LMFDB - Embedded newform 144.3.o.a.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			$-2.06288i$ of defining polynomial
Character	$\chi$	$=$	144.31
Dual form			144.3.o.a.79.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.456412 - 2.96508i) q^{3} +(4.61660 - 7.99619i) q^{5} +(-5.33093 + 3.07781i) q^{7} +(-8.58338 + 2.70659i) q^{9} +O(q^{10})$	\(q+(-0.456412 - 2.96508i) q^{3} +(4.61660 - 7.99619i) q^{5} +(-5.33093 + 3.07781i) q^{7} +(-8.58338 + 2.70659i) q^{9} +(-3.70016 + 2.13629i) q^{11} +(0.869235 - 1.50556i) q^{13} +(-25.8164 - 10.0390i) q^{15} +12.3476 q^{17} -33.9338i q^{19} +(11.5590 + 14.4019i) q^{21} +(-3.35035 - 1.93433i) q^{23} +(-30.1260 - 52.1798i) q^{25} +(11.9428 + 24.2151i) q^{27} +(17.8409 + 30.9014i) q^{29} +(38.8262 + 22.4163i) q^{31} +(8.02306 + 9.99624i) q^{33} +56.8361i q^{35} -32.7130 q^{37} +(-4.86083 - 1.89019i) q^{39} +(21.8565 - 37.8565i) q^{41} +(33.9339 - 19.5918i) q^{43} +(-17.9836 + 81.1296i) q^{45} +(39.8784 - 23.0238i) q^{47} +(-5.55415 + 9.62007i) q^{49} +(-5.63558 - 36.6116i) q^{51} +46.3143 q^{53} +39.4496i q^{55} +(-100.617 + 15.4878i) q^{57} +(23.2710 + 13.4355i) q^{59} +(23.4545 + 40.6243i) q^{61} +(37.4270 - 40.8467i) q^{63} +(-8.02582 - 13.9011i) q^{65} +(-56.9984 - 32.9080i) q^{67} +(-4.20629 + 10.8169i) q^{69} +96.7955i q^{71} -14.0622 q^{73} +(-140.967 + 113.142i) q^{75} +(13.1502 - 22.7768i) q^{77} +(34.3954 - 19.8582i) q^{79} +(66.3487 - 46.4634i) q^{81} +(81.7202 - 47.1812i) q^{83} +(57.0039 - 98.7336i) q^{85} +(83.4822 - 67.0034i) q^{87} -81.8478 q^{89} +10.7014i q^{91} +(48.7454 - 125.354i) q^{93} +(-271.341 - 156.659i) q^{95} +(-7.99028 - 13.8396i) q^{97} +(25.9778 - 28.3514i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−0.456412	−	2.96508i	−0.152137	−	0.988359i
$3$	−0.456412	−	2.96508i	−0.152137	−	0.988359i
$4$		0			0
$5$	4.61660	−	7.99619i	0.923321	−	1.59924i	0.129080	−	0.991634i	$-0.458797\pi$
$5$	4.61660	−	7.99619i	0.923321	−	1.59924i	0.794240	−	0.607604i	$-0.207869\pi$
$6$		0			0
$7$	−5.33093	+	3.07781i	−0.761561	+	0.439687i	−0.829856	−	0.557978i	$-0.811577\pi$
$7$	−5.33093	+	3.07781i	−0.761561	+	0.439687i	0.0682950	+	0.997665i	$0.478244\pi$
$8$		0			0
$9$	−8.58338	+	2.70659i	−0.953709	+	0.300732i
$10$		0			0
$11$	−3.70016	+	2.13629i	−0.336378	+	0.194208i	−0.658669	−	0.752433i	$-0.728880\pi$
$11$	−3.70016	+	2.13629i	−0.336378	+	0.194208i	0.322291	+	0.946641i	$0.395547\pi$
$12$		0			0
$13$	0.869235	−	1.50556i	0.0668642	−	0.115812i	−0.830655	−	0.556787i	$-0.812034\pi$
$13$	0.869235	−	1.50556i	0.0668642	−	0.115812i	0.897519	+	0.440975i	$0.145367\pi$
$14$		0			0
$15$	−25.8164	−	10.0390i	−1.72109	−	0.669269i
$16$		0			0
$17$	12.3476			0.726329			0.363164	−	0.931725i	$-0.381696\pi$
$17$	12.3476			0.726329			0.363164	+	0.931725i	$0.381696\pi$
$18$		0			0
$19$		−	33.9338i		−	1.78599i	−0.450065	−	0.892996i	$-0.648599\pi$
$19$		−	33.9338i		−	1.78599i	0.450065	−	0.892996i	$-0.351401\pi$
$20$		0			0
$21$	11.5590	+	14.4019i	0.550431	+	0.685803i
$22$		0			0
$23$	−3.35035	−	1.93433i	−0.145668	−	0.0841012i	0.425395	−	0.905008i	$-0.360135\pi$
$23$	−3.35035	−	1.93433i	−0.145668	−	0.0841012i	−0.571062	+	0.820907i	$0.693469\pi$
$24$		0			0
$25$	−30.1260	−	52.1798i	−1.20504	−	2.08719i
$26$		0			0
$27$	11.9428	+	24.2151i	0.442326	+	0.896854i
$28$		0			0
$29$	17.8409	+	30.9014i	0.615204	+	1.06556i	0.990349	+	0.138598i	$0.0442596\pi$
$29$	17.8409	+	30.9014i	0.615204	+	1.06556i	−0.375145	+	0.926966i	$0.622407\pi$
$30$		0			0
$31$	38.8262	+	22.4163i	1.25246	+	0.723107i	0.971597	−	0.236641i	$-0.0760466\pi$
$31$	38.8262	+	22.4163i	1.25246	+	0.723107i	0.280861	+	0.959748i	$0.409380\pi$
$32$		0			0
$33$	8.02306	+	9.99624i	0.243123	+	0.302916i
$34$		0			0
$35$			56.8361i			1.62389i
$36$		0			0
$37$	−32.7130			−0.884134			−0.442067	−	0.896982i	$-0.645755\pi$
$37$	−32.7130			−0.884134			−0.442067	+	0.896982i	$0.645755\pi$
$38$		0			0
$39$	−4.86083	−	1.89019i	−0.124637	−	0.0484665i
$40$		0			0
$41$	21.8565	−	37.8565i	0.533085	−	0.923330i	−0.466168	−	0.884696i	$-0.654366\pi$
$41$	21.8565	−	37.8565i	0.533085	−	0.923330i	0.999253	−	0.0386343i	$-0.0123007\pi$
$42$		0			0
$43$	33.9339	−	19.5918i	0.789161	−	0.455622i	−0.0505063	−	0.998724i	$-0.516084\pi$
$43$	33.9339	−	19.5918i	0.789161	−	0.455622i	0.839667	+	0.543102i	$0.182750\pi$
$44$		0			0
$45$	−17.9836	+	81.1296i	−0.399636	+	1.80288i
$46$		0			0
$47$	39.8784	−	23.0238i	0.848477	−	0.489868i	−0.0116600	−	0.999932i	$-0.503712\pi$
$47$	39.8784	−	23.0238i	0.848477	−	0.489868i	0.860137	+	0.510064i	$0.170378\pi$
$48$		0			0
$49$	−5.55415	+	9.62007i	−0.113350	+	0.196328i
$50$		0			0
$51$	−5.63558	−	36.6116i	−0.110502	−	0.717874i
$52$		0			0
$53$	46.3143			0.873854			0.436927	−	0.899497i	$-0.356067\pi$
$53$	46.3143			0.873854			0.436927	+	0.899497i	$0.356067\pi$
$54$		0			0
$55$			39.4496i			0.717265i
$56$		0			0
$57$	−100.617	+	15.4878i	−1.76520	+	0.271716i
$58$		0			0
$59$	23.2710	+	13.4355i	0.394423	+	0.227720i	0.684075	−	0.729412i	$-0.260206\pi$
$59$	23.2710	+	13.4355i	0.394423	+	0.227720i	−0.289652	+	0.957132i	$0.593539\pi$
$60$		0			0
$61$	23.4545	+	40.6243i	0.384500	+	0.665973i	0.991700	−	0.128576i	$-0.0410407\pi$
$61$	23.4545	+	40.6243i	0.384500	+	0.665973i	−0.607200	+	0.794549i	$0.707707\pi$
$62$		0			0
$63$	37.4270	−	40.8467i	0.594079	−	0.648360i
$64$		0			0
$65$	−8.02582	−	13.9011i	−0.123474	−	0.213864i
$66$		0			0
$67$	−56.9984	−	32.9080i	−0.850722	−	0.491164i	0.0101725	−	0.999948i	$-0.496762\pi$
$67$	−56.9984	−	32.9080i	−0.850722	−	0.491164i	−0.860894	+	0.508784i	$0.830095\pi$
$68$		0			0
$69$	−4.20629	+	10.8169i	−0.0609607	+	0.156767i
$70$		0			0
$71$			96.7955i			1.36332i	0.731671	+	0.681658i	$0.238741\pi$
$71$			96.7955i			1.36332i	−0.731671	+	0.681658i	$0.761259\pi$
$72$		0			0
$73$	−14.0622			−0.192633			−0.0963163	−	0.995351i	$-0.530706\pi$
$73$	−14.0622			−0.192633			−0.0963163	+	0.995351i	$0.530706\pi$
$74$		0			0
$75$	−140.967	+	113.142i	−1.87957	+	1.50855i
$76$		0			0
$77$	13.1502	−	22.7768i	0.170782	−	0.295803i
$78$		0			0
$79$	34.3954	−	19.8582i	0.435385	−	0.251369i	−0.266253	−	0.963903i	$-0.585786\pi$
$79$	34.3954	−	19.8582i	0.435385	−	0.251369i	0.701638	+	0.712534i	$0.252452\pi$
$80$		0			0
$81$	66.3487	−	46.4634i	0.819120	−	0.573622i
$82$		0			0
$83$	81.7202	−	47.1812i	0.984581	−	0.568448i	0.0809306	−	0.996720i	$-0.474211\pi$
$83$	81.7202	−	47.1812i	0.984581	−	0.568448i	0.903650	+	0.428272i	$0.140877\pi$
$84$		0			0
$85$	57.0039	−	98.7336i	0.670634	−	1.16157i
$86$		0			0
