LMFDB - Embedded newform 630.2.bk.c.101.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(101,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("630.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.bk (of order $6$, 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:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.14
Character	$\chi$	$=$	630.101
Dual form			630.2.bk.c.131.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(0.661104 + 1.60092i) q^{3} -1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(-1.60092 + 0.661104i) q^{6} +(-2.57921 + 0.589657i) q^{7} -1.00000i q^{8} +(-2.12588 + 2.11675i) q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(0.661104 + 1.60092i) q^{3} -1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(-1.60092 + 0.661104i) q^{6} +(-2.57921 + 0.589657i) q^{7} -1.00000i q^{8} +(-2.12588 + 2.11675i) q^{9} +(0.866025 + 0.500000i) q^{10} +(-2.51862 + 1.45413i) q^{11} +(-0.661104 - 1.60092i) q^{12} +(1.69585 - 0.979098i) q^{13} +(-0.589657 - 2.57921i) q^{14} +(1.71699 + 0.227927i) q^{15} +1.00000 q^{16} +(-1.68420 + 2.91713i) q^{17} +(-2.11675 - 2.12588i) q^{18} +(-6.97993 + 4.02986i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(-2.64912 - 3.73928i) q^{21} +(-1.45413 - 2.51862i) q^{22} +(-2.47278 - 1.42766i) q^{23} +(1.60092 - 0.661104i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(0.979098 + 1.69585i) q^{26} +(-4.79417 - 2.00398i) q^{27} +(2.57921 - 0.589657i) q^{28} +(1.87671 + 1.08352i) q^{29} +(-0.227927 + 1.71699i) q^{30} -2.20521i q^{31} +1.00000i q^{32} +(-3.99300 - 3.07078i) q^{33} +(-2.91713 - 1.68420i) q^{34} +(-0.778946 + 2.52849i) q^{35} +(2.12588 - 2.11675i) q^{36} +(1.68075 + 2.91115i) q^{37} +(-4.02986 - 6.97993i) q^{38} +(2.68859 + 2.06763i) q^{39} +(-0.866025 - 0.500000i) q^{40} +(4.24814 + 7.35799i) q^{41} +(3.73928 - 2.64912i) q^{42} +(0.991430 - 1.71721i) q^{43} +(2.51862 - 1.45413i) q^{44} +(0.770216 + 2.89944i) q^{45} +(1.42766 - 2.47278i) q^{46} -0.647198 q^{47} +(0.661104 + 1.60092i) q^{48} +(6.30461 - 3.04169i) q^{49} +(0.866025 - 0.500000i) q^{50} +(-5.78352 - 0.767750i) q^{51} +(-1.69585 + 0.979098i) q^{52} +(9.25368 + 5.34261i) q^{53} +(2.00398 - 4.79417i) q^{54} +2.90825i q^{55} +(0.589657 + 2.57921i) q^{56} +(-11.0659 - 8.51014i) q^{57} +(-1.08352 + 1.87671i) q^{58} +9.11655 q^{59} +(-1.71699 - 0.227927i) q^{60} -3.03785i q^{61} +2.20521 q^{62} +(4.23494 - 6.71307i) q^{63} -1.00000 q^{64} -1.95820i q^{65} +(3.07078 - 3.99300i) q^{66} -15.1391 q^{67} +(1.68420 - 2.91713i) q^{68} +(0.650802 - 4.90254i) q^{69} +(-2.52849 - 0.778946i) q^{70} +7.94202i q^{71} +(2.11675 + 2.12588i) q^{72} +(-12.5756 - 7.26053i) q^{73} +(-2.91115 + 1.68075i) q^{74} +(1.05588 - 1.37299i) q^{75} +(6.97993 - 4.02986i) q^{76} +(5.63860 - 5.23561i) q^{77} +(-2.06763 + 2.68859i) q^{78} +4.29504 q^{79} +(0.500000 - 0.866025i) q^{80} +(0.0387579 - 8.99992i) q^{81} +(-7.35799 + 4.24814i) q^{82} +(6.87362 - 11.9055i) q^{83} +(2.64912 + 3.73928i) q^{84} +(1.68420 + 2.91713i) q^{85} +(1.71721 + 0.991430i) q^{86} +(-0.493925 + 3.72078i) q^{87} +(1.45413 + 2.51862i) q^{88} +(8.43872 + 14.6163i) q^{89} +(-2.89944 + 0.770216i) q^{90} +(-3.79661 + 3.52526i) q^{91} +(2.47278 + 1.42766i) q^{92} +(3.53036 - 1.45787i) q^{93} -0.647198i q^{94} +8.05973i q^{95} +(-1.60092 + 0.661104i) q^{96} +(5.21536 + 3.01109i) q^{97} +(3.04169 + 6.30461i) q^{98} +(2.27627 - 8.42258i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 2 q^{3} - 32 q^{4} + 16 q^{5} - 2 q^{6} - 2 q^{7}+O(q^{10}) $ 32 * q - 2 * q^3 - 32 * q^4 + 16 * q^5 - 2 * q^6 - 2 * q^7	$ 32 q - 2 q^{3} - 32 q^{4} + 16 q^{5} - 2 q^{6} - 2 q^{7} - 6 q^{11} + 2 q^{12} + 6 q^{14} + 2 q^{15} + 32 q^{16} - 6 q^{17} + 8 q^{18} - 16 q^{20} + 18 q^{23} + 2 q^{24} - 16 q^{25} - 12 q^{26} - 8 q^{27} + 2 q^{28} + 6 q^{29} - 4 q^{30} + 20 q^{33} + 2 q^{35} + 2 q^{37} + 30 q^{39} + 6 q^{41} + 10 q^{42} - 28 q^{43} + 6 q^{44} + 6 q^{45} + 48 q^{47} - 2 q^{48} + 8 q^{49} + 34 q^{51} + 36 q^{53} - 46 q^{54} - 6 q^{56} + 18 q^{57} - 60 q^{59} - 2 q^{60} + 32 q^{63} - 32 q^{64} - 34 q^{66} - 8 q^{67} + 6 q^{68} - 28 q^{69} + 6 q^{70} - 8 q^{72} - 30 q^{73} - 18 q^{74} + 4 q^{75} - 6 q^{77} - 22 q^{78} - 8 q^{79} + 16 q^{80} + 20 q^{81} - 24 q^{82} - 6 q^{83} + 6 q^{85} + 30 q^{86} - 22 q^{87} + 12 q^{89} + 4 q^{90} - 66 q^{91} - 18 q^{92} - 32 q^{93} - 2 q^{96} - 96 q^{97} + 24 q^{98} - 24 q^{99}+O(q^{100}) $ 32 * q - 2 * q^3 - 32 * q^4 + 16 * q^5 - 2 * q^6 - 2 * q^7 - 6 * q^11 + 2 * q^12 + 6 * q^14 + 2 * q^15 + 32 * q^16 - 6 * q^17 + 8 * q^18 - 16 * q^20 + 18 * q^23 + 2 * q^24 - 16 * q^25 - 12 * q^26 - 8 * q^27 + 2 * q^28 + 6 * q^29 - 4 * q^30 + 20 * q^33 + 2 * q^35 + 2 * q^37 + 30 * q^39 + 6 * q^41 + 10 * q^42 - 28 * q^43 + 6 * q^44 + 6 * q^45 + 48 * q^47 - 2 * q^48 + 8 * q^49 + 34 * q^51 + 36 * q^53 - 46 * q^54 - 6 * q^56 + 18 * q^57 - 60 * q^59 - 2 * q^60 + 32 * q^63 - 32 * q^64 - 34 * q^66 - 8 * q^67 + 6 * q^68 - 28 * q^69 + 6 * q^70 - 8 * q^72 - 30 * q^73 - 18 * q^74 + 4 * q^75 - 6 * q^77 - 22 * q^78 - 8 * q^79 + 16 * q^80 + 20 * q^81 - 24 * q^82 - 6 * q^83 + 6 * q^85 + 30 * q^86 - 22 * q^87 + 12 * q^89 + 4 * q^90 - 66 * q^91 - 18 * q^92 - 32 * q^93 - 2 * q^96 - 96 * q^97 + 24 * q^98 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	0.661104	+	1.60092i	0.381689	+	0.924291i
$3$	0.661104	+	1.60092i	0.381689	+	0.924291i
$4$	−1.00000			−0.500000
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	−1.60092	+	0.661104i	−0.653572	+	0.269895i
$7$	−2.57921	+	0.589657i	−0.974848	+	0.222869i
$7$	−2.57921	+	0.589657i	−0.974848	+	0.222869i
$8$		−	1.00000i		−	0.353553i
$9$	−2.12588	+	2.11675i	−0.708628	+	0.705583i
$10$	0.866025	+	0.500000i	0.273861	+	0.158114i
$11$	−2.51862	+	1.45413i	−0.759392	+	0.438435i	−0.829077	−	0.559134i	$-0.811134\pi$
$11$	−2.51862	+	1.45413i	−0.759392	+	0.438435i	0.0696854	+	0.997569i	$0.477800\pi$
$12$	−0.661104	−	1.60092i	−0.190844	−	0.462145i
$13$	1.69585	−	0.979098i	0.470344	−	0.271553i	−0.246040	−	0.969260i	$-0.579129\pi$
$13$	1.69585	−	0.979098i	0.470344	−	0.271553i	0.716384	+	0.697707i	$0.245796\pi$
$14$	−0.589657	−	2.57921i	−0.157592	−	0.689322i
$15$	1.71699	+	0.227927i	0.443325	+	0.0588504i
$16$	1.00000			0.250000
$17$	−1.68420	+	2.91713i	−0.408479	+	0.707507i	−0.994720	−	0.102630i	$-0.967274\pi$
$17$	−1.68420	+	2.91713i	−0.408479	+	0.707507i	0.586240	+	0.810137i	$0.300607\pi$
$18$	−2.11675	−	2.12588i	−0.498922	−	0.501075i
$19$	−6.97993	+	4.02986i	−1.60131	+	0.924514i	−0.610079	+	0.792341i	$0.708862\pi$
$19$	−6.97993	+	4.02986i	−1.60131	+	0.924514i	−0.991227	+	0.132173i	$0.957804\pi$
$20$	−0.500000	+	0.866025i	−0.111803	+	0.193649i
$21$	−2.64912	−	3.73928i	−0.578084	−	0.815977i
$22$	−1.45413	−	2.51862i	−0.310020	−	0.536971i
$23$	−2.47278	−	1.42766i	−0.515609	−	0.297687i	0.219527	−	0.975606i	$-0.429549\pi$
$23$	−2.47278	−	1.42766i	−0.515609	−	0.297687i	−0.735136	+	0.677919i	$0.762882\pi$
$24$	1.60092	−	0.661104i	0.326786	−	0.134947i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	0.979098	+	1.69585i	0.192017	+	0.332583i
$27$	−4.79417	−	2.00398i	−0.922639	−	0.385665i
$28$	2.57921	−	0.589657i	0.487424	−	0.111435i
$29$	1.87671	+	1.08352i	0.348496	+	0.201204i	0.664023	−	0.747712i	$-0.268848\pi$
$29$	1.87671	+	1.08352i	0.348496	+	0.201204i	−0.315527	+	0.948917i	$0.602181\pi$
$30$	−0.227927	+	1.71699i	−0.0416135	+	0.313478i
$31$		−	2.20521i		−	0.396067i	−0.980195	−	0.198034i	$-0.936544\pi$
$31$		−	2.20521i		−	0.396067i	0.980195	−	0.198034i	$-0.0634555\pi$
$32$			1.00000i			0.176777i
$33$	−3.99300	−	3.07078i	−0.695093	−	0.534554i
$34$	−2.91713	−	1.68420i	−0.500283	−	0.288839i
$35$	−0.778946	+	2.52849i	−0.131666	+	0.427392i
$36$	2.12588	−	2.11675i	0.354314	−	0.352791i
$37$	1.68075	+	2.91115i	0.276314	+	0.478590i	0.970466	−	0.241239i	$-0.0775537\pi$
$37$	1.68075	+	2.91115i	0.276314	+	0.478590i	−0.694152	+	0.719829i	$0.744220\pi$
$38$	−4.02986	−	6.97993i	−0.653730	−	1.13229i
$39$	2.68859	+	2.06763i	0.430519	+	0.331086i
$40$	−0.866025	−	0.500000i	−0.136931	−	0.0790569i
$41$	4.24814	+	7.35799i	0.663448	+	1.14912i	0.979704	+	0.200451i	$0.0642407\pi$
$41$	4.24814	+	7.35799i	0.663448	+	1.14912i	−0.316256	+	0.948674i	$0.602426\pi$
$42$	3.73928	−	2.64912i	0.576983	−	0.408767i
$43$	0.991430	−	1.71721i	0.151192	−	0.261872i	−0.780474	−	0.625188i	$-0.785022\pi$
$43$	0.991430	−	1.71721i	0.151192	−	0.261872i	0.931666	+	0.363316i	$0.118356\pi$
$44$	2.51862	−	1.45413i	0.379696	−	0.219218i
$45$	0.770216	+	2.89944i	0.114817	+	0.432223i
$46$	1.42766	−	2.47278i	0.210497	−	0.364591i
$47$	−0.647198			−0.0944035			−0.0472018	−	0.998885i	$-0.515030\pi$
$47$	−0.647198			−0.0944035			−0.0472018	+	0.998885i	$0.515030\pi$
$48$	0.661104	+	1.60092i	0.0954221	+	0.231073i
$49$	6.30461	−	3.04169i	0.900659	−	0.434527i
$50$	0.866025	−	0.500000i	0.122474	−	0.0707107i
$51$	−5.78352	−	0.767750i	−0.809854	−	0.107506i
$52$	−1.69585	+	0.979098i	−0.235172	+	0.135776i
$53$	9.25368	+	5.34261i	1.27109	+	0.733865i	0.975193	−	0.221355i	$-0.0710480\pi$
$53$	9.25368	+	5.34261i	1.27109	+	0.733865i	0.295897	+	0.955220i	$0.404381\pi$
$54$	2.00398	−	4.79417i	0.272707	−	0.652404i
$55$			2.90825i			0.392148i
$56$	0.589657	+	2.57921i	0.0787962	+	0.344661i
$57$	−11.0659	−	8.51014i	−1.46572	−	1.12720i
