LMFDB - Embedded newform 200.3.g.g.51.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [200,3,Mod(51,200)]

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, 0]))

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

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

chi := DirichletCharacter("200.51");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 200 = 2^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	200.g (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.44960528721$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.148996000000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 7x^{6} - 2x^{5} + 12x^{3} + 47x^{2} + 114x + 81 $ x^8 - 4x^7 + 7x^6 - 2x^5 + 12x^3 + 47x^2 + 114x + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6}\cdot 3 $
Twist minimal:	no (minimal twist has level 40)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			51.1
Root			$2.49601 + 1.32738i$ of defining polynomial
Character	$\chi$	$=$	200.51
Dual form			200.3.g.g.51.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.86976 - 0.709922i) q^{2} +1.20470 q^{3} +(2.99202 + 2.65477i) q^{4} +(-2.25250 - 0.855241i) q^{6} +12.3974i q^{7} +(-3.70969 - 7.08789i) q^{8} -7.54870 q^{9} +O(q^{10})$	\(q+(-1.86976 - 0.709922i) q^{2} +1.20470 q^{3} +(2.99202 + 2.65477i) q^{4} +(-2.25250 - 0.855241i) q^{6} +12.3974i q^{7} +(-3.70969 - 7.08789i) q^{8} -7.54870 q^{9} -9.41939 q^{11} +(3.60448 + 3.19819i) q^{12} -4.18033i q^{13} +(8.80120 - 23.1802i) q^{14} +(1.90440 + 15.8863i) q^{16} -21.3875 q^{17} +(14.1143 + 5.35899i) q^{18} +0.990008 q^{19} +14.9351i q^{21} +(17.6120 + 6.68703i) q^{22} -0.480059i q^{23} +(-4.46906 - 8.53876i) q^{24} +(-2.96771 + 7.81623i) q^{26} -19.9362 q^{27} +(-32.9123 + 37.0934i) q^{28} +32.5969i q^{29} +23.2761i q^{31} +(7.71723 - 31.0555i) q^{32} -11.3475 q^{33} +(39.9895 + 15.1834i) q^{34} +(-22.5859 - 20.0401i) q^{36} +55.8927i q^{37} +(-1.85108 - 0.702828i) q^{38} -5.03604i q^{39} +16.5487 q^{41} +(10.6028 - 27.9252i) q^{42} +57.3157 q^{43} +(-28.1830 - 25.0063i) q^{44} +(-0.340804 + 0.897597i) q^{46} -17.9921i q^{47} +(2.29422 + 19.1381i) q^{48} -104.696 q^{49} -25.7654 q^{51} +(11.0978 - 12.5077i) q^{52} +26.8978i q^{53} +(37.2759 + 14.1531i) q^{54} +(87.8716 - 45.9907i) q^{56} +1.19266 q^{57} +(23.1412 - 60.9485i) q^{58} +76.8224 q^{59} -104.235i q^{61} +(16.5242 - 43.5208i) q^{62} -93.5845i q^{63} +(-36.4764 + 52.5878i) q^{64} +(21.2171 + 8.05584i) q^{66} +2.30211 q^{67} +(-63.9918 - 56.7788i) q^{68} -0.578326i q^{69} -54.2243i q^{71} +(28.0034 + 53.5044i) q^{72} -73.9447 q^{73} +(39.6794 - 104.506i) q^{74} +(2.96213 + 2.62824i) q^{76} -116.776i q^{77} +(-3.57519 + 9.41619i) q^{78} +39.5803i q^{79} +43.9213 q^{81} +(-30.9421 - 11.7483i) q^{82} +58.1742 q^{83} +(-39.6494 + 44.6863i) q^{84} +(-107.167 - 40.6897i) q^{86} +39.2694i q^{87} +(34.9430 + 66.7636i) q^{88} -28.3395 q^{89} +51.8254 q^{91} +(1.27445 - 1.43635i) q^{92} +28.0407i q^{93} +(-12.7730 + 33.6409i) q^{94} +(9.29692 - 37.4125i) q^{96} +4.84731 q^{97} +(195.757 + 74.3261i) q^{98} +71.1042 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} - 8 q^{4} - 12 q^{6} - 8 q^{8} + 24 q^{9}+O(q^{10}) $ 8 * q - 2 * q^2 - 8 * q^4 - 12 * q^6 - 8 * q^8 + 24 * q^9	$ 8 q - 2 q^{2} - 8 q^{4} - 12 q^{6} - 8 q^{8} + 24 q^{9} - 32 q^{11} - 20 q^{12} - 20 q^{14} + 8 q^{16} + 62 q^{18} + 32 q^{19} - 20 q^{22} - 8 q^{24} + 60 q^{26} + 96 q^{27} - 100 q^{28} - 72 q^{32} - 16 q^{33} + 12 q^{34} - 144 q^{36} - 60 q^{38} + 48 q^{41} - 140 q^{42} - 96 q^{43} - 88 q^{44} - 140 q^{46} + 280 q^{48} - 88 q^{49} + 64 q^{51} + 160 q^{52} + 56 q^{54} + 280 q^{56} + 176 q^{57} + 320 q^{58} + 224 q^{59} + 160 q^{62} - 128 q^{64} + 224 q^{66} - 160 q^{67} - 360 q^{68} - 152 q^{72} - 160 q^{73} + 60 q^{74} - 192 q^{76} - 600 q^{78} - 56 q^{81} - 80 q^{82} + 480 q^{83} - 40 q^{84} - 444 q^{86} + 400 q^{88} - 48 q^{89} + 60 q^{92} - 100 q^{94} + 448 q^{96} - 224 q^{97} + 442 q^{98} - 352 q^{99}+O(q^{100}) $ 8 * q - 2 * q^2 - 8 * q^4 - 12 * q^6 - 8 * q^8 + 24 * q^9 - 32 * q^11 - 20 * q^12 - 20 * q^14 + 8 * q^16 + 62 * q^18 + 32 * q^19 - 20 * q^22 - 8 * q^24 + 60 * q^26 + 96 * q^27 - 100 * q^28 - 72 * q^32 - 16 * q^33 + 12 * q^34 - 144 * q^36 - 60 * q^38 + 48 * q^41 - 140 * q^42 - 96 * q^43 - 88 * q^44 - 140 * q^46 + 280 * q^48 - 88 * q^49 + 64 * q^51 + 160 * q^52 + 56 * q^54 + 280 * q^56 + 176 * q^57 + 320 * q^58 + 224 * q^59 + 160 * q^62 - 128 * q^64 + 224 * q^66 - 160 * q^67 - 360 * q^68 - 152 * q^72 - 160 * q^73 + 60 * q^74 - 192 * q^76 - 600 * q^78 - 56 * q^81 - 80 * q^82 + 480 * q^83 - 40 * q^84 - 444 * q^86 + 400 * q^88 - 48 * q^89 + 60 * q^92 - 100 * q^94 + 448 * q^96 - 224 * q^97 + 442 * q^98 - 352 * 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 $

$2$	−1.86976	−	0.709922i	−0.934881	−	0.354961i
$2$	−1.86976	−	0.709922i	−0.934881	−	0.354961i
$3$	1.20470			0.401566			0.200783	−	0.979636i	$-0.435651\pi$
$3$	1.20470			0.401566			0.200783	+	0.979636i	$0.435651\pi$
$4$	2.99202	+	2.65477i	0.748006	+	0.663692i
$5$		0			0
$5$		0			0
$6$	−2.25250	−	0.855241i	−0.375416	−	0.142540i
$7$			12.3974i			1.77106i	0.464581	+	0.885531i	$0.346205\pi$
$7$			12.3974i			1.77106i	−0.464581	+	0.885531i	$0.653795\pi$
$8$	−3.70969	−	7.08789i	−0.463712	−	0.885986i
$9$	−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	$0.640836\pi$
$12$	3.60448	+	3.19819i	0.300373	+	0.266516i
$13$		−	4.18033i		−	0.321564i	−0.986990	−	0.160782i	$-0.948598\pi$
$13$		−	4.18033i		−	0.321564i	0.986990	−	0.160782i	$-0.0514016\pi$
$14$	8.80120	−	23.1802i	0.628657	−	1.65573i
$15$		0			0
$16$	1.90440	+	15.8863i	0.119025	+	0.992891i
$17$	−21.3875			−1.25809			−0.629043	−	0.777370i	$-0.716553\pi$
$17$	−21.3875			−1.25809			−0.629043	+	0.777370i	$0.716553\pi$
$18$	14.1143	+	5.35899i	0.784127	+	0.297722i
$19$	0.990008			0.0521057			0.0260529	−	0.999661i	$-0.491706\pi$
$19$	0.990008			0.0521057			0.0260529	+	0.999661i	$0.491706\pi$
$20$		0			0
$21$			14.9351i			0.711198i
$22$	17.6120	+	6.68703i	0.800546	+	0.303956i
$23$		−	0.480059i		−	0.0208721i	−0.999946	−	0.0104361i	$-0.996678\pi$
$23$		−	0.480059i		−	0.0208721i	0.999946	−	0.0104361i	$-0.00332197\pi$
$24$	−4.46906	−	8.53876i	−0.186211	−	0.355782i
$25$		0			0
$26$	−2.96771	+	7.81623i	−0.114143	+	0.300624i
$27$	−19.9362			−0.738377
$28$	−32.9123	+	37.0934i	−1.17544	+	1.32476i
$29$			32.5969i			1.12403i	0.827127	+	0.562016i	$0.189974\pi$
$29$			32.5969i			1.12403i	−0.827127	+	0.562016i	$0.810026\pi$
$30$		0			0
$31$			23.2761i			0.750842i	0.926854	+	0.375421i	$0.122502\pi$
$31$			23.2761i			0.750842i	−0.926854	+	0.375421i	$0.877498\pi$
$32$	7.71723	−	31.0555i	0.241163	−	0.970485i
$33$	−11.3475			−0.343864
$34$	39.9895	+	15.1834i	1.17616	+	0.446572i
$35$		0			0
$36$	−22.5859	−	20.0401i	−0.627386	−	0.556669i
$37$			55.8927i			1.51061i	0.655371	+	0.755307i	$0.272512\pi$
$37$			55.8927i			1.51061i	−0.655371	+	0.755307i	$0.727488\pi$
$38$	−1.85108	−	0.702828i	−0.0487126	−	0.0184955i
$39$		−	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	$0.435317\pi$
$42$	10.6028	−	27.9252i	0.252447	−	0.664885i