$87$	83.4822	−	67.0034i	0.959565	−	0.770154i
$88$		0			0
$89$	−81.8478			−0.919639			−0.459819	−	0.888012i	$-0.652086\pi$
$89$	−81.8478			−0.919639			−0.459819	+	0.888012i	$0.652086\pi$
$90$		0			0
$91$			10.7014i			0.117597i
$92$		0			0
$93$	48.7454	−	125.354i	0.524144	−	1.34789i
$94$		0			0
$95$	−271.341	−	156.659i	−2.85623	−	1.64904i
$96$		0			0
$97$	−7.99028	−	13.8396i	−0.0823741	−	0.142676i	0.821895	−	0.569639i	$-0.192917\pi$
$97$	−7.99028	−	13.8396i	−0.0823741	−	0.142676i	−0.904269	+	0.426963i	$0.859584\pi$
$98$		0			0
$99$	25.9778	−	28.3514i	0.262402	−	0.286378i
$100$		0			0
$101$	50.6344	+	87.7014i	0.501331	+	0.868330i	0.999999	+	0.00153723i	$0.000489314\pi$
$101$	50.6344	+	87.7014i	0.501331	+	0.868330i	−0.498668	+	0.866793i	$0.666177\pi$
$102$		0			0
$103$	−88.4092	−	51.0431i	−0.858341	−	0.495564i	0.00511517	−	0.999987i	$-0.498372\pi$
$103$	−88.4092	−	51.0431i	−0.858341	−	0.495564i	−0.863456	+	0.504423i	$0.831705\pi$
$104$		0			0
$105$	168.524	−	25.9407i	1.60499	−	0.247054i
$106$		0			0
$107$		−	73.1463i		−	0.683610i	−0.939771	−	0.341805i	$-0.888962\pi$
$107$		−	73.1463i		−	0.683610i	0.939771	−	0.341805i	$-0.111038\pi$
$108$		0			0
$109$	−33.9344			−0.311325			−0.155663	−	0.987810i	$-0.549751\pi$
$109$	−33.9344			−0.311325			−0.155663	+	0.987810i	$0.549751\pi$
$110$		0			0
$111$	14.9306	+	96.9965i	0.134510	+	0.873842i
$112$		0			0
$113$	−13.9292	+	24.1262i	−0.123268	+	0.213506i	−0.921054	−	0.389434i	$-0.872671\pi$
$113$	−13.9292	+	24.1262i	−0.123268	+	0.213506i	0.797787	+	0.602940i	$0.206004\pi$
$114$		0			0
$115$	−30.9345	+	17.8600i	−0.268996	+	0.155305i
$116$		0			0
$117$	−3.38604	+	15.2754i	−0.0289405	+	0.130559i
$118$		0			0
$119$	−65.8241	+	38.0035i	−0.553143	+	0.319358i
$120$		0			0
$121$	−51.3725	+	88.9798i	−0.424566	+	0.735371i
$122$		0			0
$123$	−122.223	−	47.5280i	−0.993684	−	0.386407i
$124$		0			0
$125$	−325.490			−2.60392
$126$		0			0
$127$			117.905i			0.928387i	0.885734	+	0.464193i	$0.153656\pi$
$127$			117.905i			0.928387i	−0.885734	+	0.464193i	$0.846344\pi$
$128$		0			0
$129$	−73.5789	−	91.6748i	−0.570379	−	0.710657i
$130$		0			0
$131$	73.5214	+	42.4476i	0.561232	+	0.324027i	0.753640	−	0.657288i	$-0.228296\pi$
$131$	73.5214	+	42.4476i	0.561232	+	0.324027i	−0.192408	+	0.981315i	$0.561630\pi$
$132$		0			0
$133$	104.442	+	180.899i	0.785278	+	1.36014i
$134$		0			0
$135$	248.763	+	16.2943i	1.84269	+	0.120699i
$136$		0			0
$137$	3.97975	+	6.89314i	0.0290493	+	0.0503149i	0.880185	−	0.474632i	$-0.157419\pi$
$137$	3.97975	+	6.89314i	0.0290493	+	0.0503149i	−0.851135	+	0.524946i	$0.824085\pi$
$138$		0			0
$139$	17.9239	+	10.3484i	0.128949	+	0.0744488i	0.563087	−	0.826398i	$-0.309614\pi$
$139$	17.9239	+	10.3484i	0.128949	+	0.0744488i	−0.434138	+	0.900846i	$0.642947\pi$
$140$		0			0
$141$	−86.4683	−	107.734i	−0.613251	−	0.764073i
$142$		0			0
$143$			7.42775i			0.0519423i
$144$		0			0
$145$	329.458			2.27212
$146$		0			0
$147$	31.0592	+	12.0778i	0.211287	+	0.0821617i
$148$		0			0
$149$	65.6122	−	113.644i	0.440350	−	0.762709i	−0.557365	−	0.830267i	$-0.688188\pi$
$149$	65.6122	−	113.644i	0.440350	−	0.762709i	0.997715	+	0.0675588i	$0.0215210\pi$
$150$		0			0
$151$	−204.949	+	118.328i	−1.35728	+	0.783627i	−0.989257	−	0.146189i	$-0.953299\pi$
$151$	−204.949	+	118.328i	−1.35728	+	0.783627i	−0.368025	+	0.929816i	$0.619966\pi$
$152$		0			0
$153$	−105.984	+	33.4199i	−0.692706	+	0.218431i
$154$		0			0
$155$	358.490	−	206.974i	2.31284	−	1.33532i
$156$		0			0
$157$	−74.8892	+	129.712i	−0.477001	+	0.826190i	−0.999653	−	0.0263562i	$-0.991610\pi$
$157$	−74.8892	+	129.712i	−0.477001	+	0.826190i	0.522651	+	0.852546i	$0.324943\pi$
$158$		0			0
$159$	−21.1384	−	137.325i	−0.132946	−	0.863682i
$160$		0			0
$161$	23.8140			0.147913
$162$		0			0
$163$		−	152.365i		−	0.934756i	−0.884057	−	0.467378i	$-0.845199\pi$
$163$		−	152.365i		−	0.934756i	0.884057	−	0.467378i	$-0.154801\pi$
$164$		0			0
$165$	116.971	−	18.0053i	0.708916	−	0.109123i
$166$		0			0
$167$	−21.5631	−	12.4494i	−0.129120	−	0.0745476i	0.434049	−	0.900889i	$-0.357085\pi$
$167$	−21.5631	−	12.4494i	−0.129120	−	0.0745476i	−0.563169	+	0.826342i	$0.690418\pi$
$168$		0			0
$169$	82.9889	+	143.741i	0.491058	+	0.850538i
$170$		0			0
$171$	91.8451	+	291.267i	0.537106	+	1.70332i
$172$		0			0
$173$	−54.0452	−	93.6091i	−0.312400	−	0.541093i	0.666481	−	0.745522i	$-0.267800\pi$
$173$	−54.0452	−	93.6091i	−0.312400	−	0.541093i	−0.978881	+	0.204429i	$0.934466\pi$
$174$		0			0
$175$	321.199	+	185.445i	1.83543	+	1.05968i
$176$		0			0
$177$	29.2162	−	75.1323i	0.165063	−	0.424477i
$178$		0			0
$179$			313.318i			1.75038i	0.483779	+	0.875190i	$0.339264\pi$
$179$			313.318i			1.75038i	−0.483779	+	0.875190i	$0.660736\pi$
$180$		0			0
$181$	20.5886			0.113749			0.0568746	−	0.998381i	$-0.481886\pi$
$181$	20.5886			0.113749			0.0568746	+	0.998381i	$0.481886\pi$
$182$		0			0
$183$	109.749	−	88.0858i	0.599724	−	0.481343i
$184$		0			0
$185$	−151.023	+	261.579i	−0.816339	+	1.41394i
$186$		0			0
$187$	−45.6881	+	26.3780i	−0.244321	+	0.141059i
$188$		0			0
$189$	−138.196	−	92.3310i	−0.731194	−	0.488524i
$190$		0			0
$191$	−23.6619	+	13.6612i	−0.123884	+	0.0715247i	−0.560662	−	0.828045i	$-0.689453\pi$
$191$	−23.6619	+	13.6612i	−0.123884	+	0.0715247i	0.436777	+	0.899570i	$0.356120\pi$
$192$		0			0
$193$	−65.7227	+	113.835i	−0.340532	+	0.589819i	−0.984532	−	0.175207i	$-0.943941\pi$
$193$	−65.7227	+	113.835i	−0.340532	+	0.589819i	0.644000	+	0.765026i	$0.277274\pi$
$194$		0			0
$195$	−37.5549	+	30.1418i	−0.192589	+	0.154574i
$196$		0			0
$197$	−126.466			−0.641961			−0.320981	−	0.947086i	$-0.604012\pi$
$197$	−126.466			−0.641961			−0.320981	+	0.947086i	$0.604012\pi$
$198$		0			0
$199$			76.0070i			0.381945i	0.981595	+	0.190972i	$0.0611641\pi$
$199$			76.0070i			0.381945i	−0.981595	+	0.190972i	$0.938836\pi$
$200$		0			0
$201$	−71.5601	+	184.024i	−0.356021	+	0.915543i
$202$		0			0
$203$	−190.217	−	109.822i	−0.937030	−	0.540995i
$204$		0			0
$205$	−201.805	−	349.537i	−0.984417	−	1.70506i
$206$		0			0
$207$	33.9928	+	7.53502i	0.164216	+	0.0364011i
$208$		0			0
$209$	72.4925	+	125.561i	0.346854	+	0.600769i
$210$		0			0
$211$	−91.8563	−	53.0332i	−0.435338	−	0.251342i	0.266280	−	0.963896i	$-0.414205\pi$
$211$	−91.8563	−	53.0332i	−0.435338	−	0.251342i	−0.701618	+	0.712553i	$0.747539\pi$
$212$		0			0
$213$	287.006	−	44.1786i	1.34745	−	0.207411i
$214$		0			0
$215$		−	361.789i		−	1.68274i
$216$		0			0
$217$	−275.973			−1.27176
$218$		0			0
$219$	6.41814	+	41.6954i	0.0293066	+	0.190390i
$220$		0			0
