LMFDB - Embedded newform 1110.2.o.a.487.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(253,1110)]

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, 1]))

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

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

chi := DirichletCharacter("1110.253");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.o (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			487.5
Character	$\chi$	$=$	1110.487
Dual form			1110.2.o.a.253.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$4$	1.00000			0.500000
$5$	1.63524	−	1.52512i	0.731300	−	0.682056i
$5$	1.63524	−	1.52512i	0.731300	−	0.682056i
$6$	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	$0.586062\pi$
$8$	−1.00000			−0.353553
$9$			1.00000i			0.333333i
$10$	−1.63524	+	1.52512i	−0.517107	+	0.482286i
$11$		−	3.01042i		−	0.907674i	−0.891085	−	0.453837i	$-0.850055\pi$
$11$		−	3.01042i		−	0.907674i	0.891085	−	0.453837i	$-0.149945\pi$
$12$	−0.707107	−	0.707107i	−0.204124	−	0.204124i
$13$	−1.82067			−0.504963			−0.252481	−	0.967602i	$-0.581247\pi$
$13$	−1.82067			−0.504963			−0.252481	+	0.967602i	$0.581247\pi$
$14$	−1.84299	−	1.84299i	−0.492559	−	0.492559i
$15$	−2.23471	−	0.0778616i	−0.577000	−	0.0201038i
$16$	1.00000			0.250000
$17$		−	5.42248i		−	1.31515i	−0.753391	−	0.657573i	$-0.771583\pi$
$17$		−	5.42248i		−	1.31515i	0.753391	−	0.657573i	$-0.228417\pi$
$18$		−	1.00000i		−	0.235702i
$19$	0.509592	−	0.509592i	0.116909	−	0.116909i	−0.646232	−	0.763141i	$-0.723656\pi$
$19$	0.509592	−	0.509592i	0.116909	−	0.116909i	0.763141	+	0.646232i	$0.223656\pi$
$20$	1.63524	−	1.52512i	0.365650	−	0.341028i
$21$		−	2.60638i		−	0.568758i
$22$			3.01042i			0.641823i
$23$	−0.0216604			−0.00451651			−0.00225825	−	0.999997i	$-0.500719\pi$
$23$	−0.0216604			−0.00451651			−0.00225825	+	0.999997i	$0.500719\pi$
$24$	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	$-0.0394412\pi$
$29$	4.67832	+	4.67832i	0.868742	+	0.868742i	−0.123591	+	0.992333i	$0.539441\pi$
$30$	2.23471	+	0.0778616i	0.408001	+	0.0142155i
$31$	1.55104	−	1.55104i	0.278574	−	0.278574i	−0.553965	−	0.832540i	$-0.686886\pi$
$31$	1.55104	−	1.55104i	0.278574	−	0.278574i	0.832540	+	0.553965i	$0.186886\pi$
$32$	−1.00000			−0.176777
$33$	−2.12868	+	2.12868i	−0.370556	+	0.370556i
$34$			5.42248i			0.929948i
$35$	5.82450	+	0.202937i	0.984520	+	0.0343025i
$36$			1.00000i			0.166667i
$37$	2.27285	+	5.64218i	0.373655	+	0.927568i
$37$	2.27285	+	5.64218i	0.373655	+	0.927568i
$38$	−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	$-0.834688\pi$
$41$		−	6.35587i		−	0.992619i	0.868146	−	0.496310i	$-0.165312\pi$
$42$			2.60638i			0.402173i
$43$	−7.86706			−1.19972			−0.599858	−	0.800107i	$-0.704776\pi$
$43$	−7.86706			−1.19972			−0.599858	+	0.800107i	$0.704776\pi$
$44$		−	3.01042i		−	0.453837i
$45$	1.52512	+	1.63524i	0.227352	+	0.243767i
$46$	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
$50$	−0.347996	+	4.98788i	−0.0492141	+	0.705392i
$51$	−3.83427	+	3.83427i	−0.536906	+	0.536906i
$52$	−1.82067			−0.252481
$53$	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
$55$	−4.59126	−	4.92274i	−0.619085	−	0.663782i
$56$	−1.84299	−	1.84299i	−0.246279	−	0.246279i
$57$	−0.720673			−0.0954554
$58$	−4.67832	−	4.67832i	−0.614293	−	0.614293i
$59$	2.84934	−	2.84934i	0.370952	−	0.370952i	−0.496872	−	0.867824i	$-0.665518\pi$
$59$	2.84934	−	2.84934i	0.370952	−	0.370952i	0.867824	+	0.496872i	$0.165518\pi$
$60$	−2.23471	−	0.0778616i	−0.288500	−	0.0100519i
$61$	4.51718	−	4.51718i	0.578366	−	0.578366i	−0.356087	−	0.934453i	$-0.615889\pi$
$61$	4.51718	−	4.51718i	0.578366	−	0.578366i	0.934453	+	0.356087i	$0.115889\pi$
$62$	−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	−0.905519	−	0.424305i	$-0.860519\pi$
$67$	−3.93891	+	3.93891i	−0.481215	+	0.481215i	0.424305	+	0.905519i	$0.360519\pi$
$68$		−	5.42248i		−	0.657573i
$69$	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	$0.320456\pi$
$72$		−	1.00000i		−	0.117851i
$73$	−8.50501	−	8.50501i	−0.995437	−	0.995437i	0.00455309	−	0.999990i	$-0.498551\pi$
$73$	−8.50501	−	8.50501i	−0.995437	−	0.995437i	−0.999990	+	0.00455309i	$0.998551\pi$
$74$	−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	$-0.694932\pi$
$79$	2.16377	−	2.16377i	0.243444	−	0.243444i	0.818273	+	0.574830i	$0.194932\pi$
$80$	1.63524	−	1.52512i	0.182825	−	0.170514i
$81$	−1.00000			−0.111111
$82$			6.35587i			0.701888i
$83$	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
$87$		−	6.61614i		−	0.709325i
$88$			3.01042i			0.320911i
$89$	−1.03976	−	1.03976i	−0.110214	−	0.110214i	0.649849	−	0.760063i	$-0.274832\pi$
$89$	−1.03976	−	1.03976i	−0.110214	−	0.110214i	−0.760063	+	0.649849i	$0.774832\pi$
$90$	−1.52512	−	1.63524i	−0.160762	−	0.172369i
$91$	−3.35547	−	3.35547i	−0.351749	−	0.351749i
$92$	−0.0216604			−0.00225825
$93$	−2.19350			−0.227455
$94$	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
$97$		−	7.65590i		−	0.777339i	−0.921377	−	0.388670i	$-0.872935\pi$
$97$		−	7.65590i		−	0.777339i	0.921377	−	0.388670i	$-0.127065\pi$
$98$			0.206804i			0.0208904i
$99$	3.01042			0.302558
$100$	0.347996	−	4.98788i	0.0347996	−	0.498788i
$101$		−	16.6519i		−	1.65693i	−0.560040	−	0.828465i	$-0.689214\pi$
$101$		−	16.6519i		−	1.65693i	0.560040	−	0.828465i	$-0.310786\pi$
$102$	3.83427	−	3.83427i	0.379650	−	0.379650i
$103$			15.2064i			1.49833i	0.662383	+	0.749165i	$0.269545\pi$
$103$			15.2064i			1.49833i	−0.662383	+	0.749165i	$0.730455\pi$
$104$	1.82067			0.178531
$105$	−3.97505	−	4.26204i	−0.387925	−	0.415933i
