LMFDB - Embedded newform 189.2.e.f.163.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(109,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("189.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.e (of order $3$, degree $2$, 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:	$1.50917259820$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			163.3
Root			$0.500000 - 0.224437i$ of defining polynomial
Character	$\chi$	$=$	189.163
Dual form			189.2.e.f.109.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.34981 - 2.33795i) q^{2} +(-2.64400 - 4.57954i) q^{4} +(-0.794182 + 1.37556i) q^{5} +(1.23855 - 2.33795i) q^{7} -8.87636 q^{8} +O(q^{10})$	\(q+(1.34981 - 2.33795i) q^{2} +(-2.64400 - 4.57954i) q^{4} +(-0.794182 + 1.37556i) q^{5} +(1.23855 - 2.33795i) q^{7} -8.87636 q^{8} +(2.14400 + 3.71351i) q^{10} +(0.150186 + 0.260130i) q^{11} +2.81089 q^{13} +(-3.79418 - 6.05146i) q^{14} +(-6.69344 + 11.5934i) q^{16} +(2.93818 + 5.08907i) q^{17} +(1.14400 - 1.98146i) q^{19} +8.39926 q^{20} +0.810892 q^{22} +(0.944368 - 1.63569i) q^{23} +(1.23855 + 2.14523i) q^{25} +(3.79418 - 6.57172i) q^{26} +(-13.9814 + 0.509538i) q^{28} -2.52290 q^{29} +(2.40545 + 4.16635i) q^{31} +(9.19344 + 15.9235i) q^{32} +15.8640 q^{34} +(2.23236 + 3.56046i) q^{35} +(2.23855 - 3.87728i) q^{37} +(-3.08836 - 5.34920i) q^{38} +(7.04944 - 12.2100i) q^{40} -8.90978 q^{41} -9.09888 q^{43} +(0.794182 - 1.37556i) q^{44} +(-2.54944 - 4.41576i) q^{46} +(-1.60507 + 2.78007i) q^{47} +(-3.93199 - 5.79133i) q^{49} +6.68725 q^{50} +(-7.43199 - 12.8726i) q^{52} +(1.00619 + 1.74277i) q^{53} -0.477100 q^{55} +(-10.9938 + 20.7524i) q^{56} +(-3.40545 + 5.89841i) q^{58} +(-2.44437 - 4.23377i) q^{59} +(-3.78799 + 6.56099i) q^{61} +12.9876 q^{62} +22.8640 q^{64} +(-2.23236 + 3.86656i) q^{65} +(-0.356004 - 0.616617i) q^{67} +(15.5371 - 26.9110i) q^{68} +(11.3374 - 0.413181i) q^{70} +12.8640 q^{71} +(5.83743 + 10.1107i) q^{73} +(-6.04325 - 10.4672i) q^{74} -12.0989 q^{76} +(0.794182 - 0.0289431i) q^{77} +(-0.833104 + 1.44298i) q^{79} +(-10.6316 - 18.4145i) q^{80} +(-12.0265 + 20.8306i) q^{82} +5.43268 q^{83} -9.33379 q^{85} +(-12.2818 + 21.2727i) q^{86} +(-1.33310 - 2.30900i) q^{88} +(-4.67673 + 8.10033i) q^{89} +(3.48143 - 6.57172i) q^{91} -9.98762 q^{92} +(4.33310 + 7.50516i) q^{94} +(1.81708 + 3.14728i) q^{95} -12.5760 q^{97} +(-18.8473 + 1.37556i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 2 q^{2} - 4 q^{4} + q^{5} + 2 q^{7} - 18 q^{8}+O(q^{10}) $ 6 * q + 2 * q^2 - 4 * q^4 + q^5 + 2 * q^7 - 18 * q^8	$ 6 q + 2 q^{2} - 4 q^{4} + q^{5} + 2 q^{7} - 18 q^{8} + q^{10} + 7 q^{11} + 4 q^{13} - 17 q^{14} - 10 q^{16} - 5 q^{19} + 26 q^{20} - 8 q^{22} + 6 q^{23} + 2 q^{25} + 17 q^{26} - 30 q^{28} - 26 q^{29} + 8 q^{31} + 25 q^{32} + 24 q^{34} - 10 q^{35} + 8 q^{37} - 7 q^{38} + 24 q^{40} - 4 q^{41} - 18 q^{43} - q^{44} + 3 q^{46} + 9 q^{47} + 12 q^{49} - 8 q^{50} - 9 q^{52} + 24 q^{53} + 8 q^{55} - 48 q^{56} - 14 q^{58} - 15 q^{59} + q^{61} + 42 q^{62} + 66 q^{64} + 10 q^{65} - 14 q^{67} + 39 q^{68} + 26 q^{70} + 6 q^{71} - 7 q^{73} - 36 q^{76} - q^{77} - 6 q^{79} - 16 q^{80} - 43 q^{82} - 6 q^{83} - 54 q^{85} - 32 q^{86} - 9 q^{88} - 5 q^{89} - 33 q^{91} - 24 q^{92} + 27 q^{94} + 16 q^{95} - 28 q^{97} - 49 q^{98}+O(q^{100}) $ 6 * q + 2 * q^2 - 4 * q^4 + q^5 + 2 * q^7 - 18 * q^8 + q^10 + 7 * q^11 + 4 * q^13 - 17 * q^14 - 10 * q^16 - 5 * q^19 + 26 * q^20 - 8 * q^22 + 6 * q^23 + 2 * q^25 + 17 * q^26 - 30 * q^28 - 26 * q^29 + 8 * q^31 + 25 * q^32 + 24 * q^34 - 10 * q^35 + 8 * q^37 - 7 * q^38 + 24 * q^40 - 4 * q^41 - 18 * q^43 - q^44 + 3 * q^46 + 9 * q^47 + 12 * q^49 - 8 * q^50 - 9 * q^52 + 24 * q^53 + 8 * q^55 - 48 * q^56 - 14 * q^58 - 15 * q^59 + q^61 + 42 * q^62 + 66 * q^64 + 10 * q^65 - 14 * q^67 + 39 * q^68 + 26 * q^70 + 6 * q^71 - 7 * q^73 - 36 * q^76 - q^77 - 6 * q^79 - 16 * q^80 - 43 * q^82 - 6 * q^83 - 54 * q^85 - 32 * q^86 - 9 * q^88 - 5 * q^89 - 33 * q^91 - 24 * q^92 + 27 * q^94 + 16 * q^95 - 28 * q^97 - 49 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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
$5$	−0.794182	+	1.37556i	−0.355169	+	0.615171i	−0.987147	−	0.159816i	$-0.948910\pi$
$5$	−0.794182	+	1.37556i	−0.355169	+	0.615171i	0.631978	+	0.774986i	$0.282243\pi$
$6$		0			0
$7$	1.23855	−	2.33795i	0.468128	−	0.883661i
$7$	1.23855	−	2.33795i	0.468128	−	0.883661i
$8$	−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	0.887778	−	0.460271i	$-0.152248\pi$
$11$	0.150186	+	0.260130i	0.0452828	+	0.0784320i	−0.842496	+	0.538703i	$0.818914\pi$
