LMFDB - Embedded newform 966.2.i.n.277.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(277,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("966.277");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.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:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.173309020416.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 5x^{6} - 28x^{5} - 4x^{4} + 70x^{3} + 51x^{2} + 406x + 841 $ x^8 - 5x^6 - 28x^5 - 4x^4 + 70x^3 + 51x^2 + 406x + 841
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			277.2
Root			$-1.61272 + 2.45863i$ of defining polynomial
Character	$\chi$	$=$	966.277
Dual form			966.2.i.n.415.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.739514 - 1.28088i) q^{5} +1.00000 q^{6} +(1.32288 - 2.29129i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.739514 - 1.28088i) q^{5} +1.00000 q^{6} +(1.32288 - 2.29129i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.739514 - 1.28088i) q^{10} +(-2.85224 + 4.94022i) q^{11} +(0.500000 + 0.866025i) q^{12} +6.35023 q^{13} +2.64575 q^{14} -1.47903 q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.06239 - 3.57216i) q^{17} +(0.500000 - 0.866025i) q^{18} +(-1.69609 - 2.93771i) q^{19} +1.47903 q^{20} +(-1.32288 - 2.29129i) q^{21} -5.70448 q^{22} +(-0.500000 - 0.866025i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(1.40624 - 2.43567i) q^{25} +(3.17511 + 5.49946i) q^{26} -1.00000 q^{27} +(1.32288 + 2.29129i) q^{28} +2.39217 q^{29} +(-0.739514 - 1.28088i) q^{30} +(3.90624 - 6.76580i) q^{31} +(0.500000 - 0.866025i) q^{32} +(2.85224 + 4.94022i) q^{33} +4.12478 q^{34} -3.91314 q^{35} +1.00000 q^{36} +(-4.17511 - 7.23151i) q^{37} +(1.69609 - 2.93771i) q^{38} +(3.17511 - 5.49946i) q^{39} +(0.739514 + 1.28088i) q^{40} +7.39217 q^{41} +(1.32288 - 2.29129i) q^{42} +2.00000 q^{43} +(-2.85224 - 4.94022i) q^{44} +(-0.739514 + 1.28088i) q^{45} +(0.500000 - 0.866025i) q^{46} +(-5.11071 - 8.85202i) q^{47} -1.00000 q^{48} +(-3.50000 - 6.06218i) q^{49} +2.81247 q^{50} +(-2.06239 - 3.57216i) q^{51} +(-3.17511 + 5.49946i) q^{52} +(-0.260486 + 0.451174i) q^{53} +(-0.500000 - 0.866025i) q^{54} +8.43709 q^{55} +(-1.32288 + 2.29129i) q^{56} -3.39217 q^{57} +(1.19609 + 2.07168i) q^{58} +(-3.68918 + 6.38985i) q^{59} +(0.739514 - 1.28088i) q^{60} +(2.52097 + 4.36645i) q^{61} +7.81247 q^{62} -2.64575 q^{63} +1.00000 q^{64} +(-4.69609 - 8.13386i) q^{65} +(-2.85224 + 4.94022i) q^{66} +(-7.70448 + 13.3445i) q^{67} +(2.06239 + 3.57216i) q^{68} -1.00000 q^{69} +(-1.95657 - 3.38888i) q^{70} +9.87120 q^{71} +(0.500000 + 0.866025i) q^{72} +(-4.46496 + 7.73354i) q^{73} +(4.17511 - 7.23151i) q^{74} +(-1.40624 - 2.43567i) q^{75} +3.39217 q^{76} +(7.54631 + 13.0706i) q^{77} +6.35023 q^{78} +(6.71505 + 11.6308i) q^{79} +(-0.739514 + 1.28088i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(3.69609 + 6.40181i) q^{82} -9.22143 q^{83} +2.64575 q^{84} -6.10067 q^{85} +(1.00000 + 1.73205i) q^{86} +(1.19609 - 2.07168i) q^{87} +(2.85224 - 4.94022i) q^{88} +(3.21706 + 5.57211i) q^{89} -1.47903 q^{90} +(8.40056 - 14.5502i) q^{91} +1.00000 q^{92} +(-3.90624 - 6.76580i) q^{93} +(5.11071 - 8.85202i) q^{94} +(-2.50856 + 4.34495i) q^{95} +(-0.500000 - 0.866025i) q^{96} -10.3640 q^{97} +(3.50000 - 6.06218i) q^{98} +5.70448 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} + 4 q^{3} - 4 q^{4} - 2 q^{5} + 8 q^{6} - 8 q^{8} - 4 q^{9}+O(q^{10}) $ 8 * q + 4 * q^2 + 4 * q^3 - 4 * q^4 - 2 * q^5 + 8 * q^6 - 8 * q^8 - 4 * q^9	$ 8 q + 4 q^{2} + 4 q^{3} - 4 q^{4} - 2 q^{5} + 8 q^{6} - 8 q^{8} - 4 q^{9} + 2 q^{10} - 6 q^{11} + 4 q^{12} - 4 q^{13} - 4 q^{15} - 4 q^{16} + 2 q^{17} + 4 q^{18} + 6 q^{19} + 4 q^{20} - 12 q^{22} - 4 q^{23} - 4 q^{24} - 6 q^{25} - 2 q^{26} - 8 q^{27} - 20 q^{29} - 2 q^{30} + 14 q^{31} + 4 q^{32} + 6 q^{33} + 4 q^{34} + 8 q^{36} - 6 q^{37} - 6 q^{38} - 2 q^{39} + 2 q^{40} + 20 q^{41} + 16 q^{43} - 6 q^{44} - 2 q^{45} + 4 q^{46} + 10 q^{47} - 8 q^{48} - 28 q^{49} - 12 q^{50} - 2 q^{51} + 2 q^{52} - 6 q^{53} - 4 q^{54} + 44 q^{55} + 12 q^{57} - 10 q^{58} - 24 q^{59} + 2 q^{60} + 28 q^{61} + 28 q^{62} + 8 q^{64} - 18 q^{65} - 6 q^{66} - 28 q^{67} + 2 q^{68} - 8 q^{69} + 32 q^{71} + 4 q^{72} - 6 q^{73} + 6 q^{74} + 6 q^{75} - 12 q^{76} - 14 q^{77} - 4 q^{78} + 4 q^{79} - 2 q^{80} - 4 q^{81} + 10 q^{82} + 28 q^{83} - 52 q^{85} + 8 q^{86} - 10 q^{87} + 6 q^{88} + 14 q^{89} - 4 q^{90} + 14 q^{91} + 8 q^{92} - 14 q^{93} - 10 q^{94} + 34 q^{95} - 4 q^{96} + 28 q^{98} + 12 q^{99}+O(q^{100}) $ 8 * q + 4 * q^2 + 4 * q^3 - 4 * q^4 - 2 * q^5 + 8 * q^6 - 8 * q^8 - 4 * q^9 + 2 * q^10 - 6 * q^11 + 4 * q^12 - 4 * q^13 - 4 * q^15 - 4 * q^16 + 2 * q^17 + 4 * q^18 + 6 * q^19 + 4 * q^20 - 12 * q^22 - 4 * q^23 - 4 * q^24 - 6 * q^25 - 2 * q^26 - 8 * q^27 - 20 * q^29 - 2 * q^30 + 14 * q^31 + 4 * q^32 + 6 * q^33 + 4 * q^34 + 8 * q^36 - 6 * q^37 - 6 * q^38 - 2 * q^39 + 2 * q^40 + 20 * q^41 + 16 * q^43 - 6 * q^44 - 2 * q^45 + 4 * q^46 + 10 * q^47 - 8 * q^48 - 28 * q^49 - 12 * q^50 - 2 * q^51 + 2 * q^52 - 6 * q^53 - 4 * q^54 + 44 * q^55 + 12 * q^57 - 10 * q^58 - 24 * q^59 + 2 * q^60 + 28 * q^61 + 28 * q^62 + 8 * q^64 - 18 * q^65 - 6 * q^66 - 28 * q^67 + 2 * q^68 - 8 * q^69 + 32 * q^71 + 4 * q^72 - 6 * q^73 + 6 * q^74 + 6 * q^75 - 12 * q^76 - 14 * q^77 - 4 * q^78 + 4 * q^79 - 2 * q^80 - 4 * q^81 + 10 * q^82 + 28 * q^83 - 52 * q^85 + 8 * q^86 - 10 * q^87 + 6 * q^88 + 14 * q^89 - 4 * q^90 + 14 * q^91 + 8 * q^92 - 14 * q^93 - 10 * q^94 + 34 * q^95 - 4 * q^96 + 28 * q^98 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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
$5$	−0.739514	−	1.28088i	−0.330721	−	0.572825i	0.651933	−	0.758277i	$-0.273959\pi$
$5$	−0.739514	−	1.28088i	−0.330721	−	0.572825i	−0.982653	+	0.185452i	$0.940625\pi$
$6$	1.00000			0.408248
$7$	1.32288	−	2.29129i	0.500000	−	0.866025i
$7$	1.32288	−	2.29129i	0.500000	−	0.866025i
$8$	−1.00000			−0.353553
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	0.739514	−	1.28088i	0.233855	−	0.405049i
$11$	−2.85224	+	4.94022i	−0.859982	+	1.48953i	0.0119622	+	0.999928i	$0.496192\pi$
$11$	−2.85224	+	4.94022i	−0.859982	+	1.48953i	−0.871945	+	0.489605i	$0.837141\pi$
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$	6.35023			1.76124			0.880618	−	0.473826i	$-0.157128\pi$
$13$	6.35023			1.76124			0.880618	+	0.473826i	$0.157128\pi$
$14$	2.64575			0.707107
$15$	−1.47903			−0.381884
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	2.06239	−	3.57216i	0.500203	−	0.866377i	−0.499797	−	0.866143i	$-0.666592\pi$
$17$	2.06239	−	3.57216i	0.500203	−	0.866377i	1.00000		0.000234490i	$-7.46404e-5\pi$
$18$	0.500000	−	0.866025i	0.117851	−	0.204124i
$19$	−1.69609	−	2.93771i	−0.389109	−	0.673956i	0.603221	−	0.797574i	$-0.293884\pi$
$19$	−1.69609	−	2.93771i	−0.389109	−	0.673956i	−0.992330	+	0.123618i	$0.960550\pi$
$20$	1.47903			0.330721
$21$	−1.32288	−	2.29129i	−0.288675	−	0.500000i
$22$	−5.70448			−1.21620
$23$	−0.500000	−	0.866025i	−0.104257	−	0.180579i
$23$	−0.500000	−	0.866025i	−0.104257	−	0.180579i
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$	1.40624	−	2.43567i	0.281247	−	0.487135i
$26$	3.17511	+	5.49946i	0.622691	+	1.07853i
$27$	−1.00000			−0.192450
$28$	1.32288	+	2.29129i	0.250000	+	0.433013i
$29$	2.39217			0.444215			0.222108	−	0.975022i	$-0.428706\pi$
$29$	2.39217			0.444215			0.222108	+	0.975022i	$0.428706\pi$
$30$	−0.739514	−	1.28088i	−0.135016	−	0.233855i
$31$	3.90624	−	6.76580i	0.701581	−	1.21517i	−0.266330	−	0.963882i	$-0.585811\pi$
$31$	3.90624	−	6.76580i	0.701581	−	1.21517i	0.967911	−	0.251292i	$-0.0808554\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	2.85224	+	4.94022i	0.496511	+	0.859982i
$34$	4.12478			0.707394
$35$	−3.91314			−0.661442
$36$	1.00000			0.166667
$37$	−4.17511	−	7.23151i	−0.686385	−	1.18885i	−0.973000	−	0.230807i	$-0.925863\pi$
$37$	−4.17511	−	7.23151i	−0.686385	−	1.18885i	0.286615	−	0.958046i	$-0.407470\pi$
$38$	1.69609	−	2.93771i	0.275141	−	0.476559i
$39$	3.17511	−	5.49946i	0.508425	−	0.880618i
$40$	0.739514	+	1.28088i	0.116927	+	0.202524i
$41$	7.39217			1.15446			0.577232	−	0.816580i	$-0.304133\pi$
$41$	7.39217			1.15446			0.577232	+	0.816580i	$0.304133\pi$
$42$	1.32288	−	2.29129i	0.204124	−	0.353553i
$43$	2.00000			0.304997			0.152499	−	0.988304i	$-0.451268\pi$
$43$	2.00000			0.304997			0.152499	+	0.988304i	$0.451268\pi$
$44$	−2.85224	−	4.94022i	−0.429991	−	0.744767i
$45$	−0.739514	+	1.28088i	−0.110240	+	0.190942i
$46$	0.500000	−	0.866025i	0.0737210	−	0.127688i
$47$	−5.11071	−	8.85202i	−0.745474	−	1.29120i	−0.949973	−	0.312333i	$-0.898890\pi$
$47$	−5.11071	−	8.85202i	−0.745474	−	1.29120i	0.204499	−	0.978867i	$-0.434444\pi$
$48$	−1.00000			−0.144338
$49$	−3.50000	−	6.06218i	−0.500000	−	0.866025i
$50$	2.81247			0.397744
$51$	−2.06239	−	3.57216i	−0.288792	−	0.500203i