$106$	−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	$-0.636384\pi$
$109$	5.15891	−	5.15891i	0.494134	−	0.494134i	0.909606	+	0.415472i	$0.136384\pi$
$110$	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
$113$			3.80319i			0.357774i	0.983870	+	0.178887i	$0.0572497\pi$
$113$			3.80319i			0.357774i	−0.983870	+	0.178887i	$0.942750\pi$
$114$	0.720673			0.0674972
$115$	−0.0354199	+	0.0330348i	−0.00330292	+	0.00308051i
$116$	4.67832	+	4.67832i	0.434371	+	0.434371i
$117$		−	1.82067i		−	0.168321i
$118$	−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
$125$	−7.03807	−	8.68709i	−0.629504	−	0.776997i
$126$	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	$0.539923\pi$
$128$	−1.00000			−0.0883883
$129$	5.56285	+	5.56285i	0.489782	+	0.489782i
$130$	2.97723	−	2.77675i	0.261120	−	0.243537i
$131$	2.21257	−	2.21257i	0.193313	−	0.193313i	−0.603813	−	0.797126i	$-0.706353\pi$
$131$	2.21257	−	2.21257i	0.193313	−	0.193313i	0.797126	+	0.603813i	$0.206353\pi$
$132$	−2.12868	+	2.12868i	−0.185278	+	0.185278i
$133$	1.87834			0.162873
$134$	3.93891	−	3.93891i	0.340270	−	0.340270i
$135$	0.0778616	−	2.23471i	0.00670126	−	0.192333i
$136$			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	$-0.556748\pi$
$139$	−4.18150			−0.354670			−0.177335	+	0.984151i	$0.556748\pi$
$140$	5.82450	+	0.202937i	0.492260	+	0.0171513i
$141$			0.249148i			0.0209820i
$142$	−9.00950			−0.756060
$143$			5.48097i			0.458342i
$144$			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
$148$	2.27285	+	5.64218i	0.186827	+	0.463784i
$149$			2.65031i			0.217122i	0.994090	+	0.108561i	$0.0346243\pi$
$149$			2.65031i			0.217122i	−0.994090	+	0.108561i	$0.965376\pi$
$150$	3.77303	−	3.28089i	0.308067	−	0.267884i
$151$			3.91246i			0.318391i	0.987247	+	0.159196i	$0.0508901\pi$
$151$			3.91246i			0.318391i	−0.987247	+	0.159196i	$0.949110\pi$
$152$	−0.509592	+	0.509592i	−0.0413334	+	0.0413334i
$153$	5.42248			0.438382
$154$	−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
$162$	1.00000			0.0785674
$163$			8.59786i			0.673437i	0.941605	+	0.336718i	$0.109317\pi$
$163$			8.59786i			0.673437i	−0.941605	+	0.336718i	$0.890683\pi$
$164$		−	6.35587i		−	0.496310i
$165$	−0.234396	+	6.72741i	−0.0182477	+	0.523728i
$166$	−0.925954	+	0.925954i	−0.0718680	+	0.0718680i
$167$			4.59086i			0.355252i	0.984098	+	0.177626i	$0.0568417\pi$
$167$			4.59086i			0.355252i	−0.984098	+	0.177626i	$0.943158\pi$
$168$			2.60638i			0.201086i
$169$	−9.68516			−0.745012
$170$	8.26996	+	8.86704i	0.634277	+	0.680071i
$171$	0.509592	+	0.509592i	0.0389695	+	0.0389695i
$172$	−7.86706			−0.599858
$173$	6.49792	+	6.49792i	0.494028	+	0.494028i	0.909573	−	0.415545i	$-0.136409\pi$
$173$	6.49792	+	6.49792i	0.494028	+	0.494028i	−0.415545	+	0.909573i	$0.636409\pi$
$174$			6.61614i			0.501568i
$175$	9.83394	−	8.55123i	0.743376	−	0.646412i
$176$		−	3.01042i		−	0.226919i
$177$	−4.02957			−0.302881
$178$	1.03976	+	1.03976i	0.0779333	+	0.0779333i
$179$	−11.1786	−	11.1786i	−0.835528	−	0.835528i	0.152738	−	0.988267i	$-0.451191\pi$
$179$	−11.1786	−	11.1786i	−0.835528	−	0.835528i	−0.988267	+	0.152738i	$0.951191\pi$
$180$	1.52512	+	1.63524i	0.113676	+	0.121883i
$181$	−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
$183$	−6.38826			−0.472234
$184$	0.0216604			0.00159683
$185$	12.3217	+	5.75991i	0.905907	+	0.423477i
$186$	2.19350			0.160835
$187$	−16.3239			−1.19372
$188$	−0.176174	−	0.176174i	−0.0128488	−	0.0128488i
$189$	2.60638			0.189586
$190$	−0.0561127	+	1.61050i	−0.00407084	+	0.116838i
$191$	15.7097	+	15.7097i	1.13672	+	1.13672i	0.989035	+	0.147683i	$0.0471814\pi$
$191$	15.7097	+	15.7097i	1.13672	+	1.13672i	0.147683	+	0.989035i	$0.452819\pi$
$192$	−0.707107	−	0.707107i	−0.0510310	−	0.0510310i
$193$	21.0634			1.51618			0.758088	−	0.652152i	$-0.226134\pi$
$193$	21.0634			1.51618			0.758088	+	0.652152i	$0.226134\pi$
$194$			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	$0.839803\pi$
$198$	−3.01042			−0.213941
$199$	5.69096	+	5.69096i	0.403421	+	0.403421i	0.879437	−	0.476015i	$-0.157919\pi$
$199$	5.69096	+	5.69096i	0.403421	+	0.403421i	−0.476015	+	0.879437i	$0.657919\pi$
$200$	−0.347996	+	4.98788i	−0.0246071	+	0.352696i
$201$	5.57046			0.392910
$202$			16.6519i			1.17163i
$203$			17.2442i			1.21030i
$204$	−3.83427	+	3.83427i	−0.268453	+	0.268453i
$205$	−9.69348	−	10.3933i	−0.677022	−	0.725903i
$206$		−	15.2064i		−	1.05948i
$207$		−	0.0216604i		−	0.00150550i
$208$	−1.82067			−0.126241
$209$	−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
$217$	5.71708			0.388101
$218$	−5.15891	+	5.15891i	−0.349405	+	0.349405i
$219$			12.0279i			0.812771i
$220$	−4.59126	−	4.92274i	−0.309542	−	0.331891i
$221$			9.87255i			0.664100i
$222$	−2.38247	+	5.59677i	−0.159901	+	0.375631i
$223$	−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
$227$		−	3.20189i		−	0.212517i	−0.994339	−	0.106258i	$-0.966113\pi$
$227$		−	3.20189i		−	0.212517i	0.994339	−	0.106258i	$-0.0338870\pi$
$228$	−0.720673			−0.0477277
$229$			21.2446i			1.40389i	0.712233	+	0.701943i	$0.247684\pi$
$229$			21.2446i			1.40389i	−0.712233	+	0.701943i	$0.752316\pi$
$230$	0.0354199	−	0.0330348i	0.00233552	−	0.00217825i
$231$	−7.84627			−0.516247
$232$	−4.67832	−	4.67832i	−0.307147	−	0.307147i
$233$	−12.0202	−	12.0202i	−0.787472	−	0.787472i	0.193607	−	0.981079i	$-0.437981\pi$
$233$	−12.0202	−	12.0202i	−0.787472	−	0.787472i	−0.981079	+	0.193607i	$0.937981\pi$
$234$			1.82067i			0.119021i
$235$	−0.556773	−	0.0193990i	−0.0363199	−	0.00126545i
$236$	2.84934	−	2.84934i	0.185476	−	0.185476i
$237$	−3.06004			−0.198771
