LMFDB - Embedded newform 144.3.o.b.79.4

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:	8.0.121550625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 4x^{6} - 9x^{5} + 23x^{4} + 18x^{3} - 16x^{2} + 8x + 16 $ x^8 - x^7 - 4x^6 - 9x^5 + 23x^4 + 18x^3 - 16x^2 + 8x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			79.4
Root			$2.25820 + 0.369600i$ of defining polynomial
Character	$\chi$	$=$	144.79
Dual form			144.3.o.b.31.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.82269 + 1.01607i) q^{3} +(1.81174 + 3.13802i) q^{5} +(1.59422 + 0.920424i) q^{7} +(6.93521 + 5.73610i) q^{9} +O(q^{10})$	\(q+(2.82269 + 1.01607i) q^{3} +(1.81174 + 3.13802i) q^{5} +(1.59422 + 0.920424i) q^{7} +(6.93521 + 5.73610i) q^{9} +(-10.0623 - 5.80948i) q^{11} +(6.43521 + 11.1461i) q^{13} +(1.92554 + 10.6985i) q^{15} +12.6235 q^{17} -25.6526i q^{19} +(3.56479 + 4.21791i) q^{21} +(-25.9012 + 14.9541i) q^{23} +(5.93521 - 10.2801i) q^{25} +(13.7477 + 23.2379i) q^{27} +(-10.8117 + 18.7265i) q^{29} +(52.4027 - 30.2547i) q^{31} +(-22.5000 - 26.6224i) q^{33} +6.67027i q^{35} -25.7409 q^{37} +(6.83944 + 38.0007i) q^{39} +(-33.3704 - 57.7993i) q^{41} +(-14.2447 - 8.22418i) q^{43} +(-5.43521 + 32.1552i) q^{45} +(-66.1505 - 38.1920i) q^{47} +(-22.8056 - 39.5005i) q^{49} +(35.6322 + 12.8263i) q^{51} +14.2591 q^{53} -42.1010i q^{55} +(26.0648 - 72.4095i) q^{57} +(-50.3115 + 29.0474i) q^{59} +(-9.43521 + 16.3423i) q^{61} +(5.77662 + 15.5279i) q^{63} +(-23.3178 + 40.3877i) q^{65} +(-20.6216 + 11.9059i) q^{67} +(-88.3056 + 15.8934i) q^{69} -46.4758i q^{71} +49.3521 q^{73} +(27.1986 - 22.9870i) q^{75} +(-10.6944 - 18.5232i) q^{77} +(52.4027 + 30.2547i) q^{79} +(15.1944 + 79.5621i) q^{81} +(86.2751 + 49.8109i) q^{83} +(22.8704 + 39.6127i) q^{85} +(-49.5456 + 41.8737i) q^{87} +154.988 q^{89} +23.6925i q^{91} +(178.658 - 32.1552i) q^{93} +(80.4984 - 46.4758i) q^{95} +(-21.1113 + 36.5658i) q^{97} +(-36.4605 - 98.0083i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 6 q^{5} - 6 q^{9}+O(q^{10}) $ 8 * q - 6 * q^5 - 6 * q^9	$ 8 q - 6 q^{5} - 6 q^{9} - 10 q^{13} + 60 q^{17} + 90 q^{21} - 14 q^{25} - 66 q^{29} - 180 q^{33} + 40 q^{37} - 144 q^{41} + 18 q^{45} + 2 q^{49} + 360 q^{53} + 270 q^{57} - 14 q^{61} - 330 q^{65} - 522 q^{69} - 220 q^{73} - 270 q^{77} + 306 q^{81} + 60 q^{85} + 912 q^{89} + 630 q^{93} + 200 q^{97}+O(q^{100}) $ 8 * q - 6 * q^5 - 6 * q^9 - 10 * q^13 + 60 * q^17 + 90 * q^21 - 14 * q^25 - 66 * q^29 - 180 * q^33 + 40 * q^37 - 144 * q^41 + 18 * q^45 + 2 * q^49 + 360 * q^53 + 270 * q^57 - 14 * q^61 - 330 * q^65 - 522 * q^69 - 220 * q^73 - 270 * q^77 + 306 * q^81 + 60 * q^85 + 912 * q^89 + 630 * q^93 + 200 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$37$	$65$	$127$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$-1$

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
$3$	2.82269	+	1.01607i	0.940898	+	0.338689i
$3$	2.82269	+	1.01607i	0.940898	+	0.338689i
$4$		0			0
$5$	1.81174	+	3.13802i	0.362348	+	0.627604i	0.988347	−	0.152219i	$-0.0486420\pi$
$5$	1.81174	+	3.13802i	0.362348	+	0.627604i	−0.625999	+	0.779824i	$0.715309\pi$
$6$		0			0
$7$	1.59422	+	0.920424i	0.227746	+	0.131489i	0.609532	−	0.792762i	$-0.291357\pi$
$7$	1.59422	+	0.920424i	0.227746	+	0.131489i	−0.381786	+	0.924251i	$0.624691\pi$
$8$		0			0
$9$	6.93521	+	5.73610i	0.770579	+	0.637344i
$10$		0			0
$11$	−10.0623	−	5.80948i	−0.914755	−	0.528134i	−0.0327970	−	0.999462i	$-0.510441\pi$
$11$	−10.0623	−	5.80948i	−0.914755	−	0.528134i	−0.881958	+	0.471328i	$0.843775\pi$
$12$		0			0
$13$	6.43521	+	11.1461i	0.495016	+	0.857394i	0.999983	−	0.00574505i	$-0.00182872\pi$
$13$	6.43521	+	11.1461i	0.495016	+	0.857394i	−0.504967	+	0.863139i	$0.668495\pi$
$14$		0			0
$15$	1.92554	+	10.6985i	0.128369	+	0.713235i
$16$		0			0
$17$	12.6235			0.742557			0.371279	−	0.928521i	$-0.378919\pi$
$17$	12.6235			0.742557			0.371279	+	0.928521i	$0.378919\pi$
$18$		0			0
$19$		−	25.6526i		−	1.35014i	−0.737755	−	0.675069i	$-0.764114\pi$
$19$		−	25.6526i		−	1.35014i	0.737755	−	0.675069i	$-0.235886\pi$
$20$		0			0
$21$	3.56479	+	4.21791i	0.169752	+	0.200853i
$22$		0			0
$23$	−25.9012	+	14.9541i	−1.12614	+	0.650178i	−0.942961	−	0.332902i	$-0.891972\pi$
$23$	−25.9012	+	14.9541i	−1.12614	+	0.650178i	−0.183179	+	0.983080i	$0.558639\pi$
$24$		0			0
$25$	5.93521	−	10.2801i	0.237409	−	0.411204i
$26$		0			0
$27$	13.7477	+	23.2379i	0.509175	+	0.860663i
$28$		0			0
$29$	−10.8117	+	18.7265i	−0.372819	+	0.645741i	−0.989998	−	0.141082i	$-0.954942\pi$
$29$	−10.8117	+	18.7265i	−0.372819	+	0.645741i	0.617179	+	0.786822i	$0.288275\pi$
$30$		0			0
$31$	52.4027	−	30.2547i	1.69041	−	0.975959i	0.736228	−	0.676733i	$-0.236605\pi$
$31$	52.4027	−	30.2547i	1.69041	−	0.975959i	0.954182	−	0.299226i	$-0.0967284\pi$
$32$		0			0
$33$	−22.5000	−	26.6224i	−0.681818	−	0.806738i
$34$		0			0
$35$			6.67027i			0.190579i
$36$		0			0
$37$	−25.7409			−0.695699			−0.347849	−	0.937550i	$-0.613088\pi$
$37$	−25.7409			−0.695699			−0.347849	+	0.937550i	$0.613088\pi$
$38$		0			0
$39$	6.83944	+	38.0007i	0.175370	+	0.974377i
$40$		0			0
$41$	−33.3704	−	57.7993i	−0.813913	−	1.40974i	−0.910106	−	0.414376i	$-0.864000\pi$
$41$	−33.3704	−	57.7993i	−0.813913	−	1.40974i	0.0961931	−	0.995363i	$-0.469333\pi$
$42$		0			0
$43$	−14.2447	−	8.22418i	−0.331272	−	0.191260i	0.325134	−	0.945668i	$-0.394591\pi$
$43$	−14.2447	−	8.22418i	−0.331272	−	0.191260i	−0.656406	+	0.754408i	$0.727924\pi$
$44$		0			0
$45$	−5.43521	+	32.1552i	−0.120783	+	0.714559i
$46$		0			0
$47$	−66.1505	−	38.1920i	−1.40746	−	0.812595i	−0.412314	−	0.911042i	$-0.635279\pi$
$47$	−66.1505	−	38.1920i	−1.40746	−	0.812595i	−0.995142	+	0.0984463i	$0.968613\pi$
$48$		0			0
$49$	−22.8056	−	39.5005i	−0.465421	−	0.806133i
$50$		0			0
$51$	35.6322	+	12.8263i	0.698671	+	0.251496i
$52$		0			0
$53$	14.2591			0.269041			0.134520	−	0.990911i	$-0.457051\pi$
$53$	14.2591			0.269041			0.134520	+	0.990911i	$0.457051\pi$
$54$		0			0
$55$		−	42.1010i		−	0.765472i
$56$		0			0
$57$	26.0648	−	72.4095i	0.457277	−	1.27034i
$58$		0			0
$59$	−50.3115	+	29.0474i	−0.852738	+	0.492328i	−0.861574	−	0.507633i	$-0.830521\pi$
$59$	−50.3115	+	29.0474i	−0.852738	+	0.492328i	0.00883587	+	0.999961i	$0.497187\pi$
$60$		0			0
$61$	−9.43521	+	16.3423i	−0.154676	+	0.267906i	−0.932941	−	0.360030i	$-0.882767\pi$
$61$	−9.43521	+	16.3423i	−0.154676	+	0.267906i	0.778265	+	0.627936i	$0.216100\pi$
$62$		0			0
$63$	5.77662	+	15.5279i	0.0916924	+	0.246475i
$64$		0			0
$65$	−23.3178	+	40.3877i	−0.358736	+	0.621349i
$66$		0			0
$67$	−20.6216	+	11.9059i	−0.307785	+	0.177700i	−0.645935	−	0.763393i	$-0.723532\pi$
$67$	−20.6216	+	11.9059i	−0.307785	+	0.177700i	0.338150	+	0.941092i	$0.390199\pi$
$68$		0			0
$69$	−88.3056	+	15.8934i	−1.27979	+	0.230339i
