LMFDB - Embedded newform 240.2.s.c.61.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [240,2,Mod(61,240)]

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([0, 3, 0, 0]))

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

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

chi := DirichletCharacter("240.61");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 240 = 2^{4} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	240.s (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:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{18} - 4 x^{17} + 7 x^{16} + 16 x^{15} + 6 x^{14} - 36 x^{13} - 42 x^{12} + 40 x^{11} + \cdots + 1024 $ x^20 - 2x^18 - 4x^17 + 7x^16 + 16x^15 + 6x^14 - 36x^13 - 42x^12 + 40x^11 + 136x^10 + 80x^9 - 168x^8 - 288x^7 + 96x^6 + 512x^5 + 448x^4 - 512x^3 - 512*x^2 + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			61.10
Root			$1.32147 - 0.503713i$ of defining polynomial
Character	$\chi$	$=$	240.61
Dual form			240.2.s.c.181.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.32147 - 0.503713i) q^{2} +(-0.707107 - 0.707107i) q^{3} +(1.49255 - 1.33128i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(-1.29060 - 0.578239i) q^{6} -2.69529i q^{7} +(1.30176 - 2.51106i) q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+(1.32147 - 0.503713i) q^{2} +(-0.707107 - 0.707107i) q^{3} +(1.49255 - 1.33128i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(-1.29060 - 0.578239i) q^{6} -2.69529i q^{7} +(1.30176 - 2.51106i) q^{8} +1.00000i q^{9} +(-0.578239 + 1.29060i) q^{10} +(2.72735 - 2.72735i) q^{11} +(-1.99675 - 0.114032i) q^{12} +(1.82449 + 1.82449i) q^{13} +(-1.35765 - 3.56173i) q^{14} +1.00000 q^{15} +(0.455385 - 3.97399i) q^{16} -7.33517 q^{17} +(0.503713 + 1.32147i) q^{18} +(3.62540 + 3.62540i) q^{19} +(-0.114032 + 1.99675i) q^{20} +(-1.90586 + 1.90586i) q^{21} +(2.23030 - 4.97791i) q^{22} +8.95345i q^{23} +(-2.69607 + 0.855099i) q^{24} -1.00000i q^{25} +(3.33002 + 1.49198i) q^{26} +(0.707107 - 0.707107i) q^{27} +(-3.58819 - 4.02284i) q^{28} +(2.84302 + 2.84302i) q^{29} +(1.32147 - 0.503713i) q^{30} -3.37977 q^{31} +(-1.39998 - 5.48088i) q^{32} -3.85706 q^{33} +(-9.69317 + 3.69482i) q^{34} +(1.90586 + 1.90586i) q^{35} +(1.33128 + 1.49255i) q^{36} +(-0.190364 + 0.190364i) q^{37} +(6.61700 + 2.96468i) q^{38} -2.58022i q^{39} +(0.855099 + 2.69607i) q^{40} +7.67786i q^{41} +(-1.55852 + 3.47853i) q^{42} +(7.98115 - 7.98115i) q^{43} +(0.439827 - 7.70158i) q^{44} +(-0.707107 - 0.707107i) q^{45} +(4.50997 + 11.8317i) q^{46} -1.31537 q^{47} +(-3.13204 + 2.48803i) q^{48} -0.264584 q^{49} +(-0.503713 - 1.32147i) q^{50} +(5.18675 + 5.18675i) q^{51} +(5.15204 + 0.294227i) q^{52} +(-6.71014 + 6.71014i) q^{53} +(0.578239 - 1.29060i) q^{54} +3.85706i q^{55} +(-6.76803 - 3.50863i) q^{56} -5.12708i q^{57} +(5.18902 + 2.32488i) q^{58} +(1.01464 - 1.01464i) q^{59} +(1.49255 - 1.33128i) q^{60} +(2.38996 + 2.38996i) q^{61} +(-4.46625 + 1.70243i) q^{62} +2.69529 q^{63} +(-4.61082 - 6.53761i) q^{64} -2.58022 q^{65} +(-5.09698 + 1.94285i) q^{66} +(-7.22173 - 7.22173i) q^{67} +(-10.9481 + 9.76516i) q^{68} +(6.33104 - 6.33104i) q^{69} +(3.47853 + 1.55852i) q^{70} +2.28859i q^{71} +(2.51106 + 1.30176i) q^{72} +1.31098i q^{73} +(-0.155670 + 0.347448i) q^{74} +(-0.707107 + 0.707107i) q^{75} +(10.2375 + 0.584650i) q^{76} +(-7.35101 - 7.35101i) q^{77} +(-1.29969 - 3.40967i) q^{78} -2.59319 q^{79} +(2.48803 + 3.13204i) q^{80} -1.00000 q^{81} +(3.86744 + 10.1460i) q^{82} +(-5.36584 - 5.36584i) q^{83} +(-0.307348 + 5.38181i) q^{84} +(5.18675 - 5.18675i) q^{85} +(6.52661 - 14.5670i) q^{86} -4.02063i q^{87} +(-3.29817 - 10.3989i) q^{88} -14.8944i q^{89} +(-1.29060 - 0.578239i) q^{90} +(4.91753 - 4.91753i) q^{91} +(11.9195 + 13.3634i) q^{92} +(2.38986 + 2.38986i) q^{93} +(-1.73822 + 0.662570i) q^{94} -5.12708 q^{95} +(-2.88563 + 4.86550i) q^{96} +0.694695 q^{97} +(-0.349639 + 0.133275i) q^{98} +(2.72735 + 2.72735i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 4 q^{4} + 12 q^{8}+O(q^{10}) $ 20 * q + 4 * q^4 + 12 * q^8	$ 20 q + 4 q^{4} + 12 q^{8} + 8 q^{11} - 4 q^{14} + 20 q^{15} - 20 q^{16} - 24 q^{17} - 4 q^{18} - 4 q^{19} - 8 q^{20} + 8 q^{22} + 28 q^{26} - 8 q^{28} + 16 q^{29} - 40 q^{32} + 16 q^{33} - 44 q^{34} + 16 q^{37} - 8 q^{38} + 12 q^{40} + 12 q^{42} - 8 q^{43} + 24 q^{44} - 12 q^{46} - 16 q^{48} - 52 q^{49} + 4 q^{50} + 4 q^{51} - 56 q^{52} - 16 q^{53} + 64 q^{56} + 72 q^{58} - 16 q^{59} + 4 q^{60} - 4 q^{61} - 44 q^{62} - 8 q^{63} - 56 q^{64} - 32 q^{66} - 8 q^{67} - 32 q^{68} - 4 q^{69} + 20 q^{70} + 4 q^{72} + 60 q^{74} + 28 q^{76} - 40 q^{77} - 28 q^{78} + 56 q^{79} - 16 q^{80} - 20 q^{81} - 24 q^{82} - 48 q^{83} + 24 q^{84} + 4 q^{85} + 64 q^{86} + 40 q^{88} - 8 q^{91} + 88 q^{92} + 16 q^{93} - 20 q^{94} + 56 q^{97} - 48 q^{98} + 8 q^{99}+O(q^{100}) $ 20 * q + 4 * q^4 + 12 * q^8 + 8 * q^11 - 4 * q^14 + 20 * q^15 - 20 * q^16 - 24 * q^17 - 4 * q^18 - 4 * q^19 - 8 * q^20 + 8 * q^22 + 28 * q^26 - 8 * q^28 + 16 * q^29 - 40 * q^32 + 16 * q^33 - 44 * q^34 + 16 * q^37 - 8 * q^38 + 12 * q^40 + 12 * q^42 - 8 * q^43 + 24 * q^44 - 12 * q^46 - 16 * q^48 - 52 * q^49 + 4 * q^50 + 4 * q^51 - 56 * q^52 - 16 * q^53 + 64 * q^56 + 72 * q^58 - 16 * q^59 + 4 * q^60 - 4 * q^61 - 44 * q^62 - 8 * q^63 - 56 * q^64 - 32 * q^66 - 8 * q^67 - 32 * q^68 - 4 * q^69 + 20 * q^70 + 4 * q^72 + 60 * q^74 + 28 * q^76 - 40 * q^77 - 28 * q^78 + 56 * q^79 - 16 * q^80 - 20 * q^81 - 24 * q^82 - 48 * q^83 + 24 * q^84 + 4 * q^85 + 64 * q^86 + 40 * q^88 - 8 * q^91 + 88 * q^92 + 16 * q^93 - 20 * q^94 + 56 * q^97 - 48 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	1.32147	−	0.503713i	0.934418	−	0.356179i
$2$	1.32147	−	0.503713i	0.934418	−	0.356179i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$4$	1.49255	−	1.33128i	0.746273	−	0.665640i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$6$	−1.29060	−	0.578239i	−0.526884	−	0.236065i
$7$		−	2.69529i		−	1.01872i	−0.860552	−	0.509362i	$-0.829882\pi$
$7$		−	2.69529i		−	1.01872i	0.860552	−	0.509362i	$-0.170118\pi$
$8$	1.30176	−	2.51106i	0.460243	−	0.887793i
$9$			1.00000i			0.333333i
$10$	−0.578239	+	1.29060i	−0.182855	+	0.408123i
$11$	2.72735	−	2.72735i	0.822328	−	0.822328i	−0.164113	−	0.986442i	$-0.552476\pi$
$11$	2.72735	−	2.72735i	0.822328	−	0.822328i	0.986442	+	0.164113i	$0.0524762\pi$
$12$	−1.99675	−	0.114032i	−0.576411	−	0.0329181i
$13$	1.82449	+	1.82449i	0.506023	+	0.506023i	0.913303	−	0.407281i	$-0.133523\pi$
$13$	1.82449	+	1.82449i	0.506023	+	0.506023i	−0.407281	+	0.913303i	$0.633523\pi$
$14$	−1.35765	−	3.56173i	−0.362848	−	0.951913i
$15$	1.00000			0.258199
$16$	0.455385	−	3.97399i	0.113846	−	0.993498i
$17$	−7.33517			−1.77904			−0.889520	−	0.456897i	$-0.848961\pi$
$17$	−7.33517			−1.77904			−0.889520	+	0.456897i	$0.848961\pi$
$18$	0.503713	+	1.32147i	0.118726	+	0.311473i
$19$	3.62540	+	3.62540i	0.831723	+	0.831723i	0.987752	−	0.156029i	$-0.0498695\pi$
$19$	3.62540	+	3.62540i	0.831723	+	0.831723i	−0.156029	+	0.987752i	$0.549869\pi$
$20$	−0.114032	+	1.99675i	−0.0254983	+	0.446486i
$21$	−1.90586	+	1.90586i	−0.415892	+	0.415892i
$22$	2.23030	−	4.97791i	0.475502	−	1.06129i
$23$			8.95345i			1.86692i	0.358678	+	0.933461i	$0.383228\pi$
$23$			8.95345i			1.86692i	−0.358678	+	0.933461i	$0.616772\pi$
$24$	−2.69607	+	0.855099i	−0.550333	+	0.174546i
$25$		−	1.00000i		−	0.200000i
$26$	3.33002	+	1.49198i	0.653071	+	0.292602i
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	−3.58819	−	4.02284i	−0.678103	−	0.760246i
$29$	2.84302	+	2.84302i	0.527935	+	0.527935i	0.919956	−	0.392021i	$-0.128224\pi$
$29$	2.84302	+	2.84302i	0.527935	+	0.527935i	−0.392021	+	0.919956i	$0.628224\pi$
$30$	1.32147	−	0.503713i	0.241266	−	0.0919651i
$31$	−3.37977			−0.607024			−0.303512	−	0.952828i	$-0.598159\pi$
$31$	−3.37977			−0.607024			−0.303512	+	0.952828i	$0.598159\pi$
$32$	−1.39998	−	5.48088i	−0.247484	−	0.968892i
$33$	−3.85706			−0.671428
$34$	−9.69317	+	3.69482i	−1.66237	+	0.633657i
$35$	1.90586	+	1.90586i	0.322149	+	0.322149i
$36$	1.33128	+	1.49255i	0.221880	+	0.248758i
$37$	−0.190364	+	0.190364i	−0.0312956	+	0.0312956i	−0.722581	−	0.691286i	$-0.757045\pi$
$37$	−0.190364	+	0.190364i	−0.0312956	+	0.0312956i	0.691286	+	0.722581i	$0.257045\pi$
$38$	6.61700	+	2.96468i	1.07342	+	0.480934i
$39$		−	2.58022i		−	0.413166i
$40$	0.855099	+	2.69607i	0.135203	+	0.426286i
$41$			7.67786i			1.19908i	0.800345	+	0.599540i	$0.204650\pi$
$41$			7.67786i			1.19908i	−0.800345	+	0.599540i	$0.795350\pi$
$42$	−1.55852	+	3.47853i	−0.240485	+	0.536749i
$43$	7.98115	−	7.98115i	1.21711	−	1.21711i	0.248477	−	0.968638i	$-0.420070\pi$
$43$	7.98115	−	7.98115i	1.21711	−	1.21711i	0.968638	−	0.248477i	$-0.0799299\pi$
$44$	0.439827	−	7.70158i	0.0663065	−	1.16106i
$45$	−0.707107	−	0.707107i	−0.105409	−	0.105409i
$46$	4.50997	+	11.8317i	0.664959	+	1.74449i
$47$	−1.31537			−0.191866			−0.0959332	−	0.995388i	$-0.530584\pi$
$47$	−1.31537			−0.191866			−0.0959332	+	0.995388i	$0.530584\pi$
$48$	−3.13204	+	2.48803i	−0.452072	+	0.359117i
$49$	−0.264584			−0.0377977
$50$	−0.503713	−	1.32147i	−0.0712358	−	0.186884i
