LMFDB - Embedded newform 1344.2.bl.l.703.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1344,2,Mod(703,1344)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1344, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 0, 1]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1344.703");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1344 = 2^{6} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1344.bl (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:	$10.7318940317$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 24x^{14} + 218x^{12} + 968x^{10} + 2241x^{8} + 2672x^{6} + 1512x^{4} + 320x^{2} + 16 $ x^16 + 24x^14 + 218x^12 + 968x^10 + 2241x^8 + 2672x^6 + 1512x^4 + 320*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{14} $
Twist minimal:	no (minimal twist has level 672)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			703.2
Root			$1.60698i$ of defining polynomial
Character	$\chi$	$=$	1344.703
Dual form			1344.2.bl.l.1279.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{3} +(-2.33837 + 1.35006i) q^{5} +(2.63871 + 0.192843i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{3} +(-2.33837 + 1.35006i) q^{5} +(2.63871 + 0.192843i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(-1.22769 - 0.708810i) q^{11} +5.69489i q^{13} +2.70012i q^{15} +(-1.69711 - 0.979828i) q^{17} +(0.361646 + 0.626389i) q^{19} +(1.48636 - 2.18877i) q^{21} +(-0.562697 + 0.324873i) q^{23} +(1.14531 - 1.98374i) q^{25} -1.00000 q^{27} -6.06459 q^{29} +(-2.49760 + 4.32597i) q^{31} +(-1.22769 + 0.708810i) q^{33} +(-6.43064 + 3.11148i) q^{35} +(0.576851 + 0.999134i) q^{37} +(4.93192 + 2.84745i) q^{39} -1.58141i q^{41} +10.8193i q^{43} +(2.33837 + 1.35006i) q^{45} +(4.81485 + 8.33956i) q^{47} +(6.92562 + 1.01771i) q^{49} +(-1.69711 + 0.979828i) q^{51} +(6.26205 - 10.8462i) q^{53} +3.82774 q^{55} +0.723292 q^{57} +(-0.434140 + 0.751953i) q^{59} +(-11.7867 + 6.80505i) q^{61} +(-1.15235 - 2.38161i) q^{63} +(-7.68844 - 13.3168i) q^{65} +(-0.0459751 - 0.0265437i) q^{67} +0.649746i q^{69} +14.0593i q^{71} +(13.5520 + 7.82422i) q^{73} +(-1.14531 - 1.98374i) q^{75} +(-3.10285 - 2.10710i) q^{77} +(-9.95371 + 5.74678i) q^{79} +(-0.500000 + 0.866025i) q^{81} -2.95860 q^{83} +5.29130 q^{85} +(-3.03229 + 5.25209i) q^{87} +(-7.13765 + 4.12092i) q^{89} +(-1.09822 + 15.0272i) q^{91} +(2.49760 + 4.32597i) q^{93} +(-1.69132 - 0.976486i) q^{95} +1.01880i q^{97} +1.41762i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{3} - 4 q^{7} - 8 q^{9}+O(q^{10}) $ 16 * q + 8 * q^3 - 4 * q^7 - 8 * q^9	$ 16 q + 8 q^{3} - 4 q^{7} - 8 q^{9} - 12 q^{11} - 4 q^{19} - 8 q^{21} + 4 q^{25} - 16 q^{27} + 4 q^{31} - 12 q^{33} - 8 q^{35} - 4 q^{37} + 12 q^{39} + 8 q^{47} + 24 q^{49} - 8 q^{53} - 16 q^{55} - 8 q^{57} - 4 q^{59} - 24 q^{61} - 4 q^{63} + 8 q^{65} + 12 q^{67} + 12 q^{73} - 4 q^{75} + 32 q^{77} + 12 q^{79} - 8 q^{81} - 8 q^{83} - 32 q^{85} + 4 q^{91} - 4 q^{93} - 48 q^{95}+O(q^{100}) $ 16 * q + 8 * q^3 - 4 * q^7 - 8 * q^9 - 12 * q^11 - 4 * q^19 - 8 * q^21 + 4 * q^25 - 16 * q^27 + 4 * q^31 - 12 * q^33 - 8 * q^35 - 4 * q^37 + 12 * q^39 + 8 * q^47 + 24 * q^49 - 8 * q^53 - 16 * q^55 - 8 * q^57 - 4 * q^59 - 24 * q^61 - 4 * q^63 + 8 * q^65 + 12 * q^67 + 12 * q^73 - 4 * q^75 + 32 * q^77 + 12 * q^79 - 8 * q^81 - 8 * q^83 - 32 * q^85 + 4 * q^91 - 4 * q^93 - 48 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times$.

$n$	$127$	$449$	$577$	$1093$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{6}\right)$	$1$

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
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$		0			0
$5$	−2.33837	+	1.35006i	−1.04575	+	0.603764i	−0.921457	−	0.388481i	$-0.873000\pi$
$5$	−2.33837	+	1.35006i	−1.04575	+	0.603764i	−0.124294	+	0.992245i	$0.539667\pi$
$6$		0			0
$7$	2.63871	+	0.192843i	0.997340	+	0.0728877i
$7$	2.63871	+	0.192843i	0.997340	+	0.0728877i
$8$		0			0
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	−1.22769	−	0.708810i	−0.370164	−	0.213714i	0.303366	−	0.952874i	$-0.401889\pi$
$11$	−1.22769	−	0.708810i	−0.370164	−	0.213714i	−0.673530	+	0.739160i	$0.735223\pi$
$12$		0			0
$13$			5.69489i			1.57948i	0.613442	+	0.789739i	$0.289784\pi$
$13$			5.69489i			1.57948i	−0.613442	+	0.789739i	$0.710216\pi$
$14$		0			0
$15$			2.70012i			0.697167i
$16$		0			0
$17$	−1.69711	−	0.979828i	−0.411610	−	0.237643i	0.279871	−	0.960038i	$-0.409708\pi$
$17$	−1.69711	−	0.979828i	−0.411610	−	0.237643i	−0.691481	+	0.722394i	$0.743042\pi$
$18$		0			0
$19$	0.361646	+	0.626389i	0.0829672	+	0.143703i	0.904523	−	0.426424i	$-0.140227\pi$
$19$	0.361646	+	0.626389i	0.0829672	+	0.143703i	−0.821556	+	0.570128i	$0.806894\pi$
$20$		0			0
$21$	1.48636	−	2.18877i	0.324351	−	0.477629i
$22$		0			0
$23$	−0.562697	+	0.324873i	−0.117330	+	0.0677407i	−0.557517	−	0.830166i	$-0.688246\pi$
$23$	−0.562697	+	0.324873i	−0.117330	+	0.0677407i	0.440186	+	0.897906i	$0.354912\pi$
$24$		0			0
$25$	1.14531	−	1.98374i	0.229063	−	0.396749i
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	−6.06459			−1.12617			−0.563083	−	0.826400i	$-0.690385\pi$
$29$	−6.06459			−1.12617			−0.563083	+	0.826400i	$0.690385\pi$
$30$		0			0
$31$	−2.49760	+	4.32597i	−0.448582	+	0.776967i	−0.998294	−	0.0583872i	$-0.981404\pi$
$31$	−2.49760	+	4.32597i	−0.448582	+	0.776967i	0.549712	+	0.835354i	$0.314738\pi$
$32$		0			0
$33$	−1.22769	+	0.708810i	−0.213714	+	0.123388i
$34$		0			0
$35$	−6.43064	+	3.11148i	−1.08698	+	0.525936i
$36$		0			0
$37$	0.576851	+	0.999134i	0.0948336	+	0.164257i	0.909539	−	0.415618i	$-0.136435\pi$
$37$	0.576851	+	0.999134i	0.0948336	+	0.164257i	−0.814706	+	0.579875i	$0.803101\pi$
$38$		0			0
$39$	4.93192	+	2.84745i	0.789739	+	0.455956i
$40$		0			0
$41$		−	1.58141i		−	0.246975i	−0.992346	−	0.123487i	$-0.960592\pi$
$41$		−	1.58141i		−	0.246975i	0.992346	−	0.123487i	$-0.0394078\pi$
$42$		0			0
$43$			10.8193i			1.64993i	0.565185	+	0.824965i	$0.308805\pi$
$43$			10.8193i			1.64993i	−0.565185	+	0.824965i	$0.691195\pi$
$44$		0			0
$45$	2.33837	+	1.35006i	0.348584	+	0.201255i
$46$		0			0
$47$	4.81485	+	8.33956i	0.702318	+	1.21645i	0.967651	+	0.252293i	$0.0811847\pi$
$47$	4.81485	+	8.33956i	0.702318	+	1.21645i	−0.265333	+	0.964157i	$0.585482\pi$
$48$		0			0
$49$	6.92562	+	1.01771i	0.989375	+	0.145388i
$50$		0			0
$51$	−1.69711	+	0.979828i	−0.237643	+	0.137203i
$52$		0			0
$53$	6.26205	−	10.8462i	0.860158	−	1.48984i	−0.0116175	−	0.999933i	$-0.503698\pi$
$53$	6.26205	−	10.8462i	0.860158	−	1.48984i	0.871776	−	0.489905i	$-0.162969\pi$
$54$		0			0
$55$	3.82774			0.516132
$56$		0			0
$57$	0.723292			0.0958023
$58$		0			0
$59$	−0.434140	+	0.751953i	−0.0565202	+	0.0978959i	−0.892901	−	0.450253i	$-0.851334\pi$
$59$	−0.434140	+	0.751953i	−0.0565202	+	0.0978959i	0.836381	+	0.548149i	$0.184667\pi$
