LMFDB - Embedded newform 1260.2.c.e.811.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1260,2,Mod(811,1260)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1260, 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("1260.811");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1260.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:	$10.0611506547$
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:	no (minimal twist has level 420)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			811.2
Root			$1.40936 + 0.117062i$ of defining polynomial
Character	$\chi$	$=$	1260.811
Dual form			1260.2.c.e.811.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40936 + 0.117062i) q^{2} +(1.97259 - 0.329965i) q^{4} +1.00000i q^{5} +(-0.776136 + 2.52935i) q^{7} +(-2.74147 + 0.695955i) q^{8} +O(q^{10})$	\(q+(-1.40936 + 0.117062i) q^{2} +(1.97259 - 0.329965i) q^{4} +1.00000i q^{5} +(-0.776136 + 2.52935i) q^{7} +(-2.74147 + 0.695955i) q^{8} +(-0.117062 - 1.40936i) q^{10} -0.556350i q^{11} +0.182384i q^{13} +(0.797764 - 3.65562i) q^{14} +(3.78225 - 1.30177i) q^{16} +2.39449i q^{17} -3.08109 q^{19} +(0.329965 + 1.97259i) q^{20} +(0.0651274 + 0.784098i) q^{22} +3.94362i q^{23} -1.00000 q^{25} +(-0.0213502 - 0.257045i) q^{26} +(-0.696403 + 5.24548i) q^{28} +3.20026 q^{29} -5.68747 q^{31} +(-5.17816 + 2.27742i) q^{32} +(-0.280303 - 3.37469i) q^{34} +(-2.52935 - 0.776136i) q^{35} -4.98180 q^{37} +(4.34237 - 0.360678i) q^{38} +(-0.695955 - 2.74147i) q^{40} -9.64809i q^{41} -0.643697i q^{43} +(-0.183576 - 1.09745i) q^{44} +(-0.461647 - 5.55798i) q^{46} -3.63668 q^{47} +(-5.79523 - 3.92624i) q^{49} +(1.40936 - 0.117062i) q^{50} +(0.0601803 + 0.359769i) q^{52} +6.97060 q^{53} +0.556350 q^{55} +(0.367437 - 7.47429i) q^{56} +(-4.51031 + 0.374628i) q^{58} -8.79962 q^{59} +14.3787i q^{61} +(8.01569 - 0.665786i) q^{62} +(7.03129 - 3.81588i) q^{64} -0.182384 q^{65} +10.0692i q^{67} +(0.790096 + 4.72335i) q^{68} +(3.65562 + 0.797764i) q^{70} +1.36136i q^{71} -10.1087i q^{73} +(7.02115 - 0.583179i) q^{74} +(-6.07774 + 1.01665i) q^{76} +(1.40721 + 0.431803i) q^{77} -13.0596i q^{79} +(1.30177 + 3.78225i) q^{80} +(1.12942 + 13.5976i) q^{82} -9.45272 q^{83} -2.39449 q^{85} +(0.0753523 + 0.907200i) q^{86} +(0.387195 + 1.52522i) q^{88} +8.01600i q^{89} +(-0.461313 - 0.141555i) q^{91} +(1.30125 + 7.77915i) q^{92} +(5.12540 - 0.425717i) q^{94} -3.08109i q^{95} -0.445387i q^{97} +(8.62718 + 4.85508i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{2} - 2 q^{4} + 4 q^{7} - 2 q^{8}+O(q^{10}) $ 16 * q - 2 * q^2 - 2 * q^4 + 4 * q^7 - 2 * q^8	$ 16 q - 2 q^{2} - 2 q^{4} + 4 q^{7} - 2 q^{8} - 10 q^{14} + 6 q^{16} + 24 q^{19} - 12 q^{22} - 16 q^{25} - 12 q^{26} - 22 q^{28} - 16 q^{29} - 8 q^{31} + 18 q^{32} - 24 q^{34} + 24 q^{37} + 28 q^{38} - 12 q^{40} + 8 q^{44} - 20 q^{46} + 16 q^{47} - 16 q^{49} + 2 q^{50} + 20 q^{52} + 32 q^{53} + 2 q^{56} - 32 q^{58} + 8 q^{59} + 16 q^{62} - 2 q^{64} + 8 q^{65} + 4 q^{68} - 20 q^{70} + 4 q^{74} - 16 q^{76} + 8 q^{77} - 16 q^{80} + 4 q^{82} + 8 q^{83} - 64 q^{86} - 52 q^{88} - 16 q^{91} - 64 q^{92} - 16 q^{94} - 2 q^{98}+O(q^{100}) $ 16 * q - 2 * q^2 - 2 * q^4 + 4 * q^7 - 2 * q^8 - 10 * q^14 + 6 * q^16 + 24 * q^19 - 12 * q^22 - 16 * q^25 - 12 * q^26 - 22 * q^28 - 16 * q^29 - 8 * q^31 + 18 * q^32 - 24 * q^34 + 24 * q^37 + 28 * q^38 - 12 * q^40 + 8 * q^44 - 20 * q^46 + 16 * q^47 - 16 * q^49 + 2 * q^50 + 20 * q^52 + 32 * q^53 + 2 * q^56 - 32 * q^58 + 8 * q^59 + 16 * q^62 - 2 * q^64 + 8 * q^65 + 4 * q^68 - 20 * q^70 + 4 * q^74 - 16 * q^76 + 8 * q^77 - 16 * q^80 + 4 * q^82 + 8 * q^83 - 64 * q^86 - 52 * q^88 - 16 * q^91 - 64 * q^92 - 16 * q^94 - 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1260\mathbb{Z}\right)^\times$.

$n$	$281$	$631$	$757$	$1081$
$\chi(n)$	$1$	$-1$	$1$	$-1$

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
$3$		0			0
$3$		0			0
$4$	1.97259	−	0.329965i	0.986297	−	0.164982i
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$		0			0
$7$	−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
$9$		0			0
$10$	−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	$-0.0267290\pi$
$12$		0			0
$13$			0.182384i			0.0505842i	0.999680	+	0.0252921i	$0.00805158\pi$
$13$			0.182384i			0.0505842i	−0.999680	+	0.0252921i	$0.991948\pi$
$14$	0.797764	−	3.65562i	0.213211	−	0.977006i
$15$		0			0
$16$	3.78225	−	1.30177i	0.945562	−	0.325443i
$17$			2.39449i			0.580748i	0.956913	+	0.290374i	$0.0937797\pi$
$17$			2.39449i			0.580748i	−0.956913	+	0.290374i	$0.906220\pi$
$18$		0			0
$19$	−3.08109			−0.706851			−0.353425	−	0.935463i	$-0.614983\pi$
$19$	−3.08109			−0.706851			−0.353425	+	0.935463i	$0.614983\pi$
$20$	0.329965	+	1.97259i	0.0737824	+	0.441085i
$21$		0			0
$22$	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	$0.865127\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$	−0.0213502	−	0.257045i	−0.00418712	−	0.0504106i
$27$		0			0
$28$	−0.696403	+	5.24548i	−0.131608	+	0.991302i
$29$	3.20026			0.594273			0.297136	−	0.954835i	$-0.403968\pi$
$29$	3.20026			0.594273			0.297136	+	0.954835i	$0.403968\pi$
$30$		0			0
$31$	−5.68747			−1.02150			−0.510750	−	0.859729i	$-0.670632\pi$
$31$	−5.68747			−1.02150			−0.510750	+	0.859729i	$0.670632\pi$
$32$	−5.17816	+	2.27742i	−0.915378	+	0.402595i
$33$		0			0
$34$	−0.280303	−	3.37469i	−0.0480716	−	0.578755i
$35$	−2.52935	−	0.776136i	−0.427538	−	0.131191i
$36$		0			0
$37$	−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			0
$40$	−0.695955	−	2.74147i	−0.110040	−	0.433464i
$41$		−	9.64809i		−	1.50678i	−0.657575	−	0.753389i	$-0.728418\pi$
$41$		−	9.64809i		−	1.50678i	0.657575	−	0.753389i	$-0.271582\pi$
$42$		0			0
$43$		−	0.643697i		−	0.0981628i	−0.998795	−	0.0490814i	$-0.984371\pi$
$43$		−	0.643697i		−	0.0981628i	0.998795	−	0.0490814i	$-0.0156294\pi$
$44$	−0.183576	−	1.09745i	−0.0276751	−	0.165447i
$45$		0			0
$46$	−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	$0.585449\pi$
$48$		0			0
$49$	−5.79523	−	3.92624i	−0.827890	−	0.560891i
