LMFDB - Embedded newform 567.2.h.l.298.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [567,2,Mod(298,567)]

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([4, 4]))

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

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

chi := DirichletCharacter("567.298");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.h (of order $3$, 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:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4x^{14} + 14x^{12} - 39x^{10} + 77x^{8} - 156x^{6} + 224x^{4} - 256x^{2} + 256 $ x^16 - 4x^14 + 14x^12 - 39x^10 + 77x^8 - 156x^6 + 224x^4 - 256*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			298.7
Root			$1.41264 - 0.0667052i$ of defining polynomial
Character	$\chi$	$=$	567.298
Dual form			567.2.h.l.352.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.52818 q^{2} +0.335323 q^{4} +(-1.41264 + 2.44676i) q^{5} +(-2.61442 + 0.405935i) q^{7} -2.54392 q^{8} +O(q^{10})$	\(q+1.52818 q^{2} +0.335323 q^{4} +(-1.41264 + 2.44676i) q^{5} +(-2.61442 + 0.405935i) q^{7} -2.54392 q^{8} +(-2.15876 + 3.73909i) q^{10} +(-1.81857 - 3.14986i) q^{11} +(2.81454 + 4.87493i) q^{13} +(-3.99530 + 0.620340i) q^{14} -4.55820 q^{16} +(-1.60110 + 2.77319i) q^{17} +(-2.03544 - 3.52548i) q^{19} +(-0.473690 + 0.820455i) q^{20} +(-2.77910 - 4.81355i) q^{22} +(-2.35159 + 4.07307i) q^{23} +(-1.49110 - 2.58266i) q^{25} +(4.30111 + 7.44975i) q^{26} +(-0.876676 + 0.136119i) q^{28} +(-2.16313 + 3.74665i) q^{29} +3.58197 q^{31} -1.87790 q^{32} +(-2.44676 + 4.23792i) q^{34} +(2.70001 - 6.97032i) q^{35} +(2.15578 + 3.73392i) q^{37} +(-3.11051 - 5.38756i) q^{38} +(3.59364 - 6.22437i) q^{40} +(-1.57596 - 2.72964i) q^{41} +(4.59663 - 7.96159i) q^{43} +(-0.609809 - 1.05622i) q^{44} +(-3.59364 + 6.22437i) q^{46} +4.84643 q^{47} +(6.67043 - 2.12257i) q^{49} +(-2.27866 - 3.94676i) q^{50} +(0.943779 + 1.63467i) q^{52} +(-7.06707 + 12.2405i) q^{53} +10.2760 q^{55} +(6.65089 - 1.03267i) q^{56} +(-3.30564 + 5.72554i) q^{58} +1.50098 q^{59} +13.2051 q^{61} +5.47388 q^{62} +6.24665 q^{64} -15.9037 q^{65} -12.6822 q^{67} +(-0.536885 + 0.929913i) q^{68} +(4.12610 - 10.6519i) q^{70} -2.91413 q^{71} +(-1.46456 + 2.53670i) q^{73} +(3.29441 + 5.70608i) q^{74} +(-0.682529 - 1.18217i) q^{76} +(6.03316 + 7.49686i) q^{77} +0.893527 q^{79} +(6.43910 - 11.1528i) q^{80} +(-2.40834 - 4.17137i) q^{82} +(-4.02432 + 6.97032i) q^{83} +(-4.52356 - 7.83503i) q^{85} +(7.02446 - 12.1667i) q^{86} +(4.62631 + 8.01300i) q^{88} +(-2.82863 - 4.89934i) q^{89} +(-9.33731 - 11.6026i) q^{91} +(-0.788541 + 1.36579i) q^{92} +7.40620 q^{94} +11.5014 q^{95} +(-2.56789 + 4.44772i) q^{97} +(10.1936 - 3.24366i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 12 q^{4} - 6 q^{7}+O(q^{10}) $ 16 * q + 12 * q^4 - 6 * q^7	$ 16 q + 12 q^{4} - 6 q^{7} - 14 q^{10} - 6 q^{13} + 12 q^{16} - 24 q^{19} - 2 q^{22} - 26 q^{28} + 40 q^{31} + 4 q^{37} - 36 q^{40} - 10 q^{43} + 36 q^{46} + 10 q^{49} - 34 q^{52} + 8 q^{55} + 22 q^{58} + 72 q^{61} + 76 q^{64} - 36 q^{67} - 46 q^{70} - 32 q^{73} - 58 q^{76} - 64 q^{79} + 2 q^{82} - 30 q^{85} + 72 q^{88} - 22 q^{91} + 108 q^{94} - 14 q^{97}+O(q^{100}) $ 16 * q + 12 * q^4 - 6 * q^7 - 14 * q^10 - 6 * q^13 + 12 * q^16 - 24 * q^19 - 2 * q^22 - 26 * q^28 + 40 * q^31 + 4 * q^37 - 36 * q^40 - 10 * q^43 + 36 * q^46 + 10 * q^49 - 34 * q^52 + 8 * q^55 + 22 * q^58 + 72 * q^61 + 76 * q^64 - 36 * q^67 - 46 * q^70 - 32 * q^73 - 58 * q^76 - 64 * q^79 + 2 * q^82 - 30 * q^85 + 72 * q^88 - 22 * q^91 + 108 * q^94 - 14 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	1.52818			1.08058			0.540292	−	0.841478i	$-0.318314\pi$
$2$	1.52818			1.08058			0.540292	+	0.841478i	$0.318314\pi$
$3$		0			0
$3$		0			0
$4$	0.335323			0.167661
$5$	−1.41264	+	2.44676i	−0.631752	+	1.09423i	0.355442	+	0.934698i	$0.384330\pi$
$5$	−1.41264	+	2.44676i	−0.631752	+	1.09423i	−0.987193	+	0.159527i	$0.949003\pi$
$6$		0			0
$7$	−2.61442	+	0.405935i	−0.988160	+	0.153429i
$7$	−2.61442	+	0.405935i	−0.988160	+	0.153429i
$8$	−2.54392			−0.899412
$9$		0			0
$10$	−2.15876	+	3.73909i	−0.682661	+	1.18240i
$11$	−1.81857	−	3.14986i	−0.548321	−	0.949719i	−0.998390	−	0.0567257i	$-0.981934\pi$
$11$	−1.81857	−	3.14986i	−0.548321	−	0.949719i	0.450069	−	0.892994i	$-0.351399\pi$
$12$		0			0
$13$	2.81454	+	4.87493i	0.780613	+	1.35206i	0.931585	+	0.363523i	$0.118426\pi$
$13$	2.81454	+	4.87493i	0.780613	+	1.35206i	−0.150972	+	0.988538i	$0.548240\pi$
$14$	−3.99530	+	0.620340i	−1.06779	+	0.165793i
$15$		0			0
$16$	−4.55820			−1.13955
$17$	−1.60110	+	2.77319i	−0.388324	+	0.672597i	−0.992224	−	0.124463i	$-0.960279\pi$
$17$	−1.60110	+	2.77319i	−0.388324	+	0.672597i	0.603900	+	0.797060i	$0.293612\pi$
$18$		0			0
$19$	−2.03544	−	3.52548i	−0.466962	−	0.808801i	0.532326	−	0.846539i	$-0.321318\pi$
$19$	−2.03544	−	3.52548i	−0.466962	−	0.808801i	−0.999288	+	0.0377382i	$0.987985\pi$
$20$	−0.473690	+	0.820455i	−0.105920	+	0.183459i
$21$		0			0
$22$	−2.77910	−	4.81355i	−0.592507	−	1.02625i
$23$	−2.35159	+	4.07307i	−0.490340	+	0.849294i	−0.999938	−	0.0111185i	$-0.996461\pi$
$23$	−2.35159	+	4.07307i	−0.490340	+	0.849294i	0.509598	+	0.860413i	$0.329794\pi$
$24$		0			0
$25$	−1.49110	−	2.58266i	−0.298220	−	0.516532i
$26$	4.30111	+	7.44975i	0.843518	+	1.46102i
$27$		0			0
$28$	−0.876676	+	0.136119i	−0.165676	+	0.0257241i
$29$	−2.16313	+	3.74665i	−0.401683	+	0.695735i	−0.993929	−	0.110022i	$-0.964908\pi$
$29$	−2.16313	+	3.74665i	−0.401683	+	0.695735i	0.592246	+	0.805757i	$0.298241\pi$
$30$		0			0
$31$	3.58197			0.643341			0.321670	−	0.946852i	$-0.395756\pi$
$31$	3.58197			0.643341			0.321670	+	0.946852i	$0.395756\pi$
$32$	−1.87790			−0.331969
$33$		0			0
$34$	−2.44676	+	4.23792i	−0.419616	+	0.726797i
$35$	2.70001	−	6.97032i	0.456386	−	1.17820i
$36$		0			0
$37$	2.15578	+	3.73392i	0.354408	+	0.613852i	0.987016	−	0.160619i	$-0.0513492\pi$
$37$	2.15578	+	3.73392i	0.354408	+	0.613852i	−0.632609	+	0.774472i	$0.718016\pi$
$38$	−3.11051	−	5.38756i	−0.504591	−	0.873977i
$39$		0			0
$40$	3.59364	−	6.22437i	0.568205	−	0.984159i
$41$	−1.57596	−	2.72964i	−0.246123	−	0.426298i	0.716324	−	0.697768i	$-0.245823\pi$
$41$	−1.57596	−	2.72964i	−0.246123	−	0.426298i	−0.962447	+	0.271470i	$0.912490\pi$
$42$		0			0
$43$	4.59663	−	7.96159i	0.700979	−	1.21413i	−0.267144	−	0.963657i	$-0.586080\pi$
$43$	4.59663	−	7.96159i	0.700979	−	1.21413i	0.968123	−	0.250475i	$-0.0805867\pi$
$44$	−0.609809	−	1.05622i	−0.0919322	−	0.159231i
$45$		0			0
$46$	−3.59364	+	6.22437i	−0.529854	+	0.917733i
$47$	4.84643			0.706924			0.353462	−	0.935449i	$-0.385004\pi$
$47$	4.84643			0.706924			0.353462	+	0.935449i	$0.385004\pi$
$48$		0			0
$49$	6.67043	−	2.12257i	0.952919	−	0.303225i
$50$	−2.27866	−	3.94676i	−0.322252	−	0.558157i
$51$		0			0
$52$	0.943779	+	1.63467i	0.130879	+	0.226688i
$53$	−7.06707	+	12.2405i	−0.970736	+	1.68136i	−0.277395	+	0.960756i	$0.589471\pi$
$53$	−7.06707	+	12.2405i	−0.970736	+	1.68136i	−0.693342	+	0.720609i	$0.743862\pi$
$54$		0			0
$55$	10.2760			1.38561
$56$	6.65089	−	1.03267i	0.888762	−	0.137996i
$57$		0			0
$58$	−3.30564	+	5.72554i	−0.434052	+	0.751800i
$59$	1.50098			0.195411			0.0977053	−	0.995215i	$-0.468850\pi$
$59$	1.50098			0.195411			0.0977053	+	0.995215i	$0.468850\pi$
$60$		0			0
$61$	13.2051			1.69074			0.845369	−	0.534183i	$-0.179381\pi$
$61$	13.2051			1.69074			0.845369	+	0.534183i	$0.179381\pi$
