LMFDB - Embedded newform 1110.2.x.e.841.1

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			841.1
Root			$-3.06293i$ of defining polynomial
Character	$\chi$	$=$	1110.841
Dual form			1110.2.x.e.751.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{5} -1.00000i q^{6} +(-1.55211 - 2.68834i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(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} +(-1.55211 - 2.68834i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} -1.00000 q^{10} -1.08193 q^{11} +(-0.500000 + 0.866025i) q^{12} +(-1.53345 + 0.885339i) q^{13} +3.10423i q^{14} +(0.866025 + 0.500000i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-4.39343 - 2.53655i) q^{17} +(0.866025 - 0.500000i) q^{18} +(-6.08559 + 3.51352i) q^{19} +(0.866025 + 0.500000i) q^{20} +(1.55211 - 2.68834i) q^{21} +(0.936982 + 0.540967i) q^{22} +8.39725i q^{23} +(0.866025 - 0.500000i) q^{24} +(0.500000 - 0.866025i) q^{25} +1.77068 q^{26} -1.00000 q^{27} +(1.55211 - 2.68834i) q^{28} -2.60820i q^{29} +(-0.500000 - 0.866025i) q^{30} +9.58996i q^{31} +(0.866025 - 0.500000i) q^{32} +(-0.540967 - 0.936982i) q^{33} +(2.53655 + 4.39343i) q^{34} +(-2.68834 - 1.55211i) q^{35} -1.00000 q^{36} +(-5.59638 - 2.38338i) q^{37} +7.02704 q^{38} +(-1.53345 - 0.885339i) q^{39} +(-0.500000 - 0.866025i) q^{40} +(5.39276 + 9.34053i) q^{41} +(-2.68834 + 1.55211i) q^{42} -0.223846i q^{43} +(-0.540967 - 0.936982i) q^{44} +1.00000i q^{45} +(4.19862 - 7.27223i) q^{46} +6.17308 q^{47} -1.00000 q^{48} +(-1.31811 + 2.28303i) q^{49} +(-0.866025 + 0.500000i) q^{50} -5.07309i q^{51} +(-1.53345 - 0.885339i) q^{52} +(-1.31966 + 2.28572i) q^{53} +(0.866025 + 0.500000i) q^{54} +(-0.936982 + 0.540967i) q^{55} +(-2.68834 + 1.55211i) q^{56} +(-6.08559 - 3.51352i) q^{57} +(-1.30410 + 2.25876i) q^{58} +(1.47494 + 0.851557i) q^{59} +1.00000i q^{60} +(-6.59715 + 3.80887i) q^{61} +(4.79498 - 8.30515i) q^{62} +3.10423 q^{63} -1.00000 q^{64} +(-0.885339 + 1.53345i) q^{65} +1.08193i q^{66} +(-0.526383 - 0.911722i) q^{67} -5.07309i q^{68} +(-7.27223 + 4.19862i) q^{69} +(1.55211 + 2.68834i) q^{70} +(-6.27647 - 10.8712i) q^{71} +(0.866025 + 0.500000i) q^{72} -13.3131 q^{73} +(3.65492 + 4.86226i) q^{74} +1.00000 q^{75} +(-6.08559 - 3.51352i) q^{76} +(1.67928 + 2.90860i) q^{77} +(0.885339 + 1.53345i) q^{78} +(-6.89265 + 3.97947i) q^{79} +1.00000i q^{80} +(-0.500000 - 0.866025i) q^{81} -10.7855i q^{82} +(8.32060 - 14.4117i) q^{83} +3.10423 q^{84} -5.07309 q^{85} +(-0.111923 + 0.193856i) q^{86} +(2.25876 - 1.30410i) q^{87} +1.08193i q^{88} +(11.8958 + 6.86806i) q^{89} +(0.500000 - 0.866025i) q^{90} +(4.76018 + 2.74829i) q^{91} +(-7.27223 + 4.19862i) q^{92} +(-8.30515 + 4.79498i) q^{93} +(-5.34605 - 3.08654i) q^{94} +(-3.51352 + 6.08559i) q^{95} +(0.866025 + 0.500000i) q^{96} -12.0709i q^{97} +(2.28303 - 1.31811i) q^{98} +(0.540967 - 0.936982i) 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
$7$	−1.55211	−	2.68834i	−0.586644	−	1.01610i	−0.994668	−	0.103126i	$-0.967116\pi$
$7$	−1.55211	−	2.68834i	−0.586644	−	1.01610i	0.408025	−	0.912971i	$-0.366218\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−1.00000			−0.316228
$11$	−1.08193			−0.326215			−0.163108	−	0.986608i	$-0.552152\pi$
$11$	−1.08193			−0.326215			−0.163108	+	0.986608i	$0.552152\pi$
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	−1.53345	+	0.885339i	−0.425303	+	0.245549i	−0.697344	−	0.716737i	$-0.745635\pi$
$13$	−1.53345	+	0.885339i	−0.425303	+	0.245549i	0.272041	+	0.962286i	$0.412302\pi$
$14$			3.10423i			0.829639i
$15$	0.866025	+	0.500000i	0.223607	+	0.129099i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−4.39343	−	2.53655i	−1.06556	−	0.615203i	−0.138597	−	0.990349i	$-0.544259\pi$
$17$	−4.39343	−	2.53655i	−1.06556	−	0.615203i	−0.926966	+	0.375146i	$0.877593\pi$
$18$	0.866025	−	0.500000i	0.204124	−	0.117851i
$19$	−6.08559	+	3.51352i	−1.39613	+	0.806056i	−0.993985	−	0.109519i	$-0.965069\pi$
$19$	−6.08559	+	3.51352i	−1.39613	+	0.806056i	−0.402146	+	0.915576i	$0.631736\pi$
$20$	0.866025	+	0.500000i	0.193649	+	0.111803i
$21$	1.55211	−	2.68834i	0.338699	−	0.586644i
$22$	0.936982	+	0.540967i	0.199765	+	0.115334i
$23$			8.39725i			1.75095i	0.483266	+	0.875474i	$0.339450\pi$
$23$			8.39725i			1.75095i	−0.483266	+	0.875474i	$0.660550\pi$
$24$	0.866025	−	0.500000i	0.176777	−	0.102062i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	1.77068			0.347259
$27$	−1.00000			−0.192450
$28$	1.55211	−	2.68834i	0.293322	−	0.508048i
$29$		−	2.60820i		−	0.484330i	−0.970235	−	0.242165i	$-0.922143\pi$
$29$		−	2.60820i		−	0.484330i	0.970235	−	0.242165i	$-0.0778575\pi$
$30$	−0.500000	−	0.866025i	−0.0912871	−	0.158114i
$31$			9.58996i			1.72241i	0.508259	+	0.861204i	$0.330289\pi$
$31$			9.58996i			1.72241i	−0.508259	+	0.861204i	$0.669711\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	−0.540967	−	0.936982i	−0.0941702	−	0.163108i
$34$	2.53655	+	4.39343i	0.435014	+	0.753467i
$35$	−2.68834	−	1.55211i	−0.454412	−	0.262355i
$36$	−1.00000			−0.166667
$37$	−5.59638	−	2.38338i	−0.920040	−	0.391825i
$37$	−5.59638	−	2.38338i	−0.920040	−	0.391825i
$38$	7.02704			1.13994
$39$	−1.53345	−	0.885339i	−0.245549	−	0.141768i
$40$	−0.500000	−	0.866025i	−0.0790569	−	0.136931i
$41$	5.39276	+	9.34053i	0.842207	+	1.45875i	0.888025	+	0.459796i	$0.152077\pi$
$41$	5.39276	+	9.34053i	0.842207	+	1.45875i	−0.0458173	+	0.998950i	$0.514589\pi$
$42$	−2.68834	+	1.55211i	−0.414820	+	0.239496i
$43$		−	0.223846i		−	0.0341362i	−0.999854	−	0.0170681i	$-0.994567\pi$
$43$		−	0.223846i		−	0.0341362i	0.999854	−	0.0170681i	$-0.00543320\pi$
$44$	−0.540967	−	0.936982i	−0.0815538	−	0.141255i
$45$			1.00000i			0.149071i
$46$	4.19862	−	7.27223i	0.619053	−	1.07223i
$47$	6.17308			0.900437			0.450218	−	0.892918i	$-0.351346\pi$
$47$	6.17308			0.900437			0.450218	+	0.892918i	$0.351346\pi$
$48$	−1.00000			−0.144338
$49$	−1.31811	+	2.28303i	−0.188302	+	0.326148i
$50$	−0.866025	+	0.500000i	−0.122474	+	0.0707107i
$51$		−	5.07309i		−	0.710375i
$52$	−1.53345	−	0.885339i	−0.212652	−	0.122774i
$53$	−1.31966	+	2.28572i	−0.181270	+	0.313968i	−0.942313	−	0.334733i	$-0.891354\pi$
$53$	−1.31966	+	2.28572i	−0.181270	+	0.313968i	0.761043	+	0.648701i	$0.224687\pi$
$54$	0.866025	+	0.500000i	0.117851	+	0.0680414i
$55$	−0.936982	+	0.540967i	−0.126343	+	0.0729439i
$56$	−2.68834	+	1.55211i	−0.359244	+	0.207410i
$57$	−6.08559	−	3.51352i	−0.806056	−	0.465377i
$58$	−1.30410	+	2.25876i	−0.171236	+	0.296590i
$59$	1.47494	+	0.851557i	0.192021	+	0.110863i	0.592928	−	0.805255i	$-0.297972\pi$
$59$	1.47494	+	0.851557i	0.192021	+	0.110863i	−0.400907	+	0.916119i	$0.631305\pi$
$60$			1.00000i			0.129099i
$61$	−6.59715	+	3.80887i	−0.844678	+	0.487675i	−0.858852	−	0.512224i	$-0.828822\pi$
$61$	−6.59715	+	3.80887i	−0.844678	+	0.487675i	0.0141734	+	0.999900i	$0.495488\pi$
$62$	4.79498	−	8.30515i	0.608963	−	1.05476i
$63$	3.10423			0.391096
$64$	−1.00000			−0.125000
$65$	−0.885339	+	1.53345i	−0.109813	+	0.190201i
$66$			1.08193i			0.133177i
$67$	−0.526383	−	0.911722i	−0.0643079	−	0.111385i	0.832079	−	0.554657i	$-0.187151\pi$
$67$	−0.526383	−	0.911722i	−0.0643079	−	0.111385i	−0.896387	+	0.443273i	$0.853817\pi$
$68$		−	5.07309i		−	0.615203i
$69$	−7.27223	+	4.19862i	−0.875474	+	0.505455i
$70$	1.55211	+	2.68834i	0.185513	+	0.321318i
$71$	−6.27647	−	10.8712i	−0.744880	−	1.29017i	−0.950251	−	0.311485i	$-0.899174\pi$
$71$	−6.27647	−	10.8712i	−0.744880	−	1.29017i	0.205371	−	0.978684i	$-0.434160\pi$
$72$	0.866025	+	0.500000i	0.102062	+	0.0589256i
$73$	−13.3131			−1.55818			−0.779091	−	0.626910i	$-0.784319\pi$
$73$	−13.3131			−1.55818			−0.779091	+	0.626910i	$0.784319\pi$
$74$	3.65492	+	4.86226i	0.424876	+	0.565226i
$75$	1.00000			0.115470
$76$	−6.08559	−	3.51352i	−0.698065	−	0.403028i
$77$	1.67928	+	2.90860i	0.191372	+	0.331466i
$78$	0.885339	+	1.53345i	0.100245	+	0.173629i
$79$	−6.89265	+	3.97947i	−0.775483	+	0.447725i	−0.834827	−	0.550512i	$-0.814432\pi$
$79$	−6.89265	+	3.97947i	−0.775483	+	0.447725i	0.0593439	+	0.998238i	$0.481099\pi$
$80$			1.00000i			0.111803i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		−	10.7855i		−	1.19106i
$83$	8.32060	−	14.4117i	0.913304	−	1.58189i	0.103939	−	0.994584i	$-0.466855\pi$
$83$	8.32060	−	14.4117i	0.913304	−	1.58189i	0.809366	−	0.587305i	$-0.199811\pi$
$84$	3.10423			0.338699
$85$	−5.07309			−0.550254
