LMFDB - Embedded newform 240.2.y.e.163.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [240,2,Mod(163,240)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(240, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0, 3]))

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

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

chi := DirichletCharacter("240.163");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 240 = 2^{4} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	240.y (of order $4$, 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:	$1.91640964851$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6 x^{15} + 14 x^{14} - 10 x^{13} - 26 x^{12} + 78 x^{11} - 66 x^{10} - 74 x^{9} + 233 x^{8} + \cdots + 256 $ x^16 - 6x^15 + 14x^14 - 10x^13 - 26x^12 + 78x^11 - 66x^10 - 74x^9 + 233x^8 - 148x^7 - 264x^6 + 624x^5 - 416x^4 - 320x^3 + 896x^2 - 768*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			163.6
Root			$1.28040 + 0.600471i$ of defining polynomial
Character	$\chi$	$=$	240.163
Dual form			240.2.y.e.187.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.812425 + 1.15757i) q^{2} +1.00000 q^{3} +(-0.679932 + 1.88088i) q^{4} +(1.45639 + 1.69674i) q^{5} +(0.812425 + 1.15757i) q^{6} +(1.12791 - 1.12791i) q^{7} +(-2.72964 + 0.741001i) q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(0.812425 + 1.15757i) q^{2} +1.00000 q^{3} +(-0.679932 + 1.88088i) q^{4} +(1.45639 + 1.69674i) q^{5} +(0.812425 + 1.15757i) q^{6} +(1.12791 - 1.12791i) q^{7} +(-2.72964 + 0.741001i) q^{8} +1.00000 q^{9} +(-0.780893 + 3.06434i) q^{10} +(-4.05250 - 4.05250i) q^{11} +(-0.679932 + 1.88088i) q^{12} -1.51085i q^{13} +(2.22197 + 0.389291i) q^{14} +(1.45639 + 1.69674i) q^{15} +(-3.07538 - 2.55774i) q^{16} +(-1.61725 + 1.61725i) q^{17} +(0.812425 + 1.15757i) q^{18} +(3.09584 + 3.09584i) q^{19} +(-4.18161 + 1.58561i) q^{20} +(1.12791 - 1.12791i) q^{21} +(1.39870 - 7.98340i) q^{22} +(1.55774 + 1.55774i) q^{23} +(-2.72964 + 0.741001i) q^{24} +(-0.757876 + 4.94223i) q^{25} +(1.74892 - 1.22746i) q^{26} +1.00000 q^{27} +(1.35455 + 2.88835i) q^{28} +(0.425907 - 0.425907i) q^{29} +(-0.780893 + 3.06434i) q^{30} -9.02889i q^{31} +(0.462239 - 5.63794i) q^{32} +(-4.05250 - 4.05250i) q^{33} +(-3.18598 - 0.558186i) q^{34} +(3.55644 + 0.271100i) q^{35} +(-0.679932 + 1.88088i) q^{36} -7.76193i q^{37} +(-1.06851 + 6.09878i) q^{38} -1.51085i q^{39} +(-5.23269 - 3.55231i) q^{40} +7.27238i q^{41} +(2.22197 + 0.389291i) q^{42} -9.30484i q^{43} +(10.3777 - 4.86682i) q^{44} +(1.45639 + 1.69674i) q^{45} +(-0.537644 + 3.06873i) q^{46} +(-1.13932 - 1.13932i) q^{47} +(-3.07538 - 2.55774i) q^{48} +4.45565i q^{49} +(-6.33669 + 3.13789i) q^{50} +(-1.61725 + 1.61725i) q^{51} +(2.84173 + 1.02728i) q^{52} -8.27183 q^{53} +(0.812425 + 1.15757i) q^{54} +(0.974046 - 12.7781i) q^{55} +(-2.24300 + 3.91456i) q^{56} +(3.09584 + 3.09584i) q^{57} +(0.839034 + 0.146999i) q^{58} +(-9.12504 + 9.12504i) q^{59} +(-4.18161 + 1.58561i) q^{60} +(4.89881 + 4.89881i) q^{61} +(10.4516 - 7.33529i) q^{62} +(1.12791 - 1.12791i) q^{63} +(6.90184 - 4.04533i) q^{64} +(2.56353 - 2.20039i) q^{65} +(1.39870 - 7.98340i) q^{66} -2.17068i q^{67} +(-1.94223 - 4.14147i) q^{68} +(1.55774 + 1.55774i) q^{69} +(2.57552 + 4.33707i) q^{70} +13.5937 q^{71} +(-2.72964 + 0.741001i) q^{72} +(-1.11750 + 1.11750i) q^{73} +(8.98497 - 6.30598i) q^{74} +(-0.757876 + 4.94223i) q^{75} +(-7.92785 + 3.71792i) q^{76} -9.14169 q^{77} +(1.74892 - 1.22746i) q^{78} +1.68922 q^{79} +(-0.139126 - 8.94319i) q^{80} +1.00000 q^{81} +(-8.41829 + 5.90826i) q^{82} -5.64544 q^{83} +(1.35455 + 2.88835i) q^{84} +(-5.09941 - 0.388718i) q^{85} +(10.7710 - 7.55948i) q^{86} +(0.425907 - 0.425907i) q^{87} +(14.0648 + 8.05895i) q^{88} +10.4975 q^{89} +(-0.780893 + 3.06434i) q^{90} +(-1.70410 - 1.70410i) q^{91} +(-3.98906 + 1.87075i) q^{92} -9.02889i q^{93} +(0.393229 - 2.24445i) q^{94} +(-0.744106 + 9.76158i) q^{95} +(0.462239 - 5.63794i) q^{96} +(-6.26114 + 6.26114i) q^{97} +(-5.15772 + 3.61988i) q^{98} +(-4.05250 - 4.05250i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{2} + 16 q^{3} - 8 q^{4} - 4 q^{5} + 2 q^{6} - 4 q^{7} - 4 q^{8} + 16 q^{9}+O(q^{10}) $ 16 * q + 2 * q^2 + 16 * q^3 - 8 * q^4 - 4 * q^5 + 2 * q^6 - 4 * q^7 - 4 * q^8 + 16 * q^9	$ 16 q + 2 q^{2} + 16 q^{3} - 8 q^{4} - 4 q^{5} + 2 q^{6} - 4 q^{7} - 4 q^{8} + 16 q^{9} - 14 q^{10} - 8 q^{12} - 4 q^{14} - 4 q^{15} - 8 q^{16} - 8 q^{17} + 2 q^{18} + 8 q^{19} - 12 q^{20} - 4 q^{21} - 8 q^{22} - 4 q^{24} + 32 q^{25} + 20 q^{26} + 16 q^{27} + 12 q^{28} + 12 q^{29} - 14 q^{30} - 28 q^{32} - 20 q^{35} - 8 q^{36} - 16 q^{38} - 44 q^{40} - 4 q^{42} + 52 q^{44} - 4 q^{45} - 16 q^{46} - 32 q^{47} - 8 q^{48} + 22 q^{50} - 8 q^{51} + 8 q^{52} + 16 q^{53} + 2 q^{54} - 4 q^{55} + 20 q^{56} + 8 q^{57} - 44 q^{58} - 24 q^{59} - 12 q^{60} + 40 q^{61} + 40 q^{62} - 4 q^{63} - 8 q^{64} - 4 q^{65} - 8 q^{66} + 24 q^{68} + 56 q^{70} - 4 q^{72} + 8 q^{73} + 64 q^{74} + 32 q^{75} + 16 q^{76} - 72 q^{77} + 20 q^{78} - 48 q^{79} + 16 q^{80} + 16 q^{81} + 8 q^{82} - 8 q^{83} + 12 q^{84} - 8 q^{85} - 8 q^{86} + 12 q^{87} - 16 q^{88} - 14 q^{90} - 40 q^{91} - 20 q^{94} + 8 q^{95} - 28 q^{96} + 48 q^{97} + 30 q^{98}+O(q^{100}) $ 16 * q + 2 * q^2 + 16 * q^3 - 8 * q^4 - 4 * q^5 + 2 * q^6 - 4 * q^7 - 4 * q^8 + 16 * q^9 - 14 * q^10 - 8 * q^12 - 4 * q^14 - 4 * q^15 - 8 * q^16 - 8 * q^17 + 2 * q^18 + 8 * q^19 - 12 * q^20 - 4 * q^21 - 8 * q^22 - 4 * q^24 + 32 * q^25 + 20 * q^26 + 16 * q^27 + 12 * q^28 + 12 * q^29 - 14 * q^30 - 28 * q^32 - 20 * q^35 - 8 * q^36 - 16 * q^38 - 44 * q^40 - 4 * q^42 + 52 * q^44 - 4 * q^45 - 16 * q^46 - 32 * q^47 - 8 * q^48 + 22 * q^50 - 8 * q^51 + 8 * q^52 + 16 * q^53 + 2 * q^54 - 4 * q^55 + 20 * q^56 + 8 * q^57 - 44 * q^58 - 24 * q^59 - 12 * q^60 + 40 * q^61 + 40 * q^62 - 4 * q^63 - 8 * q^64 - 4 * q^65 - 8 * q^66 + 24 * q^68 + 56 * q^70 - 4 * q^72 + 8 * q^73 + 64 * q^74 + 32 * q^75 + 16 * q^76 - 72 * q^77 + 20 * q^78 - 48 * q^79 + 16 * q^80 + 16 * q^81 + 8 * q^82 - 8 * q^83 + 12 * q^84 - 8 * q^85 - 8 * q^86 + 12 * q^87 - 16 * q^88 - 14 * q^90 - 40 * q^91 - 20 * q^94 + 8 * q^95 - 28 * q^96 + 48 * q^97 + 30 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/240\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$161$	$181$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.812425	+	1.15757i	0.574471	+	0.818525i
$2$	0.812425	+	1.15757i	0.574471	+	0.818525i
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	−0.679932	+	1.88088i	−0.339966	+	0.940438i
$5$	1.45639	+	1.69674i	0.651316	+	0.758807i
$5$	1.45639	+	1.69674i	0.651316	+	0.758807i
$6$	0.812425	+	1.15757i	0.331671	+	0.472576i
$7$	1.12791	−	1.12791i	0.426309	−	0.426309i	−0.461060	−	0.887369i	$-0.652531\pi$
$7$	1.12791	−	1.12791i	0.426309	−	0.426309i	0.887369	+	0.461060i	$0.152531\pi$
$8$	−2.72964	+	0.741001i	−0.965072	+	0.261983i
$9$	1.00000			0.333333
$10$	−0.780893	+	3.06434i	−0.246940	+	0.969031i
$11$	−4.05250	−	4.05250i	−1.22188	−	1.22188i	−0.966965	−	0.254911i	$-0.917954\pi$
$11$	−4.05250	−	4.05250i	−1.22188	−	1.22188i	−0.254911	−	0.966965i	$-0.582046\pi$
$12$	−0.679932	+	1.88088i	−0.196280	+	0.542962i
$13$		−	1.51085i		−	0.419036i	−0.977805	−	0.209518i	$-0.932811\pi$
$13$		−	1.51085i		−	0.419036i	0.977805	−	0.209518i	$-0.0671894\pi$
$14$	2.22197	+	0.389291i	0.593846	+	0.104042i
$15$	1.45639	+	1.69674i	0.376037	+	0.438097i
$16$	−3.07538	−	2.55774i	−0.768846	−	0.639434i
$17$	−1.61725	+	1.61725i	−0.392241	+	0.392241i	−0.875486	−	0.483244i	$-0.839458\pi$
$17$	−1.61725	+	1.61725i	−0.392241	+	0.392241i	0.483244	+	0.875486i	$0.339458\pi$
$18$	0.812425	+	1.15757i	0.191490	+	0.272842i
$19$	3.09584	+	3.09584i	0.710234	+	0.710234i	0.966584	−	0.256350i	$-0.0825200\pi$
$19$	3.09584	+	3.09584i	0.710234	+	0.710234i	−0.256350	+	0.966584i	$0.582520\pi$
$20$	−4.18161	+	1.58561i	−0.935036	+	0.354553i
$21$	1.12791	−	1.12791i	0.246130	−	0.246130i
$22$	1.39870	−	7.98340i	0.298204	−	1.70207i
$23$	1.55774	+	1.55774i	0.324810	+	0.324810i	0.850609	−	0.525799i	$-0.176233\pi$
$23$	1.55774	+	1.55774i	0.324810	+	0.324810i	−0.525799	+	0.850609i	$0.676233\pi$
$24$	−2.72964	+	0.741001i	−0.557185	+	0.151256i
$25$	−0.757876	+	4.94223i	−0.151575	+	0.988446i
$26$	1.74892	−	1.22746i	0.342991	−	0.240724i
$27$	1.00000			0.192450
$28$	1.35455	+	2.88835i	0.255986	+	0.545847i
$29$	0.425907	−	0.425907i	0.0790889	−	0.0790889i	−0.666456	−	0.745545i	$-0.732189\pi$
$29$	0.425907	−	0.425907i	0.0790889	−	0.0790889i	0.745545	+	0.666456i	$0.232189\pi$
$30$	−0.780893	+	3.06434i	−0.142571	+	0.559470i
$31$		−	9.02889i		−	1.62164i	−0.585298	−	0.810818i	$-0.699022\pi$
$31$		−	9.02889i		−	1.62164i	0.585298	−	0.810818i	$-0.300978\pi$
$32$	0.462239	−	5.63794i	0.0817130	−	0.996656i
$33$	−4.05250	−	4.05250i	−0.705450	−	0.705450i
$34$	−3.18598	−	0.558186i	−0.546391	−	0.0957281i
$35$	3.55644	+	0.271100i	0.601148	+	0.0458243i
$36$	−0.679932	+	1.88088i	−0.113322	+	0.313479i
$37$		−	7.76193i		−	1.27605i	−0.770014	−	0.638027i	$-0.779751\pi$
$37$		−	7.76193i		−	1.27605i	0.770014	−	0.638027i	$-0.220249\pi$
$38$	−1.06851	+	6.09878i	−0.173335	+	0.989353i
$39$		−	1.51085i		−	0.241930i
$40$	−5.23269	−	3.55231i	−0.827362	−	0.561670i
$41$			7.27238i			1.13576i	0.823113	+	0.567878i	$0.192235\pi$
$41$			7.27238i			1.13576i	−0.823113	+	0.567878i	$0.807765\pi$
$42$	2.22197	+	0.389291i	0.342857	+	0.0600689i
$43$		−	9.30484i		−	1.41897i	−0.704718	−	0.709487i	$-0.748927\pi$
$43$		−	9.30484i		−	1.41897i	0.704718	−	0.709487i	$-0.251073\pi$
