LMFDB - Embedded newform 570.2.f.b.341.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(341,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

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

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

chi := DirichletCharacter("570.341");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.f (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			341.3
Root			$-0.707107 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	570.341
Dual form			570.2.f.b.341.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(1.00000 + 1.41421i) q^{3} +1.00000 q^{4} -1.00000i q^{5} +(1.00000 + 1.41421i) q^{6} +0.585786 q^{7} +1.00000 q^{8} +(-1.00000 + 2.82843i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(1.00000 + 1.41421i) q^{3} +1.00000 q^{4} -1.00000i q^{5} +(1.00000 + 1.41421i) q^{6} +0.585786 q^{7} +1.00000 q^{8} +(-1.00000 + 2.82843i) q^{9} -1.00000i q^{10} +5.41421i q^{11} +(1.00000 + 1.41421i) q^{12} -2.24264i q^{13} +0.585786 q^{14} +(1.41421 - 1.00000i) q^{15} +1.00000 q^{16} +2.82843i q^{17} +(-1.00000 + 2.82843i) q^{18} +(4.24264 - 1.00000i) q^{19} -1.00000i q^{20} +(0.585786 + 0.828427i) q^{21} +5.41421i q^{22} -6.00000i q^{23} +(1.00000 + 1.41421i) q^{24} -1.00000 q^{25} -2.24264i q^{26} +(-5.00000 + 1.41421i) q^{27} +0.585786 q^{28} +5.07107 q^{29} +(1.41421 - 1.00000i) q^{30} -6.82843i q^{31} +1.00000 q^{32} +(-7.65685 + 5.41421i) q^{33} +2.82843i q^{34} -0.585786i q^{35} +(-1.00000 + 2.82843i) q^{36} -2.24264i q^{37} +(4.24264 - 1.00000i) q^{38} +(3.17157 - 2.24264i) q^{39} -1.00000i q^{40} -11.0711 q^{41} +(0.585786 + 0.828427i) q^{42} +6.58579 q^{43} +5.41421i q^{44} +(2.82843 + 1.00000i) q^{45} -6.00000i q^{46} +3.17157i q^{47} +(1.00000 + 1.41421i) q^{48} -6.65685 q^{49} -1.00000 q^{50} +(-4.00000 + 2.82843i) q^{51} -2.24264i q^{52} -3.17157 q^{53} +(-5.00000 + 1.41421i) q^{54} +5.41421 q^{55} +0.585786 q^{56} +(5.65685 + 5.00000i) q^{57} +5.07107 q^{58} -12.8284 q^{59} +(1.41421 - 1.00000i) q^{60} -4.48528 q^{61} -6.82843i q^{62} +(-0.585786 + 1.65685i) q^{63} +1.00000 q^{64} -2.24264 q^{65} +(-7.65685 + 5.41421i) q^{66} +2.82843i q^{68} +(8.48528 - 6.00000i) q^{69} -0.585786i q^{70} -2.82843 q^{71} +(-1.00000 + 2.82843i) q^{72} +2.48528 q^{73} -2.24264i q^{74} +(-1.00000 - 1.41421i) q^{75} +(4.24264 - 1.00000i) q^{76} +3.17157i q^{77} +(3.17157 - 2.24264i) q^{78} -13.3137i q^{79} -1.00000i q^{80} +(-7.00000 - 5.65685i) q^{81} -11.0711 q^{82} -12.8284i q^{83} +(0.585786 + 0.828427i) q^{84} +2.82843 q^{85} +6.58579 q^{86} +(5.07107 + 7.17157i) q^{87} +5.41421i q^{88} +10.5858 q^{89} +(2.82843 + 1.00000i) q^{90} -1.31371i q^{91} -6.00000i q^{92} +(9.65685 - 6.82843i) q^{93} +3.17157i q^{94} +(-1.00000 - 4.24264i) q^{95} +(1.00000 + 1.41421i) q^{96} -6.58579i q^{97} -6.65685 q^{98} +(-15.3137 - 5.41421i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} + 4 q^{6} + 8 q^{7} + 4 q^{8} - 4 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 + 4 * q^6 + 8 * q^7 + 4 * q^8 - 4 * q^9	$ 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} + 4 q^{6} + 8 q^{7} + 4 q^{8} - 4 q^{9} + 4 q^{12} + 8 q^{14} + 4 q^{16} - 4 q^{18} + 8 q^{21} + 4 q^{24} - 4 q^{25} - 20 q^{27} + 8 q^{28} - 8 q^{29} + 4 q^{32} - 8 q^{33} - 4 q^{36} + 24 q^{39} - 16 q^{41} + 8 q^{42} + 32 q^{43} + 4 q^{48} - 4 q^{49} - 4 q^{50} - 16 q^{51} - 24 q^{53} - 20 q^{54} + 16 q^{55} + 8 q^{56} - 8 q^{58} - 40 q^{59} + 16 q^{61} - 8 q^{63} + 4 q^{64} + 8 q^{65} - 8 q^{66} - 4 q^{72} - 24 q^{73} - 4 q^{75} + 24 q^{78} - 28 q^{81} - 16 q^{82} + 8 q^{84} + 32 q^{86} - 8 q^{87} + 48 q^{89} + 16 q^{93} - 4 q^{95} + 4 q^{96} - 4 q^{98} - 16 q^{99}+O(q^{100}) $ 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 + 4 * q^6 + 8 * q^7 + 4 * q^8 - 4 * q^9 + 4 * q^12 + 8 * q^14 + 4 * q^16 - 4 * q^18 + 8 * q^21 + 4 * q^24 - 4 * q^25 - 20 * q^27 + 8 * q^28 - 8 * q^29 + 4 * q^32 - 8 * q^33 - 4 * q^36 + 24 * q^39 - 16 * q^41 + 8 * q^42 + 32 * q^43 + 4 * q^48 - 4 * q^49 - 4 * q^50 - 16 * q^51 - 24 * q^53 - 20 * q^54 + 16 * q^55 + 8 * q^56 - 8 * q^58 - 40 * q^59 + 16 * q^61 - 8 * q^63 + 4 * q^64 + 8 * q^65 - 8 * q^66 - 4 * q^72 - 24 * q^73 - 4 * q^75 + 24 * q^78 - 28 * q^81 - 16 * q^82 + 8 * q^84 + 32 * q^86 - 8 * q^87 + 48 * q^89 + 16 * q^93 - 4 * q^95 + 4 * q^96 - 4 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$-1$	$1$

Coefficient data

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

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	1.00000	+	1.41421i	0.577350	+	0.816497i
$3$	1.00000	+	1.41421i	0.577350	+	0.816497i
$4$	1.00000			0.500000
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	1.00000	+	1.41421i	0.408248	+	0.577350i
$7$	0.585786			0.221406			0.110703	−	0.993854i	$-0.464690\pi$
$7$	0.585786			0.221406			0.110703	+	0.993854i	$0.464690\pi$
$8$	1.00000			0.353553
$9$	−1.00000	+	2.82843i	−0.333333	+	0.942809i
$10$		−	1.00000i		−	0.316228i
$11$			5.41421i			1.63245i	0.577736	+	0.816223i	$0.303936\pi$
$11$			5.41421i			1.63245i	−0.577736	+	0.816223i	$0.696064\pi$
$12$	1.00000	+	1.41421i	0.288675	+	0.408248i
$13$		−	2.24264i		−	0.621997i	−0.950410	−	0.310998i	$-0.899337\pi$
$13$		−	2.24264i		−	0.621997i	0.950410	−	0.310998i	$-0.100663\pi$
$14$	0.585786			0.156558
$15$	1.41421	−	1.00000i	0.365148	−	0.258199i
$16$	1.00000			0.250000
$17$			2.82843i			0.685994i	0.939336	+	0.342997i	$0.111442\pi$
$17$			2.82843i			0.685994i	−0.939336	+	0.342997i	$0.888558\pi$
$18$	−1.00000	+	2.82843i	−0.235702	+	0.666667i
$19$	4.24264	−	1.00000i	0.973329	−	0.229416i
$19$	4.24264	−	1.00000i	0.973329	−	0.229416i
$20$		−	1.00000i		−	0.223607i
$21$	0.585786	+	0.828427i	0.127829	+	0.180778i
$22$			5.41421i			1.15431i
$23$		−	6.00000i		−	1.25109i	−0.780189	−	0.625543i	$-0.784877\pi$
$23$		−	6.00000i		−	1.25109i	0.780189	−	0.625543i	$-0.215123\pi$
$24$	1.00000	+	1.41421i	0.204124	+	0.288675i
$25$	−1.00000			−0.200000
$26$		−	2.24264i		−	0.439818i
$27$	−5.00000	+	1.41421i	−0.962250	+	0.272166i
$28$	0.585786			0.110703
$29$	5.07107			0.941674			0.470837	−	0.882220i	$-0.343952\pi$
$29$	5.07107			0.941674			0.470837	+	0.882220i	$0.343952\pi$
$30$	1.41421	−	1.00000i	0.258199	−	0.182574i
$31$		−	6.82843i		−	1.22642i	−0.789919	−	0.613211i	$-0.789878\pi$
$31$		−	6.82843i		−	1.22642i	0.789919	−	0.613211i	$-0.210122\pi$
$32$	1.00000			0.176777
$33$	−7.65685	+	5.41421i	−1.33289	+	0.942494i
$34$			2.82843i			0.485071i
$35$		−	0.585786i		−	0.0990160i
$36$	−1.00000	+	2.82843i	−0.166667	+	0.471405i
$37$		−	2.24264i		−	0.368688i	−0.982862	−	0.184344i	$-0.940984\pi$
$37$		−	2.24264i		−	0.368688i	0.982862	−	0.184344i	$-0.0590160\pi$
$38$	4.24264	−	1.00000i	0.688247	−	0.162221i
$39$	3.17157	−	2.24264i	0.507858	−	0.359110i
$40$		−	1.00000i		−	0.158114i
$41$	−11.0711			−1.72901			−0.864505	−	0.502624i	$-0.832368\pi$
$41$	−11.0711			−1.72901			−0.864505	+	0.502624i	$0.832368\pi$
$42$	0.585786	+	0.828427i	0.0903888	+	0.127829i
$43$	6.58579			1.00432			0.502162	−	0.864774i	$-0.332538\pi$
$43$	6.58579			1.00432			0.502162	+	0.864774i	$0.332538\pi$
$44$			5.41421i			0.816223i
$45$	2.82843	+	1.00000i	0.421637	+	0.149071i
$46$		−	6.00000i		−	0.884652i
$47$			3.17157i			0.462621i	0.972880	+	0.231311i	$0.0743014\pi$
$47$			3.17157i			0.462621i	−0.972880	+	0.231311i	$0.925699\pi$
$48$	1.00000	+	1.41421i	0.144338	+	0.204124i
$49$	−6.65685			−0.950979
$50$	−1.00000			−0.141421
$51$	−4.00000	+	2.82843i	−0.560112	+	0.396059i
$52$		−	2.24264i		−	0.310998i
$53$	−3.17157			−0.435649			−0.217825	−	0.975988i	$-0.569896\pi$
$53$	−3.17157			−0.435649			−0.217825	+	0.975988i	$0.569896\pi$