$51$	5.18675	+	5.18675i	0.726290	+	0.726290i
$52$	5.15204	+	0.294227i	0.714460	+	0.0408019i
$53$	−6.71014	+	6.71014i	−0.921709	+	0.921709i	−0.997150	−	0.0754412i	$-0.975963\pi$
$53$	−6.71014	+	6.71014i	−0.921709	+	0.921709i	0.0754412	+	0.997150i	$0.475963\pi$
$54$	0.578239	−	1.29060i	0.0786883	−	0.175628i
$55$			3.85706i			0.520086i
$56$	−6.76803	−	3.50863i	−0.904415	−	0.468861i
$57$		−	5.12708i		−	0.679099i
$58$	5.18902	+	2.32488i	0.681351	+	0.305272i
$59$	1.01464	−	1.01464i	0.132094	−	0.132094i	−0.637968	−	0.770063i	$-0.720225\pi$
$59$	1.01464	−	1.01464i	0.132094	−	0.132094i	0.770063	+	0.637968i	$0.220225\pi$
$60$	1.49255	−	1.33128i	0.192687	−	0.171868i
$61$	2.38996	+	2.38996i	0.306004	+	0.306004i	0.843357	−	0.537354i	$-0.180576\pi$
$61$	2.38996	+	2.38996i	0.306004	+	0.306004i	−0.537354	+	0.843357i	$0.680576\pi$
$62$	−4.46625	+	1.70243i	−0.567214	+	0.216209i
$63$	2.69529			0.339575
$64$	−4.61082	−	6.53761i	−0.576352	−	0.817201i
$65$	−2.58022			−0.320037
$66$	−5.09698	+	1.94285i	−0.627394	+	0.239149i
$67$	−7.22173	−	7.22173i	−0.882275	−	0.882275i	0.111490	−	0.993766i	$-0.464438\pi$
$67$	−7.22173	−	7.22173i	−0.882275	−	0.882275i	−0.993766	+	0.111490i	$0.964438\pi$
$68$	−10.9481	+	9.76516i	−1.32765	+	1.18420i
$69$	6.33104	−	6.33104i	0.762168	−	0.762168i
$70$	3.47853	+	1.55852i	0.415764	+	0.186279i
$71$			2.28859i			0.271606i	0.990736	+	0.135803i	$0.0433614\pi$
$71$			2.28859i			0.271606i	−0.990736	+	0.135803i	$0.956639\pi$
$72$	2.51106	+	1.30176i	0.295931	+	0.153414i
$73$			1.31098i			0.153439i	0.997053	+	0.0767196i	$0.0244446\pi$
$73$			1.31098i			0.153439i	−0.997053	+	0.0767196i	$0.975555\pi$
$74$	−0.155670	+	0.347448i	−0.0180963	+	0.0403900i
$75$	−0.707107	+	0.707107i	−0.0816497	+	0.0816497i
$76$	10.2375	+	0.584650i	1.17432	+	0.0670640i
$77$	−7.35101	−	7.35101i	−0.837725	−	0.837725i
$78$	−1.29969	−	3.40967i	−0.147161	−	0.386069i
$79$	−2.59319			−0.291757			−0.145879	−	0.989303i	$-0.546601\pi$
$79$	−2.59319			−0.291757			−0.145879	+	0.989303i	$0.546601\pi$
$80$	2.48803	+	3.13204i	0.278170	+	0.350173i
$81$	−1.00000			−0.111111
$82$	3.86744	+	10.1460i	0.427087	+	1.12044i
$83$	−5.36584	−	5.36584i	−0.588977	−	0.588977i	0.348377	−	0.937354i	$-0.386733\pi$
$83$	−5.36584	−	5.36584i	−0.588977	−	0.588977i	−0.937354	+	0.348377i	$0.886733\pi$
$84$	−0.307348	+	5.38181i	−0.0335345	+	0.587204i
$85$	5.18675	−	5.18675i	0.562582	−	0.562582i
$86$	6.52661	−	14.5670i	0.703783	−	1.57080i
$87$		−	4.02063i		−	0.431057i
$88$	−3.29817	−	10.3989i	−0.351586	−	1.10853i
$89$		−	14.8944i		−	1.57880i	−0.613877	−	0.789402i	$-0.710391\pi$
$89$		−	14.8944i		−	1.57880i	0.613877	−	0.789402i	$-0.289609\pi$
$90$	−1.29060	−	0.578239i	−0.136041	−	0.0609517i
$91$	4.91753	−	4.91753i	0.515497	−	0.515497i
$92$	11.9195	+	13.3634i	1.24270	+	1.39323i
$93$	2.38986	+	2.38986i	0.247816	+	0.247816i
$94$	−1.73822	+	0.662570i	−0.179283	+	0.0683388i
$95$	−5.12708			−0.526028
$96$	−2.88563	+	4.86550i	−0.294514	+	0.496583i
$97$	0.694695			0.0705356			0.0352678	−	0.999378i	$-0.488772\pi$
$97$	0.694695			0.0705356			0.0352678	+	0.999378i	$0.488772\pi$
$98$	−0.349639	+	0.133275i	−0.0353189	+	0.0134628i
$99$	2.72735	+	2.72735i	0.274109	+	0.274109i
$100$	−1.33128	−	1.49255i	−0.133128	−	0.149255i
$101$	−6.88955	+	6.88955i	−0.685536	+	0.685536i	−0.961242	−	0.275706i	$-0.911088\pi$
$101$	−6.88955	+	6.88955i	−0.685536	+	0.685536i	0.275706	+	0.961242i	$0.411088\pi$
$102$	9.46674	+	4.24148i	0.937347	+	0.419969i
$103$		−	4.39299i		−	0.432854i	−0.976299	−	0.216427i	$-0.930560\pi$
$103$		−	4.39299i		−	0.432854i	0.976299	−	0.216427i	$-0.0694403\pi$
$104$	6.95646	−	2.20634i	0.682137	−	0.216350i
$105$		−	2.69529i		−	0.263033i
$106$	−5.48724	+	12.2472i	−0.532968	+	1.18955i
$107$	7.09279	−	7.09279i	0.685686	−	0.685686i	−0.275590	−	0.961275i	$-0.588873\pi$
$107$	7.09279	−	7.09279i	0.685686	−	0.685686i	0.961275	+	0.275590i	$0.0888730\pi$
$108$	0.114032	−	1.99675i	0.0109727	−	0.192137i
$109$	7.83035	+	7.83035i	0.750012	+	0.750012i	0.974481	−	0.224469i	$-0.0720649\pi$
$109$	7.83035	+	7.83035i	0.750012	+	0.750012i	−0.224469	+	0.974481i	$0.572065\pi$
$110$	1.94285	+	5.09698i	0.185244	+	0.485978i
$111$	0.269215			0.0255527
$112$	−10.7111	−	1.22739i	−1.01210	−	0.115978i
$113$	−4.63828			−0.436332			−0.218166	−	0.975912i	$-0.570007\pi$
$113$	−4.63828			−0.436332			−0.218166	+	0.975912i	$0.570007\pi$
$114$	−2.58258	−	6.77527i	−0.241881	−	0.634562i
$115$	−6.33104	−	6.33104i	−0.590373	−	0.590373i
$116$	8.02818	+	0.458479i	0.745398	+	0.0425687i
$117$	−1.82449	+	1.82449i	−0.168674	+	0.168674i
$118$	0.829722	−	1.85189i	0.0763821	−	0.170481i
$119$			19.7704i			1.81235i
$120$	1.30176	−	2.51106i	0.118834	−	0.229227i
$121$		−	3.87693i		−	0.352448i
$122$	4.36211	+	1.95440i	0.394927	+	0.176943i
$123$	5.42907	−	5.42907i	0.489523	−	0.489523i
$124$	−5.04445	+	4.49942i	−0.453005	+	0.404059i
$125$	0.707107	+	0.707107i	0.0632456	+	0.0632456i
$126$	3.56173	−	1.35765i	0.317304	−	0.120949i
$127$	−8.57901			−0.761264			−0.380632	−	0.924727i	$-0.624294\pi$
$127$	−8.57901			−0.761264			−0.380632	+	0.924727i	$0.624294\pi$
$128$	−9.38612	−	6.31670i	−0.829624	−	0.558323i
$129$	−11.2871			−0.993770
$130$	−3.40967	+	1.29969i	−0.299048	+	0.113990i
$131$	−5.33779	−	5.33779i	−0.466365	−	0.466365i	0.434370	−	0.900735i	$-0.356971\pi$
$131$	−5.33779	−	5.33779i	−0.466365	−	0.466365i	−0.900735	+	0.434370i	$0.856971\pi$
$132$	−5.75684	+	5.13483i	−0.501069	+	0.446930i
$133$	9.77149	−	9.77149i	0.847296	−	0.847296i
$134$	−13.1810	−	5.90559i	−1.13866	−	0.510165i
$135$			1.00000i			0.0860663i
$136$	−9.54866	+	18.4190i	−0.818791	+	1.57942i
$137$		−	12.2694i		−	1.04825i	−0.851642	−	0.524124i	$-0.824393\pi$
$137$		−	12.2694i		−	1.04825i	0.851642	−	0.524124i	$-0.175607\pi$
$138$	5.17723	−	11.5553i	0.440715	−	0.983652i
$139$	−12.7593	+	12.7593i	−1.08223	+	1.08223i	−0.0859285	+	0.996301i	$0.527386\pi$
$139$	−12.7593	+	12.7593i	−1.08223	+	1.08223i	−0.996301	+	0.0859285i	$0.972614\pi$
$140$	5.38181	+	0.307348i	0.454846	+	0.0259757i
$141$	0.930107	+	0.930107i	0.0783291	+	0.0783291i
$142$	1.15279	+	3.02430i	0.0967404	+	0.253793i
$143$	9.95206			0.832233
$144$	3.97399	+	0.455385i	0.331166	+	0.0379487i
$145$	−4.02063			−0.333895
$146$	0.660361	+	1.73242i	0.0546518	+	0.143376i
$147$	0.187089	+	0.187089i	0.0154309	+	0.0154309i
$148$	−0.0306990	+	0.537554i	−0.00252344	+	0.0441866i
$149$	6.47238	−	6.47238i	0.530238	−	0.530238i	−0.390405	−	0.920643i	$-0.627665\pi$
$149$	6.47238	−	6.47238i	0.530238	−	0.530238i	0.920643	+	0.390405i	$0.127665\pi$
$150$	−0.578239	+	1.29060i	−0.0472130	+	0.105377i
$151$		−	14.7782i		−	1.20263i	−0.799012	−	0.601316i	$-0.794643\pi$
$151$		−	14.7782i		−	1.20263i	0.799012	−	0.601316i	$-0.205357\pi$
$152$	13.8230	−	4.38417i	1.12119	−	0.355603i
$153$		−	7.33517i		−	0.593013i
$154$	−13.4169	−	6.01131i	−1.08117	−	0.484405i
$155$	2.38986	−	2.38986i	0.191958	−	0.191958i
$156$	−3.43499	−	3.85109i	−0.275020	−	0.308334i
$157$	14.0590	+	14.0590i	1.12203	+	1.12203i	0.991436	+	0.130592i	$0.0416878\pi$
$157$	14.0590	+	14.0590i	1.12203	+	1.12203i	0.130592	+	0.991436i	$0.458312\pi$
$158$	−3.42682	+	1.30623i	−0.272623	+	0.103918i
$159$	9.48958			0.752572
$160$	4.86550	+	2.88563i	0.384652	+	0.228129i
$161$	24.1321			1.90188
$162$	−1.32147	+	0.503713i	−0.103824	+	0.0395755i
$163$	2.09819	+	2.09819i	0.164343	+	0.164343i	0.784487	−	0.620145i	$-0.212926\pi$
$163$	2.09819	+	2.09819i	0.164343	+	0.164343i	−0.620145	+	0.784487i	$0.712926\pi$
$164$	10.2214	+	11.4596i	0.798156	+	0.894841i
$165$	2.72735	−	2.72735i	0.212324	−	0.212324i
$166$	−9.79362	−	4.38793i	−0.760132	−	0.340569i
$167$		−	15.7672i		−	1.22010i	−0.792361	−	0.610052i	$-0.791148\pi$
$167$		−	15.7672i		−	1.22010i	0.792361	−	0.610052i	$-0.208852\pi$
$168$	2.30474	+	7.26669i	0.177814	+	0.560638i
$169$		−	6.34247i		−	0.487882i
$170$	4.24148	−	9.46674i	0.325306	−	0.726066i
$171$	−3.62540	+	3.62540i	−0.277241	+	0.277241i
$172$	1.28708	−	22.5374i	0.0981391	−	1.71846i
$173$	8.73572	+	8.73572i	0.664164	+	0.664164i	0.956359	−	0.292195i	$-0.0943855\pi$
$173$	8.73572	+	8.73572i	0.664164	+	0.664164i	−0.292195	+	0.956359i	$0.594385\pi$
$174$	−2.02525	−	5.31313i	−0.153534	−	0.402787i
$175$	−2.69529			−0.203745
$176$	−9.59649	−	12.0805i	−0.723363	−	0.910601i
$177$	−1.43491			−0.107855
$178$	−7.50251	−	19.6824i	−0.562337	−	1.47526i
$179$	5.72942	+	5.72942i	0.428237	+	0.428237i	0.888027	−	0.459790i	$-0.152075\pi$
$179$	5.72942	+	5.72942i	0.428237	+	0.428237i	−0.459790	+	0.888027i	$0.652075\pi$
$180$	−1.99675	−	0.114032i	−0.148829	−	0.00849942i
$181$	−1.48317	+	1.48317i	−0.110243	+	0.110243i	−0.760077	−	0.649833i	$-0.774839\pi$
$181$	−1.48317	+	1.48317i	−0.110243	+	0.110243i	0.649833	+	0.760077i	$0.274839\pi$
$182$	4.02132	−	8.97537i	0.298080	−	0.665299i
$183$		−	3.37992i		−	0.249851i
$184$	22.4826	+	11.6553i	1.65744	+	0.859239i
$185$		−	0.269215i		−	0.0197931i
$186$	4.36191	+	1.95431i	0.319831	+	0.143297i
$187$	−20.0056	+	20.0056i	−1.46295	+	1.46295i
$188$	−1.96325	+	1.75113i	−0.143185	+	0.127714i
$189$	−1.90586	−	1.90586i	−0.138631	−	0.138631i
$190$	−6.77527	+	2.58258i	−0.491530	+	0.187360i
$191$	1.00884			0.0729970			0.0364985	−	0.999334i	$-0.488380\pi$
