LMFDB - Embedded newform 171.3.p.e.145.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [171,3,Mod(46,171)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(171, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("171.46");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 171 = 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	171.p (of order $6$, 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:	$4.65941252056$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{6})$
Coefficient field:	6.0.6967728.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 8x^{4} + 5x^{3} + 50x^{2} - 7x + 1 $ x^6 - x^5 + 8x^4 + 5x^3 + 50x^2 - 7x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 57)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			145.2
Root			$-1.13654 - 1.96854i$ of defining polynomial
Character	$\chi$	$=$	171.145
Dual form			171.3.p.e.46.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.583430 - 0.336844i) q^{2} +(-1.77307 + 3.07105i) q^{4} +(-2.27307 - 3.93708i) q^{5} +9.87987 q^{7} +5.08374i q^{8} +O(q^{10})$	\(q+(0.583430 - 0.336844i) q^{2} +(-1.77307 + 3.07105i) q^{4} +(-2.27307 - 3.93708i) q^{5} +9.87987 q^{7} +5.08374i q^{8} +(-2.65236 - 1.53134i) q^{10} +15.6384 q^{11} +(13.3053 + 7.68182i) q^{13} +(5.76421 - 3.32797i) q^{14} +(-5.37987 - 9.31820i) q^{16} +(12.4260 + 21.5225i) q^{17} +(-18.4260 - 4.63488i) q^{19} +16.1213 q^{20} +(9.12394 - 5.26771i) q^{22} +(-4.15294 + 7.19310i) q^{23} +(2.16628 - 3.75211i) q^{25} +10.3503 q^{26} +(-17.5177 + 30.3416i) q^{28} +(-27.3059 - 15.7651i) q^{29} -30.9353i q^{31} +(-23.8881 - 13.7918i) q^{32} +(14.4994 + 8.37124i) q^{34} +(-22.4577 - 38.8978i) q^{35} +17.3225i q^{37} +(-12.3115 + 3.50256i) q^{38} +(20.0151 - 11.5557i) q^{40} +(44.2502 - 25.5479i) q^{41} +(-0.773073 - 1.33900i) q^{43} +(-27.7281 + 48.0265i) q^{44} +5.59556i q^{46} +(-5.09113 + 8.81810i) q^{47} +48.6118 q^{49} -2.91879i q^{50} +(-47.1825 + 27.2408i) q^{52} +(-4.54002 - 2.62118i) q^{53} +(-35.5473 - 61.5697i) q^{55} +50.2267i q^{56} -21.2414 q^{58} +(-68.4321 + 39.5093i) q^{59} +(-53.9426 + 93.4313i) q^{61} +(-10.4204 - 18.0486i) q^{62} +24.4562 q^{64} -69.8453i q^{65} +(-16.9843 - 9.80591i) q^{67} -88.1289 q^{68} +(-26.2049 - 15.1294i) q^{70} +(45.3604 - 26.1888i) q^{71} +(-36.6301 - 63.4451i) q^{73} +(5.83498 + 10.1065i) q^{74} +(46.9046 - 48.3693i) q^{76} +154.506 q^{77} +(-27.1512 + 15.6758i) q^{79} +(-24.4577 + 42.3619i) q^{80} +(17.2113 - 29.8108i) q^{82} +42.6674 q^{83} +(56.4905 - 97.8443i) q^{85} +(-0.902068 - 0.520809i) q^{86} +79.5018i q^{88} +(-114.819 - 66.2909i) q^{89} +(131.455 + 75.8953i) q^{91} +(-14.7269 - 25.5078i) q^{92} +6.85966i q^{94} +(23.6358 + 83.0801i) q^{95} +(-70.2270 + 40.5456i) q^{97} +(28.3616 - 16.3746i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} + 5 q^{4} + 2 q^{5} + 26 q^{7}+O(q^{10}) $ 6 * q + 3 * q^2 + 5 * q^4 + 2 * q^5 + 26 * q^7	$ 6 q + 3 q^{2} + 5 q^{4} + 2 q^{5} + 26 q^{7} + 30 q^{10} - 15 q^{13} + 81 q^{14} + q^{16} + 10 q^{17} - 46 q^{19} + 124 q^{20} - 84 q^{22} + 24 q^{23} + 15 q^{25} - 58 q^{26} + 19 q^{28} - 66 q^{29} - 51 q^{32} + 90 q^{34} + 6 q^{35} - 83 q^{38} + 162 q^{40} - 24 q^{41} + 11 q^{43} - 176 q^{44} + 26 q^{47} + 96 q^{49} - 321 q^{52} - 180 q^{53} - 176 q^{55} - 188 q^{58} - 162 q^{59} - 141 q^{61} + 109 q^{62} + 166 q^{64} - 63 q^{67} - 212 q^{68} + 258 q^{70} + 372 q^{71} + 103 q^{73} + 315 q^{74} - 217 q^{76} + 16 q^{77} - 123 q^{79} - 6 q^{80} + 80 q^{82} + 252 q^{83} + 116 q^{85} + 39 q^{86} - 642 q^{89} + 87 q^{91} - 104 q^{92} + 214 q^{95} - 12 q^{97} + 264 q^{98}+O(q^{100}) $ 6 * q + 3 * q^2 + 5 * q^4 + 2 * q^5 + 26 * q^7 + 30 * q^10 - 15 * q^13 + 81 * q^14 + q^16 + 10 * q^17 - 46 * q^19 + 124 * q^20 - 84 * q^22 + 24 * q^23 + 15 * q^25 - 58 * q^26 + 19 * q^28 - 66 * q^29 - 51 * q^32 + 90 * q^34 + 6 * q^35 - 83 * q^38 + 162 * q^40 - 24 * q^41 + 11 * q^43 - 176 * q^44 + 26 * q^47 + 96 * q^49 - 321 * q^52 - 180 * q^53 - 176 * q^55 - 188 * q^58 - 162 * q^59 - 141 * q^61 + 109 * q^62 + 166 * q^64 - 63 * q^67 - 212 * q^68 + 258 * q^70 + 372 * q^71 + 103 * q^73 + 315 * q^74 - 217 * q^76 + 16 * q^77 - 123 * q^79 - 6 * q^80 + 80 * q^82 + 252 * q^83 + 116 * q^85 + 39 * q^86 - 642 * q^89 + 87 * q^91 - 104 * q^92 + 214 * q^95 - 12 * q^97 + 264 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/171\mathbb{Z}\right)^\times$.

$n$	$20$	$154$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.583430	−	0.336844i	0.291715	−	0.168422i	−0.347000	−	0.937865i	$-0.612800\pi$
$2$	0.583430	−	0.336844i	0.291715	−	0.168422i	0.638715	+	0.769443i	$0.279466\pi$
$3$		0			0
$3$		0			0
$4$	−1.77307	+	3.07105i	−0.443268	+	0.767763i
$5$	−2.27307	−	3.93708i	−0.454615	−	0.787416i	0.544051	−	0.839052i	$-0.316890\pi$
$5$	−2.27307	−	3.93708i	−0.454615	−	0.787416i	−0.998666	+	0.0516364i	$0.983556\pi$
$6$		0			0
$7$	9.87987			1.41141			0.705705	−	0.708506i	$-0.250631\pi$
$7$	9.87987			1.41141			0.705705	+	0.708506i	$0.250631\pi$
$8$			5.08374i			0.635468i
$9$		0			0
$10$	−2.65236	−	1.53134i	−0.265236	−	0.153134i
$11$	15.6384			1.42168			0.710838	−	0.703356i	$-0.248316\pi$
$11$	15.6384			1.42168			0.710838	+	0.703356i	$0.248316\pi$
$12$		0			0
$13$	13.3053	+	7.68182i	1.02348	+	0.590909i	0.915111	−	0.403201i	$-0.132103\pi$
$13$	13.3053	+	7.68182i	1.02348	+	0.590909i	0.108373	+	0.994110i	$0.465436\pi$
$14$	5.76421	−	3.32797i	0.411729	−	0.237712i
$15$		0			0
$16$	−5.37987	−	9.31820i	−0.336242	−	0.582388i
$17$	12.4260	+	21.5225i	0.730942	+	1.26603i	0.956481	+	0.291794i	$0.0942523\pi$
$17$	12.4260	+	21.5225i	0.730942	+	1.26603i	−0.225539	+	0.974234i	$0.572414\pi$
$18$		0			0
$19$	−18.4260	−	4.63488i	−0.969790	−	0.243941i
$19$	−18.4260	−	4.63488i	−0.969790	−	0.243941i
$20$	16.1213			0.806065
$21$		0			0
$22$	9.12394	−	5.26771i	0.414724	−	0.239441i
$23$	−4.15294	+	7.19310i	−0.180563	+	0.312744i	−0.942072	−	0.335410i	$-0.891125\pi$
$23$	−4.15294	+	7.19310i	−0.180563	+	0.312744i	0.761510	+	0.648154i	$0.224458\pi$
$24$		0			0
$25$	2.16628	−	3.75211i	0.0866512	−	0.150084i
$26$	10.3503			0.398088
$27$		0			0
$28$	−17.5177	+	30.3416i	−0.625633	+	1.08363i
$29$	−27.3059	−	15.7651i	−0.941582	−	0.543623i	−0.0511261	−	0.998692i	$-0.516281\pi$
$29$	−27.3059	−	15.7651i	−0.941582	−	0.543623i	−0.890456	+	0.455070i	$0.849614\pi$
$30$		0			0
$31$		−	30.9353i		−	0.997914i	−0.866627	−	0.498957i	$-0.833716\pi$
$31$		−	30.9353i		−	0.997914i	0.866627	−	0.498957i	$-0.166284\pi$
$32$	−23.8881	−	13.7918i	−0.746505	−	0.430995i
$33$		0			0
$34$	14.4994	+	8.37124i	0.426454	+	0.246213i
$35$	−22.4577	−	38.8978i	−0.641647	−	1.11137i
$36$		0			0
$37$			17.3225i			0.468176i	0.972215	+	0.234088i	$0.0752104\pi$
$37$			17.3225i			0.468176i	−0.972215	+	0.234088i	$0.924790\pi$
$38$	−12.3115	+	3.50256i	−0.323987	+	0.0921725i
$39$		0			0
$40$	20.0151	−	11.5557i	0.500377	−	0.288893i
$41$	44.2502	−	25.5479i	1.07927	−	0.623119i	0.148573	−	0.988901i	$-0.452532\pi$
$41$	44.2502	−	25.5479i	1.07927	−	0.623119i	0.930700	+	0.365783i	$0.119199\pi$
$42$		0			0
$43$	−0.773073	−	1.33900i	−0.0179784	−	0.0311396i	0.856896	−	0.515489i	$-0.172390\pi$
$43$	−0.773073	−	1.33900i	−0.0179784	−	0.0311396i	−0.874875	+	0.484349i	$0.839056\pi$
$44$	−27.7281	+	48.0265i	−0.630184	+	1.09151i
$45$		0			0
$46$			5.59556i			0.121643i
$47$	−5.09113	+	8.81810i	−0.108322	+	0.187619i	−0.915091	−	0.403248i	$-0.867881\pi$
$47$	−5.09113	+	8.81810i	−0.108322	+	0.187619i	0.806769	+	0.590867i	$0.201214\pi$
