LMFDB - Embedded newform 322.2.e.a.277.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [322,2,Mod(93,322)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(322, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("322.93");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 322 = 2 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	322.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.57118294509$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.310217769.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 4x^{6} - 2x^{5} + 15x^{4} - 4x^{3} + 5x^{2} + x + 1 $ x^8 + 4x^6 - 2x^5 + 15x^4 - 4x^3 + 5*x^2 + x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			277.1
Root			$-1.03075 + 1.78531i$ of defining polynomial
Character	$\chi$	$=$	322.277
Dual form			322.2.e.a.93.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-1.28821 + 2.23124i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.663319 - 1.14890i) q^{5} +2.57641 q^{6} +(-1.46157 - 2.20541i) q^{7} +1.00000 q^{8} +(-1.81896 - 3.15053i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.28821 + 2.23124i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.663319 - 1.14890i) q^{5} +2.57641 q^{6} +(-1.46157 - 2.20541i) q^{7} +1.00000 q^{8} +(-1.81896 - 3.15053i) q^{9} +(-0.663319 + 1.14890i) q^{10} +(-1.04567 + 1.81115i) q^{11} +(-1.28821 - 2.23124i) q^{12} +3.11142 q^{13} +(-1.17915 + 2.36846i) q^{14} +3.41797 q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.47460 - 6.01818i) q^{17} +(-1.81896 + 3.15053i) q^{18} +(-3.88326 - 6.72601i) q^{19} +1.32664 q^{20} +(6.80360 - 0.420095i) q^{21} +2.09133 q^{22} +(0.500000 + 0.866025i) q^{23} +(-1.28821 + 2.23124i) q^{24} +(1.62002 - 2.80595i) q^{25} +(-1.55571 - 2.69457i) q^{26} +1.64353 q^{27} +(2.64072 - 0.163054i) q^{28} +1.15845 q^{29} +(-1.70898 - 2.96005i) q^{30} +(4.35694 - 7.54644i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-2.69407 - 4.66626i) q^{33} -6.94919 q^{34} +(-1.56431 + 3.14209i) q^{35} +3.63791 q^{36} +(1.65472 + 2.86606i) q^{37} +(-3.88326 + 6.72601i) q^{38} +(-4.00815 + 6.94232i) q^{39} +(-0.663319 - 1.14890i) q^{40} -4.26425 q^{41} +(-3.76561 - 5.68204i) q^{42} -8.36716 q^{43} +(-1.04567 - 1.81115i) q^{44} +(-2.41310 + 4.17961i) q^{45} +(0.500000 - 0.866025i) q^{46} +(1.74065 + 3.01490i) q^{47} +2.57641 q^{48} +(-2.72763 + 6.44671i) q^{49} -3.24003 q^{50} +(8.95200 + 15.5053i) q^{51} +(-1.55571 + 2.69457i) q^{52} +(-2.12002 + 3.67198i) q^{53} +(-0.821765 - 1.42334i) q^{54} +2.77444 q^{55} +(-1.46157 - 2.20541i) q^{56} +20.0098 q^{57} +(-0.579223 - 1.00324i) q^{58} +(-4.59225 + 7.95401i) q^{59} +(-1.70898 + 2.96005i) q^{60} +(-6.01934 - 10.4258i) q^{61} -8.71388 q^{62} +(-4.28965 + 8.61625i) q^{63} +1.00000 q^{64} +(-2.06386 - 3.57471i) q^{65} +(-2.69407 + 4.66626i) q^{66} +(3.63160 - 6.29011i) q^{67} +(3.47460 + 6.01818i) q^{68} -2.57641 q^{69} +(3.50328 - 0.216314i) q^{70} -7.41708 q^{71} +(-1.81896 - 3.15053i) q^{72} +(2.18402 - 3.78284i) q^{73} +(1.65472 - 2.86606i) q^{74} +(4.17383 + 7.22929i) q^{75} +7.76653 q^{76} +(5.52262 - 0.341000i) q^{77} +8.01631 q^{78} +(0.398625 + 0.690439i) q^{79} +(-0.663319 + 1.14890i) q^{80} +(3.33966 - 5.78446i) q^{81} +(2.13212 + 3.69295i) q^{82} +10.3746 q^{83} +(-3.03798 + 6.10213i) q^{84} -9.21906 q^{85} +(4.18358 + 7.24617i) q^{86} +(-1.49232 + 2.58477i) q^{87} +(-1.04567 + 1.81115i) q^{88} +(-8.32132 - 14.4129i) q^{89} +4.82619 q^{90} +(-4.54756 - 6.86194i) q^{91} -1.00000 q^{92} +(11.2253 + 19.4428i) q^{93} +(1.74065 - 3.01490i) q^{94} +(-5.15168 + 8.92298i) q^{95} +(-1.28821 - 2.23124i) q^{96} +6.65800 q^{97} +(6.94683 - 0.861161i) q^{98} +7.60808 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} - 3 q^{3} - 4 q^{4} - 7 q^{5} + 6 q^{6} - q^{7} + 8 q^{8} + q^{9}+O(q^{10}) $ 8 * q - 4 * q^2 - 3 * q^3 - 4 * q^4 - 7 * q^5 + 6 * q^6 - q^7 + 8 * q^8 + q^9	\( 8 q - 4 q^{2} - 3 q^{3} - 4 q^{4} - 7 q^{5} + 6 q^{6} - q^{7} + 8 q^{8} + q^{9} - 7 q^{10} - 2 q^{11} - 3 q^{12} + 2 q^{13} - q^{14} + 18 q^{15} - 4 q^{16} - 5 q^{17} + q^{18} - 11 q^{19} + 14 q^{20} + q^{21} + 4 q^{22} + 4 q^{23} - 3 q^{24} - 3 q^{25} - q^{26} + 6 q^{27} + 2 q^{28} + 4 q^{29} - 9 q^{30} - 6 q^{31} - 4 q^{32} - 15 q^{33} + 10 q^{34} - 8 q^{35} - 2 q^{36} + 8 q^{37} - 11 q^{38} - 3 q^{39} - 7 q^{40} + 18 q^{41} - 2 q^{42} + 8 q^{43} - 2 q^{44} - 3 q^{45} + 4 q^{46} - 11 q^{47} + 6 q^{48} - 19 q^{49} + 6 q^{50} + 18 q^{51} - q^{52} - q^{53} - 3 q^{54} + 20 q^{55} - q^{56} + 6 q^{57} - 2 q^{58} - 12 q^{59} - 9 q^{60} - 21 q^{61} + 12 q^{62} - 15 q^{63} + 8 q^{64} + 24 q^{65} - 15 q^{66} + 3 q^{67} - 5 q^{68} - 6 q^{69} - 8 q^{70} + 22 q^{71} + q^{72} + 16 q^{73} + 8 q^{74} - 18 q^{75} + 22 q^{76} - 19 q^{77} + 6 q^{78} + 21 q^{79} - 7 q^{80} + 8 q^{81} - 9 q^{82} + 8 q^{83} + q^{84} + 20 q^{85} - 4 q^{86} + 7 q^{87} - 2 q^{88} - 27 q^{89} + 6 q^{90} - 54 q^{91} - 8 q^{92} + 27 q^{93} - 11 q^{94} - 5 q^{95} - 3 q^{96} + 12 q^{97} + 14 q^{98} + 26 q^{99}+O(q^{100}) \) 8 * q - 4 * q^2 - 3 * q^3 - 4 * q^4 - 7 * q^5 + 6 * q^6 - q^7 + 8 * q^8 + q^9 - 7 * q^10 - 2 * q^11 - 3 * q^12 + 2 * q^13 - q^14 + 18 * q^15 - 4 * q^16 - 5 * q^17 + q^18 - 11 * q^19 + 14 * q^20 + q^21 + 4 * q^22 + 4 * q^23 - 3 * q^24 - 3 * q^25 - q^26 + 6 * q^27 + 2 * q^28 + 4 * q^29 - 9 * q^30 - 6 * q^31 - 4 * q^32 - 15 * q^33 + 10 * q^34 - 8 * q^35 - 2 * q^36 + 8 * q^37 - 11 * q^38 - 3 * q^39 - 7 * q^40 + 18 * q^41 - 2 * q^42 + 8 * q^43 - 2 * q^44 - 3 * q^45 + 4 * q^46 - 11 * q^47 + 6 * q^48 - 19 * q^49 + 6 * q^50 + 18 * q^51 - q^52 - q^53 - 3 * q^54 + 20 * q^55 - q^56 + 6 * q^57 - 2 * q^58 - 12 * q^59 - 9 * q^60 - 21 * q^61 + 12 * q^62 - 15 * q^63 + 8 * q^64 + 24 * q^65 - 15 * q^66 + 3 * q^67 - 5 * q^68 - 6 * q^69 - 8 * q^70 + 22 * q^71 + q^72 + 16 * q^73 + 8 * q^74 - 18 * q^75 + 22 * q^76 - 19 * q^77 + 6 * q^78 + 21 * q^79 - 7 * q^80 + 8 * q^81 - 9 * q^82 + 8 * q^83 + q^84 + 20 * q^85 - 4 * q^86 + 7 * q^87 - 2 * q^88 - 27 * q^89 + 6 * q^90 - 54 * q^91 - 8 * q^92 + 27 * q^93 - 11 * q^94 - 5 * q^95 - 3 * q^96 + 12 * q^97 + 14 * q^98 + 26 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/322\mathbb{Z}\right)^\times$.

$n$	$185$	$281$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	−1.28821	+	2.23124i	−0.743747	+	1.28821i	0.207031	+	0.978334i	$0.433620\pi$
$3$	−1.28821	+	2.23124i	−0.743747	+	1.28821i	−0.950778	+	0.309873i	$0.899713\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−0.663319	−	1.14890i	−0.296645	−	0.513804i	0.678721	−	0.734396i	$-0.262535\pi$
$5$	−0.663319	−	1.14890i	−0.296645	−	0.513804i	−0.975366	+	0.220592i	$0.929201\pi$
$6$	2.57641			1.05182
$7$	−1.46157	−	2.20541i	−0.552422	−	0.833565i
$7$	−1.46157	−	2.20541i	−0.552422	−	0.833565i
$8$	1.00000			0.353553
$9$	−1.81896	−	3.15053i	−0.606319	−	1.05018i
$10$	−0.663319	+	1.14890i	−0.209760	+	0.363315i
$11$	−1.04567	+	1.81115i	−0.315280	+	0.546081i	−0.979497	−	0.201459i	$-0.935432\pi$
$11$	−1.04567	+	1.81115i	−0.315280	+	0.546081i	0.664217	+	0.747540i	$0.268765\pi$
$12$	−1.28821	−	2.23124i	−0.371873	−	0.644104i
$13$	3.11142			0.862952			0.431476	−	0.902124i	$-0.357993\pi$
$13$	3.11142			0.862952			0.431476	+	0.902124i	$0.357993\pi$
$14$	−1.17915	+	2.36846i	−0.315142	+	0.632997i
$15$	3.41797			0.882516
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	3.47460	−	6.01818i	0.842713	−	1.45962i	−0.0448794	−	0.998992i	$-0.514290\pi$
$17$	3.47460	−	6.01818i	0.842713	−	1.45962i	0.887593	−	0.460629i	$-0.152376\pi$
$18$	−1.81896	+	3.15053i	−0.428732	+	0.742586i
$19$	−3.88326	−	6.72601i	−0.890882	−	1.54305i	−0.838820	−	0.544409i	$-0.816754\pi$
$19$	−3.88326	−	6.72601i	−0.890882	−	1.54305i	−0.0520619	−	0.998644i	$-0.516579\pi$
$20$	1.32664			0.296645
$21$	6.80360	−	0.420095i	1.48467	−	0.0916722i
$22$	2.09133			0.445873
$23$	0.500000	+	0.866025i	0.104257	+	0.180579i
$23$	0.500000	+	0.866025i	0.104257	+	0.180579i
$24$	−1.28821	+	2.23124i	−0.262954	+	0.455450i
$25$	1.62002	−	2.80595i	0.324003	−	0.561190i
$26$	−1.55571	−	2.69457i	−0.305100	−	0.528448i
$27$	1.64353			0.316298
$28$	2.64072	−	0.163054i	0.499050	−	0.0308143i
$29$	1.15845			0.215118			0.107559	−	0.994199i	$-0.465697\pi$
$29$	1.15845			0.215118			0.107559	+	0.994199i	$0.465697\pi$
$30$	−1.70898	−	2.96005i	−0.312016	−	0.540428i
$31$	4.35694	−	7.54644i	0.782530	−	1.35538i	−0.147934	−	0.988997i	$-0.547262\pi$
$31$	4.35694	−	7.54644i	0.782530	−	1.35538i	0.930464	−	0.366384i	$-0.119404\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−2.69407	−	4.66626i	−0.468977	−	0.812292i
$34$	−6.94919			−1.19178
$35$	−1.56431	+	3.14209i	−0.264416	+	0.531110i
$36$	3.63791			0.606319
$37$	1.65472	+	2.86606i	0.272034	+	0.471177i	0.969383	−	0.245555i	$-0.0789702\pi$
$37$	1.65472	+	2.86606i	0.272034	+	0.471177i	−0.697348	+	0.716732i	$0.745637\pi$
$38$	−3.88326	+	6.72601i	−0.629949	+	1.09110i
$39$	−4.00815	+	6.94232i	−0.641818	+	1.11166i
$40$	−0.663319	−	1.14890i	−0.104880	−	0.181657i
$41$	−4.26425			−0.665964			−0.332982	−	0.942933i	$-0.608055\pi$
$41$	−4.26425			−0.665964			−0.332982	+	0.942933i	$0.608055\pi$
$42$	−3.76561	−	5.68204i	−0.581046	−	0.876758i
