LMFDB - Embedded newform 567.2.s.f.26.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [567,2,Mod(26,567)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(567, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 5]))

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

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

chi := DirichletCharacter("567.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.s (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:	$4.52751779461$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 9x^{10} + 59x^{8} - 180x^{6} + 403x^{4} - 198x^{2} + 81 $ x^12 - 9x^10 + 59x^8 - 180x^6 + 403x^4 - 198*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	no (minimal twist has level 189)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			26.5
Root			$1.90412 - 1.09935i$ of defining polynomial
Character	$\chi$	$=$	567.26
Dual form			567.2.s.f.458.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.58850 - 0.917122i) q^{2} +(0.682224 - 1.18165i) q^{4} -3.80824 q^{5} +(-2.43359 + 1.03810i) q^{7} +1.16576i q^{8} +O(q^{10})$	\(q+(1.58850 - 0.917122i) q^{2} +(0.682224 - 1.18165i) q^{4} -3.80824 q^{5} +(-2.43359 + 1.03810i) q^{7} +1.16576i q^{8} +(-6.04940 + 3.49262i) q^{10} -1.16576i q^{11} +(-4.79804 + 2.77015i) q^{13} +(-2.91370 + 3.88092i) q^{14} +(2.43359 + 4.21510i) q^{16} +(-1.58850 - 2.75136i) q^{17} +(-0.546672 - 0.315621i) q^{19} +(-2.59808 + 4.50000i) q^{20} +(-1.06914 - 1.85181i) q^{22} -1.76183i q^{23} +9.50273 q^{25} +(-5.08112 + 8.80077i) q^{26} +(-0.433589 + 3.58386i) q^{28} +(-4.18658 - 2.41712i) q^{29} +(3.70469 + 2.13891i) q^{31} +(5.71237 + 3.29804i) q^{32} +(-5.04667 - 2.91370i) q^{34} +(9.26770 - 3.95333i) q^{35} +(-2.11581 + 3.66470i) q^{37} -1.15785 q^{38} -4.43949i q^{40} +(-2.28245 - 3.95333i) q^{41} +(-3.61581 + 6.26277i) q^{43} +(-1.37751 - 0.795307i) q^{44} +(-1.61581 - 2.79867i) q^{46} +(1.27288 + 2.20469i) q^{47} +(4.84471 - 5.05260i) q^{49} +(15.0951 - 8.71516i) q^{50} +7.55945i q^{52} +(-0.0627112 + 0.0362063i) q^{53} +4.43949i q^{55} +(-1.21017 - 2.83697i) q^{56} -8.86718 q^{58} +(3.49262 - 6.04940i) q^{59} +(-7.00273 + 4.04303i) q^{61} +7.84655 q^{62} +2.36445 q^{64} +(18.2721 - 10.5494i) q^{65} +(-2.54940 + 4.41569i) q^{67} -4.33485 q^{68} +(11.0961 - 14.7795i) q^{70} -4.76183i q^{71} +(4.84744 - 2.79867i) q^{73} +7.76183i q^{74} +(-0.745906 + 0.430649i) q^{76} +(1.21017 + 2.83697i) q^{77} +(-8.54940 - 14.8080i) q^{79} +(-9.26770 - 16.0521i) q^{80} +(-7.25136 - 4.18658i) q^{82} +(-5.08112 + 8.80077i) q^{83} +(6.04940 + 10.4779i) q^{85} +13.2646i q^{86} +1.35899 q^{88} +(-5.77508 + 10.0027i) q^{89} +(8.80077 - 11.7222i) q^{91} +(-2.08186 - 1.20196i) q^{92} +(4.04394 + 2.33477i) q^{94} +(2.08186 + 1.20196i) q^{95} +(0.596074 + 0.344143i) q^{97} +(3.06197 - 12.4693i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 8 q^{4} + 4 q^{7}+O(q^{10}) $ 12 * q + 8 * q^4 + 4 * q^7	$ 12 q + 8 q^{4} + 4 q^{7} - 6 q^{10} - 24 q^{13} - 4 q^{16} - 6 q^{19} + 20 q^{22} + 48 q^{25} + 28 q^{28} + 12 q^{31} - 60 q^{34} + 8 q^{37} - 10 q^{43} + 14 q^{46} + 24 q^{49} - 40 q^{58} - 18 q^{61} + 28 q^{64} + 36 q^{67} + 66 q^{70} - 42 q^{73} - 108 q^{76} - 36 q^{79} - 54 q^{82} + 6 q^{85} + 148 q^{88} + 6 q^{91} + 114 q^{94} - 60 q^{97}+O(q^{100}) $ 12 * q + 8 * q^4 + 4 * q^7 - 6 * q^10 - 24 * q^13 - 4 * q^16 - 6 * q^19 + 20 * q^22 + 48 * q^25 + 28 * q^28 + 12 * q^31 - 60 * q^34 + 8 * q^37 - 10 * q^43 + 14 * q^46 + 24 * q^49 - 40 * q^58 - 18 * q^61 + 28 * q^64 + 36 * q^67 + 66 * q^70 - 42 * q^73 - 108 * q^76 - 36 * q^79 - 54 * q^82 + 6 * q^85 + 148 * q^88 + 6 * q^91 + 114 * q^94 - 60 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	1.58850	−	0.917122i	1.12324	−	0.648503i	0.181014	−	0.983481i	$-0.442062\pi$
$2$	1.58850	−	0.917122i	1.12324	−	0.648503i	0.942226	+	0.334978i	$0.108729\pi$
$3$		0			0
$3$		0			0
$4$	0.682224	−	1.18165i	0.341112	−	0.590823i
$5$	−3.80824			−1.70310			−0.851549	−	0.524274i	$-0.824337\pi$
$5$	−3.80824			−1.70310			−0.851549	+	0.524274i	$0.824337\pi$
$6$		0			0
$7$	−2.43359	+	1.03810i	−0.919810	+	0.392364i
$7$	−2.43359	+	1.03810i	−0.919810	+	0.392364i
$8$			1.16576i			0.412157i
$9$		0			0
$10$	−6.04940	+	3.49262i	−1.91299	+	1.10446i
$11$		−	1.16576i		−	0.351489i	−0.984436	−	0.175744i	$-0.943767\pi$
$11$		−	1.16576i		−	0.351489i	0.984436	−	0.175744i	$-0.0562332\pi$
$12$		0			0
$13$	−4.79804	+	2.77015i	−1.33074	+	0.768301i	−0.985412	−	0.170183i	$-0.945564\pi$
$13$	−4.79804	+	2.77015i	−1.33074	+	0.768301i	−0.345324	+	0.938484i	$0.612231\pi$
$14$	−2.91370	+	3.88092i	−0.778718	+	1.03722i
$15$		0			0
$16$	2.43359	+	4.21510i	0.608397	+	1.05377i
$17$	−1.58850	−	2.75136i	−0.385268	−	0.667304i	0.606538	−	0.795054i	$-0.292558\pi$
$17$	−1.58850	−	2.75136i	−0.385268	−	0.667304i	−0.991806	+	0.127750i	$0.959224\pi$
$18$		0			0
$19$	−0.546672	−	0.315621i	−0.125415	−	0.0724085i	0.435980	−	0.899956i	$-0.356402\pi$
$19$	−0.546672	−	0.315621i	−0.125415	−	0.0724085i	−0.561395	+	0.827548i	$0.689735\pi$
$20$	−2.59808	+	4.50000i	−0.580948	+	1.00623i
$21$		0			0
$22$	−1.06914	−	1.85181i	−0.227942	−	0.394806i
$23$		−	1.76183i		−	0.367367i	−0.982985	−	0.183684i	$-0.941198\pi$
$23$		−	1.76183i		−	0.367367i	0.982985	−	0.183684i	$-0.0588022\pi$
$24$		0			0
$25$	9.50273			1.90055
$26$	−5.08112	+	8.80077i	−0.996491	+	1.72597i
$27$		0			0
$28$	−0.433589	+	3.58386i	−0.0819406	+	0.677285i
$29$	−4.18658	−	2.41712i	−0.777428	−	0.448848i	0.0580901	−	0.998311i	$-0.481499\pi$
$29$	−4.18658	−	2.41712i	−0.777428	−	0.448848i	−0.835518	+	0.549463i	$0.814832\pi$
$30$		0			0
$31$	3.70469	+	2.13891i	0.665382	+	0.384159i	0.794325	−	0.607493i	$-0.207825\pi$
$31$	3.70469	+	2.13891i	0.665382	+	0.384159i	−0.128942	+	0.991652i	$0.541158\pi$
$32$	5.71237	+	3.29804i	1.00981	+	0.583016i
$33$		0			0
$34$	−5.04667	−	2.91370i	−0.865497	−	0.499695i
$35$	9.26770	−	3.95333i	1.56653	−	0.668234i
$36$		0			0
$37$	−2.11581	+	3.66470i	−0.347837	+	0.602472i	−0.985865	−	0.167541i	$-0.946417\pi$
$37$	−2.11581	+	3.66470i	−0.347837	+	0.602472i	0.638028	+	0.770014i	$0.279751\pi$
$38$	−1.15785			−0.187828
$39$		0			0
$40$		−	4.43949i		−	0.701945i
$41$	−2.28245	−	3.95333i	−0.356460	−	0.617406i	0.630907	−	0.775858i	$-0.282683\pi$
$41$	−2.28245	−	3.95333i	−0.356460	−	0.617406i	−0.987367	+	0.158452i	$0.949350\pi$
$42$		0			0
$43$	−3.61581	+	6.26277i	−0.551406	+	0.955064i	0.446767	+	0.894650i	$0.352575\pi$
$43$	−3.61581	+	6.26277i	−0.551406	+	0.955064i	−0.998173	+	0.0604134i	$0.980758\pi$
$44$	−1.37751	−	0.795307i	−0.207668	−	0.119897i
$45$		0			0
$46$	−1.61581	−	2.79867i	−0.238239	−	0.412641i
$47$	1.27288	+	2.20469i	0.185669	+	0.321587i	0.943802	−	0.330512i	$-0.107222\pi$
$47$	1.27288	+	2.20469i	0.185669	+	0.321587i	−0.758133	+	0.652100i	$0.773888\pi$
$48$		0			0
$49$	4.84471	−	5.05260i	0.692101	−	0.721800i
$50$	15.0951	−	8.71516i	2.13477	−	1.23251i
$51$		0			0
$52$			7.55945i			1.04831i
$53$	−0.0627112	+	0.0362063i	−0.00861404	+	0.00497332i	−0.504301	−	0.863528i	$-0.668250\pi$
$53$	−0.0627112	+	0.0362063i	−0.00861404	+	0.00497332i	0.495687	+	0.868501i	$0.334916\pi$
$54$		0			0
$55$			4.43949i			0.598620i
$56$	−1.21017	−	2.83697i	−0.161716	−	0.379106i
$57$		0			0
$58$	−8.86718			−1.16432
$59$	3.49262	−	6.04940i	0.454701	−	0.787565i	−0.543970	−	0.839105i	$-0.683080\pi$
$59$	3.49262	−	6.04940i	0.454701	−	0.787565i	0.998671	+	0.0515396i	$0.0164128\pi$
$60$		0			0
