LMFDB - Embedded newform 108.3.d.d.55.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [108,3,Mod(55,108)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(108, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("108.55");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	108.d (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:	$2.94278685509$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.207360000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 6x^{6} + 32x^{4} + 24x^{2} + 16 $ x^8 + 6x^6 + 32x^4 + 24*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			55.8
Root			$-0.437016 + 0.756934i$ of defining polynomial
Character	$\chi$	$=$	108.55
Dual form			108.3.d.d.55.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.85123 + 0.756934i) q^{2} +(2.85410 + 2.80252i) q^{4} +1.08036 q^{5} +6.01392i q^{7} +(3.16228 + 7.34847i) q^{8} +O(q^{10})$	\(q+(1.85123 + 0.756934i) q^{2} +(2.85410 + 2.80252i) q^{4} +1.08036 q^{5} +6.01392i q^{7} +(3.16228 + 7.34847i) q^{8} +(2.00000 + 0.817763i) q^{10} -17.7247i q^{11} +12.4164 q^{13} +(-4.55214 + 11.1331i) q^{14} +(0.291796 + 15.9973i) q^{16} -26.3786 q^{17} +5.19615i q^{19} +(3.08347 + 3.02774i) q^{20} +(13.4164 - 32.8124i) q^{22} -29.8356i q^{23} -23.8328 q^{25} +(22.9856 + 9.39840i) q^{26} +(-16.8541 + 17.1643i) q^{28} +4.32145 q^{29} -44.8403i q^{31} +(-11.5687 + 29.8356i) q^{32} +(-48.8328 - 19.9668i) q^{34} +6.49721i q^{35} -20.4164 q^{37} +(-3.93314 + 9.61927i) q^{38} +(3.41641 + 7.93901i) q^{40} +59.2393 q^{41} +19.1491i q^{43} +(49.6737 - 50.5880i) q^{44} +(22.5836 - 55.2326i) q^{46} +41.0631i q^{47} +12.8328 q^{49} +(-44.1200 - 18.0399i) q^{50} +(35.4377 + 34.7972i) q^{52} -70.0430 q^{53} -19.1491i q^{55} +(-44.1931 + 19.0177i) q^{56} +(8.00000 + 3.27105i) q^{58} +28.9521i q^{59} +18.4164 q^{61} +(33.9411 - 83.0096i) q^{62} +(-44.0000 + 46.4758i) q^{64} +13.4142 q^{65} +94.8767i q^{67} +(-75.2872 - 73.9264i) q^{68} +(-4.91796 + 12.0278i) q^{70} +83.8931i q^{71} +55.8328 q^{73} +(-37.7955 - 15.4539i) q^{74} +(-14.5623 + 14.8303i) q^{76} +106.595 q^{77} -41.0410i q^{79} +(0.315246 + 17.2829i) q^{80} +(109.666 + 44.8403i) q^{82} +35.4493i q^{83} -28.4984 q^{85} +(-14.4946 + 35.4493i) q^{86} +(130.249 - 56.0503i) q^{88} -26.3786 q^{89} +74.6712i q^{91} +(83.6148 - 85.1539i) q^{92} +(-31.0820 + 76.0172i) q^{94} +5.61373i q^{95} +76.3313 q^{97} +(23.7565 + 9.71359i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{4}+O(q^{10}) $ 8 * q - 4 * q^4	$ 8 q - 4 q^{4} + 16 q^{10} - 8 q^{13} + 56 q^{16} + 24 q^{25} - 108 q^{28} - 176 q^{34} - 56 q^{37} - 80 q^{40} + 288 q^{46} - 112 q^{49} + 364 q^{52} + 64 q^{58} + 40 q^{61} - 352 q^{64} - 576 q^{70} + 232 q^{73} - 36 q^{76} + 448 q^{82} + 416 q^{85} + 720 q^{88} + 288 q^{94} - 248 q^{97}+O(q^{100}) $ 8 * q - 4 * q^4 + 16 * q^10 - 8 * q^13 + 56 * q^16 + 24 * q^25 - 108 * q^28 - 176 * q^34 - 56 * q^37 - 80 * q^40 + 288 * q^46 - 112 * q^49 + 364 * q^52 + 64 * q^58 + 40 * q^61 - 352 * q^64 - 576 * q^70 + 232 * q^73 - 36 * q^76 + 448 * q^82 + 416 * q^85 + 720 * q^88 + 288 * q^94 - 248 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$1$	$-1$

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 $

$2$	1.85123	+	0.756934i	0.925615	+	0.378467i
$2$	1.85123	+	0.756934i	0.925615	+	0.378467i
$3$		0			0
$3$		0			0
$4$	2.85410	+	2.80252i	0.713525	+	0.700629i
$5$	1.08036			0.216073			0.108036	−	0.994147i	$-0.465544\pi$
$5$	1.08036			0.216073			0.108036	+	0.994147i	$0.465544\pi$
$6$		0			0
$7$			6.01392i			0.859131i	0.903036	+	0.429565i	$0.141333\pi$
$7$			6.01392i			0.859131i	−0.903036	+	0.429565i	$0.858667\pi$
$8$	3.16228	+	7.34847i	0.395285	+	0.918559i
$9$		0			0
$10$	2.00000	+	0.817763i	0.200000	+	0.0817763i
$11$		−	17.7247i		−	1.61133i	−0.592369	−	0.805667i	$-0.701807\pi$
$11$		−	17.7247i		−	1.61133i	0.592369	−	0.805667i	$-0.298193\pi$
$12$		0			0
$13$	12.4164			0.955108			0.477554	−	0.878602i	$-0.341523\pi$
$13$	12.4164			0.955108			0.477554	+	0.878602i	$0.341523\pi$
$14$	−4.55214	+	11.1331i	−0.325153	+	0.795224i
$15$		0			0
$16$	0.291796	+	15.9973i	0.0182373	+	0.999834i
$17$	−26.3786			−1.55168			−0.775841	−	0.630929i	$-0.782674\pi$
$17$	−26.3786			−1.55168			−0.775841	+	0.630929i	$0.782674\pi$
$18$		0			0
$19$			5.19615i			0.273482i	0.990607	+	0.136741i	$0.0436628\pi$
$19$			5.19615i			0.273482i	−0.990607	+	0.136741i	$0.956337\pi$
$20$	3.08347	+	3.02774i	0.154173	+	0.151387i
$21$		0			0
$22$	13.4164	−	32.8124i	0.609837	−	1.49147i
$23$		−	29.8356i		−	1.29720i	−0.761129	−	0.648600i	$-0.775355\pi$
$23$		−	29.8356i		−	1.29720i	0.761129	−	0.648600i	$-0.224645\pi$
$24$		0			0
$25$	−23.8328			−0.953313
$26$	22.9856	+	9.39840i	0.884062	+	0.361477i
$27$		0			0
$28$	−16.8541	+	17.1643i	−0.601932	+	0.613012i
$29$	4.32145			0.149016			0.0745078	−	0.997220i	$-0.476261\pi$
$29$	4.32145			0.149016			0.0745078	+	0.997220i	$0.476261\pi$
$30$		0			0
$31$		−	44.8403i		−	1.44646i	−0.690607	−	0.723230i	$-0.742657\pi$
$31$		−	44.8403i		−	1.44646i	0.690607	−	0.723230i	$-0.257343\pi$
$32$	−11.5687	+	29.8356i	−0.361523	+	0.932363i
$33$		0			0
$34$	−48.8328	−	19.9668i	−1.43626	−	0.587260i
$35$			6.49721i			0.185635i
$36$		0			0
$37$	−20.4164			−0.551795			−0.275897	−	0.961187i	$-0.588975\pi$
$37$	−20.4164			−0.551795			−0.275897	+	0.961187i	$0.588975\pi$
$38$	−3.93314	+	9.61927i	−0.103504	+	0.253139i
$39$		0			0
$40$	3.41641	+	7.93901i	0.0854102	+	0.198475i
$41$	59.2393			1.44486			0.722431	−	0.691443i	$-0.243025\pi$
$41$	59.2393			1.44486			0.722431	+	0.691443i	$0.243025\pi$
$42$		0			0
$43$			19.1491i			0.445328i	0.974895	+	0.222664i	$0.0714752\pi$
$43$			19.1491i			0.445328i	−0.974895	+	0.222664i	$0.928525\pi$
$44$	49.6737	−	50.5880i	1.12895	−	1.14973i
$45$		0			0
$46$	22.5836	−	55.2326i	0.490948	−	1.20071i
$47$			41.0631i			0.873683i	0.899539	+	0.436841i	$0.143903\pi$
$47$			41.0631i			0.873683i	−0.899539	+	0.436841i	$0.856097\pi$
$48$		0			0
$49$	12.8328			0.261894
$50$	−44.1200	−	18.0399i	−0.882400	−	0.360797i
$51$		0			0
$52$	35.4377	+	34.7972i	0.681494	+	0.669177i
$53$	−70.0430			−1.32157			−0.660783	−	0.750577i	$-0.729776\pi$
$53$	−70.0430			−1.32157			−0.660783	+	0.750577i	$0.729776\pi$
$54$		0			0
$55$		−	19.1491i		−	0.348165i
$56$	−44.1931	+	19.0177i	−0.789162	+	0.339601i
$57$		0			0
$58$	8.00000	+	3.27105i	0.137931	+	0.0563975i
$59$			28.9521i			0.490714i	0.969433	+	0.245357i	$0.0789052\pi$
$59$			28.9521i			0.490714i	−0.969433	+	0.245357i	$0.921095\pi$
$60$		0			0
$61$	18.4164			0.301908			0.150954	−	0.988541i	$-0.451765\pi$
$61$	18.4164			0.301908			0.150954	+	0.988541i	$0.451765\pi$
$62$	33.9411	−	83.0096i	0.547438	−	1.33887i
$63$		0			0
$64$	−44.0000	+	46.4758i	−0.687500	+	0.726184i