$48$		0			0
$49$	48.6118			0.992077
$50$		−	2.91879i		−	0.0583758i
$51$		0			0
$52$	−47.1825	+	27.2408i	−0.907356	+	0.523862i
$53$	−4.54002	−	2.62118i	−0.0856608	−	0.0494563i	0.456558	−	0.889694i	$-0.349082\pi$
$53$	−4.54002	−	2.62118i	−0.0856608	−	0.0494563i	−0.542219	+	0.840238i	$0.682416\pi$
$54$		0			0
$55$	−35.5473	−	61.5697i	−0.646315	−	1.11945i
$56$			50.2267i			0.896905i
$57$		0			0
$58$	−21.2414			−0.366232
$59$	−68.4321	+	39.5093i	−1.15987	+	0.669649i	−0.951272	−	0.308353i	$-0.900222\pi$
$59$	−68.4321	+	39.5093i	−1.15987	+	0.669649i	−0.208595	+	0.978002i	$0.566889\pi$
$60$		0			0
$61$	−53.9426	+	93.4313i	−0.884304	+	1.53166i	−0.0377957	+	0.999285i	$0.512034\pi$
$61$	−53.9426	+	93.4313i	−0.884304	+	1.53166i	−0.846509	+	0.532375i	$0.821300\pi$
$62$	−10.4204	−	18.0486i	−0.168071	−	0.291107i
$63$		0			0
$64$	24.4562			0.382128
$65$		−	69.8453i		−	1.07454i
$66$		0			0
$67$	−16.9843	−	9.80591i	−0.253498	−	0.146357i	0.367867	−	0.929878i	$-0.380088\pi$
$67$	−16.9843	−	9.80591i	−0.253498	−	0.146357i	−0.621365	+	0.783521i	$0.713421\pi$
$68$	−88.1289			−1.29601
$69$		0			0
$70$	−26.2049	−	15.1294i	−0.374356	−	0.216135i
$71$	45.3604	−	26.1888i	0.638879	−	0.368857i	−0.145304	−	0.989387i	$-0.546416\pi$
$71$	45.3604	−	26.1888i	0.638879	−	0.368857i	0.784183	+	0.620530i	$0.213083\pi$
$72$		0			0
$73$	−36.6301	−	63.4451i	−0.501782	−	0.869111i	−0.999998	−	0.00205848i	$-0.999345\pi$
$73$	−36.6301	−	63.4451i	−0.501782	−	0.869111i	0.498216	−	0.867053i	$-0.333989\pi$
$74$	5.83498	+	10.1065i	0.0788511	+	0.136574i
$75$		0			0
$76$	46.9046	−	48.3693i	0.617166	−	0.636438i
$77$	154.506			2.00657
$78$		0			0
$79$	−27.1512	+	15.6758i	−0.343686	+	0.198427i	−0.661901	−	0.749591i	$-0.730250\pi$
$79$	−27.1512	+	15.6758i	−0.343686	+	0.198427i	0.318215	+	0.948019i	$0.396917\pi$
$80$	−24.4577	+	42.3619i	−0.305721	+	0.529524i
$81$		0			0
$82$	17.2113	−	29.8108i	0.209893	−	0.363546i
$83$	42.6674			0.514066			0.257033	−	0.966403i	$-0.417255\pi$
$83$	42.6674			0.514066			0.257033	+	0.966403i	$0.417255\pi$
$84$		0			0
$85$	56.4905	−	97.8443i	0.664594	−	1.15111i
$86$	−0.902068	−	0.520809i	−0.0104892	−	0.00605592i
$87$		0			0
$88$			79.5018i			0.903429i
$89$	−114.819	−	66.2909i	−1.29010	−	0.744842i	−0.311431	−	0.950269i	$-0.600808\pi$
$89$	−114.819	−	66.2909i	−1.29010	−	0.744842i	−0.978672	+	0.205427i	$0.934142\pi$
$90$		0			0
$91$	131.455	+	75.8953i	1.44456	+	0.834015i
$92$	−14.7269	−	25.5078i	−0.160075	−	0.277259i
$93$		0			0
$94$			6.85966i			0.0729751i
$95$	23.6358	+	83.0801i	0.248798	+	0.874527i
$96$		0			0
$97$	−70.2270	+	40.5456i	−0.723990	+	0.417996i	−0.816219	−	0.577742i	$-0.803934\pi$
$97$	−70.2270	+	40.5456i	−0.723990	+	0.417996i	0.0922297	+	0.995738i	$0.470601\pi$
$98$	28.3616	−	16.3746i	0.289404	−	0.167087i
$99$		0			0
$100$	7.68194	+	13.3055i	0.0768194	+	0.133055i
$101$	44.8242	−	77.6378i	0.443804	−	0.768691i	−0.554164	−	0.832407i	$-0.686962\pi$
$101$	44.8242	−	77.6378i	0.443804	−	0.768691i	0.997968	+	0.0637166i	$0.0202954\pi$
$102$		0			0
$103$			59.2876i			0.575608i	0.957689	+	0.287804i	$0.0929251\pi$
$103$			59.2876i			0.575608i	−0.957689	+	0.287804i	$0.907075\pi$
$104$	−39.0524	+	67.6407i	−0.375504	+	0.650391i
$105$		0			0
$106$	−3.53171			−0.0333181
$107$			45.0373i			0.420910i	0.977604	+	0.210455i	$0.0674945\pi$
$107$			45.0373i			0.420910i	−0.977604	+	0.210455i	$0.932505\pi$
$108$		0			0
$109$	4.30356	−	2.48466i	0.0394822	−	0.0227950i	−0.480129	−	0.877198i	$-0.659410\pi$
$109$	4.30356	−	2.48466i	0.0394822	−	0.0227950i	0.519611	+	0.854403i	$0.326077\pi$
$110$	−41.4787	−	23.9478i	−0.377079	−	0.217707i
$111$		0			0
$112$	−53.1524	−	92.0626i	−0.474575	−	0.821987i
$113$		−	124.048i		−	1.09777i	−0.835898	−	0.548885i	$-0.815053\pi$
$113$		−	124.048i		−	1.09777i	0.835898	−	0.548885i	$-0.184947\pi$
$114$		0			0
$115$	37.7597			0.328345
$116$	96.8306	−	55.9052i	0.834747	−	0.481941i
$117$		0			0
$118$	−26.6169	+	46.1018i	−0.225567	+	0.390694i
$119$	122.767	+	212.639i	1.03166	+	1.78688i
$120$		0			0
$121$	123.561			1.02116
$122$			72.6808i			0.595744i
$123$		0			0
$124$	95.0041	+	54.8506i	0.766162	+	0.442344i
$125$	−133.350			−1.06680
$126$		0			0
$127$	99.9211	+	57.6895i	0.786780	+	0.454248i	0.838828	−	0.544397i	$-0.183241\pi$
$127$	99.9211	+	57.6895i	0.786780	+	0.454248i	−0.0520474	+	0.998645i	$0.516575\pi$
$128$	109.821	−	63.4052i	0.857977	−	0.495353i
$129$		0			0
$130$	−23.5269	−	40.7499i	−0.180976	−	0.313460i
$131$	53.1834	+	92.1164i	0.405980	+	0.703179i	0.994435	−	0.105352i	$-0.0335968\pi$
$131$	53.1834	+	92.1164i	0.405980	+	0.703179i	−0.588455	+	0.808530i	$0.700263\pi$
$132$		0			0
$133$	−182.047	−	45.7920i	−1.36877	−	0.344300i
$134$	−13.2122			−0.0985987
$135$		0			0
$136$	−109.415	+	63.1706i	−0.804520	+	0.464490i
$137$	58.9455	−	102.097i	0.430259	−	0.745230i	−0.566636	−	0.823968i	$-0.691756\pi$
$137$	58.9455	−	102.097i	0.430259	−	0.745230i	0.996895	+	0.0787376i	$0.0250889\pi$
$138$		0			0
$139$	88.9275	−	154.027i	0.639766	−	1.10811i	−0.345718	−	0.938339i	$-0.612365\pi$
$139$	88.9275	−	154.027i	0.639766	−	1.10811i	0.985484	−	0.169769i	$-0.0543021\pi$
$140$	159.276			1.13769
$141$		0			0
$142$	17.6431	−	30.5587i	0.124247	−	0.215202i
$143$	208.074	+	120.132i	1.45506	+	0.840081i
$144$		0			0
$145$			143.340i			0.988555i
$146$	−42.7422	−	24.6772i	−0.292755	−	0.169022i
$147$		0			0
$148$	−53.1984	−	30.7141i	−0.359448	−	0.207528i
$149$	−89.8593	−	155.641i	−0.603083	−	1.04457i	−0.992351	−	0.123445i	$-0.960606\pi$
$149$	−89.8593	−	155.641i	−0.603083	−	1.04457i	0.389269	−	0.921124i	$-0.372728\pi$
$150$		0			0
$151$		−	225.138i		−	1.49098i	−0.666517	−	0.745490i	$-0.732215\pi$
$151$		−	225.138i		−	1.49098i	0.666517	−	0.745490i	$-0.267785\pi$
$152$	23.5625	−	93.6731i	0.155017	−	0.616270i
$153$		0			0
$154$	90.1433	−	52.0442i	0.585346	−	0.337950i
$155$	−121.795	+	70.3183i	−0.785773	+	0.453666i
$156$		0			0
$157$	−13.5101	−	23.4002i	−0.0860517	−	0.149046i	0.819787	−	0.572668i	$-0.194092\pi$
$157$	−13.5101	−	23.4002i	−0.0860517	−	0.149046i	−0.905839	+	0.423622i	$0.860758\pi$
$158$	−10.5606	+	18.2914i	−0.0668389	+	0.115768i
$159$		0			0
$160$			125.399i			0.783746i
$161$	−41.0305	+	71.0669i	−0.254848	+	0.441409i
$162$		0			0
$163$	−151.210			−0.927667			−0.463833	−	0.885922i	$-0.653526\pi$
$163$	−151.210			−0.927667			−0.463833	+	0.885922i	$0.653526\pi$
$164$			181.193i			1.10483i
$165$		0			0
$166$	24.8935	−	14.3723i	0.149961	−	0.0865798i
$167$	−123.259	−	71.1638i	−0.738079	−	0.426130i	0.0832911	−	0.996525i	$-0.473457\pi$
$167$	−123.259	−	71.1638i	−0.738079	−	0.426130i	−0.821371	+	0.570395i	$0.806790\pi$
$168$		0			0
$169$	33.5206	+	58.0594i	0.198347	+	0.343547i
$170$		−	76.1138i		−	0.447728i
$171$		0			0
$172$	5.48286			0.0318771
$173$	−205.442	+	118.612i	−1.18753	+	0.685620i	−0.957744	−	0.287622i	$-0.907135\pi$
$173$	−205.442	+	118.612i	−1.18753	+	0.685620i	−0.229784	+	0.973242i	$0.573802\pi$
$174$		0			0
$175$	21.4026	−	37.0703i	0.122300	−	0.211830i
$176$	−84.1327	−	145.722i	−0.478027	−	0.827967i
$177$		0			0
$178$	−89.3187			−0.501790
$179$			1.84122i			0.0102862i	0.999987	+	0.00514308i	$0.00163710\pi$
$179$			1.84122i			0.0102862i	−0.999987	+	0.00514308i	$0.998363\pi$
$180$		0			0
$181$	−30.9176	−	17.8503i	−0.170816	−	0.0986205i	0.412155	−	0.911114i	$-0.364776\pi$
$181$	−30.9176	−	17.8503i	−0.170816	−	0.0986205i	−0.582970	+	0.812493i	$0.698110\pi$
$182$	102.259			0.561865
$183$		0			0
$184$	−36.5679	−	21.1125i	−0.198738	−	0.114742i
