LMFDB - Embedded newform 1110.2.i.k.211.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(121,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("1110.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{41})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 11x^{2} + 10x + 100 $ x^4 - x^3 + 11x^2 + 10x + 100
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			211.1
Root			$-1.35078 + 2.33962i$ of defining polynomial
Character	$\chi$	$=$	1110.211
Dual form			1110.2.i.k.121.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} -1.00000 q^{6} +(1.50000 - 2.59808i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} -1.00000 q^{6} +(1.50000 - 2.59808i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} -1.00000 q^{10} +2.00000 q^{11} +(-0.500000 - 0.866025i) q^{12} +(-3.20156 + 5.54527i) q^{13} +3.00000 q^{14} +(-0.500000 - 0.866025i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.00000 + 1.73205i) q^{17} +(0.500000 - 0.866025i) q^{18} +(-2.85078 + 4.93770i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(1.50000 + 2.59808i) q^{21} +(1.00000 + 1.73205i) q^{22} -7.40312 q^{23} +(0.500000 - 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} -6.40312 q^{26} +1.00000 q^{27} +(1.50000 + 2.59808i) q^{28} -1.70156 q^{29} +(0.500000 - 0.866025i) q^{30} +4.70156 q^{31} +(0.500000 - 0.866025i) q^{32} +(-1.00000 + 1.73205i) q^{33} +(-1.00000 + 1.73205i) q^{34} +(1.50000 + 2.59808i) q^{35} +1.00000 q^{36} +(3.55234 + 4.93770i) q^{37} -5.70156 q^{38} +(-3.20156 - 5.54527i) q^{39} +(0.500000 - 0.866025i) q^{40} +(-5.70156 + 9.87540i) q^{41} +(-1.50000 + 2.59808i) q^{42} -2.70156 q^{43} +(-1.00000 + 1.73205i) q^{44} +1.00000 q^{45} +(-3.70156 - 6.41129i) q^{46} -8.00000 q^{47} +1.00000 q^{48} +(-1.00000 - 1.73205i) q^{49} +(0.500000 - 0.866025i) q^{50} -2.00000 q^{51} +(-3.20156 - 5.54527i) q^{52} +(-1.70156 - 2.94719i) q^{53} +(0.500000 + 0.866025i) q^{54} +(-1.00000 + 1.73205i) q^{55} +(-1.50000 + 2.59808i) q^{56} +(-2.85078 - 4.93770i) q^{57} +(-0.850781 - 1.47360i) q^{58} +(-1.00000 - 1.73205i) q^{59} +1.00000 q^{60} +(4.70156 - 8.14334i) q^{61} +(2.35078 + 4.07167i) q^{62} -3.00000 q^{63} +1.00000 q^{64} +(-3.20156 - 5.54527i) q^{65} -2.00000 q^{66} +(5.35078 - 9.26782i) q^{67} -2.00000 q^{68} +(3.70156 - 6.41129i) q^{69} +(-1.50000 + 2.59808i) q^{70} +(-1.85078 + 3.20565i) q^{71} +(0.500000 + 0.866025i) q^{72} +5.29844 q^{73} +(-2.50000 + 5.54527i) q^{74} +1.00000 q^{75} +(-2.85078 - 4.93770i) q^{76} +(3.00000 - 5.19615i) q^{77} +(3.20156 - 5.54527i) q^{78} +(4.05234 - 7.01886i) q^{79} +1.00000 q^{80} +(-0.500000 + 0.866025i) q^{81} -11.4031 q^{82} +(3.85078 + 6.66975i) q^{83} -3.00000 q^{84} -2.00000 q^{85} +(-1.35078 - 2.33962i) q^{86} +(0.850781 - 1.47360i) q^{87} -2.00000 q^{88} +(0.701562 + 1.21514i) q^{89} +(0.500000 + 0.866025i) q^{90} +(9.60469 + 16.6358i) q^{91} +(3.70156 - 6.41129i) q^{92} +(-2.35078 + 4.07167i) q^{93} +(-4.00000 - 6.92820i) q^{94} +(-2.85078 - 4.93770i) q^{95} +(0.500000 + 0.866025i) q^{96} -14.7016 q^{97} +(1.00000 - 1.73205i) q^{98} +(-1.00000 - 1.73205i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 2 q^{3} - 2 q^{4} - 2 q^{5} - 4 q^{6} + 6 q^{7} - 4 q^{8} - 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 - 2 * q^5 - 4 * q^6 + 6 * q^7 - 4 * q^8 - 2 * q^9	$ 4 q + 2 q^{2} - 2 q^{3} - 2 q^{4} - 2 q^{5} - 4 q^{6} + 6 q^{7} - 4 q^{8} - 2 q^{9} - 4 q^{10} + 8 q^{11} - 2 q^{12} + 12 q^{14} - 2 q^{15} - 2 q^{16} + 4 q^{17} + 2 q^{18} - 5 q^{19} - 2 q^{20} + 6 q^{21} + 4 q^{22} - 4 q^{23} + 2 q^{24} - 2 q^{25} + 4 q^{27} + 6 q^{28} + 6 q^{29} + 2 q^{30} + 6 q^{31} + 2 q^{32} - 4 q^{33} - 4 q^{34} + 6 q^{35} + 4 q^{36} - 5 q^{37} - 10 q^{38} + 2 q^{40} - 10 q^{41} - 6 q^{42} + 2 q^{43} - 4 q^{44} + 4 q^{45} - 2 q^{46} - 32 q^{47} + 4 q^{48} - 4 q^{49} + 2 q^{50} - 8 q^{51} + 6 q^{53} + 2 q^{54} - 4 q^{55} - 6 q^{56} - 5 q^{57} + 3 q^{58} - 4 q^{59} + 4 q^{60} + 6 q^{61} + 3 q^{62} - 12 q^{63} + 4 q^{64} - 8 q^{66} + 15 q^{67} - 8 q^{68} + 2 q^{69} - 6 q^{70} - q^{71} + 2 q^{72} + 34 q^{73} - 10 q^{74} + 4 q^{75} - 5 q^{76} + 12 q^{77} - 3 q^{79} + 4 q^{80} - 2 q^{81} - 20 q^{82} + 9 q^{83} - 12 q^{84} - 8 q^{85} + q^{86} - 3 q^{87} - 8 q^{88} - 10 q^{89} + 2 q^{90} + 2 q^{92} - 3 q^{93} - 16 q^{94} - 5 q^{95} + 2 q^{96} - 46 q^{97} + 4 q^{98} - 4 q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 - 2 * q^5 - 4 * q^6 + 6 * q^7 - 4 * q^8 - 2 * q^9 - 4 * q^10 + 8 * q^11 - 2 * q^12 + 12 * q^14 - 2 * q^15 - 2 * q^16 + 4 * q^17 + 2 * q^18 - 5 * q^19 - 2 * q^20 + 6 * q^21 + 4 * q^22 - 4 * q^23 + 2 * q^24 - 2 * q^25 + 4 * q^27 + 6 * q^28 + 6 * q^29 + 2 * q^30 + 6 * q^31 + 2 * q^32 - 4 * q^33 - 4 * q^34 + 6 * q^35 + 4 * q^36 - 5 * q^37 - 10 * q^38 + 2 * q^40 - 10 * q^41 - 6 * q^42 + 2 * q^43 - 4 * q^44 + 4 * q^45 - 2 * q^46 - 32 * q^47 + 4 * q^48 - 4 * q^49 + 2 * q^50 - 8 * q^51 + 6 * q^53 + 2 * q^54 - 4 * q^55 - 6 * q^56 - 5 * q^57 + 3 * q^58 - 4 * q^59 + 4 * q^60 + 6 * q^61 + 3 * q^62 - 12 * q^63 + 4 * q^64 - 8 * q^66 + 15 * q^67 - 8 * q^68 + 2 * q^69 - 6 * q^70 - q^71 + 2 * q^72 + 34 * q^73 - 10 * q^74 + 4 * q^75 - 5 * q^76 + 12 * q^77 - 3 * q^79 + 4 * q^80 - 2 * q^81 - 20 * q^82 + 9 * q^83 - 12 * q^84 - 8 * q^85 + q^86 - 3 * q^87 - 8 * q^88 - 10 * q^89 + 2 * q^90 + 2 * q^92 - 3 * q^93 - 16 * q^94 - 5 * q^95 + 2 * q^96 - 46 * q^97 + 4 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$	−1.00000			−0.408248
$7$	1.50000	−	2.59808i	0.566947	−	0.981981i	−0.429919	−	0.902867i	$-0.641458\pi$
$7$	1.50000	−	2.59808i	0.566947	−	0.981981i	0.996866	−	0.0791130i	$-0.0252088\pi$
$8$	−1.00000			−0.353553
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−1.00000			−0.316228
$11$	2.00000			0.603023			0.301511	−	0.953463i	$-0.402509\pi$
$11$	2.00000			0.603023			0.301511	+	0.953463i	$0.402509\pi$
$12$	−0.500000	−	0.866025i	−0.144338	−	0.250000i
$13$	−3.20156	+	5.54527i	−0.887954	+	1.53798i	−0.0456630	+	0.998957i	$0.514540\pi$
$13$	−3.20156	+	5.54527i	−0.887954	+	1.53798i	−0.842291	+	0.539024i	$0.818793\pi$
$14$	3.00000			0.801784
$15$	−0.500000	−	0.866025i	−0.129099	−	0.223607i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.00000	+	1.73205i	0.242536	+	0.420084i	0.961436	−	0.275029i	$-0.0886875\pi$
$17$	1.00000	+	1.73205i	0.242536	+	0.420084i	−0.718900	+	0.695113i	$0.755354\pi$
$18$	0.500000	−	0.866025i	0.117851	−	0.204124i
$19$	−2.85078	+	4.93770i	−0.654014	+	1.13279i	0.328126	+	0.944634i	$0.393583\pi$
$19$	−2.85078	+	4.93770i	−0.654014	+	1.13279i	−0.982140	+	0.188152i	$0.939750\pi$
$20$	−0.500000	−	0.866025i	−0.111803	−	0.193649i
$21$	1.50000	+	2.59808i	0.327327	+	0.566947i
$22$	1.00000	+	1.73205i	0.213201	+	0.369274i
$23$	−7.40312			−1.54366			−0.771829	−	0.635830i	$-0.780658\pi$
$23$	−7.40312			−1.54366			−0.771829	+	0.635830i	$0.780658\pi$
$24$	0.500000	−	0.866025i	0.102062	−	0.176777i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−6.40312			−1.25576
$27$	1.00000			0.192450
$28$	1.50000	+	2.59808i	0.283473	+	0.490990i
$29$	−1.70156			−0.315972			−0.157986	−	0.987441i	$-0.550500\pi$
$29$	−1.70156			−0.315972			−0.157986	+	0.987441i	$0.550500\pi$
$30$	0.500000	−	0.866025i	0.0912871	−	0.158114i
$31$	4.70156			0.844425			0.422213	−	0.906497i	$-0.361254\pi$
$31$	4.70156			0.844425			0.422213	+	0.906497i	$0.361254\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−1.00000	+	1.73205i	−0.174078	+	0.301511i
$34$	−1.00000	+	1.73205i	−0.171499	+	0.297044i
$35$	1.50000	+	2.59808i	0.253546	+	0.439155i
$36$	1.00000			0.166667
$37$	3.55234	+	4.93770i	0.584002	+	0.811752i
$37$	3.55234	+	4.93770i	0.584002	+	0.811752i
$38$	−5.70156			−0.924916
$39$	−3.20156	−	5.54527i	−0.512660	−	0.887954i
$40$	0.500000	−	0.866025i	0.0790569	−	0.136931i
$41$	−5.70156	+	9.87540i	−0.890434	+	1.54228i	−0.0510790	+	0.998695i	$0.516266\pi$
$41$	−5.70156	+	9.87540i	−0.890434	+	1.54228i	−0.839355	+	0.543583i	$0.817067\pi$
$42$	−1.50000	+	2.59808i	−0.231455	+	0.400892i
$43$	−2.70156			−0.411984			−0.205992	−	0.978554i	$-0.566042\pi$
$43$	−2.70156			−0.411984			−0.205992	+	0.978554i	$0.566042\pi$
$44$	−1.00000	+	1.73205i	−0.150756	+	0.261116i
$45$	1.00000			0.149071
$46$	−3.70156	−	6.41129i	−0.545766	−	0.945294i
$47$	−8.00000			−1.16692			−0.583460	−	0.812142i	$-0.698301\pi$
$47$	−8.00000			−1.16692			−0.583460	+	0.812142i	$0.698301\pi$
$48$	1.00000			0.144338
$49$	−1.00000	−	1.73205i	−0.142857	−	0.247436i
$50$	0.500000	−	0.866025i	0.0707107	−	0.122474i
$51$	−2.00000			−0.280056
$52$	−3.20156	−	5.54527i	−0.443977	−	0.768990i
$53$	−1.70156	−	2.94719i	−0.233728	−	0.404828i	0.725175	−	0.688565i	$-0.241759\pi$
$53$	−1.70156	−	2.94719i	−0.233728	−	0.404828i	−0.958902	+	0.283737i	$0.908426\pi$
$54$	0.500000	+	0.866025i	0.0680414	+	0.117851i
$55$	−1.00000	+	1.73205i	−0.134840	+	0.233550i
