LMFDB - Embedded newform 370.2.e.d.121.2

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			121.2
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	370.121
Dual form			370.2.e.d.211.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-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} +1.46410 q^{11} +(0.500000 - 0.866025i) q^{12} +(1.23205 + 2.13397i) q^{13} -3.46410 q^{14} +(0.500000 - 0.866025i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.73205 + 4.73205i) 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} +(-0.732051 + 1.26795i) q^{22} +1.46410 q^{23} +(0.500000 + 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} -2.46410 q^{26} +5.00000 q^{27} +(1.73205 - 3.00000i) q^{28} -2.00000 q^{29} +(0.500000 + 0.866025i) q^{30} +1.53590 q^{31} +(-0.500000 - 0.866025i) q^{32} +(0.732051 + 1.26795i) q^{33} +(-2.73205 - 4.73205i) q^{34} +(1.73205 - 3.00000i) q^{35} -2.00000 q^{36} +(-5.69615 + 2.13397i) q^{37} -2.00000 q^{38} +(-1.23205 + 2.13397i) q^{39} +(-0.500000 - 0.866025i) q^{40} +(-0.964102 - 1.66987i) q^{41} +(-1.73205 - 3.00000i) q^{42} +3.92820 q^{43} +(-0.732051 - 1.26795i) q^{44} -2.00000 q^{45} +(-0.732051 + 1.26795i) q^{46} -3.46410 q^{47} -1.00000 q^{48} +(-2.50000 + 4.33013i) q^{49} +(-0.500000 - 0.866025i) q^{50} -5.46410 q^{51} +(1.23205 - 2.13397i) q^{52} +(6.23205 - 10.7942i) q^{53} +(-2.50000 + 4.33013i) q^{54} +(-0.732051 - 1.26795i) q^{55} +(1.73205 + 3.00000i) q^{56} +(-1.00000 + 1.73205i) q^{57} +(1.00000 - 1.73205i) q^{58} +(-0.732051 + 1.26795i) q^{59} -1.00000 q^{60} +(2.46410 + 4.26795i) q^{61} +(-0.767949 + 1.33013i) q^{62} +6.92820 q^{63} +1.00000 q^{64} +(1.23205 - 2.13397i) q^{65} -1.46410 q^{66} +(-0.535898 - 0.928203i) q^{67} +5.46410 q^{68} +(0.732051 + 1.26795i) q^{69} +(1.73205 + 3.00000i) q^{70} +(-7.46410 - 12.9282i) q^{71} +(1.00000 - 1.73205i) q^{72} +9.46410 q^{73} +(1.00000 - 6.00000i) q^{74} -1.00000 q^{75} +(1.00000 - 1.73205i) q^{76} +(2.53590 + 4.39230i) q^{77} +(-1.23205 - 2.13397i) q^{78} +(0.535898 + 0.928203i) q^{79} +1.00000 q^{80} +(-0.500000 - 0.866025i) q^{81} +1.92820 q^{82} +(8.92820 - 15.4641i) q^{83} +3.46410 q^{84} +5.46410 q^{85} +(-1.96410 + 3.40192i) q^{86} +(-1.00000 - 1.73205i) q^{87} +1.46410 q^{88} +(1.00000 - 1.73205i) q^{89} +(1.00000 - 1.73205i) q^{90} +(-4.26795 + 7.39230i) q^{91} +(-0.732051 - 1.26795i) q^{92} +(0.767949 + 1.33013i) 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} +(1.46410 - 2.53590i) 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} + 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}+ \cdots - 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

Character values

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

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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	0.973494	−	0.228714i	$-0.0734519\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i	−0.684819	+	0.728714i	$0.740119\pi$
$4$	−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	0.981981	+	0.188982i	$0.0605189\pi$
$7$	1.73205	+	3.00000i	0.654654	+	1.13389i	−0.327327	+	0.944911i	$0.606148\pi$
$8$	1.00000			0.353553
$9$	1.00000	−	1.73205i	0.333333	−	0.577350i
$10$	1.00000			0.316228
$11$	1.46410			0.441443			0.220722	−	0.975337i	$-0.429159\pi$
$11$	1.46410			0.441443			0.220722	+	0.975337i	$0.429159\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	1.23205	+	2.13397i	0.341709	+	0.591858i	0.984750	−	0.173974i	$-0.0556608\pi$
$13$	1.23205	+	2.13397i	0.341709	+	0.591858i	−0.643041	+	0.765832i	$0.722327\pi$
$14$	−3.46410			−0.925820
$15$	0.500000	−	0.866025i	0.129099	−	0.223607i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.73205	+	4.73205i	−0.662620	+	1.14769i	0.317305	+	0.948323i	$0.397222\pi$
$17$	−2.73205	+	4.73205i	−0.662620	+	1.14769i	−0.979925	+	0.199367i	$0.936111\pi$
$18$	1.00000	+	1.73205i	0.235702	+	0.408248i
$19$	1.00000	+	1.73205i	0.229416	+	0.397360i	0.957635	−	0.287984i	$-0.0929851\pi$
$19$	1.00000	+	1.73205i	0.229416	+	0.397360i	−0.728219	+	0.685344i	$0.759652\pi$
$20$	−0.500000	+	0.866025i	−0.111803	+	0.193649i
$21$	−1.73205	+	3.00000i	−0.377964	+	0.654654i
$22$	−0.732051	+	1.26795i	−0.156074	+	0.270328i
$23$	1.46410			0.305286			0.152643	−	0.988281i	$-0.451221\pi$
$23$	1.46410			0.305286			0.152643	+	0.988281i	$0.451221\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−2.46410			−0.483250
$27$	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
$31$	1.53590			0.275855			0.137928	−	0.990442i	$-0.455956\pi$
$31$	1.53590			0.275855			0.137928	+	0.990442i	$0.455956\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	0.732051	+	1.26795i	0.127434	+	0.220722i
$34$	−2.73205	−	4.73205i	−0.468543	−	0.811540i
$35$	1.73205	−	3.00000i	0.292770	−	0.507093i
$36$	−2.00000			−0.333333
$37$	−5.69615	+	2.13397i	−0.936442	+	0.350823i
$37$	−5.69615	+	2.13397i	−0.936442	+	0.350823i
$38$	−2.00000			−0.324443
$39$	−1.23205	+	2.13397i	−0.197286	+	0.341709i
$40$	−0.500000	−	0.866025i	−0.0790569	−	0.136931i
$41$	−0.964102	−	1.66987i	−0.150567	−	0.260790i	0.780869	−	0.624695i	$-0.214777\pi$
$41$	−0.964102	−	1.66987i	−0.150567	−	0.260790i	−0.931436	+	0.363905i	$0.881443\pi$
$42$	−1.73205	−	3.00000i	−0.267261	−	0.462910i
$43$	3.92820			0.599045			0.299523	−	0.954089i	$-0.403173\pi$
$43$	3.92820			0.599045			0.299523	+	0.954089i	$0.403173\pi$
$44$	−0.732051	−	1.26795i	−0.110361	−	0.191151i
$45$	−2.00000			−0.298142
$46$	−0.732051	+	1.26795i	−0.107935	+	0.186949i
$47$	−3.46410			−0.505291			−0.252646	−	0.967559i	$-0.581301\pi$
$47$	−3.46410			−0.505291			−0.252646	+	0.967559i	$0.581301\pi$
$48$	−1.00000			−0.144338
$49$	−2.50000	+	4.33013i	−0.357143	+	0.618590i
$50$	−0.500000	−	0.866025i	−0.0707107	−	0.122474i
$51$	−5.46410			−0.765127
$52$	1.23205	−	2.13397i	0.170855	−	0.295929i
$53$	6.23205	−	10.7942i	0.856038	−	1.48270i	−0.0196407	−	0.999807i	$-0.506252\pi$
$53$	6.23205	−	10.7942i	0.856038	−	1.48270i	0.875679	−	0.482894i	$-0.160414\pi$
$54$	−2.50000	+	4.33013i	−0.340207	+	0.589256i
$55$	−0.732051	−	1.26795i	−0.0987097	−	0.170970i
$56$	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
$59$	−0.732051	+	1.26795i	−0.0953049	+	0.165073i	−0.909736	−	0.415188i	$-0.863716\pi$
$59$	−0.732051	+	1.26795i	−0.0953049	+	0.165073i	0.814431	+	0.580261i	$0.197049\pi$
$60$	−1.00000			−0.129099
$61$	2.46410	+	4.26795i	0.315496	+	0.546455i	0.979543	−	0.201236i	$-0.0644958\pi$
$61$	2.46410	+	4.26795i	0.315496	+	0.546455i	−0.664047	+	0.747691i	$0.731162\pi$
$62$	−0.767949	+	1.33013i	−0.0975296	+	0.168926i
$63$	6.92820			0.872872
$64$	1.00000			0.125000
$65$	1.23205	−	2.13397i	0.152817	−	0.264687i
$66$	−1.46410			−0.180218
$67$	−0.535898	−	0.928203i	−0.0654704	−	0.113398i	0.831432	−	0.555626i	$-0.187521\pi$
$67$	−0.535898	−	0.928203i	−0.0654704	−	0.113398i	−0.896903	+	0.442228i	$0.854188\pi$
$68$	5.46410			0.662620
$69$	0.732051	+	1.26795i	0.0881286	+	0.152643i
$70$	1.73205	+	3.00000i	0.207020	+	0.358569i
$71$	−7.46410	−	12.9282i	−0.885826	−	1.53430i	−0.844764	−	0.535139i	$-0.820259\pi$
$71$	−7.46410	−	12.9282i	−0.885826	−	1.53430i	−0.0410618	−	0.999157i	$-0.513074\pi$
$72$	1.00000	−	1.73205i	0.117851	−	0.204124i
$73$	9.46410			1.10769			0.553845	−	0.832620i	$-0.313160\pi$
$73$	9.46410			1.10769			0.553845	+	0.832620i	$0.313160\pi$
$74$	1.00000	−	6.00000i	0.116248	−	0.697486i
$75$	−1.00000			−0.115470
$76$	1.00000	−	1.73205i	0.114708	−	0.198680i
$77$	2.53590	+	4.39230i	0.288992	+	0.500550i
$78$	−1.23205	−	2.13397i	−0.139502	−	0.241625i
$79$	0.535898	+	0.928203i	0.0602933	+	0.104431i	0.894596	−	0.446875i	$-0.147463\pi$
$79$	0.535898	+	0.928203i	0.0602933	+	0.104431i	−0.834303	+	0.551306i	$0.814130\pi$
$80$	1.00000			0.111803
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	1.92820			0.212934
$83$	8.92820	−	15.4641i	0.979998	−	1.69741i	0.317652	−	0.948207i	$-0.397106\pi$
$83$	8.92820	−	15.4641i	0.979998	−	1.69741i	0.662346	−	0.749198i	$-0.269561\pi$
$84$	3.46410			0.377964
$85$	5.46410			0.592665
$86$	−1.96410	+	3.40192i	−0.211795	+	0.366839i