$221$	10.7330	−	18.5900i	0.0485654	−	0.0841177i
$222$		0			0
$223$	55.1700	−	31.8524i	0.247399	−	0.142836i	−0.371174	−	0.928563i	$-0.621045\pi$
$223$	55.1700	−	31.8524i	0.247399	−	0.142836i	0.618573	+	0.785728i	$0.287711\pi$
$224$		0			0
$225$	399.813	+	366.340i	1.77695	+	1.62818i
$226$		0			0
$227$	−304.643	+	175.886i	−1.34204	+	0.774827i	−0.987106	−	0.160065i	$-0.948830\pi$
$227$	−304.643	+	175.886i	−1.34204	+	0.774827i	−0.354933	+	0.934892i	$0.615496\pi$
$228$		0			0
$229$	102.232	−	177.072i	0.446429	−	0.773238i	−0.551721	−	0.834029i	$-0.686029\pi$
$229$	102.232	−	177.072i	0.446429	−	0.773238i	0.998151	+	0.0607903i	$0.0193621\pi$
$230$		0			0
$231$	−73.5369	−	28.5958i	−0.318342	−	0.123791i
$232$		0			0
$233$	236.626			1.01556			0.507782	−	0.861486i	$-0.330466\pi$
$233$	236.626			1.01556			0.507782	+	0.861486i	$0.330466\pi$
$234$		0			0
$235$		−	425.167i		−	1.80922i
$236$		0			0
$237$	−74.5795	−	92.9215i	−0.314682	−	0.392074i
$238$		0			0
$239$	16.1578	+	9.32873i	0.0676060	+	0.0390324i	0.533422	−	0.845849i	$-0.320906\pi$
$239$	16.1578	+	9.32873i	0.0676060	+	0.0390324i	−0.465816	+	0.884882i	$0.654239\pi$
$240$		0			0
$241$	−37.2290	−	64.4826i	−0.154477	−	0.267562i	0.778391	−	0.627779i	$-0.216036\pi$
$241$	−37.2290	−	64.4826i	−0.154477	−	0.267562i	−0.932869	+	0.360217i	$0.882703\pi$
$242$		0			0
$243$	−168.050	−	175.523i	−0.691564	−	0.722316i
$244$		0			0
$245$	51.2826	+	88.8241i	0.209317	+	0.362547i
$246$		0			0
$247$	−51.0894	−	29.4965i	−0.206840	−	0.119419i
$248$		0			0
$249$	−177.194	−	220.773i	−0.711622	−	0.886637i
$250$		0			0
$251$			206.637i			0.823257i	0.911352	+	0.411628i	$0.135040\pi$
$251$			206.637i			0.823257i	−0.911352	+	0.411628i	$0.864960\pi$
$252$		0			0
$253$	16.5291			0.0653325
$254$		0			0
$255$	−318.770	−	123.958i	−1.25008	−	0.486109i
$256$		0			0
$257$	148.678	−	257.517i	0.578513	−	1.00201i	−0.417138	−	0.908843i	$-0.636967\pi$
$257$	148.678	−	257.517i	0.578513	−	1.00201i	0.995650	−	0.0931698i	$-0.0296999\pi$
$258$		0			0
$259$	174.390	−	100.684i	0.673322	−	0.388743i
$260$		0			0
$261$	−236.773	−	216.950i	−0.907175	−	0.831226i
$262$		0			0
$263$	123.730	−	71.4357i	0.470457	−	0.271619i	−0.245974	−	0.969276i	$-0.579108\pi$
$263$	123.730	−	71.4357i	0.470457	−	0.271619i	0.716431	+	0.697658i	$0.245774\pi$
$264$		0			0
$265$	213.815	−	370.338i	0.806847	−	1.39750i
$266$		0			0
$267$	37.3563	+	242.685i	0.139911	+	0.908934i
$268$		0			0
$269$	370.517			1.37738			0.688692	−	0.725054i	$-0.258185\pi$
$269$	370.517			1.37738			0.688692	+	0.725054i	$0.258185\pi$
$270$		0			0
$271$			368.022i			1.35801i	0.734132	+	0.679007i	$0.237589\pi$
$271$			368.022i			1.35801i	−0.734132	+	0.679007i	$0.762411\pi$
$272$		0			0
$273$	31.7304	−	4.88423i	0.116229	−	0.0178909i
$274$		0			0
$275$	222.942	+	128.716i	0.810700	+	0.468058i
$276$		0			0
$277$	−15.3234	−	26.5409i	−0.0553191	−	0.0958154i	0.837040	−	0.547142i	$-0.184284\pi$
$277$	−15.3234	−	26.5409i	−0.0553191	−	0.0958154i	−0.892359	+	0.451327i	$0.850951\pi$
$278$		0			0
$279$	−393.932	−	87.3210i	−1.41194	−	0.312979i
$280$		0			0
$281$	−231.041	−	400.176i	−0.822212	−	1.42411i	−0.904032	−	0.427465i	$-0.859407\pi$
$281$	−231.041	−	400.176i	−0.822212	−	1.42411i	0.0818203	−	0.996647i	$-0.473927\pi$
$282$		0			0
$283$	−422.693	−	244.042i	−1.49361	−	0.862339i	−0.493642	−	0.869665i	$-0.664335\pi$
$283$	−422.693	−	244.042i	−1.49361	−	0.862339i	−0.999973	+	0.00732653i	$0.997668\pi$
$284$		0			0
$285$	−340.663	+	876.050i	−1.19531	+	3.07386i
$286$		0			0
$287$			269.081i			0.937563i
$288$		0			0
$289$	−136.537			−0.472447
$290$		0			0
$291$	−37.3886	+	30.0084i	−0.128483	+	0.103122i
$292$		0			0
$293$	215.030	−	372.442i	0.733890	−	1.27113i	−0.221319	−	0.975201i	$-0.571036\pi$
$293$	215.030	−	372.442i	0.733890	−	1.27113i	0.955209	−	0.295933i	$-0.0956305\pi$
$294$		0			0
$295$	214.866	−	124.053i	0.728358	−	0.420518i
$296$		0			0
$297$	−95.9207	−	64.0863i	−0.322965	−	0.215779i
$298$		0			0
$299$	−5.82449	+	3.36277i	−0.0194799	+	0.0112467i
$300$		0			0
$301$	−120.599	+	208.884i	−0.400663	+	0.693968i
$302$		0			0
$303$	236.931	−	190.163i	0.781951	−	0.627600i
$304$		0			0
$305$	433.120			1.42007
$306$		0			0
$307$			276.184i			0.899621i	0.893124	+	0.449810i	$0.148508\pi$
$307$			276.184i			0.899621i	−0.893124	+	0.449810i	$0.851492\pi$
$308$		0			0
$309$	−110.996	+	285.437i	−0.359209	+	0.923743i
$310$		0			0
$311$	172.998	+	99.8806i	0.556264	+	0.321159i	0.751645	−	0.659568i	$-0.229261\pi$
$311$	172.998	+	99.8806i	0.556264	+	0.321159i	−0.195380	+	0.980728i	$0.562594\pi$
$312$		0			0
$313$	59.3385	+	102.777i	0.189580	+	0.328362i	0.945110	−	0.326752i	$-0.105954\pi$
$313$	59.3385	+	102.777i	0.189580	+	0.328362i	−0.755530	+	0.655114i	$0.772621\pi$
$314$		0			0
$315$	−153.832	−	487.846i	−0.488356	−	1.54872i
$316$		0			0
$317$	193.261	+	334.738i	0.609657	+	1.05596i	0.991297	+	0.131645i	$0.0420260\pi$
$317$	193.261	+	334.738i	0.609657	+	1.05596i	−0.381640	+	0.924311i	$0.624641\pi$
$318$		0			0
$319$	−132.028	−	76.2267i	−0.413882	−	0.238955i
$320$		0			0
$321$	−216.884	+	33.3848i	−0.675652	+	0.104003i
$322$		0			0
$323$		−	419.001i		−	1.29722i
$324$		0			0
$325$	−104.746			−0.322297
$326$		0			0
$327$	15.4881	+	100.618i	0.0473641	+	0.307701i
$328$		0			0
$329$	−141.726	+	245.476i	−0.430778	+	0.746129i
$330$		0			0
$331$	282.733	−	163.236i	0.854179	−	0.493161i	−0.00787942	−	0.999969i	$-0.502508\pi$
$331$	282.733	−	163.236i	0.854179	−	0.493161i	0.862059	+	0.506808i	$0.169175\pi$
$332$		0			0
$333$	280.788	−	88.5407i	0.843206	−	0.265888i
$334$		0			0
$335$	−526.278	+	303.847i	−1.57098	+	0.907005i
$336$		0			0
$337$	57.4906	−	99.5766i	0.170595	−	0.295479i	−0.768033	−	0.640410i	$-0.778764\pi$
$337$	57.4906	−	99.5766i	0.170595	−	0.295479i	0.938628	+	0.344931i	$0.112098\pi$
$338$		0			0
$339$	77.8934	+	30.2898i	0.229774	+	0.0893506i
$340$		0			0
$341$	−191.551			−0.561733
$342$		0			0
$343$		−	370.004i		−	1.07873i
$344$		0			0
$345$	67.0753	+	83.5717i	0.194421	+	0.242237i
$346$		0			0
$347$	502.945	+	290.375i	1.44941	+	0.836817i	0.998446	−	0.0557260i	$-0.0177473\pi$
$347$	502.945	+	290.375i	1.44941	+	0.836817i	0.450963	+	0.892543i	$0.351081\pi$
$348$		0			0
$349$	−175.463	−	303.912i	−0.502761	−	0.870807i	−0.999995	−	0.00319067i	$-0.998984\pi$
$349$	−175.463	−	303.912i	−0.502761	−	0.870807i	0.497234	−	0.867616i	$-0.334349\pi$
$350$		0			0
$351$	46.8383	+	3.06797i	0.133442	+	0.00874066i
$352$		0			0
$353$	−67.7870	−	117.411i	−0.192031	−	0.332608i	0.753892	−	0.656998i	$-0.228174\pi$
