LMFDB - Embedded newform 1344.2.bl.i.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:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.562828176.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + x^{6} + 2x^{5} - 6x^{4} + 4x^{3} + 4x^{2} - 16x + 16 $ x^8 - 2x^7 + x^6 + 2x^5 - 6x^4 + 4x^3 + 4x^2 - 16x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 84)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			703.2
Root			$1.40376 + 0.171630i$ of defining polynomial
Character	$\chi$	$=$	1344.703
Dual form			1344.2.bl.i.1279.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{3} +(-0.834598 + 0.481855i) q^{5} +(1.20103 + 2.35744i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{3} +(-0.834598 + 0.481855i) q^{5} +(1.20103 + 2.35744i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(4.74861 + 2.74161i) q^{11} +3.75117i q^{13} -0.963711i q^{15} +(-0.594545 - 0.343260i) q^{17} +(-2.44109 - 4.22809i) q^{19} +(-2.64212 - 0.138595i) q^{21} +(1.07465 - 0.620450i) q^{23} +(-2.03563 + 3.52582i) q^{25} +1.00000 q^{27} +2.48011 q^{29} +(2.41401 - 4.18119i) q^{31} +(-4.74861 + 2.74161i) q^{33} +(-2.13832 - 1.38879i) q^{35} +(-1.36643 - 2.36673i) q^{37} +(-3.24861 - 1.87558i) q^{39} +9.42976i q^{41} -5.97437i q^{43} +(0.834598 + 0.481855i) q^{45} +(1.80752 + 3.13072i) q^{47} +(-4.11504 + 5.66272i) q^{49} +(0.594545 - 0.343260i) q^{51} +(-2.04757 + 3.54650i) q^{53} -5.28424 q^{55} +4.88217 q^{57} +(-6.34315 + 10.9867i) q^{59} +(-9.01711 + 5.20603i) q^{61} +(1.44109 - 2.21884i) q^{63} +(-1.80752 - 3.13072i) q^{65} +(8.17396 + 4.71924i) q^{67} +1.24090i q^{69} +10.1163i q^{71} +(-5.76850 - 3.33044i) q^{73} +(-2.03563 - 3.52582i) q^{75} +(-0.759946 + 14.4873i) q^{77} +(-1.22492 + 0.707208i) q^{79} +(-0.500000 + 0.866025i) q^{81} +0.543780 q^{83} +0.661608 q^{85} +(-1.24005 + 2.14784i) q^{87} +(0.480107 - 0.277190i) q^{89} +(-8.84315 + 4.50528i) q^{91} +(2.41401 + 4.18119i) q^{93} +(4.07465 + 2.35250i) q^{95} -10.8747i q^{97} -5.48322i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{3} - 2 q^{7} - 4 q^{9}+O(q^{10}) $ 8 * q - 4 * q^3 - 2 * q^7 - 4 * q^9	$ 8 q - 4 q^{3} - 2 q^{7} - 4 q^{9} + 6 q^{11} - 6 q^{19} + 4 q^{21} + 2 q^{25} + 8 q^{27} + 16 q^{29} - 6 q^{31} - 6 q^{33} - 12 q^{35} - 6 q^{37} + 6 q^{39} - 4 q^{47} + 4 q^{49} + 4 q^{53} + 8 q^{55} + 12 q^{57} - 14 q^{59} - 12 q^{61} - 2 q^{63} + 4 q^{65} + 42 q^{67} - 18 q^{73} + 2 q^{75} - 8 q^{77} + 6 q^{79} - 4 q^{81} + 4 q^{83} + 32 q^{85} - 8 q^{87} - 34 q^{91} - 6 q^{93} + 24 q^{95}+O(q^{100}) $ 8 * q - 4 * q^3 - 2 * q^7 - 4 * q^9 + 6 * q^11 - 6 * q^19 + 4 * q^21 + 2 * q^25 + 8 * q^27 + 16 * q^29 - 6 * q^31 - 6 * q^33 - 12 * q^35 - 6 * q^37 + 6 * q^39 - 4 * q^47 + 4 * q^49 + 4 * q^53 + 8 * q^55 + 12 * q^57 - 14 * q^59 - 12 * q^61 - 2 * q^63 + 4 * q^65 + 42 * q^67 - 18 * q^73 + 2 * q^75 - 8 * q^77 + 6 * q^79 - 4 * q^81 + 4 * q^83 + 32 * q^85 - 8 * q^87 - 34 * q^91 - 6 * q^93 + 24 * 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
$5$	−0.834598	+	0.481855i	−0.373244	+	0.215492i	−0.674875	−	0.737932i	$-0.735802\pi$
$5$	−0.834598	+	0.481855i	−0.373244	+	0.215492i	0.301631	+	0.953425i	$0.402469\pi$
$6$		0			0
$7$	1.20103	+	2.35744i	0.453948	+	0.891028i
$7$	1.20103	+	2.35744i	0.453948	+	0.891028i
$8$		0			0
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	4.74861	+	2.74161i	1.43176	+	0.826626i	0.997255	−	0.0740437i	$-0.0235904\pi$
$11$	4.74861	+	2.74161i	1.43176	+	0.826626i	0.434504	+	0.900670i	$0.356924\pi$
$12$		0			0
$13$			3.75117i			1.04039i	0.854048	+	0.520193i	$0.174140\pi$
$13$			3.75117i			1.04039i	−0.854048	+	0.520193i	$0.825860\pi$
$14$		0			0
$15$		−	0.963711i		−	0.248829i
$16$		0			0
$17$	−0.594545	−	0.343260i	−0.144198	−	0.0832529i	0.426165	−	0.904645i	$-0.359864\pi$
$17$	−0.594545	−	0.343260i	−0.144198	−	0.0832529i	−0.570363	+	0.821393i	$0.693198\pi$
$18$		0			0
$19$	−2.44109	−	4.22809i	−0.560024	−	0.969989i	−0.997494	−	0.0707563i	$-0.977459\pi$
$19$	−2.44109	−	4.22809i	−0.560024	−	0.969989i	0.437470	−	0.899233i	$-0.355875\pi$
$20$		0			0
$21$	−2.64212	−	0.138595i	−0.576558	−	0.0302439i
$22$		0			0
$23$	1.07465	−	0.620450i	0.224080	−	0.129373i	−0.383758	−	0.923434i	$-0.625370\pi$
$23$	1.07465	−	0.620450i	0.224080	−	0.129373i	0.607838	+	0.794061i	$0.292037\pi$
$24$		0			0
$25$	−2.03563	+	3.52582i	−0.407126	+	0.705163i
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$	2.48011			0.460544			0.230272	−	0.973126i	$-0.426038\pi$
$29$	2.48011			0.460544			0.230272	+	0.973126i	$0.426038\pi$
$30$		0			0
$31$	2.41401	−	4.18119i	0.433569	−	0.750963i	−0.563609	−	0.826042i	$-0.690587\pi$
$31$	2.41401	−	4.18119i	0.433569	−	0.750963i	0.997178	+	0.0750787i	$0.0239208\pi$
$32$		0			0
$33$	−4.74861	+	2.74161i	−0.826626	+	0.477253i
$34$		0			0
$35$	−2.13832	−	1.38879i	−0.361443	−	0.234748i
$36$		0			0
$37$	−1.36643	−	2.36673i	−0.224640	−	0.389089i	0.731571	−	0.681765i	$-0.238787\pi$
$37$	−1.36643	−	2.36673i	−0.224640	−	0.389089i	−0.956212	+	0.292677i	$0.905454\pi$
$38$		0			0
$39$	−3.24861	−	1.87558i	−0.520193	−	0.300334i
$40$		0			0
$41$			9.42976i			1.47268i	0.676611	+	0.736340i	$0.263448\pi$
$41$			9.42976i			1.47268i	−0.676611	+	0.736340i	$0.736552\pi$
$42$		0			0
$43$		−	5.97437i		−	0.911083i	−0.890215	−	0.455541i	$-0.849446\pi$
$43$		−	5.97437i		−	0.911083i	0.890215	−	0.455541i	$-0.150554\pi$
$44$		0			0
$45$	0.834598	+	0.481855i	0.124415	+	0.0718308i
$46$		0			0
$47$	1.80752	+	3.13072i	0.263654	+	0.456662i	0.967210	−	0.253978i	$-0.0817390\pi$
$47$	1.80752	+	3.13072i	0.263654	+	0.456662i	−0.703556	+	0.710640i	$0.748406\pi$
$48$		0			0
$49$	−4.11504	+	5.66272i	−0.587863	+	0.808960i
$50$		0			0
$51$	0.594545	−	0.343260i	0.0832529	−	0.0480661i
$52$		0			0
$53$	−2.04757	+	3.54650i	−0.281256	+	0.487150i	−0.971694	−	0.236242i	$-0.924084\pi$
$53$	−2.04757	+	3.54650i	−0.281256	+	0.487150i	0.690438	+	0.723391i	$0.257418\pi$
$54$		0			0
$55$	−5.28424			−0.712526
$56$		0			0
$57$	4.88217			0.646660
$58$		0			0
$59$	−6.34315	+	10.9867i	−0.825808	+	1.43034i	0.0754923	+	0.997146i	$0.475947\pi$
$59$	−6.34315	+	10.9867i	−0.825808	+	1.43034i	−0.901300	+	0.433195i	$0.857386\pi$
$60$		0			0
$61$	−9.01711	+	5.20603i	−1.15452	+	0.666564i	−0.949985	−	0.312295i	$-0.898902\pi$
$61$	−9.01711	+	5.20603i	−1.15452	+	0.666564i	−0.204537	+	0.978859i	$0.565569\pi$
$62$		0			0
$63$	1.44109	−	2.21884i	0.181560	−	0.279548i
$64$		0			0
$65$	−1.80752	−	3.13072i	−0.224195	−	0.388318i
$66$		0			0
$67$	8.17396	+	4.71924i	0.998608	+	0.576546i	0.907836	−	0.419325i	$-0.137733\pi$
$67$	8.17396	+	4.71924i	0.998608	+	0.576546i	0.0907716	+	0.995872i	$0.471067\pi$
$68$		0			0
$69$			1.24090i			0.149387i
$70$		0			0
$71$			10.1163i			1.20058i	0.799782	+	0.600291i	$0.204948\pi$
