LMFDB - Embedded newform 336.3.bh.d.241.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,3,Mod(145,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 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("336.145");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	336.bh (of order $6$, 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:	$9.15533688251$
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:	no (minimal twist has level 21)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			241.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	336.241
Dual form			336.3.bh.d.145.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.50000 + 0.866025i) q^{3} +(4.50000 - 2.59808i) q^{5} +(-6.50000 - 2.59808i) q^{7} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(1.50000 + 0.866025i) q^{3} +(4.50000 - 2.59808i) q^{5} +(-6.50000 - 2.59808i) q^{7} +(1.50000 + 2.59808i) q^{9} +(7.50000 - 12.9904i) q^{11} -13.8564i q^{13} +9.00000 q^{15} +(9.00000 + 5.19615i) q^{17} +(9.00000 - 5.19615i) q^{19} +(-7.50000 - 9.52628i) q^{21} +(1.00000 - 1.73205i) q^{25} +5.19615i q^{27} -9.00000 q^{29} +(10.5000 + 6.06218i) q^{31} +(22.5000 - 12.9904i) q^{33} +(-36.0000 + 5.19615i) q^{35} +(-5.00000 - 8.66025i) q^{37} +(12.0000 - 20.7846i) q^{39} -10.3923i q^{41} +74.0000 q^{43} +(13.5000 + 7.79423i) q^{45} +(35.5000 + 33.7750i) q^{49} +(9.00000 + 15.5885i) q^{51} +(-16.5000 + 28.5788i) q^{53} -77.9423i q^{55} +18.0000 q^{57} +(-13.5000 - 7.79423i) q^{59} +(78.0000 - 45.0333i) q^{61} +(-3.00000 - 20.7846i) q^{63} +(-36.0000 - 62.3538i) q^{65} +(-38.0000 + 65.8179i) q^{67} -84.0000 q^{71} +(-54.0000 - 31.1769i) q^{73} +(3.00000 - 1.73205i) q^{75} +(-82.5000 + 64.9519i) q^{77} +(-21.5000 - 37.2391i) q^{79} +(-4.50000 + 7.79423i) q^{81} +119.512i q^{83} +54.0000 q^{85} +(-13.5000 - 7.79423i) q^{87} +(-63.0000 + 36.3731i) q^{89} +(-36.0000 + 90.0666i) q^{91} +(10.5000 + 18.1865i) q^{93} +(27.0000 - 46.7654i) q^{95} +185.329i q^{97} +45.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 3 q^{3} + 9 q^{5} - 13 q^{7} + 3 q^{9}+O(q^{10}) $ 2 * q + 3 * q^3 + 9 * q^5 - 13 * q^7 + 3 * q^9	$ 2 q + 3 q^{3} + 9 q^{5} - 13 q^{7} + 3 q^{9} + 15 q^{11} + 18 q^{15} + 18 q^{17} + 18 q^{19} - 15 q^{21} + 2 q^{25} - 18 q^{29} + 21 q^{31} + 45 q^{33} - 72 q^{35} - 10 q^{37} + 24 q^{39} + 148 q^{43} + 27 q^{45} + 71 q^{49} + 18 q^{51} - 33 q^{53} + 36 q^{57} - 27 q^{59} + 156 q^{61} - 6 q^{63} - 72 q^{65} - 76 q^{67} - 168 q^{71} - 108 q^{73} + 6 q^{75} - 165 q^{77} - 43 q^{79} - 9 q^{81} + 108 q^{85} - 27 q^{87} - 126 q^{89} - 72 q^{91} + 21 q^{93} + 54 q^{95} + 90 q^{99}+O(q^{100}) $ 2 * q + 3 * q^3 + 9 * q^5 - 13 * q^7 + 3 * q^9 + 15 * q^11 + 18 * q^15 + 18 * q^17 + 18 * q^19 - 15 * q^21 + 2 * q^25 - 18 * q^29 + 21 * q^31 + 45 * q^33 - 72 * q^35 - 10 * q^37 + 24 * q^39 + 148 * q^43 + 27 * q^45 + 71 * q^49 + 18 * q^51 - 33 * q^53 + 36 * q^57 - 27 * q^59 + 156 * q^61 - 6 * q^63 - 72 * q^65 - 76 * q^67 - 168 * q^71 - 108 * q^73 + 6 * q^75 - 165 * q^77 - 43 * q^79 - 9 * q^81 + 108 * q^85 - 27 * q^87 - 126 * q^89 - 72 * q^91 + 21 * q^93 + 54 * q^95 + 90 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$		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
$5$	4.50000	−	2.59808i	0.900000	−	0.519615i	0.0227998	−	0.999740i	$-0.492742\pi$
$5$	4.50000	−	2.59808i	0.900000	−	0.519615i	0.877200	+	0.480125i	$0.159409\pi$
$6$		0			0
$7$	−6.50000	−	2.59808i	−0.928571	−	0.371154i
$7$	−6.50000	−	2.59808i	−0.928571	−	0.371154i
$8$		0			0
$9$	1.50000	+	2.59808i	0.166667	+	0.288675i
$10$		0			0
$11$	7.50000	−	12.9904i	0.681818	−	1.18094i	−0.292607	−	0.956233i	$-0.594523\pi$
$11$	7.50000	−	12.9904i	0.681818	−	1.18094i	0.974425	−	0.224711i	$-0.0721438\pi$
$12$		0			0
$13$		−	13.8564i		−	1.06588i	−0.846154	−	0.532939i	$-0.821088\pi$
$13$		−	13.8564i		−	1.06588i	0.846154	−	0.532939i	$-0.178912\pi$
$14$		0			0
$15$	9.00000			0.600000
$16$		0			0
$17$	9.00000	+	5.19615i	0.529412	+	0.305656i	0.740777	−	0.671751i	$-0.234458\pi$
$17$	9.00000	+	5.19615i	0.529412	+	0.305656i	−0.211365	+	0.977407i	$0.567791\pi$
$18$		0			0
$19$	9.00000	−	5.19615i	0.473684	−	0.273482i	−0.244096	−	0.969751i	$-0.578491\pi$
$19$	9.00000	−	5.19615i	0.473684	−	0.273482i	0.717781	+	0.696269i	$0.245158\pi$
$20$		0			0
$21$	−7.50000	−	9.52628i	−0.357143	−	0.453632i
$22$		0			0
$23$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$23$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$24$		0			0
$25$	1.00000	−	1.73205i	0.0400000	−	0.0692820i
$26$		0			0
$27$			5.19615i			0.192450i
$28$		0			0
$29$	−9.00000			−0.310345			−0.155172	−	0.987887i	$-0.549593\pi$
$29$	−9.00000			−0.310345			−0.155172	+	0.987887i	$0.549593\pi$
$30$		0			0
$31$	10.5000	+	6.06218i	0.338710	+	0.195554i	0.659701	−	0.751528i	$-0.270683\pi$
$31$	10.5000	+	6.06218i	0.338710	+	0.195554i	−0.320992	+	0.947082i	$0.604016\pi$
$32$		0			0
$33$	22.5000	−	12.9904i	0.681818	−	0.393648i
$34$		0			0
$35$	−36.0000	+	5.19615i	−1.02857	+	0.148461i
$36$		0			0
$37$	−5.00000	−	8.66025i	−0.135135	−	0.234061i	0.790514	−	0.612444i	$-0.209814\pi$
$37$	−5.00000	−	8.66025i	−0.135135	−	0.234061i	−0.925649	+	0.378383i	$0.876480\pi$
$38$		0			0
$39$	12.0000	−	20.7846i	0.307692	−	0.532939i
$40$		0			0
$41$		−	10.3923i		−	0.253471i	−0.991937	−	0.126735i	$-0.959550\pi$
$41$		−	10.3923i		−	0.253471i	0.991937	−	0.126735i	$-0.0404499\pi$
$42$		0			0
$43$	74.0000			1.72093			0.860465	−	0.509509i	$-0.170173\pi$
$43$	74.0000			1.72093			0.860465	+	0.509509i	$0.170173\pi$
$44$		0			0
$45$	13.5000	+	7.79423i	0.300000	+	0.173205i
$46$		0			0
$47$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$47$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$48$		0			0
$49$	35.5000	+	33.7750i	0.724490	+	0.689286i
$50$		0			0
$51$	9.00000	+	15.5885i	0.176471	+	0.305656i
$52$		0			0
$53$	−16.5000	+	28.5788i	−0.311321	+	0.539223i	−0.978649	−	0.205541i	$-0.934105\pi$
$53$	−16.5000	+	28.5788i	−0.311321	+	0.539223i	0.667328	+	0.744764i	$0.267438\pi$
$54$		0			0
$55$		−	77.9423i		−	1.41713i
$56$		0			0
$57$	18.0000			0.315789
$58$		0			0
$59$	−13.5000	−	7.79423i	−0.228814	−	0.132106i	0.381211	−	0.924488i	$-0.375507\pi$
$59$	−13.5000	−	7.79423i	−0.228814	−	0.132106i	−0.610025	+	0.792382i	$0.708840\pi$
$60$		0			0
$61$	78.0000	−	45.0333i	1.27869	−	0.738251i	0.302081	−	0.953282i	$-0.402319\pi$
$61$	78.0000	−	45.0333i	1.27869	−	0.738251i	0.976607	+	0.215031i	$0.0689853\pi$
$62$		0			0
$63$	−3.00000	−	20.7846i	−0.0476190	−	0.329914i
$64$		0			0
$65$	−36.0000	−	62.3538i	−0.553846	−	0.959290i
$66$		0			0
$67$	−38.0000	+	65.8179i	−0.567164	+	0.982357i	0.429681	+	0.902981i	$0.358626\pi$
