LMFDB - Embedded newform 670.2.e.g.171.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [670,2,Mod(171,670)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(670, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("670.171");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 670 = 2 \cdot 5 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	670.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:	$5.34997693543$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.954288.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 2x^{4} + 3x^{3} - 6x^{2} - 9x + 27 $ x^6 - x^5 - 2x^4 + 3x^3 - 6x^2 - 9x + 27
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			171.1
Root			$0.403374 - 1.68443i$ of defining polynomial
Character	$\chi$	$=$	670.171
Dual form			670.2.e.g.431.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} -2.51414 q^{3} +(-0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(-1.25707 - 2.17731i) q^{6} +(-0.0966262 + 0.167362i) q^{7} -1.00000 q^{8} +3.32088 q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} -2.51414 q^{3} +(-0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(-1.25707 - 2.17731i) q^{6} +(-0.0966262 + 0.167362i) q^{7} -1.00000 q^{8} +3.32088 q^{9} +(0.500000 + 0.866025i) q^{10} +(2.66044 - 4.60802i) q^{11} +(1.25707 - 2.17731i) q^{12} +(-0.0966262 - 0.167362i) q^{13} -0.193252 q^{14} -2.51414 q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.91751 + 5.05328i) q^{17} +(1.66044 + 2.87597i) q^{18} +(0.500000 + 0.866025i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(0.242932 - 0.420770i) q^{21} +5.32088 q^{22} +(0.903374 + 1.56469i) q^{23} +2.51414 q^{24} +1.00000 q^{25} +(0.0966262 - 0.167362i) q^{26} -0.806748 q^{27} +(-0.0966262 - 0.167362i) q^{28} +(0.563816 - 0.976558i) q^{29} +(-1.25707 - 2.17731i) q^{30} +(-0.485863 + 0.841540i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-6.68872 + 11.5852i) q^{33} +(-2.91751 + 5.05328i) q^{34} +(-0.0966262 + 0.167362i) q^{35} +(-1.66044 + 2.87597i) q^{36} +(5.34916 + 9.26501i) q^{37} +(-0.500000 + 0.866025i) q^{38} +(0.242932 + 0.420770i) q^{39} -1.00000 q^{40} +(-0.339558 + 0.588131i) q^{41} +0.485863 q^{42} +2.51414 q^{43} +(2.66044 + 4.60802i) q^{44} +3.32088 q^{45} +(-0.903374 + 1.56469i) q^{46} +(-3.00000 + 5.19615i) q^{47} +(1.25707 + 2.17731i) q^{48} +(3.48133 + 6.02983i) q^{49} +(0.500000 + 0.866025i) q^{50} +(-7.33502 - 12.7046i) q^{51} +0.193252 q^{52} +8.83502 q^{53} +(-0.403374 - 0.698664i) q^{54} +(2.66044 - 4.60802i) q^{55} +(0.0966262 - 0.167362i) q^{56} +(-1.25707 - 2.17731i) q^{57} +1.12763 q^{58} +5.73566 q^{59} +(1.25707 - 2.17731i) q^{60} +(-0.320884 - 0.555788i) q^{61} -0.971726 q^{62} +(-0.320884 + 0.555788i) q^{63} +1.00000 q^{64} +(-0.0966262 - 0.167362i) q^{65} -13.3774 q^{66} +(-6.98133 - 4.27330i) q^{67} -5.83502 q^{68} +(-2.27121 - 3.93384i) q^{69} -0.193252 q^{70} +(4.75707 - 8.23948i) q^{71} -3.32088 q^{72} +(1.91751 + 3.32123i) q^{73} +(-5.34916 + 9.26501i) q^{74} -2.51414 q^{75} -1.00000 q^{76} +(0.514137 + 0.890511i) q^{77} +(-0.242932 + 0.420770i) q^{78} +(0.292611 - 0.506816i) q^{79} +(-0.500000 - 0.866025i) q^{80} -7.93438 q^{81} -0.679116 q^{82} +(-1.36783 - 2.36915i) q^{83} +(0.242932 + 0.420770i) q^{84} +(2.91751 + 5.05328i) q^{85} +(1.25707 + 2.17731i) q^{86} +(-1.41751 + 2.45520i) q^{87} +(-2.66044 + 4.60802i) q^{88} +8.67004 q^{89} +(1.66044 + 2.87597i) q^{90} +0.0373465 q^{91} -1.80675 q^{92} +(1.22153 - 2.11575i) q^{93} -6.00000 q^{94} +(0.500000 + 0.866025i) q^{95} +(-1.25707 + 2.17731i) q^{96} +(-7.43165 - 12.8720i) q^{97} +(-3.48133 + 6.02983i) q^{98} +(8.83502 - 15.3027i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} - 2 q^{3} - 3 q^{4} + 6 q^{5} - q^{6} - 2 q^{7} - 6 q^{8} + 4 q^{9}+O(q^{10}) $ 6 * q + 3 * q^2 - 2 * q^3 - 3 * q^4 + 6 * q^5 - q^6 - 2 * q^7 - 6 * q^8 + 4 * q^9	\( 6 q + 3 q^{2} - 2 q^{3} - 3 q^{4} + 6 q^{5} - q^{6} - 2 q^{7} - 6 q^{8} + 4 q^{9} + 3 q^{10} + 8 q^{11} + q^{12} - 2 q^{13} - 4 q^{14} - 2 q^{15} - 3 q^{16} + 3 q^{17} + 2 q^{18} + 3 q^{19} - 3 q^{20} + 8 q^{21} + 16 q^{22} + 4 q^{23} + 2 q^{24} + 6 q^{25} + 2 q^{26} - 2 q^{27} - 2 q^{28} - 6 q^{29} - q^{30} - 16 q^{31} + 3 q^{32} - 6 q^{33} - 3 q^{34} - 2 q^{35} - 2 q^{36} - 10 q^{37} - 3 q^{38} + 8 q^{39} - 6 q^{40} - 10 q^{41} + 16 q^{42} + 2 q^{43} + 8 q^{44} + 4 q^{45} - 4 q^{46} - 18 q^{47} + q^{48} - 3 q^{49} + 3 q^{50} - 15 q^{51} + 4 q^{52} + 24 q^{53} - q^{54} + 8 q^{55} + 2 q^{56} - q^{57} - 12 q^{58} - 2 q^{59} + q^{60} + 14 q^{61} - 32 q^{62} + 14 q^{63} + 6 q^{64} - 2 q^{65} - 12 q^{66} - 18 q^{67} - 6 q^{68} + 6 q^{69} - 4 q^{70} + 22 q^{71} - 4 q^{72} - 3 q^{73} + 10 q^{74} - 2 q^{75} - 6 q^{76} - 10 q^{77} - 8 q^{78} + 12 q^{79} - 3 q^{80} - 26 q^{81} - 20 q^{82} + 10 q^{83} + 8 q^{84} + 3 q^{85} + q^{86} + 6 q^{87} - 8 q^{88} - 6 q^{89} + 2 q^{90} + 48 q^{91} - 8 q^{92} - 16 q^{93} - 36 q^{94} + 3 q^{95} - q^{96} - 17 q^{97} + 3 q^{98} + 24 q^{99}+O(q^{100}) \) 6 * q + 3 * q^2 - 2 * q^3 - 3 * q^4 + 6 * q^5 - q^6 - 2 * q^7 - 6 * q^8 + 4 * q^9 + 3 * q^10 + 8 * q^11 + q^12 - 2 * q^13 - 4 * q^14 - 2 * q^15 - 3 * q^16 + 3 * q^17 + 2 * q^18 + 3 * q^19 - 3 * q^20 + 8 * q^21 + 16 * q^22 + 4 * q^23 + 2 * q^24 + 6 * q^25 + 2 * q^26 - 2 * q^27 - 2 * q^28 - 6 * q^29 - q^30 - 16 * q^31 + 3 * q^32 - 6 * q^33 - 3 * q^34 - 2 * q^35 - 2 * q^36 - 10 * q^37 - 3 * q^38 + 8 * q^39 - 6 * q^40 - 10 * q^41 + 16 * q^42 + 2 * q^43 + 8 * q^44 + 4 * q^45 - 4 * q^46 - 18 * q^47 + q^48 - 3 * q^49 + 3 * q^50 - 15 * q^51 + 4 * q^52 + 24 * q^53 - q^54 + 8 * q^55 + 2 * q^56 - q^57 - 12 * q^58 - 2 * q^59 + q^60 + 14 * q^61 - 32 * q^62 + 14 * q^63 + 6 * q^64 - 2 * q^65 - 12 * q^66 - 18 * q^67 - 6 * q^68 + 6 * q^69 - 4 * q^70 + 22 * q^71 - 4 * q^72 - 3 * q^73 + 10 * q^74 - 2 * q^75 - 6 * q^76 - 10 * q^77 - 8 * q^78 + 12 * q^79 - 3 * q^80 - 26 * q^81 - 20 * q^82 + 10 * q^83 + 8 * q^84 + 3 * q^85 + q^86 + 6 * q^87 - 8 * q^88 - 6 * q^89 + 2 * q^90 + 48 * q^91 - 8 * q^92 - 16 * q^93 - 36 * q^94 + 3 * q^95 - q^96 - 17 * q^97 + 3 * q^98 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/670\mathbb{Z}\right)^\times$.

$n$	$471$	$537$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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
$3$	−2.51414			−1.45154			−0.725769	−	0.687939i	$-0.758516\pi$
$3$	−2.51414			−1.45154			−0.725769	+	0.687939i	$0.758516\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	−1.25707	−	2.17731i	−0.513196	−	0.888882i
$7$	−0.0966262	+	0.167362i	−0.0365213	+	0.0632567i	−0.883708	−	0.468038i	$-0.844961\pi$
$7$	−0.0966262	+	0.167362i	−0.0365213	+	0.0632567i	0.847187	+	0.531295i	$0.178294\pi$
$8$	−1.00000			−0.353553
$9$	3.32088			1.10696
$10$	0.500000	+	0.866025i	0.158114	+	0.273861i
$11$	2.66044	−	4.60802i	0.802154	−	1.38937i	−0.116042	−	0.993244i	$-0.537021\pi$
$11$	2.66044	−	4.60802i	0.802154	−	1.38937i	0.918196	−	0.396126i	$-0.129646\pi$
$12$	1.25707	−	2.17731i	0.362884	−	0.628534i
$13$	−0.0966262	−	0.167362i	−0.0267993	−	0.0464177i	0.852315	−	0.523029i	$-0.175198\pi$
$13$	−0.0966262	−	0.167362i	−0.0267993	−	0.0464177i	−0.879114	+	0.476612i	$0.841865\pi$
$14$	−0.193252			−0.0516489
$15$	−2.51414			−0.649147
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	2.91751	+	5.05328i	0.707600	+	1.22560i	0.965745	+	0.259493i	$0.0835556\pi$
$17$	2.91751	+	5.05328i	0.707600	+	1.22560i	−0.258145	+	0.966106i	$0.583111\pi$
$18$	1.66044	+	2.87597i	0.391370	+	0.677873i
$19$	0.500000	+	0.866025i	0.114708	+	0.198680i	0.917663	−	0.397360i	$-0.130073\pi$
$19$	0.500000	+	0.866025i	0.114708	+	0.198680i	−0.802955	+	0.596040i	$0.796740\pi$
$20$	−0.500000	+	0.866025i	−0.111803	+	0.193649i
$21$	0.242932	−	0.420770i	0.0530120	−	0.0918195i
$22$	5.32088			1.13442
$23$	0.903374	+	1.56469i	0.188366	+	0.326260i	0.944706	−	0.327919i	$-0.106347\pi$
$23$	0.903374	+	1.56469i	0.188366	+	0.326260i	−0.756339	+	0.654180i	$0.773014\pi$
$24$	2.51414			0.513196
$25$	1.00000			0.200000
$26$	0.0966262	−	0.167362i	0.0189500	−	0.0328223i
$27$	−0.806748			−0.155259
$28$	−0.0966262	−	0.167362i	−0.0182606	−	0.0316284i
$29$	0.563816	−	0.976558i	0.104698	−	0.181342i	−0.808917	−	0.587923i	$-0.799946\pi$
$29$	0.563816	−	0.976558i	0.104698	−	0.181342i	0.913615	+	0.406581i	$0.133279\pi$
$30$	−1.25707	−	2.17731i	−0.229508	−	0.397520i
$31$	−0.485863	+	0.841540i	−0.0872636	+	0.151145i	−0.906354	−	0.422520i	$-0.861146\pi$
$31$	−0.485863	+	0.841540i	−0.0872636	+	0.151145i	0.819090	+	0.573665i	$0.194479\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−6.68872	+	11.5852i	−1.16436	+	2.01672i
$34$	−2.91751	+	5.05328i	−0.500349	+	0.866630i
$35$	−0.0966262	+	0.167362i	−0.0163328	+	0.0282893i
$36$	−1.66044	+	2.87597i	−0.276740	+	0.479328i
$37$	5.34916	+	9.26501i	0.879396	+	1.52316i	0.852005	+	0.523534i	$0.175387\pi$
$37$	5.34916	+	9.26501i	0.879396	+	1.52316i	0.0273915	+	0.999625i	$0.491280\pi$
$38$	−0.500000	+	0.866025i	−0.0811107	+	0.140488i
$39$	0.242932	+	0.420770i	0.0389002	+	0.0673771i
$40$	−1.00000			−0.158114
$41$	−0.339558	+	0.588131i	−0.0530300	+	0.0918507i	−0.891322	−	0.453371i	$-0.850221\pi$
