LMFDB - Embedded newform 1110.2.l.a.697.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(43,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("1110.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.l (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:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			697.14
Character	$\chi$	$=$	1110.697
Dual form			1110.2.l.a.43.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(-1.52512 - 1.63524i) q^{5} +(0.707107 - 0.707107i) q^{6} +(1.84299 + 1.84299i) q^{7} +1.00000i q^{8} +1.00000i q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(-1.52512 - 1.63524i) q^{5} +(0.707107 - 0.707107i) q^{6} +(1.84299 + 1.84299i) q^{7} +1.00000i q^{8} +1.00000i q^{9} +(-1.63524 + 1.52512i) q^{10} +3.01042i q^{11} +(-0.707107 - 0.707107i) q^{12} +1.82067i q^{13} +(1.84299 - 1.84299i) q^{14} +(0.0778616 - 2.23471i) q^{15} +1.00000 q^{16} -5.42248 q^{17} +1.00000 q^{18} +(-0.509592 - 0.509592i) q^{19} +(1.52512 + 1.63524i) q^{20} +2.60638i q^{21} +3.01042 q^{22} +0.0216604i q^{23} +(-0.707107 + 0.707107i) q^{24} +(-0.347996 + 4.98788i) q^{25} +1.82067 q^{26} +(-0.707107 + 0.707107i) q^{27} +(-1.84299 - 1.84299i) q^{28} +(-4.67832 + 4.67832i) q^{29} +(-2.23471 - 0.0778616i) q^{30} +(1.55104 + 1.55104i) q^{31} -1.00000i q^{32} +(-2.12868 + 2.12868i) q^{33} +5.42248i q^{34} +(0.202937 - 5.82450i) q^{35} -1.00000i q^{36} +(5.64218 + 2.27285i) q^{37} +(-0.509592 + 0.509592i) q^{38} +(-1.28741 + 1.28741i) q^{39} +(1.63524 - 1.52512i) q^{40} +6.35587i q^{41} +2.60638 q^{42} +7.86706i q^{43} -3.01042i q^{44} +(1.63524 - 1.52512i) q^{45} +0.0216604 q^{46} +(-0.176174 - 0.176174i) q^{47} +(0.707107 + 0.707107i) q^{48} -0.206804i q^{49} +(4.98788 + 0.347996i) q^{50} +(-3.83427 - 3.83427i) q^{51} -1.82067i q^{52} +(2.05089 - 2.05089i) q^{53} +(0.707107 + 0.707107i) q^{54} +(4.92274 - 4.59126i) q^{55} +(-1.84299 + 1.84299i) q^{56} -0.720673i q^{57} +(4.67832 + 4.67832i) q^{58} +(-2.84934 - 2.84934i) q^{59} +(-0.0778616 + 2.23471i) q^{60} +(4.51718 + 4.51718i) q^{61} +(1.55104 - 1.55104i) q^{62} +(-1.84299 + 1.84299i) q^{63} -1.00000 q^{64} +(2.97723 - 2.77675i) q^{65} +(2.12868 + 2.12868i) q^{66} +(3.93891 - 3.93891i) q^{67} +5.42248 q^{68} +(-0.0153162 + 0.0153162i) q^{69} +(-5.82450 - 0.202937i) q^{70} +9.00950 q^{71} -1.00000 q^{72} +(8.50501 + 8.50501i) q^{73} +(2.27285 - 5.64218i) q^{74} +(-3.77303 + 3.28089i) q^{75} +(0.509592 + 0.509592i) q^{76} +(-5.54815 + 5.54815i) q^{77} +(1.28741 + 1.28741i) q^{78} +(-2.16377 - 2.16377i) q^{79} +(-1.52512 - 1.63524i) q^{80} -1.00000 q^{81} +6.35587 q^{82} +(0.925954 - 0.925954i) q^{83} -2.60638i q^{84} +(8.26996 + 8.86704i) q^{85} +7.86706 q^{86} -6.61614 q^{87} -3.01042 q^{88} +(1.03976 - 1.03976i) q^{89} +(-1.52512 - 1.63524i) q^{90} +(-3.35547 + 3.35547i) q^{91} -0.0216604i q^{92} +2.19350i q^{93} +(-0.176174 + 0.176174i) q^{94} +(-0.0561127 + 1.61050i) q^{95} +(0.707107 - 0.707107i) q^{96} -7.65590 q^{97} -0.206804 q^{98} -3.01042 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 36 q^{4} + 4 q^{7}+O(q^{10}) $ 36 * q - 36 * q^4 + 4 * q^7	$ 36 q - 36 q^{4} + 4 q^{7} - 4 q^{10} + 4 q^{14} + 36 q^{16} - 32 q^{17} + 36 q^{18} + 4 q^{19} + 8 q^{22} - 4 q^{25} + 8 q^{26} - 4 q^{28} + 36 q^{29} - 4 q^{31} + 4 q^{33} - 12 q^{35} - 4 q^{37} + 4 q^{38} + 4 q^{39} + 4 q^{40} - 16 q^{42} + 4 q^{45} + 16 q^{47} - 16 q^{50} - 8 q^{53} + 16 q^{55} - 4 q^{56} - 36 q^{58} - 4 q^{59} - 4 q^{61} - 4 q^{62} - 4 q^{63} - 36 q^{64} + 52 q^{65} - 4 q^{66} + 16 q^{67} + 32 q^{68} - 8 q^{69} - 28 q^{70} - 8 q^{71} - 36 q^{72} - 4 q^{73} + 28 q^{74} + 16 q^{75} - 4 q^{76} + 8 q^{77} - 4 q^{78} - 12 q^{79} - 36 q^{81} - 8 q^{82} + 8 q^{83} + 8 q^{85} + 32 q^{86} - 8 q^{87} - 8 q^{88} - 24 q^{89} + 56 q^{91} + 16 q^{94} - 20 q^{95} + 40 q^{97} - 12 q^{98} - 8 q^{99}+O(q^{100}) $ 36 * q - 36 * q^4 + 4 * q^7 - 4 * q^10 + 4 * q^14 + 36 * q^16 - 32 * q^17 + 36 * q^18 + 4 * q^19 + 8 * q^22 - 4 * q^25 + 8 * q^26 - 4 * q^28 + 36 * q^29 - 4 * q^31 + 4 * q^33 - 12 * q^35 - 4 * q^37 + 4 * q^38 + 4 * q^39 + 4 * q^40 - 16 * q^42 + 4 * q^45 + 16 * q^47 - 16 * q^50 - 8 * q^53 + 16 * q^55 - 4 * q^56 - 36 * q^58 - 4 * q^59 - 4 * q^61 - 4 * q^62 - 4 * q^63 - 36 * q^64 + 52 * q^65 - 4 * q^66 + 16 * q^67 + 32 * q^68 - 8 * q^69 - 28 * q^70 - 8 * q^71 - 36 * q^72 - 4 * q^73 + 28 * q^74 + 16 * q^75 - 4 * q^76 + 8 * q^77 - 4 * q^78 - 12 * q^79 - 36 * q^81 - 8 * q^82 + 8 * q^83 + 8 * q^85 + 32 * q^86 - 8 * q^87 - 8 * q^88 - 24 * q^89 + 56 * q^91 + 16 * q^94 - 20 * q^95 + 40 * q^97 - 12 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$4$	−1.00000			−0.500000
$5$	−1.52512	−	1.63524i	−0.682056	−	0.731300i
$5$	−1.52512	−	1.63524i	−0.682056	−	0.731300i
$6$	0.707107	−	0.707107i	0.288675	−	0.288675i
$7$	1.84299	+	1.84299i	0.696583	+	0.696583i	0.963672	−	0.267089i	$-0.0860617\pi$
$7$	1.84299	+	1.84299i	0.696583	+	0.696583i	−0.267089	+	0.963672i	$0.586062\pi$
$8$			1.00000i			0.353553i
$9$			1.00000i			0.333333i
$10$	−1.63524	+	1.52512i	−0.517107	+	0.482286i
$11$			3.01042i			0.907674i	0.891085	+	0.453837i	$0.149945\pi$
$11$			3.01042i			0.907674i	−0.891085	+	0.453837i	$0.850055\pi$
$12$	−0.707107	−	0.707107i	−0.204124	−	0.204124i
$13$			1.82067i			0.504963i	0.967602	+	0.252481i	$0.0812467\pi$
$13$			1.82067i			0.504963i	−0.967602	+	0.252481i	$0.918753\pi$
$14$	1.84299	−	1.84299i	0.492559	−	0.492559i
$15$	0.0778616	−	2.23471i	0.0201038	−	0.577000i
$16$	1.00000			0.250000
$17$	−5.42248			−1.31515			−0.657573	−	0.753391i	$-0.728417\pi$
$17$	−5.42248			−1.31515			−0.657573	+	0.753391i	$0.728417\pi$
$18$	1.00000			0.235702
$19$	−0.509592	−	0.509592i	−0.116909	−	0.116909i	0.646232	−	0.763141i	$-0.276344\pi$
$19$	−0.509592	−	0.509592i	−0.116909	−	0.116909i	−0.763141	+	0.646232i	$0.776344\pi$
$20$	1.52512	+	1.63524i	0.341028	+	0.365650i
$21$			2.60638i			0.568758i
$22$	3.01042			0.641823
$23$			0.0216604i			0.00451651i	0.999997	+	0.00225825i	$0.000718825\pi$
$23$			0.0216604i			0.00451651i	−0.999997	+	0.00225825i	$0.999281\pi$
$24$	−0.707107	+	0.707107i	−0.144338	+	0.144338i
$25$	−0.347996	+	4.98788i	−0.0695993	+	0.997575i
$26$	1.82067			0.357063
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	−1.84299	−	1.84299i	−0.348292	−	0.348292i
$29$	−4.67832	+	4.67832i	−0.868742	+	0.868742i	−0.992333	−	0.123591i	$-0.960559\pi$
$29$	−4.67832	+	4.67832i	−0.868742	+	0.868742i	0.123591	+	0.992333i	$0.460559\pi$
$30$	−2.23471	−	0.0778616i	−0.408001	−	0.0142155i
$31$	1.55104	+	1.55104i	0.278574	+	0.278574i	0.832540	−	0.553965i	$-0.186886\pi$
$31$	1.55104	+	1.55104i	0.278574	+	0.278574i	−0.553965	+	0.832540i	$0.686886\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−2.12868	+	2.12868i	−0.370556	+	0.370556i
$34$			5.42248i			0.929948i
$35$	0.202937	−	5.82450i	0.0343025	−	0.984520i
$36$		−	1.00000i		−	0.166667i
$37$	5.64218	+	2.27285i	0.927568	+	0.373655i
$37$	5.64218	+	2.27285i	0.927568	+	0.373655i
$38$	−0.509592	+	0.509592i	−0.0826668	+	0.0826668i
$39$	−1.28741	+	1.28741i	−0.206150	+	0.206150i
$40$	1.63524	−	1.52512i	0.258554	−	0.241143i
$41$			6.35587i			0.992619i	0.868146	+	0.496310i	$0.165312\pi$
$41$			6.35587i			0.992619i	−0.868146	+	0.496310i	$0.834688\pi$
$42$	2.60638			0.402173
$43$			7.86706i			1.19972i	0.800107	+	0.599858i	$0.204776\pi$
$43$			7.86706i			1.19972i	−0.800107	+	0.599858i	$0.795224\pi$
$44$		−	3.01042i		−	0.453837i
$45$	1.63524	−	1.52512i	0.243767	−	0.227352i
$46$	0.0216604			0.00319365
$47$	−0.176174	−	0.176174i	−0.0256976	−	0.0256976i	0.694141	−	0.719839i	$-0.255784\pi$
$47$	−0.176174	−	0.176174i	−0.0256976	−	0.0256976i	−0.719839	+	0.694141i	$0.755784\pi$
$48$	0.707107	+	0.707107i	0.102062	+	0.102062i
$49$		−	0.206804i		−	0.0295435i
$50$	4.98788	+	0.347996i	0.705392	+	0.0492141i
$51$	−3.83427	−	3.83427i	−0.536906	−	0.536906i
$52$		−	1.82067i		−	0.252481i
$53$	2.05089	−	2.05089i	0.281711	−	0.281711i	−0.552080	−	0.833791i	$-0.686166\pi$
$53$	2.05089	−	2.05089i	0.281711	−	0.281711i	0.833791	+	0.552080i	$0.186166\pi$
$54$	0.707107	+	0.707107i	0.0962250	+	0.0962250i
$55$	4.92274	−	4.59126i	0.663782	−	0.619085i
$56$	−1.84299	+	1.84299i	−0.246279	+	0.246279i
$57$		−	0.720673i		−	0.0954554i
$58$	4.67832	+	4.67832i	0.614293	+	0.614293i
$59$	−2.84934	−	2.84934i	−0.370952	−	0.370952i	0.496872	−	0.867824i	$-0.334482\pi$
$59$	−2.84934	−	2.84934i	−0.370952	−	0.370952i	−0.867824	+	0.496872i	$0.834482\pi$
$60$	−0.0778616	+	2.23471i	−0.0100519	+	0.288500i
$61$	4.51718	+	4.51718i	0.578366	+	0.578366i	0.934453	−	0.356087i	$-0.115889\pi$
