LMFDB - Embedded newform 966.2.i.j.277.1

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:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			277.1
Root			$-0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	966.277
Dual form			966.2.i.j.415.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.207107 - 0.358719i) q^{5} -1.00000 q^{6} +(-2.62132 + 0.358719i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.207107 - 0.358719i) q^{5} -1.00000 q^{6} +(-2.62132 + 0.358719i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.207107 - 0.358719i) q^{10} +(-1.00000 + 1.73205i) q^{11} +(-0.500000 - 0.866025i) q^{12} -1.82843 q^{13} +(-1.62132 - 2.09077i) q^{14} +0.414214 q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.62132 - 2.80821i) q^{17} +(0.500000 - 0.866025i) q^{18} +(-1.82843 - 3.16693i) q^{19} +0.414214 q^{20} +(1.00000 - 2.44949i) q^{21} -2.00000 q^{22} +(-0.500000 - 0.866025i) q^{23} +(0.500000 - 0.866025i) q^{24} +(2.41421 - 4.18154i) q^{25} +(-0.914214 - 1.58346i) q^{26} +1.00000 q^{27} +(1.00000 - 2.44949i) q^{28} -1.17157 q^{29} +(0.207107 + 0.358719i) q^{30} +(1.00000 - 1.73205i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-1.00000 - 1.73205i) q^{33} +3.24264 q^{34} +(0.671573 + 0.866025i) q^{35} +1.00000 q^{36} +(1.58579 + 2.74666i) q^{37} +(1.82843 - 3.16693i) q^{38} +(0.914214 - 1.58346i) q^{39} +(0.207107 + 0.358719i) q^{40} -10.8284 q^{41} +(2.62132 - 0.358719i) q^{42} -11.6569 q^{43} +(-1.00000 - 1.73205i) q^{44} +(-0.207107 + 0.358719i) q^{45} +(0.500000 - 0.866025i) q^{46} +(-4.50000 - 7.79423i) q^{47} +1.00000 q^{48} +(6.74264 - 1.88064i) q^{49} +4.82843 q^{50} +(1.62132 + 2.80821i) q^{51} +(0.914214 - 1.58346i) q^{52} +(5.03553 - 8.72180i) q^{53} +(0.500000 + 0.866025i) q^{54} +0.828427 q^{55} +(2.62132 - 0.358719i) q^{56} +3.65685 q^{57} +(-0.585786 - 1.01461i) q^{58} +(-0.828427 + 1.43488i) q^{59} +(-0.207107 + 0.358719i) q^{60} +(1.00000 + 1.73205i) q^{61} +2.00000 q^{62} +(1.62132 + 2.09077i) q^{63} +1.00000 q^{64} +(0.378680 + 0.655892i) q^{65} +(1.00000 - 1.73205i) q^{66} +(-7.44975 + 12.9033i) q^{67} +(1.62132 + 2.80821i) q^{68} +1.00000 q^{69} +(-0.414214 + 1.01461i) q^{70} -9.82843 q^{71} +(0.500000 + 0.866025i) q^{72} +(5.32843 - 9.22911i) q^{73} +(-1.58579 + 2.74666i) q^{74} +(2.41421 + 4.18154i) q^{75} +3.65685 q^{76} +(2.00000 - 4.89898i) q^{77} +1.82843 q^{78} +(5.00000 + 8.66025i) q^{79} +(-0.207107 + 0.358719i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-5.41421 - 9.37769i) q^{82} +12.8284 q^{83} +(1.62132 + 2.09077i) q^{84} -1.34315 q^{85} +(-5.82843 - 10.0951i) q^{86} +(0.585786 - 1.01461i) q^{87} +(1.00000 - 1.73205i) q^{88} +(-0.585786 - 1.01461i) q^{89} -0.414214 q^{90} +(4.79289 - 0.655892i) q^{91} +1.00000 q^{92} +(1.00000 + 1.73205i) q^{93} +(4.50000 - 7.79423i) q^{94} +(-0.757359 + 1.31178i) q^{95} +(0.500000 + 0.866025i) q^{96} -9.65685 q^{97} +(5.00000 + 4.89898i) q^{98} +2.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{5} - 4 q^{6} - 2 q^{7} - 4 q^{8} - 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^5 - 4 * q^6 - 2 * q^7 - 4 * q^8 - 2 * q^9	\( 4 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{5} - 4 q^{6} - 2 q^{7} - 4 q^{8} - 2 q^{9} - 2 q^{10} - 4 q^{11} - 2 q^{12} + 4 q^{13} + 2 q^{14} - 4 q^{15} - 2 q^{16} - 2 q^{17} + 2 q^{18} + 4 q^{19} - 4 q^{20} + 4 q^{21} - 8 q^{22} - 2 q^{23} + 2 q^{24} + 4 q^{25} + 2 q^{26} + 4 q^{27} + 4 q^{28} - 16 q^{29} - 2 q^{30} + 4 q^{31} + 2 q^{32} - 4 q^{33} - 4 q^{34} + 14 q^{35} + 4 q^{36} + 12 q^{37} - 4 q^{38} - 2 q^{39} - 2 q^{40} - 32 q^{41} + 2 q^{42} - 24 q^{43} - 4 q^{44} + 2 q^{45} + 2 q^{46} - 18 q^{47} + 4 q^{48} + 10 q^{49} + 8 q^{50} - 2 q^{51} - 2 q^{52} + 6 q^{53} + 2 q^{54} - 8 q^{55} + 2 q^{56} - 8 q^{57} - 8 q^{58} + 8 q^{59} + 2 q^{60} + 4 q^{61} + 8 q^{62} - 2 q^{63} + 4 q^{64} + 10 q^{65} + 4 q^{66} - 10 q^{67} - 2 q^{68} + 4 q^{69} + 4 q^{70} - 28 q^{71} + 2 q^{72} + 10 q^{73} - 12 q^{74} + 4 q^{75} - 8 q^{76} + 8 q^{77} - 4 q^{78} + 20 q^{79} + 2 q^{80} - 2 q^{81} - 16 q^{82} + 40 q^{83} - 2 q^{84} - 28 q^{85} - 12 q^{86} + 8 q^{87} + 4 q^{88} - 8 q^{89} + 4 q^{90} + 22 q^{91} + 4 q^{92} + 4 q^{93} + 18 q^{94} - 20 q^{95} + 2 q^{96} - 16 q^{97} + 20 q^{98} + 8 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^5 - 4 * q^6 - 2 * q^7 - 4 * q^8 - 2 * q^9 - 2 * q^10 - 4 * q^11 - 2 * q^12 + 4 * q^13 + 2 * q^14 - 4 * q^15 - 2 * q^16 - 2 * q^17 + 2 * q^18 + 4 * q^19 - 4 * q^20 + 4 * q^21 - 8 * q^22 - 2 * q^23 + 2 * q^24 + 4 * q^25 + 2 * q^26 + 4 * q^27 + 4 * q^28 - 16 * q^29 - 2 * q^30 + 4 * q^31 + 2 * q^32 - 4 * q^33 - 4 * q^34 + 14 * q^35 + 4 * q^36 + 12 * q^37 - 4 * q^38 - 2 * q^39 - 2 * q^40 - 32 * q^41 + 2 * q^42 - 24 * q^43 - 4 * q^44 + 2 * q^45 + 2 * q^46 - 18 * q^47 + 4 * q^48 + 10 * q^49 + 8 * q^50 - 2 * q^51 - 2 * q^52 + 6 * q^53 + 2 * q^54 - 8 * q^55 + 2 * q^56 - 8 * q^57 - 8 * q^58 + 8 * q^59 + 2 * q^60 + 4 * q^61 + 8 * q^62 - 2 * q^63 + 4 * q^64 + 10 * q^65 + 4 * q^66 - 10 * q^67 - 2 * q^68 + 4 * q^69 + 4 * q^70 - 28 * q^71 + 2 * q^72 + 10 * q^73 - 12 * q^74 + 4 * q^75 - 8 * q^76 + 8 * q^77 - 4 * q^78 + 20 * q^79 + 2 * q^80 - 2 * q^81 - 16 * q^82 + 40 * q^83 - 2 * q^84 - 28 * q^85 - 12 * q^86 + 8 * q^87 + 4 * q^88 - 8 * q^89 + 4 * q^90 + 22 * q^91 + 4 * q^92 + 4 * q^93 + 18 * q^94 - 20 * q^95 + 2 * q^96 - 16 * q^97 + 20 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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
$3$	−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
$5$	−0.207107	−	0.358719i	−0.0926210	−	0.160424i	0.815992	−	0.578063i	$-0.196191\pi$
$5$	−0.207107	−	0.358719i	−0.0926210	−	0.160424i	−0.908613	+	0.417639i	$0.862858\pi$
$6$	−1.00000			−0.408248
$7$	−2.62132	+	0.358719i	−0.990766	+	0.135583i
$7$	−2.62132	+	0.358719i	−0.990766	+	0.135583i
$8$	−1.00000			−0.353553
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	0.207107	−	0.358719i	0.0654929	−	0.113437i
$11$	−1.00000	+	1.73205i	−0.301511	+	0.522233i	−0.976478	−	0.215615i	$-0.930824\pi$
$11$	−1.00000	+	1.73205i	−0.301511	+	0.522233i	0.674967	+	0.737848i	$0.264158\pi$
$12$	−0.500000	−	0.866025i	−0.144338	−	0.250000i
$13$	−1.82843			−0.507114			−0.253557	−	0.967320i	$-0.581601\pi$
$13$	−1.82843			−0.507114			−0.253557	+	0.967320i	$0.581601\pi$
$14$	−1.62132	−	2.09077i	−0.433316	−	0.558782i
$15$	0.414214			0.106949
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.62132	−	2.80821i	0.393228	−	0.681091i	−0.599645	−	0.800266i	$-0.704692\pi$
$17$	1.62132	−	2.80821i	0.393228	−	0.681091i	0.992873	+	0.119175i	$0.0380250\pi$
$18$	0.500000	−	0.866025i	0.117851	−	0.204124i
$19$	−1.82843	−	3.16693i	−0.419470	−	0.726543i	0.576416	−	0.817156i	$-0.304451\pi$
$19$	−1.82843	−	3.16693i	−0.419470	−	0.726543i	−0.995886	+	0.0906130i	$0.971117\pi$
$20$	0.414214			0.0926210
$21$	1.00000	−	2.44949i	0.218218	−	0.534522i
$22$	−2.00000			−0.426401
$23$	−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
$25$	2.41421	−	4.18154i	0.482843	−	0.836308i
$26$	−0.914214	−	1.58346i	−0.179292	−	0.310543i
$27$	1.00000			0.192450
$28$	1.00000	−	2.44949i	0.188982	−	0.462910i
$29$	−1.17157			−0.217556			−0.108778	−	0.994066i	$-0.534694\pi$
$29$	−1.17157			−0.217556			−0.108778	+	0.994066i	$0.534694\pi$
$30$	0.207107	+	0.358719i	0.0378124	+	0.0654929i
$31$	1.00000	−	1.73205i	0.179605	−	0.311086i	−0.762140	−	0.647412i	$-0.775851\pi$
$31$	1.00000	−	1.73205i	0.179605	−	0.311086i	0.941745	+	0.336327i	$0.109185\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−1.00000	−	1.73205i	−0.174078	−	0.301511i
$34$	3.24264			0.556108
$35$	0.671573	+	0.866025i	0.113517	+	0.146385i
$36$	1.00000			0.166667
$37$	1.58579	+	2.74666i	0.260702	+	0.451549i	0.966429	−	0.256935i	$-0.0827128\pi$
$37$	1.58579	+	2.74666i	0.260702	+	0.451549i	−0.705727	+	0.708484i	$0.749379\pi$
$38$	1.82843	−	3.16693i	0.296610	−	0.513744i
$39$	0.914214	−	1.58346i	0.146391	−	0.253557i
$40$	0.207107	+	0.358719i	0.0327465	+	0.0567185i
$41$	−10.8284			−1.69112			−0.845558	−	0.533883i	$-0.820732\pi$
$41$	−10.8284			−1.69112			−0.845558	+	0.533883i	$0.820732\pi$
$42$	2.62132	−	0.358719i	0.404479	−	0.0553516i
$43$	−11.6569			−1.77765			−0.888827	−	0.458243i	$-0.848479\pi$
$43$	−11.6569			−1.77765			−0.888827	+	0.458243i	$0.848479\pi$
$44$	−1.00000	−	1.73205i	−0.150756	−	0.261116i
$45$	−0.207107	+	0.358719i	−0.0308737	+	0.0534747i
$46$	0.500000	−	0.866025i	0.0737210	−	0.127688i
$47$	−4.50000	−	7.79423i	−0.656392	−	1.13691i	−0.981543	−	0.191243i	$-0.938748\pi$
$47$	−4.50000	−	7.79423i	−0.656392	−	1.13691i	0.325150	−	0.945662i	$-0.394585\pi$
$48$	1.00000			0.144338
$49$	6.74264	−	1.88064i	0.963234	−	0.268662i
$50$	4.82843			0.682843
$51$	1.62132	+	2.80821i	0.227030	+	0.393228i
$52$	0.914214	−	1.58346i	0.126779	−	0.219587i
$53$	5.03553	−	8.72180i	0.691684	−	1.19803i	−0.279602	−	0.960116i	$-0.590203\pi$
$53$	5.03553	−	8.72180i	0.691684	−	1.19803i	0.971286	−	0.237915i	$-0.0764641\pi$
$54$	0.500000	+	0.866025i	0.0680414	+	0.117851i
