LMFDB - Embedded newform 930.2.o.e.161.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(161,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 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("930.161");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.o (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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			161.9
Character	$\chi$	$=$	930.161
Dual form			930.2.o.e.491.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(1.62650 - 0.595404i) q^{3} -1.00000 q^{4} +(0.866025 + 0.500000i) q^{5} +(-0.595404 - 1.62650i) q^{6} +(-0.581871 - 1.00783i) q^{7} +1.00000i q^{8} +(2.29099 - 1.93685i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(1.62650 - 0.595404i) q^{3} -1.00000 q^{4} +(0.866025 + 0.500000i) q^{5} +(-0.595404 - 1.62650i) q^{6} +(-0.581871 - 1.00783i) q^{7} +1.00000i q^{8} +(2.29099 - 1.93685i) q^{9} +(0.500000 - 0.866025i) q^{10} +(0.0889568 - 0.154078i) q^{11} +(-1.62650 + 0.595404i) q^{12} +(-4.88952 - 2.82297i) q^{13} +(-1.00783 + 0.581871i) q^{14} +(1.70629 + 0.297614i) q^{15} +1.00000 q^{16} +(-1.93896 - 3.35837i) q^{17} +(-1.93685 - 2.29099i) q^{18} +(-2.57689 - 4.46331i) q^{19} +(-0.866025 - 0.500000i) q^{20} +(-1.54648 - 1.29279i) q^{21} +(-0.154078 - 0.0889568i) q^{22} +5.70722 q^{23} +(0.595404 + 1.62650i) q^{24} +(0.500000 + 0.866025i) q^{25} +(-2.82297 + 4.88952i) q^{26} +(2.57308 - 4.51434i) q^{27} +(0.581871 + 1.00783i) q^{28} +5.56575 q^{29} +(0.297614 - 1.70629i) q^{30} +(5.12730 - 2.17043i) q^{31} -1.00000i q^{32} +(0.0529495 - 0.303572i) q^{33} +(-3.35837 + 1.93896i) q^{34} -1.16374i q^{35} +(-2.29099 + 1.93685i) q^{36} +(0.782503 - 0.451779i) q^{37} +(-4.46331 + 2.57689i) q^{38} +(-9.63360 - 1.68031i) q^{39} +(-0.500000 + 0.866025i) q^{40} +(2.48692 + 1.43582i) q^{41} +(-1.29279 + 1.54648i) q^{42} +(0.735867 - 0.424853i) q^{43} +(-0.0889568 + 0.154078i) q^{44} +(2.95248 - 0.531863i) q^{45} -5.70722i q^{46} -4.11079i q^{47} +(1.62650 - 0.595404i) q^{48} +(2.82285 - 4.88932i) q^{49} +(0.866025 - 0.500000i) q^{50} +(-5.15329 - 4.30792i) q^{51} +(4.88952 + 2.82297i) q^{52} +(-6.25104 + 10.8271i) q^{53} +(-4.51434 - 2.57308i) q^{54} +(0.154078 - 0.0889568i) q^{55} +(1.00783 - 0.581871i) q^{56} +(-6.84878 - 5.72526i) q^{57} -5.56575i q^{58} +(-4.27376 + 2.46746i) q^{59} +(-1.70629 - 0.297614i) q^{60} -0.00227491i q^{61} +(-2.17043 - 5.12730i) q^{62} +(-3.28507 - 1.18193i) q^{63} -1.00000 q^{64} +(-2.82297 - 4.88952i) q^{65} +(-0.303572 - 0.0529495i) q^{66} +(-3.20296 + 5.54769i) q^{67} +(1.93896 + 3.35837i) q^{68} +(9.28278 - 3.39810i) q^{69} -1.16374 q^{70} +(10.9712 + 6.33424i) q^{71} +(1.93685 + 2.29099i) q^{72} +(9.32062 + 5.38127i) q^{73} +(-0.451779 - 0.782503i) q^{74} +(1.32888 + 1.11089i) q^{75} +(2.57689 + 4.46331i) q^{76} -0.207046 q^{77} +(-1.68031 + 9.63360i) q^{78} +(-2.52627 + 1.45854i) q^{79} +(0.866025 + 0.500000i) q^{80} +(1.49726 - 8.87458i) q^{81} +(1.43582 - 2.48692i) q^{82} +(-7.95846 + 13.7845i) q^{83} +(1.54648 + 1.29279i) q^{84} -3.87791i q^{85} +(-0.424853 - 0.735867i) q^{86} +(9.05268 - 3.31387i) q^{87} +(0.154078 + 0.0889568i) q^{88} -5.20790 q^{89} +(-0.531863 - 2.95248i) q^{90} +6.57041i q^{91} -5.70722 q^{92} +(7.04726 - 6.58302i) q^{93} -4.11079 q^{94} -5.15378i q^{95} +(-0.595404 - 1.62650i) q^{96} -13.7078 q^{97} +(-4.88932 - 2.82285i) q^{98} +(-0.0946257 - 0.525286i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 6 q^{3} - 40 q^{4} - 12 q^{7} - 2 q^{9}+O(q^{10}) $ 40 * q + 6 * q^3 - 40 * q^4 - 12 * q^7 - 2 * q^9	$ 40 q + 6 q^{3} - 40 q^{4} - 12 q^{7} - 2 q^{9} + 20 q^{10} - 6 q^{12} - 12 q^{13} + 40 q^{16} - 12 q^{18} - 12 q^{19} + 12 q^{21} - 24 q^{22} + 20 q^{25} + 12 q^{28} + 8 q^{31} + 52 q^{33} + 24 q^{34} + 2 q^{36} + 60 q^{37} - 8 q^{39} - 20 q^{40} + 12 q^{42} + 24 q^{43} - 12 q^{45} + 6 q^{48} - 4 q^{49} + 14 q^{51} + 12 q^{52} + 24 q^{55} - 12 q^{57} - 40 q^{64} + 8 q^{66} + 64 q^{67} - 26 q^{69} - 24 q^{70} + 12 q^{72} + 6 q^{75} + 12 q^{76} - 68 q^{78} - 48 q^{79} + 2 q^{81} + 4 q^{82} - 12 q^{84} + 36 q^{87} + 24 q^{88} + 2 q^{90} - 22 q^{93} - 40 q^{94} + 8 q^{97} - 90 q^{99}+O(q^{100}) $ 40 * q + 6 * q^3 - 40 * q^4 - 12 * q^7 - 2 * q^9 + 20 * q^10 - 6 * q^12 - 12 * q^13 + 40 * q^16 - 12 * q^18 - 12 * q^19 + 12 * q^21 - 24 * q^22 + 20 * q^25 + 12 * q^28 + 8 * q^31 + 52 * q^33 + 24 * q^34 + 2 * q^36 + 60 * q^37 - 8 * q^39 - 20 * q^40 + 12 * q^42 + 24 * q^43 - 12 * q^45 + 6 * q^48 - 4 * q^49 + 14 * q^51 + 12 * q^52 + 24 * q^55 - 12 * q^57 - 40 * q^64 + 8 * q^66 + 64 * q^67 - 26 * q^69 - 24 * q^70 + 12 * q^72 + 6 * q^75 + 12 * q^76 - 68 * q^78 - 48 * q^79 + 2 * q^81 + 4 * q^82 - 12 * q^84 + 36 * q^87 + 24 * q^88 + 2 * q^90 - 22 * q^93 - 40 * q^94 + 8 * q^97 - 90 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	1.62650	−	0.595404i	0.939059	−	0.343757i
$3$	1.62650	−	0.595404i	0.939059	−	0.343757i
$4$	−1.00000			−0.500000
$5$	0.866025	+	0.500000i	0.387298	+	0.223607i
$5$	0.866025	+	0.500000i	0.387298	+	0.223607i
$6$	−0.595404	−	1.62650i	−0.243073	−	0.664015i
$7$	−0.581871	−	1.00783i	−0.219927	−	0.380924i	0.734859	−	0.678220i	$-0.237248\pi$
$7$	−0.581871	−	1.00783i	−0.219927	−	0.380924i	−0.954785	+	0.297296i	$0.903915\pi$
$8$			1.00000i			0.353553i
$9$	2.29099	−	1.93685i	0.763663	−	0.645615i
$10$	0.500000	−	0.866025i	0.158114	−	0.273861i
$11$	0.0889568	−	0.154078i	0.0268215	−	0.0464562i	−0.852303	−	0.523048i	$-0.824795\pi$
$11$	0.0889568	−	0.154078i	0.0268215	−	0.0464562i	0.879125	+	0.476592i	$0.158128\pi$
$12$	−1.62650	+	0.595404i	−0.469529	+	0.171878i
$13$	−4.88952	−	2.82297i	−1.35611	−	0.782950i	−0.367012	−	0.930216i	$-0.619619\pi$
$13$	−4.88952	−	2.82297i	−1.35611	−	0.782950i	−0.989097	+	0.147266i	$0.952953\pi$
$14$	−1.00783	+	0.581871i	−0.269354	+	0.155512i
$15$	1.70629	+	0.297614i	0.440562	+	0.0768436i
$16$	1.00000			0.250000
$17$	−1.93896	−	3.35837i	−0.470266	−	0.814524i	0.529156	−	0.848525i	$-0.322509\pi$
$17$	−1.93896	−	3.35837i	−0.470266	−	0.814524i	−0.999422	+	0.0340003i	$0.989175\pi$
$18$	−1.93685	−	2.29099i	−0.456519	−	0.539991i
$19$	−2.57689	−	4.46331i	−0.591179	−	1.02395i	−0.994074	−	0.108706i	$-0.965329\pi$
$19$	−2.57689	−	4.46331i	−0.591179	−	1.02395i	0.402895	−	0.915246i	$-0.368004\pi$
$20$	−0.866025	−	0.500000i	−0.193649	−	0.111803i
$21$	−1.54648	−	1.29279i	−0.337469	−	0.282109i
$22$	−0.154078	−	0.0889568i	−0.0328495	−	0.0189656i
$23$	5.70722			1.19004			0.595019	−	0.803712i	$-0.297145\pi$
$23$	5.70722			1.19004			0.595019	+	0.803712i	$0.297145\pi$
$24$	0.595404	+	1.62650i	0.121536	+	0.332007i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	−2.82297	+	4.88952i	−0.553629	+	0.958914i
$27$	2.57308	−	4.51434i	0.495190	−	0.868785i
$28$	0.581871	+	1.00783i	0.109963	+	0.190462i
$29$	5.56575			1.03353			0.516767	−	0.856126i	$-0.327135\pi$
$29$	5.56575			1.03353			0.516767	+	0.856126i	$0.327135\pi$
$30$	0.297614	−	1.70629i	0.0543366	−	0.311525i
$31$	5.12730	−	2.17043i	0.920891	−	0.389821i
$31$	5.12730	−	2.17043i	0.920891	−	0.389821i
$32$		−	1.00000i		−	0.176777i
$33$	0.0529495	−	0.303572i	0.00921733	−	0.0528451i
$34$	−3.35837	+	1.93896i	−0.575956	+	0.332528i
$35$		−	1.16374i		−	0.196708i
$36$	−2.29099	+	1.93685i	−0.381831	+	0.322808i
$37$	0.782503	−	0.451779i	0.128643	−	0.0742719i	−0.434298	−	0.900769i	$-0.643003\pi$
$37$	0.782503	−	0.451779i	0.128643	−	0.0742719i	0.562940	+	0.826497i	$0.309670\pi$
$38$	−4.46331	+	2.57689i	−0.724044	+	0.418027i
$39$	−9.63360	−	1.68031i	−1.54261	−	0.269065i
$40$	−0.500000	+	0.866025i	−0.0790569	+	0.136931i
$41$	2.48692	+	1.43582i	0.388391	+	0.224238i	0.681463	−	0.731853i	$-0.261344\pi$
$41$	2.48692	+	1.43582i	0.388391	+	0.224238i	−0.293072	+	0.956091i	$0.594677\pi$
$42$	−1.29279	+	1.54648i	−0.199481	+	0.238627i
$43$	0.735867	−	0.424853i	0.112219	−	0.0647895i	−0.442840	−	0.896601i	$-0.646029\pi$
$43$	0.735867	−	0.424853i	0.112219	−	0.0647895i	0.555059	+	0.831811i	$0.312696\pi$
$44$	−0.0889568	+	0.154078i	−0.0134107	+	0.0232281i
$45$	2.95248	−	0.531863i	0.440129	−	0.0792855i
$46$		−	5.70722i		−	0.841484i
$47$		−	4.11079i		−	0.599620i	−0.953999	−	0.299810i	$-0.903077\pi$
$47$		−	4.11079i		−	0.599620i	0.953999	−	0.299810i	$-0.0969233\pi$
$48$	1.62650	−	0.595404i	0.234765	−	0.0859391i
$49$	2.82285	−	4.88932i	0.403265	−	0.698475i
$50$	0.866025	−	0.500000i	0.122474	−	0.0707107i
$51$	−5.15329	−	4.30792i	−0.721605	−	0.603229i
$52$	4.88952	+	2.82297i	0.678055	+	0.391475i
$53$	−6.25104	+	10.8271i	−0.858646	+	1.48722i	0.0145750	+	0.999894i	$0.495360\pi$
$53$	−6.25104	+	10.8271i	−0.858646	+	1.48722i	−0.873221	+	0.487325i	$0.837973\pi$
$54$	−4.51434	−	2.57308i	−0.614324	−	0.350152i
$55$	0.154078	−	0.0889568i	0.0207758	−	0.0119949i
$56$	1.00783	−	0.581871i	0.134677	−	0.0777558i
$57$	−6.84878	−	5.72526i	−0.907142	−	0.758330i
$58$		−	5.56575i		−	0.730819i
$59$	−4.27376	+	2.46746i	−0.556396	+	0.321235i	−0.751698	−	0.659508i	$-0.770765\pi$
$59$	−4.27376	+	2.46746i	−0.556396	+	0.321235i	0.195302	+	0.980743i	$0.437431\pi$
$60$	−1.70629	−	0.297614i	−0.220281	−	0.0384218i
$61$		−	0.00227491i		−	0.000291272i	−1.00000		0.000145636i	$-0.999954\pi$
