LMFDB - Embedded newform 567.2.g.l.109.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [567,2,Mod(109,567)]

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([2, 4]))

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

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

chi := DirichletCharacter("567.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.g (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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			109.7
Root			$1.41264 - 0.0667052i$ of defining polynomial
Character	$\chi$	$=$	567.109
Dual form			567.2.g.l.541.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.764088 - 1.32344i) q^{2} +(-0.167661 - 0.290398i) q^{4} -2.82528 q^{5} +(0.955663 - 2.46713i) q^{7} +2.54392 q^{8} +O(q^{10})$	\(q+(0.764088 - 1.32344i) q^{2} +(-0.167661 - 0.290398i) q^{4} -2.82528 q^{5} +(0.955663 - 2.46713i) q^{7} +2.54392 q^{8} +(-2.15876 + 3.73909i) q^{10} -3.63715 q^{11} +(2.81454 - 4.87493i) q^{13} +(-2.53488 - 3.14986i) q^{14} +(2.27910 - 3.94752i) q^{16} +(1.60110 - 2.77319i) q^{17} +(-2.03544 - 3.52548i) q^{19} +(0.473690 + 0.820455i) q^{20} +(-2.77910 + 4.81355i) q^{22} -4.70318 q^{23} +2.98220 q^{25} +(-4.30111 - 7.44975i) q^{26} +(-0.876676 + 0.136119i) q^{28} +(2.16313 + 3.74665i) q^{29} +(-1.79099 - 3.10208i) q^{31} +(-0.938949 - 1.62631i) q^{32} +(-2.44676 - 4.23792i) q^{34} +(-2.70001 + 6.97032i) q^{35} +(2.15578 + 3.73392i) q^{37} -6.22102 q^{38} -7.18728 q^{40} +(1.57596 - 2.72964i) q^{41} +(4.59663 + 7.96159i) q^{43} +(0.609809 + 1.05622i) q^{44} +(-3.59364 + 6.22437i) q^{46} +(2.42321 - 4.19713i) q^{47} +(-5.17342 - 4.71548i) q^{49} +(2.27866 - 3.94676i) q^{50} -1.88756 q^{52} +(7.06707 - 12.2405i) q^{53} +10.2760 q^{55} +(2.43113 - 6.27617i) q^{56} +6.61128 q^{58} +(0.750489 + 1.29988i) q^{59} +(-6.60254 + 11.4359i) q^{61} -5.47388 q^{62} +6.24665 q^{64} +(-7.95186 + 13.7730i) q^{65} +(6.34108 + 10.9831i) q^{67} -1.07377 q^{68} +(7.16175 + 8.89924i) q^{70} +2.91413 q^{71} +(-1.46456 + 2.53670i) q^{73} +6.58882 q^{74} +(-0.682529 + 1.18217i) q^{76} +(-3.47589 + 8.97330i) q^{77} +(-0.446763 + 0.773817i) q^{79} +(-6.43910 + 11.1528i) q^{80} +(-2.40834 - 4.17137i) q^{82} +(4.02432 + 6.97032i) q^{83} +(-4.52356 + 7.83503i) q^{85} +14.0489 q^{86} -9.25262 q^{88} +(2.82863 + 4.89934i) q^{89} +(-9.33731 - 11.6026i) q^{91} +(0.788541 + 1.36579i) q^{92} +(-3.70310 - 6.41396i) q^{94} +(5.75068 + 9.96047i) q^{95} +(-2.56789 - 4.44772i) q^{97} +(-10.1936 + 3.24366i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{4}+O(q^{10}) $ 16 * q - 6 * q^4	$ 16 q - 6 q^{4} - 14 q^{10} - 6 q^{13} - 6 q^{16} - 24 q^{19} - 2 q^{22} - 26 q^{28} - 20 q^{31} + 4 q^{37} + 72 q^{40} - 10 q^{43} + 36 q^{46} + 4 q^{49} + 68 q^{52} + 8 q^{55} - 44 q^{58} - 36 q^{61} + 76 q^{64} + 18 q^{67} + 104 q^{70} - 32 q^{73} - 58 q^{76} + 32 q^{79} + 2 q^{82} - 30 q^{85} - 144 q^{88} - 22 q^{91} - 54 q^{94} - 14 q^{97}+O(q^{100}) $ 16 * q - 6 * q^4 - 14 * q^10 - 6 * q^13 - 6 * q^16 - 24 * q^19 - 2 * q^22 - 26 * q^28 - 20 * q^31 + 4 * q^37 + 72 * q^40 - 10 * q^43 + 36 * q^46 + 4 * q^49 + 68 * q^52 + 8 * q^55 - 44 * q^58 - 36 * q^61 + 76 * q^64 + 18 * q^67 + 104 * q^70 - 32 * q^73 - 58 * q^76 + 32 * q^79 + 2 * q^82 - 30 * q^85 - 144 * q^88 - 22 * q^91 - 54 * q^94 - 14 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.764088	−	1.32344i	0.540292	−	0.935813i	−0.458595	−	0.888645i	$-0.651647\pi$
$2$	0.764088	−	1.32344i	0.540292	−	0.935813i	0.998887	−	0.0471677i	$-0.0150195\pi$
$3$		0			0
$3$		0			0
$4$	−0.167661	−	0.290398i	−0.0838307	−	0.145199i
$5$	−2.82528			−1.26350			−0.631752	−	0.775171i	$-0.717664\pi$
$5$	−2.82528			−1.26350			−0.631752	+	0.775171i	$0.717664\pi$
$6$		0			0
$7$	0.955663	−	2.46713i	0.361207	−	0.932486i
$7$	0.955663	−	2.46713i	0.361207	−	0.932486i
$8$	2.54392			0.899412
$9$		0			0
$10$	−2.15876	+	3.73909i	−0.682661	+	1.18240i
$11$	−3.63715			−1.09664			−0.548321	−	0.836268i	$-0.684733\pi$
$11$	−3.63715			−1.09664			−0.548321	+	0.836268i	$0.684733\pi$
$12$		0			0
$13$	2.81454	−	4.87493i	0.780613	−	1.35206i	−0.150972	−	0.988538i	$-0.548240\pi$
$13$	2.81454	−	4.87493i	0.780613	−	1.35206i	0.931585	−	0.363523i	$-0.118426\pi$
$14$	−2.53488	−	3.14986i	−0.677475	−	0.841836i
$15$		0			0
$16$	2.27910	−	3.94752i	0.569776	−	0.986880i
$17$	1.60110	−	2.77319i	0.388324	−	0.672597i	−0.603900	−	0.797060i	$-0.706388\pi$
$17$	1.60110	−	2.77319i	0.388324	−	0.672597i	0.992224	+	0.124463i	$0.0397209\pi$
$18$		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
$23$	−4.70318			−0.980680			−0.490340	−	0.871531i	$-0.663127\pi$
$23$	−4.70318			−0.980680			−0.490340	+	0.871531i	$0.663127\pi$
$24$		0			0
$25$	2.98220			0.596440
$26$	−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	$-0.0350921\pi$
$29$	2.16313	+	3.74665i	0.401683	+	0.695735i	−0.592246	+	0.805757i	$0.701759\pi$
$30$		0			0
$31$	−1.79099	−	3.10208i	−0.321670	−	0.557150i	0.659162	−	0.752001i	$-0.270911\pi$
$31$	−1.79099	−	3.10208i	−0.321670	−	0.557150i	−0.980833	+	0.194851i	$0.937578\pi$
$32$	−0.938949	−	1.62631i	−0.165984	−	0.287493i
$33$		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	$0.718016\pi$
$38$	−6.22102			−1.00918
$39$		0			0
$40$	−7.18728			−1.13641
$41$	1.57596	−	2.72964i	0.246123	−	0.426298i	−0.716324	−	0.697768i	$-0.754177\pi$
$41$	1.57596	−	2.72964i	0.246123	−	0.426298i	0.962447	+	0.271470i	$0.0875099\pi$
$42$		0			0
$43$	4.59663	+	7.96159i	0.700979	+	1.21413i	0.968123	+	0.250475i	$0.0805867\pi$
$43$	4.59663	+	7.96159i	0.700979	+	1.21413i	−0.267144	+	0.963657i	$0.586080\pi$
$44$	0.609809	+	1.05622i	0.0919322	+	0.159231i
$45$		0			0
$46$	−3.59364	+	6.22437i	−0.529854	+	0.917733i
$47$	2.42321	−	4.19713i	0.353462	−	0.612215i	−0.633391	−	0.773832i	$-0.718338\pi$
$47$	2.42321	−	4.19713i	0.353462	−	0.612215i	0.986854	+	0.161617i	$0.0516710\pi$
$48$		0			0
$49$	−5.17342	−	4.71548i	−0.739060	−	0.673640i
$50$	2.27866	−	3.94676i	0.322252	−	0.558157i
$51$		0			0
$52$	−1.88756			−0.261757
$53$	7.06707	−	12.2405i	0.970736	−	1.68136i	0.277395	−	0.960756i	$-0.410529\pi$
$53$	7.06707	−	12.2405i	0.970736	−	1.68136i	0.693342	−	0.720609i	$-0.256138\pi$
$54$		0			0
$55$	10.2760			1.38561
$56$	2.43113	−	6.27617i	0.324873	−	0.838689i
$57$		0			0
