LMFDB - Embedded newform 588.3.p.h.557.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [588,3,Mod(557,588)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(588, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("588.557");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 588 = 2^{2} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	588.p (of order $6$, degree $2$, not 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:	$16.0218395444$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.1090537426944.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} - 4x^{6} - 44x^{5} + 71x^{4} + 196x^{3} + 28x^{2} + 294x + 441 $ x^8 - 2x^7 - 4x^6 - 44x^5 + 71x^4 + 196x^3 + 28x^2 + 294*x + 441
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 84)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			557.3
Root			$-1.29094 - 0.204849i$ of defining polynomial
Character	$\chi$	$=$	588.557
Dual form			588.3.p.h.569.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.29094 - 1.93690i) q^{3} +(8.17193 - 4.71806i) q^{5} +(1.49684 - 8.87465i) q^{9} +O(q^{10})$	\(q+(2.29094 - 1.93690i) q^{3} +(8.17193 - 4.71806i) q^{5} +(1.49684 - 8.87465i) q^{9} +(-13.4490 - 7.76476i) q^{11} +6.22876 q^{13} +(9.58301 - 26.6370i) q^{15} +(2.89489 + 1.67137i) q^{17} +(-4.46863 - 7.73989i) q^{19} +(-16.3439 + 9.43613i) q^{23} +(32.0203 - 55.4607i) q^{25} +(-13.7601 - 23.2306i) q^{27} +41.0872i q^{29} +(2.35425 - 4.07768i) q^{31} +(-45.8504 + 8.26066i) q^{33} +(21.9373 + 37.9964i) q^{37} +(14.2697 - 12.0645i) q^{39} +46.5886i q^{41} +47.8745 q^{43} +(-29.6391 - 79.5852i) q^{45} +(-21.1081 + 12.1868i) q^{47} +(9.86931 - 1.77811i) q^{51} +(-1.86938 - 1.07929i) q^{53} -146.539 q^{55} +(-25.2288 - 9.07637i) q^{57} +(11.0668 + 6.38943i) q^{59} +(9.94837 + 17.2311i) q^{61} +(50.9009 - 29.3877i) q^{65} +(40.4170 - 70.0043i) q^{67} +(-19.1660 + 53.2740i) q^{69} -65.4608i q^{71} +(50.2693 - 87.0689i) q^{73} +(-34.0652 - 189.077i) q^{75} +(10.7085 + 18.5477i) q^{79} +(-76.5189 - 26.5679i) q^{81} +49.3392i q^{83} +31.5425 q^{85} +(79.5819 + 94.1286i) q^{87} +(40.3469 - 23.2943i) q^{89} +(-2.50460 - 13.9017i) q^{93} +(-73.0346 - 42.1665i) q^{95} +36.3320 q^{97} +(-89.0405 + 107.732i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 6 q^{3} + 4 q^{9}+O(q^{10}) $ 8 * q + 6 * q^3 + 4 * q^9	$ 8 q + 6 q^{3} + 4 q^{9} - 56 q^{13} - 8 q^{15} - 4 q^{19} + 108 q^{25} - 36 q^{27} + 40 q^{31} - 116 q^{33} + 112 q^{37} + 28 q^{39} + 256 q^{43} + 100 q^{45} - 124 q^{51} - 368 q^{55} - 96 q^{57} + 196 q^{61} + 408 q^{67} + 16 q^{69} - 358 q^{75} + 128 q^{79} - 188 q^{81} + 464 q^{85} + 140 q^{87} - 32 q^{93} - 48 q^{97} - 416 q^{99}+O(q^{100}) $ 8 * q + 6 * q^3 + 4 * q^9 - 56 * q^13 - 8 * q^15 - 4 * q^19 + 108 * q^25 - 36 * q^27 + 40 * q^31 - 116 * q^33 + 112 * q^37 + 28 * q^39 + 256 * q^43 + 100 * q^45 - 124 * q^51 - 368 * q^55 - 96 * q^57 + 196 * q^61 + 408 * q^67 + 16 * q^69 - 358 * q^75 + 128 * q^79 - 188 * q^81 + 464 * q^85 + 140 * q^87 - 32 * q^93 - 48 * q^97 - 416 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/588\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$493$