$61$		−	0.00227491i		−	0.000291272i	1.00000		0.000145636i	$-4.63574e-5\pi$
$62$	−2.17043	−	5.12730i	−0.275645	−	0.651168i
$63$	−3.28507	−	1.18193i	−0.413880	−	0.148910i
$64$	−1.00000			−0.125000
$65$	−2.82297	−	4.88952i	−0.350146	−	0.606471i
$66$	−0.303572	−	0.0529495i	−0.0373671	−	0.00651764i
$67$	−3.20296	+	5.54769i	−0.391304	+	0.677758i	−0.992622	−	0.121252i	$-0.961309\pi$
$67$	−3.20296	+	5.54769i	−0.391304	+	0.677758i	0.601318	+	0.799010i	$0.294642\pi$
$68$	1.93896	+	3.35837i	0.235133	+	0.407262i
$69$	9.28278	−	3.39810i	1.11752	−	0.409083i
$70$	−1.16374			−0.139094
$71$	10.9712	+	6.33424i	1.30204	+	0.751736i	0.980754	−	0.195245i	$-0.0625502\pi$
$71$	10.9712	+	6.33424i	1.30204	+	0.751736i	0.321290	+	0.946981i	$0.395884\pi$
$72$	1.93685	+	2.29099i	0.228259	+	0.269996i
$73$	9.32062	+	5.38127i	1.09090	+	0.629829i	0.933815	−	0.357756i	$-0.116458\pi$
$73$	9.32062	+	5.38127i	1.09090	+	0.629829i	0.157082	+	0.987586i	$0.449791\pi$
$74$	−0.451779	−	0.782503i	−0.0525182	−	0.0909642i
$75$	1.32888	+	1.11089i	0.153446	+	0.128274i
$76$	2.57689	+	4.46331i	0.295590	+	0.511976i
$77$	−0.207046			−0.0235950
$78$	−1.68031	+	9.63360i	−0.190257	+	1.09079i
$79$	−2.52627	+	1.45854i	−0.284228	+	0.164099i	−0.635336	−	0.772236i	$-0.719138\pi$
$79$	−2.52627	+	1.45854i	−0.284228	+	0.164099i	0.351108	+	0.936335i	$0.385805\pi$
$80$	0.866025	+	0.500000i	0.0968246	+	0.0559017i
$81$	1.49726	−	8.87458i	0.166362	−	0.986065i
$82$	1.43582	−	2.48692i	0.158560	−	0.274634i
$83$	−7.95846	+	13.7845i	−0.873555	+	1.51304i	−0.0152607	+	0.999884i	$0.504858\pi$
$83$	−7.95846	+	13.7845i	−0.873555	+	1.51304i	−0.858294	+	0.513158i	$0.828476\pi$
$84$	1.54648	+	1.29279i	0.168735	+	0.141054i
$85$		−	3.87791i		−	0.420618i
$86$	−0.424853	−	0.735867i	−0.0458131	−	0.0793506i
$87$	9.05268	−	3.31387i	0.970549	−	0.355284i
$88$	0.154078	+	0.0889568i	0.0164247	+	0.00948282i
$89$	−5.20790			−0.552036			−0.276018	−	0.961152i	$-0.589015\pi$
$89$	−5.20790			−0.552036			−0.276018	+	0.961152i	$0.589015\pi$
$90$	−0.531863	−	2.95248i	−0.0560633	−	0.311218i
$91$			6.57041i			0.688766i
$92$	−5.70722			−0.595019
$93$	7.04726	−	6.58302i	0.730767	−	0.682627i
$94$	−4.11079			−0.423995
$95$		−	5.15378i		−	0.528767i
$96$	−0.595404	−	1.62650i	−0.0607682	−	0.166004i
$97$	−13.7078			−1.39181			−0.695907	−	0.718132i	$-0.744997\pi$
$97$	−13.7078			−1.39181			−0.695907	+	0.718132i	$0.744997\pi$
$98$	−4.88932	−	2.82285i	−0.493896	−	0.285151i
$99$	−0.0946257	−	0.525286i	−0.00951024	−	0.0527932i
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$		−	2.34879i		−	0.233713i	−0.993149	−	0.116856i	$-0.962718\pi$
$101$		−	2.34879i		−	0.233713i	0.993149	−	0.116856i	$-0.0372817\pi$
$102$	−4.30792	+	5.15329i	−0.426547	+	0.510252i
$103$	−8.49332	+	14.7109i	−0.836872	+	1.44950i	0.0556251	+	0.998452i	$0.482285\pi$
$103$	−8.49332	+	14.7109i	−0.836872	+	1.44950i	−0.892497	+	0.451053i	$0.851048\pi$
$104$	2.82297	−	4.88952i	0.276815	−	0.479457i
$105$	−0.692897	−	1.89282i	−0.0676198	−	0.184721i
$106$	10.8271	+	6.25104i	1.05162	+	0.607154i
$107$	−4.00394	+	2.31167i	−0.387075	+	0.223478i	−0.680892	−	0.732384i	$-0.738408\pi$
$107$	−4.00394	+	2.31167i	−0.387075	+	0.223478i	0.293817	+	0.955862i	$0.405074\pi$
$108$	−2.57308	+	4.51434i	−0.247595	+	0.434392i
$109$	18.3302			1.75571			0.877856	−	0.478925i	$-0.158973\pi$
$109$	18.3302			1.75571			0.877856	+	0.478925i	$0.158973\pi$
$110$	−0.0889568	−	0.154078i	−0.00848170	−	0.0146907i
$111$	1.00375	−	1.20072i	0.0952716	−	0.113968i
$112$	−0.581871	−	1.00783i	−0.0549817	−	0.0952310i
$113$	0.376805	+	0.217548i	0.0354468	+	0.0204652i	0.517619	−	0.855611i	$-0.326819\pi$
$113$	0.376805	+	0.217548i	0.0354468	+	0.0204652i	−0.482172	+	0.876077i	$0.660152\pi$
$114$	−5.72526	+	6.84878i	−0.536220	+	0.641447i
$115$	4.94260	+	2.85361i	0.460900	+	0.266101i
$116$	−5.56575			−0.516767
$117$	−16.6695	+	3.00287i	−1.54109	+	0.277615i
$118$	2.46746	+	4.27376i	0.227148	+	0.393431i
$119$	−2.25644	+	3.90828i	−0.206848	+	0.358271i
$120$	−0.297614	+	1.70629i	−0.0271683	+	0.155762i
$121$	5.48417	+	9.49887i	0.498561	+	0.863533i
$122$	−0.00227491			−0.000205960
$123$	4.89986	+	0.854642i	0.441806	+	0.0770604i
$124$	−5.12730	+	2.17043i	−0.460445	+	0.194911i
$125$			1.00000i			0.0894427i
$126$	−1.18193	+	3.28507i	−0.105295	+	0.292657i
$127$	10.9132	−	6.30073i	0.968388	−	0.559099i	0.0696438	−	0.997572i	$-0.477814\pi$
$127$	10.9132	−	6.30073i	0.968388	−	0.559099i	0.898745	+	0.438473i	$0.144480\pi$
$128$			1.00000i			0.0883883i
$129$	0.943927	−	1.12916i	0.0831081	−	0.0994170i
$130$	−4.88952	+	2.82297i	−0.428839	+	0.247591i
$131$	−18.3335	+	10.5849i	−1.60181	+	0.924803i	−0.610679	+	0.791878i	$0.709104\pi$
$131$	−18.3335	+	10.5849i	−1.60181	+	0.924803i	−0.991126	+	0.132925i	$0.957563\pi$
$132$	−0.0529495	+	0.303572i	−0.00460867	+	0.0264226i
$133$	−2.99884	+	5.19414i	−0.260032	+	0.450389i
$134$	5.54769	+	3.20296i	0.479247	+	0.276693i
$135$	4.48552	−	2.62299i	0.386052	−	0.225751i
$136$	3.35837	−	1.93896i	0.287978	−	0.166264i
$137$	6.42120	−	11.1218i	0.548600	−	0.950203i	−0.449771	−	0.893144i	$-0.648494\pi$
$137$	6.42120	−	11.1218i	0.548600	−	0.950203i	0.998371	−	0.0570592i	$-0.0181724\pi$
$138$	−3.39810	−	9.28278i	−0.289266	−	0.790203i
$139$			0.913499i			0.0774820i	0.999249	+	0.0387410i	$0.0123347\pi$
$139$			0.913499i			0.0774820i	−0.999249	+	0.0387410i	$0.987665\pi$
$140$			1.16374i			0.0983542i
$141$	−2.44758	−	6.68619i	−0.206123	−	0.563078i
$142$	6.33424	−	10.9712i	0.531557	−	0.920685i
$143$	−0.869912	+	0.502244i	−0.0727457	+	0.0419998i
$144$	2.29099	−	1.93685i	0.190916	−	0.161404i
$145$	4.82008	+	2.78288i	0.400286	+	0.231105i
$146$	5.38127	−	9.32062i	0.445357	−	0.771380i
$147$	1.68024	−	9.63321i	0.138584	−	0.794534i
$148$	−0.782503	+	0.451779i	−0.0643214	+	0.0371360i
$149$	3.97105	−	2.29269i	0.325321	−	0.187824i	−0.328441	−	0.944525i	$-0.606523\pi$
$149$	3.97105	−	2.29269i	0.325321	−	0.187824i	0.653762	+	0.756700i	$0.273190\pi$
$150$	1.11089	−	1.32888i	0.0907035	−	0.108503i
$151$		−	18.0258i		−	1.46692i	−0.679734	−	0.733458i	$-0.737905\pi$
$151$		−	18.0258i		−	1.46692i	0.679734	−	0.733458i	$-0.262095\pi$
$152$	4.46331	−	2.57689i	0.362022	−	0.209013i
$153$	−10.9468	−	3.93853i	−0.884994	−	0.318411i
$154$			0.207046i			0.0166842i
$155$	5.52559	+	0.684001i	0.443826	+	0.0549403i
$156$	9.63360	+	1.68031i	0.771305	+	0.134532i
$157$	−9.03549			−0.721111			−0.360555	−	0.932738i	$-0.617413\pi$
$157$	−9.03549			−0.721111			−0.360555	+	0.932738i	$0.617413\pi$
$158$	1.45854	+	2.52627i	0.116036	+	0.200980i
$159$	−3.72079	+	21.3322i	−0.295078	+	1.69175i
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$	−3.32087	−	5.75191i	−0.261721	−	0.453314i
$162$	−8.87458	−	1.49726i	−0.697253	−	0.117636i
$163$	17.0876			1.33840			0.669201	−	0.743082i	$-0.266637\pi$
$163$	17.0876			1.33840			0.669201	+	0.743082i	$0.266637\pi$
$164$	−2.48692	−	1.43582i	−0.194196	−	0.112119i
$165$	0.197642	−	0.236426i	0.0153864	−	0.0184058i
$166$	13.7845	+	7.95846i	1.06988	+	0.617697i
$167$	−4.44098	−	7.69200i	−0.343653	−	0.595225i	0.641455	−	0.767161i	$-0.278331\pi$
$167$	−4.44098	−	7.69200i	−0.343653	−	0.595225i	−0.985108	+	0.171936i	$0.944998\pi$
$168$	1.29279	−	1.54648i	0.0997406	−	0.119313i
$169$	9.43828	+	16.3476i	0.726022	+	1.25751i
$170$	−3.87791			−0.297422
$171$	−14.5484	−	5.23434i	−1.11254	−	0.400280i
$172$	−0.735867	+	0.424853i	−0.0561093	+	0.0323947i
$173$	−2.18205	−	1.25981i	−0.165898	−	0.0957813i	0.414752	−	0.909934i	$-0.363868\pi$
$173$	−2.18205	−	1.25981i	−0.165898	−	0.0957813i	−0.580650	+	0.814153i	$0.697202\pi$
$174$	−3.31387	−	9.05268i	−0.251224	−	0.686282i
$175$	0.581871	−	1.00783i	0.0439853	−	0.0761848i
$176$	0.0889568	−	0.154078i	0.00670537	−	0.0116140i
$177$	−5.48213	+	6.55792i	−0.412062	+	0.492924i
$178$			5.20790i			0.390348i
$179$	7.26572	+	12.5846i	0.543065	+	0.940616i	0.998726	+	0.0504628i	$0.0160696\pi$
$179$	7.26572	+	12.5846i	0.543065	+	0.940616i	−0.455661	+	0.890153i	$0.650597\pi$
$180$	−2.95248	+	0.531863i	−0.220065	+	0.0396428i
$181$	−3.27223	−	1.88922i	−0.243223	−	0.140425i	0.373434	−	0.927657i	$-0.378180\pi$
$181$	−3.27223	−	1.88922i	−0.243223	−	0.140425i	−0.616657	+	0.787232i	$0.711513\pi$
$182$	6.57041			0.487031
$183$	−0.00135449	−	0.00370013i	−0.000100127	−	0.000273522i
$184$			5.70722i			0.420742i
$185$	0.903557			0.0664308
$186$	−6.58302	−	7.04726i	−0.482690	−	0.516730i
$187$	−0.689933			−0.0504529
$188$			4.11079i			0.299810i
$189$	−6.04689	+	0.0335334i	−0.439846	+	0.00243919i
$190$	−5.15378			−0.373895
$191$	5.58732	+	3.22584i	0.404284	+	0.233414i	0.688331	−	0.725397i	$-0.258344\pi$
$191$	5.58732	+	3.22584i	0.404284	+	0.233414i	−0.284047	+	0.958810i	$0.591677\pi$
$192$	−1.62650	+	0.595404i	−0.117382	+	0.0429696i
$193$	−1.05136	−	1.82101i	−0.0756786	−	0.131079i	0.825703	−	0.564106i	$-0.190779\pi$
$193$	−1.05136	−	1.82101i	−0.0756786	−	0.131079i	−0.901381	+	0.433027i	$0.857446\pi$
$194$			13.7078i			0.984161i
$195$	−7.50279	−	6.27199i	−0.537286	−	0.449147i
$196$	−2.82285	+	4.88932i	−0.201632	+	0.349237i
$197$	9.43359	−	16.3395i	0.672115	−	1.16414i	−0.305188	−	0.952292i	$-0.598719\pi$
