LMFDB - Embedded newform 1110.2.x.e.841.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(751,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5]))

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

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

chi := DirichletCharacter("1110.751");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.x (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 44x^{14} + 724x^{12} + 5750x^{10} + 23344x^{8} + 47024x^{6} + 43297x^{4} + 13976x^{2} + 676 $ x^16 + 44x^14 + 724x^12 + 5750x^10 + 23344x^8 + 47024x^6 + 43297x^4 + 13976*x^2 + 676
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			841.7
Root			$2.57049i$ of defining polynomial
Character	$\chi$	$=$	1110.841
Dual form			1110.2.x.e.751.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{5} +1.00000i q^{6} +(0.243282 + 0.421377i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{5} +1.00000i q^{6} +(0.243282 + 0.421377i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} -1.00000 q^{10} -3.92759 q^{11} +(-0.500000 + 0.866025i) q^{12} +(-2.50956 + 1.44890i) q^{13} +0.486564i q^{14} +(-0.866025 - 0.500000i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.21667 + 1.85715i) q^{17} +(-0.866025 + 0.500000i) q^{18} +(-4.61424 + 2.66404i) q^{19} +(-0.866025 - 0.500000i) q^{20} +(-0.243282 + 0.421377i) q^{21} +(-3.40139 - 1.96379i) q^{22} -0.619168i q^{23} +(-0.866025 + 0.500000i) q^{24} +(0.500000 - 0.866025i) q^{25} -2.89779 q^{26} -1.00000 q^{27} +(-0.243282 + 0.421377i) q^{28} +6.39653i q^{29} +(-0.500000 - 0.866025i) q^{30} -1.67688i q^{31} +(-0.866025 + 0.500000i) q^{32} +(-1.96379 - 3.40139i) q^{33} +(1.85715 + 3.21667i) q^{34} +(-0.421377 - 0.243282i) q^{35} -1.00000 q^{36} +(-6.08005 - 0.181603i) q^{37} -5.32807 q^{38} +(-2.50956 - 1.44890i) q^{39} +(-0.500000 - 0.866025i) q^{40} +(4.81213 + 8.33485i) q^{41} +(-0.421377 + 0.243282i) q^{42} -2.14314i q^{43} +(-1.96379 - 3.40139i) q^{44} -1.00000i q^{45} +(0.309584 - 0.536215i) q^{46} +9.69972 q^{47} -1.00000 q^{48} +(3.38163 - 5.85715i) q^{49} +(0.866025 - 0.500000i) q^{50} +3.71429i q^{51} +(-2.50956 - 1.44890i) q^{52} +(-2.09784 + 3.63356i) q^{53} +(-0.866025 - 0.500000i) q^{54} +(3.40139 - 1.96379i) q^{55} +(-0.421377 + 0.243282i) q^{56} +(-4.61424 - 2.66404i) q^{57} +(-3.19826 + 5.53955i) q^{58} +(-3.57217 - 2.06239i) q^{59} -1.00000i q^{60} +(0.262978 - 0.151831i) q^{61} +(0.838440 - 1.45222i) q^{62} -0.486564 q^{63} -1.00000 q^{64} +(1.44890 - 2.50956i) q^{65} -3.92759i q^{66} +(-0.713345 - 1.23555i) q^{67} +3.71429i q^{68} +(0.536215 - 0.309584i) q^{69} +(-0.243282 - 0.421377i) q^{70} +(1.39033 + 2.40811i) q^{71} +(-0.866025 - 0.500000i) q^{72} +0.964401 q^{73} +(-5.17468 - 3.19730i) q^{74} +1.00000 q^{75} +(-4.61424 - 2.66404i) q^{76} +(-0.955512 - 1.65500i) q^{77} +(-1.44890 - 2.50956i) q^{78} +(7.50415 - 4.33252i) q^{79} -1.00000i q^{80} +(-0.500000 - 0.866025i) q^{81} +9.62425i q^{82} +(-1.79705 + 3.11259i) q^{83} -0.486564 q^{84} -3.71429 q^{85} +(1.07157 - 1.85602i) q^{86} +(-5.53955 + 3.19826i) q^{87} -3.92759i q^{88} +(6.81203 + 3.93292i) q^{89} +(0.500000 - 0.866025i) q^{90} +(-1.22106 - 0.704981i) q^{91} +(0.536215 - 0.309584i) q^{92} +(1.45222 - 0.838440i) q^{93} +(8.40021 + 4.84986i) q^{94} +(2.66404 - 4.61424i) q^{95} +(-0.866025 - 0.500000i) q^{96} -3.96693i q^{97} +(5.85715 - 3.38163i) q^{98} +(1.96379 - 3.40139i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{3} + 8 q^{4} - 4 q^{7} - 8 q^{9}+O(q^{10}) $ 16 * q + 8 * q^3 + 8 * q^4 - 4 * q^7 - 8 * q^9	$ 16 q + 8 q^{3} + 8 q^{4} - 4 q^{7} - 8 q^{9} - 16 q^{10} - 4 q^{11} - 8 q^{12} - 8 q^{16} - 6 q^{17} - 6 q^{19} + 4 q^{21} + 12 q^{22} + 8 q^{25} - 8 q^{26} - 16 q^{27} + 4 q^{28} - 8 q^{30} - 2 q^{33} + 2 q^{34} + 18 q^{35} - 16 q^{36} - 12 q^{37} + 12 q^{38} - 8 q^{40} + 4 q^{41} + 18 q^{42} - 2 q^{44} + 12 q^{47} - 16 q^{48} - 42 q^{49} - 16 q^{53} - 12 q^{55} + 18 q^{56} - 6 q^{57} + 2 q^{58} + 48 q^{59} - 12 q^{61} - 4 q^{62} + 8 q^{63} - 16 q^{64} + 4 q^{65} + 6 q^{67} - 18 q^{69} + 4 q^{70} - 6 q^{71} - 52 q^{73} - 16 q^{74} + 16 q^{75} - 6 q^{76} + 10 q^{77} - 4 q^{78} + 78 q^{79} - 8 q^{81} + 36 q^{83} + 8 q^{84} - 4 q^{85} - 6 q^{86} + 12 q^{87} + 18 q^{89} + 8 q^{90} - 66 q^{91} - 18 q^{92} - 36 q^{93} + 12 q^{94} - 6 q^{95} - 12 q^{98} + 2 q^{99}+O(q^{100}) $ 16 * q + 8 * q^3 + 8 * q^4 - 4 * q^7 - 8 * q^9 - 16 * q^10 - 4 * q^11 - 8 * q^12 - 8 * q^16 - 6 * q^17 - 6 * q^19 + 4 * q^21 + 12 * q^22 + 8 * q^25 - 8 * q^26 - 16 * q^27 + 4 * q^28 - 8 * q^30 - 2 * q^33 + 2 * q^34 + 18 * q^35 - 16 * q^36 - 12 * q^37 + 12 * q^38 - 8 * q^40 + 4 * q^41 + 18 * q^42 - 2 * q^44 + 12 * q^47 - 16 * q^48 - 42 * q^49 - 16 * q^53 - 12 * q^55 + 18 * q^56 - 6 * q^57 + 2 * q^58 + 48 * q^59 - 12 * q^61 - 4 * q^62 + 8 * q^63 - 16 * q^64 + 4 * q^65 + 6 * q^67 - 18 * q^69 + 4 * q^70 - 6 * q^71 - 52 * q^73 - 16 * q^74 + 16 * q^75 - 6 * q^76 + 10 * q^77 - 4 * q^78 + 78 * q^79 - 8 * q^81 + 36 * q^83 + 8 * q^84 - 4 * q^85 - 6 * q^86 + 12 * q^87 + 18 * q^89 + 8 * q^90 - 66 * q^91 - 18 * q^92 - 36 * q^93 + 12 * q^94 - 6 * q^95 - 12 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−0.866025	+	0.500000i	−0.387298	+	0.223607i
$5$	−0.866025	+	0.500000i	−0.387298	+	0.223607i
$6$			1.00000i			0.408248i
$7$	0.243282	+	0.421377i	0.0919520	+	0.159266i	0.908332	−	0.418249i	$-0.137356\pi$
$7$	0.243282	+	0.421377i	0.0919520	+	0.159266i	−0.816380	+	0.577514i	$0.804023\pi$
$8$			1.00000i			0.353553i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−1.00000			−0.316228
$11$	−3.92759			−1.18421			−0.592106	−	0.805860i	$-0.701703\pi$
$11$	−3.92759			−1.18421			−0.592106	+	0.805860i	$0.701703\pi$
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	−2.50956	+	1.44890i	−0.696027	+	0.401851i	−0.805866	−	0.592098i	$-0.798300\pi$
$13$	−2.50956	+	1.44890i	−0.696027	+	0.401851i	0.109839	+	0.993949i	$0.464966\pi$
$14$			0.486564i			0.130040i
$15$	−0.866025	−	0.500000i	−0.223607	−	0.129099i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	3.21667	+	1.85715i	0.780157	+	0.450424i	0.836486	−	0.547988i	$-0.184606\pi$
$17$	3.21667	+	1.85715i	0.780157	+	0.450424i	−0.0563289	+	0.998412i	$0.517940\pi$
$18$	−0.866025	+	0.500000i	−0.204124	+	0.117851i
$19$	−4.61424	+	2.66404i	−1.05858	+	0.611172i	−0.925039	−	0.379872i	$-0.875968\pi$
$19$	−4.61424	+	2.66404i	−1.05858	+	0.611172i	−0.133541	+	0.991043i	$0.542635\pi$
$20$	−0.866025	−	0.500000i	−0.193649	−	0.111803i
$21$	−0.243282	+	0.421377i	−0.0530885	+	0.0919520i
$22$	−3.40139	−	1.96379i	−0.725179	−	0.418682i
$23$		−	0.619168i		−	0.129105i	−0.997914	−	0.0645527i	$-0.979438\pi$
$23$		−	0.619168i		−	0.129105i	0.997914	−	0.0645527i	$-0.0205621\pi$
$24$	−0.866025	+	0.500000i	−0.176777	+	0.102062i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	−2.89779			−0.568304
$27$	−1.00000			−0.192450
$28$	−0.243282	+	0.421377i	−0.0459760	+	0.0796328i
$29$			6.39653i			1.18781i	0.804537	+	0.593903i	$0.202414\pi$
$29$			6.39653i			1.18781i	−0.804537	+	0.593903i	$0.797586\pi$
$30$	−0.500000	−	0.866025i	−0.0912871	−	0.158114i
$31$		−	1.67688i		−	0.301176i	−0.988597	−	0.150588i	$-0.951883\pi$
$31$		−	1.67688i		−	0.301176i	0.988597	−	0.150588i	$-0.0481167\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	−1.96379	−	3.40139i	−0.341853	−	0.592106i
$34$	1.85715	+	3.21667i	0.318498	+	0.551654i
$35$	−0.421377	−	0.243282i	−0.0712257	−	0.0411222i
$36$	−1.00000			−0.166667
$37$	−6.08005	−	0.181603i	−0.999554	−	0.0298554i
$37$	−6.08005	−	0.181603i	−0.999554	−	0.0298554i
$38$	−5.32807			−0.864327
$39$	−2.50956	−	1.44890i	−0.401851	−	0.232009i
$40$	−0.500000	−	0.866025i	−0.0790569	−	0.136931i
$41$	4.81213	+	8.33485i	0.751528	+	1.30168i	0.947082	+	0.320991i	$0.104016\pi$
$41$	4.81213	+	8.33485i	0.751528	+	1.30168i	−0.195554	+	0.980693i	$0.562651\pi$
$42$	−0.421377	+	0.243282i	−0.0650199	+	0.0375392i
$43$		−	2.14314i		−	0.326826i	−0.986558	−	0.163413i	$-0.947750\pi$
$43$		−	2.14314i		−	0.326826i	0.986558	−	0.163413i	$-0.0522503\pi$
$44$	−1.96379	−	3.40139i	−0.296053	−	0.512779i
$45$		−	1.00000i		−	0.149071i
$46$	0.309584	−	0.536215i	0.0456456	−	0.0790606i
$47$	9.69972			1.41485			0.707425	−	0.706788i	$-0.249857\pi$
$47$	9.69972			1.41485			0.707425	+	0.706788i	$0.249857\pi$
$48$	−1.00000			−0.144338
$49$	3.38163	−	5.85715i	0.483090	−	0.836736i
$50$	0.866025	−	0.500000i	0.122474	−	0.0707107i
$51$			3.71429i			0.520105i
$52$	−2.50956	−	1.44890i	−0.348013	−	0.200926i
$53$	−2.09784	+	3.63356i	−0.288160	+	0.499108i	−0.973371	−	0.229237i	$-0.926377\pi$
$53$	−2.09784	+	3.63356i	−0.288160	+	0.499108i	0.685211	+	0.728345i	$0.259710\pi$
$54$	−0.866025	−	0.500000i	−0.117851	−	0.0680414i
$55$	3.40139	−	1.96379i	0.458643	−	0.264798i
$56$	−0.421377	+	0.243282i	−0.0563089	+	0.0325099i
$57$	−4.61424	−	2.66404i	−0.611172	−	0.352860i
