LMFDB - Embedded newform 1110.2.bb.d.1099.4

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			1099.4
Character	$\chi$	$=$	1110.1099
Dual form			1110.2.bb.d.1009.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-2.14608 + 0.627973i) q^{5} +1.00000 q^{6} +(2.93485 + 1.69443i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-2.14608 + 0.627973i) 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} +(2.17254 + 0.529198i) 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} +(-0.529198 + 2.17254i) q^{20} +(-1.69443 - 2.93485i) q^{21} +(-3.72017 + 2.14784i) q^{22} -4.17381i q^{23} +(0.500000 - 0.866025i) q^{24} +(4.21130 - 2.69536i) q^{25} +2.08914 q^{26} -1.00000i q^{27} +(2.93485 - 1.69443i) q^{28} +2.38887 q^{29} +(-2.14608 + 0.627973i) q^{30} +8.38482 q^{31} +(0.866025 + 0.500000i) q^{32} +(-3.72017 - 2.14784i) q^{33} +(3.19443 - 5.53292i) q^{34} +(-7.36246 - 1.79338i) q^{35} +1.00000 q^{36} +(-0.158737 - 6.08069i) q^{37} -2.14462i q^{38} +(1.04457 + 1.80925i) q^{39} +(-0.627973 - 2.14608i) 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} +(-2.29941 + 4.43990i) q^{50} +6.38887 q^{51} +(-1.80925 + 1.04457i) q^{52} +(-9.69231 + 5.59586i) q^{53} +(0.500000 + 0.866025i) q^{54} +(-9.21886 + 2.69757i) 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} +(4.53875 + 1.10557i) q^{65} +4.29568 q^{66} +(12.4237 + 7.17284i) q^{67} +6.38887i q^{68} +(-2.08690 + 3.61462i) q^{69} +(7.27277 - 2.12812i) 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} +(2.17254 + 0.529198i) 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} +(1.13493 - 4.65928i) 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 $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	−0.866025	+	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
$5$	−2.14608	+	0.627973i	−0.959755	+	0.280838i
$5$	−2.14608	+	0.627973i	−0.959755	+	0.280838i
$6$	1.00000			0.408248
$7$	2.93485	+	1.69443i	1.10927	+	0.640436i	0.938639	−	0.344900i	$-0.112087\pi$
$7$	2.93485	+	1.69443i	1.10927	+	0.640436i	0.170628	+	0.985336i	$0.445420\pi$
$8$			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	$-0.426893\pi$
$13$	−1.80925	−	1.04457i	−0.501796	−	0.289712i	−0.729455	+	0.684029i	$0.760226\pi$
$14$	−3.38887			−0.905713
$15$	2.17254	+	0.529198i	0.560949	+	0.136638i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−5.53292	+	3.19443i	−1.34193	+	0.774764i	−0.987091	−	0.160163i	$-0.948798\pi$
$17$	−5.53292	+	3.19443i	−1.34193	+	0.774764i	−0.354840	+	0.934927i	$0.615465\pi$
$18$	−0.866025	−	0.500000i	−0.204124	−	0.117851i
$19$	−1.07231	+	1.85729i	−0.246004	+	0.426092i	−0.962414	−	0.271588i	$-0.912451\pi$
$19$	−1.07231	+	1.85729i	−0.246004	+	0.426092i	0.716409	+	0.697680i	$0.245784\pi$
$20$	−0.529198	+	2.17254i	−0.118332	+	0.485796i
$21$	−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
$25$	4.21130	−	2.69536i	0.842260	−	0.539072i
$26$	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	$0.428807\pi$
$30$	−2.14608	+	0.627973i	−0.391818	+	0.114652i
$31$	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
$35$	−7.36246	−	1.79338i	−1.24448	−	0.303137i
$36$	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
$40$	−0.627973	−	2.14608i	−0.0992913	−	0.339325i
$41$	−5.28456	+	9.15313i	−0.825310	+	1.42948i	0.0763728	+	0.997079i	$0.475666\pi$
$41$	−5.28456	+	9.15313i	−0.825310	+	1.42948i	−0.901682	+	0.432399i	$0.857667\pi$
$42$	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
$50$	−2.29941	+	4.43990i	−0.325186	+	0.627897i
$51$	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	$-0.945738\pi$
$53$	−9.69231	+	5.59586i	−1.33134	+	0.768650i	−0.345836	+	0.938295i	$0.612405\pi$
$54$	0.500000	+	0.866025i	0.0680414	+	0.117851i
$55$	−9.21886	+	2.69757i	−1.24307	+	0.363741i
$56$	−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	0.726165	−	0.687521i	$-0.241301\pi$
$59$	−1.78454	−	3.09092i	−0.232328	−	0.402403i	−0.958493	+	0.285117i	$0.907968\pi$
$60$	1.54457	−	1.61688i	0.199403	−	0.208738i
$61$	−1.89207	+	3.27717i	−0.242255	+	0.419598i	−0.961356	−	0.275307i	$-0.911220\pi$
$61$	−1.89207	+	3.27717i	−0.242255	+	0.419598i	0.719101	+	0.694905i	$0.244554\pi$
$62$	−7.26147	+	4.19241i	−0.922207	+	0.532437i
$63$			3.38887i			0.426957i
$64$	−1.00000			−0.125000
$65$	4.53875	+	1.10557i	0.562963	+	0.137129i
$66$	4.29568			0.528762
$67$	12.4237	+	7.17284i	1.51780	+	0.876302i	0.999781	+	0.0209325i	$0.00666350\pi$
$67$	12.4237	+	7.17284i	1.51780	+	0.876302i	0.518019	+	0.855369i	$0.326670\pi$
$68$			6.38887i			0.774764i
$69$	−2.08690	+	3.61462i	−0.251234	+	0.435149i
$70$	7.27277	−	2.12812i	0.869263	−	0.254359i
$71$	−4.72539	+	8.18462i	−0.560801	+	0.971336i	0.436626	+	0.899643i	$0.356173\pi$
$71$	−4.72539	+	8.18462i	−0.560801	+	0.971336i	−0.997427	+	0.0716927i	$0.977160\pi$
$72$	−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	−0.990980	−	0.134008i	$-0.957215\pi$
$79$	−3.37250	+	5.84135i	−0.379436	+	0.657203i	0.611544	+	0.791210i	$0.290549\pi$