$197$	9.43359	−	16.3395i	0.672115	−	1.16414i	0.977303	−	0.211846i	$-0.0679474\pi$
$198$	−0.525286	+	0.0946257i	−0.0373304	+	0.00672476i
$199$	16.6694	+	9.62408i	1.18166	+	0.682233i	0.956398	−	0.292065i	$-0.0943425\pi$
$199$	16.6694	+	9.62408i	1.18166	+	0.682233i	0.225263	+	0.974298i	$0.427676\pi$
$200$	−0.866025	+	0.500000i	−0.0612372	+	0.0353553i
$201$	−1.90649	+	10.9304i	−0.134473	+	0.770967i
$202$	−2.34879			−0.165260
$203$	−3.23855	−	5.60933i	−0.227302	−	0.393698i
$204$	5.15329	+	4.30792i	0.360803	+	0.301615i
$205$	1.43582	+	2.48692i	0.100282	+	0.173694i
$206$	14.7109	+	8.49332i	1.02495	+	0.591758i
$207$	13.0752	−	11.0540i	0.908788	−	0.768307i
$208$	−4.88952	−	2.82297i	−0.339027	−	0.195738i
$209$	−0.916927			−0.0634252
$210$	−1.89282	+	0.692897i	−0.130617	+	0.0478144i
$211$	5.53532	+	9.58746i	0.381067	+	0.660028i	0.991215	−	0.132260i	$-0.0422233\pi$
$211$	5.53532	+	9.58746i	0.381067	+	0.660028i	−0.610148	+	0.792288i	$0.708890\pi$
$212$	6.25104	−	10.8271i	0.429323	−	0.743609i
$213$	21.6161	+	3.77031i	1.48111	+	0.258338i
$214$	2.31167	+	4.00394i	0.158023	+	0.273703i
$215$	0.849706			0.0579495
$216$	4.51434	+	2.57308i	0.307162	+	0.175076i
$217$	−5.17086	−	3.90454i	−0.351021	−	0.265057i
$218$		−	18.3302i		−	1.24148i
$219$	18.3640	+	3.20308i	1.24092	+	0.216444i
$220$	−0.154078	+	0.0889568i	−0.0103879	+	0.00599746i
$221$			21.8944i			1.47278i
$222$	−1.20072	−	1.00375i	−0.0805872	−	0.0673672i
$223$	−3.79542	+	2.19128i	−0.254160	+	0.146739i	−0.621668	−	0.783281i	$-0.713545\pi$
$223$	−3.79542	+	2.19128i	−0.254160	+	0.146739i	0.367508	+	0.930020i	$0.380211\pi$
$224$	−1.00783	+	0.581871i	−0.0673385	+	0.0388779i
$225$	2.82285	+	1.01563i	0.188190	+	0.0677088i
$226$	0.217548	−	0.376805i	0.0144711	−	0.0250647i
$227$	−14.2337	−	8.21783i	−0.944724	−	0.545436i	−0.0532857	−	0.998579i	$-0.516969\pi$
$227$	−14.2337	−	8.21783i	−0.944724	−	0.545436i	−0.891438	+	0.453143i	$0.850303\pi$
$228$	6.84878	+	5.72526i	0.453571	+	0.379165i
$229$	0.621599	−	0.358880i	0.0410764	−	0.0237155i	−0.479321	−	0.877640i	$-0.659117\pi$
$229$	0.621599	−	0.358880i	0.0410764	−	0.0237155i	0.520398	+	0.853924i	$0.325784\pi$
$230$	2.85361	−	4.94260i	0.188162	−	0.325905i
$231$	−0.336759	+	0.123276i	−0.0221571	+	0.00811095i
$232$			5.56575i			0.365410i
$233$		−	15.7057i		−	1.02891i	−0.857517	−	0.514456i	$-0.827994\pi$
$233$		−	15.7057i		−	1.02891i	0.857517	−	0.514456i	$-0.172006\pi$
$234$	3.00287	+	16.6695i	0.196303	+	1.08972i
$235$	2.05539	−	3.56005i	0.134079	−	0.232232i
$236$	4.27376	−	2.46746i	0.278198	−	0.160618i
$237$	−3.24055	+	3.87647i	−0.210497	+	0.251804i
$238$	3.90828	+	2.25644i	0.253336	+	0.146264i
$239$	−2.90971	+	5.03976i	−0.188213	+	0.325995i	−0.944655	−	0.328067i	$-0.893603\pi$
$239$	−2.90971	+	5.03976i	−0.188213	+	0.325995i	0.756441	+	0.654062i	$0.226936\pi$
$240$	1.70629	+	0.297614i	0.110141	+	0.0192109i
$241$	5.77410	−	3.33368i	0.371942	−	0.214741i	−0.302364	−	0.953192i	$-0.597776\pi$
$241$	5.77410	−	3.33368i	0.371942	−	0.214741i	0.674307	+	0.738451i	$0.264443\pi$
$242$	9.49887	−	5.48417i	0.610610	−	0.352536i
$243$	−2.84868	−	15.3260i	−0.182743	−	0.983161i
$244$			0.00227491i			0.000145636i
$245$	4.88932	−	2.82285i	0.312367	−	0.180345i
$246$	0.854642	−	4.89986i	0.0544900	−	0.312404i
$247$			29.0979i			1.85146i
$248$	2.17043	+	5.12730i	0.137823	+	0.325584i
$249$	−4.73710	+	27.1589i	−0.300201	+	1.72113i
$250$	1.00000			0.0632456
$251$	4.15063	+	7.18911i	0.261986	+	0.453773i	0.966770	−	0.255650i	$-0.0822893\pi$
$251$	4.15063	+	7.18911i	0.261986	+	0.453773i	−0.704784	+	0.709422i	$0.748956\pi$
$252$	3.28507	+	1.18193i	0.206940	+	0.0744548i
$253$	0.507696	−	0.879355i	0.0319186	−	0.0552846i
$254$	−6.30073	−	10.9132i	−0.395343	−	0.684754i
$255$	−2.30892	−	6.30741i	−0.144590	−	0.394985i
$256$	1.00000			0.0625000
$257$	20.8110	+	12.0152i	1.29815	+	0.749490i	0.980085	−	0.198577i	$-0.0636321\pi$
$257$	20.8110	+	12.0152i	1.29815	+	0.749490i	0.318070	+	0.948067i	$0.396965\pi$
$258$	−1.12916	−	0.943927i	−0.0702984	−	0.0587663i
$259$	−0.910632	−	0.525754i	−0.0565839	−	0.0326688i
$260$	2.82297	+	4.88952i	0.175073	+	0.303235i
$261$	12.7511	−	10.7800i	0.789272	−	0.667266i
$262$	10.5849	+	18.3335i	0.653934	+	1.13265i
$263$	13.3178			0.821209			0.410605	−	0.911813i	$-0.365318\pi$
$263$	13.3178			0.821209			0.410605	+	0.911813i	$0.365318\pi$
$264$	0.303572	+	0.0529495i	0.0186836	+	0.00325882i
$265$	−10.8271	+	6.25104i	−0.665104	+	0.383998i
$266$	5.19414	+	2.99884i	0.318473	+	0.183870i
$267$	−8.47063	+	3.10080i	−0.518394	+	0.189766i
$268$	3.20296	−	5.54769i	0.195652	−	0.338879i
$269$	0.769900	−	1.33351i	0.0469416	−	0.0813052i	−0.841600	−	0.540101i	$-0.818386\pi$
$269$	0.769900	−	1.33351i	0.0469416	−	0.0813052i	0.888542	+	0.458796i	$0.151719\pi$
$270$	−2.62299	−	4.48552i	−0.159630	−	0.272980i
$271$		−	8.84626i		−	0.537372i	−0.963228	−	0.268686i	$-0.913411\pi$
$271$		−	8.84626i		−	0.537372i	0.963228	−	0.268686i	$-0.0865894\pi$
$272$	−1.93896	−	3.35837i	−0.117566	−	0.203631i
$273$	3.91205	+	10.6868i	0.236768	+	0.646792i
$274$	−11.1218	−	6.42120i	−0.671895	−	0.387919i
$275$	0.177914			0.0107286
$276$	−9.28278	+	3.39810i	−0.558758	+	0.204542i
$277$		−	14.9715i		−	0.899552i	−0.893141	−	0.449776i	$-0.851504\pi$
$277$		−	14.9715i		−	0.899552i	0.893141	−	0.449776i	$-0.148496\pi$
$278$	0.913499			0.0547880
$279$	7.54280	−	14.9032i	0.451575	−	0.892233i
$280$	1.16374			0.0695469
$281$			7.32299i			0.436853i	0.975853	+	0.218426i	$0.0700924\pi$
$281$			7.32299i			0.436853i	−0.975853	+	0.218426i	$0.929908\pi$
$282$	−6.68619	+	2.44758i	−0.398157	+	0.145751i
$283$	−14.6211			−0.869133			−0.434567	−	0.900640i	$-0.643098\pi$
$283$	−14.6211			−0.869133			−0.434567	+	0.900640i	$0.643098\pi$
$284$	−10.9712	−	6.33424i	−0.651022	−	0.375868i
$285$	−3.06858	−	8.38261i	−0.181767	−	0.496543i
$286$	0.502244	+	0.869912i	0.0296983	+	0.0514390i
$287$		−	3.34186i		−	0.197263i
$288$	−1.93685	−	2.29099i	−0.114130	−	0.134998i
$289$	0.980903	−	1.69897i	0.0577002	−	0.0999397i
$290$	2.78288	−	4.82008i	0.163416	−	0.283045i
$291$	−22.2957	+	8.16166i	−1.30700	+	0.478445i
$292$	−9.32062	−	5.38127i	−0.545448	−	0.314915i
$293$	29.5457	−	17.0582i	1.72608	−	0.996551i	0.821545	−	0.570143i	$-0.193112\pi$
$293$	29.5457	−	17.0582i	1.72608	−	0.996551i	0.904531	−	0.426408i	$-0.140221\pi$
$294$	−9.63321	−	1.68024i	−0.561820	−	0.0979936i
$295$	−4.93491			−0.287322
$296$	0.451779	+	0.782503i	0.0262591	+	0.0454821i
$297$	−0.466666	−	0.798035i	−0.0270787	−	0.0463067i
$298$	−2.29269	−	3.97105i	−0.132812	−	0.230037i
$299$	−27.9056	−	16.1113i	−1.61382	−	0.931740i
$300$	−1.32888	−	1.11089i	−0.0767231	−	0.0641370i
$301$	−0.856359	−	0.494419i	−0.0493597	−	0.0284979i
$302$	−18.0258			−1.03727
$303$	−1.39848	−	3.82029i	−0.0803404	−	0.219470i
$304$	−2.57689	−	4.46331i	−0.147795	−	0.255988i
$305$	0.00113745	−	0.00197013i	6.51304e−5	−	0.000112809i
$306$	−3.93853	+	10.9468i	−0.225151	+	0.625785i
$307$	8.94582	+	15.4946i	0.510565	+	0.884324i	0.999925	+	0.0122426i	$0.00389705\pi$
$307$	8.94582	+	15.4946i	0.510565	+	0.884324i	−0.489360	+	0.872082i	$0.662770\pi$
$308$	0.207046			0.0117975
$309$	−5.05546	+	28.9841i	−0.287595	+	1.64885i
$310$	0.684001	−	5.52559i	0.0388486	−	0.313832i
$311$			14.8875i			0.844194i	0.906551	+	0.422097i	$0.138706\pi$
$311$			14.8875i			0.844194i	−0.906551	+	0.422097i	$0.861294\pi$
$312$	1.68031	−	9.63360i	0.0951287	−	0.545395i
$313$	−6.65729	+	3.84359i	−0.376293	+	0.217253i	−0.676204	−	0.736714i	$-0.736376\pi$
$313$	−6.65729	+	3.84359i	−0.376293	+	0.217253i	0.299911	+	0.953967i	$0.403043\pi$
$314$			9.03549i			0.509902i
$315$	−2.25399	−	2.66612i	−0.126998	−	0.150219i
$316$	2.52627	−	1.45854i	0.142114	−	0.0820495i
$317$	4.78141	−	2.76055i	0.268551	−	0.155048i	−0.359678	−	0.933076i	$-0.617114\pi$
$317$	4.78141	−	2.76055i	0.268551	−	0.155048i	0.628229	+	0.778029i	$0.283780\pi$
$318$	21.3322	+	3.72079i	1.19625	+	0.208652i
$319$	0.495111	−	0.857558i	0.0277209	−	0.0480140i
$320$	−0.866025	−	0.500000i	−0.0484123	−	0.0279508i
$321$	−5.13601	+	6.14389i	−0.286664	+	0.342919i
$322$	−5.75191	+	3.32087i	−0.320542	+	0.185065i
$323$	−9.99295	+	17.3083i	−0.556023	+	0.963060i
$324$	−1.49726	+	8.87458i	−0.0831809	+	0.493032i
$325$		−	5.64593i		−	0.313180i
$326$		−	17.0876i		−	0.946392i
$327$	29.8140	−	10.9139i	1.64872	−	0.603537i
$328$	−1.43582	+	2.48692i	−0.0792800	+	0.137317i
$329$	−4.14298	+	2.39195i	−0.228410	+	0.131872i
$330$	−0.236426	−	0.197642i	−0.0130148	−	0.0108798i
$331$	−7.77002	−	4.48602i	−0.427079	−	0.246574i	0.271022	−	0.962573i	$-0.412638\pi$
$331$	−7.77002	−	4.48602i	−0.427079	−	0.246574i	−0.698101	+	0.715999i	$0.745972\pi$
$332$	7.95846	−	13.7845i	0.436777	−	0.756521i
$333$	0.917681	−	2.55061i	0.0502886	−	0.139772i
$334$	−7.69200	+	4.44098i	−0.420888	+	0.243000i
$335$	−5.54769	+	3.20296i	−0.303102	+	0.174996i
$336$	−1.54648	−	1.29279i	−0.0843673	−	0.0705272i
$337$		−	2.44574i		−	0.133228i	−0.997779	−	0.0666141i	$-0.978780\pi$
$337$		−	2.44574i		−	0.133228i	0.997779	−	0.0666141i	$-0.0212196\pi$
$338$	16.3476	−	9.43828i	0.889191	−	0.513375i
$339$	0.742401	+	0.129491i	0.0403217	+	0.00703297i
$340$			3.87791i			0.210309i
$341$	0.121693	−	0.983077i	0.00659005	−	0.0532366i
