LMFDB - Embedded newform 171.3.p.c.46.2

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:	6.0.92607408.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 20x^{4} - 35x^{3} + 94x^{2} - 77x + 43 $ x^6 - 3x^5 + 20x^4 - 35x^3 + 94x^2 - 77*x + 43
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 57)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			46.2
Root			$0.500000 - 0.630453i$ of defining polynomial
Character	$\chi$	$=$	171.46
Dual form			171.3.p.c.145.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.204011 - 0.117786i) q^{2} +(-1.97225 - 3.41604i) q^{4} +(-2.88028 + 4.98878i) q^{5} +1.94451 q^{7} +1.87150i q^{8} +O(q^{10})$	\(q+(-0.204011 - 0.117786i) q^{2} +(-1.97225 - 3.41604i) q^{4} +(-2.88028 + 4.98878i) q^{5} +1.94451 q^{7} +1.87150i q^{8} +(1.17522 - 0.678513i) q^{10} -8.46561 q^{11} +(-16.7415 + 9.66573i) q^{13} +(-0.396701 - 0.229036i) q^{14} +(-7.66857 + 13.2824i) q^{16} +(-12.5365 + 21.7138i) q^{17} +(17.8181 + 6.59651i) q^{19} +22.7225 q^{20} +(1.72708 + 0.997131i) q^{22} +(-15.6408 - 27.0907i) q^{23} +(-4.09198 - 7.08751i) q^{25} +4.55395 q^{26} +(-3.83506 - 6.64251i) q^{28} +(-13.7071 + 7.91383i) q^{29} +14.4237i q^{31} +(9.61203 - 5.54951i) q^{32} +(5.11517 - 2.95325i) q^{34} +(-5.60071 + 9.70072i) q^{35} -41.6423i q^{37} +(-2.85813 - 3.44449i) q^{38} +(-9.33653 - 5.39045i) q^{40} +(-1.53439 - 0.885881i) q^{41} +(14.4358 - 25.0035i) q^{43} +(16.6963 + 28.9189i) q^{44} +7.36909i q^{46} +(-1.70506 - 2.95325i) q^{47} -45.2189 q^{49} +1.92791i q^{50} +(66.0371 + 38.1265i) q^{52} +(80.0952 - 46.2430i) q^{53} +(24.3833 - 42.2331i) q^{55} +3.63915i q^{56} +3.72855 q^{58} +(-4.27292 - 2.46697i) q^{59} +(7.45989 + 12.9209i) q^{61} +(1.69891 - 2.94259i) q^{62} +58.7340 q^{64} -111.360i q^{65} +(-70.4113 + 40.6520i) q^{67} +98.9005 q^{68} +(2.28522 - 1.31937i) q^{70} +(-52.9948 - 30.5966i) q^{71} +(-38.8299 + 67.2553i) q^{73} +(-4.90489 + 8.49551i) q^{74} +(-12.6079 - 73.8775i) q^{76} -16.4614 q^{77} +(84.0207 + 48.5094i) q^{79} +(-44.1752 - 76.5137i) q^{80} +(0.208689 + 0.361460i) q^{82} +102.323 q^{83} +(-72.2171 - 125.084i) q^{85} +(-5.89012 + 3.40067i) q^{86} -15.8434i q^{88} +(-103.596 + 59.8111i) q^{89} +(-32.5540 + 18.7951i) q^{91} +(-61.6953 + 106.859i) q^{92} +0.803328i q^{94} +(-84.2297 + 69.8911i) q^{95} +(-42.1438 - 24.3318i) q^{97} +(9.22517 + 5.32616i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} + 5 q^{4} - 4 q^{5} - 22 q^{7}+O(q^{10}) $ 6 * q - 3 * q^2 + 5 * q^4 - 4 * q^5 - 22 * q^7	$ 6 q - 3 q^{2} + 5 q^{4} - 4 q^{5} - 22 q^{7} + 54 q^{10} + 36 q^{11} - 3 q^{13} + 57 q^{14} - 23 q^{16} - 38 q^{17} - 10 q^{19} - 32 q^{20} + 36 q^{22} - 54 q^{23} - 21 q^{25} - 118 q^{26} - 101 q^{28} + 102 q^{29} + 63 q^{32} - 150 q^{34} + 24 q^{35} - 119 q^{38} + 30 q^{40} - 96 q^{41} + 107 q^{43} + 94 q^{44} + 50 q^{47} - 48 q^{49} + 399 q^{52} + 90 q^{53} + 148 q^{55} - 116 q^{58} + 27 q^{61} + 121 q^{62} + 46 q^{64} - 39 q^{67} + 388 q^{68} - 354 q^{70} - 84 q^{71} - 77 q^{73} - 219 q^{74} + 215 q^{76} - 260 q^{77} + 9 q^{79} - 312 q^{80} - 4 q^{82} + 348 q^{83} + 68 q^{85} - 249 q^{86} + 72 q^{89} - 393 q^{91} + 118 q^{92} - 104 q^{95} - 228 q^{97} - 540 q^{98}+O(q^{100}) $ 6 * q - 3 * q^2 + 5 * q^4 - 4 * q^5 - 22 * q^7 + 54 * q^10 + 36 * q^11 - 3 * q^13 + 57 * q^14 - 23 * q^16 - 38 * q^17 - 10 * q^19 - 32 * q^20 + 36 * q^22 - 54 * q^23 - 21 * q^25 - 118 * q^26 - 101 * q^28 + 102 * q^29 + 63 * q^32 - 150 * q^34 + 24 * q^35 - 119 * q^38 + 30 * q^40 - 96 * q^41 + 107 * q^43 + 94 * q^44 + 50 * q^47 - 48 * q^49 + 399 * q^52 + 90 * q^53 + 148 * q^55 - 116 * q^58 + 27 * q^61 + 121 * q^62 + 46 * q^64 - 39 * q^67 + 388 * q^68 - 354 * q^70 - 84 * q^71 - 77 * q^73 - 219 * q^74 + 215 * q^76 - 260 * q^77 + 9 * q^79 - 312 * q^80 - 4 * q^82 + 348 * q^83 + 68 * q^85 - 249 * q^86 + 72 * q^89 - 393 * q^91 + 118 * q^92 - 104 * q^95 - 228 * q^97 - 540 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−0.204011	−	0.117786i	−0.102006	−	0.0588930i	0.448129	−	0.893969i	$-0.352090\pi$
$2$	−0.204011	−	0.117786i	−0.102006	−	0.0588930i	−0.550135	+	0.835076i	$0.685424\pi$
$3$		0			0
$3$		0			0
$4$	−1.97225	−	3.41604i	−0.493063	−	0.854011i
$5$	−2.88028	+	4.98878i	−0.576055	+	0.997757i	0.419871	+	0.907584i	$0.362075\pi$
$5$	−2.88028	+	4.98878i	−0.576055	+	0.997757i	−0.995926	+	0.0901730i	$0.971258\pi$
$6$		0			0
$7$	1.94451			0.277787			0.138893	−	0.990307i	$-0.455646\pi$
$7$	1.94451			0.277787			0.138893	+	0.990307i	$0.455646\pi$
$8$			1.87150i			0.233938i
$9$		0			0
$10$	1.17522	−	0.678513i	0.117522	−	0.0678513i
$11$	−8.46561			−0.769601			−0.384800	−	0.923000i	$-0.625730\pi$
$11$	−8.46561			−0.769601			−0.384800	+	0.923000i	$0.625730\pi$
$12$		0			0
$13$	−16.7415	+	9.66573i	−1.28781	+	0.743518i	−0.978263	−	0.207366i	$-0.933511\pi$
$13$	−16.7415	+	9.66573i	−1.28781	+	0.743518i	−0.309547	+	0.950884i	$0.600178\pi$
$14$	−0.396701	−	0.229036i	−0.0283358	−	0.0163597i
$15$		0			0
$16$	−7.66857	+	13.2824i	−0.479286	+	0.830148i
$17$	−12.5365	+	21.7138i	−0.737440	+	1.27728i	0.216204	+	0.976348i	$0.430632\pi$
$17$	−12.5365	+	21.7138i	−0.737440	+	1.27728i	−0.953644	+	0.300936i	$0.902701\pi$
$18$		0			0
$19$	17.8181	+	6.59651i	0.937797	+	0.347185i
$19$	17.8181	+	6.59651i	0.937797	+	0.347185i
$20$	22.7225			1.13613
$21$		0			0
$22$	1.72708	+	0.997131i	0.0785037	+	0.0453241i
$23$	−15.6408	−	27.0907i	−0.680036	−	1.17786i	−0.974969	−	0.222339i	$-0.928631\pi$
$23$	−15.6408	−	27.0907i	−0.680036	−	1.17786i	0.294933	−	0.955518i	$-0.404703\pi$
$24$		0			0
$25$	−4.09198	−	7.08751i	−0.163679	−	0.283500i
$26$	4.55395			0.175152
$27$		0			0
$28$	−3.83506	−	6.64251i	−0.136966	−	0.237233i
$29$	−13.7071	+	7.91383i	−0.472660	+	0.272891i	−0.717353	−	0.696710i	$-0.754646\pi$
$29$	−13.7071	+	7.91383i	−0.472660	+	0.272891i	0.244692	+	0.969601i	$0.421313\pi$
$30$		0			0
$31$			14.4237i			0.465280i	0.972563	+	0.232640i	$0.0747363\pi$
$31$			14.4237i			0.465280i	−0.972563	+	0.232640i	$0.925264\pi$
$32$	9.61203	−	5.54951i	0.300376	−	0.173422i
$33$		0			0
$34$	5.11517	−	2.95325i	0.150446	−	0.0868602i
$35$	−5.60071	+	9.70072i	−0.160020	+	0.277163i
$36$		0			0
$37$		−	41.6423i		−	1.12547i	−0.826638	−	0.562734i	$-0.809749\pi$
$37$		−	41.6423i		−	1.12547i	0.826638	−	0.562734i	$-0.190251\pi$
$38$	−2.85813	−	3.44449i	−0.0752139	−	0.0906445i
$39$		0			0
$40$	−9.33653	−	5.39045i	−0.233413	−	0.134761i
$41$	−1.53439	−	0.885881i	−0.0374242	−	0.0216069i	0.481171	−	0.876627i	$-0.340212\pi$
$41$	−1.53439	−	0.885881i	−0.0374242	−	0.0216069i	−0.518595	+	0.855020i	$0.673545\pi$
$42$		0			0
$43$	14.4358	−	25.0035i	0.335716	−	0.581476i	−0.647906	−	0.761720i	$-0.724355\pi$
$43$	14.4358	−	25.0035i	0.335716	−	0.581476i	0.983622	+	0.180243i	$0.0576886\pi$
$44$	16.6963	+	28.9189i	0.379462	+	0.657247i
$45$		0			0
$46$			7.36909i			0.160198i
$47$	−1.70506	−	2.95325i	−0.0362778	−	0.0628350i	0.847316	−	0.531088i	$-0.178217\pi$
$47$	−1.70506	−	2.95325i	−0.0362778	−	0.0628350i	−0.883594	+	0.468253i	$0.844883\pi$
$48$		0			0
$49$	−45.2189			−0.922835
$50$			1.92791i			0.0385582i
$51$		0			0
$52$	66.0371	+	38.1265i	1.26994	+	0.733203i
$53$	80.0952	−	46.2430i	1.51123	−	0.872510i	0.511317	−	0.859392i	$-0.329158\pi$
$53$	80.0952	−	46.2430i	1.51123	−	0.872510i	0.999914	−	0.0131174i	$-0.00417552\pi$
$54$		0			0
$55$	24.3833	−	42.2331i	0.443333	−	0.767874i
$56$			3.63915i			0.0649848i
$57$		0			0
$58$	3.72855			0.0642854
