LMFDB - Embedded newform 144.3.o.c.31.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [144,3,Mod(31,144)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(144, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 2]))

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

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

chi := DirichletCharacter("144.31");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 144 = 2^{4} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	144.o (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:	$3.92371580679$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.856615824.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 11x^{6} + 36x^{4} + 32x^{2} + 4 $ x^8 + 11x^6 + 36x^4 + 32*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.3
Root			$-0.385731i$ of defining polynomial
Character	$\chi$	$=$	144.31
Dual form			144.3.o.c.79.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.28651 - 2.71015i) q^{3} +(-0.454613 + 0.787412i) q^{5} +(6.10709 - 3.52593i) q^{7} +(-5.68980 - 6.97325i) q^{9} +O(q^{10})$	\(q+(1.28651 - 2.71015i) q^{3} +(-0.454613 + 0.787412i) q^{5} +(6.10709 - 3.52593i) q^{7} +(-5.68980 - 6.97325i) q^{9} +(6.96661 - 4.02218i) q^{11} +(3.35952 - 5.81886i) q^{13} +(1.54914 + 2.24508i) q^{15} -26.3462 q^{17} -20.5603i q^{19} +(-1.69897 - 21.0873i) q^{21} +(21.8305 + 12.6038i) q^{23} +(12.0867 + 20.9347i) q^{25} +(-26.2185 + 6.44905i) q^{27} +(15.1693 + 26.2741i) q^{29} +(0.120040 + 0.0693050i) q^{31} +(-1.93809 - 24.0551i) q^{33} +6.41173i q^{35} +69.7588 q^{37} +(-11.4479 - 16.5908i) q^{39} +(-29.3794 + 50.8866i) q^{41} +(-2.45853 + 1.41943i) q^{43} +(8.07748 - 1.31009i) q^{45} +(-70.7583 + 40.8523i) q^{47} +(0.364383 - 0.631130i) q^{49} +(-33.8946 + 71.4022i) q^{51} -30.0259 q^{53} +7.31413i q^{55} +(-55.7213 - 26.4509i) q^{57} +(77.1442 + 44.5392i) q^{59} +(24.0688 + 41.6885i) q^{61} +(-59.3353 - 22.5244i) q^{63} +(3.05456 + 5.29066i) q^{65} +(-44.0829 - 25.4513i) q^{67} +(62.2432 - 42.9488i) q^{69} -68.4355i q^{71} -22.1474 q^{73} +(72.2857 - 5.82397i) q^{75} +(28.3638 - 49.1276i) q^{77} +(34.4343 - 19.8807i) q^{79} +(-16.2524 + 79.3527i) q^{81} +(23.0801 - 13.3253i) q^{83} +(11.9773 - 20.7453i) q^{85} +(90.7221 - 7.30936i) q^{87} -25.7926 q^{89} -47.3818i q^{91} +(0.342259 - 0.236164i) q^{93} +(16.1894 + 9.34695i) q^{95} +(-52.3697 - 90.7070i) q^{97} +(-67.6863 - 25.6946i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 3 q^{3} + 3 q^{5} - 3 q^{7} - 3 q^{9}+O(q^{10}) $ 8 * q + 3 * q^3 + 3 * q^5 - 3 * q^7 - 3 * q^9	$ 8 q + 3 q^{3} + 3 q^{5} - 3 q^{7} - 3 q^{9} - 18 q^{11} + 5 q^{13} + 21 q^{15} + 6 q^{17} - 33 q^{21} + 81 q^{23} - 23 q^{25} - 108 q^{27} + 69 q^{29} - 45 q^{31} + 72 q^{33} - 20 q^{37} + 141 q^{39} + 54 q^{41} - 117 q^{45} - 207 q^{47} + 41 q^{49} + 141 q^{51} - 252 q^{53} - 273 q^{57} + 306 q^{59} + 7 q^{61} - 441 q^{63} + 93 q^{65} - 12 q^{67} + 189 q^{69} + 74 q^{73} + 387 q^{75} + 207 q^{77} - 33 q^{79} + 117 q^{81} - 549 q^{83} - 30 q^{85} + 87 q^{87} - 168 q^{89} - 27 q^{93} + 684 q^{95} - 10 q^{97} - 585 q^{99}+O(q^{100}) $ 8 * q + 3 * q^3 + 3 * q^5 - 3 * q^7 - 3 * q^9 - 18 * q^11 + 5 * q^13 + 21 * q^15 + 6 * q^17 - 33 * q^21 + 81 * q^23 - 23 * q^25 - 108 * q^27 + 69 * q^29 - 45 * q^31 + 72 * q^33 - 20 * q^37 + 141 * q^39 + 54 * q^41 - 117 * q^45 - 207 * q^47 + 41 * q^49 + 141 * q^51 - 252 * q^53 - 273 * q^57 + 306 * q^59 + 7 * q^61 - 441 * q^63 + 93 * q^65 - 12 * q^67 + 189 * q^69 + 74 * q^73 + 387 * q^75 + 207 * q^77 - 33 * q^79 + 117 * q^81 - 549 * q^83 - 30 * q^85 + 87 * q^87 - 168 * q^89 - 27 * q^93 + 684 * q^95 - 10 * q^97 - 585 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$-1$

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			0
$2$		0			0
$3$	1.28651	−	2.71015i	0.428836	−	0.903382i
$3$	1.28651	−	2.71015i	0.428836	−	0.903382i
$4$		0			0
$5$	−0.454613	+	0.787412i	−0.0909226	+	0.157482i	−0.907900	−	0.419188i	$-0.862315\pi$
$5$	−0.454613	+	0.787412i	−0.0909226	+	0.157482i	0.816977	+	0.576670i	$0.195648\pi$
$6$		0			0
$7$	6.10709	−	3.52593i	0.872442	−	0.503704i	0.00428285	−	0.999991i	$-0.498637\pi$
$7$	6.10709	−	3.52593i	0.872442	−	0.503704i	0.868159	+	0.496286i	$0.165303\pi$
$8$		0			0
$9$	−5.68980	−	6.97325i	−0.632200	−	0.774806i
$10$		0			0
$11$	6.96661	−	4.02218i	0.633329	−	0.365652i	−0.148711	−	0.988881i	$-0.547513\pi$
$11$	6.96661	−	4.02218i	0.633329	−	0.365652i	0.782040	+	0.623228i	$0.214179\pi$
$12$		0			0
$13$	3.35952	−	5.81886i	0.258425	−	0.447605i	−0.707395	−	0.706818i	$-0.750130\pi$
$13$	3.35952	−	5.81886i	0.258425	−	0.447605i	0.965820	+	0.259213i	$0.0834632\pi$
$14$		0			0
$15$	1.54914	+	2.24508i	0.103276	+	0.149672i
$16$		0			0
$17$	−26.3462			−1.54978			−0.774889	−	0.632097i	$-0.782194\pi$
$17$	−26.3462			−1.54978			−0.774889	+	0.632097i	$0.782194\pi$
$18$		0			0
$19$		−	20.5603i		−	1.08212i	−0.840984	−	0.541059i	$-0.818023\pi$
$19$		−	20.5603i		−	1.08212i	0.840984	−	0.541059i	$-0.181977\pi$
$20$		0			0
$21$	−1.69897	−	21.0873i	−0.0809035	−	1.00416i
$22$		0			0
$23$	21.8305	+	12.6038i	0.949150	+	0.547992i	0.892817	−	0.450420i	$-0.148726\pi$
$23$	21.8305	+	12.6038i	0.949150	+	0.547992i	0.0563333	+	0.998412i	$0.482059\pi$
$24$		0			0
$25$	12.0867	+	20.9347i	0.483466	+	0.837388i
$26$		0			0
$27$	−26.2185	+	6.44905i	−0.971056	+	0.238854i
$28$		0			0
$29$	15.1693	+	26.2741i	0.523081	+	0.906002i	0.999639	+	0.0268597i	$0.00855072\pi$
$29$	15.1693	+	26.2741i	0.523081	+	0.906002i	−0.476558	+	0.879143i	$0.658116\pi$
$30$		0			0
$31$	0.120040	+	0.0693050i	0.00387225	+	0.00223565i	0.501935	−	0.864905i	$-0.332622\pi$
$31$	0.120040	+	0.0693050i	0.00387225	+	0.00223565i	−0.498063	+	0.867141i	$0.665955\pi$
$32$		0			0
$33$	−1.93809	−	24.0551i	−0.0587300	−	0.728943i
$34$		0			0
$35$			6.41173i			0.183192i
$36$		0			0
$37$	69.7588			1.88537			0.942687	−	0.333679i	$-0.108290\pi$
$37$	69.7588			1.88537			0.942687	+	0.333679i	$0.108290\pi$
$38$		0			0
$39$	−11.4479	−	16.5908i	−0.293537	−	0.425405i
$40$		0			0
$41$	−29.3794	+	50.8866i	−0.716571	+	1.24114i	0.245780	+	0.969326i	$0.420956\pi$
$41$	−29.3794	+	50.8866i	−0.716571	+	1.24114i	−0.962351	+	0.271811i	$0.912377\pi$
$42$		0			0
$43$	−2.45853	+	1.41943i	−0.0571751	+	0.0330100i	−0.528315	−	0.849048i	$-0.677176\pi$
$43$	−2.45853	+	1.41943i	−0.0571751	+	0.0330100i	0.471140	+	0.882058i	$0.343843\pi$
$44$		0			0
$45$	8.07748	−	1.31009i	0.179500	−	0.0291131i
$46$		0			0
$47$	−70.7583	+	40.8523i	−1.50550	+	0.869198i	−0.505516	+	0.862817i	$0.668698\pi$
$47$	−70.7583	+	40.8523i	−1.50550	+	0.869198i	−0.999980	+	0.00638063i	$0.997969\pi$
$48$		0			0
$49$	0.364383	−	0.631130i	0.00743639	−	0.0128802i
$50$		0			0
$51$	−33.8946	+	71.4022i	−0.664600	+	1.40004i
$52$		0			0
$53$	−30.0259			−0.566526			−0.283263	−	0.959042i	$-0.591417\pi$
$53$	−30.0259			−0.566526			−0.283263	+	0.959042i	$0.591417\pi$
$54$		0			0
$55$			7.31413i			0.132984i
$56$		0			0