$55$	0.828427			0.111705
$56$	2.62132	−	0.358719i	0.350289	−	0.0479359i
$57$	3.65685			0.484362
$58$	−0.585786	−	1.01461i	−0.0769175	−	0.133225i
$59$	−0.828427	+	1.43488i	−0.107852	+	0.186805i	−0.914900	−	0.403681i	$-0.867731\pi$
$59$	−0.828427	+	1.43488i	−0.107852	+	0.186805i	0.807048	+	0.590486i	$0.201064\pi$
$60$	−0.207107	+	0.358719i	−0.0267374	+	0.0463105i
$61$	1.00000	+	1.73205i	0.128037	+	0.221766i	0.922916	−	0.385002i	$-0.125799\pi$
$61$	1.00000	+	1.73205i	0.128037	+	0.221766i	−0.794879	+	0.606768i	$0.792466\pi$
$62$	2.00000			0.254000
$63$	1.62132	+	2.09077i	0.204267	+	0.263412i
$64$	1.00000			0.125000
$65$	0.378680	+	0.655892i	0.0469694	+	0.0813534i
$66$	1.00000	−	1.73205i	0.123091	−	0.213201i
$67$	−7.44975	+	12.9033i	−0.910132	+	1.57639i	−0.0962546	+	0.995357i	$0.530686\pi$
$67$	−7.44975	+	12.9033i	−0.910132	+	1.57639i	−0.813877	+	0.581037i	$0.802647\pi$
$68$	1.62132	+	2.80821i	0.196614	+	0.340545i
$69$	1.00000			0.120386
$70$	−0.414214	+	1.01461i	−0.0495080	+	0.121269i
$71$	−9.82843			−1.16642			−0.583210	−	0.812322i	$-0.698203\pi$
$71$	−9.82843			−1.16642			−0.583210	+	0.812322i	$0.698203\pi$
$72$	0.500000	+	0.866025i	0.0589256	+	0.102062i
$73$	5.32843	−	9.22911i	0.623645	−	1.08019i	−0.365156	−	0.930946i	$-0.618984\pi$
$73$	5.32843	−	9.22911i	0.623645	−	1.08019i	0.988801	−	0.149239i	$-0.0476823\pi$
$74$	−1.58579	+	2.74666i	−0.184344	+	0.319293i
$75$	2.41421	+	4.18154i	0.278769	+	0.482843i
$76$	3.65685			0.419470
$77$	2.00000	−	4.89898i	0.227921	−	0.558291i
$78$	1.82843			0.207029
$79$	5.00000	+	8.66025i	0.562544	+	0.974355i	0.997274	+	0.0737937i	$0.0235106\pi$
$79$	5.00000	+	8.66025i	0.562544	+	0.974355i	−0.434730	+	0.900561i	$0.643156\pi$
$80$	−0.207107	+	0.358719i	−0.0231552	+	0.0401061i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−5.41421	−	9.37769i	−0.597900	−	1.03559i
$83$	12.8284			1.40810			0.704051	−	0.710149i	$-0.251372\pi$
$83$	12.8284			1.40810			0.704051	+	0.710149i	$0.251372\pi$
$84$	1.62132	+	2.09077i	0.176901	+	0.228122i
$85$	−1.34315			−0.145685
$86$	−5.82843	−	10.0951i	−0.628495	−	1.08859i
$87$	0.585786	−	1.01461i	0.0628029	−	0.108778i
$88$	1.00000	−	1.73205i	0.106600	−	0.184637i
$89$	−0.585786	−	1.01461i	−0.0620932	−	0.107549i	0.833308	−	0.552809i	$-0.186444\pi$
$89$	−0.585786	−	1.01461i	−0.0620932	−	0.107549i	−0.895401	+	0.445261i	$0.853111\pi$
$90$	−0.414214			−0.0436619
$91$	4.79289	−	0.655892i	0.502432	−	0.0687562i
$92$	1.00000			0.104257
$93$	1.00000	+	1.73205i	0.103695	+	0.179605i
$94$	4.50000	−	7.79423i	0.464140	−	0.803913i
$95$	−0.757359	+	1.31178i	−0.0777034	+	0.134586i
$96$	0.500000	+	0.866025i	0.0510310	+	0.0883883i
$97$	−9.65685			−0.980505			−0.490252	−	0.871580i	$-0.663095\pi$
$97$	−9.65685			−0.980505			−0.490252	+	0.871580i	$0.663095\pi$
$98$	5.00000	+	4.89898i	0.505076	+	0.494872i
$99$	2.00000			0.201008
$100$	2.41421	+	4.18154i	0.241421	+	0.418154i
$101$	−1.58579	+	2.74666i	−0.157792	+	0.273303i	−0.934072	−	0.357085i	$-0.883771\pi$
$101$	−1.58579	+	2.74666i	−0.157792	+	0.273303i	0.776280	+	0.630388i	$0.217104\pi$
$102$	−1.62132	+	2.80821i	−0.160535	+	0.278054i
$103$	4.44975	+	7.70719i	0.438447	+	0.759412i	0.997570	−	0.0696727i	$-0.0221955\pi$
$103$	4.44975	+	7.70719i	0.438447	+	0.759412i	−0.559123	+	0.829085i	$0.688862\pi$
$104$	1.82843			0.179292
$105$	−1.08579	+	0.148586i	−0.105962	+	0.0145006i
$106$	10.0711			0.978189
$107$	−2.82843	−	4.89898i	−0.273434	−	0.473602i	0.696305	−	0.717746i	$-0.254826\pi$
$107$	−2.82843	−	4.89898i	−0.273434	−	0.473602i	−0.969739	+	0.244144i	$0.921493\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$	−7.41421	+	12.8418i	−0.710153	+	1.23002i	0.254647	+	0.967034i	$0.418041\pi$
$109$	−7.41421	+	12.8418i	−0.710153	+	1.23002i	−0.964799	+	0.262987i	$0.915292\pi$
$110$	0.414214	+	0.717439i	0.0394937	+	0.0684051i
$111$	−3.17157			−0.301032
$112$	1.62132	+	2.09077i	0.153200	+	0.197559i
$113$	−13.7279			−1.29141			−0.645707	−	0.763585i	$-0.723437\pi$
$113$	−13.7279			−1.29141			−0.645707	+	0.763585i	$0.723437\pi$
$114$	1.82843	+	3.16693i	0.171248	+	0.296610i
$115$	−0.207107	+	0.358719i	−0.0193128	+	0.0334508i
$116$	0.585786	−	1.01461i	0.0543889	−	0.0942043i
$117$	0.914214	+	1.58346i	0.0845191	+	0.146391i
$118$	−1.65685			−0.152526
$119$	−3.24264	+	7.94282i	−0.297252	+	0.728117i
$120$	−0.414214			−0.0378124
$121$	3.50000	+	6.06218i	0.318182	+	0.551107i
$122$	−1.00000	+	1.73205i	−0.0905357	+	0.156813i
$123$	5.41421	−	9.37769i	0.488183	−	0.845558i
$124$	1.00000	+	1.73205i	0.0898027	+	0.155543i
$125$	−4.07107			−0.364127
$126$	−1.00000	+	2.44949i	−0.0890871	+	0.218218i
$127$	4.82843			0.428454			0.214227	−	0.976784i	$-0.431277\pi$
$127$	4.82843			0.428454			0.214227	+	0.976784i	$0.431277\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	5.82843	−	10.0951i	0.513164	−	0.888827i
$130$	−0.378680	+	0.655892i	−0.0332124	+	0.0575256i
$131$	−9.57107	−	16.5776i	−0.836228	−	1.44839i	−0.893027	−	0.450004i	$-0.851423\pi$
$131$	−9.57107	−	16.5776i	−0.836228	−	1.44839i	0.0567985	−	0.998386i	$-0.481911\pi$
$132$	2.00000			0.174078
$133$	5.92893	+	7.64564i	0.514104	+	0.662961i
$134$	−14.8995			−1.28712
$135$	−0.207107	−	0.358719i	−0.0178249	−	0.0308737i
$136$	−1.62132	+	2.80821i	−0.139027	+	0.240802i
$137$	5.20711	−	9.01897i	0.444873	−	0.770543i	−0.553170	−	0.833068i	$-0.686582\pi$
$137$	5.20711	−	9.01897i	0.444873	−	0.770543i	0.998043	+	0.0625253i	$0.0199154\pi$
$138$	0.500000	+	0.866025i	0.0425628	+	0.0737210i
$139$	−13.3137			−1.12925			−0.564627	−	0.825346i	$-0.690980\pi$
$139$	−13.3137			−1.12925			−0.564627	+	0.825346i	$0.690980\pi$
$140$	−1.08579	+	0.148586i	−0.0917657	+	0.0125578i
$141$	9.00000			0.757937
$142$	−4.91421	−	8.51167i	−0.412392	−	0.714283i
$143$	1.82843	−	3.16693i	0.152901	−	0.264832i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	0.242641	+	0.420266i	0.0201502	+	0.0349012i
$146$	10.6569			0.881968
$147$	−1.74264	+	6.77962i	−0.143731	+	0.559173i
$148$	−3.17157			−0.260702
$149$	−0.378680	−	0.655892i	−0.0310226	−	0.0537328i	0.850097	−	0.526626i	$-0.176543\pi$
$149$	−0.378680	−	0.655892i	−0.0310226	−	0.0537328i	−0.881120	+	0.472893i	$0.843210\pi$
$150$	−2.41421	+	4.18154i	−0.197120	+	0.341421i
$151$	−7.07107	+	12.2474i	−0.575435	+	0.996683i	0.420559	+	0.907265i	$0.361834\pi$
$151$	−7.07107	+	12.2474i	−0.575435	+	0.996683i	−0.995994	+	0.0894180i	$0.971499\pi$
$152$	1.82843	+	3.16693i	0.148305	+	0.256872i
$153$	−3.24264			−0.262152
$154$	5.24264	−	0.717439i	0.422464	−	0.0578129i
$155$	−0.828427			−0.0665409
$156$	0.914214	+	1.58346i	0.0731957	+	0.126779i
$157$	2.17157	−	3.76127i	0.173310	−	0.300182i	−0.766265	−	0.642525i	$-0.777887\pi$
$157$	2.17157	−	3.76127i	0.173310	−	0.300182i	0.939575	+	0.342342i	$0.111220\pi$
$158$	−5.00000	+	8.66025i	−0.397779	+	0.688973i
$159$	5.03553	+	8.72180i	0.399344	+	0.691684i
$160$	−0.414214			−0.0327465
$161$	1.62132	+	2.09077i	0.127778	+	0.164776i
$162$	−1.00000			−0.0785674
$163$	4.82843	+	8.36308i	0.378192	+	0.655047i	0.990799	−	0.135340i	$-0.0432127\pi$
$163$	4.82843	+	8.36308i	0.378192	+	0.655047i	−0.612608	+	0.790387i	$0.709879\pi$
$164$	5.41421	−	9.37769i	0.422779	−	0.732275i
$165$	−0.414214	+	0.717439i	−0.0322465	+	0.0558525i
$166$	6.41421	+	11.1097i	0.497840	+	0.862283i
$167$	−14.7990			−1.14518			−0.572590	−	0.819842i	$-0.694061\pi$
$167$	−14.7990			−1.14518			−0.572590	+	0.819842i	$0.694061\pi$
$168$	−1.00000	+	2.44949i	−0.0771517	+	0.188982i
$169$	−9.65685			−0.742835
$170$	−0.671573	−	1.16320i	−0.0515073	−	0.0892132i
$171$	−1.82843	+	3.16693i	−0.139823	+	0.242181i
$172$	5.82843	−	10.0951i	0.444413	−	0.769747i
$173$	−7.65685	−	13.2621i	−0.582140	−	1.00830i	−0.995225	−	0.0976036i	$-0.968882\pi$
$173$	−7.65685	−	13.2621i	−0.582140	−	1.00830i	0.413086	−	0.910692i	$-0.364451\pi$
$174$	1.17157			0.0888167
$175$	−4.82843	+	11.8272i	−0.364995	+	0.894051i
$176$	2.00000			0.150756
$177$	−0.828427	−	1.43488i	−0.0622684	−	0.107852i
$178$	0.585786	−	1.01461i	0.0439065	−	0.0760484i
$179$	−5.98528	+	10.3668i	−0.447361	+	0.774852i	−0.998213	−	0.0597508i	$-0.980969\pi$
$179$	−5.98528	+	10.3668i	−0.447361	+	0.774852i	0.550852	+	0.834603i	$0.314303\pi$
$180$	−0.207107	−	0.358719i	−0.0154368	−	0.0267374i
$181$	13.3137			0.989600			0.494800	−	0.869007i	$-0.335241\pi$
$181$	13.3137			0.989600			0.494800	+	0.869007i	$0.335241\pi$
$182$	2.96447	+	3.82282i	0.219741	+	0.283366i
$183$	−2.00000			−0.147844
$184$	0.500000	+	0.866025i	0.0368605	+	0.0638442i
$185$	0.656854	−	1.13770i	0.0482929	−	0.0836457i
$186$	−1.00000	+	1.73205i	−0.0733236	+	0.127000i
$187$	3.24264	+	5.61642i	0.237125	+	0.410713i
$188$	9.00000			0.656392
$189$	−2.62132	+	0.358719i	−0.190673	+	0.0260930i
$190$	−1.51472			−0.109889
$191$	5.41421	+	9.37769i	0.391759	+	0.678546i	0.992682	−	0.120761i	$-0.0385335\pi$
$191$	5.41421	+	9.37769i	0.391759	+	0.678546i	−0.600923	+	0.799307i	$0.705200\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	−5.74264	+	9.94655i	−0.413364	+	0.715968i	−0.995255	−	0.0972989i	$-0.968980\pi$