$59$	−4.27292	−	2.46697i	−0.0724224	−	0.0418131i	0.463352	−	0.886175i	$-0.346647\pi$
$59$	−4.27292	−	2.46697i	−0.0724224	−	0.0418131i	−0.535774	+	0.844361i	$0.679980\pi$
$60$		0			0
$61$	7.45989	+	12.9209i	0.122293	+	0.211818i	0.920672	−	0.390338i	$-0.127642\pi$
$61$	7.45989	+	12.9209i	0.122293	+	0.211818i	−0.798378	+	0.602156i	$0.794309\pi$
$62$	1.69891	−	2.94259i	0.0274017	−	0.0474612i
$63$		0			0
$64$	58.7340			0.917718
$65$		−	111.360i		−	1.71323i
$66$		0			0
$67$	−70.4113	+	40.6520i	−1.05091	+	0.606746i	−0.922905	−	0.385027i	$-0.874192\pi$
$67$	−70.4113	+	40.6520i	−1.05091	+	0.606746i	−0.128009	+	0.991773i	$0.540859\pi$
$68$	98.9005			1.45442
$69$		0			0
$70$	2.28522	−	1.31937i	0.0326460	−	0.0188482i
$71$	−52.9948	−	30.5966i	−0.746406	−	0.430938i	0.0779878	−	0.996954i	$-0.475150\pi$
$71$	−52.9948	−	30.5966i	−0.746406	−	0.430938i	−0.824394	+	0.566017i	$0.808484\pi$
$72$		0			0
$73$	−38.8299	+	67.2553i	−0.531916	+	0.921306i	0.467390	+	0.884051i	$0.345195\pi$
$73$	−38.8299	+	67.2553i	−0.531916	+	0.921306i	−0.999306	+	0.0372545i	$0.988139\pi$
$74$	−4.90489	+	8.49551i	−0.0662822	+	0.114804i
$75$		0			0
$76$	−12.6079	−	73.8775i	−0.165894	−	0.972072i
$77$	−16.4614			−0.213785
$78$		0			0
$79$	84.0207	+	48.5094i	1.06355	+	0.614043i	0.926413	−	0.376509i	$-0.122875\pi$
$79$	84.0207	+	48.5094i	1.06355	+	0.614043i	0.137140	+	0.990552i	$0.456209\pi$
$80$	−44.1752	−	76.5137i	−0.552190	−	0.956422i
$81$		0			0
$82$	0.208689	+	0.361460i	0.00254499	+	0.00440805i
$83$	102.323			1.23280			0.616401	−	0.787432i	$-0.288590\pi$
$83$	102.323			1.23280			0.616401	+	0.787432i	$0.288590\pi$
$84$		0			0
$85$	−72.2171	−	125.084i	−0.849612	−	1.47157i
$86$	−5.89012	+	3.40067i	−0.0684898	+	0.0395426i
$87$		0			0
$88$		−	15.8434i		−	0.180039i
$89$	−103.596	+	59.8111i	−1.16400	+	0.672034i	−0.952259	−	0.305292i	$-0.901246\pi$
$89$	−103.596	+	59.8111i	−1.16400	+	0.672034i	−0.211739	+	0.977326i	$0.567913\pi$
$90$		0			0
$91$	−32.5540	+	18.7951i	−0.357737	+	0.206539i
$92$	−61.6953	+	106.859i	−0.670601	+	1.16152i
$93$		0			0
$94$			0.803328i			0.00854604i
$95$	−84.2297	+	69.8911i	−0.886629	+	0.735695i
$96$		0			0
$97$	−42.1438	−	24.3318i	−0.434473	−	0.250843i	0.266778	−	0.963758i	$-0.414041\pi$
$97$	−42.1438	−	24.3318i	−0.434473	−	0.250843i	−0.701250	+	0.712915i	$0.747374\pi$
$98$	9.22517	+	5.32616i	0.0941344	+	0.0543485i
$99$		0			0
$100$	−16.1408	+	27.9567i	−0.161408	+	0.279567i
$101$	81.5540	+	141.256i	0.807465	+	1.39857i	0.914614	+	0.404327i	$0.132494\pi$
$101$	81.5540	+	141.256i	0.807465	+	1.39857i	−0.107149	+	0.994243i	$0.534172\pi$
$102$		0			0
$103$			18.2732i			0.177410i	0.996058	+	0.0887050i	$0.0282728\pi$
$103$			18.2732i			0.177410i	−0.996058	+	0.0887050i	$0.971727\pi$
$104$	−18.0895	−	31.3319i	−0.173937	−	0.301268i
$105$		0			0
$106$	−21.7871			−0.205539
$107$		−	55.4789i		−	0.518494i	−0.965811	−	0.259247i	$-0.916526\pi$
$107$		−	55.4789i		−	0.518494i	0.965811	−	0.259247i	$-0.0834744\pi$
$108$		0			0
$109$	96.4369	+	55.6779i	0.884743	+	0.510806i	0.872219	−	0.489115i	$-0.162680\pi$
$109$	96.4369	+	55.6779i	0.884743	+	0.510806i	0.0125234	+	0.999922i	$0.496014\pi$
$110$	−9.94894	+	5.74402i	−0.0904449	+	0.0522184i
$111$		0			0
$112$	−14.9116	+	25.8276i	−0.133139	+	0.230604i
$113$			110.968i			0.982019i	0.871154	+	0.491010i	$0.163372\pi$
$113$			110.968i			0.982019i	−0.871154	+	0.491010i	$0.836628\pi$
$114$		0			0
$115$	180.200			1.56695
$116$	54.0679	+	31.2161i	0.466103	+	0.269105i
$117$		0			0
$118$	0.581150	+	1.00658i	0.00492500	+	0.00853034i
$119$	−24.3773	+	42.2227i	−0.204851	+	0.354812i
$120$		0			0
$121$	−49.3335			−0.407715
$122$		−	3.51468i		−	0.0288089i
$123$		0			0
$124$	49.2719	−	28.4471i	0.397354	−	0.229412i
$125$	−96.8697			−0.774958
$126$		0			0
$127$	−209.627	+	121.028i	−1.65061	+	0.952979i	−0.673785	+	0.738927i	$0.735333\pi$
$127$	−209.627	+	121.028i	−1.65061	+	0.952979i	−0.976822	+	0.214052i	$0.931334\pi$
$128$	−50.4305	−	29.1161i	−0.393989	−	0.227469i
$129$		0			0
$130$	−13.1166	+	22.7187i	−0.100897	+	0.174759i
$131$	−78.7288	+	136.362i	−0.600983	+	1.04093i	0.391689	+	0.920098i	$0.371891\pi$
$131$	−78.7288	+	136.362i	−0.600983	+	1.04093i	−0.992672	+	0.120836i	$0.961443\pi$
$132$		0			0
$133$	34.6475	+	12.8270i	0.260507	+	0.0964433i
$134$	19.1529			0.142932
$135$		0			0
$136$	−40.6375	−	23.4621i	−0.298805	−	0.172515i
$137$	−121.173	−	209.877i	−0.884473	−	1.53195i	−0.846317	−	0.532680i	$-0.821185\pi$
$137$	−121.173	−	209.877i	−0.884473	−	1.53195i	−0.0381558	−	0.999272i	$-0.512148\pi$
$138$		0			0
$139$	−65.0431	−	112.658i	−0.467936	−	0.810489i	0.531392	−	0.847126i	$-0.321669\pi$
$139$	−65.0431	−	112.658i	−0.467936	−	0.810489i	−0.999329	+	0.0366365i	$0.988336\pi$
$140$	44.1841			0.315601
$141$		0			0
$142$	7.20770	+	12.4841i	0.0507585	+	0.0879162i
$143$	141.727	−	81.8263i	0.991100	−	0.572212i
$144$		0			0
$145$		−	91.1760i		−	0.628800i
$146$	15.8435	−	9.14724i	0.108517	−	0.0626523i
$147$		0			0
$148$	−142.252	+	82.1292i	−0.961162	+	0.554927i
$149$	102.368	−	177.306i	0.687030	−	1.18997i	−0.285764	−	0.958300i	$-0.592247\pi$
$149$	102.368	−	177.306i	0.687030	−	1.18997i	0.972794	−	0.231672i	$-0.0744195\pi$
$150$		0			0
$151$			234.305i			1.55169i	0.630924	+	0.775845i	$0.282676\pi$
$151$			234.305i			1.55169i	−0.630924	+	0.775845i	$0.717324\pi$
$152$	−12.3454	+	33.3467i	−0.0812197	+	0.219386i
$153$		0			0
$154$	3.35832	+	1.93893i	0.0218073	+	0.0125904i
$155$	−71.9566	−	41.5441i	−0.464236	−	0.268027i
$156$		0			0
$157$	44.2955	−	76.7220i	0.282137	−	0.488675i	−0.689774	−	0.724025i	$-0.742290\pi$
$157$	44.2955	−	76.7220i	0.282137	−	0.488675i	0.971911	+	0.235349i	$0.0756234\pi$
$158$	−11.4275	−	19.7929i	−0.0723257	−	0.125272i
$159$		0			0
$160$			63.9365i			0.399603i
$161$	−30.4137	−	52.6780i	−0.188905	−	0.327193i
$162$		0			0
$163$	115.918			0.711153			0.355576	−	0.934647i	$-0.384285\pi$
$163$	115.918			0.711153			0.355576	+	0.934647i	$0.384285\pi$
$164$			6.98873i			0.0426142i
$165$		0			0
$166$	−20.8750	−	12.0522i	−0.125753	−	0.0726035i
$167$	−78.0426	+	45.0579i	−0.467321	+	0.269808i	−0.715118	−	0.699004i	$-0.753627\pi$
$167$	−78.0426	+	45.0579i	−0.467321	+	0.269808i	0.247797	+	0.968812i	$0.420293\pi$
$168$		0			0
$169$	102.353	−	177.280i	0.605638	−	1.04900i
$170$			34.0247i			0.200145i
$171$		0			0
$172$	−113.884			−0.662116
$173$	38.5739	+	22.2707i	0.222971	+	0.128732i	0.607325	−	0.794454i	$-0.292243\pi$
$173$	38.5739	+	22.2707i	0.222971	+	0.128732i	−0.384354	+	0.923186i	$0.625576\pi$
$174$		0			0
$175$	−7.95687	−	13.7817i	−0.0454678	−	0.0787526i
$176$	64.9192	−	112.443i	0.368859	−	0.638882i
$177$		0			0
$178$	28.1796			0.158313
$179$			229.632i			1.28286i	0.767181	+	0.641431i	$0.221659\pi$
$179$			229.632i			1.28286i	−0.767181	+	0.641431i	$0.778341\pi$
$180$		0			0
$181$	157.070	−	90.6845i	0.867791	−	0.501019i	0.00117734	−	0.999999i	$-0.499625\pi$
$181$	157.070	−	90.6845i	0.867791	−	0.501019i	0.866613	+	0.498980i	$0.166292\pi$
$182$	8.85519			0.0486549
$183$		0			0
$184$	50.7004	−	29.2719i	0.275545	−	0.159086i
$185$	207.745	+	119.941i	1.12294	+	0.648332i
$186$		0			0
$187$	106.129	−	183.821i	0.567535	−	0.982999i
$188$	−6.72561	+	11.6491i	−0.0357745	+	0.0619633i
$189$		0			0
$190$	25.4160	−	4.33749i	0.133769	−	0.0228289i
$191$	278.704			1.45918			0.729592	−	0.683882i	$-0.239710\pi$
$191$	278.704			1.45918			0.729592	+	0.683882i	$0.239710\pi$
$192$		0			0
$193$	−167.512	−	96.7133i	−0.867939	−	0.501105i	−0.00127645	−	0.999999i	$-0.500406\pi$
