$	7.02180			1.26115			0.630576	−	0.776128i	$-0.282819\pi$
$31$	7.02180			1.26115			0.630576	+	0.776128i	$0.282819\pi$
$32$	−0.845639	−	5.59329i	−0.149489	−	0.988763i
$33$	−3.68622			−0.641688
$34$	4.81679	+	6.22782i	0.826072	+	1.06806i
$35$	0.707107	+	0.707107i	0.119523	+	0.119523i
$36$	−3.16299	−	0.821602i	−0.527164	−	0.136934i
$37$	2.30892	−	2.30892i	0.379585	−	0.379585i	−0.491367	−	0.870952i	$-0.663503\pi$
$37$	2.30892	−	2.30892i	0.379585	−	0.379585i	0.870952	+	0.491367i	$0.163503\pi$
$38$	−0.895667	+	7.01067i	−0.145296	+	1.13728i
$39$		−	10.3852i		−	1.66297i
$40$	−1.05229	+	2.62539i	−0.166382	+	0.415111i
$41$		−	1.46358i		−	0.228573i	−0.993448	−	0.114286i	$-0.963542\pi$
$41$		−	1.46358i		−	0.228573i	0.993448	−	0.114286i	$-0.0364581\pi$
$42$	3.01979	+	0.385801i	0.465963	+	0.0595304i
$43$	−7.93729	+	7.93729i	−1.21043	+	1.21043i	−0.239538	+	0.970887i	$0.576996\pi$
$43$	−7.93729	+	7.93729i	−1.21043	+	1.21043i	−0.970887	+	0.239538i	$0.923004\pi$
$44$	1.73507	+	2.95275i	0.261571	+	0.445144i
$45$	1.15540	+	1.15540i	0.172236	+	0.172236i
$46$	8.54451	−	6.60859i	1.25982	−	0.974383i
$47$	−3.39840			−0.495707			−0.247853	−	0.968798i	$-0.579725\pi$
$47$	−3.39840			−0.495707			−0.247853	+	0.968798i	$0.579725\pi$
$48$	2.35577	+	8.28215i	0.340026	+	1.19542i
$49$	−1.00000			−0.142857
$50$	1.11867	−	0.865210i	0.158203	−	0.122359i
$51$	−8.47418	−	8.47418i	−1.18662	−	1.18662i
$52$	−8.31881	+	4.88822i	−1.15361	+	0.677874i
$53$	−3.98920	+	3.98920i	−0.547959	+	0.547959i	−0.925850	−	0.377891i	$-0.876649\pi$
$53$	−3.98920	+	3.98920i	−0.547959	+	0.547959i	0.377891	+	0.925850i	$0.376649\pi$
$54$	−4.12510	−	0.527013i	−0.561355	−	0.0717174i
$55$		−	1.71240i		−	0.230899i
$56$	−1.11235	−	2.60052i	−0.148644	−	0.347509i
$57$		−	10.7581i		−	1.42495i
$58$	−1.19336	+	9.34080i	−0.156696	+	1.22651i
$59$	4.12507	−	4.12507i	0.537038	−	0.537038i	−0.385620	−	0.922658i	$-0.626012\pi$
$59$	4.12507	−	4.12507i	0.537038	−	0.537038i	0.922658	+	0.385620i	$0.126012\pi$
$60$	1.08241	−	4.16705i	0.139739	−	0.537964i
$61$	5.67988	+	5.67988i	0.727234	+	0.727234i	0.970068	−	0.242834i	$-0.0780769\pi$
$61$	5.67988	+	5.67988i	0.727234	+	0.727234i	−0.242834	+	0.970068i	$0.578077\pi$
$62$	6.07533	+	7.85504i	0.771567	+	0.997591i
$63$	−1.63398			−0.205862
$64$	5.52536	−	5.78536i	0.690670	−	0.723170i
$65$	4.82435			0.598387
$66$	−3.18935	−	4.12364i	−0.392582	−	0.507585i
$67$	−5.68559	−	5.68559i	−0.694606	−	0.694606i	0.268636	−	0.963242i	$-0.413427\pi$
$67$	−5.68559	−	5.68559i	−0.694606	−	0.694606i	−0.963242	+	0.268636i	$0.913427\pi$
$68$	−2.79931	+	10.7767i	−0.339467	+	1.30687i
$69$	−11.6265	+	11.6265i	−1.39967	+	1.39967i
$70$	−0.179220	+	1.40281i	−0.0214209	+	0.167668i
$71$			0.786312i			0.0933181i	0.998911	+	0.0466591i	$0.0148574\pi$
$71$			0.786312i			0.0933181i	−0.998911	+	0.0466591i	$0.985143\pi$
$72$	−1.81755	−	4.24918i	−0.214200	−	0.500771i
$73$			2.82170i			0.330255i	0.986272	+	0.165128i	$0.0528036\pi$
$73$			2.82170i			0.330255i	−0.986272	+	0.165128i	$0.947196\pi$
$74$	4.58062	+	0.585209i	0.532486	+	0.0680292i
$75$	−1.52217	+	1.52217i	−0.175765	+	0.175765i
$76$	−8.61753	+	5.06375i	−0.988499	+	0.580852i
$77$	1.21085	+	1.21085i	0.137989	+	0.137989i
$78$	11.6176	−	8.98539i	1.31543	−	1.01740i
$79$	−6.07238			−0.683196			−0.341598	−	0.939846i	$-0.610968\pi$
$79$	−6.07238			−0.683196			−0.341598	+	0.939846i	$0.610968\pi$
$80$	−3.84739	+	1.09435i	−0.430151	+	0.122352i
$81$	11.2321			1.24801
$82$	1.63725	−	1.26630i	0.180805	−	0.139840i
$83$	−9.61118	−	9.61118i	−1.05496	−	1.05496i	−0.998399	−	0.0565657i	$-0.981985\pi$
$83$	−9.61118	−	9.61118i	−1.05496	−	1.05496i	−0.0565657	−	0.998399i	$-0.518015\pi$
$84$	2.18117	+	3.71193i	0.237985	+	0.405005i
$85$	3.93660	−	3.93660i	0.426984	−	0.426984i
$86$	−15.7466	−	2.01175i	−1.69800	−	0.216932i
$87$		−	14.3338i		−	1.53675i
$88$	−1.80194	+	4.49571i	−0.192088	+	0.479244i
$89$		−	7.88825i		−	0.836153i	−0.908412	−	0.418077i	$-0.862704\pi$
$89$		−	7.88825i		−	0.836153i	0.908412	−	0.418077i	$-0.137296\pi$
$90$	−0.292841	+	2.29216i	−0.0308682	+	0.241615i
$91$	−3.41133	+	3.41133i	−0.357605	+	0.357605i
$92$	14.7856	+	3.84063i	1.54150	+	0.400413i
$93$	−10.6883	−	10.6883i	−1.10833	−	1.10833i
$94$	−2.94033	−	3.80167i	−0.303271	−	0.392112i
$95$	4.99759			0.512742
$96$	−7.22671	+	9.80112i	−0.737573	+	1.00032i
$97$	−2.80418			−0.284721			−0.142361	−	0.989815i	$-0.545469\pi$
$97$	−2.80418			−0.284721			−0.142361	+	0.989815i	$0.545469\pi$
$98$	−0.865210	−	1.11867i	−0.0873994	−	0.113002i
$99$	1.97849	+	1.97849i	0.198846	+	0.198846i
$100$	1.93576	+	0.502824i	0.193576	+	0.0502824i
$101$	7.51341	−	7.51341i	0.747612	−	0.747612i	−0.226418	−	0.974030i	$-0.572702\pi$
$101$	7.51341	−	7.51341i	0.747612	−	0.747612i	0.974030	+	0.226418i	$0.0727016\pi$
$102$	2.14783	−	16.8117i	0.212667	−	1.66461i
$103$		−	14.4754i		−	1.42631i	−0.701008	−	0.713153i	$-0.747266\pi$
$103$		−	14.4754i		−	1.42631i	0.701008	−	0.713153i	$-0.252734\pi$
$104$	−12.6658	−	5.07663i	−1.24198	−	0.497805i
$105$		−	2.15267i		−	0.210079i
$106$	−7.91408	−	1.01108i	−0.768683	−	0.0982052i
$107$	−11.1448	+	11.1448i	−1.07741	+	1.07741i	−0.0806639	+	0.996741i	$0.525704\pi$
$107$	−11.1448	+	11.1448i	−1.07741	+	1.07741i	−0.996741	+	0.0806639i	$0.974296\pi$
$108$	−2.97953	−	5.07058i	−0.286705	−	0.487917i
$109$	−14.5845	−	14.5845i	−1.39694	−	1.39694i	−0.808644	−	0.588298i	$-0.799798\pi$
$109$	−14.5845	−	14.5845i	−1.39694	−	1.39694i	−0.588298	−	0.808644i	$-0.700202\pi$
$110$	1.91560	−	1.48158i	0.182645	−	0.141263i
$111$	−7.02913			−0.667176
$112$	1.94669	−	3.49434i	0.183945	−	0.330184i
$113$	−11.4813			−1.08007			−0.540034	−	0.841644i	$-0.681588\pi$
$113$	−11.4813			−1.08007			−0.540034	+	0.841644i	$0.681588\pi$
$114$	12.0348	−	9.30805i	1.12716	−	0.871779i
$115$	−5.40097	−	5.40097i	−0.503643	−	0.503643i
$116$	−11.4817	+	6.74678i	−1.06605	+	0.626423i
$117$	−5.57403	+	5.57403i	−0.515319	+	0.515319i
$118$	8.18362	+	1.04552i	0.753363	+	0.0962479i
$119$			5.56719i			0.510343i
$120$	5.59804	−	2.39452i	0.511029	−	0.218588i
$121$			8.06770i			0.733427i
$122$	−1.43960	+	11.2682i	−0.130335	+	1.02017i
$123$	−2.22781	+	2.22781i	−0.200875	+	0.200875i
$124$	−3.53072	+	13.5925i	−0.317068	+	1.22064i
$125$	−0.707107	−	0.707107i	−0.0632456	−	0.0632456i
$126$	−1.41373	−	1.82787i	−0.125945	−	0.162840i
$127$	4.16194			0.369312			0.184656	−	0.982803i	$-0.440883\pi$
$127$	4.16194			0.369312			0.184656	+	0.982803i	$0.440883\pi$
$128$	11.2525	+	1.17548i	0.994588	+	0.103899i
$129$	24.1637			2.12750
$130$	4.17407	+	5.39683i	0.366091	+	0.473333i
$131$	14.5279	+	14.5279i	1.26931	+	1.26931i	0.946447	+	0.322859i	$0.104644\pi$
$131$	14.5279	+	14.5279i	1.26931	+	1.26931i	0.322859	+	0.946447i	$0.395356\pi$
$132$	1.85352	−	7.13563i	0.161328	−	0.621077i
$133$	−3.53383	+	3.53383i	−0.306422	+	0.306422i
$134$	1.44104	−	11.2795i	0.124487	−	0.974401i
$135$			2.94060i			0.253086i
$136$	−14.4776	+	6.19265i	−1.24144	+	0.531016i
$137$			10.8424i			0.926332i	0.886272	+	0.463166i	$0.153287\pi$
$137$			10.8424i			0.926332i	−0.886272	+	0.463166i	$0.846713\pi$
$138$	−23.0655	−	2.94680i	−1.96347	−	0.250848i
$139$	4.60654	−	4.60654i	0.390722	−	0.390722i	−0.484223	−	0.874945i	$-0.660898\pi$
$139$	4.60654	−	4.60654i	0.390722	−	0.390722i	0.874945	+	0.484223i	$0.160898\pi$
$140$	−1.72434	+	1.01324i	−0.145733	+	0.0856344i
$141$	5.17292	+	5.17292i	0.435638	+	0.435638i
$142$	−0.879620	+	0.680325i	−0.0738161	+	0.0570916i
$143$	8.26119			0.690836
$144$	3.18085	−	5.70966i	0.265071	−	0.475805i
$145$	6.65863			0.552969
$146$	−3.15654	+	2.44136i	−0.261237	+	0.202049i
$147$	1.52217	+	1.52217i	0.125546	+	0.125546i
$148$	3.30854	+	5.63051i	0.271961	+	0.462825i
$149$	−0.195843	+	0.195843i	−0.0160441	+	0.0160441i	−0.715083	−	0.699039i	$-0.753611\pi$
$149$	−0.195843	+	0.195843i	−0.0160441	+	0.0160441i	0.699039	+	0.715083i	$0.253611\pi$
$150$	−3.01979	−	0.385801i	−0.246565	−	0.0315005i
$151$		−	9.12503i		−	0.742584i	−0.928516	−	0.371292i	$-0.878915\pi$
$151$		−	9.12503i		−	0.742584i	0.928516	−	0.371292i	$-0.121085\pi$