$61$	−7.00273	+	4.04303i	−0.896608	+	0.517657i	−0.876098	−	0.482133i	$-0.839862\pi$
$61$	−7.00273	+	4.04303i	−0.896608	+	0.517657i	−0.0205096	+	0.999790i	$0.506529\pi$
$62$	7.84655			0.996512
$63$		0			0
$64$	2.36445			0.295556
$65$	18.2721	−	10.5494i	2.26638	−	1.30849i
$66$		0			0
$67$	−2.54940	+	4.41569i	−0.311459	+	0.539463i	−0.978678	−	0.205398i	$-0.934151\pi$
$67$	−2.54940	+	4.41569i	−0.311459	+	0.539463i	0.667219	+	0.744861i	$0.267484\pi$
$68$	−4.33485			−0.525678
$69$		0			0
$70$	11.0961	−	14.7795i	1.32623	−	1.76649i
$71$		−	4.76183i		−	0.565125i	−0.959249	−	0.282563i	$-0.908815\pi$
$71$		−	4.76183i		−	0.565125i	0.959249	−	0.282563i	$-0.0911845\pi$
$72$		0			0
$73$	4.84744	−	2.79867i	0.567350	−	0.327560i	−0.188740	−	0.982027i	$-0.560440\pi$
$73$	4.84744	−	2.79867i	0.567350	−	0.327560i	0.756090	+	0.654467i	$0.227107\pi$
$74$			7.76183i			0.902294i
$75$		0			0
$76$	−0.745906	+	0.430649i	−0.0855612	+	0.0493988i
$77$	1.21017	+	2.83697i	0.137912	+	0.323303i
$78$		0			0
$79$	−8.54940	−	14.8080i	−0.961883	−	1.66603i	−0.717766	−	0.696284i	$-0.754835\pi$
$79$	−8.54940	−	14.8080i	−0.961883	−	1.66603i	−0.244116	−	0.969746i	$-0.578498\pi$
$80$	−9.26770	−	16.0521i	−1.03616	−	1.79468i
$81$		0			0
$82$	−7.25136	−	4.18658i	−0.800779	−	0.462330i
$83$	−5.08112	+	8.80077i	−0.557726	+	0.966010i	0.439960	+	0.898017i	$0.354993\pi$
$83$	−5.08112	+	8.80077i	−0.557726	+	0.966010i	−0.997686	+	0.0679922i	$0.978341\pi$
$84$		0			0
$85$	6.04940	+	10.4779i	0.656150	+	1.13648i
$86$			13.2646i			1.43035i
$87$		0			0
$88$	1.35899			0.144869
$89$	−5.77508	+	10.0027i	−0.612157	+	1.06029i	0.378719	+	0.925512i	$0.376365\pi$
$89$	−5.77508	+	10.0027i	−0.612157	+	1.06029i	−0.990876	+	0.134776i	$0.956969\pi$
$90$		0			0
$91$	8.80077	−	11.7222i	0.922571	−	1.22882i
$92$	−2.08186	−	1.20196i	−0.217049	−	0.125313i
$93$		0			0
$94$	4.04394	+	2.33477i	0.417101	+	0.240813i
$95$	2.08186	+	1.20196i	0.213594	+	0.123319i
$96$		0			0
$97$	0.596074	+	0.344143i	0.0605221	+	0.0349425i	0.529956	−	0.848025i	$-0.322209\pi$
$97$	0.596074	+	0.344143i	0.0605221	+	0.0349425i	−0.469434	+	0.882968i	$0.655542\pi$
$98$	3.06197	−	12.4693i	0.309306	−	1.25958i
$99$		0			0
$100$	6.48299	−	11.2289i	0.648299	−	1.12289i
$101$	−6.58406			−0.655138			−0.327569	−	0.944827i	$-0.606229\pi$
$101$	−6.58406			−0.655138			−0.327569	+	0.944827i	$0.606229\pi$
$102$		0			0
$103$			9.34854i			0.921139i	0.887624	+	0.460570i	$0.152355\pi$
$103$			9.34854i			0.921139i	−0.887624	+	0.460570i	$0.847645\pi$
$104$	−3.22932	−	5.59334i	−0.316661	−	0.548473i
$105$		0			0
$106$	−0.0664112	+	0.115028i	−0.00645043	+	0.0111725i
$107$	13.6549	+	7.88364i	1.32007	+	0.762141i	0.983739	−	0.179604i	$-0.0574818\pi$
$107$	13.6549	+	7.88364i	1.32007	+	0.762141i	0.336328	+	0.941745i	$0.390815\pi$
$108$		0			0
$109$	7.23163	+	12.5255i	0.692664	+	1.19973i	0.970962	+	0.239235i	$0.0768965\pi$
$109$	7.23163	+	12.5255i	0.692664	+	1.19973i	−0.278298	+	0.960495i	$0.589770\pi$
$110$	4.07155	+	7.05213i	0.388207	+	0.672394i
$111$		0			0
$112$	−10.2980	−	7.73152i	−0.973073	−	0.730560i
$113$	−17.1998	+	9.93032i	−1.61802	+	0.934166i	−0.630591	+	0.776115i	$0.717188\pi$
$113$	−17.1998	+	9.93032i	−1.61802	+	0.934166i	−0.987431	+	0.158051i	$0.949479\pi$
$114$		0			0
$115$			6.70948i			0.625662i
$116$	−5.71237	+	3.29804i	−0.530380	+	0.306215i
$117$		0			0
$118$		−	12.8126i		−	1.17950i
$119$	6.72194	+	5.04667i	0.616199	+	0.462628i
$120$		0			0
$121$	9.64101			0.876456
$122$	−7.41590	+	12.8447i	−0.671404	+	1.16291i
$123$		0			0
$124$	5.05486	−	2.91843i	0.453940	−	0.262082i
$125$	−17.1475			−1.53372
$126$		0			0
$127$	−8.90666			−0.790338			−0.395169	−	0.918608i	$-0.629314\pi$
$127$	−8.90666			−0.790338			−0.395169	+	0.918608i	$0.629314\pi$
$128$	−7.66881	+	4.42759i	−0.677833	+	0.391347i
$129$		0			0
$130$	19.3502	−	33.5155i	1.69712	−	2.93950i
$131$	6.75519			0.590204			0.295102	−	0.955466i	$-0.404646\pi$
$131$	6.75519			0.590204			0.295102	+	0.955466i	$0.404646\pi$
$132$		0			0
$133$	1.65802	+	0.200594i	0.143769	+	0.0173937i
$134$			9.35245i			0.807928i
$135$		0			0
$136$	3.20742	−	1.85181i	0.275034	−	0.158791i
$137$		−	16.8606i		−	1.44050i	−0.693714	−	0.720251i	$-0.744027\pi$
$137$		−	16.8606i		−	1.44050i	0.693714	−	0.720251i	$-0.255973\pi$
$138$		0			0
$139$	−0.704693	+	0.406855i	−0.0597713	+	0.0345089i	−0.529588	−	0.848255i	$-0.677653\pi$
$139$	−0.704693	+	0.406855i	−0.0597713	+	0.0345089i	0.469817	+	0.882764i	$0.344320\pi$
$140$	1.65121	−	13.6482i	0.139553	−	1.15348i
$141$		0			0
$142$	−4.36718	−	7.56417i	−0.366485	−	0.634771i
$143$	3.22932	+	5.59334i	0.270049	+	0.467739i
$144$		0			0
$145$	15.9435	+	9.20499i	1.32404	+	0.764433i
$146$	5.13344	−	8.89138i	0.424847	−	0.735856i
$147$		0			0
$148$	2.88692	+	5.00029i	0.237303	+	0.411021i
$149$			8.43032i			0.690638i	0.938485	+	0.345319i	$0.112229\pi$
$149$			8.43032i			0.690638i	−0.938485	+	0.345319i	$0.887771\pi$
$150$		0			0
$151$	3.03948			0.247349			0.123675	−	0.992323i	$-0.460532\pi$
$151$	3.03948			0.247349			0.123675	+	0.992323i	$0.460532\pi$
$152$	0.367938	−	0.637287i	0.0298437	−	0.0516908i
$153$		0			0
$154$	4.52420	+	3.39666i	0.364571	+	0.273711i
$155$	−14.1084	−	8.14548i	−1.13321	−	0.654260i
$156$		0			0
$157$	3.29804	+	1.90412i	0.263212	+	0.151966i	0.625799	−	0.779984i	$-0.284773\pi$
$157$	3.29804	+	1.90412i	0.263212	+	0.151966i	−0.362587	+	0.931950i	$0.618106\pi$
$158$	−27.1615	−	15.6817i	−2.16085	−	1.24757i
$159$		0			0
$160$	−21.7541	−	12.5597i	−1.71981	−	0.992934i
$161$	1.82895	+	4.28757i	0.144142	+	0.337908i
$162$		0			0
$163$	5.54667	−	9.60712i	0.434449	−	0.752488i	−0.562802	−	0.826592i	$-0.690276\pi$
$163$	5.54667	−	9.60712i	0.434449	−	0.752488i	0.997250	+	0.0741045i	$0.0236098\pi$
$164$	−6.22858			−0.486371
$165$		0			0
$166$			18.6400i			1.44675i
$167$	−1.85181	−	3.20742i	−0.143297	−	0.248198i	0.785439	−	0.618939i	$-0.212437\pi$
$167$	−1.85181	−	3.20742i	−0.143297	−	0.248198i	−0.928736	+	0.370741i	$0.879104\pi$
$168$		0			0
$169$	8.84744	−	15.3242i	0.680572	−	1.17879i
$170$	19.2190	+	11.0961i	1.47403	+	0.851030i
$171$		0			0
$172$	4.93359	+	8.54523i	0.376183	+	0.651567i
$173$	4.81782	+	8.34471i	0.366292	+	0.634436i	0.988983	−	0.148032i	$-0.0472938\pi$
$173$	4.81782	+	8.34471i	0.366292	+	0.634436i	−0.622691	+	0.782468i	$0.713960\pi$
$174$		0			0
$175$	−23.1257	+	9.86476i	−1.74814	+	0.745705i
$176$	4.91378	−	2.83697i	0.370390	−	0.213845i
$177$		0			0
$178$			21.1858i			1.58794i
$179$	−15.9792	+	9.22562i	−1.19435	+	0.689556i	−0.959289	−	0.282426i	$-0.908861\pi$
$179$	−15.9792	+	9.22562i	−1.19435	+	0.689556i	−0.235056	+	0.971982i	$0.575527\pi$
$180$		0			0
$181$		−	16.6209i		−	1.23542i	−0.786406	−	0.617710i	$-0.788060\pi$
$181$		−	16.6209i		−	1.23542i	0.786406	−	0.617710i	$-0.211940\pi$
$182$	3.22932	−	26.6921i	0.239373	−	1.97855i
$183$		0			0
$184$	2.05387			0.151413
$185$	8.05753	−	13.9561i	0.592402	−	1.02607i
$186$		0			0
$187$	−3.20742	+	1.85181i	−0.234550	+	0.135417i
$188$	3.47356			0.253335
$189$		0			0
$190$	4.40939			0.319890
$191$	−6.20573	+	3.58288i	−0.449031	+	0.259248i	−0.707421	−	0.706793i	$-0.750141\pi$
$191$	−6.20573	+	3.58288i	−0.449031	+	0.259248i	0.258390	+	0.966041i	$0.416808\pi$
$192$		0			0
$193$	1.58888	−	2.75202i	0.114370	−	0.198095i	−0.803158	−	0.595766i	$-0.796848\pi$
$193$	1.58888	−	2.75202i	0.114370	−	0.198095i	0.917528	+	0.397672i	$0.130182\pi$
$194$	1.26249			0.0906411
$195$		0			0