$57$	−55.7213	−	26.4509i	−0.977567	−	0.464051i
$58$		0			0
$59$	77.1442	+	44.5392i	1.30753	+	0.754902i	0.981683	−	0.190520i	$-0.0610175\pi$
$59$	77.1442	+	44.5392i	1.30753	+	0.754902i	0.325846	+	0.945423i	$0.394351\pi$
$60$		0			0
$61$	24.0688	+	41.6885i	0.394571	+	0.683417i	0.993046	−	0.117724i	$-0.0375598\pi$
$61$	24.0688	+	41.6885i	0.394571	+	0.683417i	−0.598475	+	0.801141i	$0.704226\pi$
$62$		0			0
$63$	−59.3353	−	22.5244i	−0.941830	−	0.357531i
$64$		0			0
$65$	3.05456	+	5.29066i	0.0469933	+	0.0813948i
$66$		0			0
$67$	−44.0829	−	25.4513i	−0.657953	−	0.379870i	0.133543	−	0.991043i	$-0.457364\pi$
$67$	−44.0829	−	25.4513i	−0.657953	−	0.379870i	−0.791497	+	0.611173i	$0.790698\pi$
$68$		0			0
$69$	62.2432	−	42.9488i	0.902076	−	0.622447i
$70$		0			0
$71$		−	68.4355i		−	0.963881i	−0.876204	−	0.481940i	$-0.839932\pi$
$71$		−	68.4355i		−	0.963881i	0.876204	−	0.481940i	$-0.160068\pi$
$72$		0			0
$73$	−22.1474			−0.303389			−0.151695	−	0.988427i	$-0.548473\pi$
$73$	−22.1474			−0.303389			−0.151695	+	0.988427i	$0.548473\pi$
$74$		0			0
$75$	72.2857	−	5.82397i	0.963809	−	0.0776529i
$76$		0			0
$77$	28.3638	−	49.1276i	0.368362	−	0.638021i
$78$		0			0
$79$	34.4343	−	19.8807i	0.435877	−	0.251654i	−0.265970	−	0.963981i	$-0.585692\pi$
$79$	34.4343	−	19.8807i	0.435877	−	0.251654i	0.701847	+	0.712327i	$0.252359\pi$
$80$		0			0
$81$	−16.2524	+	79.3527i	−0.200647	+	0.979664i
$82$		0			0
$83$	23.0801	−	13.3253i	0.278073	−	0.160546i	−0.354478	−	0.935065i	$-0.615341\pi$
$83$	23.0801	−	13.3253i	0.278073	−	0.160546i	0.632551	+	0.774519i	$0.282008\pi$
$84$		0			0
$85$	11.9773	−	20.7453i	0.140910	−	0.244063i
$86$		0			0
$87$	90.7221	−	7.30936i	1.04278	−	0.0840157i
$88$		0			0
$89$	−25.7926			−0.289804			−0.144902	−	0.989446i	$-0.546287\pi$
$89$	−25.7926			−0.289804			−0.144902	+	0.989446i	$0.546287\pi$
$90$		0			0
$91$		−	47.3818i		−	0.520679i
$92$		0			0
$93$	0.342259	−	0.236164i	0.00368020	−	0.00253940i
$94$		0			0
$95$	16.1894	+	9.34695i	0.170415	+	0.0983890i
$96$		0			0
$97$	−52.3697	−	90.7070i	−0.539894	−	0.935123i	−0.998909	−	0.0466950i	$-0.985131\pi$
$97$	−52.3697	−	90.7070i	−0.539894	−	0.935123i	0.459016	−	0.888428i	$-0.348202\pi$
$98$		0			0
$99$	−67.6863	−	25.6946i	−0.683700	−	0.259541i
$100$		0			0
$101$	20.4790	+	35.4707i	0.202763	+	0.351195i	0.949418	−	0.314016i	$-0.101675\pi$
$101$	20.4790	+	35.4707i	0.202763	+	0.351195i	−0.746655	+	0.665212i	$0.768341\pi$
$102$		0			0
$103$	125.278	+	72.3293i	1.21629	+	0.702227i	0.964123	−	0.265456i	$-0.0855227\pi$
$103$	125.278	+	72.3293i	1.21629	+	0.702227i	0.252169	+	0.967683i	$0.418856\pi$
$104$		0			0
$105$	17.3767	+	8.24874i	0.165493	+	0.0785595i
$106$		0			0
$107$		−	177.858i		−	1.66222i	−0.556105	−	0.831112i	$-0.687705\pi$
$107$		−	177.858i		−	1.66222i	0.556105	−	0.831112i	$-0.312295\pi$
$108$		0			0
$109$	−142.616			−1.30840			−0.654200	−	0.756322i	$-0.726994\pi$
$109$	−142.616			−1.30840			−0.654200	+	0.756322i	$0.726994\pi$
$110$		0			0
$111$	89.7452	−	189.057i	0.808516	−	1.70321i
$112$		0			0
$113$	100.147	−	173.459i	0.886254	−	1.53504i	0.0419835	−	0.999118i	$-0.486632\pi$
$113$	100.147	−	173.459i	0.886254	−	1.53504i	0.844270	−	0.535918i	$-0.180034\pi$
$114$		0			0
$115$	−19.8488	+	11.4597i	−0.172598	+	0.0996497i
$116$		0			0
$117$	−59.6914	+	9.68136i	−0.510183	+	0.0827467i
$118$		0			0
$119$	−160.899	+	92.8950i	−1.35209	+	0.780630i
$120$		0			0
$121$	−28.1442	+	48.7472i	−0.232597	+	0.402869i
$122$		0			0
$123$	100.113	+	145.089i	0.813930	+	1.17958i
$124$		0			0
$125$	−44.7096			−0.357677
$126$		0			0
$127$			181.723i			1.43089i	0.698670	+	0.715445i	$0.253776\pi$
$127$			181.723i			1.43089i	−0.698670	+	0.715445i	$0.746224\pi$
$128$		0			0
$129$	0.683954	+	8.48908i	0.00530197	+	0.0658068i
$130$		0			0
$131$	52.9361	+	30.5627i	0.404092	+	0.233303i	0.688248	−	0.725475i	$-0.258380\pi$
$131$	52.9361	+	30.5627i	0.404092	+	0.233303i	−0.284156	+	0.958778i	$0.591713\pi$
$132$		0			0
$133$	−72.4940	−	125.563i	−0.545068	−	0.944085i
$134$		0			0
$135$	6.84120	−	23.5766i	0.0506756	−	0.174641i
$136$		0			0
$137$	18.1131	+	31.3729i	0.132213	+	0.228999i	0.924529	−	0.381111i	$-0.124458\pi$
$137$	18.1131	+	31.3729i	0.132213	+	0.228999i	−0.792317	+	0.610110i	$0.791125\pi$
$138$		0			0
$139$	−154.652	−	89.2885i	−1.11261	−	0.642363i	−0.173103	−	0.984904i	$-0.555379\pi$
$139$	−154.652	−	89.2885i	−1.11261	−	0.642363i	−0.939503	+	0.342541i	$0.888713\pi$
$140$		0			0
$141$	19.6847	+	244.322i	0.139608	+	1.73278i
$142$		0			0
$143$		−	54.0504i		−	0.377975i
$144$		0			0
$145$	−27.5847			−0.190239
$146$		0			0
$147$	−1.24167	−	1.79949i	−0.00844676	−	0.0122414i
$148$		0			0
$149$	120.043	−	207.921i	0.805660	−	1.39544i	−0.110185	−	0.993911i	$-0.535144\pi$
$149$	120.043	−	207.921i	0.805660	−	1.39544i	0.915845	−	0.401533i	$-0.131522\pi$
$150$		0			0
$151$	−98.1393	+	56.6607i	−0.649929	+	0.375237i	−0.788429	−	0.615126i	$-0.789105\pi$
$151$	−98.1393	+	56.6607i	−0.649929	+	0.375237i	0.138500	+	0.990362i	$0.455772\pi$
$152$		0			0
$153$	149.905	+	183.719i	0.979769	+	1.20078i
$154$		0			0
$155$	−0.109143	+	0.0630139i	−0.000704150	+	0.000406541i
$156$		0			0
$157$	−60.3604	+	104.547i	−0.384461	+	0.665907i	−0.991694	−	0.128617i	$-0.958946\pi$
$157$	−60.3604	+	104.547i	−0.384461	+	0.665907i	0.607233	+	0.794524i	$0.292280\pi$
$158$		0			0
$159$	−38.6285	+	81.3746i	−0.242947	+	0.511790i
$160$		0			0
$161$	177.761			1.10410
$162$		0			0
$163$		−	20.3498i		−	0.124845i	−0.998050	−	0.0624226i	$-0.980117\pi$
$163$		−	20.3498i		−	0.124845i	0.998050	−	0.0624226i	$-0.0198827\pi$
$164$		0			0
$165$	19.8224	+	9.40969i	0.120136	+	0.0570284i
$166$		0			0
$167$	−151.530	−	87.4858i	−0.907365	−	0.523867i	−0.0277823	−	0.999614i	$-0.508845\pi$
$167$	−151.530	−	87.4858i	−0.907365	−	0.523867i	−0.879582	+	0.475747i	$0.842178\pi$
$168$		0			0
$169$	61.9272	+	107.261i	0.366433	+	0.634681i
$170$		0			0
$171$	−143.372	+	116.984i	−0.838431	+	0.684115i
$172$		0			0
$173$	55.9175	+	96.8520i	0.323223	+	0.559838i	0.981151	−	0.193243i	$-0.0619004\pi$
$173$	55.9175	+	96.8520i	0.323223	+	0.559838i	−0.657928	+	0.753080i	$0.728567\pi$
$174$		0			0
$175$	147.629	+	85.2334i	0.843592	+	0.487048i
$176$		0			0
$177$	219.955	−	151.772i	1.24268	−	0.857470i
$178$		0			0
$179$		−	18.6939i		−	0.104435i	−0.998636	−	0.0522176i	$-0.983371\pi$
$179$		−	18.6939i		−	0.104435i	0.998636	−	0.0522176i	$-0.0166289\pi$
$180$		0			0
$181$	−98.0536			−0.541733			−0.270866	−	0.962617i	$-0.587310\pi$
$181$	−98.0536			−0.541733			−0.270866	+	0.962617i	$0.587310\pi$
$182$		0			0
$183$	143.947	−	11.5976i	0.786594	−	0.0633748i
$184$		0			0
$185$	−31.7132	+	54.9290i	−0.171423	+	0.296913i
$186$		0			0
$187$	−183.544	+	105.969i	−0.981519	+	0.566680i
$188$		0			0
$189$	−137.380	+	131.830i	−0.726878	+	0.697511i
$190$		0			0
$191$	−240.713	+	138.976i	−1.26028	+	0.727621i	−0.973128	−	0.230265i	$-0.926041\pi$
$191$	−240.713	+	138.976i	−1.26028	+	0.727621i	−0.287149	+	0.957886i	$0.592707\pi$
$192$		0			0