$191$	1.00884			0.0729970			0.0364985	+	0.999334i	$0.488380\pi$
$192$	−1.36245	+	7.88313i	−0.0983263	+	0.568916i
$193$	−20.0273			−1.44160			−0.720798	−	0.693145i	$-0.756225\pi$
$193$	−20.0273			−1.44160			−0.720798	+	0.693145i	$0.756225\pi$
$194$	0.918015	−	0.349927i	0.0659097	−	0.0251233i
$195$	1.82449	+	1.82449i	0.130654	+	0.130654i
$196$	−0.394904	+	0.352236i	−0.0282074	+	0.0251597i
$197$	−12.7615	+	12.7615i	−0.909217	+	0.909217i	−0.996209	−	0.0869919i	$-0.972275\pi$
$197$	−12.7615	+	12.7615i	−0.909217	+	0.909217i	0.0869919	+	0.996209i	$0.472275\pi$
$198$	4.97791	+	2.23030i	0.353765	+	0.158501i
$199$			11.6629i			0.826764i	0.910558	+	0.413382i	$0.135653\pi$
$199$			11.6629i			0.826764i	−0.910558	+	0.413382i	$0.864347\pi$
$200$	−2.51106	−	1.30176i	−0.177559	−	0.0920487i
$201$			10.2131i			0.720375i
$202$	−5.63395	+	12.5747i	−0.396404	+	0.884751i
$203$	7.66275	−	7.66275i	0.537820	−	0.537820i
$204$	14.6465	+	0.836441i	1.02546	+	0.0585626i
$205$	−5.42907	−	5.42907i	−0.379183	−	0.379183i
$206$	−2.21281	−	5.80518i	−0.154174	−	0.404466i
$207$	−8.95345			−0.622308
$208$	8.08136	−	6.41967i	0.560341	−	0.445124i
$209$	19.7755			1.36790
$210$	−1.35765	−	3.56173i	−0.0936870	−	0.245783i
$211$	−0.419270	−	0.419270i	−0.0288637	−	0.0288637i	0.692528	−	0.721391i	$-0.256497\pi$
$211$	−0.419270	−	0.419270i	−0.0288637	−	0.0288637i	−0.721391	+	0.692528i	$0.756497\pi$
$212$	−1.08211	+	18.9483i	−0.0743198	+	1.30137i
$213$	1.61828	−	1.61828i	0.110883	−	0.110883i
$214$	5.80015	−	12.9456i	0.396490	−	0.884944i
$215$			11.2871i			0.769771i
$216$	−0.855099	−	2.69607i	−0.0581821	−	0.183444i
$217$			9.10945i			0.618389i
$218$	14.2918	+	6.40329i	0.967963	+	0.433686i
$219$	0.927006	−	0.927006i	0.0626413	−	0.0626413i
$220$	5.13483	+	5.75684i	0.346190	+	0.388126i
$221$	−13.3829	−	13.3829i	−0.900234	−	0.900234i
$222$	0.355758	−	0.135607i	0.0238769	−	0.00910135i
$223$	−20.3746			−1.36438			−0.682191	−	0.731174i	$-0.738973\pi$
$223$	−20.3746			−1.36438			−0.682191	+	0.731174i	$0.738973\pi$
$224$	−14.7726	+	3.77335i	−0.987033	+	0.252117i
$225$	1.00000			0.0666667
$226$	−6.12933	+	2.33636i	−0.407717	+	0.155413i
$227$	2.87480	+	2.87480i	0.190807	+	0.190807i	0.796045	−	0.605238i	$-0.206922\pi$
$227$	2.87480	+	2.87480i	0.190807	+	0.190807i	−0.605238	+	0.796045i	$0.706922\pi$
$228$	−6.82559	−	7.65241i	−0.452036	−	0.506793i
$229$	−6.78564	+	6.78564i	−0.448408	+	0.448408i	−0.894825	−	0.446417i	$-0.852700\pi$
$229$	−6.78564	+	6.78564i	−0.448408	+	0.448408i	0.446417	+	0.894825i	$0.352700\pi$
$230$	−11.5553	−	5.17723i	−0.761933	−	0.341376i
$231$			10.3959i			0.684000i
$232$	10.8399	−	3.43804i	0.711675	−	0.225718i
$233$			27.8637i			1.82541i	0.408619	+	0.912705i	$0.366010\pi$
$233$			27.8637i			1.82541i	−0.408619	+	0.912705i	$0.633990\pi$
$234$	−1.49198	+	3.33002i	−0.0975339	+	0.217690i
$235$	0.930107	−	0.930107i	0.0606735	−	0.0606735i
$236$	0.163626	−	2.86516i	0.0106511	−	0.186506i
$237$	1.83367	+	1.83367i	0.119109	+	0.119109i
$238$	9.95861	+	26.1259i	0.645521	+	1.69349i
$239$	−19.7188			−1.27550			−0.637750	−	0.770243i	$-0.720135\pi$
$239$	−19.7188			−1.27550			−0.637750	+	0.770243i	$0.720135\pi$
$240$	0.455385	−	3.97399i	0.0293950	−	0.256520i
$241$	7.74263			0.498747			0.249373	−	0.968407i	$-0.419775\pi$
$241$	7.74263			0.498747			0.249373	+	0.968407i	$0.419775\pi$
$242$	−1.95286	−	5.12323i	−0.125535	−	0.329334i
$243$	0.707107	+	0.707107i	0.0453609	+	0.0453609i
$244$	6.74884	+	0.385418i	0.432050	+	0.0246738i
$245$	0.187089	−	0.187089i	0.0119527	−	0.0119527i
$246$	4.43963	−	9.90902i	0.283061	−	0.631776i
$247$			13.2290i			0.841741i
$248$	−4.39966	+	8.48678i	−0.279379	+	0.538911i
$249$			7.58844i			0.480898i
$250$	1.29060	+	0.578239i	0.0816245	+	0.0365710i
$251$	1.46277	−	1.46277i	0.0923293	−	0.0923293i	−0.659434	−	0.751763i	$-0.729204\pi$
$251$	1.46277	−	1.46277i	0.0923293	−	0.0923293i	0.751763	+	0.659434i	$0.229204\pi$
$252$	4.02284	−	3.58819i	0.253415	−	0.226034i
$253$	24.4192	+	24.4192i	1.53522	+	1.53522i
$254$	−11.3369	+	4.32136i	−0.711338	+	0.271146i
$255$	−7.33517			−0.459346
$256$	−15.5852	−	3.61939i	−0.974078	−	0.226212i
$257$	20.6684			1.28926			0.644630	−	0.764495i	$-0.277012\pi$
$257$	20.6684			1.28926			0.644630	+	0.764495i	$0.277012\pi$
$258$	−14.9155	+	5.68544i	−0.928596	+	0.353960i
$259$	0.513085	+	0.513085i	0.0318815	+	0.0318815i
$260$	−3.85109	+	3.43499i	−0.238835	+	0.213029i
$261$	−2.84302	+	2.84302i	−0.175978	+	0.175978i
$262$	−9.74242	−	4.36499i	−0.601889	−	0.269670i
$263$			26.3239i			1.62320i	0.584215	+	0.811599i	$0.301403\pi$
$263$			26.3239i			1.62320i	−0.584215	+	0.811599i	$0.698597\pi$
$264$	−5.02099	+	9.68530i	−0.309020	+	0.596089i
$265$		−	9.48958i		−	0.582940i
$266$	7.99066	−	17.8347i	0.489939	−	1.09352i
$267$	−10.5319	+	10.5319i	−0.644544	+	0.644544i
$268$	−20.3929	−	1.16461i	−1.24570	−	0.0711401i
$269$	−17.8129	−	17.8129i	−1.08607	−	1.08607i	−0.995929	−	0.0901396i	$-0.971269\pi$
$269$	−17.8129	−	17.8129i	−1.08607	−	1.08607i	−0.0901396	−	0.995929i	$-0.528731\pi$
$270$	0.503713	+	1.32147i	0.0306550	+	0.0804219i
$271$	−7.19848			−0.437277			−0.218638	−	0.975806i	$-0.570162\pi$
$271$	−7.19848			−0.437277			−0.218638	+	0.975806i	$0.570162\pi$
$272$	−3.34032	+	29.1499i	−0.202537	+	1.76747i
$273$	−6.95444			−0.420902
$274$	−6.18027	−	16.2136i	−0.373364	−	0.979501i
$275$	−2.72735	−	2.72735i	−0.164466	−	0.164466i
$276$	1.02098	−	17.8778i	0.0614556	−	1.07611i
$277$	10.4666	−	10.4666i	0.628879	−	0.628879i	−0.318907	−	0.947786i	$-0.603316\pi$
$277$	10.4666	−	10.4666i	0.628879	−	0.628879i	0.947786	+	0.318907i	$0.103316\pi$
$278$	−10.4340	+	23.2880i	−0.625787	+	1.39672i
$279$		−	3.37977i		−	0.202341i
$280$	7.26669	−	2.30474i	0.434268	−	0.137735i
$281$		−	17.0567i		−	1.01752i	−0.860909	−	0.508759i	$-0.830104\pi$
$281$		−	17.0567i		−	1.01752i	0.860909	−	0.508759i	$-0.169896\pi$
$282$	1.69761	+	0.760598i	0.101091	+	0.0452929i
$283$	2.70727	−	2.70727i	0.160931	−	0.160931i	−0.622048	−	0.782979i	$-0.713699\pi$
$283$	2.70727	−	2.70727i	0.160931	−	0.160931i	0.782979	+	0.622048i	$0.213699\pi$
$284$	3.04676	+	3.41583i	0.180792	+	0.202692i
$285$	3.62540	+	3.62540i	0.214750	+	0.214750i
$286$	13.1513	−	5.01299i	0.777654	−	0.296424i
$287$	20.6941			1.22153
$288$	5.48088	−	1.39998i	0.322964	−	0.0824945i
$289$	36.8047			2.16498
$290$	−5.31313	+	2.02525i	−0.311998	+	0.118927i
$291$	−0.491223	−	0.491223i	−0.0287960	−	0.0287960i
$292$	1.74529	+	1.95670i	0.102135	+	0.114507i
$293$	16.6594	−	16.6594i	0.973255	−	0.973255i	−0.0263968	−	0.999652i	$-0.508403\pi$
$293$	16.6594	−	16.6594i	0.973255	−	0.973255i	0.999652	+	0.0263968i	$0.00840333\pi$
$294$	0.341471	+	0.152993i	0.0199150	+	0.00892271i
$295$			1.43491i			0.0835439i
$296$	0.230205	+	0.725822i	0.0133804	+	0.0421876i
$297$		−	3.85706i		−	0.223809i
$298$	5.29280	−	11.8133i	0.306604	−	0.684323i
$299$	−16.3355	+	16.3355i	−0.944705	+	0.944705i
$300$	−0.114032	+	1.99675i	−0.00658362	+	0.115282i
$301$	−21.5115	−	21.5115i	−1.23990	−	1.23990i
$302$	−7.44397	−	19.5289i	−0.428352	−	1.12376i
$303$	9.74330			0.559738
$304$	16.0583	−	12.7564i	0.921004	−	0.731627i
$305$	−3.37992			−0.193534
$306$	−3.69482	−	9.69317i	−0.211219	−	0.554122i
$307$	18.1991	+	18.1991i	1.03868	+	1.03868i	0.999221	+	0.0394558i	$0.0125624\pi$
$307$	18.1991	+	18.1991i	1.03868	+	1.03868i	0.0394558	+	0.999221i	$0.487438\pi$
$308$	−20.7580	−	1.18546i	−1.18280	−	0.0675479i
$309$	−3.10631	+	3.10631i	−0.176712	+	0.176712i
$310$	1.95431	−	4.36191i	0.110997	−	0.247740i
$311$		−	15.3933i		−	0.872874i	−0.899735	−	0.436437i	$-0.856240\pi$
$311$		−	15.3933i		−	0.872874i	0.899735	−	0.436437i	$-0.143760\pi$
$312$	−6.47908	−	3.35884i	−0.366805	−	0.190157i
$313$			23.7790i			1.34407i	0.740520	+	0.672034i	$0.234579\pi$
$313$			23.7790i			1.34407i	−0.740520	+	0.672034i	$0.765421\pi$
$314$	25.6602	+	11.4968i	1.44809	+	0.648800i
$315$	−1.90586	+	1.90586i	−0.107383	+	0.107383i
$316$	−3.87046	+	3.45227i	−0.217730	+	0.194205i
$317$	−9.29662	−	9.29662i	−0.522150	−	0.522150i	0.396070	−	0.918220i	$-0.370374\pi$
$317$	−9.29662	−	9.29662i	−0.522150	−	0.522150i	−0.918220	+	0.396070i	$0.870374\pi$
$318$	12.5402	−	4.78003i	0.703217	−	0.268051i
$319$	15.5078			0.868272
$320$	7.88313	+	1.36245i	0.440680	+	0.0761632i
$321$	−10.0307			−0.559860
$322$	31.8898	−	12.1557i	1.77715	−	0.677409i
$323$	−26.5929	−	26.5929i	−1.47967	−	1.47967i
$324$	−1.49255	+	1.33128i	−0.0829192	+	0.0739600i
$325$	1.82449	−	1.82449i	0.101205	−	0.101205i
$326$	3.82956	+	1.71580i	0.212100	+	0.0950292i
$327$		−	11.0738i		−	0.612382i
$328$	19.2795	+	9.99477i	1.06453	+	0.551869i
$329$			3.54530i			0.195459i
$330$	2.23030	−	4.97791i	0.122774	−	0.274025i
$331$	−15.0564	+	15.0564i	−0.827572	+	0.827572i	−0.987180	−	0.159608i	$-0.948977\pi$
$331$	−15.0564	+	15.0564i	−0.827572	+	0.827572i	0.159608	+	0.987180i	$0.448977\pi$
$332$	−15.1522	−	0.865323i	−0.831585	−	0.0474908i
$333$	−0.190364	−	0.190364i	−0.0104319	−	0.0104319i
$334$	−7.94216	−	20.8359i	−0.434576	−	1.14009i
$335$	10.2131			0.558000
$336$	6.70597	+	8.44176i	0.365840	+	0.460536i
$337$	−11.7116			−0.637969			−0.318985	−	0.947760i	$-0.603342\pi$