$152$	−13.1206	−	5.25893i	−1.06422	−	0.426555i
$153$			9.09665i			0.735421i
$154$	−0.306895	+	2.40217i	−0.0247303	+	0.193572i
$155$	4.96516	−	4.96516i	0.398811	−	0.398811i
$156$	20.1033	+	5.22193i	1.60955	+	0.418089i
$157$	−3.94939	−	3.94939i	−0.315195	−	0.315195i	0.531723	−	0.846918i	$-0.321545\pi$
$157$	−3.94939	−	3.94939i	−0.315195	−	0.315195i	−0.846918	+	0.531723i	$0.821545\pi$
$158$	−5.25388	−	6.79296i	−0.417976	−	0.540419i
$159$	12.1445			0.963118
$160$	−4.55301	−	3.35710i	−0.359947	−	0.265402i
$161$	7.63813			0.601969
$162$	9.71808	+	12.5649i	0.763525	+	0.987192i
$163$	13.2390	+	13.2390i	1.03696	+	1.03696i	0.999290	+	0.0376663i	$0.0119924\pi$
$163$	13.2390	+	13.2390i	1.03696	+	1.03696i	0.0376663	+	0.999290i	$0.488008\pi$
$164$	2.83314	+	0.735922i	0.221231	+	0.0574658i
$165$	−2.60655	+	2.60655i	−0.202920	+	0.202920i
$166$	2.43600	−	19.0674i	0.189071	−	1.47992i
$167$			6.47693i			0.501200i	0.968091	+	0.250600i	$0.0806279\pi$
$167$			6.47693i			0.501200i	−0.968091	+	0.250600i	$0.919372\pi$
$168$	−2.26524	+	5.65159i	−0.174767	+	0.436030i
$169$			10.2743i			0.790334i
$170$	7.80972	+	0.997751i	0.598978	+	0.0765240i
$171$	−5.77419	+	5.77419i	−0.441563	+	0.441563i
$172$	−11.3736	−	19.3557i	−0.867232	−	1.47586i
$173$	−5.41972	−	5.41972i	−0.412054	−	0.412054i	0.470400	−	0.882454i	$-0.344110\pi$
$173$	−5.41972	−	5.41972i	−0.412054	−	0.412054i	−0.882454	+	0.470400i	$0.844110\pi$
$174$	16.0347	−	12.4018i	1.21559	−	0.940174i
$175$	1.00000			0.0755929
$176$	−6.58825	+	1.87396i	−0.496608	+	0.141255i
$177$	−12.5581			−0.943922
$178$	8.82431	−	6.82500i	0.661410	−	0.511555i
$179$	2.98969	+	2.98969i	0.223460	+	0.223460i	0.809954	−	0.586494i	$-0.199492\pi$
$179$	2.98969	+	2.98969i	0.223460	+	0.223460i	−0.586494	+	0.809954i	$0.699492\pi$
$180$	−2.81753	+	1.65561i	−0.210006	+	0.123402i
$181$	−16.5157	+	16.5157i	−1.22760	+	1.22760i	−0.262735	+	0.964868i	$0.584625\pi$
$181$	−16.5157	+	16.5157i	−1.22760	+	1.22760i	−0.964868	+	0.262735i	$0.915375\pi$
$182$	−6.76765	−	0.864619i	−0.501652	−	0.0640899i
$183$		−	17.2914i		−	1.27822i
$184$	8.49626	+	19.8631i	0.626353	+	1.46433i
$185$		−	3.26531i		−	0.240071i
$186$	2.70901	−	21.2043i	0.198635	−	1.55478i
$187$	6.74101	−	6.74101i	0.492952	−	0.492952i
$188$	1.70879	−	6.57848i	0.124627	−	0.479785i
$189$	−2.07931	−	2.07931i	−0.151248	−	0.151248i
$190$	4.32396	+	5.59063i	0.313693	+	0.405587i
$191$	6.99534			0.506165			0.253083	−	0.967445i	$-0.418556\pi$
$191$	6.99534			0.506165			0.253083	+	0.967445i	$0.418556\pi$
$192$	−17.2168	+	0.395753i	−1.24251	+	0.0285610i
$193$	−10.6654			−0.767715			−0.383858	−	0.923392i	$-0.625405\pi$
$193$	−10.6654			−0.767715			−0.383858	+	0.923392i	$0.625405\pi$
$194$	−2.42620	−	3.13694i	−0.174191	−	0.225219i
$195$	−7.34346	−	7.34346i	−0.525876	−	0.525876i
$196$	0.502824	−	1.93576i	0.0359160	−	0.138269i
$197$	15.9669	−	15.9669i	1.13759	−	1.13759i	0.148714	−	0.988880i	$-0.452487\pi$
$197$	15.9669	−	15.9669i	1.13759	−	1.13759i	0.988880	−	0.148714i	$-0.0475133\pi$
$198$	−0.501460	+	3.92508i	−0.0356372	+	0.278944i
$199$		−	4.56536i		−	0.323630i	−0.986821	−	0.161815i	$-0.948265\pi$
$199$		−	4.56536i		−	0.323630i	0.986821	−	0.161815i	$-0.0517348\pi$
$200$	1.11235	+	2.60052i	0.0786549	+	0.183884i
$201$			17.3088i			1.22087i
$202$	14.9057	+	1.90431i	1.04876	+	0.133987i
$203$	−4.70836	+	4.70836i	−0.330462	+	0.330462i
$204$	20.6650	−	12.1430i	1.44684	−	0.850178i
$205$	−1.03491	−	1.03491i	−0.0722810	−	0.0722810i
$206$	16.1932	−	12.5243i	1.12823	−	0.872608i
$207$	12.4805			0.867456
$208$	−5.27953	−	18.5611i	−0.366069	−	1.28698i
$209$	8.55784			0.591958
$210$	2.40811	−	1.86251i	0.166176	−	0.128525i
$211$	0.886013	+	0.886013i	0.0609957	+	0.0609957i	0.736947	−	0.675951i	$-0.236267\pi$
$211$	0.886013	+	0.886013i	0.0609957	+	0.0609957i	−0.675951	+	0.736947i	$0.736267\pi$
$212$	−5.71628	−	9.72801i	−0.392595	−	0.668122i
$213$	1.19690	−	1.19690i	0.0820101	−	0.0820101i
$214$	−22.1098	−	2.82470i	−1.51140	−	0.193092i
$215$			11.2250i			0.765540i
$216$	3.09437	−	7.72021i	0.210545	−	0.525294i
$217$			7.02180i			0.476671i
$218$	3.69652	−	28.9338i	0.250360	−	1.95965i
$219$	4.29510	−	4.29510i	0.290236	−	0.290236i
$220$	3.31479	+	0.861033i	0.223483	+	0.0580508i
$221$	18.9915	+	18.9915i	1.27751	+	1.27751i
$222$	−6.08167	−	7.86325i	−0.408175	−	0.527746i
$223$	−1.51218			−0.101263			−0.0506317	−	0.998717i	$-0.516123\pi$
$223$	−1.51218			−0.101263			−0.0506317	+	0.998717i	$0.516123\pi$
$224$	5.59329	−	0.845639i	0.373717	−	0.0565016i
$225$	1.63398			0.108932
$226$	−9.93371	−	12.8437i	−0.660781	−	0.854350i
$227$	13.9414	+	13.9414i	0.925321	+	0.925321i	0.997399	−	0.0720783i	$-0.0229631\pi$
$227$	13.9414	+	13.9414i	0.925321	+	0.925321i	−0.0720783	+	0.997399i	$0.522963\pi$
$228$	20.8252	+	5.40945i	1.37918	+	0.358249i
$229$	−8.02064	+	8.02064i	−0.530019	+	0.530019i	−0.920578	−	0.390559i	$-0.872282\pi$
$229$	−8.02064	+	8.02064i	−0.530019	+	0.530019i	0.390559	+	0.920578i	$0.372282\pi$
$230$	1.36890	−	10.7149i	0.0902629	−	0.706517i
$231$		−	3.68622i		−	0.242535i
$232$	−17.4815	−	7.00683i	−1.14772	−	0.460021i
$233$		−	2.37384i		−	0.155515i	−0.996972	−	0.0777577i	$-0.975224\pi$
$233$		−	2.37384i		−	0.155515i	0.996972	−	0.0777577i	$-0.0247761\pi$
$234$	−11.0582	−	1.41277i	−0.722896	−	0.0923555i
$235$	−2.40303	+	2.40303i	−0.156756	+	0.156756i
$236$	5.91096	+	10.0593i	0.384771	+	0.654806i
$237$	9.24316	+	9.24316i	0.600408	+	0.600408i
$238$	−6.22782	+	4.81679i	−0.403690	+	0.312226i
$239$	5.04025			0.326026			0.163013	−	0.986624i	$-0.447879\pi$
$239$	5.04025			0.326026			0.163013	+	0.986624i	$0.447879\pi$
$240$	7.52214	+	4.19058i	0.485552	+	0.270501i
$241$	−0.0746993			−0.00481180			−0.00240590	−	0.999997i	$-0.500766\pi$
$241$	−0.0746993			−0.00481180			−0.00240590	+	0.999997i	$0.500766\pi$
$242$	−9.02506	+	6.98026i	−0.580153	+	0.448708i
$243$	−10.8591	−	10.8591i	−0.696611	−	0.696611i
$244$	−13.8509	+	8.13891i	−0.886711	+	0.521041i
$245$	−0.707107	+	0.707107i	−0.0451754	+	0.0451754i
$246$	−4.41970	−	0.564650i	−0.281789	−	0.0360008i
$247$			24.1101i			1.53409i
$248$	−18.2603	+	7.81068i	−1.15953	+	0.495979i
$249$			29.2596i			1.85425i
$250$	0.179220	−	1.40281i	0.0113349	−	0.0887216i
$251$	−17.6935	+	17.6935i	−1.11680	+	1.11680i	−0.124594	+	0.992208i	$0.539763\pi$
$251$	−17.6935	+	17.6935i	−1.11680	+	1.11680i	−0.992208	+	0.124594i	$0.960237\pi$
$252$	0.821602	−	3.16299i	0.0517560	−	0.199249i
$253$	−9.24860	−	9.24860i	−0.581455	−	0.581455i
$254$	3.60095	+	4.65582i	0.225944	+	0.292132i
$255$	−11.9843			−0.750486
$256$	8.42078	+	13.6048i	0.526299	+	0.850300i
$257$	−2.32431			−0.144987			−0.0724933	−	0.997369i	$-0.523096\pi$
$257$	−2.32431			−0.144987			−0.0724933	+	0.997369i	$0.523096\pi$
$258$	20.9067	+	27.0311i	1.30159	+	1.68288i
$259$	2.30892	+	2.30892i	0.143470	+	0.143470i
$260$	−2.42580	+	9.33878i	−0.150441	+	0.579167i
$261$	−7.69335	+	7.69335i	−0.476206	+	0.476206i
$262$	−3.68217	+	28.8215i	−0.227485	+	1.78060i
$263$		−	17.3695i		−	1.07105i	−0.844520	−	0.535525i	$-0.820114\pi$
$263$		−	17.3695i		−	1.07105i	0.844520	−	0.535525i	$-0.179886\pi$
$264$	9.58607	−	4.10036i	0.589982	−	0.252360i
$265$			5.64159i			0.346560i
$266$	−7.01067	−	0.895667i	−0.429852	−	0.0549169i
$267$	−12.0072	+	12.0072i	−0.734830	+	0.734830i
$268$	13.8648	−	8.14710i	0.846927	−	0.497663i
$269$	−2.51754	−	2.51754i	−0.153497	−	0.153497i	0.626181	−	0.779678i	$-0.284617\pi$
$269$	−2.51754	−	2.51754i	−0.153497	−	0.153497i	−0.779678	+	0.626181i	$0.784617\pi$
$270$	−3.28954	+	2.54423i	−0.200195	+	0.154837i
$271$	−30.0558			−1.82576			−0.912881	−	0.408226i	$-0.866148\pi$
$271$	−30.0558			−1.82576			−0.912881	+	0.408226i	$0.866148\pi$
$272$	−19.4536	−	10.8376i	−1.17955	−	0.657126i
$273$	10.3852			0.628542
$274$	−12.1291	+	9.38098i	−0.732743	+	0.566726i
$275$	−1.21085	−	1.21085i	−0.0730168	−	0.0730168i
$276$	−16.6600	−	28.3522i	−1.00282	−	1.70660i
$277$	−8.17367	+	8.17367i	−0.491108	+	0.491108i	−0.908655	−	0.417547i	$-0.862890\pi$
$277$	−8.17367	+	8.17367i	−0.491108	+	0.491108i	0.417547	+	0.908655i	$0.362890\pi$
