LMFDB - Embedded newform 547.2.c.a.40.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [547,2,Mod(40,547)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(547, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("547.40");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 547 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	547.c (of order $3$, 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:	$4.36781699056$
Analytic rank:	$0$
Dimension:	$90$
Relative dimension:	$45$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			40.7
Character	$\chi$	$=$	547.40
Dual form			547.2.c.a.506.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.983266 - 1.70307i) q^{2} -1.20089 q^{3} +(-0.933624 + 1.61708i) q^{4} +(-1.27061 + 2.20077i) q^{5} +(1.18080 + 2.04520i) q^{6} +(-0.342982 - 0.594062i) q^{7} -0.261060 q^{8} -1.55785 q^{9} +O(q^{10})$	\(q+(-0.983266 - 1.70307i) q^{2} -1.20089 q^{3} +(-0.933624 + 1.61708i) q^{4} +(-1.27061 + 2.20077i) q^{5} +(1.18080 + 2.04520i) q^{6} +(-0.342982 - 0.594062i) q^{7} -0.261060 q^{8} -1.55785 q^{9} +4.99741 q^{10} +(-0.869533 - 1.50608i) q^{11} +(1.12118 - 1.94195i) q^{12} +(1.79380 + 3.10695i) q^{13} +(-0.674484 + 1.16824i) q^{14} +(1.52587 - 2.64289i) q^{15} +(2.12394 + 3.67877i) q^{16} +(-0.0150927 - 0.0261412i) q^{17} +(1.53178 + 2.65312i) q^{18} +(1.79208 - 3.10397i) q^{19} +(-2.37255 - 4.10938i) q^{20} +(0.411885 + 0.713405i) q^{21} +(-1.70996 + 2.96175i) q^{22} +(4.51119 - 7.81362i) q^{23} +0.313506 q^{24} +(-0.728924 - 1.26253i) q^{25} +(3.52757 - 6.10993i) q^{26} +5.47350 q^{27} +1.28086 q^{28} +9.75461 q^{29} -6.00136 q^{30} -3.54692 q^{31} +(3.91574 - 6.78225i) q^{32} +(1.04422 + 1.80864i) q^{33} +(-0.0296802 + 0.0514076i) q^{34} +1.74319 q^{35} +(1.45445 - 2.51918i) q^{36} +(5.14178 + 8.90582i) q^{37} -7.04836 q^{38} +(-2.15417 - 3.73113i) q^{39} +(0.331707 - 0.574533i) q^{40} +(-4.04255 - 7.00190i) q^{41} +(0.809985 - 1.40293i) q^{42} +(-1.04743 - 1.81421i) q^{43} +3.24727 q^{44} +(1.97943 - 3.42847i) q^{45} -17.7428 q^{46} +(-5.48037 + 9.49228i) q^{47} +(-2.55063 - 4.41782i) q^{48} +(3.26473 - 5.65467i) q^{49} +(-1.43345 + 2.48281i) q^{50} +(0.0181247 + 0.0313929i) q^{51} -6.69894 q^{52} +(0.639523 + 1.10769i) q^{53} +(-5.38191 - 9.32174i) q^{54} +4.41937 q^{55} +(0.0895388 + 0.155086i) q^{56} +(-2.15210 + 3.72754i) q^{57} +(-9.59138 - 16.6127i) q^{58} +(-5.51777 - 9.55706i) q^{59} +(2.84919 + 4.93494i) q^{60} +(3.63290 + 6.29237i) q^{61} +(3.48757 + 6.04065i) q^{62} +(0.534314 + 0.925460i) q^{63} -6.90508 q^{64} -9.11692 q^{65} +(2.05349 - 3.55675i) q^{66} +(3.59933 + 6.23421i) q^{67} +0.0563635 q^{68} +(-5.41747 + 9.38333i) q^{69} +(-1.71402 - 2.96877i) q^{70} +(0.199898 + 0.346233i) q^{71} +0.406693 q^{72} +(1.09182 + 1.89109i) q^{73} +(10.1115 - 17.5136i) q^{74} +(0.875362 + 1.51617i) q^{75} +(3.34626 + 5.79588i) q^{76} +(-0.596468 + 1.03311i) q^{77} +(-4.23624 + 7.33738i) q^{78} +16.4881 q^{79} -10.7948 q^{80} -1.89954 q^{81} +(-7.94981 + 13.7695i) q^{82} +(-0.159196 - 0.275735i) q^{83} -1.53818 q^{84} +0.0767078 q^{85} +(-2.05981 + 3.56770i) q^{86} -11.7143 q^{87} +(0.227000 + 0.393176i) q^{88} -0.629391 q^{89} -7.78522 q^{90} +(1.23048 - 2.13126i) q^{91} +(8.42352 + 14.5900i) q^{92} +4.25948 q^{93} +21.5546 q^{94} +(4.55408 + 7.88790i) q^{95} +(-4.70239 + 8.14477i) q^{96} +(8.05265 - 13.9476i) q^{97} -12.8404 q^{98} +(1.35460 + 2.34624i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 90 q - q^{2} - 4 q^{3} - 47 q^{4} + q^{5} - 3 q^{6} + 2 q^{7} - 30 q^{8} + 82 q^{9}+O(q^{10}) $ 90 * q - q^2 - 4 * q^3 - 47 * q^4 + q^5 - 3 * q^6 + 2 * q^7 - 30 * q^8 + 82 * q^9	\( 90 q - q^{2} - 4 q^{3} - 47 q^{4} + q^{5} - 3 q^{6} + 2 q^{7} - 30 q^{8} + 82 q^{9} - 10 q^{10} + q^{11} + 4 q^{12} - 3 q^{13} + 2 q^{14} - 7 q^{15} - 39 q^{16} - 4 q^{17} - 11 q^{18} - 2 q^{19} + 25 q^{20} - 27 q^{21} - 7 q^{22} + q^{23} + 32 q^{24} - 40 q^{25} - 10 q^{26} - 34 q^{27} - 28 q^{28} + 26 q^{29} - 40 q^{30} - 24 q^{31} + 19 q^{32} + q^{33} - 6 q^{34} - 8 q^{35} - 36 q^{36} - 10 q^{37} + 24 q^{38} + 22 q^{39} + 20 q^{40} + 3 q^{41} + 38 q^{42} - 12 q^{43} - 30 q^{44} - 2 q^{45} - 40 q^{46} + 32 q^{47} + 14 q^{48} - 43 q^{49} + 14 q^{50} + 13 q^{51} + 46 q^{52} + 9 q^{53} - 8 q^{54} + 4 q^{55} - 8 q^{56} - 8 q^{57} + 4 q^{58} + 22 q^{59} - 2 q^{60} - 12 q^{61} + 11 q^{62} + 8 q^{63} + 22 q^{64} + 18 q^{65} + 12 q^{66} - 22 q^{67} + 6 q^{68} - q^{69} - 6 q^{70} - 4 q^{71} - 140 q^{72} + 17 q^{73} + 17 q^{74} + 39 q^{75} + 84 q^{76} - 4 q^{77} + 33 q^{78} - 72 q^{79} - 40 q^{80} + 18 q^{81} - 9 q^{82} + 24 q^{83} + 114 q^{84} + 40 q^{85} - 72 q^{86} - 78 q^{87} - 22 q^{88} + 14 q^{89} + 96 q^{90} - 8 q^{92} - 76 q^{93} + 108 q^{94} - 11 q^{95} - 34 q^{96} - 74 q^{98} - 62 q^{99}+O(q^{100}) \) 90 * q - q^2 - 4 * q^3 - 47 * q^4 + q^5 - 3 * q^6 + 2 * q^7 - 30 * q^8 + 82 * q^9 - 10 * q^10 + q^11 + 4 * q^12 - 3 * q^13 + 2 * q^14 - 7 * q^15 - 39 * q^16 - 4 * q^17 - 11 * q^18 - 2 * q^19 + 25 * q^20 - 27 * q^21 - 7 * q^22 + q^23 + 32 * q^24 - 40 * q^25 - 10 * q^26 - 34 * q^27 - 28 * q^28 + 26 * q^29 - 40 * q^30 - 24 * q^31 + 19 * q^32 + q^33 - 6 * q^34 - 8 * q^35 - 36 * q^36 - 10 * q^37 + 24 * q^38 + 22 * q^39 + 20 * q^40 + 3 * q^41 + 38 * q^42 - 12 * q^43 - 30 * q^44 - 2 * q^45 - 40 * q^46 + 32 * q^47 + 14 * q^48 - 43 * q^49 + 14 * q^50 + 13 * q^51 + 46 * q^52 + 9 * q^53 - 8 * q^54 + 4 * q^55 - 8 * q^56 - 8 * q^57 + 4 * q^58 + 22 * q^59 - 2 * q^60 - 12 * q^61 + 11 * q^62 + 8 * q^63 + 22 * q^64 + 18 * q^65 + 12 * q^66 - 22 * q^67 + 6 * q^68 - q^69 - 6 * q^70 - 4 * q^71 - 140 * q^72 + 17 * q^73 + 17 * q^74 + 39 * q^75 + 84 * q^76 - 4 * q^77 + 33 * q^78 - 72 * q^79 - 40 * q^80 + 18 * q^81 - 9 * q^82 + 24 * q^83 + 114 * q^84 + 40 * q^85 - 72 * q^86 - 78 * q^87 - 22 * q^88 + 14 * q^89 + 96 * q^90 - 8 * q^92 - 76 * q^93 + 108 * q^94 - 11 * q^95 - 34 * q^96 - 74 * q^98 - 62 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/547\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.983266	−	1.70307i	−0.695274	−	1.20425i	−0.970088	−	0.242753i	$-0.921950\pi$
$2$	−0.983266	−	1.70307i	−0.695274	−	1.20425i	0.274814	−	0.961497i	$-0.411384\pi$
$3$	−1.20089			−0.693337			−0.346668	−	0.937988i	$-0.612687\pi$
$3$	−1.20089			−0.693337			−0.346668	+	0.937988i	$0.612687\pi$
$4$	−0.933624	+	1.61708i	−0.466812	+	0.808542i
$5$	−1.27061	+	2.20077i	−0.568236	+	0.984214i	0.428504	+	0.903540i	$0.359041\pi$
$5$	−1.27061	+	2.20077i	−0.568236	+	0.984214i	−0.996741	+	0.0806743i	$0.974293\pi$
$6$	1.18080	+	2.04520i	0.482059	+	0.834951i
$7$	−0.342982	−	0.594062i	−0.129635	−	0.224534i	0.793900	−	0.608048i	$-0.208047\pi$
$7$	−0.342982	−	0.594062i	−0.129635	−	0.224534i	−0.923535	+	0.383514i	$0.874714\pi$
$8$	−0.261060			−0.0922987
$9$	−1.55785			−0.519284
$10$	4.99741			1.58032
$11$	−0.869533	−	1.50608i	−0.262174	−	0.454099i	0.704645	−	0.709560i	$-0.251106\pi$
$11$	−0.869533	−	1.50608i	−0.262174	−	0.454099i	−0.966819	+	0.255461i	$0.917773\pi$
$12$	1.12118	−	1.94195i	0.323658	−	0.560592i
$13$	1.79380	+	3.10695i	0.497511	+	0.861714i	0.999996	−	0.00287183i	$-0.000914133\pi$
$13$	1.79380	+	3.10695i	0.497511	+	0.861714i	−0.502485	+	0.864586i	$0.667581\pi$
$14$	−0.674484	+	1.16824i	−0.180264	+	0.312226i
$15$	1.52587	−	2.64289i	0.393979	−	0.682392i
$16$	2.12394	+	3.67877i	0.530985	+	0.919693i
$17$	−0.0150927	−	0.0261412i	−0.00366051	−	0.00634018i	0.864189	−	0.503167i	$-0.167832\pi$
$17$	−0.0150927	−	0.0261412i	−0.00366051	−	0.00634018i	−0.867850	+	0.496827i	$0.834499\pi$
$18$	1.53178	+	2.65312i	0.361045	+	0.625348i
$19$	1.79208	−	3.10397i	0.411131	−	0.712100i	−0.583883	−	0.811838i	$-0.698467\pi$
$19$	1.79208	−	3.10397i	0.411131	−	0.712100i	0.995014	+	0.0997383i	$0.0318006\pi$
$20$	−2.37255	−	4.10938i	−0.530519	−	0.918886i
$21$	0.411885	+	0.713405i	0.0898806	+	0.155678i
$22$	−1.70996	+	2.96175i	−0.364566	+	0.631446i
$23$	4.51119	−	7.81362i	0.940649	−	1.62925i	0.176411	−	0.984317i	$-0.443551\pi$
$23$	4.51119	−	7.81362i	0.940649	−	1.62925i	0.764237	−	0.644935i	$-0.223116\pi$
$24$	0.313506			0.0639941
$25$	−0.728924	−	1.26253i	−0.145785	−	0.252507i
$26$	3.52757	−	6.10993i	0.691813	−	1.19825i
$27$	5.47350			1.05338
$28$	1.28086			0.242060
$29$	9.75461			1.81139			0.905693	−	0.423935i	$-0.139351\pi$
$29$	9.75461			1.81139			0.905693	+	0.423935i	$0.139351\pi$
$30$	−6.00136			−1.09569
$31$	−3.54692			−0.637046			−0.318523	−	0.947915i	$-0.603187\pi$
$31$	−3.54692			−0.637046			−0.318523	+	0.947915i	$0.603187\pi$
$32$	3.91574	−	6.78225i	0.692211	−	1.19894i
$33$	1.04422	+	1.80864i	0.181775	+	0.314844i
$34$	−0.0296802	+	0.0514076i	−0.00509011	+	0.00881633i
$35$	1.74319			0.294653
$36$	1.45445	−	2.51918i	0.242408	−	0.419863i
$37$	5.14178	+	8.90582i	0.845303	+	1.46411i	0.885358	+	0.464910i	$0.153913\pi$
$37$	5.14178	+	8.90582i	0.845303	+	1.46411i	−0.0400550	+	0.999197i	$0.512753\pi$
$38$	−7.04836			−1.14339
$39$	−2.15417	−	3.73113i	−0.344943	−	0.597458i
$40$	0.331707	−	0.574533i	0.0524474	−	0.0908416i
