LMFDB - Embedded newform 200.3.e.d.99.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [200,3,Mod(99,200)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(200, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("200.99");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 200 = 2^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	200.e (of order $2$, degree $1$, 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:	$5.44960528721$
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} + 2 x^{14} - x^{12} + 4 x^{11} - 6 x^{10} + 14 x^{9} - 15 x^{8} + 28 x^{7} + \cdots + 256 $ x^16 - 2x^15 + 2x^14 - x^12 + 4x^11 - 6x^10 + 14x^9 - 15x^8 + 28x^7 - 24x^6 + 32x^5 - 16x^4 + 128x^2 - 256x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{27}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 40)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			99.8
Root			$0.579920 - 1.28984i$ of defining polynomial
Character	$\chi$	$=$	200.99
Dual form			200.3.e.d.99.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.709922 + 1.86976i) q^{2} +1.20470i q^{3} +(-2.99202 - 2.65477i) q^{4} +(-2.25250 - 0.855241i) q^{6} +12.3974 q^{7} +(7.08789 - 3.70969i) q^{8} +7.54870 q^{9} +O(q^{10})$	\(q+(-0.709922 + 1.86976i) q^{2} +1.20470i q^{3} +(-2.99202 - 2.65477i) q^{4} +(-2.25250 - 0.855241i) q^{6} +12.3974 q^{7} +(7.08789 - 3.70969i) q^{8} +7.54870 q^{9} -9.41939 q^{11} +(3.19819 - 3.60448i) q^{12} +4.18033 q^{13} +(-8.80120 + 23.1802i) q^{14} +(1.90440 + 15.8863i) q^{16} +21.3875i q^{17} +(-5.35899 + 14.1143i) q^{18} -0.990008 q^{19} +14.9351i q^{21} +(6.68703 - 17.6120i) q^{22} +0.480059 q^{23} +(4.46906 + 8.53876i) q^{24} +(-2.96771 + 7.81623i) q^{26} +19.9362i q^{27} +(-37.0934 - 32.9123i) q^{28} -32.5969i q^{29} +23.2761i q^{31} +(-31.0555 - 7.71723i) q^{32} -11.3475i q^{33} +(-39.9895 - 15.1834i) q^{34} +(-22.5859 - 20.0401i) q^{36} +55.8927 q^{37} +(0.702828 - 1.85108i) q^{38} +5.03604i q^{39} +16.5487 q^{41} +(-27.9252 - 10.6028i) q^{42} +57.3157i q^{43} +(28.1830 + 25.0063i) q^{44} +(-0.340804 + 0.897597i) q^{46} -17.9921 q^{47} +(-19.1381 + 2.29422i) q^{48} +104.696 q^{49} -25.7654 q^{51} +(-12.5077 - 11.0978i) q^{52} -26.8978 q^{53} +(-37.2759 - 14.1531i) q^{54} +(87.8716 - 45.9907i) q^{56} -1.19266i q^{57} +(60.9485 + 23.1412i) q^{58} -76.8224 q^{59} -104.235i q^{61} +(-43.5208 - 16.5242i) q^{62} +93.5845 q^{63} +(36.4764 - 52.5878i) q^{64} +(21.2171 + 8.05584i) q^{66} -2.30211i q^{67} +(56.7788 - 63.9918i) q^{68} +0.578326i q^{69} -54.2243i q^{71} +(53.5044 - 28.0034i) q^{72} -73.9447i q^{73} +(-39.6794 + 104.506i) q^{74} +(2.96213 + 2.62824i) q^{76} -116.776 q^{77} +(-9.41619 - 3.57519i) q^{78} -39.5803i q^{79} +43.9213 q^{81} +(-11.7483 + 30.9421i) q^{82} +58.1742i q^{83} +(39.6494 - 44.6863i) q^{84} +(-107.167 - 40.6897i) q^{86} +39.2694 q^{87} +(-66.7636 + 34.9430i) q^{88} +28.3395 q^{89} +51.8254 q^{91} +(-1.43635 - 1.27445i) q^{92} -28.0407 q^{93} +(12.7730 - 33.6409i) q^{94} +(9.29692 - 37.4125i) q^{96} -4.84731i q^{97} +(-74.3261 + 195.757i) q^{98} -71.1042 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{4} - 24 q^{6} - 48 q^{9}+O(q^{10}) $ 16 * q + 16 * q^4 - 24 * q^6 - 48 * q^9	$ 16 q + 16 q^{4} - 24 q^{6} - 48 q^{9} - 64 q^{11} + 40 q^{14} + 16 q^{16} - 64 q^{19} + 16 q^{24} + 120 q^{26} - 24 q^{34} - 288 q^{36} + 96 q^{41} + 176 q^{44} - 280 q^{46} + 176 q^{49} + 128 q^{51} - 112 q^{54} + 560 q^{56} - 448 q^{59} + 256 q^{64} + 448 q^{66} - 120 q^{74} - 384 q^{76} - 112 q^{81} + 80 q^{84} - 888 q^{86} + 96 q^{89} + 200 q^{94} + 896 q^{96} + 704 q^{99}+O(q^{100}) $ 16 * q + 16 * q^4 - 24 * q^6 - 48 * q^9 - 64 * q^11 + 40 * q^14 + 16 * q^16 - 64 * q^19 + 16 * q^24 + 120 * q^26 - 24 * q^34 - 288 * q^36 + 96 * q^41 + 176 * q^44 - 280 * q^46 + 176 * q^49 + 128 * q^51 - 112 * q^54 + 560 * q^56 - 448 * q^59 + 256 * q^64 + 448 * q^66 - 120 * q^74 - 384 * q^76 - 112 * q^81 + 80 * q^84 - 888 * q^86 + 96 * q^89 + 200 * q^94 + 896 * q^96 + 704 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/200\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$177$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$	−0.709922	+	1.86976i	−0.354961	+	0.934881i
$2$	−0.709922	+	1.86976i	−0.354961	+	0.934881i
$3$			1.20470i			0.401566i	0.979636	+	0.200783i	$0.0643486\pi$
$3$			1.20470i			0.401566i	−0.979636	+	0.200783i	$0.935651\pi$
$4$	−2.99202	−	2.65477i	−0.748006	−	0.663692i
$5$		0			0
$5$		0			0
$6$	−2.25250	−	0.855241i	−0.375416	−	0.142540i
$7$	12.3974			1.77106			0.885531	−	0.464581i	$-0.153795\pi$
$7$	12.3974			1.77106			0.885531	+	0.464581i	$0.153795\pi$
$8$	7.08789	−	3.70969i	0.885986	−	0.463712i
$9$	7.54870			0.838745
$10$		0			0
$11$	−9.41939			−0.856308			−0.428154	−	0.903706i	$-0.640836\pi$
$11$	−9.41939			−0.856308			−0.428154	+	0.903706i	$0.640836\pi$
$12$	3.19819	−	3.60448i	0.266516	−	0.300373i
$13$	4.18033			0.321564			0.160782	−	0.986990i	$-0.448598\pi$
$13$	4.18033			0.321564			0.160782	+	0.986990i	$0.448598\pi$
$14$	−8.80120	+	23.1802i	−0.628657	+	1.65573i
$15$		0			0
$16$	1.90440	+	15.8863i	0.119025	+	0.992891i
$17$			21.3875i			1.25809i	0.777370	+	0.629043i	$0.216553\pi$
$17$			21.3875i			1.25809i	−0.777370	+	0.629043i	$0.783447\pi$
$18$	−5.35899	+	14.1143i	−0.297722	+	0.784127i
$19$	−0.990008			−0.0521057			−0.0260529	−	0.999661i	$-0.508294\pi$
$19$	−0.990008			−0.0521057			−0.0260529	+	0.999661i	$0.508294\pi$
$20$		0			0
$21$			14.9351i			0.711198i
$22$	6.68703	−	17.6120i	0.303956	−	0.800546i
$23$	0.480059			0.0208721			0.0104361	−	0.999946i	$-0.496678\pi$
$23$	0.480059			0.0208721			0.0104361	+	0.999946i	$0.496678\pi$
$24$	4.46906	+	8.53876i	0.186211	+	0.355782i
$25$		0			0
$26$	−2.96771	+	7.81623i	−0.114143	+	0.300624i
$27$			19.9362i			0.738377i
$28$	−37.0934	−	32.9123i	−1.32476	−	1.17544i
$29$		−	32.5969i		−	1.12403i	−0.827127	−	0.562016i	$-0.810026\pi$
$29$		−	32.5969i		−	1.12403i	0.827127	−	0.562016i	$-0.189974\pi$
$30$		0			0
$31$			23.2761i			0.750842i	0.926854	+	0.375421i	$0.122502\pi$
$31$			23.2761i			0.750842i	−0.926854	+	0.375421i	$0.877498\pi$
$32$	−31.0555	−	7.71723i	−0.970485	−	0.241163i
$33$		−	11.3475i		−	0.343864i
$34$	−39.9895	−	15.1834i	−1.17616	−	0.446572i
$35$		0			0
$36$	−22.5859	−	20.0401i	−0.627386	−	0.556669i
$37$	55.8927			1.51061			0.755307	−	0.655371i	$-0.227488\pi$
$37$	55.8927			1.51061			0.755307	+	0.655371i	$0.227488\pi$
$38$	0.702828	−	1.85108i	0.0184955	−	0.0487126i
$39$			5.03604i			0.129129i
$40$		0			0
$41$	16.5487			0.403627			0.201813	−	0.979424i	$-0.435317\pi$
$41$	16.5487			0.403627			0.201813	+	0.979424i	$0.435317\pi$
$42$	−27.9252	−	10.6028i	−0.664885	−	0.252447i
$43$			57.3157i			1.33292i	0.745539	+	0.666462i	$0.232192\pi$
$43$			57.3157i			1.33292i	−0.745539	+	0.666462i	$0.767808\pi$
$44$	28.1830	+	25.0063i	0.640523	+	0.568325i
$45$		0			0
$46$	−0.340804	+	0.897597i	−0.00740879	+	0.0195130i
$47$	−17.9921			−0.382810			−0.191405	−	0.981511i	$-0.561304\pi$
$47$	−17.9921			−0.382810			−0.191405	+	0.981511i	$0.561304\pi$
$48$	−19.1381	+	2.29422i	−0.398711	+	0.0477963i
$49$	104.696			2.13666
$50$		0			0
$51$	−25.7654			−0.505205
$52$	−12.5077	−	11.0978i	−0.240532	−	0.213420i
$53$	−26.8978			−0.507506			−0.253753	−	0.967269i	$-0.581665\pi$
$53$	−26.8978			−0.507506			−0.253753	+	0.967269i	$0.581665\pi$
$54$	−37.2759	−	14.1531i	−0.690295	−	0.262095i
$55$		0			0
$56$	87.8716	−	45.9907i	1.56914	−	0.821262i