$61$	4.51718	+	4.51718i	0.578366	+	0.578366i	−0.356087	+	0.934453i	$0.615889\pi$
$62$	1.55104	−	1.55104i	0.196982	−	0.196982i
$63$	−1.84299	+	1.84299i	−0.232194	+	0.232194i
$64$	−1.00000			−0.125000
$65$	2.97723	−	2.77675i	0.369279	−	0.344413i
$66$	2.12868	+	2.12868i	0.262023	+	0.262023i
$67$	3.93891	−	3.93891i	0.481215	−	0.481215i	−0.424305	−	0.905519i	$-0.639481\pi$
$67$	3.93891	−	3.93891i	0.481215	−	0.481215i	0.905519	+	0.424305i	$0.139481\pi$
$68$	5.42248			0.657573
$69$	−0.0153162	+	0.0153162i	−0.00184386	+	0.00184386i
$70$	−5.82450	−	0.202937i	−0.696161	−	0.0242556i
$71$	9.00950			1.06923			0.534615	−	0.845095i	$-0.320456\pi$
$71$	9.00950			1.06923			0.534615	+	0.845095i	$0.320456\pi$
$72$	−1.00000			−0.117851
$73$	8.50501	+	8.50501i	0.995437	+	0.995437i	0.999990	−	0.00455309i	$-0.00144930\pi$
$73$	8.50501	+	8.50501i	0.995437	+	0.995437i	−0.00455309	+	0.999990i	$0.501449\pi$
$74$	2.27285	−	5.64218i	0.264214	−	0.655890i
$75$	−3.77303	+	3.28089i	−0.435672	+	0.378845i
$76$	0.509592	+	0.509592i	0.0584543	+	0.0584543i
$77$	−5.54815	+	5.54815i	−0.632271	+	0.632271i
$78$	1.28741	+	1.28741i	0.145770	+	0.145770i
$79$	−2.16377	−	2.16377i	−0.243444	−	0.243444i	0.574830	−	0.818273i	$-0.305068\pi$
$79$	−2.16377	−	2.16377i	−0.243444	−	0.243444i	−0.818273	+	0.574830i	$0.805068\pi$
$80$	−1.52512	−	1.63524i	−0.170514	−	0.182825i
$81$	−1.00000			−0.111111
$82$	6.35587			0.701888
$83$	0.925954	−	0.925954i	0.101637	−	0.101637i	−0.654460	−	0.756097i	$-0.727104\pi$
$83$	0.925954	−	0.925954i	0.101637	−	0.101637i	0.756097	+	0.654460i	$0.227104\pi$
$84$		−	2.60638i		−	0.284379i
$85$	8.26996	+	8.86704i	0.897003	+	0.961766i
$86$	7.86706			0.848327
$87$	−6.61614			−0.709325
$88$	−3.01042			−0.320911
$89$	1.03976	−	1.03976i	0.110214	−	0.110214i	−0.649849	−	0.760063i	$-0.725168\pi$
$89$	1.03976	−	1.03976i	0.110214	−	0.110214i	0.760063	+	0.649849i	$0.225168\pi$
$90$	−1.52512	−	1.63524i	−0.160762	−	0.172369i
$91$	−3.35547	+	3.35547i	−0.351749	+	0.351749i
$92$		−	0.0216604i		−	0.00225825i
$93$			2.19350i			0.227455i
$94$	−0.176174	+	0.176174i	−0.0181710	+	0.0181710i
$95$	−0.0561127	+	1.61050i	−0.00575704	+	0.165233i
$96$	0.707107	−	0.707107i	0.0721688	−	0.0721688i
$97$	−7.65590			−0.777339			−0.388670	−	0.921377i	$-0.627065\pi$
$97$	−7.65590			−0.777339			−0.388670	+	0.921377i	$0.627065\pi$
$98$	−0.206804			−0.0208904
$99$	−3.01042			−0.302558
$100$	0.347996	−	4.98788i	0.0347996	−	0.498788i
$101$			16.6519i			1.65693i	0.560040	+	0.828465i	$0.310786\pi$
$101$			16.6519i			1.65693i	−0.560040	+	0.828465i	$0.689214\pi$
$102$	−3.83427	+	3.83427i	−0.379650	+	0.379650i
$103$	−15.2064			−1.49833			−0.749165	−	0.662383i	$-0.769545\pi$
$103$	−15.2064			−1.49833			−0.749165	+	0.662383i	$0.769545\pi$
$104$	−1.82067			−0.178531
$105$	4.26204	−	3.97505i	0.415933	−	0.387925i
$106$	−2.05089	−	2.05089i	−0.199200	−	0.199200i
$107$	−7.85181	−	7.85181i	−0.759063	−	0.759063i	0.217089	−	0.976152i	$-0.430344\pi$
$107$	−7.85181	−	7.85181i	−0.759063	−	0.759063i	−0.976152	+	0.217089i	$0.930344\pi$
$108$	0.707107	−	0.707107i	0.0680414	−	0.0680414i
$109$	−5.15891	−	5.15891i	−0.494134	−	0.494134i	0.415472	−	0.909606i	$-0.363616\pi$
$109$	−5.15891	−	5.15891i	−0.494134	−	0.494134i	−0.909606	+	0.415472i	$0.863616\pi$
$110$	−4.59126	−	4.92274i	−0.437759	−	0.469365i
$111$	2.38247	+	5.59677i	0.226134	+	0.531222i
$112$	1.84299	+	1.84299i	0.174146	+	0.174146i
$113$	−3.80319			−0.357774			−0.178887	−	0.983870i	$-0.557250\pi$
$113$	−3.80319			−0.357774			−0.178887	+	0.983870i	$0.557250\pi$
$114$	−0.720673			−0.0674972
$115$	0.0354199	−	0.0330348i	0.00330292	−	0.00308051i
$116$	4.67832	−	4.67832i	0.434371	−	0.434371i
$117$	−1.82067			−0.168321
$118$	−2.84934	+	2.84934i	−0.262303	+	0.262303i
$119$	−9.99356	−	9.99356i	−0.916108	−	0.916108i
$120$	2.23471	+	0.0778616i	0.204000	+	0.00710776i
$121$	1.93740			0.176127
$122$	4.51718	−	4.51718i	0.408966	−	0.408966i
$123$	−4.49428	+	4.49428i	−0.405235	+	0.405235i
$124$	−1.55104	−	1.55104i	−0.139287	−	0.139287i
$125$	8.68709	−	7.03807i	0.776997	−	0.629504i
$126$	1.84299	+	1.84299i	0.164186	+	0.164186i
$127$	9.77118	+	9.77118i	0.867052	+	0.867052i	0.992145	−	0.125093i	$-0.0399229\pi$
$127$	9.77118	+	9.77118i	0.867052	+	0.867052i	−0.125093	+	0.992145i	$0.539923\pi$
$128$			1.00000i			0.0883883i
$129$	−5.56285	+	5.56285i	−0.489782	+	0.489782i
$130$	−2.77675	−	2.97723i	−0.243537	−	0.261120i
$131$	2.21257	+	2.21257i	0.193313	+	0.193313i	0.797126	−	0.603813i	$-0.206353\pi$
$131$	2.21257	+	2.21257i	0.193313	+	0.193313i	−0.603813	+	0.797126i	$0.706353\pi$
$132$	2.12868	−	2.12868i	0.185278	−	0.185278i
$133$		−	1.87834i		−	0.162873i
$134$	−3.93891	−	3.93891i	−0.340270	−	0.340270i
$135$	2.23471	+	0.0778616i	0.192333	+	0.00670126i
$136$		−	5.42248i		−	0.464974i
$137$	−5.72235	−	5.72235i	−0.488894	−	0.488894i	0.419063	−	0.907957i	$-0.362359\pi$
$137$	−5.72235	−	5.72235i	−0.488894	−	0.488894i	−0.907957	+	0.419063i	$0.862359\pi$
$138$	0.0153162	+	0.0153162i	0.00130380	+	0.00130380i
$139$	4.18150			0.354670			0.177335	−	0.984151i	$-0.443252\pi$
$139$	4.18150			0.354670			0.177335	+	0.984151i	$0.443252\pi$
$140$	−0.202937	+	5.82450i	−0.0171513	+	0.492260i
$141$		−	0.249148i		−	0.0209820i
$142$		−	9.00950i		−	0.756060i
$143$	−5.48097			−0.458342
$144$			1.00000i			0.0833333i
$145$	14.7852	+	0.515143i	1.22784	+	0.0427803i
$146$	8.50501	−	8.50501i	0.703880	−	0.703880i
$147$	0.146233	−	0.146233i	0.0120611	−	0.0120611i
$148$	−5.64218	−	2.27285i	−0.463784	−	0.186827i
$149$			2.65031i			0.217122i	0.994090	+	0.108561i	$0.0346243\pi$
$149$			2.65031i			0.217122i	−0.994090	+	0.108561i	$0.965376\pi$
$150$	3.28089	+	3.77303i	0.267884	+	0.308067i
$151$		−	3.91246i		−	0.318391i	−0.987247	−	0.159196i	$-0.949110\pi$
$151$		−	3.91246i		−	0.318391i	0.987247	−	0.159196i	$-0.0508901\pi$
$152$	0.509592	−	0.509592i	0.0413334	−	0.0413334i
$153$		−	5.42248i		−	0.438382i
$154$	5.54815	+	5.54815i	0.447083	+	0.447083i
$155$	0.170789	−	4.90183i	0.0137181	−	0.393725i
$156$	1.28741	−	1.28741i	0.103075	−	0.103075i
$157$	−12.9226	−	12.9226i	−1.03134	−	1.03134i	−0.999493	−	0.0318468i	$-0.989861\pi$
$157$	−12.9226	−	12.9226i	−1.03134	−	1.03134i	−0.0318468	−	0.999493i	$-0.510139\pi$
$158$	−2.16377	+	2.16377i	−0.172141	+	0.172141i
$159$	2.90039			0.230016
$160$	−1.63524	+	1.52512i	−0.129277	+	0.120572i
$161$	−0.0399199	+	0.0399199i	−0.00314613	+	0.00314613i
$162$			1.00000i			0.0785674i
$163$	−8.59786			−0.673437			−0.336718	−	0.941605i	$-0.609317\pi$
$163$	−8.59786			−0.673437			−0.336718	+	0.941605i	$0.609317\pi$
$164$		−	6.35587i		−	0.496310i
$165$	6.72741	+	0.234396i	0.523728	+	0.0182477i
$166$	−0.925954	−	0.925954i	−0.0718680	−	0.0718680i
$167$	4.59086			0.355252			0.177626	−	0.984098i	$-0.443158\pi$
$167$	4.59086			0.355252			0.177626	+	0.984098i	$0.443158\pi$
$168$	−2.60638			−0.201086
$169$	9.68516			0.745012
$170$	8.86704	−	8.26996i	0.680071	−	0.634277i
$171$	0.509592	−	0.509592i	0.0389695	−	0.0389695i
$172$		−	7.86706i		−	0.599858i
$173$	−6.49792	−	6.49792i	−0.494028	−	0.494028i	0.415545	−	0.909573i	$-0.363591\pi$
$173$	−6.49792	−	6.49792i	−0.494028	−	0.494028i	−0.909573	+	0.415545i	$0.863591\pi$
$174$			6.61614i			0.501568i
$175$	−9.83394	+	8.55123i	−0.743376	+	0.646412i
$176$			3.01042i			0.226919i
$177$		−	4.02957i		−	0.302881i
$178$	−1.03976	−	1.03976i	−0.0779333	−	0.0779333i
$179$	11.1786	−	11.1786i	0.835528	−	0.835528i	−0.152738	−	0.988267i	$-0.548809\pi$
$179$	11.1786	−	11.1786i	0.835528	−	0.835528i	0.988267	+	0.152738i	$0.0488092\pi$
$180$	−1.63524	+	1.52512i	−0.121883	+	0.113676i
$181$	−12.7902			−0.950689			−0.475345	−	0.879800i	$-0.657677\pi$
$181$	−12.7902			−0.950689			−0.475345	+	0.879800i	$0.657677\pi$
$182$	3.35547	+	3.35547i	0.248724	+	0.248724i
$183$			6.38826i			0.472234i
$184$	−0.0216604			−0.00159683
$185$	−4.88836	−	12.6927i	−0.359400	−	0.933184i
$186$	2.19350			0.160835
$187$		−	16.3239i		−	1.19372i
$188$	0.176174	+	0.176174i	0.0128488	+	0.0128488i
$189$	−2.60638			−0.189586
$190$	1.61050	+	0.0561127i	0.116838	+	0.00407084i
$191$	15.7097	−	15.7097i	1.13672	−	1.13672i	0.147683	−	0.989035i	$-0.452819\pi$
$191$	15.7097	−	15.7097i	1.13672	−	1.13672i	0.989035	−	0.147683i	$-0.0471814\pi$
$192$	−0.707107	−	0.707107i	−0.0510310	−	0.0510310i
$193$		−	21.0634i		−	1.51618i	−0.652152	−	0.758088i	$-0.726134\pi$
$193$		−	21.0634i		−	1.51618i	0.652152	−	0.758088i	$-0.273866\pi$
$194$			7.65590i			0.549662i
$195$	4.06867	+	0.141760i	0.291364	+	0.0101517i
$196$			0.206804i			0.0147717i
$197$	−5.52601	−	5.52601i	−0.393712	−	0.393712i	0.482296	−	0.876008i	$-0.339803\pi$