$193$	−5.74264	+	9.94655i	−0.413364	+	0.715968i	0.581891	+	0.813267i	$0.302313\pi$
$194$	−4.82843	−	8.36308i	−0.346661	−	0.600434i
$195$	−0.757359			−0.0542356
$196$	−1.74264	+	6.77962i	−0.124474	+	0.484258i
$197$	−7.17157			−0.510953			−0.255477	−	0.966815i	$-0.582232\pi$
$197$	−7.17157			−0.510953			−0.255477	+	0.966815i	$0.582232\pi$
$198$	1.00000	+	1.73205i	0.0710669	+	0.123091i
$199$	8.17157	−	14.1536i	0.579267	−	1.00332i	−0.416296	−	0.909229i	$-0.636672\pi$
$199$	8.17157	−	14.1536i	0.579267	−	1.00332i	0.995564	−	0.0940915i	$-0.0299946\pi$
$200$	−2.41421	+	4.18154i	−0.170711	+	0.295680i
$201$	−7.44975	−	12.9033i	−0.525465	−	0.910132i
$202$	−3.17157			−0.223151
$203$	3.07107	−	0.420266i	0.215547	−	0.0294969i
$204$	−3.24264			−0.227030
$205$	2.24264	+	3.88437i	0.156633	+	0.271296i
$206$	−4.44975	+	7.70719i	−0.310029	+	0.536985i
$207$	−0.500000	+	0.866025i	−0.0347524	+	0.0601929i
$208$	0.914214	+	1.58346i	0.0633893	+	0.109793i
$209$	7.31371			0.505900
$210$	−0.671573	−	0.866025i	−0.0463429	−	0.0597614i
$211$	−16.8284			−1.15852			−0.579258	−	0.815144i	$-0.696658\pi$
$211$	−16.8284			−1.15852			−0.579258	+	0.815144i	$0.696658\pi$
$212$	5.03553	+	8.72180i	0.345842	+	0.599016i
$213$	4.91421	−	8.51167i	0.336716	−	0.583210i
$214$	2.82843	−	4.89898i	0.193347	−	0.334887i
$215$	2.41421	+	4.18154i	0.164648	+	0.285179i
$216$	−1.00000			−0.0680414
$217$	−2.00000	+	4.89898i	−0.135769	+	0.332564i
$218$	−14.8284			−1.00431
$219$	5.32843	+	9.22911i	0.360062	+	0.623645i
$220$	−0.414214	+	0.717439i	−0.0279263	+	0.0483697i
$221$	−2.96447	+	5.13461i	−0.199412	+	0.345391i
$222$	−1.58579	−	2.74666i	−0.106431	−	0.184344i
$223$	4.48528			0.300357			0.150178	−	0.988659i	$-0.452015\pi$
$223$	4.48528			0.300357			0.150178	+	0.988659i	$0.452015\pi$
$224$	−1.00000	+	2.44949i	−0.0668153	+	0.163663i
$225$	−4.82843			−0.321895
$226$	−6.86396	−	11.8887i	−0.456584	−	0.790827i
$227$	−11.4853	+	19.8931i	−0.762305	+	1.32035i	0.179355	+	0.983784i	$0.442599\pi$
$227$	−11.4853	+	19.8931i	−0.762305	+	1.32035i	−0.941660	+	0.336566i	$0.890734\pi$
$228$	−1.82843	+	3.16693i	−0.121091	+	0.209735i
$229$	13.0711	+	22.6398i	0.863760	+	1.49608i	0.868273	+	0.496087i	$0.165230\pi$
$229$	13.0711	+	22.6398i	0.863760	+	1.49608i	−0.00451223	+	0.999990i	$0.501436\pi$
$230$	−0.414214			−0.0273124
$231$	3.24264	+	4.18154i	0.213350	+	0.275125i
$232$	1.17157			0.0769175
$233$	4.00000	+	6.92820i	0.262049	+	0.453882i	0.966786	−	0.255586i	$-0.0822686\pi$
$233$	4.00000	+	6.92820i	0.262049	+	0.453882i	−0.704737	+	0.709468i	$0.748935\pi$
$234$	−0.914214	+	1.58346i	−0.0597640	+	0.103514i
$235$	−1.86396	+	3.22848i	−0.121591	+	0.210603i
$236$	−0.828427	−	1.43488i	−0.0539260	−	0.0934026i
$237$	−10.0000			−0.649570
$238$	−8.50000	+	1.16320i	−0.550973	+	0.0753989i
$239$	21.6569			1.40087			0.700433	−	0.713718i	$-0.252990\pi$
$239$	21.6569			1.40087			0.700433	+	0.713718i	$0.252990\pi$
$240$	−0.207107	−	0.358719i	−0.0133687	−	0.0231552i
$241$	3.58579	−	6.21076i	0.230981	−	0.400070i	−0.727116	−	0.686514i	$-0.759140\pi$
$241$	3.58579	−	6.21076i	0.230981	−	0.400070i	0.958097	+	0.286444i	$0.0924732\pi$
$242$	−3.50000	+	6.06218i	−0.224989	+	0.389692i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	−2.00000			−0.128037
$245$	−2.07107	−	2.02922i	−0.132316	−	0.129642i
$246$	10.8284			0.690395
$247$	3.34315	+	5.79050i	0.212719	+	0.368441i
$248$	−1.00000	+	1.73205i	−0.0635001	+	0.109985i
$249$	−6.41421	+	11.1097i	−0.406484	+	0.704051i
$250$	−2.03553	−	3.52565i	−0.128738	−	0.222982i
$251$	−5.31371			−0.335398			−0.167699	−	0.985838i	$-0.553634\pi$
$251$	−5.31371			−0.335398			−0.167699	+	0.985838i	$0.553634\pi$
$252$	−2.62132	+	0.358719i	−0.165128	+	0.0225972i
$253$	2.00000			0.125739
$254$	2.41421	+	4.18154i	0.151481	+	0.262373i
$255$	0.671573	−	1.16320i	0.0420555	−	0.0728423i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−11.2426	−	19.4728i	−0.701297	−	1.21468i	−0.968011	−	0.250906i	$-0.919272\pi$
$257$	−11.2426	−	19.4728i	−0.701297	−	1.21468i	0.266715	−	0.963775i	$-0.414062\pi$
$258$	11.6569			0.725724
$259$	−5.14214	−	6.63103i	−0.319517	−	0.412032i
$260$	−0.757359			−0.0469694
$261$	0.585786	+	1.01461i	0.0362593	+	0.0628029i
$262$	9.57107	−	16.5776i	0.591303	−	1.02417i
$263$	1.65685	−	2.86976i	0.102166	−	0.176957i	−0.810411	−	0.585862i	$-0.800756\pi$
$263$	1.65685	−	2.86976i	0.102166	−	0.176957i	0.912577	+	0.408905i	$0.134089\pi$
$264$	1.00000	+	1.73205i	0.0615457	+	0.106600i
$265$	−4.17157			−0.256258
$266$	−3.65685	+	8.95743i	−0.224216	+	0.549215i
$267$	1.17157			0.0716991
$268$	−7.44975	−	12.9033i	−0.455066	−	0.788197i
$269$	6.00000	−	10.3923i	0.365826	−	0.633630i	−0.623082	−	0.782157i	$-0.714120\pi$
$269$	6.00000	−	10.3923i	0.365826	−	0.633630i	0.988908	+	0.148527i	$0.0474530\pi$
$270$	0.207107	−	0.358719i	0.0126041	−	0.0218310i
$271$	−13.1421	−	22.7628i	−0.798328	−	1.38274i	−0.920704	−	0.390261i	$-0.872385\pi$
$271$	−13.1421	−	22.7628i	−0.798328	−	1.38274i	0.122377	−	0.992484i	$-0.460948\pi$
$272$	−3.24264			−0.196614
$273$	−1.82843	+	4.47871i	−0.110661	+	0.271064i
$274$	10.4142			0.629146
$275$	4.82843	+	8.36308i	0.291165	+	0.504313i
$276$	−0.500000	+	0.866025i	−0.0300965	+	0.0521286i
$277$	15.6421	−	27.0930i	0.939845	−	1.62786i	0.174087	−	0.984730i	$-0.444303\pi$
$277$	15.6421	−	27.0930i	0.939845	−	1.62786i	0.765758	−	0.643129i	$-0.222364\pi$
$278$	−6.65685	−	11.5300i	−0.399252	−	0.691524i
$279$	−2.00000			−0.119737
$280$	−0.671573	−	0.866025i	−0.0401342	−	0.0517549i
$281$	−16.4142			−0.979190			−0.489595	−	0.871950i	$-0.662855\pi$
$281$	−16.4142			−0.979190			−0.489595	+	0.871950i	$0.662855\pi$
$282$	4.50000	+	7.79423i	0.267971	+	0.464140i
$283$	−3.69239	+	6.39540i	−0.219490	+	0.380167i	−0.954652	−	0.297724i	$-0.903773\pi$
$283$	−3.69239	+	6.39540i	−0.219490	+	0.380167i	0.735162	+	0.677891i	$0.237106\pi$
$284$	4.91421	−	8.51167i	0.291605	−	0.505075i
$285$	−0.757359	−	1.31178i	−0.0448621	−	0.0777034i
$286$	3.65685			0.216234
$287$	28.3848	−	3.88437i	1.67550	−	0.229287i
$288$	−1.00000			−0.0589256
$289$	3.24264	+	5.61642i	0.190744	+	0.330378i
$290$	−0.242641	+	0.420266i	−0.0142484	+	0.0246789i
$291$	4.82843	−	8.36308i	0.283047	−	0.490252i
$292$	5.32843	+	9.22911i	0.311823	+	0.540093i
$293$	−6.41421			−0.374722			−0.187361	−	0.982291i	$-0.559993\pi$
$293$	−6.41421			−0.374722			−0.187361	+	0.982291i	$0.559993\pi$
$294$	−6.74264	+	1.88064i	−0.393239	+	0.109681i
$295$	0.686292			0.0399574
$296$	−1.58579	−	2.74666i	−0.0921720	−	0.159647i
$297$	−1.00000	+	1.73205i	−0.0580259	+	0.100504i
$298$	0.378680	−	0.655892i	0.0219363	−	0.0379948i
$299$	0.914214	+	1.58346i	0.0528703	+	0.0915741i
$300$	−4.82843			−0.278769
$301$	30.5563	−	4.18154i	1.76124	−	0.241020i
$302$	−14.1421			−0.813788
$303$	−1.58579	−	2.74666i	−0.0911011	−	0.157792i
$304$	−1.82843	+	3.16693i	−0.104867	+	0.181636i
$305$	0.414214	−	0.717439i	0.0237178	−	0.0410804i
$306$	−1.62132	−	2.80821i	−0.0926847	−	0.160535i
$307$	14.1421			0.807134			0.403567	−	0.914950i	$-0.367770\pi$
$307$	14.1421			0.807134			0.403567	+	0.914950i	$0.367770\pi$
$308$	3.24264	+	4.18154i	0.184767	+	0.238265i
$309$	−8.89949			−0.506275
$310$	−0.414214	−	0.717439i	−0.0235257	−	0.0407478i
$311$	−3.15685	+	5.46783i	−0.179009	+	0.310052i	−0.941541	−	0.336898i	$-0.890622\pi$
$311$	−3.15685	+	5.46783i	−0.179009	+	0.310052i	0.762533	+	0.646950i	$0.223956\pi$
$312$	−0.914214	+	1.58346i	−0.0517572	+	0.0896460i
$313$	0.485281	+	0.840532i	0.0274297	+	0.0475097i	0.879414	−	0.476057i	$-0.157934\pi$
$313$	0.485281	+	0.840532i	0.0274297	+	0.0475097i	−0.851985	+	0.523567i	$0.824601\pi$
$314$	4.34315			0.245098
$315$	0.414214	−	1.01461i	0.0233383	−	0.0571669i
$316$	−10.0000			−0.562544
$317$	−6.31371	−	10.9357i	−0.354613	−	0.614208i	0.632438	−	0.774611i	$-0.282054\pi$
$317$	−6.31371	−	10.9357i	−0.354613	−	0.614208i	−0.987052	+	0.160403i	$0.948721\pi$
$318$	−5.03553	+	8.72180i	−0.282379	+	0.489094i
$319$	1.17157	−	2.02922i	0.0655955	−	0.113615i
$320$	−0.207107	−	0.358719i	−0.0115776	−	0.0200530i
$321$	5.65685			0.315735
$322$	−1.00000	+	2.44949i	−0.0557278	+	0.136505i
$323$	−11.8579			−0.659789
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	−4.41421	+	7.64564i	−0.244857	+	0.424104i
$326$	−4.82843	+	8.36308i	−0.267422	+	0.463188i
$327$	−7.41421	−	12.8418i	−0.410007	−	0.710153i
$328$	10.8284			0.597900
$329$	14.5919	+	18.8169i	0.804477	+	1.03741i
$330$	−0.828427			−0.0456034
$331$	8.75736	+	15.1682i	0.481348	+	0.833719i	0.999771	−	0.0214052i	$-0.00681400\pi$
$331$	8.75736	+	15.1682i	0.481348	+	0.833719i	−0.518423	+	0.855124i	$0.673481\pi$
$332$	−6.41421	+	11.1097i	−0.352026	+	0.609726i
$333$	1.58579	−	2.74666i	0.0869006	−	0.150516i
$334$	−7.39949	−	12.8163i	−0.404882	−	0.701277i
$335$	6.17157			0.337189
$336$	−2.62132	+	0.358719i	−0.143005	+	0.0195698i
$337$		0			0			−	1.00000i	$-0.5\pi$
$337$		0			0				1.00000i	$0.5\pi$
$338$	−4.82843	−	8.36308i	−0.262632	−	0.454892i
$339$	6.86396	−	11.8887i	0.372799	−	0.645707i
