LMFDB - Embedded newform 162.3.f.a.89.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,3,Mod(17,162)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(162, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([11]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("162.17");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	162.f (of order $18$, degree $6$, 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:	$4.41418028264$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 54)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			89.3
Character	$\chi$	$=$	162.89
Dual form			162.3.f.a.71.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39273 - 0.245576i) q^{2} +(1.87939 + 0.684040i) q^{4} +(3.55779 + 4.24001i) q^{5} +(-10.2625 + 3.73526i) q^{7} +(-2.44949 - 1.41421i) q^{8} +O(q^{10})$	\(q+(-1.39273 - 0.245576i) q^{2} +(1.87939 + 0.684040i) q^{4} +(3.55779 + 4.24001i) q^{5} +(-10.2625 + 3.73526i) q^{7} +(-2.44949 - 1.41421i) q^{8} +(-3.91380 - 6.77890i) q^{10} +(-2.64446 + 3.15155i) q^{11} +(-0.953621 - 5.40825i) q^{13} +(15.2102 - 2.68197i) q^{14} +(3.06418 + 2.57115i) q^{16} +(-4.10708 + 2.37123i) q^{17} +(-17.1665 + 29.7332i) q^{19} +(3.78613 + 10.4023i) q^{20} +(4.45696 - 3.73984i) q^{22} +(-12.6292 + 34.6986i) q^{23} +(-0.978615 + 5.55000i) q^{25} +7.76642i q^{26} -21.8423 q^{28} +(5.18449 + 0.914165i) q^{29} +(34.9235 + 12.7111i) q^{31} +(-3.63616 - 4.33340i) q^{32} +(6.30237 - 2.29387i) q^{34} +(-52.3496 - 30.2240i) q^{35} +(-12.1981 - 21.1278i) q^{37} +(31.2100 - 37.1946i) q^{38} +(-2.71850 - 15.4174i) q^{40} +(22.6189 - 3.98833i) q^{41} +(39.1915 + 32.8855i) q^{43} +(-7.12575 + 4.11406i) q^{44} +(26.1102 - 45.2243i) q^{46} +(-28.3436 - 77.8733i) q^{47} +(53.8315 - 45.1700i) q^{49} +(2.72589 - 7.48932i) q^{50} +(1.90724 - 10.8165i) q^{52} +16.2927i q^{53} -22.7711 q^{55} +(30.4205 + 5.36395i) q^{56} +(-6.99608 - 2.54637i) q^{58} +(45.6558 + 54.4105i) q^{59} +(-74.1675 + 26.9948i) q^{61} +(-45.5174 - 26.2795i) q^{62} +(4.00000 + 6.92820i) q^{64} +(19.5383 - 23.2848i) q^{65} +(-12.1162 - 68.7145i) q^{67} +(-9.34081 + 1.64704i) q^{68} +(65.4865 + 54.9497i) q^{70} +(65.9072 - 38.0516i) q^{71} +(25.5063 - 44.1783i) q^{73} +(11.8002 + 32.4208i) q^{74} +(-52.6012 + 44.1376i) q^{76} +(15.3671 - 42.2207i) q^{77} +(5.51385 - 31.2706i) q^{79} +22.1398i q^{80} -32.4815 q^{82} +(-28.7447 - 5.06847i) q^{83} +(-24.6662 - 8.97776i) q^{85} +(-46.5072 - 55.4251i) q^{86} +(10.9346 - 3.97985i) q^{88} +(69.2878 + 40.0033i) q^{89} +(29.9878 + 51.9404i) q^{91} +(-47.4704 + 56.5731i) q^{92} +(20.3511 + 115.417i) q^{94} +(-187.144 + 32.9986i) q^{95} +(36.3741 + 30.5215i) q^{97} +(-86.0653 + 49.6898i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 18 q^{5}+O(q^{10}) $ 36 * q - 18 * q^5	$ 36 q - 18 q^{5} + 18 q^{11} + 36 q^{14} + 72 q^{20} + 36 q^{22} + 180 q^{23} + 18 q^{25} - 144 q^{29} - 90 q^{31} - 72 q^{34} - 486 q^{35} - 180 q^{38} + 90 q^{41} + 90 q^{43} + 378 q^{47} + 72 q^{49} + 72 q^{56} - 252 q^{59} - 144 q^{61} + 144 q^{64} - 18 q^{65} - 594 q^{67} + 180 q^{68} - 360 q^{70} + 648 q^{71} + 126 q^{73} + 504 q^{74} - 72 q^{76} + 342 q^{77} - 72 q^{79} - 594 q^{83} + 360 q^{85} - 540 q^{86} + 144 q^{88} - 648 q^{89} - 198 q^{91} - 396 q^{92} + 504 q^{94} - 252 q^{95} + 702 q^{97} - 648 q^{98}+O(q^{100}) $ 36 * q - 18 * q^5 + 18 * q^11 + 36 * q^14 + 72 * q^20 + 36 * q^22 + 180 * q^23 + 18 * q^25 - 144 * q^29 - 90 * q^31 - 72 * q^34 - 486 * q^35 - 180 * q^38 + 90 * q^41 + 90 * q^43 + 378 * q^47 + 72 * q^49 + 72 * q^56 - 252 * q^59 - 144 * q^61 + 144 * q^64 - 18 * q^65 - 594 * q^67 + 180 * q^68 - 360 * q^70 + 648 * q^71 + 126 * q^73 + 504 * q^74 - 72 * q^76 + 342 * q^77 - 72 * q^79 - 594 * q^83 + 360 * q^85 - 540 * q^86 + 144 * q^88 - 648 * q^89 - 198 * q^91 - 396 * q^92 + 504 * q^94 - 252 * q^95 + 702 * q^97 - 648 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{1}{18}\right)$

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 $

$2$	−1.39273	−	0.245576i	−0.696364	−	0.122788i
$2$	−1.39273	−	0.245576i	−0.696364	−	0.122788i
$3$		0			0
$3$		0			0
$4$	1.87939	+	0.684040i	0.469846	+	0.171010i
$5$	3.55779	+	4.24001i	0.711559	+	0.848003i	0.993782	−	0.111346i	$-0.0355162\pi$
$5$	3.55779	+	4.24001i	0.711559	+	0.848003i	−0.282223	+	0.959349i	$0.591072\pi$
$6$		0			0
$7$	−10.2625	+	3.73526i	−1.46608	+	0.533609i	−0.947032	−	0.321138i	$-0.895935\pi$
$7$	−10.2625	+	3.73526i	−1.46608	+	0.533609i	−0.519045	+	0.854747i	$0.673712\pi$
$8$	−2.44949	−	1.41421i	−0.306186	−	0.176777i
$9$		0			0
$10$	−3.91380	−	6.77890i	−0.391380	−	0.677890i
$11$	−2.64446	+	3.15155i	−0.240406	+	0.286505i	−0.872734	−	0.488196i	$-0.837655\pi$
$11$	−2.64446	+	3.15155i	−0.240406	+	0.286505i	0.632328	+	0.774701i	$0.282099\pi$
$12$		0			0
$13$	−0.953621	−	5.40825i	−0.0733555	−	0.416020i	−0.999267	−	0.0382793i	$-0.987812\pi$
$13$	−0.953621	−	5.40825i	−0.0733555	−	0.416020i	0.925912	−	0.377740i	$-0.123299\pi$
$14$	15.2102	−	2.68197i	1.08644	−	0.191570i
$15$		0			0
$16$	3.06418	+	2.57115i	0.191511	+	0.160697i
$17$	−4.10708	+	2.37123i	−0.241593	+	0.139484i	−0.615909	−	0.787817i	$-0.711211\pi$
$17$	−4.10708	+	2.37123i	−0.241593	+	0.139484i	0.374316	+	0.927301i	$0.377878\pi$
$18$		0			0
$19$	−17.1665	+	29.7332i	−0.903499	+	1.56491i	−0.0805801	+	0.996748i	$0.525677\pi$
$19$	−17.1665	+	29.7332i	−0.903499	+	1.56491i	−0.822919	+	0.568158i	$0.807656\pi$
$20$	3.78613	+	10.4023i	0.189306	+	0.520115i
$21$		0			0
$22$	4.45696	−	3.73984i	0.202589	−	0.169993i
$23$	−12.6292	+	34.6986i	−0.549098	+	1.50863i	0.285833	+	0.958279i	$0.407730\pi$
$23$	−12.6292	+	34.6986i	−0.549098	+	1.50863i	−0.834931	+	0.550354i	$0.814493\pi$
$24$		0			0
$25$	−0.978615	+	5.55000i	−0.0391446	+	0.222000i
$26$			7.76642i			0.298708i
$27$		0			0
$28$	−21.8423			−0.780084
$29$	5.18449	+	0.914165i	0.178775	+	0.0315229i	0.262319	−	0.964981i	$-0.415513\pi$
$29$	5.18449	+	0.914165i	0.178775	+	0.0315229i	−0.0835437	+	0.996504i	$0.526624\pi$
$30$		0			0
$31$	34.9235	+	12.7111i	1.12656	+	0.410036i	0.837044	−	0.547136i	$-0.184282\pi$
$31$	34.9235	+	12.7111i	1.12656	+	0.410036i	0.289520	+	0.957172i	$0.406504\pi$
$32$	−3.63616	−	4.33340i	−0.113630	−	0.135419i
$33$		0			0
$34$	6.30237	−	2.29387i	0.185364	−	0.0674669i
$35$	−52.3496	−	30.2240i	−1.49570	−	0.863544i
$36$		0			0
$37$	−12.1981	−	21.1278i	−0.329679	−	0.571021i	0.652769	−	0.757557i	$-0.273607\pi$
$37$	−12.1981	−	21.1278i	−0.329679	−	0.571021i	−0.982448	+	0.186536i	$0.940274\pi$
$38$	31.2100	−	37.1946i	0.821316	−	0.978806i
$39$		0			0
$40$	−2.71850	−	15.4174i	−0.0679624	−	0.385434i
$41$	22.6189	−	3.98833i	0.551681	−	0.0972763i	0.109143	−	0.994026i	$-0.465189\pi$
$41$	22.6189	−	3.98833i	0.551681	−	0.0972763i	0.442538	+	0.896750i	$0.354078\pi$
$42$		0			0
$43$	39.1915	+	32.8855i	0.911430	+	0.764780i	0.972390	−	0.233360i	$-0.0749720\pi$
$43$	39.1915	+	32.8855i	0.911430	+	0.764780i	−0.0609609	+	0.998140i	$0.519416\pi$
$44$	−7.12575	+	4.11406i	−0.161949	+	0.0935013i
$45$		0			0
$46$	26.1102	−	45.2243i	0.567614	−	0.983136i
$47$	−28.3436	−	77.8733i	−0.603055	−	1.65688i	−0.745047	−	0.667012i	$-0.767573\pi$
$47$	−28.3436	−	77.8733i	−0.603055	−	1.65688i	0.141992	−	0.989868i	$-0.454649\pi$
$48$		0			0
$49$	53.8315	−	45.1700i	1.09860	−	0.921836i
$50$	2.72589	−	7.48932i	0.0545178	−	0.149786i
$51$		0			0
$52$	1.90724	−	10.8165i	0.0366777	−	0.208010i
$53$			16.2927i			0.307409i	0.988117	+	0.153704i	$0.0491204\pi$
$53$			16.2927i			0.307409i	−0.988117	+	0.153704i	$0.950880\pi$
$54$		0			0
$55$	−22.7711			−0.414020
$56$	30.4205	+	5.36395i	0.543222	+	0.0957848i
$57$		0			0
$58$	−6.99608	−	2.54637i	−0.120622	−	0.0439029i
$59$	45.6558	+	54.4105i	0.773827	+	0.922212i	0.998637	−	0.0521911i	$-0.0166205\pi$
$59$	45.6558	+	54.4105i	0.773827	+	0.922212i	−0.224810	+	0.974403i	$0.572176\pi$
$60$		0			0