$43$	−8.36716			−1.27598			−0.637990	−	0.770045i	$-0.720234\pi$
$43$	−8.36716			−1.27598			−0.637990	+	0.770045i	$0.720234\pi$
$44$	−1.04567	−	1.81115i	−0.157640	−	0.273040i
$45$	−2.41310	+	4.17961i	−0.359723	+	0.623059i
$46$	0.500000	−	0.866025i	0.0737210	−	0.127688i
$47$	1.74065	+	3.01490i	0.253900	+	0.439768i	0.964596	−	0.263731i	$-0.0849532\pi$
$47$	1.74065	+	3.01490i	0.253900	+	0.439768i	−0.710696	+	0.703499i	$0.751620\pi$
$48$	2.57641			0.371873
$49$	−2.72763	+	6.44671i	−0.389661	+	0.920958i
$50$	−3.24003			−0.458210
$51$	8.95200	+	15.5053i	1.25353	+	2.17118i
$52$	−1.55571	+	2.69457i	−0.215738	+	0.373669i
$53$	−2.12002	+	3.67198i	−0.291207	+	0.504385i	−0.974095	−	0.226138i	$-0.927390\pi$
$53$	−2.12002	+	3.67198i	−0.291207	+	0.504385i	0.682889	+	0.730522i	$0.260723\pi$
$54$	−0.821765	−	1.42334i	−0.111828	−	0.193692i
$55$	2.77444			0.374105
$56$	−1.46157	−	2.20541i	−0.195311	−	0.294710i
$57$	20.0098			2.65036
$58$	−0.579223	−	1.00324i	−0.0760557	−	0.131732i
$59$	−4.59225	+	7.95401i	−0.597860	+	1.03552i	0.395277	+	0.918562i	$0.370649\pi$
$59$	−4.59225	+	7.95401i	−0.597860	+	1.03552i	−0.993136	+	0.116961i	$0.962685\pi$
$60$	−1.70898	+	2.96005i	−0.220629	+	0.382140i
$61$	−6.01934	−	10.4258i	−0.770698	−	1.33489i	−0.937181	−	0.348844i	$-0.886574\pi$
$61$	−6.01934	−	10.4258i	−0.770698	−	1.33489i	0.166483	−	0.986044i	$-0.446759\pi$
$62$	−8.71388			−1.10666
$63$	−4.28965	+	8.61625i	−0.540446	+	1.08555i
$64$	1.00000			0.125000
$65$	−2.06386	−	3.57471i	−0.255991	−	0.443389i
$66$	−2.69407	+	4.66626i	−0.331617	+	0.574377i
$67$	3.63160	−	6.29011i	0.443670	−	0.768459i	−0.554288	−	0.832325i	$-0.687010\pi$
$67$	3.63160	−	6.29011i	0.443670	−	0.768459i	0.997959	+	0.0638656i	$0.0203429\pi$
$68$	3.47460	+	6.01818i	0.421357	+	0.729811i
$69$	−2.57641			−0.310164
$70$	3.50328	−	0.216314i	0.418722	−	0.0258544i
$71$	−7.41708			−0.880245			−0.440123	−	0.897938i	$-0.645065\pi$
$71$	−7.41708			−0.880245			−0.440123	+	0.897938i	$0.645065\pi$
$72$	−1.81896	−	3.15053i	−0.214366	−	0.371293i
$73$	2.18402	−	3.78284i	0.255621	−	0.442748i	−0.709443	−	0.704763i	$-0.751054\pi$
$73$	2.18402	−	3.78284i	0.255621	−	0.442748i	0.965064	+	0.262015i	$0.0843868\pi$
$74$	1.65472	−	2.86606i	0.192357	−	0.333173i
$75$	4.17383	+	7.22929i	0.481953	+	0.834767i
$76$	7.76653			0.890882
$77$	5.52262	−	0.341000i	0.629361	−	0.0388606i
$78$	8.01631			0.907668
$79$	0.398625	+	0.690439i	0.0448488	+	0.0776805i	0.887578	−	0.460657i	$-0.152386\pi$
$79$	0.398625	+	0.690439i	0.0448488	+	0.0776805i	−0.842730	+	0.538337i	$0.819053\pi$
$80$	−0.663319	+	1.14890i	−0.0741613	+	0.128451i
$81$	3.33966	−	5.78446i	0.371074	−	0.642718i
$82$	2.13212	+	3.69295i	0.235454	+	0.407818i
$83$	10.3746			1.13876			0.569381	−	0.822074i	$-0.307183\pi$
$83$	10.3746			1.13876			0.569381	+	0.822074i	$0.307183\pi$
$84$	−3.03798	+	6.10213i	−0.331471	+	0.665797i
$85$	−9.21906			−0.999947
$86$	4.18358	+	7.24617i	0.451127	+	0.781375i
$87$	−1.49232	+	2.58477i	−0.159993	+	0.277117i
$88$	−1.04567	+	1.81115i	−0.111468	+	0.193069i
$89$	−8.32132	−	14.4129i	−0.882058	−	1.52777i	−0.849049	−	0.528315i	$-0.822824\pi$
$89$	−8.32132	−	14.4129i	−0.882058	−	1.52777i	−0.0330095	−	0.999455i	$-0.510509\pi$
$90$	4.82619			0.508725
$91$	−4.54756	−	6.86194i	−0.476713	−	0.719327i
$92$	−1.00000			−0.104257
$93$	11.2253	+	19.4428i	1.16401	+	2.01612i
$94$	1.74065	−	3.01490i	0.179534	−	0.310963i
$95$	−5.15168	+	8.92298i	−0.528552	+	0.915478i
$96$	−1.28821	−	2.23124i	−0.131477	−	0.227725i
$97$	6.65800			0.676018			0.338009	−	0.941143i	$-0.390247\pi$
$97$	6.65800			0.676018			0.338009	+	0.941143i	$0.390247\pi$
$98$	6.94683	−	0.861161i	0.701735	−	0.0869904i
$99$	7.60808			0.764641
$100$	1.62002	+	2.80595i	0.162002	+	0.280595i
$101$	−4.57940	+	7.93175i	−0.455667	+	0.789238i	−0.998726	−	0.0504560i	$-0.983933\pi$
$101$	−4.57940	+	7.93175i	−0.455667	+	0.789238i	0.543059	+	0.839694i	$0.317266\pi$
$102$	8.95200	−	15.5053i	0.886380	−	1.53526i
$103$	−2.26606	−	3.92492i	−0.223281	−	0.386734i	0.732521	−	0.680744i	$-0.238343\pi$
$103$	−2.26606	−	3.92492i	−0.223281	−	0.386734i	−0.955802	+	0.294010i	$0.905010\pi$
$104$	3.11142			0.305100
$105$	−4.99560	−	7.53801i	−0.487521	−	0.735634i
$106$	4.24003			0.411828
$107$	6.16722	+	10.6819i	0.596207	+	1.03266i	0.993375	+	0.114916i	$0.0366597\pi$
$107$	6.16722	+	10.6819i	0.596207	+	1.03266i	−0.397168	+	0.917746i	$0.630007\pi$
$108$	−0.821765	+	1.42334i	−0.0790744	+	0.136961i
$109$	0.549920	−	0.952489i	0.0526728	−	0.0912319i	−0.838487	−	0.544922i	$-0.816559\pi$
$109$	0.549920	−	0.952489i	0.0526728	−	0.0912319i	0.891160	+	0.453690i	$0.149893\pi$
$110$	−1.38722	−	2.40273i	−0.132266	−	0.229092i
$111$	−8.52649			−0.809299
$112$	−1.17915	+	2.36846i	−0.111419	+	0.223798i
$113$	4.44278			0.417942			0.208971	−	0.977922i	$-0.432989\pi$
$113$	4.44278			0.417942			0.208971	+	0.977922i	$0.432989\pi$
$114$	−10.0049	−	17.3290i	−0.937045	−	1.62301i
$115$	0.663319	−	1.14890i	0.0618548	−	0.107136i
$116$	−0.579223	+	1.00324i	−0.0537795	+	0.0931489i
$117$	−5.65954	−	9.80260i	−0.523224	−	0.906251i
$118$	9.18450			0.845501
$119$	−18.3509	+	1.13309i	−1.68222	+	0.103871i
$120$	3.41797			0.312016
$121$	3.31317	+	5.73857i	0.301197	+	0.521689i
$122$	−6.01934	+	10.4258i	−0.544966	+	0.943908i
$123$	5.49324	−	9.51457i	0.495308	−	0.857899i
$124$	4.35694	+	7.54644i	0.391265	+	0.677691i
$125$	−10.9315			−0.977746
$126$	9.60672	−	0.593177i	0.855835	−	0.0528444i
$127$	2.41201			0.214031			0.107015	−	0.994257i	$-0.465871\pi$
$127$	2.41201			0.214031			0.107015	+	0.994257i	$0.465871\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	10.7786	−	18.6691i	0.949006	−	1.64373i
$130$	−2.06386	+	3.57471i	−0.181013	+	0.313523i
$131$	−0.761712	−	1.31932i	−0.0665511	−	0.115270i	0.830830	−	0.556526i	$-0.187866\pi$
$131$	−0.761712	−	1.31932i	−0.0665511	−	0.115270i	−0.897381	+	0.441257i	$0.854533\pi$
$132$	5.38814			0.468977
$133$	−9.15792	+	18.3947i	−0.794092	+	1.59502i
$134$	−7.26319			−0.627444
$135$	−1.09018	−	1.88825i	−0.0938281	−	0.162515i
$136$	3.47460	−	6.01818i	0.297944	−	0.516054i
$137$	−4.81334	+	8.33695i	−0.411231	+	0.712274i	−0.995025	−	0.0996287i	$-0.968235\pi$
$137$	−4.81334	+	8.33695i	−0.411231	+	0.712274i	0.583793	+	0.811902i	$0.301568\pi$
$138$	1.28821	+	2.23124i	0.109660	+	0.189936i
$139$	8.57676			0.727471			0.363736	−	0.931502i	$-0.381501\pi$
$139$	8.57676			0.727471			0.363736	+	0.931502i	$0.381501\pi$
$140$	−1.93897	−	2.92577i	−0.163873	−	0.247273i
$141$	−8.96928			−0.755349
$142$	3.70854	+	6.42338i	0.311214	+	0.539038i
$143$	−3.25350	+	5.63523i	−0.272072	+	0.471242i
$144$	−1.81896	+	3.15053i	−0.151580	+	0.262544i
$145$	−0.768419	−	1.33094i	−0.0638137	−	0.110529i
$146$	−4.36805			−0.361502
$147$	−10.8704	−	14.3907i	−0.896576	−	1.18692i
$148$	−3.30944			−0.272034
$149$	−8.01069	−	13.8749i	−0.656261	−	1.13668i	−0.981576	−	0.191072i	$-0.938804\pi$
$149$	−8.01069	−	13.8749i	−0.656261	−	1.13668i	0.325315	−	0.945606i	$-0.394530\pi$
$150$	4.17383	−	7.22929i	0.340792	−	0.590269i
$151$	6.96789	−	12.0687i	0.567039	−	0.982140i	−0.429818	−	0.902915i	$-0.641422\pi$
$151$	6.96789	−	12.0687i	0.567039	−	0.982140i	0.996857	−	0.0792244i	$-0.0252443\pi$
$152$	−3.88326	−	6.72601i	−0.314974	−	0.545552i
$153$	−25.2806			−2.04381
$154$	−3.05663	−	4.61223i	−0.246310	−	0.371664i
$155$	−11.5602			−0.928535
$156$	−4.00815	−	6.94232i	−0.320909	−	0.555831i
$157$	7.71135	−	13.3564i	0.615433	−	1.06596i	−0.374876	−	0.927075i	$-0.622315\pi$
$157$	7.71135	−	13.3564i	0.615433	−	1.06596i	0.990308	−	0.138885i	$-0.0443520\pi$
$158$	0.398625	−	0.690439i	0.0317129	−	0.0549284i
$159$	−5.46204	−	9.46053i	−0.433168	−	0.750269i
$160$	1.32664			0.104880
$161$	1.17915	−	2.36846i	0.0929302	−	0.186661i
$162$	−6.67932			−0.524777
$163$	4.30693	+	7.45983i	0.337345	+	0.584299i	0.983932	−	0.178541i	$-0.0571378\pi$
$163$	4.30693	+	7.45983i	0.337345	+	0.584299i	−0.646587	+	0.762840i	$0.723804\pi$
$164$	2.13212	−	3.69295i	0.166491	−	0.288371i
$165$	−3.57405	+	6.19044i	−0.278240	+	0.481925i
$166$	−5.18730	−	8.98468i	−0.402613	−	0.697346i
$167$	11.9693			0.926211			0.463105	−	0.886303i	$-0.346735\pi$
$167$	11.9693			0.926211			0.463105	+	0.886303i	$0.346735\pi$
$168$	6.80360	−	0.420095i	0.524909	−	0.0324110i
$169$	−3.31907			−0.255313
$170$	4.60953	+	7.98394i	0.353535	+	0.612340i
$171$	−14.1270	+	24.4686i	−1.08032	+	1.87116i
$172$	4.18358	−	7.24617i	0.318995	−	0.552515i
$173$	9.90984	+	17.1644i	0.753431	+	1.30498i	0.946150	+	0.323727i	$0.104936\pi$
$173$	9.90984	+	17.1644i	0.753431	+	1.30498i	−0.192719	+	0.981254i	$0.561731\pi$
$174$	2.98464			0.226265
$175$	−8.55603	+	0.528301i	−0.646775	+	0.0399358i
$176$	2.09133			0.157640
$177$	−11.8315	−	20.4928i	−0.889313	−	1.54033i
$178$	−8.32132	+	14.4129i	−0.623709	+	1.08030i
$179$	8.20481	−	14.2112i	0.613257	−	1.06219i	−0.377431	−	0.926038i	$-0.623193\pi$
$179$	8.20481	−	14.2112i	0.613257	−	1.06219i	0.990688	−	0.136154i	$-0.0434742\pi$
$180$	−2.41310	−	4.17961i	−0.179862	−	0.311529i
$181$	−11.2306			−0.834766			−0.417383	−	0.908731i	$-0.637053\pi$
$181$	−11.2306			−0.834766			−0.417383	+	0.908731i	$0.637053\pi$
