LMFDB - Embedded newform 171.3.p.e.46.1

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			46.1
Root			$0.0702177 - 0.121621i$ of defining polynomial
Character	$\chi$	$=$	171.46
Dual form			171.3.p.e.145.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.99014 - 1.14901i) q^{2} +(0.640435 + 1.10927i) q^{4} +(0.140435 - 0.243241i) q^{5} -5.24143 q^{7} +6.24860i q^{8} +O(q^{10})$	\(q+(-1.99014 - 1.14901i) q^{2} +(0.640435 + 1.10927i) q^{4} +(0.140435 - 0.243241i) q^{5} -5.24143 q^{7} +6.24860i q^{8} +(-0.558972 + 0.322723i) q^{10} +1.15739 q^{11} +(-6.32289 + 3.65052i) q^{13} +(10.4312 + 6.02244i) q^{14} +(9.74143 - 16.8726i) q^{16} +(-7.52230 + 13.0290i) q^{17} +(1.52230 + 18.9389i) q^{19} +0.359759 q^{20} +(-2.30336 - 1.32985i) q^{22} +(13.3819 + 23.1781i) q^{23} +(12.4606 + 21.5823i) q^{25} +16.7779 q^{26} +(-3.35679 - 5.81414i) q^{28} +(7.76372 - 4.48239i) q^{29} +11.7968i q^{31} +(-17.1278 + 9.88874i) q^{32} +(29.9408 - 17.2863i) q^{34} +(-0.736082 + 1.27493i) q^{35} +36.1681i q^{37} +(18.7314 - 39.4402i) q^{38} +(1.51992 + 0.877524i) q^{40} +(-40.3701 - 23.3077i) q^{41} +(1.64044 - 2.84132i) q^{43} +(0.741232 + 1.28385i) q^{44} -61.5034i q^{46} +(-26.3199 - 45.5874i) q^{47} -21.5274 q^{49} -57.2691i q^{50} +(-8.09880 - 4.67585i) q^{52} +(-88.0273 + 50.8226i) q^{53} +(0.162538 - 0.281524i) q^{55} -32.7516i q^{56} -20.6012 q^{58} +(39.8304 + 22.9961i) q^{59} +(-50.7162 - 87.8430i) q^{61} +(13.5547 - 23.4773i) q^{62} -32.4825 q^{64} +2.05065i q^{65} +(-50.9209 + 29.3992i) q^{67} -19.2702 q^{68} +(2.92981 - 1.69153i) q^{70} +(90.7243 + 52.3797i) q^{71} +(63.1115 - 109.312i) q^{73} +(41.5574 - 71.9796i) q^{74} +(-20.0334 + 13.8178i) q^{76} -6.06636 q^{77} +(-55.9406 - 32.2973i) q^{79} +(-2.73608 - 4.73903i) q^{80} +(53.5614 + 92.7710i) q^{82} +22.0789 q^{83} +(2.11279 + 3.65947i) q^{85} +(-6.52939 + 3.76974i) q^{86} +7.23205i q^{88} +(-107.579 + 62.1106i) q^{89} +(33.1410 - 19.1339i) q^{91} +(-17.1404 + 29.6881i) q^{92} +120.967i q^{94} +(4.82051 + 2.28941i) q^{95} +(162.700 + 93.9348i) q^{97} +(42.8426 + 24.7352i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/171\mathbb{Z}\right)^\times$.

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

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 $

$2$	−1.99014	−	1.14901i	−0.995069	−	0.574504i	−0.0882837	−	0.996095i	$-0.528138\pi$
$2$	−1.99014	−	1.14901i	−0.995069	−	0.574504i	−0.906786	+	0.421592i	$0.861472\pi$
$3$		0			0
$3$		0			0
$4$	0.640435	+	1.10927i	0.160109	+	0.277317i
$5$	0.140435	−	0.243241i	0.0280871	−	0.0486482i	−0.851640	−	0.524127i	$-0.824392\pi$
$5$	0.140435	−	0.243241i	0.0280871	−	0.0486482i	0.879727	+	0.475479i	$0.157725\pi$
$6$		0			0
$7$	−5.24143			−0.748775			−0.374388	−	0.927272i	$-0.622147\pi$
$7$	−5.24143			−0.748775			−0.374388	+	0.927272i	$0.622147\pi$
$8$			6.24860i			0.781075i
$9$		0			0
$10$	−0.558972	+	0.322723i	−0.0558972	+	0.0322723i
$11$	1.15739			0.105217			0.0526085	−	0.998615i	$-0.483246\pi$
$11$	1.15739			0.105217			0.0526085	+	0.998615i	$0.483246\pi$
$12$		0			0
$13$	−6.32289	+	3.65052i	−0.486376	+	0.280809i	−0.723070	−	0.690775i	$-0.757270\pi$
$13$	−6.32289	+	3.65052i	−0.486376	+	0.280809i	0.236694	+	0.971584i	$0.423936\pi$
$14$	10.4312	+	6.02244i	0.745083	+	0.430174i
$15$		0			0
$16$	9.74143	−	16.8726i	0.608839	−	1.05454i
$17$	−7.52230	+	13.0290i	−0.442488	+	0.766412i	−0.997873	−	0.0651813i	$-0.979237\pi$
$17$	−7.52230	+	13.0290i	−0.442488	+	0.766412i	0.555385	+	0.831593i	$0.312571\pi$
$18$		0			0
$19$	1.52230	+	18.9389i	0.0801209	+	0.996785i
$19$	1.52230	+	18.9389i	0.0801209	+	0.996785i
$20$	0.359759			0.0179880
$21$		0			0
$22$	−2.30336	−	1.32985i	−0.104698	−	0.0604476i
$23$	13.3819	+	23.1781i	0.581820	+	1.00774i	0.995264	+	0.0972122i	$0.0309926\pi$
$23$	13.3819	+	23.1781i	0.581820	+	1.00774i	−0.413444	+	0.910530i	$0.635674\pi$
$24$		0			0
$25$	12.4606	+	21.5823i	0.498422	+	0.863293i
$26$	16.7779			0.645304
$27$		0			0
$28$	−3.35679	−	5.81414i	−0.119886	−	0.207648i
$29$	7.76372	−	4.48239i	0.267715	−	0.154565i	−0.360134	−	0.932901i	$-0.617269\pi$
$29$	7.76372	−	4.48239i	0.267715	−	0.154565i	0.627849	+	0.778335i	$0.283936\pi$
$30$		0			0
$31$			11.7968i			0.380543i	0.981732	+	0.190272i	$0.0609368\pi$
$31$			11.7968i			0.380543i	−0.981732	+	0.190272i	$0.939063\pi$
$32$	−17.1278	+	9.88874i	−0.535244	+	0.309023i
$33$		0			0
$34$	29.9408	−	17.2863i	0.880613	−	0.508422i
$35$	−0.736082	+	1.27493i	−0.0210309	+	0.0364266i
$36$		0			0
$37$			36.1681i			0.977516i	0.872419	+	0.488758i	$0.162550\pi$
$37$			36.1681i			0.977516i	−0.872419	+	0.488758i	$0.837450\pi$
$38$	18.7314	−	39.4402i	0.492931	−	1.03790i
$39$		0			0
$40$	1.51992	+	0.877524i	0.0379979	+	0.0219381i
$41$	−40.3701	−	23.3077i	−0.984636	−	0.568480i	−0.0809691	−	0.996717i	$-0.525802\pi$
$41$	−40.3701	−	23.3077i	−0.984636	−	0.568480i	−0.903666	+	0.428237i	$0.859135\pi$
$42$		0			0
$43$	1.64044	−	2.84132i	0.0381497	−	0.0660771i	−0.846320	−	0.532675i	$-0.821187\pi$
$43$	1.64044	−	2.84132i	0.0381497	−	0.0660771i	0.884470	+	0.466597i	$0.154520\pi$
$44$	0.741232	+	1.28385i	0.0168462	+	0.0291784i
$45$		0			0
$46$		−	61.5034i		−	1.33703i
$47$	−26.3199	−	45.5874i	−0.559998	−	0.969946i	−0.997496	−	0.0707260i	$-0.977468\pi$
$47$	−26.3199	−	45.5874i	−0.559998	−	0.969946i	0.437497	−	0.899220i	$-0.355865\pi$
$48$		0			0
$49$	−21.5274			−0.439336
$50$		−	57.2691i		−	1.14538i
$51$		0			0
$52$	−8.09880	−	4.67585i	−0.155746	−	0.0899201i
$53$	−88.0273	+	50.8226i	−1.66089	+	0.958916i	−0.688601	+	0.725140i	$0.741775\pi$
$53$	−88.0273	+	50.8226i	−1.66089	+	0.958916i	−0.972291	+	0.233776i	$0.924892\pi$
$54$		0			0
$55$	0.162538	−	0.281524i	0.00295524	−	0.00511863i
$56$		−	32.7516i		−	0.584849i
$57$		0			0
$58$	−20.6012			−0.355193
$59$	39.8304	+	22.9961i	0.675092	+	0.389764i	0.798003	−	0.602653i	$-0.205890\pi$
$59$	39.8304	+	22.9961i	0.675092	+	0.389764i	−0.122911	+	0.992418i	$0.539223\pi$
$60$		0			0
$61$	−50.7162	−	87.8430i	−0.831413	−	1.44005i	−0.896918	−	0.442197i	$-0.854199\pi$
$61$	−50.7162	−	87.8430i	−0.831413	−	1.44005i	0.0655056	−	0.997852i	$-0.479134\pi$
$62$	13.5547	−	23.4773i	0.218623	−	0.378667i
$63$		0			0
$64$	−32.4825			−0.507539
$65$			2.05065i			0.0315485i
$66$		0			0
$67$	−50.9209	+	29.3992i	−0.760014	+	0.438794i	−0.829301	−	0.558803i	$-0.811261\pi$
$67$	−50.9209	+	29.3992i	−0.760014	+	0.438794i	0.0692870	+	0.997597i	$0.477928\pi$
$68$	−19.2702			−0.283385
$69$		0			0
$70$	2.92981	−	1.69153i	0.0418544	−	0.0241647i
$71$	90.7243	+	52.3797i	1.27781	+	0.737742i	0.976445	−	0.215768i	$-0.0692254\pi$
$71$	90.7243	+	52.3797i	1.27781	+	0.737742i	0.301362	+	0.953510i	$0.402559\pi$
$72$		0			0
$73$	63.1115	−	109.312i	0.864541	−	1.49743i	−0.00296139	−	0.999996i	$-0.500943\pi$
$73$	63.1115	−	109.312i	0.864541	−	1.49743i	0.867502	−	0.497433i	$-0.165724\pi$
$74$	41.5574	−	71.9796i	0.561587	−	0.972697i
$75$		0			0
$76$	−20.0334	+	13.8178i	−0.263597	+	0.181813i
$77$	−6.06636			−0.0787839
$78$		0			0
$79$	−55.9406	−	32.2973i	−0.708109	−	0.408827i	0.102251	−	0.994759i	$-0.467395\pi$
