LMFDB - Embedded newform 504.2.bf.b.115.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(115,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 4, 1]))

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

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

chi := DirichletCharacter("504.115");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.bf (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:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$180$
Relative dimension:	$90$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			115.16
Character	$\chi$	$=$	504.115
Dual form			504.2.bf.b.355.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.16893 + 0.795991i) q^{2} +(-0.801348 - 1.53553i) q^{3} +(0.732796 - 1.86092i) q^{4} +(1.06898 - 1.85154i) q^{5} +(2.15899 + 1.15706i) q^{6} +(2.52157 + 0.801064i) q^{7} +(0.624685 + 2.75858i) q^{8} +(-1.71568 + 2.46098i) q^{9} +O(q^{10})$	\(q+(-1.16893 + 0.795991i) q^{2} +(-0.801348 - 1.53553i) q^{3} +(0.732796 - 1.86092i) q^{4} +(1.06898 - 1.85154i) q^{5} +(2.15899 + 1.15706i) q^{6} +(2.52157 + 0.801064i) q^{7} +(0.624685 + 2.75858i) q^{8} +(-1.71568 + 2.46098i) q^{9} +(0.224237 + 3.01522i) q^{10} +(1.73850 + 3.01117i) q^{11} +(-3.44471 + 0.366014i) q^{12} +(2.54202 + 4.40291i) q^{13} +(-3.58518 + 1.07076i) q^{14} +(-3.69971 - 0.157729i) q^{15} +(-2.92602 - 2.72735i) q^{16} +(2.27003 + 1.31060i) q^{17} +(0.0465922 - 4.24238i) q^{18} +(7.04468 - 4.06725i) q^{19} +(-2.66220 - 3.34609i) q^{20} +(-0.790598 - 4.51386i) q^{21} +(-4.42905 - 2.13602i) q^{22} +(-5.90310 - 3.40816i) q^{23} +(3.73528 - 3.16980i) q^{24} +(0.214544 + 0.371601i) q^{25} +(-6.47612 - 3.12327i) q^{26} +(5.15376 + 0.662370i) q^{27} +(3.33851 - 4.10541i) q^{28} +(0.394206 + 0.227595i) q^{29} +(4.45026 - 2.76056i) q^{30} -1.37578 q^{31} +(5.59125 + 0.858993i) q^{32} +(3.23059 - 5.08251i) q^{33} +(-3.69674 + 0.274921i) q^{34} +(4.17871 - 3.81244i) q^{35} +(3.32244 + 4.99614i) q^{36} +(0.887449 - 0.512369i) q^{37} +(-4.99725 + 10.3618i) q^{38} +(4.72374 - 7.43160i) q^{39} +(5.77539 + 1.79225i) q^{40} +(-4.79267 + 2.76705i) q^{41} +(4.51715 + 4.64708i) q^{42} +(3.77476 - 6.53808i) q^{43} +(6.87750 - 1.02863i) q^{44} +(2.72256 + 5.80740i) q^{45} +(9.61318 - 0.714917i) q^{46} -10.1740 q^{47} +(-1.84315 + 6.67853i) q^{48} +(5.71659 + 4.03987i) q^{49} +(-0.546577 - 0.263600i) q^{50} +(0.193380 - 4.53594i) q^{51} +(10.0562 - 1.50405i) q^{52} +(4.63344 + 2.67512i) q^{53} +(-6.55163 + 3.32808i) q^{54} +7.43372 q^{55} +(-0.634617 + 7.45636i) q^{56} +(-11.8906 - 7.55800i) q^{57} +(-0.641964 + 0.0477419i) q^{58} -7.83247i q^{59} +(-3.00466 + 6.76927i) q^{60} -5.21493 q^{61} +(1.60819 - 1.09511i) q^{62} +(-6.29761 + 4.83116i) q^{63} +(-7.21954 + 3.44649i) q^{64} +10.8695 q^{65} +(0.269300 + 8.51262i) q^{66} -10.6663 q^{67} +(4.10240 - 3.26393i) q^{68} +(-0.502874 + 11.7955i) q^{69} +(-1.84995 + 7.78270i) q^{70} -6.60821i q^{71} +(-7.86058 - 3.19551i) q^{72} +(13.4461 + 7.76311i) q^{73} +(-0.629525 + 1.30532i) q^{74} +(0.398678 - 0.627219i) q^{75} +(-2.40649 - 16.0900i) q^{76} +(1.97160 + 8.98552i) q^{77} +(0.393768 + 12.4471i) q^{78} -7.59525i q^{79} +(-8.17765 + 2.50214i) q^{80} +(-3.11287 - 8.44453i) q^{81} +(3.39975 - 7.04941i) q^{82} +(10.4296 + 6.02151i) q^{83} +(-8.97927 - 1.83651i) q^{84} +(4.85326 - 2.80203i) q^{85} +(0.791818 + 10.6472i) q^{86} +(0.0335817 - 0.787697i) q^{87} +(-7.22054 + 6.67683i) q^{88} +(-4.49704 + 2.59637i) q^{89} +(-7.80512 - 4.62131i) q^{90} +(2.88286 + 13.1385i) q^{91} +(-10.6681 + 8.48769i) q^{92} +(1.10248 + 2.11254i) q^{93} +(11.8927 - 8.09839i) q^{94} -17.3913i q^{95} +(-3.16154 - 9.27387i) q^{96} +(-7.85340 - 4.53417i) q^{97} +(-9.89800 - 0.171974i) q^{98} +(-10.3932 - 0.887791i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 180 q - 6 q^{2} - 6 q^{3} - 2 q^{4} - 6 q^{6} + 10 q^{9}+O(q^{10}) $ 180 * q - 6 * q^2 - 6 * q^3 - 2 * q^4 - 6 * q^6 + 10 * q^9	$ 180 q - 6 q^{2} - 6 q^{3} - 2 q^{4} - 6 q^{6} + 10 q^{9} - 8 q^{11} + 12 q^{12} + 10 q^{14} + 14 q^{16} - 18 q^{17} + 8 q^{18} - 6 q^{19} + 36 q^{20} - 16 q^{22} - 12 q^{24} - 78 q^{25} - 6 q^{26} + 16 q^{28} + q^{30} - 26 q^{32} - 36 q^{33} - 12 q^{34} - 12 q^{35} + 2 q^{36} - 27 q^{38} + 24 q^{40} - 42 q^{41} + 22 q^{42} + 14 q^{43} - 21 q^{44} - 12 q^{46} - 9 q^{48} + 2 q^{49} + 15 q^{50} + 9 q^{52} - 51 q^{54} + 14 q^{56} - 26 q^{57} + 19 q^{58} + 37 q^{60} - 8 q^{64} + 24 q^{65} + 6 q^{66} + 28 q^{67} + 12 q^{68} + 27 q^{70} - 28 q^{72} + 18 q^{73} + 49 q^{74} - 18 q^{75} - 12 q^{76} - 33 q^{78} - 63 q^{80} - 22 q^{81} - 54 q^{82} + 6 q^{83} + 31 q^{84} - 13 q^{86} + 29 q^{88} - 66 q^{89} - 51 q^{90} + 2 q^{91} - 60 q^{92} - 45 q^{96} - 6 q^{97} + 31 q^{98} + 4 q^{99}+O(q^{100}) $ 180 * q - 6 * q^2 - 6 * q^3 - 2 * q^4 - 6 * q^6 + 10 * q^9 - 8 * q^11 + 12 * q^12 + 10 * q^14 + 14 * q^16 - 18 * q^17 + 8 * q^18 - 6 * q^19 + 36 * q^20 - 16 * q^22 - 12 * q^24 - 78 * q^25 - 6 * q^26 + 16 * q^28 + q^30 - 26 * q^32 - 36 * q^33 - 12 * q^34 - 12 * q^35 + 2 * q^36 - 27 * q^38 + 24 * q^40 - 42 * q^41 + 22 * q^42 + 14 * q^43 - 21 * q^44 - 12 * q^46 - 9 * q^48 + 2 * q^49 + 15 * q^50 + 9 * q^52 - 51 * q^54 + 14 * q^56 - 26 * q^57 + 19 * q^58 + 37 * q^60 - 8 * q^64 + 24 * q^65 + 6 * q^66 + 28 * q^67 + 12 * q^68 + 27 * q^70 - 28 * q^72 + 18 * q^73 + 49 * q^74 - 18 * q^75 - 12 * q^76 - 33 * q^78 - 63 * q^80 - 22 * q^81 - 54 * q^82 + 6 * q^83 + 31 * q^84 - 13 * q^86 + 29 * q^88 - 66 * q^89 - 51 * q^90 + 2 * q^91 - 60 * q^92 - 45 * q^96 - 6 * q^97 + 31 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.16893	+	0.795991i	−0.826559	+	0.562851i
$2$	−1.16893	+	0.795991i	−0.826559	+	0.562851i
$3$	−0.801348	−	1.53553i	−0.462659	−	0.886536i
$3$	−0.801348	−	1.53553i	−0.462659	−	0.886536i
$4$	0.732796	−	1.86092i	0.366398	−	0.930458i
$5$	1.06898	−	1.85154i	0.478064	−	0.828032i	−0.521619	−	0.853178i	$-0.674672\pi$
$5$	1.06898	−	1.85154i	0.478064	−	0.828032i	0.999684	+	0.0251464i	$0.00800519\pi$
$6$	2.15899	+	1.15706i	0.881402	+	0.472367i
$7$	2.52157	+	0.801064i	0.953062	+	0.302774i
$7$	2.52157	+	0.801064i	0.953062	+	0.302774i
$8$	0.624685	+	2.75858i	0.220859	+	0.975306i
$9$	−1.71568	+	2.46098i	−0.571894	+	0.820328i
$10$	0.224237	+	3.01522i	0.0709100	+	0.953496i
$11$	1.73850	+	3.01117i	0.524178	+	0.907902i	0.999604	+	0.0281466i	$0.00896052\pi$
$11$	1.73850	+	3.01117i	0.524178	+	0.907902i	−0.475426	+	0.879756i	$0.657706\pi$
$12$	−3.44471	+	0.366014i	−0.994402	+	0.105659i
$13$	2.54202	+	4.40291i	0.705030	+	1.22115i	0.966681	+	0.255985i	$0.0823996\pi$
$13$	2.54202	+	4.40291i	0.705030	+	1.22115i	−0.261651	+	0.965162i	$0.584267\pi$
$14$	−3.58518	+	1.07076i	−0.958178	+	0.286172i
$15$	−3.69971	−	0.157729i	−0.955261	−	0.0407254i
$16$	−2.92602	−	2.72735i	−0.731505	−	0.681836i
$17$	2.27003	+	1.31060i	0.550564	+	0.317868i	0.749349	−	0.662175i	$-0.230366\pi$
$17$	2.27003	+	1.31060i	0.550564	+	0.317868i	−0.198786	+	0.980043i	$0.563700\pi$
$18$	0.0465922	−	4.24238i	0.0109819	−	0.999940i
$19$	7.04468	−	4.06725i	1.61616	−	0.933090i	0.628259	−	0.778005i	$-0.283768\pi$
$19$	7.04468	−	4.06725i	1.61616	−	0.933090i	0.987901	−	0.155086i	$-0.0495653\pi$
$20$	−2.66220	−	3.34609i	−0.595287	−	0.748208i
$21$	−0.790598	−	4.51386i	−0.172523	−	0.985006i
$22$	−4.42905	−	2.13602i	−0.944277	−	0.455401i
$23$	−5.90310	−	3.40816i	−1.23088	−	0.710650i	−0.263668	−	0.964613i	$-0.584932\pi$
$23$	−5.90310	−	3.40816i	−1.23088	−	0.710650i	−0.967214	+	0.253964i	$0.918266\pi$
$24$	3.73528	−	3.16980i	0.762462	−	0.647034i
$25$	0.214544	+	0.371601i	0.0429087	+	0.0743201i
$26$	−6.47612	−	3.12327i	−1.27007	−	0.612523i
$27$	5.15376	+	0.662370i	0.991842	+	0.127473i
$28$	3.33851	−	4.10541i	0.630919	−	0.775849i
$29$	0.394206	+	0.227595i	0.0732023	+	0.0422634i	0.536154	−	0.844120i	$-0.319876\pi$
$29$	0.394206	+	0.227595i	0.0732023	+	0.0422634i	−0.462952	+	0.886383i	$0.653210\pi$
$30$	4.45026	−	2.76056i	0.812502	−	0.504007i
$31$	−1.37578			−0.247097			−0.123549	−	0.992339i	$-0.539427\pi$
$31$	−1.37578			−0.247097			−0.123549	+	0.992339i	$0.539427\pi$
$32$	5.59125	+	0.858993i	0.988404	+	0.151850i
$33$	3.23059	−	5.08251i	0.562373	−	0.884751i
$34$	−3.69674	+	0.274921i	−0.633985	+	0.0471485i
$35$	4.17871	−	3.81244i	0.706332	−	0.644421i
$36$	3.32244	+	4.99614i	0.553740	+	0.832690i
$37$	0.887449	−	0.512369i	0.145896	−	0.0842329i	−0.425275	−	0.905064i	$-0.639823\pi$
$37$	0.887449	−	0.512369i	0.145896	−	0.0842329i	0.571171	+	0.820831i	$0.306489\pi$
$38$	−4.99725	+	10.3618i	−0.810660	+	1.68091i
$39$	4.72374	−	7.43160i	0.756403	−	1.19001i
$40$	5.77539	+	1.79225i	0.913169	+	0.283380i
$41$	−4.79267	+	2.76705i	−0.748489	+	0.432140i	−0.825148	−	0.564917i	$-0.808908\pi$
$41$	−4.79267	+	2.76705i	−0.748489	+	0.432140i	0.0766586	+	0.997057i	$0.475575\pi$
$42$	4.51715	+	4.64708i	0.697011	+	0.717060i
$43$	3.77476	−	6.53808i	0.575645	−	0.997047i	−0.420326	−	0.907373i	$-0.638084\pi$
$43$	3.77476	−	6.53808i	0.575645	−	0.997047i	0.995971	−	0.0896738i	$-0.0285825\pi$
$44$	6.87750	−	1.02863i	1.03682	−	0.155072i
$45$	2.72256	+	5.80740i	0.405855	+	0.865716i
$46$	9.61318	−	0.714917i	1.41739	−	0.105409i
$47$	−10.1740			−1.48403			−0.742013	−	0.670386i	$-0.766129\pi$
$47$	−10.1740			−1.48403			−0.742013	+	0.670386i	$0.766129\pi$
$48$	−1.84315	+	6.67853i	−0.266036	+	0.963963i
$49$	5.71659	+	4.03987i	0.816656	+	0.577125i
$50$	−0.546577	−	0.263600i	−0.0772977	−	0.0372787i
$51$	0.193380	−	4.53594i	0.0270786	−	0.635159i
$52$	10.0562	−	1.50405i	1.39455	−	0.208574i
$53$	4.63344	+	2.67512i	0.636452	+	0.367456i	0.783247	−	0.621711i	$-0.213562\pi$