$87$	−1.00000	−	1.73205i	−0.107211	−	0.185695i
$88$	1.46410			0.156074
$89$	1.00000	−	1.73205i	0.106000	−	0.183597i	−0.808146	−	0.588982i	$-0.799529\pi$
$89$	1.00000	−	1.73205i	0.106000	−	0.183597i	0.914146	+	0.405385i	$0.132862\pi$
$90$	1.00000	−	1.73205i	0.105409	−	0.182574i
$91$	−4.26795	+	7.39230i	−0.447403	+	0.774924i
$92$	−0.732051	−	1.26795i	−0.0763216	−	0.132193i
$93$	0.767949	+	1.33013i	0.0796326	+	0.137928i
$94$	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
$99$	1.46410	−	2.53590i	0.147148	−	0.254867i
$100$	1.00000			0.100000
$101$	−2.53590			−0.252331			−0.126166	−	0.992009i	$-0.540267\pi$
$101$	−2.53590			−0.252331			−0.126166	+	0.992009i	$0.540267\pi$
$102$	2.73205	−	4.73205i	0.270513	−	0.468543i
$103$	−6.53590			−0.644001			−0.322001	−	0.946739i	$-0.604355\pi$
$103$	−6.53590			−0.644001			−0.322001	+	0.946739i	$0.604355\pi$
$104$	1.23205	+	2.13397i	0.120813	+	0.209253i
$105$	3.46410			0.338062
$106$	6.23205	+	10.7942i	0.605310	+	1.04843i
$107$	−9.42820	−	16.3301i	−0.911459	−	1.57869i	−0.812005	−	0.583651i	$-0.801624\pi$
$107$	−9.42820	−	16.3301i	−0.911459	−	1.57869i	−0.0994540	−	0.995042i	$-0.531710\pi$
$108$	−2.50000	−	4.33013i	−0.240563	−	0.416667i
$109$	5.00000	−	8.66025i	0.478913	−	0.829502i	−0.520794	−	0.853682i	$-0.674364\pi$
$109$	5.00000	−	8.66025i	0.478913	−	0.829502i	0.999708	+	0.0241802i	$0.00769755\pi$
$110$	1.46410			0.139597
$111$	−4.69615	−	3.86603i	−0.445739	−	0.366947i
$112$	−3.46410			−0.327327
$113$	−5.46410	+	9.46410i	−0.514019	+	0.890308i	0.485848	+	0.874043i	$0.338511\pi$
$113$	−5.46410	+	9.46410i	−0.514019	+	0.890308i	−0.999868	+	0.0162646i	$0.994823\pi$
$114$	−1.00000	−	1.73205i	−0.0936586	−	0.162221i
$115$	−0.732051	−	1.26795i	−0.0682641	−	0.118237i
$116$	1.00000	+	1.73205i	0.0928477	+	0.160817i
$117$	4.92820			0.455613
$118$	−0.732051	−	1.26795i	−0.0673907	−	0.116724i
$119$	−18.9282			−1.73515
$120$	0.500000	−	0.866025i	0.0456435	−	0.0790569i
$121$	−8.85641			−0.805128
$122$	−4.92820			−0.446179
$123$	0.964102	−	1.66987i	0.0869301	−	0.150567i
$124$	−0.767949	−	1.33013i	−0.0689639	−	0.119449i
$125$	1.00000			0.0894427
$126$	−3.46410	+	6.00000i	−0.308607	+	0.534522i
$127$	0.535898	−	0.928203i	0.0475533	−	0.0823647i	−0.841269	−	0.540617i	$-0.818191\pi$
$127$	0.535898	−	0.928203i	0.0475533	−	0.0823647i	0.888822	+	0.458252i	$0.151524\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	1.96410	+	3.40192i	0.172930	+	0.299523i
$130$	1.23205	+	2.13397i	0.108058	+	0.187162i
$131$	6.46410	−	11.1962i	0.564771	−	0.978212i	−0.432300	−	0.901730i	$-0.642298\pi$
$131$	6.46410	−	11.1962i	0.564771	−	0.978212i	0.997071	−	0.0764824i	$-0.0243689\pi$
$132$	0.732051	−	1.26795i	0.0637168	−	0.110361i
$133$	−3.46410	+	6.00000i	−0.300376	+	0.520266i
$134$	1.07180			0.0925891
$135$	−2.50000	−	4.33013i	−0.215166	−	0.372678i
$136$	−2.73205	+	4.73205i	−0.234271	+	0.405770i
$137$	5.46410			0.466830			0.233415	−	0.972377i	$-0.425010\pi$
$137$	5.46410			0.466830			0.233415	+	0.972377i	$0.425010\pi$
$138$	−1.46410			−0.124633
$139$	−2.19615	+	3.80385i	−0.186275	+	0.322638i	−0.944005	−	0.329930i	$-0.892975\pi$
$139$	−2.19615	+	3.80385i	−0.186275	+	0.322638i	0.757730	+	0.652568i	$0.226308\pi$
$140$	−3.46410			−0.292770
$141$	−1.73205	−	3.00000i	−0.145865	−	0.252646i
$142$	14.9282			1.25275
$143$	1.80385	+	3.12436i	0.150845	+	0.261272i
$144$	1.00000	+	1.73205i	0.0833333	+	0.144338i
$145$	1.00000	+	1.73205i	0.0830455	+	0.143839i
$146$	−4.73205	+	8.19615i	−0.391627	+	0.678318i
$147$	−5.00000			−0.412393
$148$	4.69615	+	3.86603i	0.386021	+	0.317785i
$149$	−6.92820			−0.567581			−0.283790	−	0.958886i	$-0.591592\pi$
$149$	−6.92820			−0.567581			−0.283790	+	0.958886i	$0.591592\pi$
$150$	0.500000	−	0.866025i	0.0408248	−	0.0707107i
$151$	7.69615	+	13.3301i	0.626304	+	1.08479i	0.988287	+	0.152606i	$0.0487665\pi$
$151$	7.69615	+	13.3301i	0.626304	+	1.08479i	−0.361983	+	0.932185i	$0.617900\pi$
$152$	1.00000	+	1.73205i	0.0811107	+	0.140488i
$153$	5.46410	+	9.46410i	0.441746	+	0.765127i
$154$	−5.07180			−0.408697
$155$	−0.767949	−	1.33013i	−0.0616832	−	0.106838i
$156$	2.46410			0.197286
$157$	−9.16025	+	15.8660i	−0.731068	+	1.26625i	0.225359	+	0.974276i	$0.427644\pi$
$157$	−9.16025	+	15.8660i	−0.731068	+	1.26625i	−0.956427	+	0.291971i	$0.905689\pi$
$158$	−1.07180			−0.0852676
$159$	12.4641			0.988468
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$	2.53590	+	4.39230i	0.199857	+	0.346162i
$162$	1.00000			0.0785674
$163$	8.42820	−	14.5981i	0.660148	−	1.14341i	−0.320429	−	0.947273i	$-0.603827\pi$
$163$	8.42820	−	14.5981i	0.660148	−	1.14341i	0.980577	−	0.196137i	$-0.0628397\pi$
$164$	−0.964102	+	1.66987i	−0.0752837	+	0.130395i
$165$	0.732051	−	1.26795i	0.0569901	−	0.0987097i
$166$	8.92820	+	15.4641i	0.692963	+	1.20025i
$167$	1.53590	+	2.66025i	0.118851	+	0.205857i	0.919313	−	0.393528i	$-0.128745\pi$
$167$	1.53590	+	2.66025i	0.118851	+	0.205857i	−0.800461	+	0.599384i	$0.795412\pi$
$168$	−1.73205	+	3.00000i	−0.133631	+	0.231455i
$169$	3.46410	−	6.00000i	0.266469	−	0.461538i
$170$	−2.73205	+	4.73205i	−0.209539	+	0.362932i
$171$	4.00000			0.305888
$172$	−1.96410	−	3.40192i	−0.149761	−	0.259394i
$173$	−5.92820	+	10.2679i	−0.450713	+	0.780658i	−0.998430	−	0.0560056i	$-0.982164\pi$
$173$	−5.92820	+	10.2679i	−0.450713	+	0.780658i	0.547718	+	0.836663i	$0.315497\pi$
$174$	2.00000			0.151620
$175$	−3.46410			−0.261861
$176$	−0.732051	+	1.26795i	−0.0551804	+	0.0955753i
$177$	−1.46410			−0.110049
$178$	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
$181$	−8.26795	−	14.3205i	−0.614552	−	1.06443i	−0.990463	−	0.137779i	$-0.956004\pi$
$181$	−8.26795	−	14.3205i	−0.614552	−	1.06443i	0.375911	−	0.926656i	$-0.377330\pi$
$182$	−4.26795	−	7.39230i	−0.316361	−	0.547954i
$183$	−2.46410	+	4.26795i	−0.182152	+	0.315496i
$184$	1.46410			0.107935
$185$	4.69615	+	3.86603i	0.345268	+	0.284236i
$186$	−1.53590			−0.112618
$187$	−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
$191$	−24.3205			−1.75977			−0.879885	−	0.475186i	$-0.842381\pi$
$191$	−24.3205			−1.75977			−0.879885	+	0.475186i	$0.842381\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	−20.3923			−1.46787			−0.733935	−	0.679220i	$-0.762318\pi$
$193$	−20.3923			−1.46787			−0.733935	+	0.679220i	$0.762318\pi$
$194$	1.00000	−	1.73205i	0.0717958	−	0.124354i
$195$	2.46410			0.176458
$196$	5.00000			0.357143
$197$	−9.16025	+	15.8660i	−0.652641	+	1.13041i	0.329839	+	0.944037i	$0.393006\pi$
$197$	−9.16025	+	15.8660i	−0.652641	+	1.13041i	−0.982480	+	0.186370i	$0.940328\pi$
$198$	1.46410	+	2.53590i	0.104049	+	0.180218i
$199$	−7.53590			−0.534206			−0.267103	−	0.963668i	$-0.586066\pi$
$199$	−7.53590			−0.534206			−0.267103	+	0.963668i	$0.586066\pi$
$200$	−0.500000	+	0.866025i	−0.0353553	+	0.0612372i
$201$	0.535898	−	0.928203i	0.0377994	−	0.0654704i
$202$	1.26795	−	2.19615i	0.0892126	−	0.154521i
$203$	−3.46410	−	6.00000i	−0.243132	−	0.421117i
$204$	2.73205	+	4.73205i	0.191282	+	0.331310i
$205$	−0.964102	+	1.66987i	−0.0673358	+	0.116629i
$206$	3.26795	−	5.66025i	0.227689	−	0.394369i
$207$	1.46410	−	2.53590i	0.101762	−	0.176257i
$208$	−2.46410			−0.170855
$209$	1.46410	+	2.53590i	0.101274	+	0.175412i
$210$	−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	$0.339947\pi$
$212$	−12.4641			−0.856038
$213$	7.46410	−	12.9282i	0.511432	−	0.885826i
$214$	18.8564			1.28900
$215$	−1.96410	−	3.40192i	−0.133951	−	0.232009i
$216$	5.00000			0.340207
$217$	2.66025	+	4.60770i	0.180590	+	0.312791i
$218$	5.00000	+	8.66025i	0.338643	+	0.586546i
$219$	4.73205	+	8.19615i	0.319762	+	0.553845i
$220$	−0.732051	+	1.26795i	−0.0493549	+	0.0854851i
$221$	−13.4641			−0.905693
$222$	5.69615	−	2.13397i	0.382301	−	0.143223i
$223$	−11.3205			−0.758077			−0.379039	−	0.925381i	$-0.623745\pi$
$223$	−11.3205			−0.758077			−0.379039	+	0.925381i	$0.623745\pi$
$224$	1.73205	−	3.00000i	0.115728	−	0.200446i
$225$	1.00000	+	1.73205i	0.0666667	+	0.115470i
$226$	−5.46410	−	9.46410i	−0.363467	−	0.629543i
$227$	6.96410	+	12.0622i	0.462224	+	0.800595i	0.999071	−	0.0430843i	$-0.0137184\pi$