$43$	57.3157			1.33292			0.666462	−	0.745539i	$-0.267808\pi$
$43$	57.3157			1.33292			0.666462	+	0.745539i	$0.267808\pi$
$44$	−28.1830	−	25.0063i	−0.640523	−	0.568325i
$45$		0			0
$46$	−0.340804	+	0.897597i	−0.00740879	+	0.0195130i
$47$		−	17.9921i		−	0.382810i	−0.981511	−	0.191405i	$-0.938696\pi$
$47$		−	17.9921i		−	0.382810i	0.981511	−	0.191405i	$-0.0613045\pi$
$48$	2.29422	+	19.1381i	0.0477963	+	0.398711i
$49$	−104.696			−2.13666
$50$		0			0
$51$	−25.7654			−0.505205
$52$	11.0978	−	12.5077i	0.213420	−	0.240532i
$53$			26.8978i			0.507506i	0.967269	+	0.253753i	$0.0816651\pi$
$53$			26.8978i			0.507506i	−0.967269	+	0.253753i	$0.918335\pi$
$54$	37.2759	+	14.1531i	0.690295	+	0.262095i
$55$		0			0
$56$	87.8716	−	45.9907i	1.56914	−	0.821262i
$57$	1.19266			0.0209239
$58$	23.1412	−	60.9485i	0.398987	−	1.05084i
$59$	76.8224			1.30207			0.651037	−	0.759046i	$-0.274334\pi$
$59$	76.8224			1.30207			0.651037	+	0.759046i	$0.274334\pi$
$60$		0			0
$61$		−	104.235i		−	1.70877i	−0.519638	−	0.854387i	$-0.673933\pi$
$61$		−	104.235i		−	1.70877i	0.519638	−	0.854387i	$-0.326067\pi$
$62$	16.5242	−	43.5208i	0.266520	−	0.701948i
$63$		−	93.5845i		−	1.48547i
$64$	−36.4764	+	52.5878i	−0.569943	+	0.821684i
$65$		0			0
$66$	21.2171	+	8.05584i	0.321472	+	0.122058i
$67$	2.30211			0.0343598			0.0171799	−	0.999852i	$-0.494531\pi$
$67$	2.30211			0.0343598			0.0171799	+	0.999852i	$0.494531\pi$
$68$	−63.9918	−	56.7788i	−0.941056	−	0.834983i
$69$		−	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	$-0.124717\pi$
$72$	28.0034	+	53.5044i	0.388936	+	0.743116i
$73$	−73.9447			−1.01294			−0.506471	−	0.862257i	$-0.669050\pi$
$73$	−73.9447			−1.01294			−0.506471	+	0.862257i	$0.669050\pi$
$74$	39.6794	−	104.506i	0.536209	−	1.41224i
$75$		0			0
$76$	2.96213	+	2.62824i	0.0389754	+	0.0345822i
$77$		−	116.776i		−	1.51657i
$78$	−3.57519	+	9.41619i	−0.0458358	+	0.120720i
$79$			39.5803i			0.501016i	0.968114	+	0.250508i	$0.0805977\pi$
$79$			39.5803i			0.501016i	−0.968114	+	0.250508i	$0.919402\pi$
$80$		0			0
$81$	43.9213			0.542238
$82$	−30.9421	−	11.7483i	−0.377343	−	0.143272i
$83$	58.1742			0.700895			0.350447	−	0.936582i	$-0.386030\pi$
$83$	58.1742			0.700895			0.350447	+	0.936582i	$0.386030\pi$
$84$	−39.6494	+	44.6863i	−0.472016	+	0.531980i
$85$		0			0
$86$	−107.167	−	40.6897i	−1.24613	−	0.473136i
$87$			39.2694i			0.451372i
$88$	34.9430	+	66.7636i	0.397080	+	0.758677i
$89$	−28.3395			−0.318422			−0.159211	−	0.987245i	$-0.550895\pi$
$89$	−28.3395			−0.318422			−0.159211	+	0.987245i	$0.550895\pi$
$90$		0			0
$91$	51.8254			0.569510
$92$	1.27445	−	1.43635i	0.0138527	−	0.0156125i
$93$			28.0407i			0.301513i
$94$	−12.7730	+	33.6409i	−0.135883	+	0.357882i
$95$		0			0
$96$	9.29692	−	37.4125i	0.0968429	−	0.389713i
$97$	4.84731			0.0499722			0.0249861	−	0.999688i	$-0.492046\pi$
$97$	4.84731			0.0499722			0.0249861	+	0.999688i	$0.492046\pi$
$98$	195.757	+	74.3261i	1.99752	+	0.758430i
$99$	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	$0.727389\pi$
$102$	48.1752	+	18.2914i	0.472306	+	0.179328i
$103$			112.926i			1.09637i	0.836357	+	0.548185i	$0.184681\pi$
$103$			112.926i			1.09637i	−0.836357	+	0.548185i	$0.815319\pi$
$104$	−29.6297	+	15.5078i	−0.284901	+	0.149113i
$105$		0			0
$106$	19.0953	−	50.2925i	0.180145	−	0.474458i
$107$	131.573			1.22966			0.614829	−	0.788660i	$-0.289225\pi$
$107$	131.573			1.22966			0.614829	+	0.788660i	$0.289225\pi$
$108$	−59.6495	−	52.9260i	−0.552310	−	0.490055i
$109$			58.7214i			0.538728i	0.963038	+	0.269364i	$0.0868135\pi$
$109$			58.7214i			0.538728i	−0.963038	+	0.269364i	$0.913186\pi$
$110$		0			0
$111$			67.3338i			0.606611i
$112$	−196.949	+	23.6097i	−1.75847	+	0.210800i
$113$	−155.198			−1.37343			−0.686715	−	0.726927i	$-0.740948\pi$
$113$	−155.198			−1.37343			−0.686715	+	0.726927i	$0.740948\pi$
$114$	−2.22999	−	0.846695i	−0.0195613	−	0.00742715i
$115$		0			0
$116$	−86.5373	+	97.5307i	−0.746011	+	0.840782i
$117$			31.5561i			0.269710i
$118$	−143.640	−	54.5379i	−1.21729	−	0.462185i
$119$		−	265.150i		−	2.22815i
$120$		0			0
$121$	−32.2752			−0.266737
$122$	−73.9988	+	194.895i	−0.606548	+	1.59750i
$123$	19.9362			0.162083
$124$	−61.7927	+	69.6427i	−0.498328	+	0.561634i
$125$		0			0
$126$	−66.4377	+	174.981i	−0.527283	+	1.38874i
$127$		−	134.542i		−	1.05939i	−0.848189	−	0.529693i	$-0.822307\pi$
$127$		−	134.542i		−	1.05939i	0.848189	−	0.529693i	$-0.177693\pi$
$128$	105.535	−	72.4313i	0.824495	−	0.565870i
$129$	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	$0.678648\pi$
$132$	−33.9520	−	30.1250i	−0.257212	−	0.228220i
$133$			12.2736i			0.0922824i
$134$	−4.30439	−	1.63431i	−0.0321223	−	0.0121964i
$135$		0			0
$136$	79.3410	+	151.592i	0.583390	+	1.11465i
$137$	87.3194			0.637368			0.318684	−	0.947861i	$-0.396759\pi$
$137$	87.3194			0.637368			0.318684	+	0.947861i	$0.396759\pi$
$138$	−0.410566	+	1.08133i	−0.00297512	+	0.00783574i
$139$	101.245			0.728380			0.364190	−	0.931325i	$-0.381346\pi$
$139$	101.245			0.728380			0.364190	+	0.931325i	$0.381346\pi$
$140$		0			0
$141$		−	21.6750i		−	0.153724i
$142$	−38.4950	+	101.386i	−0.271091	+	0.713989i
$143$			39.3762i			0.275358i
$144$	−14.3757	−	119.921i	−0.0998316	−	0.832782i
$145$		0			0
$146$	138.259	+	52.4949i	0.946980	+	0.359554i
$147$	−126.127			−0.858009
$148$	−148.382	+	167.232i	−1.00258	+	1.12995i
$149$		−	95.8745i		−	0.643453i	−0.946833	−	0.321727i	$-0.895737\pi$
$149$		−	95.8745i		−	0.643453i	0.946833	−	0.321727i	$-0.104263\pi$
$150$		0			0
$151$		−	27.7535i		−	0.183798i	−0.995768	−	0.0918991i	$-0.970706\pi$
$151$		−	27.7535i		−	0.183798i	0.995768	−	0.0918991i	$-0.0292937\pi$
$152$	−3.67263	−	7.01707i	−0.0241620	−	0.0461649i
$153$	161.448			1.05521
$154$	−82.9019	+	218.344i	−0.538324	+	1.41782i
$155$		0			0
$156$	13.3695	−	15.0679i	0.0857020	−	0.0965893i
$157$			72.4052i			0.461180i	0.973051	+	0.230590i	$0.0740656\pi$
$157$			72.4052i			0.461180i	−0.973051	+	0.230590i	$0.925934\pi$
$158$	28.0989	−	74.0057i	0.177841	−	0.468391i
$159$			32.4037i			0.203797i
$160$		0			0
$161$	5.95150			0.0369658
$162$	−82.1223	−	31.1807i	−0.506928	−	0.192473i
$163$	−66.4519			−0.407680			−0.203840	−	0.979004i	$-0.565342\pi$
$163$	−66.4519			−0.407680			−0.203840	+	0.979004i	$0.565342\pi$
$164$	49.5141	+	43.9330i	0.301915	+	0.267884i
$165$		0			0
$166$	−108.772	−	41.2992i	−0.655253	−	0.248790i
$167$			51.6512i			0.309288i	0.987970	+	0.154644i	$0.0494231\pi$
$167$			51.6512i			0.309288i	−0.987970	+	0.154644i	$0.950577\pi$
$168$	105.859	−	55.4048i	0.630111	−	0.329791i
$169$	151.525			0.896597
$170$		0			0
$171$	−7.47328			−0.0437034
$172$	171.490	+	152.160i	0.997034	+	0.884651i
$173$		−	18.5308i		−	0.107114i	−0.998565	−	0.0535571i	$-0.982944\pi$
$173$		−	18.5308i		−	0.107114i	0.998565	−	0.0535571i	$-0.0170559\pi$
$174$	27.8782	−	73.4245i	0.160220	−	0.421980i
$175$		0			0
$176$	−17.9383	−	149.639i	−0.101922	−	0.850221i
$177$	92.5478			0.522869
$178$	52.9882	+	20.1188i	0.297686	+	0.113027i
$179$	−152.782			−0.853533			−0.426767	−	0.904362i	$-0.640347\pi$
$179$	−152.782			−0.853533			−0.426767	+	0.904362i	$0.640347\pi$
$180$		0			0
$181$		−	139.334i		−	0.769801i	−0.922958	−	0.384901i	$-0.874236\pi$