$342$	−5.23434	+	14.5484i	−0.283041	+	0.786685i
$343$	−14.7163			−0.794608
$344$	0.424853	+	0.735867i	0.0229065	+	0.0396753i
$345$	9.73818	+	1.69855i	0.524286	+	0.0914468i
$346$	−1.25981	+	2.18205i	−0.0677276	+	0.117308i
$347$	−8.43977	−	14.6181i	−0.453071	−	0.784741i	0.545504	−	0.838108i	$-0.316338\pi$
$347$	−8.43977	−	14.6181i	−0.453071	−	0.784741i	−0.998575	+	0.0533666i	$0.983005\pi$
$348$	−9.05268	+	3.31387i	−0.485275	+	0.177642i
$349$	32.6846			1.74957			0.874783	−	0.484515i	$-0.161004\pi$
$349$	32.6846			1.74957			0.874783	+	0.484515i	$0.161004\pi$
$350$	−1.00783	−	0.581871i	−0.0538708	−	0.0311023i
$351$	−25.3250	+	14.8092i	−1.35175	+	0.790458i
$352$	−0.154078	−	0.0889568i	−0.00821237	−	0.00474141i
$353$	5.87229	+	10.1711i	0.312551	+	0.541353i	0.978914	−	0.204274i	$-0.0654833\pi$
$353$	5.87229	+	10.1711i	0.312551	+	0.541353i	−0.666363	+	0.745627i	$0.732150\pi$
$354$	6.55792	+	5.48213i	0.348550	+	0.291372i
$355$	6.33424	+	10.9712i	0.336186	+	0.582292i
$356$	5.20790			0.276018
$357$	−1.34310	+	7.70030i	−0.0710843	+	0.407543i
$358$	12.5846	−	7.26572i	0.665116	−	0.384005i
$359$	−9.22320	−	5.32502i	−0.486782	−	0.281044i	0.236457	−	0.971642i	$-0.424014\pi$
$359$	−9.22320	−	5.32502i	−0.486782	−	0.281044i	−0.723238	+	0.690598i	$0.757347\pi$
$360$	0.531863	+	2.95248i	0.0280317	+	0.155609i
$361$	−3.78073	+	6.54841i	−0.198986	+	0.344653i
$362$	−1.88922	+	3.27223i	−0.0992953	+	0.171984i
$363$	14.5757	+	12.1846i	0.765024	+	0.639525i
$364$		−	6.57041i		−	0.344383i
$365$	5.38127	+	9.32062i	0.281668	+	0.487864i
$366$	−0.00370013	+	0.00135449i	−0.000193409	+	7.08002e-5i
$367$	25.0136	+	14.4416i	1.30570	+	0.753847i	0.981376	−	0.192099i	$-0.0615294\pi$
$367$	25.0136	+	14.4416i	1.30570	+	0.753847i	0.324326	+	0.945946i	$0.394863\pi$
$368$	5.70722			0.297510
$369$	8.47847	−	1.52732i	0.441371	−	0.0795093i
$370$		−	0.903557i		−	0.0469737i
$371$	14.5492			0.755356
$372$	−7.04726	+	6.58302i	−0.365383	+	0.341314i
$373$	−15.4070			−0.797744			−0.398872	−	0.917007i	$-0.630598\pi$
$373$	−15.4070			−0.797744			−0.398872	+	0.917007i	$0.630598\pi$
$374$			0.689933i			0.0356756i
$375$	0.595404	+	1.62650i	0.0307465	+	0.0839920i
$376$	4.11079			0.211998
$377$	−27.2139	−	15.7119i	−1.40159	−	0.809206i
$378$	0.0335334	+	6.04689i	0.00172477	+	0.311018i
$379$	−4.66494	−	8.07991i	−0.239622	−	0.415037i	0.720984	−	0.692952i	$-0.243690\pi$
$379$	−4.66494	−	8.07991i	−0.239622	−	0.415037i	−0.960606	+	0.277915i	$0.910357\pi$
$380$			5.15378i			0.264383i
$381$	13.9988	−	16.7459i	0.717180	−	0.857917i
$382$	3.22584	−	5.58732i	0.165048	−	0.285872i
$383$	−11.7909	+	20.4225i	−0.602488	+	1.04354i	0.389955	+	0.920834i	$0.372491\pi$
$383$	−11.7909	+	20.4225i	−0.602488	+	1.04354i	−0.992443	+	0.122706i	$0.960843\pi$
$384$	0.595404	+	1.62650i	0.0303841	+	0.0830019i
$385$	−0.179307	−	0.103523i	−0.00913831	−	0.00527601i
$386$	−1.82101	+	1.05136i	−0.0926870	+	0.0535129i
$387$	0.862988	−	2.39859i	0.0438681	−	0.121927i
$388$	13.7078			0.695907
$389$	17.1562	+	29.7153i	0.869852	+	1.50663i	0.862148	+	0.506657i	$0.169119\pi$
$389$	17.1562	+	29.7153i	0.869852	+	1.50663i	0.00770372	+	0.999970i	$0.497548\pi$
$390$	−6.27199	+	7.50279i	−0.317595	+	0.379918i
$391$	−11.0660	−	19.1670i	−0.559634	−	0.969315i
$392$	4.88932	+	2.82285i	0.246948	+	0.142576i
$393$	−23.5171	+	28.1321i	−1.18628	+	1.41908i
$394$	−16.3395	−	9.43359i	−0.823170	−	0.475257i
$395$	−2.91709			−0.146775
$396$	0.0946257	+	0.525286i	0.00475512	+	0.0263966i
$397$	−13.0551	−	22.6122i	−0.655218	−	1.13487i	−0.981839	−	0.189716i	$-0.939243\pi$
$397$	−13.0551	−	22.6122i	−0.655218	−	1.13487i	0.326621	−	0.945155i	$-0.394090\pi$
$398$	9.62408	−	16.6694i	0.482411	−	0.835561i
$399$	−1.78499	+	10.2338i	−0.0893613	+	0.512329i
$400$	0.500000	+	0.866025i	0.0250000	+	0.0433013i
$401$	1.81201			0.0904873			0.0452436	−	0.998976i	$-0.485594\pi$
$401$	1.81201			0.0904873			0.0452436	+	0.998976i	$0.485594\pi$
$402$	10.9304	+	1.90649i	0.545156	+	0.0950871i
$403$	−31.1971	−	3.86182i	−1.55404	−	0.192371i
$404$			2.34879i			0.116856i
$405$	5.73395	−	6.93699i	0.284922	−	0.344702i
$406$	−5.60933	+	3.23855i	−0.278387	+	0.160727i
$407$		−	0.160755i		−	0.00796833i
$408$	4.30792	−	5.15329i	0.213274	−	0.255126i
$409$	−21.5022	+	12.4143i	−1.06322	+	0.613849i	−0.926320	−	0.376737i	$-0.877046\pi$
$409$	−21.5022	+	12.4143i	−1.06322	+	0.613849i	−0.136897	+	0.990585i	$0.543713\pi$
$410$	2.48692	−	1.43582i	0.122820	−	0.0709102i
$411$	3.82208	−	21.9129i	0.188529	−	1.08088i
$412$	8.49332	−	14.7109i	0.418436	−	0.724752i
$413$	4.97356	+	2.87148i	0.244733	+	0.141296i
$414$	−11.0540	−	13.0752i	−0.543275	−	0.642610i
$415$	−13.7845	+	7.95846i	−0.676653	+	0.390666i
$416$	−2.82297	+	4.88952i	−0.138407	+	0.239729i
$417$	0.543901	+	1.48580i	0.0266349	+	0.0727601i
$418$			0.916927i			0.0448484i
$419$			16.9548i			0.828295i	0.910210	+	0.414148i	$0.135920\pi$
$419$			16.9548i			0.828295i	−0.910210	+	0.414148i	$0.864080\pi$
$420$	0.692897	+	1.89282i	0.0338099	+	0.0923604i
$421$	14.5265	−	25.1607i	0.707980	−	1.22626i	−0.257625	−	0.966245i	$-0.582940\pi$
$421$	14.5265	−	25.1607i	0.707980	−	1.22626i	0.965605	−	0.260013i	$-0.0837267\pi$
$422$	9.58746	−	5.53532i	0.466710	−	0.269455i
$423$	−7.96196	−	9.41777i	−0.387124	−	0.457908i
$424$	−10.8271	−	6.25104i	−0.525811	−	0.303577i
$425$	1.93896	−	3.35837i	0.0940532	−	0.162905i
$426$	3.77031	−	21.6161i	0.182672	−	1.04730i
$427$	−0.00229272	+	0.00132370i	−0.000110953	+	6.40585e-5i
$428$	4.00394	−	2.31167i	0.193538	−	0.111739i
$429$	−1.11587	+	1.33485i	−0.0538748	+	0.0644471i
$430$		−	0.849706i		−	0.0409765i
$431$	−18.8864	+	10.9041i	−0.909726	+	0.525231i	−0.880343	−	0.474337i	$-0.842688\pi$
$431$	−18.8864	+	10.9041i	−0.909726	+	0.525231i	−0.0293833	+	0.999568i	$0.509354\pi$
$432$	2.57308	−	4.51434i	0.123797	−	0.217196i
$433$		−	22.8178i		−	1.09655i	−0.836297	−	0.548277i	$-0.815284\pi$
$433$		−	22.8178i		−	1.09655i	0.836297	−	0.548277i	$-0.184716\pi$
$434$	−3.90454	+	5.17086i	−0.187424	+	0.248209i
$435$	9.49679	+	1.65645i	0.455336	+	0.0794205i
$436$	−18.3302			−0.877856
$437$	−14.7069	−	25.4731i	−0.703526	−	1.21854i
$438$	3.20308	−	18.3640i	0.153049	−	0.877466i
$439$	11.9238	−	20.6527i	0.569094	−	0.985699i	−0.427562	−	0.903986i	$-0.640628\pi$
$439$	11.9238	−	20.6527i	0.569094	−	0.985699i	0.996656	−	0.0817131i	$-0.0260391\pi$
$440$	0.0889568	+	0.154078i	0.00424085	+	0.00734536i
$441$	−3.00274	−	16.6688i	−0.142988	−	0.793753i
$442$	21.8944			1.04141
$443$	−18.1698	−	10.4904i	−0.863275	−	0.498412i	0.00183237	−	0.999998i	$-0.499417\pi$
$443$	−18.1698	−	10.4904i	−0.863275	−	0.498412i	−0.865108	+	0.501586i	$0.832750\pi$
$444$	−1.00375	+	1.20072i	−0.0476358	+	0.0569838i
$445$	−4.51017	−	2.60395i	−0.213803	−	0.123439i
$446$	2.19128	+	3.79542i	0.103760	+	0.179718i
$447$	5.09383	−	6.09343i	0.240930	−	0.288209i
$448$	0.581871	+	1.00783i	0.0274908	+	0.0476155i
$449$	−30.8958			−1.45806			−0.729032	−	0.684479i	$-0.760030\pi$
$449$	−30.8958			−1.45806			−0.729032	+	0.684479i	$0.760030\pi$
$450$	1.01563	−	2.82285i	0.0478773	−	0.133071i
$451$	0.442456	−	0.255452i	0.0208345	−	0.0120288i
$452$	−0.376805	−	0.217548i	−0.0177234	−	0.0102326i
$453$	−10.7326	−	29.3189i	−0.504262	−	1.37752i
$454$	−8.21783	+	14.2337i	−0.385682	+	0.668020i
$455$	−3.28521	+	5.69014i	−0.154013	+	0.266758i
$456$	5.72526	−	6.84878i	0.268110	−	0.320723i
$457$		−	10.1581i		−	0.475177i	−0.971366	−	0.237589i	$-0.923643\pi$
$457$		−	10.1581i		−	0.475177i	0.971366	−	0.237589i	$-0.0763570\pi$
$458$	−0.358880	−	0.621599i	−0.0167694	−	0.0290454i
$459$	−20.1499	+	0.111742i	−0.940517	+	0.00521569i
$460$	−4.94260	−	2.85361i	−0.230450	−	0.133050i
$461$	19.8197			0.923095			0.461547	−	0.887116i	$-0.347294\pi$
$461$	19.8197			0.923095			0.461547	+	0.887116i	$0.347294\pi$
$462$	0.123276	+	0.336759i	0.00573530	+	0.0156674i
$463$		−	10.9325i		−	0.508074i	−0.967194	−	0.254037i	$-0.918241\pi$
$463$		−	10.9325i		−	0.508074i	0.967194	−	0.254037i	$-0.0817586\pi$
$464$	5.56575			0.258384
$465$	9.39461	−	2.17743i	0.435665	−	0.100976i
$466$	−15.7057			−0.727551
$467$			11.3377i			0.524644i	0.964980	+	0.262322i	$0.0844883\pi$
$467$			11.3377i			0.524644i	−0.964980	+	0.262322i	$0.915512\pi$
$468$	16.6695	−	3.00287i	0.770547	−	0.138808i
$469$	7.45483			0.344232
$470$	−3.56005	−	2.05539i	−0.164213	−	0.0948083i
$471$	−14.6962	+	5.37977i	−0.677166	+	0.247887i
$472$	−2.46746	−	4.27376i	−0.113574	−	0.196716i
$473$		−	0.151174i		−	0.00695100i
$474$	3.87647	+	3.24055i	0.178052	+	0.148844i
$475$	2.57689	−	4.46331i	0.118236	−	0.204790i
$476$	2.25644	−	3.90828i	0.103424	−	0.179136i
$477$	6.64940	+	36.9121i	0.304455	+	1.69009i
$478$	5.03976	+	2.90971i	0.230513	+	0.133087i
$479$	−35.3823	+	20.4280i	−1.61666	+	0.933377i	−0.628880	+	0.777502i	$0.716486\pi$
$479$	−35.3823	+	20.4280i	−1.61666	+	0.933377i	−0.987777	+	0.155875i	$0.950180\pi$
$480$	0.297614	−	1.70629i	0.0135842	−	0.0778811i
$481$	−5.10142			−0.232605
$482$	−3.33368	−	5.77410i	−0.151845	−	0.263003i
$483$	−8.82609	−	7.37821i	−0.401601	−	0.335720i
$484$	−5.48417	−	9.49887i	−0.249281	−	0.431767i
$485$	−11.8713	−	6.85389i	−0.539047	−	0.311219i