$182$	−3.66884	+	7.36927i	−0.271952	+	0.546247i
$183$	31.0167			2.29282
$184$	0.500000	+	0.866025i	0.0368605	+	0.0638442i
$185$	2.19521	−	3.80222i	0.161395	−	0.279545i
$186$	11.2253	−	19.4428i	0.823078	−	1.42561i
$187$	7.26653	+	12.5860i	0.531381	+	0.920379i
$188$	−3.48130			−0.253900
$189$	−2.40213	−	3.62465i	−0.174730	−	0.263655i
$190$	10.3034			0.747485
$191$	−3.18402	−	5.51489i	−0.230388	−	0.399044i	0.727534	−	0.686071i	$-0.240666\pi$
$191$	−3.18402	−	5.51489i	−0.230388	−	0.399044i	−0.957922	+	0.287028i	$0.907333\pi$
$192$	−1.28821	+	2.23124i	−0.0929684	+	0.161026i
$193$	7.02750	−	12.1720i	0.505850	−	0.876158i	−0.494127	−	0.869390i	$-0.664512\pi$
$193$	7.02750	−	12.1720i	0.505850	−	0.876158i	0.999977	−	0.00676850i	$-0.00215450\pi$
$194$	−3.32900	−	5.76600i	−0.239008	−	0.413975i
$195$	10.6347			0.761569
$196$	−4.21920	−	5.58555i	−0.301371	−	0.398968i
$197$	−6.95570			−0.495573			−0.247786	−	0.968815i	$-0.579703\pi$
$197$	−6.95570			−0.495573			−0.247786	+	0.968815i	$0.579703\pi$
$198$	−3.80404	−	6.58879i	−0.270341	−	0.468245i
$199$	−10.5449	+	18.2642i	−0.747506	+	1.29472i	0.201509	+	0.979487i	$0.435415\pi$
$199$	−10.5449	+	18.2642i	−0.747506	+	1.29472i	−0.949015	+	0.315231i	$0.897918\pi$
$200$	1.62002	−	2.80595i	0.114552	−	0.198411i
$201$	9.35650	+	16.2059i	0.659956	+	1.14308i
$202$	9.15879			0.644410
$203$	−1.69315	−	2.55484i	−0.118836	−	0.179315i
$204$	−17.9040			−1.25353
$205$	2.82856	+	4.89920i	0.197555	+	0.342175i
$206$	−2.26606	+	3.92492i	−0.157884	+	0.273462i
$207$	1.81896	−	3.15053i	0.126426	−	0.218977i
$208$	−1.55571	−	2.69457i	−0.107869	−	0.186835i
$209$	16.2424			1.12351
$210$	−4.03030	+	8.09532i	−0.278117	+	0.558630i
$211$	26.5036			1.82458			0.912290	−	0.409544i	$-0.134312\pi$
$211$	26.5036			1.82458			0.912290	+	0.409544i	$0.134312\pi$
$212$	−2.12002	−	3.67198i	−0.145603	−	0.252192i
$213$	9.55474	−	16.5493i	0.654680	−	1.13394i
$214$	6.16722	−	10.6819i	0.421582	−	0.730202i
$215$	5.55009	+	9.61304i	0.378513	+	0.655604i
$216$	1.64353			0.111828
$217$	−23.0109	+	1.42083i	−1.56208	+	0.0964525i
$218$	−1.09984			−0.0744906
$219$	5.62695	+	9.74617i	0.380234	+	0.658585i
$220$	−1.38722	+	2.40273i	−0.0935263	+	0.161992i
$221$	10.8109	−	18.7251i	0.727221	−	1.25958i
$222$	4.26325	+	7.38416i	0.286130	+	0.495592i
$223$	−9.80109			−0.656329			−0.328165	−	0.944621i	$-0.606430\pi$
$223$	−9.80109			−0.656329			−0.328165	+	0.944621i	$0.606430\pi$
$224$	2.64072	−	0.163054i	0.176441	−	0.0108945i
$225$	−11.7870			−0.785797
$226$	−2.22139	−	3.84756i	−0.147765	−	0.255936i
$227$	14.2481	−	24.6784i	0.945679	−	1.63796i	0.191292	−	0.981533i	$-0.438732\pi$
$227$	14.2481	−	24.6784i	0.945679	−	1.63796i	0.754387	−	0.656430i	$-0.227934\pi$
$228$	−10.0049	+	17.3290i	−0.662591	+	1.14764i
$229$	12.5957	+	21.8164i	0.832347	+	1.44167i	0.896172	+	0.443707i	$0.146337\pi$
$229$	12.5957	+	21.8164i	0.832347	+	1.44167i	−0.0638246	+	0.997961i	$0.520330\pi$
$230$	−1.32664			−0.0874759
$231$	−6.35343	+	12.7616i	−0.418025	+	0.839650i
$232$	1.15845			0.0760557
$233$	6.58123	+	11.3990i	0.431151	+	0.746775i	0.996973	−	0.0777524i	$-0.0247744\pi$
$233$	6.58123	+	11.3990i	0.431151	+	0.746775i	−0.565822	+	0.824527i	$0.691441\pi$
$234$	−5.65954	+	9.80260i	−0.369975	+	0.640816i
$235$	2.30921	−	3.99967i	0.150636	−	0.260910i
$236$	−4.59225	−	7.95401i	−0.298930	−	0.517762i
$237$	−2.05405			−0.133425
$238$	10.1567	+	15.3258i	0.658363	+	0.993423i
$239$	−8.78283			−0.568114			−0.284057	−	0.958807i	$-0.591681\pi$
$239$	−8.78283			−0.568114			−0.284057	+	0.958807i	$0.591681\pi$
$240$	−1.70898	−	2.96005i	−0.110314	−	0.191070i
$241$	−0.763776	+	1.32290i	−0.0491992	+	0.0852154i	−0.889576	−	0.456787i	$-0.849000\pi$
$241$	−0.763776	+	1.32290i	−0.0491992	+	0.0852154i	0.840377	+	0.542002i	$0.182334\pi$
$242$	3.31317	−	5.73857i	0.212978	−	0.368890i
$243$	11.0697	+	19.1732i	0.710118	+	1.22996i
$244$	12.0387			0.770698
$245$	9.21592	−	1.14245i	0.588784	−	0.0729884i
$246$	−10.9865			−0.700472
$247$	−12.0825	−	20.9274i	−0.768789	−	1.33158i
$248$	4.35694	−	7.54644i	0.276666	−	0.479200i
$249$	−13.3646	+	23.1483i	−0.846950	+	1.46696i
$250$	5.46577	+	9.46699i	0.345686	+	0.598745i
$251$	1.04230			0.0657895			0.0328947	−	0.999459i	$-0.489527\pi$
$251$	1.04230			0.0657895			0.0328947	+	0.999459i	$0.489527\pi$
$252$	−5.31707	−	8.02307i	−0.334944	−	0.505406i
$253$	−2.09133			−0.131481
$254$	−1.20600	−	2.08886i	−0.0756714	−	0.131067i
$255$	11.8761	−	20.5699i	0.743707	−	1.28814i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	3.38705	+	5.86654i	0.211278	+	0.365944i	0.952115	−	0.305741i	$-0.0989041\pi$
$257$	3.38705	+	5.86654i	0.211278	+	0.365944i	−0.740837	+	0.671685i	$0.765571\pi$
$258$	−21.5573			−1.34210
$259$	3.90234	−	7.83828i	0.242479	−	0.487047i
$260$	4.12772			0.255991
$261$	−2.10716	−	3.64972i	−0.130430	−	0.225912i
$262$	−0.761712	+	1.31932i	−0.0470588	+	0.0815082i
$263$	−0.228543	+	0.395849i	−0.0140926	+	0.0244091i	−0.872986	−	0.487746i	$-0.837819\pi$
$263$	−0.228543	+	0.395849i	−0.0140926	+	0.0244091i	0.858893	+	0.512155i	$0.171153\pi$
$264$	−2.69407	−	4.66626i	−0.165808	−	0.287189i
$265$	5.62499			0.345540
$266$	20.5092	−	1.26636i	1.25750	−	0.0776458i
$267$	42.8783			2.62411
$268$	3.63160	+	6.29011i	0.221835	+	0.384229i
$269$	−9.27674	+	16.0678i	−0.565613	+	0.979671i	0.431379	+	0.902171i	$0.358027\pi$
$269$	−9.27674	+	16.0678i	−0.565613	+	0.979671i	−0.996992	+	0.0775000i	$0.975306\pi$
$270$	−1.09018	+	1.88825i	−0.0663465	+	0.114916i
$271$	−9.14545	−	15.8404i	−0.555546	−	0.962235i	−0.997861	−	0.0653746i	$-0.979176\pi$
$271$	−9.14545	−	15.8404i	−0.555546	−	0.962235i	0.442314	−	0.896860i	$-0.354158\pi$
$272$	−6.94919			−0.421357
$273$	21.1688	−	1.30709i	1.28120	−	0.0791088i
$274$	9.62668			0.581569
$275$	3.38799	+	5.86817i	0.204304	+	0.353864i
$276$	1.28821	−	2.23124i	0.0775410	−	0.134305i
$277$	−10.0783	+	17.4562i	−0.605548	+	1.04884i	0.386416	+	0.922325i	$0.373713\pi$
$277$	−10.0783	+	17.4562i	−0.605548	+	1.04884i	−0.991965	+	0.126516i	$0.959620\pi$
$278$	−4.28838	−	7.42769i	−0.257200	−	0.445483i
$279$	−31.7004			−1.89785
$280$	−1.56431	+	3.14209i	−0.0934852	+	0.187776i
$281$	−7.27365			−0.433909			−0.216955	−	0.976182i	$-0.569612\pi$
$281$	−7.27365			−0.433909			−0.216955	+	0.976182i	$0.569612\pi$
$282$	4.48464	+	7.76762i	0.267056	+	0.462555i
$283$	1.38120	−	2.39231i	0.0821038	−	0.142208i	−0.822050	−	0.569416i	$-0.807169\pi$
$283$	1.38120	−	2.39231i	0.0821038	−	0.142208i	0.904153	+	0.427208i	$0.140503\pi$
$284$	3.70854	−	6.42338i	0.220061	−	0.381157i
$285$	−13.2729	−	22.9893i	−0.786217	−	1.36177i
$286$	6.50701			0.384767
$287$	6.23250	+	9.40440i	0.367893	+	0.555124i
$288$	3.63791			0.214366
$289$	−15.6456	−	27.0990i	−0.920331	−	1.59406i
$290$	−0.768419	+	1.33094i	−0.0451231	+	0.0781556i
$291$	−8.57689	+	14.8556i	−0.502786	+	0.870851i
$292$	2.18402	+	3.78284i	0.127810	+	0.221374i
$293$	25.3756			1.48246			0.741228	−	0.671253i	$-0.234244\pi$
$293$	25.3756			1.48246			0.741228	+	0.671253i	$0.234244\pi$
$294$	−7.02750	+	16.6094i	−0.409852	+	0.968680i
$295$	12.1845			0.709409
$296$	1.65472	+	2.86606i	0.0961787	+	0.166586i
$297$	−1.71858	+	2.97667i	−0.0997223	+	0.172724i
$298$	−8.01069	+	13.8749i	−0.464047	+	0.803753i
$299$	1.55571	+	2.69457i	0.0899690	+	0.155831i
$300$	−8.34767			−0.481953
$301$	12.2292	+	18.4530i	0.704879	+	1.06361i
$302$	−13.9358			−0.801914
$303$	−11.7984	−	20.4355i	−0.677802	−	1.17399i
$304$	−3.88326	+	6.72601i	−0.222720	+	0.385763i
$305$	−7.98549	+	13.8313i	−0.457248	+	0.791976i
$306$	12.6403	+	21.8936i	0.722597	+	1.25157i
$307$	−29.2469			−1.66921			−0.834606	−	0.550848i	$-0.814304\pi$
$307$	−29.2469			−1.66921			−0.834606	+	0.550848i	$0.814304\pi$
$308$	−2.46600	+	4.95323i	−0.140513	+	0.282237i
$309$	11.6766			0.664259
$310$	5.78008	+	10.0114i	0.328287	+	0.568609i
$311$	−13.6414	+	23.6276i	−0.773534	+	1.33980i	0.162081	+	0.986778i	$0.448180\pi$
$311$	−13.6414	+	23.6276i	−0.773534	+	1.33980i	−0.935615	+	0.353023i	$0.885154\pi$
$312$	−4.00815	+	6.94232i	−0.226917	+	0.393032i
$313$	−1.28838	−	2.23154i	−0.0728236	−	0.126134i	0.827314	−	0.561739i	$-0.189868\pi$
$313$	−1.28838	−	2.23154i	−0.0728236	−	0.126134i	−0.900138	+	0.435605i	$0.856534\pi$
$314$	−15.4227			−0.870353
$315$	12.7446	−	0.786930i	0.718079	−	0.0443385i
$316$	−0.797250			−0.0448488
$317$	6.25323	+	10.8309i	0.351216	+	0.608325i	0.986463	−	0.163985i	$-0.0524348\pi$
$317$	6.25323	+	10.8309i	0.351216	+	0.608325i	−0.635246	+	0.772310i	$0.719101\pi$
$318$	−5.46204	+	9.46053i	−0.306296	+	0.530520i
$319$	−1.21135	+	2.09812i	−0.0678224	+	0.117472i
$320$	−0.663319	−	1.14890i	−0.0370806	−	0.0642256i
$321$	−31.7786			−1.77371
$322$	−2.64072	+	0.163054i	−0.147162	+	0.00908665i
$323$	−53.9711			−3.00303
$324$	3.33966	+	5.78446i	0.185537	+	0.321359i
$325$	5.04055	−	8.73049i	0.279599	−	0.484280i
$326$	4.30693	−	7.45983i	0.238539	−	0.413162i
$327$	1.41682	+	2.45401i	0.0783504	+	0.135707i
$328$	−4.26425			−0.235454
$329$	4.10498	−	8.24532i	0.226315	−	0.454579i
$330$	7.14810			0.393490
$331$	−1.36699	−	2.36769i	−0.0751363	−	0.130140i	0.826009	−	0.563657i	$-0.190606\pi$
