LMFDB - Embedded newform 670.2.h.b.439.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [670,2,Mod(29,670)]

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([3, 4]))

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

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

chi := DirichletCharacter("670.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 670 = 2 \cdot 5 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	670.h (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:	$5.34997693543$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.89539436150784.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2x^{11} + 2x^{10} - 8x^{9} + 4x^{8} + 16x^{7} - 8x^{6} + 20x^{5} + 20x^{4} - 24x^{3} + 8x^{2} - 8x + 4 $ x^12 - 2x^11 + 2x^10 - 8x^9 + 4x^8 + 16x^7 - 8x^6 + 20x^5 + 20x^4 - 24x^3 + 8x^2 - 8*x + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			439.5
Root			$0.312819 - 1.16746i$ of defining polynomial
Character	$\chi$	$=$	670.439
Dual form			670.2.h.b.29.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +0.460811i q^{3} +(0.500000 - 0.866025i) q^{4} +(2.00000 + 1.00000i) q^{5} +(0.230406 + 0.399074i) q^{6} +(-4.22565 - 2.43968i) q^{7} -1.00000i q^{8} +2.78765 q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +0.460811i q^{3} +(0.500000 - 0.866025i) q^{4} +(2.00000 + 1.00000i) q^{5} +(0.230406 + 0.399074i) q^{6} +(-4.22565 - 2.43968i) q^{7} -1.00000i q^{8} +2.78765 q^{9} +(2.23205 - 0.133975i) q^{10} +(1.70928 - 2.96055i) q^{11} +(0.399074 + 0.230406i) q^{12} +(-1.48028 + 0.854638i) q^{13} -4.87936 q^{14} +(-0.460811 + 0.921622i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(6.50408 - 3.75513i) q^{17} +(2.41418 - 1.39383i) q^{18} +(-0.460811 - 0.798148i) q^{19} +(1.86603 - 1.23205i) q^{20} +(1.12423 - 1.94723i) q^{21} -3.41855i q^{22} +(5.02380 - 2.90049i) q^{23} +0.460811 q^{24} +(3.00000 + 4.00000i) q^{25} +(-0.854638 + 1.48028i) q^{26} +2.66701i q^{27} +(-4.22565 + 2.43968i) q^{28} +(-1.70928 + 2.96055i) q^{29} +(0.0617370 + 1.02855i) q^{30} +(-3.71594 + 6.43620i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(1.36426 + 0.787653i) q^{33} +(3.75513 - 6.50408i) q^{34} +(-6.01162 - 9.10501i) q^{35} +(1.39383 - 2.41418i) q^{36} +(-1.11780 + 0.645362i) q^{37} +(-0.798148 - 0.460811i) q^{38} +(-0.393827 - 0.682128i) q^{39} +(1.00000 - 2.00000i) q^{40} +(3.81545 - 6.60855i) q^{41} -2.24846i q^{42} +7.60197i q^{43} +(-1.70928 - 2.96055i) q^{44} +(5.57531 + 2.78765i) q^{45} +(2.90049 - 5.02380i) q^{46} +(-3.13290 - 1.80878i) q^{47} +(0.399074 - 0.230406i) q^{48} +(8.40409 + 14.5563i) q^{49} +(4.59808 + 1.96410i) q^{50} +(1.73041 + 2.99715i) q^{51} +1.70928i q^{52} +3.63090i q^{53} +(1.33351 + 2.30970i) q^{54} +(6.37910 - 4.21183i) q^{55} +(-2.43968 + 4.22565i) q^{56} +(0.367796 - 0.212347i) q^{57} +3.41855i q^{58} -7.07838 q^{59} +(0.567743 + 0.859885i) q^{60} +(-6.09530 - 10.5574i) q^{61} +7.43188i q^{62} +(-11.7797 - 6.80098i) q^{63} -1.00000 q^{64} +(-3.81519 + 0.228999i) q^{65} +1.57531 q^{66} +(-7.21126 - 3.87270i) q^{67} -7.51026i q^{68} +(1.33658 + 2.31502i) q^{69} +(-9.75872 - 4.87936i) q^{70} +(-2.79432 + 4.83990i) q^{71} -2.78765i q^{72} +(1.81147 - 1.04585i) q^{73} +(-0.645362 + 1.11780i) q^{74} +(-1.84324 + 1.38243i) q^{75} -0.921622 q^{76} +(-14.4456 + 8.34017i) q^{77} +(-0.682128 - 0.393827i) q^{78} +(-5.39383 + 9.34238i) q^{79} +(-0.133975 - 2.23205i) q^{80} +7.13397 q^{81} -7.63090i q^{82} +(9.78428 - 5.64896i) q^{83} +(-1.12423 - 1.94723i) q^{84} +(16.7633 - 1.00618i) q^{85} +(3.80098 + 6.58350i) q^{86} +(-1.36426 - 0.787653i) q^{87} +(-2.96055 - 1.70928i) q^{88} -5.00000 q^{89} +(6.22218 - 0.373475i) q^{90} +8.34017 q^{91} -5.80098i q^{92} +(-2.96587 - 1.71235i) q^{93} -3.61757 q^{94} +(-0.123474 - 2.05711i) q^{95} +(0.230406 - 0.399074i) q^{96} +(-12.3458 + 7.12783i) q^{97} +(14.5563 + 8.40409i) q^{98} +(4.76487 - 8.25299i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{4} + 24 q^{5} + 6 q^{6} - 8 q^{9}+O(q^{10}) $ 12 * q + 6 * q^4 + 24 * q^5 + 6 * q^6 - 8 * q^9	$ 12 q + 6 q^{4} + 24 q^{5} + 6 q^{6} - 8 q^{9} + 6 q^{10} - 8 q^{11} - 8 q^{14} - 12 q^{15} - 6 q^{16} - 12 q^{19} + 12 q^{20} - 4 q^{21} + 12 q^{24} + 36 q^{25} + 4 q^{26} + 8 q^{29} + 12 q^{30} - 18 q^{31} + 12 q^{34} + 4 q^{35} - 4 q^{36} + 16 q^{39} + 12 q^{40} + 38 q^{41} + 8 q^{44} - 16 q^{45} + 16 q^{46} + 14 q^{49} + 24 q^{50} + 24 q^{51} - 30 q^{54} - 16 q^{55} - 4 q^{56} - 72 q^{59} - 6 q^{60} + 4 q^{61} - 12 q^{64} + 4 q^{65} - 64 q^{66} + 40 q^{69} - 16 q^{70} + 6 q^{71} - 22 q^{74} - 48 q^{75} - 24 q^{76} - 44 q^{79} - 12 q^{80} + 140 q^{81} + 4 q^{84} + 12 q^{85} + 8 q^{86} - 60 q^{89} - 4 q^{90} + 56 q^{91} - 24 q^{94} - 24 q^{95} + 6 q^{96} + 96 q^{99}+O(q^{100}) $ 12 * q + 6 * q^4 + 24 * q^5 + 6 * q^6 - 8 * q^9 + 6 * q^10 - 8 * q^11 - 8 * q^14 - 12 * q^15 - 6 * q^16 - 12 * q^19 + 12 * q^20 - 4 * q^21 + 12 * q^24 + 36 * q^25 + 4 * q^26 + 8 * q^29 + 12 * q^30 - 18 * q^31 + 12 * q^34 + 4 * q^35 - 4 * q^36 + 16 * q^39 + 12 * q^40 + 38 * q^41 + 8 * q^44 - 16 * q^45 + 16 * q^46 + 14 * q^49 + 24 * q^50 + 24 * q^51 - 30 * q^54 - 16 * q^55 - 4 * q^56 - 72 * q^59 - 6 * q^60 + 4 * q^61 - 12 * q^64 + 4 * q^65 - 64 * q^66 + 40 * q^69 - 16 * q^70 + 6 * q^71 - 22 * q^74 - 48 * q^75 - 24 * q^76 - 44 * q^79 - 12 * q^80 + 140 * q^81 + 4 * q^84 + 12 * q^85 + 8 * q^86 - 60 * q^89 - 4 * q^90 + 56 * q^91 - 24 * q^94 - 24 * q^95 + 6 * q^96 + 96 * 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 $

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$			0.460811i			0.266049i	0.991113	+	0.133025i	$0.0424690\pi$
$3$			0.460811i			0.266049i	−0.991113	+	0.133025i	$0.957531\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	2.00000	+	1.00000i	0.894427	+	0.447214i
$5$	2.00000	+	1.00000i	0.894427	+	0.447214i
$6$	0.230406	+	0.399074i	0.0940627	+	0.162921i
$7$	−4.22565	−	2.43968i	−1.59715	−	0.922113i	−0.992034	−	0.125973i	$-0.959795\pi$
$7$	−4.22565	−	2.43968i	−1.59715	−	0.922113i	−0.605112	−	0.796140i	$-0.706872\pi$
$8$		−	1.00000i		−	0.353553i
$9$	2.78765			0.929218
$10$	2.23205	−	0.133975i	0.705836	−	0.0423665i
$11$	1.70928	−	2.96055i	0.515366	−	0.892640i	−0.484475	−	0.874805i	$-0.660989\pi$
$11$	1.70928	−	2.96055i	0.515366	−	0.892640i	0.999841	−	0.0178349i	$-0.00567731\pi$
$12$	0.399074	+	0.230406i	0.115203	+	0.0665124i
$13$	−1.48028	+	0.854638i	−0.410555	+	0.237034i	−0.691028	−	0.722828i	$-0.742842\pi$
$13$	−1.48028	+	0.854638i	−0.410555	+	0.237034i	0.280473	+	0.959862i	$0.409509\pi$
$14$	−4.87936			−1.30406
$15$	−0.460811	+	0.921622i	−0.118981	+	0.237962i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	6.50408	−	3.75513i	1.57747	−	0.910753i	0.582259	−	0.813003i	$-0.302169\pi$
$17$	6.50408	−	3.75513i	1.57747	−	0.910753i	0.995211	−	0.0977493i	$-0.0311643\pi$
$18$	2.41418	−	1.39383i	0.569027	−	0.328528i
$19$	−0.460811	−	0.798148i	−0.105717	−	0.183108i	0.808314	−	0.588752i	$-0.200381\pi$
$19$	−0.460811	−	0.798148i	−0.105717	−	0.183108i	−0.914031	+	0.405644i	$0.867047\pi$
$20$	1.86603	−	1.23205i	0.417256	−	0.275495i
$21$	1.12423	−	1.94723i	0.245328	−	0.424920i
$22$		−	3.41855i		−	0.728837i
$23$	5.02380	−	2.90049i	1.04753	−	0.604794i	0.125576	−	0.992084i	$-0.459922\pi$
$23$	5.02380	−	2.90049i	1.04753	−	0.604794i	0.921958	+	0.387290i	$0.126589\pi$
$24$	0.460811			0.0940627
$25$	3.00000	+	4.00000i	0.600000	+	0.800000i
$26$	−0.854638	+	1.48028i	−0.167608	+	0.290306i
$27$			2.66701i			0.513267i
$28$	−4.22565	+	2.43968i	−0.798573	+	0.461056i
$29$	−1.70928	+	2.96055i	−0.317404	+	0.549761i	−0.979946	−	0.199265i	$-0.936145\pi$
$29$	−1.70928	+	2.96055i	−0.317404	+	0.549761i	0.662541	+	0.749025i	$0.269478\pi$
$30$	0.0617370	+	1.02855i	0.0112716	+	0.187787i
$31$	−3.71594	+	6.43620i	−0.667403	+	1.15598i	0.311225	+	0.950336i	$0.399261\pi$
$31$	−3.71594	+	6.43620i	−0.667403	+	1.15598i	−0.978628	+	0.205639i	$0.934073\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	1.36426	+	0.787653i	0.237486	+	0.137113i
$34$	3.75513	−	6.50408i	0.643999	−	1.11544i
$35$	−6.01162	−	9.10501i	−1.01615	−	1.53903i
$36$	1.39383	−	2.41418i	0.232304	−	0.402363i
$37$	−1.11780	+	0.645362i	−0.183765	+	0.106097i	−0.589061	−	0.808089i	$-0.700502\pi$
$37$	−1.11780	+	0.645362i	−0.183765	+	0.106097i	0.405295	+	0.914186i	$0.367169\pi$
$38$	−0.798148	−	0.460811i	−0.129477	−	0.0747534i
$39$	−0.393827	−	0.682128i	−0.0630627	−	0.109228i
$40$	1.00000	−	2.00000i	0.158114	−	0.316228i
$41$	3.81545	−	6.60855i	0.595873	−	1.03208i	−0.397550	−	0.917580i	$-0.630139\pi$
$41$	3.81545	−	6.60855i	0.595873	−	1.03208i	0.993423	−	0.114502i	$-0.0365272\pi$
$42$		−	2.24846i		−	0.346946i
$43$			7.60197i			1.15929i	0.814869	+	0.579645i	$0.196809\pi$
$43$			7.60197i			1.15929i	−0.814869	+	0.579645i	$0.803191\pi$
$44$	−1.70928	−	2.96055i	−0.257683	−	0.446320i
$45$	5.57531	+	2.78765i	0.831118	+	0.415559i
$46$	2.90049	−	5.02380i	0.427654	−	0.740719i
$47$	−3.13290	−	1.80878i	−0.456981	−	0.263838i	0.253793	−	0.967259i	$-0.418322\pi$
$47$	−3.13290	−	1.80878i	−0.456981	−	0.263838i	−0.710774	+	0.703420i	$0.751655\pi$