$44$	10.3777	−	4.86682i	1.56449	−	0.733701i
$45$	1.45639	+	1.69674i	0.217105	+	0.252936i
$46$	−0.537644	+	3.06873i	−0.0792713	+	0.452460i
$47$	−1.13932	−	1.13932i	−0.166187	−	0.166187i	0.619114	−	0.785301i	$-0.287492\pi$
$47$	−1.13932	−	1.13932i	−0.166187	−	0.166187i	−0.785301	+	0.619114i	$0.787492\pi$
$48$	−3.07538	−	2.55774i	−0.443893	−	0.369177i
$49$			4.45565i			0.636522i
$50$	−6.33669	+	3.13789i	−0.896143	+	0.443765i
$51$	−1.61725	+	1.61725i	−0.226461	+	0.226461i
$52$	2.84173	+	1.02728i	0.394077	+	0.142458i
$53$	−8.27183			−1.13622			−0.568112	−	0.822952i	$-0.692326\pi$
$53$	−8.27183			−1.13622			−0.568112	+	0.822952i	$0.692326\pi$
$54$	0.812425	+	1.15757i	0.110557	+	0.157525i
$55$	0.974046	−	12.7781i	0.131340	−	1.72299i
$56$	−2.24300	+	3.91456i	−0.299733	+	0.523105i
$57$	3.09584	+	3.09584i	0.410054	+	0.410054i
$58$	0.839034	+	0.146999i	0.110171	+	0.0193020i
$59$	−9.12504	+	9.12504i	−1.18798	+	1.18798i	−0.210354	+	0.977625i	$0.567462\pi$
$59$	−9.12504	+	9.12504i	−1.18798	+	1.18798i	−0.977625	+	0.210354i	$0.932538\pi$
$60$	−4.18161	+	1.58561i	−0.539843	+	0.204701i
$61$	4.89881	+	4.89881i	0.627229	+	0.627229i	0.947370	−	0.320141i	$-0.103730\pi$
$61$	4.89881	+	4.89881i	0.627229	+	0.627229i	−0.320141	+	0.947370i	$0.603730\pi$
$62$	10.4516	−	7.33529i	1.32735	−	0.931583i
$63$	1.12791	−	1.12791i	0.142103	−	0.142103i
$64$	6.90184	−	4.04533i	0.862729	−	0.505666i
$65$	2.56353	−	2.20039i	0.317967	−	0.272925i
$66$	1.39870	−	7.98340i	0.172168	−	0.982689i
$67$		−	2.17068i		−	0.265191i	−0.991170	−	0.132596i	$-0.957669\pi$
$67$		−	2.17068i		−	0.265191i	0.991170	−	0.132596i	$-0.0423312\pi$
$68$	−1.94223	−	4.14147i	−0.235530	−	0.502228i
$69$	1.55774	+	1.55774i	0.187529	+	0.187529i
$70$	2.57552	+	4.33707i	0.307834	+	0.518379i
$71$	13.5937			1.61328			0.806641	−	0.591042i	$-0.201283\pi$
$71$	13.5937			1.61328			0.806641	+	0.591042i	$0.201283\pi$
$72$	−2.72964	+	0.741001i	−0.321691	+	0.0873278i
$73$	−1.11750	+	1.11750i	−0.130793	+	0.130793i	−0.769473	−	0.638680i	$-0.779481\pi$
$73$	−1.11750	+	1.11750i	−0.130793	+	0.130793i	0.638680	+	0.769473i	$0.279481\pi$
$74$	8.98497	−	6.30598i	1.04448	−	0.733056i
$75$	−0.757876	+	4.94223i	−0.0875120	+	0.570679i
$76$	−7.92785	+	3.71792i	−0.909386	+	0.426475i
$77$	−9.14169			−1.04179
$78$	1.74892	−	1.22746i	0.198026	−	0.138982i
$79$	1.68922			0.190052			0.0950261	−	0.995475i	$-0.469707\pi$
$79$	1.68922			0.190052			0.0950261	+	0.995475i	$0.469707\pi$
$80$	−0.139126	−	8.94319i	−0.0155548	−	0.999879i
$81$	1.00000			0.111111
$82$	−8.41829	+	5.90826i	−0.929644	+	0.652459i
$83$	−5.64544			−0.619668			−0.309834	−	0.950791i	$-0.600273\pi$
$83$	−5.64544			−0.619668			−0.309834	+	0.950791i	$0.600273\pi$
$84$	1.35455	+	2.88835i	0.147794	+	0.315145i
$85$	−5.09941	−	0.388718i	−0.553109	−	0.0421624i
$86$	10.7710	−	7.55948i	1.16147	−	0.815160i
$87$	0.425907	−	0.425907i	0.0456620	−	0.0456620i
$88$	14.0648	+	8.05895i	1.49931	+	0.859087i
$89$	10.4975			1.11273			0.556365	−	0.830938i	$-0.312196\pi$
$89$	10.4975			1.11273			0.556365	+	0.830938i	$0.312196\pi$
$90$	−0.780893	+	3.06434i	−0.0823134	+	0.323010i
$91$	−1.70410	−	1.70410i	−0.178639	−	0.178639i
$92$	−3.98906	+	1.87075i	−0.415889	+	0.195039i
$93$		−	9.02889i		−	0.936252i
$94$	0.393229	−	2.24445i	0.0405585	−	0.231497i
$95$	−0.744106	+	9.76158i	−0.0763436	+	1.00152i
$96$	0.462239	−	5.63794i	0.0471770	−	0.575420i
$97$	−6.26114	+	6.26114i	−0.635722	+	0.635722i	−0.949497	−	0.313775i	$-0.898406\pi$
$97$	−6.26114	+	6.26114i	−0.635722	+	0.635722i	0.313775	+	0.949497i	$0.398406\pi$
$98$	−5.15772	+	3.61988i	−0.521009	+	0.365663i
$99$	−4.05250	−	4.05250i	−0.407292	−	0.407292i
$100$	−8.78041	−	4.78585i	−0.878041	−	0.478585i
$101$	1.36593	−	1.36593i	0.135915	−	0.135915i	−0.635876	−	0.771791i	$-0.719361\pi$
$101$	1.36593	−	1.36593i	0.135915	−	0.135915i	0.771791	+	0.635876i	$0.219361\pi$
$102$	−3.18598	−	0.558186i	−0.315459	−	0.0552686i
$103$	−0.00181474	−	0.00181474i	−0.000178812	−	0.000178812i	0.707017	−	0.707196i	$-0.250040\pi$
$103$	−0.00181474	−	0.00181474i	−0.000178812	−	0.000178812i	−0.707196	+	0.707017i	$0.750040\pi$
$104$	1.11954	+	4.12408i	0.109780	+	0.404400i
$105$	3.55644	+	0.271100i	0.347073	+	0.0264567i
$106$	−6.72024	−	9.57521i	−0.652727	−	0.930027i
$107$	−14.5410			−1.40573			−0.702863	−	0.711325i	$-0.748096\pi$
$107$	−14.5410			−1.40573			−0.702863	+	0.711325i	$0.748096\pi$
$108$	−0.679932	+	1.88088i	−0.0654265	+	0.180987i
$109$	−11.1313	+	11.1313i	−1.06619	+	1.06619i	−0.0685378	+	0.997649i	$0.521833\pi$
$109$	−11.1313	+	11.1313i	−1.06619	+	1.06619i	−0.997649	+	0.0685378i	$0.978167\pi$
$110$	15.5828	−	9.25369i	1.48576	−	0.882305i
$111$		−	7.76193i		−	0.736730i
$112$	−6.35364	+	0.583859i	−0.600362	+	0.0551695i
$113$	9.54820	+	9.54820i	0.898219	+	0.898219i	0.995279	−	0.0970594i	$-0.0309437\pi$
$113$	9.54820	+	9.54820i	0.898219	+	0.898219i	−0.0970594	+	0.995279i	$0.530944\pi$
$114$	−1.06851	+	6.09878i	−0.100075	+	0.571203i
$115$	−0.374412	+	4.91174i	−0.0349141	+	0.458023i
$116$	0.511490	+	1.09067i	0.0474906	+	0.101266i
$117$		−	1.51085i		−	0.139679i
$118$	−17.9763	−	3.14946i	−1.65485	−	0.289931i
$119$			3.64822i			0.334432i
$120$	−5.23269	−	3.55231i	−0.477677	−	0.324280i
$121$			21.8455i			1.98596i
$122$	−1.69080	+	9.65063i	−0.153078	+	0.873727i
$123$			7.27238i			0.655729i
$124$	16.9822	+	6.13903i	1.52505	+	0.551302i
$125$	−9.48945	+	5.91187i	−0.848763	+	0.528774i
$126$	2.22197	+	0.389291i	0.197949	+	0.0346808i
$127$	7.29219	+	7.29219i	0.647077	+	0.647077i	0.952286	−	0.305209i	$-0.0987262\pi$
$127$	7.29219	+	7.29219i	0.647077	+	0.647077i	−0.305209	+	0.952286i	$0.598726\pi$
$128$	10.2900	+	4.70283i	0.909513	+	0.415675i
$129$		−	9.30484i		−	0.819246i
$130$	4.62978	+	1.17982i	0.406058	+	0.103477i
$131$	−2.59824	+	2.59824i	−0.227009	+	0.227009i	−0.811442	−	0.584433i	$-0.801317\pi$
$131$	−2.59824	+	2.59824i	−0.227009	+	0.227009i	0.584433	+	0.811442i	$0.301317\pi$
$132$	10.3777	−	4.86682i	0.903261	−	0.423603i
$133$	6.98363			0.605558
$134$	2.51272	−	1.76352i	0.217066	−	0.152345i
$135$	1.45639	+	1.69674i	0.125346	+	0.146032i
$136$	3.21613	−	5.61290i	0.275781	−	0.481302i
$137$	−13.6691	−	13.6691i	−1.16783	−	1.16783i	−0.982717	−	0.185115i	$-0.940734\pi$
$137$	−13.6691	−	13.6691i	−1.16783	−	1.16783i	−0.185115	−	0.982717i	$-0.559266\pi$
$138$	−0.537644	+	3.06873i	−0.0457673	+	0.261228i
$139$	−4.06432	+	4.06432i	−0.344731	+	0.344731i	−0.858143	−	0.513412i	$-0.828381\pi$
$139$	−4.06432	+	4.06432i	−0.344731	+	0.344731i	0.513412	+	0.858143i	$0.328381\pi$
$140$	−2.92804	+	6.50489i	−0.247465	+	0.549763i
$141$	−1.13932	−	1.13932i	−0.0959479	−	0.0959479i
$142$	11.0439	+	15.7357i	0.926783	+	1.32051i
$143$	−6.12274	+	6.12274i	−0.512009	+	0.512009i
$144$	−3.07538	−	2.55774i	−0.256282	−	0.213145i
$145$	1.34294	+	0.102370i	0.111525	+	0.00850133i
$146$	−2.20146	−	0.385698i	−0.182194	−	0.0319206i
$147$			4.45565i			0.367496i
$148$	14.5992	+	5.27759i	1.20005	+	0.433815i
$149$	−7.44842	−	7.44842i	−0.610199	−	0.610199i	0.332799	−	0.942998i	$-0.392007\pi$
$149$	−7.44842	−	7.44842i	−0.610199	−	0.610199i	−0.942998	+	0.332799i	$0.892007\pi$
$150$	−6.33669	+	3.13789i	−0.517388	+	0.256208i
$151$	−7.91377			−0.644013			−0.322007	−	0.946737i	$-0.604357\pi$
$151$	−7.91377			−0.644013			−0.322007	+	0.946737i	$0.604357\pi$
$152$	−10.7445	−	6.15650i	−0.871497	−	0.499358i
$153$	−1.61725	+	1.61725i	−0.130747	+	0.130747i
$154$	−7.42694	−	10.5821i	−0.598479	−	0.852733i
$155$	15.3197	−	13.1496i	1.23051	−	1.05620i
$156$	2.84173	+	1.02728i	0.227520	+	0.0822481i
$157$	9.30731			0.742804			0.371402	−	0.928472i	$-0.378877\pi$
$157$	9.30731			0.742804			0.371402	+	0.928472i	$0.378877\pi$
$158$	1.37236	+	1.95539i	0.109179	+	0.155562i
$159$	−8.27183			−0.655999
$160$	10.2393	−	7.42672i	0.809490	−	0.587133i
$161$	3.51396			0.276939
$162$	0.812425	+	1.15757i	0.0638301	+	0.0909472i
$163$	−3.08826			−0.241891			−0.120946	−	0.992659i	$-0.538593\pi$
$163$	−3.08826			−0.241891			−0.120946	+	0.992659i	$0.538593\pi$
$164$	−13.6784	−	4.94473i	−1.06811	−	0.386118i
$165$	0.974046	−	12.7781i	0.0758294	−	0.994771i
$166$	−4.58650	−	6.53499i	−0.355981	−	0.507213i
$167$	−4.67681	+	4.67681i	−0.361902	+	0.361902i	−0.864513	−	0.502611i	$-0.832373\pi$
$167$	−4.67681	+	4.67681i	−0.361902	+	0.361902i	0.502611	+	0.864513i	$0.332373\pi$
$168$	−2.24300	+	3.91456i	−0.173051	+	0.302015i
$169$	10.7173			0.824409
$170$	−3.69292	−	6.21872i	−0.283234	−	0.476954i
$171$	3.09584	+	3.09584i	0.236745	+	0.236745i
$172$	17.5012	+	6.32666i	1.33446	+	0.482403i
$173$		−	22.7032i		−	1.72609i	−0.505124	−	0.863047i	$-0.668553\pi$
$173$		−	22.7032i		−	1.72609i	0.505124	−	0.863047i	$-0.331447\pi$
$174$	0.839034	+	0.146999i	0.0636070	+	0.0111440i
$175$	4.71956	+	6.42919i	0.356765	+	0.486001i
$176$	2.09777	+	22.8282i	0.158125	+	1.72074i
$177$	−9.12504	+	9.12504i	−0.685880	+	0.685880i
$178$	8.52840	+	12.1515i	0.639231	+	0.910797i
$179$	5.21450	+	5.21450i	0.389750	+	0.389750i	0.874598	−	0.484848i	$-0.161125\pi$
$179$	5.21450	+	5.21450i	0.389750	+	0.389750i	−0.484848	+	0.874598i	$0.661125\pi$
$180$	−4.18161	+	1.58561i	−0.311679	+	0.118184i
$181$	14.5282	−	14.5282i	1.07987	−	1.07987i	0.0833500	−	0.996520i	$-0.473438\pi$
$181$	14.5282	−	14.5282i	1.07987	−	1.07987i	0.996520	−	0.0833500i	$-0.0265620\pi$
$182$	0.588162	−	3.35707i	0.0435975	−	0.248843i
$183$	4.89881	+	4.89881i	0.362131	+	0.362131i
$184$	−5.40634	−	3.09777i	−0.398560	−	0.228371i
$185$	13.1700	−	11.3044i	0.968278	−	0.831114i