$278$	9.13880	+	1.16755i	0.548109	+	0.0700251i
$279$			11.4734i			0.686897i
$280$	−2.62539	−	1.05229i	−0.156897	−	0.0628866i
$281$		−	17.5219i		−	1.04527i	−0.852558	−	0.522633i	$-0.824950\pi$
$281$		−	17.5219i		−	1.04527i	0.852558	−	0.522633i	$-0.175050\pi$
$282$	−1.31110	+	10.2624i	−0.0780751	+	0.611119i
$283$	−8.93977	+	8.93977i	−0.531414	+	0.531414i	−0.920993	−	0.389579i	$-0.872620\pi$
$283$	−8.93977	+	8.93977i	−0.531414	+	0.531414i	0.389579	+	0.920993i	$0.372620\pi$
$284$	−1.52211	−	0.395376i	−0.0903208	−	0.0234613i
$285$	−7.60715	−	7.60715i	−0.450609	−	0.450609i
$286$	7.14767	+	9.24151i	0.422650	+	0.546462i
$287$	1.46358			0.0863923
$288$	9.13930	−	1.38175i	0.538539	−	0.0814206i
$289$	13.9936			0.823153
$290$	5.76111	+	7.44877i	0.338304	+	0.437407i
$291$	4.26842	+	4.26842i	0.250219	+	0.250219i
$292$	−5.46214	−	1.41882i	−0.319647	−	0.0830300i
$293$	10.2100	−	10.2100i	0.596475	−	0.596475i	−0.342898	−	0.939373i	$-0.611408\pi$
$293$	10.2100	−	10.2100i	0.596475	−	0.596475i	0.939373	+	0.342898i	$0.111408\pi$
$294$	−0.385801	+	3.01979i	−0.0225004	+	0.176118i
$295$		−	5.83372i		−	0.339653i
$296$	−3.43607	+	8.57272i	−0.199717	+	0.498279i
$297$			5.03546i			0.292187i
$298$	−0.388528	−	0.0496374i	−0.0225068	−	0.00287542i
$299$	26.0562	−	26.0562i	1.50687	−	1.50687i
$300$	−2.18117	−	3.71193i	−0.125930	−	0.214308i
$301$	−7.93729	−	7.93729i	−0.457498	−	0.457498i
$302$	10.2079	−	7.89506i	0.587396	−	0.454310i
$303$	−22.8733			−1.31404
$304$	−5.46911	−	19.2277i	−0.313675	−	1.10278i
$305$	8.03257			0.459943
$306$	−10.1761	+	7.87052i	−0.581730	+	0.449927i
$307$	8.73553	+	8.73553i	0.498563	+	0.498563i	0.910991	−	0.412427i	$-0.135319\pi$
$307$	8.73553	+	8.73553i	0.498563	+	0.498563i	−0.412427	+	0.910991i	$0.635319\pi$
$308$	−2.95275	+	1.73507i	−0.168249	+	0.0988646i
$309$	−22.0340	+	22.0340i	−1.25347	+	1.25347i
$310$	9.85026	+	1.25845i	0.559457	+	0.0714749i
$311$			4.48301i			0.254208i	0.991889	+	0.127104i	$0.0405682\pi$
$311$			4.48301i			0.254208i	−0.991889	+	0.127104i	$0.959432\pi$
$312$	11.5520	+	27.0069i	0.654002	+	1.52897i
$313$		−	24.7964i		−	1.40157i	−0.713371	−	0.700786i	$-0.752833\pi$
$313$		−	24.7964i		−	1.40157i	0.713371	−	0.700786i	$-0.247167\pi$
$314$	1.00099	−	7.83509i	0.0564893	−	0.442160i
$315$	−1.15540	+	1.15540i	−0.0650992	+	0.0650992i
$316$	3.05333	−	11.7547i	0.171763	−	0.661252i
$317$	−22.8644	−	22.8644i	−1.28419	−	1.28419i	−0.938258	−	0.345936i	$-0.887561\pi$
$317$	−22.8644	−	22.8644i	−1.28419	−	1.28419i	−0.345936	−	0.938258i	$-0.612439\pi$
$318$	10.5075	+	13.5856i	0.589232	+	0.761841i
$319$	11.4022			0.638401
$320$	−0.183843	−	7.99789i	−0.0102771	−	0.447095i
$321$	33.9284			1.89370
$322$	6.60859	+	8.54451i	0.368282	+	0.476167i
$323$	19.6735	+	19.6735i	1.09466	+	1.09466i
$324$	−5.64774	+	21.7426i	−0.313763	+	1.20792i
$325$	3.41133	−	3.41133i	0.189227	−	0.189227i
$326$	−3.35549	+	26.2645i	−0.185843	+	1.45465i
$327$			44.4001i			2.45533i
$328$	1.62801	+	3.80606i	0.0898918	+	0.210154i
$329$		−	3.39840i		−	0.187360i
$330$	−5.17107	−	0.660644i	−0.284658	−	0.0363672i
$331$	−15.5702	+	15.5702i	−0.855816	+	0.855816i	−0.990842	−	0.135026i	$-0.956888\pi$
$331$	−15.5702	+	15.5702i	−0.855816	+	0.855816i	0.135026	+	0.990842i	$0.456888\pi$
$332$	23.4377	−	13.7722i	1.28631	−	0.755849i
$333$	3.77273	+	3.77273i	0.206744	+	0.206744i
$334$	−7.24552	+	5.60390i	−0.396457	+	0.306632i
$335$	−8.04064			−0.439307
$336$	−8.28215	+	2.35577i	−0.451828	+	0.128518i
$337$	−7.70484			−0.419710			−0.209855	−	0.977733i	$-0.567299\pi$
$337$	−7.70484			−0.419710			−0.209855	+	0.977733i	$0.567299\pi$
$338$	−11.4936	+	8.88947i	−0.625167	+	0.483523i
$339$	17.4764	+	17.4764i	0.949187	+	0.949187i
$340$	5.64090	+	9.59972i	0.305921	+	0.520618i
$341$	8.50232	−	8.50232i	0.460426	−	0.460426i
$342$	−11.4553	−	1.46350i	−0.619430	−	0.0791369i
$343$		−	1.00000i		−	0.0539949i
$344$	11.8120	−	29.4701i	0.636861	−	1.58892i
$345$			16.4424i			0.885226i
$346$	1.37366	−	10.7521i	0.0738483	−	0.578034i
$347$	19.1088	−	19.1088i	1.02581	−	1.02581i	0.0261542	−	0.999658i	$-0.491674\pi$
$347$	19.1088	−	19.1088i	1.02581	−	1.02581i	0.999658	−	0.0261542i	$-0.00832610\pi$
$348$	27.7468	+	7.20738i	1.48739	+	0.386356i
$349$	−25.7332	−	25.7332i	−1.37747	−	1.37747i	−0.848880	−	0.528585i	$-0.822723\pi$
$349$	−25.7332	−	25.7332i	−1.37747	−	1.37747i	−0.528585	−	0.848880i	$-0.677277\pi$
$350$	0.865210	+	1.11867i	0.0462474	+	0.0597952i
$351$	−14.1865			−0.757217
$352$	−7.79655	−	5.74868i	−0.415558	−	0.306405i
$353$	19.7720			1.05236			0.526178	−	0.850374i	$-0.323625\pi$
$353$	19.7720			1.05236			0.526178	+	0.850374i	$0.323625\pi$
$354$	−10.8654	−	14.0483i	−0.577488	−	0.746657i
$355$	0.556007	+	0.556007i	0.0295098	+	0.0295098i
$356$	15.2698	+	3.96640i	0.809296	+	0.210219i
$357$	8.47418	−	8.47418i	0.448501	−	0.448501i
$358$	−0.757753	+	5.93118i	−0.0400485	+	0.313472i
$359$		−	20.2820i		−	1.07044i	−0.844713	−	0.535220i	$-0.820229\pi$
$359$		−	20.2820i		−	1.07044i	0.844713	−	0.535220i	$-0.179771\pi$
$360$	−4.28983	−	1.71942i	−0.226094	−	0.0906215i
$361$			5.97587i			0.314520i
$362$	−32.7651	−	4.18599i	−1.72210	−	0.220011i
$363$	12.2804	−	12.2804i	0.644553	−	0.644553i
$364$	−4.88822	−	8.31881i	−0.256212	−	0.436024i
$365$	1.99524	+	1.99524i	0.104436	+	0.104436i
$366$	19.3433	−	14.9607i	1.01109	−	0.782010i
$367$	14.8645			0.775919			0.387959	−	0.921676i	$-0.373180\pi$
$367$	14.8645			0.775919			0.387959	+	0.921676i	$0.373180\pi$
$368$	−14.8691	+	26.6902i	−0.775105	+	1.39132i
$369$	2.39145			0.124494
$370$	3.65279	−	2.82518i	0.189900	−	0.146874i
$371$	−3.98920	−	3.98920i	−0.207109	−	0.207109i
$372$	26.0644	−	15.3157i	1.35138	−	0.794083i
$373$	−6.11720	+	6.11720i	−0.316736	+	0.316736i	−0.847512	−	0.530776i	$-0.821901\pi$
$373$	−6.11720	+	6.11720i	−0.316736	+	0.316736i	0.530776	+	0.847512i	$0.321901\pi$
$374$	13.3733	+	1.70854i	0.691518	+	0.0883467i
$375$			2.15267i			0.111163i
$376$	8.83758	−	3.78020i	0.455763	−	0.194949i
$377$			32.1235i			1.65445i
$378$	0.527013	−	4.12510i	0.0271066	−	0.212172i
$379$	−9.04811	+	9.04811i	−0.464770	+	0.464770i	−0.900215	−	0.435445i	$-0.856591\pi$
$379$	−9.04811	+	9.04811i	−0.464770	+	0.464770i	0.435445	+	0.900215i	$0.356591\pi$
$380$	−2.51290	+	9.67413i	−0.128909	+	0.496272i
$381$	−6.33516	−	6.33516i	−0.324560	−	0.324560i
$382$	6.05244	+	7.82545i	0.309670	+	0.400385i
$383$	−10.6002			−0.541644			−0.270822	−	0.962629i	$-0.587296\pi$
$383$	−10.6002			−0.541644			−0.270822	+	0.962629i	$0.587296\pi$
$384$	−15.3389	−	18.9174i	−0.782758	−	0.965375i
$385$	1.71240			0.0872718
$386$	−9.22784	−	11.9311i	−0.469685	−	0.607275i
$387$	−12.9693	−	12.9693i	−0.659269	−	0.659269i
$388$	1.41001	−	5.42822i	0.0715823	−	0.275576i
$389$	0.646461	−	0.646461i	0.0327768	−	0.0327768i	−0.690528	−	0.723305i	$-0.742622\pi$
$389$	0.646461	−	0.646461i	0.0327768	−	0.0327768i	0.723305	+	0.690528i	$0.242622\pi$
$390$	1.86124	−	14.5685i	0.0942474	−	0.737705i
$391$		−	42.5229i		−	2.15048i
$392$	2.60052	−	1.11235i	0.131346	−	0.0561821i
$393$		−	44.2277i		−	2.23099i
$394$	31.6763	+	4.04689i	1.59583	+	0.203879i
$395$	−4.29382	+	4.29382i	−0.216046	+	0.216046i
$396$	−4.82472	+	2.83506i	−0.242451	+	0.142467i
$397$	22.1796	+	22.1796i	1.11316	+	1.11316i	0.992721	+	0.120439i	$0.0384304\pi$
$397$	22.1796	+	22.1796i	1.11316	+	1.11316i	0.120439	+	0.992721i	$0.461570\pi$
$398$	5.10711	−	3.95000i	0.255996	−	0.197995i
$399$	10.7581			0.538581
$400$	−1.94669	+	3.49434i	−0.0973346	+	0.174717i
$401$	−6.20988			−0.310107			−0.155053	−	0.987906i	$-0.549555\pi$
$401$	−6.20988			−0.310107			−0.155053	+	0.987906i	$0.549555\pi$
$402$	−19.3628	+	14.9758i	−0.965728	+	0.746924i
$403$	23.9537	+	23.9537i	1.19322	+	1.19322i
$404$	10.7662	+	18.3221i	0.535640	+	0.911557i
$405$	7.94226	−	7.94226i	0.394654	−	0.394654i
$406$	−9.34080	−	1.19336i	−0.463576	−	0.0592254i
$407$		−	5.59151i		−	0.277161i
$408$	31.4635	+	12.6110i	1.55768	+	0.624338i
$409$		−	9.27377i		−	0.458558i	−0.973361	−	0.229279i	$-0.926363\pi$
$409$		−	9.27377i		−	0.458558i	0.973361	−	0.229279i	$-0.0736369\pi$
