LMFDB - Embedded newform 122.2.f.a.75.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [122,2,Mod(75,122)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(122, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5]))

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

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

chi := DirichletCharacter("122.75");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 122 = 2 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	122.f (of order $6$, 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:	$0.974174904660$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.110502144.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 11x^{6} - 14x^{5} + 7x^{4} + 18x^{3} - 18x^{2} - 36x + 36 $ x^8 - 4x^7 + 11x^6 - 14x^5 + 7x^4 + 18x^3 - 18x^2 - 36*x + 36
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			75.4
Root			$0.428545 + 2.13270i$ of defining polynomial
Character	$\chi$	$=$	122.75
Dual form			122.2.f.a.109.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +1.87496 q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.571455 - 0.989788i) q^{5} +(1.62376 - 0.937480i) q^{6} +(-3.92599 + 2.26667i) q^{7} -1.00000i q^{8} +0.515475 q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +1.87496 q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.571455 - 0.989788i) q^{5} +(1.62376 - 0.937480i) q^{6} +(-3.92599 + 2.26667i) q^{7} -1.00000i q^{8} +0.515475 q^{9} +(-0.989788 - 0.571455i) q^{10} +3.10462i q^{11} +(0.937480 - 1.62376i) q^{12} +(-0.437480 - 0.757738i) q^{13} +(-2.26667 + 3.92599i) q^{14} +(-1.07145 - 1.85581i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.90830 + 2.25646i) q^{17} +(0.446415 - 0.257738i) q^{18} +(3.32792 - 5.76412i) q^{19} -1.14291 q^{20} +(-7.36108 + 4.24992i) q^{21} +(1.55231 + 2.68868i) q^{22} +1.34162i q^{23} -1.87496i q^{24} +(1.84688 - 3.19889i) q^{25} +(-0.757738 - 0.437480i) q^{26} -4.65838 q^{27} +4.53334i q^{28} +(-6.69394 - 3.86475i) q^{29} +(-1.85581 - 1.07145i) q^{30} +(5.19394 + 2.99872i) q^{31} +(-0.866025 - 0.500000i) q^{32} +5.82103i q^{33} +4.51292 q^{34} +(4.48705 + 2.59060i) q^{35} +(0.257738 - 0.446415i) q^{36} +1.49505i q^{37} -6.65583i q^{38} +(-0.820258 - 1.42073i) q^{39} +(-0.989788 + 0.571455i) q^{40} -4.21402 q^{41} +(-4.24992 + 7.36108i) q^{42} +(-2.71963 + 1.57018i) q^{43} +(2.68868 + 1.55231i) q^{44} +(-0.294571 - 0.510212i) q^{45} +(0.670808 + 1.16187i) q^{46} +(-2.69522 + 4.66825i) q^{47} +(-0.937480 - 1.62376i) q^{48} +(6.77561 - 11.7357i) q^{49} -3.69376i q^{50} +(7.32792 + 4.23077i) q^{51} -0.874960 q^{52} -8.24497i q^{53} +(-4.03428 + 2.32919i) q^{54} +(3.07291 - 1.77415i) q^{55} +(2.26667 + 3.92599i) q^{56} +(6.23971 - 10.8075i) q^{57} -7.72950 q^{58} +(-4.69920 + 2.71309i) q^{59} -2.14291 q^{60} +(3.46410 - 7.00000i) q^{61} +5.99745 q^{62} +(-2.02375 + 1.16841i) q^{63} -1.00000 q^{64} +(-0.500000 + 0.866025i) q^{65} +(2.91052 + 5.04116i) q^{66} +(13.2995 - 7.67847i) q^{67} +(3.90830 - 2.25646i) q^{68} +2.51548i q^{69} +5.18120 q^{70} +(11.2056 + 6.46955i) q^{71} -0.515475i q^{72} +(-5.23971 + 9.07544i) q^{73} +(0.747526 + 1.29475i) q^{74} +(3.46282 - 5.99779i) q^{75} +(-3.32792 - 5.76412i) q^{76} +(-7.03715 - 12.1887i) q^{77} +(-1.42073 - 0.820258i) q^{78} +(-5.90336 + 3.40830i) q^{79} +(-0.571455 + 0.989788i) q^{80} -10.2807 q^{81} +(-3.64945 + 2.10701i) q^{82} +(6.66953 + 11.5520i) q^{83} +8.49984i q^{84} -5.15786i q^{85} +(-1.57018 + 2.71963i) q^{86} +(-12.5509 - 7.24625i) q^{87} +3.10462 q^{88} +1.41086i q^{89} +(-0.510212 - 0.294571i) q^{90} +(3.43509 + 1.98325i) q^{91} +(1.16187 + 0.670808i) q^{92} +(9.73843 + 5.62249i) q^{93} +5.39044i q^{94} -7.60701 q^{95} +(-1.62376 - 0.937480i) q^{96} +(2.01292 - 3.48648i) q^{97} -13.5512i q^{98} +1.60035i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{4} - 4 q^{5} + 6 q^{6} + 12 q^{7} + 4 q^{9}+O(q^{10}) $ 8 * q + 4 * q^4 - 4 * q^5 + 6 * q^6 + 12 * q^7 + 4 * q^9	$ 8 q + 4 q^{4} - 4 q^{5} + 6 q^{6} + 12 q^{7} + 4 q^{9} + 6 q^{10} + 4 q^{13} - 10 q^{14} - 8 q^{15} - 4 q^{16} - 12 q^{18} + 4 q^{19} - 8 q^{20} - 24 q^{21} + 6 q^{22} + 2 q^{25} - 6 q^{26} - 36 q^{27} - 24 q^{29} + 6 q^{30} + 12 q^{31} - 8 q^{34} - 18 q^{35} + 2 q^{36} - 14 q^{39} + 6 q^{40} + 24 q^{41} - 4 q^{42} - 6 q^{43} + 6 q^{44} + 4 q^{45} + 6 q^{46} - 14 q^{47} + 38 q^{49} + 36 q^{51} + 8 q^{52} + 18 q^{54} + 42 q^{55} + 10 q^{56} + 6 q^{57} - 4 q^{58} + 6 q^{59} - 16 q^{60} + 4 q^{62} + 6 q^{63} - 8 q^{64} - 4 q^{65} - 20 q^{66} + 30 q^{67} + 52 q^{70} - 6 q^{71} + 2 q^{73} - 8 q^{74} - 22 q^{75} - 4 q^{76} - 8 q^{77} + 18 q^{78} + 12 q^{79} - 4 q^{80} + 8 q^{81} - 36 q^{82} + 32 q^{83} + 10 q^{86} - 12 q^{87} + 12 q^{88} - 18 q^{90} + 36 q^{91} + 18 q^{92} + 12 q^{93} - 32 q^{95} - 6 q^{96} - 28 q^{97}+O(q^{100}) $ 8 * q + 4 * q^4 - 4 * q^5 + 6 * q^6 + 12 * q^7 + 4 * q^9 + 6 * q^10 + 4 * q^13 - 10 * q^14 - 8 * q^15 - 4 * q^16 - 12 * q^18 + 4 * q^19 - 8 * q^20 - 24 * q^21 + 6 * q^22 + 2 * q^25 - 6 * q^26 - 36 * q^27 - 24 * q^29 + 6 * q^30 + 12 * q^31 - 8 * q^34 - 18 * q^35 + 2 * q^36 - 14 * q^39 + 6 * q^40 + 24 * q^41 - 4 * q^42 - 6 * q^43 + 6 * q^44 + 4 * q^45 + 6 * q^46 - 14 * q^47 + 38 * q^49 + 36 * q^51 + 8 * q^52 + 18 * q^54 + 42 * q^55 + 10 * q^56 + 6 * q^57 - 4 * q^58 + 6 * q^59 - 16 * q^60 + 4 * q^62 + 6 * q^63 - 8 * q^64 - 4 * q^65 - 20 * q^66 + 30 * q^67 + 52 * q^70 - 6 * q^71 + 2 * q^73 - 8 * q^74 - 22 * q^75 - 4 * q^76 - 8 * q^77 + 18 * q^78 + 12 * q^79 - 4 * q^80 + 8 * q^81 - 36 * q^82 + 32 * q^83 + 10 * q^86 - 12 * q^87 + 12 * q^88 - 18 * q^90 + 36 * q^91 + 18 * q^92 + 12 * q^93 - 32 * q^95 - 6 * q^96 - 28 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/122\mathbb{Z}\right)^\times$.

$n$	$63$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$	1.87496			1.08251			0.541254	−	0.840859i	$-0.317950\pi$
$3$	1.87496			1.08251			0.541254	+	0.840859i	$0.317950\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−0.571455	−	0.989788i	−0.255562	−	0.442647i	0.709486	−	0.704720i	$-0.248927\pi$
$5$	−0.571455	−	0.989788i	−0.255562	−	0.442647i	−0.965048	+	0.262073i	$0.915594\pi$
$6$	1.62376	−	0.937480i	0.662898	−	0.382725i
$7$	−3.92599	+	2.26667i	−1.48389	+	0.856722i	−0.999832	−	0.0183170i	$-0.994169\pi$
$7$	−3.92599	+	2.26667i	−1.48389	+	0.856722i	−0.484053	+	0.875039i	$0.660836\pi$
$8$		−	1.00000i		−	0.353553i
$9$	0.515475			0.171825
$10$	−0.989788	−	0.571455i	−0.312999	−	0.180710i
$11$			3.10462i			0.936077i	0.883708	+	0.468039i	$0.155039\pi$
$11$			3.10462i			0.936077i	−0.883708	+	0.468039i	$0.844961\pi$
$12$	0.937480	−	1.62376i	0.270627	−	0.468740i
$13$	−0.437480	−	0.757738i	−0.121335	−	0.210159i	0.798959	−	0.601385i	$-0.205384\pi$
$13$	−0.437480	−	0.757738i	−0.121335	−	0.210159i	−0.920294	+	0.391226i	$0.872051\pi$
$14$	−2.26667	+	3.92599i	−0.605794	+	1.04927i
$15$	−1.07145	−	1.85581i	−0.276648	−	0.479169i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	3.90830	+	2.25646i	0.947903	+	0.547272i	0.892429	−	0.451188i	$-0.149000\pi$
$17$	3.90830	+	2.25646i	0.947903	+	0.547272i	0.0554742	+	0.998460i	$0.482333\pi$
$18$	0.446415	−	0.257738i	0.105221	−	0.0607493i
$19$	3.32792	−	5.76412i	0.763476	−	1.32238i	−0.177572	−	0.984108i	$-0.556824\pi$
$19$	3.32792	−	5.76412i	0.763476	−	1.32238i	0.941048	−	0.338272i	$-0.109842\pi$
$20$	−1.14291			−0.255562
$21$	−7.36108	+	4.24992i	−1.60632	+	0.927409i
$22$	1.55231	+	2.68868i	0.330953	+	0.573228i
$23$			1.34162i			0.279746i	0.990169	+	0.139873i	$0.0446695\pi$
$23$			1.34162i			0.279746i	−0.990169	+	0.139873i	$0.955331\pi$
$24$		−	1.87496i		−	0.382725i
$25$	1.84688	−	3.19889i	0.369376	−	0.639778i
$26$	−0.757738	−	0.437480i	−0.148605	−	0.0857969i
$27$	−4.65838			−0.896507
$28$			4.53334i			0.856722i
$29$	−6.69394	−	3.86475i	−1.24303	−	0.717666i	−0.273323	−	0.961922i	$-0.588123\pi$
$29$	−6.69394	−	3.86475i	−1.24303	−	0.717666i	−0.969711	+	0.244257i	$0.921456\pi$
$30$	−1.85581	−	1.07145i	−0.338824	−	0.195620i
$31$	5.19394	+	2.99872i	0.932859	+	0.538587i	0.887715	−	0.460394i	$-0.152292\pi$
$31$	5.19394	+	2.99872i	0.932859	+	0.538587i	0.0451446	+	0.998980i	$0.485625\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$			5.82103i			1.01331i
$34$	4.51292			0.773960
$35$	4.48705	+	2.59060i	0.758450	+	0.437891i
$36$	0.257738	−	0.446415i	0.0429563	−	0.0744025i
$37$			1.49505i			0.245785i	0.992420	+	0.122893i	$0.0392170\pi$
$37$			1.49505i			0.245785i	−0.992420	+	0.122893i	$0.960783\pi$
$38$		−	6.65583i		−	1.07972i
$39$	−0.820258	−	1.42073i	−0.131346	−	0.227499i
$40$	−0.989788	+	0.571455i	−0.156499	+	0.0903549i
$41$	−4.21402			−0.658120			−0.329060	−	0.944309i	$-0.606732\pi$
$41$	−4.21402			−0.658120			−0.329060	+	0.944309i	$0.606732\pi$
$42$	−4.24992	+	7.36108i	−0.655777	+	1.13584i
$43$	−2.71963	+	1.57018i	−0.414739	+	0.239450i	−0.692824	−	0.721107i	$-0.743634\pi$
$43$	−2.71963	+	1.57018i	−0.414739	+	0.239450i	0.278085	+	0.960557i	$0.410300\pi$
$44$	2.68868	+	1.55231i	0.405333	+	0.234019i