$67$	−38.0000	+	65.8179i	−0.567164	+	0.982357i	−0.996845	+	0.0793762i	$0.974707\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−84.0000			−1.18310			−0.591549	−	0.806269i	$-0.701483\pi$
$71$	−84.0000			−1.18310			−0.591549	+	0.806269i	$0.701483\pi$
$72$		0			0
$73$	−54.0000	−	31.1769i	−0.739726	−	0.427081i	0.0822437	−	0.996612i	$-0.473791\pi$
$73$	−54.0000	−	31.1769i	−0.739726	−	0.427081i	−0.821970	+	0.569531i	$0.807125\pi$
$74$		0			0
$75$	3.00000	−	1.73205i	0.0400000	−	0.0230940i
$76$		0			0
$77$	−82.5000	+	64.9519i	−1.07143	+	0.843531i
$78$		0			0
$79$	−21.5000	−	37.2391i	−0.272152	−	0.471381i	0.697261	−	0.716818i	$-0.254402\pi$
$79$	−21.5000	−	37.2391i	−0.272152	−	0.471381i	−0.969413	+	0.245437i	$0.921069\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.0555556	+	0.0962250i
$82$		0			0
$83$			119.512i			1.43990i	0.694027	+	0.719949i	$0.255835\pi$
$83$			119.512i			1.43990i	−0.694027	+	0.719949i	$0.744165\pi$
$84$		0			0
$85$	54.0000			0.635294
$86$		0			0
$87$	−13.5000	−	7.79423i	−0.155172	−	0.0895888i
$88$		0			0
$89$	−63.0000	+	36.3731i	−0.707865	+	0.408686i	−0.810270	−	0.586057i	$-0.800680\pi$
$89$	−63.0000	+	36.3731i	−0.707865	+	0.408686i	0.102405	+	0.994743i	$0.467346\pi$
$90$		0			0
$91$	−36.0000	+	90.0666i	−0.395604	+	0.989743i
$92$		0			0
$93$	10.5000	+	18.1865i	0.112903	+	0.195554i
$94$		0			0
$95$	27.0000	−	46.7654i	0.284211	−	0.492267i
$96$		0			0
$97$			185.329i			1.91061i	0.295618	+	0.955306i	$0.404475\pi$
$97$			185.329i			1.91061i	−0.295618	+	0.955306i	$0.595525\pi$
$98$		0			0
$99$	45.0000			0.454545
$100$		0			0
$101$	−126.000	−	72.7461i	−1.24752	−	0.720259i	−0.276910	−	0.960896i	$-0.589310\pi$
$101$	−126.000	−	72.7461i	−1.24752	−	0.720259i	−0.970615	+	0.240637i	$0.922644\pi$
$102$		0			0
$103$	60.0000	−	34.6410i	0.582524	−	0.336321i	−0.179612	−	0.983738i	$-0.557484\pi$
$103$	60.0000	−	34.6410i	0.582524	−	0.336321i	0.762136	+	0.647417i	$0.224151\pi$
$104$		0			0
$105$	−58.5000	−	23.3827i	−0.557143	−	0.222692i
$106$		0			0
$107$	46.5000	+	80.5404i	0.434579	+	0.752714i	0.997261	−	0.0739599i	$-0.0235637\pi$
$107$	46.5000	+	80.5404i	0.434579	+	0.752714i	−0.562682	+	0.826674i	$0.690230\pi$
$108$		0			0
$109$	4.00000	−	6.92820i	0.0366972	−	0.0635615i	−0.847093	−	0.531444i	$-0.821650\pi$
$109$	4.00000	−	6.92820i	0.0366972	−	0.0635615i	0.883791	+	0.467882i	$0.154983\pi$
$110$		0			0
$111$		−	17.3205i		−	0.156041i
$112$		0			0
$113$	42.0000			0.371681			0.185841	−	0.982580i	$-0.440499\pi$
$113$	42.0000			0.371681			0.185841	+	0.982580i	$0.440499\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	36.0000	−	20.7846i	0.307692	−	0.177646i
$118$		0			0
$119$	−45.0000	−	57.1577i	−0.378151	−	0.480317i
$120$		0			0
$121$	−52.0000	−	90.0666i	−0.429752	−	0.744352i
$122$		0			0
$123$	9.00000	−	15.5885i	0.0731707	−	0.126735i
$124$		0			0
$125$			119.512i			0.956092i
$126$		0			0
$127$	−35.0000			−0.275591			−0.137795	−	0.990461i	$-0.544002\pi$
$127$	−35.0000			−0.275591			−0.137795	+	0.990461i	$0.544002\pi$
$128$		0			0
$129$	111.000	+	64.0859i	0.860465	+	0.496790i
$130$		0			0
$131$	−148.500	+	85.7365i	−1.13359	+	0.654477i	−0.944835	−	0.327547i	$-0.893778\pi$
$131$	−148.500	+	85.7365i	−1.13359	+	0.654477i	−0.188753	+	0.982025i	$0.560445\pi$
$132$		0			0
$133$	−72.0000	+	10.3923i	−0.541353	+	0.0781376i
$134$		0			0
$135$	13.5000	+	23.3827i	0.100000	+	0.173205i
$136$		0			0
$137$	48.0000	−	83.1384i	0.350365	−	0.606850i	−0.635948	−	0.771732i	$-0.719391\pi$
$137$	48.0000	−	83.1384i	0.350365	−	0.606850i	0.986313	+	0.164882i	$0.0527242\pi$
$138$		0			0
$139$			183.597i			1.32084i	0.750894	+	0.660422i	$0.229623\pi$
$139$			183.597i			1.32084i	−0.750894	+	0.660422i	$0.770377\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−180.000	−	103.923i	−1.25874	−	0.726735i
$144$		0			0
$145$	−40.5000	+	23.3827i	−0.279310	+	0.161260i
$146$		0			0
$147$	24.0000	+	81.4064i	0.163265	+	0.553785i
$148$		0			0
$149$	93.0000	+	161.081i	0.624161	+	1.08108i	0.988702	+	0.149892i	$0.0478924\pi$
$149$	93.0000	+	161.081i	0.624161	+	1.08108i	−0.364541	+	0.931187i	$0.618774\pi$
$150$		0			0
$151$	39.5000	−	68.4160i	0.261589	−	0.453086i	−0.705075	−	0.709133i	$-0.749087\pi$
$151$	39.5000	−	68.4160i	0.261589	−	0.453086i	0.966664	+	0.256047i	$0.0824200\pi$
$152$		0			0
$153$			31.1769i			0.203771i
$154$		0			0
$155$	63.0000			0.406452
$156$		0			0
$157$	−18.0000	−	10.3923i	−0.114650	−	0.0661930i	0.441579	−	0.897223i	$-0.354419\pi$
$157$	−18.0000	−	10.3923i	−0.114650	−	0.0661930i	−0.556228	+	0.831030i	$0.687752\pi$
$158$		0			0
$159$	−49.5000	+	28.5788i	−0.311321	+	0.179741i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−104.000	−	180.133i	−0.638037	−	1.10511i	−0.985863	−	0.167553i	$-0.946413\pi$
$163$	−104.000	−	180.133i	−0.638037	−	1.10511i	0.347826	−	0.937559i	$-0.386920\pi$
$164$		0			0
$165$	67.5000	−	116.913i	0.409091	−	0.708566i
$166$		0			0
$167$			249.415i			1.49350i	0.665102	+	0.746752i	$0.268388\pi$
$167$			249.415i			1.49350i	−0.665102	+	0.746752i	$0.731612\pi$
$168$		0			0
$169$	−23.0000			−0.136095
$170$		0			0
$171$	27.0000	+	15.5885i	0.157895	+	0.0911606i
$172$		0			0
$173$	−198.000	+	114.315i	−1.14451	+	0.660782i	−0.947543	−	0.319628i	$-0.896442\pi$
$173$	−198.000	+	114.315i	−1.14451	+	0.660782i	−0.196966	+	0.980410i	$0.563109\pi$
$174$		0			0
$175$	−11.0000	+	8.66025i	−0.0628571	+	0.0494872i
$176$		0			0
$177$	−13.5000	−	23.3827i	−0.0762712	−	0.132106i
$178$		0			0
$179$	45.0000	−	77.9423i	0.251397	−	0.435432i	−0.712514	−	0.701658i	$-0.752443\pi$
$179$	45.0000	−	77.9423i	0.251397	−	0.435432i	0.963911	+	0.266226i	$0.0857768\pi$
$180$		0			0
$181$		−	10.3923i		−	0.0574160i	−0.999588	−	0.0287080i	$-0.990861\pi$
$181$		−	10.3923i		−	0.0574160i	0.999588	−	0.0287080i	$-0.00913930\pi$
$182$		0			0
$183$	156.000			0.852459
$184$		0			0
$185$	−45.0000	−	25.9808i	−0.243243	−	0.140437i
$186$		0			0
$187$	135.000	−	77.9423i	0.721925	−	0.416804i
$188$		0			0
$189$	13.5000	−	33.7750i	0.0714286	−	0.178704i
$190$		0			0
$191$	−156.000	−	270.200i	−0.816754	−	1.41466i	−0.908062	−	0.418837i	$-0.862438\pi$
$191$	−156.000	−	270.200i	−0.816754	−	1.41466i	0.0913077	−	0.995823i	$-0.470895\pi$
$192$		0			0
$193$	92.5000	−	160.215i	0.479275	−	0.830128i	−0.520443	−	0.853896i	$-0.674233\pi$
$193$	92.5000	−	160.215i	0.479275	−	0.830128i	0.999717	+	0.0237685i	$0.00756646\pi$
$194$		0			0
$195$		−	124.708i		−	0.639526i
$196$		0			0
$197$	330.000			1.67513			0.837563	−	0.546340i	$-0.183979\pi$
$197$	330.000			1.67513			0.837563	+	0.546340i	$0.183979\pi$
$198$		0			0
$199$	−6.00000	−	3.46410i	−0.0301508	−	0.0174075i	0.484849	−	0.874598i	$-0.338875\pi$