$227$	6.96410	+	12.0622i	0.462224	+	0.800595i	−0.536848	+	0.843679i	$0.680385\pi$
$228$	2.00000			0.132453
$229$	2.80385	+	4.85641i	0.185283	+	0.320920i	0.943672	−	0.330882i	$-0.107346\pi$
$229$	2.80385	+	4.85641i	0.185283	+	0.320920i	−0.758389	+	0.651803i	$0.774013\pi$
$230$	1.46410			0.0965400
$231$	−2.53590	+	4.39230i	−0.166850	+	0.288992i
$232$	−2.00000			−0.131306
$233$	−30.3923			−1.99107			−0.995533	−	0.0944137i	$-0.969902\pi$
$233$	−30.3923			−1.99107			−0.995533	+	0.0944137i	$0.969902\pi$
$234$	−2.46410	+	4.26795i	−0.161083	+	0.279005i
$235$	1.73205	+	3.00000i	0.112987	+	0.195698i
$236$	1.46410			0.0953049
$237$	−0.535898	+	0.928203i	−0.0348103	+	0.0602933i
$238$	9.46410	−	16.3923i	0.613467	−	1.06256i
$239$	−13.4641	+	23.3205i	−0.870920	+	1.50848i	−0.00987430	+	0.999951i	$0.503143\pi$
$239$	−13.4641	+	23.3205i	−0.870920	+	1.50848i	−0.861046	+	0.508527i	$0.830190\pi$
$240$	0.500000	+	0.866025i	0.0322749	+	0.0559017i
$241$	1.00000	+	1.73205i	0.0644157	+	0.111571i	0.896435	−	0.443176i	$-0.146148\pi$
$241$	1.00000	+	1.73205i	0.0644157	+	0.111571i	−0.832019	+	0.554747i	$0.812815\pi$
$242$	4.42820	−	7.66987i	0.284656	−	0.493038i
$243$	8.00000	−	13.8564i	0.513200	−	0.888889i
$244$	2.46410	−	4.26795i	0.157748	−	0.273227i
$245$	5.00000			0.319438
$246$	0.964102	+	1.66987i	0.0614689	+	0.106467i
$247$	−2.46410	+	4.26795i	−0.156787	+	0.271563i
$248$	1.53590			0.0975296
$249$	17.8564			1.13160
$250$	−0.500000	+	0.866025i	−0.0316228	+	0.0547723i
$251$	0.928203			0.0585877			0.0292938	−	0.999571i	$-0.490674\pi$
$251$	0.928203			0.0585877			0.0292938	+	0.999571i	$0.490674\pi$
$252$	−3.46410	−	6.00000i	−0.218218	−	0.377964i
$253$	2.14359			0.134767
$254$	0.535898	+	0.928203i	0.0336253	+	0.0582407i
$255$	2.73205	+	4.73205i	0.171088	+	0.296333i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	9.73205	−	16.8564i	0.607069	−	1.05147i	−0.384652	−	0.923062i	$-0.625679\pi$
$257$	9.73205	−	16.8564i	0.607069	−	1.05147i	0.991721	−	0.128412i	$-0.0409880\pi$
$258$	−3.92820			−0.244559
$259$	−16.2679	−	13.3923i	−1.01084	−	0.832157i
$260$	−2.46410			−0.152817
$261$	−2.00000	+	3.46410i	−0.123797	+	0.214423i
$262$	6.46410	+	11.1962i	0.399354	+	0.691701i
$263$	7.19615	+	12.4641i	0.443734	+	0.768569i	0.997963	−	0.0637946i	$-0.0203203\pi$
$263$	7.19615	+	12.4641i	0.443734	+	0.768569i	−0.554229	+	0.832364i	$0.686987\pi$
$264$	0.732051	+	1.26795i	0.0450546	+	0.0780369i
$265$	−12.4641			−0.765664
$266$	−3.46410	−	6.00000i	−0.212398	−	0.367884i
$267$	2.00000			0.122398
$268$	−0.535898	+	0.928203i	−0.0327352	+	0.0566990i
$269$	8.39230			0.511688			0.255844	−	0.966718i	$-0.417647\pi$
$269$	8.39230			0.511688			0.255844	+	0.966718i	$0.417647\pi$
$270$	5.00000			0.304290
$271$	15.6244	−	27.0622i	0.949112	−	1.64391i	0.201811	−	0.979424i	$-0.435317\pi$
$271$	15.6244	−	27.0622i	0.949112	−	1.64391i	0.747301	−	0.664486i	$-0.231349\pi$
$272$	−2.73205	−	4.73205i	−0.165655	−	0.286923i
$273$	−8.53590			−0.516616
$274$	−2.73205	+	4.73205i	−0.165049	+	0.285874i
$275$	−0.732051	+	1.26795i	−0.0441443	+	0.0764602i
$276$	0.732051	−	1.26795i	0.0440643	−	0.0763216i
$277$	12.7679	+	22.1147i	0.767152	+	1.32875i	0.939101	+	0.343640i	$0.111660\pi$
$277$	12.7679	+	22.1147i	0.767152	+	1.32875i	−0.171950	+	0.985106i	$0.555007\pi$
$278$	−2.19615	−	3.80385i	−0.131716	−	0.228140i
$279$	1.53590	−	2.66025i	0.0919518	−	0.159265i
$280$	1.73205	−	3.00000i	0.103510	−	0.179284i
$281$	13.3564	−	23.1340i	0.796776	−	1.38006i	−0.124929	−	0.992166i	$-0.539870\pi$
$281$	13.3564	−	23.1340i	0.796776	−	1.38006i	0.921705	−	0.387891i	$-0.126796\pi$
$282$	3.46410			0.206284
$283$	−10.9641	−	18.9904i	−0.651748	−	1.12886i	−0.982698	−	0.185213i	$-0.940703\pi$
$283$	−10.9641	−	18.9904i	−0.651748	−	1.12886i	0.330950	−	0.943648i	$-0.392631\pi$
$284$	−7.46410	+	12.9282i	−0.442913	+	0.767148i
$285$	2.00000			0.118470
$286$	−3.60770			−0.213327
$287$	3.33975	−	5.78461i	0.197139	−	0.341455i
$288$	−2.00000			−0.117851
$289$	−6.42820	−	11.1340i	−0.378130	−	0.654940i
$290$	−2.00000			−0.117444
$291$	−1.00000	−	1.73205i	−0.0586210	−	0.101535i
$292$	−4.73205	−	8.19615i	−0.276922	−	0.479644i
$293$	3.23205	+	5.59808i	0.188818	+	0.327043i	0.944857	−	0.327484i	$-0.106201\pi$
$293$	3.23205	+	5.59808i	0.188818	+	0.327043i	−0.756038	+	0.654528i	$0.772868\pi$
$294$	2.50000	−	4.33013i	0.145803	−	0.252538i
$295$	1.46410			0.0852433
$296$	−5.69615	+	2.13397i	−0.331082	+	0.124035i
$297$	7.32051			0.424779
$298$	3.46410	−	6.00000i	0.200670	−	0.347571i
$299$	1.80385	+	3.12436i	0.104319	+	0.180686i
$300$	0.500000	+	0.866025i	0.0288675	+	0.0500000i
$301$	6.80385	+	11.7846i	0.392167	+	0.679254i
$302$	−15.3923			−0.885728
$303$	−1.26795	−	2.19615i	−0.0728418	−	0.126166i
$304$	−2.00000			−0.114708
$305$	2.46410	−	4.26795i	0.141094	−	0.244382i
$306$	−10.9282			−0.624724
$307$	16.8564			0.962046			0.481023	−	0.876708i	$-0.340265\pi$
$307$	16.8564			0.962046			0.481023	+	0.876708i	$0.340265\pi$
$308$	2.53590	−	4.39230i	0.144496	−	0.250275i
$309$	−3.26795	−	5.66025i	−0.185907	−	0.322001i
$310$	1.53590			0.0872332
$311$	2.76795	−	4.79423i	0.156956	−	0.271856i	−0.776814	−	0.629731i	$-0.783165\pi$
$311$	2.76795	−	4.79423i	0.156956	−	0.271856i	0.933770	+	0.357875i	$0.116499\pi$
$312$	−1.23205	+	2.13397i	−0.0697511	+	0.120813i
$313$	2.46410	−	4.26795i	0.139279	−	0.241239i	−0.787945	−	0.615746i	$-0.788855\pi$
$313$	2.46410	−	4.26795i	0.139279	−	0.241239i	0.927224	+	0.374507i	$0.122188\pi$
$314$	−9.16025	−	15.8660i	−0.516943	−	0.895372i
$315$	−3.46410	−	6.00000i	−0.195180	−	0.338062i
$316$	0.535898	−	0.928203i	0.0301466	−	0.0522155i
$317$	12.2321	−	21.1865i	0.687020	−	1.18995i	−0.285777	−	0.958296i	$-0.592252\pi$
$317$	12.2321	−	21.1865i	0.687020	−	1.18995i	0.972797	−	0.231658i	$-0.0744151\pi$
$318$	−6.23205	+	10.7942i	−0.349476	+	0.605310i
$319$	−2.92820			−0.163948
$320$	−0.500000	−	0.866025i	−0.0279508	−	0.0484123i
$321$	9.42820	−	16.3301i	0.526231	−	0.911459i
$322$	−5.07180			−0.282640
$323$	−10.9282			−0.608061
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	−2.46410			−0.136684
$326$	8.42820	+	14.5981i	0.466795	+	0.808513i
$327$	10.0000			0.553001
$328$	−0.964102	−	1.66987i	−0.0532336	−	0.0922033i
$329$	−6.00000	−	10.3923i	−0.330791	−	0.572946i
$330$	0.732051	+	1.26795i	0.0402981	+	0.0697983i
$331$	6.12436	−	10.6077i	0.336625	−	0.583052i	−0.647171	−	0.762345i	$-0.724048\pi$
$331$	6.12436	−	10.6077i	0.336625	−	0.583052i	0.983796	+	0.179294i	$0.0573812\pi$
$332$	−17.8564			−0.979998
$333$	−2.00000	+	12.0000i	−0.109599	+	0.657596i
$334$	−3.07180			−0.168081
$335$	−0.535898	+	0.928203i	−0.0292793	+	0.0507132i
$336$	−1.73205	−	3.00000i	−0.0944911	−	0.163663i
$337$	2.46410	+	4.26795i	0.134228	+	0.232490i	0.925302	−	0.379230i	$-0.123811\pi$
$337$	2.46410	+	4.26795i	0.134228	+	0.232490i	−0.791074	+	0.611720i	$0.790478\pi$
$338$	3.46410	+	6.00000i	0.188422	+	0.326357i
$339$	−10.9282			−0.593539
$340$	−2.73205	−	4.73205i	−0.148166	−	0.256631i
$341$	2.24871			0.121775
$342$	−2.00000	+	3.46410i	−0.108148	+	0.187317i
$343$	6.92820			0.374088
$344$	3.92820			0.211795
$345$	0.732051	−	1.26795i	0.0394123	−	0.0682641i
$346$	−5.92820	−	10.2679i	−0.318702	−	0.552008i
$347$	−17.0718			−0.916462			−0.458231	−	0.888833i	$-0.651517\pi$
$347$	−17.0718			−0.916462			−0.458231	+	0.888833i	$0.651517\pi$
$348$	−1.00000	+	1.73205i	−0.0536056	+	0.0928477i
$349$	15.3923	−	26.6603i	0.823931	−	1.42709i	−0.0788022	−	0.996890i	$-0.525110\pi$
$349$	15.3923	−	26.6603i	0.823931	−	1.42709i	0.902733	−	0.430200i	$-0.141557\pi$
$350$	1.73205	−	3.00000i	0.0925820	−	0.160357i
$351$	6.16025	+	10.6699i	0.328810	+	0.569516i
$352$	−0.732051	−	1.26795i	−0.0390184	−	0.0675819i
$353$	−18.6603	+	32.3205i	−0.993185	+	1.72025i	−0.395659	+	0.918397i	$0.629484\pi$
$353$	−18.6603	+	32.3205i	−0.993185	+	1.72025i	−0.597526	+	0.801850i	$0.703849\pi$
$354$	0.732051	−	1.26795i	0.0389081	−	0.0673907i
$355$	−7.46410	+	12.9282i	−0.396153	+	0.686158i
$356$	−2.00000			−0.106000
$357$	−9.46410	−	16.3923i	−0.500893	−	0.867573i
$358$	−6.00000	+	10.3923i	−0.317110	+	0.549250i
