LMFDB - Embedded newform 370.2.e.d.211.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(121,370)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("370.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.e (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:	$2.95446487479$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			211.1
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	370.211
Dual form			370.2.e.d.121.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} -1.00000 q^{6} +(-1.73205 + 3.00000i) q^{7} +1.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} -1.00000 q^{6} +(-1.73205 + 3.00000i) q^{7} +1.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +1.00000 q^{10} -5.46410 q^{11} +(0.500000 + 0.866025i) q^{12} +(-2.23205 + 3.86603i) q^{13} +3.46410 q^{14} +(0.500000 + 0.866025i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.732051 + 1.26795i) q^{17} +(1.00000 - 1.73205i) q^{18} +(1.00000 - 1.73205i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(1.73205 + 3.00000i) q^{21} +(2.73205 + 4.73205i) q^{22} -5.46410 q^{23} +(0.500000 - 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} +4.46410 q^{26} +5.00000 q^{27} +(-1.73205 - 3.00000i) q^{28} -2.00000 q^{29} +(0.500000 - 0.866025i) q^{30} +8.46410 q^{31} +(-0.500000 + 0.866025i) q^{32} +(-2.73205 + 4.73205i) q^{33} +(0.732051 - 1.26795i) q^{34} +(-1.73205 - 3.00000i) q^{35} -2.00000 q^{36} +(4.69615 + 3.86603i) q^{37} -2.00000 q^{38} +(2.23205 + 3.86603i) q^{39} +(-0.500000 + 0.866025i) q^{40} +(5.96410 - 10.3301i) q^{41} +(1.73205 - 3.00000i) q^{42} -9.92820 q^{43} +(2.73205 - 4.73205i) q^{44} -2.00000 q^{45} +(2.73205 + 4.73205i) q^{46} +3.46410 q^{47} -1.00000 q^{48} +(-2.50000 - 4.33013i) q^{49} +(-0.500000 + 0.866025i) q^{50} +1.46410 q^{51} +(-2.23205 - 3.86603i) q^{52} +(2.76795 + 4.79423i) q^{53} +(-2.50000 - 4.33013i) q^{54} +(2.73205 - 4.73205i) q^{55} +(-1.73205 + 3.00000i) q^{56} +(-1.00000 - 1.73205i) q^{57} +(1.00000 + 1.73205i) q^{58} +(2.73205 + 4.73205i) q^{59} -1.00000 q^{60} +(-4.46410 + 7.73205i) q^{61} +(-4.23205 - 7.33013i) q^{62} -6.92820 q^{63} +1.00000 q^{64} +(-2.23205 - 3.86603i) q^{65} +5.46410 q^{66} +(-7.46410 + 12.9282i) q^{67} -1.46410 q^{68} +(-2.73205 + 4.73205i) q^{69} +(-1.73205 + 3.00000i) q^{70} +(-0.535898 + 0.928203i) q^{71} +(1.00000 + 1.73205i) q^{72} +2.53590 q^{73} +(1.00000 - 6.00000i) q^{74} -1.00000 q^{75} +(1.00000 + 1.73205i) q^{76} +(9.46410 - 16.3923i) q^{77} +(2.23205 - 3.86603i) q^{78} +(7.46410 - 12.9282i) q^{79} +1.00000 q^{80} +(-0.500000 + 0.866025i) q^{81} -11.9282 q^{82} +(-4.92820 - 8.53590i) q^{83} -3.46410 q^{84} -1.46410 q^{85} +(4.96410 + 8.59808i) q^{86} +(-1.00000 + 1.73205i) q^{87} -5.46410 q^{88} +(1.00000 + 1.73205i) q^{89} +(1.00000 + 1.73205i) q^{90} +(-7.73205 - 13.3923i) q^{91} +(2.73205 - 4.73205i) q^{92} +(4.23205 - 7.33013i) q^{93} +(-1.73205 - 3.00000i) q^{94} +(1.00000 + 1.73205i) q^{95} +(0.500000 + 0.866025i) q^{96} -2.00000 q^{97} +(-2.50000 + 4.33013i) q^{98} +(-5.46410 - 9.46410i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 4 q^{6} + 4 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 4 * q^6 + 4 * q^8 + 4 * q^9	$ 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 4 q^{6} + 4 q^{8} + 4 q^{9} + 4 q^{10} - 8 q^{11} + 2 q^{12} - 2 q^{13} + 2 q^{15} - 2 q^{16} - 4 q^{17} + 4 q^{18} + 4 q^{19} - 2 q^{20} + 4 q^{22} - 8 q^{23} + 2 q^{24} - 2 q^{25} + 4 q^{26} + 20 q^{27} - 8 q^{29} + 2 q^{30} + 20 q^{31} - 2 q^{32} - 4 q^{33} - 4 q^{34} - 8 q^{36} - 2 q^{37} - 8 q^{38} + 2 q^{39} - 2 q^{40} + 10 q^{41} - 12 q^{43} + 4 q^{44} - 8 q^{45} + 4 q^{46} - 4 q^{48} - 10 q^{49} - 2 q^{50} - 8 q^{51} - 2 q^{52} + 18 q^{53} - 10 q^{54} + 4 q^{55} - 4 q^{57} + 4 q^{58} + 4 q^{59} - 4 q^{60} - 4 q^{61} - 10 q^{62} + 4 q^{64} - 2 q^{65} + 8 q^{66} - 16 q^{67} + 8 q^{68} - 4 q^{69} - 16 q^{71} + 4 q^{72} + 24 q^{73} + 4 q^{74} - 4 q^{75} + 4 q^{76} + 24 q^{77} + 2 q^{78} + 16 q^{79} + 4 q^{80} - 2 q^{81} - 20 q^{82} + 8 q^{83} + 8 q^{85} + 6 q^{86} - 4 q^{87} - 8 q^{88} + 4 q^{89} + 4 q^{90} - 24 q^{91} + 4 q^{92} + 10 q^{93} + 4 q^{95} + 2 q^{96} - 8 q^{97} - 10 q^{98} - 8 q^{99}+O(q^{100}) $ 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 4 * q^6 + 4 * q^8 + 4 * q^9 + 4 * q^10 - 8 * q^11 + 2 * q^12 - 2 * q^13 + 2 * q^15 - 2 * q^16 - 4 * q^17 + 4 * q^18 + 4 * q^19 - 2 * q^20 + 4 * q^22 - 8 * q^23 + 2 * q^24 - 2 * q^25 + 4 * q^26 + 20 * q^27 - 8 * q^29 + 2 * q^30 + 20 * q^31 - 2 * q^32 - 4 * q^33 - 4 * q^34 - 8 * q^36 - 2 * q^37 - 8 * q^38 + 2 * q^39 - 2 * q^40 + 10 * q^41 - 12 * q^43 + 4 * q^44 - 8 * q^45 + 4 * q^46 - 4 * q^48 - 10 * q^49 - 2 * q^50 - 8 * q^51 - 2 * q^52 + 18 * q^53 - 10 * q^54 + 4 * q^55 - 4 * q^57 + 4 * q^58 + 4 * q^59 - 4 * q^60 - 4 * q^61 - 10 * q^62 + 4 * q^64 - 2 * q^65 + 8 * q^66 - 16 * q^67 + 8 * q^68 - 4 * q^69 - 16 * q^71 + 4 * q^72 + 24 * q^73 + 4 * q^74 - 4 * q^75 + 4 * q^76 + 24 * q^77 + 2 * q^78 + 16 * q^79 + 4 * q^80 - 2 * q^81 - 20 * q^82 + 8 * q^83 + 8 * q^85 + 6 * q^86 - 4 * q^87 - 8 * q^88 + 4 * q^89 + 4 * q^90 - 24 * q^91 + 4 * q^92 + 10 * q^93 + 4 * q^95 + 2 * q^96 - 8 * q^97 - 10 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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	−0.684819	−	0.728714i	$-0.740119\pi$
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i	0.973494	+	0.228714i	$0.0734519\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$	−1.00000			−0.408248
$7$	−1.73205	+	3.00000i	−0.654654	+	1.13389i	0.327327	+	0.944911i	$0.393852\pi$
$7$	−1.73205	+	3.00000i	−0.654654	+	1.13389i	−0.981981	+	0.188982i	$0.939481\pi$
$8$	1.00000			0.353553
$9$	1.00000	+	1.73205i	0.333333	+	0.577350i
$10$	1.00000			0.316228
$11$	−5.46410			−1.64749			−0.823744	−	0.566961i	$-0.808119\pi$
$11$	−5.46410			−1.64749			−0.823744	+	0.566961i	$0.808119\pi$
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$	−2.23205	+	3.86603i	−0.619060	+	1.07224i	0.370598	+	0.928793i	$0.379153\pi$
$13$	−2.23205	+	3.86603i	−0.619060	+	1.07224i	−0.989658	+	0.143449i	$0.954181\pi$
$14$	3.46410			0.925820
$15$	0.500000	+	0.866025i	0.129099	+	0.223607i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	0.732051	+	1.26795i	0.177548	+	0.307523i	0.941040	−	0.338295i	$-0.109850\pi$
$17$	0.732051	+	1.26795i	0.177548	+	0.307523i	−0.763492	+	0.645817i	$0.776517\pi$
$18$	1.00000	−	1.73205i	0.235702	−	0.408248i
$19$	1.00000	−	1.73205i	0.229416	−	0.397360i	−0.728219	−	0.685344i	$-0.759652\pi$
$19$	1.00000	−	1.73205i	0.229416	−	0.397360i	0.957635	+	0.287984i	$0.0929851\pi$
$20$	−0.500000	−	0.866025i	−0.111803	−	0.193649i
$21$	1.73205	+	3.00000i	0.377964	+	0.654654i
$22$	2.73205	+	4.73205i	0.582475	+	1.00888i
$23$	−5.46410			−1.13934			−0.569672	−	0.821872i	$-0.692930\pi$
$23$	−5.46410			−1.13934			−0.569672	+	0.821872i	$0.692930\pi$
$24$	0.500000	−	0.866025i	0.102062	−	0.176777i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	4.46410			0.875482
$27$	5.00000			0.962250
$28$	−1.73205	−	3.00000i	−0.327327	−	0.566947i
$29$	−2.00000			−0.371391			−0.185695	−	0.982607i	$-0.559454\pi$
$29$	−2.00000			−0.371391			−0.185695	+	0.982607i	$0.559454\pi$
$30$	0.500000	−	0.866025i	0.0912871	−	0.158114i
$31$	8.46410			1.52020			0.760099	−	0.649808i	$-0.225151\pi$
$31$	8.46410			1.52020			0.760099	+	0.649808i	$0.225151\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−2.73205	+	4.73205i	−0.475589	+	0.823744i
$34$	0.732051	−	1.26795i	0.125546	−	0.217451i
$35$	−1.73205	−	3.00000i	−0.292770	−	0.507093i
$36$	−2.00000			−0.333333
$37$	4.69615	+	3.86603i	0.772043	+	0.635571i
$37$	4.69615	+	3.86603i	0.772043	+	0.635571i
$38$	−2.00000			−0.324443
$39$	2.23205	+	3.86603i	0.357414	+	0.619060i
$40$	−0.500000	+	0.866025i	−0.0790569	+	0.136931i
$41$	5.96410	−	10.3301i	0.931436	−	1.61329i	0.150567	−	0.988600i	$-0.451890\pi$
$41$	5.96410	−	10.3301i	0.931436	−	1.61329i	0.780869	−	0.624695i	$-0.214777\pi$
$42$	1.73205	−	3.00000i	0.267261	−	0.462910i
$43$	−9.92820			−1.51404			−0.757018	−	0.653394i	$-0.773345\pi$
$43$	−9.92820			−1.51404			−0.757018	+	0.653394i	$0.773345\pi$
$44$	2.73205	−	4.73205i	0.411872	−	0.713384i
$45$	−2.00000			−0.298142
$46$	2.73205	+	4.73205i	0.402819	+	0.697703i
$47$	3.46410			0.505291			0.252646	−	0.967559i	$-0.418699\pi$
$47$	3.46410			0.505291			0.252646	+	0.967559i	$0.418699\pi$
$48$	−1.00000			−0.144338
$49$	−2.50000	−	4.33013i	−0.357143	−	0.618590i
$50$	−0.500000	+	0.866025i	−0.0707107	+	0.122474i
$51$	1.46410			0.205015
$52$	−2.23205	−	3.86603i	−0.309530	−	0.536121i
$53$	2.76795	+	4.79423i	0.380207	+	0.658538i	0.991092	−	0.133182i	$-0.0425194\pi$
$53$	2.76795	+	4.79423i	0.380207	+	0.658538i	−0.610885	+	0.791720i	$0.709186\pi$
$54$	−2.50000	−	4.33013i	−0.340207	−	0.589256i
$55$	2.73205	−	4.73205i	0.368390	−	0.638070i