$45$	−0.294571	−	0.510212i	−0.0439120	−	0.0760578i
$46$	0.670808	+	1.16187i	0.0989052	+	0.171309i
$47$	−2.69522	+	4.66825i	−0.393138	+	0.680935i	−0.992862	−	0.119272i	$-0.961944\pi$
$47$	−2.69522	+	4.66825i	−0.393138	+	0.680935i	0.599724	+	0.800207i	$0.295277\pi$
$48$	−0.937480	−	1.62376i	−0.135314	−	0.234370i
$49$	6.77561	−	11.7357i	0.967944	−	1.67653i
$50$		−	3.69376i		−	0.522376i
$51$	7.32792	+	4.23077i	1.02611	+	0.592427i
$52$	−0.874960			−0.121335
$53$		−	8.24497i		−	1.13253i	−0.824222	−	0.566267i	$-0.808387\pi$
$53$		−	8.24497i		−	1.13253i	0.824222	−	0.566267i	$-0.191613\pi$
$54$	−4.03428	+	2.32919i	−0.548996	+	0.316963i
$55$	3.07291	−	1.77415i	0.414352	−	0.239226i
$56$	2.26667	+	3.92599i	0.302897	+	0.524633i
$57$	6.23971	−	10.8075i	0.826470	−	1.43149i
$58$	−7.72950			−1.01493
$59$	−4.69920	+	2.71309i	−0.611784	+	0.353214i	−0.773663	−	0.633597i	$-0.781578\pi$
$59$	−4.69920	+	2.71309i	−0.611784	+	0.353214i	0.161879	+	0.986811i	$0.448245\pi$
$60$	−2.14291			−0.276648
$61$	3.46410	−	7.00000i	0.443533	−	0.896258i
$61$	3.46410	−	7.00000i	0.443533	−	0.896258i
$62$	5.99745			0.761676
$63$	−2.02375	+	1.16841i	−0.254969	+	0.147206i
$64$	−1.00000			−0.125000
$65$	−0.500000	+	0.866025i	−0.0620174	+	0.107417i
$66$	2.91052	+	5.04116i	0.358260	+	0.620524i
$67$	13.2995	−	7.67847i	1.62479	−	0.938074i	0.639178	−	0.769059i	$-0.279275\pi$
$67$	13.2995	−	7.67847i	1.62479	−	0.938074i	0.985613	−	0.169015i	$-0.0540587\pi$
$68$	3.90830	−	2.25646i	0.473952	−	0.273636i
$69$			2.51548i			0.302828i
$70$	5.18120			0.619272
$71$	11.2056	+	6.46955i	1.32986	+	0.767794i	0.985278	−	0.170963i	$-0.0546877\pi$
$71$	11.2056	+	6.46955i	1.32986	+	0.767794i	0.344581	+	0.938757i	$0.388021\pi$
$72$		−	0.515475i		−	0.0607493i
$73$	−5.23971	+	9.07544i	−0.613262	+	1.06220i	0.377425	+	0.926040i	$0.376809\pi$
$73$	−5.23971	+	9.07544i	−0.613262	+	1.06220i	−0.990687	+	0.136160i	$0.956524\pi$
$74$	0.747526	+	1.29475i	0.0868981	+	0.150512i
$75$	3.46282	−	5.99779i	0.399853	−	0.692565i
$76$	−3.32792	−	5.76412i	−0.381738	−	0.661190i
$77$	−7.03715	−	12.1887i	−0.801958	−	1.38903i
$78$	−1.42073	−	0.820258i	−0.160866	−	0.0928759i
$79$	−5.90336	+	3.40830i	−0.664180	+	0.383464i	−0.793868	−	0.608091i	$-0.791936\pi$
$79$	−5.90336	+	3.40830i	−0.664180	+	0.383464i	0.129688	+	0.991555i	$0.458602\pi$
$80$	−0.571455	+	0.989788i	−0.0638906	+	0.110662i
$81$	−10.2807			−1.14230
$82$	−3.64945	+	2.10701i	−0.403014	+	0.232680i
$83$	6.66953	+	11.5520i	0.732076	+	1.26799i	0.955994	+	0.293385i	$0.0947818\pi$
$83$	6.66953	+	11.5520i	0.732076	+	1.26799i	−0.223918	+	0.974608i	$0.571885\pi$
$84$			8.49984i			0.927409i
$85$		−	5.15786i		−	0.559448i
$86$	−1.57018	+	2.71963i	−0.169317	+	0.293265i
$87$	−12.5509	−	7.24625i	−1.34559	−	0.776879i
$88$	3.10462			0.330953
$89$			1.41086i			0.149551i	0.997200	+	0.0747753i	$0.0238240\pi$
$89$			1.41086i			0.149551i	−0.997200	+	0.0747753i	$0.976176\pi$
$90$	−0.510212	−	0.294571i	−0.0537810	−	0.0310505i
$91$	3.43509	+	1.98325i	0.360095	+	0.207901i
$92$	1.16187	+	0.670808i	0.121134	+	0.0699365i
$93$	9.73843	+	5.62249i	1.00983	+	0.583025i
$94$			5.39044i			0.555981i
$95$	−7.60701			−0.780463
$96$	−1.62376	−	0.937480i	−0.165725	−	0.0956812i
$97$	2.01292	−	3.48648i	0.204381	−	0.353999i	−0.745554	−	0.666445i	$-0.767815\pi$
$97$	2.01292	−	3.48648i	0.204381	−	0.353999i	0.949935	+	0.312446i	$0.101148\pi$
$98$		−	13.5512i		−	1.36888i
$99$			1.60035i			0.160842i
$100$	−1.84688	−	3.19889i	−0.184688	−	0.319889i
$101$	−5.32375	+	3.07367i	−0.529733	+	0.305841i	−0.740908	−	0.671607i	$-0.765604\pi$
$101$	−5.32375	+	3.07367i	−0.529733	+	0.305841i	0.211175	+	0.977448i	$0.432271\pi$
$102$	8.46155			0.837818
$103$	−0.534439	+	0.925676i	−0.0526598	+	0.0912095i	−0.891154	−	0.453701i	$-0.850103\pi$
$103$	−0.534439	+	0.925676i	−0.0526598	+	0.0912095i	0.838494	+	0.544911i	$0.183437\pi$
$104$	−0.757738	+	0.437480i	−0.0743023	+	0.0428984i
$105$	8.41304	+	4.85727i	0.821029	+	0.474021i
$106$	−4.12249	−	7.14036i	−0.400411	−	0.693533i
$107$	8.44368	+	14.6249i	0.816281	+	1.41384i	0.908404	+	0.418093i	$0.137301\pi$
$107$	8.44368	+	14.6249i	0.816281	+	1.41384i	−0.0921231	+	0.995748i	$0.529365\pi$
$108$	−2.32919	+	4.03428i	−0.224127	+	0.388199i
$109$	3.47737	+	6.02297i	0.333071	+	0.576896i	0.983112	−	0.183003i	$-0.0585817\pi$
$109$	3.47737	+	6.02297i	0.333071	+	0.576896i	−0.650041	+	0.759899i	$0.725248\pi$
$110$	1.77415	−	3.07291i	0.169158	−	0.292991i
$111$			2.80316i			0.266064i
$112$	3.92599	+	2.26667i	0.370971	+	0.214180i
$113$	−5.71418			−0.537545			−0.268772	−	0.963204i	$-0.586618\pi$
$113$	−5.71418			−0.537545			−0.268772	+	0.963204i	$0.586618\pi$
$114$		−	12.4794i		−	1.16880i
$115$	1.32792	−	0.766672i	0.123829	−	0.0714926i
$116$	−6.69394	+	3.86475i	−0.621517	+	0.358833i
$117$	−0.225510	−	0.390595i	−0.0208484	−	0.0361105i
$118$	−2.71309	+	4.69920i	−0.249760	+	0.432597i
$119$	−20.4586			−1.87544
$120$	−1.85581	+	1.07145i	−0.169412	+	0.0978100i
$121$	1.36135			0.123759
$122$	−0.500000	−	7.79423i	−0.0452679	−	0.705656i
$123$	−7.90112			−0.712420
$124$	5.19394	−	2.99872i	0.466430	−	0.269293i
$125$	−9.93618			−0.888719
$126$	−1.16841	+	2.02375i	−0.104091	+	0.180290i
$127$	−11.0116	−	19.0727i	−0.977125	−	1.69243i	−0.672735	−	0.739884i	$-0.734881\pi$
$127$	−11.0116	−	19.0727i	−0.977125	−	1.69243i	−0.304391	−	0.952547i	$-0.598453\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	−5.09919	+	2.94402i	−0.448959	+	0.259207i
$130$			1.00000i			0.0877058i
$131$	−16.5505			−1.44603			−0.723013	−	0.690834i	$-0.757243\pi$
$131$	−16.5505			−1.44603			−0.723013	+	0.690834i	$0.757243\pi$
$132$	5.04116	+	2.91052i	0.438777	+	0.253328i
$133$			30.1732i			2.61635i
$134$	7.67847	−	13.2995i	0.663318	−	1.14890i
$135$	2.66206	+	4.61082i	0.229113	+	0.396836i
$136$	2.25646	−	3.90830i	0.193490	−	0.335134i
$137$	2.19173	+	3.79619i	0.187252	+	0.324330i	0.944333	−	0.328991i	$-0.106709\pi$
$137$	2.19173	+	3.79619i	0.187252	+	0.324330i	−0.757081	+	0.653321i	$0.773375\pi$
$138$	1.25774	+	2.17847i	0.107066	+	0.185443i
$139$	−7.63288	−	4.40685i	−0.647412	−	0.373784i	0.140052	−	0.990144i	$-0.455273\pi$
$139$	−7.63288	−	4.40685i	−0.647412	−	0.373784i	−0.787464	+	0.616360i	$0.788606\pi$
$140$	4.48705	−	2.59060i	0.379225	−	0.218946i
$141$	−5.05343	+	8.75279i	−0.425575	+	0.737118i
$142$	12.9391			1.08582
$143$	2.35249	−	1.35821i	0.196725	−	0.113579i
$144$	−0.257738	−	0.446415i	−0.0214781	−	0.0372012i
$145$			8.83411i			0.733633i
$146$			10.4794i			0.867283i
$147$	12.7040	−	22.0040i	1.04781	−	1.81486i
$148$	1.29475	+	0.747526i	0.106428	+	0.0614463i
$149$	8.70429			0.713083			0.356541	−	0.934280i	$-0.383956\pi$
$149$	8.70429			0.713083			0.356541	+	0.934280i	$0.383956\pi$
$150$		−	6.92565i		−	0.565477i
$151$	2.19173	+	1.26540i	0.178360	+	0.102976i	0.586522	−	0.809933i	$-0.300497\pi$
$151$	2.19173	+	1.26540i	0.178360	+	0.102976i	−0.408162	+	0.912910i	$0.633830\pi$
$152$	−5.76412	−	3.32792i	−0.467532	−	0.269930i
$153$	2.01463	+	1.16315i	0.162874	+	0.0940351i
$154$	−12.1887	−	7.03715i	−0.982193	−	0.567070i
$155$		−	6.85454i		−	0.550570i
$156$	−1.64052			−0.131346
$157$	12.1376	+	7.00766i	0.968687	+	0.559272i	0.898836	−	0.438285i	$-0.144414\pi$
$157$	12.1376	+	7.00766i	0.968687	+	0.559272i	0.0698516	+	0.997557i	$0.477747\pi$
$158$	−3.40830	+	5.90336i	−0.271150	+	0.469646i
$159$		−	15.4590i		−	1.22598i
$160$			1.14291i			0.0903549i
$161$	−3.04100	−	5.26717i	−0.239665	−	0.415111i
$162$	−8.90336	+	5.14036i	−0.699514	+	0.403864i
$163$	4.78087			0.374467			0.187233	−	0.982315i	$-0.440048\pi$
$163$	4.78087			0.374467			0.187233	+	0.982315i	$0.440048\pi$
$164$	−2.10701	+	3.64945i	−0.164530	+	0.284974i
$165$	5.76159	−	3.32646i	0.448539	−	0.258964i
$166$	11.5520	+	6.66953i	0.896606	+	0.517656i
$167$	8.72950	+	15.1199i	0.675509	+	1.17002i	0.976320	+	0.216332i	$0.0694093\pi$
$167$	8.72950	+	15.1199i	0.675509	+	1.17002i	−0.300811	+	0.953684i	$0.597257\pi$
$168$	4.24992	+	7.36108i	0.327888	+	0.567919i
$169$	6.11722	−	10.5953i	0.470556	−	0.815026i
$170$	−2.57893	−	4.46684i	−0.197795	−	0.342591i
$171$	1.71546	−	2.97126i	0.131184	−	0.227218i
$172$			3.14036i			0.239450i
$173$	−0.0536081	−	0.0309506i	−0.00407575	−	0.00235313i	0.497961	−	0.867200i	$-0.334082\pi$
$173$	−0.0536081	−	0.0309506i	−0.00407575	−	0.00235313i	−0.502036	+	0.864846i	$0.667416\pi$
$174$	−14.4925			−1.09867
$175$			16.7451i			1.26581i
$176$	2.68868	−	1.55231i	0.202667	−	0.117010i
$177$	−8.81082	+	5.08693i	−0.662262	+	0.382357i
$178$	0.705429	+	1.22184i	0.0528742	+	0.0915807i
$179$	9.44496	−	16.3591i	0.705949	−	1.22274i	−0.260399	−	0.965501i	$-0.583854\pi$
$179$	9.44496	−	16.3591i	0.705949	−	1.22274i	0.966348	−	0.257239i	$-0.0828126\pi$
$180$	−0.589142			−0.0439120
$181$	4.14947	−	2.39570i	0.308428	−	0.178071i	−0.337795	−	0.941220i	$-0.609681\pi$
$181$	4.14947	−	2.39570i	0.308428	−	0.178071i	0.646223	+	0.763149i	$0.276348\pi$
$182$	3.96650			0.294016
$183$	6.49505	−	13.1247i	0.480128	−	0.970207i
$184$	1.34162			0.0989052