$58$	−1.08352	+	1.87671i	−0.142273	+	0.246424i
$59$	9.11655			1.18687			0.593437	−	0.804881i	$-0.297771\pi$
$59$	9.11655			1.18687			0.593437	+	0.804881i	$0.297771\pi$
$60$	−1.71699	−	0.227927i	−0.221662	−	0.0294252i
$61$		−	3.03785i		−	0.388957i	−0.980907	−	0.194478i	$-0.937699\pi$
$61$		−	3.03785i		−	0.388957i	0.980907	−	0.194478i	$-0.0623014\pi$
$62$	2.20521			0.280062
$63$	4.23494	−	6.71307i	0.533552	−	0.845767i
$64$	−1.00000			−0.125000
$65$		−	1.95820i		−	0.242884i
$66$	3.07078	−	3.99300i	0.377986	−	0.491505i
$67$	−15.1391			−1.84954			−0.924769	−	0.380529i	$-0.875742\pi$
$67$	−15.1391			−1.84954			−0.924769	+	0.380529i	$0.875742\pi$
$68$	1.68420	−	2.91713i	0.204240	−	0.353754i
$69$	0.650802	−	4.90254i	0.0783474	−	0.590197i
$70$	−2.52849	−	0.778946i	−0.302212	−	0.0931018i
$71$			7.94202i			0.942544i	0.881988	+	0.471272i	$0.156205\pi$
$71$			7.94202i			0.942544i	−0.881988	+	0.471272i	$0.843795\pi$
$72$	2.11675	+	2.12588i	0.249461	+	0.250538i
$73$	−12.5756	−	7.26053i	−1.47186	−	0.849780i	−0.472363	−	0.881404i	$-0.656599\pi$
$73$	−12.5756	−	7.26053i	−1.47186	−	0.849780i	−0.999500	+	0.0316238i	$0.989932\pi$
$74$	−2.91115	+	1.68075i	−0.338414	+	0.195384i
$75$	1.05588	−	1.37299i	0.121923	−	0.158539i
$76$	6.97993	−	4.02986i	0.800653	−	0.462257i
$77$	5.63860	−	5.23561i	0.642578	−	0.596653i
$78$	−2.06763	+	2.68859i	−0.234113	+	0.304423i
$79$	4.29504			0.483230			0.241615	−	0.970372i	$-0.422323\pi$
$79$	4.29504			0.483230			0.241615	+	0.970372i	$0.422323\pi$
$80$	0.500000	−	0.866025i	0.0559017	−	0.0968246i
$81$	0.0387579	−	8.99992i	0.00430643	−	0.999991i
$82$	−7.35799	+	4.24814i	−0.812554	+	0.469128i
$83$	6.87362	−	11.9055i	0.754477	−	1.30679i	−0.191156	−	0.981560i	$-0.561224\pi$
$83$	6.87362	−	11.9055i	0.754477	−	1.30679i	0.945634	−	0.325233i	$-0.105443\pi$
$84$	2.64912	+	3.73928i	0.289042	+	0.407988i
$85$	1.68420	+	2.91713i	0.182678	+	0.316407i
$86$	1.71721	+	0.991430i	0.185171	+	0.106909i
$87$	−0.493925	+	3.72078i	−0.0529544	+	0.398909i
$88$	1.45413	+	2.51862i	0.155010	+	0.268486i
$89$	8.43872	+	14.6163i	0.894502	+	1.54932i	0.834420	+	0.551130i	$0.185803\pi$
$89$	8.43872	+	14.6163i	0.894502	+	1.54932i	0.0600826	+	0.998193i	$0.480864\pi$
$90$	−2.89944	+	0.770216i	−0.305628	+	0.0811879i
$91$	−3.79661	+	3.52526i	−0.397993	+	0.369548i
$92$	2.47278	+	1.42766i	0.257805	+	0.148844i
$93$	3.53036	−	1.45787i	0.366081	−	0.151174i
$94$		−	0.647198i		−	0.0667534i
$95$			8.05973i			0.826911i
$96$	−1.60092	+	0.661104i	−0.163393	+	0.0674736i
$97$	5.21536	+	3.01109i	0.529539	+	0.305730i	0.740829	−	0.671694i	$-0.234433\pi$
$97$	5.21536	+	3.01109i	0.529539	+	0.305730i	−0.211289	+	0.977424i	$0.567766\pi$
$98$	3.04169	+	6.30461i	0.307257	+	0.636862i
$99$	2.27627	−	8.42258i	0.228774	−	0.846501i
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	7.83797	+	13.5758i	0.779907	+	1.35084i	0.931995	+	0.362471i	$0.118067\pi$
$101$	7.83797	+	13.5758i	0.779907	+	1.35084i	−0.152088	+	0.988367i	$0.548600\pi$
$102$	0.767750	−	5.78352i	0.0760186	−	0.572654i
$103$	−3.19529	−	1.84480i	−0.314841	−	0.181774i	0.334250	−	0.942485i	$-0.391517\pi$
$103$	−3.19529	−	1.84480i	−0.314841	−	0.181774i	−0.649091	+	0.760711i	$0.724850\pi$
$104$	−0.979098	−	1.69585i	−0.0960085	−	0.166292i
$105$	−4.56287	+	0.424564i	−0.445290	+	0.0414332i
$106$	−5.34261	+	9.25368i	−0.518921	+	0.898797i
$107$	−10.6841	+	6.16845i	−1.03287	+	0.596327i	−0.917805	−	0.397031i	$-0.870040\pi$
$107$	−10.6841	+	6.16845i	−1.03287	+	0.596327i	−0.115063	+	0.993358i	$0.536707\pi$
$108$	4.79417	+	2.00398i	0.461319	+	0.192833i
$109$	−3.48038	+	6.02819i	−0.333360	+	0.577396i	−0.983168	−	0.182702i	$-0.941516\pi$
$109$	−3.48038	+	6.02819i	−0.333360	+	0.577396i	0.649809	+	0.760098i	$0.274849\pi$
$110$	−2.90825			−0.277291
$111$	−3.54936	+	4.61532i	−0.336890	+	0.438067i
$112$	−2.57921	+	0.589657i	−0.243712	+	0.0557173i
$113$	2.35912	−	1.36204i	0.221927	−	0.128130i	−0.384915	−	0.922952i	$-0.625769\pi$
$113$	2.35912	−	1.36204i	0.221927	−	0.128130i	0.606842	+	0.794822i	$0.292436\pi$
$114$	8.51014	−	11.0659i	0.797048	−	1.03642i
$115$	−2.47278	+	1.42766i	−0.230587	+	0.133130i
$116$	−1.87671	−	1.08352i	−0.174248	−	0.100602i
$117$	−1.53267	+	5.67113i	−0.141695	+	0.524296i
$118$			9.11655i			0.839246i
$119$	2.62381	−	8.51697i	0.240524	−	0.780750i
$120$	0.227927	−	1.71699i	0.0208068	−	0.156739i
$121$	−1.27104	+	2.20151i	−0.115549	+	0.200137i
$122$	3.03785			0.275034
$123$	−8.97108	+	11.6653i	−0.808895	+	1.05183i
$124$			2.20521i			0.198034i
$125$	−1.00000			−0.0894427
$126$	6.71307	+	4.23494i	0.598048	+	0.377278i
$127$	−6.59858			−0.585529			−0.292765	−	0.956185i	$-0.594575\pi$
$127$	−6.59858			−0.585529			−0.292765	+	0.956185i	$0.594575\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	3.40455	+	0.451947i	0.299754	+	0.0397917i
$130$	1.95820			0.171745
$131$	−2.20506	+	3.81928i	−0.192657	+	0.333692i	−0.946130	−	0.323787i	$-0.895044\pi$
$131$	−2.20506	+	3.81928i	−0.192657	+	0.333692i	0.753473	+	0.657479i	$0.228377\pi$
$132$	3.99300	+	3.07078i	0.347546	+	0.267277i
$133$	15.6264	−	14.5096i	1.35498	−	1.25814i
$134$		−	15.1391i		−	1.30782i
$135$	−4.13258	+	3.14989i	−0.355676	+	0.271099i
$136$	2.91713	+	1.68420i	0.250142	+	0.144419i
$137$	−4.23640	+	2.44589i	−0.361940	+	0.208966i	−0.669932	−	0.742423i	$-0.733677\pi$
$137$	−4.23640	+	2.44589i	−0.361940	+	0.208966i	0.307991	+	0.951389i	$0.400343\pi$
$138$	4.90254	+	0.650802i	0.417332	+	0.0554000i
$139$	13.7982	−	7.96639i	1.17035	−	0.675701i	0.216586	−	0.976264i	$-0.430508\pi$
$139$	13.7982	−	7.96639i	1.17035	−	0.675701i	0.953762	+	0.300563i	$0.0971745\pi$
$140$	0.778946	−	2.52849i	0.0658329	−	0.213696i
$141$	−0.427865	−	1.03611i	−0.0360327	−	0.0872563i
$142$	−7.94202			−0.666479
$143$	−2.84746	+	4.93195i	−0.238117	+	0.412430i
$144$	−2.12588	+	2.11675i	−0.177157	+	0.176396i
$145$	1.87671	−	1.08352i	0.155852	−	0.0899813i
$146$	7.26053	−	12.5756i	0.600885	−	1.04076i
$147$	9.03750	+	8.08230i	0.745401	+	0.666617i
$148$	−1.68075	−	2.91115i	−0.138157	−	0.239295i
$149$	−6.20631	−	3.58321i	−0.508441	−	0.293548i	0.223752	−	0.974646i	$-0.428170\pi$
$149$	−6.20631	−	3.58321i	−0.508441	−	0.293548i	−0.732192	+	0.681098i	$0.761503\pi$
$150$	1.37299	+	1.05588i	0.112104	+	0.0862126i
$151$	3.38348	+	5.86035i	0.275343	+	0.476909i	0.970222	−	0.242218i	$-0.0778751\pi$
$151$	3.38348	+	5.86035i	0.275343	+	0.476909i	−0.694878	+	0.719127i	$0.744542\pi$
$152$	4.02986	+	6.97993i	0.326865	+	0.566147i
$153$	−2.59440	−	9.76650i	−0.209745	−	0.789575i
$154$	5.23561	+	5.63860i	0.421897	+	0.454372i
$155$	−1.90977	−	1.10260i	−0.153396	−	0.0885634i
$156$	−2.68859	−	2.06763i	−0.215259	−	0.165543i
$157$			10.0931i			0.805514i	0.915307	+	0.402757i	$0.131948\pi$
$157$			10.0931i			0.805514i	−0.915307	+	0.402757i	$0.868052\pi$
$158$			4.29504i			0.341695i
$159$	−2.43545	+	18.3464i	−0.193144	+	1.45497i
$160$	0.866025	+	0.500000i	0.0684653	+	0.0395285i
$161$	7.21962	+	2.22413i	0.568986	+	0.175286i
$162$	8.99992	+	0.0387579i	0.707100	+	0.00304511i
$163$	11.7073	+	20.2777i	0.916989	+	1.58827i	0.803963	+	0.594679i	$0.202721\pi$
$163$	11.7073	+	20.2777i	0.916989	+	1.58827i	0.113026	+	0.993592i	$0.463946\pi$
$164$	−4.24814	−	7.35799i	−0.331724	−	0.574562i
$165$	−4.65587	+	1.92266i	−0.362459	+	0.149679i
$166$	11.9055	+	6.87362i	0.924042	+	0.533496i
$167$	−5.38906	−	9.33412i	−0.417018	−	0.722296i	0.578620	−	0.815597i	$-0.303591\pi$
$167$	−5.38906	−	9.33412i	−0.417018	−	0.722296i	−0.995638	+	0.0933010i	$0.970258\pi$
$168$	−3.73928	+	2.64912i	−0.288491	+	0.204384i
$169$	−4.58273	+	7.93753i	−0.352518	+	0.610579i
$170$	−2.91713	+	1.68420i	−0.223733	+	0.129173i
$171$	6.30831	−	23.3418i	0.482408	−	1.78499i
$172$	−0.991430	+	1.71721i	−0.0755958	+	0.130936i
$173$	2.57885			0.196067			0.0980333	−	0.995183i	$-0.468745\pi$
$173$	2.57885			0.196067			0.0980333	+	0.995183i	$0.468745\pi$
$174$	−3.72078	−	0.493925i	−0.282071	−	0.0374444i
$175$	1.80026	+	1.93883i	0.136087	+	0.146562i
$176$	−2.51862	+	1.45413i	−0.189848	+	0.109609i
$177$	6.02699	+	14.5949i	0.453016	+	1.09702i
$178$	−14.6163	+	8.43872i	−1.09554	+	0.632509i
$179$	0.461274	+	0.266316i	0.0344772	+	0.0199054i	0.517140	−	0.855901i	$-0.326997\pi$
$179$	0.461274	+	0.266316i	0.0344772	+	0.0199054i	−0.482662	+	0.875807i	$0.660330\pi$
$180$	−0.770216	−	2.89944i	−0.0574085	−	0.216112i
$181$		−	25.2946i		−	1.88013i	−0.340993	−	0.940066i	$-0.610763\pi$
$181$		−	25.2946i		−	1.88013i	0.340993	−	0.940066i	$-0.389237\pi$
$182$	−3.52526	−	3.79661i	−0.261310	−	0.281423i
$183$	4.86335	−	2.00834i	0.359509	−	0.148460i
$184$	−1.42766	+	2.47278i	−0.105248	+	0.182295i
$185$	3.36151			0.247143
$186$	1.45787	+	3.53036i	0.106896	+	0.258859i
$187$		−	9.79617i		−	0.716367i
$188$	0.647198			0.0472018
$189$	13.5468	+	2.34175i	0.985386	+	0.170338i
$190$	−8.05973			−0.584714
$191$			23.3473i			1.68935i	0.535276	+	0.844677i	$0.320208\pi$
$191$			23.3473i			1.68935i	−0.535276	+	0.844677i	$0.679792\pi$
$192$	−0.661104	−	1.60092i	−0.0477111	−	0.115536i
$193$	4.17857			0.300780			0.150390	−	0.988627i	$-0.451947\pi$
$193$	4.17857			0.300780			0.150390	+	0.988627i	$0.451947\pi$
$194$	−3.01109	+	5.21536i	−0.216184	+	0.374441i
$195$	3.13491	−	1.29457i	0.224496	−	0.0927062i
$196$	−6.30461	+	3.04169i	−0.450329	+	0.217264i
$197$			2.79573i			0.199187i	0.995028	+	0.0995936i	$0.0317543\pi$