$50$	1.40936	−	0.117062i	0.199314	−	0.0165551i
$51$		0			0
$52$	0.0601803	+	0.359769i	0.00834550	+	0.0498910i
$53$	6.97060			0.957485			0.478743	−	0.877955i	$-0.341093\pi$
$53$	6.97060			0.957485			0.478743	+	0.877955i	$0.341093\pi$
$54$		0			0
$55$	0.556350			0.0750183
$56$	0.367437	−	7.47429i	0.0491009	−	0.998794i
$57$		0			0
$58$	−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			0
$61$			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			0
$64$	7.03129	−	3.81588i	0.878912	−	0.476984i
$65$	−0.182384			−0.0226219
$66$		0			0
$67$			10.0692i			1.23015i	0.788467	+	0.615077i	$0.210875\pi$
$67$			10.0692i			1.23015i	−0.788467	+	0.615077i	$0.789125\pi$
$68$	0.790096	+	4.72335i	0.0958132	+	0.572790i
$69$		0			0
$70$	3.65562	+	0.797764i	0.436930	+	0.0953511i
$71$			1.36136i			0.161564i	0.996732	+	0.0807821i	$0.0257418\pi$
$71$			1.36136i			0.161564i	−0.996732	+	0.0807821i	$0.974258\pi$
$72$		0			0
$73$		−	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
$75$		0			0
$76$	−6.07774	+	1.01665i	−0.697164	+	0.116618i
$77$	1.40721	+	0.431803i	0.160366	+	0.0492086i
$78$		0			0
$79$		−	13.0596i		−	1.46932i	−0.678438	−	0.734658i	$-0.737343\pi$
$79$		−	13.0596i		−	1.46932i	0.678438	−	0.734658i	$-0.262657\pi$
$80$	1.30177	+	3.78225i	0.145543	+	0.422868i
$81$		0			0
$82$	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	$0.673616\pi$
$84$		0			0
$85$	−2.39449			−0.259718
$86$	0.0753523	+	0.907200i	0.00812545	+	0.0978259i
$87$		0			0
$88$	0.387195	+	1.52522i	0.0412751	+	0.162589i
$89$			8.01600i			0.849694i	0.905265	+	0.424847i	$0.139672\pi$
$89$			8.01600i			0.849694i	−0.905265	+	0.424847i	$0.860328\pi$
$90$		0			0
$91$	−0.461313	−	0.141555i	−0.0483587	−	0.0148390i
$92$	1.30125	+	7.77915i	0.135665	+	0.811032i
$93$		0			0
$94$	5.12540	−	0.425717i	0.528645	−	0.0439094i
$95$		−	3.08109i		−	0.316113i
$96$		0			0
$97$		−	0.445387i		−	0.0452222i	−0.999744	−	0.0226111i	$-0.992802\pi$
$97$		−	0.445387i		−	0.0452222i	0.999744	−	0.0226111i	$-0.00719796\pi$
$98$	8.62718	+	4.85508i	0.871476	+	0.490437i
$99$		0			0
$100$	−1.97259	+	0.329965i	−0.197259	+	0.0329965i
$101$		−	12.8540i		−	1.27902i	−0.768781	−	0.639512i	$-0.779136\pi$
$101$		−	12.8540i		−	1.27902i	0.768781	−	0.639512i	$-0.220864\pi$
$102$		0			0
$103$	−14.3031			−1.40933			−0.704664	−	0.709542i	$-0.748902\pi$
$103$	−14.3031			−1.40933			−0.704664	+	0.709542i	$0.748902\pi$
$104$	−0.126931	−	0.500000i	−0.0124466	−	0.0490290i
$105$		0			0
$106$	−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	$0.653694\pi$
$108$		0			0
$109$	−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
$111$		0			0
$112$	0.357103	+	10.5770i	0.0337430	+	0.999431i
$113$	−3.14680			−0.296026			−0.148013	−	0.988985i	$-0.547288\pi$
$113$	−3.14680			−0.296026			−0.148013	+	0.988985i	$0.547288\pi$
$114$		0			0
$115$	−3.94362			−0.367744
$116$	6.31280	−	1.05597i	0.586129	−	0.0980445i
$117$		0			0
$118$	12.4018	−	1.03010i	1.14168	−	0.0948284i
$119$	−6.05649	−	1.85845i	−0.555198	−	0.170363i
$120$		0			0
$121$	10.6905			0.971861
$122$	−1.68319	−	20.2647i	−0.152389	−	1.83468i
$123$		0			0
$124$	−11.2191	+	1.87666i	−1.00750	+	0.168529i
$125$		−	1.00000i		−	0.0894427i
$126$		0			0
$127$			11.8445i			1.05103i	0.850784	+	0.525516i	$0.176128\pi$
$127$			11.8445i			1.05103i	−0.850784	+	0.525516i	$0.823872\pi$
$128$	−9.46293	+	6.20104i	−0.836413	+	0.548100i
$129$		0			0
$130$	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			0
$133$	2.39134	−	7.79316i	0.207356	−	0.675753i
$134$	−1.17872	−	14.1912i	−0.101826	−	1.22593i
$135$		0			0
$136$	−1.66645	−	6.56441i	−0.142897	−	0.562893i
$137$	−9.88658			−0.844667			−0.422334	−	0.906440i	$-0.638789\pi$
$137$	−9.88658			−0.844667			−0.422334	+	0.906440i	$0.638789\pi$
$138$		0			0
$139$	−20.5861			−1.74609			−0.873047	−	0.487636i	$-0.837859\pi$
$139$	−20.5861			−1.74609			−0.873047	+	0.487636i	$0.837859\pi$
$140$	−5.24548	−	0.696403i	−0.443324	−	0.0588568i
$141$		0			0
$142$	−0.159364	−	1.91865i	−0.0133735	−	0.161010i
$143$	0.101469			0.00848529
$144$		0			0
$145$			3.20026i			0.265767i
$146$	1.18335	+	14.2468i	0.0979345	+	1.17908i
$147$		0			0
$148$	−9.82706	+	1.64382i	−0.807779	+	0.135121i
$149$	−7.28607			−0.596898			−0.298449	−	0.954426i	$-0.596469\pi$
$149$	−7.28607			−0.596898			−0.298449	+	0.954426i	$0.596469\pi$
$150$		0			0
$151$			15.1807i			1.23539i	0.786418	+	0.617694i	$0.211933\pi$
$151$			15.1807i			1.23539i	−0.786418	+	0.617694i	$0.788067\pi$
$152$	8.44671	−	2.14430i	0.685119	−	0.173926i
$153$		0			0
$154$	−2.03381	−	0.443836i	−0.163889	−	0.0357654i
$155$		−	5.68747i		−	0.456829i
$156$		0			0
$157$		−	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
$159$		0			0
$160$	−2.27742	−	5.17816i	−0.180046	−	0.409370i
$161$	−9.97479	−	3.06078i	−0.786123	−	0.241223i
$162$		0			0
$163$		−	20.7486i		−	1.62515i	−0.582853	−	0.812577i	$-0.698064\pi$
$163$		−	20.7486i		−	1.62515i	0.582853	−	0.812577i	$-0.301936\pi$
$164$	−3.18353	−	19.0318i	−0.248592	−	1.48613i
$165$		0			0
$166$	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	$0.605039\pi$
$168$		0			0
$169$	12.9667			0.997441
$170$	3.37469	−	0.280303i	0.258827	−	0.0214983i
$171$		0			0
$172$	−0.212397	−	1.26975i	−0.0161951	−	0.0968176i
$173$			21.8554i			1.66163i	0.556546	+	0.830817i	$0.312126\pi$
$173$			21.8554i			1.66163i	−0.556546	+	0.830817i	$0.687874\pi$
$174$		0			0
$175$	0.776136	−	2.52935i	0.0586703	−	0.191201i
$176$	−0.724242	−	2.10425i	−0.0545918	−	0.158614i
$177$		0			0
$178$	−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			0
$181$			12.7452i			0.947341i	0.880702	+	0.473670i	$0.157071\pi$
$181$			12.7452i			0.947341i	−0.880702	+	0.473670i	$0.842929\pi$
$182$	0.666726	+	0.145499i	0.0494211	+	0.0107851i
$183$		0			0
$184$	−2.74458	−	10.8113i	−0.202333	−	0.797019i
$185$		−	4.98180i		−	0.366269i
$186$		0			0
$187$	1.33217			0.0974181
$188$	−7.17370	+	1.19998i	−0.523196	+	0.0875174i
$189$		0			0
$190$	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	$0.716932\pi$
