LMFDB - Embedded newform 798.2.j.l.457.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [798,2,Mod(457,798)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(798, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("798.457");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 798 = 2 \cdot 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	798.j (of order $3$, 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:	$6.37206208130$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.856615824.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 11x^{6} + 36x^{4} + 32x^{2} + 4 $ x^8 + 11x^6 + 36x^4 + 32*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			457.1
Root			$1.07834i$ of defining polynomial
Character	$\chi$	$=$	798.457
Dual form			798.2.j.l.571.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.24624 + 2.15855i) q^{5} +1.00000 q^{6} +(2.47720 + 0.929227i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.24624 + 2.15855i) q^{5} +1.00000 q^{6} +(2.47720 + 0.929227i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.24624 + 2.15855i) q^{10} +(1.73096 + 2.99812i) q^{11} +(0.500000 - 0.866025i) q^{12} -4.98496 q^{13} +(2.04334 - 1.68071i) q^{14} -2.49248 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.12150 - 1.94249i) q^{17} +(0.500000 + 0.866025i) q^{18} +(-0.500000 + 0.866025i) q^{19} +2.49248 q^{20} +(0.433868 + 2.60993i) q^{21} +3.46193 q^{22} +(-3.00202 + 5.19965i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-0.606223 - 1.05001i) q^{25} +(-2.49248 + 4.31710i) q^{26} -1.00000 q^{27} +(-0.433868 - 2.60993i) q^{28} -5.51156 q^{29} +(-1.24624 + 2.15855i) q^{30} +(3.64204 + 6.30819i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-1.73096 + 2.99812i) q^{33} -2.24299 q^{34} +(-5.09297 + 4.18913i) q^{35} +1.00000 q^{36} +(4.58343 - 7.93873i) q^{37} +(0.500000 + 0.866025i) q^{38} +(-2.49248 - 4.31710i) q^{39} +(1.24624 - 2.15855i) q^{40} +4.64383 q^{41} +(2.47720 + 0.929227i) q^{42} +9.54211 q^{43} +(1.73096 - 2.99812i) q^{44} +(-1.24624 - 2.15855i) q^{45} +(3.00202 + 5.19965i) q^{46} +(-2.68011 + 4.64208i) q^{47} -1.00000 q^{48} +(5.27308 + 4.60377i) q^{49} -1.21245 q^{50} +(1.12150 - 1.94249i) q^{51} +(2.49248 + 4.31710i) q^{52} +(2.93711 + 5.08723i) q^{53} +(-0.500000 + 0.866025i) q^{54} -8.62878 q^{55} +(-2.47720 - 0.929227i) q^{56} -1.00000 q^{57} +(-2.75578 + 4.77315i) q^{58} +(4.33921 + 7.51573i) q^{59} +(1.24624 + 2.15855i) q^{60} +(-2.18763 + 3.78908i) q^{61} +7.28407 q^{62} +(-2.04334 + 1.68071i) q^{63} +1.00000 q^{64} +(6.21245 - 10.7603i) q^{65} +(1.73096 + 2.99812i) q^{66} +(-7.57915 - 13.1275i) q^{67} +(-1.12150 + 1.94249i) q^{68} -6.00404 q^{69} +(1.08141 + 6.50520i) q^{70} +12.0907 q^{71} +(0.500000 - 0.866025i) q^{72} +(-7.21019 - 12.4884i) q^{73} +(-4.58343 - 7.93873i) q^{74} +(0.606223 - 1.05001i) q^{75} +1.00000 q^{76} +(1.50202 + 9.03541i) q^{77} -4.98496 q^{78} +(3.54334 - 6.13724i) q^{79} +(-1.24624 - 2.15855i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(2.32191 - 4.02167i) q^{82} -5.59823 q^{83} +(2.04334 - 1.68071i) q^{84} +5.59061 q^{85} +(4.77106 - 8.26371i) q^{86} +(-2.75578 - 4.77315i) q^{87} +(-1.73096 - 2.99812i) q^{88} +(-3.76476 + 6.52075i) q^{89} -2.49248 q^{90} +(-12.3488 - 4.63215i) q^{91} +6.00404 q^{92} +(-3.64204 + 6.30819i) q^{93} +(2.68011 + 4.64208i) q^{94} +(-1.24624 - 2.15855i) q^{95} +(-0.500000 + 0.866025i) q^{96} +7.00404 q^{97} +(6.62352 - 2.26473i) q^{98} -3.46193 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} + 4 q^{3} - 4 q^{4} + 8 q^{6} - 2 q^{7} - 8 q^{8} - 4 q^{9}+O(q^{10}) $ 8 * q + 4 * q^2 + 4 * q^3 - 4 * q^4 + 8 * q^6 - 2 * q^7 - 8 * q^8 - 4 * q^9	$ 8 q + 4 q^{2} + 4 q^{3} - 4 q^{4} + 8 q^{6} - 2 q^{7} - 8 q^{8} - 4 q^{9} + 2 q^{11} + 4 q^{12} - q^{14} - 4 q^{16} - 10 q^{17} + 4 q^{18} - 4 q^{19} - q^{21} + 4 q^{22} + 5 q^{23} - 4 q^{24} - 4 q^{25} - 8 q^{27} + q^{28} - 6 q^{29} - 9 q^{31} + 4 q^{32} - 2 q^{33} - 20 q^{34} - 9 q^{35} + 8 q^{36} + 14 q^{37} + 4 q^{38} + 8 q^{41} - 2 q^{42} + 42 q^{43} + 2 q^{44} - 5 q^{46} - 7 q^{47} - 8 q^{48} - 4 q^{49} - 8 q^{50} + 10 q^{51} + 7 q^{53} - 4 q^{54} + 2 q^{56} - 8 q^{57} - 3 q^{58} - 7 q^{59} - 23 q^{61} - 18 q^{62} + q^{63} + 8 q^{64} + 48 q^{65} + 2 q^{66} - 6 q^{67} - 10 q^{68} + 10 q^{69} + 15 q^{70} + 4 q^{71} + 4 q^{72} + 5 q^{73} - 14 q^{74} + 4 q^{75} + 8 q^{76} - 17 q^{77} + 11 q^{79} - 4 q^{81} + 4 q^{82} + 28 q^{83} - q^{84} + 12 q^{85} + 21 q^{86} - 3 q^{87} - 2 q^{88} - 10 q^{89} - 48 q^{91} - 10 q^{92} + 9 q^{93} + 7 q^{94} - 4 q^{96} - 2 q^{97} + 25 q^{98} - 4 q^{99}+O(q^{100}) $ 8 * q + 4 * q^2 + 4 * q^3 - 4 * q^4 + 8 * q^6 - 2 * q^7 - 8 * q^8 - 4 * q^9 + 2 * q^11 + 4 * q^12 - q^14 - 4 * q^16 - 10 * q^17 + 4 * q^18 - 4 * q^19 - q^21 + 4 * q^22 + 5 * q^23 - 4 * q^24 - 4 * q^25 - 8 * q^27 + q^28 - 6 * q^29 - 9 * q^31 + 4 * q^32 - 2 * q^33 - 20 * q^34 - 9 * q^35 + 8 * q^36 + 14 * q^37 + 4 * q^38 + 8 * q^41 - 2 * q^42 + 42 * q^43 + 2 * q^44 - 5 * q^46 - 7 * q^47 - 8 * q^48 - 4 * q^49 - 8 * q^50 + 10 * q^51 + 7 * q^53 - 4 * q^54 + 2 * q^56 - 8 * q^57 - 3 * q^58 - 7 * q^59 - 23 * q^61 - 18 * q^62 + q^63 + 8 * q^64 + 48 * q^65 + 2 * q^66 - 6 * q^67 - 10 * q^68 + 10 * q^69 + 15 * q^70 + 4 * q^71 + 4 * q^72 + 5 * q^73 - 14 * q^74 + 4 * q^75 + 8 * q^76 - 17 * q^77 + 11 * q^79 - 4 * q^81 + 4 * q^82 + 28 * q^83 - q^84 + 12 * q^85 + 21 * q^86 - 3 * q^87 - 2 * q^88 - 10 * q^89 - 48 * q^91 - 10 * q^92 + 9 * q^93 + 7 * q^94 - 4 * q^96 - 2 * q^97 + 25 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/798\mathbb{Z}\right)^\times$.

$n$	$115$	$211$	$533$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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 $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−1.24624	+	2.15855i	−0.557335	+	0.965333i	0.440383	+	0.897810i	$0.354843\pi$
$5$	−1.24624	+	2.15855i	−0.557335	+	0.965333i	−0.997718	+	0.0675224i	$0.978491\pi$
$6$	1.00000			0.408248
$7$	2.47720	+	0.929227i	0.936295	+	0.351215i
$7$	2.47720	+	0.929227i	0.936295	+	0.351215i
$8$	−1.00000			−0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	1.24624	+	2.15855i	0.394095	+	0.682593i
$11$	1.73096	+	2.99812i	0.521906	+	0.903967i	0.999675	+	0.0254818i	$0.00811198\pi$
$11$	1.73096	+	2.99812i	0.521906	+	0.903967i	−0.477770	+	0.878485i	$0.658555\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	−4.98496			−1.38258			−0.691289	−	0.722578i	$-0.742957\pi$
$13$	−4.98496			−1.38258			−0.691289	+	0.722578i	$0.742957\pi$
$14$	2.04334	−	1.68071i	0.546104	−	0.449188i
$15$	−2.49248			−0.643555
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.12150	−	1.94249i	−0.272003	−	0.471123i	0.697372	−	0.716710i	$-0.254353\pi$
$17$	−1.12150	−	1.94249i	−0.272003	−	0.471123i	−0.969375	+	0.245587i	$0.921019\pi$
$18$	0.500000	+	0.866025i	0.117851	+	0.204124i
$19$	−0.500000	+	0.866025i	−0.114708	+	0.198680i
$19$	−0.500000	+	0.866025i	−0.114708	+	0.198680i
$20$	2.49248			0.557335
$21$	0.433868	+	2.60993i	0.0946777	+	0.569534i
$22$	3.46193			0.738086
$23$	−3.00202	+	5.19965i	−0.625964	+	1.08420i	0.362389	+	0.932027i	$0.381961\pi$
$23$	−3.00202	+	5.19965i	−0.625964	+	1.08420i	−0.988354	+	0.152175i	$0.951372\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	−0.606223	−	1.05001i	−0.121245	−	0.210002i
$26$	−2.49248	+	4.31710i	−0.488815	+	0.846653i
$27$	−1.00000			−0.192450
$28$	−0.433868	−	2.60993i	−0.0819933	−	0.493231i
$29$	−5.51156			−1.02347			−0.511736	−	0.859143i	$-0.670997\pi$
$29$	−5.51156			−1.02347			−0.511736	+	0.859143i	$0.670997\pi$
$30$	−1.24624	+	2.15855i	−0.227531	+	0.394095i
$31$	3.64204	+	6.30819i	0.654129	+	1.13298i	0.982111	+	0.188301i	$0.0602980\pi$
$31$	3.64204	+	6.30819i	0.654129	+	1.13298i	−0.327982	+	0.944684i	$0.606369\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−1.73096	+	2.99812i	−0.301322	+	0.521906i
$34$	−2.24299			−0.384670
$35$	−5.09297	+	4.18913i	−0.860869	+	0.708092i
$36$	1.00000			0.166667
$37$	4.58343	−	7.93873i	0.753511	−	1.30512i	−0.192601	−	0.981277i	$-0.561692\pi$
$37$	4.58343	−	7.93873i	0.753511	−	1.30512i	0.946111	−	0.323842i	$-0.104974\pi$
$38$	0.500000	+	0.866025i	0.0811107	+	0.140488i
$39$	−2.49248	−	4.31710i	−0.399116	−	0.691289i
$40$	1.24624	−	2.15855i	0.197048	−	0.341297i
$41$	4.64383			0.725244			0.362622	−	0.931936i	$-0.381882\pi$
$41$	4.64383			0.725244			0.362622	+	0.931936i	$0.381882\pi$
$42$	2.47720	+	0.929227i	0.382241	+	0.143383i
$43$	9.54211			1.45516			0.727579	−	0.686024i	$-0.240645\pi$
$43$	9.54211			1.45516			0.727579	+	0.686024i	$0.240645\pi$
$44$	1.73096	−	2.99812i	0.260953	−	0.451983i
$45$	−1.24624	−	2.15855i	−0.185778	−	0.321778i
$46$	3.00202	+	5.19965i	0.442624	+	0.766647i
$47$	−2.68011	+	4.64208i	−0.390934	+	0.677117i	−0.992573	−	0.121651i	$-0.961181\pi$
$47$	−2.68011	+	4.64208i	−0.390934	+	0.677117i	0.601639	+	0.798768i	$0.294515\pi$
$48$	−1.00000			−0.144338
$49$	5.27308	+	4.60377i	0.753297	+	0.657681i
$50$	−1.21245			−0.171466