$54$	−5.00000	+	1.41421i	−0.680414	+	0.192450i
$55$	5.41421			0.730052
$56$	0.585786			0.0782790
$57$	5.65685	+	5.00000i	0.749269	+	0.662266i
$58$	5.07107			0.665864
$59$	−12.8284			−1.67012			−0.835059	−	0.550160i	$-0.814567\pi$
$59$	−12.8284			−1.67012			−0.835059	+	0.550160i	$0.814567\pi$
$60$	1.41421	−	1.00000i	0.182574	−	0.129099i
$61$	−4.48528			−0.574281			−0.287141	−	0.957888i	$-0.592705\pi$
$61$	−4.48528			−0.574281			−0.287141	+	0.957888i	$0.592705\pi$
$62$		−	6.82843i		−	0.867211i
$63$	−0.585786	+	1.65685i	−0.0738022	+	0.208744i
$64$	1.00000			0.125000
$65$	−2.24264			−0.278165
$66$	−7.65685	+	5.41421i	−0.942494	+	0.666444i
$67$		0			0		1.00000			$0$
$67$		0			0		−1.00000			$\pi$
$68$			2.82843i			0.342997i
$69$	8.48528	−	6.00000i	1.02151	−	0.722315i
$70$		−	0.585786i		−	0.0700149i
$71$	−2.82843			−0.335673			−0.167836	−	0.985815i	$-0.553678\pi$
$71$	−2.82843			−0.335673			−0.167836	+	0.985815i	$0.553678\pi$
$72$	−1.00000	+	2.82843i	−0.117851	+	0.333333i
$73$	2.48528			0.290880			0.145440	−	0.989367i	$-0.453540\pi$
$73$	2.48528			0.290880			0.145440	+	0.989367i	$0.453540\pi$
$74$		−	2.24264i		−	0.260702i
$75$	−1.00000	−	1.41421i	−0.115470	−	0.163299i
$76$	4.24264	−	1.00000i	0.486664	−	0.114708i
$77$			3.17157i			0.361434i
$78$	3.17157	−	2.24264i	0.359110	−	0.253929i
$79$		−	13.3137i		−	1.49791i	−0.662621	−	0.748955i	$-0.730556\pi$
$79$		−	13.3137i		−	1.49791i	0.662621	−	0.748955i	$-0.269444\pi$
$80$		−	1.00000i		−	0.111803i
$81$	−7.00000	−	5.65685i	−0.777778	−	0.628539i
$82$	−11.0711			−1.22259
$83$		−	12.8284i		−	1.40810i	−0.710149	−	0.704051i	$-0.751372\pi$
$83$		−	12.8284i		−	1.40810i	0.710149	−	0.704051i	$-0.248628\pi$
$84$	0.585786	+	0.828427i	0.0639145	+	0.0903888i
$85$	2.82843			0.306786
$86$	6.58579			0.710164
$87$	5.07107	+	7.17157i	0.543676	+	0.768873i
$88$			5.41421i			0.577157i
$89$	10.5858			1.12209			0.561046	−	0.827785i	$-0.310399\pi$
$89$	10.5858			1.12209			0.561046	+	0.827785i	$0.310399\pi$
$90$	2.82843	+	1.00000i	0.298142	+	0.105409i
$91$		−	1.31371i		−	0.137714i
$92$		−	6.00000i		−	0.625543i
$93$	9.65685	−	6.82843i	1.00137	−	0.708075i
$94$			3.17157i			0.327123i
$95$	−1.00000	−	4.24264i	−0.102598	−	0.435286i
$96$	1.00000	+	1.41421i	0.102062	+	0.144338i
$97$		−	6.58579i		−	0.668685i	−0.942452	−	0.334343i	$-0.891486\pi$
$97$		−	6.58579i		−	0.668685i	0.942452	−	0.334343i	$-0.108514\pi$
$98$	−6.65685			−0.672444
$99$	−15.3137	−	5.41421i	−1.53909	−	0.544149i
$100$	−1.00000			−0.100000
$101$			7.65685i			0.761885i	0.924599	+	0.380943i	$0.124401\pi$
$101$			7.65685i			0.761885i	−0.924599	+	0.380943i	$0.875599\pi$
$102$	−4.00000	+	2.82843i	−0.396059	+	0.280056i
$103$			4.34315i			0.427943i	0.976840	+	0.213971i	$0.0686399\pi$
$103$			4.34315i			0.427943i	−0.976840	+	0.213971i	$0.931360\pi$
$104$		−	2.24264i		−	0.219909i
$105$	0.828427	−	0.585786i	0.0808462	−	0.0571669i
$106$	−3.17157			−0.308050
$107$	3.65685			0.353521			0.176761	−	0.984254i	$-0.443438\pi$
$107$	3.65685			0.353521			0.176761	+	0.984254i	$0.443438\pi$
$108$	−5.00000	+	1.41421i	−0.481125	+	0.136083i
$109$		−	2.34315i		−	0.224433i	−0.993684	−	0.112216i	$-0.964205\pi$
$109$		−	2.34315i		−	0.224433i	0.993684	−	0.112216i	$-0.0357950\pi$
$110$	5.41421			0.516225
$111$	3.17157	−	2.24264i	0.301032	−	0.212862i
$112$	0.585786			0.0553516
$113$	12.8284			1.20680			0.603398	−	0.797440i	$-0.293813\pi$
$113$	12.8284			1.20680			0.603398	+	0.797440i	$0.293813\pi$
$114$	5.65685	+	5.00000i	0.529813	+	0.468293i
$115$	−6.00000			−0.559503
$116$	5.07107			0.470837
$117$	6.34315	+	2.24264i	0.586424	+	0.207332i
$118$	−12.8284			−1.18095
$119$			1.65685i			0.151884i
$120$	1.41421	−	1.00000i	0.129099	−	0.0912871i
$121$	−18.3137			−1.66488
$122$	−4.48528			−0.406078
$123$	−11.0711	−	15.6569i	−0.998245	−	1.41173i
$124$		−	6.82843i		−	0.613211i
$125$			1.00000i			0.0894427i
$126$	−0.585786	+	1.65685i	−0.0521860	+	0.147604i
$127$		−	12.8284i		−	1.13834i	−0.822220	−	0.569169i	$-0.807265\pi$
$127$		−	12.8284i		−	1.13834i	0.822220	−	0.569169i	$-0.192735\pi$
$128$	1.00000			0.0883883
$129$	6.58579	+	9.31371i	0.579846	+	0.820026i
$130$	−2.24264			−0.196693
$131$			4.92893i			0.430643i	0.976543	+	0.215321i	$0.0690799\pi$
$131$			4.92893i			0.430643i	−0.976543	+	0.215321i	$0.930920\pi$
$132$	−7.65685	+	5.41421i	−0.666444	+	0.471247i
$133$	2.48528	−	0.585786i	0.215501	−	0.0507941i
$134$		0			0
$135$	1.41421	+	5.00000i	0.121716	+	0.430331i
$136$			2.82843i			0.242536i
$137$			14.4853i			1.23756i	0.785564	+	0.618781i	$0.212373\pi$
$137$			14.4853i			1.23756i	−0.785564	+	0.618781i	$0.787627\pi$
$138$	8.48528	−	6.00000i	0.722315	−	0.510754i
$139$	18.1421			1.53880			0.769398	−	0.638770i	$-0.220556\pi$
$139$	18.1421			1.53880			0.769398	+	0.638770i	$0.220556\pi$
$140$		−	0.585786i		−	0.0495080i
$141$	−4.48528	+	3.17157i	−0.377729	+	0.267095i
$142$	−2.82843			−0.237356
$143$	12.1421			1.01538
$144$	−1.00000	+	2.82843i	−0.0833333	+	0.235702i
$145$		−	5.07107i		−	0.421129i
$146$	2.48528			0.205683
$147$	−6.65685	−	9.41421i	−0.549048	−	0.776471i
$148$		−	2.24264i		−	0.184344i
$149$		−	14.4853i		−	1.18668i	−0.804952	−	0.593340i	$-0.797809\pi$
$149$		−	14.4853i		−	1.18668i	0.804952	−	0.593340i	$-0.202191\pi$
$150$	−1.00000	−	1.41421i	−0.0816497	−	0.115470i
$151$			20.4853i			1.66707i	0.552468	+	0.833534i	$0.313686\pi$
$151$			20.4853i			1.66707i	−0.552468	+	0.833534i	$0.686314\pi$
$152$	4.24264	−	1.00000i	0.344124	−	0.0811107i
$153$	−8.00000	−	2.82843i	−0.646762	−	0.228665i
$154$			3.17157i			0.255573i
$155$	−6.82843			−0.548472
$156$	3.17157	−	2.24264i	0.253929	−	0.179555i
$157$	−23.7990			−1.89937			−0.949683	−	0.313212i	$-0.898595\pi$
$157$	−23.7990			−1.89937			−0.949683	+	0.313212i	$0.898595\pi$
$158$		−	13.3137i		−	1.05918i
$159$	−3.17157	−	4.48528i	−0.251522	−	0.355706i
$160$		−	1.00000i		−	0.0790569i
$161$		−	3.51472i		−	0.276999i
$162$	−7.00000	−	5.65685i	−0.549972	−	0.444444i
$163$	12.7279			0.996928			0.498464	−	0.866910i	$-0.333898\pi$
$163$	12.7279			0.996928			0.498464	+	0.866910i	$0.333898\pi$
$164$	−11.0711			−0.864505
$165$	5.41421	+	7.65685i	0.421496	+	0.596085i
$166$		−	12.8284i		−	0.995679i
$167$		0			0			−	1.00000i	$-0.5\pi$
$167$		0			0				1.00000i	$0.5\pi$
$168$	0.585786	+	0.828427i	0.0451944	+	0.0639145i
$169$	7.97056			0.613120
$170$	2.82843			0.216930
$171$	−1.41421	+	13.0000i	−0.108148	+	0.994135i
$172$	6.58579			0.502162
$173$	6.00000			0.456172			0.228086	−	0.973641i	$-0.426753\pi$
$173$	6.00000			0.456172			0.228086	+	0.973641i	$0.426753\pi$
$174$	5.07107	+	7.17157i	0.384437	+	0.543676i
$175$	−0.585786			−0.0442813
$176$			5.41421i			0.408112i
$177$	−12.8284	−	18.1421i	−0.964244	−	1.36365i
$178$	10.5858			0.793438
$179$	−21.7990			−1.62933			−0.814667	−	0.579930i	$-0.803080\pi$
$179$	−21.7990			−1.62933			−0.814667	+	0.579930i	$0.803080\pi$
$180$	2.82843	+	1.00000i	0.210819	+	0.0745356i
$181$			10.8284i			0.804871i	0.915448	+	0.402435i	$0.131836\pi$
$181$			10.8284i			0.804871i	−0.915448	+	0.402435i	$0.868164\pi$
$182$		−	1.31371i		−	0.0973786i
$183$	−4.48528	−	6.34315i	−0.331562	−	0.468899i
$184$		−	6.00000i		−	0.442326i
$185$	−2.24264			−0.164882
$186$	9.65685	−	6.82843i	0.708075	−	0.500685i
$187$	−15.3137			−1.11985
$188$			3.17157i			0.231311i
$189$	−2.92893	+	0.828427i	−0.213048	+	0.0602592i
$190$	−1.00000	−	4.24264i	−0.0725476	−	0.307794i
$191$			10.2426i			0.741131i	0.928806	+	0.370566i	$0.120836\pi$
$191$			10.2426i			0.741131i	−0.928806	+	0.370566i	$0.879164\pi$
$192$	1.00000	+	1.41421i	0.0721688	+	0.102062i
