LMFDB - Embedded newform 1110.2.bb.d.1009.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(1009,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("1110.1009");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.bb (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:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1009.11
Character	$\chi$	$=$	1110.1009
Dual form			1110.2.bb.d.1099.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.529198 - 2.17254i) q^{5} +1.00000 q^{6} +(-2.93485 + 1.69443i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.529198 - 2.17254i) q^{5} +1.00000 q^{6} +(-2.93485 + 1.69443i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(1.54457 - 1.61688i) q^{10} +4.29568 q^{11} +(0.866025 + 0.500000i) q^{12} +(1.80925 - 1.04457i) q^{13} -3.38887 q^{14} +(-0.627973 - 2.14608i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(5.53292 + 3.19443i) q^{17} +(0.866025 - 0.500000i) q^{18} +(-1.07231 - 1.85729i) q^{19} +(2.14608 - 0.627973i) q^{20} +(-1.69443 + 2.93485i) q^{21} +(3.72017 + 2.14784i) q^{22} -4.17381i q^{23} +(0.500000 + 0.866025i) q^{24} +(-4.43990 - 2.29941i) q^{25} +2.08914 q^{26} -1.00000i q^{27} +(-2.93485 - 1.69443i) q^{28} +2.38887 q^{29} +(0.529198 - 2.17254i) q^{30} +8.38482 q^{31} +(-0.866025 + 0.500000i) q^{32} +(3.72017 - 2.14784i) q^{33} +(3.19443 + 5.53292i) q^{34} +(2.12812 + 7.27277i) q^{35} +1.00000 q^{36} +(0.158737 - 6.08069i) q^{37} -2.14462i q^{38} +(1.04457 - 1.80925i) q^{39} +(2.17254 + 0.529198i) q^{40} +(-5.28456 - 9.15313i) q^{41} +(-2.93485 + 1.69443i) q^{42} +2.54477i q^{43} +(2.14784 + 3.72017i) q^{44} +(-1.61688 - 1.54457i) q^{45} +(2.08690 - 3.61462i) q^{46} +10.9276i q^{47} +1.00000i q^{48} +(2.24221 - 3.88362i) q^{49} +(-2.69536 - 4.21130i) q^{50} +6.38887 q^{51} +(1.80925 + 1.04457i) q^{52} +(9.69231 + 5.59586i) q^{53} +(0.500000 - 0.866025i) q^{54} +(2.27327 - 9.33256i) q^{55} +(-1.69443 - 2.93485i) q^{56} +(-1.85729 - 1.07231i) q^{57} +(2.06882 + 1.19443i) q^{58} +(-1.78454 + 3.09092i) q^{59} +(1.54457 - 1.61688i) q^{60} +(-1.89207 - 3.27717i) q^{61} +(7.26147 + 4.19241i) q^{62} +3.38887i q^{63} -1.00000 q^{64} +(-1.31193 - 4.48346i) q^{65} +4.29568 q^{66} +(-12.4237 + 7.17284i) q^{67} +6.38887i q^{68} +(-2.08690 - 3.61462i) q^{69} +(-1.79338 + 7.36246i) q^{70} +(-4.72539 - 8.18462i) q^{71} +(0.866025 + 0.500000i) q^{72} +7.65823i q^{73} +(3.17782 - 5.18666i) q^{74} +(-4.99477 + 0.228600i) q^{75} +(1.07231 - 1.85729i) q^{76} +(-12.6072 + 7.27874i) q^{77} +(1.80925 - 1.04457i) q^{78} +(-3.37250 - 5.84135i) q^{79} +(1.61688 + 1.54457i) q^{80} +(-0.500000 - 0.866025i) q^{81} -10.5691i q^{82} +(-10.0539 - 5.80463i) q^{83} -3.38887 q^{84} +(9.86806 - 10.3300i) q^{85} +(-1.27238 + 2.20383i) q^{86} +(2.06882 - 1.19443i) q^{87} +4.29568i q^{88} +(-0.462359 + 0.800829i) q^{89} +(-0.627973 - 2.14608i) q^{90} +(-3.53991 + 6.13131i) q^{91} +(3.61462 - 2.08690i) q^{92} +(7.26147 - 4.19241i) q^{93} +(-5.46381 + 9.46360i) q^{94} +(-4.60251 + 1.34676i) q^{95} +(-0.500000 + 0.866025i) q^{96} +4.99803i q^{97} +(3.88362 - 2.24221i) q^{98} +(2.14784 - 3.72017i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 14 q^{4} + 2 q^{5} + 28 q^{6} + 14 q^{9}+O(q^{10}) $ 28 * q + 14 * q^4 + 2 * q^5 + 28 * q^6 + 14 * q^9	$ 28 q + 14 q^{4} + 2 q^{5} + 28 q^{6} + 14 q^{9} + 4 q^{10} - 12 q^{11} + 8 q^{14} + 2 q^{15} - 14 q^{16} - 20 q^{19} - 2 q^{20} + 4 q^{21} + 14 q^{24} - 8 q^{25} - 20 q^{26} - 36 q^{29} + 2 q^{30} + 24 q^{31} + 38 q^{34} - 2 q^{35} + 28 q^{36} - 10 q^{39} + 2 q^{40} - 6 q^{44} + 4 q^{45} + 8 q^{46} + 50 q^{49} - 4 q^{50} + 76 q^{51} + 14 q^{54} - 28 q^{55} + 4 q^{56} - 26 q^{59} + 4 q^{60} - 28 q^{61} - 28 q^{64} + 60 q^{65} - 12 q^{66} - 8 q^{69} - 10 q^{70} - 64 q^{71} + 24 q^{74} - 8 q^{75} + 20 q^{76} + 32 q^{79} - 4 q^{80} - 14 q^{81} + 8 q^{84} + 16 q^{85} - 8 q^{86} + 76 q^{89} + 2 q^{90} - 8 q^{91} - 38 q^{94} - 70 q^{95} - 14 q^{96} - 6 q^{99}+O(q^{100}) $ 28 * q + 14 * q^4 + 2 * q^5 + 28 * q^6 + 14 * q^9 + 4 * q^10 - 12 * q^11 + 8 * q^14 + 2 * q^15 - 14 * q^16 - 20 * q^19 - 2 * q^20 + 4 * q^21 + 14 * q^24 - 8 * q^25 - 20 * q^26 - 36 * q^29 + 2 * q^30 + 24 * q^31 + 38 * q^34 - 2 * q^35 + 28 * q^36 - 10 * q^39 + 2 * q^40 - 6 * q^44 + 4 * q^45 + 8 * q^46 + 50 * q^49 - 4 * q^50 + 76 * q^51 + 14 * q^54 - 28 * q^55 + 4 * q^56 - 26 * q^59 + 4 * q^60 - 28 * q^61 - 28 * q^64 + 60 * q^65 - 12 * q^66 - 8 * q^69 - 10 * q^70 - 64 * q^71 + 24 * q^74 - 8 * q^75 + 20 * q^76 + 32 * q^79 - 4 * q^80 - 14 * q^81 + 8 * q^84 + 16 * q^85 - 8 * q^86 + 76 * q^89 + 2 * q^90 - 8 * q^91 - 38 * q^94 - 70 * q^95 - 14 * q^96 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$-1$

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 $

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	0.529198	−	2.17254i	0.236665	−	0.971591i
$5$	0.529198	−	2.17254i	0.236665	−	0.971591i
$6$	1.00000			0.408248
$7$	−2.93485	+	1.69443i	−1.10927	+	0.640436i	−0.938639	−	0.344900i	$-0.887913\pi$
$7$	−2.93485	+	1.69443i	−1.10927	+	0.640436i	−0.170628	+	0.985336i	$0.554580\pi$
$8$			1.00000i			0.353553i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	1.54457	−	1.61688i	0.488436	−	0.511302i
$11$	4.29568			1.29520			0.647598	−	0.761982i	$-0.275774\pi$
$11$	4.29568			1.29520			0.647598	+	0.761982i	$0.275774\pi$
$12$	0.866025	+	0.500000i	0.250000	+	0.144338i
$13$	1.80925	−	1.04457i	0.501796	−	0.289712i	−0.227659	−	0.973741i	$-0.573107\pi$
$13$	1.80925	−	1.04457i	0.501796	−	0.289712i	0.729455	+	0.684029i	$0.239774\pi$
$14$	−3.38887			−0.905713
$15$	−0.627973	−	2.14608i	−0.162142	−	0.554115i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	5.53292	+	3.19443i	1.34193	+	0.774764i	0.987091	−	0.160163i	$-0.0512020\pi$
$17$	5.53292	+	3.19443i	1.34193	+	0.774764i	0.354840	+	0.934927i	$0.384535\pi$
$18$	0.866025	−	0.500000i	0.204124	−	0.117851i
$19$	−1.07231	−	1.85729i	−0.246004	−	0.426092i	0.716409	−	0.697680i	$-0.245784\pi$
$19$	−1.07231	−	1.85729i	−0.246004	−	0.426092i	−0.962414	+	0.271588i	$0.912451\pi$
$20$	2.14608	−	0.627973i	0.479878	−	0.140419i
$21$	−1.69443	+	2.93485i	−0.369756	+	0.640436i
$22$	3.72017	+	2.14784i	0.793142	+	0.457921i
$23$		−	4.17381i		−	0.870299i	−0.900358	−	0.435149i	$-0.856696\pi$
$23$		−	4.17381i		−	0.870299i	0.900358	−	0.435149i	$-0.143304\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	−4.43990	−	2.29941i	−0.887980	−	0.459883i
$26$	2.08914			0.409715
$27$		−	1.00000i		−	0.192450i
$28$	−2.93485	−	1.69443i	−0.554634	−	0.320218i
$29$	2.38887			0.443602			0.221801	−	0.975092i	$-0.428807\pi$
$29$	2.38887			0.443602			0.221801	+	0.975092i	$0.428807\pi$
$30$	0.529198	−	2.17254i	0.0966179	−	0.396651i
$31$	8.38482			1.50596			0.752979	−	0.658044i	$-0.228616\pi$
$31$	8.38482			1.50596			0.752979	+	0.658044i	$0.228616\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	3.72017	−	2.14784i	0.647598	−	0.373891i
$34$	3.19443	+	5.53292i	0.547841	+	0.948888i
$35$	2.12812	+	7.27277i	0.359718	+	1.22932i
$36$	1.00000			0.166667
$37$	0.158737	−	6.08069i	0.0260962	−	0.999659i
$37$	0.158737	−	6.08069i	0.0260962	−	0.999659i
$38$		−	2.14462i		−	0.347903i
$39$	1.04457	−	1.80925i	0.167265	−	0.289712i
$40$	2.17254	+	0.529198i	0.343509	+	0.0836736i
$41$	−5.28456	−	9.15313i	−0.825310	−	1.42948i	−0.901682	−	0.432399i	$-0.857667\pi$
$41$	−5.28456	−	9.15313i	−0.825310	−	1.42948i	0.0763728	−	0.997079i	$-0.475666\pi$
$42$	−2.93485	+	1.69443i	−0.452856	+	0.261457i
$43$			2.54477i			0.388074i	0.980994	+	0.194037i	$0.0621581\pi$
$43$			2.54477i			0.388074i	−0.980994	+	0.194037i	$0.937842\pi$
$44$	2.14784	+	3.72017i	0.323799	+	0.560836i
$45$	−1.61688	−	1.54457i	−0.241030	−	0.230251i
$46$	2.08690	−	3.61462i	0.307697	−	0.532947i
$47$			10.9276i			1.59396i	0.604007	+	0.796979i	$0.293570\pi$
$47$			10.9276i			1.59396i	−0.604007	+	0.796979i	$0.706430\pi$
$48$			1.00000i			0.144338i
$49$	2.24221	−	3.88362i	0.320316	−	0.554803i
$50$	−2.69536	−	4.21130i	−0.381181	−	0.595568i
$51$	6.38887			0.894620
$52$	1.80925	+	1.04457i	0.250898	+	0.144856i
$53$	9.69231	+	5.59586i	1.33134	+	0.768650i	0.985505	−	0.169645i	$-0.0542621\pi$
$53$	9.69231	+	5.59586i	1.33134	+	0.768650i	0.345836	+	0.938295i	$0.387595\pi$
$54$	0.500000	−	0.866025i	0.0680414	−	0.117851i
$55$	2.27327	−	9.33256i	0.306527	−	1.25840i
$56$	−1.69443	−	2.93485i	−0.226428	−	0.392185i
$57$	−1.85729	−	1.07231i	−0.246004	−	0.142031i
$58$	2.06882	+	1.19443i	0.271649	+	0.156837i
$59$	−1.78454	+	3.09092i	−0.232328	+	0.402403i	−0.958493	−	0.285117i	$-0.907968\pi$
$59$	−1.78454	+	3.09092i	−0.232328	+	0.402403i	0.726165	+	0.687521i	$0.241301\pi$
$60$	1.54457	−	1.61688i	0.199403	−	0.208738i
$61$	−1.89207	−	3.27717i	−0.242255	−	0.419598i	0.719101	−	0.694905i	$-0.244554\pi$
$61$	−1.89207	−	3.27717i	−0.242255	−	0.419598i	−0.961356	+	0.275307i	$0.911220\pi$
$62$	7.26147	+	4.19241i	0.922207	+	0.532437i
$63$			3.38887i			0.426957i