$238$	−9.99356	+	9.99356i	−0.647786	+	0.647786i
$239$	−10.1337	+	10.1337i	−0.655496	+	0.655496i	−0.954311	−	0.298815i	$-0.903409\pi$
$239$	−10.1337	+	10.1337i	−0.655496	+	0.655496i	0.298815	+	0.954311i	$0.403409\pi$
$240$	−2.23471	−	0.0778616i	−0.144250	−	0.00502594i
$241$	10.2389	+	10.2389i	0.659546	+	0.659546i	0.955273	−	0.295727i	$-0.0955618\pi$
$241$	10.2389	+	10.2389i	0.659546	+	0.659546i	−0.295727	+	0.955273i	$0.595562\pi$
$242$	−1.93740			−0.124541
$243$	0.707107	+	0.707107i	0.0453609	+	0.0453609i
$244$	4.51718	−	4.51718i	0.289183	−	0.289183i
$245$	−0.315402	−	0.338174i	−0.0201503	−	0.0216052i
$246$	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	−0.575146	−	0.818051i	$-0.695055\pi$
$251$	3.84833	−	3.84833i	0.242905	−	0.242905i	0.818051	+	0.575146i	$0.195055\pi$
$252$	−1.84299	+	1.84299i	−0.116097	+	0.116097i
$253$			0.0652069i			0.00409952i
$254$	−9.77118	−	9.77118i	−0.613099	−	0.613099i
$255$	−0.422203	+	12.1177i	−0.0264394	+	0.758839i
$256$	1.00000			0.0625000
$257$		−	3.13559i		−	0.195593i	−0.995206	−	0.0977963i	$-0.968821\pi$
$257$		−	3.13559i		−	0.195593i	0.995206	−	0.0977963i	$-0.0311794\pi$
$258$	−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	$0.108405\pi$
$263$	20.7027	+	20.7027i	1.27658	+	1.27658i	0.334018	+	0.942567i	$0.391595\pi$
$264$	2.12868	−	2.12868i	0.131012	−	0.131012i
$265$	0.225829	−	6.48154i	0.0138726	−	0.398158i
$266$	−1.87834			−0.115169
$267$			1.47044i			0.0899896i
$268$	−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	$0.127633\pi$
$272$		−	5.42248i		−	0.328786i
$273$			4.74535i			0.287202i
$274$	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
$277$	14.8230			0.890629			0.445315	−	0.895374i	$-0.353092\pi$
$277$	14.8230			0.890629			0.445315	+	0.895374i	$0.353092\pi$
$278$	4.18150			0.250789
$279$	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	0.866351	+	0.499436i	$0.166459\pi$
$281$	22.8948	+	22.8948i	1.36579	+	1.36579i	0.499436	+	0.866351i	$0.333541\pi$
$282$		−	0.249148i		−	0.0148365i
$283$			23.6708i			1.40708i	0.710655	+	0.703541i	$0.248399\pi$
$283$			23.6708i			1.40708i	−0.710655	+	0.703541i	$0.751601\pi$
$284$	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
$288$		−	1.00000i		−	0.0589256i
$289$	−12.4033			−0.729607
$290$	−14.7852	−	0.515143i	−0.868215	−	0.0302503i
$291$	−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
$298$		−	2.65031i		−	0.153529i
$299$	0.0394365			0.00228067
$300$	−3.77303	+	3.28089i	−0.217836	+	0.189422i
$301$	−14.4989	−	14.4989i	−0.835701	−	0.835701i
$302$		−	3.91246i		−	0.225137i
$303$	−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	−0.0659354	−	0.997824i	$-0.521003\pi$
$307$	16.3280	−	16.3280i	0.931889	−	0.931889i	0.997824	+	0.0659354i	$0.0210031\pi$
$308$	5.54815	−	5.54815i	0.316135	−	0.316135i
$309$	10.7525	−	10.7525i	0.611691	−	0.611691i
$310$	−0.170789	+	4.90183i	−0.00970017	+	0.278405i
$311$	−20.2566	+	20.2566i	−1.14865	+	1.14865i	−0.161827	+	0.986819i	$0.551739\pi$
$311$	−20.2566	+	20.2566i	−1.14865	+	1.14865i	−0.986819	+	0.161827i	$0.948261\pi$
$312$	−1.28741	−	1.28741i	−0.0728851	−	0.0728851i
$313$	18.3942			1.03970			0.519852	−	0.854256i	$-0.325987\pi$
$313$	18.3942			1.03970			0.519852	+	0.854256i	$0.325987\pi$
$314$	12.9226	+	12.9226i	0.729267	+	0.729267i
$315$	−0.202937	+	5.82450i	−0.0114342	+	0.328173i
$316$	2.16377	−	2.16377i	0.121722	−	0.121722i
$317$	−3.40194	+	3.40194i	−0.191072	+	0.191072i	−0.796159	−	0.605087i	$-0.793138\pi$
$317$	−3.40194	+	3.40194i	−0.191072	+	0.191072i	0.605087	+	0.796159i	$0.293138\pi$
$318$	2.90039			0.162646
$319$	14.0837	−	14.0837i	0.788535	−	0.788535i
$320$	1.63524	−	1.52512i	0.0914125	−	0.0852570i
$321$			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
$325$	−0.633587	+	9.08127i	−0.0351451	+	0.503738i
$326$		−	8.59786i		−	0.476192i
$327$	−7.29580			−0.403459
$328$			6.35587i			0.350944i
$329$		−	0.649372i		−	0.0358010i
$330$	0.234396	−	6.72741i	0.0129031	−	0.370332i
$331$	2.61136	+	2.61136i	0.143533	+	0.143533i	0.775222	−	0.631689i	$-0.217638\pi$
$331$	2.61136	+	2.61136i	0.143533	+	0.143533i	−0.631689	+	0.775222i	$0.717638\pi$
$332$	0.925954	−	0.925954i	0.0508183	−	0.0508183i
$333$	−5.64218	+	2.27285i	−0.309189	+	0.124552i
$334$		−	4.59086i		−	0.251201i
$335$	−0.433725	+	12.4484i	−0.0236969	+	0.680128i
$336$		−	2.60638i		−	0.142189i
$337$	−3.23500	+	3.23500i	−0.176222	+	0.176222i	−0.789707	−	0.613485i	$-0.789767\pi$
$337$	−3.23500	+	3.23500i	−0.176222	+	0.176222i	0.613485	+	0.789707i	$0.289767\pi$
$338$	9.68516			0.526803
$339$	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
$347$	17.9326			0.962675			0.481337	−	0.876535i	$-0.340151\pi$
$347$	17.9326			0.962675			0.481337	+	0.876535i	$0.340151\pi$
$348$		−	6.61614i		−	0.354662i
$349$			34.1023i			1.82545i	0.408571	+	0.912727i	$0.366027\pi$
$349$			34.1023i			1.82545i	−0.408571	+	0.912727i	$0.633973\pi$
$350$	−9.83394	+	8.55123i	−0.525646	+	0.457083i
$351$	−1.28741	+	1.28741i	−0.0687168	+	0.0687168i
$352$			3.01042i			0.160456i
$353$			7.23850i			0.385266i	0.981271	+	0.192633i	$0.0617027\pi$
$353$			7.23850i			0.385266i	−0.981271	+	0.192633i	$0.938297\pi$
$354$	4.02957			0.214169
$355$	14.7327	−	13.7406i	0.781929	−	0.729275i
$356$	−1.03976	−	1.03976i	−0.0551071	−	0.0551071i
$357$	−14.1330			−0.747999
$358$	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
$362$	12.7902			0.672239
$363$	−1.36995	−	1.36995i	−0.0719037	−	0.0719037i
$364$	−3.35547	−	3.35547i	−0.175874	−	0.175874i
$365$	−26.8789	−	0.936512i	−1.40691	−	0.0490193i
$366$	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	$0.663138\pi$