$41$	−4.04255	−	7.00190i	−0.631340	−	1.09351i	−0.987278	−	0.159004i	$-0.949172\pi$
$41$	−4.04255	−	7.00190i	−0.631340	−	1.09351i	0.355938	−	0.934510i	$-0.384162\pi$
$42$	0.809985	−	1.40293i	0.124983	−	0.216478i
$43$	−1.04743	−	1.81421i	−0.159732	−	0.276664i	0.775040	−	0.631912i	$-0.217730\pi$
$43$	−1.04743	−	1.81421i	−0.159732	−	0.276664i	−0.934772	+	0.355248i	$0.884396\pi$
$44$	3.24727			0.489544
$45$	1.97943	−	3.42847i	0.295076	−	0.511086i
$46$	−17.7428			−2.61603
$47$	−5.48037	+	9.49228i	−0.799394	+	1.38459i	0.120617	+	0.992699i	$0.461513\pi$
$47$	−5.48037	+	9.49228i	−0.799394	+	1.38459i	−0.920011	+	0.391892i	$0.871821\pi$
$48$	−2.55063	−	4.41782i	−0.368152	−	0.637657i
$49$	3.26473	−	5.65467i	0.466390	−	0.807811i
$50$	−1.43345	+	2.48281i	−0.202721	+	0.351123i
$51$	0.0181247	+	0.0313929i	0.00253796	+	0.00439588i
$52$	−6.69894			−0.928976
$53$	0.639523	+	1.10769i	0.0878453	+	0.152153i	0.906600	−	0.421991i	$-0.138669\pi$
$53$	0.639523	+	1.10769i	0.0878453	+	0.152153i	−0.818755	+	0.574143i	$0.805335\pi$
$54$	−5.38191	−	9.32174i	−0.732385	−	1.26853i
$55$	4.41937			0.595907
$56$	0.0895388	+	0.155086i	0.0119651	+	0.0207242i
$57$	−2.15210	+	3.72754i	−0.285052	+	0.493725i
$58$	−9.59138	−	16.6127i	−1.25941	−	2.18136i
$59$	−5.51777	−	9.55706i	−0.718353	−	1.24422i	−0.961652	−	0.274272i	$-0.911563\pi$
$59$	−5.51777	−	9.55706i	−0.718353	−	1.24422i	0.243300	−	0.969951i	$-0.421770\pi$
$60$	2.84919	+	4.93494i	0.367829	+	0.637098i
$61$	3.63290	+	6.29237i	0.465145	+	0.805655i	0.999208	−	0.0397898i	$-0.0126688\pi$
$61$	3.63290	+	6.29237i	0.465145	+	0.805655i	−0.534063	+	0.845445i	$0.679336\pi$
$62$	3.48757	+	6.04065i	0.442922	+	0.767163i
$63$	0.534314	+	0.925460i	0.0673173	+	0.116597i
$64$	−6.90508			−0.863135
$65$	−9.11692			−1.13081
$66$	2.05349	−	3.55675i	0.252767	−	0.437805i
$67$	3.59933	+	6.23421i	0.439728	+	0.761631i	0.997668	−	0.0682503i	$-0.0217416\pi$
$67$	3.59933	+	6.23421i	0.439728	+	0.761631i	−0.557941	+	0.829881i	$0.688408\pi$
$68$	0.0563635			0.00683507
$69$	−5.41747	+	9.38333i	−0.652187	+	1.12962i
$70$	−1.71402	−	2.96877i	−0.204865	−	0.354836i
$71$	0.199898	+	0.346233i	0.0237235	+	0.0410903i	0.877643	−	0.479314i	$-0.159115\pi$
$71$	0.199898	+	0.346233i	0.0237235	+	0.0410903i	−0.853920	+	0.520404i	$0.825781\pi$
$72$	0.406693			0.0479292
$73$	1.09182	+	1.89109i	0.127788	+	0.221335i	0.922819	−	0.385233i	$-0.125879\pi$
$73$	1.09182	+	1.89109i	0.127788	+	0.221335i	−0.795031	+	0.606568i	$0.792546\pi$
$74$	10.1115	−	17.5136i	1.17543	−	2.03591i
$75$	0.875362	+	1.51617i	0.101078	+	0.175072i
$76$	3.34626	+	5.79588i	0.383842	+	0.664834i
$77$	−0.596468	+	1.03311i	−0.0679738	+	0.117734i
$78$	−4.23624	+	7.33738i	−0.479659	+	0.830794i
$79$	16.4881			1.85505			0.927526	−	0.373758i	$-0.121931\pi$
$79$	16.4881			1.85505			0.927526	+	0.373758i	$0.121931\pi$
$80$	−10.7948			−1.20690
$81$	−1.89954			−0.211061
$82$	−7.94981	+	13.7695i	−0.877909	+	1.52058i
$83$	−0.159196	−	0.275735i	−0.0174740	−	0.0302658i	0.857156	−	0.515057i	$-0.172229\pi$
$83$	−0.159196	−	0.275735i	−0.0174740	−	0.0302658i	−0.874630	+	0.484791i	$0.838896\pi$
$84$	−1.53818			−0.167829
$85$	0.0767078			0.00832013
$86$	−2.05981	+	3.56770i	−0.222115	+	0.384715i
$87$	−11.7143			−1.25590
$88$	0.227000	+	0.393176i	0.0241983	+	0.0419127i
$89$	−0.629391			−0.0667153			−0.0333576	−	0.999443i	$-0.510620\pi$
$89$	−0.629391			−0.0667153			−0.0333576	+	0.999443i	$0.510620\pi$
$90$	−7.78522			−0.820634
$91$	1.23048	−	2.13126i	0.128989	−	0.223416i
$92$	8.42352	+	14.5900i	0.878213	+	1.52111i
$93$	4.25948			0.441688
$94$	21.5546			2.22319
$95$	4.55408	+	7.88790i	0.467239	+	0.809282i
$96$	−4.70239	+	8.14477i	−0.479935	+	0.831273i
$97$	8.05265	−	13.9476i	0.817623	−	1.41616i	−0.0898066	−	0.995959i	$-0.528625\pi$
$97$	8.05265	−	13.9476i	0.817623	−	1.41616i	0.907429	−	0.420205i	$-0.138042\pi$
$98$	−12.8404			−1.29707
$99$	1.35460	+	2.34624i	0.136143	+	0.235806i
$100$	2.72217			0.272217
$101$	−8.48256			−0.844046			−0.422023	−	0.906585i	$-0.638680\pi$
$101$	−8.48256			−0.844046			−0.422023	+	0.906585i	$0.638680\pi$
$102$	0.0356428	−	0.0617351i	0.00352916	−	0.00611269i
$103$	17.5975			1.73393			0.866967	−	0.498366i	$-0.166066\pi$
$103$	17.5975			1.73393			0.866967	+	0.498366i	$0.166066\pi$
$104$	−0.468290	−	0.811102i	−0.0459196	−	0.0795351i
$105$	−2.09339			−0.204294
$106$	1.25764	−	2.17830i	0.122153	−	0.211575i
$107$	12.8906			1.24618			0.623092	−	0.782149i	$-0.285876\pi$
$107$	12.8906			1.24618			0.623092	+	0.782149i	$0.285876\pi$
$108$	−5.11019	+	8.85111i	−0.491729	+	0.851699i
$109$	−2.70618	+	4.68724i	−0.259205	+	0.448956i	−0.966029	−	0.258433i	$-0.916794\pi$
$109$	−2.70618	+	4.68724i	−0.259205	+	0.448956i	0.706824	+	0.707389i	$0.250127\pi$
$110$	−4.34541	−	7.52648i	−0.414319	−	0.717621i
$111$	−6.17473	−	10.6950i	−0.586080	−	1.01512i
$112$	1.45694	−	2.52350i	0.137668	−	0.238449i
$113$	−6.57994	+	11.3968i	−0.618989	+	1.07212i	0.370682	+	0.928760i	$0.379124\pi$
$113$	−6.57994	+	11.3968i	−0.618989	+	1.07212i	−0.989671	+	0.143360i	$0.954209\pi$
$114$	8.46434			0.792758
$115$	11.4640	+	19.8562i	1.06902	+	1.85160i
$116$	−9.10714	+	15.7740i	−0.845577	+	1.46458i
$117$	−2.79448	−	4.84017i	−0.258349	−	0.447474i
$118$	−10.8509	+	18.7943i	−0.998904	+	1.73015i
$119$	−0.0103530	+	0.0179319i	−0.000949058	+	0.00164382i
$120$	−0.398345	+	0.689954i	−0.0363638	+	0.0629839i
$121$	3.98782	−	6.90711i	0.362529	−	0.627919i
$122$	7.14421	−	12.3741i	0.646807	−	1.12030i
$123$	4.85468	+	8.40855i	0.437732	+	0.758173i
$124$	3.31149	−	5.73567i	0.297381	−	0.515079i
$125$	−9.00142			−0.805111
$126$	1.05075	−	1.81995i	0.0936079	−	0.162134i
$127$	−3.66591	+	6.34954i	−0.325297	+	0.563431i	−0.981572	−	0.191090i	$-0.938798\pi$
$127$	−3.66591	+	6.34954i	−0.325297	+	0.563431i	0.656275	+	0.754521i	$0.272131\pi$
$128$	−1.04194	−	1.80469i	−0.0920953	−	0.159514i
$129$	1.25786	+	2.17867i	0.110748	+	0.191821i
$130$	8.96436	+	15.5267i	0.786226	+	1.36178i
$131$	15.5254			1.35646			0.678230	−	0.734850i	$-0.262747\pi$
$131$	15.5254			1.35646			0.678230	+	0.734850i	$0.262747\pi$
$132$	−3.89963			−0.339419
$133$	−2.45860			−0.213188
$134$	7.07819	−	12.2598i	0.611462	−	1.05908i
$135$	−6.95471	+	12.0459i	−0.598566	+	1.03675i
$136$	0.00394009	+	0.00682443i	0.000337860	+	0.000585190i
$137$	9.70584	+	16.8110i	0.829226	+	1.43626i	0.898646	+	0.438674i	$0.144552\pi$
$137$	9.70584	+	16.8110i	0.829226	+	1.43626i	−0.0694204	+	0.997587i	$0.522115\pi$
$138$	21.3073			1.81379
$139$	−5.19132	−	8.99164i	−0.440322	−	0.762661i	0.557391	−	0.830250i	$-0.311802\pi$
$139$	−5.19132	−	8.99164i	−0.440322	−	0.762661i	−0.997713	+	0.0675896i	$0.978469\pi$
$140$	−1.62748	+	2.81889i	−0.137548	+	0.238239i
$141$	6.58135	−	11.3992i	0.554249	−	0.959988i
$142$	0.393106	−	0.680879i	0.0329887	−	0.0571381i
$143$	3.11954	−	5.40320i	0.260869	−	0.451838i
$144$	−3.30878	−	5.73098i	−0.275732	−	0.477582i
$145$	−12.3944	+	21.4676i	−1.02929	+	1.78279i
$146$	2.14710	−	3.71889i	0.177695	−	0.307777i
$147$	−3.92059	+	6.79067i	−0.323365	+	0.560085i
$148$	−19.2020			−1.57839
$149$	3.72293			0.304994			0.152497	−	0.988304i	$-0.451269\pi$
$149$	3.72293			0.304994			0.152497	+	0.988304i	$0.451269\pi$
$150$	1.72143	−	2.98160i	0.140554	−	0.243447i
$151$	1.16395			0.0947206			0.0473603	−	0.998878i	$-0.484919\pi$
$151$	1.16395			0.0947206			0.0473603	+	0.998878i	$0.484919\pi$
$152$	−0.467840	+	0.810323i	−0.0379468	+	0.0657258i
$153$	0.0235121	+	0.0407242i	0.00190084	+	0.00329235i
$154$	2.34595			0.189042
$155$	4.50677	−	7.80596i	0.361993	−	0.626990i
$156$	8.04473			0.644094
$157$	−8.64830	−	14.9793i	−0.690209	−	1.19548i	−0.971769	−	0.235934i	$-0.924185\pi$
$157$	−8.64830	−	14.9793i	−0.690209	−	1.19548i	0.281560	−	0.959544i	$-0.409148\pi$
$158$	−16.2122	−	28.0803i	−1.28977	−	2.23395i
$159$	−0.768000	−	1.33022i	−0.0609064	−	0.105493i
$160$	9.95079	+	17.2353i	0.786679	+	1.36257i
$161$	−6.18902			−0.487763
$162$	1.86776	+	3.23505i	0.146745	+	0.254170i
$163$	−2.33110	−	4.03758i	−0.182585	−	0.316247i	0.760175	−	0.649719i	$-0.225113\pi$
$163$	−2.33110	−	4.03758i	−0.182585	−	0.316247i	−0.942760	+	0.333471i	$0.891780\pi$
$164$	15.0969			1.17887
$165$	−5.30720			−0.413165
$166$	−0.313063	+	0.542241i	−0.0242984	+	0.0420861i
$167$	−6.13300			−0.474586			−0.237293	−	0.971438i	$-0.576260\pi$
$167$	−6.13300			−0.474586			−0.237293	+	0.971438i	$0.576260\pi$
$168$	−0.107527	−	0.186242i	−0.00829586	−	0.0143689i
$169$	0.0645565	−	0.111815i	0.00496589	−	0.00860117i
$170$	−0.0754242	−	0.130638i	−0.00578477	−	0.0100195i
$171$	−2.79179	+	4.83553i	−0.213494	+	0.369782i
$172$	3.91164			0.298259
$173$	6.81248			0.517943			0.258972	−	0.965885i	$-0.416616\pi$
$173$	6.81248			0.517943			0.258972	+	0.965885i	$0.416616\pi$
$174$	11.5182	+	19.9502i	0.873195	+	1.51242i
$175$	−0.500015	+	0.866052i	−0.0377976	+	0.0654674i
$176$	3.69367	−	6.39763i	0.278421	−	0.482239i
$177$	6.62626	+	11.4770i	0.498060	+	0.862666i
$178$	0.618859	+	1.07189i	0.0463854	+	0.0803419i
$179$	0.229883			0.0171823			0.00859114	−	0.999963i	$-0.497265\pi$