$41$	−0.339558	+	0.588131i	−0.0530300	+	0.0918507i	0.838292	+	0.545222i	$0.183555\pi$
$42$	0.485863			0.0749703
$43$	2.51414			0.383402			0.191701	−	0.981453i	$-0.438600\pi$
$43$	2.51414			0.383402			0.191701	+	0.981453i	$0.438600\pi$
$44$	2.66044	+	4.60802i	0.401077	+	0.694685i
$45$	3.32088			0.495048
$46$	−0.903374	+	1.56469i	−0.133195	+	0.230701i
$47$	−3.00000	+	5.19615i	−0.437595	+	0.757937i	−0.997503	−	0.0706177i	$-0.977503\pi$
$47$	−3.00000	+	5.19615i	−0.437595	+	0.757937i	0.559908	+	0.828554i	$0.310836\pi$
$48$	1.25707	+	2.17731i	0.181442	+	0.314267i
$49$	3.48133	+	6.02983i	0.497332	+	0.861405i
$50$	0.500000	+	0.866025i	0.0707107	+	0.122474i
$51$	−7.33502	−	12.7046i	−1.02711	−	1.77900i
$52$	0.193252			0.0267993
$53$	8.83502			1.21358			0.606792	−	0.794861i	$-0.292456\pi$
$53$	8.83502			1.21358			0.606792	+	0.794861i	$0.292456\pi$
$54$	−0.403374	−	0.698664i	−0.0548922	−	0.0950761i
$55$	2.66044	−	4.60802i	0.358734	−	0.621345i
$56$	0.0966262	−	0.167362i	0.0129122	−	0.0223646i
$57$	−1.25707	−	2.17731i	−0.166503	−	0.288391i
$58$	1.12763			0.148065
$59$	5.73566			0.746720			0.373360	−	0.927687i	$-0.378206\pi$
$59$	5.73566			0.746720			0.373360	+	0.927687i	$0.378206\pi$
$60$	1.25707	−	2.17731i	0.162287	−	0.281089i
$61$	−0.320884	−	0.555788i	−0.0410851	−	0.0711614i	0.844752	−	0.535159i	$-0.179748\pi$
$61$	−0.320884	−	0.555788i	−0.0410851	−	0.0711614i	−0.885837	+	0.463997i	$0.846415\pi$
$62$	−0.971726			−0.123409
$63$	−0.320884	+	0.555788i	−0.0404276	+	0.0700227i
$64$	1.00000			0.125000
$65$	−0.0966262	−	0.167362i	−0.0119850	−	0.0207586i
$66$	−13.3774			−1.64665
$67$	−6.98133	−	4.27330i	−0.852905	−	0.522066i
$67$	−6.98133	−	4.27330i	−0.852905	−	0.522066i
$68$	−5.83502			−0.707600
$69$	−2.27121	−	3.93384i	−0.273421	−	0.473579i
$70$	−0.193252			−0.0230981
$71$	4.75707	−	8.23948i	0.564560	−	0.977847i	−0.432530	−	0.901619i	$-0.642379\pi$
$71$	4.75707	−	8.23948i	0.564560	−	0.977847i	0.997090	−	0.0762275i	$-0.0242875\pi$
$72$	−3.32088			−0.391370
$73$	1.91751	+	3.32123i	0.224428	+	0.388720i	0.956148	−	0.292885i	$-0.0946154\pi$
$73$	1.91751	+	3.32123i	0.224428	+	0.388720i	−0.731720	+	0.681605i	$0.761282\pi$
$74$	−5.34916	+	9.26501i	−0.621827	+	1.07704i
$75$	−2.51414			−0.290308
$76$	−1.00000			−0.114708
$77$	0.514137	+	0.890511i	0.0585913	+	0.101483i
$78$	−0.242932	+	0.420770i	−0.0275066	+	0.0476428i
$79$	0.292611	−	0.506816i	0.0329213	−	0.0570213i	−0.849095	−	0.528240i	$-0.822852\pi$
$79$	0.292611	−	0.506816i	0.0329213	−	0.0570213i	0.882017	+	0.471218i	$0.156186\pi$
$80$	−0.500000	−	0.866025i	−0.0559017	−	0.0968246i
$81$	−7.93438			−0.881598
$82$	−0.679116			−0.0749958
$83$	−1.36783	−	2.36915i	−0.150139	−	0.260048i	0.781139	−	0.624357i	$-0.214639\pi$
$83$	−1.36783	−	2.36915i	−0.150139	−	0.260048i	−0.931278	+	0.364308i	$0.881305\pi$
$84$	0.242932	+	0.420770i	0.0265060	+	0.0459097i
$85$	2.91751	+	5.05328i	0.316448	+	0.548105i
$86$	1.25707	+	2.17731i	0.135553	+	0.234785i
$87$	−1.41751	+	2.45520i	−0.151973	+	0.263225i
$88$	−2.66044	+	4.60802i	−0.283604	+	0.491217i
$89$	8.67004			0.919023			0.459511	−	0.888172i	$-0.348025\pi$
$89$	8.67004			0.919023			0.459511	+	0.888172i	$0.348025\pi$
$90$	1.66044	+	2.87597i	0.175026	+	0.303154i
$91$	0.0373465			0.00391498
$92$	−1.80675			−0.188366
$93$	1.22153	−	2.11575i	0.126666	−	0.219393i
$94$	−6.00000			−0.618853
$95$	0.500000	+	0.866025i	0.0512989	+	0.0888523i
$96$	−1.25707	+	2.17731i	−0.128299	+	0.222220i
$97$	−7.43165	−	12.8720i	−0.754569	−	1.30695i	−0.945588	−	0.325366i	$-0.894512\pi$
$97$	−7.43165	−	12.8720i	−0.754569	−	1.30695i	0.191019	−	0.981586i	$-0.438821\pi$
$98$	−3.48133	+	6.02983i	−0.351667	+	0.609105i
$99$	8.83502	−	15.3027i	0.887953	−	1.53798i
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	0.563816	−	0.976558i	0.0561018	−	0.0971712i	−0.836611	−	0.547798i	$-0.815466\pi$
$101$	0.563816	−	0.976558i	0.0561018	−	0.0971712i	0.892712	+	0.450627i	$0.148800\pi$
$102$	7.33502	−	12.7046i	0.726275	−	1.25795i
$103$	7.15591	−	12.3944i	0.705092	−	1.22126i	−0.261566	−	0.965186i	$-0.584239\pi$
$103$	7.15591	−	12.3944i	0.705092	−	1.22126i	0.966658	−	0.256070i	$-0.0824278\pi$
$104$	0.0966262	+	0.167362i	0.00947498	+	0.0164111i
$105$	0.242932	−	0.420770i	0.0237077	−	0.0410629i
$106$	4.41751	+	7.65135i	0.429067	+	0.743165i
$107$	−2.25526			−0.218025			−0.109012	−	0.994040i	$-0.534769\pi$
$107$	−2.25526			−0.218025			−0.109012	+	0.994040i	$0.534769\pi$
$108$	0.403374	−	0.698664i	0.0388147	−	0.0672290i
$109$	4.48586			0.429668			0.214834	−	0.976651i	$-0.431079\pi$
$109$	4.48586			0.429668			0.214834	+	0.976651i	$0.431079\pi$
$110$	5.32088			0.507326
$111$	−13.4485	−	23.2935i	−1.27648	−	2.21092i
$112$	0.193252			0.0182606
$113$	−3.93618	+	6.81767i	−0.370285	+	0.641353i	−0.989609	−	0.143783i	$-0.954073\pi$
$113$	−3.93618	+	6.81767i	−0.370285	+	0.641353i	0.619324	+	0.785135i	$0.287407\pi$
$114$	1.25707	−	2.17731i	0.117735	−	0.203923i
$115$	0.903374	+	1.56469i	0.0842400	+	0.145908i
$116$	0.563816	+	0.976558i	0.0523490	+	0.0906711i
$117$	−0.320884	−	0.555788i	−0.0296658	−	0.0513826i
$118$	2.86783	+	4.96723i	0.264005	+	0.457271i
$119$	−1.12763			−0.103370
$120$	2.51414			0.229508
$121$	−8.65591	−	14.9925i	−0.786901	−	1.36295i
$122$	0.320884	−	0.555788i	0.0290515	−	0.0503187i
$123$	0.853695	−	1.47864i	0.0769751	−	0.133325i
$124$	−0.485863	−	0.841540i	−0.0436318	−	0.0755725i
$125$	1.00000			0.0894427
$126$	−0.641769			−0.0571733
$127$	3.19325	−	5.53088i	0.283355	−	0.490786i	−0.688854	−	0.724900i	$-0.741886\pi$
$127$	3.19325	−	5.53088i	0.283355	−	0.490786i	0.972209	+	0.234115i	$0.0752191\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	−6.32088			−0.556523
$130$	0.0966262	−	0.167362i	0.00847468	−	0.0146786i
$131$	1.70739			0.149175			0.0745877	−	0.997214i	$-0.476236\pi$
$131$	1.70739			0.149175			0.0745877	+	0.997214i	$0.476236\pi$
$132$	−6.68872	−	11.5852i	−0.582178	−	1.00836i
$133$	−0.193252			−0.0167571
$134$	0.210121	−	8.18266i	0.0181517	−	0.706874i
$135$	−0.806748			−0.0694338
$136$	−2.91751	−	5.05328i	−0.250174	−	0.433315i
$137$	−15.5990			−1.33271			−0.666354	−	0.745635i	$-0.732146\pi$
$137$	−15.5990			−1.33271			−0.666354	+	0.745635i	$0.732146\pi$
$138$	2.27121	−	3.93384i	0.193338	−	0.334871i
$139$	9.44305			0.800949			0.400475	−	0.916308i	$-0.368845\pi$
$139$	9.44305			0.800949			0.400475	+	0.916308i	$0.368845\pi$
$140$	−0.0966262	−	0.167362i	−0.00816641	−	0.0141446i
$141$	7.54241	−	13.0638i	0.635186	−	1.10017i
$142$	9.51414			0.798409
$143$	−1.02827			−0.0859886
$144$	−1.66044	−	2.87597i	−0.138370	−	0.239664i
$145$	0.563816	−	0.976558i	0.0468224	−	0.0810987i
$146$	−1.91751	+	3.32123i	−0.158694	+	0.274867i
$147$	−8.75253	−	15.1598i	−0.721897	−	1.25036i
$148$	−10.6983			−0.879396
$149$	1.02827			0.0842395			0.0421197	−	0.999113i	$-0.486589\pi$
$149$	1.02827			0.0842395			0.0421197	+	0.999113i	$0.486589\pi$
$150$	−1.25707	−	2.17731i	−0.102639	−	0.177776i
$151$	−6.37056	−	11.0341i	−0.518429	−	0.897946i	−0.999771	−	0.0214125i	$-0.993184\pi$
$151$	−6.37056	−	11.0341i	−0.518429	−	0.897946i	0.481342	−	0.876533i	$-0.340150\pi$
$152$	−0.500000	−	0.866025i	−0.0405554	−	0.0702439i
$153$	9.68872	+	16.7813i	0.783286	+	1.35669i
$154$	−0.514137	+	0.890511i	−0.0414303	+	0.0717594i
$155$	−0.485863	+	0.841540i	−0.0390255	+	0.0675941i
$156$	−0.485863			−0.0389002
$157$	9.25253	+	16.0259i	0.738432	+	1.27900i	0.953201	+	0.302338i	$0.0977670\pi$
$157$	9.25253	+	16.0259i	0.738432	+	1.27900i	−0.214768	+	0.976665i	$0.568900\pi$
$158$	0.585221			0.0465577
$159$	−22.2125			−1.76156
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$	−0.349158			−0.0275175
$162$	−3.96719	−	6.87137i	−0.311692	−	0.539866i
$163$	8.36603	−	14.4904i	0.655278	−	1.13497i	−0.326546	−	0.945181i	$-0.605885\pi$
$163$	8.36603	−	14.4904i	0.655278	−	1.13497i	0.981824	−	0.189793i	$-0.0607818\pi$
$164$	−0.339558	−	0.588131i	−0.0265150	−	0.0459253i
$165$	−6.68872	+	11.5852i	−0.520716	+	0.901906i
$166$	1.36783	−	2.36915i	0.106164	−	0.183882i
$167$	−12.3492	+	21.3894i	−0.955607	+	1.65516i	−0.222633	+	0.974902i	$0.571465\pi$
$167$	−12.3492	+	21.3894i	−0.955607	+	1.65516i	−0.732974	+	0.680257i	$0.761868\pi$
$168$	−0.242932	+	0.420770i	−0.0187426	+	0.0324631i
$169$	6.48133	−	11.2260i	0.498564	−	0.863537i
$170$	−2.91751	+	5.05328i	−0.223763	+	0.387569i
$171$	1.66044	+	2.87597i	0.126977	+	0.219931i
$172$	−1.25707	+	2.17731i	−0.0958506	+	0.166018i
$173$	11.3802	+	19.7110i	0.865218	+	1.49860i	0.866831	+	0.498603i	$0.166153\pi$
$173$	11.3802	+	19.7110i	0.865218	+	1.49860i	−0.00161283	+	0.999999i	$0.500513\pi$
$174$	−2.83502			−0.214922
$175$	−0.0966262	+	0.167362i	−0.00730426	+	0.0126513i
$176$	−5.32088			−0.401077
$177$	−14.4202			−1.08389
$178$	4.33502	+	7.50848i	0.324924	+	0.562784i
$179$	−24.4996			−1.83119			−0.915593	−	0.402106i	$-0.868278\pi$
$179$	−24.4996			−1.83119			−0.915593	+	0.402106i	$0.868278\pi$
$180$	−1.66044	+	2.87597i	−0.123762	+	0.214362i
$181$	1.53554	−	2.65964i	0.114136	−	0.197689i	−0.803298	−	0.595577i	$-0.796923\pi$
$181$	1.53554	−	2.65964i	0.114136	−	0.197689i	0.917434	+	0.397888i	$0.130257\pi$