$12$		0			0
$13$	2.81089			0.779601			0.389801	−	0.920899i	$-0.372544\pi$
$13$	2.81089			0.779601			0.389801	+	0.920899i	$0.372544\pi$
$14$	−3.79418	−	6.05146i	−1.01404	−	1.61732i
$15$		0			0
$16$	−6.69344	+	11.5934i	−1.67336	+	2.89834i
$17$	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	$0.0821360\pi$
$20$	8.39926			1.87813
$21$		0			0
$22$	0.810892			0.172883
$23$	0.944368	−	1.63569i	0.196914	−	0.341066i	−0.750612	−	0.660743i	$-0.770241\pi$
$23$	0.944368	−	1.63569i	0.196914	−	0.341066i	0.947526	+	0.319678i	$0.103575\pi$
$24$		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
$29$	−2.52290			−0.468491			−0.234245	−	0.972178i	$-0.575262\pi$
$29$	−2.52290			−0.468491			−0.234245	+	0.972178i	$0.575262\pi$
$30$		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
$34$	15.8640			2.72065
$35$	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
$41$	−8.90978			−1.39147			−0.695737	−	0.718297i	$-0.744922\pi$
$41$	−8.90978			−1.39147			−0.695737	+	0.718297i	$0.744922\pi$
$42$		0			0
$43$	−9.09888			−1.38757			−0.693783	−	0.720184i	$-0.744058\pi$
$43$	−9.09888			−1.38757			−0.693783	+	0.720184i	$0.744058\pi$
$44$	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
$49$	−3.93199	−	5.79133i	−0.561713	−	0.827332i
$50$	6.68725			0.945720
$51$		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
$56$	−10.9938	+	20.7524i	−1.46911	+	2.77316i
$57$		0			0
$58$	−3.40545	+	5.89841i	−0.447157	+	0.774499i
$59$	−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	$0.847182\pi$
$68$	15.5371	−	26.9110i	1.88415	−	3.26344i
$69$		0			0
$70$	11.3374	−	0.413181i	1.35508	−	0.0493845i
$71$	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
$76$	−12.0989			−1.38784
$77$	0.794182	−	0.0289431i	0.0905054	−	0.00329837i
$78$		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
$83$	5.43268			0.596314			0.298157	−	0.954517i	$-0.403628\pi$
$83$	5.43268			0.596314			0.298157	+	0.954517i	$0.403628\pi$
$84$		0			0
$85$	−9.33379			−1.01239
$86$	−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
$92$	−9.98762			−1.04128
$93$		0			0
$94$	4.33310	+	7.50516i	0.446926	+	0.774098i
$95$	1.81708	+	3.14728i	0.186429	+	0.322904i
$96$		0			0
$97$	−12.5760			−1.27690			−0.638449	−	0.769664i	$-0.720424\pi$
$97$	−12.5760			−1.27690			−0.638449	+	0.769664i	$0.720424\pi$
$98$	−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	−0.958210	−	0.286066i	$-0.907652\pi$
$101$	−7.30470	−	12.6521i	−0.726845	−	1.25893i	0.231365	−	0.972867i	$-0.425681\pi$
$102$		0			0
$103$	−4.59888	+	7.96550i	−0.453142	+	0.784864i	−0.998579	−	0.0532872i	$-0.983030\pi$
$103$	−4.59888	+	7.96550i	−0.453142	+	0.784864i	0.545438	+	0.838151i	$0.316363\pi$
$104$	−24.9505			−2.44660
$105$		0			0
$106$	5.43268			0.527668
$107$	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	$0.786736\pi$
$110$	−0.643996	+	1.11543i	−0.0614026	+	0.106352i
$111$		0			0
$112$	18.8145	+	30.0079i	1.77781	+	2.83548i
$113$	−9.95420			−0.936412			−0.468206	−	0.883619i	$-0.655100\pi$
$113$	−9.95420			−0.936412			−0.468206	+	0.883619i	$0.655100\pi$
$114$		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
$119$	15.5371	−	0.566231i	1.42428	−	0.0519064i
$120$		0			0
$121$	5.45489	−	9.44814i	0.495899	−	0.858922i
$122$	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
$131$	5.63781	−	9.76497i	0.492577	−	0.853169i	−0.507386	−	0.861719i	$-0.669388\pi$
$131$	5.63781	−	9.76497i	0.492577	−	0.853169i	0.999963	+	0.00854976i	$0.00272151\pi$
$132$		0			0
$133$	−3.21565	−	5.12874i	−0.278832	−	0.444718i
$134$	−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	0.935359	−	0.353701i	$-0.115077\pi$
$137$	1.88874	+	3.27139i	0.161366	+	0.279493i	−0.773993	+	0.633194i	$0.781744\pi$
$138$		0			0
$139$	16.7193			1.41811			0.709056	−	0.705152i	$-0.249121\pi$
$139$	16.7193			1.41811			0.709056	+	0.705152i	$0.249121\pi$
$140$	10.4029	−	19.6370i	0.879205	−	1.65963i
$141$		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
$146$	31.5178			2.60843
$147$		0			0
$148$	−23.6749			−1.94606
$149$	5.44437	−	9.42992i	0.446020	−	0.772529i	−0.552103	−	0.833776i	$-0.686174\pi$
$149$	5.44437	−	9.42992i	0.446020	−	0.772529i	0.998123	+	0.0612468i	$0.0195077\pi$
$150$		0			0
$151$	6.04944	+	10.4779i	0.492297	+	0.852683i	0.999961	−	0.00887237i	$-0.00282420\pi$
$151$	6.04944	+	10.4779i	0.492297	+	0.852683i	−0.507664	+	0.861555i	$0.669491\pi$
$152$	−10.1545	+	17.5881i	−0.823640	+	1.42659i
$153$		0			0
$154$	1.00433	−	1.89582i	0.0809313	−	0.152770i
$155$	−7.64145			−0.613776
$156$		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
