LMFDB - Embedded newform 966.2.i.m.415.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("966.277");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 13x^{6} + 10x^{5} + 47x^{4} + 180x^{3} + 220x^{2} + 768x + 1164 $ x^8 - 2x^7 + 13x^6 + 10x^5 + 47x^4 + 180x^3 + 220x^2 + 768*x + 1164
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			415.1
Root			$1.76655 - 2.53227i$ of defining polynomial
Character	$\chi$	$=$	966.415
Dual form			966.2.i.m.277.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.76655 + 3.05976i) q^{5} -1.00000 q^{6} +(1.80974 - 1.92999i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.76655 + 3.05976i) q^{5} -1.00000 q^{6} +(1.80974 - 1.92999i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.76655 - 3.05976i) q^{10} +(2.57629 + 4.46226i) q^{11} +(0.500000 - 0.866025i) q^{12} +6.48282 q^{13} +(0.766551 + 2.53227i) q^{14} -3.53310 q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.809736 + 1.40250i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(1.00000 - 1.73205i) q^{19} +3.53310 q^{20} +(2.57629 + 0.602283i) q^{21} -5.15257 q^{22} +(0.500000 - 0.866025i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-3.74141 - 6.48031i) q^{25} +(-3.24141 + 5.61428i) q^{26} -1.00000 q^{27} +(-2.57629 - 0.602283i) q^{28} -1.48282 q^{29} +(1.76655 - 3.05976i) q^{30} +(1.00000 + 1.73205i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-2.57629 + 4.46226i) q^{33} -1.61947 q^{34} +(2.70831 + 8.94678i) q^{35} +1.00000 q^{36} +(-5.53310 + 9.58362i) q^{37} +(1.00000 + 1.73205i) q^{38} +(3.24141 + 5.61428i) q^{39} +(-1.76655 + 3.05976i) q^{40} -5.06621 q^{41} +(-1.80974 + 1.92999i) q^{42} +2.00000 q^{43} +(2.57629 - 4.46226i) q^{44} +(-1.76655 - 3.05976i) q^{45} +(0.500000 + 0.866025i) q^{46} +(-4.65257 + 8.05850i) q^{47} -1.00000 q^{48} +(-0.449713 - 6.98554i) q^{49} +7.48282 q^{50} +(-0.809736 + 1.40250i) q^{51} +(-3.24141 - 5.61428i) q^{52} +(-5.71626 - 9.90086i) q^{53} +(0.500000 - 0.866025i) q^{54} -18.2046 q^{55} +(1.80974 - 1.92999i) q^{56} +2.00000 q^{57} +(0.741408 - 1.28416i) q^{58} +(-7.06621 - 12.2390i) q^{59} +(1.76655 + 3.05976i) q^{60} +(4.48282 - 7.76447i) q^{61} -2.00000 q^{62} +(0.766551 + 2.53227i) q^{63} +1.00000 q^{64} +(-11.4522 + 19.8358i) q^{65} +(-2.57629 - 4.46226i) q^{66} +(3.71626 + 6.43676i) q^{67} +(0.809736 - 1.40250i) q^{68} +1.00000 q^{69} +(-9.10229 - 2.12793i) q^{70} +15.2046 q^{71} +(-0.500000 + 0.866025i) q^{72} +(3.98282 + 6.89844i) q^{73} +(-5.53310 - 9.58362i) q^{74} +(3.74141 - 6.48031i) q^{75} -2.00000 q^{76} +(13.2745 + 3.10331i) q^{77} -6.48282 q^{78} +(-6.57629 + 11.3905i) q^{79} +(-1.76655 - 3.05976i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(2.53310 - 4.38746i) q^{82} +3.23894 q^{83} +(-0.766551 - 2.53227i) q^{84} -5.72176 q^{85} +(-1.00000 + 1.73205i) q^{86} +(-0.741408 - 1.28416i) q^{87} +(2.57629 + 4.46226i) q^{88} +(-0.949713 + 1.64495i) q^{89} +3.53310 q^{90} +(11.7322 - 12.5118i) q^{91} -1.00000 q^{92} +(-1.00000 + 1.73205i) q^{93} +(-4.65257 - 8.05850i) q^{94} +(3.53310 + 6.11951i) q^{95} +(0.500000 - 0.866025i) q^{96} -8.00000 q^{97} +(6.27451 + 3.10331i) q^{98} -5.15257 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} + 4 q^{3} - 4 q^{4} - 2 q^{5} - 8 q^{6} + 6 q^{7} + 8 q^{8} - 4 q^{9}+O(q^{10}) $ 8 * q - 4 * q^2 + 4 * q^3 - 4 * q^4 - 2 * q^5 - 8 * q^6 + 6 * q^7 + 8 * q^8 - 4 * q^9	$ 8 q - 4 q^{2} + 4 q^{3} - 4 q^{4} - 2 q^{5} - 8 q^{6} + 6 q^{7} + 8 q^{8} - 4 q^{9} - 2 q^{10} + 4 q^{12} + 12 q^{13} - 6 q^{14} - 4 q^{15} - 4 q^{16} - 2 q^{17} - 4 q^{18} + 8 q^{19} + 4 q^{20} + 4 q^{23} + 4 q^{24} - 10 q^{25} - 6 q^{26} - 8 q^{27} + 28 q^{29} + 2 q^{30} + 8 q^{31} - 4 q^{32} + 4 q^{34} + 26 q^{35} + 8 q^{36} - 20 q^{37} + 8 q^{38} + 6 q^{39} - 2 q^{40} + 8 q^{41} - 6 q^{42} + 16 q^{43} - 2 q^{45} + 4 q^{46} + 4 q^{47} - 8 q^{48} + 12 q^{49} + 20 q^{50} + 2 q^{51} - 6 q^{52} - 18 q^{53} + 4 q^{54} - 32 q^{55} + 6 q^{56} + 16 q^{57} - 14 q^{58} - 8 q^{59} + 2 q^{60} - 4 q^{61} - 16 q^{62} - 6 q^{63} + 8 q^{64} - 14 q^{65} + 2 q^{67} - 2 q^{68} + 8 q^{69} - 16 q^{70} + 8 q^{71} - 4 q^{72} - 8 q^{73} - 20 q^{74} + 10 q^{75} - 16 q^{76} + 62 q^{77} - 12 q^{78} - 32 q^{79} - 2 q^{80} - 4 q^{81} - 4 q^{82} - 8 q^{83} + 6 q^{84} + 28 q^{85} - 8 q^{86} + 14 q^{87} + 8 q^{89} + 4 q^{90} + 2 q^{91} - 8 q^{92} - 8 q^{93} + 4 q^{94} + 4 q^{95} + 4 q^{96} - 64 q^{97} + 6 q^{98}+O(q^{100}) $ 8 * q - 4 * q^2 + 4 * q^3 - 4 * q^4 - 2 * q^5 - 8 * q^6 + 6 * q^7 + 8 * q^8 - 4 * q^9 - 2 * q^10 + 4 * q^12 + 12 * q^13 - 6 * q^14 - 4 * q^15 - 4 * q^16 - 2 * q^17 - 4 * q^18 + 8 * q^19 + 4 * q^20 + 4 * q^23 + 4 * q^24 - 10 * q^25 - 6 * q^26 - 8 * q^27 + 28 * q^29 + 2 * q^30 + 8 * q^31 - 4 * q^32 + 4 * q^34 + 26 * q^35 + 8 * q^36 - 20 * q^37 + 8 * q^38 + 6 * q^39 - 2 * q^40 + 8 * q^41 - 6 * q^42 + 16 * q^43 - 2 * q^45 + 4 * q^46 + 4 * q^47 - 8 * q^48 + 12 * q^49 + 20 * q^50 + 2 * q^51 - 6 * q^52 - 18 * q^53 + 4 * q^54 - 32 * q^55 + 6 * q^56 + 16 * q^57 - 14 * q^58 - 8 * q^59 + 2 * q^60 - 4 * q^61 - 16 * q^62 - 6 * q^63 + 8 * q^64 - 14 * q^65 + 2 * q^67 - 2 * q^68 + 8 * q^69 - 16 * q^70 + 8 * q^71 - 4 * q^72 - 8 * q^73 - 20 * q^74 + 10 * q^75 - 16 * q^76 + 62 * q^77 - 12 * q^78 - 32 * q^79 - 2 * q^80 - 4 * q^81 - 4 * q^82 - 8 * q^83 + 6 * q^84 + 28 * q^85 - 8 * q^86 + 14 * q^87 + 8 * q^89 + 4 * q^90 + 2 * q^91 - 8 * q^92 - 8 * q^93 + 4 * q^94 + 4 * q^95 + 4 * q^96 - 64 * q^97 + 6 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−1.76655	+	3.05976i	−0.790026	+	1.36836i	0.135924	+	0.990719i	$0.456600\pi$
$5$	−1.76655	+	3.05976i	−0.790026	+	1.36836i	−0.925950	+	0.377646i	$0.876734\pi$
$6$	−1.00000			−0.408248
$7$	1.80974	−	1.92999i	0.684016	−	0.729467i
$7$	1.80974	−	1.92999i	0.684016	−	0.729467i
$8$	1.00000			0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−1.76655	−	3.05976i	−0.558633	−	0.967580i
$11$	2.57629	+	4.46226i	0.776780	+	1.34542i	0.933789	+	0.357825i	$0.116482\pi$
$11$	2.57629	+	4.46226i	0.776780	+	1.34542i	−0.157009	+	0.987597i	$0.550185\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	6.48282			1.79801			0.899005	−	0.437939i	$-0.144291\pi$
$13$	6.48282			1.79801			0.899005	+	0.437939i	$0.144291\pi$
$14$	0.766551	+	2.53227i	0.204869	+	0.676778i
$15$	−3.53310			−0.912243
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	0.809736	+	1.40250i	0.196390	+	0.340157i	0.947355	−	0.320184i	$-0.103745\pi$
$17$	0.809736	+	1.40250i	0.196390	+	0.340157i	−0.750965	+	0.660341i	$0.770412\pi$
$18$	−0.500000	−	0.866025i	−0.117851	−	0.204124i
$19$	1.00000	−	1.73205i	0.229416	−	0.397360i	−0.728219	−	0.685344i	$-0.759652\pi$
$19$	1.00000	−	1.73205i	0.229416	−	0.397360i	0.957635	+	0.287984i	$0.0929851\pi$
$20$	3.53310			0.790026
$21$	2.57629	+	0.602283i	0.562192	+	0.131429i
$22$	−5.15257			−1.09853
$23$	0.500000	−	0.866025i	0.104257	−	0.180579i
$23$	0.500000	−	0.866025i	0.104257	−	0.180579i
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	−3.74141	−	6.48031i	−0.748282	−	1.29606i
$26$	−3.24141	+	5.61428i	−0.635692	+	1.10105i
$27$	−1.00000			−0.192450
$28$	−2.57629	−	0.602283i	−0.486873	−	0.113821i
$29$	−1.48282			−0.275352			−0.137676	−	0.990477i	$-0.543963\pi$
$29$	−1.48282			−0.275352			−0.137676	+	0.990477i	$0.543963\pi$
$30$	1.76655	−	3.05976i	0.322527	−	0.558633i
$31$	1.00000	+	1.73205i	0.179605	+	0.311086i	0.941745	−	0.336327i	$-0.109185\pi$
$31$	1.00000	+	1.73205i	0.179605	+	0.311086i	−0.762140	+	0.647412i	$0.775851\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−2.57629	+	4.46226i	−0.448474	+	0.776780i
$34$	−1.61947			−0.277737
$35$	2.70831	+	8.94678i	0.457787	+	1.51228i
$36$	1.00000			0.166667
$37$	−5.53310	+	9.58362i	−0.909637	+	1.57554i	−0.0950669	+	0.995471i	$0.530306\pi$
$37$	−5.53310	+	9.58362i	−0.909637	+	1.57554i	−0.814570	+	0.580066i	$0.803027\pi$
$38$	1.00000	+	1.73205i	0.162221	+	0.280976i
$39$	3.24141	+	5.61428i	0.519041	+	0.899005i
$40$	−1.76655	+	3.05976i	−0.279316	+	0.483790i
$41$	−5.06621			−0.791208			−0.395604	−	0.918421i	$-0.629465\pi$
$41$	−5.06621			−0.791208			−0.395604	+	0.918421i	$0.629465\pi$
$42$	−1.80974	+	1.92999i	−0.279248	+	0.297804i
$43$	2.00000			0.304997			0.152499	−	0.988304i	$-0.451268\pi$
$43$	2.00000			0.304997			0.152499	+	0.988304i	$0.451268\pi$
$44$	2.57629	−	4.46226i	0.388390	−	0.672711i
$45$	−1.76655	−	3.05976i	−0.263342	−	0.456122i
$46$	0.500000	+	0.866025i	0.0737210	+	0.127688i
$47$	−4.65257	+	8.05850i	−0.678648	+	1.17545i	0.296741	+	0.954958i	$0.404100\pi$
$47$	−4.65257	+	8.05850i	−0.678648	+	1.17545i	−0.975388	+	0.220494i	$0.929233\pi$
$48$	−1.00000			−0.144338
$49$	−0.449713	−	6.98554i	−0.0642448	−	0.997934i
$50$	7.48282			1.05823
$51$	−0.809736	+	1.40250i	−0.113386	+	0.196390i
$52$	−3.24141	−	5.61428i	−0.449502	−	0.778561i
$53$	−5.71626	−	9.90086i	−0.785189	−	1.35999i	−0.928886	−	0.370366i	$-0.879232\pi$
$53$	−5.71626	−	9.90086i	−0.785189	−	1.35999i	0.143697	−	0.989622i	$-0.454101\pi$
