LMFDB - Embedded newform 567.2.h.h.352.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([4, 4]))

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

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

chi := DirichletCharacter("567.298");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.52751779461$
Analytic rank:	$0$
Dimension:	$6$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 189)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			352.1
Root			$0.500000 - 0.224437i$ of defining polynomial
Character	$\chi$	$=$	567.352
Dual form			567.2.h.h.298.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.69963 q^{2} +5.28799 q^{4} +(-0.794182 - 1.37556i) q^{5} +(-2.64400 + 0.0963576i) q^{7} -8.87636 q^{8} +(2.14400 + 3.71351i) q^{10} +(0.150186 - 0.260130i) q^{11} +(-1.40545 + 2.43430i) q^{13} +(7.13781 - 0.260130i) q^{14} +13.3869 q^{16} +(2.93818 + 5.08907i) q^{17} +(1.14400 - 1.98146i) q^{19} +(-4.19963 - 7.27397i) q^{20} +(-0.405446 + 0.702253i) q^{22} +(0.944368 + 1.63569i) q^{23} +(1.23855 - 2.14523i) q^{25} +(3.79418 - 6.57172i) q^{26} +(-13.9814 + 0.509538i) q^{28} +(1.26145 + 2.18490i) q^{29} -4.81089 q^{31} -18.3869 q^{32} +(-7.93199 - 13.7386i) q^{34} +(2.23236 + 3.56046i) q^{35} +(2.23855 - 3.87728i) q^{37} +(-3.08836 + 5.34920i) q^{38} +(7.04944 + 12.2100i) q^{40} +(4.45489 - 7.71609i) q^{41} +(4.54944 + 7.87987i) q^{43} +(0.794182 - 1.37556i) q^{44} +(-2.54944 - 4.41576i) q^{46} +3.21015 q^{47} +(6.98143 - 0.509538i) q^{49} +(-3.34362 + 5.79133i) q^{50} +(-7.43199 + 12.8726i) q^{52} +(1.00619 + 1.74277i) q^{53} -0.477100 q^{55} +(23.4691 - 0.855304i) q^{56} +(-3.40545 - 5.89841i) q^{58} +4.88874 q^{59} +7.57598 q^{61} +12.9876 q^{62} +22.8640 q^{64} +4.46472 q^{65} +0.712008 q^{67} +(15.5371 + 26.9110i) q^{68} +(-6.02654 - 9.61192i) q^{70} +12.8640 q^{71} +(5.83743 + 10.1107i) q^{73} +(-6.04325 + 10.4672i) q^{74} +(6.04944 - 10.4779i) q^{76} +(-0.372026 + 0.702253i) q^{77} +1.66621 q^{79} +(-10.6316 - 18.4145i) q^{80} +(-12.0265 + 20.8306i) q^{82} +(-2.71634 - 4.70484i) q^{83} +(4.66690 - 8.08330i) q^{85} +(-12.2818 - 21.2727i) q^{86} +(-1.33310 + 2.30900i) q^{88} +(-4.67673 + 8.10033i) q^{89} +(3.48143 - 6.57172i) q^{91} +(4.99381 + 8.64953i) q^{92} -8.66621 q^{94} -3.63416 q^{95} +(6.28799 + 10.8911i) q^{97} +(-18.8473 + 1.37556i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 4 q^{2} + 8 q^{4} + q^{5} - 4 q^{7} - 18 q^{8} + q^{10} + 7 q^{11} - 2 q^{13} + 13 q^{14} + 20 q^{16} - 5 q^{19} - 13 q^{20} + 4 q^{22} + 6 q^{23} + 2 q^{25} + 17 q^{26} - 30 q^{28} + 13 q^{29}+ \cdots - 49 q^{98}+O(q^{100}) $ 6 * q - 4 * q^2 + 8 * q^4 + q^5 - 4 * q^7 - 18 * q^8 + q^10 + 7 * q^11 - 2 * q^13 + 13 * q^14 + 20 * q^16 - 5 * q^19 - 13 * q^20 + 4 * q^22 + 6 * q^23 + 2 * q^25 + 17 * q^26 - 30 * q^28 + 13 * q^29 - 16 * q^31 - 50 * q^32 - 12 * q^34 - 10 * q^35 + 8 * q^37 - 7 * q^38 + 24 * q^40 + 2 * q^41 + 9 * q^43 - q^44 + 3 * q^46 - 18 * q^47 - 12 * q^49 + 4 * q^50 - 9 * q^52 + 24 * q^53 + 8 * q^55 + 51 * q^56 - 14 * q^58 + 30 * q^59 - 2 * q^61 + 42 * q^62 + 66 * q^64 - 20 * q^65 + 28 * q^67 + 39 * q^68 - 7 * q^70 + 6 * q^71 - 7 * q^73 + 18 * q^76 - 10 * q^77 + 12 * q^79 - 16 * q^80 - 43 * q^82 + 3 * q^83 + 27 * q^85 - 32 * q^86 - 9 * q^88 - 5 * q^89 - 33 * q^91 + 12 * q^92 - 54 * q^94 - 32 * q^95 + 14 * q^97 - 49 * q^98

Character values

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

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

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 $

$2$	−2.69963			−1.90893			−0.954463	−	0.298330i	$-0.903570\pi$
$2$	−2.69963			−1.90893			−0.954463	+	0.298330i	$0.903570\pi$
$3$		0			0
$3$		0			0
$4$	5.28799			2.64400
$5$	−0.794182	−	1.37556i	−0.355169	−	0.615171i	0.631978	−	0.774986i	$-0.282243\pi$
$5$	−0.794182	−	1.37556i	−0.355169	−	0.615171i	−0.987147	+	0.159816i	$0.948910\pi$
$6$		0			0
$7$	−2.64400	+	0.0963576i	−0.999337	+	0.0364197i
$7$	−2.64400	+	0.0963576i	−0.999337	+	0.0364197i
$8$	−8.87636			−3.13827
$9$		0			0
$10$	2.14400	+	3.71351i	0.677991	+	1.17432i
$11$	0.150186	−	0.260130i	0.0452828	−	0.0784320i	−0.842496	−	0.538703i	$-0.818914\pi$
$11$	0.150186	−	0.260130i	0.0452828	−	0.0784320i	0.887778	+	0.460271i	$0.152248\pi$
$12$		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	$0.294123\pi$
$14$	7.13781	−	0.260130i	1.90766	−	0.0695226i
$15$		0			0
$16$	13.3869			3.34672
$17$	2.93818	+	5.08907i	0.712613	+	1.23428i	0.963873	+	0.266362i	$0.0858217\pi$
$17$	2.93818	+	5.08907i	0.712613	+	1.23428i	−0.251260	+	0.967920i	$0.580845\pi$
$18$		0			0
$19$	1.14400	−	1.98146i	0.262451	−	0.454578i	−0.704442	−	0.709762i	$-0.748803\pi$
$19$	1.14400	−	1.98146i	0.262451	−	0.454578i	0.966893	+	0.255184i	$0.0821360\pi$
$20$	−4.19963	−	7.27397i	−0.939065	−	1.62651i
$21$		0			0
$22$	−0.405446	+	0.702253i	−0.0864414	+	0.149721i
$23$	0.944368	+	1.63569i	0.196914	+	0.341066i	0.947526	−	0.319678i	$-0.103575\pi$
$23$	0.944368	+	1.63569i	0.196914	+	0.341066i	−0.750612	+	0.660743i	$0.770241\pi$
$24$		0			0
$25$	1.23855	−	2.14523i	0.247710	−	0.429046i
$26$	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
$31$	−4.81089			−0.864062			−0.432031	−	0.901859i	$-0.642203\pi$
$31$	−4.81089			−0.864062			−0.432031	+	0.901859i	$0.642203\pi$
$32$	−18.3869			−3.25037
$33$		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	−0.621240	−	0.783620i	$-0.713371\pi$
$37$	2.23855	−	3.87728i	0.368015	−	0.637421i	0.989255	+	0.146199i	$0.0467041\pi$
$38$	−3.08836	+	5.34920i	−0.500999	+	0.867755i
$39$		0			0
$40$	7.04944	+	12.2100i	1.11461	+	1.93057i
$41$	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
$47$	3.21015			0.468248			0.234124	−	0.972207i	$-0.424778\pi$