$70$		0			0
$71$		−	46.4758i		−	0.654589i	−0.944922	−	0.327294i	$-0.893863\pi$
$71$		−	46.4758i		−	0.654589i	0.944922	−	0.327294i	$-0.106137\pi$
$72$		0			0
$73$	49.3521			0.676057			0.338028	−	0.941136i	$-0.390240\pi$
$73$	49.3521			0.676057			0.338028	+	0.941136i	$0.390240\pi$
$74$		0			0
$75$	27.1986	−	22.9870i	0.362648	−	0.306493i
$76$		0			0
$77$	−10.6944	−	18.5232i	−0.138888	−	0.240561i
$78$		0			0
$79$	52.4027	+	30.2547i	0.663326	+	0.382971i	0.793543	−	0.608514i	$-0.208234\pi$
$79$	52.4027	+	30.2547i	0.663326	+	0.382971i	−0.130217	+	0.991485i	$0.541567\pi$
$80$		0			0
$81$	15.1944	+	79.5621i	0.187585	+	0.982248i
$82$		0			0
$83$	86.2751	+	49.8109i	1.03946	+	0.600132i	0.919680	−	0.392669i	$-0.128448\pi$
$83$	86.2751	+	49.8109i	1.03946	+	0.600132i	0.119779	+	0.992801i	$0.461781\pi$
$84$		0			0
$85$	22.8704	+	39.6127i	0.269064	+	0.466032i
$86$		0			0
$87$	−49.5456	+	41.8737i	−0.569490	+	0.481307i
$88$		0			0
$89$	154.988			1.74144			0.870718	−	0.491783i	$-0.163655\pi$
$89$	154.988			1.74144			0.870718	+	0.491783i	$0.163655\pi$
$90$		0			0
$91$			23.6925i			0.260357i
$92$		0			0
$93$	178.658	−	32.1552i	1.92105	−	0.345754i
$94$		0			0
$95$	80.4984	−	46.4758i	0.847352	−	0.489219i
$96$		0			0
$97$	−21.1113	+	36.5658i	−0.217642	+	0.376967i	−0.954087	−	0.299531i	$-0.903170\pi$
$97$	−21.1113	+	36.5658i	−0.217642	+	0.376967i	0.736445	+	0.676498i	$0.236503\pi$
$98$		0			0
$99$	−36.4605	−	98.0083i	−0.368288	−	0.989983i
$100$		0			0
$101$	−63.1761	+	109.424i	−0.625506	+	1.08341i	0.362937	+	0.931814i	$0.381774\pi$
$101$	−63.1761	+	109.424i	−0.625506	+	1.08341i	−0.988443	+	0.151594i	$0.951559\pi$
$102$		0			0
$103$	−23.9133	+	13.8064i	−0.232168	+	0.134042i	−0.611572	−	0.791189i	$-0.709462\pi$
$103$	−23.9133	+	13.8064i	−0.232168	+	0.134042i	0.379404	+	0.925231i	$0.376129\pi$
$104$		0			0
$105$	−6.77744	+	18.8281i	−0.0645471	+	0.179316i
$106$		0			0
$107$			121.138i			1.13213i	0.824360	+	0.566066i	$0.191535\pi$
$107$			121.138i			1.13213i	−0.824360	+	0.566066i	$0.808465\pi$
$108$		0			0
$109$	61.7409			0.566430			0.283215	−	0.959056i	$-0.408599\pi$
$109$	61.7409			0.566430			0.283215	+	0.959056i	$0.408599\pi$
$110$		0			0
$111$	−72.6586	−	26.1544i	−0.654582	−	0.235626i
$112$		0			0
$113$	−43.0709	−	74.6010i	−0.381158	−	0.660186i	0.610070	−	0.792348i	$-0.291141\pi$
$113$	−43.0709	−	74.6010i	−0.381158	−	0.660186i	−0.991228	+	0.132162i	$0.957808\pi$
$114$		0			0
$115$	−93.8525	−	54.1858i	−0.816109	−	0.471180i
$116$		0			0
$117$	−19.3056	+	114.214i	−0.165005	+	0.976185i
$118$		0			0
$119$	20.1246	+	11.6190i	0.169114	+	0.0976382i
$120$		0			0
$121$	7.00000	+	12.1244i	0.0578512	+	0.100201i
$122$		0			0
$123$	−35.4666	−	197.056i	−0.288346	−	1.60208i
$124$		0			0
$125$	133.599			1.06879
$126$		0			0
$127$			183.369i			1.44385i	0.691970	+	0.721926i	$0.256743\pi$
$127$			183.369i			1.44385i	−0.691970	+	0.721926i	$0.743257\pi$
$128$		0			0
$129$	−31.8521	−	37.6879i	−0.246916	−	0.292155i
$130$		0			0
$131$	149.631	−	86.3894i	1.14222	−	0.659461i	0.195240	−	0.980755i	$-0.437451\pi$
$131$	149.631	−	86.3894i	1.14222	−	0.659461i	0.946979	+	0.321295i	$0.104118\pi$
$132$		0			0
$133$	23.6113	−	40.8959i	0.177528	−	0.307488i
$134$		0			0
$135$	−48.0138	+	85.2416i	−0.355657	+	0.631420i
$136$		0			0
$137$	−80.1235	+	138.778i	−0.584843	+	1.01298i	0.410052	+	0.912062i	$0.365511\pi$
$137$	−80.1235	+	138.778i	−0.584843	+	1.01298i	−0.994895	+	0.100915i	$0.967823\pi$
$138$		0			0
$139$	−191.971	+	110.835i	−1.38109	+	0.797371i	−0.992288	−	0.123951i	$-0.960443\pi$
$139$	−191.971	+	110.835i	−1.38109	+	0.797371i	−0.388799	+	0.921322i	$0.627110\pi$
$140$		0			0
$141$	−147.917	−	175.018i	−1.04906	−	1.24126i
$142$		0			0
$143$		−	149.541i		−	1.04574i
$144$		0			0
$145$	−78.3521			−0.540360
$146$		0			0
$147$	−24.2382	−	134.670i	−0.164885	−	0.916122i
$148$		0			0
$149$	−94.0343	−	162.872i	−0.631103	−	1.09310i	−0.987327	−	0.158701i	$-0.949269\pi$
$149$	−94.0343	−	162.872i	−0.631103	−	1.09310i	0.356224	−	0.934401i	$-0.384064\pi$
$150$		0			0
$151$	96.8344	+	55.9073i	0.641287	+	0.370247i	0.785110	−	0.619356i	$-0.212606\pi$
$151$	96.8344	+	55.9073i	0.641287	+	0.370247i	−0.143823	+	0.989603i	$0.545940\pi$
$152$		0			0
$153$	87.5465	+	72.4095i	0.572199	+	0.473265i
$154$		0			0
$155$	189.880	+	109.627i	1.22503	+	0.707273i
$156$		0			0
$157$	−51.4352	−	89.0884i	−0.327613	−	0.567442i	0.654425	−	0.756127i	$-0.272911\pi$
$157$	−51.4352	−	89.0884i	−0.327613	−	0.567442i	−0.982038	+	0.188685i	$0.939577\pi$
$158$		0			0
$159$	40.2492	+	14.4883i	0.253140	+	0.0911211i
$160$		0			0
$161$	−55.0564			−0.341965
$162$		0			0
$163$			205.221i			1.25902i	0.776991	+	0.629512i	$0.216745\pi$
$163$			205.221i			1.25902i	−0.776991	+	0.629512i	$0.783255\pi$
$164$		0			0
$165$	42.7774	−	118.838i	0.259257	−	0.720232i
$166$		0			0
$167$	46.0258	−	26.5730i	0.275604	−	0.159120i	−0.355828	−	0.934552i	$-0.615801\pi$
$167$	46.0258	−	26.5730i	0.275604	−	0.159120i	0.631432	+	0.775432i	$0.282468\pi$
$168$		0			0
$169$	1.67607	−	2.90303i	0.00991755	−	0.0171777i
$170$		0			0
$171$	147.146	−	177.906i	0.860502	−	1.04039i
$172$		0			0
$173$	94.1517	−	163.075i	0.544229	−	0.942633i	−0.454426	−	0.890785i	$-0.650155\pi$
$173$	94.1517	−	163.075i	0.544229	−	0.942633i	0.998655	−	0.0518482i	$-0.0165112\pi$
$174$		0			0
$175$	18.9241	−	10.9258i	0.108138	−	0.0624333i
$176$		0			0
$177$	−171.528	+	30.8720i	−0.969086	+	0.174418i
$178$		0			0
$179$			92.9516i			0.519283i	0.965705	+	0.259641i	$0.0836043\pi$
$179$			92.9516i			0.519283i	−0.965705	+	0.259641i	$0.916396\pi$
$180$		0			0
$181$	−240.445			−1.32843			−0.664213	−	0.747543i	$-0.731233\pi$
$181$	−240.445			−1.32843			−0.664213	+	0.747543i	$0.731233\pi$
$182$		0			0
$183$	−43.2376	+	36.5424i	−0.236271	+	0.199685i
$184$		0			0
$185$	−46.6357	−	80.7754i	−0.252085	−	0.436624i
$186$		0			0
$187$	−127.021	−	73.3358i	−0.679258	−	0.392170i
$188$		0			0
$189$	0.528196	+	49.7001i	0.00279469	+	0.262963i
$190$		0			0
$191$	−49.0077	−	28.2946i	−0.256585	−	0.148139i	0.366191	−	0.930540i	$-0.380662\pi$
$191$	−49.0077	−	28.2946i	−0.256585	−	0.148139i	−0.622776	+	0.782400i	$0.713995\pi$
$192$		0			0
$193$	50.3704	+	87.2441i	0.260987	+	0.452042i	0.966504	−	0.256650i	$-0.0826188\pi$
$193$	50.3704	+	87.2441i	0.260987	+	0.452042i	−0.705518	+	0.708692i	$0.749285\pi$
$194$		0			0
$195$	−106.856	+	90.3096i	−0.547978	+	0.463126i
$196$		0			0
$197$	−115.247			−0.585010			−0.292505	−	0.956264i	$-0.594489\pi$
$197$	−115.247			−0.585010			−0.292505	+	0.956264i	$0.594489\pi$
$198$		0			0
$199$		−	190.733i		−	0.958455i	−0.877691	−	0.479228i	$-0.840917\pi$
$199$		−	190.733i		−	0.958455i	0.877691	−	0.479228i	$-0.159083\pi$
$200$		0			0
$201$	−70.3056	+	12.6537i	−0.349779	+	0.0629539i
$202$		0			0