$486$	−15.3260	+	2.84868i	−0.695200	+	0.129219i
$487$	−31.5249	−	18.2009i	−1.42853	−	0.824761i	−0.431524	−	0.902102i	$-0.642024\pi$
$487$	−31.5249	−	18.2009i	−1.42853	−	0.824761i	−0.997005	+	0.0773402i	$0.975357\pi$
$488$	0.00227491			0.000102980
$489$	27.7929	−	10.1740i	1.25684	−	0.460084i
$490$	−2.82285	−	4.88932i	−0.127523	−	0.220877i
$491$	−16.2180	+	28.0904i	−0.731908	+	1.26770i	0.224159	+	0.974553i	$0.428037\pi$
$491$	−16.2180	+	28.0904i	−0.731908	+	1.26770i	−0.956067	+	0.293149i	$0.905297\pi$
$492$	−4.89986	−	0.854642i	−0.220903	−	0.0385302i
$493$	−10.7917	−	18.6919i	−0.486036	−	0.841839i
$494$	29.0979			1.30918
$495$	0.180695	−	0.502224i	0.00812162	−	0.0225733i
$496$	5.12730	−	2.17043i	0.230223	−	0.0974553i
$497$		−	14.7428i		−	0.661307i
$498$	27.1589	+	4.73710i	1.21702	+	0.212274i
$499$	36.8738	−	21.2891i	1.65070	−	0.953030i	0.673911	−	0.738812i	$-0.264613\pi$
$499$	36.8738	−	21.2891i	1.65070	−	0.953030i	0.976786	−	0.214218i	$-0.0687203\pi$
$500$		−	1.00000i		−	0.0447214i
$501$	−11.8031	−	9.86685i	−0.527323	−	0.440818i
$502$	7.18911	−	4.15063i	0.320866	−	0.185252i
$503$	−32.1602	+	18.5677i	−1.43395	+	0.827893i	−0.997419	−	0.0717951i	$-0.977127\pi$
$503$	−32.1602	+	18.5677i	−1.43395	+	0.827893i	−0.436533	+	0.899688i	$0.643794\pi$
$504$	1.18193	−	3.28507i	0.0526475	−	0.146329i
$505$	1.17439	−	2.03411i	0.0522598	−	0.0905166i
$506$	−0.879355	−	0.507696i	−0.0390921	−	0.0225698i
$507$	25.0848	+	20.9697i	1.11405	+	0.931298i
$508$	−10.9132	+	6.30073i	−0.484194	+	0.279550i
$509$	7.91070	−	13.7017i	0.350636	−	0.607319i	−0.635725	−	0.771915i	$-0.719299\pi$
$509$	7.91070	−	13.7017i	0.350636	−	0.607319i	0.986361	+	0.164597i	$0.0526322\pi$
$510$	−6.30741	+	2.30892i	−0.279297	+	0.102241i
$511$		−	12.5248i		−	0.554065i
$512$		−	1.00000i		−	0.0441942i
$513$	−26.7794	+	0.148507i	−1.18234	+	0.00655673i
$514$	12.0152	−	20.8110i	0.529970	−	0.917934i
$515$	−14.7109	+	8.49332i	−0.648238	+	0.374261i
$516$	−0.943927	+	1.12916i	−0.0415540	+	0.0497085i
$517$	−0.633381	−	0.365682i	−0.0278560	−	0.0160827i
$518$	−0.525754	+	0.910632i	−0.0231003	+	0.0400109i
$519$	−4.29919	−	0.749872i	−0.188713	−	0.0329157i
$520$	4.88952	−	2.82297i	0.214420	−	0.123795i
$521$	23.6227	−	13.6385i	1.03493	−	0.597515i	0.116535	−	0.993187i	$-0.462821\pi$
$521$	23.6227	−	13.6385i	1.03493	−	0.597515i	0.918392	+	0.395671i	$0.129488\pi$
$522$	−10.7800	−	12.7511i	−0.471828	−	0.558099i
$523$			18.7630i			0.820447i	0.911985	+	0.410224i	$0.134549\pi$
$523$			18.7630i			0.820447i	−0.911985	+	0.410224i	$0.865451\pi$
$524$	18.3335	−	10.5849i	0.800903	−	0.462401i
$525$	0.346346	−	1.98568i	0.0151158	−	0.0866623i
$526$		−	13.3178i		−	0.580683i
$527$	−17.2307	−	13.0110i	−0.750582	−	0.566768i
$528$	0.0529495	−	0.303572i	0.00230433	−	0.0132113i
$529$	9.57238			0.416191
$530$	6.25104	+	10.8271i	0.271528	+	0.470300i
$531$	−5.01205	+	13.9305i	−0.217505	+	0.604533i
$532$	2.99884	−	5.19414i	0.130016	−	0.225194i
$533$	−8.10656	−	14.0410i	−0.351134	−	0.608182i
$534$	3.10080	+	8.47063i	0.134185	+	0.366560i
$535$	−4.62335			−0.199885
$536$	−5.54769	−	3.20296i	−0.239624	−	0.138347i
$537$	19.3106	+	16.1428i	0.833313	+	0.696612i
$538$	−1.33351	−	0.769900i	−0.0574915	−	0.0331927i
$539$	−0.502224	−	0.869877i	−0.0216323	−	0.0374682i
$540$	−4.48552	+	2.62299i	−0.193026	+	0.112876i
$541$	9.14009	+	15.8311i	0.392963	+	0.680632i	0.992839	−	0.119461i	$-0.0381167\pi$
$541$	9.14009	+	15.8311i	0.392963	+	0.680632i	−0.599876	+	0.800093i	$0.704783\pi$
$542$	−8.84626			−0.379979
$543$	−6.44712	−	1.12452i	−0.276672	−	0.0482576i
$544$	−3.35837	+	1.93896i	−0.143989	+	0.0831320i
$545$	15.8744	+	9.16508i	0.679984	+	0.392589i
$546$	10.6868	−	3.91205i	0.457351	−	0.167420i
$547$	4.88556	−	8.46204i	0.208891	−	0.361811i	−0.742474	−	0.669875i	$-0.766348\pi$
$547$	4.88556	−	8.46204i	0.208891	−	0.361811i	0.951366	+	0.308064i	$0.0996811\pi$
$548$	−6.42120	+	11.1218i	−0.274300	+	0.475102i
$549$	−0.00440614	−	0.00521179i	−0.000188050	−	0.000222434i
$550$		−	0.177914i		−	0.00758626i
$551$	−14.3423	−	24.8417i	−0.611004	−	1.05829i
$552$	3.39810	+	9.28278i	0.144633	+	0.395101i
$553$	2.93993	+	1.69737i	0.125019	+	0.0721795i
$554$	−14.9715			−0.636080
$555$	1.46963	−	0.537981i	0.0623825	−	0.0228360i
$556$		−	0.913499i		−	0.0387410i
$557$	23.4375			0.993081			0.496540	−	0.868014i	$-0.334603\pi$
$557$	23.4375			0.993081			0.496540	+	0.868014i	$0.334603\pi$
$558$	−14.9032	−	7.54280i	−0.630904	−	0.319312i
$559$	−4.79738			−0.202908
$560$		−	1.16374i		−	0.0491771i
$561$	−1.12217	+	0.410789i	−0.0473782	+	0.0173435i
$562$	7.32299			0.308902
$563$	−3.55872	−	2.05463i	−0.149982	−	0.0865923i	0.423131	−	0.906069i	$-0.360931\pi$
$563$	−3.55872	−	2.05463i	−0.149982	−	0.0865923i	−0.573113	+	0.819476i	$0.694264\pi$
$564$	2.44758	+	6.68619i	0.103062	+	0.281539i
$565$	0.217548	+	0.376805i	0.00915232	+	0.0158523i
$566$			14.6211i			0.614570i
$567$	−9.81528	+	3.65488i	−0.412203	+	0.153491i
$568$	−6.33424	+	10.9712i	−0.265779	+	0.460342i
$569$	20.3967	−	35.3280i	0.855072	−	1.48103i	−0.0215060	−	0.999769i	$-0.506846\pi$
$569$	20.3967	−	35.3280i	0.855072	−	1.48103i	0.876578	−	0.481260i	$-0.159821\pi$
$570$	−8.38261	+	3.06858i	−0.351109	+	0.128529i
$571$	−22.6637	−	13.0849i	−0.948445	−	0.547585i	−0.0558476	−	0.998439i	$-0.517786\pi$
$571$	−22.6637	−	13.0849i	−0.948445	−	0.547585i	−0.892598	+	0.450854i	$0.851119\pi$
$572$	0.869912	−	0.502244i	0.0363729	−	0.0209999i
$573$	11.0084	+	1.92011i	0.459884	+	0.0802137i
$574$	−3.34186			−0.139486
$575$	2.85361	+	4.94260i	0.119004	+	0.206121i
$576$	−2.29099	+	1.93685i	−0.0954579	+	0.0807019i
$577$	−10.2691	−	17.7866i	−0.427509	−	0.740467i	0.569142	−	0.822239i	$-0.307275\pi$
$577$	−10.2691	−	17.7866i	−0.427509	−	0.740467i	−0.996651	+	0.0817721i	$0.973942\pi$
$578$	−1.69897	−	0.980903i	−0.0706680	−	0.0408002i
$579$	−2.79427	−	2.33589i	−0.116126	−	0.0970761i
$580$	−4.82008	−	2.78288i	−0.200143	−	0.115553i
$581$	18.5232			0.768472
$582$	8.16166	+	22.2957i	0.338312	+	0.924185i
$583$	1.11214	+	1.92629i	0.0460603	+	0.0797788i
$584$	−5.38127	+	9.32062i	−0.222678	+	0.385690i
$585$	−15.9376	−	5.73419i	−0.658940	−	0.237079i
$586$	−17.0582	−	29.5457i	−0.704668	−	1.22052i
$587$	−37.7684			−1.55887			−0.779433	−	0.626485i	$-0.784493\pi$
$587$	−37.7684			−1.55887			−0.779433	+	0.626485i	$0.784493\pi$
$588$	−1.68024	+	9.63321i	−0.0692919	+	0.397267i
$589$	−22.8998	−	17.2917i	−0.943570	−	0.712494i
$590$			4.93491i			0.203167i
$591$	5.61513	−	32.1929i	0.230976	−	1.32424i
$592$	0.782503	−	0.451779i	0.0321607	−	0.0185680i
$593$		−	37.0997i		−	1.52350i	−0.647870	−	0.761751i	$-0.724340\pi$
$593$		−	37.0997i		−	1.52350i	0.647870	−	0.761751i	$-0.275660\pi$
$594$	−0.798035	+	0.466666i	−0.0327438	+	0.0191475i
$595$	−3.90828	+	2.25644i	−0.160224	+	0.0925052i
$596$	−3.97105	+	2.29269i	−0.162661	+	0.0939121i
$597$	32.8429	+	5.72852i	1.34417	+	0.234453i
$598$	−16.1113	+	27.9056i	−0.658840	+	1.14114i
$599$	17.6250	+	10.1758i	0.720139	+	0.415773i	0.814804	−	0.579737i	$-0.196845\pi$
$599$	17.6250	+	10.1758i	0.720139	+	0.415773i	−0.0946646	+	0.995509i	$0.530178\pi$
$600$	−1.11089	+	1.32888i	−0.0453517	+	0.0542514i
$601$	−35.9489	+	20.7551i	−1.46639	+	0.846619i	−0.999293	−	0.0375894i	$-0.988032\pi$
$601$	−35.9489	+	20.7551i	−1.46639	+	0.846619i	−0.467093	+	0.884208i	$0.654699\pi$
$602$	−0.494419	+	0.856359i	−0.0201510	+	0.0349026i
$603$	3.40707	+	18.9133i	0.138747	+	0.770210i
$604$			18.0258i			0.733458i
$605$			10.9683i			0.445927i
$606$	−3.82029	+	1.39848i	−0.155189	+	0.0568092i
$607$	−9.76384	+	16.9115i	−0.396302	+	0.686415i	−0.993266	−	0.115852i	$-0.963040\pi$
$607$	−9.76384	+	16.9115i	−0.396302	+	0.686415i	0.596964	+	0.802268i	$0.296373\pi$
$608$	−4.46331	+	2.57689i	−0.181011	+	0.104507i
$609$	−8.60731	−	7.19532i	−0.348786	−	0.291569i
$610$	−0.00197013	−	0.00113745i	−7.97681e−5	−	4.60541e-5i
$611$	−11.6046	+	20.0998i	−0.469473	+	0.813150i
$612$	10.9468	+	3.93853i	0.442497	+	0.159206i
$613$	−3.94704	+	2.27883i	−0.159420	+	0.0920409i	−0.577587	−	0.816329i	$-0.696006\pi$
$613$	−3.94704	+	2.27883i	−0.159420	+	0.0920409i	0.418168	+	0.908370i	$0.362672\pi$
$614$	15.4946	−	8.94582i	0.625312	−	0.361024i
$615$	3.81608	+	3.19007i	0.153879	+	0.128636i
$616$		−	0.207046i		−	0.00834210i
$617$	−17.5553	+	10.1355i	−0.706749	+	0.408042i	−0.809856	−	0.586628i	$-0.800455\pi$
$617$	−17.5553	+	10.1355i	−0.706749	+	0.408042i	0.103107	+	0.994670i	$0.467122\pi$
$618$	28.9841	+	5.05546i	1.16591	+	0.203361i
$619$			13.7227i			0.551561i	0.961221	+	0.275781i	$0.0889363\pi$
$619$			13.7227i			0.551561i	−0.961221	+	0.275781i	$0.911064\pi$
$620$	−5.52559	−	0.684001i	−0.221913	−	0.0274701i
$621$	14.6851	−	25.7643i	0.589295	−	1.03389i
$622$	14.8875			0.596935
$623$	3.03032	+	5.24868i	0.121407	+	0.210284i
$624$	−9.63360	−	1.68031i	−0.385653	−	0.0672662i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	3.84359	+	6.65729i	0.153621	+	0.266079i
$627$	−1.49138	+	0.545942i	−0.0595600	+	0.0218028i
$628$	9.03549			0.360555
$629$	−3.03448	−	1.75196i	−0.120993	−	0.0698551i
$630$	−2.66612	+	2.25399i	−0.106221	+	0.0898011i
$631$	9.02379	+	5.20989i	0.359231	+	0.207402i	0.668743	−	0.743493i	$-0.266832\pi$
