LMFDB - Embedded newform 400.2.u.d.161.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [400,2,Mod(81,400)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(400, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("400.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	400.u (of order $5$, degree $4$, not 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:	$3.19401608085$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.58140625.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 4x^{6} - 7x^{5} + 11x^{4} + 5x^{3} - 10x^{2} - 25x + 25 $ x^8 - 3x^7 + 4x^6 - 7x^5 + 11x^4 + 5x^3 - 10x^2 - 25*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 5 $
Twist minimal:	no (minimal twist has level 50)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			161.1
Root			$1.66637 - 0.917186i$ of defining polynomial
Character	$\chi$	$=$	400.161
Dual form			400.2.u.d.241.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.529876 + 1.63079i) q^{3} +(2.02373 + 0.951057i) q^{5} +2.77447 q^{7} +(0.0483405 + 0.0351215i) q^{9} +O(q^{10})$	\(q+(-0.529876 + 1.63079i) q^{3} +(2.02373 + 0.951057i) q^{5} +2.77447 q^{7} +(0.0483405 + 0.0351215i) q^{9} +(2.24459 - 1.63079i) q^{11} +(-4.59343 - 3.33732i) q^{13} +(-2.62330 + 2.79634i) q^{15} +(1.59343 + 4.90406i) q^{17} +(-0.436451 - 1.34326i) q^{19} +(-1.47012 + 4.52458i) q^{21} +(-0.529876 + 0.384978i) q^{23} +(3.19098 + 3.84937i) q^{25} +(-4.24459 + 3.08388i) q^{27} +(1.26594 - 3.89618i) q^{29} +(2.20239 + 6.77827i) q^{31} +(1.47012 + 4.52458i) q^{33} +(5.61478 + 2.63868i) q^{35} +(0.847416 + 0.615684i) q^{37} +(7.87642 - 5.72255i) q^{39} +(-7.36789 - 5.35309i) q^{41} -9.24660 q^{43} +(0.0644258 + 0.117051i) q^{45} +(0.857358 - 2.63868i) q^{47} +0.697669 q^{49} -8.84181 q^{51} +(-0.162577 + 0.500362i) q^{53} +(6.09343 - 1.16555i) q^{55} +2.42184 q^{57} +(-3.05975 - 2.22304i) q^{59} +(8.76365 - 6.36716i) q^{61} +(0.134119 + 0.0974433i) q^{63} +(-6.12188 - 11.1224i) q^{65} +(1.33600 + 4.11180i) q^{67} +(-0.347049 - 1.06811i) q^{69} +(4.09343 - 12.5983i) q^{71} +(-3.40859 + 2.47648i) q^{73} +(-7.96834 + 3.16414i) q^{75} +(6.22754 - 4.52458i) q^{77} +(3.05975 - 9.41695i) q^{79} +(-2.72466 - 8.38563i) q^{81} +(-1.44497 - 4.44717i) q^{83} +(-1.43937 + 11.4399i) q^{85} +(5.68305 + 4.12898i) q^{87} +(7.43002 - 5.39823i) q^{89} +(-12.7443 - 9.25928i) q^{91} -12.2209 q^{93} +(0.394254 - 3.13348i) q^{95} +(-0.0278640 + 0.0857567i) q^{97} +0.165781 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 3 q^{3} - 4 q^{7} - q^{9}+O(q^{10}) $ 8 * q + 3 * q^3 - 4 * q^7 - q^9	$ 8 q + 3 q^{3} - 4 q^{7} - q^{9} - q^{11} - 13 q^{13} + 10 q^{15} - 11 q^{17} - 20 q^{19} - 19 q^{21} + 3 q^{23} + 30 q^{25} - 15 q^{27} - 15 q^{29} + 9 q^{31} + 19 q^{33} + 15 q^{35} - 6 q^{37} + 12 q^{39} - 9 q^{41} - 12 q^{43} + 15 q^{45} + q^{47} - 4 q^{49} - 26 q^{51} + 7 q^{53} + 25 q^{55} - 10 q^{59} + 6 q^{61} + 8 q^{63} - 10 q^{65} + 11 q^{67} + 43 q^{69} + 9 q^{71} - 8 q^{73} - 30 q^{75} + 33 q^{77} + 10 q^{79} - 17 q^{81} - 27 q^{83} + 5 q^{85} - 15 q^{89} - q^{91} - 46 q^{93} + 30 q^{95} - 36 q^{97} + 42 q^{99}+O(q^{100}) $ 8 * q + 3 * q^3 - 4 * q^7 - q^9 - q^11 - 13 * q^13 + 10 * q^15 - 11 * q^17 - 20 * q^19 - 19 * q^21 + 3 * q^23 + 30 * q^25 - 15 * q^27 - 15 * q^29 + 9 * q^31 + 19 * q^33 + 15 * q^35 - 6 * q^37 + 12 * q^39 - 9 * q^41 - 12 * q^43 + 15 * q^45 + q^47 - 4 * q^49 - 26 * q^51 + 7 * q^53 + 25 * q^55 - 10 * q^59 + 6 * q^61 + 8 * q^63 - 10 * q^65 + 11 * q^67 + 43 * q^69 + 9 * q^71 - 8 * q^73 - 30 * q^75 + 33 * q^77 + 10 * q^79 - 17 * q^81 - 27 * q^83 + 5 * q^85 - 15 * q^89 - q^91 - 46 * q^93 + 30 * q^95 - 36 * q^97 + 42 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$351$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.529876	+	1.63079i	−0.305924	+	0.941538i	0.673407	+	0.739272i	$0.264830\pi$
$3$	−0.529876	+	1.63079i	−0.305924	+	0.941538i	−0.979331	+	0.202265i	$0.935170\pi$
$4$		0			0
$5$	2.02373	+	0.951057i	0.905040	+	0.425325i
$5$	2.02373	+	0.951057i	0.905040	+	0.425325i
$6$		0			0
$7$	2.77447			1.04865			0.524325	−	0.851518i	$-0.324318\pi$
$7$	2.77447			1.04865			0.524325	+	0.851518i	$0.324318\pi$
$8$		0			0
$9$	0.0483405	+	0.0351215i	0.0161135	+	0.0117072i
$10$		0			0
$11$	2.24459	−	1.63079i	0.676770	−	0.491702i	−0.195515	−	0.980701i	$-0.562638\pi$
$11$	2.24459	−	1.63079i	0.676770	−	0.491702i	0.872284	+	0.488999i	$0.162638\pi$
$12$		0			0
$13$	−4.59343	−	3.33732i	−1.27399	−	0.925606i	−0.274633	−	0.961549i	$-0.588556\pi$
$13$	−4.59343	−	3.33732i	−1.27399	−	0.925606i	−0.999354	+	0.0359433i	$0.988556\pi$
$14$		0			0
$15$	−2.62330	+	2.79634i	−0.677334	+	0.722012i
$16$		0			0
$17$	1.59343	+	4.90406i	0.386462	+	1.18941i	0.935414	+	0.353555i	$0.115027\pi$
$17$	1.59343	+	4.90406i	0.386462	+	1.18941i	−0.548951	+	0.835854i	$0.684973\pi$
$18$		0			0
$19$	−0.436451	−	1.34326i	−0.100129	−	0.308164i	0.888428	−	0.459017i	$-0.151798\pi$
$19$	−0.436451	−	1.34326i	−0.100129	−	0.308164i	−0.988556	+	0.150852i	$0.951798\pi$
$20$		0			0
$21$	−1.47012	+	4.52458i	−0.320807	+	0.987343i
$22$		0			0
$23$	−0.529876	+	0.384978i	−0.110487	+	0.0802734i	−0.641657	−	0.766992i	$-0.721753\pi$
$23$	−0.529876	+	0.384978i	−0.110487	+	0.0802734i	0.531170	+	0.847265i	$0.321753\pi$
$24$		0			0
$25$	3.19098	+	3.84937i	0.638197	+	0.769873i
$26$		0			0
$27$	−4.24459	+	3.08388i	−0.816872	+	0.593492i
$28$		0			0
$29$	1.26594	−	3.89618i	0.235080	−	0.723502i	−0.762031	−	0.647541i	$-0.775798\pi$
$29$	1.26594	−	3.89618i	0.235080	−	0.723502i	0.997111	−	0.0759609i	$-0.0242024\pi$
$30$		0			0
$31$	2.20239	+	6.77827i	0.395562	+	1.21741i	0.928523	+	0.371274i	$0.121079\pi$
$31$	2.20239	+	6.77827i	0.395562	+	1.21741i	−0.532961	+	0.846140i	$0.678921\pi$
$32$		0			0
$33$	1.47012	+	4.52458i	0.255916	+	0.787628i
$34$		0			0
$35$	5.61478	+	2.63868i	0.949071	+	0.446018i
$36$		0			0
$37$	0.847416	+	0.615684i	0.139314	+	0.101218i	0.655260	−	0.755404i	$-0.272559\pi$
$37$	0.847416	+	0.615684i	0.139314	+	0.101218i	−0.515945	+	0.856622i	$0.672559\pi$
$38$		0			0
$39$	7.87642	−	5.72255i	1.26124	−	0.916342i
$40$		0			0
$41$	−7.36789	−	5.35309i	−1.15067	−	0.836012i	−0.162101	−	0.986774i	$-0.551827\pi$
$41$	−7.36789	−	5.35309i	−1.15067	−	0.836012i	−0.988570	+	0.150762i	$0.951827\pi$
$42$		0			0
$43$	−9.24660			−1.41009			−0.705047	−	0.709161i	$-0.749074\pi$
$43$	−9.24660			−1.41009			−0.705047	+	0.709161i	$0.749074\pi$
$44$		0			0
$45$	0.0644258	+	0.117051i	0.00960403	+	0.0174489i
$46$		0			0
$47$	0.857358	−	2.63868i	0.125058	−	0.384890i	−0.868853	−	0.495070i	$-0.835143\pi$
$47$	0.857358	−	2.63868i	0.125058	−	0.384890i	0.993912	+	0.110179i	$0.0351425\pi$
$48$		0			0
$49$	0.697669			0.0996670
$50$		0			0
$51$	−8.84181			−1.23810
$52$		0			0
$53$	−0.162577	+	0.500362i	−0.0223317	+	0.0687299i	−0.961601	−	0.274450i	$-0.911504\pi$
$53$	−0.162577	+	0.500362i	−0.0223317	+	0.0687299i	0.939270	+	0.343180i	$0.111504\pi$
$54$		0			0
$55$	6.09343	−	1.16555i	0.821637	−	0.157163i
$56$		0			0
$57$	2.42184			0.320780
$58$		0			0
$59$	−3.05975	−	2.22304i	−0.398346	−	0.289415i	0.370521	−	0.928824i	$-0.379179\pi$