$160$	−29.2051			−2.30886
$161$	−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
$167$	4.34108			0.335923			0.167961	−	0.985794i	$-0.446282\pi$
$167$	4.34108			0.335923			0.167961	+	0.985794i	$0.446282\pi$
$168$		0			0
$169$	−5.09888			−0.392222
$170$	−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
$175$	6.54944	−	0.238687i	0.495091	−	0.0180431i
$176$	−4.02104			−0.303097
$177$		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	$0.261267\pi$
$182$	−10.6650	−	17.0100i	−0.790545	−	1.26086i
$183$		0			0
$184$	−8.38255	+	14.5190i	−0.617969	+	1.07035i
$185$	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	$0.922313\pi$
$194$	−16.9752	+	29.4020i	−1.21875	+	2.11094i
$195$		0			0
$196$	−16.1254	+	33.3189i	−1.15182	+	2.37992i
$197$	−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
$202$	−39.4400			−2.77499
$203$	−3.12474	+	5.89841i	−0.219314	+	0.413987i
$204$		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
$209$	0.687248			0.0475380
$210$		0			0
$211$	6.67487			0.459517			0.229758	−	0.973248i	$-0.426206\pi$
$211$	6.67487			0.459517			0.229758	+	0.973248i	$0.426206\pi$
$212$	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
$218$	8.22253			0.556900
$219$		0			0
$220$	1.26145	+	2.18490i	0.0850469	+	0.147306i
$221$	8.25890	+	14.3048i	0.555554	+	0.962248i
$222$		0			0
$223$	6.34108			0.424630			0.212315	−	0.977201i	$-0.431900\pi$
$223$	6.34108			0.424630			0.212315	+	0.977201i	$0.431900\pi$
$224$	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	−0.828906	−	0.559388i	$-0.811036\pi$
$227$	−13.5433	−	23.4576i	−0.898897	−	1.55694i	−0.0699913	−	0.997548i	$-0.522297\pi$
$228$		0			0
$229$	−4.09820	+	7.09828i	−0.270816	+	0.469068i	−0.969071	−	0.246782i	$-0.920627\pi$
$229$	−4.09820	+	7.09828i	−0.270816	+	0.469068i	0.698255	+	0.715849i	$0.253960\pi$
$230$	8.09888			0.534025
$231$		0			0
$232$	22.3942			1.47025
$233$	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
$236$	−12.9258	+	22.3881i	−0.841398	+	1.45734i
$237$		0			0
$238$	19.6483	−	37.0891i	1.27361	−	2.40413i
$239$	27.8640			1.80237			0.901185	−	0.433434i	$-0.142698\pi$
$239$	27.8640			1.80237			0.901185	+	0.433434i	$0.142698\pi$
$240$		0			0
$241$	11.2651	+	19.5117i	0.725648	+	1.25686i	0.958707	+	0.284397i	$0.0917934\pi$
$241$	11.2651	+	19.5117i	0.725648	+	1.25686i	−0.233058	+	0.972463i	$0.574873\pi$
$242$	−14.7262	−	25.5065i	−0.946634	−	1.63962i
$243$		0			0
$244$	40.0617			2.56469
$245$	11.0891	−	0.809332i	0.708454	−	0.0517063i
$246$		0			0
$247$	3.21565	−	5.56967i	0.204607	−	0.354390i
$248$	−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
$257$	−5.10074	+	8.83475i	−0.318176	+	0.551096i	−0.980107	−	0.198468i	$-0.936404\pi$
$257$	−5.10074	+	8.83475i	−0.318176	+	0.551096i	0.661932	+	0.749564i	$0.269737\pi$
$258$		0			0
$259$	−6.29232	−	10.0358i	−0.390986	−	0.623595i
$260$	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	0.854086	+	0.520132i	$0.174117\pi$
$263$	14.2305	+	24.6480i	0.877490	+	1.51986i	0.0234042	+	0.999726i	$0.492550\pi$
$264$		0			0
$265$	−3.19639			−0.196353
$266$	−16.3312	+	0.595175i	−1.00133	+	0.0364925i
$267$		0			0
$268$	−1.88255	+	3.26067i	−0.114995	+	0.199177i
$269$	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	$0.167096\pi$
$272$	−78.6661			−4.76983
$273$		0			0
$274$	10.1978			0.616070
$275$	−0.372026	+	0.644367i	−0.0224340	+	0.0388568i
$276$		0			0
$277$	−7.83743	−	13.5748i	−0.470906	−	0.815633i	0.528540	−	0.848908i	$-0.322739\pi$
$277$	−7.83743	−	13.5748i	−0.470906	−	0.815633i	−0.999446	+	0.0332754i	$0.989406\pi$
$278$	22.5679	−	39.0888i	1.35353	−	2.34439i
$279$		0			0
$280$	−19.8152	−	31.6039i	−1.18419	−	1.88869i
$281$	−11.9098			−0.710478			−0.355239	−	0.934776i	$-0.615600\pi$
$281$	−11.9098			−0.710478			−0.355239	+	0.934776i	$0.615600\pi$
$282$		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
$286$	2.27933			0.134780
$287$	−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
$293$	4.95558			0.289508			0.144754	−	0.989468i	$-0.453761\pi$
$293$	4.95558			0.289508			0.144754	+	0.989468i	$0.453761\pi$
$294$		0			0
$295$	7.76509			0.452101
$296$	−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
$301$	−11.2694	+	21.2727i	−0.649559	+	1.22614i
$302$	32.6625			1.87952
$303$		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	$0.716666\pi$
$308$	−2.23236	−	3.56046i	−0.127201	−	0.202876i
$309$		0			0
$310$	−10.3145	+	17.8653i	−0.585826	+	1.01468i
$311$	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
$320$	−18.1582	+	31.4509i	−1.01507	+	1.75816i
$321$		0			0