$193$	81.1285	−	140.519i	0.420355	−	0.728076i	−0.575619	−	0.817718i	$-0.695239\pi$
$193$	81.1285	−	140.519i	0.420355	−	0.728076i	0.995974	+	0.0896419i	$0.0285722\pi$
$194$		0			0
$195$	18.2682	−	1.47184i	0.0936830	−	0.00754792i
$196$		0			0
$197$	−106.182			−0.538993			−0.269496	−	0.963001i	$-0.586857\pi$
$197$	−106.182			−0.538993			−0.269496	+	0.963001i	$0.586857\pi$
$198$		0			0
$199$			63.3880i			0.318532i	0.987236	+	0.159266i	$0.0509128\pi$
$199$			63.3880i			0.318532i	−0.987236	+	0.159266i	$0.949087\pi$
$200$		0			0
$201$	−125.690	+	86.7278i	−0.625321	+	0.431482i
$202$		0			0
$203$	185.281	+	106.972i	0.912715	+	0.526956i
$204$		0			0
$205$	−26.7125	−	46.2674i	−0.130305	−	0.225695i
$206$		0			0
$207$	−36.3213	−	223.942i	−0.175465	−	1.08185i
$208$		0			0
$209$	−82.6970	−	143.235i	−0.395679	−	0.685337i
$210$		0			0
$211$	4.98019	+	2.87531i	0.0236028	+	0.0136271i	0.511755	−	0.859131i	$-0.328996\pi$
$211$	4.98019	+	2.87531i	0.0236028	+	0.0136271i	−0.488152	+	0.872759i	$0.662329\pi$
$212$		0			0
$213$	−185.470	−	88.0428i	−0.870753	−	0.413347i
$214$		0			0
$215$		−	2.58117i		−	0.0120054i
$216$		0			0
$217$	0.977459			0.00450442
$218$		0			0
$219$	−28.4928	+	60.0228i	−0.130104	+	0.274076i
$220$		0			0
$221$	−88.5107	+	153.305i	−0.400501	+	0.693688i
$222$		0			0
$223$	179.786	−	103.799i	0.806215	−	0.465469i	−0.0394246	−	0.999223i	$-0.512552\pi$
$223$	179.786	−	103.799i	0.806215	−	0.465469i	0.845640	+	0.533754i	$0.179219\pi$
$224$		0			0
$225$	77.2123	−	203.397i	0.343166	−	0.903989i
$226$		0			0
$227$	78.8889	−	45.5465i	0.347528	−	0.200646i	−0.316068	−	0.948737i	$-0.602363\pi$
$227$	78.8889	−	45.5465i	0.347528	−	0.200646i	0.663596	+	0.748091i	$0.269029\pi$
$228$		0			0
$229$	2.04945	−	3.54974i	0.00894954	−	0.0155011i	−0.861516	−	0.507731i	$-0.830485\pi$
$229$	2.04945	−	3.54974i	0.00894954	−	0.0155011i	0.870465	+	0.492229i	$0.163818\pi$
$230$		0			0
$231$	−96.6528	−	140.073i	−0.418410	−	0.606378i
$232$		0			0
$233$	171.761			0.737170			0.368585	−	0.929594i	$-0.379842\pi$
$233$	171.761			0.737170			0.368585	+	0.929594i	$0.379842\pi$
$234$		0			0
$235$		−	74.2879i		−	0.316119i
$236$		0			0
$237$	−9.57951	−	118.899i	−0.0404199	−	0.501682i
$238$		0			0
$239$	78.9068	+	45.5569i	0.330154	+	0.190614i	0.655909	−	0.754840i	$-0.272285\pi$
$239$	78.9068	+	45.5569i	0.330154	+	0.190614i	−0.325755	+	0.945454i	$0.605619\pi$
$240$		0			0
$241$	37.2352	+	64.4933i	0.154503	+	0.267607i	0.932878	−	0.360193i	$-0.117289\pi$
$241$	37.2352	+	64.4933i	0.154503	+	0.267607i	−0.778375	+	0.627800i	$0.783956\pi$
$242$		0			0
$243$	194.149	+	146.134i	0.798966	+	0.601376i
$244$		0			0
$245$	0.331306	+	0.573840i	0.00135227	+	0.00234220i
$246$		0			0
$247$	−119.637	−	69.0726i	−0.484362	−	0.279646i
$248$		0			0
$249$	−6.42081	−	79.6935i	−0.0257864	−	0.320054i
$250$		0			0
$251$		−	216.868i		−	0.864014i	−0.901870	−	0.432007i	$-0.857806\pi$
$251$		−	216.868i		−	0.864014i	0.901870	−	0.432007i	$-0.142194\pi$
$252$		0			0
$253$	202.779			0.801499
$254$		0			0
$255$	−40.8140	−	59.1494i	−0.160055	−	0.231958i
$256$		0			0
$257$	−143.577	+	248.682i	−0.558665	+	0.967636i	0.438943	+	0.898515i	$0.355353\pi$
$257$	−143.577	+	248.682i	−0.558665	+	0.967636i	−0.997608	+	0.0691212i	$0.977980\pi$
$258$		0			0
$259$	426.023	−	245.965i	1.64488	−	0.949671i
$260$		0			0
$261$	96.9052	−	255.274i	0.371284	−	0.978060i
$262$		0			0
$263$	361.740	−	208.851i	1.37544	−	0.794108i	0.383830	−	0.923404i	$-0.374605\pi$
$263$	361.740	−	208.851i	1.37544	−	0.794108i	0.991606	+	0.129295i	$0.0412715\pi$
$264$		0			0
$265$	13.6502	−	23.6428i	0.0515100	−	0.0892180i
$266$		0			0
$267$	−33.1823	+	69.9016i	−0.124278	+	0.261804i
$268$		0			0
$269$	−489.868			−1.82107			−0.910535	−	0.413433i	$-0.864330\pi$
$269$	−489.868			−1.82107			−0.910535	+	0.413433i	$0.864330\pi$
$270$		0			0
$271$		−	325.133i		−	1.19975i	−0.800093	−	0.599876i	$-0.795216\pi$
$271$		−	325.133i		−	1.19975i	0.800093	−	0.599876i	$-0.204784\pi$
$272$		0			0
$273$	−128.412	−	60.9570i	−0.470372	−	0.223286i
$274$		0			0
$275$	168.406	+	97.2293i	0.612386	+	0.353561i
$276$		0			0
$277$	86.0882	+	149.109i	0.310788	+	0.538300i	0.978533	−	0.206089i	$-0.0660738\pi$
$277$	86.0882	+	149.109i	0.310788	+	0.538300i	−0.667745	+	0.744390i	$0.732740\pi$
$278$		0			0
$279$	−0.199721	−	1.23140i	−0.000715846	−	0.00441362i
$280$		0			0
$281$	−60.1019	−	104.100i	−0.213886	−	0.370461i	0.739042	−	0.673660i	$-0.235279\pi$
$281$	−60.1019	−	104.100i	−0.213886	−	0.370461i	−0.952927	+	0.303199i	$0.901945\pi$
$282$		0			0
$283$	−95.8910	−	55.3627i	−0.338837	−	0.195628i	0.320920	−	0.947106i	$-0.396008\pi$
$283$	−95.8910	−	55.3627i	−0.338837	−	0.195628i	−0.659758	+	0.751478i	$0.729341\pi$
$284$		0			0
$285$	46.1594	−	31.8507i	0.161963	−	0.111757i
$286$		0			0
$287$			414.359i			1.44376i
$288$		0			0
$289$	405.124			1.40181
$290$		0			0
$291$	−313.203	+	25.2344i	−1.07630	+	0.0867161i
$292$		0			0
$293$	42.3365	−	73.3289i	0.144493	−	0.250269i	−0.784691	−	0.619888i	$-0.787178\pi$
$293$	42.3365	−	73.3289i	0.144493	−	0.250269i	0.929184	+	0.369618i	$0.120512\pi$
$294$		0			0
$295$	−70.1415	+	40.4962i	−0.237768	+	0.137275i
$296$		0			0
$297$	−156.715	+	150.383i	−0.527660	+	0.506342i
$298$		0			0
$299$	146.680	−	84.6856i	0.490568	−	0.283229i
$300$		0			0
$301$	−10.0096	+	17.3372i	−0.0332546	+	0.0575987i
$302$		0			0
$303$	122.477	−	9.86784i	0.404215	−	0.0325671i
$304$		0			0
$305$	−43.7680			−0.143502
$306$		0			0
$307$		−	220.477i		−	0.718167i	−0.933306	−	0.359083i	$-0.883089\pi$
$307$		−	220.477i		−	0.718167i	0.933306	−	0.359083i	$-0.116911\pi$
$308$		0			0
$309$	357.194	−	246.470i	1.15597	−	0.797637i
$310$		0			0
$311$	−268.968	−	155.289i	−0.864849	−	0.499321i	0.000784168	−	1.00000i	$-0.499750\pi$
$311$	−268.968	−	155.289i	−0.864849	−	0.499321i	−0.865633	+	0.500679i	$0.833084\pi$
$312$		0			0
$313$	−65.5787	−	113.586i	−0.209516	−	0.362893i	0.742046	−	0.670349i	$-0.233856\pi$
$313$	−65.5787	−	113.586i	−0.209516	−	0.362893i	−0.951562	+	0.307456i	$0.900522\pi$
$314$		0			0
$315$	44.7106	−	36.4815i	0.141938	−	0.115814i
$316$		0			0
$317$	169.980	+	294.414i	0.536214	+	0.928750i	0.999104	+	0.0423342i	$0.0134794\pi$
$317$	169.980	+	294.414i	0.536214	+	0.928750i	−0.462889	+	0.886416i	$0.653187\pi$
$318$		0			0
$319$	211.358	+	122.028i	0.662564	+	0.382532i
$320$		0			0
$321$	−482.022	−	228.816i	−1.50162	−	0.712822i
$322$		0			0
$323$			541.685i			1.67704i
$324$		0			0
$325$	162.422			0.499759
$326$		0			0
$327$	−183.476	+	386.509i	−0.561089	+	1.18199i
$328$		0			0
$329$	−288.085	+	498.978i	−0.875638	+	1.51665i
$330$		0			0
$331$	−394.447	+	227.734i	−1.19168	+	0.688018i	−0.958688	−	0.284460i	$-0.908186\pi$
$331$	−394.447	+	227.734i	−1.19168	+	0.688018i	−0.232994	+	0.972478i	$0.574852\pi$
$332$		0			0
$333$	−396.913	−	486.446i	−1.19193	−	1.46080i
$334$		0			0
$335$	40.0813	−	23.1409i	0.119646	−	0.0690774i
$336$		0			0
$337$	−21.9543	+	38.0259i	−0.0651462	+	0.112837i	−0.896759	−	0.442520i	$-0.854085\pi$