$368$	−0.0216604			−0.00112913
$369$	6.35587			0.330873
$370$	−12.3217	−	5.75991i	−0.640573	−	0.299443i
$371$	7.55951			0.392470
$372$	−2.19350			−0.113728
$373$	−0.813457	−	0.813457i	−0.0421192	−	0.0421192i	0.685733	−	0.727853i	$-0.259482\pi$
$373$	−0.813457	−	0.813457i	−0.0421192	−	0.0421192i	−0.727853	+	0.685733i	$0.759482\pi$
$374$	16.3239			0.844090
$375$	−1.16604	+	11.1194i	−0.0602138	+	0.574202i
$376$	0.176174	+	0.176174i	0.00908548	+	0.00908548i
$377$	−8.51767	−	8.51767i	−0.438682	−	0.438682i
$378$	−2.60638			−0.134058
$379$		−	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
$383$	−14.8639			−0.759507			−0.379754	−	0.925088i	$-0.623991\pi$
$383$	−14.8639			−0.759507			−0.379754	+	0.925088i	$0.623991\pi$
$384$	0.707107	+	0.707107i	0.0360844	+	0.0360844i
$385$	0.610923	−	17.5342i	0.0311355	−	0.893624i
$386$	−21.0634			−1.07210
$387$		−	7.86706i		−	0.399905i
$388$		−	7.65590i		−	0.388670i
$389$	−25.0493	+	25.0493i	−1.27005	+	1.27005i	−0.323986	+	0.946062i	$0.605023\pi$
$389$	−25.0493	+	25.0493i	−1.27005	+	1.27005i	−0.946062	+	0.323986i	$0.894977\pi$
$390$	−4.06867	−	0.141760i	−0.206025	−	0.00717831i
$391$			0.117453i			0.00593987i
$392$			0.206804i			0.0104452i
$393$	−3.12905			−0.157840
$394$	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	−0.827991	−	0.560741i	$-0.810516\pi$
$397$	−5.32491	+	5.32491i	−0.267250	+	0.267250i	0.560741	+	0.827991i	$0.310516\pi$
$398$	−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	−0.822847	−	0.568263i	$-0.807616\pi$
$401$	−5.09805	+	5.09805i	−0.254584	+	0.254584i	0.568263	+	0.822847i	$0.307616\pi$
$402$	−5.57046			−0.277829
$403$	−2.82393	+	2.82393i	−0.140670	+	0.140670i
$404$		−	16.6519i		−	0.828465i
$405$	−1.63524	+	1.52512i	−0.0812556	+	0.0757840i
$406$		−	17.2442i		−	0.855813i
$407$	16.9853	−	6.84223i	0.841930	−	0.339157i
$408$	3.83427	−	3.83427i	0.189825	−	0.189825i
$409$	−15.3174	−	15.3174i	−0.757396	−	0.757396i	0.218451	−	0.975848i	$-0.429899\pi$
$409$	−15.3174	−	15.3174i	−0.757396	−	0.757396i	−0.975848	+	0.218451i	$0.929899\pi$
$410$	9.69348	+	10.3933i	0.478727	+	0.513291i
$411$			8.09263i			0.399180i
$412$			15.2064i			0.749165i
$413$	10.5026			0.516798
$414$			0.0216604i			0.00106455i
$415$	0.101960	−	2.92635i	0.00500500	−	0.143649i
$416$	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	$0.875346\pi$
$420$	−3.97505	−	4.26204i	−0.193962	−	0.207966i
$421$	15.7260	−	15.7260i	0.766440	−	0.766440i	−0.211038	−	0.977478i	$-0.567684\pi$
$421$	15.7260	−	15.7260i	0.766440	−	0.766440i	0.977478	+	0.211038i	$0.0676844\pi$
$422$	−2.18341			−0.106287
$423$	0.176174	−	0.176174i	0.00856587	−	0.00856587i
$424$	−2.05089	+	2.05089i	−0.0995998	+	0.0995998i
$425$	−27.0467	−	1.88700i	−1.31196	−	0.0915332i
$426$	6.37068	+	6.37068i	0.308660	+	0.308660i
$427$	16.6502			0.805760
$428$	−7.85181	−	7.85181i	−0.379532	−	0.379532i
$429$	3.87563	−	3.87563i	0.187117	−	0.187117i
$430$	12.8645	−	11.9982i	0.620381	−	0.578606i
$431$	7.16507	−	7.16507i	0.345129	−	0.345129i	−0.513162	−	0.858292i	$-0.671526\pi$
$431$	7.16507	−	7.16507i	0.345129	−	0.345129i	0.858292	+	0.513162i	$0.171526\pi$
$432$	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
$438$		−	12.0279i		−	0.574716i
$439$	10.5684	+	10.5684i	0.504400	+	0.504400i	0.912802	−	0.408402i	$-0.133914\pi$
$439$	10.5684	+	10.5684i	0.504400	+	0.504400i	−0.408402	+	0.912802i	$0.633914\pi$
$440$	4.59126	+	4.92274i	0.218879	+	0.234682i
$441$	0.206804			0.00984783
$442$		−	9.87255i		−	0.469589i
$443$	−17.5773	−	17.5773i	−0.835121	−	0.835121i	0.153091	−	0.988212i	$-0.451077\pi$
$443$	−17.5773	−	17.5773i	−0.835121	−	0.835121i	−0.988212	+	0.153091i	$0.951077\pi$
$444$	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	$-0.857533\pi$
$449$	−9.93203	+	9.93203i	−0.468722	+	0.468722i	0.432779	+	0.901500i	$0.357533\pi$
$450$	−4.98788	−	0.347996i	−0.235131	−	0.0164047i
$451$	−19.1338			−0.900975
$452$			3.80319i			0.178887i
$453$	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
$457$			8.27570i			0.387121i	0.981088	+	0.193560i	$0.0620036\pi$
$457$			8.27570i			0.387121i	−0.981088	+	0.193560i	$0.937996\pi$
$458$		−	21.2446i		−	0.992697i
$459$	−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	0.610499	−	0.792017i	$-0.290969\pi$
$461$	−3.89734	−	3.89734i	−0.181517	−	0.181517i	−0.792017	+	0.610499i	$0.790969\pi$
$462$	7.84627			0.365042
$463$	37.2821			1.73265			0.866323	−	0.499484i	$-0.166477\pi$
$463$	37.2821			1.73265			0.866323	+	0.499484i	$0.166477\pi$
$464$	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
$467$			11.9336i			0.552219i	0.961126	+	0.276109i	$0.0890452\pi$
$467$			11.9336i			0.552219i	−0.961126	+	0.276109i	$0.910955\pi$
$468$		−	1.82067i		−	0.0841605i
$469$	−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
$473$			23.6831i			1.08895i
$474$	3.06004			0.140552
$475$	−2.36445	−	2.71912i	−0.108488	−	0.124762i
$476$	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	$-0.740709\pi$
$479$	0.903277	−	0.903277i	0.0412718	−	0.0412718i	0.727441	+	0.686170i	$0.240709\pi$
$480$	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
$483$			0.0564552i			0.00256880i
$484$	1.93740			0.0880637
$485$	−11.6762	−	12.5192i	−0.530189	−	0.568468i
$486$	−0.707107	−	0.707107i	−0.0320750	−	0.0320750i
$487$			1.67383i			0.0758483i	0.999281	+	0.0379241i	$0.0120745\pi$
$487$			1.67383i			0.0758483i	−0.999281	+	0.0379241i	$0.987925\pi$
$488$	−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
$495$	4.92274	−	4.59126i	0.221261	−	0.206362i
