LMFDB - Embedded newform 162.4.c.g.55.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,4,Mod(55,162)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(162, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("162.55");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	162.c (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.55830942093$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 54)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			55.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	162.55
Dual form			162.4.c.g.109.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 - 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(1.50000 + 2.59808i) q^{5} +(-14.5000 + 25.1147i) q^{7} -8.00000 q^{8} +O(q^{10})$	\(q+(1.00000 - 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(1.50000 + 2.59808i) q^{5} +(-14.5000 + 25.1147i) q^{7} -8.00000 q^{8} +6.00000 q^{10} +(-28.5000 + 49.3634i) q^{11} +(-10.0000 - 17.3205i) q^{13} +(29.0000 + 50.2295i) q^{14} +(-8.00000 + 13.8564i) q^{16} +72.0000 q^{17} -106.000 q^{19} +(6.00000 - 10.3923i) q^{20} +(57.0000 + 98.7269i) q^{22} +(87.0000 + 150.688i) q^{23} +(58.0000 - 100.459i) q^{25} -40.0000 q^{26} +116.000 q^{28} +(-105.000 + 181.865i) q^{29} +(-23.5000 - 40.7032i) q^{31} +(16.0000 + 27.7128i) q^{32} +(72.0000 - 124.708i) q^{34} -87.0000 q^{35} +2.00000 q^{37} +(-106.000 + 183.597i) q^{38} +(-12.0000 - 20.7846i) q^{40} +(-3.00000 - 5.19615i) q^{41} +(-109.000 + 188.794i) q^{43} +228.000 q^{44} +348.000 q^{46} +(237.000 - 410.496i) q^{47} +(-249.000 - 431.281i) q^{49} +(-116.000 - 200.918i) q^{50} +(-40.0000 + 69.2820i) q^{52} -81.0000 q^{53} -171.000 q^{55} +(116.000 - 200.918i) q^{56} +(210.000 + 363.731i) q^{58} +(42.0000 + 72.7461i) q^{59} +(-28.0000 + 48.4974i) q^{61} -94.0000 q^{62} +64.0000 q^{64} +(30.0000 - 51.9615i) q^{65} +(71.0000 + 122.976i) q^{67} +(-144.000 - 249.415i) q^{68} +(-87.0000 + 150.688i) q^{70} -360.000 q^{71} -1159.00 q^{73} +(2.00000 - 3.46410i) q^{74} +(212.000 + 367.195i) q^{76} +(-826.500 - 1431.54i) q^{77} +(80.0000 - 138.564i) q^{79} -48.0000 q^{80} -12.0000 q^{82} +(367.500 - 636.529i) q^{83} +(108.000 + 187.061i) q^{85} +(218.000 + 377.587i) q^{86} +(228.000 - 394.908i) q^{88} +954.000 q^{89} +580.000 q^{91} +(348.000 - 602.754i) q^{92} +(-474.000 - 820.992i) q^{94} +(-159.000 - 275.396i) q^{95} +(-95.5000 + 165.411i) q^{97} -996.000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 4 q^{4} + 3 q^{5} - 29 q^{7} - 16 q^{8}+O(q^{10}) $ 2 * q + 2 * q^2 - 4 * q^4 + 3 * q^5 - 29 * q^7 - 16 * q^8	$ 2 q + 2 q^{2} - 4 q^{4} + 3 q^{5} - 29 q^{7} - 16 q^{8} + 12 q^{10} - 57 q^{11} - 20 q^{13} + 58 q^{14} - 16 q^{16} + 144 q^{17} - 212 q^{19} + 12 q^{20} + 114 q^{22} + 174 q^{23} + 116 q^{25} - 80 q^{26} + 232 q^{28} - 210 q^{29} - 47 q^{31} + 32 q^{32} + 144 q^{34} - 174 q^{35} + 4 q^{37} - 212 q^{38} - 24 q^{40} - 6 q^{41} - 218 q^{43} + 456 q^{44} + 696 q^{46} + 474 q^{47} - 498 q^{49} - 232 q^{50} - 80 q^{52} - 162 q^{53} - 342 q^{55} + 232 q^{56} + 420 q^{58} + 84 q^{59} - 56 q^{61} - 188 q^{62} + 128 q^{64} + 60 q^{65} + 142 q^{67} - 288 q^{68} - 174 q^{70} - 720 q^{71} - 2318 q^{73} + 4 q^{74} + 424 q^{76} - 1653 q^{77} + 160 q^{79} - 96 q^{80} - 24 q^{82} + 735 q^{83} + 216 q^{85} + 436 q^{86} + 456 q^{88} + 1908 q^{89} + 1160 q^{91} + 696 q^{92} - 948 q^{94} - 318 q^{95} - 191 q^{97} - 1992 q^{98}+O(q^{100}) $ 2 * q + 2 * q^2 - 4 * q^4 + 3 * q^5 - 29 * q^7 - 16 * q^8 + 12 * q^10 - 57 * q^11 - 20 * q^13 + 58 * q^14 - 16 * q^16 + 144 * q^17 - 212 * q^19 + 12 * q^20 + 114 * q^22 + 174 * q^23 + 116 * q^25 - 80 * q^26 + 232 * q^28 - 210 * q^29 - 47 * q^31 + 32 * q^32 + 144 * q^34 - 174 * q^35 + 4 * q^37 - 212 * q^38 - 24 * q^40 - 6 * q^41 - 218 * q^43 + 456 * q^44 + 696 * q^46 + 474 * q^47 - 498 * q^49 - 232 * q^50 - 80 * q^52 - 162 * q^53 - 342 * q^55 + 232 * q^56 + 420 * q^58 + 84 * q^59 - 56 * q^61 - 188 * q^62 + 128 * q^64 + 60 * q^65 + 142 * q^67 - 288 * q^68 - 174 * q^70 - 720 * q^71 - 2318 * q^73 + 4 * q^74 + 424 * q^76 - 1653 * q^77 + 160 * q^79 - 96 * q^80 - 24 * q^82 + 735 * q^83 + 216 * q^85 + 436 * q^86 + 456 * q^88 + 1908 * q^89 + 1160 * q^91 + 696 * q^92 - 948 * q^94 - 318 * q^95 - 191 * q^97 - 1992 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	1.00000	−	1.73205i	0.353553	−	0.612372i
$2$	1.00000	−	1.73205i	0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−2.00000	−	3.46410i	−0.250000	−	0.433013i
$5$	1.50000	+	2.59808i	0.134164	+	0.232379i	0.925278	−	0.379290i	$-0.123832\pi$
$5$	1.50000	+	2.59808i	0.134164	+	0.232379i	−0.791114	+	0.611669i	$0.790498\pi$
$6$		0			0
$7$	−14.5000	+	25.1147i	−0.782926	+	1.35607i	0.147304	+	0.989091i	$0.452941\pi$
$7$	−14.5000	+	25.1147i	−0.782926	+	1.35607i	−0.930230	+	0.366977i	$0.880393\pi$
$8$	−8.00000			−0.353553
$9$		0			0
$10$	6.00000			0.189737
$11$	−28.5000	+	49.3634i	−0.781188	+	1.35306i	0.150061	+	0.988677i	$0.452053\pi$
$11$	−28.5000	+	49.3634i	−0.781188	+	1.35306i	−0.931250	+	0.364381i	$0.881280\pi$
$12$		0			0
$13$	−10.0000	−	17.3205i	−0.213346	−	0.369527i	0.739413	−	0.673252i	$-0.235103\pi$
$13$	−10.0000	−	17.3205i	−0.213346	−	0.369527i	−0.952760	+	0.303725i	$0.901770\pi$
$14$	29.0000	+	50.2295i	0.553613	+	0.958885i
$15$		0			0
$16$	−8.00000	+	13.8564i	−0.125000	+	0.216506i
$17$	72.0000			1.02721			0.513605	−	0.858027i	$-0.328310\pi$
$17$	72.0000			1.02721			0.513605	+	0.858027i	$0.328310\pi$
$18$		0			0
$19$	−106.000			−1.27990			−0.639949	−	0.768417i	$-0.721045\pi$
$19$	−106.000			−1.27990			−0.639949	+	0.768417i	$0.721045\pi$
$20$	6.00000	−	10.3923i	0.0670820	−	0.116190i
$21$		0			0
$22$	57.0000	+	98.7269i	0.552384	+	0.956757i
$23$	87.0000	+	150.688i	0.788728	+	1.36612i	0.926746	+	0.375688i	$0.122594\pi$
$23$	87.0000	+	150.688i	0.788728	+	1.36612i	−0.138018	+	0.990430i	$0.544073\pi$
$24$		0			0
$25$	58.0000	−	100.459i	0.464000	−	0.803672i
$26$	−40.0000			−0.301717
$27$		0			0
$28$	116.000			0.782926
$29$	−105.000	+	181.865i	−0.672345	+	1.16454i	0.304892	+	0.952387i	$0.401380\pi$
$29$	−105.000	+	181.865i	−0.672345	+	1.16454i	−0.977237	+	0.212149i	$0.931954\pi$
$30$		0			0
$31$	−23.5000	−	40.7032i	−0.136152	−	0.235823i	0.789885	−	0.613255i	$-0.210140\pi$
$31$	−23.5000	−	40.7032i	−0.136152	−	0.235823i	−0.926037	+	0.377433i	$0.876807\pi$
$32$	16.0000	+	27.7128i	0.0883883	+	0.153093i
$33$		0			0
$34$	72.0000	−	124.708i	0.363173	−	0.629035i
$35$	−87.0000			−0.420162
$36$		0			0
$37$	2.00000			0.00888643			0.00444322	−	0.999990i	$-0.498586\pi$
$37$	2.00000			0.00888643			0.00444322	+	0.999990i	$0.498586\pi$
$38$	−106.000	+	183.597i	−0.452512	+	0.783774i
$39$		0			0
$40$	−12.0000	−	20.7846i	−0.0474342	−	0.0821584i
$41$	−3.00000	−	5.19615i	−0.0114273	−	0.0197927i	0.860255	−	0.509864i	$-0.170304\pi$
$41$	−3.00000	−	5.19615i	−0.0114273	−	0.0197927i	−0.871683	+	0.490071i	$0.836971\pi$
$42$		0			0
$43$	−109.000	+	188.794i	−0.386566	+	0.669552i	−0.991985	−	0.126355i	$-0.959672\pi$
$43$	−109.000	+	188.794i	−0.386566	+	0.669552i	0.605419	+	0.795907i	$0.293006\pi$
$44$	228.000			0.781188
$45$		0			0
$46$	348.000			1.11543
$47$	237.000	−	410.496i	0.735532	−	1.27398i	−0.218958	−	0.975734i	$-0.570266\pi$
$47$	237.000	−	410.496i	0.735532	−	1.27398i	0.954490	−	0.298244i	$-0.0964010\pi$
$48$		0			0
$49$	−249.000	−	431.281i	−0.725948	−	1.25738i
$50$	−116.000	−	200.918i	−0.328098	−	0.568282i
$51$		0			0
$52$	−40.0000	+	69.2820i	−0.106673	+	0.184763i
$53$	−81.0000			−0.209928			−0.104964	−	0.994476i	$-0.533473\pi$