$410$	0.262302	−	2.05313i	0.0129542	−	0.101397i
$411$	16.5040	−	16.5040i	0.814081	−	0.814081i
$412$	28.0210	+	7.27858i	1.38049	+	0.358590i
$413$	4.12507	+	4.12507i	0.202981	+	0.202981i
$414$	10.7983	+	13.9615i	0.530706	+	0.686171i
$415$	−13.5923			−0.667218
$416$	16.1958	−	21.9653i	0.794065	−	1.07694i
$417$	−14.0238			−0.686750
$418$	7.40433	+	9.57336i	0.362158	+	0.468248i
$419$	−18.5158	−	18.5158i	−0.904556	−	0.904556i	0.0912697	−	0.995826i	$-0.470907\pi$
$419$	−18.5158	−	18.5158i	−0.904556	−	0.904556i	−0.995826	+	0.0912697i	$0.970907\pi$
$420$	4.16705	+	1.08241i	0.203331	+	0.0528163i
$421$	16.8004	−	16.8004i	0.818804	−	0.818804i	−0.167131	−	0.985935i	$-0.553450\pi$
$421$	16.8004	−	16.8004i	0.818804	−	0.818804i	0.985935	+	0.167131i	$0.0534503\pi$
$422$	−0.224565	+	1.75774i	−0.0109316	+	0.0855654i
$423$		−	5.55290i		−	0.269991i
$424$	5.93660	−	14.8114i	0.288307	−	0.719304i
$425$		−	5.56719i		−	0.270048i
$426$	2.37450	+	0.303360i	0.115045	+	0.0146978i
$427$	−5.67988	+	5.67988i	−0.274869	+	0.274869i
$428$	−15.9697	−	27.1774i	−0.771927	−	1.31367i
$429$	−12.5749	−	12.5749i	−0.607122	−	0.607122i
$430$	−12.5570	+	9.71200i	−0.605554	+	0.468354i
$431$	26.4720			1.27511			0.637556	−	0.770404i	$-0.279945\pi$
$431$	26.4720			1.27511			0.637556	+	0.770404i	$0.279945\pi$
$432$	11.3136	−	3.21804i	0.544326	−	0.154828i
$433$	−24.9183			−1.19750			−0.598749	−	0.800937i	$-0.704335\pi$
$433$	−24.9183			−1.19750			−0.598749	+	0.800937i	$0.704335\pi$
$434$	−7.85504	+	6.07533i	−0.377054	+	0.291625i
$435$	−10.1355	−	10.1355i	−0.485962	−	0.485962i
$436$	35.5655	−	20.8987i	1.70328	−	1.00087i
$437$	26.9918	−	26.9918i	1.29119	−	1.29119i
$438$	8.52094	+	1.08861i	0.407146	+	0.0520160i
$439$			20.3230i			0.969965i	0.874524	+	0.484983i	$0.161174\pi$
$439$			20.3230i			0.969965i	−0.874524	+	0.484983i	$0.838826\pi$
$440$	1.90478	+	4.45311i	0.0908068	+	0.212294i
$441$		−	1.63398i		−	0.0778084i
$442$	−4.81350	+	37.6768i	−0.228955	+	1.79210i
$443$	−17.4088	+	17.4088i	−0.827117	+	0.827117i	−0.987117	−	0.160000i	$-0.948850\pi$
$443$	−17.4088	+	17.4088i	−0.827117	+	0.827117i	0.160000	+	0.987117i	$0.448850\pi$
$444$	3.53441	−	13.6067i	0.167736	−	0.645746i
$445$	−5.57784	−	5.57784i	−0.264415	−	0.264415i
$446$	−1.30836	−	1.69163i	−0.0619525	−	0.0801009i
$447$	0.596211			0.0281998
$448$	5.78536	+	5.52536i	0.273332	+	0.261049i
$449$	25.2328			1.19081			0.595406	−	0.803425i	$-0.296991\pi$
$449$	25.2328			1.19081			0.595406	+	0.803425i	$0.296991\pi$
$450$	1.41373	+	1.82787i	0.0666440	+	0.0861667i
$451$	−1.77217	−	1.77217i	−0.0834482	−	0.0834482i
$452$	5.77305	−	22.2250i	0.271542	−	1.04538i
$453$	−13.8898	+	13.8898i	−0.652600	+	0.652600i
$454$	−3.53351	+	27.6579i	−0.165836	+	1.29805i
$455$			4.82435i			0.226169i
$456$	11.9668	+	27.9767i	0.560397	+	1.31013i
$457$		−	4.71467i		−	0.220543i	−0.993902	−	0.110271i	$-0.964828\pi$
$457$		−	4.71467i		−	0.220543i	0.993902	−	0.110271i	$-0.0351720\pi$
$458$	−15.9120	−	2.03287i	−0.743517	−	0.0949899i
$459$	−11.5759	+	11.5759i	−0.540319	+	0.540319i
$460$	13.1707	−	7.73925i	0.614088	−	0.360845i
$461$	3.49000	+	3.49000i	0.162545	+	0.162545i	0.783693	−	0.621148i	$-0.213333\pi$
$461$	3.49000	+	3.49000i	0.162545	+	0.162545i	−0.621148	+	0.783693i	$0.713333\pi$
$462$	4.12364	−	3.18935i	0.191849	−	0.148382i
$463$	−16.6389			−0.773277			−0.386638	−	0.922231i	$-0.626364\pi$
$463$	−16.6389			−0.773277			−0.386638	+	0.922231i	$0.626364\pi$
$464$	−7.28687	−	25.6183i	−0.338285	−	1.18930i
$465$	−15.1156			−0.700969
$466$	2.65553	−	2.05387i	0.123015	−	0.0951437i
$467$	2.36036	+	2.36036i	0.109225	+	0.109225i	0.759607	−	0.650382i	$-0.225391\pi$
$467$	2.36036	+	2.36036i	0.109225	+	0.109225i	−0.650382	+	0.759607i	$0.725391\pi$
$468$	−7.98724	−	13.5927i	−0.369210	−	0.628325i
$469$	5.68559	−	5.68559i	0.262536	−	0.262536i
$470$	−4.76731	−	0.609060i	−0.219900	−	0.0280938i
$471$			12.0232i			0.554002i
$472$	−6.13879	+	15.3158i	−0.282561	+	0.704967i
$473$			19.2217i			0.883814i
$474$	−2.34273	+	18.3373i	−0.107605	+	0.842259i
$475$	3.53383	−	3.53383i	0.162143	−	0.162143i
$476$	−10.7767	−	2.79931i	−0.493951	−	0.128306i
$477$	−6.51826	−	6.51826i	−0.298451	−	0.298451i
$478$	4.36087	+	5.63835i	0.199462	+	0.257892i
$479$	2.19836			0.100445			0.0502227	−	0.998738i	$-0.484007\pi$
$479$	2.19836			0.100445			0.0502227	+	0.998738i	$0.484007\pi$
$480$	1.82038	+	12.0405i	0.0830886	+	0.549571i
$481$	15.7530			0.718275
$482$	−0.0646305	−	0.0835635i	−0.00294384	−	0.00380621i
$483$	−11.6265	−	11.6265i	−0.529024	−	0.529024i
$484$	−15.6171	−	4.05663i	−0.709870	−	0.184392i
$485$	−1.98285	+	1.98285i	−0.0900368	+	0.0900368i
$486$	2.75229	−	21.5431i	0.124847	−	0.977214i
$487$		−	25.8492i		−	1.17134i	−0.810550	−	0.585670i	$-0.800832\pi$
$487$		−	25.8492i		−	1.17134i	0.810550	−	0.585670i	$-0.199168\pi$
$488$	−21.0886	−	8.45262i	−0.954637	−	0.382632i
$489$		−	40.3038i		−	1.82260i
$490$	−1.40281	−	0.179220i	−0.0633726	−	0.00809633i
$491$	−9.97853	+	9.97853i	−0.450325	+	0.450325i	−0.895462	−	0.445138i	$-0.853155\pi$
$491$	−9.97853	+	9.97853i	−0.450325	+	0.450325i	0.445138	+	0.895462i	$0.353155\pi$
$492$	−3.19231	−	5.43270i	−0.143920	−	0.244925i
$493$	26.2123	+	26.2123i	1.18054	+	1.18054i
$494$	−26.9711	+	20.8603i	−1.21349	+	0.938549i
$495$	2.79801			0.125761
$496$	−24.5365	−	13.6693i	−1.10172	−	0.613768i
$497$	−0.786312			−0.0352709
$498$	−32.7317	+	25.3157i	−1.46674	+	1.13442i
$499$	−2.41873	−	2.41873i	−0.108277	−	0.108277i	0.650893	−	0.759170i	$-0.274395\pi$
$499$	−2.41873	−	2.41873i	−0.108277	−	0.108277i	−0.759170	+	0.650893i	$0.774395\pi$
$500$	1.72434	−	1.01324i	0.0771148	−	0.0453134i
$501$	9.85896	−	9.85896i	0.440466	−	0.440466i
$502$	−35.1016	−	4.48450i	−1.56666	−	0.200153i
$503$			25.5574i			1.13955i	0.821802	+	0.569773i	$0.192969\pi$
$503$			25.5574i			1.13955i	−0.821802	+	0.569773i	$0.807031\pi$
$504$	4.24918	−	1.81755i	0.189274	−	0.0809601i
$505$		−	10.6256i		−	0.472831i
$506$	2.34411	−	18.3481i	0.104208	−	0.815671i
$507$	15.6393	−	15.6393i	0.694564	−	0.694564i
$508$	−2.09272	+	8.05652i	−0.0928495	+	0.357450i
$509$	−20.4871	−	20.4871i	−0.908076	−	0.908076i	0.0880408	−	0.996117i	$-0.471939\pi$
$509$	−20.4871	−	20.4871i	−0.908076	−	0.908076i	−0.996117	+	0.0880408i	$0.971939\pi$
$510$	−10.3689	−	13.4064i	−0.459144	−	0.593647i
$511$	−2.82170			−0.124825
$512$	−7.93346	+	21.1910i	−0.350613	+	0.936520i
$513$	−14.6959			−0.648839
$514$	−2.01102	−	2.60013i	−0.0887022	−	0.114687i
$515$	−10.2357	−	10.2357i	−0.451038	−	0.451038i
$516$	−12.1501	+	46.7752i	−0.534878	+	2.05916i
$517$	−4.11493	+	4.11493i	−0.180975	+	0.180975i
$518$	−0.585209	+	4.58062i	−0.0257126	+	0.201261i
$519$			16.4994i			0.724245i
$520$	−12.5458	+	5.36636i	−0.550170	+	0.235330i
$521$			20.4912i			0.897737i	0.893598	+	0.448869i	$0.148173\pi$
$521$			20.4912i			0.897737i	−0.893598	+	0.448869i	$0.851827\pi$
$522$	−15.2626	−	1.94992i	−0.668028	−	0.0853456i
$523$	23.3102	−	23.3102i	1.01929	−	1.01929i	0.0194756	−	0.999810i	$-0.493800\pi$
$523$	23.3102	−	23.3102i	1.01929	−	1.01929i	0.999810	−	0.0194756i	$-0.00619965\pi$
$524$	−35.4274	+	20.8175i	−1.54765	+	0.909418i
$525$	−1.52217	−	1.52217i	−0.0664328	−	0.0664328i
$526$	19.4307	−	15.0283i	0.847217	−	0.655263i
$527$	39.0917			1.70286
$528$	12.8809	+	7.17593i	0.560569	+	0.312292i
$529$	−35.3410			−1.53657
$530$	−6.31104	+	4.88116i	−0.274134	+	0.212024i
$531$	6.74026	+	6.74026i	0.292502	+	0.292502i
$532$	−5.06375	−	8.61753i	−0.219541	−	0.373618i
$533$	4.99275	−	4.99275i	0.216260	−	0.216260i
$534$	−23.8208	−	3.04329i	−1.03083	−	0.131696i
$535$			15.7611i			0.681411i
$536$	21.1098	+	8.46112i	0.911806	+	0.365465i
$537$		−	9.10161i		−	0.392764i
$538$	0.638083	−	4.99448i	0.0275097	−	0.215327i
$539$	−1.21085	+	1.21085i	−0.0521548	+	0.0521548i
$540$	−5.69229	−	1.47860i	−0.244957	−	0.0636288i
$541$	−14.4540	−	14.4540i	−0.621425	−	0.621425i	0.324471	−	0.945896i	$-0.394814\pi$
$541$	−14.4540	−	14.4540i	−0.621425	−	0.621425i	−0.945896	+	0.324471i	$0.894814\pi$
$542$	−26.0046	−	33.6224i	−1.11699	−	1.44421i
$543$	50.2793			2.15769