$322$	−13.4814	+	0.491316i	−0.751291	+	0.0273800i
$323$	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
$328$	79.0864			4.36681
$329$	4.51169	+	7.19583i	0.248738	+	0.396719i
$330$		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
$335$	1.13093			0.0617892
$336$		0			0
$337$	−12.3855			−0.674681			−0.337341	−	0.941383i	$-0.609527\pi$
$337$	−12.3855			−0.674681			−0.337341	+	0.941383i	$0.609527\pi$
$338$	−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
$344$	80.7649			4.35455
$345$		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
$349$	−12.1891			−0.652468			−0.326234	−	0.945289i	$-0.605780\pi$
$349$	−12.1891			−0.652468			−0.326234	+	0.945289i	$0.605780\pi$
$350$	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	0.814704	−	0.579877i	$-0.196899\pi$
$353$	−1.78180	−	3.08617i	−0.0948358	−	0.164260i	−0.909540	+	0.415616i	$0.863566\pi$
$354$		0			0
$355$	−10.2163	+	17.6952i	−0.542227	+	0.939165i
$356$	49.4610			2.62143
$357$		0			0
$358$	−37.6377			−1.98922
$359$	−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
$362$	24.7570	−	42.8805i	1.30120	−	2.25375i
$363$		0			0
$364$	−39.3003	+	1.43226i	−2.05990	+	0.0750707i
$365$	−18.5439			−0.970634
$366$		0			0
$367$	−10.4771	−	18.1469i	−0.546900	−	0.947259i	−0.998485	−	0.0550305i	$-0.982474\pi$
$367$	−10.4771	−	18.1469i	−0.546900	−	0.947259i	0.451585	−	0.892228i	$-0.350859\pi$
$368$	12.6421	+	21.8968i	0.659017	+	1.14145i
$369$		0			0
$370$	19.1978			0.998044
$371$	5.32072	−	0.193908i	0.276238	−	0.0100672i
$372$		0			0
$373$	−1.00000	+	1.73205i	−0.0517780	+	0.0896822i	−0.890753	−	0.454488i	$-0.849822\pi$
$373$	−1.00000	+	1.73205i	−0.0517780	+	0.0896822i	0.838975	+	0.544170i	$0.183156\pi$
$374$	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
$383$	−5.98831	+	10.3721i	−0.305988	+	0.529987i	−0.977481	−	0.211024i	$-0.932320\pi$
$383$	−5.98831	+	10.3721i	−0.305988	+	0.529987i	0.671493	+	0.741011i	$0.265654\pi$
$384$		0			0
$385$	−0.590912	+	1.11543i	−0.0301157	+	0.0568478i
$386$	−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	0.986127	−	0.165995i	$-0.0530835\pi$
$389$	6.88942	+	11.9328i	0.349308	+	0.605019i	−0.636819	+	0.771013i	$0.719750\pi$
$390$		0			0
$391$	11.0989			0.561295
$392$	34.9017	+	51.4059i	1.76280	+	2.59639i
$393$		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	−0.951859	−	0.306535i	$-0.900830\pi$
$397$	−4.19344	+	7.26325i	−0.210463	+	0.364532i	0.741397	+	0.671067i	$0.234164\pi$
$398$	−16.0741			−0.805723
$399$		0			0
$400$	−33.1606			−1.65803
$401$	13.8083	−	23.9168i	0.689556	−	1.19435i	−0.282426	−	0.959289i	$-0.591139\pi$
$401$	13.8083	−	23.9168i	0.689556	−	1.19435i	0.971982	−	0.235057i	$-0.0755275\pi$
$402$		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
$407$	1.34479			0.0666590
$408$		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
$412$	48.6377			2.39621
$413$	−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
$419$	−21.0000			−1.02592			−0.512959	−	0.858413i	$-0.671451\pi$
$419$	−21.0000			−1.02592			−0.512959	+	0.858413i	$0.671451\pi$
$420$		0			0
$421$	34.7293			1.69260			0.846302	−	0.532703i	$-0.178824\pi$
$421$	34.7293			1.69260			0.846302	+	0.532703i	$0.178824\pi$
$422$	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
$427$	10.6476	+	16.9822i	0.515275	+	0.821828i
$428$	−66.1555			−3.19775
$429$		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	$0.549809\pi$
$434$	16.0858	−	30.3644i	0.772144	−	1.45754i
$435$		0			0
$436$	8.05308	−	13.9484i	0.385673	−	0.668005i
$437$	−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
$446$	8.55927	−	14.8251i	0.405293	−	0.701989i
$447$		0			0
$448$	28.3182	−	53.4548i	1.33791	−	2.52550i
$449$	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
$454$	−73.1235			−3.43186
$455$	6.27492	+	10.0081i	0.294173	+	0.469185i
$456$		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
$461$	40.8182			1.90109			0.950546	−	0.310584i	$-0.100525\pi$
$461$	40.8182			1.90109			0.950546	+	0.310584i	$0.100525\pi$
$462$		0			0
$463$	9.90840			0.460482			0.230241	−	0.973134i	$-0.426048\pi$
$463$	9.90840			0.460482			0.230241	+	0.973134i	$0.426048\pi$
$464$	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
$470$	−13.7651			−0.634936
$471$		0			0
$472$	21.6971	+	37.5804i	0.998689	+	1.72978i
$473$	−1.36652	−	2.36689i	−0.0628329	−	0.108830i
$474$		0			0
$475$	5.66758			0.260047
$476$	−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	−0.998938	−	0.0460744i	$-0.985329\pi$
$479$	−11.8047	−	20.4463i	−0.539371	−	0.934217i	0.459567	−	0.888143i	$-0.348004\pi$
$480$		0			0