$197$			2.79573i			0.199187i	−0.995028	+	0.0995936i	$0.968246\pi$
$198$	8.42258	+	2.27627i	0.598567	+	0.161768i
$199$	−3.02178	−	1.74463i	−0.214208	−	0.123673i	0.389057	−	0.921214i	$-0.372801\pi$
$199$	−3.02178	−	1.74463i	−0.214208	−	0.123673i	−0.603266	+	0.797540i	$0.706134\pi$
$200$	−0.866025	+	0.500000i	−0.0612372	+	0.0353553i
$201$	−10.0085	−	24.2365i	−0.705947	−	1.70951i
$202$	−13.5758	+	7.83797i	−0.955187	+	0.551477i
$203$	−5.47932	−	1.68800i	−0.384573	−	0.118475i
$204$	5.78352	+	0.767750i	0.404927	+	0.0537532i
$205$	8.49627			0.593405
$206$	1.84480	−	3.19529i	0.128533	−	0.222626i
$207$	8.27882	−	2.19921i	0.575418	−	0.152856i
$208$	1.69585	−	0.979098i	0.117586	−	0.0678882i
$209$	11.7199	−	20.2994i	0.810679	−	1.40414i
$210$	−0.424564	−	4.56287i	−0.0292977	−	0.314868i
$211$	−4.69846	−	8.13798i	−0.323455	−	0.560241i	0.657743	−	0.753242i	$-0.271511\pi$
$211$	−4.69846	−	8.13798i	−0.323455	−	0.560241i	−0.981199	+	0.193001i	$0.938178\pi$
$212$	−9.25368	−	5.34261i	−0.635545	−	0.366932i
$213$	−12.7145	+	5.25050i	−0.871185	+	0.359758i
$214$	−6.16845	−	10.6841i	−0.421667	−	0.730348i
$215$	−0.991430	−	1.71721i	−0.0676150	−	0.117113i
$216$	−2.00398	+	4.79417i	−0.136353	+	0.326202i
$217$	1.30032	+	5.68769i	0.0882712	+	0.386106i
$218$	−6.02819	−	3.48038i	−0.408281	−	0.235721i
$219$	3.30974	−	24.9325i	0.223651	−	1.68478i
$220$		−	2.90825i		−	0.196074i
$221$			6.59600i			0.443695i
$222$	−4.61532	−	3.54936i	−0.309760	−	0.238218i
$223$	14.4132	+	8.32148i	0.965181	+	0.557248i	0.897764	−	0.440477i	$-0.145191\pi$
$223$	14.4132	+	8.32148i	0.965181	+	0.557248i	0.0674174	+	0.997725i	$0.478524\pi$
$224$	−0.589657	−	2.57921i	−0.0393981	−	0.172330i
$225$	2.89610	+	0.782695i	0.193073	+	0.0521797i
$226$	1.36204	+	2.35912i	0.0906013	+	0.156926i
$227$	−0.765073	−	1.32514i	−0.0507796	−	0.0879529i	0.839518	−	0.543331i	$-0.182837\pi$
$227$	−0.765073	−	1.32514i	−0.0507796	−	0.0879529i	−0.890298	+	0.455378i	$0.849504\pi$
$228$	11.0659	+	8.51014i	0.732860	+	0.563598i
$229$	−19.5572	−	11.2914i	−1.29238	−	0.746154i	−0.313302	−	0.949654i	$-0.601435\pi$
$229$	−19.5572	−	11.2914i	−1.29238	−	0.746154i	−0.979075	+	0.203500i	$0.934768\pi$
$230$	−1.42766	−	2.47278i	−0.0941369	−	0.163050i
$231$	12.1095	+	5.56566i	0.796746	+	0.366194i
$232$	1.08352	−	1.87671i	0.0711365	−	0.123212i
$233$	−1.52031	+	0.877750i	−0.0995986	+	0.0575033i	−0.548972	−	0.835841i	$-0.684981\pi$
$233$	−1.52031	+	0.877750i	−0.0995986	+	0.0575033i	0.449373	+	0.893344i	$0.351647\pi$
$234$	−5.67113	−	1.53267i	−0.370733	−	0.100194i
$235$	−0.323599	+	0.560490i	−0.0211093	+	0.0365623i
$236$	−9.11655			−0.593437
$237$	2.83947	+	6.87602i	0.184443	+	0.446645i
$238$	8.51697	+	2.62381i	0.552073	+	0.170076i
$239$	13.5333	−	7.81348i	0.875399	−	0.505412i	0.00626059	−	0.999980i	$-0.498007\pi$
$239$	13.5333	−	7.81348i	0.875399	−	0.505412i	0.869139	+	0.494568i	$0.164674\pi$
$240$	1.71699	+	0.227927i	0.110831	+	0.0147126i
$241$	−6.76393	+	3.90516i	−0.435703	+	0.251553i	−0.701773	−	0.712400i	$-0.747608\pi$
$241$	−6.76393	+	3.90516i	−0.435703	+	0.251553i	0.266070	+	0.963954i	$0.414275\pi$
$242$	−2.20151	−	1.27104i	−0.141518	−	0.0817056i
$243$	14.4338	−	5.88783i	0.925926	−	0.377705i
$244$			3.03785i			0.194478i
$245$	0.518123	−	6.98080i	0.0331017	−	0.445987i
$246$	−11.6653	−	8.97108i	−0.743754	−	0.571975i
$247$	−7.89126	+	13.6681i	−0.502109	+	0.869678i
$248$	−2.20521			−0.140031
$249$	23.6038	+	3.13336i	1.49583	+	0.198569i
$250$		−	1.00000i		−	0.0632456i
$251$	12.4166			0.783726			0.391863	−	0.920024i	$-0.371831\pi$
$251$	12.4166			0.783726			0.391863	+	0.920024i	$0.371831\pi$
$252$	−4.23494	+	6.71307i	−0.266776	+	0.422884i
$253$	8.30397			0.522066
$254$		−	6.59858i		−	0.414032i
$255$	−3.55665	+	4.62480i	−0.222726	+	0.289616i
$256$	1.00000			0.0625000
$257$	14.7065	−	25.4724i	0.917367	−	1.58893i	0.113969	−	0.993484i	$-0.463644\pi$
$257$	14.7065	−	25.4724i	0.917367	−	1.58893i	0.803398	−	0.595442i	$-0.203023\pi$
$258$	−0.451947	+	3.40455i	−0.0281370	+	0.211958i
$259$	−6.05159	−	6.51739i	−0.376027	−	0.404971i
$260$			1.95820i			0.121442i
$261$	−6.28320	+	1.66909i	−0.388920	+	0.103314i
$262$	−3.81928	−	2.20506i	−0.235956	−	0.136229i
$263$	−22.6005	+	13.0484i	−1.39360	+	0.804598i	−0.993712	−	0.111964i	$-0.964286\pi$
$263$	−22.6005	+	13.0484i	−1.39360	+	0.804598i	−0.399892	+	0.916562i	$0.630952\pi$
$264$	−3.07078	+	3.99300i	−0.188993	+	0.245752i
$265$	9.25368	−	5.34261i	0.568449	−	0.328194i
$266$	14.5096	+	15.6264i	0.889641	+	0.958119i
$267$	−17.8206	+	23.1726i	−1.09060	+	1.41814i
$268$	15.1391			0.924769
$269$	−7.78339	+	13.4812i	−0.474562	+	0.821965i	−0.999576	−	0.0291286i	$-0.990727\pi$
$269$	−7.78339	+	13.4812i	−0.474562	+	0.821965i	0.525014	+	0.851094i	$0.324060\pi$
$270$	−3.14989	−	4.13258i	−0.191696	−	0.251501i
$271$	10.2838	−	5.93737i	0.624698	−	0.360670i	−0.153998	−	0.988071i	$-0.549215\pi$
$271$	10.2838	−	5.93737i	0.624698	−	0.360670i	0.778696	+	0.627402i	$0.215882\pi$
$272$	−1.68420	+	2.91713i	−0.102120	+	0.176877i
$273$	−8.15361	−	3.74750i	−0.493479	−	0.226809i
$274$	−2.44589	−	4.23640i	−0.147762	−	0.255931i
$275$	2.51862	+	1.45413i	0.151878	+	0.0876870i
$276$	−0.650802	+	4.90254i	−0.0391737	+	0.295098i
$277$	−13.7278	−	23.7773i	−0.824825	−	1.42864i	−0.902053	−	0.431626i	$-0.857940\pi$
$277$	−13.7278	−	23.7773i	−0.824825	−	1.42864i	0.0772275	−	0.997013i	$-0.475393\pi$
$278$	7.96639	+	13.7982i	0.477793	+	0.827561i
$279$	4.66787	+	4.68802i	0.279458	+	0.280664i
$280$	2.52849	+	0.778946i	0.151106	+	0.0465509i
$281$	−22.5302	−	13.0078i	−1.34404	−	0.775980i	−0.356639	−	0.934242i	$-0.616077\pi$
$281$	−22.5302	−	13.0078i	−1.34404	−	0.775980i	−0.987397	+	0.158263i	$0.949411\pi$
$282$	1.03611	−	0.427865i	0.0616995	−	0.0254790i
$283$			0.865094i			0.0514245i	0.999669	+	0.0257123i	$0.00818537\pi$
$283$			0.865094i			0.0514245i	−0.999669	+	0.0257123i	$0.991815\pi$
$284$		−	7.94202i		−	0.471272i
$285$	−12.9030	+	5.32832i	−0.764306	+	0.315622i
$286$	−4.93195	−	2.84746i	−0.291632	−	0.168374i
$287$	−15.2955	−	16.4728i	−0.902865	−	0.972360i
$288$	−2.11675	−	2.12588i	−0.124731	−	0.125269i
$289$	2.82692	+	4.89636i	0.166289	+	0.288021i
$290$	1.08352	+	1.87671i	0.0636264	+	0.110204i
$291$	−1.37261	+	10.3400i	−0.0804641	+	0.606142i
$292$	12.5756	+	7.26053i	0.735931	+	0.424890i
$293$	−11.3934	−	19.7339i	−0.665608	−	1.15287i	−0.979120	−	0.203283i	$-0.934839\pi$
$293$	−11.3934	−	19.7339i	−0.665608	−	1.15287i	0.313512	−	0.949584i	$-0.398495\pi$
$294$	−8.08230	+	9.03750i	−0.471369	+	0.527078i
$295$	4.55827	−	7.89516i	0.265393	−	0.459674i
$296$	2.91115	−	1.68075i	0.169207	−	0.0976918i
$297$	14.9887	−	1.92407i	0.869734	−	0.111646i
$298$	3.58321	−	6.20631i	0.207570	−	0.359522i
$299$	−5.59127			−0.323351
$300$	−1.05588	+	1.37299i	−0.0609615	+	0.0792697i
$301$	−1.54454	+	5.01364i	−0.0890258	+	0.288981i
$302$	−5.86035	+	3.38348i	−0.337226	+	0.194697i
$303$	−16.5520	+	21.5229i	−0.950886	+	1.23646i
$304$	−6.97993	+	4.02986i	−0.400326	+	0.231129i
$305$	−2.63086	−	1.51893i	−0.150642	−	0.0869734i
$306$	9.76650	−	2.59440i	0.558314	−	0.148312i
$307$			19.5794i			1.11745i	0.829352	+	0.558726i	$0.188710\pi$
$307$			19.5794i			1.11745i	−0.829352	+	0.558726i	$0.811290\pi$
$308$	−5.63860	+	5.23561i	−0.321289	+	0.298326i
$309$	0.840958	−	6.33500i	0.0478404	−	0.360386i
$310$	1.10260	−	1.90977i	0.0626237	−	0.108468i
$311$	24.7602			1.40402			0.702010	−	0.712167i	$-0.252286\pi$
$311$	24.7602			1.40402			0.702010	+	0.712167i	$0.252286\pi$
$312$	2.06763	−	2.68859i	0.117056	−	0.152211i
$313$		−	29.7074i		−	1.67916i	−0.543233	−	0.839582i	$-0.682800\pi$
$313$		−	29.7074i		−	1.67916i	0.543233	−	0.839582i	$-0.317200\pi$
$314$	−10.0931			−0.569585
$315$	−3.69622	−	7.02410i	−0.208258	−	0.395763i
$316$	−4.29504			−0.241615
$317$			5.98746i			0.336289i	0.985762	+	0.168144i	$0.0537775\pi$
$317$			5.98746i			0.336289i	−0.985762	+	0.168144i	$0.946222\pi$
$318$	−18.3464	−	2.43545i	−1.02882	−	0.136573i
$319$	−6.30228			−0.352860
$320$	−0.500000	+	0.866025i	−0.0279508	+	0.0484123i
$321$	−16.9385	−	13.0263i	−0.945414	−	0.727060i
$322$	−2.22413	+	7.21962i	−0.123946	+	0.402334i
$323$		−	27.1484i		−	1.51058i
$324$	−0.0387579	+	8.99992i	−0.00215322	+	0.499995i
$325$	−1.69585	−	0.979098i	−0.0940687	−	0.0543106i
$326$	−20.2777	+	11.7073i	−1.12308	+	0.648409i
$327$	−11.9515	−	1.58654i	−0.660922	−	0.0877360i
$328$	7.35799	−	4.24814i	0.406277	−	0.234564i
$329$	1.66926	−	0.381624i	0.0920291	−	0.0210396i
$330$	−1.92266	−	4.65587i	−0.105839	−	0.256297i
$331$	7.70669			0.423598			0.211799	−	0.977313i	$-0.432068\pi$
$331$	7.70669			0.423598			0.211799	+	0.977313i	$0.432068\pi$
$332$	−6.87362	+	11.9055i	−0.377239	+	0.653396i
$333$	−9.73525	−	2.63103i	−0.533488	−	0.144180i
$334$	9.33412	−	5.38906i	0.510741	−	0.294876i
$335$	−7.56956	+	13.1109i	−0.413569	+	0.716323i
$336$	−2.64912	−	3.73928i	−0.144521	−	0.203994i
$337$	3.29935	+	5.71465i	0.179727	+	0.311297i	0.941787	−	0.336210i	$-0.109145\pi$
$337$	3.29935	+	5.71465i	0.179727	+	0.311297i	−0.762060	+	0.647507i	$0.775812\pi$
$338$	−7.93753	−	4.58273i	−0.431745	−	0.249268i
$339$	3.74013	+	2.87631i	0.203136	+	0.156220i
$340$	−1.68420	−	2.91713i	−0.0913388	−	0.158203i
$341$	3.20665	+	5.55408i	0.173650	+	0.300770i
$342$	23.3418	+	6.30831i	1.26218	+	0.341114i
$343$	−14.4673	+	11.5627i	−0.781163	+	0.624327i
