LMFDB - Embedded newform 567.2.g.l.109.2

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			109.2
Root			$-1.41264 + 0.0667052i$ of defining polynomial
Character	$\chi$	$=$	567.109
Dual form			567.2.g.l.541.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

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	$0.348353\pi$
$2$	−0.764088	+	1.32344i	−0.540292	+	0.935813i	−0.998887	+	0.0471677i	$0.984980\pi$
$3$		0			0
$3$		0			0
$4$	−0.167661	−	0.290398i	−0.0838307	−	0.145199i
$5$	2.82528			1.26350			0.631752	−	0.775171i	$-0.282336\pi$
$5$	2.82528			1.26350			0.631752	+	0.775171i	$0.282336\pi$
$6$		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	$-0.315267\pi$
$11$	3.63715			1.09664			0.548321	+	0.836268i	$0.315267\pi$
$12$		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	−0.992224	−	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
$23$	4.70318			0.980680			0.490340	−	0.871531i	$-0.336873\pi$
$23$	4.70318			0.980680			0.490340	+	0.871531i	$0.336873\pi$
$24$		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	0.592246	−	0.805757i	$-0.298241\pi$
$29$	−2.16313	−	3.74665i	−0.401683	−	0.695735i	−0.993929	+	0.110022i	$0.964908\pi$
$30$		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	−0.962447	−	0.271470i	$-0.912490\pi$
$41$	−1.57596	+	2.72964i	−0.246123	+	0.426298i	0.716324	+	0.697768i	$0.245823\pi$
$42$		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	−0.986854	−	0.161617i	$-0.948329\pi$
$47$	−2.42321	+	4.19713i	−0.353462	+	0.612215i	0.633391	+	0.773832i	$0.281662\pi$
$48$		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	$0.589471\pi$
$53$	−7.06707	+	12.2405i	−0.970736	+	1.68136i	−0.693342	+	0.720609i	$0.743862\pi$
$54$		0			0
$55$	10.2760			1.38561
$56$	−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	0.813029	−	0.582223i	$-0.197817\pi$
$59$	−0.750489	−	1.29988i	−0.0977053	−	0.169231i	−0.910734	+	0.412992i	$0.864484\pi$
$60$		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	$-0.555321\pi$
$71$	−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	$0.221500\pi$
$74$	−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	0.556092	−	0.831121i	$-0.312300\pi$
$83$	−4.02432	−	6.97032i	−0.441726	−	0.765092i	−0.997818	+	0.0660291i	$0.978967\pi$
$84$		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	0.676263	−	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
$94$	−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	$-0.459915\pi$
$101$	2.52446			0.251193			0.125597	+	0.992081i	$0.459915\pi$
$102$		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	0.793289	−	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	$0.0238483\pi$
$110$	−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	−0.876772	−	0.480907i	$-0.840308\pi$
$113$	−0.232888	+	0.403374i	−0.0219082	+	0.0379462i	0.854863	+	0.518853i	$0.173641\pi$
$114$		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	$-0.321935\pi$
$131$	12.1479			1.06137			0.530685	+	0.847569i	$0.321935\pi$
$132$		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	$-0.470541\pi$
$137$	2.16337			0.184829			0.0924146	+	0.995721i	$0.470541\pi$
$138$		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	$-0.650204\pi$
$149$	−11.0972			−0.909121			−0.454561	+	0.890716i	$0.650204\pi$
$150$		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	$-0.598163\pi$
$167$	8.70235	−	15.0729i	0.673408	−	1.16638i	0.976931	−	0.213553i	$-0.0685036\pi$
$168$		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	$0.472202\pi$
$173$	−10.7738	+	18.6607i	−0.819116	+	1.41875i	−0.906334	+	0.422561i	$0.861131\pi$
$174$		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	−0.740738	−	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	$0.486696\pi$
$182$	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	−0.785932	−	0.618312i	$-0.787817\pi$