$71$			10.1163i			1.20058i	−0.799782	+	0.600291i	$0.795052\pi$
$72$		0			0
$73$	−5.76850	−	3.33044i	−0.675152	−	0.389799i	0.122874	−	0.992422i	$-0.460789\pi$
$73$	−5.76850	−	3.33044i	−0.675152	−	0.389799i	−0.798026	+	0.602623i	$0.794122\pi$
$74$		0			0
$75$	−2.03563	−	3.52582i	−0.235054	−	0.407126i
$76$		0			0
$77$	−0.759946	+	14.4873i	−0.0866039	+	1.65098i
$78$		0			0
$79$	−1.22492	+	0.707208i	−0.137814	+	0.0795671i	−0.567322	−	0.823496i	$-0.692020\pi$
$79$	−1.22492	+	0.707208i	−0.137814	+	0.0795671i	0.429508	+	0.903063i	$0.358687\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	0.543780			0.0596876			0.0298438	−	0.999555i	$-0.490499\pi$
$83$	0.543780			0.0596876			0.0298438	+	0.999555i	$0.490499\pi$
$84$		0			0
$85$	0.661608			0.0717614
$86$		0			0
$87$	−1.24005	+	2.14784i	−0.132948	+	0.230272i
$88$		0			0
$89$	0.480107	−	0.277190i	0.0508912	−	0.0293821i	−0.474339	−	0.880343i	$-0.657313\pi$
$89$	0.480107	−	0.277190i	0.0508912	−	0.0293821i	0.525230	+	0.850960i	$0.323979\pi$
$90$		0			0
$91$	−8.84315	+	4.50528i	−0.927014	+	0.472281i
$92$		0			0
$93$	2.41401	+	4.18119i	0.250321	+	0.433569i
$94$		0			0
$95$	4.07465	+	2.35250i	0.418050	+	0.241362i
$96$		0			0
$97$		−	10.8747i		−	1.10416i	−0.833790	−	0.552081i	$-0.813834\pi$
$97$		−	10.8747i		−	1.10416i	0.833790	−	0.552081i	$-0.186166\pi$
$98$		0			0
$99$		−	5.48322i		−	0.551084i
$100$		0			0
$101$	−12.4972	−	7.21527i	−1.24352	−	0.717946i	−0.273710	−	0.961812i	$-0.588251\pi$
$101$	−12.4972	−	7.21527i	−1.24352	−	0.717946i	−0.969809	+	0.243866i	$0.921584\pi$
$102$		0			0
$103$	−7.51235	−	13.0118i	−0.740214	−	1.28209i	−0.952398	−	0.304858i	$-0.901391\pi$
$103$	−7.51235	−	13.0118i	−0.740214	−	1.28209i	0.212184	−	0.977230i	$-0.431942\pi$
$104$		0			0
$105$	2.27189	−	1.15745i	0.221714	−	0.112955i
$106$		0			0
$107$	10.4925	−	6.05782i	1.01434	−	0.585632i	0.101883	−	0.994796i	$-0.467513\pi$
$107$	10.4925	−	6.05782i	1.01434	−	0.585632i	0.912461	+	0.409165i	$0.134180\pi$
$108$		0			0
$109$	−3.03563	+	5.25787i	−0.290761	+	0.503612i	−0.973990	−	0.226592i	$-0.927242\pi$
$109$	−3.03563	+	5.25787i	−0.290761	+	0.503612i	0.683229	+	0.730204i	$0.260575\pi$
$110$		0			0
$111$	2.73287			0.259392
$112$		0			0
$113$	−7.37939			−0.694194			−0.347097	−	0.937829i	$-0.612833\pi$
$113$	−7.37939			−0.694194			−0.347097	+	0.937829i	$0.612833\pi$
$114$		0			0
$115$	−0.597935	+	1.03565i	−0.0557577	+	0.0965752i
$116$		0			0
$117$	3.24861	−	1.87558i	0.300334	−	0.173398i
$118$		0			0
$119$	0.0951483	−	1.81387i	0.00872223	−	0.166277i
$120$		0			0
$121$	9.53284	+	16.5114i	0.866622	+	1.50103i
$122$		0			0
$123$	−8.16641	−	4.71488i	−0.736340	−	0.425126i
$124$		0			0
$125$		−	8.74207i		−	0.781915i
$126$		0			0
$127$		−	11.6431i		−	1.03316i	−0.856240	−	0.516578i	$-0.827206\pi$
$127$		−	11.6431i		−	1.03316i	0.856240	−	0.516578i	$-0.172794\pi$
$128$		0			0
$129$	5.17396	+	2.98718i	0.455541	+	0.263007i
$130$		0			0
$131$	4.63078	+	8.02074i	0.404593	+	0.700776i	0.994274	−	0.106861i	$-0.0340798\pi$
$131$	4.63078	+	8.02074i	0.404593	+	0.700776i	−0.589681	+	0.807636i	$0.700747\pi$
$132$		0			0
$133$	7.03563	−	10.8328i	0.610067	−	0.939321i
$134$		0			0
$135$	−0.834598	+	0.481855i	−0.0718308	+	0.0414715i
$136$		0			0
$137$	−3.61504	+	6.26144i	−0.308854	+	0.534951i	−0.978112	−	0.208080i	$-0.933279\pi$
$137$	−3.61504	+	6.26144i	−0.308854	+	0.534951i	0.669258	+	0.743030i	$0.266612\pi$
$138$		0			0
$139$	−5.30812			−0.450229			−0.225115	−	0.974332i	$-0.572276\pi$
$139$	−5.30812			−0.450229			−0.225115	+	0.974332i	$0.572276\pi$
$140$		0			0
$141$	−3.61504			−0.304441
$142$		0			0
$143$	−10.2842	+	17.8128i	−0.860011	+	1.48958i
$144$		0			0
$145$	−2.06989	+	1.19505i	−0.171895	+	0.0992438i
$146$		0			0
$147$	−2.84654	−	6.39509i	−0.234779	−	0.527458i
$148$		0			0
$149$	2.33080	+	4.03707i	0.190947	+	0.330730i	0.945564	−	0.325435i	$-0.105511\pi$
$149$	2.33080	+	4.03707i	0.190947	+	0.330730i	−0.754617	+	0.656165i	$0.772178\pi$
$150$		0			0
$151$	10.5709	+	6.10309i	0.860244	+	0.496662i	0.864094	−	0.503330i	$-0.167892\pi$
$151$	10.5709	+	6.10309i	0.860244	+	0.496662i	−0.00384988	+	0.999993i	$0.501225\pi$
$152$		0			0
$153$			0.686521i			0.0555019i
$154$		0			0
$155$			4.65281i			0.373723i
$156$		0			0
$157$	18.9944	+	10.9664i	1.51592	+	0.875217i	0.999825	+	0.0186856i	$0.00594816\pi$
$157$	18.9944	+	10.9664i	1.51592	+	0.875217i	0.516095	+	0.856531i	$0.327385\pi$
$158$		0			0
$159$	−2.04757	−	3.54650i	−0.162383	−	0.281256i
$160$		0			0
$161$	2.75337	+	1.78824i	0.216996	+	0.140933i
$162$		0			0
$163$	3.48011	−	2.00924i	0.272583	−	0.157376i	−0.357478	−	0.933922i	$-0.616363\pi$
$163$	3.48011	−	2.00924i	0.272583	−	0.157376i	0.630061	+	0.776546i	$0.283030\pi$
$164$		0			0
$165$	2.64212	−	4.57628i	0.205689	−	0.356263i
$166$		0			0
$167$	14.7178			1.13890			0.569448	−	0.822027i	$-0.307157\pi$
$167$	14.7178			1.13890			0.569448	+	0.822027i	$0.307157\pi$
$168$		0			0
$169$	−1.07126			−0.0824047
$170$		0			0
$171$	−2.44109	+	4.22809i	−0.186675	+	0.323330i
$172$		0			0
$173$	10.0918	−	5.82648i	0.767262	−	0.442979i	−0.0646349	−	0.997909i	$-0.520588\pi$
$173$	10.0918	−	5.82648i	0.767262	−	0.442979i	0.831897	+	0.554930i	$0.187255\pi$
$174$		0			0
$175$	−10.7568	−	0.564256i	−0.813134	−	0.0426538i
$176$		0			0
$177$	−6.34315	−	10.9867i	−0.476780	−	0.825808i
$178$		0			0
$179$	2.24663	+	1.29709i	0.167921	+	0.0969494i	0.581605	−	0.813471i	$-0.302425\pi$
$179$	2.24663	+	1.29709i	0.167921	+	0.0969494i	−0.413684	+	0.910421i	$0.635758\pi$
$180$		0			0
$181$		−	9.53343i		−	0.708615i	−0.935129	−	0.354307i	$-0.884717\pi$
$181$		−	9.53343i		−	0.708615i	0.935129	−	0.354307i	$-0.115283\pi$
$182$		0			0
$183$		−	10.4121i		−	0.769681i
$184$		0			0
$185$	2.28085	+	1.31685i	0.167691	+	0.0968166i
$186$		0			0
$187$	−1.88217	−	3.26002i	−0.137638	−	0.238396i
$188$		0			0
$189$	1.20103	+	2.35744i	0.0873623	+	0.171478i
$190$		0			0
$191$	7.21637	−	4.16637i	0.522158	−	0.301468i	−0.215659	−	0.976469i	$-0.569190\pi$
$191$	7.21637	−	4.16637i	0.522158	−	0.301468i	0.737817	+	0.675001i	$0.235857\pi$
$192$		0			0
$193$	6.18630	−	10.7150i	0.445300	−	0.771282i	−0.552773	−	0.833332i	$-0.686430\pi$
$193$	6.18630	−	10.7150i	0.445300	−	0.771282i	0.998073	+	0.0620498i	$0.0197638\pi$
$194$		0			0
$195$	3.61504			0.258878
$196$		0			0
$197$	−3.23686			−0.230617			−0.115308	−	0.993330i	$-0.536786\pi$
$197$	−3.23686			−0.230617			−0.115308	+	0.993330i	$0.536786\pi$
$198$		0			0
$199$	−9.61504	+	16.6537i	−0.681592	+	1.18055i	0.292903	+	0.956142i	$0.405379\pi$
$199$	−9.61504	+	16.6537i	−0.681592	+	1.18055i	−0.974495	+	0.224410i	$0.927955\pi$
$200$		0			0
$201$	−8.17396	+	4.71924i	−0.576546	+	0.332869i
$202$		0			0
$203$	2.97869	+	5.84670i	0.209063	+	0.410358i
$204$		0			0
$205$	−4.54378	−	7.87006i	−0.317351	−	0.549669i