$192$		0			0
$193$	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			0
$196$	−12.7271	−	5.83265i	−0.909082	−	0.416618i
$197$	8.44807			0.601900			0.300950	−	0.953640i	$-0.402696\pi$
$197$	8.44807			0.601900			0.300950	+	0.953640i	$0.402696\pi$
$198$		0			0
$199$	18.5300			1.31356			0.656778	−	0.754084i	$-0.271919\pi$
$199$	18.5300			1.31356			0.656778	+	0.754084i	$0.271919\pi$
$200$	2.74147	−	0.695955i	0.193851	−	0.0492114i
$201$		0			0
$202$	1.50472	+	18.1160i	0.105872	+	1.27463i
$203$	−2.48383	+	8.09457i	−0.174331	+	0.568127i
$204$		0			0
$205$	9.64809			0.673852
$206$	20.1582	−	1.67435i	1.40449	−	0.116657i
$207$		0			0
$208$	0.237422	+	0.689821i	0.0164623	+	0.0478305i
$209$			1.71417i			0.118571i
$210$		0			0
$211$			17.4456i			1.20101i	0.799622	+	0.600504i	$0.205033\pi$
$211$			17.4456i			1.20101i	−0.799622	+	0.600504i	$0.794967\pi$
$212$	13.7502	−	2.30005i	0.944364	−	0.157968i
$213$		0			0
$214$	−2.14493	−	25.8238i	−0.146624	−	1.76528i
$215$	0.643697			0.0438997
$216$		0			0
$217$	4.41425	−	14.3856i	0.299659	−	0.976558i
$218$	5.69085	−	0.472684i	0.385433	−	0.0320142i
$219$		0			0
$220$	1.09745	−	0.183576i	0.0739903	−	0.0123767i
$221$	−0.436716			−0.0293767
$222$		0			0
$223$	11.9173			0.798038			0.399019	−	0.916943i	$-0.369351\pi$
$223$	11.9173			0.798038			0.399019	+	0.916943i	$0.369351\pi$
$224$	−1.74145	−	14.8650i	−0.116355	−	0.993208i
$225$		0			0
$226$	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	$0.522603\pi$
$228$		0			0
$229$			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
$231$		0			0
$232$	−8.77340	+	2.22723i	−0.576002	+	0.146225i
$233$	−10.8641			−0.711732			−0.355866	−	0.934537i	$-0.615814\pi$
$233$	−10.8641			−0.711732			−0.355866	+	0.934537i	$0.615814\pi$
$234$		0			0
$235$		−	3.63668i		−	0.237231i
$236$	−17.3581	+	2.90357i	−1.12991	+	0.189006i
$237$		0			0
$238$	8.75333	+	1.91023i	0.567394	+	0.123822i
$239$		−	15.3760i		−	0.994592i	−0.867581	−	0.497296i	$-0.834326\pi$
$239$		−	15.3760i		−	0.994592i	0.867581	−	0.497296i	$-0.165674\pi$
$240$		0			0
$241$		−	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
$243$		0			0
$244$	4.74445	+	28.3633i	0.303733	+	1.81577i
$245$	3.92624	−	5.79523i	0.250838	−	0.370243i
$246$		0			0
$247$		−	0.561941i		−	0.0357555i
$248$	15.5920	−	3.95822i	0.990094	−	0.251347i
$249$		0			0
$250$	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	$0.283885\pi$
$252$		0			0
$253$	2.19403			0.137938
$254$	−1.38654	−	16.6932i	−0.0869995	−	1.04743i
$255$		0			0
$256$	12.6108	−	9.84725i	0.788174	−	0.615453i
$257$			30.1252i			1.87916i	0.342335	+	0.939578i	$0.388782\pi$
$257$			30.1252i			1.87916i	−0.342335	+	0.939578i	$0.611218\pi$
$258$		0			0
$259$	3.86655	−	12.6007i	0.240256	−	0.782970i
$260$	−0.359769	+	0.0601803i	−0.0223119	+	0.00373222i
$261$		0			0
$262$	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			0
$265$			6.97060i			0.428200i
$266$	−2.45798	+	11.2633i	−0.150709	+	0.690597i
$267$		0			0
$268$	3.32250	+	19.8625i	0.202954	+	1.21330i
$269$		−	8.40266i		−	0.512319i	−0.966634	−	0.256160i	$-0.917543\pi$
$269$		−	8.40266i		−	0.512319i	0.966634	−	0.256160i	$-0.0824573\pi$
$270$		0			0
$271$	28.7730			1.74783			0.873916	−	0.486077i	$-0.161572\pi$
$271$	28.7730			1.74783			0.873916	+	0.486077i	$0.161572\pi$
$272$	3.11708	+	9.05653i	0.189000	+	0.549133i
$273$		0			0
$274$	13.9338	−	1.15734i	0.841769	−	0.0699176i
$275$			0.556350i			0.0335492i
$276$		0			0
$277$	−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
$279$		0			0
$280$	7.47429	+	0.367437i	0.446674	+	0.0219586i
$281$	−17.8653			−1.06575			−0.532876	−	0.846193i	$-0.678889\pi$
$281$	−17.8653			−1.06575			−0.532876	+	0.846193i	$0.678889\pi$
$282$		0			0
$283$	−4.34129			−0.258063			−0.129031	−	0.991641i	$-0.541187\pi$
$283$	−4.34129			−0.258063			−0.129031	+	0.991641i	$0.541187\pi$
$284$	0.449202	+	2.68542i	0.0266552	+	0.159350i
$285$		0			0
$286$	−0.143007	+	0.0118782i	−0.00845617	+	0.000702372i
$287$	24.4034	+	7.48823i	1.44049	+	0.442016i
$288$		0			0
$289$	11.2664			0.662732
$290$	−0.374628	−	4.51031i	−0.0219989	−	0.264855i
$291$		0			0
$292$	−3.33553	−	19.9404i	−0.195197	−	1.16692i
$293$			0.535106i			0.0312612i	0.999878	+	0.0156306i	$0.00497558\pi$
$293$			0.535106i			0.0312612i	−0.999878	+	0.0156306i	$0.995024\pi$
$294$		0			0
$295$		−	8.79962i		−	0.512334i
$296$	13.6574	−	3.46711i	0.793822	−	0.201521i
$297$		0			0
$298$	10.2687	−	0.852922i	0.594850	−	0.0494084i
$299$	−0.719252			−0.0415954
$300$		0			0
$301$	1.62813	+	0.499596i	0.0938441	+	0.0287962i
$302$	−1.77708	−	21.3951i	−0.102260	−	1.23115i
$303$		0			0
$304$	−11.6534	+	4.01088i	−0.668371	+	0.230040i
$305$	−14.3787			−0.823320
$306$		0			0
$307$	20.4818			1.16896			0.584478	−	0.811409i	$-0.301299\pi$
$307$	20.4818			1.16896			0.584478	+	0.811409i	$0.301299\pi$
$308$	2.91832	+	0.387444i	0.166287	+	0.0220767i
$309$		0			0
$310$	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			0
$313$			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
$315$		0			0
$316$	−4.30920	−	25.7612i	−0.242411	−	1.44918i
$317$	16.0488			0.901388			0.450694	−	0.892678i	$-0.351177\pi$
$317$	16.0488			0.901388			0.450694	+	0.892678i	$0.351177\pi$
$318$		0			0
$319$		−	1.78046i		−	0.0996868i
$320$	3.81588	+	7.03129i	0.213314	+	0.393061i
$321$		0			0
$322$	14.4164	+	3.14608i	0.803393	+	0.175324i
$323$		−	7.37763i		−	0.410502i
$324$		0			0
$325$		−	0.182384i		−	0.0101168i
$326$	2.42887	+	29.2422i	0.134523	+	1.61958i
$327$		0			0
$328$	6.71464	+	26.4499i	0.370754	+	1.46045i
$329$	2.82256	−	9.19845i	0.155613	−	0.507127i
$330$		0			0
$331$			10.9660i			0.602746i	0.953506	+	0.301373i	$0.0974450\pi$
$331$			10.9660i			0.602746i	−0.953506	+	0.301373i	$0.902555\pi$
$332$	−18.6464	+	3.11906i	−1.02335	+	0.171181i
$333$		0			0
$334$	11.8032	−	0.980374i	0.645840	−	0.0536437i
$335$	−10.0692			−0.550142
$336$		0			0
$337$	−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
$339$		0			0
$340$	−4.72335	+	0.790096i	−0.256159	+	0.0428490i