$340$	0.671573	−	1.16320i	0.0364212	−	0.0630833i
$341$	2.00000	+	3.46410i	0.108306	+	0.187592i
$342$	−3.65685			−0.197740
$343$	−17.0000	+	7.34847i	−0.917914	+	0.396780i
$344$	11.6569			0.628495
$345$	−0.207107	−	0.358719i	−0.0111503	−	0.0193128i
$346$	7.65685	−	13.2621i	0.411635	−	0.712973i
$347$	10.6716	−	18.4837i	0.572880	−	0.992257i	−0.423388	−	0.905948i	$-0.639159\pi$
$347$	10.6716	−	18.4837i	0.572880	−	0.992257i	0.996268	−	0.0863091i	$-0.0275073\pi$
$348$	0.585786	+	1.01461i	0.0314014	+	0.0543889i
$349$	3.14214			0.168195			0.0840973	−	0.996458i	$-0.473199\pi$
$349$	3.14214			0.168195			0.0840973	+	0.996458i	$0.473199\pi$
$350$	−12.6569	+	1.73205i	−0.676537	+	0.0925820i
$351$	−1.82843			−0.0975942
$352$	1.00000	+	1.73205i	0.0533002	+	0.0923186i
$353$	13.0711	−	22.6398i	0.695703	−	1.20499i	−0.274240	−	0.961661i	$-0.588426\pi$
$353$	13.0711	−	22.6398i	0.695703	−	1.20499i	0.969943	−	0.243331i	$-0.0782402\pi$
$354$	0.828427	−	1.43488i	0.0440304	−	0.0762629i
$355$	2.03553	+	3.52565i	0.108035	+	0.187122i
$356$	1.17157			0.0620932
$357$	−5.25736	−	6.77962i	−0.278249	−	0.358815i
$358$	−11.9706			−0.632664
$359$	3.48528	+	6.03668i	0.183946	+	0.318604i	0.943221	−	0.332166i	$-0.107779\pi$
$359$	3.48528	+	6.03668i	0.183946	+	0.318604i	−0.759275	+	0.650770i	$0.774446\pi$
$360$	0.207107	−	0.358719i	0.0109155	−	0.0189062i
$361$	2.81371	−	4.87349i	0.148090	−	0.256499i
$362$	6.65685	+	11.5300i	0.349876	+	0.606004i
$363$	−7.00000			−0.367405
$364$	−1.82843	+	4.47871i	−0.0958356	+	0.234748i
$365$	−4.41421			−0.231050
$366$	−1.00000	−	1.73205i	−0.0522708	−	0.0905357i
$367$	16.3492	−	28.3177i	0.853424	−	1.47817i	−0.0246764	−	0.999695i	$-0.507856\pi$
$367$	16.3492	−	28.3177i	0.853424	−	1.47817i	0.878100	−	0.478477i	$-0.158811\pi$
$368$	−0.500000	+	0.866025i	−0.0260643	+	0.0451447i
$369$	5.41421	+	9.37769i	0.281853	+	0.488183i
$370$	1.31371			0.0682965
$371$	−10.0711	+	24.6690i	−0.522864	+	1.28075i
$372$	−2.00000			−0.103695
$373$	5.82843	+	10.0951i	0.301785	+	0.522706i	0.976540	−	0.215335i	$-0.0690844\pi$
$373$	5.82843	+	10.0951i	0.301785	+	0.522706i	−0.674756	+	0.738041i	$0.735751\pi$
$374$	−3.24264	+	5.61642i	−0.167673	+	0.290418i
$375$	2.03553	−	3.52565i	0.105115	−	0.182064i
$376$	4.50000	+	7.79423i	0.232070	+	0.401957i
$377$	2.14214			0.110326
$378$	−1.62132	−	2.09077i	−0.0833917	−	0.107538i
$379$	0.899495			0.0462040			0.0231020	−	0.999733i	$-0.492646\pi$
$379$	0.899495			0.0462040			0.0231020	+	0.999733i	$0.492646\pi$
$380$	−0.757359	−	1.31178i	−0.0388517	−	0.0672931i
$381$	−2.41421	+	4.18154i	−0.123684	+	0.214227i
$382$	−5.41421	+	9.37769i	−0.277015	+	0.479805i
$383$	3.82843	+	6.63103i	0.195623	+	0.338830i	0.947105	−	0.320925i	$-0.103994\pi$
$383$	3.82843	+	6.63103i	0.195623	+	0.338830i	−0.751481	+	0.659754i	$0.770660\pi$
$384$	−1.00000			−0.0510310
$385$	−2.17157	+	0.297173i	−0.110674	+	0.0151453i
$386$	−11.4853			−0.584585
$387$	5.82843	+	10.0951i	0.296276	+	0.513164i
$388$	4.82843	−	8.36308i	0.245126	−	0.424571i
$389$	−6.72792	+	11.6531i	−0.341119	+	0.590836i	−0.984641	−	0.174592i	$-0.944139\pi$
$389$	−6.72792	+	11.6531i	−0.341119	+	0.590836i	0.643522	+	0.765428i	$0.277473\pi$
$390$	−0.378680	−	0.655892i	−0.0191752	−	0.0332124i
$391$	−3.24264			−0.163987
$392$	−6.74264	+	1.88064i	−0.340555	+	0.0949865i
$393$	19.1421			0.965593
$394$	−3.58579	−	6.21076i	−0.180649	−	0.312894i
$395$	2.07107	−	3.58719i	0.104207	−	0.180491i
$396$	−1.00000	+	1.73205i	−0.0502519	+	0.0870388i
$397$	−1.32843	−	2.30090i	−0.0666718	−	0.115479i	0.830763	−	0.556627i	$-0.187905\pi$
$397$	−1.32843	−	2.30090i	−0.0666718	−	0.115479i	−0.897434	+	0.441148i	$0.854571\pi$
$398$	16.3431			0.819208
$399$	−9.58579	+	1.31178i	−0.479890	+	0.0656714i
$400$	−4.82843			−0.241421
$401$	−13.3492	−	23.1216i	−0.666629	−	1.15464i	−0.978841	−	0.204623i	$-0.934403\pi$
$401$	−13.3492	−	23.1216i	−0.666629	−	1.15464i	0.312211	−	0.950013i	$-0.398930\pi$
$402$	7.44975	−	12.9033i	0.371560	−	0.643560i
$403$	−1.82843	+	3.16693i	−0.0910804	+	0.157756i
$404$	−1.58579	−	2.74666i	−0.0788958	−	0.136652i
$405$	0.414214			0.0205824
$406$	1.89949	+	2.44949i	0.0942704	+	0.121566i
$407$	−6.34315			−0.314418
$408$	−1.62132	−	2.80821i	−0.0802673	−	0.139027i
$409$	−6.39949	+	11.0843i	−0.316435	+	0.548081i	−0.979741	−	0.200267i	$-0.935819\pi$
$409$	−6.39949	+	11.0843i	−0.316435	+	0.548081i	0.663307	+	0.748348i	$0.269152\pi$
$410$	−2.24264	+	3.88437i	−0.110756	+	0.191835i
$411$	5.20711	+	9.01897i	0.256848	+	0.444873i
$412$	−8.89949			−0.438447
$413$	1.65685	−	4.05845i	0.0815285	−	0.199703i
$414$	−1.00000			−0.0491473
$415$	−2.65685	−	4.60181i	−0.130420	−	0.225894i
$416$	−0.914214	+	1.58346i	−0.0448230	+	0.0776357i
$417$	6.65685	−	11.5300i	0.325988	−	0.564627i
$418$	3.65685	+	6.33386i	0.178863	+	0.309799i
$419$	24.4853			1.19618			0.598092	−	0.801427i	$-0.295926\pi$
$419$	24.4853			1.19618			0.598092	+	0.801427i	$0.295926\pi$
$420$	0.414214	−	1.01461i	0.0202116	−	0.0495080i
$421$	15.3137			0.746344			0.373172	−	0.927762i	$-0.378270\pi$
$421$	15.3137			0.746344			0.373172	+	0.927762i	$0.378270\pi$
$422$	−8.41421	−	14.5738i	−0.409598	−	0.709444i
$423$	−4.50000	+	7.79423i	−0.218797	+	0.378968i
$424$	−5.03553	+	8.72180i	−0.244547	+	0.423568i
$425$	−7.82843	−	13.5592i	−0.379734	−	0.657719i
$426$	9.82843			0.476189
$427$	−3.24264	−	4.18154i	−0.156922	−	0.202359i
$428$	5.65685			0.273434
$429$	1.82843	+	3.16693i	0.0882773	+	0.152901i
$430$	−2.41421	+	4.18154i	−0.116424	+	0.201652i
$431$	2.34315	−	4.05845i	0.112865	−	0.195489i	−0.804059	−	0.594549i	$-0.797330\pi$
$431$	2.34315	−	4.05845i	0.112865	−	0.195489i	0.916924	+	0.399061i	$0.130664\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	−14.0000			−0.672797			−0.336399	−	0.941720i	$-0.609209\pi$
$433$	−14.0000			−0.672797			−0.336399	+	0.941720i	$0.609209\pi$
$434$	−5.24264	+	0.717439i	−0.251655	+	0.0344382i
$435$	−0.485281			−0.0232675
$436$	−7.41421	−	12.8418i	−0.355076	−	0.615010i
$437$	−1.82843	+	3.16693i	−0.0874655	+	0.151495i
$438$	−5.32843	+	9.22911i	−0.254602	+	0.440984i
$439$	1.48528	+	2.57258i	0.0708886	+	0.122783i	0.899291	−	0.437351i	$-0.144083\pi$
$439$	1.48528	+	2.57258i	0.0708886	+	0.122783i	−0.828402	+	0.560133i	$0.810750\pi$
$440$	−0.828427			−0.0394937
$441$	−5.00000	−	4.89898i	−0.238095	−	0.233285i
$442$	−5.92893			−0.282011
$443$	8.57107	+	14.8455i	0.407224	+	0.705332i	0.994577	−	0.103998i	$-0.0331636\pi$
$443$	8.57107	+	14.8455i	0.407224	+	0.705332i	−0.587354	+	0.809330i	$0.699830\pi$
$444$	1.58579	−	2.74666i	0.0752581	−	0.130351i
$445$	−0.242641	+	0.420266i	−0.0115023	+	0.0199225i
$446$	2.24264	+	3.88437i	0.106192	+	0.183930i
$447$	0.757359			0.0358219
$448$	−2.62132	+	0.358719i	−0.123846	+	0.0169479i
$449$	26.4853			1.24992			0.624959	−	0.780658i	$-0.285116\pi$
$449$	26.4853			1.24992			0.624959	+	0.780658i	$0.285116\pi$
$450$	−2.41421	−	4.18154i	−0.113807	−	0.197120i
$451$	10.8284	−	18.7554i	0.509891	−	0.883157i
$452$	6.86396	−	11.8887i	0.322854	−	0.559199i
$453$	−7.07107	−	12.2474i	−0.332228	−	0.575435i
$454$	−22.9706			−1.07806
$455$	−1.22792	−	1.58346i	−0.0575659	−	0.0742340i
$456$	−3.65685			−0.171248
$457$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$457$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$458$	−13.0711	+	22.6398i	−0.610771	+	1.05789i
$459$	1.62132	−	2.80821i	0.0756768	−	0.131076i
$460$	−0.207107	−	0.358719i	−0.00965640	−	0.0167254i
$461$	14.0000			0.652045			0.326023	−	0.945362i	$-0.394291\pi$
$461$	14.0000			0.652045			0.326023	+	0.945362i	$0.394291\pi$
$462$	−2.00000	+	4.89898i	−0.0930484	+	0.227921i
$463$	10.6274			0.493898			0.246949	−	0.969028i	$-0.420572\pi$
$463$	10.6274			0.493898			0.246949	+	0.969028i	$0.420572\pi$
$464$	0.585786	+	1.01461i	0.0271945	+	0.0471022i
$465$	0.414214	−	0.717439i	0.0192087	−	0.0332704i
$466$	−4.00000	+	6.92820i	−0.185296	+	0.320943i
$467$	−5.17157	−	8.95743i	−0.239312	−	0.414500i	0.721205	−	0.692722i	$-0.243588\pi$
$467$	−5.17157	−	8.95743i	−0.239312	−	0.414500i	−0.960517	+	0.278221i	$0.910255\pi$
$468$	−1.82843			−0.0845191
$469$	14.8995	−	36.4962i	0.687995	−	1.68524i
$470$	−3.72792			−0.171956
$471$	2.17157	+	3.76127i	0.100061	+	0.173310i
$472$	0.828427	−	1.43488i	0.0381314	−	0.0660456i
$473$	11.6569	−	20.1903i	0.535983	−	0.928349i
$474$	−5.00000	−	8.66025i	−0.229658	−	0.397779i
$475$	−17.6569			−0.810152
$476$	−5.25736	−	6.77962i	−0.240971	−	0.310743i
$477$	−10.0711			−0.461123
$478$	10.8284	+	18.7554i	0.495281	+	0.857851i
$479$	−17.0711	+	29.5680i	−0.779997	+	1.35099i	0.151946	+	0.988389i	$0.451446\pi$
$479$	−17.0711	+	29.5680i	−0.779997	+	1.35099i	−0.931943	+	0.362606i	$0.881887\pi$
$480$	0.207107	−	0.358719i	0.00945309	−	0.0163732i
$481$	−2.89949	−	5.02207i	−0.132206	−	0.228987i
$482$	7.17157			0.326656
$483$	−2.62132	+	0.358719i	−0.119274	+	0.0163223i
$484$	−7.00000			−0.318182
$485$	2.00000	+	3.46410i	0.0908153	+	0.157297i
$486$	0.500000	−	0.866025i	0.0226805	−	0.0392837i
