LMFDB - Embedded newform 228.3.l.b.217.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [228,3,Mod(145,228)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(228, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5]))

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

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

chi := DirichletCharacter("228.145");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 228 = 2^{2} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	228.l (of order $6$, degree $2$, 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:	$6.21255002741$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			217.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	228.217
Dual form			228.3.l.b.145.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.50000 + 0.866025i) q^{3} +(1.00000 - 1.73205i) q^{5} -1.00000 q^{7} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(1.50000 + 0.866025i) q^{3} +(1.00000 - 1.73205i) q^{5} -1.00000 q^{7} +(1.50000 + 2.59808i) q^{9} +16.0000 q^{11} +(13.5000 - 7.79423i) q^{13} +(3.00000 - 1.73205i) q^{15} +(-11.0000 + 19.0526i) q^{17} +19.0000 q^{19} +(-1.50000 - 0.866025i) q^{21} +(-20.0000 - 34.6410i) q^{23} +(10.5000 + 18.1865i) q^{25} +5.19615i q^{27} +(15.0000 - 8.66025i) q^{29} +50.2295i q^{31} +(24.0000 + 13.8564i) q^{33} +(-1.00000 + 1.73205i) q^{35} -15.5885i q^{37} +27.0000 q^{39} +(-12.0000 - 6.92820i) q^{41} +(24.5000 - 42.4352i) q^{43} +6.00000 q^{45} +(-23.0000 - 39.8372i) q^{47} -48.0000 q^{49} +(-33.0000 + 19.0526i) q^{51} +(-42.0000 + 24.2487i) q^{53} +(16.0000 - 27.7128i) q^{55} +(28.5000 + 16.4545i) q^{57} +(-57.0000 - 32.9090i) q^{59} +(48.5000 + 84.0045i) q^{61} +(-1.50000 - 2.59808i) q^{63} -31.1769i q^{65} +(-22.5000 + 12.9904i) q^{67} -69.2820i q^{69} +(-42.0000 - 24.2487i) q^{71} +(-17.5000 + 30.3109i) q^{73} +36.3731i q^{75} -16.0000 q^{77} +(-76.5000 - 44.1673i) q^{79} +(-4.50000 + 7.79423i) q^{81} -146.000 q^{83} +(22.0000 + 38.1051i) q^{85} +30.0000 q^{87} +(-33.0000 + 19.0526i) q^{89} +(-13.5000 + 7.79423i) q^{91} +(-43.5000 + 75.3442i) q^{93} +(19.0000 - 32.9090i) q^{95} +(54.0000 + 31.1769i) q^{97} +(24.0000 + 41.5692i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 3 q^{3} + 2 q^{5} - 2 q^{7} + 3 q^{9}+O(q^{10}) $ 2 * q + 3 * q^3 + 2 * q^5 - 2 * q^7 + 3 * q^9	$ 2 q + 3 q^{3} + 2 q^{5} - 2 q^{7} + 3 q^{9} + 32 q^{11} + 27 q^{13} + 6 q^{15} - 22 q^{17} + 38 q^{19} - 3 q^{21} - 40 q^{23} + 21 q^{25} + 30 q^{29} + 48 q^{33} - 2 q^{35} + 54 q^{39} - 24 q^{41} + 49 q^{43} + 12 q^{45} - 46 q^{47} - 96 q^{49} - 66 q^{51} - 84 q^{53} + 32 q^{55} + 57 q^{57} - 114 q^{59} + 97 q^{61} - 3 q^{63} - 45 q^{67} - 84 q^{71} - 35 q^{73} - 32 q^{77} - 153 q^{79} - 9 q^{81} - 292 q^{83} + 44 q^{85} + 60 q^{87} - 66 q^{89} - 27 q^{91} - 87 q^{93} + 38 q^{95} + 108 q^{97} + 48 q^{99}+O(q^{100}) $ 2 * q + 3 * q^3 + 2 * q^5 - 2 * q^7 + 3 * q^9 + 32 * q^11 + 27 * q^13 + 6 * q^15 - 22 * q^17 + 38 * q^19 - 3 * q^21 - 40 * q^23 + 21 * q^25 + 30 * q^29 + 48 * q^33 - 2 * q^35 + 54 * q^39 - 24 * q^41 + 49 * q^43 + 12 * q^45 - 46 * q^47 - 96 * q^49 - 66 * q^51 - 84 * q^53 + 32 * q^55 + 57 * q^57 - 114 * q^59 + 97 * q^61 - 3 * q^63 - 45 * q^67 - 84 * q^71 - 35 * q^73 - 32 * q^77 - 153 * q^79 - 9 * q^81 - 292 * q^83 + 44 * q^85 + 60 * q^87 - 66 * q^89 - 27 * q^91 - 87 * q^93 + 38 * q^95 + 108 * q^97 + 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/228\mathbb{Z}\right)^\times$.

$n$	$77$	$97$	$115$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	1.50000	+	0.866025i	0.500000	+	0.288675i
$3$	1.50000	+	0.866025i	0.500000	+	0.288675i
$4$		0			0
$5$	1.00000	−	1.73205i	0.200000	−	0.346410i	−0.748528	−	0.663103i	$-0.769239\pi$
$5$	1.00000	−	1.73205i	0.200000	−	0.346410i	0.948528	+	0.316693i	$0.102572\pi$
$6$		0			0
$7$	−1.00000			−0.142857			−0.0714286	−	0.997446i	$-0.522756\pi$
$7$	−1.00000			−0.142857			−0.0714286	+	0.997446i	$0.522756\pi$
$8$		0			0
$9$	1.50000	+	2.59808i	0.166667	+	0.288675i
$10$		0			0
$11$	16.0000			1.45455			0.727273	−	0.686349i	$-0.240788\pi$
$11$	16.0000			1.45455			0.727273	+	0.686349i	$0.240788\pi$
$12$		0			0
$13$	13.5000	−	7.79423i	1.03846	−	0.599556i	0.119064	−	0.992887i	$-0.462011\pi$
$13$	13.5000	−	7.79423i	1.03846	−	0.599556i	0.919397	+	0.393330i	$0.128677\pi$
$14$		0			0
$15$	3.00000	−	1.73205i	0.200000	−	0.115470i
$16$		0			0
$17$	−11.0000	+	19.0526i	−0.647059	+	1.12074i	0.336763	+	0.941589i	$0.390668\pi$
$17$	−11.0000	+	19.0526i	−0.647059	+	1.12074i	−0.983822	+	0.179149i	$0.942665\pi$
$18$		0			0
$19$	19.0000			1.00000
$19$	19.0000			1.00000
$20$		0			0
$21$	−1.50000	−	0.866025i	−0.0714286	−	0.0412393i
$22$		0			0
$23$	−20.0000	−	34.6410i	−0.869565	−	1.50613i	−0.862442	−	0.506157i	$-0.831066\pi$
$23$	−20.0000	−	34.6410i	−0.869565	−	1.50613i	−0.00712357	−	0.999975i	$-0.502268\pi$
$24$		0			0
$25$	10.5000	+	18.1865i	0.420000	+	0.727461i
$26$		0			0
$27$			5.19615i			0.192450i
$28$		0			0
$29$	15.0000	−	8.66025i	0.517241	−	0.298629i	−0.218564	−	0.975823i	$-0.570137\pi$
$29$	15.0000	−	8.66025i	0.517241	−	0.298629i	0.735805	+	0.677193i	$0.236804\pi$
$30$		0			0
$31$			50.2295i			1.62031i	0.586219	+	0.810153i	$0.300616\pi$
$31$			50.2295i			1.62031i	−0.586219	+	0.810153i	$0.699384\pi$
$32$		0			0
$33$	24.0000	+	13.8564i	0.727273	+	0.419891i
$34$		0			0
$35$	−1.00000	+	1.73205i	−0.0285714	+	0.0494872i
$36$		0			0
$37$		−	15.5885i		−	0.421310i	−0.977561	−	0.210655i	$-0.932440\pi$
$37$		−	15.5885i		−	0.421310i	0.977561	−	0.210655i	$-0.0675596\pi$
$38$		0			0
$39$	27.0000			0.692308
$40$		0			0
$41$	−12.0000	−	6.92820i	−0.292683	−	0.168981i	0.346468	−	0.938062i	$-0.387381\pi$
$41$	−12.0000	−	6.92820i	−0.292683	−	0.168981i	−0.639151	+	0.769081i	$0.720714\pi$
$42$		0			0
$43$	24.5000	−	42.4352i	0.569767	−	0.986866i	−0.426821	−	0.904336i	$-0.640367\pi$
$43$	24.5000	−	42.4352i	0.569767	−	0.986866i	0.996589	−	0.0825301i	$-0.0263001\pi$
$44$		0			0
$45$	6.00000			0.133333
$46$		0			0
$47$	−23.0000	−	39.8372i	−0.489362	−	0.847599i	0.510563	−	0.859840i	$-0.329437\pi$
$47$	−23.0000	−	39.8372i	−0.489362	−	0.847599i	−0.999925	+	0.0122408i	$0.996104\pi$
$48$		0			0
$49$	−48.0000			−0.979592
$50$		0			0
$51$	−33.0000	+	19.0526i	−0.647059	+	0.373580i
$52$		0			0
$53$	−42.0000	+	24.2487i	−0.792453	+	0.457523i	−0.840825	−	0.541307i	$-0.817930\pi$
$53$	−42.0000	+	24.2487i	−0.792453	+	0.457523i	0.0483725	+	0.998829i	$0.484597\pi$
$54$		0			0
$55$	16.0000	−	27.7128i	0.290909	−	0.503869i
$56$		0			0
$57$	28.5000	+	16.4545i	0.500000	+	0.288675i
$58$		0			0
$59$	−57.0000	−	32.9090i	−0.966102	−	0.557779i	−0.0680561	−	0.997681i	$-0.521680\pi$