$60$		0			0
$61$	−11.7867	+	6.80505i	−1.50913	+	0.871297i	−0.509188	+	0.860655i	$0.670054\pi$
$61$	−11.7867	+	6.80505i	−1.50913	+	0.871297i	−0.999943	+	0.0106419i	$0.996613\pi$
$62$		0			0
$63$	−1.15235	−	2.38161i	−0.145182	−	0.300055i
$64$		0			0
$65$	−7.68844	−	13.3168i	−0.953633	−	1.65174i
$66$		0			0
$67$	−0.0459751	−	0.0265437i	−0.00561675	−	0.00324283i	0.497189	−	0.867642i	$-0.334366\pi$
$67$	−0.0459751	−	0.0265437i	−0.00561675	−	0.00324283i	−0.502806	+	0.864399i	$0.667699\pi$
$68$		0			0
$69$			0.649746i			0.0782202i
$70$		0			0
$71$			14.0593i			1.66853i	0.551362	+	0.834266i	$0.314108\pi$
$71$			14.0593i			1.66853i	−0.551362	+	0.834266i	$0.685892\pi$
$72$		0			0
$73$	13.5520	+	7.82422i	1.58614	+	0.915756i	0.993935	+	0.109966i	$0.0350741\pi$
$73$	13.5520	+	7.82422i	1.58614	+	0.915756i	0.592201	+	0.805790i	$0.298259\pi$
$74$		0			0
$75$	−1.14531	−	1.98374i	−0.132250	−	0.229063i
$76$		0			0
$77$	−3.10285	−	2.10710i	−0.353602	−	0.240126i
$78$		0			0
$79$	−9.95371	+	5.74678i	−1.11988	+	0.646563i	−0.941370	−	0.337375i	$-0.890461\pi$
$79$	−9.95371	+	5.74678i	−1.11988	+	0.646563i	−0.178510	+	0.983938i	$0.557128\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	−2.95860			−0.324749			−0.162375	−	0.986729i	$-0.551915\pi$
$83$	−2.95860			−0.324749			−0.162375	+	0.986729i	$0.551915\pi$
$84$		0			0
$85$	5.29130			0.573922
$86$		0			0
$87$	−3.03229	+	5.25209i	−0.325096	+	0.563083i
$88$		0			0
$89$	−7.13765	+	4.12092i	−0.756589	+	0.436817i	−0.828070	−	0.560625i	$-0.810561\pi$
$89$	−7.13765	+	4.12092i	−0.756589	+	0.436817i	0.0714806	+	0.997442i	$0.477228\pi$
$90$		0			0
$91$	−1.09822	+	15.0272i	−0.115125	+	1.57528i
$92$		0			0
$93$	2.49760	+	4.32597i	0.258989	+	0.448582i
$94$		0			0
$95$	−1.69132	−	0.976486i	−0.173526	−	0.100185i
$96$		0			0
$97$			1.01880i			0.103444i	0.998662	+	0.0517218i	$0.0164709\pi$
$97$			1.01880i			0.103444i	−0.998662	+	0.0517218i	$0.983529\pi$
$98$		0			0
$99$			1.41762i			0.142476i
$100$		0			0
$101$	10.3460	+	5.97328i	1.02947	+	0.594364i	0.916832	−	0.399273i	$-0.130737\pi$
$101$	10.3460	+	5.97328i	1.02947	+	0.594364i	0.112636	+	0.993636i	$0.464071\pi$
$102$		0			0
$103$	−8.79513	−	15.2336i	−0.866610	−	1.50101i	−0.865439	−	0.501014i	$-0.832961\pi$
$103$	−8.79513	−	15.2336i	−0.866610	−	1.50101i	−0.00117078	−	0.999999i	$-0.500373\pi$
$104$		0			0
$105$	−0.520698	+	7.12484i	−0.0508149	+	0.695313i
$106$		0			0
$107$	12.6225	−	7.28758i	1.22026	−	0.704517i	0.255286	−	0.966866i	$-0.417830\pi$
$107$	12.6225	−	7.28758i	1.22026	−	0.704517i	0.964973	+	0.262349i	$0.0844971\pi$
$108$		0			0
$109$	2.70837	−	4.69103i	0.259415	−	0.449319i	−0.706671	−	0.707543i	$-0.749804\pi$
$109$	2.70837	−	4.69103i	0.259415	−	0.449319i	0.966085	+	0.258223i	$0.0831371\pi$
$110$		0			0
$111$	1.15370			0.109504
$112$		0			0
$113$	−5.65726			−0.532190			−0.266095	−	0.963947i	$-0.585733\pi$
$113$	−5.65726			−0.532190			−0.266095	+	0.963947i	$0.585733\pi$
$114$		0			0
$115$	0.877195	−	1.51935i	0.0817989	−	0.141680i
$116$		0			0
$117$	4.93192	−	2.84745i	0.455956	−	0.263246i
$118$		0			0
$119$	−4.28924	−	2.91276i	−0.393194	−	0.267012i
$120$		0			0
$121$	−4.49518	−	7.78588i	−0.408652	−	0.707807i
$122$		0			0
$123$	−1.36954	−	0.790705i	−0.123487	−	0.0712954i
$124$		0			0
$125$		−	7.31562i		−	0.654329i
$126$		0			0
$127$		−	11.7616i		−	1.04367i	−0.853046	−	0.521835i	$-0.825247\pi$
$127$		−	11.7616i		−	1.04367i	0.853046	−	0.521835i	$-0.174753\pi$
$128$		0			0
$129$	9.36980	+	5.40965i	0.824965	+	0.476293i
$130$		0			0
$131$	10.3102	+	17.8577i	0.900804	+	1.56024i	0.826453	+	0.563006i	$0.190355\pi$
$131$	10.3102	+	17.8577i	0.900804	+	1.56024i	0.0743512	+	0.997232i	$0.476311\pi$
$132$		0			0
$133$	0.833485	+	1.72260i	0.0722723	+	0.149369i
$134$		0			0
$135$	2.33837	−	1.35006i	0.201255	−	0.116195i
$136$		0			0
$137$	−9.78488	+	16.9479i	−0.835979	+	1.44796i	0.0572523	+	0.998360i	$0.481766\pi$
$137$	−9.78488	+	16.9479i	−0.835979	+	1.44796i	−0.893231	+	0.449598i	$0.851567\pi$
$138$		0			0
$139$	19.4109			1.64641			0.823205	−	0.567745i	$-0.192184\pi$
$139$	19.4109			1.64641			0.823205	+	0.567745i	$0.192184\pi$
$140$		0			0
$141$	9.62969			0.810967
$142$		0			0
$143$	4.03660	−	6.99159i	0.337557	−	0.584666i
$144$		0			0
$145$	14.1812	−	8.18755i	1.17769	−	0.679939i
$146$		0			0
$147$	4.34418	−	5.48891i	0.358302	−	0.452718i
$148$		0			0
$149$	−9.60562	−	16.6374i	−0.786923	−	1.36299i	−0.927843	−	0.372970i	$-0.878339\pi$
$149$	−9.60562	−	16.6374i	−0.786923	−	1.36299i	0.140920	−	0.990021i	$-0.454994\pi$
$150$		0			0
$151$	1.45236	+	0.838518i	0.118191	+	0.0682376i	0.557930	−	0.829888i	$-0.311596\pi$
$151$	1.45236	+	0.838518i	0.118191	+	0.0682376i	−0.439739	+	0.898126i	$0.644929\pi$
$152$		0			0
$153$			1.95966i			0.158429i
$154$		0			0
$155$		−	13.4876i		−	1.08335i
$156$		0			0
$157$	6.81758	+	3.93613i	0.544102	+	0.314137i	0.746740	−	0.665116i	$-0.231618\pi$
$157$	6.81758	+	3.93613i	0.544102	+	0.314137i	−0.202638	+	0.979254i	$0.564951\pi$
$158$		0			0
$159$	−6.26205	−	10.8462i	−0.496613	−	0.860158i
$160$		0			0
$161$	−1.54744	+	0.748735i	−0.121956	+	0.0590086i
$162$		0			0
$163$	−3.08724	+	1.78242i	−0.241812	+	0.139610i	−0.616009	−	0.787739i	$-0.711252\pi$
$163$	−3.08724	+	1.78242i	−0.241812	+	0.139610i	0.374197	+	0.927349i	$0.377918\pi$
$164$		0			0
$165$	1.91387	−	3.31492i	0.148995	−	0.258066i
$166$		0			0
$167$	10.9594			0.848063			0.424031	−	0.905647i	$-0.360615\pi$
$167$	10.9594			0.848063			0.424031	+	0.905647i	$0.360615\pi$
$168$		0			0
$169$	−19.4318			−1.49475
$170$		0			0
$171$	0.361646	−	0.626389i	0.0276557	−	0.0479012i
$172$		0			0
$173$	−16.3996	+	9.46830i	−1.24684	+	0.719861i	−0.970477	−	0.241193i	$-0.922461\pi$
$173$	−16.3996	+	9.46830i	−1.24684	+	0.719861i	−0.276359	+	0.961054i	$0.589128\pi$
$174$		0			0
$175$	3.40471	−	5.01366i	0.257372	−	0.378997i
$176$		0			0
$177$	0.434140	+	0.751953i	0.0326320	+	0.0565202i
$178$		0			0
$179$	5.11493	+	2.95311i	0.382308	+	0.220726i	0.678822	−	0.734303i	$-0.262491\pi$
$179$	5.11493	+	2.95311i	0.382308	+	0.220726i	−0.296514	+	0.955029i	$0.595824\pi$
$180$		0			0
$181$		−	24.5302i		−	1.82331i	−0.410953	−	0.911656i	$-0.634804\pi$
$181$		−	24.5302i		−	1.82331i	0.410953	−	0.911656i	$-0.365196\pi$
$182$		0			0
$183$			13.6101i			1.00609i
$184$		0			0
$185$	−2.69778	−	1.55756i	−0.198345	−	0.114514i
$186$		0			0
$187$	1.38902	+	2.40586i	0.101575	+	0.175934i
$188$		0			0
$189$	−2.63871	−	0.192843i	−0.191938	−	0.0140272i
$190$		0			0
$191$	−6.82839	+	3.94237i	−0.494085	+	0.285260i	−0.726268	−	0.687412i	$-0.758747\pi$
$191$	−6.82839	+	3.94237i	−0.494085	+	0.285260i	0.232182	+	0.972672i	$0.425413\pi$
$192$		0			0
$193$	5.37464	−	9.30915i	0.386875	−	0.670087i	−0.605152	−	0.796110i	$-0.706888\pi$
$193$	5.37464	−	9.30915i	0.386875	−	0.670087i	0.992027	+	0.126022i	$0.0402211\pi$