$337$	−11.7116			−0.637969			−0.318985	+	0.947760i	$0.603342\pi$
$338$	−3.19479	−	8.38136i	−0.173774	−	0.455886i
$339$	3.27976	+	3.27976i	0.178132	+	0.178132i
$340$	0.836441	−	14.6465i	0.0453624	−	0.794316i
$341$	−9.21782	+	9.21782i	−0.499173	+	0.499173i
$342$	−2.96468	+	6.61700i	−0.160311	+	0.357806i
$343$		−	18.1539i		−	0.980218i
$344$	−9.65155	−	30.4307i	−0.520377	−	1.64071i
$345$			8.95345i			0.482037i
$346$	15.9443	+	7.14366i	0.857168	+	0.384045i
$347$	12.5589	−	12.5589i	0.674197	−	0.674197i	−0.284484	−	0.958681i	$-0.591822\pi$
$347$	12.5589	−	12.5589i	0.674197	−	0.674197i	0.958681	+	0.284484i	$0.0918223\pi$
$348$	−5.35259	−	6.00098i	−0.286929	−	0.321686i
$349$	−12.3114	−	12.3114i	−0.659014	−	0.659014i	0.296133	−	0.955147i	$-0.404303\pi$
$349$	−12.3114	−	12.3114i	−0.659014	−	0.659014i	−0.955147	+	0.296133i	$0.904303\pi$
$350$	−3.56173	+	1.35765i	−0.190383	+	0.0725696i
$351$	2.58022			0.137722
$352$	−18.7665	−	11.1301i	−1.00026	−	0.593235i
$353$	−5.99485			−0.319073			−0.159537	−	0.987192i	$-0.551000\pi$
$353$	−5.99485			−0.319073			−0.159537	+	0.987192i	$0.551000\pi$
$354$	−1.89619	+	0.722785i	−0.100781	+	0.0384156i
$355$	−1.61828	−	1.61828i	−0.0858894	−	0.0858894i
$356$	−19.8286	−	22.2306i	−1.05091	−	1.17822i
$357$	13.9798	−	13.9798i	0.739888	−	0.739888i
$358$	10.4572	+	4.68525i	0.552681	+	0.247623i
$359$		−	4.95429i		−	0.261477i	−0.991417	−	0.130739i	$-0.958265\pi$
$359$		−	4.95429i		−	0.261477i	0.991417	−	0.130739i	$-0.0417349\pi$
$360$	−2.69607	+	0.855099i	−0.142095	+	0.0450677i
$361$			7.28700i			0.383526i
$362$	−1.21287	+	2.70706i	−0.0637469	+	0.142280i
$363$	−2.74140	+	2.74140i	−0.143886	+	0.143886i
$364$	0.793026	−	13.8862i	0.0415659	−	0.727837i
$365$	−0.927006	−	0.927006i	−0.0485217	−	0.0485217i
$366$	−1.70251	−	4.46645i	−0.0889917	−	0.233465i
$367$	26.2297			1.36918			0.684591	−	0.728928i	$-0.259981\pi$
$367$	26.2297			1.36918			0.684591	+	0.728928i	$0.259981\pi$
$368$	35.5809	+	4.07726i	1.85478	+	0.212542i
$369$	−7.67786			−0.399693
$370$	−0.135607	−	0.355758i	−0.00704988	−	0.0184950i
$371$	18.0858	+	18.0858i	0.938967	+	0.938967i
$372$	6.74853	+	0.385400i	0.349895	+	0.0199821i
$373$	−8.58218	+	8.58218i	−0.444368	+	0.444368i	−0.893477	−	0.449109i	$-0.851742\pi$
$373$	−8.58218	+	8.58218i	−0.444368	+	0.444368i	0.449109	+	0.893477i	$0.351742\pi$
$374$	−16.3596	+	36.5138i	−0.845937	+	1.88808i
$375$		−	1.00000i		−	0.0516398i
$376$	−1.71230	+	3.30297i	−0.0883052	+	0.170338i
$377$			10.3741i			0.534294i
$378$	−3.47853	−	1.55852i	−0.178916	−	0.0801616i
$379$	4.04145	−	4.04145i	0.207595	−	0.207595i	−0.595649	−	0.803245i	$-0.703105\pi$
$379$	4.04145	−	4.04145i	0.207595	−	0.207595i	0.803245	+	0.595649i	$0.203105\pi$
$380$	−7.65241	+	6.82559i	−0.392560	+	0.350145i
$381$	6.06628	+	6.06628i	0.310785	+	0.310785i
$382$	1.33315	−	0.508165i	0.0682097	−	0.0260000i
$383$	−1.97475			−0.100905			−0.0504526	−	0.998726i	$-0.516066\pi$
$383$	−1.97475			−0.100905			−0.0504526	+	0.998726i	$0.516066\pi$
$384$	2.17041	+	11.1036i	0.110758	+	0.566627i
$385$	10.3959			0.529824
$386$	−26.4654	+	10.0880i	−1.34705	+	0.513467i
$387$	7.98115	+	7.98115i	0.405705	+	0.405705i
$388$	1.03686	−	0.924833i	0.0526388	−	0.0469513i
$389$	27.0045	−	27.0045i	1.36918	−	1.36918i	0.507579	−	0.861606i	$-0.330541\pi$
$389$	27.0045	−	27.0045i	1.36918	−	1.36918i	0.861606	−	0.507579i	$-0.169459\pi$
$390$	3.33002	+	1.49198i	0.168622	+	0.0755494i
$391$		−	65.6750i		−	3.32133i
$392$	−0.344426	+	0.664386i	−0.0173961	+	0.0335565i
$393$			7.54877i			0.380785i
$394$	−10.4357	+	23.2920i	−0.525744	+	1.17343i
$395$	1.83367	−	1.83367i	0.0922617	−	0.0922617i
$396$	7.70158	+	0.439827i	0.387019	+	0.0221022i
$397$	−13.2948	−	13.2948i	−0.667248	−	0.667248i	0.289830	−	0.957078i	$-0.406401\pi$
$397$	−13.2948	−	13.2948i	−0.667248	−	0.667248i	−0.957078	+	0.289830i	$0.906401\pi$
$398$	5.87478	+	15.4122i	0.294476	+	0.772543i
$399$	−13.8190			−0.691814
$400$	−3.97399	−	0.455385i	−0.198700	−	0.0227692i
$401$	3.97892			0.198698			0.0993490	−	0.995053i	$-0.468324\pi$
$401$	3.97892			0.198698			0.0993490	+	0.995053i	$0.468324\pi$
$402$	5.14446	+	13.4962i	0.256582	+	0.673131i
$403$	−6.16635	−	6.16635i	−0.307168	−	0.307168i
$404$	−1.11105	+	19.4549i	−0.0552766	+	0.967918i
$405$	0.707107	−	0.707107i	0.0351364	−	0.0351364i
$406$	6.26624	−	13.9859i	0.310988	−	0.694108i
$407$			1.03838i			0.0514705i
$408$	19.7761	−	6.27229i	0.979065	−	0.310525i
$409$		−	23.6091i		−	1.16740i	−0.811971	−	0.583698i	$-0.801605\pi$
$409$		−	23.6091i		−	1.16740i	0.811971	−	0.583698i	$-0.198395\pi$
$410$	−9.90902	−	4.43963i	−0.489372	−	0.219258i
$411$	−8.67579	+	8.67579i	−0.427945	+	0.427945i
$412$	−5.84830	−	6.55673i	−0.288125	−	0.323027i
$413$	−2.73474	−	2.73474i	−0.134568	−	0.134568i
$414$	−11.8317	+	4.50997i	−0.581495	+	0.221653i
$415$	7.58844			0.372502
$416$	7.44557	−	12.5541i	0.365049	−	0.615513i
$417$	18.0444			0.883637
$418$	26.1326	−	9.96118i	1.27819	−	0.487217i
$419$	−13.5761	−	13.5761i	−0.663235	−	0.663235i	0.292906	−	0.956141i	$-0.405378\pi$
$419$	−13.5761	−	13.5761i	−0.663235	−	0.663235i	−0.956141	+	0.292906i	$0.905378\pi$
$420$	−3.58819	−	4.02284i	−0.175086	−	0.196295i
$421$	9.30166	−	9.30166i	0.453335	−	0.453335i	−0.443125	−	0.896460i	$-0.646130\pi$
$421$	9.30166	−	9.30166i	0.453335	−	0.453335i	0.896460	+	0.443125i	$0.146130\pi$
$422$	−0.765242	−	0.342859i	−0.0372514	−	0.0166901i
$423$		−	1.31537i		−	0.0639555i
$424$	8.11453	+	25.5846i	0.394076	+	1.24250i
$425$			7.33517i			0.355808i
$426$	1.32335	−	2.95365i	0.0641166	−	0.143105i
$427$	6.44164	−	6.44164i	0.311733	−	0.311733i
$428$	1.14382	−	20.0288i	0.0552886	−	0.968129i
$429$	−7.03717	−	7.03717i	−0.339758	−	0.339758i
$430$	5.68544	+	14.9155i	0.274176	+	0.719287i
$431$	6.40406			0.308473			0.154236	−	0.988034i	$-0.450708\pi$
$431$	6.40406			0.308473			0.154236	+	0.988034i	$0.450708\pi$
$432$	−2.48803	−	3.13204i	−0.119706	−	0.150691i
$433$	−33.9234			−1.63025			−0.815127	−	0.579282i	$-0.803333\pi$
$433$	−33.9234			−1.63025			−0.815127	+	0.579282i	$0.803333\pi$
$434$	4.58855	+	12.0378i	0.220257	+	0.577834i
$435$	2.84302	+	2.84302i	0.136312	+	0.136312i
$436$	22.1116	+	1.26276i	1.05895	+	0.0604754i
$437$	−32.4598	+	32.4598i	−1.55276	+	1.55276i
$438$	0.758062	−	1.69195i	0.0362216	−	0.0808446i
$439$			3.97789i			0.189855i	0.995484	+	0.0949273i	$0.0302619\pi$
$439$			3.97789i			0.189855i	−0.995484	+	0.0949273i	$0.969738\pi$
$440$	9.68530	+	5.02099i	0.461729	+	0.239366i
$441$		−	0.264584i		−	0.0125992i
$442$	−24.4263	−	10.9439i	−1.16184	−	0.520550i
$443$	14.5607	−	14.5607i	0.691802	−	0.691802i	−0.270826	−	0.962628i	$-0.587297\pi$
$443$	14.5607	−	14.5607i	0.691802	−	0.691802i	0.962628	+	0.270826i	$0.0872969\pi$
$444$	0.401815	−	0.358400i	0.0190693	−	0.0170089i
$445$	10.5319	+	10.5319i	0.499261	+	0.499261i
$446$	−26.9243	+	10.2629i	−1.27490	+	0.485964i
$447$	−9.15332			−0.432937
$448$	−17.6208	+	12.4275i	−0.832502	+	0.587144i
$449$	11.3678			0.536481			0.268240	−	0.963352i	$-0.413558\pi$
$449$	11.3678			0.536481			0.268240	+	0.963352i	$0.413558\pi$
$450$	1.32147	−	0.503713i	0.0622945	−	0.0237453i
$451$	20.9402	+	20.9402i	0.986038	+	0.986038i
$452$	−6.92284	+	6.17485i	−0.325623	+	0.290440i
$453$	−10.4498	+	10.4498i	−0.490972	+	0.490972i
$454$	5.24702	+	2.35087i	0.246255	+	0.110332i
$455$			6.95444i			0.326029i
$456$	−12.8744	−	6.67426i	−0.602899	−	0.312551i
$457$			39.0892i			1.82851i	0.405135	+	0.914257i	$0.367225\pi$
$457$			39.0892i			1.82851i	−0.405135	+	0.914257i	$0.632775\pi$
$458$	−5.54898	+	12.3850i	−0.259287	+	0.578714i
$459$	−5.18675	+	5.18675i	−0.242097	+	0.242097i
$460$	−17.8778	−	1.02098i	−0.833555	−	0.0476033i
$461$	−6.05492	−	6.05492i	−0.282006	−	0.282006i	0.551903	−	0.833908i	$-0.313902\pi$
$461$	−6.05492	−	6.05492i	−0.282006	−	0.282006i	−0.833908	+	0.551903i	$0.813902\pi$
$462$	5.23655	+	13.7378i	0.243626	+	0.639142i
$463$	36.1375			1.67945			0.839725	−	0.543012i	$-0.182716\pi$
$463$	36.1375			1.67945			0.839725	+	0.543012i	$0.182716\pi$
$464$	12.5928	−	10.0035i	0.584606	−	0.464399i
$465$	−3.37977			−0.156733
$466$	14.0353	+	36.8209i	0.650173	+	1.70570i
$467$	−13.0890	−	13.0890i	−0.605689	−	0.605689i	0.336128	−	0.941816i	$-0.390883\pi$
$467$	−13.0890	−	13.0890i	−0.605689	−	0.605689i	−0.941816	+	0.336128i	$0.890883\pi$
$468$	−0.294227	+	5.15204i	−0.0136006	+	0.238153i
$469$	−19.4647	+	19.4647i	−0.898795	+	0.898795i
$470$	0.760598	−	1.69761i	0.0350838	−	0.0783050i
$471$		−	19.8824i		−	0.916132i
$472$	−1.22699	−	3.86863i	−0.0564769	−	0.178068i
$473$		−	43.5349i		−	2.00174i
$474$	3.34677	+	1.49948i	0.153722	+	0.0688736i
$475$	3.62540	−	3.62540i	0.166345	−	0.166345i
$476$	26.3199	+	29.5082i	1.20637	+	1.35251i
$477$	−6.71014	−	6.71014i	−0.307236	−	0.307236i
$478$	−26.0577	+	9.93261i	−1.19185	+	0.454307i
$479$	−3.78947			−0.173145			−0.0865726	−	0.996246i	$-0.527591\pi$
$479$	−3.78947			−0.173145			−0.0865726	+	0.996246i	$0.527591\pi$
$480$	−1.39998	−	5.48088i	−0.0639000	−	0.250167i
$481$	−0.694633			−0.0316725
$482$	10.2316	−	3.90007i	0.466038	−	0.177643i
$483$	−17.0640	−	17.0640i	−0.776438	−	0.776438i
$484$	−5.16128	−	5.78649i	−0.234603	−	0.263022i