$181$		−	139.334i		−	0.769801i	0.922958	−	0.384901i	$-0.125764\pi$
$182$	−96.9012	−	36.7920i	−0.532424	−	0.202154i
$183$		−	125.572i		−	0.686185i
$184$	−3.40261	+	1.78087i	−0.0184924	+	0.00967866i
$185$		0			0
$186$	19.9067	−	52.4294i	0.107025	−	0.281878i
$187$	201.457			1.07731
$188$	47.7648	−	53.8327i	0.254068	−	0.286344i
$189$		−	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	$0.891673\pi$
$192$	−43.9430	+	63.3524i	−0.228870	+	0.329960i
$193$	160.944			0.833908			0.416954	−	0.908928i	$-0.363098\pi$
$193$	160.944			0.833908			0.416954	+	0.908928i	$0.363098\pi$
$194$	−9.06331	−	3.44121i	−0.0467181	−	0.0177382i
$195$		0			0
$196$	−313.253	−	277.944i	−1.59823	−	1.41808i
$197$		−	149.338i		−	0.758059i	−0.925385	−	0.379030i	$-0.876258\pi$
$197$		−	149.338i		−	0.758059i	0.925385	−	0.379030i	$-0.123742\pi$
$198$	−132.948	−	50.4784i	−0.671454	−	0.254941i
$199$			350.488i			1.76125i	0.473817	+	0.880624i	$0.342876\pi$
$199$			350.488i			1.76125i	−0.473817	+	0.880624i	$0.657124\pi$
$200$		0			0
$201$	2.77334			0.0137977
$202$	108.343	−	285.350i	0.536353	−	1.41262i
$203$	−404.118			−1.99073
$204$	−77.0908	−	68.4013i	−0.377896	−	0.335300i
$205$		0			0
$206$	80.1687	−	211.145i	0.389169	−	1.02498i
$207$			3.62383i			0.0175064i
$208$	66.4099	−	7.96102i	0.319278	−	0.0382742i
$209$	−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	$0.134898\pi$
$212$	−71.4075	+	80.4789i	−0.336828	+	0.379617i
$213$		−	65.3238i		−	0.306685i
$214$	−246.011	−	93.4068i	−1.14958	−	0.436480i
$215$		0			0
$216$	73.9571	+	141.305i	0.342394	+	0.654192i
$217$	−288.564			−1.32979
$218$	41.6876	−	109.795i	0.191227	−	0.503647i
$219$	−89.0810			−0.406763
$220$		0			0
$221$			89.4068i			0.404556i
$222$	47.8017	−	125.898i	0.215323	−	0.567109i
$223$		−	59.1979i		−	0.265461i	−0.991152	−	0.132731i	$-0.957625\pi$
$223$		−	59.1979i		−	0.265461i	0.991152	−	0.132731i	$-0.0423745\pi$
$224$	385.008	+	95.6738i	1.71879	+	0.427115i
$225$		0			0
$226$	290.183	+	110.178i	1.28399	+	0.487514i
$227$	−225.689			−0.994226			−0.497113	−	0.867686i	$-0.665607\pi$
$227$	−225.689			−0.994226			−0.497113	+	0.867686i	$0.665607\pi$
$228$	3.56847	+	3.16624i	0.0156512	+	0.0138870i
$229$			147.030i			0.642051i	0.947070	+	0.321026i	$0.104028\pi$
$229$			147.030i			0.642051i	−0.947070	+	0.321026i	$0.895972\pi$
$230$		0			0
$231$		−	140.680i		−	0.609004i
$232$	231.043	−	120.925i	0.995876	−	0.521226i
$233$	154.448			0.662868			0.331434	−	0.943478i	$-0.392468\pi$
$233$	154.448			0.662868			0.331434	+	0.943478i	$0.392468\pi$
$234$	22.4024	−	59.0024i	0.0957366	−	0.252147i
$235$		0			0
$236$	229.854	+	203.946i	0.973959	+	0.864177i
$237$			47.6823i			0.201191i
$238$	−188.236	+	495.767i	−0.790905	+	2.08305i
$239$			194.606i			0.814249i	0.913373	+	0.407125i	$0.133469\pi$
$239$			194.606i			0.814249i	−0.913373	+	0.407125i	$0.866531\pi$
$240$		0			0
$241$	−101.503			−0.421176			−0.210588	−	0.977575i	$-0.567538\pi$
$241$	−101.503			−0.421176			−0.210588	+	0.977575i	$0.567538\pi$
$242$	60.3469	+	22.9128i	0.249367	+	0.0946811i
$243$	232.337			0.956121
$244$	276.720	−	311.874i	1.13410	−	1.27817i
$245$		0			0
$246$	−37.2759	−	14.1531i	−0.151528	−	0.0575330i
$247$		−	4.13857i		−	0.0167553i
$248$	164.979	−	86.3472i	0.665236	−	0.348174i
$249$	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	$0.634870\pi$
$252$	248.445	−	280.007i	0.985894	−	1.11114i
$253$			4.52186i			0.0178730i
$254$	−95.5143	+	251.562i	−0.376041	+	0.990401i
$255$		0			0
$256$	−248.747	+	60.5076i	−0.971666	+	0.236358i
$257$	74.3497			0.289298			0.144649	−	0.989483i	$-0.453795\pi$
$257$	74.3497			0.289298			0.144649	+	0.989483i	$0.453795\pi$
$258$	−129.104	−	49.0187i	−0.500401	−	0.189995i
$259$	−692.926			−2.67539
$260$		0			0
$261$		−	246.064i		−	0.942775i
$262$	260.730	+	98.9955i	0.995154	+	0.377845i
$263$			391.694i			1.48933i	0.667439	+	0.744665i	$0.267391\pi$
$263$			391.694i			1.48933i	−0.667439	+	0.744665i	$0.732609\pi$
$264$	42.0958	+	80.4299i	0.159454	+	0.304659i
$265$		0			0
$266$	8.71326	−	22.9486i	0.0327566	−	0.0862731i
$267$	−34.1405			−0.127867
$268$	6.88795	+	6.11156i	0.0257013	+	0.0228043i
$269$			268.340i			0.997548i	0.866732	+	0.498774i	$0.166216\pi$
$269$			268.340i			0.997548i	−0.866732	+	0.498774i	$0.833784\pi$
$270$		0			0
$271$		−	426.407i		−	1.57346i	−0.617300	−	0.786728i	$-0.711773\pi$
$271$		−	426.407i		−	1.57346i	0.617300	−	0.786728i	$-0.288227\pi$
$272$	−40.7303	−	339.767i	−0.149744	−	1.24914i
$273$	62.4339			0.228696
$274$	−163.267	−	61.9900i	−0.595863	−	0.226241i
$275$		0			0
$276$	1.53532	−	1.73037i	0.00556276	−	0.00626944i
$277$			3.48615i			0.0125854i	0.999980	+	0.00629269i	$0.00200304\pi$
$277$			3.48615i			0.0125854i	−0.999980	+	0.00629269i	$0.997997\pi$
$278$	−189.304	−	71.8759i	−0.680948	−	0.258546i
$279$		−	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	$0.581519\pi$
$282$	−15.3876	+	40.5271i	−0.0545658	+	0.143713i
$283$	−127.113			−0.449162			−0.224581	−	0.974455i	$-0.572101\pi$
$283$	−127.113			−0.449162			−0.224581	+	0.974455i	$0.572101\pi$
$284$	143.953	−	162.240i	0.506876	−	0.571268i
$285$		0			0
$286$	27.9540	−	73.6241i	0.0977413	−	0.257427i
$287$			205.161i			0.714848i
$288$	−58.2551	+	234.429i	−0.202274	+	0.813989i
$289$	168.424			0.582783
$290$		0			0
$291$	5.83954			0.0200671
$292$	−221.244	−	196.306i	−0.757686	−	0.672281i
$293$		−	213.860i		−	0.729898i	−0.931027	−	0.364949i	$-0.881086\pi$
$293$		−	213.860i		−	0.729898i	0.931027	−	0.364949i	$-0.118914\pi$
$294$	235.828	+	89.5405i	0.802136	+	0.304559i
$295$		0			0
$296$	396.161	−	207.345i	1.33838	−	0.700489i
$297$	187.787			0.632278
$298$	−68.0634	+	179.263i	−0.228401	+	0.601552i
$299$	−2.00681			−0.00671173
$300$		0			0
$301$			710.567i			2.36069i
$302$	−19.7028	+	51.8925i	−0.0652412	+	0.171829i
$303$			183.852i			0.606774i
$304$	1.88537	+	15.7275i	0.00620188	+	0.0517353i
$305$		0			0
$306$	−301.869	−	114.615i	−0.986500	−	0.374560i
$307$	−341.127			−1.11116			−0.555582	−	0.831462i	$-0.687504\pi$
$307$	−341.127			−1.11116			−0.555582	+	0.831462i	$0.687504\pi$
$308$	310.014	−	349.397i	1.00654	−	1.13441i
$309$			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	$0.787903\pi$
$312$	−35.6949	+	18.6822i	−0.114407	+	0.0598787i
$313$	198.197			0.633216			0.316608	−	0.948557i	$-0.397456\pi$
$313$	198.197			0.633216			0.316608	+	0.948557i	$0.397456\pi$
$314$	51.4020	−	135.381i	0.163701	−	0.431148i
$315$		0			0
$316$	−105.077	+	118.425i	−0.332521	+	0.374763i
$317$			506.683i			1.59837i	0.601087	+	0.799184i	$0.294735\pi$
$317$			506.683i			1.59837i	−0.601087	+	0.799184i	$0.705265\pi$
$318$	23.0041	−	60.5873i	0.0723400	−	0.190526i
$319$		−	307.043i		−	0.962517i
$320$		0			0
$321$	158.506			0.493789
$322$	−11.1279	−	4.22510i	−0.0345587	−	0.0131214i
$323$	−21.1738			−0.0655535
$324$	131.413	+	116.601i	0.405597	+	0.359879i
$325$		0			0
$326$	124.249	+	47.1756i	0.381133	+	0.144711i
$327$			70.7415i			0.216335i
$328$	−61.3906	−	117.295i	−0.187167	−	0.357608i
$329$	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	$0.327321\pi$
$332$	174.059	+	154.439i	0.524273	+	0.465178i