$199$	−6.00000	−	3.46410i	−0.0301508	−	0.0174075i	−0.515000	+	0.857190i	$0.672208\pi$
$200$		0			0
$201$	−114.000	+	65.8179i	−0.567164	+	0.327452i
$202$		0			0
$203$	58.5000	+	23.3827i	0.288177	+	0.115186i
$204$		0			0
$205$	−27.0000	−	46.7654i	−0.131707	−	0.228124i
$206$		0			0
$207$		0			0
$208$		0			0
$209$		−	155.885i		−	0.745859i
$210$		0			0
$211$	248.000			1.17536			0.587678	−	0.809095i	$-0.300042\pi$
$211$	248.000			1.17536			0.587678	+	0.809095i	$0.300042\pi$
$212$		0			0
$213$	−126.000	−	72.7461i	−0.591549	−	0.341531i
$214$		0			0
$215$	333.000	−	192.258i	1.54884	−	0.894222i
$216$		0			0
$217$	−52.5000	−	66.6840i	−0.241935	−	0.307299i
$218$		0			0
$219$	−54.0000	−	93.5307i	−0.246575	−	0.427081i
$220$		0			0
$221$	72.0000	−	124.708i	0.325792	−	0.564288i
$222$		0			0
$223$			192.258i			0.862142i	0.902318	+	0.431071i	$0.141864\pi$
$223$			192.258i			0.862142i	−0.902318	+	0.431071i	$0.858136\pi$
$224$		0			0
$225$	6.00000			0.0266667
$226$		0			0
$227$	76.5000	+	44.1673i	0.337004	+	0.194570i	0.658947	−	0.752190i	$-0.271002\pi$
$227$	76.5000	+	44.1673i	0.337004	+	0.194570i	−0.321942	+	0.946759i	$0.604336\pi$
$228$		0			0
$229$	285.000	−	164.545i	1.24454	−	0.718536i	0.274526	−	0.961580i	$-0.411479\pi$
$229$	285.000	−	164.545i	1.24454	−	0.718536i	0.970015	+	0.243043i	$0.0781457\pi$
$230$		0			0
$231$	−180.000	+	25.9808i	−0.779221	+	0.112471i
$232$		0			0
$233$	−135.000	−	233.827i	−0.579399	−	1.00355i	−0.995548	−	0.0942524i	$-0.969954\pi$
$233$	−135.000	−	233.827i	−0.579399	−	1.00355i	0.416149	−	0.909296i	$-0.363379\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		−	74.4782i		−	0.314254i
$238$		0			0
$239$	228.000			0.953975			0.476987	−	0.878910i	$-0.341729\pi$
$239$	228.000			0.953975			0.476987	+	0.878910i	$0.341729\pi$
$240$		0			0
$241$	385.500	+	222.569i	1.59959	+	0.923521i	0.991567	+	0.129598i	$0.0413687\pi$
$241$	385.500	+	222.569i	1.59959	+	0.923521i	0.608018	+	0.793923i	$0.291965\pi$
$242$		0			0
$243$	−13.5000	+	7.79423i	−0.0555556	+	0.0320750i
$244$		0			0
$245$	247.500	+	59.7558i	1.01020	+	0.243901i
$246$		0			0
$247$	−72.0000	−	124.708i	−0.291498	−	0.504889i
$248$		0			0
$249$	−103.500	+	179.267i	−0.415663	+	0.719949i
$250$		0			0
$251$			5.19615i			0.0207018i	0.999946	+	0.0103509i	$0.00329485\pi$
$251$			5.19615i			0.0207018i	−0.999946	+	0.0103509i	$0.996705\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$	81.0000	+	46.7654i	0.317647	+	0.183394i
$256$		0			0
$257$	99.0000	−	57.1577i	0.385214	−	0.222403i	−0.294870	−	0.955537i	$-0.595276\pi$
$257$	99.0000	−	57.1577i	0.385214	−	0.222403i	0.680084	+	0.733134i	$0.261943\pi$
$258$		0			0
$259$	10.0000	+	69.2820i	0.0386100	+	0.267498i
$260$		0			0
$261$	−13.5000	−	23.3827i	−0.0517241	−	0.0895888i
$262$		0			0
$263$	93.0000	−	161.081i	0.353612	−	0.612474i	−0.633267	−	0.773933i	$-0.718287\pi$
$263$	93.0000	−	161.081i	0.353612	−	0.612474i	0.986879	+	0.161459i	$0.0516199\pi$
$264$		0			0
$265$			171.473i			0.647068i
$266$		0			0
$267$	−126.000			−0.471910
$268$		0			0
$269$	−292.500	−	168.875i	−1.08736	−	0.627788i	−0.154488	−	0.987995i	$-0.549373\pi$
$269$	−292.500	−	168.875i	−1.08736	−	0.627788i	−0.932873	+	0.360207i	$0.882706\pi$
$270$		0			0
$271$	−79.5000	+	45.8993i	−0.293358	+	0.169370i	−0.639455	−	0.768828i	$-0.720840\pi$
$271$	−79.5000	+	45.8993i	−0.293358	+	0.169370i	0.346097	+	0.938199i	$0.387507\pi$
$272$		0			0
$273$	−132.000	+	103.923i	−0.483516	+	0.380671i
$274$		0			0
$275$	−15.0000	−	25.9808i	−0.0545455	−	0.0944755i
$276$		0			0
$277$	−190.000	+	329.090i	−0.685921	+	1.18805i	0.287226	+	0.957863i	$0.407267\pi$
$277$	−190.000	+	329.090i	−0.685921	+	1.18805i	−0.973147	+	0.230186i	$0.926066\pi$
$278$		0			0
$279$			36.3731i			0.130369i
$280$		0			0
$281$	300.000			1.06762			0.533808	−	0.845606i	$-0.320761\pi$
$281$	300.000			1.06762			0.533808	+	0.845606i	$0.320761\pi$
$282$		0			0
$283$	−177.000	−	102.191i	−0.625442	−	0.361099i	0.153543	−	0.988142i	$-0.450932\pi$
$283$	−177.000	−	102.191i	−0.625442	−	0.361099i	−0.778985	+	0.627043i	$0.784265\pi$
$284$		0			0
$285$	81.0000	−	46.7654i	0.284211	−	0.164089i
$286$		0			0
$287$	−27.0000	+	67.5500i	−0.0940767	+	0.235366i
$288$		0			0
$289$	−90.5000	−	156.751i	−0.313149	−	0.542390i
$290$		0			0
$291$	−160.500	+	277.994i	−0.551546	+	0.955306i
$292$		0			0
$293$			545.596i			1.86210i	0.364889	+	0.931051i	$0.381107\pi$
$293$			545.596i			1.86210i	−0.364889	+	0.931051i	$0.618893\pi$
$294$		0			0
$295$	−81.0000			−0.274576
$296$		0			0
$297$	67.5000	+	38.9711i	0.227273	+	0.131216i
$298$		0			0
$299$		0			0
$300$		0			0
$301$	−481.000	−	192.258i	−1.59801	−	0.638730i
$302$		0			0
$303$	−126.000	−	218.238i	−0.415842	−	0.720259i
$304$		0			0
$305$	234.000	−	405.300i	0.767213	−	1.32885i
$306$		0			0
$307$		−	173.205i		−	0.564186i	−0.959387	−	0.282093i	$-0.908971\pi$
$307$		−	173.205i		−	0.564186i	0.959387	−	0.282093i	$-0.0910287\pi$
$308$		0			0
$309$	120.000			0.388350
$310$		0			0
$311$	153.000	+	88.3346i	0.491961	+	0.284034i	0.725388	−	0.688340i	$-0.241660\pi$
$311$	153.000	+	88.3346i	0.491961	+	0.284034i	−0.233426	+	0.972374i	$0.574994\pi$
$312$		0			0
$313$	−184.500	+	106.521i	−0.589457	+	0.340323i	−0.764883	−	0.644170i	$-0.777203\pi$
$313$	−184.500	+	106.521i	−0.589457	+	0.340323i	0.175426	+	0.984493i	$0.443870\pi$
$314$		0			0
$315$	−67.5000	−	85.7365i	−0.214286	−	0.272179i
$316$		0			0
$317$	−58.5000	−	101.325i	−0.184543	−	0.319637i	0.758880	−	0.651231i	$-0.225747\pi$
$317$	−58.5000	−	101.325i	−0.184543	−	0.319637i	−0.943422	+	0.331594i	$0.892414\pi$
$318$		0			0
$319$	−67.5000	+	116.913i	−0.211599	+	0.366500i
$320$		0			0
$321$			161.081i			0.501809i
$322$		0			0
$323$	108.000			0.334365
$324$		0			0
$325$	−24.0000	−	13.8564i	−0.0738462	−	0.0426351i
$326$		0			0
$327$	12.0000	−	6.92820i	0.0366972	−	0.0211872i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	20.0000	+	34.6410i	0.0604230	+	0.104656i	0.894655	−	0.446759i	$-0.147422\pi$
$331$	20.0000	+	34.6410i	0.0604230	+	0.104656i	−0.834232	+	0.551414i	$0.814088\pi$
$332$		0			0
$333$	15.0000	−	25.9808i	0.0450450	−	0.0780203i
$334$		0			0
$335$			394.908i			1.17883i
$336$		0			0
$337$	91.0000			0.270030			0.135015	−	0.990844i	$-0.456892\pi$
$337$	91.0000			0.270030			0.135015	+	0.990844i	$0.456892\pi$
$338$		0			0
$339$	63.0000	+	36.3731i	0.185841	+	0.107295i
$340$		0			0
$341$	157.500	−	90.9327i	0.461877	−	0.266665i
$342$		0			0
$343$	−143.000	−	311.769i	−0.416910	−	0.908948i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	105.000	−	181.865i	0.302594	−	0.524108i	−0.674129	−	0.738614i	$-0.735481\pi$
$347$	105.000	−	181.865i	0.302594	−	0.524108i	0.976723	+	0.214506i	$0.0688142\pi$
$348$		0			0