$193$	−167.512	−	96.7133i	−0.867939	−	0.501105i	−0.866663	+	0.498894i	$0.833740\pi$
$194$	5.73188	+	9.92791i	0.0295458	+	0.0511748i
$195$		0			0
$196$	89.1831	+	154.470i	0.455016	+	0.788111i
$197$	96.9300			0.492030			0.246015	−	0.969266i	$-0.420879\pi$
$197$	96.9300			0.492030			0.246015	+	0.969266i	$0.420879\pi$
$198$		0			0
$199$	172.893	+	299.460i	0.868811	+	1.50482i	0.863213	+	0.504840i	$0.168449\pi$
$199$	172.893	+	299.460i	0.868811	+	1.50482i	0.00559823	+	0.999984i	$0.498218\pi$
$200$	13.2643	−	7.65815i	0.0663215	−	0.0382908i
$201$		0			0
$202$		−	38.4237i		−	0.190216i
$203$	−26.6536	+	15.3885i	−0.131299	+	0.0758053i
$204$		0			0
$205$	8.83894	−	5.10316i	0.0431168	−	0.0248935i
$206$	2.15233	−	3.72795i	0.0104482	−	0.0180968i
$207$		0			0
$208$		−	296.490i		−	1.42543i
$209$	−150.841	−	55.8435i	−0.721729	−	0.267194i
$210$		0			0
$211$	−11.1758	−	6.45233i	−0.0529657	−	0.0305798i	0.473283	−	0.880910i	$-0.343069\pi$
$211$	−11.1758	−	6.45233i	−0.0529657	−	0.0305798i	−0.526249	+	0.850330i	$0.676402\pi$
$212$	−315.936	−	182.406i	−1.49026	−	0.860405i
$213$		0			0
$214$	−6.53464	+	11.3183i	−0.0305357	+	0.0528894i
$215$	83.1580	+	144.034i	0.386781	+	0.669925i
$216$		0			0
$217$			28.0469i			0.129248i
$218$	−13.1162	−	22.7179i	−0.0601659	−	0.104210i
$219$		0			0
$220$	−192.360			−0.874364
$221$		−	484.697i		−	2.19320i
$222$		0			0
$223$	−80.3821	−	46.4086i	−0.360458	−	0.208110i	0.308824	−	0.951119i	$-0.400065\pi$
$223$	−80.3821	−	46.4086i	−0.360458	−	0.208110i	−0.669282	+	0.743009i	$0.733398\pi$
$224$	18.6907	−	10.7911i	0.0834404	−	0.0481744i
$225$		0			0
$226$	13.0705	−	22.6388i	0.0578341	−	0.100172i
$227$			280.870i			1.23731i	0.785662	+	0.618656i	$0.212323\pi$
$227$			280.870i			1.23731i	−0.785662	+	0.618656i	$0.787677\pi$
$228$		0			0
$229$	137.541			0.600615			0.300308	−	0.953842i	$-0.402911\pi$
$229$	137.541			0.600615			0.300308	+	0.953842i	$0.402911\pi$
$230$	−36.7628	−	21.2250i	−0.159838	−	0.0922826i
$231$		0			0
$232$	−14.8108	−	25.6530i	−0.0638395	−	0.110573i
$233$	183.683	−	318.148i	0.788339	−	1.36544i	−0.138645	−	0.990342i	$-0.544275\pi$
$233$	183.683	−	318.148i	0.788339	−	1.36544i	0.926984	−	0.375101i	$-0.122392\pi$
$234$		0			0
$235$	19.6441			0.0835921
$236$			19.4620i			0.0824659i
$237$		0			0
$238$	9.94648	−	5.74260i	0.0417919	−	0.0241286i
$239$	196.388			0.821707			0.410854	−	0.911701i	$-0.365231\pi$
$239$	196.388			0.821707			0.410854	+	0.911701i	$0.365231\pi$
$240$		0			0
$241$	−118.225	+	68.2572i	−0.490560	+	0.283225i	−0.724807	−	0.688952i	$-0.758071\pi$
$241$	−118.225	+	68.2572i	−0.490560	+	0.283225i	0.234247	+	0.972177i	$0.424738\pi$
$242$	10.0646	+	5.81079i	0.0415892	+	0.0240115i
$243$		0			0
$244$	29.4256	−	50.9666i	0.120597	−	0.208879i
$245$	130.243	−	225.587i	0.531604	−	0.920765i
$246$		0			0
$247$	−362.063	+	61.7896i	−1.46584	+	0.250160i
$248$	−26.9940			−0.108847
$249$		0			0
$250$	19.7625	+	11.4099i	0.0790501	+	0.0456396i
$251$	23.3322	+	40.4126i	0.0929571	+	0.161006i	0.908754	−	0.417332i	$-0.137035\pi$
$251$	23.3322	+	40.4126i	0.0929571	+	0.161006i	−0.815797	+	0.578338i	$0.803701\pi$
$252$		0			0
$253$	132.409	+	229.339i	0.523356	+	0.906480i
$254$	57.0218			0.224495
$255$		0			0
$256$	−110.609	−	191.580i	−0.432066	−	0.748361i
$257$	−4.73878	+	2.73593i	−0.0184388	+	0.0106457i	−0.509191	−	0.860653i	$-0.670055\pi$
$257$	−4.73878	+	2.73593i	−0.0184388	+	0.0106457i	0.490752	+	0.871299i	$0.336722\pi$
$258$		0			0
$259$		−	80.9737i		−	0.312640i
$260$	−380.410	+	219.630i	−1.46312	+	0.844730i
$261$		0			0
$262$	32.1232	−	18.5463i	0.122607	−	0.0707874i
$263$	−37.1071	+	64.2713i	−0.141091	+	0.244378i	−0.927908	−	0.372809i	$-0.878394\pi$
$263$	−37.1071	+	64.2713i	−0.141091	+	0.244378i	0.786816	+	0.617187i	$0.211728\pi$
$264$		0			0
$265$			532.770i			2.01045i
$266$	−5.55764	−	6.69784i	−0.0208934	−	0.0251798i
$267$		0			0
$268$	277.738	+	160.352i	1.03633	+	0.598328i
$269$	64.2197	+	37.0772i	0.238735	+	0.137834i	0.614595	−	0.788843i	$-0.289319\pi$
$269$	64.2197	+	37.0772i	0.238735	+	0.137834i	−0.375860	+	0.926676i	$0.622653\pi$
$270$		0			0
$271$	48.0380	−	83.2043i	0.177262	−	0.307027i	−0.763680	−	0.645595i	$-0.776609\pi$
$271$	48.0380	−	83.2043i	0.177262	−	0.307027i	0.940942	+	0.338568i	$0.109943\pi$
$272$	−192.274	−	333.028i	−0.706889	−	1.22437i
$273$		0			0
$274$			57.0898i			0.208357i
$275$	34.6411	+	60.0001i	0.125968	+	0.218182i
$276$		0			0
$277$	123.007			0.444068			0.222034	−	0.975039i	$-0.428730\pi$
$277$	123.007			0.444068			0.222034	+	0.975039i	$0.428730\pi$
$278$			30.6447i			0.110233i
$279$		0			0
$280$	−18.1549	−	10.4818i	−0.0648391	−	0.0374348i
$281$	−352.110	+	203.291i	−1.25306	+	0.723454i	−0.971716	−	0.236153i	$-0.924113\pi$
$281$	−352.110	+	203.291i	−1.25306	+	0.723454i	−0.281344	+	0.959607i	$0.590780\pi$
$282$		0			0
$283$	−92.7689	+	160.680i	−0.327805	+	0.567776i	−0.982076	−	0.188485i	$-0.939642\pi$
$283$	−92.7689	+	160.680i	−0.327805	+	0.567776i	0.654271	+	0.756260i	$0.272976\pi$
$284$			241.377i			0.849918i
$285$		0			0
$286$	−38.5520			−0.134797
$287$	−2.98363	−	1.72260i	−0.0103959	−	0.00600209i
$288$		0			0
$289$	−169.827	−	294.149i	−0.587636	−	1.01782i
$290$	−10.7393	+	18.6009i	−0.0370319	+	0.0641412i
$291$		0			0
$292$	306.329			1.04907
$293$			360.407i			1.23006i	0.788505	+	0.615028i	$0.210855\pi$
$293$			360.407i			1.23006i	−0.788505	+	0.615028i	$0.789145\pi$
$294$		0			0
$295$	24.6144	−	14.2111i	0.0834385	−	0.0481733i
$296$	77.9338			0.263290
$297$		0			0
$298$	−41.7683	+	24.1149i	−0.140162	+	0.0809226i
$299$	523.703	+	302.360i	1.75152	+	1.01124i
$300$		0			0
$301$	28.0704	−	48.6194i	0.0932573	−	0.161526i
$302$	27.5979	−	47.8009i	0.0913837	−	0.158281i
$303$		0			0
$304$	−224.257	+	186.081i	−0.737687	+	0.612109i
$305$	−85.9461			−0.281791
$306$		0			0
$307$	−233.152	−	134.610i	−0.759453	−	0.438470i	0.0696463	−	0.997572i	$-0.477813\pi$
$307$	−233.152	−	134.610i	−0.759453	−	0.438470i	−0.829099	+	0.559101i	$0.811146\pi$
$308$	32.4661	+	56.2329i	0.105409	+	0.182574i
$309$		0			0
$310$	9.78664	+	16.9510i	0.0315698	+	0.0546805i
$311$	−53.4530			−0.171874			−0.0859372	−	0.996301i	$-0.527388\pi$
$311$	−53.4530			−0.171874			−0.0859372	+	0.996301i	$0.527388\pi$
$312$		0			0
$313$	−119.760	−	207.430i	−0.382618	−	0.662715i	0.608817	−	0.793310i	$-0.291644\pi$
$313$	−119.760	−	207.430i	−0.382618	−	0.662715i	−0.991436	+	0.130596i	$0.958311\pi$
$314$	−18.0736	+	10.4348i	−0.0575592	+	0.0332318i
$315$		0			0
$316$		−	382.691i		−	1.21105i
$317$	−391.754	+	226.179i	−1.23582	+	0.713499i	−0.968236	−	0.250036i	$-0.919557\pi$
$317$	−391.754	+	226.179i	−1.23582	+	0.713499i	−0.267580	+	0.963536i	$0.586224\pi$
$318$		0			0
$319$	116.039	−	66.9954i	0.363760	−	0.210017i
$320$	−169.170	+	293.011i	−0.528656	+	0.915660i
$321$		0			0
$322$			14.3292i			0.0445007i
$323$	−366.612	+	304.203i	−1.13502	+	0.941805i
$324$		0			0
$325$	137.012	+	79.1039i	0.421575	+	0.243397i
$326$	−23.6486	−	13.6535i	−0.0725417	−	0.0418820i
$327$		0			0
$328$	1.65793	−	2.87162i	0.00505467	−	0.00875494i
$329$	−3.31549	−	5.74260i	−0.0100775	−	0.0174547i
$330$		0			0
$331$		−	95.4707i		−	0.288431i	−0.989546	−	0.144216i	$-0.953934\pi$
$331$		−	95.4707i		−	0.288431i	0.989546	−	0.144216i	$-0.0460659\pi$
$332$	−201.806	−	349.538i	−0.607850	−	1.05283i
$333$		0			0
$334$	21.2288			0.0635592
$335$		−	468.356i		−	1.39808i
$336$		0			0