$86$	−0.111923	+	0.193856i	−0.0120690	+	0.0209041i
$87$	2.25876	−	1.30410i	0.242165	−	0.139814i
$88$			1.08193i			0.115334i
$89$	11.8958	+	6.86806i	1.26095	+	0.728012i	0.973259	−	0.229710i	$-0.0737776\pi$
$89$	11.8958	+	6.86806i	1.26095	+	0.728012i	0.287695	+	0.957722i	$0.407111\pi$
$90$	0.500000	−	0.866025i	0.0527046	−	0.0912871i
$91$	4.76018	+	2.74829i	0.499003	+	0.288099i
$92$	−7.27223	+	4.19862i	−0.758182	+	0.437737i
$93$	−8.30515	+	4.79498i	−0.861204	+	0.497216i
$94$	−5.34605	−	3.08654i	−0.551403	−	0.318353i
$95$	−3.51352	+	6.08559i	−0.360479	+	0.624369i
$96$	0.866025	+	0.500000i	0.0883883	+	0.0510310i
$97$		−	12.0709i		−	1.22561i	−0.790234	−	0.612805i	$-0.790041\pi$
$97$		−	12.0709i		−	1.22561i	0.790234	−	0.612805i	$-0.209959\pi$
$98$	2.28303	−	1.31811i	0.230621	−	0.133149i
$99$	0.540967	−	0.936982i	0.0543692	−	0.0941702i
$100$	1.00000			0.100000
$101$	−6.54354			−0.651106			−0.325553	−	0.945524i	$-0.605551\pi$
$101$	−6.54354			−0.651106			−0.325553	+	0.945524i	$0.605551\pi$
$102$	−2.53655	+	4.39343i	−0.251156	+	0.435014i
$103$		−	1.55293i		−	0.153015i	−0.997069	−	0.0765075i	$-0.975623\pi$
$103$		−	1.55293i		−	0.153015i	0.997069	−	0.0765075i	$-0.0243769\pi$
$104$	0.885339	+	1.53345i	0.0868146	+	0.150367i
$105$		−	3.10423i		−	0.302941i
$106$	2.28572	−	1.31966i	0.222009	−	0.128177i
$107$	0.524481	+	0.908429i	0.0507035	+	0.0878211i	0.890263	−	0.455446i	$-0.150520\pi$
$107$	0.524481	+	0.908429i	0.0507035	+	0.0878211i	−0.839560	+	0.543267i	$0.817187\pi$
$108$	−0.500000	−	0.866025i	−0.0481125	−	0.0833333i
$109$	−10.9242	−	6.30710i	−1.04635	−	0.604111i	−0.124725	−	0.992191i	$-0.539805\pi$
$109$	−10.9242	−	6.30710i	−1.04635	−	0.604111i	−0.921626	+	0.388080i	$0.873138\pi$
$110$	1.08193			0.103158
$111$	−0.734124	−	6.03830i	−0.0696799	−	0.573130i
$112$	3.10423			0.293322
$113$	3.86386	+	2.23080i	0.363482	+	0.209856i	0.670607	−	0.741813i	$-0.266034\pi$
$113$	3.86386	+	2.23080i	0.363482	+	0.209856i	−0.307125	+	0.951669i	$0.599367\pi$
$114$	3.51352	+	6.08559i	0.329071	+	0.569968i
$115$	4.19862	+	7.27223i	0.391524	+	0.678139i
$116$	2.25876	−	1.30410i	0.209721	−	0.121082i
$117$		−	1.77068i		−	0.163699i
$118$	−0.851557	−	1.47494i	−0.0783922	−	0.135779i
$119$			15.7480i			1.44362i
$120$	0.500000	−	0.866025i	0.0456435	−	0.0790569i
$121$	−9.82942			−0.893584
$122$	7.61773			0.689677
$123$	−5.39276	+	9.34053i	−0.486249	+	0.842207i
$124$	−8.30515	+	4.79498i	−0.745825	+	0.430602i
$125$		−	1.00000i		−	0.0894427i
$126$	−2.68834	−	1.55211i	−0.239496	−	0.138273i
$127$	−7.67318	+	13.2903i	−0.680885	+	1.17933i	0.293826	+	0.955859i	$0.405071\pi$
$127$	−7.67318	+	13.2903i	−0.680885	+	1.17933i	−0.974711	+	0.223468i	$0.928262\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	0.193856	−	0.111923i	0.0170681	−	0.00985427i
$130$	1.53345	−	0.885339i	0.134493	−	0.0776494i
$131$	−1.94710	−	1.12416i	−0.170119	−	0.0982183i	0.412523	−	0.910947i	$-0.364648\pi$
$131$	−1.94710	−	1.12416i	−0.170119	−	0.0982183i	−0.582642	+	0.812729i	$0.697981\pi$
$132$	0.540967	−	0.936982i	0.0470851	−	0.0815538i
$133$	18.8911	+	10.9068i	1.63806	+	0.945736i
$134$			1.05277i			0.0909451i
$135$	−0.866025	+	0.500000i	−0.0745356	+	0.0430331i
$136$	−2.53655	+	4.39343i	−0.217507	+	0.376733i
$137$	−13.1110			−1.12015			−0.560075	−	0.828442i	$-0.689228\pi$
$137$	−13.1110			−1.12015			−0.560075	+	0.828442i	$0.689228\pi$
$138$	8.39725			0.714821
$139$	−3.49733	+	6.05756i	−0.296640	+	0.513795i	−0.975365	−	0.220597i	$-0.929199\pi$
$139$	−3.49733	+	6.05756i	−0.296640	+	0.513795i	0.678725	+	0.734392i	$0.262533\pi$
$140$		−	3.10423i		−	0.262355i
$141$	3.08654	+	5.34605i	0.259934	+	0.450218i
$142$			12.5529i			1.05342i
$143$	1.65909	−	0.957878i	0.138740	−	0.0801018i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	−1.30410	−	2.25876i	−0.108299	−	0.187580i
$146$	11.5295	+	6.65656i	0.954188	+	0.550901i
$147$	−2.63622			−0.217432
$148$	−0.734124	−	6.03830i	−0.0603446	−	0.496345i
$149$	3.37160			0.276213			0.138106	−	0.990417i	$-0.455898\pi$
$149$	3.37160			0.276213			0.138106	+	0.990417i	$0.455898\pi$
$150$	−0.866025	−	0.500000i	−0.0707107	−	0.0408248i
$151$	−0.650118	−	1.12604i	−0.0529058	−	0.0916356i	0.838360	−	0.545118i	$-0.183515\pi$
$151$	−0.650118	−	1.12604i	−0.0529058	−	0.0916356i	−0.891265	+	0.453482i	$0.850182\pi$
$152$	3.51352	+	6.08559i	0.284984	+	0.493607i
$153$	4.39343	−	2.53655i	0.355188	−	0.205068i
$154$		−	3.35857i		−	0.270641i
$155$	4.79498	+	8.30515i	0.385142	+	0.667086i
$156$		−	1.77068i		−	0.141768i
$157$	6.35760	−	11.0117i	0.507392	−	0.878828i	−0.492572	−	0.870272i	$-0.663943\pi$
$157$	6.35760	−	11.0117i	0.507392	−	0.878828i	0.999963	−	0.00855641i	$-0.00272362\pi$
$158$	7.95894			0.633179
$159$	−2.63933			−0.209312
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$	22.5746	−	13.0335i	1.77913	−	1.02718i
$162$			1.00000i			0.0785674i
$163$	15.7889	+	9.11574i	1.23668	+	0.714000i	0.968415	−	0.249344i	$-0.0802149\pi$
$163$	15.7889	+	9.11574i	1.23668	+	0.714000i	0.268269	+	0.963344i	$0.413548\pi$
$164$	−5.39276	+	9.34053i	−0.421104	+	0.729373i
$165$	−0.936982	−	0.540967i	−0.0729439	−	0.0421142i
$166$	−14.4117	+	8.32060i	−1.11856	+	0.645803i
$167$	10.2964	−	5.94460i	0.796756	−	0.460007i	−0.0455799	−	0.998961i	$-0.514514\pi$
$167$	10.2964	−	5.94460i	0.796756	−	0.460007i	0.842335	+	0.538954i	$0.181180\pi$
$168$	−2.68834	−	1.55211i	−0.207410	−	0.119748i
$169$	−4.93235	+	8.54308i	−0.379411	+	0.657160i
$170$	4.39343	+	2.53655i	0.336961	+	0.194544i
$171$		−	7.02704i		−	0.537371i
$172$	0.193856	−	0.111923i	0.0147814	−	0.00853404i
$173$	2.72061	−	4.71224i	0.206844	−	0.358265i	−0.743874	−	0.668319i	$-0.767014\pi$
$173$	2.72061	−	4.71224i	0.206844	−	0.358265i	0.950719	+	0.310054i	$0.100347\pi$
$174$	−2.60820			−0.197727
$175$	−3.10423			−0.234657
$176$	0.540967	−	0.936982i	0.0407769	−	0.0706277i
$177$			1.70311i			0.128014i
$178$	−6.86806	−	11.8958i	−0.514783	−	0.891629i
$179$			20.6047i			1.54007i	0.638002	+	0.770035i	$0.279761\pi$
$179$			20.6047i			1.54007i	−0.638002	+	0.770035i	$0.720239\pi$
$180$	−0.866025	+	0.500000i	−0.0645497	+	0.0372678i
$181$	−8.21109	−	14.2220i	−0.610325	−	1.05711i	−0.991185	−	0.132482i	$-0.957705\pi$
$181$	−8.21109	−	14.2220i	−0.610325	−	1.05711i	0.380860	−	0.924633i	$-0.375628\pi$
$182$	−2.74829	−	4.76018i	−0.203717	−	0.352848i
$183$	−6.59715	−	3.80887i	−0.487675	−	0.281559i
$184$	8.39725			0.619053
$185$	−6.03830	+	0.734124i	−0.443945	+	0.0539739i
$186$	9.58996			0.703170
$187$	4.75340	+	2.74437i	0.347603	+	0.200689i
$188$	3.08654	+	5.34605i	0.225109	+	0.389901i
$189$	1.55211	+	2.68834i	0.112900	+	0.195548i
$190$	6.08559	−	3.51352i	0.441495	−	0.254897i
$191$		−	4.00390i		−	0.289712i	−0.989453	−	0.144856i	$-0.953728\pi$
$191$		−	4.00390i		−	0.289712i	0.989453	−	0.144856i	$-0.0462719\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$		−	24.9397i		−	1.79520i	−0.440815	−	0.897598i	$-0.645311\pi$
$193$		−	24.9397i		−	1.79520i	0.440815	−	0.897598i	$-0.354689\pi$
$194$	−6.03543	+	10.4537i	−0.433319	+	0.750530i
$195$	−1.77068			−0.126801
$196$	−2.63622			−0.188302
$197$	9.99017	−	17.3035i	0.711770	−	1.23282i	−0.252422	−	0.967617i	$-0.581227\pi$
$197$	9.99017	−	17.3035i	0.711770	−	1.23282i	0.964192	−	0.265205i	$-0.0854397\pi$
$198$	−0.936982	+	0.540967i	−0.0665884	+	0.0384448i
$199$		−	7.74551i		−	0.549065i	−0.961578	−	0.274532i	$-0.911477\pi$
$199$		−	7.74551i		−	0.549065i	0.961578	−	0.274532i	$-0.0885230\pi$
$200$	−0.866025	−	0.500000i	−0.0612372	−	0.0353553i
$201$	0.526383	−	0.911722i	0.0371282	−	0.0643079i
$202$	5.66687	+	3.27177i	0.398720	+	0.230201i
$203$	−7.01171	+	4.04821i	−0.492126	+	0.284129i
$204$	4.39343	−	2.53655i	0.307602	−	0.177594i
$205$	9.34053	+	5.39276i	0.652371	+	0.376647i
$206$	−0.776466	+	1.34488i	−0.0540989	+	0.0937021i
$207$	−7.27223	−	4.19862i	−0.505455	−	0.291825i
$208$		−	1.77068i		−	0.122774i
$209$	6.58421	−	3.80139i	0.455439	−	0.262948i
$210$	−1.55211	+	2.68834i	−0.107106	+	0.185513i
$211$	26.1970			1.80347			0.901736	−	0.432286i	$-0.142293\pi$
$211$	26.1970			1.80347			0.901736	+	0.432286i	$0.142293\pi$
$212$	−2.63933			−0.181270
$213$	6.27647	−	10.8712i	0.430056	−	0.744880i
$214$		−	1.04896i		−	0.0717056i
$215$	−0.111923	−	0.193856i	−0.00763308	−	0.0132209i
$216$			1.00000i			0.0680414i
$217$	25.7811	−	14.8847i	1.75013	−	1.01044i