$64$	−1.00000			−0.125000
$65$	−1.31193	−	4.48346i	−0.162724	−	0.556105i
$66$	4.29568			0.528762
$67$	−12.4237	+	7.17284i	−1.51780	+	0.876302i	−0.518019	+	0.855369i	$0.673330\pi$
$67$	−12.4237	+	7.17284i	−1.51780	+	0.876302i	−0.999781	+	0.0209325i	$0.993336\pi$
$68$			6.38887i			0.774764i
$69$	−2.08690	−	3.61462i	−0.251234	−	0.435149i
$70$	−1.79338	+	7.36246i	−0.214350	+	0.879983i
$71$	−4.72539	−	8.18462i	−0.560801	−	0.971336i	−0.997427	−	0.0716927i	$-0.977160\pi$
$71$	−4.72539	−	8.18462i	−0.560801	−	0.971336i	0.436626	−	0.899643i	$-0.356173\pi$
$72$	0.866025	+	0.500000i	0.102062	+	0.0589256i
$73$			7.65823i			0.896328i	0.893951	+	0.448164i	$0.147922\pi$
$73$			7.65823i			0.896328i	−0.893951	+	0.448164i	$0.852078\pi$
$74$	3.17782	−	5.18666i	0.369414	−	0.602937i
$75$	−4.99477	+	0.228600i	−0.576747	+	0.0263964i
$76$	1.07231	−	1.85729i	0.123002	−	0.213046i
$77$	−12.6072	+	7.27874i	−1.43672	+	0.829490i
$78$	1.80925	−	1.04457i	0.204857	−	0.118274i
$79$	−3.37250	−	5.84135i	−0.379436	−	0.657203i	0.611544	−	0.791210i	$-0.290549\pi$
$79$	−3.37250	−	5.84135i	−0.379436	−	0.657203i	−0.990980	+	0.134008i	$0.957215\pi$
$80$	1.61688	+	1.54457i	0.180773	+	0.172688i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		−	10.5691i		−	1.16716i
$83$	−10.0539	−	5.80463i	−1.10356	−	0.637141i	−0.166407	−	0.986057i	$-0.553217\pi$
$83$	−10.0539	−	5.80463i	−1.10356	−	0.637141i	−0.937154	+	0.348916i	$0.886550\pi$
$84$	−3.38887			−0.369756
$85$	9.86806	−	10.3300i	1.07034	−	1.12045i
$86$	−1.27238	+	2.20383i	−0.137205	+	0.237646i
$87$	2.06882	−	1.19443i	0.221801	−	0.128057i
$88$			4.29568i			0.457921i
$89$	−0.462359	+	0.800829i	−0.0490100	+	0.0848878i	−0.889490	−	0.456955i	$-0.848940\pi$
$89$	−0.462359	+	0.800829i	−0.0490100	+	0.0848878i	0.840480	+	0.541843i	$0.182273\pi$
$90$	−0.627973	−	2.14608i	−0.0661942	−	0.226216i
$91$	−3.53991	+	6.13131i	−0.371084	+	0.642736i
$92$	3.61462	−	2.08690i	0.376851	−	0.217575i
$93$	7.26147	−	4.19241i	0.752979	−	0.434733i
$94$	−5.46381	+	9.46360i	−0.563549	+	0.976096i
$95$	−4.60251	+	1.34676i	−0.472208	+	0.138175i
$96$	−0.500000	+	0.866025i	−0.0510310	+	0.0883883i
$97$			4.99803i			0.507473i	0.967273	+	0.253737i	$0.0816596\pi$
$97$			4.99803i			0.507473i	−0.967273	+	0.253737i	$0.918340\pi$
$98$	3.88362	−	2.24221i	0.392305	−	0.226497i
$99$	2.14784	−	3.72017i	0.215866	−	0.373891i
$100$	−0.228600	−	4.99477i	−0.0228600	−	0.499477i
$101$	−5.80689			−0.577807			−0.288904	−	0.957358i	$-0.593291\pi$
$101$	−5.80689			−0.577807			−0.288904	+	0.957358i	$0.593291\pi$
$102$	5.53292	+	3.19443i	0.547841	+	0.316296i
$103$			11.8029i			1.16297i	0.813556	+	0.581486i	$0.197529\pi$
$103$			11.8029i			1.16297i	−0.813556	+	0.581486i	$0.802471\pi$
$104$	1.04457	+	1.80925i	0.102429	+	0.177412i
$105$	5.47939	+	5.23435i	0.534734	+	0.510820i
$106$	5.59586	+	9.69231i	0.543518	+	0.941400i
$107$	−10.7144	+	6.18598i	−1.03580	+	0.598021i	−0.918642	−	0.395091i	$-0.870713\pi$
$107$	−10.7144	+	6.18598i	−1.03580	+	0.598021i	−0.117162	+	0.993113i	$0.537380\pi$
$108$	0.866025	−	0.500000i	0.0833333	−	0.0481125i
$109$	6.61466	−	11.4569i	0.633569	−	1.09737i	−0.353247	−	0.935530i	$-0.614922\pi$
$109$	6.61466	−	11.4569i	0.633569	−	1.09737i	0.986816	−	0.161844i	$-0.0517442\pi$
$110$	6.63498	−	6.94560i	0.632621	−	0.662237i
$111$	−2.90288	−	5.34540i	−0.275529	−	0.507363i
$112$		−	3.38887i		−	0.320218i
$113$	−6.05799	−	3.49758i	−0.569888	−	0.329025i	0.187217	−	0.982319i	$-0.440053\pi$
$113$	−6.05799	−	3.49758i	−0.569888	−	0.329025i	−0.757104	+	0.653294i	$0.773387\pi$
$114$	−1.07231	−	1.85729i	−0.100431	−	0.173951i
$115$	−9.06778	−	2.20877i	−0.845575	−	0.205969i
$116$	1.19443	+	2.06882i	0.110900	+	0.192085i
$117$		−	2.08914i		−	0.193141i
$118$	−3.09092	+	1.78454i	−0.284542	+	0.164281i
$119$	−21.6510			−1.98475
$120$	2.14608	−	0.627973i	0.195909	−	0.0573259i
$121$	7.45286			0.677533
$122$		−	3.78415i		−	0.342601i
$123$	−9.15313	−	5.28456i	−0.825310	−	0.476493i
$124$	4.19241	+	7.26147i	0.376490	+	0.652099i
$125$	−7.34516	+	8.42903i	−0.656971	+	0.753916i
$126$	−1.69443	+	2.93485i	−0.150952	+	0.261457i
$127$	17.7444	+	10.2448i	1.57456	+	0.909075i	0.995598	+	0.0937225i	$0.0298766\pi$
$127$	17.7444	+	10.2448i	1.57456	+	0.909075i	0.578965	+	0.815352i	$0.303457\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	1.27238	+	2.20383i	0.112027	+	0.194037i
$130$	1.10557	−	4.53875i	0.0969649	−	0.398075i
$131$	−8.09647	+	14.0235i	−0.707392	+	1.22524i	0.258430	+	0.966030i	$0.416795\pi$
$131$	−8.09647	+	14.0235i	−0.707392	+	1.22524i	−0.965821	+	0.259208i	$0.916538\pi$
$132$	3.72017	+	2.14784i	0.323799	+	0.186945i
$133$	6.29412	+	3.63391i	0.545769	+	0.315100i
$134$	−14.3457			−1.23928
$135$	−2.17254	−	0.529198i	−0.186983	−	0.0455461i
$136$	−3.19443	+	5.53292i	−0.273920	+	0.474444i
$137$			19.4802i			1.66431i	0.554544	+	0.832155i	$0.312893\pi$
$137$			19.4802i			1.66431i	−0.554544	+	0.832155i	$0.687107\pi$
$138$		−	4.17381i		−	0.355298i
$139$	−0.0996490	+	0.172597i	−0.00845212	+	0.0146395i	−0.870221	−	0.492662i	$-0.836024\pi$
$139$	−0.0996490	+	0.172597i	−0.00845212	+	0.0146395i	0.861768	+	0.507302i	$0.169357\pi$
$140$	−5.23435	+	5.47939i	−0.442383	+	0.463093i
$141$	5.46381	+	9.46360i	0.460136	+	0.796979i
$142$		−	9.45079i		−	0.793092i
$143$	7.77196	−	4.48714i	0.649924	−	0.375234i
$144$	0.500000	+	0.866025i	0.0416667	+	0.0721688i
$145$	1.26418	−	5.18992i	0.104985	−	0.430999i
$146$	−3.82911	+	6.63222i	−0.316900	+	0.548886i
$147$		−	4.48442i		−	0.369869i
$148$	5.34540	−	2.90288i	0.439389	−	0.238615i
$149$	16.8868			1.38342			0.691708	−	0.722177i	$-0.256858\pi$
$149$	16.8868			1.38342			0.691708	+	0.722177i	$0.256858\pi$
$150$	−4.43990	−	2.29941i	−0.362516	−	0.187746i
$151$	10.9847	+	19.0261i	0.893926	+	1.54832i	0.835129	+	0.550054i	$0.185393\pi$
$151$	10.9847	+	19.0261i	0.893926	+	1.54832i	0.0587967	+	0.998270i	$0.481274\pi$
$152$	1.85729	−	1.07231i	0.150646	−	0.0869757i
$153$	5.53292	−	3.19443i	0.447310	−	0.258255i
$154$	−14.5575			−1.17308
$155$	4.43723	−	18.2164i	0.356407	−	1.46318i
$156$	2.08914			0.167265
$157$	−6.75998	−	3.90288i	−0.539505	−	0.311483i	0.205373	−	0.978684i	$-0.434159\pi$
$157$	−6.75998	−	3.90288i	−0.539505	−	0.311483i	−0.744878	+	0.667200i	$0.767492\pi$
$158$		−	6.74500i		−	0.536604i
$159$	11.1917			0.887561
$160$	0.627973	+	2.14608i	0.0496456	+	0.169662i
$161$	7.07224	+	12.2495i	0.557371	+	0.965394i
$162$		−	1.00000i		−	0.0785674i
$163$	9.14720	+	5.28114i	0.716464	+	0.413651i	0.813450	−	0.581635i	$-0.197587\pi$
$163$	9.14720	+	5.28114i	0.716464	+	0.413651i	−0.0969857	+	0.995286i	$0.530920\pi$
$164$	5.28456	−	9.15313i	0.412655	−	0.714739i
$165$	−2.69757	−	9.21886i	−0.210006	−	0.717687i
$166$	−5.80463	−	10.0539i	−0.450527	−	0.780335i
$167$	11.3039	−	6.52632i	0.874723	−	0.505022i	0.00580833	−	0.999983i	$-0.498151\pi$
$167$	11.3039	−	6.52632i	0.874723	−	0.505022i	0.868915	+	0.494961i	$0.164818\pi$
$168$	−2.93485	−	1.69443i	−0.226428	−	0.130728i
$169$	−4.31774	+	7.47855i	−0.332134	+	0.575273i
$170$	13.7110	−	4.01204i	1.05159	−	0.307709i
$171$	−2.14462			−0.164003
$172$	−2.20383	+	1.27238i	−0.168041	+	0.0970184i
$173$	−14.2230	−	8.21166i	−1.08136	−	0.624321i	−0.150094	−	0.988672i	$-0.547958\pi$
$173$	−14.2230	−	8.21166i	−1.08136	−	0.624321i	−0.931262	+	0.364350i	$0.881291\pi$
$174$	2.38887			0.181100
$175$	16.9266	−	0.774694i	1.27953	−	0.0585614i
$176$	−2.14784	+	3.72017i	−0.161900	+	0.280418i
$177$			3.56909i			0.268269i
$178$	−0.800829	+	0.462359i	−0.0600247	+	0.0346553i
$179$	−19.2317			−1.43745			−0.718723	−	0.695297i	$-0.755273\pi$
$179$	−19.2317			−1.43745			−0.718723	+	0.695297i	$0.755273\pi$
$180$	0.529198	−	2.17254i	0.0394441	−	0.161932i
$181$	−3.66105	−	6.34113i	−0.272124	−	0.471333i	0.697282	−	0.716797i	$-0.254393\pi$
$181$	−3.66105	−	6.34113i	−0.272124	−	0.471333i	−0.969406	+	0.245465i	$0.921059\pi$
$182$	−6.13131	+	3.53991i	−0.454483	+	0.262396i
$183$	−3.27717	−	1.89207i	−0.242255	−	0.139866i
$184$	4.17381			0.307697
$185$	−13.1266	−	3.56275i	−0.965084	−	0.261939i
$186$	8.38482			0.614805
$187$	23.7677	+	13.7223i	1.73806	+	1.00347i
$188$	−9.46360	+	5.46381i	−0.690204	+	0.398489i
$189$	1.69443	+	2.93485i	0.123252	+	0.213479i
$190$	−4.65928	−	1.13493i	−0.338019	−	0.0823363i
$191$	4.38596			0.317357			0.158679	−	0.987330i	$-0.449277\pi$
$191$	4.38596			0.317357			0.158679	+	0.987330i	$0.449277\pi$
$192$	−0.866025	+	0.500000i	−0.0625000	+	0.0360844i
$193$		−	12.6079i		−	0.907538i	−0.891119	−	0.453769i	$-0.850079\pi$
$193$		−	12.6079i		−	0.907538i	0.891119	−	0.453769i	$-0.149921\pi$
$194$	−2.49902	+	4.32842i	−0.179419	+	0.310763i
$195$	−3.37789	−	3.22683i	−0.241896	−	0.231078i
$196$	4.48442			0.320316
$197$	−22.8097	−	13.1692i	−1.62512	−	0.938264i	−0.985520	−	0.169557i	$-0.945766\pi$
$197$	−22.8097	−	13.1692i	−1.62512	−	0.938264i	−0.639601	−	0.768707i	$-0.720900\pi$
$198$	3.72017	−	2.14784i	0.264381	−	0.152640i
$199$	3.41609			0.242160			0.121080	−	0.992643i	$-0.461364\pi$