$194$		0			0
$195$	−15.3769			−1.10116
$196$		0			0
$197$	−6.22489			−0.443505			−0.221753	−	0.975103i	$-0.571178\pi$
$197$	−6.22489			−0.443505			−0.221753	+	0.975103i	$0.571178\pi$
$198$		0			0
$199$	−2.14111	+	3.70852i	−0.151780	+	0.262890i	−0.931882	−	0.362762i	$-0.881834\pi$
$199$	−2.14111	+	3.70852i	−0.151780	+	0.262890i	0.780102	+	0.625652i	$0.215167\pi$
$200$		0			0
$201$	−0.0459751	+	0.0265437i	−0.00324283	+	0.00187225i
$202$		0			0
$203$	−16.0027	−	1.16951i	−1.12317	−	0.0820836i
$204$		0			0
$205$	2.13499	+	3.69792i	0.149114	+	0.258274i
$206$		0			0
$207$	0.562697	+	0.324873i	0.0391101	+	0.0225802i
$208$		0			0
$209$		−	1.02535i		−	0.0709251i
$210$		0			0
$211$		−	17.2858i		−	1.19001i	−0.803723	−	0.595003i	$-0.797151\pi$
$211$		−	17.2858i		−	1.19001i	0.803723	−	0.595003i	$-0.202849\pi$
$212$		0			0
$213$	12.1757	+	7.02965i	0.834266	+	0.481664i
$214$		0			0
$215$	−14.6067	−	25.2995i	−0.996168	−	1.72541i
$216$		0			0
$217$	−7.42468	+	10.9334i	−0.504020	+	0.742204i
$218$		0			0
$219$	13.5520	−	7.82422i	0.915756	−	0.528712i
$220$		0			0
$221$	5.58001	−	9.66487i	0.375352	−	0.650129i
$222$		0			0
$223$	4.40635			0.295071			0.147535	−	0.989057i	$-0.452866\pi$
$223$	4.40635			0.295071			0.147535	+	0.989057i	$0.452866\pi$
$224$		0			0
$225$	−2.29063			−0.152709
$226$		0			0
$227$	3.11039	−	5.38735i	0.206444	−	0.357571i	−0.744148	−	0.668015i	$-0.767144\pi$
$227$	3.11039	−	5.38735i	0.206444	−	0.357571i	0.950592	+	0.310444i	$0.100478\pi$
$228$		0			0
$229$	−9.98807	+	5.76662i	−0.660030	+	0.381069i	−0.792289	−	0.610147i	$-0.791111\pi$
$229$	−9.98807	+	5.76662i	−0.660030	+	0.381069i	0.132258	+	0.991215i	$0.457777\pi$
$230$		0			0
$231$	−3.37622	+	1.63359i	−0.222139	+	0.107483i
$232$		0			0
$233$	−4.63846	−	8.03406i	−0.303876	−	0.526328i	0.673135	−	0.739520i	$-0.264947\pi$
$233$	−4.63846	−	8.03406i	−0.303876	−	0.526328i	−0.977010	+	0.213192i	$0.931614\pi$
$234$		0			0
$235$	−22.5178	−	13.0006i	−1.46890	−	0.848069i
$236$		0			0
$237$			11.4936i			0.746587i
$238$		0			0
$239$			3.55540i			0.229980i	0.993367	+	0.114990i	$0.0366835\pi$
$239$			3.55540i			0.229980i	−0.993367	+	0.114990i	$0.963316\pi$
$240$		0			0
$241$	7.43954	+	4.29522i	0.479223	+	0.276679i	0.720093	−	0.693878i	$-0.244099\pi$
$241$	7.43954	+	4.29522i	0.479223	+	0.276679i	−0.240870	+	0.970557i	$0.577433\pi$
$242$		0			0
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$		0			0
$245$	−17.5686	+	6.97020i	−1.12242	+	0.445310i
$246$		0			0
$247$	−3.56722	+	2.05953i	−0.226977	+	0.131045i
$248$		0			0
$249$	−1.47930	+	2.56223i	−0.0937470	+	0.162375i
$250$		0			0
$251$	−10.6135			−0.669918			−0.334959	−	0.942233i	$-0.608723\pi$
$251$	−10.6135			−0.669918			−0.334959	+	0.942233i	$0.608723\pi$
$252$		0			0
$253$	0.921093			0.0579086
$254$		0			0
$255$	2.64565	−	4.58240i	0.165677	−	0.286961i
$256$		0			0
$257$	13.7058	−	7.91303i	0.854943	−	0.493601i	−0.00737277	−	0.999973i	$-0.502347\pi$
$257$	13.7058	−	7.91303i	0.854943	−	0.493601i	0.862315	+	0.506371i	$0.169014\pi$
$258$		0			0
$259$	1.32947	+	2.74767i	0.0826091	+	0.170732i
$260$		0			0
$261$	3.03229	+	5.25209i	0.187694	+	0.325096i
$262$		0			0
$263$	0.378909	+	0.218763i	0.0233645	+	0.0134895i	0.511637	−	0.859202i	$-0.329039\pi$
$263$	0.378909	+	0.218763i	0.0233645	+	0.0134895i	−0.488272	+	0.872691i	$0.662373\pi$
$264$		0			0
$265$			33.8165i			2.07733i
$266$		0			0
$267$			8.24185i			0.504393i
$268$		0			0
$269$	−0.429647	−	0.248057i	−0.0261961	−	0.0151243i	0.486845	−	0.873489i	$-0.338148\pi$
$269$	−0.429647	−	0.248057i	−0.0261961	−	0.0151243i	−0.513041	+	0.858364i	$0.671481\pi$
$270$		0			0
$271$	1.68840	+	2.92439i	0.102563	+	0.177644i	0.912740	−	0.408541i	$-0.133962\pi$
$271$	1.68840	+	2.92439i	0.102563	+	0.177644i	−0.810177	+	0.586185i	$0.800629\pi$
$272$		0			0
$273$	12.4648	+	8.46468i	0.754405	+	0.512306i
$274$		0			0
$275$	−2.81219	+	1.62362i	−0.169582	+	0.0979080i
$276$		0			0
$277$	5.46678	−	9.46874i	0.328467	−	0.568921i	−0.653741	−	0.756718i	$-0.726801\pi$
$277$	5.46678	−	9.46874i	0.328467	−	0.568921i	0.982208	+	0.187797i	$0.0601347\pi$
$278$		0			0
$279$	4.99520			0.299055
$280$		0			0
$281$	−26.4932			−1.58045			−0.790226	−	0.612815i	$-0.790037\pi$
$281$	−26.4932			−1.58045			−0.790226	+	0.612815i	$0.790037\pi$
$282$		0			0
$283$	1.08930	−	1.88673i	0.0647524	−	0.112154i	−0.831832	−	0.555028i	$-0.812708\pi$
$283$	1.08930	−	1.88673i	0.0647524	−	0.112154i	0.896584	+	0.442873i	$0.146041\pi$
$284$		0			0
$285$	−1.69132	+	0.976486i	−0.100185	+	0.0578420i
$286$		0			0
$287$	0.304963	−	4.17289i	0.0180014	−	0.246318i
$288$		0			0
$289$	−6.57988	−	11.3967i	−0.387052	−	0.670393i
$290$		0			0
$291$	0.882307	+	0.509400i	0.0517218	+	0.0298616i
$292$		0			0
$293$		−	6.82696i		−	0.398835i	−0.979915	−	0.199418i	$-0.936095\pi$
$293$		−	6.82696i		−	0.398835i	0.979915	−	0.199418i	$-0.0639050\pi$
$294$		0			0
$295$		−	2.34446i		−	0.136500i
$296$		0			0
$297$	1.22769	+	0.708810i	0.0712381	+	0.0411293i
$298$		0			0
$299$	−1.85012	−	3.20450i	−0.106995	−	0.185321i
$300$		0			0
$301$	−2.08642	+	28.5491i	−0.120260	+	1.64554i
$302$		0			0
$303$	10.3460	−	5.97328i	0.594364	−	0.343156i
$304$		0			0
$305$	18.3744	−	31.8254i	1.05212	−	1.82232i
$306$		0			0
$307$	12.9855			0.741122			0.370561	−	0.928808i	$-0.379165\pi$
$307$	12.9855			0.741122			0.370561	+	0.928808i	$0.379165\pi$
$308$		0			0
$309$	−17.5903			−1.00068
$310$		0			0
$311$	16.3818	−	28.3741i	0.928928	−	1.60895i	0.143808	−	0.989606i	$-0.454065\pi$
$311$	16.3818	−	28.3741i	0.928928	−	1.60895i	0.785119	−	0.619344i	$-0.212602\pi$
$312$		0			0
$313$	7.92470	−	4.57533i	0.447930	−	0.258613i	−0.259025	−	0.965871i	$-0.583401\pi$
$313$	7.92470	−	4.57533i	0.447930	−	0.258613i	0.706956	+	0.707258i	$0.250068\pi$
$314$		0			0
$315$	5.90994	+	4.01336i	0.332987	+	0.226127i
$316$		0			0
$317$	12.2936	+	21.2932i	0.690479	+	1.19594i	0.971681	+	0.236296i	$0.0759334\pi$
$317$	12.2936	+	21.2932i	0.690479	+	1.19594i	−0.281203	+	0.959648i	$0.590733\pi$
$318$		0			0
$319$	7.44546	+	4.29864i	0.416866	+	0.240678i
$320$		0			0
$321$		−	14.5752i		−	0.813506i
$322$		0			0
$323$		−	1.41740i		−	0.0788664i
$324$		0			0
$325$	11.2972	+	6.52244i	0.626656	+	0.361800i
$326$		0			0
$327$	−2.70837	−	4.69103i	−0.149773	−	0.259415i
$328$		0			0
$329$	11.0968	+	22.9342i	0.611785	+	1.26440i
$330$		0			0
$331$	17.5039	−	10.1059i	0.962101	−	0.555470i	0.0652823	−	0.997867i	$-0.479205\pi$
$331$	17.5039	−	10.1059i	0.962101	−	0.555470i	0.896819	+	0.442397i	$0.145872\pi$
$332$		0			0
$333$	0.576851	−	0.999134i	0.0316112	−	0.0547522i
$334$		0			0
$335$	0.143342			0.00783163
$336$		0			0
$337$	−15.4425			−0.841209			−0.420605	−	0.907244i	$-0.638182\pi$
$337$	−15.4425			−0.841209			−0.420605	+	0.907244i	$0.638182\pi$