$56$	−1.73205	+	3.00000i	−0.231455	+	0.400892i
$57$	−1.00000	−	1.73205i	−0.132453	−	0.229416i
$58$	1.00000	+	1.73205i	0.131306	+	0.227429i
$59$	2.73205	+	4.73205i	0.355683	+	0.616061i	0.987235	−	0.159273i	$-0.0509150\pi$
$59$	2.73205	+	4.73205i	0.355683	+	0.616061i	−0.631552	+	0.775334i	$0.717582\pi$
$60$	−1.00000			−0.129099
$61$	−4.46410	+	7.73205i	−0.571570	+	0.989988i	0.424835	+	0.905271i	$0.360332\pi$
$61$	−4.46410	+	7.73205i	−0.571570	+	0.989988i	−0.996405	+	0.0847171i	$0.973001\pi$
$62$	−4.23205	−	7.33013i	−0.537471	−	0.930927i
$63$	−6.92820			−0.872872
$64$	1.00000			0.125000
$65$	−2.23205	−	3.86603i	−0.276852	−	0.479521i
$66$	5.46410			0.672584
$67$	−7.46410	+	12.9282i	−0.911885	+	1.57943i	−0.100486	+	0.994938i	$0.532040\pi$
$67$	−7.46410	+	12.9282i	−0.911885	+	1.57943i	−0.811399	+	0.584493i	$0.801293\pi$
$68$	−1.46410			−0.177548
$69$	−2.73205	+	4.73205i	−0.328900	+	0.569672i
$70$	−1.73205	+	3.00000i	−0.207020	+	0.358569i
$71$	−0.535898	+	0.928203i	−0.0635994	+	0.110157i	−0.896072	−	0.443909i	$-0.853591\pi$
$71$	−0.535898	+	0.928203i	−0.0635994	+	0.110157i	0.832472	+	0.554066i	$0.186925\pi$
$72$	1.00000	+	1.73205i	0.117851	+	0.204124i
$73$	2.53590			0.296804			0.148402	−	0.988927i	$-0.452587\pi$
$73$	2.53590			0.296804			0.148402	+	0.988927i	$0.452587\pi$
$74$	1.00000	−	6.00000i	0.116248	−	0.697486i
$75$	−1.00000			−0.115470
$76$	1.00000	+	1.73205i	0.114708	+	0.198680i
$77$	9.46410	−	16.3923i	1.07853	−	1.86808i
$78$	2.23205	−	3.86603i	0.252730	−	0.437741i
$79$	7.46410	−	12.9282i	0.839777	−	1.45454i	−0.0503039	−	0.998734i	$-0.516019\pi$
$79$	7.46410	−	12.9282i	0.839777	−	1.45454i	0.890081	−	0.455803i	$-0.150648\pi$
$80$	1.00000			0.111803
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−11.9282			−1.31725
$83$	−4.92820	−	8.53590i	−0.540941	−	0.936937i	−0.998850	−	0.0479379i	$-0.984735\pi$
$83$	−4.92820	−	8.53590i	−0.540941	−	0.936937i	0.457910	−	0.888999i	$-0.348598\pi$
$84$	−3.46410			−0.377964
$85$	−1.46410			−0.158804
$86$	4.96410	+	8.59808i	0.535293	+	0.927154i
$87$	−1.00000	+	1.73205i	−0.107211	+	0.185695i
$88$	−5.46410			−0.582475
$89$	1.00000	+	1.73205i	0.106000	+	0.183597i	0.914146	−	0.405385i	$-0.132862\pi$
$89$	1.00000	+	1.73205i	0.106000	+	0.183597i	−0.808146	+	0.588982i	$0.799529\pi$
$90$	1.00000	+	1.73205i	0.105409	+	0.182574i
$91$	−7.73205	−	13.3923i	−0.810539	−	1.40390i
$92$	2.73205	−	4.73205i	0.284836	−	0.493350i
$93$	4.23205	−	7.33013i	0.438843	−	0.760099i
$94$	−1.73205	−	3.00000i	−0.178647	−	0.309426i
$95$	1.00000	+	1.73205i	0.102598	+	0.177705i
$96$	0.500000	+	0.866025i	0.0510310	+	0.0883883i
$97$	−2.00000			−0.203069			−0.101535	−	0.994832i	$-0.532375\pi$
$97$	−2.00000			−0.203069			−0.101535	+	0.994832i	$0.532375\pi$
$98$	−2.50000	+	4.33013i	−0.252538	+	0.437409i
$99$	−5.46410	−	9.46410i	−0.549163	−	0.951178i
$100$	1.00000			0.100000
$101$	−9.46410			−0.941713			−0.470857	−	0.882210i	$-0.656055\pi$
$101$	−9.46410			−0.941713			−0.470857	+	0.882210i	$0.656055\pi$
$102$	−0.732051	−	1.26795i	−0.0724838	−	0.125546i
$103$	−13.4641			−1.32666			−0.663329	−	0.748328i	$-0.730857\pi$
$103$	−13.4641			−1.32666			−0.663329	+	0.748328i	$0.730857\pi$
$104$	−2.23205	+	3.86603i	−0.218871	+	0.379095i
$105$	−3.46410			−0.338062
$106$	2.76795	−	4.79423i	0.268847	−	0.465657i
$107$	4.42820	−	7.66987i	0.428091	−	0.741475i	−0.568613	−	0.822605i	$-0.692520\pi$
$107$	4.42820	−	7.66987i	0.428091	−	0.741475i	0.996703	+	0.0811306i	$0.0258531\pi$
$108$	−2.50000	+	4.33013i	−0.240563	+	0.416667i
$109$	5.00000	+	8.66025i	0.478913	+	0.829502i	0.999708	−	0.0241802i	$-0.00769755\pi$
$109$	5.00000	+	8.66025i	0.478913	+	0.829502i	−0.520794	+	0.853682i	$0.674364\pi$
$110$	−5.46410			−0.520982
$111$	5.69615	−	2.13397i	0.540655	−	0.202548i
$112$	3.46410			0.327327
$113$	1.46410	+	2.53590i	0.137731	+	0.238557i	0.926637	−	0.375956i	$-0.122686\pi$
$113$	1.46410	+	2.53590i	0.137731	+	0.238557i	−0.788906	+	0.614513i	$0.789352\pi$
$114$	−1.00000	+	1.73205i	−0.0936586	+	0.162221i
$115$	2.73205	−	4.73205i	0.254765	−	0.441266i
$116$	1.00000	−	1.73205i	0.0928477	−	0.160817i
$117$	−8.92820			−0.825413
$118$	2.73205	−	4.73205i	0.251506	−	0.435621i
$119$	−5.07180			−0.464931
$120$	0.500000	+	0.866025i	0.0456435	+	0.0790569i
$121$	18.8564			1.71422
$122$	8.92820			0.808322
$123$	−5.96410	−	10.3301i	−0.537765	−	0.931436i
$124$	−4.23205	+	7.33013i	−0.380049	+	0.658265i
$125$	1.00000			0.0894427
$126$	3.46410	+	6.00000i	0.308607	+	0.534522i
$127$	7.46410	+	12.9282i	0.662332	+	1.14719i	0.980001	+	0.198991i	$0.0637665\pi$
$127$	7.46410	+	12.9282i	0.662332	+	1.14719i	−0.317669	+	0.948202i	$0.602900\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−4.96410	+	8.59808i	−0.437065	+	0.757018i
$130$	−2.23205	+	3.86603i	−0.195764	+	0.339073i
$131$	−0.464102	−	0.803848i	−0.0405487	−	0.0702325i	0.845039	−	0.534705i	$-0.179577\pi$
$131$	−0.464102	−	0.803848i	−0.0405487	−	0.0702325i	−0.885588	+	0.464473i	$0.846244\pi$
$132$	−2.73205	−	4.73205i	−0.237795	−	0.411872i
$133$	3.46410	+	6.00000i	0.300376	+	0.520266i
$134$	14.9282			1.28960
$135$	−2.50000	+	4.33013i	−0.215166	+	0.372678i
$136$	0.732051	+	1.26795i	0.0627728	+	0.108726i
$137$	−1.46410			−0.125087			−0.0625433	−	0.998042i	$-0.519921\pi$
$137$	−1.46410			−0.125087			−0.0625433	+	0.998042i	$0.519921\pi$
$138$	5.46410			0.465135
$139$	8.19615	+	14.1962i	0.695189	+	1.20410i	0.970117	+	0.242637i	$0.0780125\pi$
$139$	8.19615	+	14.1962i	0.695189	+	1.20410i	−0.274929	+	0.961465i	$0.588654\pi$
$140$	3.46410			0.292770
$141$	1.73205	−	3.00000i	0.145865	−	0.252646i
$142$	1.07180			0.0899432
$143$	12.1962	−	21.1244i	1.01989	−	1.76651i
$144$	1.00000	−	1.73205i	0.0833333	−	0.144338i
$145$	1.00000	−	1.73205i	0.0830455	−	0.143839i
$146$	−1.26795	−	2.19615i	−0.104936	−	0.181755i
$147$	−5.00000			−0.412393
$148$	−5.69615	+	2.13397i	−0.468221	+	0.175412i
$149$	6.92820			0.567581			0.283790	−	0.958886i	$-0.408408\pi$
$149$	6.92820			0.567581			0.283790	+	0.958886i	$0.408408\pi$
$150$	0.500000	+	0.866025i	0.0408248	+	0.0707107i
$151$	−2.69615	+	4.66987i	−0.219410	+	0.380029i	−0.954628	−	0.297802i	$-0.903746\pi$
$151$	−2.69615	+	4.66987i	−0.219410	+	0.380029i	0.735218	+	0.677831i	$0.237080\pi$
$152$	1.00000	−	1.73205i	0.0811107	−	0.140488i
$153$	−1.46410	+	2.53590i	−0.118366	+	0.205015i
$154$	−18.9282			−1.52528
$155$	−4.23205	+	7.33013i	−0.339927	+	0.588770i
$156$	−4.46410			−0.357414
$157$	8.16025	+	14.1340i	0.651259	+	1.12801i	0.982818	+	0.184579i	$0.0590923\pi$
$157$	8.16025	+	14.1340i	0.651259	+	1.12801i	−0.331558	+	0.943435i	$0.607574\pi$
$158$	−14.9282			−1.18762
$159$	5.53590			0.439025
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$	9.46410	−	16.3923i	0.745876	−	1.29189i
$162$	1.00000			0.0785674
$163$	−5.42820	−	9.40192i	−0.425170	−	0.736416i	0.571267	−	0.820765i	$-0.306452\pi$
$163$	−5.42820	−	9.40192i	−0.425170	−	0.736416i	−0.996436	+	0.0843491i	$0.973119\pi$
$164$	5.96410	+	10.3301i	0.465718	+	0.806647i
$165$	−2.73205	−	4.73205i	−0.212690	−	0.368390i
$166$	−4.92820	+	8.53590i	−0.382503	+	0.662514i
$167$	8.46410	−	14.6603i	0.654972	−	1.13444i	−0.326929	−	0.945049i	$-0.606014\pi$
$167$	8.46410	−	14.6603i	0.654972	−	1.13444i	0.981901	−	0.189396i	$-0.0606529\pi$
$168$	1.73205	+	3.00000i	0.133631	+	0.231455i
$169$	−3.46410	−	6.00000i	−0.266469	−	0.461538i
$170$	0.732051	+	1.26795i	0.0561457	+	0.0972473i
$171$	4.00000			0.305888
$172$	4.96410	−	8.59808i	0.378509	−	0.655597i
$173$	7.92820	+	13.7321i	0.602770	+	1.04403i	0.992400	+	0.123057i	$0.0392697\pi$
$173$	7.92820	+	13.7321i	0.602770	+	1.04403i	−0.389629	+	0.920972i	$0.627397\pi$
$174$	2.00000			0.151620
$175$	3.46410			0.261861
$176$	2.73205	+	4.73205i	0.205936	+	0.356692i
$177$	5.46410			0.410707
$178$	1.00000	−	1.73205i	0.0749532	−	0.129823i
$179$	12.0000			0.896922			0.448461	−	0.893802i	$-0.351972\pi$
$179$	12.0000			0.896922			0.448461	+	0.893802i	$0.351972\pi$
$180$	1.00000	−	1.73205i	0.0745356	−	0.129099i
$181$	−11.7321	+	20.3205i	−0.872036	+	1.51041i	−0.0121500	+	0.999926i	$0.503868\pi$
$181$	−11.7321	+	20.3205i	−0.872036	+	1.51041i	−0.859886	+	0.510485i	$0.829466\pi$
$182$	−7.73205	+	13.3923i	−0.573138	+	0.992704i
$183$	4.46410	+	7.73205i	0.329996	+	0.571570i
$184$	−5.46410			−0.402819
$185$	−5.69615	+	2.13397i	−0.418789	+	0.156893i
$186$	−8.46410			−0.620618
$187$	−4.00000	−	6.92820i	−0.292509	−	0.506640i
$188$	−1.73205	+	3.00000i	−0.126323	+	0.218797i
$189$	−8.66025	+	15.0000i	−0.629941	+	1.09109i
$190$	1.00000	−	1.73205i	0.0725476	−	0.125656i
$191$	10.3205			0.746766			0.373383	−	0.927677i	$-0.378198\pi$
$191$	10.3205			0.746766			0.373383	+	0.927677i	$0.378198\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	0.392305			0.0282387			0.0141194	−	0.999900i	$-0.495506\pi$