$53$	−81.0000			−0.209928			−0.104964	+	0.994476i	$0.533473\pi$
$54$		0			0
$55$	−171.000			−0.419230
$56$	116.000	−	200.918i	0.276806	−	0.479443i
$57$		0			0
$58$	210.000	+	363.731i	0.475420	+	0.823451i
$59$	42.0000	+	72.7461i	0.0926769	+	0.160521i	0.908637	−	0.417588i	$-0.137124\pi$
$59$	42.0000	+	72.7461i	0.0926769	+	0.160521i	−0.815960	+	0.578109i	$0.803791\pi$
$60$		0			0
$61$	−28.0000	+	48.4974i	−0.0587710	+	0.101794i	−0.893914	−	0.448239i	$-0.852052\pi$
$61$	−28.0000	+	48.4974i	−0.0587710	+	0.101794i	0.835143	+	0.550033i	$0.185385\pi$
$62$	−94.0000			−0.192549
$63$		0			0
$64$	64.0000			0.125000
$65$	30.0000	−	51.9615i	0.0572468	−	0.0991544i
$66$		0			0
$67$	71.0000	+	122.976i	0.129463	+	0.224237i	0.923469	−	0.383674i	$-0.125341\pi$
$67$	71.0000	+	122.976i	0.129463	+	0.224237i	−0.794006	+	0.607910i	$0.792008\pi$
$68$	−144.000	−	249.415i	−0.256802	−	0.444795i
$69$		0			0
$70$	−87.0000	+	150.688i	−0.148550	+	0.257296i
$71$	−360.000			−0.601748			−0.300874	−	0.953664i	$-0.597278\pi$
$71$	−360.000			−0.601748			−0.300874	+	0.953664i	$0.597278\pi$
$72$		0			0
$73$	−1159.00			−1.85823			−0.929114	−	0.369793i	$-0.879429\pi$
$73$	−1159.00			−1.85823			−0.929114	+	0.369793i	$0.879429\pi$
$74$	2.00000	−	3.46410i	0.00314183	−	0.00544181i
$75$		0			0
$76$	212.000	+	367.195i	0.319975	+	0.554212i
$77$	−826.500	−	1431.54i	−1.22323	−	2.11869i
$78$		0			0
$79$	80.0000	−	138.564i	0.113933	−	0.197338i	−0.803420	−	0.595413i	$-0.796988\pi$
$79$	80.0000	−	138.564i	0.113933	−	0.197338i	0.917353	+	0.398075i	$0.130322\pi$
$80$	−48.0000			−0.0670820
$81$		0			0
$82$	−12.0000			−0.0161607
$83$	367.500	−	636.529i	0.486004	−	0.841784i	−0.513866	−	0.857870i	$-0.671787\pi$
$83$	367.500	−	636.529i	0.486004	−	0.841784i	0.999871	+	0.0160860i	$0.00512056\pi$
$84$		0			0
$85$	108.000	+	187.061i	0.137815	+	0.238702i
$86$	218.000	+	377.587i	0.273344	+	0.473445i
$87$		0			0
$88$	228.000	−	394.908i	0.276192	−	0.478378i
$89$	954.000			1.13622			0.568111	−	0.822952i	$-0.307674\pi$
$89$	954.000			1.13622			0.568111	+	0.822952i	$0.307674\pi$
$90$		0			0
$91$	580.000			0.668138
$92$	348.000	−	602.754i	0.394364	−	0.683059i
$93$		0			0
$94$	−474.000	−	820.992i	−0.520100	−	0.900839i
$95$	−159.000	−	275.396i	−0.171716	−	0.297421i
$96$		0			0
$97$	−95.5000	+	165.411i	−0.0999645	+	0.173144i	−0.911670	−	0.410924i	$-0.865206\pi$
$97$	−95.5000	+	165.411i	−0.0999645	+	0.173144i	0.811705	+	0.584067i	$0.198540\pi$
$98$	−996.000			−1.02664
$99$		0			0
$100$	−464.000			−0.464000
$101$	−181.500	+	314.367i	−0.178811	+	0.309710i	−0.941474	−	0.337087i	$-0.890558\pi$
$101$	−181.500	+	314.367i	−0.178811	+	0.309710i	0.762662	+	0.646797i	$0.223892\pi$
$102$		0			0
$103$	314.000	+	543.864i	0.300382	+	0.520277i	0.976222	−	0.216771i	$-0.0695525\pi$
$103$	314.000	+	543.864i	0.300382	+	0.520277i	−0.675841	+	0.737048i	$0.736219\pi$
$104$	80.0000	+	138.564i	0.0754293	+	0.130647i
$105$		0			0
$106$	−81.0000	+	140.296i	−0.0742209	+	0.128554i
$107$	−675.000			−0.609857			−0.304929	−	0.952375i	$-0.598633\pi$
$107$	−675.000			−0.609857			−0.304929	+	0.952375i	$0.598633\pi$
$108$		0			0
$109$	1730.00			1.52022			0.760110	−	0.649795i	$-0.225145\pi$
$109$	1730.00			1.52022			0.760110	+	0.649795i	$0.225145\pi$
$110$	−171.000	+	296.181i	−0.148220	+	0.256725i
$111$		0			0
$112$	−232.000	−	401.836i	−0.195732	−	0.339017i
$113$	933.000	+	1616.00i	0.776719	+	1.34532i	0.933823	+	0.357735i	$0.116451\pi$
$113$	933.000	+	1616.00i	0.776719	+	1.34532i	−0.157104	+	0.987582i	$0.550216\pi$
$114$		0			0
$115$	−261.000	+	452.065i	−0.211638	+	0.366568i
$116$	840.000			0.672345
$117$		0			0
$118$	168.000			0.131065
$119$	−1044.00	+	1808.26i	−0.804230	+	1.39297i
$120$		0			0
$121$	−959.000	−	1661.04i	−0.720511	−	1.24796i
$122$	56.0000	+	96.9948i	0.0415574	+	0.0719795i
$123$		0			0
$124$	−94.0000	+	162.813i	−0.0680762	+	0.117911i
$125$	723.000			0.517337
$126$		0			0
$127$	1379.00			0.963515			0.481758	−	0.876304i	$-0.339999\pi$
$127$	1379.00			0.963515			0.481758	+	0.876304i	$0.339999\pi$
$128$	64.0000	−	110.851i	0.0441942	−	0.0765466i
$129$		0			0
$130$	−60.0000	−	103.923i	−0.0404796	−	0.0701127i
$131$	289.500	+	501.429i	0.193082	+	0.334428i	0.946270	−	0.323377i	$-0.104818\pi$
$131$	289.500	+	501.429i	0.193082	+	0.334428i	−0.753188	+	0.657805i	$0.771485\pi$
$132$		0			0
$133$	1537.00	−	2662.16i	1.00207	−	1.73563i
$134$	284.000			0.183089
$135$		0			0
$136$	−576.000			−0.363173
$137$	327.000	−	566.381i	0.203923	−	0.353206i	−0.745866	−	0.666096i	$-0.767964\pi$
$137$	327.000	−	566.381i	0.203923	−	0.353206i	0.949789	+	0.312891i	$0.101297\pi$
$138$		0			0
$139$	1502.00	+	2601.54i	0.916532	+	1.58748i	0.804642	+	0.593760i	$0.202357\pi$
$139$	1502.00	+	2601.54i	0.916532	+	1.58748i	0.111890	+	0.993721i	$0.464310\pi$
$140$	174.000	+	301.377i	0.105041	+	0.181936i
$141$		0			0
$142$	−360.000	+	623.538i	−0.212750	+	0.368494i
$143$	1140.00			0.666654
$144$		0			0
$145$	−630.000			−0.360818
$146$	−1159.00	+	2007.45i	−0.656983	+	1.13793i
$147$		0			0
$148$	−4.00000	−	6.92820i	−0.00222161	−	0.00384794i
$149$	901.500	+	1561.44i	0.495663	+	0.858513i	0.999987	−	0.00500094i	$-0.00159186\pi$
$149$	901.500	+	1561.44i	0.495663	+	0.858513i	−0.504325	+	0.863514i	$0.668259\pi$
$150$		0			0
$151$	−1229.50	+	2129.56i	−0.662618	+	1.14769i	0.317307	+	0.948323i	$0.397221\pi$
$151$	−1229.50	+	2129.56i	−0.662618	+	1.14769i	−0.979925	+	0.199365i	$0.936112\pi$
$152$	848.000			0.452512
$153$		0			0
$154$	−3306.00			−1.72990
$155$	70.5000	−	122.110i	0.0365335	−	0.0632779i
$156$		0			0
$157$	98.0000	+	169.741i	0.0498169	+	0.0862854i	0.889859	−	0.456236i	$-0.150803\pi$
$157$	98.0000	+	169.741i	0.0498169	+	0.0862854i	−0.840042	+	0.542522i	$0.817470\pi$
$158$	−160.000	−	277.128i	−0.0805628	−	0.139539i
$159$		0			0
$160$	−48.0000	+	83.1384i	−0.0237171	+	0.0410792i
$161$	−5046.00			−2.47007
$162$		0			0
$163$	−1564.00			−0.751546			−0.375773	−	0.926712i	$-0.622623\pi$
$163$	−1564.00			−0.751546			−0.375773	+	0.926712i	$0.622623\pi$
$164$	−12.0000	+	20.7846i	−0.00571367	+	0.00989637i
$165$		0			0
$166$	−735.000	−	1273.06i	−0.343657	−	0.595231i
$167$	987.000	+	1709.53i	0.457343	+	0.792142i	0.998820	−	0.0485740i	$-0.0154677\pi$
$167$	987.000	+	1709.53i	0.457343	+	0.792142i	−0.541476	+	0.840716i	$0.682134\pi$
$168$		0			0
$169$	898.500	−	1556.25i	0.408967	−	0.708351i
$170$	432.000			0.194899
$171$		0			0
$172$	872.000			0.386566
$173$	−1108.50	+	1919.98i	−0.487154	+	0.843776i	−0.999891	−	0.0147700i	$-0.995298\pi$
$173$	−1108.50	+	1919.98i	−0.487154	+	0.843776i	0.512737	+	0.858546i	$0.328632\pi$
$174$		0			0
$175$	1682.00	+	2913.31i	0.726556	+	1.25843i
$176$	−456.000	−	789.815i	−0.195297	−	0.338265i
$177$		0			0
$178$	954.000	−	1652.38i	0.401715	−	0.695791i
$179$	2475.00			1.03346			0.516732	−	0.856147i	$-0.327148\pi$
$179$	2475.00			1.03346			0.516732	+	0.856147i	$0.327148\pi$
$180$		0			0
$181$	1568.00			0.643914			0.321957	−	0.946754i	$-0.395659\pi$
$181$	1568.00			0.643914			0.321957	+	0.946754i	$0.395659\pi$
$182$	580.000	−	1004.59i	0.236222	−	0.409149i
$183$		0			0
$184$	−696.000	−	1205.51i	−0.278858	−	0.482996i
$185$	3.00000	+	5.19615i	0.00119224	+	0.00206502i
$186$		0			0
$187$	−2052.00	+	3554.17i	−0.802444	+	1.38987i
$188$	−1896.00			−0.735532
$189$		0			0
$190$	−636.000			−0.242844
$191$	570.000	−	987.269i	0.215936	−	0.374012i	−0.737626	−	0.675210i	$-0.764053\pi$
$191$	570.000	−	987.269i	0.215936	−	0.374012i	0.953562	+	0.301198i	$0.0973865\pi$