$80$	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	$-0.446783\pi$
$83$	10.0539	−	5.80463i	1.10356	−	0.637141i	0.937154	+	0.348916i	$0.113450\pi$
$84$	−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	0.840480	−	0.541843i	$-0.182273\pi$
$89$	−0.462359	−	0.800829i	−0.0490100	−	0.0848878i	−0.889490	+	0.456955i	$0.848940\pi$
$90$	2.17254	+	0.529198i	0.229006	+	0.0557824i
$91$	−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
$95$	1.13493	−	4.65928i	0.116441	−	0.478032i
$96$	−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	$-0.129287\pi$
$107$	10.7144	+	6.18598i	1.03580	+	0.598021i	0.117162	+	0.993113i	$0.462620\pi$
$108$	−0.866025	−	0.500000i	−0.0833333	−	0.0481125i
$109$	6.61466	+	11.4569i	0.633569	+	1.09737i	0.986816	+	0.161844i	$0.0517442\pi$
$109$	6.61466	+	11.4569i	0.633569	+	1.09737i	−0.353247	+	0.935530i	$0.614922\pi$
$110$	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	$-0.559947\pi$
$113$	6.05799	−	3.49758i	0.569888	−	0.329025i	0.757104	+	0.653294i	$0.226613\pi$
$114$	−1.07231	+	1.85729i	−0.100431	+	0.173951i
$115$	2.62104	+	8.95731i	0.244413	+	0.835274i
$116$	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
$120$	−0.529198	+	2.17254i	−0.0483090	+	0.198325i
$121$	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	−0.578965	+	0.815352i	$0.696543\pi$
$127$	−17.7444	+	10.2448i	−1.57456	+	0.909075i	−0.995598	+	0.0937225i	$0.970123\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	1.27238	−	2.20383i	0.112027	−	0.194037i
$130$	−4.48346	+	1.31193i	−0.393226	+	0.115063i
$131$	−8.09647	−	14.0235i	−0.707392	−	1.22524i	−0.965821	−	0.259208i	$-0.916538\pi$
$131$	−8.09647	−	14.0235i	−0.707392	−	1.22524i	0.258430	−	0.966030i	$-0.416795\pi$
$132$	−3.72017	+	2.14784i	−0.323799	+	0.186945i
$133$	−6.29412	+	3.63391i	−0.545769	+	0.315100i
$134$	−14.3457			−1.23928
$135$	0.627973	+	2.14608i	0.0540473	+	0.184705i
$136$	−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	0.861768	−	0.507302i	$-0.169357\pi$
$139$	−0.0996490	−	0.172597i	−0.00845212	−	0.0146395i	−0.870221	+	0.492662i	$0.836024\pi$
$140$	−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
$145$	−5.12669	+	1.50014i	−0.425749	+	0.124580i
$146$	−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	$0.256858\pi$
$150$	4.21130	−	2.69536i	0.343851	−	0.220075i
$151$	10.9847	−	19.0261i	0.893926	−	1.54832i	0.0587967	−	0.998270i	$-0.481274\pi$
$151$	10.9847	−	19.0261i	0.893926	−	1.54832i	0.835129	−	0.550054i	$-0.185393\pi$
$152$	−1.85729	−	1.07231i	−0.150646	−	0.0869757i
$153$	−5.53292	−	3.19443i	−0.447310	−	0.258255i
$154$	−14.5575			−1.17308
$155$	−17.9945	+	5.26544i	−1.44535	+	0.422931i
$156$	2.08914			0.167265
$157$	6.75998	−	3.90288i	0.539505	−	0.311483i	−0.205373	−	0.978684i	$-0.565841\pi$
$157$	6.75998	−	3.90288i	0.539505	−	0.311483i	0.744878	+	0.667200i	$0.232508\pi$
$158$		−	6.74500i		−	0.536604i
$159$	11.1917			0.887561
$160$	−2.17254	−	0.529198i	−0.171755	−	0.0418368i
$161$	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	$-0.802413\pi$
$163$	−9.14720	+	5.28114i	−0.716464	+	0.413651i	0.0969857	+	0.995286i	$0.469080\pi$
$164$	5.28456	+	9.15313i	0.412655	+	0.714739i
$165$	9.33256	+	2.27327i	0.726538	+	0.176973i
$166$	−5.80463	+	10.0539i	−0.450527	+	0.780335i
$167$	−11.3039	−	6.52632i	−0.874723	−	0.505022i	−0.00580833	−	0.999983i	$-0.501849\pi$
$167$	−11.3039	−	6.52632i	−0.874723	−	0.505022i	−0.868915	+	0.494961i	$0.835182\pi$
$168$	2.93485	−	1.69443i	0.226428	−	0.130728i
$169$	−4.31774	−	7.47855i	−0.332134	−	0.575273i
$170$	−3.38098	+	13.8801i	−0.259309	+	1.06455i
$171$	−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	$-0.452042\pi$
$173$	14.2230	−	8.21166i	1.08136	−	0.624321i	0.931262	+	0.364350i	$0.118709\pi$
$174$	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	$0.755273\pi$
$180$	−2.14608	+	0.627973i	−0.159959	+	0.0468064i
$181$	−3.66105	+	6.34113i	−0.272124	+	0.471333i	−0.969406	−	0.245465i	$-0.921059\pi$
$181$	−3.66105	+	6.34113i	−0.272124	+	0.471333i	0.697282	+	0.716797i	$0.254393\pi$
$182$	6.13131	+	3.53991i	0.454483	+	0.262396i
$183$	3.27717	−	1.89207i	0.242255	−	0.139866i
$184$	4.17381			0.307697
$185$	4.15917	+	12.9500i	0.305789	+	0.952099i
$186$	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
$190$	1.34676	+	4.60251i	0.0977044	+	0.333902i
$191$	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	0.639601	−	0.768707i	$-0.279100\pi$
$197$	22.8097	−	13.1692i	1.62512	−	0.938264i	0.985520	−	0.169557i	$-0.0542337\pi$
$198$	−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	$0.461364\pi$
$200$	2.69536	+	4.21130i	0.190591	+	0.297784i
$201$	−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
$205$	5.59316	−	22.9619i	0.390643	−	1.60373i
$206$	−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
$210$	−7.36246	−	1.79338i	−0.508058	−	0.123755i
$211$	−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
$215$	−1.59805	−	5.46127i	−0.108986	−	0.372456i
$216$	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