$53$	4.63344	+	2.67512i	0.636452	+	0.367456i	−0.146794	+	0.989167i	$0.546896\pi$
$54$	−6.55163	+	3.32808i	−0.891564	+	0.452895i
$55$	7.43372			1.00236
$56$	−0.634617	+	7.45636i	−0.0848043	+	0.996398i
$57$	−11.8906	−	7.55800i	−1.57495	−	1.00108i
$58$	−0.641964	+	0.0477419i	−0.0842940	+	0.00626881i
$59$		−	7.83247i		−	1.01970i	−0.860263	−	0.509850i	$-0.829701\pi$
$59$		−	7.83247i		−	1.01970i	0.860263	−	0.509850i	$-0.170299\pi$
$60$	−3.00466	+	6.76927i	−0.387899	+	0.873909i
$61$	−5.21493			−0.667703			−0.333851	−	0.942626i	$-0.608348\pi$
$61$	−5.21493			−0.667703			−0.333851	+	0.942626i	$0.608348\pi$
$62$	1.60819	−	1.09511i	0.204240	−	0.139079i
$63$	−6.29761	+	4.83116i	−0.793424	+	0.608669i
$64$	−7.21954	+	3.44649i	−0.902442	+	0.430811i
$65$	10.8695			1.34820
$66$	0.269300	+	8.51262i	0.0331486	+	1.04783i
$67$	−10.6663			−1.30309			−0.651547	−	0.758608i	$-0.725880\pi$
$67$	−10.6663			−1.30309			−0.651547	+	0.758608i	$0.725880\pi$
$68$	4.10240	−	3.26393i	0.497489	−	0.395810i
$69$	−0.502874	+	11.7955i	−0.0605390	+	1.42001i
$70$	−1.84995	+	7.78270i	−0.221112	+	0.930211i
$71$		−	6.60821i		−	0.784250i	−0.919912	−	0.392125i	$-0.871740\pi$
$71$		−	6.60821i		−	0.784250i	0.919912	−	0.392125i	$-0.128260\pi$
$72$	−7.86058	−	3.19551i	−0.926378	−	0.376594i
$73$	13.4461	+	7.76311i	1.57375	+	0.908603i	0.995704	+	0.0925965i	$0.0295167\pi$
$73$	13.4461	+	7.76311i	1.57375	+	0.908603i	0.578043	+	0.816006i	$0.303817\pi$
$74$	−0.629525	+	1.30532i	−0.0731808	+	0.151741i
$75$	0.398678	−	0.627219i	0.0460354	−	0.0724250i
$76$	−2.40649	−	16.0900i	−0.276043	−	1.84565i
$77$	1.97160	+	8.98552i	0.224685	+	1.02399i
$78$	0.393768	+	12.4471i	0.0445855	+	1.40935i
$79$		−	7.59525i		−	0.854532i	−0.904126	−	0.427266i	$-0.859477\pi$
$79$		−	7.59525i		−	0.854532i	0.904126	−	0.427266i	$-0.140523\pi$
$80$	−8.17765	+	2.50214i	−0.914289	+	0.279747i
$81$	−3.11287	−	8.44453i	−0.345875	−	0.938281i
$82$	3.39975	−	7.04941i	0.375440	−	0.778477i
$83$	10.4296	+	6.02151i	1.14479	+	0.660946i	0.947613	−	0.319421i	$-0.103489\pi$
$83$	10.4296	+	6.02151i	1.14479	+	0.660946i	0.197179	+	0.980367i	$0.436822\pi$
$84$	−8.97927	−	1.83651i	−0.979718	−	0.200379i
$85$	4.85326	−	2.80203i	0.526410	−	0.303923i
$86$	0.791818	+	10.6472i	0.0853840	+	1.14812i
$87$	0.0335817	−	0.787697i	0.00360034	−	0.0844500i
$88$	−7.22054	+	6.67683i	−0.769713	+	0.711752i
$89$	−4.49704	+	2.59637i	−0.476685	+	0.275214i	−0.719034	−	0.694975i	$-0.755415\pi$
$89$	−4.49704	+	2.59637i	−0.476685	+	0.275214i	0.242349	+	0.970189i	$0.422082\pi$
$90$	−7.80512	−	4.62131i	−0.822732	−	0.487129i
$91$	2.88286	+	13.1385i	0.302206	+	1.37729i
$92$	−10.6681	+	8.48769i	−1.11222	+	0.884903i
$93$	1.10248	+	2.11254i	0.114322	+	0.219061i
$94$	11.8927	−	8.09839i	1.22663	−	0.835285i
$95$		−	17.3913i		−	1.78431i
$96$	−3.16154	−	9.27387i	−0.322673	−	0.946510i
$97$	−7.85340	−	4.53417i	−0.797392	−	0.460375i	0.0451662	−	0.998979i	$-0.485618\pi$
$97$	−7.85340	−	4.53417i	−0.797392	−	0.460375i	−0.842559	+	0.538605i	$0.818952\pi$
$98$	−9.89800	−	0.171974i	−0.999849	−	0.0173720i
$99$	−10.3932	−	0.887791i	−1.04455	−	0.0892264i
$100$	0.848734	−	0.126940i	0.0848734	−	0.0126940i
$101$	−4.24318	−	7.34940i	−0.422212	−	0.731293i	0.573944	−	0.818895i	$-0.305413\pi$
$101$	−4.24318	−	7.34940i	−0.422212	−	0.731293i	−0.996156	+	0.0876023i	$0.972080\pi$
$102$	3.38452	+	5.45613i	0.335118	+	0.540238i
$103$	1.12417	−	1.94712i	0.110768	−	0.191855i	−0.805312	−	0.592851i	$-0.798002\pi$
$103$	1.12417	−	1.94712i	0.110768	−	0.191855i	0.916080	+	0.400996i	$0.131336\pi$
$104$	−10.5578	+	9.76280i	−1.03528	+	0.957321i
$105$	−9.20271	−	3.36143i	−0.898093	−	0.328042i
$106$	−7.54554	+	0.561151i	−0.732888	+	0.0545038i
$107$	0.593860	+	1.02860i	0.0574106	+	0.0994381i	0.893302	−	0.449456i	$-0.148382\pi$
$107$	0.593860	+	1.02860i	0.0574106	+	0.0994381i	−0.835892	+	0.548894i	$0.815049\pi$
$108$	5.00927	−	9.10534i	0.482018	−	0.876162i
$109$	−10.8535	−	6.26627i	−1.03958	−	0.600200i	−0.119863	−	0.992790i	$-0.538246\pi$
$109$	−10.8535	−	6.26627i	−1.03958	−	0.600200i	−0.919713	+	0.392591i	$0.871579\pi$
$110$	−8.68950	+	5.91718i	−0.828511	+	0.564181i
$111$	−1.49791	−	0.952115i	−0.142175	−	0.0903708i
$112$	−5.19337	−	9.22111i	−0.490727	−	0.871313i
$113$	3.12960	+	5.42062i	0.294408	+	0.509929i	0.974847	−	0.222875i	$-0.0715442\pi$
$113$	3.12960	+	5.42062i	0.294408	+	0.509929i	−0.680439	+	0.732805i	$0.738211\pi$
$114$	19.9154	−	0.630032i	1.86525	−	0.0590079i
$115$	−12.6206	+	7.28654i	−1.17688	+	0.679473i
$116$	0.712409	−	0.566804i	0.0661455	−	0.0526265i
$117$	−15.1968	−	1.29812i	−1.40494	−	0.120011i
$118$	6.23457	+	9.15561i	0.573939	+	0.842842i
$119$	4.67416	+	5.12322i	0.428479	+	0.469644i
$120$	−1.87604	−	10.3045i	−0.171259	−	0.940666i
$121$	−0.544767	+	0.943564i	−0.0495242	+	0.0857785i
$122$	6.09588	−	4.15103i	0.551895	−	0.375817i
$123$	8.08947	+	5.14190i	0.729403	+	0.463629i
$124$	−1.00817	+	2.56021i	−0.0905359	+	0.229914i
$125$	11.6072			1.03818
$126$	3.51591	−	10.6601i	0.313222	−	0.949680i
$127$			6.01094i			0.533385i	0.963782	+	0.266692i	$0.0859308\pi$
$127$			6.01094i			0.533385i	−0.963782	+	0.266692i	$0.914069\pi$
$128$	5.69577	−	9.77539i	0.503439	−	0.864031i
$129$	−13.0643	−	0.556967i	−1.15025	−	0.0490382i
$130$	−12.7057	+	8.65204i	−1.11436	+	0.758834i
$131$	−1.41578	−	0.817401i	−0.123697	−	0.0714166i	0.436875	−	0.899522i	$-0.356085\pi$
$131$	−1.41578	−	0.817401i	−0.123697	−	0.0714166i	−0.560572	+	0.828106i	$0.689419\pi$
$132$	−7.09076	−	9.73630i	−0.617172	−	0.847436i
$133$	21.0217	−	4.61259i	1.82282	−	0.399962i
$134$	12.4681	−	8.49027i	1.07708	−	0.733447i
$135$	6.73569	−	8.83431i	0.579716	−	0.760336i
$136$	−2.19735	+	7.08078i	−0.188421	+	0.607172i
$137$	0.240809	+	0.417093i	0.0205737	+	0.0356346i	0.876129	−	0.482077i	$-0.160117\pi$
$137$	0.240809	+	0.417093i	0.0205737	+	0.0356346i	−0.855555	+	0.517711i	$0.826784\pi$
$138$	−8.80128	−	14.1884i	−0.749215	−	1.20780i
$139$	−0.119588	+	0.0690440i	−0.0101433	+	0.00585624i	−0.505063	−	0.863082i	$-0.668531\pi$
$139$	−0.119588	+	0.0690440i	−0.0101433	+	0.00585624i	0.494920	+	0.868939i	$0.335197\pi$
$140$	−4.03249	−	10.5700i	−0.340808	−	0.893327i
$141$	8.15289	+	15.6224i	0.686597	+	1.31564i
$142$	5.26007	+	7.72454i	0.441416	+	0.648229i
$143$	−8.83861	+	15.3089i	−0.739121	+	1.28020i
$144$	11.7321	−	2.52162i	0.977672	−	0.210135i
$145$	0.842801	−	0.486592i	0.0699908	−	0.0404092i
$146$	−21.8969	+	1.62844i	−1.81220	+	0.134771i
$147$	1.62235	−	12.0153i	0.133809	−	0.991007i
$148$	−0.303156	−	2.02693i	−0.0249193	−	0.166613i
$149$	−4.51074	−	2.60428i	−0.369534	−	0.213351i	0.303721	−	0.952761i	$-0.401771\pi$
$149$	−4.51074	−	2.60428i	−0.369534	−	0.213351i	−0.673255	+	0.739410i	$0.735104\pi$
$150$	0.0332336	+	1.05052i	0.00271351	+	0.0857746i
$151$	−13.4414	+	7.76042i	−1.09385	+	0.631534i	−0.934598	−	0.355705i	$-0.884241\pi$
$151$	−13.4414	+	7.76042i	−1.09385	+	0.631534i	−0.159250	+	0.987238i	$0.550908\pi$
$152$	15.6205	+	16.8926i	1.26699	+	1.37017i
$153$	−7.12003	+	3.33793i	−0.575620	+	0.269856i
$154$	−9.45706	−	8.93407i	−0.762071	−	0.719928i
$155$	−1.47069	+	2.54730i	−0.118128	+	0.204604i
$156$	−10.3681	−	14.2363i	−0.830108	−	1.13982i
$157$	−10.4190			−0.831524			−0.415762	−	0.909473i	$-0.636485\pi$
$157$	−10.4190			−0.831524			−0.415762	+	0.909473i	$0.636485\pi$
$158$	6.04575	+	8.87832i	0.480974	+	0.706321i
$159$	0.394714	−	9.25848i	0.0313029	−	0.734245i
$160$	7.56742	−	9.43416i	0.598257	−	0.745836i
$161$	−12.1549	−	13.3227i	−0.957941	−	1.04997i
$162$	10.3605	+	7.39324i	0.813998	+	0.580868i
$163$	2.01240	+	3.48558i	0.157623	+	0.273011i	0.934011	−	0.357244i	$-0.116284\pi$
$163$	2.01240	+	3.48558i	0.157623	+	0.273011i	−0.776388	+	0.630255i	$0.782950\pi$
$164$	1.63720	+	10.9464i	0.127843	+	0.854773i
$165$	−5.95700	−	11.4147i	−0.463752	−	0.888631i
$166$	−16.9845	+	1.26311i	−1.31825	+	0.0980364i
$167$	11.4537	+	19.8384i	0.886313	+	1.53514i	0.844202	+	0.536026i	$0.180075\pi$
$167$	11.4537	+	19.8384i	0.886313	+	1.53514i	0.0421110	+	0.999113i	$0.486592\pi$
$168$	11.9580	−	5.00067i	0.922578	−	0.385810i
$169$	−6.42374	+	11.1262i	−0.494133	+	0.855864i
$170$	−3.44273	+	7.13853i	−0.264045	+	0.547500i
$171$	−2.07700	+	24.3149i	−0.158832	+	1.85941i
$172$	−9.40068	−	11.8156i	−0.716795	−	0.900930i
$173$	6.34004			0.482025			0.241012	−	0.970522i	$-0.422521\pi$
$173$	6.34004			0.482025			0.241012	+	0.970522i	$0.422521\pi$
$174$	0.587745	+	0.947494i	0.0445569	+	0.0718294i
$175$	0.243310	+	1.10888i	0.0183925	+	0.0838233i
$176$	3.12562	−	13.5522i	0.235602	−	1.02154i
$177$	−12.0270	+	6.27654i	−0.904002	+	0.471773i
$178$	3.19004	−	6.61457i	0.239104	−	0.495783i
$179$	5.40704	−	9.36527i	0.404141	−	0.699993i	−0.590080	−	0.807345i	$-0.700904\pi$
$179$	5.40704	−	9.36527i	0.404141	−	0.699993i	0.994221	+	0.107352i	$0.0342371\pi$
$180$	12.8022	−	0.810815i	0.954217	−	0.0604346i
$181$	−12.6693			−0.941703			−0.470851	−	0.882213i	$-0.656053\pi$
$181$	−12.6693			−0.941703			−0.470851	+	0.882213i	$0.656053\pi$
$182$	−13.8280	−	13.0633i	−1.02500	−	0.968317i
$183$	4.17897	+	8.00765i	0.308918	+	0.591943i
$184$	5.71410	−	18.4132i	0.421249	−	1.35744i
$185$		−	2.19086i		−	0.161075i
$186$	−2.97029	−	1.59185i	−0.217792	−	0.116720i
$187$			9.11394i			0.666477i
$188$	−7.45545	+	18.9329i	−0.543744	+	1.38082i
$189$	12.4650	+	5.79870i	0.906692	+	0.421794i
$190$	13.8433	+	20.3292i	1.00430	+	1.47484i
$191$		−	24.6875i		−	1.78633i	−0.449734	−	0.893163i	$-0.648481\pi$
$191$		−	24.6875i		−	1.78633i	0.449734	−	0.893163i	$-0.351519\pi$
$192$	11.0775	+	8.32395i	0.799452	+	0.600730i
$193$	−13.0423			−0.938805			−0.469402	−	0.882984i	$-0.655531\pi$