$337$	−82.2367	−	47.4794i	−0.244026	−	0.140888i	0.373000	−	0.927831i	$-0.378329\pi$
$337$	−82.2367	−	47.4794i	−0.244026	−	0.140888i	−0.617026	+	0.786943i	$0.711663\pi$
$338$	−41.7623	+	24.1115i	−0.123557	+	0.0713357i
$339$		0			0
$340$	−284.861	+	493.393i	−0.837825	+	1.45116i
$341$		−	122.105i		−	0.358080i
$342$		0			0
$343$	−183.209			−0.534138
$344$	46.7941	+	27.0166i	0.136029	+	0.0785366i
$345$		0			0
$346$	−5.24635	−	9.08694i	−0.0151628	−	0.0262628i
$347$	−115.221	+	199.568i	−0.332048	+	0.575124i	−0.982913	−	0.184069i	$-0.941073\pi$
$347$	−115.221	+	199.568i	−0.332048	+	0.575124i	0.650865	+	0.759193i	$0.274406\pi$
$348$		0			0
$349$	−209.160			−0.599312			−0.299656	−	0.954047i	$-0.596872\pi$
$349$	−209.160			−0.599312			−0.299656	+	0.954047i	$0.596872\pi$
$350$			3.74884i			0.0107110i
$351$		0			0
$352$	−81.3717	+	46.9800i	−0.231170	+	0.133466i
$353$	−326.125			−0.923866			−0.461933	−	0.886915i	$-0.652844\pi$
$353$	−326.125			−0.923866			−0.461933	+	0.886915i	$0.652844\pi$
$354$		0			0
$355$	305.279	−	176.253i	0.859942	−	0.496488i
$356$	408.634	+	235.925i	1.14785	+	0.662711i
$357$		0			0
$358$	27.0475	−	46.8476i	0.0755516	−	0.130859i
$359$	268.735	−	465.463i	0.748566	−	1.29655i	−0.199945	−	0.979807i	$-0.564076\pi$
$359$	268.735	−	465.463i	0.748566	−	1.29655i	0.948510	−	0.316747i	$-0.102590\pi$
$360$		0			0
$361$	273.972	+	235.075i	0.758925	+	0.651178i
$362$	−42.7255			−0.118026
$363$		0			0
$364$	128.410	+	74.1373i	0.352773	+	0.203674i
$365$	−223.682	−	387.428i	−0.612826	−	1.06145i
$366$		0			0
$367$	−181.274	−	313.976i	−0.493935	−	0.855520i	0.506041	−	0.862509i	$-0.331108\pi$
$367$	−181.274	−	313.976i	−0.493935	−	0.855520i	−0.999976	+	0.00698970i	$0.997775\pi$
$368$	479.771			1.30373
$369$		0			0
$370$	−28.2548	−	48.9388i	−0.0763644	−	0.132267i
$371$	155.746	−	89.9198i	0.419800	−	0.242371i
$372$		0			0
$373$			336.486i			0.902108i	0.892497	+	0.451054i	$0.148952\pi$
$373$			336.486i			0.902108i	−0.892497	+	0.451054i	$0.851048\pi$
$374$	−43.3030	+	25.0010i	−0.115784	+	0.0668477i
$375$		0			0
$376$	5.52701	−	3.19102i	0.0146995	−	0.00848676i
$377$	152.986	−	264.979i	0.405798	−	0.702863i
$378$		0			0
$379$			336.744i			0.888507i	0.895901	+	0.444253i	$0.146531\pi$
$379$			336.744i			0.888507i	−0.895901	+	0.444253i	$0.853469\pi$
$380$	404.873	+	149.889i	1.06546	+	0.394446i
$381$		0			0
$382$	−56.8589	−	32.8275i	−0.148845	−	0.0859358i
$383$	193.755	+	111.865i	0.505888	+	0.292075i	0.731142	−	0.682226i	$-0.238988\pi$
$383$	193.755	+	111.865i	0.505888	+	0.292075i	−0.225254	+	0.974300i	$0.572321\pi$
$384$		0			0
$385$	47.4134	−	82.1225i	0.123152	−	0.213305i
$386$	22.7830	+	39.4612i	0.0590232	+	0.102231i
$387$		0			0
$388$			191.954i			0.494726i
$389$	−100.458	−	173.998i	−0.258246	−	0.447295i	0.707526	−	0.706687i	$-0.249811\pi$
$389$	−100.458	−	173.998i	−0.258246	−	0.447295i	−0.965772	+	0.259392i	$0.916478\pi$
$390$		0			0
$391$	784.324			2.00594
$392$		−	84.6274i		−	0.215886i
$393$		0			0
$394$	−19.7748	−	11.4170i	−0.0501899	−	0.0289772i
$395$	−484.006	+	279.441i	−1.22533	+	0.707445i
$396$		0			0
$397$	−53.1506	+	92.0595i	−0.133880	+	0.231888i	−0.925169	−	0.379555i	$-0.876077\pi$
$397$	−53.1506	+	92.0595i	−0.133880	+	0.231888i	0.791289	+	0.611443i	$0.209410\pi$
$398$		−	81.4577i		−	0.204668i
$399$		0			0
$400$	125.519			0.313796
$401$	−185.008	−	106.815i	−0.461368	−	0.266371i	0.251252	−	0.967922i	$-0.419158\pi$
$401$	−185.008	−	106.815i	−0.461368	−	0.266371i	−0.712619	+	0.701551i	$0.752491\pi$
$402$		0			0
$403$	−139.415	−	241.474i	−0.345944	−	0.599192i
$404$	321.690	−	557.184i	0.796262	−	1.37917i
$405$		0			0
$406$	7.25019			0.0178576
$407$			352.528i			0.866161i
$408$		0			0
$409$	−46.6112	+	26.9110i	−0.113964	+	0.0657970i	−0.555898	−	0.831250i	$-0.687626\pi$
$409$	−46.6112	+	26.9110i	−0.113964	+	0.0657970i	0.441935	+	0.897047i	$0.354292\pi$
$410$	−2.40433			−0.00586421
$411$		0			0
$412$	62.4221	−	36.0394i	0.151510	−	0.0874744i
$413$	−8.30872	−	4.79704i	−0.0201180	−	0.0116151i
$414$		0			0
$415$	−294.717	+	510.465i	−0.710162	+	1.23004i
$416$	−107.280	+	185.815i	−0.257885	+	0.446670i
$417$		0			0
$418$	24.1958	+	29.1597i	0.0578846	+	0.0697601i
$419$	808.890			1.93052			0.965262	−	0.261282i	$-0.0841454\pi$
$419$	808.890			1.93052			0.965262	+	0.261282i	$0.0841454\pi$
$420$		0			0
$421$	−309.086	−	178.451i	−0.734171	−	0.423874i	0.0857753	−	0.996315i	$-0.472663\pi$
$421$	−309.086	−	178.451i	−0.734171	−	0.423874i	−0.819946	+	0.572441i	$0.805997\pi$
$422$	1.51999	+	2.63270i	0.00360187	+	0.00623863i
$423$		0			0
$424$	86.5440	+	149.899i	0.204113	+	0.353534i
$425$	205.196			0.482814
$426$		0			0
$427$	14.5058	+	25.1248i	0.0339714	+	0.0588402i
$428$	−189.518	+	109.418i	−0.442800	+	0.255651i
$429$		0			0
$430$		−	39.1794i		−	0.0911149i
$431$	36.3673	−	20.9967i	0.0843789	−	0.0487162i	−0.457217	−	0.889355i	$-0.651154\pi$
$431$	36.3673	−	20.9967i	0.0843789	−	0.0487162i	0.541596	+	0.840639i	$0.317820\pi$
$432$		0			0
$433$	533.602	−	308.075i	1.23234	−	0.711491i	0.264821	−	0.964298i	$-0.414687\pi$
$433$	533.602	−	308.075i	1.23234	−	0.711491i	0.967517	+	0.252807i	$0.0813538\pi$
$434$	3.30353	−	5.72189i	0.00761183	−	0.0131841i
$435$		0			0
$436$		−	439.244i		−	1.00744i
$437$	−99.9862	−	585.881i	−0.228801	−	1.34069i
$438$		0			0
$439$	−408.012	−	235.566i	−0.929413	−	0.536597i	−0.0427870	−	0.999084i	$-0.513624\pi$
$439$	−408.012	−	235.566i	−0.929413	−	0.536597i	−0.886626	+	0.462487i	$0.846957\pi$
$440$	79.0394	+	45.6334i	0.179635	+	0.103712i
$441$		0			0
$442$	−57.0906	+	98.8838i	−0.129164	+	0.223719i
$443$	−52.2697	−	90.5338i	−0.117990	−	0.204365i	0.800981	−	0.598690i	$-0.204312\pi$
$443$	−52.2697	−	90.5338i	−0.117990	−	0.204365i	−0.918971	+	0.394325i	$0.870979\pi$
$444$		0			0
$445$		−	689.089i		−	1.54852i
$446$	10.9326	+	18.9358i	0.0245125	+	0.0424569i
$447$		0			0
$448$	114.209			0.254930
$449$			713.259i			1.58855i	0.607559	+	0.794275i	$0.292149\pi$
$449$			713.259i			1.58855i	−0.607559	+	0.794275i	$0.707851\pi$
$450$		0			0
$451$	12.9896	+	7.49952i	0.0288017	+	0.0166287i
$452$	379.072	−	218.857i	0.838655	−	0.484198i
$453$		0			0
$454$	33.0826	−	57.3007i	0.0728691	−	0.126213i
$455$		−	216.540i		−	0.475912i
$456$		0			0
$457$	−5.29457			−0.0115855			−0.00579275	−	0.999983i	$-0.501844\pi$
$457$	−5.29457			−0.0115855			−0.00579275	+	0.999983i	$0.501844\pi$
$458$	−28.0599	−	16.2004i	−0.0612662	−	0.0353721i
$459$		0			0
$460$	−355.399	−	615.569i	−0.772607	−	1.33819i
$461$	93.4120	−	161.794i	0.202629	−	0.350964i	−0.746746	−	0.665110i	$-0.768385\pi$
$461$	93.4120	−	161.794i	0.202629	−	0.350964i	0.949375	+	0.314146i	$0.101718\pi$
$462$		0			0
$463$	718.582			1.55201			0.776007	−	0.630725i	$-0.217242\pi$
$463$	718.582			1.55201			0.776007	+	0.630725i	$0.217242\pi$
$464$		−	242.751i		−	0.523170i
$465$		0			0
$466$	−74.9468	+	43.2706i	−0.160830	+	0.0928553i
$467$	−864.548			−1.85128			−0.925641	−	0.378404i	$-0.876473\pi$
$467$	−864.548			−1.85128			−0.925641	+	0.378404i	$0.876473\pi$
$468$		0			0
$469$	−136.915	+	79.0480i	−0.291930	+	0.168546i
$470$	−4.00763	−	2.31381i	−0.00852687	−	0.00492299i
$471$		0			0
$472$	4.61695	−	7.99679i	0.00978167	−	0.0169423i
$473$	−122.208	+	211.670i	−0.258367	+	0.447505i
$474$		0			0
$475$	−26.1585	−	153.279i	−0.0550706	−	0.322693i
$476$	192.313			0.404018
$477$		0			0
$478$	−40.0654	−	23.1318i	−0.0838189	−	0.0483928i
$479$	−63.1395	−	109.361i	−0.131815	−	0.228311i	0.792561	−	0.609793i	$-0.208747\pi$