$51$	1.12150	−	1.94249i	0.157041	−	0.272003i
$52$	2.49248	+	4.31710i	0.345644	+	0.598674i
$53$	2.93711	+	5.08723i	0.403443	+	0.698785i	0.994139	−	0.108110i	$-0.0344799\pi$
$53$	2.93711	+	5.08723i	0.403443	+	0.698785i	−0.590695	+	0.806895i	$0.701147\pi$
$54$	−0.500000	+	0.866025i	−0.0680414	+	0.117851i
$55$	−8.62878			−1.16350
$56$	−2.47720	−	0.929227i	−0.331030	−	0.124173i
$57$	−1.00000			−0.132453
$58$	−2.75578	+	4.77315i	−0.361852	+	0.626746i
$59$	4.33921	+	7.51573i	0.564917	+	0.978464i	0.997057	+	0.0766583i	$0.0244251\pi$
$59$	4.33921	+	7.51573i	0.564917	+	0.978464i	−0.432141	+	0.901806i	$0.642242\pi$
$60$	1.24624	+	2.15855i	0.160889	+	0.278667i
$61$	−2.18763	+	3.78908i	−0.280097	+	0.485143i	−0.971408	−	0.237415i	$-0.923700\pi$
$61$	−2.18763	+	3.78908i	−0.280097	+	0.485143i	0.691311	+	0.722557i	$0.257033\pi$
$62$	7.28407			0.925078
$63$	−2.04334	+	1.68071i	−0.257436	+	0.211749i
$64$	1.00000			0.125000
$65$	6.21245	−	10.7603i	0.770559	−	1.33465i
$66$	1.73096	+	2.99812i	0.213067	+	0.369043i
$67$	−7.57915	−	13.1275i	−0.925940	−	1.60378i	−0.790042	−	0.613053i	$-0.789941\pi$
$67$	−7.57915	−	13.1275i	−0.925940	−	1.60378i	−0.135899	−	0.990723i	$-0.543392\pi$
$68$	−1.12150	+	1.94249i	−0.136001	+	0.235561i
$69$	−6.00404			−0.722802
$70$	1.08141	+	6.50520i	0.129253	+	0.777521i
$71$	12.0907			1.43490			0.717452	−	0.696608i	$-0.245308\pi$
$71$	12.0907			1.43490			0.717452	+	0.696608i	$0.245308\pi$
$72$	0.500000	−	0.866025i	0.0589256	−	0.102062i
$73$	−7.21019	−	12.4884i	−0.843889	−	1.46166i	−0.886583	−	0.462570i	$-0.846927\pi$
$73$	−7.21019	−	12.4884i	−0.843889	−	1.46166i	0.0426940	−	0.999088i	$-0.486406\pi$
$74$	−4.58343	−	7.93873i	−0.532813	−	0.922858i
$75$	0.606223	−	1.05001i	0.0700006	−	0.121245i
$76$	1.00000			0.114708
$77$	1.50202	+	9.03541i	0.171171	+	1.02968i
$78$	−4.98496			−0.564435
$79$	3.54334	−	6.13724i	0.398656	−	0.690493i	−0.594904	−	0.803797i	$-0.702810\pi$
$79$	3.54334	−	6.13724i	0.398656	−	0.690493i	0.993560	+	0.113304i	$0.0361433\pi$
$80$	−1.24624	−	2.15855i	−0.139334	−	0.241333i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	2.32191	−	4.02167i	0.256412	−	0.444119i
$83$	−5.59823			−0.614486			−0.307243	−	0.951631i	$-0.599406\pi$
$83$	−5.59823			−0.614486			−0.307243	+	0.951631i	$0.599406\pi$
$84$	2.04334	−	1.68071i	0.222946	−	0.183380i
$85$	5.59061			0.606387
$86$	4.77106	−	8.26371i	0.514476	−	0.891099i
$87$	−2.75578	−	4.77315i	−0.295451	−	0.511736i
$88$	−1.73096	−	2.99812i	−0.184521	−	0.319601i
$89$	−3.76476	+	6.52075i	−0.399064	+	0.691198i	−0.993611	−	0.112862i	$-0.963998\pi$
$89$	−3.76476	+	6.52075i	−0.399064	+	0.691198i	0.594547	+	0.804061i	$0.297331\pi$
$90$	−2.49248			−0.262730
$91$	−12.3488	−	4.63215i	−1.29450	−	0.485582i
$92$	6.00404			0.625964
$93$	−3.64204	+	6.30819i	−0.377662	+	0.654129i
$94$	2.68011	+	4.64208i	0.276432	+	0.478794i
$95$	−1.24624	−	2.15855i	−0.127861	−	0.221462i
$96$	−0.500000	+	0.866025i	−0.0510310	+	0.0883883i
$97$	7.00404			0.711153			0.355576	−	0.934647i	$-0.384285\pi$
$97$	7.00404			0.711153			0.355576	+	0.934647i	$0.384285\pi$
$98$	6.62352	−	2.26473i	0.669076	−	0.228773i
$99$	−3.46193			−0.347937
$100$	−0.606223	+	1.05001i	−0.0606223	+	0.105001i
$101$	−3.54784	−	6.14504i	−0.353024	−	0.611455i	0.633754	−	0.773535i	$-0.281513\pi$
$101$	−3.54784	−	6.14504i	−0.353024	−	0.611455i	−0.986778	+	0.162080i	$0.948180\pi$
$102$	−1.12150	−	1.94249i	−0.111045	−	0.192335i
$103$	−3.57567	+	6.19325i	−0.352322	+	0.610239i	−0.986656	−	0.162820i	$-0.947941\pi$
$103$	−3.57567	+	6.19325i	−0.352322	+	0.610239i	0.634334	+	0.773059i	$0.281274\pi$
$104$	4.98496			0.488815
$105$	−6.17438	−	2.31608i	−0.602557	−	0.226026i
$106$	5.87423			0.570555
$107$	7.86525	−	13.6230i	0.760362	−	1.31699i	−0.182302	−	0.983243i	$-0.558355\pi$
$107$	7.86525	−	13.6230i	0.760362	−	1.31699i	0.942664	−	0.333744i	$-0.108312\pi$
$108$	0.500000	+	0.866025i	0.0481125	+	0.0833333i
$109$	−4.15854	−	7.20279i	−0.398315	−	0.689903i	0.595203	−	0.803576i	$-0.297072\pi$
$109$	−4.15854	−	7.20279i	−0.398315	−	0.689903i	−0.993518	+	0.113673i	$0.963738\pi$
$110$	−4.31439	+	7.47274i	−0.411361	+	0.712498i
$111$	9.16685			0.870079
$112$	−2.04334	+	1.68071i	−0.193077	+	0.158812i
$113$	13.3643			1.25720			0.628602	−	0.777727i	$-0.283628\pi$
$113$	13.3643			1.25720			0.628602	+	0.777727i	$0.283628\pi$
$114$	−0.500000	+	0.866025i	−0.0468293	+	0.0811107i
$115$	−7.48247	−	12.9600i	−0.697744	−	1.20853i
$116$	2.75578	+	4.77315i	0.255868	+	0.443176i
$117$	2.49248	−	4.31710i	0.230430	−	0.399116i
$118$	8.67842			0.798913
$119$	−0.973163	−	5.85407i	−0.0892097	−	0.536641i
$120$	2.49248			0.227531
$121$	−0.492478	+	0.852997i	−0.0447707	+	0.0775451i
$122$	2.18763	+	3.78908i	0.198059	+	0.343048i
$123$	2.32191	+	4.02167i	0.209360	+	0.362622i
$124$	3.64204	−	6.30819i	0.327065	−	0.566492i
$125$	−9.44040			−0.844375
$126$	0.433868	+	2.60993i	0.0386520	+	0.232511i
$127$	6.09569			0.540905			0.270452	−	0.962733i	$-0.412827\pi$
$127$	6.09569			0.540905			0.270452	+	0.962733i	$0.412827\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	4.77106	+	8.26371i	0.420068	+	0.727579i
$130$	−6.21245	−	10.7603i	−0.544868	−	0.943738i
$131$	−4.65708	+	8.06630i	−0.406891	+	0.704756i	−0.994540	−	0.104360i	$-0.966720\pi$
$131$	−4.65708	+	8.06630i	−0.406891	+	0.704756i	0.587649	+	0.809116i	$0.300054\pi$
$132$	3.46193			0.301322
$133$	−2.04334	+	1.68071i	−0.177180	+	0.145736i
$134$	−15.1583			−1.30948
$135$	1.24624	−	2.15855i	0.107259	−	0.185778i
$136$	1.12150	+	1.94249i	0.0961676	+	0.166567i
$137$	3.89255	+	6.74210i	0.332563	+	0.576016i	0.983014	−	0.183532i	$-0.0587532\pi$
$137$	3.89255	+	6.74210i	0.332563	+	0.576016i	−0.650450	+	0.759549i	$0.725420\pi$
$138$	−3.00202	+	5.19965i	−0.255549	+	0.442624i
$139$	12.5882			1.06771			0.533857	−	0.845575i	$-0.320742\pi$
$139$	12.5882			1.06771			0.533857	+	0.845575i	$0.320742\pi$
$140$	6.17438	+	2.31608i	0.521830	+	0.195744i
$141$	−5.36021			−0.451411
$142$	6.04536	−	10.4709i	0.507315	−	0.878695i
$143$	−8.62878	−	14.9455i	−0.721575	−	1.24980i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	6.86872	−	11.8970i	0.570416	−	0.987990i
$146$	−14.4204			−1.19344
$147$	−1.35044	+	6.86850i	−0.111383	+	0.566504i
$148$	−9.16685			−0.753511
$149$	−8.14608	+	14.1094i	−0.667353	+	1.15589i	0.311289	+	0.950315i	$0.399239\pi$
$149$	−8.14608	+	14.1094i	−0.667353	+	1.15589i	−0.978642	+	0.205573i	$0.934094\pi$
$150$	−0.606223	−	1.05001i	−0.0494979	−	0.0857329i
$151$	−9.98675	−	17.2976i	−0.812710	−	1.40765i	−0.910961	−	0.412493i	$-0.864658\pi$
$151$	−9.98675	−	17.2976i	−0.812710	−	1.40765i	0.0982509	−	0.995162i	$-0.468675\pi$
$152$	0.500000	−	0.866025i	0.0405554	−	0.0702439i
$153$	2.24299			0.181335
$154$	8.57590	+	3.21692i	0.691066	+	0.259227i
$155$	−18.1554			−1.45828
$156$	−2.49248	+	4.31710i	−0.199558	+	0.345644i
$157$	0.369526	+	0.640038i	0.0294914	+	0.0510806i	0.880394	−	0.474242i	$-0.157278\pi$
$157$	0.369526	+	0.640038i	0.0294914	+	0.0510806i	−0.850903	+	0.525323i	$0.823945\pi$
$158$	−3.54334	−	6.13724i	−0.281893	−	0.488252i
$159$	−2.93711	+	5.08723i	−0.232928	+	0.403443i
$160$	−2.49248			−0.197048
$161$	−12.2683	+	10.0910i	−0.966875	+	0.795285i
$162$	−1.00000			−0.0785674
$163$	2.89904	−	5.02129i	0.227071	−	0.393298i	−0.729868	−	0.683588i	$-0.760419\pi$
$163$	2.89904	−	5.02129i	0.227071	−	0.393298i	0.956939	+	0.290290i	$0.0937519\pi$
$164$	−2.32191	−	4.02167i	−0.181311	−	0.314040i
$165$	−4.31439	−	7.47274i	−0.335875	−	0.581752i
$166$	−2.79912	+	4.84821i	−0.217254	+	0.376294i
$167$	17.1058			1.32368			0.661842	−	0.749644i	$-0.269775\pi$
$167$	17.1058			1.32368			0.661842	+	0.749644i	$0.269775\pi$
$168$	−0.433868	−	2.60993i	−0.0334736	−	0.201361i
$169$	11.8498			0.911522
$170$	2.79531	−	4.84161i	0.214390	−	0.371335i
$171$	−0.500000	−	0.866025i	−0.0382360	−	0.0662266i
$172$	−4.77106	−	8.26371i	−0.363790	−	0.630102i
$173$	1.29206	−	2.23792i	0.0982336	−	0.170146i	−0.812720	−	0.582654i	$-0.802014\pi$
$173$	1.29206	−	2.23792i	0.0982336	−	0.170146i	0.910954	+	0.412509i	$0.135347\pi$
$174$	−5.51156			−0.417830
$175$	−0.526041	−	3.16440i	−0.0397650	−	0.239206i
$176$	−3.46193			−0.260953
$177$	−4.33921	+	7.51573i	−0.326155	+	0.564917i
$178$	3.76476	+	6.52075i	0.282181	+	0.488751i
$179$	1.62474	+	2.81414i	0.121439	+	0.210338i	0.920335	−	0.391130i	$-0.127916\pi$
$179$	1.62474	+	2.81414i	0.121439	+	0.210338i	−0.798896	+	0.601469i	$0.794582\pi$
$180$	−1.24624	+	2.15855i	−0.0928892	+	0.160889i
$181$	12.4559			0.925840			0.462920	−	0.886400i	$-0.346802\pi$
$181$	12.4559			0.925840			0.462920	+	0.886400i	$0.346802\pi$
$182$	−10.1859	+	8.37825i	−0.755032	+	0.621038i
$183$	−4.37526			−0.323428
$184$	3.00202	−	5.19965i	0.221312	−	0.383323i
$185$	11.4241	+	19.7871i	0.839916	+	1.45478i
$186$	3.64204	+	6.30819i	0.267047	+	0.462539i
$187$	3.88254	−	6.72476i	0.283920	−	0.491763i
$188$	5.36021			0.390934
$189$	−2.47720	−	0.929227i	−0.180190	−	0.0675913i
$190$	−2.49248			−0.180823