$57$		−	1.19266i		−	0.0209239i
$58$	60.9485	+	23.1412i	1.05084	+	0.398987i
$59$	−76.8224			−1.30207			−0.651037	−	0.759046i	$-0.725666\pi$
$59$	−76.8224			−1.30207			−0.651037	+	0.759046i	$0.725666\pi$
$60$		0			0
$61$		−	104.235i		−	1.70877i	−0.519638	−	0.854387i	$-0.673933\pi$
$61$		−	104.235i		−	1.70877i	0.519638	−	0.854387i	$-0.326067\pi$
$62$	−43.5208	−	16.5242i	−0.701948	−	0.266520i
$63$	93.5845			1.48547
$64$	36.4764	−	52.5878i	0.569943	−	0.821684i
$65$		0			0
$66$	21.2171	+	8.05584i	0.321472	+	0.122058i
$67$		−	2.30211i		−	0.0343598i	−0.999852	−	0.0171799i	$-0.994531\pi$
$67$		−	2.30211i		−	0.0343598i	0.999852	−	0.0171799i	$-0.00546880\pi$
$68$	56.7788	−	63.9918i	0.834983	−	0.941056i
$69$			0.578326i			0.00838154i
$70$		0			0
$71$		−	54.2243i		−	0.763722i	−0.924220	−	0.381861i	$-0.875283\pi$
$71$		−	54.2243i		−	0.763722i	0.924220	−	0.381861i	$-0.124717\pi$
$72$	53.5044	−	28.0034i	0.743116	−	0.388936i
$73$		−	73.9447i		−	1.01294i	−0.862257	−	0.506471i	$-0.830950\pi$
$73$		−	73.9447i		−	1.01294i	0.862257	−	0.506471i	$-0.169050\pi$
$74$	−39.6794	+	104.506i	−0.536209	+	1.41224i
$75$		0			0
$76$	2.96213	+	2.62824i	0.0389754	+	0.0345822i
$77$	−116.776			−1.51657
$78$	−9.41619	−	3.57519i	−0.120720	−	0.0458358i
$79$		−	39.5803i		−	0.501016i	−0.968114	−	0.250508i	$-0.919402\pi$
$79$		−	39.5803i		−	0.501016i	0.968114	−	0.250508i	$-0.0805977\pi$
$80$		0			0
$81$	43.9213			0.542238
$82$	−11.7483	+	30.9421i	−0.143272	+	0.377343i
$83$			58.1742i			0.700895i	0.936582	+	0.350447i	$0.113970\pi$
$83$			58.1742i			0.700895i	−0.936582	+	0.350447i	$0.886030\pi$
$84$	39.6494	−	44.6863i	0.472016	−	0.531980i
$85$		0			0
$86$	−107.167	−	40.6897i	−1.24613	−	0.473136i
$87$	39.2694			0.451372
$88$	−66.7636	+	34.9430i	−0.758677	+	0.397080i
$89$	28.3395			0.318422			0.159211	−	0.987245i	$-0.449105\pi$
$89$	28.3395			0.318422			0.159211	+	0.987245i	$0.449105\pi$
$90$		0			0
$91$	51.8254			0.569510
$92$	−1.43635	−	1.27445i	−0.0156125	−	0.0138527i
$93$	−28.0407			−0.301513
$94$	12.7730	−	33.6409i	0.135883	−	0.357882i
$95$		0			0
$96$	9.29692	−	37.4125i	0.0968429	−	0.389713i
$97$		−	4.84731i		−	0.0499722i	−0.999688	−	0.0249861i	$-0.992046\pi$
$97$		−	4.84731i		−	0.0499722i	0.999688	−	0.0249861i	$-0.00795415\pi$
$98$	−74.3261	+	195.757i	−0.758430	+	1.99752i
$99$	−71.1042			−0.718224
$100$		0			0
$101$			152.613i			1.51102i	0.655137	+	0.755510i	$0.272611\pi$
$101$			152.613i			1.51102i	−0.655137	+	0.755510i	$0.727389\pi$
$102$	18.2914	−	48.1752i	0.179328	−	0.472306i
$103$	−112.926			−1.09637			−0.548185	−	0.836357i	$-0.684681\pi$
$103$	−112.926			−1.09637			−0.548185	+	0.836357i	$0.684681\pi$
$104$	29.6297	−	15.5078i	0.284901	−	0.149113i
$105$		0			0
$106$	19.0953	−	50.2925i	0.180145	−	0.474458i
$107$		−	131.573i		−	1.22966i	−0.788660	−	0.614829i	$-0.789225\pi$
$107$		−	131.573i		−	1.22966i	0.788660	−	0.614829i	$-0.210775\pi$
$108$	52.9260	−	59.6495i	0.490055	−	0.552310i
$109$		−	58.7214i		−	0.538728i	−0.963038	−	0.269364i	$-0.913186\pi$
$109$		−	58.7214i		−	0.538728i	0.963038	−	0.269364i	$-0.0868135\pi$
$110$		0			0
$111$			67.3338i			0.606611i
$112$	23.6097	+	196.949i	0.210800	+	1.75847i
$113$		−	155.198i		−	1.37343i	−0.726927	−	0.686715i	$-0.759052\pi$
$113$		−	155.198i		−	1.37343i	0.726927	−	0.686715i	$-0.240948\pi$
$114$	2.22999	+	0.846695i	0.0195613	+	0.00742715i
$115$		0			0
$116$	−86.5373	+	97.5307i	−0.746011	+	0.840782i
$117$	31.5561			0.269710
$118$	54.5379	−	143.640i	0.462185	−	1.21729i
$119$			265.150i			2.22815i
$120$		0			0
$121$	−32.2752			−0.266737
$122$	194.895	+	73.9988i	1.59750	+	0.606548i
$123$			19.9362i			0.162083i
$124$	61.7927	−	69.6427i	0.498328	−	0.561634i
$125$		0			0
$126$	−66.4377	+	174.981i	−0.527283	+	1.38874i
$127$	−134.542			−1.05939			−0.529693	−	0.848189i	$-0.677693\pi$
$127$	−134.542			−1.05939			−0.529693	+	0.848189i	$0.677693\pi$
$128$	72.4313	+	105.535i	0.565870	+	0.824495i
$129$	−69.0481			−0.535257
$130$		0			0
$131$	−139.446			−1.06447			−0.532235	−	0.846596i	$-0.678648\pi$
$131$	−139.446			−1.06447			−0.532235	+	0.846596i	$0.678648\pi$
$132$	−30.1250	+	33.9520i	−0.228220	+	0.257212i
$133$	−12.2736			−0.0922824
$134$	4.30439	+	1.63431i	0.0321223	+	0.0121964i
$135$		0			0
$136$	79.3410	+	151.592i	0.583390	+	1.11465i
$137$		−	87.3194i		−	0.637368i	−0.947861	−	0.318684i	$-0.896759\pi$
$137$		−	87.3194i		−	0.637368i	0.947861	−	0.318684i	$-0.103241\pi$
$138$	−1.08133	−	0.410566i	−0.00783574	−	0.00297512i
$139$	−101.245			−0.728380			−0.364190	−	0.931325i	$-0.618654\pi$
$139$	−101.245			−0.728380			−0.364190	+	0.931325i	$0.618654\pi$
$140$		0			0
$141$		−	21.6750i		−	0.153724i
$142$	101.386	+	38.4950i	0.713989	+	0.271091i
$143$	−39.3762			−0.275358
$144$	14.3757	+	119.921i	0.0998316	+	0.832782i
$145$		0			0
$146$	138.259	+	52.4949i	0.946980	+	0.359554i
$147$			126.127i			0.858009i
$148$	−167.232	−	148.382i	−1.12995	−	1.00258i
$149$			95.8745i			0.643453i	0.946833	+	0.321727i	$0.104263\pi$
$149$			95.8745i			0.643453i	−0.946833	+	0.321727i	$0.895737\pi$
$150$		0			0
$151$		−	27.7535i		−	0.183798i	−0.995768	−	0.0918991i	$-0.970706\pi$
$151$		−	27.7535i		−	0.183798i	0.995768	−	0.0918991i	$-0.0292937\pi$
$152$	−7.01707	+	3.67263i	−0.0461649	+	0.0241620i
$153$			161.448i			1.05521i
$154$	82.9019	−	218.344i	0.538324	−	1.41782i
$155$		0			0
$156$	13.3695	−	15.0679i	0.0857020	−	0.0965893i
$157$	72.4052			0.461180			0.230590	−	0.973051i	$-0.425934\pi$
$157$	72.4052			0.461180			0.230590	+	0.973051i	$0.425934\pi$
$158$	74.0057	+	28.0989i	0.468391	+	0.177841i
$159$		−	32.4037i		−	0.203797i
$160$		0			0
$161$	5.95150			0.0369658
$162$	−31.1807	+	82.1223i	−0.192473	+	0.506928i
$163$		−	66.4519i		−	0.407680i	−0.979004	−	0.203840i	$-0.934658\pi$
$163$		−	66.4519i		−	0.407680i	0.979004	−	0.203840i	$-0.0653423\pi$
$164$	−49.5141	−	43.9330i	−0.301915	−	0.267884i
$165$		0			0
$166$	−108.772	−	41.2992i	−0.655253	−	0.248790i
$167$	51.6512			0.309288			0.154644	−	0.987970i	$-0.450577\pi$
$167$	51.6512			0.309288			0.154644	+	0.987970i	$0.450577\pi$
$168$	55.4048	+	105.859i	0.329791	+	0.630111i
$169$	−151.525			−0.896597
$170$		0			0
$171$	−7.47328			−0.0437034
$172$	152.160	−	171.490i	0.884651	−	0.997034i
$173$	18.5308			0.107114			0.0535571	−	0.998565i	$-0.482944\pi$
$173$	18.5308			0.107114			0.0535571	+	0.998565i	$0.482944\pi$
$174$	−27.8782	+	73.4245i	−0.160220	+	0.421980i
$175$		0			0
$176$	−17.9383	−	149.639i	−0.101922	−	0.850221i
$177$		−	92.5478i		−	0.522869i
$178$	−20.1188	+	52.9882i	−0.113027	+	0.297686i
$179$	152.782			0.853533			0.426767	−	0.904362i	$-0.359653\pi$
$179$	152.782			0.853533			0.426767	+	0.904362i	$0.359653\pi$
$180$		0			0
$181$		−	139.334i		−	0.769801i	−0.922958	−	0.384901i	$-0.874236\pi$
$181$		−	139.334i		−	0.769801i	0.922958	−	0.384901i	$-0.125764\pi$
$182$	−36.7920	+	96.9012i	−0.202154	+	0.532424i
$183$	125.572			0.686185
$184$	3.40261	−	1.78087i	0.0184924	−	0.00967866i
$185$		0			0
$186$	19.9067	−	52.4294i	0.107025	−	0.281878i
$187$		−	201.457i		−	1.07731i
$188$	53.8327	+	47.7648i	0.286344	+	0.254068i
$189$			247.157i			1.30771i
$190$		0			0
$191$			127.507i			0.667577i	0.942648	+	0.333789i	$0.108327\pi$
$191$			127.507i			0.667577i	−0.942648	+	0.333789i	$0.891673\pi$
$192$	63.3524	+	43.9430i	0.329960	+	0.228870i
$193$			160.944i			0.833908i	0.908928	+	0.416954i	$0.136902\pi$
$193$			160.944i			0.833908i	−0.908928	+	0.416954i	$0.863098\pi$