$61$	−74.1675	+	26.9948i	−1.21586	+	0.442537i	−0.868733	−	0.495281i	$-0.835065\pi$
$61$	−74.1675	+	26.9948i	−1.21586	+	0.442537i	−0.347128	+	0.937818i	$0.612843\pi$
$62$	−45.5174	−	26.2795i	−0.734151	−	0.423862i
$63$		0			0
$64$	4.00000	+	6.92820i	0.0625000	+	0.108253i
$65$	19.5383	−	23.2848i	0.300589	−	0.358228i
$66$		0			0
$67$	−12.1162	−	68.7145i	−0.180839	−	1.02559i	−0.931186	−	0.364545i	$-0.881224\pi$
$67$	−12.1162	−	68.7145i	−0.180839	−	1.02559i	0.750347	−	0.661045i	$-0.229887\pi$
$68$	−9.34081	+	1.64704i	−0.137365	+	0.0242211i
$69$		0			0
$70$	65.4865	+	54.9497i	0.935521	+	0.784995i
$71$	65.9072	−	38.0516i	0.928271	−	0.535937i	0.0420065	−	0.999117i	$-0.486625\pi$
$71$	65.9072	−	38.0516i	0.928271	−	0.535937i	0.886264	+	0.463180i	$0.153292\pi$
$72$		0			0
$73$	25.5063	−	44.1783i	0.349402	−	0.605182i	−0.636741	−	0.771077i	$-0.719718\pi$
$73$	25.5063	−	44.1783i	0.349402	−	0.605182i	0.986143	+	0.165896i	$0.0530515\pi$
$74$	11.8002	+	32.4208i	0.159462	+	0.438119i
$75$		0			0
$76$	−52.6012	+	44.1376i	−0.692121	+	0.580758i
$77$	15.3671	−	42.2207i	0.199572	−	0.548321i
$78$		0			0
$79$	5.51385	−	31.2706i	0.0697956	−	0.395830i	−0.929818	−	0.368021i	$-0.880036\pi$
$79$	5.51385	−	31.2706i	0.0697956	−	0.395830i	0.999613	−	0.0278099i	$-0.00885329\pi$
$80$			22.1398i			0.276747i
$81$		0			0
$82$	−32.4815			−0.396115
$83$	−28.7447	−	5.06847i	−0.346322	−	0.0610659i	−0.00221805	−	0.999998i	$-0.500706\pi$
$83$	−28.7447	−	5.06847i	−0.346322	−	0.0610659i	−0.344104	+	0.938932i	$0.611817\pi$
$84$		0			0
$85$	−24.6662	−	8.97776i	−0.290190	−	0.105621i
$86$	−46.5072	−	55.4251i	−0.540781	−	0.644478i
$87$		0			0
$88$	10.9346	−	3.97985i	0.124256	−	0.0452256i
$89$	69.2878	+	40.0033i	0.778514	+	0.449475i	0.835903	−	0.548877i	$-0.184944\pi$
$89$	69.2878	+	40.0033i	0.778514	+	0.449475i	−0.0573893	+	0.998352i	$0.518278\pi$
$90$		0			0
$91$	29.9878	+	51.9404i	0.329536	+	0.570774i
$92$	−47.4704	+	56.5731i	−0.515983	+	0.614925i
$93$		0			0
$94$	20.3511	+	115.417i	0.216501	+	1.22784i
$95$	−187.144	+	32.9986i	−1.96994	+	0.347353i
$96$		0			0
$97$	36.3741	+	30.5215i	0.374991	+	0.314655i	0.810732	−	0.585417i	$-0.199069\pi$
$97$	36.3741	+	30.5215i	0.374991	+	0.314655i	−0.435741	+	0.900072i	$0.643514\pi$
$98$	−86.0653	+	49.6898i	−0.878217	+	0.507039i
$99$		0			0
$100$	−5.63562	+	9.76118i	−0.0563562	+	0.0976118i
$101$	15.6059	+	42.8769i	0.154514	+	0.424524i	0.992662	−	0.120918i	$-0.0385839\pi$
$101$	15.6059	+	42.8769i	0.154514	+	0.424524i	−0.838148	+	0.545442i	$0.816362\pi$
$102$		0			0
$103$	−10.9188	+	9.16192i	−0.106007	+	0.0889507i	−0.694251	−	0.719733i	$-0.744264\pi$
$103$	−10.9188	+	9.16192i	−0.106007	+	0.0889507i	0.588243	+	0.808684i	$0.299820\pi$
$104$	−5.31254	+	14.5961i	−0.0510821	+	0.140347i
$105$		0			0
$106$	4.00108	−	22.6913i	0.0377461	−	0.214069i
$107$			105.487i			0.985863i	0.870068	+	0.492931i	$0.164075\pi$
$107$			105.487i			0.985863i	−0.870068	+	0.492931i	$0.835925\pi$
$108$		0			0
$109$	57.5260			0.527762			0.263881	−	0.964555i	$-0.414997\pi$
$109$	57.5260			0.527762			0.263881	+	0.964555i	$0.414997\pi$
$110$	31.7139	+	5.59202i	0.288308	+	0.0508366i
$111$		0			0
$112$	−41.0502	−	14.9410i	−0.366519	−	0.133402i
$113$	76.8178	+	91.5479i	0.679803	+	0.810158i	0.990082	−	0.140487i	$-0.0448670\pi$
$113$	76.8178	+	91.5479i	0.679803	+	0.810158i	−0.310279	+	0.950646i	$0.600423\pi$
$114$		0			0
$115$	−192.055	+	69.9022i	−1.67004	+	0.607845i
$116$	9.11832	+	5.26446i	0.0786062	+	0.0453833i
$117$		0			0
$118$	−50.2243	−	86.9910i	−0.425629	−	0.737212i
$119$	33.2920	−	39.6758i	0.279765	−	0.333410i
$120$		0			0
$121$	18.0724	+	102.493i	0.149358	+	0.847053i
$122$	109.924	−	19.3826i	0.901020	−	0.158874i
$123$		0			0
$124$	56.9397	+	47.7781i	0.459192	+	0.385307i
$125$	92.8213	−	53.5904i	0.742570	−	0.428723i
$126$		0			0
$127$	−68.8561	+	119.262i	−0.542174	+	0.939072i	0.456605	+	0.889669i	$0.349065\pi$
$127$	−68.8561	+	119.262i	−0.542174	+	0.939072i	−0.998779	+	0.0494029i	$0.984268\pi$
$128$	−3.86952	−	10.6314i	−0.0302306	−	0.0830579i
$129$		0			0
$130$	−32.9297	+	27.6313i	−0.253305	+	0.212549i
$131$	21.9189	−	60.2217i	0.167320	−	0.459708i	−0.827487	−	0.561484i	$-0.810231\pi$
$131$	21.9189	−	60.2217i	0.167320	−	0.459708i	0.994807	+	0.101777i	$0.0324527\pi$
$132$		0			0
$133$	65.1105	−	369.260i	0.489552	−	2.77639i
$134$			98.6761i			0.736389i
$135$		0			0
$136$	13.4137			0.0986300
$137$	−75.1710	−	13.2547i	−0.548694	−	0.0967495i	−0.107573	−	0.994197i	$-0.534308\pi$
$137$	−75.1710	−	13.2547i	−0.548694	−	0.0967495i	−0.441121	+	0.897448i	$0.645419\pi$
$138$		0			0
$139$	−100.055	−	36.4171i	−0.719821	−	0.261993i	−0.0439712	−	0.999033i	$-0.514001\pi$
$139$	−100.055	−	36.4171i	−0.719821	−	0.261993i	−0.675850	+	0.737039i	$0.736223\pi$
$140$	−77.7106	−	92.6118i	−0.555075	−	0.661513i
$141$		0			0
$142$	−101.135	+	36.8103i	−0.712221	+	0.259227i
$143$	19.5662	+	11.2966i	0.136827	+	0.0789969i
$144$		0			0
$145$	14.5693	+	25.2347i	0.100478	+	0.174032i
$146$	−46.3725	+	55.2646i	−0.317620	+	0.378525i
$147$		0			0
$148$	−8.47273	−	48.0512i	−0.0572482	−	0.324670i
$149$	84.0145	−	14.8140i	0.563856	−	0.0994230i	0.115547	−	0.993302i	$-0.463138\pi$
$149$	84.0145	−	14.8140i	0.563856	−	0.0994230i	0.448308	+	0.893879i	$0.352027\pi$
$150$		0			0
$151$	−42.4996	−	35.6614i	−0.281454	−	0.236168i	0.491121	−	0.871091i	$-0.336587\pi$
$151$	−42.4996	−	35.6614i	−0.281454	−	0.236168i	−0.772575	+	0.634923i	$0.781032\pi$
$152$	84.0983	−	48.5542i	0.553278	−	0.319435i
$153$		0			0
$154$	−31.7705	+	55.0282i	−0.206302	+	0.357326i
$155$	70.3553	+	193.299i	0.453905	+	1.24709i
$156$		0			0
$157$	−12.9857	+	10.8963i	−0.0827115	+	0.0694032i	−0.683206	−	0.730226i	$-0.739415\pi$
$157$	−12.9857	+	10.8963i	−0.0827115	+	0.0694032i	0.600494	+	0.799629i	$0.294970\pi$
$158$	−15.3586	+	42.1974i	−0.0972063	+	0.267072i
$159$		0			0
$160$	5.43699	−	30.8347i	0.0339812	−	0.192717i
$161$		−	403.269i		−	2.50478i
$162$		0			0
$163$	230.772			1.41578			0.707890	−	0.706322i	$-0.249647\pi$
$163$	230.772			1.41578			0.707890	+	0.706322i	$0.249647\pi$
$164$	45.2379	+	7.97666i	0.275841	+	0.0486382i
$165$		0			0
$166$	38.7889	+	14.1180i	0.233668	+	0.0850481i
$167$	−103.061	−	122.823i	−0.617132	−	0.735469i	0.363442	−	0.931617i	$-0.381601\pi$
$167$	−103.061	−	122.823i	−0.617132	−	0.735469i	−0.980574	+	0.196147i	$0.937157\pi$
$168$		0			0
$169$	130.468	−	47.4866i	0.772001	−	0.280986i
$170$	32.1486	+	18.5610i	0.189109	+	0.109182i
$171$		0			0
$172$	51.1608	+	88.6132i	0.297447	+	0.515193i
$173$	−204.014	+	243.135i	−1.17927	+	1.40540i	−0.284620	+	0.958640i	$0.591867\pi$
$173$	−204.014	+	243.135i	−1.17927	+	1.40540i	−0.894653	+	0.446762i	$0.852577\pi$
$174$		0			0
$175$	−10.6876	−	60.6125i	−0.0610721	−	0.346357i
$176$	−16.2062	+	2.85759i	−0.0920808	+	0.0162363i
$177$		0			0
$178$	−86.6752	−	72.7291i	−0.486939	−	0.408591i
$179$	38.5365	−	22.2490i	0.215287	−	0.124296i	−0.388479	−	0.921458i	$-0.626999\pi$
$179$	38.5365	−	22.2490i	0.215287	−	0.124296i	0.603766	+	0.797161i	$0.293666\pi$
$180$		0			0
$181$	19.0288	−	32.9588i	0.105131	−	0.182093i	−0.808661	−	0.588276i	$-0.799807\pi$
$181$	19.0288	−	32.9588i	0.105131	−	0.182093i	0.913792	+	0.406183i	$0.133140\pi$
$182$	−29.0096	−	79.7032i	−0.159393	−	0.437930i
$183$		0			0
$184$	80.0064	−	67.1333i	0.434817	−	0.364855i
$185$	46.1836	−	126.888i	0.249641	−	0.685884i
$186$		0			0
$187$	3.38800	−	19.2143i	0.0181176	−	0.102750i
$188$		−	165.742i		−	0.881607i
$189$		0			0
$190$	268.745			1.41445
$191$	−201.386	−	35.5097i	−1.05438	−	0.185915i	−0.380516	−	0.924774i	$-0.624254\pi$
$191$	−201.386	−	35.5097i	−1.05438	−	0.185915i	−0.673859	+	0.738860i	$0.735365\pi$
$192$		0			0
$193$	108.871	+	39.6259i	0.564100	+	0.205316i	0.608300	−	0.793707i	$-0.291852\pi$
$193$	108.871	+	39.6259i	0.564100	+	0.205316i	−0.0442003	+	0.999023i	$0.514074\pi$