$199$	3.41609			0.242160			0.121080	+	0.992643i	$0.461364\pi$
$200$	2.29941	−	4.43990i	0.162593	−	0.313948i
$201$	−7.17284	+	12.4237i	−0.505933	+	0.876302i
$202$	−5.02892	−	2.90345i	−0.353833	−	0.204286i
$203$	−7.01096	+	4.04778i	−0.492073	+	0.284098i
$204$	3.19443	+	5.53292i	0.223655	+	0.387382i
$205$	−22.6822	+	6.63713i	−1.58419	+	0.463557i
$206$	−5.90144	+	10.2216i	−0.411173	+	0.712172i
$207$	−3.61462	−	2.08690i	−0.251234	−	0.145050i
$208$			2.08914i			0.144856i
$209$	−4.60629	−	7.97834i	−0.318624	−	0.551873i
$210$	2.12812	+	7.27277i	0.146854	+	0.501869i
$211$	−24.2031			−1.66621			−0.833105	−	0.553115i	$-0.813439\pi$
$211$	−24.2031			−1.66621			−0.833105	+	0.553115i	$0.813439\pi$
$212$			11.1917i			0.768650i
$213$	−8.18462	−	4.72539i	−0.560801	−	0.323779i
$214$	−12.3720			−0.845730
$215$	5.52862	+	1.34669i	0.377049	+	0.0918433i
$216$	1.00000			0.0680414
$217$	−24.6082	+	14.2075i	−1.67051	+	0.964470i
$218$	11.4569	−	6.61466i	0.775961	−	0.448001i
$219$	3.82911	+	6.63222i	0.258748	+	0.448164i
$220$	9.21886	−	2.69757i	0.621536	−	0.181870i
$221$	13.3473			0.897833
$222$	0.158737	−	6.08069i	0.0106537	−	0.408109i
$223$		−	19.7702i		−	1.32391i	−0.749543	−	0.661956i	$-0.769727\pi$
$223$		−	19.7702i		−	1.32391i	0.749543	−	0.661956i	$-0.230273\pi$
$224$	1.69443	−	2.93485i	0.113214	−	0.196093i
$225$	−4.21130	+	2.69536i	−0.280753	+	0.179691i
$226$	−3.49758	−	6.05799i	−0.232656	−	0.402971i
$227$	−11.9969	+	6.92642i	−0.796263	+	0.459723i	−0.842163	−	0.539223i	$-0.818718\pi$
$227$	−11.9969	+	6.92642i	−0.796263	+	0.459723i	0.0458996	+	0.998946i	$0.485385\pi$
$228$		−	2.14462i		−	0.142031i
$229$	−6.33284	−	10.9688i	−0.418486	−	0.724839i	0.577302	−	0.816531i	$-0.304106\pi$
$229$	−6.33284	−	10.9688i	−0.418486	−	0.724839i	−0.995787	+	0.0916924i	$0.970772\pi$
$230$	−6.74854	−	6.44674i	−0.444986	−	0.425086i
$231$	−7.27874	+	12.6072i	−0.478906	+	0.829490i
$232$			2.38887i			0.156837i
$233$		−	2.09559i		−	0.137286i	−0.997641	−	0.0686432i	$-0.978133\pi$
$233$		−	2.09559i		−	0.137286i	0.997641	−	0.0686432i	$-0.0218670\pi$
$234$	1.04457	−	1.80925i	0.0682858	−	0.118274i
$235$	23.7407	+	5.78288i	1.54868	+	0.377233i
$236$	−3.56909			−0.232328
$237$	−5.84135	−	3.37250i	−0.379436	−	0.219068i
$238$	−18.7503	−	10.8255i	−1.21540	−	0.701714i
$239$	7.83955	−	13.5785i	0.507098	−	0.878320i	−0.492868	−	0.870104i	$-0.664051\pi$
$239$	7.83955	−	13.5785i	0.507098	−	0.878320i	0.999966	−	0.00821610i	$-0.00261529\pi$
$240$	2.17254	+	0.529198i	0.140237	+	0.0341596i
$241$	−7.74941	−	13.4224i	−0.499183	−	0.864611i	0.500816	−	0.865554i	$-0.333033\pi$
$241$	−7.74941	−	13.4224i	−0.499183	−	0.864611i	−1.00000		0.000942704i	$0.999700\pi$
$242$	6.45437	+	3.72643i	0.414903	+	0.239544i
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	1.89207	−	3.27717i	0.121128	−	0.209799i
$245$	−7.25077	−	6.92651i	−0.463235	−	0.442518i
$246$	−5.28456	−	9.15313i	−0.336931	−	0.583582i
$247$	−3.88015	−	2.24021i	−0.246888	−	0.142541i
$248$			8.38482i			0.532437i
$249$	−11.6093			−0.735707
$250$	−10.5756	+	3.62718i	−0.668861	+	0.229403i
$251$	−4.21275			−0.265906			−0.132953	−	0.991122i	$-0.542446\pi$
$251$	−4.21275			−0.265906			−0.132953	+	0.991122i	$0.542446\pi$
$252$	−2.93485	+	1.69443i	−0.184878	+	0.106739i
$253$		−	17.9293i		−	1.12721i
$254$	10.2448	+	17.7444i	0.642813	+	1.11338i
$255$	3.38098	−	13.8801i	0.211725	−	0.869205i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	8.32051	+	4.80385i	0.519019	+	0.299656i	0.736533	−	0.676401i	$-0.236462\pi$
$257$	8.32051	+	4.80385i	0.519019	+	0.299656i	−0.217514	+	0.976057i	$0.569795\pi$
$258$			2.54477i			0.158430i
$259$	9.83746	+	18.1149i	0.611270	+	1.12560i
$260$	3.22683	−	3.37789i	0.200119	−	0.209488i
$261$	1.19443	−	2.06882i	0.0739336	−	0.128057i
$262$	−14.0235	+	8.09647i	−0.866375	+	0.500202i
$263$	−3.97236	+	2.29344i	−0.244946	+	0.141420i	−0.617448	−	0.786612i	$-0.711833\pi$
$263$	−3.97236	+	2.29344i	−0.244946	+	0.141420i	0.372502	+	0.928031i	$0.378500\pi$
$264$	2.14784	+	3.72017i	0.132190	+	0.228960i
$265$	17.2864	−	18.0957i	1.06189	−	1.11161i
$266$	3.63391	+	6.29412i	0.222809	+	0.385917i
$267$			0.924718i			0.0565918i
$268$	−12.4237	−	7.17284i	−0.758900	−	0.438151i
$269$	4.20182			0.256190			0.128095	−	0.991762i	$-0.459114\pi$
$269$	4.20182			0.256190			0.128095	+	0.991762i	$0.459114\pi$
$270$	−1.61688	−	1.54457i	−0.0984002	−	0.0939996i
$271$	5.94377	−	10.2949i	0.361058	−	0.625372i	−0.627077	−	0.778957i	$-0.715749\pi$
$271$	5.94377	−	10.2949i	0.361058	−	0.625372i	0.988135	+	0.153586i	$0.0490821\pi$
$272$	−5.53292	+	3.19443i	−0.335483	+	0.193691i
$273$			7.07983i			0.428491i
$274$	−9.74012	+	16.8704i	−0.588422	+	1.01918i
$275$	−19.0724	−	9.87754i	−1.15011	−	0.595638i
$276$	2.08690	−	3.61462i	0.125617	−	0.217575i
$277$	0.789513	−	0.455826i	0.0474372	−	0.0273879i	−0.476094	−	0.879394i	$-0.657948\pi$
$277$	0.789513	−	0.455826i	0.0474372	−	0.0273879i	0.523531	+	0.852007i	$0.324614\pi$
$278$	−0.172597	+	0.0996490i	−0.0103517	+	0.00597655i
$279$	4.19241	−	7.26147i	0.250993	−	0.434733i
$280$	−7.27277	+	2.12812i	−0.434631	+	0.127179i
$281$	−1.60452	+	2.77912i	−0.0957178	+	0.165788i	−0.909908	−	0.414810i	$-0.863848\pi$
$281$	−1.60452	+	2.77912i	−0.0957178	+	0.165788i	0.814190	+	0.580598i	$0.197181\pi$
$282$			10.9276i			0.650730i
$283$	11.6307	−	6.71497i	0.691372	−	0.399164i	−0.112754	−	0.993623i	$-0.535967\pi$
$283$	11.6307	−	6.71497i	0.691372	−	0.399164i	0.804126	+	0.594459i	$0.202634\pi$
$284$	4.72539	−	8.18462i	0.280401	−	0.485668i
$285$	−3.31251	+	3.46759i	−0.196216	+	0.205402i
$286$	8.97429			0.530661
$287$	31.0187	+	17.9087i	1.83098	+	1.05712i
$288$			1.00000i			0.0589256i
$289$	11.9088	+	20.6267i	0.700518	+	1.21333i
$290$	3.68978	−	3.86251i	0.216671	−	0.226814i
$291$	2.49902	+	4.32842i	0.146495	+	0.253737i
$292$	−6.63222	+	3.82911i	−0.388121	+	0.224082i
$293$	4.45789	−	2.57376i	0.260432	−	0.150361i	−0.364099	−	0.931360i	$-0.618623\pi$
$293$	4.45789	−	2.57376i	0.260432	−	0.150361i	0.624532	+	0.780999i	$0.285290\pi$
$294$	2.24221	−	3.88362i	0.130768	−	0.226497i
$295$	5.77078	+	5.51271i	0.335988	+	0.320962i
$296$	6.08069	+	0.158737i	0.353433	+	0.00922641i
$297$		−	4.29568i		−	0.249261i
$298$	14.6244	+	8.44338i	0.847166	+	0.489112i
$299$	−4.35984	−	7.55146i	−0.252136	−	0.436712i
$300$	−2.69536	−	4.21130i	−0.155617	−	0.243139i
$301$	−4.31194	−	7.46850i	−0.248536	−	0.430477i
$302$			21.9695i			1.26420i
$303$	−5.02892	+	2.90345i	−0.288904	+	0.166799i
$304$	2.14462			0.123002
$305$	−8.12107	+	2.37634i	−0.465011	+	0.136069i
$306$	6.38887			0.365227
$307$			3.44266i			0.196483i	0.995163	+	0.0982416i	$0.0313218\pi$
$307$			3.44266i			0.196483i	−0.995163	+	0.0982416i	$0.968678\pi$
$308$	−12.6072	−	7.27874i	−0.718359	−	0.414745i
$309$	5.90144	+	10.2216i	0.335721	+	0.581486i
$310$	12.9510	−	13.5572i	0.735565	−	0.770000i
$311$	−14.3862	+	24.9177i	−0.815768	+	1.41295i	0.0930079	+	0.995665i	$0.470352\pi$
$311$	−14.3862	+	24.9177i	−0.815768	+	1.41295i	−0.908775	+	0.417286i	$0.862982\pi$
$312$	1.80925	+	1.04457i	0.102429	+	0.0591372i
$313$	−5.98765	−	3.45697i	−0.338442	−	0.195399i	0.321141	−	0.947031i	$-0.395934\pi$
$313$	−5.98765	−	3.45697i	−0.338442	−	0.195399i	−0.659583	+	0.751632i	$0.729267\pi$
$314$	−3.90288	−	6.75998i	−0.220252	−	0.381488i
$315$	7.36246	+	1.79338i	0.414828	+	0.101046i
$316$	3.37250	−	5.84135i	0.189718	−	0.328601i
$317$	−1.33689	−	0.771852i	−0.0750871	−	0.0433515i	0.461986	−	0.886887i	$-0.347137\pi$
$317$	−1.33689	−	0.771852i	−0.0750871	−	0.0433515i	−0.537073	+	0.843535i	$0.680470\pi$
$318$	9.69231	+	5.59586i	0.543518	+	0.313800i
$319$	10.2618			0.574551
$320$	−0.529198	+	2.17254i	−0.0295831	+	0.121449i
$321$	−6.18598	+	10.7144i	−0.345268	+	0.598021i
$322$			14.1445i			0.788241i
$323$		−	13.7017i		−	0.762382i
$324$	0.500000	−	0.866025i	0.0277778	−	0.0481125i
$325$	−10.4348	+	0.477577i	−0.578818	+	0.0264912i
$326$	5.28114	+	9.14720i	0.292495	+	0.506617i
$327$		−	13.2293i		−	0.731583i
$328$	9.15313	−	5.28456i	0.505397	−	0.291791i
$329$	−18.5161	−	32.0709i	−1.02083	−	1.76812i
$330$	2.27327	−	9.33256i	0.125139	−	0.513740i
$331$	2.95680	−	5.12132i	0.162520	−	0.281493i	−0.773252	−	0.634099i	$-0.781371\pi$
$331$	2.95680	−	5.12132i	0.162520	−	0.281493i	0.935772	+	0.352606i	$0.114704\pi$
$332$		−	11.6093i		−	0.637141i
$333$	−5.18666	−	3.17782i	−0.284227	−	0.174143i
$334$	13.0526			0.714209
$335$	9.00870	+	30.7869i	0.492198	+	1.68207i
$336$	−1.69443	−	2.93485i	−0.0924389	−	0.160109i
$337$	15.7431	−	9.08928i	0.857581	−	0.495125i	−0.00562055	−	0.999984i	$-0.501789\pi$
$337$	15.7431	−	9.08928i	0.857581	−	0.495125i	0.863201	+	0.504860i	$0.168456\pi$
$338$	−7.47855	+	4.31774i	−0.406779	+	0.234854i
$339$	−6.99516			−0.379925
$340$	13.8801	+	3.38098i	0.752754	+	0.183359i
$341$	36.0185			1.95051
$342$	−1.85729	−	1.07231i	−0.100431	−	0.0579838i
$343$		−	8.52496i		−	0.460305i
$344$	−2.54477			−0.137205
