LMFDB - Embedded newform 144.2.x.e.13.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [144,2,Mod(13,144)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(144, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 9, 4]))

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

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

chi := DirichletCharacter("144.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$144 = 2^{4} \cdot 3^{2}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	144.x (of order $12$ , degree $4$ , 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:	$1.14984578911$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			13.13
Character	$\chi$	$=$	144.13
Dual form			144.2.x.e.133.13

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.04877 + 0.948722i) q^{2} +(-1.13227 + 1.31071i) q^{3} +(0.199854 + 1.98999i) q^{4} +(0.00302457 + 0.0112878i) q^{5} +(-2.43100 + 0.300433i) q^{6} +(-1.05753 + 0.610563i) q^{7} +(-1.67835 + 2.27665i) q^{8} +(-0.435936 - 2.96816i) q^{9} +(-0.00753693 + 0.0147079i) q^{10} +(1.83070 + 0.490535i) q^{11} +(-2.83459 - 1.99125i) q^{12} +(5.06759 - 1.35786i) q^{13} +(-1.68836 - 0.362956i) q^{14} +(-0.0182197 - 0.00881653i) q^{15} +(-3.92012 + 0.795413i) q^{16} -1.54238 q^{17} +(2.35876 - 3.52651i) q^{18} +(4.06823 + 4.06823i) q^{19} +(-0.0218582 + 0.00827477i) q^{20} +(0.397131 - 2.07744i) q^{21} +(1.45461 + 2.25129i) q^{22} +(-5.20660 - 3.00603i) q^{23} +(-1.08370 - 4.77761i) q^{24} +(4.33001 - 2.49993i) q^{25} +(6.60298 + 3.38365i) q^{26} +(4.38400 + 2.78937i) q^{27} +(-1.42637 - 1.98244i) q^{28} +(0.798708 - 2.98082i) q^{29} +(-0.0107440 - 0.0265320i) q^{30} +(2.92831 - 5.07198i) q^{31} +(-4.86594 - 2.88489i) q^{32} +(-2.71580 + 1.84411i) q^{33} +(-1.61761 - 1.46329i) q^{34} +(-0.0100905 - 0.0100905i) q^{35} +(5.81948 - 1.46070i) q^{36} +(0.923082 - 0.923082i) q^{37} +(0.407035 + 8.12628i) q^{38} +(-3.95811 + 8.17961i) q^{39} +(-0.0307748 - 0.0120590i) q^{40} +(-3.20829 - 1.85231i) q^{41} +(2.38741 - 1.80199i) q^{42} +(-4.84015 - 1.29691i) q^{43} +(-0.610287 + 3.74111i) q^{44} +(0.0321856 - 0.0138982i) q^{45} +(-2.60866 - 8.09227i) q^{46} +(-1.31218 - 2.27277i) q^{47} +(3.39607 - 6.03877i) q^{48} +(-2.75442 + 4.77080i) q^{49} +(6.91294 + 1.48611i) q^{50} +(1.74639 - 2.02162i) q^{51} +(3.71490 + 9.81308i) q^{52} +(-8.88508 + 8.88508i) q^{53} +(1.95149 + 7.08461i) q^{54} +0.0221483i q^{55} +(0.384853 - 3.43236i) q^{56} +(-9.93862 + 0.725952i) q^{57} +(3.66563 - 2.36845i) q^{58} +(2.35453 + 8.78724i) q^{59} +(0.0139035 - 0.0380191i) q^{60} +(3.24737 - 12.1194i) q^{61} +(7.88303 - 2.54121i) q^{62} +(2.27326 + 2.87274i) q^{63} +(-2.36631 - 7.64203i) q^{64} +(0.0306545 + 0.0530952i) q^{65} +(-4.59780 - 0.642485i) q^{66} +(-11.8800 + 3.18324i) q^{67} +(-0.308250 - 3.06932i) q^{68} +(9.83532 - 3.42072i) q^{69} +(-0.00100958 - 0.0201557i) q^{70} -14.2363i q^{71} +(7.48912 + 3.98912i) q^{72} +4.32091i q^{73} +(1.84385 - 0.0923563i) q^{74} +(-1.62604 + 8.50599i) q^{75} +(-7.28269 + 8.90879i) q^{76} +(-2.23552 + 0.599006i) q^{77} +(-11.9113 + 4.82341i) q^{78} +(-0.261880 - 0.453589i) q^{79} +(-0.0208352 - 0.0418439i) q^{80} +(-8.61992 + 2.58785i) q^{81} +(-1.60745 - 4.98643i) q^{82} +(2.91592 - 10.8824i) q^{83} +(4.21344 + 0.375104i) q^{84} +(-0.00466503 - 0.0174101i) q^{85} +(-3.84581 - 5.95212i) q^{86} +(3.00264 + 4.42196i) q^{87} +(-4.18933 + 3.34459i) q^{88} +10.7103i q^{89} +(0.0469409 + 0.0159591i) q^{90} +(-4.53005 + 4.53005i) q^{91} +(4.94142 - 10.9619i) q^{92} +(3.33227 + 9.58101i) q^{93} +(0.780042 - 3.62852i) q^{94} +(-0.0336169 + 0.0582262i) q^{95} +(9.29082 - 3.11138i) q^{96} +(8.78820 + 15.2216i) q^{97} +(-7.41493 + 2.39031i) q^{98} +(0.657918 - 5.64765i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$72 q + 4 q^{2} + 2 q^{3} - 2 q^{4} + 4 q^{5} - 28 q^{6} - 8 q^{8} - 20 q^{10} - 2 q^{11} + 8 q^{12} - 16 q^{13} - 4 q^{14} - 20 q^{15} - 10 q^{16} - 16 q^{17} + 28 q^{19} + 12 q^{20} - 16 q^{21} - 8 q^{22}+ \cdots + 28 q^{99}+O(q^{100})$ 72 * q + 4 * q^2 + 2 * q^3 - 2 * q^4 + 4 * q^5 - 28 * q^6 - 8 * q^8 - 20 * q^10 - 2 * q^11 + 8 * q^12 - 16 * q^13 - 4 * q^14 - 20 * q^15 - 10 * q^16 - 16 * q^17 + 28 * q^19 + 12 * q^20 - 16 * q^21 - 8 * q^22 - 40 * q^24 - 4 * q^26 + 8 * q^27 - 16 * q^28 + 4 * q^29 + 18 * q^30 + 28 * q^31 - 46 * q^32 - 32 * q^33 - 14 * q^34 - 16 * q^35 + 14 * q^36 + 16 * q^37 + 2 * q^38 - 10 * q^40 + 26 * q^42 - 10 * q^43 + 60 * q^44 + 40 * q^45 + 20 * q^46 - 56 * q^47 + 2 * q^48 + 4 * q^49 - 36 * q^50 - 54 * q^51 + 6 * q^52 - 8 * q^53 + 92 * q^54 + 52 * q^56 - 14 * q^58 - 14 * q^59 + 18 * q^60 - 32 * q^61 + 16 * q^62 - 108 * q^63 - 44 * q^64 - 64 * q^65 + 26 * q^66 - 18 * q^67 + 16 * q^68 + 32 * q^69 + 14 * q^70 + 114 * q^72 + 38 * q^74 + 86 * q^75 + 10 * q^76 - 36 * q^77 + 16 * q^78 + 44 * q^79 + 144 * q^80 - 44 * q^81 - 88 * q^82 + 20 * q^83 - 58 * q^84 - 8 * q^85 + 76 * q^86 - 42 * q^88 - 80 * q^91 - 68 * q^92 - 4 * q^93 + 20 * q^94 + 48 * q^95 + 94 * q^96 + 40 * q^97 + 88 * q^98 + 28 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$ .

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	1.04877	+	0.948722i	0.741595	+	0.670848i
$2$	1.04877	+	0.948722i	0.741595	+	0.670848i
$3$	−1.13227	+	1.31071i	−0.653716	+	0.756740i
$3$	−1.13227	+	1.31071i	−0.653716	+	0.756740i
$4$	0.199854	+	1.98999i	0.0999268	+	0.994995i
$5$	0.00302457	+	0.0112878i	0.00135263	+	0.00504807i	0.966599	−	0.256294i	$-0.0825016\pi$
$5$	0.00302457	+	0.0112878i	0.00135263	+	0.00504807i	−0.965246	+	0.261342i	$0.915835\pi$
$6$	−2.43100	+	0.300433i	−0.992450	+	0.122651i
$7$	−1.05753	+	0.610563i	−0.399708	+	0.230771i	−0.686358	−	0.727264i	$-0.740792\pi$
$7$	−1.05753	+	0.610563i	−0.399708	+	0.230771i	0.286650	+	0.958035i	$0.407458\pi$
$8$	−1.67835	+	2.27665i	−0.593385	+	0.804919i
$9$	−0.435936	−	2.96816i	−0.145312	−	0.989386i
$10$	−0.00753693	+	0.0147079i	−0.00238339	+	0.00465104i
$11$	1.83070	+	0.490535i	0.551977	+	0.147902i	0.524018	−	0.851707i	$-0.324432\pi$
$11$	1.83070	+	0.490535i	0.551977	+	0.147902i	0.0279594	+	0.999609i	$0.491099\pi$
$12$	−2.83459	−	1.99125i	−0.818276	−	0.574825i
$13$	5.06759	−	1.35786i	1.40550	−	0.376602i	0.525181	−	0.850991i	$-0.323998\pi$
$13$	5.06759	−	1.35786i	1.40550	−	0.376602i	0.880315	+	0.474389i	$0.157331\pi$
$14$	−1.68836	−	0.362956i	−0.451234	−	0.0970040i
$15$	−0.0182197	−	0.00881653i	−0.00470432	−	0.00227642i
$16$	−3.92012	+	0.795413i	−0.980029	+	0.198853i
$17$	−1.54238			−0.374082			−0.187041	−	0.982352i	$-0.559890\pi$
$17$	−1.54238			−0.374082			−0.187041	+	0.982352i	$0.559890\pi$
$18$	2.35876	−	3.52651i	0.555965	−	0.831206i
$19$	4.06823	+	4.06823i	0.933317	+	0.933317i	0.997912	−	0.0645950i	$-0.0205756\pi$
$19$	4.06823	+	4.06823i	0.933317	+	0.933317i	−0.0645950	+	0.997912i	$0.520576\pi$
$20$	−0.0218582	+	0.00827477i	−0.00488764	+	0.00185030i
$21$	0.397131	−	2.07744i	0.0866611	−	0.453334i
$22$	1.45461	+	2.25129i	0.310124	+	0.479976i
$23$	−5.20660	−	3.00603i	−1.08565	−	0.626801i	−0.153236	−	0.988190i	$-0.548970\pi$
$23$	−5.20660	−	3.00603i	−1.08565	−	0.626801i	−0.932415	+	0.361388i	$0.882303\pi$
$24$	−1.08370	−	4.77761i	−0.221210	−	0.975226i
$25$	4.33001	−	2.49993i	0.866002	−	0.499986i
$26$	6.60298	+	3.38365i	1.29495	+	0.663588i
$27$	4.38400	+	2.78937i	0.843701	+	0.536814i
$28$	−1.42637	−	1.98244i	−0.269558	−	0.374647i
$29$	0.798708	−	2.98082i	0.148316	−	0.553524i	−0.851269	−	0.524730i	$-0.824166\pi$
$29$	0.798708	−	2.98082i	0.148316	−	0.553524i	0.999585	−	0.0287946i	$-0.00916687\pi$
$30$	−0.0107440	−	0.0265320i	−0.00196157	−	0.00484406i
$31$	2.92831	−	5.07198i	0.525939	−	0.910954i	−0.473604	−	0.880738i	$-0.657047\pi$
$31$	2.92831	−	5.07198i	0.525939	−	0.910954i	0.999543	−	0.0302159i	$-0.00961949\pi$
$32$	−4.86594	−	2.88489i	−0.860185	−	0.509982i
$33$	−2.71580	+	1.84411i	−0.472760	+	0.321018i
$34$	−1.61761	−	1.46329i	−0.277418	−	0.250952i
$35$	−0.0100905	−	0.0100905i	−0.00170561	−	0.00170561i
$36$	5.81948	−	1.46070i	0.969913	−	0.243451i
$37$	0.923082	−	0.923082i	0.151754	−	0.151754i	−0.627147	−	0.778901i	$-0.715777\pi$
$37$	0.923082	−	0.923082i	0.151754	−	0.151754i	0.778901	+	0.627147i	$0.215777\pi$
$38$	0.407035	+	8.12628i	0.0660298	+	1.31826i
$39$	−3.95811	+	8.17961i	−0.633805	+	1.30979i
$40$	−0.0307748	−	0.0120590i	−0.00486592	−	0.00190669i
$41$	−3.20829	−	1.85231i	−0.501051	−	0.289282i	0.228096	−	0.973639i	$-0.426750\pi$
$41$	−3.20829	−	1.85231i	−0.501051	−	0.289282i	−0.729147	+	0.684357i	$0.760083\pi$
$42$	2.38741	−	1.80199i	0.368385	−	0.278054i
$43$	−4.84015	−	1.29691i	−0.738115	−	0.197777i	−0.129875	−	0.991530i	$-0.541458\pi$
$43$	−4.84015	−	1.29691i	−0.738115	−	0.197777i	−0.608240	+	0.793753i	$0.708124\pi$
$44$	−0.610287	+	3.74111i	−0.0920043	+	0.563994i
$45$	0.0321856	−	0.0138982i	0.00479794	−	0.00207182i
$46$	−2.60866	−	8.09227i	−0.384626	−	1.19314i
$47$	−1.31218	−	2.27277i	−0.191402	−	0.331517i	0.754313	−	0.656515i	$-0.227970\pi$
$47$	−1.31218	−	2.27277i	−0.191402	−	0.331517i	−0.945715	+	0.324997i	$0.894637\pi$
$48$	3.39607	−	6.03877i	0.490180	−	0.871621i
$49$	−2.75442	+	4.77080i	−0.393489	+	0.681543i
$50$	6.91294	+	1.48611i	0.977637	+	0.210168i
$51$	1.74639	−	2.02162i	0.244543	−	0.283083i
$52$	3.71490	+	9.81308i	0.515163	+	1.36083i
$53$	−8.88508	+	8.88508i	−1.22046	+	1.22046i	−0.252991	+	0.967469i	$0.581414\pi$
