LMFDB - Embedded newform 420.2.c.a.391.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [420,2,Mod(391,420)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(420, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("420.391");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	420.c (of order $2$, degree $1$, 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:	$3.35371688489$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 3 x^{14} - 4 x^{13} + 3 x^{12} + 2 x^{11} - 7 x^{10} + 12 x^{9} - 28 x^{8} + \cdots + 256 $ x^16 - 2x^15 + 3x^14 - 4x^13 + 3x^12 + 2x^11 - 7x^10 + 12x^9 - 28x^8 + 24x^7 - 28x^6 + 16x^5 + 48x^4 - 128x^3 + 192x^2 - 256*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			391.16
Root			$1.40936 + 0.117062i$ of defining polynomial
Character	$\chi$	$=$	420.391
Dual form			420.2.c.a.391.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.40936 + 0.117062i) q^{2} -1.00000 q^{3} +(1.97259 + 0.329965i) q^{4} -1.00000i q^{5} +(-1.40936 - 0.117062i) q^{6} +(0.776136 - 2.52935i) q^{7} +(2.74147 + 0.695955i) q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(1.40936 + 0.117062i) q^{2} -1.00000 q^{3} +(1.97259 + 0.329965i) q^{4} -1.00000i q^{5} +(-1.40936 - 0.117062i) q^{6} +(0.776136 - 2.52935i) q^{7} +(2.74147 + 0.695955i) q^{8} +1.00000 q^{9} +(0.117062 - 1.40936i) q^{10} -0.556350i q^{11} +(-1.97259 - 0.329965i) q^{12} +0.182384i q^{13} +(1.38995 - 3.47391i) q^{14} +1.00000i q^{15} +(3.78225 + 1.30177i) q^{16} -2.39449i q^{17} +(1.40936 + 0.117062i) q^{18} +3.08109 q^{19} +(0.329965 - 1.97259i) q^{20} +(-0.776136 + 2.52935i) q^{21} +(0.0651274 - 0.784098i) q^{22} +3.94362i q^{23} +(-2.74147 - 0.695955i) q^{24} -1.00000 q^{25} +(-0.0213502 + 0.257045i) q^{26} -1.00000 q^{27} +(2.36560 - 4.73328i) q^{28} -3.20026 q^{29} +(-0.117062 + 1.40936i) q^{30} +5.68747 q^{31} +(5.17816 + 2.27742i) q^{32} +0.556350i q^{33} +(0.280303 - 3.37469i) q^{34} +(-2.52935 - 0.776136i) q^{35} +(1.97259 + 0.329965i) q^{36} -4.98180 q^{37} +(4.34237 + 0.360678i) q^{38} -0.182384i q^{39} +(0.695955 - 2.74147i) q^{40} +9.64809i q^{41} +(-1.38995 + 3.47391i) q^{42} +0.643697i q^{43} +(0.183576 - 1.09745i) q^{44} -1.00000i q^{45} +(-0.461647 + 5.55798i) q^{46} -3.63668 q^{47} +(-3.78225 - 1.30177i) q^{48} +(-5.79523 - 3.92624i) q^{49} +(-1.40936 - 0.117062i) q^{50} +2.39449i q^{51} +(-0.0601803 + 0.359769i) q^{52} -6.97060 q^{53} +(-1.40936 - 0.117062i) q^{54} -0.556350 q^{55} +(3.88806 - 6.39398i) q^{56} -3.08109 q^{57} +(-4.51031 - 0.374628i) q^{58} -8.79962 q^{59} +(-0.329965 + 1.97259i) q^{60} +14.3787i q^{61} +(8.01569 + 0.665786i) q^{62} +(0.776136 - 2.52935i) q^{63} +(7.03129 + 3.81588i) q^{64} +0.182384 q^{65} +(-0.0651274 + 0.784098i) q^{66} -10.0692i q^{67} +(0.790096 - 4.72335i) q^{68} -3.94362i q^{69} +(-3.47391 - 1.38995i) q^{70} +1.36136i q^{71} +(2.74147 + 0.695955i) q^{72} -10.1087i q^{73} +(-7.02115 - 0.583179i) q^{74} +1.00000 q^{75} +(6.07774 + 1.01665i) q^{76} +(-1.40721 - 0.431803i) q^{77} +(0.0213502 - 0.257045i) q^{78} +13.0596i q^{79} +(1.30177 - 3.78225i) q^{80} +1.00000 q^{81} +(-1.12942 + 13.5976i) q^{82} -9.45272 q^{83} +(-2.36560 + 4.73328i) q^{84} -2.39449 q^{85} +(-0.0753523 + 0.907200i) q^{86} +3.20026 q^{87} +(0.387195 - 1.52522i) q^{88} -8.01600i q^{89} +(0.117062 - 1.40936i) q^{90} +(0.461313 + 0.141555i) q^{91} +(-1.30125 + 7.77915i) q^{92} -5.68747 q^{93} +(-5.12540 - 0.425717i) q^{94} -3.08109i q^{95} +(-5.17816 - 2.27742i) q^{96} -0.445387i q^{97} +(-7.70795 - 6.21188i) q^{98} -0.556350i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{2} - 16 q^{3} - 2 q^{4} - 2 q^{6} - 4 q^{7} + 2 q^{8} + 16 q^{9}+O(q^{10}) $ 16 * q + 2 * q^2 - 16 * q^3 - 2 * q^4 - 2 * q^6 - 4 * q^7 + 2 * q^8 + 16 * q^9	$ 16 q + 2 q^{2} - 16 q^{3} - 2 q^{4} - 2 q^{6} - 4 q^{7} + 2 q^{8} + 16 q^{9} + 2 q^{12} - 2 q^{14} + 6 q^{16} + 2 q^{18} - 24 q^{19} + 4 q^{21} - 12 q^{22} - 2 q^{24} - 16 q^{25} - 12 q^{26} - 16 q^{27} + 14 q^{28} + 16 q^{29} + 8 q^{31} - 18 q^{32} + 24 q^{34} - 2 q^{36} + 24 q^{37} + 28 q^{38} + 12 q^{40} + 2 q^{42} - 8 q^{44} - 20 q^{46} + 16 q^{47} - 6 q^{48} - 16 q^{49} - 2 q^{50} - 20 q^{52} - 32 q^{53} - 2 q^{54} + 2 q^{56} + 24 q^{57} - 32 q^{58} + 8 q^{59} + 16 q^{62} - 4 q^{63} - 2 q^{64} - 8 q^{65} + 12 q^{66} + 4 q^{68} + 2 q^{72} - 4 q^{74} + 16 q^{75} + 16 q^{76} - 8 q^{77} + 12 q^{78} - 16 q^{80} + 16 q^{81} - 4 q^{82} + 8 q^{83} - 14 q^{84} + 64 q^{86} - 16 q^{87} - 52 q^{88} + 16 q^{91} + 64 q^{92} - 8 q^{93} + 16 q^{94} + 18 q^{96} - 86 q^{98}+O(q^{100}) $ 16 * q + 2 * q^2 - 16 * q^3 - 2 * q^4 - 2 * q^6 - 4 * q^7 + 2 * q^8 + 16 * q^9 + 2 * q^12 - 2 * q^14 + 6 * q^16 + 2 * q^18 - 24 * q^19 + 4 * q^21 - 12 * q^22 - 2 * q^24 - 16 * q^25 - 12 * q^26 - 16 * q^27 + 14 * q^28 + 16 * q^29 + 8 * q^31 - 18 * q^32 + 24 * q^34 - 2 * q^36 + 24 * q^37 + 28 * q^38 + 12 * q^40 + 2 * q^42 - 8 * q^44 - 20 * q^46 + 16 * q^47 - 6 * q^48 - 16 * q^49 - 2 * q^50 - 20 * q^52 - 32 * q^53 - 2 * q^54 + 2 * q^56 + 24 * q^57 - 32 * q^58 + 8 * q^59 + 16 * q^62 - 4 * q^63 - 2 * q^64 - 8 * q^65 + 12 * q^66 + 4 * q^68 + 2 * q^72 - 4 * q^74 + 16 * q^75 + 16 * q^76 - 8 * q^77 + 12 * q^78 - 16 * q^80 + 16 * q^81 - 4 * q^82 + 8 * q^83 - 14 * q^84 + 64 * q^86 - 16 * q^87 - 52 * q^88 + 16 * q^91 + 64 * q^92 - 8 * q^93 + 16 * q^94 + 18 * q^96 - 86 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/420\mathbb{Z}\right)^\times$.

$n$	$211$	$241$	$281$	$337$
$\chi(n)$	$-1$	$-1$	$1$	$1$

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 $

$2$	1.40936	+	0.117062i	0.996568	+	0.0827753i
$2$	1.40936	+	0.117062i	0.996568	+	0.0827753i
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	1.97259	+	0.329965i	0.986297	+	0.164982i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	−1.40936	−	0.117062i	−0.575369	−	0.0477903i
$7$	0.776136	−	2.52935i	0.293352	−	0.956005i
$7$	0.776136	−	2.52935i	0.293352	−	0.956005i
$8$	2.74147	+	0.695955i	0.969255	+	0.246057i
$9$	1.00000			0.333333
$10$	0.117062	−	1.40936i	0.0370182	−	0.445679i
$11$		−	0.556350i		−	0.167746i	−0.996476	−	0.0838730i	$-0.973271\pi$
$11$		−	0.556350i		−	0.167746i	0.996476	−	0.0838730i	$-0.0267290\pi$
$12$	−1.97259	−	0.329965i	−0.569439	−	0.0952526i
$13$			0.182384i			0.0505842i	0.999680	+	0.0252921i	$0.00805158\pi$
$13$			0.182384i			0.0505842i	−0.999680	+	0.0252921i	$0.991948\pi$
$14$	1.38995	−	3.47391i	0.371479	−	0.928442i
$15$			1.00000i			0.258199i
$16$	3.78225	+	1.30177i	0.945562	+	0.325443i
$17$		−	2.39449i		−	0.580748i	−0.956913	−	0.290374i	$-0.906220\pi$
$17$		−	2.39449i		−	0.580748i	0.956913	−	0.290374i	$-0.0937797\pi$
$18$	1.40936	+	0.117062i	0.332189	+	0.0275918i
$19$	3.08109			0.706851			0.353425	−	0.935463i	$-0.385017\pi$
$19$	3.08109			0.706851			0.353425	+	0.935463i	$0.385017\pi$
$20$	0.329965	−	1.97259i	0.0737824	−	0.441085i
$21$	−0.776136	+	2.52935i	−0.169367	+	0.551950i
$22$	0.0651274	−	0.784098i	0.0138852	−	0.167170i
$23$			3.94362i			0.822301i	0.911568	+	0.411150i	$0.134873\pi$
$23$			3.94362i			0.822301i	−0.911568	+	0.411150i	$0.865127\pi$
$24$	−2.74147	−	0.695955i	−0.559600	−	0.142061i
$25$	−1.00000			−0.200000
$26$	−0.0213502	+	0.257045i	−0.00418712	+	0.0504106i
$27$	−1.00000			−0.192450
$28$	2.36560	−	4.73328i	0.447056	−	0.894506i
$29$	−3.20026			−0.594273			−0.297136	−	0.954835i	$-0.596032\pi$
$29$	−3.20026			−0.594273			−0.297136	+	0.954835i	$0.596032\pi$
$30$	−0.117062	+	1.40936i	−0.0213725	+	0.257313i
$31$	5.68747			1.02150			0.510750	−	0.859729i	$-0.329368\pi$
$31$	5.68747			1.02150			0.510750	+	0.859729i	$0.329368\pi$
$32$	5.17816	+	2.27742i	0.915378	+	0.402595i
$33$			0.556350i			0.0968482i
$34$	0.280303	−	3.37469i	0.0480716	−	0.578755i
$35$	−2.52935	−	0.776136i	−0.427538	−	0.131191i
$36$	1.97259	+	0.329965i	0.328766	+	0.0549941i
$37$	−4.98180			−0.819002			−0.409501	−	0.912310i	$-0.634297\pi$
$37$	−4.98180			−0.819002			−0.409501	+	0.912310i	$0.634297\pi$
$38$	4.34237	+	0.360678i	0.704425	+	0.0585098i
$39$		−	0.182384i		−	0.0292048i
$40$	0.695955	−	2.74147i	0.110040	−	0.433464i
$41$			9.64809i			1.50678i	0.657575	+	0.753389i	$0.271582\pi$
$41$			9.64809i			1.50678i	−0.657575	+	0.753389i	$0.728418\pi$
$42$	−1.38995	+	3.47391i	−0.214473	+	0.536036i
$43$			0.643697i			0.0981628i	0.998795	+	0.0490814i	$0.0156294\pi$
$43$			0.643697i			0.0981628i	−0.998795	+	0.0490814i	$0.984371\pi$
$44$	0.183576	−	1.09745i	0.0276751	−	0.165447i
$45$		−	1.00000i		−	0.149071i
$46$	−0.461647	+	5.55798i	−0.0680662	+	0.819479i
