LMFDB - Embedded newform 1110.2.x.e.751.2

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			751.2
Root			$-4.20281i$ of defining polynomial
Character	$\chi$	$=$	1110.751
Dual form			1110.2.x.e.841.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{5} +1.00000i q^{6} +(-0.839478 + 1.45402i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(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} +(-0.839478 + 1.45402i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} -1.00000 q^{10} -3.11482 q^{11} +(-0.500000 - 0.866025i) q^{12} +(1.90214 + 1.09820i) q^{13} -1.67896i q^{14} +(0.866025 - 0.500000i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.49809 - 2.01962i) q^{17} +(0.866025 + 0.500000i) q^{18} +(3.21380 + 1.85549i) q^{19} +(0.866025 - 0.500000i) q^{20} +(0.839478 + 1.45402i) q^{21} +(2.69751 - 1.55741i) q^{22} +4.00110i q^{23} +(0.866025 + 0.500000i) q^{24} +(0.500000 + 0.866025i) q^{25} -2.19640 q^{26} -1.00000 q^{27} +(0.839478 + 1.45402i) q^{28} +5.04976i q^{29} +(-0.500000 + 0.866025i) q^{30} +4.94151i q^{31} +(0.866025 + 0.500000i) q^{32} +(-1.55741 + 2.69751i) q^{33} +(-2.01962 + 3.49809i) q^{34} +(-1.45402 + 0.839478i) q^{35} -1.00000 q^{36} +(5.10494 - 3.30750i) q^{37} -3.71098 q^{38} +(1.90214 - 1.09820i) q^{39} +(-0.500000 + 0.866025i) q^{40} +(1.34474 - 2.32915i) q^{41} +(-1.45402 - 0.839478i) q^{42} +5.77779i q^{43} +(-1.55741 + 2.69751i) q^{44} -1.00000i q^{45} +(-2.00055 - 3.46505i) q^{46} +5.05625 q^{47} -1.00000 q^{48} +(2.09055 + 3.62094i) q^{49} +(-0.866025 - 0.500000i) q^{50} -4.03925i q^{51} +(1.90214 - 1.09820i) q^{52} +(-6.38398 - 11.0574i) q^{53} +(0.866025 - 0.500000i) q^{54} +(-2.69751 - 1.55741i) q^{55} +(-1.45402 - 0.839478i) q^{56} +(3.21380 - 1.85549i) q^{57} +(-2.52488 - 4.37322i) q^{58} +(-4.36549 + 2.52041i) q^{59} -1.00000i q^{60} +(10.3566 + 5.97938i) q^{61} +(-2.47075 - 4.27947i) q^{62} +1.67896 q^{63} -1.00000 q^{64} +(1.09820 + 1.90214i) q^{65} -3.11482i q^{66} +(2.18318 - 3.78138i) q^{67} -4.03925i q^{68} +(3.46505 + 2.00055i) q^{69} +(0.839478 - 1.45402i) q^{70} +(-1.36159 + 2.35834i) q^{71} +(0.866025 - 0.500000i) q^{72} +2.06124 q^{73} +(-2.76726 + 5.41685i) q^{74} +1.00000 q^{75} +(3.21380 - 1.85549i) q^{76} +(2.61482 - 4.52900i) q^{77} +(-1.09820 + 1.90214i) q^{78} +(14.1746 + 8.18371i) q^{79} -1.00000i q^{80} +(-0.500000 + 0.866025i) q^{81} +2.68947i q^{82} +(2.69775 + 4.67265i) q^{83} +1.67896 q^{84} +4.03925 q^{85} +(-2.88889 - 5.00371i) q^{86} +(4.37322 + 2.52488i) q^{87} -3.11482i q^{88} +(-5.79811 + 3.34754i) q^{89} +(0.500000 + 0.866025i) q^{90} +(-3.19361 + 1.84383i) q^{91} +(3.46505 + 2.00055i) q^{92} +(4.27947 + 2.47075i) q^{93} +(-4.37884 + 2.52813i) q^{94} +(1.85549 + 3.21380i) q^{95} +(0.866025 - 0.500000i) q^{96} -6.35452i q^{97} +(-3.62094 - 2.09055i) q^{98} +(1.55741 + 2.69751i) 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 $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$

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
$7$	−0.839478	+	1.45402i	−0.317293	+	0.549567i	−0.979922	−	0.199380i	$-0.936107\pi$
$7$	−0.839478	+	1.45402i	−0.317293	+	0.549567i	0.662629	+	0.748948i	$0.269441\pi$
$8$			1.00000i			0.353553i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−1.00000			−0.316228
$11$	−3.11482			−0.939153			−0.469576	−	0.882892i	$-0.655593\pi$
$11$	−3.11482			−0.939153			−0.469576	+	0.882892i	$0.655593\pi$
$12$	−0.500000	−	0.866025i	−0.144338	−	0.250000i
$13$	1.90214	+	1.09820i	0.527558	+	0.304586i	0.740022	−	0.672583i	$-0.234815\pi$
$13$	1.90214	+	1.09820i	0.527558	+	0.304586i	−0.212463	+	0.977169i	$0.568149\pi$
$14$		−	1.67896i		−	0.448720i
$15$	0.866025	−	0.500000i	0.223607	−	0.129099i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	3.49809	−	2.01962i	0.848411	−	0.489831i	−0.0117032	−	0.999932i	$-0.503725\pi$
$17$	3.49809	−	2.01962i	0.848411	−	0.489831i	0.860115	+	0.510101i	$0.170392\pi$
$18$	0.866025	+	0.500000i	0.204124	+	0.117851i
$19$	3.21380	+	1.85549i	0.737297	+	0.425679i	0.821086	−	0.570805i	$-0.193369\pi$
$19$	3.21380	+	1.85549i	0.737297	+	0.425679i	−0.0837886	+	0.996484i	$0.526702\pi$
$20$	0.866025	−	0.500000i	0.193649	−	0.111803i
$21$	0.839478	+	1.45402i	0.183189	+	0.317293i
$22$	2.69751	−	1.55741i	0.575111	−	0.332041i
$23$			4.00110i			0.834286i	0.908841	+	0.417143i	$0.136969\pi$
$23$			4.00110i			0.834286i	−0.908841	+	0.417143i	$0.863031\pi$
$24$	0.866025	+	0.500000i	0.176777	+	0.102062i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	−2.19640			−0.430750
$27$	−1.00000			−0.192450
$28$	0.839478	+	1.45402i	0.158646	+	0.274784i
$29$			5.04976i			0.937717i	0.883273	+	0.468859i	$0.155335\pi$
$29$			5.04976i			0.937717i	−0.883273	+	0.468859i	$0.844665\pi$
$30$	−0.500000	+	0.866025i	−0.0912871	+	0.158114i
$31$			4.94151i			0.887521i	0.896145	+	0.443761i	$0.146356\pi$
$31$			4.94151i			0.887521i	−0.896145	+	0.443761i	$0.853644\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	−1.55741	+	2.69751i	−0.271110	+	0.469576i
$34$	−2.01962	+	3.49809i	−0.346362	+	0.599917i
$35$	−1.45402	+	0.839478i	−0.245774	+	0.141898i
$36$	−1.00000			−0.166667
$37$	5.10494	−	3.30750i	0.839248	−	0.543749i
$37$	5.10494	−	3.30750i	0.839248	−	0.543749i
$38$	−3.71098			−0.602001
$39$	1.90214	−	1.09820i	0.304586	−	0.175853i
$40$	−0.500000	+	0.866025i	−0.0790569	+	0.136931i
$41$	1.34474	−	2.32915i	0.210012	−	0.363752i	−0.741706	−	0.670725i	$-0.765983\pi$
$41$	1.34474	−	2.32915i	0.210012	−	0.363752i	0.951718	+	0.306973i	$0.0993162\pi$
$42$	−1.45402	−	0.839478i	−0.224360	−	0.129534i
$43$			5.77779i			0.881105i	0.897727	+	0.440552i	$0.145217\pi$
$43$			5.77779i			0.881105i	−0.897727	+	0.440552i	$0.854783\pi$
$44$	−1.55741	+	2.69751i	−0.234788	+	0.406665i
$45$		−	1.00000i		−	0.149071i
$46$	−2.00055	−	3.46505i	−0.294965	−	0.510894i
$47$	5.05625			0.737530			0.368765	−	0.929523i	$-0.379781\pi$
$47$	5.05625			0.737530			0.368765	+	0.929523i	$0.379781\pi$
$48$	−1.00000			−0.144338
$49$	2.09055	+	3.62094i	0.298650	+	0.517278i
$50$	−0.866025	−	0.500000i	−0.122474	−	0.0707107i
$51$		−	4.03925i		−	0.565608i
$52$	1.90214	−	1.09820i	0.263779	−	0.152293i
$53$	−6.38398	−	11.0574i	−0.876907	−	1.51885i	−0.854717	−	0.519094i	$-0.826269\pi$
$53$	−6.38398	−	11.0574i	−0.876907	−	1.51885i	−0.0221903	−	0.999754i	$-0.507064\pi$
$54$	0.866025	−	0.500000i	0.117851	−	0.0680414i
$55$	−2.69751	−	1.55741i	−0.363732	−	0.210001i
$56$	−1.45402	−	0.839478i	−0.194301	−	0.112180i
$57$	3.21380	−	1.85549i	0.425679	−	0.245766i
$58$	−2.52488	−	4.37322i	−0.331533	−	0.574232i
$59$	−4.36549	+	2.52041i	−0.568338	+	0.328130i	−0.756485	−	0.654011i	$-0.773085\pi$
$59$	−4.36549	+	2.52041i	−0.568338	+	0.328130i	0.188147	+	0.982141i	$0.439752\pi$
$60$		−	1.00000i		−	0.129099i
$61$	10.3566	+	5.97938i	1.32603	+	0.765581i	0.984682	−	0.174358i	$-0.0557849\pi$
$61$	10.3566	+	5.97938i	1.32603	+	0.765581i	0.341343	+	0.939939i	$0.389118\pi$
$62$	−2.47075	−	4.27947i	−0.313786	−	0.543494i
$63$	1.67896			0.211529
$64$	−1.00000			−0.125000
$65$	1.09820	+	1.90214i	0.136215	+	0.235931i
$66$		−	3.11482i		−	0.383408i
$67$	2.18318	−	3.78138i	0.266718	−	0.461969i	−0.701294	−	0.712872i	$-0.747394\pi$
$67$	2.18318	−	3.78138i	0.266718	−	0.461969i	0.968012	+	0.250903i	$0.0807274\pi$
$68$		−	4.03925i		−	0.489831i
$69$	3.46505	+	2.00055i	0.417143	+	0.240838i
$70$	0.839478	−	1.45402i	0.100337	−	0.173788i
$71$	−1.36159	+	2.35834i	−0.161591	+	0.279884i	−0.935439	−	0.353487i	$-0.884996\pi$
$71$	−1.36159	+	2.35834i	−0.161591	+	0.279884i	0.773848	+	0.633371i	$0.218329\pi$
$72$	0.866025	−	0.500000i	0.102062	−	0.0589256i
$73$	2.06124			0.241249			0.120625	−	0.992698i	$-0.461510\pi$
$73$	2.06124			0.241249			0.120625	+	0.992698i	$0.461510\pi$
$74$	−2.76726	+	5.41685i	−0.321688	+	0.629696i
$75$	1.00000			0.115470
$76$	3.21380	−	1.85549i	0.368649	−	0.212839i
$77$	2.61482	−	4.52900i	0.297987	−	0.516128i
$78$	−1.09820	+	1.90214i	−0.124347	+	0.215375i
$79$	14.1746	+	8.18371i	1.59477	+	0.920739i	0.992473	+	0.122466i	$0.0390801\pi$
$79$	14.1746	+	8.18371i	1.59477	+	0.920739i	0.602295	+	0.798274i	$0.294253\pi$
$80$		−	1.00000i		−	0.111803i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$			2.68947i			0.297002i
$83$	2.69775	+	4.67265i	0.296117	+	0.512890i	0.975244	−	0.221131i	$-0.0709748\pi$
$83$	2.69775	+	4.67265i	0.296117	+	0.512890i	−0.679127	+	0.734021i	$0.737641\pi$