$191$	8.22222	−	14.2413i	0.594939	−	1.03046i	−0.398617	−	0.917118i	$-0.630510\pi$
$191$	8.22222	−	14.2413i	0.594939	−	1.03046i	0.993556	−	0.113347i	$-0.0361571\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	9.34268	+	16.1820i	0.672501	+	1.16481i	0.977193	+	0.212355i	$0.0681133\pi$
$193$	9.34268	+	16.1820i	0.672501	+	1.16481i	−0.304692	+	0.952451i	$0.598553\pi$
$194$	3.50202	−	6.06568i	0.251430	−	0.435490i
$195$	12.4249			0.889765
$196$	1.35044	−	6.86850i	0.0964601	−	0.490607i
$197$	−15.4965			−1.10408			−0.552041	−	0.833817i	$-0.686151\pi$
$197$	−15.4965			−1.10408			−0.552041	+	0.833817i	$0.686151\pi$
$198$	−1.73096	+	2.99812i	−0.123014	+	0.213067i
$199$	0.729740	+	1.26395i	0.0517299	+	0.0895988i	0.890731	−	0.454531i	$-0.150193\pi$
$199$	0.729740	+	1.26395i	0.0517299	+	0.0895988i	−0.839001	+	0.544130i	$0.816860\pi$
$200$	0.606223	+	1.05001i	0.0428664	+	0.0742468i
$201$	7.57915	−	13.1275i	0.534592	−	0.925940i
$202$	−7.09569			−0.499251
$203$	−13.6533	−	5.12149i	−0.958271	−	0.359458i
$204$	−2.24299			−0.157041
$205$	−5.78732	+	10.0239i	−0.404204	+	0.700102i
$206$	3.57567	+	6.19325i	0.249129	+	0.431504i
$207$	−3.00202	−	5.19965i	−0.208655	−	0.361401i
$208$	2.49248	−	4.31710i	0.172822	−	0.299337i
$209$	−3.46193			−0.239467
$210$	−5.09297	+	4.18913i	−0.351448	+	0.289077i
$211$	−23.3953			−1.61060			−0.805298	−	0.592870i	$-0.797995\pi$
$211$	−23.3953			−1.61060			−0.805298	+	0.592870i	$0.797995\pi$
$212$	2.93711	−	5.08723i	0.201722	−	0.349392i
$213$	6.04536	+	10.4709i	0.414221	+	0.717452i
$214$	−7.86525	−	13.6230i	−0.537657	−	0.931250i
$215$	−11.8917	+	20.5971i	−0.811011	+	1.40471i
$216$	1.00000			0.0680414
$217$	3.16033	+	19.0110i	0.214537	+	1.29055i
$218$	−8.31707			−0.563303
$219$	7.21019	−	12.4884i	0.487219	−	0.843889i
$220$	4.31439	+	7.47274i	0.290876	+	0.503812i
$221$	5.59061	+	9.68323i	0.376065	+	0.651364i
$222$	4.58343	−	7.93873i	0.307619	−	0.532813i
$223$	14.8221			0.992564			0.496282	−	0.868161i	$-0.334698\pi$
$223$	14.8221			0.992564			0.496282	+	0.868161i	$0.334698\pi$
$224$	0.433868	+	2.60993i	0.0289890	+	0.174384i
$225$	1.21245			0.0808297
$226$	6.68213	−	11.5738i	0.444488	−	0.769877i
$227$	−8.11473	−	14.0551i	−0.538594	−	0.932872i	−0.998980	−	0.0451531i	$-0.985622\pi$
$227$	−8.11473	−	14.0551i	−0.538594	−	0.932872i	0.460386	−	0.887719i	$-0.347711\pi$
$228$	0.500000	+	0.866025i	0.0331133	+	0.0573539i
$229$	3.19740	−	5.53806i	0.211290	−	0.365965i	−0.740828	−	0.671694i	$-0.765567\pi$
$229$	3.19740	−	5.53806i	0.211290	−	0.365965i	0.952119	+	0.305729i	$0.0989001\pi$
$230$	−14.9649			−0.986759
$231$	−7.07388	+	5.81849i	−0.465427	+	0.382829i
$232$	5.51156			0.361852
$233$	10.6899	−	18.5154i	0.700317	−	1.21299i	−0.268038	−	0.963408i	$-0.586375\pi$
$233$	10.6899	−	18.5154i	0.700317	−	1.21299i	0.968355	−	0.249577i	$-0.0802915\pi$
$234$	−2.49248	−	4.31710i	−0.162938	−	0.282218i
$235$	−6.68011	−	11.5703i	−0.435762	−	0.754762i
$236$	4.33921	−	7.51573i	0.282458	−	0.489232i
$237$	7.08667			0.460329
$238$	−5.55635	−	2.08425i	−0.360165	−	0.135102i
$239$	18.8938			1.22214			0.611068	−	0.791578i	$-0.290740\pi$
$239$	18.8938			1.22214			0.611068	+	0.791578i	$0.290740\pi$
$240$	1.24624	−	2.15855i	0.0804444	−	0.139334i
$241$	−2.02505	−	3.50748i	−0.130445	−	0.225937i	0.793403	−	0.608696i	$-0.208307\pi$
$241$	−2.02505	−	3.50748i	−0.130445	−	0.225937i	−0.923848	+	0.382759i	$0.874974\pi$
$242$	0.492478	+	0.852997i	0.0316577	+	0.0548327i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	4.37526			0.280097
$245$	−16.5090	+	5.64480i	−1.05472	+	0.360633i
$246$	4.64383			0.296080
$247$	2.49248	−	4.31710i	0.158593	−	0.274690i
$248$	−3.64204	−	6.30819i	−0.231270	−	0.400571i
$249$	−2.79912	−	4.84821i	−0.177387	−	0.307243i
$250$	−4.72020	+	8.17562i	−0.298532	+	0.517072i
$251$	6.59917			0.416536			0.208268	−	0.978072i	$-0.433217\pi$
$251$	6.59917			0.416536			0.208268	+	0.978072i	$0.433217\pi$
$252$	2.47720	+	0.929227i	0.156049	+	0.0585358i
$253$	−20.7856			−1.30678
$254$	3.04784	−	5.27902i	0.191239	−	0.331235i
$255$	2.79531	+	4.84161i	0.175049	+	0.303194i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	1.32562	−	2.29605i	0.0826902	−	0.143224i	−0.821714	−	0.569899i	$-0.806982\pi$
$257$	1.32562	−	2.29605i	0.0826902	−	0.143224i	0.904405	+	0.426676i	$0.140315\pi$
$258$	9.54211			0.594066
$259$	18.7310	−	15.4068i	1.16389	−	0.957332i
$260$	−12.4249			−0.770559
$261$	2.75578	−	4.77315i	0.170579	−	0.295451i
$262$	4.65708	+	8.06630i	0.287715	+	0.498338i
$263$	0.727720	+	1.26045i	0.0448731	+	0.0777225i	0.887590	−	0.460635i	$-0.152378\pi$
$263$	0.727720	+	1.26045i	0.0448731	+	0.0777225i	−0.842716	+	0.538358i	$0.819045\pi$
$264$	1.73096	−	2.99812i	0.106534	−	0.184521i
$265$	−14.6414			−0.899413
$266$	0.433868	+	2.60993i	0.0266022	+	0.160025i
$267$	−7.52952			−0.460799
$268$	−7.57915	+	13.1275i	−0.462970	+	0.801888i
$269$	−7.16159	−	12.4042i	−0.436650	−	0.756299i	0.560779	−	0.827966i	$-0.310502\pi$
$269$	−7.16159	−	12.4042i	−0.436650	−	0.756299i	−0.997429	+	0.0716661i	$0.977168\pi$
$270$	−1.24624	−	2.15855i	−0.0758437	−	0.131365i
$271$	−10.3329	+	17.8971i	−0.627680	+	1.08717i	0.360337	+	0.932822i	$0.382662\pi$
$271$	−10.3329	+	17.8971i	−0.627680	+	1.08717i	−0.988016	+	0.154351i	$0.950671\pi$
$272$	2.24299			0.136001
$273$	−2.16281	−	13.0104i	−0.130899	−	0.787426i
$274$	7.78510			0.470315
$275$	2.09870	−	3.63506i	0.126556	−	0.219202i
$276$	3.00202	+	5.19965i	0.180700	+	0.312982i
$277$	14.2710	+	24.7182i	0.857464	+	1.48517i	0.874340	+	0.485314i	$0.161295\pi$
$277$	14.2710	+	24.7182i	0.857464	+	1.48517i	−0.0168758	+	0.999858i	$0.505372\pi$
$278$	6.29408	−	10.9017i	0.377494	−	0.653839i
$279$	−7.28407			−0.436086
$280$	5.09297	−	4.18913i	0.304363	−	0.250348i
$281$	−13.6443			−0.813950			−0.406975	−	0.913439i	$-0.633416\pi$
$281$	−13.6443			−0.813950			−0.406975	+	0.913439i	$0.633416\pi$
$282$	−2.68011	+	4.64208i	−0.159598	+	0.276432i
$283$	0.767015	+	1.32851i	0.0455943	+	0.0789717i	0.887922	−	0.459994i	$-0.152149\pi$
$283$	0.767015	+	1.32851i	0.0455943	+	0.0789717i	−0.842328	+	0.538966i	$0.818815\pi$
$284$	−6.04536	−	10.4709i	−0.358726	−	0.621331i
$285$	1.24624	−	2.15855i	0.0738208	−	0.127861i
$286$	−17.2576			−1.02046
$287$	11.5037	+	4.31517i	0.679042	+	0.254716i
$288$	−1.00000			−0.0589256
$289$	5.98449	−	10.3654i	0.352029	−	0.609732i
$290$	−6.86872	−	11.8970i	−0.403345	−	0.698615i
$291$	3.50202	+	6.06568i	0.205292	+	0.355576i
$292$	−7.21019	+	12.4884i	−0.421944	+	0.730829i
$293$	−33.3773			−1.94992			−0.974962	−	0.222373i	$-0.928620\pi$
$293$	−33.3773			−1.94992			−0.974962	+	0.222373i	$0.928620\pi$
$294$	5.27308	+	4.60377i	0.307532	+	0.268497i
$295$	−21.6308			−1.25939
$296$	−4.58343	+	7.93873i	−0.266406	+	0.461429i
$297$	−1.73096	−	2.99812i	−0.100441	−	0.173969i
$298$	8.14608	+	14.1094i	0.471890	+	0.817337i
$299$	14.9649	−	25.9200i	0.865445	−	1.49899i
$300$	−1.21245			−0.0700006
$301$	23.6378	+	8.86678i	1.36246	+	0.511073i
$302$	−19.9735			−1.14935
$303$	3.54784	−	6.14504i	0.203818	−	0.353024i
$304$	−0.500000	−	0.866025i	−0.0286770	−	0.0496700i
$305$	−5.45262	−	9.44421i	−0.312216	−	0.540774i
$306$	1.12150	−	1.94249i	0.0641117	−	0.111045i
$307$	9.52952			0.543878			0.271939	−	0.962314i	$-0.412335\pi$
$307$	9.52952			0.543878			0.271939	+	0.962314i	$0.412335\pi$
$308$	7.07388	−	5.81849i	0.403072	−	0.331539i
$309$	−7.15135			−0.406826
$310$	−9.07769	+	15.7230i	−0.515578	+	0.893008i
$311$	−8.22020	−	14.2378i	−0.466125	−	0.807352i	0.533127	−	0.846035i	$-0.321017\pi$
$311$	−8.22020	−	14.2378i	−0.466125	−	0.807352i	−0.999252	+	0.0386837i	$0.987684\pi$
$312$	2.49248	+	4.31710i	0.141109	+	0.244408i
$313$	−5.49698	+	9.52106i	−0.310708	+	0.538162i	−0.978516	−	0.206172i	$-0.933899\pi$
$313$	−5.49698	+	9.52106i	−0.310708	+	0.538162i	0.667808	+	0.744334i	$0.267233\pi$
$314$	0.739053			0.0417072
$315$	−1.08141	−	6.50520i	−0.0609303	−	0.366527i
$316$	−7.08667			−0.398656
$317$	−3.33146	+	5.77025i	−0.187113	+	0.324090i	−0.944287	−	0.329124i	$-0.893246\pi$
$317$	−3.33146	+	5.77025i	−0.187113	+	0.324090i	0.757173	+	0.653214i	$0.226580\pi$
$318$	2.93711	+	5.08723i	0.164705	+	0.285278i
$319$	−9.54032	−	16.5243i	−0.534155	−	0.925184i
$320$	−1.24624	+	2.15855i	−0.0696669	+	0.120667i
$321$	15.7305			0.877991
$322$	2.60496	+	15.6702i	0.145169	+	0.873263i
$323$	2.24299			0.124804
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	3.02199	+	5.23425i	0.167630	+	0.290344i
$326$	−2.89904	−	5.02129i	−0.160563	−	0.278103i
$327$	4.15854	−	7.20279i	0.229968	−	0.398315i
$328$	−4.64383			−0.256412
$329$	−10.9527	+	9.00895i	−0.603843	+	0.496680i
$330$	−8.62878			−0.474999
$331$	−12.9051	+	22.3523i	−0.709329	+	1.22859i	0.255778	+	0.966736i	$0.417668\pi$
$331$	−12.9051	+	22.3523i	−0.709329	+	1.22859i	−0.965107	+	0.261858i	$0.915665\pi$
$332$	2.79912	+	4.84821i	0.153622	+	0.266080i
$333$	4.58343	+	7.93873i	0.251170	+	0.435040i
$334$	8.55288	−	14.8140i	0.467993	−	0.810587i
$335$	37.7817			2.06424