$481$	6.29232	−	10.8986i	0.286905	−	0.496934i
$482$	60.8231			2.77042
$483$		0			0
$484$	−57.6908			−2.62231
$485$	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	$-0.456646\pi$
$488$	33.6236	−	58.2377i	1.52207	−	2.63630i
$489$		0			0
$490$	13.0760	−	27.0181i	0.590713	−	1.22055i
$491$	−23.2051			−1.04723			−0.523615	−	0.851955i	$-0.675417\pi$
$491$	−23.2051			−1.04723			−0.523615	+	0.851955i	$0.675417\pi$
$492$		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
$497$	15.9327	−	30.0753i	0.714678	−	1.34906i
$498$		0			0
$499$	2.66257	−	4.61170i	0.119193	−	0.206448i	−0.800255	−	0.599660i	$-0.795303\pi$
$499$	2.66257	−	4.61170i	0.119193	−	0.206448i	0.919448	+	0.393212i	$0.128636\pi$
$500$	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
$509$	0.750930	−	1.30065i	0.0332844	−	0.0576502i	−0.848903	−	0.528548i	$-0.822737\pi$
$509$	0.750930	−	1.30065i	0.0332844	−	0.0576502i	0.882188	+	0.470898i	$0.156070\pi$
$510$		0			0
$511$	30.8683	−	1.12496i	1.36553	−	0.0497654i
$512$	−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
$517$	−0.964238			−0.0424072
$518$	−31.9567	+	1.16463i	−1.40410	+	0.0511707i
$519$		0			0
$520$	19.8152	−	34.3210i	0.868955	−	1.50507i
$521$	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	$0.0382523\pi$
$524$	−59.6253			−2.60475
$525$		0			0
$526$	76.8341			3.35013
$527$	−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
$533$	−25.0444			−1.08479
$534$		0			0
$535$	9.93563	+	17.2090i	0.429555	+	0.744011i
$536$	3.16002	+	5.47331i	0.136492	+	0.236411i
$537$		0			0
$538$	40.1606			1.73145
$539$	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
$545$	−4.83784			−0.207230
$546$		0			0
$547$	30.1075			1.28731			0.643653	−	0.765318i	$-0.277418\pi$
$547$	30.1075			1.28731			0.643653	+	0.765318i	$0.277418\pi$
$548$	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
$553$	2.34176	+	3.73495i	0.0995820	+	0.158826i
$554$	−42.3163			−1.79785
$555$		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
$560$	−56.2199	+	2.04887i	−2.37572	+	0.0865807i
$561$		0			0
$562$	−16.0760	+	27.8444i	−0.678124	+	1.17455i
$563$	−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	$0.792601\pi$
$572$	2.23236	−	3.86656i	0.0933397	−	0.161669i
$573$		0			0
$574$	33.8053	+	53.9171i	1.41101	+	2.25046i
$575$	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
$580$	−21.1905			−0.879887
$581$	6.72864	−	12.7013i	0.279151	−	0.526939i
$582$		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
$587$	−38.6822			−1.59658			−0.798292	−	0.602271i	$-0.794263\pi$
$587$	−38.6822			−1.59658			−0.798292	+	0.602271i	$0.794263\pi$
$588$		0			0
$589$	11.0073			0.453547
$590$	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
$596$	−57.5795			−2.35855
$597$		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
$601$	−7.28071			−0.296986			−0.148493	−	0.988913i	$-0.547442\pi$
$601$	−7.28071			−0.296986			−0.148493	+	0.988913i	$0.547442\pi$
$602$	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	−0.489333	−	0.872097i	$-0.662760\pi$
$607$	12.5796	−	21.7886i	0.510591	−	0.884370i	0.999925	−	0.0122732i	$-0.00390679\pi$
$608$	42.0690			1.70612
$609$		0			0
$610$	−32.4858			−1.31531
$611$	−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	$0.559394\pi$
$614$	−29.7676	+	51.5589i	−1.20132	+	2.08075i
$615$		0			0
$616$	−7.04944	+	0.256909i	−0.284030	+	0.0103512i
$617$	13.7280			0.552667			0.276333	−	0.961062i	$-0.410881\pi$
$617$	13.7280			0.552667			0.276333	+	0.961062i	$0.410881\pi$
$618$		0			0
$619$	−5.90545	−	10.2285i	−0.237360	−	0.411119i	0.722596	−	0.691271i	$-0.242949\pi$
$619$	−5.90545	−	10.2285i	−0.237360	−	0.411119i	−0.959956	+	0.280151i	$0.909615\pi$
$620$	20.2040	+	34.9943i	0.811411	+	1.40540i
$621$		0			0
$622$	21.5302			0.863282
$623$	13.1458	+	20.9666i	0.526675	+	0.840009i
$624$		0			0
$625$	3.23924	−	5.61053i	0.129570	−	0.224421i
$626$	−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
$635$	10.6738	−	18.4875i	0.423576	−	0.733655i
$636$		0			0
$637$	−11.0524	−	16.2788i	−0.437912	−	0.644989i
$638$	−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	0.684291	−	0.729209i	$-0.260112\pi$
$641$	−7.32623	−	12.6894i	−0.289368	−	0.501201i	−0.973659	+	0.228008i	$0.926779\pi$
$642$		0			0
$643$	2.03714			0.0803369			0.0401685	−	0.999193i	$-0.487211\pi$
$643$	2.03714			0.0803369			0.0401685	+	0.999193i	$0.487211\pi$
$644$	−12.3702	+	23.3505i	−0.487453	+	0.920139i
$645$		0			0
$646$	18.1483	−	31.4338i	0.714036	−	1.23675i
$647$	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
$650$	18.7971			0.737284