$485$	−0.491223	+	0.491223i	−0.0223053	+	0.0223053i
$486$	1.29060	+	0.578239i	0.0585427	+	0.0262294i
$487$		−	3.39864i		−	0.154007i	−0.997031	−	0.0770036i	$-0.975465\pi$
$487$		−	3.39864i		−	0.154007i	0.997031	−	0.0770036i	$-0.0245353\pi$
$488$	9.11251	−	2.89017i	0.412504	−	0.130832i
$489$		−	2.96728i		−	0.134185i
$490$	0.152993	−	0.341471i	0.00691150	−	0.0154261i
$491$	−8.70898	+	8.70898i	−0.393031	+	0.393031i	−0.875766	−	0.482735i	$-0.839643\pi$
$491$	−8.70898	+	8.70898i	−0.393031	+	0.393031i	0.482735	+	0.875766i	$0.339643\pi$
$492$	0.875519	−	15.3307i	0.0394715	−	0.691163i
$493$	−20.8540	−	20.8540i	−0.939217	−	0.939217i
$494$	6.66362	+	17.4817i	0.299811	+	0.786538i
$495$	−3.85706			−0.173362
$496$	−1.53909	+	13.4312i	−0.0691073	+	0.603077i
$497$	6.16842			0.276691
$498$	3.82240	+	10.0279i	0.171286	+	0.449360i
$499$	−15.9542	−	15.9542i	−0.714210	−	0.714210i	0.253203	−	0.967413i	$-0.418516\pi$
$499$	−15.9542	−	15.9542i	−0.714210	−	0.714210i	−0.967413	+	0.253203i	$0.918516\pi$
$500$	1.99675	+	0.114032i	0.0892972	+	0.00509965i
$501$	−11.1491	+	11.1491i	−0.498106	+	0.498106i
$502$	1.19618	−	2.66982i	0.0533883	−	0.119160i
$503$		−	18.4604i		−	0.823107i	−0.911386	−	0.411553i	$-0.864986\pi$
$503$		−	18.4604i		−	0.823107i	0.911386	−	0.411553i	$-0.135014\pi$
$504$	3.50863	−	6.76803i	0.156287	−	0.301472i
$505$		−	9.74330i		−	0.433571i
$506$	44.5695	+	19.9689i	1.98135	+	0.887725i
$507$	−4.48480	+	4.48480i	−0.199177	+	0.199177i
$508$	−12.8046	+	11.4211i	−0.568111	+	0.506728i
$509$	8.47641	+	8.47641i	0.375710	+	0.375710i	0.869552	−	0.493841i	$-0.164408\pi$
$509$	8.47641	+	8.47641i	0.375710	+	0.375710i	−0.493841	+	0.869552i	$0.664408\pi$
$510$	−9.69317	+	3.69482i	−0.429221	+	0.163609i
$511$	3.53348			0.156312
$512$	−22.4185	+	3.06760i	−0.990768	+	0.135570i
$513$	5.12708			0.226366
$514$	27.3126	−	10.4110i	1.20471	−	0.459207i
$515$	3.10631	+	3.10631i	0.136880	+	0.136880i
$516$	−16.8464	+	15.0262i	−0.741623	+	0.661493i
$517$	−3.58748	+	3.58748i	−0.157777	+	0.157777i
$518$	0.936472	+	0.419577i	0.0411462	+	0.0184351i
$519$		−	12.3542i		−	0.542288i
$520$	−3.35884	+	6.47908i	−0.147295	+	0.284126i
$521$			22.3693i			0.980017i	0.871718	+	0.490009i	$0.163006\pi$
$521$			22.3693i			0.980017i	−0.871718	+	0.490009i	$0.836994\pi$
$522$	−2.32488	+	5.18902i	−0.101757	+	0.227117i
$523$	−2.39235	+	2.39235i	−0.104610	+	0.104610i	−0.757475	−	0.652865i	$-0.773567\pi$
$523$	−2.39235	+	2.39235i	−0.104610	+	0.104610i	0.652865	+	0.757475i	$0.273567\pi$
$524$	−15.0730	−	0.860799i	−0.658467	−	0.0376042i
$525$	1.90586	+	1.90586i	0.0831784	+	0.0831784i
$526$	13.2597	+	34.7861i	0.578149	+	1.51675i
$527$	24.7911			1.07992
$528$	−1.75645	+	15.3279i	−0.0764395	+	0.667063i
$529$	−57.1642			−2.48540
$530$	−4.78003	−	12.5402i	−0.207631	−	0.544709i
$531$	1.01464	+	1.01464i	0.0440315	+	0.0440315i
$532$	1.57580	−	27.5930i	0.0683196	−	1.19631i
$533$	−14.0082	+	14.0082i	−0.606762	+	0.606762i
$534$	−8.61251	+	19.2227i	−0.372700	+	0.831846i
$535$			10.0307i			0.433666i
$536$	−27.5352	+	8.73319i	−1.18934	+	0.377216i
$537$		−	8.10262i		−	0.349654i
$538$	−32.5117	−	14.5665i	−1.40168	−	0.628007i
$539$	−0.721614	+	0.721614i	−0.0310821	+	0.0310821i
$540$	1.33128	+	1.49255i	0.0572892	+	0.0642289i
$541$	−10.4567	−	10.4567i	−0.449570	−	0.449570i	0.445642	−	0.895211i	$-0.352976\pi$
$541$	−10.4567	−	10.4567i	−0.449570	−	0.449570i	−0.895211	+	0.445642i	$0.852976\pi$
$542$	−9.51255	+	3.62597i	−0.408599	+	0.155749i
$543$	2.09752			0.0900133
$544$	10.2691	+	40.2032i	0.440283	+	1.72370i
$545$	−11.0738			−0.474349
$546$	−9.19005	+	3.50304i	−0.393298	+	0.149916i
$547$	27.1404	+	27.1404i	1.16044	+	1.16044i	0.984379	+	0.176060i	$0.0563354\pi$
$547$	27.1404	+	27.1404i	1.16044	+	1.16044i	0.176060	+	0.984379i	$0.443665\pi$
$548$	−16.3340	−	18.3127i	−0.697756	−	0.782279i
$549$	−2.38996	+	2.38996i	−0.102001	+	0.102001i
$550$	−4.97791	−	2.23030i	−0.212259	−	0.0951004i
$551$			20.6141i			0.878191i
$552$	−7.65608	−	24.1391i	−0.325865	−	1.02743i
$553$			6.98941i			0.297220i
$554$	8.55912	−	19.1035i	0.363642	−	0.811630i
$555$	−0.190364	+	0.190364i	−0.00808048	+	0.00808048i
$556$	−2.05763	+	36.0300i	−0.0872630	+	1.52801i
$557$	−1.29047	−	1.29047i	−0.0546790	−	0.0546790i	0.679239	−	0.733918i	$-0.262310\pi$
$557$	−1.29047	−	1.29047i	−0.0546790	−	0.0546790i	−0.733918	+	0.679239i	$0.762310\pi$
$558$	−1.70243	−	4.46625i	−0.0720697	−	0.189071i
$559$	29.1231			1.23177
$560$	8.44176	−	6.70597i	0.356730	−	0.283379i
$561$	28.2922			1.19450
$562$	−8.59169	−	22.5399i	−0.362419	−	0.950787i
$563$	−3.42706	−	3.42706i	−0.144433	−	0.144433i	0.631193	−	0.775626i	$-0.282566\pi$
$563$	−3.42706	−	3.42706i	−0.144433	−	0.144433i	−0.775626	+	0.631193i	$0.782566\pi$
$564$	2.62646	+	0.149994i	0.110594	+	0.00631588i
$565$	3.27976	−	3.27976i	0.137980	−	0.137980i
$566$	2.21388	−	4.94126i	0.0930564	−	0.207697i
$567$			2.69529i			0.113192i
$568$	5.74679	+	2.97921i	0.241130	+	0.125005i
$569$			26.4853i			1.11032i	0.831743	+	0.555161i	$0.187344\pi$
$569$			26.4853i			1.11032i	−0.831743	+	0.555161i	$0.812656\pi$
$570$	6.61700	+	2.96468i	0.277156	+	0.124177i
$571$	−1.42398	+	1.42398i	−0.0595918	+	0.0595918i	−0.736275	−	0.676683i	$-0.763417\pi$
$571$	−1.42398	+	1.42398i	−0.0595918	+	0.0595918i	0.676683	+	0.736275i	$0.263417\pi$
$572$	14.8539	−	13.2490i	0.621073	−	0.553968i
$573$	−0.713357	−	0.713357i	−0.0298009	−	0.0298009i
$574$	27.3465	−	10.4239i	1.14142	−	0.435084i
$575$	8.95345			0.373385
$576$	6.53761	−	4.61082i	0.272400	−	0.192117i
$577$	37.6681			1.56814			0.784071	−	0.620671i	$-0.213140\pi$
$577$	37.6681			1.56814			0.784071	+	0.620671i	$0.213140\pi$
$578$	48.6361	−	18.5390i	2.02300	−	0.771121i
$579$	14.1614	+	14.1614i	0.588529	+	0.588529i
$580$	−6.00098	+	5.35259i	−0.249177	+	0.222254i
$581$	−14.4625	+	14.4625i	−0.600005	+	0.600005i
$582$	−0.896571	−	0.401699i	−0.0371641	−	0.0166510i
$583$			36.6019i			1.51589i
$584$	3.29196	+	1.70659i	0.136222	+	0.0706193i
$585$		−	2.58022i		−	0.106679i
$586$	13.6233	−	30.4065i	0.562773	−	1.25608i
$587$	1.99399	−	1.99399i	0.0823008	−	0.0823008i	−0.664758	−	0.747059i	$-0.731465\pi$
$587$	1.99399	−	1.99399i	0.0823008	−	0.0823008i	0.747059	+	0.664758i	$0.231465\pi$
$588$	0.528307	+	0.0301710i	0.0217870	+	0.00124423i
$589$	−12.2530	−	12.2530i	−0.504876	−	0.504876i
$590$	0.722785	+	1.89619i	0.0297566	+	0.0780649i
$591$	18.0474			0.742373
$592$	0.669815	+	0.843192i	0.0275292	+	0.0346550i
$593$	24.0023			0.985657			0.492828	−	0.870127i	$-0.335963\pi$
$593$	24.0023			0.985657			0.492828	+	0.870127i	$0.335963\pi$
$594$	−1.94285	−	5.09698i	−0.0797163	−	0.209131i
$595$	−13.9798	−	13.9798i	−0.573115	−	0.573115i
$596$	1.04377	−	18.2769i	0.0427544	−	0.748650i
$597$	8.24694	−	8.24694i	0.337525	−	0.337525i
$598$	−13.3584	+	29.8152i	−0.546265	+	1.21923i
$599$		−	34.5205i		−	1.41047i	−0.708974	−	0.705234i	$-0.750842\pi$
$599$		−	34.5205i		−	1.41047i	0.708974	−	0.705234i	$-0.249158\pi$
$600$	0.855099	+	2.69607i	0.0349093	+	0.110067i
$601$		−	3.45113i		−	0.140775i	−0.997520	−	0.0703873i	$-0.977577\pi$
$601$		−	3.45113i		−	0.140775i	0.997520	−	0.0703873i	$-0.0224235\pi$
$602$	−39.2624	−	17.5911i	−1.60022	−	0.716960i
$603$	7.22173	−	7.22173i	0.294092	−	0.294092i
$604$	−19.6739	−	22.0571i	−0.800520	−	0.897491i
$605$	2.74140	+	2.74140i	0.111454	+	0.111454i
$606$	12.8754	−	4.90783i	0.523029	−	0.199367i
$607$	−43.2408			−1.75509			−0.877545	−	0.479494i	$-0.840820\pi$
$607$	−43.2408			−1.75509			−0.877545	+	0.479494i	$0.840820\pi$
$608$	14.7949	−	24.9458i	0.600012	−	1.01169i
$609$	−10.8368			−0.439128
$610$	−4.46645	+	1.70251i	−0.180841	+	0.0689326i
$611$	−2.39988	−	2.39988i	−0.0970887	−	0.0970887i
$612$	−9.76516	−	10.9481i	−0.394733	−	0.442550i
$613$	31.4157	−	31.4157i	1.26887	−	1.26887i	0.322195	−	0.946673i	$-0.395579\pi$
$613$	31.4157	−	31.4157i	1.26887	−	1.26887i	0.946673	−	0.322195i	$-0.104421\pi$
$614$	33.2166	+	14.8824i	1.34051	+	0.600603i
$615$			7.67786i			0.309601i
$616$	−28.0281	+	8.88952i	−1.12928	+	0.358169i
$617$			26.4920i			1.06653i	0.845949	+	0.533265i	$0.179035\pi$
$617$			26.4920i			1.06653i	−0.845949	+	0.533265i	$0.820965\pi$
$618$	−2.54019	+	5.66957i	−0.102182	+	0.228064i
$619$	23.9945	−	23.9945i	0.964422	−	0.964422i	−0.0349667	−	0.999388i	$-0.511133\pi$
$619$	23.9945	−	23.9945i	0.964422	−	0.964422i	0.999388	+	0.0349667i	$0.0111325\pi$
$620$	0.385400	−	6.74853i	0.0154780	−	0.271028i
$621$	6.33104	+	6.33104i	0.254056	+	0.254056i
$622$	−7.75381	−	20.3417i	−0.310899	−	0.815629i
$623$	−40.1447			−1.60836
$624$	−10.2538	−	1.17499i	−0.410479	−	0.0470373i
$625$	−1.00000			−0.0400000
$626$	11.9778	+	31.4231i	0.478729	+	1.25592i
$627$	−13.9834	−	13.9834i	−0.558442	−	0.558442i
$628$	39.7001	+	2.26722i	1.58421	+	0.0904720i
$629$	1.39635	−	1.39635i	0.0556761	−	0.0556761i
$630$	−1.55852	+	3.47853i	−0.0620929	+	0.138588i
$631$			34.6813i			1.38064i	0.723504	+	0.690320i	$0.242530\pi$
$631$			34.6813i			1.38064i	−0.723504	+	0.690320i	$0.757470\pi$
$632$	−3.37573	+	6.51166i	−0.134279	+	0.259020i
$633$			0.592937i			0.0235671i
$634$	−16.9680	−	7.60234i	−0.673886	−	0.301927i
$635$	6.06628	−	6.06628i	0.240733	−	0.240733i