$341$			3.16423i			0.171352i
$342$		0			0
$343$	14.4287	−	11.6109i	0.779077	−	0.626928i
$344$	0.447984	+	1.76467i	0.0241537	+	0.0951448i
$345$		0			0
$346$	−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	$-0.124978\pi$
$348$		0			0
$349$		−	6.69632i		−	0.358446i	−0.983809	−	0.179223i	$-0.942642\pi$
$349$		−	6.69632i		−	0.358446i	0.983809	−	0.179223i	$-0.0573583\pi$
$350$	−0.797764	+	3.65562i	−0.0426423	+	0.195401i
$351$		0			0
$352$	1.26705	+	2.88087i	0.0675338	+	0.153551i
$353$		−	18.6741i		−	0.993920i	−0.867773	−	0.496960i	$-0.834449\pi$
$353$		−	18.6741i		−	0.993920i	0.867773	−	0.496960i	$-0.165551\pi$
$354$		0			0
$355$	−1.36136			−0.0722537
$356$	2.64500	+	15.8123i	0.140185	+	0.838051i
$357$		0			0
$358$	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			0
$361$	−9.50688			−0.500362
$362$	−1.49197	−	17.9625i	−0.0784164	−	0.944090i
$363$		0			0
$364$	−0.956690	−	0.127013i	−0.0501442	−	0.00665727i
$365$	10.1087			0.529115
$366$		0			0
$367$	21.4633			1.12038			0.560189	−	0.828365i	$-0.310729\pi$
$367$	21.4633			1.12038			0.560189	+	0.828365i	$0.310729\pi$
$368$	5.13369	+	14.9157i	0.267612	+	0.777536i
$369$		0			0
$370$	0.583179	+	7.02115i	0.0303180	+	0.365012i
$371$	−5.41013	+	17.6311i	−0.280880	+	0.915360i
$372$		0			0
$373$	−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
$375$		0			0
$376$	9.96985	−	2.53097i	0.514156	−	0.130525i
$377$			0.583675i			0.0300608i
$378$		0			0
$379$			11.1047i			0.570412i	0.958466	+	0.285206i	$0.0920621\pi$
$379$			11.1047i			0.570412i	−0.958466	+	0.285206i	$0.907938\pi$
$380$	−1.01665	−	6.07774i	−0.0521531	−	0.311781i
$381$		0			0
$382$	−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	$0.293664\pi$
$384$		0			0
$385$	−0.431803	+	1.40721i	−0.0220067	+	0.0717178i
$386$	−7.44034	+	0.617997i	−0.378704	+	0.0314552i
$387$		0			0
$388$	−0.146962	−	0.878568i	−0.00746087	−	0.0446025i
$389$	22.7913			1.15557			0.577783	−	0.816190i	$-0.303918\pi$
$389$	22.7913			1.15557			0.577783	+	0.816190i	$0.303918\pi$
$390$		0			0
$391$	−9.44293			−0.477549
$392$	18.6199	+	6.73044i	0.940448	+	0.339939i
$393$		0			0
$394$	−11.9064	+	0.988947i	−0.599834	+	0.0498224i
$395$	13.0596			0.657098
$396$		0			0
$397$			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
$399$		0			0
$400$	−3.78225	+	1.30177i	−0.189112	+	0.0650886i
$401$	28.1602			1.40625			0.703126	−	0.711065i	$-0.251787\pi$
$401$	28.1602			1.40625			0.703126	+	0.711065i	$0.251787\pi$
$402$		0			0
$403$		−	1.03730i		−	0.0516717i
$404$	−4.24138	−	25.3558i	−0.211017	−	1.26150i
$405$		0			0
$406$	2.55305	−	11.6989i	0.126706	−	0.580608i
$407$			2.77163i			0.137384i
$408$		0			0
$409$		−	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
$411$		0			0
$412$	−28.2142	+	4.71952i	−1.39001	+	0.232514i
$413$	6.82970	−	22.2573i	0.336068	−	1.09521i
$414$		0			0
$415$		−	9.45272i		−	0.464016i
$416$	−0.415365	−	0.944413i	−0.0203650	−	0.0463037i
$417$		0			0
$418$	−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	$0.310807\pi$
$420$		0			0
$421$	−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
$423$		0			0
$424$	−19.1097	+	4.85122i	−0.928048	+	0.235596i
$425$		−	2.39449i		−	0.116150i
$426$		0			0
$427$	−36.3687	−	11.1598i	−1.76000	−	0.540060i
$428$	6.04596	+	36.1439i	0.292242	+	1.74708i
$429$		0			0
$430$	−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	$0.860001\pi$
$432$		0			0
$433$			30.2797i			1.45515i	0.686029	+	0.727574i	$0.259352\pi$
$433$			30.2797i			1.45515i	−0.686029	+	0.727574i	$0.740648\pi$
$434$	−4.53726	+	20.7912i	−0.217795	+	0.998011i
$435$		0			0
$436$	−7.96513	+	1.33236i	−0.381460	+	0.0638086i
$437$		−	12.1506i		−	0.581244i
$438$		0			0
$439$	3.51474			0.167749			0.0838747	−	0.996476i	$-0.473270\pi$
$439$	3.51474			0.167749			0.0838747	+	0.996476i	$0.473270\pi$
$440$	−1.52522	+	0.387195i	−0.0727119	+	0.0184588i
$441$		0			0
$442$	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	$-0.0252829\pi$
$444$		0			0
$445$	−8.01600			−0.379995
$446$	−16.7957	+	1.39506i	−0.795300	+	0.0660578i
$447$		0			0
$448$	4.19445	+	20.7462i	0.198169	+	0.980168i
$449$	30.3020			1.43004			0.715019	−	0.699105i	$-0.246418\pi$
$449$	30.3020			1.43004			0.715019	+	0.699105i	$0.246418\pi$
$450$		0			0
$451$	−5.36772			−0.252756
$452$	−6.20736	+	1.03833i	−0.291970	+	0.0488391i
$453$		0			0
$454$	3.01315	−	0.250273i	0.141414	−	0.0117459i
$455$	0.141555	−	0.461313i	0.00663618	−	0.0216267i
$456$		0			0
$457$	−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
$459$		0			0
$460$	−7.77915	+	1.30125i	−0.362705	+	0.0606713i
$461$			7.75351i			0.361117i	0.983564	+	0.180559i	$0.0577905\pi$
$461$			7.75351i			0.361117i	−0.983564	+	0.180559i	$0.942209\pi$
$462$		0			0
$463$		−	21.4187i		−	0.995410i	−0.867346	−	0.497705i	$-0.834176\pi$
$463$		−	21.4187i		−	0.995410i	0.867346	−	0.497705i	$-0.165824\pi$
$464$	12.1042	−	4.16600i	0.561921	−	0.193402i
$465$		0			0
$466$	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			0
$469$	−25.4686	−	7.81510i	−1.17603	−	0.360868i
$470$	0.425717	+	5.12540i	0.0196369	+	0.236417i
$471$		0			0
$472$	24.1239	−	6.12414i	1.11039	−	0.281886i
$473$	−0.358121			−0.0164664
$474$		0			0
$475$	3.08109			0.141370
$476$	−12.5602	−	1.66753i	−0.575697	−	0.0764310i
$477$		0			0
$478$	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	$0.647498\pi$
$480$		0			0
$481$		−	0.908600i		−	0.0414286i
$482$	0.0607053	+	0.730858i	0.00276505	+	0.0332897i
$483$		0			0
$484$	21.0880	−	3.52748i	0.958543	−	0.160340i
$485$	0.445387			0.0202240
$486$		0			0
$487$			2.69121i			0.121950i	0.998139	+	0.0609752i	$0.0194210\pi$
$487$			2.69121i			0.121950i	−0.998139	+	0.0609752i	$0.980579\pi$
$488$	−10.0069	−	39.4187i	−0.452991	−	1.78440i
$489$		0			0
$490$	−4.85508	+	8.62718i	−0.219330	+	0.389736i
$491$		−	0.816644i		−	0.0368546i	−0.999830	−	0.0184273i	$-0.994134\pi$
$491$		−	0.816644i		−	0.0368546i	0.999830	−	0.0184273i	$-0.00586593\pi$
$492$		0			0
$493$			7.66297i			0.345123i
$494$	0.0657819	+	0.791978i	0.00295967	+	0.0356328i