$218$	6.30710	+	10.9242i	0.427171	+	0.739882i
$219$	−6.65656	−	11.5295i	−0.449809	−	0.779091i
$220$	−0.936982	−	0.540967i	−0.0631713	−	0.0364720i
$221$	8.98282			0.604250
$222$	−2.38338	+	5.59638i	−0.159962	+	0.375605i
$223$	−18.5048			−1.23917			−0.619587	−	0.784928i	$-0.712700\pi$
$223$	−18.5048			−1.23917			−0.619587	+	0.784928i	$0.712700\pi$
$224$	−2.68834	−	1.55211i	−0.179622	−	0.103705i
$225$	0.500000	+	0.866025i	0.0333333	+	0.0577350i
$226$	−2.23080	−	3.86386i	−0.148391	−	0.257020i
$227$	−19.2955	+	11.1403i	−1.28069	+	0.739404i	−0.976974	−	0.213359i	$-0.931560\pi$
$227$	−19.2955	+	11.1403i	−1.28069	+	0.739404i	−0.303712	+	0.952764i	$0.598226\pi$
$228$		−	7.02704i		−	0.465377i
$229$	1.25854	+	2.17986i	0.0831668	+	0.144049i	0.904609	−	0.426243i	$-0.140163\pi$
$229$	1.25854	+	2.17986i	0.0831668	+	0.144049i	−0.821442	+	0.570292i	$0.806830\pi$
$230$		−	8.39725i		−	0.553698i
$231$	−1.67928	+	2.90860i	−0.110489	+	0.191372i
$232$	−2.60820			−0.171236
$233$	−28.5244			−1.86870			−0.934348	−	0.356363i	$-0.884017\pi$
$233$	−28.5244			−1.86870			−0.934348	+	0.356363i	$0.884017\pi$
$234$	−0.885339	+	1.53345i	−0.0578764	+	0.100245i
$235$	5.34605	−	3.08654i	0.348738	−	0.201344i
$236$			1.70311i			0.110863i
$237$	−6.89265	−	3.97947i	−0.447725	−	0.258494i
$238$	7.87402	−	13.6382i	0.510397	−	0.884033i
$239$	1.04297	+	0.602158i	0.0674640	+	0.0389503i	0.533353	−	0.845893i	$-0.320932\pi$
$239$	1.04297	+	0.602158i	0.0674640	+	0.0389503i	−0.465889	+	0.884843i	$0.654265\pi$
$240$	−0.866025	+	0.500000i	−0.0559017	+	0.0322749i
$241$	−3.37667	+	1.94952i	−0.217510	+	0.125580i	−0.604797	−	0.796380i	$-0.706746\pi$
$241$	−3.37667	+	1.94952i	−0.217510	+	0.125580i	0.387287	+	0.921959i	$0.373412\pi$
$242$	8.51253	+	4.91471i	0.547206	+	0.315930i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−6.59715	−	3.80887i	−0.422339	−	0.243838i
$245$			2.63622i			0.168422i
$246$	9.34053	−	5.39276i	0.595530	−	0.343830i
$247$	6.22131	−	10.7756i	0.395853	−	0.685637i
$248$	9.58996			0.608963
$249$	16.6412			1.05459
$250$	−0.500000	+	0.866025i	−0.0316228	+	0.0547723i
$251$			6.61313i			0.417417i	0.977978	+	0.208709i	$0.0669260\pi$
$251$			6.61313i			0.417417i	−0.977978	+	0.208709i	$0.933074\pi$
$252$	1.55211	+	2.68834i	0.0977739	+	0.169349i
$253$		−	9.08526i		−	0.571186i
$254$	13.2903	−	7.67318i	0.833910	−	0.481458i
$255$	−2.53655	−	4.39343i	−0.158845	−	0.275127i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	2.47485	+	1.42885i	0.154377	+	0.0891294i	0.575198	−	0.818014i	$-0.304925\pi$
$257$	2.47485	+	1.42885i	0.154377	+	0.0891294i	−0.420822	+	0.907143i	$0.638258\pi$
$258$	−0.223846			−0.0139360
$259$	2.27889	+	18.7442i	0.141603	+	1.16471i
$260$	−1.77068			−0.109813
$261$	2.25876	+	1.30410i	0.139814	+	0.0807216i
$262$	1.12416	+	1.94710i	0.0694508	+	0.120292i
$263$	−7.91733	−	13.7132i	−0.488204	−	0.845593i	0.511704	−	0.859162i	$-0.329014\pi$
$263$	−7.91733	−	13.7132i	−0.488204	−	0.845593i	−0.999908	+	0.0135683i	$0.995681\pi$
$264$	−0.936982	+	0.540967i	−0.0576672	+	0.0332942i
$265$			2.63933i			0.162133i
$266$	−10.9068	−	18.8911i	−0.668736	−	1.15829i
$267$			13.7361i			0.840636i
$268$	0.526383	−	0.911722i	0.0321540	−	0.0556923i
$269$	21.8240			1.33063			0.665315	−	0.746563i	$-0.268297\pi$
$269$	21.8240			1.33063			0.665315	+	0.746563i	$0.268297\pi$
$270$	1.00000			0.0608581
$271$	−2.64564	+	4.58238i	−0.160711	+	0.278360i	−0.935124	−	0.354321i	$-0.884712\pi$
$271$	−2.64564	+	4.58238i	−0.160711	+	0.278360i	0.774413	+	0.632681i	$0.218045\pi$
$272$	4.39343	−	2.53655i	0.266391	−	0.153801i
$273$			5.49659i			0.332669i
$274$	11.3545	+	6.55551i	0.685949	+	0.396033i
$275$	−0.540967	+	0.936982i	−0.0326215	+	0.0565021i
$276$	−7.27223	−	4.19862i	−0.437737	−	0.252727i
$277$	11.7933	−	6.80885i	0.708590	−	0.409104i	−0.101949	−	0.994790i	$-0.532508\pi$
$277$	11.7933	−	6.80885i	0.708590	−	0.409104i	0.810539	+	0.585685i	$0.199175\pi$
$278$	6.05756	−	3.49733i	0.363308	−	0.209756i
$279$	−8.30515	−	4.79498i	−0.497216	−	0.287068i
$280$	−1.55211	+	2.68834i	−0.0927565	+	0.160659i
$281$	−15.1179	−	8.72835i	−0.901861	−	0.520690i	−0.0240574	−	0.999711i	$-0.507658\pi$
$281$	−15.1179	−	8.72835i	−0.901861	−	0.520690i	−0.877803	+	0.479021i	$0.840992\pi$
$282$		−	6.17308i		−	0.367602i
$283$	14.1520	−	8.17066i	0.841249	−	0.485695i	−0.0164395	−	0.999865i	$-0.505233\pi$
$283$	14.1520	−	8.17066i	0.841249	−	0.485695i	0.857689	+	0.514169i	$0.171900\pi$
$284$	6.27647	−	10.8712i	0.372440	−	0.645085i
$285$	−7.02704			−0.416246
$286$	−1.91576			−0.113281
$287$	16.7403	−	28.9951i	0.988151	−	1.71153i
$288$			1.00000i			0.0589256i
$289$	4.36814	+	7.56585i	0.256950	+	0.445050i
$290$			2.60820i			0.153158i
$291$	10.4537	−	6.03543i	0.612805	−	0.353803i
$292$	−6.65656	−	11.5295i	−0.389546	−	0.674713i
$293$	−15.1922	−	26.3137i	−0.887540	−	1.53726i	−0.842775	−	0.538266i	$-0.819079\pi$
$293$	−15.1922	−	26.3137i	−0.887540	−	1.53726i	−0.0447651	−	0.998998i	$-0.514254\pi$
$294$	2.28303	+	1.31811i	0.133149	+	0.0768738i
$295$	1.70311			0.0991592
$296$	−2.38338	+	5.59638i	−0.138531	+	0.325283i
$297$	1.08193			0.0627801
$298$	−2.91989	−	1.68580i	−0.169145	−	0.0976559i
$299$	−7.43441	−	12.8768i	−0.429943	−	0.744683i
$300$	0.500000	+	0.866025i	0.0288675	+	0.0500000i
$301$	−0.601774	+	0.347434i	−0.0346857	+	0.0200258i
$302$			1.30024i			0.0748201i
$303$	−3.27177	−	5.66687i	−0.187958	−	0.325553i
$304$		−	7.02704i		−	0.403028i
$305$	−3.80887	+	6.59715i	−0.218095	+	0.377752i
$306$	−5.07309			−0.290010
$307$	13.4246			0.766181			0.383091	−	0.923711i	$-0.374860\pi$
$307$	13.4246			0.766181			0.383091	+	0.923711i	$0.374860\pi$
$308$	−1.67928	+	2.90860i	−0.0956860	+	0.165733i
$309$	1.34488	−	0.776466i	0.0765075	−	0.0441716i
$310$		−	9.58996i		−	0.544673i
$311$	1.96496	+	1.13447i	0.111423	+	0.0643299i	0.554676	−	0.832067i	$-0.312842\pi$
$311$	1.96496	+	1.13447i	0.111423	+	0.0643299i	−0.443253	+	0.896397i	$0.646176\pi$
$312$	−0.885339	+	1.53345i	−0.0501225	+	0.0868146i
$313$	−18.1463	−	10.4768i	−1.02569	−	0.592181i	−0.109942	−	0.993938i	$-0.535066\pi$
$313$	−18.1463	−	10.4768i	−1.02569	−	0.592181i	−0.915746	+	0.401757i	$0.868400\pi$
$314$	−11.0117	+	6.35760i	−0.621425	+	0.358780i
$315$	2.68834	−	1.55211i	0.151471	−	0.0874517i
$316$	−6.89265	−	3.97947i	−0.387742	−	0.223863i
$317$	−4.15669	+	7.19960i	−0.233463	+	0.404370i	−0.958825	−	0.283998i	$-0.908339\pi$
$317$	−4.15669	+	7.19960i	−0.233463	+	0.404370i	0.725362	+	0.688368i	$0.241672\pi$
$318$	2.28572	+	1.31966i	0.128177	+	0.0740031i
$319$			2.82189i			0.157996i
$320$	−0.866025	+	0.500000i	−0.0484123	+	0.0279508i
$321$	−0.524481	+	0.908429i	−0.0292737	+	0.0507035i
$322$	−26.0670			−1.45265
$323$	35.6488			1.98355
$324$	0.500000	−	0.866025i	0.0277778	−	0.0481125i
$325$			1.77068i			0.0982196i
$326$	−9.11574	−	15.7889i	−0.504874	−	0.874468i
$327$		−	12.6142i		−	0.697567i
$328$	9.34053	−	5.39276i	0.515745	−	0.297765i
$329$	−9.58133	−	16.5953i	−0.528236	−	0.914931i
$330$	0.540967	+	0.936982i	0.0297792	+	0.0515791i
$331$	27.9593	+	16.1423i	1.53678	+	0.887263i	0.999024	+	0.0441655i	$0.0140629\pi$
$331$	27.9593	+	16.1423i	1.53678	+	0.887263i	0.537761	+	0.843098i	$0.319270\pi$
$332$	16.6412			0.913304
$333$	4.86226	−	3.65492i	0.266450	−	0.200288i
$334$	−11.8892			−0.650548
$335$	−0.911722	−	0.526383i	−0.0498127	−	0.0287594i
$336$	1.55211	+	2.68834i	0.0846747	+	0.146661i
$337$	8.61561	+	14.9227i	0.469322	+	0.812889i	0.999385	−	0.0350689i	$-0.0111651\pi$
$337$	8.61561	+	14.9227i	0.469322	+	0.812889i	−0.530063	+	0.847958i	$0.677832\pi$
$338$	8.54308	−	4.93235i	0.464682	−	0.268284i
$339$			4.46160i			0.242321i
$340$	−2.53655	−	4.39343i	−0.137564	−	0.238267i
$341$		−	10.3757i		−	0.561876i
$342$	−3.51352	+	6.08559i	−0.189989	+	0.329071i
$343$	−13.5462			−0.731424
$344$	−0.223846			−0.0120690
$345$	−4.19862	+	7.27223i	−0.226046	+	0.391524i
$346$	−4.71224	+	2.72061i	−0.253332	+	0.146261i
$347$			19.0814i			1.02435i	0.858882	+	0.512173i	$0.171159\pi$
$347$			19.0814i			1.02435i	−0.858882	+	0.512173i	$0.828841\pi$
$348$	2.25876	+	1.30410i	0.121082	+	0.0699070i
$349$	−10.8634	+	18.8160i	−0.581505	+	1.00720i	0.413797	+	0.910369i	$0.364202\pi$
$349$	−10.8634	+	18.8160i	−0.581505	+	1.00720i	−0.995301	+	0.0968262i	$0.969131\pi$
$350$	2.68834	+	1.55211i	0.143698	+	0.0829639i
$351$	1.53345	−	0.885339i	0.0818496	−	0.0472559i