$344$	−1.71721	−	0.991430i	−0.0925856	−	0.0534543i
$345$	−3.92033	−	3.01488i	−0.211063	−	0.162316i
$346$			2.57885i			0.138640i
$347$		−	12.1162i		−	0.650431i	−0.945640	−	0.325216i	$-0.894563\pi$
$347$		−	12.1162i		−	0.650431i	0.945640	−	0.325216i	$-0.105437\pi$
$348$	0.493925	−	3.72078i	0.0264772	−	0.199455i
$349$	−0.214315	−	0.123735i	−0.0114720	−	0.00662337i	0.494253	−	0.869318i	$-0.335442\pi$
$349$	−0.214315	−	0.123735i	−0.0114720	−	0.00662337i	−0.505725	+	0.862695i	$0.668775\pi$
$350$	−1.93883	+	1.80026i	−0.103635	+	0.0962280i
$351$	−10.0923	+	1.29553i	−0.538686	+	0.0691500i
$352$	−1.45413	−	2.51862i	−0.0775051	−	0.134243i
$353$	−0.0652598	−	0.113033i	−0.00347343	−	0.00601615i	0.864283	−	0.503005i	$-0.167772\pi$
$353$	−0.0652598	−	0.113033i	−0.00347343	−	0.00601615i	−0.867757	+	0.496989i	$0.834439\pi$
$354$	−14.5949	+	6.02699i	−0.775708	+	0.320331i
$355$	6.87799	+	3.97101i	0.365046	+	0.210759i
$356$	−8.43872	−	14.6163i	−0.447251	−	0.774662i
$357$	15.3696	−	1.43010i	0.813445	−	0.0756891i
$358$	−0.266316	+	0.461274i	−0.0140753	+	0.0243791i
$359$	−8.88009	+	5.12692i	−0.468673	+	0.270589i	−0.715684	−	0.698424i	$-0.753885\pi$
$359$	−8.88009	+	5.12692i	−0.468673	+	0.270589i	0.247011	+	0.969013i	$0.420552\pi$
$360$	2.89944	−	0.770216i	0.152814	−	0.0405939i
$361$	22.9796	−	39.8018i	1.20945	−	2.09483i
$362$	25.2946			1.32945
$363$	−4.36473	−	0.579408i	−0.229089	−	0.0304110i
$364$	3.79661	−	3.52526i	0.198996	−	0.184774i
$365$	−12.5756	+	7.26053i	−0.658237	+	0.380033i
$366$	2.00834	+	4.86335i	0.104977	+	0.254212i
$367$	0.374347	−	0.216129i	0.0195407	−	0.0112818i	−0.490198	−	0.871611i	$-0.663075\pi$
$367$	0.374347	−	0.216129i	0.0195407	−	0.0112818i	0.509739	+	0.860329i	$0.329742\pi$
$368$	−2.47278	−	1.42766i	−0.128902	−	0.0744218i
$369$	−24.6060	−	6.64999i	−1.28094	−	0.346185i
$370$			3.36151i			0.174756i
$371$	−27.0175	−	8.32321i	−1.40268	−	0.432120i
$372$	−3.53036	+	1.45787i	−0.183041	+	0.0755872i
$373$	−1.54641	+	2.67846i	−0.0800700	+	0.138685i	−0.903280	−	0.429052i	$-0.858848\pi$
$373$	−1.54641	+	2.67846i	−0.0800700	+	0.138685i	0.823210	+	0.567737i	$0.192181\pi$
$374$	9.79617			0.506548
$375$	−0.661104	−	1.60092i	−0.0341393	−	0.0826711i
$376$			0.647198i			0.0333767i
$377$	4.24348			0.218550
$378$	−2.34175	+	13.5468i	−0.120447	+	0.696773i
$379$	−9.20781			−0.472973			−0.236487	−	0.971635i	$-0.575996\pi$
$379$	−9.20781			−0.472973			−0.236487	+	0.971635i	$0.575996\pi$
$380$		−	8.05973i		−	0.413455i
$381$	−4.36235	−	10.5638i	−0.223490	−	0.541199i
$382$	−23.3473			−1.19455
$383$	12.2460	−	21.2108i	0.625743	−	1.08382i	−0.362653	−	0.931924i	$-0.618129\pi$
$383$	12.2460	−	21.2108i	0.625743	−	1.08382i	0.988397	−	0.151895i	$-0.0485376\pi$
$384$	1.60092	−	0.661104i	0.0816966	−	0.0337368i
$385$	−1.71487	−	7.50098i	−0.0873978	−	0.382285i
$386$			4.17857i			0.212684i
$387$	1.52723	+	5.74919i	0.0776335	+	0.292248i
$388$	−5.21536	−	3.01109i	−0.264770	−	0.152865i
$389$	−4.52023	+	2.60976i	−0.229185	+	0.132320i	−0.610196	−	0.792251i	$-0.708909\pi$
$389$	−4.52023	+	2.60976i	−0.229185	+	0.132320i	0.381011	+	0.924570i	$0.375576\pi$
$390$	1.29457	+	3.13491i	0.0655532	+	0.158743i
$391$	8.32931	−	4.80893i	0.421232	−	0.243198i
$392$	−3.04169	−	6.30461i	−0.153629	−	0.318431i
$393$	−7.57213	−	1.00518i	−0.381963	−	0.0507048i
$394$	−2.79573			−0.140847
$395$	2.14752	−	3.71962i	0.108054	−	0.187154i
$396$	−2.27627	+	8.42258i	−0.114387	+	0.423251i
$397$	8.32819	−	4.80828i	0.417980	−	0.241321i	−0.276233	−	0.961091i	$-0.589086\pi$
$397$	8.32819	−	4.80828i	0.417980	−	0.241321i	0.694213	+	0.719770i	$0.255753\pi$
$398$	1.74463	−	3.02178i	0.0874502	−	0.151468i
$399$	33.5594	+	15.4243i	1.68007	+	0.772181i
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	−15.8370	−	9.14348i	−0.790861	−	0.456604i	0.0494047	−	0.998779i	$-0.484268\pi$
$401$	−15.8370	−	9.14348i	−0.790861	−	0.456604i	−0.840266	+	0.542175i	$0.817601\pi$
$402$	24.2365	−	10.0085i	1.20881	−	0.499180i
$403$	−2.15912	−	3.73970i	−0.107553	−	0.186288i
$404$	−7.83797	−	13.5758i	−0.389953	−	0.675419i
$405$	−7.77478	−	4.53352i	−0.386332	−	0.225273i
$406$	1.68800	−	5.47932i	0.0837742	−	0.271934i
$407$	−8.46635	−	4.88805i	−0.419661	−	0.242292i
$408$	−0.767750	+	5.78352i	−0.0380093	+	0.286327i
$409$			4.06433i			0.200968i	0.994939	+	0.100484i	$0.0320391\pi$
$409$			4.06433i			0.200968i	−0.994939	+	0.100484i	$0.967961\pi$
$410$			8.49627i			0.419601i
$411$	−6.71637	−	5.16515i	−0.331294	−	0.254778i
$412$	3.19529	+	1.84480i	0.157421	+	0.0908868i
$413$	−23.5135	+	5.37563i	−1.15702	+	0.264518i
$414$	2.19921	+	8.27882i	0.108085	+	0.406882i
$415$	−6.87362	−	11.9055i	−0.337412	−	0.584416i
$416$	0.979098	+	1.69585i	0.0480042	+	0.0831458i
$417$	21.8756	+	16.8232i	1.07125	+	0.823835i
$418$	20.2994	+	11.7199i	0.992875	+	0.573237i
$419$	6.00474	+	10.4005i	0.293351	+	0.508098i	0.974600	−	0.223953i	$-0.0718963\pi$
$419$	6.00474	+	10.4005i	0.293351	+	0.508098i	−0.681249	+	0.732052i	$0.738563\pi$
$420$	4.56287	−	0.424564i	0.222645	−	0.0207166i
$421$	−6.01384	+	10.4163i	−0.293097	+	0.507658i	−0.974540	−	0.224212i	$-0.928019\pi$
$421$	−6.01384	+	10.4163i	−0.293097	+	0.507658i	0.681444	+	0.731871i	$0.261352\pi$
$422$	8.13798	−	4.69846i	0.396150	−	0.228718i
$423$	1.37587	−	1.36995i	0.0668970	−	0.0666095i
$424$	5.34261	−	9.25368i	0.259460	−	0.449398i
$425$	3.36841			0.163392
$426$	−5.25050	−	12.7145i	−0.254387	−	0.616021i
$427$	1.79129	+	7.83525i	0.0866865	+	0.379174i
$428$	10.6841	−	6.16845i	0.516434	−	0.298163i
$429$	−9.77812	−	1.29802i	−0.472092	−	0.0626692i
$430$	1.71721	−	0.991430i	0.0828111	−	0.0478110i
$431$	−8.15790	−	4.70997i	−0.392952	−	0.226871i	0.290486	−	0.956879i	$-0.406183\pi$
$431$	−8.15790	−	4.70997i	−0.392952	−	0.226871i	−0.683439	+	0.730008i	$0.739516\pi$
$432$	−4.79417	−	2.00398i	−0.230660	−	0.0964164i
$433$		−	28.8287i		−	1.38542i	−0.721216	−	0.692710i	$-0.756417\pi$
$433$		−	28.8287i		−	1.38542i	0.721216	−	0.692710i	$-0.243583\pi$
$434$	−5.68769	+	1.30032i	−0.273018	+	0.0624172i
$435$	2.97532	+	2.28814i	0.142656	+	0.109708i
$436$	3.48038	−	6.02819i	0.166680	−	0.288698i
$437$	23.0131			1.10086
$438$	24.9325	+	3.30974i	1.19132	+	0.158145i
$439$			35.2441i			1.68211i	0.540949	+	0.841055i	$0.318065\pi$
$439$			35.2441i			1.68211i	−0.540949	+	0.841055i	$0.681935\pi$
$440$	2.90825			0.138645
$441$	−6.96437	+	19.8116i	−0.331637	+	0.943407i
$442$	−6.59600			−0.313740
$443$			21.2414i			1.00921i	0.863350	+	0.504605i	$0.168362\pi$
$443$			21.2414i			1.00921i	−0.863350	+	0.504605i	$0.831638\pi$
$444$	3.54936	−	4.61532i	0.168445	−	0.219033i
$445$	16.8774			0.800067
$446$	−8.32148	+	14.4132i	−0.394034	+	0.682486i
$447$	1.63342	−	12.3047i	0.0772581	−	0.581991i
$448$	2.57921	−	0.589657i	0.121856	−	0.0278587i
$449$			16.9305i			0.799002i	0.916733	+	0.399501i	$0.130817\pi$
$449$			16.9305i			0.799002i	−0.916733	+	0.399501i	$0.869183\pi$
$450$	−0.782695	+	2.89610i	−0.0368966	+	0.136523i
$451$	−21.3989	−	12.3546i	−1.00763	−	0.581757i
$452$	−2.35912	+	1.36204i	−0.110964	+	0.0640648i
$453$	−7.14512	+	9.29098i	−0.335707	+	0.436528i
$454$	1.32514	−	0.765073i	0.0621921	−	0.0359066i
$455$	1.15466	+	5.05059i	0.0541314	+	0.236775i
$456$	−8.51014	+	11.0659i	−0.398524	+	0.518210i
$457$	33.2351			1.55467			0.777335	−	0.629086i	$-0.216571\pi$
$457$	33.2351			1.55467			0.777335	+	0.629086i	$0.216571\pi$
$458$	11.2914	−	19.5572i	0.527610	−	0.913848i
$459$	13.9202	−	10.6101i	0.649740	−	0.495237i
$460$	2.47278	−	1.42766i	0.115294	−	0.0665649i
$461$	−13.2679	+	22.9806i	−0.617946	+	1.07031i	0.371914	+	0.928267i	$0.378702\pi$
$461$	−13.2679	+	22.9806i	−0.617946	+	1.07031i	−0.989860	+	0.142047i	$0.954632\pi$
$462$	−5.56566	+	12.1095i	−0.258938	+	0.563384i
$463$	−5.25467	−	9.10135i	−0.244205	−	0.422976i	0.717703	−	0.696350i	$-0.245194\pi$
$463$	−5.25467	−	9.10135i	−0.244205	−	0.422976i	−0.961908	+	0.273374i	$0.911860\pi$
$464$	1.87671	+	1.08352i	0.0871240	+	0.0503011i
$465$	0.502626	−	3.78632i	0.0233087	−	0.175586i
$466$	−0.877750	−	1.52031i	−0.0406610	−	0.0704269i
$467$	−6.14519	−	10.6438i	−0.284366	−	0.492536i	0.688089	−	0.725626i	$-0.258450\pi$
$467$	−6.14519	−	10.6438i	−0.284366	−	0.492536i	−0.972455	+	0.233090i	$0.925116\pi$
$468$	1.53267	−	5.67113i	0.0708477	−	0.262148i
$469$	39.0469	−	8.92688i	1.80302	−	0.412205i
$470$	−0.560490	−	0.323599i	−0.0258535	−	0.0149265i
$471$	−16.1582	+	6.67256i	−0.744529	+	0.307456i
$472$		−	9.11655i		−	0.419623i
$473$			5.76665i			0.265151i
$474$	−6.87602	+	2.83947i	−0.315826	+	0.130421i
$475$	6.97993	+	4.02986i	0.320261	+	0.184903i
$476$	−2.62381	+	8.51697i	−0.120262	+	0.390375i
$477$	−30.9812	+	8.22993i	−1.41853	+	0.376823i
$478$	7.81348	+	13.5333i	0.357380	+	0.619001i
$479$	15.8696	+	27.4869i	0.725100	+	1.25591i	0.958933	+	0.283633i	$0.0915399\pi$
$479$	15.8696	+	27.4869i	0.725100	+	1.25591i	−0.233833	+	0.972277i	$0.575127\pi$
$480$	−0.227927	+	1.71699i	−0.0104034	+	0.0783694i
$481$	5.70060	+	3.29124i	0.259925	+	0.150068i
$482$	−3.90516	−	6.76393i	−0.177875	−	0.308089i
$483$	1.21226	+	13.0284i	0.0551599	+	0.592814i
$484$	1.27104	−	2.20151i	0.0577746	−	0.100069i
$485$	5.21536	−	3.01109i	0.236817	−	0.136726i
$486$	5.88783	+	14.4338i	0.267077	+	0.654729i
$487$	20.7358	−	35.9155i	0.939630	−	1.62749i	0.173468	−	0.984840i	$-0.444503\pi$
