LMFDB - Embedded newform 224.2.q.a.143.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [224,2,Mod(47,224)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(224, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 5]))

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

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

chi := DirichletCharacter("224.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 224 = 2^{5} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	224.q (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:	$1.78864900528$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.144054149089536.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3x^{11} + x^{9} + 48x^{8} - 189x^{7} + 431x^{6} - 654x^{5} + 624x^{4} - 340x^{3} + 96x^{2} - 12x + 4 $ x^12 - 3x^11 + x^9 + 48x^8 - 189x^7 + 431x^6 - 654x^5 + 624x^4 - 340x^3 + 96x^2 - 12*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 56)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			143.4
Root			$0.186445 - 1.54034i$ of defining polynomial
Character	$\chi$	$=$	224.143
Dual form			224.2.q.a.47.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.416472 + 0.240450i) q^{3} +(1.59713 + 2.76632i) q^{5} +(-0.694153 + 2.55307i) q^{7} +(-1.38437 - 2.39779i) q^{9} +O(q^{10})$	\(q+(0.416472 + 0.240450i) q^{3} +(1.59713 + 2.76632i) q^{5} +(-0.694153 + 2.55307i) q^{7} +(-1.38437 - 2.39779i) q^{9} +(-0.800840 + 1.38709i) q^{11} -1.38831 q^{13} +1.53613i q^{15} +(3.48605 + 2.01267i) q^{17} +(4.56957 - 2.63824i) q^{19} +(-0.902982 + 0.896373i) q^{21} +(3.83044 - 2.21151i) q^{23} +(-2.60168 + 4.50624i) q^{25} -2.77419i q^{27} -5.10613i q^{29} +(0.0579809 - 0.100426i) q^{31} +(-0.667055 + 0.385124i) q^{33} +(-8.17125 + 2.15734i) q^{35} +(-4.63087 + 2.67363i) q^{37} +(-0.578191 - 0.333819i) q^{39} -4.21689i q^{41} +(4.42204 - 7.65920i) q^{45} +(-5.05821 - 8.76108i) q^{47} +(-6.03630 - 3.54444i) q^{49} +(0.967895 + 1.67644i) q^{51} +(6.13514 + 3.54212i) q^{53} -5.11619 q^{55} +2.53747 q^{57} +(4.38856 + 2.53374i) q^{59} +(-4.21321 - 7.29750i) q^{61} +(7.08269 - 1.86995i) q^{63} +(-2.21731 - 3.84050i) q^{65} +(-5.01815 + 8.69169i) q^{67} +2.12703 q^{69} -5.29150i q^{71} +(9.30504 + 5.37227i) q^{73} +(-2.16706 + 1.25115i) q^{75} +(-2.98544 - 3.00745i) q^{77} +(-10.3349 + 5.96688i) q^{79} +(-3.48605 + 6.03801i) q^{81} -14.9789i q^{83} +12.8580i q^{85} +(1.22777 - 2.12656i) q^{87} +(1.50000 - 0.866025i) q^{89} +(0.963697 - 3.54444i) q^{91} +(0.0482949 - 0.0278831i) q^{93} +(14.5965 + 8.42726i) q^{95} -2.87198i q^{97} +4.43462 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{3}+O(q^{10}) $ 12 * q + 6 * q^3	$ 12 q + 6 q^{3} + 6 q^{11} - 6 q^{17} + 6 q^{19} - 6 q^{33} - 18 q^{35} - 12 q^{49} - 6 q^{51} - 36 q^{57} - 42 q^{59} - 12 q^{65} - 30 q^{67} + 18 q^{73} - 24 q^{75} + 6 q^{81} + 18 q^{89} + 72 q^{91} + 24 q^{99}+O(q^{100}) $ 12 * q + 6 * q^3 + 6 * q^11 - 6 * q^17 + 6 * q^19 - 6 * q^33 - 18 * q^35 - 12 * q^49 - 6 * q^51 - 36 * q^57 - 42 * q^59 - 12 * q^65 - 30 * q^67 + 18 * q^73 - 24 * q^75 + 6 * q^81 + 18 * q^89 + 72 * q^91 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/224\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.416472	+	0.240450i	0.240450	+	0.138824i	0.615384	−	0.788228i	$-0.289001\pi$
$3$	0.416472	+	0.240450i	0.240450	+	0.138824i	−0.374933	+	0.927052i	$0.622334\pi$
$4$		0			0
$5$	1.59713	+	2.76632i	0.714260	+	1.23714i	0.963244	+	0.268628i	$0.0865701\pi$
$5$	1.59713	+	2.76632i	0.714260	+	1.23714i	−0.248984	+	0.968508i	$0.580097\pi$
$6$		0			0
$7$	−0.694153	+	2.55307i	−0.262365	+	0.964969i
$7$	−0.694153	+	2.55307i	−0.262365	+	0.964969i
$8$		0			0
$9$	−1.38437	−	2.39779i	−0.461456	−	0.799265i
$10$		0			0
$11$	−0.800840	+	1.38709i	−0.241462	+	0.418225i	−0.961131	−	0.276093i	$-0.910960\pi$
$11$	−0.800840	+	1.38709i	−0.241462	+	0.418225i	0.719669	+	0.694318i	$0.244294\pi$
$12$		0			0
$13$	−1.38831			−0.385047			−0.192523	−	0.981292i	$-0.561667\pi$
$13$	−1.38831			−0.385047			−0.192523	+	0.981292i	$0.561667\pi$
$14$		0			0
$15$			1.53613i			0.396626i
$16$		0			0
$17$	3.48605	+	2.01267i	0.845490	+	0.488144i	0.859127	−	0.511763i	$-0.171007\pi$
$17$	3.48605	+	2.01267i	0.845490	+	0.488144i	−0.0136363	+	0.999907i	$0.504341\pi$
$18$		0			0
$19$	4.56957	−	2.63824i	1.04833	−	0.605255i	0.126150	−	0.992011i	$-0.459738\pi$
$19$	4.56957	−	2.63824i	1.04833	−	0.605255i	0.922182	+	0.386756i	$0.126405\pi$
$20$		0			0
$21$	−0.902982	+	0.896373i	−0.197047	+	0.195605i
$22$		0			0
$23$	3.83044	−	2.21151i	0.798702	−	0.461131i	−0.0443149	−	0.999018i	$-0.514110\pi$
$23$	3.83044	−	2.21151i	0.798702	−	0.461131i	0.843017	+	0.537887i	$0.180777\pi$
$24$		0			0
$25$	−2.60168	+	4.50624i	−0.520336	+	0.901248i
$26$		0			0
$27$		−	2.77419i		−	0.533893i
$28$		0			0
$29$		−	5.10613i		−	0.948185i	−0.880475	−	0.474093i	$-0.842776\pi$
$29$		−	5.10613i		−	0.948185i	0.880475	−	0.474093i	$-0.157224\pi$
$30$		0			0
$31$	0.0579809	−	0.100426i	0.0104137	−	0.0180370i	−0.860772	−	0.508991i	$-0.830018\pi$
$31$	0.0579809	−	0.100426i	0.0104137	−	0.0180370i	0.871185	+	0.490954i	$0.163352\pi$
$32$		0			0
$33$	−0.667055	+	0.385124i	−0.116119	+	0.0670416i
$34$		0			0
$35$	−8.17125	+	2.15734i	−1.38119	+	0.364658i
$36$		0			0
$37$	−4.63087	+	2.67363i	−0.761310	+	0.439543i	−0.829766	−	0.558111i	$-0.811526\pi$
$37$	−4.63087	+	2.67363i	−0.761310	+	0.439543i	0.0684556	+	0.997654i	$0.478193\pi$
$38$		0			0
$39$	−0.578191	−	0.333819i	−0.0925847	−	0.0534538i
$40$		0			0
$41$		−	4.21689i		−	0.658568i	−0.944231	−	0.329284i	$-0.893193\pi$
$41$		−	4.21689i		−	0.658568i	0.944231	−	0.329284i	$-0.106807\pi$
$42$		0			0
$43$		0			0			−	1.00000i	$-0.5\pi$
$43$		0			0				1.00000i	$0.5\pi$
$44$		0			0
$45$	4.42204	−	7.65920i	0.659199	−	1.14177i
$46$		0			0
$47$	−5.05821	−	8.76108i	−0.737816	−	1.27794i	−0.953477	−	0.301467i	$-0.902524\pi$
$47$	−5.05821	−	8.76108i	−0.737816	−	1.27794i	0.215660	−	0.976468i	$-0.430810\pi$
$48$		0			0
$49$	−6.03630	−	3.54444i	−0.862329	−	0.506348i
$50$		0			0
$51$	0.967895	+	1.67644i	0.135532	+	0.234749i
$52$		0			0
$53$	6.13514	+	3.54212i	0.842726	+	0.486548i	0.858190	−	0.513332i	$-0.171589\pi$
$53$	6.13514	+	3.54212i	0.842726	+	0.486548i	−0.0154638	+	0.999880i	$0.504922\pi$
$54$		0			0
$55$	−5.11619			−0.689868
$56$		0			0
$57$	2.53747			0.336096
$58$		0			0
$59$	4.38856	+	2.53374i	0.571342	+	0.329865i	0.757685	−	0.652620i	$-0.226330\pi$
$59$	4.38856	+	2.53374i	0.571342	+	0.329865i	−0.186343	+	0.982485i	$0.559664\pi$
$60$		0			0
$61$	−4.21321	−	7.29750i	−0.539447	−	0.934349i	−0.998934	−	0.0461646i	$-0.985300\pi$
$61$	−4.21321	−	7.29750i	−0.539447	−	0.934349i	0.459487	−	0.888184i	$-0.348033\pi$
$62$		0			0
$63$	7.08269	−	1.86995i	0.892335	−	0.235591i
$64$		0			0
$65$	−2.21731	−	3.84050i	−0.275024	−	0.476355i