$\chi(n)$	$-1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	2.29094	−	1.93690i	0.763648	−	0.645633i
$3$	2.29094	−	1.93690i	0.763648	−	0.645633i
$4$		0			0
$5$	8.17193	−	4.71806i	1.63439	−	0.943613i	0.651667	−	0.758505i	$-0.274070\pi$
$5$	8.17193	−	4.71806i	1.63439	−	0.943613i	0.982718	−	0.185108i	$-0.0592634\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	1.49684	−	8.87465i	0.166316	−	0.986073i
$10$		0			0
$11$	−13.4490	−	7.76476i	−1.22263	−	0.705887i	−0.257154	−	0.966370i	$-0.582785\pi$
$11$	−13.4490	−	7.76476i	−1.22263	−	0.705887i	−0.965478	+	0.260483i	$0.916118\pi$
$12$		0			0
$13$	6.22876			0.479135			0.239568	−	0.970880i	$-0.422994\pi$
$13$	6.22876			0.479135			0.239568	+	0.970880i	$0.422994\pi$
$14$		0			0
$15$	9.58301	−	26.6370i	0.638867	−	1.77580i
$16$		0			0
$17$	2.89489	+	1.67137i	0.170288	+	0.0983158i	0.582722	−	0.812672i	$-0.301988\pi$
$17$	2.89489	+	1.67137i	0.170288	+	0.0983158i	−0.412434	+	0.910988i	$0.635321\pi$
$18$		0			0
$19$	−4.46863	−	7.73989i	−0.235191	−	0.407363i	0.724137	−	0.689656i	$-0.242238\pi$
$19$	−4.46863	−	7.73989i	−0.235191	−	0.407363i	−0.959328	+	0.282293i	$0.908905\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−16.3439	+	9.43613i	−0.710602	+	0.410266i	−0.811284	−	0.584652i	$-0.801231\pi$
$23$	−16.3439	+	9.43613i	−0.710602	+	0.410266i	0.100682	+	0.994919i	$0.467898\pi$
$24$		0			0
$25$	32.0203	−	55.4607i	1.28081	−	2.21843i
$26$		0			0
$27$	−13.7601	−	23.2306i	−0.509634	−	0.860391i
$28$		0			0
$29$			41.0872i			1.41680i	0.705810	+	0.708401i	$0.250583\pi$
$29$			41.0872i			1.41680i	−0.705810	+	0.708401i	$0.749417\pi$
$30$		0			0
$31$	2.35425	−	4.07768i	0.0759435	−	0.131538i	−0.825553	−	0.564325i	$-0.809136\pi$
$31$	2.35425	−	4.07768i	0.0759435	−	0.131538i	0.901496	+	0.432787i	$0.142470\pi$
$32$		0			0
$33$	−45.8504	+	8.26066i	−1.38940	+	0.250323i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	21.9373	+	37.9964i	0.592899	+	1.02693i	0.993840	+	0.110827i	$0.0353499\pi$
$37$	21.9373	+	37.9964i	0.592899	+	1.02693i	−0.400941	+	0.916104i	$0.631317\pi$
$38$		0			0
$39$	14.2697	−	12.0645i	0.365890	−	0.309345i
$40$		0			0
$41$			46.5886i			1.13631i	0.822923	+	0.568153i	$0.192342\pi$
$41$			46.5886i			1.13631i	−0.822923	+	0.568153i	$0.807658\pi$
$42$		0			0
$43$	47.8745			1.11336			0.556680	−	0.830727i	$-0.312075\pi$
$43$	47.8745			1.11336			0.556680	+	0.830727i	$0.312075\pi$
$44$		0			0
$45$	−29.6391	−	79.5852i	−0.658647	−	1.76856i
$46$		0			0
$47$	−21.1081	+	12.1868i	−0.449109	+	0.259293i	−0.707454	−	0.706760i	$-0.750156\pi$
$47$	−21.1081	+	12.1868i	−0.449109	+	0.259293i	0.258345	+	0.966053i	$0.416823\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	9.86931	−	1.77811i	0.193516	−	0.0348649i
$52$		0			0
$53$	−1.86938	−	1.07929i	−0.0352714	−	0.0203639i	0.482261	−	0.876028i	$-0.339816\pi$