$56$	−1.50000	+	2.59808i	−0.200446	+	0.347183i
$57$	−2.85078	−	4.93770i	−0.377595	−	0.654014i
$58$	−0.850781	−	1.47360i	−0.111713	−	0.193493i
$59$	−1.00000	−	1.73205i	−0.130189	−	0.225494i	0.793560	−	0.608492i	$-0.208225\pi$
$59$	−1.00000	−	1.73205i	−0.130189	−	0.225494i	−0.923749	+	0.382998i	$0.874892\pi$
$60$	1.00000			0.129099
$61$	4.70156	−	8.14334i	0.601973	−	1.04265i	−0.390549	−	0.920582i	$-0.627715\pi$
$61$	4.70156	−	8.14334i	0.601973	−	1.04265i	0.992522	−	0.122066i	$-0.0389520\pi$
$62$	2.35078	+	4.07167i	0.298549	+	0.517103i
$63$	−3.00000			−0.377964
$64$	1.00000			0.125000
$65$	−3.20156	−	5.54527i	−0.397105	−	0.687806i
$66$	−2.00000			−0.246183
$67$	5.35078	−	9.26782i	0.653702	−	1.13224i	−0.328516	−	0.944499i	$-0.606548\pi$
$67$	5.35078	−	9.26782i	0.653702	−	1.13224i	0.982218	−	0.187746i	$-0.0601183\pi$
$68$	−2.00000			−0.242536
$69$	3.70156	−	6.41129i	0.445616	−	0.771829i
$70$	−1.50000	+	2.59808i	−0.179284	+	0.310530i
$71$	−1.85078	+	3.20565i	−0.219647	+	0.380440i	−0.954700	−	0.297570i	$-0.903824\pi$
$71$	−1.85078	+	3.20565i	−0.219647	+	0.380440i	0.735053	+	0.678010i	$0.237157\pi$
$72$	0.500000	+	0.866025i	0.0589256	+	0.102062i
$73$	5.29844			0.620135			0.310068	−	0.950715i	$-0.399648\pi$
$73$	5.29844			0.620135			0.310068	+	0.950715i	$0.399648\pi$
$74$	−2.50000	+	5.54527i	−0.290619	+	0.644624i
$75$	1.00000			0.115470
$76$	−2.85078	−	4.93770i	−0.327007	−	0.566393i
$77$	3.00000	−	5.19615i	0.341882	−	0.592157i
$78$	3.20156	−	5.54527i	0.362506	−	0.627878i
$79$	4.05234	−	7.01886i	0.455924	−	0.789684i	−0.542817	−	0.839851i	$-0.682642\pi$
$79$	4.05234	−	7.01886i	0.455924	−	0.789684i	0.998741	+	0.0501673i	$0.0159755\pi$
$80$	1.00000			0.111803
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−11.4031			−1.25926
$83$	3.85078	+	6.66975i	0.422678	+	0.732100i	0.996200	−	0.0870899i	$-0.0277567\pi$
$83$	3.85078	+	6.66975i	0.422678	+	0.732100i	−0.573522	+	0.819190i	$0.694423\pi$
$84$	−3.00000			−0.327327
$85$	−2.00000			−0.216930
$86$	−1.35078	−	2.33962i	−0.145658	−	0.252288i
$87$	0.850781	−	1.47360i	0.0912133	−	0.157986i
$88$	−2.00000			−0.213201
$89$	0.701562	+	1.21514i	0.0743654	+	0.128805i	0.900810	−	0.434213i	$-0.142974\pi$
$89$	0.701562	+	1.21514i	0.0743654	+	0.128805i	−0.826445	+	0.563018i	$0.809640\pi$
$90$	0.500000	+	0.866025i	0.0527046	+	0.0912871i
$91$	9.60469	+	16.6358i	1.00684	+	1.74391i
$92$	3.70156	−	6.41129i	0.385915	−	0.668424i
$93$	−2.35078	+	4.07167i	−0.243765	+	0.422213i
$94$	−4.00000	−	6.92820i	−0.412568	−	0.714590i
$95$	−2.85078	−	4.93770i	−0.292484	−	0.506597i
$96$	0.500000	+	0.866025i	0.0510310	+	0.0883883i
$97$	−14.7016			−1.49272			−0.746359	−	0.665544i	$-0.768200\pi$
$97$	−14.7016			−1.49272			−0.746359	+	0.665544i	$0.768200\pi$
$98$	1.00000	−	1.73205i	0.101015	−	0.174964i
$99$	−1.00000	−	1.73205i	−0.100504	−	0.174078i
$100$	1.00000			0.100000
$101$	−8.80625			−0.876254			−0.438127	−	0.898913i	$-0.644358\pi$
$101$	−8.80625			−0.876254			−0.438127	+	0.898913i	$0.644358\pi$
$102$	−1.00000	−	1.73205i	−0.0990148	−	0.171499i
$103$	−5.10469			−0.502980			−0.251490	−	0.967860i	$-0.580921\pi$
$103$	−5.10469			−0.502980			−0.251490	+	0.967860i	$0.580921\pi$
$104$	3.20156	−	5.54527i	0.313939	−	0.543758i
$105$	−3.00000			−0.292770
$106$	1.70156	−	2.94719i	0.165270	−	0.286257i
$107$	4.70156	−	8.14334i	0.454517	−	0.787247i	−0.544143	−	0.838992i	$-0.683145\pi$
$107$	4.70156	−	8.14334i	0.454517	−	0.787247i	0.998660	+	0.0517456i	$0.0164785\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$	8.05234	+	13.9471i	0.771275	+	1.33589i	0.936865	+	0.349692i	$0.113714\pi$
$109$	8.05234	+	13.9471i	0.771275	+	1.33589i	−0.165590	+	0.986195i	$0.552953\pi$
$110$	−2.00000			−0.190693
$111$	−6.05234	+	0.607571i	−0.574463	+	0.0576681i
$112$	−3.00000			−0.283473
$113$	6.85078	+	11.8659i	0.644467	+	1.11625i	0.984424	+	0.175809i	$0.0562541\pi$
$113$	6.85078	+	11.8659i	0.644467	+	1.11625i	−0.339957	+	0.940441i	$0.610413\pi$
$114$	2.85078	−	4.93770i	0.267000	−	0.462458i
$115$	3.70156	−	6.41129i	0.345172	−	0.597856i
$116$	0.850781	−	1.47360i	0.0789930	−	0.136820i
$117$	6.40312			0.591969
$118$	1.00000	−	1.73205i	0.0920575	−	0.159448i
$119$	6.00000			0.550019
$120$	0.500000	+	0.866025i	0.0456435	+	0.0790569i
$121$	−7.00000			−0.636364
$122$	9.40312			0.851319
$123$	−5.70156	−	9.87540i	−0.514093	−	0.890434i
$124$	−2.35078	+	4.07167i	−0.211106	+	0.365647i
$125$	1.00000			0.0894427
$126$	−1.50000	−	2.59808i	−0.133631	−	0.231455i
$127$	6.50000	+	11.2583i	0.576782	+	0.999015i	0.995846	+	0.0910585i	$0.0290250\pi$
$127$	6.50000	+	11.2583i	0.576782	+	0.999015i	−0.419064	+	0.907957i	$0.637642\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	1.35078	−	2.33962i	0.118930	−	0.205992i
$130$	3.20156	−	5.54527i	0.280796	−	0.486352i
$131$	2.70156	+	4.67924i	0.236037	+	0.408827i	0.959573	−	0.281458i	$-0.0908181\pi$
$131$	2.70156	+	4.67924i	0.236037	+	0.408827i	−0.723537	+	0.690286i	$0.757485\pi$
$132$	−1.00000	−	1.73205i	−0.0870388	−	0.150756i
$133$	8.55234	+	14.8131i	0.741582	+	1.28446i
$134$	10.7016			0.924474
$135$	−0.500000	+	0.866025i	−0.0430331	+	0.0745356i
$136$	−1.00000	−	1.73205i	−0.0857493	−	0.148522i
$137$	−9.10469			−0.777866			−0.388933	−	0.921266i	$-0.627156\pi$
$137$	−9.10469			−0.777866			−0.388933	+	0.921266i	$0.627156\pi$
$138$	7.40312			0.630196
$139$	9.75391	+	16.8943i	0.827315	+	1.43295i	0.900137	+	0.435607i	$0.143466\pi$
$139$	9.75391	+	16.8943i	0.827315	+	1.43295i	−0.0728213	+	0.997345i	$0.523200\pi$
$140$	−3.00000			−0.253546
$141$	4.00000	−	6.92820i	0.336861	−	0.583460i
$142$	−3.70156			−0.310628
$143$	−6.40312	+	11.0905i	−0.535456	+	0.927437i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	0.850781	−	1.47360i	0.0706535	−	0.122375i
$146$	2.64922	+	4.58858i	0.219251	+	0.379754i
$147$	2.00000			0.164957
$148$	−6.05234	+	0.607571i	−0.497500	+	0.0499420i
$149$	13.1047			1.07358			0.536789	−	0.843717i	$-0.319637\pi$
$149$	13.1047			1.07358			0.536789	+	0.843717i	$0.319637\pi$
$150$	0.500000	+	0.866025i	0.0408248	+	0.0707107i
$151$	6.64922	−	11.5168i	0.541106	−	0.937223i	−0.457735	−	0.889089i	$-0.651339\pi$
$151$	6.64922	−	11.5168i	0.541106	−	0.937223i	0.998841	−	0.0481341i	$-0.0153275\pi$
$152$	2.85078	−	4.93770i	0.231229	−	0.400500i
$153$	1.00000	−	1.73205i	0.0808452	−	0.140028i
$154$	6.00000			0.483494
$155$	−2.35078	+	4.07167i	−0.188819	+	0.327045i
$156$	6.40312			0.512660
$157$	−0.201562	−	0.349116i	−0.0160864	−	0.0278625i	0.857870	−	0.513867i	$-0.171787\pi$
$157$	−0.201562	−	0.349116i	−0.0160864	−	0.0278625i	−0.873957	+	0.486004i	$0.838454\pi$
$158$	8.10469			0.644774
$159$	3.40312			0.269885
$160$	0.500000	+	0.866025i	0.0395285	+	0.0684653i
$161$	−11.1047	+	19.2339i	−0.875172	+	1.51584i
$162$	−1.00000			−0.0785674
$163$	3.40312	+	5.89438i	0.266553	+	0.461684i	0.967969	−	0.251068i	$-0.0807818\pi$
$163$	3.40312	+	5.89438i	0.266553	+	0.461684i	−0.701416	+	0.712752i	$0.747449\pi$
$164$	−5.70156	−	9.87540i	−0.445217	−	0.771139i
$165$	−1.00000	−	1.73205i	−0.0778499	−	0.134840i
$166$	−3.85078	+	6.66975i	−0.298879	+	0.517673i
$167$	−7.70156	+	13.3395i	−0.595965	+	1.03224i	0.397445	+	0.917626i	$0.369897\pi$
$167$	−7.70156	+	13.3395i	−0.595965	+	1.03224i	−0.993410	+	0.114615i	$0.963436\pi$
$168$	−1.50000	−	2.59808i	−0.115728	−	0.200446i
$169$	−14.0000	−	24.2487i	−1.07692	−	1.86529i
$170$	−1.00000	−	1.73205i	−0.0766965	−	0.132842i
$171$	5.70156			0.436009
$172$	1.35078	−	2.33962i	0.102996	−	0.178394i
$173$	2.00000	+	3.46410i	0.152057	+	0.263371i	0.931984	−	0.362500i	$-0.118077\pi$
$173$	2.00000	+	3.46410i	0.152057	+	0.263371i	−0.779926	+	0.625871i	$0.784744\pi$
$174$	1.70156			0.128995
$175$	−3.00000			−0.226779
$176$	−1.00000	−	1.73205i	−0.0753778	−	0.130558i
$177$	2.00000			0.150329
$178$	−0.701562	+	1.21514i	−0.0525843	+	0.0910787i
$179$	20.2094			1.51052			0.755260	−	0.655426i	$-0.227511\pi$
$179$	20.2094			1.51052			0.755260	+	0.655426i	$0.227511\pi$
$180$	−0.500000	+	0.866025i	−0.0372678	+	0.0645497i
$181$	6.05234	−	10.4830i	0.449867	−	0.779193i	−0.548510	−	0.836144i	$-0.684805\pi$
$181$	6.05234	−	10.4830i	0.449867	−	0.779193i	0.998377	+	0.0569514i	$0.0181380\pi$
$182$	−9.60469	+	16.6358i	−0.711947	+	1.23313i
$183$	4.70156	+	8.14334i	0.347549	+	0.601973i
$184$	7.40312			0.545766
$185$	−6.05234	+	0.607571i	−0.444977	+	0.0446695i
$186$	−4.70156			−0.344735
$187$	2.00000	+	3.46410i	0.146254	+	0.253320i
$188$	4.00000	−	6.92820i	0.291730	−	0.505291i
$189$	1.50000	−	2.59808i	0.109109	−	0.188982i
$190$	2.85078	−	4.93770i	0.206817	−	0.358218i
$191$	9.40312			0.680386			0.340193	−	0.940356i	$-0.389508\pi$
$191$	9.40312			0.680386			0.340193	+	0.940356i	$0.389508\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	−16.1047			−1.15924			−0.579620	−	0.814887i	$-0.696799\pi$