$487$	20.7358	−	35.9155i	0.939630	−	1.62749i	0.766162	−	0.642647i	$-0.222164\pi$
$488$	−3.03785			−0.137517
$489$	−24.7232	+	32.1481i	−1.11802	+	1.45379i
$490$	6.98080	+	0.518123i	0.315360	+	0.0234064i
$491$	9.34197	−	5.39359i	0.421597	−	0.243409i	−0.274163	−	0.961683i	$-0.588401\pi$
$491$	9.34197	−	5.39359i	0.421597	−	0.243409i	0.695760	+	0.718274i	$0.255068\pi$
$492$	8.97108	−	11.6653i	0.404448	−	0.525913i
$493$	−6.32152	+	3.64973i	−0.284707	+	0.164376i
$494$	−13.6681	−	7.89126i	−0.614956	−	0.355045i
$495$	−6.15603	−	6.18260i	−0.276693	−	0.277887i
$496$		−	2.20521i		−	0.0990168i
$497$	−4.68306	−	20.4841i	−0.210064	−	0.918837i
$498$	−3.13336	+	23.6038i	−0.140409	+	1.05771i
$499$	−13.4335	+	23.2675i	−0.601365	+	1.04159i	0.391250	+	0.920285i	$0.372043\pi$
$499$	−13.4335	+	23.2675i	−0.601365	+	1.04159i	−0.992615	+	0.121310i	$0.961290\pi$
$500$	1.00000			0.0447214
$501$	11.3804	−	14.7983i	0.508441	−	0.661138i
$502$			12.4166i			0.554178i
$503$	36.7424			1.63826			0.819131	−	0.573606i	$-0.194456\pi$
$503$	36.7424			1.63826			0.819131	+	0.573606i	$0.194456\pi$
$504$	−6.71307	−	4.23494i	−0.299024	−	0.188639i
$505$	15.6759			0.697570
$506$			8.30397i			0.369156i
$507$	−15.7370	−	2.08905i	−0.698905	−	0.0927782i
$508$	6.59858			0.292765
$509$	−6.13530	+	10.6266i	−0.271942	+	0.471018i	−0.969359	−	0.245648i	$-0.920999\pi$
$509$	−6.13530	+	10.6266i	−0.271942	+	0.471018i	0.697417	+	0.716666i	$0.254333\pi$
$510$	−4.62480	−	3.55665i	−0.204789	−	0.157491i
$511$	36.7163	+	11.3111i	1.62423	+	0.500374i
$512$			1.00000i			0.0441942i
$513$	41.5387	−	5.33225i	1.83398	−	0.235424i
$514$	25.4724	+	14.7065i	1.12354	+	0.648676i
$515$	−3.19529	+	1.84480i	−0.140801	+	0.0812916i
$516$	−3.40455	−	0.451947i	−0.149877	−	0.0198958i
$517$	1.63004	−	0.941107i	0.0716893	−	0.0413898i
$518$	6.51739	−	6.05159i	0.286358	−	0.265891i
$519$	1.70489	+	4.12853i	0.0748363	+	0.181223i
$520$	−1.95820			−0.0858726
$521$	14.0346	−	24.3087i	0.614868	−	1.06498i	−0.375540	−	0.926806i	$-0.622543\pi$
$521$	14.0346	−	24.3087i	0.614868	−	1.06498i	0.990408	−	0.138176i	$-0.0441239\pi$
$522$	−1.66909	−	6.28320i	−0.0730539	−	0.275008i
$523$	−15.2468	+	8.80274i	−0.666696	+	0.384917i	−0.794824	−	0.606841i	$-0.792437\pi$
$523$	−15.2468	+	8.80274i	−0.666696	+	0.384917i	0.128128	+	0.991758i	$0.459103\pi$
$524$	2.20506	−	3.81928i	0.0963285	−	0.166846i
$525$	−1.91375	+	4.16384i	−0.0835229	+	0.181725i
$526$	−13.0484	−	22.6005i	−0.568937	−	0.985427i
$527$	6.43288	+	3.71402i	0.280220	+	0.161785i
$528$	−3.99300	−	3.07078i	−0.173773	−	0.133638i
$529$	−7.42359	−	12.8580i	−0.322765	−	0.559045i
$530$	5.34261	+	9.25368i	0.232068	+	0.401954i
$531$	−19.3807	+	19.2974i	−0.841051	+	0.837437i
$532$	−15.6264	+	14.5096i	−0.677492	+	0.629071i
$533$	14.4084	+	8.31869i	0.624096	+	0.360322i
$534$	−23.1726	−	17.8206i	−1.00278	−	0.771174i
$535$			12.3369i			0.533371i
$536$			15.1391i			0.653910i
$537$	−0.121401	+	0.914525i	−0.00523885	+	0.0394646i
$538$	−13.4812	−	7.78339i	−0.581217	−	0.335566i
$539$	−11.4559	+	16.8286i	−0.493441	+	0.724857i
$540$	4.13258	−	3.14989i	0.177838	−	0.135550i
$541$	−11.8477	−	20.5208i	−0.509372	−	0.882258i	−0.999941	−	0.0108558i	$-0.996544\pi$
$541$	−11.8477	−	20.5208i	−0.509372	−	0.882258i	0.490569	−	0.871402i	$-0.336789\pi$
$542$	5.93737	+	10.2838i	0.255032	+	0.441728i
$543$	40.4946	−	16.7223i	1.73779	−	0.717625i
$544$	−2.91713	−	1.68420i	−0.125071	−	0.0722096i
$545$	3.48038	+	6.02819i	0.149083	+	0.258219i
$546$	3.74750	−	8.15361i	0.160378	−	0.348942i
$547$	−16.4082	+	28.4199i	−0.701566	+	1.21515i	0.266351	+	0.963876i	$0.414182\pi$
$547$	−16.4082	+	28.4199i	−0.701566	+	1.21515i	−0.967917	+	0.251271i	$0.919151\pi$
$548$	4.23640	−	2.44589i	0.180970	−	0.104483i
$549$	6.43036	+	6.45812i	0.274441	+	0.275626i
$550$	−1.45413	+	2.51862i	−0.0620041	+	0.107394i
$551$	−17.4657			−0.744065
$552$	−4.90254	−	0.650802i	−0.208666	−	0.0277000i
$553$	−11.0778	+	2.53260i	−0.471076	+	0.107697i
$554$	23.7773	−	13.7278i	1.01020	−	0.583240i
$555$	2.22230	+	5.38150i	0.0943316	+	0.228432i
$556$	−13.7982	+	7.96639i	−0.585174	+	0.337850i
$557$	20.6283	+	11.9097i	0.874048	+	0.504632i	0.868691	−	0.495354i	$-0.164962\pi$
$557$	20.6283	+	11.9097i	0.874048	+	0.504632i	0.00535689	+	0.999986i	$0.498295\pi$
$558$	−4.68802	+	4.66787i	−0.198460	+	0.197607i
$559$		−	3.88283i		−	0.164226i
$560$	−0.778946	+	2.52849i	−0.0329165	+	0.106848i
$561$	15.6829	−	6.47629i	0.662132	−	0.273429i
$562$	13.0078	−	22.5302i	0.548700	−	0.950377i
$563$	−18.0130			−0.759157			−0.379579	−	0.925159i	$-0.623931\pi$
$563$	−18.0130			−0.759157			−0.379579	+	0.925159i	$0.623931\pi$
$564$	0.427865	+	1.03611i	0.0180164	+	0.0436282i
$565$		−	2.72407i		−	0.114603i
$566$	−0.865094			−0.0363626
$567$	5.20689	+	23.2355i	0.218669	+	0.975799i
$568$	7.94202			0.333240
$569$		−	15.9044i		−	0.666747i	−0.942795	−	0.333374i	$-0.891813\pi$
$569$		−	15.9044i		−	0.666747i	0.942795	−	0.333374i	$-0.108187\pi$
$570$	−5.32832	−	12.9030i	−0.223179	−	0.540446i
$571$	27.5270			1.15197			0.575985	−	0.817461i	$-0.304619\pi$
$571$	27.5270			1.15197			0.575985	+	0.817461i	$0.304619\pi$
$572$	2.84746	−	4.93195i	0.119058	−	0.206215i
$573$	−37.3772	+	15.4350i	−1.56146	+	0.644807i
$574$	16.4728	−	15.2955i	0.687563	−	0.638422i
$575$			2.85531i			0.119075i
$576$	2.12588	−	2.11675i	0.0885785	−	0.0881978i
$577$	−17.2512	−	9.95997i	−0.718176	−	0.414639i	0.0959051	−	0.995390i	$-0.469425\pi$
$577$	−17.2512	−	9.95997i	−0.718176	−	0.414639i	−0.814081	+	0.580752i	$0.802759\pi$
$578$	−4.89636	+	2.82692i	−0.203662	+	0.117584i
$579$	2.76247	+	6.68955i	0.114804	+	0.278008i
$580$	−1.87671	+	1.08352i	−0.0779261	+	0.0449907i
$581$	−10.7083	+	34.7597i	−0.444257	+	1.44207i
$582$	−10.3400	−	1.37261i	−0.428607	−	0.0568967i
$583$	−31.0753			−1.28701
$584$	−7.26053	+	12.5756i	−0.300443	+	0.520382i
$585$	4.14501	+	4.16290i	0.171375	+	0.172115i
$586$	19.7339	−	11.3934i	0.815200	−	0.470656i
$587$	17.0018	−	29.4479i	0.701739	−	1.21545i	−0.266117	−	0.963941i	$-0.585741\pi$
$587$	17.0018	−	29.4479i	0.701739	−	1.21545i	0.967856	−	0.251506i	$-0.0809259\pi$
$588$	−9.03750	−	8.08230i	−0.372700	−	0.333308i
$589$	8.88669	+	15.3922i	0.366170	+	0.634225i
$590$	7.89516	+	4.55827i	0.325039	+	0.187661i
$591$	−4.47573	+	1.84827i	−0.184107	+	0.0760275i
$592$	1.68075	+	2.91115i	0.0690785	+	0.119647i
$593$	5.23235	+	9.06270i	0.214867	+	0.372160i	0.953231	−	0.302241i	$-0.0977349\pi$
$593$	5.23235	+	9.06270i	0.214867	+	0.372160i	−0.738364	+	0.674402i	$0.764402\pi$
$594$	1.92407	+	14.9887i	0.0789457	+	0.614995i
$595$	−6.06401	−	6.53077i	−0.248600	−	0.267735i
$596$	6.20631	+	3.58321i	0.254220	+	0.146774i
$597$	0.795294	−	5.99101i	0.0325492	−	0.245196i
$598$		−	5.59127i		−	0.228644i
$599$			15.9493i			0.651672i	0.945426	+	0.325836i	$0.105646\pi$
$599$			15.9493i			0.651672i	−0.945426	+	0.325836i	$0.894354\pi$
$600$	−1.37299	−	1.05588i	−0.0560522	−	0.0431063i
$601$	14.6089	+	8.43447i	0.595911	+	0.344049i	0.767431	−	0.641131i	$-0.221535\pi$
$601$	14.6089	+	8.43447i	0.595911	+	0.344049i	−0.171520	+	0.985181i	$0.554868\pi$
$602$	−5.01364	−	1.54454i	−0.204341	−	0.0629508i
$603$	32.1840	−	32.0457i	1.31063	−	1.30500i
$604$	−3.38348	−	5.86035i	−0.137672	−	0.238454i
$605$	1.27104	+	2.20151i	0.0516752	+	0.0895040i
$606$	−21.5229	−	16.5520i	−0.874310	−	0.672378i
$607$	−8.28479	−	4.78322i	−0.336269	−	0.194145i	0.322352	−	0.946620i	$-0.395527\pi$
$607$	−8.28479	−	4.78322i	−0.336269	−	0.194145i	−0.658621	+	0.752475i	$0.728860\pi$
$608$	−4.02986	−	6.97993i	−0.163433	−	0.283073i
$609$	−0.920045	−	9.88790i	−0.0372821	−	0.400678i
$610$	1.51893	−	2.63086i	0.0614995	−	0.106520i
$611$	−1.09755	+	0.633670i	−0.0444021	+	0.0256356i
$612$	2.59440	+	9.76650i	0.104872	+	0.394788i
$613$	−19.3430	+	33.5030i	−0.781255	+	1.35317i	0.149956	+	0.988693i	$0.452087\pi$
$613$	−19.3430	+	33.5030i	−0.781255	+	1.35317i	−0.931211	+	0.364480i	$0.881247\pi$
$614$	−19.5794			−0.790158
$615$	5.61692	+	13.6018i	0.226496	+	0.548479i
$616$	−5.23561	−	5.63860i	−0.210949	−	0.227186i
$617$	−26.6003	+	15.3577i	−1.07089	+	0.618277i	−0.928424	−	0.371523i	$-0.878836\pi$
$617$	−26.6003	+	15.3577i	−1.07089	+	0.618277i	−0.142464	+	0.989800i	$0.545502\pi$
$618$	6.33500	+	0.840958i	0.254831	+	0.0338283i
$619$	3.13100	−	1.80768i	0.125845	−	0.0726569i	−0.435756	−	0.900065i	$-0.643519\pi$
$619$	3.13100	−	1.80768i	0.125845	−	0.0726569i	0.561601	+	0.827408i	$0.310186\pi$
$620$	1.90977	+	1.10260i	0.0766981	+	0.0442817i
$621$	8.99392	+	11.7998i	0.360913	+	0.473510i
$622$			24.7602i			0.992793i
$623$	−30.3838	−	32.7225i	−1.21730	−	1.31100i
$624$	2.68859	+	2.06763i	0.107630	+	0.0827714i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	29.7074			1.18735
$627$	40.2457	+	5.34253i	1.60726	+	0.213360i
$628$		−	10.0931i		−	0.402757i
$629$	−11.3229			−0.451474
$630$	7.02410	−	3.69622i	0.279847	−	0.147261i
$631$	40.5503			1.61428			0.807142	−	0.590358i	$-0.201013\pi$
$631$	40.5503			1.61428			0.807142	+	0.590358i	$0.201013\pi$
$632$		−	4.29504i		−	0.170848i
$633$	9.92207	−	12.9019i	0.394367	−	0.512805i
$634$	−5.98746			−0.237792
$635$	−3.29929	+	5.71454i	−0.130928	+	0.226774i
$636$	2.43545	−	18.3464i	0.0965718	−	0.727483i
$637$	7.71354	−	11.3311i	0.305622	−	0.448954i
$638$		−	6.30228i		−	0.249510i
$639$	−16.8112	−	16.8838i	−0.665043	−	0.667913i