$53$	−1.86938	−	1.07929i	−0.0352714	−	0.0203639i	−0.517532	+	0.855664i	$0.673149\pi$
$54$		0			0
$55$	−146.539			−2.66434
$56$		0			0
$57$	−25.2288	−	9.07637i	−0.442610	−	0.159234i
$58$		0			0
$59$	11.0668	+	6.38943i	0.187573	+	0.108295i	0.590846	−	0.806784i	$-0.298794\pi$
$59$	11.0668	+	6.38943i	0.187573	+	0.108295i	−0.403273	+	0.915080i	$0.632127\pi$
$60$		0			0
$61$	9.94837	+	17.2311i	0.163088	+	0.282477i	0.935975	−	0.352067i	$-0.114521\pi$
$61$	9.94837	+	17.2311i	0.163088	+	0.282477i	−0.772887	+	0.634544i	$0.781188\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	50.9009	−	29.3877i	0.783091	−	0.452118i
$66$		0			0
$67$	40.4170	−	70.0043i	0.603239	−	1.04484i	−0.389088	−	0.921200i	$-0.627210\pi$
$67$	40.4170	−	70.0043i	0.603239	−	1.04484i	0.992327	−	0.123640i	$-0.0394567\pi$
$68$		0			0
$69$	−19.1660	+	53.2740i	−0.277768	+	0.772087i
$70$		0			0
$71$		−	65.4608i		−	0.921983i	−0.887404	−	0.460992i	$-0.847494\pi$
$71$		−	65.4608i		−	0.921983i	0.887404	−	0.460992i	$-0.152506\pi$
$72$		0			0
$73$	50.2693	−	87.0689i	0.688620	−	1.19273i	−0.283664	−	0.958924i	$-0.591550\pi$
$73$	50.2693	−	87.0689i	0.688620	−	1.19273i	0.972284	−	0.233801i	$-0.0751166\pi$
$74$		0			0
$75$	−34.0652	−	189.077i	−0.454203	−	2.52103i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	10.7085	+	18.5477i	0.135551	+	0.234781i	0.925808	−	0.377995i	$-0.123386\pi$
$79$	10.7085	+	18.5477i	0.135551	+	0.234781i	−0.790257	+	0.612775i	$0.790053\pi$
$80$		0			0
$81$	−76.5189	−	26.5679i	−0.944678	−	0.327999i
$82$		0			0
$83$			49.3392i			0.594448i	0.954808	+	0.297224i	$0.0960609\pi$
$83$			49.3392i			0.594448i	−0.954808	+	0.297224i	$0.903939\pi$
$84$		0			0
$85$	31.5425			0.371088
$86$		0			0
$87$	79.5819	+	94.1286i	0.914734	+	1.08194i
$88$		0			0
$89$	40.3469	−	23.2943i	0.453336	−	0.261733i	−0.255902	−	0.966703i	$-0.582373\pi$
$89$	40.3469	−	23.2943i	0.453336	−	0.261733i	0.709238	+	0.704969i	$0.249039\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−2.50460	−	13.9017i	−0.0269312	−	0.149480i
$94$		0			0
$95$	−73.0346	−	42.1665i	−0.768785	−	0.443858i
$96$		0			0
$97$	36.3320			0.374557			0.187278	−	0.982307i	$-0.440033\pi$
$97$	36.3320			0.374557			0.187278	+	0.982307i	$0.440033\pi$
$98$		0			0
$99$	−89.0405	+	107.732i	−0.899399	+	1.08820i
$100$		0			0
$101$	−88.8657	−	51.3066i	−0.879858	−	0.507986i	−0.00924658	−	0.999957i	$-0.502943\pi$
$101$	−88.8657	−	51.3066i	−0.879858	−	0.507986i	−0.870612	+	0.491971i	$0.836277\pi$
$102$		0			0
$103$	55.8745	+	96.7775i	0.542471	+	0.939587i	0.998761	+	0.0497563i	$0.0158445\pi$
$103$	55.8745	+	96.7775i	0.542471	+	0.939587i	−0.456290	+	0.889831i	$0.650822\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	26.0540	−	15.0423i	0.243496	−	0.140582i	−0.373287	−	0.927716i	$-0.621769\pi$
$107$	26.0540	−	15.0423i	0.243496	−	0.140582i	0.616782	+	0.787134i	$0.288436\pi$
$108$		0			0
$109$	21.3542	−	36.9866i	0.195911	−	0.339327i	−0.751288	−	0.659974i	$-0.770567\pi$
$109$	21.3542	−	36.9866i	0.195911	−	0.339327i	0.947199	+	0.320647i	$0.103900\pi$