$66$		0			0
$67$	−5.01815	+	8.69169i	−0.613065	+	1.06186i	0.377656	+	0.925946i	$0.376730\pi$
$67$	−5.01815	+	8.69169i	−0.613065	+	1.06186i	−0.990721	+	0.135913i	$0.956603\pi$
$68$		0			0
$69$	2.12703			0.256064
$70$		0			0
$71$		−	5.29150i		−	0.627986i	−0.949425	−	0.313993i	$-0.898333\pi$
$71$		−	5.29150i		−	0.627986i	0.949425	−	0.313993i	$-0.101667\pi$
$72$		0			0
$73$	9.30504	+	5.37227i	1.08907	+	0.628776i	0.933329	−	0.359021i	$-0.116890\pi$
$73$	9.30504	+	5.37227i	1.08907	+	0.628776i	0.155743	+	0.987798i	$0.450223\pi$
$74$		0			0
$75$	−2.16706	+	1.25115i	−0.250230	+	0.144470i
$76$		0			0
$77$	−2.98544	−	3.00745i	−0.340223	−	0.342731i
$78$		0			0
$79$	−10.3349	+	5.96688i	−1.16277	+	0.671327i	−0.951967	−	0.306201i	$-0.900942\pi$
$79$	−10.3349	+	5.96688i	−1.16277	+	0.671327i	−0.210805	+	0.977528i	$0.567609\pi$
$80$		0			0
$81$	−3.48605	+	6.03801i	−0.387338	+	0.670890i
$82$		0			0
$83$		−	14.9789i		−	1.64415i	−0.569382	−	0.822073i	$-0.692818\pi$
$83$		−	14.9789i		−	1.64415i	0.569382	−	0.822073i	$-0.307182\pi$
$84$		0			0
$85$			12.8580i			1.39465i
$86$		0			0
$87$	1.22777	−	2.12656i	0.131631	−	0.227992i
$88$		0			0
$89$	1.50000	−	0.866025i	0.159000	−	0.0917985i	−0.418389	−	0.908268i	$-0.637405\pi$
$89$	1.50000	−	0.866025i	0.159000	−	0.0917985i	0.577389	+	0.816469i	$0.304072\pi$
$90$		0			0
$91$	0.963697	−	3.54444i	0.101023	−	0.371558i
$92$		0			0
$93$	0.0482949	−	0.0278831i	0.00500795	−	0.00289134i
$94$		0			0
$95$	14.5965	+	8.42726i	1.49756	+	0.864619i
$96$		0			0
$97$		−	2.87198i		−	0.291606i	−0.989314	−	0.145803i	$-0.953423\pi$
$97$		−	2.87198i		−	0.291606i	0.989314	−	0.145803i	$-0.0465765\pi$
$98$		0			0
$99$	4.43462			0.445696
$100$		0			0
$101$	−3.40310	+	5.89434i	−0.338621	+	0.586509i	−0.984174	−	0.177207i	$-0.943294\pi$
$101$	−3.40310	+	5.89434i	−0.338621	+	0.586509i	0.645553	+	0.763716i	$0.276627\pi$
$102$		0			0
$103$	7.02471	+	12.1672i	0.692165	+	1.19887i	0.971127	+	0.238563i	$0.0766765\pi$
$103$	7.02471	+	12.1672i	0.692165	+	1.19887i	−0.278962	+	0.960302i	$0.589990\pi$
$104$		0			0
$105$	−3.92184	−	1.06631i	−0.382732	−	0.104061i
$106$		0			0
$107$	−2.56957	−	4.45063i	−0.248410	−	0.430259i	0.714675	−	0.699457i	$-0.246575\pi$
$107$	−2.56957	−	4.45063i	−0.248410	−	0.430259i	−0.963085	+	0.269198i	$0.913241\pi$
$108$		0			0
$109$	−2.45182	−	1.41556i	−0.234842	−	0.135586i	0.377962	−	0.925821i	$-0.376625\pi$
$109$	−2.45182	−	1.41556i	−0.234842	−	0.135586i	−0.612804	+	0.790235i	$0.709958\pi$
$110$		0			0
$111$	−2.57151			−0.244077
$112$		0			0
$113$	−1.43695			−0.135177			−0.0675887	−	0.997713i	$-0.521531\pi$
$113$	−1.43695			−0.135177			−0.0675887	+	0.997713i	$0.521531\pi$
$114$		0			0
$115$	12.2355	+	7.06415i	1.14096	+	0.658735i
$116$		0			0
$117$	1.92193	+	3.32887i	0.177682	+	0.307754i
$118$		0			0
$119$	−7.55833	+	7.50301i	−0.692871	+	0.687800i
$120$		0			0
$121$	4.21731	+	7.30460i	0.383392	+	0.664054i
$122$		0			0
$123$	1.01395	−	1.75622i	0.0914251	−	0.158353i
$124$		0			0
$125$	−0.649581			−0.0581003
$126$		0			0
$127$			4.92077i			0.436647i	0.975876	+	0.218324i	$0.0700589\pi$
$127$			4.92077i			0.436647i	−0.975876	+	0.218324i	$0.929941\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	3.41647	−	1.97250i	0.298499	−	0.172338i	−0.343270	−	0.939237i	$-0.611534\pi$
$131$	3.41647	−	1.97250i	0.298499	−	0.172338i	0.641768	+	0.766899i	$0.278201\pi$
$132$		0			0
$133$	3.56363	+	13.4978i	0.309006	+	1.17041i
$134$		0			0
$135$	7.67429	−	4.43075i	0.660498	−	0.381339i
$136$		0			0
$137$	0.0514223	−	0.0890661i	0.00439331	−	0.00760943i	−0.863820	−	0.503800i	$-0.831935\pi$
$137$	0.0514223	−	0.0890661i	0.00439331	−	0.00760943i	0.868214	+	0.496190i	$0.165268\pi$
$138$		0			0
$139$			14.9789i			1.27049i	0.772310	+	0.635246i	$0.219101\pi$
$139$			14.9789i			1.27049i	−0.772310	+	0.635246i	$0.780899\pi$
$140$		0			0
$141$		−	4.86500i		−	0.409707i
$142$		0			0
$143$	1.11181	−	1.92571i	0.0929743	−	0.161036i
$144$		0			0
$145$	14.1252	−	8.15518i	1.17303	−	0.677251i
$146$		0			0
$147$	−1.66169	−	2.92759i	−0.137054	−	0.241464i
$148$		0			0
$149$	9.79164	−	5.65320i	0.802162	−	0.463129i	−0.0420645	−	0.999115i	$-0.513393\pi$
$149$	9.79164	−	5.65320i	0.802162	−	0.463129i	0.844227	+	0.535986i	$0.180060\pi$
$150$		0			0
$151$	−12.8351	−	7.41032i	−1.04450	−	0.603044i	−0.123397	−	0.992357i	$-0.539379\pi$
$151$	−12.8351	−	7.41032i	−1.04450	−	0.603044i	−0.921105	+	0.389314i	$0.872712\pi$
$152$		0			0
$153$		−	11.1451i		−	0.901028i
$154$		0			0
$155$	0.370413			0.0297523
$156$		0			0
$157$	−0.369362	+	0.639755i	−0.0294783	+	0.0510580i	−0.880388	−	0.474254i	$-0.842718\pi$
$157$	−0.369362	+	0.639755i	−0.0294783	+	0.0510580i	0.850910	+	0.525312i	$0.176051\pi$
$158$		0			0
$159$	1.70341	+	2.95039i	0.135089	+	0.233981i
$160$		0			0
$161$	2.98721	+	11.3145i	0.235425	+	0.891707i
$162$		0			0
$163$	−4.35226	−	7.53834i	−0.340895	−	0.590448i	0.643704	−	0.765275i	$-0.277397\pi$
$163$	−4.35226	−	7.53834i	−0.340895	−	0.590448i	−0.984599	+	0.174826i	$0.944064\pi$
$164$		0			0
$165$	−2.13075	−	1.23019i	−0.165879	−	0.0957703i
$166$		0			0
$167$	1.38831			0.107430			0.0537152	−	0.998556i	$-0.482894\pi$
$167$	1.38831			0.107430			0.0537152	+	0.998556i	$0.482894\pi$
$168$		0			0
$169$	−11.0726			−0.851739
$170$		0			0
$171$	−12.6519	−	7.30460i	−0.967518	−	0.558597i
$172$		0			0
$173$	0.485324	+	0.840606i	0.0368985	+	0.0639101i	0.883885	−	0.467704i	$-0.154919\pi$
$173$	0.485324	+	0.840606i	0.0368985	+	0.0639101i	−0.846986	+	0.531615i	$0.821586\pi$
$174$		0			0
$175$	−9.69877	−	9.77028i	−0.733158	−	0.738564i
$176$		0			0
$177$	1.21848	+	2.11046i	0.0915864	+	0.158632i
$178$		0			0
$179$	−7.13495	+	12.3581i	−0.533291	+	0.923687i	0.465953	+	0.884810i	$0.345712\pi$
$179$	−7.13495	+	12.3581i	−0.533291	+	0.923687i	−0.999244	+	0.0388779i	$0.987622\pi$
$180$		0			0
$181$	−15.3218			−1.13886			−0.569429	−	0.822041i	$-0.692836\pi$
$181$	−15.3218			−1.13886			−0.569429	+	0.822041i	$0.692836\pi$
$182$		0			0
$183$		−	4.05228i		−	0.299553i
$184$		0			0
$185$	−14.7922	−	8.54031i	−1.08755	−	0.627896i
$186$		0			0
$187$	−5.58353	+	3.22365i	−0.408308	+	0.235737i
$188$		0			0
$189$	7.08269	+	1.92571i	0.515190	+	0.140075i
$190$		0			0
$191$	−2.16564	+	1.25033i	−0.156700	+	0.0904709i	−0.576300	−	0.817238i	$-0.695504\pi$
$191$	−2.16564	+	1.25033i	−0.156700	+	0.0904709i	0.419599	+	0.907709i	$0.362171\pi$
$192$		0			0
$193$	1.55026	−	2.68512i	0.111590	−	0.193279i	−0.804822	−	0.593517i	$-0.797739\pi$
$193$	1.55026	−	2.68512i	0.111590	−	0.193279i	0.916411	+	0.400237i	$0.131072\pi$
$194$		0			0
$195$		−	2.13261i		−	0.152720i
$196$		0			0
$197$		−	15.6891i		−	1.11780i	−0.829233	−	0.558902i	$-0.811223\pi$
$197$		−	15.6891i		−	1.11780i	0.829233	−	0.558902i	$-0.188777\pi$
$198$		0			0