$59$	−3.05975	−	2.22304i	−0.398346	−	0.289415i	−0.768867	+	0.639409i	$0.779179\pi$
$60$		0			0
$61$	8.76365	−	6.36716i	1.12207	−	0.815232i	0.137549	−	0.990495i	$-0.456078\pi$
$61$	8.76365	−	6.36716i	1.12207	−	0.815232i	0.984522	+	0.175263i	$0.0560776\pi$
$62$		0			0
$63$	0.134119	+	0.0974433i	0.0168974	+	0.0122767i
$64$		0			0
$65$	−6.12188	−	11.1224i	−0.759326	−	1.37957i
$66$		0			0
$67$	1.33600	+	4.11180i	0.163219	+	0.502336i	0.998901	−	0.0468778i	$-0.0149271\pi$
$67$	1.33600	+	4.11180i	0.163219	+	0.502336i	−0.835682	+	0.549214i	$0.814927\pi$
$68$		0			0
$69$	−0.347049	−	1.06811i	−0.0417798	−	0.128585i
$70$		0			0
$71$	4.09343	−	12.5983i	0.485800	−	1.49514i	−0.345018	−	0.938596i	$-0.612127\pi$
$71$	4.09343	−	12.5983i	0.485800	−	1.49514i	0.830819	−	0.556543i	$-0.187873\pi$
$72$		0			0
$73$	−3.40859	+	2.47648i	−0.398945	+	0.289850i	−0.769111	−	0.639115i	$-0.779301\pi$
$73$	−3.40859	+	2.47648i	−0.398945	+	0.289850i	0.370166	+	0.928966i	$0.379301\pi$
$74$		0			0
$75$	−7.96834	+	3.16414i	−0.920105	+	0.365363i
$76$		0			0
$77$	6.22754	−	4.52458i	0.709695	−	0.515623i
$78$		0			0
$79$	3.05975	−	9.41695i	0.344249	−	1.05949i	−0.617736	−	0.786386i	$-0.711950\pi$
$79$	3.05975	−	9.41695i	0.344249	−	1.05949i	0.961985	−	0.273104i	$-0.0880502\pi$
$80$		0			0
$81$	−2.72466	−	8.38563i	−0.302740	−	0.931737i
$82$		0			0
$83$	−1.44497	−	4.44717i	−0.158606	−	0.488141i	0.839902	−	0.542738i	$-0.182612\pi$
$83$	−1.44497	−	4.44717i	−0.158606	−	0.488141i	−0.998508	+	0.0545976i	$0.982612\pi$
$84$		0			0
$85$	−1.43937	+	11.4399i	−0.156122	+	1.24084i
$86$		0			0
$87$	5.68305	+	4.12898i	0.609287	+	0.442673i
$88$		0			0
$89$	7.43002	−	5.39823i	0.787581	−	0.572211i	−0.119664	−	0.992814i	$-0.538182\pi$
$89$	7.43002	−	5.39823i	0.787581	−	0.572211i	0.907245	+	0.420603i	$0.138182\pi$
$90$		0			0
$91$	−12.7443	−	9.25928i	−1.33597	−	0.970637i
$92$		0			0
$93$	−12.2209			−1.26725
$94$		0			0
$95$	0.394254	−	3.13348i	0.0404496	−	0.321488i
$96$		0			0
$97$	−0.0278640	+	0.0857567i	−0.00282917	+	0.00870727i	−0.952461	−	0.304660i	$-0.901457\pi$
$97$	−0.0278640	+	0.0857567i	−0.00282917	+	0.00870727i	0.949632	+	0.313367i	$0.101457\pi$
$98$		0			0
$99$	0.165781			0.0166616
$100$		0			0
$101$	−7.90632			−0.786709			−0.393354	−	0.919387i	$-0.628685\pi$
$101$	−7.90632			−0.786709			−0.393354	+	0.919387i	$0.628685\pi$
$102$		0			0
$103$	−2.42091	+	7.45079i	−0.238539	+	0.734148i	0.758093	+	0.652146i	$0.226131\pi$
$103$	−2.42091	+	7.45079i	−0.238539	+	0.734148i	−0.996632	+	0.0820014i	$0.973869\pi$
$104$		0			0
$105$	−7.27826	+	7.75836i	−0.710286	+	0.757138i
$106$		0			0
$107$	10.2220			0.988194			0.494097	−	0.869407i	$-0.335499\pi$
$107$	10.2220			0.988194			0.494097	+	0.869407i	$0.335499\pi$
$108$		0			0
$109$	−3.16400	−	2.29878i	−0.303056	−	0.220183i	0.425855	−	0.904791i	$-0.359973\pi$
$109$	−3.16400	−	2.29878i	−0.303056	−	0.220183i	−0.728911	+	0.684608i	$0.759973\pi$
$110$		0			0
$111$	−1.45308	+	1.05572i	−0.137920	+	0.100205i
$112$		0			0
$113$	5.15785	+	3.74740i	0.485210	+	0.352526i	0.803339	−	0.595522i	$-0.203055\pi$
$113$	5.15785	+	3.74740i	0.485210	+	0.352526i	−0.318129	+	0.948047i	$0.603055\pi$
$114$		0			0
$115$	−1.43846	+	0.275149i	−0.134137	+	0.0256578i
$116$		0			0
$117$	−0.104837	−	0.322656i	−0.00969220	−	0.0298295i
$118$		0			0
$119$	4.42091	+	13.6062i	0.405264	+	1.24727i
$120$		0			0
$121$	−1.02048	+	3.14070i	−0.0927706	+	0.285519i
$122$		0			0
$123$	12.6338	−	9.17902i	1.13915	−	0.827644i
$124$		0			0
$125$	2.79673	+	10.8249i	0.250147	+	0.968208i
$126$		0			0
$127$	7.72525	−	5.61272i	0.685505	−	0.498049i	−0.189674	−	0.981847i	$-0.560743\pi$
$127$	7.72525	−	5.61272i	0.685505	−	0.498049i	0.875179	+	0.483798i	$0.160743\pi$
$128$		0			0
$129$	4.89955	−	15.0793i	0.431382	−	1.32766i
$130$		0			0
$131$	−1.73026	−	5.32519i	−0.151173	−	0.465264i	0.846580	−	0.532262i	$-0.178658\pi$
$131$	−1.73026	−	5.32519i	−0.151173	−	0.465264i	−0.997753	+	0.0669981i	$0.978658\pi$
$132$		0			0
$133$	−1.21092	−	3.72682i	−0.105000	−	0.323156i
$134$		0			0
$135$	−11.5229	+	2.20409i	−0.991730	+	0.189698i
$136$		0			0
$137$	−6.45931	−	4.69296i	−0.551856	−	0.400947i	0.276613	−	0.960981i	$-0.410788\pi$
$137$	−6.45931	−	4.69296i	−0.551856	−	0.400947i	−0.828469	+	0.560035i	$0.810788\pi$
$138$		0			0
$139$	−17.8699	+	12.9832i	−1.51571	+	1.10122i	−0.552140	+	0.833751i	$0.686189\pi$
$139$	−17.8699	+	12.9832i	−1.51571	+	1.10122i	−0.963565	+	0.267473i	$0.913811\pi$
$140$		0			0
$141$	3.84883	+	2.79634i	0.324130	+	0.235494i
$142$		0			0
$143$	−15.7528			−1.31732
$144$		0			0
$145$	6.26741	−	6.68083i	0.520480	−	0.554813i
$146$		0			0
$147$	−0.369678	+	1.13775i	−0.0304905	+	0.0938402i
$148$		0			0
$149$	4.18401			0.342768			0.171384	−	0.985204i	$-0.445176\pi$
$149$	4.18401			0.342768			0.171384	+	0.985204i	$0.445176\pi$
$150$		0			0
$151$	0.331561			0.0269821			0.0134910	−	0.999909i	$-0.495706\pi$
$151$	0.331561			0.0269821			0.0134910	+	0.999909i	$0.495706\pi$
$152$		0			0
$153$	−0.0952107	+	0.293028i	−0.00769733	+	0.0236899i
$154$		0			0
$155$	−1.98946	+	15.8120i	−0.159798	+	1.27005i
$156$		0			0
$157$	3.60750			0.287910			0.143955	−	0.989584i	$-0.454018\pi$
$157$	3.60750			0.287910			0.143955	+	0.989584i	$0.454018\pi$
$158$		0			0
$159$	−0.729839	−	0.530259i	−0.0578800	−	0.0420523i
$160$		0			0
$161$	−1.47012	+	1.06811i	−0.115862	+	0.0841787i
$162$		0			0
$163$	4.12101	+	2.99409i	0.322782	+	0.234515i	0.737362	−	0.675498i	$-0.236071\pi$
$163$	4.12101	+	2.99409i	0.322782	+	0.234515i	−0.414580	+	0.910013i	$0.636071\pi$
$164$		0			0
$165$	−1.32799	+	10.5547i	−0.103384	+	0.821682i
$166$		0			0
$167$	−6.44699	−	19.8418i	−0.498883	−	1.53540i	−0.810817	−	0.585300i	$-0.800977\pi$
$167$	−6.44699	−	19.8418i	−0.498883	−	1.53540i	0.311934	−	0.950104i	$-0.399023\pi$
$168$		0			0
$169$	5.94464	+	18.2957i	0.457280	+	1.40736i
$170$		0			0
$171$	0.0260789	−	0.0802625i	0.00199430	−	0.00613783i
$172$		0			0
$173$	9.69826	−	7.04620i	0.737345	−	0.535713i	−0.154533	−	0.987988i	$-0.549387\pi$
$173$	9.69826	−	7.04620i	0.737345	−	0.535713i	0.891879	+	0.452275i	$0.149387\pi$
$174$		0			0
$175$	8.85328	+	10.6799i	0.669245	+	0.807328i
$176$		0			0
$177$	5.24660	−	3.81188i	0.394359	−	0.286518i
$178$		0			0
$179$	2.63942	−	8.12330i	0.197279	−	0.607164i	−0.802663	−	0.596433i	$-0.796584\pi$
$179$	2.63942	−	8.12330i	0.197279	−	0.607164i	0.999942	−	0.0107309i	$-0.00341581\pi$
$180$		0			0
$181$	2.41912	+	7.44529i	0.179812	+	0.553404i	0.999820	−	0.0189471i	$-0.00603140\pi$
$181$	2.41912	+	7.44529i	0.179812	+	0.553404i	−0.820009	+	0.572351i	$0.806031\pi$
$182$		0			0
$183$	5.73987	+	17.6655i	0.424303	+	1.30587i
$184$		0			0
$185$	1.12939	+	2.05192i	0.0830346	+	0.150860i
$186$		0			0
$187$	11.5741	+	8.40906i	0.846381	+	0.614932i
$188$		0			0
$189$	−11.7765	+	8.55611i	−0.856613	+	0.622366i
$190$		0			0
$191$	2.72324	+	1.97855i	0.197047	+	0.143163i	0.681934	−	0.731414i	$-0.261139\pi$
$191$	2.72324	+	1.97855i	0.197047	+	0.143163i	−0.484887	+	0.874577i	$0.661139\pi$
$192$		0			0