$59$	−57.0000	−	32.9090i	−0.966102	−	0.557779i	−0.898046	+	0.439902i	$0.855013\pi$
$60$		0			0
$61$	48.5000	+	84.0045i	0.795082	+	1.37712i	0.922787	+	0.385310i	$0.125906\pi$
$61$	48.5000	+	84.0045i	0.795082	+	1.37712i	−0.127705	+	0.991812i	$0.540761\pi$
$62$		0			0
$63$	−1.50000	−	2.59808i	−0.0238095	−	0.0412393i
$64$		0			0
$65$		−	31.1769i		−	0.479645i
$66$		0			0
$67$	−22.5000	+	12.9904i	−0.335821	+	0.193886i	−0.658422	−	0.752649i	$-0.728776\pi$
$67$	−22.5000	+	12.9904i	−0.335821	+	0.193886i	0.322602	+	0.946535i	$0.395443\pi$
$68$		0			0
$69$		−	69.2820i		−	1.00409i
$70$		0			0
$71$	−42.0000	−	24.2487i	−0.591549	−	0.341531i	0.174161	−	0.984717i	$-0.444279\pi$
$71$	−42.0000	−	24.2487i	−0.591549	−	0.341531i	−0.765710	+	0.643186i	$0.777612\pi$
$72$		0			0
$73$	−17.5000	+	30.3109i	−0.239726	+	0.415218i	−0.960636	−	0.277811i	$-0.910391\pi$
$73$	−17.5000	+	30.3109i	−0.239726	+	0.415218i	0.720910	+	0.693029i	$0.243724\pi$
$74$		0			0
$75$			36.3731i			0.484974i
$76$		0			0
$77$	−16.0000			−0.207792
$78$		0			0
$79$	−76.5000	−	44.1673i	−0.968354	−	0.559080i	−0.0696203	−	0.997574i	$-0.522179\pi$
$79$	−76.5000	−	44.1673i	−0.968354	−	0.559080i	−0.898734	+	0.438494i	$0.855512\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	−146.000			−1.75904			−0.879518	−	0.475865i	$-0.842135\pi$
$83$	−146.000			−1.75904			−0.879518	+	0.475865i	$0.842135\pi$
$84$		0			0
$85$	22.0000	+	38.1051i	0.258824	+	0.448296i
$86$		0			0
$87$	30.0000			0.344828
$88$		0			0
$89$	−33.0000	+	19.0526i	−0.370787	+	0.214074i	−0.673802	−	0.738912i	$-0.735340\pi$
$89$	−33.0000	+	19.0526i	−0.370787	+	0.214074i	0.303015	+	0.952986i	$0.402007\pi$
$90$		0			0
$91$	−13.5000	+	7.79423i	−0.148352	+	0.0856509i
$92$		0			0
$93$	−43.5000	+	75.3442i	−0.467742	+	0.810153i
$94$		0			0
$95$	19.0000	−	32.9090i	0.200000	−	0.346410i
$96$		0			0
$97$	54.0000	+	31.1769i	0.556701	+	0.321411i	0.751820	−	0.659368i	$-0.229176\pi$
$97$	54.0000	+	31.1769i	0.556701	+	0.321411i	−0.195119	+	0.980780i	$0.562509\pi$
$98$		0			0
$99$	24.0000	+	41.5692i	0.242424	+	0.419891i
$100$		0			0
$101$	−14.0000	−	24.2487i	−0.138614	−	0.240086i	0.788358	−	0.615216i	$-0.210931\pi$
$101$	−14.0000	−	24.2487i	−0.138614	−	0.240086i	−0.926972	+	0.375130i	$0.877598\pi$
$102$		0			0
$103$		−	126.440i		−	1.22757i	−0.789473	−	0.613785i	$-0.789646\pi$
$103$		−	126.440i		−	1.22757i	0.789473	−	0.613785i	$-0.210354\pi$
$104$		0			0
$105$	−3.00000	+	1.73205i	−0.0285714	+	0.0164957i
$106$		0			0
$107$		−	83.1384i		−	0.776995i	−0.921450	−	0.388497i	$-0.872994\pi$
$107$		−	83.1384i		−	0.776995i	0.921450	−	0.388497i	$-0.127006\pi$
$108$		0			0
$109$	−66.0000	−	38.1051i	−0.605505	−	0.349588i	0.165699	−	0.986176i	$-0.447012\pi$
$109$	−66.0000	−	38.1051i	−0.605505	−	0.349588i	−0.771204	+	0.636588i	$0.780345\pi$
$110$		0			0
$111$	13.5000	−	23.3827i	0.121622	−	0.210655i
$112$		0			0
$113$			183.597i			1.62476i	0.583131	+	0.812378i	$0.301827\pi$
$113$			183.597i			1.62476i	−0.583131	+	0.812378i	$0.698173\pi$
$114$		0			0
$115$	−80.0000			−0.695652
$116$		0			0
$117$	40.5000	+	23.3827i	0.346154	+	0.199852i
$118$		0			0
$119$	11.0000	−	19.0526i	0.0924370	−	0.160106i
$120$		0			0
$121$	135.000			1.11570
$122$		0			0
$123$	−12.0000	−	20.7846i	−0.0975610	−	0.168981i
$124$		0			0
$125$	92.0000			0.736000
$126$		0			0
$127$	24.0000	−	13.8564i	0.188976	−	0.109106i	−0.402527	−	0.915408i	$-0.631868\pi$
$127$	24.0000	−	13.8564i	0.188976	−	0.109106i	0.591503	+	0.806303i	$0.298535\pi$
$128$		0			0
$129$	73.5000	−	42.4352i	0.569767	−	0.328955i
$130$		0			0
$131$	64.0000	−	110.851i	0.488550	−	0.846193i	−0.511364	−	0.859364i	$-0.670859\pi$
$131$	64.0000	−	110.851i	0.488550	−	0.846193i	0.999913	+	0.0131717i	$0.00419280\pi$
$132$		0			0
$133$	−19.0000			−0.142857
$134$		0			0
$135$	9.00000	+	5.19615i	0.0666667	+	0.0384900i
$136$		0			0
$137$	58.0000	+	100.459i	0.423358	+	0.733277i	0.996265	−	0.0863428i	$-0.0275180\pi$
$137$	58.0000	+	100.459i	0.423358	+	0.733277i	−0.572908	+	0.819620i	$0.694185\pi$
$138$		0			0
$139$	87.5000	+	151.554i	0.629496	+	1.09032i	0.987653	+	0.156658i	$0.0500721\pi$
$139$	87.5000	+	151.554i	0.629496	+	1.09032i	−0.358156	+	0.933662i	$0.616595\pi$
$140$		0			0
$141$		−	79.6743i		−	0.565066i
$142$		0			0
$143$	216.000	−	124.708i	1.51049	−	0.872082i
$144$		0			0
$145$		−	34.6410i		−	0.238904i
$146$		0			0
$147$	−72.0000	−	41.5692i	−0.489796	−	0.282784i
$148$		0			0
$149$	−74.0000	+	128.172i	−0.496644	+	0.860213i	−0.999993	−	0.00387051i	$-0.998768\pi$
$149$	−74.0000	+	128.172i	−0.496644	+	0.860213i	0.503348	+	0.864084i	$0.332101\pi$
$150$		0			0
$151$			193.990i			1.28470i	0.766411	+	0.642350i	$0.222040\pi$
$151$			193.990i			1.28470i	−0.766411	+	0.642350i	$0.777960\pi$
$152$		0			0
$153$	−66.0000			−0.431373
$154$		0			0
$155$	87.0000	+	50.2295i	0.561290	+	0.324061i
$156$		0			0
$157$	96.5000	−	167.143i	0.614650	−	1.06460i	−0.375796	−	0.926702i	$-0.622631\pi$
$157$	96.5000	−	167.143i	0.614650	−	1.06460i	0.990446	−	0.137902i	$-0.0440359\pi$
$158$		0			0
$159$	−84.0000			−0.528302
$160$		0			0
$161$	20.0000	+	34.6410i	0.124224	+	0.215162i
$162$		0			0
$163$	233.000			1.42945			0.714724	−	0.699407i	$-0.246552\pi$
$163$	233.000			1.42945			0.714724	+	0.699407i	$0.246552\pi$
$164$		0			0
$165$	48.0000	−	27.7128i	0.290909	−	0.167956i
$166$		0			0
$167$	63.0000	−	36.3731i	0.377246	−	0.217803i	−0.299374	−	0.954136i	$-0.596778\pi$
$167$	63.0000	−	36.3731i	0.377246	−	0.217803i	0.676619	+	0.736333i	$0.263444\pi$
$168$		0			0
$169$	37.0000	−	64.0859i	0.218935	−	0.379206i
$170$		0			0
$171$	28.5000	+	49.3634i	0.166667	+	0.288675i
$172$		0			0
$173$	99.0000	+	57.1577i	0.572254	+	0.330391i	0.758049	−	0.652197i	$-0.226153\pi$
$173$	99.0000	+	57.1577i	0.572254	+	0.330391i	−0.185795	+	0.982589i	$0.559486\pi$
$174$		0			0
$175$	−10.5000	−	18.1865i	−0.0600000	−	0.103923i
$176$		0			0
$177$	−57.0000	−	98.7269i	−0.322034	−	0.557779i
$178$		0			0
$179$			83.1384i			0.464461i	0.972661	+	0.232230i	$0.0746023\pi$
$179$			83.1384i			0.464461i	−0.972661	+	0.232230i	$0.925398\pi$
$180$		0			0
$181$	42.0000	−	24.2487i	0.232044	−	0.133971i	−0.379471	−	0.925204i	$-0.623894\pi$
$181$	42.0000	−	24.2487i	0.232044	−	0.133971i	0.611515	+	0.791233i	$0.290561\pi$
$182$		0			0
$183$			168.009i			0.918082i
$184$		0			0
$185$	−27.0000	−	15.5885i	−0.145946	−	0.0842619i
$186$		0			0
$187$	−176.000	+	304.841i	−0.941176	+	1.63017i
$188$		0			0
$189$		−	5.19615i		−	0.0274929i
$190$		0			0
$191$	70.0000			0.366492			0.183246	−	0.983067i	$-0.441339\pi$
$191$	70.0000			0.366492			0.183246	+	0.983067i	$0.441339\pi$