$199$	5.91290	−	10.2414i	0.419154	−	0.725997i	−0.576700	−	0.816956i	$-0.695660\pi$
$199$	5.91290	−	10.2414i	0.419154	−	0.725997i	0.995855	+	0.0909591i	$0.0289933\pi$
$200$		0			0
$201$	−4.17984	+	2.41323i	−0.294823	+	0.170216i
$202$		0			0
$203$	13.0363	+	3.54444i	0.914969	+	0.248771i
$204$		0			0
$205$	11.6653	−	6.73495i	0.814738	−	0.470389i
$206$		0			0
$207$	−10.6055	−	6.12307i	−0.737131	−	0.425583i
$208$		0			0
$209$			8.45124i			0.584585i
$210$		0			0
$211$	−10.0726			−0.693427			−0.346713	−	0.937971i	$-0.612702\pi$
$211$	−10.0726			−0.693427			−0.346713	+	0.937971i	$0.612702\pi$
$212$		0			0
$213$	1.27234	−	2.20376i	0.0871796	−	0.150999i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	0.216146	+	0.217740i	0.0146730	+	0.0147812i
$218$		0			0
$219$	2.58353	+	4.47480i	0.174579	+	0.302379i
$220$		0			0
$221$	−4.83970	−	2.79420i	−0.325553	−	0.187958i
$222$		0			0
$223$	24.3086			1.62783			0.813913	−	0.580987i	$-0.197333\pi$
$223$	24.3086			1.62783			0.813913	+	0.580987i	$0.197333\pi$
$224$		0			0
$225$	14.4067			0.960448
$226$		0			0
$227$	12.4048	+	7.16194i	0.823339	+	0.475355i	0.851566	−	0.524247i	$-0.175653\pi$
$227$	12.4048	+	7.16194i	0.823339	+	0.475355i	−0.0282277	+	0.999602i	$0.508986\pi$
$228$		0			0
$229$	−5.32502	−	9.22321i	−0.351887	−	0.609487i	0.634693	−	0.772765i	$-0.281127\pi$
$229$	−5.32502	−	9.22321i	−0.351887	−	0.609487i	−0.986580	+	0.163278i	$0.947793\pi$
$230$		0			0
$231$	−0.520210	−	1.97037i	−0.0342273	−	0.129641i
$232$		0			0
$233$	0.318991	+	0.552509i	0.0208978	+	0.0361961i	0.876285	−	0.481793i	$-0.160014\pi$
$233$	0.318991	+	0.552509i	0.0208978	+	0.0361961i	−0.855387	+	0.517989i	$0.826681\pi$
$234$		0			0
$235$	16.1573	−	27.9853i	1.05399	−	1.82556i
$236$		0			0
$237$	−5.73896			−0.372785
$238$		0			0
$239$		−	4.73540i		−	0.306307i	−0.988202	−	0.153154i	$-0.951057\pi$
$239$		−	4.73540i		−	0.306307i	0.988202	−	0.153154i	$-0.0489430\pi$
$240$		0			0
$241$	−10.1380	−	5.85317i	−0.653045	−	0.377036i	0.136577	−	0.990629i	$-0.456390\pi$
$241$	−10.1380	−	5.85317i	−0.653045	−	0.377036i	−0.789622	+	0.613594i	$0.789723\pi$
$242$		0			0
$243$	−10.1112	+	5.83773i	−0.648636	+	0.374490i
$244$		0			0
$245$	0.164257	−	22.3593i	0.0104940	−	1.42848i
$246$		0			0
$247$	−6.34397	+	3.66269i	−0.403657	+	0.233051i
$248$		0			0
$249$	3.60168	−	6.23829i	0.228247	−	0.395336i
$250$		0			0
$251$			11.5631i			0.729858i	0.931035	+	0.364929i	$0.118907\pi$
$251$			11.5631i			0.729858i	−0.931035	+	0.364929i	$0.881093\pi$
$252$		0			0
$253$			7.08425i			0.445383i
$254$		0			0
$255$	−3.09172	+	5.35501i	−0.193611	+	0.335344i
$256$		0			0
$257$	−20.4302	+	11.7954i	−1.27440	+	0.735777i	−0.975813	−	0.218605i	$-0.929849\pi$
$257$	−20.4302	+	11.7954i	−1.27440	+	0.735777i	−0.298589	+	0.954382i	$0.596516\pi$
$258$		0			0
$259$	−3.61144	−	13.6788i	−0.224404	−	0.849961i
$260$		0			0
$261$	−12.2435	+	7.06876i	−0.757851	+	0.437546i
$262$		0			0
$263$	9.24833	+	5.33953i	0.570277	+	0.329249i	0.757260	−	0.653114i	$-0.226538\pi$
$263$	9.24833	+	5.33953i	0.570277	+	0.329249i	−0.186983	+	0.982363i	$0.559871\pi$
$264$		0			0
$265$			22.6290i			1.39009i
$266$		0			0
$267$	0.832945			0.0509754
$268$		0			0
$269$	−11.6690	+	20.2113i	−0.711471	+	1.23230i	0.252834	+	0.967510i	$0.418637\pi$
$269$	−11.6690	+	20.2113i	−0.711471	+	1.23230i	−0.964305	+	0.264794i	$0.914696\pi$
$270$		0			0
$271$	−6.81961	−	11.8119i	−0.414262	−	0.717522i	0.581089	−	0.813840i	$-0.302627\pi$
$271$	−6.81961	−	11.8119i	−0.414262	−	0.717522i	−0.995351	+	0.0963179i	$0.969293\pi$
$272$		0			0
$273$	1.25362	−	1.24444i	0.0758722	−	0.0753169i
$274$		0			0
$275$	−4.16706	−	7.21755i	−0.251283	−	0.435235i
$276$		0			0
$277$	−0.396180	−	0.228735i	−0.0238042	−	0.0137433i	0.488051	−	0.872815i	$-0.337708\pi$
$277$	−0.396180	−	0.228735i	−0.0238042	−	0.0137433i	−0.511855	+	0.859072i	$0.671041\pi$
$278$		0			0
$279$	−0.321068			−0.0192218
$280$		0			0
$281$	1.43695			0.0857215			0.0428608	−	0.999081i	$-0.486353\pi$
$281$	1.43695			0.0857215			0.0428608	+	0.999081i	$0.486353\pi$
$282$		0			0
$283$	−27.0428	−	15.6132i	−1.60753	−	0.928108i	−0.989921	−	0.141622i	$-0.954768\pi$
$283$	−27.0428	−	15.6132i	−1.60753	−	0.928108i	−0.617609	−	0.786486i	$-0.711898\pi$
$284$		0			0
$285$	4.05268	+	7.01945i	0.240060	+	0.415796i
$286$		0			0
$287$	10.7660	+	2.92717i	0.635497	+	0.172785i
$288$		0			0
$289$	−0.398321	−	0.689912i	−0.0234306	−	0.0405831i
$290$		0			0
$291$	0.690570	−	1.19610i	0.0404819	−	0.0701168i
$292$		0			0
$293$	31.3006			1.82860			0.914299	−	0.405040i	$-0.132742\pi$
$293$	31.3006			1.82860			0.914299	+	0.405040i	$0.132742\pi$
$294$		0			0
$295$			16.1869i			0.942437i
$296$		0			0
$297$	3.84806	+	2.22168i	0.223287	+	0.128915i
$298$		0			0
$299$	−5.31783	+	3.07025i	−0.307538	+	0.177557i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−2.83459	+	1.63655i	−0.162843	+	0.0940175i
$304$		0			0
$305$	13.4581	−	23.3102i	0.770611	−	1.33474i
$306$		0			0
$307$			14.7215i			0.840202i	0.907477	+	0.420101i	$0.138005\pi$
$307$			14.7215i			0.840202i	−0.907477	+	0.420101i	$0.861995\pi$
$308$		0			0
$309$			6.75638i			0.384357i
$310$		0			0
$311$	−7.79025	+	13.4931i	−0.441745	+	0.765124i	−0.997819	−	0.0660082i	$-0.978974\pi$
$311$	−7.79025	+	13.4931i	−0.441745	+	0.765124i	0.556074	+	0.831133i	$0.312307\pi$
$312$		0			0
$313$	11.3329	−	6.54308i	0.640576	−	0.369837i	−0.144260	−	0.989540i	$-0.546080\pi$
$313$	11.3329	−	6.54308i	0.640576	−	0.369837i	0.784836	+	0.619703i	$0.212747\pi$
$314$		0			0
$315$	16.4849	+	16.6064i	0.928818	+	0.935666i
$316$		0			0
$317$	−20.3971	+	11.7763i	−1.14562	+	0.661422i	−0.947815	−	0.318821i	$-0.896713\pi$
$317$	−20.3971	+	11.7763i	−1.14562	+	0.661422i	−0.197801	+	0.980242i	$0.563380\pi$
$318$		0			0
$319$	7.08269	+	4.08919i	0.396555	+	0.228951i
$320$		0			0
$321$		−	2.47142i		−	0.137941i
$322$		0			0
$323$	21.2397			1.18181
$324$		0			0
$325$	3.61193	−	6.25604i	0.200354	−	0.347023i
$326$		0			0
$327$	−0.680744	−	1.17908i	−0.0376452	−	0.0652035i
$328$		0			0
$329$	25.8788	−	6.83243i	1.42674	−	0.376684i
$330$		0			0
$331$	16.5277	+	28.6268i	0.908445	+	1.57347i	0.816225	+	0.577735i	$0.196063\pi$
$331$	16.5277	+	28.6268i	0.908445	+	1.57347i	0.0922207	+	0.995739i	$0.470603\pi$
$332$		0			0
$333$	12.8217	+	7.40258i	0.702622	+	0.405659i
$334$		0			0
$335$	−32.0587			−1.75155
$336$		0			0
$337$	−15.5096			−0.844860			−0.422430	−	0.906396i	$-0.638823\pi$
$337$	−15.5096			−0.844860			−0.422430	+	0.906396i	$0.638823\pi$
$338$		0			0
$339$	−0.598452	−	0.345516i	−0.0325035	−	0.0187659i
$340$		0			0
$341$	0.0928668	+	0.160850i	0.00502902	+	0.00871052i
$342$		0			0
$343$	13.2393	−	12.9507i	0.714855	−	0.699272i
$344$		0			0
$345$	3.39716	+	5.88405i	0.182897	+	0.316786i
$346$		0			0
$347$	11.2494	−	19.4846i	0.603900	−	1.04599i	−0.388324	−	0.921523i	$-0.626946\pi$