$349$		−	304.841i		−	0.873470i	−0.899590	−	0.436735i	$-0.856135\pi$
$349$		−	304.841i		−	0.873470i	0.899590	−	0.436735i	$-0.143865\pi$
$350$		0			0
$351$	72.0000			0.205128
$352$		0			0
$353$	342.000	+	197.454i	0.968839	+	0.559359i	0.898882	−	0.438191i	$-0.144381\pi$
$353$	342.000	+	197.454i	0.968839	+	0.559359i	0.0699566	+	0.997550i	$0.477714\pi$
$354$		0			0
$355$	−378.000	+	218.238i	−1.06479	+	0.614756i
$356$		0			0
$357$	−18.0000	−	124.708i	−0.0504202	−	0.349321i
$358$		0			0
$359$	246.000	+	426.084i	0.685237	+	1.18686i	0.973362	+	0.229272i	$0.0736346\pi$
$359$	246.000	+	426.084i	0.685237	+	1.18686i	−0.288126	+	0.957593i	$0.593032\pi$
$360$		0			0
$361$	−126.500	+	219.104i	−0.350416	+	0.606937i
$362$		0			0
$363$		−	180.133i		−	0.496235i
$364$		0			0
$365$	−324.000			−0.887671
$366$		0			0
$367$	283.500	+	163.679i	0.772480	+	0.445991i	0.833758	−	0.552129i	$-0.186185\pi$
$367$	283.500	+	163.679i	0.772480	+	0.445991i	−0.0612789	+	0.998121i	$0.519518\pi$
$368$		0			0
$369$	27.0000	−	15.5885i	0.0731707	−	0.0422451i
$370$		0			0
$371$	181.500	−	142.894i	0.489218	−	0.385160i
$372$		0			0
$373$	−85.0000	−	147.224i	−0.227882	−	0.394703i	0.729298	−	0.684196i	$-0.239847\pi$
$373$	−85.0000	−	147.224i	−0.227882	−	0.394703i	−0.957180	+	0.289493i	$0.906513\pi$
$374$		0			0
$375$	−103.500	+	179.267i	−0.276000	+	0.478046i
$376$		0			0
$377$			124.708i			0.330790i
$378$		0			0
$379$	−82.0000			−0.216359			−0.108179	−	0.994131i	$-0.534502\pi$
$379$	−82.0000			−0.216359			−0.108179	+	0.994131i	$0.534502\pi$
$380$		0			0
$381$	−52.5000	−	30.3109i	−0.137795	−	0.0795561i
$382$		0			0
$383$	−189.000	+	109.119i	−0.493473	+	0.284907i	−0.726014	−	0.687680i	$-0.758629\pi$
$383$	−189.000	+	109.119i	−0.493473	+	0.284907i	0.232541	+	0.972587i	$0.425296\pi$
$384$		0			0
$385$	−202.500	+	506.625i	−0.525974	+	1.31591i
$386$		0			0
$387$	111.000	+	192.258i	0.286822	+	0.496790i
$388$		0			0
$389$	−153.000	+	265.004i	−0.393316	+	0.681244i	−0.992885	−	0.119080i	$-0.962006\pi$
$389$	−153.000	+	265.004i	−0.393316	+	0.681244i	0.599568	+	0.800323i	$0.295339\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$	−297.000			−0.755725
$394$		0			0
$395$	−193.500	−	111.717i	−0.489873	−	0.282829i
$396$		0			0
$397$	−222.000	+	128.172i	−0.559194	+	0.322851i	−0.752822	−	0.658224i	$-0.771308\pi$
$397$	−222.000	+	128.172i	−0.559194	+	0.322851i	0.193628	+	0.981075i	$0.437975\pi$
$398$		0			0
$399$	−117.000	−	46.7654i	−0.293233	−	0.117206i
$400$		0			0
$401$	−66.0000	−	114.315i	−0.164589	−	0.285076i	0.771921	−	0.635719i	$-0.219296\pi$
$401$	−66.0000	−	114.315i	−0.164589	−	0.285076i	−0.936509	+	0.350643i	$0.885963\pi$
$402$		0			0
$403$	84.0000	−	145.492i	0.208437	−	0.361023i
$404$		0			0
$405$			46.7654i			0.115470i
$406$		0			0
$407$	−150.000			−0.368550
$408$		0			0
$409$	−313.500	−	180.999i	−0.766504	−	0.442541i	0.0651223	−	0.997877i	$-0.479256\pi$
$409$	−313.500	−	180.999i	−0.766504	−	0.442541i	−0.831626	+	0.555336i	$0.812590\pi$
$410$		0			0
$411$	144.000	−	83.1384i	0.350365	−	0.202283i
$412$		0			0
$413$	67.5000	+	85.7365i	0.163438	+	0.207594i
$414$		0			0
$415$	310.500	+	537.802i	0.748193	+	1.29591i
$416$		0			0
$417$	−159.000	+	275.396i	−0.381295	+	0.660422i
$418$		0			0
$419$		−	644.323i		−	1.53776i	−0.639391	−	0.768882i	$-0.720813\pi$
$419$		−	644.323i		−	1.53776i	0.639391	−	0.768882i	$-0.279187\pi$
$420$		0			0
$421$	752.000			1.78622			0.893112	−	0.449835i	$-0.148517\pi$
$421$	752.000			1.78622			0.893112	+	0.449835i	$0.148517\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	18.0000	−	10.3923i	0.0423529	−	0.0244525i
$426$		0			0
$427$	−624.000	+	90.0666i	−1.46136	+	0.210929i
$428$		0			0
$429$	−180.000	−	311.769i	−0.419580	−	0.726735i
$430$		0			0
$431$	81.0000	−	140.296i	0.187935	−	0.325513i	−0.756627	−	0.653847i	$-0.773154\pi$
$431$	81.0000	−	140.296i	0.187935	−	0.325513i	0.944562	+	0.328334i	$0.106487\pi$
$432$		0			0
$433$		−	339.482i		−	0.784023i	−0.919960	−	0.392011i	$-0.871779\pi$
$433$		−	339.482i		−	0.784023i	0.919960	−	0.392011i	$-0.128221\pi$
$434$		0			0
$435$	−81.0000			−0.186207
$436$		0			0
$437$		0			0
$438$		0			0
$439$	−337.500	+	194.856i	−0.768793	+	0.443863i	−0.832444	−	0.554110i	$-0.813059\pi$
$439$	−337.500	+	194.856i	−0.768793	+	0.443863i	0.0636511	+	0.997972i	$0.479726\pi$
$440$		0			0
$441$	−34.5000	+	142.894i	−0.0782313	+	0.324023i
$442$		0			0
$443$	−148.500	−	257.210i	−0.335214	−	0.580608i	0.648312	−	0.761375i	$-0.275475\pi$
$443$	−148.500	−	257.210i	−0.335214	−	0.580608i	−0.983526	+	0.180767i	$0.942142\pi$
$444$		0			0
$445$	−189.000	+	327.358i	−0.424719	+	0.735635i
$446$		0			0
$447$			322.161i			0.720719i
$448$		0			0
$449$	−492.000			−1.09577			−0.547884	−	0.836554i	$-0.684567\pi$
$449$	−492.000			−1.09577			−0.547884	+	0.836554i	$0.684567\pi$
$450$		0			0
$451$	−135.000	−	77.9423i	−0.299335	−	0.172821i
$452$		0			0
$453$	118.500	−	68.4160i	0.261589	−	0.151029i
$454$		0			0
$455$	72.0000	+	498.831i	0.158242	+	1.09633i
$456$		0			0
$457$	221.500	+	383.649i	0.484683	+	0.839495i	0.999845	−	0.0175975i	$-0.00560174\pi$
$457$	221.500	+	383.649i	0.484683	+	0.839495i	−0.515162	+	0.857093i	$0.672268\pi$
$458$		0			0
$459$	−27.0000	+	46.7654i	−0.0588235	+	0.101885i
$460$		0			0
$461$			415.692i			0.901718i	0.892595	+	0.450859i	$0.148882\pi$
$461$			415.692i			0.901718i	−0.892595	+	0.450859i	$0.851118\pi$
$462$		0			0
$463$	82.0000			0.177106			0.0885529	−	0.996071i	$-0.471776\pi$
$463$	82.0000			0.177106			0.0885529	+	0.996071i	$0.471776\pi$
$464$		0			0
$465$	94.5000	+	54.5596i	0.203226	+	0.117332i
$466$		0			0
$467$	−234.000	+	135.100i	−0.501071	+	0.289293i	−0.729156	−	0.684348i	$-0.760087\pi$
$467$	−234.000	+	135.100i	−0.501071	+	0.289293i	0.228085	+	0.973641i	$0.426754\pi$
$468$		0			0
$469$	418.000	−	329.090i	0.891258	−	0.701684i
$470$		0			0
$471$	−18.0000	−	31.1769i	−0.0382166	−	0.0661930i
$472$		0			0
$473$	555.000	−	961.288i	1.17336	−	2.03232i
$474$		0			0
$475$		−	20.7846i		−	0.0437571i
$476$		0			0
$477$	−99.0000			−0.207547
$478$		0			0
$479$	−297.000	−	171.473i	−0.620042	−	0.357981i	0.156844	−	0.987623i	$-0.449868\pi$
$479$	−297.000	−	171.473i	−0.620042	−	0.357981i	−0.776885	+	0.629642i	$0.783202\pi$
$480$		0			0
$481$	−120.000	+	69.2820i	−0.249480	+	0.144037i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	481.500	+	833.982i	0.992784	+	1.71955i
$486$		0			0
$487$	−158.500	+	274.530i	−0.325462	+	0.563717i	−0.981606	−	0.190919i	$-0.938853\pi$
$487$	−158.500	+	274.530i	−0.325462	+	0.563717i	0.656144	+	0.754636i	$0.272186\pi$
$488$		0			0
$489$		−	360.267i		−	0.736741i
$490$		0			0
$491$	−27.0000			−0.0549898			−0.0274949	−	0.999622i	$-0.508753\pi$