$54$	0.500000	−	0.866025i	0.0680414	−	0.117851i
$55$	−18.2046			−2.45470
$56$	1.80974	−	1.92999i	0.241836	−	0.257906i
$57$	2.00000			0.264906
$58$	0.741408	−	1.28416i	0.0973517	−	0.168618i
$59$	−7.06621	−	12.2390i	−0.919942	−	1.59339i	−0.799501	−	0.600665i	$-0.794902\pi$
$59$	−7.06621	−	12.2390i	−0.919942	−	1.59339i	−0.120441	−	0.992720i	$-0.538431\pi$
$60$	1.76655	+	3.05976i	0.228061	+	0.395013i
$61$	4.48282	−	7.76447i	0.573966	−	0.994138i	−0.422187	−	0.906509i	$-0.638738\pi$
$61$	4.48282	−	7.76447i	0.573966	−	0.994138i	0.996153	−	0.0876294i	$-0.0279291\pi$
$62$	−2.00000			−0.254000
$63$	0.766551	+	2.53227i	0.0965764	+	0.319036i
$64$	1.00000			0.125000
$65$	−11.4522	+	19.8358i	−1.42047	+	2.46033i
$66$	−2.57629	−	4.46226i	−0.317119	−	0.549266i
$67$	3.71626	+	6.43676i	0.454014	+	0.786375i	0.998631	−	0.0523096i	$-0.0166583\pi$
$67$	3.71626	+	6.43676i	0.454014	+	0.786375i	−0.544617	+	0.838685i	$0.683325\pi$
$68$	0.809736	−	1.40250i	0.0981949	−	0.170079i
$69$	1.00000			0.120386
$70$	−9.10229	−	2.12793i	−1.08793	−	0.254336i
$71$	15.2046			1.80445			0.902226	−	0.431264i	$-0.141932\pi$
$71$	15.2046			1.80445			0.902226	+	0.431264i	$0.141932\pi$
$72$	−0.500000	+	0.866025i	−0.0589256	+	0.102062i
$73$	3.98282	+	6.89844i	0.466153	+	0.807401i	0.999253	−	0.0386513i	$-0.0123061\pi$
$73$	3.98282	+	6.89844i	0.466153	+	0.807401i	−0.533099	+	0.846053i	$0.678973\pi$
$74$	−5.53310	−	9.58362i	−0.643210	−	1.11407i
$75$	3.74141	−	6.48031i	0.432021	−	0.748282i
$76$	−2.00000			−0.229416
$77$	13.2745	+	3.10331i	1.51277	+	0.353655i
$78$	−6.48282			−0.734034
$79$	−6.57629	+	11.3905i	−0.739890	+	1.28153i	0.212654	+	0.977128i	$0.431789\pi$
$79$	−6.57629	+	11.3905i	−0.739890	+	1.28153i	−0.952544	+	0.304400i	$0.901544\pi$
$80$	−1.76655	−	3.05976i	−0.197506	−	0.342091i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	2.53310	−	4.38746i	0.279734	−	0.484514i
$83$	3.23894			0.355520			0.177760	−	0.984074i	$-0.443115\pi$
$83$	3.23894			0.355520			0.177760	+	0.984074i	$0.443115\pi$
$84$	−0.766551	−	2.53227i	−0.0836376	−	0.276293i
$85$	−5.72176			−0.620612
$86$	−1.00000	+	1.73205i	−0.107833	+	0.186772i
$87$	−0.741408	−	1.28416i	−0.0794873	−	0.137676i
$88$	2.57629	+	4.46226i	0.274633	+	0.475679i
$89$	−0.949713	+	1.64495i	−0.100669	+	0.174365i	−0.911961	−	0.410278i	$-0.865432\pi$
$89$	−0.949713	+	1.64495i	−0.100669	+	0.174365i	0.811291	+	0.584642i	$0.198765\pi$
$90$	3.53310			0.372422
$91$	11.7322	−	12.5118i	1.22987	−	1.31159i
$92$	−1.00000			−0.104257
$93$	−1.00000	+	1.73205i	−0.103695	+	0.179605i
$94$	−4.65257	−	8.05850i	−0.479876	−	0.831170i
$95$	3.53310	+	6.11951i	0.362489	+	0.627849i
$96$	0.500000	−	0.866025i	0.0510310	−	0.0883883i
$97$	−8.00000			−0.812277			−0.406138	−	0.913812i	$-0.633125\pi$
$97$	−8.00000			−0.812277			−0.406138	+	0.913812i	$0.633125\pi$
$98$	6.27451	+	3.10331i	0.633821	+	0.313481i
$99$	−5.15257			−0.517853
$100$	−3.74141	+	6.48031i	−0.374141	+	0.648031i
$101$	−5.74141	−	9.94441i	−0.571291	−	0.989506i	−0.996434	−	0.0843793i	$-0.973109\pi$
$101$	−5.74141	−	9.94441i	−0.571291	−	0.989506i	0.425142	−	0.905127i	$-0.360224\pi$
$102$	−0.809736	−	1.40250i	−0.0801758	−	0.138869i
$103$	0.773654	−	1.34001i	0.0762304	−	0.132035i	−0.825390	−	0.564563i	$-0.809045\pi$
$103$	0.773654	−	1.34001i	0.0762304	−	0.132035i	0.901621	+	0.432528i	$0.142378\pi$
$104$	6.48282			0.635692
$105$	−6.39398	+	6.81885i	−0.623989	+	0.665452i
$106$	11.4325			1.11043
$107$	1.15257	−	1.99632i	0.111424	−	0.192991i	−0.804921	−	0.593382i	$-0.797792\pi$
$107$	1.15257	−	1.99632i	0.111424	−	0.192991i	0.916344	+	0.400391i	$0.131126\pi$
$108$	0.500000	+	0.866025i	0.0481125	+	0.0833333i
$109$	2.52600	+	4.37516i	0.241947	+	0.419064i	0.961269	−	0.275613i	$-0.0888807\pi$
$109$	2.52600	+	4.37516i	0.241947	+	0.419064i	−0.719322	+	0.694677i	$0.755547\pi$
$110$	9.10229	−	15.7656i	0.867869	−	1.50319i
$111$	−11.0662			−1.05036
$112$	0.766551	+	2.53227i	0.0724323	+	0.239277i
$113$	8.77205			0.825205			0.412602	−	0.910911i	$-0.364620\pi$
$113$	8.77205			0.825205			0.412602	+	0.910911i	$0.364620\pi$
$114$	−1.00000	+	1.73205i	−0.0936586	+	0.162221i
$115$	1.76655	+	3.05976i	0.164732	+	0.285324i
$116$	0.741408	+	1.28416i	0.0688380	+	0.119231i
$117$	−3.24141	+	5.61428i	−0.299668	+	0.519041i
$118$	14.1324			1.30099
$119$	4.17222	+	0.975380i	0.382467	+	0.0894129i
$120$	−3.53310			−0.322527
$121$	−7.77451	+	13.4658i	−0.706774	+	1.22417i
$122$	4.48282	+	7.76447i	0.405855	+	0.702962i
$123$	−2.53310	−	4.38746i	−0.228402	−	0.395604i
$124$	1.00000	−	1.73205i	0.0898027	−	0.155543i
$125$	8.77205			0.784596
$126$	−2.57629	−	0.602283i	−0.229514	−	0.0536556i
$127$	−3.89943			−0.346018			−0.173009	−	0.984920i	$-0.555349\pi$
$127$	−3.89943			−0.346018			−0.173009	+	0.984920i	$0.555349\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	1.00000	+	1.73205i	0.0880451	+	0.152499i
$130$	−11.4522	−	19.8358i	−1.00443	−	1.73972i
$131$	5.15504	−	8.92879i	0.450398	−	0.780112i	−0.548013	−	0.836470i	$-0.684615\pi$
$131$	5.15504	−	8.92879i	0.450398	−	0.780112i	0.998411	+	0.0563579i	$0.0179488\pi$
$132$	5.15257			0.448474
$133$	−1.53310	−	5.06454i	−0.132937	−	0.439152i
$134$	−7.43253			−0.642073
$135$	1.76655	−	3.05976i	0.152041	−	0.263342i
$136$	0.809736	+	1.40250i	0.0694343	+	0.120264i
$137$	−2.89610	−	5.01620i	−0.247431	−	0.428563i	0.715381	−	0.698734i	$-0.246253\pi$
$137$	−2.89610	−	5.01620i	−0.247431	−	0.428563i	−0.962812	+	0.270171i	$0.912920\pi$
$138$	−0.500000	+	0.866025i	−0.0425628	+	0.0737210i
$139$	2.24387			0.190323			0.0951614	−	0.995462i	$-0.469663\pi$
$139$	2.24387			0.190323			0.0951614	+	0.995462i	$0.469663\pi$
$140$	6.39398	−	6.81885i	0.540390	−	0.576298i
$141$	−9.30515			−0.783635
$142$	−7.60229	+	13.1675i	−0.637970	+	1.10500i
$143$	16.7016	+	28.9280i	1.39666	+	2.41908i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	2.61947	−	4.53706i	0.217535	−	0.376782i
$146$	−7.96563			−0.659240
$147$	5.82480	−	3.88223i	0.480421	−	0.320201i
$148$	11.0662			0.909637
$149$	−9.91913	+	17.1804i	−0.812606	+	1.40748i	0.0984275	+	0.995144i	$0.468619\pi$
$149$	−9.91913	+	17.1804i	−0.812606	+	1.40748i	−0.911034	+	0.412331i	$0.864715\pi$
$150$	3.74141	+	6.48031i	0.305485	+	0.529115i
$151$	−6.01592	−	10.4199i	−0.489569	−	0.847958i	0.510359	−	0.859961i	$-0.329512\pi$
$151$	−6.01592	−	10.4199i	−0.489569	−	0.847958i	−0.999928	+	0.0120036i	$0.996179\pi$
$152$	1.00000	−	1.73205i	0.0811107	−	0.140488i
$153$	−1.61947			−0.130927
$154$	−9.32480	+	9.94441i	−0.751414	+	0.801343i
$155$	−7.06621			−0.567571
$156$	3.24141	−	5.61428i	0.259520	−	0.449502i
$157$	−6.90653	−	11.9625i	−0.551201	−	0.954708i	−0.998188	−	0.0601679i	$-0.980836\pi$
$157$	−6.90653	−	11.9625i	−0.551201	−	0.954708i	0.446987	−	0.894540i	$-0.352497\pi$
$158$	−6.57629	−	11.3905i	−0.523181	−	0.906177i
$159$	5.71626	−	9.90086i	0.453329	−	0.785189i
$160$	3.53310			0.279316
$161$	−0.766551	−	2.53227i	−0.0604127	−	0.199571i
$162$	1.00000			0.0785674
$163$	5.36088	−	9.28532i	0.419896	−	0.727282i	−0.576032	−	0.817427i	$-0.695400\pi$
$163$	5.36088	−	9.28532i	0.419896	−	0.727282i	0.995929	+	0.0901450i	$0.0287330\pi$
$164$	2.53310	+	4.38746i	0.197802	+	0.342603i
$165$	−9.10229	−	15.7656i	−0.708612	−	1.22735i
$166$	−1.61947	+	2.80501i	−0.125695	+	0.217711i
$167$	−13.4484			−1.04067			−0.520336	−	0.853962i	$-0.674193\pi$
$167$	−13.4484			−1.04067			−0.520336	+	0.853962i	$0.674193\pi$
$168$	2.57629	+	0.602283i	0.198765	+	0.0464671i
$169$	29.0269			2.23284
$170$	2.86088	−	4.95519i	0.219419	−	0.380046i
$171$	1.00000	+	1.73205i	0.0764719	+	0.132453i
$172$	−1.00000	−	1.73205i	−0.0762493	−	0.132068i
$173$	7.44725	−	12.8990i	0.566204	−	0.980694i	−0.430733	−	0.902480i	$-0.641745\pi$
$173$	7.44725	−	12.8990i	0.566204	−	0.980694i	0.996937	−	0.0782142i	$-0.0249218\pi$
$174$	1.48282			0.112412
$175$	−19.2779	−	4.50677i	−1.45727	−	0.340680i
$176$	−5.15257			−0.388390
$177$	7.06621	−	12.2390i	0.531129	−	0.919942i
$178$	−0.949713	−	1.64495i	−0.0711840	−	0.123294i
$179$	10.0135	+	17.3438i	0.748441	+	1.29634i	0.948570	+	0.316568i	$0.102530\pi$
$179$	10.0135	+	17.3438i	0.748441	+	1.29634i	−0.200129	+	0.979770i	$0.564136\pi$
$180$	−1.76655	+	3.05976i	−0.131671	+	0.228061i
$181$	18.4234			1.36940			0.684699	−	0.728826i	$-0.259934\pi$
$181$	18.4234			1.36940			0.684699	+	0.728826i	$0.259934\pi$
$182$	4.96941	+	16.4163i	0.368357	+	1.21685i
$183$	8.96563			0.662759
$184$	0.500000	−	0.866025i	0.0368605	−	0.0638442i
$185$	−19.5490	−	33.8599i	−1.43727	−	2.48943i
$186$	−1.00000	−	1.73205i	−0.0733236	−	0.127000i
$187$	−4.17222	+	7.22650i	−0.305103	+	0.528454i
$188$	9.30515			0.678648
$189$	−1.80974	+	1.92999i	−0.131639	+	0.140386i
$190$	−7.06621			−0.512636
$191$	−0.949713	+	1.64495i	−0.0687189	+	0.119025i	−0.898338	−	0.439306i	$-0.855224\pi$
$191$	−0.949713	+	1.64495i	−0.0687189	+	0.119025i	0.829619	+	0.558330i	$0.188558\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	8.30761	+	14.3892i	0.597995	+	1.03576i	0.993117	+	0.117129i	$0.0373691\pi$