$47$	−3.63668			−0.530465			−0.265232	−	0.964184i	$-0.585449\pi$
$47$	−3.63668			−0.530465			−0.265232	+	0.964184i	$0.585449\pi$
$48$	−3.78225	−	1.30177i	−0.545920	−	0.187895i
$49$	−5.79523	−	3.92624i	−0.827890	−	0.560891i
$50$	−1.40936	−	0.117062i	−0.199314	−	0.0165551i
$51$			2.39449i			0.335295i
$52$	−0.0601803	+	0.359769i	−0.00834550	+	0.0498910i
$53$	−6.97060			−0.957485			−0.478743	−	0.877955i	$-0.658907\pi$
$53$	−6.97060			−0.957485			−0.478743	+	0.877955i	$0.658907\pi$
$54$	−1.40936	−	0.117062i	−0.191790	−	0.0159301i
$55$	−0.556350			−0.0750183
$56$	3.88806	−	6.39398i	0.519564	−	0.854431i
$57$	−3.08109			−0.408100
$58$	−4.51031	−	0.374628i	−0.592233	−	0.0491911i
$59$	−8.79962			−1.14561			−0.572807	−	0.819691i	$-0.694145\pi$
$59$	−8.79962			−1.14561			−0.572807	+	0.819691i	$0.694145\pi$
$60$	−0.329965	+	1.97259i	−0.0425983	+	0.254661i
$61$			14.3787i			1.84100i	0.390743	+	0.920500i	$0.372218\pi$
$61$			14.3787i			1.84100i	−0.390743	+	0.920500i	$0.627782\pi$
$62$	8.01569	+	0.665786i	1.01799	+	0.0845549i
$63$	0.776136	−	2.52935i	0.0977839	−	0.318668i
$64$	7.03129	+	3.81588i	0.878912	+	0.476984i
$65$	0.182384			0.0226219
$66$	−0.0651274	+	0.784098i	−0.00801663	+	0.0965158i
$67$		−	10.0692i		−	1.23015i	−0.788467	−	0.615077i	$-0.789125\pi$
$67$		−	10.0692i		−	1.23015i	0.788467	−	0.615077i	$-0.210875\pi$
$68$	0.790096	−	4.72335i	0.0958132	−	0.572790i
$69$		−	3.94362i		−	0.474756i
$70$	−3.47391	−	1.38995i	−0.415212	−	0.166130i
$71$			1.36136i			0.161564i	0.996732	+	0.0807821i	$0.0257418\pi$
$71$			1.36136i			0.161564i	−0.996732	+	0.0807821i	$0.974258\pi$
$72$	2.74147	+	0.695955i	0.323085	+	0.0820191i
$73$		−	10.1087i		−	1.18314i	−0.806255	−	0.591569i	$-0.798509\pi$
$73$		−	10.1087i		−	1.18314i	0.806255	−	0.591569i	$-0.201491\pi$
$74$	−7.02115	−	0.583179i	−0.816192	−	0.0677931i
$75$	1.00000			0.115470
$76$	6.07774	+	1.01665i	0.697164	+	0.116618i
$77$	−1.40721	−	0.431803i	−0.160366	−	0.0492086i
$78$	0.0213502	−	0.257045i	0.00241743	−	0.0291046i
$79$			13.0596i			1.46932i	0.678438	+	0.734658i	$0.262657\pi$
$79$			13.0596i			1.46932i	−0.678438	+	0.734658i	$0.737343\pi$
$80$	1.30177	−	3.78225i	0.145543	−	0.422868i
$81$	1.00000			0.111111
$82$	−1.12942	+	13.5976i	−0.124724	+	1.50161i
$83$	−9.45272			−1.03757			−0.518785	−	0.854905i	$-0.673616\pi$
$83$	−9.45272			−1.03757			−0.518785	+	0.854905i	$0.673616\pi$
$84$	−2.36560	+	4.73328i	−0.258108	+	0.516443i
$85$	−2.39449			−0.259718
$86$	−0.0753523	+	0.907200i	−0.00812545	+	0.0978259i
$87$	3.20026			0.343103
$88$	0.387195	−	1.52522i	0.0412751	−	0.162589i
$89$		−	8.01600i		−	0.849694i	−0.905265	−	0.424847i	$-0.860328\pi$
$89$		−	8.01600i		−	0.849694i	0.905265	−	0.424847i	$-0.139672\pi$
$90$	0.117062	−	1.40936i	0.0123394	−	0.148560i
$91$	0.461313	+	0.141555i	0.0483587	+	0.0148390i
$92$	−1.30125	+	7.77915i	−0.135665	+	0.811032i
$93$	−5.68747			−0.589763
$94$	−5.12540	−	0.425717i	−0.528645	−	0.0439094i
$95$		−	3.08109i		−	0.316113i
$96$	−5.17816	−	2.27742i	−0.528494	−	0.232439i
$97$		−	0.445387i		−	0.0452222i	−0.999744	−	0.0226111i	$-0.992802\pi$
$97$		−	0.445387i		−	0.0452222i	0.999744	−	0.0226111i	$-0.00719796\pi$
$98$	−7.70795	−	6.21188i	−0.778621	−	0.627495i
$99$		−	0.556350i		−	0.0559153i
$100$	−1.97259	−	0.329965i	−0.197259	−	0.0329965i
$101$			12.8540i			1.27902i	0.768781	+	0.639512i	$0.220864\pi$
$101$			12.8540i			1.27902i	−0.768781	+	0.639512i	$0.779136\pi$
$102$	−0.280303	+	3.37469i	−0.0277541	+	0.334144i
$103$	14.3031			1.40933			0.704664	−	0.709542i	$-0.251098\pi$
$103$	14.3031			1.40933			0.704664	+	0.709542i	$0.251098\pi$
$104$	−0.126931	+	0.500000i	−0.0124466	+	0.0490290i
$105$	2.52935	+	0.776136i	0.246839	+	0.0757431i
$106$	−9.82408	−	0.815991i	−0.954199	−	0.0792561i
$107$			18.3230i			1.77136i	0.464301	+	0.885678i	$0.346306\pi$
$107$			18.3230i			1.77136i	−0.464301	+	0.885678i	$0.653694\pi$
$108$	−1.97259	−	0.329965i	−0.189813	−	0.0317509i
$109$	−4.03790			−0.386760			−0.193380	−	0.981124i	$-0.561945\pi$
$109$	−4.03790			−0.386760			−0.193380	+	0.981124i	$0.561945\pi$
$110$	−0.784098	−	0.0651274i	−0.0747608	−	0.00620966i
$111$	4.98180			0.472851
$112$	6.22818	−	8.55627i	0.588507	−	0.808492i
$113$	3.14680			0.296026			0.148013	−	0.988985i	$-0.452712\pi$
$113$	3.14680			0.296026			0.148013	+	0.988985i	$0.452712\pi$
$114$	−4.34237	−	0.360678i	−0.406700	−	0.0337806i
$115$	3.94362			0.367744
$116$	−6.31280	−	1.05597i	−0.586129	−	0.0980445i
$117$			0.182384i			0.0168614i
$118$	−12.4018	−	1.03010i	−1.14168	−	0.0948284i
$119$	−6.05649	−	1.85845i	−0.555198	−	0.170363i
$120$	−0.695955	+	2.74147i	−0.0635317	+	0.250261i
$121$	10.6905			0.971861
$122$	−1.68319	+	20.2647i	−0.152389	+	1.83468i
$123$		−	9.64809i		−	0.869939i
$124$	11.2191	+	1.87666i	1.00750	+	0.168529i
$125$			1.00000i			0.0894427i
$126$	1.38995	−	3.47391i	0.123826	−	0.309481i
$127$		−	11.8445i		−	1.05103i	−0.850784	−	0.525516i	$-0.823872\pi$
$127$		−	11.8445i		−	1.05103i	0.850784	−	0.525516i	$-0.176128\pi$
$128$	9.46293	+	6.20104i	0.836413	+	0.548100i
$129$		−	0.643697i		−	0.0566743i
$130$	0.257045	+	0.0213502i	0.0225443	+	0.00187254i
$131$	−16.6337			−1.45329			−0.726647	−	0.687011i	$-0.758922\pi$
$131$	−16.6337			−1.45329			−0.726647	+	0.687011i	$0.758922\pi$
$132$	−0.183576	+	1.09745i	−0.0159782	+	0.0955210i
$133$	2.39134	−	7.79316i	0.207356	−	0.675753i
$134$	1.17872	−	14.1912i	0.101826	−	1.22593i
$135$			1.00000i			0.0860663i
$136$	1.66645	−	6.56441i	0.142897	−	0.562893i
$137$	9.88658			0.844667			0.422334	−	0.906440i	$-0.361211\pi$
$137$	9.88658			0.844667			0.422334	+	0.906440i	$0.361211\pi$
$138$	0.461647	−	5.55798i	0.0392980	−	0.473126i
$139$	20.5861			1.74609			0.873047	−	0.487636i	$-0.162141\pi$
$139$	20.5861			1.74609			0.873047	+	0.487636i	$0.162141\pi$
$140$	−4.73328	−	2.36560i	−0.400035	−	0.199929i
$141$	3.63668			0.306264
$142$	−0.159364	+	1.91865i	−0.0133735	+	0.161010i
$143$	0.101469			0.00848529
$144$	3.78225	+	1.30177i	0.315187	+	0.108481i
$145$			3.20026i			0.265767i
$146$	1.18335	−	14.2468i	0.0979345	−	1.17908i
$147$	5.79523	+	3.92624i	0.477982	+	0.323831i
$148$	−9.82706	−	1.64382i	−0.807779	−	0.135121i
$149$	7.28607			0.596898			0.298449	−	0.954426i	$-0.403531\pi$
$149$	7.28607			0.596898			0.298449	+	0.954426i	$0.403531\pi$
$150$	1.40936	+	0.117062i	0.115074	+	0.00955806i
$151$		−	15.1807i		−	1.23539i	−0.786418	−	0.617694i	$-0.788067\pi$
$151$		−	15.1807i		−	1.23539i	0.786418	−	0.617694i	$-0.211933\pi$
$152$	8.44671	+	2.14430i	0.685119	+	0.173926i
$153$		−	2.39449i		−	0.193583i
$154$	−1.93271	−	0.773297i	−0.155742	−	0.0623140i
$155$		−	5.68747i		−	0.456829i
$156$	0.0601803	−	0.359769i	0.00481828	−	0.0288046i
$157$		−	10.7177i		−	0.855366i	−0.903929	−	0.427683i	$-0.859330\pi$
$157$		−	10.7177i		−	0.855366i	0.903929	−	0.427683i	$-0.140670\pi$
$158$	−1.52878	+	18.4056i	−0.121623	+	1.46427i
$159$	6.97060			0.552804
$160$	2.27742	−	5.17816i	0.180046	−	0.409370i
$161$	9.97479	+	3.06078i	0.786123	+	0.241223i
$162$	1.40936	+	0.117062i	0.110730	+	0.00919725i
$163$			20.7486i			1.62515i	0.582853	+	0.812577i	$0.301936\pi$
$163$			20.7486i			1.62515i	−0.582853	+	0.812577i	$0.698064\pi$
$164$	−3.18353	+	19.0318i	−0.248592	+	1.48613i
$165$	0.556350			0.0433118
$166$	−13.3223	−	1.10655i	−1.03401	−	0.0858852i
$167$	−8.37483			−0.648064			−0.324032	−	0.946046i	$-0.605039\pi$
$167$	−8.37483			−0.648064			−0.324032	+	0.946046i	$0.605039\pi$
$168$	−3.88806	+	6.39398i	−0.299971	+	0.493306i
$169$	12.9667			0.997441
$170$	−3.37469	−	0.280303i	−0.258827	−	0.0214983i
$171$	3.08109			0.235617
$172$	−0.212397	+	1.26975i	−0.0161951	+	0.0968176i
$173$		−	21.8554i		−	1.66163i	−0.556546	−	0.830817i	$-0.687874\pi$
$173$		−	21.8554i		−	1.66163i	0.556546	−	0.830817i	$-0.312126\pi$
$174$	4.51031	+	0.374628i	0.341926	+	0.0284005i
$175$	−0.776136	+	2.52935i	−0.0586703	+	0.191201i
$176$	0.724242	−	2.10425i	0.0545918	−	0.158614i
$177$	8.79962			0.661420
$178$	0.938368	−	11.2974i	0.0703337	−	0.846778i
$179$		−	18.3538i		−	1.37182i	−0.727684	−	0.685912i	$-0.759403\pi$
$179$		−	18.3538i		−	1.37182i	0.727684	−	0.685912i	$-0.240597\pi$
$180$	0.329965	−	1.97259i	0.0245941	−	0.147028i
$181$			12.7452i			0.947341i	0.880702	+	0.473670i	$0.157071\pi$
$181$			12.7452i			0.947341i	−0.880702	+	0.473670i	$0.842929\pi$
$182$	0.633585	+	0.253504i	0.0469645	+	0.0187909i
$183$		−	14.3787i		−	1.06290i
$184$	−2.74458	+	10.8113i	−0.202333	+	0.797019i
$185$			4.98180i			0.366269i
$186$	−8.01569	−	0.665786i	−0.587739	−	0.0488178i
$187$	−1.33217			−0.0974181