$206$		0			0
$207$	−1.07465	−	0.620450i	−0.0746934	−	0.0431243i
$208$		0			0
$209$		−	26.7700i		−	1.85172i
$210$		0			0
$211$		−	9.24637i		−	0.636546i	−0.947999	−	0.318273i	$-0.896897\pi$
$211$		−	9.24637i		−	0.636546i	0.947999	−	0.318273i	$-0.103103\pi$
$212$		0			0
$213$	−8.76095	−	5.05814i	−0.600291	−	0.346578i
$214$		0			0
$215$	2.87878	+	4.98620i	0.196331	+	0.340056i
$216$		0			0
$217$	12.7562	+	0.669139i	0.865947	+	0.0454241i
$218$		0			0
$219$	5.76850	−	3.33044i	0.389799	−	0.225051i
$220$		0			0
$221$	1.28763	−	2.23024i	0.0866152	−	0.150022i
$222$		0			0
$223$	1.94585			0.130303			0.0651517	−	0.997875i	$-0.479247\pi$
$223$	1.94585			0.130303			0.0651517	+	0.997875i	$0.479247\pi$
$224$		0			0
$225$	4.07126			0.271417
$226$		0			0
$227$	−4.32265	+	7.48706i	−0.286905	+	0.496933i	−0.973069	−	0.230513i	$-0.925960\pi$
$227$	−4.32265	+	7.48706i	−0.286905	+	0.496933i	0.686165	+	0.727446i	$0.259293\pi$
$228$		0			0
$229$	−14.5396	+	8.39446i	−0.960805	+	0.554721i	−0.896421	−	0.443204i	$-0.853842\pi$
$229$	−14.5396	+	8.39446i	−0.960805	+	0.554721i	−0.0643846	+	0.997925i	$0.520508\pi$
$230$		0			0
$231$	−12.1664	−	7.90179i	−0.800491	−	0.519900i
$232$		0			0
$233$	0.523283	+	0.906353i	0.0342814	+	0.0593772i	0.882657	−	0.470018i	$-0.155752\pi$
$233$	0.523283	+	0.906353i	0.0342814	+	0.0593772i	−0.848376	+	0.529395i	$0.822419\pi$
$234$		0			0
$235$	−3.01711	−	1.74193i	−0.196814	−	0.113631i
$236$		0			0
$237$		−	1.41442i		−	0.0918761i
$238$		0			0
$239$		−	19.2479i		−	1.24505i	−0.782602	−	0.622523i	$-0.786108\pi$
$239$		−	19.2479i		−	1.24505i	0.782602	−	0.622523i	$-0.213892\pi$
$240$		0			0
$241$	−2.38754	−	1.37844i	−0.153795	−	0.0887934i	0.421128	−	0.907001i	$-0.361634\pi$
$241$	−2.38754	−	1.37844i	−0.153795	−	0.0887934i	−0.574922	+	0.818208i	$0.694968\pi$
$242$		0			0
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$		0			0
$245$	0.705792	−	6.70895i	0.0450914	−	0.428619i
$246$		0			0
$247$	15.8603	−	9.15692i	1.00916	−	0.582641i
$248$		0			0
$249$	−0.271890	+	0.470927i	−0.0172303	+	0.0298438i
$250$		0			0
$251$	20.7493			1.30968			0.654841	−	0.755767i	$-0.272736\pi$
$251$	20.7493			1.30968			0.654841	+	0.755767i	$0.272736\pi$
$252$		0			0
$253$	6.80413			0.427772
$254$		0			0
$255$	−0.330804	+	0.572969i	−0.0207157	+	0.0358807i
$256$		0			0
$257$	6.45283	−	3.72554i	0.402516	−	0.232393i	−0.285053	−	0.958512i	$-0.592011\pi$
$257$	6.45283	−	3.72554i	0.402516	−	0.232393i	0.687569	+	0.726119i	$0.258678\pi$
$258$		0			0
$259$	3.93830	−	6.06381i	0.244714	−	0.376787i
$260$		0			0
$261$	−1.24005	−	2.14784i	−0.0767574	−	0.132948i
$262$		0			0
$263$	25.7034	+	14.8399i	1.58494	+	0.915066i	0.994123	+	0.108260i	$0.0345280\pi$
$263$	25.7034	+	14.8399i	1.58494	+	0.915066i	0.590818	+	0.806805i	$0.298805\pi$
$264$		0			0
$265$		−	3.94654i		−	0.242434i
$266$		0			0
$267$			0.554380i			0.0339275i
$268$		0			0
$269$	3.73727	+	2.15771i	0.227865	+	0.131558i	0.609587	−	0.792719i	$-0.291335\pi$
$269$	3.73727	+	2.15771i	0.227865	+	0.131558i	−0.381722	+	0.924277i	$0.624669\pi$
$270$		0			0
$271$	6.79142	+	11.7631i	0.412550	+	0.714557i	0.995168	−	0.0981892i	$-0.0313050\pi$
$271$	6.79142	+	11.7631i	0.412550	+	0.714557i	−0.582618	+	0.812746i	$0.697972\pi$
$272$		0			0
$273$	0.519893	−	9.91103i	0.0314654	−	0.599843i
$274$		0			0
$275$	−19.3328	+	11.1618i	−1.16581	+	0.673082i
$276$		0			0
$277$	1.03563	−	1.79376i	0.0622250	−	0.107777i	−0.833235	−	0.552920i	$-0.813514\pi$
$277$	1.03563	−	1.79376i	0.0622250	−	0.107777i	0.895460	+	0.445143i	$0.146847\pi$
$278$		0			0
$279$	−4.82802			−0.289046
$280$		0			0
$281$	23.7122			1.41455			0.707276	−	0.706938i	$-0.249924\pi$
$281$	23.7122			1.41455			0.707276	+	0.706938i	$0.249924\pi$
$282$		0			0
$283$	6.12739	−	10.6129i	0.364235	−	0.630874i	−0.624418	−	0.781091i	$-0.714664\pi$
$283$	6.12739	−	10.6129i	0.364235	−	0.630874i	0.988653	+	0.150216i	$0.0479970\pi$
$284$		0			0
$285$	−4.07465	+	2.35250i	−0.241362	+	0.139350i
$286$		0			0
$287$	−22.2301	+	11.3254i	−1.31220	+	0.668520i
$288$		0			0
$289$	−8.26434	−	14.3143i	−0.486138	−	0.842016i
$290$		0			0
$291$	9.41780	+	5.43737i	0.552081	+	0.318744i
$292$		0			0
$293$		−	10.7090i		−	0.625626i	−0.949815	−	0.312813i	$-0.898729\pi$
$293$		−	10.7090i		−	0.625626i	0.949815	−	0.312813i	$-0.101271\pi$
$294$		0			0
$295$		−	12.2259i		−	0.711821i
$296$		0			0
$297$	4.74861	+	2.74161i	0.275542	+	0.159084i
$298$		0			0
$299$	2.32741	+	4.03120i	0.134598	+	0.233130i
$300$		0			0
$301$	14.0842	−	7.17541i	0.811801	−	0.413584i
$302$		0			0
$303$	12.4972	−	7.21527i	0.717946	−	0.414506i
$304$		0			0
$305$	5.01711	−	8.68988i	0.287279	−	0.497581i
$306$		0			0
$307$	−4.22056			−0.240880			−0.120440	−	0.992721i	$-0.538431\pi$
$307$	−4.22056			−0.240880			−0.120440	+	0.992721i	$0.538431\pi$
$308$		0			0
$309$	15.0247			0.854725
$310$		0			0
$311$	−4.85070	+	8.40165i	−0.275058	+	0.476414i	−0.970150	−	0.242507i	$-0.922030\pi$
$311$	−4.85070	+	8.40165i	−0.275058	+	0.476414i	0.695092	+	0.718921i	$0.255364\pi$
$312$		0			0
$313$	11.8328	−	6.83168i	0.668831	−	0.386149i	−0.126803	−	0.991928i	$-0.540472\pi$
$313$	11.8328	−	6.83168i	0.668831	−	0.386149i	0.795633	+	0.605778i	$0.207138\pi$
$314$		0			0
$315$	−0.133565	+	2.54624i	−0.00752556	+	0.143464i
$316$		0			0
$317$	10.0442	+	17.3970i	0.564138	+	0.977115i	0.997129	+	0.0757171i	$0.0241246\pi$
$317$	10.0442	+	17.3970i	0.564138	+	0.977115i	−0.432992	+	0.901398i	$0.642542\pi$
$318$		0			0
$319$	11.7771	+	6.79948i	0.659388	+	0.380698i
$320$		0			0
$321$			12.1156i			0.676229i
$322$		0			0
$323$			3.35171i			0.186494i
$324$		0			0
$325$	−13.2259	−	7.63599i	−0.733642	−	0.423569i
$326$		0			0
$327$	−3.03563	−	5.25787i	−0.167871	−	0.290761i
$328$		0			0
$329$	−5.20959	+	8.02121i	−0.287214	+	0.442224i
$330$		0			0
$331$	−8.15886	+	4.71052i	−0.448452	+	0.258914i	−0.707176	−	0.707037i	$-0.750031\pi$
$331$	−8.15886	+	4.71052i	−0.448452	+	0.258914i	0.258724	+	0.965951i	$0.416698\pi$
$332$		0			0
$333$	−1.36643	+	2.36673i	−0.0748802	+	0.129696i
$334$		0			0
$335$	−9.09596			−0.496965
$336$		0			0
$337$	−13.4411			−0.732185			−0.366092	−	0.930578i	$-0.619305\pi$
$337$	−13.4411			−0.732185			−0.366092	+	0.930578i	$0.619305\pi$
$338$		0			0
$339$	3.68969	−	6.39074i	0.200397	−	0.347097i
$340$		0			0
$341$	22.9264	−	13.2365i	1.24153	−	0.716799i
$342$		0			0
$343$	−18.2918	−	2.89985i	−0.987666	−	0.156577i
$344$		0			0
$345$	−0.597935	−	1.03565i	−0.0321917	−	0.0557577i
$346$		0			0
$347$	19.5890	+	11.3097i	1.05159	+	0.607136i	0.923094	−	0.384574i	$-0.125651\pi$
$347$	19.5890	+	11.3097i	1.05159	+	0.607136i	0.128497	+	0.991710i	$0.458985\pi$
$348$		0			0
$349$		−	2.48180i		−	0.132848i	−0.997791	−	0.0664239i	$-0.978841\pi$
$349$		−	2.48180i		−	0.132848i	0.997791	−	0.0664239i	$-0.0211590\pi$