$487$	16.3848	−	28.3793i	0.742465	−	1.28599i	−0.208905	−	0.977936i	$-0.566990\pi$
$487$	16.3848	−	28.3793i	0.742465	−	1.28599i	0.951370	−	0.308051i	$-0.0996768\pi$
$488$	−1.00000	−	1.73205i	−0.0452679	−	0.0784063i
$489$	−9.65685			−0.436698
$490$	0.721825	−	2.80821i	0.0326087	−	0.126862i
$491$	−11.3431			−0.511909			−0.255955	−	0.966689i	$-0.582390\pi$
$491$	−11.3431			−0.511909			−0.255955	+	0.966689i	$0.582390\pi$
$492$	5.41421	+	9.37769i	0.244092	+	0.422779i
$493$	−1.89949	+	3.29002i	−0.0855489	+	0.148175i
$494$	−3.34315	+	5.79050i	−0.150415	+	0.260527i
$495$	−0.414214	−	0.717439i	−0.0186175	−	0.0322465i
$496$	−2.00000			−0.0898027
$497$	25.7635	−	3.52565i	1.15565	−	0.158147i
$498$	−12.8284			−0.574856
$499$	−0.585786	−	1.01461i	−0.0262234	−	0.0454203i	0.852616	−	0.522538i	$-0.175015\pi$
$499$	−0.585786	−	1.01461i	−0.0262234	−	0.0454203i	−0.878839	+	0.477118i	$0.841681\pi$
$500$	2.03553	−	3.52565i	0.0910318	−	0.157672i
$501$	7.39949	−	12.8163i	0.330585	−	0.572590i
$502$	−2.65685	−	4.60181i	−0.118581	−	0.205389i
$503$	43.6569			1.94656			0.973281	−	0.229615i	$-0.0737468\pi$
$503$	43.6569			1.94656			0.973281	+	0.229615i	$0.0737468\pi$
$504$	−1.62132	−	2.09077i	−0.0722193	−	0.0931303i
$505$	1.31371			0.0584593
$506$	1.00000	+	1.73205i	0.0444554	+	0.0769991i
$507$	4.82843	−	8.36308i	0.214438	−	0.371417i
$508$	−2.41421	+	4.18154i	−0.107113	+	0.185526i
$509$	−7.92893	−	13.7333i	−0.351444	−	0.608718i	0.635059	−	0.772464i	$-0.280976\pi$
$509$	−7.92893	−	13.7333i	−0.351444	−	0.608718i	−0.986503	+	0.163745i	$0.947642\pi$
$510$	1.34315			0.0594755
$511$	−10.6569	+	26.1039i	−0.471431	+	1.15477i
$512$	−1.00000			−0.0441942
$513$	−1.82843	−	3.16693i	−0.0807270	−	0.139823i
$514$	11.2426	−	19.4728i	0.495892	−	0.858909i
$515$	1.84315	−	3.19242i	0.0812187	−	0.140675i
$516$	5.82843	+	10.0951i	0.256582	+	0.444413i
$517$	18.0000			0.791639
$518$	3.17157	−	7.76874i	0.139351	−	0.341339i
$519$	15.3137			0.672197
$520$	−0.378680	−	0.655892i	−0.0166062	−	0.0287628i
$521$	−12.7929	+	22.1579i	−0.560467	+	0.970757i	0.436989	+	0.899467i	$0.356045\pi$
$521$	−12.7929	+	22.1579i	−0.560467	+	0.970757i	−0.997456	+	0.0712901i	$0.977288\pi$
$522$	−0.585786	+	1.01461i	−0.0256392	+	0.0444084i
$523$	7.03553	+	12.1859i	0.307642	+	0.532852i	0.977846	−	0.209325i	$-0.0671266\pi$
$523$	7.03553	+	12.1859i	0.307642	+	0.532852i	−0.670204	+	0.742177i	$0.733793\pi$
$524$	19.1421			0.836228
$525$	−7.82843	−	10.0951i	−0.341661	−	0.440588i
$526$	3.31371			0.144485
$527$	−3.24264	−	5.61642i	−0.141252	−	0.244655i
$528$	−1.00000	+	1.73205i	−0.0435194	+	0.0753778i
$529$	−0.500000	+	0.866025i	−0.0217391	+	0.0376533i
$530$	−2.08579	−	3.61269i	−0.0906008	−	0.156925i
$531$	1.65685			0.0719014
$532$	−9.58579	+	1.31178i	−0.415597	+	0.0568731i
$533$	19.7990			0.857589
$534$	0.585786	+	1.01461i	0.0253495	+	0.0439065i
$535$	−1.17157	+	2.02922i	−0.0506515	+	0.0877310i
$536$	7.44975	−	12.9033i	0.321780	−	0.557339i
$537$	−5.98528	−	10.3668i	−0.258284	−	0.447361i
$538$	12.0000			0.517357
$539$	−3.48528	+	13.5592i	−0.150122	+	0.584038i
$540$	0.414214			0.0178249
$541$	−6.42893	−	11.1352i	−0.276401	−	0.478741i	0.694086	−	0.719892i	$-0.255809\pi$
$541$	−6.42893	−	11.1352i	−0.276401	−	0.478741i	−0.970488	+	0.241151i	$0.922475\pi$
$542$	13.1421	−	22.7628i	0.564503	−	0.977748i
$543$	−6.65685	+	11.5300i	−0.285673	+	0.494800i
$544$	−1.62132	−	2.80821i	−0.0695135	−	0.120401i
$545$	6.14214			0.263100
$546$	−4.79289	+	0.655892i	−0.205117	+	0.0280696i
$547$	−34.2843			−1.46589			−0.732945	−	0.680288i	$-0.761855\pi$
$547$	−34.2843			−1.46589			−0.732945	+	0.680288i	$0.761855\pi$
$548$	5.20711	+	9.01897i	0.222437	+	0.385271i
$549$	1.00000	−	1.73205i	0.0426790	−	0.0739221i
$550$	−4.82843	+	8.36308i	−0.205885	+	0.356603i
$551$	2.14214	+	3.71029i	0.0912580	+	0.158064i
$552$	−1.00000			−0.0425628
$553$	−16.2132	−	20.9077i	−0.689456	−	0.889086i
$554$	31.2843			1.32914
$555$	0.656854	+	1.13770i	0.0278819	+	0.0482929i
$556$	6.65685	−	11.5300i	0.282314	−	0.488981i
$557$	11.8995	−	20.6105i	0.504198	−	0.873296i	−0.495790	−	0.868442i	$-0.665122\pi$
$557$	11.8995	−	20.6105i	0.504198	−	0.873296i	0.999988	−	0.00485398i	$-0.00154508\pi$
$558$	−1.00000	−	1.73205i	−0.0423334	−	0.0733236i
$559$	21.3137			0.901474
$560$	0.414214	−	1.01461i	0.0175037	−	0.0428752i
$561$	−6.48528			−0.273809
$562$	−8.20711	−	14.2151i	−0.346196	−	0.599629i
$563$	2.72792	−	4.72490i	0.114968	−	0.199131i	−0.802799	−	0.596250i	$-0.796657\pi$
$563$	2.72792	−	4.72490i	0.114968	−	0.199131i	0.917767	+	0.397119i	$0.129990\pi$
$564$	−4.50000	+	7.79423i	−0.189484	+	0.328196i
$565$	2.84315	+	4.92447i	0.119612	+	0.207174i
$566$	−7.38478			−0.310405
$567$	1.00000	−	2.44949i	0.0419961	−	0.102869i
$568$	9.82843			0.412392
$569$	−5.20711	−	9.01897i	−0.218293	−	0.378095i	0.735993	−	0.676989i	$-0.236716\pi$
$569$	−5.20711	−	9.01897i	−0.218293	−	0.378095i	−0.954286	+	0.298894i	$0.903382\pi$
$570$	0.757359	−	1.31178i	0.0317223	−	0.0549446i
$571$	10.4497	−	18.0995i	0.437308	−	0.757440i	−0.560173	−	0.828376i	$-0.689265\pi$
$571$	10.4497	−	18.0995i	0.437308	−	0.757440i	0.997481	+	0.0709357i	$0.0225985\pi$
$572$	1.82843	+	3.16693i	0.0764504	+	0.132416i
$573$	−10.8284			−0.452364
$574$	17.5563	+	22.6398i	0.732788	+	0.944965i
$575$	−4.82843			−0.201359
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	15.9706	−	27.6618i	0.664863	−	1.15158i	−0.314459	−	0.949271i	$-0.601823\pi$
$577$	15.9706	−	27.6618i	0.664863	−	1.15158i	0.979322	−	0.202306i	$-0.0648435\pi$
$578$	−3.24264	+	5.61642i	−0.134876	+	0.233612i
$579$	−5.74264	−	9.94655i	−0.238656	−	0.413364i
$580$	−0.485281			−0.0201502
$581$	−33.6274	+	4.60181i	−1.39510	+	0.190915i
$582$	9.65685			0.400289
$583$	10.0711	+	17.4436i	0.417101	+	0.722440i
$584$	−5.32843	+	9.22911i	−0.220492	+	0.381903i
$585$	0.378680	−	0.655892i	0.0156565	−	0.0271178i
$586$	−3.20711	−	5.55487i	−0.132484	−	0.229470i
$587$	1.14214			0.0471410			0.0235705	−	0.999722i	$-0.492497\pi$
$587$	1.14214			0.0471410			0.0235705	+	0.999722i	$0.492497\pi$
$588$	−5.00000	−	4.89898i	−0.206197	−	0.202031i
$589$	−7.31371			−0.301356
$590$	0.343146	+	0.594346i	0.0141271	+	0.0244688i
$591$	3.58579	−	6.21076i	0.147500	−	0.255477i
$592$	1.58579	−	2.74666i	0.0651754	−	0.112887i
$593$	1.92893	+	3.34101i	0.0792118	+	0.137199i	0.902910	−	0.429830i	$-0.141426\pi$
$593$	1.92893	+	3.34101i	0.0792118	+	0.137199i	−0.823698	+	0.567028i	$0.808093\pi$
$594$	−2.00000			−0.0820610
$595$	3.52082	−	0.481813i	0.144339	−	0.0197524i
$596$	0.757359			0.0310226
$597$	8.17157	+	14.1536i	0.334440	+	0.579267i
$598$	−0.914214	+	1.58346i	−0.0373850	+	0.0647527i
$599$	3.08579	−	5.34474i	0.126082	−	0.218380i	−0.796073	−	0.605200i	$-0.793093\pi$
$599$	3.08579	−	5.34474i	0.126082	−	0.218380i	0.922155	+	0.386820i	$0.126426\pi$
$600$	−2.41421	−	4.18154i	−0.0985599	−	0.170711i
$601$	−14.2843			−0.582668			−0.291334	−	0.956621i	$-0.594099\pi$
$601$	−14.2843			−0.582668			−0.291334	+	0.956621i	$0.594099\pi$
$602$	18.8995	+	24.3718i	0.770286	+	0.993321i
$603$	14.8995			0.606754
$604$	−7.07107	−	12.2474i	−0.287718	−	0.498342i
$605$	1.44975	−	2.51104i	0.0589406	−	0.102088i
$606$	1.58579	−	2.74666i	0.0644182	−	0.111576i
$607$	−18.0711	−	31.3000i	−0.733482	−	1.27043i	−0.955386	−	0.295360i	$-0.904561\pi$
$607$	−18.0711	−	31.3000i	−0.733482	−	1.27043i	0.221904	−	0.975068i	$-0.428773\pi$
$608$	−3.65685			−0.148305
$609$	−1.17157	+	2.86976i	−0.0474745	+	0.116288i
$610$	0.828427			0.0335420
$611$	8.22792	+	14.2512i	0.332866	+	0.576541i
$612$	1.62132	−	2.80821i	0.0655380	−	0.113515i
$613$	8.89949	−	15.4144i	0.359447	−	0.622581i	−0.628421	−	0.777873i	$-0.716299\pi$
$613$	8.89949	−	15.4144i	0.359447	−	0.622581i	0.987869	+	0.155292i	$0.0496319\pi$
$614$	7.07107	+	12.2474i	0.285365	+	0.494267i
$615$	−4.48528			−0.180864
$616$	−2.00000	+	4.89898i	−0.0805823	+	0.197386i
$617$	−36.0711			−1.45217			−0.726083	−	0.687607i	$-0.758661\pi$
$617$	−36.0711			−1.45217			−0.726083	+	0.687607i	$0.758661\pi$
$618$	−4.44975	−	7.70719i	−0.178995	−	0.310029i
$619$	−14.9645	+	25.9192i	−0.601473	+	1.04178i	0.391126	+	0.920337i	$0.372086\pi$
$619$	−14.9645	+	25.9192i	−0.601473	+	1.04178i	−0.992598	+	0.121444i	$0.961248\pi$
$620$	0.414214	−	0.717439i	0.0166352	−	0.0288130i
$621$	−0.500000	−	0.866025i	−0.0200643	−	0.0347524i
$622$	−6.31371			−0.253157
$623$	1.89949	+	2.44949i	0.0761017	+	0.0981367i
$624$	−1.82843			−0.0731957
$625$	−11.2279	−	19.4473i	−0.449117	−	0.777893i
$626$	−0.485281	+	0.840532i	−0.0193957	+	0.0335944i
$627$	−3.65685	+	6.33386i	−0.146041	+	0.252950i
$628$	2.17157	+	3.76127i	0.0866552	+	0.150091i
$629$	10.2843			0.410061
$630$	1.08579	−	0.148586i	0.0432588	−	0.00591983i
$631$	−46.5563			−1.85338			−0.926689	−	0.375828i	$-0.877358\pi$
$631$	−46.5563			−1.85338			−0.926689	+	0.375828i	$0.877358\pi$
$632$	−5.00000	−	8.66025i	−0.198889	−	0.344486i
$633$	8.41421	−	14.5738i	0.334435	−	0.579258i
$634$	6.31371	−	10.9357i	0.250749	−	0.434311i
$635$	−1.00000	−	1.73205i	−0.0396838	−	0.0687343i
$636$	−10.0711			−0.399344