$188$	−7.17370	−	1.19998i	−0.523196	−	0.0875174i
$189$	−0.776136	+	2.52935i	−0.0564556	+	0.183983i
$190$	0.360678	−	4.34237i	0.0261664	−	0.315028i
$191$			21.4663i			1.55324i	0.629967	+	0.776622i	$0.283068\pi$
$191$			21.4663i			1.55324i	−0.629967	+	0.776622i	$0.716932\pi$
$192$	−7.03129	−	3.81588i	−0.507440	−	0.275387i
$193$	5.27923			0.380008			0.190004	−	0.981783i	$-0.439150\pi$
$193$	5.27923			0.380008			0.190004	+	0.981783i	$0.439150\pi$
$194$	0.0521379	−	0.627711i	0.00374328	−	0.0450670i
$195$	−0.182384			−0.0130608
$196$	−10.1361	−	9.65709i	−0.724007	−	0.689792i
$197$	−8.44807			−0.601900			−0.300950	−	0.953640i	$-0.597304\pi$
$197$	−8.44807			−0.601900			−0.300950	+	0.953640i	$0.597304\pi$
$198$	0.0651274	−	0.784098i	0.00462841	−	0.0557234i
$199$	−18.5300			−1.31356			−0.656778	−	0.754084i	$-0.728081\pi$
$199$	−18.5300			−1.31356			−0.656778	+	0.754084i	$0.728081\pi$
$200$	−2.74147	−	0.695955i	−0.193851	−	0.0492114i
$201$			10.0692i			0.710230i
$202$	−1.50472	+	18.1160i	−0.105872	+	1.27463i
$203$	−2.48383	+	8.09457i	−0.174331	+	0.568127i
$204$	−0.790096	+	4.72335i	−0.0553178	+	0.330700i
$205$	9.64809			0.673852
$206$	20.1582	+	1.67435i	1.40449	+	0.116657i
$207$			3.94362i			0.274100i
$208$	−0.237422	+	0.689821i	−0.0164623	+	0.0478305i
$209$		−	1.71417i		−	0.118571i
$210$	3.47391	+	1.38995i	0.239723	+	0.0959153i
$211$		−	17.4456i		−	1.20101i	−0.799622	−	0.600504i	$-0.794967\pi$
$211$		−	17.4456i		−	1.20101i	0.799622	−	0.600504i	$-0.205033\pi$
$212$	−13.7502	−	2.30005i	−0.944364	−	0.157968i
$213$		−	1.36136i		−	0.0932791i
$214$	−2.14493	+	25.8238i	−0.146624	+	1.76528i
$215$	0.643697			0.0438997
$216$	−2.74147	−	0.695955i	−0.186533	−	0.0473537i
$217$	4.41425	−	14.3856i	0.299659	−	0.976558i
$218$	−5.69085	−	0.472684i	−0.385433	−	0.0320142i
$219$			10.1087i			0.683085i
$220$	−1.09745	−	0.183576i	−0.0739903	−	0.0123767i
$221$	0.436716			0.0293767
$222$	7.02115	+	0.583179i	0.471229	+	0.0391404i
$223$	−11.9173			−0.798038			−0.399019	−	0.916943i	$-0.630649\pi$
$223$	−11.9173			−0.798038			−0.399019	+	0.916943i	$0.630649\pi$
$224$	9.77936	−	11.3298i	0.653411	−	0.757004i
$225$	−1.00000			−0.0666667
$226$	4.43498	+	0.368371i	0.295010	+	0.0245037i
$227$	−2.13795			−0.141901			−0.0709505	−	0.997480i	$-0.522603\pi$
$227$	−2.13795			−0.141901			−0.0709505	+	0.997480i	$0.522603\pi$
$228$	−6.07774	−	1.01665i	−0.402508	−	0.0673294i
$229$			7.10530i			0.469531i	0.972052	+	0.234766i	$0.0754323\pi$
$229$			7.10530i			0.469531i	−0.972052	+	0.234766i	$0.924568\pi$
$230$	5.55798	+	0.461647i	0.366482	+	0.0304401i
$231$	1.40721	+	0.431803i	0.0925873	+	0.0284106i
$232$	−8.77340	−	2.22723i	−0.576002	−	0.146225i
$233$	10.8641			0.711732			0.355866	−	0.934537i	$-0.384186\pi$
$233$	10.8641			0.711732			0.355866	+	0.934537i	$0.384186\pi$
$234$	−0.0213502	+	0.257045i	−0.00139571	+	0.0168035i
$235$			3.63668i			0.237231i
$236$	−17.3581	−	2.90357i	−1.12991	−	0.189006i
$237$		−	13.0596i		−	0.848310i
$238$	−8.31823	−	3.32820i	−0.539191	−	0.215735i
$239$		−	15.3760i		−	0.994592i	−0.867581	−	0.497296i	$-0.834326\pi$
$239$		−	15.3760i		−	0.994592i	0.867581	−	0.497296i	$-0.165674\pi$
$240$	−1.30177	+	3.78225i	−0.0840291	+	0.244143i
$241$		−	0.518574i		−	0.0334043i	−0.999861	−	0.0167022i	$-0.994683\pi$
$241$		−	0.518574i		−	0.0334043i	0.999861	−	0.0167022i	$-0.00531671\pi$
$242$	15.0667	+	1.25145i	0.968526	+	0.0804461i
$243$	−1.00000			−0.0641500
$244$	−4.74445	+	28.3633i	−0.303733	+	1.81577i
$245$	−3.92624	+	5.79523i	−0.250838	+	0.370243i
$246$	1.12942	−	13.5976i	0.0720094	−	0.866954i
$247$			0.561941i			0.0357555i
$248$	15.5920	+	3.95822i	0.990094	+	0.251347i
$249$	9.45272			0.599042
$250$	−0.117062	+	1.40936i	−0.00740364	+	0.0891358i
$251$	19.8979			1.25594			0.627972	−	0.778236i	$-0.283885\pi$
$251$	19.8979			1.25594			0.627972	+	0.778236i	$0.283885\pi$
$252$	2.36560	−	4.73328i	0.149019	−	0.298169i
$253$	2.19403			0.137938
$254$	1.38654	−	16.6932i	0.0869995	−	1.04743i
$255$	2.39449			0.149948
$256$	12.6108	+	9.84725i	0.788174	+	0.615453i
$257$		−	30.1252i		−	1.87916i	−0.342335	−	0.939578i	$-0.611218\pi$
$257$		−	30.1252i		−	1.87916i	0.342335	−	0.939578i	$-0.388782\pi$
$258$	0.0753523	−	0.907200i	0.00469123	−	0.0564798i
$259$	−3.86655	+	12.6007i	−0.240256	+	0.782970i
$260$	0.359769	+	0.0601803i	0.0223119	+	0.00373222i
$261$	−3.20026			−0.198091
$262$	−23.4429	−	1.94717i	−1.44831	−	0.120297i
$263$		−	4.44397i		−	0.274027i	−0.990569	−	0.137013i	$-0.956250\pi$
$263$		−	4.44397i		−	0.274027i	0.990569	−	0.137013i	$-0.0437503\pi$
$264$	−0.387195	+	1.52522i	−0.0238302	+	0.0938706i
$265$			6.97060i			0.428200i
$266$	4.28255	−	10.7034i	0.262580	−	0.656270i
$267$			8.01600i			0.490571i
$268$	3.32250	−	19.8625i	0.202954	−	1.21330i
$269$			8.40266i			0.512319i	0.966634	+	0.256160i	$0.0824573\pi$
$269$			8.40266i			0.512319i	−0.966634	+	0.256160i	$0.917543\pi$
$270$	−0.117062	+	1.40936i	−0.00712416	+	0.0857709i
$271$	−28.7730			−1.74783			−0.873916	−	0.486077i	$-0.838428\pi$
$271$	−28.7730			−1.74783			−0.873916	+	0.486077i	$0.838428\pi$
$272$	3.11708	−	9.05653i	0.189000	−	0.549133i
$273$	−0.461313	−	0.141555i	−0.0279199	−	0.00856728i
$274$	13.9338	+	1.15734i	0.841769	+	0.0699176i
$275$			0.556350i			0.0335492i
$276$	1.30125	−	7.77915i	0.0783263	−	0.468250i
$277$	−3.93122			−0.236204			−0.118102	−	0.993001i	$-0.537681\pi$
$277$	−3.93122			−0.236204			−0.118102	+	0.993001i	$0.537681\pi$
$278$	29.0133	+	2.40985i	1.74010	+	0.144533i
$279$	5.68747			0.340500
$280$	−6.39398	−	3.88806i	−0.382113	−	0.232356i
$281$	17.8653			1.06575			0.532876	−	0.846193i	$-0.321111\pi$
$281$	17.8653			1.06575			0.532876	+	0.846193i	$0.321111\pi$
$282$	5.12540	+	0.425717i	0.305213	+	0.0253511i
$283$	4.34129			0.258063			0.129031	−	0.991641i	$-0.458813\pi$
$283$	4.34129			0.258063			0.129031	+	0.991641i	$0.458813\pi$
$284$	−0.449202	+	2.68542i	−0.0266552	+	0.159350i
$285$			3.08109i			0.182508i
$286$	0.143007	+	0.0118782i	0.00845617	+	0.000702372i
$287$	24.4034	+	7.48823i	1.44049	+	0.442016i
$288$	5.17816	+	2.27742i	0.305126	+	0.134198i
$289$	11.2664			0.662732
$290$	−0.374628	+	4.51031i	−0.0219989	+	0.264855i
$291$			0.445387i			0.0261091i
$292$	3.33553	−	19.9404i	0.195197	−	1.16692i
$293$		−	0.535106i		−	0.0312612i	−0.999878	−	0.0156306i	$-0.995024\pi$
$293$		−	0.535106i		−	0.0312612i	0.999878	−	0.0156306i	$-0.00497558\pi$
$294$	7.70795	+	6.21188i	0.449537	+	0.362284i
$295$			8.79962i			0.512334i
$296$	−13.6574	−	3.46711i	−0.793822	−	0.201521i
$297$			0.556350i			0.0322827i
$298$	10.2687	+	0.852922i	0.594850	+	0.0494084i
$299$	−0.719252			−0.0415954
$300$	1.97259	+	0.329965i	0.113888	+	0.0190505i
$301$	1.62813	+	0.499596i	0.0938441	+	0.0287962i
$302$	1.77708	−	21.3951i	0.102260	−	1.23115i
$303$		−	12.8540i		−	0.738445i
$304$	11.6534	+	4.01088i	0.668371	+	0.230040i
$305$	14.3787			0.823320
$306$	0.280303	−	3.37469i	0.0160239	−	0.192918i
$307$	−20.4818			−1.16896			−0.584478	−	0.811409i	$-0.698701\pi$
$307$	−20.4818			−1.16896			−0.584478	+	0.811409i	$0.698701\pi$
$308$	−2.63336	−	1.31610i	−0.150050	−	0.0749918i
$309$	−14.3031			−0.813675
$310$	0.665786	−	8.01569i	0.0378141	−	0.455261i
$311$	29.6598			1.68185			0.840927	−	0.541149i	$-0.182010\pi$
$311$	29.6598			1.68185			0.840927	+	0.541149i	$0.182010\pi$
$312$	0.126931	−	0.500000i	0.00718605	−	0.0283069i
$313$			11.7015i			0.661406i	0.943735	+	0.330703i	$0.107286\pi$
$313$			11.7015i			0.661406i	−0.943735	+	0.330703i	$0.892714\pi$
$314$	1.25464	−	15.1051i	0.0708032	−	0.852431i
$315$	−2.52935	−	0.776136i	−0.142513	−	0.0437303i
$316$	−4.30920	+	25.7612i	−0.242411	+	1.44918i
$317$	−16.0488			−0.901388			−0.450694	−	0.892678i	$-0.648823\pi$
$317$	−16.0488			−0.901388			−0.450694	+	0.892678i	$0.648823\pi$
$318$	9.82408	+	0.815991i	0.550907	+	0.0457585i
$319$			1.78046i			0.0996868i
$320$	3.81588	−	7.03129i	0.213314	−	0.393061i
$321$		−	18.3230i		−	1.02269i
$322$	13.6998	+	5.48141i	0.763458	+	0.305467i
$323$		−	7.37763i		−	0.410502i
$324$	1.97259	+	0.329965i	0.109589	+	0.0183314i
$325$		−	0.182384i		−	0.0101168i
$326$	−2.42887	+	29.2422i	−0.134523	+	1.61958i
$327$	4.03790			0.223296
$328$	−6.71464	+	26.4499i	−0.370754	+	1.46045i
$329$	−2.82256	+	9.19845i	−0.155613	+	0.507127i
$330$	0.784098	+	0.0651274i	0.0431632	+	0.00358515i
$331$		−	10.9660i		−	0.602746i	−0.953506	−	0.301373i	$-0.902555\pi$
$331$		−	10.9660i		−	0.602746i	0.953506	−	0.301373i	$-0.0974450\pi$
$332$	−18.6464	−	3.11906i	−1.02335	−	0.171181i
$333$	−4.98180			−0.273001
$334$	−11.8032	−	0.980374i	−0.645840	−	0.0536437i