$640$	−0.866025	−	0.500000i	−0.0342327	−	0.0197642i
$641$	30.1024	−	17.3796i	1.18897	−	0.686453i	0.230899	−	0.972978i	$-0.425833\pi$
$641$	30.1024	−	17.3796i	1.18897	−	0.686453i	0.958073	+	0.286524i	$0.0924999\pi$
$642$	13.0263	−	16.9385i	0.514109	−	0.668508i
$643$	−0.969046	+	0.559479i	−0.0382154	+	0.0220637i	−0.518986	−	0.854783i	$-0.673690\pi$
$643$	−0.969046	+	0.559479i	−0.0382154	+	0.0220637i	0.480771	+	0.876846i	$0.340357\pi$
$644$	−7.21962	−	2.22413i	−0.284493	−	0.0876432i
$645$	2.09367	−	2.72245i	0.0824382	−	0.107196i
$646$	27.1484			1.06814
$647$	8.00562	−	13.8661i	0.314734	−	0.545134i	−0.664647	−	0.747157i	$-0.731418\pi$
$647$	8.00562	−	13.8661i	0.314734	−	0.545134i	0.979381	+	0.202023i	$0.0647515\pi$
$648$	−8.99992	−	0.0387579i	−0.353550	−	0.00152255i
$649$	−22.9611	+	13.2566i	−0.901302	+	0.520367i
$650$	0.979098	−	1.69585i	0.0384034	−	0.0665166i
$651$	−8.24589	+	5.84186i	−0.323182	+	0.228960i
$652$	−11.7073	−	20.2777i	−0.458494	−	0.794136i
$653$	18.0245	+	10.4064i	0.705352	+	0.407235i	0.809338	−	0.587344i	$-0.199826\pi$
$653$	18.0245	+	10.4064i	0.705352	+	0.407235i	−0.103986	+	0.994579i	$0.533160\pi$
$654$	1.58654	−	11.9515i	0.0620387	−	0.467342i
$655$	2.20506	+	3.81928i	0.0861588	+	0.149232i
$656$	4.24814	+	7.35799i	0.165862	+	0.287281i
$657$	42.1030	−	11.1843i	1.64259	−	0.436343i
$658$	0.381624	+	1.66926i	0.0148773	+	0.0650744i
$659$	1.89741	+	1.09547i	0.0739127	+	0.0426735i	0.536501	−	0.843900i	$-0.319746\pi$
$659$	1.89741	+	1.09547i	0.0739127	+	0.0426735i	−0.462588	+	0.886573i	$0.653079\pi$
$660$	4.65587	−	1.92266i	0.181230	−	0.0748393i
$661$			18.8074i			0.731524i	0.930708	+	0.365762i	$0.119192\pi$
$661$			18.8074i			0.731524i	−0.930708	+	0.365762i	$0.880808\pi$
$662$			7.70669i			0.299529i
$663$	−10.5597	+	4.36064i	−0.410103	+	0.169353i
$664$	−11.9055	−	6.87362i	−0.462021	−	0.266748i
$665$	−4.75247	−	20.7877i	−0.184293	−	0.806112i
$666$	2.63103	−	9.73525i	0.101950	−	0.377233i
$667$	−3.09379	−	5.35859i	−0.119792	−	0.207486i
$668$	5.38906	+	9.33412i	0.208509	+	0.361148i
$669$	−3.79338	+	28.5758i	−0.146660	+	1.10480i
$670$	−13.1109	−	7.56956i	−0.506517	−	0.292438i
$671$	4.41742	+	7.65119i	0.170532	+	0.295371i
$672$	3.73928	−	2.64912i	0.144246	−	0.102192i
$673$	−18.6100	+	32.2335i	−0.717364	+	1.24251i	0.244676	+	0.969605i	$0.421318\pi$
$673$	−18.6100	+	32.2335i	−0.717364	+	1.24251i	−0.962041	+	0.272906i	$0.912015\pi$
$674$	−5.71465	+	3.29935i	−0.220120	+	0.127086i
$675$	0.661591	+	5.15386i	0.0254647	+	0.198372i
$676$	4.58273	−	7.93753i	0.176259	−	0.305290i
$677$	−41.0092			−1.57611			−0.788056	−	0.615604i	$-0.788912\pi$
$677$	−41.0092			−1.57611			−0.788056	+	0.615604i	$0.788912\pi$
$678$	−2.87631	+	3.74013i	−0.110464	+	0.143639i
$679$	−15.2270	−	4.69095i	−0.584358	−	0.180022i
$680$	2.91713	−	1.68420i	0.111867	−	0.0645863i
$681$	1.61566	−	2.10088i	0.0619121	−	0.0805058i
$682$	−5.55408	+	3.20665i	−0.212677	+	0.122789i
$683$	−28.9807	−	16.7320i	−1.10892	−	0.640233i	−0.170368	−	0.985380i	$-0.554496\pi$
$683$	−28.9807	−	16.7320i	−1.10892	−	0.640233i	−0.938549	+	0.345147i	$0.887829\pi$
$684$	−6.30831	+	23.3418i	−0.241204	+	0.892495i
$685$			4.89178i			0.186905i
$686$	−11.5627	−	14.4673i	−0.441466	−	0.552366i
$687$	5.14720	−	38.7743i	0.196378	−	1.47933i
$688$	0.991430	−	1.71721i	0.0377979	−	0.0654679i
$689$	20.9238			0.797132
$690$	3.01488	−	3.92033i	0.114775	−	0.149244i
$691$			43.1762i			1.64250i	0.570569	+	0.821250i	$0.306723\pi$
$691$			43.1762i			1.64250i	−0.570569	+	0.821250i	$0.693277\pi$
$692$	−2.57885			−0.0980333
$693$	−0.904547	+	23.0658i	−0.0343609	+	0.876197i
$694$	12.1162			0.459924
$695$		−	15.9328i		−	0.604365i
$696$	3.72078	+	0.493925i	0.141036	+	0.0187222i
$697$	−28.6189			−1.08402
$698$	0.123735	−	0.214315i	0.00468343	−	0.00811194i
$699$	−2.41029	−	1.85360i	−0.0911655	−	0.0701098i
$700$	−1.80026	−	1.93883i	−0.0680435	−	0.0732809i
$701$			23.1589i			0.874701i	0.899291	+	0.437350i	$0.144083\pi$
$701$			23.1589i			0.874701i	−0.899291	+	0.437350i	$0.855917\pi$
$702$	−1.29553	−	10.0923i	−0.0488965	−	0.380908i
$703$	−23.4631	−	13.5464i	−0.884926	−	0.510912i
$704$	2.51862	−	1.45413i	0.0949240	−	0.0548044i
$705$	−1.11123	−	0.147514i	−0.0418514	−	0.00555569i
$706$	0.113033	−	0.0652598i	0.00425406	−	0.00245608i
$707$	−28.2208	−	30.3930i	−1.06135	−	1.14305i
$708$	−6.02699	−	14.5949i	−0.226508	−	0.548508i
$709$	25.4831			0.957038			0.478519	−	0.878077i	$-0.341174\pi$
$709$	25.4831			0.957038			0.478519	+	0.878077i	$0.341174\pi$
$710$	−3.97101	+	6.87799i	−0.149029	+	0.258126i
$711$	−9.13076	+	9.09153i	−0.342430	+	0.340959i
$712$	14.6163	−	8.43872i	0.547768	−	0.316254i
$713$	−3.14828	+	5.45299i	−0.117904	+	0.204216i
$714$	1.43010	+	15.3696i	0.0535203	+	0.575193i
$715$	2.84746	+	4.93195i	0.106489	+	0.184444i
$716$	−0.461274	−	0.266316i	−0.0172386	−	0.00995271i
$717$	21.4557	+	16.5003i	0.801278	+	0.616214i
$718$	−5.12692	−	8.88009i	−0.191335	−	0.331402i
$719$	1.20759	+	2.09160i	0.0450354	+	0.0780036i	0.887664	−	0.460491i	$-0.152327\pi$
$719$	1.20759	+	2.09160i	0.0450354	+	0.0780036i	−0.842629	+	0.538495i	$0.818993\pi$
$720$	0.770216	+	2.89944i	0.0287042	+	0.108056i
$721$	9.32911	+	2.87400i	0.347434	+	0.107033i
$722$	39.8018	+	22.9796i	1.48127	+	0.855212i
$723$	−10.7235	−	8.24679i	−0.398811	−	0.306702i
$724$			25.2946i			0.940066i
$725$		−	2.16704i		−	0.0804817i
$726$	0.579408	−	4.36473i	0.0215039	−	0.161990i
$727$	23.7545	+	13.7147i	0.881006	+	0.508649i	0.870990	−	0.491301i	$-0.163478\pi$
$727$	23.7545	+	13.7147i	0.881006	+	0.508649i	0.0100163	+	0.999950i	$0.496812\pi$
$728$	3.52526	+	3.79661i	0.130655	+	0.140712i
$729$	18.9682	+	19.2148i	0.702524	+	0.711660i
$730$	−7.26053	−	12.5756i	−0.268724	−	0.465444i
$731$	3.33954	+	5.78425i	0.123517	+	0.213938i
$732$	−4.86335	+	2.00834i	−0.179755	+	0.0742302i
$733$	36.8669	+	21.2851i	1.36171	+	0.786184i	0.989852	−	0.142105i	$-0.0453871\pi$
$733$	36.8669	+	21.2851i	1.36171	+	0.786184i	0.371859	+	0.928289i	$0.378720\pi$
$734$	0.216129	+	0.374347i	0.00797747	+	0.0138174i
$735$	11.5182	−	3.78556i	0.424856	−	0.139633i
$736$	1.42766	−	2.47278i	0.0526241	−	0.0911477i
$737$	38.1297	−	22.0142i	1.40452	−	0.810903i
$738$	6.64999	−	24.6060i	0.244790	−	0.905761i
$739$	−17.3740	+	30.0927i	−0.639113	+	1.10698i	0.346514	+	0.938045i	$0.387365\pi$
$739$	−17.3740	+	30.0927i	−0.639113	+	1.10698i	−0.985628	+	0.168932i	$0.945968\pi$
$740$	−3.36151			−0.123571
$741$	−27.0984	−	3.59726i	−0.995485	−	0.132149i
$742$	8.32321	−	27.0175i	0.305555	−	0.991842i
$743$	−30.6126	+	17.6742i	−1.12307	+	0.648404i	−0.942183	−	0.335100i	$-0.891230\pi$
$743$	−30.6126	+	17.6742i	−1.12307	+	0.648404i	−0.180886	+	0.983504i	$0.557897\pi$
$744$	−1.45787	−	3.53036i	−0.0534482	−	0.129429i
$745$	−6.20631	+	3.58321i	−0.227382	+	0.131279i
$746$	−2.67846	−	1.54641i	−0.0980654	−	0.0566181i
$747$	10.5883	+	39.8593i	0.387407	+	1.45838i
$748$			9.79617i			0.358183i
$749$	23.9192	−	22.2096i	0.873987	−	0.811523i
$750$	1.60092	−	0.661104i	0.0584573	−	0.0241401i
$751$	17.3461	−	30.0443i	0.632968	−	1.09633i	−0.353974	−	0.935255i	$-0.615170\pi$
$751$	17.3461	−	30.0443i	0.632968	−	1.09633i	0.986942	−	0.161077i	$-0.0514968\pi$
$752$	−0.647198			−0.0236009
$753$	8.20863	+	19.8779i	0.299139	+	0.724391i
$754$			4.24348i			0.154539i
$755$	6.76696			0.246275
$756$	−13.5468	−	2.34175i	−0.492693	−	0.0851688i
$757$	39.4586			1.43415			0.717074	−	0.696997i	$-0.245481\pi$
$757$	39.4586			1.43415			0.717074	+	0.696997i	$0.245481\pi$
$758$		−	9.20781i		−	0.334443i
$759$	5.48979	+	13.2940i	0.199267	+	0.482541i
$760$	8.05973			0.292357
$761$	5.67608	−	9.83125i	0.205758	−	0.356383i	−0.744616	−	0.667493i	$-0.767367\pi$
$761$	5.67608	−	9.83125i	0.205758	−	0.356383i	0.950374	+	0.311110i	$0.100701\pi$
$762$	10.5638	−	4.36235i	0.382686	−	0.158031i
$763$	5.42205	−	17.6002i	0.196291	−	0.637169i
$764$		−	23.3473i		−	0.844677i
$765$	−9.75524	−	2.63644i	−0.352701	−	0.0953205i
$766$	21.2108	+	12.2460i	0.766376	+	0.442467i
$767$	15.4603	−	8.92600i	0.558238	−	0.322299i
$768$	0.661104	+	1.60092i	0.0238555	+	0.0577682i
$769$	−25.0365	+	14.4549i	−0.902841	+	0.521255i	−0.878121	−	0.478439i	$-0.841203\pi$
$769$	−25.0365	+	14.4549i	−0.902841	+	0.521255i	−0.0247199	+	0.999694i	$0.507869\pi$
$770$	7.50098	−	1.71487i	0.270316	−	0.0617996i
$771$	50.5018	+	6.70401i	1.81878	+	0.241439i
$772$	−4.17857			−0.150390
$773$	−15.3683	+	26.6187i	−0.552761	+	0.957410i	0.445313	+	0.895375i	$0.353092\pi$
$773$	−15.3683	+	26.6187i	−0.552761	+	0.957410i	−0.998074	+	0.0620349i	$0.980241\pi$
$774$	−5.74919	+	1.52723i	−0.206650	+	0.0548952i
$775$	−1.90977	+	1.10260i	−0.0686009	+	0.0396067i
$776$	3.01109	−	5.21536i	0.108092	−	0.187220i
$777$	6.43308	−	13.9968i	0.230785	−	0.502131i
$778$	−2.60976	−	4.52023i	−0.0935643	−	0.162058i
$779$	−59.3034	−	34.2388i	−2.12476	−	1.22673i
$780$	−3.13491	+	1.29457i	−0.112248	+	0.0463531i
$781$	−11.5487	−	20.0029i	−0.413244	−	0.715760i
$782$	4.80893	+	8.32931i	0.171967	+	0.297856i
$783$	−6.82592	−	8.95545i	−0.243938	−	0.320042i
$784$	6.30461	−	3.04169i	0.225165	−	0.108632i
$785$	8.74085	+	5.04653i	0.311974	+	0.180118i
$786$	1.00518	−	7.57213i	0.0358537	−	0.270089i
$787$		−	26.2583i		−	0.936007i	−0.883727	−	0.468004i	$-0.844973\pi$
$787$		−	26.2583i		−	0.936007i	0.883727	−	0.468004i	$-0.155027\pi$
