LMFDB - Embedded newform 162.4.c.b.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.b.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	0.791114	−	0.611669i	$-0.209502\pi$
$5$	−1.50000	−	2.59808i	−0.134164	−	0.232379i	−0.925278	+	0.379290i	$0.876168\pi$
$6$		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	$-0.547947\pi$
$11$	28.5000	−	49.3634i	0.781188	−	1.35306i	0.931250	−	0.364381i	$-0.118720\pi$
$12$		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	$-0.671690\pi$
$17$	−72.0000			−1.02721			−0.513605	+	0.858027i	$0.671690\pi$
$18$		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	$-0.877406\pi$
$23$	−87.0000	−	150.688i	−0.788728	−	1.36612i	0.138018	−	0.990430i	$-0.455927\pi$
$24$		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	$-0.598620\pi$
$29$	105.000	−	181.865i	0.672345	−	1.16454i	0.977237	−	0.212149i	$-0.0680463\pi$
$30$		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	0.871683	−	0.490071i	$-0.163029\pi$
$41$	3.00000	+	5.19615i	0.0114273	+	0.0197927i	−0.860255	+	0.509864i	$0.829696\pi$
$42$		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	$0.429734\pi$
$47$	−237.000	+	410.496i	−0.735532	+	1.27398i	−0.954490	+	0.298244i	$0.903599\pi$
$48$		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	$-0.466527\pi$
$53$	81.0000			0.209928			0.104964	+	0.994476i	$0.466527\pi$
$54$		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	0.815960	−	0.578109i	$-0.196209\pi$
$59$	−42.0000	−	72.7461i	−0.0926769	−	0.160521i	−0.908637	+	0.417588i	$0.862876\pi$
$60$		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	$-0.402722\pi$
$71$	360.000			0.601748			0.300874	+	0.953664i	$0.402722\pi$
$72$		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	−0.999871	−	0.0160860i	$-0.994879\pi$
$83$	−367.500	+	636.529i	−0.486004	+	0.841784i	0.513866	+	0.857870i	$0.328213\pi$
$84$		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	$-0.692326\pi$
$89$	−954.000			−1.13622			−0.568111	+	0.822952i	$0.692326\pi$
$90$		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	−0.762662	−	0.646797i	$-0.776108\pi$
$101$	181.500	−	314.367i	0.178811	−	0.309710i	0.941474	+	0.337087i	$0.109442\pi$
$102$		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	$-0.401367\pi$
$107$	675.000			0.609857			0.304929	+	0.952375i	$0.401367\pi$
$108$		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	$-0.883549\pi$
$113$	−933.000	−	1616.00i	−0.776719	−	1.34532i	0.157104	−	0.987582i	$-0.449784\pi$
$114$		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	0.753188	−	0.657805i	$-0.228515\pi$
$131$	−289.500	−	501.429i	−0.193082	−	0.334428i	−0.946270	+	0.323377i	$0.895182\pi$
$132$		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	−0.949789	−	0.312891i	$-0.898703\pi$
$137$	−327.000	+	566.381i	−0.203923	+	0.353206i	0.745866	+	0.666096i	$0.232036\pi$
$138$		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	0.504325	−	0.863514i	$-0.331741\pi$
$149$	−901.500	−	1561.44i	−0.495663	−	0.858513i	−0.999987	+	0.00500094i	$0.998408\pi$
$150$		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	0.541476	−	0.840716i	$-0.317866\pi$
$167$	−987.000	−	1709.53i	−0.457343	−	0.792142i	−0.998820	+	0.0485740i	$0.984532\pi$
$168$		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	−0.512737	−	0.858546i	$-0.671368\pi$
$173$	1108.50	−	1919.98i	0.487154	−	0.843776i	0.999891	+	0.0147700i	$0.00470159\pi$
$174$		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	$-0.672852\pi$
$179$	−2475.00			−1.03346			−0.516732	+	0.856147i	$0.672852\pi$
$180$		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	−0.953562	−	0.301198i	$-0.902614\pi$
$191$	−570.000	+	987.269i	−0.215936	+	0.374012i	0.737626	+	0.675210i	$0.235947\pi$