$197$	−5.52601	−	5.52601i	−0.393712	−	0.393712i	−0.876008	+	0.482296i	$0.839803\pi$
$198$			3.01042i			0.213941i
$199$	−5.69096	+	5.69096i	−0.403421	+	0.403421i	−0.879437	−	0.476015i	$-0.842081\pi$
$199$	−5.69096	+	5.69096i	−0.403421	+	0.403421i	0.476015	+	0.879437i	$0.342081\pi$
$200$	−4.98788	−	0.347996i	−0.352696	−	0.0246071i
$201$	5.57046			0.392910
$202$	16.6519			1.17163
$203$	−17.2442			−1.21030
$204$	3.83427	+	3.83427i	0.268453	+	0.268453i
$205$	10.3933	−	9.69348i	0.725903	−	0.677022i
$206$			15.2064i			1.05948i
$207$	−0.0216604			−0.00150550
$208$			1.82067i			0.126241i
$209$	1.53408	−	1.53408i	0.106115	−	0.106115i
$210$	−3.97505	−	4.26204i	−0.274304	−	0.294109i
$211$	2.18341			0.150312			0.0751561	−	0.997172i	$-0.476054\pi$
$211$	2.18341			0.150312			0.0751561	+	0.997172i	$0.476054\pi$
$212$	−2.05089	+	2.05089i	−0.140855	+	0.140855i
$213$	6.37068	+	6.37068i	0.436512	+	0.436512i
$214$	−7.85181	+	7.85181i	−0.536739	+	0.536739i
$215$	12.8645	−	11.9982i	0.877352	−	0.818273i
$216$	−0.707107	−	0.707107i	−0.0481125	−	0.0481125i
$217$			5.71708i			0.388101i
$218$	−5.15891	+	5.15891i	−0.349405	+	0.349405i
$219$			12.0279i			0.812771i
$220$	−4.92274	+	4.59126i	−0.331891	+	0.309542i
$221$		−	9.87255i		−	0.664100i
$222$	5.59677	−	2.38247i	0.375631	−	0.159901i
$223$	−15.3328	+	15.3328i	−1.02676	+	1.02676i	−0.0271298	+	0.999632i	$0.508637\pi$
$223$	−15.3328	+	15.3328i	−1.02676	+	1.02676i	−0.999632	+	0.0271298i	$0.991363\pi$
$224$	1.84299	−	1.84299i	0.123140	−	0.123140i
$225$	−4.98788	−	0.347996i	−0.332525	−	0.0231998i
$226$			3.80319i			0.252985i
$227$	−3.20189			−0.212517			−0.106258	−	0.994339i	$-0.533887\pi$
$227$	−3.20189			−0.212517			−0.106258	+	0.994339i	$0.533887\pi$
$228$			0.720673i			0.0477277i
$229$			21.2446i			1.40389i	0.712233	+	0.701943i	$0.247684\pi$
$229$			21.2446i			1.40389i	−0.712233	+	0.701943i	$0.752316\pi$
$230$	−0.0330348	−	0.0354199i	−0.00217825	−	0.00233552i
$231$	−7.84627			−0.516247
$232$	−4.67832	−	4.67832i	−0.307147	−	0.307147i
$233$	12.0202	+	12.0202i	0.787472	+	0.787472i	0.981079	−	0.193607i	$-0.0620188\pi$
$233$	12.0202	+	12.0202i	0.787472	+	0.787472i	−0.193607	+	0.981079i	$0.562019\pi$
$234$			1.82067i			0.119021i
$235$	−0.0193990	+	0.556773i	−0.00126545	+	0.0363199i
$236$	2.84934	+	2.84934i	0.185476	+	0.185476i
$237$		−	3.06004i		−	0.198771i
$238$	−9.99356	+	9.99356i	−0.647786	+	0.647786i
$239$	10.1337	+	10.1337i	0.655496	+	0.655496i	0.954311	−	0.298815i	$-0.0965913\pi$
$239$	10.1337	+	10.1337i	0.655496	+	0.655496i	−0.298815	+	0.954311i	$0.596591\pi$
$240$	0.0778616	−	2.23471i	0.00502594	−	0.144250i
$241$	10.2389	−	10.2389i	0.659546	−	0.659546i	−0.295727	−	0.955273i	$-0.595562\pi$
$241$	10.2389	−	10.2389i	0.659546	−	0.659546i	0.955273	+	0.295727i	$0.0955618\pi$
$242$		−	1.93740i		−	0.124541i
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$	−4.51718	−	4.51718i	−0.289183	−	0.289183i
$245$	−0.338174	+	0.315402i	−0.0216052	+	0.0201503i
$246$	4.49428	+	4.49428i	0.286545	+	0.286545i
$247$	0.927800	−	0.927800i	0.0590345	−	0.0590345i
$248$	−1.55104	+	1.55104i	−0.0984909	+	0.0984909i
$249$	1.30950			0.0829860
$250$	−7.03807	−	8.68709i	−0.445127	−	0.549420i
$251$	3.84833	+	3.84833i	0.242905	+	0.242905i	0.818051	−	0.575146i	$-0.195055\pi$
$251$	3.84833	+	3.84833i	0.242905	+	0.242905i	−0.575146	+	0.818051i	$0.695055\pi$
$252$	1.84299	−	1.84299i	0.116097	−	0.116097i
$253$	−0.0652069			−0.00409952
$254$	9.77118	−	9.77118i	0.613099	−	0.613099i
$255$	−0.422203	+	12.1177i	−0.0264394	+	0.758839i
$256$	1.00000			0.0625000
$257$	−3.13559			−0.195593			−0.0977963	−	0.995206i	$-0.531179\pi$
$257$	−3.13559			−0.195593			−0.0977963	+	0.995206i	$0.531179\pi$
$258$	5.56285	+	5.56285i	0.346328	+	0.346328i
$259$	6.20962	+	14.5873i	0.385847	+	0.906410i
$260$	−2.97723	+	2.77675i	−0.184640	+	0.172207i
$261$	−4.67832	−	4.67832i	−0.289581	−	0.289581i
$262$	2.21257	−	2.21257i	0.136693	−	0.136693i
$263$	−20.7027	−	20.7027i	−1.27658	−	1.27658i	−0.942567	−	0.334018i	$-0.891595\pi$
$263$	−20.7027	−	20.7027i	−1.27658	−	1.27658i	−0.334018	−	0.942567i	$-0.608405\pi$
$264$	−2.12868	−	2.12868i	−0.131012	−	0.131012i
$265$	−6.48154	−	0.225829i	−0.398158	−	0.0138726i
$266$	−1.87834			−0.115169
$267$	1.47044			0.0899896
$268$	−3.93891	+	3.93891i	−0.240607	+	0.240607i
$269$		−	15.5877i		−	0.950397i	−0.879879	−	0.475199i	$-0.842376\pi$
$269$		−	15.5877i		−	0.950397i	0.879879	−	0.475199i	$-0.157624\pi$
$270$	0.0778616	−	2.23471i	0.00473851	−	0.136000i
$271$	30.3127			1.84136			0.920682	−	0.390314i	$-0.127633\pi$
$271$	30.3127			1.84136			0.920682	+	0.390314i	$0.127633\pi$
$272$	−5.42248			−0.328786
$273$	−4.74535			−0.287202
$274$	−5.72235	+	5.72235i	−0.345700	+	0.345700i
$275$	−15.0156	−	1.04761i	−0.905473	−	0.0631735i
$276$	0.0153162	−	0.0153162i	0.000921929	−	0.000921929i
$277$			14.8230i			0.890629i	0.895374	+	0.445315i	$0.146908\pi$
$277$			14.8230i			0.890629i	−0.895374	+	0.445315i	$0.853092\pi$
$278$		−	4.18150i		−	0.250789i
$279$	−1.55104	+	1.55104i	−0.0928581	+	0.0928581i
$280$	5.82450	+	0.202937i	0.348080	+	0.0121278i
$281$	22.8948	−	22.8948i	1.36579	−	1.36579i	0.499436	−	0.866351i	$-0.333541\pi$
$281$	22.8948	−	22.8948i	1.36579	−	1.36579i	0.866351	−	0.499436i	$-0.166459\pi$
$282$	−0.249148			−0.0148365
$283$	−23.6708			−1.40708			−0.703541	−	0.710655i	$-0.748399\pi$
$283$	−23.6708			−1.40708			−0.703541	+	0.710655i	$0.748399\pi$
$284$	−9.00950			−0.534615
$285$	−1.17847	+	1.09911i	−0.0698065	+	0.0651059i
$286$			5.48097i			0.324097i
$287$	−11.7138	+	11.7138i	−0.691442	+	0.691442i
$288$	1.00000			0.0589256
$289$	12.4033			0.729607
$290$	0.515143	−	14.7852i	0.0302503	−	0.868215i
$291$	−5.41354	−	5.41354i	−0.317347	−	0.317347i
$292$	−8.50501	−	8.50501i	−0.497718	−	0.497718i
$293$	5.16020	−	5.16020i	0.301462	−	0.301462i	−0.540124	−	0.841586i	$-0.681623\pi$
$293$	5.16020	−	5.16020i	0.301462	−	0.301462i	0.841586	+	0.540124i	$0.181623\pi$
$294$	−0.146233	−	0.146233i	−0.00852847	−	0.00852847i
$295$	−0.313749	+	9.00493i	−0.0182672	+	0.524287i
$296$	−2.27285	+	5.64218i	−0.132107	+	0.327945i
$297$	−2.12868	−	2.12868i	−0.123519	−	0.123519i
$298$	2.65031			0.153529
$299$	−0.0394365			−0.00228067
$300$	3.77303	−	3.28089i	0.217836	−	0.189422i
$301$	−14.4989	+	14.4989i	−0.835701	+	0.835701i
$302$	−3.91246			−0.225137
$303$	−11.7747	+	11.7747i	−0.676439	+	0.676439i
$304$	−0.509592	−	0.509592i	−0.0292271	−	0.0292271i
$305$	0.497400	−	14.2759i	0.0284810	−	0.817437i
$306$	−5.42248			−0.309983
$307$	−16.3280	+	16.3280i	−0.931889	+	0.931889i	−0.997824	−	0.0659354i	$-0.978997\pi$
$307$	−16.3280	+	16.3280i	−0.931889	+	0.931889i	0.0659354	+	0.997824i	$0.478997\pi$
$308$	5.54815	−	5.54815i	0.316135	−	0.316135i
$309$	−10.7525	−	10.7525i	−0.611691	−	0.611691i
$310$	−4.90183	−	0.170789i	−0.278405	−	0.00970017i
$311$	−20.2566	−	20.2566i	−1.14865	−	1.14865i	−0.986819	−	0.161827i	$-0.948261\pi$
$311$	−20.2566	−	20.2566i	−1.14865	−	1.14865i	−0.161827	−	0.986819i	$-0.551739\pi$
$312$	−1.28741	−	1.28741i	−0.0728851	−	0.0728851i
$313$		−	18.3942i		−	1.03970i	−0.854256	−	0.519852i	$-0.825987\pi$
$313$		−	18.3942i		−	1.03970i	0.854256	−	0.519852i	$-0.174013\pi$
$314$	−12.9226	+	12.9226i	−0.729267	+	0.729267i
$315$	5.82450	+	0.202937i	0.328173	+	0.0114342i
$316$	2.16377	+	2.16377i	0.121722	+	0.121722i
$317$	3.40194	−	3.40194i	0.191072	−	0.191072i	−0.605087	−	0.796159i	$-0.706862\pi$
$317$	3.40194	−	3.40194i	0.191072	−	0.191072i	0.796159	+	0.605087i	$0.206862\pi$
$318$		−	2.90039i		−	0.162646i
$319$	−14.0837	−	14.0837i	−0.788535	−	0.788535i
$320$	1.52512	+	1.63524i	0.0852570	+	0.0914125i
$321$		−	11.1041i		−	0.619773i
$322$	0.0399199	+	0.0399199i	0.00222465	+	0.00222465i
$323$	2.76326	+	2.76326i	0.153752	+	0.153752i
$324$	1.00000			0.0555556
$325$	−9.08127	−	0.633587i	−0.503738	−	0.0351451i
$326$			8.59786i			0.476192i
$327$		−	7.29580i		−	0.403459i
$328$	−6.35587			−0.350944
$329$		−	0.649372i		−	0.0358010i
$330$	0.234396	−	6.72741i	0.0129031	−	0.370332i
$331$	2.61136	−	2.61136i	0.143533	−	0.143533i	−0.631689	−	0.775222i	$-0.717638\pi$
$331$	2.61136	−	2.61136i	0.143533	−	0.143533i	0.775222	+	0.631689i	$0.217638\pi$
$332$	−0.925954	+	0.925954i	−0.0508183	+	0.0508183i
$333$	−2.27285	+	5.64218i	−0.124552	+	0.309189i
$334$		−	4.59086i		−	0.251201i
$335$	−12.4484	−	0.433725i	−0.680128	−	0.0236969i
$336$			2.60638i			0.142189i
$337$	3.23500	−	3.23500i	0.176222	−	0.176222i	−0.613485	−	0.789707i	$-0.710233\pi$
$337$	3.23500	−	3.23500i	0.176222	−	0.176222i	0.789707	+	0.613485i	$0.210233\pi$
$338$		−	9.68516i		−	0.526803i