$350$		0			0
$351$			3.75117i			0.200223i
$352$		0			0
$353$	−7.89315	−	4.55711i	−0.420110	−	0.242551i	0.275014	−	0.961440i	$-0.411317\pi$
$353$	−7.89315	−	4.55711i	−0.420110	−	0.242551i	−0.695124	+	0.718889i	$0.744651\pi$
$354$		0			0
$355$	−4.87458	−	8.44303i	−0.258716	−	0.448109i
$356$		0			0
$357$	1.52328	+	0.989336i	0.0806207	+	0.0523612i
$358$		0			0
$359$	−6.00000	+	3.46410i	−0.316668	+	0.182828i	−0.649906	−	0.760014i	$-0.725192\pi$
$359$	−6.00000	+	3.46410i	−0.316668	+	0.182828i	0.333238	+	0.942843i	$0.391859\pi$
$360$		0			0
$361$	−2.41780	+	4.18776i	−0.127253	+	0.220408i
$362$		0			0
$363$	−19.0657			−1.00069
$364$		0			0
$365$	6.41917			0.335995
$366$		0			0
$367$	−1.91680	+	3.31999i	−0.100056	+	0.173302i	−0.911707	−	0.410840i	$-0.865235\pi$
$367$	−1.91680	+	3.31999i	−0.100056	+	0.173302i	0.811652	+	0.584142i	$0.198569\pi$
$368$		0			0
$369$	8.16641	−	4.71488i	0.425126	−	0.245447i
$370$		0			0
$371$	−10.8199	−	0.567567i	−0.561740	−	0.0294666i
$372$		0			0
$373$	−13.4150	−	23.2355i	−0.694603	−	1.20309i	−0.970314	−	0.241848i	$-0.922247\pi$
$373$	−13.4150	−	23.2355i	−0.694603	−	1.20309i	0.275711	−	0.961241i	$-0.411087\pi$
$374$		0			0
$375$	7.57086	+	4.37104i	0.390957	+	0.225719i
$376$		0			0
$377$			9.30330i			0.479144i
$378$		0			0
$379$		−	6.93692i		−	0.356325i	−0.984001	−	0.178163i	$-0.942985\pi$
$379$		−	6.93692i		−	0.356325i	0.984001	−	0.178163i	$-0.0570153\pi$
$380$		0			0
$381$	10.0832	+	5.82154i	0.516578	+	0.298247i
$382$		0			0
$383$	1.12881	+	1.95515i	0.0576793	+	0.0999035i	0.893423	−	0.449216i	$-0.148297\pi$
$383$	1.12881	+	1.95515i	0.0576793	+	0.0999035i	−0.835744	+	0.549119i	$0.814963\pi$
$384$		0			0
$385$	−6.34654	−	12.4573i	−0.323450	−	0.634881i
$386$		0			0
$387$	−5.17396	+	2.98718i	−0.263007	+	0.151847i
$388$		0			0
$389$	15.3047	−	26.5086i	0.775981	−	1.34404i	−0.158261	−	0.987397i	$-0.550589\pi$
$389$	15.3047	−	26.5086i	0.775981	−	1.34404i	0.934242	−	0.356641i	$-0.116078\pi$
$390$		0			0
$391$	−0.851904			−0.0430827
$392$		0			0
$393$	−9.26156			−0.467184
$394$		0			0
$395$	0.681544	−	1.18047i	0.0342922	−	0.0593958i
$396$		0			0
$397$	12.0368	−	6.94947i	0.604112	−	0.348784i	−0.166546	−	0.986034i	$-0.553261\pi$
$397$	12.0368	−	6.94947i	0.604112	−	0.348784i	0.770657	+	0.637250i	$0.219928\pi$
$398$		0			0
$399$	5.86365	+	11.5094i	0.293550	+	0.576192i
$400$		0			0
$401$	5.13832	+	8.89984i	0.256596	+	0.444437i	0.965328	−	0.261041i	$-0.0840658\pi$
$401$	5.13832	+	8.89984i	0.256596	+	0.444437i	−0.708732	+	0.705478i	$0.750732\pi$
$402$		0			0
$403$	15.6843	+	9.05535i	0.781292	+	0.451079i
$404$		0			0
$405$		−	0.963711i		−	0.0478872i
$406$		0			0
$407$		−	14.9849i		−	0.742775i
$408$		0			0
$409$	10.5342	+	6.08193i	0.520883	+	0.300732i	0.737296	−	0.675570i	$-0.236102\pi$
$409$	10.5342	+	6.08193i	0.520883	+	0.300732i	−0.216413	+	0.976302i	$0.569436\pi$
$410$		0			0
$411$	−3.61504	−	6.26144i	−0.178317	−	0.308854i
$412$		0			0
$413$	−33.5187	−	1.75826i	−1.64935	−	0.0865182i
$414$		0			0
$415$	−0.453838	+	0.262023i	−0.0222780	+	0.0128622i
$416$		0			0
$417$	2.65406	−	4.59697i	0.129970	−	0.225115i
$418$		0			0
$419$	−16.2245			−0.792619			−0.396310	−	0.918117i	$-0.629709\pi$
$419$	−16.2245			−0.792619			−0.396310	+	0.918117i	$0.629709\pi$
$420$		0			0
$421$	9.58477			0.467133			0.233567	−	0.972341i	$-0.424960\pi$
$421$	9.58477			0.467133			0.233567	+	0.972341i	$0.424960\pi$
$422$		0			0
$423$	1.80752	−	3.13072i	0.0878847	−	0.152221i
$424$		0			0
$425$	2.42055	−	1.39750i	0.117414	−	0.0677889i
$426$		0			0
$427$	−23.1027	−	15.0047i	−1.11802	−	0.726127i
$428$		0			0
$429$	−10.2842	−	17.8128i	−0.496528	−	0.860011i
$430$		0			0
$431$	−0.131544	−	0.0759470i	−0.00633626	−	0.00365824i	0.496829	−	0.867849i	$-0.334498\pi$
$431$	−0.131544	−	0.0759470i	−0.00633626	−	0.00365824i	−0.503165	+	0.864190i	$0.667831\pi$
$432$		0			0
$433$			9.46997i			0.455098i	0.973767	+	0.227549i	$0.0730711\pi$
$433$			9.46997i			0.455098i	−0.973767	+	0.227549i	$0.926929\pi$
$434$		0			0
$435$		−	2.39011i		−	0.114597i
$436$		0			0
$437$	−5.24663	−	3.02915i	−0.250981	−	0.144904i
$438$		0			0
$439$	−16.7373	−	28.9898i	−0.798826	−	1.38361i	−0.920381	−	0.391023i	$-0.872121\pi$
$439$	−16.7373	−	28.9898i	−0.798826	−	1.38361i	0.121555	−	0.992585i	$-0.461212\pi$
$440$		0			0
$441$	6.96158	+	0.732369i	0.331504	+	0.0348747i
$442$		0			0
$443$	22.6513	−	13.0777i	1.07619	−	0.621341i	0.146327	−	0.989236i	$-0.453255\pi$
$443$	22.6513	−	13.0777i	1.07619	−	0.621341i	0.929867	+	0.367895i	$0.119921\pi$
$444$		0			0
$445$	−0.267131	+	0.462684i	−0.0126632	+	0.0219333i
$446$		0			0
$447$	−4.66161			−0.220486
$448$		0			0
$449$	10.2918			0.485701			0.242851	−	0.970064i	$-0.421918\pi$
$449$	10.2918			0.485701			0.242851	+	0.970064i	$0.421918\pi$
$450$		0			0
$451$	−25.8527	+	44.7782i	−1.21736	+	2.10852i
$452$		0			0
$453$	−10.5709	+	6.10309i	−0.496662	+	0.286748i
$454$		0			0
$455$	5.20959	−	8.02121i	0.244229	−	0.376040i
$456$		0			0
$457$	−5.96574	−	10.3330i	−0.279065	−	0.483356i	0.692087	−	0.721814i	$-0.256691\pi$
$457$	−5.96574	−	10.3330i	−0.279065	−	0.483356i	−0.971153	+	0.238458i	$0.923358\pi$
$458$		0			0
$459$	−0.594545	−	0.343260i	−0.0277510	−	0.0160220i
$460$		0			0
$461$			30.0093i			1.39767i	0.715281	+	0.698837i	$0.246299\pi$
$461$			30.0093i			1.39767i	−0.715281	+	0.698837i	$0.753701\pi$
$462$		0			0
$463$		−	13.2736i		−	0.616875i	−0.951245	−	0.308437i	$-0.900194\pi$
$463$		−	13.2736i		−	0.616875i	0.951245	−	0.308437i	$-0.0998060\pi$
$464$		0			0
$465$	−4.02945	−	2.32641i	−0.186861	−	0.107885i
$466$		0			0
$467$	−14.8246	−	25.6770i	−0.686002	−	1.18819i	−0.973121	−	0.230295i	$-0.926031\pi$
$467$	−14.8246	−	25.6770i	−0.686002	−	1.18819i	0.287119	−	0.957895i	$-0.407303\pi$
$468$		0			0
$469$	−1.30812	+	24.9376i	−0.0604036	+	1.15151i
$470$		0			0
$471$	−18.9944	+	10.9664i	−0.875217	+	0.505307i
$472$		0			0
$473$	16.3794	−	28.3699i	0.753125	−	1.30445i
$474$		0			0
$475$	19.8766			0.912001
$476$		0			0
$477$	4.09515			0.187504
$478$		0			0
$479$	−5.76773	+	9.99001i	−0.263535	+	0.456455i	−0.967179	−	0.254097i	$-0.918222\pi$
$479$	−5.76773	+	9.99001i	−0.263535	+	0.456455i	0.703644	+	0.710553i	$0.251555\pi$
$480$		0			0
$481$	8.87802	−	5.12573i	0.404803	−	0.233713i
$482$		0			0
$483$	−2.92535	+	1.49036i	−0.133108	+	0.0678138i
$484$		0			0
$485$	5.24005	+	9.07604i	0.237939	+	0.412122i
$486$		0			0
$487$	−8.44822	−	4.87758i	−0.382825	−	0.221024i	0.296221	−	0.955119i	$-0.404273\pi$
$487$	−8.44822	−	4.87758i	−0.382825	−	0.221024i	−0.679047	+	0.734095i	$0.737607\pi$
$488$		0			0
$489$			4.01848i			0.181722i
$490$		0			0
$491$		−	40.4736i		−	1.82655i	−0.407346	−	0.913274i	$-0.633546\pi$
$491$		−	40.4736i		−	1.82655i	0.407346	−	0.913274i	$-0.366454\pi$