$53$	−8.88508	+	8.88508i	−1.22046	+	1.22046i	−0.967469	+	0.252991i	$0.918586\pi$
$54$	1.95149	+	7.08461i	0.265564	+	0.964093i
$55$			0.0221483i			0.00298648i
$56$	0.384853	−	3.43236i	0.0514282	−	0.458668i
$57$	−9.93862	+	0.725952i	−1.31640	+	0.0961547i
$58$	3.66563	−	2.36845i	0.481321	−	0.310993i
$59$	2.35453	+	8.78724i	0.306534	+	1.14400i	0.931617	+	0.363443i	$0.118399\pi$
$59$	2.35453	+	8.78724i	0.306534	+	1.14400i	−0.625082	+	0.780559i	$0.714935\pi$
$60$	0.0139035	−	0.0380191i	0.00179494	−	0.00490824i
$61$	3.24737	−	12.1194i	0.415783	−	1.55172i	−0.367478	−	0.930032i	$-0.619779\pi$
$61$	3.24737	−	12.1194i	0.415783	−	1.55172i	0.783262	−	0.621692i	$-0.213555\pi$
$62$	7.88303	−	2.54121i	1.00115	−	0.322734i
$63$	2.27326	+	2.87274i	0.286404	+	0.361931i
$64$	−2.36631	−	7.64203i	−0.295789	−	0.955253i
$65$	0.0306545	+	0.0530952i	0.00380223	+	0.00658565i
$66$	−4.59780	−	0.642485i	−0.565950	−	0.0790844i
$67$	−11.8800	+	3.18324i	−1.45137	+	0.388895i	−0.896501	−	0.443041i	$-0.853900\pi$
$67$	−11.8800	+	3.18324i	−1.45137	+	0.388895i	−0.554873	+	0.831935i	$0.687233\pi$
$68$	−0.308250	−	3.06932i	−0.0373808	−	0.372210i
$69$	9.83532	−	3.42072i	1.18403	−	0.411807i
$70$	−0.00100958	−	0.0201557i	−0.000120667	−	0.00240907i
$71$		−	14.2363i		−	1.68954i	−0.535129	−	0.844771i	$-0.679737\pi$
$71$		−	14.2363i		−	1.68954i	0.535129	−	0.844771i	$-0.320263\pi$
$72$	7.48912	+	3.98912i	0.882601	+	0.470122i
$73$			4.32091i			0.505724i	0.967502	+	0.252862i	$0.0813718\pi$
$73$			4.32091i			0.505724i	−0.967502	+	0.252862i	$0.918628\pi$
$74$	1.84385	−	0.0923563i	0.214344	−	0.0107362i
$75$	−1.62604	+	8.50599i	−0.187759	+	0.982187i
$76$	−7.28269	+	8.90879i	−0.835382	+	1.02191i
$77$	−2.23552	+	0.599006i	−0.254761	+	0.0682630i
$78$	−11.9113	+	4.82341i	−1.34869	+	0.546144i
$79$	−0.261880	−	0.453589i	−0.0294638	−	0.0510328i	0.850918	−	0.525299i	$-0.176047\pi$
$79$	−0.261880	−	0.453589i	−0.0294638	−	0.0510328i	−0.880381	+	0.474267i	$0.842713\pi$
$80$	−0.0208352	−	0.0418439i	−0.00232944	−	0.00467829i
$81$	−8.61992	+	2.58785i	−0.957769	+	0.287539i
$82$	−1.60745	−	4.98643i	−0.177513	−	0.550659i
$83$	2.91592	−	10.8824i	0.320064	−	1.19450i	−0.599117	−	0.800661i	$-0.704482\pi$
$83$	2.91592	−	10.8824i	0.320064	−	1.19450i	0.919181	−	0.393834i	$-0.128852\pi$
$84$	4.21344	+	0.375104i	0.459724	+	0.0409272i
$85$	−0.00466503	−	0.0174101i	−0.000505994	−	0.00188839i
$86$	−3.84581	−	5.95212i	−0.414704	−	0.641834i
$87$	3.00264	+	4.42196i	0.321917	+	0.474084i
$88$	−4.18933	+	3.34459i	−0.446584	+	0.356534i
$89$			10.7103i			1.13529i	0.823274	+	0.567644i	$0.192145\pi$
$89$			10.7103i			1.13529i	−0.823274	+	0.567644i	$0.807855\pi$
$90$	0.0469409	+	0.0159591i	0.00494800	+	0.00168224i
$91$	−4.53005	+	4.53005i	−0.474879	+	0.474879i
$92$	4.94142	−	10.9619i	0.515178	−	1.14285i
$93$	3.33227	+	9.58101i	0.345541	+	0.993504i
$94$	0.780042	−	3.62852i	0.0804551	−	0.374253i
$95$	−0.0336169	+	0.0582262i	−0.00344902	+	0.00597388i
$96$	9.29082	−	3.11138i	0.948240	−	0.317554i
$97$	8.78820	+	15.2216i	0.892306	+	1.54552i	0.837104	+	0.547044i	$0.184247\pi$
$97$	8.78820	+	15.2216i	0.892306	+	1.54552i	0.0552025	+	0.998475i	$0.482420\pi$
$98$	−7.41493	+	2.39031i	−0.749022	+	0.241458i
$99$	0.657918	−	5.64765i	0.0661232	−	0.567611i
$100$	5.84021	+	8.11705i	0.584021	+	0.811705i
$101$	6.73117	+	1.80361i	0.669776	+	0.179466i	0.577654	−	0.816282i	$-0.303968\pi$
$101$	6.73117	+	1.80361i	0.669776	+	0.179466i	0.0921222	+	0.995748i	$0.470635\pi$
$102$	3.74952	−	0.463382i	0.371258	−	0.0458817i
$103$	−2.20609	−	1.27369i	−0.217373	−	0.125500i	0.387360	−	0.921928i	$-0.373387\pi$
$103$	−2.20609	−	1.27369i	−0.217373	−	0.125500i	−0.604733	+	0.796428i	$0.706720\pi$
$104$	−5.41379	+	13.8161i	−0.530866	+	1.35478i
$105$	0.0246509	−	0.00180059i	0.00240568	−	0.000175720i
$106$	−17.7479	+	0.888971i	−1.72383	+	0.0863445i
$107$	3.52175	−	3.52175i	0.340460	−	0.340460i	−0.516080	−	0.856540i	$-0.672609\pi$
$107$	3.52175	−	3.52175i	0.340460	−	0.340460i	0.856540	+	0.516080i	$0.172609\pi$
$108$	−4.67465	+	9.28158i	−0.449818	+	0.893120i
$109$	3.14334	+	3.14334i	0.301077	+	0.301077i	0.841435	−	0.540358i	$-0.181711\pi$
$109$	3.14334	+	3.14334i	0.301077	+	0.301077i	−0.540358	+	0.841435i	$0.681711\pi$
$110$	−0.0210126	+	0.0232286i	−0.00200347	+	0.00221476i
$111$	0.164719	+	2.25507i	0.0156344	+	0.214042i
$112$	3.65998	−	3.23465i	0.345835	−	0.305646i
$113$	7.90904	−	13.6989i	0.744020	−	1.28868i	−0.206631	−	0.978419i	$-0.566250\pi$
$113$	7.90904	−	13.6989i	0.744020	−	1.28868i	0.950651	−	0.310262i	$-0.100417\pi$
$114$	−11.1121	−	8.66762i	−1.04074	−	0.811797i
$115$	0.0181839	−	0.0678632i	0.00169566	−	0.00632828i
$116$	6.09142	+	0.993693i	0.565574	+	0.0922621i
$117$	−6.23947	−	14.4495i	−0.576839	−	1.33585i
$118$	−5.86727	+	11.4496i	−0.540126	+	1.05402i
$119$	1.63111	−	0.941721i	0.149523	−	0.0863274i
$120$	0.0506512	−	0.0266829i	0.00462380	−	0.00243580i
$121$	−6.41543	−	3.70395i	−0.583221	−	0.336723i
$122$	14.9037	−	9.62961i	1.34931	−	0.871824i
$123$	6.06049	−	2.10784i	0.546456	−	0.190057i
$124$	10.6784	+	4.81365i	0.958950	+	0.432278i
$125$	0.0826316	+	0.0826316i	0.00739079	+	0.00739079i
$126$	−0.341293	+	5.16955i	−0.0304048	+	0.460540i
$127$	−5.72603			−0.508103			−0.254052	−	0.967191i	$-0.581763\pi$
$127$	−5.72603			−0.508103			−0.254052	+	0.967191i	$0.581763\pi$
$128$	4.76843	−	10.2597i	0.421474	−	0.906841i
$129$	7.18023	−	4.87559i	0.632184	−	0.429271i
$130$	−0.0182229	+	0.0847675i	−0.00159825	+	0.00743460i
$131$	6.56224	−	1.75835i	0.573346	−	0.153628i	0.0395151	−	0.999219i	$-0.487419\pi$
$131$	6.56224	−	1.75835i	0.573346	−	0.153628i	0.533831	+	0.845591i	$0.320752\pi$
$132$	−4.21252	−	5.03586i	−0.366652	−	0.438315i
$133$	−6.78618	−	1.81835i	−0.588436	−	0.157671i
$134$	−15.4795	−	7.93233i	−1.33722	−	0.685249i
$135$	−0.0182262	+	0.0579225i	−0.00156866	+	0.00498517i
$136$	2.58865	−	3.51147i	0.221975	−	0.301106i
$137$	−3.64923	+	2.10688i	−0.311775	+	0.180003i	−0.647720	−	0.761878i	$-0.724278\pi$
$137$	−3.64923	+	2.10688i	−0.311775	+	0.180003i	0.335946	+	0.941881i	$0.390944\pi$
$138$	13.5603	+	5.74342i	1.15433	+	0.488912i
$139$	−4.19392	−	15.6519i	−0.355724	−	1.32758i	−0.879571	−	0.475767i	$-0.842170\pi$
$139$	−4.19392	−	15.6519i	−0.355724	−	1.32758i	0.523847	−	0.851812i	$-0.324496\pi$
$140$	0.0180634	−	0.0220966i	0.00152663	−	0.00186750i
$141$	4.46469	+	0.853489i	0.375995	+	0.0718768i
$142$	13.5063	−	14.9307i	1.13342	−	1.25296i
$143$	9.94332			0.831502
$144$	4.06983	+	11.2888i	0.339153	+	0.940731i
$145$	0.0360627			0.00299485
$146$	−4.09934	+	4.53165i	−0.339264	+	0.375042i
$147$	−3.13440	−	9.01209i	−0.258521	−	0.743305i
$148$	2.02141	+	1.65244i	0.166159	+	0.135830i
$149$	1.00877	+	3.76477i	0.0826415	+	0.308422i	0.994857	−	0.101288i	$-0.0322964\pi$
$149$	1.00877	+	3.76477i	0.0826415	+	0.308422i	−0.912216	+	0.409710i	$0.865630\pi$
$150$	−9.77517	+	7.37820i	−0.798139	+	0.602428i
$151$	13.0073	−	7.50979i	1.05852	−	0.611138i	0.133499	−	0.991049i	$-0.457379\pi$
$151$	13.0073	−	7.50979i	1.05852	−	0.611138i	0.925023	+	0.379911i	$0.124045\pi$
$152$	−16.0899	+	2.43406i	−1.30506	+	0.197428i
$153$	0.672378	+	4.57803i	0.0543586	+	0.370112i
$154$	−2.91284	−	1.49266i	−0.234724	−	0.120282i
$155$	0.0661085	+	0.0177137i	0.00530996	+	0.00142280i
$156$	−17.0684	−	6.24188i	−1.36656	−	0.499750i
$157$	−9.47288	+	2.53825i	−0.756018	+	0.202574i	−0.616186	−	0.787601i	$-0.711323\pi$
$157$	−9.47288	+	2.53825i	−0.756018	+	0.202574i	−0.139832	+	0.990175i	$0.544656\pi$
$158$	0.155677	−	0.724164i	0.0123850	−	0.0576114i
$159$	−1.58549	−	21.7061i	−0.125738	−	1.72140i
$160$	0.0178468	−	0.0636515i	0.00141092	−	0.00503209i
$161$	7.34150			0.578591
$162$	−11.4955	−	5.46384i	−0.903172	−	0.429280i
$163$	5.22606	+	5.22606i	0.409336	+	0.409336i	0.881507	−	0.472171i	$-0.156529\pi$
$163$	5.22606	+	5.22606i	0.409336	+	0.409336i	−0.472171	+	0.881507i	$0.656529\pi$
$164$	3.04488	−	6.75466i	0.237766	−	0.527450i
$165$	−0.0290301	−	0.0250779i	−0.00225999	−	0.00195231i
$166$	13.3825	−	8.64675i	1.03868	−	0.671118i
$167$	−6.31476	−	3.64583i	−0.488651	−	0.282123i	0.235364	−	0.971907i	$-0.424372\pi$
$167$	−6.31476	−	3.64583i	−0.488651	−	0.282123i	−0.724015	+	0.689785i	$0.757705\pi$
$168$	4.06308	+	4.39078i	0.313473	+	0.338756i
$169$	12.5783	−	7.26211i	0.967565	−	0.558624i
$170$	0.0116248	−	0.0226851i	0.000891583	−	0.00173987i
$171$	10.3017	−	13.8486i	0.787788	−	1.05903i
$172$	1.61352	−	9.89103i	0.123030	−	0.754184i
$173$	−6.14659	+	22.9394i	−0.467317	+	1.74405i	0.181775	+	0.983340i	$0.441816\pi$
$173$	−6.14659	+	22.9394i	−0.467317	+	1.74405i	−0.649092	+	0.760710i	$0.724851\pi$
$174$	−1.04612	+	7.48632i	−0.0793060	+	0.567536i
$175$	−3.05273	+	5.28749i	−0.230765	+	0.399697i
$176$	−7.56674	−	0.466790i	−0.570365	−	0.0351856i
$177$	−14.1835	−	6.86340i	−1.06610	−	0.515885i
$178$	−10.1611	+	11.2327i	−0.761606	+	0.841925i
$179$	11.4489	+	11.4489i	0.855732	+	0.855732i	0.990832	−	0.135100i	$-0.0431356\pi$
$179$	11.4489	+	11.4489i	0.855732	+	0.855732i	−0.135100	+	0.990832i	$0.543136\pi$
$180$	0.0340896	+	0.0612713i	0.00254089	+	0.00456690i
$181$	−3.01327	+	3.01327i	−0.223974	+	0.223974i	−0.810170	−	0.586195i	$-0.800625\pi$
$181$	−3.01327	+	3.01327i	−0.223974	+	0.223974i	0.586195	+	0.810170i	$0.300625\pi$
$182$	−9.04876	+	0.453241i	−0.670739	+	0.0335965i