$339$	−2.68926	−	2.68926i	−0.146061	−	0.146061i
$340$	−8.26996	−	8.86704i	−0.448501	−	0.480883i
$341$	−4.66926	+	4.66926i	−0.252855	+	0.252855i
$342$	−0.509592	−	0.509592i	−0.0275556	−	0.0275556i
$343$	13.2820	−	13.2820i	0.717163	−	0.717163i
$344$	−7.86706			−0.424163
$345$	0.0484048	+	0.00168651i	0.00260603	+	9.07989e-5i
$346$	−6.49792	+	6.49792i	−0.349330	+	0.349330i
$347$			17.9326i			0.962675i	0.876535	+	0.481337i	$0.159849\pi$
$347$			17.9326i			0.962675i	−0.876535	+	0.481337i	$0.840151\pi$
$348$	6.61614			0.354662
$349$			34.1023i			1.82545i	0.408571	+	0.912727i	$0.366027\pi$
$349$			34.1023i			1.82545i	−0.408571	+	0.912727i	$0.633973\pi$
$350$	8.55123	+	9.83394i	0.457083	+	0.525646i
$351$	−1.28741	−	1.28741i	−0.0687168	−	0.0687168i
$352$	3.01042			0.160456
$353$	−7.23850			−0.385266			−0.192633	−	0.981271i	$-0.561703\pi$
$353$	−7.23850			−0.385266			−0.192633	+	0.981271i	$0.561703\pi$
$354$	−4.02957			−0.214169
$355$	−13.7406	−	14.7327i	−0.729275	−	0.781929i
$356$	−1.03976	+	1.03976i	−0.0551071	+	0.0551071i
$357$		−	14.1330i		−	0.747999i
$358$	−11.1786	−	11.1786i	−0.590808	−	0.590808i
$359$			29.3398i			1.54849i	0.632884	+	0.774247i	$0.281871\pi$
$359$			29.3398i			1.54849i	−0.632884	+	0.774247i	$0.718129\pi$
$360$	1.52512	+	1.63524i	0.0803811	+	0.0861845i
$361$		−	18.4806i		−	0.972665i
$362$			12.7902i			0.672239i
$363$	1.36995	+	1.36995i	0.0719037	+	0.0719037i
$364$	3.35547	−	3.35547i	0.175874	−	0.175874i
$365$	0.936512	−	26.8789i	0.0490193	−	1.40691i
$366$	6.38826			0.333920
$367$	7.30169	+	7.30169i	0.381145	+	0.381145i	0.871515	−	0.490370i	$-0.163138\pi$
$367$	7.30169	+	7.30169i	0.381145	+	0.381145i	−0.490370	+	0.871515i	$0.663138\pi$
$368$			0.0216604i			0.00112913i
$369$	−6.35587			−0.330873
$370$	−12.6927	+	4.88836i	−0.659861	+	0.254134i
$371$	7.55951			0.392470
$372$		−	2.19350i		−	0.113728i
$373$	0.813457	+	0.813457i	0.0421192	+	0.0421192i	0.727853	−	0.685733i	$-0.240518\pi$
$373$	0.813457	+	0.813457i	0.0421192	+	0.0421192i	−0.685733	+	0.727853i	$0.740518\pi$
$374$	−16.3239			−0.844090
$375$	11.1194	+	1.16604i	0.574202	+	0.0602138i
$376$	0.176174	−	0.176174i	0.00908548	−	0.00908548i
$377$	−8.51767	−	8.51767i	−0.438682	−	0.438682i
$378$			2.60638i			0.134058i
$379$		−	14.5201i		−	0.745847i	−0.927862	−	0.372924i	$-0.878355\pi$
$379$		−	14.5201i		−	0.745847i	0.927862	−	0.372924i	$-0.121645\pi$
$380$	0.0561127	−	1.61050i	0.00287852	−	0.0826167i
$381$			13.8185i			0.707945i
$382$	−15.7097	−	15.7097i	−0.803781	−	0.803781i
$383$			14.8639i			0.759507i	0.925088	+	0.379754i	$0.123991\pi$
$383$			14.8639i			0.759507i	−0.925088	+	0.379754i	$0.876009\pi$
$384$	−0.707107	+	0.707107i	−0.0360844	+	0.0360844i
$385$	17.5342	+	0.610923i	0.893624	+	0.0311355i
$386$	−21.0634			−1.07210
$387$	−7.86706			−0.399905
$388$	7.65590			0.388670
$389$	25.0493	+	25.0493i	1.27005	+	1.27005i	0.946062	+	0.323986i	$0.105023\pi$
$389$	25.0493	+	25.0493i	1.27005	+	1.27005i	0.323986	+	0.946062i	$0.394977\pi$
$390$	0.141760	−	4.06867i	0.00717831	−	0.206025i
$391$		−	0.117453i		−	0.00593987i
$392$	0.206804			0.0104452
$393$			3.12905i			0.157840i
$394$	−5.52601	+	5.52601i	−0.278396	+	0.278396i
$395$	−0.238260	+	6.83831i	−0.0119881	+	0.344073i
$396$	3.01042			0.151279
$397$	5.32491	−	5.32491i	0.267250	−	0.267250i	−0.560741	−	0.827991i	$-0.689484\pi$
$397$	5.32491	−	5.32491i	0.267250	−	0.267250i	0.827991	+	0.560741i	$0.189484\pi$
$398$	5.69096	+	5.69096i	0.285262	+	0.285262i
$399$	1.32819	−	1.32819i	0.0664926	−	0.0664926i
$400$	−0.347996	+	4.98788i	−0.0173998	+	0.249394i
$401$	−5.09805	−	5.09805i	−0.254584	−	0.254584i	0.568263	−	0.822847i	$-0.307616\pi$
$401$	−5.09805	−	5.09805i	−0.254584	−	0.254584i	−0.822847	+	0.568263i	$0.807616\pi$
$402$		−	5.57046i		−	0.277829i
$403$	−2.82393	+	2.82393i	−0.140670	+	0.140670i
$404$		−	16.6519i		−	0.828465i
$405$	1.52512	+	1.63524i	0.0757840	+	0.0812556i
$406$			17.2442i			0.855813i
$407$	−6.84223	+	16.9853i	−0.339157	+	0.841930i
$408$	3.83427	−	3.83427i	0.189825	−	0.189825i
$409$	15.3174	−	15.3174i	0.757396	−	0.757396i	−0.218451	−	0.975848i	$-0.570101\pi$
$409$	15.3174	−	15.3174i	0.757396	−	0.757396i	0.975848	+	0.218451i	$0.0701005\pi$
$410$	−9.69348	−	10.3933i	−0.478727	−	0.513291i
$411$		−	8.09263i		−	0.399180i
$412$	15.2064			0.749165
$413$		−	10.5026i		−	0.516798i
$414$			0.0216604i			0.00106455i
$415$	−2.92635	−	0.101960i	−0.143649	−	0.00500500i
$416$	1.82067			0.0892657
$417$	2.95676	+	2.95676i	0.144793	+	0.144793i
$418$	−1.53408	−	1.53408i	−0.0750345	−	0.0750345i
$419$			15.6256i			0.763360i	0.924294	+	0.381680i	$0.124654\pi$
$419$			15.6256i			0.763360i	−0.924294	+	0.381680i	$0.875346\pi$
$420$	−4.26204	+	3.97505i	−0.207966	+	0.193962i
$421$	15.7260	+	15.7260i	0.766440	+	0.766440i	0.977478	−	0.211038i	$-0.0676844\pi$
$421$	15.7260	+	15.7260i	0.766440	+	0.766440i	−0.211038	+	0.977478i	$0.567684\pi$
$422$		−	2.18341i		−	0.106287i
$423$	0.176174	−	0.176174i	0.00856587	−	0.00856587i
$424$	2.05089	+	2.05089i	0.0995998	+	0.0995998i
$425$	1.88700	−	27.0467i	0.0915332	−	1.31196i
$426$	6.37068	−	6.37068i	0.308660	−	0.308660i
$427$			16.6502i			0.805760i
$428$	7.85181	+	7.85181i	0.379532	+	0.379532i
$429$	−3.87563	−	3.87563i	−0.187117	−	0.187117i
$430$	−11.9982	−	12.8645i	−0.578606	−	0.620381i
$431$	7.16507	+	7.16507i	0.345129	+	0.345129i	0.858292	−	0.513162i	$-0.171526\pi$
$431$	7.16507	+	7.16507i	0.345129	+	0.345129i	−0.513162	+	0.858292i	$0.671526\pi$
$432$	−0.707107	+	0.707107i	−0.0340207	+	0.0340207i
$433$	12.9982	−	12.9982i	0.624652	−	0.624652i	−0.322065	−	0.946717i	$-0.604377\pi$
$433$	12.9982	−	12.9982i	0.624652	−	0.624652i	0.946717	+	0.322065i	$0.104377\pi$
$434$	5.71708			0.274429
$435$	10.0904	+	10.8190i	0.483799	+	0.518729i
$436$	5.15891	+	5.15891i	0.247067	+	0.247067i
$437$	0.0110380	−	0.0110380i	0.000528019	−	0.000528019i
$438$	12.0279			0.574716
$439$	−10.5684	+	10.5684i	−0.504400	+	0.504400i	−0.912802	−	0.408402i	$-0.866086\pi$
$439$	−10.5684	+	10.5684i	−0.504400	+	0.504400i	0.408402	+	0.912802i	$0.366086\pi$
$440$	4.59126	+	4.92274i	0.218879	+	0.234682i
$441$	0.206804			0.00984783
$442$	−9.87255			−0.469589
$443$	17.5773	+	17.5773i	0.835121	+	0.835121i	0.988212	−	0.153091i	$-0.0489227\pi$
$443$	17.5773	+	17.5773i	0.835121	+	0.835121i	−0.153091	+	0.988212i	$0.548923\pi$
$444$	−2.38247	−	5.59677i	−0.113067	−	0.265611i
$445$	−3.28601	−	0.114491i	−0.155772	−	0.00542739i
$446$	15.3328	+	15.3328i	0.726030	+	0.726030i
$447$	−1.87406	+	1.87406i	−0.0886398	+	0.0886398i
$448$	−1.84299	−	1.84299i	−0.0870729	−	0.0870729i
$449$	9.93203	+	9.93203i	0.468722	+	0.468722i	0.901500	−	0.432779i	$-0.142467\pi$
$449$	9.93203	+	9.93203i	0.468722	+	0.468722i	−0.432779	+	0.901500i	$0.642467\pi$
$450$	−0.347996	+	4.98788i	−0.0164047	+	0.235131i
$451$	−19.1338			−0.900975
$452$	3.80319			0.178887
$453$	2.76653	−	2.76653i	0.129983	−	0.129983i
$454$			3.20189i			0.150272i
$455$	10.6045	+	0.369480i	0.497146	+	0.0173215i
$456$	0.720673			0.0337486
$457$	8.27570			0.387121			0.193560	−	0.981088i	$-0.437996\pi$
$457$	8.27570			0.387121			0.193560	+	0.981088i	$0.437996\pi$
$458$	21.2446			0.992697
$459$	3.83427	−	3.83427i	0.178969	−	0.178969i
$460$	−0.0354199	+	0.0330348i	−0.00165146	+	0.00154026i
$461$	−3.89734	+	3.89734i	−0.181517	+	0.181517i	−0.792017	−	0.610499i	$-0.790969\pi$
$461$	−3.89734	+	3.89734i	−0.181517	+	0.181517i	0.610499	+	0.792017i	$0.290969\pi$
$462$			7.84627i			0.365042i
$463$		−	37.2821i		−	1.73265i	−0.499484	−	0.866323i	$-0.666477\pi$
$463$		−	37.2821i		−	1.73265i	0.499484	−	0.866323i	$-0.333523\pi$
$464$	−4.67832	+	4.67832i	−0.217185	+	0.217185i
$465$	3.58689	−	3.34535i	0.166338	−	0.155137i
$466$	12.0202	−	12.0202i	0.556827	−	0.556827i
$467$	11.9336			0.552219			0.276109	−	0.961126i	$-0.410955\pi$
$467$	11.9336			0.552219			0.276109	+	0.961126i	$0.410955\pi$
$468$	1.82067			0.0841605
$469$	14.5187			0.670412
$470$	0.556773	+	0.0193990i	0.0256820	+	0.000894810i
$471$		−	18.2754i		−	0.842085i
$472$	2.84934	−	2.84934i	0.131151	−	0.131151i
$473$	−23.6831			−1.08895
$474$	−3.06004			−0.140552
$475$	2.71912	−	2.36445i	0.124762	−	0.108488i
$476$	9.99356	+	9.99356i	0.458054	+	0.458054i
$477$	2.05089	+	2.05089i	0.0939036	+	0.0939036i
$478$	10.1337	−	10.1337i	0.463506	−	0.463506i
$479$	−0.903277	−	0.903277i	−0.0412718	−	0.0412718i	0.686170	−	0.727441i	$-0.259291\pi$
$479$	−0.903277	−	0.903277i	−0.0412718	−	0.0412718i	−0.727441	+	0.686170i	$0.759291\pi$
$480$	−2.23471	−	0.0778616i	−0.102000	−	0.00355388i
$481$	−4.13811	+	10.2725i	−0.188682	+	0.468387i