$193$	−13.0423			−0.938805			−0.469402	+	0.882984i	$0.655531\pi$
$194$	12.7892	−	0.951116i	0.918214	−	0.0682862i
$195$	−8.71027	−	16.6904i	−0.623756	−	1.19523i
$196$	11.7070	−	7.67769i	0.836212	−	0.548407i
$197$			2.57979i			0.183802i	0.995768	+	0.0919012i	$0.0292944\pi$
$197$			2.57979i			0.183802i	−0.995768	+	0.0919012i	$0.970706\pi$
$198$	12.8555	−	7.23509i	0.913604	−	0.514175i
$199$	−0.223017	+	0.386277i	−0.0158093	+	0.0273825i	−0.873822	−	0.486246i	$-0.838366\pi$
$199$	−0.223017	+	0.386277i	−0.0158093	+	0.0273825i	0.858013	+	0.513629i	$0.171699\pi$
$200$	−0.891068	+	0.823969i	−0.0630080	+	0.0582634i
$201$	8.54741	+	16.3784i	0.602888	+	1.15524i
$202$	10.8100	+	5.21340i	0.760591	+	0.366814i
$203$	0.811699	+	0.889681i	0.0569701	+	0.0624434i
$204$	−8.29930	−	3.68379i	−0.581068	−	0.257917i
$205$			11.8317i			0.826364i
$206$	0.235813	+	3.17087i	0.0164299	+	0.220925i
$207$	18.5153	−	8.68012i	1.28690	−	0.603310i
$208$	4.57025	−	19.8160i	0.316890	−	1.37399i
$209$	24.4943	+	14.1418i	1.69431	+	0.978210i
$210$	13.4330	−	3.39600i	0.926965	−	0.234346i
$211$	10.4080	+	18.0272i	0.716517	+	1.24104i	0.962372	+	0.271737i	$0.0875979\pi$
$211$	10.4080	+	18.0272i	0.716517	+	1.24104i	−0.245855	+	0.969307i	$0.579069\pi$
$212$	8.37354	−	6.66213i	0.575097	−	0.457557i
$213$	−10.1471	+	5.29548i	−0.695266	+	0.362840i
$214$	−1.51293	−	0.729649i	−0.103422	−	0.0498778i
$215$	−8.07032	−	13.9782i	−0.550391	−	0.953306i
$216$	1.39228	+	14.6308i	0.0947323	+	0.995503i
$217$	−3.46912	−	1.10209i	−0.235499	−	0.0748145i
$218$	17.6749	−	1.31445i	1.19709	−	0.0890261i
$219$	1.14545	−	26.8678i	0.0774022	−	1.81556i
$220$	5.44740	−	13.8335i	0.367264	−	0.932656i
$221$			13.3263i			0.896426i
$222$	2.50883	−	0.0793679i	0.168382	−	0.00532682i
$223$	−7.20865	+	12.4857i	−0.482727	+	0.836107i	−0.999803	−	0.0198318i	$-0.993687\pi$
$223$	−7.20865	+	12.4857i	−0.482727	+	0.836107i	0.517076	+	0.855939i	$0.327020\pi$
$224$	13.4106	+	6.64496i	0.896034	+	0.443985i
$225$	−1.28259	−	0.109560i	−0.0855061	−	0.00730400i
$226$	−7.97305	−	3.84520i	−0.530360	−	0.255779i
$227$	−1.85284	+	1.06974i	−0.122977	+	0.0710010i	−0.560227	−	0.828339i	$-0.689286\pi$
$227$	−1.85284	+	1.06974i	−0.122977	+	0.0710010i	0.437249	+	0.899340i	$0.355953\pi$
$228$	−22.7782	+	16.5889i	−1.50852	+	1.09863i
$229$	−1.23444	+	2.13812i	−0.0815744	+	0.141291i	−0.903926	−	0.427688i	$-0.859328\pi$
$229$	−1.23444	+	2.13812i	−0.0815744	+	0.141291i	0.822352	+	0.568979i	$0.192661\pi$
$230$	8.95264	−	18.5634i	0.590320	−	1.22403i
$231$	12.2176	−	10.2280i	0.803856	−	0.672951i
$232$	−0.381585	+	1.22963i	−0.0250523	+	0.0807289i
$233$	6.12391	+	10.6069i	0.401191	+	0.694883i	0.993870	−	0.110556i	$-0.0352630\pi$
$233$	6.12391	+	10.6069i	0.401191	+	0.694883i	−0.592679	+	0.805439i	$0.701930\pi$
$234$	18.7973	−	10.5791i	1.22882	−	0.691577i
$235$	−10.8758	+	18.8375i	−0.709460	+	1.22882i
$236$	−14.5756	−	5.73961i	−0.948789	−	0.373616i
$237$	−11.6627	+	6.08644i	−0.757574	+	0.395357i
$238$	−9.54180	−	2.26809i	−0.618503	−	0.147019i
$239$	1.26639	−	0.731153i	0.0819162	−	0.0472944i	−0.458482	−	0.888703i	$-0.651607\pi$
$239$	1.26639	−	0.731153i	0.0819162	−	0.0472944i	0.540399	+	0.841409i	$0.318273\pi$
$240$	10.3952	+	10.5519i	0.671010	+	0.681123i
$241$	−1.83978	+	1.06220i	−0.118511	+	0.0684223i	−0.558084	−	0.829785i	$-0.688463\pi$
$241$	−1.83978	+	1.06220i	−0.118511	+	0.0684223i	0.439573	+	0.898207i	$0.355130\pi$
$242$	−0.114274	−	1.53659i	−0.00734580	−	0.0987757i
$243$	−10.4723	+	11.5469i	−0.671798	+	0.740734i
$244$	−3.82148	+	9.70454i	−0.244645	+	0.621269i
$245$	13.5909	−	6.26591i	0.868292	−	0.400314i
$246$	−13.5489	+	0.428626i	−0.863849	+	0.0273282i
$247$	35.8154	+	20.6780i	2.27888	+	1.31571i
$248$	−0.859428	−	3.79520i	−0.0545737	−	0.240995i
$249$	0.888475	−	20.8402i	0.0563048	−	1.32069i
$250$	−13.5680	+	9.23924i	−0.858118	+	0.584341i
$251$		−	29.6562i		−	1.87188i	−0.352157	−	0.935941i	$-0.614552\pi$
$251$		−	29.6562i		−	1.87188i	0.352157	−	0.935941i	$-0.385448\pi$
$252$	4.37552	+	15.2596i	0.275632	+	0.961263i
$253$		−	23.7003i		−	1.49003i
$254$	−4.78466	−	7.02637i	−0.300216	−	0.440874i
$255$	−8.19174	−	5.20690i	−0.512987	−	0.326069i
$256$	1.12317	+	15.9605i	0.0701982	+	0.997533i
$257$	1.43195	+	0.826736i	0.0893225	+	0.0515704i	0.543996	−	0.839088i	$-0.316911\pi$
$257$	1.43195	+	0.826736i	0.0893225	+	0.0515704i	−0.454673	+	0.890658i	$0.650244\pi$
$258$	15.7146	−	9.74800i	0.978347	−	0.606884i
$259$	2.64820	−	0.581068i	0.164551	−	0.0361058i
$260$	7.96515	−	20.2273i	0.493978	−	1.25444i
$261$	−1.23644	+	0.579654i	−0.0765338	+	0.0358797i
$262$	2.30559	−	0.171463i	0.142440	−	0.0105930i
$263$	−5.56861	+	3.21504i	−0.343375	+	0.198248i	−0.661763	−	0.749713i	$-0.730192\pi$
$263$	−5.56861	+	3.21504i	−0.343375	+	0.198248i	0.318389	+	0.947960i	$0.396858\pi$
$264$	16.0386	+	5.73687i	0.987108	+	0.353080i
$265$	9.90616	−	5.71932i	0.608530	−	0.351335i
$266$	−20.9014	+	22.1249i	−1.28155	+	1.35657i
$267$	7.59048	+	4.82472i	0.464530	+	0.295268i
$268$	−7.81621	+	19.8491i	−0.477451	+	1.21247i
$269$	−2.95325	+	5.11517i	−0.180063	+	0.311878i	−0.941902	−	0.335889i	$-0.890963\pi$
$269$	−2.95325	+	5.11517i	−0.180063	+	0.311878i	0.761839	+	0.647766i	$0.224297\pi$
$270$	−0.841524	+	15.6882i	−0.0512135	+	0.954756i
$271$	12.0131	+	20.8072i	0.729741	+	1.26395i	0.956993	+	0.290112i	$0.0936927\pi$
$271$	12.0131	+	20.8072i	0.729741	+	1.26395i	−0.227252	+	0.973836i	$0.572974\pi$
$272$	−3.06769	−	10.0260i	−0.186006	−	0.607916i
$273$	17.8644	−	14.9553i	1.08120	−	0.905133i
$274$	−0.613491	−	0.295871i	−0.0370623	−	0.0178742i
$275$	−0.745968	+	1.29206i	−0.0449836	+	0.0779139i
$276$	21.5819	+	9.57950i	1.29908	+	0.576618i
$277$	15.8109	−	9.12844i	0.949986	−	0.548475i	0.0569095	−	0.998379i	$-0.481875\pi$
$277$	15.8109	−	9.12844i	0.949986	−	0.548475i	0.893077	+	0.449905i	$0.148542\pi$
$278$	0.0848314	−	0.175899i	0.00508785	−	0.0105497i
$279$	2.36040	−	3.38577i	0.141313	−	0.202701i
$280$	13.1273	+	9.14575i	0.784507	+	0.546563i
$281$	5.67336	−	9.82654i	0.338444	−	0.586202i	−0.645696	−	0.763594i	$-0.723433\pi$
$281$	5.67336	−	9.82654i	0.338444	−	0.586202i	0.984140	+	0.177392i	$0.0567661\pi$
$282$	−21.9655	−	11.7719i	−1.30802	−	0.701004i
$283$		−	16.5184i		−	0.981917i	−0.871183	−	0.490959i	$-0.836647\pi$
$283$		−	16.5184i		−	0.981917i	0.871183	−	0.490959i	$-0.163353\pi$
$284$	−12.2973	−	4.84247i	−0.729712	−	0.287348i
$285$	−26.7048	+	13.9365i	−1.58186	+	0.825526i
$286$	−1.85404	−	24.9305i	−0.109632	−	1.47417i
$287$	−14.3016	+	3.13806i	−0.844198	+	0.185234i
$288$	−11.7068	+	12.2862i	−0.689829	+	0.723973i
$289$	−5.06464	−	8.77221i	−0.297920	−	0.516012i
$290$	−0.597854	+	1.23965i	−0.0351072	+	0.0727950i
$291$	−0.669017	+	15.6926i	−0.0392185	+	0.919914i
$292$	24.2997	−	19.3333i	1.42203	−	1.13139i
$293$	3.49665	+	6.05637i	0.204276	+	0.353817i	0.949902	−	0.312548i	$-0.101183\pi$
$293$	3.49665	+	6.05637i	0.204276	+	0.353817i	−0.745626	+	0.666365i	$0.767849\pi$
$294$	7.66768	+	15.3365i	0.447188	+	0.894440i
$295$	−14.5021	−	8.37279i	−0.844345	−	0.487483i
$296$	1.96779	+	2.12803i	0.114375	+	0.123689i
$297$	6.96531	+	16.6704i	0.404168	+	0.967314i
$298$	7.34572	−	0.546290i	0.425526	−	0.0316458i
$299$		−	34.6544i		−	2.00412i
$300$	−0.875052	−	1.20153i	−0.0505211	−	0.0693704i
$301$	14.7557	−	13.4624i	0.850506	−	0.775958i
$302$	9.53488	−	19.7706i	0.548671	−	1.13767i
$303$	−7.88493	+	12.4049i	−0.452978	+	0.712645i
$304$	−31.7056	−	7.31243i	−1.81844	−	0.419397i
$305$	−5.57467	+	9.65562i	−0.319205	+	0.552879i
$306$	5.66585	−	9.56929i	0.323895	−	0.547040i
$307$			0.795805i			0.0454190i	0.999742	+	0.0227095i	$0.00722928\pi$
$307$			0.795805i			0.0454190i	−0.999742	+	0.0227095i	$0.992771\pi$
$308$	18.1661	+	2.91557i	1.03511	+	0.166130i
$309$	−3.89070	−	0.165871i	−0.221334	−	0.00943609i
$310$	−0.308501	−	4.14827i	−0.0175217	−	0.235606i
$311$	−9.08403			−0.515108			−0.257554	−	0.966264i	$-0.582917\pi$
$311$	−9.08403			−0.515108			−0.257554	+	0.966264i	$0.582917\pi$
$312$	23.4515	+	8.38841i	1.32768	+	0.474900i
$313$			16.6830i			0.942977i	0.881872	+	0.471489i	$0.156283\pi$
$313$			16.6830i			0.942977i	−0.881872	+	0.471489i	$0.843717\pi$
$314$	12.1791	−	8.29341i	0.687304	−	0.468024i
$315$	2.21302	+	16.8247i	0.124689	+	0.947964i
$316$	−14.1341	−	5.56577i	−0.795107	−	0.313099i
$317$			0.306078i			0.0171911i	0.999963	+	0.00859554i	$0.00273608\pi$
$317$			0.306078i			0.0171911i	−0.999963	+	0.00859554i	$0.997264\pi$
$318$	6.90827	+	11.1367i	0.387397	+	0.624515i
$319$			1.58270i			0.0886140i
$320$	−1.33628	+	17.0515i	−0.0747005	+	0.953206i
$321$	1.10355	−	1.73615i	0.0615940	−	0.0969025i
$322$	24.8130	+	5.89806i	1.38277	+	0.328686i
$323$	21.3222			1.18640
$324$	−17.9957	−	0.395324i	−0.999759	−	0.0219624i
$325$	−1.09075	+	1.88923i	−0.0605039	+	0.104796i
$326$	−5.12684	−	2.47254i	−0.283949	−	0.136942i
$327$	−0.924590	+	21.6873i	−0.0511299	+	1.19931i
$328$	−10.6270	−	11.4924i	−0.586780	−	0.634563i
$329$	−25.6543	−	8.15000i	−1.41437	−	0.449324i
$330$	16.0493	+	8.60124i	0.883485	+	0.473483i
$331$	−31.2531			−1.71783			−0.858913	−	0.512122i	$-0.828859\pi$
$331$	−31.2531			−1.71783			−0.858913	+	0.512122i	$0.828859\pi$
$332$	18.8483	−	14.9960i	1.03443	−	0.823012i
$333$	−0.261649	+	3.06306i	−0.0143383	+	0.167855i
$334$	−29.1797	−	14.0726i	−1.59664	−	0.770020i
$335$	−11.4021	+	19.7490i	−0.622963	+	1.07900i
$336$	−9.99756	+	15.3639i	−0.545412	+	0.838168i
$337$	−5.73132	−	9.92694i	−0.312205	−	0.540755i	0.666634	−	0.745385i	$-0.267734\pi$
$337$	−5.73132	−	9.92694i	−0.312205	−	0.540755i	−0.978839	+	0.204630i	$0.934401\pi$
$338$	−1.34748	−	18.1190i	−0.0732935	−	0.985545i