$333$		−	421.918i		−	1.26702i
$334$	36.6683	−	96.5754i	0.109785	−	0.289148i
$335$		0			0
$336$	−237.264	+	28.4425i	−0.706142	+	0.0846503i
$337$	−483.617			−1.43506			−0.717532	−	0.696525i	$-0.754729\pi$
$337$	−483.617			−1.43506			−0.717532	+	0.696525i	$0.754729\pi$
$338$	−283.315	−	107.571i	−0.838211	−	0.318257i
$339$	−186.966			−0.551523
$340$		0			0
$341$		−	219.247i		−	0.642952i
$342$	13.9733	+	5.30544i	0.0408575	+	0.0155130i
$343$		−	690.490i		−	2.01309i
$344$	−212.624	−	406.247i	−0.618092	−	1.18095i
$345$		0			0
$346$	−13.1554	+	34.6481i	−0.0380214	+	0.100139i
$347$	153.403			0.442084			0.221042	−	0.975264i	$-0.429054\pi$
$347$	153.403			0.442084			0.221042	+	0.975264i	$0.429054\pi$
$348$	−104.251	+	117.495i	−0.299572	+	0.337629i
$349$		−	470.630i		−	1.34851i	−0.738499	−	0.674254i	$-0.764465\pi$
$349$		−	470.630i		−	1.34851i	0.738499	−	0.674254i	$-0.235535\pi$
$350$		0			0
$351$			83.3399i			0.237436i
$352$	−72.6915	+	292.524i	−0.206510	+	0.831034i
$353$	−60.9892			−0.172774			−0.0863870	−	0.996262i	$-0.527532\pi$
$353$	−60.9892			−0.172774			−0.0863870	+	0.996262i	$0.527532\pi$
$354$	−173.042	−	65.7016i	−0.488820	−	0.185598i
$355$		0			0
$356$	−84.7925	−	75.2349i	−0.238181	−	0.211334i
$357$		−	319.425i		−	0.894748i
$358$	285.667	+	108.464i	0.797952	+	0.302971i
$359$			659.963i			1.83834i	0.393865	+	0.919168i	$0.371138\pi$
$359$			659.963i			1.83834i	−0.393865	+	0.919168i	$0.628862\pi$
$360$		0			0
$361$	−360.020			−0.997285
$362$	−98.9162	+	260.521i	−0.273249	+	0.719673i
$363$	−38.8818			−0.107112
$364$	155.063	+	137.584i	0.425997	+	0.377979i
$365$		0			0
$366$	−89.1462	+	234.789i	−0.243569	+	0.641501i
$367$			371.867i			1.01326i	0.862163	+	0.506630i	$0.169109\pi$
$367$			371.867i			1.01326i	−0.862163	+	0.506630i	$0.830891\pi$
$368$	7.62635	−	0.914224i	0.0207238	−	0.00248431i
$369$	−124.921			−0.338540
$370$		0			0
$371$	−333.464			−0.898824
$372$	−74.4415	+	83.8983i	−0.200112	+	0.225533i
$373$			292.195i			0.783364i	0.920101	+	0.391682i	$0.128107\pi$
$373$			292.195i			0.783364i	−0.920101	+	0.391682i	$0.871893\pi$
$374$	−376.677	−	143.019i	−1.00716	−	0.382403i
$375$		0			0
$376$	−127.526	+	66.7451i	−0.339165	+	0.177514i
$377$	136.266			0.361448
$378$	−175.462	+	462.126i	−0.464186	+	1.22255i
$379$	574.767			1.51654			0.758268	−	0.651943i	$-0.226046\pi$
$379$	574.767			1.51654			0.758268	+	0.651943i	$0.226046\pi$
$380$		0			0
$381$		−	162.083i		−	0.425413i
$382$	90.5201	−	238.408i	0.236964	−	0.624105i
$383$			80.7976i			0.210960i	0.994421	+	0.105480i	$0.0336379\pi$
$383$			80.7976i			0.210960i	−0.994421	+	0.105480i	$0.966362\pi$
$384$	127.138	−	87.2578i	0.331089	−	0.227234i
$385$		0			0
$386$	−300.928	−	114.258i	−0.779605	−	0.296005i
$387$	−432.659			−1.11798
$388$	14.5032	+	12.8685i	0.0373795	+	0.0331662i
$389$		−	295.056i		−	0.758498i	−0.925295	−	0.379249i	$-0.876182\pi$
$389$		−	295.056i		−	0.758498i	0.925295	−	0.379249i	$-0.123818\pi$
$390$		0			0
$391$			10.2673i			0.0262590i
$392$	388.391	+	742.075i	0.990793	+	1.89305i
$393$	−167.990			−0.427455
$394$	−106.018	+	279.226i	−0.269081	+	0.708695i
$395$		0			0
$396$	212.745	+	188.765i	0.537236	+	0.476680i
$397$		−	119.742i		−	0.301618i	−0.988563	−	0.150809i	$-0.951812\pi$
$397$		−	119.742i		−	0.301618i	0.988563	−	0.150809i	$-0.0481878\pi$
$398$	248.819	−	655.330i	0.625174	−	1.64656i
$399$			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	$0.636280\pi$
$402$	−5.18549	−	1.96885i	−0.0128992	−	0.00489765i
$403$	97.3019			0.241444
$404$	−405.152	+	456.622i	−1.00285	+	1.13025i
$405$		0			0
$406$	755.604	+	286.892i	1.86109	+	0.706630i
$407$		−	526.475i		−	1.29355i
$408$	95.5819	+	182.623i	0.234269	+	0.447604i
$409$	−14.2484			−0.0348373			−0.0174186	−	0.999848i	$-0.505545\pi$
$409$	−14.2484			−0.0348373			−0.0174186	+	0.999848i	$0.505545\pi$
$410$		0			0
$411$	105.194			0.255945
$412$	−299.793	+	337.878i	−0.727653	+	0.820091i
$413$			952.400i			2.30605i
$414$	2.57263	−	6.77569i	0.00621409	−	0.0163664i
$415$		0			0
$416$	−129.822	−	32.2606i	−0.312073	−	0.0775495i
$417$	121.969			0.292492
$418$	17.4360	+	6.62021i	0.0417130	+	0.0158378i
$419$	159.814			0.381417			0.190709	−	0.981647i	$-0.438921\pi$
$419$	159.814			0.381417			0.190709	+	0.981647i	$0.438921\pi$
$420$		0			0
$421$			89.1070i			0.211656i	0.994384	+	0.105828i	$0.0337492\pi$
$421$			89.1070i			0.211656i	−0.994384	+	0.105828i	$0.966251\pi$
$422$	−719.237	−	273.084i	−1.70435	−	0.647118i
$423$			135.817i			0.321080i
$424$	190.649	−	99.7827i	0.449643	−	0.235337i
$425$		0			0
$426$	−46.3748	+	122.140i	−0.108861	+	0.286714i
$427$	1292.25			3.02634
$428$	393.671	+	349.297i	0.919791	+	0.816115i
$429$			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	$0.894904\pi$
$432$	−37.9664	−	316.711i	−0.0878853	−	0.733128i
$433$	71.3709			0.164829			0.0824145	−	0.996598i	$-0.473737\pi$
$433$	71.3709			0.164829			0.0824145	+	0.996598i	$0.473737\pi$
$434$	539.546	+	204.858i	1.24319	+	0.472023i
$435$		0			0
$436$	−155.892	+	175.696i	−0.357550	+	0.402972i
$437$		−	0.475263i		−	0.00108756i
$438$	166.560	+	63.2405i	0.380275	+	0.144385i
$439$		−	385.168i		−	0.877375i	−0.898640	−	0.438688i	$-0.855444\pi$
$439$		−	385.168i		−	0.877375i	0.898640	−	0.438688i	$-0.144556\pi$
$440$		0			0
$441$	790.321			1.79211
$442$	63.4718	−	167.169i	0.143601	−	0.378211i
$443$	−194.993			−0.440165			−0.220082	−	0.975481i	$-0.570633\pi$
$443$	−194.993			−0.440165			−0.220082	+	0.975481i	$0.570633\pi$
$444$	−178.756	+	201.464i	−0.402603	+	0.453748i
$445$		0			0
$446$	−42.0259	+	110.686i	−0.0942284	+	0.248175i
$447$		−	115.500i		−	0.258389i
$448$	−651.953	−	452.213i	−1.45525	−	1.00940i
$449$	−458.520			−1.02120			−0.510602	−	0.859817i	$-0.670577\pi$
$449$	−458.520			−1.02120			−0.510602	+	0.859817i	$0.670577\pi$
$450$		0			0
$451$	−155.879			−0.345629
$452$	−464.355	−	412.014i	−1.02733	−	0.911535i
$453$		−	33.4346i		−	0.0738071i
$454$	421.985	+	160.222i	0.929483	+	0.352911i
$455$		0			0
$456$	−4.42440	−	8.45345i	−0.00970264	−	0.0185383i
$457$	283.142			0.619567			0.309784	−	0.950807i	$-0.399743\pi$
$457$	283.142			0.619567			0.309784	+	0.950807i	$0.399743\pi$
$458$	104.380	−	274.911i	0.227903	−	0.600242i
$459$	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	$-0.117384\pi$
$462$	−99.8717	+	263.038i	−0.216173	+	0.569346i
$463$			426.370i			0.920886i	0.887689	+	0.460443i	$0.152309\pi$
$463$			426.370i			0.920886i	−0.887689	+	0.460443i	$0.847691\pi$
$464$	−517.843	+	62.0775i	−1.11604	+	0.133788i
$465$		0			0
$466$	−288.781	−	109.646i	−0.619702	−	0.235292i
$467$	−365.575			−0.782815			−0.391407	−	0.920217i	$-0.628012\pi$
$467$	−365.575			−0.782815			−0.391407	+	0.920217i	$0.628012\pi$
$468$	−83.7742	+	94.4166i	−0.179005	+	0.201745i
$469$			28.5402i			0.0608533i
$470$		0			0
$471$			87.2264i			0.185194i
$472$	−284.988	−	544.509i	−0.603787	−	1.15362i
$473$	−539.879			−1.14139
$474$	33.8507	−	89.1545i	0.0714149	−	0.188090i
$475$		0			0
$476$	703.911	−	793.334i	1.47881	−	1.66667i
$477$		−	203.044i		−	0.425668i
$478$	138.155	−	363.866i	0.289027	−	0.761226i
$479$		−	657.674i		−	1.37301i	−0.727123	−	0.686507i	$-0.759143\pi$