$193$	0.392305			0.0282387			0.0141194	+	0.999900i	$0.495506\pi$
$194$	1.00000	+	1.73205i	0.0717958	+	0.124354i
$195$	−4.46410			−0.319681
$196$	5.00000			0.357143
$197$	8.16025	+	14.1340i	0.581394	+	1.00700i	0.995314	+	0.0966909i	$0.0308258\pi$
$197$	8.16025	+	14.1340i	0.581394	+	1.00700i	−0.413920	+	0.910313i	$0.635841\pi$
$198$	−5.46410	+	9.46410i	−0.388317	+	0.672584i
$199$	−14.4641			−1.02533			−0.512666	−	0.858588i	$-0.671342\pi$
$199$	−14.4641			−1.02533			−0.512666	+	0.858588i	$0.671342\pi$
$200$	−0.500000	−	0.866025i	−0.0353553	−	0.0612372i
$201$	7.46410	+	12.9282i	0.526477	+	0.911885i
$202$	4.73205	+	8.19615i	0.332946	+	0.576679i
$203$	3.46410	−	6.00000i	0.243132	−	0.421117i
$204$	−0.732051	+	1.26795i	−0.0512538	+	0.0887742i
$205$	5.96410	+	10.3301i	0.416551	+	0.721487i
$206$	6.73205	+	11.6603i	0.469044	+	0.812408i
$207$	−5.46410	−	9.46410i	−0.379781	−	0.657801i
$208$	4.46410			0.309530
$209$	−5.46410	+	9.46410i	−0.377960	+	0.654646i
$210$	1.73205	+	3.00000i	0.119523	+	0.207020i
$211$	14.0000			0.963800			0.481900	−	0.876226i	$-0.339947\pi$
$211$	14.0000			0.963800			0.481900	+	0.876226i	$0.339947\pi$
$212$	−5.53590			−0.380207
$213$	0.535898	+	0.928203i	0.0367192	+	0.0635994i
$214$	−8.85641			−0.605411
$215$	4.96410	−	8.59808i	0.338549	−	0.586384i
$216$	5.00000			0.340207
$217$	−14.6603	+	25.3923i	−0.995203	+	1.72374i
$218$	5.00000	−	8.66025i	0.338643	−	0.586546i
$219$	1.26795	−	2.19615i	0.0856801	−	0.148402i
$220$	2.73205	+	4.73205i	0.184195	+	0.319035i
$221$	−6.53590			−0.439652
$222$	−4.69615	−	3.86603i	−0.315185	−	0.259471i
$223$	23.3205			1.56166			0.780828	−	0.624746i	$-0.214797\pi$
$223$	23.3205			1.56166			0.780828	+	0.624746i	$0.214797\pi$
$224$	−1.73205	−	3.00000i	−0.115728	−	0.200446i
$225$	1.00000	−	1.73205i	0.0666667	−	0.115470i
$226$	1.46410	−	2.53590i	0.0973906	−	0.168685i
$227$	0.0358984	−	0.0621778i	0.00238266	−	0.00412689i	−0.864832	−	0.502062i	$-0.832575\pi$
$227$	0.0358984	−	0.0621778i	0.00238266	−	0.00412689i	0.867214	+	0.497935i	$0.165908\pi$
$228$	2.00000			0.132453
$229$	13.1962	−	22.8564i	0.872026	−	1.51039i	0.0121292	−	0.999926i	$-0.496139\pi$
$229$	13.1962	−	22.8564i	0.872026	−	1.51039i	0.859897	−	0.510467i	$-0.170528\pi$
$230$	−5.46410			−0.360292
$231$	−9.46410	−	16.3923i	−0.622692	−	1.07853i
$232$	−2.00000			−0.131306
$233$	−9.60770			−0.629421			−0.314711	−	0.949188i	$-0.601907\pi$
$233$	−9.60770			−0.629421			−0.314711	+	0.949188i	$0.601907\pi$
$234$	4.46410	+	7.73205i	0.291827	+	0.505460i
$235$	−1.73205	+	3.00000i	−0.112987	+	0.195698i
$236$	−5.46410			−0.355683
$237$	−7.46410	−	12.9282i	−0.484846	−	0.839777i
$238$	2.53590	+	4.39230i	0.164378	+	0.284711i
$239$	−6.53590	−	11.3205i	−0.422772	−	0.732263i	0.573437	−	0.819249i	$-0.305610\pi$
$239$	−6.53590	−	11.3205i	−0.422772	−	0.732263i	−0.996209	+	0.0869866i	$0.972276\pi$
$240$	0.500000	−	0.866025i	0.0322749	−	0.0559017i
$241$	1.00000	−	1.73205i	0.0644157	−	0.111571i	−0.832019	−	0.554747i	$-0.812815\pi$
$241$	1.00000	−	1.73205i	0.0644157	−	0.111571i	0.896435	+	0.443176i	$0.146148\pi$
$242$	−9.42820	−	16.3301i	−0.606068	−	1.04974i
$243$	8.00000	+	13.8564i	0.513200	+	0.888889i
$244$	−4.46410	−	7.73205i	−0.285785	−	0.494994i
$245$	5.00000			0.319438
$246$	−5.96410	+	10.3301i	−0.380257	+	0.658625i
$247$	4.46410	+	7.73205i	0.284044	+	0.491979i
$248$	8.46410			0.537471
$249$	−9.85641			−0.624624
$250$	−0.500000	−	0.866025i	−0.0316228	−	0.0547723i
$251$	−12.9282			−0.816021			−0.408010	−	0.912977i	$-0.633777\pi$
$251$	−12.9282			−0.816021			−0.408010	+	0.912977i	$0.633777\pi$
$252$	3.46410	−	6.00000i	0.218218	−	0.377964i
$253$	29.8564			1.87706
$254$	7.46410	−	12.9282i	0.468339	−	0.811188i
$255$	−0.732051	+	1.26795i	−0.0458428	+	0.0794021i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	6.26795	+	10.8564i	0.390984	+	0.677204i	0.992580	−	0.121597i	$-0.0388015\pi$
$257$	6.26795	+	10.8564i	0.390984	+	0.677204i	−0.601596	+	0.798801i	$0.705468\pi$
$258$	9.92820			0.618103
$259$	−19.7321	+	7.39230i	−1.22609	+	0.459335i
$260$	4.46410			0.276852
$261$	−2.00000	−	3.46410i	−0.123797	−	0.214423i
$262$	−0.464102	+	0.803848i	−0.0286723	+	0.0496619i
$263$	−3.19615	+	5.53590i	−0.197083	+	0.341358i	−0.947581	−	0.319514i	$-0.896480\pi$
$263$	−3.19615	+	5.53590i	−0.197083	+	0.341358i	0.750498	+	0.660872i	$0.229814\pi$
$264$	−2.73205	+	4.73205i	−0.168146	+	0.291238i
$265$	−5.53590			−0.340068
$266$	3.46410	−	6.00000i	0.212398	−	0.367884i
$267$	2.00000			0.122398
$268$	−7.46410	−	12.9282i	−0.455943	−	0.789716i
$269$	−12.3923			−0.755572			−0.377786	−	0.925893i	$-0.623315\pi$
$269$	−12.3923			−0.755572			−0.377786	+	0.925893i	$0.623315\pi$
$270$	5.00000			0.304290
$271$	−8.62436	−	14.9378i	−0.523892	−	0.907408i	−0.999613	−	0.0278118i	$-0.991146\pi$
$271$	−8.62436	−	14.9378i	−0.523892	−	0.907408i	0.475721	−	0.879596i	$-0.342187\pi$
$272$	0.732051	−	1.26795i	0.0443871	−	0.0768807i
$273$	−15.4641			−0.935930
$274$	0.732051	+	1.26795i	0.0442248	+	0.0765996i
$275$	2.73205	+	4.73205i	0.164749	+	0.285353i
$276$	−2.73205	−	4.73205i	−0.164450	−	0.284836i
$277$	16.2321	−	28.1147i	0.975289	−	1.68925i	0.296313	−	0.955091i	$-0.404243\pi$
$277$	16.2321	−	28.1147i	0.975289	−	1.68925i	0.678977	−	0.734160i	$-0.262424\pi$
$278$	8.19615	−	14.1962i	0.491573	−	0.851429i
$279$	8.46410	+	14.6603i	0.506733	+	0.877686i
$280$	−1.73205	−	3.00000i	−0.103510	−	0.179284i
$281$	−14.3564	−	24.8660i	−0.856431	−	1.48338i	−0.875311	−	0.483561i	$-0.839343\pi$
$281$	−14.3564	−	24.8660i	−0.856431	−	1.48338i	0.0188793	−	0.999822i	$-0.493990\pi$
$282$	−3.46410			−0.206284
$283$	−4.03590	+	6.99038i	−0.239909	+	0.415535i	−0.960688	−	0.277630i	$-0.910451\pi$
$283$	−4.03590	+	6.99038i	−0.239909	+	0.415535i	0.720779	+	0.693165i	$0.243784\pi$
$284$	−0.535898	−	0.928203i	−0.0317997	−	0.0550787i
$285$	2.00000			0.118470
$286$	−24.3923			−1.44235
$287$	20.6603	+	35.7846i	1.21954	+	2.11230i
$288$	−2.00000			−0.117851
$289$	7.42820	−	12.8660i	0.436953	−	0.756825i
$290$	−2.00000			−0.117444
$291$	−1.00000	+	1.73205i	−0.0586210	+	0.101535i
$292$	−1.26795	+	2.19615i	−0.0742011	+	0.128520i
$293$	−0.232051	+	0.401924i	−0.0135566	+	0.0234806i	−0.872724	−	0.488214i	$-0.837649\pi$
$293$	−0.232051	+	0.401924i	−0.0135566	+	0.0234806i	0.859168	+	0.511694i	$0.170982\pi$
$294$	2.50000	+	4.33013i	0.145803	+	0.252538i
$295$	−5.46410			−0.318132
$296$	4.69615	+	3.86603i	0.272958	+	0.224708i
$297$	−27.3205			−1.58530
$298$	−3.46410	−	6.00000i	−0.200670	−	0.347571i
$299$	12.1962	−	21.1244i	0.705322	−	1.22165i
$300$	0.500000	−	0.866025i	0.0288675	−	0.0500000i
$301$	17.1962	−	29.7846i	0.991170	−	1.71676i
$302$	5.39230			0.310292
$303$	−4.73205	+	8.19615i	−0.271849	+	0.470857i
$304$	−2.00000			−0.114708
$305$	−4.46410	−	7.73205i	−0.255614	−	0.442736i
$306$	2.92820			0.167394
$307$	−10.8564			−0.619608			−0.309804	−	0.950800i	$-0.600263\pi$
$307$	−10.8564			−0.619608			−0.309804	+	0.950800i	$0.600263\pi$
$308$	9.46410	+	16.3923i	0.539267	+	0.934038i
$309$	−6.73205	+	11.6603i	−0.382973	+	0.663329i
$310$	8.46410			0.480729
$311$	6.23205	+	10.7942i	0.353387	+	0.612085i	0.986841	−	0.161696i	$-0.0516965\pi$
$311$	6.23205	+	10.7942i	0.353387	+	0.612085i	−0.633453	+	0.773781i	$0.718363\pi$
$312$	2.23205	+	3.86603i	0.126365	+	0.218871i
$313$	−4.46410	−	7.73205i	−0.252326	−	0.437041i	0.711840	−	0.702342i	$-0.247862\pi$
$313$	−4.46410	−	7.73205i	−0.252326	−	0.437041i	−0.964166	+	0.265300i	$0.914529\pi$
$314$	8.16025	−	14.1340i	0.460510	−	0.797626i
$315$	3.46410	−	6.00000i	0.195180	−	0.338062i
$316$	7.46410	+	12.9282i	0.419889	+	0.727268i
$317$	8.76795	+	15.1865i	0.492457	+	0.852961i	0.999962	−	0.00868801i	$-0.00276552\pi$
$317$	8.76795	+	15.1865i	0.492457	+	0.852961i	−0.507505	+	0.861649i	$0.669432\pi$
$318$	−2.76795	−	4.79423i	−0.155219	−	0.268847i
$319$	10.9282			0.611862
$320$	−0.500000	+	0.866025i	−0.0279508	+	0.0484123i
$321$	−4.42820	−	7.66987i	−0.247158	−	0.428091i
$322$	−18.9282			−1.05483
$323$	2.92820			0.162930
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	4.46410			0.247624
$326$	−5.42820	+	9.40192i	−0.300640	+	0.520724i
$327$	10.0000			0.553001
$328$	5.96410	−	10.3301i	0.329312	−	0.570386i
$329$	−6.00000	+	10.3923i	−0.330791	+	0.572946i
$330$	−2.73205	+	4.73205i	−0.150394	+	0.260491i
$331$	−18.1244	−	31.3923i	−0.996205	−	1.72548i	−0.573483	−	0.819218i	$-0.694408\pi$
$331$	−18.1244	−	31.3923i	−0.996205	−	1.72548i	−0.422722	−	0.906259i	$-0.638925\pi$
$332$	9.85641			0.540941
$333$	−2.00000	+	12.0000i	−0.109599	+	0.657596i
$334$	−16.9282			−0.926270
$335$	−7.46410	−	12.9282i	−0.407807	−	0.706343i
$336$	1.73205	−	3.00000i	0.0944911	−	0.163663i
$337$	−4.46410	+	7.73205i	−0.243175	+	0.421192i	−0.961617	−	0.274395i	$-0.911522\pi$
$337$	−4.46410	+	7.73205i	−0.243175	+	0.421192i	0.718442	+	0.695587i	$0.244856\pi$