$352$	−0.936982	+	0.540967i	−0.0499413	+	0.0288336i
$353$	31.0850	+	17.9469i	1.65449	+	0.955218i	0.975195	+	0.221348i	$0.0710457\pi$
$353$	31.0850	+	17.9469i	1.65449	+	0.955218i	0.679291	+	0.733869i	$0.262288\pi$
$354$	0.851557	−	1.47494i	0.0452598	−	0.0783922i
$355$	−10.8712	−	6.27647i	−0.576981	−	0.333120i
$356$			13.7361i			0.728012i
$357$	−13.6382	+	7.87402i	−0.721810	+	0.416737i
$358$	10.3024	−	17.8442i	0.544497	−	0.943096i
$359$	−2.73821			−0.144517			−0.0722587	−	0.997386i	$-0.523021\pi$
$359$	−2.73821			−0.144517			−0.0722587	+	0.997386i	$0.523021\pi$
$360$	1.00000			0.0527046
$361$	15.1896	−	26.3092i	0.799454	−	1.38470i
$362$			16.4222i			0.863130i
$363$	−4.91471	−	8.51253i	−0.257955	−	0.446792i
$364$			5.49659i			0.288099i
$365$	−11.5295	+	6.65656i	−0.603482	+	0.348420i
$366$	3.80887	+	6.59715i	0.199093	+	0.344838i
$367$	12.1960	+	21.1240i	0.636625	+	1.10267i	0.986168	+	0.165746i	$0.0530033\pi$
$367$	12.1960	+	21.1240i	0.636625	+	1.10267i	−0.349544	+	0.936920i	$0.613663\pi$
$368$	−7.27223	−	4.19862i	−0.379091	−	0.218868i
$369$	−10.7855			−0.561472
$370$	5.59638	+	2.38338i	0.290942	+	0.123906i
$371$	8.19307			0.425363
$372$	−8.30515	−	4.79498i	−0.430602	−	0.248608i
$373$	17.5764	+	30.4432i	0.910070	+	1.57629i	0.813963	+	0.580917i	$0.197306\pi$
$373$	17.5764	+	30.4432i	0.910070	+	1.57629i	0.0961074	+	0.995371i	$0.469361\pi$
$374$	−2.74437	−	4.75340i	−0.141908	−	0.245792i
$375$	0.866025	−	0.500000i	0.0447214	−	0.0258199i
$376$		−	6.17308i		−	0.318353i
$377$	2.30914	+	3.99954i	0.118927	+	0.205987i
$378$		−	3.10423i		−	0.159664i
$379$	−9.72086	+	16.8370i	−0.499327	+	0.864860i	−1.00000		0.000776753i	$-0.999753\pi$
$379$	−9.72086	+	16.8370i	−0.499327	+	0.864860i	0.500673	+	0.865637i	$0.333086\pi$
$380$	−7.02704			−0.360479
$381$	−15.3464			−0.786218
$382$	−2.00195	+	3.46748i	−0.102429	+	0.177412i
$383$	−10.3337	+	5.96618i	−0.528028	+	0.304857i	−0.740213	−	0.672372i	$-0.765275\pi$
$383$	−10.3337	+	5.96618i	−0.528028	+	0.304857i	0.212185	+	0.977230i	$0.431942\pi$
$384$			1.00000i			0.0510310i
$385$	2.90860	+	1.67928i	0.148236	+	0.0855842i
$386$	−12.4698	+	21.5984i	−0.634697	+	1.09933i
$387$	0.193856	+	0.111923i	0.00985427	+	0.00568936i
$388$	10.4537	−	6.03543i	0.530705	−	0.306403i
$389$	2.58712	−	1.49367i	0.131172	−	0.0757322i	−0.432978	−	0.901404i	$-0.642537\pi$
$389$	2.58712	−	1.49367i	0.131172	−	0.0757322i	0.564150	+	0.825672i	$0.309204\pi$
$390$	1.53345	+	0.885339i	0.0776494	+	0.0448309i
$391$	21.3000	−	36.8927i	1.07719	−	1.86574i
$392$	2.28303	+	1.31811i	0.115311	+	0.0665746i
$393$		−	2.24832i		−	0.113413i
$394$	−17.3035	+	9.99017i	−0.871737	+	0.503298i
$395$	−3.97947	+	6.89265i	−0.200229	+	0.346807i
$396$	1.08193			0.0543692
$397$	7.73037			0.387976			0.193988	−	0.981004i	$-0.437858\pi$
$397$	7.73037			0.387976			0.193988	+	0.981004i	$0.437858\pi$
$398$	−3.87275	+	6.70781i	−0.194124	+	0.336232i
$399$			21.8135i			1.09204i
$400$	0.500000	+	0.866025i	0.0250000	+	0.0433013i
$401$			26.1901i			1.30787i	0.756550	+	0.653936i	$0.226884\pi$
$401$			26.1901i			1.30787i	−0.756550	+	0.653936i	$0.773116\pi$
$402$	−0.911722	+	0.526383i	−0.0454726	+	0.0262536i
$403$	−8.49037	−	14.7058i	−0.422935	−	0.732546i
$404$	−3.27177	−	5.66687i	−0.162777	−	0.281937i
$405$	−0.866025	−	0.500000i	−0.0430331	−	0.0248452i
$406$	8.09643			0.401819
$407$	6.05491	+	2.57866i	0.300131	+	0.127819i
$408$	−5.07309			−0.251156
$409$	26.7950	+	15.4701i	1.32493	+	0.764947i	0.984510	−	0.175327i	$-0.0560983\pi$
$409$	26.7950	+	15.4701i	1.32493	+	0.764947i	0.340417	+	0.940274i	$0.389432\pi$
$410$	−5.39276	−	9.34053i	−0.266329	−	0.461296i
$411$	−6.55551	−	11.3545i	−0.323359	−	0.560075i
$412$	1.34488	−	0.776466i	0.0662574	−	0.0382537i
$413$		−	5.28685i		−	0.260149i
$414$	4.19862	+	7.27223i	0.206351	+	0.357411i
$415$		−	16.6412i		−	0.816884i
$416$	−0.885339	+	1.53345i	−0.0434073	+	0.0751837i
$417$	−6.99467			−0.342530
$418$	−7.60279			−0.371864
$419$	−0.831708	+	1.44056i	−0.0406316	+	0.0703760i	−0.885626	−	0.464399i	$-0.846270\pi$
$419$	−0.831708	+	1.44056i	−0.0406316	+	0.0703760i	0.844994	+	0.534775i	$0.179604\pi$
$420$	2.68834	−	1.55211i	0.131178	−	0.0757354i
$421$		−	20.1687i		−	0.982961i	−0.870889	−	0.491480i	$-0.836456\pi$
$421$		−	20.1687i		−	0.982961i	0.870889	−	0.491480i	$-0.163544\pi$
$422$	−22.6872	−	13.0985i	−1.10440	−	0.637624i
$423$	−3.08654	+	5.34605i	−0.150073	+	0.259934i
$424$	2.28572	+	1.31966i	0.111005	+	0.0640885i
$425$	−4.39343	+	2.53655i	−0.213113	+	0.123041i
$426$	−10.8712	+	6.27647i	−0.526709	+	0.304096i
$427$	20.4790	+	11.8236i	0.991050	+	0.572183i
$428$	−0.524481	+	0.908429i	−0.0253518	+	0.0439106i
$429$	1.65909	+	0.957878i	0.0801018	+	0.0462468i
$430$			0.223846i			0.0107948i
$431$	2.39906	−	1.38510i	0.115558	−	0.0667177i	−0.441107	−	0.897455i	$-0.645414\pi$
$431$	2.39906	−	1.38510i	0.115558	−	0.0667177i	0.556665	+	0.830737i	$0.312081\pi$
$432$	0.500000	−	0.866025i	0.0240563	−	0.0416667i
$433$	−20.1141			−0.966624			−0.483312	−	0.875448i	$-0.660566\pi$
$433$	−20.1141			−0.966624			−0.483312	+	0.875448i	$0.660566\pi$
$434$	−29.7694			−1.42898
$435$	1.30410	−	2.25876i	0.0625267	−	0.108299i
$436$		−	12.6142i		−	0.604111i
$437$	−29.5039	−	51.1022i	−1.41136	−	2.44455i
$438$			13.3131i			0.636125i
$439$	−12.2885	+	7.09479i	−0.586500	+	0.338616i	−0.763712	−	0.645557i	$-0.776625\pi$
$439$	−12.2885	+	7.09479i	−0.586500	+	0.338616i	0.177213	+	0.984173i	$0.443292\pi$
$440$	0.540967	+	0.936982i	0.0257896	+	0.0446689i
$441$	−1.31811	−	2.28303i	−0.0627672	−	0.108716i
$442$	−7.77935	−	4.49141i	−0.370026	−	0.213635i
$443$	13.1816			0.626278			0.313139	−	0.949707i	$-0.398619\pi$
$443$	13.1816			0.626278			0.313139	+	0.949707i	$0.398619\pi$
$444$	4.86226	−	3.65492i	0.230753	−	0.173455i
$445$	13.7361			0.651154
$446$	16.0256	+	9.25240i	0.758836	+	0.438114i
$447$	1.68580	+	2.91989i	0.0797357	+	0.138106i
$448$	1.55211	+	2.68834i	0.0733305	+	0.127012i
$449$	20.0178	−	11.5573i	0.944699	−	0.545422i	0.0532690	−	0.998580i	$-0.483036\pi$
$449$	20.0178	−	11.5573i	0.944699	−	0.545422i	0.891430	+	0.453158i	$0.149703\pi$
$450$		−	1.00000i		−	0.0471405i
$451$	−5.83460	−	10.1058i	−0.274741	−	0.475865i
$452$			4.46160i			0.209856i
$453$	0.650118	−	1.12604i	0.0305452	−	0.0529058i
$454$	22.2805			1.04568
$455$	5.49659			0.257684
$456$	−3.51352	+	6.08559i	−0.164536	+	0.284984i
$457$	−12.3350	+	7.12163i	−0.577008	+	0.333136i	−0.759943	−	0.649989i	$-0.774773\pi$
$457$	−12.3350	+	7.12163i	−0.577008	+	0.333136i	0.182935	+	0.983125i	$0.441440\pi$
$458$		−	2.51708i		−	0.117616i
$459$	4.39343	+	2.53655i	0.205068	+	0.118396i
$460$	−4.19862	+	7.27223i	−0.195762	+	0.339069i
$461$	1.33061	+	0.768227i	0.0619726	+	0.0357799i	0.530666	−	0.847581i	$-0.321942\pi$
$461$	1.33061	+	0.768227i	0.0619726	+	0.0357799i	−0.468694	+	0.883361i	$0.655275\pi$
$462$	2.90860	−	1.67928i	0.135320	−	0.0781273i
$463$	−23.8166	+	13.7505i	−1.10685	+	0.639040i	−0.938012	−	0.346604i	$-0.887335\pi$
$463$	−23.8166	+	13.7505i	−1.10685	+	0.639040i	−0.168838	+	0.985644i	$0.554002\pi$
$464$	2.25876	+	1.30410i	0.104860	+	0.0605412i
$465$	−4.79498	+	8.30515i	−0.222362	+	0.385142i
$466$	24.7028	+	14.2622i	1.14434	+	0.660683i
$467$		−	12.9285i		−	0.598261i	−0.954212	−	0.299130i	$-0.903303\pi$
$467$		−	12.9285i		−	0.598261i	0.954212	−	0.299130i	$-0.0966966\pi$
$468$	1.53345	−	0.885339i	0.0708839	−	0.0409248i
$469$	−1.63401	+	2.83019i	−0.0754517	+	0.130686i
$470$	−6.17308			−0.284743
$471$	12.7152			0.585886
$472$	0.851557	−	1.47494i	0.0391961	−	0.0678896i
$473$			0.242186i			0.0111357i
$474$	3.97947	+	6.89265i	0.182783	+	0.316590i
$475$			7.02704i			0.322423i
$476$	−13.6382	+	7.87402i	−0.625106	+	0.360905i
$477$	−1.31966	−	2.28572i	−0.0604232	−	0.104656i
$478$	−0.602158	−	1.04297i	−0.0275420	−	0.0477042i
$479$	28.3768	+	16.3834i	1.29657	+	0.748576i	0.979810	−	0.199930i	$-0.0640715\pi$
$479$	28.3768	+	16.3834i	1.29657	+	0.748576i	0.316761	+	0.948505i	$0.397405\pi$
$480$	1.00000			0.0456435
$481$	10.6919	−	1.29990i	0.487508	−	0.0592702i
$482$	3.89904			0.177596
$483$	22.5746	+	13.0335i	1.02718	+	0.593044i
$484$	−4.91471	−	8.51253i	−0.223396	−	0.386933i
$485$	−6.03543	−	10.4537i	−0.274055	−	0.474677i
$486$	−0.866025	+	0.500000i	−0.0392837	+	0.0226805i
$487$			5.84755i			0.264978i	0.991184	+	0.132489i	$0.0422969\pi$
$487$			5.84755i			0.264978i	−0.991184	+	0.132489i	$0.957703\pi$