$194$	−43.1639	−	51.4408i	−0.222495	−	0.265159i
$195$		0			0
$196$	132.068	−	48.0689i	0.673817	−	0.245249i
$197$	76.7079	+	44.2873i	0.389380	+	0.224809i	0.681892	−	0.731453i	$-0.261158\pi$
$197$	76.7079	+	44.2873i	0.389380	+	0.224809i	−0.292511	+	0.956262i	$0.594491\pi$
$198$		0			0
$199$	134.773	+	233.434i	0.677253	+	1.17304i	0.975805	+	0.218644i	$0.0701632\pi$
$199$	134.773	+	233.434i	0.677253	+	1.17304i	−0.298551	+	0.954394i	$0.596503\pi$
$200$	10.2460	−	12.2107i	0.0512300	−	0.0610535i
$201$		0			0
$202$	−11.2053	−	63.5483i	−0.0554717	−	0.314596i
$203$	−56.6207	+	9.98375i	−0.278920	+	0.0491810i
$204$		0			0
$205$	97.3841	+	81.7149i	0.475044	+	0.398609i
$206$	17.4568	−	10.0787i	0.0847418	−	0.0489257i
$207$		0			0
$208$	10.9834	−	19.0238i	0.0528047	−	0.0914604i
$209$	−48.3096	−	132.729i	−0.231146	−	0.635069i
$210$		0			0
$211$	−107.762	+	90.4231i	−0.510721	+	0.428546i	−0.861383	−	0.507957i	$-0.830401\pi$
$211$	−107.762	+	90.4231i	−0.510721	+	0.428546i	0.350662	+	0.936502i	$0.385957\pi$
$212$	−11.1448	+	30.6202i	−0.0525700	+	0.144435i
$213$		0			0
$214$	25.9051	−	146.915i	0.121052	−	0.686520i
$215$			283.172i			1.31708i
$216$		0			0
$217$	−405.883			−1.87043
$218$	−80.1181	−	14.1270i	−0.367514	−	0.0648027i
$219$		0			0
$220$	−42.7956	−	15.5763i	−0.194526	−	0.0708015i
$221$	16.7408	+	19.9509i	0.0757502	+	0.0902756i
$222$		0			0
$223$	−324.808	+	118.221i	−1.45654	+	0.530137i	−0.944410	−	0.328770i	$-0.893366\pi$
$223$	−324.808	+	118.221i	−1.45654	+	0.530137i	−0.512130	+	0.858908i	$0.671144\pi$
$224$	53.5026	+	30.8897i	0.238851	+	0.137901i
$225$		0			0
$226$	−84.5044	−	146.366i	−0.373913	−	0.647637i
$227$	118.546	−	141.278i	0.522230	−	0.622369i	−0.438877	−	0.898547i	$-0.644624\pi$
$227$	118.546	−	141.278i	0.522230	−	0.622369i	0.961106	+	0.276178i	$0.0890680\pi$
$228$		0			0
$229$	38.3747	+	217.634i	0.167575	+	0.950365i	0.946370	+	0.323086i	$0.104720\pi$
$229$	38.3747	+	217.634i	0.167575	+	0.950365i	−0.778794	+	0.627279i	$0.784168\pi$
$230$	284.646	−	50.1908i	1.23759	−	0.218221i
$231$		0			0
$232$	−11.4065	−	9.57121i	−0.0491660	−	0.0412552i
$233$	−364.370	+	210.369i	−1.56382	+	0.902872i	−0.566955	+	0.823748i	$0.691879\pi$
$233$	−364.370	+	210.369i	−1.56382	+	0.902872i	−0.996865	+	0.0791236i	$0.974788\pi$
$234$		0			0
$235$	229.343	−	397.234i	0.975929	−	1.69036i
$236$	48.5859	+	133.489i	0.205872	+	0.565630i
$237$		0			0
$238$	−56.1101	+	47.0820i	−0.235757	+	0.197823i
$239$	27.2416	−	74.8456i	0.113981	−	0.313162i	−0.869565	−	0.493819i	$-0.835600\pi$
$239$	27.2416	−	74.8456i	0.113981	−	0.313162i	0.983546	+	0.180658i	$0.0578226\pi$
$240$		0			0
$241$	−9.36196	+	53.0943i	−0.0388463	+	0.220308i	−0.998051	−	0.0624044i	$-0.980123\pi$
$241$	−9.36196	+	53.0943i	−0.0388463	+	0.220308i	0.959205	+	0.282713i	$0.0912343\pi$
$242$		−	147.184i		−	0.608197i
$243$		0			0
$244$	−157.855			−0.646946
$245$	383.043	+	67.5407i	1.56344	+	0.275677i
$246$		0			0
$247$	177.175	+	64.4865i	0.717308	+	0.261079i
$248$	−67.5685	−	80.5250i	−0.272453	−	0.324697i
$249$		0			0
$250$	−142.435	+	51.8422i	−0.569741	+	0.207369i
$251$	179.256	+	103.494i	0.714167	+	0.412325i	0.812602	−	0.582819i	$-0.198050\pi$
$251$	179.256	+	103.494i	0.714167	+	0.412325i	−0.0984348	+	0.995144i	$0.531384\pi$
$252$		0			0
$253$	−75.9567	−	131.561i	−0.300224	−	0.520003i
$254$	125.186	−	149.190i	0.492857	−	0.587364i
$255$		0			0
$256$	2.77837	+	15.7569i	0.0108530	+	0.0615505i
$257$	−201.153	+	35.4686i	−0.782695	+	0.138010i	−0.550696	−	0.834706i	$-0.685638\pi$
$257$	−201.153	+	35.4686i	−0.782695	+	0.138010i	−0.231999	+	0.972716i	$0.574527\pi$
$258$		0			0
$259$	204.102	+	171.262i	0.788037	+	0.661241i
$260$	52.6477	−	30.3962i	0.202491	−	0.116908i
$261$		0			0
$262$	−45.3161	+	78.4897i	−0.172962	+	0.299579i
$263$	−65.2110	−	179.166i	−0.247951	−	0.681239i	−0.999761	−	0.0218596i	$-0.993041\pi$
$263$	−65.2110	−	179.166i	−0.247951	−	0.681239i	0.751810	−	0.659379i	$-0.229181\pi$
$264$		0			0
$265$	−69.0812	+	57.9660i	−0.260684	+	0.218740i
$266$	−181.362	+	498.289i	−0.681814	+	1.87327i
$267$		0			0
$268$	24.2324	−	137.429i	0.0904196	−	0.512795i
$269$			70.9150i			0.263624i	0.991275	+	0.131812i	$0.0420796\pi$
$269$			70.9150i			0.263624i	−0.991275	+	0.131812i	$0.957920\pi$
$270$		0			0
$271$	−117.923			−0.435141			−0.217570	−	0.976045i	$-0.569813\pi$
$271$	−117.923			−0.435141			−0.217570	+	0.976045i	$0.569813\pi$
$272$	−18.6816	−	3.29407i	−0.0686824	−	0.0121106i
$273$		0			0
$274$	101.438	+	36.9203i	0.370211	+	0.134746i
$275$	−14.9032	−	17.7609i	−0.0541934	−	0.0645852i
$276$		0			0
$277$	232.933	−	84.7808i	0.840915	−	0.306068i	0.114584	−	0.993414i	$-0.463446\pi$
$277$	232.933	−	84.7808i	0.840915	−	0.306068i	0.726331	+	0.687346i	$0.241224\pi$
$278$	130.406	+	75.2902i	0.469088	+	0.270828i
$279$		0			0
$280$	85.4865	+	148.067i	0.305309	+	0.528811i
$281$	−46.1416	+	54.9895i	−0.164205	+	0.195692i	−0.841872	−	0.539677i	$-0.818547\pi$
$281$	−46.1416	+	54.9895i	−0.164205	+	0.195692i	0.677667	+	0.735369i	$0.262991\pi$
$282$		0			0
$283$	−52.2646	−	296.407i	−0.184681	−	1.04738i	−0.926365	−	0.376627i	$-0.877084\pi$
$283$	−52.2646	−	296.407i	−0.184681	−	1.04738i	0.741685	−	0.670749i	$-0.234027\pi$
$284$	149.894	−	26.4303i	0.527795	−	0.0930646i
$285$		0			0
$286$	−24.4762	−	20.5380i	−0.0855813	−	0.0718112i
$287$	−217.230	+	125.418i	−0.756900	+	0.436997i
$288$		0			0
$289$	−133.255	+	230.804i	−0.461088	+	0.798629i
$290$	−14.0940	−	38.7229i	−0.0486000	−	0.133527i
$291$		0			0
$292$	78.1560	−	65.5806i	0.267657	−	0.224591i
$293$	34.3361	−	94.3376i	0.117188	−	0.321971i	−0.867206	−	0.497949i	$-0.834087\pi$
$293$	34.3361	−	94.3376i	0.117188	−	0.321971i	0.984394	+	0.175978i	$0.0563088\pi$
$294$		0			0
$295$	−68.2672	+	387.163i	−0.231414	+	1.31242i
$296$			69.0030i			0.233118i
$297$		0			0
$298$	−120.647			−0.404857
$299$	199.702	+	35.2129i	0.667900	+	0.117769i
$300$		0			0
$301$	−525.040	−	191.099i	−1.74432	−	0.634881i
$302$	50.4328	+	60.1035i	0.166996	+	0.199018i
$303$		0			0
$304$	−129.050	+	46.9703i	−0.424506	+	0.154507i
$305$	−378.331	−	218.429i	−1.24043	−	0.716162i
$306$		0			0
$307$	−136.003	−	235.565i	−0.443008	−	0.767312i	0.554903	−	0.831915i	$-0.312755\pi$
$307$	−136.003	−	235.565i	−0.443008	−	0.767312i	−0.997911	+	0.0646029i	$0.979422\pi$
$308$	57.7613	−	68.8372i	0.187537	−	0.223498i
$309$		0			0
$310$	−50.5161	−	286.491i	−0.162955	−	0.924165i
$311$	−402.304	+	70.9371i	−1.29358	+	0.228094i	−0.777738	−	0.628588i	$-0.783633\pi$
$311$	−402.304	+	70.9371i	−1.29358	+	0.228094i	−0.515845	+	0.856682i	$0.672522\pi$
$312$		0			0
$313$	186.473	+	156.470i	0.595761	+	0.499903i	0.890080	−	0.455805i	$-0.150648\pi$
$313$	186.473	+	156.470i	0.595761	+	0.499903i	−0.294319	+	0.955707i	$0.595093\pi$
$314$	20.7614	−	11.9866i	0.0661192	−	0.0381739i
$315$		0			0
$316$	31.7530	−	54.9978i	0.100484	−	0.174044i
$317$	92.9426	+	255.358i	0.293194	+	0.805545i	0.995595	+	0.0937628i	$0.0298895\pi$
$317$	92.9426	+	255.358i	0.293194	+	0.805545i	−0.702400	+	0.711782i	$0.747888\pi$
$318$		0			0
$319$	−16.5912	+	13.9217i	−0.0520101	+	0.0436417i
$320$	−15.1445	+	41.6092i	−0.0473266	+	0.130029i
$321$		0			0
$322$	−99.0331	+	561.644i	−0.307556	+	1.74424i
$323$		−	162.822i		−	0.504094i
$324$		0			0
$325$	30.9490			0.0952278
$326$	−321.403	−	56.6720i	−0.985899	−	0.173841i
$327$		0			0
$328$	−61.0452	−	22.2186i	−0.186113	−	0.0677397i
$329$	581.754	+	693.308i	1.76825	+	2.10732i
$330$		0			0
$331$	416.626	−	151.639i	1.25869	−	0.458125i	0.375360	−	0.926879i	$-0.377519\pi$
$331$	416.626	−	151.639i	1.25869	−	0.458125i	0.883329	+	0.468754i	$0.155297\pi$
$332$	−50.5553	−	29.1881i	−0.152275	−	0.0879161i
$333$		0			0
$334$	113.374	+	196.369i	0.339442	+	0.587931i
$335$	248.243	−	295.845i	0.741025	−	0.883120i
$336$		0			0
$337$	26.8736	+	152.408i	0.0797435	+	0.452248i	0.998368	+	0.0571153i	$0.0181903\pi$