$47$	3.21015			0.468248			0.234124	+	0.972207i	$0.424778\pi$
$48$		0			0
$49$	6.98143	−	0.509538i	0.997347	−	0.0727912i
$50$	−3.34362	+	5.79133i	−0.472860	+	0.819017i
$51$		0			0
$52$	−7.43199	+	12.8726i	−1.03063	+	1.78511i
$53$	1.00619	+	1.74277i	0.138211	+	0.239388i	0.926819	−	0.375507i	$-0.122532\pi$
$53$	1.00619	+	1.74277i	0.138211	+	0.239388i	−0.788609	+	0.614895i	$0.789198\pi$
$54$		0			0
$55$	−0.477100			−0.0643321
$56$	23.4691	−	0.855304i	3.13618	−	0.114295i
$57$		0			0
$58$	−3.40545	−	5.89841i	−0.447157	−	0.774499i
$59$	4.88874			0.636459			0.318230	−	0.948014i	$-0.396912\pi$
$59$	4.88874			0.636459			0.318230	+	0.948014i	$0.396912\pi$
$60$		0			0
$61$	7.57598			0.970005			0.485003	−	0.874513i	$-0.338819\pi$
$61$	7.57598			0.970005			0.485003	+	0.874513i	$0.338819\pi$
$62$	12.9876			1.64943
$63$		0			0
$64$	22.8640			2.85800
$65$	4.46472			0.553780
$66$		0			0
$67$	0.712008			0.0869856			0.0434928	−	0.999054i	$-0.486151\pi$
$67$	0.712008			0.0869856			0.0434928	+	0.999054i	$0.486151\pi$
$68$	15.5371	+	26.9110i	1.88415	+	3.26344i
$69$		0			0
$70$	−6.02654	−	9.61192i	−0.720310	−	1.14884i
$71$	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	0.973993	+	0.226580i	$0.0727543\pi$
$73$	5.83743	+	10.1107i	0.683220	+	1.18337i	−0.290773	+	0.956792i	$0.593912\pi$
$74$	−6.04325	+	10.4672i	−0.702514	+	1.21679i
$75$		0			0
$76$	6.04944	−	10.4779i	0.693919	−	1.20190i
$77$	−0.372026	+	0.702253i	−0.0423962	+	0.0800292i
$78$		0			0
$79$	1.66621			0.187463			0.0937315	−	0.995598i	$-0.470120\pi$
$79$	1.66621			0.187463			0.0937315	+	0.995598i	$0.470120\pi$
$80$	−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
$86$	−12.2818	−	21.2727i	−1.32438	−	2.29389i
$87$		0			0
$88$	−1.33310	+	2.30900i	−0.142109	+	0.246141i
$89$	−4.67673	+	8.10033i	−0.495732	+	0.858633i	−0.999988	−	0.00492107i	$-0.998434\pi$
$89$	−4.67673	+	8.10033i	−0.495732	+	0.858633i	0.504256	+	0.863554i	$0.331767\pi$
$90$		0			0
$91$	3.48143	−	6.57172i	0.364953	−	0.688903i
$92$	4.99381	+	8.64953i	0.520641	+	0.901776i
$93$		0			0
$94$	−8.66621			−0.893851
$95$	−3.63416			−0.372857
$96$		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
$101$	−7.30470	+	12.6521i	−0.726845	+	1.25893i	0.231365	+	0.972867i	$0.425681\pi$
$101$	−7.30470	+	12.6521i	−0.726845	+	1.25893i	−0.958210	+	0.286066i	$0.907652\pi$
$102$		0			0
$103$	−4.59888	−	7.96550i	−0.453142	−	0.784864i	0.545438	−	0.838151i	$-0.316363\pi$
$103$	−4.59888	−	7.96550i	−0.453142	−	0.784864i	−0.998579	+	0.0532872i	$0.983030\pi$
$104$	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	−0.387377	−	0.921921i	$-0.626619\pi$
$107$	6.25526	−	10.8344i	0.604719	−	1.04740i	0.992096	−	0.125482i	$-0.0400478\pi$
$108$		0			0
$109$	1.52290	+	2.63774i	0.145867	+	0.252650i	0.929696	−	0.368327i	$-0.120069\pi$
$109$	1.52290	+	2.63774i	0.145867	+	0.252650i	−0.783829	+	0.620977i	$0.786736\pi$
$110$	1.28799			0.122805
$111$		0			0
$112$	−35.3948	+	1.28993i	−3.34450	+	0.121887i
$113$	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
$115$	1.50000	−	2.59808i	0.139876	−	0.242272i
$116$	6.67054	+	11.5537i	0.619344	+	1.07274i
$117$		0			0
$118$	−13.1978			−1.21495
$119$	−8.25890	−	13.1724i	−0.757092	−	1.20751i
$120$		0			0
$121$	5.45489	+	9.44814i	0.495899	+	0.858922i
$122$	−20.4523			−1.85167
$123$		0			0
$124$	−25.4400			−2.28458
$125$	−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	$0.703364\pi$
$128$	−24.9505			−2.20533
$129$		0			0
$130$	−12.0531			−1.05713
$131$	5.63781	+	9.76497i	0.492577	+	0.853169i	0.999963	−	0.00854976i	$-0.00272151\pi$
$131$	5.63781	+	9.76497i	0.492577	+	0.853169i	−0.507386	+	0.861719i	$0.669388\pi$
$132$		0			0
$133$	−2.83379	+	5.34920i	−0.245721	+	0.463835i
$134$	−1.92216			−0.166049
$135$		0			0
$136$	−26.0803	−	45.1724i	−2.23637	−	3.87350i
$137$	1.88874	−	3.27139i	0.161366	−	0.279493i	−0.773993	−	0.633194i	$-0.781744\pi$
$137$	1.88874	−	3.27139i	0.161366	−	0.279493i	0.935359	+	0.353701i	$0.115077\pi$
$138$		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	$0.915788\pi$
$140$	11.8047	+	18.8277i	0.997679	+	1.59123i
$141$		0			0
$142$	−34.7280			−2.91431
$143$	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
$149$	5.44437	+	9.42992i	0.446020	+	0.772529i	0.998123	−	0.0612468i	$-0.0195077\pi$
$149$	5.44437	+	9.42992i	0.446020	+	0.772529i	−0.552103	+	0.833776i	$0.686174\pi$
$150$		0			0
$151$	6.04944	−	10.4779i	0.492297	−	0.852683i	−0.507664	−	0.861555i	$-0.669491\pi$
$151$	6.04944	−	10.4779i	0.492297	−	0.852683i	0.999961	+	0.00887237i	$0.00282420\pi$
$152$	−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
$157$	−0.189108			−0.0150924			−0.00754622	−	0.999972i	$-0.502402\pi$
$157$	−0.189108			−0.0150924			−0.00754622	+	0.999972i	$0.502402\pi$
$158$	−4.49814			−0.357853
$159$		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	−0.635650	−	0.771978i	$-0.719268\pi$
$163$	4.47779	−	7.75576i	0.350727	−	0.607478i	0.986377	+	0.164500i	$0.0526010\pi$
$164$	23.5574	−	40.8026i	1.83953	−	3.18615i
$165$		0			0
$166$	7.33310	+	12.7013i	0.569159	+	0.985813i
$167$	−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
$173$	6.30037			0.479008			0.239504	−	0.970895i	$-0.423015\pi$
$173$	6.30037			0.479008			0.239504	+	0.970895i	$0.423015\pi$
$174$		0			0
$175$	−3.06801	+	5.79133i	−0.231920	+	0.437783i
$176$	2.01052	−	3.48232i	0.151549	−	0.262490i
$177$		0			0
$178$	12.6254	−	21.8679i	0.946316	−	1.63907i
$179$	−6.97091	−	12.0740i	−0.521030	−	0.902451i	−0.999701	−	0.0244564i	$-0.992215\pi$
$179$	−6.97091	−	12.0740i	−0.521030	−	0.902451i	0.478671	−	0.877995i	$-0.341119\pi$
$180$		0			0
$181$	18.3411			1.36328			0.681641	−	0.731687i	$-0.261267\pi$
$181$	18.3411			1.36328			0.681641	+	0.731687i	$0.261267\pi$