$220$	−2.27327	+	9.33256i	−0.153264	+	0.629201i
$221$	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
$225$	4.43990	+	2.29941i	0.295993	+	0.153294i
$226$	−3.49758	+	6.05799i	−0.232656	+	0.402971i
$227$	11.9969	+	6.92642i	0.796263	+	0.459723i	0.842163	−	0.539223i	$-0.181282\pi$
$227$	11.9969	+	6.92642i	0.796263	+	0.459723i	−0.0458996	+	0.998946i	$0.514615\pi$
$228$		−	2.14462i		−	0.142031i
$229$	−6.33284	+	10.9688i	−0.418486	+	0.724839i	−0.995787	−	0.0916924i	$-0.970772\pi$
$229$	−6.33284	+	10.9688i	−0.418486	+	0.724839i	0.577302	+	0.816531i	$0.304106\pi$
$230$	−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
$235$	−6.86226	−	23.4515i	−0.447644	−	1.52981i
$236$	−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	0.999966	+	0.00821610i	$0.00261529\pi$
$239$	7.83955	+	13.5785i	0.507098	+	0.878320i	−0.492868	+	0.870104i	$0.664051\pi$
$240$	−0.627973	−	2.14608i	−0.0405355	−	0.138529i
$241$	−7.74941	+	13.4224i	−0.499183	+	0.864611i	−1.00000		0.000942704i	$-0.999700\pi$
$241$	−7.74941	+	13.4224i	−0.499183	+	0.864611i	0.500816	+	0.865554i	$0.333033\pi$
$242$	−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
$250$	2.14658	−	10.9723i	0.135762	−	0.693952i
$251$	−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
$255$	−13.7110	+	4.01204i	−0.858616	+	0.251244i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−8.32051	+	4.80385i	−0.519019	+	0.299656i	−0.736533	−	0.676401i	$-0.763538\pi$
$257$	−8.32051	+	4.80385i	−0.519019	+	0.299656i	0.217514	+	0.976057i	$0.430205\pi$
$258$			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	$-0.288167\pi$
$263$	3.97236	+	2.29344i	0.244946	+	0.141420i	−0.372502	+	0.928031i	$0.621500\pi$
$264$	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	0.988135	−	0.153586i	$-0.0490821\pi$
$271$	5.94377	+	10.2949i	0.361058	+	0.625372i	−0.627077	+	0.778957i	$0.715749\pi$
$272$	5.53292	+	3.19443i	0.335483	+	0.193691i
$273$			7.07983i			0.428491i
$274$	−9.74012	−	16.8704i	−0.588422	−	1.01918i
$275$	18.0904	−	11.5784i	1.09089	−	0.698204i
$276$	2.08690	+	3.61462i	0.125617	+	0.217575i
$277$	−0.789513	−	0.455826i	−0.0474372	−	0.0273879i	0.476094	−	0.879394i	$-0.342052\pi$
$277$	−0.789513	−	0.455826i	−0.0474372	−	0.0273879i	−0.523531	+	0.852007i	$0.675386\pi$
$278$	0.172597	+	0.0996490i	0.0103517	+	0.00597655i
$279$	4.19241	+	7.26147i	0.250993	+	0.434733i
$280$	1.79338	−	7.36246i	0.107175	−	0.439991i
$281$	−1.60452	−	2.77912i	−0.0957178	−	0.165788i	0.814190	−	0.580598i	$-0.197181\pi$
$281$	−1.60452	−	2.77912i	−0.0957178	−	0.165788i	−0.909908	+	0.414810i	$0.863848\pi$
$282$			10.9276i			0.650730i
$283$	−11.6307	−	6.71497i	−0.691372	−	0.399164i	0.112754	−	0.993623i	$-0.464033\pi$
$283$	−11.6307	−	6.71497i	−0.691372	−	0.399164i	−0.804126	+	0.594459i	$0.797366\pi$
$284$	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	$-0.381377\pi$
$293$	−4.45789	−	2.57376i	−0.260432	−	0.150361i	−0.624532	+	0.780999i	$0.714710\pi$
$294$	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
$300$	−2.29941	+	4.43990i	−0.132757	+	0.256338i
$301$	−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
$305$	2.00256	−	8.22123i	0.114666	−	0.470746i
$306$	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	−0.908775	−	0.417286i	$-0.862982\pi$
$311$	−14.3862	−	24.9177i	−0.815768	−	1.41295i	0.0930079	−	0.995665i	$-0.470352\pi$
$312$	−1.80925	+	1.04457i	−0.102429	+	0.0591372i
$313$	5.98765	−	3.45697i	0.338442	−	0.195399i	−0.321141	−	0.947031i	$-0.604066\pi$
$313$	5.98765	−	3.45697i	0.338442	−	0.195399i	0.659583	+	0.751632i	$0.270733\pi$
$314$	−3.90288	+	6.75998i	−0.220252	+	0.381488i
$315$	−2.12812	−	7.27277i	−0.119906	−	0.409774i
$316$	3.37250	+	5.84135i	0.189718	+	0.328601i
$317$	1.33689	−	0.771852i	0.0750871	−	0.0433515i	−0.461986	−	0.886887i	$-0.652863\pi$
$317$	1.33689	−	0.771852i	0.0750871	−	0.0433515i	0.537073	+	0.843535i	$0.319530\pi$
$318$	−9.69231	+	5.59586i	−0.543518	+	0.313800i
$319$	10.2618			0.574551
$320$	2.14608	−	0.627973i	0.119969	−	0.0351048i
$321$	−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
$330$	−9.21886	+	2.69757i	−0.507482	+	0.148496i
$331$	2.95680	+	5.12132i	0.162520	+	0.281493i	0.935772	−	0.352606i	$-0.114704\pi$
$331$	2.95680	+	5.12132i	0.162520	+	0.281493i	−0.773252	+	0.634099i	$0.781371\pi$
$332$		−	11.6093i		−	0.637141i
$333$	5.18666	−	3.17782i	0.284227	−	0.174143i
$334$	13.0526			0.714209
$335$	−31.1666	−	7.59171i	−1.70281	−	0.414779i
$336$	−1.69443	+	2.93485i	−0.0924389	+	0.160109i
$337$	−15.7431	−	9.08928i	−0.857581	−	0.495125i	0.00562055	−	0.999984i	$-0.498211\pi$
$337$	−15.7431	−	9.08928i	−0.857581	−	0.495125i	−0.863201	+	0.504860i	$0.831544\pi$
$338$	7.47855	+	4.31774i	0.406779	+	0.234854i
$339$	−6.99516			−0.379925
$340$	−4.01204	−	13.7110i	−0.217583	−	0.743584i
$341$	36.0185			1.95051
$342$	1.85729	−	1.07231i	0.100431	−	0.0579838i
$343$		−	8.52496i		−	0.460305i
$344$	−2.54477			−0.137205
$345$	2.20877	−	9.06778i	0.118916	−	0.488193i