$183$	12.2081	+	17.9787i	0.902448	+	1.32903i
$184$	15.5822	−	6.80848i	1.14873	−	0.501927i
$185$	0.0132115	+	0.00762768i	0.000971331	+	0.000560798i
$186$	−5.59491	+	13.2097i	−0.410239	+	0.968583i
$187$	−2.82364	−	0.756592i	−0.206485	−	0.0553275i
$188$	4.26054	−	3.06545i	0.310732	−	0.223571i
$189$	−6.33928	−	0.273120i	−0.461115	−	0.0198666i
$190$	−0.0904970	+	0.0291730i	−0.00656534	+	0.00211643i
$191$	−2.25702	−	3.90928i	−0.163313	−	0.282866i	0.772742	−	0.634720i	$-0.218885\pi$
$191$	−2.25702	−	3.90928i	−0.163313	−	0.282866i	−0.936055	+	0.351854i	$0.885551\pi$
$192$	12.6958	+	5.55127i	0.916241	+	0.400628i
$193$	−1.75793	+	3.04482i	−0.126539	+	0.219171i	−0.922333	−	0.386395i	$-0.873720\pi$
$193$	−1.75793	+	3.04482i	−0.126539	+	0.219171i	0.795795	+	0.605566i	$0.207053\pi$
$194$	−5.22424	+	24.3016i	−0.375078	+	1.74475i
$195$	−0.104302	−	0.0199387i	−0.00746920	−	0.00142784i
$196$	−10.0443	−	4.52781i	−0.717452	−	0.323415i
$197$	−4.81922	+	4.81922i	−0.343355	+	0.343355i	−0.857627	−	0.514272i	$-0.828062\pi$
$197$	−4.81922	+	4.81922i	−0.343355	+	0.343355i	0.514272	+	0.857627i	$0.328062\pi$
$198$	6.04806	−	5.29893i	0.429817	−	0.376579i
$199$		−	4.66322i		−	0.330567i	−0.986246	−	0.165284i	$-0.947146\pi$
$199$		−	4.66322i		−	0.330567i	0.986246	−	0.165284i	$-0.0528539\pi$
$200$	−1.57577	+	14.0537i	−0.111424	+	0.993746i
$201$	9.27905	−	19.1756i	0.654494	−	1.35254i
$202$	5.34835	+	8.27759i	0.376308	+	0.582409i
$203$	0.975324	+	3.63996i	0.0684543	+	0.255475i
$204$	4.37202	+	3.07127i	0.306103	+	0.215032i
$205$	0.0112049	−	0.0418171i	0.000782581	−	0.00292063i
$206$	−1.10532	−	3.42878i	−0.0770110	−	0.238894i
$207$	−6.65264	+	16.7645i	−0.462390	+	1.16521i
$208$	−18.7855	+	9.35378i	−1.30254	+	0.648568i
$209$	5.45211	+	9.44333i	0.377130	+	0.653209i
$210$	0.0275615	+	0.0214984i	0.00190192	+	0.00148353i
$211$	−17.4452	+	4.67442i	−1.20097	+	0.321800i	−0.803215	−	0.595689i	$-0.796879\pi$
$211$	−17.4452	+	4.67442i	−1.20097	+	0.321800i	−0.397760	+	0.917490i	$0.630212\pi$
$212$	−19.4569	−	15.9055i	−1.33631	−	1.09239i
$213$	18.6597	+	16.1193i	1.27854	+	1.10448i
$214$	7.03468	−	0.352358i	0.480881	−	0.0240867i
$215$		−	0.0585574i		−	0.00399358i
$216$	−13.7083	+	5.29933i	−0.932731	+	0.360574i
$217$			7.15167i			0.485487i
$218$	0.314498	+	6.27881i	0.0213005	+	0.425254i
$219$	−5.66347	−	4.89243i	−0.382702	−	0.330599i
$220$	−0.0440749	+	0.00442642i	−0.00297153	+	0.000298429i
$221$	−7.81615	+	2.09433i	−0.525771	+	0.140880i
$222$	−1.96668	+	2.52133i	−0.131995	+	0.169221i
$223$	2.85769	+	4.94966i	0.191365	+	0.331454i	0.945703	−	0.325032i	$-0.105375\pi$
$223$	2.85769	+	4.94966i	0.191365	+	0.331454i	−0.754338	+	0.656486i	$0.772042\pi$
$224$	6.90727	+	0.0798841i	0.461512	+	0.00533748i
$225$	−9.30780	−	11.7623i	−0.620520	−	0.784156i
$226$	21.2912	−	6.86353i	1.41627	−	0.456555i
$227$	−5.27233	+	19.6766i	−0.349937	+	1.30598i	0.536802	+	0.843709i	$0.319632\pi$
$227$	−5.27233	+	19.6766i	−0.349937	+	1.30598i	−0.886738	+	0.462272i	$0.847034\pi$
$228$	−3.43091	−	19.6327i	−0.227217	−	1.30020i
$229$	−0.992819	−	3.70525i	−0.0656073	−	0.244850i	0.925332	−	0.379157i	$-0.123786\pi$
$229$	−0.992819	−	3.70525i	−0.0656073	−	0.244850i	−0.990940	+	0.134307i	$0.957119\pi$
$230$	0.0834542	−	0.0539217i	0.00550280	−	0.00355549i
$231$	1.74608	−	3.60836i	0.114884	−	0.237413i
$232$	5.44579	+	6.82122i	0.357533	+	0.447835i
$233$		−	5.33043i		−	0.349208i	−0.984639	−	0.174604i	$-0.944136\pi$
$233$		−	5.33043i		−	0.349208i	0.984639	−	0.174604i	$-0.0558645\pi$
$234$	7.16472	−	21.0737i	0.468373	−	1.37763i
$235$	0.0216859	−	0.0216859i	0.00141463	−	0.00141463i
$236$	−17.0160	+	6.44166i	−1.10764	+	0.419316i
$237$	0.891043	+	0.170336i	0.0578795	+	0.0110645i
$238$	2.60410	+	0.559816i	0.168798	+	0.0362875i
$239$	−13.8380	+	23.9681i	−0.895104	+	1.55037i	−0.0614282	+	0.998112i	$0.519566\pi$
$239$	−13.8380	+	23.9681i	−0.895104	+	1.55037i	−0.833676	+	0.552254i	$0.813768\pi$
$240$	0.0784363	+	0.0200696i	0.00506304	+	0.00129549i
$241$	0.847203	+	1.46740i	0.0545731	+	0.0945234i	0.892021	−	0.451993i	$-0.149287\pi$
$241$	0.847203	+	1.46740i	0.0545731	+	0.0945234i	−0.837448	+	0.546517i	$0.815954\pi$
$242$	−3.21432	−	9.97107i	−0.206624	−	0.640965i
$243$	6.36814	−	14.2284i	0.408516	−	0.912751i
$244$	24.7664	+	4.04014i	1.58551	+	0.258643i
$245$	−0.0621830	−	0.0166619i	−0.00397273	−	0.00106449i
$246$	8.35584	+	3.53907i	0.532749	+	0.225643i
$247$	26.1402	+	15.0921i	1.66326	+	0.960284i
$248$	6.63243	+	15.1793i	0.421160	+	0.963885i
$249$	10.9621	+	16.1437i	0.694692	+	1.02307i
$250$	0.00826746	+	0.165056i	0.000522880	+	0.0104391i
$251$	0.987980	−	0.987980i	0.0623607	−	0.0623607i	−0.675239	−	0.737599i	$-0.735959\pi$
$251$	0.987980	−	0.987980i	0.0623607	−	0.0623607i	0.737599	+	0.675239i	$0.235959\pi$
$252$	−5.26240	+	5.09789i	−0.331500	+	0.321137i
$253$	−8.05717	−	8.05717i	−0.506550	−	0.506550i
$254$	−6.00531	−	5.43241i	−0.376807	−	0.340860i
$255$	0.0281018	+	0.0135984i	0.00175980	+	0.000851567i
$256$	14.7346	−	6.23623i	0.920915	−	0.389764i
$257$	11.8214	−	20.4753i	0.737401	−	1.27722i	−0.216260	−	0.976336i	$-0.569386\pi$
$257$	11.8214	−	20.4753i	0.737401	−	1.27722i	0.953662	−	0.300881i	$-0.0972806\pi$
$258$	12.1560	+	1.69865i	0.756800	+	0.105753i
$259$	−0.412584	+	1.53978i	−0.0256367	+	0.0956776i
$260$	−0.0995325	+	0.0716134i	−0.00617274	+	0.00444128i
$261$	−9.19572	−	1.07125i	−0.569201	−	0.0663085i
$262$	8.55049	+	4.38163i	0.528251	+	0.270698i
$263$	−22.2619	+	12.8529i	−1.37273	+	0.792545i	−0.991271	−	0.131841i	$-0.957911\pi$
$263$	−22.2619	+	12.8529i	−1.37273	+	0.792545i	−0.381458	+	0.924386i	$0.624578\pi$
$264$	0.359651	−	9.27798i	0.0221350	−	0.571020i
$265$	−0.127167	−	0.0734198i	−0.00781180	−	0.00451015i
$266$	−5.39206	−	8.34523i	−0.330608	−	0.511679i
$267$	−14.0381	−	12.1269i	−0.859119	−	0.742156i
$268$	−8.70888	−	23.0049i	−0.531979	−	1.40525i
$269$	−13.6891	−	13.6891i	−0.834637	−	0.834637i	0.153510	−	0.988147i	$-0.450942\pi$
$269$	−13.6891	−	13.6891i	−0.834637	−	0.834637i	−0.988147	+	0.153510i	$0.950942\pi$
$270$	−0.0740675	+	0.0434560i	−0.00450760	+	0.00264465i
$271$	−7.11000			−0.431902			−0.215951	−	0.976404i	$-0.569285\pi$
$271$	−7.11000			−0.431902			−0.215951	+	0.976404i	$0.569285\pi$
$272$	6.04631	−	1.22683i	0.366612	−	0.0743875i
$273$	−0.808361	−	11.0668i	−0.0489242	−	0.669795i
$274$	−5.82607	−	1.25246i	−0.351966	−	0.0756639i
$275$	9.15326	−	2.45261i	0.551962	−	0.147898i
$276$	8.77283	+	18.8885i	0.528062	+	1.13696i
$277$	−21.7174	−	5.81917i	−1.30487	−	0.349640i	−0.461583	−	0.887097i	$-0.652718\pi$
$277$	−21.7174	−	5.81917i	−1.30487	−	0.349640i	−0.843291	+	0.537457i	$0.819385\pi$
$278$	10.4509	−	20.3942i	0.626801	−	1.22316i
$279$	−16.3310	−	6.48062i	−0.977710	−	0.387985i
$280$	0.0399079	−	0.00603724i	0.00238496	−	0.000360794i
$281$	19.7952	−	11.4288i	1.18088	−	0.681783i	0.224664	−	0.974436i	$-0.427872\pi$
$281$	19.7952	−	11.4288i	1.18088	−	0.681783i	0.956218	+	0.292654i	$0.0945383\pi$
$282$	3.87273	+	5.13087i	0.230618	+	0.305539i
$283$	1.59958	+	5.96971i	0.0950851	+	0.354862i	0.997032	−	0.0769838i	$-0.0245290\pi$
$283$	1.59958	+	5.96971i	0.0950851	+	0.354862i	−0.901947	+	0.431846i	$0.857862\pi$
$284$	28.3301	−	2.84518i	1.68108	−	0.168830i
$285$	−0.0382544	−	0.109990i	−0.00226600	−	0.00651523i
$286$	10.4283	+	9.43344i	0.616638	+	0.557811i
$287$	4.52381			0.267032
$288$	−6.44158	+	15.7005i	−0.379574	+	0.925162i
$289$	−14.6211			−0.860063
$290$	0.0378217	+	0.0342135i	0.00222096	+	0.00200909i
$291$	−29.9017	−	5.71614i	−1.75287	−	0.335086i
$292$	−8.59856	+	0.863549i	−0.503192	+	0.0505354i
$293$	1.00950	+	3.76752i	0.0589758	+	0.220101i	0.989124	−	0.147083i	$-0.0469886\pi$
$293$	1.00950	+	3.76752i	0.0589758	+	0.220101i	−0.930148	+	0.367184i	$0.880322\pi$
$294$	5.26269	−	12.4253i	0.306926	−	0.724660i
$295$	−0.0920675	+	0.0531552i	−0.00536038	+	0.00309482i
$296$	0.552289	+	3.65079i	0.0321011	+	0.212198i
$297$	6.65751	+	7.25700i	0.386308	+	0.421094i
$298$	−2.51375	+	4.90543i	−0.145618	+	0.284164i
$299$	−30.4667	−	8.16352i	−1.76193	−	0.472109i
$300$	−17.2518	−	1.53585i	−0.996033	−	0.0886724i
$301$	5.91043	−	1.58370i	0.340672	−	0.0912827i
$302$	20.7665	+	4.46427i	1.19498	+	0.256890i
$303$	−9.98550	+	6.78045i	−0.573652	+	0.389527i
$304$	−19.1839	−	12.7120i	−1.10027	−	0.729084i
$305$	0.146623			0.00839562
$306$	−3.63810	+	5.43922i	−0.207976	+	0.310939i
$307$	10.8111	+	10.8111i	0.617023	+	0.617023i	0.944767	−	0.327743i	$-0.106288\pi$
$307$	10.8111	+	10.8111i	0.617023	+	0.617023i	−0.327743	+	0.944767i	$0.606288\pi$
$308$	−1.63879	−	4.32895i	−0.0933788	−	0.246665i
$309$	4.16733	−	1.44940i	0.237071	−	0.0824532i
$310$	0.0525275	+	0.0812963i	0.00298336	+	0.00461732i
$311$	19.5372	+	11.2798i	1.10785	+	0.639619i	0.938273	−	0.345897i	$-0.112425\pi$
$311$	19.5372	+	11.2798i	1.10785	+	0.639619i	0.169581	+	0.985516i	$0.445759\pi$
$312$	−11.9791	−	22.7395i	−0.678181	−	1.28737i
$313$	−5.17232	+	2.98624i	−0.292357	+	0.168792i	−0.639004	−	0.769203i	$-0.720653\pi$
$313$	−5.17232	+	2.98624i	−0.292357	+	0.168792i	0.346647	+	0.937996i	$0.387320\pi$
$314$	−12.3430	−	6.32508i	−0.696556	−	0.356945i
$315$	−0.0255514	+	0.0343490i	−0.00143966	+	0.00193535i
$316$	0.850300	−	0.611789i	0.0478331	−	0.0344158i
$317$	4.81751	−	17.9792i	0.270579	−	1.00981i	−0.688168	−	0.725551i	$-0.741585\pi$