$193$	−15.4211			−1.11004			−0.555018	−	0.831839i	$-0.687288\pi$
$193$	−15.4211			−1.11004			−0.555018	+	0.831839i	$0.687288\pi$
$194$		0			0
$195$	21.3822	−	4.08999i	1.53121	−	0.292891i
$196$		0			0
$197$	2.72086	−	8.37394i	0.193853	−	0.596619i	−0.806135	−	0.591732i	$-0.798444\pi$
$197$	2.72086	−	8.37394i	0.193853	−	0.596619i	0.999988	−	0.00488692i	$-0.00155556\pi$
$198$		0			0
$199$	17.6222			1.24920			0.624601	−	0.780944i	$-0.285262\pi$
$199$	17.6222			1.24920			0.624601	+	0.780944i	$0.285262\pi$
$200$		0			0
$201$	−7.41340			−0.522901
$202$		0			0
$203$	3.51232	−	10.8098i	0.246517	−	0.758700i
$204$		0			0
$205$	−9.81955	−	17.8405i	−0.685827	−	1.24603i
$206$		0			0
$207$	−0.0391355			−0.00272010
$208$		0			0
$209$	−3.17022	−	2.30330i	−0.219289	−	0.159323i
$210$		0			0
$211$	4.93617	−	3.58634i	0.339820	−	0.246894i	−0.404766	−	0.914420i	$-0.632647\pi$
$211$	4.93617	−	3.58634i	0.339820	−	0.246894i	0.744586	+	0.667527i	$0.232647\pi$
$212$		0			0
$213$	18.3761	+	13.3510i	1.25911	+	0.914798i
$214$		0			0
$215$	−18.7126	−	8.79404i	−1.27619	−	0.599749i
$216$		0			0
$217$	6.11047	+	18.8061i	0.414806	+	1.27664i
$218$		0			0
$219$	−2.23250	−	6.87092i	−0.150858	−	0.464294i
$220$		0			0
$221$	9.04713	−	27.8442i	0.608576	−	1.87300i
$222$		0			0
$223$	−4.06828	+	2.95578i	−0.272432	+	0.197933i	−0.715610	−	0.698500i	$-0.753851\pi$
$223$	−4.06828	+	2.95578i	−0.272432	+	0.197933i	0.443178	+	0.896434i	$0.353851\pi$
$224$		0			0
$225$	0.0190585	+	0.298152i	0.00127056	+	0.0198768i
$226$		0			0
$227$	−14.4314	+	10.4851i	−0.957848	+	0.695918i	−0.952650	−	0.304069i	$-0.901655\pi$
$227$	−14.4314	+	10.4851i	−0.957848	+	0.695918i	−0.00519840	+	0.999986i	$0.501655\pi$
$228$		0			0
$229$	−6.66137	+	20.5016i	−0.440195	+	1.35478i	0.447472	+	0.894298i	$0.352324\pi$
$229$	−6.66137	+	20.5016i	−0.440195	+	1.35478i	−0.887668	+	0.460485i	$0.847676\pi$
$230$		0			0
$231$	4.07881	+	12.5533i	0.268366	+	0.825946i
$232$		0			0
$233$	4.54454	+	13.9867i	0.297723	+	0.916297i	0.982293	+	0.187350i	$0.0599899\pi$
$233$	4.54454	+	13.9867i	0.297723	+	0.916297i	−0.684570	+	0.728947i	$0.740010\pi$
$234$		0			0
$235$	4.24459	−	4.52458i	0.276887	−	0.295151i
$236$		0			0
$237$	13.7358	+	9.97963i	0.892235	+	0.648247i
$238$		0			0
$239$	5.61478	−	4.07938i	0.363190	−	0.263873i	−0.391192	−	0.920309i	$-0.627937\pi$
$239$	5.61478	−	4.07938i	0.363190	−	0.263873i	0.754381	+	0.656436i	$0.227937\pi$
$240$		0			0
$241$	−2.67787	−	1.94559i	−0.172497	−	0.125326i	0.498187	−	0.867070i	$-0.333999\pi$
$241$	−2.67787	−	1.94559i	−0.172497	−	0.125326i	−0.670684	+	0.741743i	$0.733999\pi$
$242$		0			0
$243$	−0.620870			−0.0398288
$244$		0			0
$245$	1.41189	+	0.663522i	0.0902026	+	0.0423909i
$246$		0			0
$247$	−2.47807	+	7.62672i	−0.157676	+	0.485277i
$248$		0			0
$249$	8.01806			0.508124
$250$		0			0
$251$	9.46454			0.597397			0.298698	−	0.954348i	$-0.403448\pi$
$251$	9.46454			0.597397			0.298698	+	0.954348i	$0.403448\pi$
$252$		0			0
$253$	−0.561537	+	1.72823i	−0.0353036	+	0.108653i
$254$		0			0
$255$	−17.8935	−	8.40906i	−1.12053	−	0.526596i
$256$		0			0
$257$	−7.07963			−0.441615			−0.220808	−	0.975317i	$-0.570869\pi$
$257$	−7.07963			−0.441615			−0.220808	+	0.975317i	$0.570869\pi$
$258$		0			0
$259$	2.35113	+	1.70820i	0.146092	+	0.106142i
$260$		0			0
$261$	0.198036	−	0.143881i	0.0122581	−	0.00890604i
$262$		0			0
$263$	1.15969	+	0.842563i	0.0715095	+	0.0519547i	0.622966	−	0.782249i	$-0.285928\pi$
$263$	1.15969	+	0.842563i	0.0715095	+	0.0519547i	−0.551456	+	0.834204i	$0.685928\pi$
$264$		0			0
$265$	−0.804885	+	0.857977i	−0.0494437	+	0.0527051i
$266$		0			0
$267$	4.86639	+	14.9772i	0.297818	+	0.916590i
$268$		0			0
$269$	−4.41368	−	13.5839i	−0.269107	−	0.828226i	−0.990719	−	0.135928i	$-0.956598\pi$
$269$	−4.41368	−	13.5839i	−0.269107	−	0.828226i	0.721612	−	0.692298i	$-0.243402\pi$
$270$		0			0
$271$	−9.51325	+	29.2788i	−0.577889	+	1.77856i	0.0482363	+	0.998836i	$0.484640\pi$
$271$	−9.51325	+	29.2788i	−0.577889	+	1.77856i	−0.626125	+	0.779723i	$0.715360\pi$
$272$		0			0
$273$	21.8529	−	15.8770i	1.32260	−	0.960922i
$274$		0			0
$275$	13.4400	+	3.43643i	0.810460	+	0.207224i
$276$		0			0
$277$	−2.58051	+	1.87485i	−0.155048	+	0.112649i	−0.662604	−	0.748970i	$-0.730549\pi$
$277$	−2.58051	+	1.87485i	−0.155048	+	0.112649i	0.507556	+	0.861619i	$0.330549\pi$
$278$		0			0
$279$	−0.131598	+	0.405017i	−0.00787856	+	0.0242477i
$280$		0			0
$281$	6.30053	+	19.3910i	0.375858	+	1.15677i	0.942898	+	0.333081i	$0.108088\pi$
$281$	6.30053	+	19.3910i	0.375858	+	1.15677i	−0.567040	+	0.823690i	$0.691912\pi$
$282$		0			0
$283$	4.10897	+	12.6461i	0.244253	+	0.751733i	0.995758	+	0.0920063i	$0.0293280\pi$
$283$	4.10897	+	12.6461i	0.244253	+	0.751733i	−0.751506	+	0.659727i	$0.770672\pi$
$284$		0			0
$285$	4.90115	+	2.30330i	0.290319	+	0.136436i
$286$		0			0
$287$	−20.4420	−	14.8520i	−1.20665	−	0.876684i
$288$		0			0
$289$	−7.75751	+	5.63616i	−0.456324	+	0.331539i
$290$		0			0
$291$	−0.125087	−	0.0908809i	−0.00733272	−	0.00532753i
$292$		0			0
$293$	−26.0420			−1.52139			−0.760696	−	0.649108i	$-0.775142\pi$
$293$	−26.0420			−1.52139			−0.760696	+	0.649108i	$0.775142\pi$
$294$		0			0
$295$	−4.07788	−	7.40883i	−0.237423	−	0.431359i
$296$		0			0
$297$	−4.49821	+	13.8441i	−0.261013	+	0.803315i
$298$		0			0
$299$	3.71874			0.215060
$300$		0			0
$301$	−25.6544			−1.47869
$302$		0			0
$303$	4.18937	−	12.8936i	0.240673	−	0.740716i
$304$		0			0
$305$	23.7908	−	4.55071i	1.36226	−	0.260573i
$306$		0			0
$307$	−25.1000			−1.43253			−0.716267	−	0.697826i	$-0.754151\pi$
$307$	−25.1000			−1.43253			−0.716267	+	0.697826i	$0.754151\pi$
$308$		0			0
$309$	−10.8679	−	7.89599i	−0.618253	−	0.449187i
$310$		0			0
$311$	0.585185	−	0.425162i	0.0331828	−	0.0241087i	−0.571070	−	0.820901i	$-0.693472\pi$
$311$	0.585185	−	0.425162i	0.0331828	−	0.0241087i	0.604253	+	0.796792i	$0.293472\pi$
$312$		0			0
$313$	−17.4879	−	12.7057i	−0.988477	−	0.718170i	−0.0288898	−	0.999583i	$-0.509197\pi$
$313$	−17.4879	−	12.7057i	−0.988477	−	0.718170i	−0.959587	+	0.281412i	$0.909197\pi$
$314$		0			0
$315$	0.178747	+	0.324754i	0.0100713	+	0.0182978i
$316$		0			0
$317$	−5.81992	−	17.9119i	−0.326879	−	1.00603i	−0.970585	−	0.240758i	$-0.922604\pi$
$317$	−5.81992	−	17.9119i	−0.326879	−	1.00603i	0.643706	−	0.765273i	$-0.277396\pi$
$318$		0			0
$319$	−3.51232	−	10.8098i	−0.196652	−	0.605233i
$320$		0			0
$321$	−5.41637	+	16.6699i	−0.302312	+	0.930422i
$322$		0			0
$323$	5.89196	−	4.28076i	0.327837	−	0.238188i
$324$		0			0
$325$	−1.81098	−	28.3311i	−0.100455	−	1.57153i
$326$		0			0
$327$	5.42535	−	3.94175i	0.300023	−	0.217979i
$328$		0			0
$329$	2.37871	−	7.32092i	0.131143	−	0.403615i
$330$		0			0
$331$	−5.21494	−	16.0499i	−0.286639	−	0.882185i	−0.985903	−	0.167320i	$-0.946489\pi$
$331$	−5.21494	−	16.0499i	−0.286639	−	0.882185i	0.699263	−	0.714864i	$-0.253511\pi$
$332$		0			0
$333$	0.0193408	+	0.0595250i	0.00105987	+	0.00326195i
$334$		0			0
$335$	−1.20684	+	9.59180i	−0.0659366	+	0.524056i
$336$		0			0
$337$	−15.6562	−	11.3749i	−0.852845	−	0.619628i	0.0730841	−	0.997326i	$-0.476716\pi$