$182$	−9.39857	+	17.7412i	−0.696668	+	1.31506i
$183$		0			0
$184$	−8.38255	−	14.5190i	−0.617969	−	1.07035i
$185$	−7.11126			−0.522831
$186$		0			0
$187$	1.76509			0.129076
$188$	16.9752			1.23805
$189$		0			0
$190$	9.81089			0.711757
$191$	−7.60803			−0.550498			−0.275249	−	0.961373i	$-0.588760\pi$
$191$	−7.60803			−0.550498			−0.275249	+	0.961373i	$0.588760\pi$
$192$		0			0
$193$	7.66621			0.551826			0.275913	−	0.961183i	$-0.411020\pi$
$193$	7.66621			0.551826			0.275913	+	0.961183i	$0.411020\pi$
$194$	−16.9752	−	29.4020i	−1.21875	−	2.11094i
$195$		0			0
$196$	36.9177	−	2.69443i	2.63698	−	0.192460i
$197$	−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	0.741000	−	0.671505i	$-0.234352\pi$
$199$	−2.97710	−	5.15649i	−0.211041	−	0.365534i	−0.952041	+	0.305972i	$0.901019\pi$
$200$	−10.9938	+	19.0418i	−0.777380	+	1.34646i
$201$		0			0
$202$	19.7200	−	34.1560i	1.38749	−	2.40321i
$203$	−3.54580	−	5.65531i	−0.248866	−	0.396925i
$204$		0			0
$205$	−14.1520			−0.988416
$206$	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	$0.240460\pi$
$212$	5.32072	+	9.21576i	0.365429	+	0.632941i
$213$		0			0
$214$	−16.8869	+	29.2489i	−1.15436	+	1.99942i
$215$	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
$220$	−2.52290			−0.170094
$221$	−16.5178			−1.11111
$222$		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
$227$	−13.5433	+	23.4576i	−0.898897	+	1.55694i	−0.0699913	+	0.997548i	$0.522297\pi$
$227$	−13.5433	+	23.4576i	−0.898897	+	1.55694i	−0.828906	+	0.559388i	$0.811036\pi$
$228$		0			0
$229$	−4.09820	−	7.09828i	−0.270816	−	0.469068i	0.698255	−	0.715849i	$-0.253960\pi$
$229$	−4.09820	−	7.09828i	−0.270816	−	0.469068i	−0.969071	+	0.246782i	$0.920627\pi$
$230$	−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	0.0683649	−	0.997660i	$-0.478222\pi$
$233$	13.7101	−	23.7467i	0.898182	−	1.55570i	0.829817	−	0.558036i	$-0.188445\pi$
$234$		0			0
$235$	−2.54944	−	4.41576i	−0.166307	−	0.288053i
$236$	25.8516			1.68280
$237$		0			0
$238$	22.2960	+	35.5605i	1.44523	+	2.30505i
$239$	−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
$241$	11.2651	−	19.5117i	0.725648	−	1.25686i	−0.233058	−	0.972463i	$-0.574873\pi$
$241$	11.2651	−	19.5117i	0.725648	−	1.25686i	0.958707	−	0.284397i	$-0.0917934\pi$
$242$	−14.7262	−	25.5065i	−0.946634	−	1.63962i
$243$		0			0
$244$	40.0617			2.56469
$245$	−6.24543	−	9.19874i	−0.399006	−	0.587686i
$246$		0			0
$247$	3.21565	+	5.56967i	0.204607	+	0.354390i
$248$	42.7032			2.71166
$249$		0			0
$250$	32.0617			2.02776
$251$	−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
$254$	36.2829			2.27659
$255$		0			0
$256$	21.6291			1.35182
$257$	−5.10074	−	8.83475i	−0.318176	−	0.551096i	0.661932	−	0.749564i	$-0.269737\pi$
$257$	−5.10074	−	8.83475i	−0.318176	−	0.551096i	−0.980107	+	0.198468i	$0.936404\pi$
$258$		0			0
$259$	−5.54511	+	10.4672i	−0.344556	+	0.650401i
$260$	23.6094			1.46419
$261$		0			0
$262$	−15.2200	−	26.3618i	−0.940294	−	1.62864i
$263$	14.2305	−	24.6480i	0.877490	−	1.51986i	0.0234042	−	0.999726i	$-0.492550\pi$
$263$	14.2305	−	24.6480i	0.877490	−	1.51986i	0.854086	−	0.520132i	$-0.174117\pi$
$264$		0			0
$265$	1.59820	−	2.76816i	0.0981764	−	0.170046i
$266$	7.65019	−	14.4409i	0.469063	−	0.885426i
$267$		0			0
$268$	3.76509			0.229990
$269$	7.43818	+	12.8833i	0.453514	+	0.785509i	0.998601	−	0.0528702i	$-0.0168370\pi$
$269$	7.43818	+	12.8833i	0.453514	+	0.785509i	−0.545088	+	0.838379i	$0.683504\pi$
$270$		0			0
$271$	−0.0222115	+	0.0384714i	−0.00134925	+	0.00233697i	−0.866699	−	0.498831i	$-0.833763\pi$
$271$	−0.0222115	+	0.0384714i	−0.00134925	+	0.00233697i	0.865350	+	0.501168i	$0.167096\pi$
$272$	39.3330	+	68.1268i	2.38492	+	4.13079i
$273$		0			0
$274$	−5.09888	+	8.83153i	−0.308035	+	0.533532i
$275$	−0.372026	−	0.644367i	−0.0224340	−	0.0388568i
$276$		0			0
$277$	−7.83743	+	13.5748i	−0.470906	+	0.815633i	−0.999446	−	0.0332754i	$-0.989406\pi$
$277$	−7.83743	+	13.5748i	−0.470906	+	0.815633i	0.528540	+	0.848908i	$0.322739\pi$
$278$	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
$283$	6.00728			0.357096			0.178548	−	0.983931i	$-0.442860\pi$
$283$	6.00728			0.357096			0.178548	+	0.983931i	$0.442860\pi$
$284$	68.0246			4.03652
$285$		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
$290$	−5.40909	+	9.36882i	−0.317633	+	0.550156i
$291$		0			0
$292$	30.8683	+	53.4655i	1.80643	+	3.12883i
$293$	−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
$299$	−5.30903			−0.307029
$300$		0			0
$301$	−12.7880	−	20.3960i	−0.737088	−	1.17560i
$302$	−16.3312	+	28.2865i	−0.939758	+	1.62771i
$303$		0			0
$304$	15.3145	−	26.5256i	0.878349	−	1.52134i
$305$	−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	$0.716666\pi$
$308$	−1.96727	+	3.71351i	−0.112096	+	0.211597i
$309$		0			0
$310$	−10.3145	−	17.8653i	−0.585826	−	1.01468i
$311$	−7.97524			−0.452234			−0.226117	−	0.974100i	$-0.572603\pi$
$311$	−7.97524			−0.452234			−0.226117	+	0.974100i	$0.572603\pi$
$312$		0			0
$313$	−22.5302			−1.27348			−0.636741	−	0.771078i	$-0.719718\pi$
$313$	−22.5302			−1.27348			−0.636741	+	0.771078i	$0.719718\pi$
$314$	0.510520			0.0288103
$315$		0			0
$316$	8.81089			0.495651
$317$	19.9381			1.11984			0.559918	−	0.828548i	$-0.310833\pi$
$317$	19.9381			1.11984			0.559918	+	0.828548i	$0.310833\pi$
$318$		0			0
$319$	0.757808			0.0424291
$320$	−18.1582	−	31.4509i	−1.01507	−	1.75816i
$321$		0			0
$322$	7.16621	+	11.4296i	0.399357	+	0.636947i
$323$	13.4451			0.748103
$324$		0			0
$325$	3.48143	+	6.03001i	0.193115	+	0.334485i
$326$	−12.0884	+	20.9377i	−0.669513	+	1.15963i
$327$		0			0
$328$	−39.5432	+	68.4908i	−2.18341	+	3.78177i
$329$	−8.48762	+	0.309322i	−0.467938	+	0.0170535i
$330$		0			0