$84$	1.67896			0.183189
$85$	4.03925			0.438118
$86$	−2.88889	−	5.00371i	−0.311517	−	0.539564i
$87$	4.37322	+	2.52488i	0.468859	+	0.270696i
$88$		−	3.11482i		−	0.332041i
$89$	−5.79811	+	3.34754i	−0.614598	+	0.354839i	−0.774763	−	0.632252i	$-0.782131\pi$
$89$	−5.79811	+	3.34754i	−0.614598	+	0.354839i	0.160165	+	0.987090i	$0.448798\pi$
$90$	0.500000	+	0.866025i	0.0527046	+	0.0912871i
$91$	−3.19361	+	1.84383i	−0.334781	+	0.193286i
$92$	3.46505	+	2.00055i	0.361256	+	0.208572i
$93$	4.27947	+	2.47075i	0.443761	+	0.256205i
$94$	−4.37884	+	2.52813i	−0.451643	+	0.260756i
$95$	1.85549	+	3.21380i	0.190369	+	0.329729i
$96$	0.866025	−	0.500000i	0.0883883	−	0.0510310i
$97$		−	6.35452i		−	0.645203i	−0.946535	−	0.322602i	$-0.895443\pi$
$97$		−	6.35452i		−	0.645203i	0.946535	−	0.322602i	$-0.104557\pi$
$98$	−3.62094	−	2.09055i	−0.365771	−	0.211178i
$99$	1.55741	+	2.69751i	0.156525	+	0.271110i
$100$	1.00000			0.100000
$101$	2.47011			0.245785			0.122893	−	0.992420i	$-0.460783\pi$
$101$	2.47011			0.245785			0.122893	+	0.992420i	$0.460783\pi$
$102$	2.01962	+	3.49809i	0.199972	+	0.346362i
$103$		−	1.63291i		−	0.160895i	−0.996759	−	0.0804475i	$-0.974365\pi$
$103$		−	1.63291i		−	0.160895i	0.996759	−	0.0804475i	$-0.0256349\pi$
$104$	−1.09820	+	1.90214i	−0.107687	+	0.186520i
$105$			1.67896i			0.163849i
$106$	11.0574	+	6.38398i	1.07399	+	0.620067i
$107$	−3.00186	+	5.19937i	−0.290200	+	0.502642i	−0.973857	−	0.227162i	$-0.927055\pi$
$107$	−3.00186	+	5.19937i	−0.290200	+	0.502642i	0.683657	+	0.729804i	$0.260389\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$	6.20333	−	3.58149i	0.594171	−	0.343045i	−0.172574	−	0.984997i	$-0.555208\pi$
$109$	6.20333	−	3.58149i	0.594171	−	0.343045i	0.766745	+	0.641952i	$0.221875\pi$
$110$	3.11482			0.296986
$111$	−0.311905	−	6.07476i	−0.0296047	−	0.576591i
$112$	1.67896			0.158646
$113$	−5.70272	+	3.29247i	−0.536467	+	0.309729i	−0.743646	−	0.668574i	$-0.766905\pi$
$113$	−5.70272	+	3.29247i	−0.536467	+	0.309729i	0.207179	+	0.978303i	$0.433572\pi$
$114$	−1.85549	+	3.21380i	−0.173783	+	0.301000i
$115$	−2.00055	+	3.46505i	−0.186552	+	0.323118i
$116$	4.37322	+	2.52488i	0.406043	+	0.234429i
$117$		−	2.19640i		−	0.203057i
$118$	2.52041	−	4.36549i	0.232023	−	0.401876i
$119$			6.78172i			0.621679i
$120$	0.500000	+	0.866025i	0.0456435	+	0.0790569i
$121$	−1.29791			−0.117992
$122$	−11.9588			−1.08270
$123$	−1.34474	−	2.32915i	−0.121251	−	0.210012i
$124$	4.27947	+	2.47075i	0.384308	+	0.221880i
$125$			1.00000i			0.0894427i
$126$	−1.45402	+	0.839478i	−0.129534	+	0.0747867i
$127$	−9.75091	−	16.8891i	−0.865253	−	1.49866i	−0.866796	−	0.498664i	$-0.833824\pi$
$127$	−9.75091	−	16.8891i	−0.865253	−	1.49866i	0.00154226	−	0.999999i	$-0.499509\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	5.00371	+	2.88889i	0.440552	+	0.254353i
$130$	−1.90214	−	1.09820i	−0.166829	−	0.0963186i
$131$	−2.82724	+	1.63231i	−0.247017	+	0.142615i	−0.618398	−	0.785865i	$-0.712218\pi$
$131$	−2.82724	+	1.63231i	−0.247017	+	0.142615i	0.371381	+	0.928481i	$0.378885\pi$
$132$	1.55741	+	2.69751i	0.135555	+	0.234788i
$133$	−5.39584	+	3.11529i	−0.467878	+	0.270130i
$134$			4.36636i			0.377196i
$135$	−0.866025	−	0.500000i	−0.0745356	−	0.0430331i
$136$	2.01962	+	3.49809i	0.173181	+	0.299959i
$137$	−3.00916			−0.257090			−0.128545	−	0.991704i	$-0.541031\pi$
$137$	−3.00916			−0.257090			−0.128545	+	0.991704i	$0.541031\pi$
$138$	−4.00110			−0.340596
$139$	9.63217	+	16.6834i	0.816990	+	1.41507i	0.907890	+	0.419208i	$0.137692\pi$
$139$	9.63217	+	16.6834i	0.816990	+	1.41507i	−0.0909003	+	0.995860i	$0.528974\pi$
$140$			1.67896i			0.141898i
$141$	2.52813	−	4.37884i	0.212907	−	0.368765i
$142$		−	2.72318i		−	0.228524i
$143$	−5.92482	−	3.42069i	−0.495458	−	0.286053i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	−2.52488	+	4.37322i	−0.209680	+	0.363176i
$146$	−1.78508	+	1.03062i	−0.147734	+	0.0852945i
$147$	4.18111			0.344852
$148$	−0.311905	−	6.07476i	−0.0256384	−	0.499342i
$149$	−9.63414			−0.789260			−0.394630	−	0.918840i	$-0.629127\pi$
$149$	−9.63414			−0.789260			−0.394630	+	0.918840i	$0.629127\pi$
$150$	−0.866025	+	0.500000i	−0.0707107	+	0.0408248i
$151$	1.38277	−	2.39502i	0.112528	−	0.194904i	−0.804261	−	0.594276i	$-0.797439\pi$
$151$	1.38277	−	2.39502i	0.112528	−	0.194904i	0.916789	+	0.399372i	$0.130772\pi$
$152$	−1.85549	+	3.21380i	−0.150500	+	0.260674i
$153$	−3.49809	−	2.01962i	−0.282804	−	0.163277i
$154$			5.22964i			0.421417i
$155$	−2.47075	+	4.27947i	−0.198456	+	0.343736i
$156$		−	2.19640i		−	0.175853i
$157$	3.10829	+	5.38371i	0.248068	+	0.429667i	0.962990	−	0.269538i	$-0.0868709\pi$
$157$	3.10829	+	5.38371i	0.248068	+	0.429667i	−0.714921	+	0.699205i	$0.753538\pi$
$158$	−16.3674			−1.30212
$159$	−12.7680			−1.01257
$160$	0.500000	+	0.866025i	0.0395285	+	0.0684653i
$161$	−5.81767	−	3.35883i	−0.458496	−	0.264713i
$162$		−	1.00000i		−	0.0785674i
$163$	12.7927	−	7.38589i	1.00200	−	0.578507i	0.0931636	−	0.995651i	$-0.470302\pi$
$163$	12.7927	−	7.38589i	1.00200	−	0.578507i	0.908841	+	0.417143i	$0.136969\pi$
$164$	−1.34474	−	2.32915i	−0.105006	−	0.181876i
$165$	−2.69751	+	1.55741i	−0.210001	+	0.121244i
$166$	−4.67265	−	2.69775i	−0.362668	−	0.209386i
$167$	8.40730	+	4.85396i	0.650577	+	0.375611i	0.788677	−	0.614808i	$-0.210766\pi$
$167$	8.40730	+	4.85396i	0.650577	+	0.375611i	−0.138100	+	0.990418i	$0.544100\pi$
$168$	−1.45402	+	0.839478i	−0.112180	+	0.0647671i
$169$	−4.08791	−	7.08047i	−0.314455	−	0.544652i
$170$	−3.49809	+	2.01962i	−0.268291	+	0.154898i
$171$		−	3.71098i		−	0.283786i
$172$	5.00371	+	2.88889i	0.381529	+	0.220276i
$173$	5.35676	+	9.27818i	0.407267	+	0.705407i	0.994582	−	0.103951i	$-0.0331486\pi$
$173$	5.35676	+	9.27818i	0.407267	+	0.705407i	−0.587316	+	0.809358i	$0.699815\pi$
$174$	−5.04976			−0.382821
$175$	−1.67896			−0.126917
$176$	1.55741	+	2.69751i	0.117394	+	0.203333i
$177$			5.04083i			0.378892i
$178$	3.34754	−	5.79811i	0.250909	−	0.434587i
$179$		−	5.89934i		−	0.440937i	−0.975394	−	0.220469i	$-0.929241\pi$
$179$		−	5.89934i		−	0.440937i	0.975394	−	0.220469i	$-0.0707586\pi$
$180$	−0.866025	−	0.500000i	−0.0645497	−	0.0372678i
$181$	4.79487	−	8.30496i	0.356400	−	0.617303i	−0.630957	−	0.775818i	$-0.717337\pi$
$181$	4.79487	−	8.30496i	0.356400	−	0.617303i	0.987356	+	0.158515i	$0.0506708\pi$
$182$	1.84383	−	3.19361i	0.136674	−	0.236726i
$183$	10.3566	−	5.97938i	0.765581	−	0.442008i
$184$	−4.00110			−0.294965
$185$	6.07476	−	0.311905i	0.446625	−	0.0229317i
$186$	−4.94151			−0.362329
$187$	−10.8959	+	6.29076i	−0.796788	+	0.460026i
$188$	2.52813	−	4.37884i	0.184383	−	0.319360i
$189$	0.839478	−	1.45402i	0.0610631	−	0.105764i
$190$	−3.21380	−	1.85549i	−0.233154	−	0.134611i
$191$			9.39596i			0.679868i	0.940449	+	0.339934i	$0.110405\pi$
$191$			9.39596i			0.679868i	−0.940449	+	0.339934i	$0.889595\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$		−	0.591966i		−	0.0426106i	−0.999773	−	0.0213053i	$-0.993218\pi$
$193$		−	0.591966i		−	0.0426106i	0.999773	−	0.0213053i	$-0.00678221\pi$
$194$	3.17726	+	5.50317i	0.228114	+	0.395105i
$195$	2.19640			0.157288
$196$	4.18111			0.298650
$197$	−12.4021	−	21.4811i	−0.883613	−	1.53046i	−0.847295	−	0.531123i	$-0.821770\pi$
$197$	−12.4021	−	21.4811i	−0.883613	−	1.53046i	−0.0363182	−	0.999340i	$-0.511563\pi$
$198$	−2.69751	−	1.55741i	−0.191704	−	0.110680i
$199$			16.9846i			1.20401i	0.798494	+	0.602003i	$0.205630\pi$
$199$			16.9846i			1.20401i	−0.798494	+	0.602003i	$0.794370\pi$
$200$	−0.866025	+	0.500000i	−0.0612372	+	0.0353553i
$201$	−2.18318	−	3.78138i	−0.153990	−	0.266718i
$202$	−2.13918	+	1.23506i	−0.150512	+	0.0868983i
$203$	−7.34245	−	4.23916i	−0.515339	−	0.297531i
$204$	−3.49809	−	2.01962i	−0.244915	−	0.141402i
$205$	2.32915	−	1.34474i	0.162675	−	0.0939204i
$206$	0.816453	+	1.41414i	0.0568850	+	0.0985277i
$207$	3.46505	−	2.00055i	0.240838	−	0.139048i
$208$		−	2.19640i		−	0.152293i
$209$	−10.0104	−	5.77951i	−0.692435	−	0.399777i
$210$	−0.839478	−	1.45402i	−0.0579295	−	0.100337i
$211$	−15.0190			−1.03395			−0.516976	−	0.856000i	$-0.672942\pi$
$211$	−15.0190			−1.03395			−0.516976	+	0.856000i	$0.672942\pi$
$212$	−12.7680			−0.876907
$213$	1.36159	+	2.35834i	0.0932947	+	0.161591i
$214$		−	6.00371i		−	0.410405i
$215$	−2.88889	+	5.00371i	−0.197021	+	0.341250i
$216$		−	1.00000i		−	0.0680414i