$193$			19.5563i			1.40770i	0.710350	+	0.703848i	$0.248537\pi$
$193$			19.5563i			1.40770i	−0.710350	+	0.703848i	$0.751463\pi$
$194$		−	6.58579i		−	0.472832i
$195$	−2.24264	−	3.17157i	−0.160599	−	0.227121i
$196$	−6.65685			−0.475490
$197$			18.1421i			1.29257i	0.763095	+	0.646287i	$0.223679\pi$
$197$			18.1421i			1.29257i	−0.763095	+	0.646287i	$0.776321\pi$
$198$	−15.3137	−	5.41421i	−1.08830	−	0.384771i
$199$	−16.9706			−1.20301			−0.601506	−	0.798869i	$-0.705432\pi$
$199$	−16.9706			−1.20301			−0.601506	+	0.798869i	$0.705432\pi$
$200$	−1.00000			−0.0707107
$201$		0			0
$202$			7.65685i			0.538734i
$203$	2.97056			0.208493
$204$	−4.00000	+	2.82843i	−0.280056	+	0.198030i
$205$			11.0711i			0.773237i
$206$			4.34315i			0.302601i
$207$	16.9706	+	6.00000i	1.17954	+	0.417029i
$208$		−	2.24264i		−	0.155499i
$209$	5.41421	+	22.9706i	0.374509	+	1.58891i
$210$	0.828427	−	0.585786i	0.0571669	−	0.0404231i
$211$		−	2.00000i		−	0.137686i	−0.997628	−	0.0688428i	$-0.978069\pi$
$211$		−	2.00000i		−	0.137686i	0.997628	−	0.0688428i	$-0.0219307\pi$
$212$	−3.17157			−0.217825
$213$	−2.82843	−	4.00000i	−0.193801	−	0.274075i
$214$	3.65685			0.249977
$215$		−	6.58579i		−	0.449147i
$216$	−5.00000	+	1.41421i	−0.340207	+	0.0962250i
$217$		−	4.00000i		−	0.271538i
$218$		−	2.34315i		−	0.158698i
$219$	2.48528	+	3.51472i	0.167940	+	0.237503i
$220$	5.41421			0.365026
$221$	6.34315			0.426686
$222$	3.17157	−	2.24264i	0.212862	−	0.150516i
$223$		−	18.0000i		−	1.20537i	−0.797980	−	0.602685i	$-0.794098\pi$
$223$		−	18.0000i		−	1.20537i	0.797980	−	0.602685i	$-0.205902\pi$
$224$	0.585786			0.0391395
$225$	1.00000	−	2.82843i	0.0666667	−	0.188562i
$226$	12.8284			0.853334
$227$	−2.34315			−0.155520			−0.0777600	−	0.996972i	$-0.524777\pi$
$227$	−2.34315			−0.155520			−0.0777600	+	0.996972i	$0.524777\pi$
$228$	5.65685	+	5.00000i	0.374634	+	0.331133i
$229$	8.48528			0.560723			0.280362	−	0.959894i	$-0.409546\pi$
$229$	8.48528			0.560723			0.280362	+	0.959894i	$0.409546\pi$
$230$	−6.00000			−0.395628
$231$	−4.48528	+	3.17157i	−0.295110	+	0.208674i
$232$	5.07107			0.332932
$233$			17.7990i			1.16605i	0.812454	+	0.583025i	$0.198131\pi$
$233$			17.7990i			1.16605i	−0.812454	+	0.583025i	$0.801869\pi$
$234$	6.34315	+	2.24264i	0.414664	+	0.146606i
$235$	3.17157			0.206891
$236$	−12.8284			−0.835059
$237$	18.8284	−	13.3137i	1.22304	−	0.864818i
$238$			1.65685i			0.107398i
$239$		−	0.100505i		−	0.00650113i	−0.999995	−	0.00325057i	$-0.998965\pi$
$239$		−	0.100505i		−	0.00650113i	0.999995	−	0.00325057i	$-0.00103469\pi$
$240$	1.41421	−	1.00000i	0.0912871	−	0.0645497i
$241$			8.48528i			0.546585i	0.961931	+	0.273293i	$0.0881127\pi$
$241$			8.48528i			0.546585i	−0.961931	+	0.273293i	$0.911887\pi$
$242$	−18.3137			−1.17725
$243$	1.00000	−	15.5563i	0.0641500	−	0.997940i
$244$	−4.48528			−0.287141
$245$			6.65685i			0.425291i
$246$	−11.0711	−	15.6569i	−0.705866	−	0.998245i
$247$	−2.24264	−	9.51472i	−0.142696	−	0.605407i
$248$		−	6.82843i		−	0.433606i
$249$	18.1421	−	12.8284i	1.14971	−	0.812969i
$250$			1.00000i			0.0632456i
$251$			4.92893i			0.311111i	0.987827	+	0.155556i	$0.0497168\pi$
$251$			4.92893i			0.311111i	−0.987827	+	0.155556i	$0.950283\pi$
$252$	−0.585786	+	1.65685i	−0.0369011	+	0.104372i
$253$	32.4853			2.04233
$254$		−	12.8284i		−	0.804927i
$255$	2.82843	+	4.00000i	0.177123	+	0.250490i
$256$	1.00000			0.0625000
$257$	28.1421			1.75546			0.877729	−	0.479157i	$-0.159058\pi$
$257$	28.1421			1.75546			0.877729	+	0.479157i	$0.159058\pi$
$258$	6.58579	+	9.31371i	0.410013	+	0.579846i
$259$		−	1.31371i		−	0.0816299i
$260$	−2.24264			−0.139083
$261$	−5.07107	+	14.3431i	−0.313891	+	0.887818i
$262$			4.92893i			0.304510i
$263$		−	11.1716i		−	0.688869i	−0.938810	−	0.344434i	$-0.888071\pi$
$263$		−	11.1716i		−	0.688869i	0.938810	−	0.344434i	$-0.111929\pi$
$264$	−7.65685	+	5.41421i	−0.471247	+	0.333222i
$265$			3.17157i			0.194828i
$266$	2.48528	−	0.585786i	0.152382	−	0.0359169i
$267$	10.5858	+	14.9706i	0.647840	+	0.916184i
$268$		0			0
$269$	−24.3848			−1.48677			−0.743383	−	0.668866i	$-0.766780\pi$
$269$	−24.3848			−1.48677			−0.743383	+	0.668866i	$0.766780\pi$
$270$	1.41421	+	5.00000i	0.0860663	+	0.304290i
$271$	−28.9706			−1.75984			−0.879918	−	0.475125i	$-0.842403\pi$
$271$	−28.9706			−1.75984			−0.879918	+	0.475125i	$0.842403\pi$
$272$			2.82843i			0.171499i
$273$	1.85786	−	1.31371i	0.112443	−	0.0795093i
$274$			14.4853i			0.875088i
$275$		−	5.41421i		−	0.326489i
$276$	8.48528	−	6.00000i	0.510754	−	0.361158i
$277$	24.9706			1.50034			0.750168	−	0.661247i	$-0.229973\pi$
$277$	24.9706			1.50034			0.750168	+	0.661247i	$0.229973\pi$
$278$	18.1421			1.08809
$279$	19.3137	+	6.82843i	1.15628	+	0.408807i
$280$		−	0.585786i		−	0.0350074i
$281$	−0.928932			−0.0554154			−0.0277077	−	0.999616i	$-0.508821\pi$
$281$	−0.928932			−0.0554154			−0.0277077	+	0.999616i	$0.508821\pi$
$282$	−4.48528	+	3.17157i	−0.267095	+	0.188864i
$283$	12.7279			0.756596			0.378298	−	0.925684i	$-0.376509\pi$
$283$	12.7279			0.756596			0.378298	+	0.925684i	$0.376509\pi$
$284$	−2.82843			−0.167836
$285$	5.00000	−	5.65685i	0.296174	−	0.335083i
$286$	12.1421			0.717980
$287$	−6.48528			−0.382814
$288$	−1.00000	+	2.82843i	−0.0589256	+	0.166667i
$289$	9.00000			0.529412
$290$		−	5.07107i		−	0.297783i
$291$	9.31371	−	6.58579i	0.545979	−	0.386066i
$292$	2.48528			0.145440
$293$	3.17157			0.185285			0.0926426	−	0.995699i	$-0.470469\pi$
$293$	3.17157			0.185285			0.0926426	+	0.995699i	$0.470469\pi$
$294$	−6.65685	−	9.41421i	−0.388236	−	0.549048i
$295$			12.8284i			0.746900i
$296$		−	2.24264i		−	0.130351i
$297$	−7.65685	−	27.0711i	−0.444296	−	1.57082i
$298$		−	14.4853i		−	0.839110i
$299$	−13.4558			−0.778172
$300$	−1.00000	−	1.41421i	−0.0577350	−	0.0816497i
$301$	3.85786			0.222364
$302$			20.4853i			1.17880i
$303$	−10.8284	+	7.65685i	−0.622077	+	0.439875i
$304$	4.24264	−	1.00000i	0.243332	−	0.0573539i
$305$			4.48528i			0.256826i
$306$	−8.00000	−	2.82843i	−0.457330	−	0.161690i
$307$		−	18.1421i		−	1.03543i	−0.855554	−	0.517713i	$-0.826783\pi$
$307$		−	18.1421i		−	1.03543i	0.855554	−	0.517713i	$-0.173217\pi$
$308$			3.17157i			0.180717i
$309$	−6.14214	+	4.34315i	−0.349414	+	0.247073i
$310$	−6.82843			−0.387829
$311$			5.07107i			0.287554i	0.989610	+	0.143777i	$0.0459248\pi$
$311$			5.07107i			0.287554i	−0.989610	+	0.143777i	$0.954075\pi$
$312$	3.17157	−	2.24264i	0.179555	−	0.126965i
$313$	−16.8284			−0.951199			−0.475599	−	0.879662i	$-0.657769\pi$
$313$	−16.8284			−0.951199			−0.475599	+	0.879662i	$0.657769\pi$
$314$	−23.7990			−1.34305
$315$	1.65685	+	0.585786i	0.0933532	+	0.0330053i
$316$		−	13.3137i		−	0.748955i
$317$	−0.343146			−0.0192730			−0.00963649	−	0.999954i	$-0.503067\pi$
$317$	−0.343146			−0.0192730			−0.00963649	+	0.999954i	$0.503067\pi$
$318$	−3.17157	−	4.48528i	−0.177853	−	0.251522i
$319$			27.4558i			1.53723i
$320$		−	1.00000i		−	0.0559017i
$321$	3.65685	+	5.17157i	0.204106	+	0.288649i
$322$		−	3.51472i		−	0.195868i
$323$	2.82843	+	12.0000i	0.157378	+	0.667698i
$324$	−7.00000	−	5.65685i	−0.388889	−	0.314270i
$325$			2.24264i			0.124399i
$326$	12.7279			0.704934
$327$	3.31371	−	2.34315i	0.183248	−	0.129576i
$328$	−11.0711			−0.611297
$329$			1.85786i			0.102427i
$330$	5.41421	+	7.65685i	0.298043	+	0.421496i
$331$			16.9706i			0.932786i	0.884577	+	0.466393i	$0.154447\pi$
$331$			16.9706i			0.932786i	−0.884577	+	0.466393i	$0.845553\pi$
$332$		−	12.8284i		−	0.704051i
$333$	6.34315	+	2.24264i	0.347602	+	0.122896i
$334$		0			0
$335$		0			0
$336$	0.585786	+	0.828427i	0.0319573	+	0.0451944i
$337$			29.2132i			1.59134i	0.605727	+	0.795672i	$0.292882\pi$