$193$	8.30761	+	14.3892i	0.597995	+	1.03576i	−0.395122	+	0.918629i	$0.629298\pi$
$194$	4.00000	−	6.92820i	0.287183	−	0.497416i
$195$	−22.9045			−1.64022
$196$	−5.82480	+	3.88223i	−0.416057	+	0.277302i
$197$	26.4484			1.88437			0.942187	−	0.335088i	$-0.108766\pi$
$197$	26.4484			1.88437			0.942187	+	0.335088i	$0.108766\pi$
$198$	2.57629	−	4.46226i	0.183089	−	0.317119i
$199$	4.48992	+	7.77677i	0.318282	+	0.551280i	0.980130	−	0.198358i	$-0.0635608\pi$
$199$	4.48992	+	7.77677i	0.318282	+	0.551280i	−0.661848	+	0.749638i	$0.730227\pi$
$200$	−3.74141	−	6.48031i	−0.264558	−	0.458227i
$201$	−3.71626	+	6.43676i	−0.262125	+	0.454014i
$202$	11.4828			0.807928
$203$	−2.68351	+	2.86182i	−0.188345	+	0.200860i
$204$	1.61947			0.113386
$205$	8.94971	−	15.5014i	0.625075	−	1.08266i
$206$	0.773654	+	1.34001i	0.0539030	+	0.0933628i
$207$	0.500000	+	0.866025i	0.0347524	+	0.0601929i
$208$	−3.24141	+	5.61428i	−0.224751	+	0.389281i
$209$	10.3051			0.712822
$210$	−2.70831	−	8.94678i	−0.186891	−	0.617386i
$211$	−9.78797			−0.673831			−0.336916	−	0.941535i	$-0.609384\pi$
$211$	−9.78797			−0.673831			−0.336916	+	0.941535i	$0.609384\pi$
$212$	−5.71626	+	9.90086i	−0.392595	+	0.679994i
$213$	7.60229	+	13.1675i	0.520900	+	0.902226i
$214$	1.15257	+	1.99632i	0.0787884	+	0.136465i
$215$	−3.53310	+	6.11951i	−0.240956	+	0.417347i
$216$	−1.00000			−0.0680414
$217$	5.15257	+	1.20457i	0.349780	+	0.0817712i
$218$	−5.05200			−0.342165
$219$	−3.98282	+	6.89844i	−0.269134	+	0.466153i
$220$	9.10229	+	15.7656i	0.613676	+	1.06292i
$221$	5.24937	+	9.09217i	0.353111	+	0.611606i
$222$	5.53310	−	9.58362i	0.371358	−	0.643210i
$223$	−27.1986			−1.82135			−0.910677	−	0.413119i	$-0.864439\pi$
$223$	−27.1986			−1.82135			−0.910677	+	0.413119i	$0.864439\pi$
$224$	−2.57629	−	0.602283i	−0.172135	−	0.0402417i
$225$	7.48282			0.498854
$226$	−4.38602	+	7.59681i	−0.291754	+	0.505333i
$227$	−1.51008	−	2.61554i	−0.100228	−	0.173599i	0.811551	−	0.584282i	$-0.198624\pi$
$227$	−1.51008	−	2.61554i	−0.100228	−	0.173599i	−0.911778	+	0.410683i	$0.865290\pi$
$228$	−1.00000	−	1.73205i	−0.0662266	−	0.114708i
$229$	3.77915	−	6.54568i	0.249733	−	0.432550i	−0.713719	−	0.700433i	$-0.752990\pi$
$229$	3.77915	−	6.54568i	0.249733	−	0.432550i	0.963452	+	0.267882i	$0.0863238\pi$
$230$	−3.53310			−0.232966
$231$	3.94971	+	13.0477i	0.259872	+	0.858477i
$232$	−1.48282			−0.0973517
$233$	12.3051	−	21.3131i	0.806137	−	1.39627i	−0.109384	−	0.994000i	$-0.534888\pi$
$233$	12.3051	−	21.3131i	0.806137	−	1.39627i	0.915521	−	0.402271i	$-0.131779\pi$
$234$	−3.24141	−	5.61428i	−0.211897	−	0.367017i
$235$	−16.4380	−	28.4715i	−1.07230	−	1.85728i
$236$	−7.06621	+	12.2390i	−0.459971	+	0.796693i
$237$	−13.1526			−0.854352
$238$	−2.93082	+	3.12556i	−0.189977	+	0.202600i
$239$	−18.7218			−1.21101			−0.605505	−	0.795842i	$-0.707029\pi$
$239$	−18.7218			−1.21101			−0.605505	+	0.795842i	$0.707029\pi$
$240$	1.76655	−	3.05976i	0.114030	−	0.197506i
$241$	2.68568	+	4.65173i	0.173000	+	0.299644i	0.939467	−	0.342639i	$-0.111321\pi$
$241$	2.68568	+	4.65173i	0.173000	+	0.299644i	−0.766468	+	0.642283i	$0.777987\pi$
$242$	−7.77451	−	13.4658i	−0.499765	−	0.865618i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−8.96563			−0.573966
$245$	22.1685	+	10.9643i	1.41629	+	0.700483i
$246$	5.06621			0.323009
$247$	6.48282	−	11.2286i	0.412492	−	0.714457i
$248$	1.00000	+	1.73205i	0.0635001	+	0.109985i
$249$	1.61947	+	2.80501i	0.102630	+	0.177760i
$250$	−4.38602	+	7.59681i	−0.277396	+	0.480465i
$251$	27.2566			1.72042			0.860210	−	0.509940i	$-0.170332\pi$
$251$	27.2566			1.72042			0.860210	+	0.509940i	$0.170332\pi$
$252$	1.80974	−	1.92999i	0.114003	−	0.121578i
$253$	5.15257			0.323940
$254$	1.94971	−	3.37700i	0.122336	−	0.211892i
$255$	−2.86088	−	4.95519i	−0.179155	−	0.310306i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	0.685677	−	1.18763i	0.0427714	−	0.0740822i	−0.843847	−	0.536584i	$-0.819715\pi$
$257$	0.685677	−	1.18763i	0.0427714	−	0.0740822i	0.886619	+	0.462501i	$0.153048\pi$
$258$	−2.00000			−0.124515
$259$	8.48282	+	28.0226i	0.527097	+	1.74124i
$260$	22.9045			1.42047
$261$	0.741408	−	1.28416i	0.0458920	−	0.0794873i
$262$	5.15504	+	8.92879i	0.318479	+	0.551623i
$263$	6.63539	+	11.4928i	0.409156	+	0.708678i	0.994795	−	0.101893i	$-0.0324899\pi$
$263$	6.63539	+	11.4928i	0.409156	+	0.708678i	−0.585640	+	0.810572i	$0.699157\pi$
$264$	−2.57629	+	4.46226i	−0.158560	+	0.274633i
$265$	40.3923			2.48128
$266$	5.15257	+	1.20457i	0.315925	+	0.0738566i
$267$	−1.89943			−0.116243
$268$	3.71626	−	6.43676i	0.227007	−	0.393188i
$269$	−5.03064	−	8.71332i	−0.306723	−	0.531260i	0.670920	−	0.741530i	$-0.265899\pi$
$269$	−5.03064	−	8.71332i	−0.306723	−	0.531260i	−0.977644	+	0.210269i	$0.932566\pi$
$270$	1.76655	+	3.05976i	0.107509	+	0.186211i
$271$	−1.33024	+	2.30405i	−0.0808064	+	0.139961i	−0.903597	−	0.428384i	$-0.859083\pi$
$271$	−1.33024	+	2.30405i	−0.0808064	+	0.139961i	0.822790	+	0.568345i	$0.192416\pi$
$272$	−1.61947			−0.0981949
$273$	16.7016	+	3.90449i	1.01083	+	0.236310i
$274$	5.79221			0.349920
$275$	19.2779	−	33.3903i	1.16250	−	2.01351i
$276$	−0.500000	−	0.866025i	−0.0300965	−	0.0521286i
$277$	−1.44427	−	2.50155i	−0.0867777	−	0.150303i	0.819370	−	0.573266i	$-0.194324\pi$
$277$	−1.44427	−	2.50155i	−0.0867777	−	0.150303i	−0.906147	+	0.422962i	$0.860990\pi$
$278$	−1.12194	+	1.94325i	−0.0672893	+	0.116548i
$279$	−2.00000			−0.119737
$280$	2.70831	+	8.94678i	0.161852	+	0.534672i
$281$	27.3965			1.63434			0.817171	−	0.576396i	$-0.195541\pi$
$281$	27.3965			1.63434			0.817171	+	0.576396i	$0.195541\pi$
$282$	4.65257	−	8.05850i	0.277057	−	0.479876i
$283$	−1.31982	−	2.28599i	−0.0784550	−	0.135888i	0.824129	−	0.566403i	$-0.191665\pi$
$283$	−1.31982	−	2.28599i	−0.0784550	−	0.135888i	−0.902584	+	0.430515i	$0.858332\pi$
$284$	−7.60229	−	13.1675i	−0.451113	−	0.781350i
$285$	−3.53310	+	6.11951i	−0.209283	+	0.362489i
$286$	−33.4032			−1.97517
$287$	−9.16849	+	9.77772i	−0.541199	+	0.577161i
$288$	1.00000			0.0589256
$289$	7.18866	−	12.4511i	0.422862	−	0.732419i
$290$	2.61947	+	4.53706i	0.153821	+	0.266425i
$291$	−4.00000	−	6.92820i	−0.234484	−	0.406138i
$292$	3.98282	−	6.89844i	0.233077	−	0.403701i
$293$	6.29416			0.367709			0.183854	−	0.982953i	$-0.441143\pi$
$293$	6.29416			0.367709			0.183854	+	0.982953i	$0.441143\pi$
$294$	0.449713	+	6.98554i	0.0262278	+	0.407405i
$295$	49.9313			2.90711
$296$	−5.53310	+	9.58362i	−0.321605	+	0.557036i
$297$	−2.57629	−	4.46226i	−0.149491	−	0.258927i
$298$	−9.91913	−	17.1804i	−0.574600	−	0.995236i
$299$	3.24141	−	5.61428i	0.187455	−	0.324682i
$300$	−7.48282			−0.432021
$301$	3.61947	−	3.85998i	0.208623	−	0.222485i
$302$	12.0318			0.692355
$303$	5.74141	−	9.94441i	0.329835	−	0.571291i
$304$	1.00000	+	1.73205i	0.0573539	+	0.0993399i
$305$	15.8383	+	27.4327i	0.906896	+	1.57079i
$306$	0.809736	−	1.40250i	0.0462895	−	0.0801758i
$307$	−20.8223			−1.18839			−0.594197	−	0.804320i	$-0.702530\pi$
$307$	−20.8223			−1.18839			−0.594197	+	0.804320i	$0.702530\pi$
$308$	−3.94971	−	13.0477i	−0.225056	−	0.743463i
$309$	1.54731			0.0880233
$310$	3.53310	−	6.11951i	0.200667	−	0.347565i
$311$	−1.34743	−	2.33381i	−0.0764055	−	0.132338i	0.825291	−	0.564708i	$-0.191011\pi$
$311$	−1.34743	−	2.33381i	−0.0764055	−	0.132338i	−0.901697	+	0.432369i	$0.857678\pi$
$312$	3.24141	+	5.61428i	0.183509	+	0.317846i
$313$	12.3051	−	21.3131i	0.695528	−	1.20469i	−0.274474	−	0.961594i	$-0.588504\pi$
$313$	12.3051	−	21.3131i	0.695528	−	1.20469i	0.970002	−	0.243096i	$-0.0781629\pi$
$314$	13.8131			0.779516
$315$	−9.10229	−	2.12793i	−0.512856	−	0.119895i
$316$	13.1526			0.739890
$317$	11.1324	−	19.2819i	0.625259	−	1.08298i	−0.363232	−	0.931699i	$-0.618327\pi$
$317$	11.1324	−	19.2819i	0.625259	−	1.08298i	0.988491	−	0.151281i	$-0.0483398\pi$
$318$	5.71626	+	9.90086i	0.320552	+	0.555213i
$319$	−3.82016	−	6.61671i	−0.213888	−	0.370465i
$320$	−1.76655	+	3.05976i	−0.0987532	+	0.171046i
$321$	2.30515			0.128661
$322$	2.57629	+	0.602283i	0.143571	+	0.0335639i
$323$	3.23894			0.180220
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	−24.2549	−	42.0107i	−1.34542	−	2.33033i
$326$	5.36088	+	9.28532i	0.296912	+	0.514266i
$327$	−2.52600	+	4.37516i	−0.139688	+	0.241947i
$328$	−5.06621			−0.279734
$329$	7.13288	+	23.5632i	0.393248	+	1.29908i
$330$	18.2046			1.00213
$331$	1.63368	−	2.82961i	0.0897950	−	0.155529i	−0.817629	−	0.575745i	$-0.804712\pi$
$331$	1.63368	−	2.82961i	0.0897950	−	0.155529i	0.907424	+	0.420215i	$0.138045\pi$
$332$	−1.61947	−	2.80501i	−0.0888800	−	0.153945i
$333$	−5.53310	−	9.58362i	−0.303212	−	0.525179i
$334$	6.72422	−	11.6467i	0.367933	−	0.637279i
$335$	−26.2599			−1.43473
$336$	−1.80974	+	1.92999i	−0.0987292	+	0.105290i
$337$	1.03437			0.0563456			0.0281728	−	0.999603i	$-0.491031\pi$
$337$	1.03437			0.0563456			0.0281728	+	0.999603i	$0.491031\pi$
$338$	−14.5135	+	25.1380i	−0.789428	+	1.36733i