$317$	4.81751	−	17.9792i	0.270579	−	1.00981i	0.958747	−	0.284262i	$-0.0917485\pi$
$318$	18.9302	−	24.2690i	1.06155	−	1.36094i
$319$	2.92439	−	5.06520i	0.163735	−	0.283597i
$320$	0.0791049	−	0.0498244i	0.00442210	−	0.00278527i
$321$	0.628435	+	8.60356i	0.0350758	+	0.480204i
$322$	7.69957	+	6.96504i	0.429080	+	0.388146i
$323$	−6.27476	−	6.27476i	−0.349137	−	0.349137i
$324$	−6.87252	−	16.6364i	−0.381807	−	0.924242i
$325$	18.5482	−	18.5482i	1.02887	−	1.02887i
$326$	0.522878	+	10.4390i	0.0289595	+	0.578164i
$327$	−7.67912	+	0.560910i	−0.424656	+	0.0310184i
$328$	9.60169	−	4.19536i	0.530164	−	0.231650i
$329$	2.77534	+	1.60234i	0.153009	+	0.0883400i
$330$	−0.00665409	−	0.0538425i	−0.000366296	−	0.00296393i
$331$	−10.1869	−	2.72957i	−0.559923	−	0.150031i	−0.0322521	−	0.999480i	$-0.510268\pi$
$331$	−10.1869	−	2.72957i	−0.559923	−	0.150031i	−0.527671	+	0.849449i	$0.676935\pi$
$332$	22.2386	+	3.62777i	1.22050	+	0.199100i
$333$	−3.14226	−	2.33745i	−0.172195	−	0.128091i
$334$	−3.16388	−	9.81461i	−0.173120	−	0.537031i
$335$	−0.0718638	−	0.124472i	−0.00392634	−	0.00680062i
$336$	0.0956190	+	8.45967i	0.00521644	+	0.461513i
$337$	12.1222	−	20.9962i	0.660336	−	1.14374i	−0.320192	−	0.947353i	$-0.603747\pi$
$337$	12.1222	−	20.9962i	0.660336	−	1.14374i	0.980527	−	0.196382i	$-0.0629194\pi$
$338$	20.0816	+	4.31704i	1.09229	+	0.234816i
$339$	9.00011	+	25.8773i	0.488819	+	1.40546i
$340$	0.0337137	−	0.0127628i	0.00182838	−	0.000692163i
$341$	7.84884	−	7.84884i	0.425038	−	0.425038i
$342$	23.9426	−	4.75068i	1.29467	−	0.256887i
$343$		−	15.2749i		−	0.824767i
$344$	11.0761	−	8.84267i	0.597181	−	0.476765i
$345$	0.0683602	+	0.100673i	0.00368039	+	0.00542007i
$346$	−28.2095	+	18.2268i	−1.51655	+	0.979881i
$347$	4.97570	+	18.5696i	0.267110	+	0.996867i	0.960946	+	0.276735i	$0.0892523\pi$
$347$	4.97570	+	18.5696i	0.267110	+	0.996867i	−0.693837	+	0.720132i	$0.744081\pi$
$348$	−8.19957	+	6.85898i	−0.439543	+	0.367680i
$349$	−4.19134	+	15.6423i	−0.224357	+	0.837313i	0.758304	+	0.651901i	$0.226028\pi$
$349$	−4.19134	+	15.6423i	−0.224357	+	0.837313i	−0.982661	+	0.185411i	$0.940638\pi$
$350$	−8.21798	+	2.64919i	−0.439270	+	0.141605i
$351$	26.0039	+	8.18252i	1.38798	+	0.436750i
$352$	−7.49295	−	7.66829i	−0.399376	−	0.408721i
$353$	−7.69391	−	13.3262i	−0.409505	−	0.709284i	0.585329	−	0.810796i	$-0.300965\pi$
$353$	−7.69391	−	13.3262i	−0.409505	−	0.709284i	−0.994834	+	0.101512i	$0.967632\pi$
$354$	−8.36384	−	20.6544i	−0.444533	−	1.09777i
$355$	0.160697	−	0.0430587i	0.00852893	−	0.00228532i
$356$	−21.3134	+	2.14049i	−1.12961	+	0.113446i
$357$	−0.612527	+	3.20420i	−0.0324184	+	0.169584i
$358$	1.14549	+	22.8692i	0.0605409	+	1.20867i
$359$			2.97883i			0.157217i	0.996906	+	0.0786083i	$0.0250476\pi$
$359$			2.97883i			0.157217i	−0.996906	+	0.0786083i	$0.974952\pi$
$360$	−0.0223772	+	0.0966013i	−0.00117938	+	0.00509134i
$361$			14.1010i			0.742159i
$362$	−6.01899	+	0.301484i	−0.316351	+	0.0158456i
$363$	12.1188	−	4.21492i	0.636073	−	0.221226i
$364$	−9.92011	−	8.10941i	−0.519955	−	0.425049i
$365$	−0.0487737	+	0.0130689i	−0.00255293	+	0.000684056i
$366$	−4.25329	+	30.4377i	−0.222323	+	1.59101i
$367$	12.5585	+	21.7519i	0.655547	+	1.13544i	0.981756	+	0.190143i	$0.0608952\pi$
$367$	12.5585	+	21.7519i	0.655547	+	1.13544i	−0.326210	+	0.945297i	$0.605772\pi$
$368$	22.8015	+	7.64260i	1.18861	+	0.398398i
$369$	−4.09933	+	10.3302i	−0.213403	+	0.537769i
$370$	0.00661936	+	0.0205338i	0.000344124	+	0.00106750i
$371$	3.97131	−	14.8211i	0.206180	−	0.769474i
$372$	−18.4001	+	8.54599i	−0.954003	+	0.443089i
$373$	7.71816	+	28.8046i	0.399631	+	1.49144i	0.813747	+	0.581220i	$0.197424\pi$
$373$	7.71816	+	28.8046i	0.399631	+	1.49144i	−0.414116	+	0.910224i	$0.635909\pi$
$374$	−2.24356	−	3.47234i	−0.116012	−	0.179551i
$375$	−0.201867	+	0.0147451i	−0.0104244	+	0.000761435i
$376$	7.37661	+	0.827102i	0.380420	+	0.0426545i
$377$		−	16.1901i		−	0.833832i
$378$	−6.38936	−	6.30065i	−0.328633	−	0.324071i
$379$	10.1985	−	10.1985i	0.523864	−	0.523864i	−0.394872	−	0.918736i	$-0.629211\pi$
$379$	10.1985	−	10.1985i	0.523864	−	0.523864i	0.918736	+	0.394872i	$0.129211\pi$
$380$	−0.122588	−	0.0552606i	−0.00628863	−	0.00283481i
$381$	6.48341	−	7.50518i	0.332155	−	0.384502i
$382$	1.34171	−	6.24124i	0.0686479	−	0.319330i
$383$	10.5750	−	18.3164i	0.540356	−	0.935924i	−0.458528	−	0.888680i	$-0.651623\pi$
$383$	10.5750	−	18.3164i	0.540356	−	0.935924i	0.998883	−	0.0472436i	$-0.0150437\pi$
$384$	8.04842	+	17.8668i	0.410719	+	0.911762i
$385$	−0.0135230	−	0.0234224i	−0.000689194	−	0.00119372i
$386$	−4.73236	+	1.52555i	−0.240871	+	0.0776482i
$387$	−1.73945	+	14.9317i	−0.0884213	+	0.759020i
$388$	−28.5345	+	20.5305i	−1.44862	+	1.04228i
$389$	30.3488	+	8.13193i	1.53874	+	0.412305i	0.925860	−	0.377867i	$-0.123342\pi$
$389$	30.3488	+	8.13193i	1.53874	+	0.412305i	0.612884	+	0.790173i	$0.290009\pi$
$390$	−0.0904726	−	0.119865i	−0.00458126	−	0.00606958i
$391$	8.03056	+	4.63645i	0.406123	+	0.234475i
$392$	−6.23860	−	14.2779i	−0.315097	−	0.721144i
$393$	−5.12553	+	10.5921i	−0.258549	+	0.534303i
$394$	−9.62638	+	0.482173i	−0.484970	+	0.0242915i
$395$	0.00432797	−	0.00432797i	0.000217764	−	0.000217764i
$396$	11.3703	+	0.180545i	0.571377	+	0.00907272i
$397$	−3.24113	−	3.24113i	−0.162668	−	0.162668i	0.621080	−	0.783747i	$-0.286694\pi$
$397$	−3.24113	−	3.24113i	−0.162668	−	0.162668i	−0.783747	+	0.621080i	$0.786694\pi$
$398$	4.42410	−	4.89067i	0.221760	−	0.245147i
$399$	10.0671	−	6.83587i	0.503986	−	0.342221i
$400$	−14.9857	+	13.2442i	−0.749283	+	0.662209i
$401$	−10.7429	+	18.6073i	−0.536476	+	0.929203i	0.462614	+	0.886560i	$0.346911\pi$
$401$	−10.7429	+	18.6073i	−0.536476	+	0.929203i	−0.999090	+	0.0426439i	$0.986422\pi$
$402$	27.9239	−	11.3076i	1.39272	−	0.563971i
$403$	7.95244	−	29.6789i	0.396139	−	1.47841i
$404$	−2.24392	+	13.7554i	−0.111639	+	0.684357i
$405$	−0.0552828	−	0.0894731i	−0.00274702	−	0.00444596i
$406$	−2.43041	+	4.74280i	−0.120619	+	0.235381i
$407$	2.14269	−	1.23708i	0.106209	−	0.0613200i
$408$	1.67148	+	7.36890i	0.0827507	+	0.364815i
$409$	−23.1426	−	13.3614i	−1.14433	−	0.660678i	−0.196829	−	0.980438i	$-0.563064\pi$
$409$	−23.1426	−	13.3614i	−1.14433	−	0.660678i	−0.947499	+	0.319760i	$0.896398\pi$
$410$	0.0514242	−	0.0332264i	0.00253966	−	0.00164093i
$411$	1.37039	−	7.16865i	0.0675963	−	0.353604i
$412$	2.09373	−	4.64465i	0.103151	−	0.228825i
$413$	−7.85515	−	7.85515i	−0.386527	−	0.386527i
$414$	−22.8819	+	11.2706i	−1.12459	+	0.553921i
$415$	0.131658			0.00646283
$416$	−28.5759	−	8.01219i	−1.40105	−	0.392830i
$417$	25.2638	+	12.2252i	1.23718	+	0.598669i
$418$	−3.24106	+	15.0765i	−0.158526	+	0.737414i
$419$	−8.83989	+	2.36864i	−0.431857	+	0.115716i	−0.468198	−	0.883624i	$-0.655097\pi$
$419$	−8.83989	+	2.36864i	−0.431857	+	0.115716i	0.0363407	+	0.999339i	$0.488430\pi$
$420$	0.00850973	+	0.0486952i	0.000415232	+	0.00237608i
$421$	−28.9344	−	7.75295i	−1.41018	−	0.377856i	−0.528188	−	0.849127i	$-0.677128\pi$
$421$	−28.9344	−	7.75295i	−1.41018	−	0.377856i	−0.881988	+	0.471272i	$0.843795\pi$
$422$	−22.7308	−	11.6482i	−1.10652	−	0.567026i
$423$	−6.17391	+	4.88555i	−0.300186	+	0.237544i
$424$	−5.31603	−	35.1405i	−0.258169	−	1.70657i
$425$	−6.67852	+	3.85585i	−0.323956	+	0.187036i
$426$	4.27707	+	34.6085i	0.207225	+	1.67678i
$427$	3.96545	+	14.7993i	0.191902	+	0.716187i
$428$	7.71208	+	6.30441i	0.372777	+	0.304735i
$429$	−11.2585	+	13.0328i	−0.543566	+	0.629231i
$430$	0.0555547	−	0.0614135i	0.00267908	−	0.00296162i
$431$	−7.05544			−0.339849			−0.169924	−	0.985457i	$-0.554352\pi$
$431$	−7.05544			−0.339849			−0.169924	+	0.985457i	$0.554352\pi$
$432$	−19.4045	−	7.44755i	−0.933599	−	0.358320i
$433$	13.1552			0.632201			0.316100	−	0.948726i	$-0.397626\pi$
$433$	13.1552			0.632201			0.316100	+	0.948726i	$0.397626\pi$
$434$	−6.78494	+	7.50048i	−0.325688	+	0.360035i
$435$	−0.0408327	+	0.0472679i	−0.00195778	+	0.00226632i
$436$	−5.62700	+	6.88342i	−0.269485	+	0.329656i
$437$	−8.95243	−	33.4109i	−0.428253	−	1.59826i
$438$	−1.29814	−	10.5041i	−0.0620277	−	0.501905i
$439$	−12.8757	+	7.43381i	−0.614525	+	0.354796i	−0.774734	−	0.632287i	$-0.782116\pi$
$439$	−12.8757	+	7.43381i	−0.614525	+	0.354796i	0.160209	+	0.987083i	$0.448783\pi$
$440$	−0.0504241	−	0.0371725i	−0.00240387	−	0.00177213i
$441$	15.3612	+	6.09580i	0.731488	+	0.290276i
$442$	−10.1843	−	5.21887i	−0.484418	−	0.248236i
$443$	−2.97678	−	0.797625i	−0.141431	−	0.0378963i	0.187409	−	0.982282i	$-0.439991\pi$
$443$	−2.97678	−	0.797625i	−0.141431	−	0.0378963i	−0.328840	+	0.944386i	$0.606658\pi$
$444$	−4.45465	+	0.778473i	−0.211408	+	0.0369447i
$445$	−0.120896	+	0.0323940i	−0.00573102	+	0.00153562i
$446$	−1.69878	+	7.90223i	−0.0804398	+	0.374182i
$447$	−6.07673	−	2.94053i	−0.287419	−	0.139082i
$448$	7.16838	+	6.63686i	0.338674	+	0.313562i
$449$	−21.8550			−1.03140			−0.515701	−	0.856769i	$-0.672468\pi$
$449$	−21.8550			−1.03140			−0.515701	+	0.856769i	$0.672468\pi$
$450$	1.39741	−	21.1665i	0.0658748	−	0.997801i
$451$	−4.96480	−	4.96480i	−0.233783	−	0.233783i
$452$	28.8412	+	13.0011i	1.35658	+	0.611522i
$453$	−4.88462	+	25.5520i	−0.229500	+	1.20054i
$454$	−24.1971	+	15.6343i	−1.13563	+	0.733755i
$455$	−0.0648360	−	0.0374331i	−0.00303956	−	0.00175489i
$456$	15.0277	−	23.8452i	0.703736	−	1.11665i