$337$	−15.6562	−	11.3749i	−0.852845	−	0.619628i	−0.925929	+	0.377698i	$0.876716\pi$
$338$		0			0
$339$	−8.84425	+	6.42572i	−0.480353	+	0.348997i
$340$		0			0
$341$	15.9974	+	11.6228i	0.866309	+	0.629410i
$342$		0			0
$343$	−17.4856			−0.944134
$344$		0			0
$345$	0.313496	−	2.49163i	0.0168781	−	0.134145i
$346$		0			0
$347$	2.79311	−	8.59630i	0.149942	−	0.461473i	−0.847672	−	0.530521i	$-0.821996\pi$
$347$	2.79311	−	8.59630i	0.149942	−	0.461473i	0.997613	+	0.0690480i	$0.0219962\pi$
$348$		0			0
$349$	36.7305			1.96614			0.983068	−	0.183240i	$-0.0586584\pi$
$349$	36.7305			1.96614			0.983068	+	0.183240i	$0.0586584\pi$
$350$		0			0
$351$	29.7891			1.59002
$352$		0			0
$353$	5.67779	−	17.4744i	0.302198	−	0.930070i	−0.678510	−	0.734591i	$-0.737374\pi$
$353$	5.67779	−	17.4744i	0.302198	−	0.930070i	0.980708	−	0.195479i	$-0.0626261\pi$
$354$		0			0
$355$	20.2657	−	21.6024i	1.07559	−	1.14654i
$356$		0			0
$357$	−24.5313			−1.29834
$358$		0			0
$359$	−19.7609	−	14.3572i	−1.04294	−	0.757742i	−0.0720846	−	0.997399i	$-0.522965\pi$
$359$	−19.7609	−	14.3572i	−1.04294	−	0.757742i	−0.970858	+	0.239657i	$0.922965\pi$
$360$		0			0
$361$	13.7575	−	9.99539i	0.724078	−	0.526073i
$362$		0			0
$363$	−4.58111	−	3.32837i	−0.240446	−	0.174694i
$364$		0			0
$365$	−9.25334	+	1.76998i	−0.484342	+	0.0926450i
$366$		0			0
$367$	−4.48768	−	13.8117i	−0.234255	−	0.720963i	−0.997219	−	0.0745221i	$-0.976257\pi$
$367$	−4.48768	−	13.8117i	−0.234255	−	0.720963i	0.762964	−	0.646441i	$-0.223743\pi$
$368$		0			0
$369$	−0.168160	−	0.517542i	−0.00875404	−	0.0269422i
$370$		0			0
$371$	−0.451065	+	1.38824i	−0.0234182	+	0.0720737i
$372$		0			0
$373$	18.8410	−	13.6888i	0.975549	−	0.708778i	0.0188399	−	0.999823i	$-0.494003\pi$
$373$	18.8410	−	13.6888i	0.975549	−	0.708778i	0.956710	+	0.291044i	$0.0940027\pi$
$374$		0			0
$375$	−19.1351	−	1.17497i	−0.988130	−	0.0606753i
$376$		0			0
$377$	−18.8178	+	13.6719i	−0.969166	+	0.704140i
$378$		0			0
$379$	−8.84332	+	27.2169i	−0.454251	+	1.39804i	0.417762	+	0.908556i	$0.362815\pi$
$379$	−8.84332	+	27.2169i	−0.454251	+	1.39804i	−0.872013	+	0.489483i	$0.837185\pi$
$380$		0			0
$381$	5.05975	+	15.5723i	0.259219	+	0.797794i
$382$		0			0
$383$	5.13454	+	15.8025i	0.262363	+	0.807469i	0.992289	+	0.123944i	$0.0395542\pi$
$383$	5.13454	+	15.8025i	0.262363	+	0.807469i	−0.729927	+	0.683526i	$0.760446\pi$
$384$		0			0
$385$	16.9060	−	3.23378i	0.861610	−	0.164809i
$386$		0			0
$387$	−0.446986	−	0.324754i	−0.0227216	−	0.0165082i
$388$		0			0
$389$	−21.3392	+	15.5039i	−1.08194	+	0.786077i	−0.978021	−	0.208508i	$-0.933139\pi$
$389$	−21.3392	+	15.5039i	−1.08194	+	0.786077i	−0.103922	+	0.994585i	$0.533139\pi$
$390$		0			0
$391$	−2.73227	−	1.98511i	−0.138177	−	0.100391i
$392$		0			0
$393$	9.60109			0.484311
$394$		0			0
$395$	15.1482	−	16.1474i	0.762187	−	0.812463i
$396$		0			0
$397$	−5.53406	+	17.0321i	−0.277747	+	0.854816i	0.710733	+	0.703462i	$0.248363\pi$
$397$	−5.53406	+	17.0321i	−0.277747	+	0.854816i	−0.988480	+	0.151354i	$0.951637\pi$
$398$		0			0
$399$	6.71930			0.336386
$400$		0			0
$401$	32.0164			1.59882			0.799411	−	0.600785i	$-0.205145\pi$
$401$	32.0164			1.59882			0.799411	+	0.600785i	$0.205145\pi$
$402$		0			0
$403$	12.5047	−	38.4856i	0.622905	−	1.91710i
$404$		0			0
$405$	2.46123	−	19.5616i	0.122300	−	0.972022i
$406$		0			0
$407$	2.90615			0.144053
$408$		0			0
$409$	−14.5901	−	10.6003i	−0.721435	−	0.524153i	0.165407	−	0.986225i	$-0.447106\pi$
$409$	−14.5901	−	10.6003i	−0.721435	−	0.524153i	−0.886842	+	0.462072i	$0.847106\pi$
$410$		0			0
$411$	11.0759	−	8.04709i	0.546332	−	0.396934i
$412$		0			0
$413$	−8.48918	−	6.16775i	−0.417725	−	0.303495i
$414$		0			0
$415$	1.30527	−	10.3741i	0.0640733	−	0.509246i
$416$		0			0
$417$	−11.7041	−	36.0216i	−0.573153	−	1.76398i
$418$		0			0
$419$	6.03511	+	18.5742i	0.294834	+	0.907407i	0.983277	+	0.182116i	$0.0582947\pi$
$419$	6.03511	+	18.5742i	0.294834	+	0.907407i	−0.688443	+	0.725291i	$0.741705\pi$
$420$		0			0
$421$	−6.04242	+	18.5967i	−0.294490	+	0.906346i	0.688903	+	0.724854i	$0.258093\pi$
$421$	−6.04242	+	18.5967i	−0.294490	+	0.906346i	−0.983392	+	0.181492i	$0.941907\pi$
$422$		0			0
$423$	0.134119	−	0.0974433i	0.00652110	−	0.00473786i
$424$		0			0
$425$	−13.7929	+	21.7825i	−0.669055	+	1.05660i
$426$		0			0
$427$	24.3145	−	17.6655i	1.17666	−	0.854893i
$428$		0			0
$429$	8.34705	−	25.6896i	0.402999	−	1.24030i
$430$		0			0
$431$	6.55002	+	20.1589i	0.315503	+	0.971019i	0.975547	+	0.219792i	$0.0705378\pi$
$431$	6.55002	+	20.1589i	0.315503	+	0.971019i	−0.660044	+	0.751227i	$0.729462\pi$
$432$		0			0
$433$	2.64199	+	8.13122i	0.126966	+	0.390761i	0.994254	−	0.107045i	$-0.0341389\pi$
$433$	2.64199	+	8.13122i	0.126966	+	0.390761i	−0.867288	+	0.497807i	$0.834139\pi$
$434$		0			0
$435$	7.57408	+	13.7609i	0.363150	+	0.659783i
$436$		0			0
$437$	0.748388	+	0.543736i	0.0358003	+	0.0260104i
$438$		0			0
$439$	−22.7102	+	16.4999i	−1.08390	+	0.787499i	−0.978359	−	0.206916i	$-0.933657\pi$
$439$	−22.7102	+	16.4999i	−1.08390	+	0.787499i	−0.105541	+	0.994415i	$0.533657\pi$
$440$		0			0
$441$	0.0337257	+	0.0245031i	0.00160598	+	0.00116682i
$442$		0			0
$443$	33.0546			1.57047			0.785236	−	0.619197i	$-0.212542\pi$
$443$	33.0546			1.57047			0.785236	+	0.619197i	$0.212542\pi$
$444$		0			0
$445$	20.1704	−	3.85820i	0.956169	−	0.182896i
$446$		0			0
$447$	−2.21701	+	6.82325i	−0.104861	+	0.322729i
$448$		0			0
$449$	−37.1628			−1.75382			−0.876911	−	0.480652i	$-0.840400\pi$
$449$	−37.1628			−1.75382			−0.876911	+	0.480652i	$0.840400\pi$
$450$		0			0
$451$	−25.2677			−1.18981
$452$		0			0
$453$	−0.175686	+	0.540707i	−0.00825446	+	0.0254046i
$454$		0			0
$455$	−16.9850	−	30.8589i	−0.796267	−	1.44669i
$456$		0			0
$457$	29.3139			1.37125			0.685624	−	0.727956i	$-0.259529\pi$
$457$	29.3139			1.37125			0.685624	+	0.727956i	$0.259529\pi$
$458$		0			0
$459$	−21.8870	−	15.9018i	−1.02160	−	0.742233i
$460$		0			0
$461$	−7.20624	+	5.23564i	−0.335628	+	0.243848i	−0.742815	−	0.669497i	$-0.766510\pi$
$461$	−7.20624	+	5.23564i	−0.335628	+	0.243848i	0.407187	+	0.913345i	$0.366510\pi$
$462$		0			0
$463$	−14.7865	−	10.7430i	−0.687187	−	0.499271i	0.188547	−	0.982064i	$-0.439622\pi$
$463$	−14.7865	−	10.7430i	−0.687187	−	0.499271i	−0.875734	+	0.482793i	$0.839622\pi$
$464$		0			0
$465$	−24.7319	−	11.6228i	−1.14692	−	0.538995i
$466$		0			0
$467$	11.3360	+	34.8886i	0.524568	+	1.61445i	0.765169	+	0.643829i	$0.222655\pi$
$467$	11.3360	+	34.8886i	0.524568	+	1.61445i	−0.240601	+	0.970624i	$0.577345\pi$
$468$		0			0
$469$	3.70670	+	11.4081i	0.171160	+	0.526775i
$470$		0			0
$471$	−1.91153	+	5.88308i	−0.0880785	+	0.271078i
$472$		0			0
$473$	−20.7548	+	15.0793i	−0.954309	+	0.693346i
$474$		0			0
$475$	3.77798	−	5.96637i	0.173346	−	0.273756i
$476$		0			0
$477$	−0.0254325	+	0.0184778i	−0.00116447	+	0.000846040i
$478$		0			0
$479$	3.89046	−	11.9736i	0.177760	−	0.547088i	−0.821989	−	0.569503i	$-0.807136\pi$
$479$	3.89046	−	11.9736i	0.177760	−	0.547088i	0.999749	+	0.0224155i	$0.00713568\pi$
$480$		0			0
$481$	−1.83781	−	5.65620i	−0.0837969	−	0.257900i
$482$		0			0