$58$	6.61128			0.868104
$59$	0.750489	+	1.29988i	0.0977053	+	0.169231i	0.910734	−	0.412992i	$-0.135516\pi$
$59$	0.750489	+	1.29988i	0.0977053	+	0.169231i	−0.813029	+	0.582223i	$0.802183\pi$
$60$		0			0
$61$	−6.60254	+	11.4359i	−0.845369	+	1.46422i	0.0399317	+	0.999202i	$0.487286\pi$
$61$	−6.60254	+	11.4359i	−0.845369	+	1.46422i	−0.885301	+	0.465019i	$0.846047\pi$
$62$	−5.47388			−0.695184
$63$		0			0
$64$	6.24665			0.780831
$65$	−7.95186	+	13.7730i	−0.986307	+	1.70833i
$66$		0			0
$67$	6.34108	+	10.9831i	0.774686	+	1.34180i	0.934971	+	0.354725i	$0.115425\pi$
$67$	6.34108	+	10.9831i	0.774686	+	1.34180i	−0.160285	+	0.987071i	$0.551241\pi$
$68$	−1.07377			−0.130214
$69$		0			0
$70$	7.16175	+	8.89924i	0.855992	+	1.06366i
$71$	2.91413			0.345844			0.172922	−	0.984936i	$-0.444679\pi$
$71$	2.91413			0.345844			0.172922	+	0.984936i	$0.444679\pi$
$72$		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	$0.221500\pi$
$74$	6.58882			0.765935
$75$		0			0
$76$	−0.682529	+	1.18217i	−0.0782914	+	0.135605i
$77$	−3.47589	+	8.97330i	−0.396114	+	1.02260i
$78$		0			0
$79$	−0.446763	+	0.773817i	−0.0502648	+	0.0870612i	−0.890063	−	0.455837i	$-0.849340\pi$
$79$	−0.446763	+	0.773817i	−0.0502648	+	0.0870612i	0.839798	+	0.542899i	$0.182673\pi$
$80$	−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	$-0.0210330\pi$
$83$	4.02432	+	6.97032i	0.441726	+	0.765092i	−0.556092	+	0.831121i	$0.687700\pi$
$84$		0			0
$85$	−4.52356	+	7.83503i	−0.490648	+	0.849828i
$86$	14.0489			1.51493
$87$		0			0
$88$	−9.25262			−0.986332
$89$	2.82863	+	4.89934i	0.299835	+	0.519329i	0.976098	−	0.217331i	$-0.0697352\pi$
$89$	2.82863	+	4.89934i	0.299835	+	0.519329i	−0.676263	+	0.736660i	$0.736402\pi$
$90$		0			0
$91$	−9.33731	−	11.6026i	−0.978816	−	1.21628i
$92$	0.788541	+	1.36579i	0.0822111	+	0.142394i
$93$		0			0
$94$	−3.70310	−	6.41396i	−0.381946	−	0.661549i
$95$	5.75068	+	9.96047i	0.590007	+	1.02192i
$96$		0			0
$97$	−2.56789	−	4.44772i	−0.260730	−	0.451598i	0.705706	−	0.708505i	$-0.250630\pi$
$97$	−2.56789	−	4.44772i	−0.260730	−	0.451598i	−0.966436	+	0.256907i	$0.917297\pi$
$98$	−10.1936	+	3.24366i	−1.02971	+	0.327660i
$99$		0			0
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	−2.52446			−0.251193			−0.125597	−	0.992081i	$-0.540085\pi$
$101$	−2.52446			−0.251193			−0.125597	+	0.992081i	$0.540085\pi$
$102$		0			0
$103$	9.84642			0.970196			0.485098	−	0.874460i	$-0.338784\pi$
$103$	9.84642			0.970196			0.485098	+	0.874460i	$0.338784\pi$
$104$	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	0.923920	−	0.382586i	$-0.124966\pi$
$107$	1.35126	+	2.34045i	0.130631	+	0.226260i	−0.793289	+	0.608845i	$0.791633\pi$
$108$		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	$0.0238483\pi$
$110$	7.85174	−	13.5996i	0.748634	−	1.29667i
$111$		0			0
$112$	−7.56098	−	9.39533i	−0.714445	−	0.887775i
$113$	0.232888	−	0.403374i	0.0219082	−	0.0379462i	−0.854863	−	0.518853i	$-0.826359\pi$
$113$	0.232888	−	0.403374i	0.0219082	−	0.0379462i	0.876772	+	0.480907i	$0.159692\pi$
$114$		0			0
$115$	13.2878			1.23909
$116$	0.725346	−	1.25634i	0.0673467	−	0.116648i
$117$		0			0
$118$	2.29376			0.211158
$119$	−5.31169	−	6.60035i	−0.486922	−	0.605053i
$120$		0			0
$121$	2.22885			0.202623
$122$	10.0898	+	17.4761i	0.913492	+	1.58221i
$123$		0			0
$124$	−0.600558	+	1.04020i	−0.0539317	+	0.0934125i
$125$	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	$0.746426\pi$
$128$	6.65089	−	11.5197i	0.587861	−	1.01821i
$129$		0			0
$130$	12.1518	+	21.0476i	1.06579	+	1.84600i
$131$	−12.1479			−1.06137			−0.530685	−	0.847569i	$-0.678065\pi$
$131$	−12.1479			−1.06137			−0.530685	+	0.847569i	$0.678065\pi$
$132$		0			0
$133$	−10.6430	+	1.65251i	−0.922865	+	0.143291i
$134$	19.3806			1.67423
$135$		0			0
$136$	4.07307	−	7.05477i	0.349263	−	0.604941i
$137$	−2.16337			−0.184829			−0.0924146	−	0.995721i	$-0.529459\pi$
$137$	−2.16337			−0.184829			−0.0924146	+	0.995721i	$0.529459\pi$
$138$		0			0
$139$	10.7257	−	18.5775i	0.909743	−	1.57572i	0.0953212	−	0.995447i	$-0.469612\pi$
$139$	10.7257	−	18.5775i	0.909743	−	1.57572i	0.814421	−	0.580274i	$-0.197054\pi$
$140$	2.47685	−	0.384575i	0.209332	−	0.0325025i
$141$		0			0
$142$	2.22665	−	3.85668i	0.186857	−	0.323645i
$143$	−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
$149$	11.0972			0.909121			0.454561	−	0.890716i	$-0.349796\pi$
$149$	11.0972			0.909121			0.454561	+	0.890716i	$0.349796\pi$
$150$		0			0
$151$	2.08710			0.169846			0.0849228	−	0.996388i	$-0.472936\pi$
$151$	2.08710			0.169846			0.0849228	+	0.996388i	$0.472936\pi$
$152$	−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
$157$	10.8077	+	18.7194i	0.862547	+	1.49397i	0.869463	+	0.493998i	$0.164465\pi$
$157$	10.8077	+	18.7194i	0.862547	+	1.49397i	−0.00691621	+	0.999976i	$0.502202\pi$
$158$	0.682733	+	1.18253i	0.0543153	+	0.0940769i
$159$		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	$0.713566\pi$
$164$	−1.05691			−0.0825307
$165$		0			0
$166$	12.2997			0.954644
$167$	−8.70235	+	15.0729i	−0.673408	+	1.16638i	0.303523	+	0.952824i	$0.401837\pi$
$167$	−8.70235	+	15.0729i	−0.673408	+	1.16638i	−0.976931	+	0.213553i	$0.931496\pi$
$168$		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
$173$	10.7738	−	18.6607i	0.819116	−	1.41875i	−0.0872187	−	0.996189i	$-0.527798\pi$
$173$	10.7738	−	18.6607i	0.819116	−	1.41875i	0.906334	−	0.422561i	$-0.138869\pi$
$174$		0			0
$175$	2.84998	−	7.35747i	0.215438	−	0.556172i
$176$	−8.28943	+	14.3577i	−0.624840	+	1.08225i
$177$		0			0
$178$	8.64530			0.647993
$179$	−2.82863	+	4.89934i	−0.211422	+	0.366194i	−0.952160	−	0.305601i	$-0.901143\pi$
$179$	−2.82863	+	4.89934i	−0.211422	+	0.366194i	0.740738	+	0.671794i	$0.234476\pi$
$180$		0			0
$181$	1.12427			0.0835664			0.0417832	−	0.999127i	$-0.486696\pi$
$181$	1.12427			0.0835664			0.0417832	+	0.999127i	$0.486696\pi$
$182$	−22.4899	+	3.49194i	−1.66706	+	0.258840i
$183$		0			0
$184$	−11.9645			−0.882035
$185$	−6.09067	−	10.5494i	−0.447795	−	0.775604i
$186$		0			0
$187$	−5.82344	+	10.0865i	−0.425852	+	0.737597i
$188$	−1.62512			−0.118524
$189$		0			0
$190$	17.5761			1.27510
$191$	−1.96950	+	3.41127i	−0.142508	+	0.246831i	−0.928440	−	0.371481i	$-0.878850\pi$
$191$	−1.96950	+	3.41127i	−0.142508	+	0.246831i	0.785932	+	0.618312i	$0.212183\pi$
$192$		0			0