$337$	26.8736	+	152.408i	0.0797435	+	0.452248i	−0.918624	+	0.395133i	$0.870699\pi$
$338$	−193.368	+	34.0961i	−0.572096	+	0.100876i
$339$		0			0
$340$	−40.2161	−	33.7453i	−0.118283	−	0.0992510i
$341$	−132.414	+	76.4490i	−0.388310	+	0.224191i
$342$		0			0
$343$	−116.158	+	201.191i	−0.338652	+	0.586562i
$344$	−49.4919	−	135.978i	−0.143872	−	0.395285i
$345$		0			0
$346$	343.844	−	288.520i	0.993770	−	0.833872i
$347$	71.9673	−	197.728i	0.207398	−	0.569823i	−0.791760	−	0.610832i	$-0.790835\pi$
$347$	71.9673	−	197.728i	0.207398	−	0.569823i	0.999159	+	0.0410093i	$0.0130573\pi$
$348$		0			0
$349$	−74.8630	+	424.569i	−0.214507	+	1.21653i	0.667252	+	0.744832i	$0.267470\pi$
$349$	−74.8630	+	424.569i	−0.214507	+	1.21653i	−0.881760	+	0.471699i	$0.843641\pi$
$350$			87.0414i			0.248690i
$351$		0			0
$352$	23.2726			0.0661154
$353$	269.966	+	47.6023i	0.764777	+	0.134851i	0.542412	−	0.840113i	$-0.317511\pi$
$353$	269.966	+	47.6023i	0.764777	+	0.134851i	0.222365	+	0.974964i	$0.428622\pi$
$354$		0			0
$355$	395.823	+	144.068i	1.11500	+	0.405825i
$356$	102.855	+	122.577i	0.288917	+	0.344318i
$357$		0			0
$358$	−59.1346	+	21.5233i	−0.165181	+	0.0601208i
$359$	40.2168	+	23.2192i	0.112025	+	0.0646774i	0.554965	−	0.831873i	$-0.312731\pi$
$359$	40.2168	+	23.2192i	0.112025	+	0.0646774i	−0.442941	+	0.896551i	$0.646065\pi$
$360$		0			0
$361$	−408.876	−	708.195i	−1.13262	−	1.96176i
$362$	−34.5958	+	41.2296i	−0.0955685	+	0.113894i
$363$		0			0
$364$	20.8293	+	118.129i	0.0572234	+	0.324530i
$365$	278.063	−	49.0300i	0.761816	−	0.134329i
$366$		0			0
$367$	−490.518	−	411.594i	−1.33656	−	1.12151i	−0.982495	−	0.186288i	$-0.940354\pi$
$367$	−490.518	−	411.594i	−1.33656	−	1.12151i	−0.354067	−	0.935220i	$-0.615201\pi$
$368$	−127.914	+	73.8509i	−0.347591	+	0.200682i
$369$		0			0
$370$	−95.4820	+	165.380i	−0.258059	+	0.446972i
$371$	−60.8574	−	167.204i	−0.164036	−	0.450686i
$372$		0			0
$373$	−3.55616	+	2.98397i	−0.00953393	+	0.00799992i	−0.647542	−	0.762030i	$-0.724203\pi$
$373$	−3.55616	+	2.98397i	−0.00953393	+	0.00799992i	0.638008	+	0.770030i	$0.279759\pi$
$374$	−9.43713	+	25.9283i	−0.0252330	+	0.0693270i
$375$		0			0
$376$	−40.7022	+	230.834i	−0.108251	+	0.613920i
$377$		−	28.9108i		−	0.0766864i
$378$		0			0
$379$	259.991			0.685992			0.342996	−	0.939337i	$-0.388558\pi$
$379$	259.991			0.685992			0.342996	+	0.939337i	$0.388558\pi$
$380$	−374.288	−	65.9971i	−0.984969	−	0.173677i
$381$		0			0
$382$	271.755	+	98.9108i	0.711401	+	0.258929i
$383$	171.274	+	204.117i	0.447191	+	0.532942i	0.941800	−	0.336174i	$-0.109133\pi$
$383$	171.274	+	204.117i	0.447191	+	0.532942i	−0.494609	+	0.869116i	$0.664689\pi$
$384$		0			0
$385$	233.689	−	85.0559i	0.606985	−	0.220924i
$386$	−141.897	−	81.9242i	−0.367609	−	0.212239i
$387$		0			0
$388$	47.4830	+	82.2430i	0.122379	+	0.211967i
$389$	−15.2282	+	18.1483i	−0.0391471	+	0.0466538i	−0.785263	−	0.619163i	$-0.787472\pi$
$389$	−15.2282	+	18.1483i	−0.0391471	+	0.0466538i	0.746116	+	0.665816i	$0.231917\pi$
$390$		0			0
$391$	−30.4088	−	172.457i	−0.0777718	−	0.441066i
$392$	−195.740	+	34.5142i	−0.499336	+	0.0880464i
$393$		0			0
$394$	−95.9574	−	80.5178i	−0.243547	−	0.204360i
$395$	152.205	−	87.8756i	0.385329	−	0.222470i
$396$		0			0
$397$	113.459	−	196.518i	0.285792	−	0.495006i	−0.687009	−	0.726649i	$-0.741077\pi$
$397$	113.459	−	196.518i	0.285792	−	0.495006i	0.972801	+	0.231643i	$0.0744100\pi$
$398$	−130.377	−	358.208i	−0.327580	−	0.900020i
$399$		0			0
$400$	−17.2685	+	14.4900i	−0.0431713	+	0.0362251i
$401$	175.968	−	483.469i	0.438824	−	1.20566i	−0.501434	−	0.865196i	$-0.667194\pi$
$401$	175.968	−	483.469i	0.438824	−	1.20566i	0.940258	−	0.340463i	$-0.110584\pi$
$402$		0			0
$403$	35.4411	−	200.997i	0.0879432	−	0.498751i
$404$			91.2573i			0.225884i
$405$		0			0
$406$	81.3090			0.200268
$407$	98.8427	+	17.4286i	0.242857	+	0.0428222i
$408$		0			0
$409$	260.800	+	94.9234i	0.637653	+	0.232087i	0.640559	−	0.767909i	$-0.278703\pi$
$409$	260.800	+	94.9234i	0.637653	+	0.232087i	−0.00290599	+	0.999996i	$0.500925\pi$
$410$	−115.562	−	137.722i	−0.281859	−	0.335907i
$411$		0			0
$412$	−26.7877	+	9.74992i	−0.0650186	+	0.0236648i
$413$	−671.782	−	387.854i	−1.62659	−	0.939113i
$414$		0			0
$415$	−80.7773	−	139.910i	−0.194644	−	0.337134i
$416$	−19.9686	+	23.7977i	−0.0480015	+	0.0572060i
$417$		0			0
$418$	34.6870	+	196.720i	0.0829833	+	0.470622i
$419$	316.326	−	55.7768i	0.754955	−	0.133119i	0.217092	−	0.976151i	$-0.430343\pi$
$419$	316.326	−	55.7768i	0.754955	−	0.133119i	0.537863	+	0.843032i	$0.319232\pi$
$420$		0			0
$421$	−101.935	−	85.5332i	−0.242125	−	0.203167i	0.513648	−	0.858001i	$-0.328294\pi$
$421$	−101.935	−	85.5332i	−0.242125	−	0.203167i	−0.755772	+	0.654834i	$0.772738\pi$
$422$	172.289	−	99.4711i	0.408268	−	0.235714i
$423$		0			0
$424$	23.0413	−	39.9087i	0.0543427	−	0.0941244i
$425$	−9.14105	−	25.1148i	−0.0215084	−	0.0590937i
$426$		0			0
$427$	660.315	−	554.070i	1.54640	−	1.29759i
$428$	−72.1576	+	198.251i	−0.168592	+	0.463204i
$429$		0			0
$430$	69.5402	−	394.382i	0.161721	−	0.917168i
$431$			24.4994i			0.0568432i	0.999596	+	0.0284216i	$0.00904810\pi$
$431$			24.4994i			0.0568432i	−0.999596	+	0.0284216i	$0.990952\pi$
$432$		0			0
$433$	−25.7694			−0.0595137			−0.0297568	−	0.999557i	$-0.509473\pi$
$433$	−25.7694			−0.0595137			−0.0297568	+	0.999557i	$0.509473\pi$
$434$	565.285	+	99.6750i	1.30250	+	0.229666i
$435$		0			0
$436$	108.114	+	39.3501i	0.247967	+	0.0902526i
$437$	−814.901	−	971.161i	−1.86476	−	2.22234i
$438$		0			0
$439$	425.746	−	154.959i	0.969809	−	0.352981i	0.191939	−	0.981407i	$-0.438522\pi$
$439$	425.746	−	154.959i	0.969809	−	0.352981i	0.777870	+	0.628425i	$0.216300\pi$
$440$	55.7775	+	32.2032i	0.126767	+	0.0731890i
$441$		0			0
$442$	−18.4159	−	31.8973i	−0.0416650	−	0.0721659i
$443$	320.772	−	382.281i	0.724090	−	0.862937i	−0.270931	−	0.962599i	$-0.587332\pi$
$443$	320.772	−	382.281i	0.724090	−	0.862937i	0.995021	+	0.0996616i	$0.0317760\pi$
$444$		0			0
$445$	76.8970	+	436.105i	0.172802	+	0.980010i
$446$	481.402	−	84.8842i	1.07938	−	0.190323i
$447$		0			0
$448$	−66.9288	−	56.1600i	−0.149395	−	0.125357i
$449$	172.434	−	99.5548i	0.384040	−	0.221726i	−0.295534	−	0.955332i	$-0.595498\pi$
$449$	172.434	−	99.5548i	0.384040	−	0.221726i	0.679575	+	0.733606i	$0.262164\pi$
$450$		0			0
$451$	−47.2456	+	81.8317i	−0.104757	+	0.181445i
$452$	81.7478	+	224.600i	0.180858	+	0.496903i
$453$		0			0
$454$	−199.797	+	167.650i	−0.440081	+	0.369272i
$455$	−113.538	+	311.942i	−0.249533	+	0.685587i
$456$		0			0
$457$	1.65470	−	9.38428i	0.00362079	−	0.0205345i	−0.982944	−	0.183906i	$-0.941126\pi$
$457$	1.65470	−	9.38428i	0.00362079	−	0.0205345i	0.986565	+	0.163371i	$0.0522369\pi$
$458$		−	312.529i		−	0.682377i
$459$		0			0
$460$	−408.761			−0.888610
$461$	−746.412	−	131.612i	−1.61911	−	0.285493i	−0.710678	−	0.703517i	$-0.751612\pi$
$461$	−746.412	−	131.612i	−1.61911	−	0.285493i	−0.908436	+	0.418024i	$0.862723\pi$
$462$		0			0
$463$	−598.493	−	217.833i	−1.29264	−	0.470483i	−0.398048	−	0.917365i	$-0.630312\pi$
$463$	−598.493	−	217.833i	−1.29264	−	0.470483i	−0.894593	+	0.446882i	$0.852534\pi$
$464$	13.5357	+	16.1313i	0.0291718	+	0.0347656i
$465$		0			0
$466$	559.130	−	203.507i	1.19985	−	0.436710i
$467$	632.615	+	365.241i	1.35464	+	0.782100i	0.988895	−	0.148617i	$-0.0474821\pi$
$467$	632.615	+	365.241i	1.35464	+	0.782100i	0.365742	+	0.930716i	$0.380815\pi$
$468$		0			0
$469$	381.010	+	659.929i	0.812388	+	1.40710i
$470$	−416.964	+	496.919i	−0.887158	+	1.05727i
$471$		0			0
$472$	−34.8854	−	197.845i	−0.0739098	−	0.419163i
$473$	−207.281	+	36.5492i	−0.438226	+	0.0772711i
$474$		0			0
$475$	−148.220	−	124.371i	−0.312042	−	0.261834i
$476$	89.7083	−	51.7931i	0.188463	−	0.108809i
$477$		0			0
$478$	−56.3204	+	97.5497i	−0.117825	+	0.204079i
$479$	119.189	+	327.468i	0.248828	+	0.683650i	0.999730	+	0.0232359i	$0.00739687\pi$