$52$	−3.17511	+	5.49946i	−0.440309	+	0.762638i
$53$	−0.260486	+	0.451174i	−0.0357804	+	0.0619736i	−0.883361	−	0.468693i	$-0.844725\pi$
$53$	−0.260486	+	0.451174i	−0.0357804	+	0.0619736i	0.847581	+	0.530667i	$0.178058\pi$
$54$	−0.500000	−	0.866025i	−0.0680414	−	0.117851i
$55$	8.43709			1.13766
$56$	−1.32288	+	2.29129i	−0.176777	+	0.306186i
$57$	−3.39217			−0.449304
$58$	1.19609	+	2.07168i	0.157054	+	0.272025i
$59$	−3.68918	+	6.38985i	−0.480290	+	0.831887i	−0.999744	−	0.0226111i	$-0.992802\pi$
$59$	−3.68918	+	6.38985i	−0.480290	+	0.831887i	0.519454	+	0.854498i	$0.326135\pi$
$60$	0.739514	−	1.28088i	0.0954709	−	0.165360i
$61$	2.52097	+	4.36645i	0.322777	+	0.559067i	0.981060	−	0.193704i	$-0.0620502\pi$
$61$	2.52097	+	4.36645i	0.322777	+	0.559067i	−0.658283	+	0.752771i	$0.728717\pi$
$62$	7.81247			0.992185
$63$	−2.64575			−0.333333
$64$	1.00000			0.125000
$65$	−4.69609	−	8.13386i	−0.582478	−	1.00888i
$66$	−2.85224	+	4.94022i	−0.351086	+	0.608099i
$67$	−7.70448	+	13.3445i	−0.941252	+	1.63030i	−0.178164	+	0.984001i	$0.557016\pi$
$67$	−7.70448	+	13.3445i	−0.941252	+	1.63030i	−0.763088	+	0.646295i	$0.776318\pi$
$68$	2.06239	+	3.57216i	0.250102	+	0.433189i
$69$	−1.00000			−0.120386
$70$	−1.95657	−	3.38888i	−0.233855	−	0.405049i
$71$	9.87120			1.17150			0.585748	−	0.810493i	$-0.300801\pi$
$71$	9.87120			1.17150			0.585748	+	0.810493i	$0.300801\pi$
$72$	0.500000	+	0.866025i	0.0589256	+	0.102062i
$73$	−4.46496	+	7.73354i	−0.522584	+	0.905143i	0.477070	+	0.878865i	$0.341699\pi$
$73$	−4.46496	+	7.73354i	−0.522584	+	0.905143i	−0.999655	+	0.0262776i	$0.991635\pi$
$74$	4.17511	−	7.23151i	0.485347	−	0.840646i
$75$	−1.40624	−	2.43567i	−0.162378	−	0.281247i
$76$	3.39217			0.389109
$77$	7.54631	+	13.0706i	0.859982	+	1.48953i
$78$	6.35023			0.719022
$79$	6.71505	+	11.6308i	0.755502	+	1.30857i	0.945124	+	0.326710i	$0.105940\pi$
$79$	6.71505	+	11.6308i	0.755502	+	1.30857i	−0.189623	+	0.981857i	$0.560726\pi$
$80$	−0.739514	+	1.28088i	−0.0826802	+	0.143206i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	3.69609	+	6.40181i	0.408164	+	0.706961i
$83$	−9.22143			−1.01218			−0.506092	−	0.862480i	$-0.668910\pi$
$83$	−9.22143			−1.01218			−0.506092	+	0.862480i	$0.668910\pi$
$84$	2.64575			0.288675
$85$	−6.10067			−0.661710
$86$	1.00000	+	1.73205i	0.107833	+	0.186772i
$87$	1.19609	−	2.07168i	0.128234	−	0.222108i
$88$	2.85224	−	4.94022i	0.304050	−	0.526629i
$89$	3.21706	+	5.57211i	0.341007	+	0.590642i	0.984620	−	0.174709i	$-0.0558986\pi$
$89$	3.21706	+	5.57211i	0.341007	+	0.590642i	−0.643613	+	0.765351i	$0.722565\pi$
$90$	−1.47903			−0.155903
$91$	8.40056	−	14.5502i	0.880618	−	1.52528i
$92$	1.00000			0.104257
$93$	−3.90624	−	6.76580i	−0.405058	−	0.701581i
$94$	5.11071	−	8.85202i	0.527130	−	0.913016i
$95$	−2.50856	+	4.34495i	−0.257373	+	0.445783i
$96$	−0.500000	−	0.866025i	−0.0510310	−	0.0883883i
$97$	−10.3640			−1.05231			−0.526154	−	0.850389i	$-0.676367\pi$
$97$	−10.3640			−1.05231			−0.526154	+	0.850389i	$0.676367\pi$
$98$	3.50000	−	6.06218i	0.353553	−	0.612372i
$99$	5.70448			0.573322
$100$	1.40624	+	2.43567i	0.140624	+	0.243567i
$101$	−1.40624	+	2.43567i	−0.139926	+	0.242359i	−0.927468	−	0.373902i	$-0.878020\pi$
$101$	−1.40624	+	2.43567i	−0.139926	+	0.242359i	0.787543	+	0.616260i	$0.211353\pi$
$102$	2.06239	−	3.57216i	0.204207	−	0.353697i
$103$	6.27945	+	10.8763i	0.618732	+	1.07168i	0.989717	+	0.143037i	$0.0456868\pi$
$103$	6.27945	+	10.8763i	0.618732	+	1.07168i	−0.370985	+	0.928639i	$0.620980\pi$
$104$	−6.35023			−0.622691
$105$	−1.95657	+	3.38888i	−0.190942	+	0.330721i
$106$	−0.520971			−0.0506012
$107$	2.61071	+	4.52189i	0.252387	+	0.437148i	0.964183	−	0.265239i	$-0.0854510\pi$
$107$	2.61071	+	4.52189i	0.252387	+	0.437148i	−0.711795	+	0.702387i	$0.752118\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$	4.23750	−	7.33957i	0.405879	−	0.703004i	−0.588544	−	0.808465i	$-0.700299\pi$
$109$	4.23750	−	7.33957i	0.405879	−	0.703004i	0.994423	+	0.105462i	$0.0336320\pi$
$110$	4.21854	+	7.30673i	0.402222	+	0.696669i
$111$	−8.35023			−0.792569
$112$	−2.64575			−0.250000
$113$	0.725281			0.0682287			0.0341144	−	0.999418i	$-0.489139\pi$
$113$	0.725281			0.0682287			0.0341144	+	0.999418i	$0.489139\pi$
$114$	−1.69609	−	2.93771i	−0.158853	−	0.275141i
$115$	−0.739514	+	1.28088i	−0.0689601	+	0.119442i
$116$	−1.19609	+	2.07168i	−0.111054	+	0.192351i
$117$	−3.17511	−	5.49946i	−0.293539	−	0.508425i
$118$	−7.37836			−0.679233
$119$	−5.45657	−	9.45106i	−0.500203	−	0.866377i
$120$	1.47903			0.135016
$121$	−10.7705	−	18.6551i	−0.979139	−	1.69592i
$122$	−2.52097	+	4.36645i	−0.228238	+	0.395320i
$123$	3.69609	−	6.40181i	0.333265	−	0.577232i
$124$	3.90624	+	6.76580i	0.350790	+	0.607587i
$125$	−11.5549			−1.03350
$126$	−1.32288	−	2.29129i	−0.117851	−	0.204124i
$127$	0.0138109			0.00122552			0.000612760	−	1.00000i	$-0.499805\pi$
$127$	0.0138109			0.00122552			0.000612760		1.00000i	$0.499805\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	1.00000	−	1.73205i	0.0880451	−	0.152499i
$130$	4.69609	−	8.13386i	0.411874	−	0.713387i
$131$	7.24807	+	12.5540i	0.633267	+	1.09685i	0.986879	+	0.161459i	$0.0516199\pi$
$131$	7.24807	+	12.5540i	0.633267	+	1.09685i	−0.353612	+	0.935392i	$0.615047\pi$
$132$	−5.70448			−0.496511
$133$	−8.97484			−0.778217
$134$	−15.4090			−1.33113
$135$	0.739514	+	1.28088i	0.0636473	+	0.110240i
$136$	−2.06239	+	3.57216i	−0.176848	+	0.306311i
$137$	−4.01206	+	6.94908i	−0.342773	+	0.593700i	−0.984947	−	0.172859i	$-0.944700\pi$
$137$	−4.01206	+	6.94908i	−0.342773	+	0.593700i	0.642174	+	0.766559i	$0.278033\pi$
$138$	−0.500000	−	0.866025i	−0.0425628	−	0.0737210i
$139$	14.2214			1.20625			0.603123	−	0.797648i	$-0.293923\pi$
$139$	14.2214			1.20625			0.603123	+	0.797648i	$0.293923\pi$
$140$	1.95657	−	3.38888i	0.165360	−	0.286413i
$141$	−10.2214			−0.860800
$142$	4.93560	+	8.54871i	0.414186	+	0.717392i
$143$	−18.1124	+	31.3715i	−1.51463	+	2.62342i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	−1.76905	−	3.06408i	−0.146911	−	0.254458i
$146$	−8.92993			−0.739046
$147$	−7.00000			−0.577350
$148$	8.35023			0.686385
$149$	11.6417	+	20.1641i	0.953728	+	1.65190i	0.737253	+	0.675617i	$0.236123\pi$
$149$	11.6417	+	20.1641i	0.953728	+	1.65190i	0.216475	+	0.976288i	$0.430544\pi$
$150$	1.40624	−	2.43567i	0.114819	−	0.198872i
$151$	3.00691	−	5.20811i	0.244698	−	0.423830i	−0.717348	−	0.696715i	$-0.754644\pi$
$151$	3.00691	−	5.20811i	0.244698	−	0.423830i	0.962047	+	0.272884i	$0.0879777\pi$
$152$	1.69609	+	2.93771i	0.137571	+	0.238279i
$153$	−4.12478			−0.333469
$154$	−7.54631	+	13.0706i	−0.608099	+	1.05326i
$155$	−11.5549			−0.928110
$156$	3.17511	+	5.49946i	0.254213	+	0.440309i
$157$	8.93359	−	15.4734i	0.712978	−	1.23491i	−0.250756	−	0.968050i	$-0.580679\pi$
$157$	8.93359	−	15.4734i	0.712978	−	1.23491i	0.963734	−	0.266864i	$-0.0859875\pi$
$158$	−6.71505	+	11.6308i	−0.534220	+	0.925297i
$159$	0.260486	+	0.451174i	0.0206579	+	0.0357804i
$160$	−1.47903			−0.116927
$161$	−2.64575			−0.208514
$162$	−1.00000			−0.0785674
$163$	−6.93560	−	12.0128i	−0.543238	−	0.940916i	−0.998716	−	0.0506687i	$-0.983865\pi$
$163$	−6.93560	−	12.0128i	−0.543238	−	0.940916i	0.455477	−	0.890247i	$-0.349469\pi$
$164$	−3.69609	+	6.40181i	−0.288616	+	0.499897i
$165$	4.21854	−	7.30673i	0.328413	−	0.568828i
$166$	−4.61071	−	7.98599i	−0.357861	−	0.619833i
$167$	5.07551			0.392755			0.196377	−	0.980528i	$-0.437082\pi$
$167$	5.07551			0.392755			0.196377	+	0.980528i	$0.437082\pi$
$168$	1.32288	+	2.29129i	0.102062	+	0.176777i
$169$	27.3254			2.10195
$170$	−3.05033	−	5.28333i	−0.233950	−	0.405213i
$171$	−1.69609	+	2.93771i	−0.129703	+	0.224652i
$172$	−1.00000	+	1.73205i	−0.0762493	+	0.132068i
$173$	−1.46496	−	2.53739i	−0.111379	−	0.192914i	0.804947	−	0.593346i	$-0.202193\pi$
$173$	−1.46496	−	2.53739i	−0.111379	−	0.192914i	−0.916327	+	0.400432i	$0.868860\pi$
$174$	2.39217			0.181350
$175$	−3.72055	−	6.44419i	−0.281247	−	0.487135i
$176$	5.70448			0.429991
$177$	3.68918	+	6.38985i	0.277296	+	0.480290i
$178$	−3.21706	+	5.57211i	−0.241129	+	0.417647i
$179$	3.97187	−	6.87948i	0.296871	−	0.514196i	−0.678547	−	0.734557i	$-0.737390\pi$
$179$	3.97187	−	6.87948i	0.296871	−	0.514196i	0.975418	+	0.220361i	$0.0707234\pi$
$180$	−0.739514	−	1.28088i	−0.0551201	−	0.0954709i
$181$	−7.39950			−0.550000			−0.275000	−	0.961444i	$-0.588678\pi$
$181$	−7.39950			−0.550000			−0.275000	+	0.961444i	$0.588678\pi$
$182$	16.8011			1.24538
$183$	5.04194			0.372711
$184$	0.500000	+	0.866025i	0.0368605	+	0.0638442i
$185$	−6.17511	+	10.6956i	−0.454003	+	0.786357i
$186$	3.90624	−	6.76580i	0.286419	−	0.496093i
$187$	11.7649	+	20.3773i	0.860332	+	1.49014i
$188$	10.2214			0.745474
$189$	−1.32288	+	2.29129i	−0.0962250	+	0.166667i
$190$	−5.01712			−0.363980
$191$	−10.0883	−	17.4734i	−0.729961	−	1.26433i	−0.956899	−	0.290420i	$-0.906205\pi$