$65$	13.4142			0.206373
$66$		0			0
$67$			94.8767i			1.41607i	0.706177	+	0.708035i	$0.250418\pi$
$67$			94.8767i			1.41607i	−0.706177	+	0.708035i	$0.749582\pi$
$68$	−75.2872	−	73.9264i	−1.10716	−	1.08715i
$69$		0			0
$70$	−4.91796	+	12.0278i	−0.0702566	+	0.171826i
$71$			83.8931i			1.18159i	0.806821	+	0.590797i	$0.201186\pi$
$71$			83.8931i			1.18159i	−0.806821	+	0.590797i	$0.798814\pi$
$72$		0			0
$73$	55.8328			0.764833			0.382417	−	0.923990i	$-0.375092\pi$
$73$	55.8328			0.764833			0.382417	+	0.923990i	$0.375092\pi$
$74$	−37.7955	−	15.4539i	−0.510749	−	0.208836i
$75$		0			0
$76$	−14.5623	+	14.8303i	−0.191609	+	0.195136i
$77$	106.595			1.38435
$78$		0			0
$79$		−	41.0410i		−	0.519507i	−0.965675	−	0.259753i	$-0.916359\pi$
$79$		−	41.0410i		−	0.519507i	0.965675	−	0.259753i	$-0.0836413\pi$
$80$	0.315246	+	17.2829i	0.00394057	+	0.216037i
$81$		0			0
$82$	109.666	+	44.8403i	1.33739	+	0.546833i
$83$			35.4493i			0.427101i	0.976932	+	0.213550i	$0.0685027\pi$
$83$			35.4493i			0.427101i	−0.976932	+	0.213550i	$0.931497\pi$
$84$		0			0
$85$	−28.4984			−0.335276
$86$	−14.4946	+	35.4493i	−0.168542	+	0.412202i
$87$		0			0
$88$	130.249	−	56.0503i	1.48010	−	0.636936i
$89$	−26.3786			−0.296389			−0.148194	−	0.988958i	$-0.547346\pi$
$89$	−26.3786			−0.296389			−0.148194	+	0.988958i	$0.547346\pi$
$90$		0			0
$91$			74.6712i			0.820563i
$92$	83.6148	−	85.1539i	0.908857	−	0.925586i
$93$		0			0
$94$	−31.0820	+	76.0172i	−0.330660	+	0.808693i
$95$			5.61373i			0.0590919i
$96$		0			0
$97$	76.3313			0.786920			0.393460	−	0.919342i	$-0.371278\pi$
$97$	76.3313			0.786920			0.393460	+	0.919342i	$0.371278\pi$
$98$	23.7565	+	9.71359i	0.242413	+	0.0991183i
$99$		0			0
$100$	−68.0213	−	66.7919i	−0.680213	−	0.667919i
$101$	72.2037			0.714888			0.357444	−	0.933935i	$-0.383648\pi$
$101$	72.2037			0.714888			0.357444	+	0.933935i	$0.383648\pi$
$102$		0			0
$103$		−	57.9754i		−	0.562868i	−0.959581	−	0.281434i	$-0.909190\pi$
$103$		−	57.9754i		−	0.562868i	0.959581	−	0.281434i	$-0.0908101\pi$
$104$	39.2641	+	91.2416i	0.377540	+	0.877323i
$105$		0			0
$106$	−129.666	−	53.0179i	−1.22326	−	0.500169i
$107$			64.4015i			0.601883i	0.953643	+	0.300942i	$0.0973009\pi$
$107$			64.4015i			0.601883i	−0.953643	+	0.300942i	$0.902699\pi$
$108$		0			0
$109$	−43.1672			−0.396029			−0.198015	−	0.980199i	$-0.563449\pi$
$109$	−43.1672			−0.396029			−0.198015	+	0.980199i	$0.563449\pi$
$110$	14.4946	−	35.4493i	0.131769	−	0.322267i
$111$		0			0
$112$	−96.2067	+	1.75484i	−0.858988	+	0.0156682i
$113$	−81.2965			−0.719438			−0.359719	−	0.933061i	$-0.617127\pi$
$113$	−81.2965			−0.719438			−0.359719	+	0.933061i	$0.617127\pi$
$114$		0			0
$115$		−	32.2333i		−	0.280290i
$116$	12.3339	+	12.1109i	0.106326	+	0.104405i
$117$		0			0
$118$	−21.9149	+	53.5971i	−0.185719	+	0.454212i
$119$		−	158.639i		−	1.33310i
$120$		0			0
$121$	−193.164			−1.59640
$122$	34.0930	+	13.9400i	0.279451	+	0.114262i
$123$		0			0
$124$	125.666	−	127.979i	1.01343	−	1.03209i
$125$	−52.7572			−0.422057
$126$		0			0
$127$		−	191.968i		−	1.51156i	−0.654826	−	0.755780i	$-0.727258\pi$
$127$		−	191.968i		−	1.51156i	0.654826	−	0.755780i	$-0.272742\pi$
$128$	−116.633	+	52.7323i	−0.911197	+	0.411971i
$129$		0			0
$130$	24.8328	+	10.1537i	0.191022	+	0.0781053i
$131$		−	141.797i		−	1.08242i	−0.840887	−	0.541211i	$-0.817966\pi$
$131$		−	141.797i		−	1.08242i	0.840887	−	0.541211i	$-0.182034\pi$
$132$		0			0
$133$	−31.2492			−0.234957
$134$	−71.8154	+	175.639i	−0.535936	+	1.31074i
$135$		0			0
$136$	−83.4164	−	193.842i	−0.613356	−	1.42531i
$137$	−87.7787			−0.640720			−0.320360	−	0.947296i	$-0.603804\pi$
$137$	−87.7787			−0.640720			−0.320360	+	0.947296i	$0.603804\pi$
$138$		0			0
$139$			183.501i			1.32015i	0.751200	+	0.660075i	$0.229476\pi$
$139$			183.501i			1.32015i	−0.751200	+	0.660075i	$0.770524\pi$
$140$	−18.2085	+	18.5437i	−0.130061	+	0.132455i
$141$		0			0
$142$	−63.5016	+	155.305i	−0.447194	+	1.09370i
$143$		−	220.077i		−	1.53900i
$144$		0			0
$145$	4.66874			0.0321982
$146$	103.359	+	42.2618i	0.707941	+	0.289464i
$147$		0			0
$148$	−58.2705	−	57.2173i	−0.393720	−	0.386604i
$149$	−153.950			−1.03322			−0.516611	−	0.856220i	$-0.672807\pi$
$149$	−153.950			−1.03322			−0.516611	+	0.856220i	$0.672807\pi$
$150$		0			0
$151$		−	185.375i		−	1.22765i	−0.789442	−	0.613825i	$-0.789630\pi$
$151$		−	185.375i		−	1.22765i	0.789442	−	0.613825i	$-0.210370\pi$
$152$	−38.1838	+	16.4317i	−0.251209	+	0.108103i
$153$		0			0
$154$	197.331	+	80.6851i	1.28137	+	0.523930i
$155$		−	48.4438i		−	0.312540i
$156$		0			0
$157$	196.164			1.24945			0.624726	−	0.780844i	$-0.285211\pi$
$157$	196.164			1.24945			0.624726	+	0.780844i	$0.285211\pi$
$158$	31.0653	−	75.9764i	0.196616	−	0.480863i
$159$		0			0
$160$	−12.4984	+	32.2333i	−0.0781153	+	0.201458i
$161$	179.429			1.11447
$162$		0			0
$163$			129.325i			0.793403i	0.917948	+	0.396701i	$0.129845\pi$
$163$			129.325i			0.793403i	−0.917948	+	0.396701i	$0.870155\pi$
$164$	169.075	+	166.019i	1.03095	+	1.01231i
$165$		0			0
$166$	−26.8328	+	65.6249i	−0.161643	+	0.395331i
$167$			137.951i			0.826052i	0.910719	+	0.413026i	$0.135528\pi$
$167$			137.951i			0.826052i	−0.910719	+	0.413026i	$0.864472\pi$
$168$		0			0
$169$	−14.8328			−0.0877681
$170$	−52.7572	−	21.5714i	−0.310336	−	0.126891i
$171$		0			0
$172$	−53.6656	+	54.6534i	−0.312009	+	0.317753i
$173$	−160.432			−0.927354			−0.463677	−	0.886004i	$-0.653470\pi$
$173$	−160.432			−0.927354			−0.463677	+	0.886004i	$0.653470\pi$
$174$		0			0
$175$		−	143.329i		−	0.819020i
$176$	283.548	−	5.17199i	1.61107	−	0.0293863i
$177$		0			0
$178$	−48.8328	−	19.9668i	−0.274342	−	0.112173i
$179$		−	201.469i		−	1.12552i	−0.826619	−	0.562762i	$-0.809739\pi$
$179$		−	201.469i		−	1.12552i	0.826619	−	0.562762i	$-0.190261\pi$
$180$		0			0
$181$	−48.2523			−0.266587			−0.133294	−	0.991077i	$-0.542555\pi$
$181$	−48.2523			−0.266587			−0.133294	+	0.991077i	$0.542555\pi$
$182$	−56.5212	+	138.234i	−0.310556	+	0.759525i
$183$		0			0
$184$	219.246	−	94.3485i	1.19155	−	0.512764i
$185$	−22.0571			−0.119228
$186$		0			0
$187$			467.552i			2.50028i
$188$	−115.080	+	117.198i	−0.612128	+	0.623395i
$189$		0			0
$190$	−4.24922	+	10.3923i	−0.0223643	+	0.0546963i
$191$			147.411i			0.771786i	0.922544	+	0.385893i	$0.126107\pi$
$191$			147.411i			0.771786i	−0.922544	+	0.385893i	$0.873893\pi$
$192$		0			0
$193$	25.1641			0.130384			0.0651919	−	0.997873i	$-0.479234\pi$
$193$	25.1641			0.130384			0.0651919	+	0.997873i	$0.479234\pi$
$194$	141.307	+	57.7777i	0.728385	+	0.297823i
$195$		0			0
$196$	36.6262	+	35.9642i	0.186868	+	0.183491i
$197$	385.506			1.95688			0.978441	−	0.206528i	$-0.0662165\pi$
$197$	385.506			1.95688			0.978441	+	0.206528i	$0.0662165\pi$
$198$		0			0