$217$	−7.18505	−	4.14829i	−0.487753	−	0.281604i
$218$	−3.58149	+	6.20333i	−0.242569	+	0.420142i
$219$	1.03062	−	1.78508i	0.0696427	−	0.120625i
$220$	−2.69751	+	1.55741i	−0.181866	+	0.105000i
$221$	8.87180			0.596782
$222$	3.30750	+	5.10494i	0.221985	+	0.342621i
$223$	8.15114			0.545840			0.272920	−	0.962037i	$-0.412010\pi$
$223$	8.15114			0.545840			0.272920	+	0.962037i	$0.412010\pi$
$224$	−1.45402	+	0.839478i	−0.0971507	+	0.0560900i
$225$	0.500000	−	0.866025i	0.0333333	−	0.0577350i
$226$	3.29247	−	5.70272i	0.219012	−	0.379339i
$227$	−16.5765	−	9.57042i	−1.10022	−	0.635211i	−0.163940	−	0.986470i	$-0.552420\pi$
$227$	−16.5765	−	9.57042i	−1.10022	−	0.635211i	−0.936278	+	0.351259i	$0.885754\pi$
$228$		−	3.71098i		−	0.245766i
$229$	−2.10830	+	3.65168i	−0.139320	+	0.241310i	−0.927239	−	0.374469i	$-0.877825\pi$
$229$	−2.10830	+	3.65168i	−0.139320	+	0.241310i	0.787919	+	0.615779i	$0.211158\pi$
$230$		−	4.00110i		−	0.263824i
$231$	−2.61482	−	4.52900i	−0.172043	−	0.297987i
$232$	−5.04976			−0.331533
$233$	9.54038			0.625011			0.312506	−	0.949916i	$-0.398832\pi$
$233$	9.54038			0.625011			0.312506	+	0.949916i	$0.398832\pi$
$234$	1.09820	+	1.90214i	0.0717916	+	0.124347i
$235$	4.37884	+	2.52813i	0.285644	+	0.164917i
$236$			5.04083i			0.328130i
$237$	14.1746	−	8.18371i	0.920739	−	0.531589i
$238$	−3.39086	−	5.87314i	−0.219797	−	0.380699i
$239$	−0.954740	+	0.551219i	−0.0617570	+	0.0356554i	−0.530561	−	0.847647i	$-0.678019\pi$
$239$	−0.954740	+	0.551219i	−0.0617570	+	0.0356554i	0.468804	+	0.883302i	$0.344685\pi$
$240$	−0.866025	−	0.500000i	−0.0559017	−	0.0322749i
$241$	−23.3250	−	13.4667i	−1.50250	−	0.867466i	−0.999996	−	0.00288852i	$-0.999081\pi$
$241$	−23.3250	−	13.4667i	−1.50250	−	0.867466i	−0.502499	−	0.864578i	$-0.667586\pi$
$242$	1.12403	−	0.648956i	0.0722551	−	0.0417165i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	10.3566	−	5.97938i	0.663013	−	0.382791i
$245$			4.18111i			0.267121i
$246$	2.32915	+	1.34474i	0.148501	+	0.0857372i
$247$	4.07540	+	7.05880i	0.259312	+	0.449141i
$248$	−4.94151			−0.313786
$249$	5.39551			0.341927
$250$	−0.500000	−	0.866025i	−0.0316228	−	0.0547723i
$251$		−	27.4434i		−	1.73221i	−0.499862	−	0.866105i	$-0.666616\pi$
$251$		−	27.4434i		−	1.73221i	0.499862	−	0.866105i	$-0.333384\pi$
$252$	0.839478	−	1.45402i	0.0528822	−	0.0915946i
$253$		−	12.4627i		−	0.783522i
$254$	16.8891	+	9.75091i	1.05971	+	0.611826i
$255$	2.01962	−	3.49809i	0.126474	−	0.219059i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	23.1879	−	13.3875i	1.44642	−	0.835092i	0.448156	−	0.893955i	$-0.352081\pi$
$257$	23.1879	−	13.3875i	1.44642	−	0.835092i	0.998266	+	0.0588630i	$0.0187475\pi$
$258$	−5.77779			−0.359709
$259$	0.523675	+	10.1993i	0.0325396	+	0.633751i
$260$	2.19640			0.136215
$261$	4.37322	−	2.52488i	0.270696	−	0.156286i
$262$	1.63231	−	2.82724i	0.100844	−	0.174667i
$263$	10.8170	−	18.7356i	0.667006	−	1.15529i	−0.311732	−	0.950170i	$-0.600909\pi$
$263$	10.8170	−	18.7356i	0.667006	−	1.15529i	0.978737	−	0.205117i	$-0.0657576\pi$
$264$	−2.69751	−	1.55741i	−0.166020	−	0.0958519i
$265$		−	12.7680i		−	0.784330i
$266$	3.11529	−	5.39584i	0.191011	−	0.330840i
$267$			6.69508i			0.409732i
$268$	−2.18318	−	3.78138i	−0.133359	−	0.230985i
$269$	−10.2168			−0.622927			−0.311463	−	0.950258i	$-0.600819\pi$
$269$	−10.2168			−0.622927			−0.311463	+	0.950258i	$0.600819\pi$
$270$	1.00000			0.0608581
$271$	−7.41487	−	12.8429i	−0.450421	−	0.780152i	0.547991	−	0.836484i	$-0.315393\pi$
$271$	−7.41487	−	12.8429i	−0.450421	−	0.780152i	−0.998412	+	0.0563319i	$0.982060\pi$
$272$	−3.49809	−	2.01962i	−0.212103	−	0.122458i
$273$			3.68766i			0.223187i
$274$	2.60601	−	1.50458i	0.157435	−	0.0908950i
$275$	−1.55741	−	2.69751i	−0.0939153	−	0.162666i
$276$	3.46505	−	2.00055i	0.208572	−	0.120419i
$277$	−12.6694	−	7.31467i	−0.761230	−	0.439496i	0.0685074	−	0.997651i	$-0.478176\pi$
$277$	−12.6694	−	7.31467i	−0.761230	−	0.439496i	−0.829737	+	0.558154i	$0.811510\pi$
$278$	−16.6834	−	9.63217i	−1.00060	−	0.577699i
$279$	4.27947	−	2.47075i	0.256205	−	0.147920i
$280$	−0.839478	−	1.45402i	−0.0501684	−	0.0868942i
$281$	2.15090	−	1.24182i	0.128312	−	0.0740808i	−0.434470	−	0.900686i	$-0.643064\pi$
$281$	2.15090	−	1.24182i	0.128312	−	0.0740808i	0.562782	+	0.826605i	$0.309731\pi$
$282$			5.05625i			0.301095i
$283$	−11.1348	−	6.42868i	−0.661895	−	0.382145i	0.131104	−	0.991369i	$-0.458148\pi$
$283$	−11.1348	−	6.42868i	−0.661895	−	0.382145i	−0.792999	+	0.609223i	$0.791481\pi$
$284$	1.36159	+	2.35834i	0.0807956	+	0.139942i
$285$	3.71098			0.219820
$286$	6.84139			0.404540
$287$	2.25775	+	3.91054i	0.133271	+	0.230832i
$288$		−	1.00000i		−	0.0589256i
$289$	−0.342246	+	0.592787i	−0.0201321	+	0.0348698i
$290$		−	5.04976i		−	0.296532i
$291$	−5.50317	−	3.17726i	−0.322602	−	0.186254i
$292$	1.03062	−	1.78508i	0.0603123	−	0.104464i
$293$	−6.53661	+	11.3217i	−0.381873	+	0.661423i	−0.991330	−	0.131396i	$-0.958054\pi$
$293$	−6.53661	+	11.3217i	−0.381873	+	0.661423i	0.609457	+	0.792819i	$0.291388\pi$
$294$	−3.62094	+	2.09055i	−0.211178	+	0.121924i
$295$	−5.04083			−0.293488
$296$	3.30750	+	5.10494i	0.192244	+	0.296719i
$297$	3.11482			0.180740
$298$	8.34341	−	4.81707i	0.483321	−	0.279045i
$299$	−4.39401	+	7.61064i	−0.254112	+	0.440135i
$300$	0.500000	−	0.866025i	0.0288675	−	0.0500000i
$301$	−8.40101	−	4.85033i	−0.484226	−	0.279568i
$302$			2.76553i			0.159139i
$303$	1.23506	−	2.13918i	0.0709522	−	0.122893i
$304$		−	3.71098i		−	0.212839i
$305$	5.97938	+	10.3566i	0.342378	+	0.593017i
$306$	4.03925			0.230908
$307$	−26.2506			−1.49820			−0.749101	−	0.662456i	$-0.769514\pi$
$307$	−26.2506			−1.49820			−0.749101	+	0.662456i	$0.769514\pi$
$308$	−2.61482	−	4.52900i	−0.148993	−	0.258064i
$309$	−1.41414	−	0.816453i	−0.0804475	−	0.0464464i
$310$		−	4.94151i		−	0.280659i
$311$	2.63920	−	1.52374i	0.149655	−	0.0864036i	−0.423302	−	0.905988i	$-0.639129\pi$
$311$	2.63920	−	1.52374i	0.149655	−	0.0864036i	0.572958	+	0.819585i	$0.305796\pi$
$312$	1.09820	+	1.90214i	0.0621734	+	0.107687i
$313$	−12.8644	+	7.42729i	−0.727141	+	0.419815i	−0.817375	−	0.576106i	$-0.804572\pi$
$313$	−12.8644	+	7.42729i	−0.727141	+	0.419815i	0.0902344	+	0.995921i	$0.471238\pi$
$314$	−5.38371	−	3.10829i	−0.303821	−	0.175411i
$315$	1.45402	+	0.839478i	0.0819247	+	0.0472992i
$316$	14.1746	−	8.18371i	0.797384	−	0.460370i
$317$	−6.28380	−	10.8839i	−0.352933	−	0.611299i	0.633829	−	0.773474i	$-0.281482\pi$
$317$	−6.28380	−	10.8839i	−0.352933	−	0.611299i	−0.986762	+	0.162175i	$0.948149\pi$
$318$	11.0574	−	6.38398i	0.620067	−	0.357996i
$319$		−	15.7291i		−	0.880660i
$320$	−0.866025	−	0.500000i	−0.0484123	−	0.0279508i
$321$	3.00186	+	5.19937i	0.167547	+	0.290200i
$322$	6.71766			0.374361
$323$	14.9896			0.834042
$324$	0.500000	+	0.866025i	0.0277778	+	0.0481125i
$325$			2.19640i			0.121834i
$326$	−7.38589	+	12.7927i	−0.409067	+	0.708524i
$327$		−	7.16298i		−	0.396114i
$328$	2.32915	+	1.34474i	0.128606	+	0.0742506i
$329$	−4.24461	+	7.35189i	−0.234013	+	0.405323i
$330$	1.55741	−	2.69751i	0.0857325	−	0.148493i
$331$	−19.9199	+	11.5007i	−1.09490	+	0.632138i	−0.934875	−	0.354976i	$-0.884489\pi$
$331$	−19.9199	+	11.5007i	−1.09490	+	0.632138i	−0.160020	+	0.987114i	$0.551156\pi$
$332$	5.39551			0.296117
$333$	−5.41685	−	2.76726i	−0.296842	−	0.151645i
$334$	−9.70792			−0.531194
$335$	3.78138	−	2.18318i	0.206599	−	0.119280i
$336$	0.839478	−	1.45402i	0.0457973	−	0.0793232i
$337$	5.81904	−	10.0789i	0.316983	−	0.549031i	−0.662874	−	0.748731i	$-0.730663\pi$
$337$	5.81904	−	10.0789i	0.316983	−	0.549031i	0.979857	+	0.199700i	$0.0639967\pi$
$338$	7.08047	+	4.08791i	0.385127	+	0.222353i
$339$			6.58493i			0.357644i
$340$	2.01962	−	3.49809i	0.109529	−	0.189711i
$341$		−	15.3919i		−	0.833518i
$342$	1.85549	+	3.21380i	0.100333	+	0.173783i
$343$	−18.7726			−1.01362
$344$	−5.77779			−0.311517
$345$	2.00055	+	3.46505i	0.107706	+	0.186552i
$346$	−9.27818	−	5.35676i	−0.498798	−	0.287981i
$347$		−	20.2955i		−	1.08952i	−0.838593	−	0.544759i	$-0.816621\pi$
$347$		−	20.2955i		−	1.08952i	0.838593	−	0.544759i	$-0.183379\pi$
$348$	4.37322	−	2.52488i	0.234429	−	0.135348i
$349$	3.23231	+	5.59853i	0.173022	+	0.299683i	0.939475	−	0.342618i	$-0.111314\pi$
$349$	3.23231	+	5.59853i	0.173022	+	0.299683i	−0.766453	+	0.642300i	$0.777980\pi$
$350$	1.45402	−	0.839478i	0.0777206	−	0.0448720i