$479$	119.189	+	327.468i	0.248828	+	0.683650i	−0.750902	+	0.660414i	$0.770381\pi$
$480$		0			0
$481$	−102.632	+	86.1184i	−0.213372	+	0.179040i
$482$	26.0773	−	71.6469i	0.0541023	−	0.148645i
$483$		0			0
$484$	−36.1447	+	204.987i	−0.0746791	+	0.423527i
$485$			262.816i			0.541889i
$486$		0			0
$487$	−24.8144			−0.0509535			−0.0254768	−	0.999675i	$-0.508110\pi$
$487$	−24.8144			−0.0509535			−0.0254768	+	0.999675i	$0.508110\pi$
$488$	219.849	+	38.7653i	0.450510	+	0.0794371i
$489$		0			0
$490$	−516.888	−	188.132i	−1.05487	−	0.383943i
$491$	357.910	+	426.541i	0.728941	+	0.868719i	0.995467	−	0.0951093i	$-0.0303200\pi$
$491$	357.910	+	426.541i	0.728941	+	0.868719i	−0.266525	+	0.963828i	$0.585876\pi$
$492$		0			0
$493$	−23.4608	+	8.53904i	−0.0475879	+	0.0173206i
$494$	−230.921	−	133.322i	−0.467451	−	0.269883i
$495$		0			0
$496$	74.3296	+	128.743i	0.149858	+	0.259562i
$497$	−534.243	+	636.686i	−1.07494	+	1.28106i
$498$		0			0
$499$	−71.2311	−	403.972i	−0.142748	−	0.809562i	−0.969148	−	0.246479i	$-0.920726\pi$
$499$	−71.2311	−	403.972i	−0.142748	−	0.809562i	0.826400	−	0.563083i	$-0.190385\pi$
$500$	211.105	−	37.2235i	0.422210	−	0.0744470i
$501$		0			0
$502$	−224.239	−	188.159i	−0.446692	−	0.374819i
$503$	435.156	−	251.237i	0.865121	−	0.499478i	−0.000603145	−	1.00000i	$-0.500192\pi$
$503$	435.156	−	251.237i	0.865121	−	0.499478i	0.865724	+	0.500522i	$0.166859\pi$
$504$		0			0
$505$	−126.276	+	218.717i	−0.250052	+	0.433102i
$506$	73.4789	+	201.882i	0.145215	+	0.398976i
$507$		0			0
$508$	−210.987	+	177.039i	−0.415329	+	0.348503i
$509$	−40.2964	+	110.713i	−0.0791678	+	0.217512i	−0.972962	−	0.230966i	$-0.925811\pi$
$509$	−40.2964	+	110.713i	−0.0791678	+	0.217512i	0.893794	+	0.448478i	$0.148034\pi$
$510$		0			0
$511$	−96.7426	+	548.654i	−0.189320	+	1.07369i
$512$		−	22.6274i		−	0.0441942i
$513$		0			0
$514$	288.861			0.561987
$515$	−77.6934	−	13.6994i	−0.150861	−	0.0266008i
$516$		0			0
$517$	320.375	+	116.607i	0.619681	+	0.225546i
$518$	−242.200	−	288.643i	−0.467568	−	0.557226i
$519$		0			0
$520$	−80.7885	+	29.4046i	−0.155363	+	0.0565474i
$521$	−0.627494	−	0.362284i	−0.00120440	−	0.000695363i	0.499398	−	0.866373i	$-0.333555\pi$
$521$	−0.627494	−	0.362284i	−0.00120440	−	0.000695363i	−0.500602	+	0.865678i	$0.666888\pi$
$522$		0			0
$523$	290.424	+	503.029i	0.555304	+	0.961814i	0.997880	+	0.0650834i	$0.0207313\pi$
$523$	290.424	+	503.029i	0.555304	+	0.961814i	−0.442576	+	0.896731i	$0.645935\pi$
$524$	82.3881	−	98.1863i	0.157229	−	0.187379i
$525$		0			0
$526$	46.8225	+	265.544i	0.0890162	+	0.504836i
$527$	−173.575	+	30.6059i	−0.329363	+	0.0580757i
$528$		0			0
$529$	−639.256	−	536.399i	−1.20842	−	1.01399i
$530$	110.446	−	63.7662i	0.208389	−	0.120314i
$531$		0			0
$532$	374.956	−	649.443i	0.704805	−	1.22076i
$533$	−43.1398	−	118.526i	−0.0809377	−	0.222374i
$534$		0			0
$535$	−447.268	+	375.302i	−0.836014	+	0.701499i
$536$	−67.4984	+	185.450i	−0.125930	+	0.345990i
$537$		0			0
$538$	17.4150	−	98.7653i	0.0323699	−	0.183579i
$539$			289.103i			0.536369i
$540$		0			0
$541$	15.2361			0.0281629			0.0140815	−	0.999901i	$-0.495518\pi$
$541$	15.2361			0.0281629			0.0140815	+	0.999901i	$0.495518\pi$
$542$	164.235	+	28.9590i	0.303016	+	0.0534300i
$543$		0			0
$544$	25.2095	+	9.17550i	0.0463409	+	0.0168667i
$545$	204.666	+	243.911i	0.375534	+	0.447543i
$546$		0			0
$547$	−539.917	+	196.514i	−0.987051	+	0.359257i	−0.784578	−	0.620031i	$-0.787120\pi$
$547$	−539.917	+	196.514i	−0.987051	+	0.359257i	−0.202473	+	0.979288i	$0.564898\pi$
$548$	−132.209	−	76.3307i	−0.241257	−	0.139290i
$549$		0			0
$550$	16.3944	+	28.3960i	0.0298081	+	0.0516291i
$551$	−116.180	+	138.458i	−0.210854	+	0.251286i
$552$		0			0
$553$	60.2177	+	341.512i	0.108893	+	0.617562i
$554$	−345.233	+	60.8739i	−0.623164	+	0.109881i
$555$		0			0
$556$	−163.131	−	136.883i	−0.293402	−	0.246193i
$557$	276.094	−	159.403i	0.495680	−	0.286181i	−0.231248	−	0.972895i	$-0.574281\pi$
$557$	276.094	−	159.403i	0.495680	−	0.286181i	0.726928	+	0.686714i	$0.240948\pi$
$558$		0			0
$559$	140.480	−	243.318i	0.251305	−	0.435273i
$560$	−82.6979	−	227.210i	−0.147675	−	0.405733i
$561$		0			0
$562$	77.7668	−	65.2541i	0.138375	−	0.116111i
$563$	−84.4286	+	231.966i	−0.149962	+	0.412017i	−0.991814	−	0.127691i	$-0.959243\pi$
$563$	−84.4286	+	231.966i	−0.149962	+	0.412017i	0.841852	+	0.539708i	$0.181466\pi$
$564$		0			0
$565$	−114.862	+	651.417i	−0.203296	+	1.15295i
$566$			425.650i			0.752031i
$567$		0			0
$568$	−215.252			−0.378965
$569$	−165.837	−	29.2415i	−0.291454	−	0.0513911i	0.0260097	−	0.999662i	$-0.491720\pi$
$569$	−165.837	−	29.2415i	−0.291454	−	0.0513911i	−0.317463	+	0.948271i	$0.602831\pi$
$570$		0			0
$571$	−605.483	−	220.378i	−1.06039	−	0.385951i	−0.247816	−	0.968807i	$-0.579713\pi$
$571$	−605.483	−	220.378i	−1.06039	−	0.385951i	−0.812575	+	0.582856i	$0.801935\pi$
$572$	29.0451	+	34.6146i	0.0507782	+	0.0605151i
$573$		0			0
$574$	333.343	−	121.327i	0.580736	−	0.211371i
$575$	−180.218	−	104.049i	−0.313422	−	0.180955i
$576$		0			0
$577$	63.2482	+	109.549i	0.109616	+	0.189860i	0.915615	−	0.402057i	$-0.131705\pi$
$577$	63.2482	+	109.549i	0.109616	+	0.189860i	−0.805999	+	0.591917i	$0.798371\pi$
$578$	242.267	−	288.723i	0.419147	−	0.499520i
$579$		0			0
$580$	10.1197	+	57.3917i	0.0174478	+	0.0989512i
$581$	313.926	−	55.3536i	0.540320	−	0.0952730i
$582$		0			0
$583$	−51.3472	−	43.0854i	−0.0880741	−	0.0739029i
$584$	−124.955	+	72.1428i	−0.213964	+	0.123532i
$585$		0			0
$586$	−70.9878	+	122.955i	−0.121140	+	0.209820i
$587$	327.703	+	900.357i	0.558268	+	1.53383i	0.822149	+	0.569273i	$0.192775\pi$
$587$	327.703	+	900.357i	0.558268	+	1.53383i	−0.263881	+	0.964555i	$0.585003\pi$
$588$		0			0
$589$	−977.455	+	820.182i	−1.65952	+	1.39250i
$590$	190.155	−	522.448i	0.322297	−	0.885504i
$591$		0			0
$592$	16.9455	−	96.1025i	0.0286241	−	0.162335i
$593$			733.805i			1.23745i	0.785609	+	0.618723i	$0.212350\pi$
$593$			733.805i			1.23745i	−0.785609	+	0.618723i	$0.787650\pi$
$594$		0			0
$595$	286.672			0.481802
$596$	168.029	+	29.6280i	0.281928	+	0.0497115i
$597$		0			0
$598$	−269.484	−	98.0840i	−0.450641	−	0.164020i
$599$	−727.241	−	866.692i	−1.21409	−	1.44690i	−0.858930	−	0.512094i	$-0.828870\pi$
$599$	−727.241	−	866.692i	−1.21409	−	1.44690i	−0.355162	−	0.934805i	$-0.615574\pi$
$600$		0			0
$601$	713.313	−	259.625i	1.18688	−	0.431988i	0.328251	−	0.944590i	$-0.393541\pi$
$601$	713.313	−	259.625i	1.18688	−	0.431988i	0.858626	+	0.512602i	$0.171318\pi$
$602$	684.309	+	395.086i	1.13673	+	0.656289i
$603$		0			0
$604$	−55.4793	−	96.0929i	−0.0918531	−	0.159094i
$605$	−370.276	+	441.278i	−0.612026	+	0.729384i
$606$		0			0
$607$	79.5776	+	451.307i	0.131100	+	0.743504i	0.977497	+	0.210951i	$0.0676561\pi$
$607$	79.5776	+	451.307i	0.131100	+	0.743504i	−0.846397	+	0.532553i	$0.821233\pi$
$608$	191.266	−	33.7254i	0.314582	−	0.0554693i
$609$		0			0
$610$	473.271	+	397.122i	0.775855	+	0.651019i
$611$	−394.130	+	227.551i	−0.645057	+	0.372424i
$612$		0			0
$613$	44.6060	−	77.2599i	0.0727667	−	0.126036i	−0.827346	−	0.561692i	$-0.810150\pi$
$613$	44.6060	−	77.2599i	0.0727667	−	0.126036i	0.900113	+	0.435657i	$0.143484\pi$
$614$	131.567	+	361.477i	0.214278	+	0.588725i
$615$		0			0
$616$	−97.3506	+	81.6868i	−0.158037	+	0.132608i
$617$	−185.560	+	509.821i	−0.300745	+	0.826290i	0.693626	+	0.720335i	$0.256012\pi$
$617$	−185.560	+	509.821i	−0.300745	+	0.826290i	−0.994371	+	0.105955i	$0.966210\pi$
$618$		0			0
$619$	89.2899	−	506.388i	0.144249	−	0.818075i	−0.823719	−	0.566999i	$-0.808104\pi$
$619$	89.2899	−	506.388i	0.144249	−	0.818075i	0.967967	−	0.251076i	$-0.0807844\pi$
$620$			411.410i			0.663565i
$621$		0			0
$622$	577.721			0.928812
$623$	−860.491	−	151.728i	−1.38121	−	0.243544i
$624$		0			0
$625$	689.857	+	251.087i	1.10377	+	0.401740i
$626$	−221.281	−	263.713i	−0.353485	−	0.421266i