$199$			121.386i			0.609978i	0.952356	+	0.304989i	$0.0986528\pi$
$199$			121.386i			0.609978i	−0.952356	+	0.304989i	$0.901347\pi$
$200$	−75.3660	−	175.135i	−0.376830	−	0.875674i
$201$		0			0
$202$	133.666	+	54.6534i	0.661711	+	0.270562i
$203$			25.9888i			0.128024i
$204$		0			0
$205$	64.0000			0.312195
$206$	43.8836	−	107.326i	0.213027	−	0.520999i
$207$		0			0
$208$	3.62306	+	198.629i	0.0174186	+	0.954949i
$209$	92.1001			0.440670
$210$		0			0
$211$		−	261.631i		−	1.23996i	−0.784619	−	0.619978i	$-0.787141\pi$
$211$		−	261.631i		−	1.23996i	0.784619	−	0.619978i	$-0.212859\pi$
$212$	−199.910	−	196.297i	−0.942971	−	0.925928i
$213$		0			0
$214$	−48.7477	+	119.222i	−0.227793	+	0.557112i
$215$			20.6880i			0.0962231i
$216$		0			0
$217$	269.666			1.24270
$218$	−79.9124	−	32.6747i	−0.366570	−	0.149884i
$219$		0			0
$220$	53.6656	−	54.6534i	0.243935	−	0.248425i
$221$	−327.527			−1.48202
$222$		0			0
$223$		−	70.0542i		−	0.314144i	−0.987587	−	0.157072i	$-0.949794\pi$
$223$		−	70.0542i		−	0.314144i	0.987587	−	0.157072i	$-0.0502056\pi$
$224$	−179.429	−	69.5735i	−0.801022	−	0.310596i
$225$		0			0
$226$	−150.498	−	61.5361i	−0.665922	−	0.272283i
$227$			298.356i			1.31434i	0.753740	+	0.657172i	$0.228248\pi$
$227$			298.356i			1.31434i	−0.753740	+	0.657172i	$0.771752\pi$
$228$		0			0
$229$	259.666			1.13391			0.566956	−	0.823748i	$-0.308121\pi$
$229$	259.666			1.13391			0.566956	+	0.823748i	$0.308121\pi$
$230$	24.3985	−	59.6712i	0.106080	−	0.259440i
$231$		0			0
$232$	13.6656	+	31.7561i	0.0589036	+	0.136880i
$233$	7.38192			0.0316821			0.0158410	−	0.999875i	$-0.494957\pi$
$233$	7.38192			0.0316821			0.0158410	+	0.999875i	$0.494957\pi$
$234$		0			0
$235$			44.3630i			0.188779i
$236$	−81.1389	+	82.6323i	−0.343809	+	0.350137i
$237$		0			0
$238$	120.079	−	293.676i	0.504533	−	1.23393i
$239$			82.1262i			0.343624i	0.985130	+	0.171812i	$0.0549622\pi$
$239$			82.1262i			0.343624i	−0.985130	+	0.171812i	$0.945038\pi$
$240$		0			0
$241$	−415.827			−1.72542			−0.862711	−	0.505698i	$-0.831235\pi$
$241$	−415.827			−1.72542			−0.862711	+	0.505698i	$0.831235\pi$
$242$	−357.591	−	146.212i	−1.47765	−	0.604184i
$243$		0			0
$244$	52.5623	+	51.6123i	0.215419	+	0.211526i
$245$	13.8641			0.0565882
$246$		0			0
$247$			64.5175i			0.261205i
$248$	329.507	−	141.797i	1.32866	−	0.571764i
$249$		0			0
$250$	−97.6656	−	39.9337i	−0.390663	−	0.159735i
$251$			140.030i			0.557890i	0.960307	+	0.278945i	$0.0899847\pi$
$251$			140.030i			0.557890i	−0.960307	+	0.278945i	$0.910015\pi$
$252$		0			0
$253$	−528.827			−2.09022
$254$	145.307	−	355.377i	0.572075	−	1.39912i
$255$		0			0
$256$	−255.830	+	9.33592i	−0.999335	+	0.0364684i
$257$	−66.9825			−0.260632			−0.130316	−	0.991472i	$-0.541599\pi$
$257$	−66.9825			−0.260632			−0.130316	+	0.991472i	$0.541599\pi$
$258$		0			0
$259$		−	122.783i		−	0.474064i
$260$	38.2856	+	37.5936i	0.147252	+	0.144591i
$261$		0			0
$262$	107.331	−	262.500i	0.409661	−	1.00191i
$263$		−	37.2163i		−	0.141507i	−0.997494	−	0.0707534i	$-0.977460\pi$
$263$		−	37.2163i		−	0.141507i	0.997494	−	0.0707534i	$-0.0225404\pi$
$264$		0			0
$265$	−75.6718			−0.285554
$266$	−57.8495	−	23.6536i	−0.217479	−	0.0889233i
$267$		0			0
$268$	−265.894	+	270.788i	−0.992140	+	1.01040i
$269$	279.092			1.03752			0.518758	−	0.854921i	$-0.326395\pi$
$269$	279.092			1.03752			0.518758	+	0.854921i	$0.326395\pi$
$270$		0			0
$271$		−	406.305i		−	1.49928i	−0.661845	−	0.749641i	$-0.730226\pi$
$271$		−	406.305i		−	1.49928i	0.661845	−	0.749641i	$-0.269774\pi$
$272$	−7.69717	−	421.987i	−0.0282984	−	1.55142i
$273$		0			0
$274$	−162.498	−	66.4426i	−0.593060	−	0.242491i
$275$			422.429i			1.53611i
$276$		0			0
$277$	4.83282			0.0174470			0.00872349	−	0.999962i	$-0.497223\pi$
$277$	4.83282			0.0174470			0.00872349	+	0.999962i	$0.497223\pi$
$278$	−138.898	+	339.702i	−0.499633	+	1.22195i
$279$		0			0
$280$	−47.7446	+	20.5460i	−0.170516	+	0.0733785i
$281$	4.32145			0.0153788			0.00768942	−	0.999970i	$-0.497552\pi$
$281$	4.32145			0.0153788			0.00768942	+	0.999970i	$0.497552\pi$
$282$		0			0
$283$			44.3630i			0.156760i	0.996924	+	0.0783799i	$0.0249747\pi$
$283$			44.3630i			0.156760i	−0.996924	+	0.0783799i	$0.975025\pi$
$284$	−235.112	+	239.440i	−0.827859	+	0.843097i
$285$		0			0
$286$	166.584	−	407.413i	0.582460	−	1.42452i
$287$			356.260i			1.24133i
$288$		0			0
$289$	406.830			1.40772
$290$	8.64290	+	3.53393i	0.0298031	+	0.0121860i
$291$		0			0
$292$	159.353	+	156.472i	0.545728	+	0.535864i
$293$	388.927			1.32740			0.663699	−	0.748000i	$-0.268986\pi$
$293$	388.927			1.32740			0.663699	+	0.748000i	$0.268986\pi$
$294$		0			0
$295$			31.2788i			0.106030i
$296$	−64.5624	−	150.029i	−0.218116	−	0.506856i
$297$		0			0
$298$	−284.997	−	116.530i	−0.956365	−	0.391040i
$299$		−	370.451i		−	1.23897i
$300$		0			0
$301$	−115.161			−0.382595
$302$	140.317	−	343.172i	0.464625	−	1.13633i
$303$		0			0
$304$	−83.1246	+	1.51622i	−0.273436	+	0.00498756i
$305$	19.8964			0.0652341
$306$		0			0
$307$			96.6999i			0.314983i	0.987520	+	0.157492i	$0.0503407\pi$
$307$			96.6999i			0.314983i	−0.987520	+	0.157492i	$0.949659\pi$
$308$	304.232	+	298.733i	0.987767	+	0.969914i
$309$		0			0
$310$	36.6687	−	89.6805i	0.118286	−	0.289292i
$311$		−	136.184i		−	0.437890i	−0.975737	−	0.218945i	$-0.929739\pi$
$311$		−	136.184i		−	0.437890i	0.975737	−	0.218945i	$-0.0702615\pi$
$312$		0			0
$313$	282.161			0.901473			0.450736	−	0.892657i	$-0.351161\pi$
$313$	282.161			0.901473			0.450736	+	0.892657i	$0.351161\pi$
$314$	363.145	+	148.483i	1.15651	+	0.472877i
$315$		0			0
$316$	115.018	−	117.135i	0.363982	−	0.370681i
$317$	275.489			0.869051			0.434526	−	0.900659i	$-0.356916\pi$
$317$	275.489			0.869051			0.434526	+	0.900659i	$0.356916\pi$
$318$		0			0
$319$		−	76.5963i		−	0.240114i
$320$	−47.5360	+	50.2107i	−0.148550	+	0.156909i
$321$		0			0
$322$	332.164	+	135.816i	1.03157	+	0.421788i
$323$		−	137.067i		−	0.424356i
$324$		0			0
$325$	−295.918			−0.910517
$326$	−97.8902	+	239.410i	−0.300277	+	0.734385i
$327$		0			0
$328$	187.331	+	435.319i	0.571132	+	1.32719i
$329$	−246.950			−0.750608
$330$		0			0
$331$			55.5221i			0.167741i	0.996477	+	0.0838703i	$0.0267281\pi$
$331$			55.5221i			0.167741i	−0.996477	+	0.0838703i	$0.973272\pi$
$332$	−99.3474	+	101.176i	−0.299239	+	0.304747i
$333$		0			0
$334$	−104.420	+	255.378i	−0.312633	+	0.764606i
$335$			102.501i			0.305974i
$336$		0			0
$337$	−430.659			−1.27792			−0.638961	−	0.769239i	$-0.720635\pi$
$337$	−430.659			−1.27792			−0.638961	+	0.769239i	$0.720635\pi$
$338$	−27.4589	−	11.2275i	−0.0812395	−	0.0332173i
$339$		0			0
$340$	−81.3375	−	79.8674i	−0.239228	−	0.234904i
$341$	−794.779			−2.33073
$342$		0			0
$343$			371.857i			1.08413i
$344$	−140.716	+	60.5547i	−0.409059	+	0.176031i