$359$	−2.46410			−0.130050			−0.0650252	−	0.997884i	$-0.520713\pi$
$359$	−2.46410			−0.130050			−0.0650252	+	0.997884i	$0.520713\pi$
$360$	−2.00000			−0.105409
$361$	7.50000	−	12.9904i	0.394737	−	0.683704i
$362$	16.5359			0.869108
$363$	−4.42820	−	7.66987i	−0.232420	−	0.402564i
$364$	8.53590			0.447403
$365$	−4.73205	−	8.19615i	−0.247687	−	0.429006i
$366$	−2.46410	−	4.26795i	−0.128801	−	0.223089i
$367$	15.3923	+	26.6603i	0.803472	+	1.39165i	0.917318	+	0.398156i	$0.130350\pi$
$367$	15.3923	+	26.6603i	0.803472	+	1.39165i	−0.113846	+	0.993498i	$0.536317\pi$
$368$	−0.732051	+	1.26795i	−0.0381608	+	0.0660964i
$369$	−3.85641			−0.200757
$370$	−5.69615	+	2.13397i	−0.296129	+	0.110940i
$371$	43.1769			2.24163
$372$	0.767949	−	1.33013i	0.0398163	−	0.0689639i
$373$	15.7679	+	27.3109i	0.816433	+	1.41410i	0.908294	+	0.418332i	$0.137385\pi$
$373$	15.7679	+	27.3109i	0.816433	+	1.41410i	−0.0918606	+	0.995772i	$0.529281\pi$
$374$	−4.00000	−	6.92820i	−0.206835	−	0.358249i
$375$	0.500000	+	0.866025i	0.0258199	+	0.0447214i
$376$	−3.46410			−0.178647
$377$	−2.46410	−	4.26795i	−0.126908	−	0.219811i
$378$	−17.3205			−0.890871
$379$	1.80385	−	3.12436i	0.0926574	−	0.160487i	−0.815971	−	0.578093i	$-0.803797\pi$
$379$	1.80385	−	3.12436i	0.0926574	−	0.160487i	0.908629	+	0.417605i	$0.137131\pi$
$380$	−2.00000			−0.102598
$381$	1.07180			0.0549098
$382$	12.1603	−	21.0622i	0.622173	−	1.07763i
$383$	−3.73205	−	6.46410i	−0.190699	−	0.330300i	0.754783	−	0.655974i	$-0.227742\pi$
$383$	−3.73205	−	6.46410i	−0.190699	−	0.330300i	−0.945482	+	0.325674i	$0.894409\pi$
$384$	−1.00000			−0.0510310
$385$	2.53590	−	4.39230i	0.129241	−	0.223853i
$386$	10.1962	−	17.6603i	0.518970	−	0.898883i
$387$	3.92820	−	6.80385i	0.199682	−	0.345859i
$388$	1.00000	+	1.73205i	0.0507673	+	0.0879316i
$389$	15.8564	+	27.4641i	0.803952	+	1.39249i	0.916996	+	0.398895i	$0.130606\pi$
$389$	15.8564	+	27.4641i	0.803952	+	1.39249i	−0.113045	+	0.993590i	$0.536060\pi$
$390$	−1.23205	+	2.13397i	−0.0623873	+	0.108058i
$391$	−4.00000	+	6.92820i	−0.202289	+	0.350374i
$392$	−2.50000	+	4.33013i	−0.126269	+	0.218704i
$393$	12.9282			0.652142
$394$	−9.16025	−	15.8660i	−0.461487	−	0.799319i
$395$	0.535898	−	0.928203i	0.0269640	−	0.0467030i
$396$	−2.92820			−0.147148
$397$	2.46410			0.123670			0.0618349	−	0.998086i	$-0.480305\pi$
$397$	2.46410			0.123670			0.0618349	+	0.998086i	$0.480305\pi$
$398$	3.76795	−	6.52628i	0.188870	−	0.327133i
$399$	−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	$0.314889\pi$
$402$	0.535898	+	0.928203i	0.0267282	+	0.0462946i
$403$	1.89230	+	3.27757i	0.0942624	+	0.163267i
$404$	1.26795	+	2.19615i	0.0630828	+	0.109263i
$405$	−0.500000	+	0.866025i	−0.0248452	+	0.0430331i
$406$	6.92820			0.343841
$407$	−8.33975	+	3.12436i	−0.413386	+	0.154869i
$408$	−5.46410			−0.270513
$409$	5.50000	−	9.52628i	0.271957	−	0.471044i	−0.697406	−	0.716677i	$-0.745662\pi$
$409$	5.50000	−	9.52628i	0.271957	−	0.471044i	0.969363	+	0.245633i	$0.0789957\pi$
$410$	−0.964102	−	1.66987i	−0.0476136	−	0.0824691i
$411$	2.73205	+	4.73205i	0.134762	+	0.233415i
$412$	3.26795	+	5.66025i	0.161000	+	0.278861i
$413$	−5.07180			−0.249567
$414$	1.46410	+	2.53590i	0.0719567	+	0.124633i
$415$	−17.8564			−0.876537
$416$	1.23205	−	2.13397i	0.0604063	−	0.104627i
$417$	−4.39230			−0.215092
$418$	−2.92820			−0.143223
$419$	0.732051	−	1.26795i	0.0357630	−	0.0619434i	−0.847590	−	0.530652i	$-0.821947\pi$
$419$	0.732051	−	1.26795i	0.0357630	−	0.0619434i	0.883353	+	0.468708i	$0.155281\pi$
$420$	−1.73205	−	3.00000i	−0.0845154	−	0.146385i
$421$	−37.3205			−1.81889			−0.909445	−	0.415824i	$-0.863493\pi$
$421$	−37.3205			−1.81889			−0.909445	+	0.415824i	$0.863493\pi$
$422$	−7.00000	+	12.1244i	−0.340755	+	0.590204i
$423$	−3.46410	+	6.00000i	−0.168430	+	0.291730i
$424$	6.23205	−	10.7942i	0.302655	−	0.524214i
$425$	−2.73205	−	4.73205i	−0.132524	−	0.229538i
$426$	7.46410	+	12.9282i	0.361637	+	0.626373i
$427$	−8.53590	+	14.7846i	−0.413081	+	0.715477i
$428$	−9.42820	+	16.3301i	−0.455729	+	0.789346i
$429$	−1.80385	+	3.12436i	−0.0870906	+	0.150845i
$430$	3.92820			0.189435
$431$	−6.23205	−	10.7942i	−0.300187	−	0.519940i	0.675991	−	0.736910i	$-0.263716\pi$
$431$	−6.23205	−	10.7942i	−0.300187	−	0.519940i	−0.976178	+	0.216970i	$0.930383\pi$
$432$	−2.50000	+	4.33013i	−0.120281	+	0.208333i
$433$	−31.7128			−1.52402			−0.762010	−	0.647565i	$-0.775787\pi$
$433$	−31.7128			−1.52402			−0.762010	+	0.647565i	$0.775787\pi$
$434$	−5.32051			−0.255393
$435$	−1.00000	+	1.73205i	−0.0479463	+	0.0830455i
$436$	−10.0000			−0.478913
$437$	1.46410	+	2.53590i	0.0700375	+	0.121308i
$438$	−9.46410			−0.452212
$439$	−9.23205	−	15.9904i	−0.440622	−	0.763179i	0.557114	−	0.830436i	$-0.311909\pi$
$439$	−9.23205	−	15.9904i	−0.440622	−	0.763179i	−0.997736	+	0.0672568i	$0.978575\pi$
$440$	−0.732051	−	1.26795i	−0.0348992	−	0.0604471i
$441$	5.00000	+	8.66025i	0.238095	+	0.412393i
$442$	6.73205	−	11.6603i	0.320211	−	0.554622i
$443$	27.9282			1.32691			0.663454	−	0.748217i	$-0.269090\pi$
$443$	27.9282			1.32691			0.663454	+	0.748217i	$0.269090\pi$
$444$	−1.00000	+	6.00000i	−0.0474579	+	0.284747i
$445$	−2.00000			−0.0948091
$446$	5.66025	−	9.80385i	0.268021	−	0.464226i
$447$	−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	0.986937	−	0.161106i	$-0.0515060\pi$
$449$	7.50000	+	12.9904i	0.353947	+	0.613054i	−0.632990	+	0.774160i	$0.718173\pi$
$450$	−2.00000			−0.0942809
$451$	−1.41154	−	2.44486i	−0.0664670	−	0.115124i
$452$	10.9282			0.514019
$453$	−7.69615	+	13.3301i	−0.361597	+	0.626304i
$454$	−13.9282			−0.653683
$455$	8.53590			0.400169
$456$	−1.00000	+	1.73205i	−0.0468293	+	0.0811107i
$457$	−12.9282	−	22.3923i	−0.604756	−	1.04747i	−0.992090	−	0.125528i	$-0.959937\pi$
$457$	−12.9282	−	22.3923i	−0.604756	−	1.04747i	0.387334	−	0.921939i	$-0.373396\pi$
$458$	−5.60770			−0.262030
$459$	−13.6603	+	23.6603i	−0.637606	+	1.10437i
$460$	−0.732051	+	1.26795i	−0.0341320	+	0.0591184i
$461$	−0.464102	+	0.803848i	−0.0216154	+	0.0374389i	−0.876631	−	0.481164i	$-0.840214\pi$
$461$	−0.464102	+	0.803848i	−0.0216154	+	0.0374389i	0.855015	+	0.518603i	$0.173548\pi$
$462$	−2.53590	−	4.39230i	−0.117981	−	0.204349i
$463$	3.46410	+	6.00000i	0.160990	+	0.278844i	0.935224	−	0.354056i	$-0.115198\pi$
$463$	3.46410	+	6.00000i	0.160990	+	0.278844i	−0.774234	+	0.632900i	$0.781864\pi$
$464$	1.00000	−	1.73205i	0.0464238	−	0.0804084i
$465$	0.767949	−	1.33013i	0.0356128	−	0.0616832i
$466$	15.1962	−	26.3205i	0.703948	−	1.21927i
$467$	3.00000			0.138823			0.0694117	−	0.997588i	$-0.477888\pi$
$467$	3.00000			0.138823			0.0694117	+	0.997588i	$0.477888\pi$
$468$	−2.46410	−	4.26795i	−0.113903	−	0.197286i
$469$	1.85641	−	3.21539i	0.0857209	−	0.148473i
$470$	−3.46410			−0.159787
$471$	−18.3205			−0.844164
$472$	−0.732051	+	1.26795i	−0.0336954	+	0.0583621i
$473$	5.75129			0.264445
$474$	−0.535898	−	0.928203i	−0.0246146	−	0.0426338i
$475$	−2.00000			−0.0917663
$476$	9.46410	+	16.3923i	0.433786	+	0.751340i
$477$	−12.4641	−	21.5885i	−0.570692	−	0.988468i
$478$	−13.4641	−	23.3205i	−0.615834	−	1.06666i
$479$	1.83975	−	3.18653i	0.0840601	−	0.145596i	−0.820930	−	0.571029i	$-0.806545\pi$
$479$	1.83975	−	3.18653i	0.0840601	−	0.145596i	0.904990	+	0.425432i	$0.139878\pi$
$480$	−1.00000			−0.0456435
$481$	−11.5718	−	9.52628i	−0.527629	−	0.434361i
$482$	−2.00000			−0.0910975
$483$	−2.53590	+	4.39230i	−0.115387	+	0.199857i
$484$	4.42820	+	7.66987i	0.201282	+	0.348631i
$485$	1.00000	+	1.73205i	0.0454077	+	0.0786484i
$486$	8.00000	+	13.8564i	0.362887	+	0.628539i
$487$	−0.928203			−0.0420609			−0.0210305	−	0.999779i	$-0.506695\pi$
$487$	−0.928203			−0.0420609			−0.0210305	+	0.999779i	$0.506695\pi$
$488$	2.46410	+	4.26795i	0.111545	+	0.193201i
$489$	16.8564			0.762273
$490$	−2.50000	+	4.33013i	−0.112938	+	0.195615i
$491$	34.2487			1.54562			0.772811	−	0.634636i	$-0.218850\pi$
$491$	34.2487			1.54562			0.772811	+	0.634636i	$0.218850\pi$
$492$	−1.92820			−0.0869301
$493$	5.46410	−	9.46410i	0.246091	−	0.426242i
$494$	−2.46410	−	4.26795i	−0.110865	−	0.192024i