$191$	−10.0883	−	17.4734i	−0.729961	−	1.26433i	0.226939	−	0.973909i	$-0.427128\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	−6.44399	+	11.1613i	−0.463849	+	0.803409i	−0.999149	−	0.0412525i	$-0.986865\pi$
$193$	−6.44399	+	11.1613i	−0.463849	+	0.803409i	0.535300	+	0.844662i	$0.320199\pi$
$194$	−5.18202	−	8.97552i	−0.372047	−	0.644405i
$195$	−9.39217			−0.672587
$196$	7.00000			0.500000
$197$	−9.80410			−0.698513			−0.349257	−	0.937027i	$-0.613566\pi$
$197$	−9.80410			−0.698513			−0.349257	+	0.937027i	$0.613566\pi$
$198$	2.85224	+	4.94022i	0.202700	+	0.351086i
$199$	−1.65781	+	2.87141i	−0.117519	+	0.203549i	−0.918784	−	0.394761i	$-0.870827\pi$
$199$	−1.65781	+	2.87141i	−0.117519	+	0.203549i	0.801265	+	0.598310i	$0.204161\pi$
$200$	−1.40624	+	2.43567i	−0.0994360	+	0.172228i
$201$	7.70448	+	13.3445i	0.543432	+	0.941252i
$202$	−2.81247			−0.197885
$203$	3.16454	−	5.48115i	0.222108	−	0.384702i
$204$	4.12478			0.288792
$205$	−5.46662	−	9.46846i	−0.381805	−	0.661306i
$206$	−6.27945	+	10.8763i	−0.437510	+	0.757789i
$207$	−0.500000	+	0.866025i	−0.0347524	+	0.0601929i
$208$	−3.17511	−	5.49946i	−0.220155	−	0.381319i
$209$	19.3506			1.33851
$210$	−3.91314			−0.270032
$211$	−17.9638			−1.23668			−0.618340	−	0.785910i	$-0.712195\pi$
$211$	−17.9638			−1.23668			−0.618340	+	0.785910i	$0.712195\pi$
$212$	−0.260486	−	0.451174i	−0.0178902	−	0.0309868i
$213$	4.93560	−	8.54871i	0.338182	−	0.585748i
$214$	−2.61071	+	4.52189i	−0.178465	+	0.309110i
$215$	−1.47903	−	2.56175i	−0.100869	−	0.174710i
$216$	1.00000			0.0680414
$217$	−10.3349	−	17.9006i	−0.701581	−	1.21517i
$218$	8.47501			0.574000
$219$	4.46496	+	7.73354i	0.301714	+	0.522584i
$220$	−4.21854	+	7.30673i	−0.284414	+	0.492620i
$221$	13.0966	−	22.6841i	0.880976	−	1.52590i
$222$	−4.17511	−	7.23151i	−0.280215	−	0.485347i
$223$	−1.22947			−0.0823313			−0.0411657	−	0.999152i	$-0.513107\pi$
$223$	−1.22947			−0.0823313			−0.0411657	+	0.999152i	$0.513107\pi$
$224$	−1.32288	−	2.29129i	−0.0883883	−	0.153093i
$225$	−2.81247			−0.187498
$226$	0.362641	+	0.628112i	0.0241225	+	0.0417814i
$227$	−8.20649	+	14.2141i	−0.544684	+	0.943420i	0.453943	+	0.891031i	$0.350017\pi$
$227$	−8.20649	+	14.2141i	−0.544684	+	0.943420i	−0.998627	+	0.0523891i	$0.983316\pi$
$228$	1.69609	−	2.93771i	0.112326	−	0.194554i
$229$	12.7081	+	22.0111i	0.839778	+	1.45454i	0.890080	+	0.455803i	$0.150648\pi$
$229$	12.7081	+	22.0111i	0.839778	+	1.45454i	−0.0503028	+	0.998734i	$0.516019\pi$
$230$	−1.47903			−0.0975243
$231$	15.0926			0.993022
$232$	−2.39217			−0.157054
$233$	−0.275783	−	0.477670i	−0.0180671	−	0.0312932i	0.856850	−	0.515565i	$-0.172418\pi$
$233$	−0.275783	−	0.477670i	−0.0180671	−	0.0312932i	−0.874918	+	0.484272i	$0.839085\pi$
$234$	3.17511	−	5.49946i	0.207564	−	0.359511i
$235$	−7.55889	+	13.0924i	−0.493088	+	0.854053i
$236$	−3.68918	−	6.38985i	−0.240145	−	0.415944i
$237$	13.4301			0.872378
$238$	5.45657	−	9.45106i	0.353697	−	0.612621i
$239$	−11.2634			−0.728567			−0.364283	−	0.931288i	$-0.618686\pi$
$239$	−11.2634			−0.728567			−0.364283	+	0.931288i	$0.618686\pi$
$240$	0.739514	+	1.28088i	0.0477354	+	0.0826802i
$241$	14.1642	−	24.5331i	0.912396	−	1.58032i	0.101725	−	0.994813i	$-0.467564\pi$
$241$	14.1642	−	24.5331i	0.912396	−	1.58032i	0.810670	−	0.585503i	$-0.199103\pi$
$242$	10.7705	−	18.6551i	0.692356	−	1.19920i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	−5.04194			−0.322777
$245$	−5.17660	+	8.96614i	−0.330721	+	0.572825i
$246$	7.39217			0.471308
$247$	−10.7705	−	18.6551i	−0.685313	−	1.18700i
$248$	−3.90624	+	6.76580i	−0.248046	+	0.429629i
$249$	−4.61071	+	7.98599i	−0.292192	+	0.506092i
$250$	−5.77744	−	10.0068i	−0.365397	−	0.632886i
$251$	−7.83659			−0.494641			−0.247320	−	0.968934i	$-0.579550\pi$
$251$	−7.83659			−0.494641			−0.247320	+	0.968934i	$0.579550\pi$
$252$	1.32288	−	2.29129i	0.0833333	−	0.144338i
$253$	5.70448			0.358637
$254$	0.00690545	+	0.0119606i	0.000433287	+	0.000750475i
$255$	−3.05033	+	5.28333i	−0.191019	+	0.330855i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−1.86281	−	3.22648i	−0.116199	−	0.201262i	0.802060	−	0.597244i	$-0.203738\pi$
$257$	−1.86281	−	3.22648i	−0.116199	−	0.201262i	−0.918258	+	0.395982i	$0.870404\pi$
$258$	2.00000			0.124515
$259$	−22.0926			−1.37277
$260$	9.39217			0.582478
$261$	−1.19609	−	2.07168i	−0.0740358	−	0.128234i
$262$	−7.24807	+	12.5540i	−0.447787	+	0.775591i
$263$	−14.4331	+	24.9988i	−0.889981	+	1.54149i	−0.0500850	+	0.998745i	$0.515949\pi$
$263$	−14.4331	+	24.9988i	−0.889981	+	1.54149i	−0.839896	+	0.542747i	$0.817384\pi$
$264$	−2.85224	−	4.94022i	−0.175543	−	0.304050i
$265$	0.770531			0.0473334
$266$	−4.48742	−	7.77244i	−0.275141	−	0.476559i
$267$	6.43411			0.393761
$268$	−7.70448	−	13.3445i	−0.470626	−	0.815148i
$269$	0.241001	−	0.417426i	0.0146941	−	0.0254509i	−0.858585	−	0.512671i	$-0.828656\pi$
$269$	0.241001	−	0.417426i	0.0146941	−	0.0254509i	0.873279	+	0.487221i	$0.161989\pi$
$270$	−0.739514	+	1.28088i	−0.0450054	+	0.0779517i
$271$	2.44801	+	4.24008i	0.148706	+	0.257567i	0.930750	−	0.365657i	$-0.119156\pi$
$271$	2.44801	+	4.24008i	0.148706	+	0.257567i	−0.782043	+	0.623224i	$0.785822\pi$
$272$	−4.12478			−0.250102
$273$	−8.40056	−	14.5502i	−0.508425	−	0.880618i
$274$	−8.02411			−0.484754
$275$	8.02185	+	13.8942i	0.483736	+	0.837855i
$276$	0.500000	−	0.866025i	0.0300965	−	0.0521286i
$277$	−7.76320	+	13.4463i	−0.466446	+	0.807908i	−0.999265	−	0.0383211i	$-0.987799\pi$
$277$	−7.76320	+	13.4463i	−0.466446	+	0.807908i	0.532820	+	0.846229i	$0.321132\pi$
$278$	7.11071	+	12.3161i	0.426472	+	0.738672i
$279$	−7.81247			−0.467721
$280$	3.91314			0.233855
$281$	13.2003			0.787463			0.393732	−	0.919225i	$-0.371184\pi$
$281$	13.2003			0.787463			0.393732	+	0.919225i	$0.371184\pi$
$282$	−5.11071	−	8.85202i	−0.304339	−	0.527130i
$283$	1.37836	−	2.38739i	0.0819350	−	0.141916i	−0.822146	−	0.569277i	$-0.807223\pi$
$283$	1.37836	−	2.38739i	0.0819350	−	0.141916i	0.904081	+	0.427361i	$0.140557\pi$
$284$	−4.93560	+	8.54871i	−0.292874	+	0.507273i
$285$	2.50856	+	4.34495i	0.148594	+	0.257373i
$286$	−36.2247			−2.14201
$287$	9.77892	−	16.9376i	0.577232	−	0.999794i
$288$	−1.00000			−0.0589256
$289$	−0.00690545	−	0.0119606i	−0.000406203	−	0.000703565i
$290$	1.76905	−	3.06408i	0.103882	−	0.179929i
$291$	−5.18202	+	8.97552i	−0.303775	+	0.526154i
$292$	−4.46496	−	7.73354i	−0.261292	−	0.452571i
$293$	0.0976957			0.00570745			0.00285372	−	0.999996i	$-0.499092\pi$
$293$	0.0976957			0.00570745			0.00285372	+	0.999996i	$0.499092\pi$
$294$	−3.50000	−	6.06218i	−0.204124	−	0.353553i
$295$	10.9128			0.635368
$296$	4.17511	+	7.23151i	0.242674	+	0.420323i
$297$	2.85224	−	4.94022i	0.165504	−	0.286661i
$298$	−11.6417	+	20.1641i	−0.674387	+	1.16807i
$299$	−3.17511	−	5.49946i	−0.183622	−	0.318042i
$300$	2.81247			0.162378
$301$	2.64575	−	4.58258i	0.152499	−	0.264135i
$302$	6.01381			0.346056
$303$	1.40624	+	2.43567i	0.0807862	+	0.139926i
$304$	−1.69609	+	2.93771i	−0.0972772	+	0.168489i
$305$	3.72859	−	6.45811i	0.213498	−	0.369790i
$306$	−2.06239	−	3.57216i	−0.117899	−	0.204207i
$307$	−24.9467			−1.42378			−0.711892	−	0.702289i	$-0.752161\pi$
$307$	−24.9467			−1.42378			−0.711892	+	0.702289i	$0.752161\pi$
$308$	−15.0926			−0.859982
$309$	12.5589			0.714450
$310$	−5.77744	−	10.0068i	−0.328136	−	0.568349i
$311$	−13.2439	+	22.9391i	−0.750992	+	1.30076i	0.196351	+	0.980534i	$0.437091\pi$
$311$	−13.2439	+	22.9391i	−0.750992	+	1.30076i	−0.947342	+	0.320222i	$0.896242\pi$
$312$	−3.17511	+	5.49946i	−0.179755	+	0.311346i
$313$	9.61911	+	16.6608i	0.543704	+	0.941723i	0.998687	+	0.0512230i	$0.0163119\pi$
$313$	9.61911	+	16.6608i	0.543704	+	0.941723i	−0.454983	+	0.890500i	$0.650355\pi$
$314$	17.8672			1.00830
$315$	1.95657	+	3.38888i	0.110240	+	0.190942i
$316$	−13.4301			−0.755502
$317$	−12.6892	−	21.9783i	−0.712695	−	1.23442i	−0.963842	−	0.266475i	$-0.914141\pi$
$317$	−12.6892	−	21.9783i	−0.712695	−	1.23442i	0.251146	−	0.967949i	$-0.419192\pi$
$318$	−0.260486	+	0.451174i	−0.0146073	+	0.0253006i
$319$	−6.82304	+	11.8179i	−0.382017	+	0.661673i
$320$	−0.739514	−	1.28088i	−0.0413401	−	0.0716032i
$321$	5.22143			0.291432
$322$	−1.32288	−	2.29129i	−0.0737210	−	0.127688i
$323$	−13.9920			−0.778533
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	8.92993	−	15.4671i	0.495343	−	0.857960i
$326$	6.93560	−	12.0128i	0.384127	−	0.665328i
$327$	−4.23750	−	7.33957i	−0.234335	−	0.405879i
$328$	−7.39217			−0.408164
$329$	−27.0434			−1.49095
$330$	8.43709			0.464446
$331$	−1.42137	−	2.46188i	−0.0781254	−	0.135317i	0.824316	−	0.566130i	$-0.191560\pi$
$331$	−1.42137	−	2.46188i	−0.0781254	−	0.135317i	−0.902441	+	0.430813i	$0.858227\pi$
$332$	4.61071	−	7.98599i	0.253046	−	0.438288i
$333$	−4.17511	+	7.23151i	−0.228795	+	0.396284i
$334$	2.53775	+	4.39552i	0.138860	+	0.240512i
$335$	22.7903			1.24517
$336$	−1.32288	+	2.29129i	−0.0721688	+	0.125000i