$48$	0.399074	−	0.230406i	0.0576014	−	0.0332562i
$49$	8.40409	+	14.5563i	1.20058	+	2.07947i
$50$	4.59808	+	1.96410i	0.650266	+	0.277766i
$51$	1.73041	+	2.99715i	0.242305	+	0.419685i
$52$			1.70928i			0.237034i
$53$			3.63090i			0.498742i	0.968408	+	0.249371i	$0.0802239\pi$
$53$			3.63090i			0.498742i	−0.968408	+	0.249371i	$0.919776\pi$
$54$	1.33351	+	2.30970i	0.181467	+	0.314311i
$55$	6.37910	−	4.21183i	0.860158	−	0.567923i
$56$	−2.43968	+	4.22565i	−0.326016	+	0.564676i
$57$	0.367796	−	0.212347i	0.0487157	−	0.0281260i
$58$			3.41855i			0.448878i
$59$	−7.07838			−0.921526			−0.460763	−	0.887523i	$-0.652424\pi$
$59$	−7.07838			−0.921526			−0.460763	+	0.887523i	$0.652424\pi$
$60$	0.567743	+	0.859885i	0.0732953	+	0.111011i
$61$	−6.09530	−	10.5574i	−0.780424	−	1.35173i	−0.931695	−	0.363241i	$-0.881670\pi$
$61$	−6.09530	−	10.5574i	−0.780424	−	1.35173i	0.151272	−	0.988492i	$-0.451663\pi$
$62$			7.43188i			0.943850i
$63$	−11.7797	−	6.80098i	−1.48410	−	0.856843i
$64$	−1.00000			−0.125000
$65$	−3.81519	+	0.228999i	−0.473216	+	0.0284039i
$66$	1.57531			0.193907
$67$	−7.21126	−	3.87270i	−0.880995	−	0.473125i
$67$	−7.21126	−	3.87270i	−0.880995	−	0.473125i
$68$		−	7.51026i		−	0.910753i
$69$	1.33658	+	2.31502i	0.160905	+	0.278696i
$70$	−9.75872	−	4.87936i	−1.16639	−	0.583195i
$71$	−2.79432	+	4.83990i	−0.331625	+	0.574391i	−0.982831	−	0.184510i	$-0.940930\pi$
$71$	−2.79432	+	4.83990i	−0.331625	+	0.574391i	0.651206	+	0.758901i	$0.274263\pi$
$72$		−	2.78765i		−	0.328528i
$73$	1.81147	−	1.04585i	0.212017	−	0.122408i	−0.390231	−	0.920717i	$-0.627605\pi$
$73$	1.81147	−	1.04585i	0.212017	−	0.122408i	0.602248	+	0.798309i	$0.294272\pi$
$74$	−0.645362	+	1.11780i	−0.0750218	+	0.129942i
$75$	−1.84324	+	1.38243i	−0.212840	+	0.159630i
$76$	−0.921622			−0.105717
$77$	−14.4456	+	8.34017i	−1.64623	+	0.950451i
$78$	−0.682128	−	0.393827i	−0.0772357	−	0.0445921i
$79$	−5.39383	+	9.34238i	−0.606853	+	1.05110i	0.384903	+	0.922957i	$0.374235\pi$
$79$	−5.39383	+	9.34238i	−0.606853	+	1.05110i	−0.991756	+	0.128143i	$0.959098\pi$
$80$	−0.133975	−	2.23205i	−0.0149788	−	0.249551i
$81$	7.13397			0.792663
$82$		−	7.63090i		−	0.842692i
$83$	9.78428	−	5.64896i	1.07396	−	0.620054i	0.144702	−	0.989475i	$-0.453778\pi$
$83$	9.78428	−	5.64896i	1.07396	−	0.620054i	0.929262	+	0.369422i	$0.120444\pi$
$84$	−1.12423	−	1.94723i	−0.122664	−	0.212460i
$85$	16.7633	−	1.00618i	1.81823	−	0.109136i
$86$	3.80098	+	6.58350i	0.409871	+	0.709917i
$87$	−1.36426	−	0.787653i	−0.146264	−	0.0844453i
$88$	−2.96055	−	1.70928i	−0.315596	−	0.182209i
$89$	−5.00000			−0.529999			−0.264999	−	0.964249i	$-0.585372\pi$
$89$	−5.00000			−0.529999			−0.264999	+	0.964249i	$0.585372\pi$
$90$	6.22218	−	0.373475i	0.655876	−	0.0393677i
$91$	8.34017			0.874288
$92$		−	5.80098i		−	0.604794i
$93$	−2.96587	−	1.71235i	−0.307547	−	0.177562i
$94$	−3.61757			−0.373124
$95$	−0.123474	−	2.05711i	−0.0126682	−	0.211055i
$96$	0.230406	−	0.399074i	0.0235157	−	0.0407303i
$97$	−12.3458	+	7.12783i	−1.25352	+	0.723721i	−0.971807	−	0.235777i	$-0.924236\pi$
$97$	−12.3458	+	7.12783i	−1.25352	+	0.723721i	−0.281715	+	0.959498i	$0.590903\pi$
$98$	14.5563	+	8.40409i	1.47041	+	0.848941i
$99$	4.76487	−	8.25299i	0.478887	−	0.829457i
$100$	4.96410	−	0.598076i	0.496410	−	0.0598076i
$101$	3.04585	−	5.27557i	0.303074	−	0.524939i	−0.673757	−	0.738953i	$-0.735320\pi$
$101$	3.04585	−	5.27557i	0.303074	−	0.524939i	0.976831	+	0.214014i	$0.0686538\pi$
$102$	2.99715	+	1.73041i	0.296762	+	0.171336i
$103$	−1.69545	−	0.978870i	−0.167058	−	0.0964509i	0.414140	−	0.910213i	$-0.364082\pi$
$103$	−1.69545	−	0.978870i	−0.167058	−	0.0964509i	−0.581198	+	0.813762i	$0.697416\pi$
$104$	0.854638	+	1.48028i	0.0838041	+	0.145153i
$105$	4.19569	−	2.77022i	0.409458	−	0.270346i
$106$	1.81545	+	3.14445i	0.176332	+	0.305416i
$107$			0.143424i			0.0138654i	0.999976	+	0.00693268i	$0.00220676\pi$
$107$			0.143424i			0.0138654i	−0.999976	+	0.00693268i	$0.997793\pi$
$108$	2.30970	+	1.33351i	0.222251	+	0.128317i
$109$	−18.3474			−1.75736			−0.878679	−	0.477413i	$-0.841575\pi$
$109$	−18.3474			−1.75736			−0.878679	+	0.477413i	$0.841575\pi$
$110$	3.41855	−	6.83710i	0.325946	−	0.651892i
$111$	−0.297390	−	0.515095i	−0.0282270	−	0.0488906i
$112$			4.87936i			0.461056i
$113$	7.19971	+	4.15676i	0.677292	+	0.391035i	0.798834	−	0.601552i	$-0.205451\pi$
$113$	7.19971	+	4.15676i	0.677292	+	0.391035i	−0.121542	+	0.992586i	$0.538784\pi$
$114$	0.212347	−	0.367796i	0.0198881	−	0.0344472i
$115$	12.9481	−	0.777185i	1.20742	−	0.0724728i
$116$	1.70928	+	2.96055i	0.158702	+	0.274880i
$117$	−4.12650	+	2.38243i	−0.381495	+	0.220256i
$118$	−6.13005	+	3.53919i	−0.564317	+	0.325809i
$119$	−36.6453			−3.35927
$120$	0.921622	+	0.460811i	0.0841322	+	0.0420661i
$121$	−0.343245	−	0.594517i	−0.0312040	−	0.0540470i
$122$	−10.5574	−	6.09530i	−0.955820	−	0.551843i
$123$	3.04529	+	1.75820i	0.274585	+	0.158532i
$124$	3.71594	+	6.43620i	0.333701	+	0.577988i
$125$	2.00000	+	11.0000i	0.178885	+	0.983870i
$126$	−13.6020			−1.21176
$127$	5.92110	+	3.41855i	0.525413	+	0.303347i	0.739147	−	0.673545i	$-0.235229\pi$
$127$	5.92110	+	3.41855i	0.525413	+	0.303347i	−0.213734	+	0.976892i	$0.568562\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	−3.50307			−0.308428
$130$	−3.18955	+	2.10591i	−0.279742	+	0.184701i
$131$	10.3246			0.902062			0.451031	−	0.892508i	$-0.351056\pi$
$131$	10.3246			0.902062			0.451031	+	0.892508i	$0.351056\pi$
$132$	1.36426	−	0.787653i	0.118743	−	0.0685564i
$133$			4.49693i			0.389933i
$134$	−8.18148	+	0.251775i	−0.706772	+	0.0217500i
$135$	−2.66701	+	5.33403i	−0.229540	+	0.459080i
$136$	−3.75513	−	6.50408i	−0.322000	−	0.557720i
$137$			21.8504i			1.86681i	0.358827	+	0.933404i	$0.383177\pi$
$137$			21.8504i			1.86681i	−0.358827	+	0.933404i	$0.616823\pi$
$138$	2.31502	+	1.33658i	0.197068	+	0.113777i
$139$	9.60197			0.814428			0.407214	−	0.913333i	$-0.366500\pi$
$139$	9.60197			0.814428			0.407214	+	0.913333i	$0.366500\pi$
$140$	−10.8910	+	0.653711i	−0.920456	+	0.0552486i
$141$	0.833507	−	1.44368i	0.0701940	−	0.121580i
$142$			5.58864i			0.468988i
$143$			5.84324i			0.488637i
$144$	−1.39383	−	2.41418i	−0.116152	−	0.201182i
$145$	−6.37910	+	4.21183i	−0.529756	+	0.349773i
$146$	1.04585	−	1.81147i	0.0865555	−	0.149919i
$147$	−6.70771	+	3.87270i	−0.553242	+	0.319415i
$148$			1.29072i			0.106097i
$149$	−3.14342			−0.257519			−0.128760	−	0.991676i	$-0.541100\pi$
$149$	−3.14342			−0.257519			−0.128760	+	0.991676i	$0.541100\pi$
$150$	−0.905080	+	2.11884i	−0.0738995	+	0.173003i
$151$	9.84377	+	17.0499i	0.801074	+	1.38750i	0.918910	+	0.394468i	$0.129071\pi$
$151$	9.84377	+	17.0499i	0.801074	+	1.38750i	−0.117835	+	0.993033i	$0.537595\pi$
$152$	−0.798148	+	0.460811i	−0.0647384	+	0.0373767i
$153$	18.1311	−	10.4680i	1.46581	−	0.846288i
$154$	−8.34017	+	14.4456i	−0.672070	+	1.16406i
$155$	−13.8681	+	9.15646i	−1.11391	+	0.735464i
$156$	−0.787653			−0.0630627
$157$	−10.1834	+	5.87936i	−0.812720	+	0.469224i	−0.847900	−	0.530157i	$-0.822133\pi$
$157$	−10.1834	+	5.87936i	−0.812720	+	0.469224i	0.0351795	+	0.999381i	$0.488800\pi$
$158$			10.7877i			0.858220i
$159$	−1.67316			−0.132690
$160$	−1.23205	−	1.86603i	−0.0974022	−	0.147522i
$161$	−28.3051			−2.23075
$162$	6.17820	−	3.56698i	0.485405	−	0.280249i
$163$	−14.8143	−	8.55304i	−1.16035	−	0.669926i	−0.208959	−	0.977924i	$-0.567008\pi$
$163$	−14.8143	−	8.55304i	−1.16035	−	0.669926i	−0.951387	+	0.307998i	$0.900341\pi$
$164$	−3.81545	−	6.60855i	−0.297936	−	0.516041i
$165$	1.94086	+	2.93956i	0.151096	+	0.228845i
$166$	5.64896	−	9.78428i	0.438444	−	0.759407i
$167$	20.9694	+	12.1067i	1.62266	+	0.936844i	0.986204	+	0.165532i	$0.0529343\pi$
$167$	20.9694	+	12.1067i	1.62266	+	0.936844i	0.636458	+	0.771312i	$0.280399\pi$
$168$	−1.94723	−	1.12423i	−0.150232	−	0.0867364i
$169$	−5.03919	+	8.72813i	−0.387630	+	0.671395i
$170$	14.0143	−	9.25302i	1.07485	−	0.709674i
$171$	−1.28458	−	2.22496i	−0.0982344	−	0.170147i
$172$	6.58350	+	3.80098i	0.501987	+	0.289822i
$173$	9.66203	−	5.57838i	0.734591	−	0.424116i	−0.0855085	−	0.996337i	$-0.527251\pi$
$173$	9.66203	−	5.57838i	0.734591	−	0.424116i	0.820099	+	0.572221i	$0.193918\pi$
$174$	−1.57531			−0.119424
$175$	−2.91823	−	24.2216i	−0.220597	−	1.83098i
$176$	−3.41855			−0.257683
$177$		−	3.26180i		−	0.245172i
$178$	−4.33013	+	2.50000i	−0.324557	+	0.187383i
$179$	11.1350			0.832270			0.416135	−	0.909303i	$-0.363384\pi$
$179$	11.1350			0.832270			0.416135	+	0.909303i	$0.363384\pi$
$180$	5.20183	−	3.43453i	0.387722	−	0.255995i
$181$	−3.22927	+	5.59326i	−0.240030	+	0.415744i	−0.960723	−	0.277511i	$-0.910491\pi$
$181$	−3.22927	+	5.59326i	−0.240030	+	0.415744i	0.720693	+	0.693255i	$0.243824\pi$
$182$	7.22280	−	4.17009i	0.535390	−	0.309107i
$183$	4.86496	−	2.80878i	0.359628	−	0.207631i
$184$	−2.90049	−	5.02380i	−0.213827	−	0.370359i
$185$	−2.88096	+	0.172924i	−0.211813	+	0.0127136i
$186$	−3.42469			−0.251111
$187$		−	25.6742i		−	1.87748i
$188$	−3.13290	+	1.80878i	−0.228491	+	0.131919i
$189$	6.50667	−	11.2699i	0.473290	−	0.819763i
$190$	−1.13549	−	1.71977i	−0.0823768	−	0.124765i