$193$	−16.1047			−1.15924			−0.579620	+	0.814887i	$0.696799\pi$
$194$	−7.35078	−	12.7319i	−0.527755	−	0.914099i
$195$	6.40312			0.458537
$196$	2.00000			0.142857
$197$	−8.40312	−	14.5546i	−0.598698	−	1.03698i	−0.993014	−	0.118000i	$-0.962352\pi$
$197$	−8.40312	−	14.5546i	−0.598698	−	1.03698i	0.394316	−	0.918975i	$-0.370982\pi$
$198$	1.00000	−	1.73205i	0.0710669	−	0.123091i
$199$	22.1047			1.56696			0.783480	−	0.621417i	$-0.213443\pi$
$199$	22.1047			1.56696			0.783480	+	0.621417i	$0.213443\pi$
$200$	0.500000	+	0.866025i	0.0353553	+	0.0612372i
$201$	5.35078	+	9.26782i	0.377415	+	0.653702i
$202$	−4.40312	−	7.62643i	−0.309803	−	0.536594i
$203$	−2.55234	+	4.42079i	−0.179139	+	0.310278i
$204$	1.00000	−	1.73205i	0.0700140	−	0.121268i
$205$	−5.70156	−	9.87540i	−0.398214	−	0.689728i
$206$	−2.55234	−	4.42079i	−0.177830	−	0.308011i
$207$	3.70156	+	6.41129i	0.257276	+	0.445616i
$208$	6.40312			0.443977
$209$	−5.70156	+	9.87540i	−0.394385	+	0.683095i
$210$	−1.50000	−	2.59808i	−0.103510	−	0.179284i
$211$	25.2094			1.73548			0.867742	−	0.497014i	$-0.165570\pi$
$211$	25.2094			1.73548			0.867742	+	0.497014i	$0.165570\pi$
$212$	3.40312			0.233728
$213$	−1.85078	−	3.20565i	−0.126813	−	0.219647i
$214$	9.40312			0.642784
$215$	1.35078	−	2.33962i	0.0921225	−	0.159561i
$216$	−1.00000			−0.0680414
$217$	7.05234	−	12.2150i	0.478744	−	0.829209i
$218$	−8.05234	+	13.9471i	−0.545373	+	0.944615i
$219$	−2.64922	+	4.58858i	−0.179018	+	0.310068i
$220$	−1.00000	−	1.73205i	−0.0674200	−	0.116775i
$221$	−12.8062			−0.861441
$222$	−3.55234	−	4.93770i	−0.238418	−	0.331397i
$223$	7.50781			0.502760			0.251380	−	0.967888i	$-0.419116\pi$
$223$	7.50781			0.502760			0.251380	+	0.967888i	$0.419116\pi$
$224$	−1.50000	−	2.59808i	−0.100223	−	0.173591i
$225$	−0.500000	+	0.866025i	−0.0333333	+	0.0577350i
$226$	−6.85078	+	11.8659i	−0.455707	+	0.789308i
$227$	−7.25391	+	12.5641i	−0.481459	+	0.833911i	−0.999774	−	0.0212790i	$-0.993226\pi$
$227$	−7.25391	+	12.5641i	−0.481459	+	0.833911i	0.518315	+	0.855190i	$0.326559\pi$
$228$	5.70156			0.377595
$229$	13.7539	−	23.8225i	0.908884	−	1.57423i	0.0932661	−	0.995641i	$-0.470269\pi$
$229$	13.7539	−	23.8225i	0.908884	−	1.57423i	0.815618	−	0.578591i	$-0.196397\pi$
$230$	7.40312			0.488148
$231$	3.00000	+	5.19615i	0.197386	+	0.341882i
$232$	1.70156			0.111713
$233$	−14.5078			−0.950438			−0.475219	−	0.879867i	$-0.657631\pi$
$233$	−14.5078			−0.950438			−0.475219	+	0.879867i	$0.657631\pi$
$234$	3.20156	+	5.54527i	0.209293	+	0.362506i
$235$	4.00000	−	6.92820i	0.260931	−	0.451946i
$236$	2.00000			0.130189
$237$	4.05234	+	7.01886i	0.263228	+	0.455924i
$238$	3.00000	+	5.19615i	0.194461	+	0.336817i
$239$	−4.55234	−	7.88489i	−0.294467	−	0.510031i	0.680394	−	0.732846i	$-0.261809\pi$
$239$	−4.55234	−	7.88489i	−0.294467	−	0.510031i	−0.974861	+	0.222815i	$0.928475\pi$
$240$	−0.500000	+	0.866025i	−0.0322749	+	0.0559017i
$241$	2.05234	−	3.55476i	0.132203	−	0.228982i	−0.792322	−	0.610103i	$-0.791128\pi$
$241$	2.05234	−	3.55476i	0.132203	−	0.228982i	0.924526	+	0.381120i	$0.124462\pi$
$242$	−3.50000	−	6.06218i	−0.224989	−	0.389692i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	4.70156	+	8.14334i	0.300987	+	0.521324i
$245$	2.00000			0.127775
$246$	5.70156	−	9.87540i	0.363518	−	0.629632i
$247$	−18.2539	−	31.6167i	−1.16147	−	2.01172i
$248$	−4.70156			−0.298549
$249$	−7.70156			−0.488067
$250$	0.500000	+	0.866025i	0.0316228	+	0.0547723i
$251$	20.8062			1.31328			0.656639	−	0.754205i	$-0.271977\pi$
$251$	20.8062			1.31328			0.656639	+	0.754205i	$0.271977\pi$
$252$	1.50000	−	2.59808i	0.0944911	−	0.163663i
$253$	−14.8062			−0.930861
$254$	−6.50000	+	11.2583i	−0.407846	+	0.706410i
$255$	1.00000	−	1.73205i	0.0626224	−	0.108465i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	12.8508	+	22.2582i	0.801610	+	1.38843i	0.918556	+	0.395291i	$0.129356\pi$
$257$	12.8508	+	22.2582i	0.801610	+	1.38843i	−0.116946	+	0.993138i	$0.537311\pi$
$258$	2.70156			0.168192
$259$	18.1570	−	1.82271i	1.12822	−	0.113258i
$260$	6.40312			0.397105
$261$	0.850781	+	1.47360i	0.0526620	+	0.0912133i
$262$	−2.70156	+	4.67924i	−0.166903	+	0.289085i
$263$	−1.00000	+	1.73205i	−0.0616626	+	0.106803i	−0.895209	−	0.445647i	$-0.852974\pi$
$263$	−1.00000	+	1.73205i	−0.0616626	+	0.106803i	0.833546	+	0.552450i	$0.186307\pi$
$264$	1.00000	−	1.73205i	0.0615457	−	0.106600i
$265$	3.40312			0.209052
$266$	−8.55234	+	14.8131i	−0.524378	+	0.908249i
$267$	−1.40312			−0.0858698
$268$	5.35078	+	9.26782i	0.326851	+	0.566122i
$269$	−22.2984			−1.35956			−0.679780	−	0.733416i	$-0.737925\pi$
$269$	−22.2984			−1.35956			−0.679780	+	0.733416i	$0.737925\pi$
$270$	−1.00000			−0.0608581
$271$	13.1570	+	22.7886i	0.799233	+	1.38431i	0.920116	+	0.391645i	$0.128094\pi$
$271$	13.1570	+	22.7886i	0.799233	+	1.38431i	−0.120884	+	0.992667i	$0.538573\pi$
$272$	1.00000	−	1.73205i	0.0606339	−	0.105021i
$273$	−19.2094			−1.16260
$274$	−4.55234	−	7.88489i	−0.275017	−	0.476344i
$275$	−1.00000	−	1.73205i	−0.0603023	−	0.104447i
$276$	3.70156	+	6.41129i	0.222808	+	0.385915i
$277$	−2.44766	+	4.23947i	−0.147065	+	0.254725i	−0.930142	−	0.367201i	$-0.880316\pi$
$277$	−2.44766	+	4.23947i	−0.147065	+	0.254725i	0.783076	+	0.621926i	$0.213649\pi$
$278$	−9.75391	+	16.8943i	−0.585000	+	1.01325i
$279$	−2.35078	−	4.07167i	−0.140738	−	0.243765i
$280$	−1.50000	−	2.59808i	−0.0896421	−	0.155265i
$281$	−4.10469	−	7.10953i	−0.244865	−	0.424119i	0.717229	−	0.696838i	$-0.245410\pi$
$281$	−4.10469	−	7.10953i	−0.244865	−	0.424119i	−0.962094	+	0.272719i	$0.912077\pi$
$282$	8.00000			0.476393
$283$	−8.75391	+	15.1622i	−0.520366	+	0.901300i	0.479354	+	0.877622i	$0.340871\pi$
$283$	−8.75391	+	15.1622i	−0.520366	+	0.901300i	−0.999720	+	0.0236781i	$0.992462\pi$
$284$	−1.85078	−	3.20565i	−0.109824	−	0.190220i
$285$	5.70156			0.337731
$286$	−12.8062			−0.757249
$287$	17.1047	+	29.6262i	1.00966	+	1.74878i
$288$	−1.00000			−0.0589256
$289$	6.50000	−	11.2583i	0.382353	−	0.662255i
$290$	1.70156			0.0999192
$291$	7.35078	−	12.7319i	0.430910	−	0.746359i
$292$	−2.64922	+	4.58858i	−0.155034	+	0.268526i
$293$	5.70156	−	9.87540i	0.333089	−	0.576927i	−0.650027	−	0.759911i	$-0.725242\pi$
$293$	5.70156	−	9.87540i	0.333089	−	0.576927i	0.983116	+	0.182984i	$0.0585758\pi$
$294$	1.00000	+	1.73205i	0.0583212	+	0.101015i
$295$	2.00000			0.116445
$296$	−3.55234	−	4.93770i	−0.206476	−	0.286998i
$297$	2.00000			0.116052
$298$	6.55234	+	11.3490i	0.379567	+	0.657429i
$299$	23.7016	−	41.0523i	1.37070	−	2.37412i
$300$	−0.500000	+	0.866025i	−0.0288675	+	0.0500000i
$301$	−4.05234	+	7.01886i	−0.233573	+	0.404561i
$302$	13.2984			0.765239
$303$	4.40312	−	7.62643i	0.252953	−	0.438127i
$304$	5.70156			0.327007
$305$	4.70156	+	8.14334i	0.269211	+	0.466287i
$306$	2.00000			0.114332
$307$	−9.89531			−0.564755			−0.282378	−	0.959303i	$-0.591123\pi$
$307$	−9.89531			−0.564755			−0.282378	+	0.959303i	$0.591123\pi$
$308$	3.00000	+	5.19615i	0.170941	+	0.296078i
$309$	2.55234	−	4.42079i	0.145198	−	0.251490i
$310$	−4.70156			−0.267031
$311$	−10.0000	−	17.3205i	−0.567048	−	0.982156i	−0.996856	−	0.0792356i	$-0.974752\pi$
$311$	−10.0000	−	17.3205i	−0.567048	−	0.982156i	0.429808	−	0.902920i	$-0.358581\pi$
$312$	3.20156	+	5.54527i	0.181253	+	0.313939i
$313$	−3.05234	−	5.28681i	−0.172529	−	0.298828i	0.766775	−	0.641916i	$-0.221860\pi$
$313$	−3.05234	−	5.28681i	−0.172529	−	0.298828i	−0.939303	+	0.343088i	$0.888527\pi$
$314$	0.201562	−	0.349116i	0.0113748	−	0.0197017i
$315$	1.50000	−	2.59808i	0.0845154	−	0.146385i
$316$	4.05234	+	7.01886i	0.227962	+	0.394842i
$317$	−1.59688	−	2.76587i	−0.0896895	−	0.155347i	0.817690	−	0.575658i	$-0.195254\pi$
$317$	−1.59688	−	2.76587i	−0.0896895	−	0.155347i	−0.907380	+	0.420312i	$0.861921\pi$
$318$	1.70156	+	2.94719i	0.0954189	+	0.165270i
$319$	−3.40312			−0.190538
$320$	−0.500000	+	0.866025i	−0.0279508	+	0.0484123i
$321$	4.70156	+	8.14334i	0.262416	+	0.454517i
$322$	−22.2094			−1.23768
$323$	−11.4031			−0.634487
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	6.40312			0.355181
$326$	−3.40312	+	5.89438i	−0.188482	+	0.326460i
$327$	−16.1047			−0.890591
$328$	5.70156	−	9.87540i	0.314816	−	0.545277i
$329$	−12.0000	+	20.7846i	−0.661581	+	1.14589i
$330$	1.00000	−	1.73205i	0.0550482	−	0.0953463i
$331$	2.90312	+	5.02836i	0.159570	+	0.276384i	0.934714	−	0.355402i	$-0.115656\pi$
$331$	2.90312	+	5.02836i	0.159570	+	0.276384i	−0.775144	+	0.631785i	$0.782323\pi$
$332$	−7.70156			−0.422678
$333$	2.50000	−	5.54527i	0.136999	−	0.303879i
$334$	−15.4031			−0.842821
$335$	5.35078	+	9.26782i	0.292344	+	0.506355i
$336$	1.50000	−	2.59808i	0.0818317	−	0.141737i
$337$	12.7539	−	22.0904i	0.694749	−	1.20334i	−0.275516	−	0.961297i	$-0.588849\pi$
$337$	12.7539	−	22.0904i	0.694749	−	1.20334i	0.970265	−	0.242045i	$-0.0778181\pi$
$338$	14.0000	−	24.2487i	0.761500	−	1.31896i
$339$	−13.7016			−0.744167