$196$	−2.66521	−	9.17174i	−0.190372	−	0.655124i
$197$			1.93305i			0.137724i	0.997626	+	0.0688619i	$0.0219368\pi$
$197$			1.93305i			0.137724i	−0.997626	+	0.0688619i	$0.978063\pi$
$198$		0			0
$199$	−7.50000	+	4.33013i	−0.531661	+	0.306955i	−0.741693	−	0.670740i	$-0.765977\pi$
$199$	−7.50000	+	4.33013i	−0.531661	+	0.306955i	0.210032	+	0.977695i	$0.432643\pi$
$200$			11.0779i			0.783324i
$201$		0			0
$202$	−10.4588	+	6.03838i	−0.735878	+	0.424859i
$203$	12.6976	+	1.53621i	0.891198	+	0.107821i
$204$		0			0
$205$	8.69215	+	15.0552i	0.607086	+	1.05150i
$206$	8.57375	+	14.8502i	0.597361	+	1.03466i
$207$		0			0
$208$	−23.3529	−	13.4828i	−1.61923	−	0.934864i
$209$	−0.367938	+	0.637287i	−0.0254508	+	0.0440820i
$210$		0			0
$211$	−6.20916	−	10.7546i	−0.427456	−	0.740376i	0.569190	−	0.822206i	$-0.307257\pi$
$211$	−6.20916	−	10.7546i	−0.427456	−	0.740376i	−0.996646	+	0.0818303i	$0.973923\pi$
$212$			0.0988033i			0.00678584i
$213$		0			0
$214$	28.9210			1.97700
$215$	13.7699	−	23.8502i	0.939099	−	1.62657i
$216$		0			0
$217$	−11.2361	−	1.35939i	−0.762755	−	0.0922811i
$218$	22.9749	+	13.2646i	1.55606	+	0.898389i
$219$		0			0
$220$	5.24591	+	3.02873i	0.353679	+	0.204197i
$221$	15.2434	+	8.80077i	1.02538	+	0.592004i
$222$		0			0
$223$	−16.3996	−	9.46830i	−1.09820	−	0.634044i	−0.162450	−	0.986717i	$-0.551940\pi$
$223$	−16.3996	−	9.46830i	−1.09820	−	0.634044i	−0.935747	+	0.352673i	$0.885273\pi$
$224$	−17.3252	−	2.09607i	−1.15759	−	0.140050i
$225$		0			0
$226$	−18.2146	+	31.5486i	−1.21162	+	2.09858i
$227$	−5.72276			−0.379833			−0.189917	−	0.981800i	$-0.560822\pi$
$227$	−5.72276			−0.379833			−0.189917	+	0.981800i	$0.560822\pi$
$228$		0			0
$229$		−	11.1376i		−	0.735996i	−0.929827	−	0.367998i	$-0.880043\pi$
$229$		−	11.1376i		−	0.735996i	0.929827	−	0.367998i	$-0.119957\pi$
$230$	6.15341	+	10.6580i	0.405744	+	0.702769i
$231$		0			0
$232$	2.81778	−	4.88053i	0.184996	−	0.320423i
$233$	−8.95208	−	5.16849i	−0.586470	−	0.338599i	0.177230	−	0.984169i	$-0.443286\pi$
$233$	−8.95208	−	5.16849i	−0.586470	−	0.338599i	−0.763701	+	0.645571i	$0.776620\pi$
$234$		0			0
$235$	−4.84744	−	8.39601i	−0.316212	−	0.547695i
$236$	−4.76550	−	8.25409i	−0.310208	−	0.537296i
$237$		0			0
$238$	15.3062	+	1.85181i	0.992155	+	0.120035i
$239$	−14.3592	+	8.29030i	−0.928821	+	0.536255i	−0.886438	−	0.462846i	$-0.846828\pi$
$239$	−14.3592	+	8.29030i	−0.928821	+	0.536255i	−0.0423824	+	0.999101i	$0.513495\pi$
$240$		0			0
$241$			23.8932i			1.53910i	0.638587	+	0.769549i	$0.279519\pi$
$241$			23.8932i			1.53910i	−0.638587	+	0.769549i	$0.720481\pi$
$242$	15.3148	−	8.84198i	0.984470	−	0.568384i
$243$		0			0
$244$			11.0330i			0.706316i
$245$	−18.4498	+	19.2415i	−1.17872	+	1.22930i
$246$		0			0
$247$	3.49727			0.222526
$248$	−2.49344	+	4.31877i	−0.158334	+	0.274242i
$249$		0			0
$250$	−27.2388	+	15.7263i	−1.72273	+	0.994621i
$251$	−19.9233			−1.25755			−0.628774	−	0.777588i	$-0.716443\pi$
$251$	−19.9233			−1.25755			−0.628774	+	0.777588i	$0.716443\pi$
$252$		0			0
$253$	−2.05387			−0.129125
$254$	−14.1482	+	8.16849i	−0.887739	+	0.512536i
$255$		0			0
$256$	−10.4857	+	18.1618i	−0.655358	+	1.13511i
$257$	23.2049			1.44748			0.723742	−	0.690070i	$-0.242420\pi$
$257$	23.2049			1.44748			0.723742	+	0.690070i	$0.242420\pi$
$258$		0			0
$259$	1.34471	−	11.1148i	0.0835561	−	0.690639i
$260$		−	28.7882i		−	1.78537i
$261$		0			0
$262$	10.7306	−	6.19533i	0.662941	−	0.382749i
$263$			9.62246i			0.593347i	0.954979	+	0.296673i	$0.0958772\pi$
$263$			9.62246i			0.593347i	−0.954979	+	0.296673i	$0.904123\pi$
$264$		0			0
$265$	0.238820	−	0.137883i	0.0146706	−	0.00847006i
$266$	2.81774	−	1.20196i	0.172767	−	0.0736971i
$267$		0			0
$268$	3.47853	+	6.02498i	0.212485	+	0.368034i
$269$	−10.4152	−	18.0396i	−0.635024	−	1.09989i	−0.986510	−	0.163700i	$-0.947657\pi$
$269$	−10.4152	−	18.0396i	−0.635024	−	1.09989i	0.351487	−	0.936193i	$-0.385676\pi$
$270$		0			0
$271$	17.0467	+	9.84190i	1.03551	+	0.597853i	0.918559	−	0.395285i	$-0.129354\pi$
$271$	17.0467	+	9.84190i	1.03551	+	0.597853i	0.116953	+	0.993137i	$0.462687\pi$
$272$	7.73152	−	13.3914i	0.468792	−	0.811972i
$273$		0			0
$274$	−15.4633	−	26.7831i	−0.934169	−	1.61803i
$275$		−	11.0779i		−	0.668021i
$276$		0			0
$277$	8.31604			0.499662			0.249831	−	0.968289i	$-0.419625\pi$
$277$	8.31604			0.499662			0.249831	+	0.968289i	$0.419625\pi$
$278$	−0.746270	+	1.29258i	−0.0447583	+	0.0775237i
$279$		0			0
$280$	4.60862	+	10.8039i	0.275418	+	0.645656i
$281$	19.7123	+	11.3809i	1.17594	+	0.678928i	0.955072	−	0.296375i	$-0.0957780\pi$
$281$	19.7123	+	11.3809i	1.17594	+	0.678928i	0.220867	+	0.975304i	$0.429111\pi$
$282$		0			0
$283$	14.7514	+	8.51670i	0.876878	+	0.506266i	0.869628	−	0.493708i	$-0.164359\pi$
$283$	14.7514	+	8.51670i	0.876878	+	0.506266i	0.00724998	+	0.999974i	$0.497692\pi$
$284$	−5.62680	−	3.24864i	−0.333889	−	0.192771i
$285$		0			0
$286$	10.2596	+	5.92336i	0.606660	+	0.350255i
$287$	9.65849	+	7.25136i	0.570123	+	0.428035i
$288$		0			0
$289$	3.45333	−	5.98134i	0.203137	−	0.351843i
$290$	33.7684			1.98295
$291$		0			0
$292$		−	7.63728i		−	0.446938i
$293$	10.7079	+	18.5467i	0.625564	+	1.08351i	0.988432	+	0.151668i	$0.0484643\pi$
$293$	10.7079	+	18.5467i	0.625564	+	1.08351i	−0.362868	+	0.931841i	$0.618202\pi$
$294$		0			0
$295$	−13.3008	+	23.0376i	−0.774401	+	1.34130i
$296$	−4.27214	−	2.46652i	−0.248313	−	0.143364i
$297$		0			0
$298$	7.73163	+	13.3916i	0.447881	+	0.775753i
$299$	4.88053	+	8.45333i	0.282248	+	0.488869i
$300$		0			0
$301$	2.29804	−	18.9946i	0.132457	−	1.09483i
$302$	4.82821	−	2.78757i	0.277833	−	0.160407i
$303$		0			0
$304$		−	3.07237i		−	0.176212i
$305$	26.6681	−	15.3968i	1.52701	−	0.881621i
$306$		0			0
$307$			19.4537i			1.11028i	0.831756	+	0.555142i	$0.187336\pi$
$307$			19.4537i			1.11028i	−0.831756	+	0.555142i	$0.812664\pi$
$308$	4.17791	+	0.505459i	0.238058	+	0.0288012i
$309$		0			0
$310$	−29.8816			−1.69716
$311$	3.40706	−	5.90120i	0.193197	−	0.334626i	−0.753111	−	0.657893i	$-0.771448\pi$
$311$	3.40706	−	5.90120i	0.193197	−	0.334626i	0.946308	+	0.323267i	$0.104781\pi$
$312$		0			0
$313$	14.4121	−	8.32084i	0.814621	−	0.470322i	−0.0339371	−	0.999424i	$-0.510805\pi$
$313$	14.4121	−	8.32084i	0.814621	−	0.470322i	0.848558	+	0.529102i	$0.177471\pi$
$314$	6.98525			0.394200
$315$		0			0
$316$	−23.3304			−1.31244
$317$	−4.39757	+	2.53894i	−0.246992	+	0.142601i	−0.618386	−	0.785874i	$-0.712213\pi$
$317$	−4.39757	+	2.53894i	−0.246992	+	0.142601i	0.371394	+	0.928475i	$0.378880\pi$
$318$		0			0
$319$	−2.81778	+	4.88053i	−0.157765	+	0.273257i
$320$	−9.00440			−0.503361
$321$		0			0
$322$	6.83752	+	5.13344i	0.381040	+	0.286075i
$323$			2.00546i			0.111587i
$324$		0			0
$325$	−45.5944	+	26.3240i	−2.52912	+	1.46019i
$326$		−	20.3479i		−	1.12697i
$327$		0			0
$328$	4.60862	−	2.66079i	0.254468	−	0.146917i
$329$	−5.38635	−	4.04394i	−0.296959	−	0.222950i
$330$		0			0
$331$	−8.16521	−	14.1426i	−0.448801	−	0.777346i	0.549507	−	0.835489i	$-0.314815\pi$
$331$	−8.16521	−	14.1426i	−0.448801	−	0.777346i	−0.998308	+	0.0581430i	$0.981482\pi$
$332$	6.93293	+	12.0082i	0.380494	+	0.659035i
$333$		0			0
$334$	−5.88319	−	3.39666i	−0.321914	−	0.185857i
$335$	9.70875	−	16.8160i	0.530445	−	0.918758i
$336$		0			0
$337$	1.97753	+	3.42518i	0.107723	+	0.186582i	0.914847	−	0.403800i	$-0.132311\pi$
$337$	1.97753	+	3.42518i	0.107723	+	0.186582i	−0.807124	+	0.590381i	$0.798977\pi$
$338$		−	32.4567i		−	1.76541i
$339$		0			0
$340$	16.5082			0.895282