$335$	−10.0692			−0.550142
$336$	−6.22818	+	8.55627i	−0.339775	+	0.466783i
$337$	−7.87907			−0.429200			−0.214600	−	0.976702i	$-0.568845\pi$
$337$	−7.87907			−0.429200			−0.214600	+	0.976702i	$0.568845\pi$
$338$	18.2748	+	1.51791i	0.994018	+	0.0825635i
$339$	−3.14680			−0.170911
$340$	−4.72335	−	0.790096i	−0.256159	−	0.0428490i
$341$		−	3.16423i		−	0.171352i
$342$	4.34237	+	0.360678i	0.234808	+	0.0195033i
$343$	−14.4287	+	11.6109i	−0.779077	+	0.626928i
$344$	−0.447984	+	1.76467i	−0.0241537	+	0.0951448i
$345$	−3.94362			−0.212317
$346$	2.55843	−	30.8021i	0.137542	−	1.65593i
$347$		−	14.2548i		−	0.765240i	−0.923906	−	0.382620i	$-0.875022\pi$
$347$		−	14.2548i		−	0.765240i	0.923906	−	0.382620i	$-0.124978\pi$
$348$	6.31280	+	1.05597i	0.338402	+	0.0566060i
$349$		−	6.69632i		−	0.358446i	−0.983809	−	0.179223i	$-0.942642\pi$
$349$		−	6.69632i		−	0.358446i	0.983809	−	0.179223i	$-0.0573583\pi$
$350$	−1.38995	+	3.47391i	−0.0742957	+	0.185688i
$351$		−	0.182384i		−	0.00973493i
$352$	1.26705	−	2.88087i	0.0675338	−	0.153551i
$353$			18.6741i			0.993920i	0.867773	+	0.496960i	$0.165551\pi$
$353$			18.6741i			0.993920i	−0.867773	+	0.496960i	$0.834449\pi$
$354$	12.4018	+	1.03010i	0.659150	+	0.0547492i
$355$	1.36136			0.0722537
$356$	2.64500	−	15.8123i	0.140185	−	0.838051i
$357$	6.05649	+	1.85845i	0.320544	+	0.0983594i
$358$	2.14853	−	25.8671i	0.113553	−	1.36712i
$359$		−	20.9659i		−	1.10654i	−0.833003	−	0.553269i	$-0.813380\pi$
$359$		−	20.9659i		−	1.10654i	0.833003	−	0.553269i	$-0.186620\pi$
$360$	0.695955	−	2.74147i	0.0366800	−	0.144488i
$361$	−9.50688			−0.500362
$362$	−1.49197	+	17.9625i	−0.0784164	+	0.944090i
$363$	−10.6905			−0.561104
$364$	0.863274	+	0.431447i	0.0452479	+	0.0226139i
$365$	−10.1087			−0.529115
$366$	1.68319	−	20.2647i	0.0879820	−	1.05925i
$367$	−21.4633			−1.12038			−0.560189	−	0.828365i	$-0.689271\pi$
$367$	−21.4633			−1.12038			−0.560189	+	0.828365i	$0.689271\pi$
$368$	−5.13369	+	14.9157i	−0.267612	+	0.777536i
$369$			9.64809i			0.502260i
$370$	−0.583179	+	7.02115i	−0.0303180	+	0.365012i
$371$	−5.41013	+	17.6311i	−0.280880	+	0.915360i
$372$	−11.2191	−	1.87666i	−0.581681	−	0.0973005i
$373$	−36.3356			−1.88139			−0.940693	−	0.339260i	$-0.889823\pi$
$373$	−36.3356			−1.88139			−0.940693	+	0.339260i	$0.889823\pi$
$374$	−1.87751	−	0.155947i	−0.0970838	−	0.00806381i
$375$		−	1.00000i		−	0.0516398i
$376$	−9.96985	−	2.53097i	−0.514156	−	0.130525i
$377$		−	0.583675i		−	0.0300608i
$378$	−1.38995	+	3.47391i	−0.0714911	+	0.178679i
$379$		−	11.1047i		−	0.570412i	−0.958466	−	0.285206i	$-0.907938\pi$
$379$		−	11.1047i		−	0.570412i	0.958466	−	0.285206i	$-0.0920621\pi$
$380$	1.01665	−	6.07774i	0.0521531	−	0.311781i
$381$			11.8445i			0.606814i
$382$	−2.51288	+	30.2537i	−0.128570	+	1.54791i
$383$	23.6321			1.20754			0.603772	−	0.797157i	$-0.293664\pi$
$383$	23.6321			1.20754			0.603772	+	0.797157i	$0.293664\pi$
$384$	−9.46293	−	6.20104i	−0.482903	−	0.316446i
$385$	−0.431803	+	1.40721i	−0.0220067	+	0.0717178i
$386$	7.44034	+	0.617997i	0.378704	+	0.0314552i
$387$			0.643697i			0.0327209i
$388$	0.146962	−	0.878568i	0.00746087	−	0.0446025i
$389$	−22.7913			−1.15557			−0.577783	−	0.816190i	$-0.696082\pi$
$389$	−22.7913			−1.15557			−0.577783	+	0.816190i	$0.696082\pi$
$390$	−0.257045	−	0.0213502i	−0.0130160	−	0.00108111i
$391$	9.44293			0.477549
$392$	−13.1549	−	14.7969i	−0.664425	−	0.747355i
$393$	16.6337			0.839059
$394$	−11.9064	−	0.988947i	−0.599834	−	0.0498224i
$395$	13.0596			0.657098
$396$	0.183576	−	1.09745i	0.00922504	−	0.0551491i
$397$			10.5426i			0.529118i	0.964370	+	0.264559i	$0.0852264\pi$
$397$			10.5426i			0.529118i	−0.964370	+	0.264559i	$0.914774\pi$
$398$	−26.1154	−	2.16916i	−1.30905	−	0.108730i
$399$	−2.39134	+	7.79316i	−0.119717	+	0.390146i
$400$	−3.78225	−	1.30177i	−0.189112	−	0.0650886i
$401$	−28.1602			−1.40625			−0.703126	−	0.711065i	$-0.748213\pi$
$401$	−28.1602			−1.40625			−0.703126	+	0.711065i	$0.748213\pi$
$402$	−1.17872	+	14.1912i	−0.0587895	+	0.707792i
$403$			1.03730i			0.0516717i
$404$	−4.24138	+	25.3558i	−0.211017	+	1.26150i
$405$		−	1.00000i		−	0.0496904i
$406$	−4.44818	+	11.1174i	−0.220759	+	0.551747i
$407$			2.77163i			0.137384i
$408$	−1.66645	+	6.56441i	−0.0825017	+	0.324986i
$409$		−	23.3091i		−	1.15256i	−0.817253	−	0.576280i	$-0.804504\pi$
$409$		−	23.3091i		−	1.15256i	0.817253	−	0.576280i	$-0.195496\pi$
$410$	13.5976	+	1.12942i	0.671540	+	0.0557783i
$411$	−9.88658			−0.487669
$412$	28.2142	+	4.71952i	1.39001	+	0.232514i
$413$	−6.82970	+	22.2573i	−0.336068	+	1.09521i
$414$	−0.461647	+	5.55798i	−0.0226887	+	0.273160i
$415$			9.45272i			0.464016i
$416$	−0.415365	+	0.944413i	−0.0203650	+	0.0463037i
$417$	−20.5861			−1.00811
$418$	0.200664	−	2.41588i	0.00981478	−	0.118164i
$419$	22.9252			1.11997			0.559984	−	0.828503i	$-0.310807\pi$
$419$	22.9252			1.11997			0.559984	+	0.828503i	$0.310807\pi$
$420$	4.73328	+	2.36560i	0.230960	+	0.115429i
$421$	−30.2880			−1.47614			−0.738072	−	0.674722i	$-0.764264\pi$
$421$	−30.2880			−1.47614			−0.738072	+	0.674722i	$0.764264\pi$
$422$	2.04222	−	24.5872i	0.0994137	−	1.19689i
$423$	−3.63668			−0.176822
$424$	−19.1097	−	4.85122i	−0.928048	−	0.235596i
$425$			2.39449i			0.116150i
$426$	0.159364	−	1.91865i	0.00772120	−	0.0929590i
$427$	36.3687	+	11.1598i	1.76000	+	0.540060i
$428$	−6.04596	+	36.1439i	−0.292242	+	1.74708i
$429$	−0.101469			−0.00489899
$430$	0.907200	+	0.0753523i	0.0437491	+	0.00363381i
$431$			17.6787i			0.851551i	0.904829	+	0.425776i	$0.139999\pi$
$431$			17.6787i			0.851551i	−0.904829	+	0.425776i	$0.860001\pi$
$432$	−3.78225	−	1.30177i	−0.181973	−	0.0626316i
$433$			30.2797i			1.45515i	0.686029	+	0.727574i	$0.259352\pi$
$433$			30.2797i			1.45515i	−0.686029	+	0.727574i	$0.740648\pi$
$434$	7.90527	−	19.7578i	0.379465	−	0.948403i
$435$		−	3.20026i		−	0.153441i
$436$	−7.96513	−	1.33236i	−0.381460	−	0.0638086i
$437$			12.1506i			0.581244i
$438$	−1.18335	+	14.2468i	−0.0565425	+	0.680740i
$439$	−3.51474			−0.167749			−0.0838747	−	0.996476i	$-0.526730\pi$
$439$	−3.51474			−0.167749			−0.0838747	+	0.996476i	$0.526730\pi$
$440$	−1.52522	−	0.387195i	−0.0727119	−	0.0184588i
$441$	−5.79523	−	3.92624i	−0.275963	−	0.186964i
$442$	0.615490	+	0.0511228i	0.0292759	+	0.00243166i
$443$		−	3.34004i		−	0.158690i	−0.996847	−	0.0793450i	$-0.974717\pi$
$443$		−	3.34004i		−	0.158690i	0.996847	−	0.0793450i	$-0.0252829\pi$
$444$	9.82706	+	1.64382i	0.466372	+	0.0780121i
$445$	−8.01600			−0.379995
$446$	−16.7957	−	1.39506i	−0.795300	−	0.0660578i
$447$	−7.28607			−0.344619
$448$	15.1089	−	14.8230i	0.713830	−	0.700319i
$449$	−30.3020			−1.43004			−0.715019	−	0.699105i	$-0.753582\pi$
$449$	−30.3020			−1.43004			−0.715019	+	0.699105i	$0.753582\pi$
$450$	−1.40936	−	0.117062i	−0.0664379	−	0.00551835i
$451$	5.36772			0.252756
$452$	6.20736	+	1.03833i	0.291970	+	0.0488391i
$453$			15.1807i			0.713252i
$454$	−3.01315	−	0.250273i	−0.141414	−	0.0117459i
$455$	0.141555	−	0.461313i	0.00663618	−	0.0216267i
$456$	−8.44671	−	2.14430i	−0.395554	−	0.100416i
$457$	−7.65632			−0.358148			−0.179074	−	0.983836i	$-0.557310\pi$
$457$	−7.65632			−0.358148			−0.179074	+	0.983836i	$0.557310\pi$
$458$	−0.831760	+	10.0139i	−0.0388656	+	0.467920i
$459$			2.39449i			0.111765i
$460$	7.77915	+	1.30125i	0.362705	+	0.0606713i
$461$		−	7.75351i		−	0.361117i	−0.983564	−	0.180559i	$-0.942209\pi$
$461$		−	7.75351i		−	0.361117i	0.983564	−	0.180559i	$-0.0577905\pi$
$462$	1.93271	+	0.773297i	0.0899179	+	0.0359770i
$463$			21.4187i			0.995410i	0.867346	+	0.497705i	$0.165824\pi$
$463$			21.4187i			0.995410i	−0.867346	+	0.497705i	$0.834176\pi$
$464$	−12.1042	−	4.16600i	−0.561921	−	0.193402i
$465$			5.68747i			0.263750i
$466$	15.3114	+	1.27177i	0.709289	+	0.0589138i
$467$	11.8414			0.547954			0.273977	−	0.961736i	$-0.411661\pi$
$467$	11.8414			0.547954			0.273977	+	0.961736i	$0.411661\pi$
$468$	−0.0601803	+	0.359769i	−0.00278183	+	0.0166303i
$469$	−25.4686	−	7.81510i	−1.17603	−	0.360868i
$470$	−0.425717	+	5.12540i	−0.0196369	+	0.236417i
$471$			10.7177i			0.493846i
$472$	−24.1239	−	6.12414i	−1.11039	−	0.281886i
$473$	0.358121			0.0164664
$474$	1.52878	−	18.4056i	0.0702191	−	0.845399i
$475$	−3.08109			−0.141370
$476$	−11.3338	−	5.66439i	−0.519483	−	0.259627i
$477$	−6.97060			−0.319162
$478$	1.79995	−	21.6704i	0.0823276	−	0.991179i
$479$	−19.5650			−0.893948			−0.446974	−	0.894547i	$-0.647498\pi$
$479$	−19.5650			−0.893948			−0.446974	+	0.894547i	$0.647498\pi$
$480$	−2.27742	+	5.17816i	−0.103950	+	0.236350i