$338$		0			0
$339$	−2.82863	+	4.89933i	−0.153630	+	0.266095i
$340$		0			0
$341$	6.13258	−	3.54065i	0.332098	−	0.191737i
$342$		0			0
$343$	18.0785	+	4.02101i	0.976146	+	0.217114i
$344$		0			0
$345$	−0.877195	−	1.51935i	−0.0472266	−	0.0817989i
$346$		0			0
$347$	−19.8910	−	11.4841i	−1.06781	−	0.616498i	−0.140225	−	0.990120i	$-0.544783\pi$
$347$	−19.8910	−	11.4841i	−1.06781	−	0.616498i	−0.927581	+	0.373621i	$0.878116\pi$
$348$		0			0
$349$		−	2.24157i		−	0.119988i	−0.998199	−	0.0599941i	$-0.980892\pi$
$349$		−	2.24157i		−	0.119988i	0.998199	−	0.0599941i	$-0.0191082\pi$
$350$		0			0
$351$		−	5.69489i		−	0.303971i
$352$		0			0
$353$	−11.0621	−	6.38674i	−0.588779	−	0.339932i	0.175836	−	0.984420i	$-0.443737\pi$
$353$	−11.0621	−	6.38674i	−0.588779	−	0.339932i	−0.764614	+	0.644488i	$0.777071\pi$
$354$		0			0
$355$	−18.9809	−	32.8758i	−1.00740	−	1.74487i
$356$		0			0
$357$	−4.66714	+	2.25821i	−0.247011	+	0.119517i
$358$		0			0
$359$	−19.4433	+	11.2256i	−1.02618	+	0.592464i	−0.915887	−	0.401436i	$-0.868511\pi$
$359$	−19.4433	+	11.2256i	−1.02618	+	0.592464i	−0.110290	+	0.993899i	$0.535178\pi$
$360$		0			0
$361$	9.23842	−	16.0014i	0.486233	−	0.842180i
$362$		0			0
$363$	−8.99035			−0.471871
$364$		0			0
$365$	−42.2526			−2.21160
$366$		0			0
$367$	−1.98510	+	3.43829i	−0.103621	+	0.179477i	−0.913174	−	0.407570i	$-0.866376\pi$
$367$	−1.98510	+	3.43829i	−0.103621	+	0.179477i	0.809553	+	0.587047i	$0.199710\pi$
$368$		0			0
$369$	−1.36954	+	0.790705i	−0.0712954	+	0.0411624i
$370$		0			0
$371$	18.6154	−	27.4124i	0.966461	−	1.42318i
$372$		0			0
$373$	9.03872	+	15.6555i	0.468007	+	0.810612i	0.999332	−	0.0365562i	$-0.0116388\pi$
$373$	9.03872	+	15.6555i	0.468007	+	0.810612i	−0.531324	+	0.847168i	$0.678305\pi$
$374$		0			0
$375$	−6.33551	−	3.65781i	−0.327164	−	0.188888i
$376$		0			0
$377$		−	34.5372i		−	1.77876i
$378$		0			0
$379$		−	9.69206i		−	0.497848i	−0.968523	−	0.248924i	$-0.919923\pi$
$379$		−	9.69206i		−	0.497848i	0.968523	−	0.248924i	$-0.0800769\pi$
$380$		0			0
$381$	−10.1858	−	5.88079i	−0.521835	−	0.301282i
$382$		0			0
$383$	6.93009	+	12.0033i	0.354111	+	0.613338i	0.986965	−	0.160932i	$-0.0514501\pi$
$383$	6.93009	+	12.0033i	0.354111	+	0.613338i	−0.632854	+	0.774271i	$0.718117\pi$
$384$		0			0
$385$	10.1003	+	0.738152i	0.514759	+	0.0376197i
$386$		0			0
$387$	9.36980	−	5.40965i	0.476293	−	0.274988i
$388$		0			0
$389$	9.65262	−	16.7188i	0.489407	−	0.847678i	−0.510519	−	0.859867i	$-0.670547\pi$
$389$	9.65262	−	16.7188i	0.489407	−	0.847678i	0.999926	+	0.0121887i	$0.00387987\pi$
$390$		0			0
$391$	1.27328			0.0643925
$392$		0			0
$393$	20.6203			1.04016
$394$		0			0
$395$	15.5170	−	26.8762i	0.780743	−	1.35229i
$396$		0			0
$397$	0.460324	−	0.265768i	0.0231030	−	0.0133385i	−0.488404	−	0.872618i	$-0.662421\pi$
$397$	0.460324	−	0.265768i	0.0231030	−	0.0133385i	0.511507	+	0.859279i	$0.329087\pi$
$398$		0			0
$399$	1.90856	+	0.139482i	0.0955475	+	0.00698281i
$400$		0			0
$401$	0.374615	+	0.648852i	0.0187074	+	0.0324021i	0.875228	−	0.483711i	$-0.160712\pi$
$401$	0.374615	+	0.648852i	0.0187074	+	0.0324021i	−0.856520	+	0.516114i	$0.827378\pi$
$402$		0			0
$403$	−24.6359	−	14.2236i	−1.22720	−	0.708526i
$404$		0			0
$405$		−	2.70012i		−	0.134170i
$406$		0			0
$407$		−	1.63551i		−	0.0810692i
$408$		0			0
$409$	8.68982	+	5.01707i	0.429684	+	0.248078i	0.699212	−	0.714914i	$-0.253534\pi$
$409$	8.68982	+	5.01707i	0.429684	+	0.248078i	−0.269528	+	0.962993i	$0.586868\pi$
$410$		0			0
$411$	9.78488	+	16.9479i	0.482653	+	0.835979i
$412$		0			0
$413$	−1.29058	+	1.90047i	−0.0635053	+	0.0935159i
$414$		0			0
$415$	6.91831	−	3.99429i	0.339606	−	0.196072i
$416$		0			0
$417$	9.70544	−	16.8103i	0.475277	−	0.823205i
$418$		0			0
$419$	−2.20727			−0.107832			−0.0539160	−	0.998545i	$-0.517170\pi$
$419$	−2.20727			−0.107832			−0.0539160	+	0.998545i	$0.517170\pi$
$420$		0			0
$421$	21.3916			1.04256			0.521280	−	0.853386i	$-0.325455\pi$
$421$	21.3916			1.04256			0.521280	+	0.853386i	$0.325455\pi$
$422$		0			0
$423$	4.81485	−	8.33956i	0.234106	−	0.405483i
$424$		0			0
$425$	−3.88745	+	2.24442i	−0.188569	+	0.108870i
$426$		0			0
$427$	−32.4140	+	15.6836i	−1.56862	+	0.758983i
$428$		0			0
$429$	−4.03660	−	6.99159i	−0.194889	−	0.337557i
$430$		0			0
$431$	28.3217	+	16.3515i	1.36421	+	0.787626i	0.990181	−	0.139791i	$-0.0446431\pi$
$431$	28.3217	+	16.3515i	1.36421	+	0.787626i	0.374028	+	0.927417i	$0.377976\pi$
$432$		0			0
$433$		−	3.18695i		−	0.153155i	−0.997064	−	0.0765775i	$-0.975601\pi$
$433$		−	3.18695i		−	0.153155i	0.997064	−	0.0765775i	$-0.0243993\pi$
$434$		0			0
$435$		−	16.3751i		−	0.785126i
$436$		0			0
$437$	−0.406994	−	0.234978i	−0.0194691	−	0.0112405i
$438$		0			0
$439$	5.33511	+	9.24069i	0.254631	+	0.441034i	0.964795	−	0.263002i	$-0.0847126\pi$
$439$	5.33511	+	9.24069i	0.254631	+	0.441034i	−0.710164	+	0.704036i	$0.751379\pi$
$440$		0			0
$441$	−2.58145	−	6.50662i	−0.122926	−	0.309839i
$442$		0			0
$443$	−22.7383	+	13.1280i	−1.08033	+	0.623729i	−0.930985	−	0.365057i	$-0.881050\pi$
$443$	−22.7383	+	13.1280i	−1.08033	+	0.623729i	−0.149344	+	0.988785i	$0.547716\pi$
$444$		0			0
$445$	11.1270	−	19.2725i	0.527469	−	0.913603i
$446$		0			0
$447$	−19.2112			−0.908661
$448$		0			0
$449$	10.3240			0.487220			0.243610	−	0.969873i	$-0.421668\pi$
$449$	10.3240			0.487220			0.243610	+	0.969873i	$0.421668\pi$
$450$		0			0
$451$	−1.12092	+	1.94149i	−0.0527820	+	0.0914211i
$452$		0			0
$453$	1.45236	−	0.838518i	0.0682376	−	0.0393970i
$454$		0			0
$455$	−17.7195	−	36.6218i	−0.830705	−	1.71686i
$456$		0			0
$457$	12.6001	+	21.8240i	0.589407	+	1.02088i	0.994310	+	0.106523i	$0.0339718\pi$
$457$	12.6001	+	21.8240i	0.589407	+	1.02088i	−0.404903	+	0.914359i	$0.632695\pi$
$458$		0			0
$459$	1.69711	+	0.979828i	0.0792144	+	0.0457344i
$460$		0			0
$461$			20.7224i			0.965140i	0.875857	+	0.482570i	$0.160297\pi$
$461$			20.7224i			0.965140i	−0.875857	+	0.482570i	$0.839703\pi$
$462$		0			0
$463$		−	39.6594i		−	1.84313i	−0.388227	−	0.921564i	$-0.626912\pi$
$463$		−	39.6594i		−	1.84313i	0.388227	−	0.921564i	$-0.373088\pi$
$464$		0			0
$465$	−11.6806	−	6.74381i	−0.541676	−	0.312737i
$466$		0			0
$467$	16.5981	+	28.7487i	0.768068	+	1.33033i	0.938609	+	0.344982i	$0.112115\pi$
$467$	16.5981	+	28.7487i	0.768068	+	1.33033i	−0.170542	+	0.985350i	$0.554552\pi$
$468$		0			0
$469$	−0.116196	−	0.0789073i	−0.00536545	−	0.00364360i
$470$		0			0
$471$	6.81758	−	3.93613i	0.314137	−	0.181367i
$472$		0			0
$473$	7.66883	−	13.2828i	0.352613	−	0.610744i
$474$		0			0
$475$	1.65679			0.0760189
$476$		0			0
$477$	−12.5241			−0.573439
$478$		0			0
$479$	−9.09367	+	15.7507i	−0.415500	+	0.719667i	−0.995481	−	0.0949628i	$-0.969727\pi$
$479$	−9.09367	+	15.7507i	−0.415500	+	0.719667i	0.579981	+	0.814630i	$0.303060\pi$
$480$		0			0