$488$	3.80887	+	6.59715i	0.172419	+	0.298639i
$489$			18.2315i			0.824456i
$490$	1.31811	−	2.28303i	0.0595462	−	0.103137i
$491$	−13.1230			−0.592233			−0.296116	−	0.955152i	$-0.595692\pi$
$491$	−13.1230			−0.592233			−0.296116	+	0.955152i	$0.595692\pi$
$492$	−10.7855			−0.486249
$493$	−6.61581	+	11.4589i	−0.297961	+	0.516084i
$494$	−10.7756	+	6.22131i	−0.484818	+	0.279910i
$495$		−	1.08193i		−	0.0486293i
$496$	−8.30515	−	4.79498i	−0.372912	−	0.215301i
$497$	−19.4836	+	33.7465i	−0.873958	+	1.51374i
$498$	−14.4117	−	8.32060i	−0.645803	−	0.372855i
$499$	−11.4355	+	6.60230i	−0.511924	+	0.295560i	−0.733624	−	0.679555i	$-0.762173\pi$
$499$	−11.4355	+	6.60230i	−0.511924	+	0.295560i	0.221700	+	0.975115i	$0.428839\pi$
$500$	0.866025	−	0.500000i	0.0387298	−	0.0223607i
$501$	10.2964	+	5.94460i	0.460007	+	0.265585i
$502$	3.30657	−	5.72714i	0.147579	−	0.255615i
$503$	−23.2754	−	13.4380i	−1.03780	−	0.599173i	−0.118589	−	0.992943i	$-0.537837\pi$
$503$	−23.2754	−	13.4380i	−1.03780	−	0.599173i	−0.919209	+	0.393770i	$0.871171\pi$
$504$		−	3.10423i		−	0.138273i
$505$	−5.66687	+	3.27177i	−0.252172	+	0.145592i
$506$	−4.54263	+	7.86807i	−0.201945	+	0.349778i
$507$	−9.86470			−0.438107
$508$	−15.3464			−0.680885
$509$	12.7988	−	22.1682i	0.567299	−	0.982590i	−0.429533	−	0.903051i	$-0.641322\pi$
$509$	12.7988	−	22.1682i	0.567299	−	0.982590i	0.996832	−	0.0795388i	$-0.0253448\pi$
$510$			5.07309i			0.224640i
$511$	20.6635	+	35.7902i	0.914098	+	1.58326i
$512$			1.00000i			0.0441942i
$513$	6.08559	−	3.51352i	0.268685	−	0.155126i
$514$	−1.42885	−	2.47485i	−0.0630240	−	0.109161i
$515$	−0.776466	−	1.34488i	−0.0342152	−	0.0592624i
$516$	0.193856	+	0.111923i	0.00853404	+	0.00492713i
$517$	−6.67887			−0.293736
$518$	7.39855	−	17.3724i	0.325074	−	0.763301i
$519$	5.44123			0.238843
$520$	1.53345	+	0.885339i	0.0672463	+	0.0388247i
$521$	−2.18203	−	3.77938i	−0.0955964	−	0.165578i	0.814261	−	0.580499i	$-0.197142\pi$
$521$	−2.18203	−	3.77938i	−0.0955964	−	0.165578i	−0.909857	+	0.414921i	$0.863809\pi$
$522$	−1.30410	−	2.25876i	−0.0570788	−	0.0988634i
$523$	−21.6781	+	12.5159i	−0.947918	+	0.547281i	−0.892434	−	0.451179i	$-0.851004\pi$
$523$	−21.6781	+	12.5159i	−0.947918	+	0.547281i	−0.0554845	+	0.998460i	$0.517670\pi$
$524$		−	2.24832i		−	0.0982183i
$525$	−1.55211	−	2.68834i	−0.0677398	−	0.117329i
$526$			15.8347i			0.690424i
$527$	24.3254	−	42.1328i	1.05963	−	1.83533i
$528$	1.08193			0.0470851
$529$	−47.5138			−2.06582
$530$	1.31966	−	2.28572i	0.0573225	−	0.0992855i
$531$	−1.47494	+	0.851557i	−0.0640070	+	0.0369544i
$532$			21.8135i			0.945736i
$533$	−16.5391	−	9.54884i	−0.716387	−	0.413606i
$534$	6.86806	−	11.8958i	0.297210	−	0.514783i
$535$	0.908429	+	0.524481i	0.0392748	+	0.0226753i
$536$	−0.911722	+	0.526383i	−0.0393804	+	0.0227363i
$537$	−17.8442	+	10.3024i	−0.770035	+	0.444580i
$538$	−18.9001	−	10.9120i	−0.814841	−	0.470449i
$539$	1.42611	−	2.47009i	0.0614268	−	0.106394i
$540$	−0.866025	−	0.500000i	−0.0372678	−	0.0215166i
$541$			3.28188i			0.141099i	0.997508	+	0.0705496i	$0.0224753\pi$
$541$			3.28188i			0.141099i	−0.997508	+	0.0705496i	$0.977525\pi$
$542$	4.58238	−	2.64564i	0.196830	−	0.113640i
$543$	8.21109	−	14.2220i	0.352372	−	0.610325i
$544$	−5.07309			−0.217507
$545$	−12.6142			−0.540333
$546$	2.74829	−	4.76018i	0.117616	−	0.203717i
$547$			38.1935i			1.63304i	0.577320	+	0.816518i	$0.304099\pi$
$547$			38.1935i			1.63304i	−0.577320	+	0.816518i	$0.695901\pi$
$548$	−6.55551	−	11.3545i	−0.280037	−	0.485039i
$549$		−	7.61773i		−	0.325117i
$550$	0.936982	−	0.540967i	0.0399530	−	0.0230669i
$551$	9.16394	+	15.8724i	0.390397	+	0.676188i
$552$	4.19862	+	7.27223i	0.178705	+	0.309527i
$553$	21.3963	+	12.3532i	0.909865	+	0.525311i
$554$	−13.6177			−0.578561
$555$	−3.65492	−	4.86226i	−0.155143	−	0.206391i
$556$	−6.99467			−0.296640
$557$	4.11089	+	2.37342i	0.174184	+	0.100565i	0.584557	−	0.811353i	$-0.301268\pi$
$557$	4.11089	+	2.37342i	0.174184	+	0.100565i	−0.410373	+	0.911918i	$0.634602\pi$
$558$	4.79498	+	8.30515i	0.202988	+	0.351585i
$559$	0.198180	+	0.343257i	0.00838210	+	0.0145182i
$560$	2.68834	−	1.55211i	0.113603	−	0.0655888i
$561$			5.48875i			0.231735i
$562$	8.72835	+	15.1179i	0.368183	+	0.637712i
$563$			28.3773i			1.19596i	0.801511	+	0.597980i	$0.204030\pi$
$563$			28.3773i			1.19596i	−0.801511	+	0.597980i	$0.795970\pi$
$564$	−3.08654	+	5.34605i	−0.129967	+	0.225109i
$565$	4.46160			0.187701
$566$	−16.3413			−0.686877
$567$	−1.55211	+	2.68834i	−0.0651826	+	0.112900i
$568$	−10.8712	+	6.27647i	−0.456144	+	0.263355i
$569$			20.1333i			0.844034i	0.906588	+	0.422017i	$0.138678\pi$
$569$			20.1333i			0.844034i	−0.906588	+	0.422017i	$0.861322\pi$
$570$	6.08559	+	3.51352i	0.254897	+	0.147165i
$571$	−2.44862	+	4.24114i	−0.102472	+	0.177486i	−0.912702	−	0.408625i	$-0.866008\pi$
$571$	−2.44862	+	4.24114i	−0.102472	+	0.177486i	0.810231	+	0.586111i	$0.199342\pi$
$572$	1.65909	+	0.957878i	0.0693702	+	0.0400509i
$573$	3.46748	−	2.00195i	0.144856	−	0.0836327i
$574$	−28.9951	+	16.7403i	−1.21023	+	0.698728i
$575$	7.27223	+	4.19862i	0.303273	+	0.175095i
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$	14.0963	+	8.13847i	0.586835	+	0.338809i	0.763845	−	0.645400i	$-0.223309\pi$
$577$	14.0963	+	8.13847i	0.586835	+	0.338809i	−0.177010	+	0.984209i	$0.556643\pi$
$578$		−	8.73629i		−	0.363382i
$579$	21.5984	−	12.4698i	0.897598	−	0.518228i
$580$	1.30410	−	2.25876i	0.0541497	−	0.0937900i
$581$	−51.6580			−2.14314
$582$	−12.0709			−0.500354
$583$	1.42779	−	2.47300i	0.0591329	−	0.102421i
$584$			13.3131i			0.550901i
$585$	−0.885339	−	1.53345i	−0.0366043	−	0.0634005i
$586$			30.3845i			1.25517i
$587$	−21.5925	+	12.4665i	−0.891219	+	0.514546i	−0.874341	−	0.485312i	$-0.838706\pi$
$587$	−21.5925	+	12.4665i	−0.891219	+	0.514546i	−0.0168783	+	0.999858i	$0.505373\pi$
$588$	−1.31811	−	2.28303i	−0.0543580	−	0.0941508i
$589$	−33.6945	−	58.3606i	−1.38836	−	2.40471i
$590$	−1.47494	−	0.851557i	−0.0607223	−	0.0350581i
$591$	19.9803			0.821882
$592$	4.86226	−	3.65492i	0.199838	−	0.150216i
$593$	10.9110			0.448062			0.224031	−	0.974582i	$-0.428078\pi$
$593$	10.9110			0.448062			0.224031	+	0.974582i	$0.428078\pi$
$594$	−0.936982	−	0.540967i	−0.0384448	−	0.0221961i
$595$	7.87402	+	13.6382i	0.322803	+	0.559112i
$596$	1.68580	+	2.91989i	0.0690531	+	0.119604i
$597$	6.70781	−	3.87275i	0.274532	−	0.158501i
$598$			14.8688i			0.608032i
$599$	5.36219	+	9.28759i	0.219093	+	0.379481i	0.954531	−	0.298112i	$-0.0963568\pi$
$599$	5.36219	+	9.28759i	0.219093	+	0.379481i	−0.735438	+	0.677592i	$0.763023\pi$
$600$		−	1.00000i		−	0.0408248i
$601$	8.73858	−	15.1357i	0.356454	−	0.617396i	−0.630912	−	0.775855i	$-0.717319\pi$
$601$	8.73858	−	15.1357i	0.356454	−	0.617396i	0.987366	+	0.158458i	$0.0506523\pi$
$602$	0.694868			0.0283207
$603$	1.05277			0.0428720
$604$	0.650118	−	1.12604i	0.0264529	−	0.0458178i
$605$	−8.51253	+	4.91471i	−0.346083	+	0.199811i
$606$			6.54354i			0.265813i
$607$	32.8110	+	18.9434i	1.33176	+	0.768891i	0.985569	−	0.169274i	$-0.0541423\pi$
$607$	32.8110	+	18.9434i	1.33176	+	0.768891i	0.346189	+	0.938165i	$0.387476\pi$
$608$	−3.51352	+	6.08559i	−0.142492	+	0.246803i
$609$	−7.01171	−	4.04821i	−0.284129	−	0.164042i
$610$	6.59715	−	3.80887i	0.267111	−	0.154216i
$611$	−9.46613	+	5.46527i	−0.382959	+	0.221101i
$612$	4.39343	+	2.53655i	0.177594	+	0.102534i
$613$	8.83995	−	15.3112i	0.357042	−	0.618415i	−0.630423	−	0.776252i	$-0.717119\pi$
$613$	8.83995	−	15.3112i	0.357042	−	0.618415i	0.987465	+	0.157837i	$0.0504520\pi$
$614$	−11.6260	−	6.71229i	−0.469188	−	0.270886i
$615$			10.7855i			0.434914i
$616$	2.90860	−	1.67928i	0.117191	−	0.0676602i
$617$	−19.7389	+	34.1888i	−0.794658	+	1.37639i	0.128398	+	0.991723i	$0.459016\pi$
$617$	−19.7389	+	34.1888i	−0.794658	+	1.37639i	−0.923056	+	0.384665i	$0.874317\pi$
$618$	−1.55293			−0.0624681
$619$	24.5765			0.987814			0.493907	−	0.869515i	$-0.335568\pi$
$619$	24.5765			0.987814			0.493907	+	0.869515i	$0.335568\pi$
$620$	−4.79498	+	8.30515i	−0.192571	+	0.333543i
$621$		−	8.39725i		−	0.336970i
$622$	−1.13447	−	1.96496i	−0.0454881	−	0.0787877i
$623$		−	42.6400i		−	1.70834i
$624$	1.53345	−	0.885339i	0.0613872	−	0.0354419i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	10.4768	+	18.1463i	0.418735	+	0.725271i
$627$	6.58421	+	3.80139i	0.262948	+	0.151813i
$628$	12.7152			0.507392