$345$	−8.95731	+	2.62104i	−0.482246	+	0.141112i
$346$	−8.21166	−	14.2230i	−0.441462	−	0.764634i
$347$			12.9131i			0.693211i	0.938011	+	0.346605i	$0.112666\pi$
$347$			12.9131i			0.693211i	−0.938011	+	0.346605i	$0.887334\pi$
$348$	2.06882	+	1.19443i	0.110900	+	0.0640284i
$349$	−0.845677	+	1.46476i	−0.0452681	+	0.0784066i	−0.887772	−	0.460284i	$-0.847748\pi$
$349$	−0.845677	+	1.46476i	−0.0452681	+	0.0784066i	0.842504	+	0.538691i	$0.181081\pi$
$350$	15.0462	+	7.79240i	0.804255	+	0.416522i
$351$	−1.04457	−	1.80925i	−0.0557551	−	0.0965706i
$352$	−3.72017	+	2.14784i	−0.198286	+	0.114480i
$353$	4.80463	+	2.77396i	0.255725	+	0.147643i	0.622383	−	0.782713i	$-0.286165\pi$
$353$	4.80463	+	2.77396i	0.255725	+	0.147643i	−0.366658	+	0.930356i	$0.619498\pi$
$354$	−1.78454	+	3.09092i	−0.0948474	+	0.164281i
$355$	−20.2821	+	5.93484i	−1.07646	+	0.314989i
$356$	−0.924718			−0.0490100
$357$	−18.7503	+	10.8255i	−0.992373	+	0.572947i
$358$	−16.6552	−	9.61586i	−0.880252	−	0.508214i
$359$	20.3437			1.07370			0.536851	−	0.843677i	$-0.319614\pi$
$359$	20.3437			1.07370			0.536851	+	0.843677i	$0.319614\pi$
$360$	1.54457	−	1.61688i	0.0814060	−	0.0852170i
$361$	7.20031	−	12.4713i	0.378964	−	0.656384i
$362$		−	7.32211i		−	0.384841i
$363$	6.45437	−	3.72643i	0.338767	−	0.195587i
$364$	−7.07983			−0.371084
$365$	16.6378	+	4.05272i	0.870864	+	0.212129i
$366$	−1.89207	−	3.27717i	−0.0989003	−	0.171300i
$367$	0.369651	−	0.213418i	0.0192956	−	0.0111403i	−0.490321	−	0.871542i	$-0.663121\pi$
$367$	0.369651	−	0.213418i	0.0192956	−	0.0111403i	0.509617	+	0.860401i	$0.329787\pi$
$368$	3.61462	+	2.08690i	0.188425	+	0.108787i
$369$	−10.5691			−0.550206
$370$	−9.58656	−	9.64872i	−0.498382	−	0.501613i
$371$	−37.9272			−1.96908
$372$	7.26147	+	4.19241i	0.376490	+	0.217366i
$373$	−22.9294	+	13.2383i	−1.18724	+	0.685454i	−0.957679	−	0.287839i	$-0.907063\pi$
$373$	−22.9294	+	13.2383i	−1.18724	+	0.685454i	−0.229563	+	0.973294i	$0.573730\pi$
$374$	13.7223	+	23.7677i	0.709561	+	1.22900i
$375$	−2.14658	+	10.9723i	−0.110849	+	0.566609i
$376$	−10.9276			−0.563549
$377$	4.32206	−	2.49534i	0.222597	−	0.128517i
$378$			3.38887i			0.174305i
$379$	−1.48389	+	2.57017i	−0.0762222	+	0.132021i	−0.901617	−	0.432535i	$-0.857619\pi$
$379$	−1.48389	+	2.57017i	−0.0762222	+	0.132021i	0.825395	+	0.564556i	$0.190952\pi$
$380$	−3.46759	−	3.31251i	−0.177883	−	0.169928i
$381$	20.4895			1.04971
$382$	3.79836	+	2.19298i	0.194341	+	0.112203i
$383$	−30.4946	+	17.6061i	−1.55820	+	0.899628i	−0.560773	+	0.827970i	$0.689496\pi$
$383$	−30.4946	+	17.6061i	−1.55820	+	0.899628i	−0.997429	+	0.0716589i	$0.977171\pi$
$384$	−1.00000			−0.0510310
$385$	9.14171	+	31.2415i	0.465905	+	1.59221i
$386$	6.30396	−	10.9188i	0.320863	−	0.555751i
$387$	2.20383	+	1.27238i	0.112027	+	0.0646789i
$388$	−4.32842	+	2.49902i	−0.219742	+	0.126868i
$389$	13.8150	+	23.9283i	0.700450	+	1.21322i	0.968309	+	0.249757i	$0.0803508\pi$
$389$	13.8150	+	23.9283i	0.700450	+	1.21322i	−0.267858	+	0.963458i	$0.586316\pi$
$390$	−1.31193	−	4.48346i	−0.0664319	−	0.227029i
$391$	13.3330	−	23.0933i	0.674276	−	1.16788i
$392$	3.88362	+	2.24221i	0.196153	+	0.113249i
$393$			16.1929i			0.816826i
$394$	−13.1692	−	22.8097i	−0.663453	−	1.14913i
$395$	−14.4753	+	4.23568i	−0.728332	+	0.213120i
$396$	4.29568			0.215866
$397$		−	31.9573i		−	1.60389i	−0.597397	−	0.801946i	$-0.703798\pi$
$397$		−	31.9573i		−	1.60389i	0.597397	−	0.801946i	$-0.296202\pi$
$398$	2.95842	+	1.70804i	0.148292	+	0.0856165i
$399$	7.26782			0.363846
$400$	4.21130	−	2.69536i	0.210565	−	0.134768i
$401$	8.53388			0.426162			0.213081	−	0.977035i	$-0.431650\pi$
$401$	8.53388			0.426162			0.213081	+	0.977035i	$0.431650\pi$
$402$	−12.4237	+	7.17284i	−0.619639	+	0.357749i
$403$	15.1702	−	8.75854i	0.755684	−	0.436294i
$404$	−2.90345	−	5.02892i	−0.144452	−	0.250198i
$405$	−2.14608	+	0.627973i	−0.106639	+	0.0312042i
$406$	−8.09555			−0.401776
$407$	0.681884	−	26.1207i	0.0337997	−	1.29476i
$408$			6.38887i			0.316296i
$409$	15.5232	−	26.8870i	0.767573	−	1.32948i	−0.171302	−	0.985219i	$-0.554797\pi$
$409$	15.5232	−	26.8870i	0.767573	−	1.32948i	0.938875	−	0.344257i	$-0.111869\pi$
$410$	−22.9619	−	5.59316i	−1.13401	−	0.276226i
$411$	9.74012	+	16.8704i	0.480445	+	0.832155i
$412$	−10.2216	+	5.90144i	−0.503582	+	0.290743i
$413$		−	12.0952i		−	0.595164i
$414$	−2.08690	−	3.61462i	−0.102566	−	0.177649i
$415$	−17.9313	+	18.7708i	−0.880215	+	0.921422i
$416$	−1.04457	+	1.80925i	−0.0512143	+	0.0887058i
$417$			0.199298i			0.00975967i
$418$		−	9.21259i		−	0.450602i
$419$	−6.27177	+	10.8630i	−0.306396	+	0.530693i	−0.977571	−	0.210605i	$-0.932456\pi$
$419$	−6.27177	+	10.8630i	−0.306396	+	0.530693i	0.671175	+	0.741299i	$0.265790\pi$
$420$	−1.79338	+	7.36246i	−0.0875081	+	0.359251i
$421$	−24.0695			−1.17308			−0.586538	−	0.809922i	$-0.699510\pi$
$421$	−24.0695			−1.17308			−0.586538	+	0.809922i	$0.699510\pi$
$422$	−20.9605	−	12.1015i	−1.02034	−	0.589094i
$423$	9.46360	+	5.46381i	0.460136	+	0.265660i
$424$	−5.59586	+	9.69231i	−0.271759	+	0.470700i
$425$	−17.2203	−	26.9054i	−0.835307	−	1.30511i
$426$	−4.72539	−	8.18462i	−0.228946	−	0.396546i
$427$	11.1059	+	6.41199i	0.537451	+	0.310298i
$428$	−10.7144	−	6.18598i	−0.517902	−	0.299011i
$429$	4.48714	−	7.77196i	0.216641	−	0.375234i
$430$	4.11459	+	3.93058i	0.198423	+	0.189549i
$431$	10.1880	+	17.6460i	0.490736	+	0.849980i	0.999943	−	0.0106640i	$-0.00339451\pi$
$431$	10.1880	+	17.6460i	0.490736	+	0.849980i	−0.509207	+	0.860644i	$0.670061\pi$
$432$	0.866025	+	0.500000i	0.0416667	+	0.0240563i
$433$			15.6081i			0.750079i	0.927009	+	0.375039i	$0.122371\pi$
$433$			15.6081i			0.750079i	−0.927009	+	0.375039i	$0.877629\pi$
$434$	−28.4150			−1.36397
$435$	−1.50014	−	5.12669i	−0.0719264	−	0.245806i
$436$	13.2293			0.633569
$437$	−7.75198	+	4.47561i	−0.370828	+	0.214097i
$438$			7.65823i			0.365924i
$439$	−7.26387	−	12.5814i	−0.346686	−	0.600477i	0.638973	−	0.769229i	$-0.279360\pi$
$439$	−7.26387	−	12.5814i	−0.346686	−	0.600477i	−0.985659	+	0.168752i	$0.946026\pi$
$440$	9.33256	+	2.27327i	0.444912	+	0.108374i
$441$	−2.24221	−	3.88362i	−0.106772	−	0.184934i
$442$	11.5591	+	6.67363i	0.549808	+	0.317432i
$443$		−	23.3745i		−	1.11055i	−0.831665	−	0.555277i	$-0.812612\pi$
$443$		−	23.3745i		−	1.11055i	0.831665	−	0.555277i	$-0.187388\pi$
$444$	3.17782	−	5.18666i	0.150812	−	0.246148i
$445$	1.49516	+	1.42829i	0.0708773	+	0.0677076i
$446$	9.88511	−	17.1215i	0.468073	−	0.810727i
$447$	14.6244	−	8.44338i	0.691708	−	0.399358i
$448$	2.93485	−	1.69443i	0.138658	−	0.0800545i
$449$	8.00485	+	13.8648i	0.377772	+	0.654321i	0.990738	−	0.135789i	$-0.0433568\pi$
$449$	8.00485	+	13.8648i	0.377772	+	0.654321i	−0.612965	+	0.790110i	$0.710024\pi$
$450$	−4.99477	+	0.228600i	−0.235456	+	0.0107763i
$451$	−22.7008	−	39.3189i	−1.06894	−	1.85145i
$452$		−	6.99516i		−	0.329025i
$453$	19.0261	+	10.9847i	0.893926	+	0.516108i
$454$	−13.8528			−0.650146
$455$	11.4472	+	10.9353i	0.536654	+	0.512655i
$456$	1.07231	−	1.85729i	0.0502154	−	0.0869757i
$457$	13.7823	−	7.95720i	0.644708	−	0.372222i	−0.141718	−	0.989907i	$-0.545263\pi$
$457$	13.7823	−	7.95720i	0.644708	−	0.372222i	0.786426	+	0.617685i	$0.211929\pi$
$458$		−	12.6657i		−	0.591828i
$459$	3.19443	−	5.53292i	0.149103	−	0.258255i
$460$	−2.62104	−	8.95731i	−0.122207	−	0.417637i
$461$	−15.1275	+	26.2017i	−0.704559	+	1.22033i	0.262291	+	0.964989i	$0.415522\pi$
$461$	−15.1275	+	26.2017i	−0.704559	+	1.22033i	−0.966850	+	0.255344i	$0.917811\pi$
$462$	−12.6072	+	7.27874i	−0.586538	+	0.338638i
$463$	4.63056	−	2.67345i	0.215200	−	0.124246i	−0.388526	−	0.921438i	$-0.627016\pi$
$463$	4.63056	−	2.67345i	0.215200	−	0.124246i	0.603726	+	0.797192i	$0.293682\pi$
$464$	−1.19443	+	2.06882i	−0.0554502	+	0.0960425i
$465$	−5.26544	−	17.9945i	−0.244179	−	0.834474i
$466$	1.04779	−	1.81483i	0.0485381	−	0.0840704i
$467$			23.4925i			1.08710i	0.839376	+	0.543551i	$0.182920\pi$
$467$			23.4925i			1.08710i	−0.839376	+	0.543551i	$0.817080\pi$
$468$	1.80925	−	1.04457i	0.0836326	−	0.0482853i
$469$	24.3078	−	42.1024i	1.12243	−	1.94411i
$470$	17.6687	+	16.8785i	0.814994	+	0.778547i
$471$	−7.80575			−0.359670
$472$	−3.09092	−	1.78454i	−0.142271	−	0.0821403i
$473$			10.9315i			0.502631i
$474$	−3.37250	−	5.84135i	−0.154904	−	0.268302i
$475$	0.490259	+	10.7119i	0.0224946	+	0.491494i
$476$	−10.8255	−	18.7503i	−0.496187	−	0.859420i
$477$	9.69231	−	5.59586i	0.443780	−	0.256217i
$478$	13.5785	−	7.83955i	0.621066	−	0.358573i
$479$	16.8406	−	29.1687i	0.769465	−	1.33275i	−0.168388	−	0.985721i	$-0.553856\pi$
$479$	16.8406	−	29.1687i	0.769465	−	1.33275i	0.937853	−	0.347032i	$-0.112811\pi$
$480$	1.61688	+	1.54457i	0.0738001	+	0.0704997i
$481$	−6.06452	−	11.1673i	−0.276518	−	0.509185i
$482$		−	15.4988i		−	0.705952i
$483$	12.2495	+	7.07224i	0.557371	+	0.321798i
$484$	3.72643	+	6.45437i	0.169383	+	0.293380i
$485$	10.8584	+	2.64495i	0.493057	+	0.120101i