$192$		0			0
$193$	−262.500	−	151.554i	−1.36010	−	0.785256i	−0.370466	−	0.928846i	$-0.620802\pi$
$193$	−262.500	−	151.554i	−1.36010	−	0.785256i	−0.989637	+	0.143590i	$0.954135\pi$
$194$		0			0
$195$	27.0000	−	46.7654i	0.138462	−	0.239822i
$196$		0			0
$197$	−2.00000			−0.0101523			−0.00507614	−	0.999987i	$-0.501616\pi$
$197$	−2.00000			−0.0101523			−0.00507614	+	0.999987i	$0.501616\pi$
$198$		0			0
$199$	−98.5000	−	170.607i	−0.494975	−	0.857322i	0.505008	−	0.863114i	$-0.331489\pi$
$199$	−98.5000	−	170.607i	−0.494975	−	0.857322i	−0.999983	+	0.00579283i	$0.998156\pi$
$200$		0			0
$201$	−45.0000			−0.223881
$202$		0			0
$203$	−15.0000	+	8.66025i	−0.0738916	+	0.0426613i
$204$		0			0
$205$	−24.0000	+	13.8564i	−0.117073	+	0.0675922i
$206$		0			0
$207$	60.0000	−	103.923i	0.289855	−	0.502044i
$208$		0			0
$209$	304.000			1.45455
$210$		0			0
$211$	−316.500	−	182.731i	−1.50000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$211$	−316.500	−	182.731i	−1.50000	−	0.866025i	−1.00000			$\pi$
$212$		0			0
$213$	−42.0000	−	72.7461i	−0.197183	−	0.341531i
$214$		0			0
$215$	−49.0000	−	84.8705i	−0.227907	−	0.394746i
$216$		0			0
$217$		−	50.2295i		−	0.231472i
$218$		0			0
$219$	−52.5000	+	30.3109i	−0.239726	+	0.138406i
$220$		0			0
$221$			342.946i			1.55179i
$222$		0			0
$223$	211.500	+	122.110i	0.948430	+	0.547577i	0.892593	−	0.450863i	$-0.148884\pi$
$223$	211.500	+	122.110i	0.948430	+	0.547577i	0.0558375	+	0.998440i	$0.482217\pi$
$224$		0			0
$225$	−31.5000	+	54.5596i	−0.140000	+	0.242487i
$226$		0			0
$227$			148.956i			0.656195i	0.944644	+	0.328098i	$0.106408\pi$
$227$			148.956i			0.656195i	−0.944644	+	0.328098i	$0.893592\pi$
$228$		0			0
$229$	83.0000			0.362445			0.181223	−	0.983442i	$-0.441995\pi$
$229$	83.0000			0.362445			0.181223	+	0.983442i	$0.441995\pi$
$230$		0			0
$231$	−24.0000	−	13.8564i	−0.103896	−	0.0599844i
$232$		0			0
$233$	40.0000	−	69.2820i	0.171674	−	0.297348i	−0.767331	−	0.641251i	$-0.778416\pi$
$233$	40.0000	−	69.2820i	0.171674	−	0.297348i	0.939005	+	0.343903i	$0.111749\pi$
$234$		0			0
$235$	−92.0000			−0.391489
$236$		0			0
$237$	−76.5000	−	132.502i	−0.322785	−	0.559080i
$238$		0			0
$239$	58.0000			0.242678			0.121339	−	0.992611i	$-0.461281\pi$
$239$	58.0000			0.242678			0.121339	+	0.992611i	$0.461281\pi$
$240$		0			0
$241$	−244.500	+	141.162i	−1.01452	+	0.585735i	−0.912513	−	0.409048i	$-0.865861\pi$
$241$	−244.500	+	141.162i	−1.01452	+	0.585735i	−0.102010	+	0.994783i	$0.532527\pi$
$242$		0			0
$243$	−13.5000	+	7.79423i	−0.0555556	+	0.0320750i
$244$		0			0
$245$	−48.0000	+	83.1384i	−0.195918	+	0.339341i
$246$		0			0
$247$	256.500	−	148.090i	1.03846	−	0.599556i
$248$		0			0
$249$	−219.000	−	126.440i	−0.879518	−	0.507790i
$250$		0			0
$251$	133.000	+	230.363i	0.529880	+	0.917780i	0.999392	+	0.0348538i	$0.0110966\pi$
$251$	133.000	+	230.363i	0.529880	+	0.917780i	−0.469512	+	0.882926i	$0.655570\pi$
$252$		0			0
$253$	−320.000	−	554.256i	−1.26482	−	2.19074i
$254$		0			0
$255$			76.2102i			0.298864i
$256$		0			0
$257$	−162.000	+	93.5307i	−0.630350	+	0.363933i	−0.780888	−	0.624671i	$-0.785233\pi$
$257$	−162.000	+	93.5307i	−0.630350	+	0.363933i	0.150537	+	0.988604i	$0.451900\pi$
$258$		0			0
$259$			15.5885i			0.0601871i
$260$		0			0
$261$	45.0000	+	25.9808i	0.172414	+	0.0995431i
$262$		0			0
$263$	82.0000	−	142.028i	0.311787	−	0.540031i	−0.666962	−	0.745092i	$-0.732406\pi$
$263$	82.0000	−	142.028i	0.311787	−	0.540031i	0.978749	+	0.205060i	$0.0657391\pi$
$264$		0			0
$265$			96.9948i			0.366018i
$266$		0			0
$267$	−66.0000			−0.247191
$268$		0			0
$269$	−447.000	−	258.076i	−1.66171	−	0.959389i	−0.971899	−	0.235400i	$-0.924360\pi$
$269$	−447.000	−	258.076i	−1.66171	−	0.959389i	−0.689811	−	0.723989i	$-0.742307\pi$
$270$		0			0
$271$	−7.00000	+	12.1244i	−0.0258303	+	0.0447393i	−0.878652	−	0.477464i	$-0.841556\pi$
$271$	−7.00000	+	12.1244i	−0.0258303	+	0.0447393i	0.852821	+	0.522203i	$0.174890\pi$
$272$		0			0
$273$	−27.0000			−0.0989011
$274$		0			0
$275$	168.000	+	290.985i	0.610909	+	1.05813i
$276$		0			0
$277$	206.000			0.743682			0.371841	−	0.928296i	$-0.378727\pi$
$277$	206.000			0.743682			0.371841	+	0.928296i	$0.378727\pi$
$278$		0			0
$279$	−130.500	+	75.3442i	−0.467742	+	0.270051i
$280$		0			0
$281$	87.0000	−	50.2295i	0.309609	−	0.178753i	−0.337143	−	0.941454i	$-0.609461\pi$
$281$	87.0000	−	50.2295i	0.309609	−	0.178753i	0.646751	+	0.762701i	$0.276127\pi$
$282$		0			0
$283$	−271.000	+	469.386i	−0.957597	+	1.65861i	−0.229288	+	0.973359i	$0.573640\pi$
$283$	−271.000	+	469.386i	−0.957597	+	1.65861i	−0.728310	+	0.685248i	$0.759694\pi$
$284$		0			0
$285$	57.0000	−	32.9090i	0.200000	−	0.115470i
$286$		0			0
$287$	12.0000	+	6.92820i	0.0418118	+	0.0241401i
$288$		0			0
$289$	−97.5000	−	168.875i	−0.337370	−	0.584342i
$290$		0			0
$291$	54.0000	+	93.5307i	0.185567	+	0.321411i
$292$		0			0
$293$		−	481.510i		−	1.64338i	−0.569935	−	0.821690i	$-0.693032\pi$
$293$		−	481.510i		−	1.64338i	0.569935	−	0.821690i	$-0.306968\pi$
$294$		0			0
$295$	−114.000	+	65.8179i	−0.386441	+	0.223112i
$296$		0			0
$297$			83.1384i			0.279927i
$298$		0			0
$299$	−540.000	−	311.769i	−1.80602	−	1.04271i
$300$		0			0
$301$	−24.5000	+	42.4352i	−0.0813953	+	0.140981i
$302$		0			0
$303$		−	48.4974i		−	0.160058i
$304$		0			0
$305$	194.000			0.636066
$306$		0			0
$307$	−138.000	−	79.6743i	−0.449511	−	0.259526i	0.258112	−	0.966115i	$-0.416900\pi$
$307$	−138.000	−	79.6743i	−0.449511	−	0.259526i	−0.707624	+	0.706589i	$0.750233\pi$
$308$		0			0
$309$	109.500	−	189.660i	0.354369	−	0.613785i
$310$		0			0
$311$	322.000			1.03537			0.517685	−	0.855571i	$-0.326794\pi$
$311$	322.000			1.03537			0.517685	+	0.855571i	$0.326794\pi$
$312$		0			0
$313$	−13.0000	−	22.5167i	−0.0415335	−	0.0719382i	0.844511	−	0.535538i	$-0.179891\pi$
$313$	−13.0000	−	22.5167i	−0.0415335	−	0.0719382i	−0.886045	+	0.463599i	$0.846558\pi$
$314$		0			0
$315$	−6.00000			−0.0190476
$316$		0			0
$317$	−291.000	+	168.009i	−0.917981	+	0.529997i	−0.882990	−	0.469391i	$-0.844473\pi$
$317$	−291.000	+	168.009i	−0.917981	+	0.529997i	−0.0349907	+	0.999388i	$0.511140\pi$
$318$		0			0
$319$	240.000	−	138.564i	0.752351	−	0.434370i
$320$		0			0
$321$	72.0000	−	124.708i	0.224299	−	0.388497i
$322$		0			0
$323$	−209.000	+	361.999i	−0.647059	+	1.12074i
$324$		0			0
$325$	283.500	+	163.679i	0.872308	+	0.503627i
$326$		0			0
$327$	−66.0000	−	114.315i	−0.201835	−	0.349588i
$328$		0			0
$329$	23.0000	+	39.8372i	0.0699088	+	0.121086i
$330$		0			0
$331$			219.970i			0.664563i	0.943180	+	0.332282i	$0.107818\pi$
$331$			219.970i			0.664563i	−0.943180	+	0.332282i	$0.892182\pi$
$332$		0			0