$544$	−4.70783	−	31.1389i	−0.201847	−	1.33507i
$545$	−20.6256			−0.883504
$546$	8.98539	+	11.6176i	0.384539	+	0.497187i
$547$	4.96269	+	4.96269i	0.212190	+	0.212190i	0.805197	−	0.593007i	$-0.202060\pi$
$547$	4.96269	+	4.96269i	0.212190	+	0.212190i	−0.593007	+	0.805197i	$0.702060\pi$
$548$	−20.9884	−	5.45183i	−0.896578	−	0.232891i
$549$	−9.28079	+	9.28079i	−0.396095	+	0.396095i
$550$	0.306895	−	2.40217i	0.0130861	−	0.102429i
$551$			33.2771i			1.41765i
$552$	17.3022	−	43.1676i	0.736430	−	1.83734i
$553$		−	6.07238i		−	0.258224i
$554$	−16.2155	−	2.07166i	−0.688932	−	0.0880164i
$555$	−4.97035	+	4.97035i	−0.210979	+	0.210979i
$556$	6.60088	+	11.2334i	0.279940	+	0.476404i
$557$	−20.9828	−	20.9828i	−0.889072	−	0.889072i	0.105362	−	0.994434i	$-0.466400\pi$
$557$	−20.9828	−	20.9828i	−0.889072	−	0.889072i	−0.994434	+	0.105362i	$0.966400\pi$
$558$	−12.8349	+	9.92694i	−0.543346	+	0.420241i
$559$	−54.1534			−2.29045
$560$	−1.09435	−	3.84739i	−0.0462447	−	0.162582i
$561$	−20.5219			−0.866434
$562$	19.6011	−	15.1601i	0.826822	−	0.639490i
$563$	−16.5515	−	16.5515i	−0.697563	−	0.697563i	0.266322	−	0.963884i	$-0.414192\pi$
$563$	−16.5515	−	16.5515i	−0.697563	−	0.697563i	−0.963884	+	0.266322i	$0.914192\pi$
$564$	−12.6146	+	7.41247i	−0.531170	+	0.312121i
$565$	−8.11848	+	8.11848i	−0.341547	+	0.341547i
$566$	−17.7354	−	2.26583i	−0.745474	−	0.0952400i
$567$			11.2321i			0.471702i
$568$	−0.874653	−	2.04482i	−0.0366996	−	0.0857986i
$569$			11.3521i			0.475903i	0.971277	+	0.237952i	$0.0764760\pi$
$569$			11.3521i			0.475903i	−0.971277	+	0.237952i	$0.923524\pi$
$570$	1.92807	−	15.0916i	0.0807581	−	0.632119i
$571$	13.6254	−	13.6254i	0.570203	−	0.570203i	−0.361982	−	0.932185i	$-0.617900\pi$
$571$	13.6254	−	13.6254i	0.570203	−	0.570203i	0.932185	+	0.361982i	$0.117900\pi$
$572$	−4.15392	+	15.9917i	−0.173684	+	0.668646i
$573$	−10.6481	−	10.6481i	−0.444830	−	0.444830i
$574$	1.26630	+	1.63725i	0.0528545	+	0.0683377i
$575$	−7.63813			−0.318532
$576$	9.45313	+	9.02831i	0.393881	+	0.376180i
$577$	−24.0343			−1.00056			−0.500280	−	0.865863i	$-0.666770\pi$
$577$	−24.0343			−1.00056			−0.500280	+	0.865863i	$0.666770\pi$
$578$	12.1074	+	15.6542i	0.503602	+	0.651127i
$579$	16.2346	+	16.2346i	0.674685	+	0.674685i
$580$	−3.34811	+	12.8895i	−0.139023	+	0.535208i
$581$	9.61118	−	9.61118i	0.398739	−	0.398739i
$582$	−1.08185	+	8.46802i	−0.0448443	+	0.351011i
$583$			9.66062i			0.400102i
$584$	−3.13871	−	7.33788i	−0.129881	−	0.303644i
$585$			7.88287i			0.325917i
$586$	20.2554	+	2.58778i	0.836742	+	0.106900i
$587$	9.77337	−	9.77337i	0.403390	−	0.403390i	−0.476036	−	0.879426i	$-0.657927\pi$
$587$	9.77337	−	9.77337i	0.403390	−	0.403390i	0.879426	+	0.476036i	$0.157927\pi$
$588$	−3.71193	+	2.18117i	−0.153077	+	0.0899498i
$589$	24.8138	+	24.8138i	1.02244	+	1.02244i
$590$	6.52598	−	5.04740i	0.268671	−	0.207798i
$591$	−48.6085			−1.99949
$592$	−12.5629	+	3.57340i	−0.516333	+	0.146866i
$593$	10.8170			0.444201			0.222101	−	0.975024i	$-0.428709\pi$
$593$	10.8170			0.444201			0.222101	+	0.975024i	$0.428709\pi$
$594$	−5.63300	+	4.35673i	−0.231125	+	0.178759i
$595$	3.93660	+	3.93660i	0.161385	+	0.161385i
$596$	−0.280631	−	0.477580i	−0.0114951	−	0.0195624i
$597$	−6.94924	+	6.94924i	−0.284413	+	0.284413i
$598$	51.6922	+	6.60408i	2.11385	+	0.270061i
$599$		−	15.7218i		−	0.642376i	−0.947015	−	0.321188i	$-0.895918\pi$
$599$		−	15.7218i		−	0.642376i	0.947015	−	0.321188i	$-0.104082\pi$
$600$	2.26524	−	5.65159i	0.0924779	−	0.230725i
$601$		−	26.1826i		−	1.06801i	−0.845482	−	0.534005i	$-0.820686\pi$
$601$		−	26.1826i		−	1.06801i	0.845482	−	0.534005i	$-0.179314\pi$
$602$	2.01175	−	15.7466i	0.0819927	−	0.641783i
$603$	9.29012	−	9.29012i	0.378323	−	0.378323i
$604$	17.6639	+	4.58828i	0.718733	+	0.186694i
$605$	5.70473	+	5.70473i	0.231930	+	0.231930i
$606$	−19.7902	−	25.5876i	−0.803922	−	1.03942i
$607$	22.5081			0.913577			0.456789	−	0.889575i	$-0.349000\pi$
$607$	22.5081			0.913577			0.456789	+	0.889575i	$0.349000\pi$
$608$	16.7774	−	22.7541i	0.680413	−	0.922799i
$609$	14.3338			0.580835
$610$	6.94986	+	8.98575i	0.281391	+	0.363823i
$611$	−11.5930	−	11.5930i	−0.469004	−	0.469004i
$612$	−17.6089	−	4.57401i	−0.711799	−	0.184893i
$613$	−18.6642	+	18.6642i	−0.753841	+	0.753841i	−0.975194	−	0.221353i	$-0.928953\pi$
$613$	−18.6642	+	18.6642i	−0.753841	+	0.753841i	0.221353	+	0.975194i	$0.428953\pi$
$614$	−2.21407	+	17.3302i	−0.0893525	+	0.699390i
$615$			3.15060i			0.127044i
$616$	−4.49571	−	1.80194i	−0.181137	−	0.0726023i
$617$		−	22.0682i		−	0.888432i	−0.895920	−	0.444216i	$-0.853482\pi$
$617$		−	22.0682i		−	0.888432i	0.895920	−	0.444216i	$-0.146518\pi$
$618$	−43.7127	−	5.58463i	−1.75838	−	0.224647i
$619$	−13.4279	+	13.4279i	−0.539713	+	0.539713i	−0.923445	−	0.383731i	$-0.874639\pi$
$619$	−13.4279	+	13.4279i	−0.539713	+	0.539713i	0.383731	+	0.923445i	$0.374639\pi$
$620$	7.11476	+	12.1080i	0.285736	+	0.486267i
$621$	15.8821	+	15.8821i	0.637326	+	0.637326i
$622$	−5.01498	+	3.87874i	−0.201082	+	0.155523i
$623$	7.88825			0.316036
$624$	−20.2168	+	36.2895i	−0.809320	+	1.45274i
$625$	−1.00000			−0.0400000
$626$	27.7388	−	21.4541i	1.10867	−	0.857476i
$627$	−13.0265	−	13.0265i	−0.520227	−	0.520227i
$628$	9.63091	−	5.65922i	0.384315	−	0.225828i
$629$	12.8542	−	12.8542i	0.512531	−	0.512531i
$630$	−2.29216	−	0.292841i	−0.0913219	−	0.0116671i
$631$			7.21979i			0.287415i	0.989620	+	0.143708i	$0.0459025\pi$
$631$			7.21979i			0.287415i	−0.989620	+	0.143708i	$0.954097\pi$
$632$	15.7913	−	6.75460i	0.628145	−	0.268683i
$633$		−	2.69732i		−	0.107209i
$634$	5.79511	−	45.3602i	0.230153	−	1.80148i
$635$	2.94294	−	2.94294i	0.116787	−	0.116787i
$636$	−6.10652	+	23.5088i	−0.242139	+	0.932183i
$637$	−3.41133	−	3.41133i	−0.135162	−	0.135162i
$638$	9.86530	+	12.7552i	0.390571	+	0.504985i
$639$	−1.28482			−0.0508265
$640$	8.78790	−	7.12551i	0.347372	−	0.281661i
$641$	−23.6126			−0.932643			−0.466322	−	0.884615i	$-0.654421\pi$
$641$	−23.6126			−0.932643			−0.466322	+	0.884615i	$0.654421\pi$
$642$	29.3552	+	37.9545i	1.15856	+	1.49794i
$643$	33.5944	+	33.5944i	1.32484	+	1.32484i	0.909810	+	0.415026i	$0.136227\pi$
$643$	33.5944	+	33.5944i	1.32484	+	1.32484i	0.415026	+	0.909810i	$0.363773\pi$
$644$	−3.84063	+	14.7856i	−0.151342	+	0.582634i
$645$	17.0863	−	17.0863i	0.672774	−	0.672774i
$646$	−4.98635	+	39.0297i	−0.196185	+	1.53560i
$647$		−	18.0840i		−	0.710957i	−0.934685	−	0.355478i	$-0.884318\pi$
$647$		−	18.0840i		−	0.710957i	0.934685	−	0.355478i	$-0.115682\pi$
$648$	−29.2091	+	12.4939i	−1.14744	+	0.490809i
$649$		−	9.98964i		−	0.392128i
$650$	6.76765	+	0.864619i	0.265449	+	0.0339132i
$651$	10.6883	−	10.6883i	0.418909	−	0.418909i
$652$	−32.2844	+	18.9706i	−1.26435	+	0.742947i
$653$	−28.4808	−	28.4808i	−1.11454	−	1.11454i	−0.992529	−	0.122012i	$-0.961065\pi$
$653$	−28.4808	−	28.4808i	−1.11454	−	1.11454i	−0.122012	−	0.992529i	$-0.538935\pi$
$654$	−49.6688	+	38.4154i	−1.94220	+	1.50216i
$655$	20.5455			0.802780
$656$	−2.84914	+	5.11424i	−0.111240	+	0.199677i
$657$	−4.61059			−0.179876
$658$	3.80167	−	2.94033i	0.148204	−	0.114626i
$659$	−2.82673	−	2.82673i	−0.110114	−	0.110114i	0.649903	−	0.760017i	$-0.274809\pi$
$659$	−2.82673	−	2.82673i	−0.110114	−	0.110114i	−0.760017	+	0.649903i	$0.774809\pi$
$660$	−3.73502	−	6.35629i	−0.145385	−	0.247418i
$661$	−15.1445	+	15.1445i	−0.589052	+	0.589052i	−0.937375	−	0.348322i	$-0.886751\pi$
$661$	−15.1445	+	15.1445i	−0.589052	+	0.589052i	0.348322	+	0.937375i	$0.386751\pi$
$662$	−30.8893	−	3.94635i	−1.20055	−	0.153379i
$663$		−	57.8165i		−	2.24541i
$664$	35.6850	+	14.3031i	1.38485	+	0.555066i
$665$			4.99759i			0.193798i
$666$	−0.956218	+	7.48462i	−0.0370527	+	0.290023i
$667$	35.9631	−	35.9631i	1.39250	−	1.39250i
$668$	−12.5378	−	3.25675i	−0.485101	−	0.126008i
$669$	2.30179	+	2.30179i	0.0889925	+	0.0889925i
$670$	−6.95685	−	8.99479i	−0.268766	−	0.347499i
$671$	13.7549			0.531003
$672$	−9.80112	−	7.22671i	−0.378086	−	0.278776i
$673$	−41.4800			−1.59894			−0.799468	−	0.600708i	$-0.794885\pi$
$673$	−41.4800			−1.59894			−0.799468	+	0.600708i	$0.794885\pi$