$479$		−	657.674i		−	1.37301i	0.727123	−	0.686507i	$-0.240857\pi$
$480$		0			0
$481$	233.650			0.485759
$482$	189.787	+	72.0594i	0.393749	+	0.149501i
$483$	7.16976			0.0148442
$484$	−96.5680	−	85.6831i	−0.199521	−	0.177031i
$485$		0			0
$486$	−434.416	−	164.941i	−0.893860	−	0.339386i
$487$		−	599.006i		−	1.22999i	−0.788530	−	0.614996i	$-0.789157\pi$
$487$		−	599.006i		−	1.22999i	0.788530	−	0.614996i	$-0.210843\pi$
$488$	−738.807	+	386.680i	−1.51395	+	0.792378i
$489$	−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	$0.473561\pi$
$492$	59.6495	+	52.9260i	0.121239	+	0.107573i
$493$		−	697.165i		−	1.41413i
$494$	−2.93806	+	7.73813i	−0.00594748	+	0.0156642i
$495$		0			0
$496$	−369.770	+	44.3270i	−0.745505	+	0.0893690i
$497$	672.241			1.35260
$498$	−131.037	−	49.7530i	−0.263127	−	0.0999056i
$499$	−263.876			−0.528809			−0.264404	−	0.964412i	$-0.585175\pi$
$499$	−263.876			−0.528809			−0.264404	+	0.964412i	$0.585175\pi$
$500$		0			0
$501$			62.2240i			0.124200i
$502$	385.906	+	146.523i	0.768736	+	0.291878i
$503$		−	173.548i		−	0.345026i	−0.985007	−	0.172513i	$-0.944811\pi$
$503$		−	173.548i		−	0.345026i	0.985007	−	0.172513i	$-0.0551887\pi$
$504$	−663.317	+	347.170i	−1.31610	+	0.688829i
$505$		0			0
$506$	3.21017	−	8.45481i	0.00634421	−	0.0167091i
$507$	182.542			0.360042
$508$	357.178	−	402.553i	0.703107	−	0.792427i
$509$			459.387i			0.902528i	0.892390	+	0.451264i	$0.149027\pi$
$509$			459.387i			0.902528i	−0.892390	+	0.451264i	$0.850973\pi$
$510$		0			0
$511$		−	916.724i		−	1.79398i
$512$	508.053	+	63.4558i	0.992290	+	0.123937i
$513$	−19.7370			−0.0384737
$514$	−139.016	−	52.7824i	−0.270460	−	0.102690i
$515$		0			0
$516$	206.593	+	183.307i	0.400375	+	0.355246i
$517$			169.474i			0.327804i
$518$	1295.61	+	491.923i	2.50117	+	0.949659i
$519$		−	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	$0.364550\pi$
$522$	−174.686	+	460.082i	−0.334648	+	0.881383i
$523$	745.353			1.42515			0.712574	−	0.701596i	$-0.247529\pi$
$523$	745.353			1.42515			0.712574	+	0.701596i	$0.247529\pi$
$524$	−417.225	−	370.196i	−0.796230	−	0.706481i
$525$		0			0
$526$	278.072	−	732.374i	0.528654	−	1.39235i
$527$		−	497.817i		−	0.944625i
$528$	−21.6102	−	180.270i	−0.0409284	−	0.341420i
$529$	528.770			0.999564
$530$		0			0
$531$	−579.910			−1.09211
$532$	−32.5835	+	36.7228i	−0.0612471	+	0.0690277i
$533$		−	69.1791i		−	0.129792i
$534$	63.8347	+	24.2371i	0.119541	+	0.0453878i
$535$		0			0
$536$	−8.54011	−	16.3171i	−0.0159330	−	0.0304423i
$537$	−184.057			−0.342750
$538$	190.501	−	501.733i	0.354090	−	0.932588i
$539$	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	$-0.234008\pi$
$542$	−302.715	+	797.279i	−0.558515	+	1.47099i
$543$		−	167.855i		−	0.309126i
$544$	−165.052	+	664.199i	−0.303404	+	1.22095i
$545$		0			0
$546$	−116.737	−	44.3232i	−0.213803	−	0.0811780i
$547$	−92.4741			−0.169057			−0.0845284	−	0.996421i	$-0.526938\pi$
$547$	−92.4741			−0.169057			−0.0845284	+	0.996421i	$0.526938\pi$
$548$	261.262	+	231.813i	0.476755	+	0.423016i
$549$			786.840i			1.43322i
$550$		0			0
$551$			32.2712i			0.0585684i
$552$	−4.09911	+	2.14541i	−0.00742593	+	0.00388662i
$553$	−490.694			−0.887330
$554$	2.47490	−	6.51828i	0.00446732	−	0.0117658i
$555$		0			0
$556$	302.927	+	268.782i	0.544832	+	0.483420i
$557$		−	1043.87i		−	1.87409i	−0.349215	−	0.937043i	$-0.613552\pi$
$557$		−	1043.87i		−	1.87409i	0.349215	−	0.937043i	$-0.386448\pi$
$558$	−124.736	+	328.526i	−0.223542	+	0.588756i
$559$		−	239.599i		−	0.428620i
$560$		0			0
$561$	242.695			0.432611
$562$	266.181	+	101.065i	0.473631	+	0.179831i
$563$	149.723			0.265939			0.132969	−	0.991120i	$-0.457549\pi$
$563$	149.723			0.265939			0.132969	+	0.991120i	$0.457549\pi$
$564$	57.5422	−	64.8522i	0.102025	−	0.114986i
$565$		0			0
$566$	237.671	+	90.2402i	0.419913	+	0.159435i
$567$			544.511i			0.960337i
$568$	−384.336	+	201.155i	−0.676647	+	0.354147i
$569$	−814.440			−1.43135			−0.715677	−	0.698432i	$-0.753881\pi$
$569$	−814.440			−1.43135			−0.715677	+	0.698432i	$0.753881\pi$
$570$		0			0
$571$	250.759			0.439157			0.219578	−	0.975595i	$-0.429532\pi$
$571$	250.759			0.439157			0.219578	+	0.975595i	$0.429532\pi$
$572$	−104.535	+	117.814i	−0.182753	+	0.205969i
$573$			153.608i			0.268076i
$574$	145.648	−	383.603i	0.253743	−	0.668298i
$575$		0			0
$576$	275.349	−	396.970i	0.478037	−	0.689183i
$577$	−851.781			−1.47622			−0.738112	−	0.674678i	$-0.764282\pi$
$577$	−851.781			−1.47622			−0.738112	+	0.674678i	$0.764282\pi$
$578$	−314.913	−	119.568i	−0.544832	−	0.206865i
$579$	193.889			0.334869
$580$		0			0
$581$			721.211i			1.24133i
$582$	−10.9185	−	4.14561i	−0.0187604	−	0.00712305i
$583$		−	253.361i		−	0.434581i
$584$	274.312	+	524.112i	0.469713	+	0.897452i
$585$		0			0
$586$	−151.824	+	399.868i	−0.259085	+	0.682368i
$587$	426.708			0.726929			0.363465	−	0.931608i	$-0.381594\pi$
$587$	426.708			0.726929			0.363465	+	0.931608i	$0.381594\pi$
$588$	−377.376	−	334.839i	−0.641795	−	0.569454i
$589$			23.0435i			0.0391232i
$590$		0			0
$591$		−	179.907i		−	0.304411i
$592$	−887.926	+	106.442i	−1.49988	+	0.179801i
$593$	−668.977			−1.12812			−0.564061	−	0.825733i	$-0.690762\pi$
$593$	−668.977			−1.12812			−0.564061	+	0.825733i	$0.690762\pi$
$594$	−351.116	−	133.314i	−0.591105	−	0.224434i
$595$		0			0
$596$	254.525	−	286.859i	0.427055	−	0.481306i
$597$			422.232i			0.707257i
$598$	3.75225	+	1.42468i	0.00627467	+	0.00238240i
$599$		−	75.4852i		−	0.126019i	−0.998013	−	0.0630093i	$-0.979930\pi$
$599$		−	75.4852i		−	0.126019i	0.998013	−	0.0630093i	$-0.0200698\pi$
$600$		0			0
$601$	−887.728			−1.47709			−0.738543	−	0.674207i	$-0.764486\pi$
$601$	−887.728			−1.47709			−0.738543	+	0.674207i	$0.764486\pi$
$602$	504.447	−	1328.59i	0.837952	−	2.20696i
$603$	−17.3779			−0.0288191
$604$	73.6792	−	83.0392i	0.121985	−	0.137482i
$605$		0			0
$606$	130.521	−	343.760i	0.215381	−	0.567261i
$607$			560.008i			0.922583i	0.887249	+	0.461292i	$0.152614\pi$
$607$			560.008i			0.922583i	−0.887249	+	0.461292i	$0.847386\pi$
$608$	7.64012	−	30.7452i	0.0125660	−	0.0505678i
$609$	−486.840			−0.799408
$610$		0			0
$611$	−75.2129			−0.123098
$612$	483.055	+	428.607i	0.789306	+	0.700337i
$613$			28.9794i			0.0472747i	0.999721	+	0.0236374i	$0.00752471\pi$
$613$			28.9794i			0.0472747i	−0.999721	+	0.0236374i	$0.992475\pi$
$614$	637.827	+	242.173i	1.03881	+	0.394419i
$615$		0			0
$616$	−827.697	+	433.204i	−1.34366	+	0.703253i
$617$	−345.379			−0.559771			−0.279886	−	0.960033i	$-0.590297\pi$
$617$	−345.379			−0.559771			−0.279886	+	0.960033i	$0.590297\pi$
$618$	96.5791	−	254.366i	0.156277	−	0.411595i
$619$	624.297			1.00856			0.504279	−	0.863541i	$-0.331758\pi$
$619$	624.297			1.00856			0.504279	+	0.863541i	$0.331758\pi$
$620$		0			0
$621$			9.57055i			0.0154115i
$622$	272.935	−	718.845i	0.438802	−	1.15570i
$623$		−	351.337i		−	0.563944i
$624$	80.0038	−	9.59062i	0.128211	−	0.0153696i
$625$		0			0
$626$	−370.580	−	140.704i	−0.591981	−	0.224767i
$627$	−11.2341			−0.0179173
$628$	−192.219	+	216.638i	−0.306081	+	0.344965i
$629$		−	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	$0.807604\pi$