$191$	1.96950	−	3.41127i	0.142508	−	0.246831i	0.928440	+	0.371481i	$0.121150\pi$
$192$		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	$-0.862266\pi$
$197$	−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	$0.314397\pi$
$200$	−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	$-0.479618\pi$
$227$	1.92818			0.127978			0.0639890	+	0.997951i	$0.479618\pi$
$228$		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	$0.0769749\pi$
$233$	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
$236$	−0.251656	+	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	$0.451416\pi$
$239$	−12.0575	+	20.8843i	−0.779937	+	1.35089i	−0.931978	+	0.362516i	$0.881918\pi$
$240$		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	$-0.300565\pi$
$251$	18.5790			1.17270			0.586349	+	0.810058i	$0.300565\pi$
$252$		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	$-0.603261\pi$
$257$	−10.2197			−0.637490			−0.318745	+	0.947841i	$0.603261\pi$
$258$		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	$-0.409092\pi$
$263$	9.13775			0.563458			0.281729	+	0.959494i	$0.409092\pi$
$264$		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	$-0.587066\pi$
$269$	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
$275$	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	0.516552	−	0.856256i	$-0.327215\pi$
$281$	−8.10097	−	14.0313i	−0.483263	−	0.837037i	−0.999815	+	0.0192190i	$0.993882\pi$
$282$		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	−0.531285	−	0.847193i	$-0.678291\pi$
$293$	8.01170	−	13.8767i	0.468049	−	0.810684i	0.999333	+	0.0365093i	$0.0116239\pi$
$294$		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	$0.00830382\pi$
$311$	9.21297	+	15.9573i	0.522420	+	0.904857i	−0.477240	+	0.878773i	$0.658363\pi$
$312$		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	−0.974824	−	0.222974i	$-0.928424\pi$
$317$	−5.24006	+	9.07606i	−0.294311	+	0.509762i	0.680513	+	0.732736i	$0.261757\pi$
$318$		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	0.999441	−	0.0334327i	$-0.0106439\pi$
$347$	8.76942	+	15.1891i	0.470767	+	0.815392i	−0.528674	+	0.848825i	$0.677311\pi$
$348$		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	$-0.542937\pi$
$353$	−5.05338			−0.268965			−0.134482	+	0.990916i	$0.542937\pi$
$354$		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	0.609339	−	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
$362$	−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	$-0.721344\pi$
$383$	−25.0764			−1.28134			−0.640672	+	0.767814i	$0.721344\pi$
$384$		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	$-0.703138\pi$
$389$	−23.4993			−1.19146			−0.595732	+	0.803184i	$0.703138\pi$
$390$		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	$-0.616897\pi$
$401$	−14.3797			−0.718086			−0.359043	+	0.933321i	$0.616897\pi$
$402$		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	$-0.518970\pi$
$419$	17.0860	−	29.5939i	0.834708	−	1.44576i	0.894268	−	0.447532i	$-0.147697\pi$
$420$		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	−0.866940	−	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	$0.748293\pi$
$434$	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	−0.999909	−	0.0134764i	$-0.995710\pi$
$443$	−10.2772	+	17.8006i	−0.488284	+	0.845732i	0.511625	+	0.859209i	$0.329044\pi$
$444$		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	$-0.404915\pi$
$449$	12.4720			0.588588			0.294294	+	0.955715i	$0.404915\pi$
$450$		0			0
$451$	−5.73199	+	9.92810i	−0.269909	+	0.467496i
$452$	0.156185			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	0.944192	−	0.329397i	$-0.106845\pi$
$461$	4.01141	+	6.94796i	0.186830	+	0.323599i	−0.757362	+	0.652995i	$0.773512\pi$
$462$		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	0.876926	−	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
$472$	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	$-0.685846\pi$