$336$	−2.47720	−	0.929227i	−0.135143	−	0.0506935i
$337$	10.0932			0.549810			0.274905	−	0.961471i	$-0.411354\pi$
$337$	10.0932			0.549810			0.274905	+	0.961471i	$0.411354\pi$
$338$	5.92489	−	10.2622i	0.322272	−	0.558191i
$339$	6.68213	+	11.5738i	0.362923	+	0.628602i
$340$	−2.79531	−	4.84161i	−0.151597	−	0.262573i
$341$	−12.6085	+	21.8385i	−0.682787	+	1.18262i
$342$	−1.00000			−0.0540738
$343$	8.78454	+	16.3044i	0.474321	+	0.880352i
$344$	−9.54211			−0.514476
$345$	7.48247	−	12.9600i	0.402843	−	0.697744i
$346$	−1.29206	−	2.23792i	−0.0694617	−	0.120311i
$347$	0.184614	+	0.319761i	0.00991059	+	0.0171657i	0.870938	−	0.491393i	$-0.163512\pi$
$347$	0.184614	+	0.319761i	0.00991059	+	0.0171657i	−0.861028	+	0.508558i	$0.830179\pi$
$348$	−2.75578	+	4.77315i	−0.147725	+	0.255868i
$349$	31.3643			1.67889			0.839445	−	0.543445i	$-0.182880\pi$
$349$	31.3643			1.67889			0.839445	+	0.543445i	$0.182880\pi$
$350$	−3.00347	−	1.12664i	−0.160542	−	0.0602213i
$351$	4.98496			0.266077
$352$	−1.73096	+	2.99812i	−0.0922607	+	0.159800i
$353$	11.4096	+	19.7620i	0.607272	+	1.05183i	0.991688	+	0.128666i	$0.0410696\pi$
$353$	11.4096	+	19.7620i	0.607272	+	1.05183i	−0.384416	+	0.923160i	$0.625597\pi$
$354$	4.33921	+	7.51573i	0.230626	+	0.399456i
$355$	−15.0679	+	26.0984i	−0.799722	+	1.38516i
$356$	7.52952			0.399064
$357$	4.58319	−	3.76982i	0.242568	−	0.199520i
$358$	3.24948			0.171741
$359$	−12.0138	+	20.8085i	−0.634065	+	1.09823i	0.352648	+	0.935756i	$0.385281\pi$
$359$	−12.0138	+	20.8085i	−0.634065	+	1.09823i	−0.986712	+	0.162476i	$0.948052\pi$
$360$	1.24624	+	2.15855i	0.0656826	+	0.113766i
$361$	−0.500000	−	0.866025i	−0.0263158	−	0.0455803i
$362$	6.22795	−	10.7871i	0.327334	−	0.566959i
$363$	−0.984956			−0.0516968
$364$	2.16281	+	13.0104i	0.113362	+	0.681931i
$365$	35.9425			1.88131
$366$	−2.18763	+	3.78908i	−0.114349	+	0.198059i
$367$	−7.90481	−	13.6915i	−0.412628	−	0.714692i	0.582548	−	0.812796i	$-0.302056\pi$
$367$	−7.90481	−	13.6915i	−0.412628	−	0.714692i	−0.995176	+	0.0981037i	$0.968722\pi$
$368$	−3.00202	−	5.19965i	−0.156491	−	0.271051i
$369$	−2.32191	+	4.02167i	−0.120874	+	0.209360i
$370$	22.8482			1.18782
$371$	2.54864	+	15.3313i	0.132319	+	0.795964i
$372$	7.28407			0.377662
$373$	−15.4254	+	26.7175i	−0.798694	+	1.38338i	0.121772	+	0.992558i	$0.461142\pi$
$373$	−15.4254	+	26.7175i	−0.798694	+	1.38338i	−0.920467	+	0.390821i	$0.872191\pi$
$374$	−3.88254	−	6.72476i	−0.200762	−	0.347729i
$375$	−4.72020	−	8.17562i	−0.243750	−	0.422187i
$376$	2.68011	−	4.64208i	0.138216	−	0.239397i
$377$	27.4749			1.41503
$378$	−2.04334	+	1.68071i	−0.105098	+	0.0864463i
$379$	23.5450			1.20943			0.604713	−	0.796443i	$-0.293288\pi$
$379$	23.5450			1.20943			0.604713	+	0.796443i	$0.293288\pi$
$380$	−1.24624	+	2.15855i	−0.0639307	+	0.110731i
$381$	3.04784	+	5.27902i	0.156146	+	0.270452i
$382$	−8.22222	−	14.2413i	−0.420685	−	0.728648i
$383$	−2.43635	+	4.21989i	−0.124492	+	0.215626i	−0.921534	−	0.388297i	$-0.873063\pi$
$383$	−2.43635	+	4.21989i	−0.124492	+	0.215626i	0.797042	+	0.603923i	$0.206397\pi$
$384$	1.00000			0.0510310
$385$	−21.3753	−	8.01809i	−1.08938	−	0.408640i
$386$	18.6854			0.951060
$387$	−4.77106	+	8.26371i	−0.242526	+	0.420068i
$388$	−3.50202	−	6.06568i	−0.177788	−	0.307938i
$389$	14.1428	+	24.4960i	0.717068	+	1.24200i	0.962156	+	0.272498i	$0.0878497\pi$
$389$	14.1428	+	24.4960i	0.717068	+	1.24200i	−0.245088	+	0.969501i	$0.578817\pi$
$390$	6.21245	−	10.7603i	0.314579	−	0.544868i
$391$	13.4670			0.681057
$392$	−5.27308	−	4.60377i	−0.266331	−	0.232525i
$393$	−9.31416			−0.469837
$394$	−7.74826	+	13.4204i	−0.390352	+	0.676109i
$395$	8.83169	+	15.2969i	0.444370	+	0.769672i
$396$	1.73096	+	2.99812i	0.0869843	+	0.150661i
$397$	−1.32562	+	2.29605i	−0.0665312	+	0.115235i	−0.897372	−	0.441274i	$-0.854527\pi$
$397$	−1.32562	+	2.29605i	−0.0665312	+	0.115235i	0.830841	+	0.556510i	$0.187860\pi$
$398$	1.45948			0.0731571
$399$	−2.47720	−	0.929227i	−0.124015	−	0.0465195i
$400$	1.21245			0.0606223
$401$	3.72646	−	6.45441i	0.186090	−	0.322318i	−0.757853	−	0.652425i	$-0.773752\pi$
$401$	3.72646	−	6.45441i	0.186090	−	0.322318i	0.943943	+	0.330107i	$0.107085\pi$
$402$	−7.57915	−	13.1275i	−0.378014	−	0.654739i
$403$	−18.1554	−	31.4461i	−0.904384	−	1.56644i
$404$	−3.54784	+	6.14504i	−0.176512	+	0.305727i
$405$	2.49248			0.123852
$406$	−11.2620	+	9.26333i	−0.558922	+	0.459731i
$407$	31.7350			1.57305
$408$	−1.12150	+	1.94249i	−0.0555224	+	0.0961676i
$409$	−8.70187	−	15.0721i	−0.430280	−	0.745267i	0.566617	−	0.823981i	$-0.308252\pi$
$409$	−8.70187	−	15.0721i	−0.430280	−	0.745267i	−0.996897	+	0.0787145i	$0.974918\pi$
$410$	5.78732	+	10.0239i	0.285815	+	0.495047i
$411$	−3.89255	+	6.74210i	−0.192005	+	0.332563i
$412$	7.15135			0.352322
$413$	3.76529	+	22.6501i	0.185278	+	1.11454i
$414$	−6.00404			−0.295082
$415$	6.97674	−	12.0841i	0.342475	−	0.593183i
$416$	−2.49248	−	4.31710i	−0.122204	−	0.211663i
$417$	6.29408	+	10.9017i	0.308223	+	0.533857i
$418$	−1.73096	+	2.99812i	−0.0846643	+	0.146643i
$419$	−3.76105			−0.183739			−0.0918696	−	0.995771i	$-0.529284\pi$
$419$	−3.76105			−0.183739			−0.0918696	+	0.995771i	$0.529284\pi$
$420$	1.08141	+	6.50520i	0.0527672	+	0.317421i
$421$	31.6343			1.54176			0.770882	−	0.636978i	$-0.219816\pi$
$421$	31.6343			1.54176			0.770882	+	0.636978i	$0.219816\pi$
$422$	−11.6976	+	20.2609i	−0.569432	+	0.986285i
$423$	−2.68011	−	4.64208i	−0.130311	−	0.225706i
$424$	−2.93711	−	5.08723i	−0.142639	−	0.247058i
$425$	−1.35975	+	2.35516i	−0.0659578	+	0.114242i
$426$	12.0907			0.585797
$427$	−8.94012	+	7.35353i	−0.432643	+	0.355862i
$428$	−15.7305			−0.760362
$429$	8.62878	−	14.9455i	0.416602	−	0.721575i
$430$	11.8917	+	20.5971i	0.573471	+	0.993281i
$431$	0.832910	+	1.44264i	0.0401199	+	0.0694897i	0.885388	−	0.464853i	$-0.153893\pi$
$431$	0.832910	+	1.44264i	0.0401199	+	0.0694897i	−0.845268	+	0.534342i	$0.820559\pi$
$432$	0.500000	−	0.866025i	0.0240563	−	0.0416667i
$433$	16.1062			0.774015			0.387008	−	0.922076i	$-0.373509\pi$
$433$	16.1062			0.774015			0.387008	+	0.922076i	$0.373509\pi$
$434$	18.0441	+	6.76855i	0.866146	+	0.324901i
$435$	13.7374			0.658660
$436$	−4.15854	+	7.20279i	−0.199158	+	0.344951i
$437$	−3.00202	−	5.19965i	−0.143606	−	0.248733i
$438$	−7.21019	−	12.4884i	−0.344516	−	0.596719i
$439$	−10.5433	+	18.2616i	−0.503206	+	0.871578i	0.496787	+	0.867872i	$0.334513\pi$
$439$	−10.5433	+	18.2616i	−0.503206	+	0.871578i	−0.999993	+	0.00370589i	$0.998820\pi$
$440$	8.62878			0.411361
$441$	−6.62352	+	2.26473i	−0.315406	+	0.107844i
$442$	11.1812			0.531837
$443$	9.29789	−	16.1044i	0.441756	−	0.765144i	−0.556064	−	0.831140i	$-0.687689\pi$
$443$	9.29789	−	16.1044i	0.441756	−	0.765144i	0.997820	+	0.0659955i	$0.0210223\pi$
$444$	−4.58343	−	7.93873i	−0.217520	−	0.376755i
$445$	−9.38358	−	16.2528i	−0.444824	−	0.770458i
$446$	7.41107	−	12.8364i	0.350924	−	0.607819i
$447$	−16.2922			−0.770592
$448$	2.47720	+	0.929227i	0.117037	+	0.0439018i
$449$	19.7410			0.931637			0.465818	−	0.884880i	$-0.345760\pi$
$449$	19.7410			0.931637			0.465818	+	0.884880i	$0.345760\pi$
$450$	0.606223	−	1.05001i	0.0285776	−	0.0494979i
$451$	8.03830	+	13.9227i	0.378509	+	0.655596i
$452$	−6.68213	−	11.5738i	−0.314301	−	0.544385i
$453$	9.98675	−	17.2976i	0.469218	−	0.812710i
$454$	−16.2295			−0.761687
$455$	25.3882	−	20.8826i	1.19022	−	0.978992i
$456$	1.00000			0.0468293
$457$	−0.234446	+	0.406073i	−0.0109669	+	0.0189953i	−0.871457	−	0.490472i	$-0.836824\pi$
$457$	−0.234446	+	0.406073i	−0.0109669	+	0.0189953i	0.860490	+	0.509468i	$0.170158\pi$
$458$	−3.19740	−	5.53806i	−0.149405	−	0.258777i
$459$	1.12150	+	1.94249i	0.0523470	+	0.0906677i
$460$	−7.48247	+	12.9600i	−0.348872	+	0.604264i
$461$	−19.0556			−0.887510			−0.443755	−	0.896148i	$-0.646354\pi$
$461$	−19.0556			−0.887510			−0.443755	+	0.896148i	$0.646354\pi$
$462$	1.50202	+	9.03541i	0.0698803	+	0.420365i
$463$	−9.65575			−0.448741			−0.224370	−	0.974504i	$-0.572033\pi$
$463$	−9.65575			−0.448741			−0.224370	+	0.974504i	$0.572033\pi$
$464$	2.75578	−	4.77315i	0.127934	−	0.221588i
$465$	−9.07769	−	15.7230i	−0.420968	−	0.729138i
$466$	−10.6899	−	18.5154i	−0.495199	−	0.857710i
$467$	4.58141	−	7.93523i	0.212002	−	0.367199i	−0.740339	−	0.672234i	$-0.765335\pi$
$467$	4.58141	−	7.93523i	0.212002	−	0.367199i	0.952341	+	0.305035i	$0.0986683\pi$
$468$	−4.98496			−0.230430
$469$	−6.57670	−	39.5622i	−0.303684	−	1.82681i
$470$	−13.3602			−0.616261
$471$	−0.369526	+	0.640038i	−0.0170269	+	0.0294914i
$472$	−4.33921	−	7.51573i	−0.199728	−	0.345939i
$473$	16.5171	+	28.6084i	0.759455	+	1.31541i
$474$	3.54334	−	6.13724i	0.162751	−	0.281893i
$475$	1.21245			0.0556308
$476$	−4.58319	+	3.76982i	−0.210070	+	0.172789i
$477$	−5.87423			−0.268962
$478$	9.44689	−	16.3625i	0.432090	−	0.748403i
$479$	−21.4106	−	37.0843i	−0.978276	−	1.69442i	−0.668673	−	0.743557i	$-0.733137\pi$
$479$	−21.4106	−	37.0843i	−0.978276	−	1.69442i	−0.309603	−	0.950866i	$-0.600196\pi$
$480$	−1.24624	−	2.15855i	−0.0568828	−	0.0985238i