$629$	18.5418	+	24.6667i	0.739308	+	0.983526i
$630$	−3.10423			−0.123675
$631$	−12.0776	−	6.97300i	−0.480801	−	0.277591i	0.239949	−	0.970785i	$-0.422869\pi$
$631$	−12.0776	−	6.97300i	−0.480801	−	0.277591i	−0.720750	+	0.693195i	$0.756203\pi$
$632$	3.97947	+	6.89265i	0.158295	+	0.274175i
$633$	13.0985	+	22.6872i	0.520618	+	0.901736i
$634$	7.19960	−	4.15669i	0.285933	−	0.165083i
$635$			15.3464i			0.609002i
$636$	−1.31966	−	2.28572i	−0.0523281	−	0.0906349i
$637$		−	4.66790i		−	0.184949i
$638$	1.41095	−	2.44383i	0.0558599	−	0.0967522i
$639$	12.5529			0.496586
$640$	1.00000			0.0395285
$641$	−19.9121	+	34.4888i	−0.786480	+	1.36222i	0.141630	+	0.989920i	$0.454766\pi$
$641$	−19.9121	+	34.4888i	−0.786480	+	1.36222i	−0.928111	+	0.372304i	$0.878568\pi$
$642$	0.908429	−	0.524481i	0.0358528	−	0.0206996i
$643$		−	1.31829i		−	0.0519884i	−0.999662	−	0.0259942i	$-0.991725\pi$
$643$		−	1.31829i		−	0.0519884i	0.999662	−	0.0259942i	$-0.00827514\pi$
$644$	22.5746	+	13.0335i	0.889566	+	0.513591i
$645$	0.111923	−	0.193856i	0.00440696	−	0.00763308i
$646$	−30.8728	−	17.8244i	−1.21467	−	0.701292i
$647$	−24.3160	+	14.0389i	−0.955962	+	0.551925i	−0.894928	−	0.446211i	$-0.852773\pi$
$647$	−24.3160	+	14.0389i	−0.955962	+	0.551925i	−0.0610340	+	0.998136i	$0.519440\pi$
$648$	−0.866025	+	0.500000i	−0.0340207	+	0.0196419i
$649$	−1.59579	−	0.921328i	−0.0626401	−	0.0361653i
$650$	0.885339	−	1.53345i	0.0347259	−	0.0601470i
$651$	25.7811	+	14.8847i	1.01044	+	0.583378i
$652$			18.2315i			0.714000i
$653$	−27.4067	+	15.8233i	−1.07251	+	0.619212i	−0.928865	−	0.370418i	$-0.879214\pi$
$653$	−27.4067	+	15.8233i	−1.07251	+	0.619212i	−0.143641	+	0.989630i	$0.545881\pi$
$654$	−6.30710	+	10.9242i	−0.246627	+	0.427171i
$655$	−2.24832			−0.0878491
$656$	−10.7855			−0.421104
$657$	6.65656	−	11.5295i	0.259697	−	0.449809i
$658$			19.1627i			0.747038i
$659$	−20.9099	−	36.2170i	−0.814535	−	1.41082i	−0.909661	−	0.415351i	$-0.863659\pi$
$659$	−20.9099	−	36.2170i	−0.814535	−	1.41082i	0.0951266	−	0.995465i	$-0.469674\pi$
$660$		−	1.08193i		−	0.0421142i
$661$	−0.137516	+	0.0793947i	−0.00534874	+	0.00308810i	−0.502672	−	0.864477i	$-0.667650\pi$
$661$	−0.137516	+	0.0793947i	−0.00534874	+	0.00308810i	0.497323	+	0.867565i	$0.334316\pi$
$662$	−16.1423	−	27.9593i	−0.627390	−	1.08667i
$663$	4.49141	+	7.77935i	0.174432	+	0.302125i
$664$	−14.4117	−	8.32060i	−0.559282	−	0.322902i
$665$	21.8135			0.845892
$666$	−6.03830	+	0.734124i	−0.233979	+	0.0284467i
$667$	21.9017			0.848036
$668$	10.2964	+	5.94460i	0.398378	+	0.230004i
$669$	−9.25240	−	16.0256i	−0.357719	−	0.619587i
$670$	0.526383	+	0.911722i	0.0203360	+	0.0352229i
$671$	7.13767	−	4.12094i	0.275547	−	0.159087i
$672$		−	3.10423i		−	0.119748i
$673$	−10.7078	−	18.5465i	−0.412757	−	0.714916i	0.582433	−	0.812879i	$-0.302101\pi$
$673$	−10.7078	−	18.5465i	−0.412757	−	0.714916i	−0.995190	+	0.0979626i	$0.968767\pi$
$674$		−	17.2312i		−	0.663721i
$675$	−0.500000	+	0.866025i	−0.0192450	+	0.0333333i
$676$	−9.86470			−0.379411
$677$	20.2973			0.780089			0.390044	−	0.920796i	$-0.372460\pi$
$677$	20.2973			0.780089			0.390044	+	0.920796i	$0.372460\pi$
$678$	2.23080	−	3.86386i	0.0856734	−	0.148391i
$679$	−32.4506	+	18.7354i	−1.24534	+	0.718997i
$680$			5.07309i			0.194544i
$681$	−19.2955	−	11.1403i	−0.739404	−	0.426895i
$682$	−5.18785	+	8.98562i	−0.198653	+	0.344077i
$683$	−27.7947	−	16.0473i	−1.06353	−	0.614032i	−0.137127	−	0.990553i	$-0.543787\pi$
$683$	−27.7947	−	16.0473i	−1.06353	−	0.614032i	−0.926408	+	0.376521i	$0.877120\pi$
$684$	6.08559	−	3.51352i	0.232688	−	0.134343i
$685$	−11.3545	+	6.55551i	−0.433832	+	0.250473i
$686$	11.7313	+	6.77308i	0.447904	+	0.258597i
$687$	−1.25854	+	2.17986i	−0.0480164	+	0.0831668i
$688$	0.193856	+	0.111923i	0.00739070	+	0.00426702i
$689$		−	4.67340i		−	0.178042i
$690$	7.27223	−	4.19862i	0.276849	−	0.159839i
$691$	5.90971	−	10.2359i	0.224816	−	0.389393i	−0.731448	−	0.681897i	$-0.761155\pi$
$691$	5.90971	−	10.2359i	0.224816	−	0.389393i	0.956264	+	0.292504i	$0.0944886\pi$
$692$	5.44123			0.206844
$693$	−3.35857			−0.127581
$694$	9.54072	−	16.5250i	0.362161	−	0.627281i
$695$			6.99467i			0.265323i
$696$	−1.30410	−	2.25876i	−0.0494317	−	0.0856182i
$697$		−	54.7159i		−	2.07251i
$698$	18.8160	−	10.8634i	0.712195	−	0.411186i
$699$	−14.2622	−	24.7028i	−0.539446	−	0.934348i
$700$	−1.55211	−	2.68834i	−0.0586644	−	0.101610i
$701$	−9.84065	−	5.68150i	−0.371676	−	0.214587i	0.302514	−	0.953145i	$-0.402174\pi$
$701$	−9.84065	−	5.68150i	−0.371676	−	0.214587i	−0.674190	+	0.738558i	$0.735507\pi$
$702$	−1.77068			−0.0668299
$703$	42.4314	−	5.15872i	1.60033	−	0.194565i
$704$	1.08193			0.0407769
$705$	5.34605	+	3.08654i	0.201344	+	0.116246i
$706$	−17.9469	−	31.0850i	−0.675441	−	1.16990i
$707$	10.1563	+	17.5912i	0.381967	+	0.661587i
$708$	−1.47494	+	0.851557i	−0.0554317	+	0.0320035i
$709$		−	4.73086i		−	0.177671i	−0.996046	−	0.0888357i	$-0.971685\pi$
$709$		−	4.73086i		−	0.177671i	0.996046	−	0.0888357i	$-0.0283146\pi$
$710$	6.27647	+	10.8712i	0.235552	+	0.407987i
$711$		−	7.95894i		−	0.298484i
$712$	6.86806	−	11.8958i	0.257391	−	0.445815i
$713$	−80.5293			−3.01585
$714$	15.7480			0.589355
$715$	0.957878	−	1.65909i	0.0358226	−	0.0620466i
$716$	−17.8442	+	10.3024i	−0.666870	+	0.385017i
$717$			1.20432i			0.0449760i
$718$	2.37136	+	1.36911i	0.0884985	+	0.0510946i
$719$	−4.67891	+	8.10410i	−0.174494	+	0.302232i	−0.939986	−	0.341213i	$-0.889162\pi$
$719$	−4.67891	+	8.10410i	−0.174494	+	0.302232i	0.765492	+	0.643445i	$0.222496\pi$
$720$	−0.866025	−	0.500000i	−0.0322749	−	0.0186339i
$721$	−4.17481	+	2.41033i	−0.155478	+	0.0897652i
$722$	−26.3092	+	15.1896i	−0.979127	+	0.565299i
$723$	−3.37667	−	1.94952i	−0.125580	−	0.0725034i
$724$	8.21109	−	14.2220i	0.305163	−	0.528557i
$725$	−2.25876	−	1.30410i	−0.0838884	−	0.0484330i
$726$			9.82942i			0.364804i
$727$	−0.906829	+	0.523558i	−0.0336324	+	0.0194177i	−0.516722	−	0.856153i	$-0.672848\pi$
$727$	−0.906829	+	0.523558i	−0.0336324	+	0.0194177i	0.483090	+	0.875571i	$0.339515\pi$
$728$	2.74829	−	4.76018i	0.101859	−	0.176424i
$729$	1.00000			0.0370370
$730$	13.3131			0.492741
$731$	−0.567796	+	0.983451i	−0.0210007	+	0.0363742i
$732$		−	7.61773i		−	0.281559i
$733$	23.5145	+	40.7283i	0.868528	+	1.50433i	0.863501	+	0.504347i	$0.168267\pi$
$733$	23.5145	+	40.7283i	0.868528	+	1.50433i	0.00502658	+	0.999987i	$0.498400\pi$
$734$		−	24.3919i		−	0.900323i
$735$	−2.28303	+	1.31811i	−0.0842110	+	0.0486192i
$736$	4.19862	+	7.27223i	0.154763	+	0.268058i
$737$	0.569511	+	0.986423i	0.0209782	+	0.0363353i
$738$	9.34053	+	5.39276i	0.343830	+	0.198510i
$739$	−17.0984			−0.628975			−0.314487	−	0.949262i	$-0.601833\pi$
$739$	−17.0984			−0.628975			−0.314487	+	0.949262i	$0.601833\pi$
$740$	−3.65492	−	4.86226i	−0.134358	−	0.178740i
$741$	12.4426			0.457091
$742$	−7.09541	−	4.09653i	−0.260481	−	0.150389i
$743$	16.4254	+	28.4496i	0.602588	+	1.04371i	0.992428	+	0.122831i	$0.0391972\pi$
$743$	16.4254	+	28.4496i	0.602588	+	1.04371i	−0.389839	+	0.920883i	$0.627469\pi$
$744$	4.79498	+	8.30515i	0.175793	+	0.304482i
$745$	2.91989	−	1.68580i	0.106977	−	0.0617630i
$746$		−	35.1528i		−	1.28703i
$747$	8.32060	+	14.4117i	0.304435	+	0.527296i
$748$			5.48875i			0.200689i
$749$	1.62811	−	2.81997i	0.0594898	−	0.103039i
$750$	−1.00000			−0.0365148
$751$	−33.5956			−1.22592			−0.612961	−	0.790113i	$-0.710022\pi$
$751$	−33.5956			−1.22592			−0.612961	+	0.790113i	$0.710022\pi$
$752$	−3.08654	+	5.34605i	−0.112555	+	0.194950i
$753$	−5.72714	+	3.30657i	−0.208709	+	0.120498i
$754$		−	4.61827i		−	0.168188i
$755$	−1.12604	−	0.650118i	−0.0409807	−	0.0236602i
$756$	−1.55211	+	2.68834i	−0.0564498	+	0.0977739i
$757$	−17.3800	−	10.0343i	−0.631686	−	0.364704i	0.149719	−	0.988729i	$-0.452163\pi$
$757$	−17.3800	−	10.0343i	−0.631686	−	0.364704i	−0.781405	+	0.624024i	$0.785497\pi$
$758$	16.8370	−	9.72086i	0.611548	−	0.353078i
$759$	7.86807	−	4.54263i	0.285593	−	0.164887i
$760$	6.08559	+	3.51352i	0.220748	+	0.127449i
$761$	12.9992	−	22.5152i	0.471219	−	0.816175i	−0.528239	−	0.849096i	$-0.677148\pi$
$761$	12.9992	−	22.5152i	0.471219	−	0.816175i	0.999458	+	0.0329207i	$0.0104809\pi$
$762$	13.2903	+	7.67318i	0.481458	+	0.277970i
$763$			39.1573i			1.41759i
$764$	3.46748	−	2.00195i	0.125449	−	0.0724281i
$765$	2.53655	−	4.39343i	0.0917091	−	0.158845i
$766$	11.9324			0.431133
$767$	−3.01567			−0.108889
