LMFDB - Embedded newform 414.2.e.d.139.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [414,2,Mod(139,414)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(414, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("414.139");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 414 = 2 \cdot 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	414.e (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:	$3.30580664368$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.288778218147.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 7x^{8} - 4x^{7} + 34x^{6} - 19x^{5} + 64x^{4} - x^{3} + 64x^{2} - 21x + 9 $ x^10 - x^9 + 7x^8 - 4x^7 + 34x^6 - 19x^5 + 64x^4 - x^3 + 64x^2 - 21*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			139.4
Root			$1.07065 + 1.85442i$ of defining polynomial
Character	$\chi$	$=$	414.139
Dual form			414.2.e.d.277.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.278072 - 1.70958i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.69714 + 2.93953i) q^{5} +(1.34151 - 1.09561i) q^{6} +(-1.74607 - 3.02428i) q^{7} -1.00000 q^{8} +(-2.84535 + 0.950775i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.278072 - 1.70958i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.69714 + 2.93953i) q^{5} +(1.34151 - 1.09561i) q^{6} +(-1.74607 - 3.02428i) q^{7} -1.00000 q^{8} +(-2.84535 + 0.950775i) q^{9} -3.39428 q^{10} +(-2.39735 - 4.15233i) q^{11} +(1.61958 + 0.613974i) q^{12} +(2.56373 - 4.44052i) q^{13} +(1.74607 - 3.02428i) q^{14} +(5.49731 + 2.08400i) q^{15} +(-0.500000 - 0.866025i) q^{16} -6.35504 q^{17} +(-2.24607 - 1.98876i) q^{18} +3.15998 q^{19} +(-1.69714 - 2.93953i) q^{20} +(-4.68473 + 3.82602i) q^{21} +(2.39735 - 4.15233i) q^{22} +(-0.500000 + 0.866025i) q^{23} +(0.278072 + 1.70958i) q^{24} +(-3.26058 - 5.64748i) q^{25} +5.12747 q^{26} +(2.41664 + 4.59998i) q^{27} +3.49214 q^{28} +(1.22952 + 2.12959i) q^{29} +(0.943856 + 5.80281i) q^{30} +(-0.830547 + 1.43855i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-6.43212 + 5.25312i) q^{33} +(-3.17752 - 5.50362i) q^{34} +11.8533 q^{35} +(0.599280 - 2.93953i) q^{36} -9.88582 q^{37} +(1.57999 + 2.73662i) q^{38} +(-8.30434 - 3.14813i) q^{39} +(1.69714 - 2.93953i) q^{40} +(-2.74914 + 4.76165i) q^{41} +(-5.65580 - 2.14409i) q^{42} +(0.387635 + 0.671404i) q^{43} +4.79470 q^{44} +(2.03413 - 9.97761i) q^{45} -1.00000 q^{46} +(-5.55862 - 9.62781i) q^{47} +(-1.34151 + 1.09561i) q^{48} +(-2.59753 + 4.49906i) q^{49} +(3.26058 - 5.64748i) q^{50} +(1.76716 + 10.8645i) q^{51} +(2.56373 + 4.44052i) q^{52} +6.41715 q^{53} +(-2.77538 + 4.39287i) q^{54} +16.2746 q^{55} +(1.74607 + 3.02428i) q^{56} +(-0.878701 - 5.40224i) q^{57} +(-1.22952 + 2.12959i) q^{58} +(-3.08029 + 5.33522i) q^{59} +(-4.55345 + 3.71881i) q^{60} +(-0.632287 - 1.09515i) q^{61} -1.66109 q^{62} +(7.84360 + 6.94503i) q^{63} +1.00000 q^{64} +(8.70204 + 15.0724i) q^{65} +(-7.76540 - 2.94382i) q^{66} +(-1.74607 + 3.02428i) q^{67} +(3.17752 - 5.50362i) q^{68} +(1.61958 + 0.613974i) q^{69} +(5.92666 + 10.2653i) q^{70} +16.4462 q^{71} +(2.84535 - 0.950775i) q^{72} +5.89600 q^{73} +(-4.94291 - 8.56138i) q^{74} +(-8.74817 + 7.14463i) q^{75} +(-1.57999 + 2.73662i) q^{76} +(-8.37189 + 14.5005i) q^{77} +(-1.42581 - 8.76584i) q^{78} +(-3.43033 - 5.94150i) q^{79} +3.39428 q^{80} +(7.19205 - 5.41058i) q^{81} -5.49828 q^{82} +(-3.29807 - 5.71243i) q^{83} +(-0.971068 - 5.97011i) q^{84} +(10.7854 - 18.6809i) q^{85} +(-0.387635 + 0.671404i) q^{86} +(3.29881 - 2.69414i) q^{87} +(2.39735 + 4.15233i) q^{88} +14.4886 q^{89} +(9.65793 - 3.22720i) q^{90} -17.9059 q^{91} +(-0.500000 - 0.866025i) q^{92} +(2.69027 + 1.01987i) q^{93} +(5.55862 - 9.62781i) q^{94} +(-5.36292 + 9.28886i) q^{95} +(-1.61958 - 0.613974i) q^{96} +(0.770482 + 1.33451i) q^{97} -5.19506 q^{98} +(10.7692 + 9.53551i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 5 q^{2} - 3 q^{3} - 5 q^{4} - q^{5} - 3 q^{6} + 5 q^{7} - 10 q^{8} - 3 q^{9}+O(q^{10}) $ 10 * q + 5 * q^2 - 3 * q^3 - 5 * q^4 - q^5 - 3 * q^6 + 5 * q^7 - 10 * q^8 - 3 * q^9	\( 10 q + 5 q^{2} - 3 q^{3} - 5 q^{4} - q^{5} - 3 q^{6} + 5 q^{7} - 10 q^{8} - 3 q^{9} - 2 q^{10} - 11 q^{11} + 6 q^{13} - 5 q^{14} + 9 q^{15} - 5 q^{16} + 2 q^{17} - 6 q^{19} - q^{20} - 21 q^{21} + 11 q^{22} - 5 q^{23} + 3 q^{24} + 12 q^{26} + 27 q^{27} - 10 q^{28} - 8 q^{29} + 9 q^{30} + 4 q^{31} + 5 q^{32} - 24 q^{33} + q^{34} + 46 q^{35} + 3 q^{36} - 28 q^{37} - 3 q^{38} - 45 q^{39} + q^{40} - 24 q^{41} - 27 q^{42} + 27 q^{43} + 22 q^{44} + 27 q^{45} - 10 q^{46} - 9 q^{47} + 3 q^{48} - 12 q^{49} - 6 q^{51} + 6 q^{52} - 26 q^{53} + 18 q^{54} + 16 q^{55} - 5 q^{56} - 18 q^{57} + 8 q^{58} - 9 q^{59} + 3 q^{61} + 8 q^{62} + 42 q^{63} + 10 q^{64} + 5 q^{65} - 3 q^{66} + 5 q^{67} - q^{68} + 23 q^{70} + 54 q^{71} + 3 q^{72} + 34 q^{73} - 14 q^{74} - 45 q^{75} + 3 q^{76} - 13 q^{77} - 30 q^{78} - 11 q^{79} + 2 q^{80} + 33 q^{81} - 48 q^{82} - 23 q^{83} - 6 q^{84} + 23 q^{85} - 27 q^{86} + 63 q^{87} + 11 q^{88} + 78 q^{89} + 51 q^{90} - 30 q^{91} - 5 q^{92} - 27 q^{93} + 9 q^{94} - 37 q^{95} + 28 q^{97} - 24 q^{98} + 24 q^{99}+O(q^{100}) \) 10 * q + 5 * q^2 - 3 * q^3 - 5 * q^4 - q^5 - 3 * q^6 + 5 * q^7 - 10 * q^8 - 3 * q^9 - 2 * q^10 - 11 * q^11 + 6 * q^13 - 5 * q^14 + 9 * q^15 - 5 * q^16 + 2 * q^17 - 6 * q^19 - q^20 - 21 * q^21 + 11 * q^22 - 5 * q^23 + 3 * q^24 + 12 * q^26 + 27 * q^27 - 10 * q^28 - 8 * q^29 + 9 * q^30 + 4 * q^31 + 5 * q^32 - 24 * q^33 + q^34 + 46 * q^35 + 3 * q^36 - 28 * q^37 - 3 * q^38 - 45 * q^39 + q^40 - 24 * q^41 - 27 * q^42 + 27 * q^43 + 22 * q^44 + 27 * q^45 - 10 * q^46 - 9 * q^47 + 3 * q^48 - 12 * q^49 - 6 * q^51 + 6 * q^52 - 26 * q^53 + 18 * q^54 + 16 * q^55 - 5 * q^56 - 18 * q^57 + 8 * q^58 - 9 * q^59 + 3 * q^61 + 8 * q^62 + 42 * q^63 + 10 * q^64 + 5 * q^65 - 3 * q^66 + 5 * q^67 - q^68 + 23 * q^70 + 54 * q^71 + 3 * q^72 + 34 * q^73 - 14 * q^74 - 45 * q^75 + 3 * q^76 - 13 * q^77 - 30 * q^78 - 11 * q^79 + 2 * q^80 + 33 * q^81 - 48 * q^82 - 23 * q^83 - 6 * q^84 + 23 * q^85 - 27 * q^86 + 63 * q^87 + 11 * q^88 + 78 * q^89 + 51 * q^90 - 30 * q^91 - 5 * q^92 - 27 * q^93 + 9 * q^94 - 37 * q^95 + 28 * q^97 - 24 * q^98 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/414\mathbb{Z}\right)^\times$.

$n$	$47$	$235$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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
$3$	−0.278072	−	1.70958i	−0.160545	−	0.987029i
$3$	−0.278072	−	1.70958i	−0.160545	−	0.987029i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−1.69714	+	2.93953i	−0.758985	+	1.31460i	0.184384	+	0.982854i	$0.440971\pi$
$5$	−1.69714	+	2.93953i	−0.758985	+	1.31460i	−0.943369	+	0.331746i	$0.892362\pi$
$6$	1.34151	−	1.09561i	0.547668	−	0.447281i
$7$	−1.74607	−	3.02428i	−0.659953	−	1.14307i	−0.980627	−	0.195883i	$-0.937243\pi$
$7$	−1.74607	−	3.02428i	−0.659953	−	1.14307i	0.320674	−	0.947189i	$-0.396090\pi$
$8$	−1.00000			−0.353553
$9$	−2.84535	+	0.950775i	−0.948451	+	0.316925i
$10$	−3.39428			−1.07337
$11$	−2.39735	−	4.15233i	−0.722828	−	1.25198i	−0.959862	−	0.280474i	$-0.909508\pi$
$11$	−2.39735	−	4.15233i	−0.722828	−	1.25198i	0.237033	−	0.971502i	$-0.423825\pi$
$12$	1.61958	+	0.613974i	0.467532	+	0.177239i
$13$	2.56373	−	4.44052i	0.711052	−	1.23158i	−0.253410	−	0.967359i	$-0.581552\pi$
$13$	2.56373	−	4.44052i	0.711052	−	1.23158i	0.964463	−	0.264219i	$-0.0851143\pi$
$14$	1.74607	−	3.02428i	0.466657	−	0.808274i
$15$	5.49731	+	2.08400i	1.41940	+	0.538087i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−6.35504			−1.54132			−0.770662	−	0.637245i	$-0.780074\pi$
$17$	−6.35504			−1.54132			−0.770662	+	0.637245i	$0.780074\pi$
$18$	−2.24607	−	1.98876i	−0.529404	−	0.468755i
$19$	3.15998			0.724948			0.362474	−	0.931994i	$-0.381932\pi$
$19$	3.15998			0.724948			0.362474	+	0.931994i	$0.381932\pi$
$20$	−1.69714	−	2.93953i	−0.379492	−	0.657300i
$21$	−4.68473	+	3.82602i	−1.02229	+	0.834907i
$22$	2.39735	−	4.15233i	0.511117	−	0.885280i
$23$	−0.500000	+	0.866025i	−0.104257	+	0.180579i
$23$	−0.500000	+	0.866025i	−0.104257	+	0.180579i
$24$	0.278072	+	1.70958i	0.0567613	+	0.348967i
$25$	−3.26058	−	5.64748i	−0.652115	−	1.12950i
$26$	5.12747			1.00558
$27$	2.41664	+	4.59998i	0.465083	+	0.885267i
$28$	3.49214			0.659953
$29$	1.22952	+	2.12959i	0.228316	+	0.395455i	0.957309	−	0.289066i	$-0.0933448\pi$
$29$	1.22952	+	2.12959i	0.228316	+	0.395455i	−0.728993	+	0.684521i	$0.760011\pi$
$30$	0.943856	+	5.80281i	0.172324	+	1.05944i
$31$	−0.830547	+	1.43855i	−0.149171	+	0.258371i	−0.930921	−	0.365220i	$-0.880994\pi$
$31$	−0.830547	+	1.43855i	−0.149171	+	0.258371i	0.781750	+	0.623591i	$0.214327\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−6.43212	+	5.25312i	−1.11969	+	0.914451i
$34$	−3.17752	−	5.50362i	−0.544940	−	0.943864i
$35$	11.8533			2.00358
$36$	0.599280	−	2.93953i	0.0998800	−	0.489922i
$37$	−9.88582			−1.62522			−0.812610	−	0.582808i	$-0.801954\pi$
$37$	−9.88582			−1.62522			−0.812610	+	0.582808i	$0.801954\pi$
$38$	1.57999	+	2.73662i	0.256308	+	0.443938i
$39$	−8.30434	−	3.14813i	−1.32976	−	0.504105i
$40$	1.69714	−	2.93953i	0.268342	−	0.464781i
$41$	−2.74914	+	4.76165i	−0.429344	+	0.743645i	−0.996815	−	0.0797482i	$-0.974588\pi$
$41$	−2.74914	+	4.76165i	−0.429344	+	0.743645i	0.567471	+	0.823393i	$0.307922\pi$
$42$	−5.65580	−	2.14409i	−0.872709	−	0.330840i