$185$	68.2001	−	39.3753i	0.368649	−	0.212840i
$186$		0			0
$187$	194.323	+	336.578i	1.03916	+	1.79988i
$188$	−18.0539	−	31.2703i	−0.0960313	−	0.166331i
$189$		0			0
$190$	41.7748	+	40.5098i	0.219867	+	0.213210i
$191$	−166.346			−0.870919			−0.435460	−	0.900208i	$-0.643414\pi$
$191$	−166.346			−0.870919			−0.435460	+	0.900208i	$0.643414\pi$
$192$		0			0
$193$	150.645	−	86.9747i	0.780542	−	0.450646i	−0.0560803	−	0.998426i	$-0.517860\pi$
$193$	150.645	−	86.9747i	0.780542	−	0.450646i	0.836622	+	0.547780i	$0.184527\pi$
$194$	−27.3150	+	47.3110i	−0.140799	+	0.243871i
$195$		0			0
$196$	−86.1922	+	149.289i	−0.439756	+	0.761680i
$197$	86.5637			0.439410			0.219705	−	0.975566i	$-0.429491\pi$
$197$	86.5637			0.439410			0.219705	+	0.975566i	$0.429491\pi$
$198$		0			0
$199$	−125.922	+	218.103i	−0.632774	+	1.09600i	0.354208	+	0.935167i	$0.384750\pi$
$199$	−125.922	+	218.103i	−0.632774	+	1.09600i	−0.986982	+	0.160830i	$0.948583\pi$
$200$	19.0747	+	11.0128i	0.0953737	+	0.0550640i
$201$		0			0
$202$		−	60.3949i		−	0.298985i
$203$	−269.778	−	155.757i	−1.32896	−	0.767274i
$204$		0			0
$205$	−201.168	−	116.144i	−0.981306	−	0.566558i
$206$	19.9706	+	34.5902i	0.0969448	+	0.167913i
$207$		0			0
$208$		−	165.309i		−	0.794753i
$209$	−288.154	−	72.4822i	−1.37873	−	0.346805i
$210$		0			0
$211$	−143.105	+	82.6215i	−0.678221	+	0.391571i	−0.799184	−	0.601086i	$-0.794735\pi$
$211$	−143.105	+	82.6215i	−0.678221	+	0.391571i	0.120963	+	0.992657i	$0.461402\pi$
$212$	16.0996	−	9.29510i	0.0759414	−	0.0438448i
$213$		0			0
$214$	15.1705	+	26.2761i	0.0708904	+	0.122786i
$215$	−3.51450	+	6.08730i	−0.0163465	+	0.0283130i
$216$		0			0
$217$		−	305.637i		−	1.40847i
$218$	1.67388	−	2.89925i	0.00767836	−	0.0132993i
$219$		0			0
$220$	252.112			1.14596
$221$			381.817i			1.72768i
$222$		0			0
$223$	−178.604	+	103.117i	−0.800915	+	0.462408i	−0.843791	−	0.536672i	$-0.819681\pi$
$223$	−178.604	+	103.117i	−0.800915	+	0.462408i	0.0428761	+	0.999080i	$0.486348\pi$
$224$	−236.012	−	136.261i	−1.05362	−	0.608310i
$225$		0			0
$226$	−41.7847	−	72.3733i	−0.184888	−	0.320236i
$227$		−	329.381i		−	1.45102i	−0.688213	−	0.725509i	$-0.741605\pi$
$227$		−	329.381i		−	1.45102i	0.688213	−	0.725509i	$-0.258395\pi$
$228$		0			0
$229$	109.771			0.479351			0.239676	−	0.970853i	$-0.422959\pi$
$229$	109.771			0.479351			0.239676	+	0.970853i	$0.422959\pi$
$230$	22.0302	−	12.7191i	0.0957833	−	0.0553005i
$231$		0			0
$232$	80.1455	−	138.816i	0.345455	−	0.598345i
$233$	107.428	+	186.071i	0.461066	+	0.798589i	0.999014	−	0.0443883i	$-0.0141339\pi$
$233$	107.428	+	186.071i	0.461066	+	0.798589i	−0.537949	+	0.842978i	$0.680801\pi$
$234$		0			0
$235$	46.2900			0.196979
$236$		−	280.212i		−	1.18734i
$237$		0			0
$238$	143.252	+	82.7068i	0.601901	+	0.347507i
$239$	332.860			1.39272			0.696359	−	0.717694i	$-0.254802\pi$
$239$	332.860			1.39272			0.696359	+	0.717694i	$0.254802\pi$
$240$		0			0
$241$	−243.721	−	140.712i	−1.01129	−	0.583869i	−0.0997218	−	0.995015i	$-0.531795\pi$
$241$	−243.721	−	140.712i	−1.01129	−	0.583869i	−0.911569	+	0.411146i	$0.865129\pi$
$242$	72.0890	−	41.6206i	0.297889	−	0.171986i
$243$		0			0
$244$	−191.288	−	331.321i	−0.783968	−	1.35787i
$245$	−110.498	−	191.388i	−0.451013	−	0.781177i
$246$		0			0
$247$	−209.559	−	203.214i	−0.848418	−	0.822727i
$248$	157.267			0.634142
$249$		0			0
$250$	−77.8005	+	44.9181i	−0.311202	+	0.179672i
$251$	−203.986	+	353.314i	−0.812694	+	1.40763i	0.0982779	+	0.995159i	$0.468667\pi$
$251$	−203.986	+	353.314i	−0.812694	+	1.40763i	−0.910972	+	0.412468i	$0.864667\pi$
$252$		0			0
$253$	−64.9455	+	112.489i	−0.256701	+	0.444620i
$254$	77.7293			0.306021
$255$		0			0
$256$	−6.19708	+	10.7337i	−0.0242073	+	0.0419283i
$257$	−37.5180	−	21.6610i	−0.145984	−	0.0842841i	0.425229	−	0.905086i	$-0.360194\pi$
$257$	−37.5180	−	21.6610i	−0.145984	−	0.0842841i	−0.571213	+	0.820802i	$0.693527\pi$
$258$		0			0
$259$			171.144i			0.660788i
$260$	214.499	+	123.841i	0.824995	+	0.476311i
$261$		0			0
$262$	62.0576	+	35.8290i	0.236861	+	0.136752i
$263$	242.738	+	420.434i	0.922958	+	1.59861i	0.794813	+	0.606855i	$0.207569\pi$
$263$	242.738	+	420.434i	0.922958	+	1.59861i	0.128145	+	0.991755i	$0.459098\pi$
$264$		0			0
$265$			23.8326i			0.0899342i
$266$	−121.636	+	34.6048i	−0.457279	+	0.130093i
$267$		0			0
$268$	60.2289	−	34.7732i	0.224735	−	0.129751i
$269$	−335.484	+	193.692i	−1.24715	+	0.720044i	−0.970540	−	0.240938i	$-0.922545\pi$
$269$	−335.484	+	193.692i	−1.24715	+	0.720044i	−0.276612	+	0.960982i	$0.589212\pi$
$270$		0			0
$271$	173.258	+	300.091i	0.639328	+	1.10735i	0.985581	+	0.169207i	$0.0541206\pi$
$271$	173.258	+	300.091i	0.639328	+	1.10735i	−0.346253	+	0.938141i	$0.612546\pi$
$272$	133.701	−	231.576i	0.491546	−	0.851383i
$273$		0			0
$274$		−	79.4216i		−	0.289860i
$275$	33.8772	−	58.6771i	0.123190	−	0.213371i
$276$		0			0
$277$	−115.366			−0.416484			−0.208242	−	0.978077i	$-0.566774\pi$
$277$	−115.366			−0.416484			−0.208242	+	0.978077i	$0.566774\pi$
$278$		−	119.819i		−	0.431002i
$279$		0			0
$280$	197.746	−	114.169i	0.706237	−	0.407746i
$281$	377.987	+	218.231i	1.34515	+	0.776622i	0.987558	−	0.157257i	$-0.0502650\pi$
$281$	377.987	+	218.231i	1.34515	+	0.776622i	0.357591	+	0.933878i	$0.383598\pi$
$282$		0			0
$283$	217.321	+	376.411i	0.767919	+	1.33007i	0.938689	+	0.344764i	$0.112041\pi$
$283$	217.321	+	376.411i	0.767919	+	1.33007i	−0.170770	+	0.985311i	$0.554626\pi$
$284$			185.739i			0.654010i
$285$		0			0
$286$	161.862			0.565952
$287$	437.186	−	252.409i	1.52330	−	0.879475i
$288$		0			0
$289$	−164.312	+	284.596i	−0.568552	+	0.984761i
$290$	48.2833	+	83.6292i	0.166494	+	0.288376i
$291$		0			0
$292$	259.791			0.889695
$293$		−	297.624i		−	1.01578i	−0.861421	−	0.507891i	$-0.830425\pi$
$293$		−	297.624i		−	1.01578i	0.861421	−	0.507891i	$-0.169575\pi$
$294$		0			0
$295$	311.102	+	179.615i	1.05458	+	0.608865i
$296$	−88.0632			−0.297511
$297$		0			0
$298$	−104.853	−	60.5371i	−0.351857	−	0.203144i
$299$	−110.512	+	63.8042i	−0.369606	+	0.213392i
$300$		0			0
$301$	−7.63786	−	13.2292i	−0.0253749	−	0.0439507i
$302$	−75.8363	−	131.352i	−0.251114	−	0.434941i
$303$		0			0
$304$	55.9408	+	196.632i	0.184016	+	0.646817i
$305$	490.462			1.60807
$306$		0			0
$307$	69.6945	−	40.2381i	0.227018	−	0.131069i	−0.382178	−	0.924089i	$-0.624826\pi$
$307$	69.6945	−	40.2381i	0.227018	−	0.131069i	0.609196	+	0.793020i	$0.291492\pi$
$308$	−273.950	+	474.495i	−0.889447	+	1.54057i
$309$		0			0
$310$	−47.3725	+	82.0516i	−0.152815	+	0.264683i
$311$	120.522			0.387529			0.193765	−	0.981048i	$-0.437930\pi$
$311$	120.522			0.387529			0.193765	+	0.981048i	$0.437930\pi$
$312$		0			0
$313$	189.243	−	327.778i	0.604610	−	1.04721i	−0.387503	−	0.921868i	$-0.626662\pi$
$313$	189.243	−	327.778i	0.604610	−	1.04721i	0.992113	−	0.125346i	$-0.0400042\pi$
$314$	−15.7644	−	9.10159i	−0.0502052	−	0.0289860i
$315$		0			0
$316$		−	111.177i		−	0.351826i
$317$	−197.232	−	113.872i	−0.622182	−	0.359217i	0.155536	−	0.987830i	$-0.450290\pi$
$317$	−197.232	−	113.872i	−0.622182	−	0.359217i	−0.777718	+	0.628613i	$0.783623\pi$
$318$		0			0
$319$	−427.021	−	246.541i	−1.33862	−	0.772855i
$320$	−55.5907	−	96.2859i	−0.173721	−	0.300893i
$321$		0			0
$322$			55.2834i			0.171688i
$323$	−129.208	−	454.167i	−0.400024	−	1.40609i
$324$		0			0
$325$	57.6460	−	33.2819i	0.177372	−	0.102406i
$326$	−88.2203	+	50.9340i	−0.270614	+	0.156239i
$327$		0			0
$328$	129.879	+	224.957i	0.395972	+	0.685843i
$329$	−50.2997	+	87.1216i	−0.152887	+	0.264807i