$338$	−3.46410	+	6.00000i	−0.188422	+	0.326357i
$339$	2.92820			0.159038
$340$	0.732051	−	1.26795i	0.0397010	−	0.0687642i
$341$	−46.2487			−2.50451
$342$	−2.00000	−	3.46410i	−0.108148	−	0.187317i
$343$	−6.92820			−0.374088
$344$	−9.92820			−0.535293
$345$	−2.73205	−	4.73205i	−0.147089	−	0.254765i
$346$	7.92820	−	13.7321i	0.426223	−	0.738240i
$347$	−30.9282			−1.66031			−0.830156	−	0.557530i	$-0.811749\pi$
$347$	−30.9282			−1.66031			−0.830156	+	0.557530i	$0.811749\pi$
$348$	−1.00000	−	1.73205i	−0.0536056	−	0.0928477i
$349$	−5.39230	−	9.33975i	−0.288643	−	0.499945i	0.684843	−	0.728691i	$-0.259871\pi$
$349$	−5.39230	−	9.33975i	−0.288643	−	0.499945i	−0.973486	+	0.228746i	$0.926538\pi$
$350$	−1.73205	−	3.00000i	−0.0925820	−	0.160357i
$351$	−11.1603	+	19.3301i	−0.595690	+	1.03177i
$352$	2.73205	−	4.73205i	0.145619	−	0.252219i
$353$	−1.33975	−	2.32051i	−0.0713075	−	0.123508i	0.828167	−	0.560481i	$-0.189384\pi$
$353$	−1.33975	−	2.32051i	−0.0713075	−	0.123508i	−0.899475	+	0.436973i	$0.856050\pi$
$354$	−2.73205	−	4.73205i	−0.145207	−	0.251506i
$355$	−0.535898	−	0.928203i	−0.0284425	−	0.0492639i
$356$	−2.00000			−0.106000
$357$	−2.53590	+	4.39230i	−0.134214	+	0.232465i
$358$	−6.00000	−	10.3923i	−0.317110	−	0.549250i
$359$	4.46410			0.235606			0.117803	−	0.993037i	$-0.462415\pi$
$359$	4.46410			0.235606			0.117803	+	0.993037i	$0.462415\pi$
$360$	−2.00000			−0.105409
$361$	7.50000	+	12.9904i	0.394737	+	0.683704i
$362$	23.4641			1.23325
$363$	9.42820	−	16.3301i	0.494852	−	0.857109i
$364$	15.4641			0.810539
$365$	−1.26795	+	2.19615i	−0.0663675	+	0.114952i
$366$	4.46410	−	7.73205i	0.233342	−	0.404161i
$367$	−5.39230	+	9.33975i	−0.281476	+	0.487531i	−0.971749	−	0.236019i	$-0.924157\pi$
$367$	−5.39230	+	9.33975i	−0.281476	+	0.487531i	0.690272	+	0.723550i	$0.257491\pi$
$368$	2.73205	+	4.73205i	0.142418	+	0.246675i
$369$	23.8564			1.24191
$370$	4.69615	+	3.86603i	0.244141	+	0.200985i
$371$	−19.1769			−0.995616
$372$	4.23205	+	7.33013i	0.219422	+	0.380049i
$373$	19.2321	−	33.3109i	0.995798	−	1.72477i	0.418589	−	0.908176i	$-0.362525\pi$
$373$	19.2321	−	33.3109i	0.995798	−	1.72477i	0.577208	−	0.816597i	$-0.304142\pi$
$374$	−4.00000	+	6.92820i	−0.206835	+	0.358249i
$375$	0.500000	−	0.866025i	0.0258199	−	0.0447214i
$376$	3.46410			0.178647
$377$	4.46410	−	7.73205i	0.229913	−	0.398221i
$378$	17.3205			0.890871
$379$	12.1962	+	21.1244i	0.626474	+	1.08509i	0.988254	+	0.152822i	$0.0488360\pi$
$379$	12.1962	+	21.1244i	0.626474	+	1.08509i	−0.361780	+	0.932264i	$0.617831\pi$
$380$	−2.00000			−0.102598
$381$	14.9282			0.764795
$382$	−5.16025	−	8.93782i	−0.264022	−	0.457299i
$383$	−0.267949	+	0.464102i	−0.0136916	+	0.0237145i	−0.872790	−	0.488096i	$-0.837692\pi$
$383$	−0.267949	+	0.464102i	−0.0136916	+	0.0237145i	0.859098	+	0.511810i	$0.171025\pi$
$384$	−1.00000			−0.0510310
$385$	9.46410	+	16.3923i	0.482335	+	0.835429i
$386$	−0.196152	−	0.339746i	−0.00998390	−	0.0172926i
$387$	−9.92820	−	17.1962i	−0.504679	−	0.874130i
$388$	1.00000	−	1.73205i	0.0507673	−	0.0879316i
$389$	−11.8564	+	20.5359i	−0.601144	+	1.04121i	0.391505	+	0.920176i	$0.371955\pi$
$389$	−11.8564	+	20.5359i	−0.601144	+	1.04121i	−0.992648	+	0.121035i	$0.961379\pi$
$390$	2.23205	+	3.86603i	0.113024	+	0.195764i
$391$	−4.00000	−	6.92820i	−0.202289	−	0.350374i
$392$	−2.50000	−	4.33013i	−0.126269	−	0.218704i
$393$	−0.928203			−0.0468217
$394$	8.16025	−	14.1340i	0.411108	−	0.712059i
$395$	7.46410	+	12.9282i	0.375560	+	0.650488i
$396$	10.9282			0.549163
$397$	−4.46410			−0.224047			−0.112023	−	0.993706i	$-0.535733\pi$
$397$	−4.46410			−0.224047			−0.112023	+	0.993706i	$0.535733\pi$
$398$	7.23205	+	12.5263i	0.362510	+	0.627886i
$399$	6.92820			0.346844
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$	22.0000			1.09863			0.549314	−	0.835616i	$-0.314889\pi$
$401$	22.0000			1.09863			0.549314	+	0.835616i	$0.314889\pi$
$402$	7.46410	−	12.9282i	0.372276	−	0.644800i
$403$	−18.8923	+	32.7224i	−0.941093	+	1.63002i
$404$	4.73205	−	8.19615i	0.235428	−	0.407774i
$405$	−0.500000	−	0.866025i	−0.0248452	−	0.0430331i
$406$	−6.92820			−0.343841
$407$	−25.6603	−	21.1244i	−1.27193	−	1.04710i
$408$	1.46410			0.0724838
$409$	5.50000	+	9.52628i	0.271957	+	0.471044i	0.969363	−	0.245633i	$-0.0789957\pi$
$409$	5.50000	+	9.52628i	0.271957	+	0.471044i	−0.697406	+	0.716677i	$0.745662\pi$
$410$	5.96410	−	10.3301i	0.294546	−	0.510169i
$411$	−0.732051	+	1.26795i	−0.0361094	+	0.0625433i
$412$	6.73205	−	11.6603i	0.331664	−	0.574459i
$413$	−18.9282			−0.931396
$414$	−5.46410	+	9.46410i	−0.268546	+	0.465135i
$415$	9.85641			0.483832
$416$	−2.23205	−	3.86603i	−0.109435	−	0.189547i
$417$	16.3923			0.802735
$418$	10.9282			0.534516
$419$	−2.73205	−	4.73205i	−0.133469	−	0.231176i	0.791542	−	0.611114i	$-0.209278\pi$
$419$	−2.73205	−	4.73205i	−0.133469	−	0.231176i	−0.925012	+	0.379939i	$0.875945\pi$
$420$	1.73205	−	3.00000i	0.0845154	−	0.146385i
$421$	−2.67949			−0.130590			−0.0652952	−	0.997866i	$-0.520799\pi$
$421$	−2.67949			−0.130590			−0.0652952	+	0.997866i	$0.520799\pi$
$422$	−7.00000	−	12.1244i	−0.340755	−	0.590204i
$423$	3.46410	+	6.00000i	0.168430	+	0.291730i
$424$	2.76795	+	4.79423i	0.134423	+	0.232828i
$425$	0.732051	−	1.26795i	0.0355097	−	0.0615046i
$426$	0.535898	−	0.928203i	0.0259644	−	0.0449716i
$427$	−15.4641	−	26.7846i	−0.748360	−	1.29620i
$428$	4.42820	+	7.66987i	0.214045	+	0.370737i
$429$	−12.1962	−	21.1244i	−0.588836	−	1.01989i
$430$	−9.92820			−0.478780
$431$	−2.76795	+	4.79423i	−0.133327	+	0.230930i	−0.924957	−	0.380071i	$-0.875900\pi$
$431$	−2.76795	+	4.79423i	−0.133327	+	0.230930i	0.791630	+	0.611001i	$0.209233\pi$
$432$	−2.50000	−	4.33013i	−0.120281	−	0.208333i
$433$	23.7128			1.13957			0.569783	−	0.821796i	$-0.307027\pi$
$433$	23.7128			1.13957			0.569783	+	0.821796i	$0.307027\pi$
$434$	29.3205			1.40743
$435$	−1.00000	−	1.73205i	−0.0479463	−	0.0830455i
$436$	−10.0000			−0.478913
$437$	−5.46410	+	9.46410i	−0.261383	+	0.452729i
$438$	−2.53590			−0.121170
$439$	−5.76795	+	9.99038i	−0.275289	+	0.476815i	−0.970208	−	0.242273i	$-0.922107\pi$
$439$	−5.76795	+	9.99038i	−0.275289	+	0.476815i	0.694919	+	0.719088i	$0.255440\pi$
$440$	2.73205	−	4.73205i	0.130245	−	0.225592i
$441$	5.00000	−	8.66025i	0.238095	−	0.412393i
$442$	3.26795	+	5.66025i	0.155440	+	0.269231i
$443$	14.0718			0.668571			0.334286	−	0.942472i	$-0.391505\pi$
$443$	14.0718			0.668571			0.334286	+	0.942472i	$0.391505\pi$
$444$	−1.00000	+	6.00000i	−0.0474579	+	0.284747i
$445$	−2.00000			−0.0948091
$446$	−11.6603	−	20.1962i	−0.552129	−	0.956316i
$447$	3.46410	−	6.00000i	0.163846	−	0.283790i
$448$	−1.73205	+	3.00000i	−0.0818317	+	0.141737i
$449$	7.50000	−	12.9904i	0.353947	−	0.613054i	−0.632990	−	0.774160i	$-0.718173\pi$
$449$	7.50000	−	12.9904i	0.353947	−	0.613054i	0.986937	+	0.161106i	$0.0515060\pi$
$450$	−2.00000			−0.0942809
$451$	−32.5885	+	56.4449i	−1.53453	+	2.65788i
$452$	−2.92820			−0.137731
$453$	2.69615	+	4.66987i	0.126676	+	0.219410i
$454$	−0.0717968			−0.00336959
$455$	15.4641			0.724968
$456$	−1.00000	−	1.73205i	−0.0468293	−	0.0811107i
$457$	0.928203	−	1.60770i	0.0434195	−	0.0752048i	−0.843499	−	0.537131i	$-0.819508\pi$
$457$	0.928203	−	1.60770i	0.0434195	−	0.0752048i	0.886918	+	0.461926i	$0.152841\pi$
$458$	−26.3923			−1.23323
$459$	3.66025	+	6.33975i	0.170846	+	0.295914i
$460$	2.73205	+	4.73205i	0.127383	+	0.220633i
$461$	6.46410	+	11.1962i	0.301063	+	0.521457i	0.976377	−	0.216074i	$-0.0693251\pi$
$461$	6.46410	+	11.1962i	0.301063	+	0.521457i	−0.675314	+	0.737530i	$0.735992\pi$
$462$	−9.46410	+	16.3923i	−0.440310	+	0.762639i
$463$	−3.46410	+	6.00000i	−0.160990	+	0.278844i	−0.935224	−	0.354056i	$-0.884802\pi$
$463$	−3.46410	+	6.00000i	−0.160990	+	0.278844i	0.774234	+	0.632900i	$0.218136\pi$
$464$	1.00000	+	1.73205i	0.0464238	+	0.0804084i
$465$	4.23205	+	7.33013i	0.196257	+	0.339927i
$466$	4.80385	+	8.32051i	0.222534	+	0.385440i
$467$	3.00000			0.138823			0.0694117	−	0.997588i	$-0.477888\pi$
$467$	3.00000			0.138823			0.0694117	+	0.997588i	$0.477888\pi$
$468$	4.46410	−	7.73205i	0.206353	−	0.357414i
$469$	−25.8564	−	44.7846i	−1.19394	−	2.06796i
$470$	3.46410			0.159787
$471$	16.3205			0.752009
$472$	2.73205	+	4.73205i	0.125753	+	0.217810i
$473$	54.2487			2.49436
$474$	−7.46410	+	12.9282i	−0.342838	+	0.593812i
$475$	−2.00000			−0.0917663
$476$	2.53590	−	4.39230i	0.116233	−	0.201321i
$477$	−5.53590	+	9.58846i	−0.253471	+	0.439025i
$478$	−6.53590	+	11.3205i	−0.298945	+	0.517788i
$479$	19.1603	+	33.1865i	0.875454	+	1.51633i	0.856278	+	0.516515i	$0.172771\pi$
$479$	19.1603	+	33.1865i	0.875454	+	1.51633i	0.0191764	+	0.999816i	$0.493896\pi$
$480$	−1.00000			−0.0456435
$481$	−25.4282	+	9.52628i	−1.15943	+	0.434361i
$482$	−2.00000			−0.0910975
$483$	−9.46410	−	16.3923i	−0.430632	−	0.745876i
$484$	−9.42820	+	16.3301i	−0.428555	+	0.742279i