$492$		0			0
$493$	−1.47453	−	0.851323i	−0.0664097	−	0.0383416i
$494$		0			0
$495$	2.64212	+	4.57628i	0.118754	+	0.205689i
$496$		0			0
$497$	−23.8485	+	12.1500i	−1.06975	+	0.545001i
$498$		0			0
$499$	27.6827	−	15.9826i	1.23925	−	0.715480i	0.270307	−	0.962774i	$-0.412875\pi$
$499$	27.6827	−	15.9826i	1.23925	−	0.715480i	0.968941	+	0.247294i	$0.0795413\pi$
$500$		0			0
$501$	−7.35889	+	12.7460i	−0.328771	+	0.569448i
$502$		0			0
$503$	22.7110			1.01263			0.506317	−	0.862348i	$-0.331007\pi$
$503$	22.7110			1.01263			0.506317	+	0.862348i	$0.331007\pi$
$504$		0			0
$505$	13.9069			0.618847
$506$		0			0
$507$	0.535631	−	0.927740i	0.0237882	−	0.0412024i
$508$		0			0
$509$	1.98947	−	1.14862i	0.0881819	−	0.0509118i	−0.455261	−	0.890358i	$-0.650454\pi$
$509$	1.98947	−	1.14862i	0.0881819	−	0.0509118i	0.543443	+	0.839446i	$0.317121\pi$
$510$		0			0
$511$	0.923166	−	17.5989i	0.0408384	−	0.778528i
$512$		0			0
$513$	−2.44109	−	4.22809i	−0.107777	−	0.186675i
$514$		0			0
$515$	12.5396	+	7.23973i	0.552560	+	0.319021i
$516$		0			0
$517$			19.8221i			0.871773i
$518$		0			0
$519$			11.6530i			0.511508i
$520$		0			0
$521$	−32.5712	−	18.8050i	−1.42697	−	0.823862i	−0.430090	−	0.902786i	$-0.641518\pi$
$521$	−32.5712	−	18.8050i	−1.42697	−	0.823862i	−0.996881	+	0.0789240i	$0.974852\pi$
$522$		0			0
$523$	17.8444	+	30.9073i	0.780279	+	1.35148i	0.931779	+	0.363026i	$0.118256\pi$
$523$	17.8444	+	30.9073i	0.780279	+	1.35148i	−0.151500	+	0.988457i	$0.548410\pi$
$524$		0			0
$525$	5.86704	−	9.03350i	0.256059	−	0.394254i
$526$		0			0
$527$	−2.87047	+	1.65727i	−0.125040	+	0.0721917i
$528$		0			0
$529$	−10.7301	+	18.5850i	−0.466525	+	0.808046i
$530$		0			0
$531$	12.6863			0.550539
$532$		0			0
$533$	−35.3726			−1.53216
$534$		0			0
$535$	−5.83799	+	10.1117i	−0.252398	+	0.437167i
$536$		0			0
$537$	−2.24663	+	1.29709i	−0.0969494	+	0.0559738i
$538$		0			0
$539$	−35.0657	+	15.6082i	−1.51039	+	0.672293i
$540$		0			0
$541$	18.5102	+	32.0605i	0.795814	+	1.37839i	0.922321	+	0.386425i	$0.126290\pi$
$541$	18.5102	+	32.0605i	0.795814	+	1.37839i	−0.126507	+	0.991966i	$0.540377\pi$
$542$		0			0
$543$	8.25620	+	4.76672i	0.354307	+	0.204559i
$544$		0			0
$545$		−	5.85094i		−	0.250627i
$546$		0			0
$547$		−	2.09106i		−	0.0894073i	−0.999000	−	0.0447036i	$-0.985766\pi$
$547$		−	2.09106i		−	0.0894073i	0.999000	−	0.0447036i	$-0.0142344\pi$
$548$		0			0
$549$	9.01711	+	5.20603i	0.384841	+	0.222188i
$550$		0			0
$551$	−6.05415	−	10.4861i	−0.257916	−	0.446723i
$552$		0			0
$553$	−3.13837	−	2.03829i	−0.133457	−	0.0866771i
$554$		0			0
$555$	−2.28085	+	1.31685i	−0.0968166	+	0.0558971i
$556$		0			0
$557$	−8.39887	+	14.5473i	−0.355872	+	0.616388i	−0.987267	−	0.159073i	$-0.949149\pi$
$557$	−8.39887	+	14.5473i	−0.355872	+	0.616388i	0.631395	+	0.775461i	$0.282483\pi$
$558$		0			0
$559$	22.4109			0.947878
$560$		0			0
$561$	3.76434			0.158931
$562$		0			0
$563$	−8.69784	+	15.0651i	−0.366570	+	0.634918i	−0.989027	−	0.147736i	$-0.952801\pi$
$563$	−8.69784	+	15.0651i	−0.366570	+	0.634918i	0.622456	+	0.782654i	$0.286135\pi$
$564$		0			0
$565$	6.15882	−	3.55580i	0.259104	−	0.149594i
$566$		0			0
$567$	−2.64212	−	0.138595i	−0.110959	−	0.00582044i
$568$		0			0
$569$	17.1425	+	29.6917i	0.718652	+	1.24474i	0.961534	+	0.274686i	$0.0885739\pi$
$569$	17.1425	+	29.6917i	0.718652	+	1.24474i	−0.242882	+	0.970056i	$0.578093\pi$
$570$		0			0
$571$	−5.14176	−	2.96860i	−0.215176	−	0.124232i	0.388539	−	0.921432i	$-0.372980\pi$
$571$	−5.14176	−	2.96860i	−0.215176	−	0.124232i	−0.603715	+	0.797201i	$0.706313\pi$
$572$		0			0
$573$			8.33274i			0.348105i
$574$		0			0
$575$			5.05203i			0.210684i
$576$		0			0
$577$	33.7930	+	19.5104i	1.40682	+	0.812229i	0.995080	−	0.0990712i	$-0.0315871\pi$
$577$	33.7930	+	19.5104i	1.40682	+	0.812229i	0.411742	+	0.911300i	$0.364920\pi$
$578$		0			0
$579$	6.18630	+	10.7150i	0.257094	+	0.445300i
$580$		0			0
$581$	0.653097	+	1.28193i	0.0270950	+	0.0531833i
$582$		0			0
$583$	−19.4462	+	11.2273i	−0.805381	+	0.464987i
$584$		0			0
$585$	−1.80752	+	3.13072i	−0.0747318	+	0.129439i
$586$		0			0
$587$	7.71931			0.318610			0.159305	−	0.987229i	$-0.449075\pi$
$587$	7.71931			0.318610			0.159305	+	0.987229i	$0.449075\pi$
$588$		0			0
$589$	−23.5712			−0.971235
$590$		0			0
$591$	1.61843	−	2.80321i	0.0665734	−	0.115308i
$592$		0			0
$593$	0.336377	−	0.194207i	0.0138133	−	0.00797513i	−0.493077	−	0.869985i	$-0.664128\pi$
$593$	0.336377	−	0.194207i	0.0138133	−	0.00797513i	0.506891	+	0.862010i	$0.330795\pi$
$594$		0			0
$595$	0.794612	+	1.55970i	0.0325759	+	0.0639415i
$596$		0			0
$597$	−9.61504	−	16.6537i	−0.393517	−	0.681592i
$598$		0			0
$599$	18.0000	+	10.3923i	0.735460	+	0.424618i	0.820416	−	0.571767i	$-0.193742\pi$
$599$	18.0000	+	10.3923i	0.735460	+	0.424618i	−0.0849563	+	0.996385i	$0.527075\pi$
$600$		0			0
$601$			26.4110i			1.07733i	0.842521	+	0.538664i	$0.181071\pi$
$601$			26.4110i			1.07733i	−0.842521	+	0.538664i	$0.818929\pi$
$602$		0			0
$603$		−	9.43847i		−	0.384364i
$604$		0			0
$605$	−15.9122	−	9.18691i	−0.646922	−	0.373501i
$606$		0			0
$607$	20.3531	+	35.2526i	0.826106	+	1.43086i	0.901071	+	0.433671i	$0.142782\pi$
$607$	20.3531	+	35.2526i	0.826106	+	1.43086i	−0.0749655	+	0.997186i	$0.523885\pi$
$608$		0			0
$609$	−6.55274	−	0.343730i	−0.265530	−	0.0139287i
$610$		0			0
$611$	−11.7438	+	6.78031i	−0.475105	+	0.274302i
$612$		0			0
$613$	8.66920	−	15.0155i	0.350146	−	0.606470i	−0.636129	−	0.771583i	$-0.719465\pi$
$613$	8.66920	−	15.0155i	0.350146	−	0.606470i	0.986275	+	0.165113i	$0.0527988\pi$
$614$		0			0
$615$	9.08756			0.366446
$616$		0			0
$617$	−46.4753			−1.87103			−0.935513	−	0.353291i	$-0.885062\pi$
$617$	−46.4753			−1.87103			−0.935513	+	0.353291i	$0.885062\pi$
$618$		0			0
$619$	−13.1911	+	22.8476i	−0.530194	+	0.918322i	0.469186	+	0.883099i	$0.344547\pi$
$619$	−13.1911	+	22.8476i	−0.530194	+	0.918322i	−0.999379	+	0.0352227i	$0.988786\pi$
$620$		0			0
$621$	1.07465	−	0.620450i	0.0431243	−	0.0248978i
$622$		0			0
$623$	1.23008	+	0.798909i	0.0492822	+	0.0320076i
$624$		0			0
$625$	−5.96574	−	10.3330i	−0.238630	−	0.413318i
$626$		0			0
$627$	23.1835	+	13.3850i	0.925860	+	0.534546i
$628$		0			0
$629$			1.87617i			0.0748079i
$630$		0			0
$631$			41.0696i			1.63495i	0.575961	+	0.817477i	$0.304628\pi$
$631$			41.0696i			1.63495i	−0.575961	+	0.817477i	$0.695372\pi$
$632$		0			0
$633$	8.00759	+	4.62318i	0.318273	+	0.183755i
$634$		0			0
$635$	5.61028	+	9.71729i	0.222637	+	0.385619i
$636$		0			0
$637$	−21.2418	−	15.4362i	−0.841632	−	0.611605i
$638$		0			0
$639$	8.76095	−	5.05814i	0.346578	−	0.200097i
$640$		0			0
$641$	−22.7239	+	39.3590i	−0.897540	+	1.55459i	−0.0669115	+	0.997759i	$0.521315\pi$
$641$	−22.7239	+	39.3590i	−0.897540	+	1.55459i	−0.830629	+	0.556827i	$0.812019\pi$