$191$	6.57058	+	11.3806i	0.475430	+	0.823470i	0.999604	−	0.0281419i	$-0.00895902\pi$
$191$	6.57058	+	11.3806i	0.475430	+	0.823470i	−0.524174	+	0.851611i	$0.675626\pi$
$192$		−	0.460811i		−	0.0332562i
$193$			4.92881i			0.354784i	0.984140	+	0.177392i	$0.0567660\pi$
$193$			4.92881i			0.354784i	−0.984140	+	0.177392i	$0.943234\pi$
$194$	−7.12783	+	12.3458i	−0.511748	+	0.886374i
$195$	−0.105526	−	1.75808i	−0.00755684	−	0.125899i
$196$	16.8082			1.20058
$197$	10.5208	+	6.07417i	0.749574	+	0.432767i	0.825540	−	0.564344i	$-0.190871\pi$
$197$	10.5208	+	6.07417i	0.749574	+	0.432767i	−0.0759658	+	0.997110i	$0.524204\pi$
$198$		−	9.52973i		−	0.677249i
$199$	−7.23041	−	12.5234i	−0.512550	−	0.887762i	−0.999894	−	0.0145525i	$-0.995368\pi$
$199$	−7.23041	−	12.5234i	−0.512550	−	0.887762i	0.487344	−	0.873210i	$-0.337966\pi$
$200$	4.00000	−	3.00000i	0.282843	−	0.212132i
$201$	1.78458	−	3.32303i	0.125875	−	0.234388i
$202$		−	6.09171i		−	0.428611i
$203$	14.4456	−	8.34017i	1.01388	−	0.585365i
$204$	3.46081			0.242305
$205$	14.2394	−	9.40165i	0.994526	−	0.656640i
$206$	−1.95774			−0.136402
$207$	14.0046	−	8.08557i	0.973388	−	0.561986i
$208$	1.48028	+	0.854638i	0.102639	+	0.0592585i
$209$	−3.15061			−0.217932
$210$	2.24846	−	4.49693i	0.155159	−	0.310318i
$211$	0.0995079	+	0.172353i	0.00685041	+	0.0118653i	0.869430	−	0.494056i	$-0.164486\pi$
$211$	0.0995079	+	0.172353i	0.00685041	+	0.0118653i	−0.862580	+	0.505921i	$0.831153\pi$
$212$	3.14445	+	1.81545i	0.215962	+	0.124686i
$213$	−2.23028	−	1.28765i	−0.152816	−	0.0882285i
$214$	0.0717122	+	0.124209i	0.00490215	+	0.00849077i
$215$	−7.60197	+	15.2039i	−0.518450	+	1.03690i
$216$	2.66701			0.181467
$217$	31.4045	−	18.1314i	2.13188	−	1.23084i
$218$	−15.8893	+	9.17368i	−1.07616	+	0.621320i
$219$	0.481941	+	0.834747i	0.0325666	+	0.0564070i
$220$	−0.457999	−	7.63038i	−0.0308783	−	0.514440i
$221$	−6.41855	+	11.1173i	−0.431758	+	0.747828i
$222$	−0.515095	−	0.297390i	−0.0345709	−	0.0199595i
$223$		−	5.57531i		−	0.373350i	−0.982422	−	0.186675i	$-0.940229\pi$
$223$		−	5.57531i		−	0.373350i	0.982422	−	0.186675i	$-0.0597712\pi$
$224$	2.43968	+	4.22565i	0.163008	+	0.282338i
$225$	8.36296	+	11.1506i	0.557531	+	0.743374i
$226$	8.31351			0.553007
$227$	−7.00231	−	4.04278i	−0.464759	−	0.268329i	0.249284	−	0.968430i	$-0.419805\pi$
$227$	−7.00231	−	4.04278i	−0.464759	−	0.268329i	−0.714043	+	0.700101i	$0.753138\pi$
$228$		−	0.424694i		−	0.0281260i
$229$	−12.3438	−	21.3800i	−0.815699	−	1.41283i	−0.908825	−	0.417178i	$-0.863019\pi$
$229$	−12.3438	−	21.3800i	−0.815699	−	1.41283i	0.0931258	−	0.995654i	$-0.470314\pi$
$230$	10.8248	−	7.14711i	0.713765	−	0.471266i
$231$	−3.84324	−	6.65669i	−0.252867	−	0.437978i
$232$	2.96055	+	1.70928i	0.194370	+	0.112219i
$233$	−16.0481	−	9.26539i	−1.05135	−	0.606996i	−0.128321	−	0.991733i	$-0.540959\pi$
$233$	−16.0481	−	9.26539i	−1.05135	−	0.606996i	−0.923026	+	0.384737i	$0.874292\pi$
$234$	−2.38243	+	4.12650i	−0.155745	+	0.269757i
$235$	−4.45703	−	6.75047i	−0.290744	−	0.440352i
$236$	−3.53919	+	6.13005i	−0.230382	+	0.399033i
$237$	−4.30507	−	2.48554i	−0.279645	−	0.161453i
$238$	−31.7357	+	18.3226i	−2.05712	+	1.18768i
$239$	−6.83710	+	11.8422i	−0.442255	+	0.766009i	−0.997856	−	0.0654402i	$-0.979155\pi$
$239$	−6.83710	+	11.8422i	−0.442255	+	0.766009i	0.555601	+	0.831449i	$0.312488\pi$
$240$	1.02855	−	0.0617370i	0.0663929	−	0.00398511i
$241$	−9.97107			−0.642293			−0.321147	−	0.947030i	$-0.604068\pi$
$241$	−9.97107			−0.642293			−0.321147	+	0.947030i	$0.604068\pi$
$242$	−0.594517	−	0.343245i	−0.0382170	−	0.0220646i
$243$			11.2885i			0.724155i
$244$	−12.1906			−0.780424
$245$	2.25187	+	37.5167i	0.143867	+	2.39685i
$246$	3.51640			0.224198
$247$	1.36426	+	0.787653i	0.0868055	+	0.0501172i
$248$	6.43620	+	3.71594i	0.408699	+	0.235962i
$249$	2.60310	+	4.50870i	0.164965	+	0.285728i
$250$	7.23205	+	8.52628i	0.457395	+	0.539249i
$251$	−8.70148	−	15.0714i	−0.549232	−	0.951298i	−0.998327	−	0.0578143i	$-0.981587\pi$
$251$	−8.70148	−	15.0714i	−0.549232	−	0.951298i	0.449095	−	0.893484i	$-0.351746\pi$
$252$	−11.7797	+	6.80098i	−0.742048	+	0.428422i
$253$		−	19.8310i		−	1.24676i
$254$	6.83710			0.428998
$255$	0.463661	+	7.72471i	0.0290356	+	0.483740i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	0.271508	+	0.156755i	0.0169362	+	0.00977814i	0.508444	−	0.861095i	$-0.330221\pi$
$257$	0.271508	+	0.156755i	0.0169362	+	0.00977814i	−0.491508	+	0.870873i	$0.663554\pi$
$258$	−3.03375	+	1.75154i	−0.188873	+	0.109046i
$259$	6.29791			0.391333
$260$	−1.70928	+	3.41855i	−0.106005	+	0.212010i
$261$	−4.76487	+	8.25299i	−0.294938	+	0.510847i
$262$	8.94134	−	5.16229i	0.552398	−	0.318927i
$263$		−	10.8371i		−	0.668244i	−0.942530	−	0.334122i	$-0.891560\pi$
$263$		−	10.8371i		−	0.668244i	0.942530	−	0.334122i	$-0.108440\pi$
$264$	0.787653	−	1.36426i	0.0484767	−	0.0839641i
$265$	−3.63090	+	7.26180i	−0.223044	+	0.446089i
$266$	2.24846	+	3.89445i	0.137862	+	0.238784i
$267$		−	2.30406i		−	0.141006i
$268$	−6.95948	+	4.30878i	−0.425118	+	0.263201i
$269$	13.6163			0.830203			0.415102	−	0.909775i	$-0.363746\pi$
$269$	13.6163			0.830203			0.415102	+	0.909775i	$0.363746\pi$
$270$	0.357312	+	5.95291i	0.0217453	+	0.362283i
$271$	22.2423			1.35112			0.675562	−	0.737303i	$-0.263901\pi$
$271$	22.2423			1.35112			0.675562	+	0.737303i	$0.263901\pi$
$272$	−6.50408	−	3.75513i	−0.394368	−	0.227688i
$273$			3.84324i			0.232604i
$274$	10.9252	+	18.9230i	0.660016	+	1.14318i
$275$	16.9700	−	2.04455i	1.02333	−	0.123291i
$276$	2.67316			0.160905
$277$		−	11.3402i		−	0.681365i	−0.940178	−	0.340682i	$-0.889342\pi$
$277$		−	11.3402i		−	0.681365i	0.940178	−	0.340682i	$-0.110658\pi$
$278$	8.31555	−	4.80098i	0.498733	−	0.287944i
$279$	−10.3588	+	17.9419i	−0.620162	+	1.07415i
$280$	−9.10501	+	6.01162i	−0.544129	+	0.359263i
$281$	−2.48861	−	4.31039i	−0.148458	−	0.257137i	0.782200	−	0.623028i	$-0.214098\pi$
$281$	−2.48861	−	4.31039i	−0.148458	−	0.257137i	−0.930658	+	0.365891i	$0.880764\pi$
$282$		−	1.66701i		−	0.0992693i
$283$			6.57304i			0.390727i	0.980731	+	0.195363i	$0.0625886\pi$
$283$			6.57304i			0.390727i	−0.980731	+	0.195363i	$0.937411\pi$
$284$	2.79432	+	4.83990i	0.165812	+	0.287195i
$285$	0.947938	−	0.0568982i	0.0561510	−	0.00337036i
$286$	2.92162	+	5.06040i	0.172759	+	0.299228i
$287$	−32.2455	+	18.6170i	−1.90339	+	1.09892i
$288$	−2.41418	−	1.39383i	−0.142257	−	0.0821320i
$289$	19.7020	−	34.1249i	1.15894	−	2.00734i
$290$	−3.41855	+	6.83710i	−0.200744	+	0.401488i
$291$	−3.28458	−	5.68906i	−0.192546	−	0.333499i
$292$		−	2.09171i		−	0.122408i
$293$		−	9.48852i		−	0.554325i	−0.960823	−	0.277163i	$-0.910606\pi$
$293$		−	9.48852i		−	0.554325i	0.960823	−	0.277163i	$-0.0893941\pi$
$294$	−3.87270	+	6.70771i	−0.225860	+	0.391201i
$295$	−14.1568	−	7.07838i	−0.824238	−	0.412119i
$296$	0.645362	+	1.11780i	0.0375109	+	0.0649708i
$297$	7.89584	+	4.55866i	0.458163	+	0.264520i
$298$	−2.72229	+	1.57171i	−0.157698	+	0.0910468i
$299$	−4.95774	+	8.58706i	−0.286713	+	0.496602i
$300$	0.275600	+	2.28751i	0.0159118	+	0.132070i
$301$	18.5464	−	32.1233i	1.06900	−	1.85155i
$302$	17.0499	+	9.84377i	0.981112	+	0.566445i
$303$	2.43104	+	1.40356i	0.139660	+	0.0806326i
$304$	−0.460811	+	0.798148i	−0.0264293	+	0.0457769i
$305$	−1.63323	−	27.2101i	−0.0935186	−	1.55804i
$306$	10.4680	−	18.1311i	0.598416	−	1.03649i
$307$	27.1673	−	15.6851i	1.55052	−	0.895194i	0.552423	−	0.833564i	$-0.313703\pi$
$307$	27.1673	−	15.6851i	1.55052	−	0.895194i	0.998099	−	0.0616306i	$-0.0196301\pi$
$308$			16.6803i			0.950451i
$309$	0.451074	−	0.781283i	0.0256607	−	0.0444457i
$310$	−7.43188	+	14.8638i	−0.422103	+	0.844205i
$311$	8.58637			0.486888			0.243444	−	0.969915i	$-0.421723\pi$
$311$	8.58637			0.486888			0.243444	+	0.969915i	$0.421723\pi$
$312$	−0.682128	+	0.393827i	−0.0386179	+	0.0222960i
$313$			13.3607i			0.755191i	0.925971	+	0.377595i	$0.123249\pi$
$313$			13.3607i			0.755191i	−0.925971	+	0.377595i	$0.876751\pi$
$314$	−5.87936	+	10.1834i	−0.331792	+	0.574680i
$315$	−16.7583	−	25.3816i	−0.944224	−	1.43009i
$316$	5.39383	+	9.34238i	0.303426	+	0.525550i
$317$	6.37987	−	3.68342i	0.358329	−	0.206881i	−0.310019	−	0.950731i	$-0.600335\pi$
$317$	6.37987	−	3.68342i	0.358329	−	0.206881i	0.668348	+	0.743849i	$0.267002\pi$
$318$	−1.44900	+	0.836579i	−0.0812557	+	0.0469130i
$319$	5.84324	+	10.1208i	0.327159	+	0.566656i
$320$	−2.00000	−	1.00000i	−0.111803	−	0.0559017i
$321$	−0.0660916			−0.00368887
$322$	−24.5129	+	14.1526i	−1.36605	+	0.788691i
$323$	−5.99430	−	3.46081i	−0.333532	−	0.192565i
$324$	3.56698	−	6.17820i	0.198166	−	0.343233i
$325$	−7.85938	−	3.35719i	−0.435960	−	0.186223i
$326$	−17.1061			−0.947418
$327$		−	8.45467i		−	0.467544i
$328$	−6.60855	−	3.81545i	−0.364896	−	0.210673i
$329$	8.82571	+	15.2866i	0.486577	+	0.842776i
$330$	3.15061	+	1.57531i	0.173436	+	0.0867178i
$331$	−15.3474	+	26.5824i	−0.843567	+	1.46110i	0.0432924	+	0.999062i	$0.486215\pi$
$331$	−15.3474	+	26.5824i	−0.843567	+	1.46110i	−0.886860	+	0.462039i	$0.847118\pi$
$332$		−	11.2979i		−	0.620054i
$333$	−3.11604	+	1.79905i	−0.170758	+	0.0985871i
$334$	24.2134			1.32490
$335$	−10.5498	−	14.9566i	−0.576398	−	0.817169i