$192$		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	$-0.736029\pi$
$197$	−3735.00			−1.35080			−0.675400	+	0.737451i	$0.736029\pi$
$198$		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	$-0.636118\pi$
$227$	1986.00	−	3439.85i	0.580685	−	1.00578i	0.995398	−	0.0958236i	$-0.0305485\pi$
$228$		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	$-0.261672\pi$
$233$	4842.00			1.36142			0.680708	+	0.732555i	$0.261672\pi$
$234$		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	$0.0900254\pi$
$239$	2667.00	+	4619.38i	0.721815	+	1.25022i	−0.238456	+	0.971153i	$0.576641\pi$
$240$		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	$-0.540452\pi$
$251$	−1008.00			−0.253484			−0.126742	+	0.991936i	$0.540452\pi$
$252$		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	0.916631	−	0.399734i	$-0.130898\pi$
$257$	462.000	+	800.207i	0.112135	+	0.194224i	−0.804496	+	0.593958i	$0.797564\pi$
$258$		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	−0.919320	−	0.393510i	$-0.871261\pi$
$263$	−507.000	+	878.150i	−0.118871	+	0.205890i	0.800450	+	0.599400i	$0.204594\pi$
$264$		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	$-0.609273\pi$
$269$	−2970.00			−0.673175			−0.336588	+	0.941652i	$0.609273\pi$
$270$		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	−0.878482	−	0.477775i	$-0.841443\pi$
$281$	−120.000	+	207.846i	−0.0254754	+	0.0441248i	0.853007	+	0.521900i	$0.174777\pi$
$282$		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	$0.00377431\pi$
$293$	2559.00	+	4432.32i	0.510233	+	0.883750i	−0.489696	+	0.871893i	$0.662892\pi$
$294$		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	$-0.920514\pi$
$311$	−3831.00	−	6635.49i	−0.698508	−	1.20985i	0.270475	−	0.962727i	$-0.412819\pi$
$312$		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	$-0.618289\pi$
$317$	3529.50	−	6113.27i	0.625352	−	1.08314i	0.988473	−	0.151399i	$-0.0483778\pi$
$318$		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	0.781724	−	0.623625i	$-0.214341\pi$
$347$	−964.500	−	1670.56i	−0.149213	−	0.258445i	−0.930937	+	0.365180i	$0.881007\pi$
$348$		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	−0.543217	−	0.839593i	$-0.682794\pi$
$353$	3021.00	−	5232.53i	0.455500	−	0.788950i	0.998717	+	0.0506430i	$0.0161271\pi$
$354$		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	$-0.589186\pi$
$359$	−3762.00			−0.553066			−0.276533	+	0.961004i	$0.589186\pi$
$360$		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	0.983099	−	0.183075i	$-0.0586052\pi$
$383$	2496.00	+	4323.20i	0.333002	+	0.576776i	−0.650097	+	0.759851i	$0.725272\pi$
$384$		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	$-0.622066\pi$
$389$	4726.50	−	8186.54i	0.616049	−	1.06703i	0.990199	−	0.139660i	$-0.0446010\pi$
$390$		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	0.914492	−	0.404604i	$-0.132591\pi$
$401$	858.000	+	1486.10i	0.106849	+	0.185068i	−0.807643	+	0.589672i	$0.799257\pi$
$402$		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	0.657389	−	0.753551i	$-0.271661\pi$
$419$	−2778.00	−	4811.64i	−0.323900	−	0.561012i	−0.981289	+	0.192540i	$0.938328\pi$
$420$		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	$-0.360109\pi$
$431$	7614.00			0.850936			0.425468	+	0.904973i	$0.360109\pi$
$432$		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	−0.956964	−	0.290208i	$-0.906275\pi$
$443$	−2118.00	+	3668.48i	−0.227154	+	0.393442i	0.729810	+	0.683651i	$0.239609\pi$
$444$		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	$-0.818008\pi$
$449$	−16002.0			−1.68192			−0.840959	+	0.541099i	$0.818008\pi$
$450$		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	−0.999711	−	0.0240450i	$-0.992345\pi$