$345$		0			0
$346$	−296.997	−	121.437i	−0.858373	−	0.350973i
$347$		−	135.871i		−	0.391559i	−0.980648	−	0.195779i	$-0.937276\pi$
$347$		−	135.871i		−	0.391559i	0.980648	−	0.195779i	$-0.0627236\pi$
$348$		0			0
$349$	288.082			0.825450			0.412725	−	0.910856i	$-0.364577\pi$
$349$	288.082			0.825450			0.412725	+	0.910856i	$0.364577\pi$
$350$	108.490	−	265.334i	0.309972	−	0.758097i
$351$		0			0
$352$	528.827	+	205.052i	1.50235	+	0.582535i
$353$	−198.964			−0.563638			−0.281819	−	0.959468i	$-0.590938\pi$
$353$	−198.964			−0.563638			−0.281819	+	0.959468i	$0.590938\pi$
$354$		0			0
$355$			90.6350i			0.255310i
$356$	−75.2872	−	73.9264i	−0.211481	−	0.207659i
$357$		0			0
$358$	152.498	−	372.965i	0.425973	−	1.04180i
$359$		−	324.658i		−	0.904339i	−0.891932	−	0.452170i	$-0.850650\pi$
$359$		−	324.658i		−	0.904339i	0.891932	−	0.452170i	$-0.149350\pi$
$360$		0			0
$361$	334.000			0.925208
$362$	−89.3261	−	36.5238i	−0.246757	−	0.100895i
$363$		0			0
$364$	−209.267	+	213.119i	−0.574910	+	0.585493i
$365$	60.3197			0.165259
$366$		0			0
$367$		−	176.141i		−	0.479948i	−0.970779	−	0.239974i	$-0.922861\pi$
$367$		−	176.141i		−	0.479948i	0.970779	−	0.239974i	$-0.0771390\pi$
$368$	477.290	−	8.70592i	1.29699	−	0.0236574i
$369$		0			0
$370$	−40.8328	−	16.6958i	−0.110359	−	0.0451238i
$371$		−	421.233i		−	1.13540i
$372$		0			0
$373$	596.580			1.59941			0.799706	−	0.600392i	$-0.204989\pi$
$373$	596.580			1.59941			0.799706	+	0.600392i	$0.204989\pi$
$374$	−353.906	+	865.546i	−0.946272	+	2.31429i
$375$		0			0
$376$	−301.751	+	129.853i	−0.802529	+	0.345353i
$377$	53.6569			0.142326
$378$		0			0
$379$		−	30.3082i		−	0.0799689i	−0.999200	−	0.0399844i	$-0.987269\pi$
$379$		−	30.3082i		−	0.0799689i	0.999200	−	0.0399844i	$-0.0127308\pi$
$380$	−15.7326	+	16.0222i	−0.0414015	+	0.0421636i
$381$		0			0
$382$	−111.580	+	272.892i	−0.292096	+	0.714377i
$383$		−	707.220i		−	1.84653i	−0.384167	−	0.923264i	$-0.625511\pi$
$383$		−	707.220i		−	1.84653i	0.384167	−	0.923264i	$-0.374489\pi$
$384$		0			0
$385$	115.161			0.299119
$386$	46.5845	+	19.0475i	0.120685	+	0.0493460i
$387$		0			0
$388$	217.857	+	213.920i	0.561488	+	0.551339i
$389$	−577.088			−1.48352			−0.741758	−	0.670668i	$-0.766008\pi$
$389$	−577.088			−1.48352			−0.741758	+	0.670668i	$0.766008\pi$
$390$		0			0
$391$			787.021i			2.01284i
$392$	40.5809	+	94.3016i	0.103523	+	0.240565i
$393$		0			0
$394$	713.659	+	291.802i	1.81132	+	0.740615i
$395$		−	44.3392i		−	0.112251i
$396$		0			0
$397$	26.8266			0.0675733			0.0337867	−	0.999429i	$-0.489243\pi$
$397$	26.8266			0.0675733			0.0337867	+	0.999429i	$0.489243\pi$
$398$	−91.8809	+	224.713i	−0.230857	+	0.564605i
$399$		0			0
$400$	−6.95432	−	381.262i	−0.0173858	−	0.953154i
$401$	505.065			1.25951			0.629756	−	0.776793i	$-0.283155\pi$
$401$	505.065			1.25951			0.629756	+	0.776793i	$0.283155\pi$
$402$		0			0
$403$		−	556.755i		−	1.38153i
$404$	206.077	+	202.352i	0.510091	+	0.500872i
$405$		0			0
$406$	−19.6718	+	48.1113i	−0.0484528	+	0.118501i
$407$			361.874i			0.889126i
$408$		0			0
$409$	−683.328			−1.67073			−0.835364	−	0.549696i	$-0.814743\pi$
$409$	−683.328			−1.67073			−0.835364	+	0.549696i	$0.814743\pi$
$410$	118.479	+	48.4438i	0.288972	+	0.118156i
$411$		0			0
$412$	162.477	−	165.468i	0.394362	−	0.401621i
$413$	−174.116			−0.421588
$414$		0			0
$415$			38.2982i			0.0922847i
$416$	−143.642	+	370.451i	−0.345294	+	0.890508i
$417$		0			0
$418$	170.498	+	69.7137i	0.407891	+	0.166779i
$419$		−	306.620i		−	0.731791i	−0.930656	−	0.365895i	$-0.880763\pi$
$419$		−	306.620i		−	0.731791i	0.930656	−	0.365895i	$-0.119237\pi$
$420$		0			0
$421$	−18.5867			−0.0441489			−0.0220745	−	0.999756i	$-0.507027\pi$
$421$	−18.5867			−0.0441489			−0.0220745	+	0.999756i	$0.507027\pi$
$422$	198.037	−	484.339i	0.469283	−	1.14772i
$423$		0			0
$424$	−221.495	−	514.709i	−0.522395	−	1.21394i
$425$	628.676			1.47924
$426$		0			0
$427$			110.755i			0.259379i
$428$	−180.486	+	183.808i	−0.421697	+	0.429459i
$429$		0			0
$430$	−15.6594	+	38.2982i	−0.0364173	+	0.0890655i
$431$		−	308.130i		−	0.714918i	−0.933929	−	0.357459i	$-0.883643\pi$
$431$		−	308.130i		−	0.714918i	0.933929	−	0.357459i	$-0.116357\pi$
$432$		0			0
$433$	174.839			0.403785			0.201893	−	0.979408i	$-0.435291\pi$
$433$	174.839			0.403785			0.201893	+	0.979408i	$0.435291\pi$
$434$	499.213	+	204.119i	1.15026	+	0.470320i
$435$		0			0
$436$	−123.204	−	120.977i	−0.282577	−	0.277470i
$437$	155.030			0.354761
$438$		0			0
$439$			480.159i			1.09376i	0.837212	+	0.546878i	$0.184184\pi$
$439$			480.159i			1.09376i	−0.837212	+	0.546878i	$0.815816\pi$
$440$	140.716	−	60.5547i	0.319810	−	0.137624i
$441$		0			0
$442$	−606.328	−	247.917i	−1.37178	−	0.560897i
$443$			555.962i			1.25499i	0.778619	+	0.627497i	$0.215920\pi$
$443$			555.962i			1.25499i	−0.778619	+	0.627497i	$0.784080\pi$
$444$		0			0
$445$	−28.4984			−0.0640415
$446$	53.0264	−	129.686i	0.118893	−	0.290777i
$447$		0			0
$448$	−279.502	−	264.612i	−0.623887	−	0.590652i
$449$	−801.711			−1.78555			−0.892774	−	0.450504i	$-0.851244\pi$
$449$	−801.711			−1.78555			−0.892774	+	0.450504i	$0.851244\pi$
$450$		0			0
$451$		−	1050.00i		−	2.32816i
$452$	−232.028	−	227.835i	−0.513337	−	0.504059i
$453$		0			0
$454$	−225.836	+	552.326i	−0.497436	+	1.21658i
$455$			80.6720i			0.177301i
$456$		0			0
$457$	−137.830			−0.301597			−0.150798	−	0.988565i	$-0.548184\pi$
$457$	−137.830			−0.301597			−0.150798	+	0.988565i	$0.548184\pi$
$458$	480.701	+	196.550i	1.04956	+	0.429148i
$459$		0			0
$460$	90.3344	−	91.9971i	0.196379	−	0.199994i
$461$	188.341			0.408549			0.204274	−	0.978914i	$-0.434517\pi$
$461$	188.341			0.408549			0.204274	+	0.978914i	$0.434517\pi$
$462$		0			0
$463$		−	548.425i		−	1.18450i	−0.805753	−	0.592251i	$-0.798239\pi$
$463$		−	548.425i		−	1.18450i	0.805753	−	0.592251i	$-0.201761\pi$
$464$	1.26098	+	69.1317i	0.00271764	+	0.148991i
$465$		0			0
$466$	13.6656	+	5.58763i	0.0293254	+	0.0119906i
$467$			618.597i			1.32462i	0.749231	+	0.662309i	$0.230423\pi$
$467$			618.597i			1.32462i	−0.749231	+	0.662309i	$0.769577\pi$
$468$		0			0
$469$	−570.580			−1.21659
$470$	−33.5799	+	82.1262i	−0.0714466	+	0.174737i
$471$		0			0
$472$	−212.754	+	91.5547i	−0.450750	+	0.193972i
$473$	339.411			0.717571
$474$		0			0
$475$		−	123.839i		−	0.260714i
$476$	444.587	−	452.771i	0.934007	−	0.951199i
$477$		0			0
$478$	−62.1641	+	152.034i	−0.130050	+	0.318064i
$479$		−	770.425i		−	1.60840i	−0.594357	−	0.804202i	$-0.702593\pi$
$479$		−	770.425i		−	1.60840i	0.594357	−	0.804202i	$-0.297407\pi$
$480$		0			0
$481$	−253.498			−0.527024
$482$	−769.791	−	314.753i	−1.59708	−	0.653015i
$483$		0			0
$484$	−551.310	−	541.346i	−1.13907	−	1.11848i
$485$	82.4655			0.170032
$486$		0			0