$203$	−34.4726	+	19.9028i	−0.169816	+	0.0980432i
$204$		0			0
$205$	120.917	−	209.434i	0.589839	−	1.02163i
$206$		0			0
$207$	−265.409	−	44.8623i	−1.28217	−	0.216726i
$208$		0			0
$209$	−149.028	+	258.124i	−0.713054	+	1.23505i
$210$		0			0
$211$	−68.3449	+	39.4590i	−0.323910	+	0.187009i	−0.653134	−	0.757242i	$-0.726546\pi$
$211$	−68.3449	+	39.4590i	−0.323910	+	0.187009i	0.329224	+	0.944252i	$0.393213\pi$
$212$		0			0
$213$	47.2226	−	131.187i	0.221702	−	0.615901i
$214$		0			0
$215$		−	59.6003i		−	0.277211i
$216$		0			0
$217$	111.389			0.513312
$218$		0			0
$219$	139.306	+	50.1451i	0.636100	+	0.228973i
$220$		0			0
$221$	81.2348	+	140.703i	0.367578	+	0.636664i
$222$		0			0
$223$	192.074	+	110.894i	0.861321	+	0.497284i	0.864454	−	0.502711i	$-0.167664\pi$
$223$	192.074	+	110.894i	0.861321	+	0.497284i	−0.00313373	+	0.999995i	$0.500997\pi$
$224$		0			0
$225$	100.130	−	37.2497i	0.445020	−	0.165554i
$226$		0			0
$227$	−10.0623	−	5.80948i	−0.0443273	−	0.0255924i	0.477673	−	0.878538i	$-0.341481\pi$
$227$	−10.0623	−	5.80948i	−0.0443273	−	0.0255924i	−0.522000	+	0.852946i	$0.674814\pi$
$228$		0			0
$229$	24.4352	+	42.3230i	0.106704	+	0.184817i	0.914433	−	0.404737i	$-0.132637\pi$
$229$	24.4352	+	42.3230i	0.106704	+	0.184817i	−0.807729	+	0.589554i	$0.799304\pi$
$230$		0			0
$231$	−11.3661	−	63.1515i	−0.0492040	−	0.273383i
$232$		0			0
$233$	384.785			1.65144			0.825719	−	0.564082i	$-0.190770\pi$
$233$	384.785			1.65144			0.825719	+	0.564082i	$0.190770\pi$
$234$		0			0
$235$		−	276.775i		−	1.17777i
$236$		0			0
$237$	117.176	+	138.645i	0.494414	+	0.584998i
$238$		0			0
$239$	−169.755	+	98.0083i	−0.710274	+	0.410077i	−0.811162	−	0.584821i	$-0.801165\pi$
$239$	−169.755	+	98.0083i	−0.710274	+	0.410077i	0.100889	+	0.994898i	$0.467831\pi$
$240$		0			0
$241$	−130.593	+	226.194i	−0.541880	+	0.938563i	0.456917	+	0.889510i	$0.348954\pi$
$241$	−130.593	+	226.194i	−0.541880	+	0.938563i	−0.998796	+	0.0490534i	$0.984380\pi$
$242$		0			0
$243$	−37.9515	+	240.018i	−0.156179	+	0.987729i
$244$		0			0
$245$	82.6357	−	143.129i	0.337288	−	0.584201i
$246$		0			0
$247$	285.927	−	165.080i	1.15760	−	0.668340i
$248$		0			0
$249$	192.917	+	228.262i	0.774767	+	0.916716i
$250$		0			0
$251$			137.922i			0.549490i	0.961517	+	0.274745i	$0.0885934\pi$
$251$			137.922i			0.549490i	−0.961517	+	0.274745i	$0.911407\pi$
$252$		0			0
$253$	347.502			1.37352
$254$		0			0
$255$	24.3070	+	135.053i	0.0953216	+	0.529618i
$256$		0			0
$257$	−13.7348	−	23.7893i	−0.0534426	−	0.0925653i	0.838066	−	0.545568i	$-0.183686\pi$
$257$	−13.7348	−	23.7893i	−0.0534426	−	0.0925653i	−0.891509	+	0.453003i	$0.850353\pi$
$258$		0			0
$259$	−41.0366	−	23.6925i	−0.158443	−	0.0914768i
$260$		0			0
$261$	−182.399	+	67.8549i	−0.698845	+	0.259981i
$262$		0			0
$263$	−250.254	−	144.484i	−0.951535	−	0.549369i	−0.0579779	−	0.998318i	$-0.518465\pi$
$263$	−250.254	−	144.484i	−0.951535	−	0.549369i	−0.893558	+	0.448949i	$0.851799\pi$
$264$		0			0
$265$	25.8338	+	44.7455i	0.0974862	+	0.168851i
$266$		0			0
$267$	437.483	+	157.478i	1.63851	+	0.589806i
$268$		0			0
$269$	−180.235			−0.670018			−0.335009	−	0.942215i	$-0.608739\pi$
$269$	−180.235			−0.670018			−0.335009	+	0.942215i	$0.608739\pi$
$270$		0			0
$271$		−	28.9765i		−	0.106924i	−0.998570	−	0.0534622i	$-0.982974\pi$
$271$		−	28.9765i		−	0.106924i	0.998570	−	0.0534622i	$-0.0170257\pi$
$272$		0			0
$273$	−24.0732	+	66.8767i	−0.0881802	+	0.244970i
$274$		0			0
$275$	−119.444	+	68.9609i	−0.434341	+	0.250767i
$276$		0			0
$277$	−146.528	+	253.794i	−0.528983	+	0.916225i	0.470446	+	0.882429i	$0.344093\pi$
$277$	−146.528	+	253.794i	−0.528983	+	0.916225i	−0.999429	+	0.0337961i	$0.989240\pi$
$278$		0			0
$279$	536.968	+	90.7642i	1.92462	+	0.325320i
$280$		0			0
$281$	14.6700	−	25.4091i	0.0522063	−	0.0904239i	−0.838741	−	0.544530i	$-0.816708\pi$
$281$	14.6700	−	25.4091i	0.0522063	−	0.0904239i	0.890948	+	0.454106i	$0.150041\pi$
$282$		0			0
$283$	179.527	−	103.650i	0.634372	−	0.366255i	−0.148071	−	0.988977i	$-0.547307\pi$
$283$	179.527	−	103.650i	0.634372	−	0.366255i	0.782443	+	0.622722i	$0.213973\pi$
$284$		0			0
$285$	274.445	−	49.3951i	0.962965	−	0.173316i
$286$		0			0
$287$		−	122.860i		−	0.428083i
$288$		0			0
$289$	−129.648			−0.448609
$290$		0			0
$291$	−96.7440	+	81.7636i	−0.332454	+	0.280975i
$292$		0			0
$293$	248.905	+	431.116i	0.849504	+	1.47138i	0.881651	+	0.471901i	$0.156432\pi$
$293$	248.905	+	431.116i	0.849504	+	1.47138i	−0.0321473	+	0.999483i	$0.510235\pi$
$294$		0			0
$295$	−182.303	−	105.252i	−0.617975	−	0.356788i
$296$		0			0
$297$	−3.33384	−	313.694i	−0.0112250	−	1.05621i
$298$		0			0
$299$	−333.360	−	192.465i	−1.11492	−	0.643697i
$300$		0			0
$301$	−15.1395	−	26.2223i	−0.0502973	−	0.0871174i
$302$		0			0
$303$	−289.509	+	244.680i	−0.955476	+	0.807524i
$304$		0			0
$305$	−68.3765			−0.224185
$306$		0			0
$307$		−	32.7775i		−	0.106767i	−0.998574	−	0.0533835i	$-0.982999\pi$
$307$		−	32.7775i		−	0.106767i	0.998574	−	0.0533835i	$-0.0170006\pi$
$308$		0			0
$309$	−81.5282	+	14.6736i	−0.263845	+	0.0474874i
$310$		0			0
$311$	−330.752	+	190.960i	−1.06351	+	0.614019i	−0.926402	−	0.376537i	$-0.877115\pi$
$311$	−330.752	+	190.960i	−1.06351	+	0.614019i	−0.137110	+	0.990556i	$0.543782\pi$
$312$		0			0
$313$	247.593	−	428.844i	0.791032	−	1.37011i	−0.134297	−	0.990941i	$-0.542878\pi$
$313$	247.593	−	428.844i	0.791032	−	1.37011i	0.925329	−	0.379166i	$-0.123789\pi$
$314$		0			0
$315$	−38.2613	+	46.2597i	−0.121464	+	0.146856i
$316$		0			0
$317$	140.200	−	242.834i	0.442273	−	0.766039i	−0.555585	−	0.831460i	$-0.687506\pi$
$317$	140.200	−	242.834i	0.442273	−	0.766039i	0.997858	+	0.0654209i	$0.0208390\pi$
$318$		0			0
$319$	217.582	−	125.621i	0.682075	−	0.393796i
$320$		0			0
$321$	−123.085	+	341.936i	−0.383441	+	1.06522i
$322$		0			0
$323$		−	323.825i		−	1.00255i
$324$		0			0
$325$	152.777			0.470084
$326$		0			0
$327$	174.276	+	62.7329i	0.532953	+	0.191844i
$328$		0			0
$329$	−70.3056	−	121.773i	−0.213695	−	0.370131i
$330$		0			0
$331$	−4.57609	−	2.64201i	−0.0138251	−	0.00798190i	0.493072	−	0.869989i	$-0.335874\pi$
$331$	−4.57609	−	2.64201i	−0.0138251	−	0.00798190i	−0.506897	+	0.862007i	$0.669207\pi$
$332$		0			0
$333$	−178.518	−	147.652i	−0.536091	−	0.443400i
$334$		0			0
$335$	−74.7218	−	43.1407i	−0.223050	−	0.128778i
$336$		0			0
$337$	−121.945	−	211.215i	−0.361855	−	0.626751i	0.626411	−	0.779493i	$-0.284523\pi$
$337$	−121.945	−	211.215i	−0.361855	−	0.626751i	−0.988266	+	0.152742i	$0.951190\pi$
$338$		0			0
$339$	−45.7763	−	254.339i	−0.135033	−	0.750262i
$340$		0			0
$341$	−703.056			−2.06175
$342$		0			0
$343$		−	174.165i		−	0.507770i
$344$		0			0
$345$	−209.861	−	248.310i	−0.608291	−	0.719740i
$346$		0			0
$347$	−168.452	+	97.2556i	−0.485451	+	0.280275i	−0.722685	−	0.691177i	$-0.757092\pi$
