LMFDB - Embedded newform 567.2.g.i.109.3

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:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.309123.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 $ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 189)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			109.3
Root			$0.500000 - 0.224437i$ of defining polynomial
Character	$\chi$	$=$	567.109
Dual form			567.2.g.i.541.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.34981 - 2.33795i) q^{2} +(-2.64400 - 4.57954i) q^{4} +1.58836 q^{5} +(1.40545 - 2.24159i) q^{7} -8.87636 q^{8} +(2.14400 - 3.71351i) q^{10} -0.300372 q^{11} +(-1.40545 + 2.43430i) q^{13} +(-3.34362 - 6.31159i) q^{14} +(-6.69344 + 11.5934i) q^{16} +(2.93818 - 5.08907i) q^{17} +(1.14400 + 1.98146i) q^{19} +(-4.19963 - 7.27397i) q^{20} +(-0.405446 + 0.702253i) q^{22} -1.88874 q^{23} -2.47710 q^{25} +(3.79418 + 6.57172i) q^{26} +(-13.9814 - 0.509538i) q^{28} +(1.26145 + 2.18490i) q^{29} +(2.40545 + 4.16635i) q^{31} +(9.19344 + 15.9235i) q^{32} +(-7.93199 - 13.7386i) q^{34} +(2.23236 - 3.56046i) q^{35} +(2.23855 + 3.87728i) q^{37} +6.17673 q^{38} -14.0989 q^{40} +(4.45489 - 7.71609i) q^{41} +(4.54944 + 7.87987i) q^{43} +(0.794182 + 1.37556i) q^{44} +(-2.54944 + 4.41576i) q^{46} +(-1.60507 + 2.78007i) q^{47} +(-3.04944 - 6.30087i) q^{49} +(-3.34362 + 5.79133i) q^{50} +14.8640 q^{52} +(1.00619 - 1.74277i) q^{53} -0.477100 q^{55} +(-12.4752 + 19.8971i) q^{56} +6.81089 q^{58} +(-2.44437 - 4.23377i) q^{59} +(-3.78799 + 6.56099i) q^{61} +12.9876 q^{62} +22.8640 q^{64} +(-2.23236 + 3.86656i) q^{65} +(-0.356004 - 0.616617i) q^{67} -31.0741 q^{68} +(-5.31089 - 10.0251i) q^{70} +12.8640 q^{71} +(5.83743 - 10.1107i) q^{73} +12.0865 q^{74} +(6.04944 - 10.4779i) q^{76} +(-0.422156 + 0.673310i) q^{77} +(-0.833104 + 1.44298i) q^{79} +(-10.6316 + 18.4145i) q^{80} +(-12.0265 - 20.8306i) q^{82} +(-2.71634 - 4.70484i) q^{83} +(4.66690 - 8.08330i) q^{85} +24.5636 q^{86} +2.66621 q^{88} +(-4.67673 - 8.10033i) q^{89} +(3.48143 + 6.57172i) q^{91} +(4.99381 + 8.64953i) q^{92} +(4.33310 + 7.50516i) q^{94} +(1.81708 + 3.14728i) q^{95} +(6.28799 + 10.8911i) q^{97} +(-18.8473 - 1.37556i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 2 q^{2} - 4 q^{4} - 2 q^{5} + 2 q^{7} - 18 q^{8} + q^{10} - 14 q^{11} - 2 q^{13} + 4 q^{14} - 10 q^{16} - 5 q^{19} - 13 q^{20} + 4 q^{22} - 12 q^{23} - 4 q^{25} + 17 q^{26} - 30 q^{28} + 13 q^{29}+ \cdots - 49 q^{98}+O(q^{100}) $ 6 * q + 2 * q^2 - 4 * q^4 - 2 * q^5 + 2 * q^7 - 18 * q^8 + q^10 - 14 * q^11 - 2 * q^13 + 4 * q^14 - 10 * q^16 - 5 * q^19 - 13 * q^20 + 4 * q^22 - 12 * q^23 - 4 * q^25 + 17 * q^26 - 30 * q^28 + 13 * q^29 + 8 * q^31 + 25 * q^32 - 12 * q^34 - 10 * q^35 + 8 * q^37 + 14 * q^38 - 48 * q^40 + 2 * q^41 + 9 * q^43 - q^44 + 3 * q^46 + 9 * q^47 + 4 * q^50 + 18 * q^52 + 24 * q^53 + 8 * q^55 - 3 * q^56 + 28 * q^58 - 15 * q^59 + q^61 + 42 * q^62 + 66 * q^64 + 10 * q^65 - 14 * q^67 - 78 * q^68 - 19 * q^70 + 6 * q^71 - 7 * q^73 + 18 * q^76 + 11 * q^77 - 6 * q^79 - 16 * q^80 - 43 * q^82 + 3 * q^83 + 27 * q^85 + 64 * q^86 + 18 * q^88 - 5 * q^89 - 33 * q^91 + 12 * q^92 + 27 * q^94 + 16 * q^95 + 14 * q^97 - 49 * q^98

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 $

$2$	1.34981	−	2.33795i	0.954463	−	1.65318i	0.218870	−	0.975754i	$-0.429763\pi$
$2$	1.34981	−	2.33795i	0.954463	−	1.65318i	0.735593	−	0.677424i	$-0.236904\pi$
$3$		0			0
$3$		0			0
$4$	−2.64400	−	4.57954i	−1.32200	−	2.28977i
$5$	1.58836			0.710338			0.355169	−	0.934802i	$-0.384423\pi$
$5$	1.58836			0.710338			0.355169	+	0.934802i	$0.384423\pi$
$6$		0			0
$7$	1.40545	−	2.24159i	0.531209	−	0.847241i
$7$	1.40545	−	2.24159i	0.531209	−	0.847241i
$8$	−8.87636			−3.13827
$9$		0			0
$10$	2.14400	−	3.71351i	0.677991	−	1.17432i
$11$	−0.300372			−0.0905655			−0.0452828	−	0.998974i	$-0.514419\pi$
$11$	−0.300372			−0.0905655			−0.0452828	+	0.998974i	$0.514419\pi$
$12$		0			0
$13$	−1.40545	+	2.43430i	−0.389801	+	0.675154i	−0.992422	−	0.122872i	$-0.960789\pi$
$13$	−1.40545	+	2.43430i	−0.389801	+	0.675154i	0.602622	+	0.798027i	$0.294123\pi$
$14$	−3.34362	−	6.31159i	−0.893621	−	1.68684i
$15$		0			0
$16$	−6.69344	+	11.5934i	−1.67336	+	2.89834i
$17$	2.93818	−	5.08907i	0.712613	−	1.23428i	−0.251260	−	0.967920i	$-0.580845\pi$
$17$	2.93818	−	5.08907i	0.712613	−	1.23428i	0.963873	−	0.266362i	$-0.0858217\pi$
$18$		0			0
$19$	1.14400	+	1.98146i	0.262451	+	0.454578i	0.966893	−	0.255184i	$-0.0821360\pi$
$19$	1.14400	+	1.98146i	0.262451	+	0.454578i	−0.704442	+	0.709762i	$0.748803\pi$
$20$	−4.19963	−	7.27397i	−0.939065	−	1.62651i
$21$		0			0
$22$	−0.405446	+	0.702253i	−0.0864414	+	0.149721i
$23$	−1.88874			−0.393829			−0.196914	−	0.980421i	$-0.563092\pi$
$23$	−1.88874			−0.393829			−0.196914	+	0.980421i	$0.563092\pi$
$24$		0			0
$25$	−2.47710			−0.495420
$26$	3.79418	+	6.57172i	0.744100	+	1.28882i
$27$		0			0
$28$	−13.9814	−	0.509538i	−2.64224	−	0.0962937i
$29$	1.26145	+	2.18490i	0.234245	+	0.405725i	0.959053	−	0.283226i	$-0.0914047\pi$
$29$	1.26145	+	2.18490i	0.234245	+	0.405725i	−0.724808	+	0.688951i	$0.758071\pi$
$30$		0			0
$31$	2.40545	+	4.16635i	0.432031	+	0.748299i	0.997048	−	0.0767797i	$-0.0244638\pi$
$31$	2.40545	+	4.16635i	0.432031	+	0.748299i	−0.565017	+	0.825079i	$0.691130\pi$
$32$	9.19344	+	15.9235i	1.62519	+	2.81490i
$33$		0			0
$34$	−7.93199	−	13.7386i	−1.36032	−	2.35615i
$35$	2.23236	−	3.56046i	0.377338	−	0.601827i
$36$		0			0
$37$	2.23855	+	3.87728i	0.368015	+	0.637421i	0.989255	−	0.146199i	$-0.0467041\pi$
$37$	2.23855	+	3.87728i	0.368015	+	0.637421i	−0.621240	+	0.783620i	$0.713371\pi$
$38$	6.17673			1.00200
$39$		0			0
$40$	−14.0989			−2.22923
$41$	4.45489	−	7.71609i	0.695737	−	1.20505i	−0.274195	−	0.961674i	$-0.588411\pi$
$41$	4.45489	−	7.71609i	0.695737	−	1.20505i	0.969932	−	0.243377i	$-0.0782553\pi$
$42$		0			0
$43$	4.54944	+	7.87987i	0.693783	+	1.20167i	0.970589	+	0.240742i	$0.0773908\pi$
$43$	4.54944	+	7.87987i	0.693783	+	1.20167i	−0.276806	+	0.960926i	$0.589276\pi$
$44$	0.794182	+	1.37556i	0.119727	+	0.207374i
$45$		0			0
$46$	−2.54944	+	4.41576i	−0.375895	+	0.651069i
$47$	−1.60507	+	2.78007i	−0.234124	+	0.405515i	−0.959018	−	0.283346i	$-0.908556\pi$
$47$	−1.60507	+	2.78007i	−0.234124	+	0.405515i	0.724894	+	0.688861i	$0.241889\pi$
$48$		0			0
$49$	−3.04944	−	6.30087i	−0.435635	−	0.900124i
$50$	−3.34362	+	5.79133i	−0.472860	+	0.819017i
$51$		0			0
$52$	14.8640			2.06126
$53$	1.00619	−	1.74277i	0.138211	−	0.239388i	−0.788609	−	0.614895i	$-0.789198\pi$
$53$	1.00619	−	1.74277i	0.138211	−	0.239388i	0.926819	+	0.375507i	$0.122532\pi$
$54$		0			0
$55$	−0.477100			−0.0643321
$56$	−12.4752	+	19.8971i	−1.66707	+	2.65887i
$57$		0			0
$58$	6.81089			0.894314
$59$	−2.44437	−	4.23377i	−0.318230	−	0.551190i	0.661889	−	0.749602i	$-0.269755\pi$
$59$	−2.44437	−	4.23377i	−0.318230	−	0.551190i	−0.980119	+	0.198412i	$0.936422\pi$
$60$		0			0
$61$	−3.78799	+	6.56099i	−0.485003	+	0.840049i	−0.999852	−	0.0172317i	$-0.994515\pi$
$61$	−3.78799	+	6.56099i	−0.485003	+	0.840049i	0.514849	+	0.857281i	$0.327848\pi$
$62$	12.9876			1.64943
$63$		0			0
$64$	22.8640			2.85800
$65$	−2.23236	+	3.86656i	−0.276890	+	0.479588i
$66$		0			0
$67$	−0.356004	−	0.616617i	−0.0434928	−	0.0753317i	0.843460	−	0.537193i	$-0.180515\pi$