$351$	−1.90214	−	1.09820i	−0.101529	−	0.0586176i
$352$	−2.69751	−	1.55741i	−0.143778	−	0.0830102i
$353$	20.0014	−	11.5478i	1.06457	−	0.614628i	0.137875	−	0.990450i	$-0.455973\pi$
$353$	20.0014	−	11.5478i	1.06457	−	0.614628i	0.926692	+	0.375822i	$0.122639\pi$
$354$	−2.52041	−	4.36549i	−0.133959	−	0.232023i
$355$	−2.35834	+	1.36159i	−0.125168	+	0.0722657i
$356$			6.69508i			0.354839i
$357$	5.87314	+	3.39086i	0.310840	+	0.179463i
$358$	2.94967	+	5.10898i	0.155895	+	0.270018i
$359$	−23.2699			−1.22814			−0.614068	−	0.789253i	$-0.710468\pi$
$359$	−23.2699			−1.22814			−0.614068	+	0.789253i	$0.710468\pi$
$360$	1.00000			0.0527046
$361$	−2.61431	−	4.52812i	−0.137595	−	0.238322i
$362$			9.58974i			0.504025i
$363$	−0.648956	+	1.12403i	−0.0340614	+	0.0589960i
$364$			3.68766i			0.193286i
$365$	1.78508	+	1.03062i	0.0934355	+	0.0539450i
$366$	−5.97938	+	10.3566i	−0.312547	+	0.541348i
$367$	−18.5412	+	32.1143i	−0.967844	+	1.67635i	−0.266071	+	0.963954i	$0.585725\pi$
$367$	−18.5412	+	32.1143i	−0.967844	+	1.67635i	−0.701773	+	0.712401i	$0.747608\pi$
$368$	3.46505	−	2.00055i	0.180628	−	0.104286i
$369$	−2.68947			−0.140008
$370$	−5.10494	+	3.30750i	−0.265393	+	0.171949i
$371$	21.4369			1.11295
$372$	4.27947	−	2.47075i	0.221880	−	0.128103i
$373$	18.6646	−	32.3280i	0.966416	−	1.67388i	0.260656	−	0.965432i	$-0.416061\pi$
$373$	18.6646	−	32.3280i	0.966416	−	1.67388i	0.705760	−	0.708451i	$-0.250606\pi$
$374$	6.29076	−	10.8959i	0.325287	−	0.563414i
$375$	0.866025	+	0.500000i	0.0447214	+	0.0258199i
$376$			5.05625i			0.260756i
$377$	−5.54565	+	9.60535i	−0.285616	+	0.494701i
$378$			1.67896i			0.0863562i
$379$	14.0651	+	24.3615i	0.722477	+	1.25137i	0.960004	+	0.279986i	$0.0903298\pi$
$379$	14.0651	+	24.3615i	0.722477	+	1.25137i	−0.237527	+	0.971381i	$0.576337\pi$
$380$	3.71098			0.190369
$381$	−19.5018			−0.999108
$382$	−4.69798	−	8.13714i	−0.240370	−	0.416332i
$383$	−3.84862	−	2.22200i	−0.196655	−	0.113539i	0.398439	−	0.917195i	$-0.369552\pi$
$383$	−3.84862	−	2.22200i	−0.196655	−	0.113539i	−0.595094	+	0.803656i	$0.702885\pi$
$384$		−	1.00000i		−	0.0510310i
$385$	4.52900	−	2.61482i	0.230819	−	0.133264i
$386$	0.295983	+	0.512657i	0.0150651	+	0.0260936i
$387$	5.00371	−	2.88889i	0.254353	−	0.146851i
$388$	−5.50317	−	3.17726i	−0.279381	−	0.161301i
$389$	−0.525760	−	0.303548i	−0.0266571	−	0.0153905i	0.486612	−	0.873618i	$-0.338232\pi$
$389$	−0.525760	−	0.303548i	−0.0266571	−	0.0153905i	−0.513269	+	0.858228i	$0.671566\pi$
$390$	−1.90214	+	1.09820i	−0.0963186	+	0.0556095i
$391$	8.08070	+	13.9962i	0.408659	+	0.707818i
$392$	−3.62094	+	2.09055i	−0.182885	+	0.105589i
$393$			3.26462i			0.164678i
$394$	21.4811	+	12.4021i	1.08220	+	0.624809i
$395$	8.18371	+	14.1746i	0.411767	+	0.713202i
$396$	3.11482			0.156525
$397$	11.2514			0.564693			0.282347	−	0.959312i	$-0.408887\pi$
$397$	11.2514			0.564693			0.282347	+	0.959312i	$0.408887\pi$
$398$	−8.49229	−	14.7091i	−0.425680	−	0.737300i
$399$			6.23058i			0.311919i
$400$	0.500000	−	0.866025i	0.0250000	−	0.0433013i
$401$			15.2870i			0.763399i	0.924287	+	0.381699i	$0.124661\pi$
$401$			15.2870i			0.763399i	−0.924287	+	0.381699i	$0.875339\pi$
$402$	3.78138	+	2.18318i	0.188598	+	0.108887i
$403$	−5.42677	+	9.39944i	−0.270327	+	0.468219i
$404$	1.23506	−	2.13918i	0.0614464	−	0.106428i
$405$	−0.866025	+	0.500000i	−0.0430331	+	0.0248452i
$406$	8.47833			0.420772
$407$	−15.9010	+	10.3023i	−0.788182	+	0.510664i
$408$	4.03925			0.199972
$409$	−11.4321	+	6.60034i	−0.565283	+	0.326366i	−0.755263	−	0.655422i	$-0.772491\pi$
$409$	−11.4321	+	6.60034i	−0.565283	+	0.326366i	0.189980	+	0.981788i	$0.439158\pi$
$410$	−1.34474	+	2.32915i	−0.0664118	+	0.115029i
$411$	−1.50458	+	2.60601i	−0.0742155	+	0.128545i
$412$	−1.41414	−	0.816453i	−0.0696696	−	0.0402238i
$413$		−	8.46333i		−	0.416453i
$414$	−2.00055	+	3.46505i	−0.0983216	+	0.170298i
$415$			5.39551i			0.264855i
$416$	1.09820	+	1.90214i	0.0538437	+	0.0932600i
$417$	19.2643			0.943379
$418$	11.5590			0.565371
$419$	4.21451	+	7.29974i	0.205892	+	0.356616i	0.950417	−	0.310979i	$-0.100657\pi$
$419$	4.21451	+	7.29974i	0.205892	+	0.356616i	−0.744524	+	0.667595i	$0.767324\pi$
$420$	1.45402	+	0.839478i	0.0709489	+	0.0409623i
$421$		−	13.0242i		−	0.634759i	−0.948299	−	0.317379i	$-0.897197\pi$
$421$		−	13.0242i		−	0.634759i	0.948299	−	0.317379i	$-0.102803\pi$
$422$	13.0068	−	7.50951i	0.633163	−	0.365557i
$423$	−2.52813	−	4.37884i	−0.122922	−	0.212907i
$424$	11.0574	−	6.38398i	0.536994	−	0.310034i
$425$	3.49809	+	2.01962i	0.169682	+	0.0979661i
$426$	−2.35834	−	1.36159i	−0.114262	−	0.0659693i
$427$	−17.3883	+	10.0391i	−0.841477	+	0.485827i
$428$	3.00186	+	5.19937i	0.145100	+	0.251321i
$429$	−5.92482	+	3.42069i	−0.286053	+	0.165153i
$430$		−	5.77779i		−	0.278630i
$431$	−20.5049	−	11.8385i	−0.987684	−	0.570240i	−0.0831031	−	0.996541i	$-0.526483\pi$
$431$	−20.5049	−	11.8385i	−0.987684	−	0.570240i	−0.904581	+	0.426301i	$0.859816\pi$
$432$	0.500000	+	0.866025i	0.0240563	+	0.0416667i
$433$	24.5236			1.17853			0.589266	−	0.807939i	$-0.299417\pi$
$433$	24.5236			1.17853			0.589266	+	0.807939i	$0.299417\pi$
$434$	8.29658			0.398248
$435$	2.52488	+	4.37322i	0.121059	+	0.209680i
$436$		−	7.16298i		−	0.343045i
$437$	−7.42400	+	12.8587i	−0.355138	+	0.615117i
$438$			2.06124i			0.0984896i
$439$	19.2488	+	11.1133i	0.918696	+	0.530409i	0.883219	−	0.468961i	$-0.155372\pi$
$439$	19.2488	+	11.1133i	0.918696	+	0.530409i	0.0354771	+	0.999370i	$0.488705\pi$
$440$	1.55741	−	2.69751i	0.0742465	−	0.128599i
$441$	2.09055	−	3.62094i	0.0995501	−	0.172426i
$442$	−7.68321	+	4.43590i	−0.365453	+	0.210994i
$443$	−17.3757			−0.825545			−0.412773	−	0.910834i	$-0.635440\pi$
$443$	−17.3757			−0.825545			−0.412773	+	0.910834i	$0.635440\pi$
$444$	−5.41685	−	2.76726i	−0.257072	−	0.131328i
$445$	−6.69508			−0.317377
$446$	−7.05909	+	4.07557i	−0.334258	+	0.192984i
$447$	−4.81707	+	8.34341i	−0.227840	+	0.394630i
$448$	0.839478	−	1.45402i	0.0396616	−	0.0686959i
$449$	−3.38846	−	1.95633i	−0.159911	−	0.0923248i	0.417909	−	0.908489i	$-0.362763\pi$
$449$	−3.38846	−	1.95633i	−0.159911	−	0.0923248i	−0.577820	+	0.816164i	$0.696096\pi$
$450$			1.00000i			0.0471405i
$451$	−4.18861	+	7.25488i	−0.197234	+	0.341619i
$452$			6.58493i			0.309729i
$453$	−1.38277	−	2.39502i	−0.0649680	−	0.112528i
$454$	19.1408			0.898324
$455$	−3.68766			−0.172880
$456$	1.85549	+	3.21380i	0.0868913	+	0.150500i
$457$	8.02456	+	4.63298i	0.375373	+	0.216722i	0.675803	−	0.737082i	$-0.263797\pi$
$457$	8.02456	+	4.63298i	0.375373	+	0.216722i	−0.300430	+	0.953804i	$0.597130\pi$
$458$		−	4.21660i		−	0.197029i
$459$	−3.49809	+	2.01962i	−0.163277	+	0.0942679i
$460$	2.00055	+	3.46505i	0.0932760	+	0.161559i
$461$	−3.27441	+	1.89048i	−0.152504	+	0.0880484i	−0.574310	−	0.818638i	$-0.694730\pi$
$461$	−3.27441	+	1.89048i	−0.152504	+	0.0880484i	0.421806	+	0.906686i	$0.361396\pi$
$462$	4.52900	+	2.61482i	0.210708	+	0.121652i
$463$	−18.6447	−	10.7645i	−0.866494	−	0.500271i	−0.000312703	−	1.00000i	$-0.500100\pi$
$463$	−18.6447	−	10.7645i	−0.866494	−	0.500271i	−0.866182	+	0.499729i	$0.833433\pi$
$464$	4.37322	−	2.52488i	0.203022	−	0.117215i
$465$	2.47075	+	4.27947i	0.114579	+	0.198456i
$466$	−8.26221	+	4.77019i	−0.382740	+	0.220975i
$467$			6.90304i			0.319435i	0.987163	+	0.159717i	$0.0510583\pi$
$467$			6.90304i			0.319435i	−0.987163	+	0.159717i	$0.948942\pi$
$468$	−1.90214	−	1.09820i	−0.0879264	−	0.0507643i
$469$	3.66547	+	6.34878i	0.169256	+	0.293159i
$470$	−5.05625			−0.233228
$471$	6.21658			0.286445
$472$	−2.52041	−	4.36549i	−0.116011	−	0.200938i
$473$		−	17.9968i		−	0.827492i
$474$	−8.18371	+	14.1746i	−0.375890	+	0.651061i
$475$			3.71098i			0.170271i
$476$	5.87314	+	3.39086i	0.269195	+	0.155420i
$477$	−6.38398	+	11.0574i	−0.292302	+	0.506283i
$478$	0.551219	−	0.954740i	0.0252122	−	0.0436688i
$479$	23.9274	−	13.8145i	1.09327	−	0.631200i	0.158826	−	0.987307i	$-0.449229\pi$
$479$	23.9274	−	13.8145i	1.09327	−	0.631200i	0.934445	+	0.356106i	$0.115896\pi$
$480$	1.00000			0.0456435
$481$	13.3426	−	0.685068i	0.608371	−	0.0312364i
$482$	26.9334			1.22678
$483$	−5.81767	+	3.35883i	−0.264713	+	0.152832i
$484$	−0.648956	+	1.12403i	−0.0294980	+	0.0510920i
$485$	3.17726	−	5.50317i	0.144272	−	0.249886i
$486$	−0.866025	−	0.500000i	−0.0392837	−	0.0226805i
$487$		−	5.77366i		−	0.261630i	−0.991407	−	0.130815i	$-0.958241\pi$