$485$	1.00000	−	1.73205i	0.0454077	−	0.0786484i
$486$	8.00000	−	13.8564i	0.362887	−	0.628539i
$487$	12.9282			0.585833			0.292916	−	0.956138i	$-0.405374\pi$
$487$	12.9282			0.585833			0.292916	+	0.956138i	$0.405374\pi$
$488$	−4.46410	+	7.73205i	−0.202080	+	0.350013i
$489$	−10.8564			−0.490944
$490$	−2.50000	−	4.33013i	−0.112938	−	0.195615i
$491$	−14.2487			−0.643035			−0.321518	−	0.946904i	$-0.604193\pi$
$491$	−14.2487			−0.643035			−0.321518	+	0.946904i	$0.604193\pi$
$492$	11.9282			0.537765
$493$	−1.46410	−	2.53590i	−0.0659398	−	0.114211i
$494$	4.46410	−	7.73205i	0.200849	−	0.347881i
$495$	10.9282			0.491186
$496$	−4.23205	−	7.33013i	−0.190025	−	0.329132i
$497$	−1.85641	−	3.21539i	−0.0832712	−	0.144230i
$498$	4.92820	+	8.53590i	0.220838	+	0.382503i
$499$	1.46410	−	2.53590i	0.0655422	−	0.113522i	−0.831392	−	0.555686i	$-0.812456\pi$
$499$	1.46410	−	2.53590i	0.0655422	−	0.113522i	0.896934	+	0.442164i	$0.145789\pi$
$500$	−0.500000	+	0.866025i	−0.0223607	+	0.0387298i
$501$	−8.46410	−	14.6603i	−0.378148	−	0.654972i
$502$	6.46410	+	11.1962i	0.288507	+	0.499709i
$503$	2.66025	+	4.60770i	0.118615	+	0.205447i	0.919219	−	0.393747i	$-0.128821\pi$
$503$	2.66025	+	4.60770i	0.118615	+	0.205447i	−0.800604	+	0.599194i	$0.795488\pi$
$504$	−6.92820			−0.308607
$505$	4.73205	−	8.19615i	0.210573	−	0.364724i
$506$	−14.9282	−	25.8564i	−0.663640	−	1.14946i
$507$	−6.92820			−0.307692
$508$	−14.9282			−0.662332
$509$	−16.6603	−	28.8564i	−0.738453	−	1.27904i	−0.953192	−	0.302366i	$-0.902223\pi$
$509$	−16.6603	−	28.8564i	−0.738453	−	1.27904i	0.214739	−	0.976671i	$-0.431110\pi$
$510$	1.46410			0.0648315
$511$	−4.39230	+	7.60770i	−0.194304	+	0.336545i
$512$	1.00000			0.0441942
$513$	5.00000	−	8.66025i	0.220755	−	0.382360i
$514$	6.26795	−	10.8564i	0.276467	−	0.478856i
$515$	6.73205	−	11.6603i	0.296650	−	0.513812i
$516$	−4.96410	−	8.59808i	−0.218532	−	0.378509i
$517$	−18.9282			−0.832461
$518$	16.2679	+	13.3923i	0.714773	+	0.588424i
$519$	15.8564			0.696019
$520$	−2.23205	−	3.86603i	−0.0978819	−	0.169536i
$521$	−12.3564	+	21.4019i	−0.541344	+	0.937635i	0.457483	+	0.889218i	$0.348751\pi$
$521$	−12.3564	+	21.4019i	−0.541344	+	0.937635i	−0.998827	+	0.0484170i	$0.984582\pi$
$522$	−2.00000	+	3.46410i	−0.0875376	+	0.151620i
$523$	1.10770	−	1.91858i	0.0484361	−	0.0838938i	−0.840791	−	0.541360i	$-0.817910\pi$
$523$	1.10770	−	1.91858i	0.0484361	−	0.0838938i	0.889227	+	0.457466i	$0.151243\pi$
$524$	0.928203			0.0405487
$525$	1.73205	−	3.00000i	0.0755929	−	0.130931i
$526$	6.39230			0.278718
$527$	6.19615	+	10.7321i	0.269909	+	0.467495i
$528$	5.46410			0.237795
$529$	6.85641			0.298105
$530$	2.76795	+	4.79423i	0.120232	+	0.208248i
$531$	−5.46410	+	9.46410i	−0.237122	+	0.410707i
$532$	−6.92820			−0.300376
$533$	26.6244	+	46.1147i	1.15323	+	1.99745i
$534$	−1.00000	−	1.73205i	−0.0432742	−	0.0749532i
$535$	4.42820	+	7.66987i	0.191448	+	0.331598i
$536$	−7.46410	+	12.9282i	−0.322400	+	0.558413i
$537$	6.00000	−	10.3923i	0.258919	−	0.448461i
$538$	6.19615	+	10.7321i	0.267135	+	0.462692i
$539$	13.6603	+	23.6603i	0.588389	+	1.01912i
$540$	−2.50000	−	4.33013i	−0.107583	−	0.186339i
$541$	2.78461			0.119720			0.0598599	−	0.998207i	$-0.480935\pi$
$541$	2.78461			0.119720			0.0598599	+	0.998207i	$0.480935\pi$
$542$	−8.62436	+	14.9378i	−0.370448	+	0.641634i
$543$	11.7321	+	20.3205i	0.503470	+	0.872036i
$544$	−1.46410			−0.0627728
$545$	−10.0000			−0.428353
$546$	7.73205	+	13.3923i	0.330901	+	0.573138i
$547$	28.0718			1.20026			0.600132	−	0.799901i	$-0.295115\pi$
$547$	28.0718			1.20026			0.600132	+	0.799901i	$0.295115\pi$
$548$	0.732051	−	1.26795i	0.0312717	−	0.0541641i
$549$	−17.8564			−0.762093
$550$	2.73205	−	4.73205i	0.116495	−	0.201775i
$551$	−2.00000	+	3.46410i	−0.0852029	+	0.147576i
$552$	−2.73205	+	4.73205i	−0.116284	+	0.201409i
$553$	25.8564	+	44.7846i	1.09953	+	1.90444i
$554$	−32.4641			−1.37927
$555$	−1.00000	+	6.00000i	−0.0424476	+	0.254686i
$556$	−16.3923			−0.695189
$557$	−19.1603	−	33.1865i	−0.811846	−	1.40616i	−0.911571	−	0.411143i	$-0.865130\pi$
$557$	−19.1603	−	33.1865i	−0.811846	−	1.40616i	0.0997246	−	0.995015i	$-0.468204\pi$
$558$	8.46410	−	14.6603i	0.358314	−	0.620618i
$559$	22.1603	−	38.3827i	0.937279	−	1.62341i
$560$	−1.73205	+	3.00000i	−0.0731925	+	0.126773i
$561$	−8.00000			−0.337760
$562$	−14.3564	+	24.8660i	−0.605588	+	1.04891i
$563$	−1.85641			−0.0782382			−0.0391191	−	0.999235i	$-0.512455\pi$
$563$	−1.85641			−0.0782382			−0.0391191	+	0.999235i	$0.512455\pi$
$564$	1.73205	+	3.00000i	0.0729325	+	0.126323i
$565$	−2.92820			−0.123190
$566$	8.07180			0.339283
$567$	−1.73205	−	3.00000i	−0.0727393	−	0.125988i
$568$	−0.535898	+	0.928203i	−0.0224858	+	0.0389465i
$569$	−25.9282			−1.08697			−0.543483	−	0.839420i	$-0.682895\pi$
$569$	−25.9282			−1.08697			−0.543483	+	0.839420i	$0.682895\pi$
$570$	−1.00000	−	1.73205i	−0.0418854	−	0.0725476i
$571$	6.92820	+	12.0000i	0.289936	+	0.502184i	0.973794	−	0.227431i	$-0.0730325\pi$
$571$	6.92820	+	12.0000i	0.289936	+	0.502184i	−0.683858	+	0.729615i	$0.739699\pi$
$572$	12.1962	+	21.1244i	0.509947	+	0.883254i
$573$	5.16025	−	8.93782i	0.215573	−	0.373383i
$574$	20.6603	−	35.7846i	0.862342	−	1.49362i
$575$	2.73205	+	4.73205i	0.113934	+	0.197340i
$576$	1.00000	+	1.73205i	0.0416667	+	0.0721688i
$577$	−0.267949	−	0.464102i	−0.0111549	−	0.0193208i	0.860394	−	0.509629i	$-0.170217\pi$
$577$	−0.267949	−	0.464102i	−0.0111549	−	0.0193208i	−0.871549	+	0.490308i	$0.836884\pi$
$578$	−14.8564			−0.617945
$579$	0.196152	−	0.339746i	0.00815182	−	0.0141194i
$580$	1.00000	+	1.73205i	0.0415227	+	0.0719195i
$581$	34.1436			1.41651
$582$	2.00000			0.0829027
$583$	−15.1244	−	26.1962i	−0.626387	−	1.08493i
$584$	2.53590			0.104936
$585$	4.46410	−	7.73205i	0.184568	−	0.319681i
$586$	0.464102			0.0191719
$587$	−4.03590	+	6.99038i	−0.166579	+	0.288524i	−0.937215	−	0.348752i	$-0.886606\pi$
$587$	−4.03590	+	6.99038i	−0.166579	+	0.288524i	0.770636	+	0.637276i	$0.219939\pi$
$588$	2.50000	−	4.33013i	0.103098	−	0.178571i
$589$	8.46410	−	14.6603i	0.348757	−	0.604065i
$590$	2.73205	+	4.73205i	0.112477	+	0.194815i
$591$	16.3205			0.671336
$592$	1.00000	−	6.00000i	0.0410997	−	0.246598i
$593$	−36.3923			−1.49445			−0.747226	−	0.664570i	$-0.768615\pi$
$593$	−36.3923			−1.49445			−0.747226	+	0.664570i	$0.768615\pi$
$594$	13.6603	+	23.6603i	0.560487	+	0.970792i
$595$	2.53590	−	4.39230i	0.103962	−	0.180067i
$596$	−3.46410	+	6.00000i	−0.141895	+	0.245770i
$597$	−7.23205	+	12.5263i	−0.295988	+	0.512666i
$598$	−24.3923			−0.997476
$599$	−16.6244	+	28.7942i	−0.679253	+	1.17650i	0.295953	+	0.955202i	$0.404363\pi$
$599$	−16.6244	+	28.7942i	−0.679253	+	1.17650i	−0.975206	+	0.221298i	$0.928971\pi$
$600$	−1.00000			−0.0408248
$601$	10.4282	+	18.0622i	0.425375	+	0.736772i	0.996455	−	0.0841227i	$-0.0268088\pi$
$601$	10.4282	+	18.0622i	0.425375	+	0.736772i	−0.571080	+	0.820894i	$0.693475\pi$
$602$	−34.3923			−1.40173
$603$	−29.8564			−1.21585
$604$	−2.69615	−	4.66987i	−0.109705	−	0.190014i
$605$	−9.42820	+	16.3301i	−0.383311	+	0.663914i
$606$	9.46410			0.384453
$607$	6.66025	+	11.5359i	0.270331	+	0.468228i	0.968947	−	0.247270i	$-0.0795334\pi$
$607$	6.66025	+	11.5359i	0.270331	+	0.468228i	−0.698615	+	0.715498i	$0.746200\pi$
$608$	1.00000	+	1.73205i	0.0405554	+	0.0702439i
$609$	−3.46410	−	6.00000i	−0.140372	−	0.243132i
$610$	−4.46410	+	7.73205i	−0.180746	+	0.313062i
$611$	−7.73205	+	13.3923i	−0.312805	+	0.541795i
$612$	−1.46410	−	2.53590i	−0.0591828	−	0.102508i
$613$	−8.46410	−	14.6603i	−0.341862	−	0.592122i	0.642917	−	0.765936i	$-0.277724\pi$
$613$	−8.46410	−	14.6603i	−0.341862	−	0.592122i	−0.984778	+	0.173814i	$0.944391\pi$
$614$	5.42820	+	9.40192i	0.219064	+	0.379431i
$615$	11.9282			0.480992
$616$	9.46410	−	16.3923i	0.381320	−	0.660465i
$617$	−12.4641	−	21.5885i	−0.501786	−	0.869119i	−0.999998	−	0.00206334i	$-0.999343\pi$
$617$	−12.4641	−	21.5885i	−0.501786	−	0.869119i	0.498212	−	0.867055i	$-0.333990\pi$
$618$	13.4641			0.541606
$619$	14.0000			0.562708			0.281354	−	0.959604i	$-0.409217\pi$
$619$	14.0000			0.562708			0.281354	+	0.959604i	$0.409217\pi$
$620$	−4.23205	−	7.33013i	−0.169963	−	0.294385i
$621$	−27.3205			−1.09633
$622$	6.23205	−	10.7942i	0.249882	−	0.432809i
$623$	−6.92820			−0.277573
$624$	2.23205	−	3.86603i	0.0893535	−	0.154765i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−4.46410	+	7.73205i	−0.178421	+	0.309035i
$627$	5.46410	+	9.46410i	0.218215	+	0.377960i
$628$	−16.3205			−0.651259
$629$	−1.46410	+	8.78461i	−0.0583776	+	0.350265i
$630$	−6.92820			−0.276026
$631$	9.16025	+	15.8660i	0.364664	+	0.631616i	0.988722	−	0.149761i	$-0.0478505\pi$
$631$	9.16025	+	15.8660i	0.364664	+	0.631616i	−0.624058	+	0.781378i	$0.714517\pi$
$632$	7.46410	−	12.9282i	0.296906	−	0.514256i
$633$	7.00000	−	12.1244i	0.278225	−	0.481900i