$636$	14.1636	−	12.6333i	0.561624	−	0.500942i
$637$	−0.482731	−	0.482731i	−0.0191265	−	0.0191265i
$638$	20.4931	−	7.81150i	0.811328	−	0.309260i
$639$	−2.28859			−0.0905353
$640$	11.1036	−	2.17041i	0.438907	−	0.0857929i
$641$	25.5477			1.00908			0.504538	−	0.863390i	$-0.331663\pi$
$641$	25.5477			1.00908			0.504538	+	0.863390i	$0.331663\pi$
$642$	−13.2553	+	5.05261i	−0.523143	+	0.199411i
$643$	12.0319	+	12.0319i	0.474490	+	0.474490i	0.903364	−	0.428874i	$-0.141090\pi$
$643$	12.0319	+	12.0319i	0.474490	+	0.474490i	−0.428874	+	0.903364i	$0.641090\pi$
$644$	36.0183	−	32.1266i	1.41932	−	1.26597i
$645$	7.98115	−	7.98115i	0.314258	−	0.314258i
$646$	−48.5368	−	21.7464i	−1.90965	−	0.855601i
$647$		−	20.4148i		−	0.802587i	−0.915950	−	0.401293i	$-0.868561\pi$
$647$		−	20.4148i		−	0.802587i	0.915950	−	0.401293i	$-0.131439\pi$
$648$	−1.30176	+	2.51106i	−0.0511381	+	0.0986436i
$649$		−	5.53455i		−	0.217250i
$650$	1.49198	−	3.33002i	0.0585203	−	0.130614i
$651$	6.44135	−	6.44135i	0.252456	−	0.252456i
$652$	5.92491	+	0.338364i	0.232037	+	0.0132514i
$653$	15.3217	+	15.3217i	0.599586	+	0.599586i	0.940202	−	0.340616i	$-0.110636\pi$
$653$	15.3217	+	15.3217i	0.599586	+	0.599586i	−0.340616	+	0.940202i	$0.610636\pi$
$654$	−5.57802	−	14.6336i	−0.218118	−	0.572221i
$655$	7.54877			0.294955
$656$	30.5118	+	3.49638i	1.19128	+	0.136511i
$657$	−1.31098			−0.0511464
$658$	1.78582	+	4.68500i	0.0696184	+	0.182640i
$659$	3.52074	+	3.52074i	0.137148	+	0.137148i	0.772348	−	0.635200i	$-0.219082\pi$
$659$	3.52074	+	3.52074i	0.137148	+	0.137148i	−0.635200	+	0.772348i	$0.719082\pi$
$660$	0.439827	−	7.70158i	0.0171203	−	0.299783i
$661$	−23.8945	+	23.8945i	−0.929388	+	0.929388i	−0.997666	−	0.0682781i	$-0.978249\pi$
$661$	−23.8945	+	23.8945i	−0.929388	+	0.929388i	0.0682781	+	0.997666i	$0.478249\pi$
$662$	−12.3124	+	27.4806i	−0.478534	+	1.06806i
$663$			18.9263i			0.735038i
$664$	−20.4590	+	6.48887i	−0.793963	+	0.251817i
$665$			13.8190i			0.535877i
$666$	−0.347448	−	0.155670i	−0.0134633	−	0.00603210i
$667$	−25.4548	+	25.4548i	−0.985613	+	0.985613i
$668$	−20.9906	−	23.5333i	−0.812151	−	0.910531i
$669$	14.4070	+	14.4070i	0.557006	+	0.557006i
$670$	13.4962	−	5.14446i	0.521405	−	0.198748i
$671$	13.0366			0.503271
$672$	13.1139	+	7.77762i	0.505881	+	0.300028i
$673$	−25.4607			−0.981437			−0.490719	−	0.871318i	$-0.663266\pi$
$673$	−25.4607			−0.981437			−0.490719	+	0.871318i	$0.663266\pi$
$674$	−15.4764	+	5.89927i	−0.596130	+	0.227231i
$675$	−0.707107	−	0.707107i	−0.0272166	−	0.0272166i
$676$	−8.44361	−	9.46643i	−0.324754	−	0.364093i
$677$	21.1318	−	21.1318i	0.812162	−	0.812162i	−0.172796	−	0.984958i	$-0.555280\pi$
$677$	21.1318	−	21.1318i	0.812162	−	0.812162i	0.984958	+	0.172796i	$0.0552801\pi$
$678$	5.98615	+	2.68203i	0.229897	+	0.103003i
$679$		−	1.87240i		−	0.0718562i
$680$	−6.27229	−	19.7761i	−0.240531	−	0.758380i
$681$		−	4.06558i		−	0.155793i
$682$	−7.53790	+	16.8242i	−0.288641	+	0.644231i
$683$	−6.14096	+	6.14096i	−0.234977	+	0.234977i	−0.814767	−	0.579789i	$-0.803135\pi$
$683$	−6.14096	+	6.14096i	−0.234977	+	0.234977i	0.579789	+	0.814767i	$0.303135\pi$
$684$	−0.584650	+	10.2375i	−0.0223547	+	0.391440i
$685$	8.67579	+	8.67579i	0.331485	+	0.331485i
$686$	−9.14436	−	23.9898i	−0.349133	−	0.915933i
$687$	9.59635			0.366124
$688$	−28.0826	−	35.3515i	−1.07064	−	1.34777i
$689$	−24.4852			−0.932811
$690$	4.50997	+	11.8317i	0.171692	+	0.450424i
$691$	1.37557	+	1.37557i	0.0523291	+	0.0523291i	0.732787	−	0.680458i	$-0.238219\pi$
$691$	1.37557	+	1.37557i	0.0523291	+	0.0523291i	−0.680458	+	0.732787i	$0.738219\pi$
$692$	24.6681	+	1.40877i	0.937742	+	0.0535533i
$693$	7.35101	−	7.35101i	0.279242	−	0.279242i
$694$	10.2701	−	22.9222i	0.389846	−	0.870116i
$695$		−	18.0444i		−	0.684462i
$696$	−10.0960	−	5.23392i	−0.382689	−	0.198391i
$697$		−	56.3184i		−	2.13321i
$698$	−22.4705	−	10.0677i	−0.850521	−	0.381067i
$699$	19.7026	−	19.7026i	0.745220	−	0.745220i
$700$	−4.02284	+	3.58819i	−0.152049	+	0.135621i
$701$	27.0610	+	27.0610i	1.02208	+	1.02208i	0.999751	+	0.0223289i	$0.00710809\pi$
$701$	27.0610	+	27.0610i	1.02208	+	1.02208i	0.0223289	+	0.999751i	$0.492892\pi$
$702$	3.40967	−	1.29969i	0.128690	−	0.0490537i
$703$	−1.38029			−0.0520585
$704$	−30.4057	−	5.25505i	−1.14596	−	0.198057i
$705$	−1.31537			−0.0495397
$706$	−7.92199	+	3.01968i	−0.298148	+	0.113647i
$707$	18.5693	+	18.5693i	0.698372	+	0.698372i
$708$	−2.14167	+	1.91027i	−0.0804890	+	0.0717924i
$709$	−32.8479	+	32.8479i	−1.23363	+	1.23363i	−0.271068	+	0.962560i	$0.587377\pi$
$709$	−32.8479	+	32.8479i	−1.23363	+	1.23363i	−0.962560	+	0.271068i	$0.912623\pi$
$710$	−2.95365	−	1.32335i	−0.110849	−	0.0496645i
$711$		−	2.59319i		−	0.0972524i
$712$	−37.4007	−	19.3890i	−1.40165	−	0.726634i
$713$		−	30.2605i		−	1.13327i
$714$	11.4320	−	25.5156i	0.427832	−	0.954898i
$715$	−7.03717	+	7.03717i	−0.263175	+	0.263175i
$716$	16.1789	+	0.923956i	0.604633	+	0.0345298i
$717$	13.9433	+	13.9433i	0.520721	+	0.520721i
$718$	−2.49554	−	6.54692i	−0.0931327	−	0.244329i
$719$	−33.7746			−1.25958			−0.629791	−	0.776765i	$-0.716859\pi$
$719$	−33.7746			−1.25958			−0.629791	+	0.776765i	$0.716859\pi$
$720$	−3.13204	+	2.48803i	−0.116724	+	0.0927235i
$721$	−11.8404			−0.440958
$722$	3.67056	+	9.62952i	0.136604	+	0.358374i
$723$	−5.47487	−	5.47487i	−0.203612	−	0.203612i
$724$	−0.239184	+	4.18822i	−0.00888920	+	0.155654i
$725$	2.84302	−	2.84302i	0.105587	−	0.105587i
$726$	−2.24179	+	5.00355i	−0.0832006	+	0.185699i
$727$		−	7.54917i		−	0.279983i	−0.990153	−	0.139992i	$-0.955292\pi$
$727$		−	7.54917i		−	0.279983i	0.990153	−	0.139992i	$-0.0447075\pi$
$728$	−5.94673	−	18.7497i	−0.220401	−	0.694909i
$729$		−	1.00000i		−	0.0370370i
$730$	−1.69195	−	0.758062i	−0.0626220	−	0.0280571i
$731$	−58.5431	+	58.5431i	−2.16529	+	2.16529i
$732$	−4.49962	−	5.04468i	−0.166311	−	0.186457i
$733$	−13.2524	−	13.2524i	−0.489487	−	0.489487i	0.418657	−	0.908144i	$-0.362501\pi$
$733$	−13.2524	−	13.2524i	−0.489487	−	0.489487i	−0.908144	+	0.418657i	$0.862501\pi$
$734$	34.6617	−	13.2123i	1.27939	−	0.487674i
$735$	−0.264584			−0.00975933
$736$	49.0728	−	12.5346i	1.80885	−	0.462033i
$737$	−39.3925			−1.45104
$738$	−10.1460	+	3.86744i	−0.373481	+	0.142362i
$739$	4.42190	+	4.42190i	0.162662	+	0.162662i	0.783745	−	0.621083i	$-0.213307\pi$
$739$	4.42190	+	4.42190i	0.162662	+	0.162662i	−0.621083	+	0.783745i	$0.713307\pi$
$740$	−0.358400	−	0.401815i	−0.0131751	−	0.0147710i
$741$	9.35432	−	9.35432i	0.343639	−	0.343639i
$742$	33.0098	+	14.7897i	1.21183	+	0.542947i
$743$			45.5703i			1.67181i	0.548873	+	0.835906i	$0.315057\pi$
$743$			45.5703i			1.67181i	−0.548873	+	0.835906i	$0.684943\pi$
$744$	9.11209	−	2.89003i	0.334065	−	0.105954i
$745$			9.15332i			0.335352i
$746$	−7.01810	+	15.6640i	−0.256951	+	0.573501i
$747$	5.36584	−	5.36584i	0.196326	−	0.196326i
$748$	−3.22621	+	56.4923i	−0.117962	+	2.06556i
$749$	−19.1171	−	19.1171i	−0.698524	−	0.698524i
$750$	−0.503713	−	1.32147i	−0.0183930	−	0.0482531i
$751$	10.6007			0.386824			0.193412	−	0.981118i	$-0.438045\pi$
$751$	10.6007			0.386824			0.193412	+	0.981118i	$0.438045\pi$
$752$	−0.598999	+	5.22727i	−0.0218433	+	0.190619i
$753$	−2.06867			−0.0753865
$754$	5.22558	+	13.7090i	0.190304	+	0.499254i
$755$	10.4498	+	10.4498i	0.380305	+	0.380305i
$756$	−5.38181	−	0.307348i	−0.195735	−	0.0111782i
$757$	−14.7340	+	14.7340i	−0.535517	+	0.535517i	−0.922209	−	0.386692i	$-0.873618\pi$
$757$	−14.7340	+	14.7340i	−0.535517	+	0.535517i	0.386692	+	0.922209i	$0.373618\pi$
$758$	3.30491	−	7.37637i	0.120040	−	0.267922i
$759$		−	34.5340i		−	1.25350i
$760$	−6.67426	+	12.8744i	−0.242101	+	0.467004i
$761$		−	8.89182i		−	0.322328i	−0.986928	−	0.161164i	$-0.948475\pi$
$761$		−	8.89182i		−	0.322328i	0.986928	−	0.161164i	$-0.0515248\pi$
$762$	11.0720	+	4.96071i	0.401098	+	0.179708i
$763$	21.1051	−	21.1051i	0.764055	−	0.764055i
$764$	1.50574	−	1.34305i	0.0544757	−	0.0485897i
$765$	5.18675	+	5.18675i	0.187527	+	0.187527i
$766$	−2.60957	+	0.994710i	−0.0942876	+	0.0359403i
$767$	3.70239			0.133686
$768$	8.46114	+	13.5797i	0.305315	+	0.490016i
$769$	32.7022			1.17927			0.589636	−	0.807669i	$-0.299271\pi$
$769$	32.7022			1.17927			0.589636	+	0.807669i	$0.299271\pi$
$770$	13.7378	−	5.23655i	0.495077	−	0.188712i
$771$	−14.6148	−	14.6148i	−0.526338	−	0.526338i
$772$	−29.8916	+	26.6619i	−1.07582	+	0.959584i
$773$	12.4209	−	12.4209i	0.446747	−	0.446747i	−0.447525	−	0.894272i	$-0.647694\pi$
$773$	12.4209	−	12.4209i	0.446747	−	0.446747i	0.894272	+	0.447525i	$0.147694\pi$
$774$	14.5670	+	6.52661i	0.523601	+	0.234594i
$775$			3.37977i			0.121405i
$776$	0.904329	−	1.74442i	0.0324635	−	0.0626210i
$777$		−	0.725612i		−	0.0260312i
$778$	22.0830	−	49.2881i	0.791715	−	1.76706i
$779$	−27.8353	+	27.8353i	−0.997303	+	0.997303i
$780$	5.15204	+	0.294227i	0.184473	+	0.0105350i
$781$	6.24180	+	6.24180i	0.223349	+	0.223349i
$782$	−33.0814	−	86.7873i	−1.18299	−	3.10351i
$783$	4.02063			0.143686
$784$	−0.120488	+	1.05146i	−0.00430313	+	0.0375520i
$785$	−19.8824			−0.709633
$786$	3.80242	+	9.97545i	0.135628	+	0.355812i
$787$	−22.6663	−	22.6663i	−0.807965	−	0.807965i	0.176361	−	0.984326i	$-0.443567\pi$