$110$		0			0
$111$	123.852	+	44.5574i	1.11579	+	0.401418i
$112$		0			0
$113$		−	92.2027i		−	0.815953i	−0.912992	−	0.407977i	$-0.866234\pi$
$113$		−	92.2027i		−	0.815953i	0.912992	−	0.407977i	$-0.133766\pi$
$114$		0			0
$115$	−89.0405	+	154.223i	−0.774265	+	1.34107i
$116$		0			0
$117$	9.32346	−	55.2781i	0.0796877	−	0.472462i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	60.0830	+	104.067i	0.496554	+	0.860056i
$122$		0			0
$123$	90.2374	+	106.732i	0.733637	+	0.867738i
$124$		0			0
$125$		−	368.391i		−	2.94713i
$126$		0			0
$127$	159.579			1.25653			0.628264	−	0.778000i	$-0.283766\pi$
$127$	159.579			1.25653			0.628264	+	0.778000i	$0.283766\pi$
$128$		0			0
$129$	109.678	−	92.7281i	0.850215	−	0.718823i
$130$		0			0
$131$	−217.747	+	125.716i	−1.66219	+	0.959667i	−0.690526	+	0.723307i	$0.742621\pi$
$131$	−217.747	+	125.716i	−1.66219	+	0.959667i	−0.971666	+	0.236359i	$0.924046\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−222.050	−	124.917i	−1.64482	−	0.925313i
$136$		0			0
$137$	194.075	+	112.049i	1.41661	+	0.817879i	0.995999	−	0.0893636i	$-0.0284833\pi$
$137$	194.075	+	112.049i	1.41661	+	0.817879i	0.420608	+	0.907242i	$0.361817\pi$
$138$		0			0
$139$	70.5163			0.507312			0.253656	−	0.967295i	$-0.418367\pi$
$139$	70.5163			0.507312			0.253656	+	0.967295i	$0.418367\pi$
$140$		0			0
$141$	−24.7530	+	68.8036i	−0.175553	+	0.487968i
$142$		0			0
$143$	−83.7703	−	48.3648i	−0.585806	−	0.338215i
$144$		0			0
$145$	193.852	+	335.762i	1.33691	+	2.31560i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−194.257	+	112.154i	−1.30374	+	0.752713i	−0.981043	−	0.193790i	$-0.937922\pi$
$149$	−194.257	+	112.154i	−1.30374	+	0.752713i	−0.322694	+	0.946503i	$0.604589\pi$
$150$		0			0
$151$	10.0405	−	17.3907i	0.0664935	−	0.115170i	−0.830862	−	0.556478i	$-0.812152\pi$
$151$	10.0405	−	17.3907i	0.0664935	−	0.115170i	0.897356	+	0.441308i	$0.145486\pi$
$152$		0			0
$153$	19.1660	−	23.1894i	0.125268	−	0.151565i
$154$		0			0
$155$		−	44.4300i		−	0.286645i
$156$		0			0
$157$	−92.8412	+	160.806i	−0.591345	+	1.02424i	0.402707	+	0.915329i	$0.368070\pi$
$157$	−92.8412	+	160.806i	−0.591345	+	1.02424i	−0.994052	+	0.108910i	$0.965264\pi$
$158$		0			0
$159$	−6.37312	+	1.14822i	−0.0400825	+	0.00722149i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−101.184	−	175.256i	−0.620763	−	1.07519i	−0.989344	−	0.145597i	$-0.953490\pi$
$163$	−101.184	−	175.256i	−0.620763	−	1.07519i	0.368581	−	0.929595i	$-0.379844\pi$
$164$		0			0
$165$	−335.712	+	283.830i	−2.03462	+	1.72018i
$166$		0			0
$167$			207.595i			1.24308i	0.783381	+	0.621541i	$0.213493\pi$
$167$			207.595i			1.24308i	−0.783381	+	0.621541i	$0.786507\pi$
$168$		0			0
$169$	−130.203			−0.770430
$170$		0			0
$171$	−75.3777	+	28.0721i	−0.440805	+	0.164164i
$172$		0			0
$173$	148.451	−	85.7084i	0.858100	−	0.495424i	−0.00527553	−	0.999986i	$-0.501679\pi$
$173$	148.451	−	85.7084i	0.858100	−	0.495424i	0.863376	+	0.504562i	$0.168346\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	37.7291	−	6.79749i	0.213159	−	0.0384039i