$337$	−21.9543	+	38.0259i	−0.0651462	+	0.112837i	0.831613	+	0.555356i	$0.187418\pi$
$338$		0			0
$339$	−341.260	−	494.569i	−1.00667	−	1.45890i
$340$		0			0
$341$	1.11503			0.00326988
$342$		0			0
$343$			340.402i			0.992426i
$344$		0			0
$345$	5.52187	+	68.5362i	0.0160054	+	0.198656i
$346$		0			0
$347$	−340.283	−	196.462i	−0.980642	−	0.566174i	−0.0781781	−	0.996939i	$-0.524910\pi$
$347$	−340.283	−	196.462i	−0.980642	−	0.566174i	−0.902464	+	0.430766i	$0.858244\pi$
$348$		0			0
$349$	271.979	+	471.082i	0.779310	+	1.34981i	0.932340	+	0.361584i	$0.117764\pi$
$349$	271.979	+	471.082i	0.779310	+	1.34981i	−0.153029	+	0.988222i	$0.548903\pi$
$350$		0			0
$351$	−50.5555	+	174.228i	−0.144033	+	0.496375i
$352$		0			0
$353$	−63.7961	−	110.498i	−0.180725	−	0.313026i	0.761402	−	0.648280i	$-0.224511\pi$
$353$	−63.7961	−	110.498i	−0.180725	−	0.313026i	−0.942128	+	0.335254i	$0.891178\pi$
$354$		0			0
$355$	53.8870	+	31.1117i	0.151794	+	0.0876385i
$356$		0			0
$357$	44.7615	+	555.570i	0.125382	+	1.55622i
$358$		0			0
$359$			285.077i			0.794085i	0.917800	+	0.397043i	$0.129963\pi$
$359$			285.077i			0.794085i	−0.917800	+	0.397043i	$0.870037\pi$
$360$		0			0
$361$	−61.7239			−0.170980
$362$		0			0
$363$	95.9043	+	138.988i	0.264199	+	0.382888i
$364$		0			0
$365$	10.0685	−	17.4391i	0.0275849	−	0.0477785i
$366$		0			0
$367$	280.084	−	161.706i	0.763171	−	0.440617i	−0.0672623	−	0.997735i	$-0.521426\pi$
$367$	280.084	−	161.706i	0.763171	−	0.440617i	0.830433	+	0.557119i	$0.188093\pi$
$368$		0			0
$369$	522.008	−	84.6646i	1.41466	−	0.229443i
$370$		0			0
$371$	−183.371	+	105.869i	−0.494261	+	0.285362i
$372$		0			0
$373$	257.740	−	446.419i	0.690993	−	1.19683i	−0.280520	−	0.959848i	$-0.590507\pi$
$373$	257.740	−	446.419i	0.690993	−	1.19683i	0.971513	−	0.236987i	$-0.0761597\pi$
$374$		0			0
$375$	−57.5193	+	121.170i	−0.153385	+	0.323119i
$376$		0			0
$377$	203.847			0.540708
$378$		0			0
$379$			21.2535i			0.0560779i	0.999607	+	0.0280389i	$0.00892624\pi$
$379$			21.2535i			0.0560779i	−0.999607	+	0.0280389i	$0.991074\pi$
$380$		0			0
$381$	492.496	+	233.788i	1.29264	+	0.613617i
$382$		0			0
$383$	93.4125	+	53.9317i	0.243897	+	0.140814i	0.616966	−	0.786989i	$-0.288361\pi$
$383$	93.4125	+	53.9317i	0.243897	+	0.140814i	−0.373070	+	0.927803i	$0.621695\pi$
$384$		0			0
$385$	25.7891	+	44.6681i	0.0669847	+	0.116021i
$386$		0			0
$387$	23.8866	+	9.06765i	0.0617224	+	0.0234306i
$388$		0			0
$389$	75.1474	+	130.159i	0.193181	+	0.334599i	0.946303	−	0.323282i	$-0.104786\pi$
$389$	75.1474	+	130.159i	0.193181	+	0.334599i	−0.753122	+	0.657881i	$0.771453\pi$
$390$		0			0
$391$	−575.150	−	332.063i	−1.47097	−	0.849266i
$392$		0			0
$393$	150.932	−	104.145i	0.384051	−	0.265001i
$394$		0			0
$395$			36.1520i			0.0915241i
$396$		0			0
$397$	137.203			0.345600			0.172800	−	0.984957i	$-0.444719\pi$
$397$	137.203			0.345600			0.172800	+	0.984957i	$0.444719\pi$
$398$		0			0
$399$	−433.559	+	34.9313i	−1.08661	+	0.0875472i
$400$		0			0
$401$	−133.366	+	230.996i	−0.332583	+	0.576050i	−0.983017	−	0.183512i	$-0.941253\pi$
$401$	−133.366	+	230.996i	−0.332583	+	0.576050i	0.650435	+	0.759562i	$0.274587\pi$
$402$		0			0
$403$	0.806553	−	0.465664i	0.00200137	−	0.00115549i
$404$		0			0
$405$	−55.0948	−	48.8721i	−0.136037	−	0.120672i
$406$		0			0
$407$	485.983	−	280.582i	1.19406	−	0.689391i
$408$		0			0
$409$	−341.404	+	591.329i	−0.834729	+	1.44579i	0.0595226	+	0.998227i	$0.481042\pi$
$409$	−341.404	+	591.329i	−0.834729	+	1.44579i	−0.894251	+	0.447565i	$0.852291\pi$
$410$		0			0
$411$	108.328	−	8.72784i	0.263571	−	0.0212356i
$412$		0			0
$413$	628.169			1.52099
$414$		0			0
$415$			24.2314i			0.0583889i
$416$		0			0
$417$	−440.946	+	304.260i	−1.05742	+	0.729640i
$418$		0			0
$419$	−449.030	−	259.248i	−1.07167	−	0.618730i	−0.143034	−	0.989718i	$-0.545686\pi$
$419$	−449.030	−	259.248i	−1.07167	−	0.618730i	−0.928638	+	0.370988i	$0.879019\pi$
$420$		0			0
$421$	−170.758	−	295.761i	−0.405601	−	0.702521i	0.588790	−	0.808286i	$-0.299604\pi$
$421$	−170.758	−	295.761i	−0.405601	−	0.702521i	−0.994391	+	0.105765i	$0.966271\pi$
$422$		0			0
$423$	687.474	+	260.974i	1.62523	+	0.616959i
$424$		0			0
$425$	−318.438	−	551.550i	−0.749265	−	1.29777i
$426$		0			0
$427$	293.981	+	169.730i	0.688481	+	0.397495i
$428$		0			0
$429$	−146.484	−	69.5362i	−0.341456	−	0.162089i
$430$		0			0
$431$		−	166.603i		−	0.386550i	−0.981145	−	0.193275i	$-0.938089\pi$
$431$		−	166.603i		−	0.386550i	0.981145	−	0.193275i	$-0.0619110\pi$
$432$		0			0
$433$	−677.766			−1.56528			−0.782640	−	0.622475i	$-0.786127\pi$
$433$	−677.766			−1.56528			−0.782640	+	0.622475i	$0.786127\pi$
$434$		0			0
$435$	−35.4879	+	74.7586i	−0.0815815	+	0.171859i
$436$		0			0
$437$	259.138	−	448.840i	0.592992	−	1.02709i
$438$		0			0
$439$	−427.032	+	246.547i	−0.972738	+	0.561610i	−0.900070	−	0.435746i	$-0.856485\pi$
$439$	−427.032	+	246.547i	−0.972738	+	0.561610i	−0.0726678	+	0.997356i	$0.523151\pi$
$440$		0			0
$441$	−6.47429	+	1.05007i	−0.0146809	+	0.00238111i
$442$		0			0
$443$	284.084	−	164.016i	0.641273	−	0.370239i	−0.143832	−	0.989602i	$-0.545942\pi$
$443$	284.084	−	164.016i	0.641273	−	0.370239i	0.785105	+	0.619363i	$0.212609\pi$
$444$		0			0
$445$	11.7256	−	20.3094i	0.0263497	−	0.0456391i
$446$		0			0
$447$	−409.060	−	592.827i	−0.915124	−	1.32624i
$448$		0			0
$449$	19.0862			0.0425082			0.0212541	−	0.999774i	$-0.493234\pi$
$449$	19.0862			0.0425082			0.0212541	+	0.999774i	$0.493234\pi$
$450$		0			0
$451$			472.677i			1.04806i
$452$		0			0
$453$	27.3020	+	338.866i	0.0602694	+	0.748049i
$454$		0			0
$455$	37.3090	+	21.5404i	0.0819978	+	0.0473415i
$456$		0			0
$457$	−137.806	−	238.686i	−0.301544	−	0.522289i	0.674942	−	0.737871i	$-0.264169\pi$
$457$	−137.806	−	238.686i	−0.301544	−	0.522289i	−0.976486	+	0.215581i	$0.930835\pi$
$458$		0			0
$459$	690.759	−	169.908i	1.50492	−	0.370170i
$460$		0			0
$461$	−199.467	−	345.486i	−0.432683	−	0.749428i	0.564421	−	0.825487i	$-0.309100\pi$
$461$	−199.467	−	345.486i	−0.432683	−	0.749428i	−0.997103	+	0.0760589i	$0.975766\pi$
$462$		0			0
$463$	−15.7881	−	9.11524i	−0.0340995	−	0.0196873i	0.482853	−	0.875701i	$-0.339600\pi$
$463$	−15.7881	−	9.11524i	−0.0340995	−	0.0196873i	−0.516953	+	0.856014i	$0.672934\pi$
$464$		0			0
$465$	0.0303633	+	0.376862i	6.52974e−5	+	0.000810456i
$466$		0			0
$467$			499.275i			1.06911i	0.845133	+	0.534555i	$0.179521\pi$
$467$			499.275i			1.06911i	−0.845133	+	0.534555i	$0.820479\pi$
$468$		0			0
$469$	−358.958			−0.765368
$470$		0			0
$471$	205.685	+	298.087i	0.436698	+	0.632880i
$472$		0			0
$473$	−11.4184	+	19.7773i	−0.0241404	+	0.0418124i
$474$		0			0
$475$	430.423	−	248.505i	0.906153	−	0.523168i
$476$		0			0
$477$	170.841	+	209.378i	0.358158	+	0.438948i
$478$		0			0
$479$	−52.4473	+	30.2805i	−0.109493	+	0.0632160i	−0.553747	−	0.832685i	$-0.686802\pi$
$479$	−52.4473	+	30.2805i	−0.109493	+	0.0632160i	0.444253	+	0.895901i	$0.353469\pi$
$480$		0			0