$642$		0			0
$643$	30.5534			1.20491			0.602454	−	0.798154i	$-0.294190\pi$
$643$	30.5534			1.20491			0.602454	+	0.798154i	$0.294190\pi$
$644$		0			0
$645$	−5.75756			−0.226704
$646$		0			0
$647$	18.0896	−	31.3321i	0.711175	−	1.23179i	−0.253242	−	0.967403i	$-0.581497\pi$
$647$	18.0896	−	31.3321i	0.711175	−	1.23179i	0.964417	−	0.264388i	$-0.0851698\pi$
$648$		0			0
$649$	−60.2423	+	34.7809i	−2.36472	+	1.36527i
$650$		0			0
$651$	−6.95759	+	10.7126i	−0.272689	+	0.419861i
$652$		0			0
$653$	−4.11545	−	7.12816i	−0.161050	−	0.278946i	0.774196	−	0.632946i	$-0.218155\pi$
$653$	−4.11545	−	7.12816i	−0.161050	−	0.278946i	−0.935245	+	0.354000i	$0.884821\pi$
$654$		0			0
$655$	−7.72968	−	4.46273i	−0.302024	−	0.174373i
$656$		0			0
$657$			6.66089i			0.259866i
$658$		0			0
$659$		−	22.8837i		−	0.891422i	−0.895177	−	0.445711i	$-0.852951\pi$
$659$		−	22.8837i		−	0.891422i	0.895177	−	0.445711i	$-0.147049\pi$
$660$		0			0
$661$	17.7212	+	10.2313i	0.689275	+	0.397953i	0.803340	−	0.595520i	$-0.203054\pi$
$661$	17.7212	+	10.2313i	0.689275	+	0.397953i	−0.114065	+	0.993473i	$0.536387\pi$
$662$		0			0
$663$	1.28763	+	2.23024i	0.0500073	+	0.0866152i
$664$		0			0
$665$	−0.652090	+	12.4312i	−0.0252870	+	0.482060i
$666$		0			0
$667$	2.66525	−	1.53878i	0.103199	−	0.0595819i
$668$		0			0
$669$	−0.972923	+	1.68515i	−0.0376154	+	0.0651517i
$670$		0			0
$671$	−57.0916			−2.20400
$672$		0			0
$673$	4.23008			0.163058			0.0815289	−	0.996671i	$-0.474020\pi$
$673$	4.23008			0.163058			0.0815289	+	0.996671i	$0.474020\pi$
$674$		0			0
$675$	−2.03563	+	3.52582i	−0.0783515	+	0.135709i
$676$		0			0
$677$	−20.7962	+	12.0067i	−0.799262	+	0.461454i	−0.843213	−	0.537580i	$-0.819339\pi$
$677$	−20.7962	+	12.0067i	−0.799262	+	0.461454i	0.0439511	+	0.999034i	$0.486005\pi$
$678$		0			0
$679$	25.6365	−	13.0609i	0.983840	−	0.501232i
$680$		0			0
$681$	−4.32265	−	7.48706i	−0.165644	−	0.286905i
$682$		0			0
$683$	7.09951	+	4.09890i	0.271655	+	0.156840i	0.629640	−	0.776887i	$-0.283203\pi$
$683$	7.09951	+	4.09890i	0.271655	+	0.156840i	−0.357984	+	0.933728i	$0.616536\pi$
$684$		0			0
$685$		−	6.96771i		−	0.266222i
$686$		0			0
$687$		−	16.7889i		−	0.640537i
$688$		0			0
$689$	−13.3035	−	7.68079i	−0.506824	−	0.292615i
$690$		0			0
$691$	−17.9925	−	31.1638i	−0.684465	−	1.18553i	−0.973605	−	0.228242i	$-0.926702\pi$
$691$	−17.9925	−	31.1638i	−0.684465	−	1.18553i	0.289139	−	0.957287i	$-0.406631\pi$
$692$		0			0
$693$	12.9264	−	6.58552i	0.491032	−	0.250163i
$694$		0			0
$695$	4.43015	−	2.55775i	0.168045	−	0.0970209i
$696$		0			0
$697$	3.23686	−	5.60641i	0.122605	−	0.212358i
$698$		0			0
$699$	−1.04657			−0.0395848
$700$		0			0
$701$	12.9471			0.489003			0.244502	−	0.969649i	$-0.421376\pi$
$701$	12.9471			0.489003			0.244502	+	0.969649i	$0.421376\pi$
$702$		0			0
$703$	−6.67117	+	11.5548i	−0.251608	+	0.435798i
$704$		0			0
$705$	3.01711	−	1.74193i	0.113631	−	0.0656048i
$706$		0			0
$707$	2.00000	−	38.1272i	0.0752177	−	1.43392i
$708$		0			0
$709$	6.65603	+	11.5286i	0.249973	+	0.432965i	0.963518	−	0.267644i	$-0.0862450\pi$
$709$	6.65603	+	11.5286i	0.249973	+	0.432965i	−0.713545	+	0.700609i	$0.752912\pi$
$710$		0			0
$711$	1.22492	+	0.707208i	0.0459381	+	0.0265224i
$712$		0			0
$713$		−	5.99109i		−	0.224368i
$714$		0			0
$715$		−	19.8221i		−	0.741303i
$716$		0			0
$717$	16.6692	+	9.62396i	0.622523	+	0.359414i
$718$		0			0
$719$	−23.7520	−	41.1397i	−0.885800	−	1.53425i	−0.844794	−	0.535091i	$-0.820277\pi$
$719$	−23.7520	−	41.1397i	−0.885800	−	1.53425i	−0.0410056	−	0.999159i	$-0.513056\pi$
$720$		0			0
$721$	21.6519	−	33.3375i	0.806358	−	1.24155i
$722$		0			0
$723$	2.38754	−	1.37844i	0.0887934	−	0.0512649i
$724$		0			0
$725$	−5.04858	+	8.74440i	−0.187500	+	0.324759i
$726$		0			0
$727$	24.3567			0.903340			0.451670	−	0.892185i	$-0.350828\pi$
$727$	24.3567			0.903340			0.451670	+	0.892185i	$0.350828\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	−2.05076	+	3.55203i	−0.0758503	+	0.131377i
$732$		0			0
$733$	−3.35812	+	1.93881i	−0.124035	+	0.0716117i	−0.560734	−	0.827996i	$-0.689481\pi$
$733$	−3.35812	+	1.93881i	−0.124035	+	0.0716117i	0.436699	+	0.899608i	$0.356148\pi$
$734$		0			0
$735$	5.45723	+	3.96571i	0.201293	+	0.146277i
$736$		0			0
$737$	25.8766	+	44.8196i	0.953177	+	1.65095i
$738$		0			0
$739$	7.46497	+	4.30990i	0.274603	+	0.158542i	0.630978	−	0.775801i	$-0.282654\pi$
$739$	7.46497	+	4.30990i	0.274603	+	0.158542i	−0.356374	+	0.934343i	$0.615987\pi$
$740$		0			0
$741$			18.3138i			0.672776i
$742$		0			0
$743$		−	6.12929i		−	0.224862i	−0.993660	−	0.112431i	$-0.964136\pi$
$743$		−	6.12929i		−	0.224862i	0.993660	−	0.112431i	$-0.0358637\pi$
$744$		0			0
$745$	−3.89057	−	2.24622i	−0.142539	−	0.0822952i
$746$		0			0
$747$	−0.271890	−	0.470927i	−0.00994793	−	0.0172303i
$748$		0			0
$749$	26.8827	+	17.4597i	0.982273	+	0.637963i
$750$		0			0
$751$	30.7146	−	17.7331i	1.12079	−	0.647090i	0.179190	−	0.983815i	$-0.442652\pi$
$751$	30.7146	−	17.7331i	1.12079	−	0.647090i	0.941603	+	0.336725i	$0.109319\pi$
$752$		0			0
$753$	−10.3746	+	17.9694i	−0.378072	+	0.654841i
$754$		0			0
$755$	−11.7632			−0.428108
$756$		0			0
$757$	−29.4204			−1.06930			−0.534651	−	0.845073i	$-0.679557\pi$
$757$	−29.4204			−1.06930			−0.534651	+	0.845073i	$0.679557\pi$
$758$		0			0
$759$	−3.40207	+	5.89255i	−0.123487	+	0.213886i
$760$		0			0
$761$	43.5568	−	25.1475i	1.57893	−	0.911597i	0.583923	−	0.811809i	$-0.301517\pi$
$761$	43.5568	−	25.1475i	1.57893	−	0.911597i	0.995009	−	0.0997877i	$-0.0318164\pi$
$762$		0			0
$763$	−16.0410	−	0.841446i	−0.580723	−	0.0304624i
$764$		0			0
$765$	−0.330804	−	0.572969i	−0.0119602	−	0.0207157i
$766$		0			0
$767$	−41.2128	−	23.7942i	−1.48811	−	0.859160i
$768$		0			0
$769$			20.2817i			0.731377i	0.930737	+	0.365689i	$0.119167\pi$
$769$			20.2817i			0.731377i	−0.930737	+	0.365689i	$0.880833\pi$
$770$		0			0
$771$			7.45109i			0.268344i
$772$		0			0
$773$	18.8149	+	10.8628i	0.676723	+	0.390706i	0.798619	−	0.601836i	$-0.205564\pi$
$773$	18.8149	+	10.8628i	0.676723	+	0.390706i	−0.121896	+	0.992543i	$0.538897\pi$
$774$		0			0
$775$	9.82806	+	17.0227i	0.353034	+	0.611473i
$776$		0			0
$777$	3.28226	+	6.44257i	0.117751	+	0.231126i
$778$		0			0
$779$	39.8698	−	23.0189i	1.42848	−	0.824736i
$780$		0			0
$781$	−27.7349	+	48.0382i	−0.992432	+	1.71894i
$782$		0			0
$783$	2.48011			0.0886318
$784$		0			0
$785$	−21.1369			−0.754410
$786$		0			0
$787$	−0.299328	+	0.518452i	−0.0106699	+	0.0184808i	−0.871311	−	0.490731i	$-0.836730\pi$
$787$	−0.299328	+	0.518452i	−0.0106699	+	0.0184808i	0.860641	+	0.509212i	$0.170063\pi$
$788$		0			0
$789$	−25.7034	+	14.8399i	−0.915066	+	0.528313i
$790$		0			0
$791$	−8.86288	−	17.3965i	−0.315128	−	0.618547i
$792$		0			0
$793$	−19.5287	−	33.8247i	−0.693484	−	1.20115i
$794$		0			0