$331$	−1.36699	−	2.36769i	−0.0751363	−	0.130140i	−0.901146	+	0.433517i	$0.857273\pi$
$332$	−5.18730	+	8.98468i	−0.284690	+	0.493098i
$333$	6.01973	−	10.4265i	0.329879	−	0.571368i
$334$	−5.98464	−	10.3657i	−0.327465	−	0.567186i
$335$	−9.63562			−0.526450
$336$	−3.76561	−	5.68204i	−0.205431	−	0.309981i
$337$	12.4355			0.677405			0.338703	−	0.940893i	$-0.390012\pi$
$337$	12.4355			0.677405			0.338703	+	0.940893i	$0.390012\pi$
$338$	1.65954	+	2.87440i	0.0902669	+	0.156347i
$339$	−5.72323	+	9.91292i	−0.310843	+	0.538396i
$340$	4.60953	−	7.98394i	0.249987	−	0.432990i
$341$	9.11181	+	15.7821i	0.493432	+	0.854649i
$342$	28.2540			1.52780
$343$	18.2042	−	3.40680i	0.982936	−	0.183950i
$344$	−8.36716			−0.451127
$345$	1.70898	+	2.96005i	0.0920086	+	0.159364i
$346$	9.90984	−	17.1644i	0.532756	−	0.922761i
$347$	−1.10374	+	1.91173i	−0.0592518	+	0.102627i	−0.894130	−	0.447808i	$-0.852205\pi$
$347$	−1.10374	+	1.91173i	−0.0592518	+	0.102627i	0.834878	+	0.550435i	$0.185538\pi$
$348$	−1.49232	−	2.58477i	−0.0799967	−	0.138558i
$349$	10.7710			0.576558			0.288279	−	0.957546i	$-0.406917\pi$
$349$	10.7710			0.576558			0.288279	+	0.957546i	$0.406917\pi$
$350$	4.73554	+	7.14559i	0.253125	+	0.381948i
$351$	5.11371			0.272950
$352$	−1.04567	−	1.81115i	−0.0557342	−	0.0965344i
$353$	6.94849	−	12.0351i	0.369831	−	0.640566i	−0.619708	−	0.784832i	$-0.712749\pi$
$353$	6.94849	−	12.0351i	0.369831	−	0.640566i	0.989539	+	0.144267i	$0.0460823\pi$
$354$	−11.8315	+	20.4928i	−0.628839	+	1.08918i
$355$	4.91989	+	8.52149i	0.261120	+	0.452274i
$356$	16.6426			0.882058
$357$	21.1115	−	42.4049i	1.11734	−	2.24430i
$358$	−16.4096			−0.867276
$359$	9.73350	+	16.8589i	0.513714	+	0.889780i	0.999873	+	0.0159091i	$0.00506425\pi$
$359$	9.73350	+	16.8589i	0.513714	+	0.889780i	−0.486159	+	0.873870i	$0.661602\pi$
$360$	−2.41310	+	4.17961i	−0.127181	+	0.220285i
$361$	−20.6595	+	35.7833i	−1.08734	+	1.88333i
$362$	5.61532	+	9.72601i	0.295135	+	0.511188i
$363$	−17.0722			−0.896057
$364$	8.21639	−	0.507330i	0.430656	−	0.0265913i
$365$	−5.79482			−0.303315
$366$	−15.5083	−	26.8612i	−0.810633	−	1.40406i
$367$	−8.59369	+	14.8847i	−0.448587	+	0.776976i	−0.998294	−	0.0583816i	$-0.981406\pi$
$367$	−8.59369	+	14.8847i	−0.448587	+	0.776976i	0.549707	+	0.835357i	$0.314739\pi$
$368$	0.500000	−	0.866025i	0.0260643	−	0.0451447i
$369$	7.75648	+	13.4346i	0.403786	+	0.699379i
$370$	−4.39043			−0.228248
$371$	11.1967	−	0.691355i	0.581306	−	0.0358934i
$372$	−22.4506			−1.16401
$373$	4.71828	+	8.17231i	0.244303	+	0.423146i	0.961936	−	0.273276i	$-0.0881074\pi$
$373$	4.71828	+	8.17231i	0.244303	+	0.423146i	−0.717632	+	0.696422i	$0.754774\pi$
$374$	7.26653	−	12.5860i	0.375743	−	0.650806i
$375$	14.0821	−	24.3909i	0.727196	−	1.25954i
$376$	1.74065	+	3.01490i	0.0897672	+	0.155481i
$377$	3.60441			0.185637
$378$	−1.93797	+	3.89264i	−0.0996785	+	0.200216i
$379$	6.99131			0.359120			0.179560	−	0.983747i	$-0.442533\pi$
$379$	6.99131			0.359120			0.179560	+	0.983747i	$0.442533\pi$
$380$	−5.15168	−	8.92298i	−0.264276	−	0.457739i
$381$	−3.10716	+	5.38177i	−0.159185	+	0.275716i
$382$	−3.18402	+	5.51489i	−0.162909	+	0.282166i
$383$	−13.7705	−	23.8512i	−0.703640	−	1.21874i	−0.967180	−	0.254092i	$-0.918223\pi$
$383$	−13.7705	−	23.8512i	−0.703640	−	1.21874i	0.263540	−	0.964649i	$-0.415110\pi$
$384$	2.57641			0.131477
$385$	−4.05504	−	6.11876i	−0.206664	−	0.311841i
$386$	−14.0550			−0.715380
$387$	15.2195	+	26.3609i	0.773651	+	1.34000i
$388$	−3.32900	+	5.76600i	−0.169004	+	0.292724i
$389$	−3.35222	+	5.80621i	−0.169964	+	0.294386i	−0.938407	−	0.345532i	$-0.887698\pi$
$389$	−3.35222	+	5.80621i	−0.169964	+	0.294386i	0.768443	+	0.639918i	$0.221032\pi$
$390$	−5.31737	−	9.20995i	−0.269255	−	0.466364i
$391$	6.94919			0.351436
$392$	−2.72763	+	6.44671i	−0.137766	+	0.325608i
$393$	3.92497			0.197989
$394$	3.47785	+	6.02381i	0.175211	+	0.303475i
$395$	0.528831	−	0.915962i	0.0266084	−	0.0460871i
$396$	−3.80404	+	6.58879i	−0.191160	+	0.331099i
$397$	−11.3026	−	19.5767i	−0.567262	−	0.982527i	−0.996835	−	0.0794950i	$-0.974669\pi$
$397$	−11.3026	−	19.5767i	−0.567262	−	0.982527i	0.429573	−	0.903032i	$-0.358664\pi$
$398$	21.0897			1.05713
$399$	−29.2457	−	44.1297i	−1.46412	−	2.20925i
$400$	−3.24003			−0.162002
$401$	4.85413	+	8.40761i	0.242404	+	0.419856i	0.961398	−	0.275160i	$-0.0887308\pi$
$401$	4.85413	+	8.40761i	0.242404	+	0.419856i	−0.718995	+	0.695016i	$0.755397\pi$
$402$	9.35650	−	16.2059i	0.466660	−	0.808278i
$403$	13.5563	−	23.4801i	0.675286	−	1.16963i
$404$	−4.57940	−	7.93175i	−0.227833	−	0.394619i
$405$	−8.86104			−0.440309
$406$	−1.36598	+	2.74373i	−0.0677927	+	0.136169i
$407$	−6.92114			−0.343068
$408$	8.95200	+	15.5053i	0.443190	+	0.767628i
$409$	18.1680	−	31.4679i	0.898350	−	1.55599i	0.0687468	−	0.997634i	$-0.478100\pi$
$409$	18.1680	−	31.4679i	0.898350	−	1.55599i	0.829603	−	0.558354i	$-0.188567\pi$
$410$	2.82856	−	4.89920i	0.139692	−	0.241954i
$411$	−12.4012	−	21.4794i	−0.611704	−	1.05950i
$412$	4.53211			0.223281
$413$	24.2537	−	1.49757i	1.19345	−	0.0736906i
$414$	−3.63791			−0.178794
$415$	−6.88167	−	11.9194i	−0.337808	−	0.585101i
$416$	−1.55571	+	2.69457i	−0.0762749	+	0.132112i
$417$	−11.0486	+	19.1368i	−0.541055	+	0.937134i
$418$	−8.12119	−	14.0663i	−0.397220	−	0.688006i
$419$	9.98642			0.487868			0.243934	−	0.969792i	$-0.421562\pi$
$419$	9.98642			0.487868			0.243934	+	0.969792i	$0.421562\pi$
$420$	9.02590	−	0.557314i	0.440419	−	0.0271941i
$421$	14.1053			0.687448			0.343724	−	0.939071i	$-0.388312\pi$
$421$	14.1053			0.687448			0.343724	+	0.939071i	$0.388312\pi$
$422$	−13.2518	−	22.9528i	−0.645087	−	1.11732i
$423$	6.33234	−	10.9679i	0.307889	−	0.533279i
$424$	−2.12002	+	3.67198i	−0.102957	+	0.178327i
$425$	−11.2578	−	19.4991i	−0.546084	−	0.945845i
$426$	−19.1095			−0.925857
$427$	−14.1954	+	28.5131i	−0.686966	+	1.37985i
$428$	−12.3344			−0.596207
$429$	−8.38237	−	14.5187i	−0.404705	−	0.700969i
$430$	5.55009	−	9.61304i	0.267649	−	0.463582i
$431$	1.77185	−	3.06893i	0.0853468	−	0.147825i	−0.820192	−	0.572088i	$-0.806134\pi$
$431$	1.77185	−	3.06893i	0.0853468	−	0.147825i	0.905539	+	0.424263i	$0.139467\pi$
$432$	−0.821765	−	1.42334i	−0.0395372	−	0.0684804i
$433$	−16.2680			−0.781792			−0.390896	−	0.920435i	$-0.627835\pi$
$433$	−16.2680			−0.781792			−0.390896	+	0.920435i	$0.627835\pi$
$434$	12.7360	+	19.2176i	0.611345	+	0.922477i
$435$	3.95953			0.189845
$436$	0.549920	+	0.952489i	0.0263364	+	0.0456160i
$437$	3.88326	−	6.72601i	0.185762	−	0.321749i
$438$	5.62695	−	9.74617i	0.268866	−	0.465690i
$439$	−0.585013	−	1.01327i	−0.0279211	−	0.0483608i	0.851727	−	0.523985i	$-0.175555\pi$
$439$	−0.585013	−	1.01327i	−0.0279211	−	0.0483608i	−0.879648	+	0.475625i	$0.842222\pi$
$440$	2.77444			0.132266
$441$	25.2720	−	3.13283i	1.20343	−	0.149182i
$442$	−21.6218			−1.02845
$443$	−19.5037	−	33.7813i	−0.926647	−	1.60500i	−0.788891	−	0.614533i	$-0.789345\pi$
$443$	−19.5037	−	33.7813i	−0.926647	−	1.60500i	−0.137755	−	0.990466i	$-0.543989\pi$
$444$	4.26325	−	7.38416i	0.202325	−	0.350437i
$445$	−11.0394	+	19.1208i	−0.523317	+	0.906411i
$446$	4.90054	+	8.48799i	0.232047	+	0.401918i
$447$	41.2777			1.95237
$448$	−1.46157	−	2.20541i	−0.0690527	−	0.104196i
$449$	32.1714			1.51826			0.759130	−	0.650939i	$-0.225624\pi$
$449$	32.1714			1.51826			0.759130	+	0.650939i	$0.225624\pi$
$450$	5.89348	+	10.2078i	0.277821	+	0.481201i
$451$	4.45898	−	7.72318i	0.209965	−	0.363670i
$452$	−2.22139	+	3.84756i	−0.104485	+	0.180974i
$453$	17.9522	+	31.0941i	0.843467	+	1.46093i
$454$	−28.4962			−1.33739
$455$	−4.86721	+	9.77635i	−0.228179	+	0.458322i
$456$	20.0098			0.937045
$457$	17.1774	+	29.7521i	0.803524	+	1.39174i	0.917283	+	0.398236i	$0.130377\pi$
$457$	17.1774	+	29.7521i	0.803524	+	1.39174i	−0.113759	+	0.993508i	$0.536289\pi$
$458$	12.5957	−	21.8164i	0.588558	−	1.01941i
$459$	5.71060	−	9.89105i	0.266548	−	0.461675i
$460$	0.663319	+	1.14890i	0.0309274	+	0.0535678i
$461$	10.5155			0.489756			0.244878	−	0.969554i	$-0.421252\pi$
$461$	10.5155			0.489756			0.244878	+	0.969554i	$0.421252\pi$
$462$	14.2286	−	0.878558i	0.661973	−	0.0408742i
$463$	−19.9943			−0.929213			−0.464606	−	0.885517i	$-0.653804\pi$
$463$	−19.9943			−0.929213			−0.464606	+	0.885517i	$0.653804\pi$
$464$	−0.579223	−	1.00324i	−0.0268898	−	0.0465744i
$465$	14.8919	−	25.7935i	0.690595	−	1.19615i
$466$	6.58123	−	11.3990i	0.304870	−	0.528050i
$467$	13.7321	+	23.7848i	0.635448	+	1.10063i	0.986420	+	0.164242i	$0.0525177\pi$
$467$	13.7321	+	23.7848i	0.635448	+	1.10063i	−0.350973	+	0.936386i	$0.614149\pi$
$468$	11.3191			0.523224
$469$	−19.1801	+	1.18429i	−0.885653	+	0.0546856i
$470$	−4.61843			−0.213032
$471$	19.8676	+	34.4117i	0.915452	+	1.58561i
$472$	−4.59225	+	7.95401i	−0.211375	+	0.366113i
$473$	8.74925	−	15.1541i	0.402291	−	0.696788i
$474$	1.02702	+	1.77886i	0.0471728	+	0.0817056i
$475$	−25.1638			−1.15459
$476$	8.19415	−	16.4589i	0.375578	−	0.754391i
$477$	15.4249			0.706257
$478$	4.39142	+	7.60616i	0.200859	+	0.347898i
$479$	4.22275	−	7.31402i	0.192943	−	0.334186i	−0.753282	−	0.657698i	$-0.771530\pi$
$479$	4.22275	−	7.31402i	0.192943	−	0.334186i	0.946224	+	0.323512i	$0.104864\pi$