$62$	5.47388			0.695184
$63$		0			0
$64$	6.24665			0.780831
$65$	−15.9037			−1.97261
$66$		0			0
$67$	−12.6822			−1.54937			−0.774686	−	0.632346i	$-0.782092\pi$
$67$	−12.6822			−1.54937			−0.774686	+	0.632346i	$0.782092\pi$
$68$	−0.536885	+	0.929913i	−0.0651069	+	0.112768i
$69$		0			0
$70$	4.12610	−	10.6519i	0.493163	−	1.27314i
$71$	−2.91413			−0.345844			−0.172922	−	0.984936i	$-0.555321\pi$
$71$	−2.91413			−0.345844			−0.172922	+	0.984936i	$0.555321\pi$
$72$		0			0
$73$	−1.46456	+	2.53670i	−0.171414	+	0.296898i	−0.938914	−	0.344151i	$-0.888167\pi$
$73$	−1.46456	+	2.53670i	−0.171414	+	0.296898i	0.767500	+	0.641048i	$0.221500\pi$
$74$	3.29441	+	5.70608i	0.382967	+	0.663319i
$75$		0			0
$76$	−0.682529	−	1.18217i	−0.0782914	−	0.135605i
$77$	6.03316	+	7.49686i	0.687543	+	0.854346i
$78$		0			0
$79$	0.893527			0.100530			0.0502648	−	0.998736i	$-0.483993\pi$
$79$	0.893527			0.100530			0.0502648	+	0.998736i	$0.483993\pi$
$80$	6.43910	−	11.1528i	0.719913	−	1.24693i
$81$		0			0
$82$	−2.40834	−	4.17137i	−0.265957	−	0.460651i
$83$	−4.02432	+	6.97032i	−0.441726	+	0.765092i	−0.997818	−	0.0660291i	$-0.978967\pi$
$83$	−4.02432	+	6.97032i	−0.441726	+	0.765092i	0.556092	+	0.831121i	$0.312300\pi$
$84$		0			0
$85$	−4.52356	−	7.83503i	−0.490648	−	0.849828i
$86$	7.02446	−	12.1667i	0.757467	−	1.31197i
$87$		0			0
$88$	4.62631	+	8.01300i	0.493166	+	0.854189i
$89$	−2.82863	−	4.89934i	−0.299835	−	0.519329i	0.676263	−	0.736660i	$-0.263598\pi$
$89$	−2.82863	−	4.89934i	−0.299835	−	0.519329i	−0.976098	+	0.217331i	$0.930265\pi$
$90$		0			0
$91$	−9.33731	−	11.6026i	−0.978816	−	1.21628i
$92$	−0.788541	+	1.36579i	−0.0822111	+	0.142394i
$93$		0			0
$94$	7.40620			0.763891
$95$	11.5014			1.18001
$96$		0			0
$97$	−2.56789	+	4.44772i	−0.260730	+	0.451598i	−0.966436	−	0.256907i	$-0.917297\pi$
$97$	−2.56789	+	4.44772i	−0.260730	+	0.451598i	0.705706	+	0.708505i	$0.250630\pi$
$98$	10.1936	−	3.24366i	1.02971	−	0.327660i
$99$		0			0
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	−1.26223	−	2.18625i	−0.125597	−	0.217540i	0.796369	−	0.604811i	$-0.206751\pi$
$101$	−1.26223	−	2.18625i	−0.125597	−	0.217540i	−0.921966	+	0.387271i	$0.873418\pi$
$102$		0			0
$103$	−4.92321	+	8.52725i	−0.485098	+	0.840215i	−0.999853	−	0.0171225i	$-0.994549\pi$
$103$	−4.92321	+	8.52725i	−0.485098	+	0.840215i	0.514755	+	0.857337i	$0.327883\pi$
$104$	−7.15997	−	12.4014i	−0.702092	−	1.21606i
$105$		0			0
$106$	−10.7997	+	18.7057i	−1.04896	+	1.81686i
$107$	−1.35126	−	2.34045i	−0.130631	−	0.226260i	0.793289	−	0.608845i	$-0.208367\pi$
$107$	−1.35126	−	2.34045i	−0.130631	−	0.226260i	−0.923920	+	0.382586i	$0.875034\pi$
$108$		0			0
$109$	4.52873	−	7.84400i	0.433774	−	0.751319i	−0.563421	−	0.826170i	$-0.690515\pi$
$109$	4.52873	−	7.84400i	0.433774	−	0.751319i	0.997195	+	0.0748515i	$0.0238483\pi$
$110$	15.7035			1.49727
$111$		0			0
$112$	11.9171	−	1.85033i	1.12606	−	0.174840i
$113$	−0.232888	−	0.403374i	−0.0219082	−	0.0379462i	0.854863	−	0.518853i	$-0.173641\pi$
$113$	−0.232888	−	0.403374i	−0.0219082	−	0.0379462i	−0.876772	+	0.480907i	$0.840308\pi$
$114$		0			0
$115$	−6.64389	−	11.5076i	−0.619546	−	1.07309i
$116$	−0.725346	+	1.25634i	−0.0673467	+	0.116648i
$117$		0			0
$118$	2.29376			0.211158
$119$	3.06022	−	7.90023i	0.280530	−	0.724213i
$120$		0			0
$121$	−1.11442	+	1.93024i	−0.101311	+	0.175476i
$122$	20.1797			1.82698
$123$		0			0
$124$	1.20112			0.107863
$125$	−5.70084			−0.509899
$126$		0			0
$127$	−15.7574			−1.39825			−0.699123	−	0.715002i	$-0.746426\pi$
$127$	−15.7574			−1.39825			−0.699123	+	0.715002i	$0.746426\pi$
$128$	13.3018			1.17572
$129$		0			0
$130$	−24.3037			−2.13157
$131$	−6.07396	+	10.5204i	−0.530685	+	0.919173i	0.468674	+	0.883371i	$0.344732\pi$
$131$	−6.07396	+	10.5204i	−0.530685	+	0.919173i	−0.999359	+	0.0358017i	$0.988602\pi$
$132$		0			0
$133$	6.75262	+	8.39085i	0.585526	+	0.727579i
$134$	−19.3806			−1.67423
$135$		0			0
$136$	4.07307	−	7.05477i	0.349263	−	0.604941i
$137$	−1.08169	−	1.87353i	−0.0924146	−	0.160067i	0.816112	−	0.577894i	$-0.196125\pi$
$137$	−1.08169	−	1.87353i	−0.0924146	−	0.160067i	−0.908527	+	0.417827i	$0.862792\pi$
$138$		0			0
$139$	10.7257	+	18.5775i	0.909743	+	1.57572i	0.814421	+	0.580274i	$0.197054\pi$
$139$	10.7257	+	18.5775i	0.909743	+	1.57572i	0.0953212	+	0.995447i	$0.469612\pi$
$140$	0.905376	−	2.33731i	0.0765182	−	0.197538i
$141$		0			0
$142$	−4.45331			−0.373713
$143$	10.2369	−	17.7308i	0.856053	−	1.48273i
$144$		0			0
$145$	−6.11144	−	10.5853i	−0.507528	−	0.879063i
$146$	−2.23811	+	3.87652i	−0.185227	+	0.320823i
$147$		0			0
$148$	0.722881	+	1.25207i	0.0594205	+	0.102919i
$149$	5.54862	−	9.61049i	0.454561	−	0.787322i	−0.544102	−	0.839019i	$-0.683130\pi$
$149$	5.54862	−	9.61049i	0.454561	−	0.787322i	0.998663	+	0.0516967i	$0.0164629\pi$
$150$		0			0
$151$	−1.04355	−	1.80748i	−0.0849228	−	0.147091i	0.820436	−	0.571739i	$-0.193731\pi$
$151$	−1.04355	−	1.80748i	−0.0849228	−	0.147091i	−0.905358	+	0.424649i	$0.860398\pi$
$152$	5.17799	+	8.96855i	0.419991	+	0.727445i
$153$		0			0
$154$	9.21974	+	11.4565i	0.742948	+	0.923193i
$155$	−5.06003	+	8.76423i	−0.406432	+	0.703960i
$156$		0			0
$157$	−21.6154			−1.72509			−0.862547	−	0.505978i	$-0.831132\pi$
$157$	−21.6154			−1.72509			−0.862547	+	0.505978i	$0.831132\pi$
$158$	1.36547			0.108631
$159$		0			0
$160$	2.65279	−	4.59477i	0.209722	−	0.363249i
$161$	4.49465	−	11.6033i	0.354228	−	0.914471i
$162$		0			0
$163$	4.69122	+	8.12543i	0.367444	+	0.636432i	0.989165	−	0.146807i	$-0.0468995\pi$
$163$	4.69122	+	8.12543i	0.367444	+	0.636432i	−0.621721	+	0.783239i	$0.713566\pi$
$164$	−0.528454	−	0.915310i	−0.0412654	−	0.0714737i
$165$		0			0
$166$	−6.14986	+	10.6519i	−0.477322	+	0.826746i
$167$	8.70235	+	15.0729i	0.673408	+	1.16638i	0.976931	+	0.213553i	$0.0685036\pi$
$167$	8.70235	+	15.0729i	0.673408	+	1.16638i	−0.303523	+	0.952824i	$0.598163\pi$
$168$		0			0
$169$	−9.34327	+	16.1830i	−0.718713	+	1.24485i
$170$	−6.91279	−	11.9733i	−0.530187	−	0.918310i
$171$		0			0
$172$	1.54135	−	2.66970i	0.117527	−	0.203563i
$173$	21.5476			1.63823			0.819116	−	0.573628i	$-0.194465\pi$
$173$	21.5476			1.63823			0.819116	+	0.573628i	$0.194465\pi$
$174$		0			0
$175$	4.94676	+	6.14689i	0.373940	+	0.464661i
$176$	8.28943	+	14.3577i	0.624840	+	1.08225i
$177$		0			0
$178$	−4.32265	−	7.48705i	−0.323996	−	0.561178i
$179$	2.82863	−	4.89934i	0.211422	−	0.366194i	−0.740738	−	0.671794i	$-0.765524\pi$
$179$	2.82863	−	4.89934i	0.211422	−	0.366194i	0.952160	+	0.305601i	$0.0988572\pi$
$180$		0			0
$181$	1.12427			0.0835664			0.0417832	−	0.999127i	$-0.486696\pi$
$181$	1.12427			0.0835664			0.0417832	+	0.999127i	$0.486696\pi$
$182$	−14.2690	−	17.7308i	−1.05769	−	1.31430i
$183$		0			0
$184$	5.98225	−	10.3616i	0.441018	−	0.763865i
$185$	−12.1813			−0.895591
$186$		0			0
$187$	11.6469			0.851704
$188$	1.62512			0.118524
$189$		0			0
$190$	17.5761			1.27510
$191$	−3.93900			−0.285016			−0.142508	−	0.989794i	$-0.545517\pi$
$191$	−3.93900			−0.285016			−0.142508	+	0.989794i	$0.545517\pi$
$192$		0			0
$193$	18.0868			1.30191			0.650957	−	0.759114i	$-0.274368\pi$
$193$	18.0868			1.30191			0.650957	+	0.759114i	$0.274368\pi$
$194$	−3.92419	+	6.79690i	−0.281741	+	0.487989i
$195$		0			0
$196$	2.23675	−	0.711747i	0.159768	−	0.0508390i
$197$	−25.4842			−1.81567			−0.907836	−	0.419326i	$-0.862266\pi$