$336$	−2.24846			−0.122664
$337$	−12.4483	+	7.18701i	−0.678100	+	0.391501i	−0.799139	−	0.601146i	$-0.794711\pi$
$337$	−12.4483	+	7.18701i	−0.678100	+	0.391501i	0.121039	+	0.992648i	$0.461378\pi$
$338$			10.0784i			0.548191i
$339$	−1.91548	+	3.31771i	−0.104035	+	0.180193i
$340$	7.51026	−	15.0205i	0.407301	−	0.814602i
$341$	12.7031	+	22.0025i	0.687913	+	1.19150i
$342$	−2.22496	−	1.28458i	−0.120312	−	0.0694622i
$343$		−	47.8576i		−	2.58407i
$344$	7.60197			0.409871
$345$	0.358135	+	5.96662i	0.0192814	+	0.321232i
$346$	5.57838	−	9.66203i	0.299895	−	0.519434i
$347$	−8.84219	−	5.10504i	−0.474674	−	0.274053i	0.243521	−	0.969896i	$-0.421698\pi$
$347$	−8.84219	−	5.10504i	−0.474674	−	0.274053i	−0.718194	+	0.695843i	$0.755031\pi$
$348$	−1.36426	+	0.787653i	−0.0731318	+	0.0422226i
$349$	3.05172			0.163355			0.0816773	−	0.996659i	$-0.473972\pi$
$349$	3.05172			0.163355			0.0816773	+	0.996659i	$0.473972\pi$
$350$	−14.6381	−	19.5174i	−0.782439	−	1.04325i
$351$	−2.27933	−	3.94792i	−0.121662	−	0.210724i
$352$	−2.96055	+	1.70928i	−0.157798	+	0.0911047i
$353$	1.78838	−	1.03252i	0.0951860	−	0.0549557i	−0.451651	−	0.892194i	$-0.649165\pi$
$353$	1.78838	−	1.03252i	0.0951860	−	0.0549557i	0.546837	+	0.837239i	$0.315832\pi$
$354$	−1.63090	−	2.82480i	−0.0866812	−	0.150136i
$355$	−10.4285	+	6.88548i	−0.553489	+	0.365444i
$356$	−2.50000	+	4.33013i	−0.132500	+	0.229496i
$357$		−	16.8865i		−	0.893731i
$358$	9.64320	−	5.56751i	0.509659	−	0.294252i
$359$	−27.3162			−1.44169			−0.720846	−	0.693095i	$-0.756247\pi$
$359$	−27.3162			−1.44169			−0.720846	+	0.693095i	$0.756247\pi$
$360$	2.78765	−	5.57531i	0.146922	−	0.293844i
$361$	9.07531	−	15.7189i	0.477648	−	0.827310i
$362$			6.45854i			0.339454i
$363$	0.273960	−	0.158171i	0.0143792	−	0.00830182i
$364$	4.17009	−	7.22280i	0.218572	−	0.378578i
$365$	4.66880	−	0.280236i	0.244376	−	0.0146682i
$366$	2.80878	−	4.86496i	0.146817	−	0.254295i
$367$	4.38450	+	2.53139i	0.228869	+	0.132137i	0.610050	−	0.792363i	$-0.291149\pi$
$367$	4.38450	+	2.53139i	0.228869	+	0.132137i	−0.381181	+	0.924500i	$0.624483\pi$
$368$	−5.02380	−	2.90049i	−0.261884	−	0.151199i
$369$	10.6361	−	18.4223i	0.553696	−	0.959029i
$370$	−2.40852	+	1.59024i	−0.125213	+	0.0826726i
$371$	8.85823	−	15.3429i	0.459896	−	0.796564i
$372$	−2.96587	+	1.71235i	−0.153773	+	0.0887811i
$373$	4.48897	+	2.59171i	0.232430	+	0.134194i	0.611693	−	0.791096i	$-0.290489\pi$
$373$	4.48897	+	2.59171i	0.232430	+	0.134194i	−0.379263	+	0.925289i	$0.623822\pi$
$374$	−12.8371	−	22.2345i	−0.663791	−	1.14972i
$375$	−5.06892	+	0.921622i	−0.261758	+	0.0475924i
$376$	−1.80878	+	3.13290i	−0.0932809	+	0.161567i
$377$		−	5.84324i		−	0.300942i
$378$		−	13.0133i		−	0.669334i
$379$	−15.6875	−	27.1716i	−0.805814	−	1.39571i	−0.915740	−	0.401772i	$-0.868395\pi$
$379$	−15.6875	−	27.1716i	−0.805814	−	1.39571i	0.109925	−	0.993940i	$-0.464939\pi$
$380$	−1.84324	−	0.921622i	−0.0945564	−	0.0472782i
$381$	−1.57531	+	2.72851i	−0.0807054	+	0.139786i
$382$	11.3806	+	6.57058i	0.582281	+	0.336180i
$383$	20.0721	−	11.5886i	1.02564	−	0.592152i	0.109905	−	0.993942i	$-0.464945\pi$
$383$	20.0721	−	11.5886i	1.02564	−	0.592152i	0.915732	+	0.401790i	$0.131612\pi$
$384$	−0.230406	−	0.399074i	−0.0117578	−	0.0203652i
$385$	−37.2314	+	2.23474i	−1.89749	+	0.113893i
$386$	2.46441	+	4.26847i	0.125435	+	0.217260i
$387$			21.1917i			1.07723i
$388$			14.2557i			0.723721i
$389$	10.8758	+	18.8374i	0.551423	+	0.955093i	0.998172	+	0.0604338i	$0.0192484\pi$
$389$	10.8758	+	18.8374i	0.551423	+	0.955093i	−0.446749	+	0.894659i	$0.647418\pi$
$390$	−0.970429	−	1.46978i	−0.0491396	−	0.0744252i
$391$	21.7834	−	37.7300i	1.10164	−	1.90809i
$392$	14.5563	−	8.40409i	0.735204	−	0.424470i
$393$			4.75768i			0.239993i
$394$	12.1483			0.612025
$395$	−20.1300	+	13.2909i	−1.01285	+	0.668740i
$396$	−4.76487	−	8.25299i	−0.239444	−	0.414728i
$397$		−	31.9588i		−	1.60397i	−0.597347	−	0.801983i	$-0.703779\pi$
$397$		−	31.9588i		−	1.60397i	0.597347	−	0.801983i	$-0.296221\pi$
$398$	−12.5234	−	7.23041i	−0.627743	−	0.362427i
$399$	−2.07223			−0.103741
$400$	1.96410	−	4.59808i	0.0982051	−	0.229904i
$401$	26.3896			1.31783			0.658917	−	0.752215i	$-0.271015\pi$
$401$	26.3896			1.31783			0.658917	+	0.752215i	$0.271015\pi$
$402$	−0.116021	−	3.77012i	−0.00578659	−	0.188036i
$403$		−	12.7031i		−	0.632788i
$404$	−3.04585	−	5.27557i	−0.151537	−	0.262470i
$405$	14.2679	+	7.13397i	0.708980	+	0.354490i
$406$	8.34017	−	14.4456i	0.413916	−	0.716923i
$407$			4.41241i			0.218715i
$408$	2.99715	−	1.73041i	0.148381	−	0.0856678i
$409$	−18.8721	+	32.6874i	−0.933165	+	1.61629i	−0.155290	+	0.987869i	$0.549631\pi$
$409$	−18.8721	+	32.6874i	−0.933165	+	1.61629i	−0.777875	+	0.628419i	$0.783702\pi$
$410$	7.63090	−	15.2618i	0.376863	−	0.753726i
$411$	−10.0689			−0.496663
$412$	−1.69545	+	0.978870i	−0.0835289	+	0.0482255i
$413$	29.9108	+	17.2690i	1.47181	+	0.849751i
$414$	8.08557	−	14.0046i	0.397384	−	0.688289i
$415$	25.2175	−	1.51363i	1.23788	−	0.0743013i
$416$	1.70928			0.0838041
$417$			4.42469i			0.216678i
$418$	−2.72851	+	1.57531i	−0.133456	+	0.0770507i
$419$	−5.58864	−	9.67980i	−0.273023	−	0.472889i	0.696612	−	0.717448i	$-0.254690\pi$
$419$	−5.58864	−	9.67980i	−0.273023	−	0.472889i	−0.969634	+	0.244559i	$0.921357\pi$
$420$	−0.301237	−	5.01869i	−0.0146989	−	0.244887i
$421$	5.63090	+	9.75300i	0.274433	+	0.475332i	0.969992	−	0.243137i	$-0.0781765\pi$
$421$	5.63090	+	9.75300i	0.274433	+	0.475332i	−0.695559	+	0.718469i	$0.744843\pi$
$422$	0.172353	+	0.0995079i	0.00839000	+	0.00484397i
$423$	−8.73345	−	5.04226i	−0.424635	−	0.245163i
$424$	3.63090			0.176332
$425$	34.5327	+	14.7509i	1.67508	+	0.715524i
$426$	−2.57531			−0.124774
$427$			59.4824i			2.87855i
$428$	0.124209	+	0.0717122i	0.00600388	+	0.00346634i
$429$	−2.69263			−0.130002
$430$	1.01847	+	16.9680i	0.0491150	+	0.818269i
$431$	1.64896	−	2.85608i	0.0794274	−	0.137572i	−0.823576	−	0.567206i	$-0.808024\pi$
$431$	1.64896	−	2.85608i	0.0794274	−	0.137572i	0.903003	+	0.429634i	$0.141357\pi$
$432$	2.30970	−	1.33351i	0.111126	−	0.0641584i
$433$	−4.79511	−	2.76846i	−0.230439	−	0.133044i	0.380336	−	0.924848i	$-0.375808\pi$
$433$	−4.79511	−	2.76846i	−0.230439	−	0.133044i	−0.610774	+	0.791805i	$0.709142\pi$
$434$	18.1314	−	31.4045i	0.870336	−	1.50747i
$435$	−1.94086	−	2.93956i	−0.0930570	−	0.140941i
$436$	−9.17368	+	15.8893i	−0.439340	+	0.760959i
$437$	−4.63005	−	2.67316i	−0.221485	−	0.127874i
$438$	0.834747	+	0.481941i	0.0398857	+	0.0230280i
$439$	8.75206	+	15.1590i	0.417713	+	0.723500i	0.995709	−	0.0925395i	$-0.0294984\pi$
$439$	8.75206	+	15.1590i	0.417713	+	0.723500i	−0.577996	+	0.816040i	$0.696165\pi$
$440$	−4.21183	−	6.37910i	−0.200791	−	0.304112i
$441$	23.4277	+	40.5779i	1.11560	+	1.93228i
$442$			12.8371i			0.610599i
$443$	−7.19152	−	4.15203i	−0.341680	−	0.197269i	0.319335	−	0.947642i	$-0.396541\pi$
$443$	−7.19152	−	4.15203i	−0.341680	−	0.197269i	−0.661015	+	0.750373i	$0.729874\pi$
$444$	−0.594780			−0.0282270
$445$	−10.0000	−	5.00000i	−0.474045	−	0.237023i
$446$	−2.78765	−	4.82836i	−0.131999	−	0.228629i
$447$		−	1.44852i		−	0.0685129i
$448$	4.22565	+	2.43968i	0.199643	+	0.115264i
$449$	15.1803	−	26.2931i	0.716405	−	1.24085i	−0.246010	−	0.969267i	$-0.579120\pi$
$449$	15.1803	−	26.2931i	0.716405	−	1.24085i	0.962415	−	0.271582i	$-0.0875469\pi$
$450$	12.8178	+	5.47523i	0.604239	+	0.258105i
$451$	−13.0433	−	22.5917i	−0.614185	−	1.06380i
$452$	7.19971	−	4.15676i	0.338646	−	0.195517i
$453$	−7.85679	+	4.53612i	−0.369144	+	0.213125i
$454$	−8.08557			−0.379474
$455$	16.6803	+	8.34017i	0.781987	+	0.390993i
$456$	−0.212347	−	0.367796i	−0.00994405	−	0.0172236i
$457$	13.2002	+	7.62116i	0.617481	+	0.356503i	0.775888	−	0.630871i	$-0.217302\pi$
$457$	13.2002	+	7.62116i	0.617481	+	0.356503i	−0.158407	+	0.987374i	$0.550636\pi$
$458$	−21.3800	−	12.3438i	−0.999023	−	0.576786i
$459$	10.0150	+	17.3465i	0.467460	+	0.809664i
$460$	5.80098	−	11.6020i	0.270472	−	0.540945i
$461$	−21.9083			−1.02037			−0.510185	−	0.860064i	$-0.670423\pi$
$461$	−21.9083			−1.02037			−0.510185	+	0.860064i	$0.670423\pi$
$462$	−6.65669	−	3.84324i	−0.309697	−	0.178804i
$463$	−17.3926	+	10.0416i	−0.808305	+	0.466675i	−0.846367	−	0.532600i	$-0.821215\pi$
$463$	−17.3926	+	10.0416i	−0.808305	+	0.466675i	0.0380620	+	0.999275i	$0.487882\pi$
$464$	3.41855			0.158702
$465$	−4.21940	−	6.39057i	−0.195670	−	0.296355i
$466$	−18.5308			−0.858422
$467$	9.78428	−	5.64896i	0.452762	−	0.261403i	−0.256234	−	0.966615i	$-0.582482\pi$
$467$	9.78428	−	5.64896i	0.452762	−	0.261403i	0.708996	+	0.705212i	$0.249148\pi$
$468$			4.76487i			0.220256i
$469$	21.0241	+	33.9578i	0.970803	+	1.56803i
$470$	−7.23513	−	3.61757i	−0.333732	−	0.166866i
$471$	−2.70928	−	4.69260i	−0.124837	−	0.216224i
$472$			7.07838i			0.325809i
$473$	22.5060	+	12.9939i	1.03483	+	0.597458i
$474$	−4.97107			−0.228329
$475$	1.81016	−	4.23769i	0.0830558	−	0.194439i
$476$	−18.3226	+	31.7357i	−0.839817	+	1.45461i
$477$			10.1217i			0.463440i
$478$			13.6742i			0.625443i
$479$	−6.68035	−	11.5707i	−0.305233	−	0.528679i	0.672080	−	0.740478i	$-0.265401\pi$