$632$	280.541	−	146.831i	0.443893	−	0.232327i
$633$	463.408			0.732082
$634$	359.705	−	947.376i	0.567358	−	1.49428i
$635$		0			0
$636$	−86.0245	+	96.9527i	−0.135259	+	0.152441i
$637$			437.665i			0.687072i
$638$	−217.976	+	574.097i	−0.341656	+	0.899839i
$639$			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	$0.362135\pi$
$642$	−296.369	−	112.527i	−0.461634	−	0.175276i
$643$	1266.66			1.96993			0.984963	−	0.172767i	$-0.0552708\pi$
$643$	1266.66			1.96993			0.984963	+	0.172767i	$0.0552708\pi$
$644$	17.8070	+	15.7999i	0.0276507	+	0.0245339i
$645$		0			0
$646$	39.5899	+	15.0317i	0.0612847	+	0.0232689i
$647$			816.424i			1.26186i	0.775839	+	0.630930i	$0.217327\pi$
$647$			816.424i			1.26186i	−0.775839	+	0.630930i	$0.782673\pi$
$648$	−162.934	−	311.309i	−0.251442	−	0.480415i
$649$	−723.620			−1.11498
$650$		0			0
$651$	−347.632			−0.533997
$652$	−198.826	−	176.415i	−0.304947	−	0.270574i
$653$			692.042i			1.05979i	0.848064	+	0.529894i	$0.177768\pi$
$653$			692.042i			1.05979i	−0.848064	+	0.529894i	$0.822232\pi$
$654$	50.2209	−	132.270i	0.0767904	−	0.202247i
$655$		0			0
$656$	31.5153	+	262.897i	0.0480417	+	0.400758i
$657$	558.187			0.849599
$658$	−417.061	−	158.352i	−0.633831	−	0.240657i
$659$	−890.532			−1.35134			−0.675669	−	0.737205i	$-0.736145\pi$
$659$	−890.532			−1.35134			−0.675669	+	0.737205i	$0.736145\pi$
$660$		0			0
$661$			656.736i			0.993549i	0.867880	+	0.496774i	$0.165482\pi$
$661$			656.736i			0.993549i	−0.867880	+	0.496774i	$0.834518\pi$
$662$	−639.028	−	242.630i	−0.965299	−	0.366510i
$663$			107.708i			0.162456i
$664$	−215.809	−	412.333i	−0.325013	−	0.620983i
$665$		0			0
$666$	−299.528	+	788.886i	−0.449742	+	1.18451i
$667$	15.6484			0.0234609
$668$	−137.122	+	154.541i	−0.205272	+	0.231349i
$669$		−	71.3155i		−	0.106600i
$670$		0			0
$671$			981.831i			1.46324i
$672$	463.819	+	115.258i	0.690206	+	0.171515i
$673$	242.150			0.359807			0.179904	−	0.983684i	$-0.442421\pi$
$673$	242.150			0.359807			0.179904	+	0.983684i	$0.442421\pi$
$674$	904.249	+	343.330i	1.34162	+	0.509392i
$675$		0			0
$676$	453.366	+	402.263i	0.670659	+	0.595064i
$677$			592.051i			0.874521i	0.899335	+	0.437261i	$0.144051\pi$
$677$			592.051i			0.874521i	−0.899335	+	0.437261i	$0.855949\pi$
$678$	349.582	+	132.731i	0.515608	+	0.195769i
$679$			60.0941i			0.0885039i
$680$		0			0
$681$	−271.887			−0.399247
$682$	−155.648	+	409.939i	−0.228223	+	0.601084i
$683$	−640.413			−0.937647			−0.468824	−	0.883292i	$-0.655322\pi$
$683$	−640.413			−0.937647			−0.468824	+	0.883292i	$0.655322\pi$
$684$	−22.3602	−	19.8398i	−0.0326904	−	0.0290056i
$685$		0			0
$686$	−490.194	+	1291.05i	−0.714568	+	1.88200i
$687$			177.126i			0.257826i
$688$	109.152	+	910.532i	0.158651	+	1.32345i
$689$	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	$0.289657\pi$
$692$	49.1949	−	55.4445i	0.0710909	−	0.0801221i
$693$			881.509i			1.27202i
$694$	−286.827	−	108.904i	−0.413296	−	0.156922i
$695$		0			0
$696$	278.337	−	145.677i	0.399910	−	0.209307i
$697$	−353.935			−0.507798
$698$	−334.110	+	879.965i	−0.478668	+	1.26070i
$699$	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	$-0.172815\pi$
$702$	59.1648	−	155.826i	0.0842803	−	0.221974i
$703$			55.3343i			0.0787116i
$704$	343.585	−	495.345i	0.488047	−	0.703615i
$705$		0			0
$706$	114.035	+	43.2976i	0.161523	+	0.0613280i
$707$	−1892.01			−2.67611
$708$	276.905	+	245.693i	0.391109	+	0.347024i
$709$			109.289i			0.154145i	0.997026	+	0.0770723i	$0.0245572\pi$
$709$			109.289i			0.154145i	−0.997026	+	0.0770723i	$0.975443\pi$
$710$		0			0
$711$		−	298.780i		−	0.420225i
$712$	105.131	+	200.867i	0.147656	+	0.282117i
$713$	11.1739			0.0156717
$714$	−226.767	+	597.249i	−0.317601	+	0.836483i
$715$		0			0
$716$	−457.129	−	405.602i	−0.638448	−	0.566483i
$717$			234.441i			0.326975i
$718$	468.522	−	1233.97i	0.652537	−	1.71863i
$719$			794.119i			1.10448i	0.833686	+	0.552238i	$0.186226\pi$
$719$			794.119i			1.10448i	−0.833686	+	0.552238i	$0.813774\pi$
$720$		0			0
$721$	−1399.99			−1.94174
$722$	673.152	+	255.586i	0.932343	+	0.353997i
$723$	−122.281			−0.169130
$724$	369.900	−	416.890i	0.510911	−	0.575816i
$725$		0			0
$726$	72.6997	+	27.6030i	0.100137	+	0.0380207i
$727$		−	756.542i		−	1.04064i	−0.853973	−	0.520318i	$-0.825813\pi$
$727$		−	756.542i		−	1.04064i	0.853973	−	0.520318i	$-0.174187\pi$
$728$	−192.256	−	367.333i	−0.264088	−	0.504578i
$729$	−115.395			−0.158292
$730$		0			0
$731$	−1225.84			−1.67693
$732$	333.364	−	375.714i	0.455416	−	0.513270i
$733$		−	884.232i		−	1.20632i	−0.797621	−	0.603160i	$-0.793908\pi$
$733$		−	884.232i		−	1.20632i	0.797621	−	0.603160i	$-0.206092\pi$
$734$	263.996	−	695.302i	0.359668	−	0.947278i
$735$		0			0
$736$	−14.9085	−	3.70473i	−0.0202561	−	0.00503359i
$737$	−21.6844			−0.0294226
$738$	233.573	+	88.6843i	0.316495	+	0.120168i
$739$	−746.061			−1.00956			−0.504778	−	0.863249i	$-0.668426\pi$
$739$	−746.061			−1.00956			−0.504778	+	0.863249i	$0.668426\pi$
$740$		0			0
$741$		−	4.98572i		−	0.00672837i
$742$	623.498	+	236.733i	0.840294	+	0.319047i
$743$		−	47.1955i		−	0.0635202i	−0.999496	−	0.0317601i	$-0.989889\pi$
$743$		−	47.1955i		−	0.0635202i	0.999496	−	0.0317601i	$-0.0101113\pi$
$744$	198.749	−	104.022i	0.267136	−	0.139815i
$745$		0			0
$746$	207.435	−	546.335i	0.278064	−	0.732353i
$747$	−439.140			−0.587872
$748$	602.764	+	534.822i	0.805834	+	0.715002i
$749$			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	$0.805110\pi$
$752$	285.827	−	34.2641i	0.380089	−	0.0455640i
$753$	−248.641			−0.330200
$754$	−254.785	−	96.7381i	−0.337911	−	0.128300i
$755$		0			0
$756$	656.146	−	739.500i	0.867918	−	0.978175i
$757$			980.034i			1.29463i	0.762223	+	0.647314i	$0.224108\pi$
$757$			980.034i			1.29463i	−0.762223	+	0.647314i	$0.775892\pi$
$758$	−1074.68	−	408.040i	−1.41778	−	0.538311i
$759$			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	$0.194027\pi$
$762$	−115.066	+	303.056i	−0.151005	+	0.397711i
$763$	−727.994			−0.954121
$764$	−338.502	+	381.505i	−0.443066	+	0.499352i
$765$		0			0
$766$	57.3600	−	151.072i	0.0748825	−	0.197222i
$767$		−	321.143i		−	0.418701i
$768$	−299.664	+	72.8933i	−0.390188	+	0.0949131i
$769$	782.117			1.01706			0.508528	−	0.861045i	$-0.330190\pi$
$769$	782.117			1.01706			0.508528	+	0.861045i	$0.330190\pi$
$770$		0			0
$771$	89.5689			0.116172
$772$	481.549	+	427.270i	0.623768	+	0.553459i
$773$		−	673.425i		−	0.871184i	−0.900144	−	0.435592i	$-0.856539\pi$
$773$		−	673.425i		−	0.871184i	0.900144	−	0.435592i	$-0.143461\pi$
$774$	808.970	+	307.154i	1.04518	+	0.396840i
$775$		0			0
$776$	−17.9820	−	34.3572i	−0.0231727	−	0.0442747i
$777$	−834.766			−1.07435
$778$	−209.467	+	551.684i	−0.269237	+	0.709106i
$779$	16.3834			0.0210313
$780$		0			0
$781$			510.759i			0.653981i
$782$	7.28895	−	19.1973i	0.00932090	−	0.0245490i
$783$		−	649.858i		−	0.829959i
$784$	−199.383	−	1663.23i	−0.254316	−	2.12147i
$785$		0			0
$786$	314.101	+	119.260i	0.399620	+	0.151730i
$787$	−96.9208			−0.123152			−0.0615761	−	0.998102i	$-0.519613\pi$
$787$	−96.9208			−0.123152			−0.0615761	+	0.998102i	$0.519613\pi$
$788$	396.457	−	446.822i	0.503118	−	0.567033i
$789$			471.872i			0.598064i