$193$	−9.04339	−	15.6636i	−0.650957	−	1.12749i	−0.982891	−	0.184189i	$-0.941034\pi$
$193$	−9.04339	−	15.6636i	−0.650957	−	1.12749i	0.331933	−	0.943303i	$-0.392299\pi$
$194$	−7.84838			−0.563481
$195$		0			0
$196$	−0.501983	+	2.29295i	−0.0358560	+	0.163782i
$197$	25.4842			1.81567			0.907836	−	0.419326i	$-0.137734\pi$
$197$	25.4842			1.81567			0.907836	+	0.419326i	$0.137734\pi$
$198$		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	$0.314397\pi$
$200$	7.58648			0.536445
$201$		0			0
$202$	−1.92891	+	3.34097i	−0.135718	+	0.235070i
$203$	11.3107	−	1.75618i	0.793854	−	0.123260i
$204$		0			0
$205$	−4.45252	+	7.71199i	−0.310977	+	0.538629i
$206$	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	−0.903063	−	0.429508i	$-0.858687\pi$
$211$	−1.15578	+	2.00187i	−0.0795670	+	0.137814i	0.823496	+	0.567322i	$0.192020\pi$
$212$	−4.73950			−0.325510
$213$		0			0
$214$	4.12992			0.282316
$215$	−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
$220$	−1.72288	−	2.98412i	−0.116157	−	0.201189i
$221$	−9.01272	−	15.6105i	−0.606261	−	1.05008i
$222$		0			0
$223$	−4.64981	−	8.05371i	−0.311374	−	0.539316i	0.667286	−	0.744802i	$-0.267456\pi$
$223$	−4.64981	−	8.05371i	−0.311374	−	0.539316i	−0.978660	+	0.205486i	$0.934123\pi$
$224$	−4.90963	+	0.762304i	−0.328038	+	0.0509336i
$225$		0			0
$226$	−0.355894	−	0.616426i	−0.0236737	−	0.0410040i
$227$	−1.92818			−0.127978			−0.0639890	−	0.997951i	$-0.520382\pi$
$227$	−1.92818			−0.127978			−0.0639890	+	0.997951i	$0.520382\pi$
$228$		0			0
$229$	3.34118			0.220792			0.110396	−	0.993888i	$-0.464788\pi$
$229$	3.34118			0.220792			0.110396	+	0.993888i	$0.464788\pi$
$230$	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	$-0.923025\pi$
$233$	−10.5758	−	18.3178i	−0.692842	−	1.20004i	0.278061	−	0.960563i	$-0.410308\pi$
$234$		0			0
$235$	−6.84626	+	11.8581i	−0.446601	+	0.773535i
$236$	0.251656	−	0.435881i	0.0163814	−	0.0283734i
$237$		0			0
$238$	−12.7938	+	1.98645i	−0.829296	+	0.128763i
$239$	12.0575	−	20.8843i	0.779937	−	1.35089i	−0.152041	−	0.988374i	$-0.548584\pi$
$239$	12.0575	−	20.8843i	0.779937	−	1.35089i	0.931978	−	0.362516i	$-0.118082\pi$
$240$		0			0
$241$	9.23439			0.594840			0.297420	−	0.954747i	$-0.403874\pi$
$241$	9.23439			0.594840			0.297420	+	0.954747i	$0.403874\pi$
$242$	1.70304	−	2.94975i	0.109475	−	0.189617i
$243$		0			0
$244$	4.42796			0.283471
$245$	14.6163	+	13.3225i	0.933804	+	0.851146i
$246$		0			0
$247$	−22.9153			−1.45807
$248$	−4.55612	−	7.89144i	−0.289314	−	0.501107i
$249$		0			0
$250$	4.35595	−	7.54472i	0.275494	−	0.477170i
$251$	−18.5790			−1.17270			−0.586349	−	0.810058i	$-0.699435\pi$
$251$	−18.5790			−1.17270			−0.586349	+	0.810058i	$0.699435\pi$
$252$		0			0
$253$	17.1062			1.07545
$254$	−12.0401	+	20.8540i	−0.755461	+	1.30850i
$255$		0			0
$256$	−3.91708	−	6.78458i	−0.244818	−	0.424037i
$257$	10.2197			0.637490			0.318745	−	0.947841i	$-0.396739\pi$
$257$	10.2197			0.637490			0.318745	+	0.947841i	$0.396739\pi$
$258$		0			0
$259$	11.2722	−	1.75021i	0.700423	−	0.108753i
$260$	5.33288			0.330731
$261$		0			0
$262$	−9.28209	+	16.0770i	−0.573449	+	0.993243i
$263$	−9.13775			−0.563458			−0.281729	−	0.959494i	$-0.590908\pi$
$263$	−9.13775			−0.563458			−0.281729	+	0.959494i	$0.590908\pi$
$264$		0			0
$265$	−19.9664	+	34.5829i	−1.22653	+	2.12441i
$266$	−5.94519	+	15.3480i	−0.364523	+	0.941048i
$267$		0			0
$268$	2.12631	−	3.68287i	0.129885	−	0.224967i
$269$	−11.4606	+	19.8504i	−0.698767	+	1.21030i	0.270127	+	0.962825i	$0.412934\pi$
$269$	−11.4606	+	19.8504i	−0.698767	+	1.21030i	−0.968894	+	0.247475i	$0.920399\pi$
$270$		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
$275$	−10.8467			−0.654081
$276$		0			0
$277$	0.183318			0.0110145			0.00550725	−	0.999985i	$-0.498247\pi$
$277$	0.183318			0.0110145			0.00550725	+	0.999985i	$0.498247\pi$
$278$	−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	$-0.00611799\pi$
$281$	8.10097	+	14.0313i	0.483263	+	0.837037i	−0.516552	+	0.856256i	$0.672785\pi$
$282$		0			0
$283$	−10.3492	−	17.9253i	−0.615195	−	1.06555i	−0.990350	−	0.138588i	$-0.955744\pi$
$283$	−10.3492	−	17.9253i	−0.615195	−	1.06555i	0.375155	−	0.926962i	$-0.377590\pi$
$284$	−0.488588	−	0.846258i	−0.0289923	−	0.0502162i
$285$		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
$290$	−18.6787			−1.09685
$291$		0			0
$292$	0.982202			0.0574790
$293$	−8.01170	+	13.8767i	−0.468049	+	0.810684i	−0.999333	−	0.0365093i	$-0.988376\pi$
$293$	−8.01170	+	13.8767i	−0.468049	+	0.810684i	0.531285	+	0.847193i	$0.321709\pi$
$294$		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
$299$	−13.2373	+	22.9276i	−0.765532	+	1.32594i
$300$		0			0
$301$	24.0351	−	3.73186i	1.38536	−	0.215101i
$302$	1.59473	−	2.76215i	0.0917662	−	0.158944i
$303$		0			0
$304$	−18.5559			−1.06425
$305$	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	$0.548540\pi$
$308$	3.18860	−	0.495086i	0.181687	−	0.0282101i
$309$		0			0
$310$	15.4652			0.878367
$311$	−9.21297	−	15.9573i	−0.522420	−	0.904857i	−0.999660	−	0.0260843i	$-0.991696\pi$
$311$	−9.21297	−	15.9573i	−0.522420	−	0.904857i	0.477240	−	0.878773i	$-0.341637\pi$
$312$		0			0
$313$	−2.32344	+	4.02432i	−0.131329	+	0.227468i	−0.924189	−	0.381936i	$-0.875258\pi$
$313$	−2.32344	+	4.02432i	−0.131329	+	0.227468i	0.792860	+	0.609403i	$0.208591\pi$
$314$	33.0321			1.86411
$315$		0			0
$316$	0.299620			0.0168549
$317$	5.24006	−	9.07606i	0.294311	−	0.509762i	−0.680513	−	0.732736i	$-0.738243\pi$
$317$	5.24006	−	9.07606i	0.294311	−	0.509762i	0.974824	+	0.222974i	$0.0715764\pi$
$318$		0			0
$319$	−7.86762	−	13.6271i	−0.440502	−	0.762972i
$320$	−17.6485			−0.986582
$321$		0			0
$322$	11.9220	+	14.8144i	0.664387	+	0.825572i
$323$	−13.0358			−0.725329
$324$		0			0
$325$	8.39353	−	14.5380i	0.465589	−	0.806424i
$326$	14.3380			0.794109
$327$		0			0
$328$	4.00911	−	6.94398i	0.221366	−	0.383417i
$329$	−8.03907	−	9.98942i	−0.443209	−	0.550734i
$330$		0			0
$331$	−6.42677	+	11.1315i	−0.353247	+	0.611842i	−0.986816	−	0.161844i	$-0.948256\pi$
$331$	−6.42677	+	11.1315i	−0.353247	+	0.611842i	0.633569	+	0.773686i	$0.281589\pi$
$332$	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	−0.948080	−	0.318033i	$-0.896978\pi$
$337$	−3.64609	+	6.31521i	−0.198615	+	0.344012i	0.749464	+	0.662045i	$0.230311\pi$