$179$	0.229883			0.0171823			0.00859114	+	0.999963i	$0.497265\pi$
$180$	3.69609	+	6.40181i	0.275490	+	0.477163i
$181$	−9.15856	+	15.8631i	−0.680750	+	1.17909i	0.294002	+	0.955805i	$0.405013\pi$
$181$	−9.15856	+	15.8631i	−0.680750	+	1.17909i	−0.974752	+	0.223289i	$0.928321\pi$
$182$	−4.83956			−0.358732
$183$	−4.36273	−	7.55647i	−0.322502	−	0.558590i
$184$	−1.17769	+	2.03982i	−0.0868206	+	0.150378i
$185$	−26.1329			−1.92133
$186$	−4.18820	−	7.25418i	−0.307094	−	0.531902i
$187$	−0.0262471	+	0.0454613i	−0.00191938	+	0.00332446i
$188$	−10.2332	−	17.7244i	−0.746334	−	1.29269i
$189$	−1.87731	−	3.25160i	−0.136554	−	0.236519i
$190$	8.95575	−	15.5118i	0.649718	−	1.12535i
$191$	3.64625	−	6.31550i	0.263834	−	0.456973i	−0.703424	−	0.710771i	$-0.748346\pi$
$191$	3.64625	−	6.31550i	0.263834	−	0.456973i	0.967257	+	0.253797i	$0.0816797\pi$
$192$	8.29228			0.598444
$193$	−10.7608	+	18.6383i	−0.774580	+	1.34161i	0.160451	+	0.987044i	$0.448705\pi$
$193$	−10.7608	+	18.6383i	−0.774580	+	1.34161i	−0.935030	+	0.354568i	$0.884628\pi$
$194$	−31.6716			−2.27389
$195$	10.9485			0.784036
$196$	6.09606	+	10.5587i	0.435433	+	0.754191i
$197$	23.7199			1.68998			0.844988	−	0.534786i	$-0.179608\pi$
$197$	23.7199			1.68998			0.844988	+	0.534786i	$0.179608\pi$
$198$	2.66387	−	4.61396i	0.189313	−	0.327900i
$199$	−7.87874	+	13.6464i	−0.558509	+	0.967366i	0.439112	+	0.898432i	$0.355293\pi$
$199$	−7.87874	+	13.6464i	−0.558509	+	0.967366i	−0.997621	+	0.0689338i	$0.978040\pi$
$200$	0.190293	+	0.329597i	0.0134558	+	0.0233060i
$201$	−4.32241	−	7.48664i	−0.304879	−	0.528067i
$202$	8.34061	+	14.4464i	0.586843	+	1.01644i
$203$	−3.34565	−	5.79484i	−0.234819	−	0.406718i
$204$	−0.0676866			−0.00473901
$205$	20.5461			1.43500
$206$	−17.3030	−	29.9697i	−1.20556	−	2.08809i
$207$	−7.02777	+	12.1725i	−0.488464	+	0.846044i
$208$	−7.61985	+	13.1980i	−0.528342	+	0.915115i
$209$	−6.23309			−0.431152
$210$	2.05836	+	3.56518i	0.142040	+	0.246021i
$211$	8.35805	−	14.4766i	0.575392	−	0.996608i	−0.420607	−	0.907243i	$-0.638183\pi$
$211$	8.35805	−	14.4766i	0.575392	−	0.996608i	0.995999	−	0.0893649i	$-0.0284837\pi$
$212$	−2.38830			−0.164029
$213$	−0.240056	−	0.415790i	−0.0164484	−	0.0284894i
$214$	−12.6749	−	21.9536i	−0.866439	−	1.50072i
$215$	5.32354			0.363062
$216$	−1.42891			−0.0972252
$217$	1.21653	+	2.10709i	0.0825834	+	0.143039i
$218$	10.6436			0.720874
$219$	−1.31116	−	2.27100i	−0.0886001	−	0.153460i
$220$	−4.12603	+	7.14649i	−0.278177	+	0.481816i
$221$	0.0541464	−	0.0937844i	0.00364228	−	0.00630862i
$222$	−12.1428	+	21.0320i	−0.814972	+	1.41157i
$223$	−7.14730	+	12.3795i	−0.478619	+	0.828992i	−0.999699	−	0.0245157i	$-0.992196\pi$
$223$	−7.14730	+	12.3795i	−0.478619	+	0.828992i	0.521081	+	0.853507i	$0.325529\pi$
$224$	−5.37210			−0.358939
$225$	1.13556	+	1.96684i	0.0757037	+	0.131123i
$226$	25.8793			1.72147
$227$	1.42925	−	2.47553i	0.0948623	−	0.164306i	−0.814689	−	0.579898i	$-0.803092\pi$
$227$	1.42925	−	2.47553i	0.0948623	−	0.164306i	0.909551	+	0.415592i	$0.136426\pi$
$228$	−4.01850	−	6.96025i	−0.266132	−	0.460954i
$229$	12.5113	−	21.6701i	0.826767	−	1.43200i	−0.0737943	−	0.997273i	$-0.523511\pi$
$229$	12.5113	−	21.6701i	0.826767	−	1.43200i	0.900561	−	0.434729i	$-0.143156\pi$
$230$	22.5443	−	39.0478i	1.48653	−	2.57474i
$231$	0.716295	−	1.24066i	0.0471288	−	0.0816294i
$232$	−2.54654			−0.167188
$233$	5.53456	−	9.58615i	0.362581	−	0.628009i	−0.625804	−	0.779981i	$-0.715229\pi$
$233$	5.53456	−	9.58615i	0.362581	−	0.628009i	0.988385	+	0.151971i	$0.0485622\pi$
$234$	−5.49543	+	9.51836i	−0.359247	+	0.622234i
$235$	−13.9269	−	24.1221i	−0.908489	−	1.57355i
$236$	20.6061			1.34134
$237$	−19.8004			−1.28618
$238$	0.0407190			0.00263942
$239$	11.7340	+	20.3239i	0.759010	+	1.31464i	0.943356	+	0.331782i	$0.107650\pi$
$239$	11.7340	+	20.3239i	0.759010	+	1.31464i	−0.184346	+	0.982861i	$0.559017\pi$
$240$	12.9635			0.836788
$241$	5.76847	−	9.99128i	0.371580	−	0.643595i	−0.618229	−	0.785998i	$-0.712150\pi$
$241$	5.76847	−	9.99128i	0.371580	−	0.643595i	0.989809	+	0.142403i	$0.0454829\pi$
$242$	−15.6844			−1.00823
$243$	−14.1393			−0.907040
$244$	−13.5671			−0.868541
$245$	8.29642	+	14.3698i	0.530039	+	0.918054i
$246$	9.54688	−	16.5357i	0.608687	−	1.05428i
$247$	12.8585			0.818168
$248$	0.925960			0.0587985
$249$	0.191177	+	0.331129i	0.0121154	+	0.0209844i
$250$	8.85079	+	15.3300i	0.559773	+	0.969556i
$251$	−8.88813	−	15.3947i	−0.561014	−	0.971704i	−0.997408	−	0.0719489i	$-0.977078\pi$
$251$	−8.88813	−	15.3947i	−0.561014	−	0.971704i	0.436395	−	0.899755i	$-0.356255\pi$
$252$	−1.99540			−0.125698
$253$	−15.6905			−0.986455
$254$	14.4183			0.904682
$255$	−0.0921180			−0.00576865
$256$	−8.95409	+	15.5089i	−0.559631	+	0.969309i
$257$	−31.8971			−1.98969			−0.994844	−	0.101421i	$-0.967661\pi$
$257$	−31.8971			−1.98969			−0.994844	+	0.101421i	$0.967661\pi$
$258$	2.47362	−	4.28443i	0.154001	−	0.266737i
$259$	3.52707	−	6.10906i	0.219161	−	0.379599i
$260$	8.51178	−	14.7428i	0.527878	−	0.914312i
$261$	−15.1962			−0.940623
$262$	−15.2656	−	26.4408i	−0.943111	−	1.63352i
$263$	9.96379			0.614394			0.307197	−	0.951646i	$-0.400609\pi$
$263$	9.96379			0.614394			0.307197	+	0.951646i	$0.400609\pi$
$264$	−0.272604	−	0.472163i	−0.0167776	−	0.0290596i
$265$	−3.25035			−0.199668
$266$	2.41746	+	4.18716i	0.148224	+	0.256731i
$267$	0.755832			0.0462562
$268$	−13.4417			−0.821081
$269$	11.4401	−	19.8148i	0.697513	−	1.20813i	−0.271814	−	0.962350i	$-0.587623\pi$
$269$	11.4401	−	19.8148i	0.697513	−	1.20813i	0.969326	−	0.245777i	$-0.0790432\pi$
$270$	27.3533			1.66467
$271$	−5.81155	−	10.0659i	−0.353026	−	0.611460i	0.633752	−	0.773537i	$-0.281514\pi$
$271$	−5.81155	−	10.0659i	−0.353026	−	0.611460i	−0.986778	+	0.162077i	$0.948181\pi$
$272$	0.0641118	−	0.111045i	0.00388735	−	0.00673308i
$273$	−1.47768	+	2.55941i	−0.0894332	+	0.154903i
$274$	19.0868	−	33.0594i	1.15308	−	1.99719i
$275$	−1.26765	+	2.19563i	−0.0764421	+	0.132402i
$276$	−10.1158	−	17.5210i	−0.608897	−	1.05464i
$277$	5.64324			0.339069			0.169535	−	0.985524i	$-0.445774\pi$
$277$	5.64324			0.339069			0.169535	+	0.985524i	$0.445774\pi$
$278$	−10.2089	+	17.6823i	−0.612289	+	1.06052i
$279$	5.52558			0.330808
$280$	−0.455077			−0.0271961
$281$	−4.99769	−	8.65626i	−0.298137	−	0.516389i	0.677572	−	0.735456i	$-0.263032\pi$
$281$	−4.99769	−	8.65626i	−0.298137	−	0.516389i	−0.975710	+	0.219067i	$0.929699\pi$
$282$	−25.8849			−1.54142
$283$	−7.08587	−	12.2731i	−0.421211	−	0.729559i	0.574847	−	0.818261i	$-0.305062\pi$
$283$	−7.08587	−	12.2731i	−0.421211	−	0.729559i	−0.996058	+	0.0887018i	$0.971728\pi$
$284$	−0.746518			−0.0442977
$285$	−5.46897	−	9.47254i	−0.323954	−	0.561105i
$286$	−12.2693			−0.725502
$287$	−2.77304	+	4.80305i	−0.163687	+	0.283515i
$288$	−6.10014	+	10.5657i	−0.359454	+	0.622592i
$289$	8.49954	−	14.7216i	0.499973	−	0.865979i
$290$	48.7478			2.86257
$291$	−9.67039	+	16.7496i	−0.566888	+	0.981879i
$292$	−4.07740			−0.238612
$293$	−12.5147			−0.731117			−0.365558	−	0.930788i	$-0.619122\pi$
$293$	−12.5147			−0.731117			−0.365558	+	0.930788i	$0.619122\pi$
$294$	15.4199			0.899310
$295$	28.0438			1.63278
$296$	−1.34231	−	2.32495i	−0.0780203	−	0.135135i
$297$	−4.75939	−	8.24351i	−0.276168	−	0.478337i
$298$	−3.66063	−	6.34040i	−0.212055	−	0.367289i
$299$	32.3687			1.87193
$300$	−3.26904			−0.188738
$301$	−0.718501	+	1.24448i	−0.0414137	+	0.0717306i
$302$	−1.14447	−	1.98228i	−0.0658568	−	0.114067i
$303$	10.1867			0.585208
$304$	15.2251			0.873217
$305$	−18.4641			−1.05725
$306$	0.0462373	−	0.0800854i	0.00264321	−	0.00457818i
$307$	11.3697			0.648900			0.324450	−	0.945903i	$-0.394821\pi$
$307$	11.3697			0.648900			0.324450	+	0.945903i	$0.394821\pi$
$308$	−1.11375	−	1.92908i	−0.0634620	−	0.109919i
$309$	−21.1328			−1.20220
$310$	−17.7254			−1.00674
$311$	−7.62354			−0.432291			−0.216146	−	0.976361i	$-0.569349\pi$
$311$	−7.62354			−0.432291			−0.216146	+	0.976361i	$0.569349\pi$
$312$	0.562367	+	0.974048i	0.0318377	+	0.0551446i
$313$	−9.23689	+	15.9988i	−0.522100	+	0.904304i	0.477569	+	0.878594i	$0.341518\pi$
$313$	−9.23689	+	15.9988i	−0.522100	+	0.904304i	−0.999669	+	0.0257098i	$0.991815\pi$
$314$	−17.0072	+	29.4573i	−0.959769	+	1.66237i
$315$	−2.71563			−0.153008
$316$	−15.3937	+	26.6626i	−0.865961	+	1.49989i
$317$	3.34533	−	5.79427i	0.187892	−	0.325439i	−0.756655	−	0.653814i	$-0.773168\pi$
$317$	3.34533	−	5.79427i	0.187892	−	0.325439i	0.944547	+	0.328375i	$0.106501\pi$
$318$	−1.51030	+	2.61591i	−0.0846933	+	0.146693i
$319$	−8.48196	−	14.6912i	−0.474898	−	0.822548i
$320$	8.77370	−	15.1965i	0.490465	−	0.849510i
$321$	−15.4803			−0.864025
$322$	6.08546	+	10.5403i	0.339129	+	0.587389i
$323$	−0.108189			−0.00601979
$324$	1.77346	−	3.07172i	0.0985256	−	0.170651i
$325$	2.61509	−	4.52947i	0.145059	−	0.251250i
$326$	−4.58417	+	7.94002i	−0.253894	+	0.439757i
$327$	3.24984	−	5.62888i	0.179716	−	0.311278i
$328$	1.05535	+	1.82792i	0.0582719	+	0.100930i
$329$	7.51866			0.414517
$330$	5.21839	+	9.03851i	0.287263	+	0.497554i
$331$	7.30707			0.401633			0.200816	−	0.979629i	$-0.435641\pi$