$194$	9.06331	+	3.44121i	0.0467181	+	0.0177382i
$195$		0			0
$196$	−313.253	−	277.944i	−1.59823	−	1.41808i
$197$	−149.338			−0.758059			−0.379030	−	0.925385i	$-0.623742\pi$
$197$	−149.338			−0.758059			−0.379030	+	0.925385i	$0.623742\pi$
$198$	50.4784	−	132.948i	0.254941	−	0.671454i
$199$		−	350.488i		−	1.76125i	−0.473817	−	0.880624i	$-0.657124\pi$
$199$		−	350.488i		−	1.76125i	0.473817	−	0.880624i	$-0.342876\pi$
$200$		0			0
$201$	2.77334			0.0137977
$202$	−285.350	−	108.343i	−1.41262	−	0.536353i
$203$		−	404.118i		−	1.99073i
$204$	77.0908	+	68.4013i	0.377896	+	0.335300i
$205$		0			0
$206$	80.1687	−	211.145i	0.389169	−	1.02498i
$207$	3.62383			0.0175064
$208$	7.96102	+	66.4099i	0.0382742	+	0.319278i
$209$	9.32527			0.0446185
$210$		0			0
$211$	384.668			1.82307			0.911535	−	0.411224i	$-0.134898\pi$
$211$	384.668			1.82307			0.911535	+	0.411224i	$0.134898\pi$
$212$	80.4789	+	71.4075i	0.379617	+	0.336828i
$213$	65.3238			0.306685
$214$	246.011	+	93.4068i	1.14958	+	0.436480i
$215$		0			0
$216$	73.9571	+	141.305i	0.342394	+	0.654192i
$217$			288.564i			1.32979i
$218$	109.795	+	41.6876i	0.503647	+	0.191227i
$219$	89.0810			0.406763
$220$		0			0
$221$			89.4068i			0.404556i
$222$	−125.898	−	47.8017i	−0.567109	−	0.215323i
$223$	59.1979			0.265461			0.132731	−	0.991152i	$-0.457625\pi$
$223$	59.1979			0.265461			0.132731	+	0.991152i	$0.457625\pi$
$224$	−385.008	−	95.6738i	−1.71879	−	0.427115i
$225$		0			0
$226$	290.183	+	110.178i	1.28399	+	0.487514i
$227$			225.689i			0.994226i	0.867686	+	0.497113i	$0.165607\pi$
$227$			225.689i			0.994226i	−0.867686	+	0.497113i	$0.834393\pi$
$228$	−3.16624	+	3.56847i	−0.0138870	+	0.0156512i
$229$		−	147.030i		−	0.642051i	−0.947070	−	0.321026i	$-0.895972\pi$
$229$		−	147.030i		−	0.642051i	0.947070	−	0.321026i	$-0.104028\pi$
$230$		0			0
$231$		−	140.680i		−	0.609004i
$232$	−120.925	−	231.043i	−0.521226	−	0.995876i
$233$			154.448i			0.662868i	0.943478	+	0.331434i	$0.107532\pi$
$233$			154.448i			0.662868i	−0.943478	+	0.331434i	$0.892468\pi$
$234$	−22.4024	+	59.0024i	−0.0957366	+	0.252147i
$235$		0			0
$236$	229.854	+	203.946i	0.973959	+	0.864177i
$237$	47.6823			0.201191
$238$	−495.767	−	188.236i	−2.08305	−	0.790905i
$239$		−	194.606i		−	0.814249i	−0.913373	−	0.407125i	$-0.866531\pi$
$239$		−	194.606i		−	0.814249i	0.913373	−	0.407125i	$-0.133469\pi$
$240$		0			0
$241$	−101.503			−0.421176			−0.210588	−	0.977575i	$-0.567538\pi$
$241$	−101.503			−0.421176			−0.210588	+	0.977575i	$0.567538\pi$
$242$	22.9128	−	60.3469i	0.0946811	−	0.249367i
$243$			232.337i			0.956121i
$244$	−276.720	+	311.874i	−1.13410	+	1.27817i
$245$		0			0
$246$	−37.2759	−	14.1531i	−0.151528	−	0.0575330i
$247$	−4.13857			−0.0167553
$248$	86.3472	+	164.979i	0.348174	+	0.665236i
$249$	−70.0824			−0.281455
$250$		0			0
$251$	−206.393			−0.822282			−0.411141	−	0.911572i	$-0.634870\pi$
$251$	−206.393			−0.822282			−0.411141	+	0.911572i	$0.634870\pi$
$252$	−280.007	−	248.445i	−1.11114	−	0.985894i
$253$	−4.52186			−0.0178730
$254$	95.5143	−	251.562i	0.376041	−	0.990401i
$255$		0			0
$256$	−248.747	+	60.5076i	−0.971666	+	0.236358i
$257$		−	74.3497i		−	0.289298i	−0.989483	−	0.144649i	$-0.953795\pi$
$257$		−	74.3497i		−	0.289298i	0.989483	−	0.144649i	$-0.0462054\pi$
$258$	49.0187	−	129.104i	0.189995	−	0.500401i
$259$	692.926			2.67539
$260$		0			0
$261$		−	246.064i		−	0.942775i
$262$	98.9955	−	260.730i	0.377845	−	0.995154i
$263$	−391.694			−1.48933			−0.744665	−	0.667439i	$-0.767391\pi$
$263$	−391.694			−1.48933			−0.744665	+	0.667439i	$0.767391\pi$
$264$	−42.0958	−	80.4299i	−0.159454	−	0.304659i
$265$		0			0
$266$	8.71326	−	22.9486i	0.0327566	−	0.0862731i
$267$			34.1405i			0.127867i
$268$	−6.11156	+	6.88795i	−0.0228043	+	0.0257013i
$269$		−	268.340i		−	0.997548i	−0.866732	−	0.498774i	$-0.833784\pi$
$269$		−	268.340i		−	0.997548i	0.866732	−	0.498774i	$-0.166216\pi$
$270$		0			0
$271$		−	426.407i		−	1.57346i	−0.617300	−	0.786728i	$-0.711773\pi$
$271$		−	426.407i		−	1.57346i	0.617300	−	0.786728i	$-0.288227\pi$
$272$	−339.767	+	40.7303i	−1.24914	+	0.149744i
$273$			62.4339i			0.228696i
$274$	163.267	+	61.9900i	0.595863	+	0.226241i
$275$		0			0
$276$	1.53532	−	1.73037i	0.00556276	−	0.00626944i
$277$	3.48615			0.0125854			0.00629269	−	0.999980i	$-0.497997\pi$
$277$	3.48615			0.0125854			0.00629269	+	0.999980i	$0.497997\pi$
$278$	71.8759	−	189.304i	0.258546	−	0.680948i
$279$			175.705i			0.629765i
$280$		0			0
$281$	−142.361			−0.506621			−0.253311	−	0.967385i	$-0.581519\pi$
$281$	−142.361			−0.506621			−0.253311	+	0.967385i	$0.581519\pi$
$282$	40.5271	+	15.3876i	0.143713	+	0.0545658i
$283$		−	127.113i		−	0.449162i	−0.974455	−	0.224581i	$-0.927899\pi$
$283$		−	127.113i		−	0.449162i	0.974455	−	0.224581i	$-0.0721014\pi$
$284$	−143.953	+	162.240i	−0.506876	+	0.571268i
$285$		0			0
$286$	27.9540	−	73.6241i	0.0977413	−	0.257427i
$287$	205.161			0.714848
$288$	−234.429	−	58.2551i	−0.813989	−	0.202274i
$289$	−168.424			−0.582783
$290$		0			0
$291$	5.83954			0.0200671
$292$	−196.306	+	221.244i	−0.672281	+	0.757686i
$293$	213.860			0.729898			0.364949	−	0.931027i	$-0.381086\pi$
$293$	213.860			0.729898			0.364949	+	0.931027i	$0.381086\pi$
$294$	−235.828	−	89.5405i	−0.802136	−	0.304559i
$295$		0			0
$296$	396.161	−	207.345i	1.33838	−	0.700489i
$297$		−	187.787i		−	0.632278i
$298$	−179.263	−	68.0634i	−0.601552	−	0.228401i
$299$	2.00681			0.00671173
$300$		0			0
$301$			710.567i			2.36069i
$302$	51.8925	+	19.7028i	0.171829	+	0.0652412i
$303$	−183.852			−0.606774
$304$	−1.88537	−	15.7275i	−0.00620188	−	0.0517353i
$305$		0			0
$306$	−301.869	−	114.615i	−0.986500	−	0.374560i
$307$			341.127i			1.11116i	0.831462	+	0.555582i	$0.187504\pi$
$307$			341.127i			1.11116i	−0.831462	+	0.555582i	$0.812496\pi$
$308$	349.397	+	310.014i	1.13441	+	1.00654i
$309$		−	136.042i		−	0.440265i
$310$		0			0
$311$			384.458i			1.23620i	0.786100	+	0.618100i	$0.212097\pi$
$311$			384.458i			1.23620i	−0.786100	+	0.618100i	$0.787903\pi$
$312$	18.6822	+	35.6949i	0.0598787	+	0.114407i
$313$			198.197i			0.633216i	0.948557	+	0.316608i	$0.102544\pi$
$313$			198.197i			0.633216i	−0.948557	+	0.316608i	$0.897456\pi$
$314$	−51.4020	+	135.381i	−0.163701	+	0.431148i
$315$		0			0
$316$	−105.077	+	118.425i	−0.332521	+	0.374763i
$317$	506.683			1.59837			0.799184	−	0.601087i	$-0.205265\pi$
$317$	506.683			1.59837			0.799184	+	0.601087i	$0.205265\pi$
$318$	60.5873	+	23.0041i	0.190526	+	0.0723400i
$319$			307.043i			0.962517i
$320$		0			0
$321$	158.506			0.493789
$322$	−4.22510	+	11.1279i	−0.0131214	+	0.0345587i
$323$		−	21.1738i		−	0.0655535i
$324$	−131.413	−	116.601i	−0.405597	−	0.359879i
$325$		0			0
$326$	124.249	+	47.1756i	0.381133	+	0.144711i
$327$	70.7415			0.216335
$328$	117.295	−	61.3906i	0.357608	−	0.187167i
$329$	−223.056			−0.677981
$330$		0			0
$331$	341.770			1.03254			0.516268	−	0.856427i	$-0.327321\pi$
$331$	341.770			1.03254			0.516268	+	0.856427i	$0.327321\pi$
$332$	154.439	−	174.059i	0.465178	−	0.524273i
$333$	421.918			1.26702
$334$	−36.6683	+	96.5754i	−0.109785	+	0.289148i
$335$		0			0
$336$	−237.264	+	28.4425i	−0.706142	+	0.0846503i
$337$			483.617i			1.43506i	0.696525	+	0.717532i	$0.254729\pi$
$337$			483.617i			1.43506i	−0.696525	+	0.717532i	$0.745271\pi$
$338$	107.571	−	283.315i	0.318257	−	0.838211i
$339$	186.966			0.551523
$340$		0			0
$341$		−	219.247i		−	0.642952i
$342$	5.30544	−	13.9733i	0.0155130	−	0.0408575i