$340$	1.00000	−	1.73205i	0.0542326	−	0.0939336i
$341$	9.40312			0.509208
$342$	2.85078	+	4.93770i	0.154153	+	0.267000i
$343$	15.0000			0.809924
$344$	2.70156			0.145658
$345$	3.70156	+	6.41129i	0.199285	+	0.345172i
$346$	−2.00000	+	3.46410i	−0.107521	+	0.186231i
$347$	9.70156			0.520807			0.260404	−	0.965500i	$-0.416144\pi$
$347$	9.70156			0.520807			0.260404	+	0.965500i	$0.416144\pi$
$348$	0.850781	+	1.47360i	0.0456067	+	0.0789930i
$349$	2.70156	+	4.67924i	0.144611	+	0.250474i	0.929228	−	0.369507i	$-0.120473\pi$
$349$	2.70156	+	4.67924i	0.144611	+	0.250474i	−0.784617	+	0.619981i	$0.787140\pi$
$350$	−1.50000	−	2.59808i	−0.0801784	−	0.138873i
$351$	−3.20156	+	5.54527i	−0.170887	+	0.295985i
$352$	1.00000	−	1.73205i	0.0533002	−	0.0923186i
$353$	3.14922	+	5.45461i	0.167616	+	0.290319i	0.937581	−	0.347766i	$-0.113060\pi$
$353$	3.14922	+	5.45461i	0.167616	+	0.290319i	−0.769965	+	0.638086i	$0.779726\pi$
$354$	1.00000	+	1.73205i	0.0531494	+	0.0920575i
$355$	−1.85078	−	3.20565i	−0.0982293	−	0.170138i
$356$	−1.40312			−0.0743654
$357$	−3.00000	+	5.19615i	−0.158777	+	0.275010i
$358$	10.1047	+	17.5018i	0.534049	+	0.925000i
$359$	3.70156			0.195361			0.0976805	−	0.995218i	$-0.468858\pi$
$359$	3.70156			0.195361			0.0976805	+	0.995218i	$0.468858\pi$
$360$	−1.00000			−0.0527046
$361$	−6.75391	−	11.6981i	−0.355469	−	0.615690i
$362$	12.1047			0.636208
$363$	3.50000	−	6.06218i	0.183702	−	0.318182i
$364$	−19.2094			−1.00684
$365$	−2.64922	+	4.58858i	−0.138666	+	0.240177i
$366$	−4.70156	+	8.14334i	−0.245755	+	0.425659i
$367$	4.50000	−	7.79423i	0.234898	−	0.406855i	−0.724345	−	0.689438i	$-0.757858\pi$
$367$	4.50000	−	7.79423i	0.234898	−	0.406855i	0.959243	+	0.282582i	$0.0911910\pi$
$368$	3.70156	+	6.41129i	0.192957	+	0.334212i
$369$	11.4031			0.593623
$370$	−3.55234	−	4.93770i	−0.184678	−	0.256699i
$371$	−10.2094			−0.530044
$372$	−2.35078	−	4.07167i	−0.121882	−	0.211106i
$373$	−14.2016	+	24.5978i	−0.735329	+	1.27363i	0.219250	+	0.975669i	$0.429639\pi$
$373$	−14.2016	+	24.5978i	−0.735329	+	1.27363i	−0.954579	+	0.297958i	$0.903694\pi$
$374$	−2.00000	+	3.46410i	−0.103418	+	0.179124i
$375$	−0.500000	+	0.866025i	−0.0258199	+	0.0447214i
$376$	8.00000			0.412568
$377$	5.44766	−	9.43562i	0.280569	−	0.485959i
$378$	3.00000			0.154303
$379$	−12.8508	−	22.2582i	−0.660100	−	1.14333i	−0.980589	−	0.196075i	$-0.937180\pi$
$379$	−12.8508	−	22.2582i	−0.660100	−	1.14333i	0.320489	−	0.947252i	$-0.396153\pi$
$380$	5.70156			0.292484
$381$	−13.0000			−0.666010
$382$	4.70156	+	8.14334i	0.240553	+	0.416650i
$383$	15.1047	−	26.1621i	0.771813	−	1.33682i	−0.164755	−	0.986335i	$-0.552683\pi$
$383$	15.1047	−	26.1621i	0.771813	−	1.33682i	0.936568	−	0.350485i	$-0.113983\pi$
$384$	−1.00000			−0.0510310
$385$	3.00000	+	5.19615i	0.152894	+	0.264820i
$386$	−8.05234	−	13.9471i	−0.409853	−	0.709887i
$387$	1.35078	+	2.33962i	0.0686641	+	0.118930i
$388$	7.35078	−	12.7319i	0.373179	−	0.646366i
$389$	−11.1492	+	19.3110i	−0.565288	+	0.979107i	0.431735	+	0.902000i	$0.357902\pi$
$389$	−11.1492	+	19.3110i	−0.565288	+	0.979107i	−0.997023	+	0.0771068i	$0.975432\pi$
$390$	3.20156	+	5.54527i	0.162117	+	0.280796i
$391$	−7.40312	−	12.8226i	−0.374392	−	0.648466i
$392$	1.00000	+	1.73205i	0.0505076	+	0.0874818i
$393$	−5.40312			−0.272552
$394$	8.40312	−	14.5546i	0.423343	−	0.733252i
$395$	4.05234	+	7.01886i	0.203896	+	0.353157i
$396$	2.00000			0.100504
$397$	−5.29844			−0.265921			−0.132960	−	0.991121i	$-0.542448\pi$
$397$	−5.29844			−0.265921			−0.132960	+	0.991121i	$0.542448\pi$
$398$	11.0523	+	19.1432i	0.554004	+	0.959563i
$399$	−17.1047			−0.856305
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$	−18.0000			−0.898877			−0.449439	−	0.893311i	$-0.648376\pi$
$401$	−18.0000			−0.898877			−0.449439	+	0.893311i	$0.648376\pi$
$402$	−5.35078	+	9.26782i	−0.266873	+	0.462237i
$403$	−15.0523	+	26.0714i	−0.749811	+	1.29871i
$404$	4.40312	−	7.62643i	0.219064	−	0.379429i
$405$	−0.500000	−	0.866025i	−0.0248452	−	0.0430331i
$406$	−5.10469			−0.253341
$407$	7.10469	+	9.87540i	0.352166	+	0.489505i
$408$	2.00000			0.0990148
$409$	17.2016	+	29.7940i	0.850563	+	1.47322i	0.880701	+	0.473672i	$0.157072\pi$
$409$	17.2016	+	29.7940i	0.850563	+	1.47322i	−0.0301390	+	0.999546i	$0.509595\pi$
$410$	5.70156	−	9.87540i	0.281580	−	0.487711i
$411$	4.55234	−	7.88489i	0.224551	−	0.388933i
$412$	2.55234	−	4.42079i	0.125745	−	0.217797i
$413$	−6.00000			−0.295241
$414$	−3.70156	+	6.41129i	−0.181922	+	0.315098i
$415$	−7.70156			−0.378055
$416$	3.20156	+	5.54527i	0.156969	+	0.271879i
$417$	−19.5078			−0.955302
$418$	−11.4031			−0.557745
$419$	−10.1047	−	17.5018i	−0.493646	−	0.855020i	0.506327	−	0.862342i	$-0.331003\pi$
$419$	−10.1047	−	17.5018i	−0.493646	−	0.855020i	−0.999973	+	0.00732123i	$0.997670\pi$
$420$	1.50000	−	2.59808i	0.0731925	−	0.126773i
$421$	25.4031			1.23807			0.619036	−	0.785362i	$-0.287523\pi$
$421$	25.4031			1.23807			0.619036	+	0.785362i	$0.287523\pi$
$422$	12.6047	+	21.8320i	0.613587	+	1.06276i
$423$	4.00000	+	6.92820i	0.194487	+	0.336861i
$424$	1.70156	+	2.94719i	0.0826352	+	0.143128i
$425$	1.00000	−	1.73205i	0.0485071	−	0.0840168i
$426$	1.85078	−	3.20565i	0.0896706	−	0.155314i
$427$	−14.1047	−	24.4300i	−0.682574	−	1.18225i
$428$	4.70156	+	8.14334i	0.227259	+	0.393623i
$429$	−6.40312	−	11.0905i	−0.309146	−	0.535456i
$430$	2.70156			0.130281
$431$	−9.44766	+	16.3638i	−0.455078	+	0.788218i	−0.998693	−	0.0511171i	$-0.983722\pi$
$431$	−9.44766	+	16.3638i	−0.455078	+	0.788218i	0.543615	+	0.839335i	$0.317055\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	6.59688			0.317026			0.158513	−	0.987357i	$-0.449330\pi$
$433$	6.59688			0.317026			0.158513	+	0.987357i	$0.449330\pi$
$434$	14.1047			0.677047
$435$	0.850781	+	1.47360i	0.0407918	+	0.0706535i
$436$	−16.1047			−0.771275
$437$	21.1047	−	36.5544i	1.00957	−	1.74863i
$438$	−5.29844			−0.253169
$439$	−11.0523	+	19.1432i	−0.527500	+	0.913656i	0.471987	+	0.881606i	$0.343537\pi$
$439$	−11.0523	+	19.1432i	−0.527500	+	0.913656i	−0.999486	+	0.0320504i	$0.989796\pi$
$440$	1.00000	−	1.73205i	0.0476731	−	0.0825723i
$441$	−1.00000	+	1.73205i	−0.0476190	+	0.0824786i
$442$	−6.40312	−	11.0905i	−0.304566	−	0.527523i
$443$	14.5078			0.689287			0.344643	−	0.938734i	$-0.388000\pi$
$443$	14.5078			0.689287			0.344643	+	0.938734i	$0.388000\pi$
$444$	2.50000	−	5.54527i	0.118645	−	0.263167i
$445$	−1.40312			−0.0665145
$446$	3.75391	+	6.50195i	0.177753	+	0.307876i
$447$	−6.55234	+	11.3490i	−0.309915	+	0.536789i
$448$	1.50000	−	2.59808i	0.0708683	−	0.122748i
$449$	8.00000	−	13.8564i	0.377543	−	0.653924i	−0.613161	−	0.789958i	$-0.710102\pi$
$449$	8.00000	−	13.8564i	0.377543	−	0.653924i	0.990704	+	0.136034i	$0.0434356\pi$
$450$	−1.00000			−0.0471405
$451$	−11.4031	+	19.7508i	−0.536952	+	0.930028i
$452$	−13.7016			−0.644467
$453$	6.64922	+	11.5168i	0.312408	+	0.541106i
$454$	−14.5078			−0.680885
$455$	−19.2094			−0.900549
$456$	2.85078	+	4.93770i	0.133500	+	0.231229i
$457$	15.8062	−	27.3772i	0.739385	−	1.28065i	−0.213387	−	0.976968i	$-0.568450\pi$
$457$	15.8062	−	27.3772i	0.739385	−	1.28065i	0.952773	−	0.303685i	$-0.0982170\pi$
$458$	27.5078			1.28536
$459$	1.00000	+	1.73205i	0.0466760	+	0.0808452i
$460$	3.70156	+	6.41129i	0.172586	+	0.298928i
$461$	0.149219	+	0.258455i	0.00694982	+	0.0120374i	0.869479	−	0.493969i	$-0.164454\pi$
$461$	0.149219	+	0.258455i	0.00694982	+	0.0120374i	−0.862530	+	0.506007i	$0.831121\pi$
$462$	−3.00000	+	5.19615i	−0.139573	+	0.241747i
$463$	−3.79844	+	6.57909i	−0.176528	+	0.305756i	−0.940689	−	0.339270i	$-0.889820\pi$
$463$	−3.79844	+	6.57909i	−0.176528	+	0.305756i	0.764161	+	0.645026i	$0.223153\pi$
$464$	0.850781	+	1.47360i	0.0394965	+	0.0684100i
$465$	−2.35078	−	4.07167i	−0.109015	−	0.188819i
$466$	−7.25391	−	12.5641i	−0.336031	−	0.582022i
$467$	21.9109			1.01392			0.506959	−	0.861970i	$-0.330770\pi$
$467$	21.9109			1.01392			0.506959	+	0.861970i	$0.330770\pi$
$468$	−3.20156	+	5.54527i	−0.147992	+	0.256330i
$469$	−16.0523	−	27.8035i	−0.741228	−	1.28385i
$470$	8.00000			0.369012
$471$	0.403124			0.0185750
$472$	1.00000	+	1.73205i	0.0460287	+	0.0797241i
$473$	−5.40312			−0.248436
$474$	−4.05234	+	7.01886i	−0.186130	+	0.322387i
$475$	5.70156			0.261606
$476$	−3.00000	+	5.19615i	−0.137505	+	0.238165i
$477$	−1.70156	+	2.94719i	−0.0779092	+	0.134943i
$478$	4.55234	−	7.88489i	0.208219	−	0.360646i
$479$	−9.40312	−	16.2867i	−0.429640	−	0.744158i	0.567201	−	0.823579i	$-0.308026\pi$
$479$	−9.40312	−	16.2867i	−0.429640	−	0.744158i	−0.996841	+	0.0794213i	$0.974693\pi$
$480$	−1.00000			−0.0456435
$481$	−38.7539	+	3.89035i	−1.76703	+	0.177385i
$482$	4.10469			0.186963
$483$	−11.1047	−	19.2339i	−0.505281	−	0.875172i
$484$	3.50000	−	6.06218i	0.159091	−	0.275554i
$485$	7.35078	−	12.7319i	0.333782	−	0.578127i
$486$	0.500000	−	0.866025i	0.0226805	−	0.0392837i