$637$	−12.3284	+	3.43861i	−0.488470	+	0.136243i
$638$	2.34315			0.0927660
$639$	4.91421	+	8.51167i	0.194403	+	0.336716i
$640$	0.207107	−	0.358719i	0.00818661	−	0.0141796i
$641$	5.30761	−	9.19305i	0.209638	−	0.363104i	−0.741962	−	0.670441i	$-0.766105\pi$
$641$	5.30761	−	9.19305i	0.209638	−	0.363104i	0.951601	+	0.307338i	$0.0994381\pi$
$642$	2.82843	+	4.89898i	0.111629	+	0.193347i
$643$	6.68629			0.263682			0.131841	−	0.991271i	$-0.457911\pi$
$643$	6.68629			0.263682			0.131841	+	0.991271i	$0.457911\pi$
$644$	−2.62132	+	0.358719i	−0.103294	+	0.0141355i
$645$	−4.82843			−0.190119
$646$	−5.92893	−	10.2692i	−0.233271	−	0.404037i
$647$	10.8284	−	18.7554i	0.425709	−	0.737350i	−0.570777	−	0.821105i	$-0.693358\pi$
$647$	10.8284	−	18.7554i	0.425709	−	0.737350i	0.996486	+	0.0837548i	$0.0266913\pi$
$648$	0.500000	−	0.866025i	0.0196419	−	0.0340207i
$649$	−1.65685	−	2.86976i	−0.0650372	−	0.112648i
$650$	−8.82843			−0.346279
$651$	−3.24264	−	4.18154i	−0.127089	−	0.163887i
$652$	−9.65685			−0.378192
$653$	15.9706	+	27.6618i	0.624976	+	1.08249i	0.988545	+	0.150924i	$0.0482248\pi$
$653$	15.9706	+	27.6618i	0.624976	+	1.08249i	−0.363569	+	0.931567i	$0.618442\pi$
$654$	7.41421	−	12.8418i	0.289919	−	0.502154i
$655$	−3.96447	+	6.86666i	−0.154905	+	0.268302i
$656$	5.41421	+	9.37769i	0.211390	+	0.366137i
$657$	−10.6569			−0.415763
$658$	−9.00000	+	22.0454i	−0.350857	+	0.859419i
$659$	27.4558			1.06953			0.534764	−	0.845002i	$-0.320401\pi$
$659$	27.4558			1.06953			0.534764	+	0.845002i	$0.320401\pi$
$660$	−0.414214	−	0.717439i	−0.0161232	−	0.0279263i
$661$	−8.72792	+	15.1172i	−0.339477	+	0.587991i	−0.984334	−	0.176312i	$-0.943583\pi$
$661$	−8.72792	+	15.1172i	−0.339477	+	0.587991i	0.644858	+	0.764303i	$0.276917\pi$
$662$	−8.75736	+	15.1682i	−0.340364	+	0.589528i
$663$	−2.96447	−	5.13461i	−0.115130	−	0.199412i
$664$	−12.8284			−0.497840
$665$	1.51472	−	3.71029i	0.0587383	−	0.143879i
$666$	3.17157			0.122896
$667$	0.585786	+	1.01461i	0.0226817	+	0.0392859i
$668$	7.39949	−	12.8163i	0.286295	−	0.495878i
$669$	−2.24264	+	3.88437i	−0.0867055	+	0.150178i
$670$	3.08579	+	5.34474i	0.119214	+	0.206485i
$671$	−4.00000			−0.154418
$672$	−1.62132	−	2.09077i	−0.0625438	−	0.0806532i
$673$	−29.3137			−1.12996			−0.564980	−	0.825104i	$-0.691116\pi$
$673$	−29.3137			−1.12996			−0.564980	+	0.825104i	$0.691116\pi$
$674$		0			0
$675$	2.41421	−	4.18154i	0.0929231	−	0.160948i
$676$	4.82843	−	8.36308i	0.185709	−	0.321657i
$677$	10.1360	+	17.5561i	0.389560	+	0.674737i	0.992390	−	0.123132i	$-0.0392939\pi$
$677$	10.1360	+	17.5561i	0.389560	+	0.674737i	−0.602831	+	0.797869i	$0.705961\pi$
$678$	13.7279			0.527218
$679$	25.3137	−	3.46410i	0.971451	−	0.132940i
$680$	1.34315			0.0515073
$681$	−11.4853	−	19.8931i	−0.440117	−	0.762305i
$682$	−2.00000	+	3.46410i	−0.0765840	+	0.132647i
$683$	22.5711	−	39.0942i	0.863658	−	1.49590i	−0.00471573	−	0.999989i	$-0.501501\pi$
$683$	22.5711	−	39.0942i	0.863658	−	1.49590i	0.868374	−	0.495910i	$-0.165166\pi$
$684$	−1.82843	−	3.16693i	−0.0699117	−	0.121091i
$685$	−4.31371			−0.164818
$686$	−14.8640	−	11.0482i	−0.567509	−	0.421822i
$687$	−26.1421			−0.997385
$688$	5.82843	+	10.0951i	0.222207	+	0.384873i
$689$	−9.20711	+	15.9472i	−0.350763	+	0.607539i
$690$	0.207107	−	0.358719i	0.00788442	−	0.0136562i
$691$	−8.07107	−	13.9795i	−0.307038	−	0.531805i	0.670675	−	0.741751i	$-0.266005\pi$
$691$	−8.07107	−	13.9795i	−0.307038	−	0.531805i	−0.977713	+	0.209946i	$0.932671\pi$
$692$	15.3137			0.582140
$693$	−5.24264	+	0.717439i	−0.199151	+	0.0272533i
$694$	21.3431			0.810175
$695$	2.75736	+	4.77589i	0.104593	+	0.181160i
$696$	−0.585786	+	1.01461i	−0.0222042	+	0.0384588i
$697$	−17.5563	+	30.4085i	−0.664994	+	1.15180i
$698$	1.57107	+	2.72117i	0.0594658	+	0.102998i
$699$	−8.00000			−0.302588
$700$	−7.82843	−	10.0951i	−0.295887	−	0.381560i
$701$	45.3848			1.71416			0.857080	−	0.515184i	$-0.172276\pi$
$701$	45.3848			1.71416			0.857080	+	0.515184i	$0.172276\pi$
$702$	−0.914214	−	1.58346i	−0.0345048	−	0.0597640i
$703$	5.79899	−	10.0441i	0.218713	−	0.378822i
$704$	−1.00000	+	1.73205i	−0.0376889	+	0.0652791i
$705$	−1.86396	−	3.22848i	−0.0702008	−	0.121591i
$706$	26.1421			0.983872
$707$	3.17157	−	7.76874i	0.119279	−	0.292173i
$708$	1.65685			0.0622684
$709$	19.0711	+	33.0321i	0.716229	+	1.24054i	0.962484	+	0.271340i	$0.0874667\pi$
$709$	19.0711	+	33.0321i	0.716229	+	1.24054i	−0.246255	+	0.969205i	$0.579200\pi$
$710$	−2.03553	+	3.52565i	−0.0763922	+	0.132315i
$711$	5.00000	−	8.66025i	0.187515	−	0.324785i
$712$	0.585786	+	1.01461i	0.0219533	+	0.0380242i
$713$	−2.00000			−0.0749006
$714$	3.24264	−	7.94282i	0.121353	−	0.297252i
$715$	−1.51472			−0.0566473
$716$	−5.98528	−	10.3668i	−0.223680	−	0.387426i
$717$	−10.8284	+	18.7554i	−0.404395	+	0.700433i
$718$	−3.48528	+	6.03668i	−0.130070	+	0.225287i
$719$	−1.67157	−	2.89525i	−0.0623391	−	0.107975i	0.833171	−	0.553015i	$-0.186523\pi$
$719$	−1.67157	−	2.89525i	−0.0623391	−	0.107975i	−0.895511	+	0.445040i	$0.853189\pi$
$720$	0.414214			0.0154368
$721$	−14.4289	−	18.6068i	−0.537362	−	0.692953i
$722$	5.62742			0.209431
$723$	3.58579	+	6.21076i	0.133357	+	0.230981i
$724$	−6.65685	+	11.5300i	−0.247400	+	0.428509i
$725$	−2.82843	+	4.89898i	−0.105045	+	0.181944i
$726$	−3.50000	−	6.06218i	−0.129897	−	0.224989i
$727$	−42.0000			−1.55769			−0.778847	−	0.627214i	$-0.784195\pi$
$727$	−42.0000			−1.55769			−0.778847	+	0.627214i	$0.784195\pi$
$728$	−4.79289	+	0.655892i	−0.177636	+	0.0243090i
$729$	1.00000			0.0370370
$730$	−2.20711	−	3.82282i	−0.0816887	−	0.141489i
$731$	−18.8995	+	32.7349i	−0.699023	+	1.21074i
$732$	1.00000	−	1.73205i	0.0369611	−	0.0640184i
$733$	−4.24264	−	7.34847i	−0.156706	−	0.271422i	0.776973	−	0.629534i	$-0.216754\pi$
$733$	−4.24264	−	7.34847i	−0.156706	−	0.271422i	−0.933679	+	0.358112i	$0.883421\pi$
$734$	32.6985			1.20692
$735$	2.79289	−	0.778985i	0.103017	−	0.0287333i
$736$	−1.00000			−0.0368605
$737$	−14.8995	−	25.8067i	−0.548830	−	0.950601i
$738$	−5.41421	+	9.37769i	−0.199300	+	0.345198i
$739$	−22.6274	+	39.1918i	−0.832363	+	1.44169i	0.0637965	+	0.997963i	$0.479679\pi$
$739$	−22.6274	+	39.1918i	−0.832363	+	1.44169i	−0.896160	+	0.443732i	$0.853654\pi$
$740$	0.656854	+	1.13770i	0.0241464	+	0.0418229i
$741$	−6.68629			−0.245627
$742$	−26.3995	+	3.61269i	−0.969156	+	0.132626i
$743$	−35.4558			−1.30075			−0.650374	−	0.759614i	$-0.725388\pi$
$743$	−35.4558			−1.30075			−0.650374	+	0.759614i	$0.725388\pi$
$744$	−1.00000	−	1.73205i	−0.0366618	−	0.0635001i
$745$	−0.156854	+	0.271680i	−0.00574670	+	0.00995357i
$746$	−5.82843	+	10.0951i	−0.213394	+	0.369609i
$747$	−6.41421	−	11.1097i	−0.234684	−	0.406484i
$748$	−6.48528			−0.237125
$749$	9.17157	+	11.8272i	0.335122	+	0.432156i
$750$	4.07107			0.148654
$751$	20.7990	+	36.0249i	0.758966	+	1.31457i	0.943378	+	0.331719i	$0.107628\pi$
$751$	20.7990	+	36.0249i	0.758966	+	1.31457i	−0.184412	+	0.982849i	$0.559038\pi$
$752$	−4.50000	+	7.79423i	−0.164098	+	0.284226i
$753$	2.65685	−	4.60181i	0.0968212	−	0.167699i
$754$	1.07107	+	1.85514i	0.0390060	+	0.0675604i
$755$	5.85786			0.213190
$756$	1.00000	−	2.44949i	0.0363696	−	0.0890871i
$757$	−4.97056			−0.180658			−0.0903291	−	0.995912i	$-0.528792\pi$
$757$	−4.97056			−0.180658			−0.0903291	+	0.995912i	$0.528792\pi$
$758$	0.449747	+	0.778985i	0.0163356	+	0.0282940i
$759$	−1.00000	+	1.73205i	−0.0362977	+	0.0628695i
$760$	0.757359	−	1.31178i	0.0274723	−	0.0475834i
$761$	5.17157	+	8.95743i	0.187469	+	0.324706i	0.944406	−	0.328782i	$-0.106638\pi$
$761$	5.17157	+	8.95743i	0.187469	+	0.324706i	−0.756936	+	0.653488i	$0.773305\pi$
$762$	−4.82843			−0.174915
$763$	14.8284	−	36.3221i	0.536825	−	1.31495i
$764$	−10.8284			−0.391759
$765$	0.671573	+	1.16320i	0.0242808	+	0.0420555i
$766$	−3.82843	+	6.63103i	−0.138327	+	0.239589i
$767$	1.51472	−	2.62357i	0.0546933	−	0.0947316i
$768$	−0.500000	−	0.866025i	−0.0180422	−	0.0312500i
$769$	10.6863			0.385358			0.192679	−	0.981262i	$-0.438282\pi$
$769$	10.6863			0.385358			0.192679	+	0.981262i	$0.438282\pi$
$770$	−1.34315	−	1.73205i	−0.0484036	−	0.0624188i
$771$	22.4853			0.809788
$772$	−5.74264	−	9.94655i	−0.206682	−	0.357984i
$773$	4.62132	−	8.00436i	0.166217	−	0.287897i	−0.770870	−	0.636993i	$-0.780178\pi$
$773$	4.62132	−	8.00436i	0.166217	−	0.287897i	0.937087	+	0.349096i	$0.113511\pi$
$774$	−5.82843	+	10.0951i	−0.209498	+	0.362862i
$775$	−4.82843	−	8.36308i	−0.173442	−	0.300411i
$776$	9.65685			0.346661
$777$	8.31371	−	1.13770i	0.298253	−	0.0408149i
$778$	−13.4558			−0.482415
$779$	19.7990	+	34.2929i	0.709372	+	1.22867i
$780$	0.378680	−	0.655892i	0.0135589	−	0.0234847i
$781$	9.82843	−	17.0233i	0.351689	−	0.609143i
$782$	−1.62132	−	2.80821i	−0.0579783	−	0.100421i
$783$	−1.17157			−0.0418686
$784$	−5.00000	−	4.89898i	−0.178571	−	0.174964i
$785$	−1.79899			−0.0642087
$786$	9.57107	+	16.5776i	0.341389	+	0.591303i
$787$	−5.52082	+	9.56233i	−0.196796	+	0.340860i	−0.947488	−	0.319792i	$-0.896387\pi$
$787$	−5.52082	+	9.56233i	−0.196796	+	0.340860i	0.750692	+	0.660652i	$0.229720\pi$