$495$		0			0
$496$	−21.5114	+	7.40379i	−0.965891	+	0.332440i
$497$	−3.44337	−	1.05660i	−0.154456	−	0.0473951i
$498$		0			0
$499$			6.19049i			0.277124i	0.990354	+	0.138562i	$0.0442481\pi$
$499$			6.19049i			0.277124i	−0.990354	+	0.138562i	$0.955752\pi$
$500$	−0.329965	−	1.97259i	−0.0147565	−	0.0882170i
$501$		0			0
$502$	−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	$0.324573\pi$
$504$		0			0
$505$	12.8540			0.571997
$506$	−3.09218	+	0.256838i	−0.137464	+	0.0114178i
$507$		0			0
$508$	3.90828	+	23.3644i	0.173402	+	1.03663i
$509$			31.9990i			1.41833i	0.705042	+	0.709165i	$0.250928\pi$
$509$			31.9990i			1.41833i	−0.705042	+	0.709165i	$0.749072\pi$
$510$		0			0
$511$	25.5685	+	7.84575i	1.13108	+	0.347075i
$512$	−16.6204	+	15.3546i	−0.734524	+	0.678582i
$513$		0			0
$514$	−3.52651	−	42.4572i	−0.155548	−	1.87271i
$515$		−	14.3031i		−	0.630270i
$516$		0			0
$517$			2.02327i			0.0889834i
$518$	−3.97430	+	18.2116i	−0.174621	+	0.800170i
$519$		0			0
$520$	0.500000	−	0.126931i	0.0219264	−	0.00556629i
$521$			38.3707i			1.68105i	0.541773	+	0.840525i	$0.317753\pi$
$521$			38.3707i			1.68105i	−0.541773	+	0.840525i	$0.682247\pi$
$522$		0			0
$523$	−27.0855			−1.18437			−0.592183	−	0.805804i	$-0.701734\pi$
$523$	−27.0855			−1.18437			−0.592183	+	0.805804i	$0.701734\pi$
$524$	−32.8115	+	5.48854i	−1.43338	+	0.239768i
$525$		0			0
$526$	0.520219	+	6.26315i	0.0226826	+	0.273086i
$527$		−	13.6186i		−	0.593234i
$528$		0			0
$529$	7.44790			0.323822
$530$	−0.815991	−	9.82408i	−0.0354444	−	0.426731i
$531$		0			0
$532$	2.14568	−	16.1618i	0.0930271	−	0.700702i
$533$	1.75966			0.0762192
$534$		0			0
$535$	−18.3230			−0.792174
$536$	−7.00774	−	27.6045i	−0.302688	−	1.19233i
$537$		0			0
$538$	0.983632	+	11.8424i	0.0424074	+	0.510561i
$539$	−2.18436	+	3.22418i	−0.0940872	+	0.138875i
$540$		0			0
$541$	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
$543$		0			0
$544$	−5.45326	−	12.3990i	−0.233806	−	0.531604i
$545$		−	4.03790i		−	0.172964i
$546$		0			0
$547$		−	7.41113i		−	0.316877i	−0.987369	−	0.158438i	$-0.949354\pi$
$547$		−	7.41113i		−	0.316877i	0.987369	−	0.158438i	$-0.0506460\pi$
$548$	−19.5022	+	3.26222i	−0.833093	+	0.139355i
$549$		0			0
$550$	−0.0651274	−	0.784098i	−0.00277704	−	0.0334341i
$551$	−9.86028			−0.420062
$552$		0			0
$553$	33.0322	+	10.1360i	1.40467	+	0.431026i
$554$	5.54051	−	0.460196i	0.235394	−	0.0195519i
$555$		0			0
$556$	−40.6081	+	6.79270i	−1.72217	+	0.288075i
$557$	0.317738			0.0134630			0.00673149	−	0.999977i	$-0.497857\pi$
$557$	0.317738			0.0134630			0.00673149	+	0.999977i	$0.497857\pi$
$558$		0			0
$559$	0.117400			0.00496549
$560$	−10.5770	+	0.357103i	−0.446959	+	0.0150903i
$561$		0			0
$562$	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	$0.516804\pi$
$564$		0			0
$565$		−	3.14680i		−	0.132387i
$566$	6.11844	−	0.508200i	0.257177	−	0.0213612i
$567$		0			0
$568$	−0.947448	−	3.73214i	−0.0397540	−	0.156597i
$569$	−25.4990			−1.06897			−0.534487	−	0.845177i	$-0.679495\pi$
$569$	−25.4990			−1.06897			−0.534487	+	0.845177i	$0.679495\pi$
$570$		0			0
$571$			43.8357i			1.83447i	0.398350	+	0.917233i	$0.369583\pi$
$571$			43.8357i			1.83447i	−0.398350	+	0.917233i	$0.630417\pi$
$572$	0.200158	−	0.0334813i	0.00836902	−	0.00139992i
$573$		0			0
$574$	−35.2698	−	7.69690i	−1.47213	−	0.321262i
$575$		−	3.94362i		−	0.164460i
$576$		0			0
$577$			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
$579$		0			0
$580$	1.05597	+	6.31280i	0.0438468	+	0.262125i
$581$	7.33659	−	23.9092i	0.304373	−	0.991922i
$582$		0			0
$583$		−	3.87810i		−	0.160614i
$584$	7.03522	+	27.7128i	0.291119	+	1.14676i
$585$		0			0
$586$	−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	$0.754833\pi$
$588$		0			0
$589$	17.5236			0.722048
$590$	1.03010	+	12.4018i	0.0424086	+	0.510576i
$591$		0			0
$592$	−18.8424	+	6.48517i	−0.774417	+	0.266539i
$593$		−	5.30521i		−	0.217859i	−0.994049	−	0.108929i	$-0.965258\pi$
$593$		−	5.30521i		−	0.217859i	0.994049	−	0.108929i	$-0.0347423\pi$
$594$		0			0
$595$	1.85845	−	6.05649i	0.0761888	−	0.248292i
$596$	−14.3725	+	2.40415i	−0.588719	+	0.0984777i
$597$		0			0
$598$	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	$0.988539\pi$
$600$		0			0
$601$		−	20.8508i		−	0.850523i	−0.905071	−	0.425262i	$-0.860182\pi$
$601$		−	20.8508i		−	0.850523i	0.905071	−	0.425262i	$-0.139818\pi$
$602$	−2.35311	−	0.513518i	−0.0959057	−	0.0209294i
$603$		0			0
$604$	5.00910	+	29.9454i	0.203817	+	1.21846i
$605$			10.6905i			0.434630i
$606$		0			0
$607$	−5.84505			−0.237243			−0.118622	−	0.992940i	$-0.537848\pi$
$607$	−5.84505			−0.237243			−0.118622	+	0.992940i	$0.537848\pi$
$608$	15.9544	−	7.01695i	0.647036	−	0.284575i
$609$		0			0
$610$	20.2647	−	1.68319i	0.820495	−	0.0681505i
$611$		−	0.663273i		−	0.0268331i
$612$		0			0
$613$	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
$615$		0			0
$616$	−4.15832	−	0.204424i	−0.167544	−	0.00823648i
$617$	−31.3037			−1.26024			−0.630120	−	0.776497i	$-0.716994\pi$
$617$	−31.3037			−1.26024			−0.630120	+	0.776497i	$0.716994\pi$
$618$		0			0
$619$	13.7799			0.553861			0.276930	−	0.960890i	$-0.410683\pi$
$619$	13.7799			0.553861			0.276930	+	0.960890i	$0.410683\pi$
$620$	−1.87666	−	11.2191i	−0.0753687	−	0.450568i
$621$		0			0
$622$	−41.8014	+	3.47203i	−1.67608	+	0.139216i
$623$	−20.2753	−	6.22150i	−0.812312	−	0.249259i
$624$		0			0
$625$	1.00000			0.0400000
$626$	−1.36980	−	16.4916i	−0.0547481	−	0.659137i
$627$		0			0
$628$	−3.53647	−	21.1417i	−0.141120	−	0.843645i
$629$		−	11.9288i		−	0.475634i
$630$		0			0
$631$		−	15.3886i		−	0.612610i	−0.951933	−	0.306305i	$-0.900907\pi$
$631$		−	15.3886i		−	0.612610i	0.951933	−	0.306305i	$-0.0990928\pi$
$632$	9.08887	+	35.8024i	0.361536	+	1.42414i
$633$		0			0
$634$	−22.6185	+	1.87870i	−0.898295	+	0.0746126i
$635$	−11.8445			−0.470036
$636$		0			0
$637$	0.716082	−	1.05696i	0.0283722	−	0.0418781i
$638$	0.208424	+	2.50931i	0.00825160	+	0.0993447i
$639$		0			0
$640$	−6.20104	−	9.46293i	−0.245118	−	0.374055i