$457$	−2.32261	+	1.34096i	−0.108647	+	0.0627275i	−0.553339	−	0.832956i	$-0.686647\pi$
$457$	−2.32261	+	1.34096i	−0.108647	+	0.0627275i	0.444692	+	0.895684i	$0.353313\pi$
$458$	2.47401	−	4.82788i	0.115603	−	0.225592i
$459$	−6.76179	−	4.30226i	−0.315613	−	0.200812i
$460$	0.138681	+	0.0226231i	0.00646605	+	0.00105481i
$461$	2.74844	−	10.2573i	0.128008	−	0.477732i	−0.871921	−	0.489646i	$-0.837126\pi$
$461$	2.74844	−	10.2573i	0.128008	−	0.477732i	0.999929	+	0.0119146i	$0.00379262\pi$
$462$	5.25458	−	2.12780i	0.244465	−	0.0989944i
$463$	11.8249	−	20.4814i	0.549550	−	0.951849i	−0.448755	−	0.893655i	$-0.648132\pi$
$463$	11.8249	−	20.4814i	0.549550	−	0.951849i	0.998305	−	0.0581943i	$-0.0185343\pi$
$464$	−0.760046	+	12.3205i	−0.0352842	+	0.571963i
$465$	−0.0980702	+	0.0665926i	−0.00454790	+	0.00308816i
$466$	5.05709	−	5.59041i	0.234265	−	0.258971i
$467$	2.22540	+	2.22540i	0.102979	+	0.102979i	0.756719	−	0.653740i	$-0.226801\pi$
$467$	2.22540	+	2.22540i	0.102979	+	0.102979i	−0.653740	+	0.756719i	$0.726801\pi$
$468$	27.5073	−	15.3043i	1.27153	−	0.707440i
$469$	10.6199	−	10.6199i	0.490380	−	0.490380i
$470$	0.0433174	−	0.00216972i	0.00199808	−	0.000100082i
$471$	7.39893	−	15.2902i	0.340925	−	0.704536i
$472$	−23.9572	−	9.38756i	−1.10272	−	0.432098i
$473$	−8.22468	−	4.74852i	−0.378171	−	0.218337i
$474$	0.772902	+	1.02400i	0.0355006	+	0.0470337i
$475$	27.7858	+	7.44518i	1.27490	+	0.341608i
$476$	2.20000	+	3.05768i	0.100837	+	0.140149i
$477$	30.2456	+	22.4990i	1.38485	+	1.03016i
$478$	−37.2519	+	12.0087i	−1.70386	+	0.549265i
$479$	−6.23896	−	10.8062i	−0.285066	−	0.493748i	0.687559	−	0.726128i	$-0.258682\pi$
$479$	−6.23896	−	10.8062i	−0.285066	−	0.493748i	−0.972625	+	0.232380i	$0.925349\pi$
$480$	0.0632215	+	0.0954627i	0.00288565	+	0.00435726i
$481$	3.42439	−	5.93121i	0.156139	−	0.270440i
$482$	−0.503629	+	2.34273i	−0.0229397	+	0.106708i
$483$	−8.31255	+	9.62259i	−0.378234	+	0.437843i
$484$	6.08868	−	13.5069i	0.276758	−	0.613950i
$485$	−0.145238	+	0.145238i	−0.00659494	+	0.00659494i
$486$	20.1775	−	8.88077i	0.915271	−	0.402840i
$487$		−	12.5314i		−	0.567853i	−0.958846	−	0.283927i	$-0.908363\pi$
$487$		−	12.5314i		−	0.567853i	0.958846	−	0.283927i	$-0.0916372\pi$
$488$	22.1414	+	27.7336i	1.00229	+	1.25544i
$489$	−12.7672	+	0.932559i	−0.577351	+	0.0421718i
$490$	−0.0494084	−	0.0764689i	−0.00223204	−	0.00345451i
$491$	−3.93613	−	14.6898i	−0.177635	−	0.662942i	−0.996088	−	0.0883688i	$-0.971835\pi$
$491$	−3.93613	−	14.6898i	−0.177635	−	0.662942i	0.818453	−	0.574574i	$-0.194832\pi$
$492$	5.40579	+	11.6391i	0.243712	+	0.524729i
$493$	−1.23191	+	4.59756i	−0.0554825	+	0.207064i
$494$	13.0970	+	40.6279i	0.589262	+	1.82794i
$495$	0.0657397	−	0.00965524i	0.00295478	−	0.000433971i
$496$	−7.44499	+	22.2120i	−0.334290	+	0.997346i
$497$	8.69218	+	15.0553i	0.389898	+	0.675322i
$498$	−3.81917	+	27.3310i	−0.171141	+	1.22473i
$499$	29.4298	−	7.88570i	1.31746	−	0.353012i	0.469434	−	0.882967i	$-0.344458\pi$
$499$	29.4298	−	7.88570i	1.31746	−	0.353012i	0.848026	+	0.529955i	$0.177791\pi$
$500$	−0.147922	+	0.180950i	−0.00661526	+	0.00809234i
$501$	11.9286	−	4.14878i	0.532933	−	0.185354i
$502$	1.97349	−	0.0988495i	0.0880810	−	0.00441187i
$503$			1.90106i			0.0847639i	0.999101	+	0.0423820i	$0.0134946\pi$
$503$			1.90106i			0.0847639i	−0.999101	+	0.0423820i	$0.986505\pi$
$504$	−10.3556	+	0.353983i	−0.461273	+	0.0157676i
$505$			0.0814355i			0.00362383i
$506$	−0.806137	−	16.0942i	−0.0358372	−	0.715473i
$507$	−4.72352	+	24.7093i	−0.209779	+	1.09738i
$508$	−1.14437	−	11.3947i	−0.0507731	−	0.505560i
$509$	12.4896	−	3.34659i	0.553593	−	0.148335i	0.0288320	−	0.999584i	$-0.490821\pi$
$509$	12.4896	−	3.34659i	0.553593	−	0.148335i	0.524761	+	0.851249i	$0.324155\pi$
$510$	0.0165713	+	0.0409224i	0.000733788	+	0.00181208i
$511$	−2.63819	−	4.56947i	−0.116706	−	0.202142i
$512$	21.3697	+	7.43868i	0.944418	+	0.328746i
$513$	6.48734	+	29.1829i	0.286423	+	1.28846i
$514$	31.8234	−	10.2587i	1.40367	−	0.452494i
$515$	0.00770471	−	0.0287544i	0.000339510	−	0.00126707i
$516$	11.1374	+	13.3142i	0.490295	+	0.586124i
$517$	−1.28734	−	4.80444i	−0.0566174	−	0.211299i
$518$	−1.89353	+	1.22346i	−0.0831971	+	0.0537557i
$519$	−23.1074	−	34.0300i	−1.01430	−	1.49375i
$520$	−0.172328	−	0.0193223i	−0.00755710	−	0.000847339i
$521$			1.24885i			0.0547130i	0.999626	+	0.0273565i	$0.00870893\pi$
$521$			1.24885i			0.0547130i	−0.999626	+	0.0273565i	$0.991291\pi$
$522$	−8.62792	−	9.84768i	−0.377634	−	0.431021i
$523$	9.58031	−	9.58031i	0.418918	−	0.418918i	−0.465913	−	0.884831i	$-0.654274\pi$
$523$	9.58031	−	9.58031i	0.418918	−	0.418918i	0.884831	+	0.465913i	$0.154274\pi$
$524$	4.81058	+	12.7074i	0.210151	+	0.555125i
$525$	−3.47387	−	9.98811i	−0.151612	−	0.435917i
$526$	−35.5416	−	7.64056i	−1.54969	−	0.333144i
$527$	−4.51656	+	7.82292i	−0.196745	+	0.340772i
$528$	9.17941	−	9.38930i	0.399483	−	0.408617i
$529$	6.57248	+	11.3839i	0.285760	+	0.494951i
$530$	−0.0637143	−	0.197647i	−0.00276757	−	0.00858523i
$531$	25.0555	−	10.8193i	1.08732	−	0.469518i
$532$	2.26226	−	13.8678i	0.0980813	−	0.601247i
$533$	−18.7735	−	5.03034i	−0.813169	−	0.217888i
$534$	−3.21773	−	26.0367i	−0.139245	−	1.12672i
$535$	0.0504047	+	0.0291012i	0.00217918	+	0.00125815i
$536$	12.6916	−	32.3893i	0.548195	−	1.39900i
$537$	−27.9695	+	2.04299i	−1.20697	+	0.0881616i
$538$	−1.36962	−	27.3439i	−0.0590485	−	1.17888i
$539$	−7.38278	+	7.38278i	−0.317999	+	0.317999i
$540$	−0.118908	−	0.0246940i	−0.00511697	−	0.00106266i
$541$	13.0165	+	13.0165i	0.559622	+	0.559622i	0.929200	−	0.369578i	$-0.120498\pi$
$541$	13.0165	+	13.0165i	0.559622	+	0.559622i	−0.369578	+	0.929200i	$0.620498\pi$
$542$	−7.45678	−	6.74541i	−0.320296	−	0.289740i
$543$	−0.537699	−	7.36135i	−0.0230749	−	0.315906i
$544$	7.50513	+	4.44960i	0.321780	+	0.190775i
$545$	−0.0259743	+	0.0449887i	−0.00111262	+	0.00192711i
$546$	9.65156	−	12.3735i	0.413049	−	0.529538i
$547$	2.61540	−	9.76080i	0.111826	−	0.417341i	−0.887204	−	0.461378i	$-0.847355\pi$
$547$	2.61540	−	9.76080i	0.111826	−	0.417341i	0.999030	+	0.0440366i	$0.0140218\pi$
$548$	−4.92199	−	6.84086i	−0.210257	−	0.292227i
$549$	−37.3878	−	4.35545i	−1.59567	−	0.185886i
$550$	11.9265	+	6.11167i	0.508550	+	0.260602i
$551$	15.3760	−	8.87733i	0.655039	−	0.378187i
$552$	−8.71926	+	28.1328i	−0.371116	+	1.19741i
$553$	0.553890	+	0.319788i	0.0235538	+	0.0135988i
$554$	−17.2559	−	26.7068i	−0.733133	−	1.13466i
$555$	−0.0249567	+	0.00867994i	−0.00105935	+	0.000368443i
$556$	30.3090	−	11.4740i	1.28539	−	0.486604i
$557$	26.6259	+	26.6259i	1.12818	+	1.12818i	0.990474	+	0.137702i	$0.0439715\pi$
$557$	26.6259	+	26.6259i	1.12818	+	1.12818i	0.137702	+	0.990474i	$0.456029\pi$
$558$	−10.9792	−	22.2903i	−0.464786	−	0.943622i
$559$	−26.2889			−1.11190
$560$	0.0475821	+	0.0315298i	0.00201071	+	0.00133238i
$561$	4.18879	−	2.84431i	0.176851	−	0.120087i
$562$	31.6034	+	6.79395i	1.33311	+	0.286585i
$563$	−21.1660	+	5.67141i	−0.892039	+	0.239021i	−0.675594	−	0.737274i	$-0.736113\pi$
$563$	−21.1660	+	5.67141i	−0.892039	+	0.239021i	−0.216445	+	0.976295i	$0.569446\pi$
$564$	−0.806150	+	9.05526i	−0.0339450	+	0.381295i
$565$	0.178552	+	0.0478429i	0.00751174	+	0.00201276i
$566$	−3.98600	+	7.77843i	−0.167544	+	0.326952i
$567$	7.53575	−	7.99973i	0.316472	−	0.335957i
$568$	32.4112	+	23.8935i	1.35994	+	1.00255i
$569$	8.15901	−	4.71061i	0.342044	−	0.197479i	−0.319132	−	0.947710i	$-0.603391\pi$
$569$	8.15901	−	4.71061i	0.342044	−	0.197479i	0.661175	+	0.750231i	$0.270058\pi$
$570$	0.0642295	−	0.151647i	0.00269028	−	0.00635180i
$571$	7.61666	+	28.4258i	0.318747	+	1.18958i	0.920450	+	0.390861i	$0.127823\pi$
$571$	7.61666	+	28.4258i	0.318747	+	1.18958i	−0.601702	+	0.798720i	$0.705511\pi$
$572$	1.98721	+	19.7871i	0.0830894	+	0.827340i
$573$	7.67950	+	1.46805i	0.320816	+	0.0613285i
$574$	4.74445	+	4.29183i	0.198029	+	0.179138i
$575$	−30.0595			−1.25357
$576$	−21.6512	+	10.3550i	−0.902132	+	0.431459i
$577$	−42.9309			−1.78724			−0.893618	−	0.448828i	$-0.851842\pi$
$577$	−42.9309			−1.78724			−0.893618	+	0.448828i	$0.851842\pi$
$578$	−15.3342	−	13.8713i	−0.637818	−	0.576971i
$579$	−2.00044	−	5.75170i	−0.0831355	−	0.239033i
$580$	0.00720727	+	0.0717645i	0.000299266	+	0.00297986i
$581$	3.56071	+	13.2888i	0.147723	+	0.551310i
$582$	−25.9371	−	34.3634i	−1.07513	−	1.42441i
$583$	−20.6244	+	11.9075i	−0.854175	+	0.493158i
$584$	−9.83721	−	7.25197i	−0.407067	−	0.300089i
$585$	0.144232	−	0.114134i	0.00596324	−	0.00471884i
$586$	−2.51559	+	4.90901i	−0.103918	+	0.202789i
$587$	30.3611	+	8.13523i	1.25314	+	0.335777i	0.823548	−	0.567247i	$-0.191992\pi$
$587$	30.3611	+	8.13523i	1.25314	+	0.335777i	0.429589	+	0.903024i	$0.358658\pi$
$588$	17.3075	−	8.03853i	0.713751	−	0.331503i
$589$	32.5470	−	8.72095i	1.34108	−	0.359340i
$590$	−0.146988	−	0.0315987i	−0.00605138	−	0.00130090i
$591$	−0.859962	−	11.7733i	−0.0353741	−	0.484288i
$592$	−2.88436	+	4.35282i	−0.118546	+	0.178900i
$593$	0.434128			0.0178275			0.00891374	−	0.999960i	$-0.497163\pi$
$593$	0.434128			0.0178275			0.00891374	+	0.999960i	$0.497163\pi$
$594$	0.0973487	+	13.9271i	0.00399427	+	0.571435i
$595$	0.0155634	+	0.0155634i	0.000638037	+	0.000638037i
$596$	−7.29025	+	2.75984i	−0.298620	+	0.113047i
$597$	6.11215	+	5.28002i	0.250154	+	0.216097i
$598$	−24.2078	−	37.4661i	−0.989929	−	1.53210i
$599$	3.46143	+	1.99846i	0.141430	+	0.0816547i	0.569045	−	0.822306i	$-0.307313\pi$