$483$	−0.962877	−	2.96343i	−0.0438124	−	0.134841i
$484$		0			0
$485$	−0.137949	+	0.147048i	−0.00626393	+	0.00667712i
$486$		0			0
$487$	−14.8257	−	10.7715i	−0.671816	−	0.488103i	0.198816	−	0.980037i	$-0.436290\pi$
$487$	−14.8257	−	10.7715i	−0.671816	−	0.488103i	−0.870633	+	0.491934i	$0.836290\pi$
$488$		0			0
$489$	−7.06635	+	5.13401i	−0.319552	+	0.232168i
$490$		0			0
$491$	17.5595	+	12.7577i	0.792448	+	0.575747i	0.908689	−	0.417474i	$-0.137085\pi$
$491$	17.5595	+	12.7577i	0.792448	+	0.575747i	−0.116241	+	0.993221i	$0.537085\pi$
$492$		0			0
$493$	21.1243			0.951389
$494$		0			0
$495$	0.335495	+	0.157667i	0.0150794	+	0.00708659i
$496$		0			0
$497$	11.3571	−	34.9535i	0.509434	−	1.56788i
$498$		0			0
$499$	−15.8391			−0.709055			−0.354527	−	0.935046i	$-0.615358\pi$
$499$	−15.8391			−0.709055			−0.354527	+	0.935046i	$0.615358\pi$
$500$		0			0
$501$	35.7739			1.59826
$502$		0			0
$503$	−8.51433	+	26.2044i	−0.379635	+	1.16840i	0.560662	+	0.828044i	$0.310547\pi$
$503$	−8.51433	+	26.2044i	−0.379635	+	1.16840i	−0.940298	+	0.340353i	$0.889453\pi$
$504$		0			0
$505$	−16.0003	−	7.51936i	−0.712003	−	0.334607i
$506$		0			0
$507$	−32.9864			−1.46498
$508$		0			0
$509$	22.3386	+	16.2300i	0.990142	+	0.719380i	0.959952	−	0.280164i	$-0.0903889\pi$
$509$	22.3386	+	16.2300i	0.990142	+	0.719380i	0.0301894	+	0.999544i	$0.490389\pi$
$510$		0			0
$511$	−9.45701	+	6.87092i	−0.418354	+	0.303952i
$512$		0			0
$513$	5.99499	+	4.35562i	0.264685	+	0.192305i
$514$		0			0
$515$	−11.9854	+	12.7760i	−0.528139	+	0.562977i
$516$		0			0
$517$	−2.37871	−	7.32092i	−0.104616	−	0.321974i
$518$		0			0
$519$	6.35200	+	19.5495i	0.278822	+	0.858126i
$520$		0			0
$521$	5.28084	−	16.2527i	0.231358	−	0.712046i	−0.766226	−	0.642571i	$-0.777868\pi$
$521$	5.28084	−	16.2527i	0.231358	−	0.712046i	0.997584	−	0.0694747i	$-0.0221323\pi$
$522$		0			0
$523$	29.3796	−	21.3456i	1.28468	−	0.933376i	0.284999	−	0.958528i	$-0.408007\pi$
$523$	29.3796	−	21.3456i	1.28468	−	0.933376i	0.999684	+	0.0251516i	$0.00800684\pi$
$524$		0			0
$525$	−22.1079	+	8.77880i	−0.964868	+	0.383138i
$526$		0			0
$527$	−29.7317	+	21.6013i	−1.29513	+	0.940970i
$528$		0			0
$529$	−6.97483	+	21.4663i	−0.303253	+	0.933318i
$530$		0			0
$531$	−0.0698337	−	0.214926i	−0.00303052	−	0.00932699i
$532$		0			0
$533$	15.9789	+	49.1780i	0.692123	+	2.13014i
$534$		0			0
$535$	20.6865	+	9.72166i	0.894356	+	0.420304i
$536$		0			0
$537$	11.8488	+	8.60868i	0.511315	+	0.371492i
$538$		0			0
$539$	1.56598	−	1.13775i	0.0674516	−	0.0490064i
$540$		0			0
$541$	−20.1742	−	14.6574i	−0.867355	−	0.630170i	0.0625209	−	0.998044i	$-0.480086\pi$
$541$	−20.1742	−	14.6574i	−0.867355	−	0.630170i	−0.929876	+	0.367873i	$0.880086\pi$
$542$		0			0
$543$	−13.4235			−0.576060
$544$		0			0
$545$	−4.21681	−	7.66125i	−0.180628	−	0.328172i
$546$		0			0
$547$	−2.06176	+	6.34546i	−0.0881547	+	0.271312i	−0.985409	−	0.170201i	$-0.945558\pi$
$547$	−2.06176	+	6.34546i	−0.0881547	+	0.271312i	0.897255	+	0.441513i	$0.145558\pi$
$548$		0			0
$549$	0.647264			0.0276245
$550$		0			0
$551$	−5.78609			−0.246496
$552$		0			0
$553$	8.48918	−	26.1270i	0.360997	−	1.11103i
$554$		0			0
$555$	−3.94469	+	0.754541i	−0.167443	+	0.0320285i
$556$		0			0
$557$	−20.4328			−0.865765			−0.432882	−	0.901450i	$-0.642503\pi$
$557$	−20.4328			−0.865765			−0.432882	+	0.901450i	$0.642503\pi$
$558$		0			0
$559$	42.4736	+	30.8589i	1.79644	+	1.30519i
$560$		0			0
$561$	−19.8463	+	14.4192i	−0.837910	+	0.608777i
$562$		0			0
$563$	−0.487680	−	0.354320i	−0.0205532	−	0.0149328i	0.577461	−	0.816418i	$-0.304043\pi$
$563$	−0.487680	−	0.354320i	−0.0205532	−	0.0149328i	−0.598014	+	0.801485i	$0.704043\pi$
$564$		0			0
$565$	6.87412	+	12.4891i	0.289196	+	0.525422i
$566$		0			0
$567$	−7.55947	−	23.2657i	−0.317468	−	0.977066i
$568$		0			0
$569$	10.4688	+	32.2195i	0.438873	+	1.35071i	0.889065	+	0.457781i	$0.151356\pi$
$569$	10.4688	+	32.2195i	0.438873	+	1.35071i	−0.450192	+	0.892932i	$0.648644\pi$
$570$		0			0
$571$	1.92521	−	5.92520i	0.0805677	−	0.247962i	−0.902657	−	0.430361i	$-0.858386\pi$
$571$	1.92521	−	5.92520i	0.0805677	−	0.247962i	0.983225	+	0.182399i	$0.0583863\pi$
$572$		0			0
$573$	−4.66958	+	3.39265i	−0.195074	+	0.141730i
$574$		0			0
$575$	−3.17275	−	0.811231i	−0.132313	−	0.0338307i
$576$		0			0
$577$	−3.05893	+	2.22244i	−0.127345	+	0.0925214i	−0.649634	−	0.760247i	$-0.725078\pi$
$577$	−3.05893	+	2.22244i	−0.127345	+	0.0925214i	0.522290	+	0.852768i	$0.325078\pi$
$578$		0			0
$579$	8.17127	−	25.1486i	0.339587	−	1.04514i
$580$		0			0
$581$	−4.00903	−	12.3385i	−0.166323	−	0.511889i
$582$		0			0
$583$	0.451065	+	1.38824i	0.0186812	+	0.0574949i
$584$		0			0
$585$	0.0947014	−	0.752675i	0.00391542	−	0.0311193i
$586$		0			0
$587$	13.2296	+	9.61184i	0.546042	+	0.396723i	0.826324	−	0.563195i	$-0.190428\pi$
$587$	13.2296	+	9.61184i	0.546042	+	0.396723i	−0.280282	+	0.959918i	$0.590428\pi$
$588$		0			0
$589$	8.14373	−	5.91676i	0.335556	−	0.243796i
$590$		0			0
$591$	12.2144	+	8.87430i	0.502435	+	0.365040i
$592$		0			0
$593$	9.53314			0.391479			0.195740	−	0.980656i	$-0.437289\pi$
$593$	9.53314			0.391479			0.195740	+	0.980656i	$0.437289\pi$
$594$		0			0
$595$	−3.99349	+	31.7397i	−0.163717	+	1.30120i
$596$		0			0
$597$	−9.33756	+	28.7381i	−0.382161	+	1.17617i
$598$		0			0
$599$	16.0682			0.656528			0.328264	−	0.944586i	$-0.393536\pi$
$599$	16.0682			0.656528			0.328264	+	0.944586i	$0.393536\pi$
$600$		0			0
$601$	15.0380			0.613413			0.306707	−	0.951804i	$-0.400773\pi$
$601$	15.0380			0.613413			0.306707	+	0.951804i	$0.400773\pi$
$602$		0			0
$603$	−0.0798292	+	0.245689i	−0.00325090	+	0.0100052i
$604$		0			0
$605$	−5.05216	+	5.38541i	−0.205399	+	0.218948i
$606$		0			0
$607$	44.8348			1.81979			0.909894	−	0.414840i	$-0.136163\pi$
$607$	44.8348			1.81979			0.909894	+	0.414840i	$0.136163\pi$
$608$		0			0
$609$	15.7674	+	11.4557i	0.638929	+	0.464209i
$610$		0			0
$611$	−12.7443	+	9.25928i	−0.515580	+	0.374590i
$612$		0			0
$613$	12.5793	+	9.13937i	0.508072	+	0.369136i	0.812092	−	0.583530i	$-0.198329\pi$
$613$	12.5793	+	9.13937i	0.508072	+	0.369136i	−0.304020	+	0.952666i	$0.598329\pi$
$614$		0			0
$615$	34.2973	−	6.56038i	1.38300	−	0.264540i
$616$		0			0
$617$	5.43852	+	16.7380i	0.218946	+	0.673848i	0.998850	+	0.0479478i	$0.0152681\pi$
$617$	5.43852	+	16.7380i	0.218946	+	0.673848i	−0.779903	+	0.625900i	$0.784732\pi$
$618$		0			0
$619$	11.5229	+	35.4637i	0.463143	+	1.42541i	0.861303	+	0.508091i	$0.169649\pi$
$619$	11.5229	+	35.4637i	0.463143	+	1.42541i	−0.398161	+	0.917316i	$0.630351\pi$
$620$		0			0
$621$	1.06188	−	3.26814i	0.0426120	−	0.131146i
$622$		0			0
$623$	20.6144	−	14.9772i	0.825897	−	0.600049i
$624$		0			0
$625$	−4.63525	+	24.5665i	−0.185410	+	0.982661i
$626$		0			0
$627$	5.43603	−	3.94951i	0.217094	−	0.157728i
$628$		0			0
$629$	−1.66906	+	5.13683i	−0.0665496	+	0.204819i
$630$		0			0
$631$	−2.64380	−	8.13677i	−0.105248	−	0.323920i	0.884541	−	0.466463i	$-0.154472\pi$
$631$	−2.64380	−	8.13677i	−0.105248	−	0.323920i	−0.989789	+	0.142543i	$0.954472\pi$
$632$		0			0
$633$	3.23301	+	9.95017i	0.128500	+	0.395484i