$186$	10.4516	−	7.33529i	0.766346	−	0.537850i
$187$	13.1078			0.958540
$188$	2.91758	−	1.36826i	0.212786	−	0.0997904i
$189$	1.12791	−	1.12791i	0.0820432	−	0.0820432i
$190$	−11.9042	+	7.06919i	−0.863624	+	0.512853i
$191$			21.5118i			1.55654i	0.627929	+	0.778271i	$0.283903\pi$
$191$			21.5118i			1.55654i	−0.627929	+	0.778271i	$0.716097\pi$
$192$	6.90184	−	4.04533i	0.498097	−	0.291946i
$193$	−14.7523	−	14.7523i	−1.06189	−	1.06189i	−0.997954	−	0.0639410i	$-0.979633\pi$
$193$	−14.7523	−	14.7523i	−1.06189	−	1.06189i	−0.0639410	−	0.997954i	$-0.520367\pi$
$194$	−12.3344	−	2.16100i	−0.885559	−	0.155151i
$195$	2.56353	−	2.20039i	0.183578	−	0.157573i
$196$	−8.38052	−	3.02954i	−0.598609	−	0.216396i
$197$			6.41499i			0.457049i	0.973538	+	0.228524i	$0.0733901\pi$
$197$			6.41499i			0.457049i	−0.973538	+	0.228524i	$0.926610\pi$
$198$	1.39870	−	7.98340i	0.0994012	−	0.567356i
$199$			9.01442i			0.639015i	0.947584	+	0.319508i	$0.103518\pi$
$199$			9.01442i			0.639015i	−0.947584	+	0.319508i	$0.896482\pi$
$200$	−1.59347	−	14.0521i	−0.112675	−	0.993632i
$201$		−	2.17068i		−	0.153108i
$202$	2.69087	+	0.471442i	0.189329	+	0.0331706i
$203$		−	0.960767i		−	0.0674326i
$204$	−1.94223	−	4.14147i	−0.135983	−	0.289961i
$205$	−12.3394	+	10.5914i	−0.861819	+	0.739736i
$206$	0.000626348	−	0.00357503i	4.36398e−5	−	0.000249084i
$207$	1.55774	+	1.55774i	0.108270	+	0.108270i
$208$	−3.86437	+	4.64646i	−0.267946	+	0.322174i
$209$		−	25.0918i		−	1.73563i
$210$	2.57552	+	4.33707i	0.177728	+	0.299286i
$211$	−12.1263	+	12.1263i	−0.834809	+	0.834809i	−0.988170	−	0.153361i	$-0.950990\pi$
$211$	−12.1263	+	12.1263i	−0.834809	+	0.834809i	0.153361	+	0.988170i	$0.450990\pi$
$212$	5.62428	−	15.5583i	0.386277	−	1.06855i
$213$	13.5937			0.931428
$214$	−11.8134	−	16.8322i	−0.807549	−	1.15062i
$215$	15.7879	−	13.5514i	1.07673	−	0.924201i
$216$	−2.72964	+	0.741001i	−0.185728	+	0.0504187i
$217$	−10.1837	−	10.1837i	−0.691318	−	0.691318i
$218$	−21.9286	−	3.84191i	−1.48519	−	0.260207i
$219$	−1.11750	+	1.11750i	−0.0755134	+	0.0755134i
$220$	23.3717	+	10.5203i	1.57572	+	0.709277i
$221$	2.44343	+	2.44343i	0.164363	+	0.164363i
$222$	8.98497	−	6.30598i	0.603032	−	0.423230i
$223$	9.07927	−	9.07927i	0.607993	−	0.607993i	−0.334428	−	0.942421i	$-0.608543\pi$
$223$	9.07927	−	9.07927i	0.607993	−	0.607993i	0.942421	+	0.334428i	$0.108543\pi$
$224$	−5.83771	−	6.88043i	−0.390048	−	0.459718i
$225$	−0.757876	+	4.94223i	−0.0505251	+	0.329482i
$226$	−3.29551	+	18.8099i	−0.219214	+	1.25122i
$227$			0.580888i			0.0385549i	0.999814	+	0.0192774i	$0.00613658\pi$
$227$			0.580888i			0.0385549i	−0.999814	+	0.0192774i	$0.993863\pi$
$228$	−7.92785	+	3.71792i	−0.525034	+	0.246226i
$229$	8.27674	+	8.27674i	0.546942	+	0.546942i	0.925555	−	0.378613i	$-0.123599\pi$
$229$	8.27674	+	8.27674i	0.546942	+	0.546942i	−0.378613	+	0.925555i	$0.623599\pi$
$230$	−5.98987	+	3.55701i	−0.394960	+	0.234543i
$231$	−9.14169			−0.601479
$232$	−0.846974	+	1.47817i	−0.0556066	+	0.0970465i
$233$	10.8812	−	10.8812i	0.712852	−	0.712852i	−0.254279	−	0.967131i	$-0.581838\pi$
$233$	10.8812	−	10.8812i	0.712852	−	0.712852i	0.967131	+	0.254279i	$0.0818382\pi$
$234$	1.74892	−	1.22746i	0.114330	−	0.0802413i
$235$	0.273843	−	3.59242i	0.0178635	−	0.234344i
$236$	−10.9587	−	23.3675i	−0.713348	−	1.52109i
$237$	1.68922			0.109727
$238$	−4.22307	+	2.96391i	−0.273741	+	0.192121i
$239$	−10.3831			−0.671628			−0.335814	−	0.941928i	$-0.609011\pi$
$239$	−10.3831			−0.671628			−0.335814	+	0.941928i	$0.609011\pi$
$240$	−0.139126	−	8.94319i	−0.00898055	−	0.577280i
$241$	22.4691			1.44736			0.723680	−	0.690136i	$-0.242449\pi$
$241$	22.4691			1.44736			0.723680	+	0.690136i	$0.242449\pi$
$242$	−25.2877	+	17.7479i	−1.62556	+	1.14088i
$243$	1.00000			0.0641500
$244$	−12.5449	+	5.88320i	−0.803106	+	0.376633i
$245$	−7.56010	+	6.48915i	−0.482997	+	0.414577i
$246$	−8.41829	+	5.90826i	−0.536730	+	0.376697i
$247$	4.67736	−	4.67736i	0.297613	−	0.297613i
$248$	6.69041	+	24.6456i	0.424842	+	1.56500i
$249$	−5.64544			−0.357765
$250$	−14.5529	−	6.18175i	−0.920404	−	0.390968i
$251$	−16.2297	−	16.2297i	−1.02441	−	1.02441i	−0.999695	−	0.0247152i	$-0.992132\pi$
$251$	−16.2297	−	16.2297i	−1.02441	−	1.02441i	−0.0247152	−	0.999695i	$-0.507868\pi$
$252$	1.35455	+	2.88835i	0.0853288	+	0.181949i
$253$		−	12.6255i		−	0.793756i
$254$	−2.51686	+	14.3656i	−0.157922	+	0.901375i
$255$	−5.09941	−	0.388718i	−0.319337	−	0.0243424i
$256$	2.91597	+	15.7320i	0.182248	+	0.983253i
$257$	−0.223380	+	0.223380i	−0.0139341	+	0.0139341i	−0.714039	−	0.700105i	$-0.753136\pi$
$257$	−0.223380	+	0.223380i	−0.0139341	+	0.0139341i	0.700105	+	0.714039i	$0.253136\pi$
$258$	10.7710	−	7.55948i	0.670573	−	0.470633i
$259$	−8.75474	−	8.75474i	−0.543993	−	0.543993i
$260$	2.39563	+	6.31780i	0.148570	+	0.391813i
$261$	0.425907	−	0.425907i	0.0263630	−	0.0263630i
$262$	−5.11851	−	0.896767i	−0.316222	−	0.0554024i
$263$	−1.01264	−	1.01264i	−0.0624420	−	0.0624420i	0.675196	−	0.737638i	$-0.264059\pi$
$263$	−1.01264	−	1.01264i	−0.0624420	−	0.0624420i	−0.737638	+	0.675196i	$0.764059\pi$
$264$	14.0648	+	8.05895i	0.865626	+	0.495994i
$265$	−12.0470	−	14.0352i	−0.740040	−	0.862174i
$266$	5.67368	+	8.08404i	0.347875	+	0.495664i
$267$	10.4975			0.642435
$268$	4.08279	+	1.47592i	0.249396	+	0.0901561i
$269$	12.5052	−	12.5052i	0.762455	−	0.762455i	−0.214310	−	0.976766i	$-0.568750\pi$
$269$	12.5052	−	12.5052i	0.762455	−	0.762455i	0.976766	+	0.214310i	$0.0687504\pi$
$270$	−0.780893	+	3.06434i	−0.0475237	+	0.186490i
$271$		−	25.2641i		−	1.53469i	−0.641237	−	0.767343i	$-0.721578\pi$
$271$		−	25.2641i		−	1.53469i	0.641237	−	0.767343i	$-0.278422\pi$
$272$	9.11018	−	0.837167i	0.552386	−	0.0507607i
$273$	−1.70410	−	1.70410i	−0.103137	−	0.103137i
$274$	4.71782	−	26.9281i	0.285014	−	1.62678i
$275$	23.0997	−	16.9571i	1.39296	−	1.02255i
$276$	−3.98906	+	1.87075i	−0.240113	+	0.112606i
$277$			13.1100i			0.787706i	0.919174	+	0.393853i	$0.128858\pi$
$277$			13.1100i			0.787706i	−0.919174	+	0.393853i	$0.871142\pi$
$278$	−8.00668	−	1.40278i	−0.480209	−	0.0841330i
$279$		−	9.02889i		−	0.540546i
$280$	−9.90867	+	1.89532i	−0.592156	+	0.113267i
$281$		−	2.34999i		−	0.140189i	−0.997540	−	0.0700944i	$-0.977670\pi$
$281$		−	2.34999i		−	0.140189i	0.997540	−	0.0700944i	$-0.0223301\pi$
$282$	0.393229	−	2.24445i	0.0234165	−	0.133655i
$283$			16.1614i			0.960695i	0.877078	+	0.480348i	$0.159490\pi$
$283$			16.1614i			0.960695i	−0.877078	+	0.480348i	$0.840510\pi$
$284$	−9.24283	+	25.5681i	−0.548461	+	1.51719i
$285$	−0.744106	+	9.76158i	−0.0440770	+	0.578226i
$286$	−12.0618	−	2.11323i	−0.713227	−	0.124958i
$287$	8.20257	+	8.20257i	0.484183	+	0.484183i
$288$	0.462239	−	5.63794i	0.0272377	−	0.332219i
$289$			11.7690i			0.692293i
$290$	0.972537	+	1.63771i	0.0571094	+	0.0961698i
$291$	−6.26114	+	6.26114i	−0.367035	+	0.367035i
$292$	−1.34205	−	2.86169i	−0.0785375	−	0.167468i
$293$	15.9522			0.931939			0.465969	−	0.884801i	$-0.345706\pi$
$293$	15.9522			0.931939			0.465969	+	0.884801i	$0.345706\pi$
$294$	−5.15772	+	3.61988i	−0.300805	+	0.211116i
$295$	−28.7724	−	2.19327i	−1.67520	−	0.127697i
$296$	5.75160	+	21.1872i	0.334305	+	1.23148i
$297$	−4.05250	−	4.05250i	−0.235150	−	0.235150i
$298$	2.57078	−	14.6733i	0.148921	−	0.850004i
$299$	2.35351	−	2.35351i	0.136107	−	0.136107i
$300$	−8.78041	−	4.78585i	−0.506937	−	0.276311i
$301$	−10.4950	−	10.4950i	−0.604921	−	0.604921i
$302$	−6.42934	−	9.16073i	−0.369967	−	0.527141i
$303$	1.36593	−	1.36593i	0.0784705	−	0.0784705i
$304$	−1.60255	−	17.4392i	−0.0919127	−	1.00021i
$305$	−1.17746	+	15.4466i	−0.0674213	+	0.884469i
$306$	−3.18598	−	0.558186i	−0.182130	−	0.0319094i
$307$		−	24.9902i		−	1.42627i	−0.701029	−	0.713133i	$-0.747276\pi$
$307$		−	24.9902i		−	1.42627i	0.701029	−	0.713133i	$-0.252724\pi$
$308$	6.21573	−	17.1944i	0.354174	−	0.979741i
$309$	−0.00181474	−	0.00181474i	−0.000103237	−	0.000103237i
$310$	27.6676	+	7.05060i	1.57142	+	0.400447i
$311$	5.55703			0.315111			0.157555	−	0.987510i	$-0.449639\pi$
$311$	5.55703			0.315111			0.157555	+	0.987510i	$0.449639\pi$
$312$	1.11954	+	4.12408i	0.0633817	+	0.233480i
$313$	3.12705	−	3.12705i	0.176751	−	0.176751i	−0.613187	−	0.789938i	$-0.710113\pi$
$313$	3.12705	−	3.12705i	0.176751	−	0.176751i	0.789938	+	0.613187i	$0.210113\pi$
$314$	7.56148	+	10.7738i	0.426719	+	0.608003i
$315$	3.55644	+	0.271100i	0.200383	+	0.0152748i
$316$	−1.14856	+	3.17721i	−0.0646113	+	0.178732i
$317$	33.8169			1.89935			0.949674	−	0.313240i	$-0.101414\pi$
$317$	33.8169			1.89935			0.949674	+	0.313240i	$0.101414\pi$
$318$	−6.72024	−	9.57521i	−0.376852	−	0.536951i
$319$	−3.45198			−0.193274
$320$	16.9156	+	5.81909i	0.945612	+	0.325297i
$321$	−14.5410			−0.811597
$322$	2.85483	+	4.06766i	0.159093	+	0.226682i
$323$	−10.0135			−0.557166
$324$	−0.679932	+	1.88088i	−0.0377740	+	0.104493i
$325$	7.46699	+	1.14504i	0.414194	+	0.0635154i
$326$	−2.50898	−	3.57488i	−0.138960	−	0.197994i
$327$	−11.1313	+	11.1313i	−0.615563	+	0.615563i
$328$	−5.38884	−	19.8510i	−0.297549	−	1.09609i
$329$	−2.57009			−0.141694
$330$	15.5828	−	9.25369i	0.857807	−	0.509399i
$331$	13.0748	+	13.0748i	0.718658	+	0.718658i	0.968330	−	0.249672i	$-0.0803229\pi$
$331$	13.0748	+	13.0748i	0.718658	+	0.718658i	−0.249672	+	0.968330i	$0.580323\pi$
$332$	3.83852	−	10.6184i	0.210666	−	0.582759i
$333$		−	7.76193i		−	0.425351i
$334$	−9.21328	−	1.61417i	−0.504128	−	0.0883237i
$335$	3.68309	−	3.16136i	0.201229	−	0.172723i
$336$	−6.35364	+	0.583859i	−0.346619	+	0.0318521i