$481$	−22.8482	+	39.5742i	−1.04179	+	1.80443i
$482$	−4.05009			−0.184477
$483$	−14.8732	−	5.57911i	−0.676755	−	0.253858i
$484$	0.984956			0.0447707
$485$	−8.72871	+	15.1186i	−0.396350	+	0.686499i
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$	13.1576	+	22.7897i	0.596230	+	1.03270i	0.993372	+	0.114943i	$0.0366685\pi$
$487$	13.1576	+	22.7897i	0.596230	+	1.03270i	−0.397143	+	0.917757i	$0.629998\pi$
$488$	2.18763	−	3.78908i	0.0990293	−	0.171524i
$489$	5.79808			0.262198
$490$	−3.36595	+	17.1196i	−0.152058	+	0.773384i
$491$	−14.2064			−0.641127			−0.320563	−	0.947227i	$-0.603872\pi$
$491$	−14.2064			−0.641127			−0.320563	+	0.947227i	$0.603872\pi$
$492$	2.32191	−	4.02167i	0.104680	−	0.181311i
$493$	6.18120	+	10.7062i	0.278387	+	0.482181i
$494$	−2.49248	−	4.31710i	−0.112142	−	0.194235i
$495$	4.31439	−	7.47274i	0.193917	−	0.335875i
$496$	−7.28407			−0.327065
$497$	29.9512	+	11.2350i	1.34349	+	0.503959i
$498$	−5.59823			−0.250863
$499$	−17.0163	+	29.4730i	−0.761753	+	1.31939i	0.180194	+	0.983631i	$0.442327\pi$
$499$	−17.0163	+	29.4730i	−0.761753	+	1.31939i	−0.941947	+	0.335763i	$0.891006\pi$
$500$	4.72020	+	8.17562i	0.211094	+	0.365625i
$501$	8.55288	+	14.8140i	0.382114	+	0.661842i
$502$	3.29958	−	5.71505i	0.147268	−	0.255075i
$503$	18.2003			0.811512			0.405756	−	0.913981i	$-0.367008\pi$
$503$	18.2003			0.811512			0.405756	+	0.913981i	$0.367008\pi$
$504$	2.04334	−	1.68071i	0.0910174	−	0.0748647i
$505$	17.6858			0.787009
$506$	−10.3928	+	18.0008i	−0.462016	+	0.800234i
$507$	5.92489	+	10.2622i	0.263134	+	0.455761i
$508$	−3.04784	−	5.27902i	−0.135226	−	0.234219i
$509$	2.28239	−	3.95321i	0.101165	−	0.175223i	−0.811000	−	0.585046i	$-0.801076\pi$
$509$	2.28239	−	3.95321i	0.101165	−	0.175223i	0.912165	+	0.409823i	$0.134410\pi$
$510$	5.59061			0.247556
$511$	−6.25654	−	37.6362i	−0.276773	−	1.66493i
$512$	−1.00000			−0.0441942
$513$	0.500000	−	0.866025i	0.0220755	−	0.0382360i
$514$	−1.32562	−	2.29605i	−0.0584708	−	0.101274i
$515$	−8.91229	−	15.4365i	−0.392722	−	0.680215i
$516$	4.77106	−	8.26371i	0.210034	−	0.363790i
$517$	−18.5567			−0.816122
$518$	−3.97720	−	23.9249i	−0.174748	−	1.05120i
$519$	2.58412			0.113430
$520$	−6.21245	+	10.7603i	−0.272434	+	0.471869i
$521$	20.2580	+	35.0879i	0.887520	+	1.53723i	0.842798	+	0.538231i	$0.180907\pi$
$521$	20.2580	+	35.0879i	0.887520	+	1.53723i	0.0447225	+	0.998999i	$0.485760\pi$
$522$	−2.75578	−	4.77315i	−0.120617	−	0.208915i
$523$	14.7322	−	25.5170i	0.644195	−	1.11578i	−0.340292	−	0.940320i	$-0.610526\pi$
$523$	14.7322	−	25.5170i	0.644195	−	1.11578i	0.984487	−	0.175459i	$-0.0561408\pi$
$524$	9.31416			0.406891
$525$	2.47743	−	2.03777i	0.108124	−	0.0889354i
$526$	1.45544			0.0634602
$527$	8.16907	−	14.1492i	0.355850	−	0.616350i
$528$	−1.73096	−	2.99812i	−0.0753306	−	0.130476i
$529$	−6.52425	−	11.3003i	−0.283663	−	0.491319i
$530$	−7.32069	+	12.6798i	−0.317990	+	0.550776i
$531$	−8.67842			−0.376611
$532$	2.47720	+	0.929227i	0.107400	+	0.0402871i
$533$	−23.1493			−1.00271
$534$	−3.76476	+	6.52075i	−0.162917	+	0.282181i
$535$	19.6040	+	33.9551i	0.847553	+	1.46800i
$536$	7.57915	+	13.1275i	0.327369	+	0.567020i
$537$	−1.62474	+	2.81414i	−0.0701128	+	0.121439i
$538$	−14.3232			−0.617516
$539$	−4.67513	+	23.7783i	−0.201372	+	1.02420i
$540$	−2.49248			−0.107259
$541$	2.76400	−	4.78739i	0.118834	−	0.205826i	−0.800472	−	0.599370i	$-0.795418\pi$
$541$	2.76400	−	4.78739i	0.118834	−	0.205826i	0.919306	+	0.393544i	$0.128751\pi$
$542$	10.3329	+	17.8971i	0.443837	+	0.768747i
$543$	6.22795	+	10.7871i	0.267267	+	0.462920i
$544$	1.12150	−	1.94249i	0.0480838	−	0.0832836i
$545$	20.7301			0.887980
$546$	−12.3488	−	4.63215i	−0.528478	−	0.198238i
$547$	−13.7329			−0.587178			−0.293589	−	0.955932i	$-0.594850\pi$
$547$	−13.7329			−0.587178			−0.293589	+	0.955932i	$0.594850\pi$
$548$	3.89255	−	6.74210i	0.166282	−	0.288008i
$549$	−2.18763	−	3.78908i	−0.0933657	−	0.161714i
$550$	−2.09870	−	3.63506i	−0.0894889	−	0.154999i
$551$	2.75578	−	4.77315i	0.117400	−	0.203343i
$552$	6.00404			0.255549
$553$	14.4804	−	11.9106i	0.615771	−	0.506491i
$554$	28.5421			1.21264
$555$	−11.4241	+	19.7871i	−0.484926	+	0.839916i
$556$	−6.29408	−	10.9017i	−0.266929	−	0.462334i
$557$	0.199621	+	0.345753i	0.00845821	+	0.0146500i	0.870224	−	0.492657i	$-0.163974\pi$
$557$	0.199621	+	0.345753i	0.00845821	+	0.0146500i	−0.861765	+	0.507307i	$0.830641\pi$
$558$	−3.64204	+	6.30819i	−0.154180	+	0.267047i
$559$	−47.5670			−2.01187
$560$	−1.08141	−	6.50520i	−0.0456978	−	0.274895i
$561$	7.76509			0.327842
$562$	−6.82214	+	11.8163i	−0.287775	+	0.498440i
$563$	−13.0621	−	22.6242i	−0.550501	−	0.953496i	−0.998238	−	0.0593309i	$-0.981103\pi$
$563$	−13.0621	−	22.6242i	−0.550501	−	0.953496i	0.447737	−	0.894165i	$-0.352230\pi$
$564$	2.68011	+	4.64208i	0.112853	+	0.195467i
$565$	−16.6551	+	28.8474i	−0.700683	+	1.21362i
$566$	1.53403			0.0644801
$567$	−0.433868	−	2.60993i	−0.0182207	−	0.109607i
$568$	−12.0907			−0.507315
$569$	−1.53158	+	2.65278i	−0.0642072	+	0.111210i	−0.896342	−	0.443363i	$-0.853785\pi$
$569$	−1.53158	+	2.65278i	−0.0642072	+	0.111210i	0.832135	+	0.554573i	$0.187119\pi$
$570$	−1.24624	−	2.15855i	−0.0521992	−	0.0904117i
$571$	−2.94533	−	5.10146i	−0.123258	−	0.213490i	0.797792	−	0.602932i	$-0.206001\pi$
$571$	−2.94533	−	5.10146i	−0.123258	−	0.213490i	−0.921051	+	0.389443i	$0.872668\pi$
$572$	−8.62878	+	14.9455i	−0.360788	+	0.624902i
$573$	16.4444			0.686976
$574$	9.48890	−	7.80492i	0.396059	−	0.325771i
$575$	7.27957			0.303579
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	12.8948	+	22.3345i	0.536818	+	0.929795i	0.999073	+	0.0430486i	$0.0137070\pi$
$577$	12.8948	+	22.3345i	0.536818	+	0.929795i	−0.462255	+	0.886747i	$0.652960\pi$
$578$	−5.98449	−	10.3654i	−0.248922	−	0.431145i
$579$	−9.34268	+	16.1820i	−0.388269	+	0.672501i
$580$	−13.7374			−0.570416
$581$	−13.8680	−	5.20203i	−0.575340	−	0.215816i
$582$	7.00404			0.290327
$583$	−10.1681	+	17.6116i	−0.421119	+	0.729399i
$584$	7.21019	+	12.4884i	0.298360	+	0.516774i
$585$	6.21245	+	10.7603i	0.256853	+	0.444882i
$586$	−16.6887	+	28.9056i	−0.689402	+	1.19408i
$587$	0.822143			0.0339335			0.0169667	−	0.999856i	$-0.494599\pi$
$587$	0.822143			0.0339335			0.0169667	+	0.999856i	$0.494599\pi$
$588$	6.62352	−	2.26473i	0.273149	−	0.0933961i
$589$	−7.28407			−0.300135
$590$	−10.8154	+	18.7328i	−0.445262	+	0.771217i
$591$	−7.74826	−	13.4204i	−0.318721	−	0.552041i
$592$	4.58343	+	7.93873i	0.188378	+	0.326280i
$593$	8.32035	−	14.4113i	0.341676	−	0.591800i	−0.643068	−	0.765809i	$-0.722339\pi$
$593$	8.32035	−	14.4113i	0.341676	−	0.591800i	0.984744	+	0.174009i	$0.0556721\pi$
$594$	−3.46193			−0.142045
$595$	13.8491	+	5.19495i	0.567757	+	0.212972i
$596$	16.2922			0.667353
$597$	−0.729740	+	1.26395i	−0.0298663	+	0.0517299i
$598$	−14.9649	−	25.9200i	−0.611962	−	1.05995i
$599$	−4.28835	−	7.42764i	−0.175217	−	0.303485i	0.765019	−	0.644007i	$-0.222729\pi$
$599$	−4.28835	−	7.42764i	−0.175217	−	0.303485i	−0.940236	+	0.340522i	$0.889396\pi$
$600$	−0.606223	+	1.05001i	−0.0247489	+	0.0428664i
$601$	13.6993			0.558805			0.279403	−	0.960174i	$-0.409864\pi$
$601$	13.6993			0.558805			0.279403	+	0.960174i	$0.409864\pi$
$602$	19.4977	−	16.0375i	0.794668	−	0.653640i
$603$	15.1583			0.617294
$604$	−9.98675	+	17.2976i	−0.406355	+	0.703827i
$605$	−1.22749	−	2.12608i	−0.0499046	−	0.0864372i
$606$	−3.54784	−	6.14504i	−0.144121	−	0.249625i
$607$	−21.2703	+	36.8412i	−0.863333	+	1.49534i	0.00536006	+	0.999986i	$0.498294\pi$
$607$	−21.2703	+	36.8412i	−0.863333	+	1.49534i	−0.868693	+	0.495351i	$0.835040\pi$
$608$	−1.00000			−0.0405554
$609$	−2.39129	−	14.3848i	−0.0969000	−	0.582902i
$610$	−10.9052			−0.441540
$611$	13.3602	−	23.1406i	0.540496	−	0.936167i
$612$	−1.12150	−	1.94249i	−0.0453338	−	0.0785205i
$613$	−7.25479	−	12.5657i	−0.293018	−	0.507522i	0.681504	−	0.731815i	$-0.261326\pi$
$613$	−7.25479	−	12.5657i	−0.293018	−	0.507522i	−0.974522	+	0.224292i	$0.927993\pi$
$614$	4.76476	−	8.25280i	0.192290	−	0.333056i
$615$	−11.5746			−0.466734
$616$	−1.50202	−	9.03541i	−0.0605181	−	0.364047i
$617$	−25.3468			−1.02042			−0.510211	−	0.860049i	$-0.670433\pi$
$617$	−25.3468			−1.02042			−0.510211	+	0.860049i	$0.670433\pi$
$618$	−3.57567	+	6.19325i	−0.143835	+	0.249129i
$619$	7.99718	+	13.8515i	0.321434	+	0.556739i	0.980784	−	0.195096i	$-0.0625019\pi$
$619$	7.99718	+	13.8515i	0.321434	+	0.556739i	−0.659350	+	0.751836i	$0.729169\pi$
$620$	9.07769	+	15.7230i	0.364569	+	0.631452i
$621$	3.00202	−	5.19965i	0.120467	−	0.208655i
$622$	−16.4404			−0.659200
$623$	−15.3853	+	12.6549i	−0.616400	+	0.507009i
$624$	4.98496			0.199558
$625$	14.7961	−	25.6276i	0.591844	−	1.02510i
$626$	5.49698	+	9.52106i	0.219704	+	0.380538i
$627$	−1.73096	−	2.99812i	−0.0691281	−	0.119733i
$628$	0.369526	−	0.640038i	0.0147457	−	0.0255403i
$629$	−20.5612			−0.819829
$630$	−6.17438	−	2.31608i	−0.245993	−	0.0922747i
$631$	−25.6970			−1.02298			−0.511491	−	0.859288i	$-0.670907\pi$