$496$	1.55104	−	1.55104i	0.0696436	−	0.0696436i
$497$	16.6044	+	16.6044i	0.744808	+	0.744808i
$498$	1.30950			0.0586800
$499$	−11.8837	−	11.8837i	−0.531986	−	0.531986i	0.389177	−	0.921163i	$-0.372760\pi$
$499$	−11.8837	−	11.8837i	−0.531986	−	0.531986i	−0.921163	+	0.389177i	$0.872760\pi$
$500$	−7.03807	−	8.68709i	−0.314752	−	0.388499i
$501$	3.24623	−	3.24623i	0.145031	−	0.145031i
$502$	−3.84833	+	3.84833i	−0.171759	+	0.171759i
$503$	−25.4862			−1.13637			−0.568187	−	0.822900i	$-0.692355\pi$
$503$	−25.4862			−1.13637			−0.568187	+	0.822900i	$0.692355\pi$
$504$	1.84299	−	1.84299i	0.0820931	−	0.0820931i
$505$	−25.3963	−	27.2299i	−1.13012	−	1.21171i
$506$		−	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	$-0.654684\pi$
$509$	−21.0744			−0.934105			−0.467053	+	0.884230i	$0.654684\pi$
$510$	0.422203	−	12.1177i	0.0186955	−	0.536580i
$511$		−	31.3492i		−	1.38681i
$512$	−1.00000			−0.0441942
$513$		−	0.720673i		−	0.0318185i
$514$			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
$518$	6.20962	−	14.5873i	0.272835	−	0.640929i
$519$		−	9.18945i		−	0.403372i
$520$	2.97723	−	2.77675i	0.130560	−	0.121768i
$521$		−	26.1425i		−	1.14532i	−0.819792	−	0.572661i	$-0.805911\pi$
$521$		−	26.1425i		−	1.14532i	0.819792	−	0.572661i	$-0.194089\pi$
$522$	4.67832	−	4.67832i	0.204764	−	0.204764i
$523$	18.6818			0.816898			0.408449	−	0.912781i	$-0.366070\pi$
$523$	18.6818			0.816898			0.408449	+	0.912781i	$0.366070\pi$
$524$	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
$532$	1.87834			0.0814365
$533$			11.5719i			0.501236i
$534$		−	1.47044i		−	0.0636322i
$535$	−24.8146	−	0.864586i	−1.07283	−	0.0373793i
$536$	3.93891	−	3.93891i	0.170135	−	0.170135i
$537$			15.8089i			0.682206i
$538$			15.5877i			0.672032i
$539$	−0.622567			−0.0268159
$540$	0.0778616	−	2.23471i	0.00335063	−	0.0961667i
$541$	−12.5483	−	12.5483i	−0.539494	−	0.539494i	0.383887	−	0.923380i	$-0.374585\pi$
$541$	−12.5483	−	12.5483i	−0.539494	−	0.539494i	−0.923380	+	0.383887i	$0.874585\pi$
$542$	−30.3127			−1.30204
$543$	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
$547$	13.3305			0.569972			0.284986	−	0.958532i	$-0.408011\pi$
$547$	13.3305			0.569972			0.284986	+	0.958532i	$0.408011\pi$
$548$	−5.72235	−	5.72235i	−0.244447	−	0.244447i
$549$	4.51718	+	4.51718i	0.192789	+	0.192789i
$550$	15.0156	+	1.04761i	0.640266	+	0.0446704i
$551$	4.76807			0.203127
$552$	−0.0153162	−	0.0153162i	−0.000651902	−	0.000651902i
$553$	7.97561			0.339158
$554$	−14.8230			−0.629770
$555$	−4.63986	−	12.7856i	−0.196951	−	0.542719i
$556$	−4.18150			−0.177335
$557$	31.5142			1.33530			0.667650	−	0.744475i	$-0.267300\pi$
$557$	31.5142			1.33530			0.667650	+	0.744475i	$0.267300\pi$
$558$	−1.55104	−	1.55104i	−0.0656606	−	0.0656606i
$559$	14.3233			0.605812
$560$	5.82450	+	0.202937i	0.246130	+	0.00857563i
$561$	11.5428	+	11.5428i	0.487336	+	0.487336i
$562$	−22.8948	−	22.8948i	−0.965757	−	0.965757i
$563$	−23.8203			−1.00391			−0.501953	−	0.864895i	$-0.667385\pi$
$563$	−23.8203			−1.00391			−0.501953	+	0.864895i	$0.667385\pi$
$564$			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
$568$	−9.00950			−0.378030
$569$	2.20968	+	2.20968i	0.0926346	+	0.0926346i	0.751905	−	0.659271i	$-0.229135\pi$
$569$	2.20968	+	2.20968i	0.0926346	+	0.0926346i	−0.659271	+	0.751905i	$0.729135\pi$
$570$	1.17847	−	1.09911i	0.0493607	−	0.0460368i
$571$	−18.6714			−0.781372			−0.390686	−	0.920524i	$-0.627762\pi$
$571$	−18.6714			−0.781372			−0.390686	+	0.920524i	$0.627762\pi$
$572$			5.48097i			0.229171i
$573$		−	22.2169i		−	0.928126i
$574$	−11.7138	+	11.7138i	−0.488923	+	0.488923i
$575$	−0.00753775	+	0.108039i	−0.000314346	+	0.00450556i
$576$			1.00000i			0.0416667i
$577$			42.7062i			1.77788i	0.458023	+	0.888941i	$0.348558\pi$
$577$			42.7062i			1.77788i	−0.458023	+	0.888941i	$0.651442\pi$
$578$	12.4033			0.515910
$579$	−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
$587$	−14.4564			−0.596681			−0.298341	−	0.954459i	$-0.596433\pi$
$587$	−14.4564			−0.596681			−0.298341	+	0.954459i	$0.596433\pi$
$588$	−0.146233	+	0.146233i	−0.00603054	+	0.00603054i
$589$		−	1.58079i		−	0.0651354i
$590$	−0.313749	+	9.00493i	−0.0129168	+	0.370727i
$591$			7.81496i			0.321465i
$592$	2.27285	+	5.64218i	0.0934137	+	0.231892i
$593$	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
$597$		−	8.04823i		−	0.329392i
$598$	−0.0394365			−0.00161268
$599$			32.8474i			1.34211i	0.741407	+	0.671055i	$0.234159\pi$
$599$			32.8474i			1.34211i	−0.741407	+	0.671055i	$0.765841\pi$
$600$	3.77303	−	3.28089i	0.154033	−	0.133942i
$601$	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
$605$	3.16811	−	2.95477i	0.128802	−	0.120129i
$606$	11.7747	−	11.7747i	0.478315	−	0.478315i
$607$	−1.05109			−0.0426623			−0.0213312	−	0.999772i	$-0.506790\pi$
$607$	−1.05109			−0.0426623			−0.0213312	+	0.999772i	$0.506790\pi$
$608$	−0.509592	+	0.509592i	−0.0206667	+	0.0206667i
$609$	12.1935	−	12.1935i	0.494104	−	0.494104i
$610$	−0.497400	+	14.2759i	−0.0201391	+	0.578015i
$611$	0.320755	+	0.320755i	0.0129763	+	0.0129763i
$612$	5.42248			0.219191
$613$	20.8463	+	20.8463i	0.841976	+	0.841976i	0.989116	−	0.147140i	$-0.0470067\pi$
$613$	20.8463	+	20.8463i	0.841976	+	0.841976i	−0.147140	+	0.989116i	$0.547007\pi$
$614$	−16.3280	+	16.3280i	−0.658945	+	0.658945i
$615$	−0.494878	+	14.2035i	−0.0199554	+	0.572742i
$616$	−5.54815	+	5.54815i	−0.223541	+	0.223541i
$617$	11.8344	−	11.8344i	0.476435	−	0.476435i	−0.427555	−	0.903990i	$-0.640625\pi$
$617$	11.8344	−	11.8344i	0.476435	−	0.476435i	0.903990	+	0.427555i	$0.140625\pi$
$618$	−10.7525	+	10.7525i	−0.432531	+	0.432531i