$481$	234.356	−	405.917i	0.487227	−	0.843902i
$482$		0			0
$483$	228.691	−	481.758i	0.473479	−	0.997428i
$484$		0			0
$485$	95.2317			0.196354
$486$		0			0
$487$		−	852.354i		−	1.75021i	−0.483931	−	0.875106i	$-0.660791\pi$
$487$		−	852.354i		−	1.75021i	0.483931	−	0.875106i	$-0.339209\pi$
$488$		0			0
$489$	−55.1509	−	26.1801i	−0.112783	−	0.0535381i
$490$		0			0
$491$	−585.457	−	338.014i	−1.19238	−	0.688419i	−0.233532	−	0.972349i	$-0.575028\pi$
$491$	−585.457	−	338.014i	−1.19238	−	0.688419i	−0.958845	+	0.283930i	$0.908362\pi$
$492$		0			0
$493$	−399.655	−	692.223i	−0.810659	−	1.40410i
$494$		0			0
$495$	51.0033	−	41.6159i	0.103037	−	0.0840726i
$496$		0			0
$497$	−241.299	−	417.942i	−0.485511	−	0.840930i
$498$		0			0
$499$	736.084	+	424.978i	1.47512	+	0.851660i	0.999607	−	0.0280487i	$-0.00892936\pi$
$499$	736.084	+	424.978i	1.47512	+	0.851660i	0.475512	+	0.879709i	$0.342263\pi$
$500$		0			0
$501$	−432.044	+	298.117i	−0.862363	+	0.595044i
$502$		0			0
$503$		−	945.179i		−	1.87908i	−0.342433	−	0.939542i	$-0.611251\pi$
$503$		−	945.179i		−	1.87908i	0.342433	−	0.939542i	$-0.388749\pi$
$504$		0			0
$505$	−37.2401			−0.0737428
$506$		0			0
$507$	370.363	−	29.8397i	0.730499	−	0.0588554i
$508$		0			0
$509$	125.931	−	218.119i	0.247409	−	0.428524i	−0.715397	−	0.698718i	$-0.753754\pi$
$509$	125.931	−	218.119i	0.247409	−	0.428524i	0.962806	+	0.270194i	$0.0870877\pi$
$510$		0			0
$511$	−135.256	+	78.0903i	−0.264689	+	0.152819i
$512$		0			0
$513$	132.594	+	539.059i	0.258468	+	1.05080i
$514$		0			0
$515$	−113.906	+	65.7637i	−0.221177	+	0.127696i
$516$		0			0
$517$	−328.630	+	569.205i	−0.635649	+	1.10098i
$518$		0			0
$519$	334.421	−	26.9439i	0.644357	−	0.0519150i
$520$		0			0
$521$	856.423			1.64381			0.821903	−	0.569628i	$-0.192913\pi$
$521$	856.423			1.64381			0.821903	+	0.569628i	$0.192913\pi$
$522$		0			0
$523$			741.634i			1.41804i	0.705189	+	0.709019i	$0.250862\pi$
$523$			741.634i			1.41804i	−0.705189	+	0.709019i	$0.749138\pi$
$524$		0			0
$525$	420.920	−	290.442i	0.801753	−	0.553223i
$526$		0			0
$527$	−3.16260	−	1.82593i	−0.00600113	−	0.00346475i
$528$		0			0
$529$	53.2125	+	92.1667i	0.100591	+	0.174228i
$530$		0			0
$531$	−128.352	−	791.365i	−0.241717	−	1.49033i
$532$		0			0
$533$	197.402	+	341.910i	0.370359	+	0.641481i
$534$		0			0
$535$	140.048	+	80.8565i	0.261771	+	0.151134i
$536$		0			0
$537$	−50.6632	−	24.0498i	−0.0943449	−	0.0447856i
$538$		0			0
$539$		−	5.86245i		−	0.0108765i
$540$		0			0
$541$	−434.157			−0.802509			−0.401254	−	0.915967i	$-0.631426\pi$
$541$	−434.157			−0.802509			−0.401254	+	0.915967i	$0.631426\pi$
$542$		0			0
$543$	−126.147	+	265.740i	−0.232314	+	0.489392i
$544$		0			0
$545$	64.8349	−	112.297i	0.118963	−	0.206050i
$546$		0			0
$547$	−235.269	+	135.832i	−0.430107	+	0.248323i	−0.699392	−	0.714738i	$-0.746546\pi$
$547$	−235.269	+	135.832i	−0.430107	+	0.248323i	0.269285	+	0.963061i	$0.413213\pi$
$548$		0			0
$549$	153.757	−	405.037i	0.280068	−	0.737772i
$550$		0			0
$551$	540.201	−	311.885i	0.980402	−	0.566035i
$552$		0			0
$553$	140.196	−	242.826i	0.253518	−	0.439107i
$554$		0			0
$555$	108.066	+	156.614i	0.194714	+	0.282188i
$556$		0			0
$557$	41.7759			0.0750016			0.0375008	−	0.999297i	$-0.488060\pi$
$557$	41.7759			0.0750016			0.0375008	+	0.999297i	$0.488060\pi$
$558$		0			0
$559$			19.0744i			0.0341224i
$560$		0			0
$561$	51.0614	+	633.761i	0.0910185	+	1.12970i
$562$		0			0
$563$	−388.403	−	224.245i	−0.689882	−	0.398303i	0.113686	−	0.993517i	$-0.463734\pi$
$563$	−388.403	−	224.245i	−0.689882	−	0.398303i	−0.803568	+	0.595213i	$0.797068\pi$
$564$		0			0
$565$	91.0559	+	157.713i	0.161161	+	0.279139i
$566$		0			0
$567$	180.537	+	541.919i	0.318408	+	0.955766i
$568$		0			0
$569$	−180.208	−	312.130i	−0.316710	−	0.548559i	0.663089	−	0.748540i	$-0.269245\pi$
$569$	−180.208	−	312.130i	−0.316710	−	0.548559i	−0.979800	+	0.199982i	$0.935912\pi$
$570$		0			0
$571$	−665.784	−	384.391i	−1.16600	−	0.673189i	−0.213263	−	0.976995i	$-0.568409\pi$
$571$	−665.784	−	384.391i	−1.16600	−	0.673189i	−0.952734	+	0.303806i	$0.901743\pi$
$572$		0			0
$573$	66.9656	+	831.161i	0.116868	+	1.45054i
$574$		0			0
$575$			609.352i			1.05974i
$576$		0			0
$577$	−413.359			−0.716394			−0.358197	−	0.933646i	$-0.616608\pi$
$577$	−413.359			−0.716394			−0.358197	+	0.933646i	$0.616608\pi$
$578$		0			0
$579$	−276.454	−	400.649i	−0.477468	−	0.691966i
$580$		0			0
$581$	93.9682	−	162.758i	0.161735	−	0.280134i
$582$		0			0
$583$	−209.179	+	120.769i	−0.358797	+	0.207152i
$584$		0			0
$585$	19.5132	−	51.4030i	0.0333560	−	0.0878684i
$586$		0			0
$587$	−1.41240	+	0.815451i	−0.00240614	+	0.00138918i	−0.501203	−	0.865330i	$-0.667109\pi$
$587$	−1.41240	+	0.815451i	−0.00240614	+	0.00138918i	0.498796	+	0.866719i	$0.333776\pi$
$588$		0			0
$589$	1.42493	−	2.46805i	0.00241923	−	0.00419024i
$590$		0			0
$591$	−136.603	+	287.768i	−0.231139	+	0.486916i
$592$		0			0
$593$	652.407			1.10018			0.550091	−	0.835105i	$-0.314593\pi$
$593$	652.407			1.10018			0.550091	+	0.835105i	$0.314593\pi$
$594$		0			0
$595$		−	168.925i		−	0.283908i
$596$		0			0
$597$	171.791	+	81.5491i	0.287757	+	0.136598i
$598$		0			0
$599$	148.315	+	85.6298i	0.247605	+	0.142955i	0.618667	−	0.785653i	$-0.287673\pi$
$599$	148.315	+	85.6298i	0.247605	+	0.142955i	−0.371062	+	0.928608i	$0.621006\pi$
$600$		0			0
$601$	−65.9875	−	114.294i	−0.109796	−	0.190173i	0.805891	−	0.592063i	$-0.201686\pi$
$601$	−65.9875	−	114.294i	−0.109796	−	0.190173i	−0.915688	+	0.401891i	$0.868353\pi$
$602$		0			0
$603$	73.3446	+	452.213i	0.121633	+	0.749939i
$604$		0			0
$605$	−25.5894	−	44.3222i	−0.0422966	−	0.0732598i
$606$		0			0
$607$	−514.763	−	297.199i	−0.848045	−	0.489619i	0.0119458	−	0.999929i	$-0.496197\pi$
$607$	−514.763	−	297.199i	−0.848045	−	0.489619i	−0.859991	+	0.510310i	$0.829531\pi$
$608$		0			0
$609$	528.276	−	364.519i	0.867448	−	0.598553i
$610$		0			0
$611$			548.977i			0.898489i
$612$		0			0
$613$	367.632			0.599727			0.299863	−	0.953982i	$-0.403059\pi$
$613$	367.632			0.599727			0.299863	+	0.953982i	$0.403059\pi$
$614$		0			0
$615$	−159.757	+	12.8714i	−0.259768	+	0.0209292i
$616$		0			0
$617$	21.0806	−	36.5126i	0.0341662	−	0.0591776i	−0.848437	−	0.529297i	$-0.822456\pi$
$617$	21.0806	−	36.5126i	0.0341662	−	0.0591776i	0.882603	+	0.470119i	$0.155789\pi$
$618$		0			0
$619$	−214.298	+	123.725i	−0.346200	+	0.199879i	−0.663010	−	0.748610i	$-0.730721\pi$
$619$	−214.298	+	123.725i	−0.346200	+	0.199879i	0.316810	+	0.948489i	$0.397388\pi$
$620$		0			0
$621$	−653.644	−	189.668i	−1.05257	−	0.305423i
$622$		0			0
$623$	−157.518	+	90.9428i	−0.252837	+	0.145976i
$624$		0			0
$625$	−281.841	+	488.163i	−0.450945	+	0.781060i
$626$		0			0
$627$	−494.579	+	39.8476i	−0.788802	+	0.0635528i
$628$		0			0
$629$	−1837.88			−2.92191
$630$		0			0
$631$			725.556i			1.14985i	0.818206	+	0.574926i	$0.194969\pi$
$631$			725.556i			1.14985i	−0.818206	+	0.574926i	$0.805031\pi$
$632$		0			0
$633$	14.1996	−	9.79793i	0.0224322	−	0.0154786i