$487$			549.208i			1.12774i	0.825865	+	0.563868i	$0.190687\pi$
$487$			549.208i			1.12774i	−0.825865	+	0.563868i	$0.809313\pi$
$488$	58.2378	+	135.332i	0.119340	+	0.277321i
$489$		0			0
$490$	25.6656	+	10.4942i	0.0523788	+	0.0214168i
$491$			23.0256i			0.0468952i	0.999725	+	0.0234476i	$0.00746429\pi$
$491$			23.0256i			0.0468952i	−0.999725	+	0.0234476i	$0.992536\pi$
$492$		0			0
$493$	−113.994			−0.231225
$494$	−48.8355	+	119.437i	−0.0988573	+	0.241775i
$495$		0			0
$496$	717.325	−	13.0842i	1.44622	−	0.0263795i
$497$	−504.526			−1.01514
$498$		0			0
$499$		−	626.809i		−	1.25613i	−0.778160	−	0.628065i	$-0.783847\pi$
$499$		−	626.809i		−	1.25613i	0.778160	−	0.628065i	$-0.216153\pi$
$500$	−150.574	−	147.853i	−0.301149	−	0.295706i
$501$		0			0
$502$	−105.994	+	259.228i	−0.211143	+	0.516391i
$503$			732.896i			1.45705i	0.685019	+	0.728525i	$0.259794\pi$
$503$			732.896i			1.45705i	−0.685019	+	0.728525i	$0.740206\pi$
$504$		0			0
$505$	78.0062			0.154468
$506$	−978.979	−	400.287i	−1.93474	−	0.791081i
$507$		0			0
$508$	537.994	−	547.896i	1.05904	−	1.07854i
$509$	437.363			0.859259			0.429630	−	0.903005i	$-0.358644\pi$
$509$	437.363			0.859259			0.429630	+	0.903005i	$0.358644\pi$
$510$		0			0
$511$			335.774i			0.657092i
$512$	−480.666	−	176.363i	−0.938801	−	0.344459i
$513$		0			0
$514$	−124.000	−	50.7013i	−0.241245	−	0.0986407i
$515$		−	62.6345i		−	0.121620i
$516$		0			0
$517$	727.830			1.40779
$518$	92.9383	−	227.299i	0.179418	−	0.438801i
$519$		0			0
$520$	42.4195	+	98.5740i	0.0815760	+	0.189565i
$521$	−385.236			−0.739417			−0.369709	−	0.929148i	$-0.620542\pi$
$521$	−385.236			−0.739417			−0.369709	+	0.929148i	$0.620542\pi$
$522$		0			0
$523$			418.572i			0.800328i	0.916443	+	0.400164i	$0.131047\pi$
$523$			418.572i			0.800328i	−0.916443	+	0.400164i	$0.868953\pi$
$524$	397.390	−	404.704i	0.758377	−	0.772336i
$525$		0			0
$526$	28.1703	−	68.8959i	0.0535557	−	0.130981i
$527$			1182.82i			2.24445i
$528$		0			0
$529$	−361.164			−0.682730
$530$	−140.086	−	57.2786i	−0.264313	−	0.108073i
$531$		0			0
$532$	−89.1885	−	87.5765i	−0.167648	−	0.164617i
$533$	735.540			1.38000
$534$		0			0
$535$			69.5770i			0.130050i
$536$	−697.199	+	300.026i	−1.30074	+	0.559751i
$537$		0			0
$538$	516.663	+	211.254i	0.960339	+	0.392665i
$539$		−	227.457i		−	0.421999i
$540$		0			0
$541$	−23.4257			−0.0433008			−0.0216504	−	0.999766i	$-0.506892\pi$
$541$	−23.4257			−0.0433008			−0.0216504	+	0.999766i	$0.506892\pi$
$542$	307.546	−	752.164i	0.567429	−	1.38776i
$543$		0			0
$544$	305.167	−	787.021i	0.560969	−	1.44673i
$545$	−46.6362			−0.0855711
$546$		0			0
$547$		−	722.163i		−	1.32023i	−0.751167	−	0.660113i	$-0.770509\pi$
$547$		−	722.163i		−	1.32023i	0.751167	−	0.660113i	$-0.229491\pi$
$548$	−250.529	−	246.001i	−0.457170	−	0.448907i
$549$		0			0
$550$	−319.751	+	782.013i	−0.581365	+	1.42184i
$551$			22.4549i			0.0407530i
$552$		0			0
$553$	246.817			0.446324
$554$	8.94665	+	3.65812i	0.0161492	+	0.00660311i
$555$		0			0
$556$	−514.264	+	523.730i	−0.924936	+	0.941961i
$557$	−2.34135			−0.00420349			−0.00210175	−	0.999998i	$-0.500669\pi$
$557$	−2.34135			−0.00420349			−0.00210175	+	0.999998i	$0.500669\pi$
$558$		0			0
$559$			237.763i			0.425336i
$560$	−103.938	+	1.89586i	−0.185604	+	0.00338547i
$561$		0			0
$562$	8.00000	+	3.27105i	0.0142349	+	0.00582038i
$563$		−	359.794i		−	0.639066i	−0.947575	−	0.319533i	$-0.896474\pi$
$563$		−	359.794i		−	0.639066i	0.947575	−	0.319533i	$-0.103526\pi$
$564$		0			0
$565$	−87.8297			−0.155451
$566$	−33.5799	+	82.1262i	−0.0593284	+	0.145099i
$567$		0			0
$568$	−616.486	+	265.293i	−1.08536	+	0.467066i
$569$	18.6354			0.0327512			0.0163756	−	0.999866i	$-0.494787\pi$
$569$	18.6354			0.0327512			0.0163756	+	0.999866i	$0.494787\pi$
$570$		0			0
$571$			284.528i			0.498298i	0.968465	+	0.249149i	$0.0801509\pi$
$571$			284.528i			0.498298i	−0.968465	+	0.249149i	$0.919849\pi$
$572$	616.769	−	628.122i	1.07827	−	1.09811i
$573$		0			0
$574$	−269.666	+	659.520i	−0.469801	+	1.14899i
$575$			711.067i			1.23664i
$576$		0			0
$577$	664.823			1.15221			0.576104	−	0.817377i	$-0.304572\pi$
$577$	664.823			1.15221			0.576104	+	0.817377i	$0.304572\pi$
$578$	753.135	+	307.943i	1.30300	+	0.532774i
$579$		0			0
$580$	13.3251	+	13.0842i	0.0229742	+	0.0225590i
$581$	−213.189			−0.366935
$582$		0			0
$583$			1241.49i			2.12948i
$584$	176.559	+	410.286i	0.302327	+	0.702544i
$585$		0			0
$586$	719.994	+	294.392i	1.22866	+	0.502376i
$587$			754.467i			1.28529i	0.766162	+	0.642647i	$0.222164\pi$
$587$			754.467i			1.28529i	−0.766162	+	0.642647i	$0.777836\pi$
$588$		0			0
$589$	232.997			0.395580
$590$	−23.6760	+	57.9043i	−0.0401288	+	0.0981428i
$591$		0			0
$592$	−5.95743	−	326.608i	−0.0100632	−	0.551703i
$593$	550.801			0.928838			0.464419	−	0.885615i	$-0.346263\pi$
$593$	550.801			0.928838			0.464419	+	0.885615i	$0.346263\pi$
$594$		0			0
$595$		−	171.387i		−	0.288046i
$596$	−439.389	−	431.448i	−0.737230	−	0.723905i
$597$		0			0
$598$	280.407	−	685.790i	0.468908	−	1.14681i
$599$			25.9888i			0.0433871i	0.999765	+	0.0216935i	$0.00690581\pi$
$599$			25.9888i			0.0433871i	−0.999765	+	0.0216935i	$0.993094\pi$
$600$		0			0
$601$	186.170			0.309768			0.154884	−	0.987933i	$-0.450500\pi$
$601$	186.170			0.309768			0.154884	+	0.987933i	$0.450500\pi$
$602$	−213.189	−	87.1693i	−0.354135	−	0.144799i
$603$		0			0
$604$	519.517	−	529.079i	0.860127	−	0.875959i
$605$	−208.687			−0.344938
$606$		0			0
$607$		−	99.5447i		−	0.163994i	−0.996633	−	0.0819972i	$-0.973870\pi$
$607$		−	99.5447i		−	0.163994i	0.996633	−	0.0819972i	$-0.0261299\pi$
$608$	−155.030	−	60.1130i	−0.254984	−	0.0988700i
$609$		0			0
$610$	36.8328	+	15.0603i	0.0603817	+	0.0246890i
$611$			509.856i			0.834461i
$612$		0			0
$613$	−960.234			−1.56645			−0.783225	−	0.621739i	$-0.786427\pi$
$613$	−960.234			−1.56645			−0.783225	+	0.621739i	$0.786427\pi$
$614$	−73.1954	+	179.014i	−0.119211	+	0.291553i
$615$		0			0
$616$	337.082	+	783.308i	0.547211	+	1.27160i
$617$	354.625			0.574757			0.287378	−	0.957817i	$-0.407216\pi$
$617$	354.625			0.574757			0.287378	+	0.957817i	$0.407216\pi$
$618$		0			0
$619$			360.647i			0.582629i	0.956627	+	0.291314i	$0.0940926\pi$
$619$			360.647i			0.582629i	−0.956627	+	0.291314i	$0.905907\pi$
$620$	135.765	−	138.263i	0.218975	−	0.223006i
$621$		0			0
$622$	103.082	−	252.107i	0.165727	−	0.405317i
$623$		−	158.639i		−	0.254637i
$624$		0			0
$625$	538.823			0.862118
$626$	522.345	+	213.577i	0.834417	+	0.341178i
$627$		0			0
$628$	559.872	+	549.753i	0.891516	+	0.875403i
$629$	538.556			0.856210
$630$		0			0
$631$			82.7121i			0.131081i	0.997850	+	0.0655405i	$0.0208772\pi$
$631$			82.7121i			0.131081i	−0.997850	+	0.0655405i	$0.979123\pi$