$599$	3.46143	+	1.99846i	0.141430	+	0.0816547i	−0.427615	+	0.903961i	$0.640646\pi$
$600$	−16.6361	−	17.9779i	−0.679168	−	0.733946i
$601$	−3.54563	+	2.04707i	−0.144629	+	0.0835019i	−0.570569	−	0.821250i	$-0.693277\pi$
$601$	−3.54563	+	2.04707i	−0.144629	+	0.0835019i	0.425939	+	0.904752i	$0.359944\pi$
$602$	7.70119	+	3.94642i	0.313877	+	0.160844i
$603$	14.6273	+	33.8741i	0.595669	+	1.37946i
$604$	17.5440	+	24.3836i	0.713854	+	0.992155i
$605$	0.0224057	−	0.0836192i	0.000910922	−	0.00339961i
$606$	−16.9053	−	2.36230i	−0.686731	−	0.0959620i
$607$	16.8996	−	29.2709i	0.685932	−	1.18807i	−0.287211	−	0.957867i	$-0.592728\pi$
$607$	16.8996	−	29.2709i	0.685932	−	1.18807i	0.973143	−	0.230202i	$-0.0739386\pi$
$608$	−8.05937	−	31.5322i	−0.326851	−	1.27880i
$609$	−5.87527	−	2.84304i	−0.238078	−	0.115206i
$610$	0.153775	+	0.139105i	0.00622615	+	0.00563218i
$611$	−9.73570	−	9.73570i	−0.393864	−	0.393864i
$612$	−8.97585	+	2.25296i	−0.362827	+	0.0910706i
$613$	1.73094	−	1.73094i	0.0699119	−	0.0699119i	−0.671286	−	0.741198i	$-0.734258\pi$
$613$	1.73094	−	1.73094i	0.0699119	−	0.0699119i	0.741198	+	0.671286i	$0.234258\pi$
$614$	1.08168	+	21.5952i	0.0436529	+	0.871510i
$615$	0.0421233	+	0.0620346i	0.00169858	+	0.00250147i
$616$	2.38824	−	6.09484i	0.0962251	−	0.245568i
$617$	−14.9093	−	8.60788i	−0.600225	−	0.346540i	0.168905	−	0.985632i	$-0.445977\pi$
$617$	−14.9093	−	8.60788i	−0.600225	−	0.346540i	−0.769130	+	0.639092i	$0.779310\pi$
$618$	5.74566	+	2.43354i	0.231124	+	0.0978915i
$619$	6.34645	+	1.70053i	0.255085	+	0.0683499i	0.384095	−	0.923293i	$-0.374513\pi$
$619$	6.34645	+	1.70053i	0.255085	+	0.0683499i	−0.129010	+	0.991643i	$0.541180\pi$
$620$	−0.0220381	+	0.135095i	−0.000885071	+	0.00542556i
$621$	−14.4408	−	27.7016i	−0.579490	−	1.11163i
$622$	9.78871	+	30.3653i	0.392491	+	1.21754i
$623$	−6.53931	−	11.3264i	−0.261992	−	0.453783i
$624$	9.01009	−	35.2134i	0.360692	−	1.40966i
$625$	12.4990	−	21.6489i	0.499959	−	0.865954i
$626$	−8.25771	−	1.77520i	−0.330045	−	0.0709514i
$627$	−18.5507	−	3.54624i	−0.740846	−	0.141623i
$628$	−6.94428	−	18.3437i	−0.277107	−	0.731992i
$629$	−1.42374	+	1.42374i	−0.0567684	+	0.0567684i
$630$	−0.0593853	+	0.0117832i	−0.00236597	+	0.000469453i
$631$			13.3295i			0.530639i	0.964161	+	0.265319i	$0.0854774\pi$
$631$			13.3295i			0.530639i	−0.964161	+	0.265319i	$0.914523\pi$
$632$	1.47219	+	0.165069i	0.0585606	+	0.00656610i
$633$	13.6258	−	28.1583i	0.541577	−	1.11919i
$634$	22.1098	−	14.2856i	0.878091	−	0.567355i
$635$	−0.0173188	−	0.0646345i	−0.000687274	−	0.00256494i
$636$	42.8780	−	7.49315i	1.70022	−	0.297123i
$637$	−7.48023	+	27.9166i	−0.296377	+	1.10610i
$638$	7.87249	−	2.53781i	0.311675	−	0.100473i
$639$	−42.2557	+	6.20612i	−1.67161	+	0.245510i
$640$	0.130233	+	0.0227940i	0.00514790	+	0.000901012i
$641$	8.26044	+	14.3075i	0.326268	+	0.565113i	0.981768	−	0.190082i	$-0.0608755\pi$
$641$	8.26044	+	14.3075i	0.326268	+	0.565113i	−0.655500	+	0.755195i	$0.727542\pi$
$642$	−7.50330	+	9.61940i	−0.296132	+	0.379648i
$643$	−24.0050	+	6.43213i	−0.946667	+	0.253659i	−0.698947	−	0.715173i	$-0.746348\pi$
$643$	−24.0050	+	6.43213i	−0.946667	+	0.253659i	−0.247719	+	0.968832i	$0.579681\pi$
$644$	1.46722	+	14.6095i	0.0578168	+	0.575695i
$645$	0.0767519	+	0.0663027i	0.00302210	+	0.00261067i
$646$	−0.627803	−	12.5338i	−0.0247006	−	0.493136i
$647$			26.9660i			1.06014i	0.847954	+	0.530071i	$0.177835\pi$
$647$			26.9660i			1.06014i	−0.847954	+	0.530071i	$0.822165\pi$
$648$	8.57556	−	23.9679i	0.336880	−	0.941548i
$649$			17.2418i			0.676800i
$650$	37.0499	−	1.85578i	1.45322	−	0.0727897i
$651$	−9.37378	−	8.09761i	−0.367387	−	0.317370i
$652$	−9.35535	+	11.4442i	−0.366384	+	0.448191i
$653$	5.27782	−	1.41419i	0.206537	−	0.0553414i	−0.154067	−	0.988060i	$-0.549237\pi$
$653$	5.27782	−	1.41419i	0.206537	−	0.0553414i	0.360604	+	0.932719i	$0.382571\pi$
$654$	−8.58581	−	6.69708i	−0.335732	−	0.261877i
$655$	0.0396959	+	0.0687553i	0.00155105	+	0.00268649i
$656$	14.0502	+	4.70935i	0.548569	+	0.183869i
$657$	12.8251	−	1.88364i	0.500356	−	0.0734876i
$658$	1.39053	+	4.31352i	0.0542083	+	0.168159i
$659$	−0.184661	+	0.689165i	−0.00719337	+	0.0268460i	−0.969429	−	0.245371i	$-0.921090\pi$
$659$	−0.184661	+	0.689165i	−0.00719337	+	0.0268460i	0.962236	+	0.272217i	$0.0877569\pi$
$660$	0.0441029	−	0.0627815i	0.00171670	−	0.00244377i
$661$	9.89344	+	36.9228i	0.384810	+	1.43613i	0.838466	+	0.544954i	$0.183453\pi$
$661$	9.89344	+	36.9228i	0.384810	+	1.43613i	−0.453656	+	0.891177i	$0.649880\pi$
$662$	−8.09416	−	12.5272i	−0.314588	−	0.486885i
$663$	6.10491	−	12.6161i	0.237095	−	0.489968i
$664$	19.8815	+	24.9029i	0.771551	+	0.966421i
$665$		−	0.0821010i		−	0.00318374i
$666$	−1.07793	−	5.43259i	−0.0417689	−	0.210508i
$667$	−13.1190	+	13.1190i	−0.507970	+	0.507970i
$668$	5.99314	−	13.2949i	0.231881	−	0.514397i
$669$	−9.72326	−	1.85874i	−0.375923	−	0.0718630i
$670$	0.0427202	−	0.198721i	0.00165042	−	0.00767728i
$671$	11.8899	−	20.5940i	0.459006	−	0.795022i
$672$	−7.92559	+	8.96300i	−0.305736	+	0.345755i
$673$	−6.39173	−	11.0708i	−0.246383	−	0.426748i	0.716137	−	0.697960i	$-0.245909\pi$
$673$	−6.39173	−	11.0708i	−0.246383	−	0.426748i	−0.962520	+	0.271212i	$0.912575\pi$
$674$	32.6329	−	10.5197i	1.25697	−	0.405204i
$675$	25.9560	+	1.11828i	0.999046	+	0.0430427i
$676$	16.9654	+	23.5794i	0.652514	+	0.906901i
$677$	−25.4595	−	6.82184i	−0.978487	−	0.262185i	−0.266079	−	0.963951i	$-0.585728\pi$
$677$	−25.4595	−	6.82184i	−0.978487	−	0.262185i	−0.712407	+	0.701766i	$0.752395\pi$
$678$	−15.1113	+	35.6780i	−0.580344	+	1.37021i
$679$	−18.5875	−	10.7315i	−0.713323	−	0.411837i
$680$	0.0474664	+	0.0185996i	0.00182025	+	0.000713261i
$681$	−19.8207	−	29.1897i	−0.759529	−	1.11855i
$682$	15.6780	−	0.785293i	0.600343	−	0.0300704i
$683$	9.42670	−	9.42670i	0.360703	−	0.360703i	−0.503369	−	0.864072i	$-0.667906\pi$
$683$	9.42670	−	9.42670i	0.360703	−	0.360703i	0.864072	+	0.503369i	$0.167906\pi$
$684$	29.6175	+	17.7325i	1.13245	+	0.678020i
$685$	−0.0348195	−	0.0348195i	−0.00133039	−	0.00133039i
$686$	14.4916	−	16.0199i	0.553293	−	0.611643i
$687$	5.98065	+	2.89404i	0.228176	+	0.110414i
$688$	20.0055	+	1.23413i	0.762703	+	0.0470509i
$689$	−32.9613	+	57.0906i	−1.25572	+	2.17498i
$690$	−0.0238166	+	0.170438i	−0.000906683	+	0.00648848i
$691$	4.07041	−	15.1910i	0.154846	−	0.577891i	−0.844273	−	0.535913i	$-0.819967\pi$
$691$	4.07041	−	15.1910i	0.154846	−	0.577891i	0.999119	−	0.0419780i	$-0.0133660\pi$
$692$	−46.8776	−	7.64714i	−1.78202	−	0.290700i
$693$	2.75248	+	6.37425i	0.104558	+	0.242138i
$694$	−12.3990	+	24.1958i	−0.470659	+	0.918462i
$695$	0.163992	−	0.0946807i	0.00622056	−	0.00359144i
$696$	−15.1068	−	0.585597i	−0.572620	−	0.0221970i
$697$	4.94841	+	2.85696i	0.187434	+	0.108215i
$698$	−19.2360	+	12.4288i	−0.728091	+	0.470437i
$699$	6.98666	+	6.03547i	0.264260	+	0.228283i
$700$	−11.1321	−	5.01818i	−0.420756	−	0.189670i
$701$	9.62303	+	9.62303i	0.363457	+	0.363457i	0.865084	−	0.501627i	$-0.167265\pi$
$701$	9.62303	+	9.62303i	0.363457	+	0.363457i	−0.501627	+	0.865084i	$0.667265\pi$
$702$	19.5092	+	33.2520i	0.736328	+	1.25502i
$703$	7.51063			0.283269
$704$	−0.583333	−	15.1510i	−0.0219852	−	0.571026i
$705$	0.00386971	+	0.0529782i	0.000145742	+	0.00199527i
$706$	4.57372	−	21.2756i	0.172134	−	0.800717i
$707$	−8.21961	+	2.20244i	−0.309130	+	0.0828312i
$708$	10.8235	−	29.5967i	0.406771	−	1.11231i
$709$	40.3893	+	10.8223i	1.51685	+	0.406439i	0.918704	−	0.394947i	$-0.129237\pi$
$709$	40.3893	+	10.8223i	1.51685	+	0.406439i	0.598148	+	0.801386i	$0.295904\pi$
$710$	0.209386	+	0.107298i	0.00785812	+	0.00402683i
$711$	−1.23216	+	0.975036i	−0.0462097	+	0.0365667i
$712$	−24.3836	−	17.9756i	−0.913816	−	0.673663i
$713$	−30.4931	+	17.6052i	−1.14197	+	0.659319i
$714$	−3.68229	+	2.77936i	−0.137806	+	0.104015i
$715$	0.0300742	+	0.112239i	0.00112471	+	0.00419749i
$716$	−20.4951	+	25.0713i	−0.765938	+	0.936959i
$717$	−15.7470	−	45.2759i	−0.588081	−	1.69086i
$718$	−2.82608	+	3.12412i	−0.105468	+	0.116591i
$719$	48.7757			1.81903			0.909514	−	0.415674i	$-0.136454\pi$
$719$	48.7757			1.81903			0.909514	+	0.415674i	$0.136454\pi$
$720$	−0.115116	+	0.0800833i	−0.00429014	+	0.00298453i
$721$	3.11067			0.115847
$722$	−13.3780	+	14.7888i	−0.497876	+	0.550382i
$723$	−2.88260	−	0.551050i	−0.107205	−	0.0204938i
$724$	−6.59858	−	5.39416i	−0.245234	−	0.200472i
$725$	−3.99343	−	14.9037i	−0.148312	−	0.553509i
$726$	16.7087	+	7.07688i	0.620117	+	0.262648i
$727$	−34.9918	+	20.2025i	−1.29777	+	0.749270i	−0.980019	−	0.198902i	$-0.936262\pi$
$727$	−34.9918	+	20.2025i	−1.29777	+	0.749270i	−0.317755	+	0.948173i	$0.602929\pi$
$728$	−2.71037	−	17.9164i	−0.100453	−	0.664024i
$729$	11.4389	+	24.4571i	0.423662	+	0.905820i
$730$	−0.0635513	−	0.0325664i	−0.00235214	−	0.00120534i
$731$	7.46535	+	2.00033i	0.276116	+	0.0739850i
$732$	−33.3377	+	27.8871i	−1.23220	+	1.03074i
$733$	−28.4006	+	7.60991i	−1.04900	+	0.281078i	−0.741838	−	0.670579i	$-0.766046\pi$
$733$	−28.4006	+	7.60991i	−1.04900	+	0.281078i	−0.307161	+	0.951658i	$0.599379\pi$
$734$	−7.46552	+	34.7273i	−0.275557	+	1.28181i
$735$	0.0922468	−	0.0626383i	0.00340257	−	0.00231045i
$736$	16.6630	+	29.6477i	0.614205	+	1.09283i
$737$	−23.3102			−0.858644
$738$	−14.0998	+	6.94492i	−0.519019	+	0.255646i