$346$	−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	0.842504	−	0.538691i	$-0.181081\pi$
$349$	−0.845677	−	1.46476i	−0.0452681	−	0.0784066i	−0.887772	+	0.460284i	$0.847748\pi$
$350$	−14.2715	+	9.13421i	−0.762846	+	0.488244i
$351$	−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	$-0.713835\pi$
$353$	−4.80463	+	2.77396i	−0.255725	+	0.147643i	0.366658	+	0.930356i	$0.380502\pi$
$354$	−1.78454	−	3.09092i	−0.0948474	−	0.164281i
$355$	5.00134	−	20.5323i	0.265443	−	1.08974i
$356$	−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
$365$	−4.80916	−	16.4352i	−0.251723	−	0.860255i
$366$	−1.89207	+	3.27717i	−0.0989003	+	0.171300i
$367$	−0.369651	−	0.213418i	−0.0192956	−	0.0111403i	0.490321	−	0.871542i	$-0.336879\pi$
$367$	−0.369651	−	0.213418i	−0.0192956	−	0.0111403i	−0.509617	+	0.860401i	$0.670213\pi$
$368$	−3.61462	+	2.08690i	−0.188425	+	0.108787i
$369$	−10.5691			−0.550206
$370$	−10.0769	−	9.13540i	−0.523874	−	0.474927i
$371$	−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	$-0.0929369\pi$
$373$	22.9294	+	13.2383i	1.18724	+	0.685454i	0.229563	+	0.973294i	$0.426270\pi$
$374$	13.7223	−	23.7677i	0.709561	−	1.22900i
$375$	10.5756	−	3.62718i	0.546122	−	0.187307i
$376$	−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	0.825395	−	0.564556i	$-0.190952\pi$
$379$	−1.48389	−	2.57017i	−0.0762222	−	0.132021i	−0.901617	+	0.432535i	$0.857619\pi$
$380$	−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	0.997429	+	0.0716589i	$0.0228293\pi$
$383$	30.4946	+	17.6061i	1.55820	+	0.899628i	0.560773	+	0.827970i	$0.310504\pi$
$384$	−1.00000			−0.0510310
$385$	−31.6268	−	7.70379i	−1.61185	−	0.392622i
$386$	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	−0.267858	−	0.963458i	$-0.586316\pi$
$389$	13.8150	−	23.9283i	0.700450	−	1.21322i	0.968309	−	0.249757i	$-0.0803508\pi$
$390$	4.53875	+	1.10557i	0.229829	+	0.0559827i
$391$	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
$395$	3.56944	−	14.6538i	0.179598	−	0.737314i
$396$	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
$400$	−4.43990	−	2.29941i	−0.221995	−	0.114971i
$401$	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
$405$	0.529198	−	2.17254i	0.0262961	−	0.107955i
$406$	−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	0.938875	+	0.344257i	$0.111869\pi$
$409$	15.5232	+	26.8870i	0.767573	+	1.32948i	−0.171302	+	0.985219i	$0.554797\pi$
$410$	6.63713	+	22.6822i	0.327784	+	1.12019i
$411$	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	0.671175	−	0.741299i	$-0.265790\pi$
$419$	−6.27177	−	10.8630i	−0.306396	−	0.530693i	−0.977571	+	0.210605i	$0.932456\pi$
$420$	7.27277	−	2.12812i	0.354875	−	0.103842i
$421$	−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
$425$	−14.6906	+	28.3659i	−0.712601	+	1.37595i
$426$	−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	−0.509207	−	0.860644i	$-0.670061\pi$
$431$	10.1880	−	17.6460i	0.490736	−	0.849980i	0.999943	+	0.0106640i	$0.00339451\pi$
$432$	−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
$435$	5.18992	+	1.26418i	0.248838	+	0.0606130i
$436$	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	−0.985659	−	0.168752i	$-0.946026\pi$
$439$	−7.26387	+	12.5814i	−0.346686	+	0.600477i	0.638973	+	0.769229i	$0.279360\pi$
$440$	−2.69757	−	9.21886i	−0.128602	−	0.439492i
$441$	−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	−0.612965	−	0.790110i	$-0.710024\pi$
$449$	8.00485	−	13.8648i	0.377772	−	0.654321i	0.990738	+	0.135789i	$0.0433568\pi$
$450$	−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	$-0.454737\pi$
$457$	−13.7823	−	7.95720i	−0.644708	−	0.372222i	−0.786426	+	0.617685i	$0.788071\pi$
$458$		−	12.6657i		−	0.591828i
$459$	3.19443	+	5.53292i	0.149103	+	0.258255i
$460$	9.06778	+	2.20877i	0.422788	+	0.102984i
$461$	−15.1275	−	26.2017i	−0.704559	−	1.22033i	−0.966850	−	0.255344i	$-0.917811\pi$
$461$	−15.1275	−	26.2017i	−0.704559	−	1.22033i	0.262291	−	0.964989i	$-0.415522\pi$
$462$	12.6072	+	7.27874i	0.586538	+	0.338638i
$463$	−4.63056	−	2.67345i	−0.215200	−	0.124246i	0.388526	−	0.921438i	$-0.372984\pi$
$463$	−4.63056	−	2.67345i	−0.215200	−	0.124246i	−0.603726	+	0.797192i	$0.706318\pi$
$464$	−1.19443	−	2.06882i	−0.0554502	−	0.0960425i
$465$	18.2164	+	4.43723i	0.844765	+	0.205772i
$466$	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	0.937853	+	0.347032i	$0.112811\pi$
$479$	16.8406	+	29.1687i	0.769465	+	1.33275i	−0.168388	+	0.985721i	$0.553856\pi$
$480$	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
$485$	−3.13863	−	10.7262i	−0.142518	−	0.487050i
$486$	−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
$490$	9.74261	+	2.37315i	0.440126	+	0.107208i
$491$	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	−0.434642	−	0.900603i	$-0.643125\pi$
$499$	12.5681	−	21.7686i	0.562625	−	0.974494i	0.997266	−	0.0738909i	$-0.0235417\pi$
$500$	3.62718	+	10.5756i	0.162212	+	0.472956i
$501$	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	$-0.706373\pi$