$331$	23.6304			1.29885			0.649423	−	0.760427i	$-0.275010\pi$
$331$	23.6304			1.29885			0.649423	+	0.760427i	$0.275010\pi$
$332$	−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	$0.0571393\pi$
$338$	−6.88255	−	11.9209i	−0.374361	−	0.648413i
$339$		0			0
$340$	24.6785	−	42.7444i	1.33838	−	2.31814i
$341$	−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
$346$	−17.0087			−0.914391
$347$	3.84431			0.206374			0.103187	−	0.994662i	$-0.467096\pi$
$347$	3.84431			0.206374			0.103187	+	0.994662i	$0.467096\pi$
$348$		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
$353$	−1.78180	+	3.08617i	−0.0948358	+	0.164260i	−0.909540	−	0.415616i	$-0.863566\pi$
$353$	−1.78180	+	3.08617i	−0.0948358	+	0.164260i	0.814704	+	0.579877i	$0.196899\pi$
$354$		0			0
$355$	−10.2163	−	17.6952i	−0.542227	−	0.939165i
$356$	−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	−0.878515	−	0.477716i	$-0.841465\pi$
$359$	−0.483978	+	0.838275i	−0.0255434	+	0.0442425i	0.852971	+	0.521958i	$0.174798\pi$
$360$		0			0
$361$	6.88255	+	11.9209i	0.362239	+	0.627417i
$362$	−49.5141			−2.60240
$363$		0			0
$364$	18.4098	−	34.7512i	0.964934	−	1.82146i
$365$	9.27197	−	16.0595i	0.485317	−	0.840594i
$366$		0			0
$367$	−10.4771	+	18.1469i	−0.546900	+	0.947259i	0.451585	+	0.892228i	$0.350859\pi$
$367$	−10.4771	+	18.1469i	−0.546900	+	0.947259i	−0.998485	+	0.0550305i	$0.982474\pi$
$368$	12.6421	+	21.8968i	0.659017	+	1.14145i
$369$		0			0
$370$	19.1978			0.998044
$371$	−2.82829	−	4.51093i	−0.146838	−	0.234196i
$372$		0			0
$373$	−1.00000	−	1.73205i	−0.0517780	−	0.0896822i	0.838975	−	0.544170i	$-0.183156\pi$
$373$	−1.00000	−	1.73205i	−0.0517780	−	0.0896822i	−0.890753	+	0.454488i	$0.849822\pi$
$374$	−4.76509			−0.246397
$375$		0			0
$376$	−28.4944			−1.46949
$377$	−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	$0.558731\pi$
$380$	−19.2174			−0.985833
$381$		0			0
$382$	20.5388			1.05086
$383$	−5.98831	−	10.3721i	−0.305988	−	0.529987i	0.671493	−	0.741011i	$-0.265654\pi$
$383$	−5.98831	−	10.3721i	−0.305988	−	0.529987i	−0.977481	+	0.211024i	$0.932320\pi$
$384$		0			0
$385$	1.26145	−	0.0459722i	0.0642894	−	0.00234296i
$386$	−20.6959			−1.05339
$387$		0			0
$388$	33.2509	+	57.5922i	1.68806	+	2.92380i
$389$	6.88942	−	11.9328i	0.349308	−	0.605019i	−0.636819	−	0.771013i	$-0.719750\pi$
$389$	6.88942	−	11.9328i	0.349308	−	0.605019i	0.986127	+	0.165995i	$0.0530835\pi$
$390$		0			0
$391$	−5.54944	+	9.61192i	−0.280647	+	0.486095i
$392$	−61.9697	+	4.52284i	−3.12994	+	0.228438i
$393$		0			0
$394$	49.6377			2.50071
$395$	−1.32327	−	2.29197i	−0.0665810	−	0.115322i
$396$		0			0
$397$	−4.19344	+	7.26325i	−0.210463	+	0.364532i	−0.951859	−	0.306535i	$-0.900830\pi$
$397$	−4.19344	+	7.26325i	−0.210463	+	0.364532i	0.741397	+	0.671067i	$0.234164\pi$
$398$	8.03706	+	13.9206i	0.402862	+	0.697777i
$399$		0			0
$400$	16.5803	−	28.7179i	0.829016	−	1.43590i
$401$	13.8083	+	23.9168i	0.689556	+	1.19435i	0.971982	+	0.235057i	$0.0755275\pi$
$401$	13.8083	+	23.9168i	0.689556	+	1.19435i	−0.282426	+	0.959289i	$0.591139\pi$
$402$		0			0
$403$	6.76145	−	11.7112i	0.336812	−	0.583375i
$404$	−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
$409$	30.5316			1.50969			0.754844	−	0.655904i	$-0.227712\pi$
$409$	30.5316			1.50969			0.754844	+	0.655904i	$0.227712\pi$
$410$	38.2051			1.88681
$411$		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
$416$	25.8418	−	44.7592i	1.26700	−	2.19450i
$417$		0			0
$418$	0.927658	+	1.60675i	0.0453732	+	0.0785887i
$419$	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
$425$	14.5563			0.706085
$426$		0			0
$427$	−20.0309	+	0.730004i	−0.969362	+	0.0353273i
$428$	33.0778	−	57.2924i	1.59887	−	2.76933i
$429$		0			0
$430$	−19.5080	+	33.7888i	−0.940758	+	1.62944i
$431$	15.8022	+	27.3701i	0.761163	+	1.31837i	0.942251	+	0.334906i	$0.108705\pi$
$431$	15.8022	+	27.3701i	0.761163	+	1.31837i	−0.181088	+	0.983467i	$0.557962\pi$
$432$		0			0
$433$	−6.48576			−0.311686			−0.155843	−	0.987782i	$-0.549809\pi$
$433$	−6.48576			−0.311686			−0.155843	+	0.987782i	$0.549809\pi$
$434$	−34.3392	+	1.25146i	−1.64834	+	0.0600718i
$435$		0			0
$436$	8.05308	+	13.9484i	0.385673	+	0.668005i
$437$	4.32141			0.206721
$438$		0			0
$439$	−15.5760			−0.743401			−0.371701	−	0.928353i	$-0.621225\pi$
$439$	−15.5760			−0.743401			−0.371701	+	0.928353i	$0.621225\pi$
$440$	4.23491			0.201891
$441$		0			0
$442$	44.5919			2.12102
$443$	25.0741			1.19131			0.595654	−	0.803241i	$-0.296893\pi$
$443$	25.0741			1.19131			0.595654	+	0.803241i	$0.296893\pi$
$444$		0			0
$445$	14.8567			0.704275
$446$	8.55927	+	14.8251i	0.405293	+	0.701989i
$447$		0			0
$448$	−60.4523	+	2.20312i	−2.85610	+	0.104088i
$449$	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
$452$	26.3189	−	45.5856i	1.23794	−	2.14417i
$453$		0			0
$454$	36.5617	−	63.3268i	1.71593	−	2.97207i
$455$	−11.8047	+	0.430210i	−0.553413	+	0.0201685i
$456$		0			0
$457$	20.4400			0.956141			0.478071	−	0.878321i	$-0.341336\pi$
$457$	20.4400			0.956141			0.478071	+	0.878321i	$0.341336\pi$
$458$	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	$0.240618\pi$
$464$	16.8869	+	29.2489i	0.783954	+	1.35785i
$465$		0			0
$466$	−37.0123	+	64.1072i	−1.71456	+	2.96971i
$467$	−8.86948	+	15.3624i	−0.410430	+	0.710886i	−0.994937	−	0.100503i	$-0.967955\pi$
$467$	−8.86948	+	15.3624i	−0.410430	+	0.710886i	0.584506	+	0.811389i	$0.301288\pi$
$468$		0			0
$469$	−1.88255	+	0.0686074i	−0.0869279	+	0.00316799i
$470$	6.88255	+	11.9209i	0.317468	+	0.549871i
$471$		0			0
$472$	−43.3942			−1.99738
$473$	2.73305			0.125666
$474$		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
$479$	−11.8047	+	20.4463i	−0.539371	+	0.934217i	0.459567	+	0.888143i	$0.348004\pi$