$674$	−6.66631	−	8.61914i	−0.256777	−	0.331997i
$675$	2.07931	+	2.07931i	0.0800329	+	0.0800329i
$676$	−19.8887	−	5.16618i	−0.764949	−	0.198699i
$677$	2.09621	−	2.09621i	0.0805638	−	0.0805638i	−0.665677	−	0.746240i	$-0.731857\pi$
$677$	2.09621	−	2.09621i	0.0805638	−	0.0805638i	0.746240	+	0.665677i	$0.231857\pi$
$678$	−4.42948	+	34.6710i	−0.170113	+	1.33153i
$679$		−	2.80418i		−	0.107615i
$680$	−5.85832	+	14.6161i	−0.224656	+	0.560500i
$681$		−	42.4421i		−	1.62639i
$682$	16.8675	+	2.15496i	0.645891	+	0.0825175i
$683$	−27.8470	+	27.8470i	−1.06554	+	1.06554i	−0.0678407	+	0.997696i	$0.521611\pi$
$683$	−27.8470	+	27.8470i	−1.06554	+	1.06554i	−0.997696	+	0.0678407i	$0.978389\pi$
$684$	−8.27405	−	14.0808i	−0.316366	−	0.538395i
$685$	7.66676	+	7.66676i	0.292932	+	0.292932i
$686$	1.11867	−	0.865210i	0.0427108	−	0.0330339i
$687$	24.4175			0.931585
$688$	43.1870	−	12.2841i	1.64649	−	0.468327i
$689$	−27.2170			−1.03688
$690$	−18.3935	+	14.2261i	−0.700228	+	0.541578i
$691$	−18.9734	−	18.9734i	−0.721784	−	0.721784i	0.247185	−	0.968968i	$-0.420495\pi$
$691$	−18.9734	−	18.9734i	−0.721784	−	0.721784i	−0.968968	+	0.247185i	$0.920495\pi$
$692$	13.2164	−	7.76612i	0.502414	−	0.295224i
$693$	−1.97849	+	1.97849i	−0.0751568	+	0.0751568i
$694$	37.9094	+	4.84322i	1.43902	+	0.183846i
$695$		−	6.51463i		−	0.247114i
$696$	15.9442	+	37.2753i	0.604363	+	1.41292i
$697$		−	8.14802i		−	0.308628i
$698$	6.52221	−	51.0514i	0.246869	−	1.93232i
$699$	−3.61338	+	3.61338i	−0.136670	+	0.136670i
$700$	−0.502824	+	1.93576i	−0.0190049	+	0.0731649i
$701$	33.1667	+	33.1667i	1.25269	+	1.25269i	0.954510	+	0.298178i	$0.0963789\pi$
$701$	33.1667	+	33.1667i	1.25269	+	1.25269i	0.298178	+	0.954510i	$0.403621\pi$
$702$	−12.2743	−	15.8699i	−0.463262	−	0.598971i
$703$	16.3187			0.615471
$704$	−0.314812	−	13.6955i	−0.0118649	−	0.516170i
$705$	7.31561			0.275522
$706$	17.1069	+	22.1182i	0.643827	+	0.832430i
$707$	7.51341	+	7.51341i	0.282571	+	0.282571i
$708$	6.31449	−	24.3094i	0.237313	−	0.913604i
$709$	−27.8109	+	27.8109i	−1.04446	+	1.04446i	−0.0454962	+	0.998965i	$0.514487\pi$
$709$	−27.8109	+	27.8109i	−1.04446	+	1.04446i	−0.998965	+	0.0454962i	$0.985513\pi$
$710$	−0.140923	+	1.10305i	−0.00528874	+	0.0413967i
$711$		−	9.92212i		−	0.372109i
$712$	8.77448	+	20.5135i	0.328838	+	0.768777i
$713$		−	53.6334i		−	2.00859i
$714$	16.8117	+	2.14783i	0.629163	+	0.0803804i
$715$	5.84155	−	5.84155i	0.218461	−	0.218461i
$716$	−7.29061	+	4.28404i	−0.272463	+	0.160102i
$717$	−7.67209	−	7.67209i	−0.286519	−	0.286519i
$718$	22.6887	−	17.5481i	0.846735	−	0.654891i
$719$	−11.3327			−0.422637			−0.211319	−	0.977417i	$-0.567776\pi$
$719$	−11.3327			−0.422637			−0.211319	+	0.977417i	$0.567776\pi$
$720$	−1.78814	−	6.28654i	−0.0666401	−	0.234286i
$721$	14.4754			0.539093
$722$	−6.68500	+	5.17038i	−0.248790	+	0.192422i
$723$	0.113705	+	0.113705i	0.00422872	+	0.00422872i
$724$	−23.6660	−	40.2750i	−0.879539	−	1.49681i
$725$	4.70836	−	4.70836i	0.174864	−	0.174864i
$726$	24.3627	+	3.11253i	0.904186	+	0.115517i
$727$			21.5599i			0.799611i	0.916600	+	0.399805i	$0.130922\pi$
$727$			21.5599i			0.799611i	−0.916600	+	0.399805i	$0.869078\pi$
$728$	5.07663	−	12.6658i	0.188152	−	0.469426i
$729$		−	0.637467i		−	0.0236099i
$730$	−0.505705	+	3.95832i	−0.0187170	+	0.146504i
$731$	−44.1884	+	44.1884i	−1.63437	+	1.63437i
$732$	33.4721	+	8.69454i	1.23716	+	0.321360i
$733$	24.0330	+	24.0330i	0.887680	+	0.887680i	0.994300	−	0.106620i	$-0.0340029\pi$
$733$	24.0330	+	24.0330i	0.887680	+	0.887680i	−0.106620	+	0.994300i	$0.534003\pi$
$734$	12.8609	+	16.6284i	0.474704	+	0.613764i
$735$	2.15267			0.0794023
$736$	−42.7223	+	6.45910i	−1.57476	+	0.238086i
$737$	−13.7688			−0.507179
$738$	2.06911	+	2.67523i	0.0761649	+	0.0984767i
$739$	32.3430	+	32.3430i	1.18976	+	1.18976i	0.977134	+	0.212624i	$0.0682010\pi$
$739$	32.3430	+	32.3430i	1.18976	+	1.18976i	0.212624	+	0.977134i	$0.431799\pi$
$740$	6.32086	+	1.64188i	0.232360	+	0.0603566i
$741$	36.6996	−	36.6996i	1.34819	−	1.34819i
$742$	1.01108	−	7.91408i	0.0371181	−	0.290535i
$743$			4.62062i			0.169514i	0.996402	+	0.0847570i	$0.0270114\pi$
$743$			4.62062i			0.169514i	−0.996402	+	0.0847570i	$0.972989\pi$
$744$	39.6843	+	15.9060i	1.45490	+	0.583144i
$745$			0.276964i			0.0101472i
$746$	−12.1358	−	1.55044i	−0.444322	−	0.0567655i
$747$	15.7044	−	15.7044i	0.574596	−	0.574596i
$748$	9.65945	+	16.4385i	0.353184	+	0.601052i
$749$	−11.1448	−	11.1448i	−0.407221	−	0.407221i
$750$	−2.40811	+	1.86251i	−0.0879319	+	0.0680092i
$751$	10.8648			0.396463			0.198231	−	0.980155i	$-0.436480\pi$
$751$	10.8648			0.396463			0.198231	+	0.980155i	$0.436480\pi$
$752$	11.8751	+	6.61563i	0.433042	+	0.241247i
$753$	53.8648			1.96294
$754$	−35.9355	+	27.7936i	−1.30869	+	1.01218i
$755$	−6.45237	−	6.45237i	−0.234826	−	0.234826i
$756$	5.07058	−	2.97953i	0.184415	−	0.108364i
$757$	−8.20636	+	8.20636i	−0.298265	+	0.298265i	−0.840334	−	0.542069i	$-0.817641\pi$
$757$	−8.20636	+	8.20636i	−0.298265	+	0.298265i	0.542069	+	0.840334i	$0.317641\pi$
$758$	−17.9503	−	2.29329i	−0.651985	−	0.0832961i
$759$			28.1558i			1.02199i
$760$	−12.9963	+	5.55906i	−0.471425	+	0.201648i
$761$			38.1339i			1.38235i	0.722687	+	0.691176i	$0.242907\pi$
$761$			38.1339i			1.38235i	−0.722687	+	0.691176i	$0.757093\pi$
$762$	1.60568	−	12.5682i	0.0581676	−	0.455297i
$763$	14.5845	−	14.5845i	0.527995	−	0.527995i
$764$	−3.51742	+	13.5413i	−0.127256	+	0.489907i
$765$	6.43231	+	6.43231i	0.232561	+	0.232561i
$766$	−9.17139	−	11.8581i	−0.331376	−	0.428449i
$767$	28.1439			1.01622
$768$	7.89092	−	33.5266i	0.284739	−	1.20979i
$769$	27.0313			0.974773			0.487387	−	0.873186i	$-0.337950\pi$
$769$	27.0313			0.974773			0.487387	+	0.873186i	$0.337950\pi$
$770$	1.48158	+	1.91560i	0.0533925	+	0.0690333i
$771$	3.53799	+	3.53799i	0.127418	+	0.127418i
$772$	5.36283	−	20.6457i	0.193013	−	0.743056i
$773$	28.2529	−	28.2529i	1.01619	−	1.01619i	0.0163193	−	0.999867i	$-0.494805\pi$
$773$	28.2529	−	28.2529i	1.01619	−	1.01619i	0.999867	−	0.0163193i	$-0.00519483\pi$
$774$	3.28715	−	25.7296i	0.118154	−	0.924830i
$775$		−	7.02180i		−	0.252230i
$776$	7.29231	−	3.11922i	0.261779	−	0.111974i
$777$		−	7.02913i		−	0.252169i
$778$	1.28250	+	0.163849i	0.0459797	+	0.00587426i
$779$	5.17203	−	5.17203i	0.185307	−	0.185307i
$780$	17.9076	−	10.5227i	0.641196	−	0.376774i
$781$	0.952104	+	0.952104i	0.0340689	+	0.0340689i
$782$	47.5689	−	36.7913i	1.70106	−	1.31565i
$783$	−19.5803			−0.699744
$784$	3.49434	+	1.94669i	0.124798	+	0.0695247i
$785$	−5.58528			−0.199347
$786$	49.4759	−	38.2662i	1.76475	−	1.36491i
$787$	−21.7110	−	21.7110i	−0.773912	−	0.773912i	0.204876	−	0.978788i	$-0.434321\pi$
$787$	−21.7110	−	21.7110i	−0.773912	−	0.773912i	−0.978788	+	0.204876i	$0.934321\pi$
$788$	22.8795	+	38.9366i	0.815050	+	1.38706i
$789$	−26.4393	+	26.4393i	−0.941262	+	0.941262i
$790$	−8.51840	−	1.08829i	−0.303071	−	0.0387197i
$791$		−	11.4813i		−	0.408227i
$792$	−7.34588	−	2.94433i	−0.261024	−	0.104622i
$793$			38.7519i			1.37612i
$794$	−5.62152	+	44.0015i	−0.199500	+	1.56155i
$795$	8.58743	−	8.58743i	0.304565	−	0.304565i
$796$	8.83745	+	2.29557i	0.313235	+	0.0813644i
$797$	−0.301001	−	0.301001i	−0.0106620	−	0.0106620i	0.701756	−	0.712418i	$-0.252400\pi$
$797$	−0.301001	−	0.301001i	−0.0106620	−	0.0106620i	−0.712418	+	0.701756i	$0.752400\pi$
$798$	9.30805	+	12.0348i	0.329501	+	0.426026i
$799$	−18.9195			−0.669324
$800$	−5.59329	+	0.845639i	−0.197753	+	0.0298979i
$801$	12.8892			0.455418
$802$	−5.37285	−	6.94678i	−0.189722	−	0.245299i
$803$	3.41665	+	3.41665i	0.120571	+	0.120571i
$804$	−33.5057	−	8.70329i	−1.18166	−	0.306941i
$805$	5.40097	−	5.40097i	0.190359	−	0.190359i
$806$	−6.07118	+	47.5211i	−0.213848	+	1.67386i
$807$			7.66422i			0.269793i
$808$	−11.1812	+	27.8963i	−0.393354	+	0.981387i
$809$		−	51.4569i		−	1.80913i	−0.426338	−	0.904564i	$-0.640197\pi$
$809$		−	51.4569i		−	1.80913i	0.426338	−	0.904564i	$-0.359803\pi$
$810$	15.7565	+	2.01301i	0.553625	+	0.0707299i
$811$	−1.67008	+	1.67008i	−0.0586445	+	0.0586445i	−0.735821	−	0.677176i	$-0.763203\pi$