$619$	−2.66335			−0.107049			−0.0535246	−	0.998567i	$-0.517046\pi$
$619$	−2.66335			−0.107049			−0.0535246	+	0.998567i	$0.517046\pi$
$620$	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
$623$		−	3.83252i		−	0.153547i
$624$	1.28741	+	1.28741i	0.0515376	+	0.0515376i
$625$	−24.7578	−	3.47153i	−0.990312	−	0.138861i
$626$	−18.3942			−0.735182
$627$			2.16952i			0.0866424i
$628$	−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	−0.985797	−	0.167943i	$-0.946288\pi$
$631$	−20.5443	+	20.5443i	−0.817854	+	0.817854i	0.167943	+	0.985797i	$0.446288\pi$
$632$	−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
$635$	30.8805	+	1.07593i	1.22545	+	0.0426971i
$636$	−2.90039			−0.115008
$637$			0.376523i			0.0149184i
$638$	−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	$0.225706\pi$
$642$		−	11.1041i		−	0.438245i
$643$		−	33.4086i		−	1.31751i	−0.752358	−	0.658754i	$-0.771084\pi$
$643$		−	33.4086i		−	1.31751i	0.752358	−	0.658754i	$-0.228916\pi$
$644$	−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
$647$	−48.3301			−1.90005			−0.950026	−	0.312170i	$-0.898944\pi$
$647$	−48.3301			−1.90005			−0.950026	+	0.312170i	$0.898944\pi$
$648$	1.00000			0.0392837
$649$	−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
$652$			8.59786i			0.336718i
$653$			20.8734i			0.816839i	0.912794	+	0.408420i	$0.133920\pi$
$653$			20.8734i			0.816839i	−0.912794	+	0.408420i	$0.866080\pi$
$654$	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
$658$			0.649372i			0.0253152i
$659$	26.2240			1.02154			0.510771	−	0.859717i	$-0.329360\pi$
$659$	26.2240			1.02154			0.510771	+	0.859717i	$0.329360\pi$
$660$	−0.234396	+	6.72741i	−0.00912384	+	0.261864i
$661$	15.8166	−	15.8166i	0.615196	−	0.615196i	−0.329100	−	0.944295i	$-0.606745\pi$
$661$	15.8166	−	15.8166i	0.615196	−	0.615196i	0.944295	+	0.329100i	$0.106745\pi$
$662$	−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
$668$			4.59086i			0.177626i
$669$	21.6839			0.838347
$670$	0.433725	−	12.4484i	0.0167563	−	0.480923i
$671$	−13.5986	−	13.5986i	−0.524968	−	0.524968i
$672$			2.60638i			0.100543i
$673$	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	−0.618469	−	0.785809i	$-0.712247\pi$
$677$	4.35406	−	4.35406i	0.167340	−	0.167340i	0.785809	+	0.618469i	$0.212247\pi$
$678$	−2.68926	+	2.68926i	−0.103281	+	0.103281i
$679$	14.1097	−	14.1097i	0.541481	−	0.541481i
$680$	8.26996	+	8.86704i	0.317138	+	0.340036i
$681$	−2.26408	+	2.26408i	−0.0867596	+	0.0867596i
$682$	4.66926	+	4.66926i	0.178795	+	0.178795i
$683$	−28.7474			−1.09999			−0.549995	−	0.835168i	$-0.685370\pi$
$683$	−28.7474			−1.09999			−0.549995	+	0.835168i	$0.685370\pi$
$684$	0.509592	+	0.509592i	0.0194848	+	0.0194848i
$685$	−18.0847	−	0.630105i	−0.690981	−	0.0240751i
$686$	−13.2820	+	13.2820i	−0.507111	+	0.507111i
$687$	15.0222	−	15.0222i	0.573134	−	0.573134i
$688$	−7.86706			−0.299929
$689$	−3.73399	+	3.73399i	−0.142254	+	0.142254i
$690$	−0.0484048	−	0.00168651i	−0.00184274	−	6.42045e-5i
$691$			43.9902i			1.67347i	0.547610	+	0.836733i	$0.315538\pi$
$691$			43.9902i			1.67347i	−0.547610	+	0.836733i	$0.684462\pi$
$692$	6.49792	+	6.49792i	0.247014	+	0.247014i
$693$	5.54815	+	5.54815i	0.210757	+	0.210757i
$694$	−17.9326			−0.680714
$695$	−6.83773	+	6.37730i	−0.259370	+	0.241905i
$696$			6.61614i			0.250784i
$697$	−34.4646			−1.30544
$698$		−	34.1023i		−	1.29079i
$699$			16.9992i			0.642968i
$700$	9.83394	−	8.55123i	0.371688	−	0.323206i
$701$	−9.73870	−	9.73870i	−0.367826	−	0.367826i	0.498858	−	0.866684i	$-0.333753\pi$
$701$	−9.73870	−	9.73870i	−0.367826	−	0.367826i	−0.866684	+	0.498858i	$0.833753\pi$
$702$	1.28741	−	1.28741i	0.0485901	−	0.0485901i
$703$	4.03344	+	1.71698i	0.152124	+	0.0647572i
$704$		−	3.01042i		−	0.113459i
$705$	0.379981	+	0.407415i	0.0143109	+	0.0153441i
$706$		−	7.23850i		−	0.272424i
$707$	30.6893	−	30.6893i	1.15419	−	1.15419i
$708$	−4.02957			−0.151441
$709$	−10.8762	+	10.8762i	−0.408466	+	0.408466i	−0.881203	−	0.472738i	$-0.843266\pi$
$709$	−10.8762	+	10.8762i	−0.408466	+	0.408466i	0.472738	+	0.881203i	$0.343266\pi$
$710$	−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
$717$	14.3313			0.535210
$718$		−	29.3398i		−	1.09495i
$719$		−	28.4189i		−	1.05985i	−0.848045	−	0.529924i	$-0.822221\pi$
$719$		−	28.4189i		−	1.05985i	0.848045	−	0.529924i	$-0.177779\pi$
$720$	1.52512	+	1.63524i	0.0568380	+	0.0609417i
$721$	−28.0252	+	28.0252i	−1.04371	+	1.04371i
$722$		−	18.4806i		−	0.687778i
$723$		−	14.4800i		−	0.538517i
$724$	−12.7902			−0.475345
$725$	24.9629	−	21.7068i	0.927099	−	0.806171i
$726$	1.36995	+	1.36995i	0.0508436	+	0.0508436i
$727$	2.22360			0.0824686			0.0412343	−	0.999150i	$-0.486871\pi$
$727$	2.22360			0.0824686			0.0412343	+	0.999150i	$0.486871\pi$
$728$	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
$732$	−6.38826			−0.236117
$733$	11.8204	+	11.8204i	0.436598	+	0.436598i	0.890865	−	0.454268i	$-0.150099\pi$
$733$	11.8204	+	11.8204i	0.436598	+	0.436598i	−0.454268	+	0.890865i	$0.650099\pi$
$734$	−7.30169	−	7.30169i	−0.269510	−	0.269510i
$735$	−0.0161021	+	0.462148i	−0.000593936	+	0.0170466i
$736$	0.0216604			0.000798414
$737$	11.8578	+	11.8578i	0.436786	+	0.436786i
$738$	−6.35587			−0.233963
$739$	−41.0418			−1.50975			−0.754874	−	0.655870i	$-0.772302\pi$
$739$	−41.0418			−1.50975			−0.754874	+	0.655870i	$0.772302\pi$
$740$	12.3217	+	5.75991i	0.452953	+	0.211739i
$741$	1.31211			0.0482014
$742$	−7.55951			−0.277518
$743$	−21.4316	−	21.4316i	−0.786249	−	0.786249i	0.194628	−	0.980877i	$-0.437650\pi$