$634$		0			0
$635$	20.9719	−	4.01150i	0.832243	−	0.159191i
$636$		0			0
$637$	−3.20469	−	2.32834i	−0.126974	−	0.0922523i
$638$		0			0
$639$	0.640348	−	0.465240i	0.0253318	−	0.0184046i
$640$		0			0
$641$	18.4582	+	13.4107i	0.729055	+	0.529690i	0.889264	−	0.457394i	$-0.151217\pi$
$641$	18.4582	+	13.4107i	0.729055	+	0.529690i	−0.160209	+	0.987083i	$0.551217\pi$
$642$		0			0
$643$	−34.7745			−1.37137			−0.685686	−	0.727898i	$-0.740497\pi$
$643$	−34.7745			−1.37137			−0.685686	+	0.727898i	$0.740497\pi$
$644$		0			0
$645$	24.2566	−	25.8567i	0.955104	−	1.01811i
$646$		0			0
$647$	5.08583	−	15.6526i	0.199945	−	0.615366i	−0.799939	−	0.600082i	$-0.795135\pi$
$647$	5.08583	−	15.6526i	0.199945	−	0.615366i	0.999883	−	0.0152844i	$-0.00486537\pi$
$648$		0			0
$649$	−10.4932			−0.411894
$650$		0			0
$651$	−33.9066			−1.32890
$652$		0			0
$653$	9.33515	−	28.7306i	0.365313	−	1.12432i	−0.584473	−	0.811414i	$-0.698699\pi$
$653$	9.33515	−	28.7306i	0.365313	−	1.12432i	0.949785	−	0.312903i	$-0.101301\pi$
$654$		0			0
$655$	1.56298	−	12.4223i	0.0610705	−	0.485381i
$656$		0			0
$657$	−0.251751			−0.00982173
$658$		0			0
$659$	−23.0523	−	16.7485i	−0.897991	−	0.652428i	0.0399585	−	0.999201i	$-0.487277\pi$
$659$	−23.0523	−	16.7485i	−0.897991	−	0.652428i	−0.937949	+	0.346773i	$0.887277\pi$
$660$		0			0
$661$	−41.0448	+	29.8208i	−1.59646	+	1.15990i	−0.702562	+	0.711622i	$0.747961\pi$
$661$	−41.0448	+	29.8208i	−1.59646	+	1.15990i	−0.893897	+	0.448273i	$0.852039\pi$
$662$		0			0
$663$	40.6142	+	29.5080i	1.57733	+	1.14599i
$664$		0			0
$665$	1.09385	−	8.69374i	0.0424175	−	0.337129i
$666$		0			0
$667$	0.829146	+	2.55185i	0.0321047	+	0.0988080i
$668$		0			0
$669$	−2.66457	−	8.20070i	−0.103018	−	0.317057i
$670$		0			0
$671$	9.28730	−	28.5834i	0.358532	−	1.10345i
$672$		0			0
$673$	16.5401	−	12.0171i	0.637573	−	0.463224i	−0.221442	−	0.975173i	$-0.571077\pi$
$673$	16.5401	−	12.0171i	0.637573	−	0.463224i	0.859016	+	0.511949i	$0.171077\pi$
$674$		0			0
$675$	−25.4154	−	6.49839i	−0.978239	−	0.250123i
$676$		0			0
$677$	−6.90383	+	5.01592i	−0.265336	+	0.192778i	−0.712496	−	0.701676i	$-0.752435\pi$
$677$	−6.90383	+	5.01592i	−0.265336	+	0.192778i	0.447160	+	0.894454i	$0.352435\pi$
$678$		0			0
$679$	−0.0773079	+	0.237929i	−0.00296680	+	0.00913088i
$680$		0			0
$681$	−9.45206	−	29.0904i	−0.362204	−	1.11475i
$682$		0			0
$683$	15.0085	+	46.1913i	0.574283	+	1.76746i	0.638608	+	0.769532i	$0.279511\pi$
$683$	15.0085	+	46.1913i	0.574283	+	1.76746i	−0.0643246	+	0.997929i	$0.520489\pi$
$684$		0			0
$685$	−8.60863	−	15.6405i	−0.328919	−	0.597591i
$686$		0			0
$687$	−29.9041	−	21.7266i	−1.14091	−	0.828921i
$688$		0			0
$689$	2.41665	−	1.75580i	0.0920671	−	0.0668907i
$690$		0			0
$691$	36.2501	+	26.3373i	1.37902	+	1.00192i	0.996971	+	0.0777740i	$0.0247813\pi$
$691$	36.2501	+	26.3373i	1.37902	+	1.00192i	0.382048	+	0.924142i	$0.375219\pi$
$692$		0			0
$693$	0.459953			0.0174722
$694$		0			0
$695$	−48.5117	+	9.27932i	−1.84015	+	0.351985i
$696$		0			0
$697$	14.5117	−	44.6623i	0.549669	−	1.69171i
$698$		0			0
$699$	−25.2174			−0.953809
$700$		0			0
$701$	2.21913			0.0838152			0.0419076	−	0.999121i	$-0.486656\pi$
$701$	2.21913			0.0838152			0.0419076	+	0.999121i	$0.486656\pi$
$702$		0			0
$703$	0.457166	−	1.40701i	0.0172424	−	0.0530665i
$704$		0			0
$705$	5.12953	+	9.31951i	0.193189	+	0.350993i
$706$		0			0
$707$	−21.9358			−0.824982
$708$		0			0
$709$	−27.7968	−	20.1955i	−1.04393	−	0.758459i	−0.0728805	−	0.997341i	$-0.523219\pi$
$709$	−27.7968	−	20.1955i	−1.04393	−	0.758459i	−0.971049	+	0.238882i	$0.923219\pi$
$710$		0			0
$711$	0.478647	−	0.347757i	0.0179507	−	0.0130419i
$712$		0			0
$713$	−3.77648	−	2.74377i	−0.141430	−	0.102755i
$714$		0			0
$715$	−31.8795	−	14.9818i	−1.19223	−	0.560289i
$716$		0			0
$717$	3.67747	+	11.3181i	0.137338	+	0.422682i
$718$		0			0
$719$	−3.70511	−	11.4032i	−0.138177	−	0.425266i	0.857893	−	0.513828i	$-0.171773\pi$
$719$	−3.70511	−	11.4032i	−0.138177	−	0.425266i	−0.996071	+	0.0885618i	$0.971773\pi$
$720$		0			0
$721$	−6.71673	+	20.6720i	−0.250144	+	0.769864i
$722$		0			0
$723$	4.59179	−	3.33613i	0.170770	−	0.124072i
$724$		0			0
$725$	19.0374	−	7.55955i	0.707032	−	0.280754i
$726$		0			0
$727$	34.1265	−	24.7944i	1.26568	−	0.919573i	0.266661	−	0.963790i	$-0.414080\pi$
$727$	34.1265	−	24.7944i	1.26568	−	0.919573i	0.999022	+	0.0442177i	$0.0140795\pi$
$728$		0			0
$729$	8.50295	−	26.1694i	0.314924	−	0.969237i
$730$		0			0
$731$	−14.7338	−	45.3459i	−0.544948	−	1.67718i
$732$		0			0
$733$	−0.0996219	−	0.306605i	−0.00367962	−	0.0113247i	0.949200	−	0.314674i	$-0.101895\pi$
$733$	−0.0996219	−	0.306605i	−0.00367962	−	0.0113247i	−0.952879	+	0.303349i	$0.901895\pi$
$734$		0			0
$735$	−1.83020	+	1.95092i	−0.0675078	+	0.0719608i
$736$		0			0
$737$	9.70427	+	7.05056i	0.357461	+	0.259711i
$738$		0			0
$739$	−4.44942	+	3.23269i	−0.163674	+	0.118916i	−0.666607	−	0.745409i	$-0.732254\pi$
$739$	−4.44942	+	3.23269i	−0.163674	+	0.118916i	0.502933	+	0.864325i	$0.332254\pi$
$740$		0			0
$741$	−11.1245	−	8.08244i	−0.408670	−	0.296916i
$742$		0			0
$743$	6.03812			0.221517			0.110759	−	0.993847i	$-0.464672\pi$
$743$	6.03812			0.221517			0.110759	+	0.993847i	$0.464672\pi$
$744$		0			0
$745$	8.46733	+	3.97923i	0.310219	+	0.145788i
$746$		0			0
$747$	0.0863404	−	0.265728i	0.00315903	−	0.00972249i
$748$		0			0
$749$	28.3605			1.03627
$750$		0			0
$751$	13.5719			0.495244			0.247622	−	0.968857i	$-0.420351\pi$
$751$	13.5719			0.495244			0.247622	+	0.968857i	$0.420351\pi$
$752$		0			0
$753$	−5.01503	+	15.4347i	−0.182758	+	0.562471i
$754$		0			0
$755$	0.670991	+	0.315333i	0.0244199	+	0.0114762i
$756$		0			0
$757$	33.0661			1.20181			0.600904	−	0.799321i	$-0.294807\pi$
$757$	33.0661			1.20181			0.600904	+	0.799321i	$0.294807\pi$
$758$		0			0
$759$	−2.52084	−	1.83150i	−0.0915008	−	0.0664792i
$760$		0			0
$761$	−4.19767	+	3.04978i	−0.152165	+	0.110555i	−0.661263	−	0.750154i	$-0.729979\pi$
$761$	−4.19767	+	3.04978i	−0.152165	+	0.110555i	0.509098	+	0.860709i	$0.329979\pi$
$762$		0			0
$763$	−8.77840	−	6.37788i	−0.317799	−	0.230895i
$764$		0			0
$765$	−0.471367	+	0.502460i	−0.0170423	+	0.0181665i
$766$		0			0
$767$	6.63575	+	20.4227i	0.239603	+	0.737422i
$768$		0			0
$769$	10.2191	+	31.4512i	0.368511	+	1.13416i	0.947753	+	0.319005i	$0.103349\pi$
$769$	10.2191	+	31.4512i	0.368511	+	1.13416i	−0.579242	+	0.815156i	$0.696651\pi$
$770$		0			0
$771$	3.75133	−	11.5454i	0.135101	−	0.415798i
$772$		0			0
$773$	0.914961	−	0.664758i	0.0329088	−	0.0239097i	−0.571209	−	0.820804i	$-0.693526\pi$
$773$	0.914961	−	0.664758i	0.0329088	−	0.0239097i	0.604118	+	0.796895i	$0.293526\pi$
$774$		0			0
$775$	−19.0643	+	30.1072i	−0.684808	+	1.08148i
$776$		0			0
$777$	−4.03152	+	2.92907i	−0.144630	+	0.105080i
$778$		0			0
$779$	−3.97485	+	12.2333i	−0.142414	+	0.438305i
$780$		0			0
$781$	−11.3571	−	34.9535i	−0.406388	−	1.25073i
$782$		0			0
$783$	6.64191	+	20.4417i	0.237362	+	0.730526i
$784$		0			0
$785$	7.30061	+	3.43094i	0.260570	+	0.122455i
$786$		0			0
$787$	12.7509	+	9.26408i	0.454521	+	0.330229i	0.791378	−	0.611327i	$-0.209364\pi$