$461$	−4741.50	+	8212.52i	−0.479032	+	0.829707i	0.520679	+	0.853752i	$0.325679\pi$
$462$		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	$-0.459153\pi$
$467$	2583.00			0.255946			0.127973	+	0.991778i	$0.459153\pi$
$468$		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	−0.834571	−	0.550901i	$-0.814284\pi$
$479$	627.000	−	1086.00i	0.0598087	−	0.103592i	0.894379	+	0.447309i	$0.147618\pi$
$480$		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	$0.0789077\pi$
$491$	7585.50	+	13138.5i	0.697207	+	1.20760i	−0.272224	+	0.962234i	$0.587759\pi$
$492$		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	$-0.264516\pi$
$503$	15210.0			1.34827			0.674136	+	0.738608i	$0.264516\pi$
$504$		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	$-0.840114\pi$
$509$	−9820.50	−	17009.6i	−0.855179	−	1.48121i	0.0213002	−	0.999773i	$-0.493219\pi$
$510$		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	$-0.108007\pi$
$521$	22428.0			1.88597			0.942983	+	0.332840i	$0.108007\pi$
$522$		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	$-0.308812\pi$
$557$	14859.0			1.13033			0.565167	+	0.824977i	$0.308812\pi$
$558$		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	0.670973	−	0.741482i	$-0.265877\pi$
$563$	−4096.50	−	7095.35i	−0.306655	−	0.531142i	−0.977628	+	0.210339i	$0.932543\pi$
$564$		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	$-0.624307\pi$
$569$	8286.00	−	14351.8i	0.610487	−	1.05739i	0.991158	−	0.132684i	$-0.0423596\pi$
$570$		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	$-0.443108\pi$
$587$	13384.5	−	23182.6i	0.941120	−	1.63007i	0.763340	−	0.645997i	$-0.223558\pi$
$588$		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	$-0.533989\pi$
$593$	−3078.00			−0.213151			−0.106575	+	0.994305i	$0.533989\pi$
$594$		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	0.848432	−	0.529304i	$-0.177547\pi$
$599$	−501.000	−	867.757i	−0.0341741	−	0.0591913i	−0.882607	+	0.470112i	$0.844213\pi$
$600$		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	0.873654	−	0.486548i	$-0.161744\pi$
$617$	237.000	+	410.496i	0.0154640	+	0.0267844i	−0.858190	+	0.513332i	$0.828411\pi$
$618$		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	$-0.607734\pi$
$641$	10563.0	−	18295.7i	0.650879	−	1.12736i	0.982910	−	0.184087i	$-0.0589328\pi$
$642$		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	$-0.615306\pi$
$647$	−11664.0			−0.708747			−0.354373	+	0.935104i	$0.615306\pi$
$648$		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	0.911779	−	0.410681i	$-0.134709\pi$
$653$	1672.50	+	2896.85i	0.100230	+	0.173603i	−0.811550	+	0.584284i	$0.801376\pi$
$654$		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	−0.970792	−	0.239922i	$-0.922878\pi$
$659$	−4696.50	+	8134.58i	−0.277617	+	0.480847i	0.693175	+	0.720769i	$0.256211\pi$
$660$		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	$0.443186\pi$
$677$	−13449.0	+	23294.4i	−0.763496	+	1.32241i	−0.941038	+	0.338301i	$0.890148\pi$
$678$		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	$-0.266037\pi$
$683$	23940.0			1.34120			0.670599	+	0.741820i	$0.266037\pi$
$684$		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	$-0.624720\pi$
$701$	−14175.0			−0.763741			−0.381870	+	0.924216i	$0.624720\pi$
$702$		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	$-0.778012\pi$
$719$	−29556.0			−1.53304			−0.766518	+	0.642223i	$0.778012\pi$
$720$		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	0.981869	−	0.189560i	$-0.0607061\pi$
$743$	6618.00	+	11462.7i	0.326771	+	0.565984i	−0.655098	+	0.755544i	$0.727373\pi$
$744$		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	$0.246005\pi$