$481$		−	0.908600i		−	0.0414286i
$482$	0.0607053	−	0.730858i	0.00276505	−	0.0332897i
$483$	−9.97479	−	3.06078i	−0.453868	−	0.139270i
$484$	21.0880	+	3.52748i	0.958543	+	0.160340i
$485$	−0.445387			−0.0202240
$486$	−1.40936	−	0.117062i	−0.0639299	−	0.00531004i
$487$		−	2.69121i		−	0.121950i	−0.998139	−	0.0609752i	$-0.980579\pi$
$487$		−	2.69121i		−	0.121950i	0.998139	−	0.0609752i	$-0.0194210\pi$
$488$	−10.0069	+	39.4187i	−0.452991	+	1.78440i
$489$		−	20.7486i		−	0.938284i
$490$	−6.21188	+	7.70795i	−0.280624	+	0.348210i
$491$		−	0.816644i		−	0.0368546i	−0.999830	−	0.0184273i	$-0.994134\pi$
$491$		−	0.816644i		−	0.0368546i	0.999830	−	0.0184273i	$-0.00586593\pi$
$492$	3.18353	−	19.0318i	0.143525	−	0.858018i
$493$			7.66297i			0.345123i
$494$	−0.0657819	+	0.791978i	−0.00295967	+	0.0356328i
$495$	−0.556350			−0.0250061
$496$	21.5114	+	7.40379i	0.965891	+	0.332440i
$497$	3.44337	+	1.05660i	0.154456	+	0.0473951i
$498$	13.3223	+	1.10655i	0.596986	+	0.0495858i
$499$		−	6.19049i		−	0.277124i	−0.990354	−	0.138562i	$-0.955752\pi$
$499$		−	6.19049i		−	0.277124i	0.990354	−	0.138562i	$-0.0442481\pi$
$500$	−0.329965	+	1.97259i	−0.0147565	+	0.0882170i
$501$	8.37483			0.374160
$502$	28.0433	+	2.32928i	1.25163	+	0.103961i
$503$	23.4882			1.04729			0.523643	−	0.851938i	$-0.324573\pi$
$503$	23.4882			1.04729			0.523643	+	0.851938i	$0.324573\pi$
$504$	3.88806	−	6.39398i	0.173188	−	0.284810i
$505$	12.8540			0.571997
$506$	3.09218	+	0.256838i	0.137464	+	0.0114178i
$507$	−12.9667			−0.575873
$508$	3.90828	−	23.3644i	0.173402	−	1.03663i
$509$		−	31.9990i		−	1.41833i	−0.705042	−	0.709165i	$-0.749072\pi$
$509$		−	31.9990i		−	1.41833i	0.705042	−	0.709165i	$-0.250928\pi$
$510$	3.37469	+	0.280303i	0.149434	+	0.0124120i
$511$	−25.5685	−	7.84575i	−1.13108	−	0.347075i
$512$	16.6204	+	15.3546i	0.734524	+	0.678582i
$513$	−3.08109			−0.136033
$514$	3.52651	−	42.4572i	0.155548	−	1.87271i
$515$		−	14.3031i		−	0.630270i
$516$	0.212397	−	1.26975i	0.00935027	−	0.0558977i
$517$			2.02327i			0.0889834i
$518$	−6.92443	+	17.3063i	−0.304242	+	0.760396i
$519$			21.8554i			0.959345i
$520$	0.500000	+	0.126931i	0.0219264	+	0.00556629i
$521$		−	38.3707i		−	1.68105i	−0.541773	−	0.840525i	$-0.682247\pi$
$521$		−	38.3707i		−	1.68105i	0.541773	−	0.840525i	$-0.317753\pi$
$522$	−4.51031	−	0.374628i	−0.197411	−	0.0163970i
$523$	27.0855			1.18437			0.592183	−	0.805804i	$-0.298266\pi$
$523$	27.0855			1.18437			0.592183	+	0.805804i	$0.298266\pi$
$524$	−32.8115	−	5.48854i	−1.43338	−	0.239768i
$525$	0.776136	−	2.52935i	0.0338733	−	0.110390i
$526$	0.520219	−	6.26315i	0.0226826	−	0.273086i
$527$		−	13.6186i		−	0.593234i
$528$	−0.724242	+	2.10425i	−0.0315186	+	0.0915759i
$529$	7.44790			0.323822
$530$	−0.815991	+	9.82408i	−0.0354444	+	0.426731i
$531$	−8.79962			−0.381871
$532$	7.28862	−	14.5837i	0.316002	−	0.632282i
$533$	−1.75966			−0.0762192
$534$	−0.938368	+	11.2974i	−0.0406072	+	0.488888i
$535$	18.3230			0.792174
$536$	7.00774	−	27.6045i	0.302688	−	1.19233i
$537$			18.3538i			0.792023i
$538$	−0.983632	+	11.8424i	−0.0424074	+	0.510561i
$539$	−2.18436	+	3.22418i	−0.0940872	+	0.138875i
$540$	−0.329965	+	1.97259i	−0.0141994	+	0.0848869i
$541$	12.3048			0.529024			0.264512	−	0.964382i	$-0.414789\pi$
$541$	12.3048			0.529024			0.264512	+	0.964382i	$0.414789\pi$
$542$	−40.5515	−	3.36822i	−1.74183	−	0.144677i
$543$		−	12.7452i		−	0.546947i
$544$	5.45326	−	12.3990i	0.233806	−	0.531604i
$545$			4.03790i			0.172964i
$546$	−0.633585	−	0.253504i	−0.0271149	−	0.0108490i
$547$			7.41113i			0.316877i	0.987369	+	0.158438i	$0.0506460\pi$
$547$			7.41113i			0.316877i	−0.987369	+	0.158438i	$0.949354\pi$
$548$	19.5022	+	3.26222i	0.833093	+	0.139355i
$549$			14.3787i			0.613667i
$550$	−0.0651274	+	0.784098i	−0.00277704	+	0.0334341i
$551$	−9.86028			−0.420062
$552$	2.74458	−	10.8113i	0.116817	−	0.460159i
$553$	33.0322	+	10.1360i	1.40467	+	0.431026i
$554$	−5.54051	−	0.460196i	−0.235394	−	0.0195519i
$555$		−	4.98180i		−	0.211466i
$556$	40.6081	+	6.79270i	1.72217	+	0.288075i
$557$	−0.317738			−0.0134630			−0.00673149	−	0.999977i	$-0.502143\pi$
$557$	−0.317738			−0.0134630			−0.00673149	+	0.999977i	$0.502143\pi$
$558$	8.01569	+	0.665786i	0.339331	+	0.0281850i
$559$	−0.117400			−0.00496549
$560$	−8.55627	−	6.22818i	−0.361569	−	0.263188i
$561$	1.33217			0.0562444
$562$	25.1786	+	2.09134i	1.06210	+	0.0882179i
$563$	−2.50413			−0.105537			−0.0527683	−	0.998607i	$-0.516804\pi$
$563$	−2.50413			−0.105537			−0.0527683	+	0.998607i	$0.516804\pi$
$564$	7.17370	+	1.19998i	0.302067	+	0.0505282i
$565$		−	3.14680i		−	0.132387i
$566$	6.11844	+	0.508200i	0.257177	+	0.0213612i
$567$	0.776136	−	2.52935i	0.0325946	−	0.106223i
$568$	−0.947448	+	3.73214i	−0.0397540	+	0.156597i
$569$	25.4990			1.06897			0.534487	−	0.845177i	$-0.320505\pi$
$569$	25.4990			1.06897			0.534487	+	0.845177i	$0.320505\pi$
$570$	−0.360678	+	4.34237i	−0.0151072	+	0.181882i
$571$		−	43.8357i		−	1.83447i	−0.398350	−	0.917233i	$-0.630417\pi$
$571$		−	43.8357i		−	1.83447i	0.398350	−	0.917233i	$-0.369583\pi$
$572$	0.200158	+	0.0334813i	0.00836902	+	0.00139992i
$573$		−	21.4663i		−	0.896766i
$574$	33.5166	+	13.4103i	1.39896	+	0.559736i
$575$		−	3.94362i		−	0.164460i
$576$	7.03129	+	3.81588i	0.292971	+	0.158995i
$577$			4.18046i			0.174035i	0.996207	+	0.0870175i	$0.0277336\pi$
$577$			4.18046i			0.174035i	−0.996207	+	0.0870175i	$0.972266\pi$
$578$	15.8785	+	1.31887i	0.660457	+	0.0548578i
$579$	−5.27923			−0.219398
$580$	−1.05597	+	6.31280i	−0.0438468	+	0.262125i
$581$	−7.33659	+	23.9092i	−0.304373	+	0.991922i
$582$	−0.0521379	+	0.627711i	−0.00216119	+	0.0260195i
$583$			3.87810i			0.160614i
$584$	7.03522	−	27.7128i	0.291119	−	1.14676i
$585$	0.182384			0.00754065
$586$	0.0626405	−	0.754157i	0.00258766	−	0.0311540i
$587$	−34.7799			−1.43552			−0.717761	−	0.696290i	$-0.754833\pi$
$587$	−34.7799			−1.43552			−0.717761	+	0.696290i	$0.754833\pi$
$588$	10.1361	+	9.65709i	0.418006	+	0.398252i
$589$	17.5236			0.722048
$590$	−1.03010	+	12.4018i	−0.0424086	+	0.510576i
$591$	8.44807			0.347507
$592$	−18.8424	−	6.48517i	−0.774417	−	0.266539i
$593$			5.30521i			0.217859i	0.994049	+	0.108929i	$0.0347423\pi$
$593$			5.30521i			0.217859i	−0.994049	+	0.108929i	$0.965258\pi$
$594$	−0.0651274	+	0.784098i	−0.00267221	+	0.0321719i
$595$	−1.85845	+	6.05649i	−0.0761888	+	0.248292i
$596$	14.3725	+	2.40415i	0.588719	+	0.0984777i
$597$	18.5300			0.758382
$598$	−1.01369	−	0.0841970i	−0.0414527	−	0.00344307i
$599$			1.76214i			0.0719991i	0.999352	+	0.0359996i	$0.0114615\pi$
$599$			1.76214i			0.0719991i	−0.999352	+	0.0359996i	$0.988539\pi$
$600$	2.74147	+	0.695955i	0.111920	+	0.0284122i
$601$		−	20.8508i		−	0.850523i	−0.905071	−	0.425262i	$-0.860182\pi$
$601$		−	20.8508i		−	0.850523i	0.905071	−	0.425262i	$-0.139818\pi$
$602$	2.23614	+	0.894703i	0.0911384	+	0.0364654i
$603$		−	10.0692i		−	0.410051i
$604$	5.00910	−	29.9454i	0.203817	−	1.21846i
$605$		−	10.6905i		−	0.434630i
$606$	1.50472	−	18.1160i	0.0611250	−	0.735911i
$607$	5.84505			0.237243			0.118622	−	0.992940i	$-0.462152\pi$
$607$	5.84505			0.237243			0.118622	+	0.992940i	$0.462152\pi$
$608$	15.9544	+	7.01695i	0.647036	+	0.284575i
$609$	2.48383	−	8.09457i	0.100650	−	0.328008i
$610$	20.2647	+	1.68319i	0.820495	+	0.0681505i
$611$		−	0.663273i		−	0.0268331i
$612$	0.790096	−	4.72335i	0.0319377	−	0.190930i
$613$	10.6913			0.431816			0.215908	−	0.976414i	$-0.430729\pi$
$613$	10.6913			0.431816			0.215908	+	0.976414i	$0.430729\pi$
$614$	−28.8662	−	2.39764i	−1.16495	−	0.0967607i
$615$	−9.64809			−0.389049
$616$	−3.55729	−	2.16313i	−0.143327	−	0.0871549i
$617$	31.3037			1.26024			0.630120	−	0.776497i	$-0.283006\pi$
$617$	31.3037			1.26024			0.630120	+	0.776497i	$0.283006\pi$
$618$	−20.1582	−	1.67435i	−0.810883	−	0.0673522i
$619$	−13.7799			−0.553861			−0.276930	−	0.960890i	$-0.589317\pi$
$619$	−13.7799			−0.553861			−0.276930	+	0.960890i	$0.589317\pi$
$620$	1.87666	−	11.2191i	0.0753687	−	0.450568i
$621$		−	3.94362i		−	0.158252i
$622$	41.8014	+	3.47203i	1.67608	+	0.139216i
$623$	−20.2753	−	6.22150i	−0.812312	−	0.249259i
$624$	0.237422	−	0.689821i	0.00950450	−	0.0276149i
$625$	1.00000			0.0400000
$626$	−1.36980	+	16.4916i	−0.0547481	+	0.659137i
$627$			1.71417i			0.0684572i
$628$	3.53647	−	21.1417i	0.141120	−	0.843645i
$629$			11.9288i			0.475634i
$630$	−3.47391	−	1.38995i	−0.138404	−	0.0553767i
$631$			15.3886i			0.612610i	0.951933	+	0.306305i	$0.0990928\pi$
$631$			15.3886i			0.612610i	−0.951933	+	0.306305i	$0.900907\pi$
$632$	−9.08887	+	35.8024i	−0.361536	+	1.42414i