$43$	0.387635	+	0.671404i	0.0591138	+	0.102388i	0.894068	−	0.447932i	$-0.147839\pi$
$43$	0.387635	+	0.671404i	0.0591138	+	0.102388i	−0.834954	+	0.550320i	$0.814506\pi$
$44$	4.79470			0.722828
$45$	2.03413	−	9.97761i	0.303230	−	1.48737i
$46$	−1.00000			−0.147442
$47$	−5.55862	−	9.62781i	−0.810808	−	1.40436i	−0.912300	−	0.409524i	$-0.865695\pi$
$47$	−5.55862	−	9.62781i	−0.810808	−	1.40436i	0.101492	−	0.994836i	$-0.467638\pi$
$48$	−1.34151	+	1.09561i	−0.193630	+	0.158138i
$49$	−2.59753	+	4.49906i	−0.371076	+	0.642722i
$50$	3.26058	−	5.64748i	0.461115	−	0.798675i
$51$	1.76716	+	10.8645i	0.247452	+	1.52133i
$52$	2.56373	+	4.44052i	0.355526	+	0.615789i
$53$	6.41715			0.881464			0.440732	−	0.897639i	$-0.354719\pi$
$53$	6.41715			0.881464			0.440732	+	0.897639i	$0.354719\pi$
$54$	−2.77538	+	4.39287i	−0.377681	+	0.597793i
$55$	16.2746			2.19446
$56$	1.74607	+	3.02428i	0.233329	+	0.404137i
$57$	−0.878701	−	5.40224i	−0.116387	−	0.715544i
$58$	−1.22952	+	2.12959i	−0.161444	+	0.279629i
$59$	−3.08029	+	5.33522i	−0.401019	+	0.694586i	−0.993849	−	0.110742i	$-0.964677\pi$
$59$	−3.08029	+	5.33522i	−0.401019	+	0.694586i	0.592830	+	0.805328i	$0.298011\pi$
$60$	−4.55345	+	3.71881i	−0.587848	+	0.480096i
$61$	−0.632287	−	1.09515i	−0.0809561	−	0.140220i	0.822705	−	0.568469i	$-0.192464\pi$
$61$	−0.632287	−	1.09515i	−0.0809561	−	0.140220i	−0.903661	+	0.428249i	$0.859131\pi$
$62$	−1.66109			−0.210959
$63$	7.84360	+	6.94503i	0.988201	+	0.874992i
$64$	1.00000			0.125000
$65$	8.70204	+	15.0724i	1.07936	+	1.86950i
$66$	−7.76540	−	2.94382i	−0.955854	−	0.362360i
$67$	−1.74607	+	3.02428i	−0.213317	+	0.369475i	−0.952751	−	0.303754i	$-0.901760\pi$
$67$	−1.74607	+	3.02428i	−0.213317	+	0.369475i	0.739434	+	0.673229i	$0.235093\pi$
$68$	3.17752	−	5.50362i	0.385331	−	0.667412i
$69$	1.61958	+	0.613974i	0.194974	+	0.0739138i
$70$	5.92666	+	10.2653i	0.708371	+	1.22694i
$71$	16.4462			1.95180			0.975900	−	0.218218i	$-0.0700243\pi$
$71$	16.4462			1.95180			0.975900	+	0.218218i	$0.0700243\pi$
$72$	2.84535	−	0.950775i	0.335328	−	0.112050i
$73$	5.89600			0.690075			0.345037	−	0.938589i	$-0.387866\pi$
$73$	5.89600			0.690075			0.345037	+	0.938589i	$0.387866\pi$
$74$	−4.94291	−	8.56138i	−0.574602	−	0.995240i
$75$	−8.74817	+	7.14463i	−1.01015	+	0.824991i
$76$	−1.57999	+	2.73662i	−0.181237	+	0.313912i
$77$	−8.37189	+	14.5005i	−0.954066	+	1.65249i
$78$	−1.42581	−	8.76584i	−0.161441	−	0.992536i
$79$	−3.43033	−	5.94150i	−0.385942	−	0.668471i	0.605957	−	0.795497i	$-0.292790\pi$
$79$	−3.43033	−	5.94150i	−0.385942	−	0.668471i	−0.991899	+	0.127026i	$0.959457\pi$
$80$	3.39428			0.379492
$81$	7.19205	−	5.41058i	0.799117	−	0.601176i
$82$	−5.49828			−0.607183
$83$	−3.29807	−	5.71243i	−0.362010	−	0.627020i	0.626281	−	0.779597i	$-0.284576\pi$
$83$	−3.29807	−	5.71243i	−0.362010	−	0.627020i	−0.988292	+	0.152577i	$0.951243\pi$
$84$	−0.971068	−	5.97011i	−0.105952	−	0.651392i
$85$	10.7854	−	18.6809i	1.16984	−	2.02622i
$86$	−0.387635	+	0.671404i	−0.0417998	+	0.0723993i
$87$	3.29881	−	2.69414i	0.353670	−	0.288842i
$88$	2.39735	+	4.15233i	0.255558	+	0.442640i
$89$	14.4886			1.53579			0.767897	−	0.640574i	$-0.221303\pi$
$89$	14.4886			1.53579			0.767897	+	0.640574i	$0.221303\pi$
$90$	9.65793	−	3.22720i	1.01803	−	0.340177i
$91$	−17.9059			−1.87704
$92$	−0.500000	−	0.866025i	−0.0521286	−	0.0902894i
$93$	2.69027	+	1.01987i	0.278968	+	0.105756i
$94$	5.55862	−	9.62781i	0.573328	−	0.993032i
$95$	−5.36292	+	9.28886i	−0.550224	+	0.953017i
$96$	−1.61958	−	0.613974i	−0.165298	−	0.0626635i
$97$	0.770482	+	1.33451i	0.0782306	+	0.135499i	0.902487	−	0.430718i	$-0.141740\pi$
$97$	0.770482	+	1.33451i	0.0782306	+	0.135499i	−0.824256	+	0.566217i	$0.808406\pi$
$98$	−5.19506			−0.524781
$99$	10.7692	+	9.53551i	1.08235	+	0.958354i
$100$	6.52115			0.652115
$101$	−4.84505	−	8.39188i	−0.482101	−	0.835023i	0.517688	−	0.855569i	$-0.326793\pi$
$101$	−4.84505	−	8.39188i	−0.482101	−	0.835023i	−0.999789	+	0.0205465i	$0.993459\pi$
$102$	−8.52533	+	6.96264i	−0.844133	+	0.689404i
$103$	5.56148	−	9.63277i	0.547989	−	0.949145i	−0.450423	−	0.892815i	$-0.648727\pi$
$103$	5.56148	−	9.63277i	0.547989	−	0.949145i	0.998412	−	0.0563301i	$-0.0179399\pi$
$104$	−2.56373	+	4.44052i	−0.251395	+	0.435429i
$105$	−3.29608	−	20.2642i	−0.321664	−	1.97759i
$106$	3.20858	+	5.55742i	0.311644	+	0.539784i
$107$	−14.8829			−1.43879			−0.719393	−	0.694603i	$-0.755580\pi$
$107$	−14.8829			−1.43879			−0.719393	+	0.694603i	$0.755580\pi$
$108$	−5.19202	−	0.207117i	−0.499603	−	0.0199298i
$109$	−11.9775			−1.14724			−0.573618	−	0.819123i	$-0.694460\pi$
$109$	−11.9775			−1.14724			−0.573618	+	0.819123i	$0.694460\pi$
$110$	8.13728	+	14.0942i	0.775860	+	1.34383i
$111$	2.74897	+	16.9006i	0.260921	+	1.60414i
$112$	−1.74607	+	3.02428i	−0.164988	+	0.285768i
$113$	1.92838	−	3.34005i	0.181407	−	0.314205i	−0.760953	−	0.648807i	$-0.775268\pi$
$113$	1.92838	−	3.34005i	0.181407	−	0.314205i	0.942360	+	0.334601i	$0.108602\pi$
$114$	4.23913	−	3.46210i	0.397031	−	0.324255i
$115$	−1.69714	−	2.93953i	−0.158259	−	0.274113i
$116$	−2.45904			−0.228316
$117$	−3.07279	+	15.0724i	−0.284080	+	1.39344i
$118$	−6.16058			−0.567127
$119$	11.0964	+	19.2194i	1.01720	+	1.76184i
$120$	−5.49731	−	2.08400i	−0.501833	−	0.190242i
$121$	−5.99458	+	10.3829i	−0.544962	+	0.943902i
$122$	0.632287	−	1.09515i	0.0572446	−	0.0991506i
$123$	8.90490	+	3.37580i	0.802928	+	0.304386i
$124$	−0.830547	−	1.43855i	−0.0745854	−	0.129186i
$125$	5.16322			0.461812
$126$	−2.09277	+	10.2653i	−0.186439	+	0.914503i
$127$	−7.31645			−0.649230			−0.324615	−	0.945846i	$-0.605235\pi$
$127$	−7.31645			−0.649230			−0.324615	+	0.945846i	$0.605235\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	1.04003	−	0.849393i	0.0915696	−	0.0747849i
$130$	−8.70204	+	15.0724i	−0.763219	+	1.32193i
$131$	3.57550	−	6.19295i	0.312393	−	0.541080i	−0.666487	−	0.745517i	$-0.732203\pi$
$131$	3.57550	−	6.19295i	0.312393	−	0.541080i	0.978880	+	0.204436i	$0.0655361\pi$
$132$	−1.33327	−	8.19694i	−0.116047	−	0.713452i
$133$	−5.51754	−	9.55667i	−0.478432	−	0.828668i
$134$	−3.49214			−0.301675
$135$	−17.6232	−	0.703012i	−1.51676	−	0.0605057i
$136$	6.35504			0.544940
$137$	−3.38252	−	5.85869i	−0.288988	−	0.500542i	0.684581	−	0.728937i	$-0.259985\pi$
$137$	−3.38252	−	5.85869i	−0.288988	−	0.500542i	−0.973568	+	0.228395i	$0.926652\pi$
$138$	0.278072	+	1.70958i	0.0236711	+	0.145529i
$139$	−1.43310	+	2.48220i	−0.121554	+	0.210537i	−0.920381	−	0.391024i	$-0.872121\pi$
$139$	−1.43310	+	2.48220i	−0.121554	+	0.210537i	0.798827	+	0.601561i	$0.205454\pi$
$140$	−5.92666	+	10.2653i	−0.500894	+	0.867574i
$141$	−14.9138	+	12.1801i	−1.25597	+	1.02575i
$142$	8.22308	+	14.2428i	0.690066	+	1.19523i
$143$	−24.5847			−2.05587
$144$	2.24607	+	1.98876i	0.187173	+	0.165730i
$145$	−8.34666			−0.693153
$146$	2.94800	+	5.10609i	0.243978	+	0.422583i
$147$	8.41381	+	3.18963i	0.693960	+	0.263077i
$148$	4.94291	−	8.56138i	0.406305	−	0.703741i
$149$	−0.500601	+	0.867066i	−0.0410108	+	0.0710328i	−0.885802	−	0.464063i	$-0.846391\pi$
$149$	−0.500601	+	0.867066i	−0.0410108	+	0.0710328i	0.844791	+	0.535096i	$0.179724\pi$
$150$	−10.5615	−	4.00382i	−0.862344	−	0.326910i
$151$	1.31459	+	2.27694i	0.106980	+	0.185295i	0.914546	−	0.404483i	$-0.132549\pi$
$151$	1.31459	+	2.27694i	0.106980	+	0.185295i	−0.807565	+	0.589778i	$0.799215\pi$
$152$	−3.15998			−0.256308
$153$	18.0823	−	6.04221i	1.46187	−	0.488484i
$154$	−16.7438			−1.34925
$155$	−2.81911	−	4.88285i	−0.226437	−	0.392200i
$156$	6.87853	−	5.61770i	0.550724	−	0.449776i
$157$	9.45290	−	16.3729i	0.754423	−	1.30670i	−0.191237	−	0.981544i	$-0.561250\pi$
$157$	9.45290	−	16.3729i	0.754423	−	1.30670i	0.945660	−	0.325156i	$-0.105417\pi$
$158$	3.43033	−	5.94150i	0.272902	−	0.472681i
$159$	−1.78443	−	10.9707i	−0.141515	−	0.870030i
$160$	1.69714	+	2.93953i	0.134171	+	0.232391i
$161$	3.49214			0.275219
$162$	8.28173	+	3.52321i	0.650674	+	0.276810i
$163$	15.6754			1.22779			0.613896	−	0.789387i	$-0.289602\pi$
$163$	15.6754			1.22779			0.613896	+	0.789387i	$0.289602\pi$
$164$	−2.74914	−	4.76165i	−0.214672	−	0.371822i
$165$	−4.52551	−	27.8227i	−0.352310	−	2.16600i
$166$	3.29807	−	5.71243i	0.255980	−	0.443370i
$167$	6.30918	−	10.9278i	0.488219	−	0.845620i	−0.511689	−	0.859170i	$-0.670980\pi$
$167$	6.30918	−	10.9278i	0.488219	−	0.845620i	0.999908	+	0.0135508i	$0.00431350\pi$
$168$	4.68473	−	3.82602i	0.361435	−	0.295184i
$169$	−6.64547	−	11.5103i	−0.511190	−	0.885407i
$170$	21.5708			1.65440
$171$	−8.99124	+	3.00443i	−0.687577	+	0.229754i
$172$	−0.775270			−0.0591138
$173$	0.301440	+	0.522109i	0.0229180	+	0.0396952i	0.877257	−	0.480021i	$-0.159371\pi$
$173$	0.301440	+	0.522109i	0.0229180	+	0.0396952i	−0.854339	+	0.519716i	$0.826038\pi$
$174$	3.98260	+	1.50978i	0.301920	+	0.114456i
$175$	−11.3864	+	19.7218i	−0.860731	+	1.49083i
$176$	−2.39735	+	4.15233i	−0.180707	+	0.312994i
$177$	9.97754	+	3.78243i	0.749958	+	0.284305i
$178$	7.24432	+	12.5475i	0.542985	+	0.940477i
$179$	10.1600			0.759392			0.379696	−	0.925111i	$-0.376029\pi$
$179$	10.1600			0.759392			0.379696	+	0.925111i	$0.376029\pi$
$180$	7.62380	+	6.75041i	0.568245	+	0.503146i
$181$	−7.42165			−0.551647			−0.275824	−	0.961208i	$-0.588951\pi$
$181$	−7.42165			−0.551647			−0.275824	+	0.961208i	$0.588951\pi$
$182$	−8.95293	−	15.5069i	−0.663635	−	1.14945i