$333$	40.5000	−	23.3827i	0.121622	−	0.0702183i
$334$		0			0
$335$			51.9615i			0.155109i
$336$		0			0
$337$	−505.500	−	291.851i	−1.50000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$337$	−505.500	−	291.851i	−1.50000	−	0.866025i	−1.00000			$\pi$
$338$		0			0
$339$	−159.000	+	275.396i	−0.469027	+	0.812378i
$340$		0			0
$341$			803.672i			2.35681i
$342$		0			0
$343$	97.0000			0.282799
$344$		0			0
$345$	−120.000	−	69.2820i	−0.347826	−	0.200817i
$346$		0			0
$347$	235.000	−	407.032i	0.677233	−	1.17300i	−0.298577	−	0.954385i	$-0.596512\pi$
$347$	235.000	−	407.032i	0.677233	−	1.17300i	0.975811	−	0.218617i	$-0.0701546\pi$
$348$		0			0
$349$	−295.000			−0.845272			−0.422636	−	0.906299i	$-0.638895\pi$
$349$	−295.000			−0.845272			−0.422636	+	0.906299i	$0.638895\pi$
$350$		0			0
$351$	40.5000	+	70.1481i	0.115385	+	0.199852i
$352$		0			0
$353$	262.000			0.742210			0.371105	−	0.928591i	$-0.378979\pi$
$353$	262.000			0.742210			0.371105	+	0.928591i	$0.378979\pi$
$354$		0			0
$355$	−84.0000	+	48.4974i	−0.236620	+	0.136612i
$356$		0			0
$357$	33.0000	−	19.0526i	0.0924370	−	0.0533685i
$358$		0			0
$359$	232.000	−	401.836i	0.646240	−	1.11932i	−0.337774	−	0.941227i	$-0.609674\pi$
$359$	232.000	−	401.836i	0.646240	−	1.11932i	0.984014	−	0.178093i	$-0.0569926\pi$
$360$		0			0
$361$	361.000			1.00000
$362$		0			0
$363$	202.500	+	116.913i	0.557851	+	0.322076i
$364$		0			0
$365$	35.0000	+	60.6218i	0.0958904	+	0.166087i
$366$		0			0
$367$	−116.500	−	201.784i	−0.317439	−	0.549820i	0.662514	−	0.749049i	$-0.269489\pi$
$367$	−116.500	−	201.784i	−0.317439	−	0.549820i	−0.979953	+	0.199229i	$0.936156\pi$
$368$		0			0
$369$		−	41.5692i		−	0.112654i
$370$		0			0
$371$	42.0000	−	24.2487i	0.113208	−	0.0653604i
$372$		0			0
$373$			533.472i			1.43022i	0.699013	+	0.715109i	$0.253623\pi$
$373$			533.472i			1.43022i	−0.699013	+	0.715109i	$0.746377\pi$
$374$		0			0
$375$	138.000	+	79.6743i	0.368000	+	0.212465i
$376$		0			0
$377$	135.000	−	233.827i	0.358090	−	0.620230i
$378$		0			0
$379$		−	161.081i		−	0.425015i	−0.977159	−	0.212508i	$-0.931837\pi$
$379$		−	161.081i		−	0.425015i	0.977159	−	0.212508i	$-0.0681630\pi$
$380$		0			0
$381$	48.0000			0.125984
$382$		0			0
$383$	−498.000	−	287.520i	−1.30026	−	0.750706i	−0.319812	−	0.947481i	$-0.603620\pi$
$383$	−498.000	−	287.520i	−1.30026	−	0.750706i	−0.980449	+	0.196775i	$0.936953\pi$
$384$		0			0
$385$	−16.0000	+	27.7128i	−0.0415584	+	0.0719813i
$386$		0			0
$387$	147.000			0.379845
$388$		0			0
$389$	76.0000	+	131.636i	0.195373	+	0.338396i	0.947023	−	0.321167i	$-0.104075\pi$
$389$	76.0000	+	131.636i	0.195373	+	0.338396i	−0.751650	+	0.659562i	$0.770742\pi$
$390$		0			0
$391$	880.000			2.25064
$392$		0			0
$393$	192.000	−	110.851i	0.488550	−	0.282064i
$394$		0			0
$395$	−153.000	+	88.3346i	−0.387342	+	0.223632i
$396$		0			0
$397$	249.500	−	432.147i	0.628463	−	1.08853i	−0.359397	−	0.933185i	$-0.617017\pi$
$397$	249.500	−	432.147i	0.628463	−	1.08853i	0.987860	−	0.155346i	$-0.0496492\pi$
$398$		0			0
$399$	−28.5000	−	16.4545i	−0.0714286	−	0.0412393i
$400$		0			0
$401$	87.0000	+	50.2295i	0.216958	+	0.125261i	0.604541	−	0.796574i	$-0.293357\pi$
$401$	87.0000	+	50.2295i	0.216958	+	0.125261i	−0.387583	+	0.921835i	$0.626690\pi$
$402$		0			0
$403$	391.500	+	678.098i	0.971464	+	1.68263i
$404$		0			0
$405$	9.00000	+	15.5885i	0.0222222	+	0.0384900i
$406$		0			0
$407$		−	249.415i		−	0.612814i
$408$		0			0
$409$	342.000	−	197.454i	0.836186	−	0.482772i	−0.0197801	−	0.999804i	$-0.506297\pi$
$409$	342.000	−	197.454i	0.836186	−	0.482772i	0.855966	+	0.517032i	$0.172963\pi$
$410$		0			0
$411$			200.918i			0.488851i
$412$		0			0
$413$	57.0000	+	32.9090i	0.138015	+	0.0796827i
$414$		0			0
$415$	−146.000	+	252.879i	−0.351807	+	0.609348i
$416$		0			0
$417$			303.109i			0.726880i
$418$		0			0
$419$	628.000			1.49881			0.749403	−	0.662114i	$-0.230340\pi$
$419$	628.000			1.49881			0.749403	+	0.662114i	$0.230340\pi$
$420$		0			0
$421$	558.000	+	322.161i	1.32542	+	0.765229i	0.984587	−	0.174896i	$-0.0559590\pi$
$421$	558.000	+	322.161i	1.32542	+	0.765229i	0.340829	+	0.940125i	$0.389292\pi$
$422$		0			0
$423$	69.0000	−	119.512i	0.163121	−	0.282533i
$424$		0			0
$425$	−462.000			−1.08706
$426$		0			0
$427$	−48.5000	−	84.0045i	−0.113583	−	0.196732i
$428$		0			0
$429$	432.000			1.00699
$430$		0			0
$431$	−393.000	+	226.899i	−0.911833	+	0.526447i	−0.881020	−	0.473078i	$-0.843143\pi$
$431$	−393.000	+	226.899i	−0.911833	+	0.526447i	−0.0308125	+	0.999525i	$0.509809\pi$
$432$		0			0
$433$	433.500	−	250.281i	1.00115	−	0.578017i	0.0925650	−	0.995707i	$-0.470493\pi$
$433$	433.500	−	250.281i	1.00115	−	0.578017i	0.908590	+	0.417690i	$0.137160\pi$
$434$		0			0
$435$	30.0000	−	51.9615i	0.0689655	−	0.119452i
$436$		0			0
$437$	−380.000	−	658.179i	−0.869565	−	1.50613i
$438$		0			0
$439$	292.500	+	168.875i	0.666287	+	0.384681i	0.794668	−	0.607044i	$-0.207645\pi$
$439$	292.500	+	168.875i	0.666287	+	0.384681i	−0.128381	+	0.991725i	$0.540978\pi$
$440$		0			0
$441$	−72.0000	−	124.708i	−0.163265	−	0.282784i
$442$		0			0
$443$	−365.000	−	632.199i	−0.823928	−	1.42708i	−0.902736	−	0.430195i	$-0.858445\pi$
$443$	−365.000	−	632.199i	−0.823928	−	1.42708i	0.0788082	−	0.996890i	$-0.474889\pi$
$444$		0			0
$445$			76.2102i			0.171259i
$446$		0			0
$447$	−222.000	+	128.172i	−0.496644	+	0.286738i
$448$		0			0
$449$		−	446.869i		−	0.995254i	−0.867391	−	0.497627i	$-0.834205\pi$
$449$		−	446.869i		−	0.995254i	0.867391	−	0.497627i	$-0.165795\pi$
$450$		0			0
$451$	−192.000	−	110.851i	−0.425721	−	0.245790i
$452$		0			0
$453$	−168.000	+	290.985i	−0.370861	+	0.642350i
$454$		0			0
$455$			31.1769i			0.0685207i
$456$		0			0
$457$	−397.000			−0.868709			−0.434354	−	0.900742i	$-0.643023\pi$
$457$	−397.000			−0.868709			−0.434354	+	0.900742i	$0.643023\pi$
$458$		0			0
$459$	−99.0000	−	57.1577i	−0.215686	−	0.124527i
$460$		0			0
$461$	−287.000	+	497.099i	−0.622560	+	1.07830i	0.366448	+	0.930439i	$0.380574\pi$
$461$	−287.000	+	497.099i	−0.622560	+	1.07830i	−0.989007	+	0.147866i	$0.952759\pi$
$462$		0			0
$463$	−367.000			−0.792657			−0.396328	−	0.918109i	$-0.629716\pi$
$463$	−367.000			−0.792657			−0.396328	+	0.918109i	$0.629716\pi$
$464$		0			0
$465$	87.0000	+	150.688i	0.187097	+	0.324061i
$466$		0			0
$467$	424.000			0.907923			0.453961	−	0.891021i	$-0.350010\pi$
$467$	424.000			0.907923			0.453961	+	0.891021i	$0.350010\pi$
$468$		0			0
$469$	22.5000	−	12.9904i	0.0479744	−	0.0276980i
$470$		0			0
$471$	289.500	−	167.143i	0.614650	−	0.354868i
$472$		0			0
$473$	392.000	−	678.964i	0.828753	−	1.43544i
$474$		0			0
$475$	199.500	+	345.544i	0.420000	+	0.727461i
$476$		0			0