$347$	−168.452	+	97.2556i	−0.485451	+	0.280275i	0.237234	+	0.971452i	$0.423759\pi$
$348$		0			0
$349$	−202.139	+	350.116i	−0.579196	+	1.00320i	0.416376	+	0.909193i	$0.363300\pi$
$349$	−202.139	+	350.116i	−0.579196	+	1.00320i	−0.995572	+	0.0940045i	$0.970033\pi$
$350$		0			0
$351$	−170.543	+	302.775i	−0.485877	+	0.862606i
$352$		0			0
$353$	145.463	−	251.950i	0.412078	−	0.713739i	−0.583039	−	0.812444i	$-0.698137\pi$
$353$	145.463	−	251.950i	0.412078	−	0.713739i	0.995117	+	0.0987047i	$0.0314699\pi$
$354$		0			0
$355$	145.842	−	84.2020i	0.410823	−	0.237189i
$356$		0			0
$357$	45.0000	+	53.2447i	0.126050	+	0.149145i
$358$		0			0
$359$			554.699i			1.54512i	0.634941	+	0.772561i	$0.281024\pi$
$359$			554.699i			1.54512i	−0.634941	+	0.772561i	$0.718976\pi$
$360$		0			0
$361$	−297.056			−0.822871
$362$		0			0
$363$	7.43970	+	41.3358i	0.0204950	+	0.113873i
$364$		0			0
$365$	89.4131	+	154.868i	0.244967	+	0.424296i
$366$		0			0
$367$	−11.3661	−	6.56223i	−0.0309703	−	0.0178807i	0.484435	−	0.874827i	$-0.339025\pi$
$367$	−11.3661	−	6.56223i	−0.0309703	−	0.0178807i	−0.515405	+	0.856947i	$0.672359\pi$
$368$		0			0
$369$	100.111	−	592.266i	0.271304	−	1.60506i
$370$		0			0
$371$	22.7322	+	13.1245i	0.0612729	+	0.0353759i
$372$		0			0
$373$	−209.306	−	362.528i	−0.561141	−	0.971925i	−0.997397	−	0.0721024i	$-0.977029\pi$
$373$	−209.306	−	362.528i	−0.561141	−	0.971925i	0.436256	−	0.899823i	$-0.356304\pi$
$374$		0			0
$375$	377.109	+	135.746i	1.00563	+	0.361989i
$376$		0			0
$377$	−278.303			−0.738205
$378$		0			0
$379$		−	546.545i		−	1.44207i	−0.692898	−	0.721036i	$-0.743666\pi$
$379$		−	546.545i		−	1.44207i	0.692898	−	0.721036i	$-0.256334\pi$
$380$		0			0
$381$	−186.316	+	517.595i	−0.489017	+	1.35852i
$382$		0			0
$383$	511.874	−	295.530i	1.33649	−	0.771620i	0.350201	−	0.936675i	$-0.386113\pi$
$383$	511.874	−	295.530i	1.33649	−	0.771620i	0.986284	+	0.165055i	$0.0527801\pi$
$384$		0			0
$385$	38.7508	−	67.1183i	0.100651	−	0.174333i
$386$		0			0
$387$	−51.6153	−	138.746i	−0.133373	−	0.358516i
$388$		0			0
$389$	172.694	−	299.115i	0.443944	−	0.768934i	−0.554034	−	0.832494i	$-0.686912\pi$
$389$	172.694	−	299.115i	0.443944	−	0.768934i	0.997978	+	0.0635601i	$0.0202454\pi$
$390$		0			0
$391$	−326.964	+	188.773i	−0.836224	+	0.482794i
$392$		0			0
$393$	510.139	−	91.8158i	1.29806	−	0.233628i
$394$		0			0
$395$			219.255i			0.555075i
$396$		0			0
$397$	−385.741			−0.971639			−0.485820	−	0.874059i	$-0.661479\pi$
$397$	−385.741			−0.971639			−0.485820	+	0.874059i	$0.661479\pi$
$398$		0			0
$399$	108.200	−	91.4461i	0.271179	−	0.229188i
$400$		0			0
$401$	−59.0869	−	102.341i	−0.147349	−	0.255216i	0.782898	−	0.622150i	$-0.213741\pi$
$401$	−59.0869	−	102.341i	−0.147349	−	0.255216i	−0.930247	+	0.366934i	$0.880407\pi$
$402$		0			0
$403$	674.445	+	389.391i	1.67356	+	0.966231i
$404$		0			0
$405$	−222.139	+	191.826i	−0.548493	+	0.473644i
$406$		0			0
$407$	259.012	+	149.541i	0.636394	+	0.367422i
$408$		0			0
$409$	167.852	+	290.728i	0.410396	+	0.710827i	0.994933	−	0.100540i	$-0.0320570\pi$
$409$	167.852	+	290.728i	0.410396	+	0.710827i	−0.584537	+	0.811367i	$0.698724\pi$
$410$		0			0
$411$	−367.172	+	310.317i	−0.893362	+	0.755029i
$412$		0			0
$413$	−106.944			−0.258943
$414$		0			0
$415$			360.977i			0.869825i
$416$		0			0
$417$	−654.492	+	117.797i	−1.56952	+	0.282486i
$418$		0			0
$419$	28.8831	−	16.6757i	0.0689334	−	0.0397987i	−0.465137	−	0.885239i	$-0.653995\pi$
$419$	28.8831	−	16.6757i	0.0689334	−	0.0397987i	0.534071	+	0.845440i	$0.320662\pi$
$420$		0			0
$421$	138.824	−	240.450i	0.329748	−	0.571140i	−0.652714	−	0.757605i	$-0.726370\pi$
$421$	138.824	−	240.450i	0.329748	−	0.571140i	0.982462	+	0.186464i	$0.0597029\pi$
$422$		0			0
$423$	−239.695	−	644.315i	−0.566654	−	1.52320i
$424$		0			0
$425$	74.9230	−	129.770i	0.176289	−	0.305342i
$426$		0			0
$427$	−30.0836	+	17.3688i	−0.0704535	+	0.0406763i
$428$		0			0
$429$	151.944	−	422.108i	0.354181	−	0.983935i
$430$		0			0
$431$		−	368.795i		−	0.855674i	−0.903856	−	0.427837i	$-0.859276\pi$
$431$		−	368.795i		−	0.855674i	0.903856	−	0.427837i	$-0.140724\pi$
$432$		0			0
$433$	585.093			1.35125			0.675627	−	0.737244i	$-0.263873\pi$
$433$	585.093			1.35125			0.675627	+	0.737244i	$0.263873\pi$
$434$		0			0
$435$	−221.164	−	79.6111i	−0.508423	−	0.183014i
$436$		0			0
$437$	383.611	+	664.434i	0.877829	+	1.52044i
$438$		0			0
$439$	−569.640	−	328.882i	−1.29759	−	0.749161i	−0.317599	−	0.948225i	$-0.602877\pi$
$439$	−569.640	−	328.882i	−1.29759	−	0.749161i	−0.979987	+	0.199064i	$0.936210\pi$
$440$		0			0
$441$	68.4169	−	404.760i	0.155140	−	0.917823i
$442$		0			0
$443$	96.1502	+	55.5124i	0.217043	+	0.125310i	0.604581	−	0.796544i	$-0.293341\pi$
$443$	96.1502	+	55.5124i	0.217043	+	0.125310i	−0.387537	+	0.921854i	$0.626674\pi$
$444$		0			0
$445$	280.797	+	486.355i	0.631005	+	1.09293i
$446$		0			0
$447$	−99.9410	−	555.284i	−0.223582	−	1.24225i
$448$		0			0
$449$	136.056			0.303021			0.151510	−	0.988456i	$-0.451586\pi$
$449$	136.056			0.303021			0.151510	+	0.988456i	$0.451586\pi$
$450$		0			0
$451$			775.459i			1.71942i
$452$		0			0
$453$	216.528	+	256.200i	0.477987	+	0.565562i
$454$		0			0
$455$	−74.3476	+	42.9246i	−0.163401	+	0.0943398i
$456$		0			0
$457$	29.0747	−	50.3588i	0.0636208	−	0.110194i	−0.832461	−	0.554084i	$-0.813069\pi$
$457$	29.0747	−	50.3588i	0.0636208	−	0.110194i	0.896081	+	0.443890i	$0.146402\pi$
$458$		0			0
$459$	173.544	+	293.343i	0.378092	+	0.639092i
$460$		0			0
$461$	−51.4916	+	89.1861i	−0.111695	+	0.193462i	−0.916454	−	0.400140i	$-0.868961\pi$
$461$	−51.4916	+	89.1861i	−0.111695	+	0.193462i	0.804759	+	0.593602i	$0.202295\pi$
$462$		0			0
$463$	−672.083	+	388.027i	−1.45158	+	0.838072i	−0.998571	−	0.0534320i	$-0.982984\pi$
$463$	−672.083	+	388.027i	−1.45158	+	0.838072i	−0.453012	+	0.891504i	$0.649651\pi$
$464$		0			0
$465$	424.585	+	502.375i	0.913085	+	1.08038i
$466$		0			0
$467$		−	692.620i		−	1.48313i	−0.670882	−	0.741564i	$-0.734085\pi$
$467$		−	692.620i		−	1.48313i	0.670882	−	0.741564i	$-0.265915\pi$
$468$		0			0
$469$	−43.8338			−0.0934623
$470$		0			0
$471$	−54.6661	−	303.731i	−0.116064	−	0.644864i
$472$		0			0
$473$	95.5564	+	165.509i	0.202022	+	0.349912i
$474$		0			0
$475$	−263.711	−	152.254i	−0.555181	−	0.320534i
$476$		0			0
$477$	98.8902	+	81.7919i	0.207317	+	0.171471i
$478$		0			0
$479$	630.014	+	363.739i	1.31527	+	0.759371i	0.982963	−	0.183801i	$-0.0588402\pi$
$479$	630.014	+	363.739i	1.31527	+	0.759371i	0.332305	+	0.943172i	$0.392174\pi$
$480$		0			0
$481$	−165.648	−	286.911i	−0.344382	−	0.596488i
$482$		0			0
$483$	−155.407	−	55.9410i	−0.321754	−	0.115820i
$484$		0			0
$485$	−152.992			−0.315448
$486$		0			0
$487$			285.503i			0.586248i	0.956074	+	0.293124i	$0.0946948\pi$