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$			26.1574i			1.18530i	0.805459	+	0.592652i	$0.201919\pi$
$487$			26.1574i			1.18530i	−0.805459	+	0.592652i	$0.798081\pi$
$488$	3.27717	−	1.89207i	0.148350	−	0.0856501i
$489$	10.5623			0.477643
$490$	−2.81610	−	9.62392i	−0.127218	−	0.434764i
$491$	12.3778			0.558604			0.279302	−	0.960203i	$-0.409897\pi$
$491$	12.3778			0.558604			0.279302	+	0.960203i	$0.409897\pi$
$492$		−	10.5691i		−	0.476493i
$493$	13.2174	+	7.63108i	0.595282	+	0.343686i
$494$	−2.24021	−	3.88015i	−0.100792	−	0.174576i
$495$	−6.94560	−	6.63498i	−0.312181	−	0.298220i
$496$	−4.19241	+	7.26147i	−0.188245	+	0.326050i
$497$	27.7366	+	16.0137i	1.24416	+	0.718314i
$498$	−10.0539	−	5.80463i	−0.450527	−	0.260112i
$499$	12.5681	+	21.7686i	0.562625	+	0.974494i	0.997266	+	0.0738909i	$0.0235417\pi$
$499$	12.5681	+	21.7686i	0.562625	+	0.974494i	−0.434642	+	0.900603i	$0.643125\pi$
$500$	−10.9723	−	2.14658i	−0.490698	−	0.0959980i
$501$	6.52632	−	11.3039i	0.291574	−	0.505022i
$502$	−3.64835	−	2.10637i	−0.162834	−	0.0940120i
$503$	4.83312	+	2.79040i	0.215498	+	0.124418i	0.603864	−	0.797087i	$-0.293627\pi$
$503$	4.83312	+	2.79040i	0.215498	+	0.124418i	−0.388366	+	0.921505i	$0.626960\pi$
$504$	−3.38887			−0.150952
$505$	−3.07300	+	12.6157i	−0.136746	+	0.561393i
$506$	8.96467	−	15.5273i	0.398528	−	0.690271i
$507$			8.63548i			0.383515i
$508$			20.4895i			0.909075i
$509$	−4.88714	+	8.46478i	−0.216619	+	0.375195i	−0.953772	−	0.300531i	$-0.902836\pi$
$509$	−4.88714	+	8.46478i	−0.216619	+	0.375195i	0.737153	+	0.675726i	$0.236170\pi$
$510$	9.86806	−	10.3300i	0.436965	−	0.457421i
$511$	−12.9764	−	22.4757i	−0.574040	−	0.994267i
$512$		−	1.00000i		−	0.0441942i
$513$	−1.85729	+	1.07231i	−0.0820015	+	0.0473436i
$514$	4.80385	+	8.32051i	0.211889	+	0.367002i
$515$	25.6423	+	6.24606i	1.12993	+	0.275234i
$516$	−1.27238	+	2.20383i	−0.0560136	+	0.0970184i
$517$			46.9416i			2.06449i
$518$	−0.537939	+	20.6067i	−0.0236357	+	0.905404i
$519$	−16.4233			−0.720904
$520$	4.48346	−	1.31193i	0.196613	−	0.0575317i
$521$	−8.56513	−	14.8352i	−0.375245	−	0.649943i	0.615119	−	0.788435i	$-0.289108\pi$
$521$	−8.56513	−	14.8352i	−0.375245	−	0.649943i	−0.990364	+	0.138491i	$0.955775\pi$
$522$	2.06882	−	1.19443i	0.0905498	−	0.0522789i
$523$	4.79471	−	2.76822i	0.209658	−	0.121046i	−0.391495	−	0.920180i	$-0.628042\pi$
$523$	4.79471	−	2.76822i	0.209658	−	0.121046i	0.601152	+	0.799134i	$0.294708\pi$
$524$	−16.1929			−0.707392
$525$	14.2715	−	9.13421i	0.622861	−	0.398650i
$526$	−4.58688			−0.199998
$527$	46.3926	+	26.7848i	2.02089	+	1.16676i
$528$			4.29568i			0.186945i
$529$	5.57933			0.242580
$530$	24.0183	−	7.02810i	1.04329	−	0.305281i
$531$	1.78454	+	3.09092i	0.0774426	+	0.134134i
$532$			7.26782i			0.315100i
$533$	−19.1222	−	11.0402i	−0.828274	−	0.478204i
$534$	−0.462359	+	0.800829i	−0.0200082	+	0.0346553i
$535$	7.76926	+	26.5512i	0.335895	+	1.14791i
$536$	−7.17284	−	12.4237i	−0.309820	−	0.536623i
$537$	−16.6552	+	9.61586i	−0.718723	+	0.414955i
$538$	3.63889	+	2.10091i	0.156883	+	0.0905767i
$539$	9.63182	−	16.6828i	0.414872	−	0.718579i
$540$	−0.627973	−	2.14608i	−0.0270237	−	0.0923525i
$541$	8.03851			0.345602			0.172801	−	0.984957i	$-0.444718\pi$
$541$	8.03851			0.345602			0.172801	+	0.984957i	$0.444718\pi$
$542$	10.2949	−	5.94377i	0.442204	−	0.255307i
$543$	−6.34113	−	3.66105i	−0.272124	−	0.157111i
$544$	−6.38887			−0.273920
$545$	−21.3902	−	20.4336i	−0.916256	−	0.875280i
$546$	−3.53991	+	6.13131i	−0.151494	+	0.262396i
$547$			8.07970i			0.345463i	0.984969	+	0.172732i	$0.0552593\pi$
$547$			8.07970i			0.345463i	−0.984969	+	0.172732i	$0.944741\pi$
$548$	−16.8704	+	9.74012i	−0.720667	+	0.416077i
$549$	−3.78415			−0.161503
$550$	−11.5784	−	18.0904i	−0.493705	−	0.771377i
$551$	−2.56160	−	4.43683i	−0.109128	−	0.189015i
$552$	3.61462	−	2.08690i	0.153849	−	0.0888245i
$553$	19.7955	+	11.4290i	0.841792	+	0.486009i
$554$	0.911651			0.0387324
$555$	−13.1493	+	3.47785i	−0.558157	+	0.147626i
$556$	−0.199298			−0.00845212
$557$	−36.2741	−	20.9429i	−1.53698	−	0.887377i	−0.999013	−	0.0444128i	$-0.985858\pi$
$557$	−36.2741	−	20.9429i	−1.53698	−	0.887377i	−0.537969	−	0.842964i	$-0.680808\pi$
$558$	7.26147	−	4.19241i	0.307402	−	0.177479i
$559$	2.65819	+	4.60412i	0.112430	+	0.194734i
$560$	−7.36246	−	1.79338i	−0.311121	−	0.0757842i
$561$	27.4445			1.15871
$562$	−2.77912	+	1.60452i	−0.117230	+	0.0676827i
$563$		−	42.3364i		−	1.78427i	−0.451771	−	0.892134i	$-0.649208\pi$
$563$		−	42.3364i		−	1.78427i	0.451771	−	0.892134i	$-0.350792\pi$
$564$	−5.46381	+	9.46360i	−0.230068	+	0.398489i
$565$	−10.8045	+	11.3103i	−0.454550	+	0.475829i
$566$	13.4299			0.564503
$567$	2.93485	+	1.69443i	0.123252	+	0.0711595i
$568$	8.18462	−	4.72539i	0.343419	−	0.198273i
$569$	3.65368			0.153170			0.0765852	−	0.997063i	$-0.475598\pi$
$569$	3.65368			0.153170			0.0765852	+	0.997063i	$0.475598\pi$
$570$	−4.60251	+	1.34676i	−0.192778	+	0.0564097i
$571$	0.382372	−	0.662288i	0.0160018	−	0.0277159i	−0.857914	−	0.513794i	$-0.828240\pi$
$571$	0.382372	−	0.662288i	0.0160018	−	0.0277159i	0.873915	+	0.486078i	$0.161573\pi$
$572$	7.77196	+	4.48714i	0.324962	+	0.187617i
$573$	3.79836	−	2.19298i	0.158679	−	0.0916131i
$574$	17.9087	+	31.0187i	0.747494	+	1.29470i
$575$	−9.59730	+	18.5313i	−0.400235	+	0.772808i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	1.14731	+	0.662402i	0.0477633	+	0.0275761i	0.523691	−	0.851908i	$-0.324554\pi$
$577$	1.14731	+	0.662402i	0.0477633	+	0.0275761i	−0.475928	+	0.879484i	$0.657888\pi$
$578$			23.8176i			0.990683i
$579$	−6.30396	−	10.9188i	−0.261984	−	0.453769i
$580$	5.12669	−	1.50014i	0.212874	−	0.0622901i
$581$	39.3423			1.63219
$582$			4.99803i			0.207175i
$583$	41.6351	+	24.0380i	1.72435	+	0.995553i
$584$	−7.65823			−0.316900
$585$	−4.53875	−	1.10557i	−0.187654	−	0.0457097i
$586$	5.14752			0.212642
$587$	7.06825	−	4.08086i	0.291738	−	0.168435i	−0.346987	−	0.937870i	$-0.612795\pi$
$587$	7.06825	−	4.08086i	0.291738	−	0.168435i	0.638725	+	0.769435i	$0.279462\pi$
$588$	3.88362	−	2.24221i	0.160158	−	0.0924672i
$589$	−8.99112	−	15.5731i	−0.370472	−	0.641677i
$590$	2.24129	+	7.65954i	0.0922725	+	0.315338i
$591$	−26.3383			−1.08341
$592$	5.18666	+	3.17782i	0.213171	+	0.130607i
$593$			3.99327i			0.163984i	0.996633	+	0.0819919i	$0.0261282\pi$
$593$			3.99327i			0.163984i	−0.996633	+	0.0819919i	$0.973872\pi$
$594$	2.14784	−	3.72017i	0.0881269	−	0.152640i
$595$	−11.4577	+	47.0378i	−0.469719	+	1.92836i
$596$	8.44338	+	14.6244i	0.345854	+	0.599037i
$597$	2.95842	−	1.70804i	0.121080	−	0.0699056i
$598$		−	8.71968i		−	0.356574i
$599$	15.7398	+	27.2621i	0.643109	+	1.11390i	0.984735	+	0.174062i	$0.0556892\pi$
$599$	15.7398	+	27.2621i	0.643109	+	1.11390i	−0.341626	+	0.939836i	$0.610977\pi$
$600$	−0.228600	−	4.99477i	−0.00933255	−	0.203911i
$601$	−5.06605	+	8.77466i	−0.206649	+	0.357926i	−0.950657	−	0.310245i	$-0.899589\pi$
$601$	−5.06605	+	8.77466i	−0.206649	+	0.357926i	0.744008	+	0.668171i	$0.232922\pi$
$602$		−	8.62388i		−	0.351483i
$603$			14.3457i			0.584201i
$604$	−10.9847	+	19.0261i	−0.446963	+	0.774162i
$605$	3.94404	−	16.1917i	0.160348	−	0.658285i
$606$	−5.80689			−0.235889
$607$	−27.9541	−	16.1393i	−1.13462	−	0.655074i	−0.189529	−	0.981875i	$-0.560696\pi$
$607$	−27.9541	−	16.1393i	−1.13462	−	0.655074i	−0.945093	+	0.326801i	$0.894029\pi$
$608$	1.85729	+	1.07231i	0.0753232	+	0.0434879i
$609$	−4.04778	+	7.01096i	−0.164024	+	0.284098i
$610$	−8.22123	−	2.00256i	−0.332868	−	0.0810814i
$611$	11.4147	+	19.7708i	0.461789	+	0.799841i
$612$	5.53292	+	3.19443i	0.223655	+	0.129127i
$613$	2.79022	+	1.61093i	0.112696	+	0.0650650i	0.555288	−	0.831658i	$-0.312608\pi$
$613$	2.79022	+	1.61093i	0.112696	+	0.0650650i	−0.442593	+	0.896723i	$0.645941\pi$
$614$	−1.72133	+	2.98143i	−0.0694673	+	0.120321i
$615$	−16.3248	+	17.0890i	−0.658278	+	0.689095i
$616$	−7.27874	−	12.6072i	−0.293269	−	0.507957i
$617$	22.0266	+	12.7171i	0.886757	+	0.511970i	0.872880	−	0.487934i	$-0.162249\pi$
$617$	22.0266	+	12.7171i	0.886757	+	0.511970i	0.0138769	+	0.999904i	$0.495583\pi$
$618$			11.8029i			0.474781i
$619$	20.9639			0.842612			0.421306	−	0.906919i	$-0.361572\pi$
$619$	20.9639			0.842612			0.421306	+	0.906919i	$0.361572\pi$
$620$	17.9945	−	5.26544i	0.722676	−	0.211465i
$621$	−4.17381			−0.167489
$622$	−24.9177	+	14.3862i	−0.999107	+	0.576835i
$623$		−	3.13375i		−	0.125551i
$624$	1.04457	+	1.80925i	0.0418163	+	0.0724280i
$625$	14.4254	+	20.4183i	0.577016	+	0.816733i
$626$	−3.45697	−	5.98765i	−0.138168	−	0.239315i
$627$	−7.97834	−	4.60629i	−0.318624	−	0.183958i
$628$		−	7.80575i		−	0.311483i
$629$	20.3026	−	33.1369i	0.809519	−	1.32126i
$630$	5.47939	+	5.23435i	0.218304	+	0.208541i
$631$	−9.21454	+	15.9600i	−0.366825	+	0.635359i	−0.989067	−	0.147465i	$-0.952889\pi$
$631$	−9.21454	+	15.9600i	−0.366825	+	0.635359i	0.622242	+	0.782825i	$0.286222\pi$
$632$	5.84135	−	3.37250i	0.232356	−	0.134151i
$633$	−20.9605	+	12.1015i	−0.833105	+	0.480993i