$192$		0			0
$193$	−1022.50	−	1771.02i	−0.381353	−	0.660523i	0.609903	−	0.792476i	$-0.291208\pi$
$193$	−1022.50	−	1771.02i	−0.381353	−	0.660523i	−0.991256	+	0.131953i	$0.957875\pi$
$194$	191.000	+	330.822i	0.0706856	+	0.122431i
$195$		0			0
$196$	−996.000	+	1725.12i	−0.362974	+	0.628689i
$197$	3735.00			1.35080			0.675400	−	0.737451i	$-0.263971\pi$
$197$	3735.00			1.35080			0.675400	+	0.737451i	$0.263971\pi$
$198$		0			0
$199$	1163.00			0.414286			0.207143	−	0.978311i	$-0.433583\pi$
$199$	1163.00			0.414286			0.207143	+	0.978311i	$0.433583\pi$
$200$	−464.000	+	803.672i	−0.164049	+	0.284141i
$201$		0			0
$202$	363.000	+	628.734i	0.126439	+	0.218998i
$203$	−3045.00	−	5274.09i	−1.05279	−	1.82349i
$204$		0			0
$205$	9.00000	−	15.5885i	0.00306628	−	0.00531095i
$206$	1256.00			0.424804
$207$		0			0
$208$	320.000			0.106673
$209$	3021.00	−	5232.53i	0.999842	−	1.73178i
$210$		0			0
$211$	−1063.00	−	1841.17i	−0.346824	−	0.600717i	0.638859	−	0.769324i	$-0.279407\pi$
$211$	−1063.00	−	1841.17i	−0.346824	−	0.600717i	−0.985683	+	0.168606i	$0.946073\pi$
$212$	162.000	+	280.592i	0.0524821	+	0.0909017i
$213$		0			0
$214$	−675.000	+	1169.13i	−0.215617	+	0.373460i
$215$	−654.000			−0.207453
$216$		0			0
$217$	1363.00			0.426389
$218$	1730.00	−	2996.45i	0.537479	−	0.930941i
$219$		0			0
$220$	342.000	+	592.361i	0.104807	+	0.181532i
$221$	−720.000	−	1247.08i	−0.219151	−	0.379581i
$222$		0			0
$223$	1376.00	−	2383.30i	0.413201	−	0.715685i	−0.582037	−	0.813162i	$-0.697744\pi$
$223$	1376.00	−	2383.30i	0.413201	−	0.715685i	0.995238	+	0.0974776i	$0.0310774\pi$
$224$	−928.000			−0.276806
$225$		0			0
$226$	3732.00			1.09845
$227$	−1986.00	+	3439.85i	−0.580685	+	1.00578i	0.414714	+	0.909952i	$0.363882\pi$
$227$	−1986.00	+	3439.85i	−0.580685	+	1.00578i	−0.995398	+	0.0958236i	$0.969452\pi$
$228$		0			0
$229$	−2251.00	−	3898.85i	−0.649564	−	1.12508i	−0.983227	−	0.182386i	$-0.941618\pi$
$229$	−2251.00	−	3898.85i	−0.649564	−	1.12508i	0.333663	−	0.942693i	$-0.391715\pi$
$230$	522.000	+	904.131i	0.149651	+	0.259203i
$231$		0			0
$232$	840.000	−	1454.92i	0.237710	−	0.411726i
$233$	−4842.00			−1.36142			−0.680708	−	0.732555i	$-0.738328\pi$
$233$	−4842.00			−1.36142			−0.680708	+	0.732555i	$0.738328\pi$
$234$		0			0
$235$	1422.00			0.394728
$236$	168.000	−	290.985i	0.0463384	−	0.0802605i
$237$		0			0
$238$	2088.00	+	3616.52i	0.568676	+	0.984976i
$239$	−2667.00	−	4619.38i	−0.721815	−	1.25022i	−0.960271	−	0.279068i	$-0.909975\pi$
$239$	−2667.00	−	4619.38i	−0.721815	−	1.25022i	0.238456	−	0.971153i	$-0.423359\pi$
$240$		0			0
$241$	1997.00	−	3458.91i	0.533768	−	0.924513i	−0.465454	−	0.885072i	$-0.654109\pi$
$241$	1997.00	−	3458.91i	0.533768	−	0.924513i	0.999222	−	0.0394411i	$-0.0125578\pi$
$242$	−3836.00			−1.01896
$243$		0			0
$244$	224.000			0.0587710
$245$	747.000	−	1293.84i	0.194792	−	0.337390i
$246$		0			0
$247$	1060.00	+	1835.97i	0.273061	+	0.472956i
$248$	188.000	+	325.626i	0.0481371	+	0.0833760i
$249$		0			0
$250$	723.000	−	1252.27i	0.182906	−	0.316803i
$251$	1008.00			0.253484			0.126742	−	0.991936i	$-0.459548\pi$
$251$	1008.00			0.253484			0.126742	+	0.991936i	$0.459548\pi$
$252$		0			0
$253$	−9918.00			−2.46458
$254$	1379.00	−	2388.50i	0.340654	−	0.590030i
$255$		0			0
$256$	−128.000	−	221.703i	−0.0312500	−	0.0541266i
$257$	−462.000	−	800.207i	−0.112135	−	0.194224i	0.804496	−	0.593958i	$-0.202436\pi$
$257$	−462.000	−	800.207i	−0.112135	−	0.194224i	−0.916631	+	0.399734i	$0.869102\pi$
$258$		0			0
$259$	−29.0000	+	50.2295i	−0.00695742	+	0.0120506i
$260$	−240.000			−0.0572468
$261$		0			0
$262$	1158.00			0.273059
$263$	507.000	−	878.150i	0.118871	−	0.205890i	−0.800450	−	0.599400i	$-0.795406\pi$
$263$	507.000	−	878.150i	0.118871	−	0.205890i	0.919320	+	0.393510i	$0.128739\pi$
$264$		0			0
$265$	−121.500	−	210.444i	−0.0281649	−	0.0487830i
$266$	−3074.00	−	5324.32i	−0.708568	−	1.22728i
$267$		0			0
$268$	284.000	−	491.902i	0.0647316	−	0.112118i
$269$	2970.00			0.673175			0.336588	−	0.941652i	$-0.390727\pi$
$269$	2970.00			0.673175			0.336588	+	0.941652i	$0.390727\pi$
$270$		0			0
$271$	245.000			0.0549177			0.0274588	−	0.999623i	$-0.491258\pi$
$271$	245.000			0.0549177			0.0274588	+	0.999623i	$0.491258\pi$
$272$	−576.000	+	997.661i	−0.128401	+	0.222397i
$273$		0			0
$274$	−654.000	−	1132.76i	−0.144196	−	0.249754i
$275$	3306.00	+	5726.16i	0.724943	+	1.25564i
$276$		0			0
$277$	−2188.00	+	3789.73i	−0.474600	+	0.822031i	−0.999577	−	0.0290852i	$-0.990741\pi$
$277$	−2188.00	+	3789.73i	−0.474600	+	0.822031i	0.524977	+	0.851116i	$0.324074\pi$
$278$	6008.00			1.29617
$279$		0			0
$280$	696.000			0.148550
$281$	120.000	−	207.846i	0.0254754	−	0.0441248i	−0.853007	−	0.521900i	$-0.825223\pi$
$281$	120.000	−	207.846i	0.0254754	−	0.0441248i	0.878482	+	0.477775i	$0.158557\pi$
$282$		0			0
$283$	3419.00	+	5921.88i	0.718157	+	1.24388i	0.961729	+	0.274002i	$0.0883474\pi$
$283$	3419.00	+	5921.88i	0.718157	+	1.24388i	−0.243572	+	0.969883i	$0.578319\pi$
$284$	720.000	+	1247.08i	0.150437	+	0.260565i
$285$		0			0
$286$	1140.00	−	1974.54i	0.235698	−	0.408241i
$287$	174.000			0.0357871
$288$		0			0
$289$	271.000			0.0551598
$290$	−630.000	+	1091.19i	−0.127569	+	0.220955i
$291$		0			0
$292$	2318.00	+	4014.89i	0.464557	+	0.804637i
$293$	−2559.00	−	4432.32i	−0.510233	−	0.883750i	−0.999930	−	0.0118571i	$-0.996226\pi$
$293$	−2559.00	−	4432.32i	−0.510233	−	0.883750i	0.489696	−	0.871893i	$-0.337108\pi$
$294$		0			0
$295$	−126.000	+	218.238i	−0.0248678	+	0.0430723i
$296$	−16.0000			−0.00314183
$297$		0			0
$298$	3606.00			0.700973
$299$	1740.00	−	3013.77i	0.336544	−	0.582912i
$300$		0			0
$301$	−3161.00	−	5475.01i	−0.605306	−	1.04842i
$302$	2459.00	+	4259.11i	0.468542	+	0.811538i
$303$		0			0
$304$	848.000	−	1468.78i	0.159987	−	0.277106i
$305$	−168.000			−0.0315398
$306$		0			0
$307$	−5560.00			−1.03364			−0.516818	−	0.856096i	$-0.672883\pi$
$307$	−5560.00			−1.03364			−0.516818	+	0.856096i	$0.672883\pi$
$308$	−3306.00	+	5726.16i	−0.611613	+	1.05934i
$309$		0			0
$310$	−141.000	−	244.219i	−0.0258331	−	0.0447442i
$311$	3831.00	+	6635.49i	0.698508	+	1.20985i	0.968984	+	0.247125i	$0.0794858\pi$
$311$	3831.00	+	6635.49i	0.698508	+	1.20985i	−0.270475	+	0.962727i	$0.587181\pi$
$312$		0			0
$313$	−1742.50	+	3018.10i	−0.314671	+	0.545026i	−0.979367	−	0.202088i	$-0.935227\pi$
$313$	−1742.50	+	3018.10i	−0.314671	+	0.545026i	0.664697	+	0.747113i	$0.268561\pi$
$314$	392.000			0.0704517
$315$		0			0
$316$	−640.000			−0.113933
$317$	−3529.50	+	6113.27i	−0.625352	+	1.08314i	0.363121	+	0.931742i	$0.381711\pi$
$317$	−3529.50	+	6113.27i	−0.625352	+	1.08314i	−0.988473	+	0.151399i	$0.951622\pi$
$318$		0			0
$319$	−5985.00	−	10366.3i	−1.05046	−	1.81944i
$320$	96.0000	+	166.277i	0.0167705	+	0.0290474i
$321$		0			0
$322$	−5046.00	+	8739.93i	−0.873300	+	1.51260i
$323$	−7632.00			−1.31472
$324$		0			0
$325$	−2320.00			−0.395971
$326$	−1564.00	+	2708.93i	−0.265711	+	0.460226i
$327$		0			0
$328$	24.0000	+	41.5692i	0.00404018	+	0.00699779i
$329$	6873.00	+	11904.4i	1.15173	+	1.99486i
$330$		0			0
$331$	−4645.00	+	8045.38i	−0.771336	+	1.33599i	0.165495	+	0.986211i	$0.447078\pi$
$331$	−4645.00	+	8045.38i	−0.771336	+	1.33599i	−0.936831	+	0.349783i	$0.886255\pi$
$332$	−2940.00			−0.486004
$333$		0			0
$334$	3948.00			0.646781
$335$	−213.000	+	368.927i	−0.0347386	+	0.0601690i
$336$		0			0
$337$	1907.00	+	3303.02i	0.308252	+	0.533908i	0.977980	−	0.208698i	$-0.0669227\pi$
$337$	1907.00	+	3303.02i	0.308252	+	0.533908i	−0.669728	+	0.742606i	$0.733589\pi$