$480$	−1.70898	+	2.96005i	−0.0780041	+	0.135107i
$481$	5.14853	+	8.91751i	0.234753	+	0.406604i
$482$	1.52755			0.0695781
$483$	3.76561	+	5.68204i	0.171341	+	0.258542i
$484$	−6.62633			−0.301197
$485$	−4.41638	−	7.64939i	−0.200537	−	0.347341i
$486$	11.0697	−	19.1732i	0.502130	−	0.869714i
$487$	−16.6395	+	28.8205i	−0.754009	+	1.30598i	0.191856	+	0.981423i	$0.438549\pi$
$487$	−16.6395	+	28.8205i	−0.754009	+	1.30598i	−0.945865	+	0.324559i	$0.894784\pi$
$488$	−6.01934	−	10.4258i	−0.272483	−	0.471954i
$489$	−22.1929			−1.00360
$490$	−5.59735	−	7.41000i	−0.252862	−	0.334750i
$491$	15.8532			0.715444			0.357722	−	0.933828i	$-0.383553\pi$
$491$	15.8532			0.715444			0.357722	+	0.933828i	$0.383553\pi$
$492$	5.49324	+	9.51457i	0.247654	+	0.428950i
$493$	4.02513	−	6.97173i	0.181283	−	0.313991i
$494$	−12.0825	+	20.9274i	−0.543616	+	0.941570i
$495$	−5.04658	−	8.74094i	−0.226827	−	0.392876i
$496$	−8.71388			−0.391265
$497$	10.8406	+	16.3577i	0.486266	+	0.733742i
$498$	26.7293			1.19777
$499$	9.66615	+	16.7423i	0.432717	+	0.749487i	0.997106	−	0.0760215i	$-0.0242218\pi$
$499$	9.66615	+	16.7423i	0.432717	+	0.749487i	−0.564390	+	0.825509i	$0.690888\pi$
$500$	5.46577	−	9.46699i	0.244437	−	0.423377i
$501$	−15.4189	+	26.7063i	−0.688866	+	1.19315i
$502$	−0.521150	−	0.902659i	−0.0232601	−	0.0402876i
$503$	40.9220			1.82462			0.912310	−	0.409500i	$-0.134297\pi$
$503$	40.9220			1.82462			0.912310	+	0.409500i	$0.134297\pi$
$504$	−4.28965	+	8.61625i	−0.191076	+	0.383798i
$505$	12.1504			0.540686
$506$	1.04567	+	1.81115i	0.0464855	+	0.0805152i
$507$	4.27565	−	7.40565i	0.189888	−	0.328897i
$508$	−1.20600	+	2.08886i	−0.0535077	+	0.0926781i
$509$	−0.260911	−	0.451912i	−0.0115647	−	0.0200306i	0.860185	−	0.509982i	$-0.170348\pi$
$509$	−0.260911	−	0.451912i	−0.0115647	−	0.0200306i	−0.871750	+	0.489951i	$0.837015\pi$
$510$	−23.7521			−1.05176
$511$	−11.5348	+	0.712228i	−0.510270	+	0.0315071i
$512$	1.00000			0.0441942
$513$	−6.38226	−	11.0544i	−0.281784	−	0.488064i
$514$	3.38705	−	5.86654i	0.149396	−	0.258762i
$515$	−3.00623	+	5.20695i	−0.132471	+	0.229446i
$516$	10.7786	+	18.6691i	0.474503	+	0.821863i
$517$	−7.28055			−0.320198
$518$	−8.73932	+	0.539618i	−0.383983	+	0.0237095i
$519$	−51.0637			−2.24145
$520$	−2.06386	−	3.57471i	−0.0905063	−	0.156762i
$521$	−6.14887	+	10.6502i	−0.269387	+	0.466592i	−0.968704	−	0.248220i	$-0.920154\pi$
$521$	−6.14887	+	10.6502i	−0.269387	+	0.466592i	0.699317	+	0.714812i	$0.253488\pi$
$522$	−2.10716	+	3.64972i	−0.0922281	+	0.159744i
$523$	−15.6891	−	27.1742i	−0.686034	−	1.18825i	−0.973111	−	0.230339i	$-0.926017\pi$
$523$	−15.6891	−	27.1742i	−0.686034	−	1.18825i	0.287076	−	0.957908i	$-0.407317\pi$
$524$	1.52342			0.0665511
$525$	9.84317	−	19.7711i	0.429591	−	0.862882i
$526$	0.457086			0.0199299
$527$	−30.2772	−	52.4417i	−1.31890	−	2.28440i
$528$	−2.69407	+	4.66626i	−0.117244	+	0.203073i
$529$	−0.500000	+	0.866025i	−0.0217391	+	0.0376533i
$530$	−2.81249	−	4.87138i	−0.122167	−	0.211599i
$531$	33.4124			1.44997
$532$	−11.3513	−	17.1283i	−0.492142	−	0.742608i
$533$	−13.2679			−0.574695
$534$	−21.4392	−	37.1337i	−0.927764	−	1.60693i
$535$	8.18166	−	14.1711i	0.353724	−	0.612668i
$536$	3.63160	−	6.29011i	0.156861	−	0.271691i
$537$	21.1390	+	36.6138i	0.912215	+	1.58000i
$538$	18.5535			0.799898
$539$	−8.82375	−	11.6812i	−0.380066	−	0.503146i
$540$	2.18037			0.0938281
$541$	−0.375985	−	0.651226i	−0.0161649	−	0.0279984i	0.857830	−	0.513934i	$-0.171812\pi$
$541$	−0.375985	−	0.651226i	−0.0161649	−	0.0279984i	−0.873995	+	0.485935i	$0.838479\pi$
$542$	−9.14545	+	15.8404i	−0.392831	+	0.680403i
$543$	14.4674	−	25.0582i	0.620855	−	1.07535i
$544$	3.47460	+	6.01818i	0.148972	+	0.258027i
$545$	−1.45909			−0.0625005
$546$	−11.7164	−	17.6792i	−0.501415	−	0.756600i
$547$	−27.3113			−1.16775			−0.583874	−	0.811844i	$-0.698464\pi$
$547$	−27.3113			−1.16775			−0.583874	+	0.811844i	$0.698464\pi$
$548$	−4.81334	−	8.33695i	−0.205616	−	0.356137i
$549$	−21.8979	+	37.9282i	−0.934578	+	1.61874i
$550$	3.38799	−	5.86817i	0.144464	−	0.250220i
$551$	−4.49855	−	7.79172i	−0.191645	−	0.331939i
$552$	−2.57641			−0.109660
$553$	0.940079	−	1.88825i	0.0399762	−	0.0802968i
$554$	20.1567			0.856375
$555$	5.65578	+	9.79610i	0.240075	+	0.415821i
$556$	−4.28838	+	7.42769i	−0.181868	+	0.315004i
$557$	−14.6243	+	25.3300i	−0.619650	+	1.07327i	0.369899	+	0.929072i	$0.379392\pi$
$557$	−14.6243	+	25.3300i	−0.619650	+	1.07327i	−0.989549	+	0.144194i	$0.953941\pi$
$558$	15.8502	+	27.4533i	0.670992	+	1.16219i
$559$	−26.0337			−1.10111
$560$	3.50328	−	0.216314i	0.148041	−	0.00914092i
$561$	−37.4432			−1.58085
$562$	3.63682	+	6.29916i	0.153410	+	0.265714i
$563$	−0.257258	+	0.445584i	−0.0108421	+	0.0187791i	−0.871396	−	0.490581i	$-0.836785\pi$
$563$	−0.257258	+	0.445584i	−0.0108421	+	0.0187791i	0.860553	+	0.509360i	$0.170118\pi$
$564$	4.48464	−	7.76762i	0.188837	−	0.327076i
$565$	−2.94698	−	5.10432i	−0.123980	−	0.214740i
$566$	−2.76240			−0.116112
$567$	−17.6382	+	1.08909i	−0.740736	+	0.0457375i
$568$	−7.41708			−0.311214
$569$	−16.9002	−	29.2720i	−0.708493	−	1.22715i	−0.965416	−	0.260714i	$-0.916042\pi$
$569$	−16.9002	−	29.2720i	−0.708493	−	1.22715i	0.256923	−	0.966432i	$-0.417291\pi$
$570$	−13.2729	+	22.9893i	−0.555940	+	0.962915i
$571$	6.69143	−	11.5899i	0.280028	−	0.485022i	−0.691364	−	0.722507i	$-0.742990\pi$
$571$	6.69143	−	11.5899i	0.280028	−	0.485022i	0.971391	+	0.237485i	$0.0763230\pi$
$572$	−3.25350	−	5.63523i	−0.136036	−	0.235621i
$573$	16.4067			0.685401
$574$	5.02820	−	10.0997i	0.209873	−	0.421553i
$575$	3.24003			0.135119
$576$	−1.81896	−	3.15053i	−0.0757899	−	0.131272i
$577$	18.3241	−	31.7382i	0.762842	−	1.32128i	−0.178538	−	0.983933i	$-0.557137\pi$
$577$	18.3241	−	31.7382i	0.762842	−	1.32128i	0.941380	−	0.337348i	$-0.109530\pi$
$578$	−15.6456	+	27.0990i	−0.650772	+	1.12717i
$579$	18.1057	+	31.3601i	0.752449	+	1.30328i
$580$	1.53684			0.0638137
$581$	−15.1632	−	22.8802i	−0.629076	−	0.949231i
$582$	17.1538			0.711047
$583$	−4.43366	−	7.67932i	−0.183623	−	0.318045i
$584$	2.18402	−	3.78284i	0.0903756	−	0.156535i
$585$	−7.50815	+	13.0045i	−0.310424	+	0.537670i
$586$	−12.6878	−	21.9759i	−0.524127	−	0.907815i
$587$	−10.8300			−0.447003			−0.223502	−	0.974704i	$-0.571749\pi$
$587$	−10.8300			−0.447003			−0.223502	+	0.974704i	$0.571749\pi$
$588$	17.8979	−	2.21871i	0.738097	−	0.0914980i
$589$	−67.6766			−2.78857
$590$	−6.09225	−	10.5521i	−0.250814	−	0.434422i
$591$	8.96038	−	15.5198i	0.368581	−	0.638401i
$592$	1.65472	−	2.86606i	0.0680086	−	0.117794i
$593$	3.90397	+	6.76187i	0.160317	+	0.277677i	0.934982	−	0.354694i	$-0.115415\pi$
$593$	3.90397	+	6.76187i	0.160317	+	0.277677i	−0.774665	+	0.632371i	$0.782082\pi$
$594$	3.43717			0.141029
$595$	13.4743	+	20.3318i	0.552392	+	0.833521i
$596$	16.0214			0.656261
$597$	−27.1679	−	47.0563i	−1.11191	−	1.92588i
$598$	1.55571	−	2.69457i	0.0636177	−	0.110189i
$599$	17.3699	−	30.0856i	0.709715	−	1.22926i	−0.255248	−	0.966876i	$-0.582157\pi$
$599$	17.3699	−	30.0856i	0.709715	−	1.22926i	0.964963	−	0.262387i	$-0.0845097\pi$
$600$	4.17383	+	7.22929i	0.170396	+	0.295135i
$601$	−33.4939			−1.36625			−0.683123	−	0.730303i	$-0.739379\pi$
$601$	−33.4939			−1.36625			−0.683123	+	0.730303i	$0.739379\pi$
$602$	9.86615	−	19.8173i	0.402114	−	0.807692i
$603$	−26.4229			−1.07602
$604$	6.96789	+	12.0687i	0.283519	+	0.491070i
$605$	4.39537	−	7.61301i	0.178697	−	0.309513i
$606$	−11.7984	+	20.4355i	−0.479278	+	0.830134i
$607$	16.5199	+	28.6134i	0.670523	+	1.16138i	0.977756	+	0.209746i	$0.0672637\pi$
$607$	16.5199	+	28.6134i	0.670523	+	1.16138i	−0.307233	+	0.951634i	$0.599403\pi$
$608$	7.76653			0.314974
$609$	7.88160	−	0.486658i	0.319379	−	0.0197204i
$610$	15.9710			0.646646
$611$	5.41589	+	9.38060i	0.219104	+	0.379499i
$612$	12.6403	−	21.8936i	0.510953	−	0.884996i
$613$	−0.172305	+	0.298441i	−0.00695934	+	0.0120539i	−0.869484	−	0.493961i	$-0.835549\pi$
$613$	−0.172305	+	0.298441i	−0.00695934	+	0.0120539i	0.862525	+	0.506015i	$0.168882\pi$
$614$	14.6235	+	25.3286i	0.590155	+	1.02218i
$615$	−14.5751			−0.587723
$616$	5.52262	−	0.341000i	0.222513	−	0.0137393i
$617$	18.8997			0.760872			0.380436	−	0.924807i	$-0.375774\pi$
$617$	18.8997			0.760872			0.380436	+	0.924807i	$0.375774\pi$
$618$	−5.83830	−	10.1122i	−0.234851	−	0.406774i
$619$	−11.2136	+	19.4225i	−0.450712	+	0.780656i	−0.998430	−	0.0560067i	$-0.982163\pi$
$619$	−11.2136	+	19.4225i	−0.450712	+	0.780656i	0.547718	+	0.836663i	$0.315497\pi$
$620$	5.78008	−	10.0114i	0.232134	−	0.402067i
$621$	0.821765	+	1.42334i	0.0329763	+	0.0571166i
$622$	27.2828			1.09394
$623$	−19.6242	+	39.4174i	−0.786227	+	1.57923i
$624$	8.01631			0.320909
$625$	−0.848991	−	1.47050i	−0.0339596	−	0.0588198i
$626$	−1.28838	+	2.23154i	−0.0514940	+	0.0891903i
$627$	−20.9236	+	36.2407i	−0.835606	+	1.44731i
$628$	7.71135	+	13.3564i	0.307716	+	0.532980i
$629$	22.9979			0.916988
$630$	−7.05382	−	10.6437i	−0.281031	−	0.424056i
$631$	45.9749			1.83023			0.915117	−	0.403189i	$-0.132098\pi$
$631$	45.9749			1.83023			0.915117	+	0.403189i	$0.132098\pi$
$632$	0.398625	+	0.690439i	0.0158565	+	0.0274642i