$479$	−11.8047	+	20.4463i	−0.539371	+	0.934217i	−0.998938	+	0.0460744i	$0.985329\pi$
$480$		0			0
$481$	6.29232	+	10.8986i	0.286905	+	0.496934i
$482$	−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	−0.925895	−	0.377780i	$-0.876687\pi$
$487$	−17.4363	−	30.2006i	−0.790115	−	1.36852i	0.135780	−	0.990739i	$-0.456646\pi$
$488$	−67.2471			−3.04413
$489$		0			0
$490$	16.8603	+	24.8332i	0.761672	+	1.12185i
$491$	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
$493$	−7.41273	+	12.8392i	−0.333853	+	0.578250i
$494$	−8.68106	−	15.0360i	−0.390579	−	0.676503i
$495$		0			0
$496$	−64.4028			−2.89177
$497$	−34.0123	+	1.23954i	−1.52566	+	0.0556010i
$498$		0			0
$499$	2.66257	+	4.61170i	0.119193	+	0.206448i	0.919448	−	0.393212i	$-0.128636\pi$
$499$	2.66257	+	4.61170i	0.119193	+	0.206448i	−0.800255	+	0.599660i	$0.795303\pi$
$500$	−62.8021			−2.80859
$501$		0			0
$502$	84.3657			3.76542
$503$	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
$506$	−1.53156			−0.0680862
$507$		0			0
$508$	−71.0704			−3.15324
$509$	0.750930	+	1.30065i	0.0332844	+	0.0576502i	0.882188	−	0.470898i	$-0.156070\pi$
$509$	0.750930	+	1.30065i	0.0332844	+	0.0576502i	−0.848903	+	0.528548i	$0.822737\pi$
$510$		0			0
$511$	−16.4084	−	26.1703i	−0.725865	−	1.15770i
$512$	−8.48948			−0.375186
$513$		0			0
$514$	13.7701	+	23.8505i	0.607374	+	1.05200i
$515$	−7.30470	+	12.6521i	−0.321884	+	0.557519i
$516$		0			0
$517$	0.482119	−	0.835055i	0.0212036	−	0.0367257i
$518$	14.9697	−	28.2576i	0.657733	−	1.24157i
$519$		0			0
$520$	−39.6304			−1.73791
$521$	18.8709	+	32.6853i	0.826747	+	1.43197i	0.900577	+	0.434697i	$0.143145\pi$
$521$	18.8709	+	32.6853i	0.826747	+	1.43197i	−0.0738295	+	0.997271i	$0.523522\pi$
$522$		0			0
$523$	8.97779	−	15.5500i	0.392571	−	0.679953i	−0.600217	−	0.799837i	$-0.704919\pi$
$523$	8.97779	−	15.5500i	0.392571	−	0.679953i	0.992788	+	0.119884i	$0.0382523\pi$
$524$	29.8127	+	51.6371i	1.30237	+	2.25578i
$525$		0			0
$526$	−38.4171	+	66.5403i	−1.67506	+	2.90129i
$527$	−14.1353	−	24.4830i	−0.615742	−	1.06650i
$528$		0			0
$529$	9.71634	−	16.8292i	0.422449	−	0.731704i
$530$	−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
$535$	−19.8713			−0.859109
$536$	−6.32004			−0.272984
$537$		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	−0.941862	−	0.335999i	$-0.890926\pi$
$541$	−4.18547	+	7.24944i	−0.179947	+	0.311678i	0.761915	+	0.647677i	$0.224259\pi$
$542$	0.0599627	−	0.103858i	0.00257562	−	0.00446110i
$543$		0			0
$544$	−54.0239	−	93.5722i	−2.31626	−	4.01187i
$545$	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
$551$	5.77238			0.245911
$552$		0			0
$553$	−4.40545	+	0.160552i	−0.187339	+	0.00682735i
$554$	21.1582	−	36.6470i	0.898924	−	1.55698i
$555$		0			0
$556$	−44.2057	+	76.5666i	−1.87474	+	3.24715i
$557$	8.26764	+	14.3200i	0.350311	+	0.606757i	0.986304	−	0.164938i	$-0.0527425\pi$
$557$	8.26764	+	14.3200i	0.350311	+	0.606757i	−0.635993	+	0.771695i	$0.719409\pi$
$558$		0			0
$559$	−25.5760			−1.08175
$560$	29.8843	+	47.6634i	1.26284	+	2.01415i
$561$		0			0
$562$	−16.0760	−	27.8444i	−0.678124	−	1.17455i
$563$	22.2312			0.936933			0.468466	−	0.883481i	$-0.344807\pi$
$563$	22.2312			0.936933			0.468466	+	0.883481i	$0.344807\pi$
$564$		0			0
$565$	−15.8109			−0.665169
$566$	−16.2174			−0.681670
$567$		0			0
$568$	−114.185			−4.79111
$569$	−2.31275			−0.0969556			−0.0484778	−	0.998824i	$-0.515437\pi$
$569$	−2.31275			−0.0969556			−0.0484778	+	0.998824i	$0.515437\pi$
$570$		0			0
$571$	−6.09888			−0.255230			−0.127615	−	0.991824i	$-0.540732\pi$
$571$	−6.09888			−0.255230			−0.127615	+	0.991824i	$0.540732\pi$
$572$	2.23236	+	3.86656i	0.0933397	+	0.161669i
$573$		0			0
$574$	29.7909	−	56.2348i	1.24345	−	2.34720i
$575$	4.67859			0.195111
$576$		0			0
$577$	−10.1032	−	17.4993i	−0.420602	−	0.728505i	0.575396	−	0.817875i	$-0.304848\pi$
$577$	−10.1032	−	17.4993i	−0.420602	−	0.728505i	−0.995998	+	0.0893702i	$0.971515\pi$
$578$	23.6643	−	40.9879i	0.984307	−	1.70487i
$579$		0			0
$580$	10.5952	−	18.3515i	0.439944	−	0.762004i
$581$	7.63533	+	12.1778i	0.316767	+	0.505221i
$582$		0			0
$583$	0.604462			0.0250343
$584$	−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
$590$	10.4814	+	18.1544i	0.431514	+	0.747404i
$591$		0			0
$592$	29.9672	−	51.9047i	1.23164	−	2.13327i
$593$	11.8578	−	20.5383i	0.486941	−	0.843406i	−0.512946	−	0.858421i	$-0.671446\pi$
$593$	11.8578	−	20.5383i	0.486941	−	0.843406i	0.999887	+	0.0150142i	$0.00477936\pi$
$594$		0			0
$595$	−11.5604	+	21.8219i	−0.473929	+	0.894611i
$596$	28.7898	+	49.8654i	1.17928	+	2.04256i
$597$		0			0
$598$	14.3324			0.586096
$599$	34.4807			1.40884			0.704421	−	0.709783i	$-0.251207\pi$
$599$	34.4807			1.40884			0.704421	+	0.709783i	$0.251207\pi$
$600$		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
$605$	8.66435	−	15.0071i	0.352256	−	0.610125i
$606$		0			0
$607$	12.5796	+	21.7886i	0.510591	+	0.884370i	0.999925	+	0.0122732i	$0.00390679\pi$
$607$	12.5796	+	21.7886i	0.510591	+	0.884370i	−0.489333	+	0.872097i	$0.662760\pi$
$608$	−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	0.943749	+	0.330663i	$0.107272\pi$
$613$	18.7731	+	32.5159i	0.758237	+	1.31330i	−0.185512	+	0.982642i	$0.559394\pi$
$614$	59.5351			2.40264
$615$		0			0
$616$	3.30223	−	6.23345i	0.133051	−	0.251153i
$617$	−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
$619$	−5.90545	+	10.2285i	−0.237360	+	0.411119i	−0.959956	−	0.280151i	$-0.909615\pi$
$619$	−5.90545	+	10.2285i	−0.237360	+	0.411119i	0.722596	+	0.691271i	$0.242949\pi$
$620$	20.2040	+	34.9943i	0.811411	+	1.40540i
$621$		0			0
$622$	21.5302			0.863282
$623$	11.5847	−	21.8679i	0.464132	−	0.876118i
$624$		0			0
$625$	3.23924	+	5.61053i	0.129570	+	0.224421i
$626$	60.8231			2.43098
$627$		0			0