$331$	7.30707			0.401633			0.200816	+	0.979629i	$0.435641\pi$
$332$	0.594515			0.0326283
$333$	−8.01012	−	13.8739i	−0.438952	−	0.760287i
$334$	6.03037	+	10.4449i	0.329967	+	0.571520i
$335$	−18.2934			−0.999477
$336$	−1.74964	+	3.03046i	−0.0954505	+	0.165325i
$337$	12.7589	+	22.0991i	0.695023	+	1.20381i	0.970173	+	0.242413i	$0.0779390\pi$
$337$	12.7589	+	22.0991i	0.695023	+	1.20381i	−0.275150	+	0.961401i	$0.588728\pi$
$338$	−0.253905			−0.0138106
$339$	7.90182	−	13.6864i	0.429168	−	0.743341i
$340$	−0.0716162	+	0.124043i	−0.00388394	+	0.00672718i
$341$	3.08417	+	5.34193i	0.167017	+	0.289282i
$342$	10.9803			0.593746
$343$	−9.28071			−0.501111
$344$	0.273443	+	0.473617i	0.0147431	+	0.0255357i
$345$	−13.7670	−	23.8452i	−0.741192	−	1.28378i
$346$	−6.69848	−	11.6021i	−0.360113	−	0.623733i
$347$	−10.3904	−	17.9966i	−0.557784	−	0.966110i	−0.997681	−	0.0680620i	$-0.978318\pi$
$347$	−10.3904	−	17.9966i	−0.557784	−	0.966110i	0.439897	−	0.898048i	$-0.355015\pi$
$348$	10.9367	−	18.9429i	0.586270	−	1.01545i
$349$	1.19446	−	2.06887i	0.0639381	−	0.110744i	−0.832284	−	0.554349i	$-0.812967\pi$
$349$	1.19446	−	2.06887i	0.0639381	−	0.110744i	0.896222	+	0.443605i	$0.146301\pi$
$350$	1.96659			0.105119
$351$	9.81837	+	17.0059i	0.524066	+	0.907709i
$352$	−13.6194			−0.725919
$353$	−11.6690			−0.621079			−0.310540	−	0.950560i	$-0.600510\pi$
$353$	−11.6690			−0.621079			−0.310540	+	0.950560i	$0.600510\pi$
$354$	13.0308	−	22.5699i	0.692577	−	1.19958i
$355$	−1.01597			−0.0539222
$356$	0.587614	−	1.01778i	0.0311435	−	0.0539421i
$357$	0.0124329	−	0.0215344i	0.000658017	−	0.00113972i
$358$	−0.226036	−	0.391506i	−0.0119464	−	0.0206918i
$359$	5.39666	+	9.34729i	0.284825	+	0.493331i	0.972567	−	0.232624i	$-0.0747312\pi$
$359$	5.39666	+	9.34729i	0.284825	+	0.493331i	−0.687742	+	0.725955i	$0.741398\pi$
$360$	−0.516750	+	0.895037i	−0.0272351	+	0.0471726i
$361$	3.07691	+	5.32937i	0.161943	+	0.280493i
$362$	36.0212			1.89323
$363$	−4.78896	+	8.29472i	−0.251355	+	0.435360i
$364$	2.29761	+	3.97959i	0.120428	+	0.208587i
$365$	−5.54914			−0.290455
$366$	−8.57945	+	14.8600i	−0.448455	+	0.776747i
$367$	−7.23779	−	12.5362i	−0.377810	−	0.654385i	0.612934	−	0.790134i	$-0.289989\pi$
$367$	−7.23779	−	12.5362i	−0.377810	−	0.654385i	−0.990743	+	0.135749i	$0.956656\pi$
$368$	38.3260			1.99788
$369$	6.29769	+	10.9079i	0.327845	+	0.567844i
$370$	25.6956	+	44.5060i	1.33585	+	2.31376i
$371$	0.438690	−	0.759833i	0.0227756	−	0.0394485i
$372$	−3.97676	+	6.88794i	−0.206185	+	0.357123i
$373$	4.61158	+	7.98748i	0.238778	+	0.413576i	0.960364	−	0.278749i	$-0.0899197\pi$
$373$	4.61158	+	7.98748i	0.238778	+	0.413576i	−0.721586	+	0.692325i	$0.756586\pi$
$374$	0.103232			0.00533798
$375$	10.8098			0.558214
$376$	1.43071	−	2.47805i	0.0737830	−	0.127796i
$377$	17.4978	+	30.3071i	0.901184	+	1.56090i
$378$	−3.69179	+	6.39437i	−0.189885	+	0.328891i
$379$	0.0925856	+	0.160363i	0.00475580	+	0.00823730i	0.868394	−	0.495876i	$-0.165153\pi$
$379$	0.0925856	+	0.160363i	0.00475580	+	0.00823730i	−0.863638	+	0.504113i	$0.831820\pi$
$380$	−17.0072			−0.872451
$381$	4.40237	−	7.62514i	0.225540	−	0.390648i
$382$	−14.3410			−0.733747
$383$	25.3103			1.29329			0.646647	−	0.762789i	$-0.276171\pi$
$383$	25.3103			1.29329			0.646647	+	0.762789i	$0.276171\pi$
$384$	1.25126	+	2.16725i	0.0638531	+	0.110597i
$385$	−1.51576	−	2.62538i	−0.0772504	−	0.133802i
$386$	42.3229			2.15418
$387$	1.63175	+	2.82627i	0.0829463	+	0.143667i
$388$	15.0363	+	26.0436i	0.763352	+	1.32217i
$389$	−2.05589	−	3.56091i	−0.104238	−	0.180545i	0.809189	−	0.587549i	$-0.199907\pi$
$389$	−2.05589	−	3.56091i	−0.104238	−	0.180545i	−0.913427	+	0.407004i	$0.866574\pi$
$390$	−10.7653	−	18.6460i	−0.545120	−	0.944175i
$391$	−0.272343			−0.0137730
$392$	−0.852290	+	1.47621i	−0.0430471	+	0.0745598i
$393$	−18.6444			−0.940483
$394$	−23.3230	−	40.3966i	−1.17500	−	2.03515i
$395$	−20.9500	+	36.2864i	−1.05411	+	1.82577i
$396$	−5.05876			−0.254212
$397$	−7.92796	+	13.7316i	−0.397893	+	0.689171i	−0.993466	−	0.114131i	$-0.963592\pi$
$397$	−7.92796	+	13.7316i	−0.397893	+	0.689171i	0.595573	+	0.803301i	$0.296925\pi$
$398$	30.9876			1.55327
$399$	2.95252			0.147811
$400$	3.09638	−	5.36309i	0.154819	−	0.268155i
$401$	1.24431	−	2.15521i	0.0621379	−	0.107626i	−0.833283	−	0.552847i	$-0.813541\pi$
$401$	1.24431	−	2.15521i	0.0621379	−	0.107626i	0.895421	+	0.445221i	$0.146875\pi$
$402$	−8.50016	+	14.7227i	−0.423950	+	0.734302i
$403$	−6.36247	−	11.0201i	−0.316937	−	0.548952i
$404$	7.91952	−	13.7170i	0.394011	−	0.682447i
$405$	2.41359	−	4.18046i	0.119932	−	0.207729i
$406$	−6.57933	+	11.3957i	−0.326527	+	0.565561i
$407$	8.94189	−	15.4878i	0.443233	−	0.767702i
$408$	−0.00473163	−	0.00819543i	−0.000234251	−	0.000405734i
$409$	−6.33504			−0.313247			−0.156624	−	0.987658i	$-0.550061\pi$
$409$	−6.33504			−0.313247			−0.156624	+	0.987658i	$0.550061\pi$
$410$	−20.2023	−	34.9914i	−0.997720	−	1.72810i
$411$	−11.6557	−	20.1883i	−0.574933	−	0.995813i
$412$	−16.4295	+	28.4567i	−0.809421	+	1.40196i
$413$	−3.78499	+	6.55579i	−0.186247	+	0.322589i
$414$	27.6407			1.35846
$415$	0.809105			0.0397174
$416$	28.0962			1.37753
$417$	6.23423	+	10.7980i	0.305292	+	0.528781i
$418$	6.12878	+	10.6154i	0.299769	+	0.519214i
$419$	6.52147	+	11.2955i	0.318594	+	0.551822i	0.980195	−	0.198035i	$-0.0634558\pi$
$419$	6.52147	+	11.2955i	0.318594	+	0.551822i	−0.661601	+	0.749856i	$0.730123\pi$
$420$	1.95444	−	3.38519i	0.0953668	−	0.165180i
$421$	17.1584	−	29.7192i	0.836250	−	1.44843i	−0.0567590	−	0.998388i	$-0.518077\pi$
$421$	17.1584	−	29.7192i	0.836250	−	1.44843i	0.893009	−	0.450039i	$-0.148590\pi$
$422$	−32.8727			−1.60022
$423$	8.53760	−	14.7876i	0.415112	−	0.718996i
$424$	−0.166954	−	0.289173i	−0.00810800	−	0.0140435i
$425$	−0.0220028	+	0.0381100i	−0.00106729	+	0.00184861i
$426$	−0.472079	+	0.817664i	−0.0228723	+	0.0396159i
$427$	2.49203	−	4.31633i	0.120598	−	0.208882i
$428$	−12.0350	+	20.8452i	−0.581734	+	1.00759i
$429$	−3.74624	+	6.48867i	−0.180870	+	0.313276i
$430$	−5.23445	−	9.06634i	−0.252428	−	0.437218i
$431$	−8.09128	+	14.0145i	−0.389743	+	0.675055i	−0.992415	−	0.122934i	$-0.960770\pi$
$431$	−8.09128	+	14.0145i	−0.389743	+	0.675055i	0.602672	+	0.797989i	$0.294103\pi$
$432$	11.6254	+	20.1358i	0.559327	+	0.968782i
$433$	−3.05688			−0.146904			−0.0734522	−	0.997299i	$-0.523402\pi$
$433$	−3.05688			−0.146904			−0.0734522	+	0.997299i	$0.523402\pi$
$434$	2.39234	−	4.14366i	0.114836	−	0.198902i
$435$	14.8843	−	25.7804i	0.713648	−	1.23607i
$436$	−5.05311	−	8.75224i	−0.242000	−	0.419156i
$437$	−16.1688	−	28.0052i	−0.773460	−	1.33967i
$438$	−2.57844	+	4.46599i	−0.123203	+	0.213393i
$439$	−1.68417	+	2.91706i	−0.0803809	+	0.139224i	−0.903414	−	0.428770i	$-0.858947\pi$
$439$	−1.68417	+	2.91706i	−0.0803809	+	0.139224i	0.823033	+	0.567994i	$0.192280\pi$
$440$	−1.15372			−0.0550014
$441$	−5.08596	+	8.80914i	−0.242189	+	0.419483i
$442$	−0.212961			−0.0101295
$443$	3.41197	+	5.90971i	0.162108	+	0.280779i	0.935624	−	0.352997i	$-0.114837\pi$
$443$	3.41197	+	5.90971i	0.162108	+	0.280779i	−0.773517	+	0.633776i	$0.781504\pi$
$444$	23.0595			1.09436
$445$	0.799713	−	1.38514i	0.0379100	−	0.0656621i
$446$	28.1108			1.33108
$447$	−4.47085			−0.211464
$448$	2.36832	+	4.10204i	0.111892	+	0.193803i
$449$	−12.5770			−0.593546			−0.296773	−	0.954948i	$-0.595910\pi$
$449$	−12.5770			−0.593546			−0.296773	+	0.954948i	$0.595910\pi$
$450$	2.23311	−	3.86786i	0.105270	−	0.182332i
$451$	−7.03026	+	12.1768i	−0.331042	+	0.573382i
$452$	−12.2864	−	21.2806i	−0.577903	−	1.00096i
$453$	−1.39778			−0.0656733
$454$	−5.62131			−0.263821
$455$	3.12694	+	5.41601i	0.146593	+	0.253907i
$456$	0.561827	−	0.973112i	0.0263099	−	0.0455702i
$457$	−15.2779			−0.714669			−0.357334	−	0.933977i	$-0.616314\pi$
$457$	−15.2779			−0.714669			−0.357334	+	0.933977i	$0.616314\pi$
$458$	−49.2076			−2.29932
$459$	−0.0826096	−	0.143084i	−0.00385589	−	0.00667859i
$460$	−42.8122			−1.99613
$461$	−5.84714	+	10.1275i	−0.272328	+	0.471687i	−0.969458	−	0.245259i	$-0.921127\pi$
$461$	−5.84714	+	10.1275i	−0.272328	+	0.471687i	0.697129	+	0.716945i	$0.254460\pi$
$462$	−2.81723			−0.131070
$463$	12.0475			0.559896			0.279948	−	0.960015i	$-0.409683\pi$
$463$	12.0475			0.559896			0.279948	+	0.960015i	$0.409683\pi$
$464$	20.7182	+	35.8850i	0.961818	+	1.66592i
$465$	−5.41216	+	9.37414i	−0.250983	+	0.434715i
$466$	−21.7678			−1.00837
$467$	38.3333			1.77385			0.886926	−	0.461911i	$-0.152836\pi$
$467$	38.3333			1.77385			0.886926	+	0.461911i	$0.152836\pi$
$468$	10.4360			0.482402
$469$	2.46900	−	4.27644i	0.114008	−	0.197468i
$470$	−27.3876	+	47.4368i	−1.26330	+	2.18810i
$471$	10.3857	+	17.9886i	0.478548	+	0.828869i
$472$	1.44047	+	2.49497i	0.0663030	+	0.114840i
$473$	−1.82156	+	3.15503i	−0.0837552	+	0.145068i
$474$	19.4691	+	33.7215i	0.894245	+	1.54888i
$475$	−5.22516			−0.239747
$476$	−0.0193316	−	0.0334834i	−0.000886064	−	0.00153471i
$477$	−0.996283	−	1.72561i	−0.0456166	−	0.0790103i
$478$	23.0753	−	39.9676i	1.05544	−	1.82808i
$479$	4.85151			0.221671			0.110835	−	0.993839i	$-0.464647\pi$