$641$	4.57385			0.180656			0.0903282	−	0.995912i	$-0.471208\pi$
$641$	4.57385			0.180656			0.0903282	+	0.995912i	$0.471208\pi$
$642$		0			0
$643$	−40.9959			−1.61672			−0.808360	−	0.588689i	$-0.799644\pi$
$643$	−40.9959			−1.61672			−0.808360	+	0.588689i	$0.799644\pi$
$644$	−20.6861	−	2.74635i	−0.815148	−	0.108221i
$645$		0			0
$646$	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	$0.460681\pi$
$648$		0			0
$649$			4.89567i			0.192172i
$650$	0.0213502	+	0.257045i	0.000837424	+	0.0100821i
$651$		0			0
$652$	−6.84630	−	40.9285i	−0.268122	−	1.60288i
$653$	−27.6655			−1.08263			−0.541316	−	0.840819i	$-0.682074\pi$
$653$	−27.6655			−1.08263			−0.541316	+	0.840819i	$0.682074\pi$
$654$		0			0
$655$		−	16.6337i		−	0.649932i
$656$	−12.5596	−	36.4915i	−0.490371	−	1.42475i
$657$		0			0
$658$	−2.90122	+	13.2943i	−0.113101	+	0.518267i
$659$			33.8406i			1.31824i	0.752036	+	0.659122i	$0.229072\pi$
$659$			33.8406i			1.31824i	−0.752036	+	0.659122i	$0.770928\pi$
$660$		0			0
$661$		−	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			0
$664$	25.9143	−	6.57866i	1.00567	−	0.255302i
$665$	7.79316	+	2.39134i	0.302206	+	0.0927324i
$666$		0			0
$667$			12.6206i			0.488671i
$668$	−16.5201	+	2.76340i	−0.639183	+	0.106919i
$669$		0			0
$670$	14.1912	−	1.17872i	0.548254	−	0.0455381i
$671$	7.99958			0.308820
$672$		0			0
$673$	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
$675$		0			0
$676$	25.5781	−	4.27857i	0.983773	−	0.164560i
$677$		−	7.67384i		−	0.294930i	−0.989067	−	0.147465i	$-0.952889\pi$
$677$		−	7.67384i		−	0.294930i	0.989067	−	0.147465i	$-0.0471113\pi$
$678$		0			0
$679$	1.12654	+	0.345681i	0.0432327	+	0.0132660i
$680$	6.56441	−	1.66645i	0.251733	−	0.0639056i
$681$		0			0
$682$	−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	$-0.137149\pi$
$684$		0			0
$685$		−	9.88658i		−	0.377747i
$686$	−18.9761	+	18.0529i	−0.724510	+	0.689265i
$687$		0			0
$688$	−0.837947	−	2.43462i	−0.0319464	−	0.0928190i
$689$			1.27132i			0.0484336i
$690$		0			0
$691$	19.9109			0.757446			0.378723	−	0.925510i	$-0.376363\pi$
$691$	19.9109			0.757446			0.378723	+	0.925510i	$0.376363\pi$
$692$	7.21151	+	43.1118i	0.274140	+	1.63886i
$693$		0			0
$694$	1.66870	+	20.0902i	0.0633429	+	0.762614i
$695$		−	20.5861i		−	0.780877i
$696$		0			0
$697$	23.1022			0.875059
$698$	0.783884	+	9.43752i	0.0296704	+	0.357215i
$699$		0			0
$700$	0.696403	−	5.24548i	0.0263216	−	0.198260i
$701$	−41.1901			−1.55573			−0.777864	−	0.628433i	$-0.783697\pi$
$701$	−41.1901			−1.55573			−0.777864	+	0.628433i	$0.783697\pi$
$702$		0			0
$703$	15.3494			0.578912
$704$	−2.12296	−	3.91186i	−0.0800122	−	0.147434i
$705$		0			0
$706$	2.18602	+	26.3185i	0.0822720	+	0.990509i
$707$	32.5124	+	9.97647i	1.22275	+	0.375204i
$708$		0			0
$709$	−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
$711$		0			0
$712$	−5.57877	−	21.9756i	−0.209073	−	0.823571i
$713$		−	22.4292i		−	0.839980i
$714$		0			0
$715$			0.101469i			0.00379474i
$716$	−6.05610	−	36.2045i	−0.226327	−	1.35303i
$717$		0			0
$718$	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	$0.271996\pi$
$720$		0			0
$721$	11.1012	−	36.1776i	0.413429	−	1.34732i
$722$	13.3986	−	1.11289i	0.498645	−	0.0414176i
$723$		0			0
$724$	4.20546	+	25.1410i	0.156295	+	0.934359i
$725$	−3.20026			−0.118855
$726$		0			0
$727$	44.9984			1.66890			0.834449	−	0.551085i	$-0.185786\pi$
$727$	44.9984			1.66890			0.834449	+	0.551085i	$0.185786\pi$
$728$	1.36319	+	0.0670147i	0.0505232	+	0.00248373i
$729$		0			0
$730$	−14.2468	+	1.18335i	−0.527299	+	0.0437976i
$731$	1.54132			0.0570079
$732$		0			0
$733$		−	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
$735$		0			0
$736$	−8.98128	−	20.4207i	−0.331054	−	0.752716i
$737$	5.60203			0.206353
$738$		0			0
$739$			29.0684i			1.06930i	0.845075	+	0.534648i	$0.179556\pi$
$739$			29.0684i			1.06930i	−0.845075	+	0.534648i	$0.820444\pi$
$740$	−1.64382	−	9.82706i	−0.0604279	−	0.361250i
$741$		0			0
$742$	5.56089	−	25.4819i	0.204147	−	0.935469i
$743$			21.0881i			0.773647i	0.922154	+	0.386824i	$0.126428\pi$
$743$			21.0881i			0.773647i	−0.922154	+	0.386824i	$0.873572\pi$
$744$		0			0
$745$		−	7.28607i		−	0.266941i
$746$	51.2099	−	4.25351i	1.87493	−	0.155732i
$747$		0			0
$748$	2.62784	−	0.439570i	0.0960832	−	0.0160723i
$749$	−46.3454	−	14.2212i	−1.69342	−	0.519630i
$750$		0			0
$751$			41.9734i			1.53163i	0.643061	+	0.765815i	$0.277664\pi$
$751$			41.9734i			1.53163i	−0.643061	+	0.765815i	$0.722336\pi$
$752$	−13.7548	+	4.73414i	−0.501587	+	0.172636i
$753$		0			0
$754$	−0.0683261	−	0.822608i	−0.00248829	−	0.0299576i
$755$	−15.1807			−0.552483
$756$		0			0
$757$	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
$759$		0			0
$760$	2.14430	+	8.44671i	0.0777819	+	0.306394i
$761$			43.3157i			1.57019i	0.619374	+	0.785096i	$0.287387\pi$
$761$			43.3157i			1.57019i	−0.619374	+	0.785096i	$0.712613\pi$
$762$		0			0
$763$	3.13396	−	10.2133i	0.113457	−	0.369745i
$764$	7.08311	+	42.3442i	0.256258	+	1.53196i
$765$		0			0
$766$	−33.3061	+	2.76642i	−1.20340	+	0.0999548i
$767$		−	1.60491i		−	0.0579499i
$768$		0			0
$769$			36.5255i			1.31714i	0.752518	+	0.658572i	$0.228839\pi$
$769$			36.5255i			1.31714i	−0.752518	+	0.658572i	$0.771161\pi$
$770$	0.443836	−	2.03381i	0.0159948	−	0.0732933i
$771$		0			0
$772$	10.4138	−	1.74196i	0.374800	−	0.0626946i
$773$			38.9312i			1.40026i	0.714017	+	0.700128i	$0.246874\pi$
$773$			38.9312i			1.40026i	−0.714017	+	0.700128i	$0.753126\pi$
$774$		0			0
$775$	5.68747			0.204300
$776$	0.309969	+	1.22102i	0.0111273	+	0.0438319i
$777$		0			0
$778$	−32.1212	+	2.66800i	−1.15160	+	0.0956524i
$779$			29.7266i			1.06507i
$780$		0			0
$781$	0.757395			0.0271017
$782$	13.3085	−	1.10541i	0.475911	−	0.0395293i
$783$		0			0
$784$	−27.0300	−	7.30593i	−0.965359	−	0.260926i
$785$	10.7177			0.382531
$786$		0			0
$787$	−36.3954			−1.29736			−0.648679	−	0.761063i	$-0.724678\pi$
$787$	−36.3954			−1.29736			−0.648679	+	0.761063i	$0.724678\pi$
$788$	16.6646	−	2.78756i	0.593652	−	0.0993029i