$338$	−28.5563			−1.55326
$339$		0			0
$340$	3.03370			0.164526
$341$	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
$346$	−16.4642	−	28.5169i	−0.885123	−	1.53308i
$347$	−8.76942	−	15.1891i	−0.470767	−	0.815392i	0.528674	−	0.848825i	$-0.322689\pi$
$347$	−8.76942	−	15.1891i	−0.470767	−	0.815392i	−0.999441	+	0.0334327i	$0.989356\pi$
$348$		0			0
$349$	−10.5080	−	18.2004i	−0.562481	−	0.974245i	−0.997279	−	0.0737172i	$-0.976514\pi$
$349$	−10.5080	−	18.2004i	−0.562481	−	0.974245i	0.434799	−	0.900528i	$-0.356820\pi$
$350$	−7.55953	−	9.39353i	−0.404074	−	0.502105i
$351$		0			0
$352$	3.41510	+	5.91512i	0.182025	+	0.315277i
$353$	5.05338			0.268965			0.134482	−	0.990916i	$-0.457063\pi$
$353$	5.05338			0.268965			0.134482	+	0.990916i	$0.457063\pi$
$354$		0			0
$355$	−8.23324			−0.436975
$356$	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	0.991349	−	0.131249i	$-0.0418986\pi$
$359$	7.23806	+	12.5367i	0.382010	+	0.661661i	−0.609339	+	0.792910i	$0.708565\pi$
$360$		0			0
$361$	1.21398	−	2.10268i	0.0638938	−	0.110667i
$362$	0.859042	−	1.48791i	0.0451503	−	0.0782026i
$363$		0			0
$364$	−1.80387	+	4.65684i	−0.0945484	+	0.244085i
$365$	4.13780	−	7.16687i	0.216582	−	0.375131i
$366$		0			0
$367$	14.9228			0.778966			0.389483	−	0.921034i	$-0.372654\pi$
$367$	14.9228			0.778966			0.389483	+	0.921034i	$0.372654\pi$
$368$	−10.7190	+	18.5659i	−0.558768	+	0.967814i
$369$		0			0
$370$	−18.6152			−0.967761
$371$	−23.4452	−	29.1332i	−1.21721	−	1.51252i
$372$		0			0
$373$	7.82107			0.404960			0.202480	−	0.979286i	$-0.435100\pi$
$373$	7.82107			0.404960			0.202480	+	0.979286i	$0.435100\pi$
$374$	8.89924	+	15.4139i	0.460169	+	0.797036i
$375$		0			0
$376$	6.16447	−	10.6772i	0.317908	−	0.550633i
$377$	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	$0.403622\pi$
$380$	1.92833	−	3.33997i	0.0989214	−	0.171337i
$381$		0			0
$382$	3.00974	+	5.21303i	0.153992	+	0.266722i
$383$	25.0764			1.28134			0.640672	−	0.767814i	$-0.278656\pi$
$383$	25.0764			1.28134			0.640672	+	0.767814i	$0.278656\pi$
$384$		0			0
$385$	9.82035	−	25.3521i	0.500491	−	1.29206i
$386$	−27.6398			−1.40683
$387$		0			0
$388$	−0.861073	+	1.49142i	−0.0437143	+	0.0757155i
$389$	23.4993			1.19146			0.595732	−	0.803184i	$-0.296862\pi$
$389$	23.4993			1.19146			0.595732	+	0.803184i	$0.296862\pi$
$390$		0			0
$391$	−7.53026	+	13.0428i	−0.380822	+	0.659602i
$392$	−13.1608	−	11.9958i	−0.664719	−	0.605880i
$393$		0			0
$394$	19.4721	−	33.7267i	0.980992	−	1.69913i
$395$	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
$401$	14.3797			0.718086			0.359043	−	0.933321i	$-0.383103\pi$
$401$	14.3797			0.718086			0.359043	+	0.933321i	$0.383103\pi$
$402$		0			0
$403$	−20.1632			−1.00440
$404$	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
$409$	5.78795	+	10.0250i	0.286196	+	0.495705i	0.972898	−	0.231233i	$-0.0742759\pi$
$409$	5.78795	+	10.0250i	0.286196	+	0.495705i	−0.686703	+	0.726938i	$0.740943\pi$
$410$	6.80424	+	11.7853i	0.336037	+	0.582034i
$411$		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
$416$	−10.5708			−0.518278
$417$		0			0
$418$	22.6268			1.10671
$419$	−17.0860	+	29.5939i	−0.834708	+	1.44576i	0.0595598	+	0.998225i	$0.481030\pi$
$419$	−17.0860	+	29.5939i	−0.834708	+	1.44576i	−0.894268	+	0.447532i	$0.852303\pi$
$420$		0			0
$421$	5.11065	+	8.85191i	0.249078	+	0.431416i	0.963270	−	0.268534i	$-0.0865391\pi$
$421$	5.11065	+	8.85191i	0.249078	+	0.431416i	−0.714192	+	0.699950i	$0.753206\pi$
$422$	1.76623	+	3.05920i	0.0859789	+	0.148920i
$423$		0			0
$424$	17.9781	−	31.1389i	0.873092	−	1.51224i
$425$	4.77480	−	8.27020i	0.231612	−	0.401164i
$426$		0			0
$427$	21.9041	+	27.2182i	1.06001	+	1.31718i
$428$	0.453108	−	0.784806i	0.0219018	−	0.0379350i
$429$		0			0
$430$	−39.6921			−1.91412
$431$	0.0380526	−	0.0659090i	0.00183293	−	0.00317472i	−0.865107	−	0.501587i	$-0.832750\pi$
$431$	0.0380526	−	0.0659090i	0.00183293	−	0.00317472i	0.866940	+	0.498412i	$0.166083\pi$
$432$		0			0
$433$	−29.2697			−1.40661			−0.703305	−	0.710888i	$-0.748293\pi$
$433$	−29.2697			−1.40661			−0.703305	+	0.710888i	$0.748293\pi$
$434$	−5.23118	+	13.5048i	−0.251105	+	0.648249i
$435$		0			0
$436$	−3.03717			−0.145454
$437$	9.57303	+	16.5810i	0.457940	+	0.793175i
$438$		0			0
$439$	2.17263	−	3.76310i	0.103694	−	0.179603i	−0.809510	−	0.587106i	$-0.800267\pi$
$439$	2.17263	−	3.76310i	0.103694	−	0.179603i	0.913204	+	0.407503i	$0.133600\pi$
$440$	26.1412			1.24623
$441$		0			0
$442$	−27.5461			−1.31023
$443$	10.2772	−	17.8006i	0.488284	−	0.845732i	−0.511625	−	0.859209i	$-0.670956\pi$
$443$	10.2772	−	17.8006i	0.488284	−	0.845732i	0.999909	+	0.0134764i	$0.00428979\pi$
$444$		0			0
$445$	−7.99168	−	13.8420i	−0.378842	−	0.656173i
$446$	−14.2115			−0.672932
$447$		0			0
$448$	5.96969	−	15.4113i	0.282041	−	0.728114i
$449$	−12.4720			−0.588588			−0.294294	−	0.955715i	$-0.595085\pi$
$449$	−12.4720			−0.588588			−0.294294	+	0.955715i	$0.595085\pi$
$450$		0			0
$451$	−5.73199	+	9.92810i	−0.269909	+	0.467496i
$452$	−0.156185			−0.00734633
$453$		0			0
$454$	−1.47330	+	2.55183i	−0.0691455	+	0.119764i
$455$	26.3805	+	32.7806i	1.23674	+	1.53678i
$456$		0			0
$457$	15.4674	−	26.7903i	0.723534	−	1.25320i	−0.236041	−	0.971743i	$-0.575850\pi$
$457$	15.4674	−	26.7903i	0.723534	−	1.25320i	0.959575	−	0.281454i	$-0.0908168\pi$
$458$	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	$-0.226488\pi$
$461$	−4.01141	−	6.94796i	−0.186830	−	0.323599i	−0.944192	+	0.329397i	$0.893155\pi$
$462$		0			0
$463$	8.41117	−	14.5686i	0.390900	−	0.677059i	−0.601668	−	0.798746i	$-0.705497\pi$
$463$	8.41117	−	14.5686i	0.390900	−	0.677059i	0.992569	+	0.121687i	$0.0388305\pi$
$464$	19.7200			0.915476
$465$		0			0
$466$	−32.3233			−1.49735
$467$	−0.480399	−	0.832075i	−0.0222302	−	0.0385038i	0.854696	−	0.519128i	$-0.173743\pi$
$467$	−0.480399	−	0.832075i	−0.0222302	−	0.0385038i	−0.876926	+	0.480625i	$0.840410\pi$
$468$		0			0
$469$	33.1566	−	5.14813i	1.53103	−	0.237719i
$470$	10.4623	+	18.1212i	0.482589	+	0.835869i
$471$		0			0
$472$	1.90918	+	3.30680i	0.0878773	+	0.152208i
$473$	−16.7186	−	28.9575i	−0.768723	−	1.33147i
$474$		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
$479$	24.1290			1.10248			0.551242	−	0.834346i	$-0.314154\pi$