$491$	−27.0000			−0.0549898			−0.0274949	+	0.999622i	$0.508753\pi$
$492$		0			0
$493$	−81.0000	−	46.7654i	−0.164300	−	0.0948588i
$494$		0			0
$495$	202.500	−	116.913i	0.409091	−	0.236189i
$496$		0			0
$497$	546.000	+	218.238i	1.09859	+	0.439111i
$498$		0			0
$499$	−223.000	−	386.247i	−0.446894	−	0.774043i	0.551288	−	0.834315i	$-0.314136\pi$
$499$	−223.000	−	386.247i	−0.446894	−	0.774043i	−0.998182	+	0.0602721i	$0.980803\pi$
$500$		0			0
$501$	−216.000	+	374.123i	−0.431138	+	0.746752i
$502$		0			0
$503$			488.438i			0.971050i	0.874223	+	0.485525i	$0.161372\pi$
$503$			488.438i			0.971050i	−0.874223	+	0.485525i	$0.838628\pi$
$504$		0			0
$505$	−756.000			−1.49703
$506$		0			0
$507$	−34.5000	−	19.9186i	−0.0680473	−	0.0392871i
$508$		0			0
$509$	85.5000	−	49.3634i	0.167976	−	0.0969812i	−0.413655	−	0.910434i	$-0.635748\pi$
$509$	85.5000	−	49.3634i	0.167976	−	0.0969812i	0.581631	+	0.813453i	$0.302415\pi$
$510$		0			0
$511$	270.000	+	342.946i	0.528376	+	0.671127i
$512$		0			0
$513$	27.0000	+	46.7654i	0.0526316	+	0.0911606i
$514$		0			0
$515$	180.000	−	311.769i	0.349515	−	0.605377i
$516$		0			0
$517$		0			0
$518$		0			0
$519$	−396.000			−0.763006
$520$		0			0
$521$	−783.000	−	452.065i	−1.50288	−	0.867688i	−0.999994	−	0.00333410i	$-0.998939\pi$
$521$	−783.000	−	452.065i	−1.50288	−	0.867688i	−0.502885	−	0.864354i	$-0.667728\pi$
$522$		0			0
$523$	606.000	−	349.874i	1.15870	−	0.668976i	0.207708	−	0.978191i	$-0.433400\pi$
$523$	606.000	−	349.874i	1.15870	−	0.668976i	0.950992	+	0.309215i	$0.100066\pi$
$524$		0			0
$525$	−24.0000	+	3.46410i	−0.0457143	+	0.00659829i
$526$		0			0
$527$	63.0000	+	109.119i	0.119545	+	0.207057i
$528$		0			0
$529$	264.500	−	458.127i	0.500000	−	0.866025i
$530$		0			0
$531$		−	46.7654i		−	0.0880704i
$532$		0			0
$533$	−144.000			−0.270169
$534$		0			0
$535$	418.500	+	241.621i	0.782243	+	0.451628i
$536$		0			0
$537$	135.000	−	77.9423i	0.251397	−	0.145144i
$538$		0			0
$539$	705.000	−	207.846i	1.30798	−	0.385614i
$540$		0			0
$541$	−37.0000	−	64.0859i	−0.0683919	−	0.118458i	0.829802	−	0.558058i	$-0.188453\pi$
$541$	−37.0000	−	64.0859i	−0.0683919	−	0.118458i	−0.898194	+	0.439600i	$0.855120\pi$
$542$		0			0
$543$	9.00000	−	15.5885i	0.0165746	−	0.0287080i
$544$		0			0
$545$		−	41.5692i		−	0.0762738i
$546$		0			0
$547$	934.000			1.70750			0.853748	−	0.520687i	$-0.174324\pi$
$547$	934.000			1.70750			0.853748	+	0.520687i	$0.174324\pi$
$548$		0			0
$549$	234.000	+	135.100i	0.426230	+	0.246084i
$550$		0			0
$551$	−81.0000	+	46.7654i	−0.147005	+	0.0848736i
$552$		0			0
$553$	43.0000	+	297.913i	0.0777577	+	0.538721i
$554$		0			0
$555$	−45.0000	−	77.9423i	−0.0810811	−	0.140437i
$556$		0			0
$557$	−421.500	+	730.059i	−0.756732	+	1.31070i	0.187776	+	0.982212i	$0.439872\pi$
$557$	−421.500	+	730.059i	−0.756732	+	1.31070i	−0.944508	+	0.328487i	$0.893461\pi$
$558$		0			0
$559$		−	1025.37i		−	1.83430i
$560$		0			0
$561$	270.000			0.481283
$562$		0			0
$563$	−823.500	−	475.448i	−1.46270	−	0.844490i	−0.463564	−	0.886063i	$-0.653430\pi$
$563$	−823.500	−	475.448i	−1.46270	−	0.844490i	−0.999135	+	0.0415731i	$0.986763\pi$
$564$		0			0
$565$	189.000	−	109.119i	0.334513	−	0.193131i
$566$		0			0
$567$	49.5000	−	38.9711i	0.0873016	−	0.0687322i
$568$		0			0
$569$	−111.000	−	192.258i	−0.195079	−	0.337887i	0.751847	−	0.659337i	$-0.229163\pi$
$569$	−111.000	−	192.258i	−0.195079	−	0.337887i	−0.946926	+	0.321450i	$0.895830\pi$
$570$		0			0
$571$	220.000	−	381.051i	0.385289	−	0.667340i	−0.606520	−	0.795068i	$-0.707435\pi$
$571$	220.000	−	381.051i	0.385289	−	0.667340i	0.991809	+	0.127728i	$0.0407684\pi$
$572$		0			0
$573$		−	540.400i		−	0.943106i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	568.500	+	328.224i	0.985269	+	0.568845i	0.903857	−	0.427835i	$-0.140724\pi$
$577$	568.500	+	328.224i	0.985269	+	0.568845i	0.0814120	+	0.996681i	$0.474057\pi$
$578$		0			0
$579$	277.500	−	160.215i	0.479275	−	0.276709i
$580$		0			0
$581$	310.500	−	776.825i	0.534423	−	1.33705i
$582$		0			0
$583$	247.500	+	428.683i	0.424528	+	0.735305i
$584$		0			0
$585$	108.000	−	187.061i	0.184615	−	0.319763i
$586$		0			0
$587$			1054.82i			1.79697i	0.439008	+	0.898483i	$0.355330\pi$
$587$			1054.82i			1.79697i	−0.439008	+	0.898483i	$0.644670\pi$
$588$		0			0
$589$	126.000			0.213922
$590$		0			0
$591$	495.000	+	285.788i	0.837563	+	0.483567i
$592$		0			0
$593$	612.000	−	353.338i	1.03204	−	0.595849i	0.114472	−	0.993426i	$-0.463482\pi$
$593$	612.000	−	353.338i	1.03204	−	0.595849i	0.917569	+	0.397578i	$0.130149\pi$
$594$		0			0
$595$	−351.000	−	140.296i	−0.589916	−	0.235792i
$596$		0			0
$597$	−6.00000	−	10.3923i	−0.0100503	−	0.0174075i
$598$		0			0
$599$	258.000	−	446.869i	0.430718	−	0.746025i	−0.566217	−	0.824256i	$-0.691594\pi$
$599$	258.000	−	446.869i	0.430718	−	0.746025i	0.996935	+	0.0782307i	$0.0249271\pi$
$600$		0			0
$601$		−	247.683i		−	0.412119i	−0.978540	−	0.206059i	$-0.933936\pi$
$601$		−	247.683i		−	0.412119i	0.978540	−	0.206059i	$-0.0660640\pi$
$602$		0			0
$603$	−228.000			−0.378109
$604$		0			0
$605$	−468.000	−	270.200i	−0.773554	−	0.446611i
$606$		0			0
$607$	562.500	−	324.760i	0.926689	−	0.535024i	0.0409259	−	0.999162i	$-0.486969\pi$
$607$	562.500	−	324.760i	0.926689	−	0.535024i	0.885763	+	0.464138i	$0.153636\pi$
$608$		0			0
$609$	67.5000	+	85.7365i	0.110837	+	0.140782i
$610$		0			0
$611$		0			0
$612$		0			0
$613$	446.000	−	772.495i	0.727569	−	1.26019i	−0.230338	−	0.973111i	$-0.573983\pi$
$613$	446.000	−	772.495i	0.727569	−	1.26019i	0.957908	−	0.287076i	$-0.0926834\pi$
$614$		0			0
$615$		−	93.5307i		−	0.152083i
$616$		0			0
$617$	−1224.00			−1.98379			−0.991896	−	0.127050i	$-0.959449\pi$
$617$	−1224.00			−1.98379			−0.991896	+	0.127050i	$0.959449\pi$
$618$		0			0
$619$	348.000	+	200.918i	0.562197	+	0.324585i	0.754027	−	0.656844i	$-0.228109\pi$
$619$	348.000	+	200.918i	0.562197	+	0.324585i	−0.191830	+	0.981428i	$0.561442\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	504.000	−	72.7461i	0.808989	−	0.116767i
$624$		0			0
$625$	335.500	+	581.103i	0.536800	+	0.929765i
$626$		0			0
$627$	135.000	−	233.827i	0.215311	−	0.372930i
$628$		0			0
$629$		−	103.923i		−	0.165219i
$630$		0			0
$631$	−1115.00			−1.76704			−0.883518	−	0.468397i	$-0.844832\pi$
$631$	−1115.00			−1.76704			−0.883518	+	0.468397i	$0.844832\pi$
$632$		0			0
$633$	372.000	+	214.774i	0.587678	+	0.339296i
$634$		0			0
$635$	−157.500	+	90.9327i	−0.248031	+	0.143201i
$636$		0			0
$637$	468.000	−	491.902i	0.734694	−	0.772217i
$638$		0			0
$639$	−126.000	−	218.238i	−0.197183	−	0.341531i
$640$		0			0
$641$	192.000	−	332.554i	0.299532	−	0.518805i	−0.676497	−	0.736445i	$-0.736503\pi$
$641$	192.000	−	332.554i	0.299532	−	0.518805i	0.976029	+	0.217641i	$0.0698361\pi$