$477$	−126.000	−	72.7461i	−0.264151	−	0.152508i
$478$		0			0
$479$	364.000	+	630.466i	0.759916	+	1.31621i	0.942893	+	0.333097i	$0.108094\pi$
$479$	364.000	+	630.466i	0.759916	+	1.31621i	−0.182976	+	0.983117i	$0.558573\pi$
$480$		0			0
$481$	−121.500	−	210.444i	−0.252599	−	0.437514i
$482$		0			0
$483$			69.2820i			0.143441i
$484$		0			0
$485$	108.000	−	62.3538i	0.222680	−	0.128565i
$486$		0			0
$487$		−	270.200i		−	0.554825i	−0.960751	−	0.277413i	$-0.910523\pi$
$487$		−	270.200i		−	0.554825i	0.960751	−	0.277413i	$-0.0894769\pi$
$488$		0			0
$489$	349.500	+	201.784i	0.714724	+	0.412646i
$490$		0			0
$491$	−380.000	+	658.179i	−0.773931	+	1.34049i	0.161463	+	0.986879i	$0.448379\pi$
$491$	−380.000	+	658.179i	−0.773931	+	1.34049i	−0.935393	+	0.353609i	$0.884954\pi$
$492$		0			0
$493$			381.051i			0.772923i
$494$		0			0
$495$	96.0000			0.193939
$496$		0			0
$497$	42.0000	+	24.2487i	0.0845070	+	0.0487902i
$498$		0			0
$499$	231.500	−	400.970i	0.463928	−	0.803547i	−0.535225	−	0.844710i	$-0.679773\pi$
$499$	231.500	−	400.970i	0.463928	−	0.803547i	0.999152	+	0.0411632i	$0.0131064\pi$
$500$		0			0
$501$	126.000			0.251497
$502$		0			0
$503$	−65.0000	−	112.583i	−0.129225	−	0.223824i	0.794152	−	0.607720i	$-0.207916\pi$
$503$	−65.0000	−	112.583i	−0.129225	−	0.223824i	−0.923376	+	0.383896i	$0.874582\pi$
$504$		0			0
$505$	−56.0000			−0.110891
$506$		0			0
$507$	111.000	−	64.0859i	0.218935	−	0.126402i
$508$		0			0
$509$	−459.000	+	265.004i	−0.901768	+	0.520636i	−0.877773	−	0.479076i	$-0.840972\pi$
$509$	−459.000	+	265.004i	−0.901768	+	0.520636i	−0.0239947	+	0.999712i	$0.507638\pi$
$510$		0			0
$511$	17.5000	−	30.3109i	0.0342466	−	0.0593168i
$512$		0			0
$513$			98.7269i			0.192450i
$514$		0			0
$515$	−219.000	−	126.440i	−0.425243	−	0.245514i
$516$		0			0
$517$	−368.000	−	637.395i	−0.711799	−	1.23287i
$518$		0			0
$519$	99.0000	+	171.473i	0.190751	+	0.330391i
$520$		0			0
$521$			602.754i			1.15692i	0.815712	+	0.578458i	$0.196345\pi$
$521$			602.754i			1.15692i	−0.815712	+	0.578458i	$0.803655\pi$
$522$		0			0
$523$	−277.500	+	160.215i	−0.530593	+	0.306338i	−0.741258	−	0.671220i	$-0.765770\pi$
$523$	−277.500	+	160.215i	−0.530593	+	0.306338i	0.210665	+	0.977558i	$0.432437\pi$
$524$		0			0
$525$		−	36.3731i		−	0.0692820i
$526$		0			0
$527$	−957.000	−	552.524i	−1.81594	−	1.04843i
$528$		0			0
$529$	−535.500	+	927.513i	−1.01229	+	1.75333i
$530$		0			0
$531$		−	197.454i		−	0.371853i
$532$		0			0
$533$	−216.000			−0.405253
$534$		0			0
$535$	−144.000	−	83.1384i	−0.269159	−	0.155399i
$536$		0			0
$537$	−72.0000	+	124.708i	−0.134078	+	0.232230i
$538$		0			0
$539$	−768.000			−1.42486
$540$		0			0
$541$	−182.500	−	316.099i	−0.337338	−	0.584287i	0.646593	−	0.762835i	$-0.276193\pi$
$541$	−182.500	−	316.099i	−0.337338	−	0.584287i	−0.983931	+	0.178548i	$0.942860\pi$
$542$		0			0
$543$	84.0000			0.154696
$544$		0			0
$545$	−132.000	+	76.2102i	−0.242202	+	0.139835i
$546$		0			0
$547$	−199.500	+	115.181i	−0.364717	+	0.210569i	−0.671148	−	0.741324i	$-0.734198\pi$
$547$	−199.500	+	115.181i	−0.364717	+	0.210569i	0.306431	+	0.951893i	$0.400865\pi$
$548$		0			0
$549$	−145.500	+	252.013i	−0.265027	+	0.459041i
$550$		0			0
$551$	285.000	−	164.545i	0.517241	−	0.298629i
$552$		0			0
$553$	76.5000	+	44.1673i	0.138336	+	0.0798685i
$554$		0			0
$555$	−27.0000	−	46.7654i	−0.0486486	−	0.0842619i
$556$		0			0
$557$	−320.000	−	554.256i	−0.574506	−	0.995074i	−0.996095	−	0.0882870i	$-0.971861\pi$
$557$	−320.000	−	554.256i	−0.574506	−	0.995074i	0.421589	−	0.906787i	$-0.361473\pi$
$558$		0			0
$559$		−	763.834i		−	1.36643i
$560$		0			0
$561$	−528.000	+	304.841i	−0.941176	+	0.543388i
$562$		0			0
$563$		−	96.9948i		−	0.172282i	−0.996283	−	0.0861411i	$-0.972546\pi$
$563$		−	96.9948i		−	0.172282i	0.996283	−	0.0861411i	$-0.0274536\pi$
$564$		0			0
$565$	318.000	+	183.597i	0.562832	+	0.324951i
$566$		0			0
$567$	4.50000	−	7.79423i	0.00793651	−	0.0137464i
$568$		0			0
$569$		−	152.420i		−	0.267874i	−0.990990	−	0.133937i	$-0.957238\pi$
$569$		−	152.420i		−	0.267874i	0.990990	−	0.133937i	$-0.0427620\pi$
$570$		0			0
$571$	335.000			0.586690			0.293345	−	0.956007i	$-0.405232\pi$
$571$	335.000			0.586690			0.293345	+	0.956007i	$0.405232\pi$
$572$		0			0
$573$	105.000	+	60.6218i	0.183246	+	0.105797i
$574$		0			0
$575$	420.000	−	727.461i	0.730435	−	1.26515i
$576$		0			0
$577$	746.000			1.29289			0.646447	−	0.762959i	$-0.276254\pi$
$577$	746.000			1.29289			0.646447	+	0.762959i	$0.276254\pi$
$578$		0			0
$579$	−262.500	−	454.663i	−0.453368	−	0.785256i
$580$		0			0
$581$	146.000			0.251291
$582$		0			0
$583$	−672.000	+	387.979i	−1.15266	+	0.665488i
$584$		0			0
$585$	81.0000	−	46.7654i	0.138462	−	0.0799408i
$586$		0			0
$587$	−89.0000	+	154.153i	−0.151618	+	0.262611i	−0.931823	−	0.362914i	$-0.881782\pi$
$587$	−89.0000	+	154.153i	−0.151618	+	0.262611i	0.780204	+	0.625525i	$0.215115\pi$
$588$		0			0
$589$			954.360i			1.62031i
$590$		0			0
$591$	−3.00000	−	1.73205i	−0.00507614	−	0.00293071i
$592$		0			0
$593$	−137.000	−	237.291i	−0.231029	−	0.400153i	0.727082	−	0.686550i	$-0.240876\pi$
$593$	−137.000	−	237.291i	−0.231029	−	0.400153i	−0.958111	+	0.286397i	$0.907542\pi$
$594$		0			0
$595$	−22.0000	−	38.1051i	−0.0369748	−	0.0640422i
$596$		0			0
$597$		−	341.214i		−	0.571548i
$598$		0			0
$599$	−252.000	+	145.492i	−0.420701	+	0.242892i	−0.695377	−	0.718645i	$-0.744763\pi$
$599$	−252.000	+	145.492i	−0.420701	+	0.242892i	0.274676	+	0.961537i	$0.411429\pi$
$600$		0			0
$601$			1020.18i			1.69747i	0.528820	+	0.848734i	$0.322634\pi$
$601$			1020.18i			1.69747i	−0.528820	+	0.848734i	$0.677366\pi$
$602$		0			0
$603$	−67.5000	−	38.9711i	−0.111940	−	0.0646288i
$604$		0			0
$605$	135.000	−	233.827i	0.223140	−	0.386491i
$606$		0			0
$607$		−	157.617i		−	0.259665i	−0.991536	−	0.129832i	$-0.958556\pi$
$607$		−	157.617i		−	0.259665i	0.991536	−	0.129832i	$-0.0414440\pi$
$608$		0			0
$609$	−30.0000			−0.0492611
$610$		0			0
$611$	−621.000	−	358.535i	−1.01637	−	0.586800i
$612$		0			0
$613$	401.000	−	694.552i	0.654160	−	1.13304i	−0.327944	−	0.944697i	$-0.606356\pi$
$613$	401.000	−	694.552i	0.654160	−	1.13304i	0.982104	−	0.188341i	$-0.0603110\pi$
$614$		0			0
$615$	−48.0000			−0.0780488
$616$		0			0
$617$	382.000	+	661.643i	0.619125	+	1.07236i	0.989646	+	0.143531i	$0.0458458\pi$
$617$	382.000	+	661.643i	0.619125	+	1.07236i	−0.370521	+	0.928824i	$0.620821\pi$
$618$		0			0
$619$	−127.000			−0.205170			−0.102585	−	0.994724i	$-0.532711\pi$
$619$	−127.000			−0.205170			−0.102585	+	0.994724i	$0.532711\pi$
$620$		0			0
$621$	180.000	−	103.923i	0.289855	−	0.167348i
$622$		0			0