$197$	−25.4842			−1.81567			−0.907836	+	0.419326i	$0.862266\pi$
$198$		0			0
$199$	−6.31454	+	10.9371i	−0.447626	+	0.775311i	−0.998231	−	0.0594551i	$-0.981064\pi$
$199$	−6.31454	+	10.9371i	−0.447626	+	0.775311i	0.550605	+	0.834766i	$0.314397\pi$
$200$	3.79324	+	6.57009i	0.268223	+	0.464575i
$201$		0			0
$202$	−1.92891	−	3.34097i	−0.135718	−	0.235070i
$203$	4.13444	−	10.6734i	0.290181	−	0.749127i
$204$		0			0
$205$	8.90504			0.621955
$206$	−7.52353	+	13.0311i	−0.524189	+	0.907922i
$207$		0			0
$208$	−12.8292	−	22.2209i	−0.889548	−	1.54074i
$209$	−7.40319	+	12.8227i	−0.512089	+	0.886965i
$210$		0			0
$211$	−1.15578	−	2.00187i	−0.0795670	−	0.137814i	0.823496	−	0.567322i	$-0.192020\pi$
$211$	−1.15578	−	2.00187i	−0.0795670	−	0.137814i	−0.903063	+	0.429508i	$0.858687\pi$
$212$	−2.36975	+	4.10452i	−0.162755	+	0.281900i
$213$		0			0
$214$	−2.06496	−	3.57662i	−0.141158	−	0.244493i
$215$	12.9868	+	22.4937i	0.885689	+	1.53406i
$216$		0			0
$217$	−9.36479	+	1.45405i	−0.635724	+	0.0987071i
$218$	6.92070	−	11.9870i	0.468729	−	0.811863i
$219$		0			0
$220$	3.44576			0.232313
$221$	−18.0254			−1.21252
$222$		0			0
$223$	−4.64981	+	8.05371i	−0.311374	+	0.539316i	−0.978660	−	0.205486i	$-0.934123\pi$
$223$	−4.64981	+	8.05371i	−0.311374	+	0.539316i	0.667286	+	0.744802i	$0.267456\pi$
$224$	4.90963	−	0.762304i	0.328038	−	0.0509336i
$225$		0			0
$226$	−0.355894	−	0.616426i	−0.0236737	−	0.0410040i
$227$	−0.964092	−	1.66986i	−0.0639890	−	0.110832i	0.832256	−	0.554391i	$-0.187049\pi$
$227$	−0.964092	−	1.66986i	−0.0639890	−	0.110832i	−0.896245	+	0.443559i	$0.853716\pi$
$228$		0			0
$229$	−1.67059	+	2.89355i	−0.110396	+	0.191211i	−0.915930	−	0.401338i	$-0.868545\pi$
$229$	−1.67059	+	2.89355i	−0.110396	+	0.191211i	0.805534	+	0.592549i	$0.201879\pi$
$230$	−10.1530	−	17.5856i	−0.669472	−	1.15956i
$231$		0			0
$232$	5.50283	−	9.53117i	0.361278	−	0.625752i
$233$	10.5758	+	18.3178i	0.692842	+	1.20004i	0.970903	+	0.239474i	$0.0769749\pi$
$233$	10.5758	+	18.3178i	0.692842	+	1.20004i	−0.278061	+	0.960563i	$0.589692\pi$
$234$		0			0
$235$	−6.84626	+	11.8581i	−0.446601	+	0.773535i
$236$	0.503312			0.0327628
$237$		0			0
$238$	4.67656	−	12.0729i	0.303136	−	0.782573i
$239$	−12.0575	−	20.8843i	−0.779937	−	1.35089i	−0.931978	−	0.362516i	$-0.881918\pi$
$239$	−12.0575	−	20.8843i	−0.779937	−	1.35089i	0.152041	−	0.988374i	$-0.451416\pi$
$240$		0			0
$241$	−4.61720	−	7.99722i	−0.297420	−	0.515146i	0.678125	−	0.734947i	$-0.262793\pi$
$241$	−4.61720	−	7.99722i	−0.297420	−	0.515146i	−0.975545	+	0.219800i	$0.929459\pi$
$242$	−1.70304	+	2.94975i	−0.109475	+	0.189617i
$243$		0			0
$244$	4.42796			0.283471
$245$	−4.22949	+	19.3194i	−0.270212	+	1.23427i
$246$		0			0
$247$	11.4576	−	19.8452i	0.729033	−	1.26272i
$248$	−9.11225			−0.578628
$249$		0			0
$250$	−8.71189			−0.550989
$251$	18.5790			1.17270			0.586349	−	0.810058i	$-0.300565\pi$
$251$	18.5790			1.17270			0.586349	+	0.810058i	$0.300565\pi$
$252$		0			0
$253$	17.1062			1.07545
$254$	−24.0801			−1.51092
$255$		0			0
$256$	7.83416			0.489635
$257$	5.10987	−	8.85056i	0.318745	−	0.552083i	−0.661481	−	0.749962i	$-0.730072\pi$
$257$	5.10987	−	8.85056i	0.318745	−	0.552083i	0.980226	+	0.197879i	$0.0634053\pi$
$258$		0			0
$259$	−7.15185	−	8.88694i	−0.444394	−	0.552208i
$260$	−5.33288			−0.330731
$261$		0			0
$262$	−9.28209	+	16.0770i	−0.573449	+	0.993243i
$263$	−4.56887	−	7.91352i	−0.281729	−	0.487969i	0.690082	−	0.723731i	$-0.257575\pi$
$263$	−4.56887	−	7.91352i	−0.281729	−	0.487969i	−0.971811	+	0.235763i	$0.924241\pi$
$264$		0			0
$265$	−19.9664	−	34.5829i	−1.22653	−	2.12441i
$266$	10.3192	+	12.8227i	0.632710	+	0.786210i
$267$		0			0
$268$	−4.25262			−0.259770
$269$	11.4606	−	19.8504i	0.698767	−	1.21030i	−0.270127	−	0.962825i	$-0.587066\pi$
$269$	11.4606	−	19.8504i	0.698767	−	1.21030i	0.968894	−	0.247475i	$-0.0796010\pi$
$270$		0			0
$271$	4.65781	+	8.06757i	0.282942	+	0.490070i	0.972108	−	0.234533i	$-0.0753562\pi$
$271$	4.65781	+	8.06757i	0.282942	+	0.490070i	−0.689166	+	0.724604i	$0.742023\pi$
$272$	7.29814	−	12.6408i	0.442515	−	0.766458i
$273$		0			0
$274$	−1.65301	−	2.86309i	−0.0998617	−	0.172966i
$275$	−5.42336	+	9.39353i	−0.327041	+	0.566451i
$276$		0			0
$277$	−0.0916589	−	0.158758i	−0.00550725	−	0.00953884i	0.863259	−	0.504762i	$-0.168420\pi$
$277$	−0.0916589	−	0.158758i	−0.00550725	−	0.00953884i	−0.868766	+	0.495223i	$0.835086\pi$
$278$	16.3908	+	28.3896i	0.983053	+	1.70270i
$279$		0			0
$280$	−6.86862	+	17.7319i	−0.410479	+	1.05969i
$281$	−8.10097	+	14.0313i	−0.483263	+	0.837037i	−0.999815	−	0.0192190i	$-0.993882\pi$
$281$	−8.10097	+	14.0313i	−0.483263	+	0.837037i	0.516552	+	0.856256i	$0.327215\pi$
$282$		0			0
$283$	20.6984			1.23039			0.615195	−	0.788375i	$-0.289077\pi$
$283$	20.6984			1.23039			0.615195	+	0.788375i	$0.289077\pi$
$284$	−0.977175			−0.0579847
$285$		0			0
$286$	15.6438	−	27.0958i	0.925037	−	1.60221i
$287$	5.22828	+	6.49670i	0.308615	+	0.383488i
$288$		0			0
$289$	3.37296	+	5.84213i	0.198409	+	0.343655i
$290$	−9.33936	−	16.1762i	−0.548426	−	0.949902i
$291$		0			0
$292$	−0.491101	+	0.850612i	−0.0287395	+	0.0497783i
$293$	8.01170	+	13.8767i	0.468049	+	0.810684i	0.999333	−	0.0365093i	$-0.0116239\pi$
$293$	8.01170	+	13.8767i	0.468049	+	0.810684i	−0.531285	+	0.847193i	$0.678291\pi$
$294$		0			0
$295$	−2.12034	+	3.67254i	−0.123451	+	0.213823i
$296$	−5.48413	−	9.49879i	−0.318758	−	0.552106i
$297$		0			0
$298$	8.47927	−	14.6865i	0.491191	−	0.850768i
$299$	−26.4746			−1.53106
$300$		0			0
$301$	−8.78565	+	22.6809i	−0.506396	+	1.30731i
$302$	−1.59473	−	2.76215i	−0.0917662	−	0.158944i
$303$		0			0
$304$	9.27794	+	16.0699i	0.532127	+	0.921670i
$305$	−18.6540	+	32.3097i	−1.06813	+	1.85005i
$306$		0			0
$307$	−5.32307			−0.303804			−0.151902	−	0.988396i	$-0.548540\pi$
$307$	−5.32307			−0.303804			−0.151902	+	0.988396i	$0.548540\pi$
$308$	2.02306	+	2.51387i	0.115274	+	0.143241i
$309$		0			0
$310$	−7.73262	+	13.3933i	−0.439183	+	0.760688i
$311$	−18.4259			−1.04484			−0.522420	−	0.852689i	$-0.674970\pi$
$311$	−18.4259			−1.04484			−0.522420	+	0.852689i	$0.674970\pi$
$312$		0			0
$313$	4.64688			0.262657			0.131329	−	0.991339i	$-0.458076\pi$
$313$	4.64688			0.262657			0.131329	+	0.991339i	$0.458076\pi$
$314$	−33.0321			−1.86411
$315$		0			0
$316$	0.299620			0.0168549
$317$	10.4801			0.588623			0.294311	−	0.955710i	$-0.404910\pi$
$317$	10.4801			0.588623			0.294311	+	0.955710i	$0.404910\pi$
$318$		0			0
$319$	15.7352			0.881004
$320$	−8.82426	+	15.2841i	−0.493291	+	0.854405i
$321$		0			0
$322$	6.86862	−	17.7319i	0.382773	−	0.988162i
$323$	13.0358			0.725329
$324$		0			0
$325$	8.39353	−	14.5380i	0.465589	−	0.806424i
$326$	7.16901	+	12.4171i	0.397054	+	0.687719i
$327$		0			0
$328$	4.00911	+	6.94398i	0.221366	+	0.383417i
$329$	−12.6706	+	1.96733i	−0.698554	+	0.108463i
$330$		0			0
$331$	12.8535			0.706494			0.353247	−	0.935530i	$-0.385077\pi$
$331$	12.8535			0.706494			0.353247	+	0.935530i	$0.385077\pi$
$332$	−1.34944	+	2.33731i	−0.0740604	+	0.128276i
$333$		0			0
$334$	13.2987	+	23.0341i	0.727674	+	1.26037i
$335$	17.9153	−	31.0302i	0.978818	−	1.69536i
$336$		0			0
$337$	−3.64609	−	6.31521i	−0.198615	−	0.344012i	0.749464	−	0.662045i	$-0.230311\pi$
$337$	−3.64609	−	6.31521i	−0.198615	−	0.344012i	−0.948080	+	0.318033i	$0.896978\pi$
$338$	−14.2782	+	24.7305i	−0.776630	+	1.34516i
$339$		0			0
$340$	−1.51685	−	2.62726i	−0.0822628	−	0.142483i