$339$	5.81561	−	9.14939i	0.315861	−	0.496927i
$340$	−1.65789	−	11.0848i	−0.0899119	−	0.601159i
$341$	−2.39179	−	4.14270i	−0.129523	−	0.224340i
$342$	−16.9266	−	30.0757i	−0.915285	−	1.62631i
$343$	11.1786	+	14.7662i	0.603586	+	0.797298i
$344$	20.3938	+	6.32874i	1.09956	+	0.341223i
$345$	21.3022	+	13.5403i	1.14687	+	0.728984i
$346$	−7.41107	+	5.04662i	−0.398422	+	0.271308i
$347$	−31.0495			−1.66682			−0.833411	−	0.552653i	$-0.813615\pi$
$347$	−31.0495			−1.66682			−0.833411	+	0.552653i	$0.813615\pi$
$348$	−1.44123	−	0.639715i	−0.0772581	−	0.0342923i
$349$	6.32917	−	10.9625i	0.338793	−	0.586807i	−0.645413	−	0.763834i	$-0.723315\pi$
$349$	6.32917	−	10.9625i	0.338793	−	0.586807i	0.984206	+	0.177027i	$0.0566481\pi$
$350$	−1.16707	−	1.10253i	−0.0623825	−	0.0589327i
$351$	10.1846	+	24.3753i	0.543615	+	1.30106i
$352$	7.13382	+	18.3296i	0.380234	+	0.976970i
$353$	−8.41353	+	4.85755i	−0.447807	+	0.258541i	−0.706904	−	0.707310i	$-0.749909\pi$
$353$	−8.41353	+	4.85755i	−0.447807	+	0.258541i	0.259097	+	0.965851i	$0.416575\pi$
$354$	9.06261	−	16.9102i	0.481672	−	0.898766i
$355$	−12.2353	−	7.06407i	−0.649384	−	0.374922i
$356$	1.53621	+	10.2712i	0.0814187	+	0.544373i
$357$	4.12120	−	11.2828i	0.218117	−	0.597148i
$358$	1.13422	+	15.2513i	0.0599452	+	0.806056i
$359$	−20.1951	+	11.6596i	−1.06586	+	0.615372i	−0.927046	−	0.374947i	$-0.877661\pi$
$359$	−20.1951	+	11.6596i	−1.06586	+	0.615372i	−0.138809	+	0.990319i	$0.544328\pi$
$360$	−14.3194	+	11.1382i	−0.754701	+	0.587034i
$361$	23.5850	−	40.8504i	1.24131	−	2.15002i
$362$	14.8095	−	10.0847i	0.778373	−	0.530038i
$363$	1.88541	+	0.0803804i	0.0989586	+	0.00421888i
$364$	26.5623	+	4.26312i	1.39224	+	0.223448i
$365$	28.7473	−	16.5973i	1.50470	−	0.868742i
$366$	−11.2589	−	6.03397i	−0.588515	−	0.315400i
$367$	−8.08674	−	14.0066i	−0.422124	−	0.731141i	0.574023	−	0.818839i	$-0.305382\pi$
$367$	−8.08674	−	14.0066i	−0.422124	−	0.731141i	−0.996147	+	0.0876985i	$0.972049\pi$
$368$	7.97736	+	26.0721i	0.415849	+	1.35910i
$369$	1.41304	−	16.5421i	0.0735597	−	0.861145i
$370$	1.74390	+	2.56096i	0.0906612	+	0.133138i
$371$	9.54059	+	10.4572i	0.495323	+	0.542910i
$372$	4.73916	−	0.503554i	0.245714	−	0.0261081i
$373$	−20.8772	−	12.0535i	−1.08098	−	0.624105i	−0.149820	−	0.988713i	$-0.547869\pi$
$373$	−20.8772	−	12.0535i	−1.08098	−	0.624105i	−0.931161	+	0.364609i	$0.881203\pi$
$374$	−7.25461	−	10.6536i	−0.375127	−	0.550883i
$375$	−9.30143	−	17.8232i	−0.480324	−	0.920386i
$376$	−6.35552	−	28.0657i	−0.327761	−	1.44738i
$377$			2.31421i			0.119188i
$378$	−19.1864	+	3.14371i	−0.986841	+	0.161695i
$379$	1.25354			0.0643900			0.0321950	−	0.999482i	$-0.489750\pi$
$379$	1.25354			0.0643900			0.0321950	+	0.999482i	$0.489750\pi$
$380$	−32.3637	−	12.7443i	−1.66022	−	0.653768i
$381$	9.22996	−	4.81686i	0.472865	−	0.246775i
$382$	19.6510	+	28.8580i	1.00543	+	1.47650i
$383$	5.63149	−	9.75403i	0.287756	−	0.498408i	−0.685518	−	0.728056i	$-0.740424\pi$
$383$	5.63149	−	9.75403i	0.287756	−	0.498408i	0.973274	+	0.229648i	$0.0737575\pi$
$384$	−19.5747	−	0.912504i	−0.998915	−	0.0465660i
$385$	18.7446	+	5.95489i	0.955314	+	0.303489i
$386$	15.2455	−	10.3815i	0.775977	−	0.528407i
$387$	9.61380	+	20.5069i	0.488697	+	1.04242i
$388$	−14.1926	+	11.2919i	−0.720523	+	0.573260i
$389$	30.2800	−	17.4822i	1.53526	−	0.886381i	0.536150	−	0.844123i	$-0.319878\pi$
$389$	30.2800	−	17.4822i	1.53526	−	0.886381i	0.999107	−	0.0422580i	$-0.0134551\pi$
$390$	23.4671	+	12.5767i	1.18830	+	0.636844i
$391$	−8.93349	−	15.4733i	−0.451786	−	0.782516i
$392$	−7.57325	+	18.2933i	−0.382507	+	0.923953i
$393$	−0.120608	+	2.82899i	−0.00608385	+	0.142704i
$394$	−2.05349	−	3.01559i	−0.103453	−	0.151923i
$395$	−14.0629	−	8.11921i	−0.707580	−	0.408522i
$396$	−9.26817	+	18.6902i	−0.465743	+	0.939219i
$397$	13.5914	+	23.5409i	0.682131	+	1.18149i	0.974329	+	0.225128i	$0.0722801\pi$
$397$	13.5914	+	23.5409i	0.682131	+	1.18149i	−0.292198	+	0.956358i	$0.594387\pi$
$398$	−0.0467816	−	0.629051i	−0.00234495	−	0.0315315i
$399$	−23.9285	−	28.5831i	−1.19792	−	1.43095i
$400$	0.385724	−	1.67244i	0.0192862	−	0.0836222i
$401$	−5.47680	+	9.48609i	−0.273498	+	0.473713i	−0.969755	−	0.244080i	$-0.921514\pi$
$401$	−5.47680	+	9.48609i	−0.273498	+	0.473713i	0.696257	+	0.717793i	$0.254847\pi$
$402$	−23.0284	−	12.3415i	−1.14855	−	0.615538i
$403$	−3.49726	−	6.05743i	−0.174211	−	0.301742i
$404$	−16.7860	+	2.51058i	−0.835135	+	0.124906i
$405$	−18.9630	−	3.26347i	−0.942277	−	0.162163i
$406$	−1.65700	−	0.393870i	−0.0822354	−	0.0195474i
$407$	3.08566	+	1.78151i	0.152950	+	0.0883060i
$408$	12.6336	−	2.30008i	0.625455	−	0.113871i
$409$		−	8.70886i		−	0.430625i	−0.976545	−	0.215313i	$-0.930923\pi$
$409$		−	8.70886i		−	0.430625i	0.976545	−	0.215313i	$-0.0690771\pi$
$410$	−9.41795	−	13.8305i	−0.465120	−	0.683038i
$411$	0.447485	−	0.704005i	0.0220728	−	0.0347260i
$412$	−2.79963	−	3.51882i	−0.137928	−	0.173360i
$413$	6.27431	−	19.7501i	0.308739	−	0.971838i
$414$	−14.7338	+	24.8844i	−0.724124	+	1.22300i
$415$	22.2981	−	12.8738i	1.09457	−	0.631950i
$416$	10.4310	+	26.8014i	0.511423	+	1.31404i
$417$	0.201850	+	0.128302i	0.00988466	+	0.00628297i
$418$	−39.8889	+	2.96648i	−1.95103	+	0.145095i
$419$	0.313456	−	0.180974i	0.0153133	−	0.00884115i	−0.492324	−	0.870412i	$-0.663852\pi$
$419$	0.313456	−	0.180974i	0.0153133	−	0.00884115i	0.507637	+	0.861571i	$0.330519\pi$
$420$	−12.9991	+	14.6622i	−0.634289	+	0.715444i
$421$	−24.4125	−	14.0946i	−1.18979	−	0.686926i	−0.231532	−	0.972827i	$-0.574374\pi$
$421$	−24.4125	−	14.0946i	−1.18979	−	0.686926i	−0.958259	+	0.285901i	$0.907707\pi$
$422$	−26.5157	−	12.7879i	−1.29076	−	0.622503i
$423$	17.4553	−	25.0380i	0.848705	−	1.21739i
$424$	−4.48509	+	14.4528i	−0.217815	+	0.701892i
$425$			1.12473i			0.0545573i
$426$	7.64608	−	14.2670i	0.370454	−	0.691240i
$427$	−13.1498	−	4.17749i	−0.636362	−	0.202163i
$428$	2.34931	−	0.351372i	0.113558	−	0.0169842i
$429$	30.5900	+	1.30414i	1.47690	+	0.0629644i
$430$	20.5602	+	9.91564i	0.991499	+	0.478175i
$431$	−8.43356	−	4.86912i	−0.406230	−	0.234537i	0.282938	−	0.959138i	$-0.408691\pi$
$431$	−8.43356	−	4.86912i	−0.406230	−	0.234537i	−0.689169	+	0.724601i	$0.742024\pi$
$432$	−13.2735	−	15.9942i	−0.638621	−	0.769521i
$433$			15.4570i			0.742814i	0.928470	+	0.371407i	$0.121125\pi$
$433$			15.4570i			0.742814i	−0.928470	+	0.371407i	$0.878875\pi$
$434$	4.93241	−	1.47312i	0.236763	−	0.0707122i
$435$	−1.42255	−	0.904214i	−0.0682061	−	0.0433538i
$436$	−19.6144	+	15.6056i	−0.939360	+	0.747370i
$437$	−55.4473			−2.65240
$438$	20.0476	+	32.3183i	0.957910	+	1.54423i
$439$	−12.5194			−0.597519			−0.298760	−	0.954328i	$-0.596573\pi$
$439$	−12.5194			−0.597519			−0.298760	+	0.954328i	$0.596573\pi$
$440$	4.64373	+	20.5065i	0.221381	+	0.977610i
$441$	−19.7499	+	7.13730i	−0.940472	+	0.339871i
$442$	−10.6076	−	15.5775i	−0.504554	−	0.740948i
$443$	18.1150			0.860669			0.430335	−	0.902669i	$-0.358396\pi$
$443$	18.1150			0.860669			0.430335	+	0.902669i	$0.358396\pi$
$444$	−2.86947	+	2.08978i	−0.136179	+	0.0991766i
$445$			11.1019i			0.526280i
$446$	−1.51213	−	20.3330i	−0.0716016	−	0.962795i
$447$	−0.384262	+	9.01330i	−0.0181750	+	0.426314i
$448$	−20.9654	+	2.90723i	−0.990522	+	0.137354i
$449$	−10.3243			−0.487235			−0.243617	−	0.969871i	$-0.578334\pi$
$449$	−10.3243			−0.487235			−0.243617	+	0.969871i	$0.578334\pi$
$450$	1.58647	−	0.892863i	0.0747868	−	0.0420900i
$451$	−16.6641	−	9.62103i	−0.784683	−	0.453037i
$452$	12.3807	−	1.85171i	0.582339	−	0.0870970i
$453$	22.6876	+	14.4209i	1.06596	+	0.677552i
$454$	1.31434	−	2.72529i	0.0616850	−	0.127904i
$455$	27.4082	+	8.70719i	1.28492	+	0.408199i
$456$	13.4215	−	37.5226i	0.628519	−	1.75715i
$457$	5.15167			0.240985			0.120493	−	0.992714i	$-0.461553\pi$
$457$	5.15167			0.240985			0.120493	+	0.992714i	$0.461553\pi$
$458$	−0.258945	−	3.48192i	−0.0120997	−	0.162700i
$459$	10.8311	+	8.25814i	0.505553	+	0.385457i
$460$	4.31126	+	28.8255i	0.201014	+	1.34400i
$461$	−2.70721	+	4.68902i	−0.126087	+	0.218389i	−0.922157	−	0.386815i	$-0.873575\pi$
$461$	−2.70721	+	4.68902i	−0.126087	+	0.218389i	0.796070	+	0.605204i	$0.206909\pi$
$462$	−6.14010	+	21.6809i	−0.285663	+	1.00868i
$463$	−16.7625	+	9.67783i	−0.779019	+	0.449767i	−0.836083	−	0.548604i	$-0.815160\pi$
$463$	−16.7625	+	9.67783i	−0.779019	+	0.449767i	0.0570635	+	0.998371i	$0.481826\pi$
$464$	−0.532725	−	1.74109i	−0.0247311	−	0.0808279i
$465$	5.08998	+	0.217000i	0.236042	+	0.0100631i
$466$	−15.6015	−	7.52418i	−0.722723	−	0.348551i
$467$	−16.5492	+	9.55466i	−0.765804	+	0.442137i	−0.831376	−	0.555711i	$-0.812446\pi$
$467$	−16.5492	+	9.55466i	−0.765804	+	0.442137i	0.0655718	+	0.997848i	$0.479113\pi$
$468$	−13.5518	+	27.3287i	−0.626434	+	1.26327i
$469$	−26.8957	−	8.54438i	−1.24193	−	0.394543i
$470$	−2.28138	−	30.6767i	−0.105232	−	1.41501i
$471$	8.34922	+	15.9986i	0.384712	+	0.737177i
$472$	21.6065	−	4.89282i	0.994520	−	0.225210i
$473$	26.2497			1.20696
$474$	8.78814	−	16.3980i	0.403653	−	0.753187i
$475$	3.02278	+	1.74520i	0.138695	+	0.0800754i
$476$	12.9591	−	4.94394i	0.593979	−	0.226605i
$477$	−14.5329	+	6.81317i	−0.665417	+	0.311954i
$478$	−0.898335	+	1.86271i	−0.0410889	+	0.0851982i
$479$	7.29764	+	12.6399i	0.333438	+	0.577531i	0.983183	−	0.182620i	$-0.0584579\pi$
$479$	7.29764	+	12.6399i	0.333438	+	0.577531i	−0.649746	+	0.760152i	$0.725125\pi$
$480$	−20.5505	−	4.05993i	−0.937999	−	0.185309i
$481$	4.51183	+	2.60490i	0.205722	+	0.118773i
$482$	1.30508	−	2.70609i	0.0594447	−	0.123259i
$483$	−10.7170	+	29.3403i	−0.487639	+	1.33503i
$484$	1.35669	+	1.70521i	0.0616677	+	0.0775093i
$485$	−16.7903	+	9.69391i	−0.762410	+	0.440178i