$632$	301.589	−	129.783i	0.477197	−	0.205353i
$633$		0			0
$634$	509.994	+	208.527i	0.804407	+	0.328907i
$635$		−	207.395i		−	0.326607i
$636$		0			0
$637$	159.337			0.250137
$638$	57.9784	−	141.797i	0.0908752	−	0.222253i
$639$		0			0
$640$	−126.006	+	56.9700i	−0.196885	+	0.0890156i
$641$	760.569			1.18653			0.593267	−	0.805005i	$-0.297838\pi$
$641$	760.569			1.18653			0.593267	+	0.805005i	$0.297838\pi$
$642$		0			0
$643$		−	787.021i		−	1.22398i	−0.790864	−	0.611992i	$-0.790369\pi$
$643$		−	787.021i		−	1.22398i	0.790864	−	0.611992i	$-0.209631\pi$
$644$	512.108	+	502.853i	0.795199	+	0.780827i
$645$		0			0
$646$	103.751	−	253.743i	0.160605	−	0.392791i
$647$		−	978.962i		−	1.51308i	−0.653948	−	0.756539i	$-0.726889\pi$
$647$		−	978.962i		−	1.51308i	0.653948	−	0.756539i	$-0.273111\pi$
$648$		0			0
$649$	513.167			0.790704
$650$	−547.812	−	223.990i	−0.842788	−	0.344601i
$651$		0			0
$652$	−362.435	+	369.106i	−0.555881	+	0.566113i
$653$	−939.548			−1.43882			−0.719409	−	0.694587i	$-0.755587\pi$
$653$	−939.548			−1.43882			−0.719409	+	0.694587i	$0.755587\pi$
$654$		0			0
$655$		−	153.193i		−	0.233882i
$656$	17.2858	+	947.672i	0.0263503	+	1.44462i
$657$		0			0
$658$	−457.161	−	186.925i	−0.694774	−	0.284080i
$659$		−	149.491i		−	0.226845i	−0.993547	−	0.113423i	$-0.963819\pi$
$659$		−	149.491i		−	0.226845i	0.993547	−	0.113423i	$-0.0361814\pi$
$660$		0			0
$661$	337.420			0.510468			0.255234	−	0.966879i	$-0.417847\pi$
$661$	337.420			0.510468			0.255234	+	0.966879i	$0.417847\pi$
$662$	−42.0266	+	102.784i	−0.0634843	+	0.155263i
$663$		0			0
$664$	−260.498	+	112.101i	−0.392317	+	0.168826i
$665$	−33.7605			−0.0507677
$666$		0			0
$667$		−	128.933i		−	0.193303i
$668$	−386.609	+	393.725i	−0.578756	+	0.589409i
$669$		0			0
$670$	−77.5867	+	189.753i	−0.115801	+	0.283214i
$671$		−	326.425i		−	0.486475i
$672$		0			0
$673$	−321.341			−0.477475			−0.238737	−	0.971084i	$-0.576734\pi$
$673$	−321.341			−0.477475			−0.238737	+	0.971084i	$0.576734\pi$
$674$	−797.249	−	325.981i	−1.18286	−	0.483651i
$675$		0			0
$676$	−42.3344	−	41.5692i	−0.0626248	−	0.0614929i
$677$	−741.841			−1.09578			−0.547889	−	0.836551i	$-0.684568\pi$
$677$	−741.841			−1.09578			−0.547889	+	0.836551i	$0.684568\pi$
$678$		0			0
$679$			459.050i			0.676067i
$680$	−90.1200	−	209.420i	−0.132529	−	0.307971i
$681$		0			0
$682$	−1471.32	−	601.595i	−2.15736	−	0.882105i
$683$		−	1259.02i		−	1.84337i	−0.387938	−	0.921686i	$-0.626812\pi$
$683$		−	1259.02i		−	1.84337i	0.387938	−	0.921686i	$-0.373188\pi$
$684$		0			0
$685$	−94.8328			−0.138442
$686$	−281.471	+	688.393i	−0.410308	+	1.00349i
$687$		0			0
$688$	−306.334	+	5.58763i	−0.445253	+	0.00812155i
$689$	−869.682			−1.26224
$690$		0			0
$691$		−	222.770i		−	0.322387i	−0.986923	−	0.161194i	$-0.948466\pi$
$691$		−	222.770i		−	0.322387i	0.986923	−	0.161194i	$-0.0515344\pi$
$692$	−457.890	−	449.614i	−0.661691	−	0.649731i
$693$		0			0
$694$	102.845	−	251.528i	0.148192	−	0.362432i
$695$			198.248i			0.285248i
$696$		0			0
$697$	−1562.65			−2.24197
$698$	533.306	+	218.059i	0.764049	+	0.312406i
$699$		0			0
$700$	401.681	−	409.074i	0.573830	−	0.584392i
$701$	−2.34135			−0.00334001			−0.00167000	−	0.999999i	$-0.500532\pi$
$701$	−2.34135			−0.00334001			−0.00167000	+	0.999999i	$0.500532\pi$
$702$		0			0
$703$		−	106.087i		−	0.150906i
$704$	823.768	+	779.886i	1.17013	+	1.10779i
$705$		0			0
$706$	−368.328	−	150.603i	−0.521711	−	0.213318i
$707$			434.227i			0.614182i
$708$		0			0
$709$	−495.085			−0.698287			−0.349143	−	0.937069i	$-0.613527\pi$
$709$	−495.085			−0.698287			−0.349143	+	0.937069i	$0.613527\pi$
$710$	−68.6047	+	167.786i	−0.0966264	+	0.236319i
$711$		0			0
$712$	−83.4164	−	193.842i	−0.117158	−	0.272250i
$713$	−1337.84			−1.87635
$714$		0			0
$715$		−	237.763i		−	0.332535i
$716$	564.619	−	575.012i	0.788574	−	0.803089i
$717$		0			0
$718$	245.745	−	601.016i	0.342263	−	0.837070i
$719$		−	962.433i		−	1.33857i	−0.743005	−	0.669286i	$-0.766600\pi$
$719$		−	962.433i		−	1.33857i	0.743005	−	0.669286i	$-0.233400\pi$
$720$		0			0
$721$	348.659			0.483578
$722$	618.311	+	252.816i	0.856386	+	0.350161i
$723$		0			0
$724$	−137.717	−	135.228i	−0.190217	−	0.186779i
$725$	−102.992			−0.142058
$726$		0			0
$727$		−	544.625i		−	0.749141i	−0.927198	−	0.374570i	$-0.877790\pi$
$727$		−	544.625i		−	0.749141i	0.927198	−	0.374570i	$-0.122210\pi$
$728$	−548.719	+	236.131i	−0.753735	+	0.324356i
$729$		0			0
$730$	111.666	+	45.6580i	0.152967	+	0.0625453i
$731$		−	505.126i		−	0.691006i
$732$		0			0
$733$	−146.170			−0.199414			−0.0997069	−	0.995017i	$-0.531791\pi$
$733$	−146.170			−0.199414			−0.0997069	+	0.995017i	$0.531791\pi$
$734$	133.327	−	326.077i	0.181645	−	0.444247i
$735$		0			0
$736$	890.164	+	345.161i	1.20946	+	0.468968i
$737$	1681.66			2.28176
$738$		0			0
$739$		−	1172.87i		−	1.58710i	−0.608505	−	0.793550i	$-0.708231\pi$
$739$		−	1172.87i		−	1.58710i	0.608505	−	0.793550i	$-0.291769\pi$
$740$	−62.9533	−	61.8155i	−0.0850720	−	0.0835344i
$741$		0			0
$742$	318.845	−	779.798i	0.429711	−	1.05094i
$743$		−	494.837i		−	0.665998i	−0.942927	−	0.332999i	$-0.891939\pi$
$743$		−	494.837i		−	0.665998i	0.942927	−	0.332999i	$-0.108061\pi$
$744$		0			0
$745$	−166.322			−0.223251
$746$	1104.41	+	451.572i	1.48044	+	0.605324i
$747$		0			0
$748$	−1310.32	+	1334.44i	−1.75177	+	1.78401i
$749$	−387.305			−0.517096
$750$		0			0
$751$			927.250i			1.23469i	0.786693	+	0.617344i	$0.211791\pi$
$751$			927.250i			1.23469i	−0.786693	+	0.617344i	$0.788209\pi$
$752$	−656.900	+	11.9820i	−0.873537	+	0.0159336i
$753$		0			0
$754$	99.3313	+	40.6147i	0.131739	+	0.0538657i
$755$		−	200.272i		−	0.265261i
$756$		0			0
$757$	−757.748			−1.00099			−0.500494	−	0.865740i	$-0.666848\pi$
$757$	−757.748			−1.00099			−0.500494	+	0.865740i	$0.666848\pi$
$758$	22.9413	−	56.1074i	0.0302656	−	0.0740204i
$759$		0			0
$760$	−41.2523	+	17.7522i	−0.0542794	+	0.0233581i
$761$	−953.139			−1.25248			−0.626241	−	0.779629i	$-0.715408\pi$
$761$	−953.139			−1.25248			−0.626241	+	0.779629i	$0.715408\pi$
$762$		0			0
$763$		−	259.604i		−	0.340241i
$764$	−413.122	+	420.726i	−0.540736	+	0.550689i
$765$		0			0
$766$	535.319	−	1309.23i	0.698850	−	1.70917i
$767$			359.482i			0.468685i
$768$		0			0
$769$	145.675			0.189434			0.0947171	−	0.995504i	$-0.469805\pi$
$769$	145.675			0.189434			0.0947171	+	0.995504i	$0.469805\pi$
$770$	213.189	+	87.1693i	0.276869	+	0.113207i
$771$		0			0
$772$	71.8208	+	70.5228i	0.0930322	+	0.0913507i
$773$	−60.1391			−0.0777996			−0.0388998	−	0.999243i	$-0.512385\pi$
$773$	−60.1391			−0.0777996			−0.0388998	+	0.999243i	$0.512385\pi$
$774$		0			0
$775$			1068.67i			1.37893i
$776$	241.381	+	560.918i	0.311058	+	0.722832i
$777$		0			0
$778$	−1068.32	−	436.817i	−1.37316	−	0.561462i