$479$	−63.1395	−	109.361i	−0.131815	−	0.228311i	−0.924376	+	0.381482i	$0.875414\pi$
$480$		0			0
$481$	402.504	+	697.157i	0.836806	+	1.44939i
$482$	32.1590			0.0667199
$483$		0			0
$484$	97.2981	+	168.525i	0.201029	+	0.348193i
$485$	242.772	−	140.164i	0.500560	−	0.288999i
$486$		0			0
$487$		−	12.1199i		−	0.0248868i	−0.999923	−	0.0124434i	$-0.996039\pi$
$487$		−	12.1199i		−	0.0248868i	0.999923	−	0.0124434i	$-0.00396097\pi$
$488$	−24.1815	+	13.9612i	−0.0495523	+	0.0286090i
$489$		0			0
$490$	−53.1421	+	30.6816i	−0.108453	+	0.0626155i
$491$	−246.271	+	426.554i	−0.501570	+	0.868745i	0.498428	+	0.866931i	$0.333911\pi$
$491$	−246.271	+	426.554i	−0.501570	+	0.868745i	−0.999998	+	0.00181372i	$0.999423\pi$
$492$		0			0
$493$		−	396.846i		−	0.804962i
$494$	81.1430	+	30.0402i	0.164257	+	0.0608102i
$495$		0			0
$496$	−191.580	−	110.609i	−0.386251	−	0.223002i
$497$	−103.049	−	59.4952i	−0.207342	−	0.119709i
$498$		0			0
$499$	173.134	−	299.877i	0.346962	−	0.600956i	−0.638746	−	0.769417i	$-0.720547\pi$
$499$	173.134	−	299.877i	0.346962	−	0.600956i	0.985708	+	0.168462i	$0.0538800\pi$
$500$	191.052	+	330.911i	0.382103	+	0.661822i
$501$		0			0
$502$		−	10.9928i		−	0.0218981i
$503$	−166.249	−	287.952i	−0.330516	−	0.572470i	0.652098	−	0.758135i	$-0.273889\pi$
$503$	−166.249	−	287.952i	−0.330516	−	0.572470i	−0.982613	+	0.185665i	$0.940556\pi$
$504$		0			0
$505$	−939.592			−1.86058
$506$		−	62.3838i		−	0.123288i
$507$		0			0
$508$	826.876	+	477.397i	1.62771	+	0.939758i
$509$	461.493	−	266.443i	0.906666	−	0.523464i	0.0273090	−	0.999627i	$-0.491306\pi$
$509$	461.493	−	266.443i	0.906666	−	0.523464i	0.879357	+	0.476163i	$0.157973\pi$
$510$		0			0
$511$	−75.5049	+	130.778i	−0.147759	+	0.255926i
$512$			285.041i			0.556722i
$513$		0			0
$514$	1.28902			0.00250782
$515$	−91.1612	−	52.6319i	−0.177012	−	0.102198i
$516$		0			0
$517$	14.4343	+	25.0010i	0.0279194	+	0.0483579i
$518$	−9.53758	+	16.5196i	−0.0184123	+	0.0318911i
$519$		0			0
$520$	208.411			0.400789
$521$		−	74.3056i		−	0.142621i	−0.997454	−	0.0713106i	$-0.977282\pi$
$521$		−	74.3056i		−	0.142621i	0.997454	−	0.0713106i	$-0.0227181\pi$
$522$		0			0
$523$	25.3191	−	14.6180i	0.0484113	−	0.0279503i	−0.475599	−	0.879662i	$-0.657769\pi$
$523$	25.3191	−	14.6180i	0.0484113	−	0.0279503i	0.524010	+	0.851712i	$0.324435\pi$
$524$	621.092			1.18529
$525$		0			0
$526$	15.1405	−	8.74139i	0.0287843	−	0.0166186i
$527$	−313.193	−	180.822i	−0.594294	−	0.343116i
$528$		0			0
$529$	−224.771	+	389.315i	−0.424898	+	0.735945i
$530$	62.7529	−	108.691i	0.118402	−	0.205078i
$531$		0			0
$532$	−24.5162	−	143.655i	−0.0460830	−	0.270029i
$533$	34.2508			0.0642603
$534$		0			0
$535$	276.772	+	159.795i	0.517331	+	0.298681i
$536$	−76.0803	−	131.775i	−0.141941	−	0.245849i
$537$		0			0
$538$	−8.73436	−	15.1284i	−0.0162349	−	0.0281196i
$539$	382.805			0.710214
$540$		0			0
$541$	109.055	+	188.889i	0.201580	+	0.349147i	0.949038	−	0.315163i	$-0.102059\pi$
$541$	109.055	+	188.889i	0.201580	+	0.349147i	−0.747458	+	0.664310i	$0.768726\pi$
$542$	−19.6006	+	11.3164i	−0.0361635	+	0.0208790i
$543$		0			0
$544$			278.285i			0.511554i
$545$	−555.530	+	320.735i	−1.01932	+	0.588505i
$546$		0			0
$547$	−465.237	+	268.605i	−0.850525	+	0.491051i	−0.860828	−	0.508896i	$-0.830054\pi$
$547$	−465.237	+	268.605i	−0.850525	+	0.491051i	0.0103027	+	0.999947i	$0.496721\pi$
$548$	−477.967	+	827.863i	−0.872202	+	1.51070i
$549$		0			0
$550$		−	16.3209i		−	0.0296744i
$551$	−296.440	+	50.5903i	−0.538003	+	0.0918154i
$552$		0			0
$553$	163.379	+	94.3268i	0.295441	+	0.170573i
$554$	−25.0948	−	14.4885i	−0.0452975	−	0.0261525i
$555$		0			0
$556$	−256.563	+	444.380i	−0.461444	+	0.799245i
$557$	158.164	+	273.947i	0.283956	+	0.491826i	0.972355	−	0.233505i	$-0.0750197\pi$
$557$	158.164	+	273.947i	0.283956	+	0.491826i	−0.688399	+	0.725332i	$0.741686\pi$
$558$		0			0
$559$			558.129i			0.998442i
$560$	−85.8990	−	148.781i	−0.153391	−	0.265681i
$561$		0			0
$562$	95.7792			0.170426
$563$		−	595.272i		−	1.05732i	−0.848833	−	0.528661i	$-0.822694\pi$
$563$		−	595.272i		−	1.05732i	0.848833	−	0.528661i	$-0.177306\pi$
$564$		0			0
$565$	−553.596	−	319.619i	−0.979816	−	0.565697i
$566$	37.8518	−	21.8538i	0.0668760	−	0.0386109i
$567$		0			0
$568$	57.2616	−	99.1800i	0.100813	−	0.174613i
$569$			536.213i			0.942377i	0.882032	+	0.471189i	$0.156175\pi$
$569$			536.213i			0.942377i	−0.882032	+	0.471189i	$0.843825\pi$
$570$		0			0
$571$	−84.5912			−0.148146			−0.0740729	−	0.997253i	$-0.523600\pi$
$571$	−84.5912			−0.148146			−0.0740729	+	0.997253i	$0.523600\pi$
$572$	−559.044	−	322.764i	−0.977350	−	0.564273i
$573$		0			0
$574$	0.405797	+	0.702861i	0.000706963	+	0.00122450i
$575$	−128.004	+	221.709i	−0.222615	+	0.385581i
$576$		0			0
$577$	−850.008			−1.47315			−0.736575	−	0.676356i	$-0.763558\pi$
$577$	−850.008			−1.47315			−0.736575	+	0.676356i	$0.763558\pi$
$578$			80.0129i			0.138431i
$579$		0			0
$580$	−311.461	+	179.822i	−0.537002	+	0.310038i
$581$	198.967			0.342456
$582$		0			0
$583$	−678.055	+	391.475i	−1.16304	+	0.671484i
$584$	−125.869	−	72.6703i	−0.215528	−	0.124435i
$585$		0			0
$586$	42.4509	−	73.5271i	0.0724417	−	0.125473i
$587$	−229.370	+	397.281i	−0.390750	+	0.676798i	−0.992549	−	0.121849i	$-0.961117\pi$
$587$	−229.370	+	397.281i	−0.390750	+	0.676798i	0.601799	+	0.798648i	$0.294451\pi$
$588$		0			0
$589$	−95.1459	+	257.003i	−0.161538	+	0.436338i
$590$	−6.69548			−0.0113483
$591$		0			0
$592$	553.108	+	319.337i	0.934305	+	0.539421i
$593$	51.3293	+	88.9049i	0.0865586	+	0.149924i	0.906054	−	0.423161i	$-0.139080\pi$
$593$	51.3293	+	88.9049i	0.0865586	+	0.149924i	−0.819496	+	0.573085i	$0.805746\pi$
$594$		0			0
$595$	−140.426	−	243.226i	−0.236011	−	0.408783i
$596$	−807.579			−1.35500
$597$		0			0
$598$	−71.2276	−	123.370i	−0.119110	−	0.206304i
$599$	−322.250	+	186.051i	−0.537980	+	0.310603i	−0.744260	−	0.667890i	$-0.767198\pi$
$599$	−322.250	+	186.051i	−0.537980	+	0.310603i	0.206280	+	0.978493i	$0.433864\pi$
$600$		0			0
$601$		−	850.837i		−	1.41570i	−0.706362	−	0.707851i	$-0.749665\pi$
$601$		−	850.837i		−	1.41570i	0.706362	−	0.707851i	$-0.250335\pi$
$602$	−11.4534	+	6.61261i	−0.0190256	+	0.0109844i
$603$		0			0
$604$	800.396	−	462.109i	1.32516	−	0.765081i
$605$	142.094	−	246.114i	0.234866	−	0.406800i
$606$		0			0
$607$			314.498i			0.518119i	0.965861	+	0.259060i	$0.0834126\pi$
$607$			314.498i			0.518119i	−0.965861	+	0.259060i	$0.916587\pi$
$608$	207.876	−	35.4760i	0.341901	−	0.0583488i
$609$		0			0
$610$	17.5340	+	10.1233i	0.0287442	+	0.0165955i
$611$	57.0906	+	32.9613i	0.0934379	+	0.0539464i
$612$		0			0
$613$	146.198	−	253.222i	0.238495	−	0.413086i	−0.721787	−	0.692115i	$-0.756679\pi$
$613$	146.198	−	253.222i	0.238495	−	0.413086i	0.960283	+	0.279029i	$0.0900125\pi$
$614$	31.7105	+	54.9241i	0.0516457	+	0.0894530i
$615$		0			0
$616$		−	30.8076i		−	0.0500124i
$617$	438.183	+	758.955i	0.710183	+	1.23007i	0.964788	+	0.263028i	$0.0847212\pi$
$617$	438.183	+	758.955i	0.710183	+	1.23007i	−0.254605	+	0.967045i	$0.581945\pi$
$618$		0			0
$619$	−166.847			−0.269542			−0.134771	−	0.990877i	$-0.543030\pi$
$619$	−166.847			−0.269542			−0.134771	+	0.990877i	$0.543030\pi$
$620$			327.742i			0.528617i
$621$		0			0
$622$	10.9050	+	6.29601i	0.0175322	+	0.0101222i
$623$	−201.443	+	116.303i	−0.323343	+	0.186682i
$624$		0			0
$625$	381.311	−	660.450i	0.610097	−	1.05672i
$626$			56.4240i			0.0901342i
$627$		0			0
$628$	−349.448			−0.556445