$495$	−2.92820			−0.131613
$496$	−0.767949	+	1.33013i	−0.0344819	+	0.0597245i
$497$	25.8564	−	44.7846i	1.15982	−	2.00886i
$498$	−8.92820	+	15.4641i	−0.400082	+	0.692963i
$499$	−5.46410	−	9.46410i	−0.244607	−	0.423671i	0.717414	−	0.696647i	$-0.245326\pi$
$499$	−5.46410	−	9.46410i	−0.244607	−	0.423671i	−0.962021	+	0.272975i	$0.911992\pi$
$500$	−0.500000	−	0.866025i	−0.0223607	−	0.0387298i
$501$	−1.53590	+	2.66025i	−0.0686189	+	0.118851i
$502$	−0.464102	+	0.803848i	−0.0207139	+	0.0358775i
$503$	−14.6603	+	25.3923i	−0.653668	+	1.13219i	0.328557	+	0.944484i	$0.393438\pi$
$503$	−14.6603	+	25.3923i	−0.653668	+	1.13219i	−0.982226	+	0.187703i	$0.939896\pi$
$504$	6.92820			0.308607
$505$	1.26795	+	2.19615i	0.0564230	+	0.0977275i
$506$	−1.07180	+	1.85641i	−0.0476472	+	0.0825273i
$507$	6.92820			0.307692
$508$	−1.07180			−0.0475533
$509$	0.660254	−	1.14359i	0.0292652	−	0.0506889i	−0.851022	−	0.525130i	$-0.824017\pi$
$509$	0.660254	−	1.14359i	0.0292652	−	0.0506889i	0.880287	+	0.474441i	$0.157350\pi$
$510$	−5.46410			−0.241954
$511$	16.3923	+	28.3923i	0.725153	+	1.25600i
$512$	1.00000			0.0441942
$513$	5.00000	+	8.66025i	0.220755	+	0.382360i
$514$	9.73205	+	16.8564i	0.429262	+	0.743504i
$515$	3.26795	+	5.66025i	0.144003	+	0.249421i
$516$	1.96410	−	3.40192i	0.0864648	−	0.149761i
$517$	−5.07180			−0.223057
$518$	19.7321	−	7.39230i	0.866977	−	0.324799i
$519$	−11.8564			−0.520438
$520$	1.23205	−	2.13397i	0.0540290	−	0.0935810i
$521$	15.3564	+	26.5981i	0.672776	+	1.16528i	0.977114	+	0.212718i	$0.0682317\pi$
$521$	15.3564	+	26.5981i	0.672776	+	1.16528i	−0.304337	+	0.952564i	$0.598435\pi$
$522$	−2.00000	−	3.46410i	−0.0875376	−	0.151620i
$523$	21.8923	+	37.9186i	0.957284	+	1.65806i	0.729054	+	0.684457i	$0.239961\pi$
$523$	21.8923	+	37.9186i	0.957284	+	1.65806i	0.228230	+	0.973607i	$0.426706\pi$
$524$	−12.9282			−0.564771
$525$	−1.73205	−	3.00000i	−0.0755929	−	0.130931i
$526$	−14.3923			−0.627534
$527$	−4.19615	+	7.26795i	−0.182787	+	0.316597i
$528$	−1.46410			−0.0637168
$529$	−20.8564			−0.906800
$530$	6.23205	−	10.7942i	0.270703	−	0.468871i
$531$	1.46410	+	2.53590i	0.0635366	+	0.110049i
$532$	6.92820			0.300376
$533$	2.37564	−	4.11474i	0.102901	−	0.178229i
$534$	−1.00000	+	1.73205i	−0.0432742	+	0.0749532i
$535$	−9.42820	+	16.3301i	−0.407617	+	0.706013i
$536$	−0.535898	−	0.928203i	−0.0231473	−	0.0400923i
$537$	6.00000	+	10.3923i	0.258919	+	0.448461i
$538$	−4.19615	+	7.26795i	−0.180909	+	0.313344i
$539$	−3.66025	+	6.33975i	−0.157658	+	0.273072i
$540$	−2.50000	+	4.33013i	−0.107583	+	0.186339i
$541$	−38.7846			−1.66748			−0.833740	−	0.552157i	$-0.813805\pi$
$541$	−38.7846			−1.66748			−0.833740	+	0.552157i	$0.813805\pi$
$542$	15.6244	+	27.0622i	0.671124	+	1.16242i
$543$	8.26795	−	14.3205i	0.354812	−	0.614552i
$544$	5.46410			0.234271
$545$	−10.0000			−0.428353
$546$	4.26795	−	7.39230i	0.182651	−	0.316361i
$547$	41.9282			1.79272			0.896360	−	0.443326i	$-0.146202\pi$
$547$	41.9282			1.79272			0.896360	+	0.443326i	$0.146202\pi$
$548$	−2.73205	−	4.73205i	−0.116707	−	0.202143i
$549$	9.85641			0.420661
$550$	−0.732051	−	1.26795i	−0.0312148	−	0.0540655i
$551$	−2.00000	−	3.46410i	−0.0852029	−	0.147576i
$552$	0.732051	+	1.26795i	0.0311582	+	0.0539675i
$553$	−1.85641	+	3.21539i	−0.0789424	+	0.136732i
$554$	−25.5359			−1.08492
$555$	−1.00000	+	6.00000i	−0.0424476	+	0.254686i
$556$	4.39230			0.186275
$557$	−1.83975	+	3.18653i	−0.0779525	+	0.135018i	−0.902366	−	0.430970i	$-0.858172\pi$
$557$	−1.83975	+	3.18653i	−0.0779525	+	0.135018i	0.824414	+	0.565987i	$0.191505\pi$
$558$	1.53590	+	2.66025i	0.0650198	+	0.112618i
$559$	4.83975	+	8.38269i	0.204699	+	0.354550i
$560$	1.73205	+	3.00000i	0.0731925	+	0.126773i
$561$	−8.00000			−0.337760
$562$	13.3564	+	23.1340i	0.563406	+	0.975848i
$563$	25.8564			1.08972			0.544859	−	0.838528i	$-0.316583\pi$
$563$	25.8564			1.08972			0.544859	+	0.838528i	$0.316583\pi$
$564$	−1.73205	+	3.00000i	−0.0729325	+	0.126323i
$565$	10.9282			0.459753
$566$	21.9282			0.921711
$567$	1.73205	−	3.00000i	0.0727393	−	0.125988i
$568$	−7.46410	−	12.9282i	−0.313187	−	0.542455i
$569$	−12.0718			−0.506076			−0.253038	−	0.967456i	$-0.581430\pi$
$569$	−12.0718			−0.506076			−0.253038	+	0.967456i	$0.581430\pi$
$570$	−1.00000	+	1.73205i	−0.0418854	+	0.0725476i
$571$	−6.92820	+	12.0000i	−0.289936	+	0.502184i	−0.973794	−	0.227431i	$-0.926967\pi$
$571$	−6.92820	+	12.0000i	−0.289936	+	0.502184i	0.683858	+	0.729615i	$0.260301\pi$
$572$	1.80385	−	3.12436i	0.0754227	−	0.130636i
$573$	−12.1603	−	21.0622i	−0.508002	−	0.879885i
$574$	3.33975	+	5.78461i	0.139398	+	0.241445i
$575$	−0.732051	+	1.26795i	−0.0305286	+	0.0528771i
$576$	1.00000	−	1.73205i	0.0416667	−	0.0721688i
$577$	−3.73205	+	6.46410i	−0.155367	+	0.269104i	−0.933193	−	0.359376i	$-0.882989\pi$
$577$	−3.73205	+	6.46410i	−0.155367	+	0.269104i	0.777825	+	0.628480i	$0.216323\pi$
$578$	12.8564			0.534756
$579$	−10.1962	−	17.6603i	−0.423738	−	0.733935i
$580$	1.00000	−	1.73205i	0.0415227	−	0.0719195i
$581$	61.8564			2.56624
$582$	2.00000			0.0829027
$583$	9.12436	−	15.8038i	0.377892	−	0.654528i
$584$	9.46410			0.391627
$585$	−2.46410	−	4.26795i	−0.101878	−	0.176458i
$586$	−6.46410			−0.267030
$587$	−10.9641	−	18.9904i	−0.452537	−	0.783817i	0.546006	−	0.837781i	$-0.316148\pi$
$587$	−10.9641	−	18.9904i	−0.452537	−	0.783817i	−0.998543	+	0.0539644i	$0.982814\pi$
$588$	2.50000	+	4.33013i	0.103098	+	0.178571i
$589$	1.53590	+	2.66025i	0.0632856	+	0.109614i
$590$	−0.732051	+	1.26795i	−0.0301381	+	0.0522006i
$591$	−18.3205			−0.753605
$592$	1.00000	−	6.00000i	0.0410997	−	0.246598i
$593$	−15.6077			−0.640931			−0.320466	−	0.947260i	$-0.603839\pi$
$593$	−15.6077			−0.640931			−0.320466	+	0.947260i	$0.603839\pi$
$594$	−3.66025	+	6.33975i	−0.150182	+	0.260123i
$595$	9.46410	+	16.3923i	0.387990	+	0.672019i
$596$	3.46410	+	6.00000i	0.141895	+	0.245770i
$597$	−3.76795	−	6.52628i	−0.154212	−	0.267103i
$598$	−3.60770			−0.147530
$599$	7.62436	+	13.2058i	0.311523	+	0.539573i	0.978692	−	0.205333i	$-0.0658277\pi$
$599$	7.62436	+	13.2058i	0.311523	+	0.539573i	−0.667169	+	0.744906i	$0.732494\pi$
$600$	−1.00000			−0.0408248
$601$	−3.42820	+	5.93782i	−0.139839	+	0.242209i	−0.927436	−	0.373983i	$-0.877992\pi$
$601$	−3.42820	+	5.93782i	−0.139839	+	0.242209i	0.787596	+	0.616192i	$0.211325\pi$
$602$	−13.6077			−0.554608
$603$	−2.14359			−0.0872939
$604$	7.69615	−	13.3301i	0.313152	−	0.542395i
$605$	4.42820	+	7.66987i	0.180032	+	0.311825i
$606$	2.53590			0.103014
$607$	−10.6603	+	18.4641i	−0.432686	+	0.749435i	−0.997104	−	0.0760549i	$-0.975768\pi$
$607$	−10.6603	+	18.4641i	−0.432686	+	0.749435i	0.564417	+	0.825490i	$0.309101\pi$
$608$	1.00000	−	1.73205i	0.0405554	−	0.0702439i
$609$	3.46410	−	6.00000i	0.140372	−	0.243132i
$610$	2.46410	+	4.26795i	0.0997686	+	0.172804i
$611$	−4.26795	−	7.39230i	−0.172663	−	0.299061i
$612$	5.46410	−	9.46410i	0.220873	−	0.382564i
$613$	−1.53590	+	2.66025i	−0.0620344	+	0.107447i	−0.895375	−	0.445314i	$-0.853092\pi$
$613$	−1.53590	+	2.66025i	−0.0620344	+	0.107447i	0.833340	+	0.552760i	$0.186426\pi$
$614$	−8.42820	+	14.5981i	−0.340135	+	0.589130i
$615$	−1.92820			−0.0777527
$616$	2.53590	+	4.39230i	0.102174	+	0.176971i
$617$	−5.53590	+	9.58846i	−0.222867	+	0.386017i	−0.955677	−	0.294416i	$-0.904875\pi$
$617$	−5.53590	+	9.58846i	−0.222867	+	0.386017i	0.732810	+	0.680433i	$0.238208\pi$
$618$	6.53590			0.262912
$619$	14.0000			0.562708			0.281354	−	0.959604i	$-0.409217\pi$
$619$	14.0000			0.562708			0.281354	+	0.959604i	$0.409217\pi$
$620$	−0.767949	+	1.33013i	−0.0308416	+	0.0534192i
$621$	7.32051			0.293762
$622$	2.76795	+	4.79423i	0.110985	+	0.192231i
$623$	6.92820			0.277573
$624$	−1.23205	−	2.13397i	−0.0493215	−	0.0854274i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	2.46410	+	4.26795i	0.0984853	+	0.170582i
$627$	−1.46410	+	2.53590i	−0.0584706	+	0.101274i
$628$	18.3205			0.731068
$629$	5.46410	−	32.7846i	0.217868	−	1.30721i
$630$	6.92820			0.276026
$631$	−8.16025	+	14.1340i	−0.324855	+	0.562665i	−0.981483	−	0.191550i	$-0.938649\pi$
$631$	−8.16025	+	14.1340i	−0.324855	+	0.562665i	0.656628	+	0.754214i	$0.271982\pi$