$341$	−6.51408	−	11.2827i	−0.352757	−	0.610993i
$342$		0			0
$343$	−16.5777	+	8.25707i	−0.895113	+	0.445840i
$344$	−11.6935	+	20.2537i	−0.630469	+	1.09200i
$345$		0			0
$346$	32.9285			1.77025
$347$	−17.5388			−0.941534			−0.470767	−	0.882258i	$-0.656023\pi$
$347$	−17.5388			−0.941534			−0.470767	+	0.882258i	$0.656023\pi$
$348$		0			0
$349$	−10.5080	+	18.2004i	−0.562481	+	0.974245i	0.434799	+	0.900528i	$0.356820\pi$
$349$	−10.5080	+	18.2004i	−0.562481	+	0.974245i	−0.997279	+	0.0737172i	$0.976514\pi$
$350$	7.55953	+	9.39353i	0.404074	+	0.502105i
$351$		0			0
$352$	3.41510	+	5.91512i	0.182025	+	0.315277i
$353$	2.52669	+	4.37636i	0.134482	+	0.232930i	0.925400	−	0.378993i	$-0.123730\pi$
$353$	2.52669	+	4.37636i	0.134482	+	0.232930i	−0.790917	+	0.611923i	$0.790396\pi$
$354$		0			0
$355$	4.11662	−	7.13019i	0.218487	−	0.378431i
$356$	−0.948505	−	1.64286i	−0.0502707	−	0.0870713i
$357$		0			0
$358$	4.32265	−	7.48705i	0.228459	−	0.395703i
$359$	−7.23806	−	12.5367i	−0.382010	−	0.661661i	0.609339	−	0.792910i	$-0.291435\pi$
$359$	−7.23806	−	12.5367i	−0.382010	−	0.661661i	−0.991349	+	0.131249i	$0.958101\pi$
$360$		0			0
$361$	1.21398	−	2.10268i	0.0638938	−	0.110667i
$362$	1.71808			0.0903005
$363$		0			0
$364$	−3.13101	−	3.89062i	−0.164110	−	0.203924i
$365$	−4.13780	−	7.16687i	−0.216582	−	0.375131i
$366$		0			0
$367$	−7.46142	−	12.9236i	−0.389483	−	0.674604i	0.602897	−	0.797819i	$-0.294013\pi$
$367$	−7.46142	−	12.9236i	−0.389483	−	0.674604i	−0.992380	+	0.123215i	$0.960680\pi$
$368$	10.7190	−	18.5659i	0.558768	−	0.967814i
$369$		0			0
$370$	−18.6152			−0.967761
$371$	13.5075	−	34.8707i	0.701273	−	1.81040i
$372$		0			0
$373$	−3.91054	+	6.77325i	−0.202480	+	0.350705i	−0.949327	−	0.314290i	$-0.898233\pi$
$373$	−3.91054	+	6.77325i	−0.202480	+	0.350705i	0.746847	+	0.664996i	$0.231567\pi$
$374$	17.7985			0.920338
$375$		0			0
$376$	−12.3289			−0.635816
$377$	−24.3528			−1.25424
$378$		0			0
$379$	11.6097			0.596350			0.298175	−	0.954511i	$-0.403622\pi$
$379$	11.6097			0.596350			0.298175	+	0.954511i	$0.403622\pi$
$380$	3.85667			0.197843
$381$		0			0
$382$	−6.01948			−0.307984
$383$	12.5382	−	21.7168i	0.640672	−	1.10968i	−0.344611	−	0.938746i	$-0.611989\pi$
$383$	12.5382	−	21.7168i	0.640672	−	1.10968i	0.985283	−	0.170931i	$-0.0546776\pi$
$384$		0			0
$385$	−26.8657	+	4.17137i	−1.36920	+	0.212593i
$386$	27.6398			1.40683
$387$		0			0
$388$	−0.861073	+	1.49142i	−0.0437143	+	0.0757155i
$389$	11.7497	+	20.3510i	0.595732	+	1.03184i	0.993443	+	0.114327i	$0.0364711\pi$
$389$	11.7497	+	20.3510i	0.595732	+	1.03184i	−0.397712	+	0.917510i	$0.630196\pi$
$390$		0			0
$391$	−7.53026	−	13.0428i	−0.380822	−	0.659602i
$392$	−16.9691	+	5.39965i	−0.857067	+	0.272724i
$393$		0			0
$394$	−38.9443			−1.96198
$395$	−1.26223	+	2.18625i	−0.0635098	+	0.110002i
$396$		0			0
$397$	9.86170	+	17.0810i	0.494945	+	0.857269i	0.999983	−	0.00582755i	$-0.00185498\pi$
$397$	9.86170	+	17.0810i	0.494945	+	0.857269i	−0.505038	+	0.863097i	$0.668522\pi$
$398$	−9.64973	+	16.7138i	−0.483697	+	0.837788i
$399$		0			0
$400$	6.79674	+	11.7723i	0.339837	+	0.588615i
$401$	7.18983	−	12.4532i	0.359043	−	0.621881i	−0.628758	−	0.777601i	$-0.716436\pi$
$401$	7.18983	−	12.4532i	0.359043	−	0.621881i	0.987801	+	0.155720i	$0.0497698\pi$
$402$		0			0
$403$	10.0816	+	17.4618i	0.502200	+	0.869836i
$404$	−0.423255	−	0.733099i	−0.0210577	−	0.0364730i
$405$		0			0
$406$	6.31816	−	16.3109i	0.313565	−	0.809495i
$407$	7.84089	−	13.5808i	0.388658	−	0.673176i
$408$		0			0
$409$	−11.5759			−0.572391			−0.286196	−	0.958171i	$-0.592391\pi$
$409$	−11.5759			−0.572391			−0.286196	+	0.958171i	$0.592391\pi$
$410$	13.6085			0.672074
$411$		0			0
$412$	−1.65086	+	2.85938i	−0.0813322	+	0.140872i
$413$	−3.92419	+	0.609299i	−0.193097	+	0.0299816i
$414$		0			0
$415$	−11.3698	−	19.6931i	−0.558122	−	0.966696i
$416$	−5.28542	−	9.15462i	−0.259139	−	0.448842i
$417$		0			0
$418$	−11.3134	+	19.5954i	−0.553356	+	0.958440i
$419$	17.0860	+	29.5939i	0.834708	+	1.44576i	0.894268	+	0.447532i	$0.147697\pi$
$419$	17.0860	+	29.5939i	0.834708	+	1.44576i	−0.0595598	+	0.998225i	$0.518970\pi$
$420$		0			0
$421$	5.11065	−	8.85191i	0.249078	−	0.431416i	−0.714192	−	0.699950i	$-0.753206\pi$
$421$	5.11065	−	8.85191i	0.249078	−	0.431416i	0.963270	+	0.268534i	$0.0865391\pi$
$422$	−1.76623	−	3.05920i	−0.0859789	−	0.148920i
$423$		0			0
$424$	17.9781	−	31.1389i	0.873092	−	1.51224i
$425$	9.54961			0.463224
$426$		0			0
$427$	−34.5237	+	5.36040i	−1.67072	+	0.259408i
$428$	−0.453108	−	0.784806i	−0.0219018	−	0.0379350i
$429$		0			0
$430$	19.8460	+	34.3744i	0.957061	+	1.65768i
$431$	−0.0380526	+	0.0659090i	−0.00183293	+	0.00317472i	−0.866940	−	0.498412i	$-0.833917\pi$
$431$	−0.0380526	+	0.0659090i	−0.00183293	+	0.00317472i	0.865107	+	0.501587i	$0.167250\pi$
$432$		0			0
$433$	−29.2697			−1.40661			−0.703305	−	0.710888i	$-0.748293\pi$
$433$	−29.2697			−1.40661			−0.703305	+	0.710888i	$0.748293\pi$
$434$	−14.3111	+	2.22204i	−0.686953	+	0.106661i
$435$		0			0
$436$	1.51859	−	2.63027i	0.0727271	−	0.125967i
$437$	19.1461			0.915880
$438$		0			0
$439$	−4.34526			−0.207388			−0.103694	−	0.994609i	$-0.533066\pi$
$439$	−4.34526			−0.207388			−0.103694	+	0.994609i	$0.533066\pi$
$440$	−26.1412			−1.24623
$441$		0			0
$442$	−27.5461			−1.31023
$443$	20.5544			0.976567			0.488284	−	0.872685i	$-0.337623\pi$
$443$	20.5544			0.976567			0.488284	+	0.872685i	$0.337623\pi$
$444$		0			0
$445$	15.9834			0.757684
$446$	−7.10573	+	12.3075i	−0.336466	+	0.582776i
$447$		0			0
$448$	−16.3314	+	2.53573i	−0.771586	+	0.119802i
$449$	12.4720			0.588588			0.294294	−	0.955715i	$-0.404915\pi$
$449$	12.4720			0.588588			0.294294	+	0.955715i	$0.404915\pi$
$450$		0			0
$451$	−5.73199	+	9.92810i	−0.269909	+	0.467496i
$452$	−0.0780926	−	0.135260i	−0.00367317	−	0.00636211i
$453$		0			0
$454$	−1.47330	−	2.55183i	−0.0691455	−	0.119764i
$455$	41.5791	−	6.45587i	1.94926	−	0.302656i
$456$		0			0
$457$	−30.9348			−1.44707			−0.723534	−	0.690289i	$-0.757483\pi$
$457$	−30.9348			−1.44707			−0.723534	+	0.690289i	$0.757483\pi$
$458$	−2.55296	+	4.42186i	−0.119292	+	0.206620i
$459$		0			0
$460$	−2.22785	−	3.85875i	−0.103874	−	0.179915i
$461$	4.01141	−	6.94796i	0.186830	−	0.323599i	−0.757362	−	0.652995i	$-0.773512\pi$
$461$	4.01141	−	6.94796i	0.186830	−	0.323599i	0.944192	+	0.329397i	$0.106845\pi$
$462$		0			0
$463$	8.41117	+	14.5686i	0.390900	+	0.677059i	0.992569	−	0.121687i	$-0.0388305\pi$
$463$	8.41117	+	14.5686i	0.390900	+	0.677059i	−0.601668	+	0.798746i	$0.705497\pi$
$464$	9.85998	−	17.0780i	0.457738	−	0.792826i
$465$		0			0
$466$	16.1616	+	27.9928i	0.748674	+	1.29674i
$467$	0.480399	+	0.832075i	0.0222302	+	0.0385038i	0.876926	−	0.480625i	$-0.159590\pi$
$467$	0.480399	+	0.832075i	0.0222302	+	0.0385038i	−0.854696	+	0.519128i	$0.826257\pi$
$468$		0			0
$469$	33.1566	−	5.14813i	1.53103	−	0.237719i
$470$	−10.4623	+	18.1212i	−0.482589	+	0.835869i
$471$		0			0
$472$	−3.81837			−0.175755
$473$	−33.4372			−1.53745
$474$		0			0
$475$	−6.07009	+	10.5137i	−0.278515	+	0.482402i
$476$	1.02616	−	2.64913i	0.0470341	−	0.121423i
$477$		0			0
$478$	−18.4260	−	31.9148i	−0.842787	−	1.45975i
$479$	12.0645	+	20.8964i	0.551242	+	0.954779i	0.998185	+	0.0602166i	$0.0191791\pi$
$479$	12.0645	+	20.8964i	0.551242	+	0.954779i	−0.446944	+	0.894562i	$0.647488\pi$
$480$		0			0
$481$	−12.1350	+	21.0185i	−0.553311	+	0.958362i