$634$	−0.771852	−	1.33689i	−0.0306542	−	0.0530946i
$635$	31.6475	−	33.1291i	1.25589	−	1.31469i
$636$	5.59586	+	9.69231i	0.221890	+	0.384325i
$637$		−	9.36859i		−	0.371197i
$638$	8.88699	+	5.13090i	0.351839	+	0.203134i
$639$	−9.45079			−0.373867
$640$	−1.54457	+	1.61688i	−0.0610545	+	0.0639128i
$641$	−5.87842	+	10.1817i	−0.232183	+	0.402154i	−0.958450	−	0.285259i	$-0.907920\pi$
$641$	−5.87842	+	10.1817i	−0.232183	+	0.402154i	0.726267	+	0.687413i	$0.241254\pi$
$642$	−10.7144	+	6.18598i	−0.422865	+	0.244141i
$643$		−	1.38385i		−	0.0545738i	−0.999628	−	0.0272869i	$-0.991313\pi$
$643$		−	1.38385i		−	0.0545738i	0.999628	−	0.0272869i	$-0.00868677\pi$
$644$	−7.07224	+	12.2495i	−0.278685	+	0.482697i
$645$	5.46127	−	1.59805i	0.215037	−	0.0629230i
$646$	6.85084	−	11.8660i	0.269543	−	0.466861i
$647$	−26.9727	+	15.5727i	−1.06041	+	0.612226i	−0.925545	−	0.378638i	$-0.876392\pi$
$647$	−26.9727	+	15.5727i	−1.06041	+	0.612226i	−0.134862	+	0.990864i	$0.543059\pi$
$648$	0.866025	−	0.500000i	0.0340207	−	0.0196419i
$649$	−7.66583	+	13.2776i	−0.300910	+	0.521191i
$650$	−9.27558	−	4.80380i	−0.363818	−	0.188421i
$651$	−14.2075	+	24.6082i	−0.556837	+	0.964470i
$652$			10.5623i			0.413651i
$653$	36.4720	−	21.0571i	1.42726	−	0.824028i	0.430355	−	0.902660i	$-0.358388\pi$
$653$	36.4720	−	21.0571i	1.42726	−	0.824028i	0.996904	+	0.0786314i	$0.0250550\pi$
$654$	6.61466	−	11.4569i	0.258654	−	0.448001i
$655$	26.1820	+	25.0111i	1.02302	+	0.977266i
$656$	10.5691			0.412655
$657$	6.63222	+	3.82911i	0.258748	+	0.149388i
$658$		−	37.0323i		−	1.44367i
$659$	13.0406	+	22.5870i	0.507990	+	0.879864i	0.999957	+	0.00925020i	$0.00294447\pi$
$659$	13.0406	+	22.5870i	0.507990	+	0.879864i	−0.491968	+	0.870613i	$0.663722\pi$
$660$	6.63498	−	6.94560i	0.258266	−	0.270357i
$661$	9.31601	+	16.1358i	0.362351	+	0.627610i	0.988347	−	0.152216i	$-0.0486409\pi$
$661$	9.31601	+	16.1358i	0.362351	+	0.627610i	−0.625996	+	0.779826i	$0.715308\pi$
$662$	5.12132	−	2.95680i	0.199046	−	0.114919i
$663$	11.5591	−	6.67363i	0.448917	−	0.259182i
$664$	5.80463	−	10.0539i	0.225263	−	0.390168i
$665$	11.2257	−	11.7512i	0.435313	−	0.455692i
$666$	−2.90288	−	5.34540i	−0.112484	−	0.207130i
$667$		−	9.97067i		−	0.386066i
$668$	11.3039	+	6.52632i	0.437362	+	0.252511i
$669$	−9.88511	−	17.1215i	−0.382180	−	0.661956i
$670$	−7.59171	+	31.1666i	−0.293293	+	1.20407i
$671$	−8.12774	−	14.0777i	−0.313768	−	0.543462i
$672$		−	3.38887i		−	0.130728i
$673$	2.31679	−	1.33760i	0.0893056	−	0.0515606i	−0.454682	−	0.890654i	$-0.650247\pi$
$673$	2.31679	−	1.33760i	0.0893056	−	0.0515606i	0.543988	+	0.839093i	$0.316914\pi$
$674$	18.1786			0.700212
$675$	−2.29941	+	4.43990i	−0.0885044	+	0.170892i
$676$	−8.63548			−0.332134
$677$		−	18.7360i		−	0.720083i	−0.932936	−	0.360041i	$-0.882763\pi$
$677$		−	18.7360i		−	0.720083i	0.932936	−	0.360041i	$-0.117237\pi$
$678$	−6.05799	−	3.49758i	−0.232656	−	0.134324i
$679$	−8.46883	−	14.6684i	−0.325004	−	0.562923i
$680$	10.3300	+	9.86806i	0.396139	+	0.378423i
$681$	−6.92642	+	11.9969i	−0.265421	+	0.459723i
$682$	31.1929	+	18.0093i	1.19444	+	0.689610i
$683$	12.7062	+	7.33593i	0.486189	+	0.280701i	0.722992	−	0.690856i	$-0.242766\pi$
$683$	12.7062	+	7.33593i	0.486189	+	0.280701i	−0.236803	+	0.971558i	$0.576100\pi$
$684$	−1.07231	−	1.85729i	−0.0410007	−	0.0710154i
$685$	42.3217	+	10.3089i	1.61703	+	0.393883i
$686$	4.26248	−	7.38283i	0.162742	−	0.281878i
$687$	−10.9688	−	6.33284i	−0.418486	−	0.241613i
$688$	−2.20383	−	1.27238i	−0.0840204	−	0.0485092i
$689$	23.3811			0.890748
$690$	−9.06778	−	2.20877i	−0.345205	−	0.0840865i
$691$	7.39577	−	12.8098i	0.281348	−	0.487309i	−0.690369	−	0.723458i	$-0.742552\pi$
$691$	7.39577	−	12.8098i	0.281348	−	0.487309i	0.971717	+	0.236148i	$0.0758851\pi$
$692$		−	16.4233i		−	0.624321i
$693$			14.5575i			0.552993i
$694$	−6.45654	+	11.1831i	−0.245087	+	0.424503i
$695$	0.322241	+	0.307830i	0.0122233	+	0.0116767i
$696$	1.19443	+	2.06882i	0.0452749	+	0.0784184i
$697$		−	67.5247i		−	2.55768i
$698$	−1.46476	+	0.845677i	−0.0554418	+	0.0320094i
$699$	−1.04779	−	1.81483i	−0.0396312	−	0.0686432i
$700$	9.13421	+	14.2715i	0.345241	+	0.539413i
$701$	13.3246	−	23.0789i	0.503264	−	0.871678i	−0.496729	−	0.867906i	$-0.665466\pi$
$701$	13.3246	−	23.0789i	0.503264	−	0.871678i	0.999993	−	0.00377282i	$-0.00120093\pi$
$702$		−	2.08914i		−	0.0788496i
$703$	−11.4638	+	6.22556i	−0.432367	+	0.234801i
$704$	−4.29568			−0.161900
$705$	23.4515	−	6.86226i	0.883236	−	0.258447i
$706$	2.77396	+	4.80463i	0.104399	+	0.180825i
$707$	17.0423	−	9.83939i	0.640943	−	0.370048i
$708$	−3.09092	+	1.78454i	−0.116164	+	0.0670672i
$709$	−17.9366			−0.673622			−0.336811	−	0.941572i	$-0.609348\pi$
$709$	−17.9366			−0.673622			−0.336811	+	0.941572i	$0.609348\pi$
$710$	−20.5323	−	5.00134i	−0.770562	−	0.187697i
$711$	−6.74500			−0.252957
$712$	−0.800829	−	0.462359i	−0.0300124	−	0.0173276i
$713$		−	34.9966i		−	1.31063i
$714$	−21.6510			−0.810269
$715$	−5.63561	−	19.2595i	−0.210760	−	0.720265i
$716$	−9.61586	−	16.6552i	−0.359361	−	0.622432i
$717$		−	15.6791i		−	0.585547i
$718$	17.6182	+	10.1719i	0.657505	+	0.379611i
$719$	−8.52478	+	14.7654i	−0.317921	+	0.550655i	−0.980054	−	0.198731i	$-0.936318\pi$
$719$	−8.52478	+	14.7654i	−0.317921	+	0.550655i	0.662133	+	0.749386i	$0.269651\pi$
$720$	2.14608	−	0.627973i	0.0799796	−	0.0234032i
$721$	−19.9992	−	34.6396i	−0.744809	−	1.29005i
$722$	12.4713	−	7.20031i	0.464134	−	0.267968i
$723$	−13.4224	−	7.74941i	−0.499183	−	0.288204i
$724$	3.66105	−	6.34113i	0.136062	−	0.235666i
$725$	−10.6063	−	5.49299i	−0.393909	−	0.204005i
$726$	7.45286			0.276602
$727$	10.4909	−	6.05695i	0.389087	−	0.224640i	−0.292677	−	0.956211i	$-0.594546\pi$
$727$	10.4909	−	6.05695i	0.389087	−	0.224640i	0.681765	+	0.731572i	$0.261213\pi$
$728$	−6.13131	−	3.53991i	−0.227241	−	0.131198i
$729$	−1.00000			−0.0370370
$730$	12.3824	+	11.8287i	0.458294	+	0.437799i
$731$	−8.12910	+	14.0800i	−0.300665	+	0.520768i
$732$		−	3.78415i		−	0.139866i
$733$	2.80038	−	1.61680i	0.103434	−	0.0597178i	−0.447390	−	0.894339i	$-0.647647\pi$
$733$	2.80038	−	1.61680i	0.103434	−	0.0597178i	0.550825	+	0.834621i	$0.314313\pi$
$734$	0.426836			0.0157548
$735$	−9.74261	−	2.37315i	−0.359361	−	0.0875348i
$736$	2.08690	+	3.61462i	0.0769243	+	0.133237i
$737$	−53.3683	+	30.8122i	−1.96585	+	1.13498i
$738$	−9.15313	−	5.28456i	−0.336931	−	0.194527i
$739$	31.7088			1.16643			0.583214	−	0.812318i	$-0.301795\pi$
$739$	31.7088			1.16643			0.583214	+	0.812318i	$0.301795\pi$
$740$	−3.47785	−	13.1493i	−0.127848	−	0.483379i
$741$	−4.48041			−0.164592
$742$	−32.8459	−	18.9636i	−1.20581	−	0.696176i
$743$	−15.9225	+	9.19286i	−0.584140	+	0.337253i	−0.762777	−	0.646662i	$-0.776165\pi$
$743$	−15.9225	+	9.19286i	−0.584140	+	0.337253i	0.178637	+	0.983915i	$0.442831\pi$
$744$	4.19241	+	7.26147i	0.153701	+	0.266218i
$745$	8.93644	−	36.6872i	0.327406	−	1.34412i
$746$	−26.4766			−0.969379
$747$	−10.0539	+	5.80463i	−0.367854	+	0.212380i
$748$			27.4445i			1.00347i
$749$	20.9635	−	36.3098i	0.765989	−	1.32673i
$750$	−7.34516	+	8.42903i	−0.268207	+	0.307785i
$751$	2.77635			0.101310			0.0506552	−	0.998716i	$-0.483869\pi$
$751$	2.77635			0.101310			0.0506552	+	0.998716i	$0.483869\pi$
$752$	−9.46360	−	5.46381i	−0.345102	−	0.199245i
$753$	−3.64835	+	2.10637i	−0.132953	+	0.0767605i
$754$	4.99068			0.181750
$755$	47.1482	−	13.7962i	1.71590	−	0.502097i
$756$	−1.69443	+	2.93485i	−0.0616260	+	0.106739i
$757$	16.1194	+	9.30653i	0.585869	+	0.338252i	0.763462	−	0.645852i	$-0.223498\pi$
$757$	16.1194	+	9.30653i	0.585869	+	0.338252i	−0.177593	+	0.984104i	$0.556831\pi$
$758$	−2.57017	+	1.48389i	−0.0933527	+	0.0538972i
$759$	−8.96467	−	15.5273i	−0.325397	−	0.563604i
$760$	−1.34676	−	4.60251i	−0.0488522	−	0.166951i
$761$	10.6131	−	18.3824i	0.384724	−	0.666361i	−0.607007	−	0.794696i	$-0.707630\pi$
$761$	10.6131	−	18.3824i	0.384724	−	0.666361i	0.991731	+	0.128335i	$0.0409634\pi$
$762$	17.7444	+	10.2448i	0.642813	+	0.371128i
$763$			44.8324i			1.62304i
$764$	2.19298	+	3.79836i	0.0793393	+	0.137420i
$765$	−4.01204	−	13.7110i	−0.145056	−	0.495722i
$766$	−35.2122			−1.27227
$767$			7.45633i			0.269232i
$768$	−0.866025	−	0.500000i	−0.0312500	−	0.0180422i
$769$	−20.1047			−0.724993			−0.362496	−	0.931985i	$-0.618075\pi$
$769$	−20.1047			−0.724993			−0.362496	+	0.931985i	$0.618075\pi$
$770$	−7.70379	+	31.6268i	−0.277625	+	1.13975i
$771$	9.60769			0.346013
$772$	10.9188	−	6.30396i	0.392975	−	0.226884i
$773$	−36.8790	+	21.2921i	−1.32645	+	0.765823i	−0.984748	−	0.173987i	$-0.944335\pi$
$773$	−36.8790	+	21.2921i	−1.32645	+	0.765823i	−0.341697	+	0.939810i	$0.611002\pi$
$774$	1.27238	+	2.20383i	0.0457349	+	0.0792152i
$775$	−37.2278	−	19.2802i	−1.33726	−	0.692564i
$776$	−4.99803			−0.179419
$777$	17.5769	+	10.7692i	0.630568	+	0.386343i
$778$			27.6301i			0.990586i
$779$	−11.3334	+	19.6300i	−0.406060	+	0.703316i
$780$	1.10557	−	4.53875i	0.0395858	−	0.162513i
$781$	−20.2988	−	35.1585i	−0.726347	−	1.25807i