$479$	4.85151			0.221671			0.110835	+	0.993839i	$0.464647\pi$
$480$	−11.9498	−	20.6977i	−0.545433	−	0.944718i
$481$	−18.4466	+	31.9505i	−0.841095	+	1.45682i
$482$	−22.6878			−1.03340
$483$	7.43237			0.338184
$484$	7.44626	+	12.8973i	0.338466	+	0.586241i
$485$	20.4636	+	35.4441i	0.929206	+	1.60943i
$486$	13.9027	+	24.0803i	0.630641	+	1.09230i
$487$	−12.7286	−	22.0466i	−0.576789	−	0.999029i	−0.995845	−	0.0910678i	$-0.970972\pi$
$487$	−12.7286	−	22.0466i	−0.576789	−	0.999029i	0.419055	−	0.907961i	$-0.362361\pi$
$488$	−0.948405	−	1.64269i	−0.0429323	−	0.0743609i
$489$	2.79940	+	4.84870i	0.126593	+	0.219266i
$490$	16.3152	−	28.2587i	0.737045	−	1.27660i
$491$	19.5777	+	33.9095i	0.883529	+	1.53032i	0.847391	+	0.530970i	$0.178172\pi$
$491$	19.5777	+	33.9095i	0.883529	+	1.53032i	0.0361376	+	0.999347i	$0.488495\pi$
$492$	−18.1298			−0.817354
$493$	−0.147223	−	0.254998i	−0.00663059	−	0.0114845i
$494$	−12.6434	−	21.8989i	−0.568851	−	0.985279i
$495$	−6.88472			−0.309445
$496$	−7.53345	−	13.0483i	−0.338262	−	0.585887i
$497$	0.137123	−	0.237503i	0.00615079	−	0.0106535i
$498$	0.375956	−	0.651175i	0.0168470	−	0.0291798i
$499$	−8.41077	−	14.5679i	−0.376518	−	0.652148i	0.614035	−	0.789279i	$-0.289545\pi$
$499$	−8.41077	−	14.5679i	−0.376518	−	0.652148i	−0.990553	+	0.137131i	$0.956212\pi$
$500$	8.40394	−	14.5561i	0.375836	−	0.650967i
$501$	7.36509			0.329048
$502$	−17.4788	+	30.2742i	−0.780117	+	1.35120i
$503$	21.2879			0.949181			0.474590	−	0.880207i	$-0.342596\pi$
$503$	21.2879			0.949181			0.474590	+	0.880207i	$0.342596\pi$
$504$	−0.139488	−	0.241601i	−0.00621329	−	0.0107617i
$505$	10.7781	−	18.6682i	0.479618	−	0.830722i
$506$	15.4280	+	26.7220i	0.685857	+	1.18794i
$507$	−0.0775256	+	0.134278i	−0.00344303	+	0.00596351i
$508$	−6.84517	−	11.8562i	−0.303705	−	0.526033i
$509$	2.70470			0.119884			0.0599419	−	0.998202i	$-0.480908\pi$
$509$	2.70470			0.119884			0.0599419	+	0.998202i	$0.480908\pi$
$510$	0.0905765	+	0.156883i	0.00401079	+	0.00694690i
$511$	0.748949	−	1.29722i	0.0331316	−	0.0573855i
$512$	31.0493			1.37220
$513$	9.80894	−	16.9896i	0.433075	−	0.750109i
$514$	31.3633	+	54.3229i	1.38338	+	2.39608i
$515$	−22.3597	+	38.7281i	−0.985284	+	1.70656i
$516$	−4.69746			−0.206794
$517$	19.0614			0.838321
$518$	−13.8722			−0.609509
$519$	−8.18107			−0.359109
$520$	2.38006			0.104373
$521$	−1.19196	+	2.06453i	−0.0522207	+	0.0904489i	−0.890954	−	0.454093i	$-0.849963\pi$
$521$	−1.19196	+	2.06453i	−0.0522207	+	0.0904489i	0.838733	+	0.544542i	$0.183297\pi$
$522$	14.9419	+	25.8802i	0.653991	+	1.13275i
$523$	−12.7929			−0.559393			−0.279697	−	0.960088i	$-0.590234\pi$
$523$	−12.7929			−0.559393			−0.279697	+	0.960088i	$0.590234\pi$
$524$	−14.4949	+	25.1059i	−0.633212	+	1.09675i
$525$	0.600466	−	1.04004i	0.0262065	−	0.0453910i
$526$	−9.79705	−	16.9690i	−0.427172	−	0.739883i
$527$	0.0535325	+	0.0927210i	0.00233191	+	0.00403899i
$528$	−4.43571	+	7.68288i	−0.193040	+	0.334354i
$529$	−29.2017	−	50.5789i	−1.26964	−	2.19908i
$530$	3.19596	+	5.53557i	0.138824	+	0.240450i
$531$	8.59587	+	14.8885i	0.373029	+	0.646105i
$532$	2.29541	−	3.97576i	0.0995186	−	0.172371i
$533$	14.5031	−	25.1200i	0.628197	−	1.08807i
$534$	−0.743184	−	1.28723i	−0.0321607	−	0.0557040i
$535$	−16.3790	+	28.3693i	−0.708127	+	1.22651i
$536$	−0.939640	−	1.62750i	−0.0405863	−	0.0702975i
$537$	−0.276065			−0.0119131
$538$	−44.9945			−1.93985
$539$	−11.3552			−0.489101
$540$	−12.9862	−	22.4927i	−0.558836	−	0.967932i
$541$	−0.356656	−	0.617746i	−0.0153338	−	0.0265590i	0.858257	−	0.513221i	$-0.171548\pi$
$541$	−0.356656	−	0.617746i	−0.0153338	−	0.0265590i	−0.873590	+	0.486662i	$0.838214\pi$
$542$	−11.4286	+	19.7949i	−0.490900	+	0.850264i
$543$	10.9985	−	19.0499i	0.471989	−	0.817510i
$544$	−0.236395			−0.0101354
$545$	−6.87702	−	11.9113i	−0.294579	−	0.510226i
$546$	5.81181			0.248722
$547$	17.1527	+	15.8992i	0.733397	+	0.679801i
$547$	17.1527	+	15.8992i	0.733397	+	0.679801i
$548$	−36.2464			−1.54837
$549$	−5.65952	−	9.80257i	−0.241542	−	0.418364i
$550$	4.98574			0.212593
$551$	17.4810	−	30.2780i	0.744717	−	1.28989i
$552$	1.41428	−	2.44961i	0.0601960	−	0.104262i
$553$	−5.65510	−	9.79493i	−0.240479	−	0.416523i
$554$	−5.54881	−	9.61081i	−0.235746	−	0.408324i
$555$	31.3828			1.33213
$556$	19.3870			0.822191
$557$	−9.46033			−0.400847			−0.200424	−	0.979709i	$-0.564232\pi$
$557$	−9.46033			−0.400847			−0.200424	+	0.979709i	$0.564232\pi$
$558$	−5.43311	−	9.41043i	−0.230002	−	0.398375i
$559$	3.75777	−	6.50865i	0.158937	−	0.275287i
$560$	3.70243	+	6.41280i	0.156456	+	0.270990i
$561$	0.0315200	−	0.0545943i	0.00133078	−	0.00230497i
$562$	−9.82812	+	17.0228i	−0.414574	+	0.718064i
$563$	8.92881	+	15.4652i	0.376305	+	0.651779i	0.990521	−	0.137359i	$-0.0438613\pi$
$563$	8.92881	+	15.4652i	0.376305	+	0.651779i	−0.614217	+	0.789137i	$0.710528\pi$
$564$	12.2890	+	21.2852i	0.517461	+	0.896268i
$565$	−16.7211	−	28.9619i	−0.703464	−	1.21844i
$566$	−13.9346	+	24.1354i	−0.585714	+	1.01449i
$567$	0.651509	+	1.12845i	0.0273608	+	0.0473903i
$568$	−0.0521853	−	0.0903877i	−0.00218965	−	0.00379258i
$569$	−1.36985	+	2.37265i	−0.0574271	+	0.0994666i	−0.893310	−	0.449442i	$-0.851623\pi$
$569$	−1.36985	+	2.37265i	−0.0574271	+	0.0994666i	0.835883	+	0.548908i	$0.184956\pi$
$570$	−10.7549	+	18.6281i	−0.450474	+	0.780244i
$571$	−46.1724			−1.93226			−0.966128	−	0.258064i	$-0.916916\pi$
$571$	−46.1724			−1.93226			−0.966128	+	0.258064i	$0.916916\pi$
$572$	5.82495	+	10.0891i	0.243554	+	0.421847i
$573$	−4.37877	+	7.58425i	−0.182926	+	0.316837i
$574$	10.9065			0.455231
$575$	−13.1533			−0.548530
$576$	10.7571			0.448212
$577$	27.4648			1.14337			0.571687	−	0.820471i	$-0.306289\pi$
$577$	27.4648			1.14337			0.571687	+	0.820471i	$0.306289\pi$
$578$	−33.4293			−1.39047
$579$	12.9226	−	22.3826i	0.537045	−	0.930189i
$580$	−23.1433	−	40.0854i	−0.960975	−	1.66446i
$581$	−0.109202	+	0.189144i	−0.00453047	+	0.00784701i
$582$	38.0342			1.57657
$583$	1.11217	−	1.92634i	0.0460615	−	0.0797809i
$584$	−0.285031	−	0.493688i	−0.0117947	−	0.0204290i
$585$	14.2028			0.587214
$586$	12.3053	+	21.3134i	0.508327	+	0.880448i
$587$	−7.90087	+	13.6847i	−0.326104	+	0.564828i	−0.981735	−	0.190253i	$-0.939069\pi$
$587$	−7.90087	+	13.6847i	−0.326104	+	0.564828i	0.655631	+	0.755081i	$0.272403\pi$
$588$	−7.32072	−	12.6799i	−0.301902	−	0.522909i
$589$	−6.35636	+	11.0095i	−0.261909	+	0.453640i
$590$	−27.5746	−	47.7605i	−1.13523	−	1.96627i
$591$	−28.4851			−1.17172
$592$	−21.8417	+	37.8308i	−0.897686	+	1.55484i
$593$	15.5130			0.637044			0.318522	−	0.947916i	$-0.396814\pi$
$593$	15.5130			0.637044			0.318522	+	0.947916i	$0.396814\pi$
$594$	−9.35949	+	16.2111i	−0.384025	+	0.665150i
$595$	−0.0263094	−	0.0455691i	−0.00107858	−	0.00186815i
$596$	−3.47582	+	6.02029i	−0.142375	+	0.246601i
$597$	9.46154	−	16.3879i	0.387235	−	0.670711i
$598$	−31.8271	−	55.1261i	−1.30151	−	2.25427i
$599$	−19.6628			−0.803402			−0.401701	−	0.915771i	$-0.631581\pi$
$599$	−19.6628			−0.803402			−0.401701	+	0.915771i	$0.631581\pi$
$600$	−0.228522	−	0.395812i	−0.00932937	−	0.0161589i
$601$	4.23032	+	7.32713i	0.172558	+	0.298880i	0.939314	−	0.343060i	$-0.111463\pi$
$601$	4.23032	+	7.32713i	0.172558	+	0.298880i	−0.766755	+	0.641940i	$0.778130\pi$
$602$	2.82591			0.115175
$603$	−5.60721	−	9.71198i	−0.228343	−	0.395502i
$604$	−1.08669	+	1.88220i	−0.0442167	+	0.0765856i
$605$	10.1340	+	17.5526i	0.412005	+	0.713613i
$606$	−10.0162	−	17.3486i	−0.406880	−	0.704737i
$607$	−7.18378	−	12.4427i	−0.291580	−	0.505032i	0.682603	−	0.730789i	$-0.260848\pi$
$607$	−7.18378	−	12.4427i	−0.291580	−	0.505032i	−0.974184	+	0.225757i	$0.927514\pi$
$608$	−14.0346	−	24.3087i	−0.569179	−	0.985846i
$609$	4.01778	+	6.95899i	0.162808	+	0.281993i
$610$	18.1551	+	31.4455i	0.735078	+	1.27319i
$611$	−39.3228			−1.59083
$612$	−0.0878059			−0.00354934
$613$	−6.12369	+	10.6065i	−0.247334	+	0.428394i	−0.962785	−	0.270268i	$-0.912888\pi$
$613$	−6.12369	+	10.6065i	−0.247334	+	0.428394i	0.715452	+	0.698662i	$0.246221\pi$
$614$	−11.1794	−	19.3633i	−0.451164	−	0.781438i
$615$	−24.6737			−0.994940
$616$	0.155714	−	0.269704i	0.00627389	−	0.0108667i
$617$	11.7986	+	20.4357i	0.474992	+	0.822710i	0.999590	−	0.0286398i	$-0.00911758\pi$
$617$	11.7986	+	20.4357i	0.474992	+	0.822710i	−0.524598	+	0.851350i	$0.675784\pi$
$618$	20.7791	+	35.9905i	0.835859	+	1.44775i
$619$	40.0675			1.61045			0.805223	−	0.592972i	$-0.202045\pi$
$619$	40.0675			1.61045			0.805223	+	0.592972i	$0.202045\pi$
$620$	8.41527	+	14.5757i	0.337965	+	0.585373i
$621$	24.6920	−	42.7678i	0.990857	−	1.71621i
$622$	7.49597	+	12.9834i	0.300561	+	0.520587i
$623$	0.215869	+	0.373897i	0.00864863	+	0.0149799i
$624$	9.15064	−	15.8494i	0.366319	−	0.634483i
$625$	15.0820	−	26.1227i	0.603278	−	1.04491i
$626$	36.3293			1.45201
$627$	7.48528			0.298933
$628$	32.2970			1.28879
$629$	0.155206	−	0.268825i	0.00618847	−	0.0107187i
$630$	2.67019	+	4.62490i	0.106383	+	0.184260i
$631$	−26.2797			−1.04618			−0.523089	−	0.852278i	$-0.675221\pi$