$633$			17.4456i			0.693402i
$634$	−22.6185	−	1.87870i	−0.898295	−	0.0746126i
$635$	−11.8445			−0.470036
$636$	13.7502	+	2.30005i	0.545229	+	0.0912030i
$637$	0.716082	−	1.05696i	0.0283722	−	0.0418781i
$638$	−0.208424	+	2.50931i	−0.00825160	+	0.0993447i
$639$			1.36136i			0.0538547i
$640$	6.20104	−	9.46293i	0.245118	−	0.374055i
$641$	−4.57385			−0.180656			−0.0903282	−	0.995912i	$-0.528792\pi$
$641$	−4.57385			−0.180656			−0.0903282	+	0.995912i	$0.528792\pi$
$642$	2.14493	−	25.8238i	0.0846536	−	1.01918i
$643$	40.9959			1.61672			0.808360	−	0.588689i	$-0.200356\pi$
$643$	40.9959			1.61672			0.808360	+	0.588689i	$0.200356\pi$
$644$	18.6662	+	9.32900i	0.735553	+	0.367614i
$645$	−0.643697			−0.0253455
$646$	0.863639	−	10.3977i	0.0339794	−	0.409093i
$647$	6.26797			0.246419			0.123210	−	0.992381i	$-0.460681\pi$
$647$	6.26797			0.246419			0.123210	+	0.992381i	$0.460681\pi$
$648$	2.74147	+	0.695955i	0.107695	+	0.0273397i
$649$			4.89567i			0.192172i
$650$	0.0213502	−	0.257045i	0.000837424	−	0.0100821i
$651$	−4.41425	+	14.3856i	−0.173008	+	0.563816i
$652$	−6.84630	+	40.9285i	−0.268122	+	1.60288i
$653$	27.6655			1.08263			0.541316	−	0.840819i	$-0.317926\pi$
$653$	27.6655			1.08263			0.541316	+	0.840819i	$0.317926\pi$
$654$	5.69085	+	0.472684i	0.222530	+	0.0184834i
$655$			16.6337i			0.649932i
$656$	−12.5596	+	36.4915i	−0.490371	+	1.42475i
$657$		−	10.1087i		−	0.394379i
$658$	−5.05479	+	12.6335i	−0.197056	+	0.492506i
$659$			33.8406i			1.31824i	0.752036	+	0.659122i	$0.229072\pi$
$659$			33.8406i			1.31824i	−0.752036	+	0.659122i	$0.770928\pi$
$660$	1.09745	+	0.183576i	0.0427183	+	0.00714569i
$661$		−	15.9944i		−	0.622109i	−0.950392	−	0.311054i	$-0.899318\pi$
$661$		−	15.9944i		−	0.622109i	0.950392	−	0.311054i	$-0.100682\pi$
$662$	1.28370	−	15.4551i	0.0498925	−	0.600678i
$663$	−0.436716			−0.0169606
$664$	−25.9143	−	6.57866i	−1.00567	−	0.255302i
$665$	−7.79316	−	2.39134i	−0.302206	−	0.0927324i
$666$	−7.02115	−	0.583179i	−0.272064	−	0.0225977i
$667$		−	12.6206i		−	0.488671i
$668$	−16.5201	−	2.76340i	−0.639183	−	0.106919i
$669$	11.9173			0.460748
$670$	−14.1912	−	1.17872i	−0.548254	−	0.0455381i
$671$	7.99958			0.308820
$672$	−9.77936	+	11.3298i	−0.377247	+	0.437056i
$673$	1.91279			0.0737326			0.0368663	−	0.999320i	$-0.488262\pi$
$673$	1.91279			0.0737326			0.0368663	+	0.999320i	$0.488262\pi$
$674$	−11.1045	−	0.922339i	−0.427728	−	0.0355272i
$675$	1.00000			0.0384900
$676$	25.5781	+	4.27857i	0.983773	+	0.164560i
$677$			7.67384i			0.294930i	0.989067	+	0.147465i	$0.0471113\pi$
$677$			7.67384i			0.294930i	−0.989067	+	0.147465i	$0.952889\pi$
$678$	−4.43498	−	0.368371i	−0.170324	−	0.0141472i
$679$	−1.12654	−	0.345681i	−0.0432327	−	0.0132660i
$680$	−6.56441	−	1.66645i	−0.251733	−	0.0639056i
$681$	2.13795			0.0819265
$682$	0.370410	−	4.45954i	0.0141837	−	0.170764i
$683$		−	21.8303i		−	0.835314i	−0.908605	−	0.417657i	$-0.862851\pi$
$683$		−	21.8303i		−	0.835314i	0.908605	−	0.417657i	$-0.137149\pi$
$684$	6.07774	+	1.01665i	0.232388	+	0.0388726i
$685$		−	9.88658i		−	0.377747i
$686$	−21.6944	+	14.6748i	−0.828298	+	0.560288i
$687$		−	7.10530i		−	0.271084i
$688$	−0.837947	+	2.43462i	−0.0319464	+	0.0928190i
$689$		−	1.27132i		−	0.0484336i
$690$	−5.55798	−	0.461647i	−0.211588	−	0.0175746i
$691$	−19.9109			−0.757446			−0.378723	−	0.925510i	$-0.623637\pi$
$691$	−19.9109			−0.757446			−0.378723	+	0.925510i	$0.623637\pi$
$692$	7.21151	−	43.1118i	0.274140	−	1.63886i
$693$	−1.40721	−	0.431803i	−0.0534553	−	0.0164029i
$694$	1.66870	−	20.0902i	0.0633429	−	0.762614i
$695$		−	20.5861i		−	0.780877i
$696$	8.77340	+	2.22723i	0.332555	+	0.0844231i
$697$	23.1022			0.875059
$698$	0.783884	−	9.43752i	0.0296704	−	0.357215i
$699$	−10.8641			−0.410918
$700$	−2.36560	+	4.73328i	−0.0894111	+	0.178901i
$701$	41.1901			1.55573			0.777864	−	0.628433i	$-0.216303\pi$
$701$	41.1901			1.55573			0.777864	+	0.628433i	$0.216303\pi$
$702$	0.0213502	−	0.257045i	0.000805811	−	0.00970152i
$703$	−15.3494			−0.578912
$704$	2.12296	−	3.91186i	0.0800122	−	0.147434i
$705$		−	3.63668i		−	0.136965i
$706$	−2.18602	+	26.3185i	−0.0822720	+	0.990509i
$707$	32.5124	+	9.97647i	1.22275	+	0.375204i
$708$	17.3581	+	2.90357i	0.652356	+	0.109123i
$709$	−5.89330			−0.221327			−0.110664	−	0.993858i	$-0.535298\pi$
$709$	−5.89330			−0.221327			−0.110664	+	0.993858i	$0.535298\pi$
$710$	1.91865	+	0.159364i	0.0720057	+	0.00598082i
$711$			13.0596i			0.489772i
$712$	5.57877	−	21.9756i	0.209073	−	0.823571i
$713$			22.4292i			0.839980i
$714$	8.31823	+	3.32820i	0.311302	+	0.124555i
$715$		−	0.101469i		−	0.00379474i
$716$	6.05610	−	36.2045i	0.226327	−	1.35303i
$717$			15.3760i			0.574228i
$718$	2.45431	−	29.5485i	0.0915940	−	1.10274i
$719$	35.2121			1.31319			0.656595	−	0.754243i	$-0.271996\pi$
$719$	35.2121			1.31319			0.656595	+	0.754243i	$0.271996\pi$
$720$	1.30177	−	3.78225i	0.0485142	−	0.140956i
$721$	11.1012	−	36.1776i	0.413429	−	1.34732i
$722$	−13.3986	−	1.11289i	−0.498645	−	0.0414176i
$723$			0.518574i			0.0192860i
$724$	−4.20546	+	25.1410i	−0.156295	+	0.934359i
$725$	3.20026			0.118855
$726$	−15.0667	−	1.25145i	−0.559179	−	0.0464456i
$727$	−44.9984			−1.66890			−0.834449	−	0.551085i	$-0.814214\pi$
$727$	−44.9984			−1.66890			−0.834449	+	0.551085i	$0.814214\pi$
$728$	1.16616	+	0.709120i	0.0432207	+	0.0262817i
$729$	1.00000			0.0370370
$730$	−14.2468	−	1.18335i	−0.527299	−	0.0437976i
$731$	1.54132			0.0570079
$732$	4.74445	−	28.3633i	0.175360	−	1.04834i
$733$		−	4.38540i		−	0.161978i	−0.996715	−	0.0809892i	$-0.974192\pi$
$733$		−	4.38540i		−	0.161978i	0.996715	−	0.0809892i	$-0.0258079\pi$
$734$	−30.2496	−	2.51254i	−1.11653	−	0.0927395i
$735$	3.92624	−	5.79523i	0.144821	−	0.213760i
$736$	−8.98128	+	20.4207i	−0.331054	+	0.752716i
$737$	−5.60203			−0.206353
$738$	−1.12942	+	13.5976i	−0.0415747	+	0.500536i
$739$		−	29.0684i		−	1.06930i	−0.845075	−	0.534648i	$-0.820444\pi$
$739$		−	29.0684i		−	1.06930i	0.845075	−	0.534648i	$-0.179556\pi$
$740$	−1.64382	+	9.82706i	−0.0604279	+	0.361250i
$741$		−	0.561941i		−	0.0206434i
$742$	−9.68875	+	24.2152i	−0.355685	+	0.888969i
$743$			21.0881i			0.773647i	0.922154	+	0.386824i	$0.126428\pi$
$743$			21.0881i			0.773647i	−0.922154	+	0.386824i	$0.873572\pi$
$744$	−15.5920	−	3.95822i	−0.571631	−	0.145115i
$745$		−	7.28607i		−	0.266941i
$746$	−51.2099	−	4.25351i	−1.87493	−	0.155732i
$747$	−9.45272			−0.345857
$748$	−2.62784	−	0.439570i	−0.0960832	−	0.0160723i
$749$	46.3454	+	14.2212i	1.69342	+	0.519630i
$750$	0.117062	−	1.40936i	0.00427450	−	0.0514626i
$751$		−	41.9734i		−	1.53163i	−0.643061	−	0.765815i	$-0.722336\pi$
$751$		−	41.9734i		−	1.53163i	0.643061	−	0.765815i	$-0.277664\pi$
$752$	−13.7548	−	4.73414i	−0.501587	−	0.172636i
$753$	−19.8979			−0.725119
$754$	0.0683261	−	0.822608i	0.00248829	−	0.0299576i
$755$	−15.1807			−0.552483
$756$	−2.36560	+	4.73328i	−0.0860359	+	0.172148i
$757$	3.52848			0.128245			0.0641224	−	0.997942i	$-0.479575\pi$
$757$	3.52848			0.128245			0.0641224	+	0.997942i	$0.479575\pi$
$758$	1.29994	−	15.6506i	0.0472160	−	0.568455i
$759$	−2.19403			−0.0796383
$760$	2.14430	−	8.44671i	0.0777819	−	0.306394i
$761$		−	43.3157i		−	1.57019i	−0.619374	−	0.785096i	$-0.712613\pi$
$761$		−	43.3157i		−	1.57019i	0.619374	−	0.785096i	$-0.287387\pi$
$762$	−1.38654	+	16.6932i	−0.0502292	+	0.604731i
$763$	−3.13396	+	10.2133i	−0.113457	+	0.369745i
$764$	−7.08311	+	42.3442i	−0.256258	+	1.53196i
$765$	−2.39449			−0.0865728
$766$	33.3061	+	2.76642i	1.20340	+	0.0999548i
$767$		−	1.60491i		−	0.0579499i
$768$	−12.6108	−	9.84725i	−0.455052	−	0.355332i
$769$			36.5255i			1.31714i	0.752518	+	0.658572i	$0.228839\pi$
$769$			36.5255i			1.31714i	−0.752518	+	0.658572i	$0.771161\pi$
$770$	−0.773297	+	1.93271i	−0.0278677	+	0.0696501i
$771$			30.1252i			1.08493i
$772$	10.4138	+	1.74196i	0.374800	+	0.0626946i
$773$		−	38.9312i		−	1.40026i	−0.714017	−	0.700128i	$-0.753126\pi$
$773$		−	38.9312i		−	1.40026i	0.714017	−	0.700128i	$-0.246874\pi$
$774$	−0.0753523	+	0.907200i	−0.00270848	+	0.0326086i
$775$	−5.68747			−0.204300
$776$	0.309969	−	1.22102i	0.0111273	−	0.0438319i
$777$	3.86655	−	12.6007i	0.138712	−	0.452048i
$778$	−32.1212	−	2.66800i	−1.15160	−	0.0956524i
$779$			29.7266i			1.06507i
$780$	−0.359769	−	0.0601803i	−0.0128818	−	0.00215480i
$781$	0.757395			0.0271017
$782$	13.3085	+	1.10541i	0.475911	+	0.0395293i
$783$	3.20026			0.114368
$784$	−16.8079	−	22.3941i	−0.600282	−	0.799788i
$785$	−10.7177			−0.382531
$786$	23.4429	+	1.94717i	0.836180	+	0.0694533i