$487$		−	5.77366i		−	0.261630i	0.991407	−	0.130815i	$-0.0417593\pi$
$488$	−5.97938	+	10.3566i	−0.270674	+	0.468821i
$489$		−	14.7718i		−	0.668003i
$490$	−2.09055	−	3.62094i	−0.0944416	−	0.163578i
$491$	11.9996			0.541536			0.270768	−	0.962645i	$-0.412722\pi$
$491$	11.9996			0.541536			0.270768	+	0.962645i	$0.412722\pi$
$492$	−2.68947			−0.121251
$493$	10.1986	+	17.6645i	0.459322	+	0.795570i
$494$	−7.05880	−	4.07540i	−0.317591	−	0.183361i
$495$			3.11482i			0.140001i
$496$	4.27947	−	2.47075i	0.192154	−	0.110940i
$497$	−2.28605	−	3.95956i	−0.102543	−	0.177610i
$498$	−4.67265	+	2.69775i	−0.209386	+	0.120889i
$499$	−21.7771	−	12.5730i	−0.974877	−	0.562846i	−0.0741575	−	0.997247i	$-0.523627\pi$
$499$	−21.7771	−	12.5730i	−0.974877	−	0.562846i	−0.900720	+	0.434401i	$0.856960\pi$
$500$	0.866025	+	0.500000i	0.0387298	+	0.0223607i
$501$	8.40730	−	4.85396i	0.375611	−	0.216859i
$502$	13.7217	+	23.7667i	0.612429	+	1.06076i
$503$	15.7661	−	9.10258i	0.702977	−	0.405864i	−0.105478	−	0.994422i	$-0.533637\pi$
$503$	15.7661	−	9.10258i	0.702977	−	0.405864i	0.808455	+	0.588558i	$0.200304\pi$
$504$			1.67896i			0.0747867i
$505$	2.13918	+	1.23506i	0.0951923	+	0.0549593i
$506$	6.23134	+	10.7930i	0.277017	+	0.479807i
$507$	−8.17582			−0.363101
$508$	−19.5018			−0.865253
$509$	10.2075	+	17.6800i	0.452441	+	0.783651i	0.998537	−	0.0540716i	$-0.0172199\pi$
$509$	10.2075	+	17.6800i	0.452441	+	0.783651i	−0.546096	+	0.837723i	$0.683887\pi$
$510$			4.03925i			0.178861i
$511$	−1.73036	+	2.99708i	−0.0765467	+	0.132583i
$512$		−	1.00000i		−	0.0441942i
$513$	−3.21380	−	1.85549i	−0.141893	−	0.0819219i
$514$	−13.3875	+	23.1879i	−0.590499	+	1.02278i
$515$	0.816453	−	1.41414i	0.0359772	−	0.0623144i
$516$	5.00371	−	2.88889i	0.220276	−	0.127176i
$517$	−15.7493			−0.692654
$518$	−5.55314	−	8.57098i	−0.243991	−	0.376587i
$519$	10.7135			0.470271
$520$	−1.90214	+	1.09820i	−0.0834143	+	0.0481593i
$521$	−6.30711	+	10.9242i	−0.276320	+	0.478600i	−0.970467	−	0.241233i	$-0.922448\pi$
$521$	−6.30711	+	10.9242i	−0.276320	+	0.478600i	0.694148	+	0.719833i	$0.255782\pi$
$522$	−2.52488	+	4.37322i	−0.110511	+	0.191411i
$523$	−4.83979	−	2.79425i	−0.211629	−	0.122184i	0.390439	−	0.920629i	$-0.372323\pi$
$523$	−4.83979	−	2.79425i	−0.211629	−	0.122184i	−0.602068	+	0.798445i	$0.705657\pi$
$524$			3.26462i			0.142615i
$525$	−0.839478	+	1.45402i	−0.0366378	+	0.0634586i
$526$			21.6340i			0.943288i
$527$	9.97999	+	17.2858i	0.434735	+	0.752983i
$528$	3.11482			0.135555
$529$	6.99123			0.303967
$530$	6.38398	+	11.0574i	0.277302	+	0.480302i
$531$	4.36549	+	2.52041i	0.189446	+	0.109377i
$532$			6.23058i			0.270130i
$533$	5.11575	−	2.95358i	0.221588	−	0.127934i
$534$	−3.34754	−	5.79811i	−0.144862	−	0.250909i
$535$	−5.19937	+	3.00186i	−0.224788	+	0.129782i
$536$	3.78138	+	2.18318i	0.163331	+	0.0942991i
$537$	−5.10898	−	2.94967i	−0.220469	−	0.127288i
$538$	8.84797	−	5.10838i	0.381463	−	0.220238i
$539$	−6.51169	−	11.2786i	−0.280478	−	0.485803i
$540$	−0.866025	+	0.500000i	−0.0372678	+	0.0215166i
$541$		−	3.14841i		−	0.135361i	−0.997707	−	0.0676804i	$-0.978440\pi$
$541$		−	3.14841i		−	0.135361i	0.997707	−	0.0676804i	$-0.0215598\pi$
$542$	12.8429	+	7.41487i	0.551651	+	0.318496i
$543$	−4.79487	−	8.30496i	−0.205768	−	0.356400i
$544$	4.03925			0.173181
$545$	7.16298			0.306829
$546$	−1.84383	−	3.19361i	−0.0789087	−	0.136674i
$547$		−	21.3068i		−	0.911011i	−0.890233	−	0.455506i	$-0.849459\pi$
$547$		−	21.3068i		−	0.911011i	0.890233	−	0.455506i	$-0.150541\pi$
$548$	−1.50458	+	2.60601i	−0.0642725	+	0.111323i
$549$		−	11.9588i		−	0.510387i
$550$	2.69751	+	1.55741i	0.115022	+	0.0664081i
$551$	−9.36978	+	16.2289i	−0.399166	+	0.691376i
$552$	−2.00055	+	3.46505i	−0.0851490	+	0.147482i
$553$	−23.7985	+	13.7401i	−1.01202	+	0.584288i
$554$	14.6293			0.621541
$555$	2.76726	−	5.41685i	0.117464	−	0.229932i
$556$	19.2643			0.816990
$557$	3.44302	−	1.98783i	0.145885	−	0.0842269i	−0.425281	−	0.905062i	$-0.639825\pi$
$557$	3.44302	−	1.98783i	0.145885	−	0.0842269i	0.571166	+	0.820835i	$0.306491\pi$
$558$	−2.47075	+	4.27947i	−0.104595	+	0.181165i
$559$	−6.34517	+	10.9902i	−0.268372	+	0.464834i
$560$	1.45402	+	0.839478i	0.0614435	+	0.0354744i
$561$			12.5815i			0.531192i
$562$	−1.24182	+	2.15090i	−0.0523830	+	0.0907301i
$563$			25.3165i			1.06696i	0.845812	+	0.533482i	$0.179117\pi$
$563$			25.3165i			1.06696i	−0.845812	+	0.533482i	$0.820883\pi$
$564$	−2.52813	−	4.37884i	−0.106453	−	0.184383i
$565$	−6.58493			−0.277030
$566$	12.8574			0.540435
$567$	−0.839478	−	1.45402i	−0.0352548	−	0.0610631i
$568$	−2.35834	−	1.36159i	−0.0989539	−	0.0571311i
$569$			8.07490i			0.338517i	0.985572	+	0.169259i	$0.0541373\pi$
$569$			8.07490i			0.338517i	−0.985572	+	0.169259i	$0.945863\pi$
$570$	−3.21380	+	1.85549i	−0.134611	+	0.0777179i
$571$	−15.2691	−	26.4468i	−0.638991	−	1.10677i	−0.985655	−	0.168775i	$-0.946019\pi$
$571$	−15.2691	−	26.4468i	−0.638991	−	1.10677i	0.346663	−	0.937990i	$-0.387315\pi$
$572$	−5.92482	+	3.42069i	−0.247729	+	0.143026i
$573$	8.13714	+	4.69798i	0.339934	+	0.196261i
$574$	−3.91054	−	2.25775i	−0.163223	−	0.0942368i
$575$	−3.46505	+	2.00055i	−0.144503	+	0.0834286i
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$	−10.7838	+	6.22602i	−0.448935	+	0.259193i	−0.707380	−	0.706833i	$-0.750123\pi$
$577$	−10.7838	+	6.22602i	−0.448935	+	0.259193i	0.258446	+	0.966026i	$0.416790\pi$
$578$		−	0.684492i		−	0.0284711i
$579$	−0.512657	−	0.295983i	−0.0213053	−	0.0123006i
$580$	2.52488	+	4.37322i	0.104840	+	0.181588i
$581$	−9.05882			−0.375823
$582$	6.35452			0.263403
$583$	19.8849	+	34.4417i	0.823550	+	1.42643i
$584$			2.06124i			0.0852945i
$585$	1.09820	−	1.90214i	0.0454050	−	0.0786438i
$586$		−	13.0732i		−	0.540050i
$587$	−10.2420	−	5.91325i	−0.422735	−	0.244066i	0.273512	−	0.961869i	$-0.411815\pi$
$587$	−10.2420	−	5.91325i	−0.422735	−	0.244066i	−0.696247	+	0.717803i	$0.745148\pi$
$588$	2.09055	−	3.62094i	0.0862129	−	0.149325i
$589$	−9.16892	+	15.8810i	−0.377799	+	0.654367i
$590$	4.36549	−	2.52041i	0.179724	−	0.103764i
$591$	−24.8042			−1.02031
$592$	−5.41685	−	2.76726i	−0.222631	−	0.113734i
$593$	42.2434			1.73473			0.867364	−	0.497675i	$-0.165813\pi$
$593$	42.2434			1.73473			0.867364	+	0.497675i	$0.165813\pi$
$594$	−2.69751	+	1.55741i	−0.110680	+	0.0639013i
$595$	−3.39086	+	5.87314i	−0.139012	+	0.240775i
$596$	−4.81707	+	8.34341i	−0.197315	+	0.341759i
$597$	14.7091	+	8.49229i	0.602003	+	0.347566i
$598$		−	8.78801i		−	0.359368i
$599$	11.0583	−	19.1536i	0.451830	−	0.782593i	−0.546670	−	0.837348i	$-0.684105\pi$
$599$	11.0583	−	19.1536i	0.451830	−	0.782593i	0.998500	+	0.0547554i	$0.0174379\pi$
$600$			1.00000i			0.0408248i
$601$	7.49887	+	12.9884i	0.305885	+	0.529809i	0.977458	−	0.211130i	$-0.0677142\pi$
$601$	7.49887	+	12.9884i	0.305885	+	0.529809i	−0.671573	+	0.740939i	$0.734381\pi$
$602$	9.70065			0.395369
$603$	−4.36636			−0.177812
$604$	−1.38277	−	2.39502i	−0.0562640	−	0.0974521i
$605$	−1.12403	−	0.648956i	−0.0456981	−	0.0263838i
$606$			2.47011i			0.100342i
$607$	9.63929	−	5.56524i	0.391247	−	0.225886i	−0.291454	−	0.956585i	$-0.594139\pi$
$607$	9.63929	−	5.56524i	0.391247	−	0.225886i	0.682700	+	0.730699i	$0.260806\pi$
$608$	1.85549	+	3.21380i	0.0752501	+	0.130337i
$609$	−7.34245	+	4.23916i	−0.297531	+	0.171780i
$610$	−10.3566	−	5.97938i	−0.419326	−	0.242098i
$611$	9.61770	+	5.55278i	0.389090	+	0.224641i
$612$	−3.49809	+	2.01962i	−0.141402	+	0.0816384i
$613$	12.3369	+	21.3681i	0.498282	+	0.863050i	0.999998	−	0.00198245i	$-0.000631033\pi$
$613$	12.3369	+	21.3681i	0.498282	+	0.863050i	−0.501716	+	0.865032i	$0.667298\pi$
$614$	22.7337	−	13.1253i	0.917457	−	0.529694i
$615$		−	2.68947i		−	0.108450i
$616$	4.52900	+	2.61482i	0.182479	+	0.105354i
$617$	18.4446	+	31.9470i	0.742552	+	1.28614i	0.951330	+	0.308175i	$0.0997182\pi$
$617$	18.4446	+	31.9470i	0.742552	+	1.28614i	−0.208778	+	0.977963i	$0.566948\pi$
$618$	1.63291			0.0656851
$619$	20.0271			0.804959			0.402479	−	0.915429i	$-0.368149\pi$
$619$	20.0271			0.804959			0.402479	+	0.915429i	$0.368149\pi$
$620$	2.47075	+	4.27947i	0.0992279	+	0.171868i
$621$		−	4.00110i		−	0.160558i
$622$	−1.52374	+	2.63920i	−0.0610966	+	0.105822i
$623$		−	11.2407i		−	0.450351i
$624$	−1.90214	−	1.09820i	−0.0761465	−	0.0439632i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	7.42729	−	12.8644i	0.296854	−	0.514166i