$743$	−21.4316	−	21.4316i	−0.786249	−	0.786249i	−0.980877	+	0.194628i	$0.937650\pi$
$744$	2.19350			0.0804175
$745$	4.04206	+	4.33389i	0.148090	+	0.158781i
$746$	0.813457	+	0.813457i	0.0297828	+	0.0297828i
$747$	0.925954	+	0.925954i	0.0338789	+	0.0338789i
$748$	−16.3239			−0.596862
$749$		−	28.9416i		−	1.05750i
$750$	1.16604	−	11.1194i	0.0425776	−	0.406022i
$751$		−	38.7551i		−	1.41419i	−0.707117	−	0.707097i	$-0.750005\pi$
$751$		−	38.7551i		−	1.41419i	0.707117	−	0.707097i	$-0.249995\pi$
$752$	−0.176174	−	0.176174i	−0.00642440	−	0.00642440i
$753$	−5.44236			−0.198331
$754$	8.51767	+	8.51767i	0.310195	+	0.310195i
$755$	5.96698	+	6.39779i	0.217161	+	0.232840i
$756$	2.60638			0.0947930
$757$			47.4098i			1.72314i	0.507640	+	0.861569i	$0.330518\pi$
$757$			47.4098i			1.72314i	−0.507640	+	0.861569i	$0.669482\pi$
$758$			14.5201i			0.527394i
$759$	0.0461082	−	0.0461082i	0.00167362	−	0.00167362i
$760$	−0.0561127	+	1.61050i	−0.00203542	+	0.0584188i
$761$			31.8594i			1.15490i	0.816425	+	0.577452i	$0.195953\pi$
$761$			31.8594i			1.15490i	−0.816425	+	0.577452i	$0.804047\pi$
$762$			13.8185i			0.500593i
$763$	19.0156			0.688411
$764$	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	$-0.130793\pi$
$769$	14.3460	+	14.3460i	0.517329	+	0.517329i	−0.399433	+	0.916762i	$0.630793\pi$
$770$	−0.610923	+	17.5342i	−0.0220161	+	0.631887i
$771$	−2.21719	+	2.21719i	−0.0798503	+	0.0798503i
$772$	21.0634			0.758088
$773$	−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
$775$	−7.19662	−	8.27613i	−0.258510	−	0.297287i
$776$			7.65590i			0.274831i
$777$	14.7056	−	5.92391i	0.527562	−	0.212519i
$778$	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
$782$		−	0.117453i		−	0.00420012i
$783$	6.61614			0.236442
$784$		−	0.206804i		−	0.00738587i
$785$	−40.8402	−	1.42295i	−1.45765	−	0.0507873i
$786$	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
$790$	−0.238260	+	6.83831i	−0.00847689	+	0.243296i
$791$	−7.00924	+	7.00924i	−0.249220	+	0.249220i
$792$	−3.01042			−0.106970
$793$	−8.22430	+	8.22430i	−0.292053	+	0.292053i
$794$	5.32491	−	5.32491i	0.188974	−	0.188974i
$795$	−4.74282	+	4.42345i	−0.168211	+	0.156884i
$796$	5.69096	+	5.69096i	0.201711	+	0.201711i
$797$	39.3879			1.39519			0.697595	−	0.716492i	$-0.254253\pi$
$797$	39.3879			1.39519			0.697595	+	0.716492i	$0.254253\pi$
$798$	1.32819	+	1.32819i	0.0470174	+	0.0470174i
$799$	−0.955300	+	0.955300i	−0.0337961	+	0.0337961i
$800$	−0.347996	+	4.98788i	−0.0123035	+	0.176348i
$801$	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
$808$			16.6519i			0.585813i
$809$	−24.3142	−	24.3142i	−0.854841	−	0.854841i	0.135884	−	0.990725i	$-0.456613\pi$
$809$	−24.3142	−	24.3142i	−0.854841	−	0.854841i	−0.990725	+	0.135884i	$0.956613\pi$
$810$	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	$0.644021\pi$
$812$			17.2442i			0.605151i
$813$	−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
$820$	−9.69348	−	10.3933i	−0.338511	−	0.362951i
$821$	−52.1619			−1.82046			−0.910231	−	0.414101i	$-0.864096\pi$
$821$	−52.1619			−1.82046			−0.910231	+	0.414101i	$0.864096\pi$
$822$		−	8.09263i		−	0.282263i
$823$	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
$827$			30.7971i			1.07092i	0.844561	+	0.535460i	$0.179862\pi$
$827$			30.7971i			1.07092i	−0.844561	+	0.535460i	$0.820138\pi$
$828$		−	0.0216604i		−	0.000752752i
$829$	−4.01468	−	4.01468i	−0.139435	−	0.139435i	0.633944	−	0.773379i	$-0.281435\pi$
$829$	−4.01468	−	4.01468i	−0.139435	−	0.139435i	−0.773379	+	0.633944i	$0.781435\pi$
$830$	−0.101960	+	2.92635i	−0.00353907	+	0.101575i
$831$	−10.4815	−	10.4815i	−0.363598	−	0.363598i
$832$	−1.82067			−0.0631204
$833$	−1.12139			−0.0388540
$834$	−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
$837$		−	2.19350i		−	0.0758184i
$838$		−	15.6256i		−	0.539777i
$839$	−26.0337			−0.898784			−0.449392	−	0.893335i	$-0.648359\pi$
$839$	−26.0337			−0.898784			−0.449392	+	0.893335i	$0.648359\pi$
$840$	3.97505	+	4.26204i	0.137152	+	0.147054i
$841$			14.7733i			0.509425i
$842$	−15.7260	+	15.7260i	−0.541955	+	0.541955i
$843$		−	32.3781i		−	1.11516i
$844$	2.18341			0.0751561
$845$	−15.8375	+	14.7711i	−0.544828	+	0.508140i
$846$	−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
$853$			24.2328i			0.829714i	0.909887	+	0.414857i	$0.136168\pi$
$853$			24.2328i			0.829714i	−0.909887	+	0.414857i	$0.863832\pi$
$854$	−16.6502			−0.569758
$855$	1.61050	+	0.0561127i	0.0550778	+	0.00191901i
$856$	7.85181	+	7.85181i	0.268369	+	0.268369i
$857$		−	38.1314i		−	1.30254i	−0.758845	−	0.651272i	$-0.774236\pi$
$857$		−	38.1314i		−	1.30254i	0.758845	−	0.651272i	$-0.225764\pi$
$858$	−3.87563	+	3.87563i	−0.132312	+	0.132312i
$859$	17.3872	−	17.3872i	0.593243	−	0.593243i	−0.345263	−	0.938506i	$-0.612210\pi$
$859$	17.3872	−	17.3872i	0.593243	−	0.593243i	0.938506	+	0.345263i	$0.112210\pi$
$860$	−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
$865$	20.5358	+	0.715505i	0.698237	+	0.0243279i
$866$	−12.9982	+	12.9982i	−0.441696	+	0.441696i
$867$	8.77047	+	8.77047i	0.297861	+	0.297861i
$868$	5.71708			0.194050
$869$	−6.51386	−	6.51386i	−0.220968	−	0.220968i
$870$	10.0904	+	10.8190i	0.342098	+	0.366797i
$871$	7.17146	−	7.17146i	0.242996	−	0.242996i
$872$	−5.15891	+	5.15891i	−0.174703	+	0.174703i
$873$	7.65590			0.259113
$874$	0.0110380	−	0.0110380i	0.000373365	−	0.000373365i
$875$	3.03913	−	28.9813i	0.102741	−	0.979745i
$876$			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
$880$	−4.59126	−	4.92274i	−0.154771	−	0.165946i
$881$		−	6.61073i		−	0.222721i	−0.993780	−	0.111361i	$-0.964479\pi$