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$		−	29.6450i		−	1.06903i	−0.845160	−	0.534513i	$-0.820495\pi$
$769$		−	29.6450i		−	1.06903i	0.845160	−	0.534513i	$-0.179505\pi$
$770$	−1.67928	−	2.90860i	−0.0605172	−	0.104819i
$771$			2.85771i			0.102918i
$772$	21.5984	−	12.4698i	0.777342	−	0.448799i
$773$	2.38987	+	4.13937i	0.0859576	+	0.148883i	0.905799	−	0.423708i	$-0.139272\pi$
$773$	2.38987	+	4.13937i	0.0859576	+	0.148883i	−0.819841	+	0.572591i	$0.805938\pi$
$774$	−0.111923	−	0.193856i	−0.00402299	−	0.00696802i
$775$	8.30515	+	4.79498i	0.298330	+	0.172241i
$776$	−12.0709			−0.433319
$777$	−15.0936	+	11.3457i	−0.541478	+	0.407025i
$778$	−2.98735			−0.107102
$779$	−65.6363	−	37.8951i	−2.35166	−	1.35773i
$780$	−0.885339	−	1.53345i	−0.0317002	−	0.0549064i
$781$	6.79072	+	11.7619i	0.242991	+	0.420873i
$782$	−36.8927	+	21.3000i	−1.31928	+	0.761687i
$783$			2.60820i			0.0932093i
$784$	−1.31811	−	2.28303i	−0.0470754	−	0.0815369i
$785$		−	12.7152i		−	0.453825i
$786$	−1.12416	+	1.94710i	−0.0400975	+	0.0694508i
$787$	−4.03423			−0.143805			−0.0719024	−	0.997412i	$-0.522907\pi$
$787$	−4.03423			−0.143805			−0.0719024	+	0.997412i	$0.522907\pi$
$788$	19.9803			0.711770
$789$	7.91733	−	13.7132i	0.281864	−	0.488204i
$790$	6.89265	−	3.97947i	0.245229	−	0.141583i
$791$		−	13.8498i		−	0.492443i
$792$	−0.936982	−	0.540967i	−0.0332942	−	0.0192224i
$793$	6.74428	−	11.6814i	0.239496	−	0.414820i
$794$	−6.69470	−	3.86518i	−0.237586	−	0.137170i
$795$	−2.28572	+	1.31966i	−0.0810663	+	0.0468036i
$796$	6.70781	−	3.87275i	0.237752	−	0.137266i
$797$	14.7716	+	8.52842i	0.523239	+	0.302092i	0.738259	−	0.674518i	$-0.235648\pi$
$797$	14.7716	+	8.52842i	0.523239	+	0.302092i	−0.215020	+	0.976610i	$0.568982\pi$
$798$	10.9068	−	18.8911i	0.386095	−	0.668736i
$799$	−27.1210	−	15.6583i	−0.959472	−	0.553952i
$800$		−	1.00000i		−	0.0353553i
$801$	−11.8958	+	6.86806i	−0.420318	+	0.242671i
$802$	13.0951	−	22.6813i	0.462403	−	0.800905i
$803$	14.4039			0.508303
$804$	1.05277			0.0371282
$805$	13.0335	−	22.5746i	0.459370	−	0.795652i
$806$			16.9807i			0.598121i
$807$	10.9120	+	18.9001i	0.384120	+	0.665315i
$808$			6.54354i			0.230201i
$809$	19.2253	−	11.0997i	0.675925	−	0.390245i	−0.122393	−	0.992482i	$-0.539057\pi$
$809$	19.2253	−	11.0997i	0.675925	−	0.390245i	0.798318	+	0.602236i	$0.205724\pi$
$810$	0.500000	+	0.866025i	0.0175682	+	0.0304290i
$811$	2.17153	+	3.76119i	0.0762526	+	0.132073i	0.901630	−	0.432508i	$-0.142371\pi$
$811$	2.17153	+	3.76119i	0.0762526	+	0.132073i	−0.825378	+	0.564581i	$0.809038\pi$
$812$	−7.01171	−	4.04821i	−0.246063	−	0.142064i
$813$	−5.29128			−0.185573
$814$	−3.95438	−	5.26064i	−0.138601	−	0.184385i
$815$	18.2315			0.638621
$816$	4.39343	+	2.53655i	0.153801	+	0.0887969i
$817$	0.786487	+	1.36223i	0.0275157	+	0.0476586i
$818$	−15.4701	−	26.7950i	−0.540899	−	0.936865i
$819$	−4.76018	+	2.74829i	−0.166334	+	0.0960331i
$820$			10.7855i			0.376647i
$821$	23.1178	+	40.0413i	0.806818	+	1.39745i	0.915057	+	0.403325i	$0.132146\pi$
$821$	23.1178	+	40.0413i	0.806818	+	1.39745i	−0.108239	+	0.994125i	$0.534521\pi$
$822$			13.1110i			0.457299i
$823$	12.8556	−	22.2665i	0.448118	−	0.776163i	−0.550146	−	0.835069i	$-0.685428\pi$
$823$	12.8556	−	22.2665i	0.448118	−	0.776163i	0.998264	+	0.0589059i	$0.0187612\pi$
$824$	−1.55293			−0.0540989
$825$	−1.08193			−0.0376681
$826$	−2.64343	+	4.57855i	−0.0919766	+	0.159308i
$827$	25.1998	−	14.5491i	0.876282	−	0.505922i	0.00685156	−	0.999977i	$-0.497819\pi$
$827$	25.1998	−	14.5491i	0.876282	−	0.505922i	0.869431	+	0.494055i	$0.164486\pi$
$828$		−	8.39725i		−	0.291825i
$829$	−7.45210	−	4.30247i	−0.258822	−	0.149431i	0.364975	−	0.931017i	$-0.381078\pi$
$829$	−7.45210	−	4.30247i	−0.258822	−	0.149431i	−0.623797	+	0.781586i	$0.714411\pi$
$830$	−8.32060	+	14.4117i	−0.288812	+	0.500237i
$831$	11.7933	+	6.80885i	0.409104	+	0.236197i
$832$	1.53345	−	0.885339i	0.0531629	−	0.0306936i
$833$	11.5820	−	6.68690i	0.401294	−	0.231687i
$834$	6.05756	+	3.49733i	0.209756	+	0.121103i
$835$	5.94460	−	10.2964i	0.205721	−	0.356320i
$836$	6.58421	+	3.80139i	0.227720	+	0.131474i
$837$		−	9.58996i		−	0.331478i
$838$	1.44056	−	0.831708i	0.0497634	−	0.0287309i
$839$	26.0616	−	45.1399i	0.899745	−	1.55840i	0.0719248	−	0.997410i	$-0.477086\pi$
$839$	26.0616	−	45.1399i	0.899745	−	1.55840i	0.827820	−	0.560994i	$-0.189581\pi$
$840$	−3.10423			−0.107106
$841$	22.1973			0.765425
$842$	−10.0843	+	17.4666i	−0.347529	+	0.601938i
$843$		−	17.4567i		−	0.601241i
$844$	13.0985	+	22.6872i	0.450868	+	0.780927i
$845$			9.86470i			0.339356i
$846$	5.34605	−	3.08654i	0.183801	−	0.106118i
$847$	15.2564	+	26.4248i	0.524215	+	0.907967i
$848$	−1.31966	−	2.28572i	−0.0453174	−	0.0784921i
$849$	14.1520	+	8.17066i	0.485695	+	0.280416i
$850$	5.07309			0.174006
$851$	20.0138	−	46.9942i	0.686065	−	1.61094i
$852$	12.5529			0.430056
$853$	−13.8401	−	7.99058i	−0.473876	−	0.273592i	0.243985	−	0.969779i	$-0.421545\pi$
$853$	−13.8401	−	7.99058i	−0.473876	−	0.273592i	−0.717861	+	0.696187i	$0.754879\pi$
$854$	−11.8236	−	20.4790i	−0.404595	−	0.700778i
$855$	−3.51352	−	6.08559i	−0.120160	−	0.208123i
$856$	0.908429	−	0.524481i	0.0310494	−	0.0179264i
$857$		−	12.5996i		−	0.430394i	−0.976571	−	0.215197i	$-0.930961\pi$
$857$		−	12.5996i		−	0.430394i	0.976571	−	0.215197i	$-0.0690393\pi$
$858$	−0.957878	−	1.65909i	−0.0327014	−	0.0566405i
$859$		−	23.8594i		−	0.814073i	−0.913412	−	0.407036i	$-0.866562\pi$
$859$		−	23.8594i		−	0.814073i	0.913412	−	0.407036i	$-0.133438\pi$
$860$	0.111923	−	0.193856i	0.00381654	−	0.00661044i
$861$	33.4807			1.14102
$862$	−2.77019			−0.0943531
$863$	2.32455	−	4.02624i	0.0791287	−	0.137055i	−0.823746	−	0.566960i	$-0.808120\pi$
$863$	2.32455	−	4.02624i	0.0791287	−	0.137055i	0.902874	+	0.429905i	$0.141453\pi$
$864$	−0.866025	+	0.500000i	−0.0294628	+	0.0170103i
$865$		−	5.44123i		−	0.185007i
$866$	17.4194	+	10.0571i	0.591934	+	0.341753i
$867$	−4.36814	+	7.56585i	−0.148350	+	0.256950i
$868$	25.7811	+	14.8847i	0.875066	+	0.505220i
$869$	7.45738	−	4.30552i	0.252974	−	0.146055i
$870$	−2.25876	+	1.30410i	−0.0765792	+	0.0442130i
$871$	1.61437	+	0.932055i	0.0547007	+	0.0315815i
$872$	−6.30710	+	10.9242i	−0.213585	+	0.369941i
$873$	10.4537	+	6.03543i	0.353803	+	0.204268i
$874$			59.0078i			1.99597i
$875$	−2.68834	+	1.55211i	−0.0908824	+	0.0524710i
$876$	6.65656	−	11.5295i	0.224904	−	0.389546i
$877$	11.8099			0.398793			0.199396	−	0.979919i	$-0.436102\pi$
$877$	11.8099			0.398793			0.199396	+	0.979919i	$0.436102\pi$
$878$	14.1896			0.478875
$879$	15.1922	−	26.3137i	0.512421	−	0.887540i
$880$		−	1.08193i		−	0.0364720i
$881$	−27.3437	−	47.3606i	−0.921231	−	1.59562i	−0.797513	−	0.603302i	$-0.793851\pi$
$881$	−27.3437	−	47.3606i	−0.921231	−	1.59562i	−0.123718	−	0.992317i	$-0.539482\pi$
$882$			2.63622i			0.0887662i
$883$	−35.4234	+	20.4517i	−1.19209	+	0.688254i	−0.958780	−	0.284148i	$-0.908289\pi$
$883$	−35.4234	+	20.4517i	−1.19209	+	0.688254i	−0.233311	+	0.972402i	$0.574956\pi$
$884$	4.49141	+	7.77935i	0.151062	+	0.261648i
$885$	0.851557	+	1.47494i	0.0286248	+	0.0495796i
$886$	−11.4156	−	6.59082i	−0.383516	−	0.221423i
$887$	−48.0816			−1.61442			−0.807210	−	0.590264i	$-0.799024\pi$
$887$	−48.0816			−1.61442			−0.807210	+	0.590264i	$0.799024\pi$
$888$	−6.03830	+	0.734124i	−0.202632	+	0.0246356i
$889$	47.6386			1.59775
$890$	−11.8958	−	6.86806i	−0.398749	−	0.230218i
$891$	0.540967	+	0.936982i	0.0181231	+	0.0313901i
$892$	−9.25240	−	16.0256i	−0.309793	−	0.536578i
$893$	−37.5669	+	21.6892i	−1.25713	+	0.725803i
$894$		−	3.37160i		−	0.112763i
$895$	10.3024	+	17.8442i	0.344370	+	0.596466i
$896$		−	3.10423i		−	0.103705i
$897$	7.43441	−	12.8768i	0.248228	−	0.429943i
$898$	−23.1146			−0.771344
$899$	25.0125			0.834213
$900$	−0.500000	+	0.866025i	−0.0166667	+	0.0288675i
$901$	11.5957	−	6.69478i	0.386309	−	0.223035i
$902$			11.6692i			0.388542i
$903$	−0.601774	−	0.347434i	−0.0200258	−	0.0115619i
$904$	2.23080	−	3.86386i	0.0741954	−	0.128510i
$905$	−14.2220	−	8.21109i	−0.472756	−	0.272946i
$906$	−1.12604	+	0.650118i	−0.0374101	+	0.0215987i
$907$	40.0248	−	23.1083i	1.32900	−	0.767299i	0.343856	−	0.939022i	$-0.388267\pi$
$907$	40.0248	−	23.1083i	1.32900	−	0.767299i	0.985145	+	0.171723i	$0.0549334\pi$
$908$	−19.2955	−	11.1403i	−0.640343	−	0.369702i
$909$	3.27177	−	5.66687i	0.108518	−	0.187958i