$58$	−3.19826	+	5.53955i	−0.419953	+	0.727379i
$59$	−3.57217	−	2.06239i	−0.465057	−	0.268501i	0.249111	−	0.968475i	$-0.419861\pi$
$59$	−3.57217	−	2.06239i	−0.465057	−	0.268501i	−0.714168	+	0.699974i	$0.753195\pi$
$60$		−	1.00000i		−	0.129099i
$61$	0.262978	−	0.151831i	0.0336709	−	0.0194399i	−0.483070	−	0.875582i	$-0.660478\pi$
$61$	0.262978	−	0.151831i	0.0336709	−	0.0194399i	0.516741	+	0.856142i	$0.327145\pi$
$62$	0.838440	−	1.45222i	0.106482	−	0.184432i
$63$	−0.486564			−0.0613013
$64$	−1.00000			−0.125000
$65$	1.44890	−	2.50956i	0.179713	−	0.311273i
$66$		−	3.92759i		−	0.483453i
$67$	−0.713345	−	1.23555i	−0.0871490	−	0.150946i	0.819156	−	0.573571i	$-0.194442\pi$
$67$	−0.713345	−	1.23555i	−0.0871490	−	0.150946i	−0.906305	+	0.422624i	$0.861109\pi$
$68$			3.71429i			0.450424i
$69$	0.536215	−	0.309584i	0.0645527	−	0.0372695i
$70$	−0.243282	−	0.421377i	−0.0290778	−	0.0503642i
$71$	1.39033	+	2.40811i	0.165001	+	0.285791i	0.936656	−	0.350251i	$-0.113904\pi$
$71$	1.39033	+	2.40811i	0.165001	+	0.285791i	−0.771654	+	0.636042i	$0.780570\pi$
$72$	−0.866025	−	0.500000i	−0.102062	−	0.0589256i
$73$	0.964401			0.112875			0.0564373	−	0.998406i	$-0.482026\pi$
$73$	0.964401			0.112875			0.0564373	+	0.998406i	$0.482026\pi$
$74$	−5.17468	−	3.19730i	−0.601544	−	0.371678i
$75$	1.00000			0.115470
$76$	−4.61424	−	2.66404i	−0.529290	−	0.305586i
$77$	−0.955512	−	1.65500i	−0.108891	−	0.188604i
$78$	−1.44890	−	2.50956i	−0.164055	−	0.284152i
$79$	7.50415	−	4.33252i	0.844283	−	0.487447i	−0.0144351	−	0.999896i	$-0.504595\pi$
$79$	7.50415	−	4.33252i	0.844283	−	0.487447i	0.858718	+	0.512449i	$0.171262\pi$
$80$		−	1.00000i		−	0.111803i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$			9.62425i			1.06282i
$83$	−1.79705	+	3.11259i	−0.197252	+	0.341651i	−0.947637	−	0.319351i	$-0.896535\pi$
$83$	−1.79705	+	3.11259i	−0.197252	+	0.341651i	0.750384	+	0.661002i	$0.229868\pi$
$84$	−0.486564			−0.0530885
$85$	−3.71429			−0.402871
$86$	1.07157	−	1.85602i	0.115551	−	0.200139i
$87$	−5.53955	+	3.19826i	−0.593903	+	0.342890i
$88$		−	3.92759i		−	0.418682i
$89$	6.81203	+	3.93292i	0.722073	+	0.416889i	0.815515	−	0.578736i	$-0.196454\pi$
$89$	6.81203	+	3.93292i	0.722073	+	0.416889i	−0.0934420	+	0.995625i	$0.529787\pi$
$90$	0.500000	−	0.866025i	0.0527046	−	0.0912871i
$91$	−1.22106	−	0.704981i	−0.128002	−	0.0739021i
$92$	0.536215	−	0.309584i	0.0559043	−	0.0322763i
$93$	1.45222	−	0.838440i	0.150588	−	0.0869421i
$94$	8.40021	+	4.84986i	0.866415	+	0.500225i
$95$	2.66404	−	4.61424i	0.273324	−	0.473411i
$96$	−0.866025	−	0.500000i	−0.0883883	−	0.0510310i
$97$		−	3.96693i		−	0.402781i	−0.979511	−	0.201390i	$-0.935454\pi$
$97$		−	3.96693i		−	0.402781i	0.979511	−	0.201390i	$-0.0645460\pi$
$98$	5.85715	−	3.38163i	0.591662	−	0.341596i
$99$	1.96379	−	3.40139i	0.197369	−	0.341853i
$100$	1.00000			0.100000
$101$	−13.1358			−1.30706			−0.653529	−	0.756901i	$-0.726712\pi$
$101$	−13.1358			−1.30706			−0.653529	+	0.756901i	$0.726712\pi$
$102$	−1.85715	+	3.21667i	−0.183885	+	0.318498i
$103$			15.6421i			1.54126i	0.637280	+	0.770632i	$0.280059\pi$
$103$			15.6421i			1.54126i	−0.637280	+	0.770632i	$0.719941\pi$
$104$	−1.44890	−	2.50956i	−0.142076	−	0.246083i
$105$		−	0.486564i		−	0.0474838i
$106$	−3.63356	+	2.09784i	−0.352922	+	0.203760i
$107$	3.87952	+	6.71952i	0.375047	+	0.649601i	0.990334	−	0.138703i	$-0.0442932\pi$
$107$	3.87952	+	6.71952i	0.375047	+	0.649601i	−0.615287	+	0.788303i	$0.710960\pi$
$108$	−0.500000	−	0.866025i	−0.0481125	−	0.0833333i
$109$	5.05443	+	2.91818i	0.484127	+	0.279511i	0.722135	−	0.691753i	$-0.243161\pi$
$109$	5.05443	+	2.91818i	0.484127	+	0.279511i	−0.238008	+	0.971263i	$0.576494\pi$
$110$	3.92759			0.374481
$111$	−2.88275	−	5.35628i	−0.273619	−	0.508396i
$112$	−0.486564			−0.0459760
$113$	−7.10850	−	4.10409i	−0.668711	−	0.386081i	0.126877	−	0.991918i	$-0.459505\pi$
$113$	−7.10850	−	4.10409i	−0.668711	−	0.386081i	−0.795588	+	0.605838i	$0.792838\pi$
$114$	−2.66404	−	4.61424i	−0.249510	−	0.432164i
$115$	0.309584	+	0.536215i	0.0288688	+	0.0500023i
$116$	−5.53955	+	3.19826i	−0.514335	+	0.296951i
$117$		−	2.89779i		−	0.267901i
$118$	−2.06239	−	3.57217i	−0.189859	−	0.328845i
$119$			1.80724i			0.165669i
$120$	0.500000	−	0.866025i	0.0456435	−	0.0790569i
$121$	4.42595			0.402359
$122$	0.303661			0.0274922
$123$	−4.81213	+	8.33485i	−0.433895	+	0.751528i
$124$	1.45222	−	0.838440i	0.130413	−	0.0752941i
$125$			1.00000i			0.0894427i
$126$	−0.421377	−	0.243282i	−0.0375392	−	0.0216733i
$127$	4.81845	−	8.34580i	0.427569	−	0.740570i	−0.569088	−	0.822277i	$-0.692704\pi$
$127$	4.81845	−	8.34580i	0.427569	−	0.740570i	0.996656	+	0.0817062i	$0.0260369\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	1.85602	−	1.07157i	0.163413	−	0.0943466i
$130$	2.50956	−	1.44890i	0.220103	−	0.127077i
$131$	8.11818	+	4.68703i	0.709288	+	0.409508i	0.810798	−	0.585327i	$-0.199034\pi$
$131$	8.11818	+	4.68703i	0.709288	+	0.409508i	−0.101509	+	0.994835i	$0.532367\pi$
$132$	1.96379	−	3.40139i	0.170926	−	0.296053i
$133$	−2.24513	−	1.29622i	−0.194677	−	0.112397i
$134$		−	1.42669i		−	0.123247i
$135$	0.866025	−	0.500000i	0.0745356	−	0.0430331i
$136$	−1.85715	+	3.21667i	−0.159249	+	0.275827i
$137$	10.9349			0.934233			0.467117	−	0.884196i	$-0.345293\pi$
$137$	10.9349			0.934233			0.467117	+	0.884196i	$0.345293\pi$
$138$	0.619168			0.0527071
$139$	9.32007	−	16.1428i	0.790518	−	1.36922i	−0.135128	−	0.990828i	$-0.543145\pi$
$139$	9.32007	−	16.1428i	0.790518	−	1.36922i	0.925646	−	0.378390i	$-0.123522\pi$
$140$		−	0.486564i		−	0.0411222i
$141$	4.84986	+	8.40021i	0.408432	+	0.707425i
$142$			2.78065i			0.233347i
$143$	9.85652	−	5.69066i	0.824244	−	0.475877i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	−3.19826	−	5.53955i	−0.265601	−	0.460035i
$146$	0.835196	+	0.482200i	0.0691213	+	0.0399072i
$147$	6.76326			0.557824
$148$	−2.88275	−	5.35628i	−0.236961	−	0.440284i
$149$	22.0084			1.80299			0.901497	−	0.432785i	$-0.142469\pi$
$149$	22.0084			1.80299			0.901497	+	0.432785i	$0.142469\pi$
$150$	0.866025	+	0.500000i	0.0707107	+	0.0408248i
$151$	5.65964	+	9.80278i	0.460575	+	0.797739i	0.998990	−	0.0449409i	$-0.0143100\pi$
$151$	5.65964	+	9.80278i	0.460575	+	0.797739i	−0.538415	+	0.842680i	$0.680977\pi$
$152$	−2.66404	−	4.61424i	−0.216082	−	0.374265i
$153$	−3.21667	+	1.85715i	−0.260052	+	0.150141i
$154$		−	1.91102i		−	0.153995i
$155$	0.838440	+	1.45222i	0.0673451	+	0.116645i
$156$		−	2.89779i		−	0.232009i
$157$	5.84890	−	10.1306i	0.466793	−	0.808509i	−0.532488	−	0.846438i	$-0.678743\pi$
$157$	5.84890	−	10.1306i	0.466793	−	0.808509i	0.999280	+	0.0379289i	$0.0120760\pi$
$158$	8.66504			0.689354
$159$	−4.19567			−0.332738
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$	0.260903	−	0.150632i	0.0205620	−	0.0118715i
$162$		−	1.00000i		−	0.0785674i
$163$	−13.4481	−	7.76427i	−1.05334	−	0.608144i	−0.129755	−	0.991546i	$-0.541419\pi$
$163$	−13.4481	−	7.76427i	−1.05334	−	0.608144i	−0.923582	+	0.383402i	$0.874752\pi$
$164$	−4.81213	+	8.33485i	−0.375764	+	0.650842i
$165$	3.40139	+	1.96379i	0.264798	+	0.152881i
$166$	−3.11259	+	1.79705i	−0.241584	+	0.139478i
$167$	7.30124	−	4.21537i	0.564987	−	0.326195i	−0.190158	−	0.981754i	$-0.560900\pi$
$167$	7.30124	−	4.21537i	0.564987	−	0.326195i	0.755145	+	0.655558i	$0.227567\pi$
$168$	−0.421377	−	0.243282i	−0.0325099	−	0.0187696i
$169$	−2.30140	+	3.98615i	−0.177031	+	0.306627i
$170$	−3.21667	−	1.85715i	−0.246707	−	0.142437i
$171$		−	5.32807i		−	0.407448i
$172$	1.85602	−	1.07157i	0.141520	−	0.0817066i
$173$	−9.80229	+	16.9781i	−0.745254	+	1.29082i	0.204822	+	0.978799i	$0.434339\pi$
$173$	−9.80229	+	16.9781i	−0.745254	+	1.29082i	−0.950076	+	0.312019i	$0.898995\pi$
$174$	−6.39653			−0.484919
$175$	0.486564			0.0367808
$176$	1.96379	−	3.40139i	0.148027	−	0.256389i
$177$		−	4.12478i		−	0.310038i
$178$	3.93292	+	6.81203i	0.294785	+	0.510583i
$179$			5.79763i			0.433335i	0.976245	+	0.216668i	$0.0695187\pi$
$179$			5.79763i			0.433335i	−0.976245	+	0.216668i	$0.930481\pi$
$180$	0.866025	−	0.500000i	0.0645497	−	0.0372678i
$181$	−1.17814	−	2.04061i	−0.0875708	−	0.151677i	0.818913	−	0.573918i	$-0.194577\pi$
$181$	−1.17814	−	2.04061i	−0.0875708	−	0.151677i	−0.906484	+	0.422241i	$0.861244\pi$
$182$	−0.704981	−	1.22106i	−0.0522566	−	0.0905112i
$183$	0.262978	+	0.151831i	0.0194399	+	0.0112236i
$184$	0.619168			0.0456456
$185$	5.35628	−	2.88275i	0.393802	−	0.211944i
$186$	1.67688			0.122955
$187$	−12.6338	−	7.29410i	−0.923871	−	0.533397i
$188$	4.84986	+	8.40021i	0.353713	+	0.612648i
$189$	−0.243282	−	0.421377i	−0.0176962	−	0.0306507i
$190$	4.61424	−	2.66404i	0.334752	−	0.193269i
$191$			16.7408i			1.21132i	0.795723	+	0.605661i	$0.207091\pi$
$191$			16.7408i			1.21132i	−0.795723	+	0.605661i	$0.792909\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$			25.9501i			1.86793i	0.357366	+	0.933964i	$0.383675\pi$