$633$	−34.1421	+	59.1358i	−1.35703	+	2.35044i
$634$	6.25323	−	10.8309i	0.248348	−	0.430151i
$635$	−1.59993	−	2.77116i	−0.0634912	−	0.109970i
$636$	10.9241			0.433168
$637$	−8.48679	+	20.0584i	−0.336259	+	0.794743i
$638$	2.42270			0.0959154
$639$	13.4913	+	23.3677i	0.533709	+	0.924412i
$640$	−0.663319	+	1.14890i	−0.0262200	+	0.0454143i
$641$	5.92284	−	10.2587i	0.233938	−	0.405193i	−0.725025	−	0.688722i	$-0.758172\pi$
$641$	5.92284	−	10.2587i	0.233938	−	0.405193i	0.958964	+	0.283529i	$0.0915053\pi$
$642$	15.8893	+	27.5211i	0.627101	+	1.08617i
$643$	40.7199			1.60584			0.802918	−	0.596089i	$-0.203280\pi$
$643$	40.7199			1.60584			0.802918	+	0.596089i	$0.203280\pi$
$644$	1.46157	+	2.20541i	0.0575939	+	0.0869051i
$645$	−28.5987			−1.12607
$646$	26.9855	+	46.7403i	1.06173	+	1.83897i
$647$	−0.360840	+	0.624994i	−0.0141861	+	0.0245710i	−0.873031	−	0.487664i	$-0.837849\pi$
$647$	−0.360840	+	0.624994i	−0.0141861	+	0.0245710i	0.858845	+	0.512235i	$0.171182\pi$
$648$	3.33966	−	5.78446i	0.131194	−	0.227235i
$649$	−9.60391	−	16.6345i	−0.376986	−	0.652960i
$650$	−10.0811			−0.395413
$651$	26.4726	−	53.1733i	1.03754	−	2.08403i
$652$	−8.61387			−0.337345
$653$	0.373131	+	0.646282i	0.0146018	+	0.0252910i	0.873234	−	0.487301i	$-0.162019\pi$
$653$	0.373131	+	0.646282i	0.0146018	+	0.0252910i	−0.858632	+	0.512592i	$0.828685\pi$
$654$	1.41682	−	2.45401i	0.0554021	−	0.0959593i
$655$	−1.01052	+	1.75027i	−0.0394841	+	0.0683885i
$656$	2.13212	+	3.69295i	0.0832455	+	0.144185i
$657$	−15.8906			−0.619951
$658$	−9.19315	+	0.567641i	−0.358386	+	0.0221289i
$659$	6.85325			0.266965			0.133482	−	0.991051i	$-0.457384\pi$
$659$	6.85325			0.266965			0.133482	+	0.991051i	$0.457384\pi$
$660$	−3.57405	−	6.19044i	−0.139120	−	0.240963i
$661$	−16.8918	+	29.2575i	−0.657016	+	1.13798i	0.324369	+	0.945931i	$0.394848\pi$
$661$	−16.8918	+	29.2575i	−0.657016	+	1.13798i	−0.981384	+	0.192054i	$0.938485\pi$
$662$	−1.36699	+	2.36769i	−0.0531294	+	0.0920228i
$663$	27.8534	+	48.2435i	1.08174	+	1.87362i
$664$	10.3746			0.402613
$665$	27.2083	−	1.68001i	1.05509	−	0.0651478i
$666$	−12.0395			−0.466520
$667$	0.579223	+	1.00324i	0.0224276	+	0.0388458i
$668$	−5.98464	+	10.3657i	−0.231553	+	0.401061i
$669$	12.6258	−	21.8686i	0.488143	−	0.845488i
$670$	4.81781	+	8.34469i	0.186128	+	0.322384i
$671$	25.1769			0.971943
$672$	−3.03798	+	6.10213i	−0.117193	+	0.235395i
$673$	32.6054			1.25684			0.628422	−	0.777873i	$-0.283701\pi$
$673$	32.6054			1.25684			0.628422	+	0.777873i	$0.283701\pi$
$674$	−6.21775	−	10.7695i	−0.239499	−	0.414824i
$675$	2.66255	−	4.61167i	0.102481	−	0.177503i
$676$	1.65954	−	2.87440i	0.0638283	−	0.110554i
$677$	−12.5764	−	21.7829i	−0.483349	−	0.837184i	0.516469	−	0.856306i	$-0.327246\pi$
$677$	−12.5764	−	21.7829i	−0.483349	−	0.837184i	−0.999817	+	0.0191219i	$0.993913\pi$
$678$	11.4465			0.439598
$679$	−9.73114	−	14.6836i	−0.373447	−	0.563505i
$680$	−9.21906			−0.353535
$681$	36.7090	+	63.5818i	1.40669	+	2.43646i
$682$	9.11181	−	15.7821i	0.348909	−	0.604328i
$683$	16.8507	−	29.1863i	0.644776	−	1.11678i	−0.339578	−	0.940578i	$-0.610284\pi$
$683$	16.8507	−	29.1863i	0.644776	−	1.11678i	0.984353	−	0.176206i	$-0.0563825\pi$
$684$	−14.1270	−	24.4686i	−0.540159	−	0.935582i
$685$	12.7711			0.487959
$686$	−12.0525	−	14.0619i	−0.460166	−	0.536887i
$687$	−64.9035			−2.47622
$688$	4.18358	+	7.24617i	0.159497	+	0.276258i
$689$	−6.59626	+	11.4251i	−0.251297	+	0.435260i
$690$	1.70898	−	2.96005i	0.0650599	−	0.112687i
$691$	−12.5502	−	21.7376i	−0.477431	−	0.826935i	0.522234	−	0.852802i	$-0.325099\pi$
$691$	−12.5502	−	21.7376i	−0.477431	−	0.826935i	−0.999665	+	0.0258668i	$0.991765\pi$
$692$	−19.8197			−0.753431
$693$	−11.1197	−	16.7789i	−0.422404	−	0.637378i
$694$	2.20748			0.0837947
$695$	−5.68913	−	9.85385i	−0.215801	−	0.373778i
$696$	−1.49232	+	2.58477i	−0.0565662	+	0.0979756i
$697$	−14.8165	+	25.6630i	−0.561216	+	0.972055i
$698$	−5.38550	−	9.32796i	−0.203844	−	0.353069i
$699$	−33.9120			−1.28267
$700$	3.82049	−	7.67389i	0.144401	−	0.290046i
$701$	−32.8099			−1.23921			−0.619607	−	0.784912i	$-0.712708\pi$
$701$	−32.8099			−1.23921			−0.619607	+	0.784912i	$0.712708\pi$
$702$	−2.55686	−	4.42860i	−0.0965023	−	0.167147i
$703$	12.8514	−	22.2593i	0.484701	−	0.839527i
$704$	−1.04567	+	1.81115i	−0.0394100	+	0.0682601i
$705$	5.94949	+	10.3048i	0.224071	+	0.388102i
$706$	−13.8970			−0.523020
$707$	24.1858	−	1.49338i	0.909602	−	0.0561643i
$708$	23.6631			0.889313
$709$	9.54605	+	16.5343i	0.358510	+	0.620957i	0.987712	−	0.156285i	$-0.0499517\pi$
$709$	9.54605	+	16.5343i	0.358510	+	0.620957i	−0.629202	+	0.777241i	$0.716618\pi$
$710$	4.91989	−	8.52149i	0.184640	−	0.319806i
$711$	1.45016	−	2.51176i	0.0543854	−	0.0941983i
$712$	−8.32132	−	14.4129i	−0.311855	−	0.540148i
$713$	8.71388			0.326338
$714$	−47.2795	+	2.91932i	−1.76939	+	0.109253i
$715$	8.63244			0.322835
$716$	8.20481	+	14.2112i	0.306628	+	0.531096i
$717$	11.3141	−	19.5966i	0.422533	−	0.731849i
$718$	9.73350	−	16.8589i	0.363251	−	0.629169i
$719$	−10.5225	−	18.2254i	−0.392421	−	0.679693i	0.600347	−	0.799740i	$-0.295029\pi$
$719$	−10.5225	−	18.2254i	−0.392421	−	0.679693i	−0.992768	+	0.120046i	$0.961696\pi$
$720$	4.82619			0.179862
$721$	−5.34405	+	10.7341i	−0.199023	+	0.399760i
$722$	41.3190			1.53773
$723$	−1.96780	−	3.40834i	−0.0731834	−	0.126757i
$724$	5.61532	−	9.72601i	0.208692	−	0.361464i
$725$	1.87670	−	3.25054i	0.0696990	−	0.120722i
$726$	8.53609	+	14.7849i	0.316804	+	0.548721i
$727$	11.6826			0.433282			0.216641	−	0.976251i	$-0.430490\pi$
$727$	11.6826			0.433282			0.216641	+	0.976251i	$0.430490\pi$
$728$	−4.54756	−	6.86194i	−0.168544	−	0.254320i
$729$	−37.0021			−1.37045
$730$	2.89741	+	5.01846i	0.107238	+	0.185741i
$731$	−29.0725	+	50.3550i	−1.07528	+	1.86245i
$732$	−15.5083	+	26.8612i	−0.573204	+	0.992819i
$733$	12.1238	+	20.9990i	0.447802	+	0.775615i	0.998243	−	0.0592589i	$-0.0188737\pi$
$733$	12.1238	+	20.9990i	0.447802	+	0.775615i	−0.550441	+	0.834874i	$0.685540\pi$
$734$	17.1874			0.634398
$735$	−9.32294	+	22.0346i	−0.343882	+	0.812760i
$736$	−1.00000			−0.0368605
$737$	7.59487	+	13.1547i	0.279761	+	0.484560i
$738$	7.75648	−	13.4346i	0.285520	−	0.494535i
$739$	13.5595	−	23.4857i	0.498793	−	0.863935i	−0.501206	−	0.865328i	$-0.667110\pi$
$739$	13.5595	−	23.4857i	0.498793	−	0.863935i	0.999999	+	0.00139329i	$0.000443498\pi$
$740$	2.19521	+	3.80222i	0.0806977	+	0.139773i
$741$	62.2589			2.28714
$742$	−6.19711	−	9.35099i	−0.227503	−	0.343286i
$743$	−10.3281			−0.378902			−0.189451	−	0.981890i	$-0.560671\pi$
$743$	−10.3281			−0.378902			−0.189451	+	0.981890i	$0.560671\pi$
$744$	11.2253	+	19.4428i	0.411539	+	0.712807i
$745$	−10.6273	+	18.4070i	−0.389353	+	0.674380i
$746$	4.71828	−	8.17231i	0.172749	−	0.299209i
$747$	−18.8710	−	32.6855i	−0.690453	−	1.19590i
$748$	−14.5331			−0.531381
$749$	14.5442	−	29.2136i	0.531433	−	1.06744i
$750$	−28.1642			−1.02841
$751$	5.15333	+	8.92583i	0.188048	+	0.325708i	0.944599	−	0.328226i	$-0.106451\pi$
$751$	5.15333	+	8.92583i	0.188048	+	0.325708i	−0.756552	+	0.653934i	$0.773117\pi$
$752$	1.74065	−	3.01490i	0.0634750	−	0.109942i
$753$	−1.34270	+	2.32562i	−0.0489307	+	0.0847505i
$754$	−1.80221	−	3.12151i	−0.0656325	−	0.113679i
$755$	−18.4877			−0.672837
$756$	4.34011	−	0.267984i	0.157848	−	0.00974650i
$757$	−39.6243			−1.44017			−0.720084	−	0.693887i	$-0.755897\pi$
$757$	−39.6243			−1.44017			−0.720084	+	0.693887i	$0.755897\pi$
$758$	−3.49566	−	6.05465i	−0.126968	−	0.219915i
$759$	2.69407	−	4.66626i	0.0977885	−	0.169375i
$760$	−5.15168	+	8.92298i	−0.186871	+	0.323670i
$761$	26.7319	+	46.3010i	0.969031	+	1.67841i	0.698372	+	0.715735i	$0.253908\pi$
$761$	26.7319	+	46.3010i	0.969031	+	1.67841i	0.270658	+	0.962676i	$0.412759\pi$
$762$	6.21433			0.225121
$763$	−2.90437	+	0.179333i	−0.105145	+	0.00649231i
$764$	6.36805			0.230388
$765$	16.7691	+	29.0449i	0.606287	+	1.05012i
$766$	−13.7705	+	23.8512i	−0.497549	+	0.861780i
$767$	−14.2884	+	24.7482i	−0.515924	+	0.893607i
$768$	−1.28821	−	2.23124i	−0.0464842	−	0.0805130i
$769$	8.56383			0.308820			0.154410	−	0.988007i	$-0.450652\pi$
$769$	8.56383			0.308820			0.154410	+	0.988007i	$0.450652\pi$
$770$	−3.27148	+	6.57114i	−0.117896	+	0.236808i
$771$	−17.4529			−0.628550
$772$	7.02750	+	12.1720i	0.252925	+	0.438079i
$773$	15.8946	−	27.5302i	0.571688	−	0.990193i	−0.424705	−	0.905332i	$-0.639622\pi$
$773$	15.8946	−	27.5302i	0.571688	−	0.990193i	0.996393	−	0.0848607i	$-0.0270445\pi$
$774$	15.2195	−	26.3609i	0.547054	−	0.947525i
$775$	−14.1166	−	24.4507i	−0.507085	−	0.878296i
$776$	6.65800			0.239008
$777$	12.4621	+	18.8044i	0.447074	+	0.674603i
$778$	6.70443			0.240365
$779$	16.5592	+	28.6814i	0.593295	+	1.02762i
$780$	−5.31737	+	9.20995i	−0.190392	+	0.329769i
$781$	7.75578	−	13.4334i	0.277524	−	0.480685i
$782$	−3.47460	−	6.01818i	−0.124251	−	0.215210i
$783$	1.90394			0.0680413
$784$	6.94683	−	0.861161i	0.248101	−	0.0307558i
$785$	−20.4603			−0.730260
$786$	−1.96249	−	3.39913i	−0.0699996	−	0.121243i
$787$	−5.21977	+	9.04091i	−0.186065	+	0.322274i	−0.943935	−	0.330132i	$-0.892907\pi$
$787$	−5.21977	+	9.04091i	−0.186065	+	0.322274i	0.757870	+	0.652406i	$0.226240\pi$