$178$		0			0
$179$	−26.0540	−	15.0423i	−0.145553	−	0.0840353i	0.425455	−	0.904980i	$-0.360114\pi$
$179$	−26.0540	−	15.0423i	−0.145553	−	0.0840353i	−0.571008	+	0.820944i	$0.693448\pi$
$180$		0			0
$181$	253.978			1.40319			0.701596	−	0.712575i	$-0.252471\pi$
$181$	253.978			1.40319			0.701596	+	0.712575i	$0.252471\pi$
$182$		0			0
$183$	56.1660	+	20.2064i	0.306918	+	0.110418i
$184$		0			0
$185$	358.539	+	207.003i	1.93805	+	1.11893i
$186$		0			0
$187$	−25.9555	−	44.9563i	−0.138800	−	0.240408i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	183.703	−	106.061i	0.961795	−	0.555292i	0.0650698	−	0.997881i	$-0.479273\pi$
$191$	183.703	−	106.061i	0.961795	−	0.555292i	0.896725	+	0.442588i	$0.145940\pi$
$192$		0			0
$193$	−82.3098	+	142.565i	−0.426476	+	0.738677i	−0.996557	−	0.0829108i	$-0.973578\pi$
$193$	−82.3098	+	142.565i	−0.426476	+	0.738677i	0.570081	+	0.821588i	$0.306912\pi$
$194$		0			0
$195$	59.6902	−	165.915i	0.306104	−	0.850849i
$196$		0			0
$197$			173.193i			0.879153i	0.898205	+	0.439576i	$0.144871\pi$
$197$			173.193i			0.879153i	−0.898205	+	0.439576i	$0.855129\pi$
$198$		0			0
$199$	−70.1255	+	121.461i	−0.352389	+	0.610356i	−0.986668	−	0.162749i	$-0.947964\pi$
$199$	−70.1255	+	121.461i	−0.352389	+	0.610356i	0.634278	+	0.773105i	$0.281297\pi$
$200$		0			0
$201$	−42.9982	−	238.660i	−0.213921	−	1.18736i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	219.808	+	380.718i	1.07223	+	1.85716i
$206$		0			0
$207$	59.2782	+	159.170i	0.286368	+	0.768939i
$208$		0			0
$209$			138.791i			0.664073i
$210$		0			0
$211$	−256.243			−1.21442			−0.607211	−	0.794540i	$-0.707712\pi$
$211$	−256.243			−1.21442			−0.607211	+	0.794540i	$0.707712\pi$
$212$		0			0
$213$	−126.791	−	149.967i	−0.595263	−	0.704071i
$214$		0			0
$215$	391.227	−	225.875i	1.81966	−	1.05058i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−53.4797	−	296.837i	−0.244200	−	1.35542i
$220$		0			0
$221$	18.0316	+	10.4105i	0.0815909	+	0.0471065i
$222$		0			0
$223$	−185.875			−0.833518			−0.416759	−	0.909017i	$-0.636834\pi$
$223$	−185.875			−0.833518			−0.416759	+	0.909017i	$0.636834\pi$
$224$		0			0
$225$	−444.265	−	367.185i	−1.97451	−	1.63193i
$226$		0			0
$227$	68.6014	+	39.6070i	0.302209	+	0.174480i	0.643435	−	0.765501i	$-0.277509\pi$
$227$	68.6014	+	39.6070i	0.302209	+	0.174480i	−0.341226	+	0.939981i	$0.610842\pi$
$228$		0			0
$229$	87.3654	+	151.321i	0.381508	+	0.660791i	0.991278	−	0.131787i	$-0.0420715\pi$
$229$	87.3654	+	151.321i	0.381508	+	0.660791i	−0.609770	+	0.792578i	$0.708738\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	271.030	−	156.479i	1.16322	−	0.671585i	0.211146	−	0.977454i	$-0.432280\pi$
$233$	271.030	−	156.479i	1.16322	−	0.671585i	0.952074	+	0.305869i	$0.0989470\pi$
$234$		0			0
$235$	−114.996	+	199.179i	−0.489345	+	0.847570i
$236$		0			0
$237$	60.4575	+	21.7504i	0.255095	+	0.0917737i
$238$		0			0
$239$			238.654i			0.998552i	0.866443	+	0.499276i	$0.166401\pi$