$627$		0			0
$628$	−31.8587	+	11.5956i	−0.0507304	+	0.0184643i
$629$	100.197	+	57.8490i	0.159296	+	0.0919698i
$630$		0			0
$631$	317.732	+	550.327i	0.503537	+	0.872151i	0.999992	+	0.00408856i	$0.00130143\pi$
$631$	317.732	+	550.327i	0.503537	+	0.872151i	−0.496455	+	0.868062i	$0.665365\pi$
$632$	−57.7294	+	68.7993i	−0.0913440	+	0.108860i
$633$		0			0
$634$	−66.7342	−	378.469i	−0.105259	−	0.596954i
$635$	−750.649	+	132.360i	−1.18212	+	0.208440i
$636$		0			0
$637$	−295.625	−	248.059i	−0.464090	−	0.389418i
$638$	26.5259	−	15.3147i	0.0415766	−	0.0240043i
$639$		0			0
$640$	31.3104	−	54.2312i	0.0489225	−	0.0847362i
$641$	−219.882	−	604.121i	−0.343030	−	0.942466i	−0.984510	−	0.175327i	$-0.943902\pi$
$641$	−219.882	−	604.121i	−0.343030	−	0.942466i	0.641481	−	0.767139i	$-0.278320\pi$
$642$		0			0
$643$	499.083	−	418.781i	0.776179	−	0.651292i	−0.166104	−	0.986108i	$-0.553119\pi$
$643$	499.083	−	418.781i	0.776179	−	0.651292i	0.942283	+	0.334816i	$0.108674\pi$
$644$	275.852	−	757.898i	0.428342	−	1.17686i
$645$		0			0
$646$	−39.9852	+	226.768i	−0.0618966	+	0.351033i
$647$		−	736.107i		−	1.13772i	−0.822433	−	0.568862i	$-0.807384\pi$
$647$		−	736.107i		−	1.13772i	0.822433	−	0.568862i	$-0.192616\pi$
$648$		0			0
$649$	−292.213			−0.450250
$650$	−43.1036	−	7.60033i	−0.0663132	−	0.0116928i
$651$		0			0
$652$	433.710	+	157.858i	0.665199	+	0.242113i
$653$	−102.032	−	121.597i	−0.156251	−	0.186213i	0.682240	−	0.731129i	$-0.261006\pi$
$653$	−102.032	−	121.597i	−0.156251	−	0.186213i	−0.838491	+	0.544916i	$0.816562\pi$
$654$		0			0
$655$	333.324	−	121.320i	0.508891	−	0.185221i
$656$	79.5630	+	45.9357i	0.121285	+	0.0700240i
$657$		0			0
$658$	−639.966	−	1108.45i	−0.972593	−	1.68458i
$659$	813.429	−	969.407i	1.23434	−	1.47103i	0.403057	−	0.915175i	$-0.367948\pi$
$659$	813.429	−	969.407i	1.23434	−	1.47103i	0.831281	−	0.555852i	$-0.187608\pi$
$660$		0			0
$661$	−155.505	−	881.911i	−0.235257	−	1.33421i	−0.842073	−	0.539364i	$-0.818665\pi$
$661$	−155.505	−	881.911i	−0.235257	−	1.33421i	0.606816	−	0.794842i	$-0.292447\pi$
$662$	−617.486	+	108.879i	−0.932758	+	0.164470i
$663$		0			0
$664$	63.2419	+	53.0663i	0.0952439	+	0.0799191i
$665$	1797.32	−	1037.68i	2.70273	−	1.56042i
$666$		0			0
$667$	−97.1964	+	168.349i	−0.145722	+	0.252397i
$668$	−109.675	−	301.330i	−0.164185	−	0.451093i
$669$		0			0
$670$	−418.388	+	351.069i	−0.624460	+	0.523984i
$671$	111.058	−	305.129i	0.165511	−	0.454738i
$672$		0			0
$673$	198.279	−	1124.50i	0.294620	−	1.67087i	−0.374122	−	0.927380i	$-0.622056\pi$
$673$	198.279	−	1124.50i	0.294620	−	1.67087i	0.668742	−	0.743495i	$-0.266833\pi$
$674$		−	218.862i		−	0.324721i
$675$		0			0
$676$	277.683			0.410773
$677$	1228.42	+	216.603i	1.81450	+	0.319945i	0.974795	−	0.223101i	$-0.0716180\pi$
$677$	1228.42	+	216.603i	1.81450	+	0.319945i	0.839703	+	0.543046i	$0.182729\pi$
$678$		0			0
$679$	−487.297	−	177.362i	−0.717668	−	0.261210i
$680$	47.7231	+	56.8742i	0.0701811	+	0.0836385i
$681$		0			0
$682$	203.190	−	73.9552i	0.297933	−	0.108439i
$683$	779.418	+	449.997i	1.14117	+	0.658854i	0.946720	−	0.322059i	$-0.104375\pi$
$683$	779.418	+	449.997i	1.14117	+	0.658854i	0.194449	+	0.980913i	$0.437708\pi$
$684$		0			0
$685$	−211.243	−	365.884i	−0.308384	−	0.534137i
$686$	211.184	−	251.679i	0.307848	−	0.366879i
$687$		0			0
$688$	35.5359	+	201.534i	0.0516511	+	0.292928i
$689$	88.1149	−	15.5370i	0.127888	−	0.0225501i
$690$		0			0
$691$	−286.646	−	240.525i	−0.414828	−	0.348082i	0.411363	−	0.911471i	$-0.365053\pi$
$691$	−286.646	−	240.525i	−0.414828	−	0.348082i	−0.826192	+	0.563389i	$0.809497\pi$
$692$	−549.735	+	317.390i	−0.794415	+	0.458656i
$693$		0			0
$694$	−148.788	+	257.709i	−0.214392	+	0.371338i
$695$	−201.567	−	553.800i	−0.290024	−	0.796834i
$696$		0			0
$697$	−83.4406	+	70.0150i	−0.119714	+	0.100452i
$698$	208.528	−	572.925i	0.298750	−	0.820810i
$699$		0			0
$700$	21.3752	−	121.225i	0.0305361	−	0.173179i
$701$		−	574.292i		−	0.819247i	−0.912255	−	0.409624i	$-0.865660\pi$
$701$		−	574.292i		−	0.819247i	0.912255	−	0.409624i	$-0.134340\pi$
$702$		0			0
$703$	837.596			1.19146
$704$	−32.4124	−	5.71519i	−0.0460404	−	0.00811816i
$705$		0			0
$706$	−364.300	−	132.594i	−0.516005	−	0.187811i
$707$	−320.313	−	381.734i	−0.453059	−	0.539935i
$708$		0			0
$709$	−98.2153	+	35.7475i	−0.138527	+	0.0504195i	−0.410353	−	0.911927i	$-0.634595\pi$
$709$	−98.2153	+	35.7475i	−0.138527	+	0.0504195i	0.271827	+	0.962346i	$0.412372\pi$
$710$	−515.895	−	297.852i	−0.726613	−	0.419510i
$711$		0			0
$712$	−113.146	−	195.975i	−0.158914	−	0.275246i
$713$	−882.114	+	1051.26i	−1.23719	+	1.47442i
$714$		0			0
$715$	21.7150	+	123.152i	0.0303706	+	0.172240i
$716$	87.6441	−	15.4540i	0.122408	−	0.0215838i
$717$		0			0
$718$	−50.3091	−	42.2143i	−0.0700683	−	0.0587943i
$719$	−960.194	+	554.368i	−1.33546	+	0.771027i	−0.986130	−	0.165974i	$-0.946923\pi$
$719$	−960.194	+	554.368i	−1.33546	+	0.771027i	−0.349328	+	0.937001i	$0.613590\pi$
$720$		0			0
$721$	77.8320	−	134.809i	0.107950	−	0.186975i
$722$	395.539	+	1086.73i	0.547837	+	1.50517i
$723$		0			0
$724$	58.3075	−	48.9258i	0.0805353	−	0.0675771i
$725$	−10.1472	+	27.8793i	−0.0139962	+	0.0384542i
$726$		0			0
$727$	−178.676	+	1013.32i	−0.245772	+	1.39384i	0.572921	+	0.819611i	$0.305810\pi$
$727$	−178.676	+	1013.32i	−0.245772	+	1.39384i	−0.818693	+	0.574232i	$0.805301\pi$
$728$		−	169.637i		−	0.233017i
$729$		0			0
$730$	−399.307			−0.546995
$731$	−238.942	−	42.1319i	−0.326870	−	0.0576359i
$732$		0			0
$733$	315.178	+	114.715i	0.429984	+	0.156501i	0.547940	−	0.836517i	$-0.315412\pi$
$733$	315.178	+	114.715i	0.429984	+	0.156501i	−0.117956	+	0.993019i	$0.537634\pi$
$734$	582.081	+	693.697i	0.793026	+	0.945092i
$735$		0			0
$736$	196.285	−	71.4418i	0.266691	−	0.0970677i
$737$	248.598	+	143.528i	0.337311	+	0.194747i
$738$		0			0
$739$	130.983	+	226.869i	0.177244	+	0.306995i	0.940935	−	0.338586i	$-0.109949\pi$
$739$	130.983	+	226.869i	0.177244	+	0.306995i	−0.763692	+	0.645581i	$0.776615\pi$
$740$	173.594	−	206.881i	0.234586	−	0.279569i
$741$		0			0
$742$	43.6965	+	247.815i	0.0588902	+	0.333983i
$743$	477.341	−	84.1680i	0.642450	−	0.113281i	0.157074	−	0.987587i	$-0.449794\pi$
$743$	477.341	−	84.1680i	0.642450	−	0.113281i	0.485376	+	0.874305i	$0.338683\pi$
$744$		0			0
$745$	361.718	+	303.517i	0.485527	+	0.407406i
$746$	5.68555	−	3.28255i	0.00762138	−	0.00440021i
$747$		0			0
$748$	19.5107	−	33.7936i	0.0260838	−	0.0451785i
$749$	−394.023	−	1082.57i	−0.526065	−	1.44535i
$750$		0			0
$751$	668.630	−	561.047i	0.890320	−	0.747067i	−0.0779544	−	0.996957i	$-0.524839\pi$
$751$	668.630	−	561.047i	0.890320	−	0.747067i	0.968274	+	0.249890i	$0.0803944\pi$
$752$	113.374	−	311.493i	0.150764	−	0.414220i
$753$		0			0
$754$	−7.09978	+	40.2649i	−0.00941616	+	0.0534017i
$755$		−	307.075i		−	0.406722i
$756$		0			0
$757$	599.418			0.791834			0.395917	−	0.918286i	$-0.370427\pi$
$757$	599.418			0.791834			0.395917	+	0.918286i	$0.370427\pi$
$758$	−362.097	−	63.8474i	−0.477700	−	0.0842314i
$759$		0			0
$760$	505.075	+	183.832i	0.664572	+	0.241884i
$761$	754.984	+	899.755i	0.992094	+	1.18233i	0.983230	+	0.182371i	$0.0583773\pi$
$761$	754.984	+	899.755i	0.992094	+	1.18233i	0.00886470	+	0.999961i	$0.497178\pi$
$762$		0			0
$763$	−590.364	+	214.875i	−0.773740	+	0.281618i
$764$	−354.191	−	204.492i	−0.463601	−	0.267660i
$765$		0			0
$766$	−188.412	−	326.340i	−0.245969	−	0.426031i
$767$	250.727	−	298.805i	0.326894	−	0.389577i
$768$		0			0
$769$	−74.9660	−	425.153i	−0.0974850	−	0.552865i	−0.993958	−	0.109766i	$-0.964990\pi$
$769$	−74.9660	−	425.153i	−0.0974850	−	0.552865i	0.896473	−	0.443099i	$-0.146121\pi$
$770$	−346.353	+	61.0714i	−0.449809	+	0.0793135i
$771$		0			0
$772$	177.505	+	148.945i	0.229929	+	0.192933i
$773$	−1315.06	+	759.248i	−1.70124	+	0.982209i	−0.756723	+	0.653736i	$0.773201\pi$