$338$	−1797.00	−	3112.50i	−0.289183	−	0.500880i
$339$		0			0
$340$	432.000	−	748.246i	0.0689073	−	0.119351i
$341$	2679.00			0.425443
$342$		0			0
$343$	4495.00			0.707601
$344$	872.000	−	1510.35i	0.136672	−	0.236722i
$345$		0			0
$346$	2217.00	+	3839.96i	0.344470	+	0.596640i
$347$	964.500	+	1670.56i	0.149213	+	0.258445i	0.930937	−	0.365180i	$-0.118993\pi$
$347$	964.500	+	1670.56i	0.149213	+	0.258445i	−0.781724	+	0.623625i	$0.785659\pi$
$348$		0			0
$349$	3293.00	−	5703.64i	0.505072	−	0.874811i	−0.494910	−	0.868944i	$-0.664799\pi$
$349$	3293.00	−	5703.64i	0.505072	−	0.874811i	0.999983	−	0.00586698i	$-0.00186753\pi$
$350$	6728.00			1.02750
$351$		0			0
$352$	−1824.00			−0.276192
$353$	−3021.00	+	5232.53i	−0.455500	+	0.788950i	−0.998717	−	0.0506430i	$-0.983873\pi$
$353$	−3021.00	+	5232.53i	−0.455500	+	0.788950i	0.543217	+	0.839593i	$0.317206\pi$
$354$		0			0
$355$	−540.000	−	935.307i	−0.0807330	−	0.139834i
$356$	−1908.00	−	3304.75i	−0.284056	−	0.491999i
$357$		0			0
$358$	2475.00	−	4286.83i	0.365385	−	0.632865i
$359$	3762.00			0.553066			0.276533	−	0.961004i	$-0.410814\pi$
$359$	3762.00			0.553066			0.276533	+	0.961004i	$0.410814\pi$
$360$		0			0
$361$	4377.00			0.638140
$362$	1568.00	−	2715.86i	0.227658	−	0.394315i
$363$		0			0
$364$	−1160.00	−	2009.18i	−0.167034	−	0.289312i
$365$	−1738.50	−	3011.17i	−0.249308	−	0.431813i
$366$		0			0
$367$	3630.50	−	6288.21i	0.516378	−	0.894392i	−0.483442	−	0.875377i	$-0.660613\pi$
$367$	3630.50	−	6288.21i	0.516378	−	0.894392i	0.999819	−	0.0190155i	$-0.00605320\pi$
$368$	−2784.00			−0.394364
$369$		0			0
$370$	12.0000			0.00168608
$371$	1174.50	−	2034.29i	0.164358	−	0.284677i
$372$		0			0
$373$	−820.000	−	1420.28i	−0.113828	−	0.197157i	0.803482	−	0.595328i	$-0.202978\pi$
$373$	−820.000	−	1420.28i	−0.113828	−	0.197157i	−0.917311	+	0.398172i	$0.869645\pi$
$374$	4104.00	+	7108.34i	0.567414	+	0.982790i
$375$		0			0
$376$	−1896.00	+	3283.97i	−0.260050	+	0.450420i
$377$	4200.00			0.573769
$378$		0			0
$379$	−7396.00			−1.00239			−0.501197	−	0.865333i	$-0.667107\pi$
$379$	−7396.00			−1.00239			−0.501197	+	0.865333i	$0.667107\pi$
$380$	−636.000	+	1101.58i	−0.0858582	+	0.148711i
$381$		0			0
$382$	−1140.00	−	1974.54i	−0.152690	−	0.264466i
$383$	−2496.00	−	4323.20i	−0.333002	−	0.576776i	0.650097	−	0.759851i	$-0.274728\pi$
$383$	−2496.00	−	4323.20i	−0.333002	−	0.576776i	−0.983099	+	0.183075i	$0.941395\pi$
$384$		0			0
$385$	2479.50	−	4294.62i	0.328226	−	0.568504i
$386$	−4090.00			−0.539315
$387$		0			0
$388$	764.000			0.0999645
$389$	−4726.50	+	8186.54i	−0.616049	+	1.06703i	0.374150	+	0.927368i	$0.377934\pi$
$389$	−4726.50	+	8186.54i	−0.616049	+	1.06703i	−0.990199	+	0.139660i	$0.955399\pi$
$390$		0			0
$391$	6264.00	+	10849.6i	0.810190	+	1.40329i
$392$	1992.00	+	3450.25i	0.256661	+	0.444550i
$393$		0			0
$394$	3735.00	−	6469.21i	0.477580	−	0.827193i
$395$	480.000			0.0611428
$396$		0			0
$397$	8588.00			1.08569			0.542846	−	0.839833i	$-0.317347\pi$
$397$	8588.00			1.08569			0.542846	+	0.839833i	$0.317347\pi$
$398$	1163.00	−	2014.38i	0.146472	−	0.253697i
$399$		0			0
$400$	928.000	+	1607.34i	0.116000	+	0.200918i
$401$	−858.000	−	1486.10i	−0.106849	−	0.185068i	0.807643	−	0.589672i	$-0.200743\pi$
$401$	−858.000	−	1486.10i	−0.106849	−	0.185068i	−0.914492	+	0.404604i	$0.867409\pi$
$402$		0			0
$403$	−470.000	+	814.064i	−0.0580952	+	0.100624i
$404$	1452.00			0.178811
$405$		0			0
$406$	−12180.0			−1.48888
$407$	−57.0000	+	98.7269i	−0.00694198	+	0.0120239i
$408$		0			0
$409$	4944.50	+	8564.13i	0.597775	+	1.03538i	0.993149	+	0.116856i	$0.0372815\pi$
$409$	4944.50	+	8564.13i	0.597775	+	1.03538i	−0.395374	+	0.918520i	$0.629385\pi$
$410$	−18.0000	−	31.1769i	−0.00216819	−	0.00375541i
$411$		0			0
$412$	1256.00	−	2175.46i	0.150191	−	0.260138i
$413$	−2436.00			−0.290237
$414$		0			0
$415$	2205.00			0.260817
$416$	320.000	−	554.256i	0.0377146	−	0.0653237i
$417$		0			0
$418$	−6042.00	−	10465.1i	−0.706995	−	1.22455i
$419$	2778.00	+	4811.64i	0.323900	+	0.561012i	0.981289	−	0.192540i	$-0.0616725\pi$
$419$	2778.00	+	4811.64i	0.323900	+	0.561012i	−0.657389	+	0.753551i	$0.728339\pi$
$420$		0			0
$421$	1052.00	−	1822.12i	0.121785	−	0.210937i	−0.798687	−	0.601747i	$-0.794472\pi$
$421$	1052.00	−	1822.12i	0.121785	−	0.210937i	0.920472	+	0.390810i	$0.127805\pi$
$422$	−4252.00			−0.490484
$423$		0			0
$424$	648.000			0.0742209
$425$	4176.00	−	7233.04i	0.476625	−	0.825539i
$426$		0			0
$427$	−812.000	−	1406.43i	−0.0920268	−	0.159395i
$428$	1350.00	+	2338.27i	0.152464	+	0.264076i
$429$		0			0
$430$	−654.000	+	1132.76i	−0.0733458	+	0.127039i
$431$	−7614.00			−0.850936			−0.425468	−	0.904973i	$-0.639891\pi$
$431$	−7614.00			−0.850936			−0.425468	+	0.904973i	$0.639891\pi$
$432$		0			0
$433$	7805.00			0.866246			0.433123	−	0.901335i	$-0.357412\pi$
$433$	7805.00			0.866246			0.433123	+	0.901335i	$0.357412\pi$
$434$	1363.00	−	2360.79i	0.150751	−	0.261109i
$435$		0			0
$436$	−3460.00	−	5992.90i	−0.380055	−	0.658274i
$437$	−9222.00	−	15973.0i	−1.00949	−	1.74849i
$438$		0			0
$439$	2604.50	−	4511.13i	0.283157	−	0.490443i	−0.689003	−	0.724758i	$-0.741952\pi$
$439$	2604.50	−	4511.13i	0.283157	−	0.490443i	0.972161	+	0.234315i	$0.0752849\pi$
$440$	1368.00			0.148220
$441$		0			0
$442$	−2880.00			−0.309927
$443$	2118.00	−	3668.48i	0.227154	−	0.393442i	−0.729810	−	0.683651i	$-0.760391\pi$
$443$	2118.00	−	3668.48i	0.227154	−	0.393442i	0.956964	+	0.290208i	$0.0937246\pi$
$444$		0			0
$445$	1431.00	+	2478.56i	0.152440	+	0.264034i
$446$	−2752.00	−	4766.60i	−0.292177	−	0.506066i
$447$		0			0
$448$	−928.000	+	1607.34i	−0.0978658	+	0.169509i
$449$	16002.0			1.68192			0.840959	−	0.541099i	$-0.181992\pi$
$449$	16002.0			1.68192			0.840959	+	0.541099i	$0.181992\pi$
$450$		0			0
$451$	342.000			0.0357077
$452$	3732.00	−	6464.01i	0.388360	−	0.672658i
$453$		0			0
$454$	3972.00	+	6879.71i	0.410606	+	0.711191i
$455$	870.000	+	1506.88i	0.0896401	+	0.155261i
$456$		0			0
$457$	−3659.50	+	6338.44i	−0.374582	+	0.648796i	−0.990264	−	0.139199i	$-0.955547\pi$
$457$	−3659.50	+	6338.44i	−0.374582	+	0.648796i	0.615682	+	0.787995i	$0.288881\pi$
$458$	−9004.00			−0.918623
$459$		0			0
$460$	2088.00			0.211638
$461$	4741.50	−	8212.52i	0.479032	−	0.829707i	−0.520679	−	0.853752i	$-0.674321\pi$
$461$	4741.50	−	8212.52i	0.479032	−	0.829707i	0.999711	+	0.0240450i	$0.00765451\pi$
$462$		0			0
$463$	−5396.50	−	9347.01i	−0.541677	−	0.938213i	−0.998808	−	0.0488131i	$-0.984456\pi$
$463$	−5396.50	−	9347.01i	−0.541677	−	0.938213i	0.457131	−	0.889400i	$-0.348877\pi$
$464$	−1680.00	−	2909.85i	−0.168086	−	0.291134i
$465$		0			0
$466$	−4842.00	+	8386.59i	−0.481333	+	0.833694i
$467$	−2583.00			−0.255946			−0.127973	−	0.991778i	$-0.540847\pi$
$467$	−2583.00			−0.255946			−0.127973	+	0.991778i	$0.540847\pi$
$468$		0			0
$469$	−4118.00			−0.405440
$470$	1422.00	−	2462.98i	0.139557	−	0.241720i
$471$		0			0
$472$	−336.000	−	581.969i	−0.0327662	−	0.0567527i
$473$	−6213.00	−	10761.2i	−0.603962	−	1.04609i
$474$		0			0
$475$	−6148.00	+	10648.6i	−0.593873	+	1.02862i
$476$	8352.00			0.804230
$477$		0			0
$478$	−10668.0			−1.02080
$479$	−627.000	+	1086.00i	−0.0598087	+	0.103592i	−0.894379	−	0.447309i	$-0.852382\pi$
$479$	−627.000	+	1086.00i	−0.0598087	+	0.103592i	0.834571	+	0.550901i	$0.185716\pi$
$480$		0			0
$481$	−20.0000	−	34.6410i	−0.00189589	−	0.00328377i
$482$	−3994.00	−	6917.81i	−0.377431	−	0.653730i
$483$		0			0
$484$	−3836.00	+	6644.15i	−0.360255	+	0.623981i
$485$	−573.000			−0.0536466