$788$	3.58579	−	6.21076i	0.127738	−	0.221249i
$789$	1.65685	+	2.86976i	0.0589856	+	0.102166i
$790$	4.14214			0.147371
$791$	35.9853	−	4.92447i	1.27949	−	0.175094i
$792$	−2.00000			−0.0710669
$793$	−1.82843	−	3.16693i	−0.0649294	−	0.112461i
$794$	1.32843	−	2.30090i	0.0471441	−	0.0816560i
$795$	2.08579	−	3.61269i	0.0739752	−	0.128129i
$796$	8.17157	+	14.1536i	0.289634	+	0.501660i
$797$	13.8701			0.491303			0.245651	−	0.969358i	$-0.420998\pi$
$797$	13.8701			0.491303			0.245651	+	0.969358i	$0.420998\pi$
$798$	−5.92893	−	7.64564i	−0.209882	−	0.270653i
$799$	−29.1838			−1.03245
$800$	−2.41421	−	4.18154i	−0.0853553	−	0.147840i
$801$	−0.585786	+	1.01461i	−0.0206977	+	0.0358495i
$802$	13.3492	−	23.1216i	0.471378	−	0.816451i
$803$	10.6569	+	18.4582i	0.376072	+	0.651376i
$804$	14.8995			0.525465
$805$	0.414214	−	1.01461i	0.0145991	−	0.0357604i
$806$	−3.65685			−0.128807
$807$	6.00000	+	10.3923i	0.211210	+	0.365826i
$808$	1.58579	−	2.74666i	0.0557878	−	0.0966273i
$809$	−2.07107	+	3.58719i	−0.0728149	+	0.126119i	−0.900134	−	0.435613i	$-0.856532\pi$
$809$	−2.07107	+	3.58719i	−0.0728149	+	0.126119i	0.827319	+	0.561732i	$0.189865\pi$
$810$	0.207107	+	0.358719i	0.00727699	+	0.0126041i
$811$	−41.1127			−1.44366			−0.721831	−	0.692069i	$-0.756699\pi$
$811$	−41.1127			−1.44366			−0.721831	+	0.692069i	$0.756699\pi$
$812$	−1.17157	+	2.86976i	−0.0411141	+	0.100709i
$813$	26.2843			0.921830
$814$	−3.17157	−	5.49333i	−0.111164	−	0.192541i
$815$	2.00000	−	3.46410i	0.0700569	−	0.121342i
$816$	1.62132	−	2.80821i	0.0567576	−	0.0983070i
$817$	21.3137	+	36.9164i	0.745672	+	1.29154i
$818$	−12.7990			−0.447506
$819$	−2.96447	−	3.82282i	−0.103587	−	0.133580i
$820$	−4.48528			−0.156633
$821$	−27.1421	−	47.0116i	−0.947267	−	1.64071i	−0.751147	−	0.660135i	$-0.770499\pi$
$821$	−27.1421	−	47.0116i	−0.947267	−	1.64071i	−0.196120	−	0.980580i	$-0.562834\pi$
$822$	−5.20711	+	9.01897i	−0.181619	+	0.314573i
$823$	−12.8995	+	22.3426i	−0.449648	+	0.778813i	−0.998363	−	0.0571962i	$-0.981784\pi$
$823$	−12.8995	+	22.3426i	−0.449648	+	0.778813i	0.548715	+	0.836010i	$0.315117\pi$
$824$	−4.44975	−	7.70719i	−0.155014	−	0.268493i
$825$	−9.65685			−0.336209
$826$	4.34315	−	0.594346i	0.151117	−	0.0206799i
$827$	2.62742			0.0913642			0.0456821	−	0.998956i	$-0.485454\pi$
$827$	2.62742			0.0913642			0.0456821	+	0.998956i	$0.485454\pi$
$828$	−0.500000	−	0.866025i	−0.0173762	−	0.0300965i
$829$	−10.9142	+	18.9040i	−0.379066	+	0.656562i	−0.990927	−	0.134404i	$-0.957088\pi$
$829$	−10.9142	+	18.9040i	−0.379066	+	0.656562i	0.611860	+	0.790966i	$0.290421\pi$
$830$	2.65685	−	4.60181i	0.0922208	−	0.159731i
$831$	15.6421	+	27.0930i	0.542620	+	0.939845i
$832$	−1.82843			−0.0633893
$833$	5.65076	−	21.9839i	0.195787	−	0.761696i
$834$	13.3137			0.461016
$835$	3.06497	+	5.30869i	0.106068	+	0.183715i
$836$	−3.65685	+	6.33386i	−0.126475	+	0.219061i
$837$	1.00000	−	1.73205i	0.0345651	−	0.0598684i
$838$	12.2426	+	21.2049i	0.422915	+	0.732510i
$839$	−8.97056			−0.309698			−0.154849	−	0.987938i	$-0.549489\pi$
$839$	−8.97056			−0.309698			−0.154849	+	0.987938i	$0.549489\pi$
$840$	1.08579	−	0.148586i	0.0374632	−	0.00512672i
$841$	−27.6274			−0.952670
$842$	7.65685	+	13.2621i	0.263873	+	0.457041i
$843$	8.20711	−	14.2151i	0.282668	−	0.489595i
$844$	8.41421	−	14.5738i	0.289629	−	0.501652i
$845$	2.00000	+	3.46410i	0.0688021	+	0.119169i
$846$	−9.00000			−0.309426
$847$	−11.3492	−	14.6354i	−0.389965	−	0.502878i
$848$	−10.0711			−0.345842
$849$	−3.69239	−	6.39540i	−0.126722	−	0.219490i
$850$	7.82843	−	13.5592i	0.268513	−	0.465078i
$851$	1.58579	−	2.74666i	0.0543601	−	0.0941544i
$852$	4.91421	+	8.51167i	0.168358	+	0.291605i
$853$	48.9117			1.67470			0.837352	−	0.546664i	$-0.184102\pi$
$853$	48.9117			1.67470			0.837352	+	0.546664i	$0.184102\pi$
$854$	2.00000	−	4.89898i	0.0684386	−	0.167640i
$855$	1.51472			0.0518023
$856$	2.82843	+	4.89898i	0.0966736	+	0.167444i
$857$	−22.3137	+	38.6485i	−0.762222	+	1.32021i	0.179481	+	0.983761i	$0.442558\pi$
$857$	−22.3137	+	38.6485i	−0.762222	+	1.32021i	−0.941703	+	0.336445i	$0.890775\pi$
$858$	−1.82843	+	3.16693i	−0.0624215	+	0.108117i
$859$	6.34315	+	10.9867i	0.216425	+	0.374860i	0.953713	−	0.300720i	$-0.0972269\pi$
$859$	6.34315	+	10.9867i	0.216425	+	0.374860i	−0.737287	+	0.675579i	$0.763894\pi$
$860$	−4.82843			−0.164648
$861$	−10.8284	+	26.5241i	−0.369032	+	0.903940i
$862$	4.68629			0.159616
$863$	−15.6716	−	27.1440i	−0.533467	−	0.923991i	−0.999236	−	0.0390850i	$-0.987556\pi$
$863$	−15.6716	−	27.1440i	−0.533467	−	0.923991i	0.465769	−	0.884906i	$-0.345778\pi$
$864$	0.500000	−	0.866025i	0.0170103	−	0.0294628i
$865$	−3.17157	+	5.49333i	−0.107837	+	0.186779i
$866$	−7.00000	−	12.1244i	−0.237870	−	0.412002i
$867$	−6.48528			−0.220252
$868$	−3.24264	−	4.18154i	−0.110062	−	0.141931i
$869$	−20.0000			−0.678454
$870$	−0.242641	−	0.420266i	−0.00822629	−	0.0142484i
$871$	13.6213	−	23.5928i	0.461541	−	0.799412i
$872$	7.41421	−	12.8418i	0.251077	−	0.434878i
$873$	4.82843	+	8.36308i	0.163417	+	0.283047i
$874$	−3.65685			−0.123695
$875$	10.6716	−	1.46037i	0.360765	−	0.0493696i
$876$	−10.6569			−0.360062
$877$	20.1569	+	34.9127i	0.680649	+	1.17892i	0.974783	+	0.223154i	$0.0716353\pi$
$877$	20.1569	+	34.9127i	0.680649	+	1.17892i	−0.294135	+	0.955764i	$0.595031\pi$
$878$	−1.48528	+	2.57258i	−0.0501258	+	0.0868205i
$879$	3.20711	−	5.55487i	0.108173	−	0.187361i
$880$	−0.414214	−	0.717439i	−0.0139631	−	0.0241849i
$881$	−31.7279			−1.06894			−0.534470	−	0.845187i	$-0.679489\pi$
$881$	−31.7279			−1.06894			−0.534470	+	0.845187i	$0.679489\pi$
$882$	1.74264	−	6.77962i	0.0586778	−	0.228282i
$883$	12.2843			0.413399			0.206699	−	0.978405i	$-0.433728\pi$
$883$	12.2843			0.413399			0.206699	+	0.978405i	$0.433728\pi$
$884$	−2.96447	−	5.13461i	−0.0997058	−	0.172695i
$885$	−0.343146	+	0.594346i	−0.0115347	+	0.0199787i
$886$	−8.57107	+	14.8455i	−0.287951	+	0.498745i
$887$	−3.51472	−	6.08767i	−0.118013	−	0.204404i	0.800967	−	0.598708i	$-0.204319\pi$
$887$	−3.51472	−	6.08767i	−0.118013	−	0.204404i	−0.918980	+	0.394304i	$0.870986\pi$
$888$	3.17157			0.106431
$889$	−12.6569	+	1.73205i	−0.424497	+	0.0580911i
$890$	−0.485281			−0.0162667
$891$	−1.00000	−	1.73205i	−0.0335013	−	0.0580259i
$892$	−2.24264	+	3.88437i	−0.0750892	+	0.130058i
$893$	−16.4558	+	28.5024i	−0.550674	+	0.953795i
$894$	0.378680	+	0.655892i	0.0126649	+	0.0219363i
$895$	4.95837			0.165740
$896$	−1.62132	−	2.09077i	−0.0541645	−	0.0698477i
$897$	−1.82843			−0.0610494
$898$	13.2426	+	22.9369i	0.441913	+	0.765415i
$899$	−1.17157	+	2.02922i	−0.0390741	+	0.0676784i
$900$	2.41421	−	4.18154i	0.0804738	−	0.139385i
$901$	−16.3284	−	28.2817i	−0.543979	−	0.942199i
$902$	21.6569			0.721094
$903$	−11.6569	+	28.5533i	−0.387916	+	0.950196i
$904$	13.7279			0.456584
$905$	−2.75736	−	4.77589i	−0.0916577	−	0.158756i
$906$	7.07107	−	12.2474i	0.234920	−	0.406894i
$907$	−11.5503	+	20.0056i	−0.383520	+	0.664276i	−0.991563	−	0.129628i	$-0.958622\pi$
$907$	−11.5503	+	20.0056i	−0.383520	+	0.664276i	0.608043	+	0.793904i	$0.291955\pi$
$908$	−11.4853	−	19.8931i	−0.381152	−	0.660175i
$909$	3.17157			0.105194
$910$	0.757359	−	1.85514i	0.0251062	−	0.0614974i
$911$	−8.48528			−0.281130			−0.140565	−	0.990071i	$-0.544892\pi$
$911$	−8.48528			−0.281130			−0.140565	+	0.990071i	$0.544892\pi$
$912$	−1.82843	−	3.16693i	−0.0605453	−	0.104867i
$913$	−12.8284	+	22.2195i	−0.424559	+	0.735358i
$914$		0			0
$915$	0.414214	+	0.717439i	0.0136935	+	0.0237178i
$916$	−26.1421			−0.863760
$917$	31.0355	+	40.0218i	1.02488	+	1.32164i
$918$	3.24264			0.107023
$919$	−0.863961	−	1.49642i	−0.0284994	−	0.0493625i	0.851424	−	0.524478i	$-0.175740\pi$
$919$	−0.863961	−	1.49642i	−0.0284994	−	0.0493625i	−0.879923	+	0.475116i	$0.842406\pi$
$920$	0.207107	−	0.358719i	0.00682811	−	0.0118266i
$921$	−7.07107	+	12.2474i	−0.233000	+	0.403567i
$922$	7.00000	+	12.1244i	0.230533	+	0.399294i
$923$	17.9706			0.591508
$924$	−5.24264	+	0.717439i	−0.172470	+	0.0236020i
$925$	15.3137			0.503512
$926$	5.31371	+	9.20361i	0.174619	+	0.302449i
$927$	4.44975	−	7.70719i	0.146149	−	0.253137i
$928$	−0.585786	+	1.01461i	−0.0192294	+	0.0333063i
$929$	25.3137	+	43.8446i	0.830516	+	1.43850i	0.897630	+	0.440750i	$0.145288\pi$
$929$	25.3137	+	43.8446i	0.830516	+	1.43850i	−0.0671139	+	0.997745i	$0.521379\pi$
$930$	0.828427			0.0271652
$931$	−18.2843	−	17.9149i	−0.599243	−	0.587136i
$932$	−8.00000			−0.262049
$933$	−3.15685	−	5.46783i	−0.103351	−	0.179009i
$934$	5.17157	−	8.95743i	0.169219	−	0.293096i
$935$	1.34315	−	2.32640i	0.0439256	−	0.0760813i
$936$	−0.914214	−	1.58346i	−0.0298820	−	0.0517572i
$937$	−12.4853			−0.407876			−0.203938	−	0.978984i	$-0.565374\pi$
$937$	−12.4853			−0.407876			−0.203938	+	0.978984i	$0.565374\pi$
$938$	39.0563	−	5.34474i	1.27524	−	0.174512i
$939$	−0.970563			−0.0316731
$940$	−1.86396	−	3.22848i	−0.0607957	−	0.105301i
$941$	−24.2426	+	41.9895i	−0.790288	+	1.36882i	0.135501	+	0.990777i	$0.456735\pi$
$941$	−24.2426	+	41.9895i	−0.790288	+	1.36882i	−0.925789	+	0.378041i	$0.876598\pi$