$347$	11.2494	−	19.4846i	0.603900	−	1.04599i	0.992224	−	0.124463i	$-0.0397209\pi$
$348$		0			0
$349$	28.4735			1.52415			0.762077	−	0.647486i	$-0.224180\pi$
$349$	28.4735			1.52415			0.762077	+	0.647486i	$0.224180\pi$
$350$		0			0
$351$			3.85142i			0.205574i
$352$		0			0
$353$	−8.29108	−	4.78686i	−0.441290	−	0.254779i	0.262855	−	0.964835i	$-0.415336\pi$
$353$	−8.29108	−	4.78686i	−0.441290	−	0.254779i	−0.704145	+	0.710057i	$0.748669\pi$
$354$		0			0
$355$	14.6380	−	8.45124i	0.776903	−	0.448545i
$356$		0			0
$357$	−4.95194	+	1.30739i	−0.262084	+	0.0691945i
$358$		0			0
$359$	−3.25225	+	1.87769i	−0.171647	+	0.0991006i	−0.583362	−	0.812212i	$-0.698263\pi$
$359$	−3.25225	+	1.87769i	−0.171647	+	0.0991006i	0.411715	+	0.911313i	$0.364930\pi$
$360$		0			0
$361$	4.42067	−	7.65683i	0.232667	−	0.402991i
$362$		0			0
$363$			4.05622i			0.212896i
$364$		0			0
$365$			34.3209i			1.79644i
$366$		0			0
$367$	−8.41302	+	14.5718i	−0.439156	+	0.760640i	−0.997625	−	0.0688852i	$-0.978056\pi$
$367$	−8.41302	+	14.5718i	−0.439156	+	0.760640i	0.558469	+	0.829526i	$0.311389\pi$
$368$		0			0
$369$	−10.1112	+	5.83773i	−0.526370	+	0.303900i
$370$		0			0
$371$	−13.3020	+	13.2046i	−0.690606	+	0.685551i
$372$		0			0
$373$	11.1354	−	6.42901i	0.576568	−	0.332882i	−0.183200	−	0.983076i	$-0.558646\pi$
$373$	11.1354	−	6.42901i	0.576568	−	0.332882i	0.759768	+	0.650194i	$0.225312\pi$
$374$		0			0
$375$	−0.270533	−	0.156192i	−0.0139702	−	0.00806572i
$376$		0			0
$377$			7.08888i			0.365096i
$378$		0			0
$379$	−25.5822			−1.31407			−0.657034	−	0.753861i	$-0.728189\pi$
$379$	−25.5822			−1.31407			−0.657034	+	0.753861i	$0.728189\pi$
$380$		0			0
$381$	−1.18320	+	2.04936i	−0.0606172	+	0.104992i
$382$		0			0
$383$	13.4846	+	23.3561i	0.689033	+	1.19344i	0.972151	+	0.234355i	$0.0752978\pi$
$383$	13.4846	+	23.3561i	0.689033	+	1.19344i	−0.283118	+	0.959085i	$0.591369\pi$
$384$		0			0
$385$	3.55142	−	13.0620i	0.180997	−	0.665701i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−27.7043	−	15.9951i	−1.40466	−	0.810983i	−0.409796	−	0.912177i	$-0.634400\pi$
$389$	−27.7043	−	15.9951i	−1.40466	−	0.810983i	−0.994867	+	0.101195i	$0.967734\pi$
$390$		0			0
$391$	17.8041			0.900394
$392$		0			0
$393$	1.89716			0.0956988
$394$		0			0
$395$	−33.0126	−	19.0598i	−1.66104	−	0.959004i
$396$		0			0
$397$	8.51929	+	14.7558i	0.427571	+	0.740575i	0.996657	−	0.0817035i	$-0.0260360\pi$
$397$	8.51929	+	14.7558i	0.427571	+	0.740575i	−0.569086	+	0.822278i	$0.692703\pi$
$398$		0			0
$399$	−1.76139	+	6.47833i	−0.0881799	+	0.324322i
$400$		0			0
$401$	2.94858	+	5.10709i	0.147245	+	0.255036i	0.930208	−	0.367032i	$-0.119626\pi$
$401$	2.94858	+	5.10709i	0.147245	+	0.255036i	−0.782963	+	0.622068i	$0.786293\pi$
$402$		0			0
$403$	−0.0804953	+	0.139422i	−0.00400976	+	0.00694510i
$404$		0			0
$405$	−22.2707			−1.10664
$406$		0			0
$407$		−	8.56461i		−	0.424532i
$408$		0			0
$409$	−0.207751	−	0.119945i	−0.0102726	−	0.00593090i	0.494855	−	0.868976i	$-0.335221\pi$
$409$	−0.207751	−	0.119945i	−0.0102726	−	0.00593090i	−0.505128	+	0.863045i	$0.668555\pi$
$410$		0			0
$411$	0.0428320	−	0.0247290i	0.00211274	−	0.00121979i
$412$		0			0
$413$	−9.51514	+	9.44550i	−0.468210	+	0.464783i
$414$		0			0
$415$	41.4364	−	23.9233i	2.03403	−	1.17435i
$416$		0			0
$417$	−3.60168	+	6.23829i	−0.176375	+	0.305490i
$418$		0			0
$419$		−	29.4140i		−	1.43697i	−0.695544	−	0.718484i	$-0.744837\pi$
$419$		−	29.4140i		−	1.43697i	0.695544	−	0.718484i	$-0.255163\pi$
$420$		0			0
$421$		−	32.1265i		−	1.56575i	−0.622180	−	0.782874i	$-0.713753\pi$
$421$		−	32.1265i		−	1.56575i	0.622180	−	0.782874i	$-0.286247\pi$
$422$		0			0
$423$	−14.0049	+	24.2571i	−0.680939	+	1.17942i
$424$		0			0
$425$	−18.1391	+	10.4726i	−0.879878	+	0.507998i
$426$		0			0
$427$	21.5556	−	5.69103i	1.04315	−	0.275408i
$428$		0			0
$429$	0.926077	−	0.534671i	0.0447114	−	0.0258141i
$430$		0			0
$431$	−32.7662	−	18.9176i	−1.57829	−	0.911228i	−0.995098	−	0.0988962i	$-0.968469\pi$
$431$	−32.7662	−	18.9176i	−1.57829	−	0.911228i	−0.583196	−	0.812332i	$-0.698198\pi$
$432$		0			0
$433$			25.4835i			1.22466i	0.790602	+	0.612330i	$0.209768\pi$
$433$			25.4835i			1.22466i	−0.790602	+	0.612330i	$0.790232\pi$
$434$		0			0
$435$	7.84367			0.376075
$436$		0			0
$437$	11.6690	−	20.2113i	0.558204	−	0.966837i
$438$		0			0
$439$	−11.9804	−	20.7506i	−0.571792	−	0.990373i	−0.996382	−	0.0849871i	$-0.972915\pi$
$439$	−11.9804	−	20.7506i	−0.571792	−	0.990373i	0.424590	−	0.905386i	$-0.360418\pi$
$440$		0			0
$441$	−0.142375	+	19.3806i	−0.00677975	+	0.922887i
$442$		0			0
$443$	5.13495	+	8.89399i	0.243969	+	0.422566i	0.961841	−	0.273608i	$-0.0882172\pi$
$443$	5.13495	+	8.89399i	0.243969	+	0.422566i	−0.717872	+	0.696175i	$0.754884\pi$
$444$		0			0
$445$	4.79140	+	2.76632i	0.227134	+	0.131136i
$446$		0			0
$447$	5.43726			0.257174
$448$		0			0
$449$	11.5096			0.543170			0.271585	−	0.962414i	$-0.412452\pi$
$449$	11.5096			0.543170			0.271585	+	0.962414i	$0.412452\pi$
$450$		0			0
$451$	5.84923	+	3.37705i	0.275429	+	0.159019i
$452$		0			0
$453$	−3.56363	−	6.17239i	−0.167434	−	0.290004i
$454$		0			0
$455$	11.3442	−	2.99505i	0.531824	−	0.140410i
$456$		0			0
$457$	−15.3050	−	26.5091i	−0.715939	−	1.24004i	−0.962596	−	0.270941i	$-0.912665\pi$
$457$	−15.3050	−	26.5091i	−0.715939	−	1.24004i	0.246657	−	0.969103i	$-0.420668\pi$
$458$		0			0
$459$	5.58353	−	9.67095i	0.260617	−	0.451401i
$460$		0			0
$461$	−17.3671			−0.808866			−0.404433	−	0.914568i	$-0.632531\pi$
$461$	−17.3671			−0.808866			−0.404433	+	0.914568i	$0.632531\pi$
$462$		0			0
$463$		−	21.7288i		−	1.00983i	−0.863171	−	0.504913i	$-0.831525\pi$
$463$		−	21.7288i		−	1.00983i	0.863171	−	0.504913i	$-0.168475\pi$
$464$		0			0
$465$	0.154267	+	0.0890661i	0.00715396	+	0.00413034i
$466$		0			0
$467$	0.585859	−	0.338246i	0.0271103	−	0.0156521i	−0.486384	−	0.873745i	$-0.661684\pi$
$467$	0.585859	−	0.338246i	0.0271103	−	0.0156521i	0.513494	+	0.858093i	$0.328351\pi$
$468$		0			0
$469$	−18.7071	−	18.8450i	−0.863814	−	0.870183i
$470$		0			0
$471$	−0.307659	+	0.177627i	−0.0141762	+	0.00818461i
$472$		0			0
$473$		0			0
$474$		0			0
$475$			27.4555i			1.25974i
$476$		0			0
$477$		−	19.6144i		−	0.898082i
$478$		0			0
$479$	14.3839	−	24.9136i	0.657217	−	1.13833i	−0.324116	−	0.946017i	$-0.605067\pi$
$479$	14.3839	−	24.9136i	0.657217	−	1.13833i	0.981333	−	0.192316i	$-0.0615999\pi$
$480$		0			0
$481$	6.42907	−	3.71182i	0.293140	−	0.169245i
$482$		0			0
$483$	−1.47649	+	5.43045i	−0.0671824	+	0.247094i
$484$		0			0
$485$	7.94483	−	4.58695i	0.360756	−	0.208283i
$486$		0			0
$487$	−1.58745	−	0.916514i	−0.0719342	−	0.0415312i	0.463602	−	0.886044i	$-0.346557\pi$
$487$	−1.58745	−	0.916514i	−0.0719342	−	0.0415312i	−0.535536	+	0.844513i	$0.679890\pi$
$488$		0			0
$489$		−	4.18601i		−	0.189298i
$490$		0			0