$330$		0			0
$331$		−	398.204i		−	1.20303i	−0.798861	−	0.601516i	$-0.794564\pi$
$331$		−	398.204i		−	1.20303i	0.798861	−	0.601516i	$-0.205436\pi$
$332$	−75.6525	+	131.034i	−0.227869	+	0.394681i
$333$		0			0
$334$	−95.8842			−0.287079
$335$			89.1582i			0.266144i
$336$		0			0
$337$	556.961	−	321.561i	1.65270	−	0.954188i	0.676747	−	0.736216i	$-0.263389\pi$
$337$	556.961	−	321.561i	1.65270	−	0.954188i	0.975955	−	0.217972i	$-0.0699442\pi$
$338$	39.1139	+	22.5824i	0.115722	+	0.0668119i
$339$		0			0
$340$	200.323	+	346.970i	0.589186	+	1.02050i
$341$		−	483.780i		−	1.41871i
$342$		0			0
$343$	−3.83580			−0.0111831
$344$	6.80714	−	3.93010i	0.0197882	−	0.0114247i
$345$		0			0
$346$	−79.9075	+	138.404i	−0.230947	+	0.400011i
$347$	64.6475	+	111.973i	0.186304	+	0.322688i	0.944015	−	0.329902i	$-0.107016\pi$
$347$	64.6475	+	111.973i	0.186304	+	0.322688i	−0.757711	+	0.652590i	$0.773682\pi$
$348$		0			0
$349$	−10.4853			−0.0300438			−0.0150219	−	0.999887i	$-0.504782\pi$
$349$	−10.4853			−0.0300438			−0.0150219	+	0.999887i	$0.504782\pi$
$350$		−	28.8372i		−	0.0823921i
$351$		0			0
$352$	−373.573	−	215.683i	−1.06129	−	0.612735i
$353$	388.861			1.10159			0.550794	−	0.834641i	$-0.314325\pi$
$353$	388.861			1.10159			0.550794	+	0.834641i	$0.314325\pi$
$354$		0			0
$355$	−206.215	−	119.058i	−0.580887	−	0.335375i
$356$	407.166	−	235.077i	1.14372	−	0.660329i
$357$		0			0
$358$	0.620204	+	1.07422i	0.00173241	+	0.00300063i
$359$	142.019	+	245.985i	0.395597	+	0.685194i	0.993177	−	0.116615i	$-0.0372045\pi$
$359$	142.019	+	245.985i	0.395597	+	0.685194i	−0.597580	+	0.801809i	$0.703871\pi$
$360$		0			0
$361$	318.036	+	170.805i	0.880986	+	0.473143i
$362$	−24.0510			−0.0664393
$363$		0			0
$364$	−466.157	+	269.136i	−1.28065	+	0.739384i
$365$	−166.526	+	288.431i	−0.456234	+	0.790221i
$366$		0			0
$367$	81.5487	−	141.247i	0.222204	−	0.384868i	−0.733273	−	0.679934i	$-0.762008\pi$
$367$	81.5487	−	141.247i	0.222204	−	0.384868i	0.955477	+	0.295066i	$0.0953417\pi$
$368$	89.3690			0.242851
$369$		0			0
$370$	26.5267	−	45.9455i	0.0716937	−	0.124177i
$371$	−44.8548	−	25.8969i	−0.120902	−	0.0698031i
$372$		0			0
$373$			329.361i			0.883004i	0.897260	+	0.441502i	$0.145554\pi$
$373$			329.361i			0.883004i	−0.897260	+	0.441502i	$0.854446\pi$
$374$	226.748	+	130.913i	0.606279	+	0.350035i
$375$		0			0
$376$	−44.8289	−	25.8820i	−0.119226	−	0.0688351i
$377$	−242.209	−	419.518i	−0.642463	−	1.11278i
$378$		0			0
$379$			590.484i			1.55801i	0.627021	+	0.779003i	$0.284274\pi$
$379$			590.484i			1.55801i	−0.627021	+	0.779003i	$0.715726\pi$
$380$	−297.051	−	74.7202i	−0.781714	−	0.196632i
$381$		0			0
$382$	−97.0510	+	56.0324i	−0.254060	+	0.146682i
$383$	−417.346	+	240.955i	−1.08968	+	0.629125i	−0.933490	−	0.358602i	$-0.883253\pi$
$383$	−417.346	+	240.955i	−1.08968	+	0.629125i	−0.156187	+	0.987728i	$0.549920\pi$
$384$		0			0
$385$	−351.203	−	608.301i	−0.912215	−	1.58000i
$386$	58.5937	−	101.487i	0.151797	−	0.262921i
$387$		0			0
$388$		−	287.561i		−	0.741137i
$389$	86.5071	−	149.835i	0.222383	−	0.385179i	−0.733148	−	0.680069i	$-0.761950\pi$
$389$	86.5071	−	149.835i	0.222383	−	0.385179i	0.955531	+	0.294890i	$0.0952830\pi$
$390$		0			0
$391$	−206.418			−0.527923
$392$			247.130i			0.630433i
$393$		0			0
$394$	50.5039	−	29.1584i	0.128182	−	0.0740061i
$395$	123.433	+	71.2642i	0.312489	+	0.180416i
$396$		0			0
$397$	−80.0448	−	138.642i	−0.201624	−	0.349223i	0.747428	−	0.664343i	$-0.231289\pi$
$397$	−80.0448	−	138.642i	−0.201624	−	0.349223i	−0.949052	+	0.315120i	$0.897955\pi$
$398$			169.664i			0.426292i
$399$		0			0
$400$	−46.6172			−0.116543
$401$	−83.3196	+	48.1046i	−0.207780	+	0.119962i	−0.600279	−	0.799791i	$-0.704944\pi$
$401$	−83.3196	+	48.1046i	−0.207780	+	0.119962i	0.392499	+	0.919752i	$0.371610\pi$
$402$		0			0
$403$	237.640	−	411.604i	0.589677	−	1.02135i
$404$	158.953	+	275.315i	0.393448	+	0.681472i
$405$		0			0
$406$	−209.862			−0.516903
$407$			270.897i			0.665595i
$408$		0			0
$409$	−472.302	−	272.684i	−1.15477	−	0.666709i	−0.204728	−	0.978819i	$-0.565631\pi$
$409$	−472.302	−	272.684i	−1.15477	−	0.666709i	−0.950046	+	0.312110i	$0.898964\pi$
$410$	−156.490			−0.381683
$411$		0			0
$412$	−182.075	−	105.121i	−0.441930	−	0.255149i
$413$	−676.100	+	390.347i	−1.63705	+	0.945149i
$414$		0			0
$415$	−96.9862	−	167.985i	−0.233702	−	0.404783i
$416$	−211.893	−	367.009i	−0.509357	−	0.882233i
$417$		0			0
$418$	−192.533	+	54.7745i	−0.460605	+	0.131039i
$419$	−81.4631			−0.194423			−0.0972114	−	0.995264i	$-0.530992\pi$
$419$	−81.4631			−0.194423			−0.0972114	+	0.995264i	$0.530992\pi$
$420$		0			0
$421$	326.092	−	188.269i	0.774565	−	0.447196i	−0.0599354	−	0.998202i	$-0.519089\pi$
$421$	326.092	−	188.269i	0.774565	−	0.447196i	0.834501	+	0.551007i	$0.185756\pi$
$422$	−55.6610	+	96.4077i	−0.131898	+	0.228454i
$423$		0			0
$424$	13.3254	−	23.0803i	0.0314279	−	0.0544347i
$425$	107.673			0.253348
$426$		0			0
$427$	−532.945	+	923.089i	−1.24812	+	2.16180i
$428$	−138.312	−	79.8545i	−0.323159	−	0.186576i
$429$		0			0
$430$			4.73535i			0.0110124i
$431$	−504.983	−	291.552i	−1.17165	−	0.676454i	−0.217584	−	0.976042i	$-0.569818\pi$
$431$	−504.983	−	291.552i	−1.17165	−	0.676454i	−0.954069	+	0.299587i	$0.903151\pi$
$432$		0			0
$433$	552.877	+	319.204i	1.27685	+	0.737191i	0.976268	−	0.216564i	$-0.0694849\pi$
$433$	552.877	+	319.204i	1.27685	+	0.737191i	0.300585	+	0.953755i	$0.402818\pi$
$434$	−102.952	−	178.318i	−0.237216	−	0.410871i
$435$		0			0
$436$			17.6219i			0.0404173i
$437$	109.861	−	113.292i	0.251399	−	0.259249i
$438$		0			0
$439$	267.855	−	154.646i	0.610148	−	0.352269i	−0.162875	−	0.986647i	$-0.552077\pi$
$439$	267.855	−	154.646i	0.610148	−	0.352269i	0.773023	+	0.634378i	$0.218744\pi$
$440$	313.005	−	180.713i	0.711374	−	0.410712i
$441$		0			0
$442$	128.613	+	222.764i	0.290979	+	0.503990i
$443$	76.4634	−	132.438i	0.172604	−	0.298958i	−0.766726	−	0.641975i	$-0.778115\pi$
$443$	76.4634	−	132.438i	0.172604	−	0.298958i	0.939329	+	0.343017i	$0.111449\pi$
$444$		0			0
$445$			602.736i			1.35446i
$446$	−69.4686	+	120.323i	−0.155759	+	0.269783i
$447$		0			0
$448$	241.624			0.539339
$449$		−	128.150i		−	0.285413i	−0.989765	−	0.142706i	$-0.954420\pi$
$449$		−	128.150i		−	0.285413i	0.989765	−	0.142706i	$-0.0455805\pi$
$450$		0			0
$451$	692.004	−	399.529i	1.53438	−	0.885873i
$452$	380.958	+	219.946i	0.842827	+	0.486606i
$453$		0			0
$454$	−110.950	−	192.171i	−0.244383	−	0.423284i
$455$		−	690.062i		−	1.51662i
$456$		0			0
$457$	338.690			0.741117			0.370558	−	0.928809i	$-0.379166\pi$
$457$	338.690			0.741117			0.370558	+	0.928809i	$0.379166\pi$
$458$	64.0440	−	36.9758i	0.139834	−	0.0807332i
$459$		0			0
$460$	−66.9508	+	115.962i	−0.145545	+	0.252092i
$461$	−262.476	−	454.623i	−0.569363	−	0.986166i	−0.996629	−	0.0820401i	$-0.973856\pi$
$461$	−262.476	−	454.623i	−0.569363	−	0.986166i	0.427266	−	0.904126i	$-0.359477\pi$
$462$		0			0
$463$	107.360			0.231879			0.115940	−	0.993256i	$-0.463012\pi$
$463$	107.360			0.231879			0.115940	+	0.993256i	$0.463012\pi$
$464$			339.256i			0.731154i
$465$		0			0
$466$	125.354	+	72.3731i	0.269000	+	0.155307i
$467$	−60.2392			−0.128992			−0.0644959	−	0.997918i	$-0.520544\pi$
$467$	−60.2392			−0.128992			−0.0644959	+	0.997918i	$0.520544\pi$
$468$		0			0
$469$	−167.803	−	96.8811i	−0.357789	−	0.206569i
$470$	27.0070	−	15.5925i	0.0574617	−	0.0331755i
$471$		0			0
$472$	−200.855	−	347.891i	−0.425540	−	0.737058i
$473$	−12.0897	−	20.9399i	−0.0255595	−	0.0442704i
$474$		0			0