$67$	−0.356004	−	0.616617i	−0.0434928	−	0.0753317i	−0.886952	+	0.461861i	$0.847182\pi$
$68$	−31.0741			−3.76829
$69$		0			0
$70$	−5.31089	−	10.0251i	−0.634773	−	1.19823i
$71$	12.8640			1.52667			0.763337	−	0.646001i	$-0.223560\pi$
$71$	12.8640			1.52667			0.763337	+	0.646001i	$0.223560\pi$
$72$		0			0
$73$	5.83743	−	10.1107i	0.683220	−	1.18337i	−0.290773	−	0.956792i	$-0.593912\pi$
$73$	5.83743	−	10.1107i	0.683220	−	1.18337i	0.973993	−	0.226580i	$-0.0727543\pi$
$74$	12.0865			1.40503
$75$		0			0
$76$	6.04944	−	10.4779i	0.693919	−	1.20190i
$77$	−0.422156	+	0.673310i	−0.0481092	+	0.0767308i
$78$		0			0
$79$	−0.833104	+	1.44298i	−0.0937315	+	0.162348i	−0.909078	−	0.416625i	$-0.863213\pi$
$79$	−0.833104	+	1.44298i	−0.0937315	+	0.162348i	0.815347	+	0.578973i	$0.196546\pi$
$80$	−10.6316	+	18.4145i	−1.18865	+	2.05880i
$81$		0			0
$82$	−12.0265	−	20.8306i	−1.32811	−	2.30035i
$83$	−2.71634	−	4.70484i	−0.298157	−	0.516423i	0.677557	−	0.735470i	$-0.263039\pi$
$83$	−2.71634	−	4.70484i	−0.298157	−	0.516423i	−0.975714	+	0.219047i	$0.929705\pi$
$84$		0			0
$85$	4.66690	−	8.08330i	0.506196	−	0.876757i
$86$	24.5636			2.64876
$87$		0			0
$88$	2.66621			0.284219
$89$	−4.67673	−	8.10033i	−0.495732	−	0.858633i	0.504256	−	0.863554i	$-0.331767\pi$
$89$	−4.67673	−	8.10033i	−0.495732	−	0.858633i	−0.999988	+	0.00492107i	$0.998434\pi$
$90$		0			0
$91$	3.48143	+	6.57172i	0.364953	+	0.688903i
$92$	4.99381	+	8.64953i	0.520641	+	0.901776i
$93$		0			0
$94$	4.33310	+	7.50516i	0.446926	+	0.774098i
$95$	1.81708	+	3.14728i	0.186429	+	0.322904i
$96$		0			0
$97$	6.28799	+	10.8911i	0.638449	+	1.10583i	0.985773	+	0.168081i	$0.0537570\pi$
$97$	6.28799	+	10.8911i	0.638449	+	1.10583i	−0.347324	+	0.937745i	$0.612910\pi$
$98$	−18.8473	−	1.37556i	−1.90386	−	0.138953i
$99$		0			0
$100$	6.54944	+	11.3440i	0.654944	+	1.13440i
$101$	14.6094			1.45369			0.726845	−	0.686801i	$-0.240986\pi$
$101$	14.6094			1.45369			0.726845	+	0.686801i	$0.240986\pi$
$102$		0			0
$103$	9.19777			0.906283			0.453142	−	0.891439i	$-0.350303\pi$
$103$	9.19777			0.906283			0.453142	+	0.891439i	$0.350303\pi$
$104$	12.4752	−	21.6078i	1.22330	−	2.11881i
$105$		0			0
$106$	−2.71634	−	4.70484i	−0.263834	−	0.456974i
$107$	6.25526	+	10.8344i	0.604719	+	1.04740i	0.992096	+	0.125482i	$0.0400478\pi$
$107$	6.25526	+	10.8344i	0.604719	+	1.04740i	−0.387377	+	0.921921i	$0.626619\pi$
$108$		0			0
$109$	1.52290	−	2.63774i	0.145867	−	0.252650i	−0.783829	−	0.620977i	$-0.786736\pi$
$109$	1.52290	−	2.63774i	0.145867	−	0.252650i	0.929696	+	0.368327i	$0.120069\pi$
$110$	−0.643996	+	1.11543i	−0.0614026	+	0.106352i
$111$		0			0
$112$	16.5803	+	31.2978i	1.56669	+	2.95736i
$113$	4.97710	−	8.62059i	0.468206	−	0.810957i	−0.531134	−	0.847288i	$-0.678234\pi$
$113$	4.97710	−	8.62059i	0.468206	−	0.810957i	0.999340	+	0.0363312i	$0.0115671\pi$
$114$		0			0
$115$	−3.00000			−0.279751
$116$	6.67054	−	11.5537i	0.619344	−	1.07274i
$117$		0			0
$118$	−13.1978			−1.21495
$119$	−7.27816	−	13.7386i	−0.667188	−	1.25942i
$120$		0			0
$121$	−10.9098			−0.991798
$122$	10.2262	+	17.7122i	0.925834	+	1.60359i
$123$		0			0
$124$	12.7200	−	22.0317i	1.14229	−	1.97850i
$125$	−11.8764			−1.06225
$126$		0			0
$127$	−13.4400			−1.19260			−0.596302	−	0.802760i	$-0.703364\pi$
$127$	−13.4400			−1.19260			−0.596302	+	0.802760i	$0.703364\pi$
$128$	12.4752	−	21.6078i	1.10267	−	1.90987i
$129$		0			0
$130$	6.02654	+	10.4383i	0.528563	+	0.915497i
$131$	−11.2756			−0.985155			−0.492577	−	0.870269i	$-0.663945\pi$
$131$	−11.2756			−0.985155			−0.492577	+	0.870269i	$0.663945\pi$
$132$		0			0
$133$	6.04944	+	0.220465i	0.524553	+	0.0191168i
$134$	−1.92216			−0.166049
$135$		0			0
$136$	−26.0803	+	45.1724i	−2.23637	+	3.87350i
$137$	−3.77747			−0.322731			−0.161366	−	0.986895i	$-0.551590\pi$
$137$	−3.77747			−0.322731			−0.161366	+	0.986895i	$0.551590\pi$
$138$		0			0
$139$	−8.35965	+	14.4793i	−0.709056	+	1.22812i	0.256152	+	0.966637i	$0.417545\pi$
$139$	−8.35965	+	14.4793i	−0.709056	+	1.22812i	−0.965208	+	0.261484i	$0.915788\pi$
$140$	−22.2076	−	0.809332i	−1.87688	−	0.0684010i
$141$		0			0
$142$	17.3640	−	30.0753i	1.45715	−	2.52386i
$143$	0.422156	−	0.731196i	0.0353025	−	0.0611457i
$144$		0			0
$145$	2.00364	+	3.47041i	0.166393	+	0.288202i
$146$	−15.7589	−	27.2952i	−1.30422	−	2.25897i
$147$		0			0
$148$	11.8374	−	20.5030i	0.973031	−	1.68534i
$149$	−10.8887			−0.892040			−0.446020	−	0.895023i	$-0.647159\pi$
$149$	−10.8887			−0.892040			−0.446020	+	0.895023i	$0.647159\pi$
$150$		0			0
$151$	−12.0989			−0.984593			−0.492297	−	0.870427i	$-0.663842\pi$
$151$	−12.0989			−0.984593			−0.492297	+	0.870427i	$0.663842\pi$
$152$	−10.1545	−	17.5881i	−0.823640	−	1.42659i
$153$		0			0
$154$	1.00433	+	1.89582i	0.0809313	+	0.152770i
$155$	3.82072	+	6.61769i	0.306888	+	0.531546i
$156$		0			0
$157$	0.0945538	+	0.163772i	0.00754622	+	0.0130704i	0.869774	−	0.493451i	$-0.164265\pi$
$157$	0.0945538	+	0.163772i	0.00754622	+	0.0130704i	−0.862228	+	0.506521i	$0.830931\pi$
$158$	2.24907	+	3.89550i	0.178926	+	0.309910i
$159$		0			0
$160$	14.6025	+	25.2923i	1.15443	+	1.99953i
$161$	−2.65452	+	4.23377i	−0.209205	+	0.333668i
$162$		0			0
$163$	4.47779	+	7.75576i	0.350727	+	0.607478i	0.986377	−	0.164500i	$-0.0526010\pi$
$163$	4.47779	+	7.75576i	0.350727	+	0.607478i	−0.635650	+	0.771978i	$0.719268\pi$
$164$	−47.1148			−3.67905
$165$		0			0
$166$	−14.6662			−1.13832
$167$	−2.17054	+	3.75948i	−0.167961	+	0.290917i	−0.937703	−	0.347438i	$-0.887052\pi$
$167$	−2.17054	+	3.75948i	−0.167961	+	0.290917i	0.769742	+	0.638356i	$0.220385\pi$
$168$		0			0
$169$	2.54944	+	4.41576i	0.196111	+	0.339674i
$170$	−12.5989	−	21.8219i	−0.966290	−	1.67366i
$171$		0			0
$172$	24.0574	−	41.6687i	1.83436	−	3.17721i
$173$	−3.15019	+	5.45628i	−0.239504	+	0.414833i	−0.960572	−	0.278031i	$-0.910318\pi$
$173$	−3.15019	+	5.45628i	−0.239504	+	0.414833i	0.721068	+	0.692864i	$0.243652\pi$
$174$		0			0
$175$	−3.48143	+	5.55264i	−0.263171	+	0.419740i
$176$	2.01052	−	3.48232i	0.151549	−	0.262490i
$177$		0			0
$178$	−25.2509			−1.89263
$179$	−6.97091	+	12.0740i	−0.521030	+	0.902451i	0.478671	+	0.877995i	$0.341119\pi$
$179$	−6.97091	+	12.0740i	−0.521030	+	0.902451i	−0.999701	+	0.0244564i	$0.992215\pi$
$180$		0			0
$181$	18.3411			1.36328			0.681641	−	0.731687i	$-0.261267\pi$
$181$	18.3411			1.36328			0.681641	+	0.731687i	$0.261267\pi$
$182$	20.0636	+	0.731196i	1.48721	+	0.0541999i
$183$		0			0
$184$	16.7651			1.23594
$185$	3.55563	+	6.15854i	0.261415	+	0.452785i
$186$		0			0
$187$	−0.882546	+	1.52861i	−0.0645382	+	0.111783i
$188$	16.9752			1.23805
$189$		0			0
$190$	9.81089			0.711757
$191$	3.80401	−	6.58875i	0.275249	−	0.476745i	−0.694949	−	0.719059i	$-0.744573\pi$
$191$	3.80401	−	6.58875i	0.275249	−	0.476745i	0.970198	+	0.242314i	$0.0779064\pi$
$192$		0			0
$193$	−3.83310	−	6.63913i	−0.275913	−	0.477895i	0.694452	−	0.719539i	$-0.255647\pi$
$193$	−3.83310	−	6.63913i	−0.275913	−	0.477895i	−0.970365	+	0.241644i	$0.922313\pi$
$194$	33.9505			2.43750
$195$		0			0
$196$	−20.7923	+	30.6245i	−1.48517	+	2.18746i
$197$	−18.3869			−1.31001			−0.655005	−	0.755624i	$-0.727334\pi$
$197$	−18.3869			−1.31001			−0.655005	+	0.755624i	$0.727334\pi$
$198$		0			0
$199$	−2.97710	+	5.15649i	−0.211041	+	0.365534i	−0.952041	−	0.305972i	$-0.901019\pi$