$341$	2.49344	−	4.31877i	0.135028	−	0.233875i
$342$		0			0
$343$	−6.54494	+	17.3252i	−0.353393	+	0.935475i
$344$	−7.30087	−	4.21516i	−0.393636	−	0.227266i
$345$		0			0
$346$	15.3062	+	8.83705i	0.822868	+	0.475083i
$347$	−6.35400	−	3.66849i	−0.341101	−	0.196935i	0.319658	−	0.947533i	$-0.396432\pi$
$347$	−6.35400	−	3.66849i	−0.341101	−	0.196935i	−0.660759	+	0.750598i	$0.729765\pi$
$348$		0			0
$349$	22.0917	+	12.7547i	1.18254	+	0.682741i	0.956601	−	0.291400i	$-0.0941210\pi$
$349$	22.0917	+	12.7547i	1.18254	+	0.682741i	0.225941	+	0.974141i	$0.427454\pi$
$350$	−27.6881	+	36.8793i	−1.47999	+	1.97128i
$351$		0			0
$352$	3.84471	−	6.65923i	0.204924	−	0.354938i
$353$	0.0207896			0.00110652			0.000553260	−	1.00000i	$-0.499824\pi$
$353$	0.0207896			0.00110652			0.000553260		1.00000i	$0.499824\pi$
$354$		0			0
$355$			18.1342i			0.962464i
$356$	7.87979	+	13.6482i	0.417628	+	0.723353i
$357$		0			0
$358$	−16.9220	+	29.3098i	−0.894358	+	1.54907i
$359$	−31.3709	−	18.1120i	−1.65569	−	0.955915i	−0.974669	−	0.223654i	$-0.928201\pi$
$359$	−31.3709	−	18.1120i	−1.65569	−	0.955915i	−0.681024	−	0.732261i	$-0.738465\pi$
$360$		0			0
$361$	−9.30077	−	16.1094i	−0.489514	−	0.847863i
$362$	−15.2434	−	26.4023i	−0.801174	−	1.38767i
$363$		0			0
$364$	−7.84744	−	18.3966i	−0.411318	−	0.964243i
$365$	−18.4602	+	10.6580i	−0.966253	+	0.557866i
$366$		0			0
$367$		−	8.87897i		−	0.463479i	−0.972778	−	0.231739i	$-0.925558\pi$
$367$		−	8.87897i		−	0.463479i	0.972778	−	0.231739i	$-0.0744416\pi$
$368$	7.42629	−	4.28757i	0.387122	−	0.223505i
$369$		0			0
$370$		−	29.5590i		−	1.53670i
$371$	0.115028	−	0.153212i	0.00597193	−	0.00795435i
$372$		0			0
$373$	−12.8188			−0.663731			−0.331865	−	0.943327i	$-0.607678\pi$
$373$	−12.8188			−0.663731			−0.331865	+	0.943327i	$0.607678\pi$
$374$	−3.39666	+	5.88319i	−0.175637	+	0.304213i
$375$		0			0
$376$	−2.57014	+	1.48387i	−0.132545	+	0.0765247i
$377$	26.7831			1.37940
$378$		0			0
$379$	3.13828			0.161203			0.0806013	−	0.996746i	$-0.474316\pi$
$379$	3.13828			0.161203			0.0806013	+	0.996746i	$0.474316\pi$
$380$	2.84059	−	1.64002i	0.145719	−	0.0841311i
$381$		0			0
$382$	−6.57187	+	11.3828i	−0.336246	+	0.582395i
$383$	−27.5190			−1.40616			−0.703078	−	0.711113i	$-0.748192\pi$
$383$	−27.5190			−1.40616			−0.703078	+	0.711113i	$0.748192\pi$
$384$		0			0
$385$	−4.60862	−	10.8039i	−0.234877	−	0.550617i
$386$		−	5.82878i		−	0.296677i
$387$		0			0
$388$	0.813312	−	0.469566i	0.0412896	−	0.0238386i
$389$			18.2436i			0.924989i	0.886622	+	0.462494i	$0.153045\pi$
$389$			18.2436i			0.924989i	−0.886622	+	0.462494i	$0.846955\pi$
$390$		0			0
$391$	−4.84744	+	2.79867i	−0.245146	+	0.141535i
$392$	5.89011	+	5.64775i	0.297495	+	0.285255i
$393$		0			0
$394$	1.77284	+	3.07065i	0.0893143	+	0.154697i
$395$	32.5582	+	56.3925i	1.63818	+	2.83741i
$396$		0			0
$397$	1.01255	+	0.584593i	0.0508182	+	0.0293399i	0.525194	−	0.850983i	$-0.323993\pi$
$397$	1.01255	+	0.584593i	0.0508182	+	0.0293399i	−0.474376	+	0.880323i	$0.657326\pi$
$398$	−7.94251	+	13.7568i	−0.398122	+	0.689567i
$399$		0			0
$400$	23.1257	+	40.0550i	1.15629	+	2.00275i
$401$		−	13.9594i		−	0.697101i	−0.937290	−	0.348551i	$-0.886674\pi$
$401$		−	13.9594i		−	0.697101i	0.937290	−	0.348551i	$-0.113326\pi$
$402$		0			0
$403$	−23.7003			−1.18060
$404$	−4.49180	+	7.78003i	−0.223476	+	0.387071i
$405$		0			0
$406$	21.5791	−	9.20499i	1.07095	−	0.456836i
$407$	4.27214	+	2.46652i	0.211762	+	0.122261i
$408$		0			0
$409$	−17.6427	−	10.1860i	−0.872378	−	0.503667i	−0.00424001	−	0.999991i	$-0.501350\pi$
$409$	−17.6427	−	10.1860i	−0.872378	−	0.503667i	−0.868138	+	0.496324i	$0.834683\pi$
$410$	27.6150	+	15.9435i	1.36381	+	0.787394i
$411$		0			0
$412$	11.0467	+	6.37780i	0.544230	+	0.314212i
$413$	−2.21974	+	18.3474i	−0.109226	+	0.902818i
$414$		0			0
$415$	19.3502	−	33.5155i	0.949862	−	1.64521i
$416$	−36.5442			−1.79173
$417$		0			0
$418$			1.34977i			0.0660196i
$419$	−12.7603	−	22.1015i	−0.623383	−	1.07973i	−0.988851	−	0.148907i	$-0.952425\pi$
$419$	−12.7603	−	22.1015i	−0.623383	−	1.07973i	0.365469	−	0.930824i	$-0.380909\pi$
$420$		0			0
$421$	−0.0466721	+	0.0808384i	−0.00227466	+	0.00393982i	−0.867160	−	0.498029i	$-0.834057\pi$
$421$	−0.0466721	+	0.0808384i	−0.00227466	+	0.00393982i	0.864886	+	0.501969i	$0.167391\pi$
$422$	−19.7265	−	11.3891i	−0.960271	−	0.554413i
$423$		0			0
$424$	−0.0422078	−	0.0731060i	−0.00204979	−	0.00355034i
$425$	−15.0951	−	26.1455i	−0.732220	−	1.26824i
$426$		0			0
$427$	12.8447	−	17.1086i	0.621599	−	0.827942i
$428$	18.6314	−	10.7568i	0.900581	−	0.519951i
$429$		0			0
$430$		−	50.5147i		−	2.43603i
$431$	−28.7271	+	16.5856i	−1.38374	+	0.798901i	−0.992600	−	0.121432i	$-0.961251\pi$
$431$	−28.7271	+	16.5856i	−1.38374	+	0.798901i	−0.391137	+	0.920333i	$0.627918\pi$
$432$		0			0
$433$			17.9518i			0.862706i	0.902183	+	0.431353i	$0.141964\pi$
$433$			17.9518i			0.862706i	−0.902183	+	0.431353i	$0.858036\pi$
$434$	−19.0953	+	8.14548i	−0.916602	+	0.390995i
$435$		0			0
$436$	19.7344			0.945104
$437$	−0.556071	+	0.963144i	−0.0266005	+	0.0460734i
$438$		0			0
$439$	8.69215	−	5.01841i	0.414854	−	0.239516i	−0.278019	−	0.960575i	$-0.589678\pi$
$439$	8.69215	−	5.01841i	0.414854	−	0.239516i	0.692873	+	0.721060i	$0.256345\pi$
$440$	−5.17536			−0.246726
$441$		0			0
$442$	32.2855			1.53566
$443$	−22.8266	+	13.1790i	−1.08453	+	0.626151i	−0.932114	−	0.362166i	$-0.882037\pi$
$443$	−22.8266	+	13.1790i	−1.08453	+	0.626151i	−0.152412	+	0.988317i	$0.548704\pi$
$444$		0			0
$445$	21.9929	−	38.0928i	1.04256	−	1.80577i
$446$	−34.7343			−1.64472
$447$		0			0
$448$	−5.75409	+	2.45453i	−0.271855	+	0.115965i
$449$			24.0264i			1.13388i	0.823761	+	0.566938i	$0.191872\pi$
$449$			24.0264i			1.13388i	−0.823761	+	0.566938i	$0.808128\pi$
$450$		0			0
$451$	−4.60862	+	2.66079i	−0.217011	+	0.125292i
$452$			27.0988i			1.27462i
$453$		0			0
$454$	−9.09061	+	5.24847i	−0.426644	+	0.246323i
$455$	−33.5155	+	44.6411i	−1.57123	+	2.09281i
$456$		0			0
$457$	−10.4111	−	18.0326i	−0.487012	−	0.843529i	0.512877	−	0.858462i	$-0.328580\pi$
$457$	−10.4111	−	18.0326i	−0.487012	−	0.843529i	−0.999888	+	0.0149333i	$0.995246\pi$
$458$	−10.2146	−	17.6921i	−0.477295	−	0.826700i
$459$		0			0
$460$	7.92824	+	4.57737i	0.369656	+	0.213421i
$461$	4.17618	−	7.23336i	0.194504	−	0.336891i	−0.752234	−	0.658896i	$-0.771024\pi$
$461$	4.17618	−	7.23336i	0.194504	−	0.336891i	0.946738	+	0.322005i	$0.104357\pi$
$462$		0			0
$463$	−5.90666	−	10.2306i	−0.274506	−	0.475458i	0.695505	−	0.718522i	$-0.255181\pi$
$463$	−5.90666	−	10.2306i	−0.274506	−	0.475458i	−0.970010	+	0.243064i	$0.921848\pi$
$464$		−	23.5291i		−	1.09231i
$465$		0			0
$466$	−18.9605			−0.878329
$467$	14.5789	−	25.2514i	0.674630	−	1.16849i	−0.301947	−	0.953325i	$-0.597636\pi$
$467$	14.5789	−	25.2514i	0.674630	−	1.16849i	0.976577	−	0.215169i	$-0.0690302\pi$
$468$		0			0
$469$	1.62028	−	13.3925i	0.0748174	−	0.618409i
$470$	−15.4003	−	8.89138i	−0.710364	−	0.410129i
$471$		0			0
$472$	7.05213	+	4.07155i	0.324601	+	0.187408i
$473$	7.30087	+	4.21516i	0.335694	+	0.193813i
$474$		0			0
$475$	−5.19488	−	2.99926i	−0.238357	−	0.137616i
$476$	10.5493	−	4.50000i	0.483524	−	0.206257i
$477$		0			0
$478$	−15.2064	+	26.3383i	−0.695526	+	1.20469i
$479$	40.5236			1.85157			0.925785	−	0.378051i	$-0.123406\pi$
$479$	40.5236			1.85157			0.925785	+	0.378051i	$0.123406\pi$
$480$		0			0
$481$		−	23.4445i		−	1.06898i
$482$	21.9130	+	37.9544i	0.998110	+	1.72878i