$491$	−13.4370			−0.606401			−0.303201	−	0.952927i	$-0.598055\pi$
$491$	−13.4370			−0.606401			−0.303201	+	0.952927i	$0.598055\pi$
$492$		0			0
$493$	10.2770	−	17.8002i	0.462851	−	0.801682i
$494$		0			0
$495$	7.08269	+	12.2676i	0.318343	+	0.551387i
$496$		0			0
$497$	13.5096	+	3.67311i	0.605987	+	0.164762i
$498$		0			0
$499$	−5.68404	−	9.84505i	−0.254453	−	0.440725i	0.710294	−	0.703905i	$-0.248562\pi$
$499$	−5.68404	−	9.84505i	−0.254453	−	0.440725i	−0.964747	+	0.263180i	$0.915229\pi$
$500$		0			0
$501$	0.578191	+	0.333819i	0.0258317	+	0.0149139i
$502$		0			0
$503$	−13.2022			−0.588656			−0.294328	−	0.955704i	$-0.595096\pi$
$503$	−13.2022			−0.588656			−0.294328	+	0.955704i	$0.595096\pi$
$504$		0			0
$505$	−21.7408			−0.967454
$506$		0			0
$507$	−4.61144	−	2.66241i	−0.204801	−	0.118242i
$508$		0			0
$509$	13.2178	+	22.8940i	0.585870	+	1.01476i	0.994766	+	0.102176i	$0.0325804\pi$
$509$	13.2178	+	22.8940i	0.585870	+	1.01476i	−0.408896	+	0.912581i	$0.634086\pi$
$510$		0			0
$511$	−20.1749	+	20.0272i	−0.892484	+	0.885952i
$512$		0			0
$513$	−7.31899	−	12.6769i	−0.323141	−	0.559697i
$514$		0			0
$515$	−22.4388	+	38.8652i	−0.988773	+	1.71260i
$516$		0			0
$517$	16.2033			0.712619
$518$		0			0
$519$			0.466786i			0.0204896i
$520$		0			0
$521$	−10.4163	−	6.01384i	−0.456345	−	0.263471i	0.254161	−	0.967162i	$-0.418201\pi$
$521$	−10.4163	−	6.01384i	−0.456345	−	0.263471i	−0.710506	+	0.703691i	$0.751534\pi$
$522$		0			0
$523$	−2.43276	+	1.40455i	−0.106377	+	0.0614168i	−0.552245	−	0.833682i	$-0.686229\pi$
$523$	−2.43276	+	1.40455i	−0.106377	+	0.0614168i	0.445868	+	0.895099i	$0.352895\pi$
$524$		0			0
$525$	−1.69000	−	6.40113i	−0.0737577	−	0.279368i
$526$		0			0
$527$	0.404248	−	0.233393i	0.0176093	−	0.0101668i
$528$		0			0
$529$	−1.71848	+	2.97649i	−0.0747164	+	0.129413i
$530$		0			0
$531$		−	14.0305i		−	0.608872i
$532$		0			0
$533$			5.85434i			0.253580i
$534$		0			0
$535$	8.20791	−	14.2165i	0.354859	−	0.614634i
$536$		0			0
$537$	−5.94302	+	3.43120i	−0.256460	+	0.148067i
$538$		0			0
$539$	9.75058	−	5.53440i	0.419987	−	0.238383i
$540$		0			0
$541$	−1.68628	+	0.973573i	−0.0724988	+	0.0418572i	−0.535811	−	0.844338i	$-0.679994\pi$
$541$	−1.68628	+	0.973573i	−0.0724988	+	0.0418572i	0.463312	+	0.886195i	$0.346661\pi$
$542$		0			0
$543$	−6.38109	−	3.68413i	−0.273839	−	0.158101i
$544$		0			0
$545$		−	9.04336i		−	0.387375i
$546$		0			0
$547$	−28.4561			−1.21669			−0.608347	−	0.793671i	$-0.708167\pi$
$547$	−28.4561			−1.21669			−0.608347	+	0.793671i	$0.708167\pi$
$548$		0			0
$549$	−11.6653	+	20.2048i	−0.497862	+	0.862321i
$550$		0			0
$551$	−13.4712	−	23.3329i	−0.573894	−	0.994013i
$552$		0			0
$553$	−8.05982	−	30.5277i	−0.342738	−	1.29817i
$554$		0			0
$555$	−4.10704	−	7.11361i	−0.174334	−	0.301956i
$556$		0			0
$557$	−7.96630	−	4.59935i	−0.337543	−	0.194881i	0.321642	−	0.946861i	$-0.395765\pi$
$557$	−7.96630	−	4.59935i	−0.337543	−	0.194881i	−0.659185	+	0.751981i	$0.729099\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	−3.10051			−0.130904
$562$		0			0
$563$	23.5533	+	13.5985i	0.992653	+	0.573108i	0.906066	−	0.423136i	$-0.139071\pi$
$563$	23.5533	+	13.5985i	0.992653	+	0.573108i	0.0865866	+	0.996244i	$0.472404\pi$
$564$		0			0
$565$	−2.29501	−	3.97508i	−0.0965518	−	0.167233i
$566$		0			0
$567$	−12.9956	−	13.0914i	−0.545764	−	0.549788i
$568$		0			0
$569$	11.7699	+	20.3861i	0.493420	+	0.854628i	0.999971	−	0.00758149i	$-0.00241329\pi$
$569$	11.7699	+	20.3861i	0.493420	+	0.854628i	−0.506551	+	0.862210i	$0.669080\pi$
$570$		0			0
$571$	15.1713	−	26.2774i	0.634897	−	1.09967i	−0.351640	−	0.936135i	$-0.614376\pi$
$571$	15.1713	−	26.2774i	0.634897	−	1.09967i	0.986537	−	0.163539i	$-0.0522909\pi$
$572$		0			0
$573$	−1.20257			−0.0502382
$574$		0			0
$575$			23.0145i			0.959772i
$576$		0			0
$577$	24.7760	+	14.3044i	1.03144	+	0.595500i	0.917396	−	0.397976i	$-0.130287\pi$
$577$	24.7760	+	14.3044i	1.03144	+	0.595500i	0.114041	+	0.993476i	$0.463620\pi$
$578$		0			0
$579$	1.29128	−	0.745520i	0.0536637	−	0.0309828i
$580$		0			0
$581$	38.2421	+	10.3976i	1.58655	+	0.431367i
$582$		0			0
$583$	−9.82652	+	5.67335i	−0.406973	+	0.234966i
$584$		0			0
$585$	−6.13915	+	10.6333i	−0.253823	+	0.439634i
$586$		0			0
$587$			15.2362i			0.628867i	0.949280	+	0.314433i	$0.101814\pi$
$587$			15.2362i			0.628867i	−0.949280	+	0.314433i	$0.898186\pi$
$588$		0			0
$589$		−	0.611872i		−	0.0252117i
$590$		0			0
$591$	3.77246	−	6.53409i	0.155178	−	0.268777i
$592$		0			0
$593$	18.2934	−	10.5617i	0.751221	−	0.433717i	−0.0749142	−	0.997190i	$-0.523868\pi$
$593$	18.2934	−	10.5617i	0.751221	−	0.433717i	0.826135	+	0.563473i	$0.190535\pi$
$594$		0			0
$595$	−32.8274	−	8.92543i	−1.34579	−	0.365907i
$596$		0			0
$597$	4.92512	−	2.84352i	0.201572	−	0.116378i
$598$		0			0
$599$	29.1795	+	16.8468i	1.19224	+	0.688341i	0.958814	−	0.284033i	$-0.0916726\pi$
$599$	29.1795	+	16.8468i	1.19224	+	0.688341i	0.233427	+	0.972374i	$0.425006\pi$
$600$		0			0
$601$		−	24.3960i		−	0.995132i	−0.867426	−	0.497566i	$-0.834227\pi$
$601$		−	24.3960i		−	0.995132i	0.867426	−	0.497566i	$-0.165773\pi$
$602$		0			0
$603$	27.7879			1.13161
$604$		0			0
$605$	−13.4712	+	23.3329i	−0.547683	+	0.948616i
$606$		0			0
$607$	4.08757	+	7.07987i	0.165909	+	0.287363i	0.936978	−	0.349389i	$-0.113611\pi$
$607$	4.08757	+	7.07987i	0.165909	+	0.287363i	−0.771069	+	0.636752i	$0.780277\pi$
$608$		0			0
$609$	4.57700	+	4.61075i	0.185469	+	0.186837i
$610$		0			0
$611$	7.02235	+	12.1631i	0.284094	+	0.492065i
$612$		0			0
$613$	14.7221	+	8.49981i	0.594620	+	0.343304i	0.766922	−	0.641740i	$-0.221787\pi$
$613$	14.7221	+	8.49981i	0.594620	+	0.343304i	−0.172302	+	0.985044i	$0.555121\pi$
$614$		0			0
$615$	6.47768			0.261205
$616$		0			0
$617$	39.6548			1.59644			0.798221	−	0.602365i	$-0.205775\pi$
$617$	39.6548			1.59644			0.798221	+	0.602365i	$0.205775\pi$
$618$		0			0
$619$	12.4719	+	7.20065i	0.501288	+	0.289419i	0.729245	−	0.684252i	$-0.239871\pi$
$619$	12.4719	+	7.20065i	0.501288	+	0.289419i	−0.227957	+	0.973671i	$0.573205\pi$
$620$		0			0
$621$	−6.13514	−	10.6264i	−0.246195	−	0.426422i
$622$		0			0
$623$	1.16979	+	4.43075i	0.0468667	+	0.177514i
$624$		0			0
$625$	11.9709	+	20.7343i	0.478837	+	0.829370i
$626$		0			0
$627$	−2.03211	+	3.51971i	−0.0811545	+	0.140564i
$628$		0			0
$629$	−21.5246			−0.858241
$630$		0			0
$631$			36.6698i			1.45980i	0.683553	+	0.729900i	$0.260434\pi$
$631$			36.6698i			1.45980i	−0.683553	+	0.729900i	$0.739566\pi$
$632$		0			0
$633$	−4.19496	−	2.42196i	−0.166735	−	0.0962644i
$634$		0			0
$635$	−13.6124	+	7.85913i	−0.540192	+	0.311880i
$636$		0			0
$637$	8.38024	+	4.92077i	0.332037	+	0.194968i
$638$		0			0
$639$	−12.6879	+	7.32538i	−0.501927	+	0.289788i
$640$		0			0
$641$	−9.13798	+	15.8274i	−0.360929	+	0.625147i	−0.988114	−	0.153723i	$-0.950874\pi$