$627$	−10.0104	+	5.77951i	−0.399777	+	0.230812i
$628$	6.21658			0.248068
$629$	11.1777	−	21.8800i	0.445682	−	0.872412i
$630$	−1.67896			−0.0668912
$631$	32.7988	−	18.9364i	1.30570	−	0.753845i	0.324323	−	0.945946i	$-0.394863\pi$
$631$	32.7988	−	18.9364i	1.30570	−	0.753845i	0.981375	+	0.192101i	$0.0615301\pi$
$632$	−8.18371	+	14.1746i	−0.325531	+	0.563835i
$633$	−7.50951	+	13.0068i	−0.298476	+	0.516976i
$634$	10.8839	+	6.28380i	0.432253	+	0.249562i
$635$		−	19.5018i		−	0.773906i
$636$	−6.38398	+	11.0574i	−0.253141	+	0.438454i
$637$			9.18338i			0.363859i
$638$	7.86454	+	13.6218i	0.311360	+	0.539292i
$639$	2.72318			0.107727
$640$	1.00000			0.0395285
$641$	17.5151	+	30.3371i	0.691806	+	1.19824i	0.971246	+	0.238080i	$0.0765180\pi$
$641$	17.5151	+	30.3371i	0.691806	+	1.19824i	−0.279439	+	0.960163i	$0.590149\pi$
$642$	−5.19937	−	3.00186i	−0.205203	−	0.118474i
$643$			46.7340i			1.84301i	0.388368	+	0.921504i	$0.373039\pi$
$643$			46.7340i			1.84301i	−0.388368	+	0.921504i	$0.626961\pi$
$644$	−5.81767	+	3.35883i	−0.229248	+	0.132357i
$645$	2.88889	+	5.00371i	0.113750	+	0.197021i
$646$	−12.9813	+	7.49478i	−0.510744	+	0.294878i
$647$	−2.96747	−	1.71327i	−0.116663	−	0.0673556i	0.440533	−	0.897736i	$-0.354790\pi$
$647$	−2.96747	−	1.71327i	−0.116663	−	0.0673556i	−0.557196	+	0.830381i	$0.688123\pi$
$648$	−0.866025	−	0.500000i	−0.0340207	−	0.0196419i
$649$	13.5977	−	7.85063i	0.533756	−	0.308164i
$650$	−1.09820	−	1.90214i	−0.0430750	−	0.0746080i
$651$	−7.18505	+	4.14829i	−0.281604	+	0.162584i
$652$		−	14.7718i		−	0.578507i
$653$	28.0828	+	16.2136i	1.09896	+	0.634487i	0.935949	−	0.352137i	$-0.114545\pi$
$653$	28.0828	+	16.2136i	1.09896	+	0.634487i	0.163015	+	0.986624i	$0.447878\pi$
$654$	3.58149	+	6.20333i	0.140047	+	0.242569i
$655$	−3.26462			−0.127559
$656$	−2.68947			−0.105006
$657$	−1.03062	−	1.78508i	−0.0402082	−	0.0696427i
$658$		−	8.48923i		−	0.330945i
$659$	−19.1350	+	33.1427i	−0.745393	+	1.29106i	0.204619	+	0.978842i	$0.434405\pi$
$659$	−19.1350	+	33.1427i	−0.745393	+	1.29106i	−0.950011	+	0.312216i	$0.898929\pi$
$660$			3.11482i			0.121244i
$661$	−22.7914	−	13.1586i	−0.886483	−	0.511811i	−0.0136927	−	0.999906i	$-0.504359\pi$
$661$	−22.7914	−	13.1586i	−0.886483	−	0.511811i	−0.872791	+	0.488095i	$0.837692\pi$
$662$	11.5007	−	19.9199i	0.446989	−	0.774208i
$663$	4.43590	−	7.68321i	0.172276	−	0.298391i
$664$	−4.67265	+	2.69775i	−0.181334	+	0.104693i
$665$	−6.23058			−0.241611
$666$	6.07476	−	0.311905i	0.235392	−	0.0120861i
$667$	−20.2046			−0.782324
$668$	8.40730	−	4.85396i	0.325288	−	0.187805i
$669$	4.07557	−	7.05909i	0.157571	−	0.272920i
$670$	−2.18318	+	3.78138i	−0.0843437	+	0.146088i
$671$	−32.2589	−	18.6247i	−1.24534	−	0.718998i
$672$			1.67896i			0.0647671i
$673$	8.47948	−	14.6869i	0.326860	−	0.566138i	−0.655027	−	0.755605i	$-0.727343\pi$
$673$	8.47948	−	14.6869i	0.326860	−	0.566138i	0.981887	+	0.189467i	$0.0606761\pi$
$674$			11.6381i			0.448282i
$675$	−0.500000	−	0.866025i	−0.0192450	−	0.0333333i
$676$	−8.17582			−0.314455
$677$	40.1260			1.54217			0.771084	−	0.636734i	$-0.219715\pi$
$677$	40.1260			1.54217			0.771084	+	0.636734i	$0.219715\pi$
$678$	−3.29247	−	5.70272i	−0.126446	−	0.219012i
$679$	9.23958	+	5.33448i	0.354583	+	0.204718i
$680$			4.03925i			0.154898i
$681$	−16.5765	+	9.57042i	−0.635211	+	0.366739i
$682$	7.69595	+	13.3298i	0.294693	+	0.510423i
$683$	−21.6778	+	12.5157i	−0.829477	+	0.478899i	−0.853673	−	0.520809i	$-0.825631\pi$
$683$	−21.6778	+	12.5157i	−0.829477	+	0.478899i	0.0241967	+	0.999707i	$0.492297\pi$
$684$	−3.21380	−	1.85549i	−0.122883	−	0.0709465i
$685$	−2.60601	−	1.50458i	−0.0995705	−	0.0574870i
$686$	16.2575	−	9.38629i	0.620716	−	0.358370i
$687$	2.10830	+	3.65168i	0.0804366	+	0.139320i
$688$	5.00371	−	2.88889i	0.190765	−	0.110138i
$689$		−	28.0436i		−	1.06837i
$690$	−3.46505	−	2.00055i	−0.131912	−	0.0761596i
$691$	3.36977	+	5.83661i	0.128192	+	0.222035i	0.922976	−	0.384857i	$-0.125749\pi$
$691$	3.36977	+	5.83661i	0.128192	+	0.222035i	−0.794784	+	0.606892i	$0.792416\pi$
$692$	10.7135			0.407267
$693$	−5.22964			−0.198658
$694$	10.1477	+	17.5764i	0.385202	+	0.667190i
$695$			19.2643i			0.730738i
$696$	−2.52488	+	4.37322i	−0.0957054	+	0.165767i
$697$		−	10.8634i		−	0.411482i
$698$	−5.59853	−	3.23231i	−0.211908	−	0.122345i
$699$	4.77019	−	8.26221i	0.180425	−	0.312506i
$700$	−0.839478	+	1.45402i	−0.0317293	+	0.0549567i
$701$	21.9691	−	12.6839i	0.829761	−	0.479063i	−0.0240097	−	0.999712i	$-0.507643\pi$
$701$	21.9691	−	12.6839i	0.829761	−	0.479063i	0.853771	+	0.520649i	$0.174310\pi$
$702$	2.19640			0.0828978
$703$	22.5433	−	1.15747i	0.850238	−	0.0436549i
$704$	3.11482			0.117394
$705$	4.37884	−	2.52813i	0.164917	−	0.0952148i
$706$	−11.5478	+	20.0014i	−0.434608	+	0.752763i
$707$	−2.07361	+	3.59159i	−0.0779860	+	0.135076i
$708$	4.36549	+	2.52041i	0.164065	+	0.0947230i
$709$		−	32.9232i		−	1.23646i	−0.785999	−	0.618228i	$-0.787851\pi$
$709$		−	32.9232i		−	1.23646i	0.785999	−	0.618228i	$-0.212149\pi$
$710$	1.36159	−	2.35834i	0.0510996	−	0.0885071i
$711$		−	16.3674i		−	0.613826i
$712$	−3.34754	−	5.79811i	−0.125454	−	0.217293i
$713$	−19.7715			−0.740447
$714$	−6.78172			−0.253799
$715$	−3.42069	−	5.92482i	−0.127927	−	0.221576i
$716$	−5.10898	−	2.94967i	−0.190931	−	0.110234i
$717$			1.10244i			0.0411713i
$718$	20.1523	−	11.6349i	0.752077	−	0.434212i
$719$	−10.9842	−	19.0252i	−0.409641	−	0.709519i	0.585208	−	0.810883i	$-0.301013\pi$
$719$	−10.9842	−	19.0252i	−0.409641	−	0.709519i	−0.994849	+	0.101364i	$0.967679\pi$
$720$	−0.866025	+	0.500000i	−0.0322749	+	0.0186339i
$721$	2.37428	+	1.37079i	0.0884227	+	0.0510509i
$722$	4.52812	+	2.61431i	0.168519	+	0.0972945i
$723$	−23.3250	+	13.4667i	−0.867466	+	0.500832i
$724$	−4.79487	−	8.30496i	−0.178200	−	0.308651i
$725$	−4.37322	+	2.52488i	−0.162417	+	0.0937717i
$726$		−	1.29791i		−	0.0481700i
$727$	−9.30758	−	5.37373i	−0.345199	−	0.199301i	0.317370	−	0.948302i	$-0.397200\pi$
$727$	−9.30758	−	5.37373i	−0.345199	−	0.199301i	−0.662569	+	0.749001i	$0.730534\pi$
$728$	−1.84383	−	3.19361i	−0.0683369	−	0.118363i
$729$	1.00000			0.0370370
$730$	−2.06124			−0.0762898
$731$	11.6690	+	20.2112i	0.431592	+	0.747539i
$732$		−	11.9588i		−	0.442008i
$733$	13.5795	−	23.5203i	0.501569	−	0.868743i	−0.498430	−	0.866930i	$-0.666090\pi$
$733$	13.5795	−	23.5203i	0.501569	−	0.868743i	0.999998	−	0.00181241i	$-0.000576908\pi$
$734$		−	37.0824i		−	1.36874i
$735$	3.62094	+	2.09055i	0.133561	+	0.0771112i
$736$	−2.00055	+	3.46505i	−0.0737412	+	0.127723i
$737$	−6.80021	+	11.7783i	−0.250489	+	0.433860i
$738$	2.32915	−	1.34474i	0.0857372	−	0.0495004i
$739$	19.6714			0.723623			0.361811	−	0.932251i	$-0.382158\pi$
$739$	19.6714			0.723623			0.361811	+	0.932251i	$0.382158\pi$
$740$	2.76726	−	5.41685i	0.101727	−	0.199127i
$741$	8.15080			0.299427
$742$	−18.5649	+	10.7184i	−0.681537	+	0.393486i
$743$	23.2831	−	40.3275i	0.854173	−	1.47947i	−0.0232368	−	0.999730i	$-0.507397\pi$
$743$	23.2831	−	40.3275i	0.854173	−	1.47947i	0.877410	−	0.479741i	$-0.159269\pi$
$744$	−2.47075	+	4.27947i	−0.0905823	+	0.156893i
$745$	−8.34341	−	4.81707i	−0.305679	−	0.176484i
$746$			37.3292i			1.36672i
$747$	2.69775	−	4.67265i	0.0987057	−	0.170963i
$748$			12.5815i			0.460026i
$749$	−5.03998	−	8.72951i	−0.184157	−	0.318969i
$750$	−1.00000			−0.0365148
$751$	−34.9770			−1.27633			−0.638165	−	0.769900i	$-0.720306\pi$
$751$	−34.9770			−1.27633			−0.638165	+	0.769900i	$0.720306\pi$
$752$	−2.52813	−	4.37884i	−0.0921913	−	0.159680i
$753$	−23.7667	−	13.7217i	−0.866105	−	0.500046i
$754$		−	11.0913i		−	0.403921i
$755$	2.39502	−	1.38277i	0.0871638	−	0.0503240i
$756$	−0.839478	−	1.45402i	−0.0305315	−	0.0528822i
$757$	−25.8435	+	14.9207i	−0.939298	+	0.542304i	−0.889740	−	0.456468i	$-0.849114\pi$
$757$	−25.8435	+	14.9207i	−0.939298	+	0.542304i	−0.0495575	+	0.998771i	$0.515781\pi$
$758$	−24.3615	−	14.0651i	−0.884850	−	0.510868i
$759$	−10.7930	−	6.23134i	−0.391761	−	0.226183i
$760$	−3.21380	+	1.85549i	−0.116577	+	0.0673057i
$761$	15.6704	+	27.1420i	0.568053	+	0.983896i	0.996758	+	0.0804520i	$0.0256364\pi$
$761$	15.6704	+	27.1420i	0.568053	+	0.983896i	−0.428706	+	0.903444i	$0.641030\pi$
$762$	16.8891	−	9.75091i	0.611826	−	0.353238i
$763$			12.0263i			0.435383i
$764$	8.13714	+	4.69798i	0.294391	+	0.169967i
$765$	−2.01962	−	3.49809i	−0.0730196	−	0.126474i
$766$	4.44400			0.160568