$486$	3.05015	−	21.8334i	0.138358	−	0.990382i
$487$	−31.6248	−	18.2586i	−1.43306	−	0.827376i	−0.435705	−	0.900090i	$-0.643501\pi$
$487$	−31.6248	−	18.2586i	−1.43306	−	0.827376i	−0.997353	+	0.0727131i	$0.976834\pi$
$488$	−3.25768	−	14.3858i	−0.147468	−	0.651214i
$489$	3.73956	−	5.88325i	0.169109	−	0.266050i
$490$	−10.8992	+	18.1427i	−0.492377	+	0.819602i
$491$	17.0469	+	29.5260i	0.769314	+	1.33249i	0.937935	+	0.346810i	$0.112735\pi$
$491$	17.0469	+	29.5260i	0.769314	+	1.33249i	−0.168621	+	0.985681i	$0.553931\pi$
$492$	15.4966	−	11.2859i	0.698640	−	0.508806i
$493$	0.596574	+	1.03330i	0.0268684	+	0.0465374i
$494$	−58.3253	+	4.33756i	−2.62418	+	0.195156i
$495$	−12.7539	+	18.2943i	−0.573245	+	0.822266i
$496$	4.02555	+	3.75222i	0.180753	+	0.168480i
$497$	5.29360	−	16.6630i	0.237450	−	0.747439i
$498$	15.5500	+	25.0679i	0.696813	+	1.12332i
$499$	−2.96932	+	5.14301i	−0.132925	+	0.230233i	−0.924803	−	0.380447i	$-0.875770\pi$
$499$	−2.96932	+	5.14301i	−0.132925	+	0.230233i	0.791878	+	0.610679i	$0.209104\pi$
$500$	8.50573	−	21.6001i	0.380388	−	0.965984i
$501$	21.2839	−	33.4849i	0.950896	−	1.49599i
$502$	23.6061	+	34.6660i	1.05359	+	1.54722i
$503$	29.8048			1.32893			0.664465	−	0.747319i	$-0.268659\pi$
$503$	29.8048			1.32893			0.664465	+	0.747319i	$0.268659\pi$
$504$	−17.2612	−	14.3545i	−0.768873	−	0.639401i
$505$	−18.1436			−0.807378
$506$	18.8653	+	27.7040i	0.838663	+	1.23159i
$507$	22.2323	+	0.947824i	0.987370	+	0.0420943i
$508$	11.1859	+	4.40480i	0.496292	+	0.195431i
$509$	4.51459	−	7.81949i	0.200106	−	0.346593i	−0.748457	−	0.663184i	$-0.769205\pi$
$509$	4.51459	−	7.81949i	0.200106	−	0.346593i	0.948562	+	0.316591i	$0.102538\pi$
$510$	13.7202	−	0.434045i	0.607542	−	0.0192198i
$511$	27.6865	+	30.3464i	1.22478	+	1.34244i
$512$	−14.0173	−	17.7627i	−0.619485	−	0.785008i
$513$	39.0006	−	16.2954i	1.72192	−	0.719461i
$514$	−2.33192	+	0.173422i	−0.102857	+	0.00764930i
$515$	−2.40344	−	4.16288i	−0.105908	−	0.183438i
$516$	−10.6099	+	23.9034i	−0.467076	+	1.05229i
$517$	−17.6874	−	30.6356i	−0.777893	−	1.34735i
$518$	−2.63304	+	2.78717i	−0.115689	+	0.122461i
$519$	−5.08058	−	9.73530i	−0.223013	−	0.427332i
$520$	6.79002	+	29.9845i	0.297762	+	1.31491i
$521$	5.73970	+	3.31382i	0.251461	+	0.145181i	0.620433	−	0.784260i	$-0.286957\pi$
$521$	5.73970	+	3.31382i	0.251461	+	0.145181i	−0.368972	+	0.929440i	$0.620290\pi$
$522$	0.983913	−	1.66177i	0.0430647	−	0.0727338i
$523$	−18.6354	+	10.7592i	−0.814869	+	0.470465i	−0.848644	−	0.528964i	$-0.822580\pi$
$523$	−18.6354	+	10.7592i	−0.814869	+	0.470465i	0.0337747	+	0.999429i	$0.489247\pi$
$524$	−2.55859	+	2.03566i	−0.111773	+	0.0889281i
$525$	1.50774	−	1.26221i	0.0658030	−	0.0550872i
$526$	3.95017	−	8.19071i	0.172236	−	0.357132i
$527$	−3.12306	−	1.80310i	−0.136043	−	0.0785443i
$528$	−23.3145	+	6.06059i	−1.01463	+	0.263753i
$529$	11.7311	+	20.3188i	0.510047	+	0.883427i
$530$	−7.02708	+	14.5707i	−0.305237	+	0.632911i
$531$	19.2756	+	13.4380i	0.836488	+	0.583161i
$532$	6.82101	−	42.4998i	0.295728	−	1.84260i
$533$	−24.3661	−	14.0678i	−1.05541	−	0.609344i
$534$	−12.7132	+	0.402187i	−0.550153	+	0.0174043i
$535$	2.53931			0.109784
$536$	−6.66306	−	29.4238i	−0.287800	−	1.27091i
$537$	−18.7135	−	0.797810i	−0.807549	−	0.0344280i
$538$	−0.619492	−	8.33004i	−0.0267082	−	0.359133i
$539$	−2.22645	+	24.2370i	−0.0959000	+	1.04396i
$540$	−11.5040	−	19.0083i	−0.495054	−	0.817988i
$541$	9.24892	−	5.33987i	0.397642	−	0.229579i	−0.287824	−	0.957683i	$-0.592932\pi$
$541$	9.24892	−	5.33987i	0.397642	−	0.229579i	0.685466	+	0.728104i	$0.259598\pi$
$542$	−30.6048	−	14.7599i	−1.31459	−	0.633992i
$543$	10.1525	+	19.4541i	0.435687	+	0.834854i
$544$	11.5665	+	9.27786i	0.495911	+	0.397785i
$545$	−23.2044	+	13.3971i	−0.993969	+	0.573868i
$546$	−8.97800	+	31.7016i	−0.384223	+	1.35670i
$547$	21.4549	−	37.1609i	0.917343	−	1.58889i	0.113909	−	0.993491i	$-0.463663\pi$
$547$	21.4549	−	37.1609i	0.917343	−	1.58889i	0.803434	−	0.595394i	$-0.203004\pi$
$548$	0.952639	−	0.142481i	0.0406947	−	0.00608647i
$549$	8.94715	−	12.8338i	0.381855	−	0.547735i
$550$	−0.156479	−	2.10411i	−0.00667230	−	0.0897194i
$551$	3.70274			0.157742
$552$	−32.8529	+	5.98124i	−1.39831	+	0.254579i
$553$	6.08428	−	19.1519i	0.258730	−	0.814423i
$554$	−11.2157	+	23.2559i	−0.476510	+	0.988047i
$555$	−3.36412	+	1.75564i	−0.142799	+	0.0745228i
$556$	0.0408517	+	0.273138i	0.00173250	+	0.0115836i
$557$	9.07376	+	5.23874i	0.384467	+	0.221972i	0.679760	−	0.733434i	$-0.262084\pi$
$557$	9.07376	+	5.23874i	0.384467	+	0.221972i	−0.295293	+	0.955407i	$0.595417\pi$
$558$	−0.0641005	+	5.83658i	−0.00271359	+	0.247082i
$559$	38.3821			1.62339
$560$	−22.6249	−	0.241516i	−0.956074	−	0.0102059i
$561$	13.9947	−	7.30344i	0.590856	−	0.308352i
$562$	1.19008	+	16.0025i	0.0502005	+	0.675024i
$563$			27.4002i			1.15478i	0.816469	+	0.577390i	$0.195929\pi$
$563$			27.4002i			1.15478i	−0.816469	+	0.577390i	$0.804071\pi$
$564$	35.0464	−	3.72381i	1.47572	−	0.156801i
$565$	13.3820			0.562984
$566$	13.1485	+	19.3089i	0.552673	+	0.811612i
$567$	−1.08471	−	23.7870i	−0.0455534	−	0.998962i
$568$	18.2293	−	4.12805i	0.764884	−	0.173209i
$569$	−12.7459			−0.534335			−0.267168	−	0.963650i	$-0.586088\pi$
$569$	−12.7459			−0.534335			−0.267168	+	0.963650i	$0.586088\pi$
$570$	20.1227	−	37.5476i	0.842848	−	1.57269i
$571$	−0.607325			−0.0254157			−0.0127079	−	0.999919i	$-0.504045\pi$
$571$	−0.607325			−0.0254157			−0.0127079	+	0.999919i	$0.504045\pi$
$572$	22.0117	+	27.6662i	0.920356	+	1.15678i
$573$	−37.9083	+	19.7833i	−1.58364	+	0.826459i
$574$	14.2197	−	15.0521i	0.593520	−	0.628264i
$575$		−	2.92479i		−	0.121972i
$576$	3.90469	−	23.6802i	0.162695	−	0.986676i
$577$	6.93643	+	4.00475i	0.288767	+	0.166720i	0.637386	−	0.770545i	$-0.280016\pi$
$577$	6.93643	+	4.00475i	0.288767	+	0.166720i	−0.348618	+	0.937265i	$0.613349\pi$
$578$	12.9028	+	6.22269i	0.536686	+	0.258830i
$579$	10.4514	+	20.0268i	0.434346	+	0.832285i
$580$	−0.287904	−	1.92496i	−0.0119546	−	0.0799294i
$581$	21.4752	+	23.5384i	0.890941	+	0.976536i
$582$	−11.7091	−	18.8760i	−0.485358	−	0.782437i
$583$			18.6028i			0.770449i
$584$	−13.0156	+	41.9416i	−0.538589	+	1.73556i
$585$	−18.6486	+	26.7497i	−0.771026	+	1.10596i
$586$	−8.90815	−	4.29618i	−0.367992	−	0.177473i
$587$	−41.0822	−	23.7188i	−1.69564	−	0.978981i	−0.949798	−	0.312863i	$-0.898712\pi$
$587$	−41.0822	−	23.7188i	−1.69564	−	0.978981i	−0.745846	−	0.666118i	$-0.767955\pi$
$588$	−21.1707	−	11.8238i	−0.873063	−	0.487607i
$589$	−9.69191	+	5.59563i	−0.399348	+	0.230564i
$590$	23.6166	−	1.75633i	0.972280	−	0.0723070i
$591$	3.96133	−	2.06731i	0.162947	−	0.0850377i
$592$	−3.99410	−	0.921179i	−0.164156	−	0.0378602i
$593$	12.9623	−	7.48376i	0.532296	−	0.307321i	−0.209655	−	0.977775i	$-0.567234\pi$
$593$	12.9623	−	7.48376i	0.532296	−	0.307321i	0.741951	+	0.670454i	$0.233901\pi$
$594$	−21.4114	−	13.9422i	−0.878522	−	0.572055i
$595$	14.4824	−	3.17773i	0.593721	−	0.130274i
$596$	−8.15180	+	6.48571i	−0.333911	+	0.265665i
$597$	0.771853	+	0.0329062i	0.0315899	+	0.00134676i
$598$	27.5846	+	40.5086i	1.12802	+	1.65652i
$599$			39.6923i			1.62178i	0.585195	+	0.810892i	$0.301018\pi$
$599$			39.6923i			1.62178i	−0.585195	+	0.810892i	$0.698982\pi$
$600$	1.97928	+	0.707972i	0.0808039	+	0.0289028i
$601$	18.0692	+	10.4323i	0.737058	+	0.425540i	0.820998	−	0.570930i	$-0.193417\pi$
$601$	18.0692	+	10.4323i	0.737058	+	0.425540i	−0.0839409	+	0.996471i	$0.526751\pi$
$602$	−6.53249	+	27.4820i	−0.266245	+	1.12008i
$603$	18.2999	−	26.2495i	0.745231	−	1.06896i
$604$	4.59165	+	30.7002i	0.186832	+	1.24917i
$605$	1.16469	+	2.01731i	0.0473516	+	0.0820153i
$606$	−0.657284	−	20.7768i	−0.0267003	−	0.844002i
$607$	3.69369	−	6.39766i	0.149922	−	0.259673i	−0.781276	−	0.624185i	$-0.785431\pi$
$607$	3.69369	−	6.39766i	0.149922	−	0.259673i	0.931199	+	0.364512i	$0.118764\pi$
$608$	42.8823	−	16.6897i	1.73911	−	0.676856i
$609$	0.715675	−	1.95933i	0.0290006	−	0.0793961i
$610$	−1.16938	−	15.7241i	−0.0473468	−	0.636652i
$611$	−25.8624	−	44.7950i	−1.04628	−	1.81221i
$612$	0.994081	+	15.6958i	0.0401833	+	0.634465i
$613$	−27.7143	−	16.0009i	−1.11937	−	0.646269i	−0.178131	−	0.984007i	$-0.557005\pi$
$613$	−27.7143	−	16.0009i	−1.11937	−	0.646269i	−0.941240	+	0.337738i	$0.890338\pi$
$614$	−0.633453	−	0.930240i	−0.0255641	−	0.0375414i
$615$	18.1679	−	9.48134i	0.732602	−	0.382324i
$616$	−23.5556	+	11.0519i	−0.949084	+	0.445295i
$617$	−14.2551	−	24.6906i	−0.573890	−	0.994006i	−0.996161	−	0.0875368i	$-0.972100\pi$
$617$	−14.2551	−	24.6906i	−0.573890	−	0.994006i	0.422272	−	0.906469i	$-0.361233\pi$
$618$	4.67999	−	2.90307i	0.188257	−	0.116779i
$619$	20.2234	−	11.6760i	0.812849	−	0.469298i	−0.0350954	−	0.999384i	$-0.511174\pi$
$619$	20.2234	−	11.6760i	0.812849	−	0.469298i	0.847944	+	0.530085i	$0.177840\pi$
$620$	3.66260	+	4.60348i	0.147094	+	0.184880i
$621$	−28.1657	−	21.4749i	−1.13025	−	0.861757i
$622$	10.6186	−	7.23081i	0.425767	−	0.289929i
$623$	−13.4194	+	2.94449i	−0.537638	+	0.117969i
$624$	−34.0903	+	8.86174i	−1.36470	+	0.354754i
$625$	11.3352	−	19.6332i	0.453409	−	0.785327i
$626$	−13.2795	−	19.5012i	−0.530755	−	0.779426i
$627$	2.08663	−	48.9442i	0.0833319	−	1.95464i
$628$	−7.63498	+	19.3888i	−0.304669	+	0.773699i
$629$	2.68605			0.107100
$630$	−15.9792	−	17.9053i	−0.636625	−	0.713366i
$631$			29.5430i			1.17609i	0.808829	+	0.588043i	$0.200102\pi$
$631$			29.5430i			1.17609i	−0.808829	+	0.588043i	$0.799898\pi$
$632$	20.9521	−	4.74464i	0.833430	−	0.188731i
$633$	19.3408	−	30.4278i	0.768727	−	1.20940i
$634$	−0.243636	−	0.357784i	−0.00967601	−	0.0142094i
$635$	11.1295	+	6.42560i	0.441660	+	0.254992i