$337$	−4.71773	+	4.71773i	−0.256991	+	0.256991i	−0.823829	−	0.566838i	$-0.808167\pi$
$337$	−4.71773	+	4.71773i	−0.256991	+	0.256991i	0.566838	+	0.823829i	$0.308167\pi$
$338$	8.70701	+	12.4060i	0.473599	+	0.674799i
$339$	9.54820	+	9.54820i	0.518587	+	0.518587i
$340$	4.19838	−	9.32705i	0.227689	−	0.505830i
$341$	−36.5896	+	36.5896i	−1.98144	+	1.98144i
$342$	−1.06851	+	6.09878i	−0.0577785	+	0.329784i
$343$	12.9209	+	12.9209i	0.697664	+	0.697664i
$344$	6.89489	+	25.3988i	0.371748	+	1.36941i
$345$	−0.374412	+	4.91174i	−0.0201577	+	0.264439i
$346$	26.2805	−	18.4447i	1.41285	−	0.991591i
$347$	26.4531			1.42008			0.710039	−	0.704163i	$-0.248677\pi$
$347$	26.4531			1.42008			0.710039	+	0.704163i	$0.248677\pi$
$348$	0.511490	+	1.09067i	0.0274187	+	0.0584658i
$349$	−7.72146	+	7.72146i	−0.413320	+	0.413320i	−0.882893	−	0.469573i	$-0.844408\pi$
$349$	−7.72146	+	7.72146i	−0.413320	+	0.413320i	0.469573	+	0.882893i	$0.344408\pi$
$350$	−3.60794	+	10.6864i	−0.192853	+	0.571215i
$351$		−	1.51085i		−	0.0806434i
$352$	−24.7210	+	20.9745i	−1.31763	+	1.11795i
$353$	17.1761	+	17.1761i	0.914189	+	0.914189i	0.996599	−	0.0824092i	$-0.0262615\pi$
$353$	17.1761	+	17.1761i	0.914189	+	0.914189i	−0.0824092	+	0.996599i	$0.526261\pi$
$354$	−17.9763	−	3.14946i	−0.955428	−	0.167392i
$355$	19.7978	+	23.0651i	1.05076	+	1.22417i
$356$	−7.13757	+	19.7444i	−0.378290	+	1.04645i
$357$			3.64822i			0.193084i
$358$	−1.79975	+	10.2725i	−0.0951200	+	0.542920i
$359$		−	13.3611i		−	0.705173i	−0.935779	−	0.352587i	$-0.885302\pi$
$359$		−	13.3611i		−	0.705173i	0.935779	−	0.352587i	$-0.114698\pi$
$360$	−5.23269	−	3.55231i	−0.275787	−	0.187223i
$361$			0.168423i			0.00886435i
$362$	28.6204	+	5.01432i	1.50426	+	0.263547i
$363$			21.8455i			1.14659i
$364$	4.36388	−	2.04653i	0.228730	−	0.107267i
$365$	−3.52361	−	0.268598i	−0.184434	−	0.0140591i
$366$	−1.69080	+	9.65063i	−0.0883794	+	0.504447i
$367$	−2.07421	−	2.07421i	−0.108273	−	0.108273i	0.650895	−	0.759168i	$-0.274394\pi$
$367$	−2.07421	−	2.07421i	−0.108273	−	0.108273i	−0.759168	+	0.650895i	$0.774394\pi$
$368$	−0.806359	−	8.77491i	−0.0420343	−	0.457424i
$369$			7.27238i			0.378585i
$370$	23.7852	+	6.06124i	1.23653	+	0.315109i
$371$	−9.32985	+	9.32985i	−0.484382	+	0.484382i
$372$	16.9822	+	6.13903i	0.880487	+	0.318294i
$373$	−31.6636			−1.63948			−0.819739	−	0.572737i	$-0.805882\pi$
$373$	−31.6636			−1.63948			−0.819739	+	0.572737i	$0.805882\pi$
$374$	10.6491	+	15.1732i	0.550654	+	0.784589i
$375$	−9.48945	+	5.91187i	−0.490033	+	0.305288i
$376$	3.95416	+	2.26569i	0.203920	+	0.116844i
$377$	−0.643483	−	0.643483i	−0.0331411	−	0.0331411i
$378$	2.22197	+	0.389291i	0.114286	+	0.0200230i
$379$	−5.09306	+	5.09306i	−0.261613	+	0.261613i	−0.825709	−	0.564096i	$-0.809225\pi$
$379$	−5.09306	+	5.09306i	−0.261613	+	0.261613i	0.564096	+	0.825709i	$0.309225\pi$
$380$	−17.8544	−	8.03678i	−0.915910	−	0.412278i
$381$	7.29219	+	7.29219i	0.373590	+	0.373590i
$382$	−24.9014	+	17.4767i	−1.27407	+	0.894188i
$383$	−3.20359	+	3.20359i	−0.163696	+	0.163696i	−0.784202	−	0.620506i	$-0.786927\pi$
$383$	−3.20359	+	3.20359i	−0.163696	+	0.163696i	0.620506	+	0.784202i	$0.286927\pi$
$384$	10.2900	+	4.70283i	0.525108	+	0.239990i
$385$	−13.3138	−	15.5111i	−0.678536	−	0.790519i
$386$	5.09168	−	29.0620i	0.259160	−	1.47922i
$387$		−	9.30484i		−	0.472992i
$388$	−7.51927	−	16.0336i	−0.381733	−	0.813982i
$389$	−1.34936	−	1.34936i	−0.0684155	−	0.0684155i	0.672071	−	0.740487i	$-0.265405\pi$
$389$	−1.34936	−	1.34936i	−0.0684155	−	0.0684155i	−0.740487	+	0.672071i	$0.765405\pi$
$390$	4.62978	+	1.17982i	0.234438	+	0.0597423i
$391$	−5.03851			−0.254808
$392$	−3.30164	−	12.1623i	−0.166758	−	0.614289i
$393$	−2.59824	+	2.59824i	−0.131064	+	0.131064i
$394$	−7.42579	+	5.21169i	−0.374106	+	0.262561i
$395$	2.46016	+	2.86617i	0.123784	+	0.144213i
$396$	10.3777	−	4.86682i	0.521498	−	0.244567i
$397$	24.4680			1.22801			0.614007	−	0.789301i	$-0.289557\pi$
$397$	24.4680			1.22801			0.614007	+	0.789301i	$0.289557\pi$
$398$	−10.4348	+	7.32354i	−0.523050	+	0.367096i
$399$	6.98363			0.349619
$400$	14.9717	−	13.2608i	0.748584	−	0.663040i
$401$	28.5323			1.42484			0.712419	−	0.701755i	$-0.247600\pi$
$401$	28.5323			1.42484			0.712419	+	0.701755i	$0.247600\pi$
$402$	2.51272	−	1.76352i	0.125323	−	0.0879563i
$403$	−13.6413			−0.679523
$404$	1.64040	+	3.49788i	0.0816130	+	0.174026i
$405$	1.45639	+	1.69674i	0.0723684	+	0.0843119i
$406$	1.11215	−	0.780551i	0.0551953	−	0.0387381i
$407$	−31.4552	+	31.4552i	−1.55918	+	1.55918i
$408$	3.21613	−	5.61290i	0.159222	−	0.277880i
$409$	−15.1016			−0.746726			−0.373363	−	0.927685i	$-0.621795\pi$
$409$	−15.1016			−0.746726			−0.373363	+	0.927685i	$0.621795\pi$
$410$	−22.2851	−	5.67896i	−1.10058	−	0.280464i
$411$	−13.6691	−	13.6691i	−0.674248	−	0.674248i
$412$	0.00464721	−	0.00217940i	0.000228951	−	0.000107371i
$413$			20.5844i			1.01289i
$414$	−0.537644	+	3.06873i	−0.0264238	+	0.150820i
$415$	−8.22194	−	9.57886i	−0.403599	−	0.470208i
$416$	−8.51810	−	0.698375i	−0.417634	−	0.0342407i
$417$	−4.06432	+	4.06432i	−0.199030	+	0.199030i
$418$	29.0455	−	20.3852i	1.42066	−	0.997072i
$419$	1.93018	+	1.93018i	0.0942953	+	0.0942953i	0.752681	−	0.658386i	$-0.228760\pi$
$419$	1.93018	+	1.93018i	0.0942953	+	0.0942953i	−0.658386	+	0.752681i	$0.728760\pi$
$420$	−2.92804	+	6.50489i	−0.142874	+	0.317406i
$421$	11.3334	−	11.3334i	0.552355	−	0.552355i	−0.374765	−	0.927120i	$-0.622277\pi$
$421$	11.3334	−	11.3334i	0.552355	−	0.552355i	0.927120	+	0.374765i	$0.122277\pi$
$422$	−23.8887	−	4.18533i	−1.16289	−	0.203739i
$423$	−1.13932	−	1.13932i	−0.0553956	−	0.0553956i
$424$	22.5791	−	6.12943i	1.09654	−	0.297671i
$425$	−6.76716	−	9.21851i	−0.328255	−	0.447164i
$426$	11.0439	+	15.7357i	0.535078	+	0.762397i
$427$	11.0508			0.534786
$428$	9.88686	−	27.3497i	0.477900	−	1.32200i
$429$	−6.12274	+	6.12274i	−0.295609	+	0.295609i
$430$	28.5132	+	7.26609i	1.37503	+	0.350402i
$431$		−	23.3060i		−	1.12261i	−0.827609	−	0.561305i	$-0.810299\pi$
$431$		−	23.3060i		−	1.12261i	0.827609	−	0.561305i	$-0.189701\pi$
$432$	−3.07538	−	2.55774i	−0.147964	−	0.123059i
$433$	2.27419	+	2.27419i	0.109291	+	0.109291i	0.759637	−	0.650347i	$-0.225376\pi$
$433$	2.27419	+	2.27419i	0.109291	+	0.109291i	−0.650347	+	0.759637i	$0.725376\pi$
$434$	3.51486	−	20.0619i	0.168719	−	0.963003i
$435$	1.34294	+	0.102370i	0.0643890	+	0.00490825i
$436$	−13.3681	−	28.5052i	−0.640214	−	1.36515i
$437$			9.64500i			0.461383i
$438$	−2.20146	−	0.385698i	−0.105190	−	0.0184294i
$439$			9.72340i			0.464073i	0.972707	+	0.232036i	$0.0745388\pi$
$439$			9.72340i			0.464073i	−0.972707	+	0.232036i	$0.925461\pi$
$440$	6.80976	+	35.6012i	0.324643	+	1.69722i
$441$			4.45565i			0.212174i
$442$	−0.843338	+	4.81355i	−0.0401135	+	0.228957i
$443$		−	16.8029i		−	0.798332i	−0.916879	−	0.399166i	$-0.869300\pi$
$443$		−	16.8029i		−	0.798332i	0.916879	−	0.399166i	$-0.130700\pi$
$444$	14.5992	+	5.27759i	0.692848	+	0.250463i
$445$	15.2884	+	17.8115i	0.724738	+	0.844347i
$446$	17.8861	+	3.13366i	0.846932	+	0.148383i
$447$	−7.44842	−	7.44842i	−0.352298	−	0.352298i
$448$	3.22188	−	12.3474i	0.152219	−	0.583359i
$449$		−	14.6889i		−	0.693212i	−0.938011	−	0.346606i	$-0.887334\pi$
$449$		−	14.6889i		−	0.693212i	0.938011	−	0.346606i	$-0.112666\pi$
$450$	−6.33669	+	3.13789i	−0.298714	+	0.147922i
$451$	29.4713	−	29.4713i	1.38775	−	1.38775i
$452$	−24.4511	+	11.4668i	−1.15008	+	0.539355i
$453$	−7.91377			−0.371821
$454$	−0.672418	+	0.471927i	−0.0315581	+	0.0221487i
$455$	0.409593	−	5.37326i	0.0192020	−	0.251902i
$456$	−10.7445	−	6.15650i	−0.503159	−	0.288304i
$457$	−10.8605	−	10.8605i	−0.508034	−	0.508034i	0.405889	−	0.913922i	$-0.366962\pi$
$457$	−10.8605	−	10.8605i	−0.508034	−	0.508034i	−0.913922	+	0.405889i	$0.866962\pi$
$458$	−2.85667	+	16.3051i	−0.133483	+	0.761888i
$459$	−1.61725	+	1.61725i	−0.0754869	+	0.0754869i
$460$	−8.98380	−	4.04388i	−0.418872	−	0.188547i
$461$	−12.2300	−	12.2300i	−0.569608	−	0.569608i	0.362411	−	0.932019i	$-0.381954\pi$
$461$	−12.2300	−	12.2300i	−0.569608	−	0.569608i	−0.932019	+	0.362411i	$0.881954\pi$
$462$	−7.42694	−	10.5821i	−0.345532	−	0.492326i
$463$	−25.4819	+	25.4819i	−1.18424	+	1.18424i	−0.205609	+	0.978634i	$0.565918\pi$
$463$	−25.4819	+	25.4819i	−1.18424	+	1.18424i	−0.978634	+	0.205609i	$0.934082\pi$
$464$	−2.39918	+	0.220470i	−0.111379	+	0.0102351i
$465$	15.3197	−	13.1496i	0.710435	−	0.609796i
$466$	21.4359	+	3.75559i	0.993000	+	0.173974i
$467$		−	34.3316i		−	1.58868i	−0.607475	−	0.794339i	$-0.707818\pi$
$467$		−	34.3316i		−	1.58868i	0.607475	−	0.794339i	$-0.292182\pi$
$468$	2.84173	+	1.02728i	0.131359	+	0.0474860i
$469$	−2.44833	−	2.44833i	−0.113053	−	0.113053i
$470$	4.38095	−	2.60158i	0.202078	−	0.120002i
$471$	9.30731			0.428858
$472$	18.1464	−	31.6697i	0.835255	−	1.45772i
$473$	−37.7079	+	37.7079i	−1.73381	+	1.73381i
$474$	1.37236	+	1.95539i	0.0630348	+	0.0898140i
$475$	−17.6466	+	12.9541i	−0.809682	+	0.594374i
$476$	−6.86185	−	2.48054i	−0.314512	−	0.113696i
$477$	−8.27183			−0.378741
$478$	−8.43550	−	12.0192i	−0.385831	−	0.549744i
$479$	8.65519			0.395466			0.197733	−	0.980256i	$-0.436642\pi$
$479$	8.65519			0.395466			0.197733	+	0.980256i	$0.436642\pi$
$480$	10.2393	−	7.42672i	0.467359	−	0.338982i
$481$	−11.7271			−0.534712
$482$	18.2544	+	26.0095i	0.831466	+	1.18470i
$483$	3.51396			0.159891
$484$	−41.0887	−	14.8535i	−1.86767	−	0.675159i
$485$	−19.7422	−	1.50491i	−0.896447	−	0.0683343i
$486$	0.812425	+	1.15757i	0.0368523	+	0.0525084i
$487$	−7.87838	+	7.87838i	−0.357004	+	0.357004i	−0.862707	−	0.505704i	$-0.831233\pi$