$773$	−1315.06	+	759.248i	−1.70124	+	0.982209i	−0.944513	+	0.328473i	$0.893466\pi$
$774$		0			0
$775$	−104.723	+	181.386i	−0.135127	+	0.234046i
$776$	−45.9341	−	126.203i	−0.0591934	−	0.162633i
$777$		0			0
$778$	25.6656	−	21.5360i	0.0329892	−	0.0276812i
$779$	−269.702	+	740.999i	−0.346215	+	0.951219i
$780$		0			0
$781$	−54.3679	+	308.336i	−0.0696132	+	0.394796i
$782$			247.653i			0.316692i
$783$		0			0
$784$	281.088			0.358531
$785$	−92.4010	−	16.2928i	−0.117708	−	0.0207551i
$786$		0			0
$787$	1107.17	+	402.976i	1.40682	+	0.512040i	0.930195	−	0.367067i	$-0.119638\pi$
$787$	1107.17	+	402.976i	1.40682	+	0.512040i	0.476624	+	0.879107i	$0.341860\pi$
$788$	113.869	+	135.704i	0.144504	+	0.172214i
$789$		0			0
$790$	−233.560	+	85.0090i	−0.295646	+	0.107606i
$791$	−1130.30	−	652.580i	−1.42895	−	0.825006i
$792$		0			0
$793$	216.722	+	375.374i	0.273294	+	0.473359i
$794$	−206.278	+	245.833i	−0.259796	+	0.309613i
$795$		0			0
$796$	93.6126	+	530.904i	0.117604	+	0.666964i
$797$	351.259	−	61.9364i	0.440726	−	0.0777119i	0.0511179	−	0.998693i	$-0.483722\pi$
$797$	351.259	−	61.9364i	0.440726	−	0.0777119i	0.389608	+	0.920981i	$0.372610\pi$
$798$		0			0
$799$	301.065	+	252.623i	0.376802	+	0.316174i
$800$	27.6088	−	15.9399i	0.0345110	−	0.0199249i
$801$		0			0
$802$	−363.804	+	630.128i	−0.453622	+	0.785696i
$803$	71.7794	+	197.212i	0.0893891	+	0.245595i
$804$		0			0
$805$	1709.87	−	1434.75i	2.12406	−	1.78230i
$806$	−98.7197	+	271.230i	−0.122481	+	0.336514i
$807$		0			0
$808$	22.4106	−	127.097i	0.0277359	−	0.157298i
$809$		−	1097.22i		−	1.35627i	−0.734937	−	0.678135i	$-0.762788\pi$
$809$		−	1097.22i		−	1.35627i	0.734937	−	0.678135i	$-0.237212\pi$
$810$		0			0
$811$	−1027.37			−1.26680			−0.633398	−	0.773826i	$-0.718341\pi$
$811$	−1027.37			−1.26680			−0.633398	+	0.773826i	$0.718341\pi$
$812$	−113.241	−	19.9675i	−0.139460	−	0.0245905i
$813$		0			0
$814$	−133.381	−	48.5467i	−0.163859	−	0.0596397i
$815$	821.040	+	978.478i	1.00741	+	1.20059i
$816$		0			0
$817$	−1650.57	+	600.760i	−2.02029	+	0.735324i
$818$	−339.913	−	196.249i	−0.415541	−	0.239913i
$819$		0			0
$820$	127.126	+	220.189i	0.155032	+	0.268523i
$821$	595.875	−	710.137i	0.725792	−	0.864966i	−0.269388	−	0.963032i	$-0.586821\pi$
$821$	595.875	−	710.137i	0.725792	−	0.864966i	0.995180	+	0.0980663i	$0.0312657\pi$
$822$		0			0
$823$	−47.2612	−	268.032i	−0.0574255	−	0.325676i	0.942539	−	0.334096i	$-0.108431\pi$
$823$	−47.2612	−	268.032i	−0.0574255	−	0.325676i	−0.999965	+	0.00841973i	$0.997320\pi$
$824$	39.7023	−	7.00059i	0.0481824	−	0.00849586i
$825$		0			0
$826$	840.363	+	705.148i	1.01739	+	0.853690i
$827$	623.416	−	359.929i	0.753828	−	0.435223i	−0.0732475	−	0.997314i	$-0.523336\pi$
$827$	623.416	−	359.929i	0.753828	−	0.435223i	0.827075	+	0.562091i	$0.190003\pi$
$828$		0			0
$829$	−67.8015	+	117.436i	−0.0817871	+	0.141659i	−0.904018	−	0.427495i	$-0.859396\pi$
$829$	−67.8015	+	117.436i	−0.0817871	+	0.141659i	0.822231	+	0.569155i	$0.192729\pi$
$830$	78.1423	+	214.694i	0.0941474	+	0.258668i
$831$		0			0
$832$	33.6550	−	28.2399i	0.0404507	−	0.0339422i
$833$	−113.982	+	313.163i	−0.136833	+	0.375947i
$834$		0			0
$835$	154.103	−	873.961i	0.184554	−	1.04666i
$836$		−	282.496i		−	0.337913i
$837$		0			0
$838$	−454.254			−0.542069
$839$	−672.509	−	118.582i	−0.801561	−	0.141337i	−0.242162	−	0.970236i	$-0.577857\pi$
$839$	−672.509	−	118.582i	−0.801561	−	0.141337i	−0.559398	+	0.828899i	$0.688968\pi$
$840$		0			0
$841$	−764.238	−	278.160i	−0.908726	−	0.330749i
$842$	120.962	+	144.157i	0.143661	+	0.171208i
$843$		0			0
$844$	−264.380	+	96.2263i	−0.313246	+	0.114012i
$845$	665.523	+	384.240i	0.787601	+	0.454722i
$846$		0			0
$847$	−568.308	−	984.338i	−0.670966	−	1.16215i
$848$	−41.8909	+	49.9237i	−0.0493997	+	0.0588722i
$849$		0			0
$850$	6.56341	+	37.2230i	0.00772166	+	0.0437917i
$851$	887.157	−	156.430i	1.04249	−	0.183819i
$852$		0			0
$853$	515.666	+	432.695i	0.604533	+	0.507263i	0.892899	−	0.450257i	$-0.148668\pi$
$853$	515.666	+	432.695i	0.604533	+	0.507263i	−0.288366	+	0.957520i	$0.593112\pi$
$854$	−1055.71	+	609.512i	−1.23619	+	0.713714i
$855$		0			0
$856$	149.182	−	258.390i	0.174278	−	0.301858i
$857$	−266.513	−	732.238i	−0.310983	−	0.854420i	−0.992459	−	0.122579i	$-0.960884\pi$
$857$	−266.513	−	732.238i	−0.310983	−	0.854420i	0.681476	−	0.731841i	$-0.261339\pi$
$858$		0			0
$859$	−661.624	+	555.168i	−0.770226	+	0.646296i	−0.940767	−	0.339054i	$-0.889893\pi$
$859$	−661.624	+	555.168i	−0.770226	+	0.646296i	0.170541	+	0.985351i	$0.445448\pi$
$860$	−193.701	+	532.190i	−0.225234	+	0.618826i
$861$		0			0
$862$	6.01646	−	34.1211i	0.00697966	−	0.0395836i
$863$			538.992i			0.624556i	0.949991	+	0.312278i	$0.101092\pi$
$863$			538.992i			0.624556i	−0.949991	+	0.312278i	$0.898908\pi$
$864$		0			0
$865$	−1756.73			−2.03091
$866$	35.8898	+	6.32834i	0.0414432	+	0.00730755i
$867$		0			0
$868$	−762.810	−	277.640i	−0.878814	−	0.319862i
$869$	83.9697	+	100.071i	0.0966279	+	0.115157i
$870$		0			0
$871$	−360.071	+	131.055i	−0.413400	+	0.150465i
$872$	−140.909	−	81.3541i	−0.161593	−	0.0932960i
$873$		0			0
$874$	896.442	+	1552.68i	1.02568	+	1.77653i
$875$	−752.409	+	896.686i	−0.859895	+	1.02478i
$876$		0			0
$877$	−273.081	−	1548.72i	−0.311381	−	1.76593i	−0.591832	−	0.806061i	$-0.701595\pi$
$877$	−273.081	−	1548.72i	−0.311381	−	1.76593i	0.280451	−	0.959868i	$-0.409516\pi$
$878$	−631.003	+	111.263i	−0.718682	+	0.126723i
$879$		0			0
$880$	−69.7746	−	58.5479i	−0.0792893	−	0.0665317i
$881$	−399.139	+	230.443i	−0.453052	+	0.261570i	−0.709118	−	0.705090i	$-0.750907\pi$
$881$	−399.139	+	230.443i	−0.453052	+	0.261570i	0.256066	+	0.966659i	$0.417573\pi$
$882$		0			0
$883$	−225.254	+	390.151i	−0.255101	+	0.441848i	−0.964923	−	0.262533i	$-0.915442\pi$
$883$	−225.254	+	390.151i	−0.255101	+	0.441848i	0.709822	+	0.704381i	$0.248775\pi$
$884$	17.8152	+	48.9468i	0.0201529	+	0.0553697i
$885$		0			0
$886$	−540.627	+	453.640i	−0.610189	+	0.512009i
$887$	183.324	−	503.678i	0.206679	−	0.567845i	−0.792434	−	0.609957i	$-0.791187\pi$
$887$	183.324	−	503.678i	0.206679	−	0.567845i	0.999113	+	0.0421126i	$0.0134088\pi$
$888$		0			0
$889$	261.163	−	1481.13i	0.293772	−	1.66606i
$890$		−	626.259i		−	0.703662i
$891$		0			0
$892$	−691.308			−0.775009
$893$	2801.98	+	494.066i	3.13772	+	0.553265i
$894$		0			0
$895$	231.441	+	84.2376i	0.258593	+	0.0941203i
$896$	79.4222	+	94.6517i	0.0886408	+	0.105638i
$897$		0			0
$898$	−264.602	+	96.3073i	−0.294657	+	0.107246i
$899$	169.440	+	97.8263i	0.188476	+	0.108817i
$900$		0			0
$901$	−38.6336	−	66.9154i	−0.0428786	−	0.0742679i
$902$	85.8961	−	102.367i	0.0952285	−	0.113489i
$903$		0			0
$904$	−58.6961	−	332.882i	−0.0649293	−	0.368233i
$905$	207.446	−	36.5784i	0.229222	−	0.0404181i
$906$		0			0
$907$	1035.69	+	869.048i	1.14189	+	0.958157i	0.999499	−	0.0316538i	$-0.0100774\pi$
$907$	1035.69	+	869.048i	1.14189	+	0.958157i	0.142388	+	0.989811i	$0.454522\pi$
$908$	319.434	−	184.425i	0.351799	−	0.203111i
$909$		0			0
$910$	234.732	−	406.569i	0.257948	−	0.446779i
$911$	589.249	+	1618.95i	0.646816	+	1.77711i	0.629169	+	0.777268i	$0.283395\pi$
$911$	589.249	+	1618.95i	0.646816	+	1.77711i	0.0176469	+	0.999844i	$0.494383\pi$
$912$		0			0
$913$	91.9879	−	77.1870i	0.100753	−	0.0845421i
$914$	−4.60910	+	12.6634i	−0.00504278	+	0.0138549i
$915$		0			0
$916$	−76.7494	+	435.267i	−0.0837875	+	0.475183i
$917$			699.901i			0.763250i
$918$		0			0
$919$	−1327.65			−1.44467			−0.722336	−	0.691542i	$-0.756932\pi$
$919$	−1327.65			−1.44467			−0.722336	+	0.691542i	$0.756932\pi$
$920$	569.293	+	100.382i	0.618796	+	0.109110i
$921$		0			0
$922$	1007.23	+	366.601i	1.09244	+	0.397615i
$923$	−268.643	−	320.156i	−0.291054	−	0.346865i
$924$		0			0
$925$	129.196	−	47.0236i	0.139672	−	0.0508364i
$926$	780.043	+	450.358i	0.842379	+	0.486348i
$927$		0			0
$928$	−14.8902	−	25.7905i	−0.0160454	−	0.0277915i