$623$	33.0000	−	19.0526i	0.0529695	−	0.0305820i
$624$		0			0
$625$	−170.500	+	295.315i	−0.272800	+	0.472503i
$626$		0			0
$627$	456.000	+	263.272i	0.727273	+	0.419891i
$628$		0			0
$629$	297.000	+	171.473i	0.472178	+	0.272612i
$630$		0			0
$631$	−161.500	−	279.726i	−0.255943	−	0.443306i	0.709208	−	0.704999i	$-0.249053\pi$
$631$	−161.500	−	279.726i	−0.255943	−	0.443306i	−0.965151	+	0.261693i	$0.915719\pi$
$632$		0			0
$633$	−316.500	−	548.194i	−0.500000	−	0.866025i
$634$		0			0
$635$		−	55.4256i		−	0.0872845i
$636$		0			0
$637$	−648.000	+	374.123i	−1.01727	+	0.587320i
$638$		0			0
$639$		−	145.492i		−	0.227687i
$640$		0			0
$641$	−873.000	−	504.027i	−1.36193	−	0.786313i	−0.372053	−	0.928211i	$-0.621346\pi$
$641$	−873.000	−	504.027i	−1.36193	−	0.786313i	−0.989881	+	0.141898i	$0.954679\pi$
$642$		0			0
$643$	222.500	−	385.381i	0.346034	−	0.599349i	−0.639507	−	0.768785i	$-0.720861\pi$
$643$	222.500	−	385.381i	0.346034	−	0.599349i	0.985541	+	0.169437i	$0.0541948\pi$
$644$		0			0
$645$		−	169.741i		−	0.263164i
$646$		0			0
$647$	106.000			0.163833			0.0819165	−	0.996639i	$-0.473896\pi$
$647$	106.000			0.163833			0.0819165	+	0.996639i	$0.473896\pi$
$648$		0			0
$649$	−912.000	−	526.543i	−1.40524	−	0.811315i
$650$		0			0
$651$	43.5000	−	75.3442i	0.0668203	−	0.115736i
$652$		0			0
$653$	328.000			0.502297			0.251149	−	0.967949i	$-0.419192\pi$
$653$	328.000			0.502297			0.251149	+	0.967949i	$0.419192\pi$
$654$		0			0
$655$	−128.000	−	221.703i	−0.195420	−	0.338477i
$656$		0			0
$657$	−105.000			−0.159817
$658$		0			0
$659$	348.000	−	200.918i	0.528073	−	0.304883i	−0.212158	−	0.977235i	$-0.568049\pi$
$659$	348.000	−	200.918i	0.528073	−	0.304883i	0.740231	+	0.672352i	$0.234716\pi$
$660$		0			0
$661$	828.000	−	478.046i	1.25265	−	0.723216i	0.281013	−	0.959704i	$-0.409330\pi$
$661$	828.000	−	478.046i	1.25265	−	0.723216i	0.971635	+	0.236488i	$0.0759963\pi$
$662$		0			0
$663$	−297.000	+	514.419i	−0.447964	+	0.775896i
$664$		0			0
$665$	−19.0000	+	32.9090i	−0.0285714	+	0.0494872i
$666$		0			0
$667$	−600.000	−	346.410i	−0.899550	−	0.519356i
$668$		0			0
$669$	211.500	+	366.329i	0.316143	+	0.547577i
$670$		0			0
$671$	776.000	+	1344.07i	1.15648	+	2.00309i
$672$		0			0
$673$			521.347i			0.774662i	0.921941	+	0.387331i	$0.126603\pi$
$673$			521.347i			0.774662i	−0.921941	+	0.387331i	$0.873397\pi$
$674$		0			0
$675$	−94.5000	+	54.5596i	−0.140000	+	0.0808290i
$676$		0			0
$677$			439.941i			0.649839i	0.945742	+	0.324919i	$0.105337\pi$
$677$			439.941i			0.649839i	−0.945742	+	0.324919i	$0.894663\pi$
$678$		0			0
$679$	−54.0000	−	31.1769i	−0.0795287	−	0.0459159i
$680$		0			0
$681$	−129.000	+	223.435i	−0.189427	+	0.328098i
$682$		0			0
$683$			717.069i			1.04988i	0.851139	+	0.524941i	$0.175913\pi$
$683$			717.069i			1.04988i	−0.851139	+	0.524941i	$0.824087\pi$
$684$		0			0
$685$	232.000			0.338686
$686$		0			0
$687$	124.500	+	71.8801i	0.181223	+	0.104629i
$688$		0			0
$689$	−378.000	+	654.715i	−0.548621	+	0.950240i
$690$		0			0
$691$	422.000			0.610709			0.305355	−	0.952239i	$-0.401225\pi$
$691$	422.000			0.610709			0.305355	+	0.952239i	$0.401225\pi$
$692$		0			0
$693$	−24.0000	−	41.5692i	−0.0346320	−	0.0599844i
$694$		0			0
$695$	350.000			0.503597
$696$		0			0
$697$	264.000	−	152.420i	0.378766	−	0.218681i
$698$		0			0
$699$	120.000	−	69.2820i	0.171674	−	0.0991159i
$700$		0			0
$701$	−185.000	+	320.429i	−0.263909	+	0.457103i	−0.967277	−	0.253722i	$-0.918345\pi$
$701$	−185.000	+	320.429i	−0.263909	+	0.457103i	0.703368	+	0.710825i	$0.251678\pi$
$702$		0			0
$703$		−	296.181i		−	0.421310i
$704$		0			0
$705$	−138.000	−	79.6743i	−0.195745	−	0.113013i
$706$		0			0
$707$	14.0000	+	24.2487i	0.0198020	+	0.0342980i
$708$		0			0
$709$	45.5000	+	78.8083i	0.0641749	+	0.111154i	0.896328	−	0.443392i	$-0.146225\pi$
$709$	45.5000	+	78.8083i	0.0641749	+	0.111154i	−0.832153	+	0.554546i	$0.812892\pi$
$710$		0			0
$711$		−	265.004i		−	0.372720i
$712$		0			0
$713$	1740.00	−	1004.59i	2.44039	−	1.40896i
$714$		0			0
$715$		−	498.831i		−	0.697665i
$716$		0			0
$717$	87.0000	+	50.2295i	0.121339	+	0.0700551i
$718$		0			0
$719$	502.000	−	869.490i	0.698192	−	1.20930i	−0.270901	−	0.962607i	$-0.587322\pi$
$719$	502.000	−	869.490i	0.698192	−	1.20930i	0.969093	−	0.246697i	$-0.0793451\pi$
$720$		0			0
$721$			126.440i			0.175367i
$722$		0			0
$723$	−489.000			−0.676349
$724$		0			0
$725$	315.000	+	181.865i	0.434483	+	0.250849i
$726$		0			0
$727$	147.500	−	255.477i	0.202889	−	0.351413i	−0.746569	−	0.665308i	$-0.768300\pi$
$727$	147.500	−	255.477i	0.202889	−	0.351413i	0.949458	+	0.313894i	$0.101634\pi$
$728$		0			0
$729$	−27.0000			−0.0370370
$730$		0			0
$731$	539.000	+	933.575i	0.737346	+	1.27712i
$732$		0			0
$733$	−250.000			−0.341064			−0.170532	−	0.985352i	$-0.554549\pi$
$733$	−250.000			−0.341064			−0.170532	+	0.985352i	$0.554549\pi$
$734$		0			0
$735$	−144.000	+	83.1384i	−0.195918	+	0.113114i
$736$		0			0
$737$	−360.000	+	207.846i	−0.488467	+	0.282016i
$738$		0			0
$739$	285.500	−	494.501i	0.386333	−	0.669148i	−0.605620	−	0.795754i	$-0.707075\pi$
$739$	285.500	−	494.501i	0.386333	−	0.669148i	0.991953	+	0.126606i	$0.0404083\pi$
$740$		0			0
$741$	513.000			0.692308
$742$		0			0
$743$	6.00000	+	3.46410i	0.00807537	+	0.00466232i	0.504032	−	0.863685i	$-0.331849\pi$
$743$	6.00000	+	3.46410i	0.00807537	+	0.00466232i	−0.495957	+	0.868347i	$0.665183\pi$
$744$		0			0
$745$	148.000	+	256.344i	0.198658	+	0.344085i
$746$		0			0
$747$	−219.000	−	379.319i	−0.293173	−	0.507790i
$748$		0			0
$749$			83.1384i			0.110999i
$750$		0			0
$751$	−841.500	+	485.840i	−1.12051	+	0.646924i	−0.941530	−	0.336929i	$-0.890612\pi$
$751$	−841.500	+	485.840i	−1.12051	+	0.646924i	−0.178976	+	0.983853i	$0.557278\pi$
$752$		0			0
$753$			460.726i			0.611853i
$754$		0			0
$755$	336.000	+	193.990i	0.445033	+	0.256940i
$756$		0			0
$757$	−119.500	+	206.980i	−0.157860	+	0.273421i	−0.934097	−	0.357020i	$-0.883793\pi$
$757$	−119.500	+	206.980i	−0.157860	+	0.273421i	0.776237	+	0.630442i	$0.217126\pi$
$758$		0			0
$759$		−	1108.51i		−	1.46049i
$760$		0			0
$761$	1402.00			1.84231			0.921156	−	0.389193i	$-0.127246\pi$
$761$	1402.00			1.84231			0.921156	+	0.389193i	$0.127246\pi$
$762$		0			0
$763$	66.0000	+	38.1051i	0.0865007	+	0.0499412i
$764$		0			0
$765$	−66.0000	+	114.315i	−0.0862745	+	0.149432i
$766$		0			0
$767$	−1026.00			−1.33768
$768$		0			0
$769$	51.5000	+	89.2006i	0.0669701	+	0.115996i	0.897566	−	0.440880i	$-0.145333\pi$
$769$	51.5000	+	89.2006i	0.0669701	+	0.115996i	−0.830596	+	0.556875i	$0.812000\pi$
$770$		0			0
$771$	−324.000			−0.420233
$772$		0			0
$773$	−69.0000	+	39.8372i	−0.0892626	+	0.0515358i	−0.543967	−	0.839107i	$-0.683078\pi$