$486$		0			0
$487$	17336.0			1.61308			0.806539	−	0.591181i	$-0.201338\pi$
$487$	17336.0			1.61308			0.806539	+	0.591181i	$0.201338\pi$
$488$	224.000	−	387.979i	0.0207787	−	0.0359898i
$489$		0			0
$490$	−1494.00	−	2587.68i	−0.137739	−	0.238571i
$491$	−7585.50	−	13138.5i	−0.697207	−	1.20760i	−0.969431	−	0.245365i	$-0.921092\pi$
$491$	−7585.50	−	13138.5i	−0.697207	−	1.20760i	0.272224	−	0.962234i	$-0.412241\pi$
$492$		0			0
$493$	−7560.00	+	13094.3i	−0.690640	+	1.19622i
$494$	4240.00			0.386167
$495$		0			0
$496$	752.000			0.0680762
$497$	5220.00	−	9041.31i	0.471125	−	0.816012i
$498$		0			0
$499$	−4465.00	−	7733.61i	−0.400563	−	0.693795i	0.593231	−	0.805032i	$-0.297852\pi$
$499$	−4465.00	−	7733.61i	−0.400563	−	0.693795i	−0.993794	+	0.111237i	$0.964519\pi$
$500$	−1446.00	−	2504.55i	−0.129334	−	0.224013i
$501$		0			0
$502$	1008.00	−	1745.91i	0.0896200	−	0.155226i
$503$	−15210.0			−1.34827			−0.674136	−	0.738608i	$-0.735484\pi$
$503$	−15210.0			−1.34827			−0.674136	+	0.738608i	$0.735484\pi$
$504$		0			0
$505$	−1089.00			−0.0959601
$506$	−9918.00	+	17178.5i	−0.871361	+	1.50924i
$507$		0			0
$508$	−2758.00	−	4777.00i	−0.240879	−	0.417214i
$509$	9820.50	+	17009.6i	0.855179	+	1.48121i	0.876479	+	0.481440i	$0.159886\pi$
$509$	9820.50	+	17009.6i	0.855179	+	1.48121i	−0.0213002	+	0.999773i	$0.506781\pi$
$510$		0			0
$511$	16805.5	−	29108.0i	1.45486	−	2.51988i
$512$	−512.000			−0.0441942
$513$		0			0
$514$	−1848.00			−0.158583
$515$	−942.000	+	1631.59i	−0.0806009	+	0.139605i
$516$		0			0
$517$	13509.0	+	23398.3i	1.14918	+	1.99044i
$518$	58.0000	+	100.459i	0.00491964	+	0.00852107i
$519$		0			0
$520$	−240.000	+	415.692i	−0.0202398	+	0.0350564i
$521$	−22428.0			−1.88597			−0.942983	−	0.332840i	$-0.891993\pi$
$521$	−22428.0			−1.88597			−0.942983	+	0.332840i	$0.891993\pi$
$522$		0			0
$523$	−8152.00			−0.681572			−0.340786	−	0.940141i	$-0.610693\pi$
$523$	−8152.00			−0.681572			−0.340786	+	0.940141i	$0.610693\pi$
$524$	1158.00	−	2005.71i	0.0965410	−	0.167214i
$525$		0			0
$526$	−1014.00	−	1756.30i	−0.0840542	−	0.145586i
$527$	−1692.00	−	2930.63i	−0.139857	−	0.242240i
$528$		0			0
$529$	−9054.50	+	15682.9i	−0.744185	+	1.28897i
$530$	−486.000			−0.0398311
$531$		0			0
$532$	−12296.0			−1.00207
$533$	−60.0000	+	103.923i	−0.00487596	+	0.00844542i
$534$		0			0
$535$	−1012.50	−	1753.70i	−0.0818209	−	0.141718i
$536$	−568.000	−	983.805i	−0.0457721	−	0.0792797i
$537$		0			0
$538$	2970.00	−	5144.19i	0.238003	−	0.412234i
$539$	28386.0			2.26841
$540$		0			0
$541$	−2860.00			−0.227285			−0.113642	−	0.993522i	$-0.536252\pi$
$541$	−2860.00			−0.227285			−0.113642	+	0.993522i	$0.536252\pi$
$542$	245.000	−	424.352i	0.0194163	−	0.0336301i
$543$		0			0
$544$	1152.00	+	1995.32i	0.0907934	+	0.157259i
$545$	2595.00	+	4494.67i	0.203959	+	0.353267i
$546$		0			0
$547$	4832.00	−	8369.27i	0.377699	−	0.654194i	−0.613028	−	0.790061i	$-0.710049\pi$
$547$	4832.00	−	8369.27i	0.377699	−	0.654194i	0.990727	+	0.135867i	$0.0433820\pi$
$548$	−2616.00			−0.203923
$549$		0			0
$550$	13224.0			1.02522
$551$	11130.0	−	19277.7i	0.860533	−	1.49049i
$552$		0			0
$553$	2320.00	+	4018.36i	0.178402	+	0.309002i
$554$	4376.00	+	7579.45i	0.335593	+	0.581264i
$555$		0			0
$556$	6008.00	−	10406.2i	0.458266	−	0.793740i
$557$	−14859.0			−1.13033			−0.565167	−	0.824977i	$-0.691188\pi$
$557$	−14859.0			−1.13033			−0.565167	+	0.824977i	$0.691188\pi$
$558$		0			0
$559$	4360.00			0.329890
$560$	696.000	−	1205.51i	0.0525203	−	0.0909678i
$561$		0			0
$562$	−240.000	−	415.692i	−0.0180139	−	0.0312009i
$563$	4096.50	+	7095.35i	0.306655	+	0.531142i	0.977628	−	0.210339i	$-0.0674568\pi$
$563$	4096.50	+	7095.35i	0.306655	+	0.531142i	−0.670973	+	0.741482i	$0.734123\pi$
$564$		0			0
$565$	−2799.00	+	4848.01i	−0.208416	+	0.360986i
$566$	13676.0			1.01563
$567$		0			0
$568$	2880.00			0.212750
$569$	−8286.00	+	14351.8i	−0.610487	+	1.05739i	0.380671	+	0.924710i	$0.375693\pi$
$569$	−8286.00	+	14351.8i	−0.610487	+	1.05739i	−0.991158	+	0.132684i	$0.957640\pi$
$570$		0			0
$571$	3122.00	+	5407.46i	0.228812	+	0.396314i	0.957456	−	0.288578i	$-0.0931826\pi$
$571$	3122.00	+	5407.46i	0.228812	+	0.396314i	−0.728644	+	0.684892i	$0.759849\pi$
$572$	−2280.00	−	3949.08i	−0.166664	−	0.288670i
$573$		0			0
$574$	174.000	−	301.377i	0.0126526	−	0.0219150i
$575$	20184.0			1.46388
$576$		0			0
$577$	−14794.0			−1.06739			−0.533693	−	0.845678i	$-0.679196\pi$
$577$	−14794.0			−1.06739			−0.533693	+	0.845678i	$0.679196\pi$
$578$	271.000	−	469.386i	0.0195019	−	0.0337783i
$579$		0			0
$580$	1260.00	+	2182.38i	0.0902046	+	0.156239i
$581$	10657.5	+	18459.3i	0.761011	+	1.31811i
$582$		0			0
$583$	2308.50	−	3998.44i	0.163994	−	0.284045i
$584$	9272.00			0.656983
$585$		0			0
$586$	−10236.0			−0.721579
$587$	−13384.5	+	23182.6i	−0.941120	+	1.63007i	−0.177780	+	0.984070i	$0.556892\pi$
$587$	−13384.5	+	23182.6i	−0.941120	+	1.63007i	−0.763340	+	0.645997i	$0.776442\pi$
$588$		0			0
$589$	2491.00	+	4314.54i	0.174261	+	0.301829i
$590$	252.000	+	436.477i	0.0175842	+	0.0304567i
$591$		0			0
$592$	−16.0000	+	27.7128i	−0.00111080	+	0.00192397i
$593$	3078.00			0.213151			0.106575	−	0.994305i	$-0.466011\pi$
$593$	3078.00			0.213151			0.106575	+	0.994305i	$0.466011\pi$
$594$		0			0
$595$	−6264.00			−0.431595
$596$	3606.00	−	6245.78i	0.247831	−	0.429257i
$597$		0			0
$598$	−3480.00	−	6027.54i	−0.237973	−	0.412181i
$599$	501.000	+	867.757i	0.0341741	+	0.0591913i	0.882607	−	0.470112i	$-0.155787\pi$
$599$	501.000	+	867.757i	0.0341741	+	0.0591913i	−0.848432	+	0.529304i	$0.822453\pi$
$600$		0			0
$601$	10326.5	−	17886.0i	0.700876	−	1.21395i	−0.267283	−	0.963618i	$-0.586126\pi$
$601$	10326.5	−	17886.0i	0.700876	−	1.21395i	0.968159	−	0.250335i	$-0.0805409\pi$
$602$	−12644.0			−0.856032
$603$		0			0
$604$	9836.00			0.662618
$605$	2877.00	−	4983.11i	0.193333	−	0.334863i
$606$		0			0
$607$	−13564.0	−	23493.5i	−0.906995	−	1.57096i	−0.818217	−	0.574909i	$-0.805037\pi$
$607$	−13564.0	−	23493.5i	−0.906995	−	1.57096i	−0.0887776	−	0.996051i	$-0.528296\pi$
$608$	−1696.00	−	2937.56i	−0.113128	−	0.195944i
$609$		0			0
$610$	−168.000	+	290.985i	−0.0111510	+	0.0193141i
$611$	−9480.00			−0.627692
$612$		0			0
$613$	24518.0			1.61545			0.807727	−	0.589557i	$-0.200698\pi$
$613$	24518.0			1.61545			0.807727	+	0.589557i	$0.200698\pi$
$614$	−5560.00	+	9630.20i	−0.365445	+	0.632970i
$615$		0			0
$616$	6612.00	+	11452.3i	0.432476	+	0.749070i
$617$	−237.000	−	410.496i	−0.0154640	−	0.0267844i	0.858190	−	0.513332i	$-0.171589\pi$
$617$	−237.000	−	410.496i	−0.0154640	−	0.0267844i	−0.873654	+	0.486548i	$0.838256\pi$
$618$		0			0
$619$	566.000	−	980.341i	0.0367520	−	0.0636563i	−0.847064	−	0.531490i	$-0.821632\pi$
$619$	566.000	−	980.341i	0.0367520	−	0.0636563i	0.883816	+	0.467834i	$0.154966\pi$
$620$	−564.000			−0.0365335
$621$		0			0
$622$	15324.0			0.987840
$623$	−13833.0	+	23959.5i	−0.889579	+	1.54080i
$624$		0			0
$625$	−6165.50	−	10679.0i	−0.394592	−	0.683453i
$626$	3485.00	+	6036.20i	0.222506	+	0.385391i
$627$		0			0
$628$	392.000	−	678.964i	0.0249084	−	0.0431427i
$629$	144.000			0.00912823
$630$		0			0
$631$	6725.00			0.424276			0.212138	−	0.977240i	$-0.431957\pi$
$631$	6725.00			0.424276			0.212138	+	0.977240i	$0.431957\pi$
$632$	−640.000	+	1108.51i	−0.0402814	+	0.0697694i
$633$		0			0
$634$	7059.00	+	12226.5i	0.442190	+	0.765896i
$635$	2068.50	+	3582.75i	0.129269	+	0.223901i
$636$		0			0
$637$	−4980.00	+	8625.61i	−0.309756	+	0.536514i
$638$	−23940.0			−1.48557
$639$		0			0