$503$	−4.83312	+	2.79040i	−0.215498	+	0.124418i	0.388366	+	0.921505i	$0.373040\pi$
$504$	−3.38887			−0.150952
$505$	12.4620	−	3.64657i	0.554553	−	0.162270i
$506$	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	0.737153	−	0.675726i	$-0.236170\pi$
$509$	−4.88714	−	8.46478i	−0.216619	−	0.375195i	−0.953772	+	0.300531i	$0.902836\pi$
$510$	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
$515$	−7.41189	−	25.3299i	−0.326607	−	1.11617i
$516$	−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
$520$	−1.10557	+	4.53875i	−0.0484825	+	0.199038i
$521$	−8.56513	+	14.8352i	−0.375245	+	0.649943i	−0.990364	−	0.138491i	$-0.955775\pi$
$521$	−8.56513	+	14.8352i	−0.375245	+	0.649943i	0.615119	+	0.788435i	$0.289108\pi$
$522$	−2.06882	−	1.19443i	−0.0905498	−	0.0522789i
$523$	−4.79471	−	2.76822i	−0.209658	−	0.121046i	0.391495	−	0.920180i	$-0.371958\pi$
$523$	−4.79471	−	2.76822i	−0.209658	−	0.121046i	−0.601152	+	0.799134i	$0.705292\pi$
$524$	−16.1929			−0.707392
$525$	−15.0462	−	7.79240i	−0.656671	−	0.340088i
$526$	−4.58688			−0.199998
$527$	−46.3926	+	26.7848i	−2.02089	+	1.16676i
$528$			4.29568i			0.186945i
$529$	5.57933			0.242580
$530$	−5.92263	+	24.3145i	−0.257263	+	1.05615i
$531$	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
$535$	−26.8786	−	6.54722i	−1.16207	−	0.283061i
$536$	−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
$540$	2.17254	+	0.529198i	0.0934914	+	0.0227731i
$541$	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
$550$	−9.87754	+	19.0724i	−0.421180	+	0.813249i
$551$	−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
$555$	2.87303	−	13.2946i	0.121953	−	0.564323i
$556$	−0.199298			−0.00845212
$557$	36.2741	−	20.9429i	1.53698	−	0.887377i	0.537969	−	0.842964i	$-0.319192\pi$
$557$	36.2741	−	20.9429i	1.53698	−	0.887377i	0.999013	−	0.0444128i	$-0.0141417\pi$
$558$	−7.26147	−	4.19241i	−0.307402	−	0.177479i
$559$	2.65819	−	4.60412i	0.112430	−	0.194734i
$560$	2.12812	+	7.27277i	0.0899294	+	0.307331i
$561$	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	$0.475598\pi$
$570$	1.13493	−	4.65928i	0.0475369	−	0.195156i
$571$	0.382372	+	0.662288i	0.0160018	+	0.0277159i	0.873915	−	0.486078i	$-0.161573\pi$
$571$	0.382372	+	0.662288i	0.0160018	+	0.0277159i	−0.857914	+	0.513794i	$0.828240\pi$
$572$	−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
$575$	−11.2499	−	17.5772i	−0.469154	−	0.733018i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	−1.14731	+	0.662402i	−0.0477633	+	0.0275761i	−0.523691	−	0.851908i	$-0.675446\pi$
$577$	−1.14731	+	0.662402i	−0.0477633	+	0.0275761i	0.475928	+	0.879484i	$0.342112\pi$
$578$			23.8176i			0.990683i
$579$	−6.30396	+	10.9188i	−0.261984	+	0.453769i
$580$	−1.26418	+	5.18992i	−0.0524924	+	0.215500i
$581$	39.3423			1.63219
$582$			4.99803i			0.207175i
$583$	−41.6351	+	24.0380i	−1.72435	+	0.995553i
$584$	−7.65823			−0.316900
$585$	1.31193	+	4.48346i	0.0542414	+	0.185368i
$586$	5.14752			0.212642
$587$	−7.06825	−	4.08086i	−0.291738	−	0.168435i	0.346987	−	0.937870i	$-0.387205\pi$
$587$	−7.06825	−	4.08086i	−0.291738	−	0.168435i	−0.638725	+	0.769435i	$0.720538\pi$
$588$	−3.88362	−	2.24221i	−0.160158	−	0.0924672i
$589$	−8.99112	+	15.5731i	−0.370472	+	0.641677i
$590$	−7.75400	−	1.88875i	−0.319227	−	0.0777588i
$591$	−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
$595$	46.4648	−	13.5963i	1.90487	−	0.557392i
$596$	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	−0.341626	−	0.939836i	$-0.610977\pi$
$599$	15.7398	−	27.2621i	0.643109	−	1.11390i	0.984735	−	0.174062i	$-0.0556892\pi$
$600$	−0.228600	−	4.99477i	−0.00933255	−	0.203911i
$601$	−5.06605	−	8.77466i	−0.206649	−	0.357926i	0.744008	−	0.668171i	$-0.232922\pi$
$601$	−5.06605	−	8.77466i	−0.206649	−	0.357926i	−0.950657	+	0.310245i	$0.899589\pi$
$602$		−	8.62388i		−	0.351483i
$603$			14.3457i			0.584201i
$604$	−10.9847	−	19.0261i	−0.446963	−	0.774162i
$605$	−15.9944	+	4.68020i	−0.650266	+	0.190277i
$606$	−5.80689			−0.235889
$607$	27.9541	−	16.1393i	1.13462	−	0.655074i	0.189529	−	0.981875i	$-0.439304\pi$
$607$	27.9541	−	16.1393i	1.13462	−	0.655074i	0.945093	+	0.326801i	$0.105971\pi$
$608$	−1.85729	+	1.07231i	−0.0753232	+	0.0434879i
$609$	−4.04778	−	7.01096i	−0.164024	−	0.284098i
$610$	2.37634	+	8.12107i	0.0962153	+	0.328813i
$611$	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	$-0.687392\pi$
$613$	−2.79022	+	1.61093i	−0.112696	+	0.0650650i	0.442593	+	0.896723i	$0.354059\pi$
$614$	−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	$-0.837751\pi$
$617$	−22.0266	+	12.7171i	−0.886757	+	0.511970i	−0.0138769	+	0.999904i	$0.504417\pi$
$618$			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	$0.361572\pi$
$620$	−4.43723	+	18.2164i	−0.178204	+	0.731588i
$621$	−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
$625$	10.4701	−	22.7019i	0.418803	−	0.908077i
$626$	−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	0.622242	−	0.782825i	$-0.286222\pi$