$787$	−22.6663	−	22.6663i	−0.807965	−	0.807965i	−0.984326	+	0.176361i	$0.943567\pi$
$788$	−2.05798	+	36.0362i	−0.0733125	+	1.28374i
$789$	18.6138	−	18.6138i	0.662668	−	0.662668i
$790$	1.49948	−	3.34677i	0.0533493	−	0.119073i
$791$			12.5015i			0.444502i
$792$	10.3989	−	3.29817i	0.369509	−	0.117195i
$793$			8.72093i			0.309689i
$794$	−24.2655	−	10.8719i	−0.861149	−	0.385829i
$795$	−6.71014	+	6.71014i	−0.237984	+	0.237984i
$796$	15.5266	+	17.4075i	0.550327	+	0.616991i
$797$	7.47619	+	7.47619i	0.264820	+	0.264820i	0.827009	−	0.562189i	$-0.190041\pi$
$797$	7.47619	+	7.47619i	0.264820	+	0.264820i	−0.562189	+	0.827009i	$0.690041\pi$
$798$	−18.2613	+	6.96080i	−0.646443	+	0.246410i
$799$	9.64846			0.341338
$800$	−5.48088	+	1.39998i	−0.193778	+	0.0494967i
$801$	14.8944			0.526268
$802$	5.25801	−	2.00424i	0.185667	−	0.0707721i
$803$	3.57552	+	3.57552i	0.126177	+	0.126177i
$804$	13.5965	+	15.2435i	0.479510	+	0.537596i
$805$	−17.0640	+	17.0640i	−0.601427	+	0.601427i
$806$	−11.2547	−	5.04255i	−0.396430	−	0.177616i
$807$			25.1912i			0.886771i
$808$	8.33149	+	26.2686i	0.293101	+	0.924128i
$809$		−	9.20349i		−	0.323577i	−0.986825	−	0.161789i	$-0.948274\pi$
$809$		−	9.20349i		−	0.323577i	0.986825	−	0.161789i	$-0.0517263\pi$
$810$	0.578239	−	1.29060i	0.0203172	−	0.0453470i
$811$	31.0252	−	31.0252i	1.08944	−	1.08944i	0.0938555	−	0.995586i	$-0.470081\pi$
$811$	31.0252	−	31.0252i	1.08944	−	1.08944i	0.995586	−	0.0938555i	$-0.0299192\pi$
$812$	1.23573	−	21.6383i	0.0433658	−	0.759355i
$813$	5.09010	+	5.09010i	0.178517	+	0.178517i
$814$	0.523045	+	1.37218i	0.0183327	+	0.0480949i
$815$	−2.96728			−0.103939
$816$	22.9741	−	18.2501i	0.804253	−	0.638882i
$817$	57.8697			2.02460
$818$	−11.8922	−	31.1987i	−0.415802	−	1.09084i
$819$	4.91753	+	4.91753i	0.171832	+	0.171832i
$820$	−15.3307	−	0.875519i	−0.535373	−	0.0305745i
$821$	5.31973	−	5.31973i	0.185660	−	0.185660i	−0.608157	−	0.793817i	$-0.708091\pi$
$821$	5.31973	−	5.31973i	0.185660	−	0.185660i	0.793817	+	0.608157i	$0.208091\pi$
$822$	−7.09465	+	15.8349i	−0.247454	+	0.552305i
$823$			24.8425i			0.865956i	0.901404	+	0.432978i	$0.142537\pi$
$823$			24.8425i			0.865956i	−0.901404	+	0.432978i	$0.857463\pi$
$824$	−11.0310	−	5.71863i	−0.384285	−	0.199218i
$825$			3.85706i			0.134286i
$826$	−4.99139	−	2.23634i	−0.173673	−	0.0778122i
$827$	11.8871	−	11.8871i	0.413354	−	0.413354i	−0.469551	−	0.882905i	$-0.655584\pi$
$827$	11.8871	−	11.8871i	0.413354	−	0.413354i	0.882905	+	0.469551i	$0.155584\pi$
$828$	−13.3634	+	11.9195i	−0.464411	+	0.414233i
$829$	6.17740	+	6.17740i	0.214550	+	0.214550i	0.806197	−	0.591647i	$-0.201522\pi$
$829$	6.17740	+	6.17740i	0.214550	+	0.214550i	−0.591647	+	0.806197i	$0.701522\pi$
$830$	10.0279	−	3.82240i	0.348072	−	0.132677i
$831$	−14.8021			−0.513478
$832$	3.51542	−	20.3402i	0.121875	−	0.705169i
$833$	1.94077			0.0672436
$834$	23.8450	−	9.08919i	0.825686	−	0.314733i
$835$	11.1491	+	11.1491i	0.385831	+	0.385831i
$836$	29.5158	−	26.3267i	1.02083	−	0.910528i
$837$	−2.38986	+	2.38986i	−0.0826055	+	0.0826055i
$838$	−24.7788	−	11.1019i	−0.855969	−	0.383508i
$839$			8.14180i			0.281086i	0.990075	+	0.140543i	$0.0448848\pi$
$839$			8.14180i			0.281086i	−0.990075	+	0.140543i	$0.955115\pi$
$840$	−6.76803	−	3.50863i	−0.233519	−	0.121059i
$841$		−	12.8345i		−	0.442570i
$842$	7.60646	−	16.9772i	0.262136	−	0.585073i
$843$	−12.0609	+	12.0609i	−0.415400	+	0.415400i
$844$	−1.18394	−	0.0676136i	−0.0407531	−	0.00232736i
$845$	4.48480	+	4.48480i	0.154282	+	0.154282i
$846$	−0.662570	−	1.73822i	−0.0227796	−	0.0597611i
$847$	−10.4494			−0.359047
$848$	23.6104	+	29.7218i	0.810783	+	1.02065i
$849$	−3.82866			−0.131399
$850$	3.69482	+	9.69317i	0.126731	+	0.332473i
$851$	−1.70441	−	1.70441i	−0.0584264	−	0.0584264i
$852$	0.260972	−	4.56974i	0.00894076	−	0.156557i
$853$	27.9298	−	27.9298i	0.956297	−	0.956297i	−0.0427875	−	0.999084i	$-0.513624\pi$
$853$	27.9298	−	27.9298i	0.956297	−	0.956297i	0.999084	+	0.0427875i	$0.0136239\pi$
$854$	5.26767	−	11.7572i	0.180256	−	0.402322i
$855$		−	5.12708i		−	0.175343i
$856$	−8.57726	−	27.0435i	−0.293165	−	0.924329i
$857$			20.7075i			0.707356i	0.935367	+	0.353678i	$0.115069\pi$
$857$			20.7075i			0.707356i	−0.935367	+	0.353678i	$0.884931\pi$
$858$	−12.8441	−	5.75467i	−0.438490	−	0.196461i
$859$	−12.8547	+	12.8547i	−0.438597	+	0.438597i	−0.891539	−	0.452943i	$-0.850374\pi$
$859$	−12.8547	+	12.8547i	−0.438597	+	0.438597i	0.452943	+	0.891539i	$0.350374\pi$
$860$	15.0262	+	16.8464i	0.512390	+	0.574459i
$861$	−14.6329	−	14.6329i	−0.498688	−	0.498688i
$862$	8.46274	−	3.22581i	0.288242	−	0.109872i
$863$	11.9606			0.407143			0.203572	−	0.979060i	$-0.434745\pi$
$863$	11.9606			0.407143			0.203572	+	0.979060i	$0.434745\pi$
$864$	−4.86550	−	2.88563i	−0.165528	−	0.0981713i
$865$	−12.3542			−0.420054
$866$	−44.8286	+	17.0877i	−1.52334	+	0.580663i
$867$	−26.0248	−	26.0248i	−0.883850	−	0.883850i
$868$	12.1272	+	13.5963i	0.411625	+	0.461487i
$869$	−7.07256	+	7.07256i	−0.239920	+	0.239920i
$870$	5.18902	+	2.32488i	0.175924	+	0.0788210i
$871$		−	26.3520i		−	0.892902i
$872$	29.8557	−	9.46919i	1.01104	−	0.320667i
$873$			0.694695i			0.0235119i
$874$	−26.5441	+	59.2449i	−0.897867	+	2.00399i
$875$	1.90586	−	1.90586i	0.0644297	−	0.0644297i
$876$	0.149494	−	2.61770i	0.00505093	−	0.0884440i
$877$	6.15758	+	6.15758i	0.207927	+	0.207927i	0.803386	−	0.595459i	$-0.203030\pi$
$877$	6.15758	+	6.15758i	0.207927	+	0.207927i	−0.595459	+	0.803386i	$0.703030\pi$
$878$	2.00372	+	5.25665i	0.0676222	+	0.177403i
$879$	−23.5600			−0.794659
$880$	15.3279	+	1.75645i	0.516705	+	0.0592098i
$881$	−19.5267			−0.657871			−0.328936	−	0.944352i	$-0.606690\pi$
$881$	−19.5267			−0.657871			−0.328936	+	0.944352i	$0.606690\pi$
$882$	−0.133275	−	0.349639i	−0.00448759	−	0.0117730i
$883$	17.6166	+	17.6166i	0.592845	+	0.592845i	0.938399	−	0.345554i	$-0.112309\pi$
$883$	17.6166	+	17.6166i	0.592845	+	0.592845i	−0.345554	+	0.938399i	$0.612309\pi$
$884$	−37.7911	−	2.15820i	−1.27105	−	0.0725882i
$885$	1.01464	−	1.01464i	0.0341066	−	0.0341066i
$886$	11.9071	−	26.5760i	0.400027	−	0.892838i
$887$			29.2567i			0.982343i	0.871063	+	0.491172i	$0.163431\pi$
$887$			29.2567i			0.982343i	−0.871063	+	0.491172i	$0.836569\pi$
$888$	0.350454	−	0.676014i	0.0117605	−	0.0226855i
$889$			23.1229i			0.775518i
$890$	19.2227	+	8.61251i	0.644345	+	0.288692i
$891$	−2.72735	+	2.72735i	−0.0913698	+	0.0913698i
$892$	−30.4100	+	27.1242i	−1.01820	+	0.908187i
$893$	−4.76874	−	4.76874i	−0.159580	−	0.159580i
$894$	−12.0958	+	4.61065i	−0.404544	+	0.154203i
$895$	−8.10262			−0.270841
$896$	−17.0253	+	25.2983i	−0.568777	+	0.845157i
$897$	23.1018			0.771348
$898$	15.0222	−	5.72613i	0.501297	−	0.191083i
$899$	−9.60873	−	9.60873i	−0.320469	−	0.320469i
$900$	1.49255	−	1.33128i	0.0497515	−	0.0443760i
$901$	49.2200	−	49.2200i	1.63976	−	1.63976i
$902$	38.2197	+	17.1239i	1.27258	+	0.570165i
$903$			30.4219i			1.01238i
$904$	−6.03795	+	11.6470i	−0.200819	+	0.387373i
$905$		−	2.09752i		−	0.0697240i
$906$	−8.54531	+	19.0727i	−0.283899	+	0.633647i
$907$	32.6905	−	32.6905i	1.08547	−	1.08547i	0.0894835	−	0.995988i	$-0.471478\pi$
$907$	32.6905	−	32.6905i	1.08547	−	1.08547i	0.995988	−	0.0894835i	$-0.0285216\pi$
$908$	8.11793	+	0.463605i	0.269403	+	0.0153853i
$909$	−6.88955	−	6.88955i	−0.228512	−	0.228512i
$910$	3.50304	+	9.19005i	0.116125	+	0.304647i
$911$	−44.0834			−1.46055			−0.730275	−	0.683153i	$-0.760608\pi$
$911$	−44.0834			−1.46055			−0.730275	+	0.683153i	$0.760608\pi$
$912$	−20.3750	−	2.33480i	−0.674684	−	0.0773128i
$913$	−29.2691			−0.968665
$914$	19.6897	+	51.6550i	0.651279	+	1.70860i
$915$	2.38996	+	2.38996i	0.0790098	+	0.0790098i
$916$	−1.09429	+	19.1615i	−0.0361563	+	0.633113i
$917$	−14.3869	+	14.3869i	−0.475097	+	0.475097i
$918$	−4.24148	+	9.46674i	−0.139990	+	0.312449i
$919$			21.4544i			0.707716i	0.935299	+	0.353858i	$0.115130\pi$
$919$			21.4544i			0.707716i	−0.935299	+	0.353858i	$0.884870\pi$
$920$	−24.1391	+	7.65608i	−0.795844	+	0.252414i
$921$		−	25.7374i		−	0.848076i
$922$	−11.0513	−	4.95142i	−0.363956	−	0.163066i
$923$	−4.17551	+	4.17551i	−0.137439	+	0.137439i
$924$	13.8399	+	15.5164i	0.455298	+	0.510450i
$925$	0.190364	+	0.190364i	0.00625912	+	0.00625912i
$926$	47.7544	−	18.2029i	1.56931	−	0.598185i
$927$	4.39299			0.144285
$928$	11.6021	−	19.5624i	0.380857	−	0.642167i
$929$	33.6688			1.10464			0.552318	−	0.833634i	$-0.313743\pi$
$929$	33.6688			1.10464			0.552318	+	0.833634i	$0.313743\pi$
$930$	−4.46625	+	1.70243i	−0.146454	+	0.0558250i
$931$	−0.959222	−	0.959222i	−0.0314372	−	0.0314372i
$932$	37.0944	+	41.5878i	1.21507	+	1.36225i
$933$	−10.8847	+	10.8847i	−0.356349	+	0.356349i
$934$	−23.8899	−	10.7036i	−0.781700	−	0.350233i
$935$		−	28.2922i		−	0.925254i
$936$	2.20634	+	6.95646i	0.0721166	+	0.227379i
$937$		−	10.5938i		−	0.346084i	−0.984914	−	0.173042i	$-0.944640\pi$
$937$		−	10.5938i		−	0.346084i	0.984914	−	0.173042i	$-0.0553596\pi$
$938$	−15.9173	+	35.5265i	−0.519718	+	1.15998i
$939$	16.8143	−	16.8143i	0.548713	−	0.548713i
$940$	0.149994	−	2.62646i	0.00489226	−	0.0856657i
$941$	7.72584	+	7.72584i	0.251855	+	0.251855i	0.821731	−	0.569876i	$-0.193009\pi$