$631$	−25.6970			−1.02298			−0.511491	+	0.859288i	$0.670907\pi$
$632$	−3.54334	+	6.13724i	−0.140946	+	0.244126i
$633$	−11.6976	−	20.2609i	−0.464939	−	0.805298i
$634$	3.33146	+	5.77025i	0.132309	+	0.229166i
$635$	−7.59668	+	13.1578i	−0.301465	+	0.522153i
$636$	5.87423			0.232928
$637$	−26.2860	−	22.9496i	−1.04149	−	0.909295i
$638$	−19.0806			−0.755410
$639$	−6.04536	+	10.4709i	−0.239151	+	0.414221i
$640$	1.24624	+	2.15855i	0.0492619	+	0.0853241i
$641$	−22.0374	−	38.1698i	−0.870424	−	1.50762i	−0.861559	−	0.507657i	$-0.830512\pi$
$641$	−22.0374	−	38.1698i	−0.870424	−	1.50762i	−0.00886458	−	0.999961i	$-0.502822\pi$
$642$	7.86525	−	13.6230i	0.310417	−	0.537657i
$643$	22.7730			0.898078			0.449039	−	0.893512i	$-0.351766\pi$
$643$	22.7730			0.898078			0.449039	+	0.893512i	$0.351766\pi$
$644$	14.8732	+	5.57911i	0.586087	+	0.219848i
$645$	−23.7835			−0.936474
$646$	1.12150	−	1.94249i	0.0441247	−	0.0764262i
$647$	−15.1839	−	26.2993i	−0.596941	−	1.03393i	−0.993270	−	0.115824i	$-0.963049\pi$
$647$	−15.1839	−	26.2993i	−0.596941	−	1.03393i	0.396328	−	0.918109i	$-0.370284\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$	−15.0220	+	26.0189i	−0.589666	+	1.02133i
$650$	6.04399			0.237065
$651$	−14.8838	+	12.2424i	−0.583342	+	0.479817i
$652$	−5.79808			−0.227071
$653$	2.31767	−	4.01433i	0.0906976	−	0.157093i	−0.817107	−	0.576486i	$-0.804424\pi$
$653$	2.31767	−	4.01433i	0.0906976	−	0.157093i	0.907805	+	0.419393i	$0.137757\pi$
$654$	−4.15854	−	7.20279i	−0.162612	−	0.281652i
$655$	−11.6077	−	20.1051i	−0.453549	−	0.785570i
$656$	−2.32191	+	4.02167i	−0.0906555	+	0.157020i
$657$	14.4204			0.562592
$658$	2.32562	+	13.9898i	0.0906623	+	0.545379i
$659$	−18.8998			−0.736232			−0.368116	−	0.929780i	$-0.619997\pi$
$659$	−18.8998			−0.736232			−0.368116	+	0.929780i	$0.619997\pi$
$660$	−4.31439	+	7.47274i	−0.167937	+	0.290876i
$661$	−12.9021	−	22.3471i	−0.501833	−	0.869200i	−0.999998	−	0.00211793i	$-0.999326\pi$
$661$	−12.9021	−	22.3471i	−0.501833	−	0.869200i	0.498165	−	0.867082i	$-0.334007\pi$
$662$	12.9051	+	22.3523i	0.501571	+	0.868747i
$663$	−5.59061	+	9.68323i	−0.217121	+	0.376065i
$664$	5.59823			0.217254
$665$	−1.08141	−	6.50520i	−0.0419351	−	0.252261i
$666$	9.16685			0.355208
$667$	16.5458	−	28.6582i	0.640657	−	1.10965i
$668$	−8.55288	−	14.8140i	−0.330921	−	0.573172i
$669$	7.41107	+	12.8364i	0.286529	+	0.496282i
$670$	18.8909	−	32.7199i	0.729818	−	1.26408i
$671$	−15.1468			−0.584737
$672$	−2.04334	+	1.68071i	−0.0788234	+	0.0648347i
$673$	15.7844			0.608445			0.304223	−	0.952601i	$-0.401603\pi$
$673$	15.7844			0.608445			0.304223	+	0.952601i	$0.401603\pi$
$674$	5.04658	−	8.74093i	0.194387	−	0.336688i
$675$	0.606223	+	1.05001i	0.0233335	+	0.0404149i
$676$	−5.92489	−	10.2622i	−0.227880	−	0.394700i
$677$	12.0393	−	20.8527i	0.462707	−	0.801433i	−0.536387	−	0.843972i	$-0.680211\pi$
$677$	12.0393	−	20.8527i	0.462707	−	0.801433i	0.999095	+	0.0425391i	$0.0135447\pi$
$678$	13.3643			0.513251
$679$	17.3504	+	6.50834i	0.665849	+	0.249767i
$680$	−5.59061			−0.214390
$681$	8.11473	−	14.0551i	0.310957	−	0.538594i
$682$	12.6085	+	21.8385i	0.482803	+	0.836240i
$683$	−7.42531	−	12.8610i	−0.284122	−	0.492113i	0.688274	−	0.725451i	$-0.258369\pi$
$683$	−7.42531	−	12.8610i	−0.284122	−	0.492113i	−0.972396	+	0.233337i	$0.925035\pi$
$684$	−0.500000	+	0.866025i	−0.0191180	+	0.0331133i
$685$	−19.4042			−0.741396
$686$	18.5123	+	0.544542i	0.706801	+	0.0207907i
$687$	6.39480			0.243977
$688$	−4.77106	+	8.26371i	−0.181895	+	0.315051i
$689$	−14.6414	−	25.3596i	−0.557792	−	0.966124i
$690$	−7.48247	−	12.9600i	−0.284853	−	0.493379i
$691$	−19.1471	+	33.1637i	−0.728389	+	1.26161i	0.229175	+	0.973385i	$0.426397\pi$
$691$	−19.1471	+	33.1637i	−0.728389	+	1.26161i	−0.957564	+	0.288221i	$0.906936\pi$
$692$	−2.58412			−0.0982336
$693$	−8.57590	−	3.21692i	−0.325772	−	0.122201i
$694$	0.369228			0.0140157
$695$	−15.6879	+	27.1722i	−0.595074	+	1.03070i
$696$	2.75578	+	4.77315i	0.104458	+	0.180926i
$697$	−5.20804	−	9.02059i	−0.197268	−	0.341679i
$698$	15.6821	−	27.1622i	0.593577	−	1.02811i
$699$	21.3798			0.808657
$700$	−2.47743	+	2.03777i	−0.0936382	+	0.0770204i
$701$	−24.6068			−0.929385			−0.464693	−	0.885472i	$-0.653835\pi$
$701$	−24.6068			−0.929385			−0.464693	+	0.885472i	$0.653835\pi$
$702$	2.49248	−	4.31710i	0.0940725	−	0.162938i
$703$	4.58343	+	7.93873i	0.172867	+	0.299415i
$704$	1.73096	+	2.99812i	0.0652382	+	0.112996i
$705$	6.68011	−	11.5703i	0.251587	−	0.435762i
$706$	22.8192			0.858813
$707$	−3.07859	−	18.5193i	−0.115782	−	0.696489i
$708$	8.67842			0.326155
$709$	−8.63325	+	14.9532i	−0.324229	+	0.561580i	−0.981356	−	0.192199i	$-0.938438\pi$
$709$	−8.63325	+	14.9532i	−0.324229	+	0.561580i	0.657127	+	0.753780i	$0.271771\pi$
$710$	15.0679	+	26.0984i	0.565489	+	0.979455i
$711$	3.54334	+	6.13724i	0.132885	+	0.230164i
$712$	3.76476	−	6.52075i	0.141090	−	0.244376i
$713$	−43.7339			−1.63785
$714$	−0.973163	−	5.85407i	−0.0364197	−	0.219083i
$715$	43.0141			1.60864
$716$	1.62474	−	2.81414i	0.0607195	−	0.105169i
$717$	9.44689	+	16.3625i	0.352800	+	0.611068i
$718$	12.0138	+	20.8085i	0.448352	+	0.776568i
$719$	−21.6263	+	37.4579i	−0.806526	+	1.39694i	0.108730	+	0.994071i	$0.465322\pi$
$719$	−21.6263	+	37.4579i	−0.806526	+	1.39694i	−0.915256	+	0.402873i	$0.868012\pi$
$720$	2.49248			0.0928892
$721$	−14.6126	+	12.0193i	−0.544202	+	0.447623i
$722$	−1.00000			−0.0372161
$723$	2.02505	−	3.50748i	0.0753123	−	0.130445i
$724$	−6.22795	−	10.7871i	−0.231460	−	0.400900i
$725$	3.34124	+	5.78719i	0.124090	+	0.214931i
$726$	−0.492478	+	0.852997i	−0.0182776	+	0.0316577i
$727$	−26.0766			−0.967127			−0.483564	−	0.875309i	$-0.660658\pi$
$727$	−26.0766			−0.967127			−0.483564	+	0.875309i	$0.660658\pi$
$728$	12.3488	+	4.63215i	0.457675	+	0.171679i
$729$	1.00000			0.0370370
$730$	17.9712	−	31.1271i	0.665145	−	1.15207i
$731$	−10.7014	−	18.5355i	−0.395807	−	0.685558i
$732$	2.18763	+	3.78908i	0.0808571	+	0.140049i
$733$	4.10947	−	7.11781i	0.151787	−	0.262902i	−0.780098	−	0.625658i	$-0.784831\pi$
$733$	4.10947	−	7.11781i	0.151787	−	0.262902i	0.931884	+	0.362756i	$0.118164\pi$
$734$	−15.8096			−0.583544
$735$	−13.1430	−	11.4748i	−0.484788	−	0.423254i
$736$	−6.00404			−0.221312
$737$	26.2385	−	45.4464i	0.966507	−	1.67404i
$738$	2.32191	+	4.02167i	0.0854708	+	0.148040i
$739$	−19.2989	−	33.4266i	−0.709921	−	1.22962i	−0.964886	−	0.262669i	$-0.915397\pi$
$739$	−19.2989	−	33.4266i	−0.709921	−	1.22962i	0.254965	−	0.966950i	$-0.417936\pi$
$740$	11.4241	−	19.7871i	0.419958	−	0.727388i
$741$	4.98496			0.183127
$742$	14.5517	+	5.45849i	0.534208	+	0.200387i
$743$	−5.51309			−0.202256			−0.101128	−	0.994873i	$-0.532245\pi$
$743$	−5.51309			−0.202256			−0.101128	+	0.994873i	$0.532245\pi$
$744$	3.64204	−	6.30819i	0.133524	−	0.231270i
$745$	−20.3039	−	35.1674i	−0.743878	−	1.28843i
$746$	15.4254	+	26.7175i	0.564762	+	0.978197i
$747$	2.79912	−	4.84821i	0.102414	−	0.177387i
$748$	−7.76509			−0.283920
$749$	32.1427	−	26.4384i	1.17447	−	0.966037i
$750$	−9.44040			−0.344714
$751$	−9.63001	+	16.6797i	−0.351404	+	0.608649i	−0.986496	−	0.163787i	$-0.947629\pi$
$751$	−9.63001	+	16.6797i	−0.351404	+	0.608649i	0.635092	+	0.772437i	$0.280962\pi$
$752$	−2.68011	−	4.64208i	−0.0977334	−	0.169279i
$753$	3.29958	+	5.71505i	0.120244	+	0.208268i
$754$	13.7374	−	23.7940i	0.500288	−	0.866525i
$755$	49.7835			1.81181
$756$	0.433868	+	2.60993i	0.0157796	+	0.0949224i
$757$	−0.556024			−0.0202090			−0.0101045	−	0.999949i	$-0.503216\pi$
$757$	−0.556024			−0.0202090			−0.0101045	+	0.999949i	$0.503216\pi$
$758$	11.7725	−	20.3906i	0.427597	−	0.740619i
$759$	−10.3928	−	18.0008i	−0.377234	−	0.653389i
$760$	1.24624	+	2.15855i	0.0452058	+	0.0782988i
$761$	−4.58846	+	7.94745i	−0.166332	+	0.288095i	−0.937127	−	0.348988i	$-0.886526\pi$
$761$	−4.58846	+	7.94745i	−0.166332	+	0.288095i	0.770796	+	0.637082i	$0.219859\pi$
$762$	6.09569			0.220823
$763$	−3.60851	−	21.7070i	−0.130637	−	0.785847i
$764$	−16.4444			−0.594939
$765$	−2.79531	+	4.84161i	−0.101065	+	0.175049i
$766$	2.43635	+	4.21989i	0.0880291	+	0.152471i
$767$	−21.6308	−	37.4656i	−0.781041	−	1.35280i
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$	10.2515			0.369680			0.184840	−	0.982769i	$-0.440823\pi$
$769$	10.2515			0.369680			0.184840	+	0.982769i	$0.440823\pi$
$770$	−17.6315	+	14.5025i	−0.635395	+	0.522632i
$771$	2.65125			0.0954824
$772$	9.34268	−	16.1820i	0.336251	−	0.582403i
$773$	12.6864	+	21.9735i	0.456298	+	0.790332i	0.998762	−	0.0497476i	$-0.0158417\pi$
$773$	12.6864	+	21.9735i	0.456298	+	0.790332i	−0.542464	+	0.840079i	$0.682508\pi$
$774$	4.77106	+	8.26371i	0.171492	+	0.297033i
$775$	4.41577	−	7.64834i	0.158619	−	0.274736i
$776$	−7.00404			−0.251430
$777$	22.7082	+	8.51808i	0.814651	+	0.305585i
$778$	28.2856			1.01409
$779$	−2.32191	+	4.02167i	−0.0831912	+	0.144091i
$780$	−6.21245	−	10.7603i	−0.222441	−	0.385280i
$781$	20.9286	+	36.2494i	0.748884	+	1.29711i
$782$	6.73351	−	11.6628i	0.240790	−	0.417060i
$783$	5.51156			0.196967