$199$	−2.97710	+	5.15649i	−0.211041	+	0.365534i	0.741000	+	0.671505i	$0.234352\pi$
$200$	21.9876			1.55476
$201$		0			0
$202$	19.7200	−	34.1560i	1.38749	−	2.40321i
$203$	6.67054	+	0.243101i	0.468180	+	0.0170623i
$204$		0			0
$205$	7.07598	−	12.2560i	0.494208	−	0.855994i
$206$	12.4153	−	21.5039i	0.865013	−	1.49825i
$207$		0			0
$208$	−18.8145	−	32.5877i	−1.30455	−	2.25955i
$209$	−0.343624	−	0.595175i	−0.0237690	−	0.0411691i
$210$		0			0
$211$	−3.33743	+	5.78061i	−0.229758	+	0.397953i	−0.957736	−	0.287647i	$-0.907127\pi$
$211$	−3.33743	+	5.78061i	−0.229758	+	0.397953i	0.727978	+	0.685601i	$0.240460\pi$
$212$	−10.6414			−0.730858
$213$		0			0
$214$	33.7738			2.30873
$215$	7.22617	+	12.5161i	0.492821	+	0.853591i
$216$		0			0
$217$	12.7200	+	0.463566i	0.863489	+	0.0314689i
$218$	−4.11126	−	7.12092i	−0.278450	−	0.482289i
$219$		0			0
$220$	1.26145	+	2.18490i	0.0850469	+	0.147306i
$221$	8.25890	+	14.3048i	0.555554	+	0.962248i
$222$		0			0
$223$	−3.17054	−	5.49153i	−0.212315	−	0.367740i	0.740124	−	0.672471i	$-0.234767\pi$
$223$	−3.17054	−	5.49153i	−0.212315	−	0.367740i	−0.952439	+	0.304731i	$0.901434\pi$
$224$	48.6148	+	1.77172i	3.24821	+	0.118378i
$225$		0			0
$226$	−13.4363	−	23.2724i	−0.893771	−	1.54806i
$227$	27.0865			1.79779			0.898897	−	0.438160i	$-0.144370\pi$
$227$	27.0865			1.79779			0.898897	+	0.438160i	$0.144370\pi$
$228$		0			0
$229$	8.19639			0.541633			0.270816	−	0.962631i	$-0.412706\pi$
$229$	8.19639			0.541633			0.270816	+	0.962631i	$0.412706\pi$
$230$	−4.04944	+	7.01384i	−0.267012	+	0.462479i
$231$		0			0
$232$	−11.1971	−	19.3939i	−0.735124	−	1.27327i
$233$	13.7101	+	23.7467i	0.898182	+	1.55570i	0.829817	+	0.558036i	$0.188445\pi$
$233$	13.7101	+	23.7467i	0.898182	+	1.55570i	0.0683649	+	0.997660i	$0.478222\pi$
$234$		0			0
$235$	−2.54944	+	4.41576i	−0.166307	+	0.288053i
$236$	−12.9258	+	22.3881i	−0.841398	+	1.45734i
$237$		0			0
$238$	−41.9443	−	1.52861i	−2.71884	−	0.0990854i
$239$	−13.9320	+	24.1309i	−0.901185	+	1.56090i	−0.0752280	+	0.997166i	$0.523968\pi$
$239$	−13.9320	+	24.1309i	−0.901185	+	1.56090i	−0.825957	+	0.563733i	$0.809365\pi$
$240$		0			0
$241$	−22.5302			−1.45130			−0.725648	−	0.688066i	$-0.758460\pi$
$241$	−22.5302			−1.45130			−0.725648	+	0.688066i	$0.758460\pi$
$242$	−14.7262	+	25.5065i	−0.946634	+	1.63962i
$243$		0			0
$244$	40.0617			2.56469
$245$	−4.84362	−	10.0081i	−0.309448	−	0.639392i
$246$		0			0
$247$	−6.43130			−0.409214
$248$	−21.3516	−	36.9821i	−1.35583	−	2.34836i
$249$		0			0
$250$	−16.0309	+	27.7663i	−1.01388	+	1.75609i
$251$	−31.2509			−1.97254			−0.986268	−	0.165152i	$-0.947189\pi$
$251$	−31.2509			−1.97254			−0.986268	+	0.165152i	$0.947189\pi$
$252$		0			0
$253$	0.567323			0.0356673
$254$	−18.1414	+	31.4219i	−1.13830	+	1.97159i
$255$		0			0
$256$	−10.8145	−	18.7313i	−0.675908	−	1.17071i
$257$	10.2015			0.636351			0.318176	−	0.948032i	$-0.396930\pi$
$257$	10.2015			0.636351			0.318176	+	0.948032i	$0.396930\pi$
$258$		0			0
$259$	11.8374	+	0.431403i	0.735542	+	0.0268060i
$260$	23.6094			1.46419
$261$		0			0
$262$	−15.2200	+	26.3618i	−0.940294	+	1.62864i
$263$	−28.4610			−1.75498			−0.877490	−	0.479594i	$-0.840784\pi$
$263$	−28.4610			−1.75498			−0.877490	+	0.479594i	$0.840784\pi$
$264$		0			0
$265$	1.59820	−	2.76816i	0.0981764	−	0.170046i
$266$	8.68106	−	13.8457i	0.532270	−	0.848933i
$267$		0			0
$268$	−1.88255	+	3.26067i	−0.114995	+	0.199177i
$269$	7.43818	−	12.8833i	0.453514	−	0.785509i	−0.545088	−	0.838379i	$-0.683504\pi$
$269$	7.43818	−	12.8833i	0.453514	−	0.785509i	0.998601	+	0.0528702i	$0.0168370\pi$
$270$		0			0
$271$	−0.0222115	−	0.0384714i	−0.00134925	−	0.00233697i	0.865350	−	0.501168i	$-0.167096\pi$
$271$	−0.0222115	−	0.0384714i	−0.00134925	−	0.00233697i	−0.866699	+	0.498831i	$0.833763\pi$
$272$	39.3330	+	68.1268i	2.38492	+	4.13079i
$273$		0			0
$274$	−5.09888	+	8.83153i	−0.308035	+	0.533532i
$275$	0.744051			0.0448680
$276$		0			0
$277$	15.6749			0.941812			0.470906	−	0.882184i	$-0.343927\pi$
$277$	15.6749			0.941812			0.470906	+	0.882184i	$0.343927\pi$
$278$	22.5679	+	39.0888i	1.35353	+	2.34439i
$279$		0			0
$280$	−19.8152	+	31.6039i	−1.18419	+	1.88869i
$281$	5.95489	+	10.3142i	0.355239	+	0.615292i	0.987159	−	0.159742i	$-0.0510662\pi$
$281$	5.95489	+	10.3142i	0.355239	+	0.615292i	−0.631920	+	0.775034i	$0.717733\pi$
$282$		0			0
$283$	−3.00364	−	5.20246i	−0.178548	−	0.309254i	0.762835	−	0.646593i	$-0.223807\pi$
$283$	−3.00364	−	5.20246i	−0.178548	−	0.309254i	−0.941383	+	0.337339i	$0.890473\pi$
$284$	−34.0123	−	58.9110i	−2.01826	−	3.49573i
$285$		0			0
$286$	−1.13967	−	1.97396i	−0.0673898	−	0.116723i
$287$	−11.0352	−	20.8306i	−0.651387	−	1.22959i
$288$		0			0
$289$	−8.76578	−	15.1828i	−0.515634	−	0.893105i
$290$	10.8182			0.635265
$291$		0			0
$292$	−61.7366			−3.61286
$293$	−2.47779	+	4.29166i	−0.144754	+	0.250721i	−0.929281	−	0.369373i	$-0.879572\pi$
$293$	−2.47779	+	4.29166i	−0.144754	+	0.250721i	0.784527	+	0.620094i	$0.212906\pi$
$294$		0			0
$295$	−3.88255	−	6.72477i	−0.226051	−	0.391531i
$296$	−19.8702	−	34.4161i	−1.15493	−	2.00040i
$297$		0			0
$298$	−14.6978	+	25.4573i	−0.851419	+	1.47470i
$299$	2.65452	−	4.59776i	0.153515	−	0.265895i
$300$		0			0
$301$	24.0574	+	0.876747i	1.38665	+	0.0505348i
$302$	−16.3312	+	28.2865i	−0.939758	+	1.62771i
$303$		0			0
$304$	−30.6291			−1.75670
$305$	−6.01671	+	10.4212i	−0.344516	+	0.596719i
$306$		0			0
$307$	−22.0531			−1.25864			−0.629318	−	0.777148i	$-0.716666\pi$
$307$	−22.0531			−1.25864			−0.629318	+	0.777148i	$0.716666\pi$
$308$	4.19963	+	0.153051i	0.239296	+	0.00872089i
$309$		0			0
$310$	20.6291			1.17165
$311$	3.98762	+	6.90676i	0.226117	+	0.391646i	0.956654	−	0.291227i	$-0.0940634\pi$
$311$	3.98762	+	6.90676i	0.226117	+	0.391646i	−0.730537	+	0.682873i	$0.760730\pi$
$312$		0			0
$313$	11.2651	−	19.5117i	0.636741	−	1.10287i	−0.349403	−	0.936973i	$-0.613616\pi$
$313$	11.2651	−	19.5117i	0.636741	−	1.10287i	0.986143	−	0.165895i	$-0.0530511\pi$
$314$	0.510520			0.0288103
$315$		0			0
$316$	8.81089			0.495651
$317$	−9.96905	+	17.2669i	−0.559918	+	0.969806i	0.437585	+	0.899177i	$0.355834\pi$
$317$	−9.96905	+	17.2669i	−0.559918	+	0.969806i	−0.997503	+	0.0706288i	$0.977499\pi$
$318$		0			0
$319$	−0.378904	−	0.656281i	−0.0212146	−	0.0367447i
$320$	36.3163			2.03014
$321$		0			0
$322$	6.31522	+	11.9209i	0.351934	+	0.664327i
$323$	13.4451			0.748103
$324$		0			0
$325$	3.48143	−	6.03001i	0.193115	−	0.334485i
$326$	24.1767			1.33903
$327$		0			0
$328$	−39.5432	+	68.4908i	−2.18341	+	3.78177i
$329$	3.97593	+	7.50516i	0.219200	+	0.413773i
$330$		0			0
$331$	−11.8152	+	20.4646i	−0.649423	+	1.12483i	0.333837	+	0.942631i	$0.391656\pi$
$331$	−11.8152	+	20.4646i	−0.649423	+	1.12483i	−0.983261	+	0.182204i	$0.941677\pi$
$332$	−14.3640	+	24.8791i	−0.788326	+	1.36542i
$333$		0			0
$334$	5.85965	+	10.1492i	0.320626	+	0.555340i
$335$	−0.565464	−	0.979412i	−0.0308946	−	0.0535110i
$336$		0			0
$337$	6.19275	−	10.7262i	0.337341	−	0.584291i	−0.646591	−	0.762837i	$-0.723806\pi$
$337$	6.19275	−	10.7262i	0.337341	−	0.584291i	0.983932	+	0.178546i	$0.0571393\pi$
$338$	13.7651			0.748722
$339$		0			0
$340$	−49.3570			−2.67676
$341$	−0.722528	−	1.25146i	−0.0391271	−	0.0677701i
$342$		0			0
$343$	−18.4098	−	2.01993i	−0.994035	−	0.109066i
$344$	−40.3825	−	69.9445i	−2.17728	−	3.77115i