$193$			25.9501i			1.86793i	−0.357366	+	0.933964i	$0.616325\pi$
$194$	1.98347	−	3.43546i	0.142405	−	0.246652i
$195$	2.89779			0.207515
$196$	6.76326			0.483090
$197$	−7.24396	+	12.5469i	−0.516111	+	0.893930i	0.483714	+	0.875226i	$0.339287\pi$
$197$	−7.24396	+	12.5469i	−0.516111	+	0.893930i	−0.999825	+	0.0187042i	$0.994046\pi$
$198$	3.40139	−	1.96379i	0.241726	−	0.139561i
$199$		−	18.5465i		−	1.31473i	−0.753574	−	0.657363i	$-0.771672\pi$
$199$		−	18.5465i		−	1.31473i	0.753574	−	0.657363i	$-0.228328\pi$
$200$	0.866025	+	0.500000i	0.0612372	+	0.0353553i
$201$	0.713345	−	1.23555i	0.0503155	−	0.0871490i
$202$	−11.3759	−	6.56789i	−0.800407	−	0.462115i
$203$	−2.69535	+	1.55616i	−0.189176	+	0.109221i
$204$	−3.21667	+	1.85715i	−0.225212	+	0.130026i
$205$	−8.33485	−	4.81213i	−0.582131	−	0.336093i
$206$	−7.82106	+	13.5465i	−0.544919	+	0.943828i
$207$	0.536215	+	0.309584i	0.0372695	+	0.0215176i
$208$		−	2.89779i		−	0.200926i
$209$	18.1228	−	10.4632i	1.25358	−	0.723757i
$210$	0.243282	−	0.421377i	0.0167881	−	0.0290778i
$211$	19.9382			1.37261			0.686303	−	0.727316i	$-0.259233\pi$
$211$	19.9382			1.37261			0.686303	+	0.727316i	$0.259233\pi$
$212$	−4.19567			−0.288160
$213$	−1.39033	+	2.40811i	−0.0952635	+	0.165001i
$214$			7.75904i			0.530397i
$215$	1.07157	+	1.85602i	0.0730806	+	0.126579i
$216$		−	1.00000i		−	0.0680414i
$217$	0.706598	−	0.407955i	0.0479670	−	0.0276938i
$218$	2.91818	+	5.05443i	0.197644	+	0.342329i
$219$	0.482200	+	0.835196i	0.0325841	+	0.0564373i
$220$	3.40139	+	1.96379i	0.229322	+	0.132399i
$221$	−10.7632			−0.724014
$222$	0.181603	−	6.08005i	0.0121884	−	0.408066i
$223$	−9.21349			−0.616981			−0.308490	−	0.951227i	$-0.599824\pi$
$223$	−9.21349			−0.616981			−0.308490	+	0.951227i	$0.599824\pi$
$224$	−0.421377	−	0.243282i	−0.0281544	−	0.0162550i
$225$	0.500000	+	0.866025i	0.0333333	+	0.0577350i
$226$	−4.10409	−	7.10850i	−0.273000	−	0.472850i
$227$	13.7498	−	7.93847i	0.912609	−	0.526895i	0.0313390	−	0.999509i	$-0.490023\pi$
$227$	13.7498	−	7.93847i	0.912609	−	0.526895i	0.881270	+	0.472614i	$0.156690\pi$
$228$		−	5.32807i		−	0.352860i
$229$	8.29785	+	14.3723i	0.548337	+	0.949748i	0.998389	+	0.0567454i	$0.0180723\pi$
$229$	8.29785	+	14.3723i	0.548337	+	0.949748i	−0.450051	+	0.893003i	$0.648594\pi$
$230$			0.619168i			0.0408267i
$231$	0.955512	−	1.65500i	0.0628681	−	0.108891i
$232$	−6.39653			−0.419953
$233$	−16.8216			−1.10202			−0.551010	−	0.834498i	$-0.685757\pi$
$233$	−16.8216			−1.10202			−0.551010	+	0.834498i	$0.685757\pi$
$234$	1.44890	−	2.50956i	0.0947173	−	0.164055i
$235$	−8.40021	+	4.84986i	−0.547969	+	0.316370i
$236$		−	4.12478i		−	0.268501i
$237$	7.50415	+	4.33252i	0.487447	+	0.281428i
$238$	−0.903620	+	1.56512i	−0.0585730	+	0.101451i
$239$	−2.03613	−	1.17556i	−0.131706	−	0.0760408i	0.432699	−	0.901538i	$-0.357561\pi$
$239$	−2.03613	−	1.17556i	−0.131706	−	0.0760408i	−0.564406	+	0.825498i	$0.690895\pi$
$240$	0.866025	−	0.500000i	0.0559017	−	0.0322749i
$241$	4.16270	−	2.40334i	0.268143	−	0.154813i	−0.359900	−	0.932991i	$-0.617189\pi$
$241$	4.16270	−	2.40334i	0.268143	−	0.154813i	0.628044	+	0.778178i	$0.283856\pi$
$242$	3.83298	+	2.21297i	0.246393	+	0.142255i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	0.262978	+	0.151831i	0.0168355	+	0.00971996i
$245$			6.76326i			0.432089i
$246$	−8.33485	+	4.81213i	−0.531410	+	0.306810i
$247$	7.71982	−	13.3711i	0.491200	−	0.850784i
$248$	1.67688			0.106482
$249$	−3.59411			−0.227767
$250$	−0.500000	+	0.866025i	−0.0316228	+	0.0547723i
$251$		−	21.0899i		−	1.33118i	−0.746316	−	0.665592i	$-0.768179\pi$
$251$		−	21.0899i		−	1.33118i	0.746316	−	0.665592i	$-0.231821\pi$
$252$	−0.243282	−	0.421377i	−0.0153253	−	0.0265443i
$253$			2.43184i			0.152888i
$254$	8.34580	−	4.81845i	0.523662	−	0.302337i
$255$	−1.85715	−	3.21667i	−0.116299	−	0.201436i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	1.07530	+	0.620823i	0.0670752	+	0.0387259i	0.533163	−	0.846013i	$-0.321003\pi$
$257$	1.07530	+	0.620823i	0.0670752	+	0.0387259i	−0.466087	+	0.884739i	$0.654337\pi$
$258$	2.14314			0.133426
$259$	−1.40264	−	2.60617i	−0.0871561	−	0.161940i
$260$	2.89779			0.179713
$261$	−5.53955	−	3.19826i	−0.342890	−	0.197968i
$262$	4.68703	+	8.11818i	0.289566	+	0.501543i
$263$	−5.88514	−	10.1934i	−0.362893	−	0.628549i	0.625543	−	0.780190i	$-0.284878\pi$
$263$	−5.88514	−	10.1934i	−0.362893	−	0.628549i	−0.988436	+	0.151641i	$0.951544\pi$
$264$	3.40139	−	1.96379i	0.209341	−	0.120863i
$265$		−	4.19567i		−	0.257738i
$266$	−1.29622	−	2.24513i	−0.0794766	−	0.137658i
$267$			7.86585i			0.481382i
$268$	0.713345	−	1.23555i	0.0435745	−	0.0754732i
$269$	12.2032			0.744040			0.372020	−	0.928225i	$-0.378665\pi$
$269$	12.2032			0.744040			0.372020	+	0.928225i	$0.378665\pi$
$270$	1.00000			0.0608581
$271$	−0.135247	+	0.234255i	−0.00821570	+	0.0142300i	−0.870104	−	0.492868i	$-0.835948\pi$
$271$	−0.135247	+	0.234255i	−0.00821570	+	0.0142300i	0.861888	+	0.507098i	$0.169282\pi$
$272$	−3.21667	+	1.85715i	−0.195039	+	0.112606i
$273$		−	1.40996i		−	0.0853348i
$274$	9.46992	+	5.46746i	0.572099	+	0.330301i
$275$	−1.96379	+	3.40139i	−0.118421	+	0.205112i
$276$	0.536215	+	0.309584i	0.0322763	+	0.0186348i
$277$	−12.8451	+	7.41614i	−0.771789	+	0.445593i	−0.833512	−	0.552501i	$-0.813674\pi$
$277$	−12.8451	+	7.41614i	−0.771789	+	0.445593i	0.0617234	+	0.998093i	$0.480340\pi$
$278$	16.1428	−	9.32007i	0.968183	−	0.558981i
$279$	1.45222	+	0.838440i	0.0869421	+	0.0501961i
$280$	0.243282	−	0.421377i	0.0145389	−	0.0251821i
$281$	18.6841	+	10.7872i	1.11460	+	0.643513i	0.940016	−	0.341130i	$-0.110810\pi$
$281$	18.6841	+	10.7872i	1.11460	+	0.643513i	0.174581	+	0.984643i	$0.444143\pi$
$282$			9.69972i			0.577610i
$283$	6.05832	−	3.49777i	0.360130	−	0.207921i	−0.309008	−	0.951059i	$-0.599997\pi$
$283$	6.05832	−	3.49777i	0.360130	−	0.207921i	0.669138	+	0.743138i	$0.266664\pi$
$284$	−1.39033	+	2.40811i	−0.0825007	+	0.142895i
$285$	5.32807			0.315608
$286$	11.3813			0.672992
$287$	−2.34141	+	4.05544i	−0.138209	+	0.239385i
$288$		−	1.00000i		−	0.0589256i
$289$	−1.60202	−	2.77479i	−0.0942367	−	0.163223i
$290$		−	6.39653i		−	0.375617i
$291$	3.43546	−	1.98347i	0.201390	−	0.116273i
$292$	0.482200	+	0.835196i	0.0282186	+	0.0488761i
$293$	10.3100	+	17.8574i	0.602315	+	1.04324i	0.992470	+	0.122491i	$0.0390881\pi$
$293$	10.3100	+	17.8574i	0.602315	+	1.04324i	−0.390155	+	0.920749i	$0.627579\pi$
$294$	5.85715	+	3.38163i	0.341596	+	0.197221i
$295$	4.12478			0.240154
$296$	0.181603	−	6.08005i	0.0105555	−	0.353396i
$297$	3.92759			0.227902
$298$	19.0598	+	11.0042i	1.10410	+	0.637455i
$299$	0.897109	+	1.55384i	0.0518812	+	0.0898608i
$300$	0.500000	+	0.866025i	0.0288675	+	0.0500000i
$301$	0.903071	−	0.521388i	0.0520522	−	0.0300523i
$302$			11.3193i			0.651351i
$303$	−6.56789	−	11.3759i	−0.377315	−	0.653529i
$304$		−	5.32807i		−	0.305586i
$305$	−0.151831	+	0.262978i	−0.00869379	+	0.0150581i
$306$	−3.71429			−0.212332
$307$	−9.52416			−0.543572			−0.271786	−	0.962358i	$-0.587614\pi$
$307$	−9.52416			−0.543572			−0.271786	+	0.962358i	$0.587614\pi$
$308$	0.955512	−	1.65500i	0.0544453	−	0.0943021i
$309$	−13.5465	+	7.82106i	−0.770632	+	0.444925i
$310$			1.67688i			0.0952403i
$311$	9.01824	+	5.20668i	0.511378	+	0.295244i	0.733400	−	0.679798i	$-0.237932\pi$
$311$	9.01824	+	5.20668i	0.511378	+	0.295244i	−0.222022	+	0.975042i	$0.571266\pi$
$312$	1.44890	−	2.50956i	0.0820276	−	0.142076i
$313$	−15.3692	−	8.87342i	−0.868719	−	0.501555i	−0.00179670	−	0.999998i	$-0.500572\pi$
$313$	−15.3692	−	8.87342i	−0.868719	−	0.501555i	−0.866922	+	0.498443i	$0.833905\pi$
$314$	10.1306	−	5.84890i	0.571702	−	0.330072i
$315$	0.421377	−	0.243282i	0.0237419	−	0.0137074i
$316$	7.50415	+	4.33252i	0.422141	+	0.243723i
$317$	15.9690	−	27.6591i	0.896907	−	1.55349i	0.0654815	−	0.997854i	$-0.479142\pi$
$317$	15.9690	−	27.6591i	0.896907	−	1.55349i	0.831426	−	0.555635i	$-0.187525\pi$
$318$	−3.63356	−	2.09784i	−0.203760	−	0.117641i
$319$		−	25.1229i		−	1.40661i
$320$	0.866025	−	0.500000i	0.0484123	−	0.0279508i
$321$	−3.87952	+	6.71952i	−0.216534	+	0.375047i
$322$	0.301265			0.0167888
$323$	−19.7900			−1.10115
$324$	0.500000	−	0.866025i	0.0277778	−	0.0481125i
$325$			2.89779i			0.160741i
$326$	−7.76427	−	13.4481i	−0.430023	−	0.744822i
$327$			5.83635i			0.322751i
$328$	−8.33485	+	4.81213i	−0.460215	+	0.265705i
$329$	2.35977	+	4.08724i	0.130098	+	0.225337i
$330$	1.96379	+	3.40139i	0.108103	+	0.187240i
$331$	−18.0273	−	10.4081i	−0.990870	−	0.572079i	−0.0853357	−	0.996352i	$-0.527196\pi$
$331$	−18.0273	−	10.4081i	−0.990870	−	0.572079i	−0.905534	+	0.424273i	$0.860530\pi$
$332$	−3.59411			−0.197252
$333$	3.19730	−	5.17468i	0.175211	−	0.283571i
$334$	8.43074			0.461310
$335$	1.23555	+	0.713345i	0.0675053	+	0.0389742i
$336$	−0.243282	−	0.421377i	−0.0132721	−	0.0229880i
$337$	2.50724	+	4.34266i	0.136578	+	0.236560i	0.926199	−	0.377035i	$-0.123056\pi$