$481$	−5.68996	+	3.28510i	−0.259440	+	0.149788i
$482$		0			0
$483$	−0.125299	+	1.71449i	−0.00570129	+	0.0780122i
$484$		0			0
$485$	−1.37544	−	2.38233i	−0.0624555	−	0.108176i
$486$		0			0
$487$	20.7512	+	11.9807i	0.940326	+	0.542897i	0.890062	−	0.455839i	$-0.150661\pi$
$487$	20.7512	+	11.9807i	0.940326	+	0.542897i	0.0502633	+	0.998736i	$0.483994\pi$
$488$		0			0
$489$			3.56484i			0.161208i
$490$		0			0
$491$			11.5449i			0.521016i	0.965472	+	0.260508i	$0.0838900\pi$
$491$			11.5449i			0.521016i	−0.965472	+	0.260508i	$0.916110\pi$
$492$		0			0
$493$	10.2923	+	5.94225i	0.463541	+	0.267626i
$494$		0			0
$495$	−1.91387	−	3.31492i	−0.0860220	−	0.148995i
$496$		0			0
$497$	−2.71123	+	37.0985i	−0.121615	+	1.66409i
$498$		0			0
$499$	19.2101	−	11.0910i	0.859963	−	0.496500i	−0.00403674	−	0.999992i	$-0.501285\pi$
$499$	19.2101	−	11.0910i	0.859963	−	0.496500i	0.864000	+	0.503492i	$0.167952\pi$
$500$		0			0
$501$	5.47969	−	9.49111i	0.244815	−	0.424031i
$502$		0			0
$503$	1.53547			0.0684631			0.0342316	−	0.999414i	$-0.489102\pi$
$503$	1.53547			0.0684631			0.0342316	+	0.999414i	$0.489102\pi$
$504$		0			0
$505$	−32.2571			−1.43542
$506$		0			0
$507$	−9.71590	+	16.8284i	−0.431498	+	0.747377i
$508$		0			0
$509$	8.40479	−	4.85251i	0.372536	−	0.215084i	−0.302030	−	0.953298i	$-0.597664\pi$
$509$	8.40479	−	4.85251i	0.372536	−	0.215084i	0.674566	+	0.738215i	$0.264331\pi$
$510$		0			0
$511$	34.2509	+	23.2593i	1.51517	+	1.02893i
$512$		0			0
$513$	−0.361646	−	0.626389i	−0.0159671	−	0.0276557i
$514$		0			0
$515$	41.1325	+	23.7479i	1.81252	+	1.04646i
$516$		0			0
$517$		−	13.6512i		−	0.600381i
$518$		0			0
$519$			18.9366i			0.831224i
$520$		0			0
$521$	23.0675	+	13.3180i	1.01060	+	0.583473i	0.911368	−	0.411591i	$-0.135027\pi$
$521$	23.0675	+	13.3180i	1.01060	+	0.583473i	0.0992356	+	0.995064i	$0.468360\pi$
$522$		0			0
$523$	−4.74401	−	8.21687i	−0.207441	−	0.359299i	0.743467	−	0.668773i	$-0.233180\pi$
$523$	−4.74401	−	8.21687i	−0.207441	−	0.359299i	−0.950908	+	0.309474i	$0.899847\pi$
$524$		0			0
$525$	−2.63961	−	5.45540i	−0.115202	−	0.238093i
$526$		0			0
$527$	8.47741	−	4.89444i	0.369282	−	0.213205i
$528$		0			0
$529$	−11.2889	+	19.5530i	−0.490822	+	0.850129i
$530$		0			0
$531$	0.868280			0.0376802
$532$		0			0
$533$	9.00595			0.390091
$534$		0			0
$535$	−19.6773	+	34.0821i	−0.850724	+	1.47350i
$536$		0			0
$537$	5.11493	−	2.95311i	0.220726	−	0.127436i
$538$		0			0
$539$	−7.78119	−	6.15839i	−0.335159	−	0.265261i
$540$		0			0
$541$	−13.5289	−	23.4328i	−0.581654	−	1.00745i	−0.995283	−	0.0970093i	$-0.969072\pi$
$541$	−13.5289	−	23.4328i	−0.581654	−	1.00745i	0.413629	−	0.910445i	$-0.364261\pi$
$542$		0			0
$543$	−21.2437	−	12.2651i	−0.911656	−	0.526345i
$544$		0			0
$545$			14.6258i			0.626501i
$546$		0			0
$547$			32.3241i			1.38208i	0.722818	+	0.691039i	$0.242847\pi$
$547$			32.3241i			1.38208i	−0.722818	+	0.691039i	$0.757153\pi$
$548$		0			0
$549$	11.7867	+	6.80505i	0.503044	+	0.290432i
$550$		0			0
$551$	−2.19323	−	3.79879i	−0.0934349	−	0.161834i
$552$		0			0
$553$	−27.3732	+	13.2446i	−1.16403	+	0.563218i
$554$		0			0
$555$	−2.69778	+	1.55756i	−0.114514	+	0.0661149i
$556$		0			0
$557$	−2.06686	+	3.57991i	−0.0875757	+	0.151686i	−0.906486	−	0.422236i	$-0.861245\pi$
$557$	−2.06686	+	3.57991i	−0.0875757	+	0.151686i	0.818910	+	0.573922i	$0.194579\pi$
$558$		0			0
$559$	−61.6148			−2.60603
$560$		0			0
$561$	2.77805			0.117289
$562$		0			0
$563$	−16.0538	+	27.8061i	−0.676589	+	1.17189i	0.299413	+	0.954124i	$0.403209\pi$
$563$	−16.0538	+	27.8061i	−0.676589	+	1.17189i	−0.976002	+	0.217762i	$0.930124\pi$
$564$		0			0
$565$	13.2288	−	7.63763i	0.556538	−	0.321317i
$566$		0			0
$567$	−1.48636	+	2.18877i	−0.0624214	+	0.0919198i
$568$		0			0
$569$	−4.41874	−	7.65349i	−0.185243	−	0.320851i	0.758415	−	0.651772i	$-0.225974\pi$
$569$	−4.41874	−	7.65349i	−0.185243	−	0.320851i	−0.943659	+	0.330921i	$0.892641\pi$
$570$		0			0
$571$	23.1203	+	13.3485i	0.967555	+	0.558618i	0.898490	−	0.438994i	$-0.144665\pi$
$571$	23.1203	+	13.3485i	0.967555	+	0.558618i	0.0690650	+	0.997612i	$0.477998\pi$
$572$		0			0
$573$			7.88475i			0.329390i
$574$		0			0
$575$			1.48833i			0.0620675i
$576$		0			0
$577$	−17.8634	−	10.3135i	−0.743665	−	0.429355i	0.0797356	−	0.996816i	$-0.474592\pi$
$577$	−17.8634	−	10.3135i	−0.743665	−	0.429355i	−0.823400	+	0.567461i	$0.807926\pi$
$578$		0			0
$579$	−5.37464	−	9.30915i	−0.223362	−	0.386875i
$580$		0			0
$581$	−7.80691	−	0.570545i	−0.323885	−	0.0236702i
$582$		0			0
$583$	−15.3758	+	8.87720i	−0.636799	+	0.367656i
$584$		0			0
$585$	−7.68844	+	13.3168i	−0.317878	+	0.550580i
$586$		0			0
$587$	30.8831			1.27468			0.637341	−	0.770582i	$-0.280034\pi$
$587$	30.8831			1.27468			0.637341	+	0.770582i	$0.280034\pi$
$588$		0			0
$589$	−3.61299			−0.148871
$590$		0			0
$591$	−3.11244	+	5.39091i	−0.128029	+	0.221753i
$592$		0			0
$593$	−26.5083	+	15.3046i	−1.08856	+	0.628483i	−0.933194	−	0.359373i	$-0.882991\pi$
$593$	−26.5083	+	15.3046i	−1.08856	+	0.628483i	−0.155371	+	0.987856i	$0.549657\pi$
$594$		0			0
$595$	13.9622	+	1.02039i	0.572395	+	0.0418318i
$596$		0			0
$597$	2.14111	+	3.70852i	0.0876300	+	0.151780i
$598$		0			0
$599$	−2.35950	−	1.36226i	−0.0964068	−	0.0556605i	0.451021	−	0.892513i	$-0.351060\pi$
$599$	−2.35950	−	1.36226i	−0.0964068	−	0.0556605i	−0.547428	+	0.836853i	$0.684393\pi$
$600$		0			0
$601$		−	28.9310i		−	1.18012i	−0.807360	−	0.590059i	$-0.799104\pi$
$601$		−	28.9310i		−	1.18012i	0.807360	−	0.590059i	$-0.200896\pi$
$602$		0			0
$603$			0.0530875i			0.00216189i
$604$		0			0
$605$	21.0228	+	12.1375i	0.854697	+	0.493460i
$606$		0			0
$607$	16.6523	+	28.8426i	0.675896	+	1.17069i	0.976206	+	0.216845i	$0.0695767\pi$
$607$	16.6523	+	28.8426i	0.675896	+	1.17069i	−0.300310	+	0.953842i	$0.597090\pi$
$608$		0			0
$609$	−9.01418	+	13.2740i	−0.365273	+	0.537890i
$610$		0			0
$611$	−47.4929	+	27.4200i	−1.92136	+	1.10930i
$612$		0			0
$613$	−0.928335	+	1.60792i	−0.0374951	+	0.0649434i	−0.884164	−	0.467177i	$-0.845271\pi$
$613$	−0.928335	+	1.60792i	−0.0374951	+	0.0649434i	0.846669	+	0.532120i	$0.178605\pi$
$614$		0			0
$615$	4.26999			0.172183
$616$		0			0
$617$	27.4264			1.10415			0.552073	−	0.833796i	$-0.313837\pi$
$617$	27.4264			1.10415			0.552073	+	0.833796i	$0.313837\pi$
$618$		0			0
$619$	1.10474	−	1.91346i	0.0444031	−	0.0769084i	−0.842970	−	0.537961i	$-0.819195\pi$
$619$	1.10474	−	1.91346i	0.0444031	−	0.0769084i	0.887373	+	0.461053i	$0.152528\pi$
$620$		0			0
$621$	0.562697	−	0.324873i	0.0225802	−	0.0130367i
$622$		0			0
$623$	−19.6289	+	9.49749i	−0.786415	+	0.380509i
$624$		0			0
$625$	15.6031	+	27.0253i	0.624123	+	1.08101i
$626$		0			0
$627$	−0.887981	−	0.512676i	−0.0354626	−	0.0204743i
$628$		0			0
$629$		−	2.26086i		−	0.0901462i
$630$		0			0
$631$			19.7387i			0.785784i	0.919585	+	0.392892i	$0.128525\pi$