$185$	1.47979	−	0.854355i	0.108796	−	0.0628134i
$186$	11.2450			0.824521
$187$	−7.00545	+	12.1338i	−0.512289	+	0.887311i
$188$	2.69522	+	4.66825i	0.196569	+	0.340467i
$189$	18.2888	−	10.5590i	1.33031	−	0.768057i
$190$	−6.58786	+	3.80351i	−0.477934	+	0.275935i
$191$		−	8.61243i		−	0.623174i	−0.950218	−	0.311587i	$-0.899140\pi$
$191$		−	8.61243i		−	0.623174i	0.950218	−	0.311587i	$-0.100860\pi$
$192$	−1.87496			−0.135314
$193$	−22.4728	−	12.9747i	−1.61762	−	0.933936i	−0.987532	−	0.157415i	$-0.949684\pi$
$193$	−22.4728	−	12.9747i	−1.61762	−	0.933936i	−0.630092	−	0.776521i	$-0.716983\pi$
$194$		−	4.02584i		−	0.289039i
$195$	−0.937480	+	1.62376i	−0.0671343	+	0.116280i
$196$	−6.77561	−	11.7357i	−0.483972	−	0.838264i
$197$	−1.97702	+	3.42430i	−0.140857	+	0.243972i	−0.927820	−	0.373029i	$-0.878319\pi$
$197$	−1.97702	+	3.42430i	−0.140857	+	0.243972i	0.786963	+	0.617001i	$0.211652\pi$
$198$	0.800177	+	1.38595i	0.0568661	+	0.0984949i
$199$	−8.27128	−	14.3263i	−0.586335	−	1.01556i	−0.994708	−	0.102747i	$-0.967237\pi$
$199$	−8.27128	−	14.3263i	−0.586335	−	1.01556i	0.408372	−	0.912816i	$-0.366097\pi$
$200$	−3.19889	−	1.84688i	−0.226196	−	0.130594i
$201$	24.9360	−	14.3968i	1.75885	−	1.01547i
$202$	−3.07367	+	5.32375i	−0.216262	+	0.374577i
$203$	35.0405			2.45936
$204$	7.32792	−	4.23077i	0.513057	−	0.296213i
$205$	2.40812	+	4.17099i	0.168191	+	0.291315i
$206$			1.06888i			0.0744723i
$207$			0.691570i			0.0480674i
$208$	−0.437480	+	0.757738i	−0.0303338	+	0.0525397i
$209$	17.8954	+	10.3319i	1.23785	+	0.714673i
$210$	9.71455			0.670367
$211$		−	6.31932i		−	0.435040i	−0.976056	−	0.217520i	$-0.930203\pi$
$211$		−	6.31932i		−	0.435040i	0.976056	−	0.217520i	$-0.0697968\pi$
$212$	−7.14036	−	4.12249i	−0.490402	−	0.283134i
$213$	21.0100	+	12.1301i	1.43958	+	0.831144i
$214$	14.6249	+	8.44368i	0.999736	+	0.577198i
$215$	3.10829	+	1.79457i	0.211983	+	0.122389i
$216$			4.65838i			0.316963i
$217$	−27.1885			−1.84568
$218$	6.02297	+	3.47737i	0.407927	+	0.235517i
$219$	−9.82424	+	17.0161i	−0.663861	+	1.14984i
$220$		−	3.54830i		−	0.239226i
$221$		−	3.94863i		−	0.265613i
$222$	1.40158	+	2.42761i	0.0940680	+	0.162931i
$223$	−18.5509	+	10.7104i	−1.24226	+	0.717218i	−0.969553	−	0.244880i	$-0.921252\pi$
$223$	−18.5509	+	10.7104i	−1.24226	+	0.717218i	−0.272705	+	0.962098i	$0.587918\pi$
$224$	4.53334			0.302897
$225$	0.952021	−	1.64895i	0.0634680	−	0.109930i
$226$	−4.94863	+	2.85709i	−0.329178	+	0.190051i
$227$	−12.7343	−	7.35217i	−0.845207	−	0.487980i	0.0138239	−	0.999904i	$-0.495600\pi$
$227$	−12.7343	−	7.35217i	−0.845207	−	0.487980i	−0.859031	+	0.511924i	$0.828933\pi$
$228$	−6.23971	−	10.8075i	−0.413235	−	0.715744i
$229$	0.790584	+	1.36933i	0.0522432	+	0.0904880i	0.890964	−	0.454073i	$-0.150030\pi$
$229$	0.790584	+	1.36933i	0.0522432	+	0.0904880i	−0.838721	+	0.544561i	$0.816696\pi$
$230$	0.766672	−	1.32792i	0.0505529	−	0.0875602i
$231$	−13.1944	−	22.8533i	−0.868126	−	1.50364i
$232$	−3.86475	+	6.69394i	−0.253733	+	0.439479i
$233$			4.88736i			0.320181i	0.987102	+	0.160091i	$0.0511787\pi$
$233$			4.88736i			0.320181i	−0.987102	+	0.160091i	$0.948821\pi$
$234$	−0.390595	−	0.225510i	−0.0255340	−	0.0147421i
$235$	6.16078			0.401885
$236$			5.42617i			0.353214i
$237$	−11.0686	+	6.39044i	−0.718980	+	0.415103i
$238$	−17.7177	+	10.2293i	−1.14847	+	0.663068i
$239$	−7.33906	−	12.7116i	−0.474724	−	0.822247i	0.524857	−	0.851191i	$-0.324119\pi$
$239$	−7.33906	−	12.7116i	−0.474724	−	0.822247i	−0.999581	+	0.0289438i	$0.990786\pi$
$240$	−1.07145	+	1.85581i	−0.0691621	+	0.119792i
$241$	−18.0000			−1.15948			−0.579741	−	0.814801i	$-0.696846\pi$
$241$	−18.0000			−1.15948			−0.579741	+	0.814801i	$0.696846\pi$
$242$	1.17897	−	0.680677i	0.0757869	−	0.0437556i
$243$	−5.30077			−0.340045
$244$	−4.33013	−	6.50000i	−0.277208	−	0.416120i
$245$	−15.4878			−0.989480
$246$	−6.84257	+	3.95056i	−0.436267	+	0.251879i
$247$	−5.82359			−0.370546
$248$	2.99872	−	5.19394i	0.190419	−	0.329816i
$249$	12.5051	+	21.6595i	0.792479	+	1.37261i
$250$	−8.60498	+	4.96809i	−0.544227	+	0.314210i
$251$	−6.65419	+	3.84180i	−0.420009	+	0.242492i	−0.695081	−	0.718931i	$-0.744632\pi$
$251$	−6.65419	+	3.84180i	−0.420009	+	0.242492i	0.275072	+	0.961424i	$0.411298\pi$
$252$			2.33683i			0.147206i
$253$	−4.16520			−0.261864
$254$	−19.0727	−	11.0116i	−1.19673	−	0.690932i
$255$		−	9.67078i		−	0.605608i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	11.2885	+	19.5523i	0.704159	+	1.21964i	0.966994	+	0.254799i	$0.0820091\pi$
$257$	11.2885	+	19.5523i	0.704159	+	1.21964i	−0.262835	+	0.964841i	$0.584658\pi$
$258$	−2.94402	+	5.09919i	−0.183287	+	0.317462i
$259$	−3.38879	−	5.86956i	−0.210569	−	0.364717i
$260$	0.500000	+	0.866025i	0.0310087	+	0.0537086i
$261$	−3.45056	−	1.99218i	−0.213584	−	0.123313i
$262$	−14.3332	+	8.27526i	−0.885507	+	0.511248i
$263$	−12.5702	+	21.7722i	−0.775110	+	1.34253i	0.159622	+	0.987178i	$0.448972\pi$
$263$	−12.5702	+	21.7722i	−0.775110	+	1.34253i	−0.934732	+	0.355352i	$0.884361\pi$
$264$	5.82103			0.358260
$265$	−8.16078	+	4.71163i	−0.501313	+	0.289433i
$266$	15.0866	+	26.1307i	0.925018	+	1.60218i
$267$			2.64530i			0.161890i
$268$		−	15.3569i		−	0.938074i
$269$	14.7827	−	25.6045i	0.901320	−	1.56113i	0.0755368	−	0.997143i	$-0.475933\pi$
$269$	14.7827	−	25.6045i	0.901320	−	1.56113i	0.825783	−	0.563988i	$-0.190734\pi$
$270$	4.61082	+	2.66206i	0.280605	+	0.162008i
$271$	−5.60920			−0.340735			−0.170367	−	0.985381i	$-0.554495\pi$
$271$	−5.60920			−0.340735			−0.170367	+	0.985381i	$0.554495\pi$
$272$		−	4.51292i		−	0.273636i
$273$	6.44065	+	3.71851i	0.389806	+	0.225054i
$274$	3.79619	+	2.19173i	0.229336	+	0.132407i
$275$	9.93132	+	5.73385i	0.598881	+	0.345764i
$276$	2.17847	+	1.25774i	0.131128	+	0.0757069i
$277$		−	17.0565i		−	1.02482i	−0.858740	−	0.512412i	$-0.828752\pi$
$277$		−	17.0565i		−	1.02482i	0.858740	−	0.512412i	$-0.171248\pi$
$278$	−8.81369			−0.528610
$279$	2.67735	+	1.54577i	0.160289	+	0.0925427i
$280$	2.59060	−	4.48705i	0.154818	−	0.268153i
$281$		−	5.98213i		−	0.356864i	−0.983952	−	0.178432i	$-0.942898\pi$
$281$		−	5.98213i		−	0.356864i	0.983952	−	0.178432i	$-0.0571025\pi$
$282$			10.1069i			0.601854i
$283$	13.0191	+	22.5498i	0.773906	+	1.34045i	0.935407	+	0.353573i	$0.115033\pi$
$283$	13.0191	+	22.5498i	0.773906	+	1.34045i	−0.161501	+	0.986873i	$0.551633\pi$
$284$	11.2056	−	6.46955i	0.664929	−	0.383897i
$285$	−14.2628			−0.844858
$286$	1.35821	−	2.35249i	0.0803125	−	0.139105i
$287$	16.5442	−	9.55181i	0.976574	−	0.563825i
$288$	−0.446415	−	0.257738i	−0.0263052	−	0.0151873i
$289$	1.68323	+	2.91544i	0.0990136	+	0.171497i
$290$	4.41706	+	7.65057i	0.259379	+	0.449257i
$291$	3.77415	−	6.53702i	0.221244	−	0.383207i
$292$	5.23971	+	9.07544i	0.306631	+	0.531100i
$293$	2.04431	−	3.54085i	0.119430	−	0.206858i	−0.800112	−	0.599851i	$-0.795227\pi$
$293$	2.04431	−	3.54085i	0.119430	−	0.206858i	0.919542	+	0.392992i	$0.128560\pi$
$294$		−	25.4080i		−	1.48182i
$295$	5.37076	+	3.10081i	0.312698	+	0.180536i
$296$	1.49505			0.0868981
$297$		−	14.4625i		−	0.839199i
$298$	7.53813	−	4.35214i	0.436672	−	0.252113i
$299$	1.01659	−	0.586930i	0.0587911	−	0.0339430i
$300$	−3.46282	−	5.99779i	−0.199926	−	0.346282i
$301$	7.11816	−	12.3290i	0.410284	−	0.710632i
$302$	2.53079			0.145631
$303$	−9.98181	+	5.76300i	−0.573440	+	0.331076i
$304$	−6.65583			−0.381738
$305$	−8.90810	+	0.571455i	−0.510076	+	0.0327214i
$306$	2.32630			0.132986
$307$	−9.56074	+	5.51990i	−0.545661	+	0.315037i	−0.747370	−	0.664408i	$-0.768684\pi$
$307$	−9.56074	+	5.51990i	−0.545661	+	0.315037i	0.201709	+	0.979445i	$0.435350\pi$
$308$	−14.0743			−0.801958
$309$	−1.00205	+	1.73560i	−0.0570047	+	0.0987351i
$310$	−3.42727	−	5.93620i	−0.194656	−	0.337154i
$311$	−1.55807	+	0.899553i	−0.0883501	+	0.0510089i	−0.543524	−	0.839394i	$-0.682910\pi$
$311$	−1.55807	+	0.899553i	−0.0883501	+	0.0510089i	0.455174	+	0.890402i	$0.349577\pi$
$312$	−1.42073	+	0.820258i	−0.0804329	+	0.0464379i
$313$			18.5308i			1.04742i	0.851896	+	0.523711i	$0.175453\pi$
$313$			18.5308i			1.04742i	−0.851896	+	0.523711i	$0.824547\pi$
$314$	14.0153			0.790930
$315$	2.31296	+	1.33539i	0.130321	+	0.0752407i
$316$			6.81661i			0.383464i
$317$	−4.20144	+	7.27711i	−0.235977	+	0.408723i	−0.959556	−	0.281518i	$-0.909162\pi$
$317$	−4.20144	+	7.27711i	−0.235977	+	0.408723i	0.723580	+	0.690241i	$0.242496\pi$
$318$	−7.72950	−	13.3879i	−0.433449	−	0.750755i
$319$	11.9986	−	20.7821i	0.671791	−	1.16358i
$320$	0.571455	+	0.989788i	0.0319453	+	0.0553309i
$321$	15.8316	+	27.4211i	0.883632	+	1.53049i
$322$	−5.26717	−	3.04100i	−0.293528	−	0.169468i
$323$	26.0130	−	15.0186i	1.44740	−	0.835658i
$324$	−5.14036	+	8.90336i	−0.285575	+	0.494631i
$325$	−3.23189			−0.179273
$326$	4.14036	−	2.39044i	0.229313	−	0.132394i
$327$	6.51992	+	11.2928i	0.360552	+	0.624495i
$328$			4.21402i			0.232680i
$329$		−	24.4367i		−	1.34724i
$330$	3.32646	−	5.76159i	0.183115	−	0.317165i
$331$	−10.5981	−	6.11882i	−0.582524	−	0.336321i	0.179612	−	0.983738i	$-0.442516\pi$