$787$	36.3954			1.29736			0.648679	−	0.761063i	$-0.275322\pi$
$787$	36.3954			1.29736			0.648679	+	0.761063i	$0.275322\pi$
$788$	−16.6646	−	2.78756i	−0.593652	−	0.0993029i
$789$			4.44397i			0.158209i
$790$	18.4056	+	1.52878i	0.654843	+	0.0543915i
$791$	2.44235	−	7.95937i	0.0868398	−	0.283003i
$792$	0.387195	−	1.52522i	0.0137584	−	0.0541962i
$793$	−2.62244			−0.0931255
$794$	−1.23414	+	14.8583i	−0.0437979	+	0.527302i
$795$		−	6.97060i		−	0.247222i
$796$	−36.5521	−	6.11424i	−1.29556	−	0.216714i
$797$			34.6389i			1.22697i	0.789705	+	0.613486i	$0.210233\pi$
$797$			34.6389i			1.22697i	−0.789705	+	0.613486i	$0.789767\pi$
$798$	−4.28255	+	10.7034i	−0.151601	+	0.378897i
$799$			8.70799i			0.308066i
$800$	−5.17816	−	2.27742i	−0.183076	−	0.0805191i
$801$		−	8.01600i		−	0.283231i
$802$	−39.6878	−	3.29648i	−1.40143	−	0.116403i
$803$	−5.62400			−0.198467
$804$	−3.32250	+	19.8625i	−0.117175	+	0.700497i
$805$	3.06078	−	9.97479i	0.107878	−	0.351565i
$806$	−0.121429	+	1.46193i	−0.00427714	+	0.0514944i
$807$		−	8.40266i		−	0.295788i
$808$	−8.94583	+	35.2389i	−0.314713	+	1.23970i
$809$	12.5608			0.441615			0.220808	−	0.975317i	$-0.429131\pi$
$809$	12.5608			0.441615			0.220808	+	0.975317i	$0.429131\pi$
$810$	0.117062	−	1.40936i	0.00411314	−	0.0495199i
$811$	37.5695			1.31925			0.659623	−	0.751597i	$-0.270716\pi$
$811$	37.5695			1.31925			0.659623	+	0.751597i	$0.270716\pi$
$812$	−7.57051	+	15.1477i	−0.265673	+	0.531580i
$813$	28.7730			1.00911
$814$	−0.324452	+	3.90622i	−0.0113720	+	0.136913i
$815$	20.7486			0.726791
$816$	−3.11708	+	9.05653i	−0.109119	+	0.317042i
$817$			1.98329i			0.0693865i
$818$	2.72860	−	32.8509i	0.0954034	−	1.14860i
$819$	0.461313	+	0.141555i	0.0161196	+	0.00494632i
$820$	19.0318	+	3.18353i	0.664618	+	0.111174i
$821$	−35.6019			−1.24252			−0.621258	−	0.783606i	$-0.713378\pi$
$821$	−35.6019			−1.24252			−0.621258	+	0.783606i	$0.713378\pi$
$822$	−13.9338	−	1.15734i	−0.485995	−	0.0403669i
$823$			31.6851i			1.10447i	0.833688	+	0.552236i	$0.186225\pi$
$823$			31.6851i			1.10447i	−0.833688	+	0.552236i	$0.813775\pi$
$824$	39.2115	+	9.95432i	1.36600	+	0.346775i
$825$		−	0.556350i		−	0.0193696i
$826$	−12.2310	+	30.5691i	−0.425571	+	1.06363i
$827$			8.15712i			0.283651i	0.989892	+	0.141825i	$0.0452971\pi$
$827$			8.15712i			0.283651i	−0.989892	+	0.141825i	$0.954703\pi$
$828$	−1.30125	+	7.77915i	−0.0452217	+	0.270344i
$829$			39.6902i			1.37850i	0.724524	+	0.689249i	$0.242060\pi$
$829$			39.6902i			1.37850i	−0.724524	+	0.689249i	$0.757940\pi$
$830$	−1.10655	+	13.3223i	−0.0384090	+	0.462423i
$831$	3.93122			0.136373
$832$	−0.695954	+	1.28239i	−0.0241279	+	0.0444590i
$833$	−9.40132	+	13.8766i	−0.325736	+	0.480795i
$834$	−29.0133	−	2.40985i	−1.00465	−	0.0834464i
$835$			8.37483i			0.289823i
$836$	0.565615	−	3.38135i	0.0195622	−	0.116947i
$837$	−5.68747			−0.196588
$838$	32.3098	+	2.68367i	1.11613	+	0.0927057i
$839$	25.0514			0.864871			0.432436	−	0.901665i	$-0.357654\pi$
$839$	25.0514			0.864871			0.432436	+	0.901665i	$0.357654\pi$
$840$	6.39398	+	3.88806i	0.220613	+	0.134151i
$841$	−18.7584			−0.646840
$842$	−42.6866	−	3.54557i	−1.47108	−	0.122188i
$843$	−17.8653			−0.615312
$844$	5.75645	−	34.4131i	0.198145	−	1.18455i
$845$		−	12.9667i		−	0.446069i
$846$	−5.12540	−	0.425717i	−0.176215	−	0.0146365i
$847$	8.29726	−	27.0400i	0.285097	−	0.929104i
$848$	−26.3645	−	9.07413i	−0.905361	−	0.311607i
$849$	−4.34129			−0.148993
$850$	−0.280303	+	3.37469i	−0.00961431	+	0.115751i
$851$		−	19.6463i		−	0.673466i
$852$	0.449202	−	2.68542i	0.0153894	−	0.0920009i
$853$		−	47.1551i		−	1.61456i	−0.590169	−	0.807280i	$-0.700939\pi$
$853$		−	47.1551i		−	1.61456i	0.590169	−	0.807280i	$-0.299061\pi$
$854$	49.9502	+	19.9856i	1.70926	+	0.683892i
$855$		−	3.08109i		−	0.105371i
$856$	−12.7520	+	50.2320i	−0.435855	+	1.71690i
$857$		−	13.6591i		−	0.466587i	−0.972406	−	0.233293i	$-0.925050\pi$
$857$		−	13.6591i		−	0.466587i	0.972406	−	0.233293i	$-0.0749503\pi$
$858$	−0.143007	−	0.0118782i	−0.00488217	−	0.000405515i
$859$	38.2512			1.30511			0.652556	−	0.757740i	$-0.273697\pi$
$859$	38.2512			1.30511			0.652556	+	0.757740i	$0.273697\pi$
$860$	1.26975	+	0.212397i	0.0432982	+	0.00724269i
$861$	−24.4034	−	7.48823i	−0.831666	−	0.255198i
$862$	−2.06950	+	24.9156i	−0.0704874	+	0.848629i
$863$		−	41.4409i		−	1.41067i	−0.708876	−	0.705333i	$-0.750798\pi$
$863$		−	41.4409i		−	1.41067i	0.708876	−	0.705333i	$-0.249202\pi$
$864$	−5.17816	−	2.27742i	−0.176165	−	0.0774795i
$865$	−21.8554			−0.743105
$866$	−3.54460	+	42.6750i	−0.120450	+	1.45015i
$867$	−11.2664			−0.382628
$868$	13.4543	−	26.9204i	0.456667	−	0.913738i
$869$	7.26570			0.246472
$870$	0.374628	−	4.51031i	0.0127011	−	0.152914i
$871$	1.83647			0.0622263
$872$	−11.0698	−	2.81019i	−0.374870	−	0.0951652i
$873$		−	0.445387i		−	0.0150741i
$874$	−1.42238	+	17.1246i	−0.0481126	+	0.579249i
$875$	2.52935	+	0.776136i	0.0855077	+	0.0262382i
$876$	−3.33553	+	19.9404i	−0.112697	+	0.673724i
$877$	30.2930			1.02292			0.511462	−	0.859306i	$-0.329104\pi$
$877$	30.2930			1.02292			0.511462	+	0.859306i	$0.329104\pi$
$878$	−4.95353	−	0.411442i	−0.167174	−	0.0138855i
$879$			0.535106i			0.0180487i
$880$	−2.10425	−	0.724242i	−0.0709344	−	0.0244142i
$881$		−	13.0135i		−	0.438437i	−0.975676	−	0.219219i	$-0.929649\pi$
$881$		−	13.0135i		−	0.438437i	0.975676	−	0.219219i	$-0.0703508\pi$
$882$	−7.70795	−	6.21188i	−0.259540	−	0.209165i
$883$			29.3613i			0.988085i	0.869438	+	0.494043i	$0.164481\pi$
$883$			29.3613i			0.988085i	−0.869438	+	0.494043i	$0.835519\pi$
$884$	0.861462	+	0.144101i	0.0289741	+	0.00484663i
$885$		−	8.79962i		−	0.295796i
$886$	0.390991	−	4.70732i	0.0131356	−	0.158145i
$887$	4.63390			0.155591			0.0777956	−	0.996969i	$-0.475212\pi$
$887$	4.63390			0.155591			0.0777956	+	0.996969i	$0.475212\pi$
$888$	13.6574	+	3.46711i	0.458314	+	0.116348i
$889$	−29.9590	−	9.19296i	−1.00479	−	0.308322i
$890$	−11.2974	−	0.938368i	−0.378691	−	0.0314542i
$891$		−	0.556350i		−	0.0186384i
$892$	−23.5079	−	3.93227i	−0.787102	−	0.131662i
$893$	−11.2050			−0.374960
$894$	−10.2687	−	0.852922i	−0.343437	−	0.0285260i
$895$	−18.3538			−0.613499
$896$	23.0291	−	19.1222i	0.769349	−	0.638829i
$897$	0.719252			0.0240151
$898$	−42.7064	−	3.54721i	−1.42513	−	0.118372i
$899$	−18.2014			−0.607049
$900$	−1.97259	−	0.329965i	−0.0657531	−	0.0109988i
$901$			16.6910i			0.556058i
$902$	7.56505	+	0.628356i	0.251889	+	0.0209220i
$903$	−1.62813	−	0.499596i	−0.0541809	−	0.0166255i
$904$	8.62686	+	2.19003i	0.286925	+	0.0728394i
$905$	12.7452			0.423664
$906$	−1.77708	+	21.3951i	−0.0590396	+	0.710804i
$907$		−	0.827765i		−	0.0274855i	−0.999906	−	0.0137427i	$-0.995625\pi$
$907$		−	0.827765i		−	0.0274855i	0.999906	−	0.0137427i	$-0.00437459\pi$
$908$	−4.21731	−	0.705449i	−0.139956	−	0.0234112i
$909$			12.8540i			0.426341i
$910$	0.253504	−	0.633585i	0.00840356	−	0.0210031i
$911$			17.4184i			0.577096i	0.957465	+	0.288548i	$0.0931725\pi$
$911$			17.4184i			0.577096i	−0.957465	+	0.288548i	$0.906827\pi$
$912$	−11.6534	−	4.01088i	−0.385884	−	0.132813i
$913$			5.25902i			0.174048i
$914$	−10.7905	−	0.896263i	−0.356918	−	0.0296458i
$915$	−14.3787			−0.475344
$916$	−2.34450	+	14.0159i	−0.0774644	+	0.463097i
$917$	−12.9100	+	42.0725i	−0.426326	+	1.38935i
$918$	−0.280303	+	3.37469i	−0.00925138	+	0.111381i
$919$		−	47.0332i		−	1.55148i	−0.631052	−	0.775741i	$-0.717376\pi$
$919$		−	47.0332i		−	1.55148i	0.631052	−	0.775741i	$-0.282624\pi$
$920$	10.8113	+	2.74458i	0.356438	+	0.0904861i
$921$	20.4818			0.674897
$922$	0.907641	−	10.9275i	0.0298916	−	0.359878i
$923$	−0.248291			−0.00817259
$924$	2.63336	+	1.31610i	0.0866313	+	0.0432965i
$925$	4.98180			0.163800
$926$	−2.50731	+	30.1866i	−0.0823953	+	0.991994i
$927$	14.3031			0.469776
$928$	−16.5714	−	7.28834i	−0.543984	−	0.239251i
$929$			13.6389i			0.447478i	0.974649	+	0.223739i	$0.0718264\pi$
$929$			13.6389i			0.447478i	−0.974649	+	0.223739i	$0.928174\pi$
$930$	−0.665786	+	8.01569i	−0.0218320	+	0.262845i
$931$	−17.8556	−	12.0971i	−0.585194	−	0.396466i
$932$	21.4305	+	3.58477i	0.701978	+	0.117423i
$933$	−29.6598			−0.971019
$934$	16.6888	+	1.38618i	0.546074	+	0.0453571i
$935$			1.33217i			0.0435667i
$936$	−0.126931	+	0.500000i	−0.00414887	+	0.0163430i
$937$			40.8581i			1.33478i	0.744710	+	0.667388i	$0.232588\pi$
$937$			40.8581i			1.33478i	−0.744710	+	0.667388i	$0.767412\pi$
$938$	−34.9797	−	13.9957i	−1.14213	−	0.456976i
$939$		−	11.7015i		−	0.381863i
$940$	−1.19998	+	7.17370i	−0.0391390	+	0.233980i
$941$			4.38655i			0.142997i	0.997441	+	0.0714987i	$0.0227782\pi$