$634$		0			0
$635$	−143.091	−	82.6136i	−0.225340	−	0.130100i
$636$		0			0
$637$	−2.44831	−	4.24059i	−0.00384349	−	0.00665713i
$638$		0			0
$639$	−477.218	+	389.384i	−0.746820	+	0.609365i
$640$		0			0
$641$	458.006	+	793.290i	0.714518	+	1.23758i	0.963145	+	0.268983i	$0.0866875\pi$
$641$	458.006	+	793.290i	0.714518	+	1.23758i	−0.248626	+	0.968599i	$0.579979\pi$
$642$		0			0
$643$	686.803	+	396.526i	1.06812	+	0.616681i	0.927668	−	0.373406i	$-0.121810\pi$
$643$	686.803	+	396.526i	1.06812	+	0.616681i	0.140455	+	0.990087i	$0.455143\pi$
$644$		0			0
$645$	−6.99534	−	3.32069i	−0.0108455	−	0.00514836i
$646$		0			0
$647$		−	78.3837i		−	0.121150i	−0.998164	−	0.0605748i	$-0.980707\pi$
$647$		−	78.3837i		−	0.121150i	0.998164	−	0.0605748i	$-0.0192934\pi$
$648$		0			0
$649$	716.579			1.10413
$650$		0			0
$651$	1.25751	−	2.64906i	0.00193166	−	0.00406921i
$652$		0			0
$653$	131.250	−	227.332i	0.200996	−	0.348135i	−0.747854	−	0.663864i	$-0.768915\pi$
$653$	131.250	−	227.332i	0.200996	−	0.348135i	0.948850	+	0.315728i	$0.102249\pi$
$654$		0			0
$655$	−48.1308	+	27.7883i	−0.0734822	+	0.0424250i
$656$		0			0
$657$	126.014	+	154.439i	0.191803	+	0.235068i
$658$		0			0
$659$	−1116.03	+	644.339i	−1.69352	+	0.977753i	−0.741880	+	0.670533i	$0.766066\pi$
$659$	−1116.03	+	644.339i	−1.69352	+	0.977753i	−0.951638	+	0.307221i	$0.900601\pi$
$660$		0			0
$661$	−184.429	+	319.441i	−0.279016	+	0.483270i	−0.971140	−	0.238508i	$-0.923342\pi$
$661$	−184.429	+	319.441i	−0.279016	+	0.483270i	0.692125	+	0.721778i	$0.256675\pi$
$662$		0			0
$663$	301.610	+	437.105i	0.454917	+	0.659284i
$664$		0			0
$665$	131.827			0.198236
$666$		0			0
$667$			764.766i			1.14658i
$668$		0			0
$669$	−50.0159	−	620.785i	−0.0747622	−	0.927930i
$670$		0			0
$671$	335.357	+	193.618i	0.499787	+	0.288552i
$672$		0			0
$673$	127.862	+	221.463i	0.189988	+	0.329069i	0.945246	−	0.326359i	$-0.105822\pi$
$673$	127.862	+	221.463i	0.189988	+	0.329069i	−0.755258	+	0.655428i	$0.772488\pi$
$674$		0			0
$675$	−451.903	−	470.929i	−0.669486	−	0.697673i
$676$		0			0
$677$	566.571	+	981.330i	0.836885	+	1.44953i	0.892486	+	0.451074i	$0.148959\pi$
$677$	566.571	+	981.330i	0.836885	+	1.44953i	−0.0556014	+	0.998453i	$0.517708\pi$
$678$		0			0
$679$	−639.653	−	369.304i	−0.942052	−	0.543894i
$680$		0			0
$681$	−21.9466	−	272.397i	−0.0322271	−	0.399995i
$682$		0			0
$683$		−	941.046i		−	1.37781i	−0.724850	−	0.688907i	$-0.758091\pi$
$683$		−	941.046i		−	1.37781i	0.724850	−	0.688907i	$-0.241909\pi$
$684$		0			0
$685$	−32.9379			−0.0480845
$686$		0			0
$687$	−6.98370	−	10.1211i	−0.0101655	−	0.0147323i
$688$		0			0
$689$	−100.873	+	174.717i	−0.146404	+	0.253580i
$690$		0			0
$691$	1163.81	−	671.923i	1.68423	−	0.972393i	0.725441	−	0.688284i	$-0.241636\pi$
$691$	1163.81	−	671.923i	1.68423	−	0.972393i	0.958792	−	0.284109i	$-0.0916976\pi$
$692$		0			0
$693$	−503.964	+	81.7380i	−0.727220	+	0.117948i
$694$		0			0
$695$	140.614	−	81.1834i	0.202322	−	0.116811i
$696$		0			0
$697$	774.036	−	1340.67i	1.11053	−	1.92349i
$698$		0			0
$699$	220.971	−	465.497i	0.316125	−	0.665946i
$700$		0			0
$701$	−28.1783			−0.0401973			−0.0200986	−	0.999798i	$-0.506398\pi$
$701$	−28.1783			−0.0401973			−0.0200986	+	0.999798i	$0.506398\pi$
$702$		0			0
$703$		−	1434.26i		−	2.04020i
$704$		0			0
$705$	−201.331	−	95.5720i	−0.285576	−	0.135563i
$706$		0			0
$707$	250.135	+	144.415i	0.353797	+	0.204265i
$708$		0			0
$709$	624.660	+	1081.94i	0.881043	+	1.52601i	0.850183	+	0.526488i	$0.176491\pi$
$709$	624.660	+	1081.94i	0.881043	+	1.52601i	0.0308605	+	0.999524i	$0.490175\pi$
$710$		0			0
$711$	−334.557	−	127.002i	−0.470544	−	0.178625i
$712$		0			0
$713$	1.74702	+	3.02592i	0.00245023	+	0.00424393i
$714$		0			0
$715$	42.5599	+	24.5720i	0.0595244	+	0.0343664i
$716$		0			0
$717$	224.980	−	155.240i	0.313780	−	0.216513i
$718$		0			0
$719$			738.132i			1.02661i	0.858206	+	0.513305i	$0.171579\pi$
$719$			738.132i			1.02661i	−0.858206	+	0.513305i	$0.828421\pi$
$720$		0			0
$721$	1020.11			1.41486
$722$		0			0
$723$	222.690	−	17.9418i	0.308008	−	0.0248158i
$724$		0			0
$725$	−366.693	+	635.131i	−0.505784	+	0.876043i
$726$		0			0
$727$	−326.676	+	188.606i	−0.449348	+	0.259431i	−0.707555	−	0.706659i	$-0.750202\pi$
$727$	−326.676	+	188.606i	−0.449348	+	0.259431i	0.258207	+	0.966090i	$0.416868\pi$
$728$		0			0
$729$	645.820	−	338.169i	0.885898	−	0.463880i
$730$		0			0
$731$	64.7729	−	37.3967i	0.0886087	−	0.0511582i
$732$		0			0
$733$	280.849	−	486.445i	0.383150	−	0.663635i	−0.608361	−	0.793661i	$-0.708173\pi$
$733$	280.849	−	486.445i	0.383150	−	0.663635i	0.991511	+	0.130025i	$0.0415059\pi$
$734$		0			0
$735$	1.98142	−	0.159640i	0.00269581	−	0.000217198i
$736$		0			0
$737$	−409.478			−0.555601
$738$		0			0
$739$		−	912.732i		−	1.23509i	−0.786535	−	0.617545i	$-0.788127\pi$
$739$		−	912.732i		−	1.23509i	0.786535	−	0.617545i	$-0.211873\pi$
$740$		0			0
$741$	−341.111	+	235.372i	−0.460339	+	0.317641i
$742$		0			0
$743$	913.005	+	527.123i	1.22881	+	0.709453i	0.966781	−	0.255608i	$-0.0822755\pi$
$743$	913.005	+	527.123i	1.22881	+	0.709453i	0.262028	+	0.965060i	$0.415609\pi$
$744$		0			0
$745$	109.146	+	189.047i	0.146505	+	0.253755i
$746$		0			0
$747$	−224.242	−	85.1250i	−0.300190	−	0.113956i
$748$		0			0
$749$	−627.115	−	1086.20i	−0.837270	−	1.45019i
$750$		0			0
$751$	916.482	+	529.131i	1.22035	+	0.704569i	0.964992	−	0.262278i	$-0.0844737\pi$
$751$	916.482	+	529.131i	1.22035	+	0.704569i	0.255357	+	0.966847i	$0.417807\pi$
$752$		0			0
$753$	−587.743	−	279.002i	−0.780535	−	0.370520i
$754$		0			0
$755$		−	103.035i		−	0.136470i
$756$		0			0
$757$	−359.804			−0.475302			−0.237651	−	0.971351i	$-0.576377\pi$
$757$	−359.804			−0.475302			−0.237651	+	0.971351i	$0.576377\pi$
$758$		0			0
$759$	260.877	−	549.561i	0.343711	−	0.724060i
$760$		0			0
$761$	−311.474	+	539.489i	−0.409296	+	0.708921i	−0.994811	−	0.101740i	$-0.967559\pi$
$761$	−311.474	+	539.489i	−0.409296	+	0.708921i	0.585515	+	0.810661i	$0.300892\pi$
$762$		0			0
$763$	−870.966	+	502.853i	−1.14150	+	0.659047i
$764$		0			0
$765$	−212.811	+	34.5159i	−0.278184	+	0.0451188i
$766$		0			0
$767$	518.336	−	299.261i	0.675796	−	0.390171i
$768$		0			0
$769$	−534.453	+	925.699i	−0.694997	+	1.20377i	0.275185	+	0.961391i	$0.411261\pi$
$769$	−534.453	+	925.699i	−0.694997	+	1.20377i	−0.970182	+	0.242379i	$0.922072\pi$
$770$		0			0
$771$	489.253	+	709.046i	0.634570	+	0.919645i
$772$		0			0
$773$	−512.261			−0.662692			−0.331346	−	0.943509i	$-0.607503\pi$
$773$	−512.261			−0.662692			−0.331346	+	0.943509i	$0.607503\pi$
$774$		0			0
$775$			3.35066i			0.00432344i
$776$		0			0
$777$	−118.518	−	1471.02i	−0.152533	−	1.89321i
$778$		0			0
$779$	1046.24	+	604.048i	1.34306	+	0.775415i
$780$		0			0
$781$	−275.260	−	476.764i	−0.352445	−	0.610453i
$782$		0			0
$783$	−567.160	−	591.039i	−0.724343	−	0.754839i
$784$		0			0
$785$	−54.8813	−	95.0571i	−0.0699124	−	0.121092i
$786$		0			0
$787$	−153.809	−	88.8019i	−0.195438	−	0.112836i	0.399088	−	0.916913i	$-0.369327\pi$