$183$	−1.69644	+	1.38548i	−0.125404	+	0.102418i
$184$	0.500000	−	0.866025i	0.0368605	−	0.0638442i
$185$	16.7776	−	29.0597i	1.23352	−	2.13651i
$186$	0.461904	+	2.83978i	0.0338685	+	0.208223i
$187$	15.2353	+	26.3882i	1.11411	+	1.92970i
$188$	11.1172			0.810808
$189$	9.69202	−	15.3405i	0.704991	−	1.11586i
$190$	−10.7258			−0.778135
$191$	−2.15681	−	3.73570i	−0.156061	−	0.270306i	0.777384	−	0.629027i	$-0.216546\pi$
$191$	−2.15681	−	3.73570i	−0.156061	−	0.270306i	−0.933445	+	0.358721i	$0.883213\pi$
$192$	−0.278072	−	1.70958i	−0.0200681	−	0.123379i
$193$	−3.86487	+	6.69416i	−0.278200	+	0.481856i	−0.970937	−	0.239334i	$-0.923071\pi$
$193$	−3.86487	+	6.69416i	−0.278200	+	0.481856i	0.692738	+	0.721190i	$0.256404\pi$
$194$	−0.770482	+	1.33451i	−0.0553174	+	0.0958125i
$195$	23.3477	−	19.0681i	1.67196	−	1.36549i
$196$	−2.59753	−	4.49906i	−0.185538	−	0.321361i
$197$	−19.4668			−1.38695			−0.693476	−	0.720480i	$-0.743922\pi$
$197$	−19.4668			−1.38695			−0.693476	+	0.720480i	$0.743922\pi$
$198$	−2.87337	+	14.0942i	−0.204201	+	1.00163i
$199$	0.661496			0.0468922			0.0234461	−	0.999725i	$-0.492536\pi$
$199$	0.661496			0.0468922			0.0234461	+	0.999725i	$0.492536\pi$
$200$	3.26058	+	5.64748i	0.230558	+	0.399337i
$201$	5.65580	+	2.14409i	0.398929	+	0.151232i
$202$	4.84505	−	8.39188i	0.340897	−	0.590450i
$203$	4.29365	−	7.43682i	0.301355	−	0.521963i
$204$	−10.2925	−	3.90183i	−0.720618	−	0.273183i
$205$	−9.33136	−	16.1624i	−0.651730	−	1.12883i
$206$	11.1230			0.774974
$207$	0.599280	−	2.93953i	0.0416529	−	0.204312i
$208$	−5.12747			−0.355526
$209$	−7.57557	−	13.1213i	−0.524013	−	0.907617i
$210$	15.9013	−	12.9866i	1.09729	−	0.896161i
$211$	−6.05925	+	10.4949i	−0.417136	+	0.722500i	−0.995650	−	0.0931719i	$-0.970299\pi$
$211$	−6.05925	+	10.4949i	−0.417136	+	0.722500i	0.578514	+	0.815672i	$0.303633\pi$
$212$	−3.20858	+	5.55742i	−0.220366	+	0.381685i
$213$	−4.57322	−	28.1161i	−0.313352	−	1.92648i
$214$	−7.44146	−	12.8890i	−0.508688	−	0.881073i
$215$	−2.63149			−0.179466
$216$	−2.41664	−	4.59998i	−0.164432	−	0.312989i
$217$	5.80078			0.393783
$218$	−5.98874	−	10.3728i	−0.405609	−	0.702535i
$219$	−1.63951	−	10.0797i	−0.110788	−	0.681124i
$220$	−8.13728	+	14.0942i	−0.548616	+	0.950230i
$221$	−16.2926	+	28.2197i	−1.09596	+	1.89826i
$222$	−13.2619	+	10.8310i	−0.890080	+	0.726929i
$223$	−9.59774	−	16.6238i	−0.642712	−	1.11321i	−0.984825	−	0.173551i	$-0.944476\pi$
$223$	−9.59774	−	16.6238i	−0.642712	−	1.11321i	0.342113	−	0.939659i	$-0.388858\pi$
$224$	−3.49214			−0.233329
$225$	14.6470	+	12.9690i	0.976465	+	0.864600i
$226$	3.85676			0.256548
$227$	−7.78876	−	13.4905i	−0.516958	−	0.895398i	−0.999806	−	0.0196939i	$-0.993731\pi$
$227$	−7.78876	−	13.4905i	−0.516958	−	0.895398i	0.482848	−	0.875704i	$-0.339603\pi$
$228$	5.11783	+	1.94014i	0.338937	+	0.128489i
$229$	5.29223	−	9.16642i	0.349721	−	0.605734i	−0.636479	−	0.771294i	$-0.719610\pi$
$229$	5.29223	−	9.16642i	0.349721	−	0.605734i	0.986200	+	0.165560i	$0.0529432\pi$
$230$	1.69714	−	2.93953i	0.111906	−	0.193827i
$231$	27.1179	+	10.2803i	1.78423	+	0.676391i
$232$	−1.22952	−	2.12959i	−0.0807218	−	0.139814i
$233$	10.2477			0.671346			0.335673	−	0.941978i	$-0.391036\pi$
$233$	10.2477			0.671346			0.335673	+	0.941978i	$0.391036\pi$
$234$	−14.5895	+	4.87507i	−0.953742	+	0.318693i
$235$	37.7350			2.46156
$236$	−3.08029	−	5.33522i	−0.200510	−	0.347293i
$237$	−9.20362	+	7.51660i	−0.597839	+	0.488256i
$238$	−11.0964	+	19.2194i	−0.719270	+	1.24581i
$239$	−6.67263	+	11.5573i	−0.431617	+	0.747582i	−0.997013	−	0.0772376i	$-0.975390\pi$
$239$	−6.67263	+	11.5573i	−0.431617	+	0.747582i	0.565396	+	0.824820i	$0.308723\pi$
$240$	−0.943856	−	5.80281i	−0.0609256	−	0.374570i
$241$	15.0065	+	25.9919i	0.966651	+	1.67429i	0.705113	+	0.709095i	$0.250896\pi$
$241$	15.0065	+	25.9919i	0.966651	+	1.67429i	0.261538	+	0.965193i	$0.415770\pi$
$242$	−11.9892			−0.770693
$243$	−11.2497	−	10.7909i	−0.721672	−	0.692235i
$244$	1.26457			0.0809561
$245$	−8.81675	−	15.2711i	−0.563282	−	0.975633i
$246$	1.52892	+	9.39977i	0.0974803	+	0.599307i
$247$	8.10134	−	14.0319i	0.515476	−	0.892830i
$248$	0.830547	−	1.43855i	0.0527398	−	0.0913480i
$249$	−8.84877	+	7.22679i	−0.560768	+	0.457979i
$250$	2.58161	+	4.47148i	0.163275	+	0.282801i
$251$	−13.1961			−0.832929			−0.416465	−	0.909152i	$-0.636731\pi$
$251$	−13.1961			−0.832929			−0.416465	+	0.909152i	$0.636731\pi$
$252$	−9.93637	+	3.32024i	−0.625933	+	0.209156i
$253$	4.79470			0.301440
$254$	−3.65823	−	6.33623i	−0.229538	−	0.397571i
$255$	−34.9356	−	13.2439i	−2.18775	−	0.829366i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	4.89203	−	8.47325i	0.305157	−	0.528547i	−0.672140	−	0.740424i	$-0.734625\pi$
$257$	4.89203	−	8.47325i	0.305157	−	0.528547i	0.977296	+	0.211878i	$0.0679579\pi$
$258$	1.25561	+	0.475996i	0.0781710	+	0.0296342i
$259$	17.2614	+	29.8975i	1.07257	+	1.85774i
$260$	−17.4041			−1.07936
$261$	−5.52317	−	4.89043i	−0.341876	−	0.302710i
$262$	7.15100			0.441790
$263$	4.58904	+	7.94846i	0.282973	+	0.490123i	0.972116	−	0.234503i	$-0.0753461\pi$
$263$	4.58904	+	7.94846i	0.282973	+	0.490123i	−0.689143	+	0.724625i	$0.742013\pi$
$264$	6.43212	−	5.25312i	0.395870	−	0.323307i
$265$	−10.8908	+	18.8634i	−0.669017	+	1.15877i
$266$	5.51754	−	9.55667i	0.338302	−	0.585957i
$267$	−4.02889	−	24.7695i	−0.246564	−	1.51587i
$268$	−1.74607	−	3.02428i	−0.106658	−	0.184738i
$269$	−19.2842			−1.17578			−0.587889	−	0.808941i	$-0.700041\pi$
$269$	−19.2842			−1.17578			−0.587889	+	0.808941i	$0.700041\pi$
$270$	−8.20277	−	15.6136i	−0.499205	−	0.950216i
$271$	12.5171			0.760357			0.380178	−	0.924913i	$-0.375863\pi$
$271$	12.5171			0.760357			0.380178	+	0.924913i	$0.375863\pi$
$272$	3.17752	+	5.50362i	0.192665	+	0.333706i
$273$	4.97912	+	30.6116i	0.301350	+	1.85270i
$274$	3.38252	−	5.85869i	0.204345	−	0.353936i
$275$	−15.6335	+	27.0780i	−0.942735	+	1.63286i
$276$	−1.34151	+	1.09561i	−0.0807492	+	0.0659479i
$277$	12.5091	+	21.6664i	0.751598	+	1.30181i	0.947048	+	0.321092i	$0.104050\pi$
$277$	12.5091	+	21.6664i	0.751598	+	1.30181i	−0.195451	+	0.980714i	$0.562617\pi$
$278$	−2.86619			−0.171903
$279$	0.995461	−	4.88285i	0.0595967	−	0.292328i
$280$	−11.8533			−0.708371
$281$	2.20838	+	3.82502i	0.131741	+	0.228182i	0.924348	−	0.381551i	$-0.124610\pi$
$281$	2.20838	+	3.82502i	0.131741	+	0.228182i	−0.792607	+	0.609733i	$0.791277\pi$
$282$	−18.0052	−	6.82569i	−1.07220	−	0.406464i
$283$	6.50840	−	11.2729i	0.386884	−	0.670103i	−0.605145	−	0.796116i	$-0.706885\pi$
$283$	6.50840	−	11.2729i	0.386884	−	0.670103i	0.992029	+	0.126013i	$0.0402181\pi$
$284$	−8.22308	+	14.2428i	−0.487950	+	0.845154i
$285$	17.3714	+	6.58539i	1.02899	+	0.390085i
$286$	−12.2923	−	21.2910i	−0.726861	−	1.25896i
$287$	19.2008			1.13339
$288$	−0.599280	+	2.93953i	−0.0353129	+	0.173214i
$289$	23.3865			1.37568
$290$	−4.17333	−	7.22842i	−0.245066	−	0.424468i
$291$	2.06721	−	1.68829i	0.121182	−	0.0989696i
$292$	−2.94800	+	5.10609i	−0.172519	+	0.298811i
$293$	−8.65516	+	14.9912i	−0.505640	+	0.875794i	0.494339	+	0.869269i	$0.335410\pi$
$293$	−8.65516	+	14.9912i	−0.505640	+	0.875794i	−0.999979	+	0.00652448i	$0.997923\pi$
$294$	1.44460	+	8.88139i	0.0842509	+	0.517973i
$295$	−10.4554	−	18.1092i	−0.608735	−	1.05436i
$296$	9.88582			0.574602
$297$	13.3071	−	21.0625i	0.772157	−	1.22217i
$298$	−1.00120			−0.0579980
$299$	2.56373	+	4.44052i	0.148265	+	0.256802i
$300$	−1.81335	−	11.1485i	−0.104694	−	0.643656i
$301$	1.35368	−	2.34464i	0.0780247	−	0.135143i
$302$	−1.31459	+	2.27694i	−0.0756464	+	0.131023i
$303$	−12.9993	+	10.6166i	−0.746792	+	0.609906i
$304$	−1.57999	−	2.73662i	−0.0906185	−	0.156956i
$305$	4.29232			0.245778
$306$	14.2739	+	12.6386i	0.815983	+	0.722503i
$307$	−16.3885			−0.935340			−0.467670	−	0.883903i	$-0.654906\pi$
$307$	−16.3885			−0.935340			−0.467670	+	0.883903i	$0.654906\pi$
$308$	−8.37189	−	14.5005i	−0.477033	−	0.826245i
$309$	−18.0145	−	6.82922i	−1.02481	−	0.388501i
$310$	2.81911	−	4.88285i	0.160115	−	0.277327i
$311$	12.4319	−	21.5326i	0.704946	−	1.22100i	−0.261765	−	0.965132i	$-0.584305\pi$
$311$	12.4319	−	21.5326i	0.704946	−	1.22100i	0.966711	−	0.255871i	$-0.0823621\pi$
$312$	8.30434	+	3.14813i	0.470141	+	0.178228i
$313$	−0.256278	−	0.443887i	−0.0144857	−	0.0250900i	0.858692	−	0.512493i	$-0.171278\pi$
$313$	−0.256278	−	0.443887i	−0.0144857	−	0.0250900i	−0.873177	+	0.487403i	$0.837944\pi$
$314$	18.9058			1.06692
$315$	−33.7269	+	11.2698i	−1.90029	+	0.634984i
$316$	6.86066			0.385942
$317$	−6.72374	−	11.6459i	−0.377643	−	0.654097i	0.613076	−	0.790024i	$-0.289932\pi$
$317$	−6.72374	−	11.6459i	−0.377643	−	0.654097i	−0.990719	+	0.135927i	$0.956599\pi$
$318$	8.60865	−	7.03069i	0.482749	−	0.394262i
$319$	5.89517	−	10.2107i	0.330066	−	0.571692i
$320$	−1.69714	+	2.93953i	−0.0948731	+	0.164325i
$321$	4.13853	+	25.4436i	0.230990	+	1.42012i
$322$	1.74607	+	3.02428i	0.0973048	+	0.168537i
$323$	−20.0818			−1.11738
$324$	1.08967	+	8.93379i	0.0605374	+	0.496322i
$325$	−33.4370			−1.85475
$326$	7.83770	+	13.5753i	0.434090	+	0.751866i
$327$	3.33061	+	20.4765i	0.184183	+	1.13235i
$328$	2.74914	−	4.76165i	0.151796	−	0.262918i
$329$	−19.4115	+	33.6217i	−1.07019	+	1.85362i
$330$	21.8324	−	17.8306i	1.20184	−	0.981541i
$331$	0.377758	+	0.654296i	0.0207635	+	0.0359634i	0.876220	−	0.481911i	$-0.160057\pi$