$941$	7.72584	+	7.72584i	0.251855	+	0.251855i	−0.569876	+	0.821731i	$0.693009\pi$
$942$	−10.0150	−	26.2739i	−0.326307	−	0.856050i
$943$	−68.7433			−2.23859
$944$	−3.57011	−	4.49421i	−0.116197	−	0.146274i
$945$	2.69529			0.0876778
$946$	−21.9291	−	57.5299i	−0.712977	−	1.87046i
$947$	21.4749	+	21.4749i	0.697841	+	0.697841i	0.963945	−	0.266103i	$-0.0857362\pi$
$947$	21.4749	+	21.4749i	0.697841	+	0.697841i	−0.266103	+	0.963945i	$0.585736\pi$
$948$	5.17795	+	0.295706i	0.168172	+	0.00960409i
$949$	−2.39188	+	2.39188i	−0.0776437	+	0.0776437i
$950$	2.96468	−	6.61700i	0.0961868	−	0.214684i
$951$			13.1474i			0.426334i
$952$	49.6446	+	25.7364i	1.60899	+	0.834122i
$953$		−	29.0291i		−	0.940344i	−0.882575	−	0.470172i	$-0.844192\pi$
$953$		−	29.0291i		−	0.940344i	0.882575	−	0.470172i	$-0.155808\pi$
$954$	−12.2472	−	5.48724i	−0.396518	−	0.177656i
$955$	−0.713357	+	0.713357i	−0.0230837	+	0.0230837i
$956$	−29.4312	+	26.2512i	−0.951872	+	0.849025i
$957$	−10.9657	−	10.9657i	−0.354470	−	0.354470i
$958$	−5.00765	+	1.90881i	−0.161790	+	0.0616707i
$959$	−33.0696			−1.06787
$960$	−4.61082	−	6.53761i	−0.148813	−	0.211000i
$961$	−19.5772			−0.631522
$962$	−0.917934	+	0.349896i	−0.0295954	+	0.0112811i
$963$	7.09279	+	7.09279i	0.228562	+	0.228562i
$964$	11.5562	−	10.3076i	0.372201	−	0.331986i
$965$	14.1614	−	14.1614i	0.455873	−	0.455873i
$966$	−31.1448	−	13.9541i	−1.00207	−	0.448967i
$967$			4.50118i			0.144748i	0.997378	+	0.0723741i	$0.0230576\pi$
$967$			4.50118i			0.144748i	−0.997378	+	0.0723741i	$0.976942\pi$
$968$	−9.73519	−	5.04685i	−0.312901	−	0.162212i
$969$			37.6080i			1.20814i
$970$	−0.401699	+	0.896571i	−0.0128978	+	0.0287872i
$971$	30.6131	−	30.6131i	0.982420	−	0.982420i	−0.0174280	−	0.999848i	$-0.505548\pi$
$971$	30.6131	−	30.6131i	0.982420	−	0.982420i	0.999848	+	0.0174280i	$0.00554777\pi$
$972$	1.99675	+	0.114032i	0.0640457	+	0.00365757i
$973$	34.3900	+	34.3900i	1.10249	+	1.10249i
$974$	−1.71194	−	4.49119i	−0.0548542	−	0.143907i
$975$	−2.58022			−0.0826331
$976$	10.5861	−	8.40935i	0.338851	−	0.269177i
$977$	−36.6473			−1.17245			−0.586225	−	0.810148i	$-0.699387\pi$
$977$	−36.6473			−1.17245			−0.586225	+	0.810148i	$0.699387\pi$
$978$	−1.49466	−	3.92116i	−0.0477940	−	0.125385i
$979$	−40.6223	−	40.6223i	−1.29829	−	1.29829i
$980$	0.0301710	−	0.528307i	0.000963776	−	0.0168762i
$981$	−7.83035	+	7.83035i	−0.250004	+	0.250004i
$982$	−7.12180	+	15.8955i	−0.227266	+	0.507244i
$983$			16.3748i			0.522276i	0.965301	+	0.261138i	$0.0840978\pi$
$983$			16.3748i			0.522276i	−0.965301	+	0.261138i	$0.915902\pi$
$984$	−6.56533	−	20.7001i	−0.209295	−	0.659894i
$985$		−	18.0474i		−	0.575039i
$986$	−38.0623	−	17.0534i	−1.21215	−	0.543091i
$987$	2.50691	−	2.50691i	0.0797957	−	0.0797957i
$988$	17.6115	+	19.7449i	0.560297	+	0.628168i
$989$	71.4588	+	71.4588i	2.27226	+	2.27226i
$990$	−5.09698	+	1.94285i	−0.161993	+	0.0617479i
$991$	13.8052			0.438537			0.219269	−	0.975665i	$-0.429633\pi$
$991$	13.8052			0.438537			0.219269	+	0.975665i	$0.429633\pi$
$992$	4.73160	+	18.5241i	0.150228	+	0.588141i
$993$	21.2929			0.675710
$994$	8.15136	−	3.10712i	0.258545	−	0.0985517i
$995$	−8.24694	−	8.24694i	−0.261446	−	0.261446i
$996$	10.1023	+	11.3261i	0.320105	+	0.358881i
$997$	10.9547	−	10.9547i	0.346938	−	0.346938i	−0.512030	−	0.858968i	$-0.671106\pi$
$997$	10.9547	−	10.9547i	0.346938	−	0.346938i	0.858968	+	0.512030i	$0.171106\pi$
$998$	−29.1194	−	13.0466i	−0.921757	−	0.412984i
$999$			0.269215i			0.00851758i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	240.2.s.c.61.10	✓	20
3.2	odd	2		720.2.t.d.541.1		20
4.3	odd	2		960.2.s.c.721.10		20
8.3	odd	2		1920.2.s.f.1441.5		20
8.5	even	2		1920.2.s.e.1441.6		20
12.11	even	2		2880.2.t.d.721.10		20
16.3	odd	4		1920.2.s.f.481.1		20
16.5	even	4	inner	240.2.s.c.181.10	yes	20
16.11	odd	4		960.2.s.c.241.6		20
16.13	even	4		1920.2.s.e.481.10		20
48.5	odd	4		720.2.t.d.181.1		20
48.11	even	4		2880.2.t.d.2161.6		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.s.c.61.10	✓	20	1.1	even	1	trivial
240.2.s.c.181.10	yes	20	16.5	even	4	inner
720.2.t.d.181.1		20	48.5	odd	4
720.2.t.d.541.1		20	3.2	odd	2
960.2.s.c.241.6		20	16.11	odd	4
960.2.s.c.721.10		20	4.3	odd	2
1920.2.s.e.481.10		20	16.13	even	4
1920.2.s.e.1441.6		20	8.5	even	2
1920.2.s.f.481.1		20	16.3	odd	4
1920.2.s.f.1441.5		20	8.3	odd	2
2880.2.t.d.721.10		20	12.11	even	2
2880.2.t.d.2161.6		20	48.11	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.s (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.32147 - 0.503713i) q^{2} +(-0.707107 - 0.707107i) q^{3} +(1.49255 - 1.33128i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(-1.29060 - 0.578239i) q^{6} -2.69529i q^{7} +(1.30176 - 2.51106i) q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+(1.32147 - 0.503713i) q^{2} +(-0.707107 - 0.707107i) q^{3} +(1.49255 - 1.33128i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(-1.29060 - 0.578239i) q^{6} -2.69529i q^{7} +(1.30176 - 2.51106i) q^{8} +1.00000i q^{9} +(-0.578239 + 1.29060i) q^{10} +(2.72735 - 2.72735i) q^{11} +(-1.99675 - 0.114032i) q^{12} +(1.82449 + 1.82449i) q^{13} +(-1.35765 - 3.56173i) q^{14} +1.00000 q^{15} +(0.455385 - 3.97399i) q^{16} -7.33517 q^{17} +(0.503713 + 1.32147i) q^{18} +(3.62540 + 3.62540i) q^{19} +(-0.114032 + 1.99675i) q^{20} +(-1.90586 + 1.90586i) q^{21} +(2.23030 - 4.97791i) q^{22} +8.95345i q^{23} +(-2.69607 + 0.855099i) q^{24} -1.00000i q^{25} +(3.33002 + 1.49198i) q^{26} +(0.707107 - 0.707107i) q^{27} +(-3.58819 - 4.02284i) q^{28} +(2.84302 + 2.84302i) q^{29} +(1.32147 - 0.503713i) q^{30} -3.37977 q^{31} +(-1.39998 - 5.48088i) q^{32} -3.85706 q^{33} +(-9.69317 + 3.69482i) q^{34} +(1.90586 + 1.90586i) q^{35} +(1.33128 + 1.49255i) q^{36} +(-0.190364 + 0.190364i) q^{37} +(6.61700 + 2.96468i) q^{38} -2.58022i q^{39} +(0.855099 + 2.69607i) q^{40} +7.67786i q^{41} +(-1.55852 + 3.47853i) q^{42} +(7.98115 - 7.98115i) q^{43} +(0.439827 - 7.70158i) q^{44} +(-0.707107 - 0.707107i) q^{45} +(4.50997 + 11.8317i) q^{46} -1.31537 q^{47} +(-3.13204 + 2.48803i) q^{48} -0.264584 q^{49} +(-0.503713 - 1.32147i) q^{50} +(5.18675 + 5.18675i) q^{51} +(5.15204 + 0.294227i) q^{52} +(-6.71014 + 6.71014i) q^{53} +(0.578239 - 1.29060i) q^{54} +3.85706i q^{55} +(-6.76803 - 3.50863i) q^{56} -5.12708i q^{57} +(5.18902 + 2.32488i) q^{58} +(1.01464 - 1.01464i) q^{59} +(1.49255 - 1.33128i) q^{60} +(2.38996 + 2.38996i) q^{61} +(-4.46625 + 1.70243i) q^{62} +2.69529 q^{63} +(-4.61082 - 6.53761i) q^{64} -2.58022 q^{65} +(-5.09698 + 1.94285i) q^{66} +(-7.22173 - 7.22173i) q^{67} +(-10.9481 + 9.76516i) q^{68} +(6.33104 - 6.33104i) q^{69} +(3.47853 + 1.55852i) q^{70} +2.28859i q^{71} +(2.51106 + 1.30176i) q^{72} +1.31098i q^{73} +(-0.155670 + 0.347448i) q^{74} +(-0.707107 + 0.707107i) q^{75} +(10.2375 + 0.584650i) q^{76} +(-7.35101 - 7.35101i) q^{77} +(-1.29969 - 3.40967i) q^{78} -2.59319 q^{79} +(2.48803 + 3.13204i) q^{80} -1.00000 q^{81} +(3.86744 + 10.1460i) q^{82} +(-5.36584 - 5.36584i) q^{83} +(-0.307348 + 5.38181i) q^{84} +(5.18675 - 5.18675i) q^{85} +(6.52661 - 14.5670i) q^{86} -4.02063i q^{87} +(-3.29817 - 10.3989i) q^{88} -14.8944i q^{89} +(-1.29060 - 0.578239i) q^{90} +(4.91753 - 4.91753i) q^{91} +(11.9195 + 13.3634i) q^{92} +(2.38986 + 2.38986i) q^{93} +(-1.73822 + 0.662570i) q^{94} -5.12708 q^{95} +(-2.88563 + 4.86550i) q^{96} +0.694695 q^{97} +(-0.349639 + 0.133275i) q^{98} +(2.72735 + 2.72735i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{4} + 12 q^{8}+O(q^{10}) \) 20 * q + 4 * q^4 + 12 * q^8	\( 20 q + 4 q^{4} + 12 q^{8} + 8 q^{11} - 4 q^{14} + 20 q^{15} - 20 q^{16} - 24 q^{17} - 4 q^{18} - 4 q^{19} - 8 q^{20} + 8 q^{22} + 28 q^{26} - 8 q^{28} + 16 q^{29} - 40 q^{32} + 16 q^{33} - 44 q^{34} + 16 q^{37} - 8 q^{38} + 12 q^{40} + 12 q^{42} - 8 q^{43} + 24 q^{44} - 12 q^{46} - 16 q^{48} - 52 q^{49} + 4 q^{50} + 4 q^{51} - 56 q^{52} - 16 q^{53} + 64 q^{56} + 72 q^{58} - 16 q^{59} + 4 q^{60} - 4 q^{61} - 44 q^{62} - 8 q^{63} - 56 q^{64} - 32 q^{66} - 8 q^{67} - 32 q^{68} - 4 q^{69} + 20 q^{70} + 4 q^{72} + 60 q^{74} + 28 q^{76} - 40 q^{77} - 28 q^{78} + 56 q^{79} - 16 q^{80} - 20 q^{81} - 24 q^{82} - 48 q^{83} + 24 q^{84} + 4 q^{85} + 64 q^{86} + 40 q^{88} - 8 q^{91} + 88 q^{92} + 16 q^{93} - 20 q^{94} + 56 q^{97} - 48 q^{98} + 8 q^{99}+O(q^{100}) \) 20 * q + 4 * q^4 + 12 * q^8 + 8 * q^11 - 4 * q^14 + 20 * q^15 - 20 * q^16 - 24 * q^17 - 4 * q^18 - 4 * q^19 - 8 * q^20 + 8 * q^22 + 28 * q^26 - 8 * q^28 + 16 * q^29 - 40 * q^32 + 16 * q^33 - 44 * q^34 + 16 * q^37 - 8 * q^38 + 12 * q^40 + 12 * q^42 - 8 * q^43 + 24 * q^44 - 12 * q^46 - 16 * q^48 - 52 * q^49 + 4 * q^50 + 4 * q^51 - 56 * q^52 - 16 * q^53 + 64 * q^56 + 72 * q^58 - 16 * q^59 + 4 * q^60 - 4 * q^61 - 44 * q^62 - 8 * q^63 - 56 * q^64 - 32 * q^66 - 8 * q^67 - 32 * q^68 - 4 * q^69 + 20 * q^70 + 4 * q^72 + 60 * q^74 + 28 * q^76 - 40 * q^77 - 28 * q^78 + 56 * q^79 - 16 * q^80 - 20 * q^81 - 24 * q^82 - 48 * q^83 + 24 * q^84 + 4 * q^85 + 64 * q^86 + 40 * q^88 - 8 * q^91 + 88 * q^92 + 16 * q^93 - 20 * q^94 + 56 * q^97 - 48 * q^98 + 8 * q^99

Introduction

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