$632$	0.535898	+	0.928203i	0.0213169	+	0.0369219i
$633$	7.00000	+	12.1244i	0.278225	+	0.481900i
$634$	12.2321	+	21.1865i	0.485797	+	0.841425i
$635$	−1.07180			−0.0425330
$636$	−6.23205	−	10.7942i	−0.247117	−	0.428019i
$637$	−12.3205			−0.488156
$638$	1.46410	−	2.53590i	0.0579643	−	0.100397i
$639$	−29.8564			−1.18110
$640$	1.00000			0.0395285
$641$	−10.8205	+	18.7417i	−0.427384	+	0.740251i	−0.996640	−	0.0819093i	$-0.973898\pi$
$641$	−10.8205	+	18.7417i	−0.427384	+	0.740251i	0.569255	+	0.822161i	$0.307232\pi$
$642$	9.42820	+	16.3301i	0.372102	+	0.644499i
$643$	−18.0718			−0.712682			−0.356341	−	0.934356i	$-0.615976\pi$
$643$	−18.0718			−0.712682			−0.356341	+	0.934356i	$0.615976\pi$
$644$	2.53590	−	4.39230i	0.0999284	−	0.173081i
$645$	1.96410	−	3.40192i	0.0773364	−	0.133951i
$646$	5.46410	−	9.46410i	0.214982	−	0.372360i
$647$	1.46410	+	2.53590i	0.0575598	+	0.0996965i	0.893369	−	0.449323i	$-0.148335\pi$
$647$	1.46410	+	2.53590i	0.0575598	+	0.0996965i	−0.835810	+	0.549019i	$0.815001\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	−1.07180	+	1.85641i	−0.0420717	+	0.0728703i
$650$	1.23205	−	2.13397i	0.0483250	−	0.0837014i
$651$	−2.66025	+	4.60770i	−0.104264	+	0.180590i
$652$	−16.8564			−0.660148
$653$	−18.2321	−	31.5788i	−0.713475	−	1.23578i	−0.963545	−	0.267548i	$-0.913787\pi$
$653$	−18.2321	−	31.5788i	−0.713475	−	1.23578i	0.250069	−	0.968228i	$-0.419547\pi$
$654$	−5.00000	+	8.66025i	−0.195515	+	0.338643i
$655$	−12.9282			−0.505147
$656$	1.92820			0.0752837
$657$	9.46410	−	16.3923i	0.369230	−	0.639525i
$658$	12.0000			0.467809
$659$	22.3923	+	38.7846i	0.872280	+	1.51083i	0.859632	+	0.510914i	$0.170693\pi$
$659$	22.3923	+	38.7846i	0.872280	+	1.51083i	0.0126485	+	0.999920i	$0.495974\pi$
$660$	−1.46410			−0.0569901
$661$	−1.19615	−	2.07180i	−0.0465249	−	0.0805836i	0.841825	−	0.539750i	$-0.181481\pi$
$661$	−1.19615	−	2.07180i	−0.0465249	−	0.0805836i	−0.888350	+	0.459167i	$0.848148\pi$
$662$	6.12436	+	10.6077i	0.238030	+	0.412280i
$663$	−6.73205	−	11.6603i	−0.261451	−	0.452847i
$664$	8.92820	−	15.4641i	0.346481	−	0.600124i
$665$	6.92820			0.268664
$666$	−9.39230	−	7.73205i	−0.363944	−	0.299611i
$667$	−2.92820			−0.113380
$668$	1.53590	−	2.66025i	0.0594257	−	0.102928i
$669$	−5.66025	−	9.80385i	−0.218838	−	0.379039i
$670$	−0.535898	−	0.928203i	−0.0207036	−	0.0358596i
$671$	3.60770	+	6.24871i	0.139274	+	0.241229i
$672$	3.46410			0.133631
$673$	−21.0526	−	36.4641i	−0.811517	−	1.40559i	−0.911802	−	0.410629i	$-0.865309\pi$
$673$	−21.0526	−	36.4641i	−0.811517	−	1.40559i	0.100286	−	0.994959i	$-0.468024\pi$
$674$	−4.92820			−0.189827
$675$	−2.50000	+	4.33013i	−0.0962250	+	0.166667i
$676$	−6.92820			−0.266469
$677$	−38.7846			−1.49061			−0.745307	−	0.666722i	$-0.767697\pi$
$677$	−38.7846			−1.49061			−0.745307	+	0.666722i	$0.767697\pi$
$678$	5.46410	−	9.46410i	0.209848	−	0.363467i
$679$	−3.46410	−	6.00000i	−0.132940	−	0.230259i
$680$	5.46410			0.209539
$681$	−6.96410	+	12.0622i	−0.266865	+	0.462224i
$682$	−1.12436	+	1.94744i	−0.0430538	+	0.0745714i
$683$	−16.4282	+	28.4545i	−0.628608	+	1.08878i	0.359224	+	0.933252i	$0.383042\pi$
$683$	−16.4282	+	28.4545i	−0.628608	+	1.08878i	−0.987831	+	0.155529i	$0.950292\pi$
$684$	−2.00000	−	3.46410i	−0.0764719	−	0.132453i
$685$	−2.73205	−	4.73205i	−0.104386	−	0.180802i
$686$	−3.46410	+	6.00000i	−0.132260	+	0.229081i
$687$	−2.80385	+	4.85641i	−0.106973	+	0.185283i
$688$	−1.96410	+	3.40192i	−0.0748807	+	0.129697i
$689$	30.7128			1.17006
$690$	0.732051	+	1.26795i	0.0278687	+	0.0482700i
$691$	15.1962	−	26.3205i	0.578089	−	1.00128i	−0.417610	−	0.908627i	$-0.637132\pi$
$691$	15.1962	−	26.3205i	0.578089	−	1.00128i	0.995698	−	0.0926528i	$-0.0295346\pi$
$692$	11.8564			0.450713
$693$	10.1436			0.385323
$694$	8.53590	−	14.7846i	0.324018	−	0.561216i
$695$	4.39230			0.166610
$696$	−1.00000	−	1.73205i	−0.0379049	−	0.0656532i
$697$	10.5359			0.399076
$698$	15.3923	+	26.6603i	0.582607	+	1.00911i
$699$	−15.1962	−	26.3205i	−0.574771	−	0.995533i
$700$	1.73205	+	3.00000i	0.0654654	+	0.113389i
$701$	−19.0000	+	32.9090i	−0.717620	+	1.24295i	0.244320	+	0.969695i	$0.421435\pi$
$701$	−19.0000	+	32.9090i	−0.717620	+	1.24295i	−0.961940	+	0.273260i	$0.911898\pi$
$702$	−12.3205			−0.465008
$703$	−9.39230	−	7.73205i	−0.354237	−	0.291620i
$704$	1.46410			0.0551804
$705$	−1.73205	+	3.00000i	−0.0652328	+	0.112987i
$706$	−18.6603	−	32.3205i	−0.702288	−	1.21640i
$707$	−4.39230	−	7.60770i	−0.165190	−	0.286117i
$708$	0.732051	+	1.26795i	0.0275122	+	0.0476524i
$709$	−12.0000			−0.450669			−0.225335	−	0.974281i	$-0.572348\pi$
$709$	−12.0000			−0.450669			−0.225335	+	0.974281i	$0.572348\pi$
$710$	−7.46410	−	12.9282i	−0.280123	−	0.485187i
$711$	2.14359			0.0803910
$712$	1.00000	−	1.73205i	0.0374766	−	0.0649113i
$713$	2.24871			0.0842149
$714$	18.9282			0.708370
$715$	1.80385	−	3.12436i	0.0674601	−	0.116844i
$716$	−6.00000	−	10.3923i	−0.224231	−	0.388379i
$717$	−26.9282			−1.00565
$718$	1.23205	−	2.13397i	0.0459797	−	0.0796392i
$719$	−0.160254	+	0.277568i	−0.00597647	+	0.0103515i	−0.868998	−	0.494815i	$-0.835236\pi$
$719$	−0.160254	+	0.277568i	−0.00597647	+	0.0103515i	0.863022	+	0.505167i	$0.168569\pi$
$720$	1.00000	−	1.73205i	0.0372678	−	0.0645497i
$721$	−11.3205	−	19.6077i	−0.421598	−	0.730229i
$722$	7.50000	+	12.9904i	0.279121	+	0.483452i
$723$	−1.00000	+	1.73205i	−0.0371904	+	0.0644157i
$724$	−8.26795	+	14.3205i	−0.307276	+	0.532217i
$725$	1.00000	−	1.73205i	0.0371391	−	0.0643268i
$726$	8.85641			0.328692
$727$	6.00000	+	10.3923i	0.222528	+	0.385429i	0.955575	−	0.294749i	$-0.0952359\pi$
$727$	6.00000	+	10.3923i	0.222528	+	0.385429i	−0.733047	+	0.680178i	$0.761903\pi$
$728$	−4.26795	+	7.39230i	−0.158181	+	0.273977i
$729$	13.0000			0.481481
$730$	9.46410			0.350282
$731$	−10.7321	+	18.5885i	−0.396939	+	0.687519i
$732$	4.92820			0.182152
$733$	−1.92820	−	3.33975i	−0.0712198	−	0.123356i	0.828216	−	0.560408i	$-0.189356\pi$
$733$	−1.92820	−	3.33975i	−0.0712198	−	0.123356i	−0.899436	+	0.437052i	$0.856023\pi$
$734$	−30.7846			−1.13628
$735$	2.50000	+	4.33013i	0.0922139	+	0.159719i
$736$	−0.732051	−	1.26795i	−0.0269838	−	0.0467372i
$737$	−0.784610	−	1.35898i	−0.0289015	−	0.0500588i
$738$	1.92820	−	3.33975i	0.0709781	−	0.122938i
$739$	−9.46410			−0.348143			−0.174071	−	0.984733i	$-0.555692\pi$
$739$	−9.46410			−0.348143			−0.174071	+	0.984733i	$0.555692\pi$
$740$	1.00000	−	6.00000i	0.0367607	−	0.220564i
$741$	−4.92820			−0.181042
$742$	−21.5885	+	37.3923i	−0.792537	+	1.37271i
$743$	−7.12436	−	12.3397i	−0.261367	−	0.452701i	0.705238	−	0.708970i	$-0.250840\pi$
$743$	−7.12436	−	12.3397i	−0.261367	−	0.452701i	−0.966605	+	0.256269i	$0.917507\pi$
$744$	0.767949	+	1.33013i	0.0281544	+	0.0487648i
$745$	3.46410	+	6.00000i	0.126915	+	0.219823i
$746$	−31.5359			−1.15461
$747$	−17.8564	−	30.9282i	−0.653332	−	1.13160i
$748$	8.00000			0.292509
$749$	32.6603	−	56.5692i	1.19338	−	2.06699i
$750$	−1.00000			−0.0365148
$751$	5.67949			0.207248			0.103624	−	0.994617i	$-0.466956\pi$
$751$	5.67949			0.207248			0.103624	+	0.994617i	$0.466956\pi$
$752$	1.73205	−	3.00000i	0.0631614	−	0.109399i
$753$	0.464102	+	0.803848i	0.0169128	+	0.0292938i
$754$	4.92820			0.179475
$755$	7.69615	−	13.3301i	0.280092	−	0.485133i
$756$	8.66025	−	15.0000i	0.314970	−	0.545545i
$757$	10.2321	−	17.7224i	0.371890	−	0.644133i	−0.617966	−	0.786205i	$-0.712043\pi$
$757$	10.2321	−	17.7224i	0.371890	−	0.644133i	0.989856	+	0.142072i	$0.0453765\pi$
$758$	1.80385	+	3.12436i	0.0655187	+	0.113482i
$759$	1.07180	+	1.85641i	0.0389038	+	0.0673833i
$760$	1.00000	−	1.73205i	0.0362738	−	0.0628281i
$761$	−2.46410	+	4.26795i	−0.0893236	+	0.154713i	−0.907225	−	0.420645i	$-0.861804\pi$
$761$	−2.46410	+	4.26795i	−0.0893236	+	0.154713i	0.817902	+	0.575358i	$0.195137\pi$
$762$	−0.535898	+	0.928203i	−0.0194136	+	0.0336253i
$763$	34.6410			1.25409
$764$	12.1603	+	21.0622i	0.439943	+	0.762003i
$765$	5.46410	−	9.46410i	0.197555	−	0.342175i
$766$	7.46410			0.269689
$767$	−3.60770			−0.130266