$487$	−31.3141			−1.41898			−0.709488	−	0.704718i	$-0.751074\pi$
$487$	−31.3141			−1.41898			−0.709488	+	0.704718i	$0.751074\pi$
$488$	−4.70156	+	8.14334i	−0.212830	+	0.368632i
$489$	−6.80625			−0.307789
$490$	1.00000	+	1.73205i	0.0451754	+	0.0782461i
$491$	−20.5969			−0.929524			−0.464762	−	0.885436i	$-0.653860\pi$
$491$	−20.5969			−0.929524			−0.464762	+	0.885436i	$0.653860\pi$
$492$	11.4031			0.514093
$493$	−1.70156	−	2.94719i	−0.0766345	−	0.132735i
$494$	18.2539	−	31.6167i	0.821282	−	1.42250i
$495$	2.00000			0.0898933
$496$	−2.35078	−	4.07167i	−0.105553	−	0.182823i
$497$	5.55234	+	9.61694i	0.249057	+	0.431379i
$498$	−3.85078	−	6.66975i	−0.172558	−	0.298879i
$499$	−8.55234	+	14.8131i	−0.382855	+	0.663125i	−0.991469	−	0.130342i	$-0.958393\pi$
$499$	−8.55234	+	14.8131i	−0.382855	+	0.663125i	0.608614	+	0.793467i	$0.291726\pi$
$500$	−0.500000	+	0.866025i	−0.0223607	+	0.0387298i
$501$	−7.70156	−	13.3395i	−0.344080	−	0.595965i
$502$	10.4031	+	18.0187i	0.464314	+	0.804216i
$503$	−17.8062	−	30.8413i	−0.793941	−	1.37515i	−0.923509	−	0.383576i	$-0.874692\pi$
$503$	−17.8062	−	30.8413i	−0.793941	−	1.37515i	0.129568	−	0.991571i	$-0.458641\pi$
$504$	3.00000			0.133631
$505$	4.40312	−	7.62643i	0.195936	−	0.339372i
$506$	−7.40312	−	12.8226i	−0.329109	−	0.570034i
$507$	28.0000			1.24352
$508$	−13.0000			−0.576782
$509$	3.44766	+	5.97152i	0.152815	+	0.264683i	0.932261	−	0.361786i	$-0.117833\pi$
$509$	3.44766	+	5.97152i	0.152815	+	0.264683i	−0.779446	+	0.626469i	$0.784500\pi$
$510$	2.00000			0.0885615
$511$	7.94766	−	13.7657i	0.351584	−	0.608961i
$512$	−1.00000			−0.0441942
$513$	−2.85078	+	4.93770i	−0.125865	+	0.218005i
$514$	−12.8508	+	22.2582i	−0.566824	+	0.981767i
$515$	2.55234	−	4.42079i	0.112470	−	0.194803i
$516$	1.35078	+	2.33962i	0.0594648	+	0.102996i
$517$	−16.0000			−0.703679
$518$	10.6570	+	14.8131i	0.468243	+	0.650850i
$519$	−4.00000			−0.175581
$520$	3.20156	+	5.54527i	0.140398	+	0.243176i
$521$	10.7016	−	18.5356i	0.468844	−	0.812062i	−0.530522	−	0.847671i	$-0.678004\pi$
$521$	10.7016	−	18.5356i	0.468844	−	0.812062i	0.999366	+	0.0356097i	$0.0113373\pi$
$522$	−0.850781	+	1.47360i	−0.0372377	+	0.0644975i
$523$	5.64922	−	9.78473i	0.247023	−	0.427857i	−0.715675	−	0.698433i	$-0.753881\pi$
$523$	5.64922	−	9.78473i	0.247023	−	0.427857i	0.962698	+	0.270577i	$0.0872143\pi$
$524$	−5.40312			−0.236037
$525$	1.50000	−	2.59808i	0.0654654	−	0.113389i
$526$	−2.00000			−0.0872041
$527$	4.70156	+	8.14334i	0.204803	+	0.354730i
$528$	2.00000			0.0870388
$529$	31.8062			1.38288
$530$	1.70156	+	2.94719i	0.0739111	+	0.128018i
$531$	−1.00000	+	1.73205i	−0.0433963	+	0.0751646i
$532$	−17.1047			−0.741582
$533$	−36.5078	−	63.2334i	−1.58133	−	2.73894i
$534$	−0.701562	−	1.21514i	−0.0303596	−	0.0525843i
$535$	4.70156	+	8.14334i	0.203266	+	0.352067i
$536$	−5.35078	+	9.26782i	−0.231119	+	0.400309i
$537$	−10.1047	+	17.5018i	−0.436049	+	0.755260i
$538$	−11.1492	−	19.3110i	−0.480677	−	0.832557i
$539$	−2.00000	−	3.46410i	−0.0861461	−	0.149209i
$540$	−0.500000	−	0.866025i	−0.0215166	−	0.0372678i
$541$	−11.5078			−0.494759			−0.247380	−	0.968919i	$-0.579570\pi$
$541$	−11.5078			−0.494759			−0.247380	+	0.968919i	$0.579570\pi$
$542$	−13.1570	+	22.7886i	−0.565143	+	0.978856i
$543$	6.05234	+	10.4830i	0.259731	+	0.449867i
$544$	2.00000			0.0857493
$545$	−16.1047			−0.689849
$546$	−9.60469	−	16.6358i	−0.411043	−	0.711947i
$547$	6.10469			0.261018			0.130509	−	0.991447i	$-0.458339\pi$
$547$	6.10469			0.261018			0.130509	+	0.991447i	$0.458339\pi$
$548$	4.55234	−	7.88489i	0.194466	−	0.336826i
$549$	−9.40312			−0.401316
$550$	1.00000	−	1.73205i	0.0426401	−	0.0738549i
$551$	4.85078	−	8.40180i	0.206650	−	0.357929i
$552$	−3.70156	+	6.41129i	−0.157549	+	0.272883i
$553$	−12.1570	−	21.0566i	−0.516969	−	0.895417i
$554$	−4.89531			−0.207982
$555$	2.50000	−	5.54527i	0.106119	−	0.235384i
$556$	−19.5078			−0.827315
$557$	13.8062	+	23.9131i	0.584990	+	1.01323i	0.994877	+	0.101095i	$0.0322347\pi$
$557$	13.8062	+	23.9131i	0.584990	+	1.01323i	−0.409887	+	0.912136i	$0.634432\pi$
$558$	2.35078	−	4.07167i	0.0995165	−	0.172368i
$559$	8.64922	−	14.9809i	0.365823	−	0.633624i
$560$	1.50000	−	2.59808i	0.0633866	−	0.109789i
$561$	−4.00000			−0.168880
$562$	4.10469	−	7.10953i	0.173146	−	0.299897i
$563$	5.10469			0.215137			0.107568	−	0.994198i	$-0.465694\pi$
$563$	5.10469			0.215137			0.107568	+	0.994198i	$0.465694\pi$
$564$	4.00000	+	6.92820i	0.168430	+	0.291730i
$565$	−13.7016			−0.576429
$566$	−17.5078			−0.735908
$567$	1.50000	+	2.59808i	0.0629941	+	0.109109i
$568$	1.85078	−	3.20565i	0.0776570	−	0.134506i
$569$	−8.80625			−0.369177			−0.184589	−	0.982816i	$-0.559095\pi$
$569$	−8.80625			−0.369177			−0.184589	+	0.982816i	$0.559095\pi$
$570$	2.85078	+	4.93770i	0.119406	+	0.206817i
$571$	15.7984	+	27.3637i	0.661144	+	1.14514i	0.980315	+	0.197438i	$0.0632621\pi$
$571$	15.7984	+	27.3637i	0.661144	+	1.14514i	−0.319171	+	0.947697i	$0.603405\pi$
$572$	−6.40312	−	11.0905i	−0.267728	−	0.463719i
$573$	−4.70156	+	8.14334i	−0.196411	+	0.340193i
$574$	−17.1047	+	29.6262i	−0.713936	+	1.23657i
$575$	3.70156	+	6.41129i	0.154366	+	0.267369i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	16.1047	+	27.8941i	0.670447	+	1.16125i	0.977778	+	0.209645i	$0.0672309\pi$
$577$	16.1047	+	27.8941i	0.670447	+	1.16125i	−0.307331	+	0.951603i	$0.599436\pi$
$578$	13.0000			0.540729
$579$	8.05234	−	13.9471i	0.334644	−	0.579620i
$580$	0.850781	+	1.47360i	0.0353268	+	0.0611877i
$581$	23.1047			0.958544
$582$	14.7016			0.609399
$583$	−3.40312	−	5.89438i	−0.140943	−	0.244120i
$584$	−5.29844			−0.219251
$585$	−3.20156	+	5.54527i	−0.132368	+	0.229269i
$586$	11.4031			0.471059
$587$	−6.95547	+	12.0472i	−0.287083	+	0.497242i	−0.973112	−	0.230332i	$-0.926019\pi$
$587$	−6.95547	+	12.0472i	−0.287083	+	0.497242i	0.686029	+	0.727574i	$0.259352\pi$
$588$	−1.00000	+	1.73205i	−0.0412393	+	0.0714286i
$589$	−13.4031	+	23.2149i	−0.552266	+	0.956553i
$590$	1.00000	+	1.73205i	0.0411693	+	0.0713074i
$591$	16.8062			0.691317
$592$	2.50000	−	5.54527i	0.102749	−	0.227909i
$593$	−39.4031			−1.61809			−0.809046	−	0.587745i	$-0.800016\pi$
$593$	−39.4031			−1.61809			−0.809046	+	0.587745i	$0.800016\pi$
$594$	1.00000	+	1.73205i	0.0410305	+	0.0710669i
$595$	−3.00000	+	5.19615i	−0.122988	+	0.213021i
$596$	−6.55234	+	11.3490i	−0.268394	+	0.464873i
$597$	−11.0523	+	19.1432i	−0.452342	+	0.783480i
$598$	47.4031			1.93846
$599$	0.552343	−	0.956686i	0.0225681	−	0.0390891i	−0.854521	−	0.519417i	$-0.826149\pi$
$599$	0.552343	−	0.956686i	0.0225681	−	0.0390891i	0.877089	+	0.480328i	$0.159482\pi$
$600$	−1.00000			−0.0408248
$601$	21.5602	+	37.3433i	0.879457	+	1.52326i	0.851938	+	0.523643i	$0.175427\pi$
$601$	21.5602	+	37.3433i	0.879457	+	1.52326i	0.0275192	+	0.999621i	$0.491239\pi$
$602$	−8.10469			−0.330322
$603$	−10.7016			−0.435801
$604$	6.64922	+	11.5168i	0.270553	+	0.468611i
$605$	3.50000	−	6.06218i	0.142295	−	0.246463i
$606$	8.80625			0.357729
$607$	3.74609	+	6.48843i	0.152049	+	0.263357i	0.931981	−	0.362508i	$-0.118079\pi$
$607$	3.74609	+	6.48843i	0.152049	+	0.263357i	−0.779931	+	0.625865i	$0.784746\pi$
$608$	2.85078	+	4.93770i	0.115614	+	0.200250i
$609$	−2.55234	−	4.42079i	−0.103426	−	0.179139i
$610$	−4.70156	+	8.14334i	−0.190361	+	0.329714i
$611$	25.6125	−	44.3621i	1.03617	−	1.79470i
$612$	1.00000	+	1.73205i	0.0404226	+	0.0700140i
$613$	−6.74609	−	11.6846i	−0.272472	−	0.471936i	0.697022	−	0.717050i	$-0.254508\pi$
$613$	−6.74609	−	11.6846i	−0.272472	−	0.471936i	−0.969494	+	0.245114i	$0.921175\pi$
$614$	−4.94766	−	8.56959i	−0.199671	−	0.345841i
$615$	11.4031			0.459818
$616$	−3.00000	+	5.19615i	−0.120873	+	0.209359i
$617$	−7.65703	−	13.2624i	−0.308260	−	0.533923i	0.669722	−	0.742612i	$-0.266413\pi$
$617$	−7.65703	−	13.2624i	−0.308260	−	0.533923i	−0.977982	+	0.208690i	$0.933080\pi$
$618$	5.10469			0.205341
$619$	14.3141			0.575331			0.287665	−	0.957731i	$-0.407121\pi$
$619$	14.3141			0.575331			0.287665	+	0.957731i	$0.407121\pi$
$620$	−2.35078	−	4.07167i	−0.0944096	−	0.163522i
$621$	−7.40312			−0.297077
$622$	10.0000	−	17.3205i	0.400963	−	0.694489i
$623$	4.20937			0.168645
$624$	−3.20156	+	5.54527i	−0.128165	+	0.221988i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	3.05234	−	5.28681i	0.121996	−	0.211304i
$627$	−5.70156	−	9.87540i	−0.227698	−	0.394385i
$628$	0.403124			0.0160864
$629$	−5.00000	+	11.0905i	−0.199363	+	0.442209i
$630$	3.00000			0.119523
$631$	−15.4555	−	26.7697i	−0.615272	−	1.06568i	−0.990337	−	0.138684i	$-0.955713\pi$
$631$	−15.4555	−	26.7697i	−0.615272	−	1.06568i	0.375064	−	0.926999i	$-0.377621\pi$
$632$	−4.05234	+	7.01886i	−0.161194	+	0.279195i
$633$	−12.6047	+	21.8320i	−0.500991	+	0.867742i
$634$	1.59688	−	2.76587i	0.0634200	−	0.109847i
$635$	−13.0000			−0.515889
$636$	−1.70156	+	2.94719i	−0.0674713	+	0.116864i