$739$	15.4222	+	15.4222i	0.567316	+	0.567316i	0.931376	−	0.364060i	$-0.118610\pi$
$739$	15.4222	+	15.4222i	0.567316	+	0.567316i	−0.364060	+	0.931376i	$0.618610\pi$
$740$	−0.0125386	+	0.0278152i	−0.000460929	+	0.00102251i
$741$	−49.3791	+	17.1740i	−1.81399	+	0.630904i
$742$	18.2261	−	11.7763i	0.669102	−	0.432323i
$743$	−21.5896	−	12.4647i	−0.792045	−	0.457287i	0.0486373	−	0.998817i	$-0.484512\pi$
$743$	−21.5896	−	12.4647i	−0.792045	−	0.457287i	−0.840682	+	0.541529i	$0.817845\pi$
$744$	−27.4054	−	8.49380i	−1.00473	−	0.311398i
$745$	−0.0394451	+	0.0227736i	−0.00144515	+	0.000834361i
$746$	−19.2329	+	37.5319i	−0.704167	+	1.37414i
$747$	−33.5718	−	3.91091i	−1.22833	−	0.143093i
$748$	0.941295	−	5.77022i	0.0344172	−	0.210980i
$749$	−1.57409	+	5.87459i	−0.0575161	+	0.214653i
$750$	−0.225702	−	0.176052i	−0.00824148	−	0.00642850i
$751$	−21.2809	+	36.8596i	−0.776551	+	1.34503i	0.157368	+	0.987540i	$0.449699\pi$
$751$	−21.2809	+	36.8596i	−0.776551	+	1.34503i	−0.933919	+	0.357486i	$0.883634\pi$
$752$	6.95171	+	7.86579i	0.253503	+	0.286836i
$753$	0.176299	+	2.41362i	0.00642470	+	0.0879571i
$754$	15.3599	−	16.9797i	0.559374	−	0.618366i
$755$	0.124111	+	0.124111i	0.00451686	+	0.00451686i
$756$	−0.723422	−	12.6697i	−0.0263106	−	0.460792i
$757$	1.80855	−	1.80855i	0.0657328	−	0.0657328i	−0.673476	−	0.739209i	$-0.735200\pi$
$757$	1.80855	−	1.80855i	0.0657328	−	0.0657328i	0.739209	+	0.673476i	$0.235200\pi$
$758$	20.3715	−	1.02038i	0.739927	−	0.0370621i
$759$	19.6835	−	1.43775i	0.714467	−	0.0521872i
$760$	−0.0761402	−	0.174258i	−0.00276189	−	0.00632099i
$761$	18.5805	+	10.7275i	0.673543	+	0.388870i	0.797418	−	0.603428i	$-0.206199\pi$
$761$	18.5805	+	10.7275i	0.673543	+	0.388870i	−0.123875	+	0.992298i	$0.539532\pi$
$762$	13.9200	−	1.72029i	0.504267	−	0.0623196i
$763$	−5.24337	−	1.40496i	−0.189823	−	0.0508629i
$764$	7.32835	−	5.27274i	0.265130	−	0.190761i
$765$	−0.0496424	+	0.0214363i	−0.00179482	+	0.000775029i
$766$	28.4679	−	9.17705i	1.02859	−	0.331580i
$767$	23.8636	+	41.3330i	0.861665	+	1.49245i
$768$	−8.50966	+	26.3740i	−0.307066	+	0.951688i
$769$	−9.98382	+	17.2925i	−0.360026	+	0.623583i	−0.987965	−	0.154680i	$-0.950565\pi$
$769$	−9.98382	+	17.2925i	−0.360026	+	0.623583i	0.627939	+	0.778263i	$0.283899\pi$
$770$	0.00803886	−	0.0373944i	0.000289701	−	0.00134760i
$771$	13.4522	+	38.6781i	0.484471	+	1.39296i
$772$	−6.41050	−	2.88974i	−0.230719	−	0.104004i
$773$	24.8049	−	24.8049i	0.892171	−	0.892171i	−0.102557	−	0.994727i	$-0.532702\pi$
$773$	24.8049	−	24.8049i	0.892171	−	0.892171i	0.994727	+	0.102557i	$0.0327022\pi$
$774$	−15.9903	+	14.0097i	−0.574760	+	0.503569i
$775$		−	29.2823i		−	1.05185i
$776$	−49.4040	−	5.53942i	−1.77350	−	0.198853i
$777$	−1.55106	−	2.28423i	−0.0556439	−	0.0819463i
$778$	24.1141	+	37.3211i	0.864531	+	1.33803i
$779$	−5.51646	−	20.5877i	−0.197648	−	0.737631i
$780$	0.0188328	−	0.211544i	0.000674323	−	0.00757449i
$781$	6.98342	−	26.0625i	0.249886	−	0.932589i
$782$	4.02355	+	12.4814i	0.143882	+	0.446332i
$783$	11.8161	−	10.8400i	0.422274	−	0.387391i
$784$	7.00291	−	20.8930i	0.250104	−	0.746179i
$785$	−0.0573027	−	0.0992512i	−0.00204522	−	0.00354243i
$786$	−15.4245	+	6.24605i	−0.550174	+	0.222789i
$787$	10.3344	−	2.76911i	0.368383	−	0.0987080i	−0.0698783	−	0.997556i	$-0.522261\pi$
$787$	10.3344	−	2.76911i	0.368383	−	0.0987080i	0.438261	+	0.898848i	$0.355594\pi$
$788$	−10.5533	−	8.62706i	−0.375947	−	0.307326i
$789$	8.35998	−	43.7319i	0.297623	−	1.55690i
$790$	0.00864510		0.000433022i	0.000307579		1.54062e-5i
$791$			19.3159i			0.686794i
$792$	11.7535	+	10.9766i	0.417644	+	0.390035i
$793$		−	65.8254i		−	2.33753i
$794$	−0.324282	−	6.47414i	−0.0115083	−	0.229759i
$795$	0.240219	−	0.0835483i	0.00851971	−	0.00296315i
$796$	9.27977	−	0.931962i	0.328913	−	0.0330325i
$797$	46.8027	−	12.5408i	1.65784	−	0.444216i	0.696046	−	0.717997i	$-0.254941\pi$
$797$	46.8027	−	12.5408i	1.65784	−	0.444216i	0.961792	+	0.273781i	$0.0882744\pi$
$798$	17.0435	+	2.38161i	0.603332	+	0.0843080i
$799$	2.02389	+	3.50547i	0.0716000	+	0.124015i
$800$	−28.2816	−	0.327083i	−0.999906	−	0.0115641i
$801$	31.7898	−	4.66900i	1.12324	−	0.164971i
$802$	−28.9200	+	9.32279i	−1.02120	+	0.329199i
$803$	−2.11956	+	7.91029i	−0.0747975	+	0.279148i
$804$	40.0136	+	14.6329i	1.41117	+	0.516063i
$805$	0.0222048	+	0.0828696i	0.000782618	+	0.00292077i
$806$	36.4973	−	23.5818i	1.28556	−	0.830634i
$807$	33.4421	−	2.44273i	1.17722	−	0.0859883i
$808$	−15.4034	+	12.2975i	−0.541890	+	0.432623i
$809$			51.3577i			1.80564i	0.430019	+	0.902820i	$0.358507\pi$
$809$			51.3577i			1.80564i	−0.430019	+	0.902820i	$0.641493\pi$
$810$	0.0269060	−	0.146285i	0.000945380	−	0.00513993i
$811$	−2.55652	+	2.55652i	−0.0897715	+	0.0897715i	−0.750566	−	0.660795i	$-0.770219\pi$
$811$	−2.55652	+	2.55652i	−0.0897715	+	0.0897715i	0.660795	+	0.750566i	$0.270219\pi$
$812$	−7.04855	+	2.66834i	−0.247356	+	0.0936405i
$813$	8.05043	−	9.31917i	0.282341	−	0.326837i
$814$	3.42085	+	0.735398i	0.119901	+	0.0257757i
$815$	−0.0431843	+	0.0747975i	−0.00151268	+	0.00262004i
$816$	−5.23803	+	9.31408i	−0.183368	+	0.326058i
$817$	−14.4147	−	24.9670i	−0.504306	−	0.873484i
$818$	−11.5951	−	35.9690i	−0.405414	−	1.25763i
$819$	15.4207	+	11.4711i	0.538844	+	0.400833i
$820$	0.0854549	+	0.0139403i	0.00298422	+	0.000486815i
$821$	0.179113	+	0.0479933i	0.00625110	+	0.00167498i	0.261943	−	0.965083i	$-0.415637\pi$
$821$	0.179113	+	0.0479933i	0.00625110	+	0.00167498i	−0.255692	+	0.966758i	$0.582303\pi$
$822$	8.23829	−	6.21818i	0.287343	−	0.216884i
$823$	−16.8590	−	9.73353i	−0.587667	−	0.339290i	0.176508	−	0.984299i	$-0.443520\pi$
$823$	−16.8590	−	9.73353i	−0.587667	−	0.339290i	−0.764174	+	0.645010i	$0.776853\pi$
$824$	6.60233	−	2.88482i	0.230003	−	0.100497i
$825$	−7.14928	+	14.7743i	−0.248906	+	0.514375i
$826$	−0.785924	−	15.6906i	−0.0273458	−	0.545947i
$827$	7.70731	−	7.70731i	0.268009	−	0.268009i	−0.560288	−	0.828298i	$-0.689310\pi$
$827$	7.70731	−	7.70731i	0.268009	−	0.268009i	0.828298	+	0.560288i	$0.189310\pi$
$828$	−34.6906	−	9.88824i	−1.20558	−	0.343640i
$829$	−23.8166	−	23.8166i	−0.827184	−	0.827184i	0.159942	−	0.987126i	$-0.448869\pi$
$829$	−23.8166	−	23.8166i	−0.827184	−	0.827184i	−0.987126	+	0.159942i	$0.948869\pi$
$830$	0.138079	+	0.124907i	0.00479280	+	0.00433557i
$831$	32.2172	−	21.8765i	1.11760	−	0.758886i
$832$	−22.3683	−	35.5135i	−0.775480	−	1.23121i
$833$	4.24837	−	7.35839i	0.147197	−	0.254953i
$834$	14.8978	+	36.7898i	0.515868	+	1.27393i
$835$	0.0220541	−	0.0823071i	0.000763214	−	0.00284835i
$836$	−17.7025	+	12.7369i	−0.612254	+	0.440516i
$837$	26.9853	−	14.0674i	0.932748	−	0.486241i
$838$	−11.5182	−	5.90243i	−0.397891	−	0.203896i
$839$	18.6769	−	10.7831i	0.644799	−	0.372275i	−0.141662	−	0.989915i	$-0.545245\pi$
$839$	18.6769	−	10.7831i	0.644799	−	0.372275i	0.786461	+	0.617640i	$0.211911\pi$
$840$	−0.0372734	+	0.0591436i	−0.00128605	+	0.00204065i
$841$	16.8674	+	9.73839i	0.581634	+	0.335807i
$842$	−22.9903	−	35.5818i	−0.792296	−	1.22623i
$843$	−7.43366	+	38.8862i	−0.256029	+	1.33931i
$844$	−12.7885	−	33.7815i	−0.440199	−	1.16281i
$845$	0.120018	+	0.120018i	0.00412873	+	0.00412873i
$846$	−11.1101	−	0.733486i	−0.381972	−	0.0252178i
$847$	9.04599			0.310824
$848$	27.7633	−	41.8979i	0.953394	−	1.43878i
$849$	−9.63573	−	4.66273i	−0.330697	−	0.160024i
$850$	−10.6624	−	2.29215i	−0.365717	−	0.0786200i
$851$	−7.58094	+	2.03131i	−0.259871	+	0.0696323i
$852$	−28.3481	+	40.3542i	−0.971190	+	1.38251i
$853$	38.5967	+	10.3419i	1.32153	+	0.354102i	0.849549	−	0.527510i	$-0.176874\pi$
$853$	38.5967	+	10.3419i	1.32153	+	0.354102i	0.471976	+	0.881611i	$0.343541\pi$
$854$	−9.88153	+	19.2832i	−0.338139	+	0.659857i
$855$	0.187479	+	0.0743974i	0.00641166	+	0.00254434i
$856$	2.10709	+	13.9285i	0.0720190	+	0.476067i
$857$	14.5777	−	8.41643i	0.497964	−	0.287500i	−0.229908	−	0.973212i	$-0.573843\pi$
$857$	14.5777	−	8.41643i	0.497964	−	0.287500i	0.727872	+	0.685713i	$0.240509\pi$
$858$	−24.1722	+	2.98730i	−0.825224	+	0.101985i
$859$	−5.55582	−	20.7346i	−0.189562	−	0.707455i	−0.993608	−	0.112888i	$-0.963990\pi$
$859$	−5.55582	−	20.7346i	−0.189562	−	0.707455i	0.804046	−	0.594568i	$-0.202677\pi$
$860$	0.116529	−	0.0117029i	0.00397359	−	0.000399066i
$861$	−5.12216	+	5.92941i	−0.174563	+	0.202074i
$862$	−7.39956	−	6.69365i	−0.252030	−	0.227987i
$863$	20.3421			0.692455			0.346227	−	0.938151i	$-0.387463\pi$
$863$	20.3421			0.692455			0.346227	+	0.938151i	$0.387463\pi$
$864$	−13.2853	−	26.2203i	−0.451974	−	0.892031i
$865$	−0.277527			−0.00943620
$866$	13.7969	+	12.4807i	0.468837	+	0.424110i
$867$	16.5550	−	19.1640i	0.562236	−	0.650844i
$868$	−14.2317	+	1.42929i	−0.483057	+	0.0485132i
$869$	−0.256922	−	0.958848i	−0.00871550	−	0.0325267i
$870$	−0.0876684	+	0.0108345i	−0.00297224	+	0.000367322i
$871$	−55.8806	+	32.2627i	−1.89344	+	1.09318i
$872$	−12.4319	+	1.88069i	−0.420997	+	0.0636882i
$873$	41.3490	−	32.7204i	1.39945	−	1.10742i
$874$	22.3086	−	43.5339i	0.754599	−	1.47255i
$875$	−0.137837	−	0.0369333i	−0.00465974	−	0.00124857i
$876$	8.60401	−	12.2480i	0.290703	−	0.413822i
$877$	−18.6156	+	4.98805i	−0.628606	+	0.168434i	−0.559037	−	0.829143i	$-0.688829\pi$
$877$	−18.6156	+	4.98805i	−0.628606	+	0.168434i	−0.0695688	+	0.997577i	$0.522162\pi$
$878$	−20.5563	−	4.41911i	−0.693743	−	0.149138i
$879$	−6.08116	−	2.94267i	−0.205113	−	0.0992539i