$487$			285.503i			0.586248i	−0.956074	+	0.293124i	$0.905305\pi$
$488$		0			0
$489$	−208.518	+	579.276i	−0.426418	+	1.18461i
$490$		0			0
$491$	188.576	−	108.875i	0.384066	−	0.221740i	−0.295520	−	0.955337i	$-0.595493\pi$
$491$	188.576	−	108.875i	0.384066	−	0.221740i	0.679586	+	0.733596i	$0.262160\pi$
$492$		0			0
$493$	−136.482	+	236.393i	−0.276839	+	0.479499i
$494$		0			0
$495$	241.495	−	291.979i	0.487869	−	0.589857i
$496$		0			0
$497$	42.7774	−	74.0927i	0.0860713	−	0.149080i
$498$		0			0
$499$	30.1869	−	17.4284i	0.0604948	−	0.0349267i	−0.469448	−	0.882960i	$-0.655547\pi$
$499$	30.1869	−	17.4284i	0.0604948	−	0.0349267i	0.529942	+	0.848034i	$0.322214\pi$
$500$		0			0
$501$	156.917	−	28.2422i	0.313207	−	0.0563716i
$502$		0			0
$503$			345.125i			0.686134i	0.939311	+	0.343067i	$0.111466\pi$
$503$			345.125i			0.686134i	−0.939311	+	0.343067i	$0.888534\pi$
$504$		0			0
$505$	−457.834			−0.906602
$506$		0			0
$507$	7.68070	−	6.49137i	0.0151493	−	0.0128035i
$508$		0			0
$509$	189.528	+	328.272i	0.372354	+	0.644936i	0.989927	−	0.141577i	$-0.0452174\pi$
$509$	189.528	+	328.272i	0.372354	+	0.644936i	−0.617573	+	0.786513i	$0.711884\pi$
$510$		0			0
$511$	78.6782	+	45.4249i	0.153969	+	0.0888941i
$512$		0			0
$513$	596.113	−	352.665i	1.16201	−	0.687456i
$514$		0			0
$515$	−86.6493	−	50.0270i	−0.168251	−	0.0971398i
$516$		0			0
$517$	443.751	+	768.599i	0.858319	+	1.48665i
$518$		0			0
$519$	431.457	−	364.648i	0.831324	−	0.702597i
$520$		0			0
$521$	40.2028			0.0771646			0.0385823	−	0.999255i	$-0.487716\pi$
$521$	40.2028			0.0771646			0.0385823	+	0.999255i	$0.487716\pi$
$522$		0			0
$523$			623.980i			1.19308i	0.802584	+	0.596539i	$0.203458\pi$
$523$			623.980i			1.19308i	−0.802584	+	0.596539i	$0.796542\pi$
$524$		0			0
$525$	64.5183	−	11.6121i	0.122892	−	0.0221183i
$526$		0			0
$527$	661.505	−	381.920i	1.25523	−	0.724706i
$528$		0			0
$529$	182.749	−	316.531i	0.345462	−	0.598357i
$530$		0			0
$531$	−515.540	−	87.1421i	−0.970885	−	0.164109i
$532$		0			0
$533$	429.492	−	743.901i	0.805800	−	1.39569i
$534$		0			0
$535$	−380.134	+	219.471i	−0.710531	+	0.410225i
$536$		0			0
$537$	−94.4451	+	262.374i	−0.175875	+	0.488592i
$538$		0			0
$539$			529.955i			0.983219i
$540$		0			0
$541$	529.741			0.979188			0.489594	−	0.871950i	$-0.337145\pi$
$541$	529.741			0.979188			0.489594	+	0.871950i	$0.337145\pi$
$542$		0			0
$543$	−678.703	−	244.309i	−1.24991	−	0.449924i
$544$		0			0
$545$	111.858	+	193.744i	0.205244	+	0.355494i
$546$		0			0
$547$	512.558	+	295.925i	0.937035	+	0.540997i	0.889029	−	0.457850i	$-0.151380\pi$
$547$	512.558	+	295.925i	0.937035	+	0.540997i	0.0480051	+	0.998847i	$0.484714\pi$
$548$		0			0
$549$	−159.176	+	59.2158i	−0.289938	+	0.107861i
$550$		0			0
$551$	480.383	+	277.349i	0.871839	+	0.503356i
$552$		0			0
$553$	55.6944	+	96.4655i	0.100713	+	0.174440i
$554$		0			0
$555$	−49.5651	−	275.389i	−0.0893064	−	0.496197i
$556$		0			0
$557$	−682.841			−1.22593			−0.612964	−	0.790111i	$-0.710023\pi$
$557$	−682.841			−1.22593			−0.612964	+	0.790111i	$0.710023\pi$
$558$		0			0
$559$		−	211.698i		−	0.378708i
$560$		0			0
$561$	−284.028	−	336.067i	−0.506289	−	0.599049i
$562$		0			0
$563$	889.956	−	513.816i	1.58074	−	0.912640i	0.585987	−	0.810321i	$-0.300707\pi$
$563$	889.956	−	513.816i	1.58074	−	0.912640i	0.994752	−	0.102319i	$-0.0326263\pi$
$564$		0			0
$565$	156.066	−	270.315i	0.276224	−	0.478433i
$566$		0			0
$567$	−49.0077	+	140.825i	−0.0864334	+	0.248368i
$568$		0			0
$569$	−165.913	+	287.370i	−0.291587	+	0.505044i	−0.974185	−	0.225750i	$-0.927517\pi$
$569$	−165.913	+	287.370i	−0.291587	+	0.505044i	0.682598	+	0.730794i	$0.260850\pi$
$570$		0			0
$571$	289.987	−	167.424i	0.507858	−	0.293212i	−0.224095	−	0.974567i	$-0.571943\pi$
$571$	289.987	−	167.424i	0.507858	−	0.293212i	0.731953	+	0.681356i	$0.238609\pi$
$572$		0			0
$573$	−109.585	−	129.662i	−0.191247	−	0.226287i
$574$		0			0
$575$			355.023i			0.617431i
$576$		0			0
$577$	−87.6845			−0.151966			−0.0759831	−	0.997109i	$-0.524209\pi$
$577$	−87.6845			−0.151966			−0.0759831	+	0.997109i	$0.524209\pi$
$578$		0			0
$579$	53.5344	+	297.443i	0.0924601	+	0.513719i
$580$		0			0
$581$	91.6944	+	158.819i	0.157822	+	0.273355i
$582$		0			0
$583$	−143.480	−	82.8382i	−0.246106	−	0.142089i
$584$		0			0
$585$	−393.382	+	146.344i	−0.672448	+	0.250160i
$586$		0			0
$587$	−116.275	−	67.1313i	−0.198083	−	0.114363i	0.397678	−	0.917525i	$-0.369816\pi$
$587$	−116.275	−	67.1313i	−0.198083	−	0.114363i	−0.595761	+	0.803162i	$0.703149\pi$
$588$		0			0
$589$	−776.113	−	1344.27i	−1.31768	−	2.28229i
$590$		0			0
$591$	−325.307	−	117.099i	−0.550435	−	0.198137i
$592$		0			0
$593$	256.915			0.433246			0.216623	−	0.976255i	$-0.430496\pi$
$593$	256.915			0.433246			0.216623	+	0.976255i	$0.430496\pi$
$594$		0			0
$595$			84.2020i			0.141516i
$596$		0			0
$597$	193.797	−	538.380i	0.324619	−	0.901809i
$598$		0			0
$599$	−851.385	+	491.547i	−1.42134	+	0.820613i	−0.996414	−	0.0846136i	$-0.973034\pi$
$599$	−851.385	+	491.547i	−1.42134	+	0.820613i	−0.424929	+	0.905227i	$0.639701\pi$
$600$		0			0
$601$	−558.909	+	968.058i	−0.929964	+	1.61075i	−0.146588	+	0.989198i	$0.546829\pi$
$601$	−558.909	+	968.058i	−0.929964	+	1.61075i	−0.783376	+	0.621548i	$0.786504\pi$
$602$		0			0
$603$	−211.308	−	35.7176i	−0.350429	−	0.0592332i
$604$		0			0
$605$	−25.3643	+	43.9323i	−0.0419245	+	0.0726154i
$606$		0			0
$607$	−259.238	+	149.671i	−0.427081	+	0.246575i	−0.698102	−	0.715998i	$-0.745972\pi$
$607$	−259.238	+	149.671i	−0.427081	+	0.246575i	0.271021	+	0.962573i	$0.412639\pi$
$608$		0			0
$609$	−117.528	+	21.1529i	−0.192986	+	0.0347339i
$610$		0			0
$611$		−	983.094i		−	1.60899i
$612$		0			0
$613$	−468.332			−0.764001			−0.382000	−	0.924162i	$-0.624765\pi$
$613$	−468.332			−0.764001			−0.382000	+	0.924162i	$0.624765\pi$
$614$		0			0
$615$	554.111	−	468.309i	0.900993	−	0.761478i
$616$		0			0
$617$	−396.884	−	687.423i	−0.643248	−	1.11414i	−0.984703	−	0.174240i	$-0.944253\pi$
$617$	−396.884	−	687.423i	−0.643248	−	1.11414i	0.341455	−	0.939898i	$-0.389080\pi$
$618$		0			0
$619$	−782.130	−	451.563i	−1.26354	−	0.729504i	−0.289780	−	0.957093i	$-0.593582\pi$
$619$	−782.130	−	451.563i	−1.26354	−	0.729504i	−0.973757	+	0.227590i	$0.926915\pi$
$620$		0			0
$621$	−703.585	−	396.306i	−1.13299	−	0.638173i
$622$		0			0
$623$	247.085	+	142.654i	0.396605	+	0.228980i
$624$		0			0
$625$	93.6662	+	162.235i	0.149866	+	0.259575i
$626$		0			0
$627$	−682.933	+	577.184i	−1.08921	+	0.920548i
$628$		0			0
$629$	−324.939			−0.516596
$630$		0			0
$631$		−	484.076i		−	0.767156i	−0.923508	−	0.383578i	$-0.874692\pi$
$631$		−	484.076i		−	0.767156i	0.923508	−	0.383578i	$-0.125308\pi$
$632$		0			0
$633$	−233.010	+	41.9376i	−0.368104	+	0.0662521i
$634$		0			0