$782$	23.0933	−	13.3330i	0.825816	−	0.476785i
$783$		−	2.38887i		−	0.0853712i
$784$	2.24221	+	3.88362i	0.0800790	+	0.138701i
$785$	−12.0565	+	12.6210i	−0.430316	+	0.450461i
$786$	−8.09647	+	14.0235i	−0.288792	+	0.500202i
$787$			19.0582i			0.679352i	0.940542	+	0.339676i	$0.110317\pi$
$787$			19.0582i			0.679352i	−0.940542	+	0.339676i	$0.889683\pi$
$788$		−	26.3383i		−	0.938264i
$789$	−2.29344	+	3.97236i	−0.0816487	+	0.141420i
$790$	−14.6538	−	3.56944i	−0.521360	−	0.126995i
$791$	23.7057			0.842877
$792$	3.72017	+	2.14784i	0.132190	+	0.0763202i
$793$	−6.84647	−	3.95281i	−0.243125	−	0.140368i
$794$	15.9787	−	27.6758i	0.567061	−	0.982179i
$795$	5.92263	−	24.3145i	0.210054	−	0.862346i
$796$	1.70804	+	2.95842i	0.0605400	+	0.104858i
$797$	−7.05417	−	4.07272i	−0.249871	−	0.144263i	0.369834	−	0.929098i	$-0.379415\pi$
$797$	−7.05417	−	4.07272i	−0.249871	−	0.144263i	−0.619705	+	0.784835i	$0.712748\pi$
$798$	6.29412	+	3.63391i	0.222809	+	0.128639i
$799$	−34.9076	+	60.4617i	−1.23494	+	2.13898i
$800$	4.99477	−	0.228600i	0.176592	−	0.00808222i
$801$	0.462359	+	0.800829i	0.0163367	+	0.0282959i
$802$	7.39056	+	4.26694i	0.260970	+	0.150671i
$803$			32.8973i			1.16092i
$804$	−14.3457			−0.505933
$805$	30.3552	−	8.88236i	1.06988	−	0.313062i
$806$	17.5171			0.617013
$807$	3.63889	−	2.10091i	0.128095	−	0.0739556i
$808$		−	5.80689i		−	0.204286i
$809$	−7.51621	−	13.0185i	−0.264256	−	0.457704i	0.703113	−	0.711079i	$-0.251793\pi$
$809$	−7.51621	−	13.0185i	−0.264256	−	0.457704i	−0.967368	+	0.253374i	$0.918460\pi$
$810$	−2.17254	−	0.529198i	−0.0763354	−	0.0185941i
$811$	−12.6697	−	21.9445i	−0.444893	−	0.770577i	0.553152	−	0.833080i	$-0.313425\pi$
$811$	−12.6697	−	21.9445i	−0.444893	−	0.770577i	−0.998045	+	0.0625033i	$0.980092\pi$
$812$	−7.01096	−	4.04778i	−0.246036	−	0.142049i
$813$		−	11.8875i		−	0.416914i
$814$	13.6509	−	22.2802i	0.478463	−	0.780922i
$815$	16.3142	−	17.0779i	0.571461	−	0.598214i
$816$	−3.19443	+	5.53292i	−0.111828	+	0.193691i
$817$	4.72638	−	2.72878i	0.165355	−	0.0954678i
$818$	26.8870	−	15.5232i	0.940082	−	0.542756i
$819$	3.53991	+	6.13131i	0.123695	+	0.214245i
$820$	−17.0890	−	16.3248i	−0.596774	−	0.570085i
$821$	17.1091	+	29.6338i	0.597112	+	1.03423i	0.993245	+	0.116035i	$0.0370185\pi$
$821$	17.1091	+	29.6338i	0.597112	+	1.03423i	−0.396133	+	0.918193i	$0.629648\pi$
$822$			19.4802i			0.679451i
$823$	12.0345	+	6.94814i	0.419497	+	0.242197i	0.694862	−	0.719143i	$-0.255465\pi$
$823$	12.0345	+	6.94814i	0.419497	+	0.242197i	−0.275365	+	0.961340i	$0.588799\pi$
$824$	−11.8029			−0.411173
$825$	−21.4559	+	0.981991i	−0.747000	+	0.0341886i
$826$	6.04758	−	10.4747i	0.210422	−	0.364462i
$827$	−10.0570	+	5.80641i	−0.349716	+	0.201909i	−0.664560	−	0.747235i	$-0.731381\pi$
$827$	−10.0570	+	5.80641i	−0.349716	+	0.201909i	0.314844	+	0.949143i	$0.398048\pi$
$828$		−	4.17381i		−	0.145050i
$829$	−16.0993	+	27.8849i	−0.559153	+	0.968481i	0.438415	+	0.898773i	$0.355540\pi$
$829$	−16.0993	+	27.8849i	−0.559153	+	0.968481i	−0.997567	+	0.0697083i	$0.977793\pi$
$830$	−24.9144	+	7.29031i	−0.864791	+	0.253050i
$831$	0.455826	−	0.789513i	0.0158124	−	0.0273879i
$832$	−1.80925	+	1.04457i	−0.0627245	+	0.0362140i
$833$	24.8120	−	14.3252i	0.859683	−	0.496338i
$834$	−0.0996490	+	0.172597i	−0.00345056	+	0.00597655i
$835$	−8.19671	−	28.0120i	−0.283659	−	0.969394i
$836$	4.60629	−	7.97834i	0.159312	−	0.275936i
$837$		−	8.38482i		−	0.289822i
$838$	−10.8630	+	6.27177i	−0.375257	+	0.216655i
$839$	−3.94927	+	6.84034i	−0.136344	+	0.236155i	−0.926110	−	0.377253i	$-0.876869\pi$
$839$	−3.94927	+	6.84034i	−0.136344	+	0.236155i	0.789766	+	0.613408i	$0.210202\pi$
$840$	−5.23435	+	5.47939i	−0.180602	+	0.189057i
$841$	−23.2933			−0.803218
$842$	−20.8448	−	12.0348i	−0.718360	−	0.414745i
$843$			3.20905i			0.110525i
$844$	−12.1015	−	20.9605i	−0.416552	−	0.721490i
$845$	13.9625	+	13.3381i	0.480326	+	0.458845i
$846$	5.46381	+	9.46360i	0.187850	+	0.325365i
$847$	−21.8730	+	12.6284i	−0.751565	+	0.433916i
$848$	−9.69231	+	5.59586i	−0.332835	+	0.192163i
$849$	6.71497	−	11.6307i	0.230457	−	0.399164i
$850$	−1.46049	−	31.9109i	−0.0500945	−	1.09454i
$851$	−25.3796	−	0.662538i	−0.870003	−	0.0227115i
$852$		−	9.45079i		−	0.323779i
$853$	−26.1511	−	15.0983i	−0.895396	−	0.516957i	−0.0196920	−	0.999806i	$-0.506269\pi$
$853$	−26.1511	−	15.0983i	−0.895396	−	0.516957i	−0.875703	+	0.482849i	$0.839602\pi$
$854$	6.41199	+	11.1059i	0.219414	+	0.380036i
$855$	−1.13493	+	4.65928i	−0.0388137	+	0.159344i
$856$	−6.18598	−	10.7144i	−0.211433	−	0.366212i
$857$			2.92600i			0.0999504i	0.998750	+	0.0499752i	$0.0159142\pi$
$857$			2.92600i			0.0999504i	−0.998750	+	0.0499752i	$0.984086\pi$
$858$	7.77196	−	4.48714i	0.265330	−	0.153189i
$859$	44.2753			1.51065			0.755327	−	0.655348i	$-0.227478\pi$
$859$	44.2753			1.51065			0.755327	+	0.655348i	$0.227478\pi$
$860$	1.59805	+	5.46127i	0.0544929	+	0.186228i
$861$	35.8173			1.22065
$862$			20.3759i			0.694006i
$863$	16.4742	+	9.51138i	0.560788	+	0.323771i	0.753462	−	0.657492i	$-0.228382\pi$
$863$	16.4742	+	9.51138i	0.560788	+	0.323771i	−0.192674	+	0.981263i	$0.561716\pi$
$864$	0.500000	+	0.866025i	0.0170103	+	0.0294628i
$865$	−25.3670	+	26.5545i	−0.862504	+	0.902882i
$866$	−7.80406	+	13.5170i	−0.265193	+	0.459327i
$867$	20.6267	+	11.9088i	0.700518	+	0.404444i
$868$	−24.6082	−	14.2075i	−0.835255	−	0.482235i
$869$	−14.4872	−	25.0925i	−0.491444	−	0.851206i
$870$	1.26418	−	5.18992i	0.0428598	−	0.175955i
$871$	−14.9851	+	25.9549i	−0.507750	+	0.879449i
$872$	11.4569	+	6.61466i	0.387980	+	0.224001i
$873$	4.32842	+	2.49902i	0.146495	+	0.0845789i
$874$	−8.95122			−0.302779
$875$	7.27448	−	37.1838i	0.245922	−	1.25704i
$876$	−3.82911	+	6.63222i	−0.129374	+	0.224082i
$877$		−	51.7039i		−	1.74592i	−0.487795	−	0.872958i	$-0.662199\pi$
$877$		−	51.7039i		−	1.74592i	0.487795	−	0.872958i	$-0.337801\pi$
$878$		−	14.5277i		−	0.490288i
$879$	2.57376	−	4.45789i	0.0868108	−	0.150361i
$880$	6.94560	+	6.63498i	0.234136	+	0.223665i
$881$	−8.22829	−	14.2518i	−0.277218	−	0.480156i	0.693474	−	0.720481i	$-0.256079\pi$
$881$	−8.22829	−	14.2518i	−0.277218	−	0.480156i	−0.970692	+	0.240326i	$0.922746\pi$
$882$		−	4.48442i		−	0.150998i
$883$	−31.3488	+	18.0992i	−1.05497	+	0.609088i	−0.924037	−	0.382303i	$-0.875131\pi$
$883$	−31.3488	+	18.0992i	−1.05497	+	0.609088i	−0.130935	+	0.991391i	$0.541798\pi$
$884$	6.67363	+	11.5591i	0.224458	+	0.388773i
$885$	7.75400	+	1.88875i	0.260648	+	0.0634898i
$886$	11.6872	−	20.2429i	0.392640	−	0.680073i
$887$		−	48.7294i		−	1.63617i	−0.575095	−	0.818086i	$-0.695035\pi$
$887$		−	48.7294i		−	1.63617i	0.575095	−	0.818086i	$-0.304965\pi$
$888$	5.34540	−	2.90288i	0.179380	−	0.0974141i
$889$	−69.4362			−2.32882
$890$	0.580698	+	1.98452i	0.0194651	+	0.0665212i
$891$	−2.14784	−	3.72017i	−0.0719553	−	0.124630i
$892$	17.1215	−	9.88511i	0.573271	−	0.330978i
$893$	20.2958	−	11.7178i	0.679173	−	0.392121i
$894$	16.8868			0.564777
$895$	−10.1774	+	41.7818i	−0.340193	+	1.39661i
$896$	3.38887			0.113214
$897$	−7.55146	−	4.35984i	−0.252136	−	0.145571i
$898$			16.0097i			0.534251i
$899$	20.0302			0.668045
$900$	−4.43990	−	2.29941i	−0.147997	−	0.0766471i
$901$	35.7512	+	61.9229i	1.19104	+	2.06295i
$902$		−	45.4016i		−	1.51171i
$903$	−7.46850	−	4.31194i	−0.248536	−	0.143492i
$904$	3.49758	−	6.05799i	0.116328	−	0.201486i
$905$	−15.7138	+	4.59809i	−0.522345	+	0.152846i
$906$	10.9847	+	19.0261i	0.364944	+	0.632101i
$907$	28.6657	−	16.5501i	0.951828	−	0.549538i	0.0581796	−	0.998306i	$-0.481470\pi$
$907$	28.6657	−	16.5501i	0.951828	−	0.549538i	0.893648	+	0.448768i	$0.148137\pi$
$908$	−11.9969	−	6.92642i	−0.398132	−	0.229861i
$909$	−2.90345	+	5.02892i	−0.0963012	+	0.166799i
$910$	4.44594	+	15.1939i	0.147382	+	0.503671i
$911$	−13.1570			−0.435911			−0.217955	−	0.975959i	$-0.569939\pi$
$911$	−13.1570			−0.435911			−0.217955	+	0.975959i	$0.569939\pi$
$912$	1.85729	−	1.07231i	0.0615011	−	0.0355077i
$913$	−43.1884	−	24.9348i	−1.42933	−	0.825223i
$914$	15.9144			0.526402
$915$	−5.84488	+	6.11851i	−0.193226	+	0.202272i
$916$	6.33284	−	10.9688i	0.209243	−	0.362419i
$917$		−	54.8757i		−	1.81216i
$918$	5.53292	−	3.19443i	0.182614	−	0.105432i
$919$	59.2020			1.95289			0.976447	−	0.215756i	$-0.0692217\pi$
$919$	59.2020			1.95289			0.976447	+	0.215756i	$0.0692217\pi$
$920$	2.20877	−	9.06778i	0.0728210	−	0.298956i
$921$	1.72133	+	2.98143i	0.0567198	+	0.0982416i
$922$	−26.2017	+	15.1275i	−0.862906	+	0.498199i
$923$	−17.0988	−	9.87202i	−0.562815	−	0.324942i
$924$	−14.5575			−0.478906
$925$	−14.6868	+	26.6327i	−0.482899	+	0.875676i
$926$	5.34691			0.175710
$927$	10.2216	+	5.90144i	0.335721	+	0.193829i
$928$	−2.06882	+	1.19443i	−0.0679123	+	0.0392092i
$929$	14.1637	+	24.5323i	0.464697	+	0.804878i	0.999188	−	0.0402958i	$-0.0128300\pi$
$929$	14.1637	+	24.5323i	0.464697	+	0.804878i	−0.534491	+	0.845174i	$0.679497\pi$
$930$	4.43723	−	18.2164i	0.145503	−	0.597339i
$931$	−9.61737			−0.315196