$642$		0			0
$643$			6.92820i			0.0107748i	0.999985	+	0.00538741i	$0.00171487\pi$
$643$			6.92820i			0.0107748i	−0.999985	+	0.00538741i	$0.998285\pi$
$644$		0			0
$645$	666.000			1.03256
$646$		0			0
$647$	−774.000	−	446.869i	−1.19629	−	0.690679i	−0.236564	−	0.971616i	$-0.576021\pi$
$647$	−774.000	−	446.869i	−1.19629	−	0.690679i	−0.959726	+	0.280937i	$0.909355\pi$
$648$		0			0
$649$	−202.500	+	116.913i	−0.312018	+	0.180144i
$650$		0			0
$651$	−21.0000	−	145.492i	−0.0322581	−	0.223490i
$652$		0			0
$653$	−37.5000	−	64.9519i	−0.0574273	−	0.0994669i	0.835883	−	0.548908i	$-0.184956\pi$
$653$	−37.5000	−	64.9519i	−0.0574273	−	0.0994669i	−0.893310	+	0.449441i	$0.851623\pi$
$654$		0			0
$655$	−445.500	+	771.629i	−0.680153	+	1.17806i
$656$		0			0
$657$		−	187.061i		−	0.284721i
$658$		0			0
$659$	−642.000			−0.974203			−0.487102	−	0.873345i	$-0.661946\pi$
$659$	−642.000			−0.974203			−0.487102	+	0.873345i	$0.661946\pi$
$660$		0			0
$661$	−243.000	−	140.296i	−0.367625	−	0.212248i	0.304795	−	0.952418i	$-0.401412\pi$
$661$	−243.000	−	140.296i	−0.367625	−	0.212248i	−0.672420	+	0.740170i	$0.734745\pi$
$662$		0			0
$663$	216.000	−	124.708i	0.325792	−	0.188096i
$664$		0			0
$665$	−297.000	+	233.827i	−0.446617	+	0.351619i
$666$		0			0
$667$		0			0
$668$		0			0
$669$	−166.500	+	288.386i	−0.248879	+	0.431071i
$670$		0			0
$671$		−	1351.00i		−	2.01341i
$672$		0			0
$673$	13.0000			0.0193165			0.00965825	−	0.999953i	$-0.496926\pi$
$673$	13.0000			0.0193165			0.00965825	+	0.999953i	$0.496926\pi$
$674$		0			0
$675$	9.00000	+	5.19615i	0.0133333	+	0.00769800i
$676$		0			0
$677$	−1093.50	+	631.333i	−1.61521	+	0.932544i	−0.627079	+	0.778955i	$0.715750\pi$
$677$	−1093.50	+	631.333i	−1.61521	+	0.932544i	−0.988135	+	0.153589i	$0.950917\pi$
$678$		0			0
$679$	481.500	−	1204.64i	0.709131	−	1.77414i
$680$		0			0
$681$	76.5000	+	132.502i	0.112335	+	0.194570i
$682$		0			0
$683$	−484.500	+	839.179i	−0.709370	+	1.22867i	0.255721	+	0.966751i	$0.417687\pi$
$683$	−484.500	+	839.179i	−0.709370	+	1.22867i	−0.965091	+	0.261915i	$0.915646\pi$
$684$		0			0
$685$		−	498.831i		−	0.728220i
$686$		0			0
$687$	570.000			0.829694
$688$		0			0
$689$	396.000	+	228.631i	0.574746	+	0.331830i
$690$		0			0
$691$	87.0000	−	50.2295i	0.125904	−	0.0726910i	−0.435725	−	0.900080i	$-0.643508\pi$
$691$	87.0000	−	50.2295i	0.125904	−	0.0726910i	0.561629	+	0.827389i	$0.310175\pi$
$692$		0			0
$693$	−292.500	−	116.913i	−0.422078	−	0.168706i
$694$		0			0
$695$	477.000	+	826.188i	0.686331	+	1.18876i
$696$		0			0
$697$	54.0000	−	93.5307i	0.0774749	−	0.134190i
$698$		0			0
$699$		−	467.654i		−	0.669033i
$700$		0			0
$701$	597.000			0.851641			0.425820	−	0.904808i	$-0.359986\pi$
$701$	597.000			0.851641			0.425820	+	0.904808i	$0.359986\pi$
$702$		0			0
$703$	−90.0000	−	51.9615i	−0.128023	−	0.0739140i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	630.000	+	800.207i	0.891089	+	1.13184i
$708$		0			0
$709$	415.000	+	718.801i	0.585331	+	1.01382i	0.994834	+	0.101515i	$0.0323689\pi$
$709$	415.000	+	718.801i	0.585331	+	1.01382i	−0.409503	+	0.912309i	$0.634298\pi$
$710$		0			0
$711$	64.5000	−	111.717i	0.0907173	−	0.157127i
$712$		0			0
$713$		0			0
$714$		0			0
$715$	−1080.00			−1.51049
$716$		0			0
$717$	342.000	+	197.454i	0.476987	+	0.275389i
$718$		0			0
$719$	−297.000	+	171.473i	−0.413074	+	0.238488i	−0.692110	−	0.721792i	$-0.743319\pi$
$719$	−297.000	+	171.473i	−0.413074	+	0.238488i	0.279036	+	0.960281i	$0.409985\pi$
$720$		0			0
$721$	−480.000	+	69.2820i	−0.665742	+	0.0960916i
$722$		0			0
$723$	385.500	+	667.706i	0.533195	+	0.923521i
$724$		0			0
$725$	−9.00000	+	15.5885i	−0.0124138	+	0.0215013i
$726$		0			0
$727$		−	50.2295i		−	0.0690914i	−0.999403	−	0.0345457i	$-0.989002\pi$
$727$		−	50.2295i		−	0.0690914i	0.999403	−	0.0345457i	$-0.0109984\pi$
$728$		0			0
$729$	−27.0000			−0.0370370
$730$		0			0
$731$	666.000	+	384.515i	0.911081	+	0.526013i
$732$		0			0
$733$	−159.000	+	91.7987i	−0.216917	+	0.125237i	−0.604522	−	0.796589i	$-0.706636\pi$
$733$	−159.000	+	91.7987i	−0.216917	+	0.125237i	0.387605	+	0.921826i	$0.373302\pi$
$734$		0			0
$735$	319.500	+	303.975i	0.434694	+	0.413571i
$736$		0			0
$737$	570.000	+	987.269i	0.773406	+	1.33958i
$738$		0			0
$739$	−167.000	+	289.252i	−0.225981	+	0.391411i	−0.956613	−	0.291361i	$-0.905892\pi$
$739$	−167.000	+	289.252i	−0.225981	+	0.391411i	0.730632	+	0.682771i	$0.239225\pi$
$740$		0			0
$741$		−	249.415i		−	0.336593i
$742$		0			0
$743$	−84.0000			−0.113055			−0.0565276	−	0.998401i	$-0.518003\pi$
$743$	−84.0000			−0.113055			−0.0565276	+	0.998401i	$0.518003\pi$
$744$		0			0
$745$	837.000	+	483.242i	1.12349	+	0.648647i
$746$		0			0
$747$	−310.500	+	179.267i	−0.415663	+	0.239983i
$748$		0			0
$749$	−93.0000	−	644.323i	−0.124166	−	0.860244i
$750$		0			0
$751$	−179.500	−	310.903i	−0.239015	−	0.413986i	0.721417	−	0.692501i	$-0.243491\pi$
$751$	−179.500	−	310.903i	−0.239015	−	0.413986i	−0.960432	+	0.278515i	$0.910158\pi$
$752$		0			0
$753$	−4.50000	+	7.79423i	−0.00597610	+	0.0103509i
$754$		0			0
$755$		−	410.496i		−	0.543703i
$756$		0			0
$757$	−80.0000			−0.105680			−0.0528402	−	0.998603i	$-0.516827\pi$
$757$	−80.0000			−0.105680			−0.0528402	+	0.998603i	$0.516827\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−702.000	+	405.300i	−0.922470	+	0.532589i	−0.884422	−	0.466687i	$-0.845447\pi$
$761$	−702.000	+	405.300i	−0.922470	+	0.532589i	−0.0380481	+	0.999276i	$0.512114\pi$
$762$		0			0
$763$	−44.0000	+	34.6410i	−0.0576671	+	0.0454011i
$764$		0			0
$765$	81.0000	+	140.296i	0.105882	+	0.183394i
$766$		0			0
$767$	−108.000	+	187.061i	−0.140808	+	0.243887i
$768$		0			0
$769$		−	774.227i		−	1.00680i	−0.864054	−	0.503398i	$-0.832083\pi$
$769$		−	774.227i		−	1.00680i	0.864054	−	0.503398i	$-0.167917\pi$
$770$		0			0
$771$	198.000			0.256809
$772$		0			0
$773$	−630.000	−	363.731i	−0.815006	−	0.470544i	0.0336850	−	0.999433i	$-0.489276\pi$
$773$	−630.000	−	363.731i	−0.815006	−	0.470544i	−0.848691	+	0.528888i	$0.822609\pi$
$774$		0			0
$775$	21.0000	−	12.1244i	0.0270968	−	0.0156443i
$776$		0			0
$777$	−45.0000	+	112.583i	−0.0579151	+	0.144895i
$778$		0			0
$779$	−54.0000	−	93.5307i	−0.0693196	−	0.120065i
$780$		0			0
$781$	−630.000	+	1091.19i	−0.806658	+	1.39717i
$782$		0			0
$783$		−	46.7654i		−	0.0597259i
$784$		0			0
$785$	−108.000			−0.137580
$786$		0			0
$787$	1236.00	+	713.605i	1.57052	+	0.906741i	0.996105	+	0.0881773i	$0.0281042\pi$
$787$	1236.00	+	713.605i	1.57052	+	0.906741i	0.574416	+	0.818563i	$0.305229\pi$
$788$		0			0
$789$	279.000	−	161.081i	0.353612	−	0.204158i
$790$		0			0
$791$	−273.000	−	109.119i	−0.345133	−	0.137951i
$792$		0			0