$628$	−1.00000			−0.0399043
$629$	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	$0.299213\pi$
$632$	−14.7899			−0.588309
$633$		0			0
$634$	−53.8255			−2.13768
$635$	10.6738	+	18.4875i	0.423576	+	0.733655i
$636$		0			0
$637$	−8.57165	+	17.7111i	−0.339621	+	0.701737i
$638$	−2.04580			−0.0809940
$639$		0			0
$640$	19.8152	+	34.3210i	0.783265	+	1.35666i
$641$	−7.32623	+	12.6894i	−0.289368	+	0.501201i	−0.973659	−	0.228008i	$-0.926779\pi$
$641$	−7.32623	+	12.6894i	−0.289368	+	0.501201i	0.684291	+	0.729209i	$0.260112\pi$
$642$		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	$0.179456\pi$
$644$	−14.0371	−	22.3881i	−0.553138	−	0.882216i
$645$		0			0
$646$	−36.2967			−1.42807
$647$	5.89307	+	10.2071i	0.231680	+	0.401282i	0.958303	−	0.285755i	$-0.0922443\pi$
$647$	5.89307	+	10.2071i	0.231680	+	0.401282i	−0.726622	+	0.687037i	$0.758911\pi$
$648$		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
$653$	17.0920	+	29.6042i	0.668862	+	1.15850i	0.978223	+	0.207558i	$0.0665516\pi$
$653$	17.0920	+	29.6042i	0.668862	+	1.15850i	−0.309361	+	0.950945i	$0.600115\pi$
$654$		0			0
$655$	8.95489	−	15.5103i	0.349896	−	0.606038i
$656$	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
$661$	25.5388			0.993346			0.496673	−	0.867938i	$-0.334555\pi$
$661$	25.5388			0.993346			0.496673	+	0.867938i	$0.334555\pi$
$662$	−63.7934			−2.47940
$663$		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
$668$	−11.4778	+	19.8801i	−0.444089	+	0.769185i
$669$		0			0
$670$	1.52654	+	2.64405i	0.0589755	+	0.102149i
$671$	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
$677$	−17.2225			−0.661916			−0.330958	−	0.943646i	$-0.607372\pi$
$677$	−17.2225			−0.661916			−0.330958	+	0.943646i	$0.607372\pi$
$678$		0			0
$679$	−17.6749	−	28.1902i	−0.678299	−	1.08184i
$680$	−41.4250	+	71.7503i	−1.58858	+	2.75150i
$681$		0			0
$682$	1.95056	−	3.37847i	0.0746907	−	0.129368i
$683$	−16.8585	−	29.1997i	−0.645072	−	1.11730i	−0.984285	−	0.176587i	$-0.943494\pi$
$683$	−16.8585	−	29.1997i	−0.645072	−	1.11730i	0.339213	−	0.940709i	$-0.389839\pi$
$684$		0			0
$685$	−6.00000			−0.229248
$686$	49.6996	−	5.45306i	1.89754	−	0.208199i
$687$		0			0
$688$	60.9028	+	105.487i	2.32190	+	4.02165i
$689$	−5.65658			−0.215499
$690$		0			0
$691$	−25.4930			−0.969801			−0.484901	−	0.874569i	$-0.661144\pi$
$691$	−25.4930			−0.969801			−0.484901	+	0.874569i	$0.661144\pi$
$692$	33.3163			1.26650
$693$		0			0
$694$	−10.3782			−0.393952
$695$	26.5563			1.00734
$696$		0			0
$697$	52.3570			1.98316
$698$	−16.4530	−	28.4975i	−0.622756	−	1.07865i
$699$		0			0
$700$	−16.2236	+	30.6245i	−0.613195	+	1.15750i
$701$	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
$704$	3.43385	−	5.94760i	0.129418	−	0.224159i
$705$		0			0
$706$	4.81020	−	8.33152i	0.181034	−	0.313561i
$707$	18.0945	−	34.1560i	0.680513	−	1.28457i
$708$		0			0
$709$	−15.9469			−0.598899			−0.299449	−	0.954112i	$-0.596803\pi$
$709$	−15.9469			−0.598899			−0.299449	+	0.954112i	$0.596803\pi$
$710$	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
$716$	−36.8621	−	63.8471i	−1.37760	−	2.38608i
$717$		0			0
$718$	1.30656	−	2.26303i	0.0487604	−	0.0844556i
$719$	8.20877	−	14.2180i	0.306136	−	0.530242i	−0.671378	−	0.741115i	$-0.734297\pi$
$719$	8.20877	−	14.2180i	0.306136	−	0.530242i	0.977513	+	0.210873i	$0.0676306\pi$
$720$		0			0
$721$	12.9270	+	20.6176i	0.481425	+	0.767840i
$722$	−18.5803	−	32.1820i	−0.691488	−	1.19769i
$723$		0			0
$724$	96.9875			3.60451
$725$	6.24948			0.232100
$726$		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
$731$	−26.7341	+	46.3049i	−0.988798	+	1.71265i
$732$		0			0
$733$	−19.6440	−	34.0244i	−0.725568	−	1.25672i	−0.958740	−	0.284284i	$-0.908244\pi$
$733$	−19.6440	−	34.0244i	−0.725568	−	1.25672i	0.233172	−	0.972435i	$-0.425089\pi$
$734$	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	0.846163	−	0.532925i	$-0.178907\pi$
$739$	−1.04511	−	1.81019i	−0.0384451	−	0.0665888i	−0.884608	+	0.466336i	$0.845574\pi$
$740$	−37.6043			−1.38236
$741$		0			0
$742$	7.63533	+	12.1778i	0.280302	+	0.447062i
$743$	−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
$745$	8.64764	−	14.9781i	0.316825	−	0.548757i
$746$	2.69963	+	4.67589i	0.0988404	+	0.171197i
$747$		0			0
$748$	9.33379			0.341277
$749$	−15.4949	+	29.2489i	−0.566171	+	1.06873i
$750$		0			0
$751$	−10.3869	−	17.9906i	−0.379023	−	0.656486i	0.611898	−	0.790937i	$-0.290406\pi$
$751$	−10.3869	−	17.9906i	−0.379023	−	0.656486i	−0.990920	+	0.134451i	$0.957073\pi$
$752$	42.9739			1.56710
$753$		0			0
$754$	19.1447			0.697208
$755$	−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	$0.400478\pi$
$758$	19.2843			0.700436
$759$		0			0
$760$	32.2581			1.17013
$761$	−16.4196	−	28.4396i	−0.595210	−	1.03093i	−0.993517	−	0.113682i	$-0.963735\pi$
$761$	−16.4196	−	28.4396i	−0.595210	−	1.03093i	0.398307	−	0.917252i	$-0.369598\pi$
$762$		0			0
$763$	−4.28071	−	6.82743i	−0.154972	−	0.247170i
$764$	−40.2312			−1.45551
$765$		0			0
$766$	16.1662	+	28.0007i	0.584109	+	1.01171i
$767$	−6.87085	+	11.9007i	−0.248092	+	0.429708i
$768$		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	$0.972798\pi$
$770$	−3.40545	+	0.124108i	−0.122724	+	0.00447254i
$771$		0			0
$772$	40.5388			1.45902
$773$	−3.18656	−	5.51928i	−0.114613	−	0.198515i	0.803012	−	0.595963i	$-0.203229\pi$
$773$	−3.18656	−	5.51928i	−0.114613	−	0.198515i	−0.917625	+	0.397448i	$0.869896\pi$
$774$		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
$779$	−10.1927	−	17.6544i	−0.365193	−	0.632533i
$780$		0			0
$781$	1.93199	−	3.34630i	0.0691320	−	0.119740i
$782$	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
$787$	−19.8799			−0.708643			−0.354321	−	0.935124i	$-0.615288\pi$