$345$		0			0
$346$	8.50433	+	14.7299i	0.457196	+	0.791886i
$347$	−1.92216	−	3.32927i	−0.103187	−	0.178725i	0.809809	−	0.586693i	$-0.199571\pi$
$347$	−1.92216	−	3.32927i	−0.103187	−	0.178725i	−0.912996	+	0.407969i	$0.866237\pi$
$348$		0			0
$349$	6.09455	+	10.5561i	0.326234	+	0.565054i	0.981761	−	0.190118i	$-0.0608869\pi$
$349$	6.09455	+	10.5561i	0.326234	+	0.565054i	−0.655527	+	0.755171i	$0.727554\pi$
$350$	8.28249	+	15.6344i	0.442718	+	0.835695i
$351$		0			0
$352$	−2.76145	−	4.78297i	−0.147186	−	0.254933i
$353$	3.56360			0.189672			0.0948358	−	0.995493i	$-0.469767\pi$
$353$	3.56360			0.189672			0.0948358	+	0.995493i	$0.469767\pi$
$354$		0			0
$355$	20.4327			1.08445
$356$	−24.7305	+	42.8345i	−1.31071	+	2.27022i
$357$		0			0
$358$	18.8189	+	32.5952i	0.994608	+	1.72271i
$359$	−0.483978	−	0.838275i	−0.0255434	−	0.0442425i	0.852971	−	0.521958i	$-0.174798\pi$
$359$	−0.483978	−	0.838275i	−0.0255434	−	0.0442425i	−0.878515	+	0.477716i	$0.841465\pi$
$360$		0			0
$361$	6.88255	−	11.9209i	0.362239	−	0.627417i
$362$	24.7570	−	42.8805i	1.30120	−	2.25375i
$363$		0			0
$364$	20.8905	−	33.3189i	1.09496	−	1.74639i
$365$	9.27197	−	16.0595i	0.485317	−	0.840594i
$366$		0			0
$367$	20.9542			1.09380			0.546900	−	0.837198i	$-0.315808\pi$
$367$	20.9542			1.09380			0.546900	+	0.837198i	$0.315808\pi$
$368$	12.6421	−	21.8968i	0.659017	−	1.14145i
$369$		0			0
$370$	19.1978			0.998044
$371$	−2.49243	−	4.70484i	−0.129401	−	0.244263i
$372$		0			0
$373$	2.00000			0.103556			0.0517780	−	0.998659i	$-0.483511\pi$
$373$	2.00000			0.103556			0.0517780	+	0.998659i	$0.483511\pi$
$374$	2.38255	+	4.12669i	0.123199	+	0.213386i
$375$		0			0
$376$	14.2472	−	24.6769i	0.734744	−	1.27261i
$377$	−7.09160			−0.365236
$378$		0			0
$379$	−7.14331			−0.366927			−0.183464	−	0.983027i	$-0.558731\pi$
$379$	−7.14331			−0.366927			−0.183464	+	0.983027i	$0.558731\pi$
$380$	9.60872	−	16.6428i	0.492917	−	0.853757i
$381$		0			0
$382$	−10.2694	−	17.7872i	−0.525429	−	0.910070i
$383$	11.9766			0.611977			0.305988	−	0.952035i	$-0.401013\pi$
$383$	11.9766			0.611977			0.305988	+	0.952035i	$0.401013\pi$
$384$		0			0
$385$	−0.670538	+	1.06946i	−0.0341738	+	0.0545048i
$386$	−20.6959			−1.05339
$387$		0			0
$388$	33.2509	−	57.5922i	1.68806	−	2.92380i
$389$	−13.7788			−0.698615			−0.349308	−	0.937008i	$-0.613583\pi$
$389$	−13.7788			−0.698615			−0.349308	+	0.937008i	$0.613583\pi$
$390$		0			0
$391$	−5.54944	+	9.61192i	−0.280647	+	0.486095i
$392$	27.0679	+	55.9287i	1.36714	+	2.82483i
$393$		0			0
$394$	−24.8189	+	42.9875i	−1.25036	+	2.16568i
$395$	−1.32327	+	2.29197i	−0.0665810	+	0.115322i
$396$		0			0
$397$	−4.19344	−	7.26325i	−0.210463	−	0.364532i	0.741397	−	0.671067i	$-0.234164\pi$
$397$	−4.19344	−	7.26325i	−0.210463	−	0.364532i	−0.951859	+	0.306535i	$0.900830\pi$
$398$	8.03706	+	13.9206i	0.402862	+	0.697777i
$399$		0			0
$400$	16.5803	−	28.7179i	0.829016	−	1.43590i
$401$	−27.6167			−1.37911			−0.689556	−	0.724233i	$-0.742194\pi$
$401$	−27.6167			−1.37911			−0.689556	+	0.724233i	$0.742194\pi$
$402$		0			0
$403$	−13.5229			−0.673624
$404$	−38.6272	−	66.9043i	−1.92178	−	3.32861i
$405$		0			0
$406$	9.57234	−	15.2672i	0.475067	−	0.757699i
$407$	−0.672397	−	1.16463i	−0.0333295	−	0.0577284i
$408$		0			0
$409$	−15.2658	−	26.4411i	−0.754844	−	1.30743i	−0.945452	−	0.325762i	$-0.894379\pi$
$409$	−15.2658	−	26.4411i	−0.754844	−	1.30743i	0.190607	−	0.981666i	$-0.438954\pi$
$410$	−19.1025	−	33.0865i	−0.943407	−	1.63403i
$411$		0			0
$412$	−24.3189	−	42.1215i	−1.19810	−	2.07518i
$413$	−12.9258	−	0.471067i	−0.636037	−	0.0231797i
$414$		0			0
$415$	−4.31453	−	7.47299i	−0.211792	−	0.366835i
$416$	−51.6835			−2.53399
$417$		0			0
$418$	−1.85532			−0.0907464
$419$	10.5000	−	18.1865i	0.512959	−	0.888470i	−0.486928	−	0.873442i	$-0.661883\pi$
$419$	10.5000	−	18.1865i	0.512959	−	0.888470i	0.999887	−	0.0150285i	$-0.00478389\pi$
$420$		0			0
$421$	−17.3647	−	30.0765i	−0.846302	−	1.46584i	−0.884486	−	0.466567i	$-0.845491\pi$
$421$	−17.3647	−	30.0765i	−0.846302	−	1.46584i	0.0381837	−	0.999271i	$-0.487843\pi$
$422$	9.00983	+	15.6055i	0.438592	+	0.759663i
$423$		0			0
$424$	−8.93130	+	15.4695i	−0.433742	+	0.751264i
$425$	−7.27816	+	12.6061i	−0.353043	+	0.611488i
$426$		0			0
$427$	9.38323	+	17.7122i	0.454087	+	0.857156i
$428$	33.0778	−	57.2924i	1.59887	−	2.76933i
$429$		0			0
$430$	39.0159			1.88152
$431$	15.8022	−	27.3701i	0.761163	−	1.31837i	−0.181088	−	0.983467i	$-0.557962\pi$
$431$	15.8022	−	27.3701i	0.761163	−	1.31837i	0.942251	−	0.334906i	$-0.108705\pi$
$432$		0			0
$433$	−6.48576			−0.311686			−0.155843	−	0.987782i	$-0.549809\pi$
$433$	−6.48576			−0.311686			−0.155843	+	0.987782i	$0.549809\pi$
$434$	18.2534	−	29.1129i	0.876191	−	1.39746i
$435$		0			0
$436$	−16.1062			−0.771346
$437$	−2.16071	−	3.74245i	−0.103361	−	0.179026i
$438$		0			0
$439$	7.78799	−	13.4892i	0.371701	−	0.643804i	−0.618127	−	0.786078i	$-0.712108\pi$
$439$	7.78799	−	13.4892i	0.371701	−	0.643804i	0.989827	+	0.142274i	$0.0454415\pi$
$440$	4.23491			0.201891
$441$		0			0
$442$	44.5919			2.12102
$443$	−12.5371	+	21.7148i	−0.595654	+	1.03170i	0.397800	+	0.917472i	$0.369774\pi$
$443$	−12.5371	+	21.7148i	−0.595654	+	1.03170i	−0.993454	+	0.114231i	$0.963560\pi$
$444$		0			0
$445$	−7.42835	−	12.8663i	−0.352137	−	0.609920i
$446$	−17.1185			−0.810587
$447$		0			0
$448$	32.1341	−	51.2516i	1.51819	−	2.42141i
$449$	15.2967			0.721894			0.360947	−	0.932586i	$-0.382454\pi$
$449$	15.2967			0.721894			0.360947	+	0.932586i	$0.382454\pi$
$450$		0			0
$451$	−1.33812	+	2.31770i	−0.0630098	+	0.109136i
$452$	−52.6377			−2.47587
$453$		0			0
$454$	36.5617	−	63.3268i	1.71593	−	2.97207i
$455$	5.52978	+	10.4383i	0.259240	+	0.489354i
$456$		0			0
$457$	−10.2200	+	17.7015i	−0.478071	+	0.828042i	−0.999684	−	0.0251395i	$-0.991997\pi$
$457$	−10.2200	+	17.7015i	−0.478071	+	0.828042i	0.521613	+	0.853182i	$0.325330\pi$
$458$	11.0636	−	19.1627i	0.516968	−	0.895415i
$459$		0			0
$460$	7.93199	+	13.7386i	0.369831	+	0.640566i
$461$	−20.4091	−	35.3496i	−0.950546	−	1.64639i	−0.744246	−	0.667905i	$-0.767191\pi$
$461$	−20.4091	−	35.3496i	−0.950546	−	1.64639i	−0.206300	−	0.978489i	$-0.566142\pi$
$462$		0			0
$463$	−4.95420	+	8.58093i	−0.230241	+	0.398789i	−0.957879	−	0.287172i	$-0.907285\pi$
$463$	−4.95420	+	8.58093i	−0.230241	+	0.398789i	0.727638	+	0.685962i	$0.240618\pi$
$464$	−33.7738			−1.56791
$465$		0			0
$466$	74.0246			3.42912
$467$	−8.86948	−	15.3624i	−0.410430	−	0.710886i	0.584506	−	0.811389i	$-0.301288\pi$
$467$	−8.86948	−	15.3624i	−0.410430	−	0.710886i	−0.994937	+	0.100503i	$0.967955\pi$
$468$		0			0
$469$	−1.88255	−	0.0686074i	−0.0869279	−	0.00316799i
$470$	6.88255	+	11.9209i	0.317468	+	0.549871i
$471$		0			0
$472$	21.6971	+	37.5804i	0.998689	+	1.72978i
$473$	−1.36652	−	2.36689i	−0.0628329	−	0.108830i
$474$		0			0
$475$	−2.83379	−	4.90827i	−0.130023	−	0.225207i
$476$	−43.6730	+	69.6554i	−2.00175	+	3.19265i
$477$		0			0
$478$	37.6112	+	65.1445i	1.72030	+	2.97964i
$479$	23.6094			1.07874			0.539371	−	0.842068i	$-0.318662\pi$
$479$	23.6094			1.07874			0.539371	+	0.842068i	$0.318662\pi$
$480$		0			0
$481$	−12.5846			−0.573810
$482$	−30.4116	+	52.6744i	−1.38521	+	2.39925i
$483$		0			0
$484$	28.8454	+	49.9617i	1.31115	+	2.27099i
$485$	9.98762	+	17.2991i	0.453514	+	0.785510i
$486$		0			0