$479$	24.1290			1.10248			0.551242	+	0.834346i	$0.314154\pi$
$480$		0			0
$481$	24.2701			1.10662
$482$	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	$0.275505\pi$
$488$	−16.7963	+	29.0921i	−0.760335	+	1.31694i
$489$		0			0
$490$	28.7998	−	9.16426i	1.30104	−	0.413999i
$491$	−3.15192	+	5.45928i	−0.142244	+	0.246374i	−0.928341	−	0.371729i	$-0.878765\pi$
$491$	−3.15192	+	5.45928i	−0.142244	+	0.246374i	0.786097	+	0.618103i	$0.212098\pi$
$492$		0			0
$493$	13.8535			0.623932
$494$	−17.5093	+	30.3270i	−0.787781	+	1.36448i
$495$		0			0
$496$	−16.3274			−0.733120
$497$	2.78493	−	7.18953i	0.124921	−	0.322495i
$498$		0			0
$499$	−28.5971			−1.28018			−0.640092	−	0.768298i	$-0.721104\pi$
$499$	−28.5971			−1.28018			−0.640092	+	0.768298i	$0.721104\pi$
$500$	−0.955811	−	1.65551i	−0.0427452	−	0.0740368i
$501$		0			0
$502$	−14.1960	+	24.5882i	−0.633600	+	1.09743i
$503$	−35.4133			−1.57900			−0.789500	−	0.613750i	$-0.789660\pi$
$503$	−35.4133			−1.57900			−0.789500	+	0.613750i	$0.789660\pi$
$504$		0			0
$505$	7.13231			0.317384
$506$	13.0706	−	22.6390i	0.581060	−	1.00642i
$507$		0			0
$508$	2.64191	+	4.57592i	0.117216	+	0.203024i
$509$	32.4883			1.44002			0.720010	−	0.693964i	$-0.244137\pi$
$509$	32.4883			1.44002			0.720010	+	0.693964i	$0.244137\pi$
$510$		0			0
$511$	4.85872	+	6.03748i	0.214937	+	0.267083i
$512$	14.6316			0.646630
$513$		0			0
$514$	7.80878	−	13.5252i	0.344431	−	0.596571i
$515$	−27.8189			−1.22585
$516$		0			0
$517$	−8.81359	+	15.2656i	−0.387621	+	0.671380i
$518$	6.29669	−	16.2554i	0.276661	−	0.714223i
$519$		0			0
$520$	−20.2289	+	35.0375i	−0.887096	+	1.53650i
$521$	16.4909	−	28.5631i	0.722479	−	1.25137i	−0.237524	−	0.971382i	$-0.576336\pi$
$521$	16.4909	−	28.5631i	0.722479	−	1.25137i	0.960003	−	0.279989i	$-0.0903308\pi$
$522$		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
$527$	−11.4702			−0.499649
$528$		0			0
$529$	−0.880118			−0.0382660
$530$	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
$535$	−3.81768	−	6.61242i	−0.165053	−	0.285880i
$536$	16.1312	+	27.9401i	0.696762	+	1.20683i
$537$		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	$0.721700\pi$
$542$	14.2359			0.611485
$543$		0			0
$544$	−6.01341			−0.257823
$545$	−12.7949	+	22.1615i	−0.548075	+	0.949294i
$546$		0			0
$547$	16.0285	+	27.7622i	0.685330	+	1.18703i	0.973333	+	0.229397i	$0.0736754\pi$
$547$	16.0285	+	27.7622i	0.685330	+	1.18703i	−0.288003	+	0.957630i	$0.592991\pi$
$548$	0.362714	+	0.628238i	0.0154944	+	0.0268370i
$549$		0			0
$550$	−8.28784	+	14.3550i	−0.353395	+	0.612098i
$551$	8.80583	−	15.2521i	0.375141	−	0.649763i
$552$		0			0
$553$	1.48215	+	1.84173i	0.0630274	+	0.0783183i
$554$	0.140071	−	0.242610i	0.00595105	−	0.0103075i
$555$		0			0
$556$	−7.19315			−0.305057
$557$	−19.6474	+	34.0302i	−0.832486	+	1.44191i	0.0635754	+	0.997977i	$0.479750\pi$
$557$	−19.6474	+	34.0302i	−0.832486	+	1.44191i	−0.896061	+	0.443931i	$0.853584\pi$
$558$		0			0
$559$	51.7496			2.18877
$560$	21.3619	+	26.5444i	0.902704	+	1.12171i
$561$		0			0
$562$	24.7594			1.04441
$563$	17.2532	+	29.8834i	0.727134	+	1.25943i	0.958089	+	0.286469i	$0.0924816\pi$
$563$	17.2532	+	29.8834i	0.727134	+	1.25943i	−0.230955	+	0.972964i	$0.574185\pi$
$564$		0			0
$565$	−0.657973	+	1.13964i	−0.0276811	+	0.0479451i
$566$	−31.6308			−1.32954
$567$		0			0
$568$	7.41332			0.311056
$569$	−2.14203	+	3.71010i	−0.0897985	+	0.155536i	−0.907426	−	0.420212i	$-0.861956\pi$
$569$	−2.14203	+	3.71010i	−0.0897985	+	0.155536i	0.817627	+	0.575748i	$0.195289\pi$
$570$		0			0
$571$	−12.5798	−	21.7888i	−0.526447	−	0.911833i	−0.999525	−	0.0308128i	$-0.990190\pi$
$571$	−12.5798	−	21.7888i	−0.526447	−	0.911833i	0.473078	−	0.881021i	$-0.343143\pi$
$572$	6.86533			0.287054
$573$		0			0
$574$	−12.5929	+	1.95526i	−0.525616	+	0.0816109i
$575$	−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	$-0.206128\pi$
$578$	10.3089			0.428795
$579$		0			0
$580$	−2.04930	+	3.54950i	−0.0850928	+	0.147385i
$581$	21.0425	−	3.26722i	0.872992	−	0.135547i
$582$		0			0
$583$	−25.7040	+	44.5206i	−1.06455	+	1.84385i
$584$	−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	$-0.253154\pi$
$587$	−6.50229	−	11.2623i	−0.268378	−	0.464845i	−0.968443	+	0.249234i	$0.919821\pi$
$588$		0			0
$589$	−7.29088	+	12.6282i	−0.300415	+	0.520335i
$590$	−6.48051			−0.266798
$591$		0			0
$592$	19.6530			0.807731
$593$	−14.1164	−	24.4503i	−0.579691	−	1.00405i	−0.995515	−	0.0946086i	$-0.969840\pi$
$593$	−14.1164	−	24.4503i	−0.579691	−	1.00405i	0.415824	−	0.909445i	$-0.363493\pi$
$594$		0			0
$595$	15.0070	+	18.6478i	0.615227	+	0.764486i
$596$	−1.86058	−	3.22262i	−0.0762123	−	0.132004i
$597$		0			0
$598$	20.2289	+	35.0375i	0.827221	+	1.43279i
$599$	2.49768	+	4.32611i	0.102052	+	0.176760i	0.912530	−	0.409010i	$-0.134126\pi$
$599$	2.49768	+	4.32611i	0.102052	+	0.176760i	−0.810478	+	0.585769i	$0.800792\pi$
$600$		0			0
$601$	−4.07893	−	7.06492i	−0.166383	−	0.288184i	0.770762	−	0.637123i	$-0.219876\pi$
$601$	−4.07893	−	7.06492i	−0.166383	−	0.288184i	−0.937146	+	0.348939i	$0.886542\pi$
$602$	13.4260	−	34.6604i	0.547204	−	1.41265i
$603$		0			0
$604$	−0.349925	−	0.606089i	−0.0142383	−	0.0246614i
$605$	−6.29712			−0.256014
$606$		0			0
$607$	16.7277			0.678956			0.339478	−	0.940614i	$-0.389750\pi$
$607$	16.7277			0.678956			0.339478	+	0.940614i	$0.389750\pi$
$608$	−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	$0.0579358\pi$
$614$	−4.06729	+	7.04476i	−0.164143	+	0.284303i
$615$		0			0
$616$	−8.84238	+	22.8274i	−0.356270	+	0.919741i
$617$	11.8543	−	20.5322i	0.477235	−	0.826595i	−0.522425	−	0.852685i	$-0.674972\pi$
$617$	11.8543	−	20.5322i	0.477235	−	0.826595i	0.999660	+	0.0260905i	$0.00830580\pi$
$618$		0			0
$619$	−7.82412			−0.314478			−0.157239	−	0.987561i	$-0.550259\pi$
$619$	−7.82412			−0.314478			−0.157239	+	0.987561i	$0.550259\pi$
$620$	1.69674	−	2.93885i	0.0681429	−	0.118027i
$621$		0			0
$622$	−28.1581			−1.12904
$623$	14.7905	−	2.29648i	0.592569	−	0.0920066i
$624$		0			0
$625$	−31.0175			−1.24070
$626$	3.55063	+	6.14986i	0.141912	+	0.245798i
$627$		0			0
$628$	3.62406	−	6.27706i	0.144616	−	0.250482i
$629$	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	$0.516142\pi$
$632$	−1.13653	+	1.96853i	−0.0452088	+	0.0783039i
$633$		0			0
$634$	−8.00774	−	13.8698i	−0.318028	−	0.550841i