$779$			307.817i			0.395143i
$780$		0			0
$781$	1486.98			1.90394
$782$	−595.723	+	1456.96i	−0.761794	+	1.86312i
$783$		0			0
$784$	3.74457	+	205.291i	0.00477623	+	0.261851i
$785$	211.928			0.269973
$786$		0			0
$787$		−	328.312i		−	0.417169i	−0.978004	−	0.208585i	$-0.933114\pi$
$787$		−	328.312i		−	0.417169i	0.978004	−	0.208585i	$-0.0668856\pi$
$788$	1100.27	+	1080.39i	1.39628	+	1.37105i
$789$		0			0
$790$	33.5619	−	82.0821i	0.0424834	−	0.103901i
$791$		−	488.910i		−	0.618091i
$792$		0			0
$793$	228.666			0.288355
$794$	49.6622	+	20.3060i	0.0625469	+	0.0255743i
$795$		0			0
$796$	−340.185	+	346.447i	−0.427369	+	0.435235i
$797$	446.725			0.560508			0.280254	−	0.959926i	$-0.409581\pi$
$797$	446.725			0.560508			0.280254	+	0.959926i	$0.409581\pi$
$798$		0			0
$799$		−	1083.19i		−	1.35568i
$800$	275.716	−	711.067i	0.344645	−	0.888833i
$801$		0			0
$802$	934.991	+	382.301i	1.16582	+	0.476684i
$803$		−	989.618i		−	1.23240i
$804$		0			0
$805$	193.848			0.240805
$806$	421.427	−	1030.68i	0.522862	−	1.27876i
$807$		0			0
$808$	228.328	+	530.587i	0.282584	+	0.656667i
$809$	793.341			0.980644			0.490322	−	0.871541i	$-0.336879\pi$
$809$	793.341			0.980644			0.490322	+	0.871541i	$0.336879\pi$
$810$		0			0
$811$			788.930i			0.972787i	0.873740	+	0.486394i	$0.161688\pi$
$811$			788.930i			0.972787i	−0.873740	+	0.486394i	$0.838312\pi$
$812$	−72.8342	+	74.1748i	−0.0896973	+	0.0913483i
$813$		0			0
$814$	−273.915	+	669.912i	−0.336505	+	0.822988i
$815$			139.718i			0.171433i
$816$		0			0
$817$	−99.5016			−0.121789
$818$	−1265.00	−	517.234i	−1.54645	−	0.632316i
$819$		0			0
$820$	182.663	+	179.361i	0.222759	+	0.218733i
$821$	1448.75			1.76462			0.882310	−	0.470668i	$-0.155987\pi$
$821$	1448.75			1.76462			0.882310	+	0.470668i	$0.155987\pi$
$822$		0			0
$823$			129.939i			0.157884i	0.996879	+	0.0789421i	$0.0251542\pi$
$823$			129.939i			0.157884i	−0.996879	+	0.0789421i	$0.974846\pi$
$824$	426.031	−	183.334i	0.517028	−	0.222493i
$825$		0			0
$826$	−322.328	−	131.794i	−0.390228	−	0.159557i
$827$			350.389i			0.423687i	0.977304	+	0.211843i	$0.0679467\pi$
$827$			350.389i			0.423687i	−0.977304	+	0.211843i	$0.932053\pi$
$828$		0			0
$829$	167.748			0.202349			0.101175	−	0.994869i	$-0.467740\pi$
$829$	167.748			0.202349			0.101175	+	0.994869i	$0.467740\pi$
$830$	−28.9892	+	70.8987i	−0.0349267	+	0.0854201i
$831$		0			0
$832$	−546.322	+	577.062i	−0.656637	+	0.693585i
$833$	−338.512			−0.406376
$834$		0			0
$835$			149.037i			0.178487i
$836$	262.863	+	258.112i	0.314430	+	0.308747i
$837$		0			0
$838$	232.091	−	567.625i	0.276959	−	0.677356i
$839$			661.684i			0.788658i	0.918969	+	0.394329i	$0.129023\pi$
$839$			661.684i			0.788658i	−0.918969	+	0.394329i	$0.870977\pi$
$840$		0			0
$841$	−822.325			−0.977794
$842$	−34.4082	−	14.0689i	−0.0408649	−	0.0167089i
$843$		0			0
$844$	733.225	−	746.721i	0.868750	−	0.884741i
$845$	−16.0248			−0.0189643
$846$		0			0
$847$		−	1161.67i		−	1.37151i
$848$	−20.4383	−	1120.50i	−0.0241017	−	1.32135i
$849$		0			0
$850$	1163.82	+	475.866i	1.36920	+	0.559843i
$851$			609.136i			0.715789i
$852$		0			0
$853$	17.0789			0.0200222			0.0100111	−	0.999950i	$-0.496813\pi$
$853$	17.0789			0.0200222			0.0100111	+	0.999950i	$0.496813\pi$
$854$	−83.8340	+	205.032i	−0.0981663	+	0.240085i
$855$		0			0
$856$	−473.252	+	203.655i	−0.552865	+	0.237915i
$857$	−422.419			−0.492904			−0.246452	−	0.969155i	$-0.579265\pi$
$857$	−422.419			−0.492904			−0.246452	+	0.969155i	$0.579265\pi$
$858$		0			0
$859$			1323.18i			1.54037i	0.637819	+	0.770186i	$0.279837\pi$
$859$			1323.18i			1.54037i	−0.637819	+	0.770186i	$0.720163\pi$
$860$	−57.9784	+	59.0456i	−0.0674167	+	0.0686576i
$861$		0			0
$862$	233.234	−	570.418i	0.270573	−	0.661738i
$863$			1455.50i			1.68656i	0.537473	+	0.843281i	$0.319379\pi$
$863$			1455.50i			1.68656i	−0.537473	+	0.843281i	$0.680621\pi$
$864$		0			0
$865$	−173.325			−0.200376
$866$	323.667	+	132.342i	0.373750	+	0.152819i
$867$		0			0
$868$	769.653	+	755.743i	0.886697	+	0.870671i
$869$	−727.439			−0.837099
$870$		0			0
$871$			1178.03i			1.35250i
$872$	−136.507	−	317.213i	−0.156544	−	0.363776i
$873$		0			0
$874$	286.997	+	117.348i	0.328372	+	0.134265i
$875$		−	317.277i		−	0.362602i
$876$		0			0
$877$	−753.085			−0.858706			−0.429353	−	0.903137i	$-0.641258\pi$
$877$	−753.085			−0.858706			−0.429353	+	0.903137i	$0.641258\pi$
$878$	−363.448	+	888.884i	−0.413950	+	1.01240i
$879$		0			0
$880$	306.334	−	5.58763i	0.348107	−	0.00634958i
$881$	−996.177			−1.13073			−0.565367	−	0.824839i	$-0.691265\pi$
$881$	−996.177			−1.13073			−0.565367	+	0.824839i	$0.691265\pi$
$882$		0			0
$883$			950.011i			1.07589i	0.842980	+	0.537945i	$0.180799\pi$
$883$			950.011i			1.07589i	−0.842980	+	0.537945i	$0.819201\pi$
$884$	−934.796	−	917.901i	−1.05746	−	1.03835i
$885$		0			0
$886$	−420.827	+	1029.21i	−0.474974	+	1.16164i
$887$		−	433.086i		−	0.488259i	−0.969743	−	0.244129i	$-0.921498\pi$
$887$		−	433.086i		−	0.488259i	0.969743	−	0.244129i	$-0.0785022\pi$
$888$		0			0
$889$	1154.48			1.29863
$890$	−52.7572	−	21.5714i	−0.0592777	−	0.0242376i
$891$		0			0
$892$	196.328	−	199.942i	0.220099	−	0.224150i
$893$	−213.370			−0.238936
$894$		0			0
$895$		−	217.659i		−	0.243195i
$896$	−317.128	−	701.422i	−0.353937	−	0.782837i
$897$		0			0
$898$	−1484.15	−	606.842i	−1.65273	−	0.675771i
$899$		−	193.775i		−	0.215545i
$900$		0			0
$901$	1847.63			2.05065
$902$	794.779	−	1943.79i	0.881130	−	2.15498i
$903$		0			0
$904$	−257.082	−	597.405i	−0.284383	−	0.660846i
$905$	−52.1300			−0.0576022
$906$		0			0
$907$			685.704i			0.756014i	0.925803	+	0.378007i	$0.123390\pi$
$907$			685.704i			0.756014i	−0.925803	+	0.378007i	$0.876610\pi$
$908$	−836.148	+	851.539i	−0.920868	+	0.937818i
$909$		0			0
$910$	−61.0634	+	149.342i	−0.0671026	+	0.164113i
$911$			36.0750i			0.0395994i	0.999804	+	0.0197997i	$0.00630285\pi$
$911$			36.0750i			0.0395994i	−0.999804	+	0.0197997i	$0.993697\pi$
$912$		0			0
$913$	628.328			0.688202
$914$	−255.154	−	104.328i	−0.279162	−	0.114144i
$915$		0			0
$916$	741.112	+	727.717i	0.809074	+	0.794451i
$917$	852.758			0.929943
$918$		0			0
$919$		−	953.775i		−	1.03784i	−0.854823	−	0.518920i	$-0.826334\pi$
$919$		−	953.775i		−	1.03784i	0.854823	−	0.518920i	$-0.173666\pi$
$920$	236.865	−	101.931i	0.257462	−	0.110794i
$921$		0			0
$922$	348.663	+	142.562i	0.378159	+	0.154622i
$923$			1041.65i			1.12855i
$924$		0			0
$925$	486.580			0.526033
$926$	415.121	−	1015.26i	0.448295	−	1.09639i
$927$		0			0
$928$	−49.9938	+	128.933i	−0.0538726	+	0.138937i
$929$	149.629			0.161064			0.0805321	−	0.996752i	$-0.474338\pi$
$929$	149.629			0.161064			0.0805321	+	0.996752i	$0.474338\pi$
$930$		0			0
$931$			66.6813i			0.0716233i
$932$	21.0688	+	20.6880i	0.0226060	+	0.0221974i