$337$	26.7793			1.45876			0.729380	−	0.684109i	$-0.239809\pi$
$337$	26.7793			1.45876			0.729380	+	0.684109i	$0.239809\pi$
$338$	13.6627	+	23.6645i	0.743153	+	1.28718i
$339$	0.362641	−	0.628112i	0.0196959	−	0.0341144i
$340$	3.05033	−	5.28333i	0.165428	−	0.286529i
$341$	22.2830	+	38.5954i	1.20669	+	2.09006i
$342$	−3.39217			−0.183428
$343$	−18.5203			−1.00000
$344$	−2.00000			−0.107833
$345$	0.739514	+	1.28088i	0.0398141	+	0.0689601i
$346$	1.46496	−	2.53739i	0.0787569	−	0.136411i
$347$	2.81247	−	4.87135i	0.150982	−	0.261508i	−0.780607	−	0.625022i	$-0.785090\pi$
$347$	2.81247	−	4.87135i	0.150982	−	0.261508i	0.931589	+	0.363514i	$0.118423\pi$
$348$	1.19609	+	2.07168i	0.0641169	+	0.111054i
$349$	20.8011			1.11346			0.556729	−	0.830694i	$-0.312056\pi$
$349$	20.8011			1.11346			0.556729	+	0.830694i	$0.312056\pi$
$350$	3.72055	−	6.44419i	0.198872	−	0.344456i
$351$	−6.35023			−0.338950
$352$	2.85224	+	4.94022i	0.152025	+	0.263315i
$353$	17.3546	−	30.0591i	0.923692	−	1.59988i	0.130041	−	0.991509i	$-0.458489\pi$
$353$	17.3546	−	30.0591i	0.923692	−	1.59988i	0.793651	−	0.608373i	$-0.208178\pi$
$354$	−3.68918	+	6.38985i	−0.196078	+	0.339617i
$355$	−7.29989	−	12.6438i	−0.387438	−	0.671063i
$356$	−6.43411			−0.341007
$357$	−10.9131			−0.577585
$358$	7.94374			0.419840
$359$	2.89200	+	5.00910i	0.152634	+	0.264370i	0.932195	−	0.361956i	$-0.117891\pi$
$359$	2.89200	+	5.00910i	0.152634	+	0.264370i	−0.779561	+	0.626326i	$0.784558\pi$
$360$	0.739514	−	1.28088i	0.0389758	−	0.0675081i
$361$	3.74659	−	6.48928i	0.197189	−	0.341541i
$362$	−3.69975	−	6.40815i	−0.194455	−	0.336805i
$363$	−21.5411			−1.13061
$364$	8.40056	+	14.5502i	0.440309	+	0.762638i
$365$	13.2076			0.691318
$366$	2.52097	+	4.36645i	0.131773	+	0.228238i
$367$	−0.334931	+	0.580118i	−0.0174833	+	0.0302819i	−0.874635	−	0.484783i	$-0.838899\pi$
$367$	−0.334931	+	0.580118i	−0.0174833	+	0.0302819i	0.857151	+	0.515065i	$0.172232\pi$
$368$	−0.500000	+	0.866025i	−0.0260643	+	0.0451447i
$369$	−3.69609	−	6.40181i	−0.192411	−	0.333265i
$370$	−12.3502			−0.642058
$371$	0.689180	+	1.19369i	0.0357804	+	0.0619736i
$372$	7.81247			0.405058
$373$	4.90004	+	8.48712i	0.253714	+	0.439446i	0.964546	−	0.263916i	$-0.0850143\pi$
$373$	4.90004	+	8.48712i	0.253714	+	0.439446i	−0.710831	+	0.703363i	$0.751681\pi$
$374$	−11.7649	+	20.3773i	−0.608346	+	1.05369i
$375$	−5.77744	+	10.0068i	−0.298346	+	0.516750i
$376$	5.11071	+	8.85202i	0.263565	+	0.456508i
$377$	15.1908			0.782368
$378$	−2.64575			−0.136083
$379$	−0.742065			−0.0381173			−0.0190587	−	0.999818i	$-0.506067\pi$
$379$	−0.742065			−0.0381173			−0.0190587	+	0.999818i	$0.506067\pi$
$380$	−2.50856	−	4.34495i	−0.128686	−	0.222891i
$381$	0.00690545	−	0.0119606i	0.000353777	−	0.000612760i
$382$	10.0883	−	17.4734i	0.516160	−	0.894016i
$383$	−15.2057	−	26.3371i	−0.776975	−	1.34576i	−0.933677	−	0.358115i	$-0.883420\pi$
$383$	−15.2057	−	26.3371i	−0.776975	−	1.34576i	0.156702	−	0.987646i	$-0.449914\pi$
$384$	1.00000			0.0510310
$385$	11.1612	−	19.3318i	0.568828	−	0.985239i
$386$	−12.8880			−0.655981
$387$	−1.00000	−	1.73205i	−0.0508329	−	0.0880451i
$388$	5.18202	−	8.97552i	0.263077	−	0.455663i
$389$	0.337465	−	0.584506i	0.0171102	−	0.0296357i	−0.857344	−	0.514745i	$-0.827887\pi$
$389$	0.337465	−	0.584506i	0.0171102	−	0.0296357i	0.874454	+	0.485109i	$0.161220\pi$
$390$	−4.69609	−	8.13386i	−0.237796	−	0.411874i
$391$	−4.12478			−0.208599
$392$	3.50000	+	6.06218i	0.176777	+	0.306186i
$393$	14.4961			0.731234
$394$	−4.90205	−	8.49060i	−0.246962	−	0.427750i
$395$	9.93175	−	17.2023i	0.499720	−	0.865541i
$396$	−2.85224	+	4.94022i	−0.143330	+	0.248256i
$397$	−4.21304	−	7.29719i	−0.211446	−	0.366236i	0.740721	−	0.671813i	$-0.234484\pi$
$397$	−4.21304	−	7.29719i	−0.211446	−	0.366236i	−0.952167	+	0.305577i	$0.901151\pi$
$398$	−3.31561			−0.166197
$399$	−4.48742	+	7.77244i	−0.224652	+	0.389109i
$400$	−2.81247			−0.140624
$401$	−17.5596	−	30.4141i	−0.876885	−	1.51881i	−0.854741	−	0.519054i	$-0.826284\pi$
$401$	−17.5596	−	30.4141i	−0.876885	−	1.51881i	−0.0221432	−	0.999755i	$-0.507049\pi$
$402$	−7.70448	+	13.3445i	−0.384264	+	0.665565i
$403$	24.8055	−	42.9644i	1.23565	−	2.14021i
$404$	−1.40624	−	2.43567i	−0.0699629	−	0.121179i
$405$	1.47903			0.0734935
$406$	6.32909			0.314107
$407$	47.6337			2.36111
$408$	2.06239	+	3.57216i	0.102104	+	0.176848i
$409$	−9.86404	+	17.0850i	−0.487745	+	0.844800i	−0.999901	−	0.0140931i	$-0.995514\pi$
$409$	−9.86404	+	17.0850i	−0.487745	+	0.844800i	0.512155	+	0.858893i	$0.328847\pi$
$410$	5.46662	−	9.46846i	0.269977	−	0.467614i
$411$	4.01206	+	6.94908i	0.197900	+	0.342773i
$412$	−12.5589			−0.618732
$413$	9.76065	+	16.9059i	0.480290	+	0.831887i
$414$	−1.00000			−0.0491473
$415$	6.81938	+	11.8115i	0.334750	+	0.579804i
$416$	3.17511	−	5.49946i	0.155673	−	0.269633i
$417$	7.11071	−	12.3161i	0.348213	−	0.603123i
$418$	9.67528	+	16.7581i	0.473234	+	0.819664i
$419$	7.26739			0.355035			0.177518	−	0.984118i	$-0.443193\pi$
$419$	7.26739			0.355035			0.177518	+	0.984118i	$0.443193\pi$
$420$	−1.95657	−	3.38888i	−0.0954709	−	0.165360i
$421$	3.82277			0.186311			0.0931553	−	0.995652i	$-0.470305\pi$
$421$	3.82277			0.186311			0.0931553	+	0.995652i	$0.470305\pi$
$422$	−8.98191	−	15.5571i	−0.437233	−	0.757309i
$423$	−5.11071	+	8.85202i	−0.248491	+	0.430400i
$424$	0.260486	−	0.451174i	0.0126503	−	0.0219110i
$425$	−5.80042	−	10.0466i	−0.281362	−	0.487333i
$426$	9.87120			0.478261
$427$	13.3397			0.645555
$428$	−5.22143			−0.252387
$429$	18.1124	+	31.3715i	0.874473	+	1.51463i
$430$	1.47903	−	2.56175i	0.0713251	−	0.123539i
$431$	0.986189	−	1.70813i	0.0475031	−	0.0822777i	−0.841296	−	0.540574i	$-0.818207\pi$
$431$	0.986189	−	1.70813i	0.0475031	−	0.0822777i	0.888799	+	0.458297i	$0.151540\pi$
$432$	0.500000	+	0.866025i	0.0240563	+	0.0416667i
$433$	−31.3929			−1.50865			−0.754323	−	0.656504i	$-0.772035\pi$
$433$	−31.3929			−1.50865			−0.754323	+	0.656504i	$0.772035\pi$
$434$	10.3349	−	17.9006i	0.496093	−	0.859258i
$435$	−3.53809			−0.169638
$436$	4.23750	+	7.33957i	0.202940	+	0.351502i
$437$	−1.69609	+	2.93771i	−0.0811348	+	0.140530i
$438$	−4.46496	+	7.73354i	−0.213344	+	0.369523i
$439$	17.8603	+	30.9349i	0.852424	+	1.47644i	0.879014	+	0.476796i	$0.158202\pi$
$439$	17.8603	+	30.9349i	0.852424	+	1.47644i	−0.0265896	+	0.999646i	$0.508465\pi$
$440$	−8.43709			−0.402222
$441$	−3.50000	+	6.06218i	−0.166667	+	0.288675i
$442$	26.1933			1.24589
$443$	0.0572397	+	0.0991421i	0.00271954	+	0.00471038i	0.867382	−	0.497643i	$-0.165801\pi$
$443$	0.0572397	+	0.0991421i	0.00271954	+	0.00471038i	−0.864662	+	0.502353i	$0.832468\pi$
$444$	4.17511	−	7.23151i	0.198142	−	0.343192i
$445$	4.75812	−	8.24130i	0.225557	−	0.390675i
$446$	−0.614734	−	1.06475i	−0.0291085	−	0.0504174i
$447$	23.2835			1.10127
$448$	1.32288	−	2.29129i	0.0625000	−	0.108253i
$449$	−9.26006			−0.437009			−0.218505	−	0.975836i	$-0.570118\pi$
$449$	−9.26006			−0.437009			−0.218505	+	0.975836i	$0.570118\pi$
$450$	−1.40624	−	2.43567i	−0.0662906	−	0.114819i
$451$	−21.0842	+	36.5190i	−0.992818	+	1.71961i
$452$	−0.362641	+	0.628112i	−0.0170572	+	0.0295439i
$453$	−3.00691	−	5.20811i	−0.141277	−	0.244698i
$454$	−16.4130			−0.770299
$455$	−24.8493			−1.16496
$456$	3.39217			0.158853
$457$	−2.91865	−	5.05525i	−0.136529	−	0.236475i	0.789652	−	0.613555i	$-0.210261\pi$
$457$	−2.91865	−	5.05525i	−0.136529	−	0.236475i	−0.926180	+	0.377081i	$0.876928\pi$
$458$	−12.7081	+	22.0111i	−0.593812	+	1.02851i
$459$	−2.06239	+	3.57216i	−0.0962641	+	0.166734i
$460$	−0.739514	−	1.28088i	−0.0344800	−	0.0597212i
$461$	23.1660			1.07895			0.539474	−	0.842002i	$-0.318623\pi$
$461$	23.1660			1.07895			0.539474	+	0.842002i	$0.318623\pi$
$462$	7.54631	+	13.0706i	0.351086	+	0.608099i
$463$	0.140148			0.00651322			0.00325661	−	0.999995i	$-0.498963\pi$
$463$	0.140148			0.00651322			0.00325661	+	0.999995i	$0.498963\pi$
$464$	−1.19609	−	2.07168i	−0.0555269	−	0.0961754i
$465$	−5.77744	+	10.0068i	−0.267922	+	0.464055i
$466$	0.275783	−	0.477670i	0.0127754	−	0.0221276i
$467$	−7.75848	−	13.4381i	−0.359019	−	0.621840i	0.628778	−	0.777585i	$-0.283555\pi$
$467$	−7.75848	−	13.4381i	−0.359019	−	0.621840i	−0.987797	+	0.155745i	$0.950222\pi$
$468$	6.35023			0.293539
$469$	20.3841	+	35.3064i	0.941252	+	1.63030i
$470$	−15.1178			−0.697332
$471$	−8.93359	−	15.4734i	−0.411638	−	0.712978i
$472$	3.68918	−	6.38985i	0.169808	−	0.294117i
$473$	−5.70448	+	9.88044i	−0.262292	+	0.454303i
$474$	6.71505	+	11.6308i	0.308432	+	0.534220i
$475$	−9.54039			−0.437743
$476$	10.9131			0.500203
$477$	0.520971			0.0238536
$478$	−5.63169	−	9.75437i	−0.257587	−	0.446154i
$479$	−7.69609	+	13.3300i	−0.351643	+	0.609064i	−0.986538	−	0.163535i	$-0.947710\pi$
$479$	−7.69609	+	13.3300i	−0.351643	+	0.609064i	0.634894	+	0.772599i	$0.281044\pi$
$480$	−0.739514	+	1.28088i	−0.0337541	+	0.0584637i
$481$	−26.5129	−	45.9217i	−1.20889	−	2.09385i