$487$	−7.87838	+	7.87838i	−0.357004	+	0.357004i	0.505704	+	0.862707i	$0.331233\pi$
$488$	−17.0020	−	9.74196i	−0.769645	−	0.440998i
$489$	−3.08826			−0.139656
$490$	−13.6536	−	3.47939i	−0.616809	−	0.157183i
$491$	−5.87690	−	5.87690i	−0.265221	−	0.265221i	0.561950	−	0.827171i	$-0.310051\pi$
$491$	−5.87690	−	5.87690i	−0.265221	−	0.265221i	−0.827171	+	0.561950i	$0.810051\pi$
$492$	−13.6784	−	4.94473i	−0.616672	−	0.222926i
$493$			1.37760i			0.0620439i
$494$	9.21437	+	1.61436i	0.414574	+	0.0726337i
$495$	0.974046	−	12.7781i	0.0437801	−	0.574331i
$496$	−23.0935	+	27.7673i	−1.03693	+	1.24679i
$497$	15.3325	−	15.3325i	0.687756	−	0.687756i
$498$	−4.58650	−	6.53499i	−0.205526	−	0.292840i
$499$	4.52232	+	4.52232i	0.202447	+	0.202447i	0.801048	−	0.598601i	$-0.204276\pi$
$499$	4.52232	+	4.52232i	0.202447	+	0.202447i	−0.598601	+	0.801048i	$0.704276\pi$
$500$	−4.66731	−	21.8682i	−0.208728	−	0.977974i
$501$	−4.67681	+	4.67681i	−0.208944	+	0.208944i
$502$	5.60159	−	31.9724i	0.250011	−	1.42700i
$503$	7.49454	+	7.49454i	0.334165	+	0.334165i	0.854166	−	0.520001i	$-0.174068\pi$
$503$	7.49454	+	7.49454i	0.334165	+	0.334165i	−0.520001	+	0.854166i	$0.674068\pi$
$504$	−2.24300	+	3.91456i	−0.0999110	+	0.174368i
$505$	4.30695	+	0.328310i	0.191657	+	0.0146096i
$506$	14.6148	−	10.2572i	0.649709	−	0.455990i
$507$	10.7173			0.475973
$508$	−18.6739	+	8.75750i	−0.828520	+	0.388551i
$509$	2.39069	−	2.39069i	0.105965	−	0.105965i	−0.652136	−	0.758102i	$-0.726127\pi$
$509$	2.39069	−	2.39069i	0.105965	−	0.105965i	0.758102	+	0.652136i	$0.226127\pi$
$510$	−3.69292	−	6.21872i	−0.163525	−	0.275370i
$511$			2.52086i			0.111516i
$512$	−15.8419	+	16.1565i	−0.700120	+	0.714025i
$513$	3.09584	+	3.09584i	0.136685	+	0.136685i
$514$	−0.440058	−	0.0770985i	−0.0194101	−	0.00340067i
$515$	0.000436186	−	0.00572212i	1.92206e−5	−	0.000252147i
$516$	17.5012	+	6.32666i	0.770449	+	0.278516i
$517$			9.23418i			0.406119i
$518$	3.02165	−	17.2468i	0.132764	−	0.757780i
$519$		−	22.7032i		−	0.996561i
$520$	−5.36702	+	7.90584i	−0.235360	+	0.346694i
$521$		−	27.6569i		−	1.21167i	−0.795590	−	0.605835i	$-0.792839\pi$
$521$		−	27.6569i		−	1.21167i	0.795590	−	0.605835i	$-0.207161\pi$
$522$	0.839034	+	0.146999i	0.0367235	+	0.00643399i
$523$		−	5.69218i		−	0.248902i	−0.992226	−	0.124451i	$-0.960283\pi$
$523$		−	5.69218i		−	0.248902i	0.992226	−	0.124451i	$-0.0397169\pi$
$524$	−3.12033	−	6.65358i	−0.136312	−	0.290663i
$525$	4.71956	+	6.42919i	0.205979	+	0.280593i
$526$	0.349507	−	1.99489i	0.0152392	−	0.0869815i
$527$	14.6020	+	14.6020i	0.636073	+	0.636073i
$528$	2.09777	+	22.8282i	0.0912937	+	0.993471i
$529$		−	18.1469i		−	0.788996i
$530$	6.45942	−	25.3477i	0.280579	−	1.10104i
$531$	−9.12504	+	9.12504i	−0.395993	+	0.395993i
$532$	−4.74840	+	13.1353i	−0.205869	+	0.569489i
$533$	10.9875			0.475922
$534$	8.52840	+	12.1515i	0.369060	+	0.525849i
$535$	−21.1772	−	24.6723i	−0.915572	−	1.06668i
$536$	1.60848	+	5.92518i	0.0694757	+	0.255929i
$537$	5.21450	+	5.21450i	0.225022	+	0.225022i
$538$	24.6352	+	4.31610i	1.06210	+	0.186080i
$539$	18.0565	−	18.0565i	0.777750	−	0.777750i
$540$	−4.18161	+	1.58561i	−0.179948	+	0.0682338i
$541$	8.91173	+	8.91173i	0.383145	+	0.383145i	0.872234	−	0.489089i	$-0.162671\pi$
$541$	8.91173	+	8.91173i	0.383145	+	0.383145i	−0.489089	+	0.872234i	$0.662671\pi$
$542$	29.2450	−	20.5252i	1.25618	−	0.881633i
$543$	14.5282	−	14.5282i	0.623463	−	0.623463i
$544$	8.37041	+	9.86553i	0.358879	+	0.422981i
$545$	−35.0985	−	2.67549i	−1.50345	−	0.114605i
$546$	0.588162	−	3.35707i	0.0251710	−	0.143669i
$547$		−	16.9775i		−	0.725904i	−0.931808	−	0.362952i	$-0.881769\pi$
$547$		−	16.9775i		−	0.725904i	0.931808	−	0.362952i	$-0.118231\pi$
$548$	35.0040	−	16.4158i	1.49530	−	0.701250i
$549$	4.89881	+	4.89881i	0.209076	+	0.209076i
$550$	38.3958	+	12.9631i	1.63720	+	0.552749i
$551$	2.63708			0.112343
$552$	−5.40634	−	3.09777i	−0.230109	−	0.131850i
$553$	1.90528	−	1.90528i	0.0810209	−	0.0810209i
$554$	−15.1758	+	10.6509i	−0.644757	+	0.452514i
$555$	13.1700	−	11.3044i	0.559035	−	0.479844i
$556$	−4.88101	−	10.4079i	−0.207001	−	0.441395i
$557$	5.77429			0.244665			0.122332	−	0.992489i	$-0.460963\pi$
$557$	5.77429			0.244665			0.122332	+	0.992489i	$0.460963\pi$
$558$	10.4516	−	7.33529i	0.442450	−	0.310528i
$559$	−14.0583			−0.594601
$560$	−10.2440	−	9.93017i	−0.432888	−	0.419626i
$561$	13.1078			0.553414
$562$	2.72028	−	1.90919i	0.114748	−	0.0805344i
$563$	−8.76839			−0.369544			−0.184772	−	0.982781i	$-0.559155\pi$
$563$	−8.76839			−0.369544			−0.184772	+	0.982781i	$0.559155\pi$
$564$	2.91758	−	1.36826i	0.122852	−	0.0576140i
$565$	−2.29497	+	30.1067i	−0.0965503	+	1.26660i
$566$	−18.7079	+	13.1299i	−0.786353	+	0.551892i
$567$	1.12791	−	1.12791i	0.0473676	−	0.0473676i
$568$	−37.1060	+	10.0730i	−1.55693	+	0.422653i
$569$	−6.53649			−0.274024			−0.137012	−	0.990569i	$-0.543750\pi$
$569$	−6.53649			−0.274024			−0.137012	+	0.990569i	$0.543750\pi$
$570$	−11.9042	+	7.06919i	−0.498613	+	0.296096i
$571$	8.51080	+	8.51080i	0.356166	+	0.356166i	0.862397	−	0.506232i	$-0.168962\pi$
$571$	8.51080	+	8.51080i	0.356166	+	0.356166i	−0.506232	+	0.862397i	$0.668962\pi$
$572$	−7.35306	−	15.6792i	−0.307447	−	0.655579i
$573$			21.5118i			0.898670i
$574$	−2.83107	+	16.1590i	−0.118167	+	0.674464i
$575$	−8.87926	+	6.51812i	−0.370291	+	0.271824i
$576$	6.90184	−	4.04533i	0.287576	−	0.168555i
$577$	−2.50352	+	2.50352i	−0.104223	+	0.104223i	−0.757295	−	0.653072i	$-0.773480\pi$
$577$	−2.50352	+	2.50352i	−0.104223	+	0.104223i	0.653072	+	0.757295i	$0.273480\pi$
$578$	−13.6234	+	9.56141i	−0.566659	+	0.397702i
$579$	−14.7523	−	14.7523i	−0.613085	−	0.613085i
$580$	−1.10565	+	2.45630i	−0.0459097	+	0.101992i
$581$	−6.36753	+	6.36753i	−0.264170	+	0.264170i
$582$	−12.3344	−	2.16100i	−0.511278	−	0.0895762i
$583$	33.5216	+	33.5216i	1.38832	+	1.38832i
$584$	2.22229	−	3.87843i	0.0919592	−	0.160490i
$585$	2.56353	−	2.20039i	0.105989	−	0.0909749i
$586$	12.9600	+	18.4658i	0.535372	+	0.762815i
$587$	−28.0515			−1.15781			−0.578904	−	0.815396i	$-0.696519\pi$
$587$	−28.0515			−1.15781			−0.578904	+	0.815396i	$0.696519\pi$
$588$	−8.38052	−	3.02954i	−0.345607	−	0.124936i
$589$	27.9520	−	27.9520i	1.15174	−	1.15174i
$590$	−20.8366	−	35.0880i	−0.857829	−	1.44455i
$591$			6.41499i			0.263877i
$592$	−19.8530	+	23.8709i	−0.815952	+	0.981088i
$593$	10.3023	+	10.3023i	0.423066	+	0.423066i	0.886258	−	0.463192i	$-0.153296\pi$
$593$	10.3023	+	10.3023i	0.423066	+	0.423066i	−0.463192	+	0.886258i	$0.653296\pi$
$594$	1.39870	−	7.98340i	0.0573893	−	0.327563i
$595$	−6.19010	+	5.31322i	−0.253769	+	0.217821i
$596$	19.0740	−	8.94513i	0.781301	−	0.366407i
$597$			9.01442i			0.368936i
$598$	4.63640	+	0.812302i	0.189597	+	0.0332175i
$599$			16.5177i			0.674893i	0.941345	+	0.337447i	$0.109563\pi$
$599$			16.5177i			0.674893i	−0.941345	+	0.337447i	$0.890437\pi$
$600$	−1.59347	−	14.0521i	−0.0650531	−	0.573674i
$601$			28.1393i			1.14783i	0.818916	+	0.573913i	$0.194575\pi$
$601$			28.1393i			1.14783i	−0.818916	+	0.573913i	$0.805425\pi$
$602$	3.62229	−	20.6751i	0.147633	−	0.842653i
$603$		−	2.17068i		−	0.0883971i
$604$	5.38083	−	14.8848i	0.218943	−	0.605654i
$605$	−37.0663	+	31.8156i	−1.50696	+	1.29349i
$606$	2.69087	+	0.471442i	0.109309	+	0.0191510i
$607$	−7.05215	−	7.05215i	−0.286238	−	0.286238i	0.549353	−	0.835591i	$-0.314874\pi$
$607$	−7.05215	−	7.05215i	−0.286238	−	0.286238i	−0.835591	+	0.549353i	$0.814874\pi$
$608$	18.8852	−	16.0231i	0.765894	−	0.649823i
$609$		−	0.960767i		−	0.0389322i
$610$	−18.8371	+	11.1862i	−0.762692	+	0.452916i
$611$	−1.72134	+	1.72134i	−0.0696381	+	0.0696381i
$612$	−1.94223	−	4.14147i	−0.0785099	−	0.167409i
$613$	9.16257			0.370073			0.185036	−	0.982732i	$-0.440760\pi$
$613$	9.16257			0.370073			0.185036	+	0.982732i	$0.440760\pi$
$614$	28.9279	−	20.3027i	1.16743	−	0.819348i
$615$	−12.3394	+	10.5914i	−0.497571	+	0.427087i
$616$	24.9535	−	6.77400i	1.00541	−	0.272932i
$617$	1.80126	+	1.80126i	0.0725161	+	0.0725161i	0.742435	−	0.669919i	$-0.233671\pi$
$617$	1.80126	+	1.80126i	0.0725161	+	0.0725161i	−0.669919	+	0.742435i	$0.733671\pi$
$618$	0.000626348	−	0.00357503i	2.51954e−5	−	0.000143809i
$619$	22.8596	−	22.8596i	0.918804	−	0.918804i	−0.0781384	−	0.996943i	$-0.524898\pi$
$619$	22.8596	−	22.8596i	0.918804	−	0.918804i	0.996943	+	0.0781384i	$0.0248976\pi$
$620$	14.3163	+	37.7553i	0.574957	+	1.51629i
$621$	1.55774	+	1.55774i	0.0625098	+	0.0625098i
$622$	4.51467	+	6.43265i	0.181022	+	0.257926i
$623$	11.8402	−	11.8402i	0.474366	−	0.474366i
$624$	−3.86437	+	4.64646i	−0.154698	+	0.186007i
$625$	−23.8512	−	7.49119i	−0.954050	−	0.299648i
$626$	6.16027	+	1.07928i	0.246214	+	0.0431369i
$627$		−	25.0918i		−	1.00207i
$628$	−6.32834	+	17.5059i	−0.252528	+	0.698561i
$629$	12.5530	+	12.5530i	0.500521	+	0.500521i
$630$	2.57552	+	4.33707i	0.102611	+	0.172793i
$631$	−5.25748			−0.209297			−0.104648	−	0.994509i	$-0.533372\pi$
$631$	−5.25748			−0.209297			−0.104648	+	0.994509i	$0.533372\pi$
$632$	−4.61096	+	1.25171i	−0.183414	+	0.0497905i
$633$	−12.1263	+	12.1263i	−0.481977	+	0.481977i
$634$	27.4737	+	39.1454i	1.09112	+	1.55466i
$635$	−1.75273	+	22.9932i	−0.0695548	+	0.912458i
$636$	5.62428	−	15.5583i	0.223017	−	0.616926i
$637$	6.73184			0.266725
$638$	−2.80447	−	3.99590i	−0.111030	−	0.158199i
$639$	13.5937			0.537760
$640$	7.00667	+	24.3086i	0.276963	+	0.960881i
$641$	−13.7980			−0.544989			−0.272494	−	0.962157i	$-0.587849\pi$
$641$	−13.7980			−0.544989			−0.272494	+	0.962157i	$0.587849\pi$