$337$			29.2132i			1.59134i	−0.605727	+	0.795672i	$0.707118\pi$
$338$	7.97056			0.433541
$339$	12.8284	+	18.1421i	0.696745	+	0.985346i
$340$	2.82843			0.153393
$341$	36.9706			2.00207
$342$	−1.41421	+	13.0000i	−0.0764719	+	0.702959i
$343$	−8.00000			−0.431959
$344$	6.58579			0.355082
$345$	−6.00000	−	8.48528i	−0.323029	−	0.456832i
$346$	6.00000			0.322562
$347$		−	30.2843i		−	1.62574i	−0.582442	−	0.812872i	$-0.697903\pi$
$347$		−	30.2843i		−	1.62574i	0.582442	−	0.812872i	$-0.302097\pi$
$348$	5.07107	+	7.17157i	0.271838	+	0.384437i
$349$	−10.9706			−0.587241			−0.293620	−	0.955922i	$-0.594860\pi$
$349$	−10.9706			−0.587241			−0.293620	+	0.955922i	$0.594860\pi$
$350$	−0.585786			−0.0313116
$351$	3.17157	+	11.2132i	0.169286	+	0.598517i
$352$			5.41421i			0.288579i
$353$			8.82843i			0.469890i	0.972009	+	0.234945i	$0.0754910\pi$
$353$			8.82843i			0.469890i	−0.972009	+	0.234945i	$0.924509\pi$
$354$	−12.8284	−	18.1421i	−0.681823	−	0.964244i
$355$			2.82843i			0.150117i
$356$	10.5858			0.561046
$357$	−2.34315	+	1.65685i	−0.124012	+	0.0876900i
$358$	−21.7990			−1.15211
$359$			19.4142i			1.02464i	0.858794	+	0.512322i	$0.171214\pi$
$359$			19.4142i			1.02464i	−0.858794	+	0.512322i	$0.828786\pi$
$360$	2.82843	+	1.00000i	0.149071	+	0.0527046i
$361$	17.0000	−	8.48528i	0.894737	−	0.446594i
$362$			10.8284i			0.569129i
$363$	−18.3137	−	25.8995i	−0.961220	−	1.35937i
$364$		−	1.31371i		−	0.0688570i
$365$		−	2.48528i		−	0.130086i
$366$	−4.48528	−	6.34315i	−0.234449	−	0.331562i
$367$	−14.2426			−0.743460			−0.371730	−	0.928341i	$-0.621235\pi$
$367$	−14.2426			−0.743460			−0.371730	+	0.928341i	$0.621235\pi$
$368$		−	6.00000i		−	0.312772i
$369$	11.0711	−	31.3137i	0.576337	−	1.63013i
$370$	−2.24264			−0.116589
$371$	−1.85786			−0.0964555
$372$	9.65685	−	6.82843i	0.500685	−	0.354037i
$373$			14.0416i			0.727048i	0.931585	+	0.363524i	$0.118427\pi$
$373$			14.0416i			0.727048i	−0.931585	+	0.363524i	$0.881573\pi$
$374$	−15.3137			−0.791853
$375$	−1.41421	+	1.00000i	−0.0730297	+	0.0516398i
$376$			3.17157i			0.163561i
$377$		−	11.3726i		−	0.585718i
$378$	−2.92893	+	0.828427i	−0.150648	+	0.0426097i
$379$			8.00000i			0.410932i	0.978664	+	0.205466i	$0.0658711\pi$
$379$			8.00000i			0.410932i	−0.978664	+	0.205466i	$0.934129\pi$
$380$	−1.00000	−	4.24264i	−0.0512989	−	0.217643i
$381$	18.1421	−	12.8284i	0.929450	−	0.657220i
$382$			10.2426i			0.524059i
$383$	32.1421			1.64239			0.821193	−	0.570650i	$-0.193309\pi$
$383$	32.1421			1.64239			0.821193	+	0.570650i	$0.193309\pi$
$384$	1.00000	+	1.41421i	0.0510310	+	0.0721688i
$385$	3.17157			0.161638
$386$			19.5563i			0.995392i
$387$	−6.58579	+	18.6274i	−0.334774	+	0.946885i
$388$		−	6.58579i		−	0.334343i
$389$		−	20.3431i		−	1.03144i	−0.856758	−	0.515719i	$-0.827525\pi$
$389$		−	20.3431i		−	1.03144i	0.856758	−	0.515719i	$-0.172475\pi$
$390$	−2.24264	−	3.17157i	−0.113561	−	0.160599i
$391$	16.9706			0.858238
$392$	−6.65685			−0.336222
$393$	−6.97056	+	4.92893i	−0.351618	+	0.248632i
$394$			18.1421i			0.913988i
$395$	−13.3137			−0.669885
$396$	−15.3137	−	5.41421i	−0.769543	−	0.272074i
$397$	16.9706			0.851728			0.425864	−	0.904787i	$-0.359970\pi$
$397$	16.9706			0.851728			0.425864	+	0.904787i	$0.359970\pi$
$398$	−16.9706			−0.850657
$399$	3.31371	+	2.92893i	0.165893	+	0.146630i
$400$	−1.00000			−0.0500000
$401$	−18.3848			−0.918092			−0.459046	−	0.888413i	$-0.651809\pi$
$401$	−18.3848			−0.918092			−0.459046	+	0.888413i	$0.651809\pi$
$402$		0			0
$403$	−15.3137			−0.762830
$404$			7.65685i			0.380943i
$405$	−5.65685	+	7.00000i	−0.281091	+	0.347833i
$406$	2.97056			0.147427
$407$	12.1421			0.601863
$408$	−4.00000	+	2.82843i	−0.198030	+	0.140028i
$409$			4.48528i			0.221783i	0.993833	+	0.110891i	$0.0353706\pi$
$409$			4.48528i			0.221783i	−0.993833	+	0.110891i	$0.964629\pi$
$410$			11.0711i			0.546761i
$411$	−20.4853	+	14.4853i	−1.01046	+	0.714506i
$412$			4.34315i			0.213971i
$413$	−7.51472			−0.369775
$414$	16.9706	+	6.00000i	0.834058	+	0.294884i
$415$	−12.8284			−0.629723
$416$		−	2.24264i		−	0.109955i
$417$	18.1421	+	25.6569i	0.888424	+	1.25642i
$418$	5.41421	+	22.9706i	0.264818	+	1.12353i
$419$		−	6.38478i		−	0.311917i	−0.987764	−	0.155958i	$-0.950153\pi$
$419$		−	6.38478i		−	0.311917i	0.987764	−	0.155958i	$-0.0498466\pi$
$420$	0.828427	−	0.585786i	0.0404231	−	0.0285835i
$421$			24.2843i			1.18354i	0.806106	+	0.591771i	$0.201571\pi$
$421$			24.2843i			1.18354i	−0.806106	+	0.591771i	$0.798429\pi$
$422$		−	2.00000i		−	0.0973585i
$423$	−8.97056	−	3.17157i	−0.436164	−	0.154207i
$424$	−3.17157			−0.154025
$425$		−	2.82843i		−	0.137199i
$426$	−2.82843	−	4.00000i	−0.137038	−	0.193801i
$427$	−2.62742			−0.127150
$428$	3.65685			0.176761
$429$	12.1421	+	17.1716i	0.586228	+	0.829051i
$430$		−	6.58579i		−	0.317595i
$431$	−19.3137			−0.930309			−0.465154	−	0.885230i	$-0.654001\pi$
$431$	−19.3137			−0.930309			−0.465154	+	0.885230i	$0.654001\pi$
$432$	−5.00000	+	1.41421i	−0.240563	+	0.0680414i
$433$		−	14.3848i		−	0.691288i	−0.938366	−	0.345644i	$-0.887660\pi$
$433$		−	14.3848i		−	0.691288i	0.938366	−	0.345644i	$-0.112340\pi$
$434$		−	4.00000i		−	0.192006i
$435$	7.17157	−	5.07107i	0.343851	−	0.243139i
$436$		−	2.34315i		−	0.112216i
$437$	−6.00000	−	25.4558i	−0.287019	−	1.21772i
$438$	2.48528	+	3.51472i	0.118751	+	0.167940i
$439$			39.9411i			1.90629i	0.302520	+	0.953143i	$0.402172\pi$
$439$			39.9411i			1.90629i	−0.302520	+	0.953143i	$0.597828\pi$
$440$	5.41421			0.258113
$441$	6.65685	−	18.8284i	0.316993	−	0.896592i
$442$	6.34315			0.301713
$443$			18.0000i			0.855206i	0.903967	+	0.427603i	$0.140642\pi$
$443$			18.0000i			0.855206i	−0.903967	+	0.427603i	$0.859358\pi$
$444$	3.17157	−	2.24264i	0.150516	−	0.106431i
$445$		−	10.5858i		−	0.501814i
$446$		−	18.0000i		−	0.852325i
$447$	20.4853	−	14.4853i	0.968921	−	0.685130i
$448$	0.585786			0.0276758
$449$	−16.2426			−0.766538			−0.383269	−	0.923637i	$-0.625202\pi$
$449$	−16.2426			−0.766538			−0.383269	+	0.923637i	$0.625202\pi$
$450$	1.00000	−	2.82843i	0.0471405	−	0.133333i
$451$		−	59.9411i		−	2.82252i
$452$	12.8284			0.603398
$453$	−28.9706	+	20.4853i	−1.36116	+	0.962482i
$454$	−2.34315			−0.109969
$455$	−1.31371			−0.0615876
$456$	5.65685	+	5.00000i	0.264906	+	0.234146i
$457$	−0.828427			−0.0387522			−0.0193761	−	0.999812i	$-0.506168\pi$
$457$	−0.828427			−0.0387522			−0.0193761	+	0.999812i	$0.506168\pi$
$458$	8.48528			0.396491
$459$	−4.00000	−	14.1421i	−0.186704	−	0.660098i
$460$	−6.00000			−0.279751
$461$		−	28.1421i		−	1.31071i	−0.755321	−	0.655355i	$-0.772519\pi$
$461$		−	28.1421i		−	1.31071i	0.755321	−	0.655355i	$-0.227481\pi$
$462$	−4.48528	+	3.17157i	−0.208674	+	0.147555i
$463$	19.2132			0.892913			0.446457	−	0.894805i	$-0.352686\pi$
$463$	19.2132			0.892913			0.446457	+	0.894805i	$0.352686\pi$
$464$	5.07107			0.235418
$465$	−6.82843	−	9.65685i	−0.316661	−	0.447826i
$466$			17.7990i			0.824522i
$467$		−	25.7990i		−	1.19383i	−0.802303	−	0.596917i	$-0.796392\pi$
$467$		−	25.7990i		−	1.19383i	0.802303	−	0.596917i	$-0.203608\pi$
$468$	6.34315	+	2.24264i	0.293212	+	0.103666i
$469$		0			0
$470$	3.17157			0.146294
$471$	−23.7990	−	33.6569i	−1.09660	−	1.55083i
$472$	−12.8284			−0.590476
$473$			35.6569i			1.63950i
$474$	18.8284	−	13.3137i	0.864818	−	0.611519i
$475$	−4.24264	+	1.00000i	−0.194666	+	0.0458831i
$476$			1.65685i			0.0759418i
$477$	3.17157	−	8.97056i	0.145216	−	0.410734i
$478$		−	0.100505i		−	0.00459699i
$479$		−	3.41421i		−	0.155999i	−0.996953	−	0.0779997i	$-0.975147\pi$
$479$		−	3.41421i		−	0.155999i	0.996953	−	0.0779997i	$-0.0248533\pi$