$631$	9.02379	+	5.20989i	0.359231	+	0.207402i	−0.309512	+	0.950895i	$0.600166\pi$
$632$	−1.45854	−	2.52627i	−0.0580178	−	0.100490i
$633$	14.7116	+	12.2982i	0.584734	+	0.488811i
$634$	−2.76055	−	4.78141i	−0.109635	−	0.189894i
$635$	12.6015			0.500074
$636$	3.72079	−	21.3322i	0.147539	−	0.845875i
$637$	−27.6048	+	15.9376i	−1.09374	+	0.631472i
$638$	−0.857558	−	0.495111i	−0.0339510	−	0.0196016i
$639$	37.4034	−	6.73790i	1.47966	−	0.266547i
$640$	−0.500000	+	0.866025i	−0.0197642	+	0.0342327i
$641$	−10.4121	+	18.0343i	−0.411254	+	0.712313i	−0.995027	−	0.0996039i	$-0.968242\pi$
$641$	−10.4121	+	18.0343i	−0.411254	+	0.712313i	0.583773	+	0.811917i	$0.301576\pi$
$642$	6.14389	+	5.13601i	0.242480	+	0.202702i
$643$		−	45.6261i		−	1.79932i	−0.436595	−	0.899658i	$-0.643816\pi$
$643$		−	45.6261i		−	1.79932i	0.436595	−	0.899658i	$-0.356184\pi$
$644$	3.32087	+	5.75191i	0.130861	+	0.226657i
$645$	1.38204	−	0.505918i	0.0544179	−	0.0199205i
$646$	17.3083	+	9.99295i	0.680986	+	0.393167i
$647$	29.3824			1.15514			0.577570	−	0.816341i	$-0.304001\pi$
$647$	29.3824			1.15514			0.577570	+	0.816341i	$0.304001\pi$
$648$	8.87458	+	1.49726i	0.348627	+	0.0588178i
$649$			0.877988i			0.0344640i
$650$	−5.64593			−0.221452
$651$	−10.7352	−	3.27197i	−0.420744	−	0.128239i
$652$	−17.0876			−0.669201
$653$			36.5284i			1.42947i	0.699397	+	0.714734i	$0.253452\pi$
$653$			36.5284i			1.42947i	−0.699397	+	0.714734i	$0.746548\pi$
$654$	−10.9139	−	29.8140i	−0.426765	−	1.16582i
$655$	−21.1697			−0.827169
$656$	2.48692	+	1.43582i	0.0970978	+	0.0560595i
$657$	31.7761	−	5.72420i	1.23970	−	0.223322i
$658$	2.39195	+	4.14298i	0.0932479	+	0.161510i
$659$		−	18.6641i		−	0.727050i	−0.931584	−	0.363525i	$-0.881573\pi$
$659$		−	18.6641i		−	0.727050i	0.931584	−	0.363525i	$-0.118427\pi$
$660$	−0.197642	+	0.236426i	−0.00769319	+	0.00920289i
$661$	−16.6494	+	28.8377i	−0.647588	+	1.12166i	0.336109	+	0.941823i	$0.390889\pi$
$661$	−16.6494	+	28.8377i	−0.647588	+	1.12166i	−0.983697	+	0.179833i	$0.942444\pi$
$662$	−4.48602	+	7.77002i	−0.174354	+	0.301990i
$663$	13.0360	+	35.6112i	0.506277	+	1.38303i
$664$	−13.7845	−	7.95846i	−0.534941	−	0.308848i
$665$	−5.19414	+	2.99884i	−0.201420	+	0.116290i
$666$	−2.55061	−	0.917681i	−0.0988340	−	0.0355594i
$667$	31.7650			1.22995
$668$	4.44098	+	7.69200i	0.171827	+	0.297613i
$669$	−4.86854	+	5.82392i	−0.188228	+	0.225166i
$670$	3.20296	+	5.54769i	0.123741	+	0.214326i
$671$	−0.000350512	0	0.000202368i	−1.35314e−5	0	7.81234e-6i
$672$	−1.29279	+	1.54648i	−0.0498703	+	0.0596567i
$673$	28.5063	+	16.4581i	1.09884	+	0.634414i	0.935915	−	0.352225i	$-0.114575\pi$
$673$	28.5063	+	16.4581i	1.09884	+	0.634414i	0.162922	+	0.986639i	$0.447908\pi$
$674$	−2.44574			−0.0942066
$675$	5.19607	−	0.0288151i	0.199997	−	0.00110909i
$676$	−9.43828	−	16.3476i	−0.363011	−	0.628753i
$677$	−3.71782	+	6.43945i	−0.142887	+	0.247488i	−0.928583	−	0.371125i	$-0.878972\pi$
$677$	−3.71782	+	6.43945i	−0.142887	+	0.247488i	0.785695	+	0.618614i	$0.212305\pi$
$678$	0.129491	−	0.742401i	0.00497306	−	0.0285117i
$679$	7.97616	+	13.8151i	0.306097	+	0.530175i
$680$	3.87791			0.148711
$681$	−28.0440	−	4.89148i	−1.07465	−	0.187442i
$682$	−0.983077	−	0.121693i	−0.0376440	−	0.00465987i
$683$			27.8306i			1.06491i	0.846459	+	0.532453i	$0.178730\pi$
$683$			27.8306i			1.06491i	−0.846459	+	0.532453i	$0.821270\pi$
$684$	14.5484	+	5.23434i	0.556270	+	0.200140i
$685$	11.1218	−	6.42120i	0.424944	−	0.245341i
$686$			14.7163i			0.561872i
$687$	0.797350	−	0.953820i	0.0304208	−	0.0363905i
$688$	0.735867	−	0.424853i	0.0280547	−	0.0161974i
$689$	61.1292	−	35.2929i	2.32884	−	1.34455i
$690$	1.69855	−	9.73818i	0.0646626	−	0.370726i
$691$	−17.9160	+	31.0315i	−0.681558	+	1.18049i	0.292947	+	0.956129i	$0.405364\pi$
$691$	−17.9160	+	31.0315i	−0.681558	+	1.18049i	−0.974505	+	0.224365i	$0.927969\pi$
$692$	2.18205	+	1.25981i	0.0829490	+	0.0478906i
$693$	−0.474339	+	0.401015i	−0.0180186	+	0.0152333i
$694$	−14.6181	+	8.43977i	−0.554896	+	0.320369i
$695$	−0.456749	+	0.791113i	−0.0173255	+	0.0300086i
$696$	3.31387	+	9.05268i	0.125612	+	0.343141i
$697$		−	11.1360i		−	0.421806i
$698$		−	32.6846i		−	1.23713i
$699$	−9.35121	−	25.5452i	−0.353695	−	0.966209i
$700$	−0.581871	+	1.00783i	−0.0219927	+	0.0380924i
$701$	−6.49145	+	3.74784i	−0.245179	+	0.141554i	−0.617555	−	0.786528i	$-0.711877\pi$
$701$	−6.49145	+	3.74784i	−0.245179	+	0.141554i	0.372376	+	0.928082i	$0.378543\pi$
$702$	14.8092	+	25.3250i	0.558938	+	0.955829i
$703$	−4.03285	−	2.32837i	−0.152102	−	0.0878160i
$704$	−0.0889568	+	0.154078i	−0.00335268	+	0.00580702i
$705$	1.22343	−	7.01420i	0.0460769	−	0.264170i
$706$	10.1711	−	5.87229i	0.382795	−	0.221007i
$707$	−2.36718	+	1.36669i	−0.0890269	+	0.0513997i
$708$	5.48213	−	6.55792i	0.206031	−	0.246462i
$709$		−	1.59160i		−	0.0597738i	−0.999553	−	0.0298869i	$-0.990485\pi$
$709$		−	1.59160i		−	0.0597738i	0.999553	−	0.0298869i	$-0.00951471\pi$
$710$	10.9712	−	6.33424i	0.411743	−	0.237720i
$711$	−2.96269	+	8.23451i	−0.111109	+	0.308818i
$712$		−	5.20790i		−	0.195174i
$713$	29.2626	−	12.3871i	1.09589	−	0.463902i
$714$	7.70030	+	1.34310i	0.288176	+	0.0502642i
$715$	−1.00449			−0.0375657
$716$	−7.26572	−	12.5846i	−0.271533	−	0.470308i
$717$	−1.73194	+	9.92961i	−0.0646804	+	0.370828i
$718$	−5.32502	+	9.22320i	−0.198728	+	0.344207i
$719$	−1.12193	−	1.94324i	−0.0418410	−	0.0724707i	0.844347	−	0.535797i	$-0.179989\pi$
$719$	−1.12193	−	1.94324i	−0.0418410	−	0.0724707i	−0.886188	+	0.463327i	$0.846656\pi$
$720$	2.95248	−	0.531863i	0.110032	−	0.0198214i
$721$	19.7681			0.736202
$722$	6.54841	+	3.78073i	0.243707	+	0.140704i
$723$	7.40667	−	8.86013i	0.275457	−	0.329512i
$724$	3.27223	+	1.88922i	0.121611	+	0.0702124i
$725$	2.78288	+	4.82008i	0.103353	+	0.179013i
$726$	12.1846	−	14.5757i	0.452212	−	0.540953i
$727$	16.3097	+	28.2493i	0.604894	+	1.04771i	0.992068	+	0.125701i	$0.0401180\pi$
$727$	16.3097	+	28.2493i	0.604894	+	1.04771i	−0.387174	+	0.922007i	$0.626549\pi$
$728$	−6.57041			−0.243516
$729$	−13.7585	−	23.2315i	−0.509574	−	0.860427i
$730$	9.32062	−	5.38127i	0.344972	−	0.199170i
$731$	−2.85363	−	1.64754i	−0.105545	−	0.0609365i
$732$	0.00135449	+	0.00370013i	5.00633e−5	+	0.000136761i
$733$	−4.82676	+	8.36019i	−0.178280	+	0.308791i	−0.941292	−	0.337594i	$-0.890387\pi$
$733$	−4.82676	+	8.36019i	−0.178280	+	0.308791i	0.763011	+	0.646385i	$0.223720\pi$
$734$	14.4416	−	25.0136i	0.533050	−	0.923270i
$735$	6.27173	−	7.50248i	0.231336	−	0.276733i
$736$		−	5.70722i		−	0.210371i
$737$	0.569850	+	0.987008i	0.0209907	+	0.0363569i
$738$	−1.52732	−	8.47847i	−0.0562215	−	0.312097i
$739$	20.5340	+	11.8553i	0.755355	+	0.436105i	0.827626	−	0.561281i	$-0.189691\pi$
$739$	20.5340	+	11.8553i	0.755355	+	0.436105i	−0.0722704	+	0.997385i	$0.523024\pi$
$740$	−0.903557			−0.0332154
$741$	17.3250	+	47.3277i	0.636450	+	1.73863i
$742$		−	14.5492i		−	0.534118i
$743$	33.9392			1.24511			0.622555	−	0.782576i	$-0.286095\pi$
$743$	33.9392			1.24511			0.622555	+	0.782576i	$0.286095\pi$
$744$	6.58302	+	7.04726i	0.241345	+	0.258365i
$745$	4.58537			0.167995
$746$			15.4070i			0.564090i
$747$	8.46563	+	46.9944i	0.309741	+	1.71943i
$748$	0.689933			0.0252264
$749$	4.65955	+	2.69019i	0.170256	+	0.0982975i
$750$	1.62650	−	0.595404i	0.0593913	−	0.0217411i
$751$	−3.61672	−	6.26434i	−0.131976	−	0.228589i	0.792462	−	0.609921i	$-0.208799\pi$
$751$	−3.61672	−	6.26434i	−0.131976	−	0.228589i	−0.924438	+	0.381332i	$0.875466\pi$
$752$		−	4.11079i		−	0.149905i
$753$	11.0314	+	9.22176i	0.402007	+	0.336060i
$754$	−15.7119	+	27.2139i	−0.572195	+	0.991071i
$755$	9.01289	−	15.6108i	0.328013	−	0.568134i
$756$	6.04689	−	0.0335334i	0.219923	−	0.00121960i
$757$	−0.672009	−	0.387984i	−0.0244246	−	0.0141015i	0.487738	−	0.872990i	$-0.337822\pi$
$757$	−0.672009	−	0.387984i	−0.0244246	−	0.0141015i	−0.512163	+	0.858889i	$0.671155\pi$
$758$	−8.07991	+	4.66494i	−0.293475	+	0.169438i
$759$	0.302195	−	1.73255i	0.0109690	−	0.0628877i
$760$	5.15378			0.186947
$761$	3.20580	+	5.55261i	0.116210	+	0.201282i	0.918263	−	0.395971i	$-0.129592\pi$
$761$	3.20580	+	5.55261i	0.116210	+	0.201282i	−0.802053	+	0.597253i	$0.796259\pi$
$762$	−16.7459	−	13.9988i	−0.606639	−	0.507122i
$763$	−10.6658	−	18.4737i	−0.386128	−	0.668793i
$764$	−5.58732	−	3.22584i	−0.202142	−	0.116707i
$765$	−7.51092	−	8.88425i	−0.271558	−	0.321211i
$766$	20.4225	+	11.7909i	0.737895	+	0.426024i
$767$	27.8622			1.00605
$768$	1.62650	−	0.595404i	0.0586912	−	0.0214848i
$769$	9.17949	+	15.8993i	0.331021	+	0.573345i	0.982712	−	0.185139i	$-0.0592736\pi$
$769$	9.17949	+	15.8993i	0.331021	+	0.573345i	−0.651691	+	0.758484i	$0.725940\pi$
$770$	−0.103523	+	0.179307i	−0.00373070	+	0.00646176i
$771$	41.0030	+	7.15180i	1.47669	+	0.257566i
$772$	1.05136	+	1.82101i	0.0378393	+	0.0655396i
$773$	−11.5363			−0.414930			−0.207465	−	0.978242i	$-0.566521\pi$
$773$	−11.5363			−0.414930			−0.207465	+	0.978242i	$0.566521\pi$
$774$	−2.39859	−	0.862988i	−0.0862157	−	0.0310195i
$775$	4.44330	+	3.35516i	0.159608	+	0.120521i
$776$		−	13.7078i		−	0.492081i
$777$	−1.79418	−	0.312943i	−0.0643657	−	0.0112268i
$778$	29.7153	−	17.1562i	1.06535	−	0.615078i
$779$		−	14.7998i		−	0.530259i