$793$	−624.000	−	1080.80i	−0.786885	−	1.36293i
$794$		0			0
$795$	−148.500	+	257.210i	−0.186792	+	0.323534i
$796$		0			0
$797$			607.950i			0.762798i	0.924411	+	0.381399i	$0.124558\pi$
$797$			607.950i			0.762798i	−0.924411	+	0.381399i	$0.875442\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$	−189.000	−	109.119i	−0.235955	−	0.136229i
$802$		0			0
$803$	−810.000	+	467.654i	−1.00872	+	0.582383i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−292.500	−	506.625i	−0.362454	−	0.627788i
$808$		0			0
$809$	84.0000	−	145.492i	0.103832	−	0.179842i	−0.809428	−	0.587218i	$-0.800223\pi$
$809$	84.0000	−	145.492i	0.103832	−	0.179842i	0.913260	+	0.407376i	$0.133556\pi$
$810$		0			0
$811$		−	353.338i		−	0.435682i	−0.975984	−	0.217841i	$-0.930099\pi$
$811$		−	353.338i		−	0.435682i	0.975984	−	0.217841i	$-0.0699015\pi$
$812$		0			0
$813$	−159.000			−0.195572
$814$		0			0
$815$	−936.000	−	540.400i	−1.14847	−	0.663067i
$816$		0			0
$817$	666.000	−	384.515i	0.815177	−	0.470643i
$818$		0			0
$819$	−288.000	+	41.5692i	−0.351648	+	0.0507561i
$820$		0			0
$821$	−142.500	−	246.817i	−0.173569	−	0.300630i	0.766096	−	0.642726i	$-0.222197\pi$
$821$	−142.500	−	246.817i	−0.173569	−	0.300630i	−0.939665	+	0.342096i	$0.888863\pi$
$822$		0			0
$823$	−137.000	+	237.291i	−0.166464	+	0.288324i	−0.937174	−	0.348862i	$-0.886568\pi$
$823$	−137.000	+	237.291i	−0.166464	+	0.288324i	0.770710	+	0.637186i	$0.219902\pi$
$824$		0			0
$825$		−	51.9615i		−	0.0629837i
$826$		0			0
$827$	−429.000			−0.518742			−0.259371	−	0.965778i	$-0.583515\pi$
$827$	−429.000			−0.518742			−0.259371	+	0.965778i	$0.583515\pi$
$828$		0			0
$829$	−819.000	−	472.850i	−0.987937	−	0.570386i	−0.0832802	−	0.996526i	$-0.526540\pi$
$829$	−819.000	−	472.850i	−0.987937	−	0.570386i	−0.904657	+	0.426140i	$0.859873\pi$
$830$		0			0
$831$	−570.000	+	329.090i	−0.685921	+	0.396016i
$832$		0			0
$833$	144.000	+	488.438i	0.172869	+	0.586361i
$834$		0			0
$835$	648.000	+	1122.37i	0.776048	+	1.34415i
$836$		0			0
$837$	−31.5000	+	54.5596i	−0.0376344	+	0.0651847i
$838$		0			0
$839$		−	259.808i		−	0.309663i	−0.987941	−	0.154832i	$-0.950516\pi$
$839$		−	259.808i		−	0.309663i	0.987941	−	0.154832i	$-0.0494835\pi$
$840$		0			0
$841$	−760.000			−0.903686
$842$		0			0
$843$	450.000	+	259.808i	0.533808	+	0.308194i
$844$		0			0
$845$	−103.500	+	59.7558i	−0.122485	+	0.0707169i
$846$		0			0
$847$	104.000	+	720.533i	0.122786	+	0.850688i
$848$		0			0
$849$	−177.000	−	306.573i	−0.208481	−	0.361099i
$850$		0			0
$851$		0			0
$852$		0			0
$853$			997.661i			1.16959i	0.811181	+	0.584796i	$0.198825\pi$
$853$			997.661i			1.16959i	−0.811181	+	0.584796i	$0.801175\pi$
$854$		0			0
$855$	162.000			0.189474
$856$		0			0
$857$	378.000	+	218.238i	0.441074	+	0.254654i	0.704053	−	0.710148i	$-0.251372\pi$
$857$	378.000	+	218.238i	0.441074	+	0.254654i	−0.262979	+	0.964801i	$0.584705\pi$
$858$		0			0
$859$	393.000	−	226.899i	0.457509	−	0.264143i	−0.253487	−	0.967339i	$-0.581578\pi$
$859$	393.000	−	226.899i	0.457509	−	0.264143i	0.710996	+	0.703196i	$0.248244\pi$
$860$		0			0
$861$	−99.0000	+	77.9423i	−0.114983	+	0.0905253i
$862$		0			0
$863$	−195.000	−	337.750i	−0.225956	−	0.391367i	0.730650	−	0.682752i	$-0.239217\pi$
$863$	−195.000	−	337.750i	−0.225956	−	0.391367i	−0.956606	+	0.291385i	$0.905884\pi$
$864$		0			0
$865$	−594.000	+	1028.84i	−0.686705	+	1.18941i
$866$		0			0
$867$		−	313.501i		−	0.361593i
$868$		0			0
$869$	−645.000			−0.742232
$870$		0			0
$871$	912.000	+	526.543i	1.04707	+	0.604527i
$872$		0			0
$873$	−481.500	+	277.994i	−0.551546	+	0.318435i
$874$		0			0
$875$	310.500	−	776.825i	0.354857	−	0.887800i
$876$		0			0
$877$	272.000	+	471.118i	0.310148	+	0.537192i	0.978394	−	0.206748i	$-0.0662880\pi$
$877$	272.000	+	471.118i	0.310148	+	0.537192i	−0.668246	+	0.743940i	$0.732955\pi$
$878$		0			0
$879$	−472.500	+	818.394i	−0.537543	+	0.931051i
$880$		0			0
$881$		−	187.061i		−	0.212329i	−0.994349	−	0.106164i	$-0.966143\pi$
$881$		−	187.061i		−	0.212329i	0.994349	−	0.106164i	$-0.0338569\pi$
$882$		0			0
$883$	−322.000			−0.364666			−0.182333	−	0.983237i	$-0.558365\pi$
$883$	−322.000			−0.364666			−0.182333	+	0.983237i	$0.558365\pi$
$884$		0			0
$885$	−121.500	−	70.1481i	−0.137288	−	0.0792633i
$886$		0			0
$887$	−612.000	+	353.338i	−0.689966	+	0.398352i	−0.803599	−	0.595171i	$-0.797084\pi$
$887$	−612.000	+	353.338i	−0.689966	+	0.398352i	0.113633	+	0.993523i	$0.463751\pi$
$888$		0			0
$889$	227.500	+	90.9327i	0.255906	+	0.102286i
$890$		0			0
$891$	67.5000	+	116.913i	0.0757576	+	0.131216i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		−	467.654i		−	0.522518i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−94.5000	−	54.5596i	−0.105117	−	0.0606892i
$900$		0			0
$901$	−297.000	+	171.473i	−0.329634	+	0.190314i
$902$		0			0
$903$	−555.000	−	704.945i	−0.614618	−	0.780670i
$904$		0			0
$905$	−27.0000	−	46.7654i	−0.0298343	−	0.0516744i
$906$		0			0
$907$	−550.000	+	952.628i	−0.606395	+	1.05031i	0.385435	+	0.922735i	$0.374052\pi$
$907$	−550.000	+	952.628i	−0.606395	+	1.05031i	−0.991829	+	0.127571i	$0.959282\pi$
$908$		0			0
$909$		−	436.477i		−	0.480173i
$910$		0			0
$911$	−900.000			−0.987925			−0.493963	−	0.869483i	$-0.664452\pi$
$911$	−900.000			−0.987925			−0.493963	+	0.869483i	$0.664452\pi$
$912$		0			0
$913$	1552.50	+	896.336i	1.70044	+	0.981748i
$914$		0			0
$915$	702.000	−	405.300i	0.767213	−	0.442951i
$916$		0			0
$917$	1188.00	−	171.473i	1.29553	−	0.186993i
$918$		0			0
$919$	−859.000	−	1487.83i	−0.934712	−	1.61897i	−0.775147	−	0.631781i	$-0.782324\pi$
$919$	−859.000	−	1487.83i	−0.934712	−	1.61897i	−0.159564	−	0.987188i	$-0.551009\pi$
$920$		0			0
$921$	150.000	−	259.808i	0.162866	−	0.282093i
$922$		0			0
$923$			1163.94i			1.26104i
$924$		0			0
$925$	−20.0000			−0.0216216
$926$		0			0
$927$	180.000	+	103.923i	0.194175	+	0.112107i
$928$		0			0
$929$	−1287.00	+	743.050i	−1.38536	+	0.799838i	−0.992788	−	0.119883i	$-0.961748\pi$
$929$	−1287.00	+	743.050i	−1.38536	+	0.799838i	−0.392573	+	0.919721i	$0.628415\pi$
$930$		0			0
$931$	495.000	+	119.512i	0.531686	+	0.128369i
$932$		0			0
$933$	153.000	+	265.004i	0.163987	+	0.284034i
$934$		0			0
$935$	405.000	−	701.481i	0.433155	−	0.750247i
$936$		0			0
$937$		−	957.824i		−	1.02222i	−0.859514	−	0.511112i	$-0.829234\pi$
$937$		−	957.824i		−	1.02222i	0.859514	−	0.511112i	$-0.170766\pi$
$938$		0			0
$939$	−369.000			−0.392971
$940$		0			0
$941$	310.500	+	179.267i	0.329968	+	0.190507i	0.655827	−	0.754911i	$-0.272320\pi$
$941$	310.500	+	179.267i	0.329968	+	0.190507i	−0.325859	+	0.945418i	$0.605653\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$	−27.0000	−	187.061i	−0.0285714	−	0.197949i
$946$		0			0