$79$	−55.9406	−	32.2973i	−0.708109	−	0.408827i	−0.810361	+	0.585931i	$0.800729\pi$
$80$	−2.73608	−	4.73903i	−0.0342010	−	0.0592379i
$81$		0			0
$82$	53.5614	+	92.7710i	0.653187	+	1.13135i
$83$	22.0789			0.266011			0.133005	−	0.991115i	$-0.457537\pi$
$83$	22.0789			0.266011			0.133005	+	0.991115i	$0.457537\pi$
$84$		0			0
$85$	2.11279	+	3.65947i	0.0248564	+	0.0430525i
$86$	−6.52939	+	3.76974i	−0.0759231	+	0.0438342i
$87$		0			0
$88$			7.23205i			0.0821824i
$89$	−107.579	+	62.1106i	−1.20875	+	0.697872i	−0.962486	−	0.271331i	$-0.912536\pi$
$89$	−107.579	+	62.1106i	−1.20875	+	0.697872i	−0.246263	+	0.969203i	$0.579203\pi$
$90$		0			0
$91$	33.1410	−	19.1339i	0.364186	−	0.210263i
$92$	−17.1404	+	29.6881i	−0.186309	+	0.322697i
$93$		0			0
$94$			120.967i			1.28688i
$95$	4.82051	+	2.28941i	0.0507422	+	0.0240990i
$96$		0			0
$97$	162.700	+	93.9348i	1.67732	+	0.968400i	0.963360	+	0.268213i	$0.0864330\pi$
$97$	162.700	+	93.9348i	1.67732	+	0.968400i	0.713959	+	0.700188i	$0.246900\pi$
$98$	42.8426	+	24.7352i	0.437170	+	0.252400i
$99$		0			0
$100$	−15.9604	+	27.6442i	−0.159604	+	0.276442i
$101$	−19.8478	−	34.3773i	−0.196513	−	0.340370i	0.750883	−	0.660435i	$-0.229628\pi$
$101$	−19.8478	−	34.3773i	−0.196513	−	0.340370i	−0.947395	+	0.320066i	$0.896295\pi$
$102$		0			0
$103$			26.7360i			0.259573i	0.991542	+	0.129787i	$0.0414292\pi$
$103$			26.7360i			0.259573i	−0.991542	+	0.129787i	$0.958571\pi$
$104$	−22.8106	−	39.5092i	−0.219333	−	0.379896i
$105$		0			0
$106$	233.582			2.20360
$107$			61.9439i			0.578915i	0.957191	+	0.289458i	$0.0934749\pi$
$107$			61.9439i			0.578915i	−0.957191	+	0.289458i	$0.906525\pi$
$108$		0			0
$109$	30.9996	+	17.8976i	0.284400	+	0.164198i	0.635414	−	0.772172i	$-0.280830\pi$
$109$	30.9996	+	17.8976i	0.284400	+	0.164198i	−0.351014	+	0.936370i	$0.614163\pi$
$110$	−0.646947	+	0.373515i	−0.00588134	+	0.00339559i
$111$		0			0
$112$	−51.0590	+	88.4367i	−0.455884	+	0.789614i
$113$			106.018i			0.938215i	0.883141	+	0.469108i	$0.155424\pi$
$113$			106.018i			0.938215i	−0.883141	+	0.469108i	$0.844576\pi$
$114$		0			0
$115$	7.51715			0.0653665
$116$	9.94433	+	5.74136i	0.0857270	+	0.0494945i
$117$		0			0
$118$	−52.8454	−	91.5309i	−0.447842	−	0.775685i
$119$	39.4276	−	68.2906i	0.331324	−	0.573870i
$120$		0			0
$121$	−119.660			−0.988929
$122$			233.093i			1.91060i
$123$		0			0
$124$	−13.0858	+	7.55511i	−0.105531	+	0.0609283i
$125$	14.0214			0.112171
$126$		0			0
$127$	−97.9362	+	56.5435i	−0.771151	+	0.445224i	−0.833285	−	0.552844i	$-0.813543\pi$
$127$	−97.9362	+	56.5435i	−0.771151	+	0.445224i	0.0621341	+	0.998068i	$0.480209\pi$
$128$	133.156	+	76.8776i	1.04028	+	0.600606i
$129$		0			0
$130$	2.35621	−	4.08108i	0.0181247	−	0.0313929i
$131$	64.7582	−	112.164i	0.494337	−	0.856217i	−0.505641	−	0.862744i	$-0.668744\pi$
$131$	64.7582	−	112.164i	0.494337	−	0.856217i	0.999979	+	0.00652644i	$0.00207745\pi$
$132$		0			0
$133$	−7.97901	−	99.2669i	−0.0599926	−	0.746368i
$134$	135.120			1.00836
$135$		0			0
$136$	−81.4130	−	47.0038i	−0.598625	−	0.345616i
$137$	−21.4880	−	37.2183i	−0.156847	−	0.271667i	0.776883	−	0.629645i	$-0.216800\pi$
$137$	−21.4880	−	37.2183i	−0.156847	−	0.271667i	−0.933730	+	0.357978i	$0.883466\pi$
$138$		0			0
$139$	104.196	+	180.473i	0.749613	+	1.29837i	0.948008	+	0.318246i	$0.103094\pi$
$139$	104.196	+	180.473i	0.749613	+	1.29837i	−0.198395	+	0.980122i	$0.563573\pi$
$140$	−1.88565			−0.0134689
$141$		0			0
$142$	−120.369	−	208.486i	−0.847671	−	1.46821i
$143$	−7.31804	+	4.22507i	−0.0511751	+	0.0295459i
$144$		0			0
$145$		−	2.51794i		−	0.0173651i
$146$	−251.201	+	145.031i	−1.72056	+	0.993364i
$147$		0			0
$148$	−40.1201	+	23.1633i	−0.271082	+	0.156509i
$149$	69.2344	−	119.917i	0.464660	−	0.804815i	−0.534526	−	0.845152i	$-0.679510\pi$
$149$	69.2344	−	119.917i	0.464660	−	0.804815i	0.999186	+	0.0403369i	$0.0128431\pi$
$150$		0			0
$151$		−	265.635i		−	1.75917i	−0.475739	−	0.879586i	$-0.657819\pi$
$151$		−	265.635i		−	1.75917i	0.475739	−	0.879586i	$-0.342181\pi$
$152$	−118.342	+	9.51222i	−0.778564	+	0.0625804i
$153$		0			0
$154$	12.0729	+	6.97030i	0.0783955	+	0.0452617i
$155$	2.86948	+	1.65669i	0.0185128	+	0.0106883i
$156$		0			0
$157$	−52.4464	+	90.8398i	−0.334053	+	0.578597i	−0.983303	−	0.181978i	$-0.941750\pi$
$157$	−52.4464	+	90.8398i	−0.334053	+	0.578597i	0.649249	+	0.760576i	$0.275083\pi$
$158$	74.2198	+	128.552i	0.469745	+	0.813623i
$159$		0			0
$160$			5.55492i			0.0347182i
$161$	−70.1400	−	121.486i	−0.435652	−	0.754572i
$162$		0			0
$163$	89.1556			0.546967			0.273483	−	0.961877i	$-0.411824\pi$
$163$	89.1556			0.546967			0.273483	+	0.961877i	$0.411824\pi$
$164$		−	59.7082i		−	0.364074i
$165$		0			0
$166$	−43.9401	−	25.3688i	−0.264699	−	0.152824i
$167$	−20.7589	+	11.9852i	−0.124305	+	0.0717674i	−0.560863	−	0.827909i	$-0.689531\pi$
$167$	−20.7589	+	11.9852i	−0.124305	+	0.0717674i	0.436558	+	0.899676i	$0.356197\pi$
$168$		0			0
$169$	−57.8474	+	100.195i	−0.342292	+	0.592867i
$170$		−	9.71046i		−	0.0571203i
$171$		0			0
$172$	4.20237			0.0244324
$173$	−48.4169	−	27.9535i	−0.279866	−	0.161581i	0.353497	−	0.935436i	$-0.384993\pi$
$173$	−48.4169	−	27.9535i	−0.279866	−	0.161581i	−0.633363	+	0.773855i	$0.718326\pi$
$174$		0			0
$175$	−65.3111	−	113.122i	−0.373206	−	0.646412i
$176$	11.2746	−	19.5282i	0.0640603	−	0.110956i
$177$		0			0
$178$	285.462			1.60372
$179$		−	191.121i		−	1.06771i	−0.845575	−	0.533856i	$-0.820742\pi$
$179$		−	191.121i		−	1.06771i	0.845575	−	0.533856i	$-0.179258\pi$
$180$		0			0
$181$	74.2912	−	42.8920i	0.410448	−	0.236973i	−0.280534	−	0.959844i	$-0.590512\pi$
$181$	74.2912	−	42.8920i	0.410448	−	0.236973i	0.690982	+	0.722872i	$0.257178\pi$
$182$	−87.9402			−0.483188
$183$		0			0
$184$	−144.830	+	83.6179i	−0.787122	+	0.454445i
$185$	8.79757	+	5.07928i	0.0475545	+	0.0274556i
$186$		0			0
$187$	−8.70621	+	15.0796i	−0.0465573	+	0.0806396i
$188$	33.7124	−	58.3916i	0.179321	−	0.310594i
$189$		0			0
$190$	−6.96294	−	10.0950i	−0.0366470	−	0.0531318i
$191$	328.175			1.71820			0.859098	−	0.511811i	$-0.171025\pi$
$191$	328.175			1.71820			0.859098	+	0.511811i	$0.171025\pi$
$192$		0			0
$193$	−187.491	−	108.248i	−0.971456	−	0.560871i	−0.0717764	−	0.997421i	$-0.522867\pi$
$193$	−187.491	−	108.248i	−0.971456	−	0.560871i	−0.899680	+	0.436550i	$0.856200\pi$
$194$	−215.864	−	373.887i	−1.11270	−	1.92725i
$195$		0			0
$196$	−13.7869	−	23.8797i	−0.0703415	−	0.121835i
$197$	−86.2234			−0.437682			−0.218841	−	0.975761i	$-0.570228\pi$
$197$	−86.2234			−0.437682			−0.218841	+	0.975761i	$0.570228\pi$
$198$		0			0
$199$	21.2768	+	36.8525i	0.106919	+	0.185188i	0.914520	−	0.404540i	$-0.132568\pi$
$199$	21.2768	+	36.8525i	0.106919	+	0.185188i	−0.807602	+	0.589728i	$0.799235\pi$
$200$	−134.859	+	77.8610i	−0.674296	+	0.389305i
$201$		0			0
$202$			91.2209i			0.451589i
$203$	−40.6930	+	23.4941i	−0.200458	+	0.115735i
$204$		0			0
$205$	−11.3388	+	6.54644i	−0.0553111	+	0.0319339i
$206$	30.7199	−	53.2084i	0.149126	−	0.258293i
$207$		0			0
$208$			142.245i			0.683871i
$209$	1.76189	+	21.9197i	0.00843009	+	0.104879i