$482$	−7.05589	−	12.2212i	−0.321387	−	0.556659i
$483$		0			0
$484$	−0.373692	+	0.647253i	−0.0169860	+	0.0294206i
$485$	−7.25501	−	12.5661i	−0.329433	−	0.570595i
$486$		0			0
$487$	−7.39944	+	12.8162i	−0.335301	+	0.580758i	−0.983543	−	0.180677i	$-0.942171\pi$
$487$	−7.39944	+	12.8162i	−0.335301	+	0.580758i	0.648242	+	0.761435i	$0.275505\pi$
$488$	−33.5927			−1.52067
$489$		0			0
$490$	−6.46340	+	29.5235i	−0.291987	+	1.33373i
$491$	3.15192	+	5.45928i	0.142244	+	0.246374i	0.928341	−	0.371729i	$-0.121235\pi$
$491$	3.15192	+	5.45928i	0.142244	+	0.246374i	−0.786097	+	0.618103i	$0.787902\pi$
$492$		0			0
$493$	−6.92677	−	11.9975i	−0.311966	−	0.540341i
$494$	17.5093	−	30.3270i	0.787781	−	1.36448i
$495$		0			0
$496$	−16.3274			−0.733120
$497$	7.61878	−	1.18295i	0.341749	−	0.0530625i
$498$		0			0
$499$	14.2986	−	24.7658i	0.640092	−	1.10867i	−0.345320	−	0.938485i	$-0.612230\pi$
$499$	14.2986	−	24.7658i	0.640092	−	1.10867i	0.985412	−	0.170187i	$-0.0544370\pi$
$500$	−1.91162			−0.0854903
$501$		0			0
$502$	28.3921			1.26720
$503$	35.4133			1.57900			0.789500	−	0.613750i	$-0.210340\pi$
$503$	35.4133			1.57900			0.789500	+	0.613750i	$0.210340\pi$
$504$		0			0
$505$	7.13231			0.317384
$506$	26.1412			1.16212
$507$		0			0
$508$	−5.28382			−0.234432
$509$	16.2442	−	28.1357i	0.720010	−	1.24709i	−0.240985	−	0.970529i	$-0.577471\pi$
$509$	16.2442	−	28.1357i	0.720010	−	1.24709i	0.960995	−	0.276565i	$-0.0891961\pi$
$510$		0			0
$511$	2.79925	−	7.22652i	0.123832	−	0.319682i
$512$	−14.6316			−0.646630
$513$		0			0
$514$	7.80878	−	13.5252i	0.344431	−	0.596571i
$515$	−13.9094	−	24.0919i	−0.612923	−	1.06161i
$516$		0			0
$517$	−8.81359	−	15.2656i	−0.387621	−	0.671380i
$518$	−10.9293	−	13.5808i	−0.480205	−	0.596707i
$519$		0			0
$520$	40.4578			1.77419
$521$	−16.4909	+	28.5631i	−0.722479	+	1.25137i	0.237524	+	0.971382i	$0.423664\pi$
$521$	−16.4909	+	28.5631i	−0.722479	+	1.25137i	−0.960003	+	0.279989i	$0.909669\pi$
$522$		0			0
$523$	−7.13133	−	12.3518i	−0.311831	−	0.540108i	0.666928	−	0.745123i	$-0.267609\pi$
$523$	−7.13133	−	12.3518i	−0.311831	−	0.540108i	−0.978759	+	0.205015i	$0.934276\pi$
$524$	−2.03674	+	3.52773i	−0.0889753	+	0.154110i
$525$		0			0
$526$	−6.98204	−	12.0933i	−0.304432	−	0.527291i
$527$	−5.73509	+	9.93347i	−0.249825	+	0.432709i
$528$		0			0
$529$	0.440059	+	0.762205i	0.0191330	+	0.0331393i
$530$	−30.5122	−	52.8487i	−1.32537	−	2.29560i
$531$		0			0
$532$	2.26431	+	2.81364i	0.0981701	+	0.121987i
$533$	8.87119	−	15.3654i	0.384254	−	0.665547i
$534$		0			0
$535$	7.63537			0.330106
$536$	32.2624			1.39352
$537$		0			0
$538$	17.5139	−	30.3349i	0.755076	−	1.30783i
$539$	−18.8165	−	17.1509i	−0.810484	−	0.738742i
$540$		0			0
$541$	7.99105	+	13.8409i	0.343562	+	0.595067i	0.985091	−	0.172032i	$-0.0550331\pi$
$541$	7.99105	+	13.8409i	0.343562	+	0.595067i	−0.641529	+	0.767098i	$0.721700\pi$
$542$	7.11796	+	12.3287i	0.305743	+	0.529562i
$543$		0			0
$544$	3.00670	−	5.20776i	0.128911	−	0.223281i
$545$	12.7949	+	22.1615i	0.548075	+	0.949294i
$546$		0			0
$547$	16.0285	−	27.7622i	0.685330	−	1.18703i	−0.288003	−	0.957630i	$-0.592991\pi$
$547$	16.0285	−	27.7622i	0.685330	−	1.18703i	0.973333	−	0.229397i	$-0.0736754\pi$
$548$	−0.362714	−	0.628238i	−0.0154944	−	0.0268370i
$549$		0			0
$550$	−8.28784	+	14.3550i	−0.353395	+	0.612098i
$551$	17.6117			0.750282
$552$		0			0
$553$	−2.33606	+	0.362714i	−0.0993393	+	0.0154242i
$554$	−0.140071	−	0.242610i	−0.00595105	−	0.0103075i
$555$		0			0
$556$	3.59657	+	6.22945i	0.152529	+	0.264187i
$557$	19.6474	−	34.0302i	0.832486	−	1.44191i	−0.0635754	−	0.997977i	$-0.520250\pi$
$557$	19.6474	−	34.0302i	0.832486	−	1.44191i	0.896061	−	0.443931i	$-0.146416\pi$
$558$		0			0
$559$	51.7496			2.18877
$560$	−12.3072	+	31.7721i	−0.520075	+	1.34262i
$561$		0			0
$562$	−12.3797	+	21.4423i	−0.522207	+	0.904489i
$563$	34.5063			1.45427			0.727134	−	0.686495i	$-0.240852\pi$
$563$	34.5063			1.45427			0.727134	+	0.686495i	$0.240852\pi$
$564$		0			0
$565$	1.31595			0.0553623
$566$	31.6308			1.32954
$567$		0			0
$568$	7.41332			0.311056
$569$	−4.28406			−0.179597			−0.0897985	−	0.995960i	$-0.528622\pi$
$569$	−4.28406			−0.179597			−0.0897985	+	0.995960i	$0.528622\pi$
$570$		0			0
$571$	25.1596			1.05289			0.526447	−	0.850208i	$-0.323524\pi$
$571$	25.1596			1.05289			0.526447	+	0.850208i	$0.323524\pi$
$572$	3.43267	−	5.94555i	0.143527	−	0.248596i
$573$		0			0
$574$	7.98973	+	9.92810i	0.333485	+	0.414391i
$575$	14.0258			0.584917
$576$		0			0
$577$	22.1281	−	38.3271i	0.921206	−	1.59558i	0.123655	−	0.992325i	$-0.460539\pi$
$577$	22.1281	−	38.3271i	0.921206	−	1.59558i	0.797552	−	0.603251i	$-0.206128\pi$
$578$	5.15447	+	8.92781i	0.214398	+	0.371348i
$579$		0			0
$580$	−2.04930	−	3.54950i	−0.0850928	−	0.147385i
$581$	7.69177	−	19.8570i	0.319109	−	0.823806i
$582$		0			0
$583$	51.4080			2.12910
$584$	3.72573	−	6.45315i	0.154172	−	0.267033i
$585$		0			0
$586$	12.2433	+	21.2060i	0.505766	+	0.876012i
$587$	6.50229	−	11.2623i	0.268378	−	0.464845i	−0.700065	−	0.714079i	$-0.746846\pi$
$587$	6.50229	−	11.2623i	0.268378	−	0.464845i	0.968443	+	0.249234i	$0.0801789\pi$
$588$		0			0
$589$	−7.29088	−	12.6282i	−0.300415	−	0.520335i
$590$	−3.24025	+	5.61228i	−0.133399	+	0.231054i
$591$		0			0
$592$	−9.82648	−	17.0200i	−0.403866	−	0.699516i
$593$	14.1164	+	24.4503i	0.579691	+	1.00405i	0.995515	+	0.0946086i	$0.0301600\pi$
$593$	14.1164	+	24.4503i	0.579691	+	1.00405i	−0.415824	+	0.909445i	$0.636507\pi$
$594$		0			0
$595$	15.0070	+	18.6478i	0.615227	+	0.764486i
$596$	1.86058	−	3.22262i	0.0762123	−	0.132004i
$597$		0			0
$598$	−40.4578			−1.65444
$599$	4.99536			0.204105			0.102052	−	0.994779i	$-0.467459\pi$
$599$	4.99536			0.204105			0.102052	+	0.994779i	$0.467459\pi$
$600$		0			0
$601$	−4.07893	+	7.06492i	−0.166383	+	0.288184i	−0.937146	−	0.348939i	$-0.886542\pi$
$601$	−4.07893	+	7.06492i	−0.166383	+	0.288184i	0.770762	+	0.637123i	$0.219876\pi$
$602$	−13.4260	+	34.6604i	−0.547204	+	1.41265i
$603$		0			0
$604$	−0.349925	−	0.606089i	−0.0142383	−	0.0246614i
$605$	−3.14856	−	5.45347i	−0.128007	−	0.221715i
$606$		0			0
$607$	−8.36385	+	14.4866i	−0.339478	+	0.587993i	−0.984335	−	0.176310i	$-0.943584\pi$
$607$	−8.36385	+	14.4866i	−0.339478	+	0.587993i	0.644857	+	0.764304i	$0.276917\pi$
$608$	3.82235	+	6.62050i	0.155017	+	0.268497i
$609$		0			0
$610$	−28.5066	+	49.3749i	−1.15420	+	1.99913i
$611$	13.6405	+	23.6260i	0.551834	+	0.955805i
$612$		0			0
$613$	8.29381	−	14.3653i	0.334984	−	0.580209i	−0.648498	−	0.761216i	$-0.724602\pi$
$613$	8.29381	−	14.3653i	0.334984	−	0.580209i	0.983482	+	0.181007i	$0.0579358\pi$
$614$	−8.13459			−0.328285
$615$		0			0
$616$	−15.3479	−	19.0714i	−0.618384	−	0.768409i
$617$	−11.8543	−	20.5322i	−0.477235	−	0.826595i	0.522425	−	0.852685i	$-0.325028\pi$
$617$	−11.8543	−	20.5322i	−0.477235	−	0.826595i	−0.999660	+	0.0260905i	$0.991694\pi$
$618$		0			0
$619$	3.91206	+	6.77589i	0.157239	+	0.272346i	0.933872	−	0.357607i	$-0.116407\pi$
$619$	3.91206	+	6.77589i	0.157239	+	0.272346i	−0.776633	+	0.629953i	$0.783074\pi$
$620$	−1.69674	+	2.93885i	−0.0681429	+	0.118027i
$621$		0			0
$622$	−28.1581			−1.12904
$623$	9.38406	+	11.6607i	0.375964	+	0.467176i
$624$		0			0
$625$	15.5087	−	26.8619i	0.620350	−	1.07448i
$626$	7.10125			0.283823
$627$		0			0
$628$	−7.24812			−0.289231
$629$	−13.8065			−0.550500
$630$		0			0
$631$	−2.54669			−0.101382			−0.0506911	−	0.998714i	$-0.516142\pi$