$337$	2.50724	+	4.34266i	0.136578	+	0.236560i	−0.789621	+	0.613595i	$0.789723\pi$
$338$	−3.98615	+	2.30140i	−0.216818	+	0.125180i
$339$		−	8.20819i		−	0.445808i
$340$	−1.85715	−	3.21667i	−0.100718	−	0.174448i
$341$			6.58609i			0.356657i
$342$	2.66404	−	4.61424i	0.144055	−	0.249510i
$343$	6.69671			0.361588
$344$	2.14314			0.115551
$345$	−0.309584	+	0.536215i	−0.0166674	+	0.0288688i
$346$	−16.9781	+	9.80229i	−0.912746	+	0.526974i
$347$			8.21958i			0.441250i	0.975359	+	0.220625i	$0.0708097\pi$
$347$			8.21958i			0.441250i	−0.975359	+	0.220625i	$0.929190\pi$
$348$	−5.53955	−	3.19826i	−0.296951	−	0.171445i
$349$	−1.17449	+	2.03427i	−0.0628688	+	0.108892i	−0.895747	−	0.444565i	$-0.853358\pi$
$349$	−1.17449	+	2.03427i	−0.0628688	+	0.108892i	0.832878	+	0.553457i	$0.186692\pi$
$350$	0.421377	+	0.243282i	0.0225235	+	0.0130040i
$351$	2.50956	−	1.44890i	0.133950	−	0.0773363i
$352$	3.40139	−	1.96379i	0.181295	−	0.104671i
$353$	25.9556	+	14.9855i	1.38148	+	0.797596i	0.992334	−	0.123581i	$-0.0394380\pi$
$353$	25.9556	+	14.9855i	1.38148	+	0.797596i	0.389143	+	0.921177i	$0.372771\pi$
$354$	2.06239	−	3.57217i	0.109615	−	0.189859i
$355$	−2.40811	−	1.39033i	−0.127809	−	0.0737908i
$356$			7.86585i			0.416889i
$357$	−1.56512	+	0.903620i	−0.0828347	+	0.0478247i
$358$	−2.89881	+	5.02089i	−0.153207	+	0.265362i
$359$	−16.1223			−0.850903			−0.425451	−	0.904981i	$-0.639885\pi$
$359$	−16.1223			−0.850903			−0.425451	+	0.904981i	$0.639885\pi$
$360$	1.00000			0.0527046
$361$	4.69417	−	8.13054i	0.247061	−	0.427923i
$362$		−	2.35629i		−	0.123844i
$363$	2.21297	+	3.83298i	0.116151	+	0.201179i
$364$		−	1.40996i		−	0.0739021i
$365$	−0.835196	+	0.482200i	−0.0437161	+	0.0252395i
$366$	0.151831	+	0.262978i	0.00793631	+	0.0137461i
$367$	−15.2726	−	26.4529i	−0.797224	−	1.38083i	−0.921417	−	0.388574i	$-0.872968\pi$
$367$	−15.2726	−	26.4529i	−0.797224	−	1.38083i	0.124194	−	0.992258i	$-0.460366\pi$
$368$	0.536215	+	0.309584i	0.0279521	+	0.0161382i
$369$	−9.62425			−0.501019
$370$	6.08005	+	0.181603i	0.316087	+	0.00944110i
$371$	−2.04146			−0.105988
$372$	1.45222	+	0.838440i	0.0752941	+	0.0434711i
$373$	2.77228	+	4.80173i	0.143543	+	0.248624i	0.928828	−	0.370510i	$-0.120817\pi$
$373$	2.77228	+	4.80173i	0.143543	+	0.248624i	−0.785285	+	0.619134i	$0.787484\pi$
$374$	−7.29410	−	12.6338i	−0.377169	−	0.653276i
$375$	−0.866025	+	0.500000i	−0.0447214	+	0.0258199i
$376$			9.69972i			0.500225i
$377$	−9.26790	−	16.0525i	−0.477321	−	0.826744i
$378$		−	0.486564i		−	0.0250262i
$379$	11.0220	−	19.0906i	0.566160	−	0.980618i	−0.430781	−	0.902457i	$-0.641762\pi$
$379$	11.0220	−	19.0906i	0.566160	−	0.980618i	0.996941	−	0.0781614i	$-0.0249050\pi$
$380$	5.32807			0.273324
$381$	9.63691			0.493714
$382$	−8.37040	+	14.4980i	−0.428267	+	0.741780i
$383$	−17.4256	+	10.0607i	−0.890408	+	0.514077i	−0.874076	−	0.485790i	$-0.838532\pi$
$383$	−17.4256	+	10.0607i	−0.890408	+	0.514077i	−0.0163318	+	0.999867i	$0.505199\pi$
$384$		−	1.00000i		−	0.0510310i
$385$	1.65500	+	0.955512i	0.0843464	+	0.0486974i
$386$	−12.9750	+	22.4734i	−0.660413	+	1.14387i
$387$	1.85602	+	1.07157i	0.0943466	+	0.0544710i
$388$	3.43546	−	1.98347i	0.174409	−	0.100695i
$389$	12.1360	−	7.00673i	0.615320	−	0.355255i	−0.159724	−	0.987162i	$-0.551061\pi$
$389$	12.1360	−	7.00673i	0.615320	−	0.355255i	0.775045	+	0.631906i	$0.217727\pi$
$390$	2.50956	+	1.44890i	0.127077	+	0.0733677i
$391$	1.14988	−	1.99166i	0.0581521	−	0.100722i
$392$	5.85715	+	3.38163i	0.295831	+	0.170798i
$393$			9.37406i			0.472859i
$394$	−12.5469	+	7.24396i	−0.632104	+	0.364945i
$395$	−4.33252	+	7.50415i	−0.217993	+	0.377575i
$396$	3.92759			0.197369
$397$	−28.6592			−1.43836			−0.719182	−	0.694822i	$-0.755483\pi$
$397$	−28.6592			−1.43836			−0.719182	+	0.694822i	$0.755483\pi$
$398$	9.27325	−	16.0617i	0.464826	−	0.805102i
$399$		−	2.59245i		−	0.129785i
$400$	0.500000	+	0.866025i	0.0250000	+	0.0433013i
$401$			11.1459i			0.556598i	0.960495	+	0.278299i	$0.0897705\pi$
$401$			11.1459i			0.556598i	−0.960495	+	0.278299i	$0.910229\pi$
$402$	1.23555	−	0.713345i	0.0616236	−	0.0355784i
$403$	2.42962	+	4.20823i	0.121028	+	0.209627i
$404$	−6.56789	−	11.3759i	−0.326765	−	0.565973i
$405$	0.866025	+	0.500000i	0.0430331	+	0.0248452i
$406$	−3.11232			−0.154462
$407$	23.8799	+	0.713262i	1.18368	+	0.0353551i
$408$	−3.71429			−0.183885
$409$	−1.79580	−	1.03680i	−0.0887965	−	0.0512667i	0.454944	−	0.890520i	$-0.349659\pi$
$409$	−1.79580	−	1.03680i	−0.0887965	−	0.0512667i	−0.543741	+	0.839253i	$0.682993\pi$
$410$	−4.81213	−	8.33485i	−0.237654	−	0.411629i
$411$	5.46746	+	9.46992i	0.269690	+	0.467117i
$412$	−13.5465	+	7.82106i	−0.667387	+	0.385316i
$413$		−	2.00697i		−	0.0987567i
$414$	0.309584	+	0.536215i	0.0152152	+	0.0263535i
$415$		−	3.59411i		−	0.176428i
$416$	1.44890	−	2.50956i	0.0710379	−	0.123041i
$417$	18.6401			0.912812
$418$	20.9265			1.02355
$419$	16.5281	−	28.6275i	0.807449	−	1.39854i	−0.107175	−	0.994240i	$-0.534181\pi$
$419$	16.5281	−	28.6275i	0.807449	−	1.39854i	0.914625	−	0.404303i	$-0.132486\pi$
$420$	0.421377	−	0.243282i	0.0205611	−	0.0118710i
$421$			5.27415i			0.257046i	0.991707	+	0.128523i	$0.0410236\pi$
$421$			5.27415i			0.257046i	−0.991707	+	0.128523i	$0.958976\pi$
$422$	17.2670	+	9.96912i	0.840546	+	0.485289i
$423$	−4.84986	+	8.40021i	−0.235808	+	0.408432i
$424$	−3.63356	−	2.09784i	−0.176461	−	0.101880i
$425$	3.21667	−	1.85715i	0.156031	−	0.0900848i
$426$	−2.40811	+	1.39033i	−0.116674	+	0.0673615i
$427$	0.127956	+	0.0738753i	0.00619222	+	0.00357508i
$428$	−3.87952	+	6.71952i	−0.187524	+	0.324800i
$429$	9.85652	+	5.69066i	0.475877	+	0.274748i
$430$			2.14314i			0.103352i
$431$	−25.1084	+	14.4964i	−1.20943	+	0.698265i	−0.962635	−	0.270803i	$-0.912711\pi$
$431$	−25.1084	+	14.4964i	−1.20943	+	0.698265i	−0.246795	+	0.969068i	$0.579378\pi$
$432$	0.500000	−	0.866025i	0.0240563	−	0.0416667i
$433$	−9.28816			−0.446360			−0.223180	−	0.974777i	$-0.571644\pi$
$433$	−9.28816			−0.446360			−0.223180	+	0.974777i	$0.571644\pi$
$434$	0.815909			0.0391649
$435$	3.19826	−	5.53955i	0.153345	−	0.265601i
$436$			5.83635i			0.279511i
$437$	1.64948	+	2.85699i	0.0789055	+	0.136668i
$438$			0.964401i			0.0460809i
$439$	−4.78046	+	2.76000i	−0.228159	+	0.131728i	−0.609722	−	0.792615i	$-0.708719\pi$
$439$	−4.78046	+	2.76000i	−0.228159	+	0.131728i	0.381564	+	0.924343i	$0.375386\pi$
$440$	1.96379	+	3.40139i	0.0936202	+	0.162155i
$441$	3.38163	+	5.85715i	0.161030	+	0.278912i
$442$	−9.32124	−	5.38162i	−0.443366	−	0.255977i
$443$	−7.67050			−0.364436			−0.182218	−	0.983258i	$-0.558328\pi$
$443$	−7.67050			−0.364436			−0.182218	+	0.983258i	$0.558328\pi$
$444$	3.19730	−	5.17468i	0.151737	−	0.245579i
$445$	−7.86585			−0.372877
$446$	−7.97911	−	4.60674i	−0.377822	−	0.218136i
$447$	11.0042	+	19.0598i	0.520480	+	0.901497i
$448$	−0.243282	−	0.421377i	−0.0114940	−	0.0199082i
$449$	11.8125	−	6.81994i	0.557466	−	0.321853i	−0.194662	−	0.980870i	$-0.562361\pi$
$449$	11.8125	−	6.81994i	0.557466	−	0.321853i	0.752128	+	0.659017i	$0.229028\pi$
$450$			1.00000i			0.0471405i
$451$	−18.9000	−	32.7358i	−0.889968	−	1.54147i
$452$		−	8.20819i		−	0.386081i
$453$	−5.65964	+	9.80278i	−0.265913	+	0.460575i
$454$	15.8769			0.745142
$455$	1.40996			0.0661000
$456$	2.66404	−	4.61424i	0.124755	−	0.216082i
$457$	−25.6513	+	14.8098i	−1.19992	+	0.692773i	−0.960537	−	0.278152i	$-0.910278\pi$
$457$	−25.6513	+	14.8098i	−1.19992	+	0.692773i	−0.239381	+	0.970926i	$0.576945\pi$
$458$			16.5957i			0.775466i
$459$	−3.21667	−	1.85715i	−0.150141	−	0.0866841i
$460$	−0.309584	+	0.536215i	−0.0144344	+	0.0250011i
$461$	−10.1820	−	5.87858i	−0.474223	−	0.273793i	0.243783	−	0.969830i	$-0.421612\pi$
$461$	−10.1820	−	5.87858i	−0.474223	−	0.273793i	−0.718006	+	0.696037i	$0.754945\pi$
$462$	1.65500	−	0.955512i	0.0769973	−	0.0444544i
$463$	−19.5230	+	11.2716i	−0.907309	+	0.523835i	−0.879564	−	0.475780i	$-0.842166\pi$
$463$	−19.5230	+	11.2716i	−0.907309	+	0.523835i	−0.0277448	+	0.999615i	$0.508833\pi$
$464$	−5.53955	−	3.19826i	−0.257167	−	0.148476i
$465$	−0.838440	+	1.45222i	−0.0388817	+	0.0673451i
$466$	−14.5679	−	8.41081i	−0.674847	−	0.389623i
$467$		−	5.99288i		−	0.277318i	−0.990340	−	0.138659i	$-0.955721\pi$
$467$		−	5.99288i		−	0.277318i	0.990340	−	0.138659i	$-0.0442791\pi$
$468$	2.50956	−	1.44890i	0.116004	−	0.0669752i
$469$	0.347088	−	0.601175i	0.0160270	−	0.0277597i
$470$	−9.69972			−0.447415
$471$	11.6978			0.539006
$472$	2.06239	−	3.57217i	0.0949293	−	0.164422i
$473$			8.41738i			0.387032i
$474$	4.33252	+	7.50415i	0.198999	+	0.344677i
$475$			5.32807i			0.244469i
$476$	−1.56512	+	0.903620i	−0.0717370	+	0.0414174i
$477$	−2.09784	−	3.63356i	−0.0960533	−	0.166369i
$478$	−1.17556	−	2.03613i	−0.0537689	−	0.0931305i
$479$	−19.2188	−	11.0960i	−0.878131	−	0.506989i	−0.00808942	−	0.999967i	$-0.502575\pi$
$479$	−19.2188	−	11.0960i	−0.878131	−	0.506989i	−0.870042	+	0.492978i	$0.835908\pi$