$210$		0			0
$211$	278.518	+	160.803i	1.31999	+	0.762098i	0.983727	−	0.179670i	$-0.0575029\pi$
$211$	278.518	+	160.803i	1.31999	+	0.762098i	0.336265	+	0.941767i	$0.390836\pi$
$212$	−112.752	−	65.0971i	−0.531847	−	0.307062i
$213$		0			0
$214$	71.1740	−	123.277i	0.332589	−	0.576061i
$215$	−0.460750	−	0.798043i	−0.00214302	−	0.00371183i
$216$		0			0
$217$		−	61.8322i		−	0.284941i
$218$	−41.1290	−	71.2376i	−0.188665	−	0.326778i
$219$		0			0
$220$	0.416381			0.00189264
$221$		−	109.841i		−	0.497019i
$222$		0			0
$223$	227.577	+	131.392i	1.02053	+	0.589201i	0.914257	−	0.405136i	$-0.132776\pi$
$223$	227.577	+	131.392i	1.02053	+	0.589201i	0.106270	+	0.994337i	$0.466109\pi$
$224$	89.7741	−	51.8311i	0.400777	−	0.231389i
$225$		0			0
$226$	121.816	−	210.991i	0.539008	−	0.933590i
$227$			424.986i			1.87219i	0.351752	+	0.936093i	$0.385586\pi$
$227$			424.986i			1.87219i	−0.351752	+	0.936093i	$0.614414\pi$
$228$		0			0
$229$	65.9830			0.288135			0.144068	−	0.989568i	$-0.453982\pi$
$229$	65.9830			0.288135			0.144068	+	0.989568i	$0.453982\pi$
$230$	−14.9602	−	8.63726i	−0.0650442	−	0.0375533i
$231$		0			0
$232$	28.0086	+	48.5124i	0.120727	+	0.209105i
$233$	25.7144	−	44.5386i	0.110362	−	0.191153i	−0.805554	−	0.592522i	$-0.798132\pi$
$233$	25.7144	−	44.5386i	0.110362	−	0.191153i	0.915916	+	0.401369i	$0.131466\pi$
$234$		0			0
$235$	−14.7850			−0.0629149
$236$			58.9101i			0.249619i
$237$		0			0
$238$	−156.933	+	90.6051i	−0.659381	+	0.380694i
$239$	239.866			1.00362			0.501811	−	0.864977i	$-0.332667\pi$
$239$	239.866			1.00362			0.501811	+	0.864977i	$0.332667\pi$
$240$		0			0
$241$	−165.208	+	95.3831i	−0.685512	+	0.395781i	−0.801929	−	0.597420i	$-0.796193\pi$
$241$	−165.208	+	95.3831i	−0.685512	+	0.395781i	0.116416	+	0.993200i	$0.462859\pi$
$242$	238.141	+	137.491i	0.984053	+	0.568144i
$243$		0			0
$244$	64.9609	−	112.515i	0.266233	−	0.461129i
$245$	−3.02322	+	5.23636i	−0.0123397	+	0.0213729i
$246$		0			0
$247$	−78.7623	−	114.192i	−0.318876	−	0.462314i
$248$	−73.7137			−0.297233
$249$		0			0
$250$	−27.9045	−	16.1107i	−0.111618	−	0.0644427i
$251$	−103.899	−	179.959i	−0.413942	−	0.716968i	0.581375	−	0.813636i	$-0.302515\pi$
$251$	−103.899	−	179.959i	−0.413942	−	0.716968i	−0.995317	+	0.0966678i	$0.969182\pi$
$252$		0			0
$253$	15.4880	+	26.8260i	0.0612174	+	0.106032i
$254$	259.875			1.02313
$255$		0			0
$256$	−111.701	−	193.471i	−0.436331	−	0.755748i
$257$	58.1843	−	33.5927i	0.226398	−	0.130711i	−0.382511	−	0.923951i	$-0.624941\pi$
$257$	58.1843	−	33.5927i	0.226398	−	0.130711i	0.608909	+	0.793240i	$0.291607\pi$
$258$		0			0
$259$		−	189.572i		−	0.731940i
$260$	−2.27472	+	1.31331i	−0.00874891	+	0.00505119i
$261$		0			0
$262$	−257.756	+	148.815i	−0.983800	+	0.567997i
$263$	−142.093	+	246.111i	−0.540276	+	0.935785i	0.458612	+	0.888637i	$0.348347\pi$
$263$	−142.093	+	246.111i	−0.540276	+	0.935785i	−0.998888	+	0.0471484i	$0.984987\pi$
$264$		0			0
$265$			28.5491i			0.107733i
$266$	−98.1791	+	206.723i	−0.369094	+	0.777154i
$267$		0			0
$268$	−65.2231	−	37.6566i	−0.243370	−	0.140510i
$269$	−61.8223	−	35.6931i	−0.229823	−	0.132688i	0.380667	−	0.924712i	$-0.375694\pi$
$269$	−61.8223	−	35.6931i	−0.229823	−	0.132688i	−0.610490	+	0.792024i	$0.709028\pi$
$270$		0			0
$271$	35.5404	−	61.5577i	0.131145	−	0.227150i	−0.792973	−	0.609257i	$-0.791468\pi$
$271$	35.5404	−	61.5577i	0.131145	−	0.227150i	0.924118	+	0.382106i	$0.124801\pi$
$272$	146.556	+	253.842i	0.538808	+	0.933243i
$273$		0			0
$274$			98.7595i			0.360436i
$275$	14.4217	+	24.9791i	0.0524425	+	0.0908331i
$276$		0			0
$277$	−476.997			−1.72201			−0.861005	−	0.508597i	$-0.830164\pi$
$277$	−476.997			−1.72201			−0.861005	+	0.508597i	$0.830164\pi$
$278$		−	478.889i		−	1.72262i
$279$		0			0
$280$	−7.96653	−	4.59948i	−0.0284519	−	0.0164267i
$281$	−126.681	+	73.1394i	−0.450822	+	0.260282i	−0.708177	−	0.706034i	$-0.750482\pi$
$281$	−126.681	+	73.1394i	−0.450822	+	0.260282i	0.257355	+	0.966317i	$0.417149\pi$
$282$		0			0
$283$	76.0571	−	131.735i	0.268753	−	0.465494i	−0.699787	−	0.714352i	$-0.746722\pi$
$283$	76.0571	−	131.735i	0.268753	−	0.465494i	0.968540	+	0.248858i	$0.0800551\pi$
$284$			134.183i			0.472476i
$285$		0			0
$286$	19.4185			0.0678970
$287$	211.597	+	122.165i	0.737271	+	0.425663i
$288$		0			0
$289$	31.3301	+	54.2653i	0.108409	+	0.187769i
$290$	−2.89314	+	5.01106i	−0.00997633	+	0.0172795i
$291$		0			0
$292$	161.675			0.553683
$293$		−	350.693i		−	1.19690i	−0.801159	−	0.598452i	$-0.795783\pi$
$293$		−	350.693i		−	1.19690i	0.801159	−	0.598452i	$-0.204217\pi$
$294$		0			0
$295$	11.1872	−	6.45893i	0.0379227	−	0.0218947i
$296$	−226.000			−0.763513
$297$		0			0
$298$	−275.572	+	159.102i	−0.924739	+	0.533898i
$299$	−169.224	−	97.7016i	−0.565967	−	0.326761i
$300$		0			0
$301$	−8.59822	+	14.8926i	−0.0285655	+	0.0494769i
$302$	−305.217	+	528.651i	−1.01065	+	1.75050i
$303$		0			0
$304$	334.379	+	158.807i	1.09993	+	0.522391i
$305$	−28.4894			−0.0934078
$306$		0			0
$307$	412.362	+	238.077i	1.34320	+	0.775497i	0.987276	−	0.159018i	$-0.0508329\pi$
$307$	412.362	+	238.077i	1.34320	+	0.775497i	0.355924	+	0.934515i	$0.384166\pi$
$308$	−3.88511	−	6.72921i	−0.0126140	−	0.0218481i
$309$		0			0
$310$	−3.80710	−	6.59410i	−0.0122810	−	0.0212713i
$311$	468.952			1.50788			0.753942	−	0.656942i	$-0.228150\pi$
$311$	468.952			1.50788			0.753942	+	0.656942i	$0.228150\pi$
$312$		0			0
$313$	−17.6786	−	30.6203i	−0.0564812	−	0.0978284i	0.836402	−	0.548116i	$-0.184655\pi$
$313$	−17.6786	−	30.6203i	−0.0564812	−	0.0978284i	−0.892884	+	0.450288i	$0.851321\pi$
$314$	208.751	−	120.523i	0.664813	−	0.383830i
$315$		0			0
$316$		−	82.7374i		−	0.261827i
$317$	−377.554	+	217.981i	−1.19102	+	0.687637i	−0.958539	−	0.284963i	$-0.908019\pi$
$317$	−377.554	+	217.981i	−1.19102	+	0.687637i	−0.232484	+	0.972600i	$0.574685\pi$
$318$		0			0
$319$	8.98564	−	5.18786i	0.0281681	−	0.0162629i
$320$	−4.56169	+	7.90107i	−0.0142553	+	0.0246909i
$321$		0			0
$322$			322.366i			1.00114i
$323$	−258.206	−	122.630i	−0.799400	−	0.379660i
$324$		0			0
$325$	−157.573	−	90.9751i	−0.484841	−	0.279923i
$326$	−177.432	−	102.440i	−0.544270	−	0.314234i
$327$		0			0
$328$	145.640	−	252.256i	0.444025	−	0.769074i
$329$	137.954	+	238.943i	0.419313	+	0.726271i
$330$		0			0
$331$			9.06641i			0.0273910i	0.999906	+	0.0136955i	$0.00435954\pi$
$331$			9.06641i			0.0273910i	−0.999906	+	0.0136955i	$0.995640\pi$
$332$	14.1401	+	24.4914i	0.0425907	+	0.0737692i
$333$		0			0
$334$	55.0841			0.164923
$335$			16.5148i			0.0492978i
$336$		0			0
$337$	364.175	+	210.256i	1.08064	+	0.623906i	0.931068	−	0.364845i	$-0.118878\pi$
$337$	364.175	+	210.256i	1.08064	+	0.623906i	0.149569	+	0.988751i	$0.452211\pi$
$338$	230.249	−	132.934i	0.681209	−	0.393296i
$339$		0			0
$340$	−2.70621	+	4.68730i	−0.00795946	+	0.0137862i
$341$			13.6535i			0.0400396i
$342$		0			0
$343$	369.664			1.07774
$344$	17.7543	+	10.2504i	0.0516112	+	0.0297977i
$345$		0			0
$346$	64.2375	+	111.263i	0.185658	+	0.321568i
$347$	32.2864	−	55.9216i	0.0930443	−	0.161157i	−0.815746	−	0.578410i	$-0.803674\pi$