$635$	44.5191			1.76669
$636$		0			0
$637$	−37.5484	+	11.9481i	−1.48772	+	0.473402i
$638$	−24.0462			−0.951999
$639$		0			0
$640$	−18.7906	+	32.5463i	−0.742764	+	1.28651i
$641$	10.2854			0.406248			0.203124	−	0.979153i	$-0.434891\pi$
$641$	10.2854			0.406248			0.203124	+	0.979153i	$0.434891\pi$
$642$		0			0
$643$	2.46063	−	4.26194i	0.0970378	−	0.168074i	−0.813419	−	0.581678i	$-0.802397\pi$
$643$	2.46063	−	4.26194i	0.0970378	−	0.168074i	0.910457	+	0.413603i	$0.135730\pi$
$644$	4.12316	−	0.640193i	0.162475	−	0.0252271i
$645$		0			0
$646$	−9.96047	+	17.2520i	−0.391890	+	0.678773i
$647$	−4.39168	+	7.60661i	−0.172655	+	0.299047i	−0.939347	−	0.342968i	$-0.888568\pi$
$647$	−4.39168	+	7.60661i	−0.172655	+	0.299047i	0.766692	+	0.642015i	$0.221901\pi$
$648$		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
$653$	1.77459			0.0694453			0.0347226	−	0.999397i	$-0.488945\pi$
$653$	1.77459			0.0694453			0.0347226	+	0.999397i	$0.488945\pi$
$654$		0			0
$655$	34.3213			1.34104
$656$	−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	$-0.181202\pi$
$659$	−1.17184	−	2.02968i	−0.0456483	−	0.0790652i	−0.887947	+	0.459946i	$0.847869\pi$
$660$		0			0
$661$	11.4547	+	19.8401i	0.445537	+	0.771692i	0.998089	−	0.0617856i	$-0.0196795\pi$
$661$	11.4547	+	19.8401i	0.445537	+	0.771692i	−0.552553	+	0.833478i	$0.686346\pi$
$662$	9.82124	+	17.0109i	0.381713	+	0.661147i
$663$		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
$668$	5.83619			0.225809
$669$		0			0
$670$	−54.7555			−2.11539
$671$	24.0144	−	41.5942i	0.927067	−	1.60573i
$672$		0			0
$673$	14.8675	+	25.7512i	0.573098	+	0.992636i	0.996245	+	0.0865746i	$0.0275921\pi$
$673$	14.8675	+	25.7512i	0.573098	+	0.992636i	−0.423147	+	0.906061i	$0.639075\pi$
$674$	5.57187	+	9.65076i	0.214620	+	0.371733i
$675$		0			0
$676$	−3.13301	+	5.42654i	−0.120500	+	0.208713i
$677$	−12.7480	+	22.0802i	−0.489946	+	0.848611i	−0.999933	−	0.0115711i	$-0.996317\pi$
$677$	−12.7480	+	22.0802i	−0.489946	+	0.848611i	0.509987	+	0.860182i	$0.329650\pi$
$678$		0			0
$679$	−13.4271	+	2.08479i	−0.515286	+	0.0800070i
$680$	−11.5076	+	19.9317i	−0.441295	+	0.764345i
$681$		0			0
$682$	19.9093			0.762367
$683$	−5.69293	+	9.86044i	−0.217834	+	0.377299i	−0.954145	−	0.299343i	$-0.903232\pi$
$683$	−5.69293	+	9.86044i	−0.217834	+	0.377299i	0.736312	+	0.676643i	$0.236566\pi$
$684$		0			0
$685$	6.11212			0.233532
$686$	−1.73911	+	28.2487i	−0.0663997	+	1.07854i
$687$		0			0
$688$	41.9047			1.59760
$689$	−39.7811	−	68.9029i	−1.51554	−	2.62499i
$690$		0			0
$691$	16.1261	−	27.9313i	0.613468	−	1.06256i	−0.377184	−	0.926138i	$-0.623107\pi$
$691$	16.1261	−	27.9313i	0.613468	−	1.06256i	0.990651	−	0.136419i	$-0.0435592\pi$
$692$	−7.22539			−0.274668
$693$		0			0
$694$	−26.8024			−1.01741
$695$	−30.3031	+	52.4865i	−1.14946	+	1.99093i
$696$		0			0
$697$	−5.04653	−	8.74085i	−0.191151	−	0.331083i
$698$	−32.1162			−1.21561
$699$		0			0
$700$	−2.61442	+	0.405935i	−0.0988160	+	0.0153429i
$701$	15.6291			0.590302			0.295151	−	0.955451i	$-0.404630\pi$
$701$	15.6291			0.590302			0.295151	+	0.955451i	$0.404630\pi$
$702$		0			0
$703$	8.77591	−	15.2003i	0.330990	−	0.573291i
$704$	−22.7200			−0.856292
$705$		0			0
$706$	3.86123	−	6.68785i	0.145319	−	0.251700i
$707$	−2.41253	+	6.22817i	−0.0907327	+	0.234234i
$708$		0			0
$709$	5.90824	−	10.2334i	0.221888	−	0.384322i	−0.733493	−	0.679697i	$-0.762111\pi$
$709$	5.90824	−	10.2334i	0.221888	−	0.384322i	0.955381	+	0.295375i	$0.0954446\pi$
$710$	−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
$716$	1.89701			0.0708946
$717$		0			0
$718$	22.1221			0.825588
$719$	25.3616	+	43.9276i	0.945830	+	1.63822i	0.754082	+	0.656781i	$0.228082\pi$
$719$	25.3616	+	43.9276i	0.945830	+	1.63822i	0.191748	+	0.981444i	$0.438584\pi$
$720$		0			0
$721$	9.40985	−	24.2923i	0.350441	−	0.904694i
$722$	−1.85518	−	3.21326i	−0.0690426	−	0.119585i
$723$		0			0
$724$	−0.188497	−	0.326486i	−0.00700543	−	0.0121338i
$725$	6.45088	+	11.1733i	0.239580	+	0.414964i
$726$		0			0
$727$	−1.13301	−	1.96243i	−0.0420211	−	0.0727827i	0.844250	−	0.535950i	$-0.180046\pi$
$727$	−1.13301	−	1.96243i	−0.0420211	−	0.0727827i	−0.886271	+	0.463167i	$0.846713\pi$
$728$	−23.7534	−	29.5161i	−0.880358	−	1.09394i
$729$		0			0
$730$	−6.32328	−	10.9522i	−0.234035	−	0.405361i
$731$	29.4386			1.08883
$732$		0			0
$733$	−33.6524			−1.24298			−0.621490	−	0.783422i	$-0.713472\pi$
$733$	−33.6524			−1.24298			−0.621490	+	0.783422i	$0.713472\pi$
$734$	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	$0.284084\pi$
$740$	−2.04234	+	3.53744i	−0.0750780	+	0.130039i
$741$		0			0
$742$	−56.4701	+	8.76797i	−2.07308	+	0.321882i
$743$	−24.4195	+	42.2958i	−0.895865	+	1.55168i	−0.0631343	+	0.998005i	$0.520110\pi$
$743$	−24.4195	+	42.2958i	−0.895865	+	1.55168i	−0.832731	+	0.553678i	$0.813224\pi$
$744$		0			0
$745$	−31.3528			−1.14868
$746$	5.97599	−	10.3507i	0.218796	−	0.378967i
$747$		0			0
$748$	3.90546			0.142798
$749$	7.06553	−	1.09705i	0.258169	−	0.0400852i
$750$		0			0
$751$	15.8254			0.577476			0.288738	−	0.957408i	$-0.406764\pi$
$751$	15.8254			0.577476			0.288738	+	0.957408i	$0.406764\pi$
$752$	−11.0455	−	19.1314i	−0.402788	−	0.697650i
$753$		0			0
$754$	18.6077	−	32.2295i	0.677653	−	1.17373i
$755$	−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	$0.512656\pi$
$758$	8.87084	−	15.3647i	0.322203	−	0.558073i
$759$		0			0
$760$	14.6293	+	25.3386i	0.530660	+	0.919129i
$761$	−27.7562			−1.00616			−0.503081	−	0.864240i	$-0.667800\pi$
$761$	−27.7562			−1.00616			−0.503081	+	0.864240i	$0.667800\pi$
$762$		0			0
$763$	−15.0242	−	18.6692i	−0.543912	−	0.675869i
$764$	1.32084			0.0477861
$765$		0			0
$766$	19.1606	−	33.1871i	0.692300	−	1.19910i
$767$	8.44912			0.305080
$768$		0			0
$769$	−5.01030	+	8.67810i	−0.180676	+	0.312940i	−0.942111	−	0.335301i	$-0.891162\pi$
$769$	−5.01030	+	8.67810i	−0.180676	+	0.312940i	0.761435	+	0.648242i	$0.224495\pi$
$770$	−26.0483	−	32.3679i	−0.938717	−	1.16646i
$771$		0			0
$772$	−3.03245	+	5.25236i	−0.109140	+	0.189037i
$773$	21.7596	−	37.6887i	0.782639	−	1.35557i	−0.147761	−	0.989023i	$-0.547207\pi$
$773$	21.7596	−	37.6887i	0.782639	−	1.35557i	0.930400	−	0.366547i	$-0.119460\pi$
$774$		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
$779$	−12.8311			−0.459720