$784$	−6.62352	+	2.26473i	−0.236554	+	0.0808834i
$785$	−1.84207			−0.0657464
$786$	−4.65708	+	8.06630i	−0.166113	+	0.287715i
$787$	−10.6443	−	18.4364i	−0.379428	−	0.657188i	0.611551	−	0.791205i	$-0.290546\pi$
$787$	−10.6443	−	18.4364i	−0.379428	−	0.657188i	−0.990979	+	0.134017i	$0.957212\pi$
$788$	7.74826	+	13.4204i	0.276020	+	0.478081i
$789$	−0.727720	+	1.26045i	−0.0259075	+	0.0448731i
$790$	17.6634			0.628435
$791$	33.1060	+	12.4184i	1.17711	+	0.441548i
$792$	3.46193			0.123014
$793$	10.9052	−	18.8884i	0.387256	−	0.670747i
$794$	1.32562	+	2.29605i	0.0470447	+	0.0814838i
$795$	−7.32069	−	12.6798i	−0.259638	−	0.449706i
$796$	0.729740	−	1.26395i	0.0258649	−	0.0447994i
$797$	41.1949			1.45920			0.729600	−	0.683874i	$-0.239706\pi$
$797$	41.1949			1.45920			0.729600	+	0.683874i	$0.239706\pi$
$798$	−2.04334	+	1.68071i	−0.0723333	+	0.0594964i
$799$	12.0229			0.425341
$800$	0.606223	−	1.05001i	0.0214332	−	0.0371234i
$801$	−3.76476	−	6.52075i	−0.133021	−	0.230399i
$802$	−3.72646	−	6.45441i	−0.131586	−	0.227913i
$803$	24.9612	−	43.2340i	0.880860	−	1.52569i
$804$	−15.1583			−0.534592
$805$	−6.49281	−	39.0575i	−0.228841	−	1.37660i
$806$	−36.3108			−1.27899
$807$	7.16159	−	12.4042i	0.252100	−	0.436650i
$808$	3.54784	+	6.14504i	0.124813	+	0.216182i
$809$	9.19840	+	15.9321i	0.323398	+	0.560142i	0.981187	−	0.193060i	$-0.0618413\pi$
$809$	9.19840	+	15.9321i	0.323398	+	0.560142i	−0.657789	+	0.753203i	$0.728508\pi$
$810$	1.24624	−	2.15855i	0.0437884	−	0.0758437i
$811$	−18.8662			−0.662482			−0.331241	−	0.943546i	$-0.607467\pi$
$811$	−18.8662			−0.662482			−0.331241	+	0.943546i	$0.607467\pi$
$812$	2.39129	+	14.3848i	0.0839178	+	0.504808i
$813$	−20.6658			−0.724782
$814$	15.8675	−	27.4833i	0.556156	−	0.963290i
$815$	7.22580	+	12.5155i	0.253109	+	0.438397i
$816$	1.12150	+	1.94249i	0.0392602	+	0.0680007i
$817$	−4.77106	+	8.26371i	−0.166918	+	0.289111i
$818$	−17.4037			−0.608508
$819$	10.1859	−	8.37825i	0.355925	−	0.292760i
$820$	11.5746			0.404204
$821$	−8.32585	+	14.4208i	−0.290574	+	0.503290i	−0.973946	−	0.226781i	$-0.927180\pi$
$821$	−8.32585	+	14.4208i	−0.290574	+	0.503290i	0.683371	+	0.730071i	$0.260513\pi$
$822$	3.89255	+	6.74210i	0.135768	+	0.235158i
$823$	17.6947	+	30.6481i	0.616798	+	1.06832i	0.990066	+	0.140602i	$0.0449037\pi$
$823$	17.6947	+	30.6481i	0.616798	+	1.06832i	−0.373269	+	0.927723i	$0.621763\pi$
$824$	3.57567	−	6.19325i	0.124565	−	0.215752i
$825$	4.19740			0.146135
$826$	21.4982	+	8.06421i	0.748018	+	0.280590i
$827$	−2.71432			−0.0943862			−0.0471931	−	0.998886i	$-0.515028\pi$
$827$	−2.71432			−0.0943862			−0.0471931	+	0.998886i	$0.515028\pi$
$828$	−3.00202	+	5.19965i	−0.104327	+	0.180700i
$829$	−6.26453	−	10.8505i	−0.217576	−	0.376853i	0.736490	−	0.676448i	$-0.236482\pi$
$829$	−6.26453	−	10.8505i	−0.217576	−	0.376853i	−0.954066	+	0.299595i	$0.903148\pi$
$830$	−6.97674	−	12.0841i	−0.242166	−	0.419444i
$831$	−14.2710	+	24.7182i	−0.495057	+	0.857464i
$832$	−4.98496			−0.172822
$833$	3.02903	−	15.4060i	0.104950	−	0.533786i
$834$	12.5882			0.435892
$835$	−21.3179	+	36.9236i	−0.737735	+	1.27779i
$836$	1.73096	+	2.99812i	0.0598667	+	0.103692i
$837$	−3.64204	−	6.30819i	−0.125887	−	0.218043i
$838$	−1.88052	+	3.25716i	−0.0649616	+	0.112517i
$839$	5.50546			0.190070			0.0950348	−	0.995474i	$-0.469704\pi$
$839$	5.50546			0.190070			0.0950348	+	0.995474i	$0.469704\pi$
$840$	6.17438	+	2.31608i	0.213036	+	0.0799122i
$841$	1.37732			0.0474939
$842$	15.8172	−	27.3961i	0.545096	−	0.944133i
$843$	−6.82214	−	11.8163i	−0.234967	−	0.406975i
$844$	11.6976	+	20.2609i	0.402649	+	0.697409i
$845$	−14.7677	+	25.5783i	−0.508023	+	0.879922i
$846$	−5.36021			−0.184288
$847$	−2.01259	+	1.65542i	−0.0691536	+	0.0568810i
$848$	−5.87423			−0.201722
$849$	−0.767015	+	1.32851i	−0.0263239	+	0.0455943i
$850$	1.35975	+	2.35516i	0.0466392	+	0.0807814i
$851$	27.5191	+	47.6644i	0.943342	+	1.63392i
$852$	6.04536	−	10.4709i	0.207110	−	0.358726i
$853$	−47.3276			−1.62047			−0.810233	−	0.586108i	$-0.800660\pi$
$853$	−47.3276			−1.62047			−0.810233	+	0.586108i	$0.800660\pi$
$854$	1.89828	+	11.4191i	0.0649579	+	0.390755i
$855$	2.49248			0.0852409
$856$	−7.86525	+	13.6230i	−0.268829	+	0.465625i
$857$	−27.0886	−	46.9189i	−0.925331	−	1.60272i	−0.791029	−	0.611779i	$-0.790454\pi$
$857$	−27.0886	−	46.9189i	−0.925331	−	1.60272i	−0.134302	−	0.990940i	$-0.542879\pi$
$858$	−8.62878	−	14.9455i	−0.294582	−	0.510231i
$859$	25.8921	−	44.8464i	0.883426	−	1.53014i	0.0359196	−	0.999355i	$-0.488564\pi$
$859$	25.8921	−	44.8464i	0.883426	−	1.53014i	0.847507	−	0.530785i	$-0.178103\pi$
$860$	23.7835			0.811011
$861$	2.01481	+	12.1201i	0.0686645	+	0.413051i
$862$	1.66582			0.0567381
$863$	13.3339	−	23.0951i	0.453893	−	0.786165i	−0.544731	−	0.838611i	$-0.683368\pi$
$863$	13.3339	−	23.0951i	0.453893	−	0.786165i	0.998624	+	0.0524456i	$0.0167016\pi$
$864$	−0.500000	−	0.866025i	−0.0170103	−	0.0294628i
$865$	3.22043	+	5.57796i	0.109498	+	0.189656i
$866$	8.05311	−	13.9484i	0.273656	−	0.473986i
$867$	11.9690			0.406488
$868$	14.8838	−	12.2424i	0.505189	−	0.415534i
$869$	24.5336			0.832244
$870$	6.86872	−	11.8970i	0.232872	−	0.403345i
$871$	37.7817	+	65.4399i	1.28018	+	2.21735i
$872$	4.15854	+	7.20279i	0.140826	+	0.243917i
$873$	−3.50202	+	6.06568i	−0.118525	+	0.205292i
$874$	−6.00404			−0.203090
$875$	−23.3858	−	8.77227i	−0.790584	−	0.296557i
$876$	−14.4204			−0.487219
$877$	5.86591	−	10.1601i	0.198078	−	0.343081i	−0.749827	−	0.661633i	$-0.769864\pi$
$877$	5.86591	−	10.1601i	0.198078	−	0.343081i	0.947905	+	0.318553i	$0.103197\pi$
$878$	10.5433	+	18.2616i	0.355820	+	0.616299i
$879$	−16.6887	−	28.9056i	−0.562894	−	0.974962i
$880$	4.31439	−	7.47274i	0.145438	−	0.251906i
$881$	−11.8406			−0.398918			−0.199459	−	0.979906i	$-0.563919\pi$
$881$	−11.8406			−0.398918			−0.199459	+	0.979906i	$0.563919\pi$
$882$	−1.35044	+	6.86850i	−0.0454717	+	0.231274i
$883$	35.5167			1.19523			0.597616	−	0.801782i	$-0.296115\pi$
$883$	35.5167			1.19523			0.597616	+	0.801782i	$0.296115\pi$
$884$	5.59061	−	9.68323i	0.188033	−	0.325682i
$885$	−10.8154	−	18.7328i	−0.363555	−	0.629696i
$886$	−9.29789	−	16.1044i	−0.312369	−	0.541039i
$887$	19.4772	−	33.7355i	0.653980	−	1.13273i	−0.328168	−	0.944619i	$-0.606431\pi$
$887$	19.4772	−	33.7355i	0.653980	−	1.13273i	0.982148	−	0.188108i	$-0.0602354\pi$
$888$	−9.16685			−0.307619
$889$	15.1003	+	5.66427i	0.506446	+	0.189974i
$890$	−18.7672			−0.629076
$891$	1.73096	−	2.99812i	0.0579895	−	0.100441i
$892$	−7.41107	−	12.8364i	−0.248141	−	0.429793i
$893$	−2.68011	−	4.64208i	−0.0896864	−	0.155341i
$894$	−8.14608	+	14.1094i	−0.272446	+	0.471890i
$895$	−8.09927			−0.270729
$896$	2.04334	−	1.68071i	0.0682631	−	0.0561485i
$897$	29.9299			0.999329
$898$	9.87051	−	17.0962i	0.329383	−	0.570509i
$899$	−20.0733	−	34.7680i	−0.669482	−	1.15958i
$900$	−0.606223	−	1.05001i	−0.0202074	−	0.0350003i
$901$	6.58793	−	11.4106i	0.219476	−	0.380143i
$902$	16.0766			0.535292
$903$	4.14002	+	24.9043i	0.137771	+	0.828763i
$904$	−13.3643			−0.444488
$905$	−15.5230	+	26.8867i	−0.516003	+	0.893743i
$906$	−9.98675	−	17.2976i	−0.331787	−	0.574673i
$907$	−27.5714	−	47.7551i	−0.915493	−	1.58568i	−0.806178	−	0.591674i	$-0.798467\pi$
$907$	−27.5714	−	47.7551i	−0.915493	−	1.58568i	−0.109316	−	0.994007i	$-0.534866\pi$
$908$	−8.11473	+	14.0551i	−0.269297	+	0.466436i
$909$	7.09569			0.235349
$910$	−5.39076	−	32.4282i	−0.178702	−	1.07498i
$911$	11.9618			0.396313			0.198157	−	0.980170i	$-0.436505\pi$
$911$	11.9618			0.396313			0.198157	+	0.980170i	$0.436505\pi$
$912$	0.500000	−	0.866025i	0.0165567	−	0.0286770i
$913$	−9.69035	−	16.7842i	−0.320704	−	0.555475i
$914$	0.234446	+	0.406073i	0.00775480	+	0.0134317i
$915$	5.45262	−	9.44421i	0.180258	−	0.312216i
$916$	−6.39480			−0.211290
$917$	−19.0320	+	15.6544i	−0.628491	+	0.516953i
$918$	2.24299			0.0740298
$919$	−18.4682	+	31.9879i	−0.609211	+	1.05518i	0.382160	+	0.924096i	$0.375180\pi$
$919$	−18.4682	+	31.9879i	−0.609211	+	1.05518i	−0.991371	+	0.131088i	$0.958153\pi$
$920$	7.48247	+	12.9600i	0.246690	+	0.427279i
$921$	4.76476	+	8.25280i	0.157004	+	0.271939i
$922$	−9.52782	+	16.5027i	−0.313782	+	0.543487i
$923$	−60.2717			−1.98387
$924$	8.57590	+	3.21692i	0.282127	+	0.105829i
$925$	−11.1143			−0.365436
$926$	−4.82787	+	8.36212i	−0.158654	+	0.274796i
$927$	−3.57567	−	6.19325i	−0.117441	−	0.203413i
$928$	−2.75578	−	4.77315i	−0.0904630	−	0.156686i
$929$	12.1403	−	21.0276i	0.398310	−	0.689893i	−0.595208	−	0.803572i	$-0.702930\pi$
$929$	12.1403	−	21.0276i	0.398310	−	0.689893i	0.993518	+	0.113679i	$0.0362636\pi$
$930$	−18.1554			−0.595339
$931$	−6.62352	+	2.26473i	−0.217077	+	0.0742237i
$932$	−21.3798			−0.700317
$933$	8.22020	−	14.2378i	0.269117	−	0.466125i
$934$	−4.58141	−	7.93523i	−0.149908	−	0.259649i
$935$	9.67715	+	16.7613i	0.316477	+	0.548154i
$936$	−2.49248	+	4.31710i	−0.0814692	+	0.141109i
$937$	−24.5823			−0.803068			−0.401534	−	0.915844i	$-0.631523\pi$
$937$	−24.5823			−0.803068			−0.401534	+	0.915844i	$0.631523\pi$