$331$	0.377758	+	0.654296i	0.0207635	+	0.0359634i	−0.855457	+	0.517874i	$0.826724\pi$
$332$	6.59614			0.362010
$333$	28.1286	−	9.39920i	1.54144	−	0.515073i
$334$	12.6184			0.690446
$335$	−5.92666	−	10.2653i	−0.323808	−	0.560852i
$336$	5.65580	+	2.14409i	0.308549	+	0.116969i
$337$	3.72552	−	6.45279i	0.202942	−	0.351506i	−0.746533	−	0.665348i	$-0.768283\pi$
$337$	3.72552	−	6.45279i	0.202942	−	0.351506i	0.949475	+	0.313842i	$0.101616\pi$
$338$	6.64547	−	11.5103i	0.361466	−	0.626077i
$339$	−6.24632	−	2.36795i	−0.339254	−	0.128609i
$340$	10.7854	+	18.6809i	0.584920	+	1.01311i
$341$	7.96445			0.431299
$342$	−7.09753	−	6.28443i	−0.383791	−	0.339823i
$343$	−6.30310			−0.340335
$344$	−0.387635	−	0.671404i	−0.0208999	−	0.0361997i
$345$	−4.55345	+	3.71881i	−0.245150	+	0.200214i
$346$	−0.301440	+	0.522109i	−0.0162055	+	0.0280687i
$347$	0.427050	−	0.739673i	0.0229253	−	0.0397077i	−0.854335	−	0.519722i	$-0.826035\pi$
$347$	0.427050	−	0.739673i	0.0229253	−	0.0397077i	0.877260	+	0.480015i	$0.159369\pi$
$348$	0.683790	+	4.20393i	0.0366550	+	0.225354i
$349$	−18.2104	−	31.5413i	−0.974781	−	1.68837i	−0.680657	−	0.732602i	$-0.738306\pi$
$349$	−18.2104	−	31.5413i	−0.974781	−	1.68837i	−0.294124	−	0.955767i	$-0.595028\pi$
$350$	−22.7728			−1.21726
$351$	26.6219	+	1.06198i	1.42097	+	0.0566845i
$352$	−4.79470			−0.255558
$353$	−4.59723	−	7.96264i	−0.244686	−	0.423808i	0.717357	−	0.696705i	$-0.245352\pi$
$353$	−4.59723	−	7.96264i	−0.244686	−	0.423808i	−0.962043	+	0.272897i	$0.912018\pi$
$354$	1.71309	+	10.5320i	0.0910494	+	0.559771i
$355$	−27.9115	+	48.3441i	−1.48139	+	2.56584i
$356$	−7.24432	+	12.5475i	−0.383948	+	0.665018i
$357$	29.7717	−	24.3145i	1.57568	−	1.28686i
$358$	5.07999	+	8.79880i	0.268486	+	0.465031i
$359$	−27.0648			−1.42843			−0.714213	−	0.699929i	$-0.753215\pi$
$359$	−27.0648			−1.42843			−0.714213	+	0.699929i	$0.753215\pi$
$360$	−2.03413	+	9.97761i	−0.107208	+	0.525866i
$361$	−9.01455			−0.474450
$362$	−3.71083	−	6.42734i	−0.195037	−	0.337813i
$363$	19.4174	+	7.36104i	1.01915	+	0.386354i
$364$	8.95293	−	15.5069i	0.469261	−	0.812784i
$365$	−10.0063	+	17.3315i	−0.523756	+	0.907172i
$366$	−2.04808	−	0.776416i	−0.107055	−	0.0405839i
$367$	17.8506	+	30.9181i	0.931793	+	1.61391i	0.780256	+	0.625461i	$0.215089\pi$
$367$	17.8506	+	30.9181i	0.931793	+	1.61391i	0.151537	+	0.988452i	$0.451578\pi$
$368$	1.00000			0.0521286
$369$	3.29501	−	16.1624i	0.171531	−	0.841380i
$370$	33.5553			1.74446
$371$	−11.2048	−	19.4073i	−0.581725	−	1.00758i
$372$	−2.22837	+	1.81991i	−0.115536	+	0.0943580i
$373$	−15.7450	+	27.2711i	−0.815243	+	1.41204i	0.0939100	+	0.995581i	$0.470063\pi$
$373$	−15.7450	+	27.2711i	−0.815243	+	1.41204i	−0.909153	+	0.416462i	$0.863270\pi$
$374$	−15.2353	+	26.3882i	−0.787796	+	1.36450i
$375$	−1.43575	−	8.82695i	−0.0741416	−	0.455822i
$376$	5.55862	+	9.62781i	0.286664	+	0.496516i
$377$	12.6086			0.649378
$378$	18.1313	+	0.723281i	0.932573	+	0.0372016i
$379$	−9.46354			−0.486109			−0.243055	−	0.970013i	$-0.578149\pi$
$379$	−9.46354			−0.486109			−0.243055	+	0.970013i	$0.578149\pi$
$380$	−5.36292	−	9.28886i	−0.275112	−	0.476508i
$381$	2.03450	+	12.5081i	0.104231	+	0.640809i
$382$	2.15681	−	3.73570i	0.110352	−	0.191135i
$383$	11.0060	−	19.0629i	0.562378	−	0.974068i	−0.434910	−	0.900474i	$-0.643220\pi$
$383$	11.0060	−	19.0629i	0.562378	−	0.974068i	0.997288	−	0.0735937i	$-0.0234468\pi$
$384$	1.34151	−	1.09561i	0.0684585	−	0.0559101i
$385$	−28.4166	−	49.2189i	−1.44824	−	2.50843i
$386$	−7.72975			−0.393434
$387$	−1.74131	−	1.54183i	−0.0885159	−	0.0783754i
$388$	−1.54096			−0.0782306
$389$	−8.50635	−	14.7334i	−0.431289	−	0.747014i	0.565696	−	0.824614i	$-0.308608\pi$
$389$	−8.50635	−	14.7334i	−0.431289	−	0.747014i	−0.996985	+	0.0775998i	$0.975274\pi$
$390$	28.1873	+	10.6857i	1.42732	+	0.541089i
$391$	3.17752	−	5.50362i	0.160694	−	0.278330i
$392$	2.59753	−	4.49906i	0.131195	−	0.227237i
$393$	−11.5816	−	4.39053i	−0.584215	−	0.221473i
$394$	−9.73340	−	16.8587i	−0.490361	−	0.849331i
$395$	23.2870			1.17170
$396$	−13.6426	+	4.55868i	−0.685567	+	0.229083i
$397$	14.4557			0.725513			0.362756	−	0.931884i	$-0.381836\pi$
$397$	14.4557			0.725513			0.362756	+	0.931884i	$0.381836\pi$
$398$	0.330748	+	0.572872i	0.0165789	+	0.0287155i
$399$	−14.8036	+	12.0901i	−0.741109	+	0.605264i
$400$	−3.26058	+	5.64748i	−0.163029	+	0.282374i
$401$	0.340134	−	0.589129i	0.0169855	−	0.0294197i	−0.857408	−	0.514638i	$-0.827926\pi$
$401$	0.340134	−	0.589129i	0.0169855	−	0.0294197i	0.874393	+	0.485218i	$0.161260\pi$
$402$	0.971068	+	5.97011i	0.0484325	+	0.297762i
$403$	4.25861	+	7.37612i	0.212136	+	0.367431i
$404$	9.69010			0.482101
$405$	3.69866	+	30.3238i	0.183788	+	1.50680i
$406$	8.58731			0.426181
$407$	23.6998	+	41.0492i	1.17475	+	2.03474i
$408$	−1.76716	−	10.8645i	−0.0874874	−	0.537871i
$409$	8.57201	−	14.8472i	0.423859	−	0.734145i	−0.572454	−	0.819937i	$-0.694009\pi$
$409$	8.57201	−	14.8472i	0.423859	−	0.734145i	0.996313	+	0.0857918i	$0.0273420\pi$
$410$	9.33136	−	16.1624i	0.460843	−	0.798203i
$411$	−9.07534	+	7.41183i	−0.447653	+	0.365599i
$412$	5.56148	+	9.63277i	0.273995	+	0.474573i
$413$	21.5136			1.05862
$414$	2.84535	−	0.950775i	0.139841	−	0.0467281i
$415$	22.3892			1.09904
$416$	−2.56373	−	4.44052i	−0.125697	−	0.217714i
$417$	4.64203	+	1.75977i	0.227321	+	0.0861762i
$418$	7.57557	−	13.1213i	0.370533	−	0.641782i
$419$	−5.29969	+	9.17933i	−0.258907	+	0.448440i	−0.965949	−	0.258731i	$-0.916696\pi$
$419$	−5.29969	+	9.17933i	−0.258907	+	0.448440i	0.707043	+	0.707171i	$0.250029\pi$
$420$	19.1974	+	7.27763i	0.936736	+	0.355112i
$421$	3.80320	+	6.58733i	0.185356	+	0.321047i	0.943697	−	0.330812i	$-0.107323\pi$
$421$	3.80320	+	6.58733i	0.185356	+	0.321047i	−0.758340	+	0.651859i	$0.773989\pi$
$422$	−12.1185			−0.589919
$423$	24.9701	+	22.1095i	1.21409	+	1.07500i
$424$	−6.41715			−0.311644
$425$	20.7211	+	35.8900i	1.00512	+	1.74092i
$426$	22.0626	−	18.0186i	1.06894	−	0.873002i
$427$	−2.20804	+	3.82443i	−0.106854	+	0.185077i
$428$	7.44146	−	12.8890i	0.359697	−	0.623013i
$429$	6.83632	+	42.0296i	0.330061	+	2.02921i
$430$	−1.31574	−	2.27893i	−0.0634508	−	0.109900i
$431$	−33.0832			−1.59356			−0.796780	−	0.604269i	$-0.793465\pi$
$431$	−33.0832			−1.59356			−0.796780	+	0.604269i	$0.793465\pi$
$432$	2.77538	−	4.39287i	0.133531	−	0.211352i
$433$	30.6096			1.47101			0.735503	−	0.677522i	$-0.236946\pi$
$433$	30.6096			1.47101			0.735503	+	0.677522i	$0.236946\pi$
$434$	2.90039	+	5.02362i	0.139223	+	0.241142i
$435$	2.32097	+	14.2693i	0.111282	+	0.684161i
$436$	5.98874	−	10.3728i	0.286809	−	0.496767i
$437$	−1.57999	+	2.73662i	−0.0755811	+	0.130910i
$438$	7.90953	−	6.45971i	0.377932	−	0.308657i
$439$	−2.23860	−	3.87738i	−0.106843	−	0.185057i	0.807647	−	0.589666i	$-0.200741\pi$
$439$	−2.23860	−	3.87738i	−0.106843	−	0.185057i	−0.914490	+	0.404609i	$0.867407\pi$
$440$	−16.2746			−0.775860
$441$	3.11330	−	15.2711i	0.148252	−	0.727194i
$442$	−32.5853			−1.54992
$443$	6.69807	+	11.6014i	0.318235	+	0.551199i	0.980120	−	0.198406i	$-0.0635766\pi$
$443$	6.69807	+	11.6014i	0.318235	+	0.551199i	−0.661885	+	0.749606i	$0.730243\pi$
$444$	−16.0109	−	6.06964i	−0.759842	−	0.288052i
$445$	−24.5893	+	42.5899i	−1.16564	+	2.01895i
$446$	9.59774	−	16.6238i	0.454466	−	0.787159i
$447$	1.62152	+	0.614712i	0.0766955	+	0.0290749i
$448$	−1.74607	−	3.02428i	−0.0824941	−	0.142884i
$449$	7.07071			0.333687			0.166844	−	0.985983i	$-0.446642\pi$
$449$	7.07071			0.333687			0.166844	+	0.985983i	$0.446642\pi$
$450$	−3.90800	+	19.1691i	−0.184225	+	0.903642i
$451$	26.3626			1.24137
$452$	1.92838	+	3.34005i	0.0907033	+	0.157103i
$453$	3.52707	−	2.88056i	0.165716	−	0.135341i
$454$	7.78876	−	13.4905i	0.365545	−	0.633142i
$455$	30.3888	−	52.6349i	1.42465	−	2.46756i
$456$	0.878701	+	5.40224i	0.0411490	+	0.252983i
$457$	−0.00878737	−	0.0152202i	−0.000411056	−	0.000711969i	0.865820	−	0.500356i	$-0.166798\pi$
$457$	−0.00878737	−	0.0152202i	−0.000411056	−	0.000711969i	−0.866231	+	0.499644i	$0.833464\pi$
$458$	10.5845			0.494580
$459$	−15.3579	−	29.2331i	−0.716843	−	1.36448i
$460$	3.39428			0.158259
$461$	15.6892	+	27.1745i	0.730719	+	1.26564i	0.956576	+	0.291481i	$0.0941482\pi$
$461$	15.6892	+	27.1745i	0.730719	+	1.26564i	−0.225858	+	0.974160i	$0.572519\pi$
$462$	4.65598	+	28.6249i	0.216616	+	1.33175i
$463$	2.12357	−	3.67813i	0.0986907	−	0.170937i	−0.812452	−	0.583028i	$-0.801868\pi$
$463$	2.12357	−	3.67813i	0.0986907	−	0.170937i	0.911143	+	0.412090i	$0.135201\pi$
$464$	1.22952	−	2.12959i	0.0570789	−	0.0988636i
$465$	−7.56372	+	6.17729i	−0.350759	+	0.286465i
$466$	5.12383	+	8.87473i	0.237357	+	0.411114i
$467$	30.9792			1.43354			0.716772	−	0.697307i	$-0.245619\pi$
$467$	30.9792			1.43354			0.716772	+	0.697307i	$0.245619\pi$
$468$	−11.5167	−	10.1973i	−0.532358	−	0.471370i
$469$	12.1951			0.563116
$470$	18.8675	+	32.6795i	0.870293	+	1.50739i
$471$	−30.6194	−	11.6077i	−1.41087	−	0.534853i
$472$	3.08029	−	5.33522i	0.141782	−	0.245573i
$473$	1.85859	−	3.21918i	0.0854583	−	0.148018i
$474$	−11.1114	−	4.21227i	−0.510362	−	0.193476i
$475$	−10.3033	−	17.8459i	−0.472750	−	0.818826i
$476$	−22.1927			−1.01720
$477$	−18.2591	+	6.10127i	−0.836025	+	0.279358i
$478$	−13.3453			−0.610398
$479$	−13.9406	−	24.1459i	−0.636963	−	1.10325i	−0.986096	−	0.166179i	$-0.946857\pi$
$479$	−13.9406	−	24.1459i	−0.636963	−	1.10325i	0.349133	−	0.937073i	$-0.386476\pi$