$480$	1.00000			0.0456435
$481$	15.5214	−	8.35361i	0.707714	−	0.380892i
$482$	4.80667			0.218938
$483$	0.260903	+	0.150632i	0.0118715	+	0.00685401i
$484$	2.21297	+	3.83298i	0.100590	+	0.174226i
$485$	1.98347	+	3.43546i	0.0900645	+	0.155996i
$486$	0.866025	−	0.500000i	0.0392837	−	0.0226805i
$487$			37.5580i			1.70191i	0.525235	+	0.850957i	$0.323977\pi$
$487$			37.5580i			1.70191i	−0.525235	+	0.850957i	$0.676023\pi$
$488$	0.151831	+	0.262978i	0.00687305	+	0.0119045i
$489$		−	15.5285i		−	0.702224i
$490$	−3.38163	+	5.85715i	−0.152766	+	0.264599i
$491$	−17.5267			−0.790969			−0.395484	−	0.918473i	$-0.629423\pi$
$491$	−17.5267			−0.790969			−0.395484	+	0.918473i	$0.629423\pi$
$492$	−9.62425			−0.433895
$493$	−11.8793	+	20.5755i	−0.535016	+	0.926674i
$494$	13.3711	−	7.71982i	0.601595	−	0.347331i
$495$			3.92759i			0.176532i
$496$	1.45222	+	0.838440i	0.0652066	+	0.0376470i
$497$	−0.676483	+	1.17170i	−0.0303444	+	0.0525580i
$498$	−3.11259	−	1.79705i	−0.139478	−	0.0805279i
$499$	7.98284	−	4.60889i	0.357361	−	0.206322i	−0.310562	−	0.950553i	$-0.600517\pi$
$499$	7.98284	−	4.60889i	0.357361	−	0.206322i	0.667922	+	0.744231i	$0.267184\pi$
$500$	−0.866025	+	0.500000i	−0.0387298	+	0.0223607i
$501$	7.30124	+	4.21537i	0.326195	+	0.188329i
$502$	10.5450	−	18.2644i	0.470644	−	0.815180i
$503$	−9.76863	−	5.63992i	−0.435562	−	0.251472i	0.266152	−	0.963931i	$-0.414248\pi$
$503$	−9.76863	−	5.63992i	−0.435562	−	0.251472i	−0.701713	+	0.712460i	$0.747581\pi$
$504$		−	0.486564i		−	0.0216733i
$505$	11.3759	−	6.56789i	0.506222	−	0.292267i
$506$	−1.21592	+	2.10603i	−0.0540541	+	0.0936245i
$507$	−4.60281			−0.204418
$508$	9.63691			0.427569
$509$	−3.87195	+	6.70642i	−0.171621	+	0.297257i	−0.938987	−	0.343953i	$-0.888234\pi$
$509$	−3.87195	+	6.70642i	−0.171621	+	0.297257i	0.767365	+	0.641210i	$0.221567\pi$
$510$		−	3.71429i		−	0.164472i
$511$	0.234622	+	0.406376i	0.0103790	+	0.0179770i
$512$		−	1.00000i		−	0.0441942i
$513$	4.61424	−	2.66404i	0.203724	−	0.117620i
$514$	0.620823	+	1.07530i	0.0273833	+	0.0474293i
$515$	−7.82106	−	13.5465i	−0.344637	−	0.596929i
$516$	1.85602	+	1.07157i	0.0817066	+	0.0471733i
$517$	−38.0965			−1.67548
$518$	0.0883616	−	2.95834i	0.00388239	−	0.129982i
$519$	−19.6046			−0.860545
$520$	2.50956	+	1.44890i	0.110052	+	0.0635383i
$521$	−3.98180	−	6.89668i	−0.174446	−	0.302149i	0.765523	−	0.643408i	$-0.222480\pi$
$521$	−3.98180	−	6.89668i	−0.174446	−	0.302149i	−0.939969	+	0.341259i	$0.889147\pi$
$522$	−3.19826	−	5.53955i	−0.139984	−	0.242460i
$523$	4.85120	−	2.80084i	0.212128	−	0.122472i	−0.390172	−	0.920742i	$-0.627584\pi$
$523$	4.85120	−	2.80084i	0.212128	−	0.122472i	0.602300	+	0.798270i	$0.294251\pi$
$524$			9.37406i			0.409508i
$525$	0.243282	+	0.421377i	0.0106177	+	0.0183904i
$526$		−	11.7703i		−	0.513208i
$527$	3.11421	−	5.39397i	0.135657	−	0.234965i
$528$	3.92759			0.170926
$529$	22.6166			0.983332
$530$	2.09784	−	3.63356i	0.0911242	−	0.157832i
$531$	3.57217	−	2.06239i	0.155019	−	0.0895002i
$532$		−	2.59245i		−	0.112397i
$533$	−24.1526	−	13.9445i	−1.04617	−	0.604005i
$534$	−3.93292	+	6.81203i	−0.170194	+	0.294785i
$535$	−6.71952	−	3.87952i	−0.290510	−	0.167726i
$536$	1.23555	−	0.713345i	0.0533676	−	0.0308118i
$537$	−5.02089	+	2.89881i	−0.216668	+	0.125093i
$538$	10.5683	+	6.10158i	0.455630	+	0.263058i
$539$	−13.2816	+	23.0045i	−0.572081	+	0.990873i
$540$	0.866025	+	0.500000i	0.0372678	+	0.0215166i
$541$			37.9846i			1.63309i	0.577284	+	0.816544i	$0.304113\pi$
$541$			37.9846i			1.63309i	−0.577284	+	0.816544i	$0.695887\pi$
$542$	−0.234255	+	0.135247i	−0.0100621	+	0.00580937i
$543$	1.17814	−	2.04061i	0.0505590	−	0.0875708i
$544$	−3.71429			−0.159249
$545$	−5.83635			−0.250002
$546$	0.704981	−	1.22106i	0.0301704	−	0.0522566i
$547$		−	4.29803i		−	0.183770i	−0.995770	−	0.0918852i	$-0.970711\pi$
$547$		−	4.29803i		−	0.183770i	0.995770	−	0.0918852i	$-0.0292893\pi$
$548$	5.46746	+	9.46992i	0.233558	+	0.404535i
$549$			0.303661i			0.0129599i
$550$	−3.40139	+	1.96379i	−0.145036	+	0.0837365i
$551$	−17.0406	−	29.5151i	−0.725953	−	1.25739i
$552$	0.309584	+	0.536215i	0.0131768	+	0.0228228i
$553$	3.65125	+	2.10805i	0.155267	+	0.0896434i
$554$	−14.8323			−0.630163
$555$	5.17468	+	3.19730i	0.219653	+	0.135718i
$556$	18.6401			0.790518
$557$	3.26912	+	1.88743i	0.138517	+	0.0799729i	0.567657	−	0.823265i	$-0.307850\pi$
$557$	3.26912	+	1.88743i	0.138517	+	0.0799729i	−0.429140	+	0.903238i	$0.641183\pi$
$558$	0.838440	+	1.45222i	0.0354940	+	0.0614774i
$559$	3.10519	+	5.37835i	0.131336	+	0.227480i
$560$	0.421377	−	0.243282i	0.0178064	−	0.0102805i
$561$		−	14.5882i		−	0.615914i
$562$	10.7872	+	18.6841i	0.455032	+	0.788139i
$563$		−	14.0752i		−	0.593199i	−0.955002	−	0.296599i	$-0.904147\pi$
$563$		−	14.0752i		−	0.593199i	0.955002	−	0.296599i	$-0.0958526\pi$
$564$	−4.84986	+	8.40021i	−0.204216	+	0.353713i
$565$	8.20819			0.345321
$566$	6.99555			0.294045
$567$	0.243282	−	0.421377i	0.0102169	−	0.0176962i
$568$	−2.40811	+	1.39033i	−0.101042	+	0.0583368i
$569$		−	32.4515i		−	1.36044i	−0.733010	−	0.680218i	$-0.761885\pi$
$569$		−	32.4515i		−	1.36044i	0.733010	−	0.680218i	$-0.238115\pi$
$570$	4.61424	+	2.66404i	0.193269	+	0.111584i
$571$	22.0773	−	38.2390i	0.923905	−	1.60025i	0.130593	−	0.991436i	$-0.458312\pi$
$571$	22.0773	−	38.2390i	0.923905	−	1.60025i	0.793312	−	0.608815i	$-0.208355\pi$
$572$	9.85652	+	5.69066i	0.412122	+	0.237939i
$573$	−14.4980	+	8.37040i	−0.605661	+	0.349678i
$574$	−4.05544	+	2.34141i	−0.169271	+	0.0977285i
$575$	−0.536215	−	0.309584i	−0.0223617	−	0.0129105i
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$	−19.4333	−	11.2198i	−0.809017	−	0.467086i	0.0375971	−	0.999293i	$-0.488030\pi$
$577$	−19.4333	−	11.2198i	−0.809017	−	0.467086i	−0.846615	+	0.532207i	$0.821363\pi$
$578$		−	3.20405i		−	0.133271i
$579$	−22.4734	+	12.9750i	−0.933964	+	0.539225i
$580$	3.19826	−	5.53955i	0.132801	−	0.230017i
$581$	−1.74876			−0.0725510
$582$	3.96693			0.164435
$583$	8.23943	−	14.2711i	0.341242	−	0.591049i
$584$			0.964401i			0.0399072i
$585$	1.44890	+	2.50956i	0.0599045	+	0.103758i
$586$			20.6199i			0.851802i
$587$	13.6187	−	7.86277i	0.562104	−	0.324531i	−0.191885	−	0.981417i	$-0.561460\pi$
$587$	13.6187	−	7.86277i	0.562104	−	0.324531i	0.753990	+	0.656886i	$0.228127\pi$
$588$	3.38163	+	5.85715i	0.139456	+	0.241545i
$589$	4.46726	+	7.73753i	0.184070	+	0.318819i
$590$	3.57217	+	2.06239i	0.147064	+	0.0849073i
$591$	−14.4879			−0.595953
$592$	3.19730	−	5.17468i	0.131408	−	0.212678i
$593$	−11.0609			−0.454216			−0.227108	−	0.973870i	$-0.572927\pi$
$593$	−11.0609			−0.454216			−0.227108	+	0.973870i	$0.572927\pi$
$594$	3.40139	+	1.96379i	0.139561	+	0.0805754i
$595$	−0.903620	−	1.56512i	−0.0370448	−	0.0641635i
$596$	11.0042	+	19.0598i	0.450749	+	0.780720i
$597$	16.0617	−	9.27325i	0.657363	−	0.379529i
$598$			1.79422i			0.0733711i
$599$	4.07384	+	7.05609i	0.166452	+	0.288304i	0.937170	−	0.348873i	$-0.113435\pi$
$599$	4.07384	+	7.05609i	0.166452	+	0.288304i	−0.770718	+	0.637177i	$0.780102\pi$
$600$			1.00000i			0.0408248i
$601$	−15.1490	+	26.2389i	−0.617942	+	1.07031i	0.371918	+	0.928265i	$0.378700\pi$
$601$	−15.1490	+	26.2389i	−0.617942	+	1.07031i	−0.989861	+	0.142042i	$0.954633\pi$
$602$	1.04278			0.0425004
$603$	1.42669			0.0580993
$604$	−5.65964	+	9.80278i	−0.230287	+	0.398870i
$605$	−3.83298	+	2.21297i	−0.155833	+	0.0899701i
$606$		−	13.1358i		−	0.533604i
$607$	−7.88137	−	4.55031i	−0.319895	−	0.184692i	0.331451	−	0.943473i	$-0.392462\pi$
$607$	−7.88137	−	4.55031i	−0.319895	−	0.184692i	−0.651346	+	0.758781i	$0.725795\pi$
$608$	2.66404	−	4.61424i	0.108041	−	0.187132i
$609$	−2.69535	−	1.55616i	−0.109221	−	0.0630588i
$610$	−0.262978	+	0.151831i	−0.0106477	+	0.00614744i
$611$	−24.3420	+	14.0539i	−0.984774	+	0.568559i
$612$	−3.21667	−	1.85715i	−0.130026	−	0.0750706i
$613$	−0.0517598	+	0.0896506i	−0.00209056	+	0.00362095i	−0.867069	−	0.498188i	$-0.833999\pi$
$613$	−0.0517598	+	0.0896506i	−0.00209056	+	0.00362095i	0.864978	+	0.501809i	$0.167332\pi$
$614$	−8.24816	−	4.76208i	−0.332869	−	0.192182i
$615$		−	9.62425i		−	0.388087i
$616$	1.65500	−	0.955512i	0.0666817	−	0.0384987i
$617$	−23.6061	+	40.8869i	−0.950345	+	1.64605i	−0.205667	+	0.978622i	$0.565937\pi$
$617$	−23.6061	+	40.8869i	−0.950345	+	1.64605i	−0.744678	+	0.667424i	$0.767397\pi$
$618$	−15.6421			−0.629219
$619$	−14.3938			−0.578537			−0.289268	−	0.957248i	$-0.593412\pi$
$619$	−14.3938			−0.578537			−0.289268	+	0.957248i	$0.593412\pi$
$620$	−0.838440	+	1.45222i	−0.0336725	+	0.0583226i
$621$			0.619168i			0.0248463i
$622$	5.20668	+	9.01824i	0.208769	+	0.361599i
$623$			3.82724i			0.153335i
$624$	2.50956	−	1.44890i	0.100463	−	0.0580022i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−8.87342	−	15.3692i	−0.354653	−	0.614277i
$627$	18.1228	+	10.4632i	0.723757	+	0.417861i
$628$	11.6978			0.466793
$629$	−19.2203	−	11.8757i	−0.766362	−	0.473515i