$339$	4.38602	+	7.59681i	0.238216	+	0.412602i
$340$	2.86088	+	4.95519i	0.155153	+	0.268733i
$341$	−5.15257	+	8.92452i	−0.279028	+	0.483290i
$342$	−2.00000			−0.108148
$343$	−14.2959	−	11.7740i	−0.771905	−	0.635738i
$344$	2.00000			0.107833
$345$	−1.76655	+	3.05976i	−0.0951079	+	0.164732i
$346$	7.44725	+	12.8990i	0.400367	+	0.693455i
$347$	0.952179	+	1.64922i	0.0511156	+	0.0885349i	0.890451	−	0.455079i	$-0.150389\pi$
$347$	0.952179	+	1.64922i	0.0511156	+	0.0885349i	−0.839335	+	0.543614i	$0.817056\pi$
$348$	−0.741408	+	1.28416i	−0.0397436	+	0.0688380i
$349$	−30.7880			−1.64804			−0.824021	−	0.566559i	$-0.808274\pi$
$349$	−30.7880			−1.64804			−0.824021	+	0.566559i	$0.808274\pi$
$350$	13.5419	−	14.4418i	0.723846	−	0.771944i
$351$	−6.48282			−0.346027
$352$	2.57629	−	4.46226i	0.137317	−	0.237839i
$353$	−9.46690	−	16.3971i	−0.503872	−	0.872732i	−0.999990	−	0.00447689i	$-0.998575\pi$
$353$	−9.46690	−	16.3971i	−0.503872	−	0.872732i	0.496118	−	0.868255i	$-0.334758\pi$
$354$	7.06621	+	12.2390i	0.375565	+	0.650497i
$355$	−26.8597	+	46.5223i	−1.42556	+	2.46915i
$356$	1.89943			0.100669
$357$	1.24141	+	4.10094i	0.0657023	+	0.217045i
$358$	−20.0269			−1.05845
$359$	−5.08637	+	8.80985i	−0.268448	+	0.464966i	−0.968461	−	0.249164i	$-0.919844\pi$
$359$	−5.08637	+	8.80985i	−0.268448	+	0.464966i	0.700013	+	0.714130i	$0.253178\pi$
$360$	−1.76655	−	3.05976i	−0.0931054	−	0.161263i
$361$	7.50000	+	12.9904i	0.394737	+	0.683704i
$362$	−9.21168	+	15.9551i	−0.484155	+	0.838581i
$363$	−15.5490			−0.816112
$364$	−16.7016	−	3.90449i	−0.875402	−	0.204651i
$365$	−28.1434			−1.47309
$366$	−4.48282	+	7.76447i	−0.234321	+	0.405855i
$367$	−8.58888	−	14.8764i	−0.448336	−	0.776541i	0.549942	−	0.835203i	$-0.314650\pi$
$367$	−8.58888	−	14.8764i	−0.448336	−	0.776541i	−0.998278	+	0.0586621i	$0.981317\pi$
$368$	0.500000	+	0.866025i	0.0260643	+	0.0451447i
$369$	2.53310	−	4.38746i	0.131868	−	0.228402i
$370$	39.0980			2.03261
$371$	−29.4535	−	6.88561i	−1.52915	−	0.357483i
$372$	2.00000			0.103695
$373$	2.24605	−	3.89026i	0.116296	−	0.201430i	−0.802001	−	0.597322i	$-0.796231\pi$
$373$	2.24605	−	3.89026i	0.116296	−	0.201430i	0.918297	+	0.395892i	$0.129565\pi$
$374$	−4.17222	−	7.22650i	−0.215741	−	0.373674i
$375$	4.38602	+	7.59681i	0.226493	+	0.392298i
$376$	−4.65257	+	8.05850i	−0.239938	+	0.415585i
$377$	−9.61283			−0.495086
$378$	−0.766551	−	2.53227i	−0.0394272	−	0.130246i
$379$	26.6311			1.36795			0.683975	−	0.729505i	$-0.260250\pi$
$379$	26.6311			1.36795			0.683975	+	0.729505i	$0.260250\pi$
$380$	3.53310	−	6.11951i	0.181244	−	0.313924i
$381$	−1.94971	−	3.37700i	−0.0998868	−	0.173009i
$382$	−0.949713	−	1.64495i	−0.0485916	−	0.0841631i
$383$	−3.17274	+	5.49534i	−0.162119	+	0.280799i	−0.935629	−	0.352986i	$-0.885166\pi$
$383$	−3.17274	+	5.49534i	−0.162119	+	0.280799i	0.773509	+	0.633785i	$0.218500\pi$
$384$	−1.00000			−0.0510310
$385$	−32.9455	+	35.1346i	−1.67906	+	1.79063i
$386$	−16.6152			−0.845693
$387$	−1.00000	+	1.73205i	−0.0508329	+	0.0880451i
$388$	4.00000	+	6.92820i	0.203069	+	0.351726i
$389$	−9.58510	−	16.6019i	−0.485984	−	0.841749i	0.513886	−	0.857858i	$-0.328205\pi$
$389$	−9.58510	−	16.6019i	−0.485984	−	0.841749i	−0.999870	+	0.0161093i	$0.994872\pi$
$390$	11.4522	−	19.8358i	0.579906	−	1.00443i
$391$	1.61947			0.0819002
$392$	−0.449713	−	6.98554i	−0.0227140	−	0.352823i
$393$	10.3101			0.520075
$394$	−13.2242	+	22.9050i	−0.666227	+	1.15394i
$395$	−23.2347	−	40.2437i	−1.16906	−	2.02488i
$396$	2.57629	+	4.46226i	0.129463	+	0.224237i
$397$	9.10475	−	15.7699i	0.456954	−	0.791468i	−0.541844	−	0.840479i	$-0.682274\pi$
$397$	9.10475	−	15.7699i	0.456954	−	0.791468i	0.998798	+	0.0490109i	$0.0156069\pi$
$398$	−8.97984			−0.450119
$399$	3.61947	−	3.85998i	0.181200	−	0.193241i
$400$	7.48282			0.374141
$401$	−8.34284	+	14.4502i	−0.416621	+	0.721610i	−0.995597	−	0.0937352i	$-0.970119\pi$
$401$	−8.34284	+	14.4502i	−0.416621	+	0.721610i	0.578976	+	0.815345i	$0.303453\pi$
$402$	−3.71626	−	6.43676i	−0.185350	−	0.321036i
$403$	6.48282	+	11.2286i	0.322932	+	0.559335i
$404$	−5.74141	+	9.94441i	−0.285646	+	0.494753i
$405$	3.53310			0.175561
$406$	−1.13666	−	3.75489i	−0.0564112	−	0.186352i
$407$	−57.0194			−2.82635
$408$	−0.809736	+	1.40250i	−0.0400879	+	0.0694343i
$409$	12.9987	+	22.5145i	0.642746	+	1.11327i	0.984817	+	0.173595i	$0.0555383\pi$
$409$	12.9987	+	22.5145i	0.642746	+	1.11327i	−0.342071	+	0.939674i	$0.611128\pi$
$410$	8.94971	+	15.5014i	0.441995	+	0.765558i
$411$	2.89610	−	5.01620i	0.142854	−	0.247431i
$412$	−1.54731			−0.0762304
$413$	−36.4092	−	8.51171i	−1.79158	−	0.418834i
$414$	−1.00000			−0.0491473
$415$	−5.72176	+	9.91038i	−0.280870	+	0.486481i
$416$	−3.24141	−	5.61428i	−0.158923	−	0.275263i
$417$	1.12194	+	1.94325i	0.0549415	+	0.0951614i
$418$	−5.15257	+	8.92452i	−0.252021	+	0.436513i
$419$	−16.1904			−0.790951			−0.395476	−	0.918476i	$-0.629420\pi$
$419$	−16.1904			−0.790951			−0.395476	+	0.918476i	$0.629420\pi$
$420$	9.10229	+	2.12793i	0.444146	+	0.103832i
$421$	24.8474			1.21099			0.605495	−	0.795849i	$-0.292975\pi$
$421$	24.8474			1.21099			0.605495	+	0.795849i	$0.292975\pi$
$422$	4.89398	−	8.47663i	0.238235	−	0.412636i
$423$	−4.65257	−	8.05850i	−0.226216	−	0.391817i
$424$	−5.71626	−	9.90086i	−0.277606	−	0.480828i
$425$	6.05910	−	10.4947i	0.293910	−	0.509067i
$426$	−15.2046			−0.736664
$427$	−6.87262	−	22.7034i	−0.332589	−	1.09870i
$428$	−2.30515			−0.111424
$429$	−16.7016	+	28.9280i	−0.806361	+	1.39666i
$430$	−3.53310	−	6.11951i	−0.170381	−	0.295109i
$431$	−7.31008	−	12.6614i	−0.352114	−	0.609880i	0.634506	−	0.772918i	$-0.281204\pi$
$431$	−7.31008	−	12.6614i	−0.352114	−	0.609880i	−0.986620	+	0.163039i	$0.947870\pi$
$432$	0.500000	−	0.866025i	0.0240563	−	0.0416667i
$433$	21.9498			1.05484			0.527420	−	0.849604i	$-0.323159\pi$
$433$	21.9498			1.05484			0.527420	+	0.849604i	$0.323159\pi$
$434$	−3.61947	+	3.85998i	−0.173740	+	0.185285i
$435$	5.23894			0.251188
$436$	2.52600	−	4.37516i	0.120973	−	0.209532i
$437$	−1.00000	−	1.73205i	−0.0478365	−	0.0828552i
$438$	−3.98282	−	6.89844i	−0.190306	−	0.329620i
$439$	−2.25315	+	3.90257i	−0.107537	+	0.186259i	−0.914772	−	0.403971i	$-0.867630\pi$
$439$	−2.25315	+	3.90257i	−0.107537	+	0.186259i	0.807235	+	0.590230i	$0.200963\pi$
$440$	−18.2046			−0.867869
$441$	6.27451	+	3.10331i	0.298786	+	0.147776i
$442$	−10.4987			−0.499374
$443$	−18.0436	+	31.2524i	−0.857276	+	1.48485i	0.0172409	+	0.999851i	$0.494512\pi$
$443$	−18.0436	+	31.2524i	−0.857276	+	1.48485i	−0.874517	+	0.484995i	$0.838822\pi$
$444$	5.53310	+	9.58362i	0.262589	+	0.454818i
$445$	−3.35544	−	5.81178i	−0.159063	−	0.275505i
$446$	13.5993	−	23.5547i	0.643946	−	1.11535i
$447$	−19.8383			−0.938317
$448$	1.80974	−	1.92999i	0.0855020	−	0.0911834i
$449$	−21.8591			−1.03159			−0.515797	−	0.856711i	$-0.672504\pi$
$449$	−21.8591			−1.03159			−0.515797	+	0.856711i	$0.672504\pi$
$450$	−3.74141	+	6.48031i	−0.176372	+	0.305485i
$451$	−13.0520	−	22.6067i	−0.614595	−	1.06451i
$452$	−4.38602	−	7.59681i	−0.206301	−	0.357324i
$453$	6.01592	−	10.4199i	0.282653	−	0.489569i
$454$	3.02016			0.141743
$455$	17.5574	+	58.0003i	0.823106	+	2.71910i
$456$	2.00000			0.0936586
$457$	−3.06621	+	5.31082i	−0.143431	+	0.248430i	−0.928787	−	0.370615i	$-0.879147\pi$
$457$	−3.06621	+	5.31082i	−0.143431	+	0.248430i	0.785355	+	0.619045i	$0.212480\pi$
$458$	3.77915	+	6.54568i	0.176588	+	0.305859i
$459$	−0.809736	−	1.40250i	−0.0377952	−	0.0654633i
$460$	1.76655	−	3.05976i	0.0823659	−	0.142662i
$461$	6.00000			0.279448			0.139724	−	0.990190i	$-0.455378\pi$
$461$	6.00000			0.279448			0.139724	+	0.990190i	$0.455378\pi$
$462$	−13.2745	−	3.10331i	−0.617586	−	0.144379i
$463$	21.9313			1.01923			0.509616	−	0.860402i	$-0.329787\pi$
$463$	21.9313			1.01923			0.509616	+	0.860402i	$0.329787\pi$
$464$	0.741408	−	1.28416i	0.0344190	−	0.0596155i
$465$	−3.53310	−	6.11951i	−0.163844	−	0.283786i
$466$	12.3051	+	21.3131i	0.570025	+	0.987312i
$467$	3.82016	−	6.61671i	0.176776	−	0.306185i	−0.763998	−	0.645218i	$-0.776767\pi$
$467$	3.82016	−	6.61671i	0.176776	−	0.306185i	0.940774	+	0.339033i	$0.110100\pi$
$468$	6.48282			0.299668
$469$	19.1483	+	4.47648i	0.884188	+	0.206705i
$470$	32.8760			1.51646
$471$	6.90653	−	11.9625i	0.318236	−	0.551201i
$472$	−7.06621	−	12.2390i	−0.325248	−	0.563347i
$473$	5.15257	+	8.92452i	0.236916	+	0.410350i
$474$	6.57629	−	11.3905i	0.302059	−	0.523181i
$475$	−14.9656			−0.686670
$476$	−1.24141	−	4.10094i	−0.0568999	−	0.187966i
$477$	11.4325			0.523460
$478$	9.36088	−	16.2135i	0.428157	−	0.741589i
$479$	8.83825	+	15.3083i	0.403830	+	0.699454i	0.994185	−	0.107690i	$-0.0343454\pi$
$479$	8.83825	+	15.3083i	0.403830	+	0.699454i	−0.590355	+	0.807144i	$0.701012\pi$
$480$	1.76655	+	3.05976i	0.0806317	+	0.139658i
$481$	−35.8701	+	62.1288i	−1.63554	+	2.83283i
$482$	−5.37135			−0.244658
$483$	1.80974	−	1.92999i	0.0823458	−	0.0878175i
$484$	15.5490			0.706774