$811$	−1.67008	+	1.67008i	−0.0586445	+	0.0586445i	0.677176	+	0.735821i	$0.263203\pi$
$812$	−6.74678	−	11.4817i	−0.236766	−	0.402930i
$813$	45.7500	+	45.7500i	1.60452	+	1.60452i
$814$	6.25502	−	4.83783i	0.219238	−	0.169566i
$815$	18.7227			0.655829
$816$	13.1150	+	46.1083i	0.459118	+	1.61411i
$817$	−56.0980			−1.96262
$818$	10.3742	−	8.02376i	0.362727	−	0.280544i
$819$	−5.57403	−	5.57403i	−0.194772	−	0.194772i
$820$	2.52371	−	1.48296i	0.0881316	−	0.0517871i
$821$	−9.96191	+	9.96191i	−0.347673	+	0.347673i	−0.859242	−	0.511569i	$-0.829064\pi$
$821$	−9.96191	+	9.96191i	−0.347673	+	0.347673i	0.511569	+	0.859242i	$0.329064\pi$
$822$	32.7418	+	4.18302i	1.14200	+	0.145900i
$823$		−	21.1619i		−	0.737659i	−0.929497	−	0.368829i	$-0.879759\pi$
$823$		−	21.1619i		−	0.737659i	0.929497	−	0.368829i	$-0.120241\pi$
$824$	16.1017	+	37.6436i	0.560930	+	1.31138i
$825$			3.68622i			0.128338i
$826$	−1.04552	+	8.18362i	−0.0363783	+	0.284744i
$827$	−23.3973	+	23.3973i	−0.813602	+	0.813602i	−0.985172	−	0.171570i	$-0.945116\pi$
$827$	−23.3973	+	23.3973i	−0.813602	+	0.813602i	0.171570	+	0.985172i	$0.445116\pi$
$828$	−6.27550	+	24.1593i	−0.218089	+	0.839594i
$829$	−32.6833	−	32.6833i	−1.13514	−	1.13514i	−0.989310	−	0.145830i	$-0.953415\pi$
$829$	−32.6833	−	32.6833i	−1.13514	−	1.13514i	−0.145830	−	0.989310i	$-0.546585\pi$
$830$	−11.7602	−	15.2052i	−0.408201	−	0.527780i
$831$	24.8834			0.863194
$832$	38.5846	−	0.886924i	1.33768	−	0.0307485i
$833$	−5.56719			−0.192892
$834$	−12.1336	−	15.6880i	−0.420151	−	0.543230i
$835$	4.57988	+	4.57988i	0.158493	+	0.158493i
$836$	−4.30309	+	16.5659i	−0.148825	+	0.572945i
$837$	−14.6005	+	14.6005i	−0.504668	+	0.504668i
$838$	4.69293	−	36.7331i	0.162115	−	1.26892i
$839$			18.7118i			0.646003i	0.946398	+	0.323001i	$0.104692\pi$
$839$			18.7118i			0.646003i	−0.946398	+	0.323001i	$0.895308\pi$
$840$	2.39452	+	5.59804i	0.0826186	+	0.193151i
$841$			15.3373i			0.528873i
$842$	33.3300	+	4.25816i	1.14863	+	0.146746i
$843$	−26.6712	+	26.6712i	−0.918604	+	0.918604i
$844$	−2.16062	+	1.26960i	−0.0743715	+	0.0437015i
$845$	7.26506	+	7.26506i	0.249926	+	0.249926i
$846$	6.21183	−	4.80442i	0.213567	−	0.165179i
$847$	−8.06770			−0.277210
$848$	21.7054	−	6.17387i	0.745365	−	0.212012i
$849$	27.2156			0.934037
$850$	6.22782	−	4.81679i	0.213613	−	0.165214i
$851$	−17.6359	−	17.6359i	−0.604550	−	0.604550i
$852$	1.71508	+	2.91874i	0.0587576	+	0.0999942i
$853$	23.1561	−	23.1561i	0.792851	−	0.792851i	−0.189106	−	0.981957i	$-0.560559\pi$
$853$	23.1561	−	23.1561i	0.792851	−	0.792851i	0.981957	+	0.189106i	$0.0605590\pi$
$854$	−11.2682	−	1.43960i	−0.385589	−	0.0492620i
$855$			8.16594i			0.279269i
$856$	16.5853	−	41.3790i	0.566873	−	1.41431i
$857$			16.7441i			0.571967i	0.958234	+	0.285984i	$0.0923203\pi$
$857$			16.7441i			0.571967i	−0.958234	+	0.285984i	$0.907680\pi$
$858$	3.18718	−	24.9470i	0.108808	−	0.851678i
$859$	12.1610	−	12.1610i	0.414928	−	0.414928i	−0.468523	−	0.883451i	$-0.655214\pi$
$859$	12.1610	−	12.1610i	0.414928	−	0.414928i	0.883451	+	0.468523i	$0.155214\pi$
$860$	−21.7290	−	5.64421i	−0.740951	−	0.192466i
$861$	−2.22781	−	2.22781i	−0.0759235	−	0.0759235i
$862$	22.9039	+	29.6133i	0.780109	+	1.00863i
$863$	26.3610			0.897340			0.448670	−	0.893697i	$-0.351898\pi$
$863$	26.3610			0.897340			0.448670	+	0.893697i	$0.351898\pi$
$864$	13.3886	+	9.87186i	0.455488	+	0.335848i
$865$	−7.66465			−0.260606
$866$	−21.5596	−	27.8753i	−0.732625	−	0.947240i
$867$	−21.3006	−	21.3006i	−0.723406	−	0.723406i
$868$	−13.5925	−	3.53072i	−0.461360	−	0.119841i
$869$	−7.35272	+	7.35272i	−0.249424	+	0.249424i
$870$	2.56890	−	20.1076i	0.0870940	−	0.681713i
$871$		−	38.7909i		−	1.31438i
$872$	54.1503	+	21.7042i	1.83376	+	0.734997i
$873$		−	4.58196i		−	0.155076i
$874$	53.5484	+	6.84122i	1.81130	+	0.231408i
$875$	0.707107	−	0.707107i	0.0239046	−	0.0239046i
$876$	6.15460	+	10.4740i	0.207945	+	0.353882i
$877$	32.2130	+	32.2130i	1.08776	+	1.08776i	0.995759	+	0.0919974i	$0.0293252\pi$
$877$	32.2130	+	32.2130i	1.08776	+	1.08776i	0.0919974	+	0.995759i	$0.470675\pi$
$878$	−22.7347	+	17.5837i	−0.767258	+	0.593421i
$879$	−31.0826			−1.04839
$880$	−3.33351	+	5.98369i	−0.112372	+	0.201710i
$881$	22.6859			0.764306			0.382153	−	0.924099i	$-0.375183\pi$
$881$	22.6859			0.764306			0.382153	+	0.924099i	$0.375183\pi$
$882$	1.82787	−	1.41373i	0.0615477	−	0.0476028i
$883$	5.30607	+	5.30607i	0.178564	+	0.178564i	0.790729	−	0.612166i	$-0.209702\pi$
$883$	5.30607	+	5.30607i	0.178564	+	0.178564i	−0.612166	+	0.790729i	$0.709702\pi$
$884$	−46.3124	+	27.2137i	−1.55766	+	0.915294i
$885$	−8.87989	+	8.87989i	−0.298494	+	0.298494i
$886$	−34.5369	−	4.41235i	−1.16029	−	0.148236i
$887$			33.5745i			1.12732i	0.826007	+	0.563660i	$0.190607\pi$
$887$			33.5745i			1.12732i	−0.826007	+	0.563660i	$0.809393\pi$
$888$	18.2794	−	7.81884i	0.613415	−	0.262383i
$889$			4.16194i			0.139587i
$890$	1.41373	−	11.0657i	0.0473884	−	0.370924i
$891$	13.6003	−	13.6003i	0.455627	−	0.455627i
$892$	0.760362	−	2.92723i	0.0254588	−	0.0980108i
$893$	−12.0093	−	12.0093i	−0.401877	−	0.401877i
$894$	0.515848	+	0.666960i	0.0172525	+	0.0223065i
$895$	4.22806			0.141329
$896$	−1.17548	+	11.2525i	−0.0392701	+	0.375919i
$897$	−79.3236			−2.64854
$898$	21.8317	+	28.2271i	0.728534	+	0.941951i
$899$	33.0611	+	33.0611i	1.10265	+	1.10265i
$900$	−0.821602	+	3.16299i	−0.0273867	+	0.105433i
$901$	−22.2087	+	22.2087i	−0.739877	+	0.739877i
$902$	0.449166	−	3.51576i	0.0149556	−	0.117062i
$903$			24.1637i			0.804119i
$904$	29.8572	−	12.7712i	0.993036	−	0.424763i
$905$			23.3567i			0.776405i
$906$	−27.5556	−	3.52044i	−0.915475	−	0.116959i
$907$	20.0939	−	20.0939i	0.667205	−	0.667205i	−0.289863	−	0.957068i	$-0.593610\pi$
$907$	20.0939	−	20.0939i	0.667205	−	0.667205i	0.957068	+	0.289863i	$0.0936097\pi$
$908$	−33.9972	+	19.9771i	−1.12824	+	0.662963i
$909$	12.2767	+	12.2767i	0.407193	+	0.407193i
$910$	−5.39683	+	4.17407i	−0.178903	+	0.138369i
$911$	1.69885			0.0562856			0.0281428	−	0.999604i	$-0.491041\pi$
$911$	1.69885			0.0562856			0.0281428	+	0.999604i	$0.491041\pi$
$912$	−20.9428	+	37.5926i	−0.693485	+	1.24481i
$913$	−23.2753			−0.770301
$914$	5.27413	−	4.07918i	0.174453	−	0.134927i
$915$	−12.2269	−	12.2269i	−0.404209	−	0.404209i
$916$	−11.4931	−	19.5590i	−0.379742	−	0.646248i
$917$	−14.5279	+	14.5279i	−0.479753	+	0.479753i
$918$	−22.9652	−	2.93398i	−0.757965	−	0.0968359i
$919$		−	55.0327i		−	1.81536i	−0.419662	−	0.907680i	$-0.637851\pi$
$919$		−	55.0327i		−	1.81536i	0.419662	−	0.907680i	$-0.362149\pi$
$920$	20.0531	+	8.03755i	0.661130	+	0.264990i
$921$		−	26.5939i		−	0.876298i
$922$	−0.884558	+	6.92372i	−0.0291314	+	0.228021i
$923$	−2.68237	+	2.68237i	−0.0882913	+	0.0882913i
$924$	7.13563	+	1.85352i	0.234745	+	0.0609762i
$925$	−2.30892	−	2.30892i	−0.0759170	−	0.0759170i
$926$	−14.3962	−	18.6134i	−0.473087	−	0.611674i
$927$	23.6525			0.776850
$928$	22.3537	−	30.3168i	0.733795	−	0.995198i
$929$	22.5379			0.739444			0.369722	−	0.929143i	$-0.379453\pi$
$929$	22.5379			0.739444			0.369722	+	0.929143i	$0.379453\pi$
$930$	−13.0782	−	16.9093i	−0.428850	−	0.554477i
$931$	−3.53383	−	3.53383i	−0.115817	−	0.115817i
$932$	4.59518	+	1.19362i	0.150520	+	0.0390984i
$933$	6.82388	−	6.82388i	0.223404	−	0.223404i
$934$	−0.598246	+	4.68266i	−0.0195752	+	0.153221i
$935$		−	9.53323i		−	0.311770i
$936$	8.29509	−	20.6956i	0.271134	−	0.676457i
$937$			40.2659i			1.31543i	0.753267	+	0.657715i	$0.228477\pi$
$937$			40.2659i			1.31543i	−0.753267	+	0.657715i	$0.771523\pi$
$938$	11.2795	+	1.44104i	0.368289	+	0.0470517i
$939$	−37.7442	+	37.7442i	−1.23173	+	1.23173i
$940$	−3.44339	−	5.85999i	−0.112311	−	0.191132i
$941$	24.3403	+	24.3403i	0.793473	+	0.793473i	0.982057	−	0.188584i	$-0.0603899\pi$
$941$	24.3403	+	24.3403i	0.793473	+	0.793473i	−0.188584	+	0.982057i	$0.560390\pi$
$942$	−13.4500	+	10.4026i	−0.438224	+	0.338936i
$943$	−11.1790			−0.364038
$944$	−22.4446	+	6.38414i	−0.730510	+	0.207786i
$945$	−2.94060			−0.0956576
$946$	−21.5026	+	16.6308i	−0.699110	+	0.540713i