$789$		0			0
$790$	−18.4056	+	1.52878i	−0.654843	+	0.0543915i
$791$	2.44235	−	7.95937i	0.0868398	−	0.283003i
$792$		0			0
$793$	−2.62244			−0.0931255
$794$	−1.23414	−	14.8583i	−0.0437979	−	0.527302i
$795$		0			0
$796$	36.5521	−	6.11424i	1.29556	−	0.216714i
$797$		−	34.6389i		−	1.22697i	−0.789705	−	0.613486i	$-0.789767\pi$
$797$		−	34.6389i		−	1.22697i	0.789705	−	0.613486i	$-0.210233\pi$
$798$		0			0
$799$		−	8.70799i		−	0.308066i
$800$	5.17816	−	2.27742i	0.183076	−	0.0805191i
$801$		0			0
$802$	−39.6878	+	3.29648i	−1.40143	+	0.116403i
$803$	−5.62400			−0.198467
$804$		0			0
$805$	3.06078	−	9.97479i	0.107878	−	0.351565i
$806$	0.121429	+	1.46193i	0.00427714	+	0.0514944i
$807$		0			0
$808$	8.94583	+	35.2389i	0.314713	+	1.23970i
$809$	−12.5608			−0.441615			−0.220808	−	0.975317i	$-0.570869\pi$
$809$	−12.5608			−0.441615			−0.220808	+	0.975317i	$0.570869\pi$
$810$		0			0
$811$	−37.5695			−1.31925			−0.659623	−	0.751597i	$-0.729284\pi$
$811$	−37.5695			−1.31925			−0.659623	+	0.751597i	$0.729284\pi$
$812$	−2.22867	+	16.7869i	−0.0782109	+	0.589103i
$813$		0			0
$814$	−0.324452	−	3.90622i	−0.0113720	−	0.136913i
$815$	20.7486			0.726791
$816$		0			0
$817$			1.98329i			0.0693865i
$818$	2.72860	+	32.8509i	0.0954034	+	1.14860i
$819$		0			0
$820$	19.0318	−	3.18353i	0.664618	−	0.111174i
$821$	35.6019			1.24252			0.621258	−	0.783606i	$-0.286622\pi$
$821$	35.6019			1.24252			0.621258	+	0.783606i	$0.286622\pi$
$822$		0			0
$823$		−	31.6851i		−	1.10447i	−0.833688	−	0.552236i	$-0.813775\pi$
$823$		−	31.6851i		−	1.10447i	0.833688	−	0.552236i	$-0.186225\pi$
$824$	39.2115	−	9.95432i	1.36600	−	0.346775i
$825$		0			0
$826$	−7.02002	+	32.1681i	−0.244258	+	1.11927i
$827$			8.15712i			0.283651i	0.989892	+	0.141825i	$0.0452971\pi$
$827$			8.15712i			0.283651i	−0.989892	+	0.141825i	$0.954703\pi$
$828$		0			0
$829$			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
$831$		0			0
$832$	0.695954	+	1.28239i	0.0241279	+	0.0444590i
$833$	9.40132	−	13.8766i	0.325736	−	0.480795i
$834$		0			0
$835$		−	8.37483i		−	0.289823i
$836$	0.565615	+	3.38135i	0.0195622	+	0.116947i
$837$		0			0
$838$	−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	$0.357654\pi$
$840$		0			0
$841$	−18.7584			−0.646840
$842$	42.6866	−	3.54557i	1.47108	−	0.122188i
$843$		0			0
$844$	5.75645	+	34.4131i	0.198145	+	1.18455i
$845$			12.9667i			0.446069i
$846$		0			0
$847$	−8.29726	+	27.0400i	−0.285097	+	0.929104i
$848$	26.3645	−	9.07413i	0.905361	−	0.311607i
$849$		0			0
$850$	0.280303	+	3.37469i	0.00961431	+	0.115751i
$851$		−	19.6463i		−	0.673466i
$852$		0			0
$853$		−	47.1551i		−	1.61456i	−0.590169	−	0.807280i	$-0.700939\pi$
$853$		−	47.1551i		−	1.61456i	0.590169	−	0.807280i	$-0.299061\pi$
$854$	52.5630	+	11.4708i	1.79867	+	0.392522i
$855$		0			0
$856$	−12.7520	−	50.2320i	−0.435855	−	1.71690i
$857$			13.6591i			0.466587i	0.972406	+	0.233293i	$0.0749503\pi$
$857$			13.6591i			0.466587i	−0.972406	+	0.233293i	$0.925050\pi$
$858$		0			0
$859$	−38.2512			−1.30511			−0.652556	−	0.757740i	$-0.726303\pi$
$859$	−38.2512			−1.30511			−0.652556	+	0.757740i	$0.726303\pi$
$860$	1.26975	−	0.212397i	0.0432982	−	0.00724269i
$861$		0			0
$862$	−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	$-0.249202\pi$
$864$		0			0
$865$	−21.8554			−0.743105
$866$	−3.54460	−	42.6750i	−0.120450	−	1.45015i
$867$		0			0
$868$	3.96077	−	29.8335i	0.134437	−	1.01261i
$869$	−7.26570			−0.246472
$870$		0			0
$871$	−1.83647			−0.0622263
$872$	11.0698	−	2.81019i	0.374870	−	0.0951652i
$873$		0			0
$874$	1.42238	+	17.1246i	0.0481126	+	0.579249i
$875$	2.52935	+	0.776136i	0.0855077	+	0.0262382i
$876$		0			0
$877$	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			0
$880$	2.10425	−	0.724242i	0.0709344	−	0.0244142i
$881$			13.0135i			0.438437i	0.975676	+	0.219219i	$0.0703508\pi$
$881$			13.0135i			0.438437i	−0.975676	+	0.219219i	$0.929649\pi$
$882$		0			0
$883$		−	29.3613i		−	0.988085i	−0.869438	−	0.494043i	$-0.835519\pi$
$883$		−	29.3613i		−	0.988085i	0.869438	−	0.494043i	$-0.164481\pi$
$884$	−0.861462	+	0.144101i	−0.0289741	+	0.00484663i
$885$		0			0
$886$	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	$0.475212\pi$
$888$		0			0
$889$	−29.9590	−	9.19296i	−1.00479	−	0.308322i
$890$	11.2974	−	0.938368i	0.378691	−	0.0314542i
$891$		0			0
$892$	23.5079	−	3.93227i	0.787102	−	0.131662i
$893$	11.2050			0.374960
$894$		0			0
$895$	18.3538			0.613499
$896$	−8.34008	−	28.7479i	−0.278623	−	0.960401i
$897$		0			0
$898$	−42.7064	+	3.54721i	−1.42513	+	0.118372i
$899$	−18.2014			−0.607049
$900$		0			0
$901$			16.6910i			0.556058i
$902$	7.56505	−	0.628356i	0.251889	−	0.0209220i
$903$		0			0
$904$	8.62686	−	2.19003i	0.286925	−	0.0728394i
$905$	−12.7452			−0.423664
$906$		0			0
$907$			0.827765i			0.0274855i	0.999906	+	0.0137427i	$0.00437459\pi$
$907$			0.827765i			0.0274855i	−0.999906	+	0.0137427i	$0.995625\pi$
$908$	−4.21731	+	0.705449i	−0.139956	+	0.0234112i
$909$		0			0
$910$	−0.145499	+	0.666726i	−0.00482326	+	0.0221018i
$911$			17.4184i			0.577096i	0.957465	+	0.288548i	$0.0931725\pi$
$911$			17.4184i			0.577096i	−0.957465	+	0.288548i	$0.906827\pi$
$912$		0			0
$913$			5.25902i			0.174048i
$914$	10.7905	−	0.896263i	0.356918	−	0.0296458i
$915$		0			0
$916$	2.34450	+	14.0159i	0.0774644	+	0.463097i
$917$	12.9100	−	42.0725i	0.426326	−	1.38935i
$918$		0			0
$919$			47.0332i			1.55148i	0.631052	+	0.775741i	$0.282624\pi$
$919$			47.0332i			1.55148i	−0.631052	+	0.775741i	$0.717376\pi$
$920$	10.8113	−	2.74458i	0.356438	−	0.0904861i
$921$		0			0
$922$	−0.907641	−	10.9275i	−0.0298916	−	0.359878i
$923$	−0.248291			−0.00817259
$924$		0			0
$925$	4.98180			0.163800
$926$	2.50731	+	30.1866i	0.0823953	+	0.991994i
$927$		0			0
$928$	−16.5714	+	7.28834i	−0.543984	+	0.239251i
$929$		−	13.6389i		−	0.447478i	−0.974649	−	0.223739i	$-0.928174\pi$
$929$		−	13.6389i		−	0.447478i	0.974649	−	0.223739i	$-0.0718264\pi$
$930$		0			0
$931$	17.8556	+	12.0971i	0.585194	+	0.396466i
$932$	−21.4305	+	3.58477i	−0.701978	+	0.117423i