$182$	0.0186733	+	0.0323430i	0.00138415	+	0.00239742i
$183$	0.806748	+	1.39733i	0.0596365	+	0.103293i
$184$	−0.903374	−	1.56469i	−0.0665976	−	0.115350i
$185$	5.34916	+	9.26501i	0.393278	+	0.681177i
$186$	2.44305			0.179133
$187$	31.0475			2.27042
$188$	−3.00000	−	5.19615i	−0.218797	−	0.378968i
$189$	0.0779530	−	0.135018i	0.00567024	−	0.00982115i
$190$	−0.500000	+	0.866025i	−0.0362738	+	0.0628281i
$191$	8.62036	+	14.9309i	0.623748	+	1.08036i	0.988782	+	0.149368i	$0.0477240\pi$
$191$	8.62036	+	14.9309i	0.623748	+	1.08036i	−0.365034	+	0.930994i	$0.618943\pi$
$192$	−2.51414			−0.181442
$193$	−2.29261			−0.165026			−0.0825129	−	0.996590i	$-0.526295\pi$
$193$	−2.29261			−0.165026			−0.0825129	+	0.996590i	$0.526295\pi$
$194$	7.43165	−	12.8720i	0.533561	−	0.924155i
$195$	0.242932	+	0.420770i	0.0173967	+	0.0301319i
$196$	−6.96265			−0.497332
$197$	9.41478	−	16.3069i	0.670775	−	1.16182i	−0.306909	−	0.951739i	$-0.599295\pi$
$197$	9.41478	−	16.3069i	0.670775	−	1.16182i	0.977685	−	0.210078i	$-0.0673718\pi$
$198$	17.6700			1.25576
$199$	3.07795	+	5.33117i	0.218190	+	0.377917i	0.954255	−	0.298995i	$-0.0966513\pi$
$199$	3.07795	+	5.33117i	0.218190	+	0.377917i	−0.736064	+	0.676911i	$0.763318\pi$
$200$	−1.00000			−0.0707107
$201$	17.5520	+	10.7437i	1.23802	+	0.757799i
$202$	1.12763			0.0793399
$203$	0.108959	+	0.188722i	0.00764741	+	0.0132457i
$204$	14.6700			1.02711
$205$	−0.339558	+	0.588131i	−0.0237157	+	0.0410769i
$206$	14.3118			0.997151
$207$	3.00000	+	5.19615i	0.208514	+	0.361158i
$208$	−0.0966262	+	0.167362i	−0.00669982	+	0.0116044i
$209$	5.32088			0.368053
$210$	0.485863			0.0335277
$211$	5.88650	+	10.1957i	0.405244	+	0.701903i	0.994350	−	0.106153i	$-0.0338533\pi$
$211$	5.88650	+	10.1957i	0.405244	+	0.701903i	−0.589106	+	0.808056i	$0.700520\pi$
$212$	−4.41751	+	7.65135i	−0.303396	+	0.525497i
$213$	−11.9599	+	20.7152i	−0.819480	+	1.41938i
$214$	−1.12763	−	1.95312i	−0.0770833	−	0.133512i
$215$	2.51414			0.171463
$216$	0.806748			0.0548922
$217$	−0.0938942	−	0.162630i	−0.00637395	−	0.0110400i
$218$	2.24293	+	3.88487i	0.151910	+	0.263117i
$219$	−4.82088	−	8.35002i	−0.325765	−	0.564242i
$220$	2.66044	+	4.60802i	0.179367	+	0.310673i
$221$	0.563816	−	0.976558i	0.0379264	−	0.0656904i
$222$	13.4485	−	23.2935i	0.902605	−	1.56336i
$223$	−24.1751			−1.61888			−0.809442	−	0.587199i	$-0.800231\pi$
$223$	−24.1751			−1.61888			−0.809442	+	0.587199i	$0.800231\pi$
$224$	0.0966262	+	0.167362i	0.00645611	+	0.0111823i
$225$	3.32088			0.221392
$226$	−7.87237			−0.523662
$227$	−10.5593	+	18.2892i	−0.700844	+	1.21390i	0.267327	+	0.963606i	$0.413860\pi$
$227$	−10.5593	+	18.2892i	−0.700844	+	1.21390i	−0.968171	+	0.250291i	$0.919474\pi$
$228$	2.51414			0.166503
$229$	−5.47679	−	9.48608i	−0.361916	−	0.626858i	0.626360	−	0.779534i	$-0.284544\pi$
$229$	−5.47679	−	9.48608i	−0.361916	−	0.626858i	−0.988276	+	0.152676i	$0.951211\pi$
$230$	−0.903374	+	1.56469i	−0.0595667	+	0.103173i
$231$	−1.29261	−	2.23887i	−0.0850475	−	0.147307i
$232$	−0.563816	+	0.976558i	−0.0370163	+	0.0641142i
$233$	11.1390	−	19.2934i	0.729743	−	1.26395i	−0.227249	−	0.973837i	$-0.572973\pi$
$233$	11.1390	−	19.2934i	0.729743	−	1.26395i	0.956992	−	0.290115i	$-0.0936934\pi$
$234$	0.320884	−	0.555788i	0.0209769	−	0.0363330i
$235$	−3.00000	+	5.19615i	−0.195698	+	0.338960i
$236$	−2.86783	+	4.96723i	−0.186680	+	0.323339i
$237$	−0.735663	+	1.27421i	−0.0477865	+	0.0827686i
$238$	−0.563816	−	0.976558i	−0.0365468	−	0.0633009i
$239$	−5.93438	+	10.2786i	−0.383863	+	0.664870i	−0.991611	−	0.129260i	$-0.958740\pi$
$239$	−5.93438	+	10.2786i	−0.383863	+	0.664870i	0.607748	+	0.794130i	$0.292073\pi$
$240$	1.25707	+	2.17731i	0.0811434	+	0.140545i
$241$	−5.22699			−0.336700			−0.168350	−	0.985727i	$-0.553844\pi$
$241$	−5.22699			−0.336700			−0.168350	+	0.985727i	$0.553844\pi$
$242$	8.65591	−	14.9925i	0.556423	−	0.963752i
$243$	22.3684			1.43493
$244$	0.641769			0.0410851
$245$	3.48133	+	6.02983i	0.222414	+	0.385232i
$246$	1.70739			0.108859
$247$	0.0966262	−	0.167362i	0.00614818	−	0.0106490i
$248$	0.485863	−	0.841540i	0.0308523	−	0.0534378i
$249$	3.43892	+	5.95638i	0.217932	+	0.377470i
$250$	0.500000	+	0.866025i	0.0316228	+	0.0547723i
$251$	9.73113	+	16.8548i	0.614223	+	1.06387i	0.990520	+	0.137367i	$0.0438639\pi$
$251$	9.73113	+	16.8548i	0.614223	+	1.06387i	−0.376297	+	0.926499i	$0.622803\pi$
$252$	−0.320884	−	0.555788i	−0.0202138	−	0.0350114i
$253$	9.61350			0.604395
$254$	6.38650			0.400725
$255$	−7.33502	−	12.7046i	−0.459337	−	0.795595i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−3.00000	+	5.19615i	−0.187135	+	0.324127i	−0.944294	−	0.329104i	$-0.893253\pi$
$257$	−3.00000	+	5.19615i	−0.187135	+	0.324127i	0.757159	+	0.653231i	$0.226587\pi$
$258$	−3.16044	−	5.47405i	−0.196761	−	0.340799i
$259$	−2.06748			−0.128467
$260$	0.193252			0.0119850
$261$	1.87237	−	3.24304i	0.115897	−	0.200739i
$262$	0.853695	+	1.47864i	0.0527414	+	0.0913508i
$263$	−12.0511			−0.743102			−0.371551	−	0.928413i	$-0.621174\pi$
$263$	−12.0511			−0.743102			−0.371551	+	0.928413i	$0.621174\pi$
$264$	6.68872	−	11.5852i	0.411662	−	0.713020i
$265$	8.83502			0.542731
$266$	−0.0966262	−	0.167362i	−0.00592453	−	0.0102616i
$267$	−21.7977			−1.33400
$268$	7.19145	−	3.90936i	0.439288	−	0.238802i
$269$	8.15591			0.497274			0.248637	−	0.968597i	$-0.420017\pi$
$269$	8.15591			0.497274			0.248637	+	0.968597i	$0.420017\pi$
$270$	−0.403374	−	0.698664i	−0.0245485	−	0.0425193i
$271$	−2.17405			−0.132064			−0.0660321	−	0.997817i	$-0.521034\pi$
$271$	−2.17405			−0.132064			−0.0660321	+	0.997817i	$0.521034\pi$
$272$	2.91751	−	5.05328i	0.176900	−	0.306400i
$273$	−0.0938942			−0.00568274
$274$	−7.79948	−	13.5091i	−0.471184	−	0.816114i
$275$	2.66044	−	4.60802i	0.160431	−	0.277874i
$276$	4.54241			0.273421
$277$	−32.1131			−1.92949			−0.964744	−	0.263188i	$-0.915226\pi$
$277$	−32.1131			−1.92949			−0.964744	+	0.263188i	$0.915226\pi$
$278$	4.72153	+	8.17792i	0.283178	+	0.490479i
$279$	−1.61350	+	2.79466i	−0.0965974	+	0.167312i
$280$	0.0966262	−	0.167362i	0.00577452	−	0.0100018i
$281$	−5.36330	−	9.28950i	−0.319947	−	0.554165i	0.660529	−	0.750800i	$-0.270332\pi$
$281$	−5.36330	−	9.28950i	−0.319947	−	0.554165i	−0.980477	+	0.196635i	$0.936999\pi$
$282$	15.0848			0.898288
$283$	−11.5424			−0.686125			−0.343063	−	0.939313i	$-0.611464\pi$
$283$	−11.5424			−0.686125			−0.343063	+	0.939313i	$0.611464\pi$
$284$	4.75707	+	8.23948i	0.282280	+	0.488923i
$285$	−1.25707	−	2.17731i	−0.0744623	−	0.128973i
$286$	−0.514137	−	0.890511i	−0.0304016	−	0.0526570i
$287$	−0.0656204	−	0.113658i	−0.00387345	−	0.00670901i
$288$	1.66044	−	2.87597i	0.0978425	−	0.169468i
$289$	−8.52374	+	14.7635i	−0.501396	+	0.868444i
$290$	1.12763			0.0662168
$291$	18.6842	+	32.3619i	1.09529	+	1.89709i
$292$	−3.83502			−0.224428
$293$	−21.6646			−1.26566			−0.632829	−	0.774291i	$-0.718106\pi$
$293$	−21.6646			−1.26566			−0.632829	+	0.774291i	$0.718106\pi$
$294$	8.75253	−	15.1598i	0.510458	−	0.884139i
$295$	5.73566			0.333943
$296$	−5.34916	−	9.26501i	−0.310914	−	0.538518i
$297$	−2.14631	+	3.71751i	−0.124541	+	0.215712i
$298$	0.514137	+	0.890511i	0.0297832	+	0.0515859i
$299$	0.174579	−	0.302380i	0.0100962	−	0.0174871i
$300$	1.25707	−	2.17731i	0.0725769	−	0.125707i
$301$	−0.242932	+	0.420770i	−0.0140023	+	0.0242528i
$302$	6.37056	−	11.0341i	0.366585	−	0.634943i
$303$	−1.41751	+	2.45520i	−0.0814339	+	0.141048i
$304$	0.500000	−	0.866025i	0.0286770	−	0.0496700i
$305$	−0.320884	−	0.555788i	−0.0183738	−	0.0318243i
$306$	−9.68872	+	16.7813i	−0.553867	+	0.959326i
$307$	−0.238395	−	0.412913i	−0.0136059	−	0.0235662i	0.859142	−	0.511737i	$-0.170998\pi$
$307$	−0.238395	−	0.412913i	−0.0136059	−	0.0235662i	−0.872748	+	0.488171i	$0.837664\pi$
$308$	−1.02827			−0.0585913
$309$	−17.9909	+	31.1612i	−1.02347	+	1.77270i
$310$	−0.971726			−0.0551903
$311$	−0.598959			−0.0339638			−0.0169819	−	0.999856i	$-0.505406\pi$
$311$	−0.598959			−0.0339638			−0.0169819	+	0.999856i	$0.505406\pi$
$312$	−0.242932	−	0.420770i	−0.0137533	−	0.0238214i
$313$	−22.7321			−1.28489			−0.642446	−	0.766331i	$-0.722080\pi$
$313$	−22.7321			−1.28489			−0.642446	+	0.766331i	$0.722080\pi$
$314$	−9.25253	+	16.0259i	−0.522151	+	0.904391i
$315$	−0.320884	+	0.555788i	−0.0180798	+	0.0313151i
$316$	0.292611	+	0.506816i	0.0164606	+	0.0285107i
$317$	−9.76394	−	16.9116i	−0.548397	−	0.949852i	−0.998385	−	0.0568171i	$-0.981905\pi$
$317$	−9.76394	−	16.9116i	−0.548397	−	0.949852i	0.449987	−	0.893035i	$-0.351429\pi$
$318$	−11.1062	−	19.2365i	−0.622806	−	1.07873i
$319$	−3.00000	−	5.19615i	−0.167968	−	0.290929i
$320$	1.00000			0.0559017
$321$	5.67004			0.316471
$322$	−0.174579	−	0.302380i	−0.00972892	−	0.0168510i
$323$	−2.91751	+	5.05328i	−0.162335	+	0.281172i
$324$	3.96719	−	6.87137i	0.220399	−	0.381743i
$325$	−0.0966262	−	0.167362i	−0.00535986	−	0.00928355i
$326$	16.7321			0.926703
$327$	−11.2781			−0.623679
$328$	0.339558	−	0.588131i	0.0187489	−	0.0324741i
$329$	−0.579757	−	1.00417i	−0.0319631	−	0.0553616i
$330$	−13.3774			−0.736403
$331$	6.07068	−	10.5147i	0.333675	−	0.577942i	−0.649554	−	0.760315i	$-0.725045\pi$