$480$	4.55345	−	3.71881i	0.207836	−	0.169740i
$481$	−25.3446	+	43.8982i	−1.15562	+	2.00159i
$482$	−15.0065	+	25.9919i	−0.683525	+	1.18390i
$483$	−0.971068	−	5.97011i	−0.0441851	−	0.271649i
$484$	−5.99458	−	10.3829i	−0.272481	−	0.471951i
$485$	−5.23047			−0.237503
$486$	3.72030	−	15.1380i	0.168756	−	0.686674i
$487$	20.9308			0.948464			0.474232	−	0.880400i	$-0.342726\pi$
$487$	20.9308			0.948464			0.474232	+	0.880400i	$0.342726\pi$
$488$	0.632287	+	1.09515i	0.0286223	+	0.0495753i
$489$	−4.35889	−	26.7984i	−0.197116	−	1.21187i
$490$	8.81675	−	15.2711i	0.398300	−	0.689876i
$491$	18.3014	−	31.6990i	0.825932	−	1.43056i	−0.0752731	−	0.997163i	$-0.523983\pi$
$491$	18.3014	−	31.6990i	0.825932	−	1.43056i	0.901205	−	0.433393i	$-0.142684\pi$
$492$	−7.37598	+	6.02397i	−0.332535	+	0.271581i
$493$	−7.81363	−	13.5336i	−0.351908	−	0.609523i
$494$	16.2027			0.728993
$495$	−46.3069	+	15.4735i	−2.08134	+	0.695480i
$496$	1.66109			0.0745854
$497$	−28.7162	−	49.7379i	−1.28810	−	2.23105i
$498$	−10.6830	−	4.04986i	−0.478715	−	0.181479i
$499$	−3.88896	+	6.73588i	−0.174094	+	0.301540i	−0.939847	−	0.341595i	$-0.889033\pi$
$499$	−3.88896	+	6.73588i	−0.174094	+	0.301540i	0.765753	+	0.643134i	$0.222366\pi$
$500$	−2.58161	+	4.47148i	−0.115453	+	0.199970i
$501$	−20.4364	−	7.74734i	−0.913032	−	0.346126i
$502$	−6.59804	−	11.4281i	−0.294485	−	0.510063i
$503$	23.1594			1.03262			0.516312	−	0.856400i	$-0.327304\pi$
$503$	23.1594			1.03262			0.516312	+	0.856400i	$0.327304\pi$
$504$	−7.84360	−	6.94503i	−0.349382	−	0.309356i
$505$	32.8909			1.46363
$506$	2.39735	+	4.15233i	0.106575	+	0.184594i
$507$	−17.8299	+	14.5617i	−0.791853	+	0.646707i
$508$	3.65823	−	6.33623i	0.162308	−	0.281125i
$509$	7.41645	−	12.8457i	0.328728	−	0.569374i	−0.653531	−	0.756899i	$-0.726713\pi$
$509$	7.41645	−	12.8457i	0.328728	−	0.569374i	0.982260	+	0.187525i	$0.0600466\pi$
$510$	−5.99824	−	36.8771i	−0.265606	−	1.63294i
$511$	−10.2948	−	17.8312i	−0.455417	−	0.788805i
$512$	−1.00000			−0.0441942
$513$	7.63653	+	14.5358i	0.337161	+	0.641773i
$514$	9.78406			0.431557
$515$	18.8772	+	32.6964i	0.831831	+	1.44077i
$516$	0.215581	+	1.32539i	0.00949043	+	0.0583470i
$517$	−26.6519	+	46.1625i	−1.17215	+	2.03022i
$518$	−17.2614	+	29.8975i	−0.758420	+	1.31362i
$519$	0.808766	−	0.660520i	0.0355009	−	0.0289936i
$520$	−8.70204	−	15.0724i	−0.381610	−	0.660967i
$521$	−40.8448			−1.78944			−0.894722	−	0.446623i	$-0.852627\pi$
$521$	−40.8448			−1.78944			−0.894722	+	0.446623i	$0.852627\pi$
$522$	1.47365	−	7.22842i	0.0645000	−	0.316379i
$523$	5.80630			0.253892			0.126946	−	0.991910i	$-0.459483\pi$
$523$	5.80630			0.253892			0.126946	+	0.991910i	$0.459483\pi$
$524$	3.57550	+	6.19295i	0.156196	+	0.270540i
$525$	36.8823	+	13.9819i	1.60968	+	0.610220i
$526$	−4.58904	+	7.94846i	−0.200092	+	0.346569i
$527$	5.27816	−	9.14204i	0.229920	−	0.398234i
$528$	7.76540	+	2.94382i	0.337946	+	0.128113i
$529$	−0.500000	−	0.866025i	−0.0217391	−	0.0376533i
$530$	−21.7816			−0.946133
$531$	3.69191	−	18.1092i	0.160215	−	0.785873i
$532$	11.0351			0.478432
$533$	14.0961	+	24.4152i	0.610571	+	1.05754i
$534$	19.4366	−	15.8739i	0.841105	−	0.686931i
$535$	25.2584	−	43.7489i	1.09202	−	1.89143i
$536$	1.74607	−	3.02428i	0.0754188	−	0.130629i
$537$	−2.82521	−	17.3693i	−0.121917	−	0.749542i
$538$	−9.64210	−	16.7006i	−0.415701	−	0.720014i
$539$	24.9088			1.07290
$540$	9.42042	−	14.9106i	0.405390	−	0.641651i
$541$	−34.5661			−1.48611			−0.743056	−	0.669229i	$-0.766624\pi$
$541$	−34.5661			−1.48611			−0.743056	+	0.669229i	$0.766624\pi$
$542$	6.25853	+	10.8401i	0.268827	+	0.465622i
$543$	2.06376	+	12.6879i	0.0885642	+	0.544491i
$544$	−3.17752	+	5.50362i	−0.136235	+	0.235966i
$545$	20.3275	−	35.2082i	0.870734	−	1.50816i
$546$	−24.0208	+	19.6178i	−1.02800	+	0.839565i
$547$	11.0446	+	19.1299i	0.472235	+	0.817935i	0.999495	−	0.0317690i	$-0.0101141\pi$
$547$	11.0446	+	19.1299i	0.472235	+	0.817935i	−0.527260	+	0.849704i	$0.676781\pi$
$548$	6.76503			0.288988
$549$	2.84032	+	2.51493i	0.121222	+	0.107335i
$550$	−31.2670			−1.33323
$551$	3.88525	+	6.72945i	0.165517	+	0.286684i
$552$	−1.61958	−	0.613974i	−0.0689339	−	0.0261325i
$553$	−11.9792	+	20.7486i	−0.509407	+	0.882319i
$554$	−12.5091	+	21.6664i	−0.531460	+	0.920515i
$555$	−54.3454	−	20.6021i	−2.30683	−	0.874509i
$556$	−1.43310	−	2.48220i	−0.0607768	−	0.105269i
$557$	−1.57737			−0.0668353			−0.0334176	−	0.999441i	$-0.510639\pi$
$557$	−1.57737			−0.0668353			−0.0334176	+	0.999441i	$0.510639\pi$
$558$	4.72640	−	1.57933i	0.200084	−	0.0668583i
$559$	3.97517			0.168132
$560$	−5.92666	−	10.2653i	−0.250447	−	0.433787i
$561$	40.8764	−	33.3838i	1.72580	−	1.40946i
$562$	−2.20838	+	3.82502i	−0.0931547	+	0.161349i
$563$	−2.70236	+	4.68062i	−0.113891	+	0.197265i	−0.917336	−	0.398114i	$-0.869665\pi$
$563$	−2.70236	+	4.68062i	−0.113891	+	0.197265i	0.803445	+	0.595379i	$0.202998\pi$
$564$	−3.09139	−	19.0058i	−0.130171	−	0.800290i
$565$	6.54546	+	11.3371i	0.275370	+	0.476954i
$566$	13.0168			0.547137
$567$	−28.9210	−	12.3036i	−1.21457	−	0.516701i
$568$	−16.4462			−0.690066
$569$	20.8169	+	36.0559i	0.872688	+	1.51154i	0.859205	+	0.511631i	$0.170959\pi$
$569$	20.8169	+	36.0559i	0.872688	+	1.51154i	0.0134832	+	0.999909i	$0.495708\pi$
$570$	2.98256	+	18.3367i	0.124926	+	0.768041i
$571$	−20.2459	+	35.0669i	−0.847264	+	1.46750i	0.0363770	+	0.999338i	$0.488418\pi$
$571$	−20.2459	+	35.0669i	−0.847264	+	1.46750i	−0.883641	+	0.468166i	$0.844915\pi$
$572$	12.2923	−	21.2910i	0.513969	−	0.890220i
$573$	−5.78674	+	4.72604i	−0.241745	+	0.197433i
$574$	9.60039	+	16.6284i	0.400713	+	0.694055i
$575$	6.52115			0.271951
$576$	−2.84535	+	0.950775i	−0.118556	+	0.0396156i
$577$	−0.0485978			−0.00202315			−0.00101158	−	0.999999i	$-0.500322\pi$
$577$	−0.0485978			−0.00202315			−0.00101158	+	0.999999i	$0.500322\pi$
$578$	11.6933	+	20.2533i	0.486375	+	0.842427i
$579$	12.5189	+	4.74587i	0.520269	+	0.197231i
$580$	4.17333	−	7.22842i	0.173288	−	0.300144i
$581$	−11.5173	+	19.9486i	−0.477820	+	0.827608i
$582$	2.49571	+	0.946112i	0.103451	+	0.0392176i
$583$	−15.3842	−	26.6462i	−0.637147	−	1.10357i
$584$	−5.89600			−0.243978
$585$	−39.0908	−	34.6125i	−1.61621	−	1.43105i
$586$	−17.3103			−0.715083
$587$	−4.67180	−	8.09180i	−0.192826	−	0.333984i	0.753360	−	0.657609i	$-0.228432\pi$
$587$	−4.67180	−	8.09180i	−0.192826	−	0.333984i	−0.946186	+	0.323624i	$0.895099\pi$
$588$	−6.96921	+	5.69176i	−0.287405	+	0.234724i
$589$	−2.62451	+	4.54578i	−0.108141	+	0.187306i
$590$	10.4554	−	18.1092i	0.430441	−	0.745545i
$591$	5.41317	+	33.2801i	0.222668	+	1.36896i
$592$	4.94291	+	8.56138i	0.203152	+	0.351870i
$593$	−14.9859			−0.615396			−0.307698	−	0.951484i	$-0.599559\pi$
$593$	−14.9859			−0.615396			−0.307698	+	0.951484i	$0.599559\pi$
$594$	24.8942	+	0.993063i	1.02142	+	0.0407459i
$595$	−75.3283			−3.08816
$596$	−0.500601	−	0.867066i	−0.0205054	−	0.0355164i
$597$	−0.183944	−	1.13088i	−0.00752831	−	0.0462839i
$598$	−2.56373	+	4.44052i	−0.104839	+	0.181586i
$599$	11.4562	−	19.8427i	0.468088	−	0.810752i	−0.531247	−	0.847217i	$-0.678276\pi$
$599$	11.4562	−	19.8427i	0.468088	−	0.810752i	0.999335	+	0.0364650i	$0.0116097\pi$
$600$	8.74817	−	7.14463i	0.357142	−	0.291678i
$601$	−1.34709	−	2.33323i	−0.0549490	−	0.0951745i	0.837242	−	0.546832i	$-0.184166\pi$
$601$	−1.34709	−	2.33323i	−0.0549490	−	0.0951745i	−0.892191	+	0.451657i	$0.850833\pi$
$602$	2.70735			0.110344
$603$	2.09277	−	10.2653i	0.0852243	−	0.418034i
$604$	−2.62919			−0.106980
$605$	−20.3473	−	35.2426i	−0.827235	−	1.43281i
$606$	−15.6939	−	5.94947i	−0.637521	−	0.241681i
$607$	20.6865	−	35.8301i	0.839640	−	1.45430i	−0.0505565	−	0.998721i	$-0.516099\pi$
$607$	20.6865	−	35.8301i	0.839640	−	1.45430i	0.890196	−	0.455577i	$-0.150567\pi$
$608$	1.57999	−	2.73662i	0.0640770	−	0.110985i
$609$	−13.9078	−	5.27238i	−0.563573	−	0.213648i
$610$	2.14616	+	3.71726i	0.0868955	+	0.150507i
$611$	−57.0033			−2.30611
$612$	−3.80845	+	18.6809i	−0.153947	+	0.755129i
$613$	−24.0528			−0.971485			−0.485743	−	0.874102i	$-0.661451\pi$
$613$	−24.0528			−0.971485			−0.485743	+	0.874102i	$0.661451\pi$
$614$	−8.19424	−	14.1928i	−0.330693	−	0.572777i
$615$	−25.0362	+	20.4470i	−1.00956	+	0.824504i
$616$	8.37189	−	14.5005i	0.337313	−	0.584243i
$617$	−9.04957	+	15.6743i	−0.364322	+	0.631024i	−0.988667	−	0.150124i	$-0.952033\pi$
$617$	−9.04957	+	15.6743i	−0.364322	+	0.631024i	0.624345	+	0.781149i	$0.285366\pi$
$618$	−3.09299	−	19.0156i	−0.124418	−	0.764921i
$619$	5.70650	+	9.88394i	0.229364	+	0.397269i	0.957620	−	0.288036i	$-0.0930022\pi$
$619$	5.70650	+	9.88394i	0.229364	+	0.397269i	−0.728256	+	0.685305i	$0.759669\pi$
$620$	5.63822			0.226437
$621$	−5.19202	−	0.207117i	−0.208349	−	0.00831131i
$622$	24.8637			0.996944
$623$	−25.2982	−	43.8178i	−1.01355	−	1.75552i
$624$	1.42581	+	8.76584i	0.0570780	+	0.350914i
$625$	7.54017	−	13.0600i	0.301607	−	0.522398i
$626$	0.256278	−	0.443887i	0.0102429	−	0.0177413i
$627$	−20.3254	+	16.5997i	−0.811717	+	0.662929i
$628$	9.45290	+	16.3729i	0.377212	+	0.653350i
$629$	62.8248			2.50499
$630$	−26.6234	−	23.5734i	−1.06070	−	0.939187i
$631$	10.2132			0.406580			0.203290	−	0.979119i	$-0.434837\pi$
$631$	10.2132			0.406580			0.203290	+	0.979119i	$0.434837\pi$
$632$	3.43033	+	5.94150i	0.136451	+	0.236340i
$633$	19.6269	+	7.44044i	0.780097	+	0.295731i