$629$	904.214	+	522.048i	1.43754	+	0.829965i
$630$		0			0
$631$	464.592	+	804.698i	0.736280	+	1.27527i	0.954160	+	0.299298i	$0.0967525\pi$
$631$	464.592	+	804.698i	0.736280	+	1.27527i	−0.217880	+	0.975976i	$0.569914\pi$
$632$	−90.7855	+	157.245i	−0.143648	+	0.248806i
$633$		0			0
$634$	106.563			0.168080
$635$		−	1394.38i		−	2.19587i
$636$		0			0
$637$	757.034	−	437.074i	1.18844	−	0.686144i
$638$	−31.5645			−0.0494741
$639$		0			0
$640$	290.508	−	167.725i	0.453918	−	0.262070i
$641$	−425.692	−	245.773i	−0.664106	−	0.383422i	0.129734	−	0.991549i	$-0.458588\pi$
$641$	−425.692	−	245.773i	−0.664106	−	0.383422i	−0.793840	+	0.608127i	$0.791921\pi$
$642$		0			0
$643$	175.770	−	304.442i	0.273359	−	0.473472i	−0.696361	−	0.717692i	$-0.745199\pi$
$643$	175.770	−	304.442i	0.273359	−	0.473472i	0.969720	+	0.244220i	$0.0785319\pi$
$644$	−119.967	+	207.789i	−0.186284	+	0.322653i
$645$		0			0
$646$	110.624	−	18.8790i	0.171245	−	0.0292245i
$647$	−767.027			−1.18551			−0.592757	−	0.805381i	$-0.701961\pi$
$647$	−767.027			−1.18551			−0.592757	+	0.805381i	$0.701961\pi$
$648$		0			0
$649$	36.1729	+	20.8844i	0.0557363	+	0.0321794i
$650$	−18.6347	−	32.2762i	−0.0286687	−	0.0496557i
$651$		0			0
$652$	−228.619	−	395.981i	−0.350643	−	0.607332i
$653$	254.877			0.390317			0.195159	−	0.980772i	$-0.437478\pi$
$653$	254.877			0.390317			0.195159	+	0.980772i	$0.437478\pi$
$654$		0			0
$655$	−453.521	−	785.522i	−0.692399	−	1.19927i
$656$	23.5332	−	13.5869i	0.0358738	−	0.0207117i
$657$		0			0
$658$			1.56208i			0.00237398i
$659$	427.502	−	246.818i	0.648713	−	0.374535i	−0.139250	−	0.990257i	$-0.544469\pi$
$659$	427.502	−	246.818i	0.648713	−	0.374535i	0.787963	+	0.615723i	$0.211136\pi$
$660$		0			0
$661$	−1110.75	+	641.292i	−1.68041	+	0.970185i	−0.719021	+	0.694988i	$0.755410\pi$
$661$	−1110.75	+	641.292i	−1.68041	+	0.970185i	−0.961388	+	0.275197i	$0.911257\pi$
$662$	−11.2451	+	19.4771i	−0.0169866	+	0.0294216i
$663$		0			0
$664$			191.497i			0.288399i
$665$	−163.785	+	135.904i	−0.246294	+	0.204366i
$666$		0			0
$667$	428.782	+	247.558i	0.642852	+	0.371151i
$668$	307.839	+	177.731i	0.460837	+	0.266065i
$669$		0			0
$670$	−55.1658	+	95.5499i	−0.0823370	+	0.142612i
$671$	−63.1525	−	109.383i	−0.0941169	−	0.163015i
$672$		0			0
$673$			337.649i			0.501707i	0.968025	+	0.250853i	$0.0807112\pi$
$673$			337.649i			0.501707i	−0.968025	+	0.250853i	$0.919289\pi$
$674$	11.1848	+	19.3727i	0.0165947	+	0.0287428i
$675$		0			0
$676$	−807.462			−1.19447
$677$		−	394.197i		−	0.582270i	−0.956682	−	0.291135i	$-0.905967\pi$
$677$		−	394.197i		−	0.582270i	0.956682	−	0.291135i	$-0.0940329\pi$
$678$		0			0
$679$	−81.9489	−	47.3132i	−0.120691	−	0.0696808i
$680$	234.094	−	135.155i	0.344257	−	0.198757i
$681$		0			0
$682$	−14.3823	+	24.9108i	−0.0210884	+	0.0365262i
$683$		−	612.782i		−	0.897192i	−0.893735	−	0.448596i	$-0.851924\pi$
$683$		−	612.782i		−	0.897192i	0.893735	−	0.448596i	$-0.148076\pi$
$684$		0			0
$685$	1396.04			2.03802
$686$	37.3768	+	21.5795i	0.0544851	+	0.0314570i
$687$		0			0
$688$	221.404	+	383.482i	0.321807	+	0.557387i
$689$	−893.945	+	1548.36i	−1.29745	+	2.24725i
$690$		0			0
$691$	254.757			0.368678			0.184339	−	0.982863i	$-0.440986\pi$
$691$	254.757			0.368678			0.184339	+	0.982863i	$0.440986\pi$
$692$		−	175.693i		−	0.253892i
$693$		0			0
$694$	47.0127	−	27.1428i	0.0677417	−	0.0391107i
$695$	749.369			1.07823
$696$		0			0
$697$	38.4717	−	22.2117i	0.0551962	−	0.0318675i
$698$	42.6710	+	24.6361i	0.0611333	+	0.0352953i
$699$		0			0
$700$	−31.3859	+	54.3620i	−0.0448370	+	0.0776600i
$701$	3.62864	−	6.28499i	0.00517638	−	0.00896576i	−0.863426	−	0.504476i	$-0.831686\pi$
$701$	3.62864	−	6.28499i	0.00517638	−	0.00896576i	0.868602	+	0.495510i	$0.165019\pi$
$702$		0			0
$703$	274.694	−	741.989i	0.390746	−	1.05546i
$704$	−497.219			−0.706277
$705$		0			0
$706$	66.5332	+	38.4130i	0.0942396	+	0.0544093i
$707$	158.582	+	274.672i	0.224303	+	0.388504i
$708$		0			0
$709$	−522.280	−	904.615i	−0.736643	−	1.27590i	−0.953999	−	0.299810i	$-0.903077\pi$
$709$	−522.280	−	904.615i	−0.736643	−	1.27590i	0.217356	−	0.976092i	$-0.430257\pi$
$710$	−83.0407			−0.116959
$711$		0			0
$712$	−111.937	−	193.880i	−0.157214	−	0.272303i
$713$	390.747	−	225.598i	0.548033	−	0.316407i
$714$		0			0
$715$			942.729i			1.31850i
$716$	784.433	−	452.893i	1.09558	−	0.632532i
$717$		0			0
$718$	−109.650	+	63.3065i	−0.152716	+	0.0881706i
$719$	658.810	−	1141.09i	0.916286	−	1.58705i	0.111279	−	0.993789i	$-0.464505\pi$
$719$	658.810	−	1141.09i	0.916286	−	1.58705i	0.805007	−	0.593265i	$-0.202161\pi$
$720$		0			0
$721$			35.5324i			0.0492821i
$722$	−28.2049	−	80.2281i	−0.0390649	−	0.111119i
$723$		0			0
$724$	−619.564	−	357.705i	−0.855751	−	0.494068i
$725$	112.179	+	64.7664i	0.154729	+	0.0893330i
$726$		0			0
$727$	−88.8280	+	153.855i	−0.122184	+	0.211630i	−0.920629	−	0.390439i	$-0.872323\pi$
$727$	−88.8280	+	153.855i	−0.122184	+	0.211630i	0.798444	+	0.602068i	$0.205657\pi$
$728$	−35.1751	−	60.9250i	−0.0483174	−	0.0836882i
$729$		0			0
$730$			105.386i			0.144365i
$731$	361.948	+	626.912i	0.495140	+	0.857608i
$732$		0			0
$733$	321.795			0.439011			0.219505	−	0.975611i	$-0.429556\pi$
$733$	321.795			0.439011			0.219505	+	0.975611i	$0.429556\pi$
$734$			85.4062i			0.116357i
$735$		0			0
$736$	−300.680	−	173.598i	−0.408533	−	0.235867i
$737$	596.074	−	344.144i	0.808785	−	0.466952i
$738$		0			0
$739$	85.7034	−	148.443i	0.115972	−	0.200870i	−0.802196	−	0.597061i	$-0.796335\pi$
$739$	85.7034	−	148.443i	0.115972	−	0.200870i	0.918168	+	0.396191i	$0.129668\pi$
$740$		−	946.219i		−	1.27867i
$741$		0			0
$742$	−42.3652			−0.0570960
$743$	257.044	+	148.405i	0.345955	+	0.199737i	0.662902	−	0.748706i	$-0.269325\pi$
$743$	257.044	+	148.405i	0.345955	+	0.199737i	−0.316947	+	0.948443i	$0.602658\pi$
$744$		0			0
$745$	589.693	+	1021.38i	0.791535	+	1.37098i
$746$	39.6334	−	68.6471i	0.0531279	−	0.0920202i
$747$		0			0
$748$	−837.253			−1.11932
$749$		−	107.879i		−	0.144031i
$750$		0			0
$751$	−117.403	+	67.7829i	−0.156329	+	0.0902568i	−0.576124	−	0.817362i	$-0.695435\pi$
$751$	−117.403	+	67.7829i	−0.156329	+	0.0902568i	0.419795	+	0.907619i	$0.362102\pi$
$752$	52.3014			0.0695498
$753$		0			0
$754$	−62.4217	+	36.0392i	−0.0827874	+	0.0477974i
$755$	−1168.90	−	674.864i	−1.54821	−	0.893859i
$756$		0			0
$757$	4.71078	−	8.15931i	0.00622296	−	0.0107785i	−0.862897	−	0.505380i	$-0.831352\pi$
$757$	4.71078	−	8.15931i	0.00622296	−	0.0107785i	0.869120	+	0.494601i	$0.164686\pi$
$758$	39.6637	−	68.6996i	0.0523268	−	0.0906327i
$759$		0			0
$760$	−130.801	−	157.636i	−0.172107	−	0.207416i
$761$	501.946			0.659587			0.329794	−	0.944053i	$-0.393021\pi$
$761$	501.946			0.659587			0.329794	+	0.944053i	$0.393021\pi$
$762$		0			0
$763$	187.522	+	108.266i	0.245770	+	0.141895i
$764$	−549.675	−	952.066i	−0.719470	−	1.24616i
$765$		0			0
$766$	−26.3522	−	45.6433i	−0.0344023	−	0.0595866i
$767$	95.3803			0.124355
$768$		0			0
$769$	722.257	+	1250.99i	0.939216	+	1.62677i	0.766937	+	0.641722i	$0.221780\pi$
$769$	722.257	+	1250.99i	0.939216	+	1.62677i	0.172279	+	0.985048i	$0.444887\pi$
$770$	−19.3458	+	11.1693i	−0.0251244	+	0.0145056i
$771$		0			0
$772$			762.972i			0.988306i
$773$	572.771	−	330.690i	0.740972	−	0.427800i	−0.0814506	−	0.996677i	$-0.525955\pi$
$773$	572.771	−	330.690i	0.740972	−	0.427800i	0.822423	+	0.568877i	$0.192622\pi$
$774$		0			0
$775$	102.228	−	59.0213i	0.131907	−	0.0761565i
$776$	45.5370	−	78.8724i	0.0586817	−	0.101640i