$331$	6.07068	−	10.5147i	0.333675	−	0.577942i	0.983229	+	0.182373i	$0.0583779\pi$
$332$	2.73566			0.150139
$333$	17.7639	+	30.7680i	0.973458	+	1.68608i
$334$	−24.6983			−1.35143
$335$	−6.98133	−	4.27330i	−0.381431	−	0.233475i
$336$	−0.485863			−0.0265060
$337$	−0.561084	−	0.971826i	−0.0305642	−	0.0529387i	0.850339	−	0.526236i	$-0.176397\pi$
$337$	−0.561084	−	0.971826i	−0.0305642	−	0.0529387i	−0.880903	+	0.473297i	$0.843064\pi$
$338$	12.9627			0.705075
$339$	9.89611	−	17.1406i	0.537483	−	0.930947i
$340$	−5.83502			−0.316448
$341$	2.58522	+	4.47773i	0.139998	+	0.242483i
$342$	−1.66044	+	2.87597i	−0.0897864	+	0.155515i
$343$	−2.69832			−0.145695
$344$	−2.51414			−0.135553
$345$	−2.27121	−	3.93384i	−0.122278	−	0.211791i
$346$	−11.3802	+	19.7110i	−0.611801	+	1.05967i
$347$	5.65317	−	9.79158i	0.303478	−	0.525640i	−0.673443	−	0.739239i	$-0.735185\pi$
$347$	5.65317	−	9.79158i	0.303478	−	0.525640i	0.976921	+	0.213599i	$0.0685187\pi$
$348$	−1.41751	−	2.45520i	−0.0759866	−	0.131613i
$349$	3.32635			0.178055			0.0890277	−	0.996029i	$-0.471624\pi$
$349$	3.32635			0.178055			0.0890277	+	0.996029i	$0.471624\pi$
$350$	−0.193252			−0.0103298
$351$	0.0779530	+	0.135018i	0.00416082	+	0.00720675i
$352$	−2.66044	−	4.60802i	−0.141802	−	0.245608i
$353$	7.06201	+	12.2318i	0.375873	+	0.651031i	0.990457	−	0.137820i	$-0.0440096\pi$
$353$	7.06201	+	12.2318i	0.375873	+	0.651031i	−0.614584	+	0.788851i	$0.710676\pi$
$354$	−7.21012	−	12.4883i	−0.383214	−	0.663745i
$355$	4.75707	−	8.23948i	0.252479	−	0.437306i
$356$	−4.33502	+	7.50848i	−0.229756	+	0.397949i
$357$	2.83502			0.150045
$358$	−12.2498	−	21.2173i	−0.647422	−	1.12137i
$359$	−32.7549			−1.72874			−0.864368	−	0.502860i	$-0.832281\pi$
$359$	−32.7549			−1.72874			−0.864368	+	0.502860i	$0.832281\pi$
$360$	−3.32088			−0.175026
$361$	9.00000	−	15.5885i	0.473684	−	0.820445i
$362$	3.07108			0.161413
$363$	21.7621	+	37.6931i	1.14222	+	1.97838i
$364$	−0.0186733	+	0.0323430i	−0.000978744	+	0.00169523i
$365$	1.91751	+	3.32123i	0.100367	+	0.173841i
$366$	−0.806748	+	1.39733i	−0.0421694	+	0.0730395i
$367$	9.86603	−	17.0885i	0.515002	−	0.892010i	−0.484846	−	0.874600i	$-0.661124\pi$
$367$	9.86603	−	17.0885i	0.515002	−	0.892010i	0.999848	−	0.0174108i	$-0.00554232\pi$
$368$	0.903374	−	1.56469i	0.0470916	−	0.0815651i
$369$	−1.12763	+	1.95312i	−0.0587022	+	0.101675i
$370$	−5.34916	+	9.26501i	−0.278090	+	0.481665i
$371$	−0.853695	+	1.47864i	−0.0443216	+	0.0767673i
$372$	1.22153	+	2.11575i	0.0633332	+	0.109696i
$373$	19.0903	−	33.0653i	0.988458	−	1.71206i	0.363027	−	0.931778i	$-0.381743\pi$
$373$	19.0903	−	33.0653i	0.988458	−	1.71206i	0.625430	−	0.780280i	$-0.284924\pi$
$374$	15.5237	+	26.8879i	0.802713	+	1.39034i
$375$	−2.51414			−0.129829
$376$	3.00000	−	5.19615i	0.154713	−	0.267971i
$377$	−0.217918			−0.0112233
$378$	0.155906			0.00801894
$379$	−3.82542	−	6.62582i	−0.196499	−	0.340346i	0.750892	−	0.660425i	$-0.229624\pi$
$379$	−3.82542	−	6.62582i	−0.196499	−	0.340346i	−0.947391	+	0.320079i	$0.896290\pi$
$380$	−1.00000			−0.0512989
$381$	−8.02827	+	13.9054i	−0.411301	+	0.712394i
$382$	−8.62036	+	14.9309i	−0.441056	+	0.763932i
$383$	0.943452	+	1.63411i	0.0482082	+	0.0834990i	0.889123	−	0.457669i	$-0.151316\pi$
$383$	0.943452	+	1.63411i	0.0482082	+	0.0834990i	−0.840914	+	0.541168i	$0.817982\pi$
$384$	−1.25707	−	2.17731i	−0.0641495	−	0.111110i
$385$	0.514137	+	0.890511i	0.0262028	+	0.0453847i
$386$	−1.14631	−	1.98546i	−0.0583454	−	0.101057i
$387$	8.34916			0.424412
$388$	14.8633			0.754569
$389$	2.42024	+	4.19198i	0.122711	+	0.212542i	0.920836	−	0.389950i	$-0.127508\pi$
$389$	2.42024	+	4.19198i	0.122711	+	0.212542i	−0.798125	+	0.602492i	$0.794174\pi$
$390$	−0.242932	+	0.420770i	−0.0123013	+	0.0213065i
$391$	−5.27121	+	9.13000i	−0.266576	+	0.461724i
$392$	−3.48133	−	6.02983i	−0.175834	−	0.304553i
$393$	−4.29261			−0.216534
$394$	18.8296			0.948619
$395$	0.292611	−	0.506816i	0.0147228	−	0.0255007i
$396$	8.83502	+	15.3027i	0.443977	+	0.768990i
$397$	9.67551			0.485600			0.242800	−	0.970076i	$-0.421934\pi$
$397$	9.67551			0.485600			0.242800	+	0.970076i	$0.421934\pi$
$398$	−3.07795	+	5.33117i	−0.154284	+	0.267227i
$399$	0.485863			0.0243236
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	3.13310			0.156459			0.0782297	−	0.996935i	$-0.475073\pi$
$401$	3.13310			0.156459			0.0782297	+	0.996935i	$0.475073\pi$
$402$	−0.528274	+	20.5723i	−0.0263479	+	1.02605i
$403$	0.187788			0.00935441
$404$	0.563816	+	0.976558i	0.0280509	+	0.0485856i
$405$	−7.93438			−0.394262
$406$	−0.108959	+	0.188722i	−0.00540754	+	0.00936613i
$407$	56.9245			2.82164
$408$	7.33502	+	12.7046i	0.363138	+	0.628973i
$409$	−12.7694	+	22.1173i	−0.631406	+	1.09363i	0.355858	+	0.934540i	$0.384189\pi$
$409$	−12.7694	+	22.1173i	−0.631406	+	1.09363i	−0.987264	+	0.159088i	$0.949145\pi$
$410$	−0.679116			−0.0335391
$411$	39.2179			1.93448
$412$	7.15591	+	12.3944i	0.352546	+	0.610628i
$413$	−0.554215	+	0.959929i	−0.0272712	+	0.0472350i
$414$	−3.00000	+	5.19615i	−0.147442	+	0.255377i
$415$	−1.36783	−	2.36915i	−0.0671442	−	0.116297i
$416$	−0.193252			−0.00947498
$417$	−23.7411			−1.16261
$418$	2.66044	+	4.60802i	0.130126	+	0.225386i
$419$	14.7125	+	25.4827i	0.718750	+	1.24491i	0.961495	+	0.274822i	$0.0886189\pi$
$419$	14.7125	+	25.4827i	0.718750	+	1.24491i	−0.242745	+	0.970090i	$0.578048\pi$
$420$	0.242932	+	0.420770i	0.0118538	+	0.0205315i
$421$	−17.4768	−	30.2707i	−0.851767	−	1.47530i	−0.879613	−	0.475691i	$-0.842198\pi$
$421$	−17.4768	−	30.2707i	−0.851767	−	1.47530i	0.0278459	−	0.999612i	$-0.491135\pi$
$422$	−5.88650	+	10.1957i	−0.286551	+	0.496320i
$423$	−9.96265	+	17.2558i	−0.484401	+	0.839007i
$424$	−8.83502			−0.429067
$425$	2.91751	+	5.05328i	0.141520	+	0.245120i
$426$	−23.9198			−1.15892
$427$	0.124023			0.00600191
$428$	1.12763	−	1.95312i	0.0545062	−	0.0944074i
$429$	2.58522			0.124816
$430$	1.25707	+	2.17731i	0.0606212	+	0.104999i
$431$	−3.11530	+	5.39586i	−0.150059	+	0.259909i	−0.931249	−	0.364384i	$-0.881280\pi$
$431$	−3.11530	+	5.39586i	−0.150059	+	0.259909i	0.781190	+	0.624293i	$0.214613\pi$
$432$	0.403374	+	0.698664i	0.0194073	+	0.0336145i
$433$	18.2949	−	31.6878i	0.879199	−	1.52282i	0.0269773	−	0.999636i	$-0.491412\pi$
$433$	18.2949	−	31.6878i	0.879199	−	1.52282i	0.852222	−	0.523181i	$-0.175255\pi$
$434$	0.0938942	−	0.162630i	0.00450707	−	0.00780647i
$435$	−1.41751	+	2.45520i	−0.0679644	+	0.117718i
$436$	−2.24293	+	3.88487i	−0.107417	+	0.186052i
$437$	−0.903374	+	1.56469i	−0.0432142	+	0.0748492i
$438$	4.82088	−	8.35002i	0.230351	−	0.398979i
$439$	−14.1773	−	24.5558i	−0.676646	−	1.17199i	−0.975985	−	0.217839i	$-0.930099\pi$
$439$	−14.1773	−	24.5558i	−0.676646	−	1.17199i	0.299339	−	0.954147i	$-0.403234\pi$
$440$	−2.66044	+	4.60802i	−0.126832	+	0.219679i
$441$	11.5611	+	20.0244i	0.550528	+	0.953542i
$442$	1.12763			0.0536360
$443$	−7.61530	+	13.1901i	−0.361814	+	0.626680i	−0.988259	−	0.152785i	$-0.951176\pi$
$443$	−7.61530	+	13.1901i	−0.361814	+	0.626680i	0.626446	+	0.779465i	$0.284509\pi$
$444$	26.8970			1.27648
$445$	8.67004			0.410999
$446$	−12.0876	−	20.9363i	−0.572362	−	0.991360i
$447$	−2.58522			−0.122277
$448$	−0.0966262	+	0.167362i	−0.00456516	+	0.00790709i
$449$	−10.1276	+	17.5416i	−0.477953	+	0.827838i	−0.999681	−	0.0252738i	$-0.991954\pi$
$449$	−10.1276	+	17.5416i	−0.477953	+	0.827838i	0.521728	+	0.853112i	$0.325288\pi$
$450$	1.66044	+	2.87597i	0.0782740	+	0.135575i
$451$	1.80675	+	3.12938i	0.0850764	+	0.147357i
$452$	−3.93618	−	6.81767i	−0.185143	−	0.320676i
$453$	16.0165	+	27.7413i	0.752519	+	1.30340i
$454$	−21.1186			−0.991143
$455$	0.0373465			0.00175083
$456$	1.25707	+	2.17731i	0.0588676	+	0.101962i
$457$	13.3136	−	23.0599i	0.622785	−	1.07869i	−0.366180	−	0.930544i	$-0.619335\pi$
$457$	13.3136	−	23.0599i	0.622785	−	1.07869i	0.988965	−	0.148151i	$-0.0473321\pi$
$458$	5.47679	−	9.48608i	0.255914	−	0.443255i
$459$	−2.35369	−	4.07672i	−0.109861	−	0.190285i
$460$	−1.80675			−0.0842400
$461$	4.60989			0.214704			0.107352	−	0.994221i	$-0.465763\pi$
$461$	4.60989			0.214704			0.107352	+	0.994221i	$0.465763\pi$
$462$	1.29261	−	2.23887i	0.0601377	−	0.104162i
$463$	−12.2152	−	21.1573i	−0.567688	−	0.983264i	−0.996794	−	0.0800101i	$-0.974505\pi$
$463$	−12.2152	−	21.1573i	−0.567688	−	0.983264i	0.429106	−	0.903254i	$-0.358829\pi$
$464$	−1.12763			−0.0523490
$465$	1.22153	−	2.11575i	0.0566469	−	0.0981154i
$466$	22.2781			1.03201
$467$	−6.34916	−	10.9971i	−0.293804	−	0.508883i	0.680902	−	0.732375i	$-0.261588\pi$
$467$	−6.34916	−	10.9971i	−0.293804	−	0.508883i	−0.974706	+	0.223491i	$0.928255\pi$
$468$	0.641769			0.0296658
$469$	1.38976	−	0.755493i	0.0641734	−	0.0348854i
$470$	−6.00000			−0.276759
$471$	−23.2621	−	40.2912i	−1.07186	−	1.85652i
$472$	−5.73566			−0.264005
$473$	6.68872	−	11.5852i	0.307547	−	0.532688i
$474$	−1.47133			−0.0675803
$475$	0.500000	+	0.866025i	0.0229416	+	0.0397360i
$476$	0.563816	−	0.976558i	0.0258425	−	0.0447605i
$477$	29.3401			1.34339
$478$	−11.8688			−0.542864
$479$	11.6860	+	20.2407i	0.533946	+	0.924822i	0.999214	+	0.0396518i	$0.0126249\pi$