$641$	−9.13798	+	15.8274i	−0.360929	+	0.625147i	0.627185	+	0.778870i	$0.284207\pi$
$642$		0			0
$643$		−	13.6340i		−	0.537671i	−0.963186	−	0.268836i	$-0.913361\pi$
$643$		−	13.6340i		−	0.537671i	0.963186	−	0.268836i	$-0.0866389\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	8.74153	−	15.1408i	0.343665	−	0.595245i	−0.641445	−	0.767169i	$-0.721665\pi$
$647$	8.74153	−	15.1408i	0.343665	−	0.595245i	0.985110	+	0.171923i	$0.0549982\pi$
$648$		0			0
$649$	−7.02907	+	4.05824i	−0.275915	+	0.159300i
$650$		0			0
$651$	0.0376633	+	0.142655i	0.00147614	+	0.00559110i
$652$		0			0
$653$	−8.40495	+	4.85260i	−0.328911	+	0.189897i	−0.655358	−	0.755319i	$-0.727482\pi$
$653$	−8.40495	+	4.85260i	−0.328911	+	0.189897i	0.326446	+	0.945216i	$0.394149\pi$
$654$		0			0
$655$	10.9131	+	6.30070i	0.426411	+	0.246189i
$656$		0			0
$657$		−	29.7488i		−	1.16061i
$658$		0			0
$659$	28.9465			1.12760			0.563798	−	0.825913i	$-0.309340\pi$
$659$	28.9465			1.12760			0.563798	+	0.825913i	$0.309340\pi$
$660$		0			0
$661$	−6.43683	+	11.1489i	−0.250364	+	0.433643i	−0.963626	−	0.267254i	$-0.913884\pi$
$661$	−6.43683	+	11.1489i	−0.250364	+	0.433643i	0.713262	+	0.700897i	$0.247217\pi$
$662$		0			0
$663$	−1.34373	−	2.32742i	−0.0521863	−	0.0903893i
$664$		0			0
$665$	−31.6475	+	31.4159i	−1.22724	+	1.21826i
$666$		0			0
$667$	−11.2922	−	19.5587i	−0.437238	−	0.757318i
$668$		0			0
$669$	10.1239	+	5.84502i	0.391412	+	0.225982i
$670$		0			0
$671$	13.4964			0.521024
$672$		0			0
$673$	−23.6548			−0.911825			−0.455912	−	0.890025i	$-0.650687\pi$
$673$	−23.6548			−0.911825			−0.455912	+	0.890025i	$0.650687\pi$
$674$		0			0
$675$	12.5012	+	7.21755i	0.481170	+	0.277804i
$676$		0			0
$677$	−1.80224	−	3.12157i	−0.0692657	−	0.119972i	0.829313	−	0.558785i	$-0.188732\pi$
$677$	−1.80224	−	3.12157i	−0.0692657	−	0.119972i	−0.898578	+	0.438813i	$0.855399\pi$
$678$		0			0
$679$	7.33237	+	1.99360i	0.281391	+	0.0765072i
$680$		0			0
$681$	3.44419	+	5.96550i	0.131981	+	0.228599i
$682$		0			0
$683$	−3.80924	+	6.59779i	−0.145756	+	0.252457i	−0.929655	−	0.368432i	$-0.879895\pi$
$683$	−3.80924	+	6.59779i	−0.145756	+	0.252457i	0.783899	+	0.620889i	$0.213228\pi$
$684$		0			0
$685$	0.328514			0.0125519
$686$		0			0
$687$		−	5.12162i		−	0.195402i
$688$		0			0
$689$	−8.51745	−	4.91755i	−0.324489	−	0.187344i
$690$		0			0
$691$	44.9707	−	25.9639i	1.71077	−	0.987712i	0.777241	−	0.629203i	$-0.216619\pi$
$691$	44.9707	−	25.9639i	1.71077	−	0.987712i	0.933526	−	0.358509i	$-0.116715\pi$
$692$		0			0
$693$	−3.07831	+	11.3219i	−0.116935	+	0.430083i
$694$		0			0
$695$	−41.4364	+	23.9233i	−1.57177	+	0.907462i
$696$		0			0
$697$	8.48721	−	14.7003i	0.321476	−	0.556813i
$698$		0			0
$699$			0.306806i			0.0116045i
$700$		0			0
$701$			0.741474i			0.0280051i	0.999902	+	0.0140025i	$0.00445729\pi$
$701$			0.741474i			0.0280051i	−0.999902	+	0.0140025i	$0.995543\pi$
$702$		0			0
$703$	−14.1074	+	24.4347i	−0.532071	+	0.921574i
$704$		0			0
$705$	13.4581	−	7.77006i	0.506863	−	0.292637i
$706$		0			0
$707$	−12.6864	−	12.7799i	−0.477120	−	0.480638i
$708$		0			0
$709$	−35.6491	+	20.5820i	−1.33883	+	0.772974i	−0.986634	−	0.162952i	$-0.947898\pi$
$709$	−35.6491	+	20.5820i	−1.33883	+	0.772974i	−0.352196	+	0.935926i	$0.614565\pi$
$710$		0			0
$711$	28.6147	+	16.5207i	1.07314	+	0.619575i
$712$		0			0
$713$		−	0.512901i		−	0.0192083i
$714$		0			0
$715$	7.10284			0.265631
$716$		0			0
$717$	1.13863	−	1.97216i	0.0425229	−	0.0736518i
$718$		0			0
$719$	7.02471	+	12.1672i	0.261978	+	0.453758i	0.966767	−	0.255658i	$-0.0822920\pi$
$719$	7.02471	+	12.1672i	0.261978	+	0.453758i	−0.704790	+	0.709416i	$0.748959\pi$
$720$		0			0
$721$	−35.9398	+	9.48869i	−1.33847	+	0.353377i
$722$		0			0
$723$	−2.81479	−	4.87536i	−0.104683	−	0.181317i
$724$		0			0
$725$	23.0095	+	13.2845i	0.854550	+	0.493375i
$726$		0			0
$727$	13.2022			0.489642			0.244821	−	0.969568i	$-0.421271\pi$
$727$	13.2022			0.489642			0.244821	+	0.969568i	$0.421271\pi$
$728$		0			0
$729$	15.3015			0.566724
$730$		0			0
$731$		0			0
$732$		0			0
$733$	−24.9797	−	43.2661i	−0.922646	−	1.59807i	−0.795304	−	0.606211i	$-0.792689\pi$
$733$	−24.9797	−	43.2661i	−0.922646	−	1.59807i	−0.127342	−	0.991859i	$-0.540644\pi$
$734$		0			0
$735$	5.44471	−	9.27253i	0.200831	−	0.342022i
$736$		0			0
$737$	−8.03747	−	13.9213i	−0.296064	−	0.512798i
$738$		0			0
$739$	−18.2718	+	31.6476i	−0.672138	+	1.16418i	0.305159	+	0.952301i	$0.401290\pi$
$739$	−18.2718	+	31.6476i	−0.672138	+	1.16418i	−0.977297	+	0.211875i	$0.932043\pi$
$740$		0			0
$741$	−3.52278			−0.129413
$742$		0			0
$743$		−	15.1330i		−	0.555177i	−0.960700	−	0.277589i	$-0.910465\pi$
$743$		−	15.1330i		−	0.555177i	0.960700	−	0.277589i	$-0.0895352\pi$
$744$		0			0
$745$	31.2771	+	18.0579i	1.14591	+	0.661589i
$746$		0			0
$747$	−35.9163	+	20.7363i	−1.31411	+	0.758701i
$748$		0			0
$749$	13.1464	−	3.47087i	0.480360	−	0.126823i
$750$		0			0
$751$	11.9997	−	6.92806i	0.437877	−	0.252808i	−0.264820	−	0.964298i	$-0.585312\pi$
$751$	11.9997	−	6.92806i	0.437877	−	0.252808i	0.702697	+	0.711490i	$0.251979\pi$
$752$		0			0
$753$	−2.78036	+	4.81572i	−0.101322	+	0.175495i
$754$		0			0
$755$		−	47.3412i		−	1.72292i
$756$		0			0
$757$			46.6967i			1.69722i	0.529019	+	0.848610i	$0.322560\pi$
$757$			46.6967i			1.69722i	−0.529019	+	0.848610i	$0.677440\pi$
$758$		0			0
$759$	−1.70341	+	2.95039i	−0.0618299	+	0.107093i
$760$		0			0
$761$	40.7899	−	23.5501i	1.47863	−	0.853689i	0.478925	−	0.877856i	$-0.341026\pi$
$761$	40.7899	−	23.5501i	1.47863	−	0.853689i	0.999708	+	0.0241662i	$0.00769309\pi$
$762$		0			0
$763$	5.31596	−	5.27705i	0.192451	−	0.191042i
$764$		0			0
$765$	30.8309	−	17.8002i	1.11469	−	0.643568i
$766$		0			0
$767$	−6.09267	−	3.51761i	−0.219994	−	0.127013i
$768$		0			0
$769$			17.3071i			0.624110i	0.950064	+	0.312055i	$0.101017\pi$
$769$			17.3071i			0.624110i	−0.950064	+	0.312055i	$0.898983\pi$
$770$		0			0
$771$	−11.3448			−0.408574
$772$		0			0
$773$	13.5389	−	23.4501i	0.486960	−	0.843440i	−0.512927	−	0.858432i	$-0.671439\pi$
$773$	13.5389	−	23.4501i	0.486960	−	0.843440i	0.999888	+	0.0149920i	$0.00477229\pi$
$774$		0			0
$775$	0.301696	+	0.522552i	0.0108372	+	0.0187706i
$776$		0			0
$777$	1.78502	−	6.56523i	0.0640372	−	0.235526i
$778$		0			0
$779$	−11.1252	−	19.2694i	−0.398601	−	0.690398i
$780$		0			0
$781$	7.33982	+	4.23764i	0.262639	+	0.151635i
$782$		0			0
$783$	−14.1654			−0.506230
$784$		0			0
$785$	−2.35969			−0.0842208
$786$		0			0
$787$	46.9684	+	27.1172i	1.67424	+	0.966624i	0.965220	+	0.261439i	$0.0841969\pi$
$787$	46.9684	+	27.1172i	1.67424	+	0.966624i	0.709023	+	0.705186i	$0.249136\pi$
$788$		0			0
$789$	2.56778	+	4.44753i	0.0914155	+	0.158336i
$790$		0			0
$791$	0.997467	−	3.66864i	0.0354658	−	0.130442i
$792$		0			0
$793$	5.84923	+	10.1312i	0.207712	+	0.359768i