$788$		−	2.79573i		−	0.0995936i
$789$	−35.8307	−	27.5552i	−1.27561	−	0.980990i
$790$	3.71962	+	2.14752i	0.132338	+	0.0764054i
$791$	−5.28152	+	4.90404i	−0.187789	+	0.174368i
$792$	−8.42258	−	2.27627i	−0.299283	−	0.0808838i
$793$	−2.97435	−	5.15173i	−0.105622	−	0.182943i
$794$	4.80828	+	8.32819i	0.170640	+	0.295556i
$795$	14.6707	+	11.2824i	0.520317	+	0.400144i
$796$	3.02178	+	1.74463i	0.107104	+	0.0618366i
$797$	5.45013	+	9.43990i	0.193054	+	0.334379i	0.946261	−	0.323405i	$-0.104828\pi$
$797$	5.45013	+	9.43990i	0.193054	+	0.334379i	−0.753207	+	0.657783i	$0.771494\pi$
$798$	−15.4243	+	33.5594i	−0.546014	+	1.18799i
$799$	1.09001	−	1.88796i	0.0385619	−	0.0667912i
$800$	0.866025	−	0.500000i	0.0306186	−	0.0176777i
$801$	−48.8787	−	13.2099i	−1.72704	−	0.466748i
$802$	9.14348	−	15.8370i	0.322868	−	0.559223i
$803$	42.2309			1.49029
$804$	10.0085	+	24.2365i	0.352974	+	0.854756i
$805$	5.53597	−	5.14031i	0.195117	−	0.181172i
$806$	3.73970	−	2.15912i	0.131725	−	0.0760516i
$807$	−26.7280	−	3.54808i	−0.940870	−	0.124898i
$808$	13.5758	−	7.83797i	0.477594	−	0.275739i
$809$	−14.0577	−	8.11622i	−0.494243	−	0.285351i	0.232090	−	0.972694i	$-0.425444\pi$
$809$	−14.0577	−	8.11622i	−0.494243	−	0.285351i	−0.726333	+	0.687343i	$0.758777\pi$
$810$	4.53352	−	7.77478i	0.159292	−	0.273178i
$811$			34.0263i			1.19482i	0.801934	+	0.597412i	$0.203804\pi$
$811$			34.0263i			1.19482i	−0.801934	+	0.597412i	$0.796196\pi$
$812$	5.47932	+	1.68800i	0.192287	+	0.0592373i
$813$	16.3039	+	12.5384i	0.571804	+	0.439739i
$814$	4.88805	−	8.46635i	0.171326	−	0.296745i
$815$	23.4147			0.820180
$816$	−5.78352	−	0.767750i	−0.202464	−	0.0268766i
$817$			15.9813i			0.559115i
$818$	−4.06433			−0.142106
$819$	0.609054	−	15.5308i	0.0212821	−	0.542689i
$820$	−8.49627			−0.296703
$821$			34.9843i			1.22096i	0.792031	+	0.610480i	$0.209024\pi$
$821$			34.9843i			1.22096i	−0.792031	+	0.610480i	$0.790976\pi$
$822$	5.16515	−	6.71637i	0.180155	−	0.234260i
$823$	−1.46588			−0.0510975			−0.0255487	−	0.999674i	$-0.508133\pi$
$823$	−1.46588			−0.0510975			−0.0255487	+	0.999674i	$0.508133\pi$
$824$	−1.84480	+	3.19529i	−0.0642667	+	0.111313i
$825$	−0.662868	+	4.99343i	−0.0230781	+	0.173849i
$826$	−5.37563	−	23.5135i	−0.187042	−	0.818138i
$827$		−	3.05294i		−	0.106161i	−0.998590	−	0.0530805i	$-0.983096\pi$
$827$		−	3.05294i		−	0.106161i	0.998590	−	0.0530805i	$-0.0169040\pi$
$828$	−8.27882	+	2.19921i	−0.287709	+	0.0764278i
$829$	−45.1011	−	26.0391i	−1.56643	−	0.904377i	−0.996581	−	0.0826248i	$-0.973670\pi$
$829$	−45.1011	−	26.0391i	−1.56643	−	0.904377i	−0.569846	−	0.821752i	$-0.692997\pi$
$830$	11.9055	−	6.87362i	0.413244	−	0.238587i
$831$	28.9900	−	37.6964i	1.00565	−	1.30767i
$832$	−1.69585	+	0.979098i	−0.0587929	+	0.0339441i
$833$	−1.74525	+	23.5142i	−0.0604693	+	0.814718i
$834$	−16.8232	+	21.8756i	−0.582539	+	0.757490i
$835$	−10.7781			−0.372992
$836$	−11.7199	+	20.2994i	−0.405340	+	0.702069i
$837$	−4.41919	+	10.5722i	−0.152749	+	0.365427i
$838$	−10.4005	+	6.00474i	−0.359280	+	0.207430i
$839$	1.17639	−	2.03757i	0.0406135	−	0.0703447i	−0.845004	−	0.534760i	$-0.820402\pi$
$839$	1.17639	−	2.03757i	0.0406135	−	0.0703447i	0.885618	+	0.464415i	$0.153735\pi$
$840$	0.424564	+	4.56287i	0.0146488	+	0.157434i
$841$	−12.1520	−	21.0478i	−0.419034	−	0.725788i
$842$	−10.4163	−	6.01384i	−0.358969	−	0.207251i
$843$	5.92964	−	44.6684i	0.204228	−	1.53846i
$844$	4.69846	+	8.13798i	0.161728	+	0.280121i
$845$	4.58273	+	7.93753i	0.157651	+	0.273059i
$846$	1.36995	+	1.37587i	0.0471000	+	0.0473033i
$847$	1.98014	−	6.42762i	0.0680385	−	0.220856i
$848$	9.25368	+	5.34261i	0.317773	+	0.183466i
$849$	−1.38495	+	0.571917i	−0.0475312	+	0.0196281i
$850$			3.36841i			0.115535i
$851$		−	9.59815i		−	0.329021i
$852$	12.7145	−	5.25050i	0.435592	−	0.179879i
$853$	−24.1341	−	13.9338i	−0.826334	−	0.477084i	0.0262617	−	0.999655i	$-0.491640\pi$
$853$	−24.1341	−	13.9338i	−0.826334	−	0.477084i	−0.852596	+	0.522571i	$0.824973\pi$
$854$	−7.83525	+	1.79129i	−0.268117	+	0.0612966i
$855$	−17.0604	−	17.1340i	−0.583454	−	0.585972i
$856$	6.16845	+	10.6841i	0.210833	+	0.365174i
$857$	−14.5780	−	25.2499i	−0.497975	−	0.862519i	0.502022	−	0.864855i	$-0.332590\pi$
$857$	−14.5780	−	25.2499i	−0.497975	−	0.862519i	−0.999997	+	0.00233623i	$0.999256\pi$
$858$	1.29802	−	9.77812i	0.0443138	−	0.333819i
$859$	−49.7500	−	28.7232i	−1.69745	−	0.980022i	−0.948169	−	0.317767i	$-0.897067\pi$
$859$	−49.7500	−	28.7232i	−1.69745	−	0.980022i	−0.749279	−	0.662255i	$-0.769600\pi$
$860$	0.991430	+	1.71721i	0.0338075	+	0.0585563i
$861$	16.2597	−	35.3771i	0.554131	−	1.20565i
$862$	4.70997	−	8.15790i	0.160422	−	0.277859i
$863$	16.5615	−	9.56179i	0.563761	−	0.325487i	−0.190893	−	0.981611i	$-0.561138\pi$
$863$	16.5615	−	9.56179i	0.563761	−	0.325487i	0.754653	+	0.656124i	$0.227805\pi$
$864$	2.00398	−	4.79417i	0.0681767	−	0.163101i
$865$	1.28943	−	2.23335i	0.0438418	−	0.0759362i
$866$	28.8287			0.979640
$867$	−5.96979	+	7.76267i	−0.202745	+	0.263634i
$868$	−1.30032	−	5.68769i	−0.0441356	−	0.193053i
$869$	−10.8176	+	6.24553i	−0.366961	+	0.211865i
$870$	−2.28814	+	2.97532i	−0.0775752	+	0.100873i
$871$	−25.6736	+	14.8227i	−0.869918	+	0.502248i
$872$	6.02819	+	3.48038i	0.204140	+	0.117860i
$873$	−17.4610	+	4.63838i	−0.590964	+	0.156985i
$874$			23.0131i			0.778428i
$875$	2.57921	−	0.589657i	0.0871931	−	0.0199340i
$876$	−3.30974	+	24.9325i	−0.111826	+	0.842390i
$877$	−14.3773	+	24.9022i	−0.485487	+	0.840888i	−0.999861	−	0.0166782i	$-0.994691\pi$
$877$	−14.3773	+	24.9022i	−0.485487	+	0.840888i	0.514374	+	0.857566i	$0.328024\pi$
$878$	−35.2441			−1.18943
$879$	24.0602	−	31.2860i	0.811530	−	1.05525i
$880$			2.90825i			0.0980371i
$881$	−9.79497			−0.330001			−0.165001	−	0.986293i	$-0.552763\pi$
$881$	−9.79497			−0.330001			−0.165001	+	0.986293i	$0.552763\pi$
$882$	−19.8116	−	6.96437i	−0.667090	−	0.234503i
$883$	−22.0390			−0.741670			−0.370835	−	0.928699i	$-0.620929\pi$
$883$	−22.0390			−0.741670			−0.370835	+	0.928699i	$0.620929\pi$
$884$		−	6.59600i		−	0.221848i
$885$	15.6530	+	2.07790i	0.526170	+	0.0698480i
$886$	−21.2414			−0.713619
$887$	23.8142	−	41.2474i	0.799603	−	1.38495i	−0.120272	−	0.992741i	$-0.538377\pi$
$887$	23.8142	−	41.2474i	0.799603	−	1.38495i	0.919875	−	0.392212i	$-0.128290\pi$
$888$	4.61532	+	3.54936i	0.154880	+	0.119109i
$889$	17.0191	−	3.89089i	0.570802	−	0.130496i
$890$			16.8774i			0.565733i
$891$	12.9894	+	22.7237i	0.435161	+	0.761273i
$892$	−14.4132	−	8.32148i	−0.482591	−	0.278624i
$893$	4.51740	−	2.60812i	0.151169	−	0.0872774i
$894$	12.3047	+	1.63342i	0.411530	+	0.0546298i
$895$	0.461274	−	0.266316i	0.0154187	−	0.00890198i
$896$	0.589657	+	2.57921i	0.0196990	+	0.0861652i
$897$	−3.69641	−	8.95116i	−0.123419	−	0.298871i
$898$	−16.9305			−0.564980
$899$	2.38939	−	4.13854i	0.0796905	−	0.138028i
$900$	−2.89610	−	0.782695i	−0.0965366	−	0.0260898i
$901$	−31.1702	+	17.9961i	−1.03843	+	0.599537i
$902$	12.3546	−	21.3989i	0.411365	−	0.712504i
$903$	−9.04753	+	0.841850i	−0.301083	+	0.0280150i
$904$	−1.36204	−	2.35912i	−0.0453007	−	0.0784631i
$905$	−21.9057	−	12.6473i	−0.728172	−	0.420410i
$906$	−9.29098	−	7.14512i	−0.308672	−	0.237381i
$907$	3.17593	+	5.50087i	0.105455	+	0.182653i	0.913924	−	0.405885i	$-0.133037\pi$
$907$	3.17593	+	5.50087i	0.105455	+	0.182653i	−0.808469	+	0.588539i	$0.799703\pi$
$908$	0.765073	+	1.32514i	0.0253898	+	0.0439765i
$909$	−45.3991	−	12.2695i	−1.50579	−	0.406953i
$910$	−5.05059	+	1.15466i	−0.167425	+	0.0382767i
$911$	23.4087	+	13.5150i	0.775563	+	0.447772i	0.834856	−	0.550469i	$-0.185551\pi$
$911$	23.4087	+	13.5150i	0.775563	+	0.447772i	−0.0592924	+	0.998241i	$0.518884\pi$
$912$	−11.0659	−	8.51014i	−0.366430	−	0.281799i
$913$			39.9804i			1.32316i
$914$			33.2351i			1.09932i
$915$	0.692407	−	5.21596i	0.0228903	−	0.172434i
$916$	19.5572	+	11.2914i	0.646188	+	0.373077i
$917$	3.43524	−	11.1509i	0.113442	−	0.368236i
$918$	10.6101	+	13.9202i	0.350185	+	0.459436i
$919$	−18.7122	−	32.4104i	−0.617257	−	1.06912i	−0.989984	−	0.141179i	$-0.954911\pi$
$919$	−18.7122	−	32.4104i	−0.617257	−	1.06912i	0.372727	−	0.927941i	$-0.378423\pi$
$920$	1.42766	+	2.47278i	0.0470685	+	0.0815250i
$921$	−31.3450	+	12.9440i	−1.03285	+	0.426519i
$922$	−22.9806	−	13.2679i	−0.756827	−	0.436954i
$923$	7.77601	+	13.4684i	0.255951	+	0.443319i
$924$	−12.1095	−	5.56566i	−0.398373	−	0.183097i
$925$	1.68075	−	2.91115i	0.0552628	−	0.0957180i
$926$	9.10135	−	5.25467i	0.299089	−	0.172679i
$927$	10.6978	−	2.84179i	0.351361	−	0.0933366i
$928$	−1.08352	+	1.87671i	−0.0355682	+	0.0616060i
$929$	−7.79487			−0.255741			−0.127871	−	0.991791i	$-0.540814\pi$
$929$	−7.79487			−0.255741			−0.127871	+	0.991791i	$0.540814\pi$
$930$	3.78632	+	0.502626i	0.124158	+	0.0164818i
$931$	−31.7481	+	46.6375i	−1.04050	+	1.52848i
$932$	1.52031	−	0.877750i	0.0497993	−	0.0287517i
$933$	16.3691	+	39.6390i	0.535899	+	1.29772i
$934$	10.6438	−	6.14519i	0.348275	−	0.201077i
$935$	−8.48373	−	4.89809i	−0.277448	−	0.160185i
$936$	5.67113	+	1.53267i	0.185367	+	0.0500969i
$937$			55.3757i			1.80905i	0.426424	+	0.904523i	$0.359773\pi$
$937$			55.3757i			1.80905i	−0.426424	+	0.904523i	$0.640227\pi$
$938$	8.92688	+	39.0469i	0.291473	+	1.27493i
$939$	47.5592	−	19.6397i	1.55204	−	0.640918i
$940$	0.323599	−	0.560490i	0.0105546	−	0.0182812i
$941$	−29.2725			−0.954256			−0.477128	−	0.878834i	$-0.658322\pi$