$479$	11.6860	+	20.2407i	0.533946	+	0.924822i	−0.465267	+	0.885170i	$0.654042\pi$
$480$	−1.25707	+	2.17731i	−0.0573771	+	0.0993800i
$481$	1.03374	−	1.79049i	0.0471344	−	0.0816392i
$482$	−2.61350	−	4.52671i	−0.119041	−	0.206186i
$483$	0.877832			0.0399427
$484$	17.3118			0.786901
$485$	−7.43165	−	12.8720i	−0.337454	−	0.584487i
$486$	11.1842	+	19.3716i	0.507325	+	0.878712i
$487$	13.1814	+	22.8309i	0.597308	+	1.03457i	0.993217	+	0.116278i	$0.0370965\pi$
$487$	13.1814	+	22.8309i	0.597308	+	1.03457i	−0.395908	+	0.918290i	$0.629570\pi$
$488$	0.320884	+	0.555788i	0.0145258	+	0.0251594i
$489$	−21.0333	+	36.4308i	−0.951160	+	1.64746i
$490$	−3.48133	+	6.02983i	−0.157270	+	0.272400i
$491$	16.9253			0.763828			0.381914	−	0.924198i	$-0.375265\pi$
$491$	16.9253			0.763828			0.381914	+	0.924198i	$0.375265\pi$
$492$	0.853695	+	1.47864i	0.0384875	+	0.0666624i
$493$	6.57976			0.296337
$494$	0.193252			0.00869484
$495$	8.83502	−	15.3027i	0.397105	−	0.687805i
$496$	0.971726			0.0436318
$497$	0.919315	+	1.59230i	0.0412369	+	0.0714244i
$498$	−3.43892	+	5.95638i	−0.154102	+	0.266912i
$499$	19.1646	+	33.1940i	0.857924	+	1.48597i	0.873905	+	0.486096i	$0.161580\pi$
$499$	19.1646	+	33.1940i	0.857924	+	1.48597i	−0.0159809	+	0.999872i	$0.505087\pi$
$500$	−0.500000	+	0.866025i	−0.0223607	+	0.0387298i
$501$	31.0475	−	53.7758i	1.38710	−	2.40253i
$502$	−9.73113	+	16.8548i	−0.434321	+	0.752267i
$503$	−12.5734	+	21.7778i	−0.560621	+	0.971024i	0.436821	+	0.899548i	$0.356104\pi$
$503$	−12.5734	+	21.7778i	−0.560621	+	0.971024i	−0.997442	+	0.0714757i	$0.977229\pi$
$504$	0.320884	−	0.555788i	0.0142933	−	0.0247568i
$505$	0.563816	−	0.976558i	0.0250895	−	0.0434563i
$506$	4.80675	+	8.32553i	0.213686	+	0.370115i
$507$	−16.2949	+	28.2237i	−0.723684	+	1.25346i
$508$	3.19325	+	5.53088i	0.141678	+	0.245393i
$509$	−2.28715			−0.101376			−0.0506880	−	0.998715i	$-0.516141\pi$
$509$	−2.28715			−0.101376			−0.0506880	+	0.998715i	$0.516141\pi$
$510$	7.33502	−	12.7046i	0.324800	−	0.562570i
$511$	−0.741127			−0.0327855
$512$	−1.00000			−0.0441942
$513$	−0.403374	−	0.698664i	−0.0178094	−	0.0308468i
$514$	−6.00000			−0.264649
$515$	7.15591	−	12.3944i	0.315327	−	0.546162i
$516$	3.16044	−	5.47405i	0.139131	−	0.240981i
$517$	15.9627	+	27.6481i	0.702037	+	1.21596i
$518$	−1.03374	−	1.79049i	−0.0454198	−	0.0786695i
$519$	−28.6113	−	49.5562i	−1.25590	−	2.17528i
$520$	0.0966262	+	0.167362i	0.00423734	+	0.00733929i
$521$	−24.9819			−1.09447			−0.547237	−	0.836977i	$-0.684321\pi$
$521$	−24.9819			−1.09447			−0.547237	+	0.836977i	$0.684321\pi$
$522$	3.74474			0.163903
$523$	−18.3136	−	31.7201i	−0.800799	−	1.38702i	−0.919091	−	0.394045i	$-0.871075\pi$
$523$	−18.3136	−	31.7201i	−0.800799	−	1.38702i	0.118293	−	0.992979i	$-0.462258\pi$
$524$	−0.853695	+	1.47864i	−0.0372938	+	0.0645948i
$525$	0.242932	−	0.420770i	0.0106024	−	0.0183639i
$526$	−6.02554	−	10.4365i	−0.262726	−	0.455055i
$527$	−5.67004			−0.246991
$528$	13.3774			0.582178
$529$	9.86783	−	17.0916i	0.429036	−	0.743112i
$530$	4.41751	+	7.65135i	0.191884	+	0.332354i
$531$	19.0475			0.826590
$532$	0.0966262	−	0.167362i	0.00418928	−	0.00725604i
$533$	0.131241			0.00568467
$534$	−10.8988	−	18.8773i	−0.471639	−	0.816902i
$535$	−2.25526			−0.0975036
$536$	6.98133	+	4.27330i	0.301547	+	0.184578i
$537$	61.5953			2.65804
$538$	4.07795	+	7.06322i	0.175813	+	0.304517i
$539$	37.0475			1.59575
$540$	0.403374	−	0.698664i	0.0173584	−	0.0300657i
$541$	15.2589			0.656030			0.328015	−	0.944672i	$-0.393620\pi$
$541$	15.2589			0.656030			0.328015	+	0.944672i	$0.393620\pi$
$542$	−1.08703	−	1.88278i	−0.0466917	−	0.0808725i
$543$	−3.86056	+	6.68669i	−0.165673	+	0.286953i
$544$	5.83502			0.250174
$545$	4.48586			0.192153
$546$	−0.0469471	−	0.0813148i	−0.00200915	−	0.00347995i
$547$	−11.3774	+	19.7063i	−0.486464	+	0.842580i	−0.999879	−	0.0155603i	$-0.995047\pi$
$547$	−11.3774	+	19.7063i	−0.486464	+	0.842580i	0.513415	+	0.858140i	$0.328380\pi$
$548$	7.79948	−	13.5091i	0.333177	−	0.577080i
$549$	−1.06562	−	1.84571i	−0.0454796	−	0.0787729i
$550$	5.32088			0.226883
$551$	1.12763			0.0480387
$552$	2.27121	+	3.93384i	0.0966689	+	0.167435i
$553$	0.0565477	+	0.0979435i	0.00240465	+	0.00416498i
$554$	−16.0565	−	27.8108i	−0.682177	−	1.18157i
$555$	−13.4485	−	23.2935i	−0.570858	−	0.988755i
$556$	−4.72153	+	8.17792i	−0.200237	+	0.346821i
$557$	1.29261	−	2.23887i	0.0547697	−	0.0948639i	−0.837341	−	0.546681i	$-0.815891\pi$
$557$	1.29261	−	2.23887i	0.0547697	−	0.0948639i	0.892110	+	0.451818i	$0.149224\pi$
$558$	−3.22699			−0.136609
$559$	−0.242932	−	0.420770i	−0.0102749	−	0.0177967i
$560$	0.193252			0.00816641
$561$	−78.0576			−3.29559
$562$	5.36330	−	9.28950i	0.226237	−	0.391854i
$563$	30.3346			1.27845			0.639226	−	0.769019i	$-0.279255\pi$
$563$	30.3346			1.27845			0.639226	+	0.769019i	$0.279255\pi$
$564$	7.54241	+	13.0638i	0.317593	+	0.550087i
$565$	−3.93618	+	6.81767i	−0.165597	+	0.286822i
$566$	−5.77121	−	9.99602i	−0.242582	−	0.420164i
$567$	0.766669	−	1.32791i	0.0321971	−	0.0557670i
$568$	−4.75707	+	8.23948i	−0.199602	+	0.345721i
$569$	−2.18872	+	3.79097i	−0.0917558	+	0.158926i	−0.908250	−	0.418428i	$-0.862581\pi$
$569$	−2.18872	+	3.79097i	−0.0917558	+	0.158926i	0.816494	+	0.577354i	$0.195915\pi$
$570$	1.25707	−	2.17731i	0.0526528	−	0.0911973i
$571$	−14.7835	+	25.6058i	−0.618672	+	1.07157i	0.371057	+	0.928610i	$0.378996\pi$
$571$	−14.7835	+	25.6058i	−0.618672	+	1.07157i	−0.989728	+	0.142961i	$0.954338\pi$
$572$	0.514137	−	0.890511i	0.0214971	−	0.0372341i
$573$	−21.6728	−	37.5383i	−0.905393	−	1.56819i
$574$	0.0656204	−	0.113658i	0.00273894	−	0.00474398i
$575$	0.903374	+	1.56469i	0.0376733	+	0.0652521i
$576$	3.32088			0.138370
$577$	−23.5689	+	40.8225i	−0.981185	+	1.69946i	−0.323391	+	0.946266i	$0.604823\pi$
$577$	−23.5689	+	40.8225i	−0.981185	+	1.69946i	−0.657795	+	0.753197i	$0.728511\pi$
$578$	−17.0475			−0.709081
$579$	5.76394			0.239541
$580$	0.563816	+	0.976558i	0.0234112	+	0.0405494i
$581$	0.528674			0.0219331
$582$	−18.6842	+	32.3619i	−0.774484	+	1.34145i
$583$	23.5051	−	40.7120i	0.973480	−	1.68612i
$584$	−1.91751	−	3.32123i	−0.0793472	−	0.137433i
$585$	−0.320884	−	0.555788i	−0.0132669	−	0.0229790i
$586$	−10.8323	−	18.7621i	−0.447478	−	0.775054i
$587$	−3.58703	−	6.21291i	−0.148052	−	0.256434i	0.782455	−	0.622707i	$-0.213967\pi$
$587$	−3.58703	−	6.21291i	−0.148052	−	0.256434i	−0.930508	+	0.366273i	$0.880634\pi$
$588$	17.5051			0.721897
$589$	−0.971726			−0.0400393
$590$	2.86783	+	4.96723i	0.118067	+	0.204498i
$591$	−23.6700	+	40.9977i	−0.973655	+	1.68642i
$592$	5.34916	−	9.26501i	0.219849	−	0.380790i
$593$	−6.96992	−	12.0723i	−0.286220	−	0.495748i	0.686684	−	0.726956i	$-0.259066\pi$
$593$	−6.96992	−	12.0723i	−0.286220	−	0.495748i	−0.972904	+	0.231208i	$0.925732\pi$
$594$	−4.29261			−0.176128
$595$	−1.12763			−0.0462284
$596$	−0.514137	+	0.890511i	−0.0210599	+	0.0364768i
$597$	−7.73840	−	13.4033i	−0.316711	−	0.548560i
$598$	0.349158			0.0142781
$599$	−1.37743	+	2.38578i	−0.0562804	+	0.0974804i	−0.892793	−	0.450467i	$-0.851257\pi$
$599$	−1.37743	+	2.38578i	−0.0562804	+	0.0974804i	0.836513	+	0.547948i	$0.184591\pi$
$600$	2.51414			0.102639
$601$	−21.4385	−	37.1326i	−0.874495	−	1.51467i	−0.857299	−	0.514818i	$-0.827859\pi$
$601$	−21.4385	−	37.1326i	−0.874495	−	1.51467i	−0.0171959	−	0.999852i	$-0.505474\pi$
$602$	−0.485863			−0.0198023
$603$	−23.1842	−	14.1911i	−0.944133	−	0.577907i
$604$	12.7411			0.518429
$605$	−8.65591	−	14.9925i	−0.351913	−	0.609531i
$606$	−2.83502			−0.115165
$607$	9.15317	−	15.8538i	0.371516	−	0.643484i	−0.618283	−	0.785955i	$-0.712171\pi$
$607$	9.15317	−	15.8538i	0.371516	−	0.643484i	0.989799	+	0.142471i	$0.0455048\pi$
$608$	1.00000			0.0405554
$609$	−0.273937	−	0.474473i	−0.0111005	−	0.0192266i
$610$	0.320884	−	0.555788i	0.0129922	−	0.0225032i
$611$	1.15951			0.0469089
$612$	−19.3774			−0.783286
$613$	14.4148	+	24.9671i	0.582207	+	1.00841i	0.995217	+	0.0976863i	$0.0311442\pi$
$613$	14.4148	+	24.9671i	0.582207	+	1.00841i	−0.413010	+	0.910727i	$0.635522\pi$
$614$	0.238395	−	0.412913i	0.00962085	−	0.0166638i
$615$	0.853695	−	1.47864i	0.0344243	−	0.0596246i
$616$	−0.514137	−	0.890511i	−0.0207152	−	0.0358797i
$617$	−15.9819			−0.643405			−0.321703	−	0.946841i	$-0.604255\pi$
$617$	−15.9819			−0.643405			−0.321703	+	0.946841i	$0.604255\pi$
$618$	−35.9819			−1.44740
$619$	−21.8870	−	37.9095i	−0.879714	−	1.52371i	−0.851655	−	0.524103i	$-0.824401\pi$
$619$	−21.8870	−	37.9095i	−0.879714	−	1.52371i	−0.0280594	−	0.999606i	$-0.508933\pi$
$620$	−0.485863	−	0.841540i	−0.0195127	−	0.0337970i
$621$	−0.728795	−	1.26231i	−0.0292455	−	0.0506547i
$622$	−0.299479	−	0.518713i	−0.0120080	−	0.0207985i
$623$	−0.837753	+	1.45103i	−0.0335639	+	0.0581343i
$624$	0.242932	−	0.420770i	0.00972504	−	0.0168443i
$625$	1.00000			0.0400000
$626$	−11.3660	−	19.6865i	−0.454278	−	0.786832i
$627$	−13.3774			−0.534243
$628$	−18.5051			−0.738432
$629$	−31.2125	+	54.0616i	−1.24452	+	2.15558i
$630$	−0.641769			−0.0255687
$631$	16.5051	+	28.5876i	0.657056	+	1.13805i	0.981374	+	0.192107i	$0.0615319\pi$
$631$	16.5051	+	28.5876i	0.657056	+	1.13805i	−0.324318	+	0.945948i	$0.605135\pi$