$631$	−9.21454	−	15.9600i	−0.366825	−	0.635359i	−0.989067	+	0.147465i	$0.952889\pi$
$632$	−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	0.726267	−	0.687413i	$-0.241254\pi$
$641$	−5.87842	−	10.1817i	−0.232183	−	0.402154i	−0.958450	+	0.285259i	$0.907920\pi$
$642$	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
$645$	−1.34669	+	5.52862i	−0.0530257	+	0.217689i
$646$	6.85084	+	11.8660i	0.269543	+	0.466861i
$647$	26.9727	+	15.5727i	1.06041	+	0.612226i	0.925545	−	0.378638i	$-0.123608\pi$
$647$	26.9727	+	15.5727i	1.06041	+	0.612226i	0.134862	+	0.990864i	$0.456941\pi$
$648$	−0.866025	−	0.500000i	−0.0340207	−	0.0196419i
$649$	−7.66583	−	13.2776i	−0.300910	−	0.521191i
$650$	8.79800	−	5.63099i	0.345086	−	0.220866i
$651$	−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	$-0.641612\pi$
$653$	−36.4720	−	21.0571i	−1.42726	−	0.824028i	−0.996904	+	0.0786314i	$0.974945\pi$
$654$	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	−0.491968	−	0.870613i	$-0.663722\pi$
$659$	13.0406	−	22.5870i	0.507990	−	0.879864i	0.999957	−	0.00925020i	$-0.00294447\pi$
$660$	6.63498	−	6.94560i	0.258266	−	0.270357i
$661$	9.31601	−	16.1358i	0.362351	−	0.627610i	−0.625996	−	0.779826i	$-0.715308\pi$
$661$	9.31601	−	16.1358i	0.362351	−	0.627610i	0.988347	+	0.152216i	$0.0486409\pi$
$662$	−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
$670$	30.7869	−	9.00870i	1.18940	−	0.348037i
$671$	−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	$-0.349753\pi$
$673$	−2.31679	−	1.33760i	−0.0893056	−	0.0515606i	−0.543988	+	0.839093i	$0.683086\pi$
$674$	18.1786			0.700212
$675$	−2.69536	−	4.21130i	−0.103744	−	0.162093i
$676$	−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	$-0.757234\pi$
$683$	−12.7062	+	7.33593i	−0.486189	+	0.280701i	0.236803	+	0.971558i	$0.423900\pi$
$684$	−1.07231	+	1.85729i	−0.0410007	+	0.0710154i
$685$	−12.2331	−	41.8061i	−0.467402	−	1.59733i
$686$	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
$690$	2.62104	+	8.95731i	0.0997813	+	0.340999i
$691$	7.39577	+	12.8098i	0.281348	+	0.487309i	0.971717	−	0.236148i	$-0.0758851\pi$
$691$	7.39577	+	12.8098i	0.281348	+	0.487309i	−0.690369	+	0.723458i	$0.742552\pi$
$692$		−	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
$700$	7.79240	−	15.0462i	0.294525	−	0.568694i
$701$	13.3246	+	23.0789i	0.503264	+	0.871678i	0.999993	+	0.00377282i	$0.00120093\pi$
$701$	13.3246	+	23.0789i	0.503264	+	0.871678i	−0.496729	+	0.867906i	$0.665466\pi$
$702$		−	2.08914i		−	0.0788496i
$703$	11.4638	+	6.22556i	0.432367	+	0.234801i
$704$	−4.29568			−0.161900
$705$	−5.78288	+	23.7407i	−0.217796	+	0.894128i
$706$	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	$0.609348\pi$
$710$	5.93484	+	20.2821i	0.222731	+	0.761175i
$711$	−6.74500			−0.252957
$712$	0.800829	−	0.462359i	0.0300124	−	0.0173276i
$713$		−	34.9966i		−	1.31063i
$714$	−21.6510			−0.810269
$715$	19.4970	+	4.74917i	0.729148	+	0.177609i
$716$	−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	0.662133	−	0.749386i	$-0.269651\pi$
$719$	−8.52478	−	14.7654i	−0.317921	−	0.550655i	−0.980054	+	0.198731i	$0.936318\pi$
$720$	−0.529198	+	2.17254i	−0.0197220	+	0.0809660i
$721$	−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
$725$	10.0602	−	6.43885i	0.373628	−	0.239133i
$726$	7.45286			0.276602
$727$	−10.4909	−	6.05695i	−0.389087	−	0.224640i	0.292677	−	0.956211i	$-0.405454\pi$
$727$	−10.4909	−	6.05695i	−0.389087	−	0.224640i	−0.681765	+	0.731572i	$0.738787\pi$
$728$	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	$-0.352353\pi$
$733$	−2.80038	−	1.61680i	−0.103434	−	0.0597178i	−0.550825	+	0.834621i	$0.685687\pi$
$734$	0.426836			0.0157548
$735$	2.81610	+	9.62392i	0.103873	+	0.354984i
$736$	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	$0.301795\pi$
$740$	13.2946	+	2.87303i	0.488718	+	0.105615i
$741$	−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	$-0.223835\pi$
$743$	15.9225	+	9.19286i	0.584140	+	0.337253i	−0.178637	+	0.983915i	$0.557169\pi$
$744$	4.19241	−	7.26147i	0.153701	−	0.266218i
$745$	−36.2403	+	10.6044i	−1.32774	+	0.388516i
$746$	−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
$755$	−11.6262	+	47.7297i	−0.423121	+	1.73706i
$756$	−1.69443	−	2.93485i	−0.0616260	−	0.106739i
$757$	−16.1194	+	9.30653i	−0.585869	+	0.338252i	−0.763462	−	0.645852i	$-0.776502\pi$
$757$	−16.1194	+	9.30653i	−0.585869	+	0.338252i	0.177593	+	0.984104i	$0.443169\pi$
$758$	2.57017	+	1.48389i	0.0933527	+	0.0538972i
$759$	−8.96467	+	15.5273i	−0.325397	+	0.563604i
$760$	4.65928	+	1.13493i	0.169010	+	0.0411681i
$761$	10.6131	+	18.3824i	0.384724	+	0.666361i	0.991731	−	0.128335i	$-0.0409634\pi$
$761$	10.6131	+	18.3824i	0.384724	+	0.666361i	−0.607007	+	0.794696i	$0.707630\pi$
$762$	−17.7444	+	10.2448i	−0.642813	+	0.371128i
$763$			44.8324i			1.62304i
$764$	2.19298	−	3.79836i	0.0793393	−	0.137420i
$765$	13.8801	+	3.38098i	0.501836	+	0.122239i
$766$	−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	$0.618075\pi$
$770$	31.2415	−	9.14171i	1.12587	−	0.329445i