$947$	−11.3631	−	11.3631i	−0.369252	−	0.369252i	0.497952	−	0.867205i	$-0.334086\pi$
$947$	−11.3631	−	11.3631i	−0.369252	−	0.369252i	−0.867205	+	0.497952i	$0.834086\pi$
$948$	−22.5402	+	13.2449i	−0.732073	+	0.430173i
$949$	−9.62576	+	9.62576i	−0.312465	+	0.312465i
$950$	7.01067	+	0.895667i	0.227456	+	0.0290593i
$951$			69.6069i			2.25716i
$952$	−6.19265	−	14.4776i	−0.200705	−	0.469221i
$953$			54.5467i			1.76694i	0.468486	+	0.883471i	$0.344800\pi$
$953$			54.5467i			1.76694i	−0.468486	+	0.883471i	$0.655200\pi$
$954$	1.65209	−	12.9314i	0.0534883	−	0.418670i
$955$	4.94645	−	4.94645i	0.160064	−	0.160064i
$956$	−2.53435	+	9.75671i	−0.0819669	+	0.315554i
$957$	−17.3560	−	17.3560i	−0.561041	−	0.561041i
$958$	1.90204	+	2.45922i	0.0614521	+	0.0794539i
$959$	−10.8424			−0.350121
$960$	−11.8943	+	12.4539i	−0.383886	+	0.401949i
$961$	18.3056			0.590504
$962$	13.6297	+	17.6223i	0.439438	+	0.568167i
$963$	−18.2103	−	18.2103i	−0.586818	−	0.586818i
$964$	0.0375605	−	0.144600i	0.00120974	−	0.00465725i
$965$	−7.54160	+	7.54160i	−0.242773	+	0.242773i
$966$	2.94680	−	23.0655i	0.0948116	−	0.742121i
$967$		−	33.2063i		−	1.06784i	−0.845534	−	0.533921i	$-0.820718\pi$
$967$		−	33.2063i		−	1.06784i	0.845534	−	0.533921i	$-0.179282\pi$
$968$	−8.97409	−	20.9802i	−0.288438	−	0.674329i
$969$		−	59.8926i		−	1.92403i
$970$	−3.93373	−	0.502565i	−0.126305	−	0.0161364i
$971$	−6.45882	+	6.45882i	−0.207273	+	0.207273i	−0.803107	−	0.595834i	$-0.796822\pi$
$971$	−6.45882	+	6.45882i	−0.207273	+	0.207273i	0.595834	+	0.803107i	$0.296822\pi$
$972$	26.4808	−	15.5604i	0.849373	−	0.499100i
$973$	4.60654	+	4.60654i	0.147679	+	0.147679i
$974$	28.9166	−	22.3650i	0.926548	−	0.716621i
$975$	−10.3852			−0.332593
$976$	−8.79044	−	30.9044i	−0.281375	−	0.989226i
$977$	−62.4423			−1.99770			−0.998852	−	0.0478963i	$-0.984748\pi$
$977$	−62.4423			−1.99770			−0.998852	+	0.0478963i	$0.984748\pi$
$978$	45.0865	−	34.8713i	1.44171	−	1.11506i
$979$	−9.55146	−	9.55146i	−0.305266	−	0.305266i
$980$	−1.01324	−	1.72434i	−0.0323667	−	0.0550820i
$981$	23.8307	−	23.8307i	0.760857	−	0.760857i
$982$	−19.7962	−	2.52911i	−0.631721	−	0.0807071i
$983$			60.0138i			1.91414i	0.289852	+	0.957071i	$0.406394\pi$
$983$			60.0138i			1.91414i	−0.289852	+	0.957071i	$0.593606\pi$
$984$	3.31535	−	8.27155i	0.105690	−	0.263687i
$985$		−	22.5806i		−	0.719478i
$986$	−6.64365	+	52.0020i	−0.211577	+	1.65608i
$987$	−5.17292	+	5.17292i	−0.164656	+	0.164656i
$988$	−46.6714	−	12.1231i	−1.48481	−	0.385688i
$989$	60.6260	+	60.6260i	1.92780	+	1.92780i
$990$	2.42087	+	3.13004i	0.0769403	+	0.0994792i
$991$	−34.9566			−1.11043			−0.555217	−	0.831706i	$-0.687365\pi$
$991$	−34.9566			−1.11043			−0.555217	+	0.831706i	$0.687365\pi$
$992$	−5.93790	−	39.2749i	−0.188529	−	1.24698i
$993$	47.4009			1.50422
$994$	−0.680325	−	0.879620i	−0.0215786	−	0.0278999i
$995$	−3.22820	−	3.22820i	−0.102341	−	0.102341i
$996$	−56.6396	−	14.7124i	−1.79470	−	0.466181i
$997$	37.3956	−	37.3956i	1.18433	−	1.18433i	0.205720	−	0.978611i	$-0.434047\pi$
$997$	37.3956	−	37.3956i	1.18433	−	1.18433i	0.978611	−	0.205720i	$-0.0659535\pi$
$998$	0.613039	−	4.79845i	0.0194054	−	0.151892i
$999$			9.60196i			0.303793i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.bd.b.141.19	✓	52
4.3	odd	2		2240.2.bd.b.1681.21		52
16.5	even	4	inner	560.2.bd.b.421.19	yes	52
16.11	odd	4		2240.2.bd.b.561.21		52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.bd.b.141.19	✓	52	1.1	even	1	trivial
560.2.bd.b.421.19	yes	52	16.5	even	4	inner
2240.2.bd.b.561.21		52	16.11	odd	4
2240.2.bd.b.1681.21		52	4.3	odd	2

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.bd (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.865210 + 1.11867i) q^{2} +(-1.52217 - 1.52217i) q^{3} +(-0.502824 + 1.93576i) q^{4} +(0.707107 - 0.707107i) q^{5} +(0.385801 - 3.01979i) q^{6} +1.00000i q^{7} +(-2.60052 + 1.11235i) q^{8} +1.63398i q^{9} +O(q^{10})\)	\(q+(0.865210 + 1.11867i) q^{2} +(-1.52217 - 1.52217i) q^{3} +(-0.502824 + 1.93576i) q^{4} +(0.707107 - 0.707107i) q^{5} +(0.385801 - 3.01979i) q^{6} +1.00000i q^{7} +(-2.60052 + 1.11235i) q^{8} +1.63398i q^{9} +(1.40281 + 0.179220i) q^{10} +(1.21085 - 1.21085i) q^{11} +(3.71193 - 2.18117i) q^{12} +(3.41133 + 3.41133i) q^{13} +(-1.11867 + 0.865210i) q^{14} -2.15267 q^{15} +(-3.49434 - 1.94669i) q^{16} +5.56719 q^{17} +(-1.82787 + 1.41373i) q^{18} +(3.53383 + 3.53383i) q^{19} +(1.01324 + 1.72434i) q^{20} +(1.52217 - 1.52217i) q^{21} +(2.40217 + 0.306895i) q^{22} -7.63813i q^{23} +(5.65159 + 2.26524i) q^{24} -1.00000i q^{25} +(-0.864619 + 6.76765i) q^{26} +(-2.07931 + 2.07931i) q^{27} +(-1.93576 - 0.502824i) q^{28} +(4.70836 + 4.70836i) q^{29} +(-1.86251 - 2.40811i) q^{30} +7.02180 q^{31} +(-0.845639 - 5.59329i) q^{32} -3.68622 q^{33} +(4.81679 + 6.22782i) q^{34} +(0.707107 + 0.707107i) q^{35} +(-3.16299 - 0.821602i) q^{36} +(2.30892 - 2.30892i) q^{37} +(-0.895667 + 7.01067i) q^{38} -10.3852i q^{39} +(-1.05229 + 2.62539i) q^{40} -1.46358i q^{41} +(3.01979 + 0.385801i) q^{42} +(-7.93729 + 7.93729i) q^{43} +(1.73507 + 2.95275i) q^{44} +(1.15540 + 1.15540i) q^{45} +(8.54451 - 6.60859i) q^{46} -3.39840 q^{47} +(2.35577 + 8.28215i) q^{48} -1.00000 q^{49} +(1.11867 - 0.865210i) q^{50} +(-8.47418 - 8.47418i) q^{51} +(-8.31881 + 4.88822i) q^{52} +(-3.98920 + 3.98920i) q^{53} +(-4.12510 - 0.527013i) q^{54} -1.71240i q^{55} +(-1.11235 - 2.60052i) q^{56} -10.7581i q^{57} +(-1.19336 + 9.34080i) q^{58} +(4.12507 - 4.12507i) q^{59} +(1.08241 - 4.16705i) q^{60} +(5.67988 + 5.67988i) q^{61} +(6.07533 + 7.85504i) q^{62} -1.63398 q^{63} +(5.52536 - 5.78536i) q^{64} +4.82435 q^{65} +(-3.18935 - 4.12364i) q^{66} +(-5.68559 - 5.68559i) q^{67} +(-2.79931 + 10.7767i) q^{68} +(-11.6265 + 11.6265i) q^{69} +(-0.179220 + 1.40281i) q^{70} +0.786312i q^{71} +(-1.81755 - 4.24918i) q^{72} +2.82170i q^{73} +(4.58062 + 0.585209i) q^{74} +(-1.52217 + 1.52217i) q^{75} +(-8.61753 + 5.06375i) q^{76} +(1.21085 + 1.21085i) q^{77} +(11.6176 - 8.98539i) q^{78} -6.07238 q^{79} +(-3.84739 + 1.09435i) q^{80} +11.2321 q^{81} +(1.63725 - 1.26630i) q^{82} +(-9.61118 - 9.61118i) q^{83} +(2.18117 + 3.71193i) q^{84} +(3.93660 - 3.93660i) q^{85} +(-15.7466 - 2.01175i) q^{86} -14.3338i q^{87} +(-1.80194 + 4.49571i) q^{88} -7.88825i q^{89} +(-0.292841 + 2.29216i) q^{90} +(-3.41133 + 3.41133i) q^{91} +(14.7856 + 3.84063i) q^{92} +(-10.6883 - 10.6883i) q^{93} +(-2.94033 - 3.80167i) q^{94} +4.99759 q^{95} +(-7.22671 + 9.80112i) q^{96} -2.80418 q^{97} +(-0.865210 - 1.11867i) q^{98} +(1.97849 + 1.97849i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q - 8 q^{4} + 12 q^{6}+O(q^{10}) \) 52 * q - 8 * q^4 + 12 * q^6	\( 52 q - 8 q^{4} + 12 q^{6} - 4 q^{10} - 4 q^{11} + 40 q^{12} + 8 q^{15} - 4 q^{16} + 8 q^{19} + 32 q^{22} + 12 q^{24} - 12 q^{26} - 24 q^{27} + 4 q^{28} + 4 q^{29} - 16 q^{34} + 4 q^{36} - 12 q^{37} + 16 q^{38} - 4 q^{42} + 36 q^{43} + 28 q^{44} - 16 q^{46} + 32 q^{48} - 52 q^{49} - 8 q^{51} - 80 q^{52} - 4 q^{53} + 48 q^{54} - 12 q^{56} - 56 q^{58} + 24 q^{59} - 16 q^{61} - 72 q^{62} - 68 q^{63} + 4 q^{64} + 40 q^{65} - 12 q^{66} - 12 q^{67} - 72 q^{69} - 8 q^{72} + 68 q^{74} - 4 q^{77} - 4 q^{78} - 16 q^{79} - 32 q^{80} - 116 q^{81} + 104 q^{82} + 16 q^{85} - 68 q^{86} - 48 q^{88} + 36 q^{90} + 64 q^{92} + 8 q^{93} - 72 q^{94} - 32 q^{95} - 52 q^{99}+O(q^{100}) \) 52 * q - 8 * q^4 + 12 * q^6 - 4 * q^10 - 4 * q^11 + 40 * q^12 + 8 * q^15 - 4 * q^16 + 8 * q^19 + 32 * q^22 + 12 * q^24 - 12 * q^26 - 24 * q^27 + 4 * q^28 + 4 * q^29 - 16 * q^34 + 4 * q^36 - 12 * q^37 + 16 * q^38 - 4 * q^42 + 36 * q^43 + 28 * q^44 - 16 * q^46 + 32 * q^48 - 52 * q^49 - 8 * q^51 - 80 * q^52 - 4 * q^53 + 48 * q^54 - 12 * q^56 - 56 * q^58 + 24 * q^59 - 16 * q^61 - 72 * q^62 - 68 * q^63 + 4 * q^64 + 40 * q^65 - 12 * q^66 - 12 * q^67 - 72 * q^69 - 8 * q^72 + 68 * q^74 - 4 * q^77 - 4 * q^78 - 16 * q^79 - 32 * q^80 - 116 * q^81 + 104 * q^82 + 16 * q^85 - 68 * q^86 - 48 * q^88 + 36 * q^90 + 64 * q^92 + 8 * q^93 - 72 * q^94 - 32 * q^95 - 52 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more