$631$	−26.2797			−1.04618			−0.523089	+	0.852278i	$0.675221\pi$
$632$	−4.30438			−0.171219
$633$	−10.0371	+	17.3848i	−0.398940	+	0.690985i
$634$	−13.1574			−0.522546
$635$	−9.31592	−	16.1357i	−0.369691	−	0.640324i
$636$	2.86810			0.113727
$637$	23.4251			0.928136
$638$	−16.6800	+	28.8907i	−0.660369	+	1.14379i
$639$	−0.311411	−	0.539380i	−0.0123192	−	0.0213375i
$640$	5.29562			0.209328
$641$	−24.3331			−0.961098			−0.480549	−	0.876968i	$-0.659563\pi$
$641$	−24.3331			−0.961098			−0.480549	+	0.876968i	$0.659563\pi$
$642$	15.2212	+	26.3640i	0.600734	+	1.04050i
$643$	1.45967	−	2.52822i	0.0575638	−	0.0997034i	−0.835808	−	0.549023i	$-0.815000\pi$
$643$	1.45967	−	2.52822i	0.0575638	−	0.0997034i	0.893371	+	0.449319i	$0.148333\pi$
$644$	5.77822	−	10.0082i	0.227694	−	0.394377i
$645$	−6.39301			−0.251724
$646$	0.106378	+	0.184253i	0.00418540	+	0.00724933i
$647$	−16.8820			−0.663701			−0.331850	−	0.943332i	$-0.607673\pi$
$647$	−16.8820			−0.663701			−0.331850	+	0.943332i	$0.607673\pi$
$648$	0.495895			0.0194806
$649$	−9.59577	+	16.6204i	−0.376667	+	0.652406i
$650$	−10.2853			−0.403423
$651$	−1.46092	−	2.53039i	−0.0572581	−	0.0991740i
$652$	8.70547			0.340932
$653$	12.8790	−	22.3071i	0.503994	−	0.872943i	−0.495995	−	0.868325i	$-0.665197\pi$
$653$	12.8790	−	22.3071i	0.503994	−	0.872943i	0.999989	−	0.00461811i	$-0.00147000\pi$
$654$	−12.7818			−0.499808
$655$	−19.7268	+	34.1678i	−0.770789	+	1.33505i
$656$	17.1723	−	29.7432i	0.670465	−	1.16128i
$657$	−1.70090	−	2.94604i	−0.0663582	−	0.114936i
$658$	−7.39284	−	12.8048i	−0.288203	−	0.499182i
$659$	12.3045	−	21.3120i	0.479315	−	0.830198i	−0.520403	−	0.853921i	$-0.674218\pi$
$659$	12.3045	−	21.3120i	0.479315	−	0.830198i	0.999719	+	0.0237223i	$0.00755176\pi$
$660$	4.95493	−	8.58218i	0.192870	−	0.334061i
$661$	18.0662			0.702695			0.351347	−	0.936245i	$-0.385724\pi$
$661$	18.0662			0.702695			0.351347	+	0.936245i	$0.385724\pi$
$662$	−7.18479	−	12.4444i	−0.279245	−	0.483666i
$663$	−0.0650242	+	0.112625i	−0.00252533	+	0.00437400i
$664$	0.0415596	+	0.0719833i	0.00161283	+	0.00279350i
$665$	3.12393	−	5.41081i	0.121141	−	0.209822i
$666$	−15.7522	+	27.2836i	−0.610384	+	1.05722i
$667$	44.0049	−	76.2188i	1.70388	−	2.95120i
$668$	5.72592	−	9.91759i	0.221543	−	0.383723i
$669$	8.58315	−	14.8665i	0.331844	−	0.574771i
$670$	17.9873	+	31.1549i	0.694910	+	1.20362i
$671$	6.31785	−	10.9428i	0.243898	−	0.422444i
$672$	6.45133			0.248865
$673$	1.32036	−	2.28694i	0.0508963	−	0.0881550i	−0.839455	−	0.543429i	$-0.817126\pi$
$673$	1.32036	−	2.28694i	0.0508963	−	0.0881550i	0.890351	+	0.455274i	$0.150459\pi$
$674$	25.0908	−	43.4586i	0.966462	−	1.67396i
$675$	−3.98977	−	6.91048i	−0.153566	−	0.265985i
$676$	0.120543	+	0.208787i	0.00463627	+	0.00803026i
$677$	−3.34647	−	5.79626i	−0.128615	−	0.222768i	0.794525	−	0.607231i	$-0.207720\pi$
$677$	−3.34647	−	5.79626i	−0.128615	−	0.222768i	−0.923140	+	0.384463i	$0.874387\pi$
$678$	−31.0784			−1.19356
$679$	−11.0476			−0.423970
$680$	−0.0200253			−0.000767937
$681$	−1.71637	+	2.97285i	−0.0657716	+	0.113920i
$682$	6.06511	−	10.5051i	0.232245	−	0.402260i
$683$	−15.7456	−	27.2722i	−0.602490	−	1.04354i	−0.992443	−	0.122709i	$-0.960842\pi$
$683$	−15.7456	−	27.2722i	−0.602490	−	1.04354i	0.389953	−	0.920835i	$-0.372491\pi$
$684$	−5.21297	−	9.02913i	−0.199323	−	0.345237i
$685$	−49.3295			−1.88478
$686$	9.12540	+	15.8057i	0.348410	+	0.603463i
$687$	−15.0247	+	26.0235i	−0.573228	+	0.992860i
$688$	4.44937	−	7.70654i	0.169631	−	0.293809i
$689$	−2.29436	+	3.97394i	−0.0874080	+	0.151395i
$690$	−27.0733	+	46.8924i	−1.03066	+	1.78516i
$691$	−6.32341	−	10.9525i	−0.240554	−	0.416652i	0.720318	−	0.693644i	$-0.243996\pi$
$691$	−6.32341	−	10.9525i	−0.240554	−	0.416652i	−0.960872	+	0.276992i	$0.910662\pi$
$692$	−6.36030	+	11.0164i	−0.241782	+	0.418779i
$693$	0.929208	−	1.60944i	0.0352977	−	0.0611374i
$694$	−20.4330	+	35.3910i	−0.775626	+	1.34342i
$695$	26.3847			1.00083
$696$	3.05812			0.115918
$697$	−0.122026	+	0.211355i	−0.00462205	+	0.00800562i
$698$	−4.69790			−0.177818
$699$	−6.64643	+	11.5120i	−0.251391	+	0.435422i
$700$	−0.933653	−	1.61713i	−0.0352888	−	0.0611219i
$701$	−40.7829			−1.54035			−0.770175	−	0.637833i	$-0.779831\pi$
$701$	−40.7829			−1.54035			−0.770175	+	0.637833i	$0.779831\pi$
$702$	19.3081	−	33.4427i	0.728739	−	1.26221i
$703$	36.8579			1.39012
$704$	6.00420	+	10.3996i	0.226292	+	0.391949i
$705$	16.7247	+	28.9681i	0.629889	+	1.09100i
$706$	11.4737	+	19.8731i	0.431820	+	0.747934i
$707$	2.90936	+	5.03916i	0.109418	+	0.189517i
$708$	−24.7458			−0.930003
$709$	21.8624	+	37.8668i	0.821059	+	1.42212i	0.904894	+	0.425637i	$0.139950\pi$
$709$	21.8624	+	37.8668i	0.821059	+	1.42212i	−0.0838350	+	0.996480i	$0.526717\pi$
$710$	0.998972	+	1.73027i	0.0374907	+	0.0649359i
$711$	−25.6860			−0.963299
$712$	0.164309			0.00615773
$713$	−16.0009	+	27.7143i	−0.599237	+	1.03791i
$714$	−0.0488993			−0.00183001
$715$	7.92746	+	13.7308i	0.296470	+	0.513502i
$716$	−0.214624	+	0.371740i	−0.00802089	+	0.0138926i
$717$	−14.0913	−	24.4069i	−0.526250	−	0.911491i
$718$	10.6127	−	18.3817i	0.396063	−	0.686001i
$719$	22.4986			0.839057			0.419529	−	0.907742i	$-0.362195\pi$
$719$	22.4986			0.839057			0.419529	+	0.907742i	$0.362195\pi$
$720$	16.8168			0.626723
$721$	−6.03562	−	10.4540i	−0.224778	−	0.389327i
$722$	6.05084	−	10.4804i	0.225189	−	0.390039i
$723$	−6.92733	+	11.9985i	−0.257630	+	0.446228i
$724$	−17.1013	−	29.6203i	−0.635565	−	1.10083i
$725$	−7.11037	−	12.3155i	−0.264073	−	0.457387i
$726$	18.8353			0.699043
$727$	−12.9679	−	22.4611i	−0.480953	−	0.833036i	0.518808	−	0.854891i	$-0.326376\pi$
$727$	−12.9679	−	22.4611i	−0.480953	−	0.833036i	−0.999761	+	0.0218553i	$0.993043\pi$
$728$	−0.321230	+	0.556386i	−0.0119056	+	0.0206210i
$729$	22.6785			0.839945
$730$	5.45628	+	9.45055i	0.201946	+	0.349781i
$731$	−0.0316171	+	0.0547624i	−0.00116940	+	0.00202546i
$732$	16.2926			0.602192
$733$	6.99262	+	12.1116i	0.258278	+	0.447351i	0.965781	−	0.259360i	$-0.0835115\pi$
$733$	6.99262	+	12.1116i	0.258278	+	0.447351i	−0.707502	+	0.706711i	$0.750178\pi$
$734$	−14.2333	+	24.6529i	−0.525362	+	0.909954i
$735$	−9.96313	−	17.2566i	−0.367496	−	0.636521i
$736$	−35.3293	−	61.1921i	−1.30225	−	2.25557i
$737$	6.25947	−	10.8417i	0.230570	−	0.399360i
$738$	12.3846	−	21.4508i	0.455884	−	0.789614i
$739$	−16.2435			−0.597527			−0.298764	−	0.954327i	$-0.596574\pi$
$739$	−16.2435			−0.597527			−0.298764	+	0.954327i	$0.596574\pi$
$740$	24.3983	−	42.2591i	0.896899	−	1.55347i
$741$	−15.4417			−0.567266
$742$	−1.72539			−0.0633412
$743$	12.6846	+	21.9704i	0.465353	+	0.806015i	0.999217	−	0.0395549i	$-0.0125940\pi$
$743$	12.6846	+	21.9704i	0.465353	+	0.806015i	−0.533864	+	0.845570i	$0.679261\pi$
$744$	−1.11198			−0.0407672
$745$	−4.73041	+	8.19331i	−0.173309	+	0.300180i
$746$	9.06881	−	15.7076i	0.332033	−	0.575098i
$747$	0.248003	+	0.429554i	0.00907396	+	0.0157166i
$748$	−0.0490099	−	0.0848876i	−0.00179198	−	0.00310380i
$749$	−4.42125	−	7.65782i	−0.161549	−	0.279811i
$750$	−10.6289	−	18.4097i	−0.388111	−	0.672229i
$751$	−6.63088			−0.241964			−0.120982	−	0.992655i	$-0.538604\pi$
$751$	−6.63088			−0.241964			−0.120982	+	0.992655i	$0.538604\pi$
$752$	−46.5599			−1.69786
$753$	10.6737	+	18.4874i	0.388972	+	0.673719i
$754$	34.4100	−	59.5999i	1.25314	−	2.17050i
$755$	−1.47893	+	2.56158i	−0.0538237	+	0.0932253i
$756$	7.01081			0.254981
$757$	−0.425476	−	0.736945i	−0.0154642	−	0.0267847i	0.858190	−	0.513333i	$-0.171589\pi$
$757$	−0.425476	−	0.736945i	−0.0154642	−	0.0267847i	−0.873654	+	0.486548i	$0.838256\pi$
$758$	0.182073	−	0.315359i	0.00661318	−	0.0114544i
$759$	18.8427			0.683946
$760$	−1.18889	−	2.05922i	−0.0431255	−	0.0746956i
$761$	15.9407	+	27.6101i	0.577850	+	1.00087i	0.995726	+	0.0923611i	$0.0294414\pi$
$761$	15.9407	+	27.6101i	0.577850	+	1.00087i	−0.417876	+	0.908504i	$0.637225\pi$
$762$	−17.3148			−0.627250
$763$	3.71268			0.134408
$764$	6.80846	+	11.7926i	0.246322	+	0.426641i
$765$	−0.119499			−0.00432051
$766$	−24.8867	−	43.1051i	−0.899194	−	1.55745i
$767$	19.7956	−	34.2869i	0.714776	−	1.23803i
$768$	10.7529	−	18.6246i	0.388013	−	0.672058i
$769$	14.3575	−	24.8679i	0.517743	−	0.896758i	−0.482044	−	0.876147i	$-0.660106\pi$
$769$	14.3575	−	24.8679i	0.517743	−	0.896758i	0.999788	−	0.0206111i	$-0.00656117\pi$
$770$	−2.98079	+	5.16289i	−0.107420	+	0.186058i
$771$	38.3051			1.37952
$772$	−20.0931	−	34.8023i	−0.723166	−	1.25256i
$773$	45.2813			1.62866			0.814328	−	0.580405i	$-0.197106\pi$
$773$	45.2813			1.62866			0.814328	+	0.580405i	$0.197106\pi$
$774$	3.20888	−	5.55794i	0.115341	−	0.199776i
$775$	2.58544	+	4.47811i	0.0928717	+	0.160859i
$776$	−2.10222	+	3.64116i	−0.0754655	+	0.130710i
$777$	−4.23564	+	7.33634i	−0.151953	+	0.263190i
$778$	−4.04297	+	7.00263i	−0.144948	+	0.251057i
$779$	−28.9783			−1.03825
$780$	−10.2218	+	17.7046i	−0.365997	+	0.633926i
$781$	0.347636	−	0.602123i	0.0124394	−	0.0215456i
$782$	0.267786	+	0.463819i	0.00957601	+	0.0165861i
$783$	53.3919			1.90807
$784$	27.7363			0.990584
$785$	43.9546			1.56881
$786$	18.3324	+	31.7526i	0.653894	+	1.13258i