$331$	−10.5981	−	6.11882i	−0.582524	−	0.336321i	−0.762136	+	0.647417i	$0.775849\pi$
$332$	13.3391			0.732076
$333$			0.770663i			0.0422320i
$334$	15.1199	+	8.72950i	0.827326	+	0.477657i
$335$	−15.2001	−	8.77579i	−0.830471	−	0.479473i
$336$	7.36108	+	4.24992i	0.401580	+	0.231852i
$337$	21.2426	+	12.2644i	1.15716	+	0.668086i	0.950622	−	0.310352i	$-0.100447\pi$
$337$	21.2426	+	12.2644i	1.15716	+	0.668086i	0.206538	+	0.978439i	$0.433780\pi$
$338$		−	12.2344i		−	0.665466i
$339$	−10.7139			−0.581897
$340$	−4.46684	−	2.57893i	−0.242248	−	0.139862i
$341$	−9.30989	+	16.1252i	−0.504159	+	0.873228i
$342$		−	3.43092i		−	0.185523i
$343$			29.6989i			1.60359i
$344$	1.57018	+	2.71963i	0.0846583	+	0.146632i
$345$	2.48979	−	1.43748i	0.134046	−	0.0773913i
$346$	−0.0619013			−0.00332783
$347$	12.9837	−	22.4885i	0.697004	−	1.20725i	−0.272496	−	0.962157i	$-0.587849\pi$
$347$	12.9837	−	22.4885i	0.697004	−	1.20725i	0.969500	−	0.245090i	$-0.0788174\pi$
$348$	−12.5509	+	7.24625i	−0.672797	+	0.388440i
$349$	14.3028	+	8.25774i	0.765612	+	0.442027i	0.831307	−	0.555813i	$-0.187593\pi$
$349$	14.3028	+	8.25774i	0.765612	+	0.442027i	−0.0656947	+	0.997840i	$0.520926\pi$
$350$	8.37254	+	14.5017i	0.447531	+	0.775147i
$351$	2.03795	+	3.52983i	0.108778	+	0.188409i
$352$	1.55231	−	2.68868i	0.0827383	−	0.143307i
$353$	−6.28290	−	10.8823i	−0.334405	−	0.579206i	0.648965	−	0.760818i	$-0.275202\pi$
$353$	−6.28290	−	10.8823i	−0.334405	−	0.579206i	−0.983370	+	0.181611i	$0.941869\pi$
$354$	−5.08693	+	8.81082i	−0.270367	+	0.468290i
$355$		−	14.7882i		−	0.784877i
$356$	1.22184	+	0.705429i	0.0647574	+	0.0373877i
$357$	−38.3591			−2.03018
$358$		−	18.8899i		−	0.998363i
$359$	−18.1028	+	10.4517i	−0.955431	+	0.551618i	−0.894764	−	0.446540i	$-0.852656\pi$
$359$	−18.1028	+	10.4517i	−0.955431	+	0.551618i	−0.0606674	+	0.998158i	$0.519323\pi$
$360$	−0.510212	+	0.294571i	−0.0268905	+	0.0155252i
$361$	−12.6500	−	21.9105i	−0.665792	−	1.15319i
$362$	2.39570	−	4.14947i	0.125915	−	0.218091i
$363$	2.55248			0.133971
$364$	3.43509	−	1.98325i	0.180047	−	0.103950i
$365$	11.9770			0.626906
$366$	−0.937480	−	14.6139i	−0.0490029	−	0.763879i
$367$	28.6613			1.49611			0.748053	−	0.663639i	$-0.230989\pi$
$367$	28.6613			1.49611			0.748053	+	0.663639i	$0.230989\pi$
$368$	1.16187	−	0.670808i	0.0605668	−	0.0349683i
$369$	−2.17222			−0.113081
$370$	0.854355	−	1.47979i	0.0444158	−	0.0769304i
$371$	18.6887	+	32.3697i	0.970266	+	1.68055i
$372$	9.73843	−	5.62249i	0.504914	−	0.291512i
$373$	27.3109	−	15.7679i	1.41410	−	0.816433i	0.418332	−	0.908294i	$-0.362615\pi$
$373$	27.3109	−	15.7679i	1.41410	−	0.816433i	0.995772	+	0.0918609i	$0.0292815\pi$
$374$			14.0109i			0.724486i
$375$	−18.6299			−0.962046
$376$	4.66825	+	2.69522i	0.240747	+	0.138995i
$377$			6.76300i			0.348312i
$378$	10.5590	−	18.2888i	0.543098	−	0.940673i
$379$	−13.5796	−	23.5206i	−0.697538	−	1.20817i	−0.969318	−	0.245811i	$-0.920946\pi$
$379$	−13.5796	−	23.5206i	−0.697538	−	1.20817i	0.271780	−	0.962359i	$-0.412388\pi$
$380$	−3.80351	+	6.58786i	−0.195116	+	0.337950i
$381$	−20.6464	−	35.7606i	−1.05775	−	1.83207i
$382$	−4.30622	−	7.45858i	−0.220325	−	0.381614i
$383$	1.64421	+	0.949284i	0.0840152	+	0.0485062i	0.541419	−	0.840753i	$-0.317887\pi$
$383$	1.64421	+	0.949284i	0.0840152	+	0.0485062i	−0.457404	+	0.889259i	$0.651221\pi$
$384$	−1.62376	+	0.937480i	−0.0828623	+	0.0478406i
$385$	−8.04282	+	13.9306i	−0.409900	+	0.709968i
$386$	−25.9493			−1.32078
$387$	−1.40190	+	0.809388i	−0.0712626	+	0.0411435i
$388$	−2.01292	−	3.48648i	−0.102191	−	0.176999i
$389$			8.92415i			0.452472i	0.974073	+	0.226236i	$0.0726421\pi$
$389$			8.92415i			0.452472i	−0.974073	+	0.226236i	$0.927358\pi$
$390$			1.87496i			0.0949423i
$391$	−3.02730	+	5.24344i	−0.153097	+	0.265172i
$392$	−11.7357	−	6.77561i	−0.592742	−	0.342220i
$393$	−31.0316			−1.56534
$394$			3.95405i			0.199202i
$395$	6.74700	+	3.89538i	0.339478	+	0.195998i
$396$	1.38595	+	0.800177i	0.0696464	+	0.0402104i
$397$	12.8751	+	7.43347i	0.646185	+	0.373075i	0.786993	−	0.616962i	$-0.211637\pi$
$397$	12.8751	+	7.43347i	0.646185	+	0.373075i	−0.140808	+	0.990037i	$0.544970\pi$
$398$	−14.3263	−	8.27128i	−0.718111	−	0.414602i
$399$			56.5735i			2.83222i
$400$	−3.69376			−0.184688
$401$	−5.76060	−	3.32589i	−0.287671	−	0.166087i	0.349220	−	0.937041i	$-0.386447\pi$
$401$	−5.76060	−	3.32589i	−0.287671	−	0.166087i	−0.636891	+	0.770954i	$0.719780\pi$
$402$	14.3968	−	24.9360i	0.718048	−	1.24370i
$403$		−	5.24753i		−	0.261398i
$404$			6.14733i			0.305841i
$405$	5.87496	+	10.1757i	0.291929	+	0.505636i
$406$	30.3459	−	17.5202i	1.50604	−	0.869515i
$407$	−4.64156			−0.230074
$408$	4.23077	−	7.32792i	0.209455	−	0.362786i
$409$	−8.35746	+	4.82518i	−0.413250	+	0.238590i	−0.692185	−	0.721720i	$-0.743352\pi$
$409$	−8.35746	+	4.82518i	−0.413250	+	0.238590i	0.278935	+	0.960310i	$0.410018\pi$
$410$	4.17099	+	2.40812i	0.205991	+	0.118929i
$411$	4.10940	+	7.11770i	0.202702	+	0.351090i
$412$	0.534439	+	0.925676i	0.0263299	+	0.0456048i
$413$	12.2994	−	21.3031i	0.605212	−	1.04826i
$414$	0.345785	+	0.598917i	0.0169944	+	0.0294352i
$415$	7.62267	−	13.2028i	0.374182	−	0.648102i
$416$			0.874960i			0.0428984i
$417$	−14.3113	−	8.26266i	−0.700830	−	0.404624i
$418$	20.6638			1.01070
$419$			11.3635i			0.555145i	0.960705	+	0.277573i	$0.0895299\pi$
$419$			11.3635i			0.555145i	−0.960705	+	0.277573i	$0.910470\pi$
$420$	8.41304	−	4.85727i	0.410515	−	0.237011i
$421$	−6.61526	+	3.81932i	−0.322408	+	0.186142i	−0.652465	−	0.757818i	$-0.726265\pi$
$421$	−6.61526	+	3.81932i	−0.322408	+	0.186142i	0.330057	+	0.943961i	$0.392932\pi$
$422$	−3.15966	−	5.47269i	−0.153810	−	0.266407i
$423$	−1.38932	+	2.40637i	−0.0675510	+	0.117002i
$424$	−8.24497			−0.400411
$425$	14.4363	−	8.33482i	0.700265	−	0.404298i
$426$	24.2603			1.17541
$427$	2.26667	+	35.3339i	0.109692	+	1.70993i
$428$	16.8874			0.816281
$429$	4.41082	−	2.54659i	0.212956	−	0.122950i
$430$	3.58914			0.173084
$431$	14.2019	−	24.5984i	0.684082	−	1.18487i	−0.289642	−	0.957135i	$-0.593536\pi$
$431$	14.2019	−	24.5984i	0.684082	−	1.18487i	0.973724	−	0.227730i	$-0.0731304\pi$
$432$	2.32919	+	4.03428i	0.112063	+	0.194099i
$433$	14.6495	−	8.45790i	0.704011	−	0.406461i	−0.104829	−	0.994490i	$-0.533429\pi$
$433$	14.6495	−	8.45790i	0.704011	−	0.406461i	0.808840	+	0.588029i	$0.200096\pi$
$434$	−23.5459	+	13.5942i	−1.13024	+	0.652545i
$435$			16.5636i			0.794164i
$436$	6.95473			0.333071
$437$	7.73323	+	4.46478i	0.369931	+	0.213580i
$438$			19.6485i			0.938841i
$439$	−11.2078	+	19.4124i	−0.534918	+	0.926505i	0.464249	+	0.885705i	$0.346324\pi$
$439$	−11.2078	+	19.4124i	−0.534918	+	0.926505i	−0.999167	+	0.0408005i	$0.987009\pi$
$440$	−1.77415	−	3.07291i	−0.0845792	−	0.146495i
$441$	3.49266	−	6.04946i	0.166317	−	0.288070i
$442$	−1.97431	−	3.41961i	−0.0939085	−	0.162654i
$443$	−2.31866	−	4.01605i	−0.110163	−	0.190808i	0.805673	−	0.592361i	$-0.201804\pi$
$443$	−2.31866	−	4.01605i	−0.110163	−	0.190808i	−0.915836	+	0.401553i	$0.868471\pi$
$444$	2.42761	+	1.40158i	0.115209	+	0.0665161i
$445$	1.39645	−	0.806242i	0.0661981	−	0.0382195i
$446$	−10.7104	+	18.5509i	−0.507150	+	0.878409i
$447$	16.3202			0.771918
$448$	3.92599	−	2.26667i	0.185486	−	0.107090i
$449$	−17.6145	−	30.5092i	−0.831280	−	1.43982i	−0.897024	−	0.441983i	$-0.854275\pi$
$449$	−17.6145	−	30.5092i	−0.831280	−	1.43982i	0.0657435	−	0.997837i	$-0.479058\pi$
$450$		−	1.90404i		−	0.0897574i
$451$		−	13.0829i		−	0.616051i
$452$	−2.85709	+	4.94863i	−0.134386	+	0.232764i
$453$	4.10940	+	2.37257i	0.193077	+	0.111473i
$454$	−14.7043			−0.690108
$455$		−	4.53334i		−	0.212526i
$456$	−10.8075	−	6.23971i	−0.506107	−	0.292201i
$457$	13.5351	+	7.81447i	0.633143	+	0.365545i	0.781968	−	0.623318i	$-0.214216\pi$
$457$	13.5351	+	7.81447i	0.633143	+	0.365545i	−0.148825	+	0.988864i	$0.547549\pi$
$458$	1.36933	+	0.790584i	0.0639847	+	0.0369416i
$459$	−18.2064	−	10.5115i	−0.849801	−	0.490633i
$460$		−	1.53334i		−	0.0714926i
$461$	24.1997			1.12709			0.563547	−	0.826084i	$-0.309436\pi$
$461$	24.1997			1.12709			0.563547	+	0.826084i	$0.309436\pi$
$462$	−22.8533	−	13.1944i	−1.06323	−	0.613858i
$463$	0.322652	−	0.558849i	0.0149949	−	0.0259719i	−0.858431	−	0.512930i	$-0.828560\pi$
$463$	0.322652	−	0.558849i	0.0149949	−	0.0259719i	0.873425	+	0.486958i	$0.161893\pi$
$464$			7.72950i			0.358833i
$465$		−	12.8520i		−	0.595996i
$466$	2.44368	+	4.23258i	0.113201	+	0.196070i
$467$	−33.4734	+	19.3259i	−1.54896	+	0.894294i	−0.550742	+	0.834676i	$0.685655\pi$
$467$	−33.4734	+	19.3259i	−1.54896	+	0.894294i	−0.998221	+	0.0596184i	$0.981012\pi$
$468$	−0.451020			−0.0208484
$469$	−34.8091	+	60.2912i	−1.60734	+	2.78399i
$470$	5.33539	−	3.08039i	0.246103	−	0.142088i
$471$	22.7576	+	13.1391i	1.04861	+	0.605417i
$472$	2.71309	+	4.69920i	0.124880	+	0.216298i
$473$	−4.87480	−	8.44340i	−0.224144	−	0.388228i
$474$	−6.39044	+	11.0686i	−0.293522	+	0.508396i
$475$	−12.2925	−	21.2913i	−0.564019	−	0.976910i
$476$	−10.2293	+	17.7177i	−0.468860	+	0.812089i
$477$		−	4.25008i		−	0.194598i
$478$	−12.7116	−	7.33906i	−0.581416	−	0.335681i