$353$	−67.7870	−	117.411i	−0.192031	−	0.332608i	−0.945923	+	0.324390i	$0.894841\pi$
$354$		0			0
$355$	773.995	+	446.866i	2.18027	+	1.25878i
$356$		0			0
$357$	142.726	+	177.828i	0.399794	+	0.498118i
$358$		0			0
$359$		−	108.852i		−	0.303210i	−0.988441	−	0.151605i	$-0.951556\pi$
$359$		−	108.852i		−	0.303210i	0.988441	−	0.151605i	$-0.0484441\pi$
$360$		0			0
$361$	−790.506			−2.18977
$362$		0			0
$363$	287.279	+	111.712i	0.791403	+	0.307747i
$364$		0			0
$365$	−64.9195	+	112.444i	−0.177862	+	0.308065i
$366$		0			0
$367$	14.6619	−	8.46503i	0.0399506	−	0.0230655i	−0.479892	−	0.877328i	$-0.659324\pi$
$367$	14.6619	−	8.46503i	0.0399506	−	0.0230655i	0.519842	+	0.854262i	$0.325991\pi$
$368$		0			0
$369$	−85.1402	+	384.094i	−0.230732	+	1.04090i
$370$		0			0
$371$	−246.898	+	142.547i	−0.665493	+	0.384223i
$372$		0			0
$373$	−18.5300	+	32.0949i	−0.0496783	+	0.0860454i	−0.889795	−	0.456360i	$-0.849153\pi$
$373$	−18.5300	+	32.0949i	−0.0496783	+	0.0860454i	0.840117	+	0.542405i	$0.182486\pi$
$374$		0			0
$375$	148.557	+	965.102i	0.396153	+	2.57361i
$376$		0			0
$377$	62.0318			0.164540
$378$		0			0
$379$			531.193i			1.40156i	0.713375	+	0.700782i	$0.247166\pi$
$379$			531.193i			1.40156i	−0.713375	+	0.700782i	$0.752834\pi$
$380$		0			0
$381$	349.598	−	53.8133i	0.917580	−	0.141242i
$382$		0			0
$383$	324.004	+	187.064i	0.845963	+	0.488417i	0.859287	−	0.511494i	$-0.170908\pi$
$383$	324.004	+	187.064i	0.845963	+	0.488417i	−0.0133235	+	0.999911i	$0.504241\pi$
$384$		0			0
$385$	−121.418	−	210.303i	−0.315373	−	0.546241i
$386$		0			0
$387$	−238.241	+	260.009i	−0.615609	+	0.671857i
$388$		0			0
$389$	271.593	+	470.412i	0.698182	+	1.20929i	0.969096	+	0.246683i	$0.0793406\pi$
$389$	271.593	+	470.412i	0.698182	+	1.20929i	−0.270915	+	0.962603i	$0.587326\pi$
$390$		0			0
$391$	−41.3688	−	23.8843i	−0.105802	−	0.0610851i
$392$		0			0
$393$	92.3044	−	237.370i	0.234871	−	0.603995i
$394$		0			0
$395$		−	366.709i		−	0.928378i
$396$		0			0
$397$	606.097			1.52669			0.763346	−	0.645990i	$-0.223555\pi$
$397$	606.097			1.52669			0.763346	+	0.645990i	$0.223555\pi$
$398$		0			0
$399$	488.711	−	392.243i	1.22484	−	0.983065i
$400$		0			0
$401$	−293.529	+	508.408i	−0.731994	+	1.26785i	0.224036	+	0.974581i	$0.428077\pi$
$401$	−293.529	+	508.408i	−0.731994	+	1.26785i	−0.956030	+	0.293269i	$0.905257\pi$
$402$		0			0
$403$	67.4982	−	38.9701i	0.167489	−	0.0967000i
$404$		0			0
$405$	−65.2245	−	745.040i	−0.161048	−	1.83961i
$406$		0			0
$407$	121.043	−	69.8844i	0.297404	−	0.171706i
$408$		0			0
$409$	129.882	−	224.961i	0.317559	−	0.550028i	−0.662419	−	0.749133i	$-0.730470\pi$
$409$	129.882	−	224.961i	0.317559	−	0.550028i	0.979978	+	0.199105i	$0.0638036\pi$
$410$		0			0
$411$	18.6223	−	14.9464i	0.0453097	−	0.0363659i
$412$		0			0
$413$	−165.408			−0.400503
$414$		0			0
$415$		−	871.267i		−	2.09944i
$416$		0			0
$417$	22.5031	−	57.8689i	0.0539642	−	0.138774i
$418$		0			0
$419$	−297.997	−	172.049i	−0.711210	−	0.410617i	0.100299	−	0.994957i	$-0.468020\pi$
$419$	−297.997	−	172.049i	−0.711210	−	0.410617i	−0.811509	+	0.584340i	$0.801353\pi$
$420$		0			0
$421$	153.263	+	265.460i	0.364046	+	0.630546i	0.988623	−	0.150417i	$-0.0480617\pi$
$421$	153.263	+	265.460i	0.364046	+	0.630546i	−0.624576	+	0.780964i	$0.714728\pi$
$422$		0			0
$423$	−279.975	+	305.557i	−0.661880	+	0.722356i
$424$		0			0
$425$	−371.984	−	644.295i	−0.875256	−	1.51599i
$426$		0			0
$427$	−250.068	−	144.377i	−0.585640	−	0.338119i
$428$		0			0
$429$	22.0239	−	3.39011i	0.0513376	−	0.00790235i
$430$		0			0
$431$			208.029i			0.482667i	0.970442	+	0.241333i	$0.0775847\pi$
$431$			208.029i			0.482667i	−0.970442	+	0.241333i	$0.922415\pi$
$432$		0			0
$433$	353.874			0.817260			0.408630	−	0.912700i	$-0.366007\pi$
$433$	353.874			0.817260			0.408630	+	0.912700i	$0.366007\pi$
$434$		0			0
$435$	−150.368	−	976.867i	−0.345674	−	2.24567i
$436$		0			0
$437$	−65.6392	+	113.690i	−0.150204	+	0.260161i
$438$		0			0
$439$	−200.356	+	115.675i	−0.456391	+	0.263497i	−0.710525	−	0.703672i	$-0.751543\pi$
$439$	−200.356	+	115.675i	−0.456391	+	0.263497i	0.254135	+	0.967169i	$0.418209\pi$
$440$		0			0
$441$	21.6358	−	97.6055i	0.0490607	−	0.221328i
$442$		0			0
$443$	221.434	−	127.845i	0.499851	−	0.288589i	−0.228801	−	0.973473i	$-0.573480\pi$
$443$	221.434	−	127.845i	0.499851	−	0.288589i	0.728652	+	0.684884i	$0.240147\pi$
$444$		0			0
$445$	−377.859	+	654.471i	−0.849121	+	1.47072i
$446$		0			0
$447$	−366.908	−	142.677i	−0.820824	−	0.319188i
$448$		0			0
$449$	323.060			0.719509			0.359755	−	0.933047i	$-0.382860\pi$
$449$	323.060			0.719509			0.359755	+	0.933047i	$0.382860\pi$
$450$		0			0
$451$			186.767i			0.414118i
$452$		0			0
$453$	444.392	+	553.685i	0.980998	+	1.22226i
$454$		0			0
$455$	85.5702	+	49.4039i	0.188066	+	0.108580i
$456$		0			0
$457$	277.264	+	480.235i	0.606704	+	1.05084i	0.991780	+	0.127957i	$0.0408418\pi$
$457$	277.264	+	480.235i	0.606704	+	1.05084i	−0.385076	+	0.922885i	$0.625825\pi$
$458$		0			0
$459$	147.465	+	298.998i	0.321274	+	0.651411i
$460$		0			0
$461$	−368.753	−	638.699i	−0.799898	−	1.38546i	−0.919682	−	0.392664i	$-0.871553\pi$
$461$	−368.753	−	638.699i	−0.799898	−	1.38546i	0.119784	−	0.992800i	$-0.461780\pi$
$462$		0			0
$463$	−116.461	−	67.2386i	−0.251535	−	0.145224i	0.368932	−	0.929456i	$-0.379724\pi$
$463$	−116.461	−	67.2386i	−0.251535	−	0.145224i	−0.620467	+	0.784233i	$0.713057\pi$
$464$		0			0
$465$	−777.315	−	968.486i	−1.67164	−	2.08277i
$466$		0			0
$467$		−	595.000i		−	1.27409i	−0.770827	−	0.637045i	$-0.780156\pi$
$467$		−	595.000i		−	1.27409i	0.770827	−	0.637045i	$-0.219844\pi$
$468$		0			0
$469$	405.139			0.863835
$470$		0			0
$471$	418.786	+	162.850i	0.889143	+	0.345754i
$472$		0			0
$473$	−83.7073	+	144.985i	−0.176971	+	0.306523i
$474$		0			0
$475$	−1770.66	+	1022.29i	−3.72771	+	2.15219i
$476$		0			0
$477$	−397.533	+	125.354i	−0.833402	+	0.262796i
$478$		0			0
$479$	−388.924	+	224.545i	−0.811950	+	0.468779i	−0.847632	−	0.530584i	$-0.821973\pi$
$479$	−388.924	+	224.545i	−0.811950	+	0.468779i	0.0356829	+	0.999363i	$0.488639\pi$
$480$		0			0
$481$	−28.4352	+	49.2513i	−0.0591169	+	0.102394i
$482$		0			0
$483$	−10.8690	−	70.6103i	−0.0225031	−	0.146191i
$484$		0			0
$485$	−147.552			−0.304231
$486$		0			0
$487$			120.044i			0.246497i	0.992376	+	0.123249i	$0.0393312\pi$
$487$			120.044i			0.246497i	−0.992376	+	0.123249i	$0.960669\pi$
$488$		0			0
$489$	−451.775	+	69.5413i	−0.923875	+	0.142211i
$490$		0			0
$491$	−372.302	−	214.949i	−0.758252	−	0.437777i	0.0704158	−	0.997518i	$-0.477567\pi$