$942$	−2.17157	+	3.76127i	−0.0707537	+	0.122549i
$943$	5.41421	+	9.37769i	0.176311	+	0.305380i
$944$	1.65685			0.0539260
$945$	0.671573	+	0.866025i	0.0218463	+	0.0281718i
$946$	23.3137			0.757994
$947$	17.1569	+	29.7165i	0.557523	+	0.965658i	0.997702	+	0.0677482i	$0.0215814\pi$
$947$	17.1569	+	29.7165i	0.557523	+	0.965658i	−0.440180	+	0.897910i	$0.645085\pi$
$948$	5.00000	−	8.66025i	0.162392	−	0.281272i
$949$	−9.74264	+	16.8747i	−0.316259	+	0.547778i
$950$	−8.82843	−	15.2913i	−0.286432	−	0.496115i
$951$	12.6274			0.409472
$952$	3.24264	−	7.94282i	0.105095	−	0.257428i
$953$	−27.7990			−0.900498			−0.450249	−	0.892903i	$-0.648665\pi$
$953$	−27.7990			−0.900498			−0.450249	+	0.892903i	$0.648665\pi$
$954$	−5.03553	−	8.72180i	−0.163031	−	0.282379i
$955$	2.24264	−	3.88437i	0.0725701	−	0.125695i
$956$	−10.8284	+	18.7554i	−0.350216	+	0.606593i
$957$	1.17157	+	2.02922i	0.0378716	+	0.0655955i
$958$	−34.1421			−1.10308
$959$	−10.4142	+	25.5095i	−0.336292	+	0.823745i
$960$	0.414214			0.0133687
$961$	13.5000	+	23.3827i	0.435484	+	0.754280i
$962$	2.89949	−	5.02207i	0.0934835	−	0.161918i
$963$	−2.82843	+	4.89898i	−0.0911448	+	0.157867i
$964$	3.58579	+	6.21076i	0.115490	+	0.200035i
$965$	4.75736			0.153145
$966$	−1.62132	−	2.09077i	−0.0521651	−	0.0672694i
$967$	−5.17157			−0.166307			−0.0831533	−	0.996537i	$-0.526499\pi$
$967$	−5.17157			−0.166307			−0.0831533	+	0.996537i	$0.526499\pi$
$968$	−3.50000	−	6.06218i	−0.112494	−	0.194846i
$969$	5.92893	−	10.2692i	0.190465	−	0.329895i
$970$	−2.00000	+	3.46410i	−0.0642161	+	0.111226i
$971$	−1.17157	−	2.02922i	−0.0375976	−	0.0651209i	0.846614	−	0.532207i	$-0.178637\pi$
$971$	−1.17157	−	2.02922i	−0.0375976	−	0.0651209i	−0.884212	+	0.467086i	$0.845304\pi$
$972$	1.00000			0.0320750
$973$	34.8995	−	4.77589i	1.11883	−	0.153108i
$974$	32.7696			1.05000
$975$	−4.41421	−	7.64564i	−0.141368	−	0.244857i
$976$	1.00000	−	1.73205i	0.0320092	−	0.0554416i
$977$	23.1777	−	40.1449i	0.741519	−	1.28435i	−0.210284	−	0.977640i	$-0.567439\pi$
$977$	23.1777	−	40.1449i	0.741519	−	1.28435i	0.951803	−	0.306709i	$-0.0992278\pi$
$978$	−4.82843	−	8.36308i	−0.154396	−	0.267422i
$979$	2.34315			0.0748873
$980$	2.79289	−	0.778985i	0.0892157	−	0.0248838i
$981$	14.8284			0.473435
$982$	−5.67157	−	9.82345i	−0.180987	−	0.313479i
$983$	−25.7279	+	44.5621i	−0.820593	+	1.42131i	0.0846478	+	0.996411i	$0.473023\pi$
$983$	−25.7279	+	44.5621i	−0.820593	+	1.42131i	−0.905241	+	0.424898i	$0.860310\pi$
$984$	−5.41421	+	9.37769i	−0.172599	+	0.298950i
$985$	1.48528	+	2.57258i	0.0473250	+	0.0819693i
$986$	−3.79899			−0.120984
$987$	−23.5919	+	3.22848i	−0.750938	+	0.102763i
$988$	−6.68629			−0.212719
$989$	5.82843	+	10.0951i	0.185333	+	0.321007i
$990$	0.414214	−	0.717439i	0.0131646	−	0.0228017i
$991$	23.9706	−	41.5182i	0.761450	−	1.31887i	−0.180653	−	0.983547i	$-0.557821\pi$
$991$	23.9706	−	41.5182i	0.761450	−	1.31887i	0.942103	−	0.335323i	$-0.108846\pi$
$992$	−1.00000	−	1.73205i	−0.0317500	−	0.0549927i
$993$	−17.5147			−0.555813
$994$	15.9350	+	20.5490i	0.505428	+	0.651774i
$995$	−6.76955			−0.214609
$996$	−6.41421	−	11.1097i	−0.203242	−	0.352026i
$997$	−10.3137	+	17.8639i	−0.326638	+	0.565754i	−0.981843	−	0.189698i	$-0.939249\pi$
$997$	−10.3137	+	17.8639i	−0.326638	+	0.565754i	0.655204	+	0.755452i	$0.272583\pi$
$998$	0.585786	−	1.01461i	0.0185427	−	0.0321170i
$999$	1.58579	+	2.74666i	0.0501721	+	0.0869006i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.i.j.277.1	✓	4
7.2	even	3	inner	966.2.i.j.415.1	yes	4
7.3	odd	6		6762.2.a.bt.1.1		2
7.4	even	3		6762.2.a.bv.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.i.j.277.1	✓	4	1.1	even	1	trivial
966.2.i.j.415.1	yes	4	7.2	even	3	inner
6762.2.a.bt.1.1		2	7.3	odd	6
6762.2.a.bv.1.2		2	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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.207107 - 0.358719i) q^{5} -1.00000 q^{6} +(-2.62132 + 0.358719i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.207107 - 0.358719i) q^{5} -1.00000 q^{6} +(-2.62132 + 0.358719i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.207107 - 0.358719i) q^{10} +(-1.00000 + 1.73205i) q^{11} +(-0.500000 - 0.866025i) q^{12} -1.82843 q^{13} +(-1.62132 - 2.09077i) q^{14} +0.414214 q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.62132 - 2.80821i) q^{17} +(0.500000 - 0.866025i) q^{18} +(-1.82843 - 3.16693i) q^{19} +0.414214 q^{20} +(1.00000 - 2.44949i) q^{21} -2.00000 q^{22} +(-0.500000 - 0.866025i) q^{23} +(0.500000 - 0.866025i) q^{24} +(2.41421 - 4.18154i) q^{25} +(-0.914214 - 1.58346i) q^{26} +1.00000 q^{27} +(1.00000 - 2.44949i) q^{28} -1.17157 q^{29} +(0.207107 + 0.358719i) q^{30} +(1.00000 - 1.73205i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-1.00000 - 1.73205i) q^{33} +3.24264 q^{34} +(0.671573 + 0.866025i) q^{35} +1.00000 q^{36} +(1.58579 + 2.74666i) q^{37} +(1.82843 - 3.16693i) q^{38} +(0.914214 - 1.58346i) q^{39} +(0.207107 + 0.358719i) q^{40} -10.8284 q^{41} +(2.62132 - 0.358719i) q^{42} -11.6569 q^{43} +(-1.00000 - 1.73205i) q^{44} +(-0.207107 + 0.358719i) q^{45} +(0.500000 - 0.866025i) q^{46} +(-4.50000 - 7.79423i) q^{47} +1.00000 q^{48} +(6.74264 - 1.88064i) q^{49} +4.82843 q^{50} +(1.62132 + 2.80821i) q^{51} +(0.914214 - 1.58346i) q^{52} +(5.03553 - 8.72180i) q^{53} +(0.500000 + 0.866025i) q^{54} +0.828427 q^{55} +(2.62132 - 0.358719i) q^{56} +3.65685 q^{57} +(-0.585786 - 1.01461i) q^{58} +(-0.828427 + 1.43488i) q^{59} +(-0.207107 + 0.358719i) q^{60} +(1.00000 + 1.73205i) q^{61} +2.00000 q^{62} +(1.62132 + 2.09077i) q^{63} +1.00000 q^{64} +(0.378680 + 0.655892i) q^{65} +(1.00000 - 1.73205i) q^{66} +(-7.44975 + 12.9033i) q^{67} +(1.62132 + 2.80821i) q^{68} +1.00000 q^{69} +(-0.414214 + 1.01461i) q^{70} -9.82843 q^{71} +(0.500000 + 0.866025i) q^{72} +(5.32843 - 9.22911i) q^{73} +(-1.58579 + 2.74666i) q^{74} +(2.41421 + 4.18154i) q^{75} +3.65685 q^{76} +(2.00000 - 4.89898i) q^{77} +1.82843 q^{78} +(5.00000 + 8.66025i) q^{79} +(-0.207107 + 0.358719i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-5.41421 - 9.37769i) q^{82} +12.8284 q^{83} +(1.62132 + 2.09077i) q^{84} -1.34315 q^{85} +(-5.82843 - 10.0951i) q^{86} +(0.585786 - 1.01461i) q^{87} +(1.00000 - 1.73205i) q^{88} +(-0.585786 - 1.01461i) q^{89} -0.414214 q^{90} +(4.79289 - 0.655892i) q^{91} +1.00000 q^{92} +(1.00000 + 1.73205i) q^{93} +(4.50000 - 7.79423i) q^{94} +(-0.757359 + 1.31178i) q^{95} +(0.500000 + 0.866025i) q^{96} -9.65685 q^{97} +(5.00000 + 4.89898i) q^{98} +2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{5} - 4 q^{6} - 2 q^{7} - 4 q^{8} - 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^5 - 4 * q^6 - 2 * q^7 - 4 * q^8 - 2 * q^9	\( 4 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{5} - 4 q^{6} - 2 q^{7} - 4 q^{8} - 2 q^{9} - 2 q^{10} - 4 q^{11} - 2 q^{12} + 4 q^{13} + 2 q^{14} - 4 q^{15} - 2 q^{16} - 2 q^{17} + 2 q^{18} + 4 q^{19} - 4 q^{20} + 4 q^{21} - 8 q^{22} - 2 q^{23} + 2 q^{24} + 4 q^{25} + 2 q^{26} + 4 q^{27} + 4 q^{28} - 16 q^{29} - 2 q^{30} + 4 q^{31} + 2 q^{32} - 4 q^{33} - 4 q^{34} + 14 q^{35} + 4 q^{36} + 12 q^{37} - 4 q^{38} - 2 q^{39} - 2 q^{40} - 32 q^{41} + 2 q^{42} - 24 q^{43} - 4 q^{44} + 2 q^{45} + 2 q^{46} - 18 q^{47} + 4 q^{48} + 10 q^{49} + 8 q^{50} - 2 q^{51} - 2 q^{52} + 6 q^{53} + 2 q^{54} - 8 q^{55} + 2 q^{56} - 8 q^{57} - 8 q^{58} + 8 q^{59} + 2 q^{60} + 4 q^{61} + 8 q^{62} - 2 q^{63} + 4 q^{64} + 10 q^{65} + 4 q^{66} - 10 q^{67} - 2 q^{68} + 4 q^{69} + 4 q^{70} - 28 q^{71} + 2 q^{72} + 10 q^{73} - 12 q^{74} + 4 q^{75} - 8 q^{76} + 8 q^{77} - 4 q^{78} + 20 q^{79} + 2 q^{80} - 2 q^{81} - 16 q^{82} + 40 q^{83} - 2 q^{84} - 28 q^{85} - 12 q^{86} + 8 q^{87} + 4 q^{88} - 8 q^{89} + 4 q^{90} + 22 q^{91} + 4 q^{92} + 4 q^{93} + 18 q^{94} - 20 q^{95} + 2 q^{96} - 16 q^{97} + 20 q^{98} + 8 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^5 - 4 * q^6 - 2 * q^7 - 4 * q^8 - 2 * q^9 - 2 * q^10 - 4 * q^11 - 2 * q^12 + 4 * q^13 + 2 * q^14 - 4 * q^15 - 2 * q^16 - 2 * q^17 + 2 * q^18 + 4 * q^19 - 4 * q^20 + 4 * q^21 - 8 * q^22 - 2 * q^23 + 2 * q^24 + 4 * q^25 + 2 * q^26 + 4 * q^27 + 4 * q^28 - 16 * q^29 - 2 * q^30 + 4 * q^31 + 2 * q^32 - 4 * q^33 - 4 * q^34 + 14 * q^35 + 4 * q^36 + 12 * q^37 - 4 * q^38 - 2 * q^39 - 2 * q^40 - 32 * q^41 + 2 * q^42 - 24 * q^43 - 4 * q^44 + 2 * q^45 + 2 * q^46 - 18 * q^47 + 4 * q^48 + 10 * q^49 + 8 * q^50 - 2 * q^51 - 2 * q^52 + 6 * q^53 + 2 * q^54 - 8 * q^55 + 2 * q^56 - 8 * q^57 - 8 * q^58 + 8 * q^59 + 2 * q^60 + 4 * q^61 + 8 * q^62 - 2 * q^63 + 4 * q^64 + 10 * q^65 + 4 * q^66 - 10 * q^67 - 2 * q^68 + 4 * q^69 + 4 * q^70 - 28 * q^71 + 2 * q^72 + 10 * q^73 - 12 * q^74 + 4 * q^75 - 8 * q^76 + 8 * q^77 - 4 * q^78 + 20 * q^79 + 2 * q^80 - 2 * q^81 - 16 * q^82 + 40 * q^83 - 2 * q^84 - 28 * q^85 - 12 * q^86 + 8 * q^87 + 4 * q^88 - 8 * q^89 + 4 * q^90 + 22 * q^91 + 4 * q^92 + 4 * q^93 + 18 * q^94 - 20 * q^95 + 2 * q^96 - 16 * q^97 + 20 * q^98 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more