$479$	9.02142			0.412199			0.206100	−	0.978531i	$-0.433923\pi$
$479$	9.02142			0.412199			0.206100	+	0.978531i	$0.433923\pi$
$480$			2.14291i			0.0978100i
$481$	1.13286	−	0.654056i	0.0516539	−	0.0298224i
$482$	−15.5885	+	9.00000i	−0.710035	+	0.409939i
$483$	−5.70176	−	9.87574i	−0.259439	−	0.449362i
$484$	0.680677	−	1.17897i	0.0309399	−	0.0535894i
$485$	−4.60117			−0.208929
$486$	−4.59060	+	2.65038i	−0.208234	+	0.120224i
$487$	−1.56689			−0.0710028			−0.0355014	−	0.999370i	$-0.511303\pi$
$487$	−1.56689			−0.0710028			−0.0355014	+	0.999370i	$0.511303\pi$
$488$	−7.00000	−	3.46410i	−0.316875	−	0.156813i
$489$	8.96394			0.405363
$490$	−13.4128	+	7.74390i	−0.605930	+	0.349834i
$491$	8.03063			0.362417			0.181209	−	0.983445i	$-0.441999\pi$
$491$	8.03063			0.362417			0.181209	+	0.983445i	$0.441999\pi$
$492$	−3.95056	+	6.84257i	−0.178105	+	0.308487i
$493$	−17.4413	−	30.2092i	−0.785517	−	1.36056i
$494$	−5.04337	+	2.91179i	−0.226912	+	0.131008i
$495$	1.58401	−	0.914529i	0.0711960	−	0.0411050i
$496$		−	5.99745i		−	0.269293i
$497$	−58.6574			−2.63114
$498$	21.6595	+	12.5051i	0.970584	+	0.560367i
$499$			12.1094i			0.542091i	0.962566	+	0.271046i	$0.0873695\pi$
$499$			12.1094i			0.542091i	−0.962566	+	0.271046i	$0.912631\pi$
$500$	−4.96809	+	8.60498i	−0.222180	+	0.384826i
$501$	16.3675	+	28.3493i	0.731244	+	1.26655i
$502$	−3.84180	+	6.65419i	−0.171468	+	0.296991i
$503$	−17.2439	−	29.8673i	−0.768867	−	1.33172i	−0.938178	−	0.346153i	$-0.887488\pi$
$503$	−17.2439	−	29.8673i	−0.768867	−	1.33172i	0.169311	−	0.985563i	$-0.445846\pi$
$504$	1.16841	+	2.02375i	0.0520453	+	0.0901451i
$505$	6.08456	+	3.51292i	0.270759	+	0.156323i
$506$	−3.60717	+	2.08260i	−0.160358	+	0.0925829i
$507$	11.4695	−	19.8658i	0.509381	−	0.882273i
$508$	−22.0233			−0.977125
$509$	18.4070	−	10.6273i	0.815875	−	0.471046i	−0.0331169	−	0.999451i	$-0.510543\pi$
$509$	18.4070	−	10.6273i	0.815875	−	0.471046i	0.848992	+	0.528406i	$0.177210\pi$
$510$	−4.83539	−	8.37514i	−0.214115	−	0.370858i
$511$		−	47.5068i		−	2.10158i
$512$			1.00000i			0.0441942i
$513$	−15.5027	+	26.8515i	−0.684461	+	1.18552i
$514$	19.5523	+	11.2885i	0.862415	+	0.497916i
$515$	1.22163			0.0538315
$516$			5.88804i			0.259207i
$517$	−14.4931	−	8.36762i	−0.637408	−	0.368007i
$518$	−5.86956	−	3.38879i	−0.257894	−	0.148895i
$519$	−0.100513	−	0.0580312i	−0.00441203	−	0.00254729i
$520$	0.866025	+	0.500000i	0.0379777	+	0.0219265i
$521$		−	26.6166i		−	1.16609i	−0.812438	−	0.583047i	$-0.801860\pi$
$521$		−	26.6166i		−	1.16609i	0.812438	−	0.583047i	$-0.198140\pi$
$522$	−3.98437			−0.174391
$523$	−4.66889	−	2.69558i	−0.204156	−	0.117870i	0.394436	−	0.918923i	$-0.370940\pi$
$523$	−4.66889	−	2.69558i	−0.204156	−	0.117870i	−0.598593	+	0.801054i	$0.704273\pi$
$524$	−8.27526	+	14.3332i	−0.361507	+	0.626148i
$525$			31.3964i			1.37025i
$526$			25.1404i			1.09617i
$527$	13.5330	+	23.4398i	0.589507	+	1.02106i
$528$	5.04116	−	2.91052i	0.219388	−	0.126664i
$529$	21.2001			0.921742
$530$	−4.71163	+	8.16078i	−0.204660	+	0.354482i
$531$	−2.42232	+	1.39853i	−0.105120	+	0.0606910i
$532$	26.1307	+	15.0866i	1.13291	+	0.654087i
$533$	1.84355	+	3.19312i	0.0798530	+	0.138310i
$534$	1.32265	+	2.29090i	0.0572367	+	0.0991369i
$535$	9.65036	−	16.7149i	0.417221	−	0.722649i
$536$	−7.67847	−	13.2995i	−0.331659	−	0.574451i
$537$	17.7089	−	30.6727i	0.764196	−	1.32363i
$538$		−	29.5655i		−	1.27466i
$539$	36.4348	+	21.0357i	1.56936	+	0.906070i
$540$	5.32411			0.229113
$541$			12.2001i			0.524522i	0.964997	+	0.262261i	$0.0844681\pi$
$541$			12.2001i			0.524522i	−0.964997	+	0.262261i	$0.915532\pi$
$542$	−4.85771	+	2.80460i	−0.208656	+	0.120468i
$543$	7.78010	−	4.49184i	0.333876	−	0.192763i
$544$	−2.25646	−	3.90830i	−0.0967450	−	0.167567i
$545$	3.97431	−	6.88371i	0.170241	−	0.294866i
$546$	7.43702			0.318275
$547$	−4.14731	+	2.39445i	−0.177326	+	0.102379i	−0.586036	−	0.810285i	$-0.699312\pi$
$547$	−4.14731	+	2.39445i	−0.177326	+	0.102379i	0.408710	+	0.912664i	$0.365979\pi$
$548$	4.38346			0.187252
$549$	1.78566	−	3.60833i	0.0762101	−	0.154000i
$550$	11.4677			0.488985
$551$	−44.5537	+	25.7231i	−1.89805	+	1.09584i
$552$	2.51548			0.107066
$553$	15.4510	−	26.7620i	0.657044	−	1.13803i
$554$	−8.52824	−	14.7713i	−0.362330	−	0.627574i
$555$	2.77454	−	1.60188i	0.117773	−	0.0679960i
$556$	−7.63288	+	4.40685i	−0.323706	+	0.186892i
$557$			4.39303i			0.186139i	0.995660	+	0.0930694i	$0.0296679\pi$
$557$			4.39303i			0.186139i	−0.995660	+	0.0930694i	$0.970332\pi$
$558$	3.09154			0.130875
$559$	2.37957	+	1.37384i	0.100645	+	0.0581074i
$560$		−	5.18120i		−	0.218946i
$561$	−13.1349	+	22.7504i	−0.554557	+	0.960521i
$562$	−2.99107	−	5.18068i	−0.126170	−	0.218534i
$563$	−5.68042	+	9.83878i	−0.239401	+	0.414655i	−0.960543	−	0.278133i	$-0.910284\pi$
$563$	−5.68042	+	9.83878i	−0.239401	+	0.414655i	0.721141	+	0.692788i	$0.243618\pi$
$564$	5.05343	+	8.75279i	0.212788	+	0.368559i
$565$	3.26540	+	5.65583i	0.137376	+	0.237943i
$566$	22.5498	+	13.0191i	0.947838	+	0.547234i
$567$	40.3620	−	23.3030i	1.69504	−	0.978634i
$568$	6.46955	−	11.2056i	0.271456	−	0.470176i
$569$	−5.70023			−0.238966			−0.119483	−	0.992836i	$-0.538124\pi$
$569$	−5.70023			−0.238966			−0.119483	+	0.992836i	$0.538124\pi$
$570$	−12.3520	+	7.13142i	−0.517368	+	0.298702i
$571$	−4.11996	−	7.13598i	−0.172415	−	0.298631i	0.766849	−	0.641828i	$-0.221824\pi$
$571$	−4.11996	−	7.13598i	−0.172415	−	0.298631i	−0.939264	+	0.343197i	$0.888490\pi$
$572$		−	2.71642i		−	0.113579i
$573$		−	16.1480i		−	0.674591i
$574$	9.55181	−	16.5442i	0.398685	−	0.690542i
$575$	4.29168	+	2.47780i	0.178975	+	0.103331i
$576$	−0.515475			−0.0214781
$577$			40.7445i			1.69622i	0.529824	+	0.848108i	$0.322258\pi$
$577$			40.7445i			1.69622i	−0.529824	+	0.848108i	$0.677742\pi$
$578$	2.91544	+	1.68323i	0.121266	+	0.0700132i
$579$	−42.1355	−	24.3270i	−1.75109	−	1.01099i
$580$	7.65057	+	4.41706i	0.317673	+	0.183408i
$581$	−52.3690	−	30.2353i	−2.17263	−	1.25437i
$582$		−	7.54830i		−	0.312887i
$583$	25.5975			1.06014
$584$	9.07544	+	5.23971i	0.375544	+	0.216821i
$585$	−0.257738	+	0.446415i	−0.0106561	+	0.0184570i
$586$		−	4.08862i		−	0.168899i
$587$		−	12.9595i		−	0.534897i	−0.963572	−	0.267448i	$-0.913820\pi$
$587$		−	12.9595i		−	0.534897i	0.963572	−	0.267448i	$-0.0861805\pi$
$588$	−12.7040	−	22.0040i	−0.523904	−	0.907428i
$589$	34.5700	−	19.9590i	1.42443	−	0.822396i
$590$	6.20162			0.255317
$591$	−3.70684	+	6.42043i	−0.152479	+	0.264101i
$592$	1.29475	−	0.747526i	0.0532140	−	0.0307231i
$593$	2.81114	+	1.62301i	0.115440	+	0.0666491i	0.556608	−	0.830775i	$-0.312103\pi$
$593$	2.81114	+	1.62301i	0.115440	+	0.0666491i	−0.441168	+	0.897424i	$0.645436\pi$
$594$	−7.23125	−	12.5249i	−0.296702	−	0.513903i
$595$	11.6912	+	20.2497i	0.479292	+	0.830157i
$596$	4.35214	−	7.53813i	0.178271	−	0.308774i
$597$	−15.5083	−	26.8612i	−0.634713	−	1.09936i
$598$	0.586930	−	1.01659i	0.0240014	−	0.0415716i
$599$			12.4951i			0.510534i	0.966871	+	0.255267i	$0.0821634\pi$
$599$			12.4951i			0.510534i	−0.966871	+	0.255267i	$0.917837\pi$
$600$	−5.99779	−	3.46282i	−0.244859	−	0.141369i
$601$	41.3773			1.68782			0.843908	−	0.536488i	$-0.180249\pi$
$601$	41.3773			1.68782			0.843908	+	0.536488i	$0.180249\pi$
$602$		−	14.2363i		−	0.580229i
$603$	6.85556	−	3.95806i	0.279180	−	0.161185i
$604$	2.19173	−	1.26540i	0.0891802	−	0.0514882i
$605$	−0.777952	−	1.34745i	−0.0316283	−	0.0547817i
$606$	−5.76300	+	9.98181i	−0.234106	+	0.405483i
$607$	−15.7659			−0.639917			−0.319958	−	0.947432i	$-0.603669\pi$
$607$	−15.7659			−0.639917			−0.319958	+	0.947432i	$0.603669\pi$
$608$	−5.76412	+	3.32792i	−0.233766	+	0.134965i
$609$	65.6995			2.66228
$610$	−7.42891	+	4.94894i	−0.300788	+	0.200377i
$611$	4.71642			0.190806
$612$	2.01463	−	1.16315i	0.0814368	−	0.0470175i
$613$	26.6683			1.07712			0.538561	−	0.842587i	$-0.318968\pi$
$613$	26.6683			1.07712			0.538561	+	0.842587i	$0.318968\pi$
$614$	−5.51990	+	9.56074i	−0.222765	+	0.385840i
$615$	4.51513	+	7.82044i	0.182068	+	0.315351i
$616$	−12.1887	+	7.03715i	−0.491097	+	0.283535i
$617$	−20.5869	+	11.8859i	−0.828797	+	0.478506i	−0.853441	−	0.521190i	$-0.825488\pi$
$617$	−20.5869	+	11.8859i	−0.828797	+	0.478506i	0.0246433	+	0.999696i	$0.492155\pi$
$618$			2.00410i			0.0806169i
$619$	23.2358			0.933926			0.466963	−	0.884277i	$-0.345348\pi$
$619$	23.2358			0.933926			0.466963	+	0.884277i	$0.345348\pi$
$620$	−5.93620	−	3.42727i	−0.238404	−	0.137642i
$621$		−	6.24976i		−	0.250794i
$622$	−0.899553	+	1.55807i	−0.0360688	+	0.0624729i
$623$	−3.19795	−	5.53902i	−0.128123	−	0.221916i
$624$	−0.820258	+	1.42073i	−0.0328366	+	0.0568746i
$625$	−3.55632	−	6.15973i	−0.142253	−	0.246389i
$626$	9.26540	+	16.0481i	0.370320	+	0.641413i
$627$	33.5531	+	19.3719i	1.33998	+	0.773639i
$628$	12.1376	−	7.00766i	0.484344	−	0.279636i
$629$	−3.37353	+	5.84312i	−0.134511	+	0.232980i
$630$	2.67078			0.106406
$631$	7.82432	−	4.51737i	0.311481	−	0.179834i	−0.336108	−	0.941823i	$-0.609111\pi$
$631$	7.82432	−	4.51737i	0.311481	−	0.179834i	0.647589	+	0.761990i	$0.275777\pi$