$487$	−17.4363	+	30.2006i	−0.790115	+	1.36852i	0.135780	+	0.990739i	$0.456646\pi$
$487$	−17.4363	+	30.2006i	−0.790115	+	1.36852i	−0.925895	+	0.377780i	$0.876687\pi$
$488$	33.6236	−	58.2377i	1.52207	−	2.63630i
$489$		0			0
$490$	−29.9363	−	2.18490i	−1.35239	−	0.0987035i
$491$	11.6025	−	20.0962i	0.523615	−	0.906927i	−0.476008	−	0.879441i	$-0.657916\pi$
$491$	11.6025	−	20.0962i	0.523615	−	0.906927i	0.999622	−	0.0274860i	$-0.00875017\pi$
$492$		0			0
$493$	14.8255			0.667705
$494$	−8.68106	+	15.0360i	−0.390579	+	0.676503i
$495$		0			0
$496$	−64.4028			−2.89177
$497$	18.0796	−	28.8357i	0.810982	−	1.29346i
$498$		0			0
$499$	−5.32513			−0.238386			−0.119193	−	0.992871i	$-0.538031\pi$
$499$	−5.32513			−0.238386			−0.119193	+	0.992871i	$0.538031\pi$
$500$	31.4010	+	54.3882i	1.40430	+	2.43231i
$501$		0			0
$502$	−42.1828	+	73.0628i	−1.88271	+	3.26095i
$503$	10.4313			0.465109			0.232554	−	0.972583i	$-0.425292\pi$
$503$	10.4313			0.465109			0.232554	+	0.972583i	$0.425292\pi$
$504$		0			0
$505$	23.2051			1.03261
$506$	0.765781	−	1.32637i	0.0340431	−	0.0589644i
$507$		0			0
$508$	35.5352	+	61.5488i	1.57662	+	2.73079i
$509$	−1.50186			−0.0665687			−0.0332844	−	0.999446i	$-0.510597\pi$
$509$	−1.50186			−0.0665687			−0.0332844	+	0.999446i	$0.510597\pi$
$510$		0			0
$511$	−14.4599	−	27.2952i	−0.639669	−	1.20747i
$512$	−8.48948			−0.375186
$513$		0			0
$514$	13.7701	−	23.8505i	0.607374	−	1.05200i
$515$	14.6094			0.643767
$516$		0			0
$517$	0.482119	−	0.835055i	0.0212036	−	0.0367257i
$518$	16.9869	−	27.0930i	0.746363	−	1.19040i
$519$		0			0
$520$	19.8152	−	34.3210i	0.868955	−	1.50507i
$521$	18.8709	−	32.6853i	0.826747	−	1.43197i	−0.0738295	−	0.997271i	$-0.523522\pi$
$521$	18.8709	−	32.6853i	0.826747	−	1.43197i	0.900577	−	0.434697i	$-0.143145\pi$
$522$		0			0
$523$	8.97779	+	15.5500i	0.392571	+	0.679953i	0.992788	−	0.119884i	$-0.0382523\pi$
$523$	8.97779	+	15.5500i	0.392571	+	0.679953i	−0.600217	+	0.799837i	$0.704919\pi$
$524$	29.8127	+	51.6371i	1.30237	+	2.25578i
$525$		0			0
$526$	−38.4171	+	66.5403i	−1.67506	+	2.90129i
$527$	28.2705			1.23148
$528$		0			0
$529$	−19.4327			−0.844899
$530$	−4.31453	−	7.47299i	−0.187411	−	0.324606i
$531$		0			0
$532$	−14.9851	−	28.2865i	−0.649685	−	1.22638i
$533$	12.5222	+	21.6891i	0.542397	+	0.939459i
$534$		0			0
$535$	9.93563	+	17.2090i	0.429555	+	0.744011i
$536$	3.16002	+	5.47331i	0.136492	+	0.236411i
$537$		0			0
$538$	−20.0803	−	34.7801i	−0.865724	−	1.49948i
$539$	0.915967	+	1.89260i	0.0394535	+	0.0815202i
$540$		0			0
$541$	−4.18547	−	7.24944i	−0.179947	−	0.311678i	0.761915	−	0.647677i	$-0.224259\pi$
$541$	−4.18547	−	7.24944i	−0.179947	−	0.311678i	−0.941862	+	0.335999i	$0.890926\pi$
$542$	−0.119925			−0.00515123
$543$		0			0
$544$	108.048			4.63251
$545$	2.41892	−	4.18969i	0.103615	−	0.179467i
$546$		0			0
$547$	−15.0538	−	26.0739i	−0.643653	−	1.11484i	−0.984611	−	0.174761i	$-0.944085\pi$
$547$	−15.0538	−	26.0739i	−0.643653	−	1.11484i	0.340958	−	0.940079i	$-0.389249\pi$
$548$	9.98762	+	17.2991i	0.426650	+	0.738979i
$549$		0			0
$550$	1.00433	−	1.73955i	0.0428248	−	0.0741747i
$551$	−2.88619	+	4.99902i	−0.122956	+	0.212966i
$552$		0			0
$553$	2.06368	+	3.89550i	0.0877567	+	0.165654i
$554$	21.1582	−	36.6470i	0.898924	−	1.55698i
$555$		0			0
$556$	88.4115			3.74948
$557$	8.26764	−	14.3200i	0.350311	−	0.606757i	−0.635993	−	0.771695i	$-0.719409\pi$
$557$	8.26764	−	14.3200i	0.350311	−	0.606757i	0.986304	+	0.164938i	$0.0527425\pi$
$558$		0			0
$559$	−25.5760			−1.08175
$560$	26.3356	+	49.7123i	1.11288	+	2.10073i
$561$		0			0
$562$	32.1520			1.35625
$563$	−11.1156	−	19.2528i	−0.468466	−	0.811408i	0.530884	−	0.847444i	$-0.321860\pi$
$563$	−11.1156	−	19.2528i	−0.468466	−	0.811408i	−0.999350	+	0.0360368i	$0.988527\pi$
$564$		0			0
$565$	7.90545	−	13.6926i	0.332585	−	0.576053i
$566$	−16.2174			−0.681670
$567$		0			0
$568$	−114.185			−4.79111
$569$	1.15638	−	2.00290i	0.0484778	−	0.0839660i	−0.840768	−	0.541395i	$-0.817896\pi$
$569$	1.15638	−	2.00290i	0.0484778	−	0.0839660i	0.889246	+	0.457429i	$0.151230\pi$
$570$		0			0
$571$	3.04944	+	5.28179i	0.127615	+	0.221036i	0.922752	−	0.385394i	$-0.125934\pi$
$571$	3.04944	+	5.28179i	0.127615	+	0.221036i	−0.795137	+	0.606430i	$0.792601\pi$
$572$	−4.46472			−0.186679
$573$		0			0
$574$	−63.5963	−	2.31770i	−2.65446	−	0.0967388i
$575$	4.67859			0.195111
$576$		0			0
$577$	−10.1032	+	17.4993i	−0.420602	+	0.728505i	−0.995998	−	0.0893702i	$-0.971515\pi$
$577$	−10.1032	+	17.4993i	−0.420602	+	0.728505i	0.575396	+	0.817875i	$0.304848\pi$
$578$	−47.3287			−1.96861
$579$		0			0
$580$	10.5952	−	18.3515i	0.439944	−	0.762004i
$581$	−14.3640	−	0.523480i	−0.595918	−	0.0217176i
$582$		0			0
$583$	−0.302231	+	0.523480i	−0.0125171	+	0.0216803i
$584$	−51.8151	+	89.7465i	−2.14413	+	3.71374i
$585$		0			0
$586$	6.68911	+	11.5859i	0.276324	+	0.478608i
$587$	19.3411	+	33.4997i	0.798292	+	1.38268i	0.920728	+	0.390205i	$0.127596\pi$
$587$	19.3411	+	33.4997i	0.798292	+	1.38268i	−0.122436	+	0.992476i	$0.539071\pi$
$588$		0			0
$589$	−5.50364	+	9.53259i	−0.226774	+	0.392783i
$590$	−20.9629			−0.863027
$591$		0			0
$592$	−59.9344			−2.46329
$593$	11.8578	+	20.5383i	0.486941	+	0.843406i	0.999887	−	0.0150142i	$-0.00477936\pi$
$593$	11.8578	+	20.5383i	0.486941	+	0.843406i	−0.512946	+	0.858421i	$0.671446\pi$
$594$		0			0
$595$	−11.5604	−	21.8219i	−0.473929	−	0.894611i
$596$	28.7898	+	49.8654i	1.17928	+	2.04256i
$597$		0			0
$598$	−7.16621	−	12.4122i	−0.293048	−	0.507574i
$599$	−17.2403	−	29.8611i	−0.704421	−	1.22009i	−0.966900	−	0.255155i	$-0.917873\pi$
$599$	−17.2403	−	29.8611i	−0.704421	−	1.22009i	0.262479	−	0.964938i	$-0.415460\pi$
$600$		0			0
$601$	3.64035	+	6.30528i	0.148493	+	0.257198i	0.930671	−	0.365858i	$-0.119224\pi$
$601$	3.64035	+	6.30528i	0.148493	+	0.257198i	−0.782178	+	0.623056i	$0.785891\pi$
$602$	34.5228	−	55.0615i	1.40705	−	2.24414i
$603$		0			0
$604$	31.9894	+	55.4073i	1.30163	+	2.25449i
$605$	−17.3287			−0.704512
$606$		0			0
$607$	−25.1593			−1.02118			−0.510591	−	0.859824i	$-0.670573\pi$
$607$	−25.1593			−1.02118			−0.510591	+	0.859824i	$0.670573\pi$
$608$	−21.0345	+	36.4328i	−0.853062	+	1.47755i
$609$		0			0
$610$	16.2429	+	28.1335i	0.657655	+	1.13909i
$611$	−4.51169	−	7.81448i	−0.182523	−	0.316140i
$612$		0			0
$613$	18.7731	−	32.5159i	0.758237	−	1.31330i	−0.185512	−	0.982642i	$-0.559394\pi$
$613$	18.7731	−	32.5159i	0.758237	−	1.31330i	0.943749	−	0.330663i	$-0.107272\pi$
$614$	−29.7676	+	51.5589i	−1.20132	+	2.08075i
$615$		0			0
$616$	3.74721	−	5.97654i	0.150979	−	0.240802i
$617$	−6.86398	+	11.8888i	−0.276333	+	0.478623i	−0.970471	−	0.241219i	$-0.922453\pi$
$617$	−6.86398	+	11.8888i	−0.276333	+	0.478623i	0.694137	+	0.719843i	$0.255786\pi$
$618$		0			0
$619$	11.8109			0.474720			0.237360	−	0.971422i	$-0.423718\pi$
$619$	11.8109			0.474720			0.237360	+	0.971422i	$0.423718\pi$
$620$	20.2040	−	34.9943i	0.811411	−	1.40540i
$621$		0			0
$622$	21.5302			0.863282
$623$	−24.7305	−	0.901276i	−0.990807	−	0.0361089i
$624$		0			0
$625$	−6.47848			−0.259139
$626$	−30.4116	−	52.6744i	−1.21549	−	2.10529i
$627$		0			0
$628$	0.500000	−	0.866025i	0.0199522	−	0.0345582i
$629$	26.3090			1.04901
$630$		0			0
$631$	29.6304			1.17957			0.589785	−	0.807561i	$-0.299213\pi$
$631$	29.6304			1.17957			0.589785	+	0.807561i	$0.299213\pi$