$631$	−2.54669			−0.101382			−0.0506911	+	0.998714i	$0.516142\pi$
$632$	−2.27306			−0.0904175
$633$		0			0
$634$	16.0155			0.636056
$635$	22.2596	−	38.5547i	0.883344	−	1.53000i
$636$		0			0
$637$	29.1216	+	26.5438i	1.15384	+	1.05170i
$638$	24.0462			0.951999
$639$		0			0
$640$	−18.7906	+	32.5463i	−0.742764	+	1.28651i
$641$	5.14269	+	8.90739i	0.203124	+	0.351821i	0.949533	−	0.313666i	$-0.101557\pi$
$641$	5.14269	+	8.90739i	0.203124	+	0.351821i	−0.746409	+	0.665487i	$0.768224\pi$
$642$		0			0
$643$	2.46063	+	4.26194i	0.0970378	+	0.168074i	0.910457	−	0.413603i	$-0.135730\pi$
$643$	2.46063	+	4.26194i	0.0970378	+	0.168074i	−0.813419	+	0.581678i	$0.802397\pi$
$644$	1.50716	−	3.89086i	0.0593904	−	0.153321i
$645$		0			0
$646$	19.9209			0.783779
$647$	4.39168	−	7.60661i	0.172655	−	0.299047i	−0.766692	−	0.642015i	$-0.778099\pi$
$647$	4.39168	−	7.60661i	0.172655	−	0.299047i	0.939347	+	0.342968i	$0.111432\pi$
$648$		0			0
$649$	−2.72964	−	4.72787i	−0.107148	−	0.185585i
$650$	12.8268	−	22.2166i	0.503108	−	0.871409i
$651$		0			0
$652$	1.57307	+	2.72464i	0.0616062	+	0.106705i
$653$	0.887297	−	1.53684i	0.0347226	−	0.0601414i	−0.848142	−	0.529769i	$-0.822279\pi$
$653$	0.887297	−	1.53684i	0.0347226	−	0.0601414i	0.882864	+	0.469628i	$0.155612\pi$
$654$		0			0
$655$	−17.1606	−	29.7231i	−0.670522	−	1.16138i
$656$	7.18354	+	12.4423i	0.280470	+	0.485788i
$657$		0			0
$658$	−19.3630	+	3.00643i	−0.754846	+	0.117203i
$659$	1.17184	−	2.02968i	0.0456483	−	0.0790652i	−0.842298	−	0.539011i	$-0.818798\pi$
$659$	1.17184	−	2.02968i	0.0456483	−	0.0790652i	0.887947	+	0.459946i	$0.152131\pi$
$660$		0			0
$661$	−22.9094			−0.891074			−0.445537	−	0.895264i	$-0.646987\pi$
$661$	−22.9094			−0.891074			−0.445537	+	0.895264i	$0.646987\pi$
$662$	19.6425			0.763426
$663$		0			0
$664$	10.2375	−	17.7319i	0.397293	−	0.688133i
$665$	−30.0694	+	4.66880i	−1.16604	+	0.181048i
$666$		0			0
$667$	−10.1736	−	17.6212i	−0.393922	−	0.682294i
$668$	2.91810	+	5.05429i	0.112905	+	0.195556i
$669$		0			0
$670$	27.3778	−	47.4197i	1.05770	−	1.83198i
$671$	−24.0144	−	41.5942i	−0.927067	−	1.60573i
$672$		0			0
$673$	14.8675	−	25.7512i	0.573098	−	0.992636i	−0.423147	−	0.906061i	$-0.639075\pi$
$673$	14.8675	−	25.7512i	0.573098	−	0.992636i	0.996245	−	0.0865746i	$-0.0275921\pi$
$674$	−5.57187	−	9.65076i	−0.214620	−	0.371733i
$675$		0			0
$676$	−3.13301	+	5.42654i	−0.120500	+	0.208713i
$677$	−25.4960			−0.979891			−0.489946	−	0.871753i	$-0.662983\pi$
$677$	−25.4960			−0.979891			−0.489946	+	0.871753i	$0.662983\pi$
$678$		0			0
$679$	4.90808	−	12.6706i	0.188355	−	0.486254i
$680$	11.5076	+	19.9317i	0.441295	+	0.764345i
$681$		0			0
$682$	−9.95466	−	17.2420i	−0.381184	−	0.660230i
$683$	5.69293	−	9.86044i	0.217834	−	0.377299i	−0.736312	−	0.676643i	$-0.763434\pi$
$683$	5.69293	−	9.86044i	0.217834	−	0.377299i	0.954145	+	0.299343i	$0.0967676\pi$
$684$		0			0
$685$	6.11212			0.233532
$686$	−25.3337	+	12.6183i	−0.967244	+	0.481767i
$687$		0			0
$688$	−20.9524	+	36.2906i	−0.798801	+	1.38356i
$689$	−79.5622			−3.03108
$690$		0			0
$691$	−32.2523			−1.22694			−0.613468	−	0.789720i	$-0.710226\pi$
$691$	−32.2523			−1.22694			−0.613468	+	0.789720i	$0.710226\pi$
$692$	7.22539			0.274668
$693$		0			0
$694$	−26.8024			−1.01741
$695$	−60.6062			−2.29893
$696$		0			0
$697$	10.0931			0.382302
$698$	−16.0581	+	27.8134i	−0.607807	+	1.05275i
$699$		0			0
$700$	1.65876	+	2.06119i	0.0626953	+	0.0779057i
$701$	−15.6291			−0.590302			−0.295151	−	0.955451i	$-0.595370\pi$
$701$	−15.6291			−0.590302			−0.295151	+	0.955451i	$0.595370\pi$
$702$		0			0
$703$	8.77591	−	15.2003i	0.330990	−	0.573291i
$704$	−11.3600	−	19.6761i	−0.428146	−	0.741570i
$705$		0			0
$706$	3.86123	+	6.68785i	0.145319	+	0.251700i
$707$	4.18748	+	5.20340i	0.157487	+	0.195694i
$708$		0			0
$709$	−11.8165			−0.443777			−0.221888	−	0.975072i	$-0.571222\pi$
$709$	−11.8165			−0.443777			−0.221888	+	0.975072i	$0.571222\pi$
$710$	6.29092	−	10.8962i	0.236094	−	0.408927i
$711$		0			0
$712$	7.19582	+	12.4635i	0.269675	+	0.467090i
$713$	−8.42332	+	14.5896i	−0.315456	+	0.546386i
$714$		0			0
$715$	28.9221	+	50.0946i	1.08163	+	1.87343i
$716$	0.948505	−	1.64286i	0.0354473	−	0.0613965i
$717$		0			0
$718$	−11.0610	−	19.1583i	−0.412794	−	0.714980i
$719$	−25.3616	−	43.9276i	−0.945830	−	1.63822i	−0.754082	−	0.656781i	$-0.771918\pi$
$719$	−25.3616	−	43.9276i	−0.945830	−	1.63822i	−0.191748	−	0.981444i	$-0.561416\pi$
$720$		0			0
$721$	9.40985	−	24.2923i	0.350441	−	0.904694i
$722$	1.85518	−	3.21326i	0.0690426	−	0.119585i
$723$		0			0
$724$	0.376994			0.0140109
$725$	12.9018			0.479160
$726$		0			0
$727$	−1.13301	+	1.96243i	−0.0420211	+	0.0727827i	−0.886271	−	0.463167i	$-0.846713\pi$
$727$	−1.13301	+	1.96243i	−0.0420211	+	0.0727827i	0.844250	+	0.535950i	$0.180046\pi$
$728$	23.7534	+	29.5161i	0.880358	+	1.09394i
$729$		0			0
$730$	−6.32328	−	10.9522i	−0.234035	−	0.405361i
$731$	14.7193	+	25.4946i	0.544414	+	0.942952i
$732$		0			0
$733$	16.8262	−	29.1439i	0.621490	−	1.07645i	−0.367718	−	0.929937i	$-0.619861\pi$
$733$	16.8262	−	29.1439i	0.621490	−	1.07645i	0.989208	−	0.146515i	$-0.0468058\pi$
$734$	−11.4024	−	19.7495i	−0.420869	−	0.728966i
$735$		0			0
$736$	4.41605	−	7.64882i	0.162778	−	0.281939i
$737$	23.0634	+	39.9471i	0.849553	+	1.47147i
$738$		0			0
$739$	−9.80187	+	16.9773i	−0.360568	+	0.624521i	−0.988054	−	0.154106i	$-0.950750\pi$
$739$	−9.80187	+	16.9773i	−0.360568	+	0.624521i	0.627487	+	0.778627i	$0.284084\pi$
$740$	−4.08468			−0.150156
$741$		0			0
$742$	20.6418	−	53.2886i	0.757784	−	1.95628i
$743$	24.4195	+	42.2958i	0.895865	+	1.55168i	0.832731	+	0.553678i	$0.186776\pi$
$743$	24.4195	+	42.2958i	0.895865	+	1.55168i	0.0631343	+	0.998005i	$0.479890\pi$
$744$		0			0
$745$	15.6764	+	27.1523i	0.574339	+	0.994784i
$746$	−5.97599	+	10.3507i	−0.218796	+	0.378967i
$747$		0			0
$748$	3.90546			0.142798
$749$	4.48283	+	5.57040i	0.163799	+	0.203538i
$750$		0			0
$751$	−7.91269	+	13.7052i	−0.288738	+	0.500109i	−0.973509	−	0.228649i	$-0.926569\pi$
$751$	−7.91269	+	13.7052i	−0.288738	+	0.500109i	0.684771	+	0.728759i	$0.259902\pi$
$752$	−22.0910			−0.805576
$753$		0			0
$754$	−37.2154			−1.35531
$755$	5.89663			0.214600
$756$		0			0
$757$	−2.18728			−0.0794982			−0.0397491	−	0.999210i	$-0.512656\pi$
$757$	−2.18728			−0.0794982			−0.0397491	+	0.999210i	$0.512656\pi$
$758$	17.7417			0.644407
$759$		0			0
$760$	−29.2585			−1.06132
$761$	−13.8781	+	24.0376i	−0.503081	+	0.871361i	0.496913	+	0.867800i	$0.334467\pi$
$761$	−13.8781	+	24.0376i	−0.503081	+	0.871361i	−0.999994	+	0.00356072i	$0.998867\pi$
$762$		0			0
$763$	−8.65588	+	22.3459i	−0.313364	+	0.808976i
$764$	−1.32084			−0.0477861
$765$		0			0
$766$	19.1606	−	33.1871i	0.692300	−	1.19910i
$767$	4.22456	+	7.31715i	0.152540	+	0.264207i
$768$		0			0
$769$	−5.01030	−	8.67810i	−0.180676	−	0.312940i	0.761435	−	0.648242i	$-0.224495\pi$
$769$	−5.01030	−	8.67810i	−0.180676	−	0.312940i	−0.942111	+	0.335301i	$0.891162\pi$
$770$	−41.0556	+	6.37459i	−1.47954	+	0.229724i
$771$		0			0
$772$	6.06491			0.218281
$773$	−21.7596	+	37.6887i	−0.782639	+	1.35557i	0.147761	+	0.989023i	$0.452793\pi$
$773$	−21.7596	+	37.6887i	−0.782639	+	1.35557i	−0.930400	+	0.366547i	$0.880540\pi$
$774$		0			0
$775$	−5.34108	−	9.25102i	−0.191857	−	0.332306i
$776$	6.53251	−	11.3146i	0.234504	−	0.406172i
$777$		0			0
$778$	17.9556	+	31.0999i	0.643738	+	1.11499i