$482$	28.3284			1.29032
$483$	−1.32288	+	2.29129i	−0.0601929	+	0.104257i
$484$	21.5411			0.979139
$485$	7.66436	+	13.2751i	0.348021	+	0.602789i
$486$	−0.500000	+	0.866025i	−0.0226805	+	0.0392837i
$487$	0.277269	−	0.480245i	0.0125643	−	0.0217620i	−0.859675	−	0.510842i	$-0.829334\pi$
$487$	0.277269	−	0.480245i	0.0125643	−	0.0217620i	0.872239	+	0.489080i	$0.162667\pi$
$488$	−2.52097	−	4.36645i	−0.114119	−	0.197660i
$489$	−13.8712			−0.627277
$490$	−10.3532			−0.467710
$491$	43.1966			1.94944			0.974718	−	0.223440i	$-0.0717286\pi$
$491$	43.1966			1.94944			0.974718	+	0.223440i	$0.0717286\pi$
$492$	3.69609	+	6.40181i	0.166632	+	0.288616i
$493$	4.93359	−	8.54523i	0.222198	−	0.384858i
$494$	10.7705	−	18.6551i	0.484589	−	0.839333i
$495$	−4.21854	−	7.30673i	−0.189609	−	0.328413i
$496$	−7.81247			−0.350790
$497$	13.0584	−	22.6178i	0.585748	−	1.01455i
$498$	−9.22143			−0.413222
$499$	10.4471	+	18.0950i	0.467678	+	0.810042i	0.999318	−	0.0369286i	$-0.0117574\pi$
$499$	10.4471	+	18.0950i	0.467678	+	0.810042i	−0.531640	+	0.846970i	$0.678424\pi$
$500$	5.77744	−	10.0068i	0.258375	−	0.447518i
$501$	2.53775	−	4.39552i	0.113379	−	0.196377i
$502$	−3.91829	−	6.78668i	−0.174882	−	0.302904i
$503$	−10.1657			−0.453265			−0.226633	−	0.973980i	$-0.572772\pi$
$503$	−10.1657			−0.453265			−0.226633	+	0.973980i	$0.572772\pi$
$504$	2.64575			0.117851
$505$	4.15973			0.185106
$506$	2.85224	+	4.94022i	0.126797	+	0.219620i
$507$	13.6627	−	23.6645i	0.606782	−	1.05098i
$508$	−0.00690545	+	0.0119606i	−0.000306380	+	0.000530666i
$509$	6.86595	+	11.8922i	0.304328	+	0.527111i	0.977111	−	0.212728i	$-0.0682348\pi$
$509$	6.86595	+	11.8922i	0.304328	+	0.527111i	−0.672784	+	0.739839i	$0.734902\pi$
$510$	−6.10067			−0.270142
$511$	11.8132	+	20.4610i	0.522584	+	0.905143i
$512$	−1.00000			−0.0441942
$513$	1.69609	+	2.93771i	0.0748840	+	0.129703i
$514$	1.86281	−	3.22648i	0.0821649	−	0.142314i
$515$	9.28748	−	16.0864i	0.409255	−	0.708851i
$516$	1.00000	+	1.73205i	0.0440225	+	0.0762493i
$517$	58.3079			2.56438
$518$	−11.0463	−	19.1328i	−0.485347	−	0.840646i
$519$	−2.92993			−0.128609
$520$	4.69609	+	8.13386i	0.205937	+	0.356693i
$521$	1.81247	−	3.13930i	0.0794059	−	0.137535i	−0.823588	−	0.567189i	$-0.808031\pi$
$521$	1.81247	−	3.13930i	0.0794059	−	0.137535i	0.902994	+	0.429654i	$0.141364\pi$
$522$	1.19609	−	2.07168i	0.0523512	−	0.0906750i
$523$	14.4710	+	25.0645i	0.632772	+	1.09599i	0.986982	+	0.160828i	$0.0514164\pi$
$523$	14.4710	+	25.0645i	0.632772	+	1.09599i	−0.354210	+	0.935166i	$0.615250\pi$
$524$	−14.4961			−0.633267
$525$	−7.44111			−0.324757
$526$	−28.8661			−1.25862
$527$	−16.1124	−	27.9074i	−0.701866	−	1.21567i
$528$	2.85224	−	4.94022i	0.124128	−	0.214996i
$529$	−0.500000	+	0.866025i	−0.0217391	+	0.0376533i
$530$	0.385266	+	0.667300i	0.0167349	+	0.0289857i
$531$	7.37836			0.320194
$532$	4.48742	−	7.77244i	0.194554	−	0.336978i
$533$	46.9420			2.03328
$534$	3.21706	+	5.57211i	0.139216	+	0.241129i
$535$	3.86132	−	6.68801i	0.166939	−	0.289148i
$536$	7.70448	−	13.3445i	0.332783	−	0.576397i
$537$	−3.97187	−	6.87948i	−0.171399	−	0.296871i
$538$	0.482002			0.0207806
$539$	39.9313			1.71996
$540$	−1.47903			−0.0636473
$541$	16.5086	+	28.5937i	0.709758	+	1.22934i	0.964947	+	0.262446i	$0.0845292\pi$
$541$	16.5086	+	28.5937i	0.709758	+	1.22934i	−0.255188	+	0.966891i	$0.582137\pi$
$542$	−2.44801	+	4.24008i	−0.105151	+	0.182127i
$543$	−3.69975	+	6.40815i	−0.158771	+	0.275000i
$544$	−2.06239	−	3.57216i	−0.0884242	−	0.153155i
$545$	−12.5348			−0.536931
$546$	8.40056	−	14.5502i	0.359511	−	0.622691i
$547$	36.6891			1.56871			0.784357	−	0.620310i	$-0.212993\pi$
$547$	36.6891			1.56871			0.784357	+	0.620310i	$0.212993\pi$
$548$	−4.01206	−	6.94908i	−0.171387	−	0.296850i
$549$	2.52097	−	4.36645i	0.107592	−	0.186356i
$550$	−8.02185	+	13.8942i	−0.342053	+	0.592453i
$551$	−4.05733	−	7.02750i	−0.172848	−	0.299381i
$552$	1.00000			0.0425628
$553$	35.5327			1.51100
$554$	−15.5264			−0.659654
$555$	6.17511	+	10.6956i	0.262119	+	0.454003i
$556$	−7.11071	+	12.3161i	−0.301561	+	0.522320i
$557$	−15.4681	+	26.7915i	−0.655405	+	1.13519i	0.326388	+	0.945236i	$0.394169\pi$
$557$	−15.4681	+	26.7915i	−0.655405	+	1.13519i	−0.981792	+	0.189958i	$0.939165\pi$
$558$	−3.90624	−	6.76580i	−0.165364	−	0.286419i
$559$	12.7005			0.537172
$560$	1.95657	+	3.38888i	0.0826802	+	0.143206i
$561$	23.5297			0.993425
$562$	6.60014	+	11.4318i	0.278410	+	0.482221i
$563$	−0.276561	+	0.479018i	−0.0116557	+	0.0201882i	−0.871794	−	0.489872i	$-0.837044\pi$
$563$	−0.276561	+	0.479018i	−0.0116557	+	0.0201882i	0.860139	+	0.510060i	$0.170377\pi$
$564$	5.11071	−	8.85202i	0.215200	−	0.372737i
$565$	−0.536356	−	0.928996i	−0.0225647	−	0.0390831i
$566$	2.75672			0.115874
$567$	1.32288	+	2.29129i	0.0555556	+	0.0962250i
$568$	−9.87120			−0.414186
$569$	−1.19083	−	2.06259i	−0.0499224	−	0.0864681i	0.839984	−	0.542611i	$-0.182564\pi$
$569$	−1.19083	−	2.06259i	−0.0499224	−	0.0864681i	−0.889907	+	0.456143i	$0.849231\pi$
$570$	−2.50856	+	4.34495i	−0.105072	+	0.181990i
$571$	−13.2831	+	23.0070i	−0.555881	+	0.962814i	0.441954	+	0.897038i	$0.354286\pi$
$571$	−13.2831	+	23.0070i	−0.555881	+	0.962814i	−0.997834	+	0.0657760i	$0.979048\pi$
$572$	−18.1124	−	31.3715i	−0.757316	−	1.31171i
$573$	−20.1765			−0.842886
$574$	19.5578			0.816329
$575$	−2.81247			−0.117288
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	2.86158	−	4.95640i	0.119129	−	0.206337i	−0.800294	−	0.599608i	$-0.795323\pi$
$577$	2.86158	−	4.95640i	0.119129	−	0.206337i	0.919423	+	0.393271i	$0.128656\pi$
$578$	0.00690545	−	0.0119606i	0.000287229	−	0.000497495i
$579$	6.44399	+	11.1613i	0.267803	+	0.463849i
$580$	3.53809			0.146911
$581$	−12.1988	+	21.1289i	−0.506092	+	0.876576i
$582$	−10.3640			−0.429603
$583$	−1.48593	−	2.57371i	−0.0615411	−	0.106592i
$584$	4.46496	−	7.73354i	0.184761	−	0.320016i
$585$	−4.69609	+	8.13386i	−0.194159	+	0.336294i
$586$	0.0488479	+	0.0846070i	0.00201789	+	0.00349508i
$587$	19.2323			0.793801			0.396900	−	0.917862i	$-0.370086\pi$
$587$	19.2323			0.793801			0.396900	+	0.917862i	$0.370086\pi$
$588$	3.50000	−	6.06218i	0.144338	−	0.250000i
$589$	−26.5012			−1.09196
$590$	5.45640	+	9.45077i	0.224637	+	0.389082i
$591$	−4.90205	+	8.49060i	−0.201643	+	0.349257i
$592$	−4.17511	+	7.23151i	−0.171596	+	0.297213i
$593$	10.3429	+	17.9144i	0.424732	+	0.735657i	0.996395	−	0.0848308i	$-0.0270350\pi$
$593$	10.3429	+	17.9144i	0.424732	+	0.735657i	−0.571663	+	0.820488i	$0.693702\pi$
$594$	5.70448			0.234058
$595$	−8.07043	+	13.9784i	−0.330855	+	0.573058i
$596$	−23.2835			−0.953728
$597$	1.65781	+	2.87141i	0.0678495	+	0.117519i
$598$	3.17511	−	5.49946i	0.129840	−	0.224890i
$599$	9.80977	−	16.9910i	0.400816	−	0.694234i	−0.593008	−	0.805196i	$-0.702060\pi$
$599$	9.80977	−	16.9910i	0.400816	−	0.694234i	0.993825	+	0.110962i	$0.0353932\pi$
$600$	1.40624	+	2.43567i	0.0574094	+	0.0994360i
$601$	−8.88798			−0.362548			−0.181274	−	0.983433i	$-0.558022\pi$
$601$	−8.88798			−0.362548			−0.181274	+	0.983433i	$0.558022\pi$
$602$	5.29150			0.215666
$603$	15.4090			0.627501
$604$	3.00691	+	5.20811i	0.122349	+	0.211915i
$605$	−15.9299	+	27.5914i	−0.647644	+	1.12175i
$606$	−1.40624	+	2.43567i	−0.0571245	+	0.0989425i
$607$	5.88945	+	10.2008i	0.239046	+	0.414039i	0.960441	−	0.278485i	$-0.0898321\pi$
$607$	5.88945	+	10.2008i	0.239046	+	0.414039i	−0.721395	+	0.692524i	$0.756499\pi$
$608$	−3.39217			−0.137571
$609$	−3.16454	−	5.48115i	−0.128234	−	0.222108i
$610$	7.45718			0.301932
$611$	−32.4542	−	56.2123i	−1.31296	−	2.27411i
$612$	2.06239	−	3.57216i	0.0833672	−	0.144396i
$613$	−12.3593	+	21.4070i	−0.499188	+	0.864619i	−1.00000		0.000937480i	$-0.999702\pi$
$613$	−12.3593	+	21.4070i	−0.499188	+	0.864619i	0.500812	+	0.865556i	$0.333035\pi$
$614$	−12.4734	−	21.6045i	−0.503384	−	0.871886i
$615$	−10.9332			−0.440871
$616$	−7.54631	−	13.0706i	−0.304050	−	0.526629i
$617$	−19.0580			−0.767247			−0.383623	−	0.923490i	$-0.625324\pi$
$617$	−19.0580			−0.767247			−0.383623	+	0.923490i	$0.625324\pi$
$618$	6.27945	+	10.8763i	0.252596	+	0.437510i
$619$	9.75481	−	16.8958i	0.392079	−	0.679101i	−0.600645	−	0.799516i	$-0.705089\pi$
$619$	9.75481	−	16.8958i	0.392079	−	0.679101i	0.992724	+	0.120415i	$0.0384227\pi$
$620$	5.77744	−	10.0068i	0.232027	−	0.401883i
$621$	0.500000	+	0.866025i	0.0200643	+	0.0347524i
$622$	−26.4878			−1.06206
$623$	17.0231			0.682015
$624$	−6.35023			−0.254213
$625$	1.51381	+	2.62200i	0.0605524	+	0.104880i
$626$	−9.61911	+	16.6608i	−0.384457	+	0.665899i
$627$	9.67528	−	16.7581i	0.386394	−	0.669253i
$628$	8.93359	+	15.4734i	0.356489	+	0.617457i
$629$	−34.4429			−1.37333
$630$	−1.95657	+	3.38888i	−0.0779517	+	0.135016i
$631$	−46.6443			−1.85688			−0.928441	−	0.371481i	$-0.878850\pi$
$631$	−46.6443			−1.85688			−0.928441	+	0.371481i	$0.878850\pi$
$632$	−6.71505	−	11.6308i	−0.267110	−	0.462648i
$633$	−8.98191	+	15.5571i	−0.356999	+	0.618340i