$483$		0			0
$484$	6.57733	−	11.3923i	0.298970	−	0.517830i
$485$	−2.26999	−	1.31058i	−0.103075	−	0.0595105i
$486$		0			0
$487$	−6.20916	−	10.7546i	−0.281364	−	0.487336i	0.690357	−	0.723469i	$-0.257453\pi$
$487$	−6.20916	−	10.7546i	−0.281364	−	0.487336i	−0.971721	+	0.236132i	$0.924120\pi$
$488$	−4.71319	−	8.16348i	−0.213356	−	0.369543i
$489$		0			0
$490$	−11.6608	+	47.4860i	−0.526779	+	2.14520i
$491$	−5.34443	+	3.08561i	−0.241191	+	0.139252i	−0.615724	−	0.787962i	$-0.711136\pi$
$491$	−5.34443	+	3.08561i	−0.241191	+	0.139252i	0.374533	+	0.927214i	$0.377803\pi$
$492$		0			0
$493$			15.3584i			0.691708i
$494$	5.55542	−	3.20742i	0.249950	−	0.144309i
$495$		0			0
$496$			20.8209i			0.934884i
$497$	4.94324	+	11.5883i	0.221735	+	0.519808i
$498$		0			0
$499$	−2.96052			−0.132531			−0.0662656	−	0.997802i	$-0.521108\pi$
$499$	−2.96052			−0.132531			−0.0662656	+	0.997802i	$0.521108\pi$
$500$	−11.6984	+	20.2623i	−0.523170	+	0.906157i
$501$		0			0
$502$	−31.6482	+	18.2721i	−1.41253	+	0.815524i
$503$	−4.33485			−0.193282			−0.0966408	−	0.995319i	$-0.530810\pi$
$503$	−4.33485			−0.193282			−0.0966408	+	0.995319i	$0.530810\pi$
$504$		0			0
$505$	25.0737			1.11577
$506$	−3.26257	+	1.88364i	−0.145039	+	0.0837382i
$507$		0			0
$508$	−6.07633	+	10.5245i	−0.269594	+	0.466950i
$509$	28.9485			1.28312			0.641560	−	0.767073i	$-0.278288\pi$
$509$	28.9485			1.28312			0.641560	+	0.767073i	$0.278288\pi$
$510$		0			0
$511$	−8.89138	+	11.8429i	−0.393332	+	0.523900i
$512$			20.7564i			0.917311i
$513$		0			0
$514$	36.8611	−	21.2818i	1.62587	−	0.938698i
$515$		−	35.6015i		−	1.56879i
$516$		0			0
$517$	2.57014	−	1.48387i	0.113034	−	0.0652605i
$518$	−8.05753	−	18.8891i	−0.354028	−	0.829940i
$519$		0			0
$520$	12.2980	+	21.3008i	0.539305	+	0.934103i
$521$	−6.08031	−	10.5314i	−0.266383	−	0.461389i	0.701542	−	0.712628i	$-0.252495\pi$
$521$	−6.08031	−	10.5314i	−0.266383	−	0.461389i	−0.967925	+	0.251239i	$0.919162\pi$
$522$		0			0
$523$	−33.1564	−	19.1429i	−1.44983	−	0.837059i	−0.451357	−	0.892343i	$-0.649060\pi$
$523$	−33.1564	−	19.1429i	−1.44983	−	0.837059i	−0.998471	+	0.0552848i	$0.982393\pi$
$524$	4.60855	−	7.98225i	0.201326	−	0.348706i
$525$		0			0
$526$	8.82497	+	15.2853i	0.384787	+	0.666471i
$527$		−	13.5906i		−	0.592016i
$528$		0			0
$529$	19.8960			0.865041
$530$	0.252910	−	0.438053i	0.0109857	−	0.0190278i
$531$		0			0
$532$	1.36817	−	1.82234i	0.0593178	−	0.0790087i
$533$	21.9026	+	12.6455i	0.948707	+	0.547736i
$534$		0			0
$535$	−52.0011	−	30.0229i	−2.24820	−	1.29800i
$536$	−5.14762	−	2.97198i	−0.222344	−	0.128370i
$537$		0			0
$538$	−33.0890	−	19.1039i	−1.42657	−	0.823629i
$539$	−5.89011	−	5.64775i	−0.253705	−	0.243266i
$540$		0			0
$541$	−0.254094	+	0.440104i	−0.0109244	+	0.0189216i	−0.871436	−	0.490509i	$-0.836811\pi$
$541$	−0.254094	+	0.440104i	−0.0109244	+	0.0189216i	0.860512	+	0.509431i	$0.170144\pi$
$542$	36.1049			1.55084
$543$		0			0
$544$		−	20.9557i		−	0.898470i
$545$	−27.5398	−	47.7003i	−1.17968	−	2.04326i
$546$		0			0
$547$	20.1482	−	34.8977i	0.861475	−	1.49212i	−0.00903012	−	0.999959i	$-0.502874\pi$
$547$	20.1482	−	34.8977i	0.861475	−	1.49212i	0.870505	−	0.492159i	$-0.163792\pi$
$548$	−19.9233	−	11.5027i	−0.851082	−	0.491372i
$549$		0			0
$550$	−10.1598	−	17.5972i	−0.433213	−	0.750348i
$551$	1.52579	+	2.64275i	0.0650008	+	0.112585i
$552$		0			0
$553$	36.1779	+	27.1615i	1.53844	+	1.15502i
$554$	13.2100	−	7.62682i	0.561241	−	0.324033i
$555$		0			0
$556$			1.11026i			0.0470857i
$557$	37.6165	−	21.7179i	1.59386	−	0.920216i	0.601226	−	0.799079i	$-0.294679\pi$
$557$	37.6165	−	21.7179i	1.59386	−	0.920216i	0.992636	−	0.121137i	$-0.0386541\pi$
$558$		0			0
$559$		−	40.0653i		−	1.69458i
$560$	39.2174	+	29.4435i	1.65724	+	1.24422i
$561$		0			0
$562$	41.7507			1.76115
$563$	−3.16661	+	5.48473i	−0.133457	+	0.231154i	−0.925007	−	0.379951i	$-0.875941\pi$
$563$	−3.16661	+	5.48473i	−0.133457	+	0.231154i	0.791550	+	0.611104i	$0.209274\pi$
$564$		0			0
$565$	65.5011	−	37.8171i	2.75565	−	1.59098i
$566$	31.2434			1.31326
$567$		0			0
$568$	5.55114			0.232921
$569$	7.12974	−	4.11636i	0.298894	−	0.172567i	−0.343052	−	0.939316i	$-0.611461\pi$
$569$	7.12974	−	4.11636i	0.298894	−	0.172567i	0.641946	+	0.766750i	$0.278127\pi$
$570$		0			0
$571$	−4.24864	+	7.35885i	−0.177800	+	0.307958i	−0.941127	−	0.338054i	$-0.890231\pi$
$571$	−4.24864	+	7.35885i	−0.177800	+	0.307958i	0.763327	+	0.646013i	$0.223565\pi$
$572$	8.81248			0.368468
$573$		0			0
$574$	21.9929	+	2.66079i	0.917966	+	0.111059i
$575$		−	16.7422i		−	0.698198i
$576$		0			0
$577$	34.1905	−	19.7399i	1.42337	−	0.821783i	0.426785	−	0.904353i	$-0.359646\pi$
$577$	34.1905	−	19.7399i	1.42337	−	0.821783i	0.996585	+	0.0825702i	$0.0263129\pi$
$578$		−	12.6685i		−	0.526940i
$579$		0			0
$580$	21.7541	−	12.5597i	0.903290	−	0.521514i
$581$	3.22932	−	26.6921i	0.133975	−	1.10738i
$582$		0			0
$583$	0.0422078	+	0.0731060i	0.00174807	+	0.00302774i
$584$	3.26257	+	5.65093i	0.135006	+	0.233837i
$585$		0			0
$586$	34.0191	+	19.6409i	1.40532	+	0.811360i
$587$	12.0560	−	20.8816i	0.497603	−	0.861874i	−0.502393	−	0.864640i	$-0.667547\pi$
$587$	12.0560	−	20.8816i	0.497603	−	0.861874i	0.999996	+	0.00276510i	$0.000880160\pi$
$588$		0			0
$589$	−1.35017	−	2.33856i	−0.0556327	−	0.0963587i
$590$			48.7937i			2.00880i
$591$		0			0
$592$	−20.5961			−0.846493
$593$	9.46830	−	16.3996i	0.388816	−	0.673450i	−0.603474	−	0.797382i	$-0.706217\pi$
$593$	9.46830	−	16.3996i	0.388816	−	0.673450i	0.992291	+	0.123933i	$0.0395507\pi$
$594$		0			0
$595$	−25.5988	−	19.2190i	−1.04945	−	0.787901i
$596$	9.96166	+	5.75136i	0.408045	+	0.235585i
$597$		0			0
$598$	15.5055	+	8.95208i	0.634065	+	0.366078i
$599$	30.0332	+	17.3397i	1.22713	+	0.708481i	0.966427	−	0.256939i	$-0.0827141\pi$
$599$	30.0332	+	17.3397i	1.22713	+	0.708481i	0.260698	+	0.965420i	$0.416047\pi$
$600$		0			0
$601$	−11.4929	−	6.63544i	−0.468806	−	0.270665i	0.246934	−	0.969032i	$-0.420577\pi$
$601$	−11.4929	−	6.63544i	−0.468806	−	0.270665i	−0.715740	+	0.698367i	$0.753910\pi$
$602$	−13.7699	−	32.2805i	−0.561219	−	1.31565i
$603$		0			0
$604$	2.07361	−	3.59159i	0.0843738	−	0.146140i
$605$	−36.7153			−1.49269
$606$		0			0
$607$			25.0148i			1.01532i	0.861557	+	0.507660i	$0.169490\pi$
$607$			25.0148i			1.01532i	−0.861557	+	0.507660i	$0.830510\pi$
$608$	−2.08186	−	3.60589i	−0.0844306	−	0.146238i
$609$		0			0
$610$	28.2415	−	48.9158i	1.14347	−	1.98054i
$611$	−12.2146	−	7.05213i	−0.494152	−	0.285299i
$612$		0			0
$613$	22.0549	+	38.2001i	0.890787	+	1.54289i	0.838933	+	0.544234i	$0.183180\pi$
$613$	22.0549	+	38.2001i	0.890787	+	1.54289i	0.0518543	+	0.998655i	$0.483487\pi$
$614$	17.8415	+	30.9023i	0.720022	+	1.24712i
$615$		0			0
$616$	−3.30722	+	1.41076i	−0.133252	+	0.0568412i
$617$	16.7463	−	9.66849i	0.674181	−	0.389239i	−0.123478	−	0.992347i	$-0.539405\pi$
$617$	16.7463	−	9.66849i	0.674181	−	0.389239i	0.797659	+	0.603109i	$0.206071\pi$
$618$		0			0
$619$			11.0598i			0.444531i	0.974986	+	0.222265i	$0.0713452\pi$
$619$			11.0598i			0.444531i	−0.974986	+	0.222265i	$0.928655\pi$
$620$	−19.2501	+	11.1141i	−0.773105	+	0.446352i
$621$		0			0
$622$		−	12.4987i		−	0.501154i
$623$	3.67036	−	30.3376i	0.147050	−	1.21545i
$624$		0			0
$625$	17.7882			0.711529
$626$	15.2624	−	26.4353i	0.610010	−	1.05657i
$627$		0			0
$628$	4.50000	−	2.59808i	0.179570	−	0.103675i
$629$	13.4439			0.536043
$630$		0			0
$631$	−27.6015			−1.09880			−0.549400	−	0.835560i	$-0.685144\pi$