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$	−42.7846			−1.54285			−0.771426	−	0.636319i	$-0.780456\pi$
$769$	−42.7846			−1.54285			−0.771426	+	0.636319i	$0.780456\pi$
$770$	2.53590	+	4.39230i	0.0913874	+	0.158288i
$771$	19.4641			0.700982
$772$	10.1962	+	17.6603i	0.366968	+	0.635606i
$773$	−11.0885	−	19.2058i	−0.398824	−	0.690784i	0.594757	−	0.803906i	$-0.297248\pi$
$773$	−11.0885	−	19.2058i	−0.398824	−	0.690784i	−0.993581	+	0.113122i	$0.963915\pi$
$774$	3.92820	+	6.80385i	0.141196	+	0.244559i
$775$	−0.767949	+	1.33013i	−0.0275855	+	0.0477796i
$776$	−2.00000			−0.0717958
$777$	3.46410	−	20.7846i	0.124274	−	0.745644i
$778$	−31.7128			−1.13696
$779$	1.92820	−	3.33975i	0.0690851	−	0.119659i
$780$	−1.23205	−	2.13397i	−0.0441145	−	0.0764085i
$781$	−10.9282	−	18.9282i	−0.391042	−	0.677304i
$782$	−4.00000	−	6.92820i	−0.143040	−	0.247752i
$783$	−10.0000			−0.357371
$784$	−2.50000	−	4.33013i	−0.0892857	−	0.154647i
$785$	18.3205			0.653887
$786$	−6.46410	+	11.1962i	−0.230567	+	0.399354i
$787$	2.21539			0.0789701			0.0394851	−	0.999220i	$-0.487428\pi$
$787$	2.21539			0.0789701			0.0394851	+	0.999220i	$0.487428\pi$
$788$	18.3205			0.652641
$789$	−7.19615	+	12.4641i	−0.256190	+	0.443734i
$790$	0.535898	+	0.928203i	0.0190664	+	0.0330240i
$791$	−37.8564			−1.34602
$792$	1.46410	−	2.53590i	0.0520246	−	0.0901092i
$793$	−6.07180	+	10.5167i	−0.215616	+	0.373458i
$794$	−1.23205	+	2.13397i	−0.0437238	+	0.0757319i
$795$	−6.23205	−	10.7942i	−0.221028	−	0.382832i
$796$	3.76795	+	6.52628i	0.133551	+	0.231318i
$797$	−13.2321	+	22.9186i	−0.468703	+	0.811818i	−0.999360	−	0.0357689i	$-0.988612\pi$
$797$	−13.2321	+	22.9186i	−0.468703	+	0.811818i	0.530657	+	0.847587i	$0.321945\pi$
$798$	3.46410	−	6.00000i	0.122628	−	0.212398i
$799$	9.46410	−	16.3923i	0.334816	−	0.579918i
$800$	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
$804$	−1.07180			−0.0377994
$805$	2.53590	−	4.39230i	0.0893787	−	0.154808i
$806$	−3.78461			−0.133307
$807$	4.19615	+	7.26795i	0.147712	+	0.255844i
$808$	−2.53590			−0.0892126
$809$	8.35641	+	14.4737i	0.293796	+	0.508869i	0.974704	−	0.223500i	$-0.0717482\pi$
$809$	8.35641	+	14.4737i	0.293796	+	0.508869i	−0.680908	+	0.732369i	$0.738415\pi$
$810$	−0.500000	−	0.866025i	−0.0175682	−	0.0304290i
$811$	13.3205	+	23.0718i	0.467746	+	0.810160i	0.999321	−	0.0368512i	$-0.0117328\pi$
$811$	13.3205	+	23.0718i	0.467746	+	0.810160i	−0.531574	+	0.847012i	$0.678399\pi$
$812$	−3.46410	+	6.00000i	−0.121566	+	0.210559i
$813$	31.2487			1.09594
$814$	1.46410	−	8.78461i	0.0513167	−	0.307900i
$815$	−16.8564			−0.590454
$816$	2.73205	−	4.73205i	0.0956409	−	0.165655i
$817$	3.92820	+	6.80385i	0.137430	+	0.238036i
$818$	5.50000	+	9.52628i	0.192303	+	0.333079i
$819$	8.53590	+	14.7846i	0.298268	+	0.516616i
$820$	1.92820			0.0673358
$821$	−18.4641	−	31.9808i	−0.644402	−	1.11614i	−0.984439	−	0.175725i	$-0.943773\pi$
$821$	−18.4641	−	31.9808i	−0.644402	−	1.11614i	0.340038	−	0.940412i	$-0.389560\pi$
$822$	−5.46410			−0.190582
$823$	8.26795	−	14.3205i	0.288203	−	0.499182i	−0.685178	−	0.728375i	$-0.740276\pi$
$823$	8.26795	−	14.3205i	0.288203	−	0.499182i	0.973381	+	0.229194i	$0.0736090\pi$
$824$	−6.53590			−0.227689
$825$	−1.46410			−0.0509735
$826$	2.53590	−	4.39230i	0.0882352	−	0.152828i
$827$	−22.3923	−	38.7846i	−0.778657	−	1.34867i	−0.932716	−	0.360611i	$-0.882568\pi$
$827$	−22.3923	−	38.7846i	−0.778657	−	1.34867i	0.154059	−	0.988062i	$-0.450765\pi$
$828$	−2.92820			−0.101762
$829$	27.9808	−	48.4641i	0.971812	−	1.68323i	0.281734	−	0.959492i	$-0.409090\pi$
$829$	27.9808	−	48.4641i	0.971812	−	1.68323i	0.690078	−	0.723735i	$-0.257576\pi$
$830$	8.92820	−	15.4641i	0.309902	−	0.536767i
$831$	−12.7679	+	22.1147i	−0.442915	+	0.767152i
$832$	1.23205	+	2.13397i	0.0427137	+	0.0739823i
$833$	−13.6603	−	23.6603i	−0.473300	−	0.819779i
$834$	2.19615	−	3.80385i	0.0760465	−	0.131716i
$835$	1.53590	−	2.66025i	0.0531520	−	0.0920619i
$836$	1.46410	−	2.53590i	0.0506370	−	0.0877059i
$837$	7.67949			0.265442
$838$	0.732051	+	1.26795i	0.0252883	+	0.0438006i
$839$	−27.0167	+	46.7942i	−0.932719	+	1.61552i	−0.154066	+	0.988060i	$0.549237\pi$
$839$	−27.0167	+	46.7942i	−0.932719	+	1.61552i	−0.778652	+	0.627456i	$0.784096\pi$
$840$	3.46410			0.119523
$841$	−25.0000			−0.862069
$842$	18.6603	−	32.3205i	0.643075	−	1.11384i
$843$	26.7128			0.920038
$844$	−7.00000	−	12.1244i	−0.240950	−	0.417338i
$845$	−6.92820			−0.238337
$846$	−3.46410	−	6.00000i	−0.119098	−	0.206284i
$847$	−15.3397	−	26.5692i	−0.527080	−	0.912929i
$848$	6.23205	+	10.7942i	0.214010	+	0.370675i
$849$	10.9641	−	18.9904i	0.376287	−	0.651748i
$850$	5.46410			0.187417
$851$	−8.33975	+	3.12436i	−0.285883	+	0.107102i
$852$	−14.9282			−0.511432
$853$	16.6244	−	28.7942i	0.569207	−	0.985896i	−0.427438	−	0.904045i	$-0.640584\pi$
$853$	16.6244	−	28.7942i	0.569207	−	0.985896i	0.996645	−	0.0818507i	$-0.0260831\pi$
$854$	−8.53590	−	14.7846i	−0.292092	−	0.505919i
$855$	−2.00000	−	3.46410i	−0.0683986	−	0.118470i
$856$	−9.42820	−	16.3301i	−0.322249	−	0.558152i
$857$	42.2487			1.44319			0.721594	−	0.692316i	$-0.243410\pi$
$857$	42.2487			1.44319			0.721594	+	0.692316i	$0.243410\pi$
$858$	−1.80385	−	3.12436i	−0.0615823	−	0.106664i
$859$	5.07180			0.173047			0.0865237	−	0.996250i	$-0.472424\pi$
$859$	5.07180			0.173047			0.0865237	+	0.996250i	$0.472424\pi$
$860$	−1.96410	+	3.40192i	−0.0669753	+	0.116005i
$861$	6.67949			0.227636
$862$	12.4641			0.424529
$863$	8.53590	−	14.7846i	0.290565	−	0.503274i	−0.683378	−	0.730065i	$-0.739490\pi$
$863$	8.53590	−	14.7846i	0.290565	−	0.503274i	0.973944	+	0.226791i	$0.0728233\pi$
$864$	−2.50000	−	4.33013i	−0.0850517	−	0.147314i
$865$	11.8564			0.403130
$866$	15.8564	−	27.4641i	0.538823	−	0.933268i
$867$	6.42820	−	11.1340i	0.218313	−	0.378130i
$868$	2.66025	−	4.60770i	0.0902949	−	0.156395i
$869$	0.784610	+	1.35898i	0.0266161	+	0.0461004i
$870$	−1.00000	−	1.73205i	−0.0339032	−	0.0587220i
$871$	1.32051	−	2.28719i	0.0447437	−	0.0774984i
$872$	5.00000	−	8.66025i	0.169321	−	0.293273i
$873$	−2.00000	+	3.46410i	−0.0676897	+	0.117242i
$874$	−2.92820			−0.0990480
$875$	1.73205	+	3.00000i	0.0585540	+	0.101419i
$876$	4.73205	−	8.19615i	0.159881	−	0.276922i
$877$	−27.2487			−0.920124			−0.460062	−	0.887887i	$-0.652173\pi$
$877$	−27.2487			−0.920124			−0.460062	+	0.887887i	$0.652173\pi$
$878$	18.4641			0.623133
$879$	−3.23205	+	5.59808i	−0.109014	+	0.188818i
$880$	1.46410			0.0493549
$881$	17.5359	+	30.3731i	0.590799	+	1.02329i	0.994125	+	0.108238i	$0.0345209\pi$
$881$	17.5359	+	30.3731i	0.590799	+	1.02329i	−0.403326	+	0.915057i	$0.632146\pi$
$882$	−10.0000			−0.336718
$883$	11.5718	+	20.0429i	0.389422	+	0.674499i	0.992372	−	0.123280i	$-0.0393415\pi$
$883$	11.5718	+	20.0429i	0.389422	+	0.674499i	−0.602950	+	0.797779i	$0.706008\pi$
$884$	6.73205	+	11.6603i	0.226423	+	0.392177i
$885$	0.732051	+	1.26795i	0.0246076	+	0.0426216i
$886$	−13.9641	+	24.1865i	−0.469133	+	0.812562i
$887$	−4.14359			−0.139128			−0.0695641	−	0.997577i	$-0.522161\pi$
$887$	−4.14359			−0.139128			−0.0695641	+	0.997577i	$0.522161\pi$
$888$	−4.69615	−	3.86603i	−0.157593	−	0.129735i
$889$	3.71281			0.124524
$890$	1.00000	−	1.73205i	0.0335201	−	0.0580585i
$891$	−0.732051	−	1.26795i	−0.0245246	−	0.0424779i
$892$	5.66025	+	9.80385i	0.189519	+	0.328257i
$893$	−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
$897$	−1.80385	+	3.12436i	−0.0602287	+	0.104319i
$898$	−15.0000			−0.500556
$899$	−3.07180			−0.102450
$900$	1.00000	−	1.73205i	0.0333333	−	0.0577350i
$901$	34.0526	+	58.9808i	1.13446	+	1.96493i
$902$	2.82309			0.0939985
$903$	−6.80385	+	11.7846i	−0.226418	+	0.392167i
$904$	−5.46410	+	9.46410i	−0.181733	+	0.314771i
$905$	−8.26795	+	14.3205i	−0.274836	+	0.476030i
$906$	−7.69615	−	13.3301i	−0.255688	−	0.442864i
$907$	−1.60770	−	2.78461i	−0.0533826	−	0.0924614i	0.838099	−	0.545518i	$-0.183667\pi$
$907$	−1.60770	−	2.78461i	−0.0533826	−	0.0924614i	−0.891482	+	0.453056i	$0.850334\pi$
$908$	6.96410	−	12.0622i	0.231112	−	0.400297i
$909$	−2.53590	+	4.39230i	−0.0841104	+	0.145684i
$910$	−4.26795	+	7.39230i	−0.141481	+	0.245053i