$780$		0			0
$781$	−10.5991			−0.379267
$782$	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
$787$	2.91819	+	5.05445i	0.104022	+	0.180172i	0.913338	−	0.407202i	$-0.133495\pi$
$787$	2.91819	+	5.05445i	0.104022	+	0.180172i	−0.809316	+	0.587373i	$0.800162\pi$
$788$	−4.27271	−	7.40055i	−0.152209	−	0.263634i
$789$		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
$794$	30.1408			1.06966
$795$		0			0
$796$	4.23482			0.150099
$797$	−18.2900	+	31.6792i	−0.647865	+	1.12214i	0.335766	+	0.941945i	$0.391005\pi$
$797$	−18.2900	+	31.6792i	−0.647865	+	1.12214i	−0.983632	+	0.180191i	$0.942329\pi$
$798$		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
$803$	5.32683	−	9.22634i	0.187980	−	0.325590i
$804$		0			0
$805$	12.6986	−	32.7826i	0.447568	−	1.15544i
$806$	−15.4065	+	26.6848i	−0.542670	+	0.939931i
$807$		0			0
$808$	−6.42203			−0.225926
$809$	11.0249	−	19.0957i	0.387616	−	0.671370i	−0.604513	−	0.796596i	$-0.706632\pi$
$809$	11.0249	−	19.0957i	0.387616	−	0.671370i	0.992128	+	0.125225i	$0.0399654\pi$
$810$		0			0
$811$	−12.6451			−0.444029			−0.222015	−	0.975043i	$-0.571263\pi$
$811$	−12.6451			−0.444029			−0.222015	+	0.975043i	$0.571263\pi$
$812$	−2.40635	−	2.99015i	−0.0844464	−	0.104934i
$813$		0			0
$814$	−23.9645			−0.839956
$815$	−13.2540	−	22.9566i	−0.464267	−	0.804134i
$816$		0			0
$817$	18.7123	−	32.4107i	0.654660	−	1.13391i
$818$	17.6900			0.618517
$819$		0			0
$820$	2.98606			0.104278
$821$	15.5479	−	26.9298i	0.542625	−	0.939855i	−0.456127	−	0.889915i	$-0.650764\pi$
$821$	15.5479	−	26.9298i	0.542625	−	0.939855i	0.998752	−	0.0499401i	$-0.0159030\pi$
$822$		0			0
$823$	24.4819	+	42.4039i	0.853385	+	1.47811i	0.878135	+	0.478412i	$0.158788\pi$
$823$	24.4819	+	42.4039i	0.853385	+	1.47811i	−0.0247505	+	0.999694i	$0.507879\pi$
$824$	25.0485			0.872606
$825$		0			0
$826$	2.19206	−	5.65899i	0.0762715	−	0.196901i
$827$	−36.3827			−1.26515			−0.632575	−	0.774499i	$-0.718002\pi$
$827$	−36.3827			−1.26515			−0.632575	+	0.774499i	$0.718002\pi$
$828$		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	$0.874496\pi$
$830$	−34.7502			−1.20620
$831$		0			0
$832$	17.5814	−	30.4520i	0.609527	−	1.05573i
$833$	−21.3601	+	6.79690i	−0.740082	+	0.235499i
$834$		0			0
$835$	24.5866	−	42.5852i	0.850853	−	1.47372i
$836$	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	$-0.0213688\pi$
$839$	12.7674	+	22.1138i	0.440779	+	0.763452i	−0.556968	+	0.830534i	$0.688035\pi$
$840$		0			0
$841$	5.14175	−	8.90578i	0.177302	−	0.307096i
$842$	15.6200			0.538299
$843$		0			0
$844$	0.775117			0.0266806
$845$	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
$850$	−7.29674	−	12.6383i	−0.250276	−	0.433491i
$851$	−10.1390	−	17.5613i	−0.347561	−	0.601993i
$852$		0			0
$853$	0.923367	+	1.59932i	0.0316155	+	0.0547596i	0.881400	−	0.472370i	$-0.156601\pi$
$853$	0.923367	+	1.59932i	0.0316155	+	0.0547596i	−0.849785	+	0.527130i	$0.823268\pi$
$854$	52.7583	−	8.19164i	1.80535	−	0.280312i
$855$		0			0
$856$	3.43749	+	5.95391i	0.117491	+	0.203501i
$857$	−22.4848			−0.768066			−0.384033	−	0.923319i	$-0.625465\pi$
$857$	−22.4848			−0.768066			−0.384033	+	0.923319i	$0.625465\pi$
$858$		0			0
$859$	−1.14761			−0.0391561			−0.0195781	−	0.999808i	$-0.506232\pi$
$859$	−1.14761			−0.0391561			−0.0195781	+	0.999808i	$0.506232\pi$
$860$	−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	0.850343	−	0.526229i	$-0.176394\pi$
$863$	−0.897635	−	1.55475i	−0.0305558	−	0.0529243i	−0.880899	+	0.473304i	$0.843061\pi$
$864$		0			0
$865$	−30.4390	+	52.7218i	−1.03496	+	1.79260i
$866$	−22.3646	+	38.7366i	−0.759980	+	1.31632i
$867$		0			0
$868$	1.99237	+	2.47573i	0.0676253	+	0.0840317i
$869$	1.62494	−	2.81449i	0.0551225	−	0.0954749i
$870$		0			0
$871$	71.3889			2.41892
$872$	11.5207	−	19.9545i	0.390141	−	0.675745i
$873$		0			0
$874$	29.2585			0.989685
$875$	5.44808	−	14.0647i	0.184179	−	0.475474i
$876$		0			0
$877$	8.57997			0.289725			0.144862	−	0.989452i	$-0.453726\pi$
$877$	8.57997			0.289725			0.144862	+	0.989452i	$0.453726\pi$
$878$	−3.32016	−	5.75069i	−0.112050	−	0.194076i
$879$		0			0
$880$	23.4200	−	40.5646i	0.789487	−	1.36743i
$881$	−16.5346			−0.557066			−0.278533	−	0.960427i	$-0.589848\pi$
$881$	−16.5346			−0.557066			−0.278533	+	0.960427i	$0.589848\pi$
$882$		0			0
$883$	−27.4948			−0.925273			−0.462636	−	0.886548i	$-0.653096\pi$
$883$	−27.4948			−0.925273			−0.462636	+	0.886548i	$0.653096\pi$
$884$	−3.02217	+	5.23455i	−0.101647	+	0.176057i
$885$		0			0
$886$	−15.7053	−	27.2025i	−0.527631	−	0.913885i
$887$	−43.4419			−1.45864			−0.729318	−	0.684175i	$-0.760163\pi$
$887$	−43.4419			−1.45864			−0.729318	+	0.684175i	$0.760163\pi$
$888$		0			0
$889$	−15.0588	+	38.8755i	−0.505055	+	1.30384i
$890$	−24.4254			−0.818741
$891$		0			0
$892$	−1.55919	+	2.70059i	−0.0522054	+	0.0904225i
$893$	−19.7292			−0.660213
$894$		0			0
$895$	7.99168	−	13.8420i	0.267132	−	0.462687i
$896$	−22.0645	−	27.4175i	−0.737123	−	0.915954i
$897$		0			0
$898$	−9.52968	+	16.5059i	−0.318010	+	0.550809i
$899$	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
$905$	−3.17638			−0.105586
$906$		0			0
$907$	11.2952			0.375052			0.187526	−	0.982260i	$-0.439953\pi$
$907$	11.2952			0.375052			0.187526	+	0.982260i	$0.439953\pi$
$908$	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	$-0.219822\pi$
$911$	−5.01690	−	8.68953i	−0.166217	−	0.287897i	−0.937087	+	0.349096i	$0.886489\pi$
$912$		0			0
$913$	−14.6370	−	25.3521i	−0.484415	−	0.839032i
$914$	−23.6369	−	40.9403i	−0.781839	−	1.35418i
$915$		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	$0.831454\pi$
$920$	33.8031			1.11445
$921$		0			0
$922$	−12.2603			−0.403770
$923$	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
$929$	−16.7632	+	29.0347i	−0.549983	+	0.952599i	0.448292	+	0.893887i	$0.352033\pi$
$929$	−16.7632	+	29.0347i	−0.549983	+	0.952599i	−0.998275	+	0.0587116i	$0.981301\pi$
$930$		0			0
$931$	−6.09417	+	27.8369i	−0.199728	+	0.912316i
$932$	−3.54630	+	6.14236i	−0.116163	+	0.201200i
$933$		0			0
$934$	−1.46827			−0.0480432
$935$	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	$0.432543\pi$
$938$	18.5213	−	47.8143i	0.604742	−	1.56119i
$939$		0			0
$940$	4.59141			0.149755
$941$	16.0492	+	27.7980i	0.523189	+	0.906190i	0.999636	+	0.0269868i	$0.00859120\pi$