$475$	−57.3064	+	59.0959i	−0.120645	+	0.124412i
$476$	−870.702			−1.82921
$477$		0			0
$478$	194.200	−	112.122i	0.406277	−	0.234564i
$479$	−38.8318	+	67.2586i	−0.0810684	+	0.140415i	−0.903709	−	0.428147i	$-0.859167\pi$
$479$	−38.8318	+	67.2586i	−0.0810684	+	0.140415i	0.822641	+	0.568562i	$0.192500\pi$
$480$		0			0
$481$	−133.068	+	230.481i	−0.276650	+	0.479171i
$482$	−189.592			−0.393345
$483$		0			0
$484$	−219.082	+	379.461i	−0.452649	+	0.784011i
$485$	319.262	+	184.326i	0.658272	+	0.380054i
$486$		0			0
$487$			248.267i			0.509789i	0.966969	+	0.254895i	$0.0820408\pi$
$487$			248.267i			0.509789i	−0.966969	+	0.254895i	$0.917959\pi$
$488$	−474.980	−	274.230i	−0.973320	−	0.561947i
$489$		0			0
$490$	−128.936	−	74.4411i	−0.263134	−	0.151921i
$491$	176.358	+	305.461i	0.359182	+	0.622121i	0.987824	−	0.155573i	$-0.0497225\pi$
$491$	176.358	+	305.461i	0.359182	+	0.622121i	−0.628643	+	0.777694i	$0.716389\pi$
$492$		0			0
$493$		−	783.587i		−	1.58943i
$494$	−190.714	−	47.9723i	−0.386062	−	0.0971099i
$495$		0			0
$496$	−288.262	+	166.428i	−0.581173	+	0.335540i
$497$	448.155	−	258.742i	0.901720	−	0.520608i
$498$		0			0
$499$	103.370	+	179.043i	0.207155	+	0.358803i	0.950817	−	0.309753i	$-0.100246\pi$
$499$	103.370	+	179.043i	0.207155	+	0.358803i	−0.743662	+	0.668555i	$0.766913\pi$
$500$	236.439	−	409.525i	0.472879	−	0.819050i
$501$		0			0
$502$			274.846i			0.547501i
$503$	−292.748	+	507.055i	−0.582005	+	1.00806i	0.413237	+	0.910624i	$0.364398\pi$
$503$	−292.748	+	507.055i	−0.582005	+	1.00806i	−0.995242	+	0.0974382i	$0.968935\pi$
$504$		0			0
$505$	−407.555			−0.807039
$506$			87.5059i			0.172936i
$507$		0			0
$508$	−354.335	+	204.575i	−0.697510	+	0.402707i
$509$	−436.147	−	251.810i	−0.856870	−	0.494714i	0.00609272	−	0.999981i	$-0.498061\pi$
$509$	−436.147	−	251.810i	−0.856870	−	0.494714i	−0.862963	+	0.505267i	$0.831394\pi$
$510$		0			0
$511$	−361.900	−	626.829i	−0.708219	−	1.22667i
$512$			515.592i			1.00701i
$513$		0			0
$514$	−29.1855			−0.0567811
$515$	233.420	−	134.765i	0.453242	−	0.261680i
$516$		0			0
$517$	−79.6173	+	137.901i	−0.153999	+	0.266734i
$518$	57.6488	+	99.8507i	0.111291	+	0.192762i
$519$		0			0
$520$	355.076			0.682838
$521$			622.860i			1.19551i	0.801679	+	0.597754i	$0.203940\pi$
$521$			622.860i			1.19551i	−0.801679	+	0.597754i	$0.796060\pi$
$522$		0			0
$523$	197.688	+	114.136i	0.377989	+	0.218232i	0.676943	−	0.736035i	$-0.263304\pi$
$523$	197.688	+	114.136i	0.377989	+	0.218232i	−0.298954	+	0.954268i	$0.596638\pi$
$524$	−377.192			−0.719833
$525$		0			0
$526$	283.241	+	163.529i	0.538481	+	0.310892i
$527$	665.805	−	384.403i	1.26339	−	0.729417i
$528$		0			0
$529$	230.006	+	398.382i	0.434794	+	0.753086i
$530$	8.02784	+	13.9046i	0.0151469	+	0.0262352i
$531$		0			0
$532$	463.411	−	477.882i	0.871074	−	0.898274i
$533$	785.016			1.47283
$534$		0			0
$535$	177.316	−	102.373i	0.331431	−	0.191352i
$536$	49.8507	−	86.3440i	0.0930051	−	0.161089i
$537$		0			0
$538$	−130.488	+	226.011i	−0.242542	+	0.420095i
$539$	760.212			1.41041
$540$		0			0
$541$	156.080	−	270.338i	0.288502	−	0.499701i	−0.684950	−	0.728590i	$-0.740176\pi$
$541$	156.080	−	270.338i	0.288502	−	0.499701i	0.973452	+	0.228889i	$0.0735094\pi$
$542$	202.168	+	116.722i	0.373003	+	0.215353i
$543$		0			0
$544$		−	685.510i		−	1.26013i
$545$	−19.5646	−	11.2956i	−0.0358983	−	0.0207259i
$546$		0			0
$547$	−588.922	−	340.015i	−1.07664	−	0.621599i	−0.146652	−	0.989188i	$-0.546850\pi$
$547$	−588.922	−	340.015i	−1.07664	−	0.621599i	−0.929988	+	0.367589i	$0.880183\pi$
$548$	209.029	+	362.049i	0.381440	+	0.660674i
$549$		0			0
$550$		−	45.6453i		−	0.0829915i
$551$	430.069	+	417.046i	0.780525	+	0.756890i
$552$		0			0
$553$	−268.250	+	154.874i	−0.485082	+	0.280062i
$554$	−67.3080	+	38.8603i	−0.121495	+	0.0701450i
$555$		0			0
$556$	315.350	+	546.202i	0.567176	+	0.982378i
$557$	452.880	−	784.411i	0.813070	−	1.40828i	−0.0976363	−	0.995222i	$-0.531128\pi$
$557$	452.880	−	784.411i	0.813070	−	1.40828i	0.910706	−	0.413056i	$-0.135538\pi$
$558$		0			0
$559$		−	23.7544i		−	0.0424945i
$560$	−241.638	+	418.530i	−0.431497	+	0.747375i
$561$		0			0
$562$	294.038			0.523200
$563$			190.842i			0.338974i	0.985532	+	0.169487i	$0.0542110\pi$
$563$			190.842i			0.338974i	−0.985532	+	0.169487i	$0.945789\pi$
$564$		0			0
$565$	−488.386	+	281.970i	−0.864401	+	0.499062i
$566$	253.583	+	146.406i	0.448027	+	0.258669i
$567$		0			0
$568$	133.137	+	230.601i	0.234397	+	0.405987i
$569$			283.587i			0.498396i	0.968453	+	0.249198i	$0.0801669\pi$
$569$			283.587i			0.498396i	−0.968453	+	0.249198i	$0.919833\pi$
$570$		0			0
$571$	−147.076			−0.257576			−0.128788	−	0.991672i	$-0.541109\pi$
$571$	−147.076			−0.257576			−0.128788	+	0.991672i	$0.541109\pi$
$572$	−737.861	+	426.004i	−1.28997	+	0.744763i
$573$		0			0
$574$	170.045	−	294.527i	0.296246	−	0.513112i
$575$	17.9929	+	31.1645i	0.0312919	+	0.0541992i
$576$		0			0
$577$	270.982			0.469639			0.234819	−	0.972039i	$-0.424550\pi$
$577$	270.982			0.469639			0.234819	+	0.972039i	$0.424550\pi$
$578$			221.389i			0.383026i
$579$		0			0
$580$	−440.206	−	254.153i	−0.758976	−	0.438195i
$581$	421.549			0.725557
$582$		0			0
$583$	−70.9988	−	40.9912i	−0.121782	−	0.0703108i
$584$	322.539	−	186.218i	0.552292	−	0.318866i
$585$		0			0
$586$	−100.253	−	173.643i	−0.171080	−	0.296319i
$587$	−83.4124	−	144.475i	−0.142100	−	0.246124i	0.786188	−	0.617988i	$-0.212052\pi$
$587$	−83.4124	−	144.475i	−0.142100	−	0.246124i	−0.928287	+	0.371864i	$0.878719\pi$
$588$		0			0
$589$	−143.382	+	570.015i	−0.243432	+	0.967767i
$590$	242.009			0.410184
$591$		0			0
$592$	161.415	−	93.1928i	0.272660	−	0.157420i
$593$	153.105	−	265.186i	0.258188	−	0.447194i	−0.707569	−	0.706644i	$-0.750208\pi$
$593$	153.105	−	265.186i	0.258188	−	0.447194i	0.965756	+	0.259450i	$0.0835414\pi$
$594$		0			0
$595$	558.118	−	966.689i	0.938014	−	1.62469i
$596$	637.308			1.06931
$597$		0			0
$598$	−42.9841	+	74.4506i	−0.0718797	+	0.124499i
$599$	40.3854	+	23.3165i	0.0674213	+	0.0389257i	0.533332	−	0.845906i	$-0.320940\pi$
$599$	40.3854	+	23.3165i	0.0674213	+	0.0389257i	−0.465910	+	0.884832i	$0.654273\pi$
$600$		0			0
$601$		−	47.7571i		−	0.0794627i	−0.999210	−	0.0397314i	$-0.987350\pi$
$601$		−	47.7571i		−	0.0794627i	0.999210	−	0.0397314i	$-0.0126502\pi$
$602$	−8.91231	−	5.14553i	−0.0148045	−	0.00854738i
$603$		0			0
$604$	691.411	+	399.186i	1.14472	+	0.660904i
$605$	−280.863	−	486.468i	−0.464236	−	0.804080i
$606$		0			0
$607$		−	304.461i		−	0.501583i	−0.968041	−	0.250792i	$-0.919309\pi$
$607$		−	304.461i		−	0.501583i	0.968041	−	0.250792i	$-0.0806909\pi$
$608$	376.240	+	364.847i	0.618816	+	0.600077i
$609$		0			0
$610$	286.150	−	165.209i	0.469098	−	0.270834i
$611$	−135.478	+	78.2183i	−0.221732	+	0.128017i
$612$		0			0
$613$	−411.325	−	712.436i	−0.671004	−	1.16221i	−0.977620	−	0.210379i	$-0.932530\pi$
$613$	−411.325	−	712.436i	−0.671004	−	1.16221i	0.306616	−	0.951833i	$-0.400803\pi$
$614$	27.1079	−	46.9523i	0.0441497	−	0.0764695i
$615$		0			0
$616$			785.467i			1.27511i
$617$	279.527	−	484.154i	0.453042	−	0.784691i	−0.545532	−	0.838090i	$-0.683672\pi$
$617$	279.527	−	484.154i	0.453042	−	0.784691i	0.998573	+	0.0533993i	$0.0170056\pi$
$618$		0			0
$619$	582.672			0.941311			0.470656	−	0.882317i	$-0.344017\pi$
$619$	582.672			0.941311			0.470656	+	0.882317i	$0.344017\pi$
$620$		−	498.718i		−	0.804384i
$621$		0			0
$622$	70.3160	−	40.5969i	0.113048	−	0.0652684i
$623$	−1134.40	−	654.945i	−1.82086	−	1.05128i
$624$		0			0