$642$	−11.8134	−	16.8322i	−0.466239	−	0.664312i
$643$	−10.3483			−0.408098			−0.204049	−	0.978961i	$-0.565410\pi$
$643$	−10.3483			−0.408098			−0.204049	+	0.978961i	$0.565410\pi$
$644$	−2.38926	+	6.60933i	−0.0941499	+	0.260444i
$645$	15.7879	−	13.5514i	0.621649	−	0.533588i
$646$	−8.13522	−	11.5913i	−0.320076	−	0.456055i
$647$	5.33727	−	5.33727i	0.209830	−	0.209830i	−0.594365	−	0.804195i	$-0.702597\pi$
$647$	5.33727	−	5.33727i	0.209830	−	0.209830i	0.804195	+	0.594365i	$0.202597\pi$
$648$	−2.72964	+	0.741001i	−0.107230	+	0.0291093i
$649$	73.9585			2.90312
$650$	4.74090	+	9.57381i	0.185953	+	0.375516i
$651$	−10.1837	−	10.1837i	−0.399133	−	0.399133i
$652$	2.09981	−	5.80864i	0.0822349	−	0.227484i
$653$			30.3415i			1.18735i	0.804703	+	0.593677i	$0.202324\pi$
$653$			30.3415i			1.18735i	−0.804703	+	0.593677i	$0.797676\pi$
$654$	−21.9286	−	3.84191i	−0.857477	−	0.150231i
$655$	−8.19258	−	0.624504i	−0.320110	−	0.0244014i
$656$	18.6008	−	22.3654i	0.726241	−	0.873221i
$657$	−1.11750	+	1.11750i	−0.0435977	+	0.0435977i
$658$	−2.08801	−	2.97506i	−0.0813989	−	0.115980i
$659$	22.0703	+	22.0703i	0.859738	+	0.859738i	0.991307	−	0.131569i	$-0.0420016\pi$
$659$	22.0703	+	22.0703i	0.859738	+	0.859738i	−0.131569	+	0.991307i	$0.542002\pi$
$660$	23.3717	+	10.5203i	0.909741	+	0.409501i
$661$	12.8058	−	12.8058i	0.498089	−	0.498089i	−0.412753	−	0.910843i	$-0.635433\pi$
$661$	12.8058	−	12.8058i	0.498089	−	0.498089i	0.910843	+	0.412753i	$0.135433\pi$
$662$	−4.51271	+	25.7574i	−0.175391	+	1.00109i
$663$	2.44343	+	2.44343i	0.0948951	+	0.0948951i
$664$	15.4100	−	4.18328i	0.598024	−	0.162343i
$665$	10.1709	+	11.8494i	0.394409	+	0.459501i
$666$	8.98497	−	6.30598i	0.348161	−	0.244352i
$667$	1.32690			0.0513778
$668$	−5.61658	−	11.9764i	−0.217312	−	0.463381i
$669$	9.07927	−	9.07927i	0.351025	−	0.351025i
$670$	6.65172	+	1.69507i	0.256979	+	0.0654864i
$671$		−	39.7049i		−	1.53279i
$672$	−5.83771	−	6.88043i	−0.225194	−	0.265418i
$673$	5.19258	+	5.19258i	0.200159	+	0.200159i	0.800068	−	0.599909i	$-0.204797\pi$
$673$	5.19258	+	5.19258i	0.200159	+	0.200159i	−0.599909	+	0.800068i	$0.704797\pi$
$674$	−9.29391	−	1.62830i	−0.357988	−	0.0627198i
$675$	−0.757876	+	4.94223i	−0.0291707	+	0.190226i
$676$	−7.28705	+	20.1579i	−0.280271	+	0.775305i
$677$		−	34.5001i		−	1.32595i	−0.748643	−	0.662973i	$-0.769294\pi$
$677$		−	34.5001i		−	1.32595i	0.748643	−	0.662973i	$-0.230706\pi$
$678$	−3.29551	+	18.8099i	−0.126563	+	0.722390i
$679$			14.1240i			0.542028i
$680$	14.2076	−	2.71761i	0.544836	−	0.104215i
$681$			0.580888i			0.0222597i
$682$	−72.0813	−	12.6287i	−2.76013	−	0.483578i
$683$		−	16.4252i		−	0.628494i	−0.949341	−	0.314247i	$-0.898248\pi$
$683$		−	16.4252i		−	0.628494i	0.949341	−	0.314247i	$-0.101752\pi$
$684$	−7.92785	+	3.71792i	−0.303129	+	0.142158i
$685$	3.28547	−	43.1005i	0.125531	−	1.64679i
$686$	−4.45958	+	25.4541i	−0.170268	+	0.971843i
$687$	8.27674	+	8.27674i	0.315777	+	0.315777i
$688$	−23.7993	+	28.6160i	−0.907341	+	1.09097i
$689$			12.4975i			0.476118i
$690$	−5.98987	+	3.55701i	−0.228030	+	0.135413i
$691$	−9.38248	+	9.38248i	−0.356926	+	0.356926i	−0.862679	−	0.505752i	$-0.831215\pi$
$691$	−9.38248	+	9.38248i	−0.356926	+	0.356926i	0.505752	+	0.862679i	$0.331215\pi$
$692$	42.7019	+	15.4367i	1.62328	+	0.586814i
$693$	−9.14169			−0.347264
$694$	21.4912	+	30.6213i	0.815793	+	1.16237i
$695$	−12.8153	−	0.976886i	−0.486113	−	0.0370554i
$696$	−0.846974	+	1.47817i	−0.0321045	+	0.0560298i
$697$	−11.7613	−	11.7613i	−0.445490	−	0.445490i
$698$	−15.2112	−	2.66502i	−0.575753	−	0.100872i
$699$	10.8812	−	10.8812i	0.411565	−	0.411565i
$700$	−15.3015	+	4.50549i	−0.578342	+	0.170292i
$701$	−9.83481	−	9.83481i	−0.371455	−	0.371455i	0.496552	−	0.868007i	$-0.334599\pi$
$701$	−9.83481	−	9.83481i	−0.371455	−	0.371455i	−0.868007	+	0.496552i	$0.834599\pi$
$702$	1.74892	−	1.22746i	0.0660087	−	0.0463273i
$703$	24.0297	−	24.0297i	0.906296	−	0.906296i
$704$	−44.3634	−	11.5760i	−1.67201	−	0.436287i
$705$	0.273843	−	3.59242i	0.0103135	−	0.135298i
$706$	−5.92822	+	33.8367i	−0.223112	+	1.27346i
$707$		−	3.08128i		−	0.115883i
$708$	−10.9587	−	23.3675i	−0.411851	−	0.878204i
$709$	−23.8550	−	23.8550i	−0.895894	−	0.895894i	0.0991761	−	0.995070i	$-0.468379\pi$
$709$	−23.8550	−	23.8550i	−0.895894	−	0.895894i	−0.995070	+	0.0991761i	$0.968379\pi$
$710$	−10.6153	+	41.6559i	−0.398384	+	1.56332i
$711$	1.68922			0.0633507
$712$	−28.6543	+	7.77863i	−1.07386	+	0.291517i
$713$	14.0646	−	14.0646i	0.526724	−	0.526724i
$714$	−4.22307	+	2.96391i	−0.158044	+	0.110921i
$715$	−19.3058	−	1.47164i	−0.721996	−	0.0550363i
$716$	−13.3533	+	6.26231i	−0.499037	+	0.234034i
$717$	−10.3831			−0.387765
$718$	15.4664	−	10.8549i	0.577202	−	0.405101i
$719$	−15.7928			−0.588971			−0.294485	−	0.955656i	$-0.595148\pi$
$719$	−15.7928			−0.588971			−0.294485	+	0.955656i	$0.595148\pi$
$720$	−0.139126	−	8.94319i	−0.00518492	−	0.333293i
$721$	−0.00409372			−0.000152458
$722$	−0.194961	+	0.136831i	−0.00725569	+	0.00509231i
$723$	22.4691			0.835634
$724$	17.4475	+	37.2038i	0.648431	+	1.38267i
$725$	1.78214	+	2.42771i	0.0661872	+	0.0901630i
$726$	−25.2877	+	17.7479i	−0.938515	+	0.658685i
$727$	2.18456	−	2.18456i	0.0810208	−	0.0810208i	−0.665435	−	0.746456i	$-0.731754\pi$
$727$	2.18456	−	2.18456i	0.0810208	−	0.0810208i	0.746456	+	0.665435i	$0.231754\pi$
$728$	5.91433	+	3.38884i	0.219199	+	0.125599i
$729$	1.00000			0.0370370
$730$	−2.55175	−	4.29704i	−0.0944445	−	0.159041i
$731$	15.0483	+	15.0483i	0.556581	+	0.556581i
$732$	−12.5449	+	5.88320i	−0.463674	+	0.217449i
$733$		−	27.2805i		−	1.00763i	−0.863812	−	0.503815i	$-0.831929\pi$
$733$		−	27.2805i		−	1.00763i	0.863812	−	0.503815i	$-0.168071\pi$
$734$	0.715901	−	4.08618i	0.0264244	−	0.150824i
$735$	−7.56010	+	6.48915i	−0.278858	+	0.239356i
$736$	9.50246	−	8.06237i	0.350265	−	0.297183i
$737$	−8.79670	+	8.79670i	−0.324031	+	0.324031i
$738$	−8.41829	+	5.90826i	−0.309881	+	0.217486i
$739$	35.5998	+	35.5998i	1.30956	+	1.30956i	0.921733	+	0.387826i	$0.126774\pi$
$739$	35.5998	+	35.5998i	1.30956	+	1.30956i	0.387826	+	0.921733i	$0.373226\pi$
$740$	12.3074	+	32.4573i	0.452429	+	1.19316i
$741$	4.67736	−	4.67736i	0.171827	−	0.171827i
$742$	−18.3798	−	3.22015i	−0.674742	−	0.118215i
$743$	−25.0052	−	25.0052i	−0.917352	−	0.917352i	0.0794841	−	0.996836i	$-0.474673\pi$
$743$	−25.0052	−	25.0052i	−0.917352	−	0.917352i	−0.996836	+	0.0794841i	$0.974673\pi$
$744$	6.69041	+	24.6456i	0.245282	+	0.903551i
$745$	1.79028	−	23.4858i	0.0655907	−	0.860455i
$746$	−25.7243	−	36.6528i	−0.941833	−	1.34195i
$747$	−5.64544			−0.206556
$748$	−8.91245	+	24.6542i	−0.325871	+	0.901447i
$749$	−16.4008	+	16.4008i	−0.599274	+	0.599274i
$750$	−14.5529	−	6.18175i	−0.531396	−	0.225725i
$751$			35.0837i			1.28022i	0.768283	+	0.640111i	$0.221112\pi$
$751$			35.0837i			1.28022i	−0.768283	+	0.640111i	$0.778888\pi$
$752$	0.589766	+	6.41792i	0.0215065	+	0.234037i
$753$	−16.2297	−	16.2297i	−0.591443	−	0.591443i
$754$	0.222095	−	1.26766i	0.00808821	−	0.0461654i
$755$	−11.5255	−	13.4276i	−0.419456	−	0.488682i
$756$	1.35455	+	2.88835i	0.0492646	+	0.105048i
$757$			18.8071i			0.683554i	0.939781	+	0.341777i	$0.111029\pi$
$757$			18.8071i			0.683554i	−0.939781	+	0.341777i	$0.888971\pi$
$758$	−10.0333	−	1.75784i	−0.364426	−	0.0638477i
$759$		−	12.6255i		−	0.458275i
$760$	−5.20220	−	27.1969i	−0.188704	−	0.986537i
$761$			0.986222i			0.0357505i	0.999840	+	0.0178753i	$0.00569017\pi$
$761$			0.986222i			0.0357505i	−0.999840	+	0.0178753i	$0.994310\pi$
$762$	−2.51686	+	14.3656i	−0.0911761	+	0.520409i
$763$			25.1102i			0.909049i
$764$	−40.4611	−	14.6266i	−1.46383	−	0.529172i
$765$	−5.09941	−	0.388718i	−0.184370	−	0.0140541i
$766$	−6.31106	−	1.10570i	−0.228028	−	0.0399506i
$767$	13.7866	+	13.7866i	0.497806	+	0.497806i
$768$	2.91597	+	15.7320i	0.105221	+	0.567681i
$769$			43.7365i			1.57718i	0.614921	+	0.788589i	$0.289188\pi$
$769$			43.7365i			1.57718i	−0.614921	+	0.788589i	$0.710812\pi$
$770$	7.13869	−	28.0133i	0.257260	−	1.00953i
$771$	−0.223380	+	0.223380i	−0.00804485	+	0.00804485i
$772$	37.7778	−	17.7167i	1.35965	−	0.637637i
$773$	33.7211			1.21286			0.606431	−	0.795136i	$-0.292601\pi$
$773$	33.7211			1.21286			0.606431	+	0.795136i	$0.292601\pi$
$774$	10.7710	−	7.55948i	0.387155	−	0.271720i
$775$	44.6228	+	6.84278i	1.60290	+	0.245800i
$776$	12.4511	−	21.7302i	0.446970	−	0.780067i
$777$	−8.75474	−	8.75474i	−0.314074	−	0.314074i
$778$	0.465725	−	2.65824i	0.0166971	−	0.0953025i
$779$	−22.5141	+	22.5141i	−0.806652	+	0.806652i
$780$	2.39563	+	6.31780i	0.0857772	+	0.226214i
$781$	−55.0887	−	55.0887i	−1.97123	−	1.97123i
$782$	−4.09341	−	5.83242i	−0.146380	−	0.208567i
$783$	0.425907	−	0.425907i	0.0152207	−	0.0152207i
$784$	11.3964	−	13.7028i	0.407014	−	0.489387i
$785$	13.5550	+	15.7921i	0.483800	+	0.563645i
$786$	−5.11851	−	0.896767i	−0.182571	−	0.0319866i
$787$			27.5235i			0.981106i	0.871411	+	0.490553i	$0.163205\pi$
$787$			27.5235i			0.981106i	−0.871411	+	0.490553i	$0.836795\pi$
$788$	−12.0658	−	4.36176i	−0.429826	−	0.155381i
$789$	−1.01264	−	1.01264i	−0.0360509	−	0.0360509i
$790$	−1.31910	+	5.17635i	−0.0469315	+	0.184166i
$791$	21.5390			0.765838
$792$	14.0648	+	8.05895i	0.499770	+	0.286362i
$793$	7.40139	−	7.40139i	0.262831	−	0.262831i
$794$	19.8784	+	28.3234i	0.705458	+	1.00516i
$795$	−12.0470	−	14.0352i	−0.427262	−	0.497776i
$796$	−16.9550	−	6.12920i	−0.600954	−	0.217244i
$797$	21.0022			0.743937			0.371969	−	0.928245i	$-0.378683\pi$
$797$	21.0022			0.743937			0.371969	+	0.928245i	$0.378683\pi$