$787$	−19.8799			−0.708643			−0.354321	+	0.935124i	$0.615288\pi$
$788$	−97.2297			−3.46366
$789$		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
$794$	11.3207	−	19.6081i	0.401757	−	0.695864i
$795$		0			0
$796$	−15.7429	−	27.2675i	−0.557992	−	0.966470i
$797$	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
$803$	3.50680			0.123752
$804$		0			0
$805$	−3.71565	+	7.01384i	−0.130959	+	0.247205i
$806$	−18.2534	+	31.6158i	−0.642949	+	1.11362i
$807$		0			0
$808$	64.8391	−	112.305i	2.28103	−	3.95087i
$809$	−1.06113	−	1.83794i	−0.0373075	−	0.0646184i	0.846769	−	0.531961i	$-0.178545\pi$
$809$	−1.06113	−	1.83794i	−0.0373075	−	0.0646184i	−0.884076	+	0.467343i	$0.845211\pi$
$810$		0			0
$811$	−18.4327			−0.647259			−0.323629	−	0.946184i	$-0.604903\pi$
$811$	−18.4327			−0.647259			−0.323629	+	0.946184i	$0.604903\pi$
$812$	−18.7502	−	29.9052i	−0.658002	−	1.04947i
$813$		0			0
$814$	1.81522	+	3.14406i	0.0636235	+	0.110199i
$815$	−14.2247			−0.498270
$816$		0			0
$817$	20.8182			0.728336
$818$	−82.4239			−2.88188
$819$		0			0
$820$	−74.8355			−2.61337
$821$	−45.1555			−1.57594			−0.787969	−	0.615714i	$-0.788868\pi$
$821$	−45.1555			−1.57594			−0.787969	+	0.615714i	$0.788868\pi$
$822$		0			0
$823$	25.0517			0.873248			0.436624	−	0.899644i	$-0.356174\pi$
$823$	25.0517			0.873248			0.436624	+	0.899644i	$0.356174\pi$
$824$	40.8213	+	70.7046i	1.42208	+	2.46311i
$825$		0			0
$826$	34.8948	−	1.27171i	1.21415	−	0.0442483i
$827$	−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	−0.998081	−	0.0619285i	$-0.980275\pi$
$829$	−15.9127	−	27.5617i	−0.552672	−	0.957256i	0.445409	−	0.895327i	$-0.353058\pi$
$830$	11.6476	−	20.1743i	0.404295	−	0.700260i
$831$		0			0
$832$	−32.1341	+	55.6579i	−1.11405	+	1.92959i
$833$	23.1058	+	34.0319i	0.800567	+	1.17914i
$834$		0			0
$835$	6.89521			0.238619
$836$	−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
$842$	46.8781	+	81.1953i	1.61553	+	2.79818i
$843$		0			0
$844$	−17.6483	+	30.5678i	−0.607480	+	1.05219i
$845$	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
$850$	−39.2967			−1.34786
$851$	8.45606			0.289870
$852$		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
$857$	19.5815	−	33.9161i	0.668891	−	1.15855i	−0.309324	−	0.950957i	$-0.600103\pi$
$857$	19.5815	−	33.9161i	0.668891	−	1.15855i	0.978215	−	0.207596i	$-0.0665640\pi$
$858$		0			0
$859$	−4.73422	−	8.19991i	−0.161529	−	0.279777i	0.773888	−	0.633323i	$-0.218309\pi$
$859$	−4.73422	−	8.19991i	−0.161529	−	0.279777i	−0.935417	+	0.353545i	$0.884976\pi$
$860$	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	−0.882643	−	0.470044i	$-0.844238\pi$
$863$	−1.00619	+	1.74277i	−0.0342511	+	0.0593246i	0.848392	+	0.529369i	$0.177571\pi$
$864$		0			0
$865$	−5.00364	−	8.66656i	−0.170129	−	0.294672i
$866$	17.5091			0.594985
$867$		0			0
$868$	67.2632	−	2.45133i	2.28306	−	0.0832037i
$869$	0.250241	−	0.433430i	0.00848884	−	0.0147031i
$870$		0			0
$871$	−1.00069	+	1.73324i	−0.0339070	+	0.0587287i
$872$	−13.5178	−	23.4135i	−0.457771	−	0.792882i
$873$		0			0
$874$	−11.6662			−0.394615
$875$	31.4010	−	1.14438i	1.06155	−	0.0386870i
$876$		0			0
$877$	−22.3497	−	38.7109i	−0.754697	−	1.30717i	−0.945525	−	0.325550i	$-0.894451\pi$
$877$	−22.3497	−	38.7109i	−0.754697	−	1.30717i	0.190828	−	0.981624i	$-0.438883\pi$
$878$	42.0494			1.41910
$879$		0			0
$880$	−6.38688			−0.215302
$881$	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	$0.592349\pi$
$884$	−87.3460			−2.93776
$885$		0			0
$886$	−67.6908			−2.27412
$887$	−0.600744	−	1.04052i	−0.0201710	−	0.0349372i	0.855764	−	0.517367i	$-0.173088\pi$
$887$	−0.600744	−	1.04052i	−0.0201710	−	0.0349372i	−0.875935	+	0.482430i	$0.839754\pi$
$888$		0			0
$889$	35.5352	−	1.29504i	1.19181	−	0.0434343i
$890$	−40.1075			−1.34441
$891$		0			0
$892$	−16.7658	−	29.0392i	−0.561360	−	0.972304i
$893$	3.67240	−	6.36078i	0.122892	−	0.212855i
$894$		0			0
$895$	−11.0723	+	19.1779i	−0.370108	+	0.641045i
$896$	65.9690	−	2.40417i	2.20387	−	0.0803176i
$897$		0			0
$898$	−41.2953			−1.37804
$899$	−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
$905$	−14.5662	−	25.2293i	−0.484195	−	0.838651i
$906$		0			0
$907$	−8.53156	+	14.7771i	−0.283286	+	0.490665i	−0.972192	−	0.234185i	$-0.924758\pi$
$907$	−8.53156	+	14.7771i	−0.283286	+	0.490665i	0.688906	+	0.724850i	$0.258091\pi$
$908$	−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
$913$	−1.63182			−0.0540055
$914$	−55.1803			−1.82520
$915$		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	−0.511854	−	0.859072i	$-0.671041\pi$
$919$	14.7953	−	25.6262i	0.488051	−	0.845329i	0.999906	+	0.0137429i	$0.00437462\pi$
$920$	−13.3145	+	23.0614i	−0.438967	+	0.760313i
$921$		0			0
$922$	55.0969	+	95.4307i	1.81452	+	3.14284i
$923$	−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
$929$	−2.69963			−0.0885719			−0.0442860	−	0.999019i	$-0.514101\pi$
$929$	−2.69963			−0.0885719			−0.0442860	+	0.999019i	$0.514101\pi$
$930$		0			0
$931$	6.97710	−	14.4163i	0.228665	−	0.472476i
$932$	72.4992	−	125.572i	2.37479	−	4.11325i
$933$		0			0
$934$	23.9443	−	41.4727i	0.783481	−	1.35703i
$935$	−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	$0.277131\pi$
$938$	5.08217	−	0.185214i	0.165939	−	0.00604746i
$939$		0			0
$940$	−13.4814	−	23.3505i	−0.439716	−	0.761610i
$941$	−39.7244			−1.29498			−0.647489	−	0.762075i	$-0.724181\pi$
$941$	−39.7244			−1.29498			−0.647489	+	0.762075i	$0.724181\pi$
$942$		0			0
$943$	16.8282			0.548002
$944$	65.4449			2.13005
$945$		0			0
$946$	−7.37822			−0.239886
$947$	15.7303			0.511166			0.255583	−	0.966787i	$-0.417733\pi$
$947$	15.7303			0.511166			0.255583	+	0.966787i	$0.417733\pi$
$948$		0			0
$949$	−32.8168			−1.06528
$950$	7.65019	+	13.2505i	0.248205	+	0.429903i
$951$		0			0