$631$			19.7387i			0.785784i	−0.919585	+	0.392892i	$0.871475\pi$
$632$		0			0
$633$	−14.9700	−	8.64292i	−0.595003	−	0.343525i
$634$		0			0
$635$	15.8788	+	27.5029i	0.630131	+	1.09142i
$636$		0			0
$637$	−5.79577	+	39.4407i	−0.229637	+	1.56270i
$638$		0			0
$639$	12.1757	−	7.02965i	0.481664	−	0.278089i
$640$		0			0
$641$	9.48629	−	16.4307i	0.374686	−	0.648975i	−0.615594	−	0.788063i	$-0.711084\pi$
$641$	9.48629	−	16.4307i	0.374686	−	0.648975i	0.990280	+	0.139088i	$0.0444172\pi$
$642$		0			0
$643$	−17.5988			−0.694027			−0.347013	−	0.937860i	$-0.612804\pi$
$643$	−17.5988			−0.694027			−0.347013	+	0.937860i	$0.612804\pi$
$644$		0			0
$645$	−29.2134			−1.15028
$646$		0			0
$647$	−3.01648	+	5.22469i	−0.118590	+	0.205404i	−0.919209	−	0.393770i	$-0.871171\pi$
$647$	−3.01648	+	5.22469i	−0.118590	+	0.205404i	0.800619	+	0.599174i	$0.204504\pi$
$648$		0			0
$649$	1.06598	−	0.615446i	0.0418435	−	0.0241584i
$650$		0			0
$651$	5.75622	+	11.8966i	0.225604	+	0.466266i
$652$		0			0
$653$	−0.795336	−	1.37756i	−0.0311239	−	0.0539082i	0.850044	−	0.526712i	$-0.176575\pi$
$653$	−0.795336	−	1.37756i	−0.0311239	−	0.0539082i	−0.881168	+	0.472804i	$0.843242\pi$
$654$		0			0
$655$	−48.2180	−	27.8387i	−1.88403	−	1.08775i
$656$		0			0
$657$		−	15.6484i		−	0.610504i
$658$		0			0
$659$			8.83213i			0.344051i	0.985093	+	0.172025i	$0.0550311\pi$
$659$			8.83213i			0.344051i	−0.985093	+	0.172025i	$0.944969\pi$
$660$		0			0
$661$	1.26457	+	0.730101i	0.0491862	+	0.0283976i	0.524391	−	0.851477i	$-0.324293\pi$
$661$	1.26457	+	0.730101i	0.0491862	+	0.0283976i	−0.475205	+	0.879875i	$0.657626\pi$
$662$		0			0
$663$	−5.58001	−	9.66487i	−0.216710	−	0.375352i
$664$		0			0
$665$	−4.27461	−	2.90283i	−0.165762	−	0.112567i
$666$		0			0
$667$	3.41252	−	1.97022i	0.132133	−	0.0762873i
$668$		0			0
$669$	2.20317	−	3.81601i	0.0851796	−	0.147535i
$670$		0			0
$671$	19.2939			0.744835
$672$		0			0
$673$	−31.7279			−1.22302			−0.611510	−	0.791237i	$-0.709438\pi$
$673$	−31.7279			−1.22302			−0.611510	+	0.791237i	$0.709438\pi$
$674$		0			0
$675$	−1.14531	+	1.98374i	−0.0440832	+	0.0763543i
$676$		0			0
$677$	5.46898	−	3.15752i	0.210190	−	0.121353i	−0.391210	−	0.920302i	$-0.627943\pi$
$677$	5.46898	−	3.15752i	0.210190	−	0.121353i	0.601400	+	0.798948i	$0.294610\pi$
$678$		0			0
$679$	−0.196468	+	2.68832i	−0.00753976	+	0.103168i
$680$		0			0
$681$	−3.11039	−	5.38735i	−0.119190	−	0.206444i
$682$		0			0
$683$	−3.00339	−	1.73401i	−0.114921	−	0.0663499i	0.441438	−	0.897292i	$-0.354469\pi$
$683$	−3.00339	−	1.73401i	−0.114921	−	0.0663499i	−0.556359	+	0.830942i	$0.687802\pi$
$684$		0			0
$685$		−	52.8406i		−	2.01894i
$686$		0			0
$687$			11.5332i			0.440020i
$688$		0			0
$689$	61.7678	+	35.6617i	2.35317	+	1.35860i
$690$		0			0
$691$	−4.28609	−	7.42372i	−0.163050	−	0.282412i	0.772911	−	0.634515i	$-0.218800\pi$
$691$	−4.28609	−	7.42372i	−0.163050	−	0.282412i	−0.935961	+	0.352103i	$0.885467\pi$
$692$		0			0
$693$	−0.273378	+	3.74069i	−0.0103848	+	0.142097i
$694$		0			0
$695$	−45.3898	+	26.2058i	−1.72173	+	0.994043i
$696$		0			0
$697$	−1.54951	+	2.68383i	−0.0586918	+	0.101657i
$698$		0			0
$699$	−9.27693			−0.350886
$700$		0			0
$701$	6.08683			0.229896			0.114948	−	0.993371i	$-0.463330\pi$
$701$	6.08683			0.229896			0.114948	+	0.993371i	$0.463330\pi$
$702$		0			0
$703$	−0.417231	+	0.722665i	−0.0157362	+	0.0272558i
$704$		0			0
$705$	−22.5178	+	13.0006i	−0.848069	+	0.489633i
$706$		0			0
$707$	26.1483	+	17.7569i	0.983408	+	0.667818i
$708$		0			0
$709$	−18.4284	−	31.9189i	−0.692092	−	1.19874i	−0.971151	−	0.238464i	$-0.923356\pi$
$709$	−18.4284	−	31.9189i	−0.692092	−	1.19874i	0.279060	−	0.960274i	$-0.409977\pi$
$710$		0			0
$711$	9.95371	+	5.74678i	0.373293	+	0.215521i
$712$		0			0
$713$		−	3.24561i		−	0.121549i
$714$		0			0
$715$			21.7986i			0.815220i
$716$		0			0
$717$	3.07906	+	1.77770i	0.114990	+	0.0663894i
$718$		0			0
$719$	22.7917	+	39.4764i	0.849988	+	1.47222i	0.881218	+	0.472710i	$0.156724\pi$
$719$	22.7917	+	39.4764i	0.849988	+	1.47222i	−0.0312297	+	0.999512i	$0.509942\pi$
$720$		0			0
$721$	−20.2701	−	41.8932i	−0.754900	−	1.56019i
$722$		0			0
$723$	7.43954	−	4.29522i	0.276679	−	0.159741i
$724$		0			0
$725$	−6.94586	+	12.0306i	−0.257963	+	0.446805i
$726$		0			0
$727$	9.02124			0.334579			0.167290	−	0.985908i	$-0.446498\pi$
$727$	9.02124			0.334579			0.167290	+	0.985908i	$0.446498\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	10.6011	−	18.3616i	0.392094	−	0.679127i
$732$		0			0
$733$	−26.9079	+	15.5353i	−0.993865	+	0.573808i	−0.906427	−	0.422362i	$-0.861201\pi$
$733$	−26.9079	+	15.5353i	−0.993865	+	0.573808i	−0.0874376	+	0.996170i	$0.527868\pi$
$734$		0			0
$735$	−2.74795	+	18.7000i	−0.101359	+	0.689760i
$736$		0			0
$737$	0.0376289	+	0.0651752i	0.00138608	+	0.00240076i
$738$		0			0
$739$	32.6812	+	18.8685i	1.20220	+	0.694089i	0.961043	−	0.276398i	$-0.0891409\pi$
$739$	32.6812	+	18.8685i	1.20220	+	0.694089i	0.241154	+	0.970487i	$0.422474\pi$
$740$		0			0
$741$			4.11907i			0.151318i
$742$		0			0
$743$		−	43.6664i		−	1.60197i	−0.598687	−	0.800983i	$-0.704311\pi$
$743$		−	43.6664i		−	1.60197i	0.598687	−	0.800983i	$-0.295689\pi$
$744$		0			0
$745$	44.9230	+	25.9363i	1.64585	+	0.950233i
$746$		0			0
$747$	1.47930	+	2.56223i	0.0541248	+	0.0937470i
$748$		0			0
$749$	34.7124	−	16.7957i	1.26836	−	0.613701i
$750$		0			0
$751$	40.5829	−	23.4306i	1.48089	−	0.854993i	0.481126	−	0.876651i	$-0.340228\pi$
$751$	40.5829	−	23.4306i	1.48089	−	0.854993i	0.999765	+	0.0216580i	$0.00689450\pi$
$752$		0			0
$753$	−5.30675	+	9.19156i	−0.193389	+	0.334959i
$754$		0			0
$755$	−4.52819			−0.164798
$756$		0			0
$757$	−20.1824			−0.733543			−0.366771	−	0.930311i	$-0.619537\pi$
$757$	−20.1824			−0.733543			−0.366771	+	0.930311i	$0.619537\pi$
$758$		0			0
$759$	0.460546	−	0.797690i	0.0167168	−	0.0289543i
$760$		0			0
$761$	−3.87020	+	2.23446i	−0.140295	+	0.0809991i	−0.568504	−	0.822680i	$-0.692478\pi$
$761$	−3.87020	+	2.23446i	−0.140295	+	0.0809991i	0.428210	+	0.903679i	$0.359144\pi$
$762$		0			0
$763$	8.05124	−	11.8560i	0.291474	−	0.429216i
$764$		0			0
$765$	−2.64565	−	4.58240i	−0.0956536	−	0.165677i
$766$		0			0
$767$	−4.28229	−	2.47238i	−0.154625	−	0.0892725i
$768$		0			0
$769$			25.5449i			0.921173i	0.887615	+	0.460587i	$0.152361\pi$
$769$			25.5449i			0.921173i	−0.887615	+	0.460587i	$0.847639\pi$
$770$		0			0
$771$		−	15.8261i		−	0.569962i
$772$		0			0
$773$	15.6854	+	9.05597i	0.564165	+	0.325721i	0.754815	−	0.655937i	$-0.227726\pi$
$773$	15.6854	+	9.05597i	0.564165	+	0.325721i	−0.190651	+	0.981658i	$0.561060\pi$
$774$		0			0
$775$	5.72108	+	9.90919i	0.205507	+	0.355949i
$776$		0			0
$777$	3.04429	+	0.222483i	0.109213	+	0.00798153i
$778$		0			0
$779$	0.990577	−	0.571910i	0.0354911	−	0.0204908i