$798$	5.67368	+	8.08404i	0.200846	+	0.286172i
$799$	3.68513			0.130371
$800$	27.5137	+	6.55735i	0.972755	+	0.231837i
$801$	10.4975			0.370910
$802$	23.1804	+	33.0282i	0.818528	+	1.16627i
$803$	9.05731			0.319626
$804$	4.08279	+	1.47592i	0.143989	+	0.0520516i
$805$	5.11769	+	5.96229i	0.180375	+	0.210143i
$806$	−11.0826	−	15.7908i	−0.390367	−	0.556207i
$807$	12.5052	−	12.5052i	0.440204	−	0.440204i
$808$	−2.71633	+	4.74064i	−0.0955602	+	0.166775i
$809$	−17.2682			−0.607117			−0.303559	−	0.952813i	$-0.598175\pi$
$809$	−17.2682			−0.607117			−0.303559	+	0.952813i	$0.598175\pi$
$810$	−0.780893	+	3.06434i	−0.0274378	+	0.107670i
$811$	12.8011	+	12.8011i	0.449507	+	0.449507i	0.895191	−	0.445683i	$-0.147039\pi$
$811$	12.8011	+	12.8011i	0.449507	+	0.449507i	−0.445683	+	0.895191i	$0.647039\pi$
$812$	1.80708	+	0.653256i	0.0634162	+	0.0229248i
$813$		−	25.2641i		−	0.886052i
$814$	−61.9666	−	10.8566i	−2.17193	−	0.380524i
$815$	−4.49770	−	5.23999i	−0.157548	−	0.183549i
$816$	9.11018	−	0.837167i	0.318920	−	0.0293067i
$817$	28.8063	−	28.8063i	1.00780	−	1.00780i
$818$	−12.2689	−	17.4811i	−0.428972	−	0.611214i
$819$	−1.70410	−	1.70410i	−0.0595462	−	0.0595462i
$820$	−11.5312	−	30.4102i	−0.402686	−	1.06197i
$821$	25.3693	−	25.3693i	0.885395	−	0.885395i	−0.108682	−	0.994077i	$-0.534663\pi$
$821$	25.3693	−	25.3693i	0.885395	−	0.885395i	0.994077	+	0.108682i	$0.0346629\pi$
$822$	4.71782	−	26.9281i	0.164553	−	0.939225i
$823$	−12.8031	−	12.8031i	−0.446288	−	0.446288i	0.447830	−	0.894119i	$-0.352197\pi$
$823$	−12.8031	−	12.8031i	−0.446288	−	0.446288i	−0.894119	+	0.447830i	$0.852197\pi$
$824$	0.00629832	+	0.00360886i	0.000219412	+	0.000125721i
$825$	23.0997	−	16.9571i	0.804228	−	0.590370i
$826$	−23.8279	+	16.7233i	−0.829077	+	0.581877i
$827$	−22.8624			−0.795005			−0.397502	−	0.917601i	$-0.630123\pi$
$827$	−22.8624			−0.795005			−0.397502	+	0.917601i	$0.630123\pi$
$828$	−3.98906	+	1.87075i	−0.138630	+	0.0650131i
$829$	−32.1620	+	32.1620i	−1.11703	+	1.11703i	−0.124857	+	0.992175i	$0.539847\pi$
$829$	−32.1620	+	32.1620i	−1.11703	+	1.11703i	−0.992175	+	0.124857i	$0.960153\pi$
$830$	4.40849	−	17.2996i	0.153021	−	0.600477i
$831$			13.1100i			0.454782i
$832$	−6.11190	−	10.4277i	−0.211892	−	0.361514i
$833$	−7.20592	−	7.20592i	−0.249670	−	0.249670i
$834$	−8.00668	−	1.40278i	−0.277249	−	0.0485742i
$835$	−14.7466	−	1.12410i	−0.510326	−	0.0389012i
$836$	47.1945	+	17.0607i	1.63226	+	0.590057i
$837$		−	9.02889i		−	0.312084i
$838$	−0.666189	+	3.80243i	−0.0230131	+	0.131353i
$839$		−	19.2953i		−	0.666147i	−0.942901	−	0.333073i	$-0.891914\pi$
$839$		−	19.2953i		−	0.666147i	0.942901	−	0.333073i	$-0.108086\pi$
$840$	−9.90867	+	1.89532i	−0.341882	+	0.0653947i
$841$			28.6372i			0.987490i
$842$	22.3267	+	3.91165i	0.769428	+	0.134804i
$843$		−	2.34999i		−	0.0809381i
$844$	−14.5630	−	31.0531i	−0.501279	−	1.06889i
$845$	15.6086	+	18.1845i	0.536951	+	0.625567i
$846$	0.393229	−	2.24445i	0.0135195	−	0.0771658i
$847$	24.6397	+	24.6397i	0.846631	+	0.846631i
$848$	25.4390	+	21.1572i	0.873580	+	0.726540i
$849$			16.1614i			0.554658i
$850$	5.17326	−	15.3228i	0.177441	−	0.525568i
$851$	12.0910	−	12.0910i	0.414475	−	0.414475i
$852$	−9.24283	+	25.5681i	−0.316654	+	0.875950i
$853$	−42.4336			−1.45290			−0.726449	−	0.687220i	$-0.758831\pi$
$853$	−42.4336			−1.45290			−0.726449	+	0.687220i	$0.758831\pi$
$854$	8.97795	+	12.7921i	0.307219	+	0.437736i
$855$	−0.744106	+	9.76158i	−0.0254479	+	0.333839i
$856$	39.6915	−	10.7749i	1.35663	−	0.368277i
$857$	7.60830	+	7.60830i	0.259894	+	0.259894i	0.825011	−	0.565117i	$-0.191169\pi$
$857$	7.60830	+	7.60830i	0.259894	+	0.259894i	−0.565117	+	0.825011i	$0.691169\pi$
$858$	−12.0618	−	2.11323i	−0.411782	−	0.0721445i
$859$	11.8598	−	11.8598i	0.404651	−	0.404651i	−0.475217	−	0.879869i	$-0.657631\pi$
$859$	11.8598	−	11.8598i	0.404651	−	0.404651i	0.879869	+	0.475217i	$0.157631\pi$
$860$	14.7539	+	38.9092i	0.503102	+	1.32679i
$861$	8.20257	+	8.20257i	0.279543	+	0.279543i
$862$	26.9783	−	18.9344i	0.918884	−	0.644907i
$863$	5.07126	−	5.07126i	0.172628	−	0.172628i	−0.615505	−	0.788133i	$-0.711048\pi$
$863$	5.07126	−	5.07126i	0.172628	−	0.172628i	0.788133	+	0.615505i	$0.211048\pi$
$864$	0.462239	−	5.63794i	0.0157257	−	0.191807i
$865$	38.5215	−	33.0647i	1.30977	−	1.12423i
$866$	−0.784924	+	4.48014i	−0.0266728	+	0.152241i
$867$			11.7690i			0.399696i
$868$	26.0786	−	12.2301i	0.885166	−	0.415117i
$869$	−6.84557	−	6.84557i	−0.232220	−	0.232220i
$870$	0.972537	+	1.63771i	0.0329721	+	0.0555237i
$871$	−3.27959			−0.111125
$872$	22.1361	−	38.6328i	0.749624	−	1.30827i
$873$	−6.26114	+	6.26114i	−0.211907	+	0.211907i
$874$	−11.1647	+	7.83583i	−0.377653	+	0.265051i
$875$	−4.03518	+	17.3713i	−0.136414	+	0.587256i
$876$	−1.34205	−	2.86169i	−0.0453437	−	0.0966877i
$877$	10.2891			0.347437			0.173719	−	0.984795i	$-0.444422\pi$
$877$	10.2891			0.347437			0.173719	+	0.984795i	$0.444422\pi$
$878$	−11.2555	+	7.89953i	−0.379855	+	0.266596i
$879$	15.9522			0.538055
$880$	−35.6785	+	36.8061i	−1.20272	+	1.24073i
$881$	−11.5441			−0.388932			−0.194466	−	0.980909i	$-0.562297\pi$
$881$	−11.5441			−0.388932			−0.194466	+	0.980909i	$0.562297\pi$
$882$	−5.15772	+	3.61988i	−0.173670	+	0.121888i
$883$	−38.5099			−1.29596			−0.647981	−	0.761657i	$-0.724386\pi$
$883$	−38.5099			−1.29596			−0.647981	+	0.761657i	$0.724386\pi$
$884$	−6.25716	+	2.93442i	−0.210451	+	0.0986954i
$885$	−28.7724	−	2.19327i	−0.967175	−	0.0737258i
$886$	19.4506	−	13.6511i	0.653455	−	0.458618i
$887$	−5.56002	+	5.56002i	−0.186687	+	0.186687i	−0.794262	−	0.607575i	$-0.792142\pi$
$887$	−5.56002	+	5.56002i	−0.186687	+	0.186687i	0.607575	+	0.794262i	$0.292142\pi$
$888$	5.75160	+	21.1872i	0.193011	+	0.710998i
$889$	16.4498			0.551709
$890$	−8.19740	+	32.1679i	−0.274778	+	1.07827i
$891$	−4.05250	−	4.05250i	−0.135764	−	0.135764i
$892$	10.9037	+	23.2503i	0.365082	+	0.778477i
$893$		−	7.05429i		−	0.236063i
$894$	2.57078	−	14.6733i	0.0859798	−	0.490750i
$895$	−1.25334	+	16.4420i	−0.0418945	+	0.549595i
$896$	16.9105	−	6.30177i	0.564939	−	0.210527i
$897$	2.35351	−	2.35351i	0.0785815	−	0.0785815i
$898$	17.0034	−	11.9336i	0.567411	−	0.398230i
$899$	−3.84547	−	3.84547i	−0.128253	−	0.128253i
$900$	−8.78041	−	4.78585i	−0.292680	−	0.159528i
$901$	13.3776	−	13.3776i	0.445674	−	0.445674i
$902$	58.0584	+	10.1719i	1.93313	+	0.338686i
$903$	−10.4950	−	10.4950i	−0.349252	−	0.349252i
$904$	−33.1383	−	18.9879i	−1.10216	−	0.631528i
$905$	45.8092	+	3.49194i	1.52275	+	0.116076i
$906$	−6.42934	−	9.16073i	−0.213601	−	0.304345i
$907$	−30.0758			−0.998649			−0.499325	−	0.866415i	$-0.666419\pi$
$907$	−30.0758			−0.998649			−0.499325	+	0.866415i	$0.666419\pi$
$908$	−1.09258	−	0.394964i	−0.0362584	−	0.0131074i
$909$	1.36593	−	1.36593i	0.0453049	−	0.0453049i
$910$	6.55268	−	3.89124i	0.217219	−	0.128993i
$911$			39.1493i			1.29707i	0.761183	+	0.648537i	$0.224619\pi$
$911$			39.1493i			1.29707i	−0.761183	+	0.648537i	$0.775381\pi$
$912$	−1.60255	−	17.4392i	−0.0530658	−	0.577470i
$913$	22.8782	+	22.8782i	0.757157	+	0.757157i
$914$	3.74845	−	21.3951i	0.123988	−	0.707689i
$915$	−1.17746	+	15.4466i	−0.0389257	+	0.510649i
$916$	−21.1951	+	9.93989i	−0.700307	+	0.328423i
$917$			5.86114i			0.193552i
$918$	−3.18598	−	0.558186i	−0.105153	−	0.0184229i
$919$		−	49.7130i		−	1.63988i	−0.572448	−	0.819941i	$-0.694006\pi$
$919$		−	49.7130i		−	1.63988i	0.572448	−	0.819941i	$-0.305994\pi$
$920$	−2.61760	−	13.6847i	−0.0862996	−	0.451172i
$921$		−	24.9902i		−	0.823455i
$922$	4.22112	−	24.0930i	0.139015	−	0.793461i
$923$		−	20.5382i		−	0.676022i
$924$	6.21573	−	17.1944i	0.204483	−	0.565654i
$925$	38.3612	+	5.88258i	1.26131	+	0.193418i
$926$	−50.1991	−	8.79493i	−1.64965	−	0.289019i
$927$	−0.00181474	−	0.00181474i	−5.96040e−5	−	5.96040e-5i
$928$	−2.20437	−	2.59811i	−0.0723618	−	0.0852870i
$929$		−	0.175895i		−	0.00577094i	−0.999996	−	0.00288547i	$-0.999082\pi$
$929$		−	0.175895i		−	0.00577094i	0.999996	−	0.00288547i	$-0.000918475\pi$
$930$	27.6676	+	7.05060i	0.907257	+	0.231198i
$931$	−13.7940	+	13.7940i	−0.452079	+	0.452079i
$932$	13.0677	+	27.8647i	0.428047	+	0.912738i
$933$	5.55703			0.181929
$934$	39.7412	−	27.8918i	1.30037	−	0.912649i
$935$	19.0901	+	22.2406i	0.624313	+	0.727347i
$936$	1.11954	+	4.12408i	0.0365934	+	0.134800i
$937$	−30.8310	−	30.8310i	−1.00720	−	1.00720i	−0.999974	−	0.00722969i	$-0.997699\pi$
$937$	−30.8310	−	30.8310i	−1.00720	−	1.00720i	−0.00722969	−	0.999974i	$-0.502301\pi$
$938$	0.845028	−	4.82320i	0.0275911	−	0.157483i
$939$	3.12705	−	3.12705i	0.102048	−	0.102048i
$940$	6.57070	+	2.95767i	0.214313	+	0.0964685i
$941$	−38.5292	−	38.5292i	−1.25602	−	1.25602i	−0.952979	−	0.303037i	$-0.902000\pi$
$941$	−38.5292	−	38.5292i	−1.25602	−	1.25602i	−0.303037	−	0.952979i	$-0.598000\pi$
$942$	7.56148	+	10.7738i	0.246366	+	0.351031i
$943$	−11.3285	+	11.3285i	−0.368905	+	0.368905i
$944$	51.4025	−	4.72356i	1.67301	−	0.153739i
$945$	3.55644	+	0.271100i	0.115691	+	0.00881889i
$946$	−74.2843	−	13.0147i	−2.41519	−	0.423143i
$947$			57.6451i			1.87321i	0.350382	+	0.936607i	$0.386052\pi$
$947$			57.6451i			1.87321i	−0.350382	+	0.936607i	$0.613948\pi$
$948$	−1.14856	+	3.17721i	−0.0373033	+	0.103191i
$949$	1.68837	+	1.68837i	0.0548070	+	0.0548070i
$950$	−29.3318	−	9.90295i	−0.951648	−	0.321294i
$951$	33.8169			1.09659
$952$	−2.70334	−	9.95832i	−0.0876156	−	0.322751i
$953$	−31.1076	+	31.1076i	−1.00767	+	1.00767i	−0.00770207	+	0.999970i	$0.502452\pi$
$953$	−31.1076	+	31.1076i	−1.00767	+	1.00767i	−0.999970	+	0.00770207i	$0.997548\pi$