$795$	3.41780	+	1.97327i	0.121217	+	0.0699847i
$796$		0			0
$797$		−	36.1789i		−	1.28152i	−0.767741	−	0.640760i	$-0.778619\pi$
$797$		−	36.1789i		−	1.28152i	0.767741	−	0.640760i	$-0.221381\pi$
$798$		0			0
$799$		−	2.48180i		−	0.0877998i
$800$		0			0
$801$	−0.480107	−	0.277190i	−0.0169637	−	0.00979402i
$802$		0			0
$803$	−18.2616	−	31.6299i	−0.644436	−	1.11620i
$804$		0			0
$805$	−3.15963	−	0.165741i	−0.111362	−	0.00584162i
$806$		0			0
$807$	−3.73727	+	2.15771i	−0.131558	+	0.0759551i
$808$		0			0
$809$	15.0603	−	26.0852i	0.529491	−	0.917106i	−0.469917	−	0.882711i	$-0.655716\pi$
$809$	15.0603	−	26.0852i	0.529491	−	0.917106i	0.999408	−	0.0343953i	$-0.0109505\pi$
$810$		0			0
$811$	−21.5947			−0.758292			−0.379146	−	0.925337i	$-0.623782\pi$
$811$	−21.5947			−0.758292			−0.379146	+	0.925337i	$0.623782\pi$
$812$		0			0
$813$	−13.5828			−0.476371
$814$		0			0
$815$	−1.93633	+	3.35382i	−0.0678266	+	0.117479i
$816$		0			0
$817$	−25.2601	+	14.5839i	−0.883740	+	0.510228i
$818$		0			0
$819$	8.32326	+	5.40576i	0.290838	+	0.188892i
$820$		0			0
$821$	25.1264	+	43.5202i	0.876918	+	1.51887i	0.854705	+	0.519114i	$0.173738\pi$
$821$	25.1264	+	43.5202i	0.876918	+	1.51887i	0.0222131	+	0.999753i	$0.492929\pi$
$822$		0			0
$823$	2.87338	+	1.65894i	0.100160	+	0.0578272i	0.549243	−	0.835663i	$-0.314916\pi$
$823$	2.87338	+	1.65894i	0.100160	+	0.0578272i	−0.449084	+	0.893490i	$0.648249\pi$
$824$		0			0
$825$		−	22.3236i		−	0.777209i
$826$		0			0
$827$			29.3948i			1.02216i	0.859534	+	0.511078i	$0.170754\pi$
$827$			29.3948i			1.02216i	−0.859534	+	0.511078i	$0.829246\pi$
$828$		0			0
$829$	−28.2980	−	16.3379i	−0.982830	−	0.567437i	−0.0797067	−	0.996818i	$-0.525398\pi$
$829$	−28.2980	−	16.3379i	−0.982830	−	0.567437i	−0.903123	+	0.429381i	$0.858732\pi$
$830$		0			0
$831$	1.03563	+	1.79376i	0.0359256	+	0.0622250i
$832$		0			0
$833$	4.39036	−	1.95421i	0.152117	−	0.0677094i
$834$		0			0
$835$	−12.2834	+	7.09184i	−0.425086	+	0.245423i
$836$		0			0
$837$	2.41401	−	4.18119i	0.0834403	−	0.144523i
$838$		0			0
$839$	8.66161			0.299032			0.149516	−	0.988759i	$-0.452228\pi$
$839$	8.66161			0.299032			0.149516	+	0.988759i	$0.452228\pi$
$840$		0			0
$841$	−22.8491			−0.787899
$842$		0			0
$843$	−11.8561	+	20.5354i	−0.408346	+	0.707276i
$844$		0			0
$845$	0.894073	−	0.516193i	0.0307570	−	0.0177576i
$846$		0			0
$847$	−27.4753	+	42.3038i	−0.944062	+	1.45358i
$848$		0			0
$849$	6.12739	+	10.6129i	0.210291	+	0.364235i
$850$		0			0
$851$	−2.93688	−	1.69561i	−0.100675	−	0.0581248i
$852$		0			0
$853$			7.17809i			0.245773i	0.992421	+	0.122887i	$0.0392151\pi$
$853$			7.17809i			0.245773i	−0.992421	+	0.122887i	$0.960785\pi$
$854$		0			0
$855$		−	4.70500i		−	0.160908i
$856$		0			0
$857$	39.5334	+	22.8246i	1.35044	+	0.779675i	0.988311	−	0.152454i	$-0.0487176\pi$
$857$	39.5334	+	22.8246i	1.35044	+	0.779675i	0.362126	+	0.932129i	$0.382051\pi$
$858$		0			0
$859$	6.77944	+	11.7423i	0.231311	+	0.400643i	0.958194	−	0.286118i	$-0.0923651\pi$
$859$	6.77944	+	11.7423i	0.231311	+	0.400643i	−0.726883	+	0.686761i	$0.759032\pi$
$860$		0			0
$861$	1.30692	−	24.9145i	0.0445396	−	0.849085i
$862$		0			0
$863$	36.0550	−	20.8163i	1.22733	−	0.708597i	0.260856	−	0.965378i	$-0.415995\pi$
$863$	36.0550	−	20.8163i	1.22733	−	0.708597i	0.966470	+	0.256781i	$0.0826620\pi$
$864$		0			0
$865$	−5.61504	+	9.72554i	−0.190917	+	0.330678i
$866$		0			0
$867$	16.5287			0.561344
$868$		0			0
$869$	−7.75555			−0.263089
$870$		0			0
$871$	−17.7026	+	30.6619i	−0.599831	+	1.03894i
$872$		0			0
$873$	−9.41780	+	5.43737i	−0.318744	+	0.184027i
$874$		0			0
$875$	20.6089	−	10.4995i	0.696708	−	0.354948i
$876$		0			0
$877$	−9.84239	−	17.0475i	−0.332354	−	0.575654i	0.650619	−	0.759404i	$-0.274509\pi$
$877$	−9.84239	−	17.0475i	−0.332354	−	0.575654i	−0.982973	+	0.183751i	$0.941176\pi$
$878$		0			0
$879$	9.27427	+	5.35450i	0.312813	+	0.180603i
$880$		0			0
$881$			7.24606i			0.244126i	0.992522	+	0.122063i	$0.0389510\pi$
$881$			7.24606i			0.244126i	−0.992522	+	0.122063i	$0.961049\pi$
$882$		0			0
$883$			35.4533i			1.19310i	0.802577	+	0.596549i	$0.203462\pi$
$883$			35.4533i			1.19310i	−0.802577	+	0.596549i	$0.796538\pi$
$884$		0			0
$885$	10.5880	+	6.11296i	0.355911	+	0.205485i
$886$		0			0
$887$	8.98684	+	15.5657i	0.301749	+	0.522644i	0.976532	−	0.215372i	$-0.0690964\pi$
$887$	8.98684	+	15.5657i	0.301749	+	0.522644i	−0.674784	+	0.738016i	$0.735763\pi$
$888$		0			0
$889$	27.4479	−	13.9837i	0.920572	−	0.468999i
$890$		0			0
$891$	−4.74861	+	2.74161i	−0.159084	+	0.0918474i
$892$		0			0
$893$	8.82463	−	15.2847i	0.295305	−	0.511483i
$894$		0			0
$895$	−2.50005			−0.0835674
$896$		0			0
$897$	−4.65483			−0.155420
$898$		0			0
$899$	5.98700	−	10.3698i	0.199678	−	0.345852i
$900$		0			0
$901$	2.43475	−	1.40570i	0.0811132	−	0.0468307i
$902$		0			0
$903$	−0.828017	+	15.7850i	−0.0275547	+	0.525292i
$904$		0			0
$905$	4.59374	+	7.95658i	0.152701	+	0.264486i
$906$		0			0
$907$	7.60870	+	4.39289i	0.252643	+	0.145863i	0.620974	−	0.783831i	$-0.286737\pi$
$907$	7.60870	+	4.39289i	0.252643	+	0.145863i	−0.368331	+	0.929695i	$0.620071\pi$
$908$		0			0
$909$			14.4305i			0.478631i
$910$		0			0
$911$		−	21.5478i		−	0.713911i	−0.934121	−	0.356955i	$-0.883815\pi$
$911$		−	21.5478i		−	0.713911i	0.934121	−	0.356955i	$-0.116185\pi$
$912$		0			0
$913$	2.58220	+	1.49083i	0.0854582	+	0.0493393i
$914$		0			0
$915$	5.01711	+	8.68988i	0.165860	+	0.287279i
$916$		0			0
$917$	−13.3467	+	20.5500i	−0.440747	+	0.678619i
$918$		0			0
$919$	−27.5939	+	15.9314i	−0.910240	+	0.525527i	−0.880508	−	0.474031i	$-0.842799\pi$
$919$	−27.5939	+	15.9314i	−0.910240	+	0.525527i	−0.0297316	+	0.999558i	$0.509465\pi$
$920$		0			0
$921$	2.11028	−	3.65512i	0.0695362	−	0.120440i
$922$		0			0
$923$	−37.9479			−1.24907
$924$		0			0
$925$	11.1262			0.365828
$926$		0			0
$927$	−7.51235	+	13.0118i	−0.246738	+	0.427363i
$928$		0			0
$929$	44.1750	−	25.5044i	1.44933	−	0.836773i	0.450892	−	0.892579i	$-0.351106\pi$
$929$	44.1750	−	25.5044i	1.44933	−	0.836773i	0.998442	+	0.0558058i	$0.0177728\pi$
$930$		0			0
$931$	33.9876	+	3.57555i	1.11390	+	0.117184i
$932$		0			0
$933$	−4.85070	−	8.40165i	−0.158805	−	0.275058i
$934$		0			0
$935$	3.14171	+	1.81387i	0.102745	+	0.0593199i
$936$		0			0
$937$			2.65742i			0.0868141i	0.999057	+	0.0434071i	$0.0138212\pi$
$937$			2.65742i			0.0868141i	−0.999057	+	0.0434071i	$0.986179\pi$
$938$		0			0
$939$			13.6634i			0.445887i
$940$		0			0
$941$	−26.2920	−	15.1797i	−0.857096	−	0.494844i	0.00594304	−	0.999982i	$-0.498108\pi$
$941$	−26.2920	−	15.1797i	−0.857096	−	0.494844i	−0.863039	+	0.505138i	$0.831442\pi$
$942$		0			0
$943$	5.85070	+	10.1337i	0.190525	+	0.329999i
$944$		0			0
$945$	−2.13832	−	1.38879i	−0.0695597	−	0.0451774i
$946$		0			0