$634$	12.6892	−	21.9783i	0.503952	−	0.872870i
$635$	−0.0102134	−	0.0176901i	−0.000405305	−	0.000702009i
$636$	−0.520971			−0.0206579
$637$	−22.2258	−	38.4962i	−0.880618	−	1.52528i
$638$	−13.6461			−0.540254
$639$	−4.93560	−	8.54871i	−0.195249	−	0.338182i
$640$	0.739514	−	1.28088i	0.0292319	−	0.0506311i
$641$	13.2670	−	22.9792i	0.524016	−	0.907623i	−0.475593	−	0.879666i	$-0.657766\pi$
$641$	13.2670	−	22.9792i	0.524016	−	0.907623i	0.999609	−	0.0279574i	$-0.00890028\pi$
$642$	2.61071	+	4.52189i	0.103037	+	0.178465i
$643$	1.53826			0.0606632			0.0303316	−	0.999540i	$-0.490344\pi$
$643$	1.53826			0.0606632			0.0303316	+	0.999540i	$0.490344\pi$
$644$	1.32288	−	2.29129i	0.0521286	−	0.0902894i
$645$	−2.95806			−0.116473
$646$	−6.99598	−	12.1174i	−0.275253	−	0.476752i
$647$	−18.5310	+	32.0967i	−0.728529	+	1.26185i	0.228975	+	0.973432i	$0.426463\pi$
$647$	−18.5310	+	32.0967i	−0.728529	+	1.26185i	−0.957505	+	0.288418i	$0.906871\pi$
$648$	0.500000	−	0.866025i	0.0196419	−	0.0340207i
$649$	−21.0448	−	36.4507i	−0.826082	−	1.43082i
$650$	17.8599			0.700521
$651$	−20.6699			−0.810116
$652$	13.8712			0.543238
$653$	−4.09542	−	7.09347i	−0.160266	−	0.277589i	0.774698	−	0.632331i	$-0.217902\pi$
$653$	−4.09542	−	7.09347i	−0.160266	−	0.277589i	−0.934964	+	0.354742i	$0.884569\pi$
$654$	4.23750	−	7.33957i	0.165700	−	0.287000i
$655$	10.7201	−	18.5678i	0.418869	−	0.725503i
$656$	−3.69609	−	6.40181i	−0.144308	−	0.249949i
$657$	8.92993			0.348390
$658$	−13.5217	−	23.4202i	−0.527130	−	0.913016i
$659$	24.2174			0.943376			0.471688	−	0.881765i	$-0.343645\pi$
$659$	24.2174			0.943376			0.471688	+	0.881765i	$0.343645\pi$
$660$	4.21854	+	7.30673i	0.164207	+	0.284414i
$661$	18.7964	−	32.5563i	0.731095	−	1.26629i	−0.225320	−	0.974285i	$-0.572343\pi$
$661$	18.7964	−	32.5563i	0.731095	−	1.26629i	0.956416	−	0.292009i	$-0.0943238\pi$
$662$	1.42137	−	2.46188i	0.0552430	−	0.0956837i
$663$	−13.0966	−	22.6841i	−0.508632	−	0.880976i
$664$	9.22143			0.357861
$665$	6.63702	+	11.4957i	0.257373	+	0.445783i
$666$	−8.35023			−0.323565
$667$	−1.19609	−	2.07168i	−0.0463126	−	0.0802158i
$668$	−2.53775	+	4.39552i	−0.0981887	+	0.170068i
$669$	−0.614734	+	1.06475i	−0.0237670	+	0.0411657i
$670$	11.3951	+	19.7370i	0.440233	+	0.762506i
$671$	−28.7616			−1.11033
$672$	−2.64575			−0.102062
$673$	4.15939			0.160333			0.0801664	−	0.996781i	$-0.474455\pi$
$673$	4.15939			0.160333			0.0801664	+	0.996781i	$0.474455\pi$
$674$	13.3896	+	23.1915i	0.515750	+	0.893304i
$675$	−1.40624	+	2.43567i	−0.0541261	+	0.0937491i
$676$	−13.6627	+	23.6645i	−0.525489	+	0.910173i
$677$	−6.17258	−	10.6912i	−0.237232	−	0.410897i	0.722687	−	0.691175i	$-0.242907\pi$
$677$	−6.17258	−	10.6912i	−0.237232	−	0.410897i	−0.959919	+	0.280278i	$0.909573\pi$
$678$	0.725281			0.0278543
$679$	−13.7103	+	23.7470i	−0.526154	+	0.911326i
$680$	6.10067			0.233950
$681$	8.20649	+	14.2141i	0.314473	+	0.544684i
$682$	−22.2830	+	38.5954i	−0.853262	+	1.47789i
$683$	−20.5731	+	35.6337i	−0.787209	+	1.36349i	0.140461	+	0.990086i	$0.455142\pi$
$683$	−20.5731	+	35.6337i	−0.787209	+	1.36349i	−0.927670	+	0.373401i	$0.878192\pi$
$684$	−1.69609	−	2.93771i	−0.0648515	−	0.112326i
$685$	11.8679			0.453449
$686$	−9.26013	−	16.0390i	−0.353553	−	0.612372i
$687$	25.4163			0.969692
$688$	−1.00000	−	1.73205i	−0.0381246	−	0.0660338i
$689$	−1.65414	+	2.86506i	−0.0630178	+	0.109150i
$690$	−0.739514	+	1.28088i	−0.0281528	+	0.0487621i
$691$	3.08118	+	5.33677i	0.117214	+	0.203020i	0.918663	−	0.395043i	$-0.129270\pi$
$691$	3.08118	+	5.33677i	0.117214	+	0.203020i	−0.801449	+	0.598063i	$0.795937\pi$
$692$	2.92993			0.111379
$693$	7.54631	−	13.0706i	0.286661	−	0.496511i
$694$	5.62495			0.213520
$695$	−10.5170	−	18.2159i	−0.398931	−	0.690968i
$696$	−1.19609	+	2.07168i	−0.0453375	+	0.0785269i
$697$	15.2455	−	26.4061i	0.577466	−	1.00020i
$698$	10.4006	+	18.0143i	0.393667	+	0.681851i
$699$	−0.551566			−0.0208621
$700$	7.44111			0.281247
$701$	−27.6447			−1.04413			−0.522063	−	0.852907i	$-0.674837\pi$
$701$	−27.6447			−1.04413			−0.522063	+	0.852907i	$0.674837\pi$
$702$	−3.17511	−	5.49946i	−0.119837	−	0.207564i
$703$	−14.1627	+	24.5305i	−0.534156	+	0.925186i
$704$	−2.85224	+	4.94022i	−0.107498	+	0.186192i
$705$	7.55889	+	13.0924i	0.284684	+	0.493088i
$706$	34.7092			1.30630
$707$	3.72055	+	6.44419i	0.139926	+	0.242359i
$708$	−7.37836			−0.277296
$709$	−12.6213	−	21.8607i	−0.474002	−	0.820996i	0.525555	−	0.850760i	$-0.323858\pi$
$709$	−12.6213	−	21.8607i	−0.474002	−	0.820996i	−0.999557	+	0.0297638i	$0.990524\pi$
$710$	7.29989	−	12.6438i	0.273960	−	0.474513i
$711$	6.71505	−	11.6308i	0.251834	−	0.436189i
$712$	−3.21706	−	5.57211i	−0.120564	−	0.208823i
$713$	−7.81247			−0.292579
$714$	−5.45657	−	9.45106i	−0.204207	−	0.353697i
$715$	53.5774			2.00368
$716$	3.97187	+	6.87948i	0.148436	+	0.257098i
$717$	−5.63169	+	9.75437i	−0.210319	+	0.364283i
$718$	−2.89200	+	5.00910i	−0.107929	+	0.186938i
$719$	−19.7038	−	34.1279i	−0.734826	−	1.27276i	−0.954799	−	0.297251i	$-0.903930\pi$
$719$	−19.7038	−	34.1279i	−0.734826	−	1.27276i	0.219973	−	0.975506i	$-0.429403\pi$
$720$	1.47903			0.0551201
$721$	33.2277			1.23746
$722$	7.49317			0.278867
$723$	−14.1642	−	24.5331i	−0.526772	−	0.912396i
$724$	3.69975	−	6.40815i	0.137500	−	0.238157i
$725$	3.36396	−	5.82655i	0.124934	−	0.216393i
$726$	−10.7705	−	18.6551i	−0.399732	−	0.692356i
$727$	33.9963			1.26085			0.630427	−	0.776248i	$-0.282880\pi$
$727$	33.9963			1.26085			0.630427	+	0.776248i	$0.282880\pi$
$728$	−8.40056	+	14.5502i	−0.311346	+	0.539266i
$729$	1.00000			0.0370370
$730$	6.60381	+	11.4381i	0.244418	+	0.423344i
$731$	4.12478	−	7.14433i	0.152561	−	0.264243i
$732$	−2.52097	+	4.36645i	−0.0931778	+	0.161389i
$733$	1.24590	+	2.15796i	0.0460182	+	0.0797059i	0.888117	−	0.459617i	$-0.152013\pi$
$733$	1.24590	+	2.15796i	0.0460182	+	0.0797059i	−0.842099	+	0.539323i	$0.818680\pi$
$734$	−0.669863			−0.0247251
$735$	5.17660	+	8.96614i	0.190942	+	0.330721i
$736$	−1.00000			−0.0368605
$737$	−43.9500	−	76.1237i	−1.61892	−	2.80405i
$738$	3.69609	−	6.40181i	0.136055	−	0.235654i
$739$	−23.6488	+	40.9609i	−0.869935	+	1.50677i	−0.00787354	+	0.999969i	$0.502506\pi$
$739$	−23.6488	+	40.9609i	−0.869935	+	1.50677i	−0.862062	+	0.506803i	$0.830827\pi$
$740$	−6.17511	−	10.6956i	−0.227002	−	0.393179i
$741$	−21.5411			−0.791331
$742$	−0.689180	+	1.19369i	−0.0253006	+	0.0438219i
$743$	44.5435			1.63414			0.817072	−	0.576536i	$-0.195596\pi$
$743$	44.5435			1.63414			0.817072	+	0.576536i	$0.195596\pi$
$744$	3.90624	+	6.76580i	0.143210	+	0.248046i
$745$	17.2185	−	29.8232i	0.630835	−	1.09264i
$746$	−4.90004	+	8.48712i	−0.179403	+	0.310735i
$747$	4.61071	+	7.98599i	0.168697	+	0.292192i
$748$	−23.5297			−0.860332
$749$	13.8146			0.504775
$750$	−11.5549			−0.421924
$751$	6.75523	+	11.7004i	0.246502	+	0.426954i	0.962553	−	0.271094i	$-0.0873855\pi$
$751$	6.75523	+	11.7004i	0.246502	+	0.426954i	−0.716051	+	0.698048i	$0.754052\pi$
$752$	−5.11071	+	8.85202i	−0.186369	+	0.322800i
$753$	−3.91829	+	6.78668i	−0.142791	+	0.247320i
$754$	7.59542	+	13.1556i	0.276609	+	0.479100i
$755$	−8.89460			−0.323708
$756$	−1.32288	−	2.29129i	−0.0481125	−	0.0833333i
$757$	−24.9895			−0.908259			−0.454129	−	0.890936i	$-0.650050\pi$
$757$	−24.9895			−0.908259			−0.454129	+	0.890936i	$0.650050\pi$
$758$	−0.371032	−	0.642647i	−0.0134765	−	0.0233420i
$759$	2.85224	−	4.94022i	0.103530	−	0.179319i
$760$	2.50856	−	4.34495i	0.0909950	−	0.157608i
$761$	1.26930	+	2.19849i	0.0460121	+	0.0796953i	0.888114	−	0.459623i	$-0.152015\pi$
$761$	1.26930	+	2.19849i	0.0460121	+	0.0796953i	−0.842102	+	0.539318i	$0.818682\pi$
$762$	0.0138109			0.000500316
$763$	−11.2114	−	19.4187i	−0.405879	−	0.703004i
$764$	20.1765			0.729961
$765$	3.05033	+	5.28333i	0.110285	+	0.191019i
$766$	15.2057	−	26.3371i	0.549405	−	0.951597i
$767$	−23.4271	+	40.5770i	−0.845905	+	1.46515i
$768$	0.500000	+	0.866025i	0.0180422	+	0.0312500i
$769$	−7.59435			−0.273859			−0.136930	−	0.990581i	$-0.543723\pi$
$769$	−7.59435			−0.273859			−0.136930	+	0.990581i	$0.543723\pi$
$770$	22.3224			0.804445
$771$	−3.72562			−0.134175
$772$	−6.44399	−	11.1613i	−0.231924	−	0.401705i
$773$	10.7843	−	18.6790i	0.387886	−	0.671838i	−0.604279	−	0.796773i	$-0.706539\pi$
$773$	10.7843	−	18.6790i	0.387886	−	0.671838i	0.992165	+	0.124935i	$0.0398721\pi$
$774$	1.00000	−	1.73205i	0.0359443	−	0.0622573i
$775$	−10.9862	−	19.0286i	−0.394636	−	0.683529i
$776$	10.3640			0.372047
$777$	−11.0463	+	19.1328i	−0.396284	+	0.686385i
$778$	0.674930			0.0241974
$779$	−12.5378	−	21.7160i	−0.449212	−	0.778057i
$780$	4.69609	−	8.13386i	0.168147	−	0.291239i
$781$	−28.1550	+	48.7659i	−1.00747	+	1.74498i
$782$	−2.06239	−	3.57216i	−0.0737509	−	0.127740i
$783$	−2.39217			−0.0854892
$784$	−3.50000	+	6.06218i	−0.125000	+	0.216506i
$785$	−26.4261			−0.943187
$786$	7.24807	+	12.5540i	0.258530	+	0.447787i