$651$		0			0
$652$	−47.3570			−1.85464
$653$	17.0920	−	29.6042i	0.668862	−	1.15850i	−0.309361	−	0.950945i	$-0.600115\pi$
$653$	17.0920	−	29.6042i	0.668862	−	1.15850i	0.978223	−	0.207558i	$-0.0665516\pi$
$654$		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
$659$	24.8640			0.968563			0.484282	−	0.874912i	$-0.339081\pi$
$659$	24.8640			0.968563			0.484282	+	0.874912i	$0.339081\pi$
$660$		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
$664$	−48.2224			−1.87139
$665$	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
$671$	−2.27561			−0.0878490
$672$		0			0
$673$	−3.81955			−0.147233			−0.0736165	−	0.997287i	$-0.523454\pi$
$673$	−3.81955			−0.147233			−0.0736165	+	0.997287i	$0.523454\pi$
$674$	−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
$679$	−15.5760	+	29.4020i	−0.597751	+	1.12834i
$680$	82.8501			3.17715
$681$		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
$686$	−20.1273	+	45.7676i	−0.768463	+	1.74742i
$687$		0			0
$688$	60.9028	−	105.487i	2.32190	−	4.02165i
$689$	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
$698$	−16.4530	+	28.4975i	−0.622756	+	1.07865i
$699$		0			0
$700$	−18.4098	−	29.3623i	−0.695824	−	1.10979i
$701$	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
$706$	−9.62041			−0.362069
$707$	−38.6272	+	1.40773i	−1.45273	+	0.0529430i
$708$		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
$713$	9.08650			0.340292
$714$		0			0
$715$	−1.34108			−0.0501534
$716$	−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
$722$	37.1606			1.38298
$723$		0			0
$724$	−48.4937	−	83.9936i	−1.80226	−	3.12160i
$725$	−3.12474	−	5.41220i	−0.116050	−	0.201004i
$726$		0			0
$727$	−35.8282			−1.32879			−0.664397	−	0.747379i	$-0.731312\pi$
$727$	−35.8282			−1.32879			−0.664397	+	0.747379i	$0.731312\pi$
$728$	−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	0.233172	+	0.972435i	$0.425089\pi$
$733$	−19.6440	+	34.0244i	−0.725568	+	1.25672i	−0.958740	+	0.284284i	$0.908244\pi$
$734$	−56.5685			−2.08798
$735$		0			0
$736$	34.7280			1.28009
$737$	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	$0.845574\pi$
$740$	18.8022	−	32.5663i	0.691181	−	1.19716i
$741$		0			0
$742$	6.72864	−	12.7013i	0.247016	−	0.466280i
$743$	30.7266			1.12725			0.563624	−	0.826031i	$-0.309407\pi$
$743$	30.7266			1.12725			0.563624	+	0.826031i	$0.309407\pi$
$744$		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
$749$	−17.5829	−	28.0434i	−0.642464	−	1.02469i
$750$		0			0
$751$	−10.3869	+	17.9906i	−0.379023	+	0.656486i	−0.990920	−	0.134451i	$-0.957073\pi$
$751$	−10.3869	+	17.9906i	−0.379023	+	0.656486i	0.611898	+	0.790937i	$0.290406\pi$
$752$	−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
$761$	−16.4196	+	28.4396i	−0.595210	+	1.03093i	0.398307	+	0.917252i	$0.369598\pi$
$761$	−16.4196	+	28.4396i	−0.595210	+	1.03093i	−0.993517	+	0.113682i	$0.963735\pi$
$762$		0			0
$763$	8.05308	−	0.293486i	0.291541	−	0.0106249i
$764$	−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
$769$	31.7293			1.14419			0.572094	−	0.820188i	$-0.306131\pi$
$769$	31.7293			1.14419			0.572094	+	0.820188i	$0.306131\pi$
$770$	1.81020	+	2.88715i	0.0652352	+	0.104046i
$771$		0			0
$772$	−20.2694	+	35.1077i	−0.729512	+	1.26355i
$773$	−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
$776$	111.629			4.00724
$777$		0			0
$778$	37.1978			1.33360
$779$	−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
$785$	−0.300372			−0.0107207
$786$		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
$790$	−7.14468			−0.254196
$791$	−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
$797$	−5.81955			−0.206139			−0.103070	−	0.994674i	$-0.532866\pi$
$797$	−5.81955			−0.206139			−0.103070	+	0.994674i	$0.532866\pi$
$798$		0			0
$799$	−18.8640			−0.667360
$800$	−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
$805$	7.93199	−	0.289073i	0.279566	−	0.0101885i
$806$	36.5068			1.28590
$807$		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	$0.604903\pi$
$812$	35.2738	−	1.28551i	1.23787	−	0.0451127i
$813$		0			0
$814$	1.81522	−	3.14406i	0.0636235	−	0.110199i
$815$	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	$0.977159\pi$
$824$	40.8213	−	70.7046i	1.42208	−	2.46311i
$825$		0			0
$826$	−16.3461	+	30.8557i	−0.568753	+	1.07361i
$827$	−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
$832$	64.2682			2.22810
$833$	17.9196	−	37.0261i	0.620878	−	1.28288i
$834$		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
$839$	16.4785			0.568900			0.284450	−	0.958691i	$-0.408189\pi$
$839$	16.4785			0.568900			0.284450	+	0.958691i	$0.408189\pi$