$485$	14.1324	−	24.4781i	0.641720	−	1.11149i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	−3.92955	−	6.80618i	−0.178065	−	0.308418i	0.763153	−	0.646218i	$-0.223650\pi$
$487$	−3.92955	−	6.80618i	−0.178065	−	0.308418i	−0.941218	+	0.337801i	$0.890317\pi$
$488$	4.48282	−	7.76447i	0.202928	−	0.351481i
$489$	10.7218			0.484855
$490$	−20.5796	+	13.7163i	−0.929692	+	0.619641i
$491$	−38.3321			−1.72990			−0.864951	−	0.501857i	$-0.832650\pi$
$491$	−38.3321			−1.72990			−0.864951	+	0.501857i	$0.832650\pi$
$492$	−2.53310	+	4.38746i	−0.114201	+	0.197802i
$493$	−1.20069	−	2.07965i	−0.0540763	−	0.0936629i
$494$	6.48282	+	11.2286i	0.291676	+	0.505197i
$495$	9.10229	−	15.7656i	0.409117	−	0.708612i
$496$	−2.00000			−0.0898027
$497$	27.5163	−	29.3447i	1.23427	−	1.31629i
$498$	−3.23894			−0.145140
$499$	−11.1329	+	19.2828i	−0.498378	+	0.863216i	−0.999998	−	0.00187170i	$-0.999404\pi$
$499$	−11.1329	+	19.2828i	−0.498378	+	0.863216i	0.501620	+	0.865088i	$0.332738\pi$
$500$	−4.38602	−	7.59681i	−0.196149	−	0.339740i
$501$	−6.72422	−	11.6467i	−0.300416	−	0.520336i
$502$	−13.6283	+	23.6049i	−0.608260	+	1.05354i
$503$	−8.93722			−0.398491			−0.199246	−	0.979950i	$-0.563849\pi$
$503$	−8.93722			−0.398491			−0.199246	+	0.979950i	$0.563849\pi$
$504$	0.766551	+	2.53227i	0.0341449	+	0.112796i
$505$	40.5700			1.80534
$506$	−2.57629	+	4.46226i	−0.114530	+	0.198372i
$507$	14.5135	+	25.1380i	0.644565	+	1.11642i
$508$	1.94971	+	3.37700i	0.0865045	+	0.149830i
$509$	4.56374	−	7.90463i	0.202284	−	0.350367i	−0.746980	−	0.664847i	$-0.768497\pi$
$509$	4.56374	−	7.90463i	0.202284	−	0.350367i	0.949264	+	0.314480i	$0.101830\pi$
$510$	5.72176			0.253364
$511$	20.5218	+	4.79756i	0.907829	+	0.212232i
$512$	1.00000			0.0441942
$513$	−1.00000	+	1.73205i	−0.0441511	+	0.0764719i
$514$	0.685677	+	1.18763i	0.0302439	+	0.0523840i
$515$	2.73340	+	4.73439i	0.120448	+	0.208622i
$516$	1.00000	−	1.73205i	0.0440225	−	0.0762493i
$517$	−47.9455			−2.10864
$518$	−28.5097	−	6.66498i	−1.25265	−	0.292843i
$519$	14.8945			0.653796
$520$	−11.4522	+	19.8358i	−0.502213	+	0.869859i
$521$	−9.55280	−	16.5459i	−0.418516	−	0.724891i	0.577275	−	0.816550i	$-0.304116\pi$
$521$	−9.55280	−	16.5459i	−0.418516	−	0.724891i	−0.995790	+	0.0916594i	$0.970783\pi$
$522$	0.741408	+	1.28416i	0.0324506	+	0.0562060i
$523$	17.6912	−	30.6420i	0.773581	−	1.33988i	−0.162008	−	0.986789i	$-0.551797\pi$
$523$	17.6912	−	30.6420i	0.773581	−	1.33988i	0.935589	−	0.353092i	$-0.114870\pi$
$524$	−10.3101			−0.450398
$525$	−5.73596	−	18.9485i	−0.250338	−	0.826981i
$526$	−13.2708			−0.578634
$527$	−1.61947	+	2.80501i	−0.0705453	+	0.122188i
$528$	−2.57629	−	4.46226i	−0.112119	−	0.194195i
$529$	−0.500000	−	0.866025i	−0.0217391	−	0.0376533i
$530$	−20.1962	+	34.9808i	−0.877265	+	1.51947i
$531$	14.1324			0.613294
$532$	−3.61947	+	3.85998i	−0.156924	+	0.167351i
$533$	−32.8433			−1.42260
$534$	0.949713	−	1.64495i	0.0410981	−	0.0711840i
$535$	4.07216	+	7.05319i	0.176055	+	0.304936i
$536$	3.71626	+	6.43676i	0.160518	+	0.278026i
$537$	−10.0135	+	17.3438i	−0.432112	+	0.748441i
$538$	10.0613			0.433772
$539$	30.0127	−	20.0035i	1.29274	−	0.861611i
$540$	−3.53310			−0.152041
$541$	−4.06867	+	7.04715i	−0.174926	+	0.302980i	−0.940136	−	0.340801i	$-0.889302\pi$
$541$	−4.06867	+	7.04715i	−0.174926	+	0.302980i	0.765210	+	0.643781i	$0.222635\pi$
$542$	−1.33024	−	2.30405i	−0.0571388	−	0.0989673i
$543$	9.21168	+	15.9551i	0.395311	+	0.684699i
$544$	0.809736	−	1.40250i	0.0347171	−	0.0601318i
$545$	−17.8492			−0.764577
$546$	−11.7322	+	12.5118i	−0.502091	+	0.535454i
$547$	−1.55498			−0.0664861			−0.0332431	−	0.999447i	$-0.510584\pi$
$547$	−1.55498			−0.0664861			−0.0332431	+	0.999447i	$0.510584\pi$
$548$	−2.89610	+	5.01620i	−0.123715	+	0.214281i
$549$	4.48282	+	7.76447i	0.191322	+	0.331379i
$550$	19.2779	+	33.3903i	0.822012	+	1.42377i
$551$	−1.48282	+	2.56831i	−0.0631701	+	0.109414i
$552$	1.00000			0.0425628
$553$	10.0821	+	33.3059i	0.428736	+	1.41631i
$554$	2.88854			0.122722
$555$	19.5490	−	33.8599i	0.829810	−	1.43727i
$556$	−1.12194	−	1.94325i	−0.0475807	−	0.0824122i
$557$	−12.5080	−	21.6645i	−0.529981	−	0.917955i	−0.999388	−	0.0349727i	$-0.988866\pi$
$557$	−12.5080	−	21.6645i	−0.529981	−	0.917955i	0.469407	−	0.882982i	$-0.344468\pi$
$558$	1.00000	−	1.73205i	0.0423334	−	0.0733236i
$559$	12.9656			0.548388
$560$	−9.10229	−	2.12793i	−0.384642	−	0.0899213i
$561$	−8.34445			−0.352303
$562$	−13.6983	+	23.7261i	−0.577827	+	1.00083i
$563$	14.0230	+	24.2886i	0.591000	+	1.02364i	0.994098	+	0.108485i	$0.0346000\pi$
$563$	14.0230	+	24.2886i	0.591000	+	1.02364i	−0.403098	+	0.915157i	$0.632067\pi$
$564$	4.65257	+	8.05850i	0.195909	+	0.339324i
$565$	−15.4963	+	26.8403i	−0.651933	+	1.12918i
$566$	2.63963			0.110952
$567$	−2.57629	−	0.602283i	−0.108194	−	0.0252935i
$568$	15.2046			0.637970
$569$	−6.09186	+	10.5514i	−0.255384	+	0.442338i	−0.965000	−	0.262251i	$-0.915535\pi$
$569$	−6.09186	+	10.5514i	−0.255384	+	0.442338i	0.709616	+	0.704589i	$0.248869\pi$
$570$	−3.53310	−	6.11951i	−0.147985	−	0.256318i
$571$	5.35590	+	9.27669i	0.224137	+	0.388217i	0.956060	−	0.293170i	$-0.0947102\pi$
$571$	5.35590	+	9.27669i	0.224137	+	0.388217i	−0.731923	+	0.681387i	$0.761377\pi$
$572$	16.7016	−	28.9280i	0.698329	−	1.20954i
$573$	−1.89943			−0.0793497
$574$	−3.88351	−	12.8290i	−0.162094	−	0.535472i
$575$	−7.48282			−0.312055
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	6.69112	+	11.5894i	0.278555	+	0.482471i	0.971026	−	0.238974i	$-0.0768112\pi$
$577$	6.69112	+	11.5894i	0.278555	+	0.482471i	−0.692471	+	0.721446i	$0.743478\pi$
$578$	7.18866	+	12.4511i	0.299009	+	0.517898i
$579$	−8.30761	+	14.3892i	−0.345253	+	0.597995i
$580$	−5.23894			−0.217535
$581$	5.86163	−	6.25112i	0.243181	−	0.259340i
$582$	8.00000			0.331611
$583$	29.4535	−	51.0149i	1.21984	−	2.11282i
$584$	3.98282	+	6.89844i	0.164810	+	0.285459i
$585$	−11.4522	−	19.8358i	−0.473491	−	0.820111i
$586$	−3.14708	+	5.45090i	−0.130005	+	0.225175i
$587$	40.1912			1.65887			0.829433	−	0.558606i	$-0.188664\pi$
$587$	40.1912			1.65887			0.829433	+	0.558606i	$0.188664\pi$
$588$	−6.27451	−	3.10331i	−0.258756	−	0.127978i
$589$	4.00000			0.164817
$590$	−24.9656	+	43.2417i	−1.02782	+	1.78023i
$591$	13.2242	+	22.9050i	0.543972	+	0.942187i
$592$	−5.53310	−	9.58362i	−0.227409	−	0.393884i
$593$	2.27996	−	3.94900i	0.0936265	−	0.162166i	−0.815408	−	0.578887i	$-0.803487\pi$
$593$	2.27996	−	3.94900i	0.0936265	−	0.162166i	0.909035	+	0.416721i	$0.136821\pi$
$594$	5.15257			0.211413
$595$	−10.3549	+	11.0429i	−0.424508	+	0.452716i
$596$	19.8383			0.812606
$597$	−4.48992	+	7.77677i	−0.183760	+	0.318282i
$598$	3.24141	+	5.61428i	0.132551	+	0.229585i
$599$	−1.66849	−	2.88992i	−0.0681728	−	0.118079i	0.829924	−	0.557876i	$-0.188384\pi$
$599$	−1.66849	−	2.88992i	−0.0681728	−	0.118079i	−0.898097	+	0.439797i	$0.855050\pi$
$600$	3.74141	−	6.48031i	0.152742	−	0.264558i
$601$	0.132412			0.00540119			0.00270059	−	0.999996i	$-0.499140\pi$
$601$	0.132412			0.00540119			0.00270059	+	0.999996i	$0.499140\pi$
$602$	1.53310	+	5.06454i	0.0624846	+	0.206415i
$603$	−7.43253			−0.302676
$604$	−6.01592	+	10.4199i	−0.244784	+	0.423979i
$605$	−27.4681	−	47.5762i	−1.11674	−	1.93425i
$606$	5.74141	+	9.94441i	0.233229	+	0.403964i
$607$	10.0821	−	17.4628i	0.409221	−	0.708791i	−0.585582	−	0.810613i	$-0.699134\pi$
$607$	10.0821	−	17.4628i	0.409221	−	0.708791i	0.994803	+	0.101822i	$0.0324672\pi$
$608$	−2.00000			−0.0811107
$609$	−3.82016	−	0.893075i	−0.154801	−	0.0361892i
$610$	−31.6765			−1.28254
$611$	−30.1618	+	52.2417i	−1.22022	+	2.11347i
$612$	0.809736	+	1.40250i	0.0327316	+	0.0566928i
$613$	−11.1958	−	19.3916i	−0.452192	−	0.783220i	0.546330	−	0.837570i	$-0.316025\pi$
$613$	−11.1958	−	19.3916i	−0.452192	−	0.783220i	−0.998522	+	0.0543501i	$0.982691\pi$
$614$	10.4112	−	18.0327i	0.420160	−	0.727739i
$615$	17.8994			0.721775
$616$	13.2745	+	3.10331i	0.534845	+	0.125036i
$617$	−15.0192			−0.604652			−0.302326	−	0.953205i	$-0.597763\pi$
$617$	−15.0192			−0.604652			−0.302326	+	0.953205i	$0.597763\pi$
$618$	−0.773654	+	1.34001i	−0.0311209	+	0.0539030i
$619$	5.14215	+	8.90646i	0.206680	+	0.357981i	0.950667	−	0.310214i	$-0.100401\pi$
$619$	5.14215	+	8.90646i	0.206680	+	0.357981i	−0.743986	+	0.668195i	$0.767067\pi$
$620$	3.53310	+	6.11951i	0.141893	+	0.245766i
$621$	−0.500000	+	0.866025i	−0.0200643	+	0.0347524i
$622$	2.69485			0.108054
$623$	1.45601	+	4.80986i	0.0583337	+	0.192703i
$624$	−6.48282			−0.259520
$625$	3.21077	−	5.56122i	0.128431	−	0.222449i
$626$	12.3051	+	21.3131i	0.491813	+	0.851845i
$627$	5.15257	+	8.92452i	0.205774	+	0.356411i
$628$	−6.90653	+	11.9625i	−0.275601	+	0.477354i
$629$	−17.9214			−0.714573
$630$	6.39398	−	6.81885i	0.254742	−	0.271669i
$631$	−3.67972			−0.146487			−0.0732437	−	0.997314i	$-0.523335\pi$
$631$	−3.67972			−0.146487			−0.0732437	+	0.997314i	$0.523335\pi$
$632$	−6.57629	+	11.3905i	−0.261591	+	0.453088i
$633$	−4.89398	−	8.47663i	−0.194518	−	0.336916i
$634$	11.1324	+	19.2819i	0.442125	+	0.765782i