$636$	−16.9400	−	7.51911i	−0.671715	−	0.298152i
$637$	−3.25550	+	35.4391i	−0.128988	+	1.40415i
$638$	−1.25981	−	1.85006i	−0.0498765	−	0.0732447i
$639$	16.2627	+	11.3376i	0.643342	+	0.448508i
$640$	−12.0108	−	20.9957i	−0.474769	−	0.829926i
$641$	13.9238	+	24.1168i	0.549958	+	0.952556i	0.998277	+	0.0586820i	$0.0186898\pi$
$641$	13.9238	+	24.1168i	0.549958	+	0.952556i	−0.448318	+	0.893874i	$0.647977\pi$
$642$	0.0919911	+	2.90785i	0.00363060	+	0.114764i
$643$	29.8516	−	17.2349i	1.17723	−	0.679676i	0.221861	−	0.975078i	$-0.428787\pi$
$643$	29.8516	−	17.2349i	1.17723	−	0.679676i	0.955373	+	0.295402i	$0.0954536\pi$
$644$	−33.6994	+	12.8565i	−1.32794	+	0.506616i
$645$	−14.9968	+	23.5936i	−0.590497	+	0.928997i
$646$	−24.9242	+	16.9723i	−0.980628	+	0.667765i
$647$	17.3591	−	30.0668i	0.682456	−	1.18205i	−0.291774	−	0.956487i	$-0.594245\pi$
$647$	17.3591	−	30.0668i	0.682456	−	1.18205i	0.974229	−	0.225560i	$-0.0724212\pi$
$648$	21.3503	−	13.8623i	0.838721	−	0.544562i
$649$	23.5849	−	13.6167i	0.925788	−	0.534504i
$650$	−0.228803	−	3.07661i	−0.00897438	−	0.120674i
$651$	1.08769	+	6.21008i	0.0426298	+	0.243392i
$652$	7.96104	−	1.19069i	0.311778	−	0.0466309i
$653$	−11.7219	−	6.76762i	−0.458712	−	0.264837i	0.252791	−	0.967521i	$-0.418652\pi$
$653$	−11.7219	−	6.76762i	−0.458712	−	0.264837i	−0.711502	+	0.702684i	$0.751985\pi$
$654$	−16.1821	−	26.0869i	−0.632771	−	1.02008i
$655$	−3.02689	+	1.74758i	−0.118270	+	0.0682835i
$656$	21.5701	+	4.97483i	0.842172	+	0.194234i
$657$	−42.1741	+	19.7716i	−1.64537	+	0.771363i
$658$	36.4755	−	10.8938i	1.42196	−	0.424686i
$659$	−17.2124	+	29.8127i	−0.670499	+	1.16134i	0.307264	+	0.951624i	$0.400587\pi$
$659$	−17.2124	+	29.8127i	−0.670499	+	1.16134i	−0.977763	+	0.209714i	$0.932747\pi$
$660$	−25.6070	+	2.72085i	−0.996752	+	0.105909i
$661$	14.7241			0.572703			0.286351	−	0.958125i	$-0.407558\pi$
$661$	14.7241			0.572703			0.286351	+	0.958125i	$0.407558\pi$
$662$	36.5327	−	24.8772i	1.41988	−	0.966879i
$663$	20.4629	−	10.6790i	0.794714	−	0.414739i
$664$	−10.0956	+	32.5323i	−0.391786	+	1.26250i
$665$	13.9315	−	43.8533i	0.540242	−	1.70056i
$666$	−2.13232	−	3.78877i	−0.0826256	−	0.146812i
$667$	−1.55136	−	2.68704i	−0.0600689	−	0.104042i
$668$	45.3108	−	6.77686i	1.75313	−	0.262205i
$669$	24.9488	+	1.06364i	0.964578	+	0.0411226i
$670$	−2.39178	−	32.1612i	−0.0924024	−	1.24249i
$671$	−9.06615	−	15.7030i	−0.349995	−	0.606209i
$672$	−0.543059	−	25.9173i	−0.0209489	−	0.999781i
$673$	−2.90448	+	5.03071i	−0.111959	+	0.193919i	−0.916560	−	0.399897i	$-0.869046\pi$
$673$	−2.90448	+	5.03071i	−0.111959	+	0.193919i	0.804601	+	0.593816i	$0.202379\pi$
$674$	14.6013	+	7.04182i	0.562420	+	0.271241i
$675$	0.859570	+	2.05725i	0.0330849	+	0.0791835i
$676$	15.9977	+	20.1073i	0.615296	+	0.773358i
$677$	28.0519			1.07812			0.539061	−	0.842266i	$-0.318779\pi$
$677$	28.0519			1.07812			0.539061	+	0.842266i	$0.318779\pi$
$678$	0.484787	+	15.3242i	0.0186181	+	0.588521i
$679$	−16.1707	−	17.7243i	−0.620575	−	0.680195i
$680$	10.7614	+	11.6377i	0.412680	+	0.446286i
$681$	3.12738	+	1.98785i	0.119842	+	0.0761747i
$682$	6.09339	+	2.93869i	0.233328	+	0.112528i
$683$	6.52433	−	11.3005i	0.249647	−	0.432401i	−0.713781	−	0.700369i	$-0.753019\pi$
$683$	6.52433	−	11.3005i	0.249647	−	0.432401i	0.963428	+	0.267968i	$0.0863522\pi$
$684$	43.7260	+	21.6830i	1.67191	+	0.829071i
$685$	1.02968			0.0393422
$686$	−24.8207	−	8.36258i	−0.947659	−	0.319285i
$687$	4.27236	+	0.182143i	0.163001	+	0.00694918i
$688$	−28.8766	+	8.83546i	−1.10091	+	0.336849i
$689$			27.2008i			1.03627i
$690$	−35.6787	+	1.12871i	−1.35827	+	0.0429693i
$691$		−	32.1183i		−	1.22184i	−0.791694	−	0.610918i	$-0.790801\pi$
$691$		−	32.1183i		−	1.22184i	0.791694	−	0.610918i	$-0.209199\pi$
$692$	4.64596	−	11.7983i	0.176613	−	0.448504i
$693$	−25.4958	−	10.5642i	−0.968507	−	0.401301i
$694$	36.2947	−	24.7151i	1.37773	−	0.938172i
$695$			0.295228i			0.0111986i
$696$	2.19391	−	0.399425i	0.0831598	−	0.0151401i
$697$	−14.5060			−0.549455
$698$	1.32765	+	17.8523i	0.0502523	+	0.675720i
$699$	11.3798	−	17.9033i	0.430425	−	0.677164i
$700$	2.24183	+	0.359802i	0.0847331	+	0.0135993i
$701$			19.3558i			0.731058i	0.930800	+	0.365529i	$0.119112\pi$
$701$			19.3558i			0.731058i	−0.930800	+	0.365529i	$0.880888\pi$
$702$	−31.3076	−	20.3862i	−1.18163	−	0.769426i
$703$	4.16786	−	7.21895i	0.157194	−	0.272268i
$704$	−22.9291	−	15.7475i	−0.864174	−	0.593508i
$705$	37.6407	+	1.60473i	1.41763	+	0.0604376i
$706$	5.96826	−	12.3752i	0.224618	−	0.465748i
$707$	−4.81211	−	21.9311i	−0.180978	−	0.824802i
$708$	2.86679	+	26.9806i	0.107741	+	1.01399i
$709$		−	22.2711i		−	0.836408i	−0.908353	−	0.418204i	$-0.862660\pi$
$709$		−	22.2711i		−	0.836408i	0.908353	−	0.418204i	$-0.137340\pi$
$710$	19.9252	−	1.48181i	0.747779	−	0.0556112i
$711$	18.6918	+	13.0310i	0.700997	+	0.488702i
$712$	−9.97151	−	10.7835i	−0.373698	−	0.404130i
$713$	8.12136	+	4.68887i	0.304147	+	0.175600i
$714$	4.16359	+	16.4692i	0.155818	+	0.616345i
$715$	18.8967	+	32.7300i	0.706695	+	1.22403i
$716$	−13.4657	−	16.9249i	−0.503237	−	0.632513i
$717$	−2.13753	−	1.35867i	−0.0798274	−	0.0507406i
$718$	14.3257	−	29.7044i	0.534630	−	1.10856i
$719$	−21.2576	−	36.8192i	−0.792775	−	1.37313i	−0.924243	−	0.381806i	$-0.875302\pi$
$719$	−21.2576	−	36.8192i	−0.792775	−	1.37313i	0.131468	−	0.991320i	$-0.458031\pi$
$720$	7.87252	−	24.4179i	0.293392	−	0.910002i
$721$	4.39443	−	4.00925i	0.163657	−	0.149312i
$722$	4.94734	+	66.5247i	0.184121	+	2.47579i
$723$	3.10534	+	1.97384i	0.115489	+	0.0734081i
$724$	−9.28403	+	23.5765i	−0.345038	+	0.876215i
$725$			0.195316i			0.00725387i
$726$	−2.26790	+	1.40681i	−0.0841697	+	0.0522118i
$727$	−9.34846	+	16.1920i	−0.346715	+	0.600529i	−0.985664	−	0.168721i	$-0.946036\pi$
$727$	−9.34846	+	16.1920i	−0.346715	+	0.600529i	0.638949	+	0.769249i	$0.279370\pi$
$728$	−34.4429	+	16.1601i	−1.27654	+	0.598931i
$729$	26.1225	+	6.82739i	0.967501	+	0.252866i
$730$	−20.3923	+	42.2837i	−0.754755	+	1.56499i
$731$	17.1377	−	9.89443i	0.633859	−	0.365959i
$732$	17.9639	−	1.90874i	0.663965	−	0.0705489i
$733$	−17.2708	+	29.9139i	−0.637911	+	1.10489i	0.347979	+	0.937502i	$0.386868\pi$
$733$	−17.2708	+	29.9139i	−0.637911	+	1.10489i	−0.985890	+	0.167392i	$0.946465\pi$
$734$	20.6020	+	9.93582i	0.760434	+	0.366738i
$735$	−20.5125	−	15.8480i	−0.756616	−	0.584564i
$736$	−30.0782	−	24.1266i	−1.10870	−	0.889318i
$737$	−18.5433	−	32.1180i	−0.683053	−	1.18308i
$738$	11.5156	+	20.4613i	0.423895	+	0.753190i
$739$	−5.00581	+	8.67033i	−0.184142	+	0.318943i	−0.943287	−	0.331978i	$-0.892284\pi$
$739$	−5.00581	+	8.67033i	−0.184142	+	0.318943i	0.759145	+	0.650921i	$0.225617\pi$
$740$	−4.07700	−	1.60545i	−0.149874	−	0.0590176i
$741$	3.05105	−	71.5658i	0.112083	−	2.62904i
$742$	−19.4761	−	4.62949i	−0.714990	−	0.169954i
$743$	−29.5323	+	17.0505i	−1.08344	+	0.625522i	−0.931821	−	0.362918i	$-0.881781\pi$
$743$	−29.5323	+	17.0505i	−1.08344	+	0.625522i	−0.151615	+	0.988440i	$0.548447\pi$
$744$	−5.13892	+	4.36095i	−0.188402	+	0.159880i
$745$	−9.64383	+	5.56787i	−0.353322	+	0.203991i
$746$	33.9985	−	2.52841i	1.24477	−	0.0925718i
$747$	−32.7126	+	15.3360i	−1.19689	+	0.561114i
$748$	16.9603	+	6.67866i	0.620129	+	0.244196i
$749$	0.673486	+	3.06939i	0.0246086	+	0.112153i
$750$	25.0598	+	13.4302i	0.915055	+	0.490402i
$751$	1.37947	+	0.796435i	0.0503374	+	0.0290623i	0.524958	−	0.851128i	$-0.324081\pi$
$751$	1.37947	+	0.796435i	0.0503374	+	0.0290623i	−0.474620	+	0.880191i	$0.657415\pi$
$752$	29.7692	+	27.7479i	1.08557	+	1.01186i
$753$	−45.5379	+	23.7649i	−1.65949	+	0.866043i
$754$	−1.84209	−	2.70515i	−0.0670849	−	0.0985156i
$755$			33.1831i			1.20766i
$756$	19.9252	−	18.9470i	0.724672	−	0.689094i
$757$		−	19.7086i		−	0.716323i	−0.933660	−	0.358161i	$-0.883404\pi$
$757$		−	19.7086i		−	0.716323i	0.933660	−	0.358161i	$-0.116596\pi$
$758$	−1.46530	+	0.997806i	−0.0532221	+	0.0362420i
$759$	−36.3925	+	18.9922i	−1.32096	+	0.689374i
$760$	47.9753	−	10.8641i	1.74025	−	0.394081i
$761$	24.3156	+	14.0386i	0.881441	+	0.508900i	0.871133	−	0.491047i	$-0.163386\pi$
$761$	24.3156	+	14.0386i	0.881441	+	0.508900i	0.0103075	+	0.999947i	$0.496719\pi$
$762$	−6.95500	+	12.9775i	−0.251953	+	0.470126i
$763$	−22.3481	−	24.4952i	−0.809057	−	0.886785i
$764$	−45.9414	−	18.0909i	−1.66210	−	0.654506i
$765$	−1.43090	+	16.7512i	−0.0517343	+	0.605640i
$766$	1.18130	+	15.8844i	0.0426821	+	0.573927i
$767$	34.4856	−	19.9103i	1.24520	−	0.718919i
$768$	23.6078	−	14.5146i	0.851872	−	0.523751i
$769$	−8.59535	+	4.96253i	−0.309956	+	0.178953i	−0.646907	−	0.762569i	$-0.723938\pi$
$769$	−8.59535	+	4.96253i	−0.309956	+	0.178953i	0.336951	+	0.941522i	$0.390604\pi$
$770$	−26.6512	+	7.95970i	−0.960442	+	0.286848i
$771$	0.121985	−	2.86130i	0.00439319	−	0.103047i
$772$	−9.55735	+	24.2706i	−0.343976	+	0.873518i
$773$	5.95467	−	10.3138i	0.214175	−	0.370961i	−0.738842	−	0.673878i	$-0.764627\pi$
$773$	5.95467	−	10.3138i	0.214175	−	0.370961i	0.953017	+	0.302917i	$0.0979605\pi$
$774$	−27.5612	−	16.3186i	−0.990665	−	0.586560i
$775$	−0.295165	−	0.511240i	−0.0106026	−	0.0183643i
$776$	7.60196	−	24.4967i	0.272894	−	0.879379i
$777$	−3.01438	−	3.60074i	−0.108140	−	0.129176i
$778$	−21.4796	+	44.5380i	−0.770079	+	1.59677i
$779$	−22.5085	+	38.9859i	−0.806452	+	1.39682i
$780$	−37.4424	+	3.97840i	−1.34065	+	0.142449i
$781$	19.8984	−	11.4884i	0.712022	−	0.411086i
$782$	22.7592	+	10.9762i	0.813867	+	0.392507i
$783$	1.88089	+	1.43408i	0.0672177	+	0.0512499i
$784$	−5.70872	−	27.4119i	−0.203883	−	0.978995i
$785$	−11.1377	+	19.2911i	−0.397522	+	0.688529i
$786$	−2.11087	−	3.40289i	−0.0752922	−	0.121377i