$947$	81.0000	+	140.296i	0.0855333	+	0.148148i	0.905618	−	0.424094i	$-0.139407\pi$
$947$	81.0000	+	140.296i	0.0855333	+	0.148148i	−0.820085	+	0.572242i	$0.806074\pi$
$948$		0			0
$949$	−432.000	+	748.246i	−0.455216	+	0.788457i
$950$		0			0
$951$		−	202.650i		−	0.213091i
$952$		0			0
$953$	−954.000			−1.00105			−0.500525	−	0.865722i	$-0.666860\pi$
$953$	−954.000			−1.00105			−0.500525	+	0.865722i	$0.666860\pi$
$954$		0			0
$955$	−1404.00	−	810.600i	−1.47016	−	0.848796i
$956$		0			0
$957$	−202.500	+	116.913i	−0.211599	+	0.122167i
$958$		0			0
$959$	−528.000	+	415.692i	−0.550574	+	0.433464i
$960$		0			0
$961$	−407.000	−	704.945i	−0.423517	−	0.733553i
$962$		0			0
$963$	−139.500	+	241.621i	−0.144860	+	0.250905i
$964$		0			0
$965$		−	961.288i		−	0.996154i
$966$		0			0
$967$	751.000			0.776629			0.388314	−	0.921527i	$-0.373057\pi$
$967$	751.000			0.776629			0.388314	+	0.921527i	$0.373057\pi$
$968$		0			0
$969$	162.000	+	93.5307i	0.167183	+	0.0965230i
$970$		0			0
$971$	247.500	−	142.894i	0.254892	−	0.147162i	−0.367110	−	0.930177i	$-0.619653\pi$
$971$	247.500	−	142.894i	0.254892	−	0.147162i	0.622002	+	0.783016i	$0.286320\pi$
$972$		0			0
$973$	477.000	−	1193.38i	0.490236	−	1.22650i
$974$		0			0
$975$	−24.0000	−	41.5692i	−0.0246154	−	0.0426351i
$976$		0			0
$977$	9.00000	−	15.5885i	0.00921187	−	0.0159554i	−0.861383	−	0.507957i	$-0.830401\pi$
$977$	9.00000	−	15.5885i	0.00921187	−	0.0159554i	0.870595	+	0.492001i	$0.163734\pi$
$978$		0			0
$979$			1091.19i			1.11460i
$980$		0			0
$981$	24.0000			0.0244648
$982$		0			0
$983$	855.000	+	493.634i	0.869786	+	0.502171i	0.867277	−	0.497825i	$-0.165868\pi$
$983$	855.000	+	493.634i	0.869786	+	0.502171i	0.00250913	+	0.999997i	$0.499201\pi$
$984$		0			0
$985$	1485.00	−	857.365i	1.50761	−	0.870421i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	351.500	−	608.816i	0.354692	−	0.614345i	−0.632373	−	0.774664i	$-0.717919\pi$
$991$	351.500	−	608.816i	0.354692	−	0.614345i	0.987065	+	0.160319i	$0.0512523\pi$
$992$		0			0
$993$			69.2820i			0.0697704i
$994$		0			0
$995$	−36.0000			−0.0361809
$996$		0			0
$997$	186.000	+	107.387i	0.186560	+	0.107710i	0.590371	−	0.807132i	$-0.298981\pi$
$997$	186.000	+	107.387i	0.186560	+	0.107710i	−0.403811	+	0.914842i	$0.632315\pi$
$998$		0			0
$999$	45.0000	−	25.9808i	0.0450450	−	0.0260068i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.3.bh.d.241.1		2
3.2	odd	2		1008.3.cg.a.577.1		2
4.3	odd	2		21.3.f.a.10.1	✓	2
7.3	odd	6		2352.3.f.a.97.2		2
7.4	even	3		2352.3.f.a.97.1		2
7.5	odd	6	inner	336.3.bh.d.145.1		2
12.11	even	2		63.3.m.d.10.1		2
20.3	even	4		525.3.s.e.199.1		4
20.7	even	4		525.3.s.e.199.2		4
20.19	odd	2		525.3.o.h.451.1		2
21.5	even	6		1008.3.cg.a.145.1		2
28.3	even	6		147.3.d.c.97.1		2
28.11	odd	6		147.3.d.c.97.2		2
28.19	even	6		21.3.f.a.19.1	yes	2
28.23	odd	6		147.3.f.a.19.1		2
28.27	even	2		147.3.f.a.31.1		2
84.11	even	6		441.3.d.a.244.1		2
84.23	even	6		441.3.m.g.19.1		2
84.47	odd	6		63.3.m.d.19.1		2
84.59	odd	6		441.3.d.a.244.2		2
84.83	odd	2		441.3.m.g.325.1		2
140.19	even	6		525.3.o.h.376.1		2
140.47	odd	12		525.3.s.e.124.1		4
140.103	odd	12		525.3.s.e.124.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.3.f.a.10.1	✓	2	4.3	odd	2
21.3.f.a.19.1	yes	2	28.19	even	6
63.3.m.d.10.1		2	12.11	even	2
63.3.m.d.19.1		2	84.47	odd	6
147.3.d.c.97.1		2	28.3	even	6
147.3.d.c.97.2		2	28.11	odd	6
147.3.f.a.19.1		2	28.23	odd	6
147.3.f.a.31.1		2	28.27	even	2
336.3.bh.d.145.1		2	7.5	odd	6	inner
336.3.bh.d.241.1		2	1.1	even	1	trivial
441.3.d.a.244.1		2	84.11	even	6
441.3.d.a.244.2		2	84.59	odd	6
441.3.m.g.19.1		2	84.23	even	6
441.3.m.g.325.1		2	84.83	odd	2
525.3.o.h.376.1		2	140.19	even	6
525.3.o.h.451.1		2	20.19	odd	2
525.3.s.e.124.1		4	140.47	odd	12
525.3.s.e.124.2		4	140.103	odd	12
525.3.s.e.199.1		4	20.3	even	4
525.3.s.e.199.2		4	20.7	even	4
1008.3.cg.a.145.1		2	21.5	even	6
1008.3.cg.a.577.1		2	3.2	odd	2
2352.3.f.a.97.1		2	7.4	even	3
2352.3.f.a.97.2		2	7.3	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:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	336.bh (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.50000 + 0.866025i) q^{3} +(4.50000 - 2.59808i) q^{5} +(-6.50000 - 2.59808i) q^{7} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(1.50000 + 0.866025i) q^{3} +(4.50000 - 2.59808i) q^{5} +(-6.50000 - 2.59808i) q^{7} +(1.50000 + 2.59808i) q^{9} +(7.50000 - 12.9904i) q^{11} -13.8564i q^{13} +9.00000 q^{15} +(9.00000 + 5.19615i) q^{17} +(9.00000 - 5.19615i) q^{19} +(-7.50000 - 9.52628i) q^{21} +(1.00000 - 1.73205i) q^{25} +5.19615i q^{27} -9.00000 q^{29} +(10.5000 + 6.06218i) q^{31} +(22.5000 - 12.9904i) q^{33} +(-36.0000 + 5.19615i) q^{35} +(-5.00000 - 8.66025i) q^{37} +(12.0000 - 20.7846i) q^{39} -10.3923i q^{41} +74.0000 q^{43} +(13.5000 + 7.79423i) q^{45} +(35.5000 + 33.7750i) q^{49} +(9.00000 + 15.5885i) q^{51} +(-16.5000 + 28.5788i) q^{53} -77.9423i q^{55} +18.0000 q^{57} +(-13.5000 - 7.79423i) q^{59} +(78.0000 - 45.0333i) q^{61} +(-3.00000 - 20.7846i) q^{63} +(-36.0000 - 62.3538i) q^{65} +(-38.0000 + 65.8179i) q^{67} -84.0000 q^{71} +(-54.0000 - 31.1769i) q^{73} +(3.00000 - 1.73205i) q^{75} +(-82.5000 + 64.9519i) q^{77} +(-21.5000 - 37.2391i) q^{79} +(-4.50000 + 7.79423i) q^{81} +119.512i q^{83} +54.0000 q^{85} +(-13.5000 - 7.79423i) q^{87} +(-63.0000 + 36.3731i) q^{89} +(-36.0000 + 90.0666i) q^{91} +(10.5000 + 18.1865i) q^{93} +(27.0000 - 46.7654i) q^{95} +185.329i q^{97} +45.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 3 q^{3} + 9 q^{5} - 13 q^{7} + 3 q^{9}+O(q^{10}) \) 2 * q + 3 * q^3 + 9 * q^5 - 13 * q^7 + 3 * q^9	\( 2 q + 3 q^{3} + 9 q^{5} - 13 q^{7} + 3 q^{9} + 15 q^{11} + 18 q^{15} + 18 q^{17} + 18 q^{19} - 15 q^{21} + 2 q^{25} - 18 q^{29} + 21 q^{31} + 45 q^{33} - 72 q^{35} - 10 q^{37} + 24 q^{39} + 148 q^{43} + 27 q^{45} + 71 q^{49} + 18 q^{51} - 33 q^{53} + 36 q^{57} - 27 q^{59} + 156 q^{61} - 6 q^{63} - 72 q^{65} - 76 q^{67} - 168 q^{71} - 108 q^{73} + 6 q^{75} - 165 q^{77} - 43 q^{79} - 9 q^{81} + 108 q^{85} - 27 q^{87} - 126 q^{89} - 72 q^{91} + 21 q^{93} + 54 q^{95} + 90 q^{99}+O(q^{100}) \) 2 * q + 3 * q^3 + 9 * q^5 - 13 * q^7 + 3 * q^9 + 15 * q^11 + 18 * q^15 + 18 * q^17 + 18 * q^19 - 15 * q^21 + 2 * q^25 - 18 * q^29 + 21 * q^31 + 45 * q^33 - 72 * q^35 - 10 * q^37 + 24 * q^39 + 148 * q^43 + 27 * q^45 + 71 * q^49 + 18 * q^51 - 33 * q^53 + 36 * q^57 - 27 * q^59 + 156 * q^61 - 6 * q^63 - 72 * q^65 - 76 * q^67 - 168 * q^71 - 108 * q^73 + 6 * q^75 - 165 * q^77 - 43 * q^79 - 9 * q^81 + 108 * q^85 - 27 * q^87 - 126 * q^89 - 72 * q^91 + 21 * q^93 + 54 * q^95 + 90 * q^99

Introduction

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