$787$	−10.0530			−0.358350			−0.179175	−	0.983817i	$-0.557343\pi$
$787$	−10.0530			−0.358350			−0.179175	+	0.983817i	$0.557343\pi$
$788$	−22.1455	+	38.3571i	−0.788901	+	1.36642i
$789$	−11.9655			−0.425982
$790$	82.3976			2.93158
$791$	9.02720			0.320970
$792$	−0.353633	−	0.612510i	−0.0125658	−	0.0217646i
$793$	−13.0334	+	22.5745i	−0.462829	+	0.801644i
$794$	31.1812			1.10658
$795$	3.90333			0.138437
$796$	−14.7116	−	25.4812i	−0.521438	−	0.903156i
$797$	11.2428	+	19.4730i	0.398239	+	0.689770i	0.993509	−	0.113756i	$-0.0362881\pi$
$797$	11.2428	+	19.4730i	0.398239	+	0.689770i	−0.595270	+	0.803526i	$0.702955\pi$
$798$	−2.90311	−	5.02834i	−0.102769	−	0.178001i
$799$	0.330853			0.0117047
$800$	−11.4171			−0.403656
$801$	0.980497			0.0346442
$802$	−4.89396			−0.172812
$803$	1.89875	−	3.28873i	0.0670054	−	0.116057i
$804$	16.1420			0.569286
$805$	7.86387	−	13.6206i	0.277165	−	0.480064i
$806$	−12.5120	+	21.6714i	−0.440717	+	0.763344i
$807$	−13.7383	+	23.7954i	−0.483611	+	0.837639i
$808$	2.21446			0.0779043
$809$	17.3046	+	29.9725i	0.608398	+	1.05378i	0.991504	+	0.130072i	$0.0415210\pi$
$809$	17.3046	+	29.9725i	0.608398	+	1.05378i	−0.383106	+	0.923704i	$0.625146\pi$
$810$	−9.49280			−0.333543
$811$	9.60522	+	16.6367i	0.337285	+	0.584194i	0.983921	−	0.178604i	$-0.0571581\pi$
$811$	9.60522	+	16.6367i	0.337285	+	0.584194i	−0.646636	+	0.762799i	$0.723825\pi$
$812$	12.4943			0.438465
$813$	6.97906	+	12.0881i	0.244766	+	0.423948i
$814$	−35.1690			−1.23267
$815$	11.8477			0.415007
$816$	−0.0769915	+	0.133353i	−0.00269524	+	0.00466830i
$817$	−7.50833			−0.262683
$818$	6.22903	+	10.7890i	0.217793	+	0.377228i
$819$	−1.91691	+	3.32018i	−0.0669822	+	0.116016i
$820$	−19.1823	+	33.2248i	−0.669876	+	1.16026i
$821$	−10.8402	+	18.7758i	−0.378326	+	0.655280i	−0.990819	−	0.135196i	$-0.956833\pi$
$821$	−10.8402	+	18.7758i	−0.378326	+	0.655280i	0.612493	+	0.790476i	$0.290167\pi$
$822$	−22.9213	+	39.7009i	−0.799472	+	1.38473i
$823$	−5.06765	−	8.77743i	−0.176647	−	0.305962i	0.764083	−	0.645118i	$-0.223192\pi$
$823$	−5.06765	−	8.77743i	−0.176647	−	0.305962i	−0.940730	+	0.339156i	$0.889858\pi$
$824$	−4.59401			−0.160040
$825$	1.52231	−	2.63672i	0.0530001	−	0.0917989i
$826$	14.8866			0.517971
$827$	−12.3450			−0.429276			−0.214638	−	0.976694i	$-0.568857\pi$
$827$	−12.3450			−0.429276			−0.214638	+	0.976694i	$0.568857\pi$
$828$	−13.1226	−	22.7290i	−0.456042	−	0.789887i
$829$	39.8323			1.38343			0.691717	−	0.722169i	$-0.256855\pi$
$829$	39.8323			1.38343			0.691717	+	0.722169i	$0.256855\pi$
$830$	−0.795566	−	1.37796i	−0.0276145	−	0.0478297i
$831$	−6.77694			−0.235089
$832$	−12.3863	−	21.4538i	−0.429419	−	0.743776i
$833$	−0.197094			−0.00682889
$834$	12.2598	−	21.2346i	0.424523	−	0.735295i
$835$	7.79269	−	13.4973i	0.269677	−	0.467094i
$836$	5.81936	−	10.0794i	0.201267	−	0.348604i
$837$	−19.4141			−0.671049
$838$	12.8247	−	22.2130i	0.443021	−	0.767335i
$839$	−13.2801			−0.458481			−0.229241	−	0.973370i	$-0.573624\pi$
$839$	−13.2801			−0.458481			−0.229241	+	0.973370i	$0.573624\pi$
$840$	0.546500			0.0188560
$841$	66.1524			2.28112
$842$	−67.4851			−2.32569
$843$	6.00170	+	10.3953i	0.206710	+	0.358032i
$844$	15.6066	+	27.0313i	0.537200	+	0.930457i
$845$	0.164053	+	0.284148i	0.00564359	+	0.00977499i
$846$	−33.5789			−1.15447
$847$	−5.47100			−0.187986
$848$	−2.71662	+	4.70532i	−0.0932891	+	0.161581i
$849$	8.50938	+	14.7387i	0.292041	+	0.505830i
$850$	0.0865384			0.00296824
$851$	92.7822			3.18053
$852$	0.896490			0.0307132
$853$	9.99483	−	17.3116i	0.342217	−	0.592736i	−0.642627	−	0.766179i	$-0.722156\pi$
$853$	9.99483	−	17.3116i	0.342217	−	0.592736i	0.984844	+	0.173442i	$0.0554890\pi$
$854$	−9.80133			−0.335395
$855$	−7.09458	−	12.2882i	−0.242630	−	0.420247i
$856$	−3.36523			−0.115021
$857$	−12.2456			−0.418301			−0.209150	−	0.977883i	$-0.567070\pi$
$857$	−12.2456			−0.418301			−0.209150	+	0.977883i	$0.567070\pi$
$858$	14.7342			0.503017
$859$	19.6169	+	33.9775i	0.669321	+	1.15930i	0.978094	+	0.208162i	$0.0667482\pi$
$859$	19.6169	+	33.9775i	0.669321	+	1.15930i	−0.308773	+	0.951136i	$0.599918\pi$
$860$	−4.97018	+	8.60861i	−0.169482	+	0.293551i
$861$	3.33013	−	5.76796i	0.113491	−	0.196571i
$862$	31.8235			1.08391
$863$	9.07604	−	15.7202i	0.308952	−	0.535120i	−0.669181	−	0.743099i	$-0.733355\pi$
$863$	9.07604	−	15.7202i	0.308952	−	0.535120i	0.978133	+	0.207979i	$0.0666884\pi$
$864$	21.4328	−	37.1227i	0.729158	−	1.26294i
$865$	−8.65604	+	14.9927i	−0.294314	+	0.509767i
$866$	3.00573	+	5.20608i	0.102139	+	0.176910i
$867$	−10.2071	+	17.6791i	−0.346650	+	0.600415i
$868$	−4.54312			−0.154204
$869$	−14.3369	−	24.8323i	−0.486347	−	0.842377i
$870$	−58.5410			−1.98472
$871$	−12.9129	+	22.3659i	−0.437539	+	0.757839i
$872$	0.706475	−	1.22365i	0.0239243	−	0.0414380i
$873$	−12.5448	+	21.7283i	−0.424578	+	0.735391i
$874$	−31.7965	+	55.0732i	−1.07553	+	1.86288i
$875$	3.08732	+	5.34740i	0.104371	+	0.180775i
$876$	4.89653			0.165438
$877$	−7.68680	−	13.3139i	−0.259565	−	0.449579i	0.706561	−	0.707652i	$-0.250246\pi$
$877$	−7.68680	−	13.3139i	−0.259565	−	0.449579i	−0.966125	+	0.258073i	$0.916912\pi$
$878$	6.62394			0.223547
$879$	15.0288			0.506910
$880$	9.38647	+	16.2578i	0.316418	+	0.548052i
$881$	15.1621	+	26.2616i	0.510826	+	0.884776i	0.999921	+	0.0125457i	$0.00399351\pi$
$881$	15.1621	+	26.2616i	0.510826	+	0.884776i	−0.489096	+	0.872230i	$0.662673\pi$
$882$	20.0034			0.673550
$883$	−11.4966	+	19.9127i	−0.386892	+	0.670117i	−0.992030	−	0.126004i	$-0.959785\pi$
$883$	−11.4966	+	19.9127i	−0.386892	+	0.670117i	0.605138	+	0.796121i	$0.293118\pi$
$884$	0.101105	+	0.175119i	0.00340052	+	0.00588988i
$885$	−33.6777			−1.13206
$886$	6.70975	−	11.6216i	0.225418	−	0.390436i
$887$	6.44116	−	11.1564i	0.216273	−	0.374596i	−0.737393	−	0.675464i	$-0.763943\pi$
$887$	6.44116	−	11.1564i	0.216273	−	0.374596i	0.953666	+	0.300869i	$0.0972765\pi$
$888$	1.61198	+	2.79202i	0.0540944	+	0.0936942i
$889$	5.02936			0.168679
$890$	−3.14532			−0.105431
$891$	1.65172	+	2.86086i	0.0553346	+	0.0958423i
$892$	−13.3458	−	23.1156i	−0.446850	−	0.773967i
$893$	19.6425	+	34.0218i	0.657311	+	1.13850i
$894$	4.39603	+	7.61415i	0.147025	+	0.254655i
$895$	−0.292093	+	0.505920i	−0.00976359	+	0.0169110i
$896$	−0.714732	+	1.23795i	−0.0238775	+	0.0413571i
$897$	−38.8714			−1.29788
$898$	12.3665	+	21.4195i	0.412677	+	0.714778i
$899$	−34.5988			−1.15394
$900$	−4.24073			−0.141358
$901$	0.0193042	−	0.0334359i	0.000643116	−	0.00111391i
$902$	27.6505			0.920660
$903$	0.862844	−	1.49449i	0.0287136	−	0.0497335i
$904$	1.71776	−	2.97525i	0.0571319	−	0.0989553i
$905$	−23.2740	−	40.3118i	−0.773654	−	1.34001i
$906$	1.37439	+	2.38051i	0.0456609	+	0.0790871i
$907$	20.5597	−	35.6105i	0.682675	−	1.18243i	−0.291487	−	0.956575i	$-0.594150\pi$
$907$	20.5597	−	35.6105i	0.682675	−	1.18243i	0.974162	−	0.225852i	$-0.0725167\pi$
$908$	2.66876	+	4.62242i	0.0885658	+	0.153400i
$909$	13.2146			0.438299
$910$	6.14922	−	10.6508i	0.203845	−	0.353069i
$911$	−0.694065	−	1.20216i	−0.0229954	−	0.0398292i	0.854299	−	0.519782i	$-0.173987\pi$
$911$	−0.694065	−	1.20216i	−0.0229954	−	0.0398292i	−0.877294	+	0.479953i	$0.840654\pi$
$912$	−18.2837			−0.605434
$913$	−0.276852	+	0.479521i	−0.00916245	+	0.0158698i
$914$	15.0222	+	26.0192i	0.496891	+	0.860640i
$915$	22.1734			0.733030
$916$	23.3616	+	40.4635i	0.771890	+	1.33695i
$917$	−5.32492	−	9.22303i	−0.175844	−	0.304571i
$918$	−0.162454	+	0.281379i	−0.00536180	+	0.00928690i
$919$	−26.0615	+	45.1399i	−0.859691	+	1.48903i	0.0125330	+	0.999921i	$0.496011\pi$
$919$	−26.0615	+	45.1399i	−0.859691	+	1.48903i	−0.872224	+	0.489107i	$0.837323\pi$
$920$	−2.99279	−	5.18366i	−0.0986693	−	0.170900i
$921$	−13.6538			−0.449907
$922$	22.9972			0.757371
$923$	−0.717154	+	1.24215i	−0.0236054	+	0.0408858i
$924$	1.33750	+	2.31662i	0.0440005	+	0.0762112i
$925$	7.49593	−	12.9833i	0.246465	−	0.426890i
$926$	−11.8459	−	20.5177i	−0.389281	−	0.674255i
$927$	−27.4143			−0.900404
$928$	38.1965	−	66.1582i	1.25386	−	2.17175i
$929$	−12.9986			−0.426471			−0.213235	−	0.977001i	$-0.568400\pi$
$929$	−12.9986			−0.426471			−0.213235	+	0.977001i	$0.568400\pi$
$930$	21.2864			0.698008
$931$	−11.7013	−	20.2672i	−0.383494	−	0.664232i
$932$	10.3344	+	17.8997i	0.338515	+	0.586325i
$933$	9.15507			0.299724
$934$	−37.6918	−	65.2841i	−1.23331	−	2.13616i
$935$	−0.0667000	−	0.115528i	−0.00218132	−	0.00377816i
$936$	0.729526	+	1.26358i	0.0238453	+	0.0413013i
$937$	−11.3446	−	19.6494i	−0.370611	−	0.641917i	0.619049	−	0.785353i	$-0.287518\pi$
$937$	−11.3446	−	19.6494i	−0.370611	−	0.641917i	−0.989660	+	0.143435i	$0.954185\pi$
$938$	−9.71075			−0.317067
$939$	11.0925	−	19.2128i	0.361991	−	0.626987i
$940$	52.0099			1.69638
$941$	−15.7894	−	27.3481i	−0.514721	−	0.891522i	−0.999854	−	0.0170822i	$-0.994562\pi$
$941$	−15.7894	−	27.3481i	−0.514721	−	0.891522i	0.485133	−	0.874440i	$-0.338771\pi$
$942$	20.4238	−	35.3751i	0.665443	−	1.15258i
$943$	−72.9469			−2.37548
$944$	23.4388	−	40.5972i	0.762869	−	1.32133i
$945$	9.54135			0.310380
$946$	7.16430			0.232931