$929$	1056.80	−	1259.44i	1.13757	−	1.35570i	0.211930	−	0.977285i	$-0.432025\pi$
$929$	1056.80	−	1259.44i	1.13757	−	1.35570i	0.925636	−	0.378414i	$-0.123531\pi$
$930$		0			0
$931$	418.952	+	2375.99i	0.450002	+	2.55209i
$932$	−828.693	+	146.121i	−0.889155	+	0.156782i
$933$		0			0
$934$	−791.367	−	664.036i	−0.847288	−	0.710959i
$935$	93.5227	−	53.9954i	0.100024	−	0.0577491i
$936$		0			0
$937$	269.132	−	466.150i	0.287227	−	0.497492i	−0.685920	−	0.727677i	$-0.740600\pi$
$937$	269.132	−	466.150i	0.287227	−	0.497492i	0.973147	+	0.230185i	$0.0739332\pi$
$938$	−368.581	−	1012.67i	−0.392944	−	1.07960i
$939$		0			0
$940$	702.749	−	589.676i	0.747605	−	0.627315i
$941$	−408.125	+	1121.31i	−0.433714	+	1.19162i	0.509802	+	0.860292i	$0.329719\pi$
$941$	−408.125	+	1121.31i	−0.433714	+	1.19162i	−0.943516	+	0.331327i	$0.892504\pi$
$942$		0			0
$943$	−147.271	+	835.214i	−0.156173	+	0.885699i
$944$			284.111i			0.300965i
$945$		0			0
$946$	297.662			0.314653
$947$	−1715.44	−	302.478i	−1.81145	−	0.319407i	−0.837543	−	0.546372i	$-0.816009\pi$
$947$	−1715.44	−	302.478i	−1.81145	−	0.319407i	−0.973903	+	0.226965i	$0.927120\pi$
$948$		0			0
$949$	−263.251	−	95.8154i	−0.277398	−	0.100965i
$950$	175.888	+	209.615i	0.185145	+	0.220647i
$951$		0			0
$952$	−137.659	+	50.1036i	−0.144599	+	0.0526298i
$953$	−264.703	−	152.826i	−0.277758	−	0.160364i	0.354650	−	0.934999i	$-0.384600\pi$
$953$	−264.703	−	152.826i	−0.277758	−	0.160364i	−0.632408	+	0.774636i	$0.717933\pi$
$954$		0			0
$955$	−565.927	−	980.214i	−0.592594	−	1.02640i
$956$	102.395	−	122.029i	0.107108	−	0.127646i
$957$		0			0
$958$	−85.5793	−	485.344i	−0.0893312	−	0.506622i
$959$	820.956	−	144.757i	0.856054	−	0.150945i
$960$		0			0
$961$	321.908	+	270.113i	0.334972	+	0.281075i
$962$	164.087	−	94.7357i	0.170569	−	0.0984779i
$963$		0			0
$964$	−53.9134	+	93.3807i	−0.0559267	+	0.0968679i
$965$	219.327	+	602.596i	0.227282	+	0.624452i
$966$		0			0
$967$	−340.677	+	285.862i	−0.352303	+	0.295617i	−0.801714	−	0.597708i	$-0.796078\pi$
$967$	−340.677	+	285.862i	−0.352303	+	0.295617i	0.449411	+	0.893325i	$0.351634\pi$
$968$	100.680	−	276.615i	0.104008	−	0.285759i
$969$		0			0
$970$	64.5412	−	366.031i	0.0665373	−	0.377352i
$971$		−	455.670i		−	0.469279i	−0.972083	−	0.234639i	$-0.924609\pi$
$971$		−	455.670i		−	0.469279i	0.972083	−	0.234639i	$-0.0753909\pi$
$972$		0			0
$973$	1162.85			1.19512
$974$	34.5597	+	6.09381i	0.0354822	+	0.00625647i
$975$		0			0
$976$	−296.670	−	107.979i	−0.303965	−	0.110634i
$977$	−1075.29	−	1281.49i	−1.10061	−	1.31165i	−0.946176	−	0.323651i	$-0.895090\pi$
$977$	−1075.29	−	1281.49i	−1.10061	−	1.31165i	−0.154432	−	0.988003i	$-0.549355\pi$
$978$		0			0
$979$	−309.301	+	112.577i	−0.315936	+	0.114991i
$980$	673.684	+	388.952i	0.687433	+	0.396889i
$981$		0			0
$982$	−393.724	−	681.950i	−0.400941	−	0.694450i
$983$	−145.881	+	173.854i	−0.148403	+	0.176860i	−0.835125	−	0.550060i	$-0.814605\pi$
$983$	−145.881	+	173.854i	−0.148403	+	0.176860i	0.686722	+	0.726921i	$0.259049\pi$
$984$		0			0
$985$	85.1321	+	482.808i	0.0864285	+	0.490160i
$986$	34.7715	−	6.13116i	0.0352652	−	0.00621821i
$987$		0			0
$988$	288.869	+	242.390i	0.292378	+	0.245334i
$989$	−1636.04	+	944.568i	−1.65424	+	0.955074i
$990$		0			0
$991$	76.9538	−	133.288i	0.0776527	−	0.134498i	−0.824584	−	0.565739i	$-0.808591\pi$
$991$	76.9538	−	133.288i	0.0776527	−	0.134498i	0.902237	+	0.431241i	$0.141924\pi$
$992$	−71.9049	−	197.557i	−0.0724847	−	0.199150i
$993$		0			0
$994$	900.411	−	755.534i	0.905846	−	0.760095i
$995$	−510.269	+	1401.95i	−0.512833	+	1.40900i
$996$		0			0
$997$	−183.930	+	1043.12i	−0.184483	+	1.04626i	0.742134	+	0.670251i	$0.233814\pi$
$997$	−183.930	+	1043.12i	−0.184483	+	1.04626i	−0.926617	+	0.376005i	$0.877297\pi$
$998$			580.115i			0.581278i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.3.f.a.89.3		36
3.2	odd	2		54.3.f.a.29.6	✓	36
12.11	even	2		432.3.bc.c.353.1		36
27.11	odd	18		1458.3.b.c.1457.22		36
27.13	even	9		54.3.f.a.41.6	yes	36
27.14	odd	18	inner	162.3.f.a.71.3		36
27.16	even	9		1458.3.b.c.1457.15		36
108.67	odd	18		432.3.bc.c.257.1		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.3.f.a.29.6	✓	36	3.2	odd	2
54.3.f.a.41.6	yes	36	27.13	even	9
162.3.f.a.71.3		36	27.14	odd	18	inner
162.3.f.a.89.3		36	1.1	even	1	trivial
432.3.bc.c.257.1		36	108.67	odd	18
432.3.bc.c.353.1		36	12.11	even	2
1458.3.b.c.1457.15		36	27.16	even	9
1458.3.b.c.1457.22		36	27.11	odd	18

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:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	162.f (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.39273 - 0.245576i) q^{2} +(1.87939 + 0.684040i) q^{4} +(3.55779 + 4.24001i) q^{5} +(-10.2625 + 3.73526i) q^{7} +(-2.44949 - 1.41421i) q^{8} +O(q^{10})\)	\(q+(-1.39273 - 0.245576i) q^{2} +(1.87939 + 0.684040i) q^{4} +(3.55779 + 4.24001i) q^{5} +(-10.2625 + 3.73526i) q^{7} +(-2.44949 - 1.41421i) q^{8} +(-3.91380 - 6.77890i) q^{10} +(-2.64446 + 3.15155i) q^{11} +(-0.953621 - 5.40825i) q^{13} +(15.2102 - 2.68197i) q^{14} +(3.06418 + 2.57115i) q^{16} +(-4.10708 + 2.37123i) q^{17} +(-17.1665 + 29.7332i) q^{19} +(3.78613 + 10.4023i) q^{20} +(4.45696 - 3.73984i) q^{22} +(-12.6292 + 34.6986i) q^{23} +(-0.978615 + 5.55000i) q^{25} +7.76642i q^{26} -21.8423 q^{28} +(5.18449 + 0.914165i) q^{29} +(34.9235 + 12.7111i) q^{31} +(-3.63616 - 4.33340i) q^{32} +(6.30237 - 2.29387i) q^{34} +(-52.3496 - 30.2240i) q^{35} +(-12.1981 - 21.1278i) q^{37} +(31.2100 - 37.1946i) q^{38} +(-2.71850 - 15.4174i) q^{40} +(22.6189 - 3.98833i) q^{41} +(39.1915 + 32.8855i) q^{43} +(-7.12575 + 4.11406i) q^{44} +(26.1102 - 45.2243i) q^{46} +(-28.3436 - 77.8733i) q^{47} +(53.8315 - 45.1700i) q^{49} +(2.72589 - 7.48932i) q^{50} +(1.90724 - 10.8165i) q^{52} +16.2927i q^{53} -22.7711 q^{55} +(30.4205 + 5.36395i) q^{56} +(-6.99608 - 2.54637i) q^{58} +(45.6558 + 54.4105i) q^{59} +(-74.1675 + 26.9948i) q^{61} +(-45.5174 - 26.2795i) q^{62} +(4.00000 + 6.92820i) q^{64} +(19.5383 - 23.2848i) q^{65} +(-12.1162 - 68.7145i) q^{67} +(-9.34081 + 1.64704i) q^{68} +(65.4865 + 54.9497i) q^{70} +(65.9072 - 38.0516i) q^{71} +(25.5063 - 44.1783i) q^{73} +(11.8002 + 32.4208i) q^{74} +(-52.6012 + 44.1376i) q^{76} +(15.3671 - 42.2207i) q^{77} +(5.51385 - 31.2706i) q^{79} +22.1398i q^{80} -32.4815 q^{82} +(-28.7447 - 5.06847i) q^{83} +(-24.6662 - 8.97776i) q^{85} +(-46.5072 - 55.4251i) q^{86} +(10.9346 - 3.97985i) q^{88} +(69.2878 + 40.0033i) q^{89} +(29.9878 + 51.9404i) q^{91} +(-47.4704 + 56.5731i) q^{92} +(20.3511 + 115.417i) q^{94} +(-187.144 + 32.9986i) q^{95} +(36.3741 + 30.5215i) q^{97} +(-86.0653 + 49.6898i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 18 q^{5}+O(q^{10}) \) 36 * q - 18 * q^5	\( 36 q - 18 q^{5} + 18 q^{11} + 36 q^{14} + 72 q^{20} + 36 q^{22} + 180 q^{23} + 18 q^{25} - 144 q^{29} - 90 q^{31} - 72 q^{34} - 486 q^{35} - 180 q^{38} + 90 q^{41} + 90 q^{43} + 378 q^{47} + 72 q^{49} + 72 q^{56} - 252 q^{59} - 144 q^{61} + 144 q^{64} - 18 q^{65} - 594 q^{67} + 180 q^{68} - 360 q^{70} + 648 q^{71} + 126 q^{73} + 504 q^{74} - 72 q^{76} + 342 q^{77} - 72 q^{79} - 594 q^{83} + 360 q^{85} - 540 q^{86} + 144 q^{88} - 648 q^{89} - 198 q^{91} - 396 q^{92} + 504 q^{94} - 252 q^{95} + 702 q^{97} - 648 q^{98}+O(q^{100}) \) 36 * q - 18 * q^5 + 18 * q^11 + 36 * q^14 + 72 * q^20 + 36 * q^22 + 180 * q^23 + 18 * q^25 - 144 * q^29 - 90 * q^31 - 72 * q^34 - 486 * q^35 - 180 * q^38 + 90 * q^41 + 90 * q^43 + 378 * q^47 + 72 * q^49 + 72 * q^56 - 252 * q^59 - 144 * q^61 + 144 * q^64 - 18 * q^65 - 594 * q^67 + 180 * q^68 - 360 * q^70 + 648 * q^71 + 126 * q^73 + 504 * q^74 - 72 * q^76 + 342 * q^77 - 72 * q^79 - 594 * q^83 + 360 * q^85 - 540 * q^86 + 144 * q^88 - 648 * q^89 - 198 * q^91 - 396 * q^92 + 504 * q^94 - 252 * q^95 + 702 * q^97 - 648 * q^98

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