$630$	0.486564			0.0193852
$631$	17.6927	+	10.2149i	0.704336	+	0.406648i	0.808960	−	0.587863i	$-0.200031\pi$
$631$	17.6927	+	10.2149i	0.704336	+	0.406648i	−0.104624	+	0.994512i	$0.533364\pi$
$632$	4.33252	+	7.50415i	0.172338	+	0.298499i
$633$	9.96912	+	17.2670i	0.396237	+	0.686303i
$634$	27.6591	−	15.9690i	1.09848	−	0.634209i
$635$			9.63691i			0.382429i
$636$	−2.09784	−	3.63356i	−0.0831846	−	0.144080i
$637$			19.5985i			0.776521i
$638$	12.5615	−	21.7571i	0.497313	−	0.861371i
$639$	−2.78065			−0.110001
$640$	1.00000			0.0395285
$641$	16.3817	−	28.3739i	0.647037	−	1.12070i	−0.336790	−	0.941580i	$-0.609341\pi$
$641$	16.3817	−	28.3739i	0.647037	−	1.12070i	0.983827	−	0.179121i	$-0.0573253\pi$
$642$	−6.71952	+	3.87952i	−0.265198	+	0.153112i
$643$		−	8.08539i		−	0.318857i	−0.987210	−	0.159428i	$-0.949035\pi$
$643$		−	8.08539i		−	0.318857i	0.987210	−	0.159428i	$-0.0509651\pi$
$644$	0.260903	+	0.150632i	0.0102810	+	0.00593575i
$645$	−1.07157	+	1.85602i	−0.0421931	+	0.0730806i
$646$	−17.1386	−	9.89500i	−0.674311	−	0.389314i
$647$	−35.4812	+	20.4851i	−1.39491	+	0.805353i	−0.993854	−	0.110700i	$-0.964691\pi$
$647$	−35.4812	+	20.4851i	−1.39491	+	0.805353i	−0.401058	+	0.916053i	$0.631357\pi$
$648$	0.866025	−	0.500000i	0.0340207	−	0.0196419i
$649$	14.0300	+	8.10023i	0.550726	+	0.317962i
$650$	−1.44890	+	2.50956i	−0.0568304	+	0.0984331i
$651$	0.706598	+	0.407955i	0.0276938	+	0.0159890i
$652$		−	15.5285i		−	0.608144i
$653$	−16.4490	+	9.49683i	−0.643699	+	0.371640i	−0.786038	−	0.618178i	$-0.787871\pi$
$653$	−16.4490	+	9.49683i	−0.643699	+	0.371640i	0.142339	+	0.989818i	$0.454538\pi$
$654$	−2.91818	+	5.05443i	−0.114110	+	0.197644i
$655$	−9.37406			−0.366275
$656$	−9.62425			−0.375764
$657$	−0.482200	+	0.835196i	−0.0188124	+	0.0325841i
$658$			4.71954i			0.183987i
$659$	−5.24714	−	9.08831i	−0.204400	−	0.354030i	0.745542	−	0.666459i	$-0.232191\pi$
$659$	−5.24714	−	9.08831i	−0.204400	−	0.354030i	−0.949941	+	0.312429i	$0.898858\pi$
$660$			3.92759i			0.152881i
$661$	28.5631	−	16.4909i	1.11098	−	0.641423i	0.171895	−	0.985115i	$-0.445011\pi$
$661$	28.5631	−	16.4909i	1.11098	−	0.641423i	0.939082	+	0.343692i	$0.111678\pi$
$662$	−10.4081	−	18.0273i	−0.404521	−	0.700651i
$663$	−5.38162	−	9.32124i	−0.209005	−	0.362007i
$664$	−3.11259	−	1.79705i	−0.120792	−	0.0697392i
$665$	2.59245			0.100531
$666$	5.35628	−	2.88275i	0.207552	−	0.111704i
$667$	3.96052			0.153352
$668$	7.30124	+	4.21537i	0.282493	+	0.163098i
$669$	−4.60674	−	7.97911i	−0.178107	−	0.308490i
$670$	0.713345	+	1.23555i	0.0275589	+	0.0477335i
$671$	−1.03287	+	0.596328i	−0.0398735	+	0.0230210i
$672$		−	0.486564i		−	0.0187696i
$673$	8.85403	+	15.3356i	0.341298	+	0.591145i	0.984674	−	0.174405i	$-0.0558003\pi$
$673$	8.85403	+	15.3356i	0.341298	+	0.591145i	−0.643376	+	0.765550i	$0.722467\pi$
$674$			5.01448i			0.193150i
$675$	−0.500000	+	0.866025i	−0.0192450	+	0.0333333i
$676$	−4.60281			−0.177031
$677$	9.67072			0.371676			0.185838	−	0.982580i	$-0.440500\pi$
$677$	9.67072			0.371676			0.185838	+	0.982580i	$0.440500\pi$
$678$	4.10409	−	7.10850i	0.157617	−	0.273000i
$679$	1.67157	−	0.965083i	0.0641491	−	0.0370365i
$680$		−	3.71429i		−	0.142437i
$681$	13.7498	+	7.93847i	0.526895	+	0.304203i
$682$	−3.29304	+	5.70372i	−0.126097	+	0.218407i
$683$	−17.6117	−	10.1681i	−0.673892	−	0.389072i	0.123658	−	0.992325i	$-0.460537\pi$
$683$	−17.6117	−	10.1681i	−0.673892	−	0.389072i	−0.797550	+	0.603253i	$0.793871\pi$
$684$	4.61424	−	2.66404i	0.176430	−	0.101862i
$685$	−9.46992	+	5.46746i	−0.361827	+	0.208901i
$686$	5.79952	+	3.34835i	0.221427	+	0.127841i
$687$	−8.29785	+	14.3723i	−0.316583	+	0.548337i
$688$	1.85602	+	1.07157i	0.0707600	+	0.0408533i
$689$		−	12.1582i		−	0.463190i
$690$	−0.536215	+	0.309584i	−0.0204134	+	0.0117857i
$691$	4.62514	−	8.01097i	0.175948	−	0.304752i	−0.764541	−	0.644576i	$-0.777034\pi$
$691$	4.62514	−	8.01097i	0.175948	−	0.304752i	0.940489	+	0.339824i	$0.110367\pi$
$692$	−19.6046			−0.745254
$693$	1.91102			0.0725938
$694$	−4.10979	+	7.11836i	−0.156005	+	0.270209i
$695$			18.6401i			0.707061i
$696$	−3.19826	−	5.53955i	−0.121230	−	0.209976i
$697$			35.7473i			1.35402i
$698$	−2.03427	+	1.17449i	−0.0769983	+	0.0444550i
$699$	−8.41081	−	14.5679i	−0.318126	−	0.551010i
$700$	0.243282	+	0.421377i	0.00919520	+	0.0159266i
$701$	−21.3846	−	12.3464i	−0.807684	−	0.466316i	0.0384672	−	0.999260i	$-0.487753\pi$
$701$	−21.3846	−	12.3464i	−0.807684	−	0.466316i	−0.846151	+	0.532943i	$0.821086\pi$
$702$	2.89779			0.109370
$703$	28.5386	−	15.3595i	1.07636	−	0.579295i
$704$	3.92759			0.148027
$705$	−8.40021	−	4.84986i	−0.316370	−	0.182656i
$706$	14.9855	+	25.9556i	0.563986	+	0.976852i
$707$	−3.19570	−	5.53511i	−0.120187	−	0.208169i
$708$	3.57217	−	2.06239i	0.134250	−	0.0775094i
$709$			32.2139i			1.20982i	0.796294	+	0.604910i	$0.206791\pi$
$709$			32.2139i			1.20982i	−0.796294	+	0.604910i	$0.793209\pi$
$710$	−1.39033	−	2.40811i	−0.0521780	−	0.0903749i
$711$			8.66504i			0.324965i
$712$	−3.93292	+	6.81203i	−0.147393	+	0.255291i
$713$	−1.03827			−0.0388835
$714$	−1.80724			−0.0676343
$715$	−5.69066	+	9.85652i	−0.212819	+	0.368613i
$716$	−5.02089	+	2.89881i	−0.187640	+	0.108334i
$717$		−	2.35112i		−	0.0878043i
$718$	−13.9623	−	8.06115i	−0.521069	−	0.300840i
$719$	−16.2324	+	28.1154i	−0.605367	+	1.04853i	0.386626	+	0.922237i	$0.373640\pi$
$719$	−16.2324	+	28.1154i	−0.605367	+	1.04853i	−0.991993	+	0.126291i	$0.959693\pi$
$720$	0.866025	+	0.500000i	0.0322749	+	0.0186339i
$721$	−6.59123	+	3.80545i	−0.245470	+	0.141722i
$722$	8.13054	−	4.69417i	0.302587	−	0.174699i
$723$	4.16270	+	2.40334i	0.154813	+	0.0893811i
$724$	1.17814	−	2.04061i	0.0437854	−	0.0758385i
$725$	5.53955	+	3.19826i	0.205734	+	0.118781i
$726$			4.42595i			0.164262i
$727$	−10.5216	+	6.07467i	−0.390226	+	0.225297i	−0.682258	−	0.731111i	$-0.739002\pi$
$727$	−10.5216	+	6.07467i	−0.390226	+	0.225297i	0.292032	+	0.956409i	$0.405669\pi$
$728$	0.704981	−	1.22106i	0.0261283	−	0.0452556i
$729$	1.00000			0.0370370
$730$	−0.964401			−0.0356941
$731$	3.98013	−	6.89378i	0.147210	−	0.254976i
$732$			0.303661i			0.0112236i
$733$	−1.24546	−	2.15721i	−0.0460023	−	0.0796783i	0.842107	−	0.539310i	$-0.181315\pi$
$733$	−1.24546	−	2.15721i	−0.0460023	−	0.0796783i	−0.888110	+	0.459632i	$0.847981\pi$
$734$		−	30.5452i		−	1.12744i
$735$	−5.85715	+	3.38163i	−0.216044	+	0.124733i
$736$	0.309584	+	0.536215i	0.0114114	+	0.0197651i
$737$	2.80173	+	4.85273i	0.103203	+	0.178753i
$738$	−8.33485	−	4.81213i	−0.306810	−	0.177137i
$739$	24.5537			0.903223			0.451611	−	0.892215i	$-0.350849\pi$
$739$	24.5537			0.903223			0.451611	+	0.892215i	$0.350849\pi$
$740$	5.17468	+	3.19730i	0.190225	+	0.117535i
$741$	15.4396			0.567189
$742$	−1.76796	−	1.02073i	−0.0649038	−	0.0374722i
$743$	−22.1669	−	38.3941i	−0.813224	−	1.40854i	−0.910597	−	0.413296i	$-0.864377\pi$
$743$	−22.1669	−	38.3941i	−0.813224	−	1.40854i	0.0973730	−	0.995248i	$-0.468956\pi$
$744$	0.838440	+	1.45222i	0.0307387	+	0.0532410i
$745$	−19.0598	+	11.0042i	−0.698297	+	0.403162i
$746$			5.54456i			0.203001i
$747$	−1.79705	−	3.11259i	−0.0657508	−	0.113884i
$748$		−	14.5882i		−	0.533397i
$749$	−1.88763	+	3.26948i	−0.0689727	+	0.119464i
$750$	−1.00000			−0.0365148
$751$	14.9997			0.547346			0.273673	−	0.961823i	$-0.411761\pi$
$751$	14.9997			0.547346			0.273673	+	0.961823i	$0.411761\pi$
$752$	−4.84986	+	8.40021i	−0.176856	+	0.306324i
$753$	18.2644	−	10.5450i	0.665592	−	0.384280i
$754$		−	18.5358i		−	0.675034i
$755$	−9.80278	−	5.65964i	−0.356760	−	0.205975i
$756$	0.243282	−	0.421377i	0.00884809	−	0.0153253i
$757$	−31.0416	−	17.9219i	−1.12823	−	0.651381i	−0.184737	−	0.982788i	$-0.559143\pi$
$757$	−31.0416	−	17.9219i	−1.12823	−	0.651381i	−0.943488	+	0.331407i	$0.892477\pi$
$758$	19.0906	−	11.0220i	0.693402	−	0.400336i
$759$	−2.10603	+	1.21592i	−0.0764441	+	0.0441350i
$760$	4.61424	+	2.66404i	0.167376	+	0.0966347i
$761$	17.0485	−	29.5289i	0.618008	−	1.07042i	−0.371841	−	0.928297i	$-0.621273\pi$
$761$	17.0485	−	29.5289i	0.618008	−	1.07042i	0.989849	−	0.142125i	$-0.0453935\pi$
$762$	8.34580	+	4.81845i	0.302337	+	0.174554i
$763$			2.83976i			0.102806i
$764$	−14.4980	+	8.37040i	−0.524517	+	0.302830i
$765$	1.85715	−	3.21667i	0.0671452	−	0.116299i
$766$	−20.1214			−0.727015
$767$	11.9528			0.431589
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$			2.83002i			0.102053i	0.998697	+	0.0510266i	$0.0162493\pi$
$769$			2.83002i			0.102053i	−0.998697	+	0.0510266i	$0.983751\pi$
$770$	0.955512	+	1.65500i	0.0344343	+	0.0596419i
$771$			1.24165i			0.0447168i
$772$	−22.4734	+	12.9750i	−0.808837	+	0.466982i
$773$	−3.16209	−	5.47691i	−0.113733	−	0.196991i	0.803540	−	0.595251i	$-0.202947\pi$
$773$	−3.16209	−	5.47691i	−0.113733	−	0.196991i	−0.917272	+	0.398260i	$0.869614\pi$
$774$	1.07157	+	1.85602i	0.0385168	+	0.0667131i
$775$	−1.45222	−	0.838440i	−0.0521653	−	0.0301176i
$776$	3.96693			0.142405