$635$	−575.417	+	332.217i	−0.906168	+	0.523176i
$636$		0			0
$637$	293.518	−	508.389i	0.460782	−	0.798098i
$638$		0			0
$639$	266.590	−	322.320i	0.417198	−	0.504412i
$640$		0			0
$641$	−173.864	+	301.142i	−0.271239	+	0.469800i	−0.969179	−	0.246356i	$-0.920767\pi$
$641$	−173.864	+	301.142i	−0.271239	+	0.469800i	0.697940	+	0.716156i	$0.254100\pi$
$642$		0			0
$643$	162.862	−	94.0285i	0.253285	−	0.146234i	−0.367983	−	0.929833i	$-0.619951\pi$
$643$	162.862	−	94.0285i	0.253285	−	0.146234i	0.621267	+	0.783599i	$0.286618\pi$
$644$		0			0
$645$	60.5579	−	168.233i	0.0938882	−	0.260827i
$646$		0			0
$647$			853.348i			1.31893i	0.751735	+	0.659465i	$0.229217\pi$
$647$			853.348i			1.31893i	−0.751735	+	0.659465i	$0.770783\pi$
$648$		0			0
$649$	675.000			1.04006
$650$		0			0
$651$	314.416	+	113.178i	0.482974	+	0.173853i
$652$		0			0
$653$	−599.678	−	1038.67i	−0.918342	−	1.59062i	−0.801933	−	0.597414i	$-0.796195\pi$
$653$	−599.678	−	1038.67i	−0.918342	−	1.59062i	−0.116410	−	0.993201i	$-0.537139\pi$
$654$		0			0
$655$	542.183	+	313.030i	0.827761	+	0.477908i
$656$		0			0
$657$	342.268	+	283.089i	0.520955	+	0.430881i
$658$		0			0
$659$	−534.606	−	308.655i	−0.811238	−	0.468369i	0.0361474	−	0.999346i	$-0.488491\pi$
$659$	−534.606	−	308.655i	−0.811238	−	0.468369i	−0.847386	+	0.530978i	$0.821825\pi$
$660$		0			0
$661$	−109.880	−	190.318i	−0.166233	−	0.287925i	0.770859	−	0.637006i	$-0.219827\pi$
$661$	−109.880	−	190.318i	−0.166233	−	0.287925i	−0.937093	+	0.349081i	$0.886494\pi$
$662$		0			0
$663$	86.3374	+	479.701i	0.130222	+	0.723531i
$664$		0			0
$665$	171.110			0.257308
$666$		0			0
$667$		−	646.719i		−	0.969593i
$668$		0			0
$669$	429.492	+	508.181i	0.641990	+	0.759613i
$670$		0			0
$671$	189.880	−	109.627i	0.282981	−	0.163379i
$672$		0			0
$673$	−289.492	+	501.414i	−0.430151	+	0.745043i	−0.996886	−	0.0788568i	$-0.974873\pi$
$673$	−289.492	+	501.414i	−0.430151	+	0.745043i	0.566735	+	0.823900i	$0.308206\pi$
$674$		0			0
$675$	320.483	−	3.40599i	0.474790	−	0.00504591i
$676$		0			0
$677$	351.528	−	608.865i	0.519244	−	0.899357i	−0.480506	−	0.876992i	$-0.659547\pi$
$677$	351.528	−	608.865i	0.519244	−	0.899357i	0.999750	−	0.0223655i	$-0.00711975\pi$
$678$		0			0
$679$	−67.3121	+	38.8627i	−0.0991342	+	0.0572351i
$680$		0			0
$681$	−22.5000	−	26.6224i	−0.0330396	−	0.0390930i
$682$		0			0
$683$		−	881.535i		−	1.29068i	−0.763895	−	0.645340i	$-0.776716\pi$
$683$		−	881.535i		−	1.29068i	0.763895	−	0.645340i	$-0.223284\pi$
$684$		0			0
$685$	−580.651			−0.847666
$686$		0			0
$687$	25.9701	+	144.293i	0.0378022	+	0.210033i
$688$		0			0
$689$	91.7607	+	158.934i	0.133179	+	0.230674i
$690$		0			0
$691$	890.846	+	514.330i	1.28921	+	0.744328i	0.978514	−	0.206181i	$-0.0661034\pi$
$691$	890.846	+	514.330i	1.28921	+	0.744328i	0.310699	+	0.950508i	$0.399437\pi$
$692$		0			0
$693$	32.0831	−	189.806i	0.0462959	−	0.273890i
$694$		0			0
$695$	−695.603	−	401.607i	−1.00087	−	0.577851i
$696$		0			0
$697$	−421.251	−	729.628i	−0.604377	−	1.04681i
$698$		0			0
$699$	1086.13	+	390.968i	1.55384	+	0.559324i
$700$		0			0
$701$	813.287			1.16018			0.580090	−	0.814552i	$-0.303017\pi$
$701$	813.287			1.16018			0.580090	+	0.814552i	$0.303017\pi$
$702$		0			0
$703$			660.320i			0.939289i
$704$		0			0
$705$	281.223	−	781.253i	0.398897	−	1.10816i
$706$		0			0
$707$	−201.433	+	116.298i	−0.284913	+	0.164494i
$708$		0			0
$709$	82.4916	−	142.880i	0.116349	−	0.201523i	−0.801969	−	0.597366i	$-0.796214\pi$
$709$	82.4916	−	142.880i	0.116349	−	0.201523i	0.918318	+	0.395843i	$0.129547\pi$
$710$		0			0
$711$	189.880	+	510.410i	0.267060	+	0.717876i
$712$		0			0
$713$	−904.864	+	1567.27i	−1.26909	+	2.19813i
$714$		0			0
$715$	469.262	−	270.929i	0.656311	−	0.378921i
$716$		0			0
$717$	−578.751	+	104.165i	−0.807184	+	0.145278i
$718$		0			0
$719$			179.881i			0.250182i	0.992145	+	0.125091i	$0.0399223\pi$
$719$			179.881i			0.250182i	−0.992145	+	0.125091i	$0.960078\pi$
$720$		0			0
$721$	−50.8308			−0.0705004
$722$		0			0
$723$	−598.452	+	505.784i	−0.827735	+	0.699564i
$724$		0			0
$725$	128.340	+	222.291i	0.177021	+	0.306609i
$726$		0			0
$727$	−664.674	−	383.749i	−0.914269	−	0.527853i	−0.0324668	−	0.999473i	$-0.510336\pi$
$727$	−664.674	−	383.749i	−0.914269	−	0.527853i	−0.881802	+	0.471619i	$0.843670\pi$
$728$		0			0
$729$	−351.000	+	638.937i	−0.481481	+	0.876456i
$730$		0			0
$731$	−179.818	−	103.818i	−0.245989	−	0.142022i
$732$		0			0
$733$	505.139	+	874.927i	0.689140	+	1.19363i	0.972117	+	0.234498i	$0.0753448\pi$
$733$	505.139	+	874.927i	0.689140	+	1.19363i	−0.282977	+	0.959127i	$0.591322\pi$
$734$		0			0
$735$	378.684	−	320.047i	0.515217	−	0.435438i
$736$		0			0
$737$	276.668			0.375397
$738$		0			0
$739$		−	941.306i		−	1.27376i	−0.770964	−	0.636878i	$-0.780225\pi$
$739$		−	941.306i		−	1.27376i	0.770964	−	0.636878i	$-0.219775\pi$
$740$		0			0
$741$	974.817	−	175.449i	1.31554	−	0.236774i
$742$		0			0
$743$	94.8464	−	54.7596i	0.127653	−	0.0737007i	−0.434814	−	0.900521i	$-0.643186\pi$
$743$	94.8464	−	54.7596i	0.127653	−	0.0737007i	0.562467	+	0.826820i	$0.309852\pi$
$744$		0			0
$745$	340.731	−	590.163i	0.457357	−	0.792166i
$746$		0			0
$747$	312.616	+	840.332i	0.418495	+	1.12494i
$748$		0			0
$749$	−111.498	+	193.121i	−0.148863	+	0.257839i
$750$		0			0
$751$	706.330	−	407.800i	0.940519	−	0.543009i	0.0503961	−	0.998729i	$-0.483952\pi$
$751$	706.330	−	407.800i	0.940519	−	0.543009i	0.890123	+	0.455720i	$0.150618\pi$
$752$		0			0
$753$	−140.138	+	389.311i	−0.186106	+	0.517014i
$754$		0			0
$755$			405.158i			0.536633i
$756$		0			0
$757$	1253.34			1.65566			0.827830	−	0.560978i	$-0.189575\pi$
$757$	1253.34			1.65566			0.827830	+	0.560978i	$0.189575\pi$
$758$		0			0
$759$	980.891	+	353.085i	1.29235	+	0.465198i
$760$		0			0
$761$	−183.095	−	317.130i	−0.240598	−	0.416728i	0.720287	−	0.693677i	$-0.244010\pi$
$761$	−183.095	−	317.130i	−0.240598	−	0.416728i	−0.960885	+	0.276948i	$0.910677\pi$
$762$		0			0
$763$	98.4286	+	56.8278i	0.129002	+	0.0744794i
$764$		0			0
$765$	−68.6113	+	405.910i	−0.0896879	+	0.530601i
$766$		0			0
$767$	−647.531	−	373.852i	−0.844238	−	0.487421i
$768$		0			0
$769$	539.066	+	933.690i	0.700996	+	1.21416i	0.968117	+	0.250498i	$0.0805945\pi$
$769$	539.066	+	933.690i	0.700996	+	1.21416i	−0.267121	+	0.963663i	$0.586072\pi$
$770$		0			0
$771$	−14.5975	−	81.1054i	−0.0189332	−	0.105195i
$772$		0			0
$773$	283.085			0.366217			0.183108	−	0.983093i	$-0.441384\pi$
$773$	283.085			0.366217			0.183108	+	0.983093i	$0.441384\pi$
$774$		0			0
$775$		−	718.273i		−	0.926804i
$776$		0			0
$777$	−91.7607	−	108.573i	−0.118096	−	0.139733i
$778$		0			0
$779$	−1482.70	+	856.039i	−1.90334	+	1.09889i
$780$		0			0
$781$	−270.000	+	467.654i	−0.345711	+	0.598788i
$782$		0			0
$783$	−583.801	+	6.20444i	−0.745595	+	0.00792394i