$933$		0			0
$934$	−16.6888	+	1.38618i	−0.546074	+	0.0453571i
$935$			1.33217i			0.0435667i
$936$		0			0
$937$			40.8581i			1.33478i	0.744710	+	0.667388i	$0.232588\pi$
$937$			40.8581i			1.33478i	−0.744710	+	0.667388i	$0.767412\pi$
$938$	36.8094	+	8.03288i	1.20187	+	0.262283i
$939$		0			0
$940$	−1.19998	−	7.17370i	−0.0391390	−	0.233980i
$941$		−	4.38655i		−	0.142997i	−0.997441	−	0.0714987i	$-0.977222\pi$
$941$		−	4.38655i		−	0.142997i	0.997441	−	0.0714987i	$-0.0227782\pi$
$942$		0			0
$943$	38.0484			1.23903
$944$	−33.2823	+	11.4551i	−1.08325	+	0.372832i
$945$		0			0
$946$	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	$-0.0556539\pi$
$948$		0			0
$949$	1.84367			0.0598480
$950$	−4.34237	+	0.360678i	−0.140885	+	0.0117020i
$951$		0			0
$952$	17.8971	+	0.879823i	0.580048	+	0.0285152i
$953$	26.6394			0.862935			0.431468	−	0.902128i	$-0.357996\pi$
$953$	26.6394			0.862935			0.431468	+	0.902128i	$0.357996\pi$
$954$		0			0
$955$	−21.4663			−0.694632
$956$	−5.07355	−	30.3306i	−0.164090	−	0.980963i
$957$		0			0
$958$	27.5742	−	2.29032i	0.890881	−	0.0739968i
$959$	7.67333	−	25.0066i	0.247785	−	0.807506i
$960$		0			0
$961$	1.34731			0.0434616
$962$	0.106362	+	1.28054i	0.00342926	+	0.0412864i
$963$		0			0
$964$	−0.171111	−	1.02294i	−0.00551112	−	0.0329466i
$965$			5.27923i			0.169945i
$966$		0			0
$967$		−	13.1899i		−	0.424158i	−0.977253	−	0.212079i	$-0.931977\pi$
$967$		−	13.1899i		−	0.424158i	0.977253	−	0.212079i	$-0.0680233\pi$
$968$	−29.3076	+	7.44009i	−0.941982	+	0.239133i
$969$		0			0
$970$	−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	$0.538717\pi$
$972$		0			0
$973$	15.9776	−	52.0696i	0.512220	−	1.66927i
$974$	−0.315038	−	3.79288i	−0.0100945	−	0.121532i
$975$		0			0
$976$	18.7178	+	54.3837i	0.599141	+	1.74078i
$977$	26.1229			0.835745			0.417873	−	0.908506i	$-0.362776\pi$
$977$	26.1229			0.835745			0.417873	+	0.908506i	$0.362776\pi$
$978$		0			0
$979$	4.45971			0.142533
$980$	5.83265	−	12.7271i	0.186317	−	0.406554i
$981$		0			0
$982$	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	$0.679144\pi$
$984$		0			0
$985$			8.44807i			0.269178i
$986$	−0.897041	−	10.7999i	−0.0285676	−	0.343938i
$987$		0			0
$988$	−0.185421	−	1.10848i	−0.00589902	−	0.0352655i
$989$	2.53849			0.0807193
$990$		0			0
$991$		−	58.4657i		−	1.85722i	−0.371053	−	0.928612i	$-0.621003\pi$
$991$		−	58.4657i		−	1.85722i	0.371053	−	0.928612i	$-0.378997\pi$
$992$	29.4506	−	12.9528i	0.935058	−	0.411251i
$993$		0			0
$994$	4.97663	+	1.08605i	0.157849	+	0.0344473i
$995$			18.5300i			0.587440i
$996$		0			0
$997$			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
$999$		0			0

Twists

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

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

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:	\( N \)	\(=\)	\( 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1260.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40936 + 0.117062i) q^{2} +(1.97259 - 0.329965i) q^{4} +1.00000i q^{5} +(-0.776136 + 2.52935i) q^{7} +(-2.74147 + 0.695955i) q^{8} +O(q^{10})\)	\(q+(-1.40936 + 0.117062i) q^{2} +(1.97259 - 0.329965i) q^{4} +1.00000i q^{5} +(-0.776136 + 2.52935i) q^{7} +(-2.74147 + 0.695955i) q^{8} +(-0.117062 - 1.40936i) q^{10} -0.556350i q^{11} +0.182384i q^{13} +(0.797764 - 3.65562i) q^{14} +(3.78225 - 1.30177i) q^{16} +2.39449i q^{17} -3.08109 q^{19} +(0.329965 + 1.97259i) q^{20} +(0.0651274 + 0.784098i) q^{22} +3.94362i q^{23} -1.00000 q^{25} +(-0.0213502 - 0.257045i) q^{26} +(-0.696403 + 5.24548i) q^{28} +3.20026 q^{29} -5.68747 q^{31} +(-5.17816 + 2.27742i) q^{32} +(-0.280303 - 3.37469i) q^{34} +(-2.52935 - 0.776136i) q^{35} -4.98180 q^{37} +(4.34237 - 0.360678i) q^{38} +(-0.695955 - 2.74147i) q^{40} -9.64809i q^{41} -0.643697i q^{43} +(-0.183576 - 1.09745i) q^{44} +(-0.461647 - 5.55798i) q^{46} -3.63668 q^{47} +(-5.79523 - 3.92624i) q^{49} +(1.40936 - 0.117062i) q^{50} +(0.0601803 + 0.359769i) q^{52} +6.97060 q^{53} +0.556350 q^{55} +(0.367437 - 7.47429i) q^{56} +(-4.51031 + 0.374628i) q^{58} -8.79962 q^{59} +14.3787i q^{61} +(8.01569 - 0.665786i) q^{62} +(7.03129 - 3.81588i) q^{64} -0.182384 q^{65} +10.0692i q^{67} +(0.790096 + 4.72335i) q^{68} +(3.65562 + 0.797764i) q^{70} +1.36136i q^{71} -10.1087i q^{73} +(7.02115 - 0.583179i) q^{74} +(-6.07774 + 1.01665i) q^{76} +(1.40721 + 0.431803i) q^{77} -13.0596i q^{79} +(1.30177 + 3.78225i) q^{80} +(1.12942 + 13.5976i) q^{82} -9.45272 q^{83} -2.39449 q^{85} +(0.0753523 + 0.907200i) q^{86} +(0.387195 + 1.52522i) q^{88} +8.01600i q^{89} +(-0.461313 - 0.141555i) q^{91} +(1.30125 + 7.77915i) q^{92} +(5.12540 - 0.425717i) q^{94} -3.08109i q^{95} -0.445387i q^{97} +(8.62718 + 4.85508i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{2} - 2 q^{4} + 4 q^{7} - 2 q^{8}+O(q^{10}) \) 16 * q - 2 * q^2 - 2 * q^4 + 4 * q^7 - 2 * q^8	\( 16 q - 2 q^{2} - 2 q^{4} + 4 q^{7} - 2 q^{8} - 10 q^{14} + 6 q^{16} + 24 q^{19} - 12 q^{22} - 16 q^{25} - 12 q^{26} - 22 q^{28} - 16 q^{29} - 8 q^{31} + 18 q^{32} - 24 q^{34} + 24 q^{37} + 28 q^{38} - 12 q^{40} + 8 q^{44} - 20 q^{46} + 16 q^{47} - 16 q^{49} + 2 q^{50} + 20 q^{52} + 32 q^{53} + 2 q^{56} - 32 q^{58} + 8 q^{59} + 16 q^{62} - 2 q^{64} + 8 q^{65} + 4 q^{68} - 20 q^{70} + 4 q^{74} - 16 q^{76} + 8 q^{77} - 16 q^{80} + 4 q^{82} + 8 q^{83} - 64 q^{86} - 52 q^{88} - 16 q^{91} - 64 q^{92} - 16 q^{94} - 2 q^{98}+O(q^{100}) \) 16 * q - 2 * q^2 - 2 * q^4 + 4 * q^7 - 2 * q^8 - 10 * q^14 + 6 * q^16 + 24 * q^19 - 12 * q^22 - 16 * q^25 - 12 * q^26 - 22 * q^28 - 16 * q^29 - 8 * q^31 + 18 * q^32 - 24 * q^34 + 24 * q^37 + 28 * q^38 - 12 * q^40 + 8 * q^44 - 20 * q^46 + 16 * q^47 - 16 * q^49 + 2 * q^50 + 20 * q^52 + 32 * q^53 + 2 * q^56 - 32 * q^58 + 8 * q^59 + 16 * q^62 - 2 * q^64 + 8 * q^65 + 4 * q^68 - 20 * q^70 + 4 * q^74 - 16 * q^76 + 8 * q^77 - 16 * q^80 + 4 * q^82 + 8 * q^83 - 64 * q^86 - 52 * q^88 - 16 * q^91 - 64 * q^92 - 16 * q^94 - 2 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more