$767$	−11.0717			−0.399775
$768$	0.500000	+	0.866025i	0.0180422	+	0.0312500i
$769$		−	42.2148i		−	1.52230i	−0.648573	−	0.761152i	$-0.724634\pi$
$769$		−	42.2148i		−	1.52230i	0.648573	−	0.761152i	$-0.275366\pi$
$770$	−2.61482	+	4.52900i	−0.0942316	+	0.163214i
$771$		−	26.7751i		−	0.964282i
$772$	−0.512657	−	0.295983i	−0.0184509	−	0.0106527i
$773$	−21.1596	+	36.6495i	−0.761058	+	1.31819i	0.181247	+	0.983438i	$0.441987\pi$
$773$	−21.1596	+	36.6495i	−0.761058	+	1.31819i	−0.942306	+	0.334754i	$0.891347\pi$
$774$	−2.88889	+	5.00371i	−0.103839	+	0.179855i
$775$	−4.27947	+	2.47075i	−0.153723	+	0.0887521i
$776$	6.35452			0.228114
$777$	9.09465	+	4.64611i	0.326269	+	0.166678i
$778$	0.607096			0.0217654
$779$	8.64343	−	4.99029i	0.309683	−	0.178796i
$780$	1.09820	−	1.90214i	0.0393219	−	0.0681075i
$781$	4.24111	−	7.34581i	0.151759	−	0.262854i
$782$	−13.9962	−	8.08070i	−0.500503	−	0.288965i
$783$		−	5.04976i		−	0.180464i
$784$	2.09055	−	3.62094i	0.0746626	−	0.129319i
$785$			6.21658i			0.221879i
$786$	−1.63231	−	2.82724i	−0.0582225	−	0.100844i
$787$	−22.3240			−0.795765			−0.397882	−	0.917436i	$-0.630255\pi$
$787$	−22.3240			−0.795765			−0.397882	+	0.917436i	$0.630255\pi$
$788$	−24.8042			−0.883613
$789$	−10.8170	−	18.7356i	−0.385096	−	0.667006i
$790$	−14.1746	−	8.18371i	−0.504310	−	0.291163i
$791$		−	11.0558i		−	0.393099i
$792$	−2.69751	+	1.55741i	−0.0958519	+	0.0553401i
$793$	13.1331	+	22.7472i	0.466371	+	0.807777i
$794$	−9.74402	+	5.62571i	−0.345802	+	0.199649i
$795$	−11.0574	−	6.38398i	−0.392165	−	0.226416i
$796$	14.7091	+	8.49229i	0.521350	+	0.301001i
$797$	44.1318	−	25.4795i	1.56323	−	0.902531i	0.566302	−	0.824198i	$-0.308374\pi$
$797$	44.1318	−	25.4795i	1.56323	−	0.902531i	0.996927	−	0.0783332i	$-0.0249598\pi$
$798$	−3.11529	−	5.39584i	−0.110280	−	0.191011i
$799$	17.6872	−	10.2117i	0.625729	−	0.361265i
$800$			1.00000i			0.0353553i
$801$	5.79811	+	3.34754i	0.204866	+	0.118280i
$802$	−7.64352	−	13.2390i	−0.269902	−	0.467484i
$803$	−6.42037			−0.226570
$804$	−4.36636			−0.153990
$805$	−3.35883	−	5.81767i	−0.118383	−	0.205046i
$806$		−	10.8535i		−	0.382299i
$807$	−5.10838	+	8.84797i	−0.179823	+	0.311463i
$808$			2.47011i			0.0868983i
$809$	14.6095	+	8.43483i	0.513644	+	0.296553i	0.734330	−	0.678792i	$-0.237496\pi$
$809$	14.6095	+	8.43483i	0.513644	+	0.296553i	−0.220686	+	0.975345i	$0.570830\pi$
$810$	0.500000	−	0.866025i	0.0175682	−	0.0304290i
$811$	17.9724	−	31.1291i	0.631095	−	1.09309i	−0.356233	−	0.934397i	$-0.615939\pi$
$811$	17.9724	−	31.1291i	0.631095	−	1.09309i	0.987328	−	0.158692i	$-0.0507277\pi$
$812$	−7.34245	+	4.23916i	−0.257669	+	0.148765i
$813$	−14.8297			−0.520102
$814$	8.61952	−	16.8725i	0.302114	−	0.591381i
$815$	14.7718			0.517433
$816$	−3.49809	+	2.01962i	−0.122458	+	0.0707009i
$817$	−10.7206	+	18.5687i	−0.375067	+	0.649636i
$818$	6.60034	−	11.4321i	0.230776	−	0.399715i
$819$	3.19361	+	1.84383i	0.111594	+	0.0644287i
$820$		−	2.68947i		−	0.0939204i
$821$	22.7904	−	39.4742i	0.795392	−	1.37766i	−0.127199	−	0.991877i	$-0.540599\pi$
$821$	22.7904	−	39.4742i	0.795392	−	1.37766i	0.922590	−	0.385781i	$-0.126068\pi$
$822$		−	3.00916i		−	0.104957i
$823$	3.82120	+	6.61851i	0.133199	+	0.230707i	0.924908	−	0.380191i	$-0.124142\pi$
$823$	3.82120	+	6.61851i	0.133199	+	0.230707i	−0.791709	+	0.610898i	$0.790809\pi$
$824$	1.63291			0.0568850
$825$	−3.11482			−0.108444
$826$	4.23167	+	7.32946i	0.147238	+	0.255025i
$827$	8.47127	+	4.89089i	0.294575	+	0.170073i	0.640003	−	0.768372i	$-0.278933\pi$
$827$	8.47127	+	4.89089i	0.294575	+	0.170073i	−0.345428	+	0.938445i	$0.612266\pi$
$828$		−	4.00110i		−	0.139048i
$829$	5.85315	−	3.37932i	0.203288	−	0.117369i	−0.394900	−	0.918724i	$-0.629221\pi$
$829$	5.85315	−	3.37932i	0.203288	−	0.117369i	0.598188	+	0.801356i	$0.295887\pi$
$830$	−2.69775	−	4.67265i	−0.0936404	−	0.162190i
$831$	−12.6694	+	7.31467i	−0.439496	+	0.253743i
$832$	−1.90214	−	1.09820i	−0.0659448	−	0.0380733i
$833$	14.6259	+	8.44426i	0.506757	+	0.292576i
$834$	−16.6834	+	9.63217i	−0.577699	+	0.333535i
$835$	4.85396	+	8.40730i	0.167978	+	0.290947i
$836$	−10.0104	+	5.77951i	−0.346217	+	0.199889i
$837$		−	4.94151i		−	0.170804i
$838$	−7.29974	−	4.21451i	−0.252165	−	0.145588i
$839$	−23.5010	−	40.7049i	−0.811344	−	1.40529i	−0.911924	−	0.410360i	$-0.865403\pi$
$839$	−23.5010	−	40.7049i	−0.811344	−	1.40529i	0.100580	−	0.994929i	$-0.467930\pi$
$840$	−1.67896			−0.0579295
$841$	3.49991			0.120687
$842$	6.51208	+	11.2793i	0.224421	+	0.388709i
$843$		−	2.48364i		−	0.0855411i
$844$	−7.50951	+	13.0068i	−0.258488	+	0.447714i
$845$		−	8.17582i		−	0.281257i
$846$	4.37884	+	2.52813i	0.150548	+	0.0869188i
$847$	1.08957	−	1.88719i	0.0374380	−	0.0648446i
$848$	−6.38398	+	11.0574i	−0.219227	+	0.379712i
$849$	−11.1348	+	6.42868i	−0.382145	+	0.220632i
$850$	−4.03925			−0.138545
$851$	13.2336	+	20.4254i	0.453642	+	0.700173i
$852$	2.72318			0.0932947
$853$	14.3406	−	8.27954i	0.491012	−	0.283486i	−0.233982	−	0.972241i	$-0.575176\pi$
$853$	14.3406	−	8.27954i	0.491012	−	0.283486i	0.724994	+	0.688755i	$0.241842\pi$
$854$	10.0391	−	17.3883i	0.343531	−	0.595014i
$855$	1.85549	−	3.21380i	0.0634564	−	0.109910i
$856$	−5.19937	−	3.00186i	−0.177711	−	0.102601i
$857$			11.0540i			0.377599i	0.982016	+	0.188799i	$0.0604596\pi$
$857$			11.0540i			0.377599i	−0.982016	+	0.188799i	$0.939540\pi$
$858$	3.42069	−	5.92482i	0.116781	−	0.202270i
$859$		−	35.6899i		−	1.21772i	−0.793276	−	0.608862i	$-0.791626\pi$
$859$		−	35.6899i		−	1.21772i	0.793276	−	0.608862i	$-0.208374\pi$
$860$	2.88889	+	5.00371i	0.0985105	+	0.170625i
$861$	4.51550			0.153888
$862$	23.6770			0.806441
$863$	4.77067	+	8.26304i	0.162395	+	0.281277i	0.935727	−	0.352724i	$-0.114745\pi$
$863$	4.77067	+	8.26304i	0.162395	+	0.281277i	−0.773332	+	0.634001i	$0.781411\pi$
$864$	−0.866025	−	0.500000i	−0.0294628	−	0.0170103i
$865$			10.7135i			0.364270i
$866$	−21.2381	+	12.2618i	−0.721700	+	0.416674i
$867$	0.342246	+	0.592787i	0.0116233	+	0.0201321i
$868$	−7.18505	+	4.14829i	−0.243876	+	0.140802i
$869$	−44.1513	−	25.4908i	−1.49773	−	0.864715i
$870$	−4.37322	−	2.52488i	−0.148266	−	0.0856015i
$871$	8.30543	−	4.79514i	0.281419	−	0.162477i
$872$	3.58149	+	6.20333i	0.121285	+	0.210071i
$873$	−5.50317	+	3.17726i	−0.186254	+	0.107534i
$874$		−	14.8480i		−	0.502241i
$875$	−1.45402	−	0.839478i	−0.0491548	−	0.0283795i
$876$	−1.03062	−	1.78508i	−0.0348213	−	0.0603123i
$877$	−41.7067			−1.40834			−0.704168	−	0.710034i	$-0.748680\pi$
$877$	−41.7067			−1.40834			−0.704168	+	0.710034i	$0.748680\pi$
$878$	−22.2266			−0.750112
$879$	6.53661	+	11.3217i	0.220474	+	0.381873i
$880$			3.11482i			0.105000i
$881$	7.08826	−	12.2772i	0.238810	−	0.413630i	−0.721563	−	0.692348i	$-0.756576\pi$
$881$	7.08826	−	12.2772i	0.238810	−	0.413630i	0.960373	+	0.278718i	$0.0899095\pi$
$882$			4.18111i			0.140785i
$883$	24.4196	+	14.0987i	0.821785	+	0.474458i	0.851031	−	0.525115i	$-0.175978\pi$
$883$	24.4196	+	14.0987i	0.821785	+	0.474458i	−0.0292469	+	0.999572i	$0.509311\pi$
$884$	4.43590	−	7.68321i	0.149196	−	0.258414i
$885$	−2.52041	+	4.36549i	−0.0847228	+	0.146744i
$886$	15.0478	−	8.68786i	0.505541	−	0.291874i
$887$	28.5132			0.957378			0.478689	−	0.877984i	$-0.341112\pi$
$887$	28.5132			0.957378			0.478689	+	0.877984i	$0.341112\pi$
$888$	6.07476	−	0.311905i	0.203856	−	0.0104668i
$889$	32.7427			1.09815
$890$	5.79811	−	3.34754i	0.194353	−	0.112210i
$891$	1.55741	−	2.69751i	0.0521752	−	0.0903700i
$892$	4.07557	−	7.05909i	0.136460	−	0.236356i
$893$	16.2498	+	9.38183i	0.543779	+	0.313951i
$894$		−	9.63414i		−	0.322214i
$895$	2.94967	−	5.10898i	0.0985965	−	0.170774i
$896$			1.67896i			0.0560900i
$897$	4.39401	+	7.61064i	0.146712	+	0.254112i
$898$	3.91266			0.130567
$899$	−24.9534			−0.832244
$900$	−0.500000	−	0.866025i	−0.0166667	−	0.0288675i
$901$	−44.6635	−	25.7865i	−1.48796	−	0.859072i
$902$		−	8.37721i		−	0.278931i
$903$	−8.40101	+	4.85033i	−0.279568	+	0.161409i
$904$	−3.29247	−	5.70272i	−0.109506	−	0.189670i
$905$	8.30496	−	4.79487i	0.276066	−	0.159387i
$906$	2.39502	+	1.38277i	0.0795693	+	0.0459393i
$907$	−19.1792	−	11.0731i	−0.636834	−	0.367676i	0.146560	−	0.989202i	$-0.453180\pi$
$907$	−19.1792	−	11.0731i	−0.636834	−	0.367676i	−0.783394	+	0.621526i	$0.786513\pi$
$908$	−16.5765	+	9.57042i	−0.550109	+	0.317606i
$909$	−1.23506	−	2.13918i	−0.0409642	−	0.0709522i