$794$		0			0
$795$	−5.44115	+	9.42435i	−0.192978	+	0.334247i
$796$		0			0
$797$	−20.1437			−0.713527			−0.356763	−	0.934195i	$-0.616120\pi$
$797$	−20.1437			−0.713527			−0.356763	+	0.934195i	$0.616120\pi$
$798$		0			0
$799$		−	40.7221i		−	1.44064i
$800$		0			0
$801$	−4.15310	−	2.39779i	−0.146743	−	0.0847219i
$802$		0			0
$803$	−14.9037	+	8.60465i	−0.525940	+	0.303651i
$804$		0			0
$805$	−26.5285	+	26.3344i	−0.935008	+	0.928164i
$806$		0			0
$807$	−9.71963	+	5.61163i	−0.342147	+	0.197539i
$808$		0			0
$809$	−17.2771	+	29.9249i	−0.607432	+	1.05210i	0.384231	+	0.923237i	$0.374467\pi$
$809$	−17.2771	+	29.9249i	−0.607432	+	1.05210i	−0.991662	+	0.128865i	$0.958867\pi$
$810$		0			0
$811$			13.6340i			0.478754i	0.970927	+	0.239377i	$0.0769431\pi$
$811$			13.6340i			0.478754i	−0.970927	+	0.239377i	$0.923057\pi$
$812$		0			0
$813$		−	6.55911i		−	0.230038i
$814$		0			0
$815$	13.9023	−	24.0795i	0.486976	−	0.843468i
$816$		0			0
$817$		0			0
$818$		0			0
$819$	−9.83294	+	2.59606i	−0.343591	+	0.0907136i
$820$		0			0
$821$	27.7311	−	16.0106i	0.967822	−	0.558772i	0.0692505	−	0.997599i	$-0.477939\pi$
$821$	27.7311	−	16.0106i	0.967822	−	0.558772i	0.898572	+	0.438827i	$0.144606\pi$
$822$		0			0
$823$	−26.8399	−	15.4960i	−0.935580	−	0.540158i	−0.0470083	−	0.998894i	$-0.514969\pi$
$823$	−26.8399	−	15.4960i	−0.935580	−	0.540158i	−0.888572	+	0.458737i	$0.848302\pi$
$824$		0			0
$825$		−	4.00788i		−	0.139537i
$826$		0			0
$827$	11.0191			0.383172			0.191586	−	0.981476i	$-0.438637\pi$
$827$	11.0191			0.383172			0.191586	+	0.981476i	$0.438637\pi$
$828$		0			0
$829$	18.9836	−	32.8806i	0.659328	−	1.14199i	−0.321462	−	0.946922i	$-0.604174\pi$
$829$	18.9836	−	32.8806i	0.659328	−	1.14199i	0.980790	−	0.195067i	$-0.0624924\pi$
$830$		0			0
$831$	−0.109999	−	0.190524i	−0.00381582	−	0.00660919i
$832$		0			0
$833$	−13.9090	−	24.5052i	−0.481920	−	0.849054i
$834$		0			0
$835$	2.21731	+	3.84050i	0.0767332	+	0.132906i
$836$		0			0
$837$	−0.278601	−	0.160850i	−0.00962984	−	0.00555979i
$838$		0			0
$839$	−8.32984			−0.287578			−0.143789	−	0.989608i	$-0.545929\pi$
$839$	−8.32984			−0.287578			−0.143789	+	0.989608i	$0.545929\pi$
$840$		0			0
$841$	2.92739			0.100945
$842$		0			0
$843$	0.598452	+	0.345516i	0.0206118	+	0.0119002i
$844$		0			0
$845$	−17.6844	−	30.6304i	−0.608363	−	1.05372i
$846$		0			0
$847$	−21.5766	+	5.69657i	−0.741380	+	0.195736i
$848$		0			0
$849$	−7.50840	−	13.0049i	−0.257687	−	0.446328i
$850$		0			0
$851$	−11.8255	+	20.4824i	−0.405374	+	0.702128i
$852$		0			0
$853$	6.94153			0.237673			0.118837	−	0.992914i	$-0.462083\pi$
$853$	6.94153			0.237673			0.118837	+	0.992914i	$0.462083\pi$
$854$		0			0
$855$		−	46.6657i		−	1.59593i
$856$		0			0
$857$	1.91744	+	1.10704i	0.0654986	+	0.0378156i	0.532392	−	0.846498i	$-0.321293\pi$
$857$	1.91744	+	1.10704i	0.0654986	+	0.0378156i	−0.466893	+	0.884314i	$0.654627\pi$
$858$		0			0
$859$	−5.26337	+	3.03881i	−0.179584	+	0.103683i	−0.587097	−	0.809516i	$-0.699729\pi$
$859$	−5.26337	+	3.03881i	−0.179584	+	0.103683i	0.407513	+	0.913199i	$0.366396\pi$
$860$		0			0
$861$	3.77991	+	3.80778i	0.128819	+	0.129769i
$862$		0			0
$863$	−7.64747	+	4.41527i	−0.260323	+	0.150298i	−0.624482	−	0.781039i	$-0.714690\pi$
$863$	−7.64747	+	4.41527i	−0.260323	+	0.150298i	0.364159	+	0.931337i	$0.381357\pi$
$864$		0			0
$865$	−1.55026	+	2.68512i	−0.0527103	+	0.0912969i
$866$		0			0
$867$		−	0.383106i		−	0.0130110i
$868$		0			0
$869$		−	19.1141i		−	0.648400i
$870$		0			0
$871$	6.96673	−	12.0667i	0.236059	−	0.408866i
$872$		0			0
$873$	−6.88643	+	3.97588i	−0.233070	+	0.134563i
$874$		0			0
$875$	0.450909	−	1.65842i	0.0152435	−	0.0560650i
$876$		0			0
$877$	10.3059	−	5.95011i	0.348005	−	0.200921i	−0.315801	−	0.948825i	$-0.602273\pi$
$877$	10.3059	−	5.95011i	0.348005	−	0.200921i	0.663806	+	0.747905i	$0.268940\pi$
$878$		0			0
$879$	13.0358	+	7.52623i	0.439687	+	0.253854i
$880$		0			0
$881$		−	53.9142i		−	1.81642i	−0.418519	−	0.908208i	$-0.637451\pi$
$881$		−	53.9142i		−	1.81642i	0.418519	−	0.908208i	$-0.362549\pi$
$882$		0			0
$883$	−11.1987			−0.376866			−0.188433	−	0.982086i	$-0.560341\pi$
$883$	−11.1987			−0.376866			−0.188433	+	0.982086i	$0.560341\pi$
$884$		0			0
$885$	−3.89215	+	6.74139i	−0.130833	+	0.226609i
$886$		0			0
$887$	18.1832	+	31.4942i	0.610531	+	1.05747i	0.991151	+	0.132740i	$0.0423774\pi$
$887$	18.1832	+	31.4942i	0.610531	+	1.05747i	−0.380620	+	0.924732i	$0.624289\pi$
$888$		0			0
$889$	−12.5630	−	3.41576i	−0.421351	−	0.114561i
$890$		0			0
$891$	−5.58353	−	9.67095i	−0.187055	−	0.323989i
$892$		0			0
$893$	−46.2278	−	26.6896i	−1.54695	−	0.893134i
$894$		0			0
$895$	−45.5819			−1.52364
$896$		0			0
$897$	−2.95297			−0.0985968
$898$		0			0
$899$	−0.512788	−	0.296058i	−0.0171024	−	0.00987410i
$900$		0			0
$901$	14.2583	+	24.6960i	0.475011	+	0.822744i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−24.4709	−	42.3849i	−0.813441	−	1.40892i
$906$		0			0
$907$	−8.92370	+	15.4563i	−0.296307	+	0.513218i	−0.975288	−	0.220937i	$-0.929088\pi$
$907$	−8.92370	+	15.4563i	−0.296307	+	0.513218i	0.678981	+	0.734156i	$0.262422\pi$
$908$		0			0
$909$	18.8446			0.625034
$910$		0			0
$911$			11.1458i			0.369278i	0.982806	+	0.184639i	$0.0591116\pi$
$911$			11.1458i			0.369278i	−0.982806	+	0.184639i	$0.940888\pi$
$912$		0			0
$913$	20.7771	+	11.9957i	0.687623	+	0.396999i
$914$		0			0
$915$	11.2099	−	6.47203i	0.370587	−	0.213959i
$916$		0			0
$917$	2.66437	+	10.0917i	0.0879854	+	0.333257i
$918$		0			0
$919$	28.2802	−	16.3276i	0.932879	−	0.538598i	0.0451579	−	0.998980i	$-0.485621\pi$
$919$	28.2802	−	16.3276i	0.932879	−	0.538598i	0.887721	+	0.460382i	$0.152288\pi$
$920$		0			0
$921$	−3.53980	+	6.13111i	−0.116640	+	0.202027i
$922$		0			0
$923$			7.34623i			0.241804i
$924$		0			0
$925$		−	27.8238i		−	0.914839i
$926$		0			0
$927$	19.4496	−	33.6876i	0.638807	−	1.10645i
$928$		0			0
$929$	−23.3027	+	13.4538i	−0.764537	+	0.441406i	−0.830922	−	0.556388i	$-0.812187\pi$
$929$	−23.3027	+	13.4538i	−0.764537	+	0.441406i	0.0663853	+	0.997794i	$0.478853\pi$
$930$		0			0
$931$	−36.9344	−	0.271329i	−1.21048	−	0.00889246i
$932$		0			0
$933$	−6.48885	+	3.74634i	−0.212435	+	0.122650i
$934$		0			0
$935$	−17.8353	−	10.2972i	−0.583276	−	0.336755i
$936$		0			0
$937$			32.6476i			1.06655i	0.845942	+	0.533275i	$0.179039\pi$
$937$			32.6476i			1.06655i	−0.845942	+	0.533275i	$0.820961\pi$
$938$		0			0
$939$	6.29315			0.205369
$940$		0			0
$941$	6.32087	−	10.9481i	0.206055	−	0.356897i	−0.744414	−	0.667719i	$-0.767271\pi$
$941$	6.32087	−	10.9481i	0.206055	−	0.356897i	0.950468	+	0.310822i	$0.100604\pi$
$942$		0			0
$943$	−9.32569	−	16.1526i	−0.303686	−	0.526000i
$944$		0			0
$945$	5.98488	+	22.6686i	0.194688	+	0.737410i
$946$		0			0
$947$	−21.1271	−	36.5931i	−0.686537	−	1.18912i	−0.972951	−	0.231011i	$-0.925797\pi$