$482$	−10.2389	−	10.2389i	−0.466369	−	0.466369i
$483$	−0.0564552			−0.00256880
$484$	−1.93740			−0.0880637
$485$	11.6762	+	12.5192i	0.530189	+	0.568468i
$486$	−0.707107	+	0.707107i	−0.0320750	+	0.0320750i
$487$	1.67383			0.0758483			0.0379241	−	0.999281i	$-0.487925\pi$
$487$	1.67383			0.0758483			0.0379241	+	0.999281i	$0.487925\pi$
$488$	−4.51718	+	4.51718i	−0.204483	+	0.204483i
$489$	−6.07961	−	6.07961i	−0.274929	−	0.274929i
$490$	0.315402	+	0.338174i	0.0142484	+	0.0152772i
$491$	9.36601			0.422682			0.211341	−	0.977412i	$-0.432217\pi$
$491$	9.36601			0.422682			0.211341	+	0.977412i	$0.432217\pi$
$492$	4.49428	−	4.49428i	0.202618	−	0.202618i
$493$	25.3681	−	25.3681i	1.14252	−	1.14252i
$494$	−0.927800	−	0.927800i	−0.0417437	−	0.0417437i
$495$	4.59126	+	4.92274i	0.206362	+	0.221261i
$496$	1.55104	+	1.55104i	0.0696436	+	0.0696436i
$497$	16.6044	+	16.6044i	0.744808	+	0.744808i
$498$		−	1.30950i		−	0.0586800i
$499$	11.8837	−	11.8837i	0.531986	−	0.531986i	−0.389177	−	0.921163i	$-0.627240\pi$
$499$	11.8837	−	11.8837i	0.531986	−	0.531986i	0.921163	+	0.389177i	$0.127240\pi$
$500$	−8.68709	+	7.03807i	−0.388499	+	0.314752i
$501$	3.24623	+	3.24623i	0.145031	+	0.145031i
$502$	3.84833	−	3.84833i	0.171759	−	0.171759i
$503$			25.4862i			1.13637i	0.822900	+	0.568187i	$0.192355\pi$
$503$			25.4862i			1.13637i	−0.822900	+	0.568187i	$0.807645\pi$
$504$	−1.84299	−	1.84299i	−0.0820931	−	0.0820931i
$505$	27.2299	−	25.3963i	1.21171	−	1.13012i
$506$			0.0652069i			0.00289880i
$507$	6.84844	+	6.84844i	0.304150	+	0.304150i
$508$	−9.77118	−	9.77118i	−0.433526	−	0.433526i
$509$	21.0744			0.934105			0.467053	−	0.884230i	$-0.345316\pi$
$509$	21.0744			0.934105			0.467053	+	0.884230i	$0.345316\pi$
$510$	12.1177	+	0.422203i	0.536580	+	0.0186955i
$511$			31.3492i			1.38681i
$512$		−	1.00000i		−	0.0441942i
$513$	0.720673			0.0318185
$514$			3.13559i			0.138305i
$515$	23.1916	+	24.8660i	1.02195	+	1.09573i
$516$	5.56285	−	5.56285i	0.244891	−	0.244891i
$517$	0.530357	−	0.530357i	0.0233251	−	0.0233251i
$518$	14.5873	−	6.20962i	0.640929	−	0.272835i
$519$		−	9.18945i		−	0.403372i
$520$	2.77675	+	2.97723i	0.121768	+	0.130560i
$521$			26.1425i			1.14532i	0.819792	+	0.572661i	$0.194089\pi$
$521$			26.1425i			1.14532i	−0.819792	+	0.572661i	$0.805911\pi$
$522$	−4.67832	+	4.67832i	−0.204764	+	0.204764i
$523$		−	18.6818i		−	0.816898i	−0.912781	−	0.408449i	$-0.866070\pi$
$523$		−	18.6818i		−	0.816898i	0.912781	−	0.408449i	$-0.133930\pi$
$524$	−2.21257	−	2.21257i	−0.0966567	−	0.0966567i
$525$	−13.0003	−	0.907010i	−0.567379	−	0.0395851i
$526$	−20.7027	+	20.7027i	−0.902682	+	0.902682i
$527$	−8.41047	−	8.41047i	−0.366366	−	0.366366i
$528$	−2.12868	+	2.12868i	−0.0926391	+	0.0926391i
$529$	22.9995			0.999980
$530$	−0.225829	+	6.48154i	−0.00980939	+	0.281540i
$531$	2.84934	−	2.84934i	0.123651	−	0.123651i
$532$			1.87834i			0.0814365i
$533$	−11.5719			−0.501236
$534$		−	1.47044i		−	0.0636322i
$535$	−0.864586	+	24.8146i	−0.0373793	+	1.07283i
$536$	3.93891	+	3.93891i	0.170135	+	0.170135i
$537$	15.8089			0.682206
$538$	−15.5877			−0.672032
$539$	0.622567			0.0268159
$540$	−2.23471	−	0.0778616i	−0.0961667	−	0.00335063i
$541$	−12.5483	+	12.5483i	−0.539494	+	0.539494i	−0.923380	−	0.383887i	$-0.874585\pi$
$541$	−12.5483	+	12.5483i	−0.539494	+	0.539494i	0.383887	+	0.923380i	$0.374585\pi$
$542$		−	30.3127i		−	1.30204i
$543$	−9.04405	−	9.04405i	−0.388117	−	0.388117i
$544$			5.42248i			0.232487i
$545$	−0.568062	+	16.3040i	−0.0243331	+	0.698387i
$546$			4.74535i			0.203082i
$547$			13.3305i			0.569972i	0.958532	+	0.284986i	$0.0919889\pi$
$547$			13.3305i			0.569972i	−0.958532	+	0.284986i	$0.908011\pi$
$548$	5.72235	+	5.72235i	0.244447	+	0.244447i
$549$	−4.51718	+	4.51718i	−0.192789	+	0.192789i
$550$	−1.04761	+	15.0156i	−0.0446704	+	0.640266i
$551$	4.76807			0.203127
$552$	−0.0153162	−	0.0153162i	−0.000651902	−	0.000651902i
$553$		−	7.97561i		−	0.339158i
$554$	14.8230			0.629770
$555$	5.51848	−	12.4317i	0.234246	−	0.527695i
$556$	−4.18150			−0.177335
$557$			31.5142i			1.33530i	0.744475	+	0.667650i	$0.232700\pi$
$557$			31.5142i			1.33530i	−0.744475	+	0.667650i	$0.767300\pi$
$558$	1.55104	+	1.55104i	0.0656606	+	0.0656606i
$559$	−14.3233			−0.605812
$560$	0.202937	−	5.82450i	0.00857563	−	0.246130i
$561$	11.5428	−	11.5428i	0.487336	−	0.487336i
$562$	−22.8948	−	22.8948i	−0.965757	−	0.965757i
$563$			23.8203i			1.00391i	0.864895	+	0.501953i	$0.167385\pi$
$563$			23.8203i			1.00391i	−0.864895	+	0.501953i	$0.832615\pi$
$564$			0.249148i			0.0104910i
$565$	5.80034	+	6.21912i	0.244022	+	0.261640i
$566$			23.6708i			0.994957i
$567$	−1.84299	−	1.84299i	−0.0773981	−	0.0773981i
$568$			9.00950i			0.378030i
$569$	−2.20968	+	2.20968i	−0.0926346	+	0.0926346i	−0.751905	−	0.659271i	$-0.770865\pi$
$569$	−2.20968	+	2.20968i	−0.0926346	+	0.0926346i	0.659271	+	0.751905i	$0.270865\pi$
$570$	1.09911	+	1.17847i	0.0460368	+	0.0493607i
$571$	−18.6714			−0.781372			−0.390686	−	0.920524i	$-0.627762\pi$
$571$	−18.6714			−0.781372			−0.390686	+	0.920524i	$0.627762\pi$
$572$	5.48097			0.229171
$573$	22.2169			0.928126
$574$	11.7138	+	11.7138i	0.488923	+	0.488923i
$575$	−0.108039	−	0.00753775i	−0.00450556	−	0.000314346i
$576$		−	1.00000i		−	0.0416667i
$577$	42.7062			1.77788			0.888941	−	0.458023i	$-0.151442\pi$
$577$	42.7062			1.77788			0.888941	+	0.458023i	$0.151442\pi$
$578$		−	12.4033i		−	0.515910i
$579$	14.8941	−	14.8941i	0.618976	−	0.618976i
$580$	−14.7852	−	0.515143i	−0.613921	−	0.0213902i
$581$	3.41304			0.141597
$582$	−5.41354	+	5.41354i	−0.224398	+	0.224398i
$583$	6.17402	+	6.17402i	0.255702	+	0.255702i
$584$	−8.50501	+	8.50501i	−0.351940	+	0.351940i
$585$	2.77675	+	2.97723i	0.114804	+	0.123093i
$586$	−5.16020	−	5.16020i	−0.213166	−	0.213166i
$587$		−	14.4564i		−	0.596681i	−0.954459	−	0.298341i	$-0.903567\pi$
$587$		−	14.4564i		−	0.596681i	0.954459	−	0.298341i	$-0.0964331\pi$
$588$	−0.146233	+	0.146233i	−0.00603054	+	0.00603054i
$589$		−	1.58079i		−	0.0651354i
$590$	9.00493	+	0.313749i	0.370727	+	0.0129168i
$591$		−	7.81496i		−	0.321465i
$592$	5.64218	+	2.27285i	0.231892	+	0.0934137i
$593$	14.3909	−	14.3909i	0.590963	−	0.590963i	−0.346928	−	0.937892i	$-0.612775\pi$
$593$	14.3909	−	14.3909i	0.590963	−	0.590963i	0.937892	+	0.346928i	$0.112775\pi$
$594$	−2.12868	+	2.12868i	−0.0873410	+	0.0873410i
$595$	−1.10042	+	31.5832i	−0.0451128	+	1.29479i
$596$		−	2.65031i		−	0.108561i
$597$	−8.04823			−0.329392
$598$			0.0394365i			0.00161268i
$599$			32.8474i			1.34211i	0.741407	+	0.671055i	$0.234159\pi$
$599$			32.8474i			1.34211i	−0.741407	+	0.671055i	$0.765841\pi$
$600$	−3.28089	−	3.77303i	−0.133942	−	0.154033i
$601$	42.6376			1.73922			0.869611	−	0.493737i	$-0.164369\pi$
$601$	42.6376			1.73922			0.869611	+	0.493737i	$0.164369\pi$
$602$	14.4989	+	14.4989i	0.590930	+	0.590930i
$603$	3.93891	+	3.93891i	0.160405	+	0.160405i
$604$			3.91246i			0.159196i
$605$	−2.95477	−	3.16811i	−0.120129	−	0.128802i
$606$	11.7747	+	11.7747i	0.478315	+	0.478315i
$607$		−	1.05109i		−	0.0426623i	−0.999772	−	0.0213312i	$-0.993210\pi$
$607$		−	1.05109i		−	0.0426623i	0.999772	−	0.0213312i	$-0.00679044\pi$
$608$	−0.509592	+	0.509592i	−0.0206667	+	0.0206667i
$609$	−12.1935	−	12.1935i	−0.494104	−	0.494104i
$610$	−14.2759	−	0.497400i	−0.578015	−	0.0201391i
$611$	0.320755	−	0.320755i	0.0129763	−	0.0129763i
$612$			5.42248i			0.219191i
$613$	−20.8463	−	20.8463i	−0.841976	−	0.841976i	0.147140	−	0.989116i	$-0.452993\pi$
$613$	−20.8463	−	20.8463i	−0.841976	−	0.841976i	−0.989116	+	0.147140i	$0.952993\pi$
$614$	16.3280	+	16.3280i	0.658945	+	0.658945i
$615$	14.2035	+	0.494878i	0.572742	+	0.0199554i
$616$	−5.54815	−	5.54815i	−0.223541	−	0.223541i
$617$	−11.8344	+	11.8344i	−0.476435	+	0.476435i	−0.903990	−	0.427555i	$-0.859375\pi$
$617$	−11.8344	+	11.8344i	−0.476435	+	0.476435i	0.427555	+	0.903990i	$0.359375\pi$
$618$	−10.7525	+	10.7525i	−0.432531	+	0.432531i
$619$	2.66335			0.107049			0.0535246	−	0.998567i	$-0.482954\pi$
$619$	2.66335			0.107049			0.0535246	+	0.998567i	$0.482954\pi$
$620$	−0.170789	+	4.90183i	−0.00685906	+	0.196862i
$621$	−0.0153162	−	0.0153162i	−0.000614619	−	0.000614619i
$622$	−20.2566	+	20.2566i	−0.812216	+	0.812216i
$623$	3.83252			0.153547
$624$	−1.28741	+	1.28741i	−0.0515376	+	0.0515376i
$625$	−24.7578	−	3.47153i	−0.990312	−	0.138861i
$626$	−18.3942			−0.735182
$627$	2.16952			0.0866424
$628$	12.9226	+	12.9226i	0.515670	+	0.515670i
$629$	−30.5946	−	12.3245i	−1.21989	−	0.491410i
$630$	0.202937	−	5.82450i	0.00808519	−	0.232054i
$631$	−20.5443	−	20.5443i	−0.817854	−	0.817854i	0.167943	−	0.985797i	$-0.446288\pi$