$787$	−153.809	−	88.8019i	−0.195438	−	0.112836i	−0.594526	+	0.804077i	$0.702660\pi$
$788$		0			0
$789$	−100.635	−	1249.06i	−0.127547	−	1.58309i
$790$		0			0
$791$		−	1412.44i		−	1.78564i
$792$		0			0
$793$	323.439			0.407868
$794$		0			0
$795$	−46.5143	−	67.4105i	−0.0585086	−	0.0847931i
$796$		0			0
$797$	−190.381	+	329.750i	−0.238872	+	0.413739i	−0.960391	−	0.278656i	$-0.910111\pi$
$797$	−190.381	+	329.750i	−0.238872	+	0.413739i	0.721519	+	0.692395i	$0.243444\pi$
$798$		0			0
$799$	1864.21	−	1076.30i	2.33318	−	1.34706i
$800$		0			0
$801$	146.754	+	179.858i	0.183214	+	0.224542i
$802$		0			0
$803$	−154.292	+	89.0808i	−0.192145	+	0.110935i
$804$		0			0
$805$	−80.8123	+	139.971i	−0.100388	+	0.173877i
$806$		0			0
$807$	−630.218	+	1327.61i	−0.780940	+	1.64512i
$808$		0			0
$809$	−720.850			−0.891039			−0.445519	−	0.895272i	$-0.646981\pi$
$809$	−720.850			−0.891039			−0.445519	+	0.895272i	$0.646981\pi$
$810$		0			0
$811$		−	1048.82i		−	1.29324i	−0.762813	−	0.646619i	$-0.776182\pi$
$811$		−	1048.82i		−	1.29324i	0.762813	−	0.646619i	$-0.223818\pi$
$812$		0			0
$813$	−881.158	−	418.286i	−1.08384	−	0.514497i
$814$		0			0
$815$	16.0237	+	9.25127i	0.0196609	+	0.0113512i
$816$		0			0
$817$	29.1839	+	50.5479i	0.0357208	+	0.0618702i
$818$		0			0
$819$	−330.405	+	269.593i	−0.403425	+	0.329173i
$820$		0			0
$821$	361.666	+	626.424i	0.440519	+	0.763001i	0.997728	−	0.0673712i	$-0.0214612\pi$
$821$	361.666	+	626.424i	0.440519	+	0.763001i	−0.557209	+	0.830372i	$0.688128\pi$
$822$		0			0
$823$	−1074.90	−	620.596i	−1.30608	−	0.754066i	−0.324640	−	0.945838i	$-0.605243\pi$
$823$	−1074.90	−	620.596i	−1.30608	−	0.754066i	−0.981440	+	0.191772i	$0.938577\pi$
$824$		0			0
$825$	480.162	−	331.319i	0.582014	−	0.401599i
$826$		0			0
$827$		−	348.111i		−	0.420932i	−0.977601	−	0.210466i	$-0.932502\pi$
$827$		−	348.111i		−	0.420932i	0.977601	−	0.210466i	$-0.0674981\pi$
$828$		0			0
$829$	731.151			0.881968			0.440984	−	0.897515i	$-0.354630\pi$
$829$	731.151			0.881968			0.440984	+	0.897515i	$0.354630\pi$
$830$		0			0
$831$	514.861	−	41.4817i	0.619568	−	0.0499178i
$832$		0			0
$833$	−9.60012	+	16.6279i	−0.0115248	+	0.0199615i
$834$		0			0
$835$	137.775	−	79.5443i	0.165000	−	0.0952627i
$836$		0			0
$837$	−3.59422	−	1.04293i	−0.00429416	−	0.00124603i
$838$		0			0
$839$	−563.141	+	325.130i	−0.671205	+	0.387520i	−0.796533	−	0.604595i	$-0.793335\pi$
$839$	−563.141	+	325.130i	−0.671205	+	0.387520i	0.125328	+	0.992115i	$0.460002\pi$
$840$		0			0
$841$	−39.7179	+	68.7934i	−0.0472269	+	0.0817995i
$842$		0			0
$843$	−359.447	+	28.9602i	−0.426390	+	0.0343537i
$844$		0			0
$845$	−112.612			−0.133268
$846$		0			0
$847$			396.938i			0.468640i
$848$		0			0
$849$	−273.406	+	188.654i	−0.322032	+	0.222208i
$850$		0			0
$851$	1522.87	+	879.227i	1.78950	+	1.03317i
$852$		0			0
$853$	−664.274	−	1150.56i	−0.778750	−	1.34884i	−0.932662	−	0.360751i	$-0.882521\pi$
$853$	−664.274	−	1150.56i	−0.778750	−	1.34884i	0.153912	−	0.988085i	$-0.450813\pi$
$854$		0			0
$855$	−26.9357	−	166.075i	−0.0315038	−	0.194240i
$856$		0			0
$857$	−323.338	−	560.038i	−0.377290	−	0.653486i	0.613377	−	0.789791i	$-0.289811\pi$
$857$	−323.338	−	560.038i	−0.377290	−	0.653486i	−0.990667	+	0.136304i	$0.956477\pi$
$858$		0			0
$859$	527.482	+	304.542i	0.614065	+	0.354530i	0.774555	−	0.632507i	$-0.217974\pi$
$859$	527.482	+	304.542i	0.614065	+	0.354530i	−0.160490	+	0.987037i	$0.551307\pi$
$860$		0			0
$861$	1122.97	+	533.076i	1.30427	+	0.619136i
$862$		0			0
$863$		−	93.0849i		−	0.107862i	−0.998545	−	0.0539310i	$-0.982825\pi$
$863$		−	93.0849i		−	0.107862i	0.998545	−	0.0539310i	$-0.0171751\pi$
$864$		0			0
$865$	−101.683			−0.117553
$866$		0			0
$867$	521.195	−	1097.94i	0.601147	−	1.26637i
$868$		0			0
$869$	159.927	−	277.002i	0.184036	−	0.318759i
$870$		0			0
$871$	−296.195	+	171.008i	−0.340063	+	0.196335i
$872$		0			0
$873$	−334.549	+	881.291i	−0.383218	+	1.00950i
$874$		0			0
$875$	−273.046	+	157.643i	−0.312052	+	0.180164i
$876$		0			0
$877$	330.684	−	572.762i	0.377063	−	0.653092i	−0.613571	−	0.789640i	$-0.710267\pi$
$877$	330.684	−	572.762i	0.377063	−	0.653092i	0.990633	+	0.136548i	$0.0436008\pi$
$878$		0			0
$879$	−144.266	−	209.076i	−0.164125	−	0.237857i
$880$		0			0
$881$	−659.388			−0.748455			−0.374227	−	0.927337i	$-0.622092\pi$
$881$	−659.388			−0.748455			−0.374227	+	0.927337i	$0.622092\pi$
$882$		0			0
$883$			776.943i			0.879890i	0.898025	+	0.439945i	$0.145002\pi$
$883$			776.943i			0.879890i	−0.898025	+	0.439945i	$0.854998\pi$
$884$		0			0
$885$	19.5131	+	242.193i	0.0220488	+	0.273664i
$886$		0			0
$887$	−598.849	−	345.745i	−0.675139	−	0.389792i	0.122882	−	0.992421i	$-0.460786\pi$
$887$	−598.849	−	345.745i	−0.675139	−	0.389792i	−0.798021	+	0.602629i	$0.794120\pi$
$888$		0			0
$889$	640.743	+	1109.80i	0.720745	+	1.24837i
$890$		0			0
$891$	205.946	+	618.190i	0.231141	+	0.693816i
$892$		0			0
$893$	839.934	+	1454.81i	0.940575	+	1.62912i
$894$		0			0
$895$	14.7198	+	8.49849i	0.0164467	+	0.00949552i
$896$		0			0
$897$	−40.8058	−	506.473i	−0.0454915	−	0.564629i
$898$		0			0
$899$			4.20525i			0.00467769i
$900$		0			0
$901$	791.069			0.877990
$902$		0			0
$903$	34.1089	+	49.4320i	0.0377729	+	0.0547420i
$904$		0			0
$905$	44.5764	−	77.2087i	0.0492557	−	0.0853134i
$906$		0			0
$907$	81.4675	−	47.0353i	0.0898209	−	0.0518581i	−0.454417	−	0.890789i	$-0.650152\pi$
$907$	81.4675	−	47.0353i	0.0898209	−	0.0518581i	0.544238	+	0.838931i	$0.316819\pi$
$908$		0			0
$909$	130.825	−	344.627i	0.143922	−	0.379127i
$910$		0			0
$911$	−818.478	+	472.549i	−0.898440	+	0.518714i	−0.876694	−	0.481049i	$-0.840256\pi$
$911$	−818.478	+	472.549i	−0.898440	+	0.518714i	−0.0217460	+	0.999764i	$0.506923\pi$
$912$		0			0
$913$	107.193	−	185.664i	0.117408	−	0.203356i
$914$		0			0
$915$	−56.3079	+	118.618i	−0.0615387	+	0.129637i
$916$		0			0
$917$	431.047			0.470062
$918$		0			0
$919$			29.1099i			0.0316757i	0.999875	+	0.0158378i	$0.00504155\pi$
$919$			29.1099i			0.0316757i	−0.999875	+	0.0158378i	$0.994958\pi$
$920$		0			0
$921$	−597.525	−	283.645i	−0.648779	−	0.307976i
$922$		0			0
$923$	−398.217	−	229.911i	−0.431438	−	0.249091i
$924$		0			0
$925$	843.151	+	1460.38i	0.911514	+	1.57879i
$926$		0			0
$927$	−208.436	−	1285.13i	−0.224850	−	1.38634i
$928$		0			0
$929$	383.769	+	664.707i	0.413099	+	0.715508i	0.995227	−	0.0975893i	$-0.0311131\pi$
$929$	383.769	+	664.707i	0.413099	+	0.715508i	−0.582128	+	0.813097i	$0.697780\pi$
$930$		0			0
$931$	−12.9762	−	7.49181i	−0.0139379	−	0.00804705i
$932$		0			0
$933$	−766.885	+	529.163i	−0.821956	+	0.567163i
$934$		0			0
$935$		−	192.700i		−	0.206096i
$936$		0			0
$937$	−736.778			−0.786316			−0.393158	−	0.919471i	$-0.628617\pi$
$937$	−736.778			−0.786316			−0.393158	+	0.919471i	$0.628617\pi$
$938$		0			0
$939$	−392.201	+	31.5991i	−0.417679	+	0.0336519i
$940$		0			0
$941$	531.351	−	920.327i	0.564667	−	0.978031i	−0.432414	−	0.901675i	$-0.642338\pi$