$840$		0			0
$841$	−22.6350			−0.780516
$842$	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
$848$	−26.9395			−0.925106
$849$		0			0
$850$	19.6483	+	34.0319i	0.673932	+	1.16728i
$851$	−4.22803	−	7.32316i	−0.144935	−	0.251035i
$852$		0			0
$853$	−26.9986			−0.924415			−0.462208	−	0.886772i	$-0.652943\pi$
$853$	−26.9986			−0.924415			−0.462208	+	0.886772i	$0.652943\pi$
$854$	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	0.978215	+	0.207596i	$0.0665640\pi$
$857$	19.5815	+	33.9161i	0.668891	+	1.15855i	−0.309324	+	0.950957i	$0.600103\pi$
$858$		0			0
$859$	−4.73422	+	8.19991i	−0.161529	+	0.279777i	−0.935417	−	0.353545i	$-0.884976\pi$
$859$	−4.73422	+	8.19991i	−0.161529	+	0.279777i	0.773888	+	0.633323i	$0.218309\pi$
$860$	−76.4239			−2.60603
$861$		0			0
$862$	85.3199			2.90601
$863$	−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
$866$	−8.75457	+	15.1634i	−0.297492	+	0.515272i
$867$		0			0
$868$	−35.7545	−	57.0259i	−1.21359	−	1.93559i
$869$	−0.500482			−0.0169777
$870$		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
$875$	−14.7095	+	27.7663i	−0.497271	+	0.938672i
$876$		0			0
$877$	−22.3497	+	38.7109i	−0.754697	+	1.30717i	0.190828	+	0.981624i	$0.438883\pi$
$877$	−22.3497	+	38.7109i	−0.754697	+	1.30717i	−0.945525	+	0.325550i	$0.894451\pi$
$878$	−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
$887$	−0.600744	+	1.04052i	−0.0201710	+	0.0349372i	−0.875935	−	0.482430i	$-0.839754\pi$
$887$	−0.600744	+	1.04052i	−0.0201710	+	0.0349372i	0.855764	+	0.517367i	$0.173088\pi$
$888$		0			0
$889$	−16.6461	+	31.4219i	−0.558291	+	1.05386i
$890$	−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
$895$	22.1447			0.740215
$896$	−35.0666	−	55.9287i	−1.17149	−	1.86845i
$897$		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
$902$	−7.22487			−0.240562
$903$		0			0
$904$	88.3570			2.93871
$905$	−14.5662	+	25.2293i	−0.484195	+	0.838651i
$906$		0			0
$907$	−8.53156	−	14.7771i	−0.283286	−	0.490665i	0.688906	−	0.724850i	$-0.258091\pi$
$907$	−8.53156	−	14.7771i	−0.283286	−	0.490665i	−0.972192	+	0.234185i	$0.924758\pi$
$908$	−71.6166	+	124.044i	−2.37668	+	4.11653i
$909$		0			0
$910$	31.8683	−	1.16141i	1.05642	−	0.0385002i
$911$	22.0014			0.728938			0.364469	−	0.931215i	$-0.381250\pi$
$911$	22.0014			0.728938			0.364469	+	0.931215i	$0.381250\pi$
$912$		0			0
$913$	0.815912	+	1.41320i	0.0270027	+	0.0467701i
$914$	27.5901	+	47.7875i	0.912601	+	1.58067i
$915$		0			0
$916$	43.3425			1.43207
$917$	−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
$923$	36.1593			1.19020
$924$		0			0
$925$	11.0902			0.364644
$926$	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
$931$	−15.9735	+	1.16582i	−0.523509	+	0.0382082i
$932$	−144.998			−4.74958
$933$		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	$0.277131\pi$
$938$	−2.38069	+	4.49390i	−0.0777322	+	0.146731i
$939$		0			0
$940$	−13.4814	+	23.3505i	−0.439716	+	0.761610i
$941$	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
$950$	7.65019	−	13.2505i	0.248205	−	0.429903i
$951$		0			0
$952$	−137.913	+	5.02607i	−4.46977	+	0.162896i
$953$	−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
$958$	−63.7366			−2.05924
$959$	9.98762	−	0.363988i	0.322517	−	0.0117538i
$960$		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
$965$	12.1767			0.391983
$966$		0			0
$967$	−6.18911			−0.199028			−0.0995141	−	0.995036i	$-0.531729\pi$
$967$	−6.18911			−0.199028			−0.0995141	+	0.995036i	$0.531729\pi$
$968$	−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
$974$	−94.1432			−3.01654
$975$		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
$979$	−2.80951			−0.0897925
$980$	−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	0.963159	+	0.268933i	$0.0866710\pi$
$983$	22.4010	+	38.7997i	0.714482	+	1.23752i	−0.248677	+	0.968587i	$0.579996\pi$
$984$		0			0
$985$	14.6025	−	25.2923i	0.465275	−	0.805880i
$986$	−40.0232			−1.27460
$987$		0			0
$988$	−34.0087			−1.08196
$989$	−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	$0.707230\pi$
$992$	−44.2286	+	76.6063i	−1.40426	+	2.43225i
$993$		0			0
$994$	−48.8083	−	77.8458i	−1.54810	−	2.46912i
$995$	9.45744			0.299821
$996$		0			0
$997$	5.66257	+	9.80785i	0.179335	+	0.310618i	0.941653	−	0.336585i	$-0.109272\pi$
$997$	5.66257	+	9.80785i	0.179335	+	0.310618i	−0.762318	+	0.647203i	$0.775939\pi$
$998$	−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	189.2.e.f.163.3	yes	6
3.2	odd	2		189.2.e.e.163.1	yes	6
7.2	even	3		1323.2.a.x.1.1		3
7.4	even	3	inner	189.2.e.f.109.3	yes	6