$941$			4.38655i			0.142997i	−0.997441	+	0.0714987i	$0.977222\pi$
$942$	−1.25464	+	15.1051i	−0.0408782	+	0.492151i
$943$	−38.0484			−1.23903
$944$	−33.2823	−	11.4551i	−1.08325	−	0.372832i
$945$	2.52935	+	0.776136i	0.0822798	+	0.0252477i
$946$	0.504721	+	0.0419223i	0.0164099	+	0.00136301i
$947$		−	10.7062i		−	0.347905i	−0.984754	−	0.173952i	$-0.944346\pi$
$947$		−	10.7062i		−	0.347905i	0.984754	−	0.173952i	$-0.0556539\pi$
$948$	4.30920	−	25.7612i	0.139956	−	0.836685i
$949$	1.84367			0.0598480
$950$	−4.34237	−	0.360678i	−0.140885	−	0.0117020i
$951$	16.0488			0.520417
$952$	−15.3103	−	9.30991i	−0.496209	−	0.301736i
$953$	−26.6394			−0.862935			−0.431468	−	0.902128i	$-0.642004\pi$
$953$	−26.6394			−0.862935			−0.431468	+	0.902128i	$0.642004\pi$
$954$	−9.82408	−	0.815991i	−0.318066	−	0.0264187i
$955$	21.4663			0.694632
$956$	5.07355	−	30.3306i	0.164090	−	0.980963i
$957$		−	1.78046i		−	0.0575542i
$958$	−27.5742	−	2.29032i	−0.890881	−	0.0739968i
$959$	7.67333	−	25.0066i	0.247785	−	0.807506i
$960$	−3.81588	+	7.03129i	−0.123157	+	0.226934i
$961$	1.34731			0.0434616
$962$	0.106362	−	1.28054i	0.00342926	−	0.0412864i
$963$			18.3230i			0.590452i
$964$	0.171111	−	1.02294i	0.00551112	−	0.0329466i
$965$		−	5.27923i		−	0.169945i
$966$	−13.6998	−	5.48141i	−0.440783	−	0.176361i
$967$			13.1899i			0.424158i	0.977253	+	0.212079i	$0.0680233\pi$
$967$			13.1899i			0.424158i	−0.977253	+	0.212079i	$0.931977\pi$
$968$	29.3076	+	7.44009i	0.941982	+	0.239133i
$969$			7.37763i			0.237004i
$970$	−0.627711	−	0.0521379i	−0.0201546	−	0.00167405i
$971$	−7.56164			−0.242665			−0.121332	−	0.992612i	$-0.538717\pi$
$971$	−7.56164			−0.242665			−0.121332	+	0.992612i	$0.538717\pi$
$972$	−1.97259	−	0.329965i	−0.0632710	−	0.0105836i
$973$	15.9776	−	52.0696i	0.512220	−	1.66927i
$974$	0.315038	−	3.79288i	0.0100945	−	0.121532i
$975$			0.182384i			0.00584096i
$976$	−18.7178	+	54.3837i	−0.599141	+	1.74078i
$977$	−26.1229			−0.835745			−0.417873	−	0.908506i	$-0.637224\pi$
$977$	−26.1229			−0.835745			−0.417873	+	0.908506i	$0.637224\pi$
$978$	2.42887	−	29.2422i	0.0776667	−	0.935064i
$979$	−4.45971			−0.142533
$980$	−9.65709	+	10.1361i	−0.308484	+	0.323786i
$981$	−4.03790			−0.128920
$982$	0.0955979	−	1.15095i	0.00305065	−	0.0367281i
$983$	−33.4569			−1.06711			−0.533555	−	0.845765i	$-0.679144\pi$
$983$	−33.4569			−1.06711			−0.533555	+	0.845765i	$0.679144\pi$
$984$	6.71464	−	26.4499i	0.214055	−	0.843193i
$985$			8.44807i			0.269178i
$986$	−0.897041	+	10.7999i	−0.0285676	+	0.343938i
$987$	2.82256	−	9.19845i	0.0898431	−	0.292790i
$988$	−0.185421	+	1.10848i	−0.00589902	+	0.0352655i
$989$	−2.53849			−0.0807193
$990$	−0.784098	−	0.0651274i	−0.0249203	−	0.00206989i
$991$			58.4657i			1.85722i	0.371053	+	0.928612i	$0.378997\pi$
$991$			58.4657i			1.85722i	−0.371053	+	0.928612i	$0.621003\pi$
$992$	29.4506	+	12.9528i	0.935058	+	0.411251i
$993$			10.9660i			0.347996i
$994$	4.72926	+	1.89222i	0.150003	+	0.0600176i
$995$			18.5300i			0.587440i
$996$	18.6464	+	3.11906i	0.590833	+	0.0988313i
$997$			34.3451i			1.08772i	0.839176	+	0.543860i	$0.183038\pi$
$997$			34.3451i			1.08772i	−0.839176	+	0.543860i	$0.816962\pi$
$998$	0.724670	−	8.72463i	0.0229390	−	0.276173i
$999$	4.98180			0.157617

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	420.2.c.a.391.16	yes	16
3.2	odd	2		1260.2.c.d.811.1		16
4.3	odd	2		420.2.c.b.391.15	yes	16
7.6	odd	2		420.2.c.b.391.16	yes	16
12.11	even	2		1260.2.c.e.811.2		16
21.20	even	2		1260.2.c.e.811.1		16
28.27	even	2	inner	420.2.c.a.391.15	✓	16
84.83	odd	2		1260.2.c.d.811.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.c.a.391.15	✓	16	28.27	even	2	inner
420.2.c.a.391.16	yes	16	1.1	even	1	trivial
420.2.c.b.391.15	yes	16	4.3	odd	2
420.2.c.b.391.16	yes	16	7.6	odd	2
1260.2.c.d.811.1		16	3.2	odd	2
1260.2.c.d.811.2		16	84.83	odd	2
1260.2.c.e.811.1		16	21.20	even	2
1260.2.c.e.811.2		16	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	420.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.40936 + 0.117062i) q^{2} -1.00000 q^{3} +(1.97259 + 0.329965i) q^{4} -1.00000i q^{5} +(-1.40936 - 0.117062i) q^{6} +(0.776136 - 2.52935i) q^{7} +(2.74147 + 0.695955i) q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(1.40936 + 0.117062i) q^{2} -1.00000 q^{3} +(1.97259 + 0.329965i) q^{4} -1.00000i q^{5} +(-1.40936 - 0.117062i) q^{6} +(0.776136 - 2.52935i) q^{7} +(2.74147 + 0.695955i) q^{8} +1.00000 q^{9} +(0.117062 - 1.40936i) q^{10} -0.556350i q^{11} +(-1.97259 - 0.329965i) q^{12} +0.182384i q^{13} +(1.38995 - 3.47391i) q^{14} +1.00000i q^{15} +(3.78225 + 1.30177i) q^{16} -2.39449i q^{17} +(1.40936 + 0.117062i) q^{18} +3.08109 q^{19} +(0.329965 - 1.97259i) q^{20} +(-0.776136 + 2.52935i) q^{21} +(0.0651274 - 0.784098i) q^{22} +3.94362i q^{23} +(-2.74147 - 0.695955i) q^{24} -1.00000 q^{25} +(-0.0213502 + 0.257045i) q^{26} -1.00000 q^{27} +(2.36560 - 4.73328i) q^{28} -3.20026 q^{29} +(-0.117062 + 1.40936i) q^{30} +5.68747 q^{31} +(5.17816 + 2.27742i) q^{32} +0.556350i q^{33} +(0.280303 - 3.37469i) q^{34} +(-2.52935 - 0.776136i) q^{35} +(1.97259 + 0.329965i) q^{36} -4.98180 q^{37} +(4.34237 + 0.360678i) q^{38} -0.182384i q^{39} +(0.695955 - 2.74147i) q^{40} +9.64809i q^{41} +(-1.38995 + 3.47391i) q^{42} +0.643697i q^{43} +(0.183576 - 1.09745i) q^{44} -1.00000i q^{45} +(-0.461647 + 5.55798i) q^{46} -3.63668 q^{47} +(-3.78225 - 1.30177i) q^{48} +(-5.79523 - 3.92624i) q^{49} +(-1.40936 - 0.117062i) q^{50} +2.39449i q^{51} +(-0.0601803 + 0.359769i) q^{52} -6.97060 q^{53} +(-1.40936 - 0.117062i) q^{54} -0.556350 q^{55} +(3.88806 - 6.39398i) q^{56} -3.08109 q^{57} +(-4.51031 - 0.374628i) q^{58} -8.79962 q^{59} +(-0.329965 + 1.97259i) q^{60} +14.3787i q^{61} +(8.01569 + 0.665786i) q^{62} +(0.776136 - 2.52935i) q^{63} +(7.03129 + 3.81588i) q^{64} +0.182384 q^{65} +(-0.0651274 + 0.784098i) q^{66} -10.0692i q^{67} +(0.790096 - 4.72335i) q^{68} -3.94362i q^{69} +(-3.47391 - 1.38995i) q^{70} +1.36136i q^{71} +(2.74147 + 0.695955i) q^{72} -10.1087i q^{73} +(-7.02115 - 0.583179i) q^{74} +1.00000 q^{75} +(6.07774 + 1.01665i) q^{76} +(-1.40721 - 0.431803i) q^{77} +(0.0213502 - 0.257045i) q^{78} +13.0596i q^{79} +(1.30177 - 3.78225i) q^{80} +1.00000 q^{81} +(-1.12942 + 13.5976i) q^{82} -9.45272 q^{83} +(-2.36560 + 4.73328i) q^{84} -2.39449 q^{85} +(-0.0753523 + 0.907200i) q^{86} +3.20026 q^{87} +(0.387195 - 1.52522i) q^{88} -8.01600i q^{89} +(0.117062 - 1.40936i) q^{90} +(0.461313 + 0.141555i) q^{91} +(-1.30125 + 7.77915i) q^{92} -5.68747 q^{93} +(-5.12540 - 0.425717i) q^{94} -3.08109i q^{95} +(-5.17816 - 2.27742i) q^{96} -0.445387i q^{97} +(-7.70795 - 6.21188i) q^{98} -0.556350i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{2} - 16 q^{3} - 2 q^{4} - 2 q^{6} - 4 q^{7} + 2 q^{8} + 16 q^{9}+O(q^{10}) \) 16 * q + 2 * q^2 - 16 * q^3 - 2 * q^4 - 2 * q^6 - 4 * q^7 + 2 * q^8 + 16 * q^9	\( 16 q + 2 q^{2} - 16 q^{3} - 2 q^{4} - 2 q^{6} - 4 q^{7} + 2 q^{8} + 16 q^{9} + 2 q^{12} - 2 q^{14} + 6 q^{16} + 2 q^{18} - 24 q^{19} + 4 q^{21} - 12 q^{22} - 2 q^{24} - 16 q^{25} - 12 q^{26} - 16 q^{27} + 14 q^{28} + 16 q^{29} + 8 q^{31} - 18 q^{32} + 24 q^{34} - 2 q^{36} + 24 q^{37} + 28 q^{38} + 12 q^{40} + 2 q^{42} - 8 q^{44} - 20 q^{46} + 16 q^{47} - 6 q^{48} - 16 q^{49} - 2 q^{50} - 20 q^{52} - 32 q^{53} - 2 q^{54} + 2 q^{56} + 24 q^{57} - 32 q^{58} + 8 q^{59} + 16 q^{62} - 4 q^{63} - 2 q^{64} - 8 q^{65} + 12 q^{66} + 4 q^{68} + 2 q^{72} - 4 q^{74} + 16 q^{75} + 16 q^{76} - 8 q^{77} + 12 q^{78} - 16 q^{80} + 16 q^{81} - 4 q^{82} + 8 q^{83} - 14 q^{84} + 64 q^{86} - 16 q^{87} - 52 q^{88} + 16 q^{91} + 64 q^{92} - 8 q^{93} + 16 q^{94} + 18 q^{96} - 86 q^{98}+O(q^{100}) \) 16 * q + 2 * q^2 - 16 * q^3 - 2 * q^4 - 2 * q^6 - 4 * q^7 + 2 * q^8 + 16 * q^9 + 2 * q^12 - 2 * q^14 + 6 * q^16 + 2 * q^18 - 24 * q^19 + 4 * q^21 - 12 * q^22 - 2 * q^24 - 16 * q^25 - 12 * q^26 - 16 * q^27 + 14 * q^28 + 16 * q^29 + 8 * q^31 - 18 * q^32 + 24 * q^34 - 2 * q^36 + 24 * q^37 + 28 * q^38 + 12 * q^40 + 2 * q^42 - 8 * q^44 - 20 * q^46 + 16 * q^47 - 6 * q^48 - 16 * q^49 - 2 * q^50 - 20 * q^52 - 32 * q^53 - 2 * q^54 + 2 * q^56 + 24 * q^57 - 32 * q^58 + 8 * q^59 + 16 * q^62 - 4 * q^63 - 2 * q^64 - 8 * q^65 + 12 * q^66 + 4 * q^68 + 2 * q^72 - 4 * q^74 + 16 * q^75 + 16 * q^76 - 8 * q^77 + 12 * q^78 - 16 * q^80 + 16 * q^81 - 4 * q^82 + 8 * q^83 - 14 * q^84 + 64 * q^86 - 16 * q^87 - 52 * q^88 + 16 * q^91 + 64 * q^92 - 8 * q^93 + 16 * q^94 + 18 * q^96 - 86 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more