$787$			7.93246i			0.282762i	0.989955	+	0.141381i	$0.0451542\pi$
$787$			7.93246i			0.282762i	−0.989955	+	0.141381i	$0.954846\pi$
$788$	4.80077	+	1.89046i	0.171020	+	0.0673449i
$789$	9.39917	+	5.97438i	0.334619	+	0.212693i
$790$	22.9013	−	1.70314i	0.814793	−	0.0605949i
$791$	3.54922	+	16.1755i	0.126196	+	0.575134i
$792$	−4.04340	−	29.2249i	−0.143676	−	1.03846i
$793$	−13.2564	−	22.9608i	−0.470750	−	0.815363i
$794$	−34.6258	−	16.6991i	−1.22882	−	0.592630i
$795$	−16.7205	−	10.6280i	−0.593013	−	0.376936i
$796$	0.555403	+	0.698079i	0.0196857	+	0.0247428i
$797$	16.8171	+	29.1281i	0.595692	+	1.03177i	0.993449	+	0.114278i	$0.0364554\pi$
$797$	16.8171	+	29.1281i	0.595692	+	1.03177i	−0.397757	+	0.917491i	$0.630211\pi$
$798$	50.7227	+	14.3648i	1.79556	+	0.508510i
$799$	−23.0952	−	13.3340i	−0.817051	−	0.471724i
$800$	0.880366	+	2.26200i	0.0311256	+	0.0799739i
$801$	1.32587	−	15.5217i	0.0468474	−	0.548431i
$802$	−1.14885	−	15.4481i	−0.0405673	−	0.545490i
$803$			53.9847i			1.90508i
$804$	36.7423	−	3.90401i	1.29580	−	0.137684i
$805$	−37.6608	+	8.26353i	−1.32737	+	0.291251i
$806$	8.90971	+	4.29693i	0.313831	+	0.151353i
$807$	10.2211	+	0.435752i	0.359798	+	0.0153392i
$808$	17.6233	−	16.2962i	0.619984	−	0.573299i
$809$	0.384877	−	0.666626i	0.0135315	−	0.0234373i	−0.859180	−	0.511673i	$-0.829026\pi$
$809$	0.384877	−	0.666626i	0.0135315	−	0.0234373i	0.872712	+	0.488236i	$0.162359\pi$
$810$	24.7641	−	11.2796i	0.870121	−	0.396324i
$811$		−	13.7780i		−	0.483810i	−0.970300	−	0.241905i	$-0.922228\pi$
$811$		−	13.7780i		−	0.483810i	0.970300	−	0.241905i	$-0.0777723\pi$
$812$	2.25043	−	0.858549i	0.0789747	−	0.0301292i
$813$	22.3234	−	35.1202i	0.782915	−	1.23172i
$814$	−5.02499	+	0.373701i	−0.176126	+	0.0130982i
$815$	8.60489			0.301416
$816$	−12.9369	+	12.7448i	−0.452883	+	0.446159i
$817$		−	61.4115i		−	2.14852i
$818$	6.93217	+	10.1801i	0.242378	+	0.355937i
$819$	−37.2798	−	15.4469i	−1.30266	−	0.539758i
$820$	22.0179	+	8.67025i	0.768897	+	0.302778i
$821$			9.71838i			0.339174i	0.985515	+	0.169587i	$0.0542434\pi$
$821$			9.71838i			0.339174i	−0.985515	+	0.169587i	$0.945757\pi$
$822$	0.0373022	+	1.17913i	0.00130106	+	0.0411268i
$823$		−	40.9493i		−	1.42740i	−0.700451	−	0.713701i	$-0.747018\pi$
$823$		−	40.9493i		−	1.42740i	0.700451	−	0.713701i	$-0.252982\pi$
$824$	6.07353	+	1.88478i	0.211581	+	0.0656593i
$825$	2.58177	+	0.110068i	0.0898855	+	0.00383207i
$826$	8.38666	+	28.0808i	0.291809	+	0.977055i
$827$	6.32932			0.220092			0.110046	−	0.993926i	$-0.464900\pi$
$827$	6.32932			0.220092			0.110046	+	0.993926i	$0.464900\pi$
$828$	−2.58506	−	40.8161i	−0.0898369	−	1.41846i
$829$	−16.5800	+	28.7174i	−0.575846	+	0.997395i	0.420103	+	0.907477i	$0.361994\pi$
$829$	−16.5800	+	28.7174i	−0.575846	+	0.997395i	−0.995949	+	0.0899187i	$0.971339\pi$
$830$	−15.8175	+	32.7976i	−0.549032	+	1.13842i
$831$	−26.6870	−	16.9630i	−0.925762	−	0.588441i
$832$	−33.5268	−	23.0259i	−1.16233	−	0.798280i
$833$	7.68218	+	16.6628i	0.266172	+	0.577333i
$834$	−0.338076	+	0.0106952i	−0.0117066	+	0.000370344i
$835$	48.9752			1.69486
$836$	44.2661	−	35.2189i	1.53098	−	1.21807i
$837$	−7.09044	−	0.911274i	−0.245081	−	0.0314982i
$838$	−0.222355	+	0.461054i	−0.00768111	+	0.0159268i
$839$	−5.61926	+	9.73284i	−0.193998	+	0.336015i	−0.946572	−	0.322493i	$-0.895479\pi$
$839$	−5.61926	+	9.73284i	−0.193998	+	0.336015i	0.752573	+	0.658508i	$0.228812\pi$
$840$	3.52398	−	27.4863i	0.121589	−	0.948366i
$841$	−14.3964	−	24.9353i	−0.496428	−	0.859838i
$842$	39.7556	−	2.95657i	1.37007	−	0.101890i
$843$	−19.6352	−	0.837105i	−0.676274	−	0.0288314i
$844$	41.1740	−	6.15816i	1.41727	−	0.211973i
$845$	13.7337	+	23.7876i	0.472455	+	0.818317i
$846$	−0.474027	+	43.1619i	−0.0162974	+	1.48394i
$847$	−2.12952	+	1.94286i	−0.0731712	+	0.0667576i
$848$	−6.26156	−	20.4645i	−0.215023	−	0.702752i
$849$	−25.3644	+	13.2370i	−0.870505	+	0.454293i
$850$	−0.895273	−	1.31473i	−0.0307076	−	0.0450948i
$851$	−6.98493			−0.239440
$852$	2.41870	+	22.7634i	0.0828632	+	0.779860i
$853$	7.50178	−	12.9935i	0.256856	−	0.444888i	−0.708542	−	0.705669i	$-0.750647\pi$
$853$	7.50178	−	12.9935i	0.256856	−	0.444888i	0.965398	+	0.260781i	$0.0839801\pi$
$854$	18.6964	−	5.58391i	0.639778	−	0.191078i
$855$	42.7997	+	29.8379i	1.46372	+	1.02044i
$856$	−2.46649	+	2.28076i	−0.0843028	+	0.0779547i
$857$	−37.4057	+	21.5962i	−1.27775	+	0.737711i	−0.976435	−	0.215812i	$-0.930760\pi$
$857$	−37.4057	+	21.5962i	−1.27775	+	0.737711i	−0.301319	+	0.953524i	$0.597427\pi$
$858$	−36.7957	+	22.8250i	−1.25618	+	0.779231i
$859$	27.3403	+	15.7849i	0.932838	+	0.538574i	0.887708	−	0.460407i	$-0.152296\pi$
$859$	27.3403	+	15.7849i	0.932838	+	0.538574i	0.0451300	+	0.998981i	$0.485630\pi$
$860$	−31.9262	+	4.77501i	−1.08867	+	0.162827i
$861$	16.2792	+	19.4458i	0.554792	+	0.662712i
$862$	13.7340	−	1.02138i	0.467783	−	0.0347883i
$863$	−42.7135	+	24.6606i	−1.45398	+	0.839458i	−0.998704	−	0.0508904i	$-0.983794\pi$
$863$	−42.7135	+	24.6606i	−1.45398	+	0.839458i	−0.455280	+	0.890348i	$0.650461\pi$
$864$	28.2470	+	8.13052i	0.960983	+	0.276606i
$865$	6.77741	−	11.7388i	0.230439	−	0.399132i
$866$	−12.3036	−	18.0681i	−0.418093	−	0.613979i
$867$	−9.41142	+	14.8065i	−0.319628	+	0.502854i
$868$	−4.59305	+	5.64813i	−0.155898	+	0.191710i
$869$	22.8706	−	13.2043i	0.775832	−	0.447927i
$870$	2.38261	−	0.0753749i	0.0807781	−	0.00255545i
$871$	−27.1139	−	46.9627i	−0.918720	−	1.59127i
$872$	10.5060	−	33.8547i	0.355778	−	1.14646i
$873$	24.6324	−	11.5479i	0.833682	−	0.390837i
$874$	64.8140	−	44.1355i	2.19237	−	1.49291i
$875$	29.2684	+	9.29813i	0.989452	+	0.314334i
$876$	−49.1593	−	21.8202i	−1.66094	−	0.737236i
$877$	48.2941	+	27.8826i	1.63078	+	0.941529i	0.983854	+	0.178973i	$0.0572774\pi$
$877$	48.2941	+	27.8826i	1.63078	+	0.941529i	0.646922	+	0.762556i	$0.276056\pi$
$878$	14.6343	−	9.96534i	0.493885	−	0.336314i
$879$	6.49768	−	10.2225i	0.219161	−	0.344795i
$880$	−21.7512	−	20.2743i	−0.733233	−	0.683447i
$881$			0.494631i			0.0166645i	0.999965	+	0.00833227i	$0.00265227\pi$
$881$			0.494631i			0.0166645i	−0.999965	+	0.00833227i	$0.997348\pi$
$882$	17.4050	−	24.0638i	0.586058	−	0.810269i
$883$	−43.5451			−1.46541			−0.732704	−	0.680547i	$-0.761742\pi$
$883$	−43.5451			−1.46541			−0.732704	+	0.680547i	$0.761742\pi$
$884$	24.7992	+	9.76548i	0.834087	+	0.328449i
$885$	−1.23541	+	28.9779i	−0.0415277	+	0.974080i
$886$	−21.1752	+	14.4194i	−0.711394	+	0.484428i
$887$	8.34443	−	14.4530i	0.280179	−	0.485283i	−0.691250	−	0.722616i	$-0.742940\pi$
$887$	8.34443	−	14.4530i	0.280179	−	0.485283i	0.971429	+	0.237332i	$0.0762730\pi$
$888$	1.69076	−	4.72688i	0.0567383	−	0.158624i
$889$	−4.81515	+	15.1570i	−0.161495	+	0.508349i
$890$	−8.83701	−	12.9773i	−0.296217	−	0.435002i
$891$	20.0162	−	24.0542i	0.670567	−	0.805846i
$892$	17.9525	+	22.5642i	0.601093	+	0.755505i
$893$	−71.6723	+	41.3800i	−2.39842	+	1.38473i
$894$	−6.72533	−	10.8418i	−0.224929	−	0.362604i
$895$	−11.5601	−	20.0227i	−0.386411	−	0.669283i
$896$	22.1930	−	20.0866i	0.741415	−	0.671047i
$897$	−53.2128	+	27.7703i	−1.77672	+	0.927222i
$898$	12.0684	−	8.21806i	0.402728	−	0.274240i
$899$	−0.542341	−	0.313121i	−0.0180881	−	0.0104432i
$900$	−1.14376	+	2.30651i	−0.0381253	+	0.0768837i
$901$	7.01204	+	12.1452i	0.233605	+	0.404616i
$902$	27.1374	−	2.01817i	0.903578	−	0.0671977i
$903$	−32.4963	−	11.8698i	−1.08141	−	0.395001i
$904$	−12.9982	+	12.0194i	−0.432314	+	0.399760i
$905$	−13.5433	+	23.4577i	−0.450195	+	0.779760i
$906$	−37.9991	+	1.20212i	−1.26244	+	0.0399377i
$907$	27.2967	+	47.2793i	0.906372	+	1.56988i	0.819065	+	0.573701i	$0.194493\pi$
$907$	27.2967	+	47.2793i	0.906372	+	1.56988i	0.0873072	+	0.996181i	$0.472174\pi$
$908$	0.632938	+	4.23188i	0.0210048	+	0.140440i
$909$	25.3667	+	2.16684i	0.841360	+	0.0718696i
$910$	−38.9691	+	11.6386i	−1.29181	+	0.385816i
$911$	−6.96825	−	4.02312i	−0.230868	−	0.133292i	0.380104	−	0.924944i	$-0.375888\pi$
$911$	−6.96825	−	4.02312i	−0.230868	−	0.133292i	−0.610973	+	0.791652i	$0.709221\pi$
$912$	14.1788	+	54.5446i	0.469508	+	1.80615i
$913$			41.8736i			1.38581i
$914$	−6.02195	+	4.10069i	−0.199188	+	0.135639i
$915$	19.2937	+	0.822545i	0.637831	+	0.0271925i
$916$	3.07427	+	3.86401i	0.101577	+	0.127670i
$917$	−2.91519	−	3.19526i	−0.0962681	−	0.105517i
$918$	−19.2342	−	1.03173i	−0.634824	−	0.0340522i
$919$	−49.5963	+	28.6344i	−1.63603	+	0.944563i	−0.653851	+	0.756623i	$0.726848\pi$
$919$	−49.5963	+	28.6344i	−1.63603	+	0.944563i	−0.982180	+	0.187940i	$0.939819\pi$
$920$	−27.9844	−	30.2633i	−0.922619	−	0.997751i
$921$	1.22198	−	0.637717i	0.0402656	−	0.0210135i
$922$	−0.567882	−	7.63605i	−0.0187022	−	0.251480i
$923$	29.0953	−	16.7982i	0.957685	−	0.552920i
$924$	−10.0804	−	30.2309i	−0.331622	−	0.994523i
$925$	0.380793	+	0.219851i	0.0125204	+	0.00722866i
$926$	11.8907	−	24.6555i	0.390753	−	0.810230i
$927$	2.86311	+	6.10719i	0.0940367	+	0.200587i
$928$	2.00861	+	1.61116i	0.0659357	+	0.0528890i
$929$		−	30.6044i		−	1.00410i	−0.864839	−	0.502049i	$-0.832580\pi$
$929$		−	30.6044i		−	1.00410i	0.864839	−	0.502049i	$-0.167420\pi$
$930$	−6.12257	+	3.79792i	−0.200767	+	0.124539i
$931$	56.7027	+	5.20881i	1.85836	+	0.170712i
$932$	24.2262	−	3.62337i	0.793555	−	0.118687i
$933$	7.27947	+	13.9488i	0.238319	+	0.456662i
$934$	11.7394	−	24.3417i	0.384125	−	0.796485i
$935$	16.8748	+	9.74266i	0.551864	+	0.318619i
$936$	−5.91222	−	42.7325i	−0.193247	−	1.39675i
$937$			21.1158i			0.689822i	0.938635	+	0.344911i	$0.112091\pi$
$937$			21.1158i			0.689822i	−0.938635	+	0.344911i	$0.887909\pi$
$938$	38.2405	−	11.4210i	1.24860	−	0.372908i
$939$	25.6171	−	13.3689i	0.835984	−	0.436277i
$940$	27.0852	+	34.0430i	0.883421	+	1.11036i