$640$	384.000			0.0237171
$641$	−10563.0	+	18295.7i	−0.650879	+	1.12736i	0.332031	+	0.943268i	$0.392266\pi$
$641$	−10563.0	+	18295.7i	−0.650879	+	1.12736i	−0.982910	+	0.184087i	$0.941067\pi$
$642$		0			0
$643$	−9730.00	−	16852.9i	−0.596755	−	1.03361i	−0.993297	−	0.115594i	$-0.963123\pi$
$643$	−9730.00	−	16852.9i	−0.596755	−	1.03361i	0.396541	−	0.918017i	$-0.370210\pi$
$644$	10092.0	+	17479.9i	0.617516	+	1.06957i
$645$		0			0
$646$	−7632.00	+	13219.0i	−0.464825	+	0.805101i
$647$	11664.0			0.708747			0.354373	−	0.935104i	$-0.384694\pi$
$647$	11664.0			0.708747			0.354373	+	0.935104i	$0.384694\pi$
$648$		0			0
$649$	−4788.00			−0.289592
$650$	−2320.00	+	4018.36i	−0.139997	+	0.242481i
$651$		0			0
$652$	3128.00	+	5417.85i	0.187886	+	0.325429i
$653$	−1672.50	−	2896.85i	−0.100230	−	0.173603i	0.811550	−	0.584284i	$-0.198624\pi$
$653$	−1672.50	−	2896.85i	−0.100230	−	0.173603i	−0.911779	+	0.410681i	$0.865291\pi$
$654$		0			0
$655$	−868.500	+	1504.29i	−0.0518093	+	0.0897364i
$656$	96.0000			0.00571367
$657$		0			0
$658$	27492.0			1.62880
$659$	4696.50	−	8134.58i	0.277617	−	0.480847i	−0.693175	−	0.720769i	$-0.743789\pi$
$659$	4696.50	−	8134.58i	0.277617	−	0.480847i	0.970792	+	0.239922i	$0.0771220\pi$
$660$		0			0
$661$	881.000	+	1525.94i	0.0518410	+	0.0897913i	0.890781	−	0.454432i	$-0.150158\pi$
$661$	881.000	+	1525.94i	0.0518410	+	0.0897913i	−0.838940	+	0.544223i	$0.816824\pi$
$662$	9290.00	+	16090.8i	0.545417	+	0.944690i
$663$		0			0
$664$	−2940.00	+	5092.23i	−0.171829	+	0.297616i
$665$	9222.00			0.537765
$666$		0			0
$667$	−36540.0			−2.12119
$668$	3948.00	−	6838.14i	0.228672	−	0.396071i
$669$		0			0
$670$	426.000	+	737.854i	0.0245639	+	0.0425459i
$671$	−1596.00	−	2764.35i	−0.0918225	−	0.159041i
$672$		0			0
$673$	−12758.5	+	22098.4i	−0.730764	+	1.26572i	0.225793	+	0.974175i	$0.427503\pi$
$673$	−12758.5	+	22098.4i	−0.730764	+	1.26572i	−0.956557	+	0.291545i	$0.905831\pi$
$674$	7628.00			0.435934
$675$		0			0
$676$	−7188.00			−0.408967
$677$	13449.0	−	23294.4i	0.763496	−	1.32241i	−0.177541	−	0.984113i	$-0.556814\pi$
$677$	13449.0	−	23294.4i	0.763496	−	1.32241i	0.941038	−	0.338301i	$-0.109852\pi$
$678$		0			0
$679$	−2769.50	−	4796.91i	−0.156530	−	0.271117i
$680$	−864.000	−	1496.49i	−0.0487248	−	0.0843939i
$681$		0			0
$682$	2679.00	−	4640.16i	0.150417	−	0.260529i
$683$	−23940.0			−1.34120			−0.670599	−	0.741820i	$-0.733963\pi$
$683$	−23940.0			−1.34120			−0.670599	+	0.741820i	$0.733963\pi$
$684$		0			0
$685$	1962.00			0.109437
$686$	4495.00	−	7785.57i	0.250175	−	0.433315i
$687$		0			0
$688$	−1744.00	−	3020.70i	−0.0966415	−	0.167388i
$689$	810.000	+	1402.96i	0.0447874	+	0.0775741i
$690$		0			0
$691$	−11530.0	+	19970.5i	−0.634764	+	1.09944i	0.351801	+	0.936075i	$0.385569\pi$
$691$	−11530.0	+	19970.5i	−0.634764	+	1.09944i	−0.986565	+	0.163369i	$0.947764\pi$
$692$	8868.00			0.487154
$693$		0			0
$694$	3858.00			0.211020
$695$	−4506.00	+	7804.62i	−0.245931	+	0.425966i
$696$		0			0
$697$	−216.000	−	374.123i	−0.0117383	−	0.0203313i
$698$	−6586.00	−	11407.3i	−0.357140	−	0.618585i
$699$		0			0
$700$	6728.00	−	11653.2i	0.363278	−	0.629216i
$701$	14175.0			0.763741			0.381870	−	0.924216i	$-0.375280\pi$
$701$	14175.0			0.763741			0.381870	+	0.924216i	$0.375280\pi$
$702$		0			0
$703$	−212.000			−0.0113737
$704$	−1824.00	+	3159.26i	−0.0976486	+	0.169132i
$705$		0			0
$706$	6042.00	+	10465.1i	0.322087	+	0.557872i
$707$	−5263.50	−	9116.65i	−0.279992	−	0.484960i
$708$		0			0
$709$	4346.00	−	7527.49i	0.230208	−	0.398732i	−0.727661	−	0.685937i	$-0.759393\pi$
$709$	4346.00	−	7527.49i	0.230208	−	0.398732i	0.957869	+	0.287205i	$0.0927260\pi$
$710$	−2160.00			−0.114174
$711$		0			0
$712$	−7632.00			−0.401715
$713$	4089.00	−	7082.36i	0.214775	−	0.372000i
$714$		0			0
$715$	1710.00	+	2961.81i	0.0894411	+	0.154916i
$716$	−4950.00	−	8573.65i	−0.258366	−	0.447503i
$717$		0			0
$718$	3762.00	−	6515.98i	0.195538	−	0.338682i
$719$	29556.0			1.53304			0.766518	−	0.642223i	$-0.221988\pi$
$719$	29556.0			1.53304			0.766518	+	0.642223i	$0.221988\pi$
$720$		0			0
$721$	−18212.0			−0.940708
$722$	4377.00	−	7581.19i	0.225616	−	0.390779i
$723$		0			0
$724$	−3136.00	−	5431.71i	−0.160979	−	0.278823i
$725$	12180.0	+	21096.4i	0.623936	+	1.08069i
$726$		0			0
$727$	18345.5	−	31775.3i	0.935897	−	1.62102i	0.162870	−	0.986648i	$-0.447925\pi$
$727$	18345.5	−	31775.3i	0.935897	−	1.62102i	0.773027	−	0.634373i	$-0.218742\pi$
$728$	−4640.00			−0.236222
$729$		0			0
$730$	−6954.00			−0.352574
$731$	−7848.00	+	13593.1i	−0.397084	+	0.687771i
$732$		0			0
$733$	9899.00	+	17145.6i	0.498810	+	0.863965i	0.999999	−	0.00137327i	$-0.000437125\pi$
$733$	9899.00	+	17145.6i	0.498810	+	0.863965i	−0.501189	+	0.865338i	$0.667104\pi$
$734$	−7261.00	−	12576.4i	−0.365134	−	0.632431i
$735$		0			0
$736$	−2784.00	+	4822.03i	−0.139429	+	0.241498i
$737$	−8094.00			−0.404540
$738$		0			0
$739$	−21976.0			−1.09391			−0.546955	−	0.837162i	$-0.684213\pi$
$739$	−21976.0			−1.09391			−0.546955	+	0.837162i	$0.684213\pi$
$740$	12.0000	−	20.7846i	0.000596120	−	0.00103251i
$741$		0			0
$742$	−2349.00	−	4068.59i	−0.116219	−	0.201297i
$743$	−6618.00	−	11462.7i	−0.326771	−	0.565984i	0.655098	−	0.755544i	$-0.272627\pi$
$743$	−6618.00	−	11462.7i	−0.326771	−	0.565984i	−0.981869	+	0.189560i	$0.939294\pi$
$744$		0			0
$745$	−2704.50	+	4684.33i	−0.133000	+	0.230363i
$746$	−3280.00			−0.160978
$747$		0			0
$748$	16416.0			0.802444
$749$	9787.50	−	16952.4i	0.477473	−	0.827008i
$750$		0			0
$751$	3162.50	+	5477.61i	0.153663	+	0.266153i	0.932572	−	0.360985i	$-0.117560\pi$
$751$	3162.50	+	5477.61i	0.153663	+	0.266153i	−0.778908	+	0.627138i	$0.784226\pi$
$752$	3792.00	+	6567.94i	0.183883	+	0.318495i
$753$		0			0
$754$	4200.00	−	7274.61i	0.202858	−	0.351360i
$755$	−7377.00			−0.355598
$756$		0			0
$757$	−3238.00			−0.155465			−0.0777326	−	0.996974i	$-0.524768\pi$
$757$	−3238.00			−0.155465			−0.0777326	+	0.996974i	$0.524768\pi$
$758$	−7396.00	+	12810.2i	−0.354399	+	0.613838i
$759$		0			0
$760$	1272.00	+	2203.17i	0.0607109	+	0.105154i
$761$	−20208.0	−	35001.3i	−0.962601	−	1.66727i	−0.715927	−	0.698176i	$-0.753995\pi$
$761$	−20208.0	−	35001.3i	−0.962601	−	1.66727i	−0.246675	−	0.969098i	$-0.579338\pi$
$762$		0			0
$763$	−25085.0	+	43448.5i	−1.19022	+	2.06152i
$764$	−4560.00			−0.215936
$765$		0			0
$766$	−9984.00			−0.470935
$767$	840.000	−	1454.92i	0.0395445	−	0.0684931i
$768$		0			0
$769$	2379.50	+	4121.41i	0.111583	+	0.193267i	0.916408	−	0.400244i	$-0.131075\pi$
$769$	2379.50	+	4121.41i	0.111583	+	0.193267i	−0.804826	+	0.593511i	$0.797741\pi$
$770$	−4959.00	−	8589.24i	−0.232091	−	0.401993i
$771$		0			0
$772$	−4090.00	+	7084.09i	−0.190677	+	0.330262i
$773$	−27414.0			−1.27557			−0.637783	−	0.770216i	$-0.720148\pi$
$773$	−27414.0			−1.27557			−0.637783	+	0.770216i	$0.720148\pi$
$774$		0			0
$775$	−5452.00			−0.252699
$776$	764.000	−	1323.29i	0.0353428	−	0.0612155i
$777$		0			0
$778$	9453.00	+	16373.1i	0.435612	+	0.754503i
$779$	318.000	+	550.792i	0.0146258	+	0.0253327i
$780$		0			0
$781$	10260.0	−	17770.8i	0.470079	−	0.814201i
$782$	25056.0			1.14578
$783$		0			0
$784$	7968.00			0.362974
$785$	−294.000	+	509.223i	−0.0133673	+	0.0231528i
$786$		0			0
$787$	−3088.00	−	5348.57i	−0.139867	−	0.242257i	0.787579	−	0.616214i	$-0.211334\pi$
$787$	−3088.00	−	5348.57i	−0.139867	−	0.242257i	−0.927446	+	0.373957i	$0.878001\pi$
$788$	−7470.00	−	12938.4i	−0.337700	−	0.584914i
$789$		0			0
$790$	480.000	−	831.384i	0.0216173	−	0.0374422i
$791$	−54114.0			−2.43246