$881$		−	6.61073i		−	0.222721i	0.993780	−	0.111361i	$-0.0355209\pi$
$882$	−0.206804			−0.00696347
$883$			49.4983i			1.66575i	0.553460	+	0.832876i	$0.313307\pi$
$883$			49.4983i			1.66575i	−0.553460	+	0.832876i	$0.686693\pi$
$884$			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	−0.933204	−	0.359346i	$-0.883000\pi$
$887$	−17.0910	+	17.0910i	−0.573859	+	0.573859i	0.359346	+	0.933204i	$0.383000\pi$
$888$	−2.38247	+	5.59677i	−0.0799505	+	0.187815i
$889$			36.0163i			1.20795i
$890$	3.28601	+	0.114491i	0.110147	+	0.00383774i
$891$			3.01042i			0.100853i
$892$	−15.3328	+	15.3328i	−0.513381	+	0.513381i
$893$	−0.179554			−0.00600854
$894$	−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
$902$	19.1338			0.637086
$903$			20.5045i			0.682347i
$904$		−	3.80319i		−	0.126492i
$905$	−20.9150	+	19.5067i	−0.695239	+	0.648423i
$906$	−2.76653	+	2.76653i	−0.0919117	+	0.0919117i
$907$			6.83317i			0.226892i	0.993544	+	0.113446i	$0.0361888\pi$
$907$			6.83317i			0.226892i	−0.993544	+	0.113446i	$0.963811\pi$
$908$		−	3.20189i		−	0.106258i
$909$	16.6519			0.552310
$910$	10.6045	+	0.369480i	0.351535	+	0.0122482i
$911$	35.7866	+	35.7866i	1.18566	+	1.18566i	0.978254	+	0.207410i	$0.0665033\pi$
$911$	35.7866	+	35.7866i	1.18566	+	1.18566i	0.207410	+	0.978254i	$0.433497\pi$
$912$	−0.720673			−0.0238639
$913$	−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
$917$	8.15548			0.269318
$918$	3.83427	+	3.83427i	0.126550	+	0.126550i
$919$	−19.0445	−	19.0445i	−0.628220	−	0.628220i	0.319400	−	0.947620i	$-0.396519\pi$
$919$	−19.0445	−	19.0445i	−0.628220	−	0.628220i	−0.947620	+	0.319400i	$0.896519\pi$
$920$	0.0354199	−	0.0330348i	0.00116776	−	0.00108913i
$921$	−23.0913			−0.760884
$922$	3.89734	+	3.89734i	0.128352	+	0.128352i
$923$	−16.4033			−0.539922
$924$	−7.84627			−0.258123
$925$	28.9334	−	9.37325i	0.951325	−	0.308190i
$926$	−37.2821			−1.22517
$927$	−15.2064			−0.499443
$928$	−4.67832	−	4.67832i	−0.153573	−	0.153573i
$929$	9.46135			0.310417			0.155208	−	0.987882i	$-0.450395\pi$
$929$	9.46135			0.310417			0.155208	+	0.987882i	$0.450395\pi$
$930$	3.58689	−	3.34535i	0.117619	−	0.109698i
$931$	−0.105386	−	0.105386i	−0.00345389	−	0.00345389i
$932$	−12.0202	−	12.0202i	−0.393736	−	0.393736i
$933$	28.6472			0.937866
$934$		−	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	$0.394205\pi$
$938$	14.5187			0.474053
$939$	−13.0067	−	13.0067i	−0.424457	−	0.424457i
$940$	−0.556773	−	0.0193990i	−0.0181599	−	0.000632726i
$941$	36.7551			1.19818			0.599090	−	0.800682i	$-0.295529\pi$
$941$	36.7551			1.19818			0.599090	+	0.800682i	$0.295529\pi$
$942$		−	18.2754i		−	0.595444i
$943$			0.137671i			0.00448318i
$944$	2.84934	−	2.84934i	0.0927380	−	0.0927380i
$945$	4.26204	−	3.97505i	0.138644	−	0.129308i
$946$		−	23.6831i		−	0.770004i
$947$			18.0935i			0.587961i	0.955811	+	0.293980i	$0.0949800\pi$
$947$			18.0935i			0.587961i	−0.955811	+	0.293980i	$0.905020\pi$
$948$	−3.06004			−0.0993855
$949$	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	0.918486	−	0.395454i	$-0.129413\pi$
$953$	16.1464	+	16.1464i	0.523032	+	0.523032i	−0.395454	+	0.918486i	$0.629413\pi$
$954$	−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
$957$	−19.9173			−0.643836
$958$	−0.903277	+	0.903277i	−0.0291836	+	0.0291836i
$959$		−	21.0924i		−	0.681110i
$960$	−2.23471	−	0.0778616i	−0.0721250	−	0.00251297i
$961$			26.1886i			0.844793i
$962$	4.13811	+	10.2725i	0.133418	+	0.331200i
$963$	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
$967$		−	15.5615i		−	0.500424i	−0.968191	−	0.250212i	$-0.919500\pi$
$967$		−	15.5615i		−	0.500424i	0.968191	−	0.250212i	$-0.0805003\pi$
$968$	−1.93740			−0.0622704
$969$			3.90783i			0.125538i
$970$	11.6762	+	12.5192i	0.374900	+	0.401968i
$971$	−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
$975$	6.86944	−	5.97342i	0.219998	−	0.191302i
$976$	4.51718	−	4.51718i	0.144591	−	0.144591i
$977$	39.5332			1.26478			0.632389	−	0.774651i	$-0.282074\pi$
$977$	39.5332			1.26478			0.632389	+	0.774651i	$0.282074\pi$
$978$	−6.07961	+	6.07961i	−0.194404	+	0.194404i
$979$	−3.13011	+	3.13011i	−0.100039	+	0.100039i
$980$	−0.315402	−	0.338174i	−0.0100752	−	0.0108026i
$981$	5.15891	+	5.15891i	0.164711	+	0.164711i
$982$	−9.36601			−0.298881
$983$	14.9967	+	14.9967i	0.478321	+	0.478321i	0.904594	−	0.426274i	$-0.140174\pi$
$983$	14.9967	+	14.9967i	0.478321	+	0.478321i	−0.426274	+	0.904594i	$0.640174\pi$
$984$	4.49428	−	4.49428i	0.143272	−	0.143272i
$985$	−17.4642	−	0.608485i	−0.556455	−	0.0193880i
$986$	−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	−0.429194	−	0.903212i	$-0.641202\pi$
$991$	14.9222	−	14.9222i	0.474018	−	0.474018i	0.903212	+	0.429194i	$0.141202\pi$
$992$	−1.55104	+	1.55104i	−0.0492455	+	0.0492455i
$993$		−	3.69302i		−	0.117194i
$994$	−16.6044	−	16.6044i	−0.526659	−	0.526659i
$995$	17.9855	+	0.626648i	0.570178	+	0.0198661i
$996$	−1.30950			−0.0414930
$997$			51.9341i			1.64477i	0.568932	+	0.822385i	$0.307357\pi$
$997$			51.9341i			1.64477i	−0.568932	+	0.822385i	$0.692643\pi$
$998$	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.o.a.487.5	yes	36
5.3	odd	4		1110.2.l.a.43.14	✓	36
37.31	odd	4		1110.2.l.a.697.14	yes	36
185.68	even	4	inner	1110.2.o.a.253.5	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.l.a.43.14	✓	36	5.3	odd	4
1110.2.l.a.697.14	yes	36	37.31	odd	4
1110.2.o.a.253.5	yes	36	185.68	even	4	inner
1110.2.o.a.487.5	yes	36	1.1	even	1	trivial

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

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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