$947$	−21.1271	−	36.5931i	−0.686537	−	1.18912i	0.286414	−	0.958106i	$-0.407537\pi$
$948$		0			0
$949$	−12.9182	−	7.45835i	−0.419344	−	0.242108i
$950$		0			0
$951$	−11.3264			−0.367285
$952$		0			0
$953$	−44.4561			−1.44007			−0.720037	−	0.693936i	$-0.755875\pi$
$953$	−44.4561			−1.44007			−0.720037	+	0.693936i	$0.755875\pi$
$954$		0			0
$955$	−6.91764	−	3.99390i	−0.223850	−	0.129240i
$956$		0			0
$957$	1.96650	+	3.40607i	0.0635678	+	0.110103i
$958$		0			0
$959$	0.191697	+	0.193110i	0.00619021	+	0.00623585i
$960$		0			0
$961$	15.4933	+	26.8351i	0.499783	+	0.865650i
$962$		0			0
$963$	−7.11447	+	12.3226i	−0.229261	+	0.397091i
$964$		0			0
$965$	9.90388			0.318817
$966$		0			0
$967$			25.7160i			0.826972i	0.910510	+	0.413486i	$0.135689\pi$
$967$			25.7160i			0.826972i	−0.910510	+	0.413486i	$0.864311\pi$
$968$		0			0
$969$	8.84573	+	5.10709i	0.284166	+	0.164063i
$970$		0			0
$971$	40.2746	−	23.2526i	1.29247	−	0.746210i	0.313381	−	0.949627i	$-0.398538\pi$
$971$	40.2746	−	23.2526i	1.29247	−	0.746210i	0.979092	+	0.203417i	$0.0652048\pi$
$972$		0			0
$973$	−38.2421	−	10.3976i	−1.22599	−	0.333333i
$974$		0			0
$975$	3.00854	−	1.73698i	0.0963503	−	0.0556278i
$976$		0			0
$977$	−17.1348	+	29.6783i	−0.548189	+	0.949492i	0.450209	+	0.892923i	$0.351349\pi$
$977$	−17.1348	+	29.6783i	−0.548189	+	0.949492i	−0.998399	+	0.0565688i	$0.981984\pi$
$978$		0			0
$979$			2.77419i			0.0886635i
$980$		0			0
$981$			7.83862i			0.250268i
$982$		0			0
$983$	−0.777334	+	1.34638i	−0.0247931	+	0.0429429i	−0.878156	−	0.478375i	$-0.841226\pi$
$983$	−0.777334	+	1.34638i	−0.0247931	+	0.0429429i	0.853363	+	0.521318i	$0.174559\pi$
$984$		0			0
$985$	43.4012	−	25.0577i	1.38288	−	0.798404i
$986$		0			0
$987$	12.4207	+	3.37705i	0.395354	+	0.107493i
$988$		0			0
$989$		0			0
$990$		0			0
$991$	22.6482	+	13.0759i	0.719443	+	0.415371i	0.814548	−	0.580097i	$-0.196985\pi$
$991$	22.6482	+	13.0759i	0.719443	+	0.415371i	−0.0951047	+	0.995467i	$0.530319\pi$
$992$		0			0
$993$			15.8964i			0.504457i
$994$		0			0
$995$	37.7748			1.19754
$996$		0			0
$997$	−18.1467	+	31.4310i	−0.574711	+	0.995429i	0.421362	+	0.906893i	$0.361552\pi$
$997$	−18.1467	+	31.4310i	−0.574711	+	0.995429i	−0.996073	+	0.0885360i	$0.971781\pi$
$998$		0			0
$999$	7.41717	+	12.8469i	0.234669	+	0.406458i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	224.2.q.a.143.4		12
3.2	odd	2		2016.2.bs.a.1711.1		12
4.3	odd	2		56.2.m.a.3.4	✓	12
7.2	even	3		1568.2.q.g.1391.4		12
7.3	odd	6		1568.2.e.e.783.8		12
7.4	even	3		1568.2.e.e.783.5		12
7.5	odd	6	inner	224.2.q.a.47.3		12
7.6	odd	2		1568.2.q.g.815.3		12
8.3	odd	2	inner	224.2.q.a.143.3		12
8.5	even	2		56.2.m.a.3.6	yes	12
12.11	even	2		504.2.bk.a.451.3		12
21.5	even	6		2016.2.bs.a.271.6		12
24.5	odd	2		504.2.bk.a.451.1		12
24.11	even	2		2016.2.bs.a.1711.6		12
28.3	even	6		392.2.e.e.195.1		12
28.11	odd	6		392.2.e.e.195.2		12
28.19	even	6		56.2.m.a.19.5	yes	12
28.23	odd	6		392.2.m.g.19.5		12
28.27	even	2		392.2.m.g.227.4		12
56.3	even	6		1568.2.e.e.783.7		12
56.5	odd	6		56.2.m.a.19.3	yes	12
56.11	odd	6		1568.2.e.e.783.6		12
56.13	odd	2		392.2.m.g.227.6		12
56.19	even	6	inner	224.2.q.a.47.4		12
56.27	even	2		1568.2.q.g.815.4		12
56.37	even	6		392.2.m.g.19.3		12
56.45	odd	6		392.2.e.e.195.3		12
56.51	odd	6		1568.2.q.g.1391.3		12
56.53	even	6		392.2.e.e.195.4		12
84.47	odd	6		504.2.bk.a.19.2		12
168.5	even	6		504.2.bk.a.19.4		12
168.131	odd	6		2016.2.bs.a.271.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.2.m.a.3.4	✓	12	4.3	odd	2
56.2.m.a.3.6	yes	12	8.5	even	2
56.2.m.a.19.3	yes	12	56.5	odd	6
56.2.m.a.19.5	yes	12	28.19	even	6
224.2.q.a.47.3		12	7.5	odd	6	inner
224.2.q.a.47.4		12	56.19	even	6	inner
224.2.q.a.143.3		12	8.3	odd	2	inner
224.2.q.a.143.4		12	1.1	even	1	trivial
392.2.e.e.195.1		12	28.3	even	6
392.2.e.e.195.2		12	28.11	odd	6
392.2.e.e.195.3		12	56.45	odd	6
392.2.e.e.195.4		12	56.53	even	6
392.2.m.g.19.3		12	56.37	even	6
392.2.m.g.19.5		12	28.23	odd	6
392.2.m.g.227.4		12	28.27	even	2
392.2.m.g.227.6		12	56.13	odd	2
504.2.bk.a.19.2		12	84.47	odd	6
504.2.bk.a.19.4		12	168.5	even	6
504.2.bk.a.451.1		12	24.5	odd	2
504.2.bk.a.451.3		12	12.11	even	2
1568.2.e.e.783.5		12	7.4	even	3
1568.2.e.e.783.6		12	56.11	odd	6
1568.2.e.e.783.7		12	56.3	even	6
1568.2.e.e.783.8		12	7.3	odd	6
1568.2.q.g.815.3		12	7.6	odd	2
1568.2.q.g.815.4		12	56.27	even	2
1568.2.q.g.1391.3		12	56.51	odd	6
1568.2.q.g.1391.4		12	7.2	even	3
2016.2.bs.a.271.1		12	168.131	odd	6
2016.2.bs.a.271.6		12	21.5	even	6
2016.2.bs.a.1711.1		12	3.2	odd	2
2016.2.bs.a.1711.6		12	24.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 224 = 2^{5} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	224.q (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.416472 + 0.240450i) q^{3} +(1.59713 + 2.76632i) q^{5} +(-0.694153 + 2.55307i) q^{7} +(-1.38437 - 2.39779i) q^{9} +O(q^{10})\)	\(q+(0.416472 + 0.240450i) q^{3} +(1.59713 + 2.76632i) q^{5} +(-0.694153 + 2.55307i) q^{7} +(-1.38437 - 2.39779i) q^{9} +(-0.800840 + 1.38709i) q^{11} -1.38831 q^{13} +1.53613i q^{15} +(3.48605 + 2.01267i) q^{17} +(4.56957 - 2.63824i) q^{19} +(-0.902982 + 0.896373i) q^{21} +(3.83044 - 2.21151i) q^{23} +(-2.60168 + 4.50624i) q^{25} -2.77419i q^{27} -5.10613i q^{29} +(0.0579809 - 0.100426i) q^{31} +(-0.667055 + 0.385124i) q^{33} +(-8.17125 + 2.15734i) q^{35} +(-4.63087 + 2.67363i) q^{37} +(-0.578191 - 0.333819i) q^{39} -4.21689i q^{41} +(4.42204 - 7.65920i) q^{45} +(-5.05821 - 8.76108i) q^{47} +(-6.03630 - 3.54444i) q^{49} +(0.967895 + 1.67644i) q^{51} +(6.13514 + 3.54212i) q^{53} -5.11619 q^{55} +2.53747 q^{57} +(4.38856 + 2.53374i) q^{59} +(-4.21321 - 7.29750i) q^{61} +(7.08269 - 1.86995i) q^{63} +(-2.21731 - 3.84050i) q^{65} +(-5.01815 + 8.69169i) q^{67} +2.12703 q^{69} -5.29150i q^{71} +(9.30504 + 5.37227i) q^{73} +(-2.16706 + 1.25115i) q^{75} +(-2.98544 - 3.00745i) q^{77} +(-10.3349 + 5.96688i) q^{79} +(-3.48605 + 6.03801i) q^{81} -14.9789i q^{83} +12.8580i q^{85} +(1.22777 - 2.12656i) q^{87} +(1.50000 - 0.866025i) q^{89} +(0.963697 - 3.54444i) q^{91} +(0.0482949 - 0.0278831i) q^{93} +(14.5965 + 8.42726i) q^{95} -2.87198i q^{97} +4.43462 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{3}+O(q^{10}) \) 12 * q + 6 * q^3	\( 12 q + 6 q^{3} + 6 q^{11} - 6 q^{17} + 6 q^{19} - 6 q^{33} - 18 q^{35} - 12 q^{49} - 6 q^{51} - 36 q^{57} - 42 q^{59} - 12 q^{65} - 30 q^{67} + 18 q^{73} - 24 q^{75} + 6 q^{81} + 18 q^{89} + 72 q^{91} + 24 q^{99}+O(q^{100}) \) 12 * q + 6 * q^3 + 6 * q^11 - 6 * q^17 + 6 * q^19 - 6 * q^33 - 18 * q^35 - 12 * q^49 - 6 * q^51 - 36 * q^57 - 42 * q^59 - 12 * q^65 - 30 * q^67 + 18 * q^73 - 24 * q^75 + 6 * q^81 + 18 * q^89 + 72 * q^91 + 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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