$479$	−6.68035	−	11.5707i	−0.305233	−	0.528679i	−0.977313	+	0.211800i	$0.932068\pi$
$480$	0.859885	−	0.567743i	0.0392482	−	0.0259138i
$481$	1.10310	−	1.91063i	0.0502971	−	0.0871172i
$482$	−8.63520	+	4.98554i	−0.393323	+	0.227085i
$483$		−	13.0433i		−	0.593491i
$484$	−0.686489			−0.0312040
$485$	−31.8193	+	1.90990i	−1.44484	+	0.0867239i
$486$	5.64423	+	9.77609i	0.256027	+	0.443452i
$487$	6.30241	−	3.63870i	0.285589	−	0.164885i	−0.350362	−	0.936614i	$-0.613941\pi$
$487$	6.30241	−	3.63870i	0.285589	−	0.164885i	0.635951	+	0.771729i	$0.280608\pi$
$488$	−10.5574	+	6.09530i	−0.477910	+	0.275921i
$489$	3.94134	−	6.82660i	0.178233	−	0.308709i
$490$	20.7085	+	31.3645i	0.935516	+	1.41690i
$491$	−39.5018			−1.78269			−0.891347	−	0.453322i	$-0.850239\pi$
$491$	−39.5018			−1.78269			−0.891347	+	0.453322i	$0.850239\pi$
$492$	3.04529	−	1.75820i	0.137292	−	0.0792658i
$493$			25.6742i			1.15631i
$494$	1.57531			0.0708764
$495$	17.7827	−	11.7411i	0.799274	−	0.527724i
$496$	7.43188			0.333701
$497$	23.6156	−	13.6345i	1.05931	−	0.611591i
$498$	4.50870	+	2.60310i	0.202040	+	0.116648i
$499$	−5.06505	−	8.77292i	−0.226743	−	0.392730i	0.730098	−	0.683342i	$-0.239474\pi$
$499$	−5.06505	−	8.77292i	−0.226743	−	0.392730i	−0.956841	+	0.290612i	$0.906141\pi$
$500$	10.5263	+	3.76795i	0.470750	+	0.168508i
$501$	−5.57890	+	9.66294i	−0.249247	+	0.431708i
$502$	−15.0714	−	8.70148i	−0.672669	−	0.388366i
$503$	−3.54975	−	2.04945i	−0.158275	−	0.0913804i	0.418770	−	0.908092i	$-0.362461\pi$
$503$	−3.54975	−	2.04945i	−0.158275	−	0.0913804i	−0.577046	+	0.816712i	$0.695795\pi$
$504$	−6.80098	+	11.7797i	−0.302940	+	0.524707i
$505$	11.3673	−	7.50529i	0.505837	−	0.333981i
$506$	−9.91548	−	17.1741i	−0.440797	−	0.763482i
$507$	−4.02202	−	2.32211i	−0.178624	−	0.103129i
$508$	5.92110	−	3.41855i	0.262706	−	0.151674i
$509$	4.82991			0.214082			0.107041	−	0.994255i	$-0.465862\pi$
$509$	4.82991			0.214082			0.107041	+	0.994255i	$0.465862\pi$
$510$	4.26390	+	6.45796i	0.188808	+	0.285963i
$511$	−10.2062			−0.451496
$512$			1.00000i			0.0441942i
$513$	2.12867	−	1.22899i	0.0939832	−	0.0542612i
$514$	0.313511			0.0138284
$515$	−2.41203	−	3.65319i	−0.106287	−	0.160979i
$516$	−1.75154	+	3.03375i	−0.0771071	+	0.133553i
$517$	−10.7100	+	6.18342i	−0.471025	+	0.271946i
$518$	5.45415	−	3.14896i	0.239642	−	0.138357i
$519$	2.57058	+	4.45237i	0.112836	+	0.195437i
$520$	0.228999	+	3.81519i	0.0100423	+	0.167307i
$521$	−30.9711			−1.35687			−0.678434	−	0.734662i	$-0.737341\pi$
$521$	−30.9711			−1.35687			−0.678434	+	0.734662i	$0.737341\pi$
$522$			9.52973i			0.417105i
$523$	1.37580	−	0.794319i	0.0601595	−	0.0347331i	−0.469619	−	0.882869i	$-0.655609\pi$
$523$	1.37580	−	0.794319i	0.0601595	−	0.0347331i	0.529778	+	0.848136i	$0.322275\pi$
$524$	5.16229	−	8.94134i	0.225516	−	0.390604i
$525$	11.1616	−	1.34475i	0.487132	−	0.0586898i
$526$	−5.41855	−	9.38521i	−0.236260	−	0.409214i
$527$			55.8154i			2.43136i
$528$		−	1.57531i		−	0.0685564i
$529$	5.32571	−	9.22440i	0.231553	−	0.401061i
$530$	0.486448	+	8.10435i	0.0211300	+	0.352030i
$531$	−19.7321			−0.856299
$532$	3.89445	+	2.24846i	0.168846	+	0.0974833i
$533$			13.0433i			0.564968i
$534$	−1.15203	−	1.99537i	−0.0498531	−	0.0863481i
$535$	−0.143424	+	0.286849i	−0.00620078	+	0.0124016i
$536$	−3.87270	+	7.21126i	−0.167275	+	0.311479i
$537$			5.13114i			0.221425i
$538$	11.7921	−	6.80817i	0.508394	−	0.293521i
$539$	57.4596			2.47496
$540$	3.28590	+	4.97672i	0.141403	+	0.214164i
$541$	37.3028			1.60377			0.801887	−	0.597476i	$-0.203830\pi$
$541$	37.3028			1.60377			0.801887	+	0.597476i	$0.203830\pi$
$542$	19.2624	−	11.1212i	0.827392	−	0.477695i
$543$	−2.57744	−	1.48808i	−0.110608	−	0.0638598i
$544$	−7.51026			−0.322000
$545$	−36.6947	−	18.3474i	−1.57183	−	0.785915i
$546$	1.92162	+	3.32835i	0.0822378	+	0.142440i
$547$	13.0236	+	7.51919i	0.556850	+	0.321497i	0.751880	−	0.659300i	$-0.229147\pi$
$547$	13.0236	+	7.51919i	0.556850	+	0.321497i	−0.195030	+	0.980797i	$0.562481\pi$
$548$	18.9230	+	10.9252i	0.808352	+	0.466702i
$549$	−16.9916	−	29.4303i	−0.725183	−	1.25605i
$550$	13.6742	−	10.2557i	0.583070	−	0.437302i
$551$	3.15061			0.134221
$552$	2.31502	−	1.33658i	0.0985339	−	0.0568886i
$553$	45.5849	−	26.3184i	1.93847	−	1.11917i
$554$	−5.67009	−	9.82088i	−0.240899	−	0.417249i
$555$	−0.0796854	−	1.32758i	−0.00338246	−	0.0563526i
$556$	4.80098	−	8.31555i	0.203607	−	0.352658i
$557$	−25.0613	−	14.4691i	−1.06188	−	0.613077i	−0.135928	−	0.990719i	$-0.543402\pi$
$557$	−25.0613	−	14.4691i	−1.06188	−	0.613077i	−0.925952	+	0.377642i	$0.876735\pi$
$558$			20.7175i			0.877042i
$559$	−6.49693	−	11.2530i	−0.274791	−	0.475952i
$560$	−4.87936	+	9.75872i	−0.206191	+	0.412381i
$561$	11.8310			0.499503
$562$	−4.31039	−	2.48861i	−0.181823	−	0.104976i
$563$		−	14.3268i		−	0.603804i	−0.953339	−	0.301902i	$-0.902378\pi$
$563$		−	14.3268i		−	0.603804i	0.953339	−	0.301902i	$-0.0976216\pi$
$564$	−0.833507	−	1.44368i	−0.0350970	−	0.0607898i
$565$	10.2427	+	15.5132i	0.430912	+	0.652646i
$566$	3.28652	+	5.69242i	0.138143	+	0.239270i
$567$	−30.1457	−	17.4046i	−1.26600	−	0.730925i
$568$	4.83990	+	2.79432i	0.203078	+	0.117247i
$569$	1.63203	−	2.82676i	0.0684183	−	0.118504i	−0.829787	−	0.558080i	$-0.811538\pi$
$569$	1.63203	−	2.82676i	0.0684183	−	0.118504i	0.898205	+	0.439576i	$0.144871\pi$
$570$	0.792489	−	0.523244i	0.0331937	−	0.0219163i
$571$	−14.8010	+	25.6361i	−0.619402	+	1.07284i	0.370193	+	0.928955i	$0.379292\pi$
$571$	−14.8010	+	25.6361i	−0.619402	+	1.07284i	−0.989595	+	0.143881i	$0.954042\pi$
$572$	5.06040	+	2.92162i	0.211586	+	0.122159i
$573$	−5.24430	+	3.02780i	−0.219084	+	0.126488i
$574$	−18.6170	+	32.2455i	−0.777057	+	1.34590i
$575$	26.6734	+	11.3937i	1.11236	+	0.475151i
$576$	−2.78765			−0.116152
$577$	−3.65619	−	2.11090i	−0.152209	−	0.0878780i	0.421961	−	0.906614i	$-0.361342\pi$
$577$	−3.65619	−	2.11090i	−0.152209	−	0.0878780i	−0.574170	+	0.818736i	$0.694675\pi$
$578$		−	39.4040i		−	1.63899i
$579$	−2.27125			−0.0943900
$580$	0.457999	+	7.63038i	0.0190174	+	0.316834i
$581$	−55.1266			−2.28704
$582$	−5.68906	−	3.28458i	−0.235819	−	0.136150i
$583$	10.7495	+	6.20620i	0.445197	+	0.257035i
$584$	−1.04585	−	1.81147i	−0.0432778	−	0.0749593i
$585$	−10.6354	+	0.638371i	−0.439721	+	0.0263934i
$586$	−4.74426	−	8.21730i	−0.195984	−	0.339453i
$587$	−5.62224	+	3.24600i	−0.232055	+	0.133977i	−0.611520	−	0.791229i	$-0.709441\pi$
$587$	−5.62224	+	3.24600i	−0.232055	+	0.133977i	0.379465	+	0.925206i	$0.376108\pi$
$588$			7.74539i			0.319415i
$589$	6.84939			0.282224
$590$	−15.7993	+	0.948323i	−0.650447	+	0.0390418i
$591$	−2.79905	+	4.84809i	−0.115137	+	0.199424i
$592$	1.11780	+	0.645362i	0.0459413	+	0.0265242i
$593$	−18.7203	+	10.8082i	−0.768751	+	0.443838i	−0.832429	−	0.554132i	$-0.813050\pi$
$593$	−18.7203	+	10.8082i	−0.768751	+	0.443838i	0.0636781	+	0.997970i	$0.479717\pi$
$594$	9.11733			0.374088
$595$	−73.2905	−	36.6453i	−3.00462	−	1.50231i
$596$	−1.57171	+	2.72229i	−0.0643798	+	0.111509i
$597$	5.77094	−	3.33185i	0.236189	−	0.136364i
$598$			9.91548i			0.405474i
$599$	7.44521	−	12.8955i	0.304203	−	0.526895i	−0.672880	−	0.739751i	$-0.734943\pi$
$599$	7.44521	−	12.8955i	0.304203	−	0.526895i	0.977084	+	0.212856i	$0.0682765\pi$
$600$	1.38243	+	1.84324i	0.0564376	+	0.0752501i
$601$	−20.0319	−	34.6963i	−0.817119	−	1.41529i	−0.907797	−	0.419411i	$-0.862237\pi$
$601$	−20.0319	−	34.6963i	−0.817119	−	1.41529i	0.0906778	−	0.995880i	$-0.471097\pi$
$602$		−	37.0928i		−	1.51179i
$603$	−20.1025	−	10.7957i	−0.818636	−	0.439636i
$604$	19.6875			0.801074
$605$	−0.0919721	−	1.53228i	−0.00373920	−	0.0622960i
$606$	2.80713			0.114032
$607$	14.6546	+	8.46081i	0.594810	+	0.343414i	0.766997	−	0.641651i	$-0.221750\pi$
$607$	14.6546	+	8.46081i	0.594810	+	0.343414i	−0.172187	+	0.985064i	$0.555083\pi$
$608$			0.921622i			0.0373767i
$609$	3.84324	+	6.65669i	0.155736	+	0.269743i
$610$	−15.0194	−	22.7480i	−0.608120	−	0.921039i
$611$	6.18342			0.250154
$612$		−	20.9360i		−	0.846288i
$613$	−15.3472	+	8.86069i	−0.619866	+	0.357880i	−0.776817	−	0.629726i	$-0.783167\pi$
$613$	−15.3472	+	8.86069i	−0.619866	+	0.357880i	0.156951	+	0.987606i	$0.449834\pi$
$614$	15.6851	−	27.1673i	0.632998	−	1.09638i
$615$	4.33239	+	6.56170i	0.174699	+	0.264593i
$616$	8.34017	+	14.4456i	0.336035	+	0.582030i
$617$			10.0917i			0.406277i	0.979150	+	0.203138i	$0.0651142\pi$
$617$			10.0917i			0.406277i	−0.979150	+	0.203138i	$0.934886\pi$
$618$		−	0.902148i		−	0.0362897i
$619$	6.02832	+	10.4414i	0.242299	+	0.419673i	0.961369	−	0.275264i	$-0.0887653\pi$
$619$	6.02832	+	10.4414i	0.242299	+	0.419673i	−0.719070	+	0.694938i	$0.755432\pi$
$620$	0.995683	+	16.5883i	0.0399876	+	0.666204i
$621$	7.73566	+	13.3985i	0.310421	+	0.537665i
$622$	7.43601	−	4.29318i	0.298157	−	0.172141i
$623$	21.1283	+	12.1984i	0.846486	+	0.488719i
$624$	−0.393827	+	0.682128i	−0.0157657	+	0.0273070i
$625$	−7.00000	+	24.0000i	−0.280000	+	0.960000i
$626$	6.68035	+	11.5707i	0.267000	+	0.462458i
$627$		−	1.45184i		−	0.0579808i
$628$			11.7587i			0.469224i
$629$	−4.84684	+	8.39497i	−0.193256	+	0.334729i
$630$	−27.2039	−	13.6020i	−1.08383	−	0.541915i