$632$	−0.292611	+	0.506816i	−0.0116394	+	0.0201601i
$633$	−14.7995	−	25.6334i	−0.588226	−	1.01884i
$634$	9.76394	−	16.9116i	0.387775	−	0.671647i
$635$	3.19325	−	5.53088i	0.126720	−	0.219486i
$636$	11.1062	−	19.2365i	0.440391	−	0.762779i
$637$	0.672775	−	1.16528i	0.0266563	−	0.0461701i
$638$	3.00000	−	5.19615i	0.118771	−	0.205718i
$639$	15.7977	−	27.3624i	0.624946	−	1.08244i
$640$	0.500000	+	0.866025i	0.0197642	+	0.0342327i
$641$	−6.10803	+	10.5794i	−0.241253	+	0.417862i	−0.961071	−	0.276300i	$-0.910892\pi$
$641$	−6.10803	+	10.5794i	−0.241253	+	0.417862i	0.719819	+	0.694162i	$0.244225\pi$
$642$	2.83502	+	4.91040i	0.111889	+	0.193798i
$643$	2.84409			0.112160			0.0560801	−	0.998426i	$-0.482140\pi$
$643$	2.84409			0.112160			0.0560801	+	0.998426i	$0.482140\pi$
$644$	0.174579	−	0.302380i	0.00687938	−	0.0119154i
$645$	−6.32088			−0.248885
$646$	−5.83502			−0.229576
$647$	−2.22153	−	3.84780i	−0.0873372	−	0.151272i	0.819048	−	0.573726i	$-0.194502\pi$
$647$	−2.22153	−	3.84780i	−0.0873372	−	0.151272i	−0.906385	+	0.422453i	$0.861169\pi$
$648$	7.93438			0.311692
$649$	15.2594	−	26.4301i	0.598984	−	1.03747i
$650$	0.0966262	−	0.167362i	0.00378999	−	0.00656446i
$651$	0.236063	+	0.408873i	0.00925204	+	0.0160250i
$652$	8.36603	+	14.4904i	0.327639	+	0.567487i
$653$	−12.1586	−	21.0594i	−0.475804	−	0.824117i	0.523812	−	0.851834i	$-0.324510\pi$
$653$	−12.1586	−	21.0594i	−0.475804	−	0.824117i	−0.999616	+	0.0277170i	$0.991176\pi$
$654$	−5.63904	−	9.76710i	−0.220504	−	0.381924i
$655$	1.70739			0.0667132
$656$	0.679116			0.0265150
$657$	6.36783	+	11.0294i	0.248433	+	0.430298i
$658$	0.579757	−	1.00417i	0.0226013	−	0.0391466i
$659$	15.1514	−	26.2429i	0.590214	−	1.02228i	−0.403990	−	0.914764i	$-0.632377\pi$
$659$	15.1514	−	26.2429i	0.590214	−	1.02228i	0.994203	−	0.107516i	$-0.0342898\pi$
$660$	−6.68872	−	11.5852i	−0.260358	−	0.450953i
$661$	−21.4394			−0.833898			−0.416949	−	0.908930i	$-0.636901\pi$
$661$	−21.4394			−0.833898			−0.416949	+	0.908930i	$0.636901\pi$
$662$	12.1414			0.471888
$663$	−1.41751	+	2.45520i	−0.0550516	+	0.0953521i
$664$	1.36783	+	2.36915i	0.0530822	+	0.0919410i
$665$	−0.193252			−0.00749401
$666$	−17.7639	+	30.7680i	−0.688339	+	1.19224i
$667$	2.03735			0.0788864
$668$	−12.3492	−	21.3894i	−0.477803	−	0.827580i
$669$	60.7795			2.34987
$670$	0.210121	−	8.18266i	0.00811770	−	0.316124i
$671$	−3.41478			−0.131826
$672$	−0.242932	−	0.420770i	−0.00937129	−	0.0162315i
$673$	−38.5635			−1.48651			−0.743256	−	0.669007i	$-0.766720\pi$
$673$	−38.5635			−1.48651			−0.743256	+	0.669007i	$0.766720\pi$
$674$	0.561084	−	0.971826i	0.0216121	−	0.0374333i
$675$	−0.806748			−0.0310517
$676$	6.48133	+	11.2260i	0.249282	+	0.431769i
$677$	12.7785	−	22.1330i	0.491117	−	0.850639i	−0.508831	−	0.860866i	$-0.669922\pi$
$677$	12.7785	−	22.1330i	0.491117	−	0.850639i	0.999948	+	0.0102274i	$0.00325555\pi$
$678$	19.7922			0.760115
$679$	2.87237			0.110231
$680$	−2.91751	−	5.05328i	−0.111881	−	0.193784i
$681$	26.5475	−	45.9816i	1.01730	−	1.76202i
$682$	−2.58522	+	4.47773i	−0.0989932	+	0.171461i
$683$	−24.6814	−	42.7495i	−0.944409	−	1.63576i	−0.756930	−	0.653497i	$-0.773301\pi$
$683$	−24.6814	−	42.7495i	−0.944409	−	1.63576i	−0.187480	−	0.982268i	$-0.560032\pi$
$684$	−3.32088			−0.126977
$685$	−15.5990			−0.596006
$686$	−1.34916	−	2.33681i	−0.0515111	−	0.0892199i
$687$	13.7694	+	23.8493i	0.525335	+	0.909908i
$688$	−1.25707	−	2.17731i	−0.0479253	−	0.0830090i
$689$	−0.853695	−	1.47864i	−0.0325232	−	0.0563318i
$690$	2.27121	−	3.93384i	0.0864633	−	0.149759i
$691$	−5.33409	+	9.23892i	−0.202918	+	0.351465i	−0.949468	−	0.313865i	$-0.898376\pi$
$691$	−5.33409	+	9.23892i	−0.202918	+	0.351465i	0.746549	+	0.665330i	$0.231709\pi$
$692$	−22.7603			−0.865218
$693$	1.70739	+	2.95729i	0.0648584	+	0.112338i
$694$	11.3063			0.429183
$695$	9.44305			0.358195
$696$	1.41751	−	2.45520i	0.0537306	−	0.0930641i
$697$	−3.96265			−0.150096
$698$	1.66317	+	2.88070i	0.0629521	+	0.109036i
$699$	−28.0051	+	48.5062i	−1.05925	+	1.83467i
$700$	−0.0966262	−	0.167362i	−0.00365213	−	0.00632567i
$701$	11.6363	−	20.1547i	0.439497	−	0.761231i	−0.558154	−	0.829738i	$-0.688490\pi$
$701$	11.6363	−	20.1547i	0.439497	−	0.761231i	0.997651	+	0.0685063i	$0.0218233\pi$
$702$	−0.0779530	+	0.135018i	−0.00294215	+	0.00509594i
$703$	−5.34916	+	9.26501i	−0.201747	+	0.349437i
$704$	2.66044	−	4.60802i	0.100269	−	0.173671i
$705$	7.54241	−	13.0638i	0.284064	−	0.492013i
$706$	−7.06201	+	12.2318i	−0.265782	+	0.460348i
$707$	0.108959	+	0.188722i	0.00409782	+	0.00709763i
$708$	7.21012	−	12.4883i	0.270973	−	0.469339i
$709$	18.2781	+	31.6586i	0.686447	+	1.18896i	0.972980	+	0.230891i	$0.0741642\pi$
$709$	18.2781	+	31.6586i	0.686447	+	1.18896i	−0.286532	+	0.958071i	$0.592503\pi$
$710$	9.51414			0.357059
$711$	0.971726	−	1.68308i	0.0364426	−	0.0631204i
$712$	−8.67004			−0.324924
$713$	−1.75566			−0.0657501
$714$	1.41751	+	2.45520i	0.0530490	+	0.0918836i
$715$	−1.02827			−0.0384553
$716$	12.2498	−	21.2173i	0.457797	−	0.792927i
$717$	14.9198	−	25.8419i	0.557192	−	0.965084i
$718$	−16.3774	−	28.3665i	−0.611200	−	1.05863i
$719$	11.8013	+	20.4404i	0.440114	+	0.762299i	0.997697	−	0.0678215i	$-0.0216048\pi$
$719$	11.8013	+	20.4404i	0.440114	+	0.762299i	−0.557584	+	0.830121i	$0.688271\pi$
$720$	−1.66044	−	2.87597i	−0.0618810	−	0.107181i
$721$	1.38290	+	2.39525i	0.0515017	+	0.0892036i
$722$	18.0000			0.669891
$723$	13.1414			0.488733
$724$	1.53554	+	2.65964i	0.0570680	+	0.0988446i
$725$	0.563816	−	0.976558i	0.0209396	−	0.0362685i
$726$	−21.7621	+	37.6931i	−0.807668	+	1.39892i
$727$	17.5990	+	30.4823i	0.652709	+	1.13053i	0.982463	+	0.186459i	$0.0597010\pi$
$727$	17.5990	+	30.4823i	0.652709	+	1.13053i	−0.329754	+	0.944067i	$0.606966\pi$
$728$	−0.0373465			−0.00138415
$729$	−32.4340			−1.20126
$730$	−1.91751	+	3.32123i	−0.0709703	+	0.122924i
$731$	7.33502	+	12.7046i	0.271296	+	0.469898i
$732$	−1.61350			−0.0596365
$733$	24.3118	−	42.1093i	0.897977	−	1.55534i	0.0679012	−	0.997692i	$-0.478370\pi$
$733$	24.3118	−	42.1093i	0.897977	−	1.55534i	0.830076	−	0.557650i	$-0.188297\pi$
$734$	19.7321			0.728323
$735$	−8.75253	−	15.1598i	−0.322842	−	0.559179i
$736$	1.80675			0.0665976
$737$	−38.2649	+	20.8012i	−1.40950	+	0.766223i
$738$	−2.25526			−0.0830174
$739$	−18.6710	−	32.3391i	−0.686823	−	1.18961i	−0.972860	−	0.231393i	$-0.925672\pi$
$739$	−18.6710	−	32.3391i	−0.686823	−	1.18961i	0.286037	−	0.958218i	$-0.407662\pi$
$740$	−10.6983			−0.393278
$741$	−0.242932	+	0.420770i	−0.00892431	+	0.0154574i
$742$	−1.70739			−0.0626802
$743$	−3.92258	−	6.79410i	−0.143905	−	0.249251i	0.785059	−	0.619421i	$-0.212633\pi$
$743$	−3.92258	−	6.79410i	−0.143905	−	0.249251i	−0.928964	+	0.370170i	$0.879299\pi$
$744$	−1.22153	+	2.11575i	−0.0447833	+	0.0775670i
$745$	1.02827			0.0376730
$746$	38.1806			1.39789
$747$	−4.54241	−	7.86769i	−0.166198	−	0.287864i
$748$	−15.5237	+	26.8879i	−0.567604	+	0.983119i
$749$	0.217918	−	0.377444i	0.00796254	−	0.0137915i
$750$	−1.25707	−	2.17731i	−0.0459017	−	0.0795040i
$751$	−31.7831			−1.15978			−0.579892	−	0.814694i	$-0.696905\pi$
$751$	−31.7831			−1.15978			−0.579892	+	0.814694i	$0.696905\pi$
$752$	6.00000			0.218797
$753$	−24.4654	−	42.3753i	−0.891568	−	1.54424i
$754$	−0.108959	−	0.188722i	−0.00396805	−	0.00687286i
$755$	−6.37056	−	11.0341i	−0.231849	−	0.401573i
$756$	0.0779530	+	0.135018i	0.00283512	+	0.00491058i
$757$	−5.35823	+	9.28073i	−0.194748	+	0.337314i	−0.946818	−	0.321770i	$-0.895722\pi$
$757$	−5.35823	+	9.28073i	−0.194748	+	0.337314i	0.752070	+	0.659084i	$0.229056\pi$
$758$	3.82542	−	6.62582i	0.138946	−	0.240661i
$759$	−24.1696			−0.877302
$760$	−0.500000	−	0.866025i	−0.0181369	−	0.0314140i
$761$	16.5935			0.601514			0.300757	−	0.953701i	$-0.402761\pi$
$761$	16.5935			0.601514			0.300757	+	0.953701i	$0.402761\pi$
$762$	−16.0565			−0.581667
$763$	−0.433452	+	0.750761i	−0.0156920	+	0.0271794i
$764$	−17.2407			−0.623748
$765$	9.68872	+	16.7813i	0.350296	+	0.606731i
$766$	−0.943452	+	1.63411i	−0.0340883	+	0.0590427i
$767$	−0.554215	−	0.959929i	−0.0200116	−	0.0346610i
$768$	1.25707	−	2.17731i	0.0453606	−	0.0785668i
$769$	−6.63723	+	11.4960i	−0.239345	+	0.414557i	−0.960526	−	0.278189i	$-0.910266\pi$
$769$	−6.63723	+	11.4960i	−0.239345	+	0.414557i	0.721182	+	0.692746i	$0.243599\pi$
$770$	−0.514137	+	0.890511i	−0.0185282	+	0.0320918i
$771$	7.54241	−	13.0638i	0.271633	−	0.470483i
$772$	1.14631	−	1.98546i	0.0412564	−	0.0714582i
$773$	−7.82595	+	13.5549i	−0.281480	+	0.487537i	−0.971749	−	0.236015i	$-0.924159\pi$
$773$	−7.82595	+	13.5549i	−0.281480	+	0.487537i	0.690270	+	0.723552i	$0.257492\pi$
$774$	4.17458	+	7.23058i	0.150052	+	0.259898i
$775$	−0.485863	+	0.841540i	−0.0174527	+	0.0302290i
$776$	7.43165	+	12.8720i	0.266781	+	0.462078i
$777$	5.19792			0.186474
$778$	−2.42024	+	4.19198i	−0.0867699	+	0.150290i
$779$	−0.679116			−0.0243318
$780$	−0.485863			−0.0173967
$781$	−25.3118	−	43.8413i	−0.905728	−	1.56877i
$782$	−10.5424			−0.376996
$783$	−0.454857	+	0.787836i	−0.0162553	+	0.0281550i
$784$	3.48133	−	6.02983i	0.124333	−	0.215351i
$785$	9.25253	+	16.0259i	0.330237	+	0.571987i