$347$	32.2864	−	55.9216i	0.0930443	−	0.161157i	0.908791	+	0.417252i	$0.137007\pi$
$348$		0			0
$349$	−242.722			−0.695477			−0.347739	−	0.937592i	$-0.613050\pi$
$349$	−242.722			−0.695477			−0.347739	+	0.937592i	$0.613050\pi$
$350$			300.172i			0.857633i
$351$		0			0
$352$	−19.8235	+	11.4451i	−0.0563168	+	0.0325145i
$353$	560.267			1.58716			0.793579	−	0.608467i	$-0.208215\pi$
$353$	560.267			1.58716			0.793579	+	0.608467i	$0.208215\pi$
$354$		0			0
$355$	25.4818	−	14.7119i	0.0717797	−	0.0414420i
$356$	−137.794	−	79.5556i	−0.387063	−	0.223471i
$357$		0			0
$358$	−219.599	+	380.356i	−0.613405	+	1.06245i
$359$	−219.906	+	380.889i	−0.612552	+	1.06097i	0.378256	+	0.925701i	$0.376524\pi$
$359$	−219.906	+	380.889i	−0.612552	+	1.06097i	−0.990809	+	0.135271i	$0.956810\pi$
$360$		0			0
$361$	−356.365	+	57.6613i	−0.987161	+	0.159727i
$362$	−197.133			−0.544566
$363$		0			0
$364$	42.4493	+	24.5081i	0.116619	+	0.0673300i
$365$	−17.7262	−	30.7026i	−0.0485648	−	0.0841168i
$366$		0			0
$367$	−66.5853	−	115.329i	−0.181431	−	0.314248i	0.760937	−	0.648826i	$-0.224740\pi$
$367$	−66.5853	−	115.329i	−0.181431	−	0.314248i	−0.942368	+	0.334578i	$0.891406\pi$
$368$	521.434			1.41694
$369$		0			0
$370$	−11.6723	−	20.2170i	−0.0315467	−	0.0546404i
$371$	461.388	−	266.383i	1.24363	−	0.718013i
$372$		0			0
$373$		−	340.051i		−	0.911666i	−0.890065	−	0.455833i	$-0.849341\pi$
$373$		−	340.051i		−	0.911666i	0.890065	−	0.455833i	$-0.150659\pi$
$374$	34.6532	−	20.0070i	0.0926555	−	0.0534947i
$375$		0			0
$376$	284.858	−	164.463i	0.757600	−	0.437401i
$377$	−32.7261	+	56.6833i	−0.0868067	+	0.150354i
$378$		0			0
$379$			71.0281i			0.187409i	0.995600	+	0.0937046i	$0.0298709\pi$
$379$			71.0281i			0.187409i	−0.995600	+	0.0937046i	$0.970129\pi$
$380$	0.547660	+	6.81345i	0.00144121	+	0.0179301i
$381$		0			0
$382$	−653.115	−	377.076i	−1.70972	−	0.987110i
$383$	−296.523	−	171.198i	−0.774213	−	0.446992i	0.0601627	−	0.998189i	$-0.480838\pi$
$383$	−296.523	−	171.198i	−0.774213	−	0.446992i	−0.834375	+	0.551197i	$0.814171\pi$
$384$		0			0
$385$	−0.851932	+	1.47559i	−0.00221281	+	0.00383270i
$386$	248.756	+	430.857i	0.644444	+	1.11621i
$387$		0			0
$388$			240.637i			0.620198i
$389$	−38.8478	−	67.2864i	−0.0998659	−	0.172973i	0.811763	−	0.583987i	$-0.198508\pi$
$389$	−38.8478	−	67.2864i	−0.0998659	−	0.172973i	−0.911629	+	0.411014i	$0.865175\pi$
$390$		0			0
$391$	−402.649			−1.02979
$392$		−	134.516i		−	0.343154i
$393$		0			0
$394$	171.596	+	99.0713i	0.435524	+	0.251450i
$395$	−15.7121	+	9.07138i	−0.0397774	+	0.0229655i
$396$		0			0
$397$	47.6985	−	82.6162i	0.120147	−	0.208101i	−0.799678	−	0.600429i	$-0.794997\pi$
$397$	47.6985	−	82.6162i	0.120147	−	0.208101i	0.919826	+	0.392327i	$0.128330\pi$
$398$		−	97.7888i		−	0.245700i
$399$		0			0
$400$	485.534			1.21384
$401$	93.1614	+	53.7868i	0.232323	+	0.134132i	0.611643	−	0.791134i	$-0.290509\pi$
$401$	93.1614	+	53.7868i	0.232323	+	0.134132i	−0.379320	+	0.925265i	$0.623842\pi$
$402$		0			0
$403$	−43.0646	−	74.5901i	−0.106860	−	0.185087i
$404$	25.4224	−	44.0329i	0.0629268	−	0.108992i
$405$		0			0
$406$	107.980			0.265960
$407$			41.8605i			0.102851i
$408$		0			0
$409$	423.796	−	244.679i	1.03618	−	0.598237i	0.117428	−	0.993081i	$-0.462535\pi$
$409$	423.796	−	244.679i	1.03618	−	0.598237i	0.918748	+	0.394845i	$0.129202\pi$
$410$	30.0876			0.0733845
$411$		0			0
$412$	−29.6574	+	17.1227i	−0.0719840	+	0.0415600i
$413$	−208.768	−	120.532i	−0.505492	−	0.291846i
$414$		0			0
$415$	3.10066	−	5.37050i	0.00747146	−	0.0129410i
$416$	72.1982	−	125.051i	0.173553	−	0.300603i
$417$		0			0
$418$	21.6795	−	45.6476i	0.0518647	−	0.109205i
$419$	160.772			0.383705			0.191853	−	0.981424i	$-0.438550\pi$
$419$	160.772			0.383705			0.191853	+	0.981424i	$0.438550\pi$
$420$		0			0
$421$	304.122	+	175.585i	0.722381	+	0.417067i	0.815628	−	0.578576i	$-0.196392\pi$
$421$	304.122	+	175.585i	0.722381	+	0.417067i	−0.0932477	+	0.995643i	$0.529725\pi$
$422$	−369.527	−	640.039i	−0.875656	−	1.51668i
$423$		0			0
$424$	−317.570	−	550.047i	−0.748985	−	1.29728i
$425$	−374.928			−0.882184
$426$		0			0
$427$	265.825	+	460.423i	0.622541	+	1.07827i
$428$	−68.7123	+	39.6711i	−0.160543	+	0.0926894i
$429$		0			0
$430$			2.11762i			0.00492470i
$431$	−14.5476	+	8.39908i	−0.0337532	+	0.0194874i	−0.516782	−	0.856117i	$-0.672870\pi$
$431$	−14.5476	+	8.39908i	−0.0337532	+	0.0194874i	0.483028	+	0.875605i	$0.339537\pi$
$432$		0			0
$433$	−360.314	+	208.027i	−0.832133	+	0.480432i	−0.854582	−	0.519316i	$-0.826187\pi$
$433$	−360.314	+	208.027i	−0.832133	+	0.480432i	0.0224496	+	0.999748i	$0.492853\pi$
$434$	−71.0457	+	123.055i	−0.163700	+	0.283536i
$435$		0			0
$436$			45.8491i			0.105159i
$437$	−418.596	+	288.722i	−0.957886	+	0.660691i
$438$		0			0
$439$	−561.428	−	324.140i	−1.27888	−	0.738361i	−0.302237	−	0.953233i	$-0.597733\pi$
$439$	−561.428	−	324.140i	−1.27888	−	0.738361i	−0.976642	+	0.214872i	$0.931067\pi$
$440$	1.75913	+	1.01564i	0.00399803	+	0.00230826i
$441$		0			0
$442$	−126.208	+	218.599i	−0.285539	+	0.494569i
$443$	−341.171	−	590.925i	−0.770137	−	1.33392i	−0.937488	−	0.348019i	$-0.886855\pi$
$443$	−341.171	−	590.925i	−0.770137	−	1.33392i	0.167351	−	0.985897i	$-0.446479\pi$
$444$		0			0
$445$			34.8901i			0.0784047i
$446$	−301.941	−	522.976i	−0.676997	−	1.17259i
$447$		0			0
$448$	170.254			0.380032
$449$		−	185.741i		−	0.413677i	−0.978375	−	0.206839i	$-0.933682\pi$
$449$		−	185.741i		−	0.413677i	0.978375	−	0.206839i	$-0.0663175\pi$
$450$		0			0
$451$	−46.7238	−	26.9760i	−0.103600	−	0.0598138i
$452$	−117.603	+	67.8979i	−0.260183	+	0.150217i
$453$		0			0
$454$	488.312	−	845.782i	1.07558	−	1.86296i
$455$		−	10.7483i		−	0.0236227i
$456$		0			0
$457$	−311.871			−0.682430			−0.341215	−	0.939985i	$-0.610838\pi$
$457$	−311.871			−0.682430			−0.341215	+	0.939985i	$0.610838\pi$
$458$	−131.315	−	75.8149i	−0.286715	−	0.165535i
$459$		0			0
$460$	4.81425	+	8.33852i	0.0104658	+	0.0181272i
$461$	428.769	−	742.649i	0.930084	−	1.61095i	0.146910	−	0.989150i	$-0.453067\pi$
$461$	428.769	−	742.649i	0.930084	−	1.61095i	0.783174	−	0.621803i	$-0.213600\pi$
$462$		0			0
$463$	140.408			0.303258			0.151629	−	0.988438i	$-0.451548\pi$
$463$	140.408			0.303258			0.151629	+	0.988438i	$0.451548\pi$
$464$		−	174.659i		−	0.376421i
$465$		0			0
$466$	−102.350	+	59.0920i	−0.219636	+	0.126807i
$467$	−416.647			−0.892178			−0.446089	−	0.894989i	$-0.647183\pi$
$467$	−416.647			−0.892178			−0.446089	+	0.894989i	$0.647183\pi$
$468$		0			0
$469$	266.898	−	154.094i	0.569079	−	0.328558i
$470$	29.4242	+	16.9881i	0.0626047	+	0.0361448i
$471$		0			0
$472$	−143.693	+	248.884i	−0.304435	+	0.527297i
$473$	1.89862	−	3.28851i	0.00401400	−	0.00695244i
$474$		0			0
$475$	−389.777	+	268.844i	−0.820583	+	0.565988i
$476$	101.003			0.212192
$477$		0			0
$478$	−477.366	−	275.608i	−0.998674	−	0.576585i
$479$	78.9373	+	136.723i	0.164796	+	0.285435i	0.936583	−	0.350446i	$-0.113970\pi$
$479$	78.9373	+	136.723i	0.164796	+	0.285435i	−0.771787	+	0.635881i	$0.780637\pi$
$480$		0			0