$787$	12.7509	+	9.26408i	0.454521	+	0.330229i	−0.336857	+	0.941556i	$0.609364\pi$
$788$		0			0
$789$	−1.98854	+	1.44476i	−0.0707938	+	0.0514347i
$790$		0			0
$791$	14.3103	+	10.3970i	0.508815	+	0.369676i
$792$		0			0
$793$	−61.5044			−2.18409
$794$		0			0
$795$	−0.972693	−	1.76722i	−0.0344978	−	0.0626769i
$796$		0			0
$797$	−7.15055	+	22.0071i	−0.253285	+	0.779532i	0.740877	+	0.671640i	$0.234410\pi$
$797$	−7.15055	+	22.0071i	−0.253285	+	0.779532i	−0.994163	+	0.107892i	$0.965590\pi$
$798$		0			0
$799$	14.3064			0.506122
$800$		0			0
$801$	0.548765			0.0193897
$802$		0			0
$803$	−3.61226	+	11.1174i	−0.127474	+	0.392324i
$804$		0			0
$805$	−3.99097	+	0.763393i	−0.140663	+	0.0269061i
$806$		0			0
$807$	24.4912			0.862132
$808$		0			0
$809$	−27.1345	−	19.7143i	−0.953997	−	0.693119i	−0.00224811	−	0.999997i	$-0.500716\pi$
$809$	−27.1345	−	19.7143i	−0.953997	−	0.693119i	−0.951749	+	0.306878i	$0.900716\pi$
$810$		0			0
$811$	−9.67796	+	7.03145i	−0.339839	+	0.246907i	−0.744594	−	0.667518i	$-0.767357\pi$
$811$	−9.67796	+	7.03145i	−0.339839	+	0.246907i	0.404755	+	0.914425i	$0.367357\pi$
$812$		0			0
$813$	−42.7067	−	31.0282i	−1.49779	−	1.08821i
$814$		0			0
$815$	5.49227	+	9.97854i	0.192386	+	0.349533i
$816$		0			0
$817$	4.03569	+	12.4206i	0.141191	+	0.434540i
$818$		0			0
$819$	−0.290867	−	0.895198i	−0.0101637	−	0.0312807i
$820$		0			0
$821$	−3.30466	+	10.1707i	−0.115333	+	0.354960i	−0.992016	−	0.126109i	$-0.959751\pi$
$821$	−3.30466	+	10.1707i	−0.115333	+	0.354960i	0.876683	+	0.481068i	$0.159751\pi$
$822$		0			0
$823$	−9.72525	+	7.06581i	−0.339001	+	0.246299i	−0.744240	−	0.667912i	$-0.767188\pi$
$823$	−9.72525	+	7.06581i	−0.339001	+	0.246299i	0.405239	+	0.914211i	$0.367188\pi$
$824$		0			0
$825$	−12.7256	+	20.0969i	−0.443049	+	0.699684i
$826$		0			0
$827$	−3.34912	+	2.43328i	−0.116460	+	0.0846133i	−0.644491	−	0.764612i	$-0.722931\pi$
$827$	−3.34912	+	2.43328i	−0.116460	+	0.0846133i	0.528031	+	0.849225i	$0.322931\pi$
$828$		0			0
$829$	−6.28859	+	19.3543i	−0.218412	+	0.672203i	0.780482	+	0.625178i	$0.214974\pi$
$829$	−6.28859	+	19.3543i	−0.218412	+	0.672203i	−0.998894	+	0.0470242i	$0.985026\pi$
$830$		0			0
$831$	−1.69014	−	5.20171i	−0.0586303	−	0.180445i
$832$		0			0
$833$	1.11168	+	3.42141i	0.0385175	+	0.118545i
$834$		0			0
$835$	5.82368	−	46.2859i	0.201537	−	1.60179i
$836$		0			0
$837$	−30.2516	−	21.9791i	−1.04565	−	0.759708i
$838$		0			0
$839$	2.53639	−	1.84279i	0.0875658	−	0.0636203i	−0.543141	−	0.839642i	$-0.682765\pi$
$839$	2.53639	−	1.84279i	0.0875658	−	0.0636203i	0.630707	+	0.776021i	$0.282765\pi$
$840$		0			0
$841$	9.88393	+	7.18109i	0.340825	+	0.247624i
$842$		0			0
$843$	−34.9612			−1.20413
$844$		0			0
$845$	−5.36990	+	42.6793i	−0.184730	+	1.46821i
$846$		0			0
$847$	−2.83128	+	8.71378i	−0.0972839	+	0.299409i
$848$		0			0
$849$	−22.8004			−0.782508
$850$		0			0
$851$	−0.686050			−0.0235175
$852$		0			0
$853$	7.21464	−	22.2044i	0.247025	−	0.760263i	−0.748272	−	0.663392i	$-0.769116\pi$
$853$	7.21464	−	22.2044i	0.247025	−	0.760263i	0.995297	−	0.0968717i	$-0.0308837\pi$
$854$		0			0
$855$	0.129111	−	0.137627i	0.00441550	−	0.00470676i
$856$		0			0
$857$	15.3036			0.522762			0.261381	−	0.965236i	$-0.415822\pi$
$857$	15.3036			0.522762			0.261381	+	0.965236i	$0.415822\pi$
$858$		0			0
$859$	−2.39576	−	1.74062i	−0.0817422	−	0.0593892i	0.546164	−	0.837679i	$-0.316088\pi$
$859$	−2.39576	−	1.74062i	−0.0817422	−	0.0593892i	−0.627906	+	0.778289i	$0.716088\pi$
$860$		0			0
$861$	35.0522	−	25.4669i	1.19457	−	0.867909i
$862$		0			0
$863$	−30.5987	−	22.2312i	−1.04159	−	0.756760i	−0.0709954	−	0.997477i	$-0.522618\pi$
$863$	−30.5987	−	22.2312i	−1.04159	−	0.756760i	−0.970595	+	0.240717i	$0.922618\pi$
$864$		0			0
$865$	26.3280	−	5.03603i	0.895180	−	0.171230i
$866$		0			0
$867$	−5.08088	−	15.6373i	−0.172556	−	0.531072i
$868$		0			0
$869$	−8.48918	−	26.1270i	−0.287976	−	0.886298i
$870$		0			0
$871$	7.58555	−	23.3459i	0.257027	−	0.791046i
$872$		0			0
$873$	−0.00435886	+	0.00316690i	−0.000147525	+	0.000107183i
$874$		0			0
$875$	7.75943	+	30.0333i	0.262317	+	1.01531i
$876$		0			0
$877$	12.6215	−	9.17007i	0.426198	−	0.309651i	−0.353929	−	0.935272i	$-0.615154\pi$
$877$	12.6215	−	9.17007i	0.426198	−	0.309651i	0.780127	+	0.625621i	$0.215154\pi$
$878$		0			0
$879$	13.7991	−	42.4691i	0.465430	−	1.43245i
$880$		0			0
$881$	0.359812	+	1.10739i	0.0121224	+	0.0373089i	0.956935	−	0.290303i	$-0.0937561\pi$
$881$	0.359812	+	1.10739i	0.0121224	+	0.0373089i	−0.944812	+	0.327612i	$0.893756\pi$
$882$		0			0
$883$	−15.1063	−	46.4925i	−0.508368	−	1.56460i	−0.795033	−	0.606566i	$-0.792547\pi$
$883$	−15.1063	−	46.4925i	−0.508368	−	1.56460i	0.286665	−	0.958031i	$-0.407453\pi$
$884$		0			0
$885$	14.2430	−	2.72441i	0.478774	−	0.0915800i
$886$		0			0
$887$	6.98094	+	5.07195i	0.234397	+	0.170299i	0.698783	−	0.715333i	$-0.253725\pi$
$887$	6.98094	+	5.07195i	0.234397	+	0.170299i	−0.464386	+	0.885633i	$0.653725\pi$
$888$		0			0
$889$	21.4335	−	15.5723i	0.718855	−	0.522279i
$890$		0			0
$891$	−19.7909	−	14.3790i	−0.663022	−	0.481713i
$892$		0			0
$893$	−3.91861			−0.131131
$894$		0			0
$895$	13.0672	−	13.9291i	0.436788	−	0.465600i
$896$		0			0
$897$	−1.97047	+	6.06449i	−0.0657921	+	0.202487i
$898$		0			0
$899$	29.1975			0.973790
$900$		0			0
$901$	−2.71286			−0.0903784
$902$		0			0
$903$	13.5937	−	41.8370i	0.452368	−	1.39225i
$904$		0			0
$905$	−2.18524	+	17.3680i	−0.0726398	+	0.577332i
$906$		0			0
$907$	−29.5085			−0.979815			−0.489907	−	0.871774i	$-0.662969\pi$
$907$	−29.5085			−0.979815			−0.489907	+	0.871774i	$0.662969\pi$
$908$		0			0
$909$	−0.382196	−	0.277682i	−0.0126766	−	0.00921012i
$910$		0			0
$911$	−31.0734	+	22.5761i	−1.02951	+	0.747981i	−0.968210	−	0.250139i	$-0.919524\pi$
$911$	−31.0734	+	22.5761i	−1.02951	+	0.747981i	−0.0612971	+	0.998120i	$0.519524\pi$
$912$		0			0
$913$	−10.4958	−	7.62563i	−0.347360	−	0.252372i
$914$		0			0
$915$	−5.18493	+	41.2092i	−0.171408	+	1.36233i
$916$		0			0
$917$	−4.80055	−	14.7746i	−0.158528	−	0.487899i
$918$		0			0
$919$	−12.8831	−	39.6500i	−0.424974	−	1.30793i	−0.903020	−	0.429600i	$-0.858655\pi$
$919$	−12.8831	−	39.6500i	−0.424974	−	1.30793i	0.478046	−	0.878335i	$-0.341345\pi$
$920$		0			0
$921$	13.2999	−	40.9329i	0.438247	−	1.34879i
$922$		0			0
$923$	−60.8473	+	44.2081i	−2.00281	+	1.45513i
$924$		0			0
$925$	0.334097	+	5.22665i	0.0109851	+	0.171851i
$926$		0			0
$927$	−0.378710	+	0.275149i	−0.0124385	+	0.00903709i
$928$		0			0
$929$	8.68484	−	26.7292i	0.284940	−	0.876956i	−0.701476	−	0.712693i	$-0.747475\pi$
$929$	8.68484	−	26.7292i	0.284940	−	0.876956i	0.986417	−	0.164263i	$-0.0525247\pi$
$930$		0			0
$931$	−0.304498	−	0.937148i	−0.00997952	−	0.0307138i
$932$		0			0
$933$	0.383274	+	1.17960i	0.0125478	+	0.0386183i
$934$		0			0
$935$	15.4254	+	28.0253i	0.504463	+	0.916525i
$936$		0			0
$937$	10.4164	+	7.56796i	0.340289	+	0.247234i	0.744784	−	0.667306i	$-0.232553\pi$
$937$	10.4164	+	7.56796i	0.340289	+	0.247234i	−0.404495	+	0.914540i	$0.632553\pi$
$938$		0			0
$939$	29.9868	−	21.7867i	0.978583	−	0.710982i