$787$	22.6096	−	39.1609i	0.805944	−	1.39594i	−0.109707	−	0.993964i	$-0.534991\pi$
$787$	22.6096	−	39.1609i	0.805944	−	1.39594i	0.915652	−	0.401973i	$-0.131675\pi$
$788$	4.90205	−	8.49060i	0.174628	−	0.302465i
$789$	14.4331	+	24.9988i	0.513831	+	0.889981i
$790$	19.8635			0.706711
$791$	0.959457	−	1.66183i	0.0341144	−	0.0590878i
$792$	−5.70448			−0.202700
$793$	16.0087	+	27.7280i	0.568487	+	0.984649i
$794$	4.21304	−	7.29719i	0.149515	−	0.258968i
$795$	0.385266	−	0.667300i	0.0136640	−	0.0236667i
$796$	−1.65781	−	2.87141i	−0.0587594	−	0.101774i
$797$	26.6028			0.942318			0.471159	−	0.882048i	$-0.343836\pi$
$797$	26.6028			0.942318			0.471159	+	0.882048i	$0.343836\pi$
$798$	−8.97484			−0.317706
$799$	−42.1611			−1.49155
$800$	−1.40624	−	2.43567i	−0.0497180	−	0.0861141i
$801$	3.21706	−	5.57211i	0.113669	−	0.196881i
$802$	17.5596	−	30.4141i	0.620051	−	1.07396i
$803$	−25.4703	−	44.1158i	−0.898827	−	1.55681i
$804$	−15.4090			−0.543432
$805$	1.95657	+	3.38888i	0.0689601	+	0.119442i
$806$	49.6110			1.74747
$807$	−0.241001	−	0.417426i	−0.00848363	−	0.0146941i
$808$	1.40624	−	2.43567i	0.0494712	−	0.0856867i
$809$	20.2791	−	35.1244i	0.712975	−	1.23491i	−0.250761	−	0.968049i	$-0.580681\pi$
$809$	20.2791	−	35.1244i	0.712975	−	1.23491i	0.963735	−	0.266860i	$-0.0859860\pi$
$810$	0.739514	+	1.28088i	0.0259839	+	0.0450054i
$811$	17.7894			0.624672			0.312336	−	0.949972i	$-0.398889\pi$
$811$	17.7894			0.624672			0.312336	+	0.949972i	$0.398889\pi$
$812$	3.16454	+	5.48115i	0.111054	+	0.192351i
$813$	4.89602			0.171711
$814$	23.8168	+	41.2520i	0.834780	+	1.44588i
$815$	−10.2580	+	17.7673i	−0.359320	+	0.622361i
$816$	−2.06239	+	3.57216i	−0.0721981	+	0.125051i
$817$	−3.39217	−	5.87541i	−0.118677	−	0.205555i
$818$	−19.7281			−0.689776
$819$	−16.8011			−0.587079
$820$	10.9332			0.381805
$821$	−1.72003	−	2.97918i	−0.0600294	−	0.103974i	0.834449	−	0.551085i	$-0.185786\pi$
$821$	−1.72003	−	2.97918i	−0.0600294	−	0.103974i	−0.894478	+	0.447111i	$0.852453\pi$
$822$	−4.01206	+	6.94908i	−0.139937	+	0.242377i
$823$	−3.64244	+	6.30890i	−0.126968	+	0.219914i	−0.922500	−	0.385996i	$-0.873858\pi$
$823$	−3.64244	+	6.30890i	−0.126968	+	0.219914i	0.795533	+	0.605911i	$0.207191\pi$
$824$	−6.27945	−	10.8763i	−0.218755	−	0.378895i
$825$	16.0437			0.558570
$826$	−9.76065	+	16.9059i	−0.339617	+	0.588233i
$827$	−25.4665			−0.885556			−0.442778	−	0.896631i	$-0.646007\pi$
$827$	−25.4665			−0.885556			−0.442778	+	0.896631i	$0.646007\pi$
$828$	−0.500000	−	0.866025i	−0.0173762	−	0.0300965i
$829$	−0.00330791	+	0.00572947i	−0.000114889	+	0.000198993i	−0.866083	−	0.499901i	$-0.833370\pi$
$829$	−0.00330791	+	0.00572947i	−0.000114889	+	0.000198993i	0.865968	+	0.500099i	$0.166703\pi$
$830$	−6.81938	+	11.8115i	−0.236704	+	0.409984i
$831$	7.76320	+	13.4463i	0.269303	+	0.466446i
$832$	6.35023			0.220155
$833$	−28.8735			−1.00041
$834$	14.2214			0.492448
$835$	−3.75341	−	6.50110i	−0.129892	−	0.224980i
$836$	−9.67528	+	16.7581i	−0.334627	+	0.579590i
$837$	−3.90624	+	6.76580i	−0.135019	+	0.233860i
$838$	3.63370	+	6.29375i	0.125524	+	0.217414i
$839$	14.8092			0.511269			0.255635	−	0.966773i	$-0.417716\pi$
$839$	14.8092			0.511269			0.255635	+	0.966773i	$0.417716\pi$
$840$	1.95657	−	3.38888i	0.0675081	−	0.116927i
$841$	−23.2775			−0.802673
$842$	1.91139	+	3.31062i	0.0658708	+	0.114091i
$843$	6.60014	−	11.4318i	0.227321	−	0.393732i
$844$	8.98191	−	15.5571i	0.309170	−	0.535499i
$845$	−20.2075	−	35.0005i	−0.695160	−	1.20405i
$846$	−10.2214			−0.351420
$847$	−56.9923			−1.95828
$848$	0.520971			0.0178902
$849$	−1.37836	−	2.38739i	−0.0473052	−	0.0819350i
$850$	5.80042	−	10.0466i	0.198953	−	0.344596i
$851$	−4.17511	+	7.23151i	−0.143121	+	0.247893i
$852$	4.93560	+	8.54871i	0.169091	+	0.292874i
$853$	−13.5264			−0.463135			−0.231568	−	0.972819i	$-0.574385\pi$
$853$	−13.5264			−0.463135			−0.231568	+	0.972819i	$0.574385\pi$
$854$	6.66986	+	11.5525i	0.228238	+	0.395320i
$855$	5.01712			0.171582
$856$	−2.61071	−	4.52189i	−0.0892324	−	0.154555i
$857$	−4.31371	+	7.47156i	−0.147353	+	0.255224i	−0.930248	−	0.366930i	$-0.880409\pi$
$857$	−4.31371	+	7.47156i	−0.147353	+	0.255224i	0.782895	+	0.622154i	$0.213742\pi$
$858$	−18.1124	+	31.3715i	−0.618346	+	1.07101i
$859$	−12.1537	−	21.0509i	−0.414680	−	0.718246i	0.580715	−	0.814107i	$-0.302773\pi$
$859$	−12.1537	−	21.0509i	−0.414680	−	0.718246i	−0.995395	+	0.0958607i	$0.969440\pi$
$860$	2.95806			0.100869
$861$	−9.77892	−	16.9376i	−0.333265	−	0.577232i
$862$	1.97238			0.0671795
$863$	7.38981	+	12.7995i	0.251552	+	0.435701i	0.963953	−	0.266072i	$-0.0857258\pi$
$863$	7.38981	+	12.7995i	0.251552	+	0.435701i	−0.712401	+	0.701772i	$0.752392\pi$
$864$	−0.500000	+	0.866025i	−0.0170103	+	0.0294628i
$865$	−2.16672	+	3.75287i	−0.0736708	+	0.127602i
$866$	−15.6964	−	27.1870i	−0.533387	−	0.923853i
$867$	−0.0138109			−0.000469043
$868$	20.6699			0.701581
$869$	−76.6117			−2.59887
$870$	−1.76905	−	3.06408i	−0.0599762	−	0.103882i
$871$	−48.9252	+	84.7409i	−1.65777	+	2.87134i
$872$	−4.23750	+	7.33957i	−0.143500	+	0.248549i
$873$	5.18202	+	8.97552i	0.175385	+	0.303775i
$874$	−3.39217			−0.114742
$875$	−15.2857	+	26.4755i	−0.516750	+	0.895037i
$876$	−8.92993			−0.301714
$877$	26.3546	+	45.6475i	0.889932	+	1.54141i	0.839955	+	0.542656i	$0.182581\pi$
$877$	26.3546	+	45.6475i	0.889932	+	1.54141i	0.0499769	+	0.998750i	$0.484085\pi$
$878$	−17.8603	+	30.9349i	−0.602755	+	1.04400i
$879$	0.0488479	−	0.0846070i	0.00164760	−	0.00285372i
$880$	−4.21854	−	7.30673i	−0.142207	−	0.246310i
$881$	35.2594			1.18792			0.593959	−	0.804495i	$-0.297564\pi$
$881$	35.2594			1.18792			0.593959	+	0.804495i	$0.297564\pi$
$882$	−7.00000			−0.235702
$883$	6.05906			0.203904			0.101952	−	0.994789i	$-0.467491\pi$
$883$	6.05906			0.203904			0.101952	+	0.994789i	$0.467491\pi$
$884$	13.0966	+	22.6841i	0.440488	+	0.762948i
$885$	5.45640	−	9.45077i	0.183415	−	0.317684i
$886$	−0.0572397	+	0.0991421i	−0.00192301	+	0.00333074i
$887$	2.45764	+	4.25675i	0.0825193	+	0.142928i	0.904331	−	0.426831i	$-0.140370\pi$
$887$	2.45764	+	4.25675i	0.0825193	+	0.142928i	−0.821812	+	0.569759i	$0.807037\pi$
$888$	8.35023			0.280215
$889$	0.0182701	−	0.0316448i	0.000612760	−	0.00106133i
$890$	9.51624			0.318985
$891$	−2.85224	−	4.94022i	−0.0955536	−	0.165504i
$892$	0.614734	−	1.06475i	0.0205828	−	0.0356505i
$893$	−17.3364	+	30.0276i	−0.580141	+	1.00483i
$894$	11.6417	+	20.1641i	0.389358	+	0.674387i
$895$	−11.7490			−0.392726
$896$	2.64575			0.0883883
$897$	−6.35023			−0.212028
$898$	−4.63003	−	8.01945i	−0.154506	−	0.267613i
$899$	9.34439	−	16.1850i	0.311653	−	0.539798i
$900$	1.40624	−	2.43567i	0.0468746	−	0.0811891i
$901$	1.07445	+	1.86099i	0.0357950	+	0.0619987i
$902$	−42.1685			−1.40406
$903$	−2.64575	−	4.58258i	−0.0880451	−	0.152499i
$904$	−0.725281			−0.0241225
$905$	5.47204	+	9.47784i	0.181897	+	0.315054i
$906$	3.00691	−	5.20811i	0.0998977	−	0.173028i
$907$	−17.0769	+	29.5781i	−0.567029	+	0.982124i	0.429828	+	0.902911i	$0.358574\pi$
$907$	−17.0769	+	29.5781i	−0.567029	+	0.982124i	−0.996858	+	0.0792132i	$0.974759\pi$
$908$	−8.20649	−	14.2141i	−0.272342	−	0.471710i
$909$	2.81247			0.0932839
$910$	−12.4247	−	21.5202i	−0.411874	−	0.713387i
$911$	−52.3590			−1.73473			−0.867365	−	0.497672i	$-0.834188\pi$
$911$	−52.3590			−1.73473			−0.867365	+	0.497672i	$0.834188\pi$
$912$	1.69609	+	2.93771i	0.0561630	+	0.0972772i
$913$	26.3017	−	45.5559i	0.870460	−	1.50768i
$914$	2.91865	−	5.05525i	0.0965403	−	0.167213i
$915$	−3.72859	−	6.45811i	−0.123263	−	0.213498i
$916$	−25.4163			−0.839778
$917$	38.3532			1.26653
$918$	−4.12478			−0.136138
$919$	−18.2232	−	31.5635i	−0.601127	−	1.04118i	−0.992651	−	0.121015i	$-0.961385\pi$
$919$	−18.2232	−	31.5635i	−0.601127	−	1.04118i	0.391523	−	0.920168i	$-0.371948\pi$
$920$	0.739514	−	1.28088i	0.0243811	−	0.0422292i
$921$	−12.4734	+	21.6045i	−0.411011	+	0.711892i
$922$	11.5830	+	20.0624i	0.381466	+	0.660718i
$923$	62.6844			2.06328
$924$	−7.54631	+	13.0706i	−0.248256	+	0.429991i
$925$	−23.4848			−0.772175
$926$	0.0700739	+	0.121372i	0.00230277	+	0.00398852i
$927$	6.27945	−	10.8763i	0.206244	−	0.357225i
$928$	1.19609	−	2.07168i	0.0392634	−	0.0680063i
$929$	27.7227	+	48.0171i	0.909551	+	1.57539i	0.814689	+	0.579898i	$0.196908\pi$
$929$	27.7227	+	48.0171i	0.909551	+	1.57539i	0.0948619	+	0.995490i	$0.469759\pi$
$930$	−11.5549			−0.378899
$931$	−11.8726	+	20.5639i	−0.389109	+	0.673956i
$932$	0.551566			0.0180671
$933$	13.2439	+	22.9391i	0.433585	+	0.750992i
$934$	7.75848	−	13.4381i	0.253865	−	0.439707i
$935$	17.4006	−	30.1387i	0.569059	−	0.985640i
$936$	3.17511	+	5.49946i	0.103782	+	0.179755i
$937$	−0.308796			−0.0100879			−0.00504396	−	0.999987i	$-0.501606\pi$
$937$	−0.308796			−0.0100879			−0.00504396	+	0.999987i	$0.501606\pi$
$938$	−20.3841	+	35.3064i	−0.665565	+	1.15279i
$939$	19.2382			0.627815
$940$	−7.55889	−	13.0924i	−0.246544	−	0.427027i