$631$	6.59583	+	11.4243i	0.262576	+	0.454794i	0.966926	−	0.255059i	$-0.0820947\pi$
$631$	6.59583	+	11.4243i	0.262576	+	0.454794i	−0.704350	+	0.709853i	$0.748761\pi$
$632$	9.34238	+	5.39383i	0.371620	+	0.214555i
$633$	−0.0794221	+	0.0458544i	−0.00315675	+	0.00182255i
$634$	3.68342	−	6.37987i	0.146287	−	0.253377i
$635$	8.42366	+	12.7582i	0.334283	+	0.506294i
$636$	−0.836579	+	1.44900i	−0.0331725	+	0.0574565i
$637$	−24.8807	−	14.3649i	−0.985810	−	0.569158i
$638$	10.1208	+	5.84324i	0.400686	+	0.231336i
$639$	−7.78959	+	13.4920i	−0.308151	+	0.533734i
$640$	−2.23205	+	0.133975i	−0.0882296	+	0.00529581i
$641$	3.93302	−	6.81218i	0.155345	−	0.269065i	−0.777840	−	0.628463i	$-0.783684\pi$
$641$	3.93302	−	6.81218i	0.155345	−	0.269065i	0.933185	+	0.359398i	$0.117018\pi$
$642$	−0.0572370	+	0.0330458i	−0.00225896	+	0.00130421i
$643$			5.93722i			0.234141i	0.993124	+	0.117071i	$0.0373504\pi$
$643$			5.93722i			0.234141i	−0.993124	+	0.117071i	$0.962650\pi$
$644$	−14.1526	+	24.5129i	−0.557689	+	0.965945i
$645$	−7.00614	−	3.50307i	−0.275867	−	0.137933i
$646$	−6.92162			−0.272328
$647$	3.80488	−	2.19675i	0.149585	−	0.0863631i	−0.423339	−	0.905971i	$-0.639142\pi$
$647$	3.80488	−	2.19675i	0.149585	−	0.0863631i	0.572924	+	0.819608i	$0.305809\pi$
$648$		−	7.13397i		−	0.280249i
$649$	−12.0989	+	20.9559i	−0.474923	+	0.822591i
$650$	−8.48502	+	1.02228i	−0.332810	+	0.0400970i
$651$	8.35516	+	14.4716i	0.327465	+	0.567185i
$652$	−14.8143	+	8.55304i	−0.580173	+	0.334963i
$653$	−23.3061	+	13.4558i	−0.912039	+	0.526566i	−0.881087	−	0.472955i	$-0.843187\pi$
$653$	−23.3061	+	13.4558i	−0.912039	+	0.526566i	−0.0309527	+	0.999521i	$0.509854\pi$
$654$	−4.22733	−	7.32196i	−0.165302	−	0.286311i
$655$	20.6491	+	10.3246i	0.806829	+	0.403415i
$656$	−7.63090			−0.297936
$657$	5.04976	−	2.91548i	0.197010	−	0.113744i
$658$	15.2866	+	8.82571i	0.595933	+	0.344062i
$659$	−4.18342	+	7.24589i	−0.162963	+	0.282260i	−0.935930	−	0.352186i	$-0.885438\pi$
$659$	−4.18342	+	7.24589i	−0.162963	+	0.282260i	0.772967	+	0.634446i	$0.218772\pi$
$660$	3.51616	−	0.211051i	0.136866	−	0.00821515i
$661$	1.93495			0.0752610			0.0376305	−	0.999292i	$-0.488019\pi$
$661$	1.93495			0.0752610			0.0376305	+	0.999292i	$0.488019\pi$
$662$			30.6947i			1.19298i
$663$	−5.12296	−	2.95774i	−0.198959	−	0.114869i
$664$	−5.64896	−	9.78428i	−0.219222	−	0.379704i
$665$	−4.49693	+	8.99386i	−0.174383	+	0.348767i
$666$	−1.79905	+	3.11604i	−0.0697116	+	0.120744i
$667$			19.8310i			0.767858i
$668$	20.9694	−	12.1067i	0.811331	−	0.468422i
$669$	2.56916			0.0993296
$670$	−16.6147	−	7.67793i	−0.641883	−	0.296624i
$671$	−41.6742			−1.60881
$672$	−1.94723	+	1.12423i	−0.0751159	+	0.0433682i
$673$		−	43.8141i		−	1.68891i	−0.535626	−	0.844455i	$-0.679924\pi$
$673$		−	43.8141i		−	1.68891i	0.535626	−	0.844455i	$-0.320076\pi$
$674$	−7.18701	+	12.4483i	−0.276833	+	0.479489i
$675$	−10.6681	+	8.00104i	−0.410614	+	0.307960i
$676$	5.03919	+	8.72813i	0.193815	+	0.335697i
$677$	−5.60874	−	3.23820i	−0.215561	−	0.124454i	0.388332	−	0.921520i	$-0.373051\pi$
$677$	−5.60874	−	3.23820i	−0.215561	−	0.124454i	−0.603893	+	0.797065i	$0.706385\pi$
$678$			3.83096i			0.147127i
$679$	69.5585			2.66941
$680$	−1.00618	−	16.7633i	−0.0385854	−	0.642842i
$681$	1.86296	−	3.22674i	0.0713888	−	0.123649i
$682$	22.0025	+	12.7031i	0.842518	+	0.486428i
$683$	−14.3642	+	8.29318i	−0.549632	+	0.317330i	−0.748973	−	0.662600i	$-0.769453\pi$
$683$	−14.3642	+	8.29318i	−0.549632	+	0.317330i	0.199342	+	0.979930i	$0.436120\pi$
$684$	−2.56916			−0.0982344
$685$	−21.8504	+	43.7009i	−0.834862	+	1.66972i
$686$	−23.9288	−	41.4459i	−0.913606	−	1.58241i
$687$	9.85216	−	5.68815i	0.375883	−	0.217016i
$688$	6.58350	−	3.80098i	0.250993	−	0.144911i
$689$	−3.10310	−	5.37473i	−0.118219	−	0.204761i
$690$	3.29347	+	4.98818i	0.125380	+	0.189897i
$691$	−13.1906	+	22.8468i	−0.501794	+	0.869133i	0.498204	+	0.867060i	$0.333993\pi$
$691$	−13.1906	+	22.8468i	−0.501794	+	0.869133i	−0.999998	+	0.00207309i	$0.999340\pi$
$692$		−	11.1568i		−	0.424116i
$693$	−40.2693	+	23.2495i	−1.52971	+	0.883176i
$694$	−10.2101			−0.387569
$695$	19.2039	+	9.60197i	0.728447	+	0.364223i
$696$	−0.787653	+	1.36426i	−0.0298559	+	0.0517120i
$697$		−	57.3100i		−	2.17077i
$698$	2.64286	−	1.52586i	0.100034	−	0.0577546i
$699$	4.26959	−	7.39515i	0.161491	−	0.279710i
$700$	−22.4357	−	9.58356i	−0.847989	−	0.362225i
$701$	14.4947	−	25.1055i	0.547456	−	0.948221i	−0.450992	−	0.892528i	$-0.648930\pi$
$701$	14.4947	−	25.1055i	0.547456	−	0.948221i	0.998448	−	0.0556933i	$-0.0177369\pi$
$702$	−3.94792	−	2.27933i	−0.149005	−	0.0860278i
$703$	1.03019	+	0.594780i	0.0388543	+	0.0224326i
$704$	−1.70928	+	2.96055i	−0.0644207	+	0.111580i
$705$	3.11069	−	2.05385i	0.117155	−	0.0773524i
$706$	1.03252	−	1.78838i	0.0388595	−	0.0673067i
$707$	−25.7414	+	14.8618i	−0.968106	+	0.558936i
$708$	−2.82480	−	1.63090i	−0.106162	−	0.0612929i
$709$	−23.4947	−	40.6939i	−0.882361	−	1.52829i	−0.848709	−	0.528860i	$-0.822620\pi$
$709$	−23.4947	−	40.6939i	−0.882361	−	1.52829i	−0.0336512	−	0.999434i	$-0.510714\pi$
$710$	−5.58864	+	11.1773i	−0.209738	+	0.419476i
$711$	−15.0361	+	26.0433i	−0.563898	+	0.976701i
$712$			5.00000i			0.187383i
$713$			43.1122i			1.61457i
$714$	−8.44327	−	14.6242i	−0.315982	−	0.547296i
$715$	−5.84324	+	11.6865i	−0.218525	+	0.437050i
$716$	5.56751	−	9.64320i	0.208068	−	0.360383i
$717$	−5.45702	−	3.15061i	−0.203796	−	0.117662i
$718$	−23.6565	+	13.6581i	−0.882852	+	0.509715i
$719$	16.3830	+	28.3761i	0.610981	+	1.05825i	0.991075	+	0.133303i	$0.0425582\pi$
$719$	16.3830	+	28.3761i	0.610981	+	1.05825i	−0.380094	+	0.924948i	$0.624108\pi$
$720$	−0.373475	−	6.22218i	−0.0139186	−	0.231887i
$721$	4.77626	+	8.27272i	0.177877	+	0.308092i
$722$		−	18.1506i		−	0.675496i
$723$		−	4.59478i		−	0.170882i
$724$	3.22927	+	5.59326i	0.120015	+	0.207872i
$725$	−16.9700	+	2.04455i	−0.630251	+	0.0759328i
$726$	0.158171	−	0.273960i	0.00587027	−	0.0101676i
$727$	5.50320	−	3.17727i	0.204102	−	0.117839i	−0.394465	−	0.918911i	$-0.629070\pi$
$727$	5.50320	−	3.17727i	0.204102	−	0.117839i	0.598568	+	0.801072i	$0.295737\pi$
$728$		−	8.34017i		−	0.309107i
$729$	16.2001			0.600002
$730$	3.90318	−	2.57709i	0.144463	−	0.0953824i
$731$	28.5464	+	49.4438i	1.05583	+	1.82874i
$732$		−	5.61757i		−	0.207631i
$733$	−24.3791	−	14.0753i	−0.900464	−	0.519883i	−0.0231135	−	0.999733i	$-0.507358\pi$
$733$	−24.3791	−	14.0753i	−0.900464	−	0.519883i	−0.877351	+	0.479850i	$0.840691\pi$
$734$	5.06278			0.186871
$735$	−17.2881	+	1.03769i	−0.637682	+	0.0382756i
$736$	−5.80098			−0.213827
$737$	−23.7913	+	14.7298i	−0.876365	+	0.542579i
$738$		−	21.2723i		−	0.783044i
$739$	3.78047	+	6.54796i	0.139067	+	0.240871i	0.927144	−	0.374706i	$-0.122256\pi$
$739$	3.78047	+	6.54796i	0.139067	+	0.240871i	−0.788077	+	0.615577i	$0.788923\pi$
$740$	−1.29072	+	2.58145i	−0.0474480	+	0.0948960i
$741$	−0.362959	+	0.628664i	−0.0133336	+	0.0230945i
$742$		−	17.7165i		−	0.650392i
$743$	−32.6499	+	18.8504i	−1.19781	+	0.691555i	−0.960066	−	0.279773i	$-0.909741\pi$
$743$	−32.6499	+	18.8504i	−1.19781	+	0.691555i	−0.237743	+	0.971328i	$0.576408\pi$
$744$	−1.71235	+	2.96587i	−0.0627777	+	0.108734i
$745$	−6.28685	−	3.14342i	−0.230332	−	0.115166i
$746$	5.18342			0.189778
$747$	27.2752	−	15.7473i	0.997947	−	0.576165i
$748$	−22.2345	−	12.8371i	−0.812974	−	0.469371i
$749$	0.349910	−	0.606062i	0.0127854	−	0.0221450i
$750$	−3.92900	+	3.33261i	−0.143467	+	0.121690i
$751$	29.0033			1.05835			0.529173	−	0.848514i	$-0.322502\pi$
$751$	29.0033			1.05835			0.529173	+	0.848514i	$0.322502\pi$
$752$			3.61757i			0.131919i
$753$	6.94507	−	4.00974i	0.253092	−	0.146123i
$754$	−2.92162	−	5.06040i	−0.106399	−	0.184289i
$755$	2.63763	+	43.9436i	0.0959932	+	1.59927i
$756$	−6.50667	−	11.2699i	−0.236645	−	0.409881i
$757$	27.5769	+	15.9215i	1.00230	+	0.578678i	0.908928	−	0.416953i	$-0.136902\pi$
$757$	27.5769	+	15.9215i	1.00230	+	0.578678i	0.0933718	+	0.995631i	$0.470235\pi$
$758$	−27.1716	−	15.6875i	−0.986917	−	0.569797i
$759$	9.13833			0.331700
$760$	−2.05711	+	0.123474i	−0.0746191	+	0.00447887i
$761$	23.5236			0.852729			0.426365	−	0.904551i	$-0.359794\pi$
$761$	23.5236			0.852729			0.426365	+	0.904551i	$0.359794\pi$
$762$			3.15061i			0.114135i
$763$	77.5295	+	44.7617i	2.80676	+	1.62048i
$764$	13.1412			0.475430
$765$	46.7302	−	2.80489i	1.68953	−	0.101411i
$766$	11.5886	−	20.0721i	0.418714	−	0.725235i
$767$	10.4780	−	6.04945i	0.378337	−	0.218433i
$768$	−0.399074	−	0.230406i	−0.0144003	−	0.00831404i
$769$	−2.08977	+	3.61959i	−0.0753591	+	0.130526i	−0.901242	−	0.433315i	$-0.857344\pi$
$769$	−2.08977	+	3.61959i	−0.0753591	+	0.130526i	0.825883	+	0.563841i	$0.190677\pi$
$770$	−31.1259	+	20.5510i	−1.12170	+	0.740608i
$771$	−0.0722347	+	0.125114i	−0.00260147	+	0.00450588i
$772$	4.26847	+	2.46441i	0.153626	+	0.0886959i
$773$	−41.2620	−	23.8226i	−1.48409	−	0.856841i	−0.484255	−	0.874927i	$-0.660909\pi$
$773$	−41.2620	−	23.8226i	−1.48409	−	0.856841i	−0.999836	+	0.0180861i	$0.994243\pi$
$774$	10.5958	+	18.3525i	0.380859	+	0.659667i
$775$	−36.8926	+	4.44483i	−1.32522	+	0.159663i
$776$	7.12783	+	12.3458i	0.255874	+	0.443187i