$784$		0			0
$785$	186.374	−	322.810i	0.237419	−	0.411222i
$786$		0			0
$787$	255.224	−	147.353i	0.324299	−	0.187234i	−0.329008	−	0.944327i	$-0.606714\pi$
$787$	255.224	−	147.353i	0.324299	−	0.187234i	0.653307	+	0.757093i	$0.273381\pi$
$788$		0			0
$789$	−559.585	−	662.109i	−0.709233	−	0.839175i
$790$		0			0
$791$		−	158.574i		−	0.200473i
$792$		0			0
$793$	−242.870			−0.306268
$794$		0			0
$795$	27.4566	+	152.552i	0.0345366	+	0.191889i
$796$		0			0
$797$	396.653	+	687.023i	0.497683	+	0.862012i	0.999996	−	0.00267363i	$-0.000851044\pi$
$797$	396.653	+	687.023i	0.497683	+	0.862012i	−0.502314	+	0.864685i	$0.667518\pi$
$798$		0			0
$799$	−835.049	−	482.116i	−1.04512	−	0.603399i
$800$		0			0
$801$	1074.87	+	889.025i	1.34191	+	1.10989i
$802$		0			0
$803$	−496.596	−	286.710i	−0.618426	−	0.357049i
$804$		0			0
$805$	−99.7477	−	172.768i	−0.123910	−	0.214619i
$806$		0			0
$807$	−508.748	−	183.131i	−0.630418	−	0.226928i
$808$		0			0
$809$	1215.12			1.50200			0.751000	−	0.660303i	$-0.229572\pi$
$809$	1215.12			1.50200			0.751000	+	0.660303i	$0.229572\pi$
$810$		0			0
$811$		−	429.447i		−	0.529527i	−0.964313	−	0.264764i	$-0.914706\pi$
$811$		−	429.447i		−	0.529527i	0.964313	−	0.264764i	$-0.0852939\pi$
$812$		0			0
$813$	29.4421	−	81.7919i	0.0362141	−	0.100605i
$814$		0			0
$815$	−643.988	+	371.806i	−0.790169	+	0.456204i
$816$		0			0
$817$	−210.972	+	365.414i	−0.258227	+	0.447263i
$818$		0			0
$819$	−135.902	+	164.313i	−0.165937	+	0.200626i
$820$		0			0
$821$	3.68216	−	6.37769i	0.00448497	−	0.00776820i	−0.863774	−	0.503879i	$-0.831906\pi$
$821$	3.68216	−	6.37769i	0.00448497	−	0.00776820i	0.868259	+	0.496111i	$0.165239\pi$
$822$		0			0
$823$	1169.36	−	675.132i	1.42085	−	0.820331i	0.424483	−	0.905436i	$-0.360456\pi$
$823$	1169.36	−	675.132i	1.42085	−	0.820331i	0.996372	+	0.0851049i	$0.0271225\pi$
$824$		0			0
$825$	−407.223	+	73.2927i	−0.493603	+	0.0888396i
$826$		0			0
$827$			571.482i			0.691031i	0.938413	+	0.345515i	$0.112296\pi$
$827$			571.482i			0.691031i	−0.938413	+	0.345515i	$0.887704\pi$
$828$		0			0
$829$	−888.445			−1.07171			−0.535854	−	0.844311i	$-0.680010\pi$
$829$	−888.445			−1.07171			−0.535854	+	0.844311i	$0.680010\pi$
$830$		0			0
$831$	−671.477	+	567.501i	−0.808034	+	0.682914i
$832$		0			0
$833$	−287.886	−	498.634i	−0.345602	−	0.598600i
$834$		0			0
$835$	166.774	+	96.2867i	0.199729	+	0.115313i
$836$		0			0
$837$	1423.47	+	801.796i	1.70069	+	0.957940i
$838$		0			0
$839$	506.659	+	292.519i	0.603884	+	0.348652i	0.770568	−	0.637358i	$-0.219973\pi$
$839$	506.659	+	292.519i	0.603884	+	0.348652i	−0.166684	+	0.986010i	$0.553306\pi$
$840$		0			0
$841$	186.713	+	323.396i	0.222013	+	0.384537i
$842$		0			0
$843$	67.2262	−	56.8165i	0.0797464	−	0.0673980i
$844$		0			0
$845$	12.1464			0.0143744
$846$		0			0
$847$			25.7719i			0.0304272i
$848$		0			0
$849$	612.066	−	110.161i	0.720926	−	0.129754i
$850$		0			0
$851$	666.720	−	384.931i	0.783455	−	0.452328i
$852$		0			0
$853$	437.917	−	758.494i	0.513384	−	0.889208i	−0.486495	−	0.873683i	$-0.661725\pi$
$853$	437.917	−	758.494i	0.513384	−	0.889208i	0.999879	−	0.0155246i	$-0.00494183\pi$
$854$		0			0
$855$	824.864	+	139.427i	0.964753	+	0.163073i
$856$		0			0
$857$	−186.836	+	323.610i	−0.218012	+	0.377608i	−0.954200	−	0.299169i	$-0.903290\pi$
$857$	−186.836	+	323.610i	−0.218012	+	0.377608i	0.736188	+	0.676777i	$0.236624\pi$
$858$		0			0
$859$	253.378	−	146.288i	0.294968	−	0.170300i	−0.345212	−	0.938525i	$-0.612193\pi$
$859$	253.378	−	146.288i	0.294968	−	0.170300i	0.640180	+	0.768225i	$0.278860\pi$
$860$		0			0
$861$	124.834	−	346.796i	0.144987	−	0.402782i
$862$		0			0
$863$		−	1461.41i		−	1.69341i	−0.532066	−	0.846703i	$-0.678584\pi$
$863$		−	1461.41i		−	1.69341i	0.532066	−	0.846703i	$-0.321416\pi$
$864$		0			0
$865$	682.313			0.788801
$866$		0			0
$867$	−365.956	−	131.731i	−0.422095	−	0.151939i
$868$		0			0
$869$	−351.528	−	608.865i	−0.404520	−	0.700650i
$870$		0			0
$871$	−265.409	−	153.234i	−0.304717	−	0.175929i
$872$		0			0
$873$	−356.156	+	132.495i	−0.407968	+	0.151770i
$874$		0			0
$875$	212.986	+	122.968i	0.243413	+	0.140535i
$876$		0			0
$877$	38.5648	+	66.7962i	0.0439735	+	0.0761644i	0.887174	−	0.461434i	$-0.152665\pi$
$877$	38.5648	+	66.7962i	0.0439735	+	0.0761644i	−0.843201	+	0.537599i	$0.819332\pi$
$878$		0			0
$879$	264.539	+	1469.81i	0.300955	+	1.67214i
$880$		0			0
$881$	371.927			0.422164			0.211082	−	0.977468i	$-0.432301\pi$
$881$	371.927			0.422164			0.211082	+	0.977468i	$0.432301\pi$
$882$		0			0
$883$			875.990i			0.992061i	0.868305	+	0.496030i	$0.165210\pi$
$883$			875.990i			0.992061i	−0.868305	+	0.496030i	$0.834790\pi$
$884$		0			0
$885$	−407.641	−	482.327i	−0.460611	−	0.545003i
$886$		0			0
$887$	−247.646	+	142.979i	−0.279195	+	0.161193i	−0.633059	−	0.774104i	$-0.718201\pi$
$887$	−247.646	+	142.979i	−0.279195	+	0.161193i	0.353864	+	0.935297i	$0.384868\pi$
$888$		0			0
$889$	−168.777	+	292.331i	−0.189851	+	0.328831i
$890$		0			0
$891$	309.324	−	888.850i	0.347165	−	0.997587i
$892$		0			0
$893$	−979.724	+	1696.93i	−1.09712	+	1.90026i
$894$		0			0
$895$	−291.684	+	168.404i	−0.325904	+	0.188161i
$896$		0			0
$897$	−745.415	−	881.987i	−0.831009	−	0.983264i
$898$		0			0
$899$			1308.42i			1.45542i
$900$		0			0
$901$	180.000			0.199778
$902$		0			0
$903$	−16.0904	−	89.4004i	−0.0178189	−	0.0990038i
$904$		0			0
$905$	−435.623	−	754.522i	−0.481352	−	0.833726i
$906$		0			0
$907$	615.208	+	355.190i	0.678289	+	0.391610i	0.799210	−	0.601052i	$-0.205252\pi$
$907$	615.208	+	355.190i	0.678289	+	0.391610i	−0.120921	+	0.992662i	$0.538585\pi$
$908$		0			0
$909$	−1065.81	+	396.496i	−1.17251	+	0.436189i
$910$		0			0
$911$	−167.148	−	96.5028i	−0.183477	−	0.105931i	0.405448	−	0.914118i	$-0.367115\pi$
$911$	−167.148	−	96.5028i	−0.183477	−	0.105931i	−0.588925	+	0.808187i	$0.700449\pi$
$912$		0			0
$913$	−578.751	−	1002.43i	−0.633900	−	1.09795i
$914$		0			0
$915$	−193.006	−	69.4752i	−0.210936	−	0.0759292i
$916$		0			0
$917$	318.059			0.346848
$918$		0			0
$919$		−	1106.39i		−	1.20390i	−0.798533	−	0.601951i	$-0.794390\pi$
$919$		−	1106.39i		−	1.20390i	0.798533	−	0.601951i	$-0.205610\pi$
$920$		0			0
$921$	33.3041	−	92.5208i	0.0361608	−	0.100457i
$922$		0			0
$923$	518.025	−	299.082i	0.561240	−	0.324032i
$924$		0			0
$925$	−152.777	+	264.618i	−0.165165	+	0.286074i
$926$		0			0
$927$	−245.039	−	41.4191i	−0.264335	−	0.0446808i
$928$		0			0
$929$	54.4108	−	94.2423i	0.0585692	−	0.101445i	−0.835254	−	0.549864i	$-0.814679\pi$
$929$	54.4108	−	94.2423i	0.0585692	−	0.101445i	0.893823	+	0.448419i	$0.148013\pi$
$930$		0			0
$931$	−1013.29	+	585.024i	−1.08839	+	0.628383i
$932$		0			0
$933$	−1127.64	+	202.955i	−1.20862	+	0.217529i
$934$		0			0
$935$		−	531.461i		−	0.568407i
$936$		0			0