$480$	1.41421	−	1.00000i	0.0645497	−	0.0456435i
$481$	−5.02944			−0.229323
$482$			8.48528i			0.386494i
$483$	4.97056	−	3.51472i	0.226168	−	0.159925i
$484$	−18.3137			−0.832441
$485$	−6.58579			−0.299045
$486$	1.00000	−	15.5563i	0.0453609	−	0.705650i
$487$			36.1421i			1.63776i	0.573967	+	0.818878i	$0.305404\pi$
$487$			36.1421i			1.63776i	−0.573967	+	0.818878i	$0.694596\pi$
$488$	−4.48528			−0.203039
$489$	12.7279	+	18.0000i	0.575577	+	0.813988i
$490$			6.65685i			0.300726i
$491$		−	43.5563i		−	1.96567i	−0.184485	−	0.982835i	$-0.559062\pi$
$491$		−	43.5563i		−	1.96567i	0.184485	−	0.982835i	$-0.440938\pi$
$492$	−11.0711	−	15.6569i	−0.499122	−	0.705866i
$493$			14.3431i			0.645983i
$494$	−2.24264	−	9.51472i	−0.100901	−	0.428087i
$495$	−5.41421	+	15.3137i	−0.243351	+	0.688300i
$496$		−	6.82843i		−	0.306605i
$497$	−1.65685			−0.0743201
$498$	18.1421	−	12.8284i	0.812969	−	0.574856i
$499$	−25.6569			−1.14856			−0.574279	−	0.818659i	$-0.694718\pi$
$499$	−25.6569			−1.14856			−0.574279	+	0.818659i	$0.694718\pi$
$500$			1.00000i			0.0447214i
$501$		0			0
$502$			4.92893i			0.219989i
$503$		−	14.2843i		−	0.636904i	−0.947939	−	0.318452i	$-0.896837\pi$
$503$		−	14.2843i		−	0.636904i	0.947939	−	0.318452i	$-0.103163\pi$
$504$	−0.585786	+	1.65685i	−0.0260930	+	0.0738022i
$505$	7.65685			0.340726
$506$	32.4853			1.44415
$507$	7.97056	+	11.2721i	0.353985	+	0.500611i
$508$		−	12.8284i		−	0.569169i
$509$	4.10051			0.181752			0.0908758	−	0.995862i	$-0.471033\pi$
$509$	4.10051			0.181752			0.0908758	+	0.995862i	$0.471033\pi$
$510$	2.82843	+	4.00000i	0.125245	+	0.177123i
$511$	1.45584			0.0644028
$512$	1.00000			0.0441942
$513$	−19.7990	+	11.0000i	−0.874147	+	0.485662i
$514$	28.1421			1.24130
$515$	4.34315			0.191382
$516$	6.58579	+	9.31371i	0.289923	+	0.410013i
$517$	−17.1716			−0.755205
$518$		−	1.31371i		−	0.0577210i
$519$	6.00000	+	8.48528i	0.263371	+	0.372463i
$520$	−2.24264			−0.0983463
$521$	14.3848			0.630208			0.315104	−	0.949057i	$-0.397961\pi$
$521$	14.3848			0.630208			0.315104	+	0.949057i	$0.397961\pi$
$522$	−5.07107	+	14.3431i	−0.221955	+	0.627782i
$523$		−	8.97056i		−	0.392255i	−0.980578	−	0.196128i	$-0.937163\pi$
$523$		−	8.97056i		−	0.392255i	0.980578	−	0.196128i	$-0.0628367\pi$
$524$			4.92893i			0.215321i
$525$	−0.585786	−	0.828427i	−0.0255658	−	0.0361555i
$526$		−	11.1716i		−	0.487104i
$527$	19.3137			0.841318
$528$	−7.65685	+	5.41421i	−0.333222	+	0.235623i
$529$	−13.0000			−0.565217
$530$			3.17157i			0.137764i
$531$	12.8284	−	36.2843i	0.556706	−	1.57460i
$532$	2.48528	−	0.585786i	0.107751	−	0.0253971i
$533$			24.8284i			1.07544i
$534$	10.5858	+	14.9706i	0.458092	+	0.647840i
$535$		−	3.65685i		−	0.158100i
$536$		0			0
$537$	−21.7990	−	30.8284i	−0.940696	−	1.33034i
$538$	−24.3848			−1.05130
$539$		−	36.0416i		−	1.55242i
$540$	1.41421	+	5.00000i	0.0608581	+	0.215166i
$541$	−42.9706			−1.84745			−0.923724	−	0.383058i	$-0.874871\pi$
$541$	−42.9706			−1.84745			−0.923724	+	0.383058i	$0.874871\pi$
$542$	−28.9706			−1.24439
$543$	−15.3137	+	10.8284i	−0.657174	+	0.464692i
$544$			2.82843i			0.121268i
$545$	−2.34315			−0.100369
$546$	1.85786	−	1.31371i	0.0795093	−	0.0562215i
$547$		−	13.1716i		−	0.563176i	−0.959535	−	0.281588i	$-0.909139\pi$
$547$		−	13.1716i		−	0.563176i	0.959535	−	0.281588i	$-0.0908611\pi$
$548$			14.4853i			0.618781i
$549$	4.48528	−	12.6863i	0.191427	−	0.541438i
$550$		−	5.41421i		−	0.230863i
$551$	21.5147	−	5.07107i	0.916558	−	0.216035i
$552$	8.48528	−	6.00000i	0.361158	−	0.255377i
$553$		−	7.79899i		−	0.331647i
$554$	24.9706			1.06090
$555$	−2.24264	−	3.17157i	−0.0951948	−	0.134626i
$556$	18.1421			0.769398
$557$			28.6274i			1.21298i	0.795090	+	0.606491i	$0.207424\pi$
$557$			28.6274i			1.21298i	−0.795090	+	0.606491i	$0.792576\pi$
$558$	19.3137	+	6.82843i	0.817614	+	0.289070i
$559$		−	14.7696i		−	0.624686i
$560$		−	0.585786i		−	0.0247540i
$561$	−15.3137	−	21.6569i	−0.646545	−	0.914353i
$562$	−0.928932			−0.0391846
$563$	−13.6569			−0.575568			−0.287784	−	0.957695i	$-0.592918\pi$
$563$	−13.6569			−0.575568			−0.287784	+	0.957695i	$0.592918\pi$
$564$	−4.48528	+	3.17157i	−0.188864	+	0.133547i
$565$		−	12.8284i		−	0.539696i
$566$	12.7279			0.534994
$567$	−4.10051	−	3.31371i	−0.172205	−	0.139163i
$568$	−2.82843			−0.118678
$569$	−28.9289			−1.21276			−0.606382	−	0.795174i	$-0.707380\pi$
$569$	−28.9289			−1.21276			−0.606382	+	0.795174i	$0.707380\pi$
$570$	5.00000	−	5.65685i	0.209427	−	0.236940i
$571$	−1.65685			−0.0693372			−0.0346686	−	0.999399i	$-0.511038\pi$
$571$	−1.65685			−0.0693372			−0.0346686	+	0.999399i	$0.511038\pi$
$572$	12.1421			0.507688
$573$	−14.4853	+	10.2426i	−0.605131	+	0.427892i
$574$	−6.48528			−0.270690
$575$			6.00000i			0.250217i
$576$	−1.00000	+	2.82843i	−0.0416667	+	0.117851i
$577$	−19.1716			−0.798123			−0.399062	−	0.916924i	$-0.630664\pi$
$577$	−19.1716			−0.798123			−0.399062	+	0.916924i	$0.630664\pi$
$578$	9.00000			0.374351
$579$	−27.6569	+	19.5563i	−1.14938	+	0.812734i
$580$		−	5.07107i		−	0.210565i
$581$		−	7.51472i		−	0.311763i
$582$	9.31371	−	6.58579i	0.386066	−	0.272990i
$583$		−	17.1716i		−	0.711174i
$584$	2.48528			0.102842
$585$	2.24264	−	6.34315i	0.0927218	−	0.262257i
$586$	3.17157			0.131016
$587$		−	3.17157i		−	0.130905i	−0.997856	−	0.0654524i	$-0.979151\pi$
$587$		−	3.17157i		−	0.130905i	0.997856	−	0.0654524i	$-0.0208491\pi$
$588$	−6.65685	−	9.41421i	−0.274524	−	0.388236i
$589$	−6.82843	−	28.9706i	−0.281360	−	1.19371i
$590$			12.8284i			0.528138i
$591$	−25.6569	+	18.1421i	−1.05538	+	0.746268i
$592$		−	2.24264i		−	0.0921720i
$593$		−	12.1421i		−	0.498618i	−0.968424	−	0.249309i	$-0.919797\pi$
$593$		−	12.1421i		−	0.498618i	0.968424	−	0.249309i	$-0.0802034\pi$
$594$	−7.65685	−	27.0711i	−0.314165	−	1.11074i
$595$	1.65685			0.0679244
$596$		−	14.4853i		−	0.593340i
$597$	−16.9706	−	24.0000i	−0.694559	−	0.982255i
$598$	−13.4558			−0.550250
$599$	21.1716			0.865047			0.432524	−	0.901623i	$-0.357623\pi$
$599$	21.1716			0.865047			0.432524	+	0.901623i	$0.357623\pi$
$600$	−1.00000	−	1.41421i	−0.0408248	−	0.0577350i
$601$			4.00000i			0.163163i	0.996667	+	0.0815817i	$0.0259972\pi$
$601$			4.00000i			0.163163i	−0.996667	+	0.0815817i	$0.974003\pi$
$602$	3.85786			0.157235
$603$		0			0
$604$			20.4853i			0.833534i
$605$			18.3137i			0.744558i
$606$	−10.8284	+	7.65685i	−0.439875	+	0.311038i
$607$		−	1.51472i		−	0.0614805i	−0.999527	−	0.0307403i	$-0.990214\pi$
$607$		−	1.51472i		−	0.0614805i	0.999527	−	0.0307403i	$-0.00978647\pi$
$608$	4.24264	−	1.00000i	0.172062	−	0.0405554i
$609$	2.97056	+	4.20101i	0.120373	+	0.170234i
$610$			4.48528i			0.181604i
$611$	7.11270			0.287749
$612$	−8.00000	−	2.82843i	−0.323381	−	0.114332i
$613$	−23.1127			−0.933513			−0.466757	−	0.884386i	$-0.654578\pi$
$613$	−23.1127			−0.933513			−0.466757	+	0.884386i	$0.654578\pi$
$614$		−	18.1421i		−	0.732157i
$615$	−15.6569	+	11.0711i	−0.631345	+	0.446429i
$616$			3.17157i			0.127786i
$617$		−	18.8284i		−	0.758004i	−0.925396	−	0.379002i	$-0.876267\pi$
$617$		−	18.8284i		−	0.758004i	0.925396	−	0.379002i	$-0.123733\pi$
$618$	−6.14214	+	4.34315i	−0.247073	+	0.174707i
$619$	41.4558			1.66625			0.833126	−	0.553084i	$-0.186549\pi$
$619$	41.4558			1.66625			0.833126	+	0.553084i	$0.186549\pi$
$620$	−6.82843			−0.274236
$621$	8.48528	+	30.0000i	0.340503	+	1.20386i
$622$			5.07107i			0.203331i
$623$	6.20101			0.248438
$624$	3.17157	−	2.24264i	0.126965	−	0.0897775i
$625$	1.00000			0.0400000
$626$	−16.8284			−0.672599
$627$	−27.0711	+	30.6274i	−1.08111	+	1.22314i
$628$	−23.7990			−0.949683
$629$	6.34315			0.252918
$630$	1.65685	+	0.585786i	0.0660107	+	0.0233383i