$343$	690.490			2.01309
$344$	212.624	+	406.247i	0.618092	+	1.18095i
$345$		0			0
$346$	−13.1554	+	34.6481i	−0.0380214	+	0.100139i
$347$		−	153.403i		−	0.442084i	−0.975264	−	0.221042i	$-0.929054\pi$
$347$		−	153.403i		−	0.442084i	0.975264	−	0.221042i	$-0.0709457\pi$
$348$	−117.495	−	104.251i	−0.337629	−	0.299572i
$349$			470.630i			1.34851i	0.738499	+	0.674254i	$0.235535\pi$
$349$			470.630i			1.34851i	−0.738499	+	0.674254i	$0.764465\pi$
$350$		0			0
$351$			83.3399i			0.237436i
$352$	292.524	+	72.6915i	0.831034	+	0.206510i
$353$		−	60.9892i		−	0.172774i	−0.996262	−	0.0863870i	$-0.972468\pi$
$353$		−	60.9892i		−	0.172774i	0.996262	−	0.0863870i	$-0.0275322\pi$
$354$	173.042	+	65.7016i	0.488820	+	0.185598i
$355$		0			0
$356$	−84.7925	−	75.2349i	−0.238181	−	0.211334i
$357$	−319.425			−0.894748
$358$	−108.464	+	285.667i	−0.302971	+	0.797952i
$359$		−	659.963i		−	1.83834i	−0.393865	−	0.919168i	$-0.628862\pi$
$359$		−	659.963i		−	1.83834i	0.393865	−	0.919168i	$-0.371138\pi$
$360$		0			0
$361$	−360.020			−0.997285
$362$	260.521	+	98.9162i	0.719673	+	0.273249i
$363$		−	38.8818i		−	0.107112i
$364$	−155.063	−	137.584i	−0.425997	−	0.377979i
$365$		0			0
$366$	−89.1462	+	234.789i	−0.243569	+	0.641501i
$367$	371.867			1.01326			0.506630	−	0.862163i	$-0.330891\pi$
$367$	371.867			1.01326			0.506630	+	0.862163i	$0.330891\pi$
$368$	0.914224	+	7.62635i	0.00248431	+	0.0207238i
$369$	124.921			0.338540
$370$		0			0
$371$	−333.464			−0.898824
$372$	83.8983	+	74.4415i	0.225533	+	0.200112i
$373$	−292.195			−0.783364			−0.391682	−	0.920101i	$-0.628107\pi$
$373$	−292.195			−0.783364			−0.391682	+	0.920101i	$0.628107\pi$
$374$	376.677	+	143.019i	1.00716	+	0.382403i
$375$		0			0
$376$	−127.526	+	66.7451i	−0.339165	+	0.177514i
$377$		−	136.266i		−	0.361448i
$378$	−462.126	−	175.462i	−1.22255	−	0.464186i
$379$	−574.767			−1.51654			−0.758268	−	0.651943i	$-0.773954\pi$
$379$	−574.767			−1.51654			−0.758268	+	0.651943i	$0.773954\pi$
$380$		0			0
$381$		−	162.083i		−	0.425413i
$382$	−238.408	−	90.5201i	−0.624105	−	0.236964i
$383$	−80.7976			−0.210960			−0.105480	−	0.994421i	$-0.533638\pi$
$383$	−80.7976			−0.210960			−0.105480	+	0.994421i	$0.533638\pi$
$384$	−127.138	+	87.2578i	−0.331089	+	0.227234i
$385$		0			0
$386$	−300.928	−	114.258i	−0.779605	−	0.296005i
$387$			432.659i			1.11798i
$388$	−12.8685	+	14.5032i	−0.0331662	+	0.0373795i
$389$			295.056i			0.758498i	0.925295	+	0.379249i	$0.123818\pi$
$389$			295.056i			0.758498i	−0.925295	+	0.379249i	$0.876182\pi$
$390$		0			0
$391$			10.2673i			0.0262590i
$392$	742.075	−	388.391i	1.89305	−	0.990793i
$393$		−	167.990i		−	0.427455i
$394$	106.018	−	279.226i	0.269081	−	0.708695i
$395$		0			0
$396$	212.745	+	188.765i	0.537236	+	0.476680i
$397$	−119.742			−0.301618			−0.150809	−	0.988563i	$-0.548188\pi$
$397$	−119.742			−0.301618			−0.150809	+	0.988563i	$0.548188\pi$
$398$	655.330	+	248.819i	1.64656	+	0.625174i
$399$		−	14.7859i		−	0.0370575i
$400$		0			0
$401$	−332.970			−0.830350			−0.415175	−	0.909742i	$-0.636280\pi$
$401$	−332.970			−0.830350			−0.415175	+	0.909742i	$0.636280\pi$
$402$	−1.96885	+	5.18549i	−0.00489765	+	0.0128992i
$403$			97.3019i			0.241444i
$404$	405.152	−	456.622i	1.00285	−	1.13025i
$405$		0			0
$406$	755.604	+	286.892i	1.86109	+	0.706630i
$407$	−526.475			−1.29355
$408$	−182.623	+	95.5819i	−0.447604	+	0.234269i
$409$	14.2484			0.0348373			0.0174186	−	0.999848i	$-0.494455\pi$
$409$	14.2484			0.0348373			0.0174186	+	0.999848i	$0.494455\pi$
$410$		0			0
$411$	105.194			0.255945
$412$	337.878	+	299.793i	0.820091	+	0.727653i
$413$	−952.400			−2.30605
$414$	−2.57263	+	6.77569i	−0.00621409	+	0.0163664i
$415$		0			0
$416$	−129.822	−	32.2606i	−0.312073	−	0.0775495i
$417$		−	121.969i		−	0.292492i
$418$	−6.62021	+	17.4360i	−0.0158378	+	0.0417130i
$419$	−159.814			−0.381417			−0.190709	−	0.981647i	$-0.561079\pi$
$419$	−159.814			−0.381417			−0.190709	+	0.981647i	$0.561079\pi$
$420$		0			0
$421$			89.1070i			0.211656i	0.994384	+	0.105828i	$0.0337492\pi$
$421$			89.1070i			0.211656i	−0.994384	+	0.105828i	$0.966251\pi$
$422$	−273.084	+	719.237i	−0.647118	+	1.70435i
$423$	−135.817			−0.321080
$424$	−190.649	+	99.7827i	−0.449643	+	0.235337i
$425$		0			0
$426$	−46.3748	+	122.140i	−0.108861	+	0.286714i
$427$		−	1292.25i		−	3.02634i
$428$	−349.297	+	393.671i	−0.816115	+	0.919791i
$429$		−	47.4364i		−	0.110574i
$430$		0			0
$431$			279.464i			0.648408i	0.945987	+	0.324204i	$0.105096\pi$
$431$			279.464i			0.648408i	−0.945987	+	0.324204i	$0.894904\pi$
$432$	−316.711	+	37.9664i	−0.733128	+	0.0878853i
$433$			71.3709i			0.164829i	0.996598	+	0.0824145i	$0.0262631\pi$
$433$			71.3709i			0.164829i	−0.996598	+	0.0824145i	$0.973737\pi$
$434$	−539.546	−	204.858i	−1.24319	−	0.472023i
$435$		0			0
$436$	−155.892	+	175.696i	−0.357550	+	0.402972i
$437$	−0.475263			−0.00108756
$438$	−63.2405	+	166.560i	−0.144385	+	0.380275i
$439$			385.168i			0.877375i	0.898640	+	0.438688i	$0.144556\pi$
$439$			385.168i			0.877375i	−0.898640	+	0.438688i	$0.855444\pi$
$440$		0			0
$441$	790.321			1.79211
$442$	−167.169	−	63.4718i	−0.378211	−	0.143601i
$443$		−	194.993i		−	0.440165i	−0.975481	−	0.220082i	$-0.929367\pi$
$443$		−	194.993i		−	0.440165i	0.975481	−	0.220082i	$-0.0706326\pi$
$444$	178.756	−	201.464i	0.402603	−	0.453748i
$445$		0			0
$446$	−42.0259	+	110.686i	−0.0942284	+	0.248175i
$447$	−115.500			−0.258389
$448$	452.213	−	651.953i	1.00940	−	1.45525i
$449$	458.520			1.02120			0.510602	−	0.859817i	$-0.329423\pi$
$449$	458.520			1.02120			0.510602	+	0.859817i	$0.329423\pi$
$450$		0			0
$451$	−155.879			−0.345629
$452$	−412.014	+	464.355i	−0.911535	+	1.02733i
$453$	33.4346			0.0738071
$454$	−421.985	−	160.222i	−0.929483	−	0.352911i
$455$		0			0
$456$	−4.42440	−	8.45345i	−0.00970264	−	0.0185383i
$457$		−	283.142i		−	0.619567i	−0.950807	−	0.309784i	$-0.899743\pi$
$457$		−	283.142i		−	0.619567i	0.950807	−	0.309784i	$-0.100257\pi$
$458$	274.911	+	104.380i	0.600242	+	0.227903i
$459$	−426.385			−0.928943
$460$		0			0
$461$		−	332.355i		−	0.720943i	−0.932770	−	0.360472i	$-0.882616\pi$
$461$		−	332.355i		−	0.720943i	0.932770	−	0.360472i	$-0.117384\pi$
$462$	263.038	+	99.8717i	0.569346	+	0.216173i
$463$	−426.370			−0.920886			−0.460443	−	0.887689i	$-0.652309\pi$
$463$	−426.370			−0.920886			−0.460443	+	0.887689i	$0.652309\pi$
$464$	517.843	−	62.0775i	1.11604	−	0.133788i
$465$		0			0
$466$	−288.781	−	109.646i	−0.619702	−	0.235292i
$467$			365.575i			0.782815i	0.920217	+	0.391407i	$0.128012\pi$
$467$			365.575i			0.782815i	−0.920217	+	0.391407i	$0.871988\pi$
$468$	−94.4166	−	83.7742i	−0.201745	−	0.179005i
$469$		−	28.5402i		−	0.0608533i
$470$		0			0
$471$			87.2264i			0.185194i
$472$	−544.509	+	284.988i	−1.15362	+	0.603787i
$473$		−	539.879i		−	1.14139i
$474$	−33.8507	+	89.1545i	−0.0714149	+	0.188090i
$475$		0			0
$476$	703.911	−	793.334i	1.47881	−	1.66667i
$477$	−203.044			−0.425668
$478$	363.866	+	138.155i	0.761226	+	0.289027i
$479$			657.674i			1.37301i	0.727123	+	0.686507i	$0.240857\pi$
$479$			657.674i			1.37301i	−0.727123	+	0.686507i	$0.759143\pi$
$480$		0			0
$481$	233.650			0.485759
$482$	72.0594	−	189.787i	0.149501	−	0.393749i
$483$			7.16976i			0.0148442i
$484$	96.5680	+	85.6831i	0.199521	+	0.177031i
$485$		0			0
$486$	−434.416	−	164.941i	−0.893860	−	0.339386i
$487$	−599.006			−1.22999			−0.614996	−	0.788530i	$-0.710843\pi$
$487$	−599.006			−1.22999			−0.614996	+	0.788530i	$0.710843\pi$