$632$	7.39493	−	12.8084i	0.294154	−	0.509490i
$633$		0			0
$634$	26.9127	+	46.6142i	1.06884	+	1.85129i
$635$	−21.3475			−0.847152
$636$		0			0
$637$	19.6240	+	1.43226i	0.777533	+	0.0567481i
$638$	−2.04580			−0.0809940
$639$		0			0
$640$	19.8152	−	34.3210i	0.783265	−	1.35666i
$641$	14.6525			0.578737			0.289368	−	0.957218i	$-0.406555\pi$
$641$	14.6525			0.578737			0.289368	+	0.957218i	$0.406555\pi$
$642$		0			0
$643$	−1.01857	+	1.76421i	−0.0401685	+	0.0695738i	−0.885411	−	0.464810i	$-0.846123\pi$
$643$	−1.01857	+	1.76421i	−0.0401685	+	0.0695738i	0.845242	+	0.534383i	$0.179456\pi$
$644$	26.4072	+	0.962383i	1.04059	+	0.0379232i
$645$		0			0
$646$	18.1483	−	31.4338i	0.714036	−	1.23675i
$647$	5.89307	−	10.2071i	0.231680	−	0.401282i	−0.726622	−	0.687037i	$-0.758911\pi$
$647$	5.89307	−	10.2071i	0.231680	−	0.401282i	0.958303	+	0.285755i	$0.0922443\pi$
$648$		0			0
$649$	0.734219	+	1.27171i	0.0288206	+	0.0499188i
$650$	−9.39857	−	16.2788i	−0.368642	−	0.638507i
$651$		0			0
$652$	23.6785	−	41.0124i	0.927322	−	1.60617i
$653$	−34.1840			−1.33772			−0.668862	−	0.743387i	$-0.733218\pi$
$653$	−34.1840			−1.33772			−0.668862	+	0.743387i	$0.733218\pi$
$654$		0			0
$655$	−17.9098			−0.699793
$656$	59.6370	+	103.294i	2.32844	+	4.03297i
$657$		0			0
$658$	22.9134	+	0.835055i	0.893258	+	0.0325538i
$659$	−12.4320	−	21.5328i	−0.484282	−	0.838800i	0.515555	−	0.856856i	$-0.327586\pi$
$659$	−12.4320	−	21.5328i	−0.484282	−	0.838800i	−0.999837	+	0.0180560i	$0.994252\pi$
$660$		0			0
$661$	−12.7694	−	22.1173i	−0.496673	−	0.860263i	0.503320	−	0.864100i	$-0.332112\pi$
$661$	−12.7694	−	22.1173i	−0.496673	−	0.860263i	−0.999993	+	0.00383747i	$0.998778\pi$
$662$	31.8967	+	55.2467i	1.23970	+	2.14722i
$663$		0			0
$664$	24.1112	+	41.7618i	0.935696	+	1.62067i
$665$	9.60872	+	0.350179i	0.372610	+	0.0135794i
$666$		0			0
$667$	−2.38255	−	4.12669i	−0.0922525	−	0.159786i
$668$	22.9556			0.888178
$669$		0			0
$670$	−3.05308			−0.117951
$671$	1.13781	−	1.97074i	0.0439245	−	0.0760795i
$672$		0			0
$673$	1.90978	+	3.30783i	0.0736165	+	0.127507i	0.900484	−	0.434890i	$-0.143213\pi$
$673$	1.90978	+	3.30783i	0.0736165	+	0.127507i	−0.826867	+	0.562397i	$0.809879\pi$
$674$	−16.7181	−	28.9566i	−0.643958	−	1.11537i
$675$		0			0
$676$	13.4814	−	23.3505i	0.518517	−	0.898097i
$677$	8.61126	−	14.9151i	0.330958	−	0.573236i	−0.651742	−	0.758441i	$-0.725962\pi$
$677$	8.61126	−	14.9151i	0.330958	−	0.573236i	0.982700	+	0.185205i	$0.0592949\pi$
$678$		0			0
$679$	33.2509	+	1.21179i	1.27605	+	0.0465043i
$680$	−41.4250	+	71.7503i	−1.58858	+	2.75150i
$681$		0			0
$682$	−3.90112			−0.149381
$683$	−16.8585	+	29.1997i	−0.645072	+	1.11730i	0.339213	+	0.940709i	$0.389839\pi$
$683$	−16.8585	+	29.1997i	−0.645072	+	1.11730i	−0.984285	+	0.176587i	$0.943494\pi$
$684$		0			0
$685$	−6.00000			−0.229248
$686$	−29.5723	+	40.3145i	−1.12907	+	1.53922i
$687$		0			0
$688$	−121.806			−4.64380
$689$	2.82829	+	4.89874i	0.107749	+	0.186627i
$690$		0			0
$691$	12.7465	−	22.0776i	0.484901	−	0.839872i	−0.514949	−	0.857221i	$-0.672189\pi$
$691$	12.7465	−	22.0776i	0.484901	−	0.839872i	0.999850	+	0.0173484i	$0.00552246\pi$
$692$	33.3163			1.26650
$693$		0			0
$694$	−10.3782			−0.393952
$695$	−13.2782	+	22.9984i	−0.503669	+	0.872381i
$696$		0			0
$697$	−26.1785	−	45.3425i	−0.991582	−	1.71747i
$698$	32.9061			1.24551
$699$		0			0
$700$	34.6334	+	1.26218i	1.30902	+	0.0477058i
$701$	10.1606			0.383762			0.191881	−	0.981418i	$-0.438541\pi$
$701$	10.1606			0.383762			0.191881	+	0.981418i	$0.438541\pi$
$702$		0			0
$703$	−5.12178	+	8.87119i	−0.193172	+	0.334583i
$704$	−6.86769			−0.258836
$705$		0			0
$706$	4.81020	−	8.33152i	0.181034	−	0.313561i
$707$	20.5327	−	32.7483i	0.772213	−	1.23163i
$708$		0			0
$709$	7.97346	−	13.8104i	0.299449	−	0.518662i	−0.676561	−	0.736387i	$-0.736530\pi$
$709$	7.97346	−	13.8104i	0.299449	−	0.518662i	0.976010	+	0.217725i	$0.0698637\pi$
$710$	27.5803	−	47.7705i	1.03507	−	1.79280i
$711$		0			0
$712$	41.5123	+	71.9014i	1.55574	+	2.69462i
$713$	−4.54325	−	7.86914i	−0.170146	−	0.294702i
$714$		0			0
$715$	0.670538	−	1.16141i	0.0250767	−	0.0434341i
$716$	73.7242			2.75520
$717$		0			0
$718$	−2.61312			−0.0975209
$719$	8.20877	+	14.2180i	0.306136	+	0.530242i	0.977513	−	0.210873i	$-0.0676306\pi$
$719$	8.20877	+	14.2180i	0.306136	+	0.530242i	−0.671378	+	0.741115i	$0.734297\pi$
$720$		0			0
$721$	12.9270	−	20.6176i	0.481425	−	0.767840i
$722$	−18.5803	−	32.1820i	−0.691488	−	1.19769i
$723$		0			0
$724$	−48.4937	−	83.9936i	−1.80226	−	3.12160i
$725$	−3.12474	−	5.41220i	−0.116050	−	0.201004i
$726$		0			0
$727$	17.9141	+	31.0281i	0.664397	+	1.15077i	0.979448	+	0.201695i	$0.0646451\pi$
$727$	17.9141	+	31.0281i	0.664397	+	1.15077i	−0.315051	+	0.949075i	$0.602022\pi$
$728$	−30.9024	−	58.3329i	−1.14532	−	2.16196i
$729$		0			0
$730$	−25.0309	−	43.3547i	−0.926434	−	1.60463i
$731$	53.4683			1.97760
$732$		0			0
$733$	39.2880			1.45114			0.725568	−	0.688151i	$-0.241577\pi$
$733$	39.2880			1.45114			0.725568	+	0.688151i	$0.241577\pi$
$734$	28.2843	−	48.9898i	1.04399	−	1.80825i
$735$		0			0
$736$	−17.3640	−	30.0753i	−0.640045	−	1.10859i
$737$	0.106934	+	0.185214i	0.00393895	+	0.00682246i
$738$		0			0
$739$	−1.04511	+	1.81019i	−0.0384451	+	0.0665888i	−0.884608	−	0.466336i	$-0.845574\pi$
$739$	−1.04511	+	1.81019i	−0.0384451	+	0.0665888i	0.846163	+	0.532925i	$0.178907\pi$
$740$	18.8022	−	32.5663i	0.691181	−	1.19716i
$741$		0			0
$742$	−14.3640	−	0.523480i	−0.527318	−	0.0192175i
$743$	−15.3633	+	26.6100i	−0.563624	+	0.976226i	0.433552	+	0.901129i	$0.357260\pi$
$743$	−15.3633	+	26.6100i	−0.563624	+	0.976226i	−0.997176	+	0.0750974i	$0.976073\pi$
$744$		0			0
$745$	−17.2953			−0.633650
$746$	2.69963	−	4.67589i	0.0988404	−	0.171197i
$747$		0			0
$748$	9.33379			0.341277
$749$	33.0778	+	1.20548i	1.20864	+	0.0440474i
$750$		0			0
$751$	20.7738			0.758045			0.379023	−	0.925387i	$-0.376260\pi$
$751$	20.7738			0.758045			0.379023	+	0.925387i	$0.376260\pi$
$752$	−21.4869	−	37.2165i	−0.783548	−	1.35714i
$753$		0			0
$754$	−9.57234	+	16.5798i	−0.348604	+	0.603800i
$755$	−19.2174			−0.699394
$756$		0			0
$757$	16.9257			0.615176			0.307588	−	0.951520i	$-0.400478\pi$
$757$	16.9257			0.615176			0.307588	+	0.951520i	$0.400478\pi$
$758$	−9.64214	+	16.7007i	−0.350218	+	0.606596i
$759$		0			0
$760$	−16.1291	−	27.9364i	−0.585063	−	1.01336i
$761$	32.8392			1.19042			0.595210	−	0.803570i	$-0.297069\pi$
$761$	32.8392			1.19042			0.595210	+	0.803570i	$0.297069\pi$
$762$		0			0
$763$	−3.77238	−	7.12092i	−0.136569	−	0.257795i
$764$	−40.2312			−1.45551
$765$		0			0
$766$	16.1662	−	28.0007i	0.584109	−	1.01171i
$767$	13.7417			0.496184
$768$		0			0
$769$	−15.8647	+	27.4784i	−0.572094	+	0.990897i	0.424256	+	0.905542i	$0.360536\pi$
$769$	−15.8647	+	27.4784i	−0.572094	+	0.990897i	−0.996351	+	0.0853545i	$0.972798\pi$
$770$	1.59524	+	3.01126i	0.0574886	+	0.108518i
$771$		0			0
$772$	−20.2694	+	35.1077i	−0.729512	+	1.26355i
$773$	−3.18656	+	5.51928i	−0.114613	+	0.198515i	−0.917625	−	0.397448i	$-0.869896\pi$
$773$	−3.18656	+	5.51928i	−0.114613	+	0.198515i	0.803012	+	0.595963i	$0.203229\pi$
$774$		0			0
$775$	−5.95853	−	10.3205i	−0.214037	−	0.370722i
$776$	−55.8145	−	96.6735i	−2.00362	−	3.47038i
$777$		0			0
$778$	−18.5989	+	32.2142i	−0.666802	+	1.15494i