$631$	23.5147			0.936106			0.468053	−	0.883700i	$-0.344956\pi$
$631$	23.5147			0.936106			0.468053	+	0.883700i	$0.344956\pi$
$632$		−	13.3137i		−	0.529591i
$633$	2.82843	−	2.00000i	0.112420	−	0.0794929i
$634$	−0.343146			−0.0136281
$635$	−12.8284			−0.509081
$636$	−3.17157	−	4.48528i	−0.125761	−	0.177853i
$637$			14.9289i			0.591506i
$638$			27.4558i			1.08699i
$639$	2.82843	−	8.00000i	0.111891	−	0.316475i
$640$		−	1.00000i		−	0.0395285i
$641$	−11.2721			−0.445220			−0.222610	−	0.974908i	$-0.571458\pi$
$641$	−11.2721			−0.445220			−0.222610	+	0.974908i	$0.571458\pi$
$642$	3.65685	+	5.17157i	0.144325	+	0.204106i
$643$	−20.7279			−0.817429			−0.408715	−	0.912662i	$-0.634023\pi$
$643$	−20.7279			−0.817429			−0.408715	+	0.912662i	$0.634023\pi$
$644$		−	3.51472i		−	0.138499i
$645$	9.31371	−	6.58579i	0.366727	−	0.259315i
$646$	2.82843	+	12.0000i	0.111283	+	0.472134i
$647$			2.68629i			0.105609i	0.998605	+	0.0528045i	$0.0168160\pi$
$647$			2.68629i			0.105609i	−0.998605	+	0.0528045i	$0.983184\pi$
$648$	−7.00000	−	5.65685i	−0.274986	−	0.222222i
$649$		−	69.4558i		−	2.72638i
$650$			2.24264i			0.0879636i
$651$	5.65685	−	4.00000i	0.221710	−	0.156772i
$652$	12.7279			0.498464
$653$		−	15.1127i		−	0.591406i	−0.955280	−	0.295703i	$-0.904446\pi$
$653$		−	15.1127i		−	0.591406i	0.955280	−	0.295703i	$-0.0955538\pi$
$654$	3.31371	−	2.34315i	0.129576	−	0.0916242i
$655$	4.92893			0.192589
$656$	−11.0711			−0.432253
$657$	−2.48528	+	7.02944i	−0.0969601	+	0.274244i
$658$			1.85786i			0.0724271i
$659$	−8.82843			−0.343907			−0.171953	−	0.985105i	$-0.555008\pi$
$659$	−8.82843			−0.343907			−0.171953	+	0.985105i	$0.555008\pi$
$660$	5.41421	+	7.65685i	0.210748	+	0.298043i
$661$			3.51472i			0.136707i	0.997661	+	0.0683534i	$0.0217745\pi$
$661$			3.51472i			0.136707i	−0.997661	+	0.0683534i	$0.978225\pi$
$662$			16.9706i			0.659580i
$663$	6.34315	+	8.97056i	0.246347	+	0.348388i
$664$		−	12.8284i		−	0.497840i
$665$	−0.585786	−	2.48528i	−0.0227158	−	0.0963751i
$666$	6.34315	+	2.24264i	0.245792	+	0.0869006i
$667$		−	30.4264i		−	1.17812i
$668$		0			0
$669$	25.4558	−	18.0000i	0.984180	−	0.695920i
$670$		0			0
$671$		−	24.2843i		−	0.937484i
$672$	0.585786	+	0.828427i	0.0225972	+	0.0319573i
$673$			37.6985i			1.45317i	0.687077	+	0.726585i	$0.258894\pi$
$673$			37.6985i			1.45317i	−0.687077	+	0.726585i	$0.741106\pi$
$674$			29.2132i			1.12525i
$675$	5.00000	−	1.41421i	0.192450	−	0.0544331i
$676$	7.97056			0.306560
$677$	−37.5980			−1.44501			−0.722504	−	0.691367i	$-0.757009\pi$
$677$	−37.5980			−1.44501			−0.722504	+	0.691367i	$0.757009\pi$
$678$	12.8284	+	18.1421i	0.492673	+	0.696745i
$679$		−	3.85786i		−	0.148051i
$680$	2.82843			0.108465
$681$	−2.34315	−	3.31371i	−0.0897895	−	0.126982i
$682$	36.9706			1.41568
$683$	39.2548			1.50204			0.751022	−	0.660277i	$-0.229561\pi$
$683$	39.2548			1.50204			0.751022	+	0.660277i	$0.229561\pi$
$684$	−1.41421	+	13.0000i	−0.0540738	+	0.497067i
$685$	14.4853			0.553454
$686$	−8.00000			−0.305441
$687$	8.48528	+	12.0000i	0.323734	+	0.457829i
$688$	6.58579			0.251081
$689$			7.11270i			0.270972i
$690$	−6.00000	−	8.48528i	−0.228416	−	0.323029i
$691$	36.9706			1.40643			0.703213	−	0.710979i	$-0.251748\pi$
$691$	36.9706			1.40643			0.703213	+	0.710979i	$0.251748\pi$
$692$	6.00000			0.228086
$693$	−8.97056	−	3.17157i	−0.340764	−	0.120478i
$694$		−	30.2843i		−	1.14958i
$695$		−	18.1421i		−	0.688170i
$696$	5.07107	+	7.17157i	0.192218	+	0.271838i
$697$		−	31.3137i		−	1.18609i
$698$	−10.9706			−0.415242
$699$	−25.1716	+	17.7990i	−0.952076	+	0.673220i
$700$	−0.585786			−0.0221406
$701$			2.48528i			0.0938678i	0.998898	+	0.0469339i	$0.0149450\pi$
$701$			2.48528i			0.0938678i	−0.998898	+	0.0469339i	$0.985055\pi$
$702$	3.17157	+	11.2132i	0.119703	+	0.423215i
$703$	−2.24264	−	9.51472i	−0.0845828	−	0.358854i
$704$			5.41421i			0.204056i
$705$	3.17157	+	4.48528i	0.119448	+	0.168925i
$706$			8.82843i			0.332262i
$707$			4.48528i			0.168686i
$708$	−12.8284	−	18.1421i	−0.482122	−	0.681823i
$709$	19.5147			0.732891			0.366445	−	0.930440i	$-0.380575\pi$
$709$	19.5147			0.732891			0.366445	+	0.930440i	$0.380575\pi$
$710$			2.82843i			0.106149i
$711$	37.6569	+	13.3137i	1.41224	+	0.499303i
$712$	10.5858			0.396719
$713$	−40.9706			−1.53436
$714$	−2.34315	+	1.65685i	−0.0876900	+	0.0620062i
$715$		−	12.1421i		−	0.454090i
$716$	−21.7990			−0.814667
$717$	0.142136	−	0.100505i	0.00530815	−	0.00375343i
$718$			19.4142i			0.724532i
$719$		−	30.7279i		−	1.14596i	−0.819570	−	0.572979i	$-0.805788\pi$
$719$		−	30.7279i		−	1.14596i	0.819570	−	0.572979i	$-0.194212\pi$
$720$	2.82843	+	1.00000i	0.105409	+	0.0372678i
$721$			2.54416i			0.0947493i
$722$	17.0000	−	8.48528i	0.632674	−	0.315789i
$723$	−12.0000	+	8.48528i	−0.446285	+	0.315571i
$724$			10.8284i			0.402435i
$725$	−5.07107			−0.188335
$726$	−18.3137	−	25.8995i	−0.679685	−	0.961220i
$727$	25.5563			0.947833			0.473916	−	0.880570i	$-0.342840\pi$
$727$	25.5563			0.947833			0.473916	+	0.880570i	$0.342840\pi$
$728$		−	1.31371i		−	0.0486893i
$729$	23.0000	−	14.1421i	0.851852	−	0.523783i
$730$		−	2.48528i		−	0.0919844i
$731$			18.6274i			0.688960i
$732$	−4.48528	−	6.34315i	−0.165781	−	0.234449i
$733$	−15.5147			−0.573049			−0.286525	−	0.958073i	$-0.592500\pi$
$733$	−15.5147			−0.573049			−0.286525	+	0.958073i	$0.592500\pi$
$734$	−14.2426			−0.525705
$735$	−9.41421	+	6.65685i	−0.347248	+	0.245542i
$736$		−	6.00000i		−	0.221163i
$737$		0			0
$738$	11.0711	−	31.3137i	0.407532	−	1.15267i
$739$	−20.4853			−0.753563			−0.376782	−	0.926302i	$-0.622969\pi$
$739$	−20.4853			−0.753563			−0.376782	+	0.926302i	$0.622969\pi$
$740$	−2.24264			−0.0824411
$741$	11.2132	−	12.6863i	0.411927	−	0.466043i
$742$	−1.85786			−0.0682043
$743$	−43.1716			−1.58381			−0.791906	−	0.610643i	$-0.790911\pi$
$743$	−43.1716			−1.58381			−0.791906	+	0.610643i	$0.790911\pi$
$744$	9.65685	−	6.82843i	0.354037	−	0.250342i
$745$	−14.4853			−0.530700
$746$			14.0416i			0.514101i
$747$	36.2843	+	12.8284i	1.32757	+	0.469368i
$748$	−15.3137			−0.559925
$749$	2.14214			0.0782719
$750$	−1.41421	+	1.00000i	−0.0516398	+	0.0365148i
$751$			48.4853i			1.76925i	0.466300	+	0.884627i	$0.345587\pi$
$751$			48.4853i			1.76925i	−0.466300	+	0.884627i	$0.654413\pi$
$752$			3.17157i			0.115655i
$753$	−6.97056	+	4.92893i	−0.254021	+	0.179620i
$754$		−	11.3726i		−	0.414165i
$755$	20.4853			0.745536
$756$	−2.92893	+	0.828427i	−0.106524	+	0.0301296i
$757$	49.6569			1.80481			0.902405	−	0.430890i	$-0.141800\pi$
$757$	49.6569			1.80481			0.902405	+	0.430890i	$0.141800\pi$
$758$			8.00000i			0.290573i
$759$	32.4853	+	45.9411i	1.17914	+	1.66756i
$760$	−1.00000	−	4.24264i	−0.0362738	−	0.153897i
$761$		−	1.17157i		−	0.0424695i	−0.999775	−	0.0212347i	$-0.993240\pi$
$761$		−	1.17157i		−	0.0424695i	0.999775	−	0.0212347i	$-0.00675974\pi$
$762$	18.1421	−	12.8284i	0.657220	−	0.464725i
$763$		−	1.37258i		−	0.0496908i
$764$			10.2426i			0.370566i
$765$	−2.82843	+	8.00000i	−0.102262	+	0.289241i
$766$	32.1421			1.16134
$767$			28.7696i			1.03881i
$768$	1.00000	+	1.41421i	0.0360844	+	0.0510310i
$769$	−13.3137			−0.480105			−0.240052	−	0.970760i	$-0.577165\pi$
$769$	−13.3137			−0.480105			−0.240052	+	0.970760i	$0.577165\pi$
$770$	3.17157			0.114296
$771$	28.1421	+	39.7990i	1.01351	+	1.43333i
$772$			19.5563i			0.703848i
$773$	0.343146			0.0123421			0.00617105	−	0.999981i	$-0.498036\pi$
$773$	0.343146			0.0123421			0.00617105	+	0.999981i	$0.498036\pi$
$774$	−6.58579	+	18.6274i	−0.236721	+	0.669549i
$775$			6.82843i			0.245284i
$776$		−	6.58579i		−	0.236416i
$777$	1.85786	−	1.31371i	0.0666505	−	0.0471290i