$625$	248.957	+	431.207i	0.398332	+	0.689931i
$626$		−	254.981i		−	0.407318i
$627$		0			0
$628$	95.8177			0.152576
$629$	−372.824	+	215.250i	−0.592724	+	0.342210i
$630$		0			0
$631$	−421.987	+	730.904i	−0.668760	+	1.15833i	0.309492	+	0.950902i	$0.399841\pi$
$631$	−421.987	+	730.904i	−0.668760	+	1.15833i	−0.978251	+	0.207424i	$0.933492\pi$
$632$	−79.6915	−	138.030i	−0.126094	−	0.218401i
$633$		0			0
$634$	−153.428			−0.242000
$635$		−	524.530i		−	0.826031i
$636$		0			0
$637$	646.794	+	373.427i	1.01538	+	0.586227i
$638$	−332.183			−0.520663
$639$		0			0
$640$	−499.263	−	288.249i	−0.780098	−	0.450390i
$641$	−386.782	+	223.309i	−0.603404	+	0.348375i	−0.770380	−	0.637586i	$-0.779933\pi$
$641$	−386.782	+	223.309i	−0.603404	+	0.348375i	0.166976	+	0.985961i	$0.446600\pi$
$642$		0			0
$643$	502.768	+	870.820i	0.781910	+	1.35431i	0.930828	+	0.365458i	$0.119088\pi$
$643$	502.768	+	870.820i	0.781910	+	1.35431i	−0.148918	+	0.988850i	$0.547579\pi$
$644$	−145.500	−	252.014i	−0.225932	−	0.391325i
$645$		0			0
$646$	−228.367	−	221.452i	−0.353509	−	0.342804i
$647$	189.919			0.293538			0.146769	−	0.989171i	$-0.453113\pi$
$647$	189.919			0.293538			0.146769	+	0.989171i	$0.453113\pi$
$648$		0			0
$649$	−1070.17	+	617.864i	−1.64895	+	0.952024i
$650$	22.4216	−	38.8354i	0.0344948	−	0.0597467i
$651$		0			0
$652$	268.106	−	464.373i	0.411205	−	0.712228i
$653$	−1018.29			−1.55940			−0.779700	−	0.626153i	$-0.784629\pi$
$653$	−1018.29			−1.55940			−0.779700	+	0.626153i	$0.784629\pi$
$654$		0			0
$655$	241.780	−	418.775i	0.369129	−	0.639350i
$656$	−476.120	−	274.888i	−0.725793	−	0.419037i
$657$		0			0
$658$			67.7725i			0.102998i
$659$	979.725	+	565.644i	1.48668	+	0.858338i	0.999885	−	0.0151763i	$-0.00483095\pi$
$659$	979.725	+	565.644i	1.48668	+	0.858338i	0.486799	+	0.873514i	$0.338164\pi$
$660$		0			0
$661$	105.628	+	60.9841i	0.159800	+	0.0922604i	0.577767	−	0.816202i	$-0.303924\pi$
$661$	105.628	+	60.9841i	0.159800	+	0.0922604i	−0.417968	+	0.908462i	$0.637257\pi$
$662$	−134.132	−	232.324i	−0.202617	−	0.350943i
$663$		0			0
$664$			216.910i			0.326672i
$665$	233.519	+	820.820i	0.351156	+	1.23432i
$666$		0			0
$667$	226.799	−	130.943i	0.340029	−	0.196316i
$668$	437.095	−	252.357i	0.654334	−	0.377780i
$669$		0			0
$670$	30.0324	+	52.0176i	0.0448244	+	0.0776382i
$671$	−843.578	+	1461.12i	−1.25719	+	2.17752i
$672$		0			0
$673$		−	353.592i		−	0.525397i	−0.964878	−	0.262699i	$-0.915387\pi$
$673$		−	353.592i		−	0.525397i	0.964878	−	0.262699i	$-0.0846125\pi$
$674$	216.632	−	375.217i	0.321412	−	0.556702i
$675$		0			0
$676$	−237.738			−0.351684
$677$			333.896i			0.493199i	0.969118	+	0.246599i	$0.0793132\pi$
$677$			333.896i			0.493199i	−0.969118	+	0.246599i	$0.920687\pi$
$678$		0			0
$679$	−693.833	+	400.585i	−1.02185	+	0.589963i
$680$	497.415	+	287.183i	0.731493	+	0.422328i
$681$		0			0
$682$	−162.958	−	282.252i	−0.238942	−	0.413859i
$683$		−	160.520i		−	0.235022i	−0.993072	−	0.117511i	$-0.962509\pi$
$683$		−	160.520i		−	0.235022i	0.993072	−	0.117511i	$-0.0374915\pi$
$684$		0			0
$685$	−535.949			−0.782408
$686$	−2.23792	+	1.29206i	−0.00326227	+	0.00188347i
$687$		0			0
$688$	−8.31806	+	14.4073i	−0.0120902	+	0.0209408i
$689$	−40.2709	−	69.7512i	−0.0584483	−	0.101235i
$690$		0			0
$691$	−417.343			−0.603969			−0.301985	−	0.953313i	$-0.597649\pi$
$691$	−417.343			−0.603969			−0.301985	+	0.953313i	$0.597649\pi$
$692$		−	841.232i		−	1.21565i
$693$		0			0
$694$	75.4346	+	43.5522i	0.108695	+	0.0627553i
$695$	−808.555			−1.16339
$696$		0			0
$697$	1099.71	+	634.916i	1.57777	+	0.910927i
$698$	−6.11743	+	3.53190i	−0.00876423	+	0.00506003i
$699$		0			0
$700$	75.8966	+	131.457i	0.108424	+	0.187795i
$701$	546.106	+	945.883i	0.779039	+	1.34933i	0.932496	+	0.361179i	$0.117626\pi$
$701$	546.106	+	945.883i	0.779039	+	1.34933i	−0.153458	+	0.988155i	$0.549041\pi$
$702$		0			0
$703$	80.2877	−	319.185i	0.114207	−	0.454033i
$704$	382.456			0.543262
$705$		0			0
$706$	226.873	−	130.985i	0.321350	−	0.185532i
$707$	442.857	−	767.051i	0.626389	−	1.08494i
$708$		0			0
$709$	255.378	−	442.327i	0.360194	−	0.623875i	−0.627798	−	0.778376i	$-0.716044\pi$
$709$	255.378	−	442.327i	0.360194	−	0.623875i	0.987993	+	0.154501i	$0.0493771\pi$
$710$	−160.416			−0.225938
$711$		0			0
$712$	337.006	−	583.711i	0.473323	−	0.819819i
$713$	222.521	+	128.473i	0.312091	+	0.180186i
$714$		0			0
$715$		−	1092.27i		−	1.52765i
$716$	−5.65449	−	3.26462i	−0.00789733	−	0.00455952i
$717$		0			0
$718$	165.717	+	95.6765i	0.230803	+	0.133254i
$719$	−143.484	−	248.522i	−0.199561	−	0.345649i	0.748825	−	0.662767i	$-0.230618\pi$
$719$	−143.484	−	248.522i	−0.199561	−	0.345649i	−0.948386	+	0.317118i	$0.897285\pi$
$720$		0			0
$721$			585.753i			0.812418i
$722$	243.086	−	7.47577i	0.336684	−	0.0103543i
$723$		0			0
$724$	109.638	−	63.2998i	0.151434	−	0.0874306i
$725$	−118.304	+	68.3030i	−0.163178	+	0.0942111i
$726$		0			0
$727$	−358.442	−	620.840i	−0.493043	−	0.853975i	0.506925	−	0.861990i	$-0.330782\pi$
$727$	−358.442	−	620.840i	−0.493043	−	0.853975i	−0.999968	+	0.00801511i	$0.997449\pi$
$728$	−385.832	+	668.281i	−0.529989	+	0.917968i
$729$		0			0
$730$			224.372i			0.307359i
$731$	19.2124	−	33.2769i	0.0262824	−	0.0455224i
$732$		0			0
$733$	−534.712			−0.729484			−0.364742	−	0.931109i	$-0.618843\pi$
$733$	−534.712			−0.729484			−0.364742	+	0.931109i	$0.618843\pi$
$734$		−	109.877i		−	0.149696i
$735$		0			0
$736$	198.412	−	114.553i	0.269582	−	0.155643i
$737$	−265.608	−	153.349i	−0.360391	−	0.208072i
$738$		0			0
$739$	337.022	+	583.739i	0.456051	+	0.789904i	0.998748	−	0.0500248i	$-0.0159300\pi$
$739$	337.022	+	583.739i	0.456051	+	0.789904i	−0.542697	+	0.839929i	$0.682597\pi$
$740$			279.261i			0.377380i
$741$		0			0
$742$	−34.8929			−0.0470254
$743$	794.193	−	458.527i	1.06890	−	0.617130i	0.141019	−	0.990007i	$-0.454962\pi$
$743$	794.193	−	458.527i	1.06890	−	0.617130i	0.927881	+	0.372877i	$0.121629\pi$
$744$		0			0
$745$	−408.514	+	707.566i	−0.548340	+	0.949753i
$746$	110.943	+	192.159i	0.148717	+	0.257586i
$747$		0			0
$748$	−1378.20			−1.84251
$749$			444.963i			0.594076i
$750$		0			0
$751$	−387.655	−	223.813i	−0.516185	−	0.298019i	0.219188	−	0.975683i	$-0.429659\pi$
$751$	−387.655	−	223.813i	−0.516185	−	0.298019i	−0.735372	+	0.677663i	$0.762993\pi$
$752$	109.558			0.145689
$753$		0			0
$754$	−282.624	−	163.173i	−0.374832	−	0.216410i
$755$	−886.386	+	511.755i	−1.17402	+	0.677821i
$756$		0			0
$757$	−118.319	−	204.934i	−0.156299	−	0.270718i	0.777232	−	0.629214i	$-0.216623\pi$
$757$	−118.319	−	204.934i	−0.156299	−	0.270718i	−0.933531	+	0.358496i	$0.883290\pi$
$758$	198.901	+	344.506i	0.262402	+	0.454494i
$759$		0			0
$760$	−422.357	+	120.158i	−0.555734	+	0.158103i
$761$	213.593			0.280674			0.140337	−	0.990104i	$-0.455181\pi$
$761$	213.593			0.280674			0.140337	+	0.990104i	$0.455181\pi$
$762$		0			0
$763$	42.5186	−	24.5481i	0.0557255	−	0.0321731i
$764$	294.943	−	510.856i	0.386051	−	0.668660i
$765$		0			0
$766$	−162.328	+	281.161i	−0.211917	+	0.367051i
$767$	−1214.01			−1.58281
$768$		0			0
$769$	442.292	−	766.072i	0.575152	−	0.996192i	−0.420873	−	0.907119i	$-0.638276\pi$
$769$	442.292	−	766.072i	0.575152	−	0.996192i	0.996025	−	0.0890727i	$-0.0283903\pi$
$770$	−409.804	−	236.601i	−0.532214	−	0.307274i
$771$		0			0
$772$			616.850i			0.799029i
$773$	−1110.22	−	640.988i	−1.43625	−	0.829222i	−0.438667	−	0.898650i	$-0.644549\pi$
$773$	−1110.22	−	640.988i	−1.43625	−	0.829222i	−0.997587	+	0.0694281i	$0.977883\pi$