$634$	8.76795	−	15.1865i	0.348220	−	0.603134i
$635$	−14.9282			−0.592408
$636$	−2.76795	+	4.79423i	−0.109756	+	0.190104i
$637$	22.3205			0.884371
$638$	−5.46410	−	9.46410i	−0.216326	−	0.374687i
$639$	−2.14359			−0.0847992
$640$	1.00000			0.0395285
$641$	23.8205	+	41.2583i	0.940854	+	1.62961i	0.763848	+	0.645396i	$0.223308\pi$
$641$	23.8205	+	41.2583i	0.940854	+	1.62961i	0.177006	+	0.984210i	$0.443359\pi$
$642$	−4.42820	+	7.66987i	−0.174767	+	0.302706i
$643$	−31.9282			−1.25913			−0.629563	−	0.776950i	$-0.716766\pi$
$643$	−31.9282			−1.25913			−0.629563	+	0.776950i	$0.716766\pi$
$644$	9.46410	+	16.3923i	0.372938	+	0.645947i
$645$	−4.96410	−	8.59808i	−0.195461	−	0.338549i
$646$	−1.46410	−	2.53590i	−0.0576043	−	0.0997736i
$647$	−5.46410	+	9.46410i	−0.214816	+	0.372072i	−0.953216	−	0.302291i	$-0.902249\pi$
$647$	−5.46410	+	9.46410i	−0.214816	+	0.372072i	0.738400	+	0.674363i	$0.235582\pi$
$648$	−0.500000	+	0.866025i	−0.0196419	+	0.0340207i
$649$	−14.9282	−	25.8564i	−0.585983	−	1.01495i
$650$	−2.23205	−	3.86603i	−0.0875482	−	0.151638i
$651$	14.6603	+	25.3923i	0.574581	+	0.995203i
$652$	10.8564			0.425170
$653$	−14.7679	+	25.5788i	−0.577915	+	1.00098i	0.417804	+	0.908537i	$0.362800\pi$
$653$	−14.7679	+	25.5788i	−0.577915	+	1.00098i	−0.995718	+	0.0924400i	$0.970533\pi$
$654$	−5.00000	−	8.66025i	−0.195515	−	0.338643i
$655$	0.928203			0.0362679
$656$	−11.9282			−0.465718
$657$	2.53590	+	4.39230i	0.0989348	+	0.171360i
$658$	12.0000			0.467809
$659$	1.60770	−	2.78461i	0.0626269	−	0.108473i	−0.833012	−	0.553255i	$-0.813386\pi$
$659$	1.60770	−	2.78461i	0.0626269	−	0.108473i	0.895639	+	0.444782i	$0.146719\pi$
$660$	5.46410			0.212690
$661$	9.19615	−	15.9282i	0.357689	−	0.619535i	−0.629885	−	0.776688i	$-0.716898\pi$
$661$	9.19615	−	15.9282i	0.357689	−	0.619535i	0.987574	+	0.157153i	$0.0502315\pi$
$662$	−18.1244	+	31.3923i	−0.704423	+	1.22010i
$663$	−3.26795	+	5.66025i	−0.126917	+	0.219826i
$664$	−4.92820	−	8.53590i	−0.191251	−	0.331257i
$665$	−6.92820			−0.268664
$666$	11.3923	−	4.26795i	0.441443	−	0.165380i
$667$	10.9282			0.423142
$668$	8.46410	+	14.6603i	0.327486	+	0.567222i
$669$	11.6603	−	20.1962i	0.450811	−	0.780828i
$670$	−7.46410	+	12.9282i	−0.288363	+	0.499460i
$671$	24.3923	−	42.2487i	0.941654	−	1.63099i
$672$	−3.46410			−0.133631
$673$	17.0526	−	29.5359i	0.657328	−	1.13853i	−0.323977	−	0.946065i	$-0.605020\pi$
$673$	17.0526	−	29.5359i	0.657328	−	1.13853i	0.981305	−	0.192460i	$-0.0616466\pi$
$674$	8.92820			0.343902
$675$	−2.50000	−	4.33013i	−0.0962250	−	0.166667i
$676$	6.92820			0.266469
$677$	2.78461			0.107021			0.0535106	−	0.998567i	$-0.482959\pi$
$677$	2.78461			0.107021			0.0535106	+	0.998567i	$0.482959\pi$
$678$	−1.46410	−	2.53590i	−0.0562285	−	0.0973906i
$679$	3.46410	−	6.00000i	0.132940	−	0.230259i
$680$	−1.46410			−0.0561457
$681$	−0.0358984	−	0.0621778i	−0.00137563	−	0.00238266i
$682$	23.1244	+	40.0526i	0.885477	+	1.53369i
$683$	−2.57180	−	4.45448i	−0.0984071	−	0.170446i	0.812618	−	0.582796i	$-0.198041\pi$
$683$	−2.57180	−	4.45448i	−0.0984071	−	0.170446i	−0.911025	+	0.412350i	$0.864708\pi$
$684$	−2.00000	+	3.46410i	−0.0764719	+	0.132453i
$685$	0.732051	−	1.26795i	0.0279702	−	0.0484458i
$686$	3.46410	+	6.00000i	0.132260	+	0.229081i
$687$	−13.1962	−	22.8564i	−0.503465	−	0.872026i
$688$	4.96410	+	8.59808i	0.189255	+	0.327799i
$689$	−24.7128			−0.941483
$690$	−2.73205	+	4.73205i	−0.104007	+	0.180146i
$691$	4.80385	+	8.32051i	0.182747	+	0.316527i	0.942815	−	0.333316i	$-0.108168\pi$
$691$	4.80385	+	8.32051i	0.182747	+	0.316527i	−0.760068	+	0.649844i	$0.774834\pi$
$692$	−15.8564			−0.602770
$693$	37.8564			1.43805
$694$	15.4641	+	26.7846i	0.587009	+	1.01673i
$695$	−16.3923			−0.621796
$696$	−1.00000	+	1.73205i	−0.0379049	+	0.0656532i
$697$	17.4641			0.661500
$698$	−5.39230	+	9.33975i	−0.204102	+	0.353515i
$699$	−4.80385	+	8.32051i	−0.181698	+	0.314711i
$700$	−1.73205	+	3.00000i	−0.0654654	+	0.113389i
$701$	−19.0000	−	32.9090i	−0.717620	−	1.24295i	−0.961940	−	0.273260i	$-0.911898\pi$
$701$	−19.0000	−	32.9090i	−0.717620	−	1.24295i	0.244320	−	0.969695i	$-0.421435\pi$
$702$	22.3205			0.842433
$703$	11.3923	−	4.26795i	0.429669	−	0.160969i
$704$	−5.46410			−0.205936
$705$	1.73205	+	3.00000i	0.0652328	+	0.112987i
$706$	−1.33975	+	2.32051i	−0.0504220	+	0.0873335i
$707$	16.3923	−	28.3923i	0.616496	−	1.06780i
$708$	−2.73205	+	4.73205i	−0.102677	+	0.177841i
$709$	−12.0000			−0.450669			−0.225335	−	0.974281i	$-0.572348\pi$
$709$	−12.0000			−0.450669			−0.225335	+	0.974281i	$0.572348\pi$
$710$	−0.535898	+	0.928203i	−0.0201119	+	0.0348348i
$711$	29.8564			1.11970
$712$	1.00000	+	1.73205i	0.0374766	+	0.0649113i
$713$	−46.2487			−1.73203
$714$	5.07180			0.189807
$715$	12.1962	+	21.1244i	0.456110	+	0.790006i
$716$	−6.00000	+	10.3923i	−0.224231	+	0.388379i
$717$	−13.0718			−0.488175
$718$	−2.23205	−	3.86603i	−0.0832994	−	0.144279i
$719$	17.1603	+	29.7224i	0.639969	+	1.10846i	0.985439	+	0.170030i	$0.0543864\pi$
$719$	17.1603	+	29.7224i	0.639969	+	1.10846i	−0.345469	+	0.938430i	$0.612280\pi$
$720$	1.00000	+	1.73205i	0.0372678	+	0.0645497i
$721$	23.3205	−	40.3923i	0.868501	−	1.50429i
$722$	7.50000	−	12.9904i	0.279121	−	0.483452i
$723$	−1.00000	−	1.73205i	−0.0371904	−	0.0644157i
$724$	−11.7321	−	20.3205i	−0.436018	−	0.755206i
$725$	1.00000	+	1.73205i	0.0371391	+	0.0643268i
$726$	−18.8564			−0.699827
$727$	6.00000	−	10.3923i	0.222528	−	0.385429i	−0.733047	−	0.680178i	$-0.761903\pi$
$727$	6.00000	−	10.3923i	0.222528	−	0.385429i	0.955575	+	0.294749i	$0.0952359\pi$
$728$	−7.73205	−	13.3923i	−0.286569	−	0.496352i
$729$	13.0000			0.481481
$730$	2.53590			0.0938578
$731$	−7.26795	−	12.5885i	−0.268815	−	0.465601i
$732$	−8.92820			−0.329996
$733$	11.9282	−	20.6603i	0.440578	−	0.763104i	−0.557154	−	0.830409i	$-0.688107\pi$
$733$	11.9282	−	20.6603i	0.440578	−	0.763104i	0.997732	+	0.0673052i	$0.0214401\pi$
$734$	10.7846			0.398067
$735$	2.50000	−	4.33013i	0.0922139	−	0.159719i
$736$	2.73205	−	4.73205i	0.100705	−	0.174426i
$737$	40.7846	−	70.6410i	1.50232	−	2.60210i
$738$	−11.9282	−	20.6603i	−0.439083	−	0.760514i
$739$	−2.53590			−0.0932845			−0.0466423	−	0.998912i	$-0.514852\pi$
$739$	−2.53590			−0.0932845			−0.0466423	+	0.998912i	$0.514852\pi$
$740$	1.00000	−	6.00000i	0.0367607	−	0.220564i
$741$	8.92820			0.327986
$742$	9.58846	+	16.6077i	0.352003	+	0.609688i
$743$	17.1244	−	29.6603i	0.628232	−	1.08813i	−0.359675	−	0.933078i	$-0.617112\pi$
$743$	17.1244	−	29.6603i	0.628232	−	1.08813i	0.987906	−	0.155051i	$-0.0495543\pi$
$744$	4.23205	−	7.33013i	0.155155	−	0.268735i
$745$	−3.46410	+	6.00000i	−0.126915	+	0.219823i
$746$	−38.4641			−1.40827
$747$	9.85641	−	17.0718i	0.360627	−	0.624624i
$748$	8.00000			0.292509
$749$	15.3397	+	26.5692i	0.560502	+	0.970818i
$750$	−1.00000			−0.0365148
$751$	40.3205			1.47132			0.735658	−	0.677353i	$-0.236873\pi$
$751$	40.3205			1.47132			0.735658	+	0.677353i	$0.236873\pi$
$752$	−1.73205	−	3.00000i	−0.0631614	−	0.109399i
$753$	−6.46410	+	11.1962i	−0.235565	+	0.408010i
$754$	−8.92820			−0.325146
$755$	−2.69615	−	4.66987i	−0.0981230	−	0.169954i
$756$	−8.66025	−	15.0000i	−0.314970	−	0.545545i
$757$	6.76795	+	11.7224i	0.245985	+	0.426059i	0.962408	−	0.271607i	$-0.0875552\pi$
$757$	6.76795	+	11.7224i	0.245985	+	0.426059i	−0.716423	+	0.697666i	$0.754222\pi$
$758$	12.1962	−	21.1244i	0.442984	−	0.767271i
$759$	14.9282	−	25.8564i	0.541859	−	0.938528i
$760$	1.00000	+	1.73205i	0.0362738	+	0.0628281i
$761$	4.46410	+	7.73205i	0.161824	+	0.280287i	0.935523	−	0.353267i	$-0.114929\pi$
$761$	4.46410	+	7.73205i	0.161824	+	0.280287i	−0.773699	+	0.633553i	$0.781596\pi$
$762$	−7.46410	−	12.9282i	−0.270396	−	0.468339i
$763$	−34.6410			−1.25409
$764$	−5.16025	+	8.93782i	−0.186691	+	0.323359i
$765$	−1.46410	−	2.53590i	−0.0529347	−	0.0916856i
$766$	0.535898			0.0193628
$767$	−24.3923			−0.880755
$768$	0.500000	+	0.866025i	0.0180422	+	0.0312500i
$769$	−1.21539			−0.0438281			−0.0219140	−	0.999760i	$-0.506976\pi$
$769$	−1.21539			−0.0438281			−0.0219140	+	0.999760i	$0.506976\pi$
$770$	9.46410	−	16.3923i	0.341063	−	0.590738i
$771$	12.5359			0.451469
$772$	−0.196152	+	0.339746i	−0.00705968	+	0.0122277i
$773$	20.0885	−	34.7942i	0.722532	−	1.25146i	−0.237450	−	0.971400i	$-0.576312\pi$
$773$	20.0885	−	34.7942i	0.722532	−	1.25146i	0.959982	−	0.280062i	$-0.0903549\pi$
$774$	−9.92820	+	17.1962i	−0.356862	+	0.618103i
$775$	−4.23205	−	7.33013i	−0.152020	−	0.263306i
$776$	−2.00000			−0.0717958
$777$	−3.46410	+	20.7846i	−0.124274	+	0.745644i
$778$	23.7128			0.850146
$779$	−11.9282	−	20.6603i	−0.427372	−	0.740230i
$780$	2.23205	−	3.86603i	0.0799202	−	0.138426i
$781$	2.92820	−	5.07180i	0.104779	−	0.181483i
$782$	−4.00000	+	6.92820i	−0.143040	+	0.247752i
$783$	−10.0000			−0.357371
$784$	−2.50000	+	4.33013i	−0.0892857	+	0.154647i
$785$	−16.3205			−0.582504