$792$		0			0
$793$	1120.00			0.0501543
$794$	8588.00	−	14874.9i	0.383850	−	0.664847i
$795$		0			0
$796$	−2326.00	−	4028.75i	−0.103571	−	0.179391i
$797$	3439.50	+	5957.39i	0.152865	+	0.264770i	0.932280	−	0.361739i	$-0.117817\pi$
$797$	3439.50	+	5957.39i	0.152865	+	0.264770i	−0.779415	+	0.626508i	$0.784483\pi$
$798$		0			0
$799$	17064.0	−	29555.7i	0.755546	−	1.30864i
$800$	3712.00			0.164049
$801$		0			0
$802$	−3432.00			−0.151107
$803$	33031.5	−	57212.2i	1.45163	−	2.51429i
$804$		0			0
$805$	−7569.00	−	13109.9i	−0.331394	−	0.573991i
$806$	940.000	+	1628.13i	0.0410795	+	0.0711518i
$807$		0			0
$808$	1452.00	−	2514.94i	0.0632193	−	0.109499i
$809$	16902.0			0.734540			0.367270	−	0.930114i	$-0.380293\pi$
$809$	16902.0			0.734540			0.367270	+	0.930114i	$0.380293\pi$
$810$		0			0
$811$	24086.0			1.04288			0.521439	−	0.853289i	$-0.325395\pi$
$811$	24086.0			1.04288			0.521439	+	0.853289i	$0.325395\pi$
$812$	−12180.0	+	21096.4i	−0.526397	+	0.911746i
$813$		0			0
$814$	114.000	+	197.454i	0.00490872	+	0.00850215i
$815$	−2346.00	−	4063.39i	−0.100830	−	0.174643i
$816$		0			0
$817$	11554.0	−	20012.1i	0.494765	−	0.856959i
$818$	19778.0			0.845381
$819$		0			0
$820$	−72.0000			−0.00306628
$821$	3927.00	−	6801.76i	0.166935	−	0.289139i	−0.770406	−	0.637554i	$-0.779946\pi$
$821$	3927.00	−	6801.76i	0.166935	−	0.289139i	0.937341	+	0.348414i	$0.113280\pi$
$822$		0			0
$823$	−2885.50	−	4997.83i	−0.122214	−	0.211681i	0.798426	−	0.602092i	$-0.205666\pi$
$823$	−2885.50	−	4997.83i	−0.122214	−	0.211681i	−0.920641	+	0.390411i	$0.872333\pi$
$824$	−2512.00	−	4350.91i	−0.106201	−	0.183946i
$825$		0			0
$826$	−2436.00	+	4219.28i	−0.102614	+	0.177733i
$827$	17568.0			0.738693			0.369347	−	0.929292i	$-0.379582\pi$
$827$	17568.0			0.738693			0.369347	+	0.929292i	$0.379582\pi$
$828$		0			0
$829$	31322.0			1.31225			0.656127	−	0.754651i	$-0.272194\pi$
$829$	31322.0			1.31225			0.656127	+	0.754651i	$0.272194\pi$
$830$	2205.00	−	3819.17i	0.0922129	−	0.159717i
$831$		0			0
$832$	−640.000	−	1108.51i	−0.0266683	−	0.0461908i
$833$	−17928.0	−	31052.2i	−0.745700	−	1.29159i
$834$		0			0
$835$	−2961.00	+	5128.60i	−0.122718	+	0.212554i
$836$	−24168.0			−0.999842
$837$		0			0
$838$	11112.0			0.458064
$839$	20928.0	−	36248.4i	0.861162	−	1.49158i	−0.00964650	−	0.999953i	$-0.503071\pi$
$839$	20928.0	−	36248.4i	0.861162	−	1.49158i	0.870808	−	0.491623i	$-0.163596\pi$
$840$		0			0
$841$	−9855.50	−	17070.2i	−0.404096	−	0.699915i
$842$	−2104.00	−	3644.23i	−0.0861148	−	0.149155i
$843$		0			0
$844$	−4252.00	+	7364.68i	−0.173412	+	0.300359i
$845$	5391.00			0.219475
$846$		0			0
$847$	55622.0			2.25643
$848$	648.000	−	1122.37i	0.0262411	−	0.0454508i
$849$		0			0
$850$	−8352.00	−	14466.1i	−0.337025	−	0.583744i
$851$	174.000	+	301.377i	0.00700898	+	0.0121399i
$852$		0			0
$853$	−7831.00	+	13563.7i	−0.314336	+	0.544445i	−0.979296	−	0.202433i	$-0.935115\pi$
$853$	−7831.00	+	13563.7i	−0.314336	+	0.544445i	0.664960	+	0.746879i	$0.268448\pi$
$854$	−3248.00			−0.130146
$855$		0			0
$856$	5400.00			0.215617
$857$	−19932.0	+	34523.2i	−0.794474	+	1.37607i	0.128699	+	0.991684i	$0.458920\pi$
$857$	−19932.0	+	34523.2i	−0.794474	+	1.37607i	−0.923173	+	0.384385i	$0.874413\pi$
$858$		0			0
$859$	4580.00	+	7932.79i	0.181918	+	0.315091i	0.942534	−	0.334111i	$-0.108436\pi$
$859$	4580.00	+	7932.79i	0.181918	+	0.315091i	−0.760616	+	0.649202i	$0.775103\pi$
$860$	1308.00	+	2265.52i	0.0518633	+	0.0898299i
$861$		0			0
$862$	−7614.00	+	13187.8i	−0.300851	+	0.521090i
$863$	−5076.00			−0.200219			−0.100110	−	0.994976i	$-0.531919\pi$
$863$	−5076.00			−0.200219			−0.100110	+	0.994976i	$0.531919\pi$
$864$		0			0
$865$	−6651.00			−0.261434
$866$	7805.00	−	13518.7i	0.306264	−	0.530465i
$867$		0			0
$868$	−2726.00	−	4721.57i	−0.106597	−	0.184632i
$869$	4560.00	+	7898.15i	0.178006	+	0.308316i
$870$		0			0
$871$	1420.00	−	2459.51i	0.0552409	−	0.0956801i
$872$	−13840.0			−0.537479
$873$		0			0
$874$	−36888.0			−1.42764
$875$	−10483.5	+	18158.0i	−0.405037	+	0.701544i
$876$		0			0
$877$	−7489.00	−	12971.3i	−0.288353	−	0.499442i	0.685064	−	0.728483i	$-0.259774\pi$
$877$	−7489.00	−	12971.3i	−0.288353	−	0.499442i	−0.973417	+	0.229041i	$0.926441\pi$
$878$	−5209.00	−	9022.25i	−0.200222	−	0.346795i
$879$		0			0
$880$	1368.00	−	2369.45i	0.0524037	−	0.0907659i
$881$	22860.0			0.874203			0.437102	−	0.899412i	$-0.356005\pi$
$881$	22860.0			0.874203			0.437102	+	0.899412i	$0.356005\pi$
$882$		0			0
$883$	−32506.0			−1.23886			−0.619430	−	0.785052i	$-0.712636\pi$
$883$	−32506.0			−1.23886			−0.619430	+	0.785052i	$0.712636\pi$
$884$	−2880.00	+	4988.31i	−0.109576	+	0.189791i
$885$		0			0
$886$	−4236.00	−	7336.97i	−0.160622	−	0.278206i
$887$	17934.0	+	31062.6i	0.678878	+	1.17585i	0.975319	+	0.220800i	$0.0708668\pi$
$887$	17934.0	+	31062.6i	0.678878	+	1.17585i	−0.296441	+	0.955051i	$0.595800\pi$
$888$		0			0
$889$	−19995.5	+	34633.2i	−0.754362	+	1.30659i
$890$	5724.00			0.215583
$891$		0			0
$892$	−11008.0			−0.413201
$893$	−25122.0	+	43512.6i	−0.941406	+	1.63056i
$894$		0			0
$895$	3712.50	+	6430.24i	0.138654	+	0.240155i
$896$	1856.00	+	3214.69i	0.0692016	+	0.119861i
$897$		0			0
$898$	16002.0	−	27716.3i	0.594648	−	1.02996i
$899$	9870.00			0.366166
$900$		0			0
$901$	−5832.00			−0.215640
$902$	342.000	−	592.361i	0.0126246	−	0.0218664i
$903$		0			0
$904$	−7464.00	−	12928.0i	−0.274612	−	0.475641i
$905$	2352.00	+	4073.78i	0.0863902	+	0.149632i
$906$		0			0
$907$	16793.0	−	29086.3i	0.614777	−	1.06482i	−0.375647	−	0.926763i	$-0.622579\pi$
$907$	16793.0	−	29086.3i	0.614777	−	1.06482i	0.990424	−	0.138062i	$-0.0440872\pi$
$908$	15888.0			0.580685
$909$		0			0
$910$	3480.00			0.126770
$911$	−14451.0	+	25029.9i	−0.525558	+	0.910292i	0.473999	+	0.880525i	$0.342810\pi$
$911$	−14451.0	+	25029.9i	−0.525558	+	0.910292i	−0.999557	+	0.0297672i	$0.990523\pi$
$912$		0			0
$913$	20947.5	+	36282.1i	0.759322	+	1.31518i
$914$	7319.00	+	12676.9i	0.264870	+	0.458768i
$915$		0			0
$916$	−9004.00	+	15595.4i	−0.324782	+	0.562539i
$917$	−16791.0			−0.604676
$918$		0			0
$919$	28271.0			1.01477			0.507385	−	0.861719i	$-0.330612\pi$
$919$	28271.0			1.01477			0.507385	+	0.861719i	$0.330612\pi$
$920$	2088.00	−	3616.52i	0.0748253	−	0.129601i
$921$		0			0
$922$	−9483.00	−	16425.0i	−0.338727	−	0.586692i
$923$	3600.00	+	6235.38i	0.128381	+	0.222362i
$924$		0			0
$925$	116.000	−	200.918i	0.00412330	−	0.00714177i
$926$	−21586.0			−0.766047
$927$		0			0
$928$	−6720.00			−0.237710
$929$	9570.00	−	16575.7i	0.337978	−	0.585395i	−0.646074	−	0.763275i	$-0.723590\pi$
$929$	9570.00	−	16575.7i	0.337978	−	0.585395i	0.984052	+	0.177880i	$0.0569237\pi$
$930$		0			0
$931$	26394.0	+	45715.7i	0.929139	+	1.60932i
$932$	9684.00	+	16773.2i	0.340354	+	0.589510i
$933$		0			0
$934$	−2583.00	+	4473.89i	−0.0904907	+	0.156735i
$935$	−12312.0			−0.430637
$936$		0			0
$937$	31619.0			1.10240			0.551199	−	0.834374i	$-0.314170\pi$
$937$	31619.0			1.10240			0.551199	+	0.834374i	$0.314170\pi$
$938$	−4118.00	+	7132.59i	−0.143345	+	0.248281i
$939$		0			0
$940$	−2844.00	−	4925.95i	−0.0986820	−	0.170922i
$941$	−10456.5	−	18111.2i	−0.362245	−	0.627426i	0.626085	−	0.779755i	$-0.284656\pi$
$941$	−10456.5	−	18111.2i	−0.362245	−	0.627426i	−0.988330	+	0.152329i	$0.951323\pi$
$942$		0			0
$943$	522.000	−	904.131i	0.0180261	−	0.0312222i
$944$	−1344.00			−0.0463384
$945$		0			0
$946$	−24852.0			−0.854131
$947$	8764.50	−	15180.6i	0.300748	−	0.520910i	−0.675558	−	0.737307i	$-0.736097\pi$
$947$	8764.50	−	15180.6i	0.300748	−	0.520910i	0.976305	+	0.216397i	$0.0694305\pi$