$941$	531.351	−	920.327i	0.564667	−	0.978031i	0.997081	−	0.0763560i	$-0.0243285\pi$
$942$		0			0
$943$	−1282.73	+	740.585i	−1.36027	+	0.785350i
$944$		0			0
$945$	−41.3496	−	168.106i	−0.0437562	−	0.177890i
$946$		0			0
$947$	−499.283	+	288.261i	−0.527226	+	0.304394i	−0.739886	−	0.672732i	$-0.765121\pi$
$947$	−499.283	+	288.261i	−0.527226	+	0.304394i	0.212660	+	0.977126i	$0.431787\pi$
$948$		0			0
$949$	−74.4047	+	128.873i	−0.0784033	+	0.135799i
$950$		0			0
$951$	1016.59	−	81.9050i	1.06896	−	0.0861251i
$952$		0			0
$953$	677.961			0.711397			0.355698	−	0.934601i	$-0.384243\pi$
$953$	677.961			0.711397			0.355698	+	0.934601i	$0.384243\pi$
$954$		0			0
$955$		−	252.720i		−	0.264629i
$956$		0			0
$957$	602.626	−	415.822i	0.629703	−	0.434505i
$958$		0			0
$959$	221.237	+	127.731i	0.230696	+	0.133192i
$960$		0			0
$961$	−480.490	−	832.234i	−0.499990	−	0.866008i
$962$		0			0
$963$	−1240.25	+	1011.98i	−1.28790	+	1.05086i
$964$		0			0
$965$	73.7641	+	127.763i	0.0764395	+	0.132397i
$966$		0			0
$967$	1153.25	+	665.830i	1.19261	+	0.688552i	0.958897	−	0.283755i	$-0.0915801\pi$
$967$	1153.25	+	665.830i	1.19261	+	0.688552i	0.233710	+	0.972306i	$0.424913\pi$
$968$		0			0
$969$	1468.05	+	696.882i	1.51501	+	0.719176i
$970$		0			0
$971$		−	385.062i		−	0.396563i	−0.980145	−	0.198281i	$-0.936464\pi$
$971$		−	385.062i		−	0.396563i	0.980145	−	0.198281i	$-0.0635360\pi$
$972$		0			0
$973$	−1259.30			−1.29424
$974$		0			0
$975$	208.957	−	440.186i	0.214314	−	0.451473i
$976$		0			0
$977$	142.550	−	246.905i	0.145906	−	0.252717i	−0.783804	−	0.621008i	$-0.786724\pi$
$977$	142.550	−	246.905i	0.145906	−	0.252717i	0.929711	+	0.368291i	$0.120057\pi$
$978$		0			0
$979$	−179.687	+	103.742i	−0.183541	+	0.105968i
$980$		0			0
$981$	811.454	+	994.494i	0.827170	+	1.01376i
$982$		0			0
$983$	−1164.42	+	672.280i	−1.18456	+	0.683907i	−0.957065	−	0.289872i	$-0.906387\pi$
$983$	−1164.42	+	672.280i	−1.18456	+	0.683907i	−0.227496	+	0.973779i	$0.573054\pi$
$984$		0			0
$985$	48.2715	−	83.6087i	0.0490066	−	0.0848819i
$986$		0			0
$987$	981.680	+	1422.69i	0.994610	+	1.44143i
$988$		0			0
$989$	−71.5610			−0.0723570
$990$		0			0
$991$			1457.00i			1.47023i	0.677944	+	0.735114i	$0.262871\pi$
$991$			1457.00i			1.47023i	−0.677944	+	0.735114i	$0.737129\pi$
$992$		0			0
$993$	109.734	+	1361.99i	0.110507	+	1.37159i
$994$		0			0
$995$	−49.9125	−	28.8170i	−0.0501633	−	0.0289618i
$996$		0			0
$997$	160.689	+	278.322i	0.161173	+	0.279160i	0.935290	−	0.353883i	$-0.115139\pi$
$997$	160.689	+	278.322i	0.161173	+	0.279160i	−0.774117	+	0.633043i	$0.781806\pi$
$998$		0			0
$999$	−1828.97	+	449.878i	−1.83080	+	0.450328i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	144.3.o.c.31.3	yes	8
3.2	odd	2		432.3.o.a.415.3		8
4.3	odd	2		144.3.o.a.31.2	✓	8
8.3	odd	2		576.3.o.f.319.3		8
8.5	even	2		576.3.o.d.319.2		8
9.2	odd	6		432.3.o.b.127.3		8
9.4	even	3		1296.3.g.j.1135.6		8
9.5	odd	6		1296.3.g.k.1135.4		8
9.7	even	3		144.3.o.a.79.2	yes	8
12.11	even	2		432.3.o.b.415.3		8
24.5	odd	2		1728.3.o.e.1279.2		8
24.11	even	2		1728.3.o.f.1279.2		8
36.7	odd	6	inner	144.3.o.c.79.3	yes	8
36.11	even	6		432.3.o.a.127.3		8
36.23	even	6		1296.3.g.k.1135.3		8
36.31	odd	6		1296.3.g.j.1135.5		8
72.11	even	6		1728.3.o.e.127.2		8
72.29	odd	6		1728.3.o.f.127.2		8
72.43	odd	6		576.3.o.d.511.2		8
72.61	even	6		576.3.o.f.511.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.3.o.a.31.2	✓	8	4.3	odd	2
144.3.o.a.79.2	yes	8	9.7	even	3
144.3.o.c.31.3	yes	8	1.1	even	1	trivial
144.3.o.c.79.3	yes	8	36.7	odd	6	inner
432.3.o.a.127.3		8	36.11	even	6
432.3.o.a.415.3		8	3.2	odd	2
432.3.o.b.127.3		8	9.2	odd	6
432.3.o.b.415.3		8	12.11	even	2
576.3.o.d.319.2		8	8.5	even	2
576.3.o.d.511.2		8	72.43	odd	6
576.3.o.f.319.3		8	8.3	odd	2
576.3.o.f.511.3		8	72.61	even	6
1296.3.g.j.1135.5		8	36.31	odd	6
1296.3.g.j.1135.6		8	9.4	even	3
1296.3.g.k.1135.3		8	36.23	even	6
1296.3.g.k.1135.4		8	9.5	odd	6
1728.3.o.e.127.2		8	72.11	even	6
1728.3.o.e.1279.2		8	24.5	odd	2
1728.3.o.f.127.2		8	72.29	odd	6
1728.3.o.f.1279.2		8	24.11	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:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	144.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.28651 - 2.71015i) q^{3} +(-0.454613 + 0.787412i) q^{5} +(6.10709 - 3.52593i) q^{7} +(-5.68980 - 6.97325i) q^{9} +O(q^{10})\)	\(q+(1.28651 - 2.71015i) q^{3} +(-0.454613 + 0.787412i) q^{5} +(6.10709 - 3.52593i) q^{7} +(-5.68980 - 6.97325i) q^{9} +(6.96661 - 4.02218i) q^{11} +(3.35952 - 5.81886i) q^{13} +(1.54914 + 2.24508i) q^{15} -26.3462 q^{17} -20.5603i q^{19} +(-1.69897 - 21.0873i) q^{21} +(21.8305 + 12.6038i) q^{23} +(12.0867 + 20.9347i) q^{25} +(-26.2185 + 6.44905i) q^{27} +(15.1693 + 26.2741i) q^{29} +(0.120040 + 0.0693050i) q^{31} +(-1.93809 - 24.0551i) q^{33} +6.41173i q^{35} +69.7588 q^{37} +(-11.4479 - 16.5908i) q^{39} +(-29.3794 + 50.8866i) q^{41} +(-2.45853 + 1.41943i) q^{43} +(8.07748 - 1.31009i) q^{45} +(-70.7583 + 40.8523i) q^{47} +(0.364383 - 0.631130i) q^{49} +(-33.8946 + 71.4022i) q^{51} -30.0259 q^{53} +7.31413i q^{55} +(-55.7213 - 26.4509i) q^{57} +(77.1442 + 44.5392i) q^{59} +(24.0688 + 41.6885i) q^{61} +(-59.3353 - 22.5244i) q^{63} +(3.05456 + 5.29066i) q^{65} +(-44.0829 - 25.4513i) q^{67} +(62.2432 - 42.9488i) q^{69} -68.4355i q^{71} -22.1474 q^{73} +(72.2857 - 5.82397i) q^{75} +(28.3638 - 49.1276i) q^{77} +(34.4343 - 19.8807i) q^{79} +(-16.2524 + 79.3527i) q^{81} +(23.0801 - 13.3253i) q^{83} +(11.9773 - 20.7453i) q^{85} +(90.7221 - 7.30936i) q^{87} -25.7926 q^{89} -47.3818i q^{91} +(0.342259 - 0.236164i) q^{93} +(16.1894 + 9.34695i) q^{95} +(-52.3697 - 90.7070i) q^{97} +(-67.6863 - 25.6946i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 3 q^{3} + 3 q^{5} - 3 q^{7} - 3 q^{9}+O(q^{10}) \) 8 * q + 3 * q^3 + 3 * q^5 - 3 * q^7 - 3 * q^9	\( 8 q + 3 q^{3} + 3 q^{5} - 3 q^{7} - 3 q^{9} - 18 q^{11} + 5 q^{13} + 21 q^{15} + 6 q^{17} - 33 q^{21} + 81 q^{23} - 23 q^{25} - 108 q^{27} + 69 q^{29} - 45 q^{31} + 72 q^{33} - 20 q^{37} + 141 q^{39} + 54 q^{41} - 117 q^{45} - 207 q^{47} + 41 q^{49} + 141 q^{51} - 252 q^{53} - 273 q^{57} + 306 q^{59} + 7 q^{61} - 441 q^{63} + 93 q^{65} - 12 q^{67} + 189 q^{69} + 74 q^{73} + 387 q^{75} + 207 q^{77} - 33 q^{79} + 117 q^{81} - 549 q^{83} - 30 q^{85} + 87 q^{87} - 168 q^{89} - 27 q^{93} + 684 q^{95} - 10 q^{97} - 585 q^{99}+O(q^{100}) \) 8 * q + 3 * q^3 + 3 * q^5 - 3 * q^7 - 3 * q^9 - 18 * q^11 + 5 * q^13 + 21 * q^15 + 6 * q^17 - 33 * q^21 + 81 * q^23 - 23 * q^25 - 108 * q^27 + 69 * q^29 - 45 * q^31 + 72 * q^33 - 20 * q^37 + 141 * q^39 + 54 * q^41 - 117 * q^45 - 207 * q^47 + 41 * q^49 + 141 * q^51 - 252 * q^53 - 273 * q^57 + 306 * q^59 + 7 * q^61 - 441 * q^63 + 93 * q^65 - 12 * q^67 + 189 * q^69 + 74 * q^73 + 387 * q^75 + 207 * q^77 - 33 * q^79 + 117 * q^81 - 549 * q^83 - 30 * q^85 + 87 * q^87 - 168 * q^89 - 27 * q^93 + 684 * q^95 - 10 * q^97 - 585 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more