$773$	−69.0000	+	39.8372i	−0.0892626	+	0.0515358i	0.454704	+	0.890642i	$0.349745\pi$
$774$		0			0
$775$	−913.500	+	527.409i	−1.17871	+	0.680528i
$776$		0			0
$777$	−13.5000	+	23.3827i	−0.0173745	+	0.0300935i
$778$		0			0
$779$	−228.000	−	131.636i	−0.292683	−	0.168981i
$780$		0			0
$781$	−672.000	−	387.979i	−0.860435	−	0.496773i
$782$		0			0
$783$	45.0000	+	77.9423i	0.0574713	+	0.0995431i
$784$		0			0
$785$	−193.000	−	334.286i	−0.245860	−	0.425842i
$786$		0			0
$787$		−	188.794i		−	0.239890i	−0.992781	−	0.119945i	$-0.961728\pi$
$787$		−	188.794i		−	0.239890i	0.992781	−	0.119945i	$-0.0382718\pi$
$788$		0			0
$789$	246.000	−	142.028i	0.311787	−	0.180010i
$790$		0			0
$791$		−	183.597i		−	0.232108i
$792$		0			0
$793$	1309.50	+	756.040i	1.65132	+	0.953392i
$794$		0			0
$795$	−84.0000	+	145.492i	−0.105660	+	0.183009i
$796$		0			0
$797$			630.466i			0.791050i	0.918455	+	0.395525i	$0.129437\pi$
$797$			630.466i			0.791050i	−0.918455	+	0.395525i	$0.870563\pi$
$798$		0			0
$799$	1012.00			1.26658
$800$		0			0
$801$	−99.0000	−	57.1577i	−0.123596	−	0.0713579i
$802$		0			0
$803$	−280.000	+	484.974i	−0.348692	+	0.603953i
$804$		0			0
$805$	80.0000			0.0993789
$806$		0			0
$807$	−447.000	−	774.227i	−0.553903	−	0.959389i
$808$		0			0
$809$	1054.00			1.30284			0.651422	−	0.758716i	$-0.274173\pi$
$809$	1054.00			1.30284			0.651422	+	0.758716i	$0.274173\pi$
$810$		0			0
$811$	960.000	−	554.256i	1.18372	−	0.683423i	0.226851	−	0.973930i	$-0.427157\pi$
$811$	960.000	−	554.256i	1.18372	−	0.683423i	0.956873	+	0.290506i	$0.0938237\pi$
$812$		0			0
$813$	−21.0000	+	12.1244i	−0.0258303	+	0.0149131i
$814$		0			0
$815$	233.000	−	403.568i	0.285890	−	0.495175i
$816$		0			0
$817$	465.500	−	806.270i	0.569767	−	0.986866i
$818$		0			0
$819$	−40.5000	−	23.3827i	−0.0494505	−	0.0285503i
$820$		0			0
$821$	487.000	+	843.509i	0.593179	+	1.02742i	0.993801	+	0.111173i	$0.0354607\pi$
$821$	487.000	+	843.509i	0.593179	+	1.02742i	−0.400622	+	0.916243i	$0.631206\pi$
$822$		0			0
$823$	317.000	+	549.060i	0.385176	+	0.667145i	0.991794	−	0.127849i	$-0.0408073\pi$
$823$	317.000	+	549.060i	0.385176	+	0.667145i	−0.606617	+	0.794994i	$0.707474\pi$
$824$		0			0
$825$			581.969i			0.705417i
$826$		0			0
$827$	1155.00	−	666.840i	1.39661	−	0.806336i	0.402578	−	0.915386i	$-0.368114\pi$
$827$	1155.00	−	666.840i	1.39661	−	0.806336i	0.994036	+	0.109050i	$0.0347809\pi$
$828$		0			0
$829$		−	296.181i		−	0.357275i	−0.983915	−	0.178637i	$-0.942831\pi$
$829$		−	296.181i		−	0.357275i	0.983915	−	0.178637i	$-0.0571689\pi$
$830$		0			0
$831$	309.000	+	178.401i	0.371841	+	0.214683i
$832$		0			0
$833$	528.000	−	914.523i	0.633854	−	1.09787i
$834$		0			0
$835$		−	145.492i		−	0.174242i
$836$		0			0
$837$	−261.000			−0.311828
$838$		0			0
$839$	1395.00	+	805.404i	1.66269	+	0.959957i	0.971421	+	0.237363i	$0.0762829\pi$
$839$	1395.00	+	805.404i	1.66269	+	0.959957i	0.691273	+	0.722594i	$0.257050\pi$
$840$		0			0
$841$	−270.500	+	468.520i	−0.321641	+	0.557098i
$842$		0			0
$843$	174.000			0.206406
$844$		0			0
$845$	−74.0000	−	128.172i	−0.0875740	−	0.151683i
$846$		0			0
$847$	−135.000			−0.159386
$848$		0			0
$849$	−813.000	+	469.386i	−0.957597	+	0.552869i
$850$		0			0
$851$	−540.000	+	311.769i	−0.634548	+	0.366356i
$852$		0			0
$853$	219.500	−	380.185i	0.257327	−	0.445704i	−0.708198	−	0.706014i	$-0.750492\pi$
$853$	219.500	−	380.185i	0.257327	−	0.445704i	0.965525	+	0.260310i	$0.0838249\pi$
$854$		0			0
$855$	114.000			0.133333
$856$		0			0
$857$	531.000	+	306.573i	0.619603	+	0.357728i	0.776715	−	0.629853i	$-0.216885\pi$
$857$	531.000	+	306.573i	0.619603	+	0.357728i	−0.157111	+	0.987581i	$0.550218\pi$
$858$		0			0
$859$	−278.500	−	482.376i	−0.324214	−	0.561555i	0.657139	−	0.753770i	$-0.271767\pi$
$859$	−278.500	−	482.376i	−0.324214	−	0.561555i	−0.981353	+	0.192214i	$0.938433\pi$
$860$		0			0
$861$	12.0000	+	20.7846i	0.0139373	+	0.0241401i
$862$		0			0
$863$			1340.61i			1.55343i	0.629854	+	0.776713i	$0.283115\pi$
$863$			1340.61i			1.55343i	−0.629854	+	0.776713i	$0.716885\pi$
$864$		0			0
$865$	198.000	−	114.315i	0.228902	−	0.132156i
$866$		0			0
$867$		−	337.750i		−	0.389562i
$868$		0			0
$869$	−1224.00	−	706.677i	−1.40852	−	0.813207i
$870$		0			0
$871$	−202.500	+	350.740i	−0.232491	+	0.402687i
$872$		0			0
$873$			187.061i			0.214274i
$874$		0			0
$875$	−92.0000			−0.105143
$876$		0			0
$877$	−397.500	−	229.497i	−0.453250	−	0.261684i	0.255952	−	0.966690i	$-0.417611\pi$
$877$	−397.500	−	229.497i	−0.453250	−	0.261684i	−0.709202	+	0.705006i	$0.750944\pi$
$878$		0			0
$879$	417.000	−	722.265i	0.474403	−	0.821690i
$880$		0			0
$881$	910.000			1.03292			0.516459	−	0.856312i	$-0.327250\pi$
$881$	910.000			1.03292			0.516459	+	0.856312i	$0.327250\pi$
$882$		0			0
$883$	−2.50000	−	4.33013i	−0.00283126	−	0.00490388i	0.864606	−	0.502450i	$-0.167568\pi$
$883$	−2.50000	−	4.33013i	−0.00283126	−	0.00490388i	−0.867438	+	0.497546i	$0.834235\pi$
$884$		0			0
$885$	−228.000			−0.257627
$886$		0			0
$887$	−927.000	+	535.204i	−1.04510	+	0.603386i	−0.921272	−	0.388918i	$-0.872849\pi$
$887$	−927.000	+	535.204i	−1.04510	+	0.603386i	−0.123823	+	0.992304i	$0.539516\pi$
$888$		0			0
$889$	−24.0000	+	13.8564i	−0.0269966	+	0.0155865i
$890$		0			0
$891$	−72.0000	+	124.708i	−0.0808081	+	0.139964i
$892$		0			0
$893$	−437.000	−	756.906i	−0.489362	−	0.847599i
$894$		0			0
$895$	144.000	+	83.1384i	0.160894	+	0.0928921i
$896$		0			0
$897$	−540.000	−	935.307i	−0.602007	−	1.04271i
$898$		0			0
$899$	435.000	+	753.442i	0.483871	+	0.838089i
$900$		0			0
$901$		−	1066.94i		−	1.18418i
$902$		0			0
$903$	−73.5000	+	42.4352i	−0.0813953	+	0.0469936i
$904$		0			0
$905$		−	96.9948i		−	0.107177i
$906$		0			0
$907$	180.000	+	103.923i	0.198456	+	0.114579i	0.595935	−	0.803032i	$-0.296781\pi$
$907$	180.000	+	103.923i	0.198456	+	0.114579i	−0.397479	+	0.917611i	$0.630115\pi$
$908$		0			0
$909$	42.0000	−	72.7461i	0.0462046	−	0.0800288i
$910$		0			0
$911$			782.887i			0.859371i	0.902979	+	0.429685i	$0.141376\pi$
$911$			782.887i			0.859371i	−0.902979	+	0.429685i	$0.858624\pi$
$912$		0			0
$913$	−2336.00			−2.55860
$914$		0			0
$915$	291.000	+	168.009i	0.318033	+	0.183616i
$916$		0			0
$917$	−64.0000	+	110.851i	−0.0697928	+	0.120885i
$918$		0			0
$919$	−1225.00			−1.33297			−0.666485	−	0.745518i	$-0.732202\pi$
$919$	−1225.00			−1.33297			−0.666485	+	0.745518i	$0.732202\pi$
$920$		0			0
$921$	−138.000	−	239.023i	−0.149837	−	0.259526i
$922$		0			0
$923$	−756.000			−0.819068
$924$		0			0
$925$	283.500	−	163.679i	0.306486	−	0.176950i
$926$		0			0
$927$	328.500	−	189.660i	0.354369	−	0.204595i