$488$	−386.680	−	738.807i	−0.792378	−	1.51395i
$489$	80.0544			0.163711
$490$		0			0
$491$	81.4721			0.165931			0.0829655	−	0.996552i	$-0.473561\pi$
$491$	81.4721			0.165931			0.0829655	+	0.996552i	$0.473561\pi$
$492$	52.9260	−	59.6495i	0.107573	−	0.121239i
$493$	697.165			1.41413
$494$	2.93806	−	7.73813i	0.00594748	−	0.0156642i
$495$		0			0
$496$	−369.770	+	44.3270i	−0.745505	+	0.0893690i
$497$		−	672.241i		−	1.35260i
$498$	49.7530	−	131.037i	0.0999056	−	0.263127i
$499$	263.876			0.528809			0.264404	−	0.964412i	$-0.414825\pi$
$499$	263.876			0.528809			0.264404	+	0.964412i	$0.414825\pi$
$500$		0			0
$501$			62.2240i			0.124200i
$502$	146.523	−	385.906i	0.291878	−	0.768736i
$503$	173.548			0.345026			0.172513	−	0.985007i	$-0.444811\pi$
$503$	173.548			0.345026			0.172513	+	0.985007i	$0.444811\pi$
$504$	663.317	−	347.170i	1.31610	−	0.688829i
$505$		0			0
$506$	3.21017	−	8.45481i	0.00634421	−	0.0167091i
$507$		−	182.542i		−	0.360042i
$508$	402.553	+	357.178i	0.792427	+	0.703107i
$509$		−	459.387i		−	0.902528i	−0.892390	−	0.451264i	$-0.850973\pi$
$509$		−	459.387i		−	0.902528i	0.892390	−	0.451264i	$-0.149027\pi$
$510$		0			0
$511$		−	916.724i		−	1.79398i
$512$	63.4558	−	508.053i	0.123937	−	0.992290i
$513$		−	19.7370i		−	0.0384737i
$514$	139.016	+	52.7824i	0.270460	+	0.102690i
$515$		0			0
$516$	206.593	+	183.307i	0.400375	+	0.355246i
$517$	169.474			0.327804
$518$	−491.923	+	1295.61i	−0.949659	+	2.50117i
$519$			22.3240i			0.0430134i
$520$		0			0
$521$	430.141			0.825606			0.412803	−	0.910820i	$-0.364550\pi$
$521$	430.141			0.825606			0.412803	+	0.910820i	$0.364550\pi$
$522$	460.082	+	174.686i	0.881383	+	0.334648i
$523$			745.353i			1.42515i	0.701596	+	0.712574i	$0.252471\pi$
$523$			745.353i			1.42515i	−0.701596	+	0.712574i	$0.747529\pi$
$524$	417.225	+	370.196i	0.796230	+	0.706481i
$525$		0			0
$526$	278.072	−	732.374i	0.528654	−	1.39235i
$527$	−497.817			−0.944625
$528$	180.270	−	21.6102i	0.341420	−	0.0409284i
$529$	−528.770			−0.999564
$530$		0			0
$531$	−579.910			−1.09211
$532$	36.7228	+	32.5835i	0.0690277	+	0.0612471i
$533$	69.1791			0.129792
$534$	−63.8347	−	24.2371i	−0.119541	−	0.0453878i
$535$		0			0
$536$	−8.54011	−	16.3171i	−0.0159330	−	0.0304423i
$537$			184.057i			0.342750i
$538$	501.733	+	190.501i	0.932588	+	0.354090i
$539$	−986.174			−1.82964
$540$		0			0
$541$		−	725.703i		−	1.34141i	−0.741724	−	0.670705i	$-0.765992\pi$
$541$		−	725.703i		−	1.34141i	0.741724	−	0.670705i	$-0.234008\pi$
$542$	797.279	+	302.715i	1.47099	+	0.558515i
$543$	167.855			0.309126
$544$	165.052	−	664.199i	0.303404	−	1.22095i
$545$		0			0
$546$	−116.737	−	44.3232i	−0.213803	−	0.0811780i
$547$			92.4741i			0.169057i	0.996421	+	0.0845284i	$0.0269384\pi$
$547$			92.4741i			0.169057i	−0.996421	+	0.0845284i	$0.973062\pi$
$548$	−231.813	+	261.262i	−0.423016	+	0.476755i
$549$		−	786.840i		−	1.43322i
$550$		0			0
$551$			32.2712i			0.0585684i
$552$	2.14541	+	4.09911i	0.00388662	+	0.00742593i
$553$		−	490.694i		−	0.887330i
$554$	−2.47490	+	6.51828i	−0.00446732	+	0.0117658i
$555$		0			0
$556$	302.927	+	268.782i	0.544832	+	0.483420i
$557$	−1043.87			−1.87409			−0.937043	−	0.349215i	$-0.886448\pi$
$557$	−1043.87			−1.87409			−0.937043	+	0.349215i	$0.886448\pi$
$558$	−328.526	−	124.736i	−0.588756	−	0.223542i
$559$			239.599i			0.428620i
$560$		0			0
$561$	242.695			0.432611
$562$	101.065	−	266.181i	0.179831	−	0.473631i
$563$			149.723i			0.265939i	0.991120	+	0.132969i	$0.0424512\pi$
$563$			149.723i			0.265939i	−0.991120	+	0.132969i	$0.957549\pi$
$564$	−57.5422	+	64.8522i	−0.102025	+	0.114986i
$565$		0			0
$566$	237.671	+	90.2402i	0.419913	+	0.159435i
$567$	544.511			0.960337
$568$	−201.155	−	384.336i	−0.354147	−	0.676647i
$569$	814.440			1.43135			0.715677	−	0.698432i	$-0.246119\pi$
$569$	814.440			1.43135			0.715677	+	0.698432i	$0.246119\pi$
$570$		0			0
$571$	250.759			0.439157			0.219578	−	0.975595i	$-0.429532\pi$
$571$	250.759			0.439157			0.219578	+	0.975595i	$0.429532\pi$
$572$	117.814	+	104.535i	0.205969	+	0.182753i
$573$	−153.608			−0.268076
$574$	−145.648	+	383.603i	−0.253743	+	0.668298i
$575$		0			0
$576$	275.349	−	396.970i	0.478037	−	0.689183i
$577$			851.781i			1.47622i	0.674678	+	0.738112i	$0.264282\pi$
$577$			851.781i			1.47622i	−0.674678	+	0.738112i	$0.735718\pi$
$578$	119.568	−	314.913i	0.206865	−	0.544832i
$579$	−193.889			−0.334869
$580$		0			0
$581$			721.211i			1.24133i
$582$	−4.14561	+	10.9185i	−0.00712305	+	0.0187604i
$583$	253.361			0.434581
$584$	−274.312	−	524.112i	−0.469713	−	0.897452i
$585$		0			0
$586$	−151.824	+	399.868i	−0.259085	+	0.682368i
$587$		−	426.708i		−	0.726929i	−0.931608	−	0.363465i	$-0.881594\pi$
$587$		−	426.708i		−	0.726929i	0.931608	−	0.363465i	$-0.118406\pi$
$588$	334.839	−	377.376i	0.569454	−	0.641795i
$589$		−	23.0435i		−	0.0391232i
$590$		0			0
$591$		−	179.907i		−	0.304411i
$592$	106.442	+	887.926i	0.179801	+	1.49988i
$593$		−	668.977i		−	1.12812i	−0.825733	−	0.564061i	$-0.809238\pi$
$593$		−	668.977i		−	1.12812i	0.825733	−	0.564061i	$-0.190762\pi$
$594$	351.116	+	133.314i	0.591105	+	0.224434i
$595$		0			0
$596$	254.525	−	286.859i	0.427055	−	0.481306i
$597$	422.232			0.707257
$598$	−1.42468	+	3.75225i	−0.00238240	+	0.00627467i
$599$			75.4852i			0.126019i	0.998013	+	0.0630093i	$0.0200698\pi$
$599$			75.4852i			0.126019i	−0.998013	+	0.0630093i	$0.979930\pi$
$600$		0			0
$601$	−887.728			−1.47709			−0.738543	−	0.674207i	$-0.764486\pi$
$601$	−887.728			−1.47709			−0.738543	+	0.674207i	$0.764486\pi$
$602$	−1328.59	−	504.447i	−2.20696	−	0.837952i
$603$		−	17.3779i		−	0.0288191i
$604$	−73.6792	+	83.0392i	−0.121985	+	0.137482i
$605$		0			0
$606$	130.521	−	343.760i	0.215381	−	0.567261i
$607$	560.008			0.922583			0.461292	−	0.887249i	$-0.347386\pi$
$607$	560.008			0.922583			0.461292	+	0.887249i	$0.347386\pi$
$608$	30.7452	+	7.64012i	0.0505678	+	0.0125660i
$609$	486.840			0.799408
$610$		0			0
$611$	−75.2129			−0.123098
$612$	428.607	−	483.055i	0.700337	−	0.789306i
$613$	−28.9794			−0.0472747			−0.0236374	−	0.999721i	$-0.507525\pi$
$613$	−28.9794			−0.0472747			−0.0236374	+	0.999721i	$0.507525\pi$
$614$	−637.827	−	242.173i	−1.03881	−	0.394419i
$615$		0			0
$616$	−827.697	+	433.204i	−1.34366	+	0.703253i
$617$			345.379i			0.559771i	0.960033	+	0.279886i	$0.0902965\pi$
$617$			345.379i			0.559771i	−0.960033	+	0.279886i	$0.909703\pi$
$618$	254.366	+	96.5791i	0.411595	+	0.156277i
$619$	−624.297			−1.00856			−0.504279	−	0.863541i	$-0.668242\pi$
$619$	−624.297			−1.00856			−0.504279	+	0.863541i	$0.668242\pi$
$620$		0			0
$621$			9.57055i			0.0154115i
$622$	−718.845	−	272.935i	−1.15570	−	0.438802i
$623$	351.337			0.563944
$624$	−80.0038	+	9.59062i	−0.128211	+	0.0153696i
$625$		0			0
$626$	−370.580	−	140.704i	−0.591981	−	0.224767i
$627$			11.2341i			0.0179173i
$628$	−216.638	−	192.219i	−0.344965	−	0.306081i
$629$			1195.40i			1.90048i
$630$		0			0
$631$			717.185i			1.13658i	0.822827	+	0.568292i	$0.192396\pi$
$631$			717.185i			1.13658i	−0.822827	+	0.568292i	$0.807604\pi$
$632$	−146.831	−	280.541i	−0.232327	−	0.443893i
$633$			463.408i			0.732082i
$634$	−359.705	+	947.376i	−0.567358	+	1.49428i
$635$		0			0
$636$	−86.0245	+	96.9527i	−0.135259	+	0.152441i
$637$	437.665			0.687072
$638$	−574.097	−	217.976i	−0.899839	−	0.341656i
$639$		−	409.323i		−	0.640568i
$640$		0			0
$641$	538.058			0.839404			0.419702	−	0.907662i	$-0.362135\pi$