$777$			2.90215i			0.104114i
$778$	18.8374	+	10.8758i	0.675353	+	0.389915i
$779$	−7.03281			−0.251976
$780$	−1.57531	−	0.787653i	−0.0564050	−	0.0282025i
$781$	9.55252	+	16.5454i	0.341816	+	0.592043i
$782$		−	43.5669i		−	1.55795i
$783$	−7.89584	−	4.55866i	−0.282174	−	0.162913i
$784$	8.40409	−	14.5563i	0.300146	−	0.519868i
$785$	−26.2461	+	1.57537i	−0.936762	+	0.0562274i
$786$	2.37884	+	4.12027i	0.0848504	+	0.146965i
$787$	−23.1675	+	13.3758i	−0.825833	+	0.476795i	−0.852424	−	0.522852i	$-0.824868\pi$
$787$	−23.1675	+	13.3758i	−0.825833	+	0.476795i	0.0265911	+	0.999646i	$0.491535\pi$
$788$	10.5208	−	6.07417i	0.374787	−	0.216383i
$789$	4.99386			0.177786
$790$	−10.7877	+	21.5753i	−0.383807	+	0.767615i
$791$	−20.2823	−	35.1300i	−0.721156	−	1.24908i
$792$	−8.25299	−	4.76487i	−0.293257	−	0.169312i
$793$	18.0455	+	10.4186i	0.640813	+	0.369974i
$794$	−15.9794	−	27.6771i	−0.567087	−	0.982224i
$795$	−3.34632	−	1.67316i	−0.118682	−	0.0593408i
$796$	−14.4608			−0.512550
$797$	−2.18746	−	1.26293i	−0.0774837	−	0.0447352i	0.460758	−	0.887526i	$-0.347578\pi$
$797$	−2.18746	−	1.26293i	−0.0774837	−	0.0447352i	−0.538241	+	0.842791i	$0.680911\pi$
$798$	−1.79461	+	1.03612i	−0.0635284	+	0.0366782i
$799$	−27.1689			−0.961165
$800$	−0.598076	−	4.96410i	−0.0211452	−	0.175507i
$801$	−13.9383			−0.492484
$802$	22.8541	−	13.1948i	0.807006	−	0.465925i
$803$		−	7.15061i		−	0.252340i
$804$	−1.98554	−	3.20701i	−0.0700244	−	0.113102i
$805$	−56.6102	−	28.3051i	−1.99525	−	0.997624i
$806$	−6.35157	−	11.0012i	−0.223724	−	0.387502i
$807$			6.27456i			0.220875i
$808$	−5.27557	−	3.04585i	−0.185594	−	0.107153i
$809$	26.3752			0.927304			0.463652	−	0.886017i	$-0.346539\pi$
$809$	26.3752			0.927304			0.463652	+	0.886017i	$0.346539\pi$
$810$	15.9234	−	0.955771i	0.559491	−	0.0335824i
$811$	14.9861	−	25.9566i	0.526232	−	0.911460i	−0.473301	−	0.880901i	$-0.656938\pi$
$811$	14.9861	−	25.9566i	0.526232	−	0.911460i	0.999533	−	0.0305594i	$-0.00972886\pi$
$812$		−	16.6803i		−	0.585365i
$813$			10.2495i			0.359466i
$814$	2.20620	+	3.82126i	0.0773274	+	0.133935i
$815$	−21.0756	−	31.9204i	−0.738245	−	1.11812i
$816$	1.73041	−	2.99715i	0.0605763	−	0.104921i
$817$	6.06750	−	3.50307i	0.212275	−	0.122557i
$818$			37.7442i			1.31969i
$819$	23.2495			0.812404
$820$	−1.02235	−	17.0326i	−0.0357019	−	0.594802i
$821$	9.89855	+	17.1448i	0.345462	+	0.598358i	0.985438	−	0.170038i	$-0.0543889\pi$
$821$	9.89855	+	17.1448i	0.345462	+	0.598358i	−0.639976	+	0.768395i	$0.721056\pi$
$822$	−8.71994	+	5.03446i	−0.304143	+	0.175597i
$823$	−12.9957	+	7.50307i	−0.453002	+	0.261541i	−0.709097	−	0.705111i	$-0.750897\pi$
$823$	−12.9957	+	7.50307i	−0.453002	+	0.261541i	0.256095	+	0.966652i	$0.417564\pi$
$824$	−0.978870	+	1.69545i	−0.0341005	+	0.0590639i
$825$	0.942153	+	7.81998i	0.0328016	+	0.272257i
$826$	34.5380			1.20173
$827$	−33.2430	+	19.1929i	−1.15597	+	0.667402i	−0.950336	−	0.311227i	$-0.899260\pi$
$827$	−33.2430	+	19.1929i	−1.15597	+	0.667402i	−0.205638	+	0.978628i	$0.565927\pi$
$828$		−	16.1711i		−	0.561986i
$829$	−48.2050			−1.67423			−0.837114	−	0.547028i	$-0.815759\pi$
$829$	−48.2050			−1.67423			−0.837114	+	0.547028i	$0.815759\pi$
$830$	21.0822	−	13.9196i	0.731774	−	0.483156i
$831$	5.22568			0.181277
$832$	1.48028	−	0.854638i	0.0513193	−	0.0296292i
$833$	109.322	+	63.1169i	3.78777	+	2.18687i
$834$	2.21235	+	3.83190i	0.0766073	+	0.132688i
$835$	29.8321	+	45.1828i	1.03238	+	1.56362i
$836$	−1.57531	+	2.72851i	−0.0544831	+	0.0943675i
$837$	−17.1654	−	9.91047i	−0.593324	−	0.342556i
$838$	−9.67980	−	5.58864i	−0.334383	−	0.193056i
$839$	3.58618	−	6.21144i	0.123809	−	0.214443i	−0.797458	−	0.603374i	$-0.793822\pi$
$839$	3.58618	−	6.21144i	0.123809	−	0.214443i	0.921267	+	0.388932i	$0.127156\pi$
$840$	−2.77022	−	4.19569i	−0.0955817	−	0.144765i
$841$	8.65676	+	14.9939i	0.298509	+	0.517032i
$842$	9.75300	+	5.63090i	0.336111	+	0.194054i
$843$	1.98628	−	1.14678i	0.0684110	−	0.0394971i
$844$	0.199016			0.00685041
$845$	−18.8065	+	12.4171i	−0.646964	+	0.427160i
$846$	−10.0845			−0.346713
$847$			3.34963i			0.115095i
$848$	3.14445	−	1.81545i	0.107981	−	0.0623428i
$849$	−3.02893			−0.103953
$850$	37.2817	−	4.49171i	1.27875	−	0.154064i
$851$	−3.74374	+	6.48434i	−0.128334	+	0.222280i
$852$	−2.23028	+	1.28765i	−0.0764082	+	0.0441143i
$853$	28.8892	−	16.6792i	0.989149	−	0.571085i	0.0841291	−	0.996455i	$-0.473189\pi$
$853$	28.8892	−	16.6792i	0.989149	−	0.571085i	0.905020	+	0.425370i	$0.139856\pi$
$854$	29.7412	+	51.5132i	1.01772	+	1.76275i
$855$	−0.344203	−	5.73450i	−0.0117715	−	0.196116i
$856$	0.143424			0.00490215
$857$		−	48.1906i		−	1.64616i	−0.567926	−	0.823080i	$-0.692254\pi$
$857$		−	48.1906i		−	1.64616i	0.567926	−	0.823080i	$-0.307746\pi$
$858$	−2.33189	+	1.34632i	−0.0796093	+	0.0459625i
$859$	16.8732	−	29.2253i	0.575707	−	0.997153i	−0.420258	−	0.907405i	$-0.638060\pi$
$859$	16.8732	−	29.2253i	0.575707	−	0.997153i	0.995964	−	0.0897486i	$-0.0286064\pi$
$860$	9.36601	+	14.1855i	0.319378	+	0.483720i
$861$	−8.57890	−	14.8591i	−0.292368	−	0.506396i
$862$		−	3.29791i		−	0.112327i
$863$		−	46.5802i		−	1.58561i	−0.609476	−	0.792805i	$-0.708620\pi$
$863$		−	46.5802i		−	1.58561i	0.609476	−	0.792805i	$-0.291380\pi$
$864$	1.33351	−	2.30970i	0.0453668	−	0.0785777i
$865$	24.9024	−	1.49472i	0.846709	−	0.0508221i
$866$	−5.53692			−0.188152
$867$	15.7251	+	9.07890i	0.534053	+	0.308336i
$868$		−	36.2628i		−	1.23084i
$869$	18.4391	+	31.9374i	0.625503	+	1.08340i
$870$	−3.15061	−	1.57531i	−0.106816	−	0.0534079i
$871$	13.9844	−	0.430353i	0.473843	−	0.0145819i
$872$			18.3474i			0.621320i
$873$	−34.4157	+	19.8699i	−1.16479	+	0.672494i
$874$	−5.34632			−0.180842
$875$	18.3852	−	51.3615i	0.621533	−	1.73634i
$876$	0.963883			0.0325666
$877$	−22.4092	+	12.9379i	−0.756704	+	0.436883i	−0.828111	−	0.560564i	$-0.810584\pi$
$877$	−22.4092	+	12.9379i	−0.756704	+	0.436883i	0.0714073	+	0.997447i	$0.477251\pi$
$878$	15.1590	+	8.75206i	0.511592	+	0.295368i
$879$	4.37241			0.147478
$880$	−6.83710	−	3.41855i	−0.230479	−	0.115239i
$881$	10.2987	+	17.8379i	0.346973	+	0.600974i	0.985710	−	0.168451i	$-0.0538764\pi$
$881$	10.2987	+	17.8379i	0.346973	+	0.600974i	−0.638738	+	0.769425i	$0.720543\pi$
$882$	40.5779	+	23.4277i	1.36633	+	0.788851i
$883$	6.85501	+	3.95774i	0.230689	+	0.133189i	0.610890	−	0.791715i	$-0.290812\pi$
$883$	6.85501	+	3.95774i	0.230689	+	0.133189i	−0.380201	+	0.924904i	$0.624145\pi$
$884$	6.41855	+	11.1173i	0.215879	+	0.373914i
$885$	3.26180	−	6.52359i	0.109644	−	0.219288i
$886$	−8.30406			−0.278980
$887$	−21.3834	+	12.3457i	−0.717984	+	0.414528i	−0.814010	−	0.580851i	$-0.802720\pi$
$887$	−21.3834	+	12.3457i	−0.717984	+	0.414528i	0.0960263	+	0.995379i	$0.469387\pi$
$888$	−0.515095	+	0.297390i	−0.0172855	+	0.00997976i
$889$	−16.6803	−	28.8912i	−0.559441	−	0.968980i
$890$	−11.1603	+	0.669873i	−0.374093	+	0.0224542i
$891$	12.1939	−	21.1205i	0.408512	−	0.707563i
$892$	−4.82836	−	2.78765i	−0.161665	−	0.0933375i
$893$			3.33403i			0.111569i
$894$	−0.724262	−	1.25446i	−0.0242230	−	0.0419554i
$895$	22.2700	+	11.1350i	0.744405	+	0.372202i
$896$	4.87936			0.163008
$897$	−3.95701	−	2.28458i	−0.132121	−	0.0762800i
$898$		−	30.3607i		−	1.01315i
$899$	−12.7031	−	22.0025i	−0.423673	−	0.733823i
$900$	13.8382	−	1.66723i	0.461273	−	0.0555743i
$901$	13.6345	+	23.6156i	0.454231	+	0.786751i
$902$	−22.5917	−	13.0433i	−0.752220	−	0.434295i
$903$	14.8028	+	8.54638i	0.492605	+	0.284406i
$904$	4.15676	−	7.19971i	0.138252	−	0.239459i
$905$	−12.0518	+	7.95725i	−0.400616	+	0.264508i
$906$	−4.53612	+	7.85679i	−0.150702	+	0.261024i
$907$	35.0328	+	20.2262i	1.16325	+	0.671600i	0.952080	−	0.305850i	$-0.0989407\pi$
$907$	35.0328	+	20.2262i	1.16325	+	0.671600i	0.211166	+	0.977450i	$0.432274\pi$
$908$	−7.00231	+	4.04278i	−0.232380	+	0.134164i
$909$	8.49079	−	14.7065i	0.281622	−	0.487783i
$910$	18.6157	−	1.11737i	0.617104	−	0.0370405i
$911$	−3.92493			−0.130039			−0.0650194	−	0.997884i	$-0.520711\pi$
$911$	−3.92493			−0.130039			−0.0650194	+	0.997884i	$0.520711\pi$
$912$	−0.367796	−	0.212347i	−0.0121789	−	0.00703151i
$913$		−	38.6225i		−	1.27822i
$914$	15.2423			0.504171
$915$	12.5387	−	0.752611i	0.414516	−	0.0248806i
$916$	−24.6875			−0.815699
$917$	−43.6281	−	25.1887i	−1.44073	−	0.831803i
$918$	17.3465	+	10.0150i	0.572519	+	0.330544i
$919$	−28.1931	−	48.8318i	−0.930003	−	1.61081i	−0.783310	−	0.621631i	$-0.786470\pi$
$919$	−28.1931	−	48.8318i	−0.930003	−	1.61081i	−0.146693	−	0.989182i	$-0.546863\pi$
$920$	−0.777185	−	12.9481i	−0.0256230	−	0.426886i
$921$	7.22786	+	12.5190i	0.238166	+	0.412516i
$922$	−18.9731	+	10.9541i	−0.624847	+	0.360756i
$923$		−	9.55252i		−	0.314425i
$924$	−7.68649			−0.252867
$925$	−5.93485	−	2.53511i	−0.195137	−	0.0833540i
$926$	−10.0416	+	17.3926i	−0.329989	+	0.571558i
$927$	−4.72633	−	2.72875i	−0.155233	−	0.0896239i
$928$	2.96055	−	1.70928i	0.0971849	−	0.0561097i
$929$	19.2313			0.630957			0.315479	−	0.948933i	$-0.397835\pi$
$929$	19.2313			0.630957			0.315479	+	0.948933i	$0.397835\pi$
$930$	−6.84939	−	3.42469i	−0.224600	−	0.112300i
$931$	7.74539	−	13.4154i	0.253845	−	0.439672i