$947$	−37.6505	+	21.7375i	−1.22348	+	0.706374i	−0.965657	−	0.259819i	$-0.916337\pi$
$947$	−37.6505	+	21.7375i	−1.22348	+	0.706374i	−0.257818	+	0.966193i	$0.583004\pi$
$948$		0			0
$949$	12.4931	−	21.6386i	0.405542	−	0.702419i
$950$		0			0
$951$	−20.0884			−0.651410
$952$		0			0
$953$	−53.8683			−1.74497			−0.872483	−	0.488645i	$-0.837491\pi$
$953$	−53.8683			−1.74497			−0.872483	+	0.488645i	$0.837491\pi$
$954$		0			0
$955$	−4.01518	+	6.95449i	−0.129928	+	0.225042i
$956$		0			0
$957$	−11.7771	+	6.79948i	−0.380698	+	0.219796i
$958$		0			0
$959$	−19.1027	−	1.00205i	−0.616860	−	0.0323580i
$960$		0			0
$961$	3.84512	+	6.65995i	0.124036	+	0.214837i
$962$		0			0
$963$	−10.4925	−	6.05782i	−0.338115	−	0.195211i
$964$		0			0
$965$			11.9236i			0.383835i
$966$		0			0
$967$		−	44.9529i		−	1.44559i	−0.691064	−	0.722794i	$-0.742858\pi$
$967$		−	44.9529i		−	1.44559i	0.691064	−	0.722794i	$-0.257142\pi$
$968$		0			0
$969$	−2.90267	−	1.67586i	−0.0932472	−	0.0538363i
$970$		0			0
$971$	−0.641758	−	1.11156i	−0.0205950	−	0.0356716i	0.855544	−	0.517730i	$-0.173223\pi$
$971$	−0.641758	−	1.11156i	−0.0205950	−	0.0356716i	−0.876139	+	0.482058i	$0.839889\pi$
$972$		0			0
$973$	−6.37523	−	12.5136i	−0.204381	−	0.401167i
$974$		0			0
$975$	13.2259	−	7.63599i	0.423569	−	0.244547i
$976$		0			0
$977$	−9.67678	+	16.7607i	−0.309588	+	0.536222i	−0.978272	−	0.207325i	$-0.933524\pi$
$977$	−9.67678	+	16.7607i	−0.309588	+	0.536222i	0.668684	+	0.743546i	$0.266858\pi$
$978$		0			0
$979$	3.03979			0.0971520
$980$		0			0
$981$	6.07126			0.193840
$982$		0			0
$983$	−4.21637	+	7.30296i	−0.134481	+	0.232928i	−0.925399	−	0.378994i	$-0.876270\pi$
$983$	−4.21637	+	7.30296i	−0.134481	+	0.232928i	0.790918	+	0.611922i	$0.209603\pi$
$984$		0			0
$985$	2.70148	−	1.55970i	0.0860763	−	0.0496962i
$986$		0			0
$987$	−4.34178	−	8.52224i	−0.138200	−	0.271266i
$988$		0			0
$989$	−3.70680	−	6.42036i	−0.117869	−	0.204156i
$990$		0			0
$991$	21.1967	+	12.2379i	0.673334	+	0.388750i	0.797339	−	0.603532i	$-0.206240\pi$
$991$	21.1967	+	12.2379i	0.673334	+	0.388750i	−0.124005	+	0.992282i	$0.539574\pi$
$992$		0			0
$993$		−	9.42104i		−	0.298968i
$994$		0			0
$995$		−	18.5322i		−	0.587511i
$996$		0			0
$997$	29.0273	+	16.7589i	0.919304	+	0.530761i	0.883413	−	0.468595i	$-0.155240\pi$
$997$	29.0273	+	16.7589i	0.919304	+	0.530761i	0.0358914	+	0.999356i	$0.488573\pi$
$998$		0			0
$999$	−1.36643	−	2.36673i	−0.0432321	−	0.0748802i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1344.2.bl.i.703.2		8
4.3	odd	2		1344.2.bl.j.703.2		8
7.5	odd	6		1344.2.bl.j.1279.2		8
8.3	odd	2		84.2.o.a.31.3	yes	8
8.5	even	2		84.2.o.b.31.3	yes	8
24.5	odd	2		252.2.bf.f.199.2		8
24.11	even	2		252.2.bf.g.199.2		8
28.19	even	6	inner	1344.2.bl.i.1279.2		8
56.3	even	6		588.2.b.a.391.2		8
56.5	odd	6		84.2.o.a.19.3	✓	8
56.11	odd	6		588.2.b.b.391.2		8
56.13	odd	2		588.2.o.b.31.3		8
56.19	even	6		84.2.o.b.19.3	yes	8
56.27	even	2		588.2.o.d.31.3		8
56.37	even	6		588.2.o.d.19.3		8
56.45	odd	6		588.2.b.b.391.1		8
56.51	odd	6		588.2.o.b.19.3		8
56.53	even	6		588.2.b.a.391.1		8
168.5	even	6		252.2.bf.g.19.2		8
168.11	even	6		1764.2.b.i.1567.7		8
168.53	odd	6		1764.2.b.j.1567.8		8
168.59	odd	6		1764.2.b.j.1567.7		8
168.101	even	6		1764.2.b.i.1567.8		8
168.131	odd	6		252.2.bf.f.19.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.2.o.a.19.3	✓	8	56.5	odd	6
84.2.o.a.31.3	yes	8	8.3	odd	2
84.2.o.b.19.3	yes	8	56.19	even	6
84.2.o.b.31.3	yes	8	8.5	even	2
252.2.bf.f.19.2		8	168.131	odd	6
252.2.bf.f.199.2		8	24.5	odd	2
252.2.bf.g.19.2		8	168.5	even	6
252.2.bf.g.199.2		8	24.11	even	2
588.2.b.a.391.1		8	56.53	even	6
588.2.b.a.391.2		8	56.3	even	6
588.2.b.b.391.1		8	56.45	odd	6
588.2.b.b.391.2		8	56.11	odd	6
588.2.o.b.19.3		8	56.51	odd	6
588.2.o.b.31.3		8	56.13	odd	2
588.2.o.d.19.3		8	56.37	even	6
588.2.o.d.31.3		8	56.27	even	2
1344.2.bl.i.703.2		8	1.1	even	1	trivial
1344.2.bl.i.1279.2		8	28.19	even	6	inner
1344.2.bl.j.703.2		8	4.3	odd	2
1344.2.bl.j.1279.2		8	7.5	odd	6
1764.2.b.i.1567.7		8	168.11	even	6
1764.2.b.i.1567.8		8	168.101	even	6
1764.2.b.j.1567.7		8	168.59	odd	6
1764.2.b.j.1567.8		8	168.53	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:	\( N \)	\(=\)	\( 1344 = 2^{6} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1344.bl (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{3} +(-0.834598 + 0.481855i) q^{5} +(1.20103 + 2.35744i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{3} +(-0.834598 + 0.481855i) q^{5} +(1.20103 + 2.35744i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(4.74861 + 2.74161i) q^{11} +3.75117i q^{13} -0.963711i q^{15} +(-0.594545 - 0.343260i) q^{17} +(-2.44109 - 4.22809i) q^{19} +(-2.64212 - 0.138595i) q^{21} +(1.07465 - 0.620450i) q^{23} +(-2.03563 + 3.52582i) q^{25} +1.00000 q^{27} +2.48011 q^{29} +(2.41401 - 4.18119i) q^{31} +(-4.74861 + 2.74161i) q^{33} +(-2.13832 - 1.38879i) q^{35} +(-1.36643 - 2.36673i) q^{37} +(-3.24861 - 1.87558i) q^{39} +9.42976i q^{41} -5.97437i q^{43} +(0.834598 + 0.481855i) q^{45} +(1.80752 + 3.13072i) q^{47} +(-4.11504 + 5.66272i) q^{49} +(0.594545 - 0.343260i) q^{51} +(-2.04757 + 3.54650i) q^{53} -5.28424 q^{55} +4.88217 q^{57} +(-6.34315 + 10.9867i) q^{59} +(-9.01711 + 5.20603i) q^{61} +(1.44109 - 2.21884i) q^{63} +(-1.80752 - 3.13072i) q^{65} +(8.17396 + 4.71924i) q^{67} +1.24090i q^{69} +10.1163i q^{71} +(-5.76850 - 3.33044i) q^{73} +(-2.03563 - 3.52582i) q^{75} +(-0.759946 + 14.4873i) q^{77} +(-1.22492 + 0.707208i) q^{79} +(-0.500000 + 0.866025i) q^{81} +0.543780 q^{83} +0.661608 q^{85} +(-1.24005 + 2.14784i) q^{87} +(0.480107 - 0.277190i) q^{89} +(-8.84315 + 4.50528i) q^{91} +(2.41401 + 4.18119i) q^{93} +(4.07465 + 2.35250i) q^{95} -10.8747i q^{97} -5.48322i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{3} - 2 q^{7} - 4 q^{9}+O(q^{10}) \) 8 * q - 4 * q^3 - 2 * q^7 - 4 * q^9	\( 8 q - 4 q^{3} - 2 q^{7} - 4 q^{9} + 6 q^{11} - 6 q^{19} + 4 q^{21} + 2 q^{25} + 8 q^{27} + 16 q^{29} - 6 q^{31} - 6 q^{33} - 12 q^{35} - 6 q^{37} + 6 q^{39} - 4 q^{47} + 4 q^{49} + 4 q^{53} + 8 q^{55} + 12 q^{57} - 14 q^{59} - 12 q^{61} - 2 q^{63} + 4 q^{65} + 42 q^{67} - 18 q^{73} + 2 q^{75} - 8 q^{77} + 6 q^{79} - 4 q^{81} + 4 q^{83} + 32 q^{85} - 8 q^{87} - 34 q^{91} - 6 q^{93} + 24 q^{95}+O(q^{100}) \) 8 * q - 4 * q^3 - 2 * q^7 - 4 * q^9 + 6 * q^11 - 6 * q^19 + 4 * q^21 + 2 * q^25 + 8 * q^27 + 16 * q^29 - 6 * q^31 - 6 * q^33 - 12 * q^35 - 6 * q^37 + 6 * q^39 - 4 * q^47 + 4 * q^49 + 4 * q^53 + 8 * q^55 + 12 * q^57 - 14 * q^59 - 12 * q^61 - 2 * q^63 + 4 * q^65 + 42 * q^67 - 18 * q^73 + 2 * q^75 - 8 * q^77 + 6 * q^79 - 4 * q^81 + 4 * q^83 + 32 * q^85 - 8 * q^87 - 34 * q^91 - 6 * q^93 + 24 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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