$631$	−20.5443	−	20.5443i	−0.817854	−	0.817854i	−0.985797	+	0.167943i	$0.946288\pi$
$632$	2.16377	−	2.16377i	0.0860703	−	0.0860703i
$633$	1.54391	+	1.54391i	0.0613647	+	0.0613647i
$634$	−3.40194	−	3.40194i	−0.135108	−	0.135108i
$635$	1.07593	−	30.8805i	0.0426971	−	1.22545i
$636$	−2.90039			−0.115008
$637$	0.376523			0.0149184
$638$	−14.0837	+	14.0837i	−0.557578	+	0.557578i
$639$			9.00950i			0.356410i
$640$	1.63524	−	1.52512i	0.0646384	−	0.0602858i
$641$	38.4309			1.51793			0.758964	−	0.651132i	$-0.225706\pi$
$641$	38.4309			1.51793			0.758964	+	0.651132i	$0.225706\pi$
$642$	−11.1041			−0.438245
$643$	33.4086			1.31751			0.658754	−	0.752358i	$-0.271084\pi$
$643$	33.4086			1.31751			0.658754	+	0.752358i	$0.271084\pi$
$644$	0.0399199	−	0.0399199i	0.00157306	−	0.00157306i
$645$	17.5806	+	0.612542i	0.692236	+	0.0241188i
$646$	2.76326	−	2.76326i	0.108719	−	0.108719i
$647$		−	48.3301i		−	1.90005i	−0.312170	−	0.950026i	$-0.601056\pi$
$647$		−	48.3301i		−	1.90005i	0.312170	−	0.950026i	$-0.398944\pi$
$648$		−	1.00000i		−	0.0392837i
$649$	8.57769	−	8.57769i	0.336704	−	0.336704i
$650$	−0.633587	+	9.08127i	−0.0248513	+	0.356197i
$651$	−4.04258	+	4.04258i	−0.158441	+	0.158441i
$652$	8.59786			0.336718
$653$	−20.8734			−0.816839			−0.408420	−	0.912794i	$-0.633920\pi$
$653$	−20.8734			−0.816839			−0.408420	+	0.912794i	$0.633920\pi$
$654$	−7.29580			−0.285288
$655$	0.243633	−	6.99253i	0.00951952	−	0.273221i
$656$			6.35587i			0.248155i
$657$	−8.50501	+	8.50501i	−0.331812	+	0.331812i
$658$	−0.649372			−0.0253152
$659$	−26.2240			−1.02154			−0.510771	−	0.859717i	$-0.670640\pi$
$659$	−26.2240			−1.02154			−0.510771	+	0.859717i	$0.670640\pi$
$660$	−6.72741	−	0.234396i	−0.261864	−	0.00912384i
$661$	15.8166	+	15.8166i	0.615196	+	0.615196i	0.944295	−	0.329100i	$-0.106745\pi$
$661$	15.8166	+	15.8166i	0.615196	+	0.615196i	−0.329100	+	0.944295i	$0.606745\pi$
$662$	−2.61136	−	2.61136i	−0.101493	−	0.101493i
$663$	6.98095	−	6.98095i	0.271118	−	0.271118i
$664$	0.925954	+	0.925954i	0.0359340	+	0.0359340i
$665$	−3.07154	+	2.86471i	−0.119109	+	0.111089i
$666$	5.64218	+	2.27285i	0.218630	+	0.0880712i
$667$	−0.101334	−	0.101334i	−0.00392368	−	0.00392368i
$668$	−4.59086			−0.177626
$669$	−21.6839			−0.838347
$670$	−0.433725	+	12.4484i	−0.0167563	+	0.480923i
$671$	−13.5986	+	13.5986i	−0.524968	+	0.524968i
$672$	2.60638			0.100543
$673$	19.5631	−	19.5631i	0.754102	−	0.754102i	−0.221140	−	0.975242i	$-0.570978\pi$
$673$	19.5631	−	19.5631i	0.754102	−	0.754102i	0.975242	+	0.221140i	$0.0709779\pi$
$674$	−3.23500	−	3.23500i	−0.124608	−	0.124608i
$675$	−3.28089	−	3.77303i	−0.126282	−	0.145224i
$676$	−9.68516			−0.372506
$677$	−4.35406	+	4.35406i	−0.167340	+	0.167340i	−0.785809	−	0.618469i	$-0.787753\pi$
$677$	−4.35406	+	4.35406i	−0.167340	+	0.167340i	0.618469	+	0.785809i	$0.287753\pi$
$678$	−2.68926	+	2.68926i	−0.103281	+	0.103281i
$679$	−14.1097	−	14.1097i	−0.541481	−	0.541481i
$680$	−8.86704	+	8.26996i	−0.340036	+	0.317138i
$681$	−2.26408	−	2.26408i	−0.0867596	−	0.0867596i
$682$	4.66926	+	4.66926i	0.178795	+	0.178795i
$683$			28.7474i			1.09999i	0.835168	+	0.549995i	$0.185370\pi$
$683$			28.7474i			1.09999i	−0.835168	+	0.549995i	$0.814630\pi$
$684$	−0.509592	+	0.509592i	−0.0194848	+	0.0194848i
$685$	−0.630105	+	18.0847i	−0.0240751	+	0.690981i
$686$	−13.2820	−	13.2820i	−0.507111	−	0.507111i
$687$	−15.0222	+	15.0222i	−0.573134	+	0.573134i
$688$			7.86706i			0.299929i
$689$	3.73399	+	3.73399i	0.142254	+	0.142254i
$690$	0.00168651	−	0.0484048i	6.42045e−5	−	0.00184274i
$691$		−	43.9902i		−	1.67347i	−0.547610	−	0.836733i	$-0.684462\pi$
$691$		−	43.9902i		−	1.67347i	0.547610	−	0.836733i	$-0.315538\pi$
$692$	6.49792	+	6.49792i	0.247014	+	0.247014i
$693$	−5.54815	−	5.54815i	−0.210757	−	0.210757i
$694$	17.9326			0.680714
$695$	−6.37730	−	6.83773i	−0.241905	−	0.259370i
$696$		−	6.61614i		−	0.250784i
$697$		−	34.4646i		−	1.30544i
$698$	34.1023			1.29079
$699$			16.9992i			0.642968i
$700$	9.83394	−	8.55123i	0.371688	−	0.323206i
$701$	−9.73870	+	9.73870i	−0.367826	+	0.367826i	−0.866684	−	0.498858i	$-0.833753\pi$
$701$	−9.73870	+	9.73870i	−0.367826	+	0.367826i	0.498858	+	0.866684i	$0.333753\pi$
$702$	−1.28741	+	1.28741i	−0.0485901	+	0.0485901i
$703$	−1.71698	−	4.03344i	−0.0647572	−	0.152124i
$704$		−	3.01042i		−	0.113459i
$705$	−0.407415	+	0.379981i	−0.0153441	+	0.0143109i
$706$			7.23850i			0.272424i
$707$	−30.6893	+	30.6893i	−1.15419	+	1.15419i
$708$			4.02957i			0.151441i
$709$	10.8762	+	10.8762i	0.408466	+	0.408466i	0.881203	−	0.472738i	$-0.156734\pi$
$709$	10.8762	+	10.8762i	0.408466	+	0.408466i	−0.472738	+	0.881203i	$0.656734\pi$
$710$	−14.7327	+	13.7406i	−0.552907	+	0.515676i
$711$	2.16377	−	2.16377i	0.0811479	−	0.0811479i
$712$	1.03976	+	1.03976i	0.0389666	+	0.0389666i
$713$	−0.0335961	+	0.0335961i	−0.00125818	+	0.00125818i
$714$	−14.1330			−0.528915
$715$	8.35916	+	8.96269i	0.312615	+	0.335185i
$716$	−11.1786	+	11.1786i	−0.417764	+	0.417764i
$717$			14.3313i			0.535210i
$718$	29.3398			1.09495
$719$		−	28.4189i		−	1.05985i	−0.848045	−	0.529924i	$-0.822221\pi$
$719$		−	28.4189i		−	1.05985i	0.848045	−	0.529924i	$-0.177779\pi$
$720$	1.63524	−	1.52512i	0.0609417	−	0.0568380i
$721$	−28.0252	−	28.0252i	−1.04371	−	1.04371i
$722$	−18.4806			−0.687778
$723$	14.4800			0.538517
$724$	12.7902			0.475345
$725$	−21.7068	−	24.9629i	−0.806171	−	0.927099i
$726$	1.36995	−	1.36995i	0.0508436	−	0.0508436i
$727$			2.22360i			0.0824686i	0.999150	+	0.0412343i	$0.0131290\pi$
$727$			2.22360i			0.0824686i	−0.999150	+	0.0412343i	$0.986871\pi$
$728$	−3.35547	−	3.35547i	−0.124362	−	0.124362i
$729$		−	1.00000i		−	0.0370370i
$730$	−26.8789	−	0.936512i	−0.994833	−	0.0346619i
$731$		−	42.6590i		−	1.57780i
$732$		−	6.38826i		−	0.236117i
$733$	−11.8204	−	11.8204i	−0.436598	−	0.436598i	0.454268	−	0.890865i	$-0.349901\pi$
$733$	−11.8204	−	11.8204i	−0.436598	−	0.436598i	−0.890865	+	0.454268i	$0.849901\pi$
$734$	7.30169	−	7.30169i	0.269510	−	0.269510i
$735$	−0.462148	−	0.0161021i	−0.0170466	−	0.000593936i
$736$	0.0216604			0.000798414
$737$	11.8578	+	11.8578i	0.436786	+	0.436786i
$738$			6.35587i			0.233963i
$739$	41.0418			1.50975			0.754874	−	0.655870i	$-0.227698\pi$
$739$	41.0418			1.50975			0.754874	+	0.655870i	$0.227698\pi$
$740$	4.88836	+	12.6927i	0.179700	+	0.466592i
$741$	1.31211			0.0482014
$742$		−	7.55951i		−	0.277518i
$743$	21.4316	+	21.4316i	0.786249	+	0.786249i	0.980877	−	0.194628i	$-0.0623499\pi$
$743$	21.4316	+	21.4316i	0.786249	+	0.786249i	−0.194628	+	0.980877i	$0.562350\pi$
$744$	−2.19350			−0.0804175
$745$	4.33389	−	4.04206i	0.158781	−	0.148090i
$746$	0.813457	−	0.813457i	0.0297828	−	0.0297828i
$747$	0.925954	+	0.925954i	0.0338789	+	0.0338789i
$748$			16.3239i			0.596862i
$749$		−	28.9416i		−	1.05750i
$750$	1.16604	−	11.1194i	0.0425776	−	0.406022i
$751$			38.7551i			1.41419i	0.707117	+	0.707097i	$0.249995\pi$
$751$			38.7551i			1.41419i	−0.707117	+	0.707097i	$0.750005\pi$
$752$	−0.176174	−	0.176174i	−0.00642440	−	0.00642440i
$753$			5.44236i			0.198331i
$754$	−8.51767	+	8.51767i	−0.310195	+	0.310195i
$755$	−6.39779	+	5.96698i	−0.232840	+	0.217161i
$756$	2.60638			0.0947930
$757$	47.4098			1.72314			0.861569	−	0.507640i	$-0.169482\pi$
$757$	47.4098			1.72314			0.861569	+	0.507640i	$0.169482\pi$
$758$	−14.5201			−0.527394
$759$	−0.0461082	−	0.0461082i	−0.00167362	−	0.00167362i
$760$	−1.61050	−	0.0561127i	−0.0584188	−	0.00203542i
$761$		−	31.8594i		−	1.15490i	−0.816425	−	0.577452i	$-0.804047\pi$
$761$		−	31.8594i		−	1.15490i	0.816425	−	0.577452i	$-0.195953\pi$
$762$	13.8185			0.500593
$763$		−	19.0156i		−	0.688411i
$764$	−15.7097	+	15.7097i	−0.568359	+	0.568359i
$765$	−8.86704	+	8.26996i	−0.320589	+	0.299001i
$766$	14.8639			0.537053
$767$	5.18770	−	5.18770i	0.187317	−	0.187317i
$768$	0.707107	+	0.707107i	0.0255155	+	0.0255155i
$769$	−14.3460	+	14.3460i	−0.517329	+	0.517329i	−0.916762	−	0.399433i	$-0.869207\pi$
$769$	−14.3460	+	14.3460i	−0.517329	+	0.517329i	0.399433	+	0.916762i	$0.369207\pi$
$770$	0.610923	−	17.5342i	0.0220161	−	0.631887i
$771$	−2.21719	−	2.21719i	−0.0798503	−	0.0798503i
$772$			21.0634i			0.758088i
$773$	−14.7324	+	14.7324i	−0.529887	+	0.529887i	−0.920539	−	0.390652i	$-0.872250\pi$
$773$	−14.7324	+	14.7324i	−0.529887	+	0.529887i	0.390652	+	0.920539i	$0.372250\pi$
$774$			7.86706i			0.282776i
$775$	−8.27613	+	7.19662i	−0.297287	+	0.258510i
$776$		−	7.65590i		−	0.274831i
$777$	−5.92391	+	14.7056i	−0.212519	+	0.527562i
$778$	25.0493	−	25.0493i	0.898060	−	0.898060i
$779$	3.23890	−	3.23890i	0.116046	−	0.116046i
$780$	−4.06867	−	0.141760i	−0.145682	−	0.00507583i