$932$	−16.0481	+	9.26539i	−0.525674	+	0.303498i
$933$			3.95669i			0.129536i
$934$	5.64896	−	9.78428i	0.184839	−	0.320151i
$935$	25.6742	−	51.3484i	0.839636	−	1.67927i
$936$	2.38243	+	4.12650i	0.0778723	+	0.134879i
$937$			22.7675i			0.743782i	0.928276	+	0.371891i	$0.121291\pi$
$937$			22.7675i			0.743782i	−0.928276	+	0.371891i	$0.878709\pi$
$938$	35.1863	+	18.8963i	1.14887	+	0.616986i
$939$	−6.15676			−0.200918
$940$	−8.07459	+	0.484662i	−0.263364	+	0.0158079i
$941$	−11.8843			−0.387417			−0.193708	−	0.981059i	$-0.562052\pi$
$941$	−11.8843			−0.387417			−0.193708	+	0.981059i	$0.562052\pi$
$942$	−4.69260	−	2.70928i	−0.152893	−	0.0882730i
$943$		−	44.2667i		−	1.44152i
$944$	3.53919	+	6.13005i	0.115191	+	0.199516i
$945$	24.2832	−	16.0331i	0.789933	−	0.521556i
$946$	25.9877			0.844933
$947$		−	8.08452i		−	0.262712i	−0.991335	−	0.131356i	$-0.958067\pi$
$947$		−	8.08452i		−	0.262712i	0.991335	−	0.131356i	$-0.0419330\pi$
$948$	−4.30507	+	2.48554i	−0.139822	+	0.0807264i
$949$	−1.78765	+	3.09631i	−0.0580297	+	0.100510i
$950$	−0.551200	−	4.57503i	−0.0178833	−	0.148433i
$951$	1.69736	+	2.93991i	0.0550407	+	0.0953332i
$952$			36.6453i			1.18768i
$953$			18.2146i			0.590029i	0.955493	+	0.295015i	$0.0953245\pi$
$953$			18.2146i			0.590029i	−0.955493	+	0.295015i	$0.904675\pi$
$954$	5.06084	+	8.76563i	0.163851	+	0.283798i
$955$	1.76058	+	29.3317i	0.0569711	+	0.949153i
$956$	6.83710	+	11.8422i	0.221128	+	0.383004i
$957$	−4.66378	+	2.69263i	−0.150758	+	0.0870404i
$958$	−11.5707	−	6.68035i	−0.373832	−	0.215832i
$959$	53.3081	−	92.3323i	1.72141	−	2.98157i
$960$	0.460811	−	0.921622i	0.0148726	−	0.0297452i
$961$	−12.1164	−	20.9863i	−0.390853	−	0.676977i
$962$		−	2.20620i		−	0.0711309i
$963$			0.399818i			0.0128839i
$964$	−4.98554	+	8.63520i	−0.160573	+	0.278121i
$965$	−4.92881	+	9.85762i	−0.158664	+	0.317328i
$966$	−6.52165	−	11.2958i	−0.209831	−	0.363437i
$967$	−3.75764	−	2.16948i	−0.120838	−	0.0697656i	0.438363	−	0.898798i	$-0.355558\pi$
$967$	−3.75764	−	2.16948i	−0.120838	−	0.0697656i	−0.559201	+	0.829032i	$0.688892\pi$
$968$	−0.594517	+	0.343245i	−0.0191085	+	0.0110323i
$969$	1.59478	−	2.76224i	0.0512317	−	0.0887359i
$970$	−26.6014	+	17.5637i	−0.854120	+	0.563936i
$971$	−0.192873	+	0.334066i	−0.00618958	+	0.0107207i	−0.869104	−	0.494630i	$-0.835304\pi$
$971$	−0.192873	+	0.334066i	−0.00618958	+	0.0107207i	0.862914	+	0.505351i	$0.168637\pi$
$972$	9.77609	+	5.64423i	0.313568	+	0.181039i
$973$	−40.5746	−	23.4257i	−1.30076	−	0.750995i
$974$	3.63870	−	6.30241i	0.116591	−	0.201942i
$975$	1.54703	−	3.62169i	0.0495446	−	0.115987i
$976$	−6.09530	+	10.5574i	−0.195106	+	0.337933i
$977$	−3.71482	+	2.14475i	−0.118848	+	0.0686167i	−0.558245	−	0.829676i	$-0.688525\pi$
$977$	−3.71482	+	2.14475i	−0.118848	+	0.0686167i	0.439398	+	0.898293i	$0.355192\pi$
$978$		−	7.88267i		−	0.252060i
$979$	−8.54638	+	14.8028i	−0.273143	+	0.473098i
$980$	33.6163	+	16.8082i	1.07383	+	0.536917i
$981$	−51.1461			−1.63297
$982$	−34.2096	+	19.7509i	−1.09167	+	0.630277i
$983$			11.1473i			0.355544i	0.984072	+	0.177772i	$0.0568889\pi$
$983$			11.1473i			0.355544i	−0.984072	+	0.177772i	$0.943111\pi$
$984$	1.75820	−	3.04529i	0.0560494	−	0.0970804i
$985$	14.9674	+	22.6691i	0.476900	+	0.722298i
$986$	12.8371	+	22.2345i	0.408817	+	0.708091i
$987$	−7.04422	+	4.06698i	−0.224220	+	0.129454i
$988$	1.36426	−	0.787653i	0.0434027	−	0.0250586i
$989$	22.0494	+	38.1908i	0.701132	+	1.21440i
$990$	9.52973	−	19.0595i	0.302875	−	0.605750i
$991$	45.0033			1.42958			0.714789	−	0.699341i	$-0.246523\pi$
$991$	45.0033			1.42958			0.714789	+	0.699341i	$0.246523\pi$
$992$	6.43620	−	3.71594i	0.204350	−	0.117981i
$993$	−12.2495	−	7.07223i	−0.388725	−	0.224431i
$994$	13.6345	−	23.6156i	0.432460	−	0.749042i
$995$	−1.93738	−	32.2773i	−0.0614191	−	1.02326i
$996$	5.20620			0.164965
$997$			37.0821i			1.17440i	0.809441	+	0.587201i	$0.199770\pi$
$997$			37.0821i			1.17440i	−0.809441	+	0.587201i	$0.800230\pi$
$998$	−8.77292	−	5.06505i	−0.277702	−	0.160331i
$999$	−1.72119	−	2.98119i	−0.0544561	−	0.0943207i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	670.2.h.b.439.5	yes	12
5.4	even	2	inner	670.2.h.b.439.2	yes	12
67.29	even	3	inner	670.2.h.b.29.2	✓	12
335.29	even	6	inner	670.2.h.b.29.5	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
670.2.h.b.29.2	✓	12	67.29	even	3	inner
670.2.h.b.29.5	yes	12	335.29	even	6	inner
670.2.h.b.439.2	yes	12	5.4	even	2	inner
670.2.h.b.439.5	yes	12	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 670 = 2 \cdot 5 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	670.h (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +0.460811i q^{3} +(0.500000 - 0.866025i) q^{4} +(2.00000 + 1.00000i) q^{5} +(0.230406 + 0.399074i) q^{6} +(-4.22565 - 2.43968i) q^{7} -1.00000i q^{8} +2.78765 q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +0.460811i q^{3} +(0.500000 - 0.866025i) q^{4} +(2.00000 + 1.00000i) q^{5} +(0.230406 + 0.399074i) q^{6} +(-4.22565 - 2.43968i) q^{7} -1.00000i q^{8} +2.78765 q^{9} +(2.23205 - 0.133975i) q^{10} +(1.70928 - 2.96055i) q^{11} +(0.399074 + 0.230406i) q^{12} +(-1.48028 + 0.854638i) q^{13} -4.87936 q^{14} +(-0.460811 + 0.921622i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(6.50408 - 3.75513i) q^{17} +(2.41418 - 1.39383i) q^{18} +(-0.460811 - 0.798148i) q^{19} +(1.86603 - 1.23205i) q^{20} +(1.12423 - 1.94723i) q^{21} -3.41855i q^{22} +(5.02380 - 2.90049i) q^{23} +0.460811 q^{24} +(3.00000 + 4.00000i) q^{25} +(-0.854638 + 1.48028i) q^{26} +2.66701i q^{27} +(-4.22565 + 2.43968i) q^{28} +(-1.70928 + 2.96055i) q^{29} +(0.0617370 + 1.02855i) q^{30} +(-3.71594 + 6.43620i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(1.36426 + 0.787653i) q^{33} +(3.75513 - 6.50408i) q^{34} +(-6.01162 - 9.10501i) q^{35} +(1.39383 - 2.41418i) q^{36} +(-1.11780 + 0.645362i) q^{37} +(-0.798148 - 0.460811i) q^{38} +(-0.393827 - 0.682128i) q^{39} +(1.00000 - 2.00000i) q^{40} +(3.81545 - 6.60855i) q^{41} -2.24846i q^{42} +7.60197i q^{43} +(-1.70928 - 2.96055i) q^{44} +(5.57531 + 2.78765i) q^{45} +(2.90049 - 5.02380i) q^{46} +(-3.13290 - 1.80878i) q^{47} +(0.399074 - 0.230406i) q^{48} +(8.40409 + 14.5563i) q^{49} +(4.59808 + 1.96410i) q^{50} +(1.73041 + 2.99715i) q^{51} +1.70928i q^{52} +3.63090i q^{53} +(1.33351 + 2.30970i) q^{54} +(6.37910 - 4.21183i) q^{55} +(-2.43968 + 4.22565i) q^{56} +(0.367796 - 0.212347i) q^{57} +3.41855i q^{58} -7.07838 q^{59} +(0.567743 + 0.859885i) q^{60} +(-6.09530 - 10.5574i) q^{61} +7.43188i q^{62} +(-11.7797 - 6.80098i) q^{63} -1.00000 q^{64} +(-3.81519 + 0.228999i) q^{65} +1.57531 q^{66} +(-7.21126 - 3.87270i) q^{67} -7.51026i q^{68} +(1.33658 + 2.31502i) q^{69} +(-9.75872 - 4.87936i) q^{70} +(-2.79432 + 4.83990i) q^{71} -2.78765i q^{72} +(1.81147 - 1.04585i) q^{73} +(-0.645362 + 1.11780i) q^{74} +(-1.84324 + 1.38243i) q^{75} -0.921622 q^{76} +(-14.4456 + 8.34017i) q^{77} +(-0.682128 - 0.393827i) q^{78} +(-5.39383 + 9.34238i) q^{79} +(-0.133975 - 2.23205i) q^{80} +7.13397 q^{81} -7.63090i q^{82} +(9.78428 - 5.64896i) q^{83} +(-1.12423 - 1.94723i) q^{84} +(16.7633 - 1.00618i) q^{85} +(3.80098 + 6.58350i) q^{86} +(-1.36426 - 0.787653i) q^{87} +(-2.96055 - 1.70928i) q^{88} -5.00000 q^{89} +(6.22218 - 0.373475i) q^{90} +8.34017 q^{91} -5.80098i q^{92} +(-2.96587 - 1.71235i) q^{93} -3.61757 q^{94} +(-0.123474 - 2.05711i) q^{95} +(0.230406 - 0.399074i) q^{96} +(-12.3458 + 7.12783i) q^{97} +(14.5563 + 8.40409i) q^{98} +(4.76487 - 8.25299i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{4} + 24 q^{5} + 6 q^{6} - 8 q^{9}+O(q^{10}) \) 12 * q + 6 * q^4 + 24 * q^5 + 6 * q^6 - 8 * q^9	\( 12 q + 6 q^{4} + 24 q^{5} + 6 q^{6} - 8 q^{9} + 6 q^{10} - 8 q^{11} - 8 q^{14} - 12 q^{15} - 6 q^{16} - 12 q^{19} + 12 q^{20} - 4 q^{21} + 12 q^{24} + 36 q^{25} + 4 q^{26} + 8 q^{29} + 12 q^{30} - 18 q^{31} + 12 q^{34} + 4 q^{35} - 4 q^{36} + 16 q^{39} + 12 q^{40} + 38 q^{41} + 8 q^{44} - 16 q^{45} + 16 q^{46} + 14 q^{49} + 24 q^{50} + 24 q^{51} - 30 q^{54} - 16 q^{55} - 4 q^{56} - 72 q^{59} - 6 q^{60} + 4 q^{61} - 12 q^{64} + 4 q^{65} - 64 q^{66} + 40 q^{69} - 16 q^{70} + 6 q^{71} - 22 q^{74} - 48 q^{75} - 24 q^{76} - 44 q^{79} - 12 q^{80} + 140 q^{81} + 4 q^{84} + 12 q^{85} + 8 q^{86} - 60 q^{89} - 4 q^{90} + 56 q^{91} - 24 q^{94} - 24 q^{95} + 6 q^{96} + 96 q^{99}+O(q^{100}) \) 12 * q + 6 * q^4 + 24 * q^5 + 6 * q^6 - 8 * q^9 + 6 * q^10 - 8 * q^11 - 8 * q^14 - 12 * q^15 - 6 * q^16 - 12 * q^19 + 12 * q^20 - 4 * q^21 + 12 * q^24 + 36 * q^25 + 4 * q^26 + 8 * q^29 + 12 * q^30 - 18 * q^31 + 12 * q^34 + 4 * q^35 - 4 * q^36 + 16 * q^39 + 12 * q^40 + 38 * q^41 + 8 * q^44 - 16 * q^45 + 16 * q^46 + 14 * q^49 + 24 * q^50 + 24 * q^51 - 30 * q^54 - 16 * q^55 - 4 * q^56 - 72 * q^59 - 6 * q^60 + 4 * q^61 - 12 * q^64 + 4 * q^65 - 64 * q^66 + 40 * q^69 - 16 * q^70 + 6 * q^71 - 22 * q^74 - 48 * q^75 - 24 * q^76 - 44 * q^79 - 12 * q^80 + 140 * q^81 + 4 * q^84 + 12 * q^85 + 8 * q^86 - 60 * q^89 - 4 * q^90 + 56 * q^91 - 24 * q^94 - 24 * q^95 + 6 * q^96 + 96 * q^99

Introduction

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