$481$	−132.032	−	228.687i	−0.274496	−	0.475441i
$482$	438.384			0.909510
$483$		0			0
$484$	−76.6348	−	132.735i	−0.158336	−	0.274247i
$485$	45.6976	−	26.3835i	0.0942219	−	0.0543991i
$486$		0			0
$487$		−	69.9652i		−	0.143666i	−0.997417	−	0.0718329i	$-0.977115\pi$
$487$		−	69.9652i		−	0.143666i	0.997417	−	0.0718329i	$-0.0228848\pi$
$488$	548.895	−	316.905i	1.12479	−	0.649395i
$489$		0			0
$490$	12.0332	−	6.94739i	0.0245576	−	0.0141784i
$491$	−187.193	+	324.228i	−0.381249	+	0.660342i	−0.991241	−	0.132065i	$-0.957839\pi$
$491$	−187.193	+	324.228i	−0.381249	+	0.660342i	0.609992	+	0.792407i	$0.291172\pi$
$492$		0			0
$493$			134.871i			0.273573i
$494$	25.5410	+	317.755i	0.0517024	+	0.643230i
$495$		0			0
$496$	199.044	+	114.918i	0.401298	+	0.231690i
$497$	−475.525	−	274.544i	−0.956790	−	0.552403i
$498$		0			0
$499$	269.212	−	466.288i	0.539502	−	0.934446i	−0.459428	−	0.888215i	$-0.651946\pi$
$499$	269.212	−	466.288i	0.539502	−	0.934446i	0.998931	−	0.0462308i	$-0.0147210\pi$
$500$	8.97979	+	15.5534i	0.0179596	+	0.0311069i
$501$		0			0
$502$			477.524i			0.951244i
$503$	370.028	+	640.906i	0.735641	+	1.27417i	0.954441	+	0.298398i	$0.0964523\pi$
$503$	370.028	+	640.906i	0.735641	+	1.27417i	−0.218800	+	0.975770i	$0.570214\pi$
$504$		0			0
$505$	−11.1493			−0.0220778
$506$		−	71.1833i		−	0.140678i
$507$		0			0
$508$	−125.444	−	72.4249i	−0.246936	−	0.142569i
$509$	−36.2456	+	20.9264i	−0.0712094	+	0.0411128i	−0.535182	−	0.844737i	$-0.679757\pi$
$509$	−36.2456	+	20.9264i	−0.0712094	+	0.0411128i	0.463973	+	0.885850i	$0.346424\pi$
$510$		0			0
$511$	−330.794	+	572.952i	−0.647347	+	1.12124i
$512$		−	101.640i		−	0.198516i
$513$		0			0
$514$	−154.393			−0.300375
$515$	6.50331	+	3.75469i	0.0126278	+	0.00729065i
$516$		0			0
$517$	−30.4624	−	52.7624i	−0.0589214	−	0.102055i
$518$	−217.820	+	377.276i	−0.420502	+	0.728331i
$519$		0			0
$520$	−12.8137			−0.0246417
$521$			881.594i			1.69212i	0.533089	+	0.846059i	$0.321031\pi$
$521$			881.594i			1.69212i	−0.533089	+	0.846059i	$0.678969\pi$
$522$		0			0
$523$	447.114	−	258.142i	0.854903	−	0.493578i	−0.00739916	−	0.999973i	$-0.502355\pi$
$523$	447.114	−	258.142i	0.854903	−	0.493578i	0.862302	+	0.506394i	$0.169022\pi$
$524$	165.894			0.316591
$525$		0			0
$526$	565.568	−	326.531i	1.07522	−	0.620781i
$527$	−153.701	−	88.7393i	−0.291653	−	0.168386i
$528$		0			0
$529$	−93.6485	+	162.204i	−0.177029	+	0.306624i
$530$	32.8032	−	56.8168i	0.0618928	−	0.107201i
$531$		0			0
$532$	105.003	−	72.4249i	0.197375	−	0.136137i
$533$	340.341			0.638538
$534$		0			0
$535$	15.0673	+	8.69912i	0.0281632	+	0.0162600i
$536$	−183.704	−	318.184i	−0.342731	−	0.593628i
$537$		0			0
$538$	82.0234	+	142.069i	0.152460	+	0.264068i
$539$	−24.9156			−0.0462256
$540$		0			0
$541$	163.097	+	282.493i	0.301474	+	0.522168i	0.976470	−	0.215654i	$-0.0691882\pi$
$541$	163.097	+	282.493i	0.301474	+	0.522168i	−0.674996	+	0.737821i	$0.735855\pi$
$542$	−141.461	+	81.6723i	−0.260997	+	0.150687i
$543$		0			0
$544$		−	297.544i		−	0.546956i
$545$	8.70688	−	5.02692i	0.0159759	−	0.00922371i
$546$		0			0
$547$	−420.124	+	242.559i	−0.768052	+	0.443435i	−0.832179	−	0.554507i	$-0.812907\pi$
$547$	−420.124	+	242.559i	−0.768052	+	0.443435i	0.0641274	+	0.997942i	$0.479574\pi$
$548$	27.5234	−	47.6718i	0.0502251	−	0.0869924i
$549$		0			0
$550$		−	66.2825i		−	0.120514i
$551$	96.7103	+	140.213i	0.175518	+	0.254470i
$552$		0			0
$553$	293.209	+	169.284i	0.530215	+	0.306120i
$554$	949.290	+	548.073i	1.71352	+	0.989301i
$555$		0			0
$556$	−133.462	+	231.163i	−0.240039	+	0.415760i
$557$	−45.2381	−	78.3548i	−0.0812175	−	0.140673i	0.822556	−	0.568685i	$-0.192548\pi$
$557$	−45.2381	−	78.3548i	−0.0812175	−	0.140673i	−0.903773	+	0.428012i	$0.859214\pi$
$558$		0			0
$559$			23.9538i			0.0428511i
$560$	14.3410	+	24.8393i	0.0256089	+	0.0443559i
$561$		0			0
$562$	336.151			0.598133
$563$			126.463i			0.224624i	0.993673	+	0.112312i	$0.0358256\pi$
$563$			126.463i			0.224624i	−0.993673	+	0.112312i	$0.964174\pi$
$564$		0			0
$565$	25.7880	+	14.8887i	0.0456425	+	0.0263517i
$566$	−302.728	+	174.780i	−0.534856	+	0.308799i
$567$		0			0
$568$	−327.300	+	566.900i	−0.576232	+	0.998063i
$569$			857.322i			1.50672i	0.657610	+	0.753359i	$0.271568\pi$
$569$			857.322i			1.50672i	−0.657610	+	0.753359i	$0.728432\pi$
$570$		0			0
$571$	−99.1009			−0.173557			−0.0867784	−	0.996228i	$-0.527657\pi$
$571$	−99.1009			−0.173557			−0.0867784	+	0.996228i	$0.527657\pi$
$572$	−9.37346	−	5.41177i	−0.0163872	−	0.00946113i
$573$		0			0
$574$	−280.738	−	486.252i	−0.489090	−	0.847129i
$575$	−333.491	+	577.623i	−0.579984	+	1.00456i
$576$		0			0
$577$	777.423			1.34735			0.673677	−	0.739026i	$-0.264714\pi$
$577$	777.423			1.34735			0.673677	+	0.739026i	$0.264714\pi$
$578$		−	143.994i		−	0.249125i
$579$		0			0
$580$	2.79307	−	1.61258i	0.00481564	−	0.00278031i
$581$	−115.725			−0.199182
$582$		0			0
$583$	−101.882	+	58.8214i	−0.174754	+	0.100894i
$584$	683.049	+	394.358i	1.16960	+	0.675271i
$585$		0			0
$586$	−402.948	+	697.927i	−0.687625	+	1.19100i
$587$	265.805	−	460.388i	0.452820	−	0.784307i	−0.545740	−	0.837955i	$-0.683751\pi$
$587$	265.805	−	460.388i	0.452820	−	0.784307i	0.998560	+	0.0536475i	$0.0170847\pi$
$588$		0			0
$589$	−223.419	+	17.9583i	−0.379320	+	0.0304895i
$590$	−29.6854			−0.0503143
$591$		0			0
$592$	610.252	+	352.329i	1.03083	+	0.595150i
$593$	340.521	+	589.799i	0.574234	+	0.994603i	0.996124	+	0.0879557i	$0.0280334\pi$
$593$	340.521	+	589.799i	0.574234	+	0.994603i	−0.421890	+	0.906647i	$0.638633\pi$
$594$		0			0
$595$	−11.0741	−	19.1808i	−0.0186118	−	0.0322367i
$596$	177.361			0.297585
$597$		0			0
$598$	224.520	+	388.879i	0.375451	+	0.650300i
$599$	281.589	−	162.575i	0.470098	−	0.271411i	−0.246183	−	0.969223i	$-0.579176\pi$
$599$	281.589	−	162.575i	0.470098	−	0.271411i	0.716281	+	0.697812i	$0.245843\pi$
$600$		0			0
$601$			331.221i			0.551117i	0.961284	+	0.275558i	$0.0888628\pi$
$601$			331.221i			0.551117i	−0.961284	+	0.275558i	$0.911137\pi$
$602$	34.2233	−	19.7588i	0.0568494	−	0.0328220i
$603$		0			0
$604$	294.660	−	170.122i	0.487848	−	0.281659i
$605$	−16.8046	+	29.1064i	−0.0277761	+	0.0481097i
$606$		0			0
$607$		−	819.129i		−	1.34947i	−0.738060	−	0.674735i	$-0.764258\pi$
$607$		−	819.129i		−	1.34947i	0.738060	−	0.674735i	$-0.235742\pi$
$608$	−213.356	−	309.328i	−0.350914	−	0.508764i
$609$		0			0
$610$	56.6978	+	32.7345i	0.0929472	+	0.0536631i
$611$	332.836	+	192.163i	0.544740	+	0.314506i
$612$		0			0
$613$	161.068	−	278.978i	0.262754	−	0.455103i	−0.704219	−	0.709983i	$-0.748703\pi$
$613$	161.068	−	278.978i	0.262754	−	0.455103i	0.966973	+	0.254880i	$0.0820359\pi$
$614$	−547.106	−	947.615i	−0.891051	−	1.54335i
$615$		0			0
$616$		−	37.9063i		−	0.0615361i
$617$	570.525	+	988.179i	0.924676	+	1.60159i	0.792081	+	0.610416i	$0.208998\pi$
$617$	570.525	+	988.179i	0.924676	+	1.60159i	0.132595	+	0.991170i	$0.457669\pi$
$618$		0			0
$619$	−56.7606			−0.0916972			−0.0458486	−	0.998948i	$-0.514599\pi$
$619$	−56.7606			−0.0916972			−0.0458486	+	0.998948i	$0.514599\pi$