$637$	12.8062			0.507402
$638$	−1.70156	−	2.94719i	−0.0673655	−	0.116680i
$639$	3.70156			0.146432
$640$	−1.00000			−0.0395285
$641$	20.0000	+	34.6410i	0.789953	+	1.36824i	0.925995	+	0.377535i	$0.123228\pi$
$641$	20.0000	+	34.6410i	0.789953	+	1.36824i	−0.136043	+	0.990703i	$0.543438\pi$
$642$	−4.70156	+	8.14334i	−0.185556	+	0.321392i
$643$	17.8953			0.705722			0.352861	−	0.935676i	$-0.385209\pi$
$643$	17.8953			0.705722			0.352861	+	0.935676i	$0.385209\pi$
$644$	−11.1047	−	19.2339i	−0.437586	−	0.757921i
$645$	1.35078	+	2.33962i	0.0531870	+	0.0921225i
$646$	−5.70156	−	9.87540i	−0.224325	−	0.388542i
$647$	12.4031	−	21.4828i	0.487617	−	0.844578i	−0.512281	−	0.858818i	$-0.671200\pi$
$647$	12.4031	−	21.4828i	0.487617	−	0.844578i	0.999899	+	0.0142400i	$0.00453288\pi$
$648$	0.500000	−	0.866025i	0.0196419	−	0.0340207i
$649$	−2.00000	−	3.46410i	−0.0785069	−	0.135978i
$650$	3.20156	+	5.54527i	0.125576	+	0.217503i
$651$	7.05234	+	12.2150i	0.276403	+	0.478744i
$652$	−6.80625			−0.266553
$653$	−17.0000	+	29.4449i	−0.665261	+	1.15227i	0.313953	+	0.949439i	$0.398347\pi$
$653$	−17.0000	+	29.4449i	−0.665261	+	1.15227i	−0.979214	+	0.202828i	$0.934987\pi$
$654$	−8.05234	−	13.9471i	−0.314872	−	0.545373i
$655$	−5.40312			−0.211118
$656$	11.4031			0.445217
$657$	−2.64922	−	4.58858i	−0.103356	−	0.179018i
$658$	−24.0000			−0.935617
$659$	−9.59688	+	16.6223i	−0.373841	+	0.647512i	−0.990153	−	0.139990i	$-0.955293\pi$
$659$	−9.59688	+	16.6223i	−0.373841	+	0.647512i	0.616312	+	0.787502i	$0.288626\pi$
$660$	2.00000			0.0778499
$661$	15.3508	−	26.5883i	0.597076	−	1.03417i	−0.396174	−	0.918175i	$-0.629662\pi$
$661$	15.3508	−	26.5883i	0.597076	−	1.03417i	0.993250	−	0.115991i	$-0.0370043\pi$
$662$	−2.90312	+	5.02836i	−0.112833	+	0.195433i
$663$	6.40312	−	11.0905i	0.248677	−	0.430721i
$664$	−3.85078	−	6.66975i	−0.149439	−	0.258836i
$665$	−17.1047			−0.663291
$666$	6.05234	−	0.607571i	0.234524	−	0.0235429i
$667$	12.5969			0.487753
$668$	−7.70156	−	13.3395i	−0.297982	−	0.516121i
$669$	−3.75391	+	6.50195i	−0.145134	+	0.251380i
$670$	−5.35078	+	9.26782i	−0.206719	+	0.358047i
$671$	9.40312	−	16.2867i	0.363004	−	0.628741i
$672$	3.00000			0.115728
$673$	0.193752	−	0.335587i	0.00746857	−	0.0129359i	−0.862267	−	0.506454i	$-0.830956\pi$
$673$	0.193752	−	0.335587i	0.00746857	−	0.0129359i	0.869736	+	0.493518i	$0.164289\pi$
$674$	25.5078			0.982524
$675$	−0.500000	−	0.866025i	−0.0192450	−	0.0333333i
$676$	28.0000			1.07692
$677$	−22.5969			−0.868468			−0.434234	−	0.900800i	$-0.642981\pi$
$677$	−22.5969			−0.868468			−0.434234	+	0.900800i	$0.642981\pi$
$678$	−6.85078	−	11.8659i	−0.263103	−	0.455707i
$679$	−22.0523	+	38.1958i	−0.846291	+	1.46582i
$680$	2.00000			0.0766965
$681$	−7.25391	−	12.5641i	−0.277970	−	0.481459i
$682$	4.70156	+	8.14334i	0.180032	+	0.311825i
$683$	20.0000	+	34.6410i	0.765279	+	1.32550i	0.940099	+	0.340901i	$0.110732\pi$
$683$	20.0000	+	34.6410i	0.765279	+	1.32550i	−0.174820	+	0.984600i	$0.555934\pi$
$684$	−2.85078	+	4.93770i	−0.109002	+	0.188798i
$685$	4.55234	−	7.88489i	0.173936	−	0.301266i
$686$	7.50000	+	12.9904i	0.286351	+	0.495975i
$687$	13.7539	+	23.8225i	0.524744	+	0.908884i
$688$	1.35078	+	2.33962i	0.0514980	+	0.0891972i
$689$	21.7906			0.830157
$690$	−3.70156	+	6.41129i	−0.140916	+	0.244074i
$691$	0.201562	+	0.349116i	0.00766778	+	0.0132810i	0.869834	−	0.493345i	$-0.164226\pi$
$691$	0.201562	+	0.349116i	0.00766778	+	0.0132810i	−0.862166	+	0.506626i	$0.830893\pi$
$692$	−4.00000			−0.152057
$693$	−6.00000			−0.227921
$694$	4.85078	+	8.40180i	0.184133	+	0.318928i
$695$	−19.5078			−0.739973
$696$	−0.850781	+	1.47360i	−0.0322488	+	0.0558565i
$697$	−22.8062			−0.863848
$698$	−2.70156	+	4.67924i	−0.102256	+	0.177112i
$699$	7.25391	−	12.5641i	0.274368	−	0.475219i
$700$	1.50000	−	2.59808i	0.0566947	−	0.0981981i
$701$	−19.8062	−	34.3054i	−0.748072	−	1.29570i	−0.948746	−	0.316040i	$-0.897647\pi$
$701$	−19.8062	−	34.3054i	−0.748072	−	1.29570i	0.200674	−	0.979658i	$-0.435687\pi$
$702$	−6.40312			−0.241670
$703$	−34.5078	+	3.46410i	−1.30149	+	0.130651i
$704$	2.00000			0.0753778
$705$	4.00000	+	6.92820i	0.150649	+	0.260931i
$706$	−3.14922	+	5.45461i	−0.118522	+	0.205287i
$707$	−13.2094	+	22.8793i	−0.496790	+	0.860465i
$708$	−1.00000	+	1.73205i	−0.0375823	+	0.0650945i
$709$	9.50781			0.357073			0.178537	−	0.983933i	$-0.442864\pi$
$709$	9.50781			0.357073			0.178537	+	0.983933i	$0.442864\pi$
$710$	1.85078	−	3.20565i	0.0694586	−	0.120306i
$711$	−8.10469			−0.303949
$712$	−0.701562	−	1.21514i	−0.0262922	−	0.0455393i
$713$	−34.8062			−1.30350
$714$	−6.00000			−0.224544
$715$	−6.40312	−	11.0905i	−0.239463	−	0.414763i
$716$	−10.1047	+	17.5018i	−0.377630	+	0.654074i
$717$	9.10469			0.340021
$718$	1.85078	+	3.20565i	0.0690705	+	0.119634i
$719$	−16.5523	−	28.6695i	−0.617298	−	1.06919i	−0.989977	−	0.141231i	$-0.954894\pi$
$719$	−16.5523	−	28.6695i	−0.617298	−	1.06919i	0.372678	−	0.927961i	$-0.378439\pi$
$720$	−0.500000	−	0.866025i	−0.0186339	−	0.0322749i
$721$	−7.65703	+	13.2624i	−0.285163	+	0.493916i
$722$	6.75391	−	11.6981i	0.251354	−	0.435358i
$723$	2.05234	+	3.55476i	0.0763275	+	0.132203i
$724$	6.05234	+	10.4830i	0.224934	+	0.389596i
$725$	0.850781	+	1.47360i	0.0315972	+	0.0547280i
$726$	7.00000			0.259794
$727$	−12.6047	+	21.8320i	−0.467482	+	0.809702i	−0.999310	−	0.0371501i	$-0.988172\pi$
$727$	−12.6047	+	21.8320i	−0.467482	+	0.809702i	0.531828	+	0.846853i	$0.321505\pi$
$728$	−9.60469	−	16.6358i	−0.355973	−	0.616564i
$729$	1.00000			0.0370370
$730$	−5.29844			−0.196104
$731$	−2.70156	−	4.67924i	−0.0999209	−	0.173068i
$732$	−9.40312			−0.347549
$733$	3.94766	−	6.83754i	0.145810	−	0.252550i	−0.783865	−	0.620931i	$-0.786755\pi$
$733$	3.94766	−	6.83754i	0.145810	−	0.252550i	0.929675	+	0.368381i	$0.120088\pi$
$734$	9.00000			0.332196
$735$	−1.00000	+	1.73205i	−0.0368856	+	0.0638877i
$736$	−3.70156	+	6.41129i	−0.136441	+	0.236323i
$737$	10.7016	−	18.5356i	0.394197	−	0.682769i
$738$	5.70156	+	9.87540i	0.209877	+	0.363518i
$739$	−37.7016			−1.38687			−0.693437	−	0.720517i	$-0.743905\pi$
$739$	−37.7016			−1.38687			−0.693437	+	0.720517i	$0.743905\pi$
$740$	2.50000	−	5.54527i	0.0919018	−	0.203848i
$741$	36.5078			1.34115
$742$	−5.10469	−	8.84158i	−0.187399	−	0.324584i
$743$	10.1047	−	17.5018i	0.370705	−	0.642080i	−0.618969	−	0.785415i	$-0.712449\pi$
$743$	10.1047	−	17.5018i	0.370705	−	0.642080i	0.989674	+	0.143335i	$0.0457828\pi$
$744$	2.35078	−	4.07167i	0.0861838	−	0.149275i
$745$	−6.55234	+	11.3490i	−0.240059	+	0.415795i
$746$	−28.4031			−1.03991
$747$	3.85078	−	6.66975i	0.140893	−	0.244033i
$748$	−4.00000			−0.146254
$749$	−14.1047	−	24.4300i	−0.515374	−	0.892654i
$750$	−1.00000			−0.0365148
$751$	−38.3141			−1.39810			−0.699050	−	0.715073i	$-0.746393\pi$
$751$	−38.3141			−1.39810			−0.699050	+	0.715073i	$0.746393\pi$
$752$	4.00000	+	6.92820i	0.145865	+	0.252646i
$753$	−10.4031	+	18.0187i	−0.379111	+	0.656639i
$754$	10.8953			0.396784
$755$	6.64922	+	11.5168i	0.241990	+	0.419139i
$756$	1.50000	+	2.59808i	0.0545545	+	0.0944911i
$757$	−8.90312	−	15.4207i	−0.323590	−	0.560474i	0.657636	−	0.753336i	$-0.271556\pi$
$757$	−8.90312	−	15.4207i	−0.323590	−	0.560474i	−0.981226	+	0.192862i	$0.938223\pi$
$758$	12.8508	−	22.2582i	0.466761	−	0.808454i
$759$	7.40312	−	12.8226i	0.268716	−	0.465430i
$760$	2.85078	+	4.93770i	0.103409	+	0.179109i
$761$	−16.4031	−	28.4110i	−0.594613	−	1.02990i	−0.993601	−	0.112944i	$-0.963972\pi$
$761$	−16.4031	−	28.4110i	−0.594613	−	1.02990i	0.398989	−	0.916956i	$-0.369361\pi$
$762$	−6.50000	−	11.2583i	−0.235470	−	0.407846i
$763$	48.3141			1.74909
$764$	−4.70156	+	8.14334i	−0.170097	+	0.294616i
$765$	1.00000	+	1.73205i	0.0361551	+	0.0626224i
$766$	30.2094			1.09151
$767$	12.8062			0.462407
$768$	−0.500000	−	0.866025i	−0.0180422	−	0.0312500i
$769$	25.8062			0.930597			0.465299	−	0.885154i	$-0.345947\pi$
$769$	25.8062			0.930597			0.465299	+	0.885154i	$0.345947\pi$
$770$	−3.00000	+	5.19615i	−0.108112	+	0.187256i
$771$	−25.7016			−0.925619
$772$	8.05234	−	13.9471i	0.289810	−	0.501966i
$773$	−2.59688	+	4.49792i	−0.0934031	+	0.161779i	−0.908941	−	0.416925i	$-0.863108\pi$
$773$	−2.59688	+	4.49792i	−0.0934031	+	0.161779i	0.815538	+	0.578704i	$0.196441\pi$
$774$	−1.35078	+	2.33962i	−0.0485528	+	0.0840960i
$775$	−2.35078	−	4.07167i	−0.0844425	−	0.146259i
$776$	14.7016			0.527755
$777$	−7.50000	+	16.6358i	−0.269061	+	0.596806i
$778$	−22.2984			−0.799438
$779$	−32.5078	−	56.3052i	−1.16471	−	2.01734i
$780$	−3.20156	+	5.54527i	−0.114634	+	0.198552i
$781$	−3.70156	+	6.41129i	−0.132452	+	0.229414i
$782$	7.40312	−	12.8226i	0.264735	−	0.458535i
$783$	−1.70156			−0.0608089
$784$	−1.00000	+	1.73205i	−0.0357143	+	0.0618590i
$785$	0.403124			0.0143881
$786$	−2.70156	−	4.67924i	−0.0963615	−	0.166903i