$880$	−0.0176171	−	0.0868240i	−0.000593871	−	0.00292684i
$881$	37.3378			1.25794			0.628972	−	0.777428i	$-0.283476\pi$
$881$	37.3378			1.25794			0.628972	+	0.777428i	$0.283476\pi$
$882$	10.3273	+	20.9667i	0.347737	+	0.705985i
$883$	−16.7468	−	16.7468i	−0.563576	−	0.563576i	0.366745	−	0.930321i	$-0.380472\pi$
$883$	−16.7468	−	16.7468i	−0.563576	−	0.563576i	−0.930321	+	0.366745i	$0.880472\pi$
$884$	−5.72978	−	15.1355i	−0.192713	−	0.509062i
$885$	0.0345740	−	0.180860i	0.00116219	−	0.00607954i
$886$	−2.36524	−	3.66066i	−0.0794619	−	0.122982i
$887$	36.4841	+	21.0641i	1.22502	+	0.707263i	0.965983	−	0.258606i	$-0.0832630\pi$
$887$	36.4841	+	21.0641i	1.22502	+	0.707263i	0.259033	+	0.965869i	$0.416596\pi$
$888$	−5.41048	−	3.40978i	−0.181564	−	0.114425i
$889$	6.05543	−	3.49611i	0.203093	−	0.117256i
$890$	−0.157526	−	0.0807228i	−0.00528027	−	0.00270583i
$891$	−17.0499	+	0.509210i	−0.571194	+	0.0170592i
$892$	−9.27866	+	6.67598i	−0.310673	+	0.223528i
$893$	3.90788	−	14.5844i	0.130772	−	0.488049i
$894$	−3.58337	−	8.84908i	−0.119846	−	0.295957i
$895$	−0.0946055	+	0.163862i	−0.00316231	+	0.00547729i
$896$	1.22148	+	13.7614i	0.0408066	+	0.459735i
$897$	45.1965	−	30.6898i	1.50907	−	1.02470i
$898$	−22.9210	−	20.7343i	−0.764882	−	0.691913i
$899$	−12.7798	−	12.7798i	−0.426229	−	0.426229i
$900$	21.5467	−	20.8732i	0.718225	−	0.695772i
$901$	13.7042	−	13.7042i	0.456552	−	0.456552i
$902$	−0.496739	−	9.91717i	−0.0165396	−	0.330206i
$903$	−4.61643	+	9.54004i	−0.153625	+	0.317473i
$904$	17.9135	+	40.9976i	0.595793	+	1.36356i
$905$	−0.0431271	−	0.0248994i	−0.00143359	−	0.000827685i
$906$	−29.3646	+	22.1641i	−0.975573	+	0.736353i
$907$	1.02635	+	0.275009i	0.0340794	+	0.00913154i	0.275818	−	0.961210i	$-0.411051\pi$
$907$	1.02635	+	0.275009i	0.0340794	+	0.00913154i	−0.241739	+	0.970341i	$0.577718\pi$
$908$	−40.2099	−	6.55943i	−1.33441	−	0.217682i
$909$	2.41905	−	20.7654i	0.0802347	−	0.688746i
$910$	−0.0324847	−	0.100770i	−0.00107686	−	0.00334050i
$911$	1.91307	+	3.31354i	0.0633829	+	0.109782i	0.895976	−	0.444103i	$-0.146478\pi$
$911$	1.91307	+	3.31354i	0.0633829	+	0.109782i	−0.832593	+	0.553886i	$0.813144\pi$
$912$	38.3831	−	10.7511i	1.27099	−	0.356005i
$913$	10.6764	−	18.4920i	0.353336	−	0.611996i
$914$	−3.70809	−	0.797148i	−0.122653	−	0.0263673i
$915$	−0.166017	+	0.192181i	−0.00548835	+	0.00635330i
$916$	7.17499	−	2.71621i	0.237068	−	0.0897460i
$917$	−5.86616	+	5.86616i	−0.193718	+	0.193718i
$918$	−3.00994	−	10.9272i	−0.0993429	−	0.360650i
$919$		−	5.73779i		−	0.189272i	−0.995512	−	0.0946361i	$-0.969831\pi$
$919$		−	5.73779i		−	0.189272i	0.995512	−	0.0946361i	$-0.0301688\pi$
$920$	0.123982	+	0.155296i	0.00408758	+	0.00511997i
$921$	−26.4114	+	1.92918i	−0.870284	+	0.0635687i
$922$	12.6139	−	8.15011i	0.415415	−	0.268410i
$923$	−19.3309	−	72.1438i	−0.636284	−	2.37464i
$924$	7.52956	+	2.75355i	0.247704	+	0.0905850i
$925$	1.68931	−	6.30460i	0.0555442	−	0.207294i
$926$	31.8328	−	10.2618i	1.04609	−	0.337222i
$927$	−2.81879	+	7.10327i	−0.0925813	+	0.233302i
$928$	−12.4858	+	12.2003i	−0.409867	+	0.400495i
$929$	−20.2911	−	35.1451i	−0.665728	−	1.15307i	−0.979087	−	0.203440i	$-0.934788\pi$
$929$	−20.2911	−	35.1451i	−0.665728	−	1.15307i	0.313359	−	0.949635i	$-0.398546\pi$
$930$	−0.166031	−	0.0232008i	−0.00544438	−	0.000760784i
$931$	−30.6144	+	8.20310i	−1.00335	+	0.268846i
$932$	10.6075	−	1.06531i	0.347460	−	0.0348952i
$933$	−36.9060	+	12.8359i	−1.20825	+	0.420228i
$934$	0.222656	+	4.44522i	0.00728552	+	0.145452i
$935$		−	0.0341611i		−	0.00111719i
$936$	43.3684	+	10.0461i	1.41754	+	0.328366i
$937$			27.9974i			0.914635i	0.889304	+	0.457317i	$0.151190\pi$
$937$			27.9974i			0.914635i	−0.889304	+	0.457317i	$0.848810\pi$
$938$	21.2131	−	1.06254i	0.692633	−	0.0346931i
$939$	1.94235	−	10.1607i	0.0633863	−	0.331581i
$940$	0.0474886	+	0.0388206i	0.00154891	+	0.00126619i
$941$	−36.1343	+	9.68215i	−1.17794	+	0.315629i	−0.794111	−	0.607773i	$-0.792063\pi$
$941$	−36.1343	+	9.68215i	−1.17794	+	0.315629i	−0.383833	+	0.923402i	$0.625396\pi$
$942$	22.2660	−	9.01645i	0.725464	−	0.293772i
$943$	11.1362	+	19.2885i	0.362645	+	0.628119i
$944$	−16.2195	−	32.5742i	−0.527901	−	1.06020i
$945$	−0.0160906	−	0.0723828i	−0.000523429	−	0.00235461i
$946$	−4.12081	−	12.7831i	−0.133979	−	0.415613i
$947$	−4.92887	+	18.3948i	−0.160167	+	0.597751i	0.838441	+	0.544993i	$0.183468\pi$
$947$	−4.92887	+	18.3948i	−0.160167	+	0.597751i	−0.998607	+	0.0527575i	$0.983199\pi$
$948$	−0.160888	+	1.80721i	−0.00522539	+	0.0586954i
$949$	5.86717	+	21.8966i	0.190456	+	0.710793i
$950$	22.0776	+	34.1693i	0.716292	+	1.10860i
$951$	18.1109	+	26.6717i	0.587285	+	0.864888i
$952$	−0.593590	+	5.29400i	−0.0192384	+	0.171580i
$953$		−	2.49861i		−	0.0809380i	−0.999181	−	0.0404690i	$-0.987115\pi$
$953$		−	2.49861i		−	0.0809380i	0.999181	−	0.0404690i	$-0.0128852\pi$
$954$	10.3756	+	52.2911i	0.335921	+	1.69299i
$955$	0.0373008	−	0.0373008i	0.00120703	−	0.00120703i
$956$	−50.4618	−	22.7473i	−1.63205	−	0.735701i
$957$	3.32782	+	9.56820i	0.107573	+	0.309296i
$958$	3.70882	−	17.2523i	0.119826	−	0.557397i
$959$	2.57277	−	4.45617i	0.0830792	−	0.143897i
$960$	−0.0242625	+	0.160098i	−0.000783069	+	0.00516715i
$961$	−1.64996	−	2.85782i	−0.0532246	−	0.0921877i
$962$	9.21848	−	2.97171i	0.297216	−	0.0958118i
$963$	−11.9884	−	8.91785i	−0.386319	−	0.287374i
$964$	−2.75079	+	1.97919i	−0.0885970	+	0.0637454i
$965$	−0.0396865	−	0.0106340i	−0.00127755	−	0.000342319i
$966$	−17.8471	+	2.20563i	−0.574222	+	0.0709650i
$967$	−3.08638	−	1.78192i	−0.0992513	−	0.0573028i	0.449553	−	0.893254i	$-0.351583\pi$
$967$	−3.08638	−	1.78192i	−0.0992513	−	0.0573028i	−0.548804	+	0.835951i	$0.684917\pi$
$968$	19.1999	−	8.38922i	0.617109	−	0.269640i
$969$	15.3291	−	1.11969i	0.492442	−	0.0359698i
$970$	−0.290113	+	0.0145314i	−0.00931498	+	0.000466576i
$971$	−0.578866	+	0.578866i	−0.0185767	+	0.0185767i	−0.716334	−	0.697757i	$-0.754181\pi$
$971$	−0.578866	+	0.578866i	−0.0185767	+	0.0185767i	0.697757	+	0.716334i	$0.254181\pi$
$972$	29.5870	+	9.82893i	0.949004	+	0.315263i
$973$	13.9917	+	13.9917i	0.448553	+	0.448553i
$974$	11.8888	−	13.1426i	0.380943	−	0.421117i
$975$	3.30981	+	45.3128i	0.105999	+	1.45117i
$976$	−3.09018	+	50.0923i	−0.0989142	+	1.60342i
$977$	10.3841	−	17.9859i	0.332218	−	0.575418i	−0.650728	−	0.759310i	$-0.725536\pi$
$977$	10.3841	−	17.9859i	0.332218	−	0.575418i	0.982946	+	0.183892i	$0.0588697\pi$
$978$	−14.2746	−	11.1344i	−0.456452	−	0.356040i
$979$	−5.25377	+	19.6074i	−0.167911	+	0.626654i
$980$	0.0207295	−	0.127073i	0.000662179	−	0.00405921i
$981$	7.95963	−	10.7002i	0.254132	−	0.341632i
$982$	9.80845	−	19.1406i	0.313000	−	0.610801i
$983$	9.13353	−	5.27325i	0.291314	−	0.168190i	−0.347220	−	0.937784i	$-0.612874\pi$
$983$	9.13353	−	5.27325i	0.291314	−	0.168190i	0.638534	+	0.769593i	$0.279541\pi$
$984$	−5.37278	+	17.3353i	−0.171278	+	0.552630i
$985$	−0.0689747	−	0.0398225i	−0.00219772	−	0.00126885i
$986$	−5.65380	+	3.65306i	−0.180054	+	0.116337i
$987$	−5.24264	+	1.82339i	−0.166875	+	0.0580391i
$988$	−24.8088	+	55.0349i	−0.789273	+	1.75089i
$989$	21.3022	+	21.3022i	0.677369	+	0.677369i
$990$	0.0781062	+	0.0522425i	0.00248238	+	0.00166038i
$991$	−24.1374			−0.766749			−0.383374	−	0.923593i	$-0.625238\pi$
$991$	−24.1374			−0.766749			−0.383374	+	0.923593i	$0.625238\pi$
$992$	−28.8811	+	16.2321i	−0.916975	+	0.515370i
$993$	15.1120	−	10.2615i	0.479565	−	0.325639i
$994$	−5.16716	+	24.0361i	−0.163892	+	0.762378i
$995$	0.0526377	−	0.0141042i	0.00166873	−	0.000447134i
$996$	−29.9350	+	25.0408i	−0.948527	+	0.793447i
$997$	−22.4986	−	6.02848i	−0.712538	−	0.190924i	−0.115698	−	0.993284i	$-0.536910\pi$
$997$	−22.4986	−	6.02848i	−0.712538	−	0.190924i	−0.596840	+	0.802361i	$0.703577\pi$
$998$	38.3466	+	19.6504i	1.21384	+	0.622023i
$999$	6.62161	−	1.47198i	0.209498	−	0.0465713i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	144.2.x.e.13.13	✓	72
3.2	odd	2		432.2.y.e.253.6		72
4.3	odd	2		576.2.bb.e.337.14		72
9.2	odd	6		432.2.y.e.397.7		72
9.7	even	3	inner	144.2.x.e.61.12	yes	72
12.11	even	2		1728.2.bc.e.145.10		72
16.5	even	4	inner	144.2.x.e.85.12	yes	72
16.11	odd	4		576.2.bb.e.49.4		72
36.7	odd	6		576.2.bb.e.529.4		72
36.11	even	6		1728.2.bc.e.721.9		72
48.5	odd	4		432.2.y.e.37.7		72
48.11	even	4		1728.2.bc.e.1009.9		72
144.11	even	12		1728.2.bc.e.1585.10		72
144.43	odd	12		576.2.bb.e.241.14		72
144.101	odd	12		432.2.y.e.181.6		72
144.133	even	12	inner	144.2.x.e.133.13	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.x.e.13.13	✓	72	1.1	even	1	trivial
144.2.x.e.61.12	yes	72	9.7	even	3	inner
144.2.x.e.85.12	yes	72	16.5	even	4	inner
144.2.x.e.133.13	yes	72	144.133	even	12	inner
432.2.y.e.37.7		72	48.5	odd	4
432.2.y.e.181.6		72	144.101	odd	12
432.2.y.e.253.6		72	3.2	odd	2
432.2.y.e.397.7		72	9.2	odd	6
576.2.bb.e.49.4		72	16.11	odd	4
576.2.bb.e.241.14		72	144.43	odd	12
576.2.bb.e.337.14		72	4.3	odd	2
576.2.bb.e.529.4		72	36.7	odd	6
1728.2.bc.e.145.10		72	12.11	even	2
1728.2.bc.e.721.9		72	36.11	even	6
1728.2.bc.e.1009.9		72	48.11	even	4
1728.2.bc.e.1585.10		72	144.11	even	12

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 $\F_{q}$

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	144.2.x.e.13.13

Level	$144$
Weight	$2$
Character	144.13
Analytic conductor	$1.150$
Analytic rank	$0$
Dimension	$72$
Inner twists	$4$