$938$	−37.5502	−	14.0855i	−1.22606	−	0.459908i
$939$	−10.9940			−0.358775
$940$	−6.68011	+	11.5703i	−0.217881	+	0.377381i
$941$	3.67861	+	6.37155i	0.119919	+	0.207707i	0.919736	−	0.392539i	$-0.128403\pi$
$941$	3.67861	+	6.37155i	0.119919	+	0.207707i	−0.799816	+	0.600245i	$0.795070\pi$
$942$	0.369526	+	0.640038i	0.0120398	+	0.0208536i
$943$	−13.9409	+	24.1463i	−0.453977	+	0.786311i
$944$	−8.67842			−0.282458
$945$	5.09297	−	4.18913i	0.165674	−	0.136272i
$946$	33.0341			1.07403
$947$	14.5231	−	25.1548i	0.471938	−	0.817420i	−0.527547	−	0.849526i	$-0.676888\pi$
$947$	14.5231	−	25.1548i	0.471938	−	0.817420i	0.999484	+	0.0321057i	$0.0102213\pi$
$948$	−3.54334	−	6.13724i	−0.115082	−	0.199328i
$949$	35.9425	+	62.2542i	1.16674	+	2.02086i
$950$	0.606223	−	1.05001i	0.0196685	−	0.0340668i
$951$	−6.66291			−0.216060
$952$	0.973163	+	5.85407i	0.0315404	+	0.189731i
$953$	−5.84772			−0.189426			−0.0947131	−	0.995505i	$-0.530193\pi$
$953$	−5.84772			−0.189426			−0.0947131	+	0.995505i	$0.530193\pi$
$954$	−2.93711	+	5.08723i	−0.0950925	+	0.164705i
$955$	20.4937	+	35.4961i	0.663160	+	1.14863i
$956$	−9.44689	−	16.3625i	−0.305534	−	0.529201i
$957$	9.54032	−	16.5243i	0.308395	−	0.534155i
$958$	−42.8212			−1.38349
$959$	3.37771	+	20.3186i	0.109072	+	0.656122i
$960$	−2.49248			−0.0804444
$961$	−11.0289	+	19.1025i	−0.355770	+	0.616211i
$962$	22.8482	+	39.5742i	0.736655	+	1.27592i
$963$	7.86525	+	13.6230i	0.253454	+	0.438995i
$964$	−2.02505	+	3.50748i	−0.0652224	+	0.112968i
$965$	−46.5729			−1.49923
$966$	−12.2683	+	10.0910i	−0.394725	+	0.324674i
$967$	11.7775			0.378738			0.189369	−	0.981906i	$-0.439356\pi$
$967$	11.7775			0.378738			0.189369	+	0.981906i	$0.439356\pi$
$968$	0.492478	−	0.852997i	0.0158288	−	0.0274163i
$969$	1.12150	+	1.94249i	0.0360277	+	0.0624018i
$970$	8.72871	+	15.1186i	0.280262	+	0.485428i
$971$	16.7405	−	28.9954i	0.537228	−	0.930507i	−0.461824	−	0.886972i	$-0.652805\pi$
$971$	16.7405	−	28.9954i	0.537228	−	0.930507i	0.999052	−	0.0435348i	$-0.0138619\pi$
$972$	−1.00000			−0.0320750
$973$	31.1834	+	11.6973i	0.999695	+	0.374997i
$974$	26.3153			0.843196
$975$	−3.02199	+	5.23425i	−0.0967813	+	0.167630i
$976$	−2.18763	−	3.78908i	−0.0700243	−	0.121286i
$977$	8.69843	+	15.0661i	0.278288	+	0.482008i	0.970959	−	0.239245i	$-0.0768999\pi$
$977$	8.69843	+	15.0661i	0.278288	+	0.482008i	−0.692672	+	0.721253i	$0.743567\pi$
$978$	2.89904	−	5.02129i	0.0927012	−	0.160563i
$979$	−26.0667			−0.833094
$980$	13.1430	+	11.4748i	0.419839	+	0.366549i
$981$	8.31707			0.265544
$982$	−7.10321	+	12.3031i	−0.226672	+	0.392608i
$983$	−6.96090	−	12.0566i	−0.222018	−	0.384547i	0.733403	−	0.679795i	$-0.237931\pi$
$983$	−6.96090	−	12.0566i	−0.222018	−	0.384547i	−0.955421	+	0.295248i	$0.904598\pi$
$984$	−2.32191	−	4.02167i	−0.0740199	−	0.128206i
$985$	19.3124	−	33.4500i	0.615343	−	1.06581i
$986$	12.3624			0.393699
$987$	−13.2783	−	4.98085i	−0.422654	−	0.158542i
$988$	−4.98496			−0.158593
$989$	−28.6456	+	49.6157i	−0.910877	+	1.57769i
$990$	−4.31439	−	7.47274i	−0.137120	−	0.237499i
$991$	19.9847	+	34.6145i	0.634834	+	1.09957i	0.986550	+	0.163459i	$0.0522650\pi$
$991$	19.9847	+	34.6145i	0.634834	+	1.09957i	−0.351716	+	0.936107i	$0.614402\pi$
$992$	−3.64204	+	6.30819i	−0.115635	+	0.200285i
$993$	−25.8102			−0.819062
$994$	24.7054	−	20.3210i	0.783607	−	0.644542i
$995$	−3.63772			−0.115324
$996$	−2.79912	+	4.84821i	−0.0886934	+	0.153622i
$997$	−17.6638	−	30.5947i	−0.559419	−	0.968942i	−0.997545	−	0.0700287i	$-0.977691\pi$
$997$	−17.6638	−	30.5947i	−0.559419	−	0.968942i	0.438126	−	0.898914i	$-0.355642\pi$
$998$	17.0163	+	29.4730i	0.538640	+	0.932952i
$999$	−4.58343	+	7.93873i	−0.145013	+	0.251170i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	798.2.j.l.457.1	✓	8
7.2	even	3		5586.2.a.bw.1.4		4
7.4	even	3	inner	798.2.j.l.571.1	yes	8
7.5	odd	6		5586.2.a.bz.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.j.l.457.1	✓	8	1.1	even	1	trivial
798.2.j.l.571.1	yes	8	7.4	even	3	inner
5586.2.a.bw.1.4		4	7.2	even	3
5586.2.a.bz.1.1		4	7.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 798 = 2 \cdot 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	798.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.24624 + 2.15855i) q^{5} +1.00000 q^{6} +(2.47720 + 0.929227i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.24624 + 2.15855i) q^{5} +1.00000 q^{6} +(2.47720 + 0.929227i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.24624 + 2.15855i) q^{10} +(1.73096 + 2.99812i) q^{11} +(0.500000 - 0.866025i) q^{12} -4.98496 q^{13} +(2.04334 - 1.68071i) q^{14} -2.49248 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.12150 - 1.94249i) q^{17} +(0.500000 + 0.866025i) q^{18} +(-0.500000 + 0.866025i) q^{19} +2.49248 q^{20} +(0.433868 + 2.60993i) q^{21} +3.46193 q^{22} +(-3.00202 + 5.19965i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-0.606223 - 1.05001i) q^{25} +(-2.49248 + 4.31710i) q^{26} -1.00000 q^{27} +(-0.433868 - 2.60993i) q^{28} -5.51156 q^{29} +(-1.24624 + 2.15855i) q^{30} +(3.64204 + 6.30819i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-1.73096 + 2.99812i) q^{33} -2.24299 q^{34} +(-5.09297 + 4.18913i) q^{35} +1.00000 q^{36} +(4.58343 - 7.93873i) q^{37} +(0.500000 + 0.866025i) q^{38} +(-2.49248 - 4.31710i) q^{39} +(1.24624 - 2.15855i) q^{40} +4.64383 q^{41} +(2.47720 + 0.929227i) q^{42} +9.54211 q^{43} +(1.73096 - 2.99812i) q^{44} +(-1.24624 - 2.15855i) q^{45} +(3.00202 + 5.19965i) q^{46} +(-2.68011 + 4.64208i) q^{47} -1.00000 q^{48} +(5.27308 + 4.60377i) q^{49} -1.21245 q^{50} +(1.12150 - 1.94249i) q^{51} +(2.49248 + 4.31710i) q^{52} +(2.93711 + 5.08723i) q^{53} +(-0.500000 + 0.866025i) q^{54} -8.62878 q^{55} +(-2.47720 - 0.929227i) q^{56} -1.00000 q^{57} +(-2.75578 + 4.77315i) q^{58} +(4.33921 + 7.51573i) q^{59} +(1.24624 + 2.15855i) q^{60} +(-2.18763 + 3.78908i) q^{61} +7.28407 q^{62} +(-2.04334 + 1.68071i) q^{63} +1.00000 q^{64} +(6.21245 - 10.7603i) q^{65} +(1.73096 + 2.99812i) q^{66} +(-7.57915 - 13.1275i) q^{67} +(-1.12150 + 1.94249i) q^{68} -6.00404 q^{69} +(1.08141 + 6.50520i) q^{70} +12.0907 q^{71} +(0.500000 - 0.866025i) q^{72} +(-7.21019 - 12.4884i) q^{73} +(-4.58343 - 7.93873i) q^{74} +(0.606223 - 1.05001i) q^{75} +1.00000 q^{76} +(1.50202 + 9.03541i) q^{77} -4.98496 q^{78} +(3.54334 - 6.13724i) q^{79} +(-1.24624 - 2.15855i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(2.32191 - 4.02167i) q^{82} -5.59823 q^{83} +(2.04334 - 1.68071i) q^{84} +5.59061 q^{85} +(4.77106 - 8.26371i) q^{86} +(-2.75578 - 4.77315i) q^{87} +(-1.73096 - 2.99812i) q^{88} +(-3.76476 + 6.52075i) q^{89} -2.49248 q^{90} +(-12.3488 - 4.63215i) q^{91} +6.00404 q^{92} +(-3.64204 + 6.30819i) q^{93} +(2.68011 + 4.64208i) q^{94} +(-1.24624 - 2.15855i) q^{95} +(-0.500000 + 0.866025i) q^{96} +7.00404 q^{97} +(6.62352 - 2.26473i) q^{98} -3.46193 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} + 4 q^{3} - 4 q^{4} + 8 q^{6} - 2 q^{7} - 8 q^{8} - 4 q^{9}+O(q^{10}) \) 8 * q + 4 * q^2 + 4 * q^3 - 4 * q^4 + 8 * q^6 - 2 * q^7 - 8 * q^8 - 4 * q^9	\( 8 q + 4 q^{2} + 4 q^{3} - 4 q^{4} + 8 q^{6} - 2 q^{7} - 8 q^{8} - 4 q^{9} + 2 q^{11} + 4 q^{12} - q^{14} - 4 q^{16} - 10 q^{17} + 4 q^{18} - 4 q^{19} - q^{21} + 4 q^{22} + 5 q^{23} - 4 q^{24} - 4 q^{25} - 8 q^{27} + q^{28} - 6 q^{29} - 9 q^{31} + 4 q^{32} - 2 q^{33} - 20 q^{34} - 9 q^{35} + 8 q^{36} + 14 q^{37} + 4 q^{38} + 8 q^{41} - 2 q^{42} + 42 q^{43} + 2 q^{44} - 5 q^{46} - 7 q^{47} - 8 q^{48} - 4 q^{49} - 8 q^{50} + 10 q^{51} + 7 q^{53} - 4 q^{54} + 2 q^{56} - 8 q^{57} - 3 q^{58} - 7 q^{59} - 23 q^{61} - 18 q^{62} + q^{63} + 8 q^{64} + 48 q^{65} + 2 q^{66} - 6 q^{67} - 10 q^{68} + 10 q^{69} + 15 q^{70} + 4 q^{71} + 4 q^{72} + 5 q^{73} - 14 q^{74} + 4 q^{75} + 8 q^{76} - 17 q^{77} + 11 q^{79} - 4 q^{81} + 4 q^{82} + 28 q^{83} - q^{84} + 12 q^{85} + 21 q^{86} - 3 q^{87} - 2 q^{88} - 10 q^{89} - 48 q^{91} - 10 q^{92} + 9 q^{93} + 7 q^{94} - 4 q^{96} - 2 q^{97} + 25 q^{98} - 4 q^{99}+O(q^{100}) \) 8 * q + 4 * q^2 + 4 * q^3 - 4 * q^4 + 8 * q^6 - 2 * q^7 - 8 * q^8 - 4 * q^9 + 2 * q^11 + 4 * q^12 - q^14 - 4 * q^16 - 10 * q^17 + 4 * q^18 - 4 * q^19 - q^21 + 4 * q^22 + 5 * q^23 - 4 * q^24 - 4 * q^25 - 8 * q^27 + q^28 - 6 * q^29 - 9 * q^31 + 4 * q^32 - 2 * q^33 - 20 * q^34 - 9 * q^35 + 8 * q^36 + 14 * q^37 + 4 * q^38 + 8 * q^41 - 2 * q^42 + 42 * q^43 + 2 * q^44 - 5 * q^46 - 7 * q^47 - 8 * q^48 - 4 * q^49 - 8 * q^50 + 10 * q^51 + 7 * q^53 - 4 * q^54 + 2 * q^56 - 8 * q^57 - 3 * q^58 - 7 * q^59 - 23 * q^61 - 18 * q^62 + q^63 + 8 * q^64 + 48 * q^65 + 2 * q^66 - 6 * q^67 - 10 * q^68 + 10 * q^69 + 15 * q^70 + 4 * q^71 + 4 * q^72 + 5 * q^73 - 14 * q^74 + 4 * q^75 + 8 * q^76 - 17 * q^77 + 11 * q^79 - 4 * q^81 + 4 * q^82 + 28 * q^83 - q^84 + 12 * q^85 + 21 * q^86 - 3 * q^87 - 2 * q^88 - 10 * q^89 - 48 * q^91 - 10 * q^92 + 9 * q^93 + 7 * q^94 - 4 * q^96 - 2 * q^97 + 25 * q^98 - 4 * q^99

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