$777$		0			0
$778$			47.3301i			0.0608356i
$779$	−21.4963	−	25.9064i	−0.0275947	−	0.0332559i
$780$		0			0
$781$	448.633	+	259.019i	0.574435	+	0.331650i
$782$	−160.011	−	92.3824i	−0.204618	−	0.118136i
$783$		0			0
$784$	346.764	−	600.614i	0.442302	−	0.766089i
$785$	255.166	+	441.961i	0.325053	+	0.563008i
$786$		0			0
$787$		−	1319.00i		−	1.67598i	−0.545686	−	0.837990i	$-0.683731\pi$
$787$		−	1319.00i		−	1.67598i	0.545686	−	0.837990i	$-0.316269\pi$
$788$	−191.170	−	331.117i	−0.242602	−	0.420199i
$789$		0			0
$790$	131.657			0.166654
$791$			215.778i			0.272792i
$792$		0			0
$793$	−249.780	−	144.211i	−0.314981	−	0.181854i
$794$	21.6866	−	12.5208i	0.0273132	−	0.0157693i
$795$		0			0
$796$	681.979	−	1181.22i	0.856757	−	1.48395i
$797$			512.600i			0.643162i	0.946882	+	0.321581i	$0.104214\pi$
$797$			512.600i			0.643162i	−0.946882	+	0.321581i	$0.895786\pi$
$798$		0			0
$799$	85.5017			0.107011
$800$	−78.6644	−	45.4169i	−0.0983306	−	0.0567712i
$801$		0			0
$802$	25.1626	+	43.5828i	0.0313748	+	0.0543427i
$803$	328.719	−	569.357i	0.409363	−	0.709038i
$804$		0			0
$805$	350.399			0.435278
$806$			65.6847i			0.0814947i
$807$		0			0
$808$	−264.360	+	152.629i	−0.327179	+	0.188897i
$809$	−368.489			−0.455487			−0.227743	−	0.973721i	$-0.573135\pi$
$809$	−368.489			−0.455487			−0.227743	+	0.973721i	$0.573135\pi$
$810$		0			0
$811$	−5.72688	+	3.30642i	−0.00706150	+	0.00407696i	−0.503527	−	0.863980i	$-0.667964\pi$
$811$	−5.72688	+	3.30642i	−0.00706150	+	0.00407696i	0.496465	+	0.868057i	$0.334631\pi$
$812$	105.135	+	60.7000i	0.129477	+	0.0747536i
$813$		0			0
$814$	41.5228	−	71.9197i	0.0510109	−	0.0883534i
$815$	−333.876	+	578.290i	−0.409663	+	0.709558i
$816$		0			0
$817$	422.154	−	350.290i	0.516713	−	0.428751i
$818$	12.6789			0.0154999
$819$		0			0
$820$	−34.8652	−	20.1295i	−0.0425186	−	0.0245481i
$821$	541.742	+	938.324i	0.659856	+	1.14290i	0.980653	+	0.195756i	$0.0627161\pi$
$821$	541.742	+	938.324i	0.659856	+	1.14290i	−0.320796	+	0.947148i	$0.603951\pi$
$822$		0			0
$823$	−160.542	−	278.067i	−0.195069	−	0.337869i	0.751854	−	0.659329i	$-0.229160\pi$
$823$	−160.542	−	278.067i	−0.195069	−	0.337869i	−0.946923	+	0.321460i	$0.895826\pi$
$824$	−34.1984			−0.0415029
$825$		0			0
$826$	1.13005	+	1.95730i	0.00136810	+	0.00236961i
$827$	710.535	−	410.228i	0.859172	−	0.496043i	−0.00456293	−	0.999990i	$-0.501452\pi$
$827$	710.535	−	410.228i	0.859172	−	0.496043i	0.863735	+	0.503946i	$0.168119\pi$
$828$		0			0
$829$		−	1041.55i		−	1.25640i	−0.778053	−	0.628199i	$-0.783792\pi$
$829$		−	1041.55i		−	1.25640i	0.778053	−	0.628199i	$-0.216208\pi$
$830$	120.251	−	69.4272i	0.144881	−	0.0836472i
$831$		0			0
$832$	−983.297	+	567.707i	−1.18185	+	0.682340i
$833$	566.886	−	981.875i	0.680535	−	1.17872i
$834$		0			0
$835$		−	519.117i		−	0.621697i
$836$	106.734	+	625.418i	0.127672	+	0.748108i
$837$		0			0
$838$	−165.023	−	95.2760i	−0.196925	−	0.113694i
$839$	−791.650	−	457.059i	−0.943564	−	0.544767i	−0.0524880	−	0.998622i	$-0.516715\pi$
$839$	−791.650	−	457.059i	−0.943564	−	0.544767i	−0.891076	+	0.453855i	$0.850048\pi$
$840$		0			0
$841$	−295.243	+	511.375i	−0.351061	+	0.608056i
$842$	42.0380	+	72.8120i	0.0499264	+	0.0864751i
$843$		0			0
$844$			50.9025i			0.0603111i
$845$	589.608	+	1021.23i	0.697761	+	1.20856i
$846$		0			0
$847$	−95.9292			−0.113258
$848$			1418.47i			1.67273i
$849$		0			0
$850$	−41.8623	−	24.1692i	−0.0492498	−	0.0284344i
$851$	−1128.12	+	651.320i	−1.32564	+	0.765359i
$852$		0			0
$853$	−3.45117	+	5.97759i	−0.00404592	+	0.00700773i	−0.868041	−	0.496492i	$-0.834621\pi$
$853$	−3.45117	+	5.97759i	−0.00404592	+	0.00700773i	0.863995	+	0.503500i	$0.167955\pi$
$854$		−	6.83432i		−	0.00800272i
$855$		0			0
$856$	103.829			0.121296
$857$	−543.649	−	313.876i	−0.634363	−	0.366250i	0.148077	−	0.988976i	$-0.452692\pi$
$857$	−543.649	−	313.876i	−0.634363	−	0.366250i	−0.782440	+	0.622726i	$0.786025\pi$
$858$		0			0
$859$	347.688	+	602.214i	0.404759	+	0.701064i	0.994293	−	0.106680i	$-0.0340220\pi$
$859$	347.688	+	602.214i	0.404759	+	0.701064i	−0.589534	+	0.807743i	$0.700689\pi$
$860$	328.017	−	568.142i	0.381415	−	0.660631i
$861$		0			0
$862$	−9.89246			−0.0114762
$863$			636.029i			0.736998i	0.929628	+	0.368499i	$0.120128\pi$
$863$			636.029i			0.736998i	−0.929628	+	0.368499i	$0.879872\pi$
$864$		0			0
$865$	−222.207	+	128.291i	−0.256887	+	0.148314i
$866$	−145.148			−0.167607
$867$		0			0
$868$	95.8094	−	55.3156i	0.110380	−	0.0637276i
$869$	−711.287	−	410.662i	−0.818512	−	0.472568i
$870$		0			0
$871$	785.862	−	1361.15i	0.902253	−	1.56275i
$872$	−104.201	+	180.482i	−0.119497	+	0.206975i
$873$		0			0
$874$	−48.6103	+	131.303i	−0.0556182	+	0.150233i
$875$	−188.364			−0.215273
$876$		0			0
$877$	−710.586	−	410.257i	−0.810246	−	0.467796i	0.0367954	−	0.999323i	$-0.488285\pi$
$877$	−710.586	−	410.257i	−0.810246	−	0.467796i	−0.847041	+	0.531527i	$0.821618\pi$
$878$	55.4928	+	96.1163i	0.0632036	+	0.109472i
$879$		0			0
$880$	373.970	+	647.735i	0.424966	+	0.736063i
$881$	−1473.56			−1.67260			−0.836301	−	0.548271i	$-0.815286\pi$
$881$	−1473.56			−1.67260			−0.836301	+	0.548271i	$0.815286\pi$
$882$		0			0
$883$	204.732	+	354.606i	0.231859	+	0.401592i	0.958355	−	0.285578i	$-0.0921857\pi$
$883$	204.732	+	354.606i	0.231859	+	0.401592i	−0.726496	+	0.687171i	$0.758852\pi$
$884$	−1655.75	+	955.945i	−1.87302	+	1.08139i
$885$		0			0
$886$			24.6266i			0.0277952i
$887$	1177.32	−	679.728i	1.32731	−	0.766322i	0.342426	−	0.939545i	$-0.388751\pi$
$887$	1177.32	−	679.728i	1.32731	−	0.766322i	0.984883	+	0.173223i	$0.0554181\pi$
$888$		0			0
$889$	−407.621	+	235.340i	−0.458517	+	0.264725i
$890$	−81.1651	+	140.582i	−0.0911968	+	0.157957i
$891$		0			0
$892$			366.118i			0.410446i
$893$	−10.8998	−	63.8688i	−0.0122058	−	0.0715216i
$894$		0			0
$895$	−1145.59	−	661.404i	−1.27998	−	0.738999i
$896$	−98.0625	−	56.6164i	−0.109445	−	0.0631879i
$897$		0			0
$898$	84.0119	−	145.513i	0.0935545	−	0.162041i
$899$	−114.146	−	197.707i	−0.126970	−	0.219919i
$900$		0			0
$901$			2318.90i			2.57369i
$902$	−1.76668	−	3.05998i	−0.00195862	−	0.00339244i
$903$		0			0
$904$	−207.677			−0.229732
$905$			1044.79i			1.15446i
$906$		0			0
$907$	1396.68	+	806.372i	1.53989	+	0.889054i	0.998845	+	0.0480579i	$0.0153032\pi$
$907$	1396.68	+	806.372i	1.53989	+	0.889054i	0.541042	+	0.840996i	$0.318030\pi$
$908$	959.463	−	553.946i	1.05668	−	0.610073i
$909$		0			0
$910$	−25.5054	+	44.1766i	−0.0280279	+	0.0485458i
$911$			5.81037i			0.00637801i	0.999995	+	0.00318901i	$0.00101509\pi$
$911$			5.81037i			0.00637801i	−0.999995	+	0.00318901i	$0.998985\pi$
$912$		0			0
$913$	−866.223			−0.948766
$914$	1.08015	+	0.623627i	0.00118179	+	0.000682305i
$915$		0			0
$916$	−271.265	−	469.846i	−0.296141	−	0.512932i
$917$	−153.089	+	265.157i	−0.166945	+	0.289157i
$918$		0			0
$919$	−223.733			−0.243452			−0.121726	−	0.992564i	$-0.538843\pi$
$919$	−223.733			−0.243452			−0.121726	+	0.992564i	$0.538843\pi$
$920$			337.244i			0.366570i
$921$		0			0
$922$	−38.1142	+	22.0053i	−0.0413386	+	0.0238669i
$923$	1182.95			1.28164
$924$		0			0
$925$	−295.140	+	170.399i	−0.319071	+	0.184216i
$926$	−146.599	−	84.6390i	−0.158314	−	0.0914028i
$927$		0			0
$928$	−87.8357	+	152.136i	−0.0946506	+	0.163940i
$929$	87.0368	−	150.752i	0.0936887	−	0.162274i	−0.815372	−	0.578938i	$-0.803467\pi$
$929$	87.0368	−	150.752i	0.0936887	−	0.162274i	0.909061	+	0.416664i	$0.136801\pi$
$930$		0			0