$634$	6.72374	−	11.6459i	0.267034	−	0.462516i
$635$	12.4171	−	21.5070i	0.492756	−	0.853478i
$636$	10.3931	+	3.93997i	0.412113	+	0.156230i
$637$	13.3188	+	23.0688i	0.527709	+	0.914018i
$638$	11.7903			0.466784
$639$	−46.7951	+	15.6366i	−1.85119	+	0.618575i
$640$	−3.39428			−0.134171
$641$	23.5815	+	40.8443i	0.931412	+	1.61325i	0.780910	+	0.624644i	$0.214756\pi$
$641$	23.5815	+	40.8443i	0.931412	+	1.61325i	0.150503	+	0.988610i	$0.451911\pi$
$642$	−19.9655	+	16.3059i	−0.787977	+	0.643542i
$643$	18.4669	−	31.9856i	0.728264	−	1.26139i	−0.229352	−	0.973343i	$-0.573661\pi$
$643$	18.4669	−	31.9856i	0.728264	−	1.26139i	0.957616	−	0.288047i	$-0.0930059\pi$
$644$	−1.74607	+	3.02428i	−0.0688049	+	0.119174i
$645$	0.731743	+	4.49875i	0.0288124	+	0.177138i
$646$	−10.0409	−	17.3913i	−0.395053	−	0.684252i
$647$	14.4649			0.568674			0.284337	−	0.958724i	$-0.408226\pi$
$647$	14.4649			0.568674			0.284337	+	0.958724i	$0.408226\pi$
$648$	−7.19205	+	5.41058i	−0.282531	+	0.212548i
$649$	29.5381			1.15947
$650$	−16.7185	−	28.9573i	−0.655754	−	1.13580i
$651$	−1.61304	−	9.91692i	−0.0632199	−	0.388675i
$652$	−7.83770	+	13.5753i	−0.306948	+	0.531649i
$653$	−0.262054	+	0.453890i	−0.0102550	+	0.0177621i	−0.871107	−	0.491093i	$-0.836598\pi$
$653$	−0.262054	+	0.453890i	−0.0102550	+	0.0177621i	0.860852	+	0.508855i	$0.169931\pi$
$654$	−16.0679	+	13.1226i	−0.628304	+	0.513136i
$655$	12.1363	+	21.0206i	0.474203	+	0.821343i
$656$	5.49828			0.214672
$657$	−16.7762	+	5.60577i	−0.654502	+	0.218702i
$658$	−38.8230			−1.51348
$659$	18.3309	+	31.7501i	0.714072	+	1.23681i	0.963317	+	0.268368i	$0.0864842\pi$
$659$	18.3309	+	31.7501i	0.714072	+	1.23681i	−0.249245	+	0.968440i	$0.580182\pi$
$660$	26.3579	+	9.99217i	1.02598	+	0.388945i
$661$	8.68530	−	15.0434i	0.337819	−	0.585119i	−0.646203	−	0.763165i	$-0.723644\pi$
$661$	8.68530	−	15.0434i	0.337819	−	0.585119i	0.984022	+	0.178046i	$0.0569775\pi$
$662$	−0.377758	+	0.654296i	−0.0146820	+	0.0254299i
$663$	52.7744	+	20.0065i	2.04959	+	0.776988i
$664$	3.29807	+	5.71243i	0.127990	+	0.221685i
$665$	37.4562			1.45249
$666$	22.2043	+	19.6605i	0.860398	+	0.761830i
$667$	−2.45904			−0.0952143
$668$	6.30918	+	10.9278i	0.244109	+	0.422810i
$669$	−25.7509	+	21.0307i	−0.995586	+	0.813096i
$670$	5.92666	−	10.2653i	0.228967	−	0.396582i
$671$	−3.03163	+	5.25093i	−0.117035	+	0.202710i
$672$	0.971068	+	5.97011i	0.0374598	+	0.230302i
$673$	−20.3892	−	35.3152i	−0.785946	−	1.36130i	−0.928432	−	0.371502i	$-0.878843\pi$
$673$	−20.3892	−	35.3152i	−0.785946	−	1.36130i	0.142486	−	0.989797i	$-0.454491\pi$
$674$	7.45104			0.287003
$675$	18.0987	−	28.6465i	0.696618	−	1.10261i
$676$	13.2909			0.511190
$677$	−1.30376	−	2.25817i	−0.0501075	−	0.0867887i	0.839884	−	0.542766i	$-0.182623\pi$
$677$	−1.30376	−	2.25817i	−0.0501075	−	0.0867887i	−0.889991	+	0.455978i	$0.849290\pi$
$678$	−1.07246	−	6.59345i	−0.0411875	−	0.253220i
$679$	2.69063	−	4.66031i	0.103257	−	0.178846i
$680$	−10.7854	+	18.6809i	−0.413601	+	0.716378i
$681$	−20.8974	+	17.0669i	−0.800789	+	0.654005i
$682$	3.98223	+	6.89742i	0.152487	+	0.264116i
$683$	−16.2295			−0.621006			−0.310503	−	0.950572i	$-0.600498\pi$
$683$	−16.2295			−0.621006			−0.310503	+	0.950572i	$0.600498\pi$
$684$	1.89371	−	9.28886i	0.0724078	−	0.355168i
$685$	22.9624			0.877350
$686$	−3.15155	−	5.45865i	−0.120327	−	0.208412i
$687$	−17.1424	−	6.49859i	−0.654023	−	0.247937i
$688$	0.387635	−	0.671404i	0.0147785	−	0.0255970i
$689$	16.4519	−	28.4955i	0.626767	−	1.08559i
$690$	−5.49731	−	2.08400i	−0.209279	−	0.0793366i
$691$	−9.69924	−	16.7996i	−0.368977	−	0.639086i	0.620429	−	0.784262i	$-0.286958\pi$
$691$	−9.69924	−	16.7996i	−0.368977	−	0.639086i	−0.989406	+	0.145176i	$0.953625\pi$
$692$	−0.602879			−0.0229180
$693$	10.0342	−	49.2189i	0.381168	−	1.86967i
$694$	0.854101			0.0324212
$695$	−4.86433	−	8.42528i	−0.184515	−	0.319589i
$696$	−3.29881	+	2.69414i	−0.125041	+	0.102121i
$697$	17.4709	−	30.2605i	0.661757	−	1.14620i
$698$	18.2104	−	31.5413i	0.689274	−	1.19386i
$699$	−2.84959	−	17.5192i	−0.107781	−	0.662638i
$700$	−11.3864	−	19.7218i	−0.430365	−	0.745415i
$701$	27.9645			1.05621			0.528103	−	0.849180i	$-0.322903\pi$
$701$	27.9645			1.05621			0.528103	+	0.849180i	$0.322903\pi$
$702$	12.3913	+	23.5863i	0.467678	+	0.890206i
$703$	−31.2390			−1.17820
$704$	−2.39735	−	4.15233i	−0.0903536	−	0.156497i
$705$	−10.4931	−	64.5112i	−0.395192	−	2.42963i
$706$	4.59723	−	7.96264i	0.173019	−	0.299678i
$707$	−16.9196	+	29.3056i	−0.636327	+	1.10215i
$708$	−8.26445	+	6.74959i	−0.310597	+	0.253665i
$709$	−1.23996	−	2.14768i	−0.0465678	−	0.0806578i	0.841802	−	0.539786i	$-0.181495\pi$
$709$	−1.23996	−	2.14768i	−0.0465678	−	0.0806578i	−0.888370	+	0.459129i	$0.848162\pi$
$710$	−55.8229			−2.09500
$711$	15.4095	+	13.6442i	0.577902	+	0.511697i
$712$	−14.4886			−0.542985
$713$	−0.830547	−	1.43855i	−0.0311042	−	0.0538741i
$714$	35.9428	+	13.6257i	1.34513	+	0.509931i
$715$	41.7237	−	72.2675i	1.56038	−	2.70265i
$716$	−5.07999	+	8.79880i	−0.189848	+	0.328826i
$717$	21.6137	+	8.19365i	0.807179	+	0.305997i
$718$	−13.5324	−	23.4388i	−0.505025	−	0.874728i
$719$	15.9388			0.594416			0.297208	−	0.954813i	$-0.403944\pi$
$719$	15.9388			0.594416			0.297208	+	0.954813i	$0.403944\pi$
$720$	−9.65793	+	3.22720i	−0.359930	+	0.120271i
$721$	−38.8430			−1.44659
$722$	−4.50728	−	7.80683i	−0.167743	−	0.290540i
$723$	40.2625	−	32.8824i	1.49738	−	1.22291i
$724$	3.71083	−	6.42734i	0.137912	−	0.238870i
$725$	8.01787	−	13.8874i	0.297776	−	0.515764i
$726$	3.33385	+	20.4965i	0.123731	+	0.760696i
$727$	−13.6715	−	23.6797i	−0.507048	−	0.878233i	−0.999967	−	0.00815739i	$-0.997403\pi$
$727$	−13.6715	−	23.6797i	−0.507048	−	0.878233i	0.492919	−	0.870075i	$-0.335930\pi$
$728$	17.9059			0.663635
$729$	−15.3197	+	22.2330i	−0.567395	+	0.823446i
$730$	−20.0127			−0.740703
$731$	−2.46344	−	4.26680i	−0.0911135	−	0.157813i
$732$	−0.351643	−	2.16190i	−0.0129971	−	0.0799060i
$733$	10.5709	−	18.3094i	0.390446	−	0.676271i	−0.602063	−	0.798449i	$-0.705654\pi$
$733$	10.5709	−	18.3094i	0.390446	−	0.676271i	0.992508	+	0.122177i	$0.0389877\pi$
$734$	−17.8506	+	30.9181i	−0.658877	+	1.14121i
$735$	−23.6555	+	19.3194i	−0.872545	+	0.712608i
$736$	0.500000	+	0.866025i	0.0184302	+	0.0319221i
$737$	16.7438			0.616765
$738$	15.6445	−	5.22763i	0.575884	−	0.192432i
$739$	−4.66746			−0.171695			−0.0858476	−	0.996308i	$-0.527360\pi$
$739$	−4.66746			−0.171695			−0.0858476	+	0.996308i	$0.527360\pi$
$740$	16.7776	+	29.0597i	0.616758	+	1.06826i
$741$	−26.2415	−	9.94803i	−0.964006	−	0.365450i
$742$	11.2048	−	19.4073i	0.411341	−	0.712464i
$743$	−2.59731	+	4.49867i	−0.0952861	+	0.165040i	−0.909728	−	0.415205i	$-0.863710\pi$
$743$	−2.59731	+	4.49867i	−0.0952861	+	0.165040i	0.814442	+	0.580245i	$0.197043\pi$
$744$	−2.69027	−	1.01987i	−0.0986302	−	0.0373902i
$745$	−1.69918	−	2.94307i	−0.0622531	−	0.107826i
$746$	−31.4899			−1.15293
$747$	14.8154	+	13.1181i	0.542067	+	0.479967i
$748$	−30.4705			−1.11411
$749$	25.9867	+	45.0102i	0.949532	+	1.64464i
$750$	6.92649	−	5.65687i	0.252920	−	0.206560i
$751$	12.9794	−	22.4810i	0.473625	−	0.820342i	−0.525920	−	0.850534i	$-0.676279\pi$
$751$	12.9794	−	22.4810i	0.473625	−	0.820342i	0.999544	+	0.0301925i	$0.00961203\pi$
$752$	−5.55862	+	9.62781i	−0.202702	+	0.351090i
$753$	3.66946	+	22.5598i	0.133723	+	0.822125i
$754$	6.30432	+	10.9194i	0.229590	+	0.397661i
$755$	−8.92421			−0.324785
$756$	8.43926	+	16.0638i	0.306933	+	0.584235i
$757$	−11.6767			−0.424397			−0.212198	−	0.977227i	$-0.568062\pi$
$757$	−11.6767			−0.424397			−0.212198	+	0.977227i	$0.568062\pi$
$758$	−4.73177	−	8.19566i	−0.171866	−	0.297680i
$759$	−1.33327	−	8.19694i	−0.0483948	−	0.297530i
$760$	5.36292	−	9.28886i	0.194534	−	0.336942i
$761$	−11.5862	+	20.0679i	−0.420000	+	0.727461i	−0.995939	−	0.0900318i	$-0.971303\pi$
$761$	−11.5862	+	20.0679i	−0.420000	+	0.727461i	0.575939	+	0.817492i	$0.304636\pi$
$762$	−9.81507	+	8.01597i	−0.355562	+	0.290388i
$763$	20.9136	+	36.2233i	0.757121	+	1.31137i
$764$	4.31361			0.156061
$765$	−12.9269	+	63.4081i	−0.467375	+	2.29252i
$766$	22.0119			0.795323
$767$	15.7941	+	27.3562i	0.570291	+	0.987774i
$768$	1.61958	+	0.613974i	0.0584415	+	0.0221549i
$769$	−15.4780	+	26.8086i	−0.558150	+	0.966744i	0.439501	+	0.898242i	$0.355155\pi$
$769$	−15.4780	+	26.8086i	−0.558150	+	0.966744i	−0.997651	+	0.0685023i	$0.978178\pi$
$770$	28.4166	−	49.2189i	1.02406	−	1.77373i
$771$	−15.8461	−	6.00716i	−0.570682	−	0.216343i
$772$	−3.86487	−	6.69416i	−0.139100	−	0.240928i
$773$	−35.6701			−1.28296			−0.641482	−	0.767138i	$-0.721680\pi$
$773$	−35.6701			−1.28296			−0.641482	+	0.767138i	$0.721680\pi$
$774$	0.464604	−	2.27893i	0.0166999	−	0.0819146i
$775$	10.8322			0.389106
$776$	−0.770482	−	1.33451i	−0.0276587	−	0.0479063i
$777$	46.3124	−	37.8234i	1.66145	−	1.35691i
$778$	8.50635	−	14.7334i	0.304967	−	0.528219i
$779$	−8.68722	+	15.0467i	−0.311252	+	0.539104i
$780$	4.83959	+	29.7537i	0.173285	+	1.06535i
$781$	−39.4272	−	68.2899i	−1.41082	−	2.44361i
$782$	6.35504			0.227256
$783$	−6.82476	+	10.8022i	−0.243897	+	0.386040i
$784$	5.19506			0.185538
$785$	32.0858	+	55.5742i	1.14519	+	1.98353i
$786$	−1.98849	−	12.2252i	−0.0709272	−	0.436060i
$787$	18.5980	−	32.2127i	0.662947	−	1.14826i	−0.316890	−	0.948462i	$-0.602639\pi$
$787$	18.5980	−	32.2127i	0.662947	−	1.14826i	0.979838	−	0.199796i	$-0.0640279\pi$