$239$			238.654i			0.998552i	−0.866443	+	0.499276i	$0.833599\pi$
$240$		0			0
$241$	−73.1255	+	126.657i	−0.303425	+	0.525548i	−0.976909	−	0.213654i	$-0.931464\pi$
$241$	−73.1255	+	126.657i	−0.303425	+	0.525548i	0.673484	+	0.739202i	$0.264797\pi$
$242$		0			0
$243$	−226.760	+	87.3439i	−0.933168	+	0.359440i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−27.8340	−	48.2099i	−0.112688	−	0.195182i
$248$		0			0
$249$	95.5651	+	113.033i	0.383796	+	0.453949i
$250$		0			0
$251$			38.3366i			0.152735i	0.997080	+	0.0763677i	$0.0243323\pi$
$251$			38.3366i			0.152735i	−0.997080	+	0.0763677i	$0.975668\pi$
$252$		0			0
$253$	293.077			1.15841
$254$		0			0
$255$	72.2620	−	61.0946i	0.283381	−	0.239587i
$256$		0			0
$257$	−204.811	+	118.248i	−0.796930	+	0.460108i	−0.842396	−	0.538858i	$-0.818856\pi$
$257$	−204.811	+	118.248i	−0.796930	+	0.460108i	0.0454667	+	0.998966i	$0.485522\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	364.635	+	61.5011i	1.39707	+	0.235636i
$262$		0			0
$263$	−72.0091	−	41.5745i	−0.273799	−	0.158078i	0.356814	−	0.934175i	$-0.383863\pi$
$263$	−72.0091	−	41.5745i	−0.273799	−	0.158078i	−0.630613	+	0.776098i	$0.717196\pi$
$264$		0			0
$265$	−20.3686			−0.0768627
$266$		0			0
$267$	47.3137	−	131.514i	0.177205	−	0.492561i
$268$		0			0
$269$	−288.731	−	166.699i	−1.07335	−	0.619698i	−0.144254	−	0.989541i	$-0.546078\pi$
$269$	−288.731	−	166.699i	−1.07335	−	0.619698i	−0.929094	+	0.369843i	$0.879412\pi$
$270$		0			0
$271$	109.225	+	189.183i	0.403044	+	0.698092i	0.994092	−	0.108544i	$-0.0346190\pi$
$271$	109.225	+	189.183i	0.403044	+	0.698092i	−0.591048	+	0.806636i	$0.701286\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−861.278	+	497.259i	−3.13192	+	1.80822i
$276$		0			0
$277$	−48.6235	+	84.2184i	−0.175536	+	0.304038i	−0.940347	−	0.340218i	$-0.889499\pi$
$277$	−48.6235	+	84.2184i	−0.175536	+	0.304038i	0.764811	+	0.644255i	$0.222833\pi$
$278$		0			0
$279$	−32.6640	−	26.9968i	−0.117075	−	0.0967627i
$280$		0			0
$281$			386.079i			1.37395i	0.726682	+	0.686974i	$0.241061\pi$
$281$			386.079i			1.37395i	−0.726682	+	0.686974i	$0.758939\pi$
$282$		0			0
$283$	132.675	−	229.800i	0.468817	−	0.812015i	−0.530548	−	0.847655i	$-0.678014\pi$
$283$	132.675	−	229.800i	0.468817	−	0.812015i	0.999365	+	0.0356404i	$0.0113471\pi$
$284$		0			0
$285$	−248.990	+	44.8595i	−0.873651	+	0.157402i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−138.913	−	240.604i	−0.480668	−	0.832541i
$290$		0			0
$291$	83.2346	−	70.3715i	0.286030	−	0.241826i
$292$		0			0
$293$			250.458i			0.854807i	0.904061	+	0.427403i	$0.140572\pi$
$293$			250.458i			0.854807i	−0.904061	+	0.427403i	$0.859428\pi$
$294$		0			0
$295$	120.583			0.408756
$296$		0			0
$297$	4.67971	+	419.271i	0.0157566	+	1.41169i
$298$		0			0
$299$	−101.802	+	58.7753i	−0.340475	+	0.196573i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−302.962	+	54.5833i	−0.999875	+	0.180143i
$304$		0			0
$305$	162.595	+	93.8741i	0.533097	+	0.307784i
$306$		0			0
$307$	−407.225			−1.32647			−0.663233	−	0.748413i	$-0.730816\pi$