$788$	3.47785	−	6.02381i	0.123893	−	0.214589i
$789$	−0.588822	−	1.01987i	−0.0209626	−	0.0363083i
$790$	−1.05766			−0.0376299
$791$	−6.49344	−	9.79814i	−0.230880	−	0.348382i
$792$	7.60808			0.270341
$793$	−18.7287	−	32.4391i	−0.665076	−	1.15194i
$794$	−11.3026	+	19.5767i	−0.401115	+	0.694752i
$795$	−7.24615	+	12.5507i	−0.256994	+	0.445127i
$796$	−10.5449	−	18.2642i	−0.373753	−	0.647359i
$797$	2.70514			0.0958211			0.0479105	−	0.998852i	$-0.484744\pi$
$797$	2.70514			0.0958211			0.0479105	+	0.998852i	$0.484744\pi$
$798$	−23.5946	+	47.3924i	−0.835240	+	1.67767i
$799$	24.1922			0.855860
$800$	1.62002	+	2.80595i	0.0572762	+	0.0992054i
$801$	−30.2722	+	52.4331i	−1.06962	+	1.85263i
$802$	4.85413	−	8.40761i	0.171405	−	0.296883i
$803$	4.56752	+	7.91117i	0.161184	+	0.279179i
$804$	−18.7130			−0.659956
$805$	−3.50328	+	0.216314i	−0.123474	+	0.00762406i
$806$	−27.1125			−0.954999
$807$	−23.9007	−	41.3973i	−0.841346	−	1.45725i
$808$	−4.57940	+	7.93175i	−0.161103	+	0.279038i
$809$	−11.1968	+	19.3935i	−0.393659	+	0.681837i	−0.992929	−	0.118710i	$-0.962124\pi$
$809$	−11.1968	+	19.3935i	−0.393659	+	0.681837i	0.599270	+	0.800547i	$0.295458\pi$
$810$	4.43052	+	7.67389i	0.155673	+	0.269633i
$811$	−23.7712			−0.834719			−0.417359	−	0.908742i	$-0.637044\pi$
$811$	−23.7712			−0.834719			−0.417359	+	0.908742i	$0.637044\pi$
$812$	3.05914	−	0.188889i	0.107355	−	0.00662872i
$813$	47.1249			1.65274
$814$	3.46057	+	5.99388i	0.121293	+	0.210085i
$815$	5.71374	−	9.89649i	0.200144	−	0.346659i
$816$	8.95200	−	15.5053i	0.313383	−	0.542795i
$817$	32.4919	+	56.2776i	1.13675	+	1.96890i
$818$	−36.3360			−1.27046
$819$	−13.3469	+	26.8088i	−0.466379	+	0.936774i
$820$	−5.65711			−0.197555
$821$	10.9377	+	18.9447i	0.381729	+	0.661175i	0.991310	−	0.131550i	$-0.0419953\pi$
$821$	10.9377	+	18.9447i	0.381729	+	0.661175i	−0.609580	+	0.792724i	$0.708662\pi$
$822$	−12.4012	+	21.4794i	−0.432540	+	0.749182i
$823$	13.8484	−	23.9861i	0.482724	−	0.836103i	−0.517079	−	0.855938i	$-0.672981\pi$
$823$	13.8484	−	23.9861i	0.482724	−	0.836103i	0.999803	+	0.0198345i	$0.00631394\pi$
$824$	−2.26606	−	3.92492i	−0.0789418	−	0.136731i
$825$	−17.4577			−0.607801
$826$	−13.4238	−	20.2555i	−0.467073	−	0.704780i
$827$	44.6016			1.55095			0.775475	−	0.631378i	$-0.217510\pi$
$827$	44.6016			1.55095			0.775475	+	0.631378i	$0.217510\pi$
$828$	1.81896	+	3.15053i	0.0632131	+	0.109488i
$829$	18.1647	−	31.4621i	0.630884	−	1.09272i	−0.356487	−	0.934300i	$-0.616026\pi$
$829$	18.1647	−	31.4621i	0.630884	−	1.09272i	0.987371	−	0.158424i	$-0.0506411\pi$
$830$	−6.88167	+	11.9194i	−0.238866	+	0.413729i
$831$	−25.9660	−	44.9744i	−0.900749	−	1.56014i
$832$	3.11142			0.107869
$833$	29.3200	+	38.8150i	1.01588	+	1.34486i
$834$	22.0973			0.765167
$835$	−7.93945	−	13.7515i	−0.274756	−	0.475891i
$836$	−8.12119	+	14.0663i	−0.280877	+	0.486494i
$837$	7.16077	−	12.4028i	0.247512	−	0.428704i
$838$	−4.99321	−	8.64849i	−0.172488	−	0.298757i
$839$	51.3975			1.77444			0.887219	−	0.461348i	$-0.152634\pi$
$839$	51.3975			1.77444			0.887219	+	0.461348i	$0.152634\pi$
$840$	−4.99560	−	7.53801i	−0.172365	−	0.260086i
$841$	−27.6580			−0.953724
$842$	−7.05263	−	12.2155i	−0.243050	−	0.420974i
$843$	9.36997	−	16.2293i	0.322719	−	0.558965i
$844$	−13.2518	+	22.9528i	−0.456145	+	0.790067i
$845$	2.20160	+	3.81329i	0.0757375	+	0.131181i
$846$	−12.6647			−0.435421
$847$	7.81346	−	15.6942i	0.268474	−	0.539259i
$848$	4.24003			0.145603
$849$	3.55855	+	6.16358i	0.122129	+	0.211534i
$850$	−11.2578	+	19.4991i	−0.386139	+	0.668813i
$851$	−1.65472	+	2.86606i	−0.0567231	+	0.0982473i
$852$	9.55474	+	16.5493i	0.327340	+	0.566969i
$853$	−36.8505			−1.26174			−0.630868	−	0.775890i	$-0.717301\pi$
$853$	−36.8505			−1.26174			−0.630868	+	0.775890i	$0.717301\pi$
$854$	31.7908	−	1.96296i	1.08786	−	0.0671710i
$855$	37.4828			1.28188
$856$	6.16722	+	10.6819i	0.210791	+	0.365101i
$857$	7.89362	−	13.6722i	0.269641	−	0.467032i	−0.699128	−	0.714996i	$-0.746428\pi$
$857$	7.89362	−	13.6722i	0.269641	−	0.467032i	0.968769	+	0.247965i	$0.0797617\pi$
$858$	−8.38237	+	14.5187i	−0.286170	+	0.495660i
$859$	−15.1034	−	26.1599i	−0.515322	−	0.892563i	−0.999842	−	0.0177833i	$-0.994339\pi$
$859$	−15.1034	−	26.1599i	−0.515322	−	0.892563i	0.484520	−	0.874780i	$-0.338994\pi$
$860$	−11.1002			−0.378513
$861$	−29.0122	+	1.79139i	−0.988734	+	0.0610504i
$862$	−3.54369			−0.120699
$863$	−25.9658	−	44.9741i	−0.883886	−	1.53094i	−0.846985	−	0.531617i	$-0.821584\pi$
$863$	−25.9658	−	44.9741i	−0.883886	−	1.53094i	−0.0369017	−	0.999319i	$-0.511749\pi$
$864$	−0.821765	+	1.42334i	−0.0279570	+	0.0484230i
$865$	13.1468	−	22.7709i	0.447004	−	0.774233i
$866$	8.13402	+	14.0885i	0.276405	+	0.478748i
$867$	80.6192			2.73797
$868$	10.2750	−	20.6385i	0.348756	−	0.700516i
$869$	−1.66731			−0.0565598
$870$	−1.97977	−	3.42906i	−0.0671204	−	0.116256i
$871$	11.2994	−	19.5712i	0.382866	−	0.663143i
$872$	0.549920	−	0.952489i	0.0186226	−	0.0322554i
$873$	−12.1106	−	20.9762i	−0.409882	−	0.709937i
$874$	−7.76653			−0.262707
$875$	15.9772	+	24.1085i	0.540128	+	0.815015i
$876$	−11.2539			−0.380234
$877$	5.65061	+	9.78714i	0.190807	+	0.330488i	0.945518	−	0.325570i	$-0.105556\pi$
$877$	5.65061	+	9.78714i	0.190807	+	0.330488i	−0.754711	+	0.656058i	$0.772223\pi$
$878$	−0.585013	+	1.01327i	−0.0197432	+	0.0341963i
$879$	−32.6890	+	56.6190i	−1.10257	+	1.90971i
$880$	−1.38722	−	2.40273i	−0.0467631	−	0.0809961i
$881$	17.4345			0.587384			0.293692	−	0.955900i	$-0.405116\pi$
$881$	17.4345			0.587384			0.293692	+	0.955900i	$0.405116\pi$
$882$	−15.3491	−	20.3197i	−0.516831	−	0.684201i
$883$	48.0567			1.61724			0.808618	−	0.588333i	$-0.200216\pi$
$883$	48.0567			1.61724			0.808618	+	0.588333i	$0.200216\pi$
$884$	10.8109	+	18.7251i	0.363611	+	0.629792i
$885$	−15.6962	+	27.1865i	−0.527621	+	0.913866i
$886$	−19.5037	+	33.7813i	−0.655238	+	1.13491i
$887$	1.09716	+	1.90034i	0.0368391	+	0.0638073i	0.883857	−	0.467757i	$-0.154938\pi$
$887$	1.09716	+	1.90034i	0.0368391	+	0.0638073i	−0.847018	+	0.531564i	$0.821604\pi$
$888$	−8.52649			−0.286130
$889$	−3.52532	−	5.31945i	−0.118235	−	0.178409i
$890$	22.0787			0.740081
$891$	6.98434	+	12.0972i	0.233984	+	0.405272i
$892$	4.90054	−	8.48799i	0.164082	−	0.284199i
$893$	13.5188	−	23.4153i	0.452390	−	0.783562i
$894$	−20.6389	−	35.7476i	−0.690267	−	1.19558i
$895$	−21.7696			−0.727678
$896$	−1.17915	+	2.36846i	−0.0393927	+	0.0791247i
$897$	−8.01631			−0.267657
$898$	−16.0857	−	27.8612i	−0.536786	−	0.929741i
$899$	5.04728	−	8.74215i	0.168336	−	0.291567i
$900$	5.89348	−	10.2078i	0.196449	−	0.340260i
$901$	14.7324	+	25.5173i	0.490807	+	0.850103i
$902$	−8.91796			−0.296935
$903$	−56.9268	+	3.51500i	−1.89440	+	0.116972i
$904$	4.44278			0.147765
$905$	7.44949	+	12.9029i	0.247629	+	0.428907i
$906$	17.9522	−	31.0941i	0.596421	−	1.03303i
$907$	15.1785	−	26.2899i	0.503993	−	0.872942i	−0.495996	−	0.868325i	$-0.665197\pi$
$907$	15.1785	−	26.2899i	0.503993	−	0.872942i	0.999989	−	0.00461698i	$-0.00146963\pi$
$908$	14.2481	+	24.6784i	0.472839	+	0.818982i
$909$	33.3189			1.10512
$910$	10.9002	−	0.673042i	0.361337	−	0.0223111i
$911$	−1.09959			−0.0364309			−0.0182155	−	0.999834i	$-0.505798\pi$
$911$	−1.09959			−0.0364309			−0.0182155	+	0.999834i	$0.505798\pi$
$912$	−10.0049	−	17.3290i	−0.331295	−	0.573820i
$913$	−10.8484	+	18.7899i	−0.359029	+	0.621856i
$914$	17.1774	−	29.7521i	0.568177	−	0.984112i
$915$	−20.5739	−	35.6351i	−0.680153	−	1.17806i
$916$	−25.1914			−0.832347
$917$	−1.79635	+	3.60817i	−0.0593207	+	0.119152i
$918$	−11.4212			−0.376956
$919$	4.83671	+	8.37743i	0.159548	+	0.276346i	0.934706	−	0.355422i	$-0.115663\pi$
$919$	4.83671	+	8.37743i	0.159548	+	0.276346i	−0.775158	+	0.631768i	$0.782330\pi$
$920$	0.663319	−	1.14890i	0.0218690	−	0.0378782i
$921$	37.6761	−	65.2570i	1.24147	−	2.15029i
$922$	−5.25776	−	9.10670i	−0.173155	−	0.299913i
$923$	−23.0776			−0.759610
$924$	−7.87514	−	11.8830i	−0.259073	−	0.390923i
$925$	10.7227			0.352560
$926$	9.99714	+	17.3155i	0.328526	+	0.569024i
$927$	−8.24372	+	14.2785i	−0.270759	+	0.468969i
$928$	−0.579223	+	1.00324i	−0.0190139	+	0.0329331i
$929$	−5.67186	−	9.82395i	−0.186088	−	0.322313i	0.757855	−	0.652423i	$-0.226248\pi$
$929$	−5.67186	−	9.82395i	−0.186088	−	0.322313i	−0.943943	+	0.330110i	$0.892914\pi$
$930$	−29.7838			−0.976649
$931$	53.9527	−	6.68823i	1.76823	−	0.219198i
$932$	−13.1625			−0.431151
$933$	−35.1460	−	60.8746i	−1.15063	−	1.99294i
$934$	13.7321	−	23.7848i	0.449329	−	0.778261i
$935$	9.64005	−	16.6971i	0.315263	−	0.546052i
$936$	−5.65954	−	9.80260i	−0.184988	−	0.320408i
$937$	−1.06500			−0.0347921			−0.0173960	−	0.999849i	$-0.505538\pi$
$937$	−1.06500			−0.0347921			−0.0173960	+	0.999849i	$0.505538\pi$
$938$	10.6157	+	16.0183i	0.346614	+	0.523015i
$939$	6.63880			0.216649
$940$	2.30921	+	3.99967i	0.0753182	+	0.130455i
$941$	−23.3540	+	40.4502i	−0.761317	+	1.31864i	0.180854	+	0.983510i	$0.442114\pi$
$941$	−23.3540	+	40.4502i	−0.761317	+	1.31864i	−0.942172	+	0.335130i	$0.891220\pi$
$942$	19.8676	−	34.4117i	0.647322	−	1.12120i
$943$	−2.13212	−	3.69295i	−0.0694315	−	0.120259i