$788$	9.73340	−	16.8587i	0.346738	−	0.600568i
$789$	12.3125	−	10.0556i	0.438335	−	0.357989i
$790$	11.6435	+	20.1671i	0.414257	+	0.717515i
$791$	−13.4683			−0.478879
$792$	−10.7692	−	9.53551i	−0.382668	−	0.338829i
$793$	−6.48407			−0.230256
$794$	7.22787	+	12.5190i	0.256507	+	0.444284i
$795$	35.2771	+	13.3734i	1.25115	+	0.474304i
$796$	−0.330748	+	0.572872i	−0.0117230	+	0.0203049i
$797$	11.0075	−	19.0656i	0.389907	−	0.675339i	−0.602529	−	0.798097i	$-0.705840\pi$
$797$	11.0075	−	19.0656i	0.389907	−	0.675339i	0.992437	+	0.122757i	$0.0391737\pi$
$798$	−17.8722	−	6.77526i	−0.632669	−	0.239842i
$799$	35.3252	+	61.1851i	1.24972	+	2.16457i
$800$	−6.52115			−0.230558
$801$	−41.2253	+	13.7754i	−1.45662	+	0.486731i
$802$	0.680268			0.0240211
$803$	−14.1348	−	24.4822i	−0.498806	−	0.863957i
$804$	−4.68473	+	3.82602i	−0.165218	+	0.134933i
$805$	−5.92666	+	10.2653i	−0.208887	+	0.361803i
$806$	−4.25861	+	7.37612i	−0.150003	+	0.259813i
$807$	5.36240	+	32.9680i	0.188765	+	1.16053i
$808$	4.84505	+	8.39188i	0.170448	+	0.295225i
$809$	−32.3565			−1.13759			−0.568797	−	0.822478i	$-0.692591\pi$
$809$	−32.3565			−1.13759			−0.568797	+	0.822478i	$0.692591\pi$
$810$	−24.4119	+	18.3650i	−0.857745	+	0.645282i
$811$	−53.8736			−1.89176			−0.945879	−	0.324520i	$-0.894797\pi$
$811$	−53.8736			−1.89176			−0.945879	+	0.324520i	$0.894797\pi$
$812$	4.29365	+	7.43682i	0.150678	+	0.260981i
$813$	−3.48064	−	21.3989i	−0.122072	−	0.750494i
$814$	−23.6998	+	41.0492i	−0.830677	+	1.43878i
$815$	−26.6033	+	46.0784i	−0.931875	+	1.61405i
$816$	8.52533	−	6.96264i	0.298446	−	0.243741i
$817$	1.22492	+	2.12162i	0.0428544	+	0.0742261i
$818$	17.1440			0.599427
$819$	50.9485	−	17.0244i	1.78028	−	0.594882i
$820$	18.6627			0.651730
$821$	−17.6853	−	30.6319i	−0.617222	−	1.06906i	−0.989990	−	0.141135i	$-0.954925\pi$
$821$	−17.6853	−	30.6319i	−0.617222	−	1.06906i	0.372768	−	0.927924i	$-0.378409\pi$
$822$	−10.9565	−	4.15356i	−0.382152	−	0.144872i
$823$	−11.6367	+	20.1554i	−0.405630	+	0.702572i	−0.994395	−	0.105733i	$-0.966281\pi$
$823$	−11.6367	+	20.1554i	−0.405630	+	0.702572i	0.588765	+	0.808305i	$0.299615\pi$
$824$	−5.56148	+	9.63277i	−0.193744	+	0.335574i
$825$	50.6393	+	19.1971i	1.76304	+	0.668358i
$826$	10.7568	+	18.6313i	0.374277	+	0.648267i
$827$	8.57319			0.298119			0.149060	−	0.988828i	$-0.452375\pi$
$827$	8.57319			0.298119			0.149060	+	0.988828i	$0.452375\pi$
$828$	2.24607	+	1.98876i	0.0780564	+	0.0691142i
$829$	31.4933			1.09381			0.546903	−	0.837196i	$-0.315806\pi$
$829$	31.4933			1.09381			0.546903	+	0.837196i	$0.315806\pi$
$830$	11.1946	+	19.3896i	0.388570	+	0.673022i
$831$	33.5620	−	27.4101i	1.16425	−	0.950847i
$832$	2.56373	−	4.44052i	0.0888815	−	0.153947i
$833$	16.5074	−	28.5917i	0.571948	−	0.990643i
$834$	0.797009	+	4.90000i	0.0275982	+	0.169673i
$835$	21.4151	+	37.0921i	0.741101	+	1.28362i
$836$	15.1511			0.524013
$837$	−8.62444	−	0.344040i	−0.298104	−	0.0118918i
$838$	−10.5994			−0.366150
$839$	−3.74560	−	6.48757i	−0.129312	−	0.223976i	0.794098	−	0.607790i	$-0.207944\pi$
$839$	−3.74560	−	6.48757i	−0.129312	−	0.223976i	−0.923410	+	0.383814i	$0.874610\pi$
$840$	3.29608	+	20.2642i	0.113726	+	0.699183i
$841$	11.4766	−	19.8780i	0.395744	−	0.685448i
$842$	−3.80320	+	6.58733i	−0.131067	+	0.227014i
$843$	5.92510	−	4.83903i	0.204071	−	0.166665i
$844$	−6.05925	−	10.4949i	−0.208568	−	0.361250i
$845$	45.1132			1.55194
$846$	−6.66234	+	32.6795i	−0.229056	+	1.12354i
$847$	41.8679			1.43860
$848$	−3.20858	−	5.55742i	−0.110183	−	0.190842i
$849$	−21.0817	−	7.99197i	−0.723523	−	0.274284i
$850$	−20.7211	+	35.8900i	−0.710727	+	1.23102i
$851$	4.94291	−	8.56138i	0.169441	−	0.293480i
$852$	26.6359	+	10.0975i	0.912529	+	0.345935i
$853$	11.2986	+	19.5698i	0.386858	+	0.670058i	0.992025	−	0.126041i	$-0.0402270\pi$
$853$	11.2986	+	19.5698i	0.386858	+	0.670058i	−0.605167	+	0.796099i	$0.706894\pi$
$854$	−4.41607			−0.151115
$855$	6.42779	−	31.5290i	0.219826	−	1.07827i
$856$	14.8829			0.508688
$857$	18.2605	+	31.6281i	0.623766	+	1.08039i	0.988778	+	0.149392i	$0.0477316\pi$
$857$	18.2605	+	31.6281i	0.623766	+	1.08039i	−0.365012	+	0.931003i	$0.618935\pi$
$858$	−32.9805	+	26.9352i	−1.12594	+	0.919553i
$859$	0.936765	−	1.62252i	0.0319620	−	0.0553598i	−0.849602	−	0.527424i	$-0.823158\pi$
$859$	0.936765	−	1.62252i	0.0319620	−	0.0553598i	0.881564	+	0.472065i	$0.156491\pi$
$860$	1.31574	−	2.27893i	0.0448665	−	0.0777110i
$861$	−5.33920	−	32.8253i	−0.181960	−	1.11868i
$862$	−16.5416	−	28.6509i	−0.563409	−	0.975852i
$863$	−25.6962			−0.874710			−0.437355	−	0.899289i	$-0.644085\pi$
$863$	−25.6962			−0.874710			−0.437355	+	0.899289i	$0.644085\pi$
$864$	5.19202	+	0.207117i	0.176636	+	0.00704625i
$865$	−2.04634			−0.0695777
$866$	15.3048	+	26.5087i	0.520079	+	0.900803i
$867$	−6.50314	−	39.9812i	−0.220858	−	1.35783i
$868$	−2.90039	+	5.02362i	−0.0984457	+	0.170513i
$869$	−16.4474	+	28.4877i	−0.557940	+	0.966380i
$870$	−11.1971	+	9.14468i	−0.379617	+	0.310034i
$871$	8.95293	+	15.5069i	0.303358	+	0.525432i
$872$	11.9775			0.405609
$873$	−3.46111	−	3.06461i	−0.117141	−	0.103721i
$874$	−3.15998			−0.106888
$875$	−9.01534	−	15.6150i	−0.304774	−	0.527884i
$876$	9.54904	+	3.61999i	0.322632	+	0.122308i
$877$	−15.2805	+	26.4666i	−0.515985	+	0.893713i	0.483842	+	0.875155i	$0.339241\pi$
$877$	−15.2805	+	26.4666i	−0.515985	+	0.893713i	−0.999828	+	0.0185578i	$0.994093\pi$
$878$	2.23860	−	3.87738i	0.0755492	−	0.130855i
$879$	28.0354	+	10.6281i	0.945611	+	0.358476i
$880$	−8.13728	−	14.0942i	−0.274308	−	0.475115i
$881$	−10.3977			−0.350309			−0.175154	−	0.984541i	$-0.556042\pi$
$881$	−10.3977			−0.350309			−0.175154	+	0.984541i	$0.556042\pi$
$882$	14.7818	−	4.93934i	0.497728	−	0.166316i
$883$	11.5454			0.388535			0.194267	−	0.980949i	$-0.437767\pi$
$883$	11.5454			0.388535			0.194267	+	0.980949i	$0.437767\pi$
$884$	−16.2926	−	28.2197i	−0.547980	−	0.949130i
$885$	−28.0519	+	22.9100i	−0.942954	+	0.770111i
$886$	−6.69807	+	11.6014i	−0.225026	+	0.389757i
$887$	−2.86979	+	4.97062i	−0.0963581	+	0.166897i	−0.910175	−	0.414225i	$-0.864053\pi$
$887$	−2.86979	+	4.97062i	−0.0963581	+	0.166897i	0.813817	+	0.581122i	$0.197386\pi$
$888$	−2.74897	−	16.9006i	−0.0922495	−	0.567148i
$889$	12.7751	+	22.1270i	0.428461	+	0.742117i
$890$	−49.1785			−1.64847
$891$	−39.7084	−	16.8927i	−1.33028	−	0.565928i
$892$	19.1955			0.642712
$893$	−17.5651	−	30.4236i	−0.587793	−	1.01809i
$894$	0.278406	+	1.71164i	0.00931130	+	0.0572457i
$895$	−17.2429	+	29.8656i	−0.576367	+	0.998297i
$896$	1.74607	−	3.02428i	0.0583322	−	0.101034i
$897$	6.87853	−	5.61770i	0.229668	−	0.187570i
$898$	3.53535	+	6.12341i	0.117976	+	0.204341i
$899$	−4.08469			−0.136232
$900$	−18.5550	+	6.20015i	−0.618499	+	0.206672i
$901$	−40.7812			−1.35862
$902$	13.1813	+	22.8307i	0.438890	+	0.760179i
$903$	−4.38477	−	1.66225i	−0.145916	−	0.0553161i
$904$	−1.92838	+	3.34005i	−0.0641369	+	0.111088i
$905$	12.5956	−	21.8162i	0.418692	−	0.725195i
$906$	4.25818	+	1.61425i	0.141469	+	0.0536300i
$907$	−1.37140	−	2.37533i	−0.0455366	−	0.0788717i	0.842359	−	0.538917i	$-0.181166\pi$
$907$	−1.37140	−	2.37533i	−0.0455366	−	0.0788717i	−0.887895	+	0.460046i	$0.847833\pi$
$908$	15.5775			0.516958
$909$	21.7647	+	19.2713i	0.721888	+	0.639188i
$910$	60.7775			2.01476
$911$	−23.1894	−	40.1653i	−0.768301	−	1.33074i	−0.938484	−	0.345323i	$-0.887769\pi$
$911$	−23.1894	−	40.1653i	−0.768301	−	1.33074i	0.170183	−	0.985412i	$-0.445564\pi$
$912$	−4.23913	+	3.46210i	−0.140372	+	0.114642i
$913$	−15.8133	+	27.3894i	−0.523343	+	0.906456i
$914$	0.00878737	−	0.0152202i	0.000290660	−	0.000503438i
$915$	−1.19358	−	7.33808i	−0.0394584	−	0.242590i
$916$	5.29223	+	9.16642i	0.174860	+	0.302867i
$917$	−24.9723			−0.824658
$918$	17.6376	−	27.9168i	0.582129	−	0.921393i
$919$	3.46521			0.114307			0.0571534	−	0.998365i	$-0.481798\pi$
$919$	3.46521			0.114307			0.0571534	+	0.998365i	$0.481798\pi$
$920$	1.69714	+	2.93953i	0.0559531	+	0.0969136i
$921$	4.55718	+	28.0175i	0.150164	+	0.923208i
$922$	−15.6892	+	27.1745i	−0.516696	+	0.894944i
$923$	42.1636	−	73.0295i	1.38783	−	2.40379i
$924$	−22.4619	+	18.3446i	−0.738942	+	0.603495i
$925$	32.2335	+	55.8300i	1.05983	+	1.83568i
$926$	4.24714			0.139570
$927$	−6.66578	+	32.6964i	−0.218933	+	1.07389i
$928$	2.45904			0.0807218
$929$	−2.97858	−	5.15905i	−0.0977240	−	0.169263i	0.813018	−	0.582238i	$-0.197823\pi$
$929$	−2.97858	−	5.15905i	−0.0977240	−	0.169263i	−0.910742	+	0.412975i	$0.864490\pi$
$930$	−9.13155	−	3.46172i	−0.299435	−	0.113514i
$931$	−8.20814	+	14.2169i	−0.269011	+	0.465940i
$932$	−5.12383	+	8.87473i	−0.167837	+	0.290702i
$933$	−40.2687	−	15.2657i	−1.31834	−	0.499776i
$934$	15.4896	+	26.8287i	0.506835	+	0.877863i
$935$	−103.426			−3.38238
$936$	3.07279	−	15.0724i	0.100437	−	0.492656i
$937$	24.1914			0.790299			0.395149	−	0.918617i	$-0.370693\pi$
$937$	24.1914			0.790299			0.395149	+	0.918617i	$0.370693\pi$
$938$	6.09753	+	10.5612i	0.199091	+	0.344837i
$939$	−0.687598	+	0.561562i	−0.0224389	+	0.0183259i
$940$	−18.8675	+	32.6795i	−0.615390	+	1.06589i
$941$	−2.91264	+	5.04485i	−0.0949495	+	0.164457i	−0.909588	−	0.415512i	$-0.863602\pi$
$941$	−2.91264	+	5.04485i	−0.0949495	+	0.164457i	0.814638	+	0.579970i	$0.196936\pi$
$942$	−5.25718	−	32.3210i	−0.171288	−	1.05308i
$943$	−2.74914	−	4.76165i	−0.0895243	−	0.155061i