$778$		−	20.3431i		−	0.729337i
$779$	−46.9706	+	11.0711i	−1.68290	+	0.396662i
$780$	−2.24264	−	3.17157i	−0.0802994	−	0.113561i
$781$		−	15.3137i		−	0.547968i
$782$	16.9706			0.606866
$783$	−25.3553	+	7.17157i	−0.906126	+	0.256291i
$784$	−6.65685			−0.237745
$785$			23.7990i			0.849422i
$786$	−6.97056	+	4.92893i	−0.248632	+	0.175809i
$787$			44.9706i			1.60303i	0.597976	+	0.801514i	$0.295972\pi$
$787$			44.9706i			1.60303i	−0.597976	+	0.801514i	$0.704028\pi$
$788$			18.1421i			0.646287i
$789$	15.7990	−	11.1716i	0.562459	−	0.397719i
$790$	−13.3137			−0.473680
$791$	7.51472			0.267193
$792$	−15.3137	−	5.41421i	−0.544149	−	0.192386i
$793$			10.0589i			0.357201i
$794$	16.9706			0.602263
$795$	−4.48528	+	3.17157i	−0.159077	+	0.112484i
$796$	−16.9706			−0.601506
$797$	−24.3431			−0.862278			−0.431139	−	0.902285i	$-0.641888\pi$
$797$	−24.3431			−0.862278			−0.431139	+	0.902285i	$0.641888\pi$
$798$	3.31371	+	2.92893i	0.117304	+	0.103683i
$799$	−8.97056			−0.317356
$800$	−1.00000			−0.0353553
$801$	−10.5858	+	29.9411i	−0.374030	+	1.05792i
$802$	−18.3848			−0.649189
$803$			13.4558i			0.474846i
$804$		0			0
$805$	−3.51472			−0.123878
$806$	−15.3137			−0.539402
$807$	−24.3848	−	34.4853i	−0.858385	−	1.21394i
$808$			7.65685i			0.269367i
$809$			35.3137i			1.24156i	0.783983	+	0.620782i	$0.213185\pi$
$809$			35.3137i			1.24156i	−0.783983	+	0.620782i	$0.786815\pi$
$810$	−5.65685	+	7.00000i	−0.198762	+	0.245955i
$811$		−	13.0294i		−	0.457525i	−0.973482	−	0.228763i	$-0.926532\pi$
$811$		−	13.0294i		−	0.457525i	0.973482	−	0.228763i	$-0.0734680\pi$
$812$	2.97056			0.104246
$813$	−28.9706	−	40.9706i	−1.01604	−	1.43690i
$814$	12.1421			0.425582
$815$		−	12.7279i		−	0.445840i
$816$	−4.00000	+	2.82843i	−0.140028	+	0.0990148i
$817$	27.9411	−	6.58579i	0.977536	−	0.230408i
$818$			4.48528i			0.156824i
$819$	3.71573	+	1.31371i	0.129838	+	0.0459047i
$820$			11.0711i			0.386618i
$821$			11.6569i			0.406827i	0.979093	+	0.203414i	$0.0652036\pi$
$821$			11.6569i			0.406827i	−0.979093	+	0.203414i	$0.934796\pi$
$822$	−20.4853	+	14.4853i	−0.714506	+	0.505232i
$823$	18.2426			0.635898			0.317949	−	0.948108i	$-0.397006\pi$
$823$	18.2426			0.635898			0.317949	+	0.948108i	$0.397006\pi$
$824$			4.34315i			0.151301i
$825$	7.65685	−	5.41421i	0.266577	−	0.188499i
$826$	−7.51472			−0.261471
$827$	−36.2843			−1.26173			−0.630864	−	0.775894i	$-0.717299\pi$
$827$	−36.2843			−1.26173			−0.630864	+	0.775894i	$0.717299\pi$
$828$	16.9706	+	6.00000i	0.589768	+	0.208514i
$829$		−	35.5980i		−	1.23637i	−0.786033	−	0.618184i	$-0.787868\pi$
$829$		−	35.5980i		−	1.23637i	0.786033	−	0.618184i	$-0.212132\pi$
$830$	−12.8284			−0.445281
$831$	24.9706	+	35.3137i	0.866219	+	1.22502i
$832$		−	2.24264i		−	0.0777496i
$833$		−	18.8284i		−	0.652366i
$834$	18.1421	+	25.6569i	0.628211	+	0.888424i
$835$		0			0
$836$	5.41421	+	22.9706i	0.187254	+	0.794454i
$837$	9.65685	+	34.1421i	0.333790	+	1.18012i
$838$		−	6.38478i		−	0.220558i
$839$	2.82843			0.0976481			0.0488241	−	0.998807i	$-0.484453\pi$
$839$	2.82843			0.0976481			0.0488241	+	0.998807i	$0.484453\pi$
$840$	0.828427	−	0.585786i	0.0285835	−	0.0202116i
$841$	−3.28427			−0.113251
$842$			24.2843i			0.836891i
$843$	−0.928932	−	1.31371i	−0.0319941	−	0.0452465i
$844$		−	2.00000i		−	0.0688428i
$845$		−	7.97056i		−	0.274196i
$846$	−8.97056	−	3.17157i	−0.308414	−	0.109041i
$847$	−10.7279			−0.368616
$848$	−3.17157			−0.108912
$849$	12.7279	+	18.0000i	0.436821	+	0.617758i
$850$		−	2.82843i		−	0.0970143i
$851$	−13.4558			−0.461260
$852$	−2.82843	−	4.00000i	−0.0969003	−	0.137038i
$853$	−12.0000			−0.410872			−0.205436	−	0.978671i	$-0.565861\pi$
$853$	−12.0000			−0.410872			−0.205436	+	0.978671i	$0.565861\pi$
$854$	−2.62742			−0.0899084
$855$	13.0000	+	1.41421i	0.444591	+	0.0483651i
$856$	3.65685			0.124989
$857$	4.82843			0.164936			0.0824680	−	0.996594i	$-0.473720\pi$
$857$	4.82843			0.164936			0.0824680	+	0.996594i	$0.473720\pi$
$858$	12.1421	+	17.1716i	0.414526	+	0.586228i
$859$	11.0294			0.376320			0.188160	−	0.982138i	$-0.439748\pi$
$859$	11.0294			0.376320			0.188160	+	0.982138i	$0.439748\pi$
$860$		−	6.58579i		−	0.224573i
$861$	−6.48528	−	9.17157i	−0.221018	−	0.312566i
$862$	−19.3137			−0.657828
$863$	56.8284			1.93446			0.967231	−	0.253898i	$-0.0817127\pi$
$863$	56.8284			1.93446			0.967231	+	0.253898i	$0.0817127\pi$
$864$	−5.00000	+	1.41421i	−0.170103	+	0.0481125i
$865$		−	6.00000i		−	0.204006i
$866$		−	14.3848i		−	0.488815i
$867$	9.00000	+	12.7279i	0.305656	+	0.432263i
$868$		−	4.00000i		−	0.135769i
$869$	72.0833			2.44526
$870$	7.17157	−	5.07107i	0.243139	−	0.171925i
$871$		0			0
$872$		−	2.34315i		−	0.0793489i
$873$	18.6274	+	6.58579i	0.630443	+	0.222895i
$874$	−6.00000	−	25.4558i	−0.202953	−	0.861057i
$875$			0.585786i			0.0198032i
$876$	2.48528	+	3.51472i	0.0839699	+	0.118751i
$877$		−	40.8701i		−	1.38008i	−0.723769	−	0.690042i	$-0.757592\pi$
$877$		−	40.8701i		−	1.38008i	0.723769	−	0.690042i	$-0.242408\pi$
$878$			39.9411i			1.34795i
$879$	3.17157	+	4.48528i	0.106974	+	0.151285i
$880$	5.41421			0.182513
$881$			28.2843i			0.952921i	0.879196	+	0.476461i	$0.158081\pi$
$881$			28.2843i			0.952921i	−0.879196	+	0.476461i	$0.841919\pi$
$882$	6.65685	−	18.8284i	0.224148	−	0.633986i
$883$	21.4142			0.720646			0.360323	−	0.932828i	$-0.382667\pi$
$883$	21.4142			0.720646			0.360323	+	0.932828i	$0.382667\pi$
$884$	6.34315			0.213343
$885$	−18.1421	+	12.8284i	−0.609841	+	0.431223i
$886$			18.0000i			0.604722i
$887$	48.8284			1.63950			0.819749	−	0.572723i	$-0.194113\pi$
$887$	48.8284			1.63950			0.819749	+	0.572723i	$0.194113\pi$
$888$	3.17157	−	2.24264i	0.106431	−	0.0752581i
$889$		−	7.51472i		−	0.252036i
$890$		−	10.5858i		−	0.354836i
$891$	30.6274	−	37.8995i	1.02606	−	1.26968i
$892$		−	18.0000i		−	0.602685i
$893$	3.17157	+	13.4558i	0.106133	+	0.450283i
$894$	20.4853	−	14.4853i	0.685130	−	0.484460i
$895$			21.7990i			0.728660i
$896$	0.585786			0.0195698
$897$	−13.4558	−	19.0294i	−0.449278	−	0.635374i
$898$	−16.2426			−0.542024
$899$		−	34.6274i		−	1.15489i
$900$	1.00000	−	2.82843i	0.0333333	−	0.0942809i
$901$		−	8.97056i		−	0.298853i
$902$		−	59.9411i		−	1.99582i
$903$	3.85786	+	5.45584i	0.128382	+	0.181559i
$904$	12.8284			0.426667
$905$	10.8284			0.359949
$906$	−28.9706	+	20.4853i	−0.962482	+	0.680578i
$907$			12.9706i			0.430680i	0.976539	+	0.215340i	$0.0690860\pi$
$907$			12.9706i			0.430680i	−0.976539	+	0.215340i	$0.930914\pi$
$908$	−2.34315			−0.0777600
$909$	−21.6569	−	7.65685i	−0.718313	−	0.253962i
$910$	−1.31371			−0.0435490
$911$	23.3137			0.772418			0.386209	−	0.922411i	$-0.373784\pi$
$911$	23.3137			0.772418			0.386209	+	0.922411i	$0.373784\pi$
$912$	5.65685	+	5.00000i	0.187317	+	0.165567i
$913$	69.4558			2.29865
$914$	−0.828427			−0.0274019
$915$	−6.34315	+	4.48528i	−0.209698	+	0.148279i
$916$	8.48528			0.280362
$917$			2.88730i			0.0953471i
$918$	−4.00000	−	14.1421i	−0.132020	−	0.466760i
$919$	37.4558			1.23555			0.617777	−	0.786353i	$-0.288033\pi$
$919$	37.4558			1.23555			0.617777	+	0.786353i	$0.288033\pi$
$920$	−6.00000			−0.197814
$921$	25.6569	−	18.1421i	0.845422	−	0.597804i
$922$		−	28.1421i		−	0.926812i
$923$			6.34315i			0.208787i
$924$	−4.48528	+	3.17157i	−0.147555	+	0.104337i
$925$			2.24264i			0.0737376i
$926$	19.2132			0.631385
$927$	−12.2843	−	4.34315i	−0.403468	−	0.142648i
$928$	5.07107			0.166466
$929$			33.1716i			1.08832i	0.838980	+	0.544162i	$0.183152\pi$
$929$			33.1716i			1.08832i	−0.838980	+	0.544162i	$0.816848\pi$
$930$	−6.82843	−	9.65685i	−0.223913	−	0.316661i
$931$	−28.2426	+	6.65685i	−0.925615	+	0.218170i