$777$	1.55569	−	2.51781i	0.0558101	−	0.0903260i
$778$	14.0135			0.502407
$779$	−44.4086	−	25.6393i	−1.59111	−	0.918625i
$780$	1.44890	+	2.50956i	0.0518788	+	0.0898567i
$781$	−5.46063	−	9.45808i	−0.195397	−	0.338437i
$782$	1.99166	−	1.14988i	0.0712215	−	0.0411198i
$783$		−	6.39653i		−	0.228593i
$784$	3.38163	+	5.85715i	0.120772	+	0.209184i
$785$			11.6978i			0.417512i
$786$	−4.68703	+	8.11818i	−0.167181	+	0.289566i
$787$	36.2186			1.29105			0.645526	−	0.763738i	$-0.276638\pi$
$787$	36.2186			1.29105			0.645526	+	0.763738i	$0.276638\pi$
$788$	−14.4879			−0.516111
$789$	5.88514	−	10.1934i	0.209516	−	0.362893i
$790$	−7.50415	+	4.33252i	−0.266986	+	0.154144i
$791$		−	3.99381i		−	0.142004i
$792$	3.40139	+	1.96379i	0.120863	+	0.0697804i
$793$	−0.439973	+	0.762056i	−0.0156239	+	0.0270614i
$794$	−24.8196	−	14.3296i	−0.880814	−	0.508538i
$795$	3.63356	−	2.09784i	0.128869	−	0.0744026i
$796$	16.0617	−	9.27325i	0.569293	−	0.328682i
$797$	40.1554	+	23.1837i	1.42238	+	0.821210i	0.996502	−	0.0835724i	$-0.0266330\pi$
$797$	40.1554	+	23.1837i	1.42238	+	0.821210i	0.425875	+	0.904782i	$0.359966\pi$
$798$	1.29622	−	2.24513i	0.0458858	−	0.0794766i
$799$	31.2008	+	18.0138i	1.10381	+	0.637282i
$800$			1.00000i			0.0353553i
$801$	−6.81203	+	3.93292i	−0.240691	+	0.138963i
$802$	−5.57293	+	9.65260i	−0.196787	+	0.340845i
$803$	−3.78777			−0.133667
$804$	1.42669			0.0503155
$805$	−0.150632	+	0.260903i	−0.00530910	+	0.00919562i
$806$			4.85925i			0.171160i
$807$	6.10158	+	10.5683i	0.214786	+	0.372020i
$808$		−	13.1358i		−	0.462115i
$809$	−12.5702	+	7.25741i	−0.441945	+	0.255157i	−0.704422	−	0.709781i	$-0.748794\pi$
$809$	−12.5702	+	7.25741i	−0.441945	+	0.255157i	0.262478	+	0.964938i	$0.415460\pi$
$810$	0.500000	+	0.866025i	0.0175682	+	0.0304290i
$811$	−8.56867	−	14.8414i	−0.300887	−	0.521151i	0.675450	−	0.737405i	$-0.263949\pi$
$811$	−8.56867	−	14.8414i	−0.300887	−	0.521151i	−0.976337	+	0.216254i	$0.930616\pi$
$812$	−2.69535	−	1.55616i	−0.0945882	−	0.0546105i
$813$	−0.270495			−0.00948667
$814$	20.3240	+	12.5577i	0.712356	+	0.440146i
$815$	15.5285			0.543941
$816$	−3.21667	−	1.85715i	−0.112606	−	0.0650131i
$817$	5.70941	+	9.88899i	0.199747	+	0.345972i
$818$	−1.03680	−	1.79580i	−0.0362510	−	0.0627886i
$819$	1.22106	−	0.704981i	0.0426674	−	0.0246340i
$820$		−	9.62425i		−	0.336093i
$821$	−15.1681	−	26.2719i	−0.529370	−	0.916896i	−0.999413	−	0.0342527i	$-0.989095\pi$
$821$	−15.1681	−	26.2719i	−0.529370	−	0.916896i	0.470043	−	0.882644i	$-0.344238\pi$
$822$			10.9349i			0.381399i
$823$	20.2199	−	35.0219i	0.704822	−	1.22079i	−0.261933	−	0.965086i	$-0.584360\pi$
$823$	20.2199	−	35.0219i	0.704822	−	1.22079i	0.966756	−	0.255702i	$-0.0823067\pi$
$824$	−15.6421			−0.544919
$825$	−3.92759			−0.136741
$826$	1.00349	−	1.73809i	0.0349158	−	0.0604759i
$827$	−6.31821	+	3.64782i	−0.219706	+	0.126847i	−0.605814	−	0.795606i	$-0.707152\pi$
$827$	−6.31821	+	3.64782i	−0.219706	+	0.126847i	0.386108	+	0.922453i	$0.373819\pi$
$828$			0.619168i			0.0215176i
$829$	14.5355	+	8.39207i	0.504838	+	0.291469i	0.730709	−	0.682689i	$-0.239189\pi$
$829$	14.5355	+	8.39207i	0.504838	+	0.291469i	−0.225871	+	0.974157i	$0.572523\pi$
$830$	1.79705	−	3.11259i	0.0623767	−	0.108040i
$831$	−12.8451	−	7.41614i	−0.445593	−	0.257263i
$832$	2.50956	−	1.44890i	0.0870034	−	0.0502314i
$833$	21.7552	−	12.5603i	0.753772	−	0.435190i
$834$	16.1428	+	9.32007i	0.558981	+	0.322728i
$835$	−4.21537	+	7.30124i	−0.145879	+	0.252670i
$836$	18.1228	+	10.4632i	0.626792	+	0.361878i
$837$			1.67688i			0.0579614i
$838$	28.6275	−	16.5281i	0.988920	−	0.570953i
$839$	−16.8525	+	29.1894i	−0.581812	+	1.00773i	0.413452	+	0.910526i	$0.364323\pi$
$839$	−16.8525	+	29.1894i	−0.581812	+	1.00773i	−0.995265	+	0.0972026i	$0.969011\pi$
$840$	0.486564			0.0167881
$841$	−11.9155			−0.410881
$842$	−2.63707	+	4.56754i	−0.0908795	+	0.157408i
$843$			21.5745i			0.743065i
$844$	9.96912	+	17.2670i	0.343151	+	0.594355i
$845$		−	4.60281i		−	0.158341i
$846$	−8.40021	+	4.84986i	−0.288805	+	0.166742i
$847$	1.07675	+	1.86499i	0.0369977	+	0.0640819i
$848$	−2.09784	−	3.63356i	−0.0720400	−	0.124777i
$849$	6.05832	+	3.49777i	0.207921	+	0.120043i
$850$	3.71429			0.127399
$851$	−0.112443	+	3.76457i	−0.00385449	+	0.129048i
$852$	−2.78065			−0.0952635
$853$	−26.2043	−	15.1291i	−0.897218	−	0.518009i	−0.0209214	−	0.999781i	$-0.506660\pi$
$853$	−26.2043	−	15.1291i	−0.897218	−	0.518009i	−0.876297	+	0.481772i	$0.839993\pi$
$854$	0.0738753	+	0.127956i	0.00252796	+	0.00437856i
$855$	2.66404	+	4.61424i	0.0911081	+	0.157804i
$856$	−6.71952	+	3.87952i	−0.229669	+	0.132599i
$857$		−	32.6455i		−	1.11515i	−0.830127	−	0.557574i	$-0.811732\pi$
$857$		−	32.6455i		−	1.11515i	0.830127	−	0.557574i	$-0.188268\pi$
$858$	5.69066	+	9.85652i	0.194276	+	0.336496i
$859$			25.4385i			0.867950i	0.900925	+	0.433975i	$0.142889\pi$
$859$			25.4385i			0.867950i	−0.900925	+	0.433975i	$0.857111\pi$
$860$	−1.07157	+	1.85602i	−0.0365403	+	0.0632896i
$861$	−4.68282			−0.159590
$862$	−28.9927			−0.987496
$863$	−19.0918	+	33.0680i	−0.649894	+	1.12565i	0.333254	+	0.942837i	$0.391853\pi$
$863$	−19.0918	+	33.0680i	−0.649894	+	1.12565i	−0.983148	+	0.182812i	$0.941480\pi$
$864$	0.866025	−	0.500000i	0.0294628	−	0.0170103i
$865$		−	19.6046i		−	0.666576i
$866$	−8.04378	−	4.64408i	−0.273339	−	0.157812i
$867$	1.60202	−	2.77479i	0.0544076	−	0.0942367i
$868$	0.706598	+	0.407955i	0.0239835	+	0.0138469i
$869$	−29.4732	+	17.0164i	−0.999810	+	0.577240i
$870$	5.53955	−	3.19826i	0.187808	−	0.108431i
$871$	3.58037	+	2.06713i	0.121316	+	0.0700419i
$872$	−2.91818	+	5.05443i	−0.0988219	+	0.171165i
$873$	3.43546	+	1.98347i	0.116273	+	0.0671301i
$874$			3.29897i			0.111589i
$875$	−0.421377	+	0.243282i	−0.0142451	+	0.00822444i
$876$	−0.482200	+	0.835196i	−0.0162920	+	0.0282186i
$877$	29.8318			1.00735			0.503675	−	0.863893i	$-0.331981\pi$
$877$	29.8318			1.00735			0.503675	+	0.863893i	$0.331981\pi$
$878$	−5.52000			−0.186291
$879$	−10.3100	+	17.8574i	−0.347747	+	0.602315i
$880$			3.92759i			0.132399i
$881$	1.07347	+	1.85931i	0.0361663	+	0.0626418i	0.883542	−	0.468352i	$-0.155152\pi$
$881$	1.07347	+	1.85931i	0.0361663	+	0.0626418i	−0.847376	+	0.530994i	$0.821819\pi$
$882$			6.76326i			0.227731i
$883$	17.6797	−	10.2074i	0.594969	−	0.343506i	−0.172091	−	0.985081i	$-0.555052\pi$
$883$	17.6797	−	10.2074i	0.594969	−	0.343506i	0.767060	+	0.641575i	$0.221719\pi$
$884$	−5.38162	−	9.32124i	−0.181003	−	0.313507i
$885$	2.06239	+	3.57217i	0.0693266	+	0.120077i
$886$	−6.64285	−	3.83525i	−0.223171	−	0.128848i
$887$	36.0747			1.21127			0.605635	−	0.795743i	$-0.292919\pi$
$887$	36.0747			1.21127			0.605635	+	0.795743i	$0.292919\pi$
$888$	5.35628	−	2.88275i	0.179745	−	0.0967388i
$889$	4.68897			0.157263
$890$	−6.81203	−	3.93292i	−0.228340	−	0.131832i
$891$	1.96379	+	3.40139i	0.0657896	+	0.113951i
$892$	−4.60674	−	7.97911i	−0.154245	−	0.267161i
$893$	−44.7569	+	25.8404i	−1.49773	+	0.864716i
$894$			22.0084i			0.736070i
$895$	−2.89881	−	5.02089i	−0.0968967	−	0.167830i
$896$		−	0.486564i		−	0.0162550i
$897$	−0.897109	+	1.55384i	−0.0299536	+	0.0518812i
$898$	13.6399			0.455169
$899$	10.7262			0.357739
$900$	−0.500000	+	0.866025i	−0.0166667	+	0.0288675i
$901$	−13.4961	+	7.79197i	−0.449620	+	0.259588i
$902$		−	37.8001i		−	1.25861i
$903$	0.903071	+	0.521388i	0.0300523	+	0.0173507i
$904$	4.10409	−	7.10850i	0.136500	−	0.236425i
$905$	2.04061	+	1.17814i	0.0678320	+	0.0391628i
$906$	−9.80278	+	5.65964i	−0.325676	+	0.188029i
$907$	−21.3925	+	12.3509i	−0.710325	+	0.410106i	−0.811181	−	0.584795i	$-0.801175\pi$
$907$	−21.3925	+	12.3509i	−0.710325	+	0.410106i	0.100856	+	0.994901i	$0.467842\pi$
$908$	13.7498	+	7.93847i	0.456304	+	0.263447i
$909$	6.56789	−	11.3759i	0.217843	−	0.377315i
$910$	1.22106	+	0.704981i	0.0404778	+	0.0233699i
$911$			8.44643i			0.279843i	0.990163	+	0.139921i	$0.0446850\pi$
$911$			8.44643i			0.279843i	−0.990163	+	0.139921i	$0.955315\pi$
$912$	4.61424	−	2.66404i	0.152793	−	0.0882150i
$913$	7.05809	−	12.2250i	0.233589	−	0.404587i
$914$	−29.6196			−0.979729
$915$	−0.303661			−0.0100387
$916$	−8.29785	+	14.3723i	−0.274169	+	0.474874i
$917$			4.56108i			0.150620i
$918$	−1.85715	−	3.21667i	−0.0612949	−	0.106166i
$919$			46.9476i			1.54866i	0.632782	+	0.774330i	$0.281913\pi$
$919$			46.9476i			1.54866i	−0.632782	+	0.774330i	$0.718087\pi$
$920$	−0.536215	+	0.309584i	−0.0176785	+	0.0102067i
$921$	−4.76208	−	8.24816i	−0.156916	−	0.271786i
$922$	−5.87858	−	10.1820i	−0.193601	−	0.335326i
$923$	−6.97821	−	4.02887i	−0.229691	−	0.132612i
$924$	1.91102			0.0628681
$925$	−3.19730	+	5.17468i	−0.105127	+	0.170142i
$926$	−22.5432			−0.740815
$927$	−13.5465	−	7.82106i	−0.444925	−	0.256877i
$928$	−3.19826	−	5.53955i	−0.104988	−	0.181845i
$929$	28.4866	+	49.3403i	0.934616	+	1.61880i	0.775317	+	0.631573i	$0.217590\pi$
$929$	28.4866	+	49.3403i	0.934616	+	1.61880i	0.159300	+	0.987230i	$0.449076\pi$