$631$	−27.6015			−1.09880			−0.549400	+	0.835560i	$0.685144\pi$
$632$	17.2625	−	9.96652i	0.686666	−	0.396447i
$633$		0			0
$634$	−4.65703	+	8.06621i	−0.184954	+	0.320350i
$635$	33.9187			1.34602
$636$		0			0
$637$	−9.24864	+	37.6631i	−0.366444	+	1.49227i
$638$			10.3370i			0.409245i
$639$		0			0
$640$	29.2047	−	16.8613i	1.15442	−	0.666503i
$641$		−	6.07241i		−	0.239846i	−0.992783	−	0.119923i	$-0.961735\pi$
$641$		−	6.07241i		−	0.239846i	0.992783	−	0.119923i	$-0.0382648\pi$
$642$		0			0
$643$	−11.4929	+	6.63544i	−0.453236	+	0.261676i	−0.709196	−	0.705011i	$-0.750942\pi$
$643$	−11.4929	+	6.63544i	−0.453236	+	0.261676i	0.255960	+	0.966687i	$0.417609\pi$
$644$	6.31415	+	0.763910i	0.248812	+	0.0301023i
$645$		0			0
$646$	1.83925	+	3.18567i	0.0723643	+	0.125339i
$647$	−15.3688	−	26.6195i	−0.604210	−	1.04652i	−0.992176	−	0.124848i	$-0.960156\pi$
$647$	−15.3688	−	26.6195i	−0.604210	−	1.04652i	0.387966	−	0.921674i	$-0.373178\pi$
$648$		0			0
$649$	−7.05213	−	4.07155i	−0.276820	−	0.159822i
$650$	−48.2846	+	83.6313i	−1.89388	+	3.28029i
$651$		0			0
$652$	−7.56815	−	13.1084i	−0.296391	−	0.513365i
$653$			37.2185i			1.45647i	0.685325	+	0.728237i	$0.259660\pi$
$653$			37.2185i			1.45647i	−0.685325	+	0.728237i	$0.740340\pi$
$654$		0			0
$655$	−25.7254			−1.00518
$656$	11.1091	−	19.2415i	0.433738	−	0.751256i
$657$		0			0
$658$	−12.2650	−	1.48387i	−0.478140	−	0.0578472i
$659$	−40.0576	−	23.1273i	−1.56042	−	0.900911i	−0.997214	−	0.0745963i	$-0.976233\pi$
$659$	−40.0576	−	23.1273i	−1.56042	−	0.900911i	−0.563209	−	0.826314i	$-0.690433\pi$
$660$		0			0
$661$	−11.4219	−	6.59445i	−0.444262	−	0.256495i	0.261142	−	0.965300i	$-0.415901\pi$
$661$	−11.4219	−	6.59445i	−0.444262	−	0.256495i	−0.705404	+	0.708806i	$0.749234\pi$
$662$	−25.9409	−	14.9770i	−1.00822	−	0.582097i
$663$		0			0
$664$	−10.2596	−	5.92336i	−0.398148	−	0.229871i
$665$	−6.31415	−	0.763910i	−0.244852	−	0.0296232i
$666$		0			0
$667$	−4.25856	+	7.37604i	−0.164892	+	0.285601i
$668$	−5.05339			−0.195521
$669$		0			0
$670$		−	35.6164i		−	1.37598i
$671$	4.71319	+	8.16348i	0.181951	+	0.315148i
$672$		0			0
$673$	−20.4633	+	35.4434i	−0.788800	+	1.36624i	0.137902	+	0.990446i	$0.455964\pi$
$673$	−20.4633	+	35.4434i	−0.788800	+	1.36624i	−0.926702	+	0.375796i	$0.877369\pi$
$674$	6.28262	+	3.62727i	0.241998	+	0.139717i
$675$		0			0
$676$	−12.0719	−	20.9091i	−0.464303	−	0.804196i
$677$	−0.808981	−	1.40120i	−0.0310917	−	0.0538524i	0.850061	−	0.526684i	$-0.176565\pi$
$677$	−0.808981	−	1.40120i	−0.0310917	−	0.0538524i	−0.881153	+	0.472832i	$0.843232\pi$
$678$		0			0
$679$	−1.80785	−	0.218721i	−0.0693790	−	0.00839374i
$680$	−12.2146	+	7.05213i	−0.468410	+	0.270437i
$681$		0			0
$682$		−	9.14716i		−	0.350263i
$683$	−22.9977	+	13.2778i	−0.879984	+	0.508059i	−0.870653	−	0.491897i	$-0.836304\pi$
$683$	−22.9977	+	13.2778i	−0.879984	+	0.508059i	−0.00933109	+	0.999956i	$0.502970\pi$
$684$		0			0
$685$			64.2094i			2.45332i
$686$	5.49271	+	33.5237i	0.209713	+	1.27994i
$687$		0			0
$688$	−35.1976			−1.34190
$689$	0.200594	−	0.347439i	0.00764201	−	0.0132364i
$690$		0			0
$691$	−32.5917	+	18.8168i	−1.23985	+	0.715826i	−0.969063	−	0.246814i	$-0.920616\pi$
$691$	−32.5917	+	18.8168i	−1.23985	+	0.715826i	−0.270784	+	0.962640i	$0.587283\pi$
$692$	13.1473			0.499787
$693$		0			0
$694$	−13.4578			−0.510851
$695$	2.68364	−	1.54940i	0.101796	−	0.0587722i
$696$		0			0
$697$	−7.25136	+	12.5597i	−0.274665	+	0.475734i
$698$	46.7903			1.77104
$699$		0			0
$700$	−4.12028	+	34.0564i	−0.155732	+	1.28721i
$701$			24.3228i			0.918659i	0.888266	+	0.459330i	$0.151910\pi$
$701$			24.3228i			0.918659i	−0.888266	+	0.459330i	$0.848090\pi$
$702$		0			0
$703$	2.31331	−	1.33559i	0.0872482	−	0.0503728i
$704$		−	2.75637i		−	0.103885i
$705$		0			0
$706$	0.0330243	−	0.0190666i	0.00124289	−	0.000717581i
$707$	16.0229	−	6.83489i	0.602603	−	0.257053i
$708$		0			0
$709$	−0.517010	−	0.895487i	−0.0194167	−	0.0336307i	0.856154	−	0.516721i	$-0.172848\pi$
$709$	−0.517010	−	0.895487i	−0.0194167	−	0.0336307i	−0.875570	+	0.483090i	$0.839514\pi$
$710$	16.6313	+	28.8062i	0.624161	+	1.08108i
$711$		0			0
$712$	−11.6608	−	6.73234i	−0.437005	−	0.252305i
$713$	3.76839	−	6.52704i	0.141127	−	0.244440i
$714$		0			0
$715$	−12.2980	−	21.3008i	−0.459921	−	0.796606i
$716$			25.1758i			0.940863i
$717$		0			0
$718$	−66.4436			−2.47965
$719$	−8.37315	+	14.5027i	−0.312266	+	0.540861i	−0.978853	−	0.204567i	$-0.934421\pi$
$719$	−8.37315	+	14.5027i	−0.312266	+	0.540861i	0.666587	+	0.745428i	$0.267755\pi$
$720$		0			0
$721$	−9.70469	−	22.7505i	−0.361422	−	0.847273i
$722$	−29.5486	−	17.0599i	−1.09968	−	0.634903i
$723$		0			0
$724$	−19.6400	−	11.3392i	−0.729915	−	0.421417i
$725$	−39.7839	−	22.9693i	−1.47754	−	0.853057i
$726$		0			0
$727$	28.4902	+	16.4488i	1.05664	+	0.610053i	0.924502	−	0.381178i	$-0.124482\pi$
$727$	28.4902	+	16.4488i	1.05664	+	0.610053i	0.132141	+	0.991231i	$0.457815\pi$
$728$	13.6653	+	10.2596i	0.506469	+	0.380244i
$729$		0			0
$730$	−19.5494	+	33.8606i	−0.723556	+	1.25324i
$731$	22.9749			0.849757
$732$		0			0
$733$			19.9120i			0.735466i	0.929931	+	0.367733i	$0.119866\pi$
$733$			19.9120i			0.735466i	−0.929931	+	0.367733i	$0.880134\pi$
$734$	−8.14310	−	14.1043i	−0.300567	−	0.520598i
$735$		0			0
$736$	5.81058	−	10.0642i	0.214181	−	0.370972i
$737$	5.14762	+	2.97198i	0.189615	+	0.109474i
$738$		0			0
$739$	25.3349	+	43.8813i	0.931959	+	1.61420i	0.779969	+	0.625819i	$0.215235\pi$
$739$	25.3349	+	43.8813i	0.931959	+	1.61420i	0.151990	+	0.988382i	$0.451432\pi$
$740$	−10.9941	−	19.0423i	−0.404151	−	0.700009i
$741$		0			0
$742$	0.0422078	−	0.348871i	0.00154950	−	0.0128075i
$743$	38.3208	−	22.1245i	1.40586	−	0.811671i	0.410870	−	0.911694i	$-0.365225\pi$
$743$	38.3208	−	22.1245i	1.40586	−	0.811671i	0.994985	+	0.100023i	$0.0318917\pi$
$744$		0			0
$745$		−	32.1047i		−	1.17623i
$746$	−20.3626	+	11.7564i	−0.745529	+	0.430431i
$747$		0			0
$748$			5.05339i			0.184770i
$749$	−41.4143	−	5.01047i	−1.51325	−	0.183078i
$750$		0			0
$751$	2.34460			0.0855557			0.0427779	−	0.999085i	$-0.486379\pi$
$751$	2.34460			0.0855557			0.0427779	+	0.999085i	$0.486379\pi$
$752$	−6.19533	+	10.7306i	−0.225921	+	0.391306i
$753$		0			0
$754$	42.5450	−	24.5634i	1.54940	−	0.894546i
$755$	−11.5751			−0.421260
$756$		0			0
$757$	−24.8530			−0.903298			−0.451649	−	0.892196i	$-0.649164\pi$
$757$	−24.8530			−0.903298			−0.451649	+	0.892196i	$0.649164\pi$
$758$	4.98516	−	2.87819i	0.181069	−	0.104540i
$759$		0			0
$760$	−1.40120	+	2.42694i	−0.0508267	+	0.0880345i
$761$	−0.882087			−0.0319756			−0.0159878	−	0.999872i	$-0.505089\pi$
$761$	−0.882087			−0.0319756			−0.0159878	+	0.999872i	$0.505089\pi$
$762$		0			0
$763$	−30.6015	−	22.9749i	−1.10785	−	0.831747i
$764$			9.77730i			0.353730i
$765$		0			0
$766$	−43.7140	+	25.2383i	−1.57945	+	0.911896i
$767$			38.7003i			1.39739i
$768$		0			0
$769$	17.9310	−	10.3524i	0.646607	−	0.373319i	−0.140548	−	0.990074i	$-0.544886\pi$
$769$	17.9310	−	10.3524i	0.646607	−	0.373319i	0.787155	+	0.616755i	$0.211553\pi$
$770$	−17.2293	−	12.9353i	−0.620900	−	0.466157i
$771$		0			0
$772$	−2.16794	−	3.75499i	−0.0780260	−	0.135145i
$773$	−4.70279	−	8.14548i	−0.169148	−	0.292972i	0.768973	−	0.639282i	$-0.220768\pi$
$773$	−4.70279	−	8.14548i	−0.169148	−	0.292972i	−0.938120	+	0.346309i	$0.887435\pi$
$774$		0			0
$775$	35.2047	+	20.3254i	1.26459	+	0.730111i
$776$	−0.401187	+	0.694877i	−0.0144018	+	0.0249446i