$940$		0			0
$941$	−8.21234	−	5.96661i	−0.267714	−	0.194506i	0.445827	−	0.895119i	$-0.352910\pi$
$941$	−8.21234	−	5.96661i	−0.267714	−	0.194506i	−0.713541	+	0.700613i	$0.752910\pi$
$942$		0			0
$943$	5.96489			0.194243
$944$		0			0
$945$	−31.9698	+	6.11518i	−1.03998	+	0.198927i
$946$		0			0
$947$	17.7298	−	54.5669i	0.576143	−	1.77318i	−0.0561124	−	0.998424i	$-0.517871\pi$
$947$	17.7298	−	54.5669i	0.576143	−	1.77318i	0.632255	−	0.774760i	$-0.282129\pi$
$948$		0			0
$949$	23.9219			0.776538
$950$		0			0
$951$	32.2944			1.04722
$952$		0			0
$953$	1.59843	−	4.91947i	0.0517784	−	0.159357i	−0.921824	−	0.387609i	$-0.873301\pi$
$953$	1.59843	−	4.91947i	0.0517784	−	0.159357i	0.973602	+	0.228252i	$0.0733010\pi$
$954$		0			0
$955$	3.62939	+	6.59401i	0.117444	+	0.213377i
$956$		0			0
$957$	19.4896			0.630010
$958$		0			0
$959$	−17.9211	−	13.0205i	−0.578704	−	0.420453i
$960$		0			0
$961$	−16.0149	+	11.6355i	−0.516611	+	0.375340i
$962$		0			0
$963$	0.494135	+	0.359010i	0.0159233	+	0.0115689i
$964$		0			0
$965$	−31.2082	−	14.6663i	−1.00463	−	0.472126i
$966$		0			0
$967$	12.7927	+	39.3718i	0.411384	+	1.26611i	0.915445	+	0.402443i	$0.131839\pi$
$967$	12.7927	+	39.3718i	0.411384	+	1.26611i	−0.504061	+	0.863668i	$0.668161\pi$
$968$		0			0
$969$	3.85901	+	11.8768i	0.123969	+	0.381539i
$970$		0			0
$971$	−13.3139	+	40.9761i	−0.427265	+	1.31499i	0.473544	+	0.880770i	$0.342975\pi$
$971$	−13.3139	+	40.9761i	−0.427265	+	1.31499i	−0.900809	+	0.434216i	$0.857025\pi$
$972$		0			0
$973$	−49.5795	+	36.0216i	−1.58944	+	1.15480i
$974$		0			0
$975$	47.1617	+	12.0587i	1.51038	+	0.386186i
$976$		0			0
$977$	−32.7340	+	23.7826i	−1.04725	+	0.760874i	−0.971688	−	0.236267i	$-0.924076\pi$
$977$	−32.7340	+	23.7826i	−1.04725	+	0.760874i	−0.0755652	+	0.997141i	$0.524076\pi$
$978$		0			0
$979$	7.87398	−	24.2336i	0.251654	−	0.774510i
$980$		0			0
$981$	−0.0722128	−	0.222248i	−0.00230558	−	0.00709584i
$982$		0			0
$983$	−12.4777	−	38.4023i	−0.397976	−	1.22484i	−0.926620	−	0.376000i	$-0.877299\pi$
$983$	−12.4777	−	38.4023i	−0.397976	−	1.22484i	0.528644	−	0.848844i	$-0.322701\pi$
$984$		0			0
$985$	13.4704	−	14.3589i	0.429202	−	0.457513i
$986$		0			0
$987$	10.6785	+	7.75836i	0.339899	+	0.246951i
$988$		0			0
$989$	4.89955	−	3.55973i	0.155797	−	0.113193i
$990$		0			0
$991$	−47.0391	−	34.1759i	−1.49424	−	1.08563i	−0.972604	−	0.232467i	$-0.925320\pi$
$991$	−47.0391	−	34.1759i	−1.49424	−	1.08563i	−0.521641	−	0.853165i	$-0.674680\pi$
$992$		0			0
$993$	28.9374			0.918300
$994$		0			0
$995$	35.6625	+	16.7597i	1.13058	+	0.531317i
$996$		0			0
$997$	12.1434	−	37.3735i	0.384585	−	1.18363i	−0.552197	−	0.833714i	$-0.686210\pi$
$997$	12.1434	−	37.3735i	0.384585	−	1.18363i	0.936781	−	0.349916i	$-0.113790\pi$
$998$		0			0
$999$	−5.49563			−0.173874

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.2.u.d.161.1		8
4.3	odd	2		50.2.d.b.11.2	✓	8
12.11	even	2		450.2.h.e.361.1		8
20.3	even	4		250.2.e.c.199.4		16
20.7	even	4		250.2.e.c.199.1		16
20.19	odd	2		250.2.d.d.51.1		8
25.4	even	10		10000.2.a.x.1.3		4
25.16	even	5	inner	400.2.u.d.241.1		8
25.21	even	5		10000.2.a.t.1.2		4
100.3	even	20		1250.2.b.e.1249.3		8
100.47	even	20		1250.2.b.e.1249.6		8
100.59	odd	10		250.2.d.d.201.1		8
100.63	even	20		250.2.e.c.49.1		16
100.71	odd	10		1250.2.a.l.1.3		4
100.79	odd	10		1250.2.a.f.1.2		4
100.87	even	20		250.2.e.c.49.4		16
100.91	odd	10		50.2.d.b.41.2	yes	8
300.191	even	10		450.2.h.e.91.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
50.2.d.b.11.2	✓	8	4.3	odd	2
50.2.d.b.41.2	yes	8	100.91	odd	10
250.2.d.d.51.1		8	20.19	odd	2
250.2.d.d.201.1		8	100.59	odd	10
250.2.e.c.49.1		16	100.63	even	20
250.2.e.c.49.4		16	100.87	even	20
250.2.e.c.199.1		16	20.7	even	4
250.2.e.c.199.4		16	20.3	even	4
400.2.u.d.161.1		8	1.1	even	1	trivial
400.2.u.d.241.1		8	25.16	even	5	inner
450.2.h.e.91.1		8	300.191	even	10
450.2.h.e.361.1		8	12.11	even	2
1250.2.a.f.1.2		4	100.79	odd	10
1250.2.a.l.1.3		4	100.71	odd	10
1250.2.b.e.1249.3		8	100.3	even	20
1250.2.b.e.1249.6		8	100.47	even	20
10000.2.a.t.1.2		4	25.21	even	5
10000.2.a.x.1.3		4	25.4	even	10

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:	\( N \)	\(=\)	\( 400 = 2^{4} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	400.u (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.529876 + 1.63079i) q^{3} +(2.02373 + 0.951057i) q^{5} +2.77447 q^{7} +(0.0483405 + 0.0351215i) q^{9} +O(q^{10})\)	\(q+(-0.529876 + 1.63079i) q^{3} +(2.02373 + 0.951057i) q^{5} +2.77447 q^{7} +(0.0483405 + 0.0351215i) q^{9} +(2.24459 - 1.63079i) q^{11} +(-4.59343 - 3.33732i) q^{13} +(-2.62330 + 2.79634i) q^{15} +(1.59343 + 4.90406i) q^{17} +(-0.436451 - 1.34326i) q^{19} +(-1.47012 + 4.52458i) q^{21} +(-0.529876 + 0.384978i) q^{23} +(3.19098 + 3.84937i) q^{25} +(-4.24459 + 3.08388i) q^{27} +(1.26594 - 3.89618i) q^{29} +(2.20239 + 6.77827i) q^{31} +(1.47012 + 4.52458i) q^{33} +(5.61478 + 2.63868i) q^{35} +(0.847416 + 0.615684i) q^{37} +(7.87642 - 5.72255i) q^{39} +(-7.36789 - 5.35309i) q^{41} -9.24660 q^{43} +(0.0644258 + 0.117051i) q^{45} +(0.857358 - 2.63868i) q^{47} +0.697669 q^{49} -8.84181 q^{51} +(-0.162577 + 0.500362i) q^{53} +(6.09343 - 1.16555i) q^{55} +2.42184 q^{57} +(-3.05975 - 2.22304i) q^{59} +(8.76365 - 6.36716i) q^{61} +(0.134119 + 0.0974433i) q^{63} +(-6.12188 - 11.1224i) q^{65} +(1.33600 + 4.11180i) q^{67} +(-0.347049 - 1.06811i) q^{69} +(4.09343 - 12.5983i) q^{71} +(-3.40859 + 2.47648i) q^{73} +(-7.96834 + 3.16414i) q^{75} +(6.22754 - 4.52458i) q^{77} +(3.05975 - 9.41695i) q^{79} +(-2.72466 - 8.38563i) q^{81} +(-1.44497 - 4.44717i) q^{83} +(-1.43937 + 11.4399i) q^{85} +(5.68305 + 4.12898i) q^{87} +(7.43002 - 5.39823i) q^{89} +(-12.7443 - 9.25928i) q^{91} -12.2209 q^{93} +(0.394254 - 3.13348i) q^{95} +(-0.0278640 + 0.0857567i) q^{97} +0.165781 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 3 q^{3} - 4 q^{7} - q^{9}+O(q^{10}) \) 8 * q + 3 * q^3 - 4 * q^7 - q^9	\( 8 q + 3 q^{3} - 4 q^{7} - q^{9} - q^{11} - 13 q^{13} + 10 q^{15} - 11 q^{17} - 20 q^{19} - 19 q^{21} + 3 q^{23} + 30 q^{25} - 15 q^{27} - 15 q^{29} + 9 q^{31} + 19 q^{33} + 15 q^{35} - 6 q^{37} + 12 q^{39} - 9 q^{41} - 12 q^{43} + 15 q^{45} + q^{47} - 4 q^{49} - 26 q^{51} + 7 q^{53} + 25 q^{55} - 10 q^{59} + 6 q^{61} + 8 q^{63} - 10 q^{65} + 11 q^{67} + 43 q^{69} + 9 q^{71} - 8 q^{73} - 30 q^{75} + 33 q^{77} + 10 q^{79} - 17 q^{81} - 27 q^{83} + 5 q^{85} - 15 q^{89} - q^{91} - 46 q^{93} + 30 q^{95} - 36 q^{97} + 42 q^{99}+O(q^{100}) \) 8 * q + 3 * q^3 - 4 * q^7 - q^9 - q^11 - 13 * q^13 + 10 * q^15 - 11 * q^17 - 20 * q^19 - 19 * q^21 + 3 * q^23 + 30 * q^25 - 15 * q^27 - 15 * q^29 + 9 * q^31 + 19 * q^33 + 15 * q^35 - 6 * q^37 + 12 * q^39 - 9 * q^41 - 12 * q^43 + 15 * q^45 + q^47 - 4 * q^49 - 26 * q^51 + 7 * q^53 + 25 * q^55 - 10 * q^59 + 6 * q^61 + 8 * q^63 - 10 * q^65 + 11 * q^67 + 43 * q^69 + 9 * q^71 - 8 * q^73 - 30 * q^75 + 33 * q^77 + 10 * q^79 - 17 * q^81 - 27 * q^83 + 5 * q^85 - 15 * q^89 - q^91 - 46 * q^93 + 30 * q^95 - 36 * q^97 + 42 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more