$774$		0			0
$775$	−116.073	−	67.0146i	−0.149771	−	0.0864705i
$776$	−206.123	−	357.016i	−0.265623	−	0.460072i
$777$		0			0
$778$		−	116.557i		−	0.149817i
$779$	−933.766	+	265.651i	−1.19867	+	0.341015i
$780$		0			0
$781$	709.366	−	409.553i	0.908279	−	0.524395i
$782$	−120.430	+	69.5305i	−0.154003	+	0.0889137i
$783$		0			0
$784$	−261.525	−	452.974i	−0.333577	−	0.577773i
$785$	−61.4190	+	106.381i	−0.0782407	+	0.135517i
$786$		0			0
$787$		−	282.196i		−	0.358572i	−0.983797	−	0.179286i	$-0.942621\pi$
$787$		−	282.196i		−	0.358572i	0.983797	−	0.179286i	$-0.0573787\pi$
$788$	−153.484	+	265.842i	−0.194776	+	0.337362i
$789$		0			0
$790$	96.0196			0.121544
$791$		−	1225.58i		−	1.54940i
$792$		0			0
$793$	−1435.44	+	828.754i	−1.81014	+	1.04509i
$794$	−93.4011	−	53.9251i	−0.117634	−	0.0679158i
$795$		0			0
$796$	−446.538	−	773.426i	−0.560977	−	0.971641i
$797$			1021.78i			1.28203i	0.767527	+	0.641016i	$0.221487\pi$
$797$			1021.78i			1.28203i	−0.767527	+	0.641016i	$0.778513\pi$
$798$		0			0
$799$	−253.050			−0.316708
$800$	−103.497	+	59.7539i	−0.129371	+	0.0746924i
$801$		0			0
$802$	−32.4074	+	56.1313i	−0.0404083	+	0.0699892i
$803$	−572.837	−	992.183i	−0.713371	−	1.23559i
$804$		0			0
$805$	373.061			0.463430
$806$		−	320.190i		−	0.397258i
$807$		0			0
$808$	394.690	+	227.875i	0.488478	+	0.282023i
$809$	6.57043			0.00812167			0.00406083	−	0.999992i	$-0.498707\pi$
$809$	6.57043			0.00812167			0.00406083	+	0.999992i	$0.498707\pi$
$810$		0			0
$811$	127.276	+	73.4831i	0.156938	+	0.0906080i	0.576412	−	0.817159i	$-0.304452\pi$
$811$	127.276	+	73.4831i	0.156938	+	0.0906080i	−0.419474	+	0.907767i	$0.637786\pi$
$812$	956.674	−	552.336i	1.17817	−	0.680216i
$813$		0			0
$814$	91.2499	+	158.050i	0.112101	+	0.194164i
$815$	343.711	+	595.324i	0.421731	+	0.730459i
$816$		0			0
$817$	8.03854	+	28.2556i	0.00983910	+	0.0345845i
$818$	−367.407			−0.449153
$819$		0			0
$820$	713.370	−	411.865i	0.869964	−	0.502274i
$821$	120.857	−	209.330i	0.147206	−	0.254969i	−0.782987	−	0.622037i	$-0.786305\pi$
$821$	120.857	−	209.330i	0.147206	−	0.254969i	0.930194	+	0.367068i	$0.119638\pi$
$822$		0			0
$823$	−148.726	+	257.601i	−0.180712	+	0.313003i	−0.942123	−	0.335267i	$-0.891174\pi$
$823$	−148.726	+	257.601i	−0.180712	+	0.313003i	0.761411	+	0.648269i	$0.224507\pi$
$824$	−301.403			−0.365780
$825$		0			0
$826$	−262.972	+	455.480i	−0.318367	+	0.551429i
$827$	587.474	+	339.179i	0.710368	+	0.410131i	0.811197	−	0.584773i	$-0.198816\pi$
$827$	587.474	+	339.179i	0.710368	+	0.410131i	−0.100829	+	0.994904i	$0.532150\pi$
$828$		0			0
$829$			924.892i			1.11567i	0.829951	+	0.557836i	$0.188368\pi$
$829$			924.892i			1.11567i	−0.829951	+	0.557836i	$0.811632\pi$
$830$	−113.169	−	65.3384i	−0.136349	−	0.0787209i
$831$		0			0
$832$	325.397	+	187.868i	0.391102	+	0.225803i
$833$	604.050	+	1046.25i	0.725150	+	1.25600i
$834$		0			0
$835$			647.042i			0.774900i
$836$	733.515	−	756.420i	0.877410	−	0.904808i
$837$		0			0
$838$	−47.5281	+	27.4403i	−0.0567161	+	0.0327450i
$839$	−294.467	+	170.011i	−0.350974	+	0.202635i	−0.665114	−	0.746742i	$-0.731617\pi$
$839$	−294.467	+	170.011i	−0.350974	+	0.202635i	0.314140	+	0.949377i	$0.398284\pi$
$840$		0			0
$841$	76.5740	+	132.630i	0.0910511	+	0.157705i
$842$	126.835	−	219.684i	0.150635	−	0.260907i
$843$		0			0
$844$		−	585.976i		−	0.694284i
$845$	152.390	−	263.947i	0.180343	−	0.312363i
$846$		0			0
$847$	1220.76			1.44128
$848$			56.4064i			0.0665170i
$849$		0			0
$850$	62.8196	−	36.2689i	0.0739054	−	0.0426693i
$851$	−124.603	−	71.9394i	−0.146419	−	0.0845351i
$852$		0			0
$853$	−436.122	−	755.386i	−0.511280	−	0.885564i	−0.999915	−	0.0130749i	$-0.995838\pi$
$853$	−436.122	−	755.386i	−0.511280	−	0.885564i	0.488634	−	0.872489i	$-0.337495\pi$
$854$			718.077i			0.840839i
$855$		0			0
$856$	−228.958			−0.267475
$857$	429.491	−	247.967i	0.501156	−	0.289343i	−0.228035	−	0.973653i	$-0.573230\pi$
$857$	429.491	−	247.967i	0.501156	−	0.289343i	0.729191	+	0.684310i	$0.239897\pi$
$858$		0			0
$859$	707.860	−	1226.05i	0.824051	−	1.42730i	−0.0785919	−	0.996907i	$-0.525042\pi$
$859$	707.860	−	1226.05i	0.824051	−	1.42730i	0.902643	−	0.430391i	$-0.141624\pi$
$860$	−12.4629	−	21.5864i	−0.0144918	−	0.0251005i
$861$		0			0
$862$	−392.829			−0.455719
$863$		−	1132.56i		−	1.31236i	−0.754605	−	0.656179i	$-0.772172\pi$
$863$		−	1132.56i		−	1.31236i	0.754605	−	0.656179i	$-0.227828\pi$
$864$		0			0
$865$	933.971	+	539.228i	1.07974	+	0.623385i
$866$	430.087			0.496636
$867$		0			0
$868$	938.627	+	541.917i	1.08137	+	0.624328i
$869$	−424.602	+	245.144i	−0.488610	+	0.282099i
$870$		0			0
$871$	−150.654	−	260.941i	−0.172967	−	0.299588i
$872$	12.6314	+	21.8782i	0.0144855	+	0.0250896i
$873$		0			0
$874$	25.9347	−	103.104i	0.0296736	−	0.117968i
$875$	−1317.48			−1.50569
$876$		0			0
$877$	−879.491	+	507.775i	−1.00284	+	0.578990i	−0.909088	−	0.416605i	$-0.863220\pi$
$877$	−879.491	+	507.775i	−1.00284	+	0.578990i	−0.0937531	+	0.995595i	$0.529886\pi$
$878$	104.183	−	180.450i	0.118660	−	0.205524i
$879$		0			0
$880$	−382.480	+	662.474i	−0.434636	+	0.752811i
$881$	−356.912			−0.405121			−0.202561	−	0.979270i	$-0.564926\pi$
$881$	−356.912			−0.405121			−0.202561	+	0.979270i	$0.564926\pi$
$882$		0			0
$883$	466.592	−	808.161i	0.528416	−	0.915244i	−0.471035	−	0.882115i	$-0.656119\pi$
$883$	466.592	−	808.161i	0.528416	−	0.915244i	0.999451	−	0.0331294i	$-0.0105474\pi$
$884$	−1172.58	−	676.990i	−1.32645	−	0.765826i
$885$		0			0
$886$		−	103.025i		−	0.116281i
$887$	610.275	+	352.343i	0.688022	+	0.397229i	0.802870	−	0.596154i	$-0.203305\pi$
$887$	610.275	+	352.343i	0.688022	+	0.397229i	−0.114849	+	0.993383i	$0.536638\pi$
$888$		0			0
$889$	987.207	+	569.964i	1.11047	+	0.641130i
$890$	203.028	+	351.654i	0.228121	+	0.395117i
$891$		0			0
$892$		−	731.336i		−	0.819884i
$893$	134.680	−	138.886i	0.150817	−	0.155527i
$894$		0			0
$895$	7.24903	−	4.18523i	0.00809948	−	0.00467624i
$896$	1085.02	−	626.435i	1.21096	−	0.699146i
$897$		0			0
$898$	−43.1666	−	74.7668i	−0.0480697	−	0.0832592i
$899$	−487.697	+	844.717i	−0.542489	+	0.939618i
$900$		0			0
$901$		−	130.283i		−	0.144599i
$902$	269.157	−	466.194i	0.298401	−	0.516845i
$903$		0			0
$904$	630.627			0.697597
$905$			162.300i			0.179337i
$906$		0			0
$907$	−1101.29	+	635.829i	−1.21421	+	0.701024i	−0.963673	−	0.267084i	$-0.913940\pi$
$907$	−1101.29	+	635.829i	−1.21421	+	0.701024i	−0.250535	+	0.968107i	$0.580607\pi$
$908$	1011.55	+	584.016i	1.11404	+	0.643190i
$909$		0			0
$910$	−232.443	−	402.603i	−0.255432	−	0.442421i
$911$			340.787i			0.374080i	0.982352	+	0.187040i	$0.0598894\pi$
$911$			340.787i			0.374080i	−0.982352	+	0.187040i	$0.940111\pi$
$912$		0			0
$913$	667.252			0.730835
$914$	197.602	−	114.086i	0.216195	−	0.124820i
$915$		0			0
$916$	−194.633	+	337.114i	−0.212481	+	0.368028i
$917$	525.445	+	910.098i	0.573004	+	0.992473i
$918$		0			0
$919$	204.788			0.222837			0.111419	−	0.993774i	$-0.464461\pi$
$919$	204.788			0.222837			0.111419	+	0.993774i	$0.464461\pi$
$920$			191.961i			0.208653i
$921$		0			0
$922$	−306.273	−	176.827i	−0.332184	−	0.191786i
$923$	804.712			0.871843
$924$		0			0
$925$	64.9959	+	37.5254i	0.0702659	+	0.0405680i
$926$	62.6371	−	36.1636i	0.0676427	−	0.0390535i
$927$		0			0
$928$	434.858	+	753.196i	0.468597	+	0.811634i
$929$	807.733	+	1399.03i	0.869465	+	1.50596i	0.862545	+	0.505981i	$0.168869\pi$
$929$	807.733	+	1399.03i	0.869465	+	1.50596i	0.00692012	+	0.999976i	$0.497797\pi$
$930$		0			0
$931$	−895.721	−	225.310i	−0.962106	−	0.242008i