$632$	3.40830	+	5.90336i	0.135575	+	0.234823i
$633$		−	11.8485i		−	0.470935i
$634$			8.40288i			0.333721i
$635$	−12.5853	+	21.7984i	−0.499433	+	0.865043i
$636$	−13.3879	−	7.72950i	−0.530864	−	0.306494i
$637$	−11.8568			−0.469782
$638$		−	23.9971i		−	0.950055i
$639$	5.77620	+	3.33489i	0.228503	+	0.131926i
$640$	0.989788	+	0.571455i	0.0391248	+	0.0225887i
$641$	−10.5000	−	6.06218i	−0.414725	−	0.239442i	0.278093	−	0.960554i	$-0.410298\pi$
$641$	−10.5000	−	6.06218i	−0.414725	−	0.239442i	−0.692818	+	0.721113i	$0.743631\pi$
$642$	27.4211	+	15.8316i	1.08222	+	0.624822i
$643$		−	16.7853i		−	0.661947i	−0.943640	−	0.330974i	$-0.892623\pi$
$643$		−	16.7853i		−	0.661947i	0.943640	−	0.330974i	$-0.107377\pi$
$644$	−6.08201			−0.239665
$645$	5.82792	+	3.36475i	0.229474	+	0.132487i
$646$	15.0186	−	26.0130i	0.590900	−	1.02347i
$647$			12.2125i			0.480122i	0.970758	+	0.240061i	$0.0771674\pi$
$647$			12.2125i			0.480122i	−0.970758	+	0.240061i	$0.922833\pi$
$648$			10.2807i			0.403864i
$649$	−8.42310	−	14.5892i	−0.330635	−	0.572677i
$650$	−2.79890	+	1.61595i	−0.109782	+	0.0633826i
$651$	−50.9773			−1.99796
$652$	2.39044	−	4.14036i	0.0936167	−	0.162149i
$653$	−9.61084	+	5.54882i	−0.376101	+	0.217142i	−0.676121	−	0.736791i	$-0.736340\pi$
$653$	−9.61084	+	5.54882i	−0.376101	+	0.217142i	0.300019	+	0.953933i	$0.403007\pi$
$654$	11.2928	+	6.51992i	0.441585	+	0.254949i
$655$	9.45788	+	16.3815i	0.369550	+	0.640079i
$656$	2.10701	+	3.64945i	0.0822650	+	0.142487i
$657$	−2.70094	+	4.67817i	−0.105374	+	0.182513i
$658$	−12.2184	−	21.1628i	−0.476321	−	0.825012i
$659$	−16.8526	+	29.1896i	−0.656486	+	1.13707i	0.325033	+	0.945703i	$0.394624\pi$
$659$	−16.8526	+	29.1896i	−0.656486	+	1.13707i	−0.981519	+	0.191364i	$0.938709\pi$
$660$		−	6.65291i		−	0.258964i
$661$	−20.6220	−	11.9061i	−0.802103	−	0.463094i	0.0421031	−	0.999113i	$-0.486594\pi$
$661$	−20.6220	−	11.9061i	−0.802103	−	0.463094i	−0.844206	+	0.536019i	$0.819928\pi$
$662$	−12.2376			−0.475629
$663$		−	7.40352i		−	0.287529i
$664$	11.5520	−	6.66953i	0.448303	−	0.258828i
$665$	29.8651	−	17.2426i	1.15812	−	0.668639i
$666$	0.385331	+	0.667413i	0.0149313	+	0.0258617i
$667$	5.18501	−	8.98069i	0.200764	−	0.347734i
$668$	17.4590			0.675509
$669$	−34.7821	+	20.0815i	−1.34476	+	0.776395i
$670$	−17.5516			−0.678077
$671$	21.7323	+	10.7547i	0.838967	+	0.415181i
$672$	8.49984			0.327888
$673$	−39.2161	+	22.6414i	−1.51167	+	0.872763i	−0.511762	+	0.859127i	$0.671007\pi$
$673$	−39.2161	+	22.6414i	−1.51167	+	0.872763i	−0.999907	+	0.0136357i	$0.995659\pi$
$674$	24.5289			0.944817
$675$	−8.60347	+	14.9017i	−0.331148	+	0.573565i
$676$	−6.11722	−	10.5953i	−0.235278	−	0.407513i
$677$	28.0310	−	16.1837i	1.07732	−	0.621990i	0.147147	−	0.989115i	$-0.452991\pi$
$677$	28.0310	−	16.1837i	1.07732	−	0.621990i	0.930172	+	0.367124i	$0.119658\pi$
$678$	−9.27848	+	5.35693i	−0.356338	+	0.205732i
$679$			18.2505i			0.700391i
$680$	−5.15786			−0.197795
$681$	−23.8764	−	13.7850i	−0.914944	−	0.528243i
$682$			18.6198i			0.712988i
$683$	7.28579	−	12.6194i	0.278783	−	0.482866i	−0.692299	−	0.721610i	$-0.743402\pi$
$683$	7.28579	−	12.6194i	0.278783	−	0.482866i	0.971083	+	0.238744i	$0.0767356\pi$
$684$	−1.71546	−	2.97126i	−0.0655922	−	0.113609i
$685$	2.50495	−	4.33870i	0.0957091	−	0.165773i
$686$	14.8495	+	25.7200i	0.566955	+	0.981995i
$687$	1.48231	+	2.56744i	0.0565538	+	0.0979540i
$688$	2.71963	+	1.57018i	0.103685	+	0.0598625i
$689$	−6.24753	+	3.60701i	−0.238012	+	0.137416i
$690$	1.43748	−	2.48979i	0.0547239	−	0.0947846i
$691$	−6.19323			−0.235602			−0.117801	−	0.993037i	$-0.537584\pi$
$691$	−6.19323			−0.235602			−0.117801	+	0.993037i	$0.537584\pi$
$692$	−0.0536081	+	0.0309506i	−0.00203787	+	0.00117657i
$693$	−3.62748	−	6.28297i	−0.137796	−	0.238670i
$694$		−	25.9675i		−	0.985713i
$695$			10.0732i			0.382100i
$696$	−7.24625	+	12.5509i	−0.274668	+	0.475740i
$697$	−16.4697	−	9.50878i	−0.623834	−	0.360171i
$698$	16.5155			0.625120
$699$			9.16360i			0.346599i
$700$	14.5017	+	8.37254i	0.548111	+	0.316452i
$701$	34.6110	+	19.9827i	1.30724	+	0.754734i	0.981634	−	0.190772i	$-0.0610991\pi$
$701$	34.6110	+	19.9827i	1.30724	+	0.754734i	0.325604	+	0.945506i	$0.394432\pi$
$702$	3.52983	+	2.03795i	0.133225	+	0.0769175i
$703$	8.61766	+	4.97541i	0.325021	+	0.187651i
$704$		−	3.10462i		−	0.117010i
$705$	11.5512			0.435044
$706$	−10.8823	−	6.28290i	−0.409561	−	0.236460i
$707$	13.9340	−	24.1344i	0.524042	−	0.907667i
$708$			10.1739i			0.382357i
$709$		−	0.515156i		−	0.0193471i	−0.999953	−	0.00967355i	$-0.996921\pi$
$709$		−	0.515156i		−	0.0193471i	0.999953	−	0.00967355i	$-0.00307923\pi$
$710$	−7.39411	−	12.8070i	−0.277496	−	0.480637i
$711$	−3.04303	+	1.75690i	−0.114123	+	0.0658888i
$712$	1.41086			0.0528742
$713$	−4.02313	+	6.96827i	−0.150668	+	0.260964i
$714$	−33.2200	+	19.1796i	−1.24323	+	0.717777i
$715$	−2.68868	−	1.55231i	−0.100551	−	0.0580530i
$716$	−9.44496	−	16.3591i	−0.352975	−	0.611370i
$717$	−13.7604	−	23.8338i	−0.513893	−	0.890089i
$718$	−10.4517	+	18.1028i	−0.390053	+	0.675592i
$719$	16.7746	+	29.0545i	0.625589	+	1.08355i	0.988427	+	0.151699i	$0.0484745\pi$
$719$	16.7746	+	29.0545i	0.625589	+	1.08355i	−0.362838	+	0.931852i	$0.618192\pi$
$720$	−0.294571	+	0.510212i	−0.0109780	+	0.0190145i
$721$		−	4.84559i		−	0.180459i
$722$	−21.9105	−	12.6500i	−0.815425	−	0.470786i
$723$	−33.7493			−1.25515
$724$		−	4.79140i		−	0.178071i
$725$	−24.7258	+	14.2754i	−0.918293	+	0.530177i
$726$	2.21052	−	1.27624i	0.0820400	−	0.0473658i
$727$	−2.66570	−	4.61713i	−0.0988655	−	0.171240i	0.812350	−	0.583170i	$-0.198188\pi$
$727$	−2.66570	−	4.61713i	−0.0988655	−	0.171240i	−0.911215	+	0.411930i	$0.864855\pi$
$728$	1.98325	−	3.43509i	0.0735041	−	0.127313i
$729$	20.9034			0.774200
$730$	10.3724	−	5.98851i	0.383900	−	0.221645i
$731$	−14.1722			−0.524177
$732$	−8.11882	−	12.1872i	−0.300080	−	0.450453i
$733$	3.38825			0.125148			0.0625739	−	0.998040i	$-0.480069\pi$
$733$	3.38825			0.125148			0.0625739	+	0.998040i	$0.480069\pi$
$734$	24.8214	−	14.3306i	0.916174	−	0.528953i
$735$	−29.0390			−1.07112
$736$	0.670808	−	1.16187i	0.0247263	−	0.0428272i
$737$	23.8387	+	41.2898i	0.878110	+	1.52093i
$738$	−1.88120	+	1.08611i	−0.0692480	+	0.0399803i
$739$	−28.6385	+	16.5344i	−1.05348	+	0.608229i	−0.923623	−	0.383303i	$-0.874787\pi$
$739$	−28.6385	+	16.5344i	−1.05348	+	0.608229i	−0.129861	+	0.991532i	$0.541453\pi$
$740$		−	1.70871i		−	0.0628134i
$741$	−10.9190			−0.401119
$742$	32.3697	+	18.6887i	1.18833	+	0.686082i
$743$		−	23.5534i		−	0.864089i	−0.901852	−	0.432044i	$-0.857792\pi$
$743$		−	23.5534i		−	0.864089i	0.901852	−	0.432044i	$-0.142208\pi$
$744$	5.62249	−	9.73843i	0.206130	−	0.357028i
$745$	−4.97410	−	8.61540i	−0.182237	−	0.315644i
$746$	15.7679	−	27.3109i	0.577306	−	0.999922i
$747$	3.43798	+	5.95475i	0.125789	+	0.217873i
$748$	7.00545	+	12.1338i	0.256144	+	0.443655i
$749$	−66.2996	−	38.2781i	−2.42254	−	1.39865i
$750$	−16.1340	+	9.31497i	−0.589130	+	0.340135i
$751$	9.35691	−	16.2066i	0.341438	−	0.591389i	−0.643262	−	0.765646i	$-0.722419\pi$
$751$	9.35691	−	16.2066i	0.341438	−	0.591389i	0.984700	+	0.174258i	$0.0557526\pi$
$752$	5.39044			0.196569
$753$	−12.4763	+	7.20322i	−0.454663	+	0.262500i
$754$	3.38150	+	5.85693i	0.123147	+	0.213297i
$755$		−	2.89246i		−	0.105268i
$756$		−	21.1181i		−	0.768057i
$757$	11.4006	−	19.7465i	0.414363	−	0.717699i	−0.580998	−	0.813905i	$-0.697338\pi$
$757$	11.4006	−	19.7465i	0.414363	−	0.717699i	0.995361	+	0.0962065i	$0.0306709\pi$
$758$	−23.5206	−	13.5796i	−0.854306	−	0.493234i
$759$	−7.80959			−0.283470
$760$			7.60701i			0.275935i
$761$	27.9745	+	16.1511i	1.01407	+	0.585476i	0.912382	−	0.409340i	$-0.134241\pi$
$761$	27.9745	+	16.1511i	1.01407	+	0.585476i	0.101692	+	0.994816i	$0.467574\pi$
$762$	−35.7606	−	20.6464i	−1.29547	−	0.747940i
$763$	−27.3042	−	15.7641i	−0.988479	−	0.570699i
$764$	−7.45858	−	4.30622i	−0.269842	−	0.155793i
$765$		−	2.65875i		−	0.0961273i
$766$	1.89857			0.0685981
$767$	4.11162	+	2.37384i	0.148462	+	0.0857145i
$768$	−0.937480	+	1.62376i	−0.0338284	+	0.0585925i
$769$			7.09533i			0.255864i	0.991783	+	0.127932i	$0.0408339\pi$
$769$			7.09533i			0.255864i	−0.991783	+	0.127932i	$0.959166\pi$
$770$			16.0856i			0.579686i
$771$	21.1655	+	36.6598i	0.762258	+	1.32027i
$772$	−22.4728	+	12.9747i	−0.808812	+	0.466968i
$773$	18.2628			0.656869			0.328434	−	0.944527i	$-0.393479\pi$
$773$	18.2628			0.656869			0.328434	+	0.944527i	$0.393479\pi$
$774$	−0.809388	+	1.40190i	−0.0290928	+	0.0503903i
$775$	19.1852	−	11.0766i	0.689151	−	0.397882i
$776$	−3.48648	−	2.01292i	−0.125157	−	0.0722597i
$777$	−6.35385	−	11.0052i	−0.227943	−	0.394809i
$778$	4.46207	+	7.72854i	0.159973	+	0.277081i
$779$	−14.0239	+	24.2901i	−0.502459	+	0.870284i
$780$	0.937480	+	1.62376i	0.0335672	+	0.0581400i
$781$	−20.0855	+	34.7890i	−0.718715	+	1.24485i
$782$			6.05461i			0.216512i
$783$	31.1830	+	18.0035i	1.11439	+	0.643392i
$784$	−13.5512			−0.483972
$785$		−	16.0182i		−	0.571715i
$786$	−26.8741	+	15.5158i	−0.958569	+	0.553430i