$780$	7.50279	+	6.27199i	0.268643	+	0.224573i
$781$	1.95193	−	1.12695i	0.0698455	−	0.0403253i
$782$	−19.1670	+	11.0660i	−0.685409	+	0.395721i
$783$	14.3211	−	25.1257i	0.511796	−	0.897919i
$784$	2.82285	−	4.88932i	0.100816	−	0.174619i
$785$	−7.82497	−	4.51775i	−0.279285	−	0.161245i
$786$	28.1321	+	23.5171i	1.00344	+	0.838828i
$787$	−15.4169	+	8.90097i	−0.549554	+	0.317285i	−0.748942	−	0.662635i	$-0.769438\pi$
$787$	−15.4169	+	8.90097i	−0.549554	+	0.317285i	0.199388	+	0.979921i	$0.436105\pi$
$788$	−9.43359	+	16.3395i	−0.336058	+	0.582069i
$789$	21.6613	−	7.92946i	0.771164	−	0.282296i
$790$			2.91709i			0.103785i
$791$		−	0.506340i		−	0.0180034i
$792$	0.525286	−	0.0946257i	0.0186652	−	0.00336238i
$793$	−0.00642199	+	0.0111232i	−0.000228051	+	0.000394997i
$794$	−22.6122	+	13.0551i	−0.802475	+	0.463309i
$795$	−13.8884	+	16.6138i	−0.492570	+	0.589231i
$796$	−16.6694	−	9.62408i	−0.590831	−	0.341116i
$797$	−18.5843	+	32.1890i	−0.658291	+	1.14019i	0.322767	+	0.946479i	$0.395387\pi$
$797$	−18.5843	+	32.1890i	−0.658291	+	1.14019i	−0.981058	+	0.193715i	$0.937946\pi$
$798$	10.2338	+	1.78499i	0.362272	+	0.0631880i
$799$	−13.8055	+	7.97063i	−0.488405	+	0.281981i
$800$	0.866025	−	0.500000i	0.0306186	−	0.0176777i
$801$	−11.9312	+	10.0869i	−0.421569	+	0.356403i
$802$		−	1.81201i		−	0.0639842i
$803$	1.65827	−	0.957400i	0.0585189	−	0.0337859i
$804$	1.90649	−	10.9304i	0.0672367	−	0.385484i
$805$		−	6.64174i		−	0.234090i
$806$	−3.86182	+	31.1971i	−0.136027	+	1.09887i
$807$	0.458266	−	2.62734i	0.0161317	−	0.0924869i
$808$	2.34879			0.0826300
$809$	−6.71526	−	11.6312i	−0.236096	−	0.408930i	0.723495	−	0.690330i	$-0.242535\pi$
$809$	−6.71526	−	11.6312i	−0.236096	−	0.408930i	−0.959591	+	0.281400i	$0.909201\pi$
$810$	−6.93699	−	5.73395i	−0.243741	−	0.201471i
$811$	−4.22401	+	7.31619i	−0.148325	+	0.256906i	−0.930608	−	0.366016i	$-0.880721\pi$
$811$	−4.22401	+	7.31619i	−0.148325	+	0.256906i	0.782284	+	0.622922i	$0.214055\pi$
$812$	3.23855	+	5.60933i	0.113651	+	0.196849i
$813$	−5.26710	−	14.3884i	−0.184725	−	0.504624i
$814$	−0.160755			−0.00563446
$815$	14.7983	+	8.54378i	0.518360	+	0.299276i
$816$	−5.15329	−	4.30792i	−0.180401	−	0.150807i
$817$	−3.79250	−	2.18960i	−0.132683	−	0.0766044i
$818$	12.4143	+	21.5022i	0.434056	+	0.751808i
$819$	12.7259	+	15.0527i	0.444678	+	0.525985i
$820$	−1.43582	−	2.48692i	−0.0501411	−	0.0868469i
$821$	21.5718			0.752861			0.376431	−	0.926445i	$-0.377151\pi$
$821$	21.5718			0.752861			0.376431	+	0.926445i	$0.377151\pi$
$822$	−21.9129	−	3.82208i	−0.764299	−	0.133310i
$823$	−23.2067	+	13.3984i	−0.808934	+	0.467038i	−0.846586	−	0.532253i	$-0.821346\pi$
$823$	−23.2067	+	13.3984i	−0.808934	+	0.467038i	0.0376515	+	0.999291i	$0.488012\pi$
$824$	−14.7109	−	8.49332i	−0.512477	−	0.295879i
$825$	0.289376	−	0.105930i	0.0100748	−	0.00368802i
$826$	2.87148	−	4.97356i	0.0999117	−	0.173052i
$827$	−8.45553	+	14.6454i	−0.294028	+	0.509271i	−0.974758	−	0.223263i	$-0.928329\pi$
$827$	−8.45553	+	14.6454i	−0.294028	+	0.509271i	0.680731	+	0.732534i	$0.261662\pi$
$828$	−13.0752	+	11.0540i	−0.454394	+	0.384153i
$829$			6.47384i			0.224846i	0.993660	+	0.112423i	$0.0358611\pi$
$829$			6.47384i			0.224846i	−0.993660	+	0.112423i	$0.964139\pi$
$830$	7.95846	+	13.7845i	0.276242	+	0.478466i
$831$	−8.91411	−	24.3512i	−0.309227	−	0.844732i
$832$	4.88952	+	2.82297i	0.169514	+	0.0978688i
$833$	−21.8935			−0.758566
$834$	1.48580	−	0.543901i	0.0514492	−	0.0188337i
$835$		−	8.88196i		−	0.307373i
$836$	0.916927			0.0317126
$837$	3.39490	−	28.7311i	0.117345	−	0.993091i
$838$	16.9548			0.585693
$839$		−	43.6645i		−	1.50747i	−0.657180	−	0.753734i	$-0.728251\pi$
$839$		−	43.6645i		−	1.50747i	0.657180	−	0.753734i	$-0.271749\pi$
$840$	1.89282	−	0.692897i	0.0653086	−	0.0239072i
$841$	1.97760			0.0681931
$842$	−25.1607	−	14.5265i	−0.867095	−	0.500618i
$843$	4.36013	+	11.9108i	0.150171	+	0.410230i
$844$	−5.53532	−	9.58746i	−0.190534	−	0.330014i
$845$			18.8766i			0.649374i
$846$	−9.41777	+	7.96196i	−0.323790	+	0.273738i
$847$	6.38216	−	11.0542i	0.219294	−	0.379828i
$848$	−6.25104	+	10.8271i	−0.214661	+	0.371805i
$849$	−23.7812	+	8.70545i	−0.816167	+	0.298770i
$850$	−3.35837	−	1.93896i	−0.115191	−	0.0665056i
$851$	4.46592	−	2.57840i	0.153090	−	0.0883864i
$852$	−21.6161	−	3.77031i	−0.740555	−	0.129169i
$853$	34.3980			1.17776			0.588882	−	0.808219i	$-0.299568\pi$
$853$	34.3980			1.17776			0.588882	+	0.808219i	$0.299568\pi$
$854$	0.00132370	+	0.00229272i	4.52962e−5	+	7.84553e-5i
$855$	−9.98208	−	11.8073i	−0.341380	−	0.403800i
$856$	−2.31167	−	4.00394i	−0.0790114	−	0.136852i
$857$	−14.9622	−	8.63842i	−0.511098	−	0.295083i	0.222187	−	0.975004i	$-0.428681\pi$
$857$	−14.9622	−	8.63842i	−0.511098	−	0.295083i	−0.733285	+	0.679921i	$0.762014\pi$
$858$	1.33485	+	1.11587i	0.0455710	+	0.0380952i
$859$	4.18085	+	2.41382i	0.142649	+	0.0823583i	0.569626	−	0.821904i	$-0.307088\pi$
$859$	4.18085	+	2.41382i	0.142649	+	0.0823583i	−0.426977	+	0.904262i	$0.640421\pi$
$860$	−0.849706			−0.0289747
$861$	−1.98975	−	5.43552i	−0.0678106	−	0.185242i
$862$	10.9041	+	18.8864i	0.371394	+	0.643274i
$863$	8.63393	−	14.9544i	0.293902	−	0.509054i	−0.680827	−	0.732445i	$-0.738379\pi$
$863$	8.63393	−	14.9544i	0.293902	−	0.509054i	0.974729	+	0.223391i	$0.0717126\pi$
$864$	−4.51434	−	2.57308i	−0.153581	−	0.0875380i
$865$	−1.25981	−	2.18205i	−0.0428347	−	0.0741919i
$866$	−22.8178			−0.775380
$867$	0.583861	−	3.34741i	0.0198290	−	0.113684i
$868$	5.17086	+	3.90454i	0.175510	+	0.132529i
$869$			0.518990i			0.0176055i
$870$	1.65645	−	9.49679i	0.0561588	−	0.321971i
$871$	31.3219	−	18.0837i	1.06130	−	0.612742i
$872$			18.3302i			0.620738i
$873$	−31.4044	+	26.5499i	−1.06288	+	0.898576i
$874$	−25.4731	+	14.7069i	−0.861640	+	0.497468i
$875$	1.00783	−	0.581871i	0.0340709	−	0.0196708i
$876$	−18.3640	−	3.20308i	−0.620462	−	0.108222i
$877$	−21.8659	+	37.8729i	−0.738359	+	1.27888i	0.214874	+	0.976642i	$0.431066\pi$
$877$	−21.8659	+	37.8729i	−0.738359	+	1.27888i	−0.953234	+	0.302234i	$0.902268\pi$
$878$	−20.6527	−	11.9238i	−0.696994	−	0.402410i
$879$	37.8994	−	45.3367i	1.27832	−	1.52917i
$880$	0.154078	−	0.0889568i	0.00519396	−	0.00299873i
$881$	18.1740	−	31.4783i	0.612298	−	1.06053i	−0.378555	−	0.925579i	$-0.623579\pi$
$881$	18.1740	−	31.4783i	0.612298	−	1.06053i	0.990852	−	0.134951i	$-0.0430879\pi$
$882$	−16.6688	+	3.00274i	−0.561268	+	0.101108i
$883$		−	51.2633i		−	1.72515i	−0.505931	−	0.862574i	$-0.668851\pi$
$883$		−	51.2633i		−	1.72515i	0.505931	−	0.862574i	$-0.331149\pi$
$884$		−	21.8944i		−	0.736389i
$885$	−8.02662	+	2.93827i	−0.269812	+	0.0987687i
$886$	−10.4904	+	18.1698i	−0.352431	+	0.610428i
$887$	−15.9684	+	9.21935i	−0.536166	+	0.309556i	−0.743524	−	0.668710i	$-0.766847\pi$
$887$	−15.9684	+	9.21935i	−0.536166	+	0.309556i	0.207358	+	0.978265i	$0.433514\pi$
$888$	1.20072	+	1.00375i	0.0402936	+	0.0336836i
$889$	−12.7001	−	7.33242i	−0.425949	−	0.245922i
$890$	−2.60395	+	4.51017i	−0.0872846	+	0.151181i
$891$	−1.23418	−	1.02015i	−0.0413467	−	0.0341762i
$892$	3.79542	−	2.19128i	0.127080	−	0.0733696i
$893$	−18.3477	+	10.5930i	−0.613982	+	0.354483i
$894$	−6.09343	−	5.09383i	−0.203795	−	0.170363i
$895$			14.5314i			0.485732i
$896$	1.00783	−	0.581871i	0.0336693	−	0.0194390i
$897$	−54.9811	−	9.58989i	−1.83577	−	0.320197i
$898$			30.8958i			1.03101i
$899$	28.5373	−	12.0801i	0.951772	−	0.402894i
$900$	−2.82285	−	1.01563i	−0.0940951	−	0.0338544i
$901$	48.4819			1.61517
$902$	−0.255452	−	0.442456i	−0.00850563	−	0.0147322i
$903$	−1.68725	−	0.294292i	−0.0561480	−	0.00979343i
$904$	−0.217548	+	0.376805i	−0.00723555	+	0.0125323i
$905$	−1.88922	−	3.27223i	−0.0627998	−	0.108773i
$906$	−29.3189	+	10.7326i	−0.974054	+	0.356567i
$907$	−4.08947			−0.135789			−0.0678943	−	0.997693i	$-0.521628\pi$
$907$	−4.08947			−0.135789			−0.0678943	+	0.997693i	$0.521628\pi$
$908$	14.2337	+	8.21783i	0.472362	+	0.272718i
$909$	−4.54924	−	5.38104i	−0.150889	−	0.178478i
$910$	5.69014	+	3.28521i	0.188626	+	0.108904i
$911$	27.6813	+	47.9455i	0.917124	+	1.58851i	0.803761	+	0.594952i	$0.202829\pi$
$911$	27.6813	+	47.9455i	0.917124	+	1.58851i	0.113363	+	0.993554i	$0.463838\pi$
$912$	−6.84878	−	5.72526i	−0.226786	−	0.189582i
$913$	1.41592	+	2.45244i	0.0468601	+	0.0811640i
$914$	−10.1581			−0.336001
$915$	0.000677044	−	0.00388165i	2.23824e−5	−	0.000128323i
$916$	−0.621599	+	0.358880i	−0.0205382	+	0.0118577i
$917$	21.3355	+	12.3180i	0.704559	+	0.406778i
$918$	0.111742	+	20.1499i	0.00368805	+	0.665046i
$919$	9.34101	−	16.1791i	0.308132	−	0.533700i	−0.669822	−	0.742522i	$-0.733630\pi$
$919$	9.34101	−	16.1791i	0.308132	−	0.533700i	0.977954	+	0.208822i	$0.0669630\pi$
$920$	−2.85361	+	4.94260i	−0.0940808	+	0.162953i
$921$	23.7759	+	19.8756i	0.783443	+	0.654923i
$922$		−	19.8197i		−	0.652727i
$923$	−35.7627	−	61.9428i	−1.17714	−	2.03887i
$924$	0.336759	−	0.123276i	0.0110786	−	0.00405547i
$925$	0.782503	+	0.451779i	0.0257286	+	0.0148544i
$926$	−10.9325			−0.359263
$927$	9.03458	+	50.1527i	0.296734	+	1.64723i
$928$		−	5.56575i		−	0.182705i
$929$	11.9745			0.392870			0.196435	−	0.980517i	$-0.437063\pi$
$929$	11.9745			0.392870			0.196435	+	0.980517i	$0.437063\pi$