$781$			27.1223i			0.970513i
$782$	−0.117453			−0.00420012
$783$		−	6.61614i		−	0.236442i
$784$		−	0.206804i		−	0.00738587i
$785$	−1.42295	+	40.8402i	−0.0507873	+	1.45765i
$786$	3.12905			0.111610
$787$	−20.6588	−	20.6588i	−0.736408	−	0.736408i	0.235473	−	0.971881i	$-0.424336\pi$
$787$	−20.6588	−	20.6588i	−0.736408	−	0.736408i	−0.971881	+	0.235473i	$0.924336\pi$
$788$	5.52601	+	5.52601i	0.196856	+	0.196856i
$789$		−	29.2781i		−	1.04233i
$790$	6.83831	+	0.238260i	0.243296	+	0.00847689i
$791$	−7.00924	−	7.00924i	−0.249220	−	0.249220i
$792$		−	3.01042i		−	0.106970i
$793$	−8.22430	+	8.22430i	−0.292053	+	0.292053i
$794$	−5.32491	−	5.32491i	−0.188974	−	0.188974i
$795$	−4.42345	−	4.74282i	−0.156884	−	0.168211i
$796$	5.69096	−	5.69096i	0.201711	−	0.201711i
$797$			39.3879i			1.39519i	0.716492	+	0.697595i	$0.245747\pi$
$797$			39.3879i			1.39519i	−0.716492	+	0.697595i	$0.754253\pi$
$798$	−1.32819	−	1.32819i	−0.0470174	−	0.0470174i
$799$	0.955300	+	0.955300i	0.0337961	+	0.0337961i
$800$	4.98788	+	0.347996i	0.176348	+	0.0123035i
$801$	1.03976	+	1.03976i	0.0367381	+	0.0367381i
$802$	−5.09805	+	5.09805i	−0.180018	+	0.180018i
$803$	−25.6036	+	25.6036i	−0.903532	+	0.903532i
$804$	−5.57046			−0.196455
$805$	0.126161	+	0.00439569i	0.00444659	+	0.000154928i
$806$	2.82393	+	2.82393i	0.0994685	+	0.0994685i
$807$	11.0221	−	11.0221i	0.387998	−	0.387998i
$808$	−16.6519			−0.585813
$809$	24.3142	−	24.3142i	0.854841	−	0.854841i	−0.135884	−	0.990725i	$-0.543387\pi$
$809$	24.3142	−	24.3142i	0.854841	−	0.854841i	0.990725	+	0.135884i	$0.0433874\pi$
$810$	1.63524	−	1.52512i	0.0574564	−	0.0535874i
$811$	−24.8998			−0.874351			−0.437176	−	0.899376i	$-0.644021\pi$
$811$	−24.8998			−0.874351			−0.437176	+	0.899376i	$0.644021\pi$
$812$	17.2442			0.605151
$813$	21.4343	+	21.4343i	0.751734	+	0.751734i
$814$	16.9853	+	6.84223i	0.595334	+	0.239820i
$815$	13.1128	+	14.0595i	0.459321	+	0.492484i
$816$	−3.83427	−	3.83427i	−0.134226	−	0.134226i
$817$	4.00899	−	4.00899i	0.140257	−	0.140257i
$818$	−15.3174	−	15.3174i	−0.535560	−	0.535560i
$819$	−3.35547	−	3.35547i	−0.117250	−	0.117250i
$820$	−10.3933	+	9.69348i	−0.362951	+	0.338511i
$821$	−52.1619			−1.82046			−0.910231	−	0.414101i	$-0.864096\pi$
$821$	−52.1619			−1.82046			−0.910231	+	0.414101i	$0.864096\pi$
$822$	−8.09263			−0.282263
$823$	0.798711	−	0.798711i	0.0278413	−	0.0278413i	−0.693049	−	0.720890i	$-0.743733\pi$
$823$	0.798711	−	0.798711i	0.0278413	−	0.0278413i	0.720890	+	0.693049i	$0.243733\pi$
$824$		−	15.2064i		−	0.529740i
$825$	−9.87684	−	11.3584i	−0.343867	−	0.395448i
$826$	−10.5026			−0.365431
$827$	30.7971			1.07092			0.535460	−	0.844561i	$-0.320138\pi$
$827$	30.7971			1.07092			0.535460	+	0.844561i	$0.320138\pi$
$828$	0.0216604			0.000752752
$829$	4.01468	−	4.01468i	0.139435	−	0.139435i	−0.633944	−	0.773379i	$-0.718565\pi$
$829$	4.01468	−	4.01468i	0.139435	−	0.139435i	0.773379	+	0.633944i	$0.218565\pi$
$830$	−0.101960	+	2.92635i	−0.00353907	+	0.101575i
$831$	−10.4815	+	10.4815i	−0.363598	+	0.363598i
$832$		−	1.82067i		−	0.0631204i
$833$			1.12139i			0.0388540i
$834$	2.95676	−	2.95676i	0.102384	−	0.102384i
$835$	−7.00164	−	7.50715i	−0.242302	−	0.259796i
$836$	−1.53408	+	1.53408i	−0.0530574	+	0.0530574i
$837$	−2.19350			−0.0758184
$838$	15.6256			0.539777
$839$	26.0337			0.898784			0.449392	−	0.893335i	$-0.351641\pi$
$839$	26.0337			0.898784			0.449392	+	0.893335i	$0.351641\pi$
$840$	3.97505	+	4.26204i	0.137152	+	0.147054i
$841$		−	14.7733i		−	0.509425i
$842$	15.7260	−	15.7260i	0.541955	−	0.541955i
$843$	32.3781			1.11516
$844$	−2.18341			−0.0751561
$845$	−14.7711	−	15.8375i	−0.508140	−	0.544828i
$846$	−0.176174	−	0.176174i	−0.00605698	−	0.00605698i
$847$	3.57060	+	3.57060i	0.122687	+	0.122687i
$848$	2.05089	−	2.05089i	0.0704277	−	0.0704277i
$849$	−16.7378	−	16.7378i	−0.574439	−	0.574439i
$850$	−27.0467	−	1.88700i	−0.927693	−	0.0647237i
$851$	−0.0492309	+	0.122212i	−0.00168761	+	0.00418937i
$852$	−6.37068	−	6.37068i	−0.218256	−	0.218256i
$853$	−24.2328			−0.829714			−0.414857	−	0.909887i	$-0.636168\pi$
$853$	−24.2328			−0.829714			−0.414857	+	0.909887i	$0.636168\pi$
$854$	16.6502			0.569758
$855$	−1.61050	−	0.0561127i	−0.0550778	−	0.00191901i
$856$	7.85181	−	7.85181i	0.268369	−	0.268369i
$857$	−38.1314			−1.30254			−0.651272	−	0.758845i	$-0.725764\pi$
$857$	−38.1314			−1.30254			−0.651272	+	0.758845i	$0.725764\pi$
$858$	−3.87563	+	3.87563i	−0.132312	+	0.132312i
$859$	−17.3872	−	17.3872i	−0.593243	−	0.593243i	0.345263	−	0.938506i	$-0.387790\pi$
$859$	−17.3872	−	17.3872i	−0.593243	−	0.593243i	−0.938506	+	0.345263i	$0.887790\pi$
$860$	−12.8645	+	11.9982i	−0.438676	+	0.409136i
$861$	−16.5658			−0.564560
$862$	7.16507	−	7.16507i	0.244043	−	0.244043i
$863$	−36.1097	+	36.1097i	−1.22919	+	1.22919i	−0.264920	+	0.964270i	$0.585345\pi$
$863$	−36.1097	+	36.1097i	−1.22919	+	1.22919i	−0.964270	+	0.264920i	$0.914655\pi$
$864$	0.707107	+	0.707107i	0.0240563	+	0.0240563i
$865$	−0.715505	+	20.5358i	−0.0243279	+	0.698237i
$866$	−12.9982	−	12.9982i	−0.441696	−	0.441696i
$867$	8.77047	+	8.77047i	0.297861	+	0.297861i
$868$		−	5.71708i		−	0.194050i
$869$	6.51386	−	6.51386i	0.220968	−	0.220968i
$870$	10.8190	−	10.0904i	0.366797	−	0.342098i
$871$	7.17146	+	7.17146i	0.242996	+	0.242996i
$872$	5.15891	−	5.15891i	0.174703	−	0.174703i
$873$		−	7.65590i		−	0.259113i
$874$	−0.0110380	−	0.0110380i	−0.000373365	−	0.000373365i
$875$	28.9813	+	3.03913i	0.979745	+	0.102741i
$876$		−	12.0279i		−	0.406385i
$877$	−35.8135	−	35.8135i	−1.20934	−	1.20934i	−0.971242	−	0.238096i	$-0.923477\pi$
$877$	−35.8135	−	35.8135i	−1.20934	−	1.20934i	−0.238096	−	0.971242i	$-0.576523\pi$
$878$	10.5684	+	10.5684i	0.356665	+	0.356665i
$879$	7.29762			0.246143
$880$	4.92274	−	4.59126i	0.165946	−	0.154771i
$881$			6.61073i			0.222721i	0.993780	+	0.111361i	$0.0355209\pi$
$881$			6.61073i			0.222721i	−0.993780	+	0.111361i	$0.964479\pi$
$882$		−	0.206804i		−	0.00696347i
$883$	−49.4983			−1.66575			−0.832876	−	0.553460i	$-0.813307\pi$
$883$	−49.4983			−1.66575			−0.832876	+	0.553460i	$0.813307\pi$
$884$			9.87255i			0.332050i
$885$	−6.58930	+	6.14559i	−0.221497	+	0.206582i
$886$	17.5773	−	17.5773i	0.590520	−	0.590520i
$887$	17.0910	−	17.0910i	0.573859	−	0.573859i	−0.359346	−	0.933204i	$-0.617000\pi$
$887$	17.0910	−	17.0910i	0.573859	−	0.573859i	0.933204	+	0.359346i	$0.117000\pi$
$888$	−5.59677	+	2.38247i	−0.187815	+	0.0799505i
$889$			36.0163i			1.20795i
$890$	−0.114491	+	3.28601i	−0.00383774	+	0.110147i
$891$		−	3.01042i		−	0.100853i
$892$	15.3328	−	15.3328i	0.513381	−	0.513381i
$893$			0.179554i			0.00600854i
$894$	1.87406	+	1.87406i	0.0626778	+	0.0626778i
$895$	−35.3284	−	1.23091i	−1.18090	−	0.0411447i
$896$	−1.84299	+	1.84299i	−0.0615698	+	0.0615698i
$897$	−0.0278858	−	0.0278858i	−0.000931080	−	0.000931080i
$898$	9.93203	−	9.93203i	0.331436	−	0.331436i
$899$	−14.5125			−0.484018
$900$	4.98788	+	0.347996i	0.166263	+	0.0115999i
$901$	−11.1209	+	11.1209i	−0.370491	+	0.370491i
$902$			19.1338i			0.637086i
$903$	−20.5045			−0.682347
$904$		−	3.80319i		−	0.126492i
$905$	19.5067	+	20.9150i	0.648423	+	0.695239i
$906$	−2.76653	−	2.76653i	−0.0919117	−	0.0919117i
$907$	6.83317			0.226892			0.113446	−	0.993544i	$-0.463811\pi$
$907$	6.83317			0.226892			0.113446	+	0.993544i	$0.463811\pi$
$908$	3.20189			0.106258
$909$	−16.6519			−0.552310
$910$	0.369480	−	10.6045i	0.0122482	−	0.351535i
$911$	35.7866	−	35.7866i	1.18566	−	1.18566i	0.207410	−	0.978254i	$-0.433497\pi$
$911$	35.7866	−	35.7866i	1.18566	−	1.18566i	0.978254	−	0.207410i	$-0.0665033\pi$
$912$		−	0.720673i		−	0.0238639i
$913$	2.78751	+	2.78751i	0.0922530	+	0.0922530i
$914$		−	8.27570i		−	0.273736i
$915$	10.4463	−	9.74288i	0.345344	−	0.322090i
$916$		−	21.2446i		−	0.701943i
$917$			8.15548i			0.269318i
$918$	−3.83427	−	3.83427i	−0.126550	−	0.126550i
$919$	19.0445	−	19.0445i	0.628220	−	0.628220i	−0.319400	−	0.947620i	$-0.603481\pi$
$919$	19.0445	−	19.0445i	0.628220	−	0.628220i	0.947620	+	0.319400i	$0.103481\pi$
$920$	0.0330348	+	0.0354199i	0.00108913	+	0.00116776i
$921$	−23.0913			−0.760884
$922$	3.89734	+	3.89734i	0.128352	+	0.128352i
$923$			16.4033i			0.539922i
$924$	7.84627			0.258123
$925$	−13.3002	+	27.3515i	−0.437307	+	0.899312i
$926$	−37.2821			−1.22517
$927$		−	15.2064i		−	0.499443i
$928$	4.67832	+	4.67832i	0.153573	+	0.153573i
$929$	−9.46135			−0.310417			−0.155208	−	0.987882i	$-0.549605\pi$
$929$	−9.46135			−0.310417			−0.155208	+	0.987882i	$0.549605\pi$
$930$	−3.34535	−	3.58689i	−0.109698	−	0.117619i
$931$	−0.105386	+	0.105386i	−0.00345389	+	0.00345389i