$932$	1.81483	−	1.04779i	0.0594468	−	0.0343216i
$933$			28.7724i			0.941967i
$934$	−11.7462	+	20.3451i	−0.384348	+	0.665711i
$935$	42.3900	−	44.3745i	1.38630	−	1.45120i
$936$	2.08914			0.0682858
$937$	11.1520	+	6.43859i	0.364319	+	0.210340i	0.670974	−	0.741481i	$-0.265876\pi$
$937$	11.1520	+	6.43859i	0.364319	+	0.210340i	−0.306655	+	0.951821i	$0.599210\pi$
$938$	42.1024	−	24.3078i	1.37469	−	0.793678i
$939$	−6.91394			−0.225628
$940$	6.86226	+	23.4515i	0.223822	+	0.764904i
$941$	21.7499	−	37.6719i	0.709026	−	1.22807i	−0.256193	−	0.966626i	$-0.582468\pi$
$941$	21.7499	−	37.6719i	0.709026	−	1.22807i	0.965219	−	0.261444i	$-0.0841985\pi$
$942$	−6.75998	−	3.90288i	−0.220252	−	0.127163i
$943$	−38.2034	+	22.0567i	−1.24407	+	0.718266i
$944$	−1.78454	−	3.09092i	−0.0580819	−	0.100601i
$945$	7.27277	−	2.12812i	0.236583	−	0.0692277i
$946$	−5.46576	+	9.46697i	−0.177707	+	0.307798i
$947$	−8.96199	−	5.17421i	−0.291225	−	0.168139i	0.347269	−	0.937766i	$-0.387109\pi$
$947$	−8.96199	−	5.17421i	−0.291225	−	0.168139i	−0.638494	+	0.769626i	$0.720442\pi$
$948$		−	6.74500i		−	0.219068i
$949$	7.99957	+	13.8557i	0.259677	+	0.449774i
$950$	−4.93136	+	9.52188i	−0.159994	+	0.308931i
$951$	−1.54370			−0.0500580
$952$		−	21.6510i		−	0.701714i
$953$	45.3038	+	26.1562i	1.46754	+	0.847282i	0.999339	−	0.0363424i	$-0.0115707\pi$
$953$	45.3038	+	26.1562i	1.46754	+	0.847282i	0.468196	+	0.883625i	$0.344904\pi$
$954$	11.1917			0.362345
$955$	2.32104	−	9.52870i	0.0751072	−	0.308341i
$956$	15.6791			0.507098
$957$	8.88699	−	5.13090i	0.287275	−	0.165859i
$958$	29.1687	−	16.8406i	0.942399	−	0.544094i
$959$	−33.0080	−	57.1715i	−1.06588	−	1.84616i
$960$	0.627973	+	2.14608i	0.0202678	+	0.0692644i
$961$	39.3052			1.26791
$962$	0.331625	−	12.7034i	0.0106920	−	0.409575i
$963$			12.3720i			0.398681i
$964$	7.74941	−	13.4224i	0.249592	−	0.432305i
$965$	−27.3913	−	6.67208i	−0.881756	−	0.214782i
$966$	7.07224	+	12.2495i	0.227546	+	0.394121i
$967$	−36.7360	+	21.2095i	−1.18135	+	0.682053i	−0.956327	−	0.292300i	$-0.905579\pi$
$967$	−36.7360	+	21.2095i	−1.18135	+	0.682053i	−0.225024	+	0.974353i	$0.572246\pi$
$968$			7.45286i			0.239544i
$969$	−6.85084	−	11.8660i	−0.220081	−	0.381191i
$970$	8.08122	+	7.71982i	0.259472	+	0.247868i
$971$	−22.2989	+	38.6229i	−0.715606	+	1.23947i	0.247119	+	0.968985i	$0.420516\pi$
$971$	−22.2989	+	38.6229i	−0.715606	+	1.23947i	−0.962725	+	0.270482i	$0.912817\pi$
$972$		−	1.00000i		−	0.0320750i
$973$		−	0.675395i		−	0.0216522i
$974$	−13.0787	+	22.6529i	−0.419068	+	0.725847i
$975$	−8.79800	+	5.63099i	−0.281762	+	0.180336i
$976$	3.78415			0.121128
$977$	10.8151	+	6.24409i	0.346005	+	0.199766i	0.662924	−	0.748686i	$-0.269315\pi$
$977$	10.8151	+	6.24409i	0.346005	+	0.199766i	−0.316919	+	0.948452i	$0.602648\pi$
$978$	9.14720	+	5.28114i	0.292495	+	0.168872i
$979$	−1.98615	+	3.44011i	−0.0634775	+	0.109946i
$980$	2.37315	−	9.74261i	0.0758074	−	0.311216i
$981$	−6.61466	−	11.4569i	−0.211190	−	0.365791i
$982$	10.7195	+	6.18892i	0.342074	+	0.197496i
$983$	−30.7417	−	17.7487i	−0.980509	−	0.566097i	−0.0780852	−	0.996947i	$-0.524881\pi$
$983$	−30.7417	−	17.7487i	−0.980509	−	0.566097i	−0.902424	+	0.430850i	$0.858214\pi$
$984$	5.28456	−	9.15313i	0.168466	−	0.291791i
$985$	−40.6814	+	42.5859i	−1.29622	+	1.35690i
$986$	7.63108	+	13.2174i	0.243023	+	0.420928i
$987$	−32.0709	−	18.5161i	−1.02083	−	0.589375i
$988$		−	4.48041i		−	0.142541i
$989$	10.6214			0.337740
$990$	−2.69757	−	9.21886i	−0.0857345	−	0.292995i
$991$	−36.1764			−1.14918			−0.574591	−	0.818440i	$-0.694839\pi$
$991$	−36.1764			−1.14918			−0.574591	+	0.818440i	$0.694839\pi$
$992$	−7.26147	+	4.19241i	−0.230552	+	0.133109i
$993$		−	5.91359i		−	0.187662i
$994$	16.0137	+	27.7366i	0.507925	+	0.879751i
$995$	1.80779	−	7.42161i	0.0573107	−	0.235281i
$996$	−5.80463	−	10.0539i	−0.183927	−	0.318571i
$997$	−6.02143	−	3.47648i	−0.190701	−	0.110101i	0.401610	−	0.915811i	$-0.368451\pi$
$997$	−6.02143	−	3.47648i	−0.190701	−	0.110101i	−0.592311	+	0.805710i	$0.701784\pi$
$998$			25.1362i			0.795671i
$999$	−6.08069	−	0.158737i	−0.192385	−	0.00502222i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.bb.d.1009.11	yes	28
5.4	even	2	inner	1110.2.bb.d.1009.4	✓	28
37.26	even	3	inner	1110.2.bb.d.1099.4	yes	28
185.174	even	6	inner	1110.2.bb.d.1099.11	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.bb.d.1009.4	✓	28	5.4	even	2	inner
1110.2.bb.d.1009.11	yes	28	1.1	even	1	trivial
1110.2.bb.d.1099.4	yes	28	37.26	even	3	inner
1110.2.bb.d.1099.11	yes	28	185.174	even	6	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:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.bb (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.529198 - 2.17254i) q^{5} +1.00000 q^{6} +(-2.93485 + 1.69443i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.529198 - 2.17254i) q^{5} +1.00000 q^{6} +(-2.93485 + 1.69443i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(1.54457 - 1.61688i) q^{10} +4.29568 q^{11} +(0.866025 + 0.500000i) q^{12} +(1.80925 - 1.04457i) q^{13} -3.38887 q^{14} +(-0.627973 - 2.14608i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(5.53292 + 3.19443i) q^{17} +(0.866025 - 0.500000i) q^{18} +(-1.07231 - 1.85729i) q^{19} +(2.14608 - 0.627973i) q^{20} +(-1.69443 + 2.93485i) q^{21} +(3.72017 + 2.14784i) q^{22} -4.17381i q^{23} +(0.500000 + 0.866025i) q^{24} +(-4.43990 - 2.29941i) q^{25} +2.08914 q^{26} -1.00000i q^{27} +(-2.93485 - 1.69443i) q^{28} +2.38887 q^{29} +(0.529198 - 2.17254i) q^{30} +8.38482 q^{31} +(-0.866025 + 0.500000i) q^{32} +(3.72017 - 2.14784i) q^{33} +(3.19443 + 5.53292i) q^{34} +(2.12812 + 7.27277i) q^{35} +1.00000 q^{36} +(0.158737 - 6.08069i) q^{37} -2.14462i q^{38} +(1.04457 - 1.80925i) q^{39} +(2.17254 + 0.529198i) q^{40} +(-5.28456 - 9.15313i) q^{41} +(-2.93485 + 1.69443i) q^{42} +2.54477i q^{43} +(2.14784 + 3.72017i) q^{44} +(-1.61688 - 1.54457i) q^{45} +(2.08690 - 3.61462i) q^{46} +10.9276i q^{47} +1.00000i q^{48} +(2.24221 - 3.88362i) q^{49} +(-2.69536 - 4.21130i) q^{50} +6.38887 q^{51} +(1.80925 + 1.04457i) q^{52} +(9.69231 + 5.59586i) q^{53} +(0.500000 - 0.866025i) q^{54} +(2.27327 - 9.33256i) q^{55} +(-1.69443 - 2.93485i) q^{56} +(-1.85729 - 1.07231i) q^{57} +(2.06882 + 1.19443i) q^{58} +(-1.78454 + 3.09092i) q^{59} +(1.54457 - 1.61688i) q^{60} +(-1.89207 - 3.27717i) q^{61} +(7.26147 + 4.19241i) q^{62} +3.38887i q^{63} -1.00000 q^{64} +(-1.31193 - 4.48346i) q^{65} +4.29568 q^{66} +(-12.4237 + 7.17284i) q^{67} +6.38887i q^{68} +(-2.08690 - 3.61462i) q^{69} +(-1.79338 + 7.36246i) q^{70} +(-4.72539 - 8.18462i) q^{71} +(0.866025 + 0.500000i) q^{72} +7.65823i q^{73} +(3.17782 - 5.18666i) q^{74} +(-4.99477 + 0.228600i) q^{75} +(1.07231 - 1.85729i) q^{76} +(-12.6072 + 7.27874i) q^{77} +(1.80925 - 1.04457i) q^{78} +(-3.37250 - 5.84135i) q^{79} +(1.61688 + 1.54457i) q^{80} +(-0.500000 - 0.866025i) q^{81} -10.5691i q^{82} +(-10.0539 - 5.80463i) q^{83} -3.38887 q^{84} +(9.86806 - 10.3300i) q^{85} +(-1.27238 + 2.20383i) q^{86} +(2.06882 - 1.19443i) q^{87} +4.29568i q^{88} +(-0.462359 + 0.800829i) q^{89} +(-0.627973 - 2.14608i) q^{90} +(-3.53991 + 6.13131i) q^{91} +(3.61462 - 2.08690i) q^{92} +(7.26147 - 4.19241i) q^{93} +(-5.46381 + 9.46360i) q^{94} +(-4.60251 + 1.34676i) q^{95} +(-0.500000 + 0.866025i) q^{96} +4.99803i q^{97} +(3.88362 - 2.24221i) q^{98} +(2.14784 - 3.72017i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 14 q^{4} + 2 q^{5} + 28 q^{6} + 14 q^{9}+O(q^{10}) \) 28 * q + 14 * q^4 + 2 * q^5 + 28 * q^6 + 14 * q^9	\( 28 q + 14 q^{4} + 2 q^{5} + 28 q^{6} + 14 q^{9} + 4 q^{10} - 12 q^{11} + 8 q^{14} + 2 q^{15} - 14 q^{16} - 20 q^{19} - 2 q^{20} + 4 q^{21} + 14 q^{24} - 8 q^{25} - 20 q^{26} - 36 q^{29} + 2 q^{30} + 24 q^{31} + 38 q^{34} - 2 q^{35} + 28 q^{36} - 10 q^{39} + 2 q^{40} - 6 q^{44} + 4 q^{45} + 8 q^{46} + 50 q^{49} - 4 q^{50} + 76 q^{51} + 14 q^{54} - 28 q^{55} + 4 q^{56} - 26 q^{59} + 4 q^{60} - 28 q^{61} - 28 q^{64} + 60 q^{65} - 12 q^{66} - 8 q^{69} - 10 q^{70} - 64 q^{71} + 24 q^{74} - 8 q^{75} + 20 q^{76} + 32 q^{79} - 4 q^{80} - 14 q^{81} + 8 q^{84} + 16 q^{85} - 8 q^{86} + 76 q^{89} + 2 q^{90} - 8 q^{91} - 38 q^{94} - 70 q^{95} - 14 q^{96} - 6 q^{99}+O(q^{100}) \) 28 * q + 14 * q^4 + 2 * q^5 + 28 * q^6 + 14 * q^9 + 4 * q^10 - 12 * q^11 + 8 * q^14 + 2 * q^15 - 14 * q^16 - 20 * q^19 - 2 * q^20 + 4 * q^21 + 14 * q^24 - 8 * q^25 - 20 * q^26 - 36 * q^29 + 2 * q^30 + 24 * q^31 + 38 * q^34 - 2 * q^35 + 28 * q^36 - 10 * q^39 + 2 * q^40 - 6 * q^44 + 4 * q^45 + 8 * q^46 + 50 * q^49 - 4 * q^50 + 76 * q^51 + 14 * q^54 - 28 * q^55 + 4 * q^56 - 26 * q^59 + 4 * q^60 - 28 * q^61 - 28 * q^64 + 60 * q^65 - 12 * q^66 - 8 * q^69 - 10 * q^70 - 64 * q^71 + 24 * q^74 - 8 * q^75 + 20 * q^76 + 32 * q^79 - 4 * q^80 - 14 * q^81 + 8 * q^84 + 16 * q^85 - 8 * q^86 + 76 * q^89 + 2 * q^90 - 8 * q^91 - 38 * q^94 - 70 * q^95 - 14 * q^96 - 6 * q^99

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