$790$		0			0
$791$		−	1924.05i		−	2.43243i
$792$	−263.775	−	503.978i	−0.333049	−	0.636336i
$793$	−435.738			−0.549480
$794$	−85.0076	+	223.890i	−0.107062	+	0.281977i
$795$		0			0
$796$	−930.465	+	1048.67i	−1.16893	+	1.31742i
$797$		−	100.960i		−	0.126675i	−0.997992	−	0.0633373i	$-0.979826\pi$
$797$		−	100.960i		−	0.126675i	0.997992	−	0.0633373i	$-0.0201744\pi$
$798$	10.4968	−	27.6462i	0.0131539	−	0.0346443i
$799$			384.805i			0.481609i
$800$		0			0
$801$	213.927			0.267074
$802$	622.575	+	236.383i	0.776278	+	0.294742i
$803$	696.514			0.867390
$804$	8.29790	+	7.36258i	0.0103208	+	0.00915744i
$805$		0			0
$806$	−181.931	−	69.0767i	−0.225721	−	0.0857032i
$807$			323.269i			0.400581i
$808$	1081.70	−	566.147i	1.33874	−	0.700677i
$809$	−125.149			−0.154696			−0.0773480	−	0.997004i	$-0.524645\pi$
$809$	−125.149			−0.154696			−0.0773480	+	0.997004i	$0.524645\pi$
$810$		0			0
$811$	1504.84			1.85554			0.927769	−	0.373156i	$-0.121724\pi$
$811$	1504.84			1.85554			0.927769	+	0.373156i	$0.121724\pi$
$812$	−1209.13	−	1072.84i	−1.48908	−	1.32123i
$813$		−	513.691i		−	0.631846i
$814$	−373.756	+	984.383i	−0.459160	+	1.20932i
$815$		0			0
$816$	−49.0677	−	409.316i	−0.0601320	−	0.501613i
$817$	56.7430			0.0694529
$818$	26.6412	+	10.1153i	0.0325687	+	0.0123659i
$819$	−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	$-0.0756611\pi$
$822$	−196.687	−	74.6791i	−0.239278	−	0.0908505i
$823$			737.692i			0.896345i	0.893947	+	0.448173i	$0.147925\pi$
$823$			737.692i			0.896345i	−0.893947	+	0.448173i	$0.852075\pi$
$824$	800.408	−	418.921i	0.971369	−	0.508400i
$825$		0			0
$826$	676.130	−	1780.76i	0.818559	−	2.15589i
$827$	1339.34			1.61952			0.809758	−	0.586764i	$-0.199598\pi$
$827$	1339.34			1.61952			0.809758	+	0.586764i	$0.199598\pi$
$828$	−9.62042	+	10.8426i	−0.0116189	+	0.0130949i
$829$		−	1103.12i		−	1.33066i	−0.746548	−	0.665331i	$-0.768290\pi$
$829$		−	1103.12i		−	1.33066i	0.746548	−	0.665331i	$-0.231710\pi$
$830$		0			0
$831$			4.19976i			0.00505386i
$832$	219.835	+	152.483i	0.264224	+	0.183273i
$833$	2239.19			2.68810
$834$	−228.054	−	86.5887i	−0.273446	−	0.103823i
$835$		0			0
$836$	−27.9014	−	24.7564i	−0.0333749	−	0.0296130i
$837$		−	464.037i		−	0.554405i
$838$	−298.814	−	113.455i	−0.356580	−	0.135388i
$839$		−	1401.49i		−	1.67043i	−0.549927	−	0.835213i	$-0.685345\pi$
$839$		−	1401.49i		−	1.67043i	0.549927	−	0.835213i	$-0.314655\pi$
$840$		0			0
$841$	−221.558			−0.263446
$842$	63.2590	−	166.609i	0.0751295	−	0.197873i
$843$	−171.501			−0.203442
$844$	1150.93	+	1021.20i	1.36367	+	1.20996i
$845$		0			0
$846$	96.4194	−	253.945i	0.113971	−	0.300172i
$847$		−	400.129i		−	0.472407i
$848$	−427.306	+	51.2242i	−0.503898	+	0.0604059i
$849$	−153.133			−0.180368
$850$		0			0
$851$	26.8318			0.0315298
$852$	173.420	−	195.450i	0.203544	−	0.229402i
$853$		−	493.813i		−	0.578913i	−0.957191	−	0.289456i	$-0.906525\pi$
$853$		−	493.813i		−	0.578913i	0.957191	−	0.289456i	$-0.0934745\pi$
$854$	−2416.20	−	917.395i	−2.82927	−	1.07423i
$855$		0			0
$856$	−488.097	−	932.578i	−0.570207	−	1.08946i
$857$	1179.48			1.37628			0.688142	−	0.725576i	$-0.258427\pi$
$857$	1179.48			1.37628			0.688142	+	0.725576i	$0.258427\pi$
$858$	33.6761	−	88.6948i	0.0392495	−	0.103374i
$859$	−1057.63			−1.23123			−0.615616	−	0.788046i	$-0.711093\pi$
$859$	−1057.63			−1.23123			−0.615616	+	0.788046i	$0.711093\pi$
$860$		0			0
$861$			247.157i			0.287059i
$862$	198.397	−	522.531i	0.230159	−	0.606184i
$863$			29.0807i			0.0336972i	0.999858	+	0.0168486i	$0.00536333\pi$
$863$			29.0807i			0.0336972i	−0.999858	+	0.0168486i	$0.994637\pi$
$864$	−153.852	+	619.128i	−0.178069	+	0.716584i
$865$		0			0
$866$	−133.447	−	50.6678i	−0.154095	−	0.0585078i
$867$	202.900			0.234026
$868$	−863.390	−	766.071i	−0.994689	−	0.882570i
$869$		−	372.822i		−	0.429024i
$870$		0			0
$871$		−	9.62357i		−	0.0110489i
$872$	416.211	−	217.838i	0.477306	−	0.249815i
$873$	−36.5909			−0.0419139
$874$	−0.337399	+	0.888628i	−0.000386040	+	0.00101674i
$875$		0			0
$876$	−266.532	−	236.490i	−0.304261	−	0.269965i
$877$		−	656.995i		−	0.749139i	−0.927199	−	0.374570i	$-0.877790\pi$
$877$		−	656.995i		−	0.749139i	0.927199	−	0.374570i	$-0.122210\pi$
$878$	−273.439	+	720.172i	−0.311434	+	0.820241i
$879$		−	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	$0.527413\pi$
$882$	−1477.71	−	561.066i	−1.67541	−	0.636129i
$883$	−1139.07			−1.29001			−0.645003	−	0.764180i	$-0.723144\pi$
$883$	−1139.07			−1.29001			−0.645003	+	0.764180i	$0.723144\pi$
$884$	−237.354	+	267.507i	−0.268500	+	0.302610i
$885$		0			0
$886$	364.591	+	138.430i	0.411502	+	0.156241i
$887$			1559.13i			1.75776i	0.477041	+	0.878881i	$0.341709\pi$
$887$			1559.13i			1.75776i	−0.477041	+	0.878881i	$0.658291\pi$
$888$	477.255	−	249.788i	0.537449	−	0.281293i
$889$	1667.98			1.87624
$890$		0			0
$891$	−413.711			−0.464323
$892$	157.157	−	177.121i	0.176185	−	0.198567i
$893$		−	17.8123i		−	0.0199466i
$894$	−81.9958	+	215.957i	−0.0917179	+	0.241563i
$895$		0			0
$896$	897.962	+	1308.37i	1.00219	+	1.46023i
$897$	−2.41760			−0.00269520
$898$	857.324	+	325.514i	0.954704	+	0.362487i
$899$	−758.729			−0.843970
$900$		0			0
$901$		−	575.277i		−	0.638487i
$902$	291.456	+	110.662i	0.323122	+	0.122685i
$903$			856.019i			0.947972i
$904$	575.736	+	1100.02i	0.636876	+	1.21684i
$905$		0			0
$906$	−23.7359	+	62.5148i	−0.0261986	+	0.0690008i
$907$	1295.44			1.42827			0.714133	−	0.700010i	$-0.246821\pi$
$907$	1295.44			1.42827			0.714133	+	0.700010i	$0.246821\pi$
$908$	−675.267	−	599.153i	−0.743686	−	0.659860i
$909$		−	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	$-0.216250\pi$
$912$	2.27130	+	18.9469i	0.00249046	+	0.0207751i
$913$	−547.966			−0.600182
$914$	−529.409	−	201.009i	−0.579222	−	0.219922i
$915$		0			0
$916$	−390.330	+	439.916i	−0.426125	+	0.480258i
$917$		−	1728.77i		−	1.88524i
$918$	−797.238	−	302.700i	−0.868451	−	0.329738i
$919$			1735.96i			1.88897i	0.328557	+	0.944484i	$0.393438\pi$
$919$			1735.96i			1.88897i	−0.328557	+	0.944484i	$0.606562\pi$
$920$		0			0
$921$	−410.955			−0.446205
$922$	−235.946	+	621.425i	−0.255907	+	0.673996i
$923$	−226.675			−0.245586
$924$	373.473	−	420.918i	0.404191	−	0.455539i
$925$		0			0
$926$	302.689	−	797.211i	0.326878	−	0.860919i
$927$		−	852.446i		−	0.919575i
$928$	1012.31	+	251.558i	1.09085	+	0.271075i
$929$	1547.16			1.66540			0.832701	−	0.553724i	$-0.186794\pi$
$929$	1547.16			1.66540			0.832701	+	0.553724i	$0.186794\pi$
$930$		0			0
$931$	−103.650			−0.111332
$932$	462.112	+	410.024i	0.495829	+	0.439940i
$933$			463.156i			0.496416i
$934$	683.538	+	259.529i	0.731839	+	0.277869i
$935$		0			0
$936$	223.666	−	117.063i	0.238960	−	0.125068i
$937$	−11.0709			−0.0118153			−0.00590764	−	0.999983i	$-0.501880\pi$
$937$	−11.0709			−0.0118153			−0.00590764	+	0.999983i	$0.501880\pi$
$938$	20.2613	−	53.3634i	0.0216005	−	0.0568906i
$939$	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	$0.959765\pi$
$942$	61.9239	−	163.093i	0.0657366	−	0.173134i
$943$		−	7.94436i		−	0.00842456i
$944$	146.301	+	1220.42i	0.154979	+	1.29282i
$945$		0			0
$946$	1009.45	+	383.272i	1.06707	+	0.405150i