$941$	−29.2725			−0.954256			−0.477128	+	0.878834i	$0.658322\pi$
$942$	−6.67256	−	16.1582i	−0.217404	−	0.526462i
$943$		−	24.2595i		−	0.789999i
$944$	9.11655			0.296718
$945$	8.80143	−	10.5610i	0.286310	−	0.343550i
$946$	−5.76665			−0.187490
$947$		−	43.5322i		−	1.41461i	−0.706911	−	0.707303i	$-0.749912\pi$
$947$		−	43.5322i		−	1.41461i	0.706911	−	0.707303i	$-0.250088\pi$
$948$	−2.83947	−	6.87602i	−0.0922217	−	0.223323i
$949$	−28.4351			−0.923041
$950$	−4.02986	+	6.97993i	−0.130746	+	0.226459i
$951$	−9.58543	+	3.95833i	−0.310829	+	0.128358i
$952$	−8.51697	−	2.62381i	−0.276037	−	0.0850381i
$953$		−	19.9323i		−	0.645672i	−0.946455	−	0.322836i	$-0.895364\pi$
$953$		−	19.9323i		−	0.645672i	0.946455	−	0.322836i	$-0.104636\pi$
$954$	−8.22993	−	30.9812i	−0.266454	−	1.00305i
$955$	20.2194	+	11.6737i	0.654284	+	0.377751i
$956$	−13.5333	+	7.81348i	−0.437700	+	0.252706i
$957$	−4.16647	−	10.0894i	−0.134683	−	0.326146i
$958$	−27.4869	+	15.8696i	−0.888063	+	0.512723i
$959$	9.48433	−	8.80648i	0.306265	−	0.284376i
$960$	−1.71699	−	0.227927i	−0.0554156	−	0.00735630i
$961$	26.1370			0.843131
$962$	−3.29124	+	5.70060i	−0.106114	+	0.183795i
$963$	9.65603	−	35.7289i	0.311161	−	1.15135i
$964$	6.76393	−	3.90516i	0.217852	−	0.125777i
$965$	2.08929	−	3.61875i	0.0672565	−	0.116492i
$966$	−13.0284	+	1.21226i	−0.419182	+	0.0390039i
$967$	13.3577	+	23.1362i	0.429555	+	0.744011i	0.996834	−	0.0795148i	$-0.0253371\pi$
$967$	13.3577	+	23.1362i	0.429555	+	0.744011i	−0.567279	+	0.823526i	$0.692004\pi$
$968$	2.20151	+	1.27104i	0.0707591	+	0.0408528i
$969$	43.4625	−	17.9479i	1.39622	−	0.576571i
$970$	3.01109	+	5.21536i	0.0966802	+	0.167455i
$971$	−1.77474	−	3.07394i	−0.0569541	−	0.0986475i	0.836143	−	0.548512i	$-0.184806\pi$
$971$	−1.77474	−	3.07394i	−0.0569541	−	0.0986475i	−0.893097	+	0.449865i	$0.851472\pi$
$972$	−14.4338	+	5.88783i	−0.462963	+	0.188852i
$973$	−30.8910	+	28.6832i	−0.990319	+	0.919540i
$974$	35.9155	+	20.7358i	1.15081	+	0.664419i
$975$	0.446325	−	3.36220i	0.0142938	−	0.107677i
$976$		−	3.03785i		−	0.0972392i
$977$			51.3465i			1.64272i	0.570411	+	0.821360i	$0.306784\pi$
$977$			51.3465i			1.64272i	−0.570411	+	0.821360i	$0.693216\pi$
$978$	−32.1481	−	24.7232i	−1.02798	−	0.790560i
$979$	−42.5078	−	24.5419i	−1.35856	−	0.784362i
$980$	−0.518123	+	6.98080i	−0.0165508	+	0.222993i
$981$	−5.36128	−	20.1823i	−0.171173	−	0.644372i
$982$	5.39359	+	9.34197i	0.172116	+	0.298114i
$983$	20.7452	+	35.9317i	0.661669	+	1.14604i	0.980177	+	0.198124i	$0.0634850\pi$
$983$	20.7452	+	35.9317i	0.661669	+	1.14604i	−0.318508	+	0.947920i	$0.603182\pi$
$984$	11.6653	+	8.97108i	0.371877	+	0.285988i
$985$	2.42117	+	1.39786i	0.0771449	+	0.0445396i
$986$	−3.64973	−	6.32152i	−0.116231	−	0.201318i
$987$	1.71450	+	2.42005i	0.0545732	+	0.0770311i
$988$	7.89126	−	13.6681i	0.251055	−	0.434839i
$989$	−4.90317	+	2.83085i	−0.155912	+	0.0900156i
$990$	6.18260	−	6.15603i	0.196496	−	0.195652i
$991$	12.9670	−	22.4595i	0.411911	−	0.713451i	−0.583188	−	0.812337i	$-0.698195\pi$
$991$	12.9670	−	22.4595i	0.411911	−	0.713451i	0.995099	+	0.0988866i	$0.0315281\pi$
$992$	2.20521			0.0700155
$993$	5.09492	+	12.3378i	0.161682	+	0.391528i
$994$	20.4841	−	4.68306i	0.649716	−	0.148538i
$995$	−3.02178	+	1.74463i	−0.0957969	+	0.0553084i
$996$	−23.6038	−	3.13336i	−0.747916	−	0.0992843i
$997$	18.3703	−	10.6061i	0.581792	−	0.335898i	−0.180053	−	0.983657i	$-0.557627\pi$
$997$	18.3703	−	10.6061i	0.581792	−	0.335898i	0.761845	+	0.647759i	$0.224294\pi$
$998$	−23.2675	−	13.4335i	−0.736519	−	0.425229i
$999$	−2.22394	−	17.3247i	−0.0703624	−	0.548130i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.bk.c.101.14	yes	32
3.2	odd	2		1890.2.bk.c.521.13		32
7.5	odd	6		630.2.t.c.551.16	yes	32
9.4	even	3		1890.2.t.c.1151.6		32
9.5	odd	6		630.2.t.c.311.16	✓	32
21.5	even	6		1890.2.t.c.1601.6		32
63.5	even	6	inner	630.2.bk.c.131.6	yes	32
63.40	odd	6		1890.2.bk.c.341.13		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.t.c.311.16	✓	32	9.5	odd	6
630.2.t.c.551.16	yes	32	7.5	odd	6
630.2.bk.c.101.14	yes	32	1.1	even	1	trivial
630.2.bk.c.131.6	yes	32	63.5	even	6	inner
1890.2.t.c.1151.6		32	9.4	even	3
1890.2.t.c.1601.6		32	21.5	even	6
1890.2.bk.c.341.13		32	63.40	odd	6
1890.2.bk.c.521.13		32	3.2	odd	2

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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.bk (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(0.661104 + 1.60092i) q^{3} -1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(-1.60092 + 0.661104i) q^{6} +(-2.57921 + 0.589657i) q^{7} -1.00000i q^{8} +(-2.12588 + 2.11675i) q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(0.661104 + 1.60092i) q^{3} -1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(-1.60092 + 0.661104i) q^{6} +(-2.57921 + 0.589657i) q^{7} -1.00000i q^{8} +(-2.12588 + 2.11675i) q^{9} +(0.866025 + 0.500000i) q^{10} +(-2.51862 + 1.45413i) q^{11} +(-0.661104 - 1.60092i) q^{12} +(1.69585 - 0.979098i) q^{13} +(-0.589657 - 2.57921i) q^{14} +(1.71699 + 0.227927i) q^{15} +1.00000 q^{16} +(-1.68420 + 2.91713i) q^{17} +(-2.11675 - 2.12588i) q^{18} +(-6.97993 + 4.02986i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(-2.64912 - 3.73928i) q^{21} +(-1.45413 - 2.51862i) q^{22} +(-2.47278 - 1.42766i) q^{23} +(1.60092 - 0.661104i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(0.979098 + 1.69585i) q^{26} +(-4.79417 - 2.00398i) q^{27} +(2.57921 - 0.589657i) q^{28} +(1.87671 + 1.08352i) q^{29} +(-0.227927 + 1.71699i) q^{30} -2.20521i q^{31} +1.00000i q^{32} +(-3.99300 - 3.07078i) q^{33} +(-2.91713 - 1.68420i) q^{34} +(-0.778946 + 2.52849i) q^{35} +(2.12588 - 2.11675i) q^{36} +(1.68075 + 2.91115i) q^{37} +(-4.02986 - 6.97993i) q^{38} +(2.68859 + 2.06763i) q^{39} +(-0.866025 - 0.500000i) q^{40} +(4.24814 + 7.35799i) q^{41} +(3.73928 - 2.64912i) q^{42} +(0.991430 - 1.71721i) q^{43} +(2.51862 - 1.45413i) q^{44} +(0.770216 + 2.89944i) q^{45} +(1.42766 - 2.47278i) q^{46} -0.647198 q^{47} +(0.661104 + 1.60092i) q^{48} +(6.30461 - 3.04169i) q^{49} +(0.866025 - 0.500000i) q^{50} +(-5.78352 - 0.767750i) q^{51} +(-1.69585 + 0.979098i) q^{52} +(9.25368 + 5.34261i) q^{53} +(2.00398 - 4.79417i) q^{54} +2.90825i q^{55} +(0.589657 + 2.57921i) q^{56} +(-11.0659 - 8.51014i) q^{57} +(-1.08352 + 1.87671i) q^{58} +9.11655 q^{59} +(-1.71699 - 0.227927i) q^{60} -3.03785i q^{61} +2.20521 q^{62} +(4.23494 - 6.71307i) q^{63} -1.00000 q^{64} -1.95820i q^{65} +(3.07078 - 3.99300i) q^{66} -15.1391 q^{67} +(1.68420 - 2.91713i) q^{68} +(0.650802 - 4.90254i) q^{69} +(-2.52849 - 0.778946i) q^{70} +7.94202i q^{71} +(2.11675 + 2.12588i) q^{72} +(-12.5756 - 7.26053i) q^{73} +(-2.91115 + 1.68075i) q^{74} +(1.05588 - 1.37299i) q^{75} +(6.97993 - 4.02986i) q^{76} +(5.63860 - 5.23561i) q^{77} +(-2.06763 + 2.68859i) q^{78} +4.29504 q^{79} +(0.500000 - 0.866025i) q^{80} +(0.0387579 - 8.99992i) q^{81} +(-7.35799 + 4.24814i) q^{82} +(6.87362 - 11.9055i) q^{83} +(2.64912 + 3.73928i) q^{84} +(1.68420 + 2.91713i) q^{85} +(1.71721 + 0.991430i) q^{86} +(-0.493925 + 3.72078i) q^{87} +(1.45413 + 2.51862i) q^{88} +(8.43872 + 14.6163i) q^{89} +(-2.89944 + 0.770216i) q^{90} +(-3.79661 + 3.52526i) q^{91} +(2.47278 + 1.42766i) q^{92} +(3.53036 - 1.45787i) q^{93} -0.647198i q^{94} +8.05973i q^{95} +(-1.60092 + 0.661104i) q^{96} +(5.21536 + 3.01109i) q^{97} +(3.04169 + 6.30461i) q^{98} +(2.27627 - 8.42258i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 2 q^{3} - 32 q^{4} + 16 q^{5} - 2 q^{6} - 2 q^{7}+O(q^{10}) \) 32 * q - 2 * q^3 - 32 * q^4 + 16 * q^5 - 2 * q^6 - 2 * q^7	\( 32 q - 2 q^{3} - 32 q^{4} + 16 q^{5} - 2 q^{6} - 2 q^{7} - 6 q^{11} + 2 q^{12} + 6 q^{14} + 2 q^{15} + 32 q^{16} - 6 q^{17} + 8 q^{18} - 16 q^{20} + 18 q^{23} + 2 q^{24} - 16 q^{25} - 12 q^{26} - 8 q^{27} + 2 q^{28} + 6 q^{29} - 4 q^{30} + 20 q^{33} + 2 q^{35} + 2 q^{37} + 30 q^{39} + 6 q^{41} + 10 q^{42} - 28 q^{43} + 6 q^{44} + 6 q^{45} + 48 q^{47} - 2 q^{48} + 8 q^{49} + 34 q^{51} + 36 q^{53} - 46 q^{54} - 6 q^{56} + 18 q^{57} - 60 q^{59} - 2 q^{60} + 32 q^{63} - 32 q^{64} - 34 q^{66} - 8 q^{67} + 6 q^{68} - 28 q^{69} + 6 q^{70} - 8 q^{72} - 30 q^{73} - 18 q^{74} + 4 q^{75} - 6 q^{77} - 22 q^{78} - 8 q^{79} + 16 q^{80} + 20 q^{81} - 24 q^{82} - 6 q^{83} + 6 q^{85} + 30 q^{86} - 22 q^{87} + 12 q^{89} + 4 q^{90} - 66 q^{91} - 18 q^{92} - 32 q^{93} - 2 q^{96} - 96 q^{97} + 24 q^{98} - 24 q^{99}+O(q^{100}) \) 32 * q - 2 * q^3 - 32 * q^4 + 16 * q^5 - 2 * q^6 - 2 * q^7 - 6 * q^11 + 2 * q^12 + 6 * q^14 + 2 * q^15 + 32 * q^16 - 6 * q^17 + 8 * q^18 - 16 * q^20 + 18 * q^23 + 2 * q^24 - 16 * q^25 - 12 * q^26 - 8 * q^27 + 2 * q^28 + 6 * q^29 - 4 * q^30 + 20 * q^33 + 2 * q^35 + 2 * q^37 + 30 * q^39 + 6 * q^41 + 10 * q^42 - 28 * q^43 + 6 * q^44 + 6 * q^45 + 48 * q^47 - 2 * q^48 + 8 * q^49 + 34 * q^51 + 36 * q^53 - 46 * q^54 - 6 * q^56 + 18 * q^57 - 60 * q^59 - 2 * q^60 + 32 * q^63 - 32 * q^64 - 34 * q^66 - 8 * q^67 + 6 * q^68 - 28 * q^69 + 6 * q^70 - 8 * q^72 - 30 * q^73 - 18 * q^74 + 4 * q^75 - 6 * q^77 - 22 * q^78 - 8 * q^79 + 16 * q^80 + 20 * q^81 - 24 * q^82 - 6 * q^83 + 6 * q^85 + 30 * q^86 - 22 * q^87 + 12 * q^89 + 4 * q^90 - 66 * q^91 - 18 * q^92 - 32 * q^93 - 2 * q^96 - 96 * q^97 + 24 * q^98 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more