$944$	9.18450			0.298930
$945$	−2.57099	+	5.16412i	−0.0836342	+	0.167989i
$946$	−17.4985			−0.568925
$947$	−23.4346	−	40.5900i	−0.761523	−	1.31900i	−0.942065	−	0.335429i	$-0.891119\pi$
$947$	−23.4346	−	40.5900i	−0.761523	−	1.31900i	0.180543	−	0.983567i	$-0.442215\pi$
$948$	1.02702	−	1.77886i	0.0333562	−	0.0577746i
$949$	6.79541	−	11.7700i	0.220588	−	0.382070i
$950$	12.5819	+	21.7925i	0.408211	+	0.707042i
$951$	−32.2218			−1.04486
$952$	−18.3509	+	1.13309i	−0.594755	+	0.0367238i
$953$	−42.2926			−1.36999			−0.684996	−	0.728547i	$-0.740196\pi$
$953$	−42.2926			−1.36999			−0.684996	+	0.728547i	$0.740196\pi$
$954$	−7.71244	−	13.3583i	−0.249699	−	0.432492i
$955$	−4.22405	+	7.31626i	−0.136687	+	0.236749i
$956$	4.39142	−	7.60616i	0.142029	−	0.246001i
$957$	−3.12093	−	5.40562i	−0.100885	−	0.174739i
$958$	−8.44551			−0.272862
$959$	25.4214	−	1.56967i	0.820899	−	0.0506873i
$960$	3.41797			0.110314
$961$	−22.4659	−	38.9121i	−0.724706	−	1.25523i
$962$	5.14853	−	8.91751i	0.165995	−	0.287512i
$963$	22.4358	−	38.8600i	0.722984	−	1.25224i
$964$	−0.763776	−	1.32290i	−0.0245996	−	0.0426077i
$965$	−18.6459			−0.600232
$966$	3.03798	−	6.10213i	0.0977456	−	0.196333i
$967$	42.5007			1.36673			0.683366	−	0.730076i	$-0.260515\pi$
$967$	42.5007			1.36673			0.683366	+	0.730076i	$0.260515\pi$
$968$	3.31317	+	5.73857i	0.106489	+	0.184445i
$969$	69.5259	−	120.422i	2.23350	−	3.86853i
$970$	−4.41638	+	7.64939i	−0.141801	+	0.245607i
$971$	−0.516162	−	0.894019i	−0.0165644	−	0.0286904i	0.857624	−	0.514277i	$-0.171940\pi$
$971$	−0.516162	−	0.894019i	−0.0165644	−	0.0286904i	−0.874189	+	0.485586i	$0.838606\pi$
$972$	−22.1393			−0.710118
$973$	−12.5355	−	18.9152i	−0.401871	−	0.606395i
$974$	33.2791			1.06633
$975$	12.9865	+	22.4934i	0.415902	+	0.720364i
$976$	−6.01934	+	10.4258i	−0.192674	+	0.333722i
$977$	−0.426210	+	0.738218i	−0.0136357	+	0.0236177i	−0.872763	−	0.488145i	$-0.837674\pi$
$977$	−0.426210	+	0.738218i	−0.0136357	+	0.0236177i	0.859127	+	0.511762i	$0.171007\pi$
$978$	11.0964	+	19.2196i	0.354825	+	0.614575i
$979$	34.8053			1.11238
$980$	−3.61857	+	8.55245i	−0.115591	+	0.273198i
$981$	−4.00112			−0.127746
$982$	−7.92659	−	13.7293i	−0.252948	−	0.438118i
$983$	3.46068	−	5.99407i	0.110379	−	0.191181i	−0.805544	−	0.592535i	$-0.798127\pi$
$983$	3.46068	−	5.99407i	0.110379	−	0.191181i	0.915923	+	0.401354i	$0.131460\pi$
$984$	5.49324	−	9.51457i	0.175118	−	0.303313i
$985$	4.61384	+	7.99141i	0.147009	+	0.254628i
$986$	−8.05027			−0.256373
$987$	13.1092	+	19.7809i	0.417271	+	0.629633i
$988$	24.1649			0.768789
$989$	−4.18358	−	7.24617i	−0.133030	−	0.230415i
$990$	−5.04658	+	8.74094i	−0.160391	+	0.277805i
$991$	0.672979	−	1.16563i	0.0213779	−	0.0370276i	−0.855139	−	0.518400i	$-0.826528\pi$
$991$	0.672979	−	1.16563i	0.0213779	−	0.0370276i	0.876516	+	0.481372i	$0.159861\pi$
$992$	4.35694	+	7.54644i	0.138333	+	0.239600i
$993$	7.04384			0.223530
$994$	8.74586	−	17.5670i	0.277402	−	0.557193i
$995$	27.9784			0.886976
$996$	−13.3646	−	23.1483i	−0.423475	−	0.733480i
$997$	−2.42089	+	4.19311i	−0.0766705	+	0.132797i	−0.901811	−	0.432130i	$-0.857762\pi$
$997$	−2.42089	+	4.19311i	−0.0766705	+	0.132797i	0.825141	+	0.564927i	$0.191096\pi$
$998$	9.66615	−	16.7423i	0.305977	−	0.529967i
$999$	2.71958	+	4.71046i	0.0860438	+	0.149032i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	322.2.e.a.277.1	yes	8
7.2	even	3	inner	322.2.e.a.93.1	✓	8
7.3	odd	6		2254.2.a.x.1.1		4
7.4	even	3		2254.2.a.z.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
322.2.e.a.93.1	✓	8	7.2	even	3	inner
322.2.e.a.277.1	yes	8	1.1	even	1	trivial
2254.2.a.x.1.1		4	7.3	odd	6
2254.2.a.z.1.4		4	7.4	even	3

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:	\( N \)	\(=\)	\( 322 = 2 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	322.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.28821 + 2.23124i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.663319 - 1.14890i) q^{5} +2.57641 q^{6} +(-1.46157 - 2.20541i) q^{7} +1.00000 q^{8} +(-1.81896 - 3.15053i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.28821 + 2.23124i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.663319 - 1.14890i) q^{5} +2.57641 q^{6} +(-1.46157 - 2.20541i) q^{7} +1.00000 q^{8} +(-1.81896 - 3.15053i) q^{9} +(-0.663319 + 1.14890i) q^{10} +(-1.04567 + 1.81115i) q^{11} +(-1.28821 - 2.23124i) q^{12} +3.11142 q^{13} +(-1.17915 + 2.36846i) q^{14} +3.41797 q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.47460 - 6.01818i) q^{17} +(-1.81896 + 3.15053i) q^{18} +(-3.88326 - 6.72601i) q^{19} +1.32664 q^{20} +(6.80360 - 0.420095i) q^{21} +2.09133 q^{22} +(0.500000 + 0.866025i) q^{23} +(-1.28821 + 2.23124i) q^{24} +(1.62002 - 2.80595i) q^{25} +(-1.55571 - 2.69457i) q^{26} +1.64353 q^{27} +(2.64072 - 0.163054i) q^{28} +1.15845 q^{29} +(-1.70898 - 2.96005i) q^{30} +(4.35694 - 7.54644i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-2.69407 - 4.66626i) q^{33} -6.94919 q^{34} +(-1.56431 + 3.14209i) q^{35} +3.63791 q^{36} +(1.65472 + 2.86606i) q^{37} +(-3.88326 + 6.72601i) q^{38} +(-4.00815 + 6.94232i) q^{39} +(-0.663319 - 1.14890i) q^{40} -4.26425 q^{41} +(-3.76561 - 5.68204i) q^{42} -8.36716 q^{43} +(-1.04567 - 1.81115i) q^{44} +(-2.41310 + 4.17961i) q^{45} +(0.500000 - 0.866025i) q^{46} +(1.74065 + 3.01490i) q^{47} +2.57641 q^{48} +(-2.72763 + 6.44671i) q^{49} -3.24003 q^{50} +(8.95200 + 15.5053i) q^{51} +(-1.55571 + 2.69457i) q^{52} +(-2.12002 + 3.67198i) q^{53} +(-0.821765 - 1.42334i) q^{54} +2.77444 q^{55} +(-1.46157 - 2.20541i) q^{56} +20.0098 q^{57} +(-0.579223 - 1.00324i) q^{58} +(-4.59225 + 7.95401i) q^{59} +(-1.70898 + 2.96005i) q^{60} +(-6.01934 - 10.4258i) q^{61} -8.71388 q^{62} +(-4.28965 + 8.61625i) q^{63} +1.00000 q^{64} +(-2.06386 - 3.57471i) q^{65} +(-2.69407 + 4.66626i) q^{66} +(3.63160 - 6.29011i) q^{67} +(3.47460 + 6.01818i) q^{68} -2.57641 q^{69} +(3.50328 - 0.216314i) q^{70} -7.41708 q^{71} +(-1.81896 - 3.15053i) q^{72} +(2.18402 - 3.78284i) q^{73} +(1.65472 - 2.86606i) q^{74} +(4.17383 + 7.22929i) q^{75} +7.76653 q^{76} +(5.52262 - 0.341000i) q^{77} +8.01631 q^{78} +(0.398625 + 0.690439i) q^{79} +(-0.663319 + 1.14890i) q^{80} +(3.33966 - 5.78446i) q^{81} +(2.13212 + 3.69295i) q^{82} +10.3746 q^{83} +(-3.03798 + 6.10213i) q^{84} -9.21906 q^{85} +(4.18358 + 7.24617i) q^{86} +(-1.49232 + 2.58477i) q^{87} +(-1.04567 + 1.81115i) q^{88} +(-8.32132 - 14.4129i) q^{89} +4.82619 q^{90} +(-4.54756 - 6.86194i) q^{91} -1.00000 q^{92} +(11.2253 + 19.4428i) q^{93} +(1.74065 - 3.01490i) q^{94} +(-5.15168 + 8.92298i) q^{95} +(-1.28821 - 2.23124i) q^{96} +6.65800 q^{97} +(6.94683 - 0.861161i) q^{98} +7.60808 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} - 3 q^{3} - 4 q^{4} - 7 q^{5} + 6 q^{6} - q^{7} + 8 q^{8} + q^{9}+O(q^{10}) \) 8 * q - 4 * q^2 - 3 * q^3 - 4 * q^4 - 7 * q^5 + 6 * q^6 - q^7 + 8 * q^8 + q^9	\( 8 q - 4 q^{2} - 3 q^{3} - 4 q^{4} - 7 q^{5} + 6 q^{6} - q^{7} + 8 q^{8} + q^{9} - 7 q^{10} - 2 q^{11} - 3 q^{12} + 2 q^{13} - q^{14} + 18 q^{15} - 4 q^{16} - 5 q^{17} + q^{18} - 11 q^{19} + 14 q^{20} + q^{21} + 4 q^{22} + 4 q^{23} - 3 q^{24} - 3 q^{25} - q^{26} + 6 q^{27} + 2 q^{28} + 4 q^{29} - 9 q^{30} - 6 q^{31} - 4 q^{32} - 15 q^{33} + 10 q^{34} - 8 q^{35} - 2 q^{36} + 8 q^{37} - 11 q^{38} - 3 q^{39} - 7 q^{40} + 18 q^{41} - 2 q^{42} + 8 q^{43} - 2 q^{44} - 3 q^{45} + 4 q^{46} - 11 q^{47} + 6 q^{48} - 19 q^{49} + 6 q^{50} + 18 q^{51} - q^{52} - q^{53} - 3 q^{54} + 20 q^{55} - q^{56} + 6 q^{57} - 2 q^{58} - 12 q^{59} - 9 q^{60} - 21 q^{61} + 12 q^{62} - 15 q^{63} + 8 q^{64} + 24 q^{65} - 15 q^{66} + 3 q^{67} - 5 q^{68} - 6 q^{69} - 8 q^{70} + 22 q^{71} + q^{72} + 16 q^{73} + 8 q^{74} - 18 q^{75} + 22 q^{76} - 19 q^{77} + 6 q^{78} + 21 q^{79} - 7 q^{80} + 8 q^{81} - 9 q^{82} + 8 q^{83} + q^{84} + 20 q^{85} - 4 q^{86} + 7 q^{87} - 2 q^{88} - 27 q^{89} + 6 q^{90} - 54 q^{91} - 8 q^{92} + 27 q^{93} - 11 q^{94} - 5 q^{95} - 3 q^{96} + 12 q^{97} + 14 q^{98} + 26 q^{99}+O(q^{100}) \) 8 * q - 4 * q^2 - 3 * q^3 - 4 * q^4 - 7 * q^5 + 6 * q^6 - q^7 + 8 * q^8 + q^9 - 7 * q^10 - 2 * q^11 - 3 * q^12 + 2 * q^13 - q^14 + 18 * q^15 - 4 * q^16 - 5 * q^17 + q^18 - 11 * q^19 + 14 * q^20 + q^21 + 4 * q^22 + 4 * q^23 - 3 * q^24 - 3 * q^25 - q^26 + 6 * q^27 + 2 * q^28 + 4 * q^29 - 9 * q^30 - 6 * q^31 - 4 * q^32 - 15 * q^33 + 10 * q^34 - 8 * q^35 - 2 * q^36 + 8 * q^37 - 11 * q^38 - 3 * q^39 - 7 * q^40 + 18 * q^41 - 2 * q^42 + 8 * q^43 - 2 * q^44 - 3 * q^45 + 4 * q^46 - 11 * q^47 + 6 * q^48 - 19 * q^49 + 6 * q^50 + 18 * q^51 - q^52 - q^53 - 3 * q^54 + 20 * q^55 - q^56 + 6 * q^57 - 2 * q^58 - 12 * q^59 - 9 * q^60 - 21 * q^61 + 12 * q^62 - 15 * q^63 + 8 * q^64 + 24 * q^65 - 15 * q^66 + 3 * q^67 - 5 * q^68 - 6 * q^69 - 8 * q^70 + 22 * q^71 + q^72 + 16 * q^73 + 8 * q^74 - 18 * q^75 + 22 * q^76 - 19 * q^77 + 6 * q^78 + 21 * q^79 - 7 * q^80 + 8 * q^81 - 9 * q^82 + 8 * q^83 + q^84 + 20 * q^85 - 4 * q^86 + 7 * q^87 - 2 * q^88 - 27 * q^89 + 6 * q^90 - 54 * q^91 - 8 * q^92 + 27 * q^93 - 11 * q^94 - 5 * q^95 - 3 * q^96 + 12 * q^97 + 14 * q^98 + 26 * q^99

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