$947$	−923.233			−0.974903			−0.487451	−	0.873150i	$-0.662073\pi$
$947$	−923.233			−0.974903			−0.487451	+	0.873150i	$0.662073\pi$
$948$	−126.585	+	142.666i	−0.133529	+	0.150492i
$949$			309.114i			0.325726i
$950$		0			0
$951$			610.399i			0.641850i
$952$	−1879.35	+	983.624i	−1.97411	+	1.03322i
$953$	1616.56			1.69629			0.848144	−	0.529765i	$-0.177720\pi$
$953$	1616.56			1.69629			0.848144	+	0.529765i	$0.177720\pi$
$954$	−144.145	+	379.644i	−0.151096	+	0.397949i
$955$		0			0
$956$	−516.633	+	582.264i	−0.540411	+	0.609063i
$957$		−	369.894i		−	0.386514i
$958$	−466.897	+	1229.69i	−0.487366	+	1.28361i
$959$			1082.54i			1.12882i
$960$		0			0
$961$	419.222			0.436236
$962$	−436.870	−	165.873i	−0.454127	−	0.172426i
$963$	−993.209			−1.03137
$964$	−303.700	−	269.468i	−0.315042	−	0.279531i
$965$		0			0
$966$	−13.4057	−	5.08997i	−0.0138776	−	0.00526912i
$967$		−	714.006i		−	0.738373i	−0.929355	−	0.369186i	$-0.879636\pi$
$967$		−	714.006i		−	0.738373i	0.929355	−	0.369186i	$-0.120364\pi$
$968$	119.731	+	228.763i	0.123689	+	0.236325i
$969$	−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	$0.408613\pi$
$972$	695.159	+	616.802i	0.715184	+	0.634570i
$973$			1255.17i			1.29000i
$974$	−425.248	+	1120.00i	−0.436599	+	1.14990i
$975$		0			0
$976$	1655.91	−	198.505i	1.69663	−	0.203387i
$977$	−391.158			−0.400366			−0.200183	−	0.979758i	$-0.564154\pi$
$977$	−391.158			−0.400366			−0.200183	+	0.979758i	$0.564154\pi$
$978$	149.683	+	56.8324i	0.153050	+	0.0581108i
$979$	266.941			0.272667
$980$		0			0
$981$		−	443.270i		−	0.451856i
$982$	−152.333	−	57.8388i	−0.155126	−	0.0588990i
$983$			1452.94i			1.47806i	0.673670	+	0.739032i	$0.264717\pi$
$983$			1452.94i			1.47806i	−0.673670	+	0.739032i	$0.735283\pi$
$984$	−73.9571	−	141.305i	−0.0751597	−	0.143603i
$985$		0			0
$986$	−494.933	+	1303.53i	−0.501960	+	1.32204i
$987$	268.715			0.272254
$988$	10.9869	−	12.3827i	0.0111204	−	0.0125331i
$989$		−	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	$-0.0198170\pi$
$992$	722.852	+	179.627i	0.728681	+	0.181076i
$993$	411.729			0.414631
$994$	−1256.93	−	477.239i	−1.26452	−	0.480119i
$995$		0			0
$996$	209.688	+	186.053i	0.210530	+	0.186800i
$997$		−	1235.61i		−	1.23933i	−0.784868	−	0.619663i	$-0.787269\pi$
$997$		−	1235.61i		−	1.23933i	0.784868	−	0.619663i	$-0.212731\pi$
$998$	493.385	+	187.331i	0.494373	+	0.187706i
$999$		−	1114.29i		−	1.11540i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.3.g.a.11.7	✓	8	40.19	odd	2
40.3.g.a.11.8	yes	8	5.4	even	2
160.3.g.a.111.5		8	40.29	even	2
160.3.g.a.111.6		8	20.19	odd	2
200.3.e.d.99.7		16	40.27	even	4
200.3.e.d.99.8		16	5.3	odd	4
200.3.e.d.99.9		16	5.2	odd	4
200.3.e.d.99.10		16	40.3	even	4
200.3.g.g.51.1		8	1.1	even	1	trivial
200.3.g.g.51.2		8	8.3	odd	2	inner
360.3.g.a.91.1		8	15.14	odd	2
360.3.g.a.91.2		8	120.59	even	2
800.3.e.d.399.7		16	20.3	even	4
800.3.e.d.399.8		16	40.13	odd	4
800.3.e.d.399.9		16	40.37	odd	4
800.3.e.d.399.10		16	20.7	even	4
800.3.g.g.751.3		8	4.3	odd	2
800.3.g.g.751.4		8	8.5	even	2
1280.3.b.i.511.7		16	80.59	odd	4
1280.3.b.i.511.8		16	80.29	even	4
1280.3.b.i.511.9		16	80.69	even	4
1280.3.b.i.511.10		16	80.19	odd	4
1440.3.g.a.271.4		8	60.59	even	2
1440.3.g.a.271.5		8	120.29	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 200 = 2^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	200.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.86976 - 0.709922i) q^{2} +1.20470 q^{3} +(2.99202 + 2.65477i) q^{4} +(-2.25250 - 0.855241i) q^{6} +12.3974i q^{7} +(-3.70969 - 7.08789i) q^{8} -7.54870 q^{9} +O(q^{10})\)	\(q+(-1.86976 - 0.709922i) q^{2} +1.20470 q^{3} +(2.99202 + 2.65477i) q^{4} +(-2.25250 - 0.855241i) q^{6} +12.3974i q^{7} +(-3.70969 - 7.08789i) q^{8} -7.54870 q^{9} -9.41939 q^{11} +(3.60448 + 3.19819i) q^{12} -4.18033i q^{13} +(8.80120 - 23.1802i) q^{14} +(1.90440 + 15.8863i) q^{16} -21.3875 q^{17} +(14.1143 + 5.35899i) q^{18} +0.990008 q^{19} +14.9351i q^{21} +(17.6120 + 6.68703i) q^{22} -0.480059i q^{23} +(-4.46906 - 8.53876i) q^{24} +(-2.96771 + 7.81623i) q^{26} -19.9362 q^{27} +(-32.9123 + 37.0934i) q^{28} +32.5969i q^{29} +23.2761i q^{31} +(7.71723 - 31.0555i) q^{32} -11.3475 q^{33} +(39.9895 + 15.1834i) q^{34} +(-22.5859 - 20.0401i) q^{36} +55.8927i q^{37} +(-1.85108 - 0.702828i) q^{38} -5.03604i q^{39} +16.5487 q^{41} +(10.6028 - 27.9252i) q^{42} +57.3157 q^{43} +(-28.1830 - 25.0063i) q^{44} +(-0.340804 + 0.897597i) q^{46} -17.9921i q^{47} +(2.29422 + 19.1381i) q^{48} -104.696 q^{49} -25.7654 q^{51} +(11.0978 - 12.5077i) q^{52} +26.8978i q^{53} +(37.2759 + 14.1531i) q^{54} +(87.8716 - 45.9907i) q^{56} +1.19266 q^{57} +(23.1412 - 60.9485i) q^{58} +76.8224 q^{59} -104.235i q^{61} +(16.5242 - 43.5208i) q^{62} -93.5845i q^{63} +(-36.4764 + 52.5878i) q^{64} +(21.2171 + 8.05584i) q^{66} +2.30211 q^{67} +(-63.9918 - 56.7788i) q^{68} -0.578326i q^{69} -54.2243i q^{71} +(28.0034 + 53.5044i) q^{72} -73.9447 q^{73} +(39.6794 - 104.506i) q^{74} +(2.96213 + 2.62824i) q^{76} -116.776i q^{77} +(-3.57519 + 9.41619i) q^{78} +39.5803i q^{79} +43.9213 q^{81} +(-30.9421 - 11.7483i) q^{82} +58.1742 q^{83} +(-39.6494 + 44.6863i) q^{84} +(-107.167 - 40.6897i) q^{86} +39.2694i q^{87} +(34.9430 + 66.7636i) q^{88} -28.3395 q^{89} +51.8254 q^{91} +(1.27445 - 1.43635i) q^{92} +28.0407i q^{93} +(-12.7730 + 33.6409i) q^{94} +(9.29692 - 37.4125i) q^{96} +4.84731 q^{97} +(195.757 + 74.3261i) q^{98} +71.1042 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} - 8 q^{4} - 12 q^{6} - 8 q^{8} + 24 q^{9}+O(q^{10}) \) 8 * q - 2 * q^2 - 8 * q^4 - 12 * q^6 - 8 * q^8 + 24 * q^9	\( 8 q - 2 q^{2} - 8 q^{4} - 12 q^{6} - 8 q^{8} + 24 q^{9} - 32 q^{11} - 20 q^{12} - 20 q^{14} + 8 q^{16} + 62 q^{18} + 32 q^{19} - 20 q^{22} - 8 q^{24} + 60 q^{26} + 96 q^{27} - 100 q^{28} - 72 q^{32} - 16 q^{33} + 12 q^{34} - 144 q^{36} - 60 q^{38} + 48 q^{41} - 140 q^{42} - 96 q^{43} - 88 q^{44} - 140 q^{46} + 280 q^{48} - 88 q^{49} + 64 q^{51} + 160 q^{52} + 56 q^{54} + 280 q^{56} + 176 q^{57} + 320 q^{58} + 224 q^{59} + 160 q^{62} - 128 q^{64} + 224 q^{66} - 160 q^{67} - 360 q^{68} - 152 q^{72} - 160 q^{73} + 60 q^{74} - 192 q^{76} - 600 q^{78} - 56 q^{81} - 80 q^{82} + 480 q^{83} - 40 q^{84} - 444 q^{86} + 400 q^{88} - 48 q^{89} + 60 q^{92} - 100 q^{94} + 448 q^{96} - 224 q^{97} + 442 q^{98} - 352 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 - 8 * q^4 - 12 * q^6 - 8 * q^8 + 24 * q^9 - 32 * q^11 - 20 * q^12 - 20 * q^14 + 8 * q^16 + 62 * q^18 + 32 * q^19 - 20 * q^22 - 8 * q^24 + 60 * q^26 + 96 * q^27 - 100 * q^28 - 72 * q^32 - 16 * q^33 + 12 * q^34 - 144 * q^36 - 60 * q^38 + 48 * q^41 - 140 * q^42 - 96 * q^43 - 88 * q^44 - 140 * q^46 + 280 * q^48 - 88 * q^49 + 64 * q^51 + 160 * q^52 + 56 * q^54 + 280 * q^56 + 176 * q^57 + 320 * q^58 + 224 * q^59 + 160 * q^62 - 128 * q^64 + 224 * q^66 - 160 * q^67 - 360 * q^68 - 152 * q^72 - 160 * q^73 + 60 * q^74 - 192 * q^76 - 600 * q^78 - 56 * q^81 - 80 * q^82 + 480 * q^83 - 40 * q^84 - 444 * q^86 + 400 * q^88 - 48 * q^89 + 60 * q^92 - 100 * q^94 + 448 * q^96 - 224 * q^97 + 442 * q^98 - 352 * q^99

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