$931$	−805.717	−	298.287i	−0.865431	−	0.320394i
$932$	−1449.08			−1.55480
$933$		0			0
$934$	176.378	+	101.832i	0.188841	+	0.109028i
$935$	611.361	+	1058.91i	0.653862	+	1.13252i
$936$		0			0
$937$	71.6605	+	124.120i	0.0764786	+	0.132465i	0.901728	−	0.432303i	$-0.142299\pi$
$937$	71.6605	+	124.120i	0.0764786	+	0.132465i	−0.825250	+	0.564768i	$0.808966\pi$
$938$	37.2430			0.0397047
$939$		0			0
$940$	−38.7432	−	67.1052i	−0.0412162	−	0.0713885i
$941$	133.495	−	77.0732i	0.141865	−	0.0819057i	−0.427388	−	0.904068i	$-0.640566\pi$
$941$	133.495	−	77.0732i	0.141865	−	0.0819057i	0.569252	+	0.822163i	$0.307233\pi$
$942$		0			0
$943$			55.4237i			0.0587738i
$944$	65.5344	−	37.8363i	0.0694220	−	0.0400808i
$945$		0			0
$946$	49.8635	−	28.7887i	0.0527098	−	0.0304320i
$947$	79.3787	−	137.488i	0.0838213	−	0.145183i	−0.821067	−	0.570832i	$-0.806621\pi$
$947$	79.3787	−	137.488i	0.0838213	−	0.145183i	0.904888	+	0.425649i	$0.139954\pi$
$948$		0			0
$949$		−	1501.28i		−	1.58196i
$950$	−12.7175	+	34.3518i	−0.0133868	+	0.0361598i
$951$		0			0
$952$	−79.0199	−	45.6221i	−0.0830041	−	0.0479224i
$953$	−191.938	−	110.815i	−0.201404	−	0.116280i	0.395906	−	0.918291i	$-0.370430\pi$
$953$	−191.938	−	110.815i	−0.201404	−	0.116280i	−0.597310	+	0.802010i	$0.703764\pi$
$954$		0			0
$955$	−802.745	+	1390.40i	−0.840571	+	1.45591i
$956$	−387.327	−	670.870i	−0.405154	−	0.701747i
$957$		0			0
$958$			29.7478i			0.0310520i
$959$	−235.621	−	408.108i	−0.245695	−	0.425556i
$960$		0			0
$961$	752.958			0.783515
$962$		−	189.637i		−	0.197128i
$963$		0			0
$964$	466.339	+	269.241i	0.483754	+	0.279295i
$965$	964.963	−	557.122i	0.999962	−	0.577328i
$966$		0			0
$967$	−252.311	+	437.015i	−0.260921	+	0.451929i	−0.966487	−	0.256716i	$-0.917360\pi$
$967$	−252.311	+	437.015i	−0.260921	+	0.451929i	0.705566	+	0.708645i	$0.250693\pi$
$968$		−	92.3278i		−	0.0953799i
$969$		0			0
$970$	−66.0376			−0.0680800
$971$	1145.39	+	661.292i	1.17960	+	0.681042i	0.955922	−	0.293621i	$-0.0948603\pi$
$971$	1145.39	+	661.292i	1.17960	+	0.681042i	0.223678	+	0.974663i	$0.428194\pi$
$972$		0			0
$973$	−126.477	−	219.064i	−0.129986	−	0.225143i
$974$	−1.42755	+	2.47260i	−0.00146566	+	0.00253860i
$975$		0			0
$976$	−228.827			−0.234454
$977$			1211.93i			1.24046i	0.784419	+	0.620231i	$0.212961\pi$
$977$			1211.93i			1.24046i	−0.784419	+	0.620231i	$0.787039\pi$
$978$		0			0
$979$	877.001	−	506.337i	0.895814	−	0.517198i
$980$	−1027.49			−1.04846
$981$		0			0
$982$	100.484	−	58.0145i	0.102326	−	0.0590779i
$983$	−924.023	−	533.485i	−0.940003	−	0.542711i	−0.0500419	−	0.998747i	$-0.515935\pi$
$983$	−924.023	−	533.485i	−0.940003	−	0.542711i	−0.889961	+	0.456036i	$0.849269\pi$
$984$		0			0
$985$	−279.185	+	483.563i	−0.283437	+	0.490927i
$986$	−46.7430	+	80.9612i	−0.0474066	+	0.0821107i
$987$		0			0
$988$	925.156	+	1114.96i	0.936393	+	1.12850i
$989$	−903.150			−0.913195
$990$		0			0
$991$	−225.943	−	130.448i	−0.227995	−	0.131633i	0.381652	−	0.924306i	$-0.375355\pi$
$991$	−225.943	−	130.448i	−0.227995	−	0.131633i	−0.609647	+	0.792673i	$0.708689\pi$
$992$	80.0443	+	138.641i	0.0806898	+	0.139759i
$993$		0			0
$994$	14.0154	+	24.2754i	0.0141000	+	0.0244219i
$995$	−1991.92			−2.00193
$996$		0			0
$997$	361.653	+	626.401i	0.362741	+	0.628286i	0.988411	−	0.151802i	$-0.0485076\pi$
$997$	361.653	+	626.401i	0.362741	+	0.628286i	−0.625670	+	0.780088i	$0.715174\pi$
$998$	−70.6426	+	40.7855i	−0.0707842	+	0.0408673i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	171.3.p.c.46.2		6
3.2	odd	2		57.3.g.b.46.2	yes	6
12.11	even	2		912.3.be.f.673.3		6
19.12	odd	6	inner	171.3.p.c.145.2		6
57.50	even	6		57.3.g.b.31.2	✓	6
228.107	odd	6		912.3.be.f.145.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
57.3.g.b.31.2	✓	6	57.50	even	6
57.3.g.b.46.2	yes	6	3.2	odd	2
171.3.p.c.46.2		6	1.1	even	1	trivial
171.3.p.c.145.2		6	19.12	odd	6	inner
912.3.be.f.145.3		6	228.107	odd	6
912.3.be.f.673.3		6	12.11	even	2

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)

\(f(q)\)	\(=\)	\(q+(-0.204011 - 0.117786i) q^{2} +(-1.97225 - 3.41604i) q^{4} +(-2.88028 + 4.98878i) q^{5} +1.94451 q^{7} +1.87150i q^{8} +O(q^{10})\)	\(q+(-0.204011 - 0.117786i) q^{2} +(-1.97225 - 3.41604i) q^{4} +(-2.88028 + 4.98878i) q^{5} +1.94451 q^{7} +1.87150i q^{8} +(1.17522 - 0.678513i) q^{10} -8.46561 q^{11} +(-16.7415 + 9.66573i) q^{13} +(-0.396701 - 0.229036i) q^{14} +(-7.66857 + 13.2824i) q^{16} +(-12.5365 + 21.7138i) q^{17} +(17.8181 + 6.59651i) q^{19} +22.7225 q^{20} +(1.72708 + 0.997131i) q^{22} +(-15.6408 - 27.0907i) q^{23} +(-4.09198 - 7.08751i) q^{25} +4.55395 q^{26} +(-3.83506 - 6.64251i) q^{28} +(-13.7071 + 7.91383i) q^{29} +14.4237i q^{31} +(9.61203 - 5.54951i) q^{32} +(5.11517 - 2.95325i) q^{34} +(-5.60071 + 9.70072i) q^{35} -41.6423i q^{37} +(-2.85813 - 3.44449i) q^{38} +(-9.33653 - 5.39045i) q^{40} +(-1.53439 - 0.885881i) q^{41} +(14.4358 - 25.0035i) q^{43} +(16.6963 + 28.9189i) q^{44} +7.36909i q^{46} +(-1.70506 - 2.95325i) q^{47} -45.2189 q^{49} +1.92791i q^{50} +(66.0371 + 38.1265i) q^{52} +(80.0952 - 46.2430i) q^{53} +(24.3833 - 42.2331i) q^{55} +3.63915i q^{56} +3.72855 q^{58} +(-4.27292 - 2.46697i) q^{59} +(7.45989 + 12.9209i) q^{61} +(1.69891 - 2.94259i) q^{62} +58.7340 q^{64} -111.360i q^{65} +(-70.4113 + 40.6520i) q^{67} +98.9005 q^{68} +(2.28522 - 1.31937i) q^{70} +(-52.9948 - 30.5966i) q^{71} +(-38.8299 + 67.2553i) q^{73} +(-4.90489 + 8.49551i) q^{74} +(-12.6079 - 73.8775i) q^{76} -16.4614 q^{77} +(84.0207 + 48.5094i) q^{79} +(-44.1752 - 76.5137i) q^{80} +(0.208689 + 0.361460i) q^{82} +102.323 q^{83} +(-72.2171 - 125.084i) q^{85} +(-5.89012 + 3.40067i) q^{86} -15.8434i q^{88} +(-103.596 + 59.8111i) q^{89} +(-32.5540 + 18.7951i) q^{91} +(-61.6953 + 106.859i) q^{92} +0.803328i q^{94} +(-84.2297 + 69.8911i) q^{95} +(-42.1438 - 24.3318i) q^{97} +(9.22517 + 5.32616i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} + 5 q^{4} - 4 q^{5} - 22 q^{7}+O(q^{10}) \) 6 * q - 3 * q^2 + 5 * q^4 - 4 * q^5 - 22 * q^7	\( 6 q - 3 q^{2} + 5 q^{4} - 4 q^{5} - 22 q^{7} + 54 q^{10} + 36 q^{11} - 3 q^{13} + 57 q^{14} - 23 q^{16} - 38 q^{17} - 10 q^{19} - 32 q^{20} + 36 q^{22} - 54 q^{23} - 21 q^{25} - 118 q^{26} - 101 q^{28} + 102 q^{29} + 63 q^{32} - 150 q^{34} + 24 q^{35} - 119 q^{38} + 30 q^{40} - 96 q^{41} + 107 q^{43} + 94 q^{44} + 50 q^{47} - 48 q^{49} + 399 q^{52} + 90 q^{53} + 148 q^{55} - 116 q^{58} + 27 q^{61} + 121 q^{62} + 46 q^{64} - 39 q^{67} + 388 q^{68} - 354 q^{70} - 84 q^{71} - 77 q^{73} - 219 q^{74} + 215 q^{76} - 260 q^{77} + 9 q^{79} - 312 q^{80} - 4 q^{82} + 348 q^{83} + 68 q^{85} - 249 q^{86} + 72 q^{89} - 393 q^{91} + 118 q^{92} - 104 q^{95} - 228 q^{97} - 540 q^{98}+O(q^{100}) \) 6 * q - 3 * q^2 + 5 * q^4 - 4 * q^5 - 22 * q^7 + 54 * q^10 + 36 * q^11 - 3 * q^13 + 57 * q^14 - 23 * q^16 - 38 * q^17 - 10 * q^19 - 32 * q^20 + 36 * q^22 - 54 * q^23 - 21 * q^25 - 118 * q^26 - 101 * q^28 + 102 * q^29 + 63 * q^32 - 150 * q^34 + 24 * q^35 - 119 * q^38 + 30 * q^40 - 96 * q^41 + 107 * q^43 + 94 * q^44 + 50 * q^47 - 48 * q^49 + 399 * q^52 + 90 * q^53 + 148 * q^55 - 116 * q^58 + 27 * q^61 + 121 * q^62 + 46 * q^64 - 39 * q^67 + 388 * q^68 - 354 * q^70 - 84 * q^71 - 77 * q^73 - 219 * q^74 + 215 * q^76 - 260 * q^77 + 9 * q^79 - 312 * q^80 - 4 * q^82 + 348 * q^83 + 68 * q^85 - 249 * q^86 + 72 * q^89 - 393 * q^91 + 118 * q^92 - 104 * q^95 - 228 * q^97 - 540 * q^98

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