$787$	−37.5078			−1.33701			−0.668505	−	0.743708i	$-0.733065\pi$
$787$	−37.5078			−1.33701			−0.668505	+	0.743708i	$0.733065\pi$
$788$	16.8062			0.598698
$789$	−1.00000	−	1.73205i	−0.0356009	−	0.0616626i
$790$	−4.05234	+	7.01886i	−0.144176	+	0.249720i
$791$	41.1047			1.46151
$792$	1.00000	+	1.73205i	0.0355335	+	0.0615457i
$793$	30.1047	+	52.1428i	1.06905	+	1.85165i
$794$	−2.64922	−	4.58858i	−0.0940173	−	0.162843i
$795$	−1.70156	+	2.94719i	−0.0603482	+	0.104526i
$796$	−11.0523	+	19.1432i	−0.391740	+	0.678513i
$797$	9.00000	+	15.5885i	0.318796	+	0.552171i	0.980237	−	0.197826i	$-0.0633881\pi$
$797$	9.00000	+	15.5885i	0.318796	+	0.552171i	−0.661441	+	0.749997i	$0.730055\pi$
$798$	−8.55234	−	14.8131i	−0.302750	−	0.524378i
$799$	−8.00000	−	13.8564i	−0.283020	−	0.490204i
$800$	−1.00000			−0.0353553
$801$	0.701562	−	1.21514i	0.0247885	−	0.0429349i
$802$	−9.00000	−	15.5885i	−0.317801	−	0.550448i
$803$	10.5969			0.373956
$804$	−10.7016			−0.377415
$805$	−11.1047	−	19.2339i	−0.391389	−	0.677905i
$806$	−30.1047			−1.06039
$807$	11.1492	−	19.3110i	0.392471	−	0.679780i
$808$	8.80625			0.309803
$809$	2.59688	−	4.49792i	0.0913013	−	0.158138i	−0.816758	−	0.576981i	$-0.804231\pi$
$809$	2.59688	−	4.49792i	0.0913013	−	0.158138i	0.908059	+	0.418842i	$0.137564\pi$
$810$	0.500000	−	0.866025i	0.0175682	−	0.0304290i
$811$	2.00000	−	3.46410i	0.0702295	−	0.121641i	−0.828772	−	0.559586i	$-0.810960\pi$
$811$	2.00000	−	3.46410i	0.0702295	−	0.121641i	0.899002	+	0.437945i	$0.144294\pi$
$812$	−2.55234	−	4.42079i	−0.0895697	−	0.155139i
$813$	−26.3141			−0.922874
$814$	−5.00000	+	11.0905i	−0.175250	+	0.388723i
$815$	−6.80625			−0.238412
$816$	1.00000	+	1.73205i	0.0350070	+	0.0606339i
$817$	7.70156	−	13.3395i	0.269444	−	0.466690i
$818$	−17.2016	+	29.7940i	−0.601439	+	1.04172i
$819$	9.60469	−	16.6358i	0.335615	−	0.581302i
$820$	11.4031			0.398214
$821$	−15.2539	+	26.4205i	−0.532365	+	0.922083i	0.466921	+	0.884299i	$0.345363\pi$
$821$	−15.2539	+	26.4205i	−0.532365	+	0.922083i	−0.999286	+	0.0377841i	$0.987970\pi$
$822$	9.10469			0.317562
$823$	−10.3062	−	17.8509i	−0.359253	−	0.622245i	0.628583	−	0.777742i	$-0.283635\pi$
$823$	−10.3062	−	17.8509i	−0.359253	−	0.622245i	−0.987836	+	0.155498i	$0.950302\pi$
$824$	5.10469			0.177830
$825$	2.00000			0.0696311
$826$	−3.00000	−	5.19615i	−0.104383	−	0.180797i
$827$	−4.74609	+	8.22048i	−0.165038	+	0.285854i	−0.936669	−	0.350217i	$-0.886108\pi$
$827$	−4.74609	+	8.22048i	−0.165038	+	0.285854i	0.771631	+	0.636071i	$0.219441\pi$
$828$	−7.40312			−0.257276
$829$	27.7539	+	48.0712i	0.963933	+	1.66958i	0.712455	+	0.701718i	$0.247583\pi$
$829$	27.7539	+	48.0712i	0.963933	+	1.66958i	0.251478	+	0.967863i	$0.419083\pi$
$830$	−3.85078	−	6.66975i	−0.133663	−	0.231510i
$831$	−2.44766	−	4.23947i	−0.0849083	−	0.147065i
$832$	−3.20156	+	5.54527i	−0.110994	+	0.192248i
$833$	2.00000	−	3.46410i	0.0692959	−	0.120024i
$834$	−9.75391	−	16.8943i	−0.337750	−	0.585000i
$835$	−7.70156	−	13.3395i	−0.266524	−	0.461632i
$836$	−5.70156	−	9.87540i	−0.197193	−	0.341548i
$837$	4.70156			0.162510
$838$	10.1047	−	17.5018i	0.349061	−	0.604591i
$839$	28.2094	+	48.8601i	0.973896	+	1.68684i	0.683532	+	0.729920i	$0.260443\pi$
$839$	28.2094	+	48.8601i	0.973896	+	1.68684i	0.290364	+	0.956916i	$0.406224\pi$
$840$	3.00000			0.103510
$841$	−26.1047			−0.900162
$842$	12.7016	+	21.9998i	0.437725	+	0.758161i
$843$	8.20937			0.282746
$844$	−12.6047	+	21.8320i	−0.433871	+	0.751487i
$845$	28.0000			0.963229
$846$	−4.00000	+	6.92820i	−0.137523	+	0.238197i
$847$	−10.5000	+	18.1865i	−0.360784	+	0.624897i
$848$	−1.70156	+	2.94719i	−0.0584319	+	0.101207i
$849$	−8.75391	−	15.1622i	−0.300433	−	0.520366i
$850$	2.00000			0.0685994
$851$	−26.2984	−	36.5544i	−0.901499	−	1.25307i
$852$	3.70156			0.126813
$853$	−16.4031	−	28.4110i	−0.561632	−	0.972776i	−0.997354	−	0.0726943i	$-0.976840\pi$
$853$	−16.4031	−	28.4110i	−0.561632	−	0.972776i	0.435722	−	0.900081i	$-0.356493\pi$
$854$	14.1047	−	24.4300i	0.482652	−	0.835979i
$855$	−2.85078	+	4.93770i	−0.0974947	+	0.168866i
$856$	−4.70156	+	8.14334i	−0.160696	+	0.278334i
$857$	31.7016			1.08290			0.541452	−	0.840731i	$-0.317875\pi$
$857$	31.7016			1.08290			0.541452	+	0.840731i	$0.317875\pi$
$858$	6.40312	−	11.0905i	0.218599	−	0.378625i
$859$	−5.20937			−0.177742			−0.0888708	−	0.996043i	$-0.528326\pi$
$859$	−5.20937			−0.177742			−0.0888708	+	0.996043i	$0.528326\pi$
$860$	1.35078	+	2.33962i	0.0460613	+	0.0797804i
$861$	−34.2094			−1.16585
$862$	−18.8953			−0.643577
$863$	16.1047	+	27.8941i	0.548210	+	0.949527i	0.998397	+	0.0565933i	$0.0180238\pi$
$863$	16.1047	+	27.8941i	0.548210	+	0.949527i	−0.450187	+	0.892934i	$0.648643\pi$
$864$	0.500000	−	0.866025i	0.0170103	−	0.0294628i
$865$	−4.00000			−0.136004
$866$	3.29844	+	5.71306i	0.112085	+	0.194138i
$867$	6.50000	+	11.2583i	0.220752	+	0.382353i
$868$	7.05234	+	12.2150i	0.239372	+	0.414605i
$869$	8.10469	−	14.0377i	0.274933	−	0.476197i
$870$	−0.850781	+	1.47360i	−0.0288442	+	0.0499596i
$871$	34.2617	+	59.3430i	1.16091	+	2.01076i
$872$	−8.05234	−	13.9471i	−0.272687	−	0.472307i
$873$	7.35078	+	12.7319i	0.248786	+	0.430910i
$874$	42.2094			1.42775
$875$	1.50000	−	2.59808i	0.0507093	−	0.0878310i
$876$	−2.64922	−	4.58858i	−0.0895088	−	0.155034i
$877$	34.0156			1.14863			0.574313	−	0.818636i	$-0.305269\pi$
$877$	34.0156			1.14863			0.574313	+	0.818636i	$0.305269\pi$
$878$	−22.1047			−0.745997
$879$	5.70156	+	9.87540i	0.192309	+	0.333089i
$880$	2.00000			0.0674200
$881$	−7.80625	+	13.5208i	−0.262999	+	0.455528i	−0.967037	−	0.254634i	$-0.918045\pi$
$881$	−7.80625	+	13.5208i	−0.262999	+	0.455528i	0.704038	+	0.710162i	$0.251378\pi$
$882$	−2.00000			−0.0673435
$883$	−16.2094	+	28.0755i	−0.545489	+	0.944814i	0.453087	+	0.891466i	$0.350323\pi$
$883$	−16.2094	+	28.0755i	−0.545489	+	0.944814i	−0.998576	+	0.0533481i	$0.983011\pi$
$884$	6.40312	−	11.0905i	0.215360	−	0.373015i
$885$	−1.00000	+	1.73205i	−0.0336146	+	0.0582223i
$886$	7.25391	+	12.5641i	0.243700	+	0.422100i
$887$	43.0156			1.44432			0.722162	−	0.691724i	$-0.243149\pi$
$887$	43.0156			1.44432			0.722162	+	0.691724i	$0.243149\pi$
$888$	6.05234	−	0.607571i	0.203103	−	0.0203887i
$889$	39.0000			1.30802
$890$	−0.701562	−	1.21514i	−0.0235164	−	0.0407316i
$891$	−1.00000	+	1.73205i	−0.0335013	+	0.0580259i
$892$	−3.75391	+	6.50195i	−0.125690	+	0.217702i
$893$	22.8062	−	39.5016i	0.763182	−	1.32187i
$894$	−13.1047			−0.438286
$895$	−10.1047	+	17.5018i	−0.337762	+	0.585022i
$896$	3.00000			0.100223
$897$	23.7016	+	41.0523i	0.791372	+	1.37070i
$898$	16.0000			0.533927
$899$	−8.00000			−0.266815
$900$	−0.500000	−	0.866025i	−0.0166667	−	0.0288675i
$901$	3.40312	−	5.89438i	0.113375	−	0.196370i
$902$	−22.8062			−0.759365
$903$	−4.05234	−	7.01886i	−0.134854	−	0.233573i
$904$	−6.85078	−	11.8659i	−0.227854	−	0.394654i
$905$	6.05234	+	10.4830i	0.201187	+	0.348466i
$906$	−6.64922	+	11.5168i	−0.220906	+	0.382620i
$907$	−7.85859	+	13.6115i	−0.260940	+	0.451962i	−0.966492	−	0.256697i	$-0.917366\pi$
$907$	−7.85859	+	13.6115i	−0.260940	+	0.451962i	0.705552	+	0.708658i	$0.250699\pi$
$908$	−7.25391	−	12.5641i	−0.240729	−	0.416955i
$909$	4.40312	+	7.62643i	0.146042	+	0.252953i
$910$	−9.60469	−	16.6358i	−0.318392	−	0.551472i
$911$	28.1203			0.931667			0.465834	−	0.884872i	$-0.345755\pi$
$911$	28.1203			0.931667			0.465834	+	0.884872i	$0.345755\pi$
$912$	−2.85078	+	4.93770i	−0.0943988	+	0.163504i
$913$	7.70156	+	13.3395i	0.254885	+	0.441473i
$914$	31.6125			1.04565
$915$	−9.40312			−0.310858
$916$	13.7539	+	23.8225i	0.454442	+	0.787116i
$917$	16.2094			0.535281
$918$	−1.00000	+	1.73205i	−0.0330049	+	0.0571662i
$919$	9.89531			0.326416			0.163208	−	0.986592i	$-0.447816\pi$
$919$	9.89531			0.326416			0.163208	+	0.986592i	$0.447816\pi$
$920$	−3.70156	+	6.41129i	−0.122037	+	0.211374i
$921$	4.94766	−	8.56959i	0.163031	−	0.282378i
$922$	−0.149219	+	0.258455i	−0.00491426	+	0.00851176i
$923$	−11.8508	−	20.5262i	−0.390073	−	0.675627i
$924$	−6.00000			−0.197386
$925$	2.50000	−	5.54527i	0.0821995	−	0.182327i
$926$	−7.59688			−0.249649
$927$	2.55234	+	4.42079i	0.0838299	+	0.145198i
$928$	−0.850781	+	1.47360i	−0.0279283	+	0.0483732i
$929$	−25.1047	+	43.4826i	−0.823658	+	1.42662i	0.0792825	+	0.996852i	$0.474737\pi$
$929$	−25.1047	+	43.4826i	−0.823658	+	1.42662i	−0.902941	+	0.429765i	$0.858596\pi$
$930$	2.35078	−	4.07167i	0.0770851	−	0.133515i
$931$	11.4031			0.373722
$932$	7.25391	−	12.5641i	0.237610	−	0.411552i
$933$	20.0000			0.654771
$934$	10.9555	+	18.9754i	0.358474	+	0.620895i
$935$	−4.00000			−0.130814
$936$	−6.40312			−0.209293
$937$	−8.45547	−	14.6453i	−0.276228	−	0.478441i	0.694216	−	0.719767i	$-0.255751\pi$
$937$	−8.45547	−	14.6453i	−0.276228	−	0.478441i	−0.970444	+	0.241326i	$0.922418\pi$
$938$	16.0523	−	27.8035i	0.524128	−	0.907816i
$939$	6.10469			0.199219
$940$	4.00000	+	6.92820i	0.130466	+	0.225973i