$786$	−2.14631	−	3.71751i	−0.0765562	−	0.132599i
$787$	0.840485	+	1.45576i	0.0299601	+	0.0518924i	0.880617	−	0.473829i	$-0.157129\pi$
$787$	0.840485	+	1.45576i	0.0299601	+	0.0518924i	−0.850657	+	0.525722i	$0.823795\pi$
$788$	9.41478	+	16.3069i	0.335388	+	0.580908i
$789$	30.2981			1.07864
$790$	0.585221			0.0208212
$791$	−0.760677	−	1.31753i	−0.0270466	−	0.0468460i
$792$	−8.83502	+	15.3027i	−0.313939	+	0.543758i
$793$	−0.0620117	+	0.107407i	−0.00220210	+	0.00381415i
$794$	4.83775	+	8.37923i	0.171685	+	0.297368i
$795$	−22.2125			−0.787795
$796$	−6.15591			−0.218190
$797$	22.6017	−	39.1473i	0.800593	−	1.38667i	−0.118633	−	0.992938i	$-0.537851\pi$
$797$	22.6017	−	39.1473i	0.800593	−	1.38667i	0.919226	−	0.393730i	$-0.128815\pi$
$798$	0.242932	+	0.420770i	0.00859968	+	0.0148951i
$799$	−35.0101			−1.23857
$800$	0.500000	−	0.866025i	0.0176777	−	0.0306186i
$801$	28.7922			1.01732
$802$	1.56655	+	2.71334i	0.0553167	+	0.0958114i
$803$	20.4057			0.720102
$804$	−18.0803	+	9.82866i	−0.637642	+	0.346630i
$805$	−0.349158			−0.0123062
$806$	0.0938942	+	0.162630i	0.00330728	+	0.00572838i
$807$	−20.5051			−0.721812
$808$	−0.563816	+	0.976558i	−0.0198350	+	0.0343552i
$809$	38.7357			1.36187			0.680937	−	0.732342i	$-0.261573\pi$
$809$	38.7357			1.36187			0.680937	+	0.732342i	$0.261573\pi$
$810$	−3.96719	−	6.87137i	−0.139393	−	0.241435i
$811$	−15.1655	+	26.2674i	−0.532533	+	0.922374i	0.466745	+	0.884392i	$0.345426\pi$
$811$	−15.1655	+	26.2674i	−0.532533	+	0.922374i	−0.999278	+	0.0379824i	$0.987907\pi$
$812$	−0.217918			−0.00764741
$813$	5.46586			0.191696
$814$	28.4623	+	49.2981i	0.997601	+	1.72790i
$815$	8.36603	−	14.4904i	0.293049	−	0.507576i
$816$	−7.33502	+	12.7046i	−0.256777	+	0.444751i
$817$	1.25707	+	2.17731i	0.0439793	+	0.0761743i
$818$	−25.5388			−0.892943
$819$	0.124023			0.00433373
$820$	−0.339558	−	0.588131i	−0.0118579	−	0.0205384i
$821$	15.8296	+	27.4176i	0.552455	+	0.956881i	0.998097	+	0.0616691i	$0.0196424\pi$
$821$	15.8296	+	27.4176i	0.552455	+	0.956881i	−0.445641	+	0.895212i	$0.647024\pi$
$822$	19.6090	+	33.9637i	0.683941	+	1.18462i
$823$	−10.6135	−	18.3831i	−0.369963	−	0.640795i	0.619596	−	0.784921i	$-0.287296\pi$
$823$	−10.6135	−	18.3831i	−0.369963	−	0.640795i	−0.989559	+	0.144126i	$0.953963\pi$
$824$	−7.15591	+	12.3944i	−0.249288	+	0.431779i
$825$	−6.68872	+	11.5852i	−0.232871	+	0.403345i
$826$	−1.10843			−0.0385672
$827$	−16.7411	−	28.9965i	−0.582146	−	1.00831i	−0.995225	−	0.0976111i	$-0.968880\pi$
$827$	−16.7411	−	28.9965i	−0.582146	−	1.00831i	0.413079	−	0.910695i	$-0.364453\pi$
$828$	−6.00000			−0.208514
$829$	−20.5743			−0.714575			−0.357287	−	0.933995i	$-0.616298\pi$
$829$	−20.5743			−0.714575			−0.357287	+	0.933995i	$0.616298\pi$
$830$	1.36783	−	2.36915i	0.0474781	−	0.0822345i
$831$	80.7367			2.80073
$832$	−0.0966262	−	0.167362i	−0.00334991	−	0.00580222i
$833$	−20.3136	+	35.1842i	−0.703825	+	1.21906i
$834$	−11.8706	−	20.5604i	−0.411044	−	0.711949i
$835$	−12.3492	+	21.3894i	−0.427360	+	0.740210i
$836$	−2.66044	+	4.60802i	−0.0920133	+	0.159372i
$837$	0.391969	−	0.678910i	0.0135484	−	0.0234666i
$838$	−14.7125	+	25.4827i	−0.508233	+	0.880286i
$839$	−5.42024	+	9.38814i	−0.187128	+	0.324114i	−0.944291	−	0.329111i	$-0.893251\pi$
$839$	−5.42024	+	9.38814i	−0.187128	+	0.324114i	0.757164	+	0.653225i	$0.226584\pi$
$840$	−0.242932	+	0.420770i	−0.00838193	+	0.0145179i
$841$	13.8642	+	24.0135i	0.478077	+	0.828053i
$842$	17.4768	−	30.2707i	0.602290	−	1.04320i
$843$	13.4841	+	23.3551i	0.464416	+	0.804392i
$844$	−11.7730			−0.405244
$845$	6.48133	−	11.2260i	0.222964	−	0.386186i
$846$	−19.9253			−0.685046
$847$	3.34555			0.114954
$848$	−4.41751	−	7.65135i	−0.151698	−	0.262749i
$849$	29.0192			0.995936
$850$	−2.91751	+	5.05328i	−0.100070	+	0.173326i
$851$	−9.66458	+	16.7395i	−0.331297	+	0.573824i
$852$	−11.9599	−	20.7152i	−0.409740	−	0.709691i
$853$	12.1933	+	21.1193i	0.417489	+	0.723112i	0.995686	−	0.0927849i	$-0.0295769\pi$
$853$	12.1933	+	21.1193i	0.417489	+	0.723112i	−0.578197	+	0.815897i	$0.696244\pi$
$854$	0.0620117	+	0.107407i	0.00212200	+	0.00367541i
$855$	1.66044	+	2.87597i	0.0567859	+	0.0983561i
$856$	2.25526			0.0770833
$857$	−47.0101			−1.60584			−0.802918	−	0.596090i	$-0.796720\pi$
$857$	−47.0101			−1.60584			−0.802918	+	0.596090i	$0.796720\pi$
$858$	1.29261	+	2.23887i	0.0441290	+	0.0764337i
$859$	11.7311	−	20.3189i	0.400261	−	0.693272i	−0.593496	−	0.804837i	$-0.702253\pi$
$859$	11.7311	−	20.3189i	0.400261	−	0.693272i	0.993757	+	0.111565i	$0.0355862\pi$
$860$	−1.25707	+	2.17731i	−0.0428657	+	0.0742455i
$861$	0.164979	+	0.285751i	0.00562245	+	0.00973838i
$862$	−6.23060			−0.212215
$863$	−20.8223			−0.708801			−0.354400	−	0.935094i	$-0.615315\pi$
$863$	−20.8223			−0.708801			−0.354400	+	0.935094i	$0.615315\pi$
$864$	−0.403374	+	0.698664i	−0.0137231	+	0.0237690i
$865$	11.3802	+	19.7110i	0.386937	+	0.670195i
$866$	36.5899			1.24337
$867$	21.4298	−	37.1176i	0.727796	−	1.26058i
$868$	0.187788			0.00637395
$869$	−1.55695	−	2.69671i	−0.0528158	−	0.0914797i
$870$	−2.83502			−0.0961162
$871$	−0.0406065	+	1.58132i	−0.00137590	+	0.0535809i
$872$	−4.48586			−0.151910
$873$	−24.6796	−	42.7464i	−0.835279	−	1.44675i
$874$	−1.80675			−0.0611141
$875$	−0.0966262	+	0.167362i	−0.00326656	+	0.00565785i
$876$	9.64177			0.325765
$877$	20.3892	+	35.3152i	0.688496	+	1.19251i	0.972325	+	0.233634i	$0.0750619\pi$
$877$	20.3892	+	35.3152i	0.688496	+	1.19251i	−0.283829	+	0.958875i	$0.591605\pi$
$878$	14.1773	−	24.5558i	0.478461	−	0.828719i
$879$	54.4677			1.83715
$880$	−5.32088			−0.179367
$881$	−2.72606	−	4.72168i	−0.0918434	−	0.159077i	0.816443	−	0.577425i	$-0.195943\pi$
$881$	−2.72606	−	4.72168i	−0.0918434	−	0.159077i	−0.908287	+	0.418348i	$0.862609\pi$
$882$	−11.5611	+	20.0244i	−0.389282	+	0.674256i
$883$	0.542411	−	0.939483i	0.0182536	−	0.0316161i	−0.856754	−	0.515725i	$-0.827523\pi$
$883$	0.542411	−	0.939483i	0.0182536	−	0.0316161i	0.875008	+	0.484109i	$0.160856\pi$
$884$	0.563816	+	0.976558i	0.0189632	+	0.0328452i
$885$	−14.4202			−0.484731
$886$	−15.2306			−0.511682
$887$	12.5734	+	21.7778i	0.422174	+	0.731227i	0.996152	−	0.0876440i	$-0.0279338\pi$
$887$	12.5734	+	21.7778i	0.422174	+	0.731227i	−0.573978	+	0.818871i	$0.694600\pi$
$888$	13.4485	+	23.2935i	0.451303	+	0.781679i
$889$	0.617104	+	1.06886i	0.0206970	+	0.0358483i
$890$	4.33502	+	7.50848i	0.145310	+	0.251685i
$891$	−21.1090	+	36.5618i	−0.707177	+	1.22487i
$892$	12.0876	−	20.9363i	0.404721	−	0.700998i
$893$	−6.00000			−0.200782
$894$	−1.29261	−	2.23887i	−0.0432314	−	0.0748789i
$895$	−24.4996			−0.818931
$896$	−0.193252			−0.00645611
$897$	−0.438916	+	0.760225i	−0.0146550	+	0.0253832i
$898$	−20.2553			−0.675927
$899$	0.547875	+	0.948947i	0.0182726	+	0.0316492i
$900$	−1.66044	+	2.87597i	−0.0553481	+	0.0958657i
$901$	25.7763	+	44.6458i	0.858732	+	1.48737i
$902$	−1.80675	+	3.12938i	−0.0601581	+	0.104197i
$903$	0.610763	−	1.05787i	0.0203249	−	0.0352038i
$904$	3.93618	−	6.81767i	0.130916	−	0.226752i
$905$	1.53554	−	2.65964i	0.0510431	−	0.0884093i
$906$	−16.0165	+	27.7413i	−0.532112	+	0.921644i
$907$	−2.89157	+	5.00834i	−0.0960130	+	0.166299i	−0.910031	−	0.414540i	$-0.863942\pi$
$907$	−2.89157	+	5.00834i	−0.0960130	+	0.166299i	0.814018	+	0.580840i	$0.197276\pi$
$908$	−10.5593	−	18.2892i	−0.350422	−	0.606949i
$909$	1.87237	−	3.24304i	0.0621025	−	0.107565i
$910$	0.0186733	+	0.0323430i	0.000619012	+	0.00107216i
$911$	45.5207			1.50817			0.754083	−	0.656779i	$-0.228081\pi$
$911$	45.5207			1.50817			0.754083	+	0.656779i	$0.228081\pi$
$912$	−1.25707	+	2.17731i	−0.0416257	+	0.0720978i
$913$	−14.5561			−0.481738
$914$	26.6272			0.880751
$915$	0.806748	+	1.39733i	0.0266703	+	0.0461942i
$916$	10.9536			0.361916
$917$	−0.164979	+	0.285751i	−0.00544807	+	0.00943634i
$918$	2.35369	−	4.07672i	0.0776835	−	0.134552i
$919$	−7.23386	−	12.5294i	−0.238623	−	0.413307i	0.721696	−	0.692210i	$-0.243363\pi$
$919$	−7.23386	−	12.5294i	−0.238623	−	0.413307i	−0.960319	+	0.278903i	$0.910029\pi$
$920$	−0.903374	−	1.56469i	−0.0297834	−	0.0515863i
$921$	0.599358	+	1.03812i	0.0197495	+	0.0342072i
$922$	2.30494	+	3.99228i	0.0759093	+	0.131479i
$923$	−1.83863			−0.0605192
$924$	2.58522			0.0850475
$925$	5.34916	+	9.26501i	0.175879	+	0.304632i
$926$	12.2152	−	21.1573i	0.401416	−	0.695273i
$927$	23.7639	−	41.1603i	0.780510	−	1.35188i
$928$	−0.563816	−	0.976558i	−0.0185082	−	0.0320571i
$929$	24.6519			0.808803			0.404401	−	0.914582i	$-0.367480\pi$
$929$	24.6519			0.808803			0.404401	+	0.914582i	$0.367480\pi$
$930$	2.44305			0.0801108
$931$	−3.48133	+	6.02983i	−0.114096	+	0.197620i
$932$	11.1390	+	19.2934i	0.364871	+	0.631976i
$933$	1.50586			0.0492998
$934$	6.34916	−	10.9971i	0.207751	−	0.359835i
$935$	31.0475			1.01536
$936$	0.320884	+	0.555788i	0.0104884	+	0.0181665i
$937$	40.7549			1.33140			0.665702	−	0.746218i	$-0.268132\pi$
$937$	40.7549			1.33140			0.665702	+	0.746218i	$0.268132\pi$
$938$	1.34916	+	0.825825i	0.0440516	+	0.0269642i
$939$	57.1515			1.86507
$940$	−3.00000	−	5.19615i	−0.0978492	−	0.169480i
$941$	15.8825			0.517755			0.258877	−	0.965910i	$-0.416647\pi$