$947$	−22.6996	+	39.3169i	−0.737639	+	1.27763i	0.215916	+	0.976412i	$0.430726\pi$
$947$	−22.6996	+	39.3169i	−0.737639	+	1.27763i	−0.953556	+	0.301217i	$0.902607\pi$
$948$	18.4862	−	32.0190i	0.600403	−	1.03993i
$949$	−3.91702	+	6.78448i	−0.127152	+	0.220233i
$950$	5.13772	+	8.89879i	0.166690	+	0.288715i
$951$	−4.01738	+	6.95831i	−0.130273	+	0.225639i
$952$	0.00270276	−	0.00468131i	8.75968e−5	−	0.000151722i
$953$	7.18461	−	12.4441i	0.232732	−	0.403104i	−0.725879	−	0.687822i	$-0.758567\pi$
$953$	7.18461	−	12.4441i	0.232732	−	0.403104i	0.958611	+	0.284718i	$0.0919001\pi$
$954$	−1.95922	+	3.39347i	−0.0634321	+	0.109868i
$955$	9.26597	+	16.0491i	0.299840	+	0.519338i
$956$	−43.8206			−1.41726
$957$	10.1859	+	17.6426i	0.329265	+	0.570303i
$958$	−4.77032	−	8.26244i	−0.154122	−	0.266947i
$959$	6.65785	−	11.5317i	0.214993	−	0.372379i
$960$	−10.5363	+	18.2494i	−0.340057	+	0.588997i
$961$	−18.4193			−0.594172
$962$	72.5519			2.33917
$963$	−20.0817			−0.647123
$964$	10.7712	+	18.6562i	0.346916	+	0.600876i
$965$	−27.3457	−	47.3641i	−0.880289	−	1.52470i
$966$	−7.30800	−	12.6578i	−0.235131	−	0.407259i
$967$	1.52250	−	2.63705i	0.0489603	−	0.0848017i	−0.840507	−	0.541801i	$-0.817743\pi$
$967$	1.52250	−	2.63705i	0.0489603	−	0.0848017i	0.889467	+	0.456999i	$0.151076\pi$
$968$	−1.04106	+	1.80317i	−0.0334610	+	0.0579561i
$969$	0.129923			0.00417374
$970$	40.2424	−	69.7019i	1.29211	−	2.23799i
$971$	−3.89654	−	6.74901i	−0.125046	−	0.216586i	0.796705	−	0.604368i	$-0.206574\pi$
$971$	−3.89654	−	6.74901i	−0.125046	−	0.216586i	−0.921751	+	0.387783i	$0.873241\pi$
$972$	13.2008	−	22.8645i	0.423417	−	0.733380i
$973$	−3.56106	+	6.16793i	−0.114162	+	0.197735i
$974$	−25.0313	+	43.3554i	−0.802053	+	1.38920i
$975$	−3.14045	+	5.43942i	−0.100575	+	0.174201i
$976$	−15.4321	+	26.7292i	−0.493970	+	0.855581i
$977$	−29.1046	−	50.4107i	−0.931140	−	1.61278i	−0.781377	−	0.624060i	$-0.785482\pi$
$977$	−29.1046	−	50.4107i	−0.931140	−	1.61278i	−0.149763	−	0.988722i	$-0.547851\pi$
$978$	5.50511	−	9.53513i	0.176034	−	0.304900i
$979$	0.547276	+	0.947910i	0.0174910	+	0.0302953i
$980$	−30.9830			−0.989714
$981$	4.21582	−	7.30202i	0.134601	−	0.233136i
$982$	38.5001	−	66.6842i	1.22859	−	2.12798i
$983$	28.9766	+	50.1890i	0.924211	+	1.60078i	0.792826	+	0.609449i	$0.208609\pi$
$983$	28.9766	+	50.1890i	0.924211	+	1.60078i	0.131385	+	0.991331i	$0.458058\pi$
$984$	−1.26736	−	2.19514i	−0.0404020	−	0.0699784i
$985$	−30.1389	+	52.2021i	−0.960305	+	1.66330i
$986$	−0.289519	+	0.501461i	−0.00922015	+	0.0159698i
$987$	−9.02912			−0.287400
$988$	−12.0050	+	20.7933i	−0.381931	+	0.661524i
$989$	−18.9007			−0.601007
$990$	6.76951	+	11.7251i	0.215149	+	0.372649i
$991$	−54.6925			−1.73736			−0.868682	−	0.495371i	$-0.835032\pi$
$991$	−54.6925			−1.73736			−0.868682	+	0.495371i	$0.835032\pi$
$992$	−13.8888	+	24.0561i	−0.440970	+	0.763783i
$993$	−8.77502			−0.278467
$994$	−0.539312			−0.0171059
$995$	−20.0217	−	34.6786i	−0.634730	−	1.09938i
$996$	−0.713951			−0.0226224
$997$	5.17430	−	8.96216i	0.163872	−	0.283834i	−0.772382	−	0.635158i	$-0.780935\pi$
$997$	5.17430	−	8.96216i	0.163872	−	0.283834i	0.936254	+	0.351324i	$0.114268\pi$
$998$	−16.5400	+	28.6482i	−0.523566	+	0.906843i
$999$	28.1435	+	48.7460i	0.890422	+	1.54226i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	547.2.c.a.40.7	✓	90
547.506	even	3	inner	547.2.c.a.506.7	yes	90

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
547.2.c.a.40.7	✓	90	1.1	even	1	trivial
547.2.c.a.506.7	yes	90	547.506	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 547 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	547.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.983266 - 1.70307i) q^{2} -1.20089 q^{3} +(-0.933624 + 1.61708i) q^{4} +(-1.27061 + 2.20077i) q^{5} +(1.18080 + 2.04520i) q^{6} +(-0.342982 - 0.594062i) q^{7} -0.261060 q^{8} -1.55785 q^{9} +O(q^{10})\)	\(q+(-0.983266 - 1.70307i) q^{2} -1.20089 q^{3} +(-0.933624 + 1.61708i) q^{4} +(-1.27061 + 2.20077i) q^{5} +(1.18080 + 2.04520i) q^{6} +(-0.342982 - 0.594062i) q^{7} -0.261060 q^{8} -1.55785 q^{9} +4.99741 q^{10} +(-0.869533 - 1.50608i) q^{11} +(1.12118 - 1.94195i) q^{12} +(1.79380 + 3.10695i) q^{13} +(-0.674484 + 1.16824i) q^{14} +(1.52587 - 2.64289i) q^{15} +(2.12394 + 3.67877i) q^{16} +(-0.0150927 - 0.0261412i) q^{17} +(1.53178 + 2.65312i) q^{18} +(1.79208 - 3.10397i) q^{19} +(-2.37255 - 4.10938i) q^{20} +(0.411885 + 0.713405i) q^{21} +(-1.70996 + 2.96175i) q^{22} +(4.51119 - 7.81362i) q^{23} +0.313506 q^{24} +(-0.728924 - 1.26253i) q^{25} +(3.52757 - 6.10993i) q^{26} +5.47350 q^{27} +1.28086 q^{28} +9.75461 q^{29} -6.00136 q^{30} -3.54692 q^{31} +(3.91574 - 6.78225i) q^{32} +(1.04422 + 1.80864i) q^{33} +(-0.0296802 + 0.0514076i) q^{34} +1.74319 q^{35} +(1.45445 - 2.51918i) q^{36} +(5.14178 + 8.90582i) q^{37} -7.04836 q^{38} +(-2.15417 - 3.73113i) q^{39} +(0.331707 - 0.574533i) q^{40} +(-4.04255 - 7.00190i) q^{41} +(0.809985 - 1.40293i) q^{42} +(-1.04743 - 1.81421i) q^{43} +3.24727 q^{44} +(1.97943 - 3.42847i) q^{45} -17.7428 q^{46} +(-5.48037 + 9.49228i) q^{47} +(-2.55063 - 4.41782i) q^{48} +(3.26473 - 5.65467i) q^{49} +(-1.43345 + 2.48281i) q^{50} +(0.0181247 + 0.0313929i) q^{51} -6.69894 q^{52} +(0.639523 + 1.10769i) q^{53} +(-5.38191 - 9.32174i) q^{54} +4.41937 q^{55} +(0.0895388 + 0.155086i) q^{56} +(-2.15210 + 3.72754i) q^{57} +(-9.59138 - 16.6127i) q^{58} +(-5.51777 - 9.55706i) q^{59} +(2.84919 + 4.93494i) q^{60} +(3.63290 + 6.29237i) q^{61} +(3.48757 + 6.04065i) q^{62} +(0.534314 + 0.925460i) q^{63} -6.90508 q^{64} -9.11692 q^{65} +(2.05349 - 3.55675i) q^{66} +(3.59933 + 6.23421i) q^{67} +0.0563635 q^{68} +(-5.41747 + 9.38333i) q^{69} +(-1.71402 - 2.96877i) q^{70} +(0.199898 + 0.346233i) q^{71} +0.406693 q^{72} +(1.09182 + 1.89109i) q^{73} +(10.1115 - 17.5136i) q^{74} +(0.875362 + 1.51617i) q^{75} +(3.34626 + 5.79588i) q^{76} +(-0.596468 + 1.03311i) q^{77} +(-4.23624 + 7.33738i) q^{78} +16.4881 q^{79} -10.7948 q^{80} -1.89954 q^{81} +(-7.94981 + 13.7695i) q^{82} +(-0.159196 - 0.275735i) q^{83} -1.53818 q^{84} +0.0767078 q^{85} +(-2.05981 + 3.56770i) q^{86} -11.7143 q^{87} +(0.227000 + 0.393176i) q^{88} -0.629391 q^{89} -7.78522 q^{90} +(1.23048 - 2.13126i) q^{91} +(8.42352 + 14.5900i) q^{92} +4.25948 q^{93} +21.5546 q^{94} +(4.55408 + 7.88790i) q^{95} +(-4.70239 + 8.14477i) q^{96} +(8.05265 - 13.9476i) q^{97} -12.8404 q^{98} +(1.35460 + 2.34624i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 90 q - q^{2} - 4 q^{3} - 47 q^{4} + q^{5} - 3 q^{6} + 2 q^{7} - 30 q^{8} + 82 q^{9}+O(q^{10}) \) 90 * q - q^2 - 4 * q^3 - 47 * q^4 + q^5 - 3 * q^6 + 2 * q^7 - 30 * q^8 + 82 * q^9	\( 90 q - q^{2} - 4 q^{3} - 47 q^{4} + q^{5} - 3 q^{6} + 2 q^{7} - 30 q^{8} + 82 q^{9} - 10 q^{10} + q^{11} + 4 q^{12} - 3 q^{13} + 2 q^{14} - 7 q^{15} - 39 q^{16} - 4 q^{17} - 11 q^{18} - 2 q^{19} + 25 q^{20} - 27 q^{21} - 7 q^{22} + q^{23} + 32 q^{24} - 40 q^{25} - 10 q^{26} - 34 q^{27} - 28 q^{28} + 26 q^{29} - 40 q^{30} - 24 q^{31} + 19 q^{32} + q^{33} - 6 q^{34} - 8 q^{35} - 36 q^{36} - 10 q^{37} + 24 q^{38} + 22 q^{39} + 20 q^{40} + 3 q^{41} + 38 q^{42} - 12 q^{43} - 30 q^{44} - 2 q^{45} - 40 q^{46} + 32 q^{47} + 14 q^{48} - 43 q^{49} + 14 q^{50} + 13 q^{51} + 46 q^{52} + 9 q^{53} - 8 q^{54} + 4 q^{55} - 8 q^{56} - 8 q^{57} + 4 q^{58} + 22 q^{59} - 2 q^{60} - 12 q^{61} + 11 q^{62} + 8 q^{63} + 22 q^{64} + 18 q^{65} + 12 q^{66} - 22 q^{67} + 6 q^{68} - q^{69} - 6 q^{70} - 4 q^{71} - 140 q^{72} + 17 q^{73} + 17 q^{74} + 39 q^{75} + 84 q^{76} - 4 q^{77} + 33 q^{78} - 72 q^{79} - 40 q^{80} + 18 q^{81} - 9 q^{82} + 24 q^{83} + 114 q^{84} + 40 q^{85} - 72 q^{86} - 78 q^{87} - 22 q^{88} + 14 q^{89} + 96 q^{90} - 8 q^{92} - 76 q^{93} + 108 q^{94} - 11 q^{95} - 34 q^{96} - 74 q^{98} - 62 q^{99}+O(q^{100}) \) 90 * q - q^2 - 4 * q^3 - 47 * q^4 + q^5 - 3 * q^6 + 2 * q^7 - 30 * q^8 + 82 * q^9 - 10 * q^10 + q^11 + 4 * q^12 - 3 * q^13 + 2 * q^14 - 7 * q^15 - 39 * q^16 - 4 * q^17 - 11 * q^18 - 2 * q^19 + 25 * q^20 - 27 * q^21 - 7 * q^22 + q^23 + 32 * q^24 - 40 * q^25 - 10 * q^26 - 34 * q^27 - 28 * q^28 + 26 * q^29 - 40 * q^30 - 24 * q^31 + 19 * q^32 + q^33 - 6 * q^34 - 8 * q^35 - 36 * q^36 - 10 * q^37 + 24 * q^38 + 22 * q^39 + 20 * q^40 + 3 * q^41 + 38 * q^42 - 12 * q^43 - 30 * q^44 - 2 * q^45 - 40 * q^46 + 32 * q^47 + 14 * q^48 - 43 * q^49 + 14 * q^50 + 13 * q^51 + 46 * q^52 + 9 * q^53 - 8 * q^54 + 4 * q^55 - 8 * q^56 - 8 * q^57 + 4 * q^58 + 22 * q^59 - 2 * q^60 - 12 * q^61 + 11 * q^62 + 8 * q^63 + 22 * q^64 + 18 * q^65 + 12 * q^66 - 22 * q^67 + 6 * q^68 - q^69 - 6 * q^70 - 4 * q^71 - 140 * q^72 + 17 * q^73 + 17 * q^74 + 39 * q^75 + 84 * q^76 - 4 * q^77 + 33 * q^78 - 72 * q^79 - 40 * q^80 + 18 * q^81 - 9 * q^82 + 24 * q^83 + 114 * q^84 + 40 * q^85 - 72 * q^86 - 78 * q^87 - 22 * q^88 + 14 * q^89 + 96 * q^90 - 8 * q^92 - 76 * q^93 + 108 * q^94 - 11 * q^95 - 34 * q^96 - 74 * q^98 - 62 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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