$930$	−2.17743	−	9.39461i	−0.0714008	−	0.308062i
$931$	−29.0967			−0.953606
$932$			15.7057i			0.514456i
$933$	8.86409	+	24.2145i	0.290197	+	0.792748i
$934$	11.3377			0.370980
$935$	−0.597499	−	0.344966i	−0.0195403	−	0.0112816i
$936$	−3.00287	−	16.6695i	−0.0981517	−	0.544859i
$937$	4.88152	+	8.45503i	0.159472	+	0.276214i	0.934678	−	0.355494i	$-0.115687\pi$
$937$	4.88152	+	8.45503i	0.159472	+	0.276214i	−0.775206	+	0.631708i	$0.782354\pi$
$938$		−	7.45483i		−	0.243409i
$939$	−8.53958	+	10.2154i	−0.278679	+	0.333366i
$940$	−2.05539	+	3.56005i	−0.0670396	+	0.116116i
$941$	3.76669	−	6.52409i	0.122790	−	0.212679i	−0.798077	−	0.602556i	$-0.794149\pi$
$941$	3.76669	−	6.52409i	0.122790	−	0.212679i	0.920867	+	0.389877i	$0.127482\pi$
$942$	5.37977	+	14.6962i	0.175282	+	0.478828i
$943$	14.1934	+	8.19456i	0.462200	+	0.266852i
$944$	−4.27376	+	2.46746i	−0.139099	+	0.0803089i
$945$	−5.25353	−	2.99440i	−0.170897	−	0.0974080i
$946$	−0.151174			−0.00491510
$947$	17.9100	+	31.0211i	0.581997	+	1.00805i	0.995242	+	0.0974291i	$0.0310619\pi$
$947$	17.9100	+	31.0211i	0.581997	+	1.00805i	−0.413245	+	0.910620i	$0.635605\pi$
$948$	3.24055	−	3.87647i	0.105248	−	0.125902i
$949$	−30.3823	−	52.6236i	−0.986250	−	1.70824i
$950$	−4.46331	−	2.57689i	−0.144809	−	0.0836054i
$951$	6.13331	−	7.33689i	0.198886	−	0.237915i
$952$	−3.90828	−	2.25644i	−0.126668	−	0.0731318i
$953$	8.04230			0.260516			0.130258	−	0.991480i	$-0.458419\pi$
$953$	8.04230			0.260516			0.130258	+	0.991480i	$0.458419\pi$
$954$	36.9121	−	6.64940i	1.19507	−	0.215282i
$955$	3.22584	+	5.58732i	0.104386	+	0.180801i
$956$	2.90971	−	5.03976i	0.0941067	−	0.162998i
$957$	0.294704	−	1.68961i	0.00952643	−	0.0546172i
$958$	20.4280	+	35.3823i	0.659997	+	1.14315i
$959$	−14.9452			−0.482607
$960$	−1.70629	−	0.297614i	−0.0550703	−	0.00960545i
$961$	21.5784	−	22.2569i	0.696079	−	0.717965i
$962$			5.10142i			0.164476i
$963$	−4.69562	+	13.0510i	−0.151314	+	0.420563i
$964$	−5.77410	+	3.33368i	−0.185971	+	0.107370i
$965$		−	2.10272i		−	0.0676890i
$966$	−7.37821	+	8.82609i	−0.237390	+	0.283975i
$967$	0.283683	−	0.163784i	0.00912262	−	0.00526695i	−0.495432	−	0.868647i	$-0.664990\pi$
$967$	0.283683	−	0.163784i	0.00912262	−	0.00526695i	0.504554	+	0.863380i	$0.331657\pi$
$968$	−9.49887	+	5.48417i	−0.305305	+	0.176268i
$969$	−5.94808	+	34.1017i	−0.191080	+	1.09551i
$970$	−6.85389	+	11.8713i	−0.220065	+	0.381164i
$971$	−9.78490	−	5.64932i	−0.314013	−	0.181295i	0.334708	−	0.942322i	$-0.391362\pi$
$971$	−9.78490	−	5.64932i	−0.314013	−	0.181295i	−0.648721	+	0.761027i	$0.724696\pi$
$972$	2.84868	+	15.3260i	0.0913714	+	0.491580i
$973$	0.920652	−	0.531539i	0.0295147	−	0.0170403i
$974$	−18.2009	+	31.5249i	−0.583194	+	1.01012i
$975$	−3.36161	−	9.18310i	−0.107658	−	0.294094i
$976$		−	0.00227491i		−	7.28180e-5i
$977$			34.7208i			1.11082i	0.831578	+	0.555409i	$0.187438\pi$
$977$			34.7208i			1.11082i	−0.831578	+	0.555409i	$0.812562\pi$
$978$	−10.1740	−	27.7929i	−0.325329	−	0.888718i
$979$	−0.463278	+	0.802421i	−0.0148064	+	0.0256455i
$980$	−4.88932	+	2.82285i	−0.156184	+	0.0901727i
$981$	41.9942	−	35.5027i	1.34077	−	1.13351i
$982$	28.0904	+	16.2180i	0.896400	+	0.517537i
$983$	19.9164	−	34.4963i	0.635235	−	1.10026i	−0.351230	−	0.936289i	$-0.614236\pi$
$983$	19.9164	−	34.4963i	0.635235	−	1.10026i	0.986465	−	0.163971i	$-0.0524302\pi$
$984$	−0.854642	+	4.89986i	−0.0272450	+	0.156202i
$985$	16.3395	−	9.43359i	0.520618	−	0.300579i
$986$	−18.6919	+	10.7917i	−0.595270	+	0.343679i
$987$	−5.31437	+	6.35724i	−0.169158	+	0.202353i
$988$		−	29.0979i		−	0.925728i
$989$	4.19976	−	2.42473i	0.133544	−	0.0771019i
$990$	−0.502224	−	0.180695i	−0.0159617	−	0.00574285i
$991$		−	5.61866i		−	0.178483i	−0.996010	−	0.0892413i	$-0.971556\pi$
$991$		−	5.61866i		−	0.178483i	0.996010	−	0.0892413i	$-0.0284442\pi$
$992$	−2.17043	−	5.12730i	−0.0689113	−	0.162792i
$993$	−15.3089	−	2.67021i	−0.485814	−	0.0847364i
$994$	−14.7428			−0.467615
$995$	9.62408	+	16.6694i	0.305104	+	0.528455i
$996$	4.73710	−	27.1589i	0.150101	−	0.860563i
$997$	−4.87015	+	8.43535i	−0.154239	+	0.267150i	−0.932782	−	0.360442i	$-0.882626\pi$
$997$	−4.87015	+	8.43535i	−0.154239	+	0.267150i	0.778542	+	0.627592i	$0.215959\pi$
$998$	−21.2891	−	36.8738i	−0.673894	−	1.16722i
$999$	−0.0260361	−	4.69495i	−0.000823745	−	0.148542i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.o.e.161.9	✓	40
3.2	odd	2	inner	930.2.o.e.161.18	yes	40
31.26	odd	6	inner	930.2.o.e.491.8	yes	40
93.26	even	6	inner	930.2.o.e.491.19	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.o.e.161.9	✓	40	1.1	even	1	trivial
930.2.o.e.161.18	yes	40	3.2	odd	2	inner
930.2.o.e.491.8	yes	40	31.26	odd	6	inner
930.2.o.e.491.19	yes	40	93.26	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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(1.62650 - 0.595404i) q^{3} -1.00000 q^{4} +(0.866025 + 0.500000i) q^{5} +(-0.595404 - 1.62650i) q^{6} +(-0.581871 - 1.00783i) q^{7} +1.00000i q^{8} +(2.29099 - 1.93685i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(1.62650 - 0.595404i) q^{3} -1.00000 q^{4} +(0.866025 + 0.500000i) q^{5} +(-0.595404 - 1.62650i) q^{6} +(-0.581871 - 1.00783i) q^{7} +1.00000i q^{8} +(2.29099 - 1.93685i) q^{9} +(0.500000 - 0.866025i) q^{10} +(0.0889568 - 0.154078i) q^{11} +(-1.62650 + 0.595404i) q^{12} +(-4.88952 - 2.82297i) q^{13} +(-1.00783 + 0.581871i) q^{14} +(1.70629 + 0.297614i) q^{15} +1.00000 q^{16} +(-1.93896 - 3.35837i) q^{17} +(-1.93685 - 2.29099i) q^{18} +(-2.57689 - 4.46331i) q^{19} +(-0.866025 - 0.500000i) q^{20} +(-1.54648 - 1.29279i) q^{21} +(-0.154078 - 0.0889568i) q^{22} +5.70722 q^{23} +(0.595404 + 1.62650i) q^{24} +(0.500000 + 0.866025i) q^{25} +(-2.82297 + 4.88952i) q^{26} +(2.57308 - 4.51434i) q^{27} +(0.581871 + 1.00783i) q^{28} +5.56575 q^{29} +(0.297614 - 1.70629i) q^{30} +(5.12730 - 2.17043i) q^{31} -1.00000i q^{32} +(0.0529495 - 0.303572i) q^{33} +(-3.35837 + 1.93896i) q^{34} -1.16374i q^{35} +(-2.29099 + 1.93685i) q^{36} +(0.782503 - 0.451779i) q^{37} +(-4.46331 + 2.57689i) q^{38} +(-9.63360 - 1.68031i) q^{39} +(-0.500000 + 0.866025i) q^{40} +(2.48692 + 1.43582i) q^{41} +(-1.29279 + 1.54648i) q^{42} +(0.735867 - 0.424853i) q^{43} +(-0.0889568 + 0.154078i) q^{44} +(2.95248 - 0.531863i) q^{45} -5.70722i q^{46} -4.11079i q^{47} +(1.62650 - 0.595404i) q^{48} +(2.82285 - 4.88932i) q^{49} +(0.866025 - 0.500000i) q^{50} +(-5.15329 - 4.30792i) q^{51} +(4.88952 + 2.82297i) q^{52} +(-6.25104 + 10.8271i) q^{53} +(-4.51434 - 2.57308i) q^{54} +(0.154078 - 0.0889568i) q^{55} +(1.00783 - 0.581871i) q^{56} +(-6.84878 - 5.72526i) q^{57} -5.56575i q^{58} +(-4.27376 + 2.46746i) q^{59} +(-1.70629 - 0.297614i) q^{60} -0.00227491i q^{61} +(-2.17043 - 5.12730i) q^{62} +(-3.28507 - 1.18193i) q^{63} -1.00000 q^{64} +(-2.82297 - 4.88952i) q^{65} +(-0.303572 - 0.0529495i) q^{66} +(-3.20296 + 5.54769i) q^{67} +(1.93896 + 3.35837i) q^{68} +(9.28278 - 3.39810i) q^{69} -1.16374 q^{70} +(10.9712 + 6.33424i) q^{71} +(1.93685 + 2.29099i) q^{72} +(9.32062 + 5.38127i) q^{73} +(-0.451779 - 0.782503i) q^{74} +(1.32888 + 1.11089i) q^{75} +(2.57689 + 4.46331i) q^{76} -0.207046 q^{77} +(-1.68031 + 9.63360i) q^{78} +(-2.52627 + 1.45854i) q^{79} +(0.866025 + 0.500000i) q^{80} +(1.49726 - 8.87458i) q^{81} +(1.43582 - 2.48692i) q^{82} +(-7.95846 + 13.7845i) q^{83} +(1.54648 + 1.29279i) q^{84} -3.87791i q^{85} +(-0.424853 - 0.735867i) q^{86} +(9.05268 - 3.31387i) q^{87} +(0.154078 + 0.0889568i) q^{88} -5.20790 q^{89} +(-0.531863 - 2.95248i) q^{90} +6.57041i q^{91} -5.70722 q^{92} +(7.04726 - 6.58302i) q^{93} -4.11079 q^{94} -5.15378i q^{95} +(-0.595404 - 1.62650i) q^{96} -13.7078 q^{97} +(-4.88932 - 2.82285i) q^{98} +(-0.0946257 - 0.525286i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 6 q^{3} - 40 q^{4} - 12 q^{7} - 2 q^{9}+O(q^{10}) \) 40 * q + 6 * q^3 - 40 * q^4 - 12 * q^7 - 2 * q^9	\( 40 q + 6 q^{3} - 40 q^{4} - 12 q^{7} - 2 q^{9} + 20 q^{10} - 6 q^{12} - 12 q^{13} + 40 q^{16} - 12 q^{18} - 12 q^{19} + 12 q^{21} - 24 q^{22} + 20 q^{25} + 12 q^{28} + 8 q^{31} + 52 q^{33} + 24 q^{34} + 2 q^{36} + 60 q^{37} - 8 q^{39} - 20 q^{40} + 12 q^{42} + 24 q^{43} - 12 q^{45} + 6 q^{48} - 4 q^{49} + 14 q^{51} + 12 q^{52} + 24 q^{55} - 12 q^{57} - 40 q^{64} + 8 q^{66} + 64 q^{67} - 26 q^{69} - 24 q^{70} + 12 q^{72} + 6 q^{75} + 12 q^{76} - 68 q^{78} - 48 q^{79} + 2 q^{81} + 4 q^{82} - 12 q^{84} + 36 q^{87} + 24 q^{88} + 2 q^{90} - 22 q^{93} - 40 q^{94} + 8 q^{97} - 90 q^{99}+O(q^{100}) \) 40 * q + 6 * q^3 - 40 * q^4 - 12 * q^7 - 2 * q^9 + 20 * q^10 - 6 * q^12 - 12 * q^13 + 40 * q^16 - 12 * q^18 - 12 * q^19 + 12 * q^21 - 24 * q^22 + 20 * q^25 + 12 * q^28 + 8 * q^31 + 52 * q^33 + 24 * q^34 + 2 * q^36 + 60 * q^37 - 8 * q^39 - 20 * q^40 + 12 * q^42 + 24 * q^43 - 12 * q^45 + 6 * q^48 - 4 * q^49 + 14 * q^51 + 12 * q^52 + 24 * q^55 - 12 * q^57 - 40 * q^64 + 8 * q^66 + 64 * q^67 - 26 * q^69 - 24 * q^70 + 12 * q^72 + 6 * q^75 + 12 * q^76 - 68 * q^78 - 48 * q^79 + 2 * q^81 + 4 * q^82 - 12 * q^84 + 36 * q^87 + 24 * q^88 + 2 * q^90 - 22 * q^93 - 40 * q^94 + 8 * q^97 - 90 * q^99

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