$941$	15.8825			0.517755			0.258877	+	0.965910i	$0.416647\pi$
$942$	23.2621	−	40.2912i	0.757921	−	1.31276i
$943$	−1.22699			−0.0399563
$944$	−2.86783	−	4.96723i	−0.0933400	−	0.161670i
$945$	0.0779530	−	0.135018i	0.00253581	−	0.00439215i
$946$	13.3774			0.434938
$947$	−49.8625			−1.62031			−0.810157	−	0.586213i	$-0.800618\pi$
$947$	−49.8625			−1.62031			−0.810157	+	0.586213i	$0.800618\pi$
$948$	−0.735663	−	1.27421i	−0.0238932	−	0.0413843i
$949$	0.370564	−	0.641835i	0.0120290	−	0.0208348i
$950$	−0.500000	+	0.866025i	−0.0162221	+	0.0280976i
$951$	24.5479	+	42.5182i	0.796019	+	1.37875i
$952$	1.12763			0.0365468
$953$	−31.6099			−1.02394			−0.511972	−	0.859002i	$-0.671085\pi$
$953$	−31.6099			−1.02394			−0.511972	+	0.859002i	$0.671085\pi$
$954$	14.6700	+	25.4093i	0.474960	+	0.822655i
$955$	8.62036	+	14.9309i	0.278948	+	0.483153i
$956$	−5.93438	−	10.2786i	−0.191932	−	0.332435i
$957$	7.54241	+	13.0638i	0.243812	+	0.422294i
$958$	−11.6860	+	20.2407i	−0.377557	+	0.653948i
$959$	1.50727	−	2.61067i	0.0486722	−	0.0843028i
$960$	−2.51414			−0.0811434
$961$	15.0279	+	26.0290i	0.484770	+	0.839647i
$962$	2.06748			0.0666581
$963$	−7.48947			−0.241345
$964$	2.61350	−	4.52671i	0.0841750	−	0.145795i
$965$	−2.29261			−0.0738017
$966$	0.438916	+	0.760225i	0.0141219	+	0.0244598i
$967$	−18.3546	+	31.7911i	−0.590245	+	1.02233i	0.403954	+	0.914779i	$0.367635\pi$
$967$	−18.3546	+	31.7911i	−0.590245	+	1.02233i	−0.994199	+	0.107555i	$0.965698\pi$
$968$	8.65591	+	14.9925i	0.278211	+	0.481876i
$969$	7.33502	−	12.7046i	0.235635	−	0.408132i
$970$	7.43165	−	12.8720i	0.238616	−	0.413295i
$971$	−10.7498	+	18.6192i	−0.344978	+	0.597519i	−0.985350	−	0.170546i	$-0.945447\pi$
$971$	−10.7498	+	18.6192i	−0.344978	+	0.597519i	0.640372	+	0.768065i	$0.278780\pi$
$972$	−11.1842	+	19.3716i	−0.358733	+	0.621343i
$973$	−0.912446	+	1.58040i	−0.0292517	+	0.0506654i
$974$	−13.1814	+	22.8309i	−0.422361	+	0.731550i
$975$	0.242932	+	0.420770i	0.00778004	+	0.0134754i
$976$	−0.320884	+	0.555788i	−0.0102713	+	0.0177903i
$977$	−24.0529	−	41.6609i	−0.769522	−	1.33285i	−0.937823	−	0.347115i	$-0.887161\pi$
$977$	−24.0529	−	41.6609i	−0.769522	−	1.33285i	0.168301	−	0.985736i	$-0.446172\pi$
$978$	−42.0667			−1.34514
$979$	23.0661	−	39.9517i	0.737197	−	1.27686i
$980$	−6.96265			−0.222414
$981$	14.8970			0.475626
$982$	8.46265	+	14.6577i	0.270054	+	0.467747i
$983$	26.4540			0.843751			0.421875	−	0.906654i	$-0.361372\pi$
$983$	26.4540			0.843751			0.421875	+	0.906654i	$0.361372\pi$
$984$	−0.853695	+	1.47864i	−0.0272148	+	0.0471374i
$985$	9.41478	−	16.3069i	0.299980	−	0.519580i
$986$	3.28988	+	5.69824i	0.104771	+	0.181469i
$987$	1.45759	+	2.52462i	0.0463956	+	0.0803595i
$988$	0.0966262	+	0.167362i	0.00307409	+	0.00532448i
$989$	2.27121	+	3.93384i	0.0722201	+	0.125089i
$990$	17.6700			0.561591
$991$	13.1386			0.417360			0.208680	−	0.977984i	$-0.433083\pi$
$991$	13.1386			0.417360			0.208680	+	0.977984i	$0.433083\pi$
$992$	0.485863	+	0.841540i	0.0154262	+	0.0267189i
$993$	−15.2625	+	26.4355i	−0.484342	+	0.838905i
$994$	−0.919315	+	1.59230i	−0.0291589	+	0.0505047i
$995$	3.07795	+	5.33117i	0.0975777	+	0.169009i
$996$	−6.87783			−0.217932
$997$	−7.59710			−0.240603			−0.120301	−	0.992737i	$-0.538386\pi$
$997$	−7.59710			−0.240603			−0.120301	+	0.992737i	$0.538386\pi$
$998$	−19.1646	+	33.1940i	−0.606644	+	1.05074i
$999$	−4.31542	−	7.47453i	−0.136534	−	0.236484i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	670.2.e.g.171.1	✓	6
67.29	even	3	inner	670.2.e.g.431.1	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
670.2.e.g.171.1	✓	6	1.1	even	1	trivial
670.2.e.g.431.1	yes	6	67.29	even	3	inner

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:	\( N \)	\(=\)	\( 670 = 2 \cdot 5 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	670.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} -2.51414 q^{3} +(-0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(-1.25707 - 2.17731i) q^{6} +(-0.0966262 + 0.167362i) q^{7} -1.00000 q^{8} +3.32088 q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} -2.51414 q^{3} +(-0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(-1.25707 - 2.17731i) q^{6} +(-0.0966262 + 0.167362i) q^{7} -1.00000 q^{8} +3.32088 q^{9} +(0.500000 + 0.866025i) q^{10} +(2.66044 - 4.60802i) q^{11} +(1.25707 - 2.17731i) q^{12} +(-0.0966262 - 0.167362i) q^{13} -0.193252 q^{14} -2.51414 q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.91751 + 5.05328i) q^{17} +(1.66044 + 2.87597i) q^{18} +(0.500000 + 0.866025i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(0.242932 - 0.420770i) q^{21} +5.32088 q^{22} +(0.903374 + 1.56469i) q^{23} +2.51414 q^{24} +1.00000 q^{25} +(0.0966262 - 0.167362i) q^{26} -0.806748 q^{27} +(-0.0966262 - 0.167362i) q^{28} +(0.563816 - 0.976558i) q^{29} +(-1.25707 - 2.17731i) q^{30} +(-0.485863 + 0.841540i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-6.68872 + 11.5852i) q^{33} +(-2.91751 + 5.05328i) q^{34} +(-0.0966262 + 0.167362i) q^{35} +(-1.66044 + 2.87597i) q^{36} +(5.34916 + 9.26501i) q^{37} +(-0.500000 + 0.866025i) q^{38} +(0.242932 + 0.420770i) q^{39} -1.00000 q^{40} +(-0.339558 + 0.588131i) q^{41} +0.485863 q^{42} +2.51414 q^{43} +(2.66044 + 4.60802i) q^{44} +3.32088 q^{45} +(-0.903374 + 1.56469i) q^{46} +(-3.00000 + 5.19615i) q^{47} +(1.25707 + 2.17731i) q^{48} +(3.48133 + 6.02983i) q^{49} +(0.500000 + 0.866025i) q^{50} +(-7.33502 - 12.7046i) q^{51} +0.193252 q^{52} +8.83502 q^{53} +(-0.403374 - 0.698664i) q^{54} +(2.66044 - 4.60802i) q^{55} +(0.0966262 - 0.167362i) q^{56} +(-1.25707 - 2.17731i) q^{57} +1.12763 q^{58} +5.73566 q^{59} +(1.25707 - 2.17731i) q^{60} +(-0.320884 - 0.555788i) q^{61} -0.971726 q^{62} +(-0.320884 + 0.555788i) q^{63} +1.00000 q^{64} +(-0.0966262 - 0.167362i) q^{65} -13.3774 q^{66} +(-6.98133 - 4.27330i) q^{67} -5.83502 q^{68} +(-2.27121 - 3.93384i) q^{69} -0.193252 q^{70} +(4.75707 - 8.23948i) q^{71} -3.32088 q^{72} +(1.91751 + 3.32123i) q^{73} +(-5.34916 + 9.26501i) q^{74} -2.51414 q^{75} -1.00000 q^{76} +(0.514137 + 0.890511i) q^{77} +(-0.242932 + 0.420770i) q^{78} +(0.292611 - 0.506816i) q^{79} +(-0.500000 - 0.866025i) q^{80} -7.93438 q^{81} -0.679116 q^{82} +(-1.36783 - 2.36915i) q^{83} +(0.242932 + 0.420770i) q^{84} +(2.91751 + 5.05328i) q^{85} +(1.25707 + 2.17731i) q^{86} +(-1.41751 + 2.45520i) q^{87} +(-2.66044 + 4.60802i) q^{88} +8.67004 q^{89} +(1.66044 + 2.87597i) q^{90} +0.0373465 q^{91} -1.80675 q^{92} +(1.22153 - 2.11575i) q^{93} -6.00000 q^{94} +(0.500000 + 0.866025i) q^{95} +(-1.25707 + 2.17731i) q^{96} +(-7.43165 - 12.8720i) q^{97} +(-3.48133 + 6.02983i) q^{98} +(8.83502 - 15.3027i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} - 2 q^{3} - 3 q^{4} + 6 q^{5} - q^{6} - 2 q^{7} - 6 q^{8} + 4 q^{9}+O(q^{10}) \) 6 * q + 3 * q^2 - 2 * q^3 - 3 * q^4 + 6 * q^5 - q^6 - 2 * q^7 - 6 * q^8 + 4 * q^9	\( 6 q + 3 q^{2} - 2 q^{3} - 3 q^{4} + 6 q^{5} - q^{6} - 2 q^{7} - 6 q^{8} + 4 q^{9} + 3 q^{10} + 8 q^{11} + q^{12} - 2 q^{13} - 4 q^{14} - 2 q^{15} - 3 q^{16} + 3 q^{17} + 2 q^{18} + 3 q^{19} - 3 q^{20} + 8 q^{21} + 16 q^{22} + 4 q^{23} + 2 q^{24} + 6 q^{25} + 2 q^{26} - 2 q^{27} - 2 q^{28} - 6 q^{29} - q^{30} - 16 q^{31} + 3 q^{32} - 6 q^{33} - 3 q^{34} - 2 q^{35} - 2 q^{36} - 10 q^{37} - 3 q^{38} + 8 q^{39} - 6 q^{40} - 10 q^{41} + 16 q^{42} + 2 q^{43} + 8 q^{44} + 4 q^{45} - 4 q^{46} - 18 q^{47} + q^{48} - 3 q^{49} + 3 q^{50} - 15 q^{51} + 4 q^{52} + 24 q^{53} - q^{54} + 8 q^{55} + 2 q^{56} - q^{57} - 12 q^{58} - 2 q^{59} + q^{60} + 14 q^{61} - 32 q^{62} + 14 q^{63} + 6 q^{64} - 2 q^{65} - 12 q^{66} - 18 q^{67} - 6 q^{68} + 6 q^{69} - 4 q^{70} + 22 q^{71} - 4 q^{72} - 3 q^{73} + 10 q^{74} - 2 q^{75} - 6 q^{76} - 10 q^{77} - 8 q^{78} + 12 q^{79} - 3 q^{80} - 26 q^{81} - 20 q^{82} + 10 q^{83} + 8 q^{84} + 3 q^{85} + q^{86} + 6 q^{87} - 8 q^{88} - 6 q^{89} + 2 q^{90} + 48 q^{91} - 8 q^{92} - 16 q^{93} - 36 q^{94} + 3 q^{95} - q^{96} - 17 q^{97} + 3 q^{98} + 24 q^{99}+O(q^{100}) \) 6 * q + 3 * q^2 - 2 * q^3 - 3 * q^4 + 6 * q^5 - q^6 - 2 * q^7 - 6 * q^8 + 4 * q^9 + 3 * q^10 + 8 * q^11 + q^12 - 2 * q^13 - 4 * q^14 - 2 * q^15 - 3 * q^16 + 3 * q^17 + 2 * q^18 + 3 * q^19 - 3 * q^20 + 8 * q^21 + 16 * q^22 + 4 * q^23 + 2 * q^24 + 6 * q^25 + 2 * q^26 - 2 * q^27 - 2 * q^28 - 6 * q^29 - q^30 - 16 * q^31 + 3 * q^32 - 6 * q^33 - 3 * q^34 - 2 * q^35 - 2 * q^36 - 10 * q^37 - 3 * q^38 + 8 * q^39 - 6 * q^40 - 10 * q^41 + 16 * q^42 + 2 * q^43 + 8 * q^44 + 4 * q^45 - 4 * q^46 - 18 * q^47 + q^48 - 3 * q^49 + 3 * q^50 - 15 * q^51 + 4 * q^52 + 24 * q^53 - q^54 + 8 * q^55 + 2 * q^56 - q^57 - 12 * q^58 - 2 * q^59 + q^60 + 14 * q^61 - 32 * q^62 + 14 * q^63 + 6 * q^64 - 2 * q^65 - 12 * q^66 - 18 * q^67 - 6 * q^68 + 6 * q^69 - 4 * q^70 + 22 * q^71 - 4 * q^72 - 3 * q^73 + 10 * q^74 - 2 * q^75 - 6 * q^76 - 10 * q^77 - 8 * q^78 + 12 * q^79 - 3 * q^80 - 26 * q^81 - 20 * q^82 + 10 * q^83 + 8 * q^84 + 3 * q^85 + q^86 + 6 * q^87 - 8 * q^88 - 6 * q^89 + 2 * q^90 + 48 * q^91 - 8 * q^92 - 16 * q^93 - 36 * q^94 + 3 * q^95 - q^96 - 17 * q^97 + 3 * q^98 + 24 * q^99

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