$930$	−1.45222	+	0.838440i	−0.0476202	+	0.0274935i
$931$			36.0351i			1.18100i
$932$	−8.41081	−	14.5679i	−0.275505	−	0.477189i
$933$			10.4134i			0.340918i
$934$	2.99644	−	5.18999i	0.0980466	−	0.169822i
$935$	14.5882			0.477085
$936$	2.89779			0.0947173
$937$	24.3035	−	42.0949i	0.793961	−	1.37518i	−0.129535	−	0.991575i	$-0.541349\pi$
$937$	24.3035	−	42.0949i	0.793961	−	1.37518i	0.923497	−	0.383607i	$-0.125318\pi$
$938$	0.601175	−	0.347088i	0.0196290	−	0.0113328i
$939$		−	17.7468i		−	0.579146i
$940$	−8.40021	−	4.84986i	−0.273985	−	0.158185i
$941$	5.30141	−	9.18232i	0.172821	−	0.299335i	−0.766584	−	0.642144i	$-0.778045\pi$
$941$	5.30141	−	9.18232i	0.172821	−	0.299335i	0.939405	+	0.342809i	$0.111378\pi$
$942$	10.1306	+	5.84890i	0.330072	+	0.190567i
$943$	5.16067	−	2.97951i	0.168054	−	0.0970263i
$944$	3.57217	−	2.06239i	0.116264	−	0.0671251i
$945$	0.421377	+	0.243282i	0.0137074	+	0.00791397i
$946$	−4.20869	+	7.28967i	−0.136836	+	0.237008i
$947$	16.9599	+	9.79179i	0.551122	+	0.318190i	0.749574	−	0.661920i	$-0.230258\pi$
$947$	16.9599	+	9.79179i	0.551122	+	0.318190i	−0.198452	+	0.980111i	$0.563592\pi$
$948$			8.66504i			0.281428i
$949$	−2.42022	+	1.39732i	−0.0785638	+	0.0453588i
$950$	−2.66404	+	4.61424i	−0.0864327	+	0.149706i
$951$	31.9380			1.03566
$952$	−1.80724			−0.0585730
$953$	18.4629	−	31.9788i	0.598073	−	1.03589i	−0.395032	−	0.918667i	$-0.629266\pi$
$953$	18.4629	−	31.9788i	0.598073	−	1.03589i	0.993105	−	0.117226i	$-0.0374002\pi$
$954$		−	4.19567i		−	0.135840i
$955$	−8.37040	−	14.4980i	−0.270860	−	0.469143i
$956$		−	2.35112i		−	0.0760408i
$957$	21.7571	−	12.5615i	0.703307	−	0.406054i
$958$	−11.0960	−	19.2188i	−0.358496	−	0.620933i
$959$	2.66027	+	4.60772i	0.0859046	+	0.148791i
$960$	0.866025	+	0.500000i	0.0279508	+	0.0161374i
$961$	28.1881			0.909293
$962$	17.6187	+	0.526248i	0.568050	+	0.0169669i
$963$	−7.75904			−0.250031
$964$	4.16270	+	2.40334i	0.134072	+	0.0774063i
$965$	−12.9750	−	22.4734i	−0.417682	−	0.723446i
$966$	0.150632	+	0.260903i	0.00484652	+	0.00839442i
$967$	14.4795	−	8.35976i	0.465630	−	0.268832i	−0.248778	−	0.968560i	$-0.580029\pi$
$967$	14.4795	−	8.35976i	0.465630	−	0.268832i	0.714409	+	0.699729i	$0.246696\pi$
$968$			4.42595i			0.142255i
$969$	−9.89500	−	17.1386i	−0.317873	−	0.550573i
$970$			3.96693i			0.127370i
$971$	27.0841	−	46.9111i	0.869172	−	1.50545i	0.00632715	−	0.999980i	$-0.497986\pi$
$971$	27.0841	−	46.9111i	0.869172	−	1.50545i	0.862844	−	0.505469i	$-0.168681\pi$
$972$	1.00000			0.0320750
$973$	9.06963			0.290759
$974$	−18.7790	+	32.5262i	−0.601717	+	1.04221i
$975$	−2.50956	+	1.44890i	−0.0803703	+	0.0464018i
$976$			0.303661i			0.00971996i
$977$	14.6640	+	8.46627i	0.469143	+	0.270860i	0.715881	−	0.698222i	$-0.246025\pi$
$977$	14.6640	+	8.46627i	0.469143	+	0.270860i	−0.246738	+	0.969082i	$0.579359\pi$
$978$	7.76427	−	13.4481i	0.248274	−	0.430023i
$979$	−26.7548	−	15.4469i	−0.855088	−	0.493685i
$980$	−5.85715	+	3.38163i	−0.187100	+	0.108022i
$981$	−5.05443	+	2.91818i	−0.161376	+	0.0931702i
$982$	−15.1786	−	8.76335i	−0.484367	−	0.279650i
$983$	22.9610	−	39.7696i	0.732341	−	1.26845i	−0.223539	−	0.974695i	$-0.571761\pi$
$983$	22.9610	−	39.7696i	0.732341	−	1.26845i	0.955880	−	0.293757i	$-0.0949057\pi$
$984$	−8.33485	−	4.81213i	−0.265705	−	0.153405i
$985$		−	14.4879i		−	0.461624i
$986$	−20.5755	+	11.8793i	−0.655258	+	0.378313i
$987$	−2.35977	+	4.08724i	−0.0751123	+	0.130098i
$988$	15.4396			0.491200
$989$	−1.32696			−0.0421950
$990$	−1.96379	+	3.40139i	−0.0624135	+	0.108103i
$991$			47.2859i			1.50209i	0.660253	+	0.751043i	$0.270449\pi$
$991$			47.2859i			1.50209i	−0.660253	+	0.751043i	$0.729551\pi$
$992$	0.838440	+	1.45222i	0.0266205	+	0.0461080i
$993$		−	20.8161i		−	0.660580i
$994$	−1.17170	+	0.676483i	−0.0371641	+	0.0214567i
$995$	9.27325	+	16.0617i	0.293982	+	0.509191i
$996$	−1.79705	−	3.11259i	−0.0569418	−	0.0986262i
$997$	40.7626	+	23.5343i	1.29096	+	0.745338i	0.978825	−	0.204699i	$-0.0656215\pi$
$997$	40.7626	+	23.5343i	1.29096	+	0.745338i	0.312138	+	0.950037i	$0.398955\pi$
$998$	9.21779			0.291784
$999$	6.08005	+	0.181603i	0.192364	+	0.00574567i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.x.e.841.7	yes	16
37.11	even	6	inner	1110.2.x.e.751.7	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.x.e.751.7	✓	16	37.11	even	6	inner
1110.2.x.e.841.7	yes	16	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.x (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{5} +1.00000i q^{6} +(0.243282 + 0.421377i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{5} +1.00000i q^{6} +(0.243282 + 0.421377i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} -1.00000 q^{10} -3.92759 q^{11} +(-0.500000 + 0.866025i) q^{12} +(-2.50956 + 1.44890i) q^{13} +0.486564i q^{14} +(-0.866025 - 0.500000i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.21667 + 1.85715i) q^{17} +(-0.866025 + 0.500000i) q^{18} +(-4.61424 + 2.66404i) q^{19} +(-0.866025 - 0.500000i) q^{20} +(-0.243282 + 0.421377i) q^{21} +(-3.40139 - 1.96379i) q^{22} -0.619168i q^{23} +(-0.866025 + 0.500000i) q^{24} +(0.500000 - 0.866025i) q^{25} -2.89779 q^{26} -1.00000 q^{27} +(-0.243282 + 0.421377i) q^{28} +6.39653i q^{29} +(-0.500000 - 0.866025i) q^{30} -1.67688i q^{31} +(-0.866025 + 0.500000i) q^{32} +(-1.96379 - 3.40139i) q^{33} +(1.85715 + 3.21667i) q^{34} +(-0.421377 - 0.243282i) q^{35} -1.00000 q^{36} +(-6.08005 - 0.181603i) q^{37} -5.32807 q^{38} +(-2.50956 - 1.44890i) q^{39} +(-0.500000 - 0.866025i) q^{40} +(4.81213 + 8.33485i) q^{41} +(-0.421377 + 0.243282i) q^{42} -2.14314i q^{43} +(-1.96379 - 3.40139i) q^{44} -1.00000i q^{45} +(0.309584 - 0.536215i) q^{46} +9.69972 q^{47} -1.00000 q^{48} +(3.38163 - 5.85715i) q^{49} +(0.866025 - 0.500000i) q^{50} +3.71429i q^{51} +(-2.50956 - 1.44890i) q^{52} +(-2.09784 + 3.63356i) q^{53} +(-0.866025 - 0.500000i) q^{54} +(3.40139 - 1.96379i) q^{55} +(-0.421377 + 0.243282i) q^{56} +(-4.61424 - 2.66404i) q^{57} +(-3.19826 + 5.53955i) q^{58} +(-3.57217 - 2.06239i) q^{59} -1.00000i q^{60} +(0.262978 - 0.151831i) q^{61} +(0.838440 - 1.45222i) q^{62} -0.486564 q^{63} -1.00000 q^{64} +(1.44890 - 2.50956i) q^{65} -3.92759i q^{66} +(-0.713345 - 1.23555i) q^{67} +3.71429i q^{68} +(0.536215 - 0.309584i) q^{69} +(-0.243282 - 0.421377i) q^{70} +(1.39033 + 2.40811i) q^{71} +(-0.866025 - 0.500000i) q^{72} +0.964401 q^{73} +(-5.17468 - 3.19730i) q^{74} +1.00000 q^{75} +(-4.61424 - 2.66404i) q^{76} +(-0.955512 - 1.65500i) q^{77} +(-1.44890 - 2.50956i) q^{78} +(7.50415 - 4.33252i) q^{79} -1.00000i q^{80} +(-0.500000 - 0.866025i) q^{81} +9.62425i q^{82} +(-1.79705 + 3.11259i) q^{83} -0.486564 q^{84} -3.71429 q^{85} +(1.07157 - 1.85602i) q^{86} +(-5.53955 + 3.19826i) q^{87} -3.92759i q^{88} +(6.81203 + 3.93292i) q^{89} +(0.500000 - 0.866025i) q^{90} +(-1.22106 - 0.704981i) q^{91} +(0.536215 - 0.309584i) q^{92} +(1.45222 - 0.838440i) q^{93} +(8.40021 + 4.84986i) q^{94} +(2.66404 - 4.61424i) q^{95} +(-0.866025 - 0.500000i) q^{96} -3.96693i q^{97} +(5.85715 - 3.38163i) q^{98} +(1.96379 - 3.40139i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{3} + 8 q^{4} - 4 q^{7} - 8 q^{9}+O(q^{10}) \) 16 * q + 8 * q^3 + 8 * q^4 - 4 * q^7 - 8 * q^9	\( 16 q + 8 q^{3} + 8 q^{4} - 4 q^{7} - 8 q^{9} - 16 q^{10} - 4 q^{11} - 8 q^{12} - 8 q^{16} - 6 q^{17} - 6 q^{19} + 4 q^{21} + 12 q^{22} + 8 q^{25} - 8 q^{26} - 16 q^{27} + 4 q^{28} - 8 q^{30} - 2 q^{33} + 2 q^{34} + 18 q^{35} - 16 q^{36} - 12 q^{37} + 12 q^{38} - 8 q^{40} + 4 q^{41} + 18 q^{42} - 2 q^{44} + 12 q^{47} - 16 q^{48} - 42 q^{49} - 16 q^{53} - 12 q^{55} + 18 q^{56} - 6 q^{57} + 2 q^{58} + 48 q^{59} - 12 q^{61} - 4 q^{62} + 8 q^{63} - 16 q^{64} + 4 q^{65} + 6 q^{67} - 18 q^{69} + 4 q^{70} - 6 q^{71} - 52 q^{73} - 16 q^{74} + 16 q^{75} - 6 q^{76} + 10 q^{77} - 4 q^{78} + 78 q^{79} - 8 q^{81} + 36 q^{83} + 8 q^{84} - 4 q^{85} - 6 q^{86} + 12 q^{87} + 18 q^{89} + 8 q^{90} - 66 q^{91} - 18 q^{92} - 36 q^{93} + 12 q^{94} - 6 q^{95} - 12 q^{98} + 2 q^{99}+O(q^{100}) \) 16 * q + 8 * q^3 + 8 * q^4 - 4 * q^7 - 8 * q^9 - 16 * q^10 - 4 * q^11 - 8 * q^12 - 8 * q^16 - 6 * q^17 - 6 * q^19 + 4 * q^21 + 12 * q^22 + 8 * q^25 - 8 * q^26 - 16 * q^27 + 4 * q^28 - 8 * q^30 - 2 * q^33 + 2 * q^34 + 18 * q^35 - 16 * q^36 - 12 * q^37 + 12 * q^38 - 8 * q^40 + 4 * q^41 + 18 * q^42 - 2 * q^44 + 12 * q^47 - 16 * q^48 - 42 * q^49 - 16 * q^53 - 12 * q^55 + 18 * q^56 - 6 * q^57 + 2 * q^58 + 48 * q^59 - 12 * q^61 - 4 * q^62 + 8 * q^63 - 16 * q^64 + 4 * q^65 + 6 * q^67 - 18 * q^69 + 4 * q^70 - 6 * q^71 - 52 * q^73 - 16 * q^74 + 16 * q^75 - 6 * q^76 + 10 * q^77 - 4 * q^78 + 78 * q^79 - 8 * q^81 + 36 * q^83 + 8 * q^84 - 4 * q^85 - 6 * q^86 + 12 * q^87 + 18 * q^89 + 8 * q^90 - 66 * q^91 - 18 * q^92 - 36 * q^93 + 12 * q^94 - 6 * q^95 - 12 * q^98 + 2 * q^99

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