$491$	−372.302	−	214.949i	−0.758252	−	0.437777i	−0.828668	+	0.559741i	$0.810901\pi$
$492$		0			0
$493$	220.292	+	381.557i	0.446840	+	0.773950i
$494$		0			0
$495$	−106.774	−	338.611i	−0.215705	−	0.684062i
$496$		0			0
$497$	−297.918	−	516.010i	−0.599433	−	1.03825i
$498$		0			0
$499$	639.117	+	368.994i	1.28080	+	0.739467i	0.976994	−	0.213268i	$-0.0684107\pi$
$499$	639.117	+	368.994i	1.28080	+	0.739467i	0.303802	+	0.952735i	$0.401744\pi$
$500$		0			0
$501$	−27.0719	+	69.6182i	−0.0540358	+	0.138959i
$502$		0			0
$503$		−	951.782i		−	1.89221i	−0.323859	−	0.946105i	$-0.604980\pi$
$503$		−	951.782i		−	1.89221i	0.323859	−	0.946105i	$-0.395020\pi$
$504$		0			0
$505$	935.036			1.85156
$506$		0			0
$507$	388.326	−	311.673i	0.765929	−	0.614741i
$508$		0			0
$509$	37.8898	−	65.6271i	0.0744398	−	0.128933i	−0.826403	−	0.563079i	$-0.809616\pi$
$509$	37.8898	−	65.6271i	0.0744398	−	0.128933i	0.900843	+	0.434146i	$0.142950\pi$
$510$		0			0
$511$	74.9644	−	43.2807i	0.146701	−	0.0846981i
$512$		0			0
$513$	821.710	−	405.265i	1.60177	−	0.789991i
$514$		0			0
$515$	−816.300	+	471.291i	−1.58505	+	0.915128i
$516$		0			0
$517$	−98.3710	+	170.384i	−0.190273	+	0.329562i
$518$		0			0
$519$	−252.891	+	202.973i	−0.487267	+	0.391084i
$520$		0			0
$521$	24.6152			0.0472461			0.0236230	−	0.999721i	$-0.492480\pi$
$521$	24.6152			0.0472461			0.0236230	+	0.999721i	$0.492480\pi$
$522$		0			0
$523$		−	165.798i		−	0.317013i	−0.987358	−	0.158506i	$-0.949332\pi$
$523$		−	165.798i		−	0.317013i	0.987358	−	0.158506i	$-0.0506678\pi$
$524$		0			0
$525$	403.259	−	1037.02i	0.768111	−	1.97528i
$526$		0			0
$527$	479.410	+	276.787i	0.909696	+	0.525213i
$528$		0			0
$529$	−257.017	−	445.166i	−0.485854	−	0.841524i
$530$		0			0
$531$	−236.108	−	52.3369i	−0.444648	−	0.0985630i
$532$		0			0
$533$	−37.9968	−	65.8124i	−0.0712886	−	0.123476i
$534$		0			0
$535$	−584.892	−	337.687i	−1.09326	−	0.631191i
$536$		0			0
$537$	929.013	−	143.002i	1.73001	−	0.266298i
$538$		0			0
$539$		−	47.4611i		−	0.0880539i
$540$		0			0
$541$	−184.323			−0.340708			−0.170354	−	0.985383i	$-0.554491\pi$
$541$	−184.323			−0.340708			−0.170354	+	0.985383i	$0.554491\pi$
$542$		0			0
$543$	−9.39688	−	61.0469i	−0.0173055	−	0.112425i
$544$		0			0
$545$	−156.662	+	271.346i	−0.287453	+	0.497883i
$546$		0			0
$547$	803.354	−	463.817i	1.46865	−	0.847928i	0.469272	−	0.883054i	$-0.344517\pi$
$547$	803.354	−	463.817i	1.46865	−	0.847928i	0.999383	+	0.0351259i	$0.0111832\pi$
$548$		0			0
$549$	−311.272	−	285.212i	−0.566980	−	0.519512i
$550$		0			0
$551$	1048.60	−	605.411i	1.90309	−	1.09875i
$552$		0			0
$553$	−122.240	+	211.725i	−0.221048	+	0.382866i
$554$		0			0
$555$	844.531	+	328.407i	1.52168	+	0.591724i
$556$		0			0
$557$	−492.087			−0.883459			−0.441730	−	0.897148i	$-0.645635\pi$
$557$	−492.087			−0.883459			−0.441730	+	0.897148i	$0.645635\pi$
$558$		0			0
$559$		−	68.1193i		−	0.121859i
$560$		0			0
$561$	99.0654	+	123.429i	0.176587	+	0.220017i
$562$		0			0
$563$	−626.453	−	361.683i	−1.11271	−	0.642421i	−0.173177	−	0.984891i	$-0.555403\pi$
$563$	−626.453	−	361.683i	−1.11271	−	0.642421i	−0.939529	+	0.342470i	$0.888736\pi$
$564$		0			0
$565$	128.612	+	222.762i	0.227631	+	0.394269i
$566$		0			0
$567$	−210.695	+	451.902i	−0.371595	+	0.797005i
$568$		0			0
$569$	435.816	+	754.855i	0.765933	+	1.32664i	0.939752	+	0.341857i	$0.111056\pi$
$569$	435.816	+	754.855i	0.765933	+	1.32664i	−0.173819	+	0.984778i	$0.555611\pi$
$570$		0			0
$571$	−210.649	−	121.618i	−0.368912	−	0.212991i	0.304071	−	0.952649i	$-0.401654\pi$
$571$	−210.649	−	121.618i	−0.368912	−	0.212991i	−0.672983	+	0.739658i	$0.734987\pi$
$572$		0			0
$573$	51.3061	+	63.9243i	0.0895395	+	0.111561i
$574$		0			0
$575$			233.094i			0.405382i
$576$		0			0
$577$	−201.625			−0.349436			−0.174718	−	0.984619i	$-0.555901\pi$
$577$	−201.625			−0.349436			−0.174718	+	0.984619i	$0.555901\pi$
$578$		0			0
$579$	367.526	+	142.917i	0.634761	+	0.246835i
$580$		0			0
$581$	−290.430	+	503.039i	−0.499879	+	0.865815i
$582$		0			0
$583$	−171.370	+	98.9406i	−0.293945	+	0.169710i
$584$		0			0
$585$	106.513	+	97.5960i	0.182074	+	0.166831i
$586$		0			0
$587$	−688.983	+	397.784i	−1.17374	+	0.677656i	−0.954557	−	0.298029i	$-0.903671\pi$
$587$	−688.983	+	397.784i	−1.17374	+	0.677656i	−0.219178	+	0.975685i	$0.570338\pi$
$588$		0			0
$589$	760.672	−	1317.52i	1.29146	−	2.23688i
$590$		0			0
$591$	57.7207	+	374.983i	0.0976662	+	0.634489i
$592$		0			0
$593$	−1078.05			−1.81796			−0.908980	−	0.416839i	$-0.863138\pi$
$593$	−1078.05			−1.81796			−0.908980	+	0.416839i	$0.863138\pi$
$594$		0			0
$595$			701.789i			1.17948i
$596$		0			0
$597$	225.367	−	34.6905i	0.377499	−	0.0581080i
$598$		0			0
$599$	209.699	+	121.070i	0.350082	+	0.202120i	0.664722	−	0.747091i	$-0.268550\pi$
$599$	209.699	+	121.070i	0.350082	+	0.202120i	−0.314639	+	0.949211i	$0.601883\pi$
$600$		0			0
$601$	135.406	+	234.529i	0.225300	+	0.390232i	0.956410	−	0.292029i	$-0.0943303\pi$
$601$	135.406	+	234.529i	0.225300	+	0.390232i	−0.731109	+	0.682261i	$0.760997\pi$
$602$		0			0
$603$	578.307	+	128.191i	0.959050	+	0.212588i
$604$		0			0
$605$	474.333	+	821.569i	0.784022	+	1.35797i
$606$		0			0
$607$	335.657	+	193.792i	0.552977	+	0.319261i	0.750322	−	0.661073i	$-0.229899\pi$
$607$	335.657	+	193.792i	0.552977	+	0.319261i	−0.197345	+	0.980334i	$0.563232\pi$
$608$		0			0
$609$	−238.813	+	614.133i	−0.392140	+	1.00843i
$610$		0			0
$611$		−	80.0524i		−	0.131019i
$612$		0			0
$613$	−1120.09			−1.82722			−0.913610	−	0.406591i	$-0.866718\pi$
$613$	−1120.09			−1.82722			−0.913610	+	0.406591i	$0.866718\pi$
$614$		0			0
$615$	−944.299	+	757.902i	−1.53545	+	1.23236i
$616$		0			0
$617$	−266.289	+	461.226i	−0.431587	+	0.747530i	−0.997010	−	0.0772706i	$-0.975379\pi$
$617$	−266.289	+	461.226i	−0.431587	+	0.747530i	0.565423	+	0.824801i	$0.308713\pi$
$618$		0			0
$619$	761.814	−	439.833i	1.23072	−	0.710555i	0.263537	−	0.964649i	$-0.415111\pi$
$619$	761.814	−	439.833i	1.23072	−	0.710555i	0.967179	+	0.254095i	$0.0817774\pi$
$620$		0			0
$621$	6.82723	−	104.230i	0.0109939	−	0.167843i
$622$		0			0
$623$	436.325	−	251.912i	0.700361	−	0.404354i
$624$		0			0
$625$	−749.506	+	1298.18i	−1.19921	+	2.07709i
$626$		0			0
$627$	339.211	−	272.253i	0.541006	−	0.434216i
$628$		0			0
$629$	−403.926			−0.642172
$630$		0			0
$631$			310.499i			0.492075i	0.969260	+	0.246037i	$0.0791286\pi$
$631$			310.499i			0.492075i	−0.969260	+	0.246037i	$0.920871\pi$
$632$		0			0
$633$	−115.323	+	296.566i	−0.182186	+	0.468509i
$634$		0			0
$635$	942.792	+	544.321i	1.48471	+	0.857199i