$779$	−6.41553	+	11.1120i	−0.229860	+	0.398130i
$780$		0			0
$781$	5.29957	+	9.17912i	0.189633	+	0.328455i
$782$	−11.5076	−	19.9317i	−0.411510	−	0.712756i
$783$		0			0
$784$	−30.4052	+	9.67512i	−1.08590	+	0.345540i
$785$	30.5347	−	52.8877i	1.08983	−	1.88764i
$786$		0			0
$787$	−5.83638			−0.208044			−0.104022	−	0.994575i	$-0.533171\pi$
$787$	−5.83638			−0.208044			−0.104022	+	0.994575i	$0.533171\pi$
$788$	−8.54542			−0.304418
$789$		0			0
$790$	−1.92891	+	3.34097i	−0.0686276	+	0.118867i
$791$	0.772611	+	0.960053i	0.0274709	+	0.0341355i
$792$		0			0
$793$	37.1662	+	64.3738i	1.31981	+	2.28598i
$794$	15.0704	+	26.1027i	0.534829	+	0.926351i
$795$		0			0
$796$	−2.11741	+	3.66746i	−0.0750496	+	0.129990i
$797$	18.2900	+	31.6792i	0.647865	+	1.12214i	0.983632	+	0.180191i	$0.0576714\pi$
$797$	18.2900	+	31.6792i	0.647865	+	1.12214i	−0.335766	+	0.941945i	$0.608995\pi$
$798$		0			0
$799$	−7.75962	+	13.4401i	−0.274516	+	0.475475i
$800$	2.80014	+	4.84998i	0.0989998	+	0.171473i
$801$		0			0
$802$	10.9873	−	19.0306i	0.387976	−	0.671994i
$803$	10.6537			0.375959
$804$		0			0
$805$	22.0413	+	27.3887i	0.776853	+	0.965324i
$806$	15.4065	+	26.6848i	0.542670	+	0.939931i
$807$		0			0
$808$	3.21102	+	5.56164i	0.112963	+	0.195658i
$809$	−11.0249	+	19.0957i	−0.387616	+	0.671370i	−0.992128	−	0.125225i	$-0.960035\pi$
$809$	−11.0249	+	19.0957i	−0.387616	+	0.671370i	0.604513	+	0.796596i	$0.293368\pi$
$810$		0			0
$811$	−12.6451			−0.444029			−0.222015	−	0.975043i	$-0.571263\pi$
$811$	−12.6451			−0.444029			−0.222015	+	0.975043i	$0.571263\pi$
$812$	1.38637	−	3.57904i	0.0486521	−	0.125600i
$813$		0			0
$814$	11.9823	−	20.7539i	0.419978	−	0.727423i
$815$	−26.5080			−0.928534
$816$		0			0
$817$	−37.4246			−1.30932
$818$	−17.6900			−0.618517
$819$		0			0
$820$	2.98606			0.104278
$821$	31.0958			1.08525			0.542625	−	0.839975i	$-0.317430\pi$
$821$	31.0958			1.08525			0.542625	+	0.839975i	$0.317430\pi$
$822$		0			0
$823$	−48.9638			−1.70677			−0.853385	−	0.521281i	$-0.825454\pi$
$823$	−48.9638			−1.70677			−0.853385	+	0.521281i	$0.825454\pi$
$824$	12.5242	−	21.6926i	0.436303	−	0.755699i
$825$		0			0
$826$	−5.99686	+	0.931116i	−0.208657	+	0.0323977i
$827$	36.3827			1.26515			0.632575	−	0.774499i	$-0.281998\pi$
$827$	36.3827			1.26515			0.632575	+	0.774499i	$0.281998\pi$
$828$		0			0
$829$	−22.8702	+	39.6124i	−0.794316	+	1.37580i	0.128957	+	0.991650i	$0.458837\pi$
$829$	−22.8702	+	39.6124i	−0.794316	+	1.37580i	−0.923273	+	0.384145i	$0.874496\pi$
$830$	−17.3751	−	30.0945i	−0.603098	−	1.04460i
$831$		0			0
$832$	17.5814	+	30.4520i	0.609527	+	1.05573i
$833$	−4.79375	+	21.8968i	−0.166093	+	0.758680i
$834$		0			0
$835$	−49.1731			−1.70171
$836$	−2.48246	+	4.29974i	−0.0858576	+	0.148710i
$837$		0			0
$838$	26.1105	+	45.2247i	0.901972	+	1.56226i
$839$	−12.7674	+	22.1138i	−0.440779	+	0.763452i	−0.997747	−	0.0670815i	$-0.978631\pi$
$839$	−12.7674	+	22.1138i	−0.440779	+	0.763452i	0.556968	+	0.830534i	$0.311965\pi$
$840$		0			0
$841$	5.14175	+	8.90578i	0.177302	+	0.307096i
$842$	7.80998	−	13.5273i	0.269150	−	0.466181i
$843$		0			0
$844$	−0.387559	−	0.671271i	−0.0133403	−	0.0231061i
$845$	−26.3974	−	45.7216i	−0.908097	−	1.57287i
$846$		0			0
$847$	2.13003	−	5.49885i	0.0731886	−	0.188943i
$848$	32.2131	−	55.7948i	1.10620	−	1.91600i
$849$		0			0
$850$	14.5935			0.500552
$851$	−20.2780			−0.695121
$852$		0			0
$853$	0.923367	−	1.59932i	0.0316155	−	0.0547596i	−0.849785	−	0.527130i	$-0.823268\pi$
$853$	0.923367	−	1.59932i	0.0316155	−	0.0547596i	0.881400	+	0.472370i	$0.156601\pi$
$854$	−52.7583	+	8.19164i	−1.80535	+	0.280312i
$855$		0			0
$856$	3.43749	+	5.95391i	0.117491	+	0.203501i
$857$	−11.2424	−	19.4724i	−0.384033	−	0.665165i	0.607601	−	0.794242i	$-0.292132\pi$
$857$	−11.2424	−	19.4724i	−0.384033	−	0.665165i	−0.991635	+	0.129077i	$0.958798\pi$
$858$		0			0
$859$	0.573807	−	0.993864i	0.0195781	−	0.0339102i	−0.856070	−	0.516859i	$-0.827101\pi$
$859$	0.573807	−	0.993864i	0.0195781	−	0.0339102i	0.875648	+	0.482949i	$0.160434\pi$
$860$	4.35475	+	7.54265i	0.148496	+	0.257202i
$861$		0			0
$862$	−0.0581510	+	0.100721i	−0.00198063	+	0.00343055i
$863$	0.897635	+	1.55475i	0.0305558	+	0.0529243i	0.880899	−	0.473304i	$-0.156939\pi$
$863$	0.897635	+	1.55475i	0.0305558	+	0.0529243i	−0.850343	+	0.526229i	$0.823606\pi$
$864$		0			0
$865$	−30.4390	+	52.7218i	−1.03496	+	1.79260i
$866$	−44.7292			−1.51996
$867$		0			0
$868$	−3.14023	+	0.487575i	−0.106586	+	0.0165494i
$869$	−1.62494	−	2.81449i	−0.0551225	−	0.0954749i
$870$		0			0
$871$	−35.6944	−	61.8246i	−1.20946	−	2.09485i
$872$	−11.5207	+	19.9545i	−0.390141	+	0.675745i
$873$		0			0
$874$	29.2585			0.989685
$875$	14.9044	−	2.31417i	0.503862	−	0.0782332i
$876$		0			0
$877$	−4.28998	+	7.43047i	−0.144862	+	0.250909i	−0.929322	−	0.369271i	$-0.879607\pi$
$877$	−4.28998	+	7.43047i	−0.144862	+	0.250909i	0.784459	+	0.620180i	$0.212941\pi$
$878$	−6.64032			−0.224100
$879$		0			0
$880$	−46.8399			−1.57897
$881$	16.5346			0.557066			0.278533	−	0.960427i	$-0.410152\pi$
$881$	16.5346			0.557066			0.278533	+	0.960427i	$0.410152\pi$
$882$		0			0
$883$	−27.4948			−0.925273			−0.462636	−	0.886548i	$-0.653096\pi$
$883$	−27.4948			−0.925273			−0.462636	+	0.886548i	$0.653096\pi$
$884$	−6.04434			−0.203293
$885$		0			0
$886$	31.4107			1.05526
$887$	−21.7210	+	37.6218i	−0.729318	+	1.26322i	0.227853	+	0.973695i	$0.426829\pi$
$887$	−21.7210	+	37.6218i	−0.729318	+	1.26322i	−0.957172	+	0.289521i	$0.906504\pi$
$888$		0			0
$889$	41.1966	−	6.39649i	1.38169	−	0.214531i
$890$	24.4254			0.818741
$891$		0			0
$892$	−1.55919	+	2.70059i	−0.0522054	+	0.0904225i
$893$	−9.86461	−	17.0860i	−0.330107	−	0.571761i
$894$		0			0
$895$	7.99168	+	13.8420i	0.267132	+	0.462687i
$896$	−34.7765	+	5.39965i	−1.16180	+	0.180390i
$897$		0			0
$898$	19.0594			0.636019
$899$	−7.74826	+	13.4204i	−0.258419	+	0.447595i
$900$		0			0
$901$	−22.6302	−	39.1966i	−0.753920	−	1.30583i
$902$	−8.75949	+	15.1719i	−0.291659	+	0.505169i
$903$		0			0
$904$	0.592448	+	1.02615i	0.0197045	+	0.0341292i
$905$	−1.58819	+	2.75083i	−0.0527932	+	0.0914406i
$906$		0			0
$907$	−5.64761	−	9.78196i	−0.187526	−	0.324805i	0.756899	−	0.653532i	$-0.226714\pi$
$907$	−5.64761	−	9.78196i	−0.187526	−	0.324805i	−0.944425	+	0.328728i	$0.893380\pi$
$908$	−0.323282	−	0.559941i	−0.0107285	−	0.0185823i
$909$		0			0
$910$	63.5402	−	9.86571i	2.10634	−	0.327045i
$911$	5.01690	−	8.68953i	0.166217	−	0.287897i	−0.770870	−	0.636993i	$-0.780178\pi$
$911$	5.01690	−	8.68953i	0.166217	−	0.287897i	0.937087	+	0.349096i	$0.113511\pi$
$912$		0			0
$913$	29.2741			0.968830
$914$	−47.2738			−1.56368
$915$		0			0
$916$	−0.560188	+	0.970273i	−0.0185091	+	0.0320587i
$917$	11.6093	−	29.9705i	0.383373	−	0.989712i
$918$		0			0
$919$	0.178967	+	0.309980i	0.00590358	+	0.0102253i	0.868962	−	0.494879i	$-0.164787\pi$
$919$	0.178967	+	0.309980i	0.00590358	+	0.0102253i	−0.863059	+	0.505104i	$0.831454\pi$
$920$	16.9015	+	29.2743i	0.557227	+	0.965146i
$921$		0			0
$922$	6.13013	−	10.6177i	0.201885	−	0.349675i
$923$	−8.20195	−	14.2062i	−0.269970	−	0.467602i
$924$		0			0
$925$	6.42897	−	11.1353i	0.211383	−	0.366126i
$926$	12.8537	+	22.2633i	0.422400	+	0.731619i
$927$		0			0
$928$	4.06214	−	7.03583i	0.133346	−	0.230962i
$929$	−33.5264			−1.09997			−0.549983	−	0.835176i	$-0.685366\pi$
$929$	−33.5264			−1.09997			−0.549983	+	0.835176i	$0.685366\pi$
$930$		0			0