$779$	20.3855			0.730386
$780$		0			0
$781$	−3.86398			−0.138264
$782$	14.9814	+	25.9486i	0.535735	+	0.927920i
$783$		0			0
$784$	93.4595	+	6.82112i	3.33784	+	0.243612i
$785$	0.150186	+	0.260130i	0.00536037	+	0.00928443i
$786$		0			0
$787$	9.93996	+	17.2165i	0.354321	+	0.613703i	0.987002	−	0.160711i	$-0.0513786\pi$
$787$	9.93996	+	17.2165i	0.354321	+	0.613703i	−0.632680	+	0.774413i	$0.718045\pi$
$788$	48.6148	+	84.2034i	1.73183	+	2.99962i
$789$		0			0
$790$	3.57234	+	6.18748i	0.127098	+	0.220141i
$791$	−12.3288	−	23.2724i	−0.438361	−	0.827471i
$792$		0			0
$793$	−10.6476	−	18.4422i	−0.378109	−	0.654903i
$794$	−22.6414			−0.803515
$795$		0			0
$796$	31.4858			1.11598
$797$	2.90978	−	5.03988i	0.103070	−	0.178522i	−0.809878	−	0.586598i	$-0.800467\pi$
$797$	2.90978	−	5.03988i	0.103070	−	0.178522i	0.912948	+	0.408076i	$0.133800\pi$
$798$		0			0
$799$	9.43199	+	16.3367i	0.333680	+	0.577950i
$800$	−22.7731	−	39.4441i	−0.805149	−	1.39456i
$801$		0			0
$802$	−37.2774	+	64.5663i	−1.31631	+	2.27992i
$803$	−1.75340	+	3.03698i	−0.0618762	+	0.107173i
$804$		0			0
$805$	−4.21634	+	6.72477i	−0.148606	+	0.237017i
$806$	−18.2534	+	31.6158i	−0.642949	+	1.11362i
$807$		0			0
$808$	−129.678			−4.56207
$809$	−1.06113	+	1.83794i	−0.0373075	+	0.0646184i	−0.884076	−	0.467343i	$-0.845211\pi$
$809$	−1.06113	+	1.83794i	−0.0373075	+	0.0646184i	0.846769	+	0.531961i	$0.178545\pi$
$810$		0			0
$811$	−18.4327			−0.647259			−0.323629	−	0.946184i	$-0.604903\pi$
$811$	−18.4327			−0.647259			−0.323629	+	0.946184i	$0.604903\pi$
$812$	−16.5236	−	31.1907i	−0.579864	−	1.09458i
$813$		0			0
$814$	−3.63045			−0.127247
$815$	7.11236	+	12.3190i	0.249135	+	0.431515i
$816$		0			0
$817$	−10.4091	+	18.0291i	−0.364168	+	0.630757i
$818$	−82.4239			−2.88188
$819$		0			0
$820$	−74.8355			−2.61337
$821$	22.5778	−	39.1058i	0.787969	−	1.36480i	−0.139239	−	0.990259i	$-0.544466\pi$
$821$	22.5778	−	39.1058i	0.787969	−	1.36480i	0.927209	−	0.374544i	$-0.122201\pi$
$822$		0			0
$823$	−12.5259	−	21.6954i	−0.436624	−	0.756255i	0.560803	−	0.827949i	$-0.310493\pi$
$823$	−12.5259	−	21.6954i	−0.436624	−	0.756255i	−0.997427	+	0.0716948i	$0.977159\pi$
$824$	−81.6427			−2.84416
$825$		0			0
$826$	−18.5488	+	29.5840i	−0.645394	+	1.02936i
$827$	−14.2953			−0.497095			−0.248548	−	0.968620i	$-0.579953\pi$
$827$	−14.2953			−0.497095			−0.248548	+	0.968620i	$0.579953\pi$
$828$		0			0
$829$	−15.9127	+	27.5617i	−0.552672	+	0.957256i	0.445409	+	0.895327i	$0.353058\pi$
$829$	−15.9127	+	27.5617i	−0.552672	+	0.957256i	−0.998081	+	0.0619285i	$0.980275\pi$
$830$	−23.2953			−0.808591
$831$		0			0
$832$	−32.1341	+	55.6579i	−1.11405	+	1.92959i
$833$	−41.0254	−	2.99423i	−1.42144	−	0.103744i
$834$		0			0
$835$	−3.44760	+	5.97143i	−0.119309	+	0.206650i
$836$	−1.81708	+	3.14728i	−0.0628451	+	0.108851i
$837$		0			0
$838$	−28.3461	−	49.0969i	−0.979200	−	1.69602i
$839$	−8.23924	−	14.2708i	−0.284450	−	0.492682i	0.688026	−	0.725686i	$-0.258478\pi$
$839$	−8.23924	−	14.2708i	−0.284450	−	0.492682i	−0.972476	+	0.233004i	$0.925144\pi$
$840$		0			0
$841$	11.3175	−	19.6025i	0.390258	−	0.675947i
$842$	−93.7563			−3.23105
$843$		0			0
$844$	35.2967			1.21496
$845$	4.04944	+	7.01384i	0.139305	+	0.241283i
$846$		0			0
$847$	−15.3331	+	24.4552i	−0.526852	+	0.840292i
$848$	13.4697	+	23.3303i	0.462553	+	0.801165i
$849$		0			0
$850$	19.6483	+	34.0319i	0.673932	+	1.16728i
$851$	−4.22803	−	7.32316i	−0.144935	−	0.251035i
$852$		0			0
$853$	13.4993	+	23.3815i	0.462208	+	0.800567i	0.999071	−	0.0431023i	$-0.0137242\pi$
$853$	13.4993	+	23.3815i	0.462208	+	0.800567i	−0.536863	+	0.843669i	$0.680391\pi$
$854$	54.0759	+	1.97074i	1.85044	+	0.0674373i
$855$		0			0
$856$	−55.5239	−	96.1702i	−1.89777	−	3.28703i
$857$	−39.1630			−1.33778			−0.668891	−	0.743361i	$-0.733231\pi$
$857$	−39.1630			−1.33778			−0.668891	+	0.743361i	$0.733231\pi$
$858$		0			0
$859$	9.46844			0.323059			0.161529	−	0.986868i	$-0.448357\pi$
$859$	9.46844			0.323059			0.161529	+	0.986868i	$0.448357\pi$
$860$	38.2119	−	66.1850i	1.30302	−	2.25689i
$861$		0			0
$862$	−42.6599	−	73.8892i	−1.45300	−	2.51668i
$863$	−1.00619	−	1.74277i	−0.0342511	−	0.0593246i	0.848392	−	0.529369i	$-0.177571\pi$
$863$	−1.00619	−	1.74277i	−0.0342511	−	0.0593246i	−0.882643	+	0.470044i	$0.844238\pi$
$864$		0			0
$865$	−5.00364	+	8.66656i	−0.170129	+	0.294672i
$866$	−8.75457	+	15.1634i	−0.297492	+	0.515272i
$867$		0			0
$868$	−31.5087	−	59.4773i	−1.06947	−	2.01879i
$869$	0.250241	−	0.433430i	0.00848884	−	0.0147031i
$870$		0			0
$871$	2.00138			0.0678141
$872$	−13.5178	+	23.4135i	−0.457771	+	0.792882i
$873$		0			0
$874$	−11.6662			−0.394615
$875$	−16.6916	+	26.6219i	−0.564278	+	0.899985i
$876$		0			0
$877$	44.6995			1.50939			0.754697	−	0.656073i	$-0.227784\pi$
$877$	44.6995			1.50939			0.754697	+	0.656073i	$0.227784\pi$
$878$	−21.0247	−	36.4158i	−0.709549	−	1.22897i
$879$		0			0
$880$	3.19344	−	5.53120i	0.107651	−	0.186457i
$881$	12.7047			0.428033			0.214017	−	0.976830i	$-0.431345\pi$
$881$	12.7047			0.428033			0.214017	+	0.976830i	$0.431345\pi$
$882$		0			0
$883$	−17.0014			−0.572142			−0.286071	−	0.958208i	$-0.592349\pi$
$883$	−17.0014			−0.572142			−0.286071	+	0.958208i	$0.592349\pi$
$884$	43.6730	−	75.6439i	1.46888	−	2.54418i
$885$		0			0
$886$	33.8454	+	58.6220i	1.13706	+	1.96944i
$887$	1.20149			0.0403420			0.0201710	−	0.999797i	$-0.493579\pi$
$887$	1.20149			0.0403420			0.0201710	+	0.999797i	$0.493579\pi$
$888$		0			0
$889$	−18.8891	+	30.1269i	−0.633521	+	1.01042i
$890$	−40.1075			−1.34441
$891$		0			0
$892$	−16.7658	+	29.0392i	−0.561360	+	0.972304i
$893$	−7.34479			−0.245784
$894$		0			0
$895$	−11.0723	+	19.1779i	−0.370108	+	0.641045i
$896$	−30.9024	−	58.3329i	−1.03238	−	1.94877i
$897$		0			0
$898$	20.6476	−	35.7628i	0.689021	−	1.19342i
$899$	−6.06870	+	10.5113i	−0.202402	+	0.350571i
$900$		0			0
$901$	−5.91273	−	10.2411i	−0.196982	−	0.341182i
$902$	3.61243	+	6.25692i	0.120281	+	0.208333i
$903$		0			0
$904$	−44.1785	+	76.5194i	−1.46936	+	2.54500i
$905$	29.1323			0.968391
$906$		0			0
$907$	17.0631			0.566572			0.283286	−	0.959036i	$-0.408575\pi$
$907$	17.0631			0.566572			0.283286	+	0.959036i	$0.408575\pi$
$908$	−71.6166	−	124.044i	−2.37668	−	4.11653i
$909$		0			0
$910$	31.8683	+	1.16141i	1.05642	+	0.0385002i
$911$	−11.0007	−	19.0538i	−0.364469	−	0.631279i	0.624222	−	0.781247i	$-0.285416\pi$
$911$	−11.0007	−	19.0538i	−0.364469	−	0.631279i	−0.988691	+	0.149968i	$0.952083\pi$
$912$		0			0
$913$	0.815912	+	1.41320i	0.0270027	+	0.0467701i
$914$	27.5901	+	47.7875i	0.912601	+	1.58067i
$915$		0			0
$916$	−21.6712	−	37.5357i	−0.716037	−	1.24021i
$917$	−15.8473	+	25.2753i	−0.523323	+	0.834664i
$918$		0			0
$919$	14.7953	+	25.6262i	0.488051	+	0.845329i	0.999906	−	0.0137429i	$-0.00437462\pi$
$919$	14.7953	+	25.6262i	0.488051	+	0.845329i	−0.511854	+	0.859072i	$0.671041\pi$
$920$	26.6291			0.877934
$921$		0			0
$922$	−110.194			−3.62904
$923$	−18.0796	+	31.3148i	−0.595098	+	1.03074i
$924$		0			0
$925$	−5.54511	−	9.60442i	−0.182322	−	0.315791i
$926$	13.3745	+	23.1653i	0.439513	+	0.761259i
$927$		0			0
$928$	−23.1941	+	40.1734i	−0.761385	+	1.31876i
$929$	1.34981	−	2.33795i	0.0442860	−	0.0767055i	−0.843033	−	0.537862i	$-0.819232\pi$
$929$	1.34981	−	2.33795i	0.0442860	−	0.0767055i	0.887319	+	0.461157i	$0.152565\pi$
$930$		0			0