$937$	−1530.74			−1.63366			−0.816832	−	0.576875i	$-0.804272\pi$
$937$	−1530.74			−1.63366			−0.816832	+	0.576875i	$0.804272\pi$
$938$		0			0
$939$	1134.61	−	958.923i	1.20832	−	1.02122i
$940$		0			0
$941$	−730.350	−	1265.00i	−0.776142	−	1.34432i	−0.934150	−	0.356880i	$-0.883841\pi$
$941$	−730.350	−	1265.00i	−0.776142	−	1.34432i	0.158008	−	0.987438i	$-0.449493\pi$
$942$		0			0
$943$	1728.67	+	998.048i	1.83316	+	1.05838i
$944$		0			0
$945$	−155.003	+	91.7010i	−0.164024	+	0.0970381i
$946$		0			0
$947$	292.181	+	168.691i	0.308533	+	0.178132i	0.646270	−	0.763109i	$-0.276328\pi$
$947$	292.181	+	168.691i	0.308533	+	0.178132i	−0.337737	+	0.941241i	$0.609661\pi$
$948$		0			0
$949$	317.591	+	550.085i	0.334659	+	0.579647i
$950$		0			0
$951$	642.479	−	542.994i	0.675583	−	0.570972i
$952$		0			0
$953$	−11.6997			−0.0122767			−0.00613834	−	0.999981i	$-0.501954\pi$
$953$	−11.6997			−0.0122767			−0.00613834	+	0.999981i	$0.501954\pi$
$954$		0			0
$955$		−	205.050i		−	0.214712i
$956$		0			0
$957$	741.807	−	133.512i	0.775138	−	0.139511i
$958$		0			0
$959$	−255.469	+	147.495i	−0.266391	+	0.153801i
$960$		0			0
$961$	1350.20	−	2338.61i	1.40499	−	2.43352i
$962$		0			0
$963$	−694.860	+	840.119i	−0.721558	+	0.872398i
$964$		0			0
$965$	−182.516	+	316.127i	−0.189136	+	0.327593i
$966$		0			0
$967$	−1072.38	+	619.139i	−1.10898	+	0.640268i	−0.938564	−	0.345104i	$-0.887844\pi$
$967$	−1072.38	+	619.139i	−1.10898	+	0.640268i	−0.170413	+	0.985373i	$0.554510\pi$
$968$		0			0
$969$	329.028	−	914.059i	0.339554	−	0.943302i
$970$		0			0
$971$			52.4978i			0.0540658i	0.999635	+	0.0270329i	$0.00860588\pi$
$971$			52.4978i			0.0540658i	−0.999635	+	0.0270329i	$0.991394\pi$
$972$		0			0
$973$	−408.059			−0.419383
$974$		0			0
$975$	431.244	+	155.232i	0.442302	+	0.159213i
$976$		0			0
$977$	−52.7789	−	91.4158i	−0.0540214	−	0.0935679i	0.837750	−	0.546054i	$-0.183871\pi$
$977$	−52.7789	−	91.4158i	−0.0540214	−	0.0935679i	−0.891772	+	0.452486i	$0.850537\pi$
$978$		0			0
$979$	−1559.53	−	900.398i	−1.59299	−	0.919712i
$980$		0			0
$981$	428.186	+	354.152i	0.436479	+	0.361011i
$982$		0			0
$983$	5.77662	+	3.33513i	0.00587652	+	0.00339281i	0.502935	−	0.864324i	$-0.332253\pi$
$983$	5.77662	+	3.33513i	0.00587652	+	0.00339281i	−0.497059	+	0.867717i	$0.665587\pi$
$984$		0			0
$985$	−208.797	−	361.647i	−0.211977	−	0.367155i
$986$		0			0
$987$	−74.7218	−	415.163i	−0.0757060	−	0.420631i
$988$		0			0
$989$	491.941			0.497412
$990$		0			0
$991$			1394.27i			1.40694i	0.710727	+	0.703468i	$0.248366\pi$
$991$			1394.27i			1.40694i	−0.710727	+	0.703468i	$0.751634\pi$
$992$		0			0
$993$	−10.2325	−	12.1072i	−0.0103046	−	0.0121926i
$994$		0			0
$995$	598.523	−	345.557i	0.601531	−	0.347294i
$996$		0			0
$997$	−634.771	+	1099.45i	−0.636681	+	1.10276i	0.349476	+	0.936945i	$0.386360\pi$
$997$	−634.771	+	1099.45i	−0.636681	+	1.10276i	−0.986156	+	0.165818i	$0.946974\pi$
$998$		0			0
$999$	−353.878	−	598.163i	−0.354232	−	0.598762i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	144.3.o.b.79.4	yes	8
3.2	odd	2		432.3.o.c.127.2		8
4.3	odd	2	inner	144.3.o.b.79.1	yes	8
8.3	odd	2		576.3.o.e.511.4		8
8.5	even	2		576.3.o.e.511.1		8
9.2	odd	6		1296.3.g.d.1135.3		4
9.4	even	3	inner	144.3.o.b.31.1	✓	8
9.5	odd	6		432.3.o.c.415.1		8
9.7	even	3		1296.3.g.h.1135.1		4
12.11	even	2		432.3.o.c.127.1		8
24.5	odd	2		1728.3.o.d.127.4		8
24.11	even	2		1728.3.o.d.127.3		8
36.7	odd	6		1296.3.g.h.1135.2		4
36.11	even	6		1296.3.g.d.1135.4		4
36.23	even	6		432.3.o.c.415.2		8
36.31	odd	6	inner	144.3.o.b.31.4	yes	8
72.5	odd	6		1728.3.o.d.1279.3		8
72.13	even	6		576.3.o.e.319.4		8
72.59	even	6		1728.3.o.d.1279.4		8
72.67	odd	6		576.3.o.e.319.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.3.o.b.31.1	✓	8	9.4	even	3	inner
144.3.o.b.31.4	yes	8	36.31	odd	6	inner
144.3.o.b.79.1	yes	8	4.3	odd	2	inner
144.3.o.b.79.4	yes	8	1.1	even	1	trivial
432.3.o.c.127.1		8	12.11	even	2
432.3.o.c.127.2		8	3.2	odd	2
432.3.o.c.415.1		8	9.5	odd	6
432.3.o.c.415.2		8	36.23	even	6
576.3.o.e.319.1		8	72.67	odd	6
576.3.o.e.319.4		8	72.13	even	6
576.3.o.e.511.1		8	8.5	even	2
576.3.o.e.511.4		8	8.3	odd	2
1296.3.g.d.1135.3		4	9.2	odd	6
1296.3.g.d.1135.4		4	36.11	even	6
1296.3.g.h.1135.1		4	9.7	even	3
1296.3.g.h.1135.2		4	36.7	odd	6
1728.3.o.d.127.3		8	24.11	even	2
1728.3.o.d.127.4		8	24.5	odd	2
1728.3.o.d.1279.3		8	72.5	odd	6
1728.3.o.d.1279.4		8	72.59	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	144.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.82269 + 1.01607i) q^{3} +(1.81174 + 3.13802i) q^{5} +(1.59422 + 0.920424i) q^{7} +(6.93521 + 5.73610i) q^{9} +O(q^{10})\)	\(q+(2.82269 + 1.01607i) q^{3} +(1.81174 + 3.13802i) q^{5} +(1.59422 + 0.920424i) q^{7} +(6.93521 + 5.73610i) q^{9} +(-10.0623 - 5.80948i) q^{11} +(6.43521 + 11.1461i) q^{13} +(1.92554 + 10.6985i) q^{15} +12.6235 q^{17} -25.6526i q^{19} +(3.56479 + 4.21791i) q^{21} +(-25.9012 + 14.9541i) q^{23} +(5.93521 - 10.2801i) q^{25} +(13.7477 + 23.2379i) q^{27} +(-10.8117 + 18.7265i) q^{29} +(52.4027 - 30.2547i) q^{31} +(-22.5000 - 26.6224i) q^{33} +6.67027i q^{35} -25.7409 q^{37} +(6.83944 + 38.0007i) q^{39} +(-33.3704 - 57.7993i) q^{41} +(-14.2447 - 8.22418i) q^{43} +(-5.43521 + 32.1552i) q^{45} +(-66.1505 - 38.1920i) q^{47} +(-22.8056 - 39.5005i) q^{49} +(35.6322 + 12.8263i) q^{51} +14.2591 q^{53} -42.1010i q^{55} +(26.0648 - 72.4095i) q^{57} +(-50.3115 + 29.0474i) q^{59} +(-9.43521 + 16.3423i) q^{61} +(5.77662 + 15.5279i) q^{63} +(-23.3178 + 40.3877i) q^{65} +(-20.6216 + 11.9059i) q^{67} +(-88.3056 + 15.8934i) q^{69} -46.4758i q^{71} +49.3521 q^{73} +(27.1986 - 22.9870i) q^{75} +(-10.6944 - 18.5232i) q^{77} +(52.4027 + 30.2547i) q^{79} +(15.1944 + 79.5621i) q^{81} +(86.2751 + 49.8109i) q^{83} +(22.8704 + 39.6127i) q^{85} +(-49.5456 + 41.8737i) q^{87} +154.988 q^{89} +23.6925i q^{91} +(178.658 - 32.1552i) q^{93} +(80.4984 - 46.4758i) q^{95} +(-21.1113 + 36.5658i) q^{97} +(-36.4605 - 98.0083i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 6 q^{5} - 6 q^{9}+O(q^{10}) \) 8 * q - 6 * q^5 - 6 * q^9	\( 8 q - 6 q^{5} - 6 q^{9} - 10 q^{13} + 60 q^{17} + 90 q^{21} - 14 q^{25} - 66 q^{29} - 180 q^{33} + 40 q^{37} - 144 q^{41} + 18 q^{45} + 2 q^{49} + 360 q^{53} + 270 q^{57} - 14 q^{61} - 330 q^{65} - 522 q^{69} - 220 q^{73} - 270 q^{77} + 306 q^{81} + 60 q^{85} + 912 q^{89} + 630 q^{93} + 200 q^{97}+O(q^{100}) \) 8 * q - 6 * q^5 - 6 * q^9 - 10 * q^13 + 60 * q^17 + 90 * q^21 - 14 * q^25 - 66 * q^29 - 180 * q^33 + 40 * q^37 - 144 * q^41 + 18 * q^45 + 2 * q^49 + 360 * q^53 + 270 * q^57 - 14 * q^61 - 330 * q^65 - 522 * q^69 - 220 * q^73 - 270 * q^77 + 306 * q^81 + 60 * q^85 + 912 * q^89 + 630 * q^93 + 200 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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