$620$			4.24402i			0.00684519i
$621$		0			0
$622$	−933.279	−	538.829i	−1.50045	−	0.866284i
$623$	563.866	−	325.548i	0.905082	−	0.522549i
$624$		0			0
$625$	−309.545	+	536.147i	−0.495272	+	0.857836i
$626$			81.2515i			0.129795i
$627$		0			0
$628$	−134.354			−0.213940
$629$	−471.234	−	272.067i	−0.749180	−	0.432539i
$630$		0			0
$631$	568.803	+	985.195i	0.901430	+	1.56132i	0.825638	+	0.564200i	$0.190815\pi$
$631$	568.803	+	985.195i	0.901430	+	1.56132i	0.0757921	+	0.997124i	$0.475851\pi$
$632$	201.813	−	349.551i	0.319325	−	0.553086i
$633$		0			0
$634$	1001.85			1.58020
$635$			31.7628i			0.0500202i
$636$		0			0
$637$	136.116	−	78.5864i	0.213682	−	0.123370i
$638$	−23.8436			−0.0373724
$639$		0			0
$640$	37.3996	−	21.5927i	0.0584368	−	0.0337385i
$641$	−65.0480	−	37.5555i	−0.101479	−	0.0585889i	0.448402	−	0.893832i	$-0.351993\pi$
$641$	−65.0480	−	37.5555i	−0.101479	−	0.0585889i	−0.549881	+	0.835243i	$0.685327\pi$
$642$		0			0
$643$	−154.393	+	267.417i	−0.240114	+	0.415889i	−0.960746	−	0.277428i	$-0.910518\pi$
$643$	−154.393	+	267.417i	−0.240114	+	0.415889i	0.720633	+	0.693317i	$0.243851\pi$
$644$	89.8403	−	155.608i	0.139504	−	0.241627i
$645$		0			0
$646$	372.964	+	540.732i	0.577343	+	0.837046i
$647$	−121.571			−0.187900			−0.0939498	−	0.995577i	$-0.529949\pi$
$647$	−121.571			−0.187900			−0.0939498	+	0.995577i	$0.529949\pi$
$648$		0			0
$649$	46.0992	+	26.6154i	0.0710312	+	0.0410099i
$650$	209.062	+	362.106i	0.321634	+	0.557086i
$651$		0			0
$652$	57.0984	+	98.8973i	0.0875742	+	0.151683i
$653$	−1258.75			−1.92764			−0.963819	−	0.266559i	$-0.914113\pi$
$653$	−1258.75			−1.92764			−0.963819	+	0.266559i	$0.914113\pi$
$654$		0			0
$655$	−18.1887	−	31.5037i	−0.0277690	−	0.0480973i
$656$	−786.524	+	454.100i	−1.19897	+	0.692225i
$657$		0			0
$658$		−	634.040i		−	0.963587i
$659$	−851.135	+	491.403i	−1.29156	+	0.745680i	−0.978930	−	0.204197i	$-0.934542\pi$
$659$	−851.135	+	491.403i	−1.29156	+	0.745680i	−0.312625	+	0.949876i	$0.601208\pi$
$660$		0			0
$661$	249.208	−	143.880i	0.377017	−	0.217671i	−0.299503	−	0.954095i	$-0.596821\pi$
$661$	249.208	−	143.880i	0.377017	−	0.217671i	0.676519	+	0.736425i	$0.263487\pi$
$662$	10.4174	−	18.0434i	0.0157362	−	0.0272559i
$663$		0			0
$664$			137.962i			0.207774i
$665$	−25.2663	−	11.9998i	−0.0379945	−	0.0180448i
$666$		0			0
$667$	207.786	+	119.965i	0.311523	+	0.179858i
$668$	−26.5895	−	15.3514i	−0.0398046	−	0.0229812i
$669$		0			0
$670$	18.9756	−	32.8667i	0.0283217	−	0.0490547i
$671$	−58.6983	−	101.668i	−0.0874788	−	0.151518i
$672$		0			0
$673$		−	252.012i		−	0.374460i	−0.982316	−	0.187230i	$-0.940049\pi$
$673$		−	252.012i		−	0.374460i	0.982316	−	0.187230i	$-0.0599510\pi$
$674$	−483.172	−	836.879i	−0.716873	−	1.24166i
$675$		0			0
$676$	−148.190			−0.219216
$677$		−	293.002i		−	0.432795i	−0.976305	−	0.216397i	$-0.930569\pi$
$677$		−	293.002i		−	0.432795i	0.976305	−	0.216397i	$-0.0694306\pi$
$678$		0			0
$679$	−852.780	−	492.353i	−1.25593	−	0.725114i
$680$	−22.8665	+	13.2020i	−0.0336272	+	0.0194147i
$681$		0			0
$682$	15.6880	−	27.1724i	0.0230029	−	0.0398422i
$683$		−	532.042i		−	0.778979i	−0.921031	−	0.389489i	$-0.872651\pi$
$683$		−	532.042i		−	0.778979i	0.921031	−	0.389489i	$-0.127349\pi$
$684$		0			0
$685$	−12.0707			−0.0176215
$686$	−735.684	−	424.747i	−1.07243	−	0.619165i
$687$		0			0
$688$	−31.9604	−	55.3570i	−0.0464540	−	0.0804607i
$689$	371.058	−	642.691i	0.538545	−	0.932788i
$690$		0			0
$691$	−806.065			−1.16652			−0.583260	−	0.812286i	$-0.698223\pi$
$691$	−806.065			−1.16652			−0.583260	+	0.812286i	$0.698223\pi$
$692$		−	71.6096i		−	0.103482i
$693$		0			0
$694$	−128.509	+	74.1945i	−0.185171	+	0.106909i
$695$	58.5314			0.0842178
$696$		0			0
$697$	607.351	−	350.654i	0.871379	−	0.503091i
$698$	483.050	+	278.889i	0.692048	+	0.399554i
$699$		0			0
$700$	83.6551	−	144.895i	0.119507	−	0.206993i
$701$	395.041	−	684.230i	0.563539	−	0.976077i	−0.433645	−	0.901084i	$-0.642773\pi$
$701$	395.041	−	684.230i	0.563539	−	0.976077i	0.997184	−	0.0749939i	$-0.0238937\pi$
$702$		0			0
$703$	−684.985	+	55.0586i	−0.974374	+	0.0783195i
$704$	−37.5948			−0.0534017
$705$		0			0
$706$	−1115.01	−	643.750i	−1.57933	−	0.911828i
$707$	104.031	+	180.186i	0.147144	+	0.254860i
$708$		0			0
$709$	−497.856	−	862.312i	−0.702195	−	1.21624i	−0.967694	−	0.252126i	$-0.918870\pi$
$709$	−497.856	−	862.312i	−0.702195	−	1.21624i	0.265499	−	0.964111i	$-0.414463\pi$
$710$	−67.6164			−0.0952344
$711$		0			0
$712$	−388.104	−	672.216i	−0.545090	−	0.944124i
$713$	−273.428	+	157.864i	−0.383489	+	0.221408i
$714$		0			0
$715$			2.37340i			0.00331944i
$716$	212.004	−	122.400i	0.296094	−	0.170950i
$717$		0			0
$718$	875.288	−	505.348i	1.21906	−	0.703827i
$719$	600.858	−	1040.72i	0.835686	−	1.44745i	−0.0577845	−	0.998329i	$-0.518404\pi$
$719$	600.858	−	1040.72i	0.835686	−	1.44745i	0.893471	−	0.449122i	$-0.148263\pi$
$720$		0			0
$721$		−	140.135i		−	0.194362i
$722$	775.470	+	294.712i	1.07406	+	0.408189i
$723$		0			0
$724$	95.1574	+	54.9391i	0.131433	+	0.0758828i
$725$	193.481	+	111.706i	0.266870	+	0.154077i
$726$		0			0
$727$	12.3246	−	21.3468i	0.0169527	−	0.0293629i	−0.857425	−	0.514610i	$-0.827937\pi$
$727$	12.3246	−	21.3468i	0.0169527	−	0.0293629i	0.874377	+	0.485247i	$0.161270\pi$
$728$	119.560	+	207.085i	0.164231	+	0.284457i
$729$		0			0
$730$			81.4700i			0.111603i
$731$	24.6797	+	42.7465i	0.0337615	+	0.0584767i
$732$		0			0
$733$	68.8594			0.0939419			0.0469710	−	0.998896i	$-0.485043\pi$
$733$	68.8594			0.0939419			0.0469710	+	0.998896i	$0.485043\pi$
$734$			306.028i			0.416932i
$735$		0			0
$736$	−458.404	−	264.660i	−0.622831	−	0.359592i
$737$	−58.9352	+	34.0263i	−0.0799664	+	0.0461686i
$738$		0			0
$739$	−497.408	+	861.536i	−0.673083	+	1.16581i	0.303943	+	0.952690i	$0.401697\pi$
$739$	−497.408	+	861.536i	−0.673083	+	1.16581i	−0.977025	+	0.213123i	$0.931636\pi$
$740$			13.0118i			0.0175835i
$741$		0			0
$742$	−1224.30			−1.65000
$743$	−341.188	−	196.985i	−0.459204	−	0.265121i	0.252506	−	0.967595i	$-0.418745\pi$
$743$	−341.188	−	196.985i	−0.459204	−	0.265121i	−0.711709	+	0.702474i	$0.752079\pi$
$744$		0			0
$745$	−19.4459	−	33.6813i	−0.0261019	−	0.0452098i
$746$	−390.721	+	676.749i	−0.523755	+	0.907171i
$747$		0			0
$748$	−22.3031			−0.0298169
$749$		−	324.674i		−	0.433477i
$750$		0			0
$751$	153.043	−	88.3594i	0.203786	−	0.117656i	−0.394634	−	0.918838i	$-0.629129\pi$
$751$	153.043	−	88.3594i	0.203786	−	0.117656i	0.598420	+	0.801183i	$0.295795\pi$
$752$	−1025.57			−1.36380
$753$		0			0
$754$	130.259	−	75.2051i	0.172757	−	0.0997415i
$755$	−64.6134	−	37.3046i	−0.0855807	−	0.0494100i
$756$		0			0
$757$	591.818	−	1025.06i	0.781793	−	1.35411i	−0.149103	−	0.988822i	$-0.547639\pi$
$757$	591.818	−	1025.06i	0.781793	−	1.35411i	0.930896	−	0.365284i	$-0.119028\pi$
$758$	81.6118	−	141.356i	0.107667	−	0.186485i
$759$		0			0
$760$	−14.3056	+	30.1214i	−0.0188232	+	0.0396335i
$761$	517.695			0.680282			0.340141	−	0.940374i	$-0.389525\pi$
$761$	517.695			0.680282			0.340141	+	0.940374i	$0.389525\pi$
$762$		0			0
$763$	−162.482	−	93.8091i	−0.212952	−	0.122948i