$307$	−407.225			−1.32647			−0.663233	+	0.748413i	$0.730816\pi$
$308$		0			0
$309$	315.454	+	113.488i	1.02089	+	0.367276i
$310$		0			0
$311$	89.5601	+	51.7075i	0.287975	+	0.166262i	0.637028	−	0.770841i	$-0.280164\pi$
$311$	89.5601	+	51.7075i	0.287975	+	0.166262i	−0.349054	+	0.937103i	$0.613497\pi$
$312$		0			0
$313$	129.642	+	224.546i	0.414191	+	0.717400i	0.995343	−	0.0963950i	$-0.0307312\pi$
$313$	129.642	+	224.546i	0.414191	+	0.717400i	−0.581152	+	0.813795i	$0.697398\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	197.996	−	114.313i	0.624592	−	0.360608i	−0.154063	−	0.988061i	$-0.549236\pi$
$317$	197.996	−	114.313i	0.624592	−	0.360608i	0.778655	+	0.627453i	$0.215902\pi$
$318$		0			0
$319$	319.033	−	552.581i	1.00010	−	1.73223i
$320$		0			0
$321$	30.5529	−	84.9252i	0.0951804	−	0.264564i
$322$		0			0
$323$		−	29.8749i		−	0.0924919i
$324$		0			0
$325$	199.446	−	345.451i	0.613681	−	1.06293i
$326$		0			0
$327$	−22.7180	−	126.095i	−0.0694741	−	0.385613i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	30.8157	+	53.3744i	0.0930988	+	0.161252i	0.908814	−	0.417203i	$-0.136989\pi$
$331$	30.8157	+	53.3744i	0.0930988	+	0.161252i	−0.815715	+	0.578454i	$0.803656\pi$
$332$		0			0
$333$	370.042	−	137.811i	1.11124	−	0.413846i
$334$		0			0
$335$		−	762.760i		−	2.27690i
$336$		0			0
$337$	269.195			0.798797			0.399399	−	0.916777i	$-0.369219\pi$
$337$	269.195			0.798797			0.399399	+	0.916777i	$0.369219\pi$
$338$		0			0
$339$	−178.587	−	211.231i	−0.526806	−	0.623101i
$340$		0			0
$341$	−63.3244	+	36.5604i	−0.185702	+	0.107215i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	94.7271	+	525.778i	0.274571	+	1.52399i
$346$		0			0
$347$	−265.059	−	153.032i	−0.763858	−	0.441014i	0.0668211	−	0.997765i	$-0.478714\pi$
$347$	−265.059	−	153.032i	−0.763858	−	0.441014i	−0.830679	+	0.556751i	$0.812048\pi$
$348$		0			0
$349$	418.759			1.19988			0.599942	−	0.800044i	$-0.295190\pi$
$349$	418.759			1.19988			0.599942	+	0.800044i	$0.295190\pi$
$350$		0			0
$351$	−85.7085	−	144.697i	−0.244184	−	0.412244i
$352$		0			0
$353$	−225.919	−	130.434i	−0.639997	−	0.369503i	0.144616	−	0.989488i	$-0.453805\pi$
$353$	−225.919	−	130.434i	−0.639997	−	0.369503i	−0.784614	+	0.619985i	$0.787139\pi$
$354$		0			0
$355$	−308.848	−	534.941i	−0.869995	−	1.50688i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	604.723	−	349.137i	1.68446	−	0.972526i	0.725834	−	0.687870i	$-0.241454\pi$
$359$	604.723	−	349.137i	1.68446	−	0.972526i	0.958630	−	0.284656i	$-0.0918795\pi$
$360$		0			0
$361$	140.563	−	243.462i	0.389370	−	0.674409i
$362$		0			0
$363$	339.214	+	122.036i	0.934473	+	0.336189i
$364$		0			0
$365$		−	948.695i		−	2.59916i
$366$		0			0
$367$	−245.808	+	425.752i	−0.669776	+	1.16009i	0.308190	+	0.951325i	$0.400277\pi$
$367$	−245.808	+	425.752i	−0.669776	+	1.16009i	−0.977967	+	0.208762i	$0.933057\pi$
$368$		0			0
$369$	413.457	+	69.7357i	1.12048	+	0.188986i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−95.4575	−	165.337i	−0.255918	−	0.443263i	0.709226	−	0.704981i	$-0.249044\pi$