$641$	538.058			0.839404			0.419702	+	0.907662i	$0.362135\pi$
$642$	−112.527	+	296.369i	−0.175276	+	0.461634i
$643$			1266.66i			1.96993i	0.172767	+	0.984963i	$0.444729\pi$
$643$			1266.66i			1.96993i	−0.172767	+	0.984963i	$0.555271\pi$
$644$	−17.8070	−	15.7999i	−0.0276507	−	0.0245339i
$645$		0			0
$646$	39.5899	+	15.0317i	0.0612847	+	0.0232689i
$647$	816.424			1.26186			0.630930	−	0.775839i	$-0.282673\pi$
$647$	816.424			1.26186			0.630930	+	0.775839i	$0.282673\pi$
$648$	311.309	−	162.934i	0.480415	−	0.251442i
$649$	723.620			1.11498
$650$		0			0
$651$	−347.632			−0.533997
$652$	−176.415	+	198.826i	−0.270574	+	0.304947i
$653$	−692.042			−1.05979			−0.529894	−	0.848064i	$-0.677768\pi$
$653$	−692.042			−1.05979			−0.529894	+	0.848064i	$0.677768\pi$
$654$	−50.2209	+	132.270i	−0.0767904	+	0.202247i
$655$		0			0
$656$	31.5153	+	262.897i	0.0480417	+	0.400758i
$657$		−	558.187i		−	0.849599i
$658$	158.352	−	417.061i	0.240657	−	0.633831i
$659$	890.532			1.35134			0.675669	−	0.737205i	$-0.263855\pi$
$659$	890.532			1.35134			0.675669	+	0.737205i	$0.263855\pi$
$660$		0			0
$661$			656.736i			0.993549i	0.867880	+	0.496774i	$0.165482\pi$
$661$			656.736i			0.993549i	−0.867880	+	0.496774i	$0.834518\pi$
$662$	−242.630	+	639.028i	−0.366510	+	0.965299i
$663$	−107.708			−0.162456
$664$	215.809	+	412.333i	0.325013	+	0.620983i
$665$		0			0
$666$	−299.528	+	788.886i	−0.449742	+	1.18451i
$667$		−	15.6484i		−	0.0234609i
$668$	−154.541	−	137.122i	−0.231349	−	0.205272i
$669$			71.3155i			0.106600i
$670$		0			0
$671$			981.831i			1.46324i
$672$	115.258	−	463.819i	0.171515	−	0.690206i
$673$			242.150i			0.359807i	0.983684	+	0.179904i	$0.0575786\pi$
$673$			242.150i			0.359807i	−0.983684	+	0.179904i	$0.942421\pi$
$674$	−904.249	−	343.330i	−1.34162	−	0.509392i
$675$		0			0
$676$	453.366	+	402.263i	0.670659	+	0.595064i
$677$	592.051			0.874521			0.437261	−	0.899335i	$-0.355949\pi$
$677$	592.051			0.874521			0.437261	+	0.899335i	$0.355949\pi$
$678$	−132.731	+	349.582i	−0.195769	+	0.515608i
$679$		−	60.0941i		−	0.0885039i
$680$		0			0
$681$	−271.887			−0.399247
$682$	409.939	+	155.648i	0.601084	+	0.228223i
$683$		−	640.413i		−	0.937647i	−0.883292	−	0.468824i	$-0.844678\pi$
$683$		−	640.413i		−	0.937647i	0.883292	−	0.468824i	$-0.155322\pi$
$684$	22.3602	+	19.8398i	0.0326904	+	0.0290056i
$685$		0			0
$686$	−490.194	+	1291.05i	−0.714568	+	1.88200i
$687$	177.126			0.257826
$688$	−910.532	+	109.152i	−1.32345	+	0.158651i
$689$	−112.442			−0.163196
$690$		0			0
$691$	848.214			1.22752			0.613759	−	0.789494i	$-0.289657\pi$
$691$	848.214			1.22752			0.613759	+	0.789494i	$0.289657\pi$
$692$	−55.4445	−	49.1949i	−0.0801221	−	0.0710909i
$693$	−881.509			−1.27202
$694$	286.827	+	108.904i	0.413296	+	0.156922i
$695$		0			0
$696$	278.337	−	145.677i	0.399910	−	0.209307i
$697$			353.935i			0.507798i
$698$	−879.965	−	334.110i	−1.26070	−	0.478668i
$699$	−186.063			−0.266185
$700$		0			0
$701$		−	724.318i		−	1.03326i	−0.856207	−	0.516632i	$-0.827185\pi$
$701$		−	724.318i		−	1.03326i	0.856207	−	0.516632i	$-0.172815\pi$
$702$	−155.826	−	59.1648i	−0.221974	−	0.0842803i
$703$	−55.3343			−0.0787116
$704$	−343.585	+	495.345i	−0.488047	+	0.703615i
$705$		0			0
$706$	114.035	+	43.2976i	0.161523	+	0.0613280i
$707$			1892.01i			2.67611i
$708$	−245.693	+	276.905i	−0.347024	+	0.391109i
$709$		−	109.289i		−	0.154145i	−0.997026	−	0.0770723i	$-0.975443\pi$
$709$		−	109.289i		−	0.154145i	0.997026	−	0.0770723i	$-0.0245572\pi$
$710$		0			0
$711$		−	298.780i		−	0.420225i
$712$	200.867	−	105.131i	0.282117	−	0.147656i
$713$			11.1739i			0.0156717i
$714$	226.767	−	597.249i	0.317601	−	0.836483i
$715$		0			0
$716$	−457.129	−	405.602i	−0.638448	−	0.566483i
$717$	234.441			0.326975
$718$	1233.97	+	468.522i	1.71863	+	0.652537i
$719$		−	794.119i		−	1.10448i	−0.833686	−	0.552238i	$-0.813774\pi$
$719$		−	794.119i		−	1.10448i	0.833686	−	0.552238i	$-0.186226\pi$
$720$		0			0
$721$	−1399.99			−1.94174
$722$	255.586	−	673.152i	0.353997	−	0.932343i
$723$		−	122.281i		−	0.169130i
$724$	−369.900	+	416.890i	−0.510911	+	0.575816i
$725$		0			0
$726$	72.6997	+	27.6030i	0.100137	+	0.0380207i
$727$	−756.542			−1.04064			−0.520318	−	0.853973i	$-0.674187\pi$
$727$	−756.542			−1.04064			−0.520318	+	0.853973i	$0.674187\pi$
$728$	367.333	−	192.256i	0.504578	−	0.264088i
$729$	115.395			0.158292
$730$		0			0
$731$	−1225.84			−1.67693
$732$	−375.714	−	333.364i	−0.513270	−	0.455416i
$733$	884.232			1.20632			0.603160	−	0.797621i	$-0.293908\pi$
$733$	884.232			1.20632			0.603160	+	0.797621i	$0.293908\pi$
$734$	−263.996	+	695.302i	−0.359668	+	0.947278i
$735$		0			0
$736$	−14.9085	−	3.70473i	−0.0202561	−	0.00503359i
$737$			21.6844i			0.0294226i
$738$	−88.6843	+	233.573i	−0.120168	+	0.316495i
$739$	746.061			1.00956			0.504778	−	0.863249i	$-0.331574\pi$
$739$	746.061			1.00956			0.504778	+	0.863249i	$0.331574\pi$
$740$		0			0
$741$		−	4.98572i		−	0.00672837i
$742$	236.733	−	623.498i	0.319047	−	0.840294i
$743$	47.1955			0.0635202			0.0317601	−	0.999496i	$-0.489889\pi$
$743$	47.1955			0.0635202			0.0317601	+	0.999496i	$0.489889\pi$
$744$	−198.749	+	104.022i	−0.267136	+	0.139815i
$745$		0			0
$746$	207.435	−	546.335i	0.278064	−	0.732353i
$747$			439.140i			0.587872i
$748$	−534.822	+	602.764i	−0.715002	+	0.805834i
$749$		−	1631.17i		−	2.17780i
$750$		0			0
$751$			863.233i			1.14945i	0.818348	+	0.574723i	$0.194890\pi$
$751$			863.233i			1.14945i	−0.818348	+	0.574723i	$0.805110\pi$
$752$	−34.2641	−	285.827i	−0.0455640	−	0.380089i
$753$		−	248.641i		−	0.330200i
$754$	254.785	+	96.7381i	0.337911	+	0.128300i
$755$		0			0
$756$	656.146	−	739.500i	0.867918	−	0.978175i
$757$	980.034			1.29463			0.647314	−	0.762223i	$-0.275892\pi$
$757$	980.034			1.29463			0.647314	+	0.762223i	$0.275892\pi$
$758$	408.040	−	1074.68i	0.538311	−	1.41778i
$759$		−	5.44748i		−	0.00717718i
$760$		0			0
$761$	1247.89			1.63981			0.819903	−	0.572502i	$-0.194027\pi$
$761$	1247.89			1.63981			0.819903	+	0.572502i	$0.194027\pi$
$762$	303.056	+	115.066i	0.397711	+	0.151005i
$763$		−	727.994i		−	0.954121i
$764$	338.502	−	381.505i	0.443066	−	0.499352i
$765$		0			0
$766$	57.3600	−	151.072i	0.0748825	−	0.197222i
$767$	−321.143			−0.418701
$768$	−72.8933	−	299.664i	−0.0949131	−	0.390188i
$769$	−782.117			−1.01706			−0.508528	−	0.861045i	$-0.669810\pi$
$769$	−782.117			−1.01706			−0.508528	+	0.861045i	$0.669810\pi$
$770$		0			0
$771$	89.5689			0.116172
$772$	427.270	−	481.549i	0.553459	−	0.623768i
$773$	673.425			0.871184			0.435592	−	0.900144i	$-0.356539\pi$
$773$	673.425			0.871184			0.435592	+	0.900144i	$0.356539\pi$
$774$	−808.970	−	307.154i	−1.04518	−	0.396840i
$775$		0			0
$776$	−17.9820	−	34.3572i	−0.0231727	−	0.0442747i
$777$			834.766i			1.07435i
$778$	−551.684	−	209.467i	−0.709106	−	0.269237i
$779$	−16.3834			−0.0210313
$780$		0			0
$781$			510.759i			0.653981i
$782$	−19.1973	−	7.28895i	−0.0245490	−	0.00932090i
$783$	649.858			0.829959
$784$	199.383	+	1663.23i	0.254316	+	2.12147i
$785$		0			0
$786$	314.101	+	119.260i	0.399620	+	0.151730i
$787$			96.9208i			0.123152i	0.998102	+	0.0615761i	$0.0196127\pi$
$787$			96.9208i			0.123152i	−0.998102	+	0.0615761i	$0.980387\pi$
$788$	446.822	+	396.457i	0.567033	+	0.503118i
$789$		−	471.872i		−	0.598064i
$790$		0			0
$791$		−	1924.05i		−	2.43243i
$792$	−503.978	+	263.775i	−0.636336	+	0.333049i
$793$		−	435.738i		−	0.549480i
$794$	85.0076	−	223.890i	0.107062	−	0.281977i
$795$		0			0