$780$		0			0
$781$	9.96537	−	17.2605i	0.356589	−	0.617630i
$782$		0			0
$783$	6.06459			0.216731
$784$		0			0
$785$	−21.2560			−0.758660
$786$		0			0
$787$	−22.3136	+	38.6483i	−0.795394	+	1.37766i	0.127195	+	0.991878i	$0.459403\pi$
$787$	−22.3136	+	38.6483i	−0.795394	+	1.37766i	−0.922589	+	0.385785i	$0.873931\pi$
$788$		0			0
$789$	0.378909	−	0.218763i	0.0134895	−	0.00778818i
$790$		0			0
$791$	−14.9279	−	1.09096i	−0.530774	−	0.0387901i
$792$		0			0
$793$	−38.7540	−	67.1239i	−1.37620	−	2.38364i
$794$		0			0
$795$	29.2860	+	16.9083i	1.03867	+	0.599674i
$796$		0			0
$797$			24.9941i			0.885335i	0.896686	+	0.442668i	$0.145968\pi$
$797$			24.9941i			0.885335i	−0.896686	+	0.442668i	$0.854032\pi$
$798$		0			0
$799$		−	18.8709i		−	0.667604i
$800$		0			0
$801$	7.13765	+	4.12092i	0.252196	+	0.145606i
$802$		0			0
$803$	−11.0918	−	19.2115i	−0.391420	−	0.677960i
$804$		0			0
$805$	2.60766	−	3.83996i	0.0919080	−	0.135341i
$806$		0			0
$807$	−0.429647	+	0.248057i	−0.0151243	+	0.00873202i
$808$		0			0
$809$	−13.3434	+	23.1115i	−0.469129	+	0.812556i	−0.999377	−	0.0352870i	$-0.988765\pi$
$809$	−13.3434	+	23.1115i	−0.469129	+	0.812556i	0.530248	+	0.847843i	$0.322099\pi$
$810$		0			0
$811$	12.1884			0.427994			0.213997	−	0.976834i	$-0.431352\pi$
$811$	12.1884			0.427994			0.213997	+	0.976834i	$0.431352\pi$
$812$		0			0
$813$	3.37679			0.118429
$814$		0			0
$815$	4.81274	−	8.33592i	0.168583	−	0.291994i
$816$		0			0
$817$	−6.77709	+	3.91276i	−0.237101	+	0.136890i
$818$		0			0
$819$	13.5630	−	6.56251i	0.473931	−	0.229313i
$820$		0			0
$821$	8.04570	+	13.9356i	0.280797	+	0.486355i	0.971581	−	0.236706i	$-0.0760679\pi$
$821$	8.04570	+	13.9356i	0.280797	+	0.486355i	−0.690784	+	0.723061i	$0.742735\pi$
$822$		0			0
$823$	15.9992	+	9.23714i	0.557697	+	0.321986i	0.752221	−	0.658911i	$-0.228983\pi$
$823$	15.9992	+	9.23714i	0.557697	+	0.321986i	−0.194524	+	0.980898i	$0.562316\pi$
$824$		0			0
$825$			3.24724i			0.113054i
$826$		0			0
$827$		−	50.1954i		−	1.74547i	−0.488198	−	0.872733i	$-0.662346\pi$
$827$		−	50.1954i		−	1.74547i	0.488198	−	0.872733i	$-0.337654\pi$
$828$		0			0
$829$	−17.6810	−	10.2081i	−0.614085	−	0.354542i	0.160477	−	0.987040i	$-0.448697\pi$
$829$	−17.6810	−	10.2081i	−0.614085	−	0.354542i	−0.774563	+	0.632497i	$0.782030\pi$
$830$		0			0
$831$	−5.46678	−	9.46874i	−0.189640	−	0.328467i
$832$		0			0
$833$	−10.7564	−	8.51309i	−0.372686	−	0.294961i
$834$		0			0
$835$	−25.6271	+	14.7958i	−0.886862	+	0.512030i
$836$		0			0
$837$	2.49760	−	4.32597i	0.0863297	−	0.149527i
$838$		0			0
$839$	20.8855			0.721048			0.360524	−	0.932750i	$-0.382598\pi$
$839$	20.8855			0.721048			0.360524	+	0.932750i	$0.382598\pi$
$840$		0			0
$841$	7.77923			0.268249
$842$		0			0
$843$	−13.2466	+	22.9438i	−0.456237	+	0.790226i
$844$		0			0
$845$	45.4387	−	26.2341i	1.56314	−	0.902479i
$846$		0			0
$847$	−10.3600	−	21.4116i	−0.355975	−	0.735710i
$848$		0			0
$849$	−1.08930	−	1.88673i	−0.0373848	−	0.0647524i
$850$		0			0
$851$	−0.649184	−	0.374806i	−0.0222537	−	0.0128482i
$852$		0			0
$853$			23.6666i			0.810329i	0.914244	+	0.405165i	$0.132786\pi$
$853$			23.6666i			0.810329i	−0.914244	+	0.405165i	$0.867214\pi$
$854$		0			0
$855$			1.95297i			0.0667902i
$856$		0			0
$857$	−2.71294	−	1.56631i	−0.0926721	−	0.0535043i	0.452948	−	0.891537i	$-0.350372\pi$
$857$	−2.71294	−	1.56631i	−0.0926721	−	0.0535043i	−0.545620	+	0.838033i	$0.683706\pi$
$858$		0			0
$859$	9.15051	+	15.8491i	0.312211	+	0.540766i	0.978841	−	0.204623i	$-0.0655970\pi$
$859$	9.15051	+	15.8491i	0.312211	+	0.540766i	−0.666629	+	0.745389i	$0.732264\pi$
$860$		0			0
$861$	−3.46134	−	2.35055i	−0.117962	−	0.0801065i
$862$		0			0
$863$	4.26257	−	2.46099i	0.145099	−	0.0837732i	−0.425693	−	0.904868i	$-0.639970\pi$
$863$	4.26257	−	2.46099i	0.145099	−	0.0837732i	0.570792	+	0.821095i	$0.306636\pi$
$864$		0			0
$865$	25.5655	−	44.2807i	0.869253	−	1.50559i
$866$		0			0
$867$	−13.1598			−0.446929
$868$		0			0
$869$	16.2935			0.552719
$870$		0			0
$871$	0.151164	−	0.261823i	0.00512199	−	0.00887154i
$872$		0			0
$873$	0.882307	−	0.509400i	0.0298616	−	0.0172406i
$874$		0			0
$875$	1.41076	−	19.3038i	0.0476925	−	0.652588i
$876$		0			0
$877$	−19.8882	−	34.4474i	−0.671578	−	1.16321i	−0.977457	−	0.211136i	$-0.932284\pi$
$877$	−19.8882	−	34.4474i	−0.671578	−	1.16321i	0.305879	−	0.952070i	$-0.401050\pi$
$878$		0			0
$879$	−5.91232	−	3.41348i	−0.199418	−	0.115134i
$880$		0			0
$881$			21.2750i			0.716774i	0.933573	+	0.358387i	$0.116673\pi$
$881$			21.2750i			0.716774i	−0.933573	+	0.358387i	$0.883327\pi$
$882$		0			0
$883$			22.6054i			0.760733i	0.924836	+	0.380366i	$0.124202\pi$
$883$			22.6054i			0.760733i	−0.924836	+	0.380366i	$0.875798\pi$
$884$		0			0
$885$	−2.03036	−	1.17223i	−0.0682498	−	0.0394041i
$886$		0			0
$887$	15.8162	+	27.3945i	0.531057	+	0.919817i	0.999343	+	0.0362405i	$0.0115382\pi$
$887$	15.8162	+	27.3945i	0.531057	+	0.919817i	−0.468286	+	0.883577i	$0.655128\pi$
$888$		0			0
$889$	2.26813	−	31.0354i	0.0760708	−	1.04089i
$890$		0			0
$891$	1.22769	−	0.708810i	0.0411293	−	0.0237460i
$892$		0			0
$893$	−3.48254	+	6.03193i	−0.116539	+	0.201851i
$894$		0			0
$895$	−15.9475			−0.533065
$896$		0			0
$897$	−3.70023			−0.123547
$898$		0			0
$899$	15.1469	−	26.2352i	0.505178	−	0.874994i
$900$		0			0
$901$	−21.2548	+	12.2715i	−0.708099	+	0.408821i
$902$		0			0
$903$	23.6810	+	16.0814i	0.788054	+	0.535156i
$904$		0			0
$905$	33.1172	+	57.3606i	1.10085	+	1.90673i
$906$		0			0
$907$	−15.5515	−	8.97867i	−0.516380	−	0.298132i	0.219073	−	0.975709i	$-0.429697\pi$
$907$	−15.5515	−	8.97867i	−0.516380	−	0.298132i	−0.735452	+	0.677577i	$0.763030\pi$
$908$		0			0
$909$		−	11.9466i		−	0.396242i
$910$		0			0
$911$			38.5199i			1.27622i	0.769945	+	0.638110i	$0.220284\pi$
$911$			38.5199i			1.27622i	−0.769945	+	0.638110i	$0.779716\pi$
$912$		0			0
$913$	3.63226	+	2.09709i	0.120210	+	0.0694035i
$914$		0			0
$915$	−18.3744	−	31.8254i	−0.607440	−	1.05212i
$916$		0			0
$917$	23.7619	+	49.1097i	0.784686	+	1.62175i
$918$		0			0
$919$	3.26565	−	1.88542i	0.107724	−	0.0621944i	−0.445170	−	0.895446i	$-0.646857\pi$
$919$	3.26565	−	1.88542i	0.107724	−	0.0621944i	0.552894	+	0.833252i	$0.313523\pi$
$920$		0			0
$921$	6.49275	−	11.2458i	0.213943	−	0.370561i
$922$		0			0
$923$	−80.0662			−2.63541
$924$		0			0
$925$	2.64270			0.0868915
$926$		0			0
$927$	−8.79513	+	15.2336i	−0.288870	+	0.500338i
$928$		0			0
$929$	−9.54078	+	5.50837i	−0.313023	+	0.180724i	−0.648278	−	0.761403i	$-0.724511\pi$
$929$	−9.54078	+	5.50837i	−0.313023	+	0.180724i	0.335255	+	0.942127i	$0.391177\pi$
$930$		0			0
$931$	1.86714	+	4.70619i	0.0611930	+	0.154239i
$932$		0			0
$933$	−16.3818	−	28.3741i	−0.536317	−	0.928928i
$934$		0			0
$935$	−6.49610	−	3.75052i	−0.212445	−	0.122655i
$936$		0			0