7.5	odd	6		1323.2.a.y.1.1		3
9.2	odd	6		567.2.h.i.352.3		6
9.4	even	3		567.2.g.i.541.3		6
9.5	odd	6		567.2.g.h.541.1		6
9.7	even	3		567.2.h.h.352.1		6
21.2	odd	6		1323.2.a.ba.1.3		3
21.5	even	6		1323.2.a.z.1.3		3
21.11	odd	6		189.2.e.e.109.1	✓	6
63.4	even	3		567.2.h.h.298.1		6
63.11	odd	6		567.2.g.h.109.1		6
63.25	even	3		567.2.g.i.109.3		6
63.32	odd	6		567.2.h.i.298.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.e.e.109.1	✓	6	21.11	odd	6
189.2.e.e.163.1	yes	6	3.2	odd	2
189.2.e.f.109.3	yes	6	7.4	even	3	inner
189.2.e.f.163.3	yes	6	1.1	even	1	trivial
567.2.g.h.109.1		6	63.11	odd	6
567.2.g.h.541.1		6	9.5	odd	6
567.2.g.i.109.3		6	63.25	even	3
567.2.g.i.541.3		6	9.4	even	3
567.2.h.h.298.1		6	63.4	even	3
567.2.h.h.352.1		6	9.7	even	3
567.2.h.i.298.3		6	63.32	odd	6
567.2.h.i.352.3		6	9.2	odd	6
1323.2.a.x.1.1		3	7.2	even	3
1323.2.a.y.1.1		3	7.5	odd	6
1323.2.a.z.1.3		3	21.5	even	6
1323.2.a.ba.1.3		3	21.2	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:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.34981 - 2.33795i) q^{2} +(-2.64400 - 4.57954i) q^{4} +(-0.794182 + 1.37556i) q^{5} +(1.23855 - 2.33795i) q^{7} -8.87636 q^{8} +O(q^{10})\)	\(q+(1.34981 - 2.33795i) q^{2} +(-2.64400 - 4.57954i) q^{4} +(-0.794182 + 1.37556i) q^{5} +(1.23855 - 2.33795i) q^{7} -8.87636 q^{8} +(2.14400 + 3.71351i) q^{10} +(0.150186 + 0.260130i) q^{11} +2.81089 q^{13} +(-3.79418 - 6.05146i) q^{14} +(-6.69344 + 11.5934i) q^{16} +(2.93818 + 5.08907i) q^{17} +(1.14400 - 1.98146i) q^{19} +8.39926 q^{20} +0.810892 q^{22} +(0.944368 - 1.63569i) q^{23} +(1.23855 + 2.14523i) q^{25} +(3.79418 - 6.57172i) q^{26} +(-13.9814 + 0.509538i) q^{28} -2.52290 q^{29} +(2.40545 + 4.16635i) q^{31} +(9.19344 + 15.9235i) q^{32} +15.8640 q^{34} +(2.23236 + 3.56046i) q^{35} +(2.23855 - 3.87728i) q^{37} +(-3.08836 - 5.34920i) q^{38} +(7.04944 - 12.2100i) q^{40} -8.90978 q^{41} -9.09888 q^{43} +(0.794182 - 1.37556i) q^{44} +(-2.54944 - 4.41576i) q^{46} +(-1.60507 + 2.78007i) q^{47} +(-3.93199 - 5.79133i) q^{49} +6.68725 q^{50} +(-7.43199 - 12.8726i) q^{52} +(1.00619 + 1.74277i) q^{53} -0.477100 q^{55} +(-10.9938 + 20.7524i) q^{56} +(-3.40545 + 5.89841i) q^{58} +(-2.44437 - 4.23377i) q^{59} +(-3.78799 + 6.56099i) q^{61} +12.9876 q^{62} +22.8640 q^{64} +(-2.23236 + 3.86656i) q^{65} +(-0.356004 - 0.616617i) q^{67} +(15.5371 - 26.9110i) q^{68} +(11.3374 - 0.413181i) q^{70} +12.8640 q^{71} +(5.83743 + 10.1107i) q^{73} +(-6.04325 - 10.4672i) q^{74} -12.0989 q^{76} +(0.794182 - 0.0289431i) q^{77} +(-0.833104 + 1.44298i) q^{79} +(-10.6316 - 18.4145i) q^{80} +(-12.0265 + 20.8306i) q^{82} +5.43268 q^{83} -9.33379 q^{85} +(-12.2818 + 21.2727i) q^{86} +(-1.33310 - 2.30900i) q^{88} +(-4.67673 + 8.10033i) q^{89} +(3.48143 - 6.57172i) q^{91} -9.98762 q^{92} +(4.33310 + 7.50516i) q^{94} +(1.81708 + 3.14728i) q^{95} -12.5760 q^{97} +(-18.8473 + 1.37556i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 2 q^{2} - 4 q^{4} + q^{5} + 2 q^{7} - 18 q^{8}+O(q^{10}) \) 6 * q + 2 * q^2 - 4 * q^4 + q^5 + 2 * q^7 - 18 * q^8	\( 6 q + 2 q^{2} - 4 q^{4} + q^{5} + 2 q^{7} - 18 q^{8} + q^{10} + 7 q^{11} + 4 q^{13} - 17 q^{14} - 10 q^{16} - 5 q^{19} + 26 q^{20} - 8 q^{22} + 6 q^{23} + 2 q^{25} + 17 q^{26} - 30 q^{28} - 26 q^{29} + 8 q^{31} + 25 q^{32} + 24 q^{34} - 10 q^{35} + 8 q^{37} - 7 q^{38} + 24 q^{40} - 4 q^{41} - 18 q^{43} - q^{44} + 3 q^{46} + 9 q^{47} + 12 q^{49} - 8 q^{50} - 9 q^{52} + 24 q^{53} + 8 q^{55} - 48 q^{56} - 14 q^{58} - 15 q^{59} + q^{61} + 42 q^{62} + 66 q^{64} + 10 q^{65} - 14 q^{67} + 39 q^{68} + 26 q^{70} + 6 q^{71} - 7 q^{73} - 36 q^{76} - q^{77} - 6 q^{79} - 16 q^{80} - 43 q^{82} - 6 q^{83} - 54 q^{85} - 32 q^{86} - 9 q^{88} - 5 q^{89} - 33 q^{91} - 24 q^{92} + 27 q^{94} + 16 q^{95} - 28 q^{97} - 49 q^{98}+O(q^{100}) \) 6 * q + 2 * q^2 - 4 * q^4 + q^5 + 2 * q^7 - 18 * q^8 + q^10 + 7 * q^11 + 4 * q^13 - 17 * q^14 - 10 * q^16 - 5 * q^19 + 26 * q^20 - 8 * q^22 + 6 * q^23 + 2 * q^25 + 17 * q^26 - 30 * q^28 - 26 * q^29 + 8 * q^31 + 25 * q^32 + 24 * q^34 - 10 * q^35 + 8 * q^37 - 7 * q^38 + 24 * q^40 - 4 * q^41 - 18 * q^43 - q^44 + 3 * q^46 + 9 * q^47 + 12 * q^49 - 8 * q^50 - 9 * q^52 + 24 * q^53 + 8 * q^55 - 48 * q^56 - 14 * q^58 - 15 * q^59 + q^61 + 42 * q^62 + 66 * q^64 + 10 * q^65 - 14 * q^67 + 39 * q^68 + 26 * q^70 + 6 * q^71 - 7 * q^73 - 36 * q^76 - q^77 - 6 * q^79 - 16 * q^80 - 43 * q^82 - 6 * q^83 - 54 * q^85 - 32 * q^86 - 9 * q^88 - 5 * q^89 - 33 * q^91 - 24 * q^92 + 27 * q^94 + 16 * q^95 - 28 * q^97 - 49 * q^98

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