$952$	73.3090	+	116.923i	2.37596	+	3.78949i
$953$	−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
$956$	−73.6722	+	127.604i	−2.38273	+	4.12701i
$957$		0			0
$958$	31.8683	−	55.1975i	1.02962	−	1.78335i
$959$	−4.67859	+	8.83153i	−0.151079	+	0.285185i
$960$		0			0
$961$	−7.85532			−0.253397
$962$	−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	$0.134938\pi$
$968$	−48.4195	−	83.8651i	−1.55626	−	2.69553i
$969$		0			0
$970$	−26.9629	+	46.7010i	−0.865725	+	1.49948i
$971$	−1.08582	+	1.88069i	−0.0348455	+	0.0603542i	−0.882922	−	0.469519i	$-0.844427\pi$
$971$	−1.08582	+	1.88069i	−0.0348455	+	0.0603542i	0.848077	+	0.529873i	$0.177761\pi$
$972$		0			0
$973$	20.7077	−	39.0888i	0.663858	−	1.25313i
$974$	47.0716	+	81.5304i	1.50827	+	2.61240i
$975$		0			0
$976$	101.419			3.24634
$977$	11.4561			0.366512			0.183256	−	0.983065i	$-0.441336\pi$
$977$	11.4561			0.366512			0.183256	+	0.983065i	$0.441336\pi$
$978$		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
$983$	22.4010	−	38.7997i	0.714482	−	1.23752i	−0.248677	−	0.968587i	$-0.579996\pi$
$983$	22.4010	−	38.7997i	0.714482	−	1.23752i	0.963159	−	0.268933i	$-0.0866710\pi$
$984$		0			0
$985$	14.6025	+	25.2923i	0.465275	+	0.805880i
$986$	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	0.991891	−	0.127090i	$-0.0405637\pi$
$991$	12.1476	+	21.0403i	0.385882	+	0.668368i	−0.606009	+	0.795458i	$0.707230\pi$
$992$	88.4573			2.80852
$993$		0			0
$994$	91.8206	−	3.34630i	2.91237	−	0.106138i
$995$	−4.72872	+	8.19038i	−0.149910	+	0.259653i
$996$		0			0
$997$	5.66257	−	9.80785i	0.179335	−	0.310618i	−0.762318	−	0.647203i	$-0.775939\pi$
$997$	5.66257	−	9.80785i	0.179335	−	0.310618i	0.941653	+	0.336585i	$0.109272\pi$
$998$	−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.h.h.352.1		6
3.2	odd	2		567.2.h.i.352.3		6
7.4	even	3		567.2.g.i.109.3		6
9.2	odd	6		567.2.g.h.541.1		6
9.4	even	3		189.2.e.f.163.3	yes	6
9.5	odd	6		189.2.e.e.163.1	yes	6
9.7	even	3		567.2.g.i.541.3		6
21.11	odd	6		567.2.g.h.109.1		6
63.4	even	3		189.2.e.f.109.3	yes	6
63.5	even	6		1323.2.a.z.1.3		3
63.11	odd	6		567.2.h.i.298.3		6
63.23	odd	6		1323.2.a.ba.1.3		3
63.25	even	3	inner	567.2.h.h.298.1		6
63.32	odd	6		189.2.e.e.109.1	✓	6
63.40	odd	6		1323.2.a.y.1.1		3
63.58	even	3		1323.2.a.x.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.e.e.109.1	✓	6	63.32	odd	6
189.2.e.e.163.1	yes	6	9.5	odd	6
189.2.e.f.109.3	yes	6	63.4	even	3
189.2.e.f.163.3	yes	6	9.4	even	3
567.2.g.h.109.1		6	21.11	odd	6
567.2.g.h.541.1		6	9.2	odd	6
567.2.g.i.109.3		6	7.4	even	3
567.2.g.i.541.3		6	9.7	even	3
567.2.h.h.298.1		6	63.25	even	3	inner
567.2.h.h.352.1		6	1.1	even	1	trivial
567.2.h.i.298.3		6	63.11	odd	6
567.2.h.i.352.3		6	3.2	odd	2
1323.2.a.x.1.1		3	63.58	even	3
1323.2.a.y.1.1		3	63.40	odd	6
1323.2.a.z.1.3		3	63.5	even	6
1323.2.a.ba.1.3		3	63.23	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.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-2.69963 q^{2} +5.28799 q^{4} +(-0.794182 - 1.37556i) q^{5} +(-2.64400 + 0.0963576i) q^{7} -8.87636 q^{8} +(2.14400 + 3.71351i) q^{10} +(0.150186 - 0.260130i) q^{11} +(-1.40545 + 2.43430i) q^{13} +(7.13781 - 0.260130i) q^{14} +13.3869 q^{16} +(2.93818 + 5.08907i) q^{17} +(1.14400 - 1.98146i) q^{19} +(-4.19963 - 7.27397i) q^{20} +(-0.405446 + 0.702253i) q^{22} +(0.944368 + 1.63569i) q^{23} +(1.23855 - 2.14523i) q^{25} +(3.79418 - 6.57172i) q^{26} +(-13.9814 + 0.509538i) q^{28} +(1.26145 + 2.18490i) q^{29} -4.81089 q^{31} -18.3869 q^{32} +(-7.93199 - 13.7386i) q^{34} +(2.23236 + 3.56046i) q^{35} +(2.23855 - 3.87728i) q^{37} +(-3.08836 + 5.34920i) q^{38} +(7.04944 + 12.2100i) q^{40} +(4.45489 - 7.71609i) q^{41} +(4.54944 + 7.87987i) q^{43} +(0.794182 - 1.37556i) q^{44} +(-2.54944 - 4.41576i) q^{46} +3.21015 q^{47} +(6.98143 - 0.509538i) q^{49} +(-3.34362 + 5.79133i) q^{50} +(-7.43199 + 12.8726i) q^{52} +(1.00619 + 1.74277i) q^{53} -0.477100 q^{55} +(23.4691 - 0.855304i) q^{56} +(-3.40545 - 5.89841i) q^{58} +4.88874 q^{59} +7.57598 q^{61} +12.9876 q^{62} +22.8640 q^{64} +4.46472 q^{65} +0.712008 q^{67} +(15.5371 + 26.9110i) q^{68} +(-6.02654 - 9.61192i) q^{70} +12.8640 q^{71} +(5.83743 + 10.1107i) q^{73} +(-6.04325 + 10.4672i) q^{74} +(6.04944 - 10.4779i) q^{76} +(-0.372026 + 0.702253i) q^{77} +1.66621 q^{79} +(-10.6316 - 18.4145i) q^{80} +(-12.0265 + 20.8306i) q^{82} +(-2.71634 - 4.70484i) q^{83} +(4.66690 - 8.08330i) q^{85} +(-12.2818 - 21.2727i) q^{86} +(-1.33310 + 2.30900i) q^{88} +(-4.67673 + 8.10033i) q^{89} +(3.48143 - 6.57172i) q^{91} +(4.99381 + 8.64953i) q^{92} -8.66621 q^{94} -3.63416 q^{95} +(6.28799 + 10.8911i) q^{97} +(-18.8473 + 1.37556i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 4 q^{2} + 8 q^{4} + q^{5} - 4 q^{7} - 18 q^{8} + q^{10} + 7 q^{11} - 2 q^{13} + 13 q^{14} + 20 q^{16} - 5 q^{19} - 13 q^{20} + 4 q^{22} + 6 q^{23} + 2 q^{25} + 17 q^{26} - 30 q^{28} + 13 q^{29}+ \cdots - 49 q^{98}+O(q^{100}) \) 6 * q - 4 * q^2 + 8 * q^4 + q^5 - 4 * q^7 - 18 * q^8 + q^10 + 7 * q^11 - 2 * q^13 + 13 * q^14 + 20 * q^16 - 5 * q^19 - 13 * q^20 + 4 * q^22 + 6 * q^23 + 2 * q^25 + 17 * q^26 - 30 * q^28 + 13 * q^29 - 16 * q^31 - 50 * q^32 - 12 * q^34 - 10 * q^35 + 8 * q^37 - 7 * q^38 + 24 * q^40 + 2 * q^41 + 9 * q^43 - q^44 + 3 * q^46 - 18 * q^47 - 12 * q^49 + 4 * q^50 - 9 * q^52 + 24 * q^53 + 8 * q^55 + 51 * q^56 - 14 * q^58 + 30 * q^59 - 2 * q^61 + 42 * q^62 + 66 * q^64 - 20 * q^65 + 28 * q^67 + 39 * q^68 - 7 * q^70 + 6 * q^71 - 7 * q^73 + 18 * q^76 - 10 * q^77 + 12 * q^79 - 16 * q^80 - 43 * q^82 + 3 * q^83 + 27 * q^85 - 32 * q^86 - 9 * q^88 - 5 * q^89 - 33 * q^91 + 12 * q^92 - 54 * q^94 - 32 * q^95 + 14 * q^97 - 49 * q^98

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