$479$	−24.1290			−1.10248			−0.551242	+	0.834346i	$0.685846\pi$
$480$		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	−0.786097	−	0.618103i	$-0.787902\pi$
$491$	3.15192	−	5.45928i	0.142244	−	0.246374i	0.928341	+	0.371729i	$0.121235\pi$
$492$		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	$-0.210340\pi$
$503$	35.4133			1.57900			0.789500	+	0.613750i	$0.210340\pi$
$504$		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	$-0.755863\pi$
$509$	−32.4883			−1.44002			−0.720010	+	0.693964i	$0.755863\pi$
$510$		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	$0.423664\pi$
$521$	−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
$527$	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	$-0.520250\pi$
$557$	19.6474	−	34.0302i	0.832486	−	1.44191i	0.896061	−	0.443931i	$-0.146416\pi$
$558$		0			0
$559$	51.7496			2.18877
$560$	−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	$-0.907518\pi$
$563$	−17.2532	−	29.8834i	−0.727134	−	1.25943i	0.230955	−	0.972964i	$-0.425815\pi$
$564$		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	−0.817627	−	0.575748i	$-0.804711\pi$
$569$	2.14203	−	3.71010i	0.0897985	−	0.155536i	0.907426	+	0.420212i	$0.138044\pi$
$570$		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	0.968443	−	0.249234i	$-0.0801789\pi$
$587$	6.50229	+	11.2623i	0.268378	+	0.464845i	−0.700065	+	0.714079i	$0.746846\pi$
$588$		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	$0.0301600\pi$
$593$	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
$598$	20.2289	+	35.0375i	0.827221	+	1.43279i
$599$	−2.49768	−	4.32611i	−0.102052	−	0.176760i	0.810478	−	0.585769i	$-0.199208\pi$
$599$	−2.49768	−	4.32611i	−0.102052	−	0.176760i	−0.912530	+	0.409010i	$0.865874\pi$
$600$		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	−0.999660	−	0.0260905i	$-0.991694\pi$
$617$	−11.8543	+	20.5322i	−0.477235	+	0.826595i	0.522425	+	0.852685i	$0.325028\pi$
$618$		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	$-0.565109\pi$
$641$	−10.2854			−0.406248			−0.203124	+	0.979153i	$0.565109\pi$
$642$		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	−0.766692	−	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
$653$	−1.77459			−0.0694453			−0.0347226	−	0.999397i	$-0.511055\pi$
$653$	−1.77459			−0.0694453			−0.0347226	+	0.999397i	$0.511055\pi$
$654$		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	0.887947	−	0.459946i	$-0.152131\pi$
$659$	1.17184	+	2.02968i	0.0456483	+	0.0790652i	−0.842298	+	0.539011i	$0.818798\pi$
$660$		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	−0.509987	−	0.860182i	$-0.670350\pi$
$677$	12.7480	−	22.0802i	0.489946	−	0.848611i	0.999933	+	0.0115711i	$0.00368327\pi$
$678$		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	−0.736312	−	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
$686$	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	$-0.595370\pi$
$701$	−15.6291			−0.590302			−0.295151	+	0.955451i	$0.595370\pi$
$702$		0			0
$703$	8.77591	−	15.2003i	0.330990	−	0.573291i
$704$	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	$-0.771918\pi$
$719$	−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
$724$	−0.188497	−	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	$-0.479890\pi$
$743$	24.4195	−	42.2958i	0.895865	−	1.55168i	0.832731	−	0.553678i	$-0.186776\pi$
$744$		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	$-0.332200\pi$
$761$	27.7562			1.00616			0.503081	+	0.864240i	$0.332200\pi$
$762$		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	$0.452793\pi$
$773$	−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
$779$	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	$-0.608995\pi$
$797$	18.2900	−	31.6792i	0.647865	−	1.12214i	0.983632	−	0.180191i	$-0.0576714\pi$