$941$	16.0492	+	27.7980i	0.523189	+	0.906190i	−0.476447	+	0.879203i	$0.658075\pi$
$942$		0			0
$943$	−7.41201	+	12.8380i	−0.241368	+	0.418062i
$944$	6.84176			0.222680
$945$		0			0
$946$	−51.0980			−1.66134
$947$	8.39928	−	14.5480i	0.272940	−	0.472746i	−0.696673	−	0.717389i	$-0.745337\pi$
$947$	8.39928	−	14.5480i	0.272940	−	0.472746i	0.969613	+	0.244642i	$0.0786706\pi$
$948$		0			0
$949$	8.24414	+	14.2793i	0.267616	+	0.463524i
$950$	−18.5523			−0.601917
$951$		0			0
$952$	−13.5125	−	16.7908i	−0.437943	−	0.544192i
$953$	2.69574			0.0873237			0.0436619	−	0.999046i	$-0.486098\pi$
$953$	2.69574			0.0873237			0.0436619	+	0.999046i	$0.486098\pi$
$954$		0			0
$955$	5.56438	−	9.63780i	0.180059	−	0.311872i
$956$	−8.08633			−0.261531
$957$		0			0
$958$	18.4367	−	31.9333i	0.595663	−	1.03172i
$959$	−2.06745	+	5.33731i	−0.0667615	+	0.172351i
$960$		0			0
$961$	9.08474	−	15.7352i	0.293056	−	0.507588i
$962$	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	−0.954783	−	0.297304i	$-0.903913\pi$
$967$	−6.83873	+	11.8450i	−0.219919	+	0.380910i	0.734864	+	0.678214i	$0.237246\pi$
$968$	5.67002			0.182241
$969$		0			0
$970$	22.1739			0.711960
$971$	21.3133	+	36.9157i	0.683977	+	1.18468i	0.973757	+	0.227589i	$0.0730843\pi$
$971$	21.3133	+	36.9157i	0.683977	+	1.18468i	−0.289781	+	0.957093i	$0.593582\pi$
$972$		0			0
$973$	−35.5828	−	44.2155i	−1.14073	−	1.41748i
$974$	11.3077	+	19.5854i	0.362321	+	0.627558i
$975$		0			0
$976$	30.0957	+	52.1273i	0.963341	+	1.66856i
$977$	2.52841	+	4.37934i	0.0808911	+	0.140108i	0.903633	−	0.428308i	$-0.140890\pi$
$977$	2.52841	+	4.37934i	0.0808911	+	0.140108i	−0.822742	+	0.568415i	$0.807557\pi$
$978$		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
$983$	−33.2884			−1.06174			−0.530868	−	0.847455i	$-0.678134\pi$
$983$	−33.2884			−1.06174			−0.530868	+	0.847455i	$0.678134\pi$
$984$		0			0
$985$	−71.9999			−2.29411
$986$	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	$0.996440\pi$
$992$	−3.36329	+	5.82539i	−0.106785	+	0.184956i
$993$		0			0
$994$	−7.38698	−	9.17912i	−0.234301	−	0.291144i
$995$	17.8403	−	30.9004i	0.565577	−	0.979608i
$996$		0			0
$997$	−43.2566			−1.36995			−0.684975	−	0.728567i	$-0.740187\pi$
$997$	−43.2566			−1.36995			−0.684975	+	0.728567i	$0.740187\pi$
$998$	−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.g.l.109.7		16
3.2	odd	2	inner	567.2.g.l.109.2		16
7.2	even	3		567.2.h.l.352.2		16
9.2	odd	6		567.2.h.l.298.7		16
9.4	even	3		567.2.e.g.487.7	yes	16
9.5	odd	6		567.2.e.g.487.2	yes	16
9.7	even	3		567.2.h.l.298.2		16
21.2	odd	6		567.2.h.l.352.7		16
63.2	odd	6	inner	567.2.g.l.541.2		16
63.4	even	3		3969.2.a.bg.1.2		8
63.16	even	3	inner	567.2.g.l.541.7		16
63.23	odd	6		567.2.e.g.163.2	✓	16
63.31	odd	6		3969.2.a.bf.1.2		8
63.32	odd	6		3969.2.a.bg.1.7		8
63.58	even	3		567.2.e.g.163.7	yes	16
63.59	even	6		3969.2.a.bf.1.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
567.2.e.g.163.2	✓	16	63.23	odd	6
567.2.e.g.163.7	yes	16	63.58	even	3
567.2.e.g.487.2	yes	16	9.5	odd	6
567.2.e.g.487.7	yes	16	9.4	even	3
567.2.g.l.109.2		16	3.2	odd	2	inner
567.2.g.l.109.7		16	1.1	even	1	trivial
567.2.g.l.541.2		16	63.2	odd	6	inner
567.2.g.l.541.7		16	63.16	even	3	inner
567.2.h.l.298.2		16	9.7	even	3
567.2.h.l.298.7		16	9.2	odd	6
567.2.h.l.352.2		16	7.2	even	3
567.2.h.l.352.7		16	21.2	odd	6
3969.2.a.bf.1.2		8	63.31	odd	6
3969.2.a.bf.1.7		8	63.59	even	6
3969.2.a.bg.1.2		8	63.4	even	3
3969.2.a.bg.1.7		8	63.32	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.g (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.764088 - 1.32344i) q^{2} +(-0.167661 - 0.290398i) q^{4} -2.82528 q^{5} +(0.955663 - 2.46713i) q^{7} +2.54392 q^{8} +O(q^{10})\)	\(q+(0.764088 - 1.32344i) q^{2} +(-0.167661 - 0.290398i) q^{4} -2.82528 q^{5} +(0.955663 - 2.46713i) q^{7} +2.54392 q^{8} +(-2.15876 + 3.73909i) q^{10} -3.63715 q^{11} +(2.81454 - 4.87493i) q^{13} +(-2.53488 - 3.14986i) q^{14} +(2.27910 - 3.94752i) q^{16} +(1.60110 - 2.77319i) q^{17} +(-2.03544 - 3.52548i) q^{19} +(0.473690 + 0.820455i) q^{20} +(-2.77910 + 4.81355i) q^{22} -4.70318 q^{23} +2.98220 q^{25} +(-4.30111 - 7.44975i) q^{26} +(-0.876676 + 0.136119i) q^{28} +(2.16313 + 3.74665i) q^{29} +(-1.79099 - 3.10208i) q^{31} +(-0.938949 - 1.62631i) q^{32} +(-2.44676 - 4.23792i) q^{34} +(-2.70001 + 6.97032i) q^{35} +(2.15578 + 3.73392i) q^{37} -6.22102 q^{38} -7.18728 q^{40} +(1.57596 - 2.72964i) q^{41} +(4.59663 + 7.96159i) q^{43} +(0.609809 + 1.05622i) q^{44} +(-3.59364 + 6.22437i) q^{46} +(2.42321 - 4.19713i) q^{47} +(-5.17342 - 4.71548i) q^{49} +(2.27866 - 3.94676i) q^{50} -1.88756 q^{52} +(7.06707 - 12.2405i) q^{53} +10.2760 q^{55} +(2.43113 - 6.27617i) q^{56} +6.61128 q^{58} +(0.750489 + 1.29988i) q^{59} +(-6.60254 + 11.4359i) q^{61} -5.47388 q^{62} +6.24665 q^{64} +(-7.95186 + 13.7730i) q^{65} +(6.34108 + 10.9831i) q^{67} -1.07377 q^{68} +(7.16175 + 8.89924i) q^{70} +2.91413 q^{71} +(-1.46456 + 2.53670i) q^{73} +6.58882 q^{74} +(-0.682529 + 1.18217i) q^{76} +(-3.47589 + 8.97330i) q^{77} +(-0.446763 + 0.773817i) q^{79} +(-6.43910 + 11.1528i) q^{80} +(-2.40834 - 4.17137i) q^{82} +(4.02432 + 6.97032i) q^{83} +(-4.52356 + 7.83503i) q^{85} +14.0489 q^{86} -9.25262 q^{88} +(2.82863 + 4.89934i) q^{89} +(-9.33731 - 11.6026i) q^{91} +(0.788541 + 1.36579i) q^{92} +(-3.70310 - 6.41396i) q^{94} +(5.75068 + 9.96047i) q^{95} +(-2.56789 - 4.44772i) q^{97} +(-10.1936 + 3.24366i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{4}+O(q^{10}) \) 16 * q - 6 * q^4	\( 16 q - 6 q^{4} - 14 q^{10} - 6 q^{13} - 6 q^{16} - 24 q^{19} - 2 q^{22} - 26 q^{28} - 20 q^{31} + 4 q^{37} + 72 q^{40} - 10 q^{43} + 36 q^{46} + 4 q^{49} + 68 q^{52} + 8 q^{55} - 44 q^{58} - 36 q^{61} + 76 q^{64} + 18 q^{67} + 104 q^{70} - 32 q^{73} - 58 q^{76} + 32 q^{79} + 2 q^{82} - 30 q^{85} - 144 q^{88} - 22 q^{91} - 54 q^{94} - 14 q^{97}+O(q^{100}) \) 16 * q - 6 * q^4 - 14 * q^10 - 6 * q^13 - 6 * q^16 - 24 * q^19 - 2 * q^22 - 26 * q^28 - 20 * q^31 + 4 * q^37 + 72 * q^40 - 10 * q^43 + 36 * q^46 + 4 * q^49 + 68 * q^52 + 8 * q^55 - 44 * q^58 - 36 * q^61 + 76 * q^64 + 18 * q^67 + 104 * q^70 - 32 * q^73 - 58 * q^76 + 32 * q^79 + 2 * q^82 - 30 * q^85 - 144 * q^88 - 22 * q^91 - 54 * q^94 - 14 * q^97

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