$796$	−930.465	+	1048.67i	−1.16893	+	1.31742i
$797$	−100.960			−0.126675			−0.0633373	−	0.997992i	$-0.520174\pi$
$797$	−100.960			−0.126675			−0.0633373	+	0.997992i	$0.520174\pi$
$798$	27.6462	+	10.4968i	0.0346443	+	0.0131539i
$799$		−	384.805i		−	0.481609i
$800$		0			0
$801$	213.927			0.267074
$802$	236.383	−	622.575i	0.294742	−	0.776278i
$803$			696.514i			0.867390i
$804$	−8.29790	−	7.36258i	−0.0103208	−	0.00915744i
$805$		0			0
$806$	−181.931	−	69.0767i	−0.225721	−	0.0857032i
$807$	323.269			0.400581
$808$	566.147	+	1081.70i	0.700677	+	1.33874i
$809$	125.149			0.154696			0.0773480	−	0.997004i	$-0.475355\pi$
$809$	125.149			0.154696			0.0773480	+	0.997004i	$0.475355\pi$
$810$		0			0
$811$	1504.84			1.85554			0.927769	−	0.373156i	$-0.121724\pi$
$811$	1504.84			1.85554			0.927769	+	0.373156i	$0.121724\pi$
$812$	−1072.84	+	1209.13i	−1.32123	+	1.48908i
$813$	513.691			0.631846
$814$	373.756	−	984.383i	0.459160	−	1.20932i
$815$		0			0
$816$	−49.0677	−	409.316i	−0.0601320	−	0.501613i
$817$		−	56.7430i		−	0.0694529i
$818$	−10.1153	+	26.6412i	−0.0123659	+	0.0325687i
$819$	391.215			0.477673
$820$		0			0
$821$		−	386.633i		−	0.470929i	−0.971883	−	0.235464i	$-0.924339\pi$
$821$		−	386.633i		−	0.470929i	0.971883	−	0.235464i	$-0.0756611\pi$
$822$	−74.6791	+	196.687i	−0.0908505	+	0.239278i
$823$	−737.692			−0.896345			−0.448173	−	0.893947i	$-0.647925\pi$
$823$	−737.692			−0.896345			−0.448173	+	0.893947i	$0.647925\pi$
$824$	−800.408	+	418.921i	−0.971369	+	0.508400i
$825$		0			0
$826$	676.130	−	1780.76i	0.818559	−	2.15589i
$827$		−	1339.34i		−	1.61952i	−0.586764	−	0.809758i	$-0.699598\pi$
$827$		−	1339.34i		−	1.61952i	0.586764	−	0.809758i	$-0.300402\pi$
$828$	−10.8426	−	9.62042i	−0.0130949	−	0.0116189i
$829$			1103.12i			1.33066i	0.746548	+	0.665331i	$0.231710\pi$
$829$			1103.12i			1.33066i	−0.746548	+	0.665331i	$0.768290\pi$
$830$		0			0
$831$			4.19976i			0.00505386i
$832$	152.483	−	219.835i	0.183273	−	0.264224i
$833$			2239.19i			2.68810i
$834$	228.054	+	86.5887i	0.273446	+	0.103823i
$835$		0			0
$836$	−27.9014	−	24.7564i	−0.0333749	−	0.0296130i
$837$	−464.037			−0.554405
$838$	113.455	−	298.814i	0.135388	−	0.356580i
$839$			1401.49i			1.67043i	0.549927	+	0.835213i	$0.314655\pi$
$839$			1401.49i			1.67043i	−0.549927	+	0.835213i	$0.685345\pi$
$840$		0			0
$841$	−221.558			−0.263446
$842$	−166.609	−	63.2590i	−0.197873	−	0.0751295i
$843$		−	171.501i		−	0.203442i
$844$	−1150.93	−	1021.20i	−1.36367	−	1.20996i
$845$		0			0
$846$	96.4194	−	253.945i	0.113971	−	0.300172i
$847$	−400.129			−0.472407
$848$	−51.2242	−	427.306i	−0.0604059	−	0.503898i
$849$	153.133			0.180368
$850$		0			0
$851$	26.8318			0.0315298
$852$	−195.450	−	173.420i	−0.229402	−	0.203544i
$853$	493.813			0.578913			0.289456	−	0.957191i	$-0.406525\pi$
$853$	493.813			0.578913			0.289456	+	0.957191i	$0.406525\pi$
$854$	2416.20	+	917.395i	2.82927	+	1.07423i
$855$		0			0
$856$	−488.097	−	932.578i	−0.570207	−	1.08946i
$857$		−	1179.48i		−	1.37628i	−0.725576	−	0.688142i	$-0.758427\pi$
$857$		−	1179.48i		−	1.37628i	0.725576	−	0.688142i	$-0.241573\pi$
$858$	88.6948	+	33.6761i	0.103374	+	0.0392495i
$859$	1057.63			1.23123			0.615616	−	0.788046i	$-0.288907\pi$
$859$	1057.63			1.23123			0.615616	+	0.788046i	$0.288907\pi$
$860$		0			0
$861$			247.157i			0.287059i
$862$	−522.531	−	198.397i	−0.606184	−	0.230159i
$863$	−29.0807			−0.0336972			−0.0168486	−	0.999858i	$-0.505363\pi$
$863$	−29.0807			−0.0336972			−0.0168486	+	0.999858i	$0.505363\pi$
$864$	153.852	−	619.128i	0.178069	−	0.716584i
$865$		0			0
$866$	−133.447	−	50.6678i	−0.154095	−	0.0585078i
$867$		−	202.900i		−	0.234026i
$868$	766.071	−	863.390i	0.882570	−	0.994689i
$869$			372.822i			0.429024i
$870$		0			0
$871$		−	9.62357i		−	0.0110489i
$872$	−217.838	−	416.211i	−0.249815	−	0.477306i
$873$		−	36.5909i		−	0.0419139i
$874$	0.337399	−	0.888628i	0.000386040	−	0.00101674i
$875$		0			0
$876$	−266.532	−	236.490i	−0.304261	−	0.269965i
$877$	−656.995			−0.749139			−0.374570	−	0.927199i	$-0.622210\pi$
$877$	−656.995			−0.749139			−0.374570	+	0.927199i	$0.622210\pi$
$878$	−720.172	−	273.439i	−0.820241	−	0.311434i
$879$			257.637i			0.293102i
$880$		0			0
$881$	−151.559			−0.172030			−0.0860152	−	0.996294i	$-0.527413\pi$
$881$	−151.559			−0.172030			−0.0860152	+	0.996294i	$0.527413\pi$
$882$	−561.066	+	1477.71i	−0.636129	+	1.67541i
$883$		−	1139.07i		−	1.29001i	−0.764180	−	0.645003i	$-0.776856\pi$
$883$		−	1139.07i		−	1.29001i	0.764180	−	0.645003i	$-0.223144\pi$
$884$	237.354	−	267.507i	0.268500	−	0.302610i
$885$		0			0
$886$	364.591	+	138.430i	0.411502	+	0.156241i
$887$	1559.13			1.75776			0.878881	−	0.477041i	$-0.158291\pi$
$887$	1559.13			1.75776			0.878881	+	0.477041i	$0.158291\pi$
$888$	249.788	+	477.255i	0.281293	+	0.537449i
$889$	−1667.98			−1.87624
$890$		0			0
$891$	−413.711			−0.464323
$892$	−177.121	−	157.157i	−0.198567	−	0.176185i
$893$	17.8123			0.0199466
$894$	81.9958	−	215.957i	0.0917179	−	0.241563i
$895$		0			0
$896$	897.962	+	1308.37i	1.00219	+	1.46023i
$897$			2.41760i			0.00269520i
$898$	−325.514	+	857.324i	−0.362487	+	0.954704i
$899$	758.729			0.843970
$900$		0			0
$901$		−	575.277i		−	0.638487i
$902$	110.662	−	291.456i	0.122685	−	0.323122i
$903$	−856.019			−0.947972
$904$	−575.736	−	1100.02i	−0.636876	−	1.21684i
$905$		0			0
$906$	−23.7359	+	62.5148i	−0.0261986	+	0.0690008i
$907$		−	1295.44i		−	1.42827i	−0.700010	−	0.714133i	$-0.746821\pi$
$907$		−	1295.44i		−	1.42827i	0.700010	−	0.714133i	$-0.253179\pi$
$908$	599.153	−	675.267i	0.659860	−	0.743686i
$909$			1152.03i			1.26736i
$910$		0			0
$911$		−	1144.77i		−	1.25661i	−0.777969	−	0.628303i	$-0.783750\pi$
$911$		−	1144.77i		−	1.25661i	0.777969	−	0.628303i	$-0.216250\pi$
$912$	18.9469	−	2.27130i	0.0207751	−	0.00249046i
$913$		−	547.966i		−	0.600182i
$914$	529.409	+	201.009i	0.579222	+	0.219922i
$915$		0			0
$916$	−390.330	+	439.916i	−0.426125	+	0.480258i
$917$	−1728.77			−1.88524
$918$	302.700	−	797.238i	0.329738	−	0.868451i
$919$		−	1735.96i		−	1.88897i	−0.328557	−	0.944484i	$-0.606562\pi$
$919$		−	1735.96i		−	1.88897i	0.328557	−	0.944484i	$-0.393438\pi$
$920$		0			0
$921$	−410.955			−0.446205
$922$	621.425	+	235.946i	0.673996	+	0.255907i
$923$		−	226.675i		−	0.245586i
$924$	−373.473	+	420.918i	−0.404191	+	0.455539i
$925$		0			0
$926$	302.689	−	797.211i	0.326878	−	0.860919i
$927$	−852.446			−0.919575
$928$	−251.558	+	1012.31i	−0.271075	+	1.09085i
$929$	−1547.16			−1.66540			−0.832701	−	0.553724i	$-0.813206\pi$
$929$	−1547.16			−1.66540			−0.832701	+	0.553724i	$0.813206\pi$
$930$		0			0
$931$	−103.650			−0.111332
$932$	410.024	−	462.112i	0.439940	−	0.495829i
$933$	−463.156			−0.496416
$934$	−683.538	−	259.529i	−0.731839	−	0.277869i
$935$		0			0
$936$	223.666	−	117.063i	0.238960	−	0.125068i
$937$			11.0709i			0.0118153i	0.999983	+	0.00590764i	$0.00188047\pi$
$937$			11.0709i			0.0118153i	−0.999983	+	0.00590764i	$0.998120\pi$
$938$	53.3634	+	20.2613i	0.0568906	+	0.0216005i
$939$	−238.767			−0.254278
$940$		0			0
$941$			237.253i			0.252129i	0.992022	+	0.126064i	$0.0402346\pi$
$941$			237.253i			0.252129i	−0.992022	+	0.126064i	$0.959765\pi$
$942$	−163.093	−	61.9239i	−0.173134	−	0.0657366i
$943$	7.94436			0.00842456
$944$	−146.301	−	1220.42i	−0.154979	−	1.29282i
$945$		0			0
$946$	1009.45	+	383.272i	1.06707	+	0.405150i
$947$			923.233i			0.974903i	0.873150	+	0.487451i	$0.162073\pi$
$947$			923.233i			0.974903i	−0.873150	+	0.487451i	$0.837927\pi$