$787$	−0.872700	+	0.503853i	−0.0311084	+	0.0179604i	−0.515474	−	0.856905i	$-0.672384\pi$
$787$	−0.872700	+	0.503853i	−0.0311084	+	0.0179604i	0.484365	+	0.874866i	$0.339051\pi$
$788$	1.97702	+	3.42430i	0.0704285	+	0.121986i
$789$	−23.5686	+	40.8220i	−0.839064	+	1.45330i
$790$	7.79077			0.277183
$791$	22.4338	−	12.9522i	0.797655	−	0.460526i
$792$	1.60035			0.0568661
$793$	−6.81964	+	0.437480i	−0.242172	+	0.0155354i
$794$	14.8669			0.527608
$795$	−15.3011	+	8.83411i	−0.542675	+	0.313314i
$796$	−16.5426			−0.586335
$797$	−8.45042	+	14.6366i	−0.299329	+	0.518454i	−0.975983	−	0.217848i	$-0.930096\pi$
$797$	−8.45042	+	14.6366i	−0.299329	+	0.518454i	0.676653	+	0.736302i	$0.263430\pi$
$798$	28.2868	+	48.9941i	1.00134	+	1.73437i
$799$	−21.0675	+	12.1633i	−0.745313	+	0.430307i
$800$	−3.19889	+	1.84688i	−0.113098	+	0.0652970i
$801$			0.727263i			0.0256966i
$802$	−6.65177			−0.234882
$803$	−28.1758	−	16.2673i	−0.994301	−	0.574060i
$804$		−	28.7936i		−	1.01547i
$805$	−3.47559	+	6.01990i	−0.122498	+	0.212174i
$806$	−2.62376	−	4.54449i	−0.0924181	−	0.160073i
$807$	27.7170	−	48.0073i	0.975686	−	1.68994i
$808$	3.07367	+	5.32375i	0.108131	+	0.187289i
$809$	−2.01053	−	3.48234i	−0.0706864	−	0.122432i	0.828516	−	0.559966i	$-0.189186\pi$
$809$	−2.01053	−	3.48234i	−0.0706864	−	0.122432i	−0.899202	+	0.437533i	$0.855852\pi$
$810$	10.1757	+	5.87496i	0.357539	+	0.206425i
$811$	−7.70616	+	4.44915i	−0.270600	+	0.156231i	−0.629160	−	0.777276i	$-0.716601\pi$
$811$	−7.70616	+	4.44915i	−0.270600	+	0.156231i	0.358560	+	0.933507i	$0.383268\pi$
$812$	17.5202	−	30.3459i	0.614840	−	1.06493i
$813$	−10.5170			−0.368848
$814$	−4.01971	+	2.32078i	−0.140891	+	0.0813434i
$815$	−2.73205	−	4.73205i	−0.0956996	−	0.165757i
$816$		−	8.46155i		−	0.296213i
$817$			20.9017i			0.731257i
$818$	−4.82518	+	8.35746i	−0.168708	+	0.292212i
$819$	1.77070	+	1.02232i	0.0618733	+	0.0357226i
$820$	4.81624			0.168191
$821$			35.1518i			1.22681i	0.789770	+	0.613403i	$0.210200\pi$
$821$			35.1518i			1.22681i	−0.789770	+	0.613403i	$0.789800\pi$
$822$	7.11770	+	4.10940i	0.248258	+	0.143332i
$823$	18.6730	+	10.7809i	0.650900	+	0.375798i	0.788801	−	0.614649i	$-0.210702\pi$
$823$	18.6730	+	10.7809i	0.650900	+	0.375798i	−0.137901	+	0.990446i	$0.544035\pi$
$824$	0.925676	+	0.534439i	0.0322474	+	0.0186181i
$825$	18.6208	+	10.7507i	0.648294	+	0.374293i
$826$		−	24.5987i		−	0.855899i
$827$	0.0847012			0.00294535			0.00147268	−	0.999999i	$-0.499531\pi$
$827$	0.0847012			0.00294535			0.00147268	+	0.999999i	$0.499531\pi$
$828$	0.598917	+	0.345785i	0.0208138	+	0.0120169i
$829$	−9.44149	+	16.3531i	−0.327916	+	0.567968i	−0.982098	−	0.188369i	$-0.939680\pi$
$829$	−9.44149	+	16.3531i	−0.327916	+	0.567968i	0.654182	+	0.756337i	$0.273013\pi$
$830$		−	15.2453i		−	0.529173i
$831$		−	31.9802i		−	1.10938i
$832$	0.437480	+	0.757738i	0.0151669	+	0.0262698i
$833$	52.9623	−	30.5778i	1.83503	−	1.05946i
$834$	−16.5253			−0.572225
$835$	9.97702	−	17.2807i	0.345269	−	0.598024i
$836$	17.8954	−	10.3319i	0.618925	−	0.357336i
$837$	−24.1954	−	13.9692i	−0.836314	−	0.482846i
$838$	5.68177	+	9.84112i	0.196274	+	0.339956i
$839$	1.31789	+	2.28265i	0.0454985	+	0.0788057i	0.887878	−	0.460079i	$-0.152179\pi$
$839$	1.31789	+	2.28265i	0.0454985	+	0.0788057i	−0.842379	+	0.538885i	$0.818846\pi$
$840$	4.85727	−	8.41304i	0.167592	−	0.290278i
$841$	15.3726	+	26.6261i	0.530088	+	0.918140i
$842$	−3.81932	+	6.61526i	−0.131623	+	0.227977i
$843$		−	11.2163i		−	0.386308i
$844$	−5.47269	−	3.15966i	−0.188378	−	0.108760i
$845$	−13.9829			−0.481025
$846$			2.77864i			0.0955315i
$847$	−5.34467	+	3.08574i	−0.183645	+	0.106027i
$848$	−7.14036	+	4.12249i	−0.245201	+	0.141567i
$849$	24.4103	+	42.2799i	0.837760	+	1.45104i
$850$	8.33482	−	14.4363i	0.285882	−	0.495162i
$851$	−2.00579			−0.0687574
$852$	21.0100	−	12.1301i	0.719792	−	0.415572i
$853$	−9.01663			−0.308724			−0.154362	−	0.988014i	$-0.549332\pi$
$853$	−9.01663			−0.308724			−0.154362	+	0.988014i	$0.549332\pi$
$854$	19.6300	+	29.4667i	0.671723	+	1.00833i
$855$	−3.92123			−0.134103
$856$	14.6249	−	8.44368i	0.499868	−	0.288599i
$857$	−24.4297			−0.834504			−0.417252	−	0.908791i	$-0.637007\pi$
$857$	−24.4297			−0.834504			−0.417252	+	0.908791i	$0.637007\pi$
$858$	2.54659	−	4.41082i	0.0869390	−	0.150583i
$859$	−6.91603	−	11.9789i	−0.235972	−	0.408716i	0.723583	−	0.690238i	$-0.242494\pi$
$859$	−6.91603	−	11.9789i	−0.235972	−	0.408716i	−0.959555	+	0.281522i	$0.909161\pi$
$860$	3.10829	−	1.79457i	0.105992	−	0.0611944i
$861$	31.0197	−	17.9093i	1.05715	−	0.610346i
$862$		−	28.4038i		−	0.967438i
$863$	4.25231			0.144750			0.0723752	−	0.997377i	$-0.476942\pi$
$863$	4.25231			0.144750			0.0723752	+	0.997377i	$0.476942\pi$
$864$	4.03428	+	2.32919i	0.137249	+	0.0792407i
$865$			0.0707476i			0.00240549i
$866$	8.45790	−	14.6495i	0.287411	−	0.497811i
$867$	3.15599	+	5.46634i	0.107183	+	0.185647i
$868$	−13.5942	+	23.5459i	−0.461419	+	0.799201i
$869$	−10.5815	−	18.3277i	−0.358952	−	0.621723i
$870$	8.28181	+	14.3445i	0.280780	+	0.486324i
$871$	−11.6365	−	6.71835i	−0.394289	−	0.227643i
$872$	6.02297	−	3.47737i	0.203964	−	0.117758i
$873$	1.03761	−	1.79720i	0.0351178	−	0.0608259i
$874$	8.92957			0.302047
$875$	39.0093	−	22.5221i	1.31876	−	0.761385i
$876$	9.82424	+	17.0161i	0.331930	+	0.574920i
$877$		−	3.22902i		−	0.109036i	−0.998513	−	0.0545182i	$-0.982638\pi$
$877$		−	3.22902i		−	0.109036i	0.998513	−	0.0545182i	$-0.0173623\pi$
$878$			22.4155i			0.756488i
$879$	3.83300	−	6.63895i	0.129284	−	0.223926i
$880$	−3.07291	−	1.77415i	−0.103588	−	0.0598065i
$881$	34.8013			1.17249			0.586243	−	0.810135i	$-0.300607\pi$
$881$	34.8013			1.17249			0.586243	+	0.810135i	$0.300607\pi$
$882$		−	6.98532i		−	0.235208i
$883$	−21.4924	−	12.4086i	−0.723277	−	0.417584i	0.0926806	−	0.995696i	$-0.470456\pi$
$883$	−21.4924	−	12.4086i	−0.723277	−	0.417584i	−0.815958	+	0.578112i	$0.803790\pi$
$884$	−3.41961	−	1.97431i	−0.115014	−	0.0664033i
$885$	10.0700	+	5.81390i	0.338498	+	0.195432i
$886$	−4.01605	−	2.31866i	−0.134922	−	0.0778971i
$887$		−	31.4277i		−	1.05524i	−0.849481	−	0.527619i	$-0.823085\pi$
$887$		−	31.4277i		−	1.05524i	0.849481	−	0.527619i	$-0.176915\pi$
$888$	2.80316			0.0940680
$889$	86.4633	+	49.9196i	2.89988	+	1.67425i
$890$	0.806242	−	1.39645i	0.0270253	−	0.0468092i
$891$		−	31.9177i		−	1.06928i
$892$			21.4207i			0.717218i
$893$	17.9389	+	31.0711i	0.600303	+	1.03976i
$894$	14.1337	−	8.16009i	0.472702	−	0.272914i
$895$	−21.5895			−0.721656
$896$	2.26667	−	3.92599i	0.0757242	−	0.131158i
$897$	1.90607	−	1.10047i	0.0636418	−	0.0367436i
$898$	−30.5092	−	17.6145i	−1.01811	−	0.587804i
$899$	−23.1786	−	40.1466i	−0.773050	−	1.33896i
$900$	−0.952021	−	1.64895i	−0.0317340	−	0.0549649i
$901$	18.6045	−	32.2239i	0.619804	−	1.07353i
$902$	−6.54146	−	11.3301i	−0.217807	−	0.377253i
$903$	13.3463	−	23.1164i	0.444136	−	0.769266i
$904$			5.71418i			0.190051i
$905$	−4.74247	−	2.73807i	−0.157645	−	0.0910164i
$906$	4.74513			0.157646
$907$			36.9173i			1.22582i	0.790153	+	0.612909i	$0.210001\pi$
$907$			36.9173i			1.22582i	−0.790153	+	0.612909i	$0.789999\pi$
$908$	−12.7343	+	7.35217i	−0.422603	+	0.243990i
$909$	−2.74426	+	1.58440i	−0.0910213	+	0.0525512i
$910$	−2.26667	−	3.92599i	−0.0751395	−	0.130145i
$911$	2.76045	−	4.78124i	0.0914577	−	0.158409i	−0.816667	−	0.577109i	$-0.804181\pi$
$911$	2.76045	−	4.78124i	0.0914577	−	0.158409i	0.908125	+	0.418700i	$0.137514\pi$
$912$	−12.4794			−0.413235
$913$	−35.8644	+	20.7063i	−1.18694	+	0.685280i
$914$	15.6289			0.516959
$915$	−16.7023	+	1.07145i	−0.552162	+	0.0354212i
$916$	1.58117			0.0522432
$917$	64.9772	−	37.5146i	2.14574	−	1.23884i
$918$	−21.0229			−0.693860
$919$	15.8866	−	27.5164i	0.524051	−	0.907683i	−0.475557	−	0.879685i	$-0.657754\pi$
$919$	15.8866	−	27.5164i	0.524051	−	0.907683i	0.999608	−	0.0279977i	$-0.00891312\pi$
$920$	−0.766672	−	1.32792i	−0.0252764	−	0.0437801i
$921$	−17.9260	+	10.3496i	−0.590682	+	0.341031i
$922$	20.9576	−	12.0999i	0.690202	−	0.398488i
$923$		−	11.3212i		−	0.372642i
$924$	−26.3887			−0.868126
$925$	4.78251	+	2.76118i	0.157248	+	0.0907871i
$926$		−	0.645303i		−	0.0212060i
$927$	−0.275490	+	0.477163i	−0.00904828	+	0.0156721i
$928$	3.86475	+	6.69394i	0.126867	+	0.219739i
$929$	−1.34162	+	2.32375i	−0.0440170	+	0.0762396i	−0.887195	−	0.461396i	$-0.847349\pi$
$929$	−1.34162	+	2.32375i	−0.0440170	+	0.0762396i	0.843178	+	0.537635i	$0.180682\pi$
$930$	−6.42599	−	11.1301i	−0.210717	−	0.364972i
$931$	−45.0973	−	78.1108i	−1.47800	−	2.55998i
$932$	4.23258	+	2.44368i	0.138643	+	0.0800454i
$933$	−2.92132	+	1.68663i	−0.0956397	+	0.0552176i
$934$	−19.3259	+	33.4734i	−0.632361	+	1.09528i
$935$	16.0132			0.523687
$936$	−0.390595	+	0.225510i	−0.0127670	+	0.00737103i
$937$	−21.5221	−	37.2774i	−0.703097	−	1.21780i	−0.967374	−	0.253353i	$-0.918466\pi$
$937$	−21.5221	−	37.2774i	−0.703097	−	1.21780i	0.264276	−	0.964447i	$-0.414867\pi$
$938$			69.6183i			2.27312i
$939$			34.7445i			1.13384i
$940$	3.08039	−	5.33539i	0.100471	−	0.174021i