$777$		0			0
$778$	16.7316	+	28.9800i	0.599858	+	1.03898i
$779$			2.88157i			0.103243i
$780$		0			0
$781$	−5.55114			−0.198635
$782$	−5.13344	+	8.89138i	−0.183571	+	0.317955i
$783$		0			0
$784$	33.0873	+	8.12497i	1.18169	+	0.290178i
$785$	−12.5597	−	7.25136i	−0.448276	−	0.258812i
$786$		0			0
$787$	21.7855	+	12.5779i	0.776569	+	0.448352i	0.835213	−	0.549927i	$-0.185344\pi$
$787$	21.7855	+	12.5779i	0.776569	+	0.448352i	−0.0586440	+	0.998279i	$0.518678\pi$
$788$	2.28418	+	1.31877i	0.0813705	+	0.0469793i
$789$		0			0
$790$	103.438	+	59.7197i	3.68014	+	2.12473i
$791$	31.5486	−	42.0214i	1.12174	−	1.49411i
$792$		0			0
$793$	22.3996	−	38.7972i	0.795432	−	1.37773i
$794$	2.14457			0.0761080
$795$		0			0
$796$			11.8165i			0.418824i
$797$	−15.3584	−	26.6015i	−0.544023	−	0.942275i	−0.998668	−	0.0516020i	$-0.983567\pi$
$797$	−15.3584	−	26.6015i	−0.544023	−	0.942275i	0.454645	−	0.890673i	$-0.349766\pi$
$798$		0			0
$799$	4.04394	−	7.00431i	0.143064	−	0.247795i
$800$	54.2831	+	31.3404i	1.91920	+	1.10805i
$801$		0			0
$802$	−12.8025	−	22.1746i	−0.452072	−	0.783012i
$803$	−3.26257	−	5.65093i	−0.115134	−	0.199417i
$804$		0			0
$805$	−6.96509	−	16.3281i	−0.245487	−	0.575491i
$806$	−37.6480	+	21.7361i	−1.32609	+	0.765621i
$807$		0			0
$808$		−	7.67541i		−	0.270020i
$809$	−12.3629	+	7.13774i	−0.434657	+	0.250950i	−0.701329	−	0.712838i	$-0.747409\pi$
$809$	−12.3629	+	7.13774i	−0.434657	+	0.250950i	0.266671	+	0.963788i	$0.414076\pi$
$810$		0			0
$811$		−	10.0160i		−	0.351711i	−0.984416	−	0.175855i	$-0.943731\pi$
$811$		−	10.0160i		−	0.351711i	0.984416	−	0.175855i	$-0.0562691\pi$
$812$	10.4779	−	13.9561i	0.367701	−	0.489762i
$813$		0			0
$814$	9.04841			0.317146
$815$	−21.1231	+	36.5863i	−0.739909	+	1.28156i
$816$		0			0
$817$	3.95333	−	2.28245i	0.138309	−	0.0798530i
$818$	−37.3674			−1.30652
$819$		0			0
$820$	23.7200			0.828337
$821$	10.7914	−	6.23043i	0.376623	−	0.217444i	−0.299725	−	0.954026i	$-0.596895\pi$
$821$	10.7914	−	6.23043i	0.376623	−	0.217444i	0.676348	+	0.736582i	$0.263562\pi$
$822$		0			0
$823$	2.29804	−	3.98032i	0.0801045	−	0.138745i	−0.823190	−	0.567766i	$-0.807808\pi$
$823$	2.29804	−	3.98032i	0.0801045	−	0.138745i	0.903295	+	0.429021i	$0.141141\pi$
$824$	−10.8981			−0.379654
$825$		0			0
$826$	13.3008	+	31.1807i	0.462793	+	1.08492i
$827$			37.9330i			1.31906i	0.751678	+	0.659531i	$0.229245\pi$
$827$			37.9330i			1.31906i	−0.751678	+	0.659531i	$0.770755\pi$
$828$		0			0
$829$	−31.8690	+	18.3996i	−1.10686	+	0.639044i	−0.938013	−	0.346599i	$-0.887337\pi$
$829$	−31.8690	+	18.3996i	−1.10686	+	0.639044i	−0.168843	+	0.985643i	$0.554003\pi$
$830$		−	70.9858i		−	2.46395i
$831$		0			0
$832$	−11.3447	+	6.54987i	−0.393307	+	0.227076i
$833$	−21.5974	−	5.30350i	−0.748305	−	0.183755i
$834$		0			0
$835$	7.05213	+	12.2146i	0.244049	+	0.422705i
$836$	0.502032	+	0.869545i	0.0173631	+	0.0300738i
$837$		0			0
$838$	−40.5396	−	23.4055i	−1.40042	−	0.808531i
$839$	10.6785	−	18.4956i	0.368662	−	0.638541i	−0.620695	−	0.784052i	$-0.713149\pi$
$839$	10.6785	−	18.4956i	0.368662	−	0.638541i	0.989357	+	0.145512i	$0.0464828\pi$
$840$		0			0
$841$	−2.81505	−	4.87580i	−0.0970706	−	0.168131i
$842$			0.171216i			0.00590049i
$843$		0			0
$844$	−16.9441			−0.583242
$845$	−33.6932	+	58.3584i	−1.15908	+	2.00759i
$846$		0			0
$847$	−23.4623	+	10.0083i	−0.806173	+	0.343889i
$848$	−0.305226	−	0.176223i	−0.0104815	−	0.00605151i
$849$		0			0
$850$	−47.9572	−	27.6881i	−1.64492	−	0.949693i
$851$	6.45657	+	3.72770i	0.221328	+	0.127784i
$852$		0			0
$853$	42.8709	+	24.7515i	1.46787	+	0.847476i	0.999353	−	0.0359772i	$-0.0114544\pi$
$853$	42.8709	+	24.7515i	1.46787	+	0.847476i	0.468519	+	0.883453i	$0.344788\pi$
$854$	4.71319	−	38.9572i	0.161282	−	1.33309i
$855$		0			0
$856$	−9.19041	+	15.9183i	−0.314122	+	0.544075i
$857$	−14.0162			−0.478784			−0.239392	−	0.970923i	$-0.576948\pi$
$857$	−14.0162			−0.478784			−0.239392	+	0.970923i	$0.576948\pi$
$858$		0			0
$859$		−	1.21490i		−	0.0414517i	−0.999785	−	0.0207259i	$-0.993402\pi$
$859$		−	1.21490i		−	0.0414517i	0.999785	−	0.0207259i	$-0.00659772\pi$
$860$	−18.7883	−	32.5423i	−0.640676	−	1.10968i
$861$		0			0
$862$	−30.4220	+	52.6925i	−1.03618	+	1.79471i
$863$	31.2396	+	18.0362i	1.06341	+	0.613960i	0.926373	−	0.376606i	$-0.122909\pi$
$863$	31.2396	+	18.0362i	1.06341	+	0.613960i	0.137036	+	0.990566i	$0.456242\pi$
$864$		0			0
$865$	−18.3474	−	31.7787i	−0.623832	−	1.08051i
$866$	16.4639	+	28.5164i	0.559467	+	0.969026i
$867$		0			0
$868$	−9.27184	+	12.3497i	−0.314707	+	0.419176i
$869$	−17.2625	+	9.96652i	−0.585591	+	0.338091i
$870$		0			0
$871$		−	28.2489i		−	0.957177i
$872$	−14.6017	+	8.43032i	−0.494477	+	0.285487i
$873$		0			0
$874$			2.03994i			0.0690020i
$875$	41.7300	−	17.8008i	1.41073	−	0.601776i
$876$		0			0
$877$	−11.1921			−0.377932			−0.188966	−	0.981984i	$-0.560514\pi$
$877$	−11.1921			−0.377932			−0.188966	+	0.981984i	$0.560514\pi$
$878$	9.20499	−	15.9435i	0.310653	−	0.538067i
$879$		0			0
$880$	−18.7129	+	10.8039i	−0.630811	+	0.364199i
$881$	−4.16372			−0.140279			−0.0701397	−	0.997537i	$-0.522345\pi$
$881$	−4.16372			−0.140279			−0.0701397	+	0.997537i	$0.522345\pi$
$882$		0			0
$883$	−38.7433			−1.30382			−0.651908	−	0.758298i	$-0.726031\pi$
$883$	−38.7433			−1.30382			−0.651908	+	0.758298i	$0.726031\pi$
$884$	20.7988	−	12.0082i	0.699539	−	0.403879i
$885$		0			0
$886$	−24.1734	+	41.8696i	−0.812121	+	1.40664i
$887$	−38.0824			−1.27868			−0.639342	−	0.768923i	$-0.720793\pi$
$887$	−38.0824			−1.27868			−0.639342	+	0.768923i	$0.720793\pi$
$888$		0			0
$889$	21.6751	−	9.24597i	0.726961	−	0.310100i
$890$		−	80.6807i		−	2.70442i
$891$		0			0
$892$	−22.3764	+	12.9190i	−0.749216	+	0.432560i
$893$		−	1.60699i		−	0.0537759i
$894$		0			0
$895$	60.8529	−	35.1334i	2.03409	−	1.17438i
$896$	14.0665	−	18.7359i	0.469927	−	0.625922i
$897$		0			0
$898$	22.0351	+	38.1660i	0.735322	+	1.27361i
$899$	−10.3400	−	17.9094i	−0.344858	−	0.597311i
$900$		0			0
$901$	0.199234	+	0.115028i	0.00663743	+	0.00383212i
$902$	−4.88053	+	8.45333i	−0.162504	+	0.281465i
$903$		0			0
$904$	−11.5763	−	20.0508i	−0.385023	−	0.666880i
$905$			63.2964i			2.10404i
$906$		0			0
$907$	1.54767			0.0513894			0.0256947	−	0.999670i	$-0.491820\pi$
$907$	1.54767			0.0513894			0.0256947	+	0.999670i	$0.491820\pi$
$908$	−3.90421	+	6.76228i	−0.129566	+	0.224414i
$909$		0			0
$910$	−12.2980	+	101.650i	−0.407676	+	3.36967i
$911$	33.7493	+	19.4852i	1.11816	+	0.645573i	0.940932	−	0.338596i	$-0.109952\pi$
$911$	33.7493	+	19.4852i	1.11816	+	0.645573i	0.177233	+	0.984169i	$0.443285\pi$
$912$		0			0
$913$	10.2596	+	5.92336i	0.339542	+	0.196034i
$914$	−33.0762	−	19.0965i	−1.09406	−	0.631657i
$915$		0			0
$916$	−13.1608	−	7.59836i	−0.434843	−	0.251057i
$917$	−16.4394	+	7.01255i	−0.542875	+	0.231575i
$918$		0			0
$919$	−5.86991	+	10.1670i	−0.193630	+	0.335378i	−0.946451	−	0.322848i	$-0.895360\pi$
$919$	−5.86991	+	10.1670i	−0.193630	+	0.335378i	0.752820	+	0.658226i	$0.228693\pi$
$920$	−7.82162			−0.257871
$921$		0			0
$922$		−	15.3203i		−	0.504546i
$923$	13.1910	+	22.8474i	0.434186	+	0.752033i
$924$		0			0
$925$	−20.1060	+	34.8246i	−0.661081	+	1.14503i
$926$	−18.7655	−	10.8342i	−0.616671	−	0.356035i
$927$		0			0
$928$	−15.9435	−	27.6150i	−0.523371	−	0.906506i
$929$	22.3142	+	38.6493i	0.732105	+	1.26804i	0.955982	+	0.293425i	$0.0947952\pi$
$929$	22.3142	+	38.6493i	0.732105	+	1.26804i	−0.223877	+	0.974617i	$0.571871\pi$
$930$		0			0