$941$	18.7928			0.612627			0.306313	−	0.951931i	$-0.400904\pi$
$941$	18.7928			0.612627			0.306313	+	0.951931i	$0.400904\pi$
$942$	−22.4944	−	12.0553i	−0.732907	−	0.392784i
$943$	37.7222			1.22840
$944$	−21.3618	+	22.9179i	−0.695269	+	0.745916i
$945$	24.0614	−	16.8806i	0.782716	−	0.549125i
$946$	−30.6841	+	20.8945i	−0.997625	+	0.679339i
$947$	−25.1259			−0.816483			−0.408242	−	0.912874i	$-0.633858\pi$
$947$	−25.1259			−0.816483			−0.408242	+	0.912874i	$0.633858\pi$
$948$	2.77997	+	26.1634i	0.0902891	+	0.849749i
$949$			78.9359i			2.56237i
$950$	−4.92259	+	0.366085i	−0.159710	+	0.0118774i
$951$	0.469992	−	0.245275i	0.0152405	−	0.00795360i
$952$	−11.2129	+	16.0944i	−0.363413	+	0.521624i
$953$	9.21172			0.298397			0.149198	−	0.988807i	$-0.452331\pi$
$953$	9.21172			0.298397			0.149198	+	0.988807i	$0.452331\pi$
$954$	11.5648	−	19.5322i	0.374423	−	0.632379i
$955$	−45.7098	−	26.3906i	−1.47913	−	0.853979i
$956$	−0.432605	−	2.89244i	−0.0139915	−	0.0935482i
$957$	2.43027	−	1.26829i	0.0785596	−	0.0409981i
$958$	−18.5917	−	8.96629i	−0.600670	−	0.289688i
$959$	0.273097	+	1.24463i	0.00881876	+	0.0401912i
$960$	27.2538	−	11.6123i	0.879613	−	0.374784i
$961$	−29.1072			−0.938943
$962$	−7.34749	+	0.546422i	−0.236893	+	0.0176173i
$963$	−3.55023	−	0.303263i	−0.114405	−	0.00977253i
$964$	0.628478	+	4.20206i	0.0202419	+	0.135339i
$965$	−13.9420	+	24.1483i	−0.448809	+	0.777360i
$966$	−10.8272	−	42.8274i	−0.348359	−	1.37795i
$967$	12.1615	−	7.02143i	0.391087	−	0.225794i	−0.291544	−	0.956557i	$-0.594169\pi$
$967$	12.1615	−	7.02143i	0.391087	−	0.225794i	0.682631	+	0.730763i	$0.260836\pi$
$968$	−2.94320	−	0.913353i	−0.0945982	−	0.0293563i
$969$	−17.0865	−	32.7408i	−0.548898	−	1.05179i
$970$	11.9105	−	24.6965i	0.382422	−	0.792956i
$971$	−39.1866	+	22.6244i	−1.25756	+	0.726051i	−0.972599	−	0.232488i	$-0.925313\pi$
$971$	−39.1866	+	22.6244i	−1.25756	+	0.726051i	−0.284959	+	0.958540i	$0.591980\pi$
$972$	13.8138	+	27.9496i	0.443077	+	0.896484i
$973$	−0.356857	+	0.0783016i	−0.0114403	+	0.00251023i
$974$	51.5009	−	3.83005i	1.65020	−	0.122723i
$975$	3.77504	+	0.160940i	0.120898	+	0.00515421i
$976$	15.2590	+	14.2229i	0.488428	+	0.455264i
$977$	21.1700			0.677288			0.338644	−	0.940914i	$-0.390032\pi$
$977$	21.1700			0.677288			0.338644	+	0.940914i	$0.390032\pi$
$978$	0.311728	+	9.85377i	0.00996796	+	0.315089i
$979$	−15.6362	−	9.02756i	−0.499735	−	0.288522i
$980$	−1.70096	−	29.8832i	−0.0543352	−	0.954584i
$981$	34.0423	−	15.9593i	1.08689	−	0.509543i
$982$	−43.4290	−	20.9447i	−1.38588	−	0.668373i
$983$	15.4989	+	26.8449i	0.494339	+	0.856220i	0.999979	−	0.00652472i	$-0.00207690\pi$
$983$	15.4989	+	26.8449i	0.494339	+	0.856220i	−0.505640	+	0.862745i	$0.668744\pi$
$984$	−9.13098	+	25.5275i	−0.291085	+	0.813788i
$985$	4.77657	+	2.75775i	0.152194	+	0.0878694i
$986$	−1.51985	−	0.732984i	−0.0484019	−	0.0233430i
$987$	8.04352	+	45.9239i	0.256028	+	1.46177i
$988$	64.7255	−	51.4967i	2.05919	−	1.63833i
$989$	−44.5656	+	25.7299i	−1.41710	+	0.818165i
$990$	0.346353	−	31.5367i	0.0110078	−	1.00230i
$991$	0.352487	+	0.203509i	0.0111971	+	0.00646467i	0.505588	−	0.862775i	$-0.331276\pi$
$991$	0.352487	+	0.203509i	0.0111971	+	0.00646467i	−0.494391	+	0.869240i	$0.664609\pi$
$992$	−7.69233	−	1.18178i	−0.244232	−	0.0375217i
$993$	25.0446	+	47.9899i	0.794767	+	1.52291i
$994$	7.07578	+	23.6916i	0.224430	+	0.751451i
$995$	0.476804	+	0.825849i	0.0151157	+	0.0261812i
$996$	−38.1308	−	16.9250i	−1.20822	−	0.536289i
$997$	13.8611	+	24.0081i	0.438984	+	0.760343i	0.997611	−	0.0690762i	$-0.0220051\pi$
$997$	13.8611	+	24.0081i	0.438984	+	0.760343i	−0.558627	+	0.829419i	$0.688672\pi$
$998$	−0.622863	−	8.37537i	−0.0197164	−	0.265118i
$999$	4.91308	−	2.05281i	0.155443	−	0.0649480i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.bf.b.115.16	yes	180
7.5	odd	6		504.2.cz.b.187.76	yes	180
8.3	odd	2	inner	504.2.bf.b.115.15	✓	180
9.4	even	3		504.2.cz.b.283.45	yes	180
56.19	even	6		504.2.cz.b.187.45	yes	180
63.40	odd	6	inner	504.2.bf.b.355.16	yes	180
72.67	odd	6		504.2.cz.b.283.76	yes	180
504.355	even	6	inner	504.2.bf.b.355.15	yes	180

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bf.b.115.15	✓	180	8.3	odd	2	inner
504.2.bf.b.115.16	yes	180	1.1	even	1	trivial
504.2.bf.b.355.15	yes	180	504.355	even	6	inner
504.2.bf.b.355.16	yes	180	63.40	odd	6	inner
504.2.cz.b.187.45	yes	180	56.19	even	6
504.2.cz.b.187.76	yes	180	7.5	odd	6
504.2.cz.b.283.45	yes	180	9.4	even	3
504.2.cz.b.283.76	yes	180	72.67	odd	6

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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.bf (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.16893 + 0.795991i) q^{2} +(-0.801348 - 1.53553i) q^{3} +(0.732796 - 1.86092i) q^{4} +(1.06898 - 1.85154i) q^{5} +(2.15899 + 1.15706i) q^{6} +(2.52157 + 0.801064i) q^{7} +(0.624685 + 2.75858i) q^{8} +(-1.71568 + 2.46098i) q^{9} +O(q^{10})\)	\(q+(-1.16893 + 0.795991i) q^{2} +(-0.801348 - 1.53553i) q^{3} +(0.732796 - 1.86092i) q^{4} +(1.06898 - 1.85154i) q^{5} +(2.15899 + 1.15706i) q^{6} +(2.52157 + 0.801064i) q^{7} +(0.624685 + 2.75858i) q^{8} +(-1.71568 + 2.46098i) q^{9} +(0.224237 + 3.01522i) q^{10} +(1.73850 + 3.01117i) q^{11} +(-3.44471 + 0.366014i) q^{12} +(2.54202 + 4.40291i) q^{13} +(-3.58518 + 1.07076i) q^{14} +(-3.69971 - 0.157729i) q^{15} +(-2.92602 - 2.72735i) q^{16} +(2.27003 + 1.31060i) q^{17} +(0.0465922 - 4.24238i) q^{18} +(7.04468 - 4.06725i) q^{19} +(-2.66220 - 3.34609i) q^{20} +(-0.790598 - 4.51386i) q^{21} +(-4.42905 - 2.13602i) q^{22} +(-5.90310 - 3.40816i) q^{23} +(3.73528 - 3.16980i) q^{24} +(0.214544 + 0.371601i) q^{25} +(-6.47612 - 3.12327i) q^{26} +(5.15376 + 0.662370i) q^{27} +(3.33851 - 4.10541i) q^{28} +(0.394206 + 0.227595i) q^{29} +(4.45026 - 2.76056i) q^{30} -1.37578 q^{31} +(5.59125 + 0.858993i) q^{32} +(3.23059 - 5.08251i) q^{33} +(-3.69674 + 0.274921i) q^{34} +(4.17871 - 3.81244i) q^{35} +(3.32244 + 4.99614i) q^{36} +(0.887449 - 0.512369i) q^{37} +(-4.99725 + 10.3618i) q^{38} +(4.72374 - 7.43160i) q^{39} +(5.77539 + 1.79225i) q^{40} +(-4.79267 + 2.76705i) q^{41} +(4.51715 + 4.64708i) q^{42} +(3.77476 - 6.53808i) q^{43} +(6.87750 - 1.02863i) q^{44} +(2.72256 + 5.80740i) q^{45} +(9.61318 - 0.714917i) q^{46} -10.1740 q^{47} +(-1.84315 + 6.67853i) q^{48} +(5.71659 + 4.03987i) q^{49} +(-0.546577 - 0.263600i) q^{50} +(0.193380 - 4.53594i) q^{51} +(10.0562 - 1.50405i) q^{52} +(4.63344 + 2.67512i) q^{53} +(-6.55163 + 3.32808i) q^{54} +7.43372 q^{55} +(-0.634617 + 7.45636i) q^{56} +(-11.8906 - 7.55800i) q^{57} +(-0.641964 + 0.0477419i) q^{58} -7.83247i q^{59} +(-3.00466 + 6.76927i) q^{60} -5.21493 q^{61} +(1.60819 - 1.09511i) q^{62} +(-6.29761 + 4.83116i) q^{63} +(-7.21954 + 3.44649i) q^{64} +10.8695 q^{65} +(0.269300 + 8.51262i) q^{66} -10.6663 q^{67} +(4.10240 - 3.26393i) q^{68} +(-0.502874 + 11.7955i) q^{69} +(-1.84995 + 7.78270i) q^{70} -6.60821i q^{71} +(-7.86058 - 3.19551i) q^{72} +(13.4461 + 7.76311i) q^{73} +(-0.629525 + 1.30532i) q^{74} +(0.398678 - 0.627219i) q^{75} +(-2.40649 - 16.0900i) q^{76} +(1.97160 + 8.98552i) q^{77} +(0.393768 + 12.4471i) q^{78} -7.59525i q^{79} +(-8.17765 + 2.50214i) q^{80} +(-3.11287 - 8.44453i) q^{81} +(3.39975 - 7.04941i) q^{82} +(10.4296 + 6.02151i) q^{83} +(-8.97927 - 1.83651i) q^{84} +(4.85326 - 2.80203i) q^{85} +(0.791818 + 10.6472i) q^{86} +(0.0335817 - 0.787697i) q^{87} +(-7.22054 + 6.67683i) q^{88} +(-4.49704 + 2.59637i) q^{89} +(-7.80512 - 4.62131i) q^{90} +(2.88286 + 13.1385i) q^{91} +(-10.6681 + 8.48769i) q^{92} +(1.10248 + 2.11254i) q^{93} +(11.8927 - 8.09839i) q^{94} -17.3913i q^{95} +(-3.16154 - 9.27387i) q^{96} +(-7.85340 - 4.53417i) q^{97} +(-9.89800 - 0.171974i) q^{98} +(-10.3932 - 0.887791i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 180 q - 6 q^{2} - 6 q^{3} - 2 q^{4} - 6 q^{6} + 10 q^{9}+O(q^{10}) \) 180 * q - 6 * q^2 - 6 * q^3 - 2 * q^4 - 6 * q^6 + 10 * q^9	\( 180 q - 6 q^{2} - 6 q^{3} - 2 q^{4} - 6 q^{6} + 10 q^{9} - 8 q^{11} + 12 q^{12} + 10 q^{14} + 14 q^{16} - 18 q^{17} + 8 q^{18} - 6 q^{19} + 36 q^{20} - 16 q^{22} - 12 q^{24} - 78 q^{25} - 6 q^{26} + 16 q^{28} + q^{30} - 26 q^{32} - 36 q^{33} - 12 q^{34} - 12 q^{35} + 2 q^{36} - 27 q^{38} + 24 q^{40} - 42 q^{41} + 22 q^{42} + 14 q^{43} - 21 q^{44} - 12 q^{46} - 9 q^{48} + 2 q^{49} + 15 q^{50} + 9 q^{52} - 51 q^{54} + 14 q^{56} - 26 q^{57} + 19 q^{58} + 37 q^{60} - 8 q^{64} + 24 q^{65} + 6 q^{66} + 28 q^{67} + 12 q^{68} + 27 q^{70} - 28 q^{72} + 18 q^{73} + 49 q^{74} - 18 q^{75} - 12 q^{76} - 33 q^{78} - 63 q^{80} - 22 q^{81} - 54 q^{82} + 6 q^{83} + 31 q^{84} - 13 q^{86} + 29 q^{88} - 66 q^{89} - 51 q^{90} + 2 q^{91} - 60 q^{92} - 45 q^{96} - 6 q^{97} + 31 q^{98} + 4 q^{99}+O(q^{100}) \) 180 * q - 6 * q^2 - 6 * q^3 - 2 * q^4 - 6 * q^6 + 10 * q^9 - 8 * q^11 + 12 * q^12 + 10 * q^14 + 14 * q^16 - 18 * q^17 + 8 * q^18 - 6 * q^19 + 36 * q^20 - 16 * q^22 - 12 * q^24 - 78 * q^25 - 6 * q^26 + 16 * q^28 + q^30 - 26 * q^32 - 36 * q^33 - 12 * q^34 - 12 * q^35 + 2 * q^36 - 27 * q^38 + 24 * q^40 - 42 * q^41 + 22 * q^42 + 14 * q^43 - 21 * q^44 - 12 * q^46 - 9 * q^48 + 2 * q^49 + 15 * q^50 + 9 * q^52 - 51 * q^54 + 14 * q^56 - 26 * q^57 + 19 * q^58 + 37 * q^60 - 8 * q^64 + 24 * q^65 + 6 * q^66 + 28 * q^67 + 12 * q^68 + 27 * q^70 - 28 * q^72 + 18 * q^73 + 49 * q^74 - 18 * q^75 - 12 * q^76 - 33 * q^78 - 63 * q^80 - 22 * q^81 - 54 * q^82 + 6 * q^83 + 31 * q^84 - 13 * q^86 + 29 * q^88 - 66 * q^89 - 51 * q^90 + 2 * q^91 - 60 * q^92 - 45 * q^96 - 6 * q^97 + 31 * q^98 + 4 * q^99

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