$635$	6.88854	−	11.9313i	0.273363	−	0.473479i
$636$	−11.4325			−0.453329
$637$	−2.91541	−	45.2860i	−0.115513	−	1.79430i
$638$	7.64032			0.302483
$639$	−7.60229	+	13.1675i	−0.300742	+	0.520900i
$640$	−1.76655	−	3.05976i	−0.0698291	−	0.120948i
$641$	14.4593	+	25.0443i	0.571109	+	0.989190i	0.996452	+	0.0841581i	$0.0268201\pi$
$641$	14.4593	+	25.0443i	0.571109	+	0.989190i	−0.425343	+	0.905032i	$0.639847\pi$
$642$	−1.15257	+	1.99632i	−0.0454885	+	0.0787884i
$643$	−3.03437			−0.119664			−0.0598319	−	0.998208i	$-0.519056\pi$
$643$	−3.03437			−0.119664			−0.0598319	+	0.998208i	$0.519056\pi$
$644$	−1.80974	+	1.92999i	−0.0713136	+	0.0760522i
$645$	−7.06621			−0.278232
$646$	−1.61947	+	2.80501i	−0.0637172	+	0.110362i
$647$	−12.9443	−	22.4201i	−0.508892	−	0.881426i	−0.999947	−	0.0102979i	$-0.996722\pi$
$647$	−12.9443	−	22.4201i	−0.508892	−	0.881426i	0.491055	−	0.871128i	$-0.336611\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	36.4092	−	63.0625i	1.42918	−	2.47542i
$650$	48.5097			1.90271
$651$	1.53310	+	5.06454i	0.0600870	+	0.198495i
$652$	−10.7218			−0.419896
$653$	6.99627	−	12.1179i	0.273785	−	0.474210i	−0.696043	−	0.718000i	$-0.745058\pi$
$653$	6.99627	−	12.1179i	0.273785	−	0.474210i	0.969828	+	0.243790i	$0.0783909\pi$
$654$	−2.52600	−	4.37516i	−0.0987744	−	0.171082i
$655$	18.2133	+	31.5463i	0.711652	+	1.23262i
$656$	2.53310	−	4.38746i	0.0989011	−	0.171302i
$657$	−7.96563			−0.310769
$658$	−23.9727	−	5.60433i	−0.934555	−	0.218480i
$659$	33.9674			1.32318			0.661592	−	0.749864i	$-0.269881\pi$
$659$	33.9674			1.32318			0.661592	+	0.749864i	$0.269881\pi$
$660$	−9.10229	+	15.7656i	−0.354306	+	0.613676i
$661$	18.8454	+	32.6411i	0.732999	+	1.26959i	0.955596	+	0.294681i	$0.0952135\pi$
$661$	18.8454	+	32.6411i	0.732999	+	1.26959i	−0.222596	+	0.974911i	$0.571453\pi$
$662$	1.63368	+	2.82961i	0.0634946	+	0.109976i
$663$	−5.24937	+	9.09217i	−0.203869	+	0.353111i
$664$	3.23894			0.125695
$665$	18.2046	+	4.25585i	0.705943	+	0.165035i
$666$	11.0662			0.428807
$667$	−0.741408	+	1.28416i	−0.0287074	+	0.0497227i
$668$	6.72422	+	11.6467i	0.260168	+	0.450624i
$669$	−13.5993	−	23.5547i	−0.525780	−	0.910677i
$670$	13.1299	−	22.7417i	0.507254	−	0.878590i
$671$	46.1961			1.78338
$672$	−0.766551	−	2.53227i	−0.0295704	−	0.0976845i
$673$	−7.37033			−0.284105			−0.142053	−	0.989859i	$-0.545370\pi$
$673$	−7.37033			−0.284105			−0.142053	+	0.989859i	$0.545370\pi$
$674$	−0.517184	+	0.895788i	−0.0199212	+	0.0345045i
$675$	3.74141	+	6.48031i	0.144007	+	0.249427i
$676$	−14.5135	−	25.1380i	−0.558210	−	0.966848i
$677$	−5.75235	+	9.96336i	−0.221081	+	0.382923i	−0.955136	−	0.296166i	$-0.904292\pi$
$677$	−5.75235	+	9.96336i	−0.221081	+	0.382923i	0.734056	+	0.679089i	$0.237625\pi$
$678$	−8.77205			−0.336888
$679$	−14.4779	+	15.4399i	−0.555610	+	0.592529i
$680$	−5.72176			−0.219419
$681$	1.51008	−	2.61554i	0.0578664	−	0.100228i
$682$	−5.15257	−	8.92452i	−0.197302	−	0.341738i
$683$	−5.71002	−	9.89004i	−0.218488	−	0.378432i	0.735858	−	0.677136i	$-0.236779\pi$
$683$	−5.71002	−	9.89004i	−0.218488	−	0.378432i	−0.954346	+	0.298704i	$0.903446\pi$
$684$	1.00000	−	1.73205i	0.0382360	−	0.0662266i
$685$	20.4645			0.781907
$686$	17.3446	−	6.49357i	0.662218	−	0.247926i
$687$	7.55830			0.288367
$688$	−1.00000	+	1.73205i	−0.0381246	+	0.0660338i
$689$	−37.0575	−	64.1855i	−1.41178	−	2.44527i
$690$	−1.76655	−	3.05976i	−0.0672515	−	0.116483i
$691$	−11.3106	+	19.5905i	−0.430275	+	0.745259i	−0.996897	−	0.0787196i	$-0.974917\pi$
$691$	−11.3106	+	19.5905i	−0.430275	+	0.745259i	0.566622	+	0.823978i	$0.308250\pi$
$692$	−14.8945			−0.566204
$693$	−9.32480	+	9.94441i	−0.354220	+	0.377757i
$694$	−1.90436			−0.0722884
$695$	−3.96392	+	6.86571i	−0.150360	+	0.260431i
$696$	−0.741408	−	1.28416i	−0.0281030	−	0.0486758i
$697$	−4.10229	−	7.10537i	−0.155385	−	0.269135i
$698$	15.3940	−	26.6632i	0.582671	−	1.00922i
$699$	24.6103			0.930847
$700$	5.73596	+	18.9485i	0.216799	+	0.716187i
$701$	−12.2942			−0.464344			−0.232172	−	0.972675i	$-0.574583\pi$
$701$	−12.2942			−0.464344			−0.232172	+	0.972675i	$0.574583\pi$
$702$	3.24141	−	5.61428i	0.122339	−	0.211897i
$703$	11.0662	+	19.1672i	0.417370	+	0.722906i
$704$	2.57629	+	4.46226i	0.0970975	+	0.168178i
$705$	16.4380	−	28.4715i	0.619092	−	1.07230i
$706$	18.9338			0.712583
$707$	−29.5830	−	6.91590i	−1.11258	−	0.260099i
$708$	−14.1324			−0.531129
$709$	−0.439632	+	0.761465i	−0.0165107	+	0.0285974i	−0.874163	−	0.485633i	$-0.838589\pi$
$709$	−0.439632	+	0.761465i	−0.0165107	+	0.0285974i	0.857652	+	0.514231i	$0.171922\pi$
$710$	−26.8597	−	46.5223i	−1.00803	−	1.74595i
$711$	−6.57629	−	11.3905i	−0.246630	−	0.427176i
$712$	−0.949713	+	1.64495i	−0.0355920	+	0.0616472i
$713$	2.00000			0.0749006
$714$	−4.17222	−	0.975380i	−0.156142	−	0.0365027i
$715$	−118.017			−4.41358
$716$	10.0135	−	17.3438i	0.374220	−	0.648169i
$717$	−9.36088	−	16.2135i	−0.349588	−	0.605505i
$718$	−5.08637	−	8.80985i	−0.189822	−	0.328781i
$719$	−1.59684	+	2.76581i	−0.0595522	+	0.103147i	−0.894264	−	0.447539i	$-0.852301\pi$
$719$	−1.59684	+	2.76581i	−0.0595522	+	0.103147i	0.834712	+	0.550686i	$0.185634\pi$
$720$	3.53310			0.131671
$721$	−1.18609	−	3.91820i	−0.0441723	−	0.145922i
$722$	−15.0000			−0.558242
$723$	−2.68568	+	4.65173i	−0.0998814	+	0.173000i
$724$	−9.21168	−	15.9551i	−0.342349	−	0.592966i
$725$	5.54782	+	9.60911i	0.206041	+	0.356873i
$726$	7.77451	−	13.4658i	0.288539	−	0.499765i
$727$	−7.48613			−0.277645			−0.138823	−	0.990317i	$-0.544332\pi$
$727$	−7.48613			−0.277645			−0.138823	+	0.990317i	$0.544332\pi$
$728$	11.7322	−	12.5118i	0.434824	−	0.463717i
$729$	1.00000			0.0370370
$730$	14.0717	−	24.3729i	0.520817	−	0.902081i
$731$	1.61947	+	2.80501i	0.0598983	+	0.103747i
$732$	−4.48282	−	7.76447i	−0.165690	−	0.286983i
$733$	4.30722	−	7.46032i	0.159091	−	0.275553i	−0.775450	−	0.631409i	$-0.782477\pi$
$733$	4.30722	−	7.46032i	0.159091	−	0.275553i	0.934541	+	0.355855i	$0.115810\pi$
$734$	17.1778			0.634043
$735$	1.58888	+	24.6806i	0.0586069	+	0.910359i
$736$	−1.00000			−0.0368605
$737$	−19.1483	+	33.1659i	−0.705338	+	1.22168i
$738$	2.53310	+	4.38746i	0.0932448	+	0.161505i
$739$	4.36581	+	7.56181i	0.160599	+	0.278166i	0.935084	−	0.354427i	$-0.115324\pi$
$739$	4.36581	+	7.56181i	0.160599	+	0.278166i	−0.774485	+	0.632593i	$0.781991\pi$
$740$	−19.5490	+	33.8599i	−0.718636	+	1.24471i
$741$	12.9656			0.476304
$742$	20.6899	−	22.0647i	0.759549	−	0.810019i
$743$	−18.2046			−0.667861			−0.333931	−	0.942598i	$-0.608375\pi$
$743$	−18.2046			−0.667861			−0.333931	+	0.942598i	$0.608375\pi$
$744$	−1.00000	+	1.73205i	−0.0366618	+	0.0635001i
$745$	−35.0453	−	60.7002i	−1.28396	−	2.22388i
$746$	2.24605	+	3.89026i	0.0822336	+	0.142433i
$747$	−1.61947	+	2.80501i	−0.0592534	+	0.102630i
$748$	8.34445			0.305103
$749$	−1.76702	−	5.83726i	−0.0645653	−	0.213289i
$750$	−8.77205			−0.320310
$751$	6.09130	−	10.5504i	0.222275	−	0.384991i	−0.733224	−	0.679988i	$-0.761985\pi$
$751$	6.09130	−	10.5504i	0.222275	−	0.384991i	0.955498	+	0.294997i	$0.0953185\pi$
$752$	−4.65257	−	8.05850i	−0.169662	−	0.293863i
$753$	13.6283	+	23.6049i	0.496642	+	0.860210i
$754$	4.80641	−	8.32495i	0.175039	−	0.303177i
$755$	42.5097			1.54709
$756$	2.57629	+	0.602283i	0.0936987	+	0.0219048i
$757$	16.0000			0.581530			0.290765	−	0.956795i	$-0.406090\pi$
$757$	16.0000			0.581530			0.290765	+	0.956795i	$0.406090\pi$
$758$	−13.3156	+	23.0633i	−0.483643	+	0.837695i
$759$	2.57629	+	4.46226i	0.0935133	+	0.161970i
$760$	3.53310	+	6.11951i	0.128159	+	0.221978i
$761$	−0.330242	+	0.571996i	−0.0119713	+	0.0207348i	−0.871949	−	0.489597i	$-0.837144\pi$
$761$	−0.330242	+	0.571996i	−0.0119713	+	0.0207348i	0.859978	+	0.510332i	$0.170477\pi$
$762$	3.89943			0.141261
$763$	13.0154	+	3.04273i	0.471189	+	0.110154i
$764$	1.89943			0.0687189
$765$	2.86088	−	4.95519i	0.103435	−	0.179155i
$766$	−3.17274	−	5.49534i	−0.114636	−	0.198555i
$767$	−45.8089	−	79.3434i	−1.65406	−	2.86492i
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$	−7.12645			−0.256986			−0.128493	−	0.991710i	$-0.541014\pi$
$769$	−7.12645			−0.256986			−0.128493	+	0.991710i	$0.541014\pi$
$770$	−13.9547	−	46.0989i	−0.502894	−	1.66129i
$771$	1.37135			0.0493881
$772$	8.30761	−	14.3892i	0.298998	−	0.517879i
$773$	15.8345	+	27.4261i	0.569526	+	0.986449i	0.996613	+	0.0822378i	$0.0262067\pi$
$773$	15.8345	+	27.4261i	0.569526	+	0.986449i	−0.427086	+	0.904211i	$0.640460\pi$
$774$	−1.00000	−	1.73205i	−0.0359443	−	0.0622573i
$775$	7.48282	−	12.9606i	0.268791	−	0.465559i
$776$	−8.00000			−0.287183
$777$	−20.0269	+	21.3577i	−0.718461	+	0.766202i
$778$	19.1702			0.687285
$779$	−5.06621	+	8.77493i	−0.181516	+	0.314394i
$780$	11.4522	+	19.8358i	0.410056	+	0.710237i
$781$	39.1714	+	67.8468i	1.40166	+	2.42775i
$782$	−0.809736	+	1.40250i	−0.0289561	+	0.0501534i
$783$	1.48282			0.0529915
$784$	6.27451	+	3.10331i	0.224090	+	0.110832i
$785$	48.8030			1.74185
$786$	−5.15504	+	8.92879i	−0.183874	+	0.318479i