$911$	−38.1769			−1.26486			−0.632429	−	0.774618i	$-0.717942\pi$
$911$	−38.1769			−1.26486			−0.632429	+	0.774618i	$0.717942\pi$
$912$	−1.00000	−	1.73205i	−0.0331133	−	0.0573539i
$913$	13.0718	−	22.6410i	0.432613	−	0.749308i
$914$	25.8564			0.855254
$915$	4.92820			0.162921
$916$	2.80385	−	4.85641i	0.0926417	−	0.160460i
$917$	44.7846			1.47892
$918$	−13.6603	−	23.6603i	−0.450856	−	0.780905i
$919$	30.9282			1.02023			0.510114	−	0.860107i	$-0.329603\pi$
$919$	30.9282			1.02023			0.510114	+	0.860107i	$0.329603\pi$
$920$	−0.732051	−	1.26795i	−0.0241350	−	0.0418030i
$921$	8.42820	+	14.5981i	0.277719	+	0.481023i
$922$	−0.464102	−	0.803848i	−0.0152844	−	0.0264733i
$923$	18.3923	−	31.8564i	0.605390	−	1.04857i
$924$	5.07180			0.166850
$925$	1.00000	−	6.00000i	0.0328798	−	0.197279i
$926$	−6.92820			−0.227675
$927$	−6.53590	+	11.3205i	−0.214667	+	0.371814i
$928$	1.00000	+	1.73205i	0.0328266	+	0.0568574i
$929$	10.5718	+	18.3109i	0.346849	+	0.600761i	0.985688	−	0.168580i	$-0.0539182\pi$
$929$	10.5718	+	18.3109i	0.346849	+	0.600761i	−0.638839	+	0.769341i	$0.720585\pi$
$930$	0.767949	+	1.33013i	0.0251820	+	0.0436166i
$931$	−10.0000			−0.327737
$932$	15.1962	+	26.3205i	0.497767	+	0.862157i
$933$	5.53590			0.181237
$934$	−1.50000	+	2.59808i	−0.0490815	+	0.0850117i
$935$	8.00000			0.261628
$936$	4.92820			0.161083
$937$	−25.9282	+	44.9090i	−0.847037	+	1.46711i	0.0368025	+	0.999323i	$0.488283\pi$
$937$	−25.9282	+	44.9090i	−0.847037	+	1.46711i	−0.883840	+	0.467789i	$0.845051\pi$
$938$	1.85641	+	3.21539i	0.0606138	+	0.104986i
$939$	4.92820			0.160826
$940$	1.73205	−	3.00000i	0.0564933	−	0.0978492i
$941$	3.80385	−	6.58846i	0.124002	−	0.214778i	−0.797340	−	0.603530i	$-0.793760\pi$
$941$	3.80385	−	6.58846i	0.124002	−	0.214778i	0.921342	+	0.388752i	$0.127094\pi$
$942$	9.16025	−	15.8660i	0.298457	−	0.516943i
$943$	−1.41154	−	2.44486i	−0.0459662	−	0.0796157i
$944$	−0.732051	−	1.26795i	−0.0238262	−	0.0412682i
$945$	8.66025	−	15.0000i	0.281718	−	0.487950i
$946$	−2.87564	+	4.98076i	−0.0934953	+	0.161939i
$947$	−9.03590	+	15.6506i	−0.293627	+	0.508577i	−0.974665	−	0.223671i	$-0.928196\pi$
$947$	−9.03590	+	15.6506i	−0.293627	+	0.508577i	0.681037	+	0.732249i	$0.261529\pi$
$948$	1.07180			0.0348103
$949$	11.6603	+	20.1962i	0.378508	+	0.655595i
$950$	1.00000	−	1.73205i	0.0324443	−	0.0561951i
$951$	24.4641			0.793303
$952$	−18.9282			−0.613467
$953$	−12.1962	+	21.1244i	−0.395072	+	0.684285i	−0.993110	−	0.117183i	$-0.962614\pi$
$953$	−12.1962	+	21.1244i	−0.395072	+	0.684285i	0.598038	+	0.801468i	$0.295947\pi$
$954$	24.9282			0.807080
$955$	12.1603	+	21.0622i	0.393497	+	0.681556i
$956$	26.9282			0.870920
$957$	−1.46410	−	2.53590i	−0.0473277	−	0.0819740i
$958$	1.83975	+	3.18653i	0.0594395	+	0.102952i
$959$	9.46410	+	16.3923i	0.305612	+	0.529335i
$960$	0.500000	−	0.866025i	0.0161374	−	0.0279508i
$961$	−28.6410			−0.923904
$962$	14.0359	−	5.25833i	0.452536	−	0.169535i
$963$	−37.7128			−1.21528
$964$	1.00000	−	1.73205i	0.0322078	−	0.0557856i
$965$	10.1962	+	17.6603i	0.328226	+	0.568504i
$966$	−2.53590	−	4.39230i	−0.0815912	−	0.141320i
$967$	−2.39230	−	4.14359i	−0.0769313	−	0.133249i	0.824993	−	0.565143i	$-0.191179\pi$
$967$	−2.39230	−	4.14359i	−0.0769313	−	0.133249i	−0.901925	+	0.431894i	$0.857846\pi$
$968$	−8.85641			−0.284656
$969$	−5.46410	−	9.46410i	−0.175532	−	0.304031i
$970$	−2.00000			−0.0642161
$971$	19.6603	−	34.0526i	0.630928	−	1.09280i	−0.356435	−	0.934320i	$-0.616008\pi$
$971$	19.6603	−	34.0526i	0.630928	−	1.09280i	0.987362	−	0.158478i	$-0.0506588\pi$
$972$	−16.0000			−0.513200
$973$	−15.2154			−0.487783
$974$	0.464102	−	0.803848i	0.0148708	−	0.0257569i
$975$	−1.23205	−	2.13397i	−0.0394572	−	0.0683419i
$976$	−4.92820			−0.157748
$977$	−1.00000	+	1.73205i	−0.0319928	+	0.0554132i	−0.881579	−	0.472037i	$-0.843519\pi$
$977$	−1.00000	+	1.73205i	−0.0319928	+	0.0554132i	0.849586	+	0.527451i	$0.176852\pi$
$978$	−8.42820	+	14.5981i	−0.269504	+	0.466795i
$979$	1.46410	−	2.53590i	0.0467929	−	0.0810477i
$980$	−2.50000	−	4.33013i	−0.0798596	−	0.138321i
$981$	−10.0000	−	17.3205i	−0.319275	−	0.553001i
$982$	−17.1244	+	29.6603i	−0.546460	+	0.946497i
$983$	16.8564	−	29.1962i	0.537636	−	0.931213i	−0.461395	−	0.887195i	$-0.652651\pi$
$983$	16.8564	−	29.1962i	0.537636	−	0.931213i	0.999031	−	0.0440178i	$-0.0140158\pi$
$984$	0.964102	−	1.66987i	0.0307344	−	0.0532336i
$985$	18.3205			0.583740
$986$	5.46410	+	9.46410i	0.174012	+	0.301398i
$987$	6.00000	−	10.3923i	0.190982	−	0.330791i
$988$	4.92820			0.156787
$989$	5.75129			0.182880
$990$	1.46410	−	2.53590i	0.0465322	−	0.0805961i
$991$	−23.2487			−0.738520			−0.369260	−	0.929326i	$-0.620389\pi$
$991$	−23.2487			−0.738520			−0.369260	+	0.929326i	$0.620389\pi$
$992$	−0.767949	−	1.33013i	−0.0243824	−	0.0422316i
$993$	12.2487			0.388701
$994$	25.8564	+	44.7846i	0.820115	+	1.42048i
$995$	3.76795	+	6.52628i	0.119452	+	0.206897i
$996$	−8.92820	−	15.4641i	−0.282901	−	0.489999i
$997$	18.6962	−	32.3827i	0.592113	−	1.02557i	−0.401834	−	0.915712i	$-0.631627\pi$
$997$	18.6962	−	32.3827i	0.592113	−	1.02557i	0.993947	−	0.109858i	$-0.0350395\pi$
$998$	10.9282			0.345926
$999$	−28.4808	+	10.6699i	−0.901091	+	0.337580i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.e.d.121.2	✓	4
37.26	even	3	inner	370.2.e.d.211.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.e.d.121.2	✓	4	1.1	even	1	trivial
370.2.e.d.211.2	yes	4	37.26	even	3	inner

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} +1.00000 q^{10} +1.46410 q^{11} +(0.500000 - 0.866025i) q^{12} +(1.23205 + 2.13397i) q^{13} -3.46410 q^{14} +(0.500000 - 0.866025i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.73205 + 4.73205i) 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} +(-0.732051 + 1.26795i) q^{22} +1.46410 q^{23} +(0.500000 + 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} -2.46410 q^{26} +5.00000 q^{27} +(1.73205 - 3.00000i) q^{28} -2.00000 q^{29} +(0.500000 + 0.866025i) q^{30} +1.53590 q^{31} +(-0.500000 - 0.866025i) q^{32} +(0.732051 + 1.26795i) q^{33} +(-2.73205 - 4.73205i) q^{34} +(1.73205 - 3.00000i) q^{35} -2.00000 q^{36} +(-5.69615 + 2.13397i) q^{37} -2.00000 q^{38} +(-1.23205 + 2.13397i) q^{39} +(-0.500000 - 0.866025i) q^{40} +(-0.964102 - 1.66987i) q^{41} +(-1.73205 - 3.00000i) q^{42} +3.92820 q^{43} +(-0.732051 - 1.26795i) q^{44} -2.00000 q^{45} +(-0.732051 + 1.26795i) q^{46} -3.46410 q^{47} -1.00000 q^{48} +(-2.50000 + 4.33013i) q^{49} +(-0.500000 - 0.866025i) q^{50} -5.46410 q^{51} +(1.23205 - 2.13397i) q^{52} +(6.23205 - 10.7942i) q^{53} +(-2.50000 + 4.33013i) q^{54} +(-0.732051 - 1.26795i) q^{55} +(1.73205 + 3.00000i) q^{56} +(-1.00000 + 1.73205i) q^{57} +(1.00000 - 1.73205i) q^{58} +(-0.732051 + 1.26795i) q^{59} -1.00000 q^{60} +(2.46410 + 4.26795i) q^{61} +(-0.767949 + 1.33013i) q^{62} +6.92820 q^{63} +1.00000 q^{64} +(1.23205 - 2.13397i) q^{65} -1.46410 q^{66} +(-0.535898 - 0.928203i) q^{67} +5.46410 q^{68} +(0.732051 + 1.26795i) q^{69} +(1.73205 + 3.00000i) q^{70} +(-7.46410 - 12.9282i) q^{71} +(1.00000 - 1.73205i) q^{72} +9.46410 q^{73} +(1.00000 - 6.00000i) q^{74} -1.00000 q^{75} +(1.00000 - 1.73205i) q^{76} +(2.53590 + 4.39230i) q^{77} +(-1.23205 - 2.13397i) q^{78} +(0.535898 + 0.928203i) q^{79} +1.00000 q^{80} +(-0.500000 - 0.866025i) q^{81} +1.92820 q^{82} +(8.92820 - 15.4641i) q^{83} +3.46410 q^{84} +5.46410 q^{85} +(-1.96410 + 3.40192i) q^{86} +(-1.00000 - 1.73205i) q^{87} +1.46410 q^{88} +(1.00000 - 1.73205i) q^{89} +(1.00000 - 1.73205i) q^{90} +(-4.26795 + 7.39230i) q^{91} +(-0.732051 - 1.26795i) q^{92} +(0.767949 + 1.33013i) 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} +(1.46410 - 2.53590i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 4 q^{6} + 4 q^{8} + 4 q^{9} + 4 q^{10} - 8 q^{11} + 2 q^{12} - 2 q^{13} + 2 q^{15} - 2 q^{16} - 4 q^{17} + 4 q^{18} + 4 q^{19} - 2 q^{20} + 4 q^{22} - 8 q^{23}+ \cdots - 8 q^{99}+O(q^{100}) \) 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

Varieties

Fields

Representations

Groups

Database

Properties

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