$786$	0.464102	+	0.803848i	0.0165540	+	0.0286723i
$787$	43.7846			1.56075			0.780376	−	0.625310i	$-0.215027\pi$
$787$	43.7846			1.56075			0.780376	+	0.625310i	$0.215027\pi$
$788$	−16.3205			−0.581394
$789$	3.19615	+	5.53590i	0.113786	+	0.197083i
$790$	7.46410	−	12.9282i	0.265561	−	0.459965i
$791$	−10.1436			−0.360665
$792$	−5.46410	−	9.46410i	−0.194158	−	0.336292i
$793$	−19.9282	−	34.5167i	−0.707671	−	1.22572i
$794$	2.23205	+	3.86603i	0.0792125	+	0.137200i
$795$	−2.76795	+	4.79423i	−0.0981690	+	0.170034i
$796$	7.23205	−	12.5263i	0.256333	−	0.443982i
$797$	−9.76795	−	16.9186i	−0.345999	−	0.599287i	0.639536	−	0.768761i	$-0.279126\pi$
$797$	−9.76795	−	16.9186i	−0.345999	−	0.599287i	−0.985535	+	0.169474i	$0.945793\pi$
$798$	−3.46410	−	6.00000i	−0.122628	−	0.212398i
$799$	2.53590	+	4.39230i	0.0897136	+	0.155389i
$800$	1.00000			0.0353553
$801$	−2.00000	+	3.46410i	−0.0706665	+	0.122398i
$802$	−11.0000	−	19.0526i	−0.388424	−	0.672769i
$803$	−13.8564			−0.488982
$804$	−14.9282			−0.526477
$805$	9.46410	+	16.3923i	0.333566	+	0.577753i
$806$	37.7846			1.33091
$807$	−6.19615	+	10.7321i	−0.218115	+	0.377786i
$808$	−9.46410			−0.332946
$809$	−19.3564	+	33.5263i	−0.680535	+	1.17872i	0.294283	+	0.955718i	$0.404919\pi$
$809$	−19.3564	+	33.5263i	−0.680535	+	1.17872i	−0.974818	+	0.223003i	$0.928414\pi$
$810$	−0.500000	+	0.866025i	−0.0175682	+	0.0304290i
$811$	−21.3205	+	36.9282i	−0.748664	+	1.29672i	0.199799	+	0.979837i	$0.435971\pi$
$811$	−21.3205	+	36.9282i	−0.748664	+	1.29672i	−0.948463	+	0.316888i	$0.897362\pi$
$812$	3.46410	+	6.00000i	0.121566	+	0.210559i
$813$	−17.2487			−0.604939
$814$	−5.46410	+	32.7846i	−0.191517	+	1.14910i
$815$	10.8564			0.380283
$816$	−0.732051	−	1.26795i	−0.0256269	−	0.0443871i
$817$	−9.92820	+	17.1962i	−0.347344	+	0.601617i
$818$	5.50000	−	9.52628i	0.192303	−	0.333079i
$819$	15.4641	−	26.7846i	0.540359	−	0.935930i
$820$	−11.9282			−0.416551
$821$	−11.5359	+	19.9808i	−0.402606	+	0.697333i	−0.994040	−	0.109020i	$-0.965229\pi$
$821$	−11.5359	+	19.9808i	−0.402606	+	0.697333i	0.591434	+	0.806353i	$0.298562\pi$
$822$	1.46410			0.0510664
$823$	11.7321	+	20.3205i	0.408954	+	0.708328i	0.994773	−	0.102113i	$-0.0325605\pi$
$823$	11.7321	+	20.3205i	0.408954	+	0.708328i	−0.585819	+	0.810442i	$0.699227\pi$
$824$	−13.4641			−0.469044
$825$	5.46410			0.190236
$826$	9.46410	+	16.3923i	0.329298	+	0.570361i
$827$	−1.60770	+	2.78461i	−0.0559050	+	0.0968304i	−0.892624	−	0.450803i	$-0.851138\pi$
$827$	−1.60770	+	2.78461i	−0.0559050	+	0.0968304i	0.836718	+	0.547633i	$0.184471\pi$
$828$	10.9282			0.379781
$829$	−23.9808	−	41.5359i	−0.832886	−	1.44260i	−0.895740	−	0.444579i	$-0.853353\pi$
$829$	−23.9808	−	41.5359i	−0.832886	−	1.44260i	0.0628535	−	0.998023i	$-0.479980\pi$
$830$	−4.92820	−	8.53590i	−0.171060	−	0.296285i
$831$	−16.2321	−	28.1147i	−0.563084	−	0.975289i
$832$	−2.23205	+	3.86603i	−0.0773824	+	0.134030i
$833$	3.66025	−	6.33975i	0.126820	−	0.219659i
$834$	−8.19615	−	14.1962i	−0.283810	−	0.491573i
$835$	8.46410	+	14.6603i	0.292912	+	0.507339i
$836$	−5.46410	−	9.46410i	−0.188980	−	0.327323i
$837$	42.3205			1.46281
$838$	−2.73205	+	4.73205i	−0.0943771	+	0.163466i
$839$	18.0167	+	31.2058i	0.622004	+	1.07734i	0.989112	+	0.147164i	$0.0470147\pi$
$839$	18.0167	+	31.2058i	0.622004	+	1.07734i	−0.367108	+	0.930178i	$0.619652\pi$
$840$	−3.46410			−0.119523
$841$	−25.0000			−0.862069
$842$	1.33975	+	2.32051i	0.0461707	+	0.0799700i
$843$	−28.7128			−0.988922
$844$	−7.00000	+	12.1244i	−0.240950	+	0.417338i
$845$	6.92820			0.238337
$846$	3.46410	−	6.00000i	0.119098	−	0.206284i
$847$	−32.6603	+	56.5692i	−1.12222	+	1.94374i
$848$	2.76795	−	4.79423i	0.0950518	−	0.164634i
$849$	4.03590	+	6.99038i	0.138512	+	0.239909i
$850$	−1.46410			−0.0502183
$851$	−25.6603	−	21.1244i	−0.879622	−	0.724134i
$852$	−1.07180			−0.0367192
$853$	−7.62436	−	13.2058i	−0.261053	−	0.452157i	0.705469	−	0.708741i	$-0.250736\pi$
$853$	−7.62436	−	13.2058i	−0.261053	−	0.452157i	−0.966522	+	0.256584i	$0.917403\pi$
$854$	−15.4641	+	26.7846i	−0.529171	+	0.916550i
$855$	−2.00000	+	3.46410i	−0.0683986	+	0.118470i
$856$	4.42820	−	7.66987i	0.151353	−	0.262151i
$857$	−6.24871			−0.213452			−0.106726	−	0.994288i	$-0.534037\pi$
$857$	−6.24871			−0.213452			−0.106726	+	0.994288i	$0.534037\pi$
$858$	−12.1962	+	21.1244i	−0.416370	+	0.721174i
$859$	18.9282			0.645822			0.322911	−	0.946429i	$-0.395339\pi$
$859$	18.9282			0.645822			0.322911	+	0.946429i	$0.395339\pi$
$860$	4.96410	+	8.59808i	0.169274	+	0.293192i
$861$	41.3205			1.40820
$862$	5.53590			0.188553
$863$	15.4641	+	26.7846i	0.526404	+	0.911759i	0.999527	+	0.0307621i	$0.00979343\pi$
$863$	15.4641	+	26.7846i	0.526404	+	0.911759i	−0.473123	+	0.880997i	$0.656873\pi$
$864$	−2.50000	+	4.33013i	−0.0850517	+	0.147314i
$865$	−15.8564			−0.539134
$866$	−11.8564	−	20.5359i	−0.402897	−	0.697838i
$867$	−7.42820	−	12.8660i	−0.252275	−	0.436953i
$868$	−14.6603	−	25.3923i	−0.497601	−	0.861871i
$869$	−40.7846	+	70.6410i	−1.38352	+	2.39633i
$870$	−1.00000	+	1.73205i	−0.0339032	+	0.0587220i
$871$	−33.3205	−	57.7128i	−1.12902	−	1.95552i
$872$	5.00000	+	8.66025i	0.169321	+	0.293273i
$873$	−2.00000	−	3.46410i	−0.0676897	−	0.117242i
$874$	10.9282			0.369652
$875$	−1.73205	+	3.00000i	−0.0585540	+	0.101419i
$876$	1.26795	+	2.19615i	0.0428400	+	0.0742011i
$877$	21.2487			0.717518			0.358759	−	0.933430i	$-0.383200\pi$
$877$	21.2487			0.717518			0.358759	+	0.933430i	$0.383200\pi$
$878$	11.5359			0.389318
$879$	0.232051	+	0.401924i	0.00782688	+	0.0135566i
$880$	−5.46410			−0.184195
$881$	24.4641	−	42.3731i	0.824217	−	1.42758i	−0.0783001	−	0.996930i	$-0.524949\pi$
$881$	24.4641	−	42.3731i	0.824217	−	1.42758i	0.902517	−	0.430655i	$-0.141717\pi$
$882$	−10.0000			−0.336718
$883$	25.4282	−	44.0429i	0.855727	−	1.48216i	−0.0202416	−	0.999795i	$-0.506444\pi$
$883$	25.4282	−	44.0429i	0.855727	−	1.48216i	0.875969	−	0.482368i	$-0.160223\pi$
$884$	3.26795	−	5.66025i	0.109913	−	0.190375i
$885$	−2.73205	+	4.73205i	−0.0918369	+	0.159066i
$886$	−7.03590	−	12.1865i	−0.236376	−	0.409415i
$887$	−31.8564			−1.06963			−0.534817	−	0.844968i	$-0.679619\pi$
$887$	−31.8564			−1.06963			−0.534817	+	0.844968i	$0.679619\pi$
$888$	5.69615	−	2.13397i	0.191150	−	0.0716115i
$889$	−51.7128			−1.73439
$890$	1.00000	+	1.73205i	0.0335201	+	0.0580585i
$891$	2.73205	−	4.73205i	0.0915271	−	0.158530i
$892$	−11.6603	+	20.1962i	−0.390414	+	0.676217i
$893$	3.46410	−	6.00000i	0.115922	−	0.200782i
$894$	−6.92820			−0.231714
$895$	−6.00000	+	10.3923i	−0.200558	+	0.347376i
$896$	3.46410			0.115728
$897$	−12.1962	−	21.1244i	−0.407218	−	0.705322i
$898$	−15.0000			−0.500556
$899$	−16.9282			−0.564587
$900$	1.00000	+	1.73205i	0.0333333	+	0.0577350i
$901$	−4.05256	+	7.01924i	−0.135010	+	0.233845i
$902$	65.1769			2.17015
$903$	−17.1962	−	29.7846i	−0.572252	−	0.991170i
$904$	1.46410	+	2.53590i	0.0486953	+	0.0843427i
$905$	−11.7321	−	20.3205i	−0.389987	−	0.675477i
$906$	2.69615	−	4.66987i	0.0895737	−	0.155146i
$907$	−22.3923	+	38.7846i	−0.743524	+	1.28782i	0.207357	+	0.978265i	$0.433514\pi$
$907$	−22.3923	+	38.7846i	−0.743524	+	1.28782i	−0.950881	+	0.309556i	$0.899819\pi$
$908$	0.0358984	+	0.0621778i	0.00119133	+	0.00206344i
$909$	−9.46410	−	16.3923i	−0.313904	−	0.543698i
$910$	−7.73205	−	13.3923i	−0.256315	−	0.443951i
$911$	24.1769			0.801017			0.400508	−	0.916293i	$-0.368834\pi$
$911$	24.1769			0.801017			0.400508	+	0.916293i	$0.368834\pi$
$912$	−1.00000	+	1.73205i	−0.0331133	+	0.0573539i
$913$	26.9282	+	46.6410i	0.891193	+	1.54359i
$914$	−1.85641			−0.0614045
$915$	−8.92820			−0.295157
$916$	13.1962	+	22.8564i	0.436013	+	0.755197i
$917$	3.21539			0.106182
$918$	3.66025	−	6.33975i	0.120806	−	0.209243i
$919$	17.0718			0.563147			0.281573	−	0.959540i	$-0.409144\pi$
$919$	17.0718			0.563147			0.281573	+	0.959540i	$0.409144\pi$
$920$	2.73205	−	4.73205i	0.0900730	−	0.156011i
$921$	−5.42820	+	9.40192i	−0.178865	+	0.309804i
$922$	6.46410	−	11.1962i	0.212884	−	0.368726i
$923$	−2.39230	−	4.14359i	−0.0787437	−	0.136388i
$924$	18.9282			0.622692
$925$	1.00000	−	6.00000i	0.0328798	−	0.197279i
$926$	6.92820			0.227675
$927$	−13.4641	−	23.3205i	−0.442219	−	0.765946i
$928$	1.00000	−	1.73205i	0.0328266	−	0.0568574i
$929$	24.4282	−	42.3109i	0.801463	−	1.38818i	−0.117190	−	0.993110i	$-0.537388\pi$
$929$	24.4282	−	42.3109i	0.801463	−	1.38818i	0.918653	−	0.395066i	$-0.129278\pi$
$930$	4.23205	−	7.33013i	0.138774	−	0.240364i
$931$	−10.0000			−0.327737
$932$	4.80385	−	8.32051i	0.157355	−	0.272547i
$933$	12.4641			0.408056
$934$	−1.50000	−	2.59808i	−0.0490815	−	0.0850117i
$935$	8.00000			0.261628
$936$	−8.92820			−0.291827
$937$	−12.0718	−	20.9090i	−0.394368	−	0.683066i	0.598652	−	0.801009i	$-0.295703\pi$
$937$	−12.0718	−	20.9090i	−0.394368	−	0.683066i	−0.993020	+	0.117943i	$0.962370\pi$