$948$	−142.666	−	126.585i	−0.150492	−	0.133529i
$949$		−	309.114i		−	0.325726i
$950$		0			0
$951$			610.399i			0.641850i
$952$	983.624	+	1879.35i	1.03322	+	1.97411i
$953$			1616.56i			1.69629i	0.529765	+	0.848144i	$0.322280\pi$
$953$			1616.56i			1.69629i	−0.529765	+	0.848144i	$0.677720\pi$
$954$	144.145	−	379.644i	0.151096	−	0.397949i
$955$		0			0
$956$	−516.633	+	582.264i	−0.540411	+	0.609063i
$957$	−369.894			−0.386514
$958$	−1229.69	−	466.897i	−1.28361	−	0.487366i
$959$		−	1082.54i		−	1.12882i
$960$		0			0
$961$	419.222			0.436236
$962$	−165.873	+	436.870i	−0.172426	+	0.454127i
$963$		−	993.209i		−	1.03137i
$964$	303.700	+	269.468i	0.315042	+	0.279531i
$965$		0			0
$966$	−13.4057	−	5.08997i	−0.0138776	−	0.00526912i
$967$	−714.006			−0.738373			−0.369186	−	0.929355i	$-0.620364\pi$
$967$	−714.006			−0.738373			−0.369186	+	0.929355i	$0.620364\pi$
$968$	−228.763	+	119.731i	−0.236325	+	0.123689i
$969$	25.5080			0.0263240
$970$		0			0
$971$	549.922			0.566346			0.283173	−	0.959069i	$-0.408613\pi$
$971$	549.922			0.566346			0.283173	+	0.959069i	$0.408613\pi$
$972$	616.802	−	695.159i	0.634570	−	0.715184i
$973$	−1255.17			−1.29000
$974$	425.248	−	1120.00i	0.436599	−	1.14990i
$975$		0			0
$976$	1655.91	−	198.505i	1.69663	−	0.203387i
$977$			391.158i			0.400366i	0.979758	+	0.200183i	$0.0641537\pi$
$977$			391.158i			0.400366i	−0.979758	+	0.200183i	$0.935846\pi$
$978$	−56.8324	+	149.683i	−0.0581108	+	0.153050i
$979$	−266.941			−0.272667
$980$		0			0
$981$		−	443.270i		−	0.451856i
$982$	−57.8388	+	152.333i	−0.0588990	+	0.155126i
$983$	−1452.94			−1.47806			−0.739032	−	0.673670i	$-0.764717\pi$
$983$	−1452.94			−1.47806			−0.739032	+	0.673670i	$0.764717\pi$
$984$	73.9571	+	141.305i	0.0751597	+	0.143603i
$985$		0			0
$986$	−494.933	+	1303.53i	−0.501960	+	1.32204i
$987$		−	268.715i		−	0.272254i
$988$	12.3827	+	10.9869i	0.0125331	+	0.0111204i
$989$			27.5149i			0.0278210i
$990$		0			0
$991$		−	123.313i		−	0.124433i	−0.998063	−	0.0622167i	$-0.980183\pi$
$991$		−	123.313i		−	0.124433i	0.998063	−	0.0622167i	$-0.0198170\pi$
$992$	179.627	−	722.852i	0.181076	−	0.728681i
$993$			411.729i			0.414631i
$994$	1256.93	+	477.239i	1.26452	+	0.480119i
$995$		0			0
$996$	209.688	+	186.053i	0.210530	+	0.186800i
$997$	−1235.61			−1.23933			−0.619663	−	0.784868i	$-0.712731\pi$
$997$	−1235.61			−1.23933			−0.619663	+	0.784868i	$0.712731\pi$
$998$	−187.331	+	493.385i	−0.187706	+	0.494373i
$999$			1114.29i			1.11540i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	200.3.e.d.99.8		16
4.3	odd	2		800.3.e.d.399.7		16
5.2	odd	4		200.3.g.g.51.1		8
5.3	odd	4		40.3.g.a.11.8	yes	8
5.4	even	2	inner	200.3.e.d.99.9		16
8.3	odd	2	inner	200.3.e.d.99.10		16
8.5	even	2		800.3.e.d.399.8		16
15.8	even	4		360.3.g.a.91.1		8
20.3	even	4		160.3.g.a.111.6		8
20.7	even	4		800.3.g.g.751.3		8
20.19	odd	2		800.3.e.d.399.10		16
40.3	even	4		40.3.g.a.11.7	✓	8
40.13	odd	4		160.3.g.a.111.5		8
40.19	odd	2	inner	200.3.e.d.99.7		16
40.27	even	4		200.3.g.g.51.2		8
40.29	even	2		800.3.e.d.399.9		16
40.37	odd	4		800.3.g.g.751.4		8
60.23	odd	4		1440.3.g.a.271.4		8
80.3	even	4		1280.3.b.i.511.10		16
80.13	odd	4		1280.3.b.i.511.8		16
80.43	even	4		1280.3.b.i.511.7		16
80.53	odd	4		1280.3.b.i.511.9		16
120.53	even	4		1440.3.g.a.271.5		8
120.83	odd	4		360.3.g.a.91.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.3.g.a.11.7	✓	8	40.3	even	4
40.3.g.a.11.8	yes	8	5.3	odd	4
160.3.g.a.111.5		8	40.13	odd	4
160.3.g.a.111.6		8	20.3	even	4
200.3.e.d.99.7		16	40.19	odd	2	inner
200.3.e.d.99.8		16	1.1	even	1	trivial
200.3.e.d.99.9		16	5.4	even	2	inner
200.3.e.d.99.10		16	8.3	odd	2	inner
200.3.g.g.51.1		8	5.2	odd	4
200.3.g.g.51.2		8	40.27	even	4
360.3.g.a.91.1		8	15.8	even	4
360.3.g.a.91.2		8	120.83	odd	4
800.3.e.d.399.7		16	4.3	odd	2
800.3.e.d.399.8		16	8.5	even	2
800.3.e.d.399.9		16	40.29	even	2
800.3.e.d.399.10		16	20.19	odd	2
800.3.g.g.751.3		8	20.7	even	4
800.3.g.g.751.4		8	40.37	odd	4
1280.3.b.i.511.7		16	80.43	even	4
1280.3.b.i.511.8		16	80.13	odd	4
1280.3.b.i.511.9		16	80.53	odd	4
1280.3.b.i.511.10		16	80.3	even	4
1440.3.g.a.271.4		8	60.23	odd	4
1440.3.g.a.271.5		8	120.53	even	4

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:	\( N \)	\(=\)	\( 200 = 2^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	200.e (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.709922 + 1.86976i) q^{2} +1.20470i q^{3} +(-2.99202 - 2.65477i) q^{4} +(-2.25250 - 0.855241i) q^{6} +12.3974 q^{7} +(7.08789 - 3.70969i) q^{8} +7.54870 q^{9} +O(q^{10})\)	\(q+(-0.709922 + 1.86976i) q^{2} +1.20470i q^{3} +(-2.99202 - 2.65477i) q^{4} +(-2.25250 - 0.855241i) q^{6} +12.3974 q^{7} +(7.08789 - 3.70969i) q^{8} +7.54870 q^{9} -9.41939 q^{11} +(3.19819 - 3.60448i) q^{12} +4.18033 q^{13} +(-8.80120 + 23.1802i) q^{14} +(1.90440 + 15.8863i) q^{16} +21.3875i q^{17} +(-5.35899 + 14.1143i) q^{18} -0.990008 q^{19} +14.9351i q^{21} +(6.68703 - 17.6120i) q^{22} +0.480059 q^{23} +(4.46906 + 8.53876i) q^{24} +(-2.96771 + 7.81623i) q^{26} +19.9362i q^{27} +(-37.0934 - 32.9123i) q^{28} -32.5969i q^{29} +23.2761i q^{31} +(-31.0555 - 7.71723i) q^{32} -11.3475i q^{33} +(-39.9895 - 15.1834i) q^{34} +(-22.5859 - 20.0401i) q^{36} +55.8927 q^{37} +(0.702828 - 1.85108i) q^{38} +5.03604i q^{39} +16.5487 q^{41} +(-27.9252 - 10.6028i) q^{42} +57.3157i q^{43} +(28.1830 + 25.0063i) q^{44} +(-0.340804 + 0.897597i) q^{46} -17.9921 q^{47} +(-19.1381 + 2.29422i) q^{48} +104.696 q^{49} -25.7654 q^{51} +(-12.5077 - 11.0978i) q^{52} -26.8978 q^{53} +(-37.2759 - 14.1531i) q^{54} +(87.8716 - 45.9907i) q^{56} -1.19266i q^{57} +(60.9485 + 23.1412i) q^{58} -76.8224 q^{59} -104.235i q^{61} +(-43.5208 - 16.5242i) q^{62} +93.5845 q^{63} +(36.4764 - 52.5878i) q^{64} +(21.2171 + 8.05584i) q^{66} -2.30211i q^{67} +(56.7788 - 63.9918i) q^{68} +0.578326i q^{69} -54.2243i q^{71} +(53.5044 - 28.0034i) q^{72} -73.9447i q^{73} +(-39.6794 + 104.506i) q^{74} +(2.96213 + 2.62824i) q^{76} -116.776 q^{77} +(-9.41619 - 3.57519i) q^{78} -39.5803i q^{79} +43.9213 q^{81} +(-11.7483 + 30.9421i) q^{82} +58.1742i q^{83} +(39.6494 - 44.6863i) q^{84} +(-107.167 - 40.6897i) q^{86} +39.2694 q^{87} +(-66.7636 + 34.9430i) q^{88} +28.3395 q^{89} +51.8254 q^{91} +(-1.43635 - 1.27445i) q^{92} -28.0407 q^{93} +(12.7730 - 33.6409i) q^{94} +(9.29692 - 37.4125i) q^{96} -4.84731i q^{97} +(-74.3261 + 195.757i) q^{98} -71.1042 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{4} - 24 q^{6} - 48 q^{9}+O(q^{10}) \) 16 * q + 16 * q^4 - 24 * q^6 - 48 * q^9	\( 16 q + 16 q^{4} - 24 q^{6} - 48 q^{9} - 64 q^{11} + 40 q^{14} + 16 q^{16} - 64 q^{19} + 16 q^{24} + 120 q^{26} - 24 q^{34} - 288 q^{36} + 96 q^{41} + 176 q^{44} - 280 q^{46} + 176 q^{49} + 128 q^{51} - 112 q^{54} + 560 q^{56} - 448 q^{59} + 256 q^{64} + 448 q^{66} - 120 q^{74} - 384 q^{76} - 112 q^{81} + 80 q^{84} - 888 q^{86} + 96 q^{89} + 200 q^{94} + 896 q^{96} + 704 q^{99}+O(q^{100}) \) 16 * q + 16 * q^4 - 24 * q^6 - 48 * q^9 - 64 * q^11 + 40 * q^14 + 16 * q^16 - 64 * q^19 + 16 * q^24 + 120 * q^26 - 24 * q^34 - 288 * q^36 + 96 * q^41 + 176 * q^44 - 280 * q^46 + 176 * q^49 + 128 * q^51 - 112 * q^54 + 560 * q^56 - 448 * q^59 + 256 * q^64 + 448 * q^66 - 120 * q^74 - 384 * q^76 - 112 * q^81 + 80 * q^84 - 888 * q^86 + 96 * q^89 + 200 * q^94 + 896 * q^96 + 704 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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