$761$	20208.0	+	35001.3i	0.962601	+	1.66727i	0.246675	+	0.969098i	$0.420662\pi$
$762$		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	$-0.279852\pi$
$773$	27414.0			1.27557			0.637783	+	0.770216i	$0.279852\pi$
$774$		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	0.779415	−	0.626508i	$-0.215517\pi$
$797$	−3439.50	−	5957.39i	−0.152865	−	0.264770i	−0.932280	+	0.361739i	$0.882183\pi$
$798$		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	$-0.619707\pi$
$809$	−16902.0			−0.734540			−0.367270	+	0.930114i	$0.619707\pi$
$810$		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	−0.937341	−	0.348414i	$-0.886720\pi$
$821$	−3927.00	+	6801.76i	−0.166935	+	0.289139i	0.770406	+	0.637554i	$0.220054\pi$
$822$		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	$-0.620418\pi$
$827$	−17568.0			−0.738693			−0.369347	+	0.929292i	$0.620418\pi$
$828$		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	$0.496929\pi$
$839$	−20928.0	+	36248.4i	−0.861162	+	1.49158i	−0.870808	+	0.491623i	$0.836404\pi$
$840$		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	$-0.541080\pi$
$857$	19932.0	−	34523.2i	0.794474	−	1.37607i	0.923173	−	0.384385i	$-0.125587\pi$
$858$		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	$-0.468081\pi$
$863$	5076.00			0.200219			0.100110	+	0.994976i	$0.468081\pi$
$864$		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	$-0.643995\pi$
$881$	−22860.0			−0.874203			−0.437102	+	0.899412i	$0.643995\pi$
$882$		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	$-0.929133\pi$
$887$	−17934.0	−	31062.6i	−0.678878	−	1.17585i	0.296441	−	0.955051i	$-0.404200\pi$
$888$		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	$-0.657190\pi$
$911$	14451.0	−	25029.9i	0.525558	−	0.910292i	0.999557	−	0.0297672i	$-0.00947661\pi$
$912$		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	−0.984052	−	0.177880i	$-0.943076\pi$
$929$	−9570.00	+	16575.7i	−0.337978	+	0.585395i	0.646074	+	0.763275i	$0.276410\pi$
$930$		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	0.988330	−	0.152329i	$-0.0486772\pi$
$941$	10456.5	+	18111.2i	0.362245	+	0.627426i	−0.626085	+	0.779755i	$0.715344\pi$
$942$		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	−0.976305	−	0.216397i	$-0.930570\pi$
$947$	−8764.50	+	15180.6i	−0.300748	+	0.520910i	0.675558	+	0.737307i	$0.263903\pi$
$948$		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	$-0.864704\pi$
$953$	−53604.0			−1.82204			−0.911020	+	0.412362i	$0.864704\pi$
$954$		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	$-0.648962\pi$
$971$	−27297.0			−0.902165			−0.451083	+	0.892482i	$0.648962\pi$
$972$		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	0.584237	−	0.811583i	$-0.301394\pi$
$977$	−12543.0	−	21725.1i	−0.410733	−	0.711410i	−0.994970	+	0.100173i	$0.968060\pi$
$978$		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	−0.644109	−	0.764934i	$-0.722772\pi$
$983$	10491.0	−	18170.9i	0.340398	−	0.589586i	0.984507	+	0.175348i	$0.0561050\pi$
$984$		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.b.55.1		2
3.2	odd	2		162.4.c.g.55.1		2
9.2	odd	6		54.4.a.b.1.1	✓	1
9.4	even	3	inner	162.4.c.b.109.1		2
9.5	odd	6		162.4.c.g.109.1		2
9.7	even	3		54.4.a.c.1.1	yes	1
36.7	odd	6		432.4.a.j.1.1		1
36.11	even	6		432.4.a.e.1.1		1
45.2	even	12		1350.4.c.s.649.1		2
45.7	odd	12		1350.4.c.b.649.2		2
45.29	odd	6		1350.4.a.o.1.1		1
45.34	even	6		1350.4.a.a.1.1		1
45.38	even	12		1350.4.c.s.649.2		2
45.43	odd	12		1350.4.c.b.649.1		2
72.11	even	6		1728.4.a.u.1.1		1
72.29	odd	6		1728.4.a.v.1.1		1
72.43	odd	6		1728.4.a.k.1.1		1
72.61	even	6		1728.4.a.l.1.1		1

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