$938$	−25.8564	+	44.7846i	−0.844242	+	1.46227i
$939$	−8.92820			−0.291361
$940$	−1.73205	−	3.00000i	−0.0564933	−	0.0978492i
$941$	14.1962	+	24.5885i	0.462781	+	0.801561i	0.999098	−	0.0424558i	$-0.0135182\pi$
$941$	14.1962	+	24.5885i	0.462781	+	0.801561i	−0.536317	+	0.844017i	$0.680185\pi$
$942$	−8.16025	−	14.1340i	−0.265875	−	0.460510i
$943$	−32.5885	+	56.4449i	−1.06123	+	1.83810i
$944$	2.73205	−	4.73205i	0.0889207	−	0.154015i
$945$	−8.66025	−	15.0000i	−0.281718	−	0.487950i
$946$	−27.1244	−	46.9808i	−0.881889	−	1.52748i
$947$	−15.9641	−	27.6506i	−0.518764	−	0.898525i	−0.999762	−	0.0218036i	$-0.993059\pi$
$947$	−15.9641	−	27.6506i	−0.518764	−	0.898525i	0.480999	−	0.876721i	$-0.340274\pi$
$948$	14.9282			0.484846
$949$	−5.66025	+	9.80385i	−0.183740	+	0.318246i
$950$	1.00000	+	1.73205i	0.0324443	+	0.0561951i
$951$	17.5359			0.568640
$952$	−5.07180			−0.164378
$953$	−1.80385	−	3.12436i	−0.0584324	−	0.101208i	0.835330	−	0.549750i	$-0.185277\pi$
$953$	−1.80385	−	3.12436i	−0.0584324	−	0.101208i	−0.893762	+	0.448542i	$0.851944\pi$
$954$	11.0718			0.358463
$955$	−5.16025	+	8.93782i	−0.166982	+	0.289221i
$956$	13.0718			0.422772
$957$	5.46410	−	9.46410i	0.176629	−	0.305931i
$958$	19.1603	−	33.1865i	0.619040	−	1.07221i
$959$	2.53590	−	4.39230i	0.0818884	−	0.141835i
$960$	0.500000	+	0.866025i	0.0161374	+	0.0279508i
$961$	40.6410			1.31100
$962$	20.9641	+	17.2583i	0.675910	+	0.556431i
$963$	17.7128			0.570787
$964$	1.00000	+	1.73205i	0.0322078	+	0.0557856i
$965$	−0.196152	+	0.339746i	−0.00631437	+	0.0109368i
$966$	−9.46410	+	16.3923i	−0.304502	+	0.527414i
$967$	18.3923	−	31.8564i	0.591457	−	1.02443i	−0.402580	−	0.915385i	$-0.631886\pi$
$967$	18.3923	−	31.8564i	0.591457	−	1.02443i	0.994036	−	0.109048i	$-0.0347802\pi$
$968$	18.8564			0.606068
$969$	1.46410	−	2.53590i	0.0470337	−	0.0814648i
$970$	−2.00000			−0.0642161
$971$	2.33975	+	4.05256i	0.0750860	+	0.130053i	0.901124	−	0.433562i	$-0.142744\pi$
$971$	2.33975	+	4.05256i	0.0750860	+	0.130053i	−0.826038	+	0.563615i	$0.809410\pi$
$972$	−16.0000			−0.513200
$973$	−56.7846			−1.82043
$974$	−6.46410	−	11.1962i	−0.207123	−	0.358748i
$975$	2.23205	−	3.86603i	0.0714828	−	0.123812i
$976$	8.92820			0.285785
$977$	−1.00000	−	1.73205i	−0.0319928	−	0.0554132i	0.849586	−	0.527451i	$-0.176852\pi$
$977$	−1.00000	−	1.73205i	−0.0319928	−	0.0554132i	−0.881579	+	0.472037i	$0.843519\pi$
$978$	5.42820	+	9.40192i	0.173575	+	0.300640i
$979$	−5.46410	−	9.46410i	−0.174633	−	0.302474i
$980$	−2.50000	+	4.33013i	−0.0798596	+	0.138321i
$981$	−10.0000	+	17.3205i	−0.319275	+	0.553001i
$982$	7.12436	+	12.3397i	0.227347	+	0.393777i
$983$	−10.8564	−	18.8038i	−0.346266	−	0.599750i	0.639317	−	0.768943i	$-0.279217\pi$
$983$	−10.8564	−	18.8038i	−0.346266	−	0.599750i	−0.985583	+	0.169193i	$0.945884\pi$
$984$	−5.96410	−	10.3301i	−0.190129	−	0.329312i
$985$	−16.3205			−0.520015
$986$	−1.46410	+	2.53590i	−0.0466265	+	0.0807595i
$987$	6.00000	+	10.3923i	0.190982	+	0.330791i
$988$	−8.92820			−0.284044
$989$	54.2487			1.72501
$990$	−5.46410	−	9.46410i	−0.173661	−	0.300789i
$991$	25.2487			0.802052			0.401026	−	0.916067i	$-0.368654\pi$
$991$	25.2487			0.802052			0.401026	+	0.916067i	$0.368654\pi$
$992$	−4.23205	+	7.33013i	−0.134368	+	0.232732i
$993$	−36.2487			−1.15032
$994$	−1.85641	+	3.21539i	−0.0588816	+	0.101986i
$995$	7.23205	−	12.5263i	0.229271	−	0.397110i
$996$	4.92820	−	8.53590i	0.156156	−	0.270470i
$997$	8.30385	+	14.3827i	0.262985	+	0.455504i	0.967034	−	0.254648i	$-0.0819595\pi$
$997$	8.30385	+	14.3827i	0.262985	+	0.455504i	−0.704048	+	0.710152i	$0.748626\pi$
$998$	−2.92820			−0.0926907
$999$	23.4808	+	19.3301i	0.742898	+	0.611578i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.e.d.211.1	yes	4
37.10	even	3	inner	370.2.e.d.121.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.e.d.121.1	✓	4	37.10	even	3	inner
370.2.e.d.211.1	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:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} -1.00000 q^{6} +(-1.73205 + 3.00000i) q^{7} +1.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} -1.00000 q^{6} +(-1.73205 + 3.00000i) q^{7} +1.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +1.00000 q^{10} -5.46410 q^{11} +(0.500000 + 0.866025i) q^{12} +(-2.23205 + 3.86603i) q^{13} +3.46410 q^{14} +(0.500000 + 0.866025i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.732051 + 1.26795i) q^{17} +(1.00000 - 1.73205i) q^{18} +(1.00000 - 1.73205i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(1.73205 + 3.00000i) q^{21} +(2.73205 + 4.73205i) q^{22} -5.46410 q^{23} +(0.500000 - 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} +4.46410 q^{26} +5.00000 q^{27} +(-1.73205 - 3.00000i) q^{28} -2.00000 q^{29} +(0.500000 - 0.866025i) q^{30} +8.46410 q^{31} +(-0.500000 + 0.866025i) q^{32} +(-2.73205 + 4.73205i) q^{33} +(0.732051 - 1.26795i) q^{34} +(-1.73205 - 3.00000i) q^{35} -2.00000 q^{36} +(4.69615 + 3.86603i) q^{37} -2.00000 q^{38} +(2.23205 + 3.86603i) q^{39} +(-0.500000 + 0.866025i) q^{40} +(5.96410 - 10.3301i) q^{41} +(1.73205 - 3.00000i) q^{42} -9.92820 q^{43} +(2.73205 - 4.73205i) q^{44} -2.00000 q^{45} +(2.73205 + 4.73205i) q^{46} +3.46410 q^{47} -1.00000 q^{48} +(-2.50000 - 4.33013i) q^{49} +(-0.500000 + 0.866025i) q^{50} +1.46410 q^{51} +(-2.23205 - 3.86603i) q^{52} +(2.76795 + 4.79423i) q^{53} +(-2.50000 - 4.33013i) q^{54} +(2.73205 - 4.73205i) q^{55} +(-1.73205 + 3.00000i) q^{56} +(-1.00000 - 1.73205i) q^{57} +(1.00000 + 1.73205i) q^{58} +(2.73205 + 4.73205i) q^{59} -1.00000 q^{60} +(-4.46410 + 7.73205i) q^{61} +(-4.23205 - 7.33013i) q^{62} -6.92820 q^{63} +1.00000 q^{64} +(-2.23205 - 3.86603i) q^{65} +5.46410 q^{66} +(-7.46410 + 12.9282i) q^{67} -1.46410 q^{68} +(-2.73205 + 4.73205i) q^{69} +(-1.73205 + 3.00000i) q^{70} +(-0.535898 + 0.928203i) q^{71} +(1.00000 + 1.73205i) q^{72} +2.53590 q^{73} +(1.00000 - 6.00000i) q^{74} -1.00000 q^{75} +(1.00000 + 1.73205i) q^{76} +(9.46410 - 16.3923i) q^{77} +(2.23205 - 3.86603i) q^{78} +(7.46410 - 12.9282i) q^{79} +1.00000 q^{80} +(-0.500000 + 0.866025i) q^{81} -11.9282 q^{82} +(-4.92820 - 8.53590i) q^{83} -3.46410 q^{84} -1.46410 q^{85} +(4.96410 + 8.59808i) q^{86} +(-1.00000 + 1.73205i) q^{87} -5.46410 q^{88} +(1.00000 + 1.73205i) q^{89} +(1.00000 + 1.73205i) q^{90} +(-7.73205 - 13.3923i) q^{91} +(2.73205 - 4.73205i) q^{92} +(4.23205 - 7.33013i) q^{93} +(-1.73205 - 3.00000i) q^{94} +(1.00000 + 1.73205i) q^{95} +(0.500000 + 0.866025i) q^{96} -2.00000 q^{97} +(-2.50000 + 4.33013i) q^{98} +(-5.46410 - 9.46410i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 4 q^{6} + 4 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 4 * q^6 + 4 * q^8 + 4 * q^9	\( 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 4 q^{6} + 4 q^{8} + 4 q^{9} + 4 q^{10} - 8 q^{11} + 2 q^{12} - 2 q^{13} + 2 q^{15} - 2 q^{16} - 4 q^{17} + 4 q^{18} + 4 q^{19} - 2 q^{20} + 4 q^{22} - 8 q^{23} + 2 q^{24} - 2 q^{25} + 4 q^{26} + 20 q^{27} - 8 q^{29} + 2 q^{30} + 20 q^{31} - 2 q^{32} - 4 q^{33} - 4 q^{34} - 8 q^{36} - 2 q^{37} - 8 q^{38} + 2 q^{39} - 2 q^{40} + 10 q^{41} - 12 q^{43} + 4 q^{44} - 8 q^{45} + 4 q^{46} - 4 q^{48} - 10 q^{49} - 2 q^{50} - 8 q^{51} - 2 q^{52} + 18 q^{53} - 10 q^{54} + 4 q^{55} - 4 q^{57} + 4 q^{58} + 4 q^{59} - 4 q^{60} - 4 q^{61} - 10 q^{62} + 4 q^{64} - 2 q^{65} + 8 q^{66} - 16 q^{67} + 8 q^{68} - 4 q^{69} - 16 q^{71} + 4 q^{72} + 24 q^{73} + 4 q^{74} - 4 q^{75} + 4 q^{76} + 24 q^{77} + 2 q^{78} + 16 q^{79} + 4 q^{80} - 2 q^{81} - 20 q^{82} + 8 q^{83} + 8 q^{85} + 6 q^{86} - 4 q^{87} - 8 q^{88} + 4 q^{89} + 4 q^{90} - 24 q^{91} + 4 q^{92} + 10 q^{93} + 4 q^{95} + 2 q^{96} - 8 q^{97} - 10 q^{98} - 8 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 4 * q^6 + 4 * q^8 + 4 * q^9 + 4 * q^10 - 8 * q^11 + 2 * q^12 - 2 * q^13 + 2 * q^15 - 2 * q^16 - 4 * q^17 + 4 * q^18 + 4 * q^19 - 2 * q^20 + 4 * q^22 - 8 * q^23 + 2 * q^24 - 2 * q^25 + 4 * q^26 + 20 * q^27 - 8 * q^29 + 2 * q^30 + 20 * q^31 - 2 * q^32 - 4 * q^33 - 4 * q^34 - 8 * q^36 - 2 * q^37 - 8 * q^38 + 2 * q^39 - 2 * q^40 + 10 * q^41 - 12 * q^43 + 4 * q^44 - 8 * q^45 + 4 * q^46 - 4 * q^48 - 10 * q^49 - 2 * q^50 - 8 * q^51 - 2 * q^52 + 18 * q^53 - 10 * q^54 + 4 * q^55 - 4 * q^57 + 4 * q^58 + 4 * q^59 - 4 * q^60 - 4 * q^61 - 10 * q^62 + 4 * q^64 - 2 * q^65 + 8 * q^66 - 16 * q^67 + 8 * q^68 - 4 * q^69 - 16 * q^71 + 4 * q^72 + 24 * q^73 + 4 * q^74 - 4 * q^75 + 4 * q^76 + 24 * q^77 + 2 * q^78 + 16 * q^79 + 4 * q^80 - 2 * q^81 - 20 * q^82 + 8 * q^83 + 8 * q^85 + 6 * q^86 - 4 * q^87 - 8 * q^88 + 4 * q^89 + 4 * q^90 - 24 * q^91 + 4 * q^92 + 10 * q^93 + 4 * q^95 + 2 * q^96 - 8 * q^97 - 10 * q^98 - 8 * q^99

Introduction

L-functions

Modular forms

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Database

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