$771$	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	$-0.0556650\pi$
$773$	36.8790	+	21.2921i	1.32645	+	0.765823i	0.341697	+	0.939810i	$0.388998\pi$
$774$	1.27238	−	2.20383i	0.0457349	−	0.0792152i
$775$	35.3110	−	22.6001i	1.26841	−	0.811820i
$776$	−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
$780$	−4.48346	+	1.31193i	−0.160534	+	0.0469745i
$781$	−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
$790$	4.23568	+	14.4753i	0.150699	+	0.515008i
$791$	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
$795$	−24.0183	+	7.02810i	−0.851841	+	0.249261i
$796$	1.70804	−	2.95842i	0.0605400	−	0.104858i
$797$	7.05417	−	4.07272i	0.249871	−	0.144263i	−0.369834	−	0.929098i	$-0.620585\pi$
$797$	7.05417	−	4.07272i	0.249871	−	0.144263i	0.619705	+	0.784835i	$0.287252\pi$
$798$	−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
$805$	−7.48523	+	30.7295i	−0.263820	+	1.08307i
$806$	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	−0.967368	−	0.253374i	$-0.918460\pi$
$809$	−7.51621	+	13.0185i	−0.264256	+	0.457704i	0.703113	+	0.711079i	$0.251793\pi$
$810$	0.627973	+	2.14608i	0.0220647	+	0.0754055i
$811$	−12.6697	+	21.9445i	−0.444893	+	0.770577i	−0.998045	−	0.0625033i	$-0.980092\pi$
$811$	−12.6697	+	21.9445i	−0.444893	+	0.770577i	0.553152	+	0.833080i	$0.313425\pi$
$812$	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	−0.396133	−	0.918193i	$-0.629648\pi$
$821$	17.1091	−	29.6338i	0.597112	−	1.03423i	0.993245	−	0.116035i	$-0.0370185\pi$
$822$			19.4802i			0.679451i
$823$	−12.0345	+	6.94814i	−0.419497	+	0.242197i	−0.694862	−	0.719143i	$-0.744535\pi$
$823$	−12.0345	+	6.94814i	−0.419497	+	0.242197i	0.275365	+	0.961340i	$0.411201\pi$
$824$	−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	$-0.268619\pi$
$827$	10.0570	+	5.80641i	0.349716	+	0.201909i	−0.314844	+	0.949143i	$0.601952\pi$
$828$		−	4.17381i		−	0.145050i
$829$	−16.0993	−	27.8849i	−0.559153	−	0.968481i	−0.997567	−	0.0697083i	$-0.977793\pi$
$829$	−16.0993	−	27.8849i	−0.559153	−	0.968481i	0.438415	−	0.898773i	$-0.355540\pi$
$830$	6.14360	−	25.2216i	0.213247	−	0.875456i
$831$	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
$835$	28.3574	+	6.90743i	0.981350	+	0.239041i
$836$	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	0.789766	−	0.613408i	$-0.210202\pi$
$839$	−3.94927	−	6.84034i	−0.136344	−	0.236155i	−0.926110	+	0.377253i	$0.876869\pi$
$840$	−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	$-0.493731\pi$
$853$	26.1511	−	15.0983i	0.895396	−	0.516957i	0.875703	+	0.482849i	$0.160398\pi$
$854$	6.41199	−	11.1059i	0.219414	−	0.380036i
$855$	4.60251	−	1.34676i	0.157403	−	0.0460583i
$856$	−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	$0.227478\pi$
$860$	−5.52862	−	1.34669i	−0.188524	−	0.0459216i
$861$	35.8173			1.22065
$862$			20.3759i			0.694006i
$863$	−16.4742	+	9.51138i	−0.560788	+	0.323771i	−0.753462	−	0.657492i	$-0.771618\pi$
$863$	−16.4742	+	9.51138i	−0.560788	+	0.323771i	0.192674	+	0.981263i	$0.438284\pi$
$864$	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
$870$	−5.12669	+	1.50014i	−0.173811	+	0.0508597i
$871$	−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
$875$	−35.8393	+	12.2920i	−1.21159	+	0.415546i
$876$	−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	−0.970692	−	0.240326i	$-0.922746\pi$
$881$	−8.22829	+	14.2518i	−0.277218	+	0.480156i	0.693474	+	0.720481i	$0.256079\pi$
$882$		−	4.48442i		−	0.150998i
$883$	31.3488	+	18.0992i	1.05497	+	0.609088i	0.924037	−	0.382303i	$-0.124869\pi$
$883$	31.3488	+	18.0992i	1.05497	+	0.609088i	0.130935	+	0.991391i	$0.458202\pi$
$884$	6.67363	−	11.5591i	0.224458	−	0.388773i
$885$	−2.24129	−	7.65954i	−0.0753402	−	0.257473i
$886$	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
$890$	−2.00899	−	0.489359i	−0.0673415	−	0.0164034i
$891$	−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
$895$	41.2728	−	12.0770i	1.37960	−	0.403690i
$896$	3.38887			0.113214
$897$	7.55146	−	4.35984i	0.252136	−	0.145571i
$898$			16.0097i			0.534251i
$899$	20.0302			0.668045
$900$	4.21130	−	2.69536i	0.140377	−	0.0898453i
$901$	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
$905$	3.87485	−	15.9076i	0.128804	−	0.528787i
$906$	10.9847	−	19.0261i	0.364944	−	0.632101i
$907$	−28.6657	−	16.5501i	−0.951828	−	0.549538i	−0.0581796	−	0.998306i	$-0.518530\pi$
$907$	−28.6657	−	16.5501i	−0.951828	−	0.549538i	−0.893648	+	0.448768i	$0.851863\pi$
$908$	11.9969	−	6.92642i	0.398132	−	0.229861i
$909$	−2.90345	−	5.02892i	−0.0963012	−	0.166799i
$910$	−15.3812	−	3.74663i	−0.509883	−	0.124200i
$911$	−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	$0.0692217\pi$
$920$	−8.95731	+	2.62104i	−0.295314	+	0.0864131i
$921$	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
$925$	−17.0581	−	25.1798i	−0.560868	−	0.827905i
$926$	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	−0.534491	−	0.845174i	$-0.679497\pi$
$929$	14.1637	−	24.5323i	0.464697	−	0.804878i	0.999188	+	0.0402958i	$0.0128300\pi$