$787$	−17.6048	−	30.4924i	−0.627543	−	1.08694i	−0.988043	−	0.154178i	$-0.950727\pi$
$787$	−17.6048	−	30.4924i	−0.627543	−	1.08694i	0.360500	−	0.932759i	$-0.382606\pi$
$788$	−13.2242	−	22.9050i	−0.471093	−	0.815958i
$789$	−6.63539	+	11.4928i	−0.236226	+	0.409156i
$790$	46.4694			1.65331
$791$	15.8751	−	16.9299i	0.564453	−	0.601960i
$792$	−5.15257			−0.183089
$793$	29.0613	−	50.3356i	1.03200	−	1.78747i
$794$	9.10475	+	15.7699i	0.323116	+	0.559653i
$795$	20.1962	+	34.9808i	0.716284	+	1.24064i
$796$	4.48992	−	7.77677i	0.159141	−	0.275640i
$797$	−5.01695			−0.177709			−0.0888547	−	0.996045i	$-0.528321\pi$
$797$	−5.01695			−0.177709			−0.0888547	+	0.996045i	$0.528321\pi$
$798$	1.53310	+	5.06454i	0.0542713	+	0.179283i
$799$	−15.0694			−0.533118
$800$	−3.74141	+	6.48031i	−0.132279	+	0.229114i
$801$	−0.949713	−	1.64495i	−0.0335565	−	0.0581215i
$802$	−8.34284	−	14.4502i	−0.294596	−	0.510255i
$803$	−20.5218	+	35.5447i	−0.724197	+	1.25435i
$804$	7.43253			0.262125
$805$	9.10229	+	2.12793i	0.320813	+	0.0749996i
$806$	−12.9656			−0.456695
$807$	5.03064	−	8.71332i	0.177087	−	0.306723i
$808$	−5.74141	−	9.94441i	−0.201982	−	0.349843i
$809$	21.9816	+	38.0732i	0.772830	+	1.33858i	0.936006	+	0.351984i	$0.114493\pi$
$809$	21.9816	+	38.0732i	0.772830	+	1.33858i	−0.163176	+	0.986597i	$0.552174\pi$
$810$	−1.76655	+	3.05976i	−0.0620703	+	0.107509i
$811$	−16.2659			−0.571171			−0.285586	−	0.958353i	$-0.592188\pi$
$811$	−16.2659			−0.571171			−0.285586	+	0.958353i	$0.592188\pi$
$812$	3.82016	+	0.893075i	0.134061	+	0.0313408i
$813$	−2.66048			−0.0933072
$814$	28.5097	−	49.3803i	0.999265	−	1.73078i
$815$	18.9405	+	32.8060i	0.663458	+	1.14914i
$816$	−0.809736	−	1.40250i	−0.0283464	−	0.0490974i
$817$	2.00000	−	3.46410i	0.0699711	−	0.121194i
$818$	−25.9975			−0.908980
$819$	4.96941	+	16.4163i	0.173645	+	0.573630i
$820$	−17.8994			−0.625075
$821$	13.8186	−	23.9345i	0.482273	−	0.835321i	−0.517520	−	0.855671i	$-0.673145\pi$
$821$	13.8186	−	23.9345i	0.482273	−	0.835321i	0.999793	+	0.0203503i	$0.00647816\pi$
$822$	2.89610	+	5.01620i	0.101013	+	0.174960i
$823$	−5.04101	−	8.73129i	−0.175719	−	0.304354i	0.764691	−	0.644397i	$-0.222892\pi$
$823$	−5.04101	−	8.73129i	−0.175719	−	0.304354i	−0.940410	+	0.340043i	$0.889558\pi$
$824$	0.773654	−	1.34001i	0.0269515	−	0.0466814i
$825$	38.5558			1.34234
$826$	25.5759	−	27.2754i	0.889900	−	0.949032i
$827$	12.0779			0.419989			0.209995	−	0.977703i	$-0.432655\pi$
$827$	12.0779			0.419989			0.209995	+	0.977703i	$0.432655\pi$
$828$	0.500000	−	0.866025i	0.0173762	−	0.0300965i
$829$	−23.8566	−	41.3209i	−0.828575	−	1.43513i	−0.899156	−	0.437628i	$-0.855819\pi$
$829$	−23.8566	−	41.3209i	−0.828575	−	1.43513i	0.0705807	−	0.997506i	$-0.477515\pi$
$830$	−5.72176	−	9.91038i	−0.198605	−	0.343994i
$831$	1.44427	−	2.50155i	0.0501011	−	0.0867777i
$832$	6.48282			0.224751
$833$	9.43309	−	6.28717i	0.326837	−	0.217837i
$834$	−2.24387			−0.0776990
$835$	23.7574	−	41.1490i	0.822158	−	1.42402i
$836$	−5.15257	−	8.92452i	−0.178206	−	0.308661i
$837$	−1.00000	−	1.73205i	−0.0345651	−	0.0598684i
$838$	8.09519	−	14.0213i	0.279644	−	0.484357i
$839$	−17.7869			−0.614073			−0.307037	−	0.951698i	$-0.599337\pi$
$839$	−17.7869			−0.614073			−0.307037	+	0.951698i	$0.599337\pi$
$840$	−6.39398	+	6.81885i	−0.220613	+	0.235273i
$841$	−26.8013			−0.924181
$842$	−12.4237	+	21.5185i	−0.428149	+	0.741577i
$843$	13.6983	+	23.7261i	0.471794	+	0.817171i
$844$	4.89398	+	8.47663i	0.168458	+	0.291778i
$845$	−51.2775	+	88.8153i	−1.76400	+	3.05534i
$846$	9.30515			0.319918
$847$	11.9191	+	39.3743i	0.409546	+	1.35292i
$848$	11.4325			0.392595
$849$	1.31982	−	2.28599i	0.0452960	−	0.0784550i
$850$	6.05910	+	10.4947i	0.207826	+	0.359964i
$851$	5.53310	+	9.58362i	0.189672	+	0.328522i
$852$	7.60229	−	13.1675i	0.260450	−	0.451113i
$853$	−19.6163			−0.671648			−0.335824	−	0.941925i	$-0.609015\pi$
$853$	−19.6163			−0.671648			−0.335824	+	0.941925i	$0.609015\pi$
$854$	23.0980	+	5.39985i	0.790399	+	0.184779i
$855$	−7.06621			−0.241659
$856$	1.15257	−	1.99632i	0.0393942	−	0.0682327i
$857$	−12.3964	−	21.4713i	−0.423455	−	0.733445i	0.572820	−	0.819681i	$-0.305849\pi$
$857$	−12.3964	−	21.4713i	−0.423455	−	0.733445i	−0.996275	+	0.0862362i	$0.972516\pi$
$858$	−16.7016	−	28.9280i	−0.570183	−	0.987586i
$859$	3.87806	−	6.71700i	0.132318	−	0.229181i	−0.792252	−	0.610194i	$-0.791091\pi$
$859$	3.87806	−	6.71700i	0.132318	−	0.229181i	0.924570	+	0.381013i	$0.124425\pi$
$860$	7.06621			0.240956
$861$	−13.0520	−	3.05129i	−0.444811	−	0.103988i
$862$	14.6202			0.497965
$863$	2.58637	−	4.47972i	0.0880410	−	0.152491i	−0.818642	−	0.574304i	$-0.805273\pi$
$863$	2.58637	−	4.47972i	0.0880410	−	0.152491i	0.906683	+	0.421813i	$0.138606\pi$
$864$	0.500000	+	0.866025i	0.0170103	+	0.0294628i
$865$	26.3119	+	45.5735i	0.894631	+	1.54955i
$866$	−10.9749	+	19.0091i	−0.372943	+	0.645955i
$867$	14.3773			0.488279
$868$	−1.53310	−	5.06454i	−0.0520369	−	0.171902i
$869$	−67.7696			−2.29893
$870$	−2.61947	+	4.53706i	−0.0888084	+	0.153821i
$871$	24.0919	+	41.7283i	0.816322	+	1.41391i
$872$	2.52600	+	4.37516i	0.0855412	+	0.148162i
$873$	4.00000	−	6.92820i	0.135379	−	0.234484i
$874$	2.00000			0.0676510
$875$	15.8751	−	16.9299i	0.536676	−	0.572337i
$876$	7.96563			0.269134
$877$	14.7401	−	25.5307i	0.497739	−	0.862110i	−0.502257	−	0.864718i	$-0.667497\pi$
$877$	14.7401	−	25.5307i	0.497739	−	0.862110i	0.999997	+	0.00260848i	$0.000830306\pi$
$878$	−2.25315	−	3.90257i	−0.0760400	−	0.131705i
$879$	3.14708	+	5.45090i	0.106148	+	0.183854i
$880$	9.10229	−	15.7656i	0.306838	−	0.531459i
$881$	3.13172			0.105510			0.0527552	−	0.998607i	$-0.483200\pi$
$881$	3.13172			0.105510			0.0527552	+	0.998607i	$0.483200\pi$
$882$	−5.82480	+	3.88223i	−0.196131	+	0.130722i
$883$	56.3285			1.89560			0.947802	−	0.318858i	$-0.103299\pi$
$883$	56.3285			1.89560			0.947802	+	0.318858i	$0.103299\pi$
$884$	5.24937	−	9.09217i	0.176555	−	0.305803i
$885$	24.9656	+	43.2417i	0.839211	+	1.45356i
$886$	−18.0436	−	31.2524i	−0.606186	−	1.04994i
$887$	25.7984	−	44.6842i	0.866227	−	1.50035i	0.000403008	−	1.00000i	$-0.499872\pi$
$887$	25.7984	−	44.6842i	0.866227	−	1.50035i	0.865824	−	0.500349i	$-0.166795\pi$
$888$	−11.0662			−0.371358
$889$	−7.05693	+	7.52585i	−0.236682	+	0.252409i
$890$	6.71087			0.224949
$891$	2.57629	−	4.46226i	0.0863089	−	0.149491i
$892$	13.5993	+	23.5547i	0.455339	+	0.788669i
$893$	9.30515	+	16.1170i	0.311385	+	0.539335i
$894$	9.91913	−	17.1804i	0.331745	−	0.574600i
$895$	−70.7571			−2.36515
$896$	0.766551	+	2.53227i	0.0256087	+	0.0845973i
$897$	6.48282			0.216455
$898$	10.9296	−	18.9305i	0.364724	−	0.631720i
$899$	−1.48282	−	2.56831i	−0.0494547	−	0.0856580i
$900$	−3.74141	−	6.48031i	−0.124714	−	0.216010i
$901$	9.25733	−	16.0342i	0.308406	−	0.534175i
$902$	26.1040			0.869168
$903$	5.15257	+	1.20457i	0.171467	+	0.0400854i
$904$	8.77205			0.291754
$905$	−32.5458	+	56.3710i	−1.08186	+	1.87384i
$906$	6.01592	+	10.4199i	0.199866	+	0.346177i
$907$	17.9191	+	31.0368i	0.594995	+	1.03056i	0.993548	+	0.113416i	$0.0361792\pi$
$907$	17.9191	+	31.0368i	0.594995	+	1.03056i	−0.398553	+	0.917145i	$0.630487\pi$
$908$	−1.51008	+	2.61554i	−0.0501138	+	0.0867997i
$909$	11.4828			0.380861
$910$	−59.0085	−	13.7950i	−1.95611	−	0.457298i
$911$	3.83069			0.126916			0.0634582	−	0.997984i	$-0.479787\pi$
$911$	3.83069			0.126916			0.0634582	+	0.997984i	$0.479787\pi$
$912$	−1.00000	+	1.73205i	−0.0331133	+	0.0573539i
$913$	8.34445	+	14.4530i	0.276161	+	0.478325i
$914$	−3.06621	−	5.31082i	−0.101421	−	0.175666i
$915$	−15.8383	+	27.4327i	−0.523596	+	0.906896i
$916$	−7.55830			−0.249733
$917$	−7.90321	−	26.1079i	−0.260987	−	0.862159i
$918$	1.61947			0.0534505
$919$	−4.20618	+	7.28532i	−0.138749	+	0.240321i	−0.927023	−	0.375003i	$-0.877642\pi$
$919$	−4.20618	+	7.28532i	−0.138749	+	0.240321i	0.788274	+	0.615324i	$0.210975\pi$
$920$	1.76655	+	3.05976i	0.0582415	+	0.100877i
$921$	−10.4112	−	18.0327i	−0.343060	−	0.594197i
$922$	−3.00000	+	5.19615i	−0.0987997	+	0.171126i
$923$	98.5685			3.24442
$924$	9.32480	−	9.94441i	0.306763	−	0.327147i
$925$	82.8064			2.72266
$926$	−10.9656	+	18.9930i	−0.360353	+	0.624150i
$927$	0.773654	+	1.34001i	0.0254101	+	0.0440116i
$928$	0.741408	+	1.28416i	0.0243379	+	0.0421545i
$929$	23.7629	−	41.1585i	0.779635	−	1.35037i	−0.152518	−	0.988301i	$-0.548738\pi$
$929$	23.7629	−	41.1585i	0.779635	−	1.35037i	0.932152	−	0.362066i	$-0.117928\pi$
$930$	7.06621			0.231710
$931$	−12.5490	−	6.20661i	−0.411278	−	0.203414i
$932$	−24.6103			−0.806137
$933$	1.34743	−	2.33381i	0.0441127	−	0.0764055i
$934$	3.82016	+	6.61671i	0.124999	+	0.216505i
$935$	−14.7409	−	25.5320i	−0.482079	−	0.834985i
$936$	−3.24141	+	5.61428i	−0.105949	+	0.183509i
$937$	55.8089			1.82320			0.911599	−	0.411081i	$-0.134849\pi$
$937$	55.8089			1.82320			0.911599	+	0.411081i	$0.134849\pi$
$938$	−13.4509	+	14.3447i	−0.439188	+	0.468371i
$939$	24.6103			0.803127
$940$	−16.4380	+	28.4715i	−0.536149	+	0.928638i