$931$	−4.24318	+	1.23302i	−0.139064	+	0.0404107i
$932$	−12.2146	+	7.05213i	−0.400104	+	0.231000i
$933$		0			0
$934$		−	53.4824i		−	1.75000i
$935$	12.2146	−	7.05213i	0.399462	−	0.230629i
$936$		0			0
$937$			33.3351i			1.08901i	0.838758	+	0.544505i	$0.183282\pi$
$937$			33.3351i			1.08901i	−0.838758	+	0.544505i	$0.816718\pi$
$938$	−9.70875	−	22.7600i	−0.317002	−	0.743141i
$939$		0			0
$940$	−13.2282			−0.431455
$941$	16.9992	−	29.4435i	0.554159	−	0.959831i	−0.443810	−	0.896121i	$-0.646373\pi$
$941$	16.9992	−	29.4435i	0.554159	−	0.959831i	0.997968	−	0.0637100i	$-0.0202933\pi$
$942$		0			0
$943$	−6.96509	+	4.02130i	−0.226815	+	0.130952i
$944$	33.9984			1.10655
$945$		0			0
$946$	15.4633			0.502754
$947$	−39.9637	+	23.0731i	−1.29865	+	0.749774i	−0.980170	−	0.198157i	$-0.936504\pi$
$947$	−39.9637	+	23.0731i	−1.29865	+	0.749774i	−0.318476	+	0.947931i	$0.603171\pi$
$948$		0			0
$949$	−15.5055	+	26.8562i	−0.503329	+	0.871791i
$950$	−11.0028			−0.356977
$951$		0			0
$952$	−5.88319	+	7.83615i	−0.190675	+	0.253971i
$953$			35.1143i			1.13746i	0.822523	+	0.568731i	$0.192566\pi$
$953$			35.1143i			1.13746i	−0.822523	+	0.568731i	$0.807434\pi$
$954$		0			0
$955$	23.6329	−	13.6445i	0.764744	−	0.441525i
$956$			22.6234i			0.731692i
$957$		0			0
$958$	64.3717	−	37.1650i	2.07976	−	1.20075i
$959$	17.5030	+	41.0318i	0.565201	+	1.32499i
$960$		0			0
$961$	−6.35017	−	10.9988i	−0.204844	−	0.354800i
$962$	−21.5014	−	37.2415i	−0.693234	−	1.20072i
$963$		0			0
$964$	28.2334	+	16.3005i	0.909335	+	0.525005i
$965$	−6.05084	+	10.4804i	−0.194784	+	0.337375i
$966$		0			0
$967$	6.70742	+	11.6176i	0.215696	+	0.373597i	0.953488	−	0.301432i	$-0.0974646\pi$
$967$	6.70742	+	11.6176i	0.215696	+	0.373597i	−0.737792	+	0.675029i	$0.764131\pi$
$968$			11.2391i			0.361238i
$969$		0			0
$970$	−4.80785			−0.154371
$971$	9.19460	−	15.9255i	0.295069	−	0.511074i	−0.679932	−	0.733275i	$-0.737991\pi$
$971$	9.19460	−	15.9255i	0.295069	−	0.511074i	0.975001	+	0.222201i	$0.0713241\pi$
$972$		0			0
$973$	1.29258	−	1.72166i	0.0414381	−	0.0551938i
$974$	−19.7265	−	11.3891i	−0.632078	−	0.364930i
$975$		0			0
$976$	−34.0835	−	19.6781i	−1.09099	−	0.629882i
$977$	−19.6181	−	11.3265i	−0.627638	−	0.362367i	0.152199	−	0.988350i	$-0.451365\pi$
$977$	−19.6181	−	11.3265i	−0.627638	−	0.362367i	−0.779837	+	0.625983i	$0.784698\pi$
$978$		0			0
$979$	11.6608	+	6.73234i	0.372679	+	0.215166i
$980$	10.1498	+	34.9282i	0.324223	+	1.11574i
$981$		0			0
$982$	−5.65976	+	9.80298i	−0.180610	+	0.312826i
$983$	−39.3408			−1.25478			−0.627388	−	0.778707i	$-0.715876\pi$
$983$	−39.3408			−1.25478			−0.627388	+	0.778707i	$0.715876\pi$
$984$		0			0
$985$		−	7.36151i		−	0.234557i
$986$	14.0855	+	24.3968i	0.448574	+	0.776954i
$987$		0			0
$988$	2.38592	−	4.13254i	0.0759063	−	0.131474i
$989$	11.0339	+	6.37045i	0.350859	+	0.202569i
$990$		0			0
$991$	−0.475797	−	0.824104i	−0.0151142	−	0.0261785i	0.858369	−	0.513032i	$-0.171478\pi$
$991$	−0.475797	−	0.824104i	−0.0151142	−	0.0261785i	−0.873484	+	0.486854i	$0.838145\pi$
$992$	14.1084	+	24.4364i	0.447941	+	0.775857i
$993$		0			0
$994$	18.4803	+	13.8745i	0.586158	+	0.440073i
$995$	28.5618	−	16.4902i	0.905471	−	0.522774i
$996$		0			0
$997$		−	31.4640i		−	0.996475i	−0.867041	−	0.498238i	$-0.833981\pi$
$997$		−	31.4640i		−	0.996475i	0.867041	−	0.498238i	$-0.166019\pi$
$998$	−4.70279	+	2.71516i	−0.148864	+	0.0859468i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.s.f.26.5		12
3.2	odd	2	inner	567.2.s.f.26.2		12
7.3	odd	6		567.2.i.f.269.5		12
9.2	odd	6		189.2.p.d.26.5	yes	12
9.4	even	3		567.2.i.f.215.5		12
9.5	odd	6		567.2.i.f.215.2		12
9.7	even	3		189.2.p.d.26.2	✓	12
21.17	even	6		567.2.i.f.269.2		12
63.2	odd	6		1323.2.c.d.1322.4		12
63.16	even	3		1323.2.c.d.1322.9		12
63.31	odd	6	inner	567.2.s.f.458.2		12
63.38	even	6		189.2.p.d.80.2	yes	12
63.47	even	6		1323.2.c.d.1322.3		12
63.52	odd	6		189.2.p.d.80.5	yes	12
63.59	even	6	inner	567.2.s.f.458.5		12
63.61	odd	6		1323.2.c.d.1322.10		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.p.d.26.2	✓	12	9.7	even	3
189.2.p.d.26.5	yes	12	9.2	odd	6
189.2.p.d.80.2	yes	12	63.38	even	6
189.2.p.d.80.5	yes	12	63.52	odd	6
567.2.i.f.215.2		12	9.5	odd	6
567.2.i.f.215.5		12	9.4	even	3
567.2.i.f.269.2		12	21.17	even	6
567.2.i.f.269.5		12	7.3	odd	6
567.2.s.f.26.2		12	3.2	odd	2	inner
567.2.s.f.26.5		12	1.1	even	1	trivial
567.2.s.f.458.2		12	63.31	odd	6	inner
567.2.s.f.458.5		12	63.59	even	6	inner
1323.2.c.d.1322.3		12	63.47	even	6
1323.2.c.d.1322.4		12	63.2	odd	6
1323.2.c.d.1322.9		12	63.16	even	3
1323.2.c.d.1322.10		12	63.61	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:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.58850 - 0.917122i) q^{2} +(0.682224 - 1.18165i) q^{4} -3.80824 q^{5} +(-2.43359 + 1.03810i) q^{7} +1.16576i q^{8} +O(q^{10})\)	\(q+(1.58850 - 0.917122i) q^{2} +(0.682224 - 1.18165i) q^{4} -3.80824 q^{5} +(-2.43359 + 1.03810i) q^{7} +1.16576i q^{8} +(-6.04940 + 3.49262i) q^{10} -1.16576i q^{11} +(-4.79804 + 2.77015i) q^{13} +(-2.91370 + 3.88092i) q^{14} +(2.43359 + 4.21510i) q^{16} +(-1.58850 - 2.75136i) q^{17} +(-0.546672 - 0.315621i) q^{19} +(-2.59808 + 4.50000i) q^{20} +(-1.06914 - 1.85181i) q^{22} -1.76183i q^{23} +9.50273 q^{25} +(-5.08112 + 8.80077i) q^{26} +(-0.433589 + 3.58386i) q^{28} +(-4.18658 - 2.41712i) q^{29} +(3.70469 + 2.13891i) q^{31} +(5.71237 + 3.29804i) q^{32} +(-5.04667 - 2.91370i) q^{34} +(9.26770 - 3.95333i) q^{35} +(-2.11581 + 3.66470i) q^{37} -1.15785 q^{38} -4.43949i q^{40} +(-2.28245 - 3.95333i) q^{41} +(-3.61581 + 6.26277i) q^{43} +(-1.37751 - 0.795307i) q^{44} +(-1.61581 - 2.79867i) q^{46} +(1.27288 + 2.20469i) q^{47} +(4.84471 - 5.05260i) q^{49} +(15.0951 - 8.71516i) q^{50} +7.55945i q^{52} +(-0.0627112 + 0.0362063i) q^{53} +4.43949i q^{55} +(-1.21017 - 2.83697i) q^{56} -8.86718 q^{58} +(3.49262 - 6.04940i) q^{59} +(-7.00273 + 4.04303i) q^{61} +7.84655 q^{62} +2.36445 q^{64} +(18.2721 - 10.5494i) q^{65} +(-2.54940 + 4.41569i) q^{67} -4.33485 q^{68} +(11.0961 - 14.7795i) q^{70} -4.76183i q^{71} +(4.84744 - 2.79867i) q^{73} +7.76183i q^{74} +(-0.745906 + 0.430649i) q^{76} +(1.21017 + 2.83697i) q^{77} +(-8.54940 - 14.8080i) q^{79} +(-9.26770 - 16.0521i) q^{80} +(-7.25136 - 4.18658i) q^{82} +(-5.08112 + 8.80077i) q^{83} +(6.04940 + 10.4779i) q^{85} +13.2646i q^{86} +1.35899 q^{88} +(-5.77508 + 10.0027i) q^{89} +(8.80077 - 11.7222i) q^{91} +(-2.08186 - 1.20196i) q^{92} +(4.04394 + 2.33477i) q^{94} +(2.08186 + 1.20196i) q^{95} +(0.596074 + 0.344143i) q^{97} +(3.06197 - 12.4693i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 8 q^{4} + 4 q^{7}+O(q^{10}) \) 12 * q + 8 * q^4 + 4 * q^7	\( 12 q + 8 q^{4} + 4 q^{7} - 6 q^{10} - 24 q^{13} - 4 q^{16} - 6 q^{19} + 20 q^{22} + 48 q^{25} + 28 q^{28} + 12 q^{31} - 60 q^{34} + 8 q^{37} - 10 q^{43} + 14 q^{46} + 24 q^{49} - 40 q^{58} - 18 q^{61} + 28 q^{64} + 36 q^{67} + 66 q^{70} - 42 q^{73} - 108 q^{76} - 36 q^{79} - 54 q^{82} + 6 q^{85} + 148 q^{88} + 6 q^{91} + 114 q^{94} - 60 q^{97}+O(q^{100}) \) 12 * q + 8 * q^4 + 4 * q^7 - 6 * q^10 - 24 * q^13 - 4 * q^16 - 6 * q^19 + 20 * q^22 + 48 * q^25 + 28 * q^28 + 12 * q^31 - 60 * q^34 + 8 * q^37 - 10 * q^43 + 14 * q^46 + 24 * q^49 - 40 * q^58 - 18 * q^61 + 28 * q^64 + 36 * q^67 + 66 * q^70 - 42 * q^73 - 108 * q^76 - 36 * q^79 - 54 * q^82 + 6 * q^85 + 148 * q^88 + 6 * q^91 + 114 * q^94 - 60 * q^97

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