$941$	7.75228	−	13.4273i	0.252717	−	0.437719i	−0.711556	−	0.702629i	$-0.752009\pi$
$941$	7.75228	−	13.4273i	0.252717	−	0.437719i	0.964273	+	0.264911i	$0.0853425\pi$
$942$	8.93359	−	15.4734i	0.291072	−	0.504152i
$943$	−3.69609	−	6.40181i	−0.120361	−	0.208472i
$944$	7.37836			0.240145
$945$	3.91314			0.127295
$946$	−11.4090			−0.370937
$947$	−29.3462	−	50.8291i	−0.953624	−	1.65172i	−0.737487	−	0.675362i	$-0.763988\pi$
$947$	−29.3462	−	50.8291i	−0.953624	−	1.65172i	−0.216137	−	0.976363i	$-0.569346\pi$
$948$	−6.71505	+	11.6308i	−0.218095	+	0.377751i
$949$	−28.3535	+	49.1098i	−0.920395	+	1.59417i
$950$	−4.77020	−	8.26222i	−0.154766	−	0.268062i
$951$	−25.3784			−0.822950
$952$	5.45657	+	9.45106i	0.176848	+	0.306311i
$953$	28.6120			0.926835			0.463417	−	0.886140i	$-0.346623\pi$
$953$	28.6120			0.926835			0.463417	+	0.886140i	$0.346623\pi$
$954$	0.260486	+	0.451174i	0.00843353	+	0.0146073i
$955$	−14.9208	+	25.8436i	−0.482826	+	0.836280i
$956$	5.63169	−	9.75437i	0.182142	−	0.315479i
$957$	6.82304	+	11.8179i	0.220558	+	0.382017i
$958$	−15.3922			−0.497298
$959$	10.6149	+	18.3855i	0.342773	+	0.593700i
$960$	−1.47903			−0.0477354
$961$	−15.0174	−	26.0109i	−0.484431	−	0.839060i
$962$	26.5129	−	45.9217i	0.854811	−	1.48058i
$963$	2.61071	−	4.52189i	0.0841291	−	0.145716i
$964$	14.1642	+	24.5331i	0.456198	+	0.790158i
$965$	19.0617			0.613618
$966$	−2.64575			−0.0851257
$967$	−15.7059			−0.505067			−0.252534	−	0.967588i	$-0.581264\pi$
$967$	−15.7059			−0.505067			−0.252534	+	0.967588i	$0.581264\pi$
$968$	10.7705	+	18.6551i	0.346178	+	0.599598i
$969$	−6.99598	+	12.1174i	−0.224743	+	0.389267i
$970$	−7.66436	+	13.2751i	−0.246088	+	0.426236i
$971$	−8.38300	−	14.5198i	−0.269023	−	0.465962i	0.699587	−	0.714548i	$-0.253368\pi$
$971$	−8.38300	−	14.5198i	−0.269023	−	0.465962i	−0.968610	+	0.248586i	$0.920034\pi$
$972$	−1.00000			−0.0320750
$973$	18.8132	−	32.5854i	0.603123	−	1.04464i
$974$	0.554539			0.0177686
$975$	−8.92993	−	15.4671i	−0.285987	−	0.495343i
$976$	2.52097	−	4.36645i	0.0806943	−	0.139767i
$977$	−8.68665	+	15.0457i	−0.277910	+	0.481355i	−0.970865	−	0.239626i	$-0.922975\pi$
$977$	−8.68665	+	15.0457i	−0.277910	+	0.481355i	0.692955	+	0.720981i	$0.256309\pi$
$978$	−6.93560	−	12.0128i	−0.221776	−	0.384127i
$979$	−36.7033			−1.17304
$980$	−5.17660	−	8.96614i	−0.165360	−	0.286413i
$981$	−8.47501			−0.270586
$982$	21.5983	+	37.4094i	0.689230	+	1.19378i
$983$	−12.0433	+	20.8597i	−0.384123	+	0.665320i	−0.991647	−	0.128981i	$-0.958829\pi$
$983$	−12.0433	+	20.8597i	−0.384123	+	0.665320i	0.607524	+	0.794301i	$0.292163\pi$
$984$	−3.69609	+	6.40181i	−0.117827	+	0.204082i
$985$	7.25027	+	12.5578i	0.231013	+	0.400126i
$986$	9.86718			0.314235
$987$	−13.5217	+	23.4202i	−0.430400	+	0.745474i
$988$	21.5411			0.685313
$989$	−1.00000	−	1.73205i	−0.0317982	−	0.0550760i
$990$	4.21854	−	7.30673i	0.134074	−	0.232223i
$991$	−28.3396	+	49.0857i	−0.900238	+	1.55926i	−0.0730538	+	0.997328i	$0.523274\pi$
$991$	−28.3396	+	49.0857i	−0.900238	+	1.55926i	−0.827184	+	0.561930i	$0.810059\pi$
$992$	−3.90624	−	6.76580i	−0.124023	−	0.214814i
$993$	−2.84273			−0.0902114
$994$	26.1167			0.828373
$995$	4.90389			0.155464
$996$	−4.61071	−	7.98599i	−0.146096	−	0.253046i
$997$	−20.7019	+	35.8567i	−0.655634	+	1.13559i	0.326100	+	0.945335i	$0.394265\pi$
$997$	−20.7019	+	35.8567i	−0.655634	+	1.13559i	−0.981734	+	0.190257i	$0.939068\pi$
$998$	−10.4471	+	18.0950i	−0.330698	+	0.572786i
$999$	4.17511	+	7.23151i	0.132095	+	0.228795i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.i.n.277.2	✓	8
7.2	even	3	inner	966.2.i.n.415.2	yes	8
7.3	odd	6		6762.2.a.ch.1.2		4
7.4	even	3		6762.2.a.cg.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.i.n.277.2	✓	8	1.1	even	1	trivial
966.2.i.n.415.2	yes	8	7.2	even	3	inner
6762.2.a.cg.1.3		4	7.4	even	3
6762.2.a.ch.1.2		4	7.3	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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.739514 - 1.28088i) q^{5} +1.00000 q^{6} +(1.32288 - 2.29129i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.739514 - 1.28088i) q^{5} +1.00000 q^{6} +(1.32288 - 2.29129i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.739514 - 1.28088i) q^{10} +(-2.85224 + 4.94022i) q^{11} +(0.500000 + 0.866025i) q^{12} +6.35023 q^{13} +2.64575 q^{14} -1.47903 q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.06239 - 3.57216i) q^{17} +(0.500000 - 0.866025i) q^{18} +(-1.69609 - 2.93771i) q^{19} +1.47903 q^{20} +(-1.32288 - 2.29129i) q^{21} -5.70448 q^{22} +(-0.500000 - 0.866025i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(1.40624 - 2.43567i) q^{25} +(3.17511 + 5.49946i) q^{26} -1.00000 q^{27} +(1.32288 + 2.29129i) q^{28} +2.39217 q^{29} +(-0.739514 - 1.28088i) q^{30} +(3.90624 - 6.76580i) q^{31} +(0.500000 - 0.866025i) q^{32} +(2.85224 + 4.94022i) q^{33} +4.12478 q^{34} -3.91314 q^{35} +1.00000 q^{36} +(-4.17511 - 7.23151i) q^{37} +(1.69609 - 2.93771i) q^{38} +(3.17511 - 5.49946i) q^{39} +(0.739514 + 1.28088i) q^{40} +7.39217 q^{41} +(1.32288 - 2.29129i) q^{42} +2.00000 q^{43} +(-2.85224 - 4.94022i) q^{44} +(-0.739514 + 1.28088i) q^{45} +(0.500000 - 0.866025i) q^{46} +(-5.11071 - 8.85202i) q^{47} -1.00000 q^{48} +(-3.50000 - 6.06218i) q^{49} +2.81247 q^{50} +(-2.06239 - 3.57216i) q^{51} +(-3.17511 + 5.49946i) q^{52} +(-0.260486 + 0.451174i) q^{53} +(-0.500000 - 0.866025i) q^{54} +8.43709 q^{55} +(-1.32288 + 2.29129i) q^{56} -3.39217 q^{57} +(1.19609 + 2.07168i) q^{58} +(-3.68918 + 6.38985i) q^{59} +(0.739514 - 1.28088i) q^{60} +(2.52097 + 4.36645i) q^{61} +7.81247 q^{62} -2.64575 q^{63} +1.00000 q^{64} +(-4.69609 - 8.13386i) q^{65} +(-2.85224 + 4.94022i) q^{66} +(-7.70448 + 13.3445i) q^{67} +(2.06239 + 3.57216i) q^{68} -1.00000 q^{69} +(-1.95657 - 3.38888i) q^{70} +9.87120 q^{71} +(0.500000 + 0.866025i) q^{72} +(-4.46496 + 7.73354i) q^{73} +(4.17511 - 7.23151i) q^{74} +(-1.40624 - 2.43567i) q^{75} +3.39217 q^{76} +(7.54631 + 13.0706i) q^{77} +6.35023 q^{78} +(6.71505 + 11.6308i) q^{79} +(-0.739514 + 1.28088i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(3.69609 + 6.40181i) q^{82} -9.22143 q^{83} +2.64575 q^{84} -6.10067 q^{85} +(1.00000 + 1.73205i) q^{86} +(1.19609 - 2.07168i) q^{87} +(2.85224 - 4.94022i) q^{88} +(3.21706 + 5.57211i) q^{89} -1.47903 q^{90} +(8.40056 - 14.5502i) q^{91} +1.00000 q^{92} +(-3.90624 - 6.76580i) q^{93} +(5.11071 - 8.85202i) q^{94} +(-2.50856 + 4.34495i) q^{95} +(-0.500000 - 0.866025i) q^{96} -10.3640 q^{97} +(3.50000 - 6.06218i) q^{98} +5.70448 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} + 4 q^{3} - 4 q^{4} - 2 q^{5} + 8 q^{6} - 8 q^{8} - 4 q^{9}+O(q^{10}) \) 8 * q + 4 * q^2 + 4 * q^3 - 4 * q^4 - 2 * q^5 + 8 * q^6 - 8 * q^8 - 4 * q^9	\( 8 q + 4 q^{2} + 4 q^{3} - 4 q^{4} - 2 q^{5} + 8 q^{6} - 8 q^{8} - 4 q^{9} + 2 q^{10} - 6 q^{11} + 4 q^{12} - 4 q^{13} - 4 q^{15} - 4 q^{16} + 2 q^{17} + 4 q^{18} + 6 q^{19} + 4 q^{20} - 12 q^{22} - 4 q^{23} - 4 q^{24} - 6 q^{25} - 2 q^{26} - 8 q^{27} - 20 q^{29} - 2 q^{30} + 14 q^{31} + 4 q^{32} + 6 q^{33} + 4 q^{34} + 8 q^{36} - 6 q^{37} - 6 q^{38} - 2 q^{39} + 2 q^{40} + 20 q^{41} + 16 q^{43} - 6 q^{44} - 2 q^{45} + 4 q^{46} + 10 q^{47} - 8 q^{48} - 28 q^{49} - 12 q^{50} - 2 q^{51} + 2 q^{52} - 6 q^{53} - 4 q^{54} + 44 q^{55} + 12 q^{57} - 10 q^{58} - 24 q^{59} + 2 q^{60} + 28 q^{61} + 28 q^{62} + 8 q^{64} - 18 q^{65} - 6 q^{66} - 28 q^{67} + 2 q^{68} - 8 q^{69} + 32 q^{71} + 4 q^{72} - 6 q^{73} + 6 q^{74} + 6 q^{75} - 12 q^{76} - 14 q^{77} - 4 q^{78} + 4 q^{79} - 2 q^{80} - 4 q^{81} + 10 q^{82} + 28 q^{83} - 52 q^{85} + 8 q^{86} - 10 q^{87} + 6 q^{88} + 14 q^{89} - 4 q^{90} + 14 q^{91} + 8 q^{92} - 14 q^{93} - 10 q^{94} + 34 q^{95} - 4 q^{96} + 28 q^{98} + 12 q^{99}+O(q^{100}) \) 8 * q + 4 * q^2 + 4 * q^3 - 4 * q^4 - 2 * q^5 + 8 * q^6 - 8 * q^8 - 4 * q^9 + 2 * q^10 - 6 * q^11 + 4 * q^12 - 4 * q^13 - 4 * q^15 - 4 * q^16 + 2 * q^17 + 4 * q^18 + 6 * q^19 + 4 * q^20 - 12 * q^22 - 4 * q^23 - 4 * q^24 - 6 * q^25 - 2 * q^26 - 8 * q^27 - 20 * q^29 - 2 * q^30 + 14 * q^31 + 4 * q^32 + 6 * q^33 + 4 * q^34 + 8 * q^36 - 6 * q^37 - 6 * q^38 - 2 * q^39 + 2 * q^40 + 20 * q^41 + 16 * q^43 - 6 * q^44 - 2 * q^45 + 4 * q^46 + 10 * q^47 - 8 * q^48 - 28 * q^49 - 12 * q^50 - 2 * q^51 + 2 * q^52 - 6 * q^53 - 4 * q^54 + 44 * q^55 + 12 * q^57 - 10 * q^58 - 24 * q^59 + 2 * q^60 + 28 * q^61 + 28 * q^62 + 8 * q^64 - 18 * q^65 - 6 * q^66 - 28 * q^67 + 2 * q^68 - 8 * q^69 + 32 * q^71 + 4 * q^72 - 6 * q^73 + 6 * q^74 + 6 * q^75 - 12 * q^76 - 14 * q^77 - 4 * q^78 + 4 * q^79 - 2 * q^80 - 4 * q^81 + 10 * q^82 + 28 * q^83 - 52 * q^85 + 8 * q^86 - 10 * q^87 + 6 * q^88 + 14 * q^89 - 4 * q^90 + 14 * q^91 + 8 * q^92 - 14 * q^93 - 10 * q^94 + 34 * q^95 - 4 * q^96 + 28 * q^98 + 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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