$937$			5.09549i			0.166462i	0.996530	+	0.0832312i	$0.0265240\pi$
$937$			5.09549i			0.166462i	−0.996530	+	0.0832312i	$0.973476\pi$
$938$		0			0
$939$		−	9.15065i		−	0.298620i
$940$		0			0
$941$	−8.96326	−	5.17494i	−0.292194	−	0.168698i	0.346737	−	0.937962i	$-0.387290\pi$
$941$	−8.96326	−	5.17494i	−0.292194	−	0.168698i	−0.638931	+	0.769264i	$0.720623\pi$
$942$		0			0
$943$	0.513757	+	0.889854i	0.0167302	+	0.0289776i
$944$		0			0
$945$	6.43064	−	3.11148i	0.209189	−	0.101216i
$946$		0			0
$947$	−40.5816	+	23.4298i	−1.31873	+	0.761367i	−0.983524	−	0.180780i	$-0.942138\pi$
$947$	−40.5816	+	23.4298i	−1.31873	+	0.761367i	−0.335202	+	0.942146i	$0.608805\pi$
$948$		0			0
$949$	−44.5581	+	77.1769i	−1.44642	+	2.50527i
$950$		0			0
$951$	24.5872			0.797296
$952$		0			0
$953$	41.3560			1.33965			0.669825	−	0.742519i	$-0.266369\pi$
$953$	41.3560			1.33965			0.669825	+	0.742519i	$0.266369\pi$
$954$		0			0
$955$	10.6449	−	18.4375i	0.344460	−	0.596622i
$956$		0			0
$957$	7.44546	−	4.29864i	0.240678	−	0.138955i
$958$		0			0
$959$	−29.0878	+	42.8337i	−0.939293	+	1.38317i
$960$		0			0
$961$	3.02399	+	5.23770i	0.0975479	+	0.168958i
$962$		0			0
$963$	−12.6225	−	7.28758i	−0.406753	−	0.234839i
$964$		0			0
$965$			29.0243i			0.934326i
$966$		0			0
$967$			23.6169i			0.759467i	0.925096	+	0.379733i	$0.123984\pi$
$967$			23.6169i			0.759467i	−0.925096	+	0.379733i	$0.876016\pi$
$968$		0			0
$969$	−1.22751	−	0.708701i	−0.0394332	−	0.0227668i
$970$		0			0
$971$	23.1664	+	40.1254i	0.743446	+	1.28769i	0.950917	+	0.309445i	$0.100143\pi$
$971$	23.1664	+	40.1254i	0.743446	+	1.28769i	−0.207472	+	0.978241i	$0.566524\pi$
$972$		0			0
$973$	51.2198	+	3.74325i	1.64203	+	0.120003i
$974$		0			0
$975$	11.2972	−	6.52244i	0.361800	−	0.208885i
$976$		0			0
$977$	6.17019	−	10.6871i	0.197402	−	0.341910i	−0.750283	−	0.661116i	$-0.770083\pi$
$977$	6.17019	−	10.6871i	0.197402	−	0.341910i	0.947685	+	0.319206i	$0.103416\pi$
$978$		0			0
$979$	11.6838			0.373416
$980$		0			0
$981$	−5.41674			−0.172943
$982$		0			0
$983$	9.59504	−	16.6191i	0.306034	−	0.530067i	−0.671457	−	0.741044i	$-0.734331\pi$
$983$	9.59504	−	16.6191i	0.306034	−	0.530067i	0.977491	+	0.210977i	$0.0676644\pi$
$984$		0			0
$985$	14.5561	−	8.40396i	0.463796	−	0.267773i
$986$		0			0
$987$	25.4100	+	1.85702i	0.808810	+	0.0591095i
$988$		0			0
$989$	−3.51490	−	6.08799i	−0.111767	−	0.193587i
$990$		0			0
$991$	−8.65548	−	4.99724i	−0.274950	−	0.158743i	0.356185	−	0.934416i	$-0.384077\pi$
$991$	−8.65548	−	4.99724i	−0.274950	−	0.158743i	−0.631135	+	0.775673i	$0.717411\pi$
$992$		0			0
$993$		−	20.2118i		−	0.641401i
$994$		0			0
$995$		−	11.5625i		−	0.366556i
$996$		0			0
$997$	−33.3809	−	19.2725i	−1.05718	−	0.610365i	−0.132532	−	0.991179i	$-0.542311\pi$
$997$	−33.3809	−	19.2725i	−1.05718	−	0.610365i	−0.924652	+	0.380814i	$0.875644\pi$
$998$		0			0
$999$	−0.576851	−	0.999134i	−0.0182507	−	0.0316112i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1344.2.bl.l.703.2		16
4.3	odd	2		1344.2.bl.k.703.2		16
7.5	odd	6		1344.2.bl.k.1279.2		16
8.3	odd	2		672.2.bl.b.31.7	yes	16
8.5	even	2		672.2.bl.a.31.7	✓	16
24.5	odd	2		2016.2.cs.a.703.2		16
24.11	even	2		2016.2.cs.c.703.2		16
28.19	even	6	inner	1344.2.bl.l.1279.2		16
56.3	even	6		4704.2.b.e.1567.3		16
56.5	odd	6		672.2.bl.b.607.7	yes	16
56.11	odd	6		4704.2.b.d.1567.14		16
56.19	even	6		672.2.bl.a.607.7	yes	16
56.45	odd	6		4704.2.b.d.1567.3		16
56.53	even	6		4704.2.b.e.1567.14		16
168.5	even	6		2016.2.cs.c.1279.2		16
168.131	odd	6		2016.2.cs.a.1279.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
672.2.bl.a.31.7	✓	16	8.5	even	2
672.2.bl.a.607.7	yes	16	56.19	even	6
672.2.bl.b.31.7	yes	16	8.3	odd	2
672.2.bl.b.607.7	yes	16	56.5	odd	6
1344.2.bl.k.703.2		16	4.3	odd	2
1344.2.bl.k.1279.2		16	7.5	odd	6
1344.2.bl.l.703.2		16	1.1	even	1	trivial
1344.2.bl.l.1279.2		16	28.19	even	6	inner
2016.2.cs.a.703.2		16	24.5	odd	2
2016.2.cs.a.1279.2		16	168.131	odd	6
2016.2.cs.c.703.2		16	24.11	even	2
2016.2.cs.c.1279.2		16	168.5	even	6
4704.2.b.d.1567.3		16	56.45	odd	6
4704.2.b.d.1567.14		16	56.11	odd	6
4704.2.b.e.1567.3		16	56.3	even	6
4704.2.b.e.1567.14		16	56.53	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1344 = 2^{6} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1344.bl (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{3} +(-2.33837 + 1.35006i) q^{5} +(2.63871 + 0.192843i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{3} +(-2.33837 + 1.35006i) q^{5} +(2.63871 + 0.192843i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(-1.22769 - 0.708810i) q^{11} +5.69489i q^{13} +2.70012i q^{15} +(-1.69711 - 0.979828i) q^{17} +(0.361646 + 0.626389i) q^{19} +(1.48636 - 2.18877i) q^{21} +(-0.562697 + 0.324873i) q^{23} +(1.14531 - 1.98374i) q^{25} -1.00000 q^{27} -6.06459 q^{29} +(-2.49760 + 4.32597i) q^{31} +(-1.22769 + 0.708810i) q^{33} +(-6.43064 + 3.11148i) q^{35} +(0.576851 + 0.999134i) q^{37} +(4.93192 + 2.84745i) q^{39} -1.58141i q^{41} +10.8193i q^{43} +(2.33837 + 1.35006i) q^{45} +(4.81485 + 8.33956i) q^{47} +(6.92562 + 1.01771i) q^{49} +(-1.69711 + 0.979828i) q^{51} +(6.26205 - 10.8462i) q^{53} +3.82774 q^{55} +0.723292 q^{57} +(-0.434140 + 0.751953i) q^{59} +(-11.7867 + 6.80505i) q^{61} +(-1.15235 - 2.38161i) q^{63} +(-7.68844 - 13.3168i) q^{65} +(-0.0459751 - 0.0265437i) q^{67} +0.649746i q^{69} +14.0593i q^{71} +(13.5520 + 7.82422i) q^{73} +(-1.14531 - 1.98374i) q^{75} +(-3.10285 - 2.10710i) q^{77} +(-9.95371 + 5.74678i) q^{79} +(-0.500000 + 0.866025i) q^{81} -2.95860 q^{83} +5.29130 q^{85} +(-3.03229 + 5.25209i) q^{87} +(-7.13765 + 4.12092i) q^{89} +(-1.09822 + 15.0272i) q^{91} +(2.49760 + 4.32597i) q^{93} +(-1.69132 - 0.976486i) q^{95} +1.01880i q^{97} +1.41762i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{3} - 4 q^{7} - 8 q^{9}+O(q^{10}) \) 16 * q + 8 * q^3 - 4 * q^7 - 8 * q^9	\( 16 q + 8 q^{3} - 4 q^{7} - 8 q^{9} - 12 q^{11} - 4 q^{19} - 8 q^{21} + 4 q^{25} - 16 q^{27} + 4 q^{31} - 12 q^{33} - 8 q^{35} - 4 q^{37} + 12 q^{39} + 8 q^{47} + 24 q^{49} - 8 q^{53} - 16 q^{55} - 8 q^{57} - 4 q^{59} - 24 q^{61} - 4 q^{63} + 8 q^{65} + 12 q^{67} + 12 q^{73} - 4 q^{75} + 32 q^{77} + 12 q^{79} - 8 q^{81} - 8 q^{83} - 32 q^{85} + 4 q^{91} - 4 q^{93} - 48 q^{95}+O(q^{100}) \) 16 * q + 8 * q^3 - 4 * q^7 - 8 * q^9 - 12 * q^11 - 4 * q^19 - 8 * q^21 + 4 * q^25 - 16 * q^27 + 4 * q^31 - 12 * q^33 - 8 * q^35 - 4 * q^37 + 12 * q^39 + 8 * q^47 + 24 * q^49 - 8 * q^53 - 16 * q^55 - 8 * q^57 - 4 * q^59 - 24 * q^61 - 4 * q^63 + 8 * q^65 + 12 * q^67 + 12 * q^73 - 4 * q^75 + 32 * q^77 + 12 * q^79 - 8 * q^81 - 8 * q^83 - 32 * q^85 + 4 * q^91 - 4 * q^93 - 48 * q^95

Introduction

L-functions

Modular forms

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Database

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