$932$	−761.913			−0.817503
$933$		0			0
$934$	−35.1454	+	20.2912i	−0.0376289	+	0.0217250i
$935$	883.423	−	1530.13i	0.944837	−	1.63651i
$936$		0			0
$937$	−269.027	+	465.968i	−0.287115	+	0.497298i	−0.973120	−	0.230299i	$-0.926030\pi$
$937$	−269.027	+	465.968i	−0.287115	+	0.497298i	0.686005	+	0.727597i	$0.259363\pi$
$938$	−130.535			−0.139163
$939$		0			0
$940$	−82.0756	+	142.159i	−0.0873145	+	0.151233i
$941$	−389.138	−	224.669i	−0.413537	−	0.238756i	0.278771	−	0.960358i	$-0.410073\pi$
$941$	−389.138	−	224.669i	−0.413537	−	0.238756i	−0.692308	+	0.721602i	$0.743406\pi$
$942$		0			0
$943$			424.395i			0.450048i
$944$	736.311	+	425.110i	0.779991	+	0.450328i
$945$		0			0
$946$	−14.1069	−	8.14464i	−0.0149122	−	0.00860956i
$947$	767.818	+	1329.90i	0.810789	+	1.40433i	0.912312	+	0.409495i	$0.134295\pi$
$947$	767.818	+	1329.90i	0.810789	+	1.40433i	−0.101523	+	0.994833i	$0.532371\pi$
$948$		0			0
$949$		−	1125.54i		−	1.18603i
$950$	−13.5282	+	53.7816i	−0.0142402	+	0.0566123i
$951$		0			0
$952$	−1081.00	+	624.117i	−1.13551	+	0.655585i
$953$	1343.91	−	775.904i	1.41018	−	0.814170i	0.414779	−	0.909922i	$-0.363859\pi$
$953$	1343.91	−	775.904i	1.41018	−	0.814170i	0.995405	+	0.0957525i	$0.0305257\pi$
$954$		0			0
$955$	378.116	+	654.915i	0.395933	+	0.685775i
$956$	−590.184	+	1022.23i	−0.617348	+	1.06928i
$957$		0			0
$958$			52.3209i			0.0546148i
$959$	582.373	−	1008.70i	0.607272	−	1.05183i
$960$		0			0
$961$	4.00437			0.00416687
$962$			179.293i			0.186375i
$963$		0			0
$964$	864.271	−	498.987i	0.896547	−	0.517621i
$965$	−684.852	−	395.400i	−0.709692	−	0.409741i
$966$		0			0
$967$	379.617	+	657.515i	0.392571	+	0.679954i	0.992788	−	0.119884i	$-0.0382523\pi$
$967$	379.617	+	657.515i	0.392571	+	0.679954i	−0.600217	+	0.799838i	$0.704919\pi$
$968$			628.151i			0.648916i
$969$		0			0
$970$	248.356			0.256037
$971$	−691.147	+	399.034i	−0.711788	+	0.410951i	−0.811723	−	0.584043i	$-0.801470\pi$
$971$	−691.147	+	399.034i	−0.711788	+	0.410951i	0.0999344	+	0.994994i	$0.468137\pi$
$972$		0			0
$973$	878.592	−	1521.77i	0.902972	−	1.56399i
$974$	83.6272	+	144.847i	0.0858596	+	0.148713i
$975$		0			0
$976$	1160.82			1.18936
$977$			1031.50i			1.05578i	0.849313	+	0.527889i	$0.177016\pi$
$977$			1031.50i			1.05578i	−0.849313	+	0.527889i	$0.822984\pi$
$978$		0			0
$979$	−1795.59	−	1036.69i	−1.83411	−	1.05892i
$980$	783.684			0.799678
$981$		0			0
$982$	205.785	+	118.810i	0.209557	+	0.120988i
$983$	630.248	−	363.874i	0.641148	−	0.370167i	−0.143909	−	0.989591i	$-0.545967\pi$
$983$	630.248	−	363.874i	0.641148	−	0.370167i	0.785056	+	0.619424i	$0.212634\pi$
$984$		0			0
$985$	−196.766	−	340.808i	−0.199762	−	0.345998i
$986$	−263.946	−	457.168i	−0.267694	−	0.463660i
$987$		0			0
$988$	995.644	−	283.255i	1.00774	−	0.286695i
$989$	12.8421			0.0129849
$990$		0			0
$991$	−122.900	+	70.9565i	−0.124016	+	0.0716009i	−0.560725	−	0.828002i	$-0.689477\pi$
$991$	−122.900	+	70.9565i	−0.124016	+	0.0716009i	0.436708	+	0.899603i	$0.356144\pi$
$992$	−426.655	+	738.988i	−0.430096	+	0.744948i
$993$		0			0
$994$	174.311	−	301.916i	0.175363	−	0.303738i
$995$	1144.92			1.15067
$996$		0			0
$997$	−908.384	+	1573.37i	−0.911118	+	1.57810i	−0.0986299	+	0.995124i	$0.531446\pi$
$997$	−908.384	+	1573.37i	−0.911118	+	1.57810i	−0.812488	+	0.582978i	$0.801887\pi$
$998$	120.619	+	69.6392i	0.120860	+	0.0697788i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	171.3.p.e.145.2		6
3.2	odd	2		57.3.g.a.31.2	✓	6
12.11	even	2		912.3.be.d.145.3		6
19.8	odd	6	inner	171.3.p.e.46.2		6
57.8	even	6		57.3.g.a.46.2	yes	6
228.179	odd	6		912.3.be.d.673.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
57.3.g.a.31.2	✓	6	3.2	odd	2
57.3.g.a.46.2	yes	6	57.8	even	6
171.3.p.e.46.2		6	19.8	odd	6	inner
171.3.p.e.145.2		6	1.1	even	1	trivial
912.3.be.d.145.3		6	12.11	even	2
912.3.be.d.673.3		6	228.179	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:	\( N \)	\(=\)	\( 171 = 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	171.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.583430 - 0.336844i) q^{2} +(-1.77307 + 3.07105i) q^{4} +(-2.27307 - 3.93708i) q^{5} +9.87987 q^{7} +5.08374i q^{8} +O(q^{10})\)	\(q+(0.583430 - 0.336844i) q^{2} +(-1.77307 + 3.07105i) q^{4} +(-2.27307 - 3.93708i) q^{5} +9.87987 q^{7} +5.08374i q^{8} +(-2.65236 - 1.53134i) q^{10} +15.6384 q^{11} +(13.3053 + 7.68182i) q^{13} +(5.76421 - 3.32797i) q^{14} +(-5.37987 - 9.31820i) q^{16} +(12.4260 + 21.5225i) q^{17} +(-18.4260 - 4.63488i) q^{19} +16.1213 q^{20} +(9.12394 - 5.26771i) q^{22} +(-4.15294 + 7.19310i) q^{23} +(2.16628 - 3.75211i) q^{25} +10.3503 q^{26} +(-17.5177 + 30.3416i) q^{28} +(-27.3059 - 15.7651i) q^{29} -30.9353i q^{31} +(-23.8881 - 13.7918i) q^{32} +(14.4994 + 8.37124i) q^{34} +(-22.4577 - 38.8978i) q^{35} +17.3225i q^{37} +(-12.3115 + 3.50256i) q^{38} +(20.0151 - 11.5557i) q^{40} +(44.2502 - 25.5479i) q^{41} +(-0.773073 - 1.33900i) q^{43} +(-27.7281 + 48.0265i) q^{44} +5.59556i q^{46} +(-5.09113 + 8.81810i) q^{47} +48.6118 q^{49} -2.91879i q^{50} +(-47.1825 + 27.2408i) q^{52} +(-4.54002 - 2.62118i) q^{53} +(-35.5473 - 61.5697i) q^{55} +50.2267i q^{56} -21.2414 q^{58} +(-68.4321 + 39.5093i) q^{59} +(-53.9426 + 93.4313i) q^{61} +(-10.4204 - 18.0486i) q^{62} +24.4562 q^{64} -69.8453i q^{65} +(-16.9843 - 9.80591i) q^{67} -88.1289 q^{68} +(-26.2049 - 15.1294i) q^{70} +(45.3604 - 26.1888i) q^{71} +(-36.6301 - 63.4451i) q^{73} +(5.83498 + 10.1065i) q^{74} +(46.9046 - 48.3693i) q^{76} +154.506 q^{77} +(-27.1512 + 15.6758i) q^{79} +(-24.4577 + 42.3619i) q^{80} +(17.2113 - 29.8108i) q^{82} +42.6674 q^{83} +(56.4905 - 97.8443i) q^{85} +(-0.902068 - 0.520809i) q^{86} +79.5018i q^{88} +(-114.819 - 66.2909i) q^{89} +(131.455 + 75.8953i) q^{91} +(-14.7269 - 25.5078i) q^{92} +6.85966i q^{94} +(23.6358 + 83.0801i) q^{95} +(-70.2270 + 40.5456i) q^{97} +(28.3616 - 16.3746i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} + 5 q^{4} + 2 q^{5} + 26 q^{7}+O(q^{10}) \) 6 * q + 3 * q^2 + 5 * q^4 + 2 * q^5 + 26 * q^7	\( 6 q + 3 q^{2} + 5 q^{4} + 2 q^{5} + 26 q^{7} + 30 q^{10} - 15 q^{13} + 81 q^{14} + q^{16} + 10 q^{17} - 46 q^{19} + 124 q^{20} - 84 q^{22} + 24 q^{23} + 15 q^{25} - 58 q^{26} + 19 q^{28} - 66 q^{29} - 51 q^{32} + 90 q^{34} + 6 q^{35} - 83 q^{38} + 162 q^{40} - 24 q^{41} + 11 q^{43} - 176 q^{44} + 26 q^{47} + 96 q^{49} - 321 q^{52} - 180 q^{53} - 176 q^{55} - 188 q^{58} - 162 q^{59} - 141 q^{61} + 109 q^{62} + 166 q^{64} - 63 q^{67} - 212 q^{68} + 258 q^{70} + 372 q^{71} + 103 q^{73} + 315 q^{74} - 217 q^{76} + 16 q^{77} - 123 q^{79} - 6 q^{80} + 80 q^{82} + 252 q^{83} + 116 q^{85} + 39 q^{86} - 642 q^{89} + 87 q^{91} - 104 q^{92} + 214 q^{95} - 12 q^{97} + 264 q^{98}+O(q^{100}) \) 6 * q + 3 * q^2 + 5 * q^4 + 2 * q^5 + 26 * q^7 + 30 * q^10 - 15 * q^13 + 81 * q^14 + q^16 + 10 * q^17 - 46 * q^19 + 124 * q^20 - 84 * q^22 + 24 * q^23 + 15 * q^25 - 58 * q^26 + 19 * q^28 - 66 * q^29 - 51 * q^32 + 90 * q^34 + 6 * q^35 - 83 * q^38 + 162 * q^40 - 24 * q^41 + 11 * q^43 - 176 * q^44 + 26 * q^47 + 96 * q^49 - 321 * q^52 - 180 * q^53 - 176 * q^55 - 188 * q^58 - 162 * q^59 - 141 * q^61 + 109 * q^62 + 166 * q^64 - 63 * q^67 - 212 * q^68 + 258 * q^70 + 372 * q^71 + 103 * q^73 + 315 * q^74 - 217 * q^76 + 16 * q^77 - 123 * q^79 - 6 * q^80 + 80 * q^82 + 252 * q^83 + 116 * q^85 + 39 * q^86 - 642 * q^89 + 87 * q^91 - 104 * q^92 + 214 * q^95 - 12 * q^97 + 264 * q^98

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