$932$			17.7990i			0.583025i
$933$	−7.17157	+	5.07107i	−0.234787	+	0.166019i
$934$		−	25.7990i		−	0.844169i
$935$			15.3137i			0.500812i
$936$	6.34315	+	2.24264i	0.207332	+	0.0733030i
$937$	−5.02944			−0.164305			−0.0821523	−	0.996620i	$-0.526179\pi$
$937$	−5.02944			−0.164305			−0.0821523	+	0.996620i	$0.526179\pi$
$938$		0			0
$939$	−16.8284	−	23.7990i	−0.549175	−	0.776651i
$940$	3.17157			0.103445
$941$	−20.8701			−0.680344			−0.340172	−	0.940363i	$-0.610485\pi$
$941$	−20.8701			−0.680344			−0.340172	+	0.940363i	$0.610485\pi$
$942$	−23.7990	−	33.6569i	−0.775413	−	1.09660i
$943$			66.4264i			2.16314i
$944$	−12.8284			−0.417530
$945$	0.828427	+	2.92893i	0.0269487	+	0.0952782i
$946$			35.6569i			1.15930i
$947$			2.68629i			0.0872927i	0.999047	+	0.0436464i	$0.0138975\pi$
$947$			2.68629i			0.0872927i	−0.999047	+	0.0436464i	$0.986103\pi$
$948$	18.8284	−	13.3137i	0.611519	−	0.432409i
$949$		−	5.57359i		−	0.180926i
$950$	−4.24264	+	1.00000i	−0.137649	+	0.0324443i
$951$	−0.343146	−	0.485281i	−0.0111273	−	0.0157363i
$952$			1.65685i			0.0536990i
$953$	−15.9411			−0.516384			−0.258192	−	0.966094i	$-0.583127\pi$
$953$	−15.9411			−0.516384			−0.258192	+	0.966094i	$0.583127\pi$
$954$	3.17157	−	8.97056i	0.102683	−	0.290433i
$955$	10.2426			0.331444
$956$		−	0.100505i		−	0.00325057i
$957$	−38.8284	+	27.4558i	−1.25514	+	0.887521i
$958$		−	3.41421i		−	0.110308i
$959$			8.48528i			0.274004i
$960$	1.41421	−	1.00000i	0.0456435	−	0.0322749i
$961$	−15.6274			−0.504110
$962$	−5.02944			−0.162156
$963$	−3.65685	+	10.3431i	−0.117840	+	0.333303i
$964$			8.48528i			0.273293i
$965$	19.5563			0.629541
$966$	4.97056	−	3.51472i	0.159925	−	0.113084i
$967$	50.2426			1.61569			0.807847	−	0.589392i	$-0.200633\pi$
$967$	50.2426			1.61569			0.807847	+	0.589392i	$0.200633\pi$
$968$	−18.3137			−0.588625
$969$	−14.1421	+	16.0000i	−0.454311	+	0.513994i
$970$	−6.58579			−0.211457
$971$	61.1127			1.96120			0.980600	−	0.196020i	$-0.0628017\pi$
$971$	61.1127			1.96120			0.980600	+	0.196020i	$0.0628017\pi$
$972$	1.00000	−	15.5563i	0.0320750	−	0.498970i
$973$	10.6274			0.340699
$974$			36.1421i			1.15807i
$975$	−3.17157	+	2.24264i	−0.101572	+	0.0718220i
$976$	−4.48528			−0.143570
$977$	10.2843			0.329023			0.164511	−	0.986375i	$-0.447395\pi$
$977$	10.2843			0.329023			0.164511	+	0.986375i	$0.447395\pi$
$978$	12.7279	+	18.0000i	0.406994	+	0.575577i
$979$			57.3137i			1.83175i
$980$			6.65685i			0.212645i
$981$	6.62742	+	2.34315i	0.211597	+	0.0748109i
$982$		−	43.5563i		−	1.38994i
$983$		0			0			−	1.00000i	$-0.5\pi$
$983$		0			0				1.00000i	$0.5\pi$
$984$	−11.0711	−	15.6569i	−0.352933	−	0.499122i
$985$	18.1421			0.578057
$986$			14.3431i			0.456779i
$987$	−2.62742	+	1.85786i	−0.0836316	+	0.0591365i
$988$	−2.24264	−	9.51472i	−0.0713479	−	0.302704i
$989$		−	39.5147i		−	1.25649i
$990$	−5.41421	+	15.3137i	−0.172075	+	0.486702i
$991$			2.97056i			0.0943630i	0.998886	+	0.0471815i	$0.0150239\pi$
$991$			2.97056i			0.0943630i	−0.998886	+	0.0471815i	$0.984976\pi$
$992$		−	6.82843i		−	0.216803i
$993$	−24.0000	+	16.9706i	−0.761617	+	0.538545i
$994$	−1.65685			−0.0525522
$995$			16.9706i			0.538003i
$996$	18.1421	−	12.8284i	0.574856	−	0.406484i
$997$	0.485281			0.0153690			0.00768451	−	0.999970i	$-0.497554\pi$
$997$	0.485281			0.0153690			0.00768451	+	0.999970i	$0.497554\pi$
$998$	−25.6569			−0.812154
$999$	3.17157	+	11.2132i	0.100344	+	0.354770i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.f.b.341.3	yes	4
3.2	odd	2		570.2.f.a.341.4	yes	4
19.18	odd	2		570.2.f.a.341.1	✓	4
57.56	even	2	inner	570.2.f.b.341.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.f.a.341.1	✓	4	19.18	odd	2
570.2.f.a.341.4	yes	4	3.2	odd	2
570.2.f.b.341.2	yes	4	57.56	even	2	inner
570.2.f.b.341.3	yes	4	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(1.00000 + 1.41421i) q^{3} +1.00000 q^{4} -1.00000i q^{5} +(1.00000 + 1.41421i) q^{6} +0.585786 q^{7} +1.00000 q^{8} +(-1.00000 + 2.82843i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(1.00000 + 1.41421i) q^{3} +1.00000 q^{4} -1.00000i q^{5} +(1.00000 + 1.41421i) q^{6} +0.585786 q^{7} +1.00000 q^{8} +(-1.00000 + 2.82843i) q^{9} -1.00000i q^{10} +5.41421i q^{11} +(1.00000 + 1.41421i) q^{12} -2.24264i q^{13} +0.585786 q^{14} +(1.41421 - 1.00000i) q^{15} +1.00000 q^{16} +2.82843i q^{17} +(-1.00000 + 2.82843i) q^{18} +(4.24264 - 1.00000i) q^{19} -1.00000i q^{20} +(0.585786 + 0.828427i) q^{21} +5.41421i q^{22} -6.00000i q^{23} +(1.00000 + 1.41421i) q^{24} -1.00000 q^{25} -2.24264i q^{26} +(-5.00000 + 1.41421i) q^{27} +0.585786 q^{28} +5.07107 q^{29} +(1.41421 - 1.00000i) q^{30} -6.82843i q^{31} +1.00000 q^{32} +(-7.65685 + 5.41421i) q^{33} +2.82843i q^{34} -0.585786i q^{35} +(-1.00000 + 2.82843i) q^{36} -2.24264i q^{37} +(4.24264 - 1.00000i) q^{38} +(3.17157 - 2.24264i) q^{39} -1.00000i q^{40} -11.0711 q^{41} +(0.585786 + 0.828427i) q^{42} +6.58579 q^{43} +5.41421i q^{44} +(2.82843 + 1.00000i) q^{45} -6.00000i q^{46} +3.17157i q^{47} +(1.00000 + 1.41421i) q^{48} -6.65685 q^{49} -1.00000 q^{50} +(-4.00000 + 2.82843i) q^{51} -2.24264i q^{52} -3.17157 q^{53} +(-5.00000 + 1.41421i) q^{54} +5.41421 q^{55} +0.585786 q^{56} +(5.65685 + 5.00000i) q^{57} +5.07107 q^{58} -12.8284 q^{59} +(1.41421 - 1.00000i) q^{60} -4.48528 q^{61} -6.82843i q^{62} +(-0.585786 + 1.65685i) q^{63} +1.00000 q^{64} -2.24264 q^{65} +(-7.65685 + 5.41421i) q^{66} +2.82843i q^{68} +(8.48528 - 6.00000i) q^{69} -0.585786i q^{70} -2.82843 q^{71} +(-1.00000 + 2.82843i) q^{72} +2.48528 q^{73} -2.24264i q^{74} +(-1.00000 - 1.41421i) q^{75} +(4.24264 - 1.00000i) q^{76} +3.17157i q^{77} +(3.17157 - 2.24264i) q^{78} -13.3137i q^{79} -1.00000i q^{80} +(-7.00000 - 5.65685i) q^{81} -11.0711 q^{82} -12.8284i q^{83} +(0.585786 + 0.828427i) q^{84} +2.82843 q^{85} +6.58579 q^{86} +(5.07107 + 7.17157i) q^{87} +5.41421i q^{88} +10.5858 q^{89} +(2.82843 + 1.00000i) q^{90} -1.31371i q^{91} -6.00000i q^{92} +(9.65685 - 6.82843i) q^{93} +3.17157i q^{94} +(-1.00000 - 4.24264i) q^{95} +(1.00000 + 1.41421i) q^{96} -6.58579i q^{97} -6.65685 q^{98} +(-15.3137 - 5.41421i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} + 4 q^{6} + 8 q^{7} + 4 q^{8} - 4 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 + 4 * q^6 + 8 * q^7 + 4 * q^8 - 4 * q^9	\( 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} + 4 q^{6} + 8 q^{7} + 4 q^{8} - 4 q^{9} + 4 q^{12} + 8 q^{14} + 4 q^{16} - 4 q^{18} + 8 q^{21} + 4 q^{24} - 4 q^{25} - 20 q^{27} + 8 q^{28} - 8 q^{29} + 4 q^{32} - 8 q^{33} - 4 q^{36} + 24 q^{39} - 16 q^{41} + 8 q^{42} + 32 q^{43} + 4 q^{48} - 4 q^{49} - 4 q^{50} - 16 q^{51} - 24 q^{53} - 20 q^{54} + 16 q^{55} + 8 q^{56} - 8 q^{58} - 40 q^{59} + 16 q^{61} - 8 q^{63} + 4 q^{64} + 8 q^{65} - 8 q^{66} - 4 q^{72} - 24 q^{73} - 4 q^{75} + 24 q^{78} - 28 q^{81} - 16 q^{82} + 8 q^{84} + 32 q^{86} - 8 q^{87} + 48 q^{89} + 16 q^{93} - 4 q^{95} + 4 q^{96} - 4 q^{98} - 16 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 + 4 * q^6 + 8 * q^7 + 4 * q^8 - 4 * q^9 + 4 * q^12 + 8 * q^14 + 4 * q^16 - 4 * q^18 + 8 * q^21 + 4 * q^24 - 4 * q^25 - 20 * q^27 + 8 * q^28 - 8 * q^29 + 4 * q^32 - 8 * q^33 - 4 * q^36 + 24 * q^39 - 16 * q^41 + 8 * q^42 + 32 * q^43 + 4 * q^48 - 4 * q^49 - 4 * q^50 - 16 * q^51 - 24 * q^53 - 20 * q^54 + 16 * q^55 + 8 * q^56 - 8 * q^58 - 40 * q^59 + 16 * q^61 - 8 * q^63 + 4 * q^64 + 8 * q^65 - 8 * q^66 - 4 * q^72 - 24 * q^73 - 4 * q^75 + 24 * q^78 - 28 * q^81 - 16 * q^82 + 8 * q^84 + 32 * q^86 - 8 * q^87 + 48 * q^89 + 16 * q^93 - 4 * q^95 + 4 * q^96 - 4 * q^98 - 16 * q^99

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