$941$	39.3026	+	22.6914i	1.28123	+	0.739717i	0.977073	−	0.212905i	$-0.0682926\pi$
$941$	39.3026	+	22.6914i	1.28123	+	0.739717i	0.304155	+	0.952623i	$0.401626\pi$
$942$	26.2782			0.856189
$943$		−	5.65360i		−	0.184106i
$944$	4.69920	+	2.71309i	0.152946	+	0.0883035i
$945$	−20.9024	−	12.0680i	−0.679956	−	0.392573i
$946$	−8.44340	−	4.87480i	−0.274519	−	0.158493i
$947$	38.3261	+	22.1276i	1.24543	+	0.719049i	0.970194	−	0.242328i	$-0.0779109\pi$
$947$	38.3261	+	22.1276i	1.24543	+	0.719049i	0.275235	+	0.961377i	$0.411244\pi$
$948$			12.7809i			0.415103i
$949$	9.16907			0.297641
$950$	−21.2913	−	12.2925i	−0.690780	−	0.398822i
$951$	−7.87754	+	13.6443i	−0.255447	+	0.442447i
$952$			20.4586i			0.663068i
$953$			19.8287i			0.642314i	0.947026	+	0.321157i	$0.104072\pi$
$953$			19.8287i			0.642314i	−0.947026	+	0.321157i	$0.895928\pi$
$954$	−2.12504	−	3.68068i	−0.0688007	−	0.119166i
$955$	−8.52448	+	4.92161i	−0.275846	+	0.159260i
$956$	−14.6781			−0.474724
$957$	22.4968	−	38.9656i	0.727219	−	1.25958i
$958$	7.81278	−	4.51071i	0.252419	−	0.145734i
$959$	−17.2094	−	9.93586i	−0.555721	−	0.320846i
$960$	1.07145	+	1.85581i	0.0345810	+	0.0598961i
$961$	2.48468	+	4.30359i	0.0801510	+	0.138826i
$962$	0.654056	−	1.13286i	0.0210876	−	0.0365248i
$963$	4.35251	+	7.53876i	0.140258	+	0.242933i
$964$	−9.00000	+	15.5885i	−0.289870	+	0.502070i
$965$			29.6577i			0.954715i
$966$	−9.87574	−	5.70176i	−0.317747	−	0.183451i
$967$	52.6491			1.69308			0.846540	−	0.532325i	$-0.178681\pi$
$967$	52.6491			1.69308			0.846540	+	0.532325i	$0.178681\pi$
$968$		−	1.36135i		−	0.0437556i
$969$	48.7734	−	28.1593i	1.56683	−	0.904608i
$970$	−3.98473	+	2.30059i	−0.127942	+	0.0738674i
$971$	−19.2361	−	33.3178i	−0.617315	−	1.06922i	−0.989974	−	0.141252i	$-0.954887\pi$
$971$	−19.2361	−	33.3178i	−0.617315	−	1.06922i	0.372659	−	0.927968i	$-0.378446\pi$
$972$	−2.65038	+	4.59060i	−0.0850111	+	0.147244i
$973$	39.9555			1.28091
$974$	−1.35697	+	0.783447i	−0.0434801	+	0.0251033i
$975$	−6.05967			−0.194065
$976$	−7.79423	+	0.500000i	−0.249487	+	0.0160046i
$977$	−35.4188			−1.13315			−0.566574	−	0.824011i	$-0.691731\pi$
$977$	−35.4188			−1.13315			−0.566574	+	0.824011i	$0.691731\pi$
$978$	7.76300	−	4.48197i	0.248233	−	0.143318i
$979$	−4.38017			−0.139991
$980$	−7.74390	+	13.4128i	−0.247370	+	0.428457i
$981$	1.79250	+	3.10469i	0.0572300	+	0.0991253i
$982$	6.95473	−	4.01532i	0.221934	−	0.128134i
$983$	8.89278	−	5.13425i	0.283636	−	0.163757i	−0.351432	−	0.936213i	$-0.614305\pi$
$983$	8.89278	−	5.13425i	0.283636	−	0.163757i	0.635068	+	0.772456i	$0.280972\pi$
$984$			7.90112i			0.251879i
$985$	4.51912			0.143991
$986$	−30.2092	−	17.4413i	−0.962058	−	0.555444i
$987$		−	45.8178i		−	1.45840i
$988$	−2.91179	+	5.04337i	−0.0926365	+	0.160451i
$989$	−2.10657	−	3.64869i	−0.0669852	−	0.116022i
$990$	0.914529	−	1.58401i	0.0290657	−	0.0503432i
$991$	27.5570	+	47.7302i	0.875378	+	1.51620i	0.856359	+	0.516381i	$0.172721\pi$
$991$	27.5570	+	47.7302i	0.875378	+	1.51620i	0.0190192	+	0.999819i	$0.493946\pi$
$992$	−2.99872	−	5.19394i	−0.0952096	−	0.164908i
$993$	−19.8710	−	11.4725i	−0.630588	−	0.364070i
$994$	−50.7988	+	29.3287i	−1.61124	+	0.930250i
$995$	−9.45332	+	16.3736i	−0.299690	+	0.519079i
$996$	25.0102			0.792479
$997$	−50.7047	+	29.2744i	−1.60584	+	0.927129i	−0.615547	+	0.788100i	$0.711065\pi$
$997$	−50.7047	+	29.2744i	−1.60584	+	0.927129i	−0.990288	+	0.139029i	$0.955602\pi$
$998$	6.05470	+	10.4871i	0.191658	+	0.331962i
$999$		−	6.96453i		−	0.220348i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	122.2.f.a.75.4	✓	8
3.2	odd	2		1098.2.o.a.685.2		8
4.3	odd	2		976.2.ba.b.929.1		8
61.29	odd	12		7442.2.a.l.1.1		4
61.32	odd	12		7442.2.a.m.1.1		4
61.48	even	6	inner	122.2.f.a.109.4	yes	8
183.170	odd	6		1098.2.o.a.109.2		8
244.231	odd	6		976.2.ba.b.353.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
122.2.f.a.75.4	✓	8	1.1	even	1	trivial
122.2.f.a.109.4	yes	8	61.48	even	6	inner
976.2.ba.b.353.1		8	244.231	odd	6
976.2.ba.b.929.1		8	4.3	odd	2
1098.2.o.a.109.2		8	183.170	odd	6
1098.2.o.a.685.2		8	3.2	odd	2
7442.2.a.l.1.1		4	61.29	odd	12
7442.2.a.m.1.1		4	61.32	odd	12

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:	\( N \)	\(=\)	\( 122 = 2 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	122.f (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +1.87496 q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.571455 - 0.989788i) q^{5} +(1.62376 - 0.937480i) q^{6} +(-3.92599 + 2.26667i) q^{7} -1.00000i q^{8} +0.515475 q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +1.87496 q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.571455 - 0.989788i) q^{5} +(1.62376 - 0.937480i) q^{6} +(-3.92599 + 2.26667i) q^{7} -1.00000i q^{8} +0.515475 q^{9} +(-0.989788 - 0.571455i) q^{10} +3.10462i q^{11} +(0.937480 - 1.62376i) q^{12} +(-0.437480 - 0.757738i) q^{13} +(-2.26667 + 3.92599i) q^{14} +(-1.07145 - 1.85581i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.90830 + 2.25646i) q^{17} +(0.446415 - 0.257738i) q^{18} +(3.32792 - 5.76412i) q^{19} -1.14291 q^{20} +(-7.36108 + 4.24992i) q^{21} +(1.55231 + 2.68868i) q^{22} +1.34162i q^{23} -1.87496i q^{24} +(1.84688 - 3.19889i) q^{25} +(-0.757738 - 0.437480i) q^{26} -4.65838 q^{27} +4.53334i q^{28} +(-6.69394 - 3.86475i) q^{29} +(-1.85581 - 1.07145i) q^{30} +(5.19394 + 2.99872i) q^{31} +(-0.866025 - 0.500000i) q^{32} +5.82103i q^{33} +4.51292 q^{34} +(4.48705 + 2.59060i) q^{35} +(0.257738 - 0.446415i) q^{36} +1.49505i q^{37} -6.65583i q^{38} +(-0.820258 - 1.42073i) q^{39} +(-0.989788 + 0.571455i) q^{40} -4.21402 q^{41} +(-4.24992 + 7.36108i) q^{42} +(-2.71963 + 1.57018i) q^{43} +(2.68868 + 1.55231i) q^{44} +(-0.294571 - 0.510212i) q^{45} +(0.670808 + 1.16187i) q^{46} +(-2.69522 + 4.66825i) q^{47} +(-0.937480 - 1.62376i) q^{48} +(6.77561 - 11.7357i) q^{49} -3.69376i q^{50} +(7.32792 + 4.23077i) q^{51} -0.874960 q^{52} -8.24497i q^{53} +(-4.03428 + 2.32919i) q^{54} +(3.07291 - 1.77415i) q^{55} +(2.26667 + 3.92599i) q^{56} +(6.23971 - 10.8075i) q^{57} -7.72950 q^{58} +(-4.69920 + 2.71309i) q^{59} -2.14291 q^{60} +(3.46410 - 7.00000i) q^{61} +5.99745 q^{62} +(-2.02375 + 1.16841i) q^{63} -1.00000 q^{64} +(-0.500000 + 0.866025i) q^{65} +(2.91052 + 5.04116i) q^{66} +(13.2995 - 7.67847i) q^{67} +(3.90830 - 2.25646i) q^{68} +2.51548i q^{69} +5.18120 q^{70} +(11.2056 + 6.46955i) q^{71} -0.515475i q^{72} +(-5.23971 + 9.07544i) q^{73} +(0.747526 + 1.29475i) q^{74} +(3.46282 - 5.99779i) q^{75} +(-3.32792 - 5.76412i) q^{76} +(-7.03715 - 12.1887i) q^{77} +(-1.42073 - 0.820258i) q^{78} +(-5.90336 + 3.40830i) q^{79} +(-0.571455 + 0.989788i) q^{80} -10.2807 q^{81} +(-3.64945 + 2.10701i) q^{82} +(6.66953 + 11.5520i) q^{83} +8.49984i q^{84} -5.15786i q^{85} +(-1.57018 + 2.71963i) q^{86} +(-12.5509 - 7.24625i) q^{87} +3.10462 q^{88} +1.41086i q^{89} +(-0.510212 - 0.294571i) q^{90} +(3.43509 + 1.98325i) q^{91} +(1.16187 + 0.670808i) q^{92} +(9.73843 + 5.62249i) q^{93} +5.39044i q^{94} -7.60701 q^{95} +(-1.62376 - 0.937480i) q^{96} +(2.01292 - 3.48648i) q^{97} -13.5512i q^{98} +1.60035i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{4} - 4 q^{5} + 6 q^{6} + 12 q^{7} + 4 q^{9}+O(q^{10}) \) 8 * q + 4 * q^4 - 4 * q^5 + 6 * q^6 + 12 * q^7 + 4 * q^9	\( 8 q + 4 q^{4} - 4 q^{5} + 6 q^{6} + 12 q^{7} + 4 q^{9} + 6 q^{10} + 4 q^{13} - 10 q^{14} - 8 q^{15} - 4 q^{16} - 12 q^{18} + 4 q^{19} - 8 q^{20} - 24 q^{21} + 6 q^{22} + 2 q^{25} - 6 q^{26} - 36 q^{27} - 24 q^{29} + 6 q^{30} + 12 q^{31} - 8 q^{34} - 18 q^{35} + 2 q^{36} - 14 q^{39} + 6 q^{40} + 24 q^{41} - 4 q^{42} - 6 q^{43} + 6 q^{44} + 4 q^{45} + 6 q^{46} - 14 q^{47} + 38 q^{49} + 36 q^{51} + 8 q^{52} + 18 q^{54} + 42 q^{55} + 10 q^{56} + 6 q^{57} - 4 q^{58} + 6 q^{59} - 16 q^{60} + 4 q^{62} + 6 q^{63} - 8 q^{64} - 4 q^{65} - 20 q^{66} + 30 q^{67} + 52 q^{70} - 6 q^{71} + 2 q^{73} - 8 q^{74} - 22 q^{75} - 4 q^{76} - 8 q^{77} + 18 q^{78} + 12 q^{79} - 4 q^{80} + 8 q^{81} - 36 q^{82} + 32 q^{83} + 10 q^{86} - 12 q^{87} + 12 q^{88} - 18 q^{90} + 36 q^{91} + 18 q^{92} + 12 q^{93} - 32 q^{95} - 6 q^{96} - 28 q^{97}+O(q^{100}) \) 8 * q + 4 * q^4 - 4 * q^5 + 6 * q^6 + 12 * q^7 + 4 * q^9 + 6 * q^10 + 4 * q^13 - 10 * q^14 - 8 * q^15 - 4 * q^16 - 12 * q^18 + 4 * q^19 - 8 * q^20 - 24 * q^21 + 6 * q^22 + 2 * q^25 - 6 * q^26 - 36 * q^27 - 24 * q^29 + 6 * q^30 + 12 * q^31 - 8 * q^34 - 18 * q^35 + 2 * q^36 - 14 * q^39 + 6 * q^40 + 24 * q^41 - 4 * q^42 - 6 * q^43 + 6 * q^44 + 4 * q^45 + 6 * q^46 - 14 * q^47 + 38 * q^49 + 36 * q^51 + 8 * q^52 + 18 * q^54 + 42 * q^55 + 10 * q^56 + 6 * q^57 - 4 * q^58 + 6 * q^59 - 16 * q^60 + 4 * q^62 + 6 * q^63 - 8 * q^64 - 4 * q^65 - 20 * q^66 + 30 * q^67 + 52 * q^70 - 6 * q^71 + 2 * q^73 - 8 * q^74 - 22 * q^75 - 4 * q^76 - 8 * q^77 + 18 * q^78 + 12 * q^79 - 4 * q^80 + 8 * q^81 - 36 * q^82 + 32 * q^83 + 10 * q^86 - 12 * q^87 + 12 * q^88 - 18 * q^90 + 36 * q^91 + 18 * q^92 + 12 * q^93 - 32 * q^95 - 6 * q^96 - 28 * q^97

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