$944$	6.16058			0.200510
$945$	28.6452	+	54.5251i	0.931830	+	1.77370i
$946$	3.71719			0.120856
$947$	1.38014	+	2.39047i	0.0448485	+	0.0776799i	0.887578	−	0.460657i	$-0.152386\pi$
$947$	1.38014	+	2.39047i	0.0448485	+	0.0776799i	−0.842730	+	0.538337i	$0.819053\pi$
$948$	−1.90776	−	11.7289i	−0.0619611	−	0.380936i
$949$	15.1158	−	26.1813i	0.490679	−	0.849881i
$950$	10.3033	−	17.8459i	0.334284	−	0.578998i
$951$	−18.0399	+	14.7332i	−0.584983	+	0.477756i
$952$	−11.0964	−	19.2194i	−0.359635	−	0.622906i
$953$	14.0362			0.454679			0.227339	−	0.973816i	$-0.426997\pi$
$953$	14.0362			0.454679			0.227339	+	0.973816i	$0.426997\pi$
$954$	−14.4134	−	12.7622i	−0.466651	−	0.413191i
$955$	14.6416			0.473792
$956$	−6.67263	−	11.5573i	−0.215808	−	0.373791i
$957$	−19.0954	−	7.23897i	−0.617266	−	0.234003i
$958$	13.9406	−	24.1459i	0.450401	−	0.780117i
$959$	−11.8122	+	20.4594i	−0.381437	+	0.660668i
$960$	5.49731	+	2.08400i	0.177425	+	0.0672609i
$961$	14.1204	+	24.4572i	0.455496	+	0.788943i
$962$	−50.6893			−1.63429
$963$	42.3472	−	14.1503i	1.36462	−	0.455988i
$964$	−30.0129			−0.966651
$965$	−13.1185	−	22.7219i	−0.422299	−	0.731443i
$966$	4.68473	−	3.82602i	0.150729	−	0.123100i
$967$	1.97836	−	3.42662i	0.0636197	−	0.110193i	−0.832461	−	0.554083i	$-0.813069\pi$
$967$	1.97836	−	3.42662i	0.0636197	−	0.110193i	0.896081	+	0.443891i	$0.146402\pi$
$968$	5.99458	−	10.3829i	0.192673	−	0.333720i
$969$	5.58418	+	34.3315i	0.179390	+	1.10289i
$970$	−2.61523	−	4.52972i	−0.0839701	−	0.145440i
$971$	15.3862			0.493767			0.246884	−	0.969045i	$-0.420593\pi$
$971$	15.3862			0.493767			0.246884	+	0.969045i	$0.420593\pi$
$972$	14.9701	−	4.34713i	0.480165	−	0.139434i
$973$	10.0092			0.320879
$974$	10.4654	+	18.1266i	0.335332	+	0.580813i
$975$	9.29790	+	57.1633i	0.297771	+	1.83069i
$976$	−0.632287	+	1.09515i	−0.0202390	+	0.0350550i
$977$	13.0757	−	22.6477i	0.418327	−	0.724564i	−0.577444	−	0.816430i	$-0.695950\pi$
$977$	13.0757	−	22.6477i	0.418327	−	0.724564i	0.995771	+	0.0918663i	$0.0292832\pi$
$978$	21.0286	−	17.1741i	0.672422	−	0.549167i
$979$	−34.7344	−	60.1617i	−1.11012	−	1.92278i
$980$	17.6335			0.563282
$981$	34.0802	−	11.3879i	1.08810	−	0.363588i
$982$	36.6029			1.16804
$983$	−23.6315	−	40.9310i	−0.753728	−	1.30550i	−0.946004	−	0.324155i	$-0.894920\pi$
$983$	−23.6315	−	40.9310i	−0.753728	−	1.30550i	0.192276	−	0.981341i	$-0.438413\pi$
$984$	−8.90490	−	3.37580i	−0.283878	−	0.107617i
$985$	33.0379	−	57.2233i	1.05267	−	1.82329i
$986$	7.81363	−	13.5336i	0.248837	−	0.430998i
$987$	62.8769	+	23.8363i	2.00139	+	0.758718i
$988$	8.10134	+	14.0319i	0.257738	+	0.446415i
$989$	−0.775270			−0.0246522
$990$	−36.5538	−	32.3662i	−1.16176	−	1.02867i
$991$	−2.89228			−0.0918763			−0.0459382	−	0.998944i	$-0.514628\pi$
$991$	−2.89228			−0.0918763			−0.0459382	+	0.998944i	$0.514628\pi$
$992$	0.830547	+	1.43855i	0.0263699	+	0.0456740i
$993$	1.01353	−	0.827751i	0.0321634	−	0.0262679i
$994$	28.7162	−	49.7379i	0.910822	−	1.57759i
$995$	−1.12265	+	1.94449i	−0.0355905	+	0.0616445i
$996$	−1.83420	−	11.2767i	−0.0581190	−	0.357314i
$997$	−16.0958	−	27.8787i	−0.509758	−	0.882927i	−0.999936	−	0.0113048i	$-0.996402\pi$
$997$	−16.0958	−	27.8787i	−0.509758	−	0.882927i	0.490178	−	0.871622i	$-0.336932\pi$
$998$	−7.77793			−0.246206
$999$	−23.8905	−	45.4746i	−0.755862	−	1.43875i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	414.2.e.d.139.4	✓	10
3.2	odd	2		1242.2.e.b.415.5		10
9.2	odd	6		1242.2.e.b.829.5		10
9.4	even	3		3726.2.a.r.1.5		5
9.5	odd	6		3726.2.a.u.1.1		5
9.7	even	3	inner	414.2.e.d.277.4	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
414.2.e.d.139.4	✓	10	1.1	even	1	trivial
414.2.e.d.277.4	yes	10	9.7	even	3	inner
1242.2.e.b.415.5		10	3.2	odd	2
1242.2.e.b.829.5		10	9.2	odd	6
3726.2.a.r.1.5		5	9.4	even	3
3726.2.a.u.1.1		5	9.5	odd	6

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:	\( N \)	\(=\)	\( 414 = 2 \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	414.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.278072 - 1.70958i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.69714 + 2.93953i) q^{5} +(1.34151 - 1.09561i) q^{6} +(-1.74607 - 3.02428i) q^{7} -1.00000 q^{8} +(-2.84535 + 0.950775i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.278072 - 1.70958i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.69714 + 2.93953i) q^{5} +(1.34151 - 1.09561i) q^{6} +(-1.74607 - 3.02428i) q^{7} -1.00000 q^{8} +(-2.84535 + 0.950775i) q^{9} -3.39428 q^{10} +(-2.39735 - 4.15233i) q^{11} +(1.61958 + 0.613974i) q^{12} +(2.56373 - 4.44052i) q^{13} +(1.74607 - 3.02428i) q^{14} +(5.49731 + 2.08400i) q^{15} +(-0.500000 - 0.866025i) q^{16} -6.35504 q^{17} +(-2.24607 - 1.98876i) q^{18} +3.15998 q^{19} +(-1.69714 - 2.93953i) q^{20} +(-4.68473 + 3.82602i) q^{21} +(2.39735 - 4.15233i) q^{22} +(-0.500000 + 0.866025i) q^{23} +(0.278072 + 1.70958i) q^{24} +(-3.26058 - 5.64748i) q^{25} +5.12747 q^{26} +(2.41664 + 4.59998i) q^{27} +3.49214 q^{28} +(1.22952 + 2.12959i) q^{29} +(0.943856 + 5.80281i) q^{30} +(-0.830547 + 1.43855i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-6.43212 + 5.25312i) q^{33} +(-3.17752 - 5.50362i) q^{34} +11.8533 q^{35} +(0.599280 - 2.93953i) q^{36} -9.88582 q^{37} +(1.57999 + 2.73662i) q^{38} +(-8.30434 - 3.14813i) q^{39} +(1.69714 - 2.93953i) q^{40} +(-2.74914 + 4.76165i) q^{41} +(-5.65580 - 2.14409i) q^{42} +(0.387635 + 0.671404i) q^{43} +4.79470 q^{44} +(2.03413 - 9.97761i) q^{45} -1.00000 q^{46} +(-5.55862 - 9.62781i) q^{47} +(-1.34151 + 1.09561i) q^{48} +(-2.59753 + 4.49906i) q^{49} +(3.26058 - 5.64748i) q^{50} +(1.76716 + 10.8645i) q^{51} +(2.56373 + 4.44052i) q^{52} +6.41715 q^{53} +(-2.77538 + 4.39287i) q^{54} +16.2746 q^{55} +(1.74607 + 3.02428i) q^{56} +(-0.878701 - 5.40224i) q^{57} +(-1.22952 + 2.12959i) q^{58} +(-3.08029 + 5.33522i) q^{59} +(-4.55345 + 3.71881i) q^{60} +(-0.632287 - 1.09515i) q^{61} -1.66109 q^{62} +(7.84360 + 6.94503i) q^{63} +1.00000 q^{64} +(8.70204 + 15.0724i) q^{65} +(-7.76540 - 2.94382i) q^{66} +(-1.74607 + 3.02428i) q^{67} +(3.17752 - 5.50362i) q^{68} +(1.61958 + 0.613974i) q^{69} +(5.92666 + 10.2653i) q^{70} +16.4462 q^{71} +(2.84535 - 0.950775i) q^{72} +5.89600 q^{73} +(-4.94291 - 8.56138i) q^{74} +(-8.74817 + 7.14463i) q^{75} +(-1.57999 + 2.73662i) q^{76} +(-8.37189 + 14.5005i) q^{77} +(-1.42581 - 8.76584i) q^{78} +(-3.43033 - 5.94150i) q^{79} +3.39428 q^{80} +(7.19205 - 5.41058i) q^{81} -5.49828 q^{82} +(-3.29807 - 5.71243i) q^{83} +(-0.971068 - 5.97011i) q^{84} +(10.7854 - 18.6809i) q^{85} +(-0.387635 + 0.671404i) q^{86} +(3.29881 - 2.69414i) q^{87} +(2.39735 + 4.15233i) q^{88} +14.4886 q^{89} +(9.65793 - 3.22720i) q^{90} -17.9059 q^{91} +(-0.500000 - 0.866025i) q^{92} +(2.69027 + 1.01987i) q^{93} +(5.55862 - 9.62781i) q^{94} +(-5.36292 + 9.28886i) q^{95} +(-1.61958 - 0.613974i) q^{96} +(0.770482 + 1.33451i) q^{97} -5.19506 q^{98} +(10.7692 + 9.53551i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 5 q^{2} - 3 q^{3} - 5 q^{4} - q^{5} - 3 q^{6} + 5 q^{7} - 10 q^{8} - 3 q^{9}+O(q^{10}) \) 10 * q + 5 * q^2 - 3 * q^3 - 5 * q^4 - q^5 - 3 * q^6 + 5 * q^7 - 10 * q^8 - 3 * q^9	\( 10 q + 5 q^{2} - 3 q^{3} - 5 q^{4} - q^{5} - 3 q^{6} + 5 q^{7} - 10 q^{8} - 3 q^{9} - 2 q^{10} - 11 q^{11} + 6 q^{13} - 5 q^{14} + 9 q^{15} - 5 q^{16} + 2 q^{17} - 6 q^{19} - q^{20} - 21 q^{21} + 11 q^{22} - 5 q^{23} + 3 q^{24} + 12 q^{26} + 27 q^{27} - 10 q^{28} - 8 q^{29} + 9 q^{30} + 4 q^{31} + 5 q^{32} - 24 q^{33} + q^{34} + 46 q^{35} + 3 q^{36} - 28 q^{37} - 3 q^{38} - 45 q^{39} + q^{40} - 24 q^{41} - 27 q^{42} + 27 q^{43} + 22 q^{44} + 27 q^{45} - 10 q^{46} - 9 q^{47} + 3 q^{48} - 12 q^{49} - 6 q^{51} + 6 q^{52} - 26 q^{53} + 18 q^{54} + 16 q^{55} - 5 q^{56} - 18 q^{57} + 8 q^{58} - 9 q^{59} + 3 q^{61} + 8 q^{62} + 42 q^{63} + 10 q^{64} + 5 q^{65} - 3 q^{66} + 5 q^{67} - q^{68} + 23 q^{70} + 54 q^{71} + 3 q^{72} + 34 q^{73} - 14 q^{74} - 45 q^{75} + 3 q^{76} - 13 q^{77} - 30 q^{78} - 11 q^{79} + 2 q^{80} + 33 q^{81} - 48 q^{82} - 23 q^{83} - 6 q^{84} + 23 q^{85} - 27 q^{86} + 63 q^{87} + 11 q^{88} + 78 q^{89} + 51 q^{90} - 30 q^{91} - 5 q^{92} - 27 q^{93} + 9 q^{94} - 37 q^{95} + 28 q^{97} - 24 q^{98} + 24 q^{99}+O(q^{100}) \) 10 * q + 5 * q^2 - 3 * q^3 - 5 * q^4 - q^5 - 3 * q^6 + 5 * q^7 - 10 * q^8 - 3 * q^9 - 2 * q^10 - 11 * q^11 + 6 * q^13 - 5 * q^14 + 9 * q^15 - 5 * q^16 + 2 * q^17 - 6 * q^19 - q^20 - 21 * q^21 + 11 * q^22 - 5 * q^23 + 3 * q^24 + 12 * q^26 + 27 * q^27 - 10 * q^28 - 8 * q^29 + 9 * q^30 + 4 * q^31 + 5 * q^32 - 24 * q^33 + q^34 + 46 * q^35 + 3 * q^36 - 28 * q^37 - 3 * q^38 - 45 * q^39 + q^40 - 24 * q^41 - 27 * q^42 + 27 * q^43 + 22 * q^44 + 27 * q^45 - 10 * q^46 - 9 * q^47 + 3 * q^48 - 12 * q^49 - 6 * q^51 + 6 * q^52 - 26 * q^53 + 18 * q^54 + 16 * q^55 - 5 * q^56 - 18 * q^57 + 8 * q^58 - 9 * q^59 + 3 * q^61 + 8 * q^62 + 42 * q^63 + 10 * q^64 + 5 * q^65 - 3 * q^66 + 5 * q^67 - q^68 + 23 * q^70 + 54 * q^71 + 3 * q^72 + 34 * q^73 - 14 * q^74 - 45 * q^75 + 3 * q^76 - 13 * q^77 - 30 * q^78 - 11 * q^79 + 2 * q^80 + 33 * q^81 - 48 * q^82 - 23 * q^83 - 6 * q^84 + 23 * q^85 - 27 * q^86 + 63 * q^87 + 11 * q^88 + 78 * q^89 + 51 * q^90 - 30 * q^91 - 5 * q^92 - 27 * q^93 + 9 * q^94 - 37 * q^95 + 28 * q^97 - 24 * q^98 + 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more