$764$	210.175	+	364.034i	0.275098	+	0.476484i
$765$		0			0
$766$	393.415	+	681.415i	0.513597	+	0.889576i
$767$	−335.791			−0.437798
$768$		0			0
$769$	476.376	+	825.107i	0.619474	+	1.07296i	0.989582	+	0.143972i	$0.0459875\pi$
$769$	476.376	+	825.107i	0.619474	+	1.07296i	−0.370107	+	0.928989i	$0.620679\pi$
$770$	3.39093	−	1.95775i	0.00440380	−	0.00254254i
$771$		0			0
$772$		−	277.303i		−	0.359201i
$773$	1088.18	−	628.259i	1.40773	−	0.812754i	0.412561	−	0.910930i	$-0.364634\pi$
$773$	1088.18	−	628.259i	1.40773	−	0.812754i	0.995169	+	0.0981762i	$0.0313009\pi$
$774$		0			0
$775$	−254.603	+	146.995i	−0.328520	+	0.189671i
$776$	−586.961	+	1016.65i	−0.756393	+	1.31011i
$777$		0			0
$778$			178.546i			0.229493i
$779$	379.967	−	800.046i	0.487762	−	1.02702i
$780$		0			0
$781$	105.003	+	60.6236i	0.134447	+	0.0776231i
$782$	801.328	+	462.647i	1.02472	+	0.591620i
$783$		0			0
$784$	−209.708	+	363.225i	−0.267485	+	0.463297i
$785$	14.7307	+	25.5142i	0.0187652	+	0.0325022i
$786$		0			0
$787$		−	981.332i		−	1.24693i	−0.781852	−	0.623464i	$-0.785725\pi$
$787$		−	981.332i		−	1.24693i	0.781852	−	0.623464i	$-0.214275\pi$
$788$	−55.2205	−	95.6447i	−0.0700768	−	0.121377i
$789$		0			0
$790$	41.6923			0.0527751
$791$		−	555.687i		−	0.702512i
$792$		0			0
$793$	641.345	+	370.281i	0.808758	+	0.466937i
$794$	−189.853	+	109.612i	−0.239110	+	0.138050i
$795$		0			0
$796$	−27.2528	+	47.2033i	−0.0342372	+	0.0593006i
$797$		−	943.008i		−	1.18320i	−0.806233	−	0.591599i	$-0.798497\pi$
$797$		−	943.008i		−	1.18320i	0.806233	−	0.591599i	$-0.201503\pi$
$798$		0			0
$799$	791.945			0.991171
$800$	−426.844	−	246.438i	−0.533555	−	0.308048i
$801$		0			0
$802$	−123.603	−	214.086i	−0.154118	−	0.266941i
$803$	73.0445	−	126.517i	0.0909645	−	0.157555i
$804$		0			0
$805$	−39.4006			−0.0489448
$806$			197.926i			0.245566i
$807$		0			0
$808$	214.810	−	124.021i	0.265854	−	0.153491i
$809$	−942.078			−1.16450			−0.582249	−	0.813011i	$-0.697827\pi$
$809$	−942.078			−1.16450			−0.582249	+	0.813011i	$0.697827\pi$
$810$		0			0
$811$	556.679	−	321.399i	0.686411	−	0.396300i	−0.115855	−	0.993266i	$-0.536961\pi$
$811$	556.679	−	321.399i	0.686411	−	0.396300i	0.802266	+	0.596967i	$0.203627\pi$
$812$	−52.1225	−	30.0929i	−0.0641902	−	0.0370602i
$813$		0			0
$814$	48.0980	−	83.3083i	0.0590885	−	0.102344i
$815$	12.5206	−	21.6863i	0.0153627	−	0.0266090i
$816$		0			0
$817$	56.3087	+	26.7427i	0.0689213	+	0.0327329i
$818$	−1124.55			−1.37476
$819$		0			0
$820$	−14.5235	−	8.38514i	−0.0177116	−	0.0102258i
$821$	428.109	+	741.507i	0.521449	+	0.903176i	0.999689	+	0.0249465i	$0.00794155\pi$
$821$	428.109	+	741.507i	0.521449	+	0.903176i	−0.478240	+	0.878229i	$0.658725\pi$
$822$		0			0
$823$	705.555	+	1222.06i	0.857297	+	1.48488i	0.874498	+	0.485029i	$0.161191\pi$
$823$	705.555	+	1222.06i	0.857297	+	1.48488i	−0.0172014	+	0.999852i	$0.505476\pi$
$824$	−167.063			−0.202746
$825$		0			0
$826$	276.985	+	479.752i	0.335333	+	0.580814i
$827$	790.058	−	456.140i	0.955330	−	0.551560i	0.0605975	−	0.998162i	$-0.480699\pi$
$827$	790.058	−	456.140i	0.955330	−	0.551560i	0.894733	+	0.446602i	$0.147366\pi$
$828$		0			0
$829$			1182.75i			1.42672i	0.700799	+	0.713359i	$0.252827\pi$
$829$			1182.75i			1.42672i	−0.700799	+	0.713359i	$0.747173\pi$
$830$	−12.3415	+	7.12535i	−0.0148692	+	0.00858476i
$831$		0			0
$832$	205.383	−	118.578i	0.246855	−	0.142522i
$833$	161.936	−	280.481i	0.194401	−	0.336712i
$834$		0			0
$835$			6.73256i			0.00806295i
$836$	−23.1864	+	15.9925i	−0.0277349	+	0.0191298i
$837$		0			0
$838$	−319.960	−	184.729i	−0.381813	−	0.220440i
$839$	−791.646	−	457.057i	−0.943559	−	0.544764i	−0.0524848	−	0.998622i	$-0.516714\pi$
$839$	−791.646	−	457.057i	−0.943559	−	0.544764i	−0.891074	+	0.453858i	$0.850047\pi$
$840$		0			0
$841$	−380.316	+	658.727i	−0.452219	+	0.783267i
$842$	−403.497	−	698.877i	−0.479213	−	0.830020i
$843$		0			0
$844$			411.935i			0.488074i
$845$	16.2476	+	28.1417i	0.0192280	+	0.0333038i
$846$		0			0
$847$	627.191			0.740486
$848$			1980.34i			2.33530i
$849$		0			0
$850$	746.159	+	430.795i	0.877834	+	0.506818i
$851$	−838.307	+	483.997i	−0.985084	+	0.568739i
$852$		0			0
$853$	241.160	−	417.701i	0.282720	−	0.489685i	−0.689334	−	0.724444i	$-0.742097\pi$
$853$	241.160	−	417.701i	0.282720	−	0.489685i	0.972054	+	0.234759i	$0.0754301\pi$
$854$		−	1221.74i		−	1.43061i
$855$		0			0
$856$	−387.063			−0.452176
$857$	965.678	+	557.534i	1.12681	+	0.650565i	0.943131	−	0.332421i	$-0.107865\pi$
$857$	965.678	+	557.534i	1.12681	+	0.650565i	0.183681	+	0.982986i	$0.441199\pi$
$858$		0			0
$859$	−103.471	−	179.217i	−0.120455	−	0.208635i	0.799492	−	0.600677i	$-0.205102\pi$
$859$	−103.471	−	179.217i	−0.120455	−	0.208635i	−0.919947	+	0.392042i	$0.871769\pi$
$860$	0.590162	−	1.02219i	0.000686234	−	0.00118859i
$861$		0			0
$862$	38.6024			0.0447824
$863$		−	562.589i		−	0.651899i	−0.945387	−	0.325949i	$-0.894316\pi$
$863$		−	562.589i		−	0.651899i	0.945387	−	0.325949i	$-0.105684\pi$
$864$		0			0
$865$	−13.5989	+	7.85132i	−0.0157213	+	0.00907667i
$866$	956.099			1.10404
$867$		0			0
$868$	68.5884	−	39.5996i	0.0790189	−	0.0456216i
$869$	−64.7450	−	37.3806i	−0.0745052	−	0.0430156i
$870$		0			0
$871$	214.645	−	371.776i	0.246435	−	0.426838i
$872$	−111.835	+	193.704i	−0.128251	+	0.222138i
$873$		0			0
$874$	1164.81	−	93.6265i	1.33273	−	0.107124i
$875$	−73.4920			−0.0839909
$876$		0			0
$877$	−446.560	−	257.821i	−0.509190	−	0.293981i	0.223311	−	0.974747i	$-0.428314\pi$
$877$	−446.560	−	257.821i	−0.509190	−	0.293981i	−0.732501	+	0.680766i	$0.761647\pi$
$878$	744.880	+	1290.17i	0.848382	+	1.46944i
$879$		0			0
$880$	−3.16671	−	5.48490i	−0.00359853	−	0.00623284i
$881$	830.527			0.942709			0.471355	−	0.881944i	$-0.343765\pi$
$881$	830.527			0.942709			0.471355	+	0.881944i	$0.343765\pi$
$882$		0			0
$883$	−387.441	−	671.068i	−0.438778	−	0.759986i	0.558817	−	0.829291i	$-0.311255\pi$
$883$	−387.441	−	671.068i	−0.438778	−	0.759986i	−0.997596	+	0.0693046i	$0.977922\pi$
$884$	121.843	−	70.3462i	0.137832	−	0.0795772i
$885$		0			0
$886$			1568.03i			1.76979i
$887$	−419.897	+	242.428i	−0.473390	+	0.273312i	−0.717658	−	0.696396i	$-0.754786\pi$
$887$	−419.897	+	242.428i	−0.473390	+	0.273312i	0.244268	+	0.969708i	$0.421452\pi$
$888$		0			0
$889$	513.325	−	296.368i	0.577419	−	0.333373i
$890$	40.0890	−	69.4361i	0.0450438	−	0.0780181i
$891$		0			0
$892$			336.592i			0.377345i
$893$	823.310	−	567.869i	0.921960	−	0.635911i
$894$		0			0
$895$	−46.4884	−	26.8401i	−0.0519423	−	0.0299889i
$896$	−697.927	−	402.948i	−0.778936	−	0.449719i
$897$		0			0
$898$	−213.418	+	369.651i	−0.237659	+	0.411638i
$899$	52.8780	+	91.5874i	0.0588187	+	0.101877i
$900$		0			0
$901$		−	1529.21i		−	1.69724i
$902$	61.9913	+	107.372i	0.0687264	+	0.119038i
$903$		0			0
$904$	−662.466			−0.732816
$905$		−	24.0942i		−	0.0266235i
$906$		0			0
$907$	−606.666	−	350.259i	−0.668871	−	0.386173i	0.126778	−	0.991931i	$-0.459536\pi$
$907$	−606.666	−	350.259i	−0.668871	−	0.386173i	−0.795649	+	0.605759i	$0.792870\pi$
$908$	−471.423	+	272.176i	−0.519188	+	0.299754i