$910$	−4.76018	−	2.74829i	−0.157799	−	0.0911050i
$911$		−	12.2210i		−	0.404900i	−0.979293	−	0.202450i	$-0.935110\pi$
$911$		−	12.2210i		−	0.404900i	0.979293	−	0.202450i	$-0.0648904\pi$
$912$	6.08559	−	3.51352i	0.201514	−	0.116344i
$913$	−9.00233	+	15.5925i	−0.297934	+	0.516036i
$914$	14.2433			0.471125
$915$	−7.61773			−0.251834
$916$	−1.25854	+	2.17986i	−0.0415834	+	0.0720246i
$917$			6.97929i			0.230477i
$918$	−2.53655	−	4.39343i	−0.0837185	−	0.145005i
$919$		−	2.71772i		−	0.0896493i	−0.998995	−	0.0448247i	$-0.985727\pi$
$919$		−	2.71772i		−	0.0896493i	0.998995	−	0.0448247i	$-0.0142729\pi$
$920$	7.27223	−	4.19862i	0.239758	−	0.138425i
$921$	6.71229	+	11.6260i	0.221178	+	0.383091i
$922$	−0.768227	−	1.33061i	−0.0253002	−	0.0438212i
$923$	19.2493	+	11.1136i	0.633599	+	0.365809i
$924$	−3.35857			−0.110489
$925$	−4.86226	+	3.65492i	−0.159870	+	0.120173i
$926$	27.5010			0.903739
$927$	1.34488	+	0.776466i	0.0441716	+	0.0255025i
$928$	−1.30410	−	2.25876i	−0.0428091	−	0.0741475i
$929$	−7.02639	−	12.1701i	−0.230528	−	0.399287i	0.727435	−	0.686176i	$-0.240712\pi$
$929$	−7.02639	−	12.1701i	−0.230528	−	0.399287i	−0.957964	+	0.286889i	$0.907379\pi$
$930$	8.30515	−	4.79498i	0.272337	−	0.157234i
$931$		−	18.5248i		−	0.607127i
$932$	−14.2622	−	24.7028i	−0.467174	−	0.809169i
$933$			2.26894i			0.0742818i
$934$	−6.46426	+	11.1964i	−0.211517	+	0.366358i
$935$	5.48875			0.179501
$936$	−1.77068			−0.0578764
$937$	−8.19702	+	14.1977i	−0.267785	+	0.463817i	−0.968290	−	0.249831i	$-0.919625\pi$
$937$	−8.19702	+	14.1977i	−0.267785	+	0.463817i	0.700504	+	0.713648i	$0.252958\pi$
$938$	2.83019	−	1.63401i	0.0924091	−	0.0533524i
$939$		−	20.9535i		−	0.683792i
$940$	5.34605	+	3.08654i	0.174369	+	0.100672i
$941$	3.05488	−	5.29121i	0.0995863	−	0.172488i	−0.811927	−	0.583759i	$-0.801581\pi$
$941$	3.05488	−	5.29121i	0.0995863	−	0.172488i	0.911513	+	0.411270i	$0.134915\pi$
$942$	−11.0117	−	6.35760i	−0.358780	−	0.207142i
$943$	−78.4348	+	45.2843i	−2.55419	+	1.47466i
$944$	−1.47494	+	0.851557i	−0.0480052	+	0.0277158i
$945$	2.68834	+	1.55211i	0.0874517	+	0.0504902i
$946$	0.121093	−	0.209739i	0.00393708	−	0.00681922i
$947$	17.6635	+	10.1980i	0.573987	+	0.331391i	0.758740	−	0.651393i	$-0.225815\pi$
$947$	17.6635	+	10.1980i	0.573987	+	0.331391i	−0.184753	+	0.982785i	$0.559149\pi$
$948$		−	7.95894i		−	0.258494i
$949$	20.4150	−	11.7866i	0.662700	−	0.382610i
$950$	3.51352	−	6.08559i	0.113994	−	0.197443i
$951$	−8.31338			−0.269580
$952$	15.7480			0.510397
$953$	−16.3050	+	28.2412i	−0.528172	+	0.914821i	0.471288	+	0.881979i	$0.343789\pi$
$953$	−16.3050	+	28.2412i	−0.528172	+	0.914821i	−0.999461	+	0.0328419i	$0.989544\pi$
$954$			2.63933i			0.0854514i
$955$	−2.00195	−	3.46748i	−0.0647816	−	0.112205i
$956$			1.20432i			0.0389503i
$957$	−2.44383	+	1.41095i	−0.0789978	+	0.0456094i
$958$	−16.3834	−	28.3768i	−0.529323	−	0.916814i
$959$	20.3498	+	35.2469i	0.657129	+	1.13818i
$960$	−0.866025	−	0.500000i	−0.0279508	−	0.0161374i
$961$	−60.9674			−1.96669
$962$	−9.90939	−	4.22020i	−0.319492	−	0.136065i
$963$	−1.04896			−0.0338024
$964$	−3.37667	−	1.94952i	−0.108755	−	0.0627898i
$965$	−12.4698	−	21.5984i	−0.401418	−	0.695276i
$966$	−13.0335	−	22.5746i	−0.419345	−	0.726327i
$967$	−3.69534	+	2.13351i	−0.118834	+	0.0686089i	−0.558239	−	0.829680i	$-0.688523\pi$
$967$	−3.69534	+	2.13351i	−0.118834	+	0.0686089i	0.439405	+	0.898289i	$0.355189\pi$
$968$			9.82942i			0.315930i
$969$	17.8244	+	30.8728i	0.572603	+	0.991777i
$970$			12.0709i			0.387572i
$971$	13.7627	−	23.8377i	0.441667	−	0.764990i	−0.556146	−	0.831084i	$-0.687721\pi$
$971$	13.7627	−	23.8377i	0.441667	−	0.764990i	0.997813	+	0.0660946i	$0.0210539\pi$
$972$	1.00000			0.0320750
$973$	21.7130			0.696088
$974$	2.92378	−	5.06413i	0.0936838	−	0.162265i
$975$	−1.53345	+	0.885339i	−0.0491098	+	0.0283535i
$976$		−	7.61773i		−	0.243838i
$977$	−3.16163	−	1.82537i	−0.101149	−	0.0583987i	0.448572	−	0.893747i	$-0.351933\pi$
$977$	−3.16163	−	1.82537i	−0.101149	−	0.0583987i	−0.549721	+	0.835348i	$0.685266\pi$
$978$	9.11574	−	15.7889i	0.291489	−	0.504874i
$979$	−12.8705	−	7.43078i	−0.411342	−	0.237489i
$980$	−2.28303	+	1.31811i	−0.0729289	+	0.0421055i
$981$	10.9242	−	6.30710i	0.348784	−	0.201370i
$982$	11.3649	+	6.56150i	0.362667	+	0.209386i
$983$	1.73078	−	2.99780i	0.0552034	−	0.0956151i	−0.837103	−	0.547045i	$-0.815753\pi$
$983$	1.73078	−	2.99780i	0.0552034	−	0.0956151i	0.892307	+	0.451430i	$0.149086\pi$
$984$	9.34053	+	5.39276i	0.297765	+	0.171915i
$985$		−	19.9803i		−	0.636627i
$986$	11.4589	−	6.61581i	0.364926	−	0.210690i
$987$	9.58133	−	16.5953i	0.304977	−	0.528236i
$988$	12.4426			0.395853
$989$	1.87969			0.0597706
$990$	−0.540967	+	0.936982i	−0.0171930	+	0.0297792i
$991$			5.19516i			0.165030i	0.996590	+	0.0825148i	$0.0262952\pi$
$991$			5.19516i			0.165030i	−0.996590	+	0.0825148i	$0.973705\pi$
$992$	4.79498	+	8.30515i	0.152241	+	0.263689i
$993$			32.2847i			1.02452i
$994$	33.7465	−	19.4836i	1.07038	−	0.617981i
$995$	−3.87275	−	6.70781i	−0.122775	−	0.212652i
$996$	8.32060	+	14.4117i	0.263648	+	0.456652i
$997$	−16.4088	−	9.47365i	−0.519673	−	0.300033i	0.217128	−	0.976143i	$-0.430331\pi$
$997$	−16.4088	−	9.47365i	−0.519673	−	0.300033i	−0.736801	+	0.676110i	$0.763664\pi$
$998$	13.2046			0.417985
$999$	5.59638	+	2.38338i	0.177062	+	0.0754068i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.x.e.841.1	yes	16
37.11	even	6	inner	1110.2.x.e.751.1	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.x.e.751.1	✓	16	37.11	even	6	inner
1110.2.x.e.841.1	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)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{5} -1.00000i q^{6} +(-1.55211 - 2.68834i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(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} +(-1.55211 - 2.68834i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} -1.00000 q^{10} -1.08193 q^{11} +(-0.500000 + 0.866025i) q^{12} +(-1.53345 + 0.885339i) q^{13} +3.10423i q^{14} +(0.866025 + 0.500000i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-4.39343 - 2.53655i) q^{17} +(0.866025 - 0.500000i) q^{18} +(-6.08559 + 3.51352i) q^{19} +(0.866025 + 0.500000i) q^{20} +(1.55211 - 2.68834i) q^{21} +(0.936982 + 0.540967i) q^{22} +8.39725i q^{23} +(0.866025 - 0.500000i) q^{24} +(0.500000 - 0.866025i) q^{25} +1.77068 q^{26} -1.00000 q^{27} +(1.55211 - 2.68834i) q^{28} -2.60820i q^{29} +(-0.500000 - 0.866025i) q^{30} +9.58996i q^{31} +(0.866025 - 0.500000i) q^{32} +(-0.540967 - 0.936982i) q^{33} +(2.53655 + 4.39343i) q^{34} +(-2.68834 - 1.55211i) q^{35} -1.00000 q^{36} +(-5.59638 - 2.38338i) q^{37} +7.02704 q^{38} +(-1.53345 - 0.885339i) q^{39} +(-0.500000 - 0.866025i) q^{40} +(5.39276 + 9.34053i) q^{41} +(-2.68834 + 1.55211i) q^{42} -0.223846i q^{43} +(-0.540967 - 0.936982i) q^{44} +1.00000i q^{45} +(4.19862 - 7.27223i) q^{46} +6.17308 q^{47} -1.00000 q^{48} +(-1.31811 + 2.28303i) q^{49} +(-0.866025 + 0.500000i) q^{50} -5.07309i q^{51} +(-1.53345 - 0.885339i) q^{52} +(-1.31966 + 2.28572i) q^{53} +(0.866025 + 0.500000i) q^{54} +(-0.936982 + 0.540967i) q^{55} +(-2.68834 + 1.55211i) q^{56} +(-6.08559 - 3.51352i) q^{57} +(-1.30410 + 2.25876i) q^{58} +(1.47494 + 0.851557i) q^{59} +1.00000i q^{60} +(-6.59715 + 3.80887i) q^{61} +(4.79498 - 8.30515i) q^{62} +3.10423 q^{63} -1.00000 q^{64} +(-0.885339 + 1.53345i) q^{65} +1.08193i q^{66} +(-0.526383 - 0.911722i) q^{67} -5.07309i q^{68} +(-7.27223 + 4.19862i) q^{69} +(1.55211 + 2.68834i) q^{70} +(-6.27647 - 10.8712i) q^{71} +(0.866025 + 0.500000i) q^{72} -13.3131 q^{73} +(3.65492 + 4.86226i) q^{74} +1.00000 q^{75} +(-6.08559 - 3.51352i) q^{76} +(1.67928 + 2.90860i) q^{77} +(0.885339 + 1.53345i) q^{78} +(-6.89265 + 3.97947i) q^{79} +1.00000i q^{80} +(-0.500000 - 0.866025i) q^{81} -10.7855i q^{82} +(8.32060 - 14.4117i) q^{83} +3.10423 q^{84} -5.07309 q^{85} +(-0.111923 + 0.193856i) q^{86} +(2.25876 - 1.30410i) q^{87} +1.08193i q^{88} +(11.8958 + 6.86806i) q^{89} +(0.500000 - 0.866025i) q^{90} +(4.76018 + 2.74829i) q^{91} +(-7.27223 + 4.19862i) q^{92} +(-8.30515 + 4.79498i) q^{93} +(-5.34605 - 3.08654i) q^{94} +(-3.51352 + 6.08559i) q^{95} +(0.866025 + 0.500000i) q^{96} -12.0709i q^{97} +(2.28303 - 1.31811i) q^{98} +(0.540967 - 0.936982i) 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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