$798$		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	−0.992128	−	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	$0.571263\pi$
$812$	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	$0.349236\pi$
$821$	−15.5479	+	26.9298i	−0.542625	+	0.939855i	−0.998752	+	0.0499401i	$0.984097\pi$
$822$		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	$-0.281998\pi$
$827$	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	$0.874496\pi$
$830$	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	0.556968	−	0.830534i	$-0.311965\pi$
$839$	−12.7674	−	22.1138i	−0.440779	−	0.763452i	−0.997747	+	0.0670815i	$0.978631\pi$
$840$		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	$-0.374535\pi$
$857$	22.4848			0.768066			0.384033	+	0.923319i	$0.374535\pi$
$858$		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	0.880899	−	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
$866$	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	$-0.410152\pi$
$881$	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	$0.653096\pi$
$884$	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	$-0.239837\pi$
$887$	43.4419			1.45864			0.729318	+	0.684175i	$0.239837\pi$
$888$		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	0.937087	−	0.349096i	$-0.113511\pi$
$911$	5.01690	+	8.68953i	0.166217	+	0.287897i	−0.770870	+	0.636993i	$0.780178\pi$
$912$		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	$-0.647967\pi$
$929$	16.7632	−	29.0347i	0.549983	−	0.952599i	0.998275	−	0.0587116i	$-0.0186992\pi$
$930$		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	$-0.991409\pi$
$941$	−16.0492	−	27.7980i	−0.523189	−	0.906190i	0.476447	−	0.879203i	$-0.341925\pi$
$942$		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	−0.969613	−	0.244642i	$-0.921329\pi$
$947$	−8.39928	+	14.5480i	−0.272940	+	0.472746i	0.696673	+	0.717389i	$0.254663\pi$
$948$		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	$-0.513902\pi$
$953$	−2.69574			−0.0873237			−0.0436619	+	0.999046i	$0.513902\pi$
$954$		0			0
$955$	5.56438	−	9.63780i	0.180059	−	0.311872i
$956$	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	$-0.926916\pi$
$971$	−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
$976$	30.0957	+	52.1273i	0.963341	+	1.66856i
$977$	−2.52841	−	4.37934i	−0.0808911	−	0.140108i	0.822742	−	0.568415i	$-0.192443\pi$
$977$	−2.52841	−	4.37934i	−0.0808911	−	0.140108i	−0.903633	+	0.428308i	$0.859110\pi$
$978$		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	$-0.321866\pi$
$983$	33.2884			1.06174			0.530868	+	0.847455i	$0.321866\pi$
$984$		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.109.2		16
3.2	odd	2	inner	567.2.g.l.109.7		16
7.2	even	3		567.2.h.l.352.7		16
9.2	odd	6		567.2.h.l.298.2		16
9.4	even	3		567.2.e.g.487.2	yes	16
9.5	odd	6		567.2.e.g.487.7	yes	16
9.7	even	3		567.2.h.l.298.7		16
21.2	odd	6		567.2.h.l.352.2		16
63.2	odd	6	inner	567.2.g.l.541.7		16
63.4	even	3		3969.2.a.bg.1.7		8
63.16	even	3	inner	567.2.g.l.541.2		16
63.23	odd	6		567.2.e.g.163.7	yes	16
63.31	odd	6		3969.2.a.bf.1.7		8
63.32	odd	6		3969.2.a.bg.1.2		8
63.58	even	3		567.2.e.g.163.2	✓	16
63.59	even	6		3969.2.a.bf.1.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
567.2.e.g.163.2	✓	16	63.58	even	3
567.2.e.g.163.7	yes	16	63.23	odd	6
567.2.e.g.487.2	yes	16	9.4	even	3
567.2.e.g.487.7	yes	16	9.5	odd	6
567.2.g.l.109.2		16	1.1	even	1	trivial
567.2.g.l.109.7		16	3.2	odd	2	inner
567.2.g.l.541.2		16	63.16	even	3	inner
567.2.g.l.541.7		16	63.2	odd	6	inner
567.2.h.l.298.2		16	9.2	odd	6
567.2.h.l.298.7		16	9.7	even	3
567.2.h.l.352.2		16	21.2	odd	6
567.2.h.l.352.7		16	7.2	even	3
3969.2.a.bf.1.2		8	63.59	even	6
3969.2.a.bf.1.7		8	63.31	odd	6
3969.2.a.bg.1.2		8	63.32	odd	6
3969.2.a.bg.1.7		8	63.4	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.g (of order \(3\), degree \(2\), not minimal)

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