$932$	−12.0202	−	12.0202i	−0.393736	−	0.393736i
$933$		−	28.6472i		−	0.937866i
$934$		−	11.9336i		−	0.390478i
$935$	−26.6935	+	24.8960i	−0.872970	+	0.814186i
$936$		−	1.82067i		−	0.0595105i
$937$	38.9228	+	38.9228i	1.27155	+	1.27155i	0.945274	+	0.326279i	$0.105795\pi$
$937$	38.9228	+	38.9228i	1.27155	+	1.27155i	0.326279	+	0.945274i	$0.394205\pi$
$938$		−	14.5187i		−	0.474053i
$939$	13.0067	−	13.0067i	0.424457	−	0.424457i
$940$	0.0193990	−	0.556773i	0.000632726	−	0.0181599i
$941$	36.7551			1.19818			0.599090	−	0.800682i	$-0.295529\pi$
$941$	36.7551			1.19818			0.599090	+	0.800682i	$0.295529\pi$
$942$	−18.2754			−0.595444
$943$	−0.137671			−0.00448318
$944$	−2.84934	−	2.84934i	−0.0927380	−	0.0927380i
$945$	3.97505	+	4.26204i	0.129308	+	0.138644i
$946$			23.6831i			0.770004i
$947$	18.0935			0.587961			0.293980	−	0.955811i	$-0.405020\pi$
$947$	18.0935			0.587961			0.293980	+	0.955811i	$0.405020\pi$
$948$			3.06004i			0.0993855i
$949$	−15.4848	+	15.4848i	−0.502659	+	0.502659i
$950$	−2.36445	−	2.71912i	−0.0767128	−	0.0882199i
$951$	4.81106			0.156009
$952$	9.99356	−	9.99356i	0.323893	−	0.323893i
$953$	−16.1464	−	16.1464i	−0.523032	−	0.523032i	0.395454	−	0.918486i	$-0.370587\pi$
$953$	−16.1464	−	16.1464i	−0.523032	−	0.523032i	−0.918486	+	0.395454i	$0.870587\pi$
$954$	2.05089	−	2.05089i	0.0663999	−	0.0663999i
$955$	−49.6485	−	1.72985i	−1.60659	−	0.0559765i
$956$	−10.1337	−	10.1337i	−0.327748	−	0.327748i
$957$		−	19.9173i		−	0.643836i
$958$	−0.903277	+	0.903277i	−0.0291836	+	0.0291836i
$959$		−	21.0924i		−	0.681110i
$960$	−0.0778616	+	2.23471i	−0.00251297	+	0.0721250i
$961$		−	26.1886i		−	0.844793i
$962$	10.2725	+	4.13811i	0.331200	+	0.133418i
$963$	7.85181	−	7.85181i	0.253021	−	0.253021i
$964$	−10.2389	+	10.2389i	−0.329773	+	0.329773i
$965$	−34.4436	+	32.1243i	−1.10878	+	1.03412i
$966$			0.0564552i			0.00181642i
$967$	−15.5615			−0.500424			−0.250212	−	0.968191i	$-0.580500\pi$
$967$	−15.5615			−0.500424			−0.250212	+	0.968191i	$0.580500\pi$
$968$			1.93740i			0.0622704i
$969$			3.90783i			0.125538i
$970$	12.5192	−	11.6762i	0.401968	−	0.374900i
$971$	−20.1860			−0.647799			−0.323900	−	0.946091i	$-0.604994\pi$
$971$	−20.1860			−0.647799			−0.323900	+	0.946091i	$0.604994\pi$
$972$	0.707107	+	0.707107i	0.0226805	+	0.0226805i
$973$	7.70644	+	7.70644i	0.247057	+	0.247057i
$974$		−	1.67383i		−	0.0536328i
$975$	−5.97342	−	6.86944i	−0.191302	−	0.219998i
$976$	4.51718	+	4.51718i	0.144591	+	0.144591i
$977$			39.5332i			1.26478i	0.774651	+	0.632389i	$0.217926\pi$
$977$			39.5332i			1.26478i	−0.774651	+	0.632389i	$0.782074\pi$
$978$	−6.07961	+	6.07961i	−0.194404	+	0.194404i
$979$	3.13011	+	3.13011i	0.100039	+	0.100039i
$980$	0.338174	−	0.315402i	0.0108026	−	0.0100752i
$981$	5.15891	−	5.15891i	0.164711	−	0.164711i
$982$		−	9.36601i		−	0.298881i
$983$	−14.9967	−	14.9967i	−0.478321	−	0.478321i	0.426274	−	0.904594i	$-0.359826\pi$
$983$	−14.9967	−	14.9967i	−0.478321	−	0.478321i	−0.904594	+	0.426274i	$0.859826\pi$
$984$	−4.49428	−	4.49428i	−0.143272	−	0.143272i
$985$	−0.608485	+	17.4642i	−0.0193880	+	0.556455i
$986$	−25.3681	−	25.3681i	−0.807885	−	0.807885i
$987$	0.459175	−	0.459175i	0.0146157	−	0.0146157i
$988$	−0.927800	+	0.927800i	−0.0295172	+	0.0295172i
$989$	−0.170404			−0.00541853
$990$	4.92274	−	4.59126i	0.156455	−	0.145920i
$991$	14.9222	+	14.9222i	0.474018	+	0.474018i	0.903212	−	0.429194i	$-0.141202\pi$
$991$	14.9222	+	14.9222i	0.474018	+	0.474018i	−0.429194	+	0.903212i	$0.641202\pi$
$992$	1.55104	−	1.55104i	0.0492455	−	0.0492455i
$993$	3.69302			0.117194
$994$	16.6044	−	16.6044i	0.526659	−	0.526659i
$995$	17.9855	+	0.626648i	0.570178	+	0.0198661i
$996$	−1.30950			−0.0414930
$997$	51.9341			1.64477			0.822385	−	0.568932i	$-0.192643\pi$
$997$	51.9341			1.64477			0.822385	+	0.568932i	$0.192643\pi$
$998$	−11.8837	−	11.8837i	−0.376171	−	0.376171i
$999$	−5.59677	+	2.38247i	−0.177074	+	0.0753781i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.l.a.697.14	yes	36
5.3	odd	4		1110.2.o.a.253.5	yes	36
37.6	odd	4		1110.2.o.a.487.5	yes	36
185.43	even	4	inner	1110.2.l.a.43.14	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.l.a.43.14	✓	36	185.43	even	4	inner
1110.2.l.a.697.14	yes	36	1.1	even	1	trivial
1110.2.o.a.253.5	yes	36	5.3	odd	4
1110.2.o.a.487.5	yes	36	37.6	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(-1.52512 - 1.63524i) q^{5} +(0.707107 - 0.707107i) q^{6} +(1.84299 + 1.84299i) q^{7} +1.00000i q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(-1.52512 - 1.63524i) q^{5} +(0.707107 - 0.707107i) q^{6} +(1.84299 + 1.84299i) q^{7} +1.00000i q^{8} +1.00000i q^{9} +(-1.63524 + 1.52512i) q^{10} +3.01042i q^{11} +(-0.707107 - 0.707107i) q^{12} +1.82067i q^{13} +(1.84299 - 1.84299i) q^{14} +(0.0778616 - 2.23471i) q^{15} +1.00000 q^{16} -5.42248 q^{17} +1.00000 q^{18} +(-0.509592 - 0.509592i) q^{19} +(1.52512 + 1.63524i) q^{20} +2.60638i q^{21} +3.01042 q^{22} +0.0216604i q^{23} +(-0.707107 + 0.707107i) q^{24} +(-0.347996 + 4.98788i) q^{25} +1.82067 q^{26} +(-0.707107 + 0.707107i) q^{27} +(-1.84299 - 1.84299i) q^{28} +(-4.67832 + 4.67832i) q^{29} +(-2.23471 - 0.0778616i) q^{30} +(1.55104 + 1.55104i) q^{31} -1.00000i q^{32} +(-2.12868 + 2.12868i) q^{33} +5.42248i q^{34} +(0.202937 - 5.82450i) q^{35} -1.00000i q^{36} +(5.64218 + 2.27285i) q^{37} +(-0.509592 + 0.509592i) q^{38} +(-1.28741 + 1.28741i) q^{39} +(1.63524 - 1.52512i) q^{40} +6.35587i q^{41} +2.60638 q^{42} +7.86706i q^{43} -3.01042i q^{44} +(1.63524 - 1.52512i) q^{45} +0.0216604 q^{46} +(-0.176174 - 0.176174i) q^{47} +(0.707107 + 0.707107i) q^{48} -0.206804i q^{49} +(4.98788 + 0.347996i) q^{50} +(-3.83427 - 3.83427i) q^{51} -1.82067i q^{52} +(2.05089 - 2.05089i) q^{53} +(0.707107 + 0.707107i) q^{54} +(4.92274 - 4.59126i) q^{55} +(-1.84299 + 1.84299i) q^{56} -0.720673i q^{57} +(4.67832 + 4.67832i) q^{58} +(-2.84934 - 2.84934i) q^{59} +(-0.0778616 + 2.23471i) q^{60} +(4.51718 + 4.51718i) q^{61} +(1.55104 - 1.55104i) q^{62} +(-1.84299 + 1.84299i) q^{63} -1.00000 q^{64} +(2.97723 - 2.77675i) q^{65} +(2.12868 + 2.12868i) q^{66} +(3.93891 - 3.93891i) q^{67} +5.42248 q^{68} +(-0.0153162 + 0.0153162i) q^{69} +(-5.82450 - 0.202937i) q^{70} +9.00950 q^{71} -1.00000 q^{72} +(8.50501 + 8.50501i) q^{73} +(2.27285 - 5.64218i) q^{74} +(-3.77303 + 3.28089i) q^{75} +(0.509592 + 0.509592i) q^{76} +(-5.54815 + 5.54815i) q^{77} +(1.28741 + 1.28741i) q^{78} +(-2.16377 - 2.16377i) q^{79} +(-1.52512 - 1.63524i) q^{80} -1.00000 q^{81} +6.35587 q^{82} +(0.925954 - 0.925954i) q^{83} -2.60638i q^{84} +(8.26996 + 8.86704i) q^{85} +7.86706 q^{86} -6.61614 q^{87} -3.01042 q^{88} +(1.03976 - 1.03976i) q^{89} +(-1.52512 - 1.63524i) q^{90} +(-3.35547 + 3.35547i) q^{91} -0.0216604i q^{92} +2.19350i q^{93} +(-0.176174 + 0.176174i) q^{94} +(-0.0561127 + 1.61050i) q^{95} +(0.707107 - 0.707107i) q^{96} -7.65590 q^{97} -0.206804 q^{98} -3.01042 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 36 q^{4} + 4 q^{7}+O(q^{10}) \) 36 * q - 36 * q^4 + 4 * q^7	\( 36 q - 36 q^{4} + 4 q^{7} - 4 q^{10} + 4 q^{14} + 36 q^{16} - 32 q^{17} + 36 q^{18} + 4 q^{19} + 8 q^{22} - 4 q^{25} + 8 q^{26} - 4 q^{28} + 36 q^{29} - 4 q^{31} + 4 q^{33} - 12 q^{35} - 4 q^{37} + 4 q^{38} + 4 q^{39} + 4 q^{40} - 16 q^{42} + 4 q^{45} + 16 q^{47} - 16 q^{50} - 8 q^{53} + 16 q^{55} - 4 q^{56} - 36 q^{58} - 4 q^{59} - 4 q^{61} - 4 q^{62} - 4 q^{63} - 36 q^{64} + 52 q^{65} - 4 q^{66} + 16 q^{67} + 32 q^{68} - 8 q^{69} - 28 q^{70} - 8 q^{71} - 36 q^{72} - 4 q^{73} + 28 q^{74} + 16 q^{75} - 4 q^{76} + 8 q^{77} - 4 q^{78} - 12 q^{79} - 36 q^{81} - 8 q^{82} + 8 q^{83} + 8 q^{85} + 32 q^{86} - 8 q^{87} - 8 q^{88} - 24 q^{89} + 56 q^{91} + 16 q^{94} - 20 q^{95} + 40 q^{97} - 12 q^{98} - 8 q^{99}+O(q^{100}) \) 36 * q - 36 * q^4 + 4 * q^7 - 4 * q^10 + 4 * q^14 + 36 * q^16 - 32 * q^17 + 36 * q^18 + 4 * q^19 + 8 * q^22 - 4 * q^25 + 8 * q^26 - 4 * q^28 + 36 * q^29 - 4 * q^31 + 4 * q^33 - 12 * q^35 - 4 * q^37 + 4 * q^38 + 4 * q^39 + 4 * q^40 - 16 * q^42 + 4 * q^45 + 16 * q^47 - 16 * q^50 - 8 * q^53 + 16 * q^55 - 4 * q^56 - 36 * q^58 - 4 * q^59 - 4 * q^61 - 4 * q^62 - 4 * q^63 - 36 * q^64 + 52 * q^65 - 4 * q^66 + 16 * q^67 + 32 * q^68 - 8 * q^69 - 28 * q^70 - 8 * q^71 - 36 * q^72 - 4 * q^73 + 28 * q^74 + 16 * q^75 - 4 * q^76 + 8 * q^77 - 4 * q^78 - 12 * q^79 - 36 * q^81 - 8 * q^82 + 8 * q^83 + 8 * q^85 + 32 * q^86 - 8 * q^87 - 8 * q^88 - 24 * q^89 + 56 * q^91 + 16 * q^94 - 20 * q^95 + 40 * q^97 - 12 * q^98 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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