$941$	8.60527	+	14.9048i	0.280524	+	0.485881i	0.971514	−	0.236983i	$-0.0761585\pi$
$941$	8.60527	+	14.9048i	0.280524	+	0.485881i	−0.690990	+	0.722864i	$0.742825\pi$
$942$	6.90653	+	11.9625i	0.225027	+	0.389758i
$943$	−2.53310	+	4.38746i	−0.0824892	+	0.142875i
$944$	14.1324			0.459971
$945$	−2.70831	−	8.94678i	−0.0881012	−	0.291039i
$946$	−10.3051			−0.335049
$947$	14.0939	−	24.4113i	0.457989	−	0.793260i	−0.540866	−	0.841109i	$-0.681903\pi$
$947$	14.0939	−	24.4113i	0.457989	−	0.793260i	0.998855	+	0.0478488i	$0.0152366\pi$
$948$	6.57629	+	11.3905i	0.213588	+	0.369945i
$949$	25.8199	+	44.7213i	0.838148	+	1.45172i
$950$	7.48282	−	12.9606i	0.242775	−	0.420498i
$951$	22.2648			0.721986
$952$	4.17222	+	0.975380i	0.135223	+	0.0316122i
$953$	19.7310			0.639151			0.319575	−	0.947561i	$-0.396460\pi$
$953$	19.7310			0.639151			0.319575	+	0.947561i	$0.396460\pi$
$954$	−5.71626	+	9.90086i	−0.185071	+	0.320552i
$955$	−3.35544	−	5.81178i	−0.108579	−	0.188065i
$956$	9.36088	+	16.2135i	0.302752	+	0.524383i
$957$	3.82016	−	6.61671i	0.123488	−	0.213888i
$958$	−17.6765			−0.571102
$959$	−14.9224	−	3.48855i	−0.481869	−	0.112651i
$960$	−3.53310			−0.114030
$961$	13.5000	−	23.3827i	0.435484	−	0.754280i
$962$	−35.8701	−	62.1288i	−1.15650	−	2.00311i
$963$	1.15257	+	1.99632i	0.0371412	+	0.0643304i
$964$	2.68568	−	4.65173i	0.0864998	−	0.149822i
$965$	−58.7033			−1.88973
$966$	0.766551	+	2.53227i	0.0246634	+	0.0814745i
$967$	−55.6646			−1.79005			−0.895026	−	0.446014i	$-0.852843\pi$
$967$	−55.6646			−1.79005			−0.895026	+	0.446014i	$0.852843\pi$
$968$	−7.77451	+	13.4658i	−0.249882	+	0.432809i
$969$	1.61947	+	2.80501i	0.0520249	+	0.0901098i
$970$	14.1324	+	24.4781i	0.453764	+	0.785943i
$971$	−6.22588	+	10.7835i	−0.199798	+	0.346060i	−0.948463	−	0.316888i	$-0.897362\pi$
$971$	−6.22588	+	10.7835i	−0.199798	+	0.346060i	0.748665	+	0.662949i	$0.230695\pi$
$972$	−1.00000			−0.0320750
$973$	4.06082	−	4.33065i	0.130184	−	0.138834i
$974$	7.85910			0.251822
$975$	24.2549	−	42.0107i	0.776777	−	1.34542i
$976$	4.48282	+	7.76447i	0.143491	+	0.248534i
$977$	−2.86884	−	4.96898i	−0.0917823	−	0.158972i	0.816479	−	0.577375i	$-0.195923\pi$
$977$	−2.86884	−	4.96898i	−0.0917823	−	0.158972i	−0.908261	+	0.418404i	$0.862590\pi$
$978$	−5.36088	+	9.28532i	−0.171422	+	0.296912i
$979$	−9.78694			−0.312792
$980$	−1.58888	−	24.6806i	−0.0507550	−	0.788394i
$981$	−5.05200			−0.161298
$982$	19.1660	−	33.1965i	0.611613	−	1.05934i
$983$	10.9841	+	19.0250i	0.350338	+	0.606803i	0.986309	−	0.164910i	$-0.0527335\pi$
$983$	10.9841	+	19.0250i	0.350338	+	0.606803i	−0.635971	+	0.771713i	$0.719400\pi$
$984$	−2.53310	−	4.38746i	−0.0807524	−	0.139867i
$985$	−46.7225	+	80.9258i	−1.48870	+	2.57851i
$986$	2.40138			0.0764755
$987$	−16.8399	+	17.9588i	−0.536019	+	0.571636i
$988$	−12.9656			−0.412492
$989$	1.00000	−	1.73205i	0.0317982	−	0.0550760i
$990$	9.10229	+	15.7656i	0.289290	+	0.501064i
$991$	−26.4577	−	45.8261i	−0.840457	−	1.45571i	−0.889509	−	0.456918i	$-0.848953\pi$
$991$	−26.4577	−	45.8261i	−0.840457	−	1.45571i	0.0490513	−	0.998796i	$-0.484380\pi$
$992$	1.00000	−	1.73205i	0.0317500	−	0.0549927i
$993$	3.26735			0.103686
$994$	11.6551	+	38.5021i	0.369677	+	1.22121i
$995$	−31.7267			−1.00580
$996$	1.61947	−	2.80501i	0.0513149	−	0.0888800i
$997$	−13.0613	−	22.6228i	−0.413655	−	0.716471i	0.581631	−	0.813452i	$-0.302415\pi$
$997$	−13.0613	−	22.6228i	−0.413655	−	0.716471i	−0.995286	+	0.0969814i	$0.969081\pi$
$998$	−11.1329	−	19.2828i	−0.352407	−	0.610386i
$999$	5.53310	−	9.58362i	0.175060	−	0.303212i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.i.m.415.1	yes	8
7.2	even	3		6762.2.a.cl.1.4		4
7.4	even	3	inner	966.2.i.m.277.1	✓	8
7.5	odd	6		6762.2.a.cr.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.i.m.277.1	✓	8	7.4	even	3	inner
966.2.i.m.415.1	yes	8	1.1	even	1	trivial
6762.2.a.cl.1.4		4	7.2	even	3
6762.2.a.cr.1.1		4	7.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.76655 + 3.05976i) q^{5} -1.00000 q^{6} +(1.80974 - 1.92999i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.76655 + 3.05976i) q^{5} -1.00000 q^{6} +(1.80974 - 1.92999i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.76655 - 3.05976i) q^{10} +(2.57629 + 4.46226i) q^{11} +(0.500000 - 0.866025i) q^{12} +6.48282 q^{13} +(0.766551 + 2.53227i) q^{14} -3.53310 q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.809736 + 1.40250i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(1.00000 - 1.73205i) q^{19} +3.53310 q^{20} +(2.57629 + 0.602283i) q^{21} -5.15257 q^{22} +(0.500000 - 0.866025i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-3.74141 - 6.48031i) q^{25} +(-3.24141 + 5.61428i) q^{26} -1.00000 q^{27} +(-2.57629 - 0.602283i) q^{28} -1.48282 q^{29} +(1.76655 - 3.05976i) q^{30} +(1.00000 + 1.73205i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-2.57629 + 4.46226i) q^{33} -1.61947 q^{34} +(2.70831 + 8.94678i) q^{35} +1.00000 q^{36} +(-5.53310 + 9.58362i) q^{37} +(1.00000 + 1.73205i) q^{38} +(3.24141 + 5.61428i) q^{39} +(-1.76655 + 3.05976i) q^{40} -5.06621 q^{41} +(-1.80974 + 1.92999i) q^{42} +2.00000 q^{43} +(2.57629 - 4.46226i) q^{44} +(-1.76655 - 3.05976i) q^{45} +(0.500000 + 0.866025i) q^{46} +(-4.65257 + 8.05850i) q^{47} -1.00000 q^{48} +(-0.449713 - 6.98554i) q^{49} +7.48282 q^{50} +(-0.809736 + 1.40250i) q^{51} +(-3.24141 - 5.61428i) q^{52} +(-5.71626 - 9.90086i) q^{53} +(0.500000 - 0.866025i) q^{54} -18.2046 q^{55} +(1.80974 - 1.92999i) q^{56} +2.00000 q^{57} +(0.741408 - 1.28416i) q^{58} +(-7.06621 - 12.2390i) q^{59} +(1.76655 + 3.05976i) q^{60} +(4.48282 - 7.76447i) q^{61} -2.00000 q^{62} +(0.766551 + 2.53227i) q^{63} +1.00000 q^{64} +(-11.4522 + 19.8358i) q^{65} +(-2.57629 - 4.46226i) q^{66} +(3.71626 + 6.43676i) q^{67} +(0.809736 - 1.40250i) q^{68} +1.00000 q^{69} +(-9.10229 - 2.12793i) q^{70} +15.2046 q^{71} +(-0.500000 + 0.866025i) q^{72} +(3.98282 + 6.89844i) q^{73} +(-5.53310 - 9.58362i) q^{74} +(3.74141 - 6.48031i) q^{75} -2.00000 q^{76} +(13.2745 + 3.10331i) q^{77} -6.48282 q^{78} +(-6.57629 + 11.3905i) q^{79} +(-1.76655 - 3.05976i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(2.53310 - 4.38746i) q^{82} +3.23894 q^{83} +(-0.766551 - 2.53227i) q^{84} -5.72176 q^{85} +(-1.00000 + 1.73205i) q^{86} +(-0.741408 - 1.28416i) q^{87} +(2.57629 + 4.46226i) q^{88} +(-0.949713 + 1.64495i) q^{89} +3.53310 q^{90} +(11.7322 - 12.5118i) q^{91} -1.00000 q^{92} +(-1.00000 + 1.73205i) q^{93} +(-4.65257 - 8.05850i) q^{94} +(3.53310 + 6.11951i) q^{95} +(0.500000 - 0.866025i) q^{96} -8.00000 q^{97} +(6.27451 + 3.10331i) q^{98} -5.15257 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} + 4 q^{3} - 4 q^{4} - 2 q^{5} - 8 q^{6} + 6 q^{7} + 8 q^{8} - 4 q^{9}+O(q^{10}) \) 8 * q - 4 * q^2 + 4 * q^3 - 4 * q^4 - 2 * q^5 - 8 * q^6 + 6 * q^7 + 8 * q^8 - 4 * q^9	\( 8 q - 4 q^{2} + 4 q^{3} - 4 q^{4} - 2 q^{5} - 8 q^{6} + 6 q^{7} + 8 q^{8} - 4 q^{9} - 2 q^{10} + 4 q^{12} + 12 q^{13} - 6 q^{14} - 4 q^{15} - 4 q^{16} - 2 q^{17} - 4 q^{18} + 8 q^{19} + 4 q^{20} + 4 q^{23} + 4 q^{24} - 10 q^{25} - 6 q^{26} - 8 q^{27} + 28 q^{29} + 2 q^{30} + 8 q^{31} - 4 q^{32} + 4 q^{34} + 26 q^{35} + 8 q^{36} - 20 q^{37} + 8 q^{38} + 6 q^{39} - 2 q^{40} + 8 q^{41} - 6 q^{42} + 16 q^{43} - 2 q^{45} + 4 q^{46} + 4 q^{47} - 8 q^{48} + 12 q^{49} + 20 q^{50} + 2 q^{51} - 6 q^{52} - 18 q^{53} + 4 q^{54} - 32 q^{55} + 6 q^{56} + 16 q^{57} - 14 q^{58} - 8 q^{59} + 2 q^{60} - 4 q^{61} - 16 q^{62} - 6 q^{63} + 8 q^{64} - 14 q^{65} + 2 q^{67} - 2 q^{68} + 8 q^{69} - 16 q^{70} + 8 q^{71} - 4 q^{72} - 8 q^{73} - 20 q^{74} + 10 q^{75} - 16 q^{76} + 62 q^{77} - 12 q^{78} - 32 q^{79} - 2 q^{80} - 4 q^{81} - 4 q^{82} - 8 q^{83} + 6 q^{84} + 28 q^{85} - 8 q^{86} + 14 q^{87} + 8 q^{89} + 4 q^{90} + 2 q^{91} - 8 q^{92} - 8 q^{93} + 4 q^{94} + 4 q^{95} + 4 q^{96} - 64 q^{97} + 6 q^{98}+O(q^{100}) \) 8 * q - 4 * q^2 + 4 * q^3 - 4 * q^4 - 2 * q^5 - 8 * q^6 + 6 * q^7 + 8 * q^8 - 4 * q^9 - 2 * q^10 + 4 * q^12 + 12 * q^13 - 6 * q^14 - 4 * q^15 - 4 * q^16 - 2 * q^17 - 4 * q^18 + 8 * q^19 + 4 * q^20 + 4 * q^23 + 4 * q^24 - 10 * q^25 - 6 * q^26 - 8 * q^27 + 28 * q^29 + 2 * q^30 + 8 * q^31 - 4 * q^32 + 4 * q^34 + 26 * q^35 + 8 * q^36 - 20 * q^37 + 8 * q^38 + 6 * q^39 - 2 * q^40 + 8 * q^41 - 6 * q^42 + 16 * q^43 - 2 * q^45 + 4 * q^46 + 4 * q^47 - 8 * q^48 + 12 * q^49 + 20 * q^50 + 2 * q^51 - 6 * q^52 - 18 * q^53 + 4 * q^54 - 32 * q^55 + 6 * q^56 + 16 * q^57 - 14 * q^58 - 8 * q^59 + 2 * q^60 - 4 * q^61 - 16 * q^62 - 6 * q^63 + 8 * q^64 - 14 * q^65 + 2 * q^67 - 2 * q^68 + 8 * q^69 - 16 * q^70 + 8 * q^71 - 4 * q^72 - 8 * q^73 - 20 * q^74 + 10 * q^75 - 16 * q^76 + 62 * q^77 - 12 * q^78 - 32 * q^79 - 2 * q^80 - 4 * q^81 - 4 * q^82 - 8 * q^83 + 6 * q^84 + 28 * q^85 - 8 * q^86 + 14 * q^87 + 8 * q^89 + 4 * q^90 + 2 * q^91 - 8 * q^92 - 8 * q^93 + 4 * q^94 + 4 * q^95 + 4 * q^96 - 64 * q^97 + 6 * q^98

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