$931$	8.99636	−	13.2505i	0.294844	−	0.434268i
$932$	72.4992	−	125.572i	2.37479	−	4.11325i
$933$		0			0
$934$	−47.8886			−1.56696
$935$	−1.40180	+	2.42800i	−0.0458439	+	0.0794040i
$936$		0			0
$937$	39.4472			1.28869			0.644343	−	0.764737i	$-0.277131\pi$
$937$	39.4472			1.28869			0.644343	+	0.764737i	$0.277131\pi$
$938$	−2.70149	+	4.30868i	−0.0882067	+	0.140684i
$939$		0			0
$940$	26.9629			0.879432
$941$	19.8622	+	34.4023i	0.647489	+	1.12148i	0.983721	+	0.179705i	$0.0575142\pi$
$941$	19.8622	+	34.4023i	0.647489	+	1.12148i	−0.336232	+	0.941779i	$0.609152\pi$
$942$		0			0
$943$	−8.41411	+	14.5737i	−0.274001	+	0.474584i
$944$	65.4449			2.13005
$945$		0			0
$946$	−7.37822			−0.239886
$947$	−7.86515	+	13.6228i	−0.255583	+	0.442683i	−0.965054	−	0.262052i	$-0.915601\pi$
$947$	−7.86515	+	13.6228i	−0.255583	+	0.442683i	0.709471	+	0.704735i	$0.248934\pi$
$948$		0			0
$949$	16.4084	+	28.4202i	0.532639	+	0.922558i
$950$	−15.3004			−0.496410
$951$		0			0
$952$	64.6035	+	121.949i	2.09381	+	3.95238i
$953$	−30.2064			−0.978482			−0.489241	−	0.872149i	$-0.662726\pi$
$953$	−30.2064			−0.978482			−0.489241	+	0.872149i	$0.662726\pi$
$954$		0			0
$955$	6.04216	−	10.4653i	0.195520	−	0.338650i
$956$	147.344			4.76546
$957$		0			0
$958$	31.8683	−	55.1975i	1.02962	−	1.78335i
$959$	−5.30903	+	8.46754i	−0.171438	+	0.273431i
$960$		0			0
$961$	3.92766	−	6.80290i	0.126699	−	0.219448i
$962$	−16.9869	+	29.4222i	−0.547681	+	0.948611i
$963$		0			0
$964$	59.5697	+	103.178i	1.91861	+	3.32313i
$965$	−6.08836	−	10.5454i	−0.195991	−	0.339467i
$966$		0			0
$967$	3.09455	−	5.35992i	0.0995141	−	0.172364i	−0.811970	−	0.583700i	$-0.801604\pi$
$967$	3.09455	−	5.35992i	0.0995141	−	0.172364i	0.911484	+	0.411336i	$0.134938\pi$
$968$	96.8391			3.11253
$969$		0			0
$970$	53.9257			1.73145
$971$	−1.08582	−	1.88069i	−0.0348455	−	0.0603542i	0.848077	−	0.529873i	$-0.177761\pi$
$971$	−1.08582	−	1.88069i	−0.0348455	−	0.0603542i	−0.882922	+	0.469519i	$0.844427\pi$
$972$		0			0
$973$	20.7077	+	39.0888i	0.663858	+	1.25313i
$974$	47.0716	+	81.5304i	1.50827	+	2.61240i
$975$		0			0
$976$	−50.7094	−	87.8312i	−1.62317	−	2.81141i
$977$	−5.72803	−	9.92124i	−0.183256	−	0.317409i	0.759732	−	0.650237i	$-0.225330\pi$
$977$	−5.72803	−	9.92124i	−0.183256	−	0.317409i	−0.942987	+	0.332828i	$0.891997\pi$
$978$		0			0
$979$	1.40476	+	2.43311i	0.0448962	+	0.0777626i
$980$	−33.0258	+	48.6428i	−1.05497	+	1.55384i
$981$		0			0
$982$	−31.3225	−	54.2522i	−0.999541	−	1.73126i
$983$	−44.8021			−1.42896			−0.714482	−	0.699654i	$-0.753338\pi$
$983$	−44.8021			−1.42896			−0.714482	+	0.699654i	$0.753338\pi$
$984$		0			0
$985$	−29.2051			−0.930550
$986$	20.0116	−	34.6611i	0.637300	−	1.10384i
$987$		0			0
$988$	17.0043	+	29.4524i	0.540980	+	0.937005i
$989$	−8.59269	−	14.8830i	−0.273232	−	0.473251i
$990$		0			0
$991$	12.1476	−	21.0403i	0.385882	−	0.668368i	−0.606009	−	0.795458i	$-0.707230\pi$
$991$	12.1476	−	21.0403i	0.385882	−	0.668368i	0.991891	+	0.127090i	$0.0405637\pi$
$992$	−44.2286	+	76.6063i	−1.40426	+	2.43225i
$993$		0			0
$994$	−43.0123	−	81.1921i	−1.36427	−	2.57526i
$995$	−4.72872	+	8.19038i	−0.149910	+	0.259653i
$996$		0			0
$997$	−11.3251			−0.358671			−0.179335	−	0.983788i	$-0.557395\pi$
$997$	−11.3251			−0.358671			−0.179335	+	0.983788i	$0.557395\pi$
$998$	−7.18794	+	12.4499i	−0.227530	+	0.394094i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.g.i.109.3		6
3.2	odd	2		567.2.g.h.109.1		6
7.2	even	3		567.2.h.h.352.1		6
9.2	odd	6		567.2.h.i.298.3		6
9.4	even	3		189.2.e.f.109.3	yes	6
9.5	odd	6		189.2.e.e.109.1	✓	6
9.7	even	3		567.2.h.h.298.1		6
21.2	odd	6		567.2.h.i.352.3		6
63.2	odd	6		567.2.g.h.541.1		6
63.4	even	3		1323.2.a.x.1.1		3
63.16	even	3	inner	567.2.g.i.541.3		6
63.23	odd	6		189.2.e.e.163.1	yes	6
63.31	odd	6		1323.2.a.y.1.1		3
63.32	odd	6		1323.2.a.ba.1.3		3
63.58	even	3		189.2.e.f.163.3	yes	6
63.59	even	6		1323.2.a.z.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.e.e.109.1	✓	6	9.5	odd	6
189.2.e.e.163.1	yes	6	63.23	odd	6
189.2.e.f.109.3	yes	6	9.4	even	3
189.2.e.f.163.3	yes	6	63.58	even	3
567.2.g.h.109.1		6	3.2	odd	2
567.2.g.h.541.1		6	63.2	odd	6
567.2.g.i.109.3		6	1.1	even	1	trivial
567.2.g.i.541.3		6	63.16	even	3	inner
567.2.h.h.298.1		6	9.7	even	3
567.2.h.h.352.1		6	7.2	even	3
567.2.h.i.298.3		6	9.2	odd	6
567.2.h.i.352.3		6	21.2	odd	6
1323.2.a.x.1.1		3	63.4	even	3
1323.2.a.y.1.1		3	63.31	odd	6
1323.2.a.z.1.3		3	63.59	even	6
1323.2.a.ba.1.3		3	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)

\(f(q)\)	\(=\)	\(q+(1.34981 - 2.33795i) q^{2} +(-2.64400 - 4.57954i) q^{4} +1.58836 q^{5} +(1.40545 - 2.24159i) q^{7} -8.87636 q^{8} +(2.14400 - 3.71351i) q^{10} -0.300372 q^{11} +(-1.40545 + 2.43430i) q^{13} +(-3.34362 - 6.31159i) q^{14} +(-6.69344 + 11.5934i) q^{16} +(2.93818 - 5.08907i) q^{17} +(1.14400 + 1.98146i) q^{19} +(-4.19963 - 7.27397i) q^{20} +(-0.405446 + 0.702253i) q^{22} -1.88874 q^{23} -2.47710 q^{25} +(3.79418 + 6.57172i) q^{26} +(-13.9814 - 0.509538i) q^{28} +(1.26145 + 2.18490i) q^{29} +(2.40545 + 4.16635i) q^{31} +(9.19344 + 15.9235i) q^{32} +(-7.93199 - 13.7386i) q^{34} +(2.23236 - 3.56046i) q^{35} +(2.23855 + 3.87728i) q^{37} +6.17673 q^{38} -14.0989 q^{40} +(4.45489 - 7.71609i) q^{41} +(4.54944 + 7.87987i) q^{43} +(0.794182 + 1.37556i) q^{44} +(-2.54944 + 4.41576i) q^{46} +(-1.60507 + 2.78007i) q^{47} +(-3.04944 - 6.30087i) q^{49} +(-3.34362 + 5.79133i) q^{50} +14.8640 q^{52} +(1.00619 - 1.74277i) q^{53} -0.477100 q^{55} +(-12.4752 + 19.8971i) q^{56} +6.81089 q^{58} +(-2.44437 - 4.23377i) q^{59} +(-3.78799 + 6.56099i) q^{61} +12.9876 q^{62} +22.8640 q^{64} +(-2.23236 + 3.86656i) q^{65} +(-0.356004 - 0.616617i) q^{67} -31.0741 q^{68} +(-5.31089 - 10.0251i) q^{70} +12.8640 q^{71} +(5.83743 - 10.1107i) q^{73} +12.0865 q^{74} +(6.04944 - 10.4779i) q^{76} +(-0.422156 + 0.673310i) q^{77} +(-0.833104 + 1.44298i) q^{79} +(-10.6316 + 18.4145i) q^{80} +(-12.0265 - 20.8306i) q^{82} +(-2.71634 - 4.70484i) q^{83} +(4.66690 - 8.08330i) q^{85} +24.5636 q^{86} +2.66621 q^{88} +(-4.67673 - 8.10033i) q^{89} +(3.48143 + 6.57172i) q^{91} +(4.99381 + 8.64953i) q^{92} +(4.33310 + 7.50516i) q^{94} +(1.81708 + 3.14728i) q^{95} +(6.28799 + 10.8911i) q^{97} +(-18.8473 - 1.37556i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 2 q^{2} - 4 q^{4} - 2 q^{5} + 2 q^{7} - 18 q^{8} + q^{10} - 14 q^{11} - 2 q^{13} + 4 q^{14} - 10 q^{16} - 5 q^{19} - 13 q^{20} + 4 q^{22} - 12 q^{23} - 4 q^{25} + 17 q^{26} - 30 q^{28} + 13 q^{29}+ \cdots - 49 q^{98}+O(q^{100}) \) 6 * q + 2 * q^2 - 4 * q^4 - 2 * q^5 + 2 * q^7 - 18 * q^8 + q^10 - 14 * q^11 - 2 * q^13 + 4 * q^14 - 10 * q^16 - 5 * q^19 - 13 * q^20 + 4 * q^22 - 12 * q^23 - 4 * q^25 + 17 * q^26 - 30 * q^28 + 13 * q^29 + 8 * q^31 + 25 * q^32 - 12 * q^34 - 10 * q^35 + 8 * q^37 + 14 * q^38 - 48 * q^40 + 2 * q^41 + 9 * q^43 - q^44 + 3 * q^46 + 9 * q^47 + 4 * q^50 + 18 * q^52 + 24 * q^53 + 8 * q^55 - 3 * q^56 + 28 * q^58 - 15 * q^59 + q^61 + 42 * q^62 + 66 * q^64 + 10 * q^65 - 14 * q^67 - 78 * q^68 - 19 * q^70 + 6 * q^71 - 7 * q^73 + 18 * q^76 + 11 * q^77 - 6 * q^79 - 16 * q^80 - 43 * q^82 + 3 * q^83 + 27 * q^85 + 64 * q^86 + 18 * q^88 - 5 * q^89 - 33 * q^91 + 12 * q^92 + 27 * q^94 + 16 * q^95 + 14 * q^97 - 49 * q^98

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