$930$	−17.9945	+	5.26544i	−0.590062	+	0.172661i
$931$	−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	$-0.734124\pi$
$937$	−11.1520	+	6.43859i	−0.364319	+	0.210340i	0.306655	+	0.951821i	$0.400790\pi$
$938$	−42.1024	−	24.3078i	−1.37469	−	0.793678i
$939$	−6.91394			−0.225628
$940$	−23.7407	−	5.78288i	−0.774338	−	0.188617i
$941$	21.7499	+	37.6719i	0.709026	+	1.22807i	0.965219	+	0.261444i	$0.0841985\pi$
$941$	21.7499	+	37.6719i	0.709026	+	1.22807i	−0.256193	+	0.966626i	$0.582468\pi$
$942$	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
$945$	−1.79338	+	7.36246i	−0.0583387	+	0.239501i
$946$	−5.46576	−	9.46697i	−0.177707	−	0.307798i
$947$	8.96199	−	5.17421i	0.291225	−	0.168139i	−0.347269	−	0.937766i	$-0.612891\pi$
$947$	8.96199	−	5.17421i	0.291225	−	0.168139i	0.638494	+	0.769626i	$0.279558\pi$
$948$		−	6.74500i		−	0.219068i
$949$	7.99957	−	13.8557i	0.259677	−	0.449774i
$950$	−5.78051	−	9.03162i	−0.187545	−	0.293025i
$951$	−1.54370			−0.0500580
$952$		−	21.6510i		−	0.701714i
$953$	−45.3038	+	26.1562i	−1.46754	+	0.847282i	−0.999339	−	0.0363424i	$-0.988429\pi$
$953$	−45.3038	+	26.1562i	−1.46754	+	0.847282i	−0.468196	+	0.883625i	$0.655096\pi$
$954$	11.1917			0.362345
$955$	−9.41262	+	2.75427i	−0.304585	+	0.0891260i
$956$	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
$960$	−2.17254	−	0.529198i	−0.0701186	−	0.0170798i
$961$	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
$965$	7.91743	+	27.0576i	0.254871	+	0.871014i
$966$	7.07224	−	12.2495i	0.227546	−	0.394121i
$967$	36.7360	+	21.2095i	1.18135	+	0.682053i	0.956327	−	0.292300i	$-0.0944206\pi$
$967$	36.7360	+	21.2095i	1.18135	+	0.682053i	0.225024	+	0.974353i	$0.427754\pi$
$968$			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	−0.962725	−	0.270482i	$-0.912817\pi$
$971$	−22.2989	−	38.6229i	−0.715606	−	1.23947i	0.247119	−	0.968985i	$-0.420516\pi$
$972$		−	1.00000i		−	0.0320750i
$973$		−	0.675395i		−	0.0216522i
$974$	−13.0787	−	22.6529i	−0.419068	−	0.725847i
$975$	9.27558	+	4.80380i	0.297056	+	0.153845i
$976$	3.78415			0.121128
$977$	−10.8151	+	6.24409i	−0.346005	+	0.199766i	−0.662924	−	0.748686i	$-0.730685\pi$
$977$	−10.8151	+	6.24409i	−0.346005	+	0.199766i	0.316919	+	0.948452i	$0.397352\pi$
$978$	−9.14720	+	5.28114i	−0.292495	+	0.168872i
$979$	−1.98615	−	3.44011i	−0.0634775	−	0.109946i
$980$	−9.62392	+	2.81610i	−0.307425	+	0.0899569i
$981$	−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	$-0.475119\pi$
$983$	30.7417	−	17.7487i	0.980509	−	0.566097i	0.902424	+	0.430850i	$0.141786\pi$
$984$	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
$990$	9.33256	+	2.27327i	0.296608	+	0.0722491i
$991$	−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
$995$	−7.33119	+	2.14521i	−0.232414	+	0.0680078i
$996$	−5.80463	+	10.0539i	−0.183927	+	0.318571i
$997$	6.02143	−	3.47648i	0.190701	−	0.110101i	−0.401610	−	0.915811i	$-0.631549\pi$
$997$	6.02143	−	3.47648i	0.190701	−	0.110101i	0.592311	+	0.805710i	$0.298216\pi$
$998$			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.1099.4	yes	28
5.4	even	2	inner	1110.2.bb.d.1099.11	yes	28
37.10	even	3	inner	1110.2.bb.d.1009.11	yes	28
185.84	even	6	inner	1110.2.bb.d.1009.4	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.bb.d.1009.4	✓	28	185.84	even	6	inner
1110.2.bb.d.1009.11	yes	28	37.10	even	3	inner
1110.2.bb.d.1099.4	yes	28	1.1	even	1	trivial
1110.2.bb.d.1099.11	yes	28	5.4	even	2	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)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-2.14608 + 0.627973i) q^{5} +1.00000 q^{6} +(2.93485 + 1.69443i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-2.14608 + 0.627973i) 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} +(2.17254 + 0.529198i) 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} +(-0.529198 + 2.17254i) q^{20} +(-1.69443 - 2.93485i) q^{21} +(-3.72017 + 2.14784i) q^{22} -4.17381i q^{23} +(0.500000 - 0.866025i) q^{24} +(4.21130 - 2.69536i) q^{25} +2.08914 q^{26} -1.00000i q^{27} +(2.93485 - 1.69443i) q^{28} +2.38887 q^{29} +(-2.14608 + 0.627973i) q^{30} +8.38482 q^{31} +(0.866025 + 0.500000i) q^{32} +(-3.72017 - 2.14784i) q^{33} +(3.19443 - 5.53292i) q^{34} +(-7.36246 - 1.79338i) q^{35} +1.00000 q^{36} +(-0.158737 - 6.08069i) q^{37} -2.14462i q^{38} +(1.04457 + 1.80925i) q^{39} +(-0.627973 - 2.14608i) 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} +(-2.29941 + 4.43990i) q^{50} +6.38887 q^{51} +(-1.80925 + 1.04457i) q^{52} +(-9.69231 + 5.59586i) q^{53} +(0.500000 + 0.866025i) q^{54} +(-9.21886 + 2.69757i) 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} +(4.53875 + 1.10557i) q^{65} +4.29568 q^{66} +(12.4237 + 7.17284i) q^{67} +6.38887i q^{68} +(-2.08690 + 3.61462i) q^{69} +(7.27277 - 2.12812i) 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} +(2.17254 + 0.529198i) 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} +(1.13493 - 4.65928i) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more