$909$		0			0
$910$	−12.3499	+	21.3907i	−0.0135713	+	0.0235062i
$911$			1216.56i			1.33541i	0.744426	+	0.667706i	$0.232723\pi$
$911$			1216.56i			1.33541i	−0.744426	+	0.667706i	$0.767277\pi$
$912$		0			0
$913$	25.5538			0.0279889
$914$	620.666	+	358.341i	0.679065	+	0.392059i
$915$		0			0
$916$	42.2578	+	73.1927i	0.0461330	+	0.0799047i
$917$	−339.425	+	587.902i	−0.370148	+	0.641114i
$918$		0			0
$919$	−1332.61			−1.45006			−0.725030	−	0.688717i	$-0.758174\pi$
$919$	−1332.61			−1.45006			−0.725030	+	0.688717i	$0.758174\pi$
$920$			46.9716i			0.0510561i
$921$		0			0
$922$	−1706.62	+	985.317i	−1.85100	+	1.06867i
$923$	−764.853			−0.828660
$924$		0			0
$925$	−780.592	+	450.675i	−0.843883	+	0.487216i
$926$	−279.432	−	161.330i	−0.301762	−	0.174223i
$927$		0			0
$928$	−88.6504	+	153.547i	−0.0955284	+	0.165460i
$929$	−297.945	+	516.056i	−0.320716	+	0.555497i	−0.980636	−	0.195839i	$-0.937257\pi$
$929$	−297.945	+	516.056i	−0.320716	+	0.555497i	0.659920	+	0.751336i	$0.270590\pi$
$930$		0			0
$931$	−32.7712	−	407.707i	−0.0352000	−	0.437923i
$932$	65.8736			0.0706798
$933$		0			0
$934$	829.186	+	478.730i	0.887779	+	0.512559i
$935$	2.44532	+	4.23542i	0.00261532	+	0.00452986i
$936$		0			0
$937$	−330.843	−	573.037i	−0.353087	−	0.611565i	0.633701	−	0.773578i	$-0.281535\pi$
$937$	−330.843	−	573.037i	−0.353087	−	0.611565i	−0.986789	+	0.162013i	$0.948201\pi$
$938$	−708.219			−0.755031
$939$		0			0
$940$	−9.46883	−	16.4005i	−0.0100732	−	0.0174473i
$941$	289.896	−	167.371i	0.308072	−	0.177865i	−0.337992	−	0.941149i	$-0.609748\pi$
$941$	289.896	−	167.371i	0.308072	−	0.177865i	0.646063	+	0.763284i	$0.276414\pi$
$942$		0			0
$943$		−	1247.60i		−	1.32301i
$944$	776.010	−	448.030i	0.822045	−	0.474608i
$945$		0			0
$946$	−7.55703	+	4.36306i	−0.00798841	+	0.00461211i
$947$	−523.600	+	906.901i	−0.552904	+	0.957657i	0.445160	+	0.895451i	$0.353147\pi$
$947$	−523.600	+	906.901i	−0.552904	+	0.957657i	−0.998063	+	0.0622060i	$0.980186\pi$
$948$		0			0
$949$			921.560i			0.971085i
$950$	1084.61	−	87.1806i	1.14170	−	0.0917690i
$951$		0			0
$952$	426.720	+	246.367i	0.448236	+	0.258789i
$953$	1349.22	+	778.975i	1.41577	+	0.817393i	0.995923	−	0.0902041i	$-0.0287520\pi$
$953$	1349.22	+	778.975i	1.41577	+	0.817393i	0.419843	+	0.907597i	$0.362085\pi$
$954$		0			0
$955$	46.0874	−	79.8258i	0.0482591	−	0.0835872i
$956$	153.619	+	266.075i	0.160689	+	0.278321i
$957$		0			0
$958$		−	362.798i		−	0.378704i
$959$	112.628	+	195.077i	0.117443	+	0.203417i
$960$		0			0
$961$	821.835			0.855187
$962$			606.825i			0.630795i
$963$		0			0
$964$	−211.611	−	122.173i	−0.219513	−	0.126736i
$965$	−52.6608	+	30.4037i	−0.0545707	+	0.0315064i
$966$		0			0
$967$	575.086	−	996.077i	0.594711	−	1.03007i	−0.398877	−	0.917005i	$-0.630600\pi$
$967$	575.086	−	996.077i	0.594711	−	1.03007i	0.993588	−	0.113065i	$-0.0360668\pi$
$968$		−	747.710i		−	0.772428i
$969$		0			0
$970$	−121.260			−0.125010
$971$	970.030	+	560.047i	0.999001	+	0.576774i	0.907953	−	0.419073i	$-0.137645\pi$
$971$	970.030	+	560.047i	0.999001	+	0.576774i	0.0910487	+	0.995846i	$0.470978\pi$
$972$		0			0
$973$	−546.137	−	945.937i	−0.561292	−	0.972186i
$974$	−80.3906	+	139.241i	−0.0825365	+	0.142957i
$975$		0			0
$976$	−1976.19			−2.02479
$977$			106.000i			0.108496i	0.998528	+	0.0542478i	$0.0172761\pi$
$977$			106.000i			0.108496i	−0.998528	+	0.0542478i	$0.982724\pi$
$978$		0			0
$979$	−124.510	+	71.8860i	−0.127181	+	0.0734280i
$980$	−7.74470			−0.00790275
$981$		0			0
$982$	745.080	−	430.172i	0.758738	−	0.438057i
$983$	−1529.14	−	882.852i	−1.55559	−	0.898120i	−0.997670	−	0.0682241i	$-0.978267\pi$
$983$	−1529.14	−	882.852i	−1.55559	−	0.898120i	−0.557919	−	0.829896i	$-0.688400\pi$
$984$		0			0
$985$	−12.1088	+	20.9731i	−0.0122932	+	0.0212925i
$986$	154.968	−	268.413i	0.157169	−	0.272224i
$987$		0			0
$988$	76.2267	−	160.501i	0.0771525	−	0.162450i
$989$	87.8083			0.0887850
$990$		0			0
$991$	1144.85	+	660.979i	1.15525	+	0.666982i	0.950160	−	0.311762i	$-0.100919\pi$
$991$	1144.85	+	660.979i	1.15525	+	0.666982i	0.205087	+	0.978744i	$0.434252\pi$
$992$	−116.656	−	202.054i	−0.117597	−	0.203683i
$993$		0			0
$994$	630.907	+	1092.76i	0.634715	+	1.09936i
$995$	11.9521			0.0120121
$996$		0			0
$997$	42.4622	+	73.5468i	0.0425900	+	0.0737681i	0.886535	−	0.462662i	$-0.153106\pi$
$997$	42.4622	+	73.5468i	0.0425900	+	0.0737681i	−0.843945	+	0.536430i	$0.819772\pi$
$998$	−1071.54	+	618.652i	−1.07368	+	0.619892i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	171.3.p.e.46.1		6
3.2	odd	2		57.3.g.a.46.3	yes	6
12.11	even	2		912.3.be.d.673.2		6
19.12	odd	6	inner	171.3.p.e.145.1		6
57.50	even	6		57.3.g.a.31.3	✓	6
228.107	odd	6		912.3.be.d.145.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
57.3.g.a.31.3	✓	6	57.50	even	6
57.3.g.a.46.3	yes	6	3.2	odd	2
171.3.p.e.46.1		6	1.1	even	1	trivial
171.3.p.e.145.1		6	19.12	odd	6	inner
912.3.be.d.145.2		6	228.107	odd	6
912.3.be.d.673.2		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)

\(f(q)\)	\(=\)	\(q+(-1.99014 - 1.14901i) q^{2} +(0.640435 + 1.10927i) q^{4} +(0.140435 - 0.243241i) q^{5} -5.24143 q^{7} +6.24860i q^{8} +O(q^{10})\)	\(q+(-1.99014 - 1.14901i) q^{2} +(0.640435 + 1.10927i) q^{4} +(0.140435 - 0.243241i) q^{5} -5.24143 q^{7} +6.24860i q^{8} +(-0.558972 + 0.322723i) q^{10} +1.15739 q^{11} +(-6.32289 + 3.65052i) q^{13} +(10.4312 + 6.02244i) q^{14} +(9.74143 - 16.8726i) q^{16} +(-7.52230 + 13.0290i) q^{17} +(1.52230 + 18.9389i) q^{19} +0.359759 q^{20} +(-2.30336 - 1.32985i) q^{22} +(13.3819 + 23.1781i) q^{23} +(12.4606 + 21.5823i) q^{25} +16.7779 q^{26} +(-3.35679 - 5.81414i) q^{28} +(7.76372 - 4.48239i) q^{29} +11.7968i q^{31} +(-17.1278 + 9.88874i) q^{32} +(29.9408 - 17.2863i) q^{34} +(-0.736082 + 1.27493i) q^{35} +36.1681i q^{37} +(18.7314 - 39.4402i) q^{38} +(1.51992 + 0.877524i) q^{40} +(-40.3701 - 23.3077i) q^{41} +(1.64044 - 2.84132i) q^{43} +(0.741232 + 1.28385i) q^{44} -61.5034i q^{46} +(-26.3199 - 45.5874i) q^{47} -21.5274 q^{49} -57.2691i q^{50} +(-8.09880 - 4.67585i) q^{52} +(-88.0273 + 50.8226i) q^{53} +(0.162538 - 0.281524i) q^{55} -32.7516i q^{56} -20.6012 q^{58} +(39.8304 + 22.9961i) q^{59} +(-50.7162 - 87.8430i) q^{61} +(13.5547 - 23.4773i) q^{62} -32.4825 q^{64} +2.05065i q^{65} +(-50.9209 + 29.3992i) q^{67} -19.2702 q^{68} +(2.92981 - 1.69153i) q^{70} +(90.7243 + 52.3797i) q^{71} +(63.1115 - 109.312i) q^{73} +(41.5574 - 71.9796i) q^{74} +(-20.0334 + 13.8178i) q^{76} -6.06636 q^{77} +(-55.9406 - 32.2973i) q^{79} +(-2.73608 - 4.73903i) q^{80} +(53.5614 + 92.7710i) q^{82} +22.0789 q^{83} +(2.11279 + 3.65947i) q^{85} +(-6.52939 + 3.76974i) q^{86} +7.23205i q^{88} +(-107.579 + 62.1106i) q^{89} +(33.1410 - 19.1339i) q^{91} +(-17.1404 + 29.6881i) q^{92} +120.967i q^{94} +(4.82051 + 2.28941i) q^{95} +(162.700 + 93.9348i) q^{97} +(42.8426 + 24.7352i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} + 5 q^{4} + 2 q^{5} + 26 q^{7}+O(q^{10}) \) 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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