$910$	3.19361	−	1.84383i	0.105867	−	0.0611224i
$911$			4.08737i			0.135421i	0.997705	+	0.0677103i	$0.0215694\pi$
$911$			4.08737i			0.135421i	−0.997705	+	0.0677103i	$0.978431\pi$
$912$	−3.21380	−	1.85549i	−0.106420	−	0.0614414i
$913$	−8.40301	−	14.5544i	−0.278099	−	0.481682i
$914$	−9.26596			−0.306491
$915$	11.9588			0.395344
$916$	2.10830	+	3.65168i	0.0696601	+	0.120655i
$917$		−	5.48115i		−	0.181003i
$918$	2.01962	−	3.49809i	0.0666575	−	0.115454i
$919$			28.2670i			0.932443i	0.884668	+	0.466221i	$0.154385\pi$
$919$			28.2670i			0.932443i	−0.884668	+	0.466221i	$0.845615\pi$
$920$	−3.46505	−	2.00055i	−0.114239	−	0.0659561i
$921$	−13.1253	+	22.7337i	−0.432494	+	0.749101i
$922$	1.89048	−	3.27441i	0.0622596	−	0.107837i
$923$	−5.17987	+	2.99060i	−0.170498	+	0.0984368i
$924$	−5.22964			−0.172043
$925$	5.41685	+	2.76726i	0.178105	+	0.0909870i
$926$	21.5291			0.707490
$927$	−1.41414	+	0.816453i	−0.0464464	+	0.0268158i
$928$	−2.52488	+	4.37322i	−0.0828833	+	0.143558i
$929$	−15.4997	+	26.8463i	−0.508530	+	0.880799i	0.491421	+	0.870922i	$0.336477\pi$
$929$	−15.4997	+	26.8463i	−0.508530	+	0.880799i	−0.999951	+	0.00987745i	$0.996856\pi$
$930$	−4.27947	−	2.47075i	−0.140329	−	0.0810192i
$931$			15.5160i			0.508517i
$932$	4.77019	−	8.26221i	0.156253	−	0.270638i
$933$		−	3.04749i		−	0.0997703i
$934$	−3.45152	−	5.97821i	−0.112937	−	0.195613i
$935$	−12.5815			−0.411459
$936$	2.19640			0.0717916
$937$	−10.5220	−	18.2247i	−0.343740	−	0.595376i	0.641384	−	0.767220i	$-0.278361\pi$
$937$	−10.5220	−	18.2247i	−0.343740	−	0.595376i	−0.985124	+	0.171845i	$0.945027\pi$
$938$	−6.34878	−	3.66547i	−0.207295	−	0.119682i
$939$			14.8546i			0.484761i
$940$	4.37884	−	2.52813i	0.142822	−	0.0824584i
$941$	−18.4334	−	31.9276i	−0.600911	−	1.04081i	−0.992683	−	0.120747i	$-0.961471\pi$
$941$	−18.4334	−	31.9276i	−0.600911	−	1.04081i	0.391772	−	0.920062i	$-0.371862\pi$
$942$	−5.38371	+	3.10829i	−0.175411	+	0.101274i
$943$	9.31915	+	5.38042i	0.303473	+	0.175210i
$944$	4.36549	+	2.52041i	0.142084	+	0.0820325i
$945$	1.45402	−	0.839478i	0.0472992	−	0.0273082i
$946$	8.99838	+	15.5856i	0.292563	+	0.506733i
$947$	4.93092	−	2.84687i	0.160233	−	0.0925107i	−0.417739	−	0.908567i	$-0.637177\pi$
$947$	4.93092	−	2.84687i	0.160233	−	0.0925107i	0.577972	+	0.816056i	$0.303844\pi$
$948$		−	16.3674i		−	0.531589i
$949$	3.92076	+	2.26365i	0.127273	+	0.0734812i
$950$	−1.85549	−	3.21380i	−0.0602001	−	0.104270i
$951$	−12.5676			−0.407532
$952$	−6.78172			−0.219797
$953$	−1.61822	−	2.80283i	−0.0524191	−	0.0907926i	0.838625	−	0.544709i	$-0.183360\pi$
$953$	−1.61822	−	2.80283i	−0.0524191	−	0.0907926i	−0.891044	+	0.453916i	$0.850027\pi$
$954$		−	12.7680i		−	0.413378i
$955$	−4.69798	+	8.13714i	−0.152023	+	0.263312i
$956$			1.10244i			0.0356554i
$957$	−13.6218	−	7.86454i	−0.440330	−	0.254225i
$958$	−13.8145	+	23.9274i	−0.446326	+	0.773059i
$959$	2.52612	−	4.37538i	0.0815728	−	0.141288i
$960$	−0.866025	+	0.500000i	−0.0279508	+	0.0161374i
$961$	6.58149			0.212306
$962$	−11.2125	+	7.26459i	−0.361506	+	0.234220i
$963$	6.00371			0.193467
$964$	−23.3250	+	13.4667i	−0.751248	+	0.433733i
$965$	0.295983	−	0.512657i	0.00952803	−	0.0165030i
$966$	3.35883	−	5.81767i	0.108069	−	0.187180i
$967$	−34.2654	−	19.7831i	−1.10190	−	0.636182i	−0.165181	−	0.986263i	$-0.552821\pi$
$967$	−34.2654	−	19.7831i	−1.10190	−	0.636182i	−0.936719	+	0.350081i	$0.886154\pi$
$968$		−	1.29791i		−	0.0417165i
$969$	7.49478	−	12.9813i	0.240767	−	0.417021i
$970$			6.35452i			0.204031i
$971$	−1.61187	−	2.79184i	−0.0517274	−	0.0895945i	0.839002	−	0.544128i	$-0.183139\pi$
$971$	−1.61187	−	2.79184i	−0.0517274	−	0.0895945i	−0.890730	+	0.454533i	$0.849806\pi$
$972$	1.00000			0.0320750
$973$	−32.3440			−1.03690
$974$	2.88683	+	5.00014i	0.0925000	+	0.160215i
$975$	1.90214	+	1.09820i	0.0609172	+	0.0351706i
$976$		−	11.9588i		−	0.382791i
$977$	−4.04716	+	2.33663i	−0.129480	+	0.0747555i	−0.563341	−	0.826224i	$-0.690484\pi$
$977$	−4.04716	+	2.33663i	−0.129480	+	0.0747555i	0.433861	+	0.900980i	$0.357151\pi$
$978$	7.38589	+	12.7927i	0.236175	+	0.409067i
$979$	18.0601	−	10.4270i	0.577202	−	0.333248i
$980$	3.62094	+	2.09055i	0.115667	+	0.0667803i
$981$	−6.20333	−	3.58149i	−0.198057	−	0.114348i
$982$	−10.3920	+	5.99982i	−0.331622	+	0.191462i
$983$	7.50400	+	12.9973i	0.239341	+	0.414550i	0.960525	−	0.278193i	$-0.0897354\pi$
$983$	7.50400	+	12.9973i	0.239341	+	0.414550i	−0.721185	+	0.692743i	$0.756402\pi$
$984$	2.32915	−	1.34474i	0.0742506	−	0.0428686i
$985$		−	24.8042i		−	0.790328i
$986$	−17.6645	−	10.1986i	−0.562553	−	0.324790i
$987$	4.24461	+	7.35189i	0.135108	+	0.234013i
$988$	8.15080			0.259312
$989$	−23.1175			−0.735093
$990$	−1.55741	−	2.69751i	−0.0494977	−	0.0857325i
$991$			43.4622i			1.38062i	0.723513	+	0.690311i	$0.242526\pi$
$991$			43.4622i			1.38062i	−0.723513	+	0.690311i	$0.757474\pi$
$992$	−2.47075	+	4.27947i	−0.0784465	+	0.135873i
$993$			23.0015i			0.729930i
$994$	3.95956	+	2.28605i	0.125590	+	0.0725092i
$995$	−8.49229	+	14.7091i	−0.269224	+	0.466309i
$996$	2.69775	−	4.67265i	0.0854816	−	0.148059i
$997$	51.4720	−	29.7174i	1.63013	−	0.941158i	0.646084	−	0.763266i	$-0.276406\pi$
$997$	51.4720	−	29.7174i	1.63013	−	0.941158i	0.984050	−	0.177892i	$-0.0569278\pi$
$998$	25.1460			0.795984
$999$	−5.10494	+	3.30750i	−0.161513	+	0.104645i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.x.e.751.2	✓	16
37.27	even	6	inner	1110.2.x.e.841.2	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.x.e.751.2	✓	16	1.1	even	1	trivial
1110.2.x.e.841.2	yes	16	37.27	even	6	inner

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)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{5} +1.00000i q^{6} +(-0.839478 + 1.45402i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(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} +(-0.839478 + 1.45402i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} -1.00000 q^{10} -3.11482 q^{11} +(-0.500000 - 0.866025i) q^{12} +(1.90214 + 1.09820i) q^{13} -1.67896i q^{14} +(0.866025 - 0.500000i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.49809 - 2.01962i) q^{17} +(0.866025 + 0.500000i) q^{18} +(3.21380 + 1.85549i) q^{19} +(0.866025 - 0.500000i) q^{20} +(0.839478 + 1.45402i) q^{21} +(2.69751 - 1.55741i) q^{22} +4.00110i q^{23} +(0.866025 + 0.500000i) q^{24} +(0.500000 + 0.866025i) q^{25} -2.19640 q^{26} -1.00000 q^{27} +(0.839478 + 1.45402i) q^{28} +5.04976i q^{29} +(-0.500000 + 0.866025i) q^{30} +4.94151i q^{31} +(0.866025 + 0.500000i) q^{32} +(-1.55741 + 2.69751i) q^{33} +(-2.01962 + 3.49809i) q^{34} +(-1.45402 + 0.839478i) q^{35} -1.00000 q^{36} +(5.10494 - 3.30750i) q^{37} -3.71098 q^{38} +(1.90214 - 1.09820i) q^{39} +(-0.500000 + 0.866025i) q^{40} +(1.34474 - 2.32915i) q^{41} +(-1.45402 - 0.839478i) q^{42} +5.77779i q^{43} +(-1.55741 + 2.69751i) q^{44} -1.00000i q^{45} +(-2.00055 - 3.46505i) q^{46} +5.05625 q^{47} -1.00000 q^{48} +(2.09055 + 3.62094i) q^{49} +(-0.866025 - 0.500000i) q^{50} -4.03925i q^{51} +(1.90214 - 1.09820i) q^{52} +(-6.38398 - 11.0574i) q^{53} +(0.866025 - 0.500000i) q^{54} +(-2.69751 - 1.55741i) q^{55} +(-1.45402 - 0.839478i) q^{56} +(3.21380 - 1.85549i) q^{57} +(-2.52488 - 4.37322i) q^{58} +(-4.36549 + 2.52041i) q^{59} -1.00000i q^{60} +(10.3566 + 5.97938i) q^{61} +(-2.47075 - 4.27947i) q^{62} +1.67896 q^{63} -1.00000 q^{64} +(1.09820 + 1.90214i) q^{65} -3.11482i q^{66} +(2.18318 - 3.78138i) q^{67} -4.03925i q^{68} +(3.46505 + 2.00055i) q^{69} +(0.839478 - 1.45402i) q^{70} +(-1.36159 + 2.35834i) q^{71} +(0.866025 - 0.500000i) q^{72} +2.06124 q^{73} +(-2.76726 + 5.41685i) q^{74} +1.00000 q^{75} +(3.21380 - 1.85549i) q^{76} +(2.61482 - 4.52900i) q^{77} +(-1.09820 + 1.90214i) q^{78} +(14.1746 + 8.18371i) q^{79} -1.00000i q^{80} +(-0.500000 + 0.866025i) q^{81} +2.68947i q^{82} +(2.69775 + 4.67265i) q^{83} +1.67896 q^{84} +4.03925 q^{85} +(-2.88889 - 5.00371i) q^{86} +(4.37322 + 2.52488i) q^{87} -3.11482i q^{88} +(-5.79811 + 3.34754i) q^{89} +(0.500000 + 0.866025i) q^{90} +(-3.19361 + 1.84383i) q^{91} +(3.46505 + 2.00055i) q^{92} +(4.27947 + 2.47075i) q^{93} +(-4.37884 + 2.52813i) q^{94} +(1.85549 + 3.21380i) q^{95} +(0.866025 - 0.500000i) q^{96} -6.35452i q^{97} +(-3.62094 - 2.09055i) q^{98} +(1.55741 + 2.69751i) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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