$948$		0			0
$949$	11590.0	+	20074.5i	0.396446	+	0.686665i
$950$	12296.0	+	21297.3i	0.419931	+	0.727343i
$951$		0			0
$952$	8352.00	−	14466.1i	0.284338	−	0.492488i
$953$	53604.0			1.82204			0.911020	−	0.412362i	$-0.135296\pi$
$953$	53604.0			1.82204			0.911020	+	0.412362i	$0.135296\pi$
$954$		0			0
$955$	3420.00			0.115883
$956$	−10668.0	+	18477.5i	−0.360908	+	0.625111i
$957$		0			0
$958$	1254.00	+	2171.99i	0.0422911	+	0.0732504i
$959$	9483.00	+	16425.0i	0.319314	+	0.553068i
$960$		0			0
$961$	13791.0	−	23886.7i	0.462925	−	0.801810i
$962$	−80.0000			−0.00268119
$963$		0			0
$964$	−15976.0			−0.533768
$965$	3067.50	−	5313.07i	0.102328	−	0.177237i
$966$		0			0
$967$	−5558.50	−	9627.60i	−0.184849	−	0.320168i	0.758676	−	0.651468i	$-0.225846\pi$
$967$	−5558.50	−	9627.60i	−0.184849	−	0.320168i	−0.943526	+	0.331299i	$0.892513\pi$
$968$	7672.00	+	13288.3i	0.254739	+	0.441221i
$969$		0			0
$970$	−573.000	+	992.465i	−0.0189669	+	0.0328517i
$971$	27297.0			0.902165			0.451083	−	0.892482i	$-0.351038\pi$
$971$	27297.0			0.902165			0.451083	+	0.892482i	$0.351038\pi$
$972$		0			0
$973$	−87116.0			−2.87031
$974$	17336.0	−	30026.8i	0.570309	−	0.987805i
$975$		0			0
$976$	−448.000	−	775.959i	−0.0146928	−	0.0254486i
$977$	12543.0	+	21725.1i	0.410733	+	0.711410i	0.994970	−	0.100173i	$-0.0319395\pi$
$977$	12543.0	+	21725.1i	0.410733	+	0.711410i	−0.584237	+	0.811583i	$0.698606\pi$
$978$		0			0
$979$	−27189.0	+	47092.7i	−0.887604	+	1.53738i
$980$	−5976.00			−0.194792
$981$		0			0
$982$	−30342.0			−0.986000
$983$	−10491.0	+	18170.9i	−0.340398	+	0.589586i	−0.984507	−	0.175348i	$-0.943895\pi$
$983$	−10491.0	+	18170.9i	−0.340398	+	0.589586i	0.644109	+	0.764934i	$0.277228\pi$
$984$		0			0
$985$	5602.50	+	9703.81i	0.181229	+	0.313898i
$986$	15120.0	+	26188.6i	0.488356	+	0.845857i
$987$		0			0
$988$	4240.00	−	7343.90i	0.136531	−	0.236478i
$989$	−37932.0			−1.21958
$990$		0			0
$991$	11477.0			0.367890			0.183945	−	0.982937i	$-0.441113\pi$
$991$	11477.0			0.367890			0.183945	+	0.982937i	$0.441113\pi$
$992$	752.000	−	1302.50i	0.0240686	−	0.0416880i
$993$		0			0
$994$	−10440.0	−	18082.6i	−0.333136	−	0.577008i
$995$	1744.50	+	3021.56i	0.0555823	+	0.0962713i
$996$		0			0
$997$	−4294.00	+	7437.43i	−0.136402	+	0.236254i	−0.926132	−	0.377200i	$-0.876887\pi$
$997$	−4294.00	+	7437.43i	−0.136402	+	0.236254i	0.789730	+	0.613454i	$0.210220\pi$
$998$	−17860.0			−0.566481
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.4.c.g.55.1		2
3.2	odd	2		162.4.c.b.55.1		2
9.2	odd	6		54.4.a.c.1.1	yes	1
9.4	even	3	inner	162.4.c.g.109.1		2
9.5	odd	6		162.4.c.b.109.1		2
9.7	even	3		54.4.a.b.1.1	✓	1
36.7	odd	6		432.4.a.e.1.1		1
36.11	even	6		432.4.a.j.1.1		1
45.2	even	12		1350.4.c.b.649.2		2
45.7	odd	12		1350.4.c.s.649.1		2
45.29	odd	6		1350.4.a.a.1.1		1
45.34	even	6		1350.4.a.o.1.1		1
45.38	even	12		1350.4.c.b.649.1		2
45.43	odd	12		1350.4.c.s.649.2		2
72.11	even	6		1728.4.a.k.1.1		1
72.29	odd	6		1728.4.a.l.1.1		1
72.43	odd	6		1728.4.a.u.1.1		1
72.61	even	6		1728.4.a.v.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.4.a.b.1.1	✓	1	9.7	even	3
54.4.a.c.1.1	yes	1	9.2	odd	6
162.4.c.b.55.1		2	3.2	odd	2
162.4.c.b.109.1		2	9.5	odd	6
162.4.c.g.55.1		2	1.1	even	1	trivial
162.4.c.g.109.1		2	9.4	even	3	inner
432.4.a.e.1.1		1	36.7	odd	6
432.4.a.j.1.1		1	36.11	even	6
1350.4.a.a.1.1		1	45.29	odd	6
1350.4.a.o.1.1		1	45.34	even	6
1350.4.c.b.649.1		2	45.38	even	12
1350.4.c.b.649.2		2	45.2	even	12
1350.4.c.s.649.1		2	45.7	odd	12
1350.4.c.s.649.2		2	45.43	odd	12
1728.4.a.k.1.1		1	72.11	even	6
1728.4.a.l.1.1		1	72.29	odd	6
1728.4.a.u.1.1		1	72.43	odd	6
1728.4.a.v.1.1		1	72.61	even	6

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:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	162.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(1.50000 + 2.59808i) q^{5} +(-14.5000 + 25.1147i) q^{7} -8.00000 q^{8} +O(q^{10})\)	\(q+(1.00000 - 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(1.50000 + 2.59808i) q^{5} +(-14.5000 + 25.1147i) q^{7} -8.00000 q^{8} +6.00000 q^{10} +(-28.5000 + 49.3634i) q^{11} +(-10.0000 - 17.3205i) q^{13} +(29.0000 + 50.2295i) q^{14} +(-8.00000 + 13.8564i) q^{16} +72.0000 q^{17} -106.000 q^{19} +(6.00000 - 10.3923i) q^{20} +(57.0000 + 98.7269i) q^{22} +(87.0000 + 150.688i) q^{23} +(58.0000 - 100.459i) q^{25} -40.0000 q^{26} +116.000 q^{28} +(-105.000 + 181.865i) q^{29} +(-23.5000 - 40.7032i) q^{31} +(16.0000 + 27.7128i) q^{32} +(72.0000 - 124.708i) q^{34} -87.0000 q^{35} +2.00000 q^{37} +(-106.000 + 183.597i) q^{38} +(-12.0000 - 20.7846i) q^{40} +(-3.00000 - 5.19615i) q^{41} +(-109.000 + 188.794i) q^{43} +228.000 q^{44} +348.000 q^{46} +(237.000 - 410.496i) q^{47} +(-249.000 - 431.281i) q^{49} +(-116.000 - 200.918i) q^{50} +(-40.0000 + 69.2820i) q^{52} -81.0000 q^{53} -171.000 q^{55} +(116.000 - 200.918i) q^{56} +(210.000 + 363.731i) q^{58} +(42.0000 + 72.7461i) q^{59} +(-28.0000 + 48.4974i) q^{61} -94.0000 q^{62} +64.0000 q^{64} +(30.0000 - 51.9615i) q^{65} +(71.0000 + 122.976i) q^{67} +(-144.000 - 249.415i) q^{68} +(-87.0000 + 150.688i) q^{70} -360.000 q^{71} -1159.00 q^{73} +(2.00000 - 3.46410i) q^{74} +(212.000 + 367.195i) q^{76} +(-826.500 - 1431.54i) q^{77} +(80.0000 - 138.564i) q^{79} -48.0000 q^{80} -12.0000 q^{82} +(367.500 - 636.529i) q^{83} +(108.000 + 187.061i) q^{85} +(218.000 + 377.587i) q^{86} +(228.000 - 394.908i) q^{88} +954.000 q^{89} +580.000 q^{91} +(348.000 - 602.754i) q^{92} +(-474.000 - 820.992i) q^{94} +(-159.000 - 275.396i) q^{95} +(-95.5000 + 165.411i) q^{97} -996.000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 4 q^{4} + 3 q^{5} - 29 q^{7} - 16 q^{8}+O(q^{10}) \) 2 * q + 2 * q^2 - 4 * q^4 + 3 * q^5 - 29 * q^7 - 16 * q^8	\( 2 q + 2 q^{2} - 4 q^{4} + 3 q^{5} - 29 q^{7} - 16 q^{8} + 12 q^{10} - 57 q^{11} - 20 q^{13} + 58 q^{14} - 16 q^{16} + 144 q^{17} - 212 q^{19} + 12 q^{20} + 114 q^{22} + 174 q^{23} + 116 q^{25} - 80 q^{26} + 232 q^{28} - 210 q^{29} - 47 q^{31} + 32 q^{32} + 144 q^{34} - 174 q^{35} + 4 q^{37} - 212 q^{38} - 24 q^{40} - 6 q^{41} - 218 q^{43} + 456 q^{44} + 696 q^{46} + 474 q^{47} - 498 q^{49} - 232 q^{50} - 80 q^{52} - 162 q^{53} - 342 q^{55} + 232 q^{56} + 420 q^{58} + 84 q^{59} - 56 q^{61} - 188 q^{62} + 128 q^{64} + 60 q^{65} + 142 q^{67} - 288 q^{68} - 174 q^{70} - 720 q^{71} - 2318 q^{73} + 4 q^{74} + 424 q^{76} - 1653 q^{77} + 160 q^{79} - 96 q^{80} - 24 q^{82} + 735 q^{83} + 216 q^{85} + 436 q^{86} + 456 q^{88} + 1908 q^{89} + 1160 q^{91} + 696 q^{92} - 948 q^{94} - 318 q^{95} - 191 q^{97} - 1992 q^{98}+O(q^{100}) \) 2 * q + 2 * q^2 - 4 * q^4 + 3 * q^5 - 29 * q^7 - 16 * q^8 + 12 * q^10 - 57 * q^11 - 20 * q^13 + 58 * q^14 - 16 * q^16 + 144 * q^17 - 212 * q^19 + 12 * q^20 + 114 * q^22 + 174 * q^23 + 116 * q^25 - 80 * q^26 + 232 * q^28 - 210 * q^29 - 47 * q^31 + 32 * q^32 + 144 * q^34 - 174 * q^35 + 4 * q^37 - 212 * q^38 - 24 * q^40 - 6 * q^41 - 218 * q^43 + 456 * q^44 + 696 * q^46 + 474 * q^47 - 498 * q^49 - 232 * q^50 - 80 * q^52 - 162 * q^53 - 342 * q^55 + 232 * q^56 + 420 * q^58 + 84 * q^59 - 56 * q^61 - 188 * q^62 + 128 * q^64 + 60 * q^65 + 142 * q^67 - 288 * q^68 - 174 * q^70 - 720 * q^71 - 2318 * q^73 + 4 * q^74 + 424 * q^76 - 1653 * q^77 + 160 * q^79 - 96 * q^80 - 24 * q^82 + 735 * q^83 + 216 * q^85 + 436 * q^86 + 456 * q^88 + 1908 * q^89 + 1160 * q^91 + 696 * q^92 - 948 * q^94 - 318 * q^95 - 191 * q^97 - 1992 * q^98

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