$636$		0			0
$637$	9.65572	+	16.7242i	0.0151581	+	0.0262546i
$638$		0			0
$639$	−261.986	−	830.832i	−0.409994	−	1.30021i
$640$		0			0
$641$	−275.610	−	477.371i	−0.429969	−	0.744728i	0.566901	−	0.823786i	$-0.308142\pi$
$641$	−275.610	−	477.371i	−0.429969	−	0.744728i	−0.996870	+	0.0790578i	$0.974809\pi$
$642$		0			0
$643$	−352.044	−	203.253i	−0.547503	−	0.316101i	0.200611	−	0.979671i	$-0.435707\pi$
$643$	−352.044	−	203.253i	−0.547503	−	0.316101i	−0.748114	+	0.663570i	$0.769041\pi$
$644$		0			0
$645$	−1072.73	+	165.125i	−1.66315	+	0.256008i
$646$		0			0
$647$			652.891i			1.00910i	0.863381	+	0.504552i	$0.168342\pi$
$647$			652.891i			1.00910i	−0.863381	+	0.504552i	$0.831658\pi$
$648$		0			0
$649$	−114.808			−0.176900
$650$		0			0
$651$	125.957	+	818.281i	0.193483	+	1.25696i
$652$		0			0
$653$	513.767	−	889.870i	0.786779	−	1.36274i	−0.141151	−	0.989988i	$-0.545080\pi$
$653$	513.767	−	889.870i	0.786779	−	1.36274i	0.927930	−	0.372754i	$-0.121586\pi$
$654$		0			0
$655$	678.838	−	391.927i	1.03639	−	0.598362i
$656$		0			0
$657$	120.701	−	38.0606i	0.183715	−	0.0579309i
$658$		0			0
$659$	20.5780	−	11.8807i	0.0312261	−	0.0180284i	−0.484306	−	0.874899i	$-0.660928\pi$
$659$	20.5780	−	11.8807i	0.0312261	−	0.0180284i	0.515532	+	0.856870i	$0.327594\pi$
$660$		0			0
$661$	328.164	−	568.396i	0.496465	−	0.859903i	−0.503526	−	0.863980i	$-0.667964\pi$
$661$	328.164	−	568.396i	0.496465	−	0.859903i	0.999992	+	0.00407665i	$0.00129764\pi$
$662$		0			0
$663$	−60.0195	−	23.3393i	−0.0905271	−	0.0352026i
$664$		0			0
$665$	1928.67			2.90025
$666$		0			0
$667$		−	138.041i		−	0.206957i
$668$		0			0
$669$	−119.625	−	149.046i	−0.178812	−	0.222789i
$670$		0			0
$671$	−173.571	−	100.211i	−0.258675	−	0.149346i
$672$		0			0
$673$	405.169	+	701.773i	0.602034	+	1.04275i	0.992513	+	0.122141i	$0.0389760\pi$
$673$	405.169	+	701.773i	0.602034	+	1.04275i	−0.390479	+	0.920612i	$0.627691\pi$
$674$		0			0
$675$	903.748	−	1352.68i	1.33889	−	2.00397i
$676$		0			0
$677$	−199.580	−	345.683i	−0.294801	−	0.510610i	0.680138	−	0.733084i	$-0.261920\pi$
$677$	−199.580	−	345.683i	−0.294801	−	0.510610i	−0.974939	+	0.222474i	$0.928587\pi$
$678$		0			0
$679$	85.1912	+	49.1852i	0.125466	+	0.0724377i
$680$		0			0
$681$	660.557	+	823.014i	0.969981	+	1.20854i
$682$		0			0
$683$		−	203.612i		−	0.298114i	−0.988829	−	0.149057i	$-0.952376\pi$
$683$		−	203.612i		−	0.298114i	0.988829	−	0.149057i	$-0.0476238\pi$
$684$		0			0
$685$	73.4918			0.107287
$686$		0			0
$687$	−571.691	−	222.309i	−0.832156	−	0.323594i
$688$		0			0
$689$	40.2580	−	69.7288i	0.0584296	−	0.101203i
$690$		0			0
$691$	−255.646	+	147.597i	−0.369965	+	0.213599i	−0.673443	−	0.739239i	$-0.735185\pi$
$691$	−255.646	+	147.597i	−0.369965	+	0.213599i	0.303478	+	0.952838i	$0.401852\pi$
$692$		0			0
$693$	−51.2255	+	231.094i	−0.0739185	+	0.333469i
$694$		0			0
$695$	165.495	−	95.5487i	0.238123	−	0.137480i
$696$		0			0
$697$	269.875	−	467.437i	0.387195	−	0.670641i
$698$		0			0
$699$	−107.999	−	701.615i	−0.154505	−	1.00374i
$700$		0			0
$701$	283.069			0.403808			0.201904	−	0.979405i	$-0.435287\pi$
$701$	283.069			0.403808			0.201904	+	0.979405i	$0.435287\pi$
$702$		0			0
$703$			1110.08i			1.57906i
$704$		0			0
$705$	−1260.65	+	194.051i	−1.78816	+	0.275250i
$706$		0			0
$707$	−539.857	−	311.686i	−0.763588	−	0.440858i
$708$		0			0
$709$	−209.399	−	362.690i	−0.295344	−	0.511551i	0.679721	−	0.733471i	$-0.262101\pi$
$709$	−209.399	−	362.690i	−0.295344	−	0.511551i	−0.975065	+	0.221920i	$0.928768\pi$
$710$		0			0
$711$	−241.481	+	263.545i	−0.339635	+	0.370667i
$712$		0			0
$713$	−86.7210	−	150.205i	−0.121628	−	0.210666i
$714$		0			0
$715$	59.3937	+	34.2910i	0.0830681	+	0.0479594i
$716$		0			0
$717$	20.2858	−	52.1670i	0.0282926	−	0.0727573i
$718$		0			0
$719$			454.879i			0.632655i	0.948650	+	0.316328i	$0.102450\pi$
$719$			454.879i			0.632655i	−0.948650	+	0.316328i	$0.897550\pi$
$720$		0			0
$721$	628.404			0.871572
$722$		0			0
$723$	−174.204	+	139.818i	−0.240946	+	0.193385i
$724$		0			0
$725$	1074.95	−	1861.87i	1.48269	−	2.56810i
$726$		0			0
$727$	−207.375	+	119.728i	−0.285247	+	0.164688i	−0.635797	−	0.771857i	$-0.719328\pi$
$727$	−207.375	+	119.728i	−0.285247	+	0.164688i	0.350549	+	0.936544i	$0.385995\pi$
$728$		0			0
$729$	−443.739	+	578.392i	−0.608695	+	0.793404i
$730$		0			0
$731$	419.002	−	241.911i	0.573190	−	0.330931i
$732$		0			0
$733$	−210.973	+	365.416i	−0.287822	+	0.498522i	−0.973289	−	0.229581i	$-0.926264\pi$
$733$	−210.973	+	365.416i	−0.287822	+	0.498522i	0.685468	+	0.728103i	$0.259598\pi$
$734$		0			0
$735$	239.964	−	192.597i	0.326482	−	0.262037i
$736$		0			0
$737$	281.204			0.381552
$738$		0			0
$739$			150.203i			0.203251i	0.994823	+	0.101626i	$0.0324044\pi$
$739$			150.203i			0.203251i	−0.994823	+	0.101626i	$0.967596\pi$
$740$		0			0
$741$	−64.1416	+	164.947i	−0.0865608	+	0.222600i
$742$		0			0
$743$	726.756	+	419.593i	0.978137	+	0.564728i	0.901707	−	0.432347i	$-0.142315\pi$
$743$	726.756	+	419.593i	0.978137	+	0.564728i	0.0764298	+	0.997075i	$0.475648\pi$
$744$		0			0
$745$	−605.810	−	1049.29i	−0.813168	−	1.40845i
$746$		0			0
$747$	−573.735	+	626.157i	−0.768052	+	0.838229i
$748$		0			0
$749$	225.130	+	389.937i	0.300575	+	0.520611i
$750$		0			0
$751$	−634.488	−	366.322i	−0.844858	−	0.487779i	0.0140549	−	0.999901i	$-0.495526\pi$
$751$	−634.488	−	366.322i	−0.844858	−	0.487779i	−0.858912	+	0.512122i	$0.828859\pi$
$752$		0			0
$753$	612.696	−	94.3117i	0.813673	−	0.125248i
$754$		0			0
$755$			2185.09i			2.89415i
$756$		0			0
$757$	−1455.19			−1.92231			−0.961153	−	0.276015i	$-0.910986\pi$
$757$	−1455.19			−1.92231			−0.961153	+	0.276015i	$0.910986\pi$
$758$		0			0
$759$	−7.54409	−	49.0102i	−0.00993951	−	0.0645720i
$760$		0			0
$761$	365.230	−	632.596i	0.479934	−	0.831270i	−0.519801	−	0.854287i	$-0.673994\pi$
$761$	365.230	−	632.596i	0.479934	−	0.831270i	0.999735	+	0.0230176i	$0.00732737\pi$
$762$		0			0
$763$	180.902	−	104.444i	0.237093	−	0.136886i
$764$		0			0
$765$	−222.054	+	1001.75i	−0.290267	+	1.30948i
$766$		0			0
$767$	40.4559	−	23.3572i	0.0527456	−	0.0304527i
$768$		0			0
$769$	430.746	−	746.074i	0.560138	−	0.970187i	−0.437346	−	0.899293i	$-0.644082\pi$
$769$	430.746	−	746.074i	0.560138	−	0.970187i	0.997484	−	0.0708938i	$-0.0225851\pi$
$770$		0			0
$771$	−831.417	−	323.307i	−1.07836	−	0.419335i
$772$		0			0
$773$	−981.517			−1.26975			−0.634875	−	0.772615i	$-0.718948\pi$
$773$	−981.517			−1.26975			−0.634875	+	0.772615i	$0.718948\pi$
$774$		0			0
$775$		−	2701.26i		−	3.48550i
$776$		0			0