$931$	−21.0603	−	19.1961i	−0.690225	−	0.629128i
$932$	3.54630	+	6.14236i	0.116163	+	0.201200i
$933$		0			0
$934$	0.734134	+	1.27156i	0.0240216	+	0.0416066i
$935$	−16.4528	+	28.4972i	−0.538065	+	0.931957i
$936$		0			0
$937$	12.8772			0.420680			0.210340	−	0.977628i	$-0.432543\pi$
$937$	12.8772			0.420680			0.210340	+	0.977628i	$0.432543\pi$
$938$	50.6691	−	7.86725i	1.65440	−	0.256875i
$939$		0			0
$940$	−2.29571	+	3.97628i	−0.0748777	+	0.129692i
$941$	32.0984			1.04638			0.523189	−	0.852217i	$-0.324742\pi$
$941$	32.0984			1.04638			0.523189	+	0.852217i	$0.324742\pi$
$942$		0			0
$943$	14.8240			0.482736
$944$	−6.84176			−0.222680
$945$		0			0
$946$	−51.0980			−1.66134
$947$	16.7986			0.545880			0.272940	−	0.962031i	$-0.412004\pi$
$947$	16.7986			0.545880			0.272940	+	0.962031i	$0.412004\pi$
$948$		0			0
$949$	−16.4883			−0.535232
$950$	−9.27616	+	16.0668i	−0.300958	+	0.521275i
$951$		0			0
$952$	−7.78496	+	20.0976i	−0.252312	+	0.651366i
$953$	−2.69574			−0.0873237			−0.0436619	−	0.999046i	$-0.513902\pi$
$953$	−2.69574			−0.0873237			−0.0436619	+	0.999046i	$0.513902\pi$
$954$		0			0
$955$	5.56438	−	9.63780i	0.180059	−	0.311872i
$956$	−4.04316	−	7.00297i	−0.130765	−	0.226492i
$957$		0			0
$958$	18.4367	+	31.9333i	0.595663	+	1.03172i
$959$	3.58852	+	4.45912i	0.115879	+	0.143992i
$960$		0			0
$961$	−18.1695			−0.586112
$962$	−18.5445	+	32.1200i	−0.597898	+	1.03559i
$963$		0			0
$964$	−1.54825	−	2.68165i	−0.0498658	−	0.0863701i
$965$	−25.5501	+	44.2541i	−0.822487	+	1.42459i
$966$		0			0
$967$	−6.83873	−	11.8450i	−0.219919	−	0.380910i	0.734864	−	0.678214i	$-0.237246\pi$
$967$	−6.83873	−	11.8450i	−0.219919	−	0.380910i	−0.954783	+	0.297304i	$0.903913\pi$
$968$	2.83501	−	4.91038i	0.0911206	−	0.157826i
$969$		0			0
$970$	−11.0869	−	19.2031i	−0.355980	−	0.616576i
$971$	−21.3133	−	36.9157i	−0.683977	−	1.18468i	−0.973757	−	0.227589i	$-0.926916\pi$
$971$	−21.3133	−	36.9157i	−0.683977	−	1.18468i	0.289781	−	0.957093i	$-0.406418\pi$
$972$		0			0
$973$	−35.5828	−	44.2155i	−1.14073	−	1.41748i
$974$	−11.3077	+	19.5854i	−0.362321	+	0.627558i
$975$		0			0
$976$	−60.1915			−1.92668
$977$	5.05683			0.161782			0.0808911	−	0.996723i	$-0.474223\pi$
$977$	5.05683			0.161782			0.0808911	+	0.996723i	$0.474223\pi$
$978$		0			0
$979$	−10.2882	+	17.8196i	−0.328811	+	0.569517i
$980$	−1.41824	+	6.47823i	−0.0453041	+	0.206940i
$981$		0			0
$982$	4.81668	+	8.34274i	0.153707	+	0.266227i
$983$	−16.6442	−	28.8286i	−0.530868	−	0.919490i	−0.999351	−	0.0360177i	$-0.988533\pi$
$983$	−16.6442	−	28.8286i	−0.530868	−	0.919490i	0.468483	−	0.883472i	$-0.344801\pi$
$984$		0			0
$985$	35.9999	−	62.3537i	1.14705	−	1.98675i
$986$	−10.5853	−	18.3343i	−0.337105	−	0.583884i
$987$		0			0
$988$	3.84201	−	6.65455i	0.122231	−	0.211710i
$989$	21.6188	+	37.4448i	0.687436	+	1.19067i
$990$		0			0
$991$	−16.0440	+	27.7890i	−0.509653	+	0.882746i	0.490284	+	0.871563i	$0.336893\pi$
$991$	−16.0440	+	27.7890i	−0.509653	+	0.882746i	−0.999937	+	0.0111829i	$0.996440\pi$
$992$	−6.72658			−0.213569
$993$		0			0
$994$	11.6428	−	1.80775i	0.369289	−	0.0573384i
$995$	−17.8403	−	30.9004i	−0.565577	−	0.979608i
$996$		0			0
$997$	21.6283	+	37.4613i	0.684975	+	1.18641i	0.973445	+	0.228922i	$0.0735202\pi$
$997$	21.6283	+	37.4613i	0.684975	+	1.18641i	−0.288470	+	0.957489i	$0.593146\pi$
$998$	21.8507	−	37.8466i	0.691673	−	1.19801i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.h.l.298.7		16
3.2	odd	2	inner	567.2.h.l.298.2		16
7.2	even	3		567.2.g.l.541.2		16
9.2	odd	6		567.2.e.g.487.7	yes	16
9.4	even	3		567.2.g.l.109.2		16
9.5	odd	6		567.2.g.l.109.7		16
9.7	even	3		567.2.e.g.487.2	yes	16
21.2	odd	6		567.2.g.l.541.7		16
63.2	odd	6		567.2.e.g.163.7	yes	16
63.11	odd	6		3969.2.a.bg.1.2		8
63.16	even	3		567.2.e.g.163.2	✓	16
63.23	odd	6	inner	567.2.h.l.352.2		16
63.25	even	3		3969.2.a.bg.1.7		8
63.38	even	6		3969.2.a.bf.1.2		8
63.52	odd	6		3969.2.a.bf.1.7		8
63.58	even	3	inner	567.2.h.l.352.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
567.2.e.g.163.2	✓	16	63.16	even	3
567.2.e.g.163.7	yes	16	63.2	odd	6
567.2.e.g.487.2	yes	16	9.7	even	3
567.2.e.g.487.7	yes	16	9.2	odd	6
567.2.g.l.109.2		16	9.4	even	3
567.2.g.l.109.7		16	9.5	odd	6
567.2.g.l.541.2		16	7.2	even	3
567.2.g.l.541.7		16	21.2	odd	6
567.2.h.l.298.2		16	3.2	odd	2	inner
567.2.h.l.298.7		16	1.1	even	1	trivial
567.2.h.l.352.2		16	63.23	odd	6	inner
567.2.h.l.352.7		16	63.58	even	3	inner
3969.2.a.bf.1.2		8	63.38	even	6
3969.2.a.bf.1.7		8	63.52	odd	6
3969.2.a.bg.1.2		8	63.11	odd	6
3969.2.a.bg.1.7		8	63.25	even	3

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.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.52818 q^{2} +0.335323 q^{4} +(-1.41264 + 2.44676i) q^{5} +(-2.61442 + 0.405935i) q^{7} -2.54392 q^{8} +O(q^{10})\)	\(q+1.52818 q^{2} +0.335323 q^{4} +(-1.41264 + 2.44676i) q^{5} +(-2.61442 + 0.405935i) q^{7} -2.54392 q^{8} +(-2.15876 + 3.73909i) q^{10} +(-1.81857 - 3.14986i) q^{11} +(2.81454 + 4.87493i) q^{13} +(-3.99530 + 0.620340i) q^{14} -4.55820 q^{16} +(-1.60110 + 2.77319i) q^{17} +(-2.03544 - 3.52548i) q^{19} +(-0.473690 + 0.820455i) q^{20} +(-2.77910 - 4.81355i) q^{22} +(-2.35159 + 4.07307i) q^{23} +(-1.49110 - 2.58266i) q^{25} +(4.30111 + 7.44975i) q^{26} +(-0.876676 + 0.136119i) q^{28} +(-2.16313 + 3.74665i) q^{29} +3.58197 q^{31} -1.87790 q^{32} +(-2.44676 + 4.23792i) q^{34} +(2.70001 - 6.97032i) q^{35} +(2.15578 + 3.73392i) q^{37} +(-3.11051 - 5.38756i) q^{38} +(3.59364 - 6.22437i) q^{40} +(-1.57596 - 2.72964i) q^{41} +(4.59663 - 7.96159i) q^{43} +(-0.609809 - 1.05622i) q^{44} +(-3.59364 + 6.22437i) q^{46} +4.84643 q^{47} +(6.67043 - 2.12257i) q^{49} +(-2.27866 - 3.94676i) q^{50} +(0.943779 + 1.63467i) q^{52} +(-7.06707 + 12.2405i) q^{53} +10.2760 q^{55} +(6.65089 - 1.03267i) q^{56} +(-3.30564 + 5.72554i) q^{58} +1.50098 q^{59} +13.2051 q^{61} +5.47388 q^{62} +6.24665 q^{64} -15.9037 q^{65} -12.6822 q^{67} +(-0.536885 + 0.929913i) q^{68} +(4.12610 - 10.6519i) q^{70} -2.91413 q^{71} +(-1.46456 + 2.53670i) q^{73} +(3.29441 + 5.70608i) q^{74} +(-0.682529 - 1.18217i) q^{76} +(6.03316 + 7.49686i) q^{77} +0.893527 q^{79} +(6.43910 - 11.1528i) q^{80} +(-2.40834 - 4.17137i) q^{82} +(-4.02432 + 6.97032i) q^{83} +(-4.52356 - 7.83503i) q^{85} +(7.02446 - 12.1667i) q^{86} +(4.62631 + 8.01300i) q^{88} +(-2.82863 - 4.89934i) q^{89} +(-9.33731 - 11.6026i) q^{91} +(-0.788541 + 1.36579i) q^{92} +7.40620 q^{94} +11.5014 q^{95} +(-2.56789 + 4.44772i) q^{97} +(10.1936 - 3.24366i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 12 q^{4} - 6 q^{7}+O(q^{10}) \) 16 * q + 12 * q^4 - 6 * q^7	\( 16 q + 12 q^{4} - 6 q^{7} - 14 q^{10} - 6 q^{13} + 12 q^{16} - 24 q^{19} - 2 q^{22} - 26 q^{28} + 40 q^{31} + 4 q^{37} - 36 q^{40} - 10 q^{43} + 36 q^{46} + 10 q^{49} - 34 q^{52} + 8 q^{55} + 22 q^{58} + 72 q^{61} + 76 q^{64} - 36 q^{67} - 46 q^{70} - 32 q^{73} - 58 q^{76} - 64 q^{79} + 2 q^{82} - 30 q^{85} + 72 q^{88} - 22 q^{91} + 108 q^{94} - 14 q^{97}+O(q^{100}) \) 16 * q + 12 * q^4 - 6 * q^7 - 14 * q^10 - 6 * q^13 + 12 * q^16 - 24 * q^19 - 2 * q^22 - 26 * q^28 + 40 * q^31 + 4 * q^37 - 36 * q^40 - 10 * q^43 + 36 * q^46 + 10 * q^49 - 34 * q^52 + 8 * q^55 + 22 * q^58 + 72 * q^61 + 76 * q^64 - 36 * q^67 - 46 * q^70 - 32 * q^73 - 58 * q^76 - 64 * q^79 + 2 * q^82 - 30 * q^85 + 72 * q^88 - 22 * q^91 + 108 * q^94 - 14 * q^97

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