$941$	19.0602	+	33.0132i	0.621343	+	1.07620i	0.989236	+	0.146330i	$0.0467461\pi$
$941$	19.0602	+	33.0132i	0.621343	+	1.07620i	−0.367893	+	0.929868i	$0.619921\pi$
$942$	0.201562	+	0.349116i	0.00656725	+	0.0113748i
$943$	42.2094	−	73.1088i	1.37453	−	2.38075i
$944$	−1.00000	+	1.73205i	−0.0325472	+	0.0563735i
$945$	1.50000	+	2.59808i	0.0487950	+	0.0845154i
$946$	−2.70156	−	4.67924i	−0.0878354	−	0.152135i
$947$	0.657030	+	1.13801i	0.0213506	+	0.0369803i	0.876503	−	0.481396i	$-0.159870\pi$
$947$	0.657030	+	1.13801i	0.0213506	+	0.0369803i	−0.855153	+	0.518376i	$0.826537\pi$
$948$	−8.10469			−0.263228
$949$	−16.9633	+	29.3813i	−0.550651	+	0.953756i
$950$	2.85078	+	4.93770i	0.0924916	+	0.160200i
$951$	3.19375			0.103564
$952$	−6.00000			−0.194461
$953$	18.5523	+	32.1336i	0.600969	+	1.04091i	0.992675	+	0.120819i	$0.0385520\pi$
$953$	18.5523	+	32.1336i	0.600969	+	1.04091i	−0.391705	+	0.920091i	$0.628115\pi$
$954$	−3.40312			−0.110180
$955$	−4.70156	+	8.14334i	−0.152139	+	0.263512i
$956$	9.10469			0.294467
$957$	1.70156	−	2.94719i	0.0550037	−	0.0952692i
$958$	9.40312	−	16.2867i	0.303801	−	0.526199i
$959$	−13.6570	+	23.6547i	−0.441008	+	0.763849i
$960$	−0.500000	−	0.866025i	−0.0161374	−	0.0279508i
$961$	−8.89531			−0.286946
$962$	−22.7461	−	31.6167i	−0.733364	−	1.01936i
$963$	−9.40312			−0.303011
$964$	2.05234	+	3.55476i	0.0661015	+	0.114491i
$965$	8.05234	−	13.9471i	0.259214	−	0.448972i
$966$	11.1047	−	19.2339i	0.357287	−	0.618840i
$967$	−12.2016	+	21.1337i	−0.392376	+	0.679615i	−0.992762	−	0.120095i	$-0.961680\pi$
$967$	−12.2016	+	21.1337i	−0.392376	+	0.679615i	0.600387	+	0.799710i	$0.295013\pi$
$968$	7.00000			0.224989
$969$	5.70156	−	9.87540i	0.183161	−	0.317243i
$970$	14.7016			0.472039
$971$	−29.4031	−	50.9277i	−0.943591	−	1.63435i	−0.758548	−	0.651617i	$-0.774091\pi$
$971$	−29.4031	−	50.9277i	−0.943591	−	1.63435i	−0.185043	−	0.982730i	$-0.559243\pi$
$972$	1.00000			0.0320750
$973$	58.5234			1.87618
$974$	−15.6570	−	27.1188i	−0.501684	−	0.868941i
$975$	−3.20156	+	5.54527i	−0.102532	+	0.177591i
$976$	−9.40312			−0.300987
$977$	−20.5523	−	35.5977i	−0.657528	−	1.13887i	−0.981254	−	0.192721i	$-0.938269\pi$
$977$	−20.5523	−	35.5977i	−0.657528	−	1.13887i	0.323726	−	0.946151i	$-0.395064\pi$
$978$	−3.40312	−	5.89438i	−0.108820	−	0.188482i
$979$	1.40312	+	2.43028i	0.0448440	+	0.0776722i
$980$	−1.00000	+	1.73205i	−0.0319438	+	0.0553283i
$981$	8.05234	−	13.9471i	0.257092	−	0.445296i
$982$	−10.2984	−	17.8374i	−0.328636	−	0.569215i
$983$	−22.0000	−	38.1051i	−0.701691	−	1.21536i	−0.967872	−	0.251442i	$-0.919095\pi$
$983$	−22.0000	−	38.1051i	−0.701691	−	1.21536i	0.266181	−	0.963923i	$-0.414238\pi$
$984$	5.70156	+	9.87540i	0.181759	+	0.314816i
$985$	16.8062			0.535492
$986$	1.70156	−	2.94719i	0.0541888	−	0.0938577i
$987$	−12.0000	−	20.7846i	−0.381964	−	0.661581i
$988$	36.5078			1.16147
$989$	20.0000			0.635963
$990$	1.00000	+	1.73205i	0.0317821	+	0.0550482i
$991$	−34.2094			−1.08670			−0.543348	−	0.839507i	$-0.682844\pi$
$991$	−34.2094			−1.08670			−0.543348	+	0.839507i	$0.682844\pi$
$992$	2.35078	−	4.07167i	0.0746374	−	0.129276i
$993$	−5.80625			−0.184256
$994$	−5.55234	+	9.61694i	−0.176110	+	0.305031i
$995$	−11.0523	+	19.1432i	−0.350383	+	0.606881i
$996$	3.85078	−	6.66975i	0.122017	−	0.211339i
$997$	2.95547	+	5.11902i	0.0936006	+	0.162121i	0.909024	−	0.416744i	$-0.136829\pi$
$997$	2.95547	+	5.11902i	0.0936006	+	0.162121i	−0.815423	+	0.578865i	$0.803496\pi$
$998$	−17.1047			−0.541439
$999$	3.55234	+	4.93770i	0.112391	+	0.156222i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.i.k.211.1	yes	4
37.10	even	3	inner	1110.2.i.k.121.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.i.k.121.1	✓	4	37.10	even	3	inner
1110.2.i.k.211.1	yes	4	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.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} -1.00000 q^{6} +(1.50000 - 2.59808i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} -1.00000 q^{6} +(1.50000 - 2.59808i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} -1.00000 q^{10} +2.00000 q^{11} +(-0.500000 - 0.866025i) q^{12} +(-3.20156 + 5.54527i) q^{13} +3.00000 q^{14} +(-0.500000 - 0.866025i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.00000 + 1.73205i) q^{17} +(0.500000 - 0.866025i) q^{18} +(-2.85078 + 4.93770i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(1.50000 + 2.59808i) q^{21} +(1.00000 + 1.73205i) q^{22} -7.40312 q^{23} +(0.500000 - 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} -6.40312 q^{26} +1.00000 q^{27} +(1.50000 + 2.59808i) q^{28} -1.70156 q^{29} +(0.500000 - 0.866025i) q^{30} +4.70156 q^{31} +(0.500000 - 0.866025i) q^{32} +(-1.00000 + 1.73205i) q^{33} +(-1.00000 + 1.73205i) q^{34} +(1.50000 + 2.59808i) q^{35} +1.00000 q^{36} +(3.55234 + 4.93770i) q^{37} -5.70156 q^{38} +(-3.20156 - 5.54527i) q^{39} +(0.500000 - 0.866025i) q^{40} +(-5.70156 + 9.87540i) q^{41} +(-1.50000 + 2.59808i) q^{42} -2.70156 q^{43} +(-1.00000 + 1.73205i) q^{44} +1.00000 q^{45} +(-3.70156 - 6.41129i) q^{46} -8.00000 q^{47} +1.00000 q^{48} +(-1.00000 - 1.73205i) q^{49} +(0.500000 - 0.866025i) q^{50} -2.00000 q^{51} +(-3.20156 - 5.54527i) q^{52} +(-1.70156 - 2.94719i) q^{53} +(0.500000 + 0.866025i) q^{54} +(-1.00000 + 1.73205i) q^{55} +(-1.50000 + 2.59808i) q^{56} +(-2.85078 - 4.93770i) q^{57} +(-0.850781 - 1.47360i) q^{58} +(-1.00000 - 1.73205i) q^{59} +1.00000 q^{60} +(4.70156 - 8.14334i) q^{61} +(2.35078 + 4.07167i) q^{62} -3.00000 q^{63} +1.00000 q^{64} +(-3.20156 - 5.54527i) q^{65} -2.00000 q^{66} +(5.35078 - 9.26782i) q^{67} -2.00000 q^{68} +(3.70156 - 6.41129i) q^{69} +(-1.50000 + 2.59808i) q^{70} +(-1.85078 + 3.20565i) q^{71} +(0.500000 + 0.866025i) q^{72} +5.29844 q^{73} +(-2.50000 + 5.54527i) q^{74} +1.00000 q^{75} +(-2.85078 - 4.93770i) q^{76} +(3.00000 - 5.19615i) q^{77} +(3.20156 - 5.54527i) q^{78} +(4.05234 - 7.01886i) q^{79} +1.00000 q^{80} +(-0.500000 + 0.866025i) q^{81} -11.4031 q^{82} +(3.85078 + 6.66975i) q^{83} -3.00000 q^{84} -2.00000 q^{85} +(-1.35078 - 2.33962i) q^{86} +(0.850781 - 1.47360i) q^{87} -2.00000 q^{88} +(0.701562 + 1.21514i) q^{89} +(0.500000 + 0.866025i) q^{90} +(9.60469 + 16.6358i) q^{91} +(3.70156 - 6.41129i) q^{92} +(-2.35078 + 4.07167i) q^{93} +(-4.00000 - 6.92820i) q^{94} +(-2.85078 - 4.93770i) q^{95} +(0.500000 + 0.866025i) q^{96} -14.7016 q^{97} +(1.00000 - 1.73205i) q^{98} +(-1.00000 - 1.73205i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 2 q^{3} - 2 q^{4} - 2 q^{5} - 4 q^{6} + 6 q^{7} - 4 q^{8} - 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 - 2 * q^5 - 4 * q^6 + 6 * q^7 - 4 * q^8 - 2 * q^9	\( 4 q + 2 q^{2} - 2 q^{3} - 2 q^{4} - 2 q^{5} - 4 q^{6} + 6 q^{7} - 4 q^{8} - 2 q^{9} - 4 q^{10} + 8 q^{11} - 2 q^{12} + 12 q^{14} - 2 q^{15} - 2 q^{16} + 4 q^{17} + 2 q^{18} - 5 q^{19} - 2 q^{20} + 6 q^{21} + 4 q^{22} - 4 q^{23} + 2 q^{24} - 2 q^{25} + 4 q^{27} + 6 q^{28} + 6 q^{29} + 2 q^{30} + 6 q^{31} + 2 q^{32} - 4 q^{33} - 4 q^{34} + 6 q^{35} + 4 q^{36} - 5 q^{37} - 10 q^{38} + 2 q^{40} - 10 q^{41} - 6 q^{42} + 2 q^{43} - 4 q^{44} + 4 q^{45} - 2 q^{46} - 32 q^{47} + 4 q^{48} - 4 q^{49} + 2 q^{50} - 8 q^{51} + 6 q^{53} + 2 q^{54} - 4 q^{55} - 6 q^{56} - 5 q^{57} + 3 q^{58} - 4 q^{59} + 4 q^{60} + 6 q^{61} + 3 q^{62} - 12 q^{63} + 4 q^{64} - 8 q^{66} + 15 q^{67} - 8 q^{68} + 2 q^{69} - 6 q^{70} - q^{71} + 2 q^{72} + 34 q^{73} - 10 q^{74} + 4 q^{75} - 5 q^{76} + 12 q^{77} - 3 q^{79} + 4 q^{80} - 2 q^{81} - 20 q^{82} + 9 q^{83} - 12 q^{84} - 8 q^{85} + q^{86} - 3 q^{87} - 8 q^{88} - 10 q^{89} + 2 q^{90} + 2 q^{92} - 3 q^{93} - 16 q^{94} - 5 q^{95} + 2 q^{96} - 46 q^{97} + 4 q^{98} - 4 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 - 2 * q^5 - 4 * q^6 + 6 * q^7 - 4 * q^8 - 2 * q^9 - 4 * q^10 + 8 * q^11 - 2 * q^12 + 12 * q^14 - 2 * q^15 - 2 * q^16 + 4 * q^17 + 2 * q^18 - 5 * q^19 - 2 * q^20 + 6 * q^21 + 4 * q^22 - 4 * q^23 + 2 * q^24 - 2 * q^25 + 4 * q^27 + 6 * q^28 + 6 * q^29 + 2 * q^30 + 6 * q^31 + 2 * q^32 - 4 * q^33 - 4 * q^34 + 6 * q^35 + 4 * q^36 - 5 * q^37 - 10 * q^38 + 2 * q^40 - 10 * q^41 - 6 * q^42 + 2 * q^43 - 4 * q^44 + 4 * q^45 - 2 * q^46 - 32 * q^47 + 4 * q^48 - 4 * q^49 + 2 * q^50 - 8 * q^51 + 6 * q^53 + 2 * q^54 - 4 * q^55 - 6 * q^56 - 5 * q^57 + 3 * q^58 - 4 * q^59 + 4 * q^60 + 6 * q^61 + 3 * q^62 - 12 * q^63 + 4 * q^64 - 8 * q^66 + 15 * q^67 - 8 * q^68 + 2 * q^69 - 6 * q^70 - q^71 + 2 * q^72 + 34 * q^73 - 10 * q^74 + 4 * q^75 - 5 * q^76 + 12 * q^77 - 3 * q^79 + 4 * q^80 - 2 * q^81 - 20 * q^82 + 9 * q^83 - 12 * q^84 - 8 * q^85 + q^86 - 3 * q^87 - 8 * q^88 - 10 * q^89 + 2 * q^90 + 2 * q^92 - 3 * q^93 - 16 * q^94 - 5 * q^95 + 2 * q^96 - 46 * q^97 + 4 * q^98 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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