$933$		0			0
$934$	−468.237	+	1145.16i	−0.501324	+	1.22609i
$935$			505.126i			0.540241i
$936$		0			0
$937$	−661.158			−0.705611			−0.352806	−	0.935697i	$-0.614772\pi$
$937$	−661.158			−0.705611			−0.352806	+	0.935697i	$0.614772\pi$
$938$	−1056.28	−	431.892i	−1.12609	−	0.460439i
$939$		0			0
$940$	−124.328	+	126.617i	−0.132264	+	0.134699i
$941$	466.713			0.495976			0.247988	−	0.968763i	$-0.420231\pi$
$941$	466.713			0.495976			0.247988	+	0.968763i	$0.420231\pi$
$942$		0			0
$943$		−	1767.44i		−	1.87428i
$944$	−463.157	+	8.44812i	−0.490633	+	0.00894928i
$945$		0			0
$946$	628.328	+	256.912i	0.664195	+	0.271577i
$947$			1302.74i			1.37565i	0.725879	+	0.687823i	$0.241433\pi$
$947$			1302.74i			1.37565i	−0.725879	+	0.687823i	$0.758567\pi$
$948$		0			0
$949$	693.243			0.730498
$950$	93.7379	−	229.254i	0.0986715	−	0.241320i
$951$		0			0
$952$	1165.75	−	501.659i	1.22453	−	0.526953i
$953$	21.6959			0.0227659			0.0113829	−	0.999935i	$-0.496377\pi$
$953$	21.6959			0.0227659			0.0113829	+	0.999935i	$0.496377\pi$
$954$		0			0
$955$			159.258i			0.166762i
$956$	−230.160	+	234.396i	−0.240753	+	0.245185i
$957$		0			0
$958$	583.161	−	1426.23i	0.608728	−	1.48876i
$959$		−	527.893i		−	0.550462i
$960$		0			0
$961$	−1049.65			−1.09225
$962$	−469.284	−	191.882i	−0.487821	−	0.199461i
$963$		0			0
$964$	−1186.81	−	1165.36i	−1.23113	−	1.20888i
$965$	27.1863			0.0281724
$966$		0			0
$967$			640.899i			0.662770i	0.943496	+	0.331385i	$0.107516\pi$
$967$			640.899i			0.662770i	−0.943496	+	0.331385i	$0.892484\pi$
$968$	−610.838	−	1419.46i	−0.631031	−	1.46638i
$969$		0			0
$970$	152.663	+	62.4209i	0.157384	+	0.0643515i
$971$			1396.09i			1.43779i	0.695121	+	0.718893i	$0.255351\pi$
$971$			1396.09i			1.43779i	−0.695121	+	0.718893i	$0.744649\pi$
$972$		0			0
$973$	−1103.56			−1.13418
$974$	−415.714	+	1016.71i	−0.426811	+	1.04385i
$975$		0			0
$976$	5.37384	+	294.614i	0.00550598	+	0.301858i
$977$	1009.95			1.03373			0.516864	−	0.856068i	$-0.327099\pi$
$977$	1009.95			1.03373			0.516864	+	0.856068i	$0.327099\pi$
$978$		0			0
$979$			467.552i			0.477581i
$980$	39.5696	+	38.8544i	0.0403771	+	0.0396473i
$981$		0			0
$982$	−17.4288	+	42.6256i	−0.0177483	+	0.0434069i
$983$		−	485.376i		−	0.493770i	−0.969045	−	0.246885i	$-0.920593\pi$
$983$		−	485.376i		−	0.493770i	0.969045	−	0.246885i	$-0.0794071\pi$
$984$		0			0
$985$	416.486			0.422828
$986$	−211.029	−	86.2858i	−0.214025	−	0.0875109i
$987$		0			0
$988$	−180.812	+	184.140i	−0.183008	+	0.186376i
$989$	571.325			0.577679
$990$		0			0
$991$			265.720i			0.268133i	0.990972	+	0.134066i	$0.0428035\pi$
$991$			265.720i			0.268133i	−0.990972	+	0.134066i	$0.957196\pi$
$992$	1337.84	+	518.746i	1.34863	+	0.522929i
$993$		0			0
$994$	−933.994	−	381.893i	−0.939632	−	0.384198i
$995$			131.141i			0.131800i
$996$		0			0
$997$	−1715.81			−1.72097			−0.860487	−	0.509472i	$-0.829841\pi$
$997$	−1715.81			−1.72097			−0.860487	+	0.509472i	$0.829841\pi$
$998$	474.453	−	1160.37i	0.475404	−	1.16269i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.3.d.d.55.8	yes	8
3.2	odd	2	inner	108.3.d.d.55.1	✓	8
4.3	odd	2	inner	108.3.d.d.55.7	yes	8
8.3	odd	2		1728.3.g.l.703.3		8
8.5	even	2		1728.3.g.l.703.4		8
9.2	odd	6		324.3.f.o.271.3		8
9.4	even	3		324.3.f.p.55.2		8
9.5	odd	6		324.3.f.p.55.3		8
9.7	even	3		324.3.f.o.271.2		8
12.11	even	2	inner	108.3.d.d.55.2	yes	8
24.5	odd	2		1728.3.g.l.703.6		8
24.11	even	2		1728.3.g.l.703.5		8
36.7	odd	6		324.3.f.p.271.1		8
36.11	even	6		324.3.f.p.271.4		8
36.23	even	6		324.3.f.o.55.3		8
36.31	odd	6		324.3.f.o.55.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.3.d.d.55.1	✓	8	3.2	odd	2	inner
108.3.d.d.55.2	yes	8	12.11	even	2	inner
108.3.d.d.55.7	yes	8	4.3	odd	2	inner
108.3.d.d.55.8	yes	8	1.1	even	1	trivial
324.3.f.o.55.2		8	36.31	odd	6
324.3.f.o.55.3		8	36.23	even	6
324.3.f.o.271.2		8	9.7	even	3
324.3.f.o.271.3		8	9.2	odd	6
324.3.f.p.55.2		8	9.4	even	3
324.3.f.p.55.3		8	9.5	odd	6
324.3.f.p.271.1		8	36.7	odd	6
324.3.f.p.271.4		8	36.11	even	6
1728.3.g.l.703.3		8	8.3	odd	2
1728.3.g.l.703.4		8	8.5	even	2
1728.3.g.l.703.5		8	24.11	even	2
1728.3.g.l.703.6		8	24.5	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:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	108.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.85123 + 0.756934i) q^{2} +(2.85410 + 2.80252i) q^{4} +1.08036 q^{5} +6.01392i q^{7} +(3.16228 + 7.34847i) q^{8} +O(q^{10})\)	\(q+(1.85123 + 0.756934i) q^{2} +(2.85410 + 2.80252i) q^{4} +1.08036 q^{5} +6.01392i q^{7} +(3.16228 + 7.34847i) q^{8} +(2.00000 + 0.817763i) q^{10} -17.7247i q^{11} +12.4164 q^{13} +(-4.55214 + 11.1331i) q^{14} +(0.291796 + 15.9973i) q^{16} -26.3786 q^{17} +5.19615i q^{19} +(3.08347 + 3.02774i) q^{20} +(13.4164 - 32.8124i) q^{22} -29.8356i q^{23} -23.8328 q^{25} +(22.9856 + 9.39840i) q^{26} +(-16.8541 + 17.1643i) q^{28} +4.32145 q^{29} -44.8403i q^{31} +(-11.5687 + 29.8356i) q^{32} +(-48.8328 - 19.9668i) q^{34} +6.49721i q^{35} -20.4164 q^{37} +(-3.93314 + 9.61927i) q^{38} +(3.41641 + 7.93901i) q^{40} +59.2393 q^{41} +19.1491i q^{43} +(49.6737 - 50.5880i) q^{44} +(22.5836 - 55.2326i) q^{46} +41.0631i q^{47} +12.8328 q^{49} +(-44.1200 - 18.0399i) q^{50} +(35.4377 + 34.7972i) q^{52} -70.0430 q^{53} -19.1491i q^{55} +(-44.1931 + 19.0177i) q^{56} +(8.00000 + 3.27105i) q^{58} +28.9521i q^{59} +18.4164 q^{61} +(33.9411 - 83.0096i) q^{62} +(-44.0000 + 46.4758i) q^{64} +13.4142 q^{65} +94.8767i q^{67} +(-75.2872 - 73.9264i) q^{68} +(-4.91796 + 12.0278i) q^{70} +83.8931i q^{71} +55.8328 q^{73} +(-37.7955 - 15.4539i) q^{74} +(-14.5623 + 14.8303i) q^{76} +106.595 q^{77} -41.0410i q^{79} +(0.315246 + 17.2829i) q^{80} +(109.666 + 44.8403i) q^{82} +35.4493i q^{83} -28.4984 q^{85} +(-14.4946 + 35.4493i) q^{86} +(130.249 - 56.0503i) q^{88} -26.3786 q^{89} +74.6712i q^{91} +(83.6148 - 85.1539i) q^{92} +(-31.0820 + 76.0172i) q^{94} +5.61373i q^{95} +76.3313 q^{97} +(23.7565 + 9.71359i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{4}+O(q^{10}) \) 8 * q - 4 * q^4	\( 8 q - 4 q^{4} + 16 q^{10} - 8 q^{13} + 56 q^{16} + 24 q^{25} - 108 q^{28} - 176 q^{34} - 56 q^{37} - 80 q^{40} + 288 q^{46} - 112 q^{49} + 364 q^{52} + 64 q^{58} + 40 q^{61} - 352 q^{64} - 576 q^{70} + 232 q^{73} - 36 q^{76} + 448 q^{82} + 416 q^{85} + 720 q^{88} + 288 q^{94} - 248 q^{97}+O(q^{100}) \) 8 * q - 4 * q^4 + 16 * q^10 - 8 * q^13 + 56 * q^16 + 24 * q^25 - 108 * q^28 - 176 * q^34 - 56 * q^37 - 80 * q^40 + 288 * q^46 - 112 * q^49 + 364 * q^52 + 64 * q^58 + 40 * q^61 - 352 * q^64 - 576 * q^70 + 232 * q^73 - 36 * q^76 + 448 * q^82 + 416 * q^85 + 720 * q^88 + 288 * q^94 - 248 * q^97

Introduction

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