$928$		0			0
$929$	145.000	−	251.147i	0.156082	−	0.270342i	−0.777371	−	0.629043i	$-0.783447\pi$
$929$	145.000	−	251.147i	0.156082	−	0.270342i	0.933452	+	0.358701i	$0.116780\pi$
$930$		0			0
$931$	−912.000			−0.979592
$932$		0			0
$933$	483.000	+	278.860i	0.517685	+	0.298886i
$934$		0			0
$935$	352.000	+	609.682i	0.376471	+	0.652066i
$936$		0			0
$937$	276.500	+	478.912i	0.295091	+	0.511112i	0.975006	−	0.222179i	$-0.0713168\pi$
$937$	276.500	+	478.912i	0.295091	+	0.511112i	−0.679915	+	0.733291i	$0.737983\pi$
$938$		0			0
$939$		−	45.0333i		−	0.0479588i
$940$		0			0
$941$	972.000	−	561.184i	1.03294	−	0.596370i	0.115117	−	0.993352i	$-0.463276\pi$
$941$	972.000	−	561.184i	1.03294	−	0.596370i	0.917827	+	0.396982i	$0.129942\pi$
$942$		0			0
$943$			554.256i			0.587758i
$944$		0			0
$945$	−9.00000	−	5.19615i	−0.00952381	−	0.00549857i
$946$		0			0
$947$	370.000	−	640.859i	0.390707	−	0.676725i	−0.601836	−	0.798620i	$-0.705564\pi$
$947$	370.000	−	640.859i	0.390707	−	0.676725i	0.992543	+	0.121895i	$0.0388971\pi$
$948$		0			0
$949$			545.596i			0.574917i
$950$		0			0
$951$	−582.000			−0.611987
$952$		0			0
$953$	−1086.00	−	627.002i	−1.13956	−	0.657925i	−0.193238	−	0.981152i	$-0.561899\pi$
$953$	−1086.00	−	627.002i	−1.13956	−	0.657925i	−0.946321	+	0.323227i	$0.895232\pi$
$954$		0			0
$955$	70.0000	−	121.244i	0.0732984	−	0.126957i
$956$		0			0
$957$	480.000			0.501567
$958$		0			0
$959$	−58.0000	−	100.459i	−0.0604797	−	0.104754i
$960$		0			0
$961$	−1562.00			−1.62539
$962$		0			0
$963$	216.000	−	124.708i	0.224299	−	0.129499i
$964$		0			0
$965$	−525.000	+	303.109i	−0.544041	+	0.314102i
$966$		0			0
$967$	−167.500	+	290.119i	−0.173216	+	0.300019i	−0.939542	−	0.342432i	$-0.888749\pi$
$967$	−167.500	+	290.119i	−0.173216	+	0.300019i	0.766326	+	0.642451i	$0.222083\pi$
$968$		0			0
$969$	−627.000	+	361.999i	−0.647059	+	0.373580i
$970$		0			0
$971$	1083.00	+	625.270i	1.11535	+	0.643945i	0.940209	−	0.340599i	$-0.110630\pi$
$971$	1083.00	+	625.270i	1.11535	+	0.643945i	0.175136	+	0.984544i	$0.443963\pi$
$972$		0			0
$973$	−87.5000	−	151.554i	−0.0899281	−	0.155760i
$974$		0			0
$975$	283.500	+	491.036i	0.290769	+	0.503627i
$976$		0			0
$977$		−	1292.11i		−	1.32253i	−0.750153	−	0.661264i	$-0.770020\pi$
$977$		−	1292.11i		−	1.32253i	0.750153	−	0.661264i	$-0.229980\pi$
$978$		0			0
$979$	−528.000	+	304.841i	−0.539326	+	0.311380i
$980$		0			0
$981$		−	228.631i		−	0.233059i
$982$		0			0
$983$	−414.000	−	239.023i	−0.421160	−	0.243157i	0.274414	−	0.961612i	$-0.411516\pi$
$983$	−414.000	−	239.023i	−0.421160	−	0.243157i	−0.695573	+	0.718455i	$0.744850\pi$
$984$		0			0
$985$	−2.00000	+	3.46410i	−0.00203046	+	0.00351685i
$986$		0			0
$987$			79.6743i			0.0807237i
$988$		0			0
$989$	−1960.00			−1.98180
$990$		0			0
$991$	955.500	+	551.658i	0.964178	+	0.556668i	0.897456	−	0.441103i	$-0.145413\pi$
$991$	955.500	+	551.658i	0.964178	+	0.556668i	0.0667213	+	0.997772i	$0.478746\pi$
$992$		0			0
$993$	−190.500	+	329.956i	−0.191843	+	0.332282i
$994$		0			0
$995$	−394.000			−0.395980
$996$		0			0
$997$	270.500	+	468.520i	0.271314	+	0.469930i	0.969199	−	0.246281i	$-0.0792085\pi$
$997$	270.500	+	468.520i	0.271314	+	0.469930i	−0.697885	+	0.716210i	$0.745875\pi$
$998$		0			0
$999$	81.0000			0.0810811

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	228.3.l.b.217.1	yes	2
3.2	odd	2		684.3.y.a.217.1		2
4.3	odd	2		912.3.be.c.673.1		2
19.12	odd	6	inner	228.3.l.b.145.1	✓	2
57.50	even	6		684.3.y.a.145.1		2
76.31	even	6		912.3.be.c.145.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
228.3.l.b.145.1	✓	2	19.12	odd	6	inner
228.3.l.b.217.1	yes	2	1.1	even	1	trivial
684.3.y.a.145.1		2	57.50	even	6
684.3.y.a.217.1		2	3.2	odd	2
912.3.be.c.145.1		2	76.31	even	6
912.3.be.c.673.1		2	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 228 = 2^{2} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	228.l (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.50000 + 0.866025i) q^{3} +(1.00000 - 1.73205i) q^{5} -1.00000 q^{7} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(1.50000 + 0.866025i) q^{3} +(1.00000 - 1.73205i) q^{5} -1.00000 q^{7} +(1.50000 + 2.59808i) q^{9} +16.0000 q^{11} +(13.5000 - 7.79423i) q^{13} +(3.00000 - 1.73205i) q^{15} +(-11.0000 + 19.0526i) q^{17} +19.0000 q^{19} +(-1.50000 - 0.866025i) q^{21} +(-20.0000 - 34.6410i) q^{23} +(10.5000 + 18.1865i) q^{25} +5.19615i q^{27} +(15.0000 - 8.66025i) q^{29} +50.2295i q^{31} +(24.0000 + 13.8564i) q^{33} +(-1.00000 + 1.73205i) q^{35} -15.5885i q^{37} +27.0000 q^{39} +(-12.0000 - 6.92820i) q^{41} +(24.5000 - 42.4352i) q^{43} +6.00000 q^{45} +(-23.0000 - 39.8372i) q^{47} -48.0000 q^{49} +(-33.0000 + 19.0526i) q^{51} +(-42.0000 + 24.2487i) q^{53} +(16.0000 - 27.7128i) q^{55} +(28.5000 + 16.4545i) q^{57} +(-57.0000 - 32.9090i) q^{59} +(48.5000 + 84.0045i) q^{61} +(-1.50000 - 2.59808i) q^{63} -31.1769i q^{65} +(-22.5000 + 12.9904i) q^{67} -69.2820i q^{69} +(-42.0000 - 24.2487i) q^{71} +(-17.5000 + 30.3109i) q^{73} +36.3731i q^{75} -16.0000 q^{77} +(-76.5000 - 44.1673i) q^{79} +(-4.50000 + 7.79423i) q^{81} -146.000 q^{83} +(22.0000 + 38.1051i) q^{85} +30.0000 q^{87} +(-33.0000 + 19.0526i) q^{89} +(-13.5000 + 7.79423i) q^{91} +(-43.5000 + 75.3442i) q^{93} +(19.0000 - 32.9090i) q^{95} +(54.0000 + 31.1769i) q^{97} +(24.0000 + 41.5692i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 3 q^{3} + 2 q^{5} - 2 q^{7} + 3 q^{9}+O(q^{10}) \) 2 * q + 3 * q^3 + 2 * q^5 - 2 * q^7 + 3 * q^9	\( 2 q + 3 q^{3} + 2 q^{5} - 2 q^{7} + 3 q^{9} + 32 q^{11} + 27 q^{13} + 6 q^{15} - 22 q^{17} + 38 q^{19} - 3 q^{21} - 40 q^{23} + 21 q^{25} + 30 q^{29} + 48 q^{33} - 2 q^{35} + 54 q^{39} - 24 q^{41} + 49 q^{43} + 12 q^{45} - 46 q^{47} - 96 q^{49} - 66 q^{51} - 84 q^{53} + 32 q^{55} + 57 q^{57} - 114 q^{59} + 97 q^{61} - 3 q^{63} - 45 q^{67} - 84 q^{71} - 35 q^{73} - 32 q^{77} - 153 q^{79} - 9 q^{81} - 292 q^{83} + 44 q^{85} + 60 q^{87} - 66 q^{89} - 27 q^{91} - 87 q^{93} + 38 q^{95} + 108 q^{97} + 48 q^{99}+O(q^{100}) \) 2 * q + 3 * q^3 + 2 * q^5 - 2 * q^7 + 3 * q^9 + 32 * q^11 + 27 * q^13 + 6 * q^15 - 22 * q^17 + 38 * q^19 - 3 * q^21 - 40 * q^23 + 21 * q^25 + 30 * q^29 + 48 * q^33 - 2 * q^35 + 54 * q^39 - 24 * q^41 + 49 * q^43 + 12 * q^45 - 46 * q^47 - 96 * q^49 - 66 * q^51 - 84 * q^53 + 32 * q^55 + 57 * q^57 - 114 * q^59 + 97 * q^61 - 3 * q^63 - 45 * q^67 - 84 * q^71 - 35 * q^73 - 32 * q^77 - 153 * q^79 - 9 * q^81 - 292 * q^83 + 44 * q^85 + 60 * q^87 - 66 * q^89 - 27 * q^91 - 87 * q^93 + 38 * q^95 + 108 * q^97 + 48 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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