$777$	−378.131	−	471.128i	−0.486655	−	0.606342i
$778$		0			0
$779$	−1284.62	−	741.675i	−1.64906	−	0.952085i
$780$		0			0
$781$	−206.783	−	358.159i	−0.264767	−	0.458590i
$782$		0			0
$783$	−535.208	+	801.068i	−0.683535	+	1.02308i
$784$		0			0
$785$	691.467	+	1197.66i	0.880850	+	1.52568i
$786$		0			0
$787$	614.292	+	354.662i	0.780549	+	0.450650i	0.836625	−	0.547776i	$-0.184526\pi$
$787$	614.292	+	354.662i	0.780549	+	0.450650i	−0.0560758	+	0.998427i	$0.517859\pi$
$788$		0			0
$789$	−268.284	−	334.266i	−0.340031	−	0.423658i
$790$		0			0
$791$		−	171.486i		−	0.216797i
$792$		0			0
$793$	81.5498			0.102837
$794$		0			0
$795$	−1195.67	−	464.950i	−1.50398	−	0.584843i
$796$		0			0
$797$	−591.856	+	1025.12i	−0.742605	+	1.28623i	0.208701	+	0.977980i	$0.433076\pi$
$797$	−591.856	+	1025.12i	−0.742605	+	1.28623i	−0.951306	+	0.308249i	$0.900257\pi$
$798$		0			0
$799$	492.402	−	284.288i	0.616273	−	0.355805i
$800$		0			0
$801$	702.531	−	221.529i	0.877067	−	0.276565i
$802$		0			0
$803$	52.0323	−	30.0409i	0.0647974	−	0.0374108i
$804$		0			0
$805$	109.940	−	190.421i	0.136571	−	0.236548i
$806$		0			0
$807$	−169.108	−	1098.61i	−0.209551	−	1.36135i
$808$		0			0
$809$	522.491			0.645847			0.322924	−	0.946425i	$-0.395334\pi$
$809$	522.491			0.645847			0.322924	+	0.946425i	$0.395334\pi$
$810$		0			0
$811$		−	115.368i		−	0.142254i	−0.997467	−	0.0711271i	$-0.977340\pi$
$811$		−	115.368i		−	0.142254i	0.997467	−	0.0711271i	$-0.0226596\pi$
$812$		0			0
$813$	1091.21	−	167.969i	1.34221	−	0.206604i
$814$		0			0
$815$	−1218.34	−	703.410i	−1.49490	−	0.863080i
$816$		0			0
$817$	−664.823	−	1151.51i	−0.813737	−	1.40943i
$818$		0			0
$819$	−28.9642	−	91.8538i	−0.0353654	−	0.112154i
$820$		0			0
$821$	417.973	+	723.951i	0.509102	+	0.881791i	0.999944	+	0.0105427i	$0.00335589\pi$
$821$	417.973	+	723.951i	0.509102	+	0.881791i	−0.490842	+	0.871249i	$0.663311\pi$
$822$		0			0
$823$	−629.895	−	363.670i	−0.765364	−	0.441883i	0.0658543	−	0.997829i	$-0.479023\pi$
$823$	−629.895	−	363.670i	−0.765364	−	0.441883i	−0.831218	+	0.555946i	$0.812356\pi$
$824$		0			0
$825$	279.899	−	719.789i	0.339272	−	0.872472i
$826$		0			0
$827$		−	1271.70i		−	1.53773i	−0.639413	−	0.768864i	$-0.720822\pi$
$827$		−	1271.70i		−	1.53773i	0.639413	−	0.768864i	$-0.279178\pi$
$828$		0			0
$829$	577.896			0.697100			0.348550	−	0.937290i	$-0.386674\pi$
$829$	577.896			0.697100			0.348550	+	0.937290i	$0.386674\pi$
$830$		0			0
$831$	−71.7020	+	57.5486i	−0.0862840	+	0.0692522i
$832$		0			0
$833$	−68.5803	+	118.785i	−0.0823293	+	0.142599i
$834$		0			0
$835$	−199.096	+	114.948i	−0.238439	+	0.137663i
$836$		0			0
$837$	−79.1186	+	1207.89i	−0.0945264	+	1.44312i
$838$		0			0
$839$	−620.279	+	358.118i	−0.739308	+	0.426839i	−0.821818	−	0.569751i	$-0.807040\pi$
$839$	−620.279	+	358.118i	−0.739308	+	0.426839i	0.0825099	+	0.996590i	$0.473706\pi$
$840$		0			0
$841$	−216.096	+	374.289i	−0.256951	+	0.445053i
$842$		0			0
$843$	−1081.10	+	867.701i	−1.28245	+	1.02930i
$844$		0			0
$845$	1532.51			1.81362
$846$		0			0
$847$		−	632.460i		−	0.746706i
$848$		0			0
$849$	−530.681	+	1364.70i	−0.625066	+	1.60742i
$850$		0			0
$851$	109.600	+	63.2776i	0.128790	+	0.0743567i
$852$		0			0
$853$	−522.638	−	905.235i	−0.612705	−	1.06124i	−0.990782	−	0.135463i	$-0.956748\pi$
$853$	−522.638	−	905.235i	−0.612705	−	1.06124i	0.378077	−	0.925774i	$-0.376585\pi$
$854$		0			0
$855$	2753.04	+	610.253i	3.21993	+	0.713746i
$856$		0			0
$857$	−411.368	−	712.510i	−0.480009	−	0.831400i	0.519728	−	0.854332i	$-0.326033\pi$
$857$	−411.368	−	712.510i	−0.480009	−	0.831400i	−0.999737	+	0.0229317i	$0.992700\pi$
$858$		0			0
$859$	53.7624	+	31.0397i	0.0625871	+	0.0361347i	0.530967	−	0.847392i	$-0.321829\pi$
$859$	53.7624	+	31.0397i	0.0625871	+	0.0361347i	−0.468380	+	0.883527i	$0.655162\pi$
$860$		0			0
$861$	797.845	−	122.811i	0.926649	−	0.142638i
$862$		0			0
$863$			1250.20i			1.44867i	0.689448	+	0.724335i	$0.257853\pi$
$863$			1250.20i			1.44867i	−0.689448	+	0.724335i	$0.742147\pi$
$864$		0			0
$865$	−998.022			−1.15378
$866$		0			0
$867$	62.3171	+	404.843i	0.0718767	+	0.466947i
$868$		0			0
$869$	−84.8456	+	146.957i	−0.0976360	+	0.169110i
$870$		0			0
$871$	−99.0899	+	57.2096i	−0.113766	+	0.0656827i
$872$		0			0
$873$	106.042	+	97.1639i	0.121468	+	0.111299i
$874$		0			0
$875$	1735.16	−	1001.80i	1.98304	−	1.14491i
$876$		0			0
$877$	−105.302	+	182.388i	−0.120071	+	0.207968i	−0.919795	−	0.392398i	$-0.871645\pi$
$877$	−105.302	+	182.388i	−0.120071	+	0.207968i	0.799725	+	0.600367i	$0.204979\pi$
$878$		0			0
$879$	−1202.46	−	467.593i	−1.36799	−	0.531960i
$880$		0			0
$881$	−366.361			−0.415846			−0.207923	−	0.978145i	$-0.566670\pi$
$881$	−366.361			−0.415846			−0.207923	+	0.978145i	$0.566670\pi$
$882$		0			0
$883$		−	266.329i		−	0.301619i	−0.988563	−	0.150809i	$-0.951812\pi$
$883$		−	266.329i		−	0.301619i	0.988563	−	0.150809i	$-0.0481879\pi$
$884$		0			0
$885$	−465.893	−	580.474i	−0.526433	−	0.655903i
$886$		0			0
$887$	−175.292	−	101.205i	−0.197623	−	0.114098i	0.397923	−	0.917419i	$-0.369731\pi$
$887$	−175.292	−	101.205i	−0.197623	−	0.114098i	−0.595546	+	0.803321i	$0.703064\pi$
$888$		0			0
$889$	−362.890	−	628.544i	−0.408200	−	0.707023i
$890$		0			0
$891$	−146.242	+	313.662i	−0.164132	+	0.352034i
$892$		0			0
$893$	−781.286	−	1353.23i	−0.874901	−	1.51537i
$894$		0			0
$895$	2505.35	+	1446.47i	2.79928	+	1.61616i
$896$		0			0
$897$	12.6292	+	15.7353i	0.0140794	+	0.0175421i
$898$		0			0
$899$			1599.71i			1.77943i
$900$		0			0
$901$	571.869			0.634705
$902$		0			0
$903$	674.401	+	262.250i	0.746845	+	0.290420i
$904$		0			0
$905$	95.0495	−	164.630i	0.105027	−	0.181912i
$906$		0			0
$907$	−1048.89	+	605.576i	−1.15644	+	0.667669i	−0.950448	−	0.310885i	$-0.899375\pi$
$907$	−1048.89	+	605.576i	−1.15644	+	0.667669i	−0.205989	+	0.978554i	$0.566041\pi$
$908$		0			0
$909$	−671.986	−	615.727i	−0.739258	−	0.677368i
$910$		0			0
$911$	−640.792	+	369.962i	−0.703394	+	0.406105i	−0.808610	−	0.588344i	$-0.799780\pi$
$911$	−640.792	+	369.962i	−0.703394	+	0.406105i	0.105216	+	0.994449i	$0.466447\pi$
$912$		0			0
$913$	−201.585	+	349.156i	−0.220794	+	0.382427i
$914$		0			0
$915$	−197.681	−	1284.23i	−0.216045	−	1.40353i
$916$		0			0
$917$	−522.583			−0.569883
$918$		0			0
$919$			1080.71i			1.17596i	0.808874	+	0.587982i	$0.200078\pi$
$919$			1080.71i			1.17596i	−0.808874	+	0.587982i	$0.799922\pi$
$920$		0			0
$921$	818.906	−	126.053i	0.889149	−	0.136866i
$922$		0			0
$923$	145.731	+	84.1380i	0.157889	+	0.0911571i
$924$		0			0
$925$	985.512	+	1706.96i	1.06542	+	1.84536i