$954$	−6.72024	−	9.57521i	−0.217576	−	0.310009i
$955$	−36.5001	+	31.3296i	−1.18111	+	1.01380i
$956$	7.05982	−	19.5293i	0.228331	−	0.631624i
$957$	−3.45198			−0.111587
$958$	7.03169	+	10.0190i	0.227184	+	0.323699i
$959$	−30.8350			−0.995714
$960$	16.9156	+	5.81909i	0.545949	+	0.187810i
$961$	−50.5209			−1.62971
$962$	−9.52742	−	13.5750i	−0.307176	−	0.437675i
$963$	−14.5410			−0.468576
$964$	−15.2775	+	42.2615i	−0.492054	+	1.36115i
$965$	3.54582	−	46.5160i	0.114144	−	1.49740i
$966$	2.85483	+	4.06766i	0.0918527	+	0.130875i
$967$	37.9194	−	37.9194i	1.21941	−	1.21941i	0.251567	−	0.967840i	$-0.419054\pi$
$967$	37.9194	−	37.9194i	1.21941	−	1.21941i	0.967840	−	0.251567i	$-0.0809460\pi$
$968$	−16.1876	−	59.6304i	−0.520288	−	1.91659i
$969$	−10.0135			−0.321680
$970$	−14.2970	−	24.0756i	−0.459049	−	0.773020i
$971$	26.9668	+	26.9668i	0.865404	+	0.865404i	0.991960	−	0.126555i	$-0.0403921\pi$
$971$	26.9668	+	26.9668i	0.865404	+	0.865404i	−0.126555	+	0.991960i	$0.540392\pi$
$972$	−0.679932	+	1.88088i	−0.0218088	+	0.0603291i
$973$			9.16835i			0.293924i
$974$	−15.5204	−	2.71918i	−0.497305	−	0.0871282i
$975$	7.46699	+	1.14504i	0.239135	+	0.0366706i
$976$	−2.53586	−	27.5956i	−0.0811709	−	0.883314i
$977$	−13.1778	+	13.1778i	−0.421596	+	0.421596i	−0.885753	−	0.464157i	$-0.846357\pi$
$977$	−13.1778	+	13.1778i	−0.421596	+	0.421596i	0.464157	+	0.885753i	$0.346357\pi$
$978$	−2.50898	−	3.57488i	−0.0802283	−	0.114312i
$979$	−42.5410	−	42.5410i	−1.35962	−	1.35962i
$980$	−7.06493	−	18.6318i	−0.225681	−	0.595170i
$981$	−11.1313	+	11.1313i	−0.355395	+	0.355395i
$982$	2.02838	−	11.5775i	0.0647282	−	0.369452i
$983$	−33.1704	−	33.1704i	−1.05797	−	1.05797i	−0.998213	−	0.0597600i	$-0.980966\pi$
$983$	−33.1704	−	33.1704i	−1.05797	−	1.05797i	−0.0597600	−	0.998213i	$-0.519034\pi$
$984$	−5.38884	−	19.8510i	−0.171790	−	0.632826i
$985$	−10.8846	+	9.34270i	−0.346812	+	0.297683i
$986$	−1.59467	+	1.11919i	−0.0507845	+	0.0356424i
$987$	−2.57009			−0.0818069
$988$	5.61724	+	11.9778i	0.178708	+	0.381065i
$989$	14.4945	−	14.4945i	0.460898	−	0.460898i
$990$	15.5828	−	9.25369i	0.495255	−	0.294102i
$991$			10.3297i			0.328135i	0.986449	+	0.164067i	$0.0524615\pi$
$991$			10.3297i			0.328135i	−0.986449	+	0.164067i	$0.947539\pi$
$992$	−50.9043	−	4.17350i	−1.61621	−	0.132509i
$993$	13.0748	+	13.0748i	0.414917	+	0.414917i
$994$	30.2049	+	5.29192i	0.958041	+	0.167850i
$995$	−15.2952	+	13.1285i	−0.484889	+	0.416201i
$996$	3.83852	−	10.6184i	0.121628	−	0.336456i
$997$		−	37.9110i		−	1.20065i	−0.799755	−	0.600327i	$-0.795037\pi$
$997$		−	37.9110i		−	1.20065i	0.799755	−	0.600327i	$-0.204963\pi$
$998$	−1.56085	+	8.90894i	−0.0494079	+	0.282008i
$999$		−	7.76193i		−	0.245577i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	240.2.y.e.163.6	✓	16
3.2	odd	2		720.2.z.f.163.3		16
4.3	odd	2		960.2.y.e.943.6		16
5.2	odd	4		240.2.bc.e.67.2	yes	16
8.3	odd	2		1920.2.y.j.223.3		16
8.5	even	2		1920.2.y.i.223.3		16
15.2	even	4		720.2.bd.f.307.7		16
16.3	odd	4		1920.2.bc.i.1183.7		16
16.5	even	4		960.2.bc.e.463.2		16
16.11	odd	4		240.2.bc.e.43.2	yes	16
16.13	even	4		1920.2.bc.j.1183.7		16
20.7	even	4		960.2.bc.e.367.2		16
40.27	even	4		1920.2.bc.j.607.7		16
40.37	odd	4		1920.2.bc.i.607.7		16
48.11	even	4		720.2.bd.f.523.7		16
80.27	even	4	inner	240.2.y.e.187.6	yes	16
80.37	odd	4		960.2.y.e.847.6		16
80.67	even	4		1920.2.y.i.1567.3		16
80.77	odd	4		1920.2.y.j.1567.3		16
240.107	odd	4		720.2.z.f.667.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.y.e.163.6	✓	16	1.1	even	1	trivial
240.2.y.e.187.6	yes	16	80.27	even	4	inner
240.2.bc.e.43.2	yes	16	16.11	odd	4
240.2.bc.e.67.2	yes	16	5.2	odd	4
720.2.z.f.163.3		16	3.2	odd	2
720.2.z.f.667.3		16	240.107	odd	4
720.2.bd.f.307.7		16	15.2	even	4
720.2.bd.f.523.7		16	48.11	even	4
960.2.y.e.847.6		16	80.37	odd	4
960.2.y.e.943.6		16	4.3	odd	2
960.2.bc.e.367.2		16	20.7	even	4
960.2.bc.e.463.2		16	16.5	even	4
1920.2.y.i.223.3		16	8.5	even	2
1920.2.y.i.1567.3		16	80.67	even	4
1920.2.y.j.223.3		16	8.3	odd	2
1920.2.y.j.1567.3		16	80.77	odd	4
1920.2.bc.i.607.7		16	40.37	odd	4
1920.2.bc.i.1183.7		16	16.3	odd	4
1920.2.bc.j.607.7		16	40.27	even	4
1920.2.bc.j.1183.7		16	16.13	even	4

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:	\( N \)	\(=\)	\( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	240.y (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.812425 + 1.15757i) q^{2} +1.00000 q^{3} +(-0.679932 + 1.88088i) q^{4} +(1.45639 + 1.69674i) q^{5} +(0.812425 + 1.15757i) q^{6} +(1.12791 - 1.12791i) q^{7} +(-2.72964 + 0.741001i) q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(0.812425 + 1.15757i) q^{2} +1.00000 q^{3} +(-0.679932 + 1.88088i) q^{4} +(1.45639 + 1.69674i) q^{5} +(0.812425 + 1.15757i) q^{6} +(1.12791 - 1.12791i) q^{7} +(-2.72964 + 0.741001i) q^{8} +1.00000 q^{9} +(-0.780893 + 3.06434i) q^{10} +(-4.05250 - 4.05250i) q^{11} +(-0.679932 + 1.88088i) q^{12} -1.51085i q^{13} +(2.22197 + 0.389291i) q^{14} +(1.45639 + 1.69674i) q^{15} +(-3.07538 - 2.55774i) q^{16} +(-1.61725 + 1.61725i) q^{17} +(0.812425 + 1.15757i) q^{18} +(3.09584 + 3.09584i) q^{19} +(-4.18161 + 1.58561i) q^{20} +(1.12791 - 1.12791i) q^{21} +(1.39870 - 7.98340i) q^{22} +(1.55774 + 1.55774i) q^{23} +(-2.72964 + 0.741001i) q^{24} +(-0.757876 + 4.94223i) q^{25} +(1.74892 - 1.22746i) q^{26} +1.00000 q^{27} +(1.35455 + 2.88835i) q^{28} +(0.425907 - 0.425907i) q^{29} +(-0.780893 + 3.06434i) q^{30} -9.02889i q^{31} +(0.462239 - 5.63794i) q^{32} +(-4.05250 - 4.05250i) q^{33} +(-3.18598 - 0.558186i) q^{34} +(3.55644 + 0.271100i) q^{35} +(-0.679932 + 1.88088i) q^{36} -7.76193i q^{37} +(-1.06851 + 6.09878i) q^{38} -1.51085i q^{39} +(-5.23269 - 3.55231i) q^{40} +7.27238i q^{41} +(2.22197 + 0.389291i) q^{42} -9.30484i q^{43} +(10.3777 - 4.86682i) q^{44} +(1.45639 + 1.69674i) q^{45} +(-0.537644 + 3.06873i) q^{46} +(-1.13932 - 1.13932i) q^{47} +(-3.07538 - 2.55774i) q^{48} +4.45565i q^{49} +(-6.33669 + 3.13789i) q^{50} +(-1.61725 + 1.61725i) q^{51} +(2.84173 + 1.02728i) q^{52} -8.27183 q^{53} +(0.812425 + 1.15757i) q^{54} +(0.974046 - 12.7781i) q^{55} +(-2.24300 + 3.91456i) q^{56} +(3.09584 + 3.09584i) q^{57} +(0.839034 + 0.146999i) q^{58} +(-9.12504 + 9.12504i) q^{59} +(-4.18161 + 1.58561i) q^{60} +(4.89881 + 4.89881i) q^{61} +(10.4516 - 7.33529i) q^{62} +(1.12791 - 1.12791i) q^{63} +(6.90184 - 4.04533i) q^{64} +(2.56353 - 2.20039i) q^{65} +(1.39870 - 7.98340i) q^{66} -2.17068i q^{67} +(-1.94223 - 4.14147i) q^{68} +(1.55774 + 1.55774i) q^{69} +(2.57552 + 4.33707i) q^{70} +13.5937 q^{71} +(-2.72964 + 0.741001i) q^{72} +(-1.11750 + 1.11750i) q^{73} +(8.98497 - 6.30598i) q^{74} +(-0.757876 + 4.94223i) q^{75} +(-7.92785 + 3.71792i) q^{76} -9.14169 q^{77} +(1.74892 - 1.22746i) q^{78} +1.68922 q^{79} +(-0.139126 - 8.94319i) q^{80} +1.00000 q^{81} +(-8.41829 + 5.90826i) q^{82} -5.64544 q^{83} +(1.35455 + 2.88835i) q^{84} +(-5.09941 - 0.388718i) q^{85} +(10.7710 - 7.55948i) q^{86} +(0.425907 - 0.425907i) q^{87} +(14.0648 + 8.05895i) q^{88} +10.4975 q^{89} +(-0.780893 + 3.06434i) q^{90} +(-1.70410 - 1.70410i) q^{91} +(-3.98906 + 1.87075i) q^{92} -9.02889i q^{93} +(0.393229 - 2.24445i) q^{94} +(-0.744106 + 9.76158i) q^{95} +(0.462239 - 5.63794i) q^{96} +(-6.26114 + 6.26114i) q^{97} +(-5.15772 + 3.61988i) q^{98} +(-4.05250 - 4.05250i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{2} + 16 q^{3} - 8 q^{4} - 4 q^{5} + 2 q^{6} - 4 q^{7} - 4 q^{8} + 16 q^{9}+O(q^{10}) \) 16 * q + 2 * q^2 + 16 * q^3 - 8 * q^4 - 4 * q^5 + 2 * q^6 - 4 * q^7 - 4 * q^8 + 16 * q^9	\( 16 q + 2 q^{2} + 16 q^{3} - 8 q^{4} - 4 q^{5} + 2 q^{6} - 4 q^{7} - 4 q^{8} + 16 q^{9} - 14 q^{10} - 8 q^{12} - 4 q^{14} - 4 q^{15} - 8 q^{16} - 8 q^{17} + 2 q^{18} + 8 q^{19} - 12 q^{20} - 4 q^{21} - 8 q^{22} - 4 q^{24} + 32 q^{25} + 20 q^{26} + 16 q^{27} + 12 q^{28} + 12 q^{29} - 14 q^{30} - 28 q^{32} - 20 q^{35} - 8 q^{36} - 16 q^{38} - 44 q^{40} - 4 q^{42} + 52 q^{44} - 4 q^{45} - 16 q^{46} - 32 q^{47} - 8 q^{48} + 22 q^{50} - 8 q^{51} + 8 q^{52} + 16 q^{53} + 2 q^{54} - 4 q^{55} + 20 q^{56} + 8 q^{57} - 44 q^{58} - 24 q^{59} - 12 q^{60} + 40 q^{61} + 40 q^{62} - 4 q^{63} - 8 q^{64} - 4 q^{65} - 8 q^{66} + 24 q^{68} + 56 q^{70} - 4 q^{72} + 8 q^{73} + 64 q^{74} + 32 q^{75} + 16 q^{76} - 72 q^{77} + 20 q^{78} - 48 q^{79} + 16 q^{80} + 16 q^{81} + 8 q^{82} - 8 q^{83} + 12 q^{84} - 8 q^{85} - 8 q^{86} + 12 q^{87} - 16 q^{88} - 14 q^{90} - 40 q^{91} - 20 q^{94} + 8 q^{95} - 28 q^{96} + 48 q^{97} + 30 q^{98}+O(q^{100}) \) 16 * q + 2 * q^2 + 16 * q^3 - 8 * q^4 - 4 * q^5 + 2 * q^6 - 4 * q^7 - 4 * q^8 + 16 * q^9 - 14 * q^10 - 8 * q^12 - 4 * q^14 - 4 * q^15 - 8 * q^16 - 8 * q^17 + 2 * q^18 + 8 * q^19 - 12 * q^20 - 4 * q^21 - 8 * q^22 - 4 * q^24 + 32 * q^25 + 20 * q^26 + 16 * q^27 + 12 * q^28 + 12 * q^29 - 14 * q^30 - 28 * q^32 - 20 * q^35 - 8 * q^36 - 16 * q^38 - 44 * q^40 - 4 * q^42 + 52 * q^44 - 4 * q^45 - 16 * q^46 - 32 * q^47 - 8 * q^48 + 22 * q^50 - 8 * q^51 + 8 * q^52 + 16 * q^53 + 2 * q^54 - 4 * q^55 + 20 * q^56 + 8 * q^57 - 44 * q^58 - 24 * q^59 - 12 * q^60 + 40 * q^61 + 40 * q^62 - 4 * q^63 - 8 * q^64 - 4 * q^65 - 8 * q^66 + 24 * q^68 + 56 * q^70 - 4 * q^72 + 8 * q^73 + 64 * q^74 + 32 * q^75 + 16 * q^76 - 72 * q^77 + 20 * q^78 - 48 * q^79 + 16 * q^80 + 16 * q^81 + 8 * q^82 - 8 * q^83 + 12 * q^84 - 8 * q^85 - 8 * q^86 + 12 * q^87 - 16 * q^88 - 14 * q^90 - 40 * q^91 - 20 * q^94 + 8 * q^95 - 28 * q^96 + 48 * q^97 + 30 * q^98

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