$926$		0			0
$927$	897.002	+	198.834i	0.967640	+	0.214492i
$928$		0			0
$929$	594.530	+	1029.76i	0.639968	+	1.10846i	0.985439	+	0.170027i	$0.0543856\pi$
$929$	594.530	+	1029.76i	0.639968	+	1.10846i	−0.345472	+	0.938429i	$0.612281\pi$
$930$		0			0
$931$	326.446	+	188.474i	0.350640	+	0.202442i
$932$		0			0
$933$	217.195	−	558.540i	0.232792	−	0.598649i
$934$		0			0
$935$			487.107i			0.520970i
$936$		0			0
$937$	1165.30			1.24364			0.621822	−	0.783158i	$-0.286393\pi$
$937$	1165.30			1.24364			0.621822	+	0.783158i	$0.286393\pi$
$938$		0			0
$939$	277.660	−	222.852i	0.295698	−	0.237329i
$940$		0			0
$941$	431.742	−	747.800i	0.458812	−	0.794686i	−0.540086	−	0.841610i	$-0.681608\pi$
$941$	431.742	−	747.800i	0.458812	−	0.794686i	0.998898	+	0.0469234i	$0.0149417\pi$
$942$		0			0
$943$	−146.454	+	84.5552i	−0.155306	+	0.0896662i
$944$		0			0
$945$	−1376.29	+	678.783i	−1.45639	+	0.718289i
$946$		0			0
$947$	994.656	−	574.265i	1.05032	−	0.606404i	0.127583	−	0.991828i	$-0.459278\pi$
$947$	994.656	−	574.265i	1.05032	−	0.606404i	0.922740	+	0.385423i	$0.125945\pi$
$948$		0			0
$949$	−12.2233	+	21.1714i	−0.0128802	+	0.0223092i
$950$		0			0
$951$	904.318	−	725.813i	0.950913	−	0.763210i
$952$		0			0
$953$	−1447.80			−1.51920			−0.759600	−	0.650391i	$-0.774605\pi$
$953$	−1447.80			−1.51920			−0.759600	+	0.650391i	$0.774605\pi$
$954$		0			0
$955$			252.274i			0.264161i
$956$		0			0
$957$	−165.759	+	426.266i	−0.173207	+	0.445419i
$958$		0			0
$959$	−42.4316	−	24.4979i	−0.0442456	−	0.0255452i
$960$		0			0
$961$	524.483	+	908.431i	0.545768	+	0.945297i
$962$		0			0
$963$	197.977	+	627.842i	0.205584	+	0.651965i
$964$		0			0
$965$	606.831	+	1051.06i	0.628840	+	1.08918i
$966$		0			0
$967$	−1318.80	−	761.408i	−1.36380	−	0.787392i	−0.373675	−	0.927560i	$-0.621903\pi$
$967$	−1318.80	−	761.408i	−1.36380	−	0.787392i	−0.990128	+	0.140168i	$0.955236\pi$
$968$		0			0
$969$	−1242.37	+	191.237i	−1.28212	+	0.197355i
$970$		0			0
$971$		−	266.782i		−	0.274750i	−0.990519	−	0.137375i	$-0.956133\pi$
$971$		−	266.782i		−	0.274750i	0.990519	−	0.137375i	$-0.0438666\pi$
$972$		0			0
$973$	−127.401			−0.130937
$974$		0			0
$975$	47.8075	+	310.581i	0.0490333	+	0.318545i
$976$		0			0
$977$	874.915	−	1515.40i	0.895512	−	1.55107i	0.0623423	−	0.998055i	$-0.480143\pi$
$977$	874.915	−	1515.40i	0.895512	−	1.55107i	0.833170	−	0.553017i	$-0.186524\pi$
$978$		0			0
$979$	302.850	−	174.851i	0.309347	−	0.178601i
$980$		0			0
$981$	291.272	−	91.8467i	0.296913	−	0.0936256i
$982$		0			0
$983$	1127.06	−	650.711i	1.14656	−	0.661964i	0.198510	−	0.980099i	$-0.436390\pi$
$983$	1127.06	−	650.711i	1.14656	−	0.661964i	0.948046	+	0.318135i	$0.103056\pi$
$984$		0			0
$985$	−583.845	+	1011.25i	−0.592736	+	1.02665i
$986$		0			0
$987$	792.542	+	308.190i	0.802981	+	0.312249i
$988$		0			0
$989$	−151.587			−0.153273
$990$		0			0
$991$		−	136.009i		−	0.137245i	−0.997643	−	0.0686223i	$-0.978140\pi$
$991$		−	136.009i		−	0.137245i	0.997643	−	0.0686223i	$-0.0218603\pi$
$992$		0			0
$993$	−613.051	−	763.824i	−0.617372	−	0.769208i
$994$		0			0
$995$	607.766	+	350.894i	0.610820	+	0.352657i
$996$		0			0
$997$	637.348	+	1103.92i	0.639266	+	1.10724i	0.985594	+	0.169128i	$0.0540950\pi$
$997$	637.348	+	1103.92i	0.639266	+	1.10724i	−0.346328	+	0.938113i	$0.612572\pi$
$998$		0			0
$999$	−390.685	−	792.147i	−0.391076	−	0.792940i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	144.3.o.a.31.3	✓	8
3.2	odd	2		432.3.o.b.415.1		8
4.3	odd	2		144.3.o.c.31.2	yes	8
8.3	odd	2		576.3.o.d.319.3		8
8.5	even	2		576.3.o.f.319.2		8
9.2	odd	6		432.3.o.a.127.1		8
9.4	even	3		1296.3.g.j.1135.1		8
9.5	odd	6		1296.3.g.k.1135.7		8
9.7	even	3		144.3.o.c.79.2	yes	8
12.11	even	2		432.3.o.a.415.1		8
24.5	odd	2		1728.3.o.f.1279.4		8
24.11	even	2		1728.3.o.e.1279.4		8
36.7	odd	6	inner	144.3.o.a.79.3	yes	8
36.11	even	6		432.3.o.b.127.1		8
36.23	even	6		1296.3.g.k.1135.8		8
36.31	odd	6		1296.3.g.j.1135.2		8
72.11	even	6		1728.3.o.f.127.4		8
72.29	odd	6		1728.3.o.e.127.4		8
72.43	odd	6		576.3.o.f.511.2		8
72.61	even	6		576.3.o.d.511.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.3.o.a.31.3	✓	8	1.1	even	1	trivial
144.3.o.a.79.3	yes	8	36.7	odd	6	inner
144.3.o.c.31.2	yes	8	4.3	odd	2
144.3.o.c.79.2	yes	8	9.7	even	3
432.3.o.a.127.1		8	9.2	odd	6
432.3.o.a.415.1		8	12.11	even	2
432.3.o.b.127.1		8	36.11	even	6
432.3.o.b.415.1		8	3.2	odd	2
576.3.o.d.319.3		8	8.3	odd	2
576.3.o.d.511.3		8	72.61	even	6
576.3.o.f.319.2		8	8.5	even	2
576.3.o.f.511.2		8	72.43	odd	6
1296.3.g.j.1135.1		8	9.4	even	3
1296.3.g.j.1135.2		8	36.31	odd	6
1296.3.g.k.1135.7		8	9.5	odd	6
1296.3.g.k.1135.8		8	36.23	even	6
1728.3.o.e.127.4		8	72.29	odd	6
1728.3.o.e.1279.4		8	24.11	even	2
1728.3.o.f.127.4		8	72.11	even	6
1728.3.o.f.1279.4		8	24.5	odd	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)

\(f(q)\)	\(=\)	\(q+(-0.456412 - 2.96508i) q^{3} +(4.61660 - 7.99619i) q^{5} +(-5.33093 + 3.07781i) q^{7} +(-8.58338 + 2.70659i) q^{9} +O(q^{10})\)	\(q+(-0.456412 - 2.96508i) q^{3} +(4.61660 - 7.99619i) q^{5} +(-5.33093 + 3.07781i) q^{7} +(-8.58338 + 2.70659i) q^{9} +(-3.70016 + 2.13629i) q^{11} +(0.869235 - 1.50556i) q^{13} +(-25.8164 - 10.0390i) q^{15} +12.3476 q^{17} -33.9338i q^{19} +(11.5590 + 14.4019i) q^{21} +(-3.35035 - 1.93433i) q^{23} +(-30.1260 - 52.1798i) q^{25} +(11.9428 + 24.2151i) q^{27} +(17.8409 + 30.9014i) q^{29} +(38.8262 + 22.4163i) q^{31} +(8.02306 + 9.99624i) q^{33} +56.8361i q^{35} -32.7130 q^{37} +(-4.86083 - 1.89019i) q^{39} +(21.8565 - 37.8565i) q^{41} +(33.9339 - 19.5918i) q^{43} +(-17.9836 + 81.1296i) q^{45} +(39.8784 - 23.0238i) q^{47} +(-5.55415 + 9.62007i) q^{49} +(-5.63558 - 36.6116i) q^{51} +46.3143 q^{53} +39.4496i q^{55} +(-100.617 + 15.4878i) q^{57} +(23.2710 + 13.4355i) q^{59} +(23.4545 + 40.6243i) q^{61} +(37.4270 - 40.8467i) q^{63} +(-8.02582 - 13.9011i) q^{65} +(-56.9984 - 32.9080i) q^{67} +(-4.20629 + 10.8169i) q^{69} +96.7955i q^{71} -14.0622 q^{73} +(-140.967 + 113.142i) q^{75} +(13.1502 - 22.7768i) q^{77} +(34.3954 - 19.8582i) q^{79} +(66.3487 - 46.4634i) q^{81} +(81.7202 - 47.1812i) q^{83} +(57.0039 - 98.7336i) q^{85} +(83.4822 - 67.0034i) q^{87} -81.8478 q^{89} +10.7014i q^{91} +(48.7454 - 125.354i) q^{93} +(-271.341 - 156.659i) q^{95} +(-7.99028 - 13.8396i) q^{97} +(25.9778 - 28.3514i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 3 q^{3} + 3 q^{5} + 3 q^{7} - 3 q^{9}+O(q^{10}) \) 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

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