$373$	−95.4575	−	165.337i	−0.255918	−	0.443263i	−0.965145	+	0.261717i	$0.915711\pi$
$374$		0			0
$375$	−713.537	−	843.964i	−1.90277	−	2.25057i
$376$		0			0
$377$			255.922i			0.678839i
$378$		0			0
$379$	−333.454			−0.879825			−0.439912	−	0.898041i	$-0.644991\pi$
$379$	−333.454			−0.879825			−0.439912	+	0.898041i	$0.644991\pi$
$380$		0			0
$381$	365.587	−	309.089i	0.959545	−	0.811256i
$382$		0			0
$383$	−15.3183	+	8.84405i	−0.0399957	+	0.0230915i	−0.519865	−	0.854249i	$-0.674018\pi$
$383$	−15.3183	+	8.84405i	−0.0399957	+	0.0230915i	0.479869	+	0.877340i	$0.340684\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	71.6606	−	424.870i	0.185169	−	1.09785i
$388$		0			0
$389$	−439.051	−	253.486i	−1.12867	−	0.651636i	−0.185068	−	0.982726i	$-0.559250\pi$
$389$	−439.051	−	253.486i	−1.12867	−	0.651636i	−0.943599	+	0.331090i	$0.892584\pi$
$390$		0			0
$391$	−63.0850			−0.161343
$392$		0			0
$393$	−255.346	+	709.763i	−0.649736	+	1.80601i
$394$		0			0
$395$	175.018	+	101.047i	0.443084	+	0.255815i
$396$		0			0
$397$	−322.797	−	559.100i	−0.813090	−	1.40831i	−0.910691	−	0.413088i	$-0.864450\pi$
$397$	−322.797	−	559.100i	−0.813090	−	1.40831i	0.0976014	−	0.995226i	$-0.468883\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−60.7928	+	35.0987i	−0.151603	+	0.0875280i	−0.573883	−	0.818938i	$-0.694563\pi$
$401$	−60.7928	+	35.0987i	−0.151603	+	0.0875280i	0.422280	+	0.906466i	$0.361230\pi$
$402$		0			0
$403$	14.6640	−	25.3989i	0.0363872	−	0.0630245i
$404$		0			0
$405$	−750.656	+	143.910i	−1.85347	+	0.355334i
$406$		0			0
$407$		−	681.350i		−	1.67408i
$408$		0			0
$409$	240.933	−	417.309i	0.589079	−	1.02031i	−0.405274	−	0.914195i	$-0.632824\pi$
$409$	240.933	−	417.309i	0.589079	−	1.02031i	0.994353	−	0.106120i	$-0.0338427\pi$
$410$		0			0
$411$	661.644	−	119.205i	1.60984	−	0.290037i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	232.786	+	403.196i	0.560929	+	0.971558i
$416$		0			0
$417$	161.549	−	136.583i	0.387407	−	0.327537i
$418$		0			0
$419$			168.074i			0.401131i	0.979680	+	0.200566i	$0.0642780\pi$
$419$			168.074i			0.401131i	−0.979680	+	0.200566i	$0.935722\pi$
$420$		0			0
$421$	453.336			1.07681			0.538404	−	0.842687i	$-0.319028\pi$
$421$	453.336			1.07681			0.538404	+	0.842687i	$0.319028\pi$
$422$		0			0
$423$	76.5579	+	205.569i	0.180988	+	0.485979i
$424$		0			0
$425$	185.391	−	107.035i	0.436213	−	0.251848i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−285.591	+	51.4536i	−0.665713	+	0.119938i
$430$		0			0
$431$	620.041	+	357.981i	1.43861	+	0.830582i	0.997753	−	0.0669956i	$-0.0213413\pi$
$431$	620.041	+	357.981i	1.43861	+	0.830582i	0.440857	+	0.897577i	$0.354675\pi$
$432$		0			0
$433$	−255.992			−0.591206			−0.295603	−	0.955311i	$-0.595521\pi$
$433$	−255.992			−0.591206			−0.295603	+	0.955311i	$0.595521\pi$
$434$		0			0
$435$	1094.44	+	393.739i	2.51596	+	0.905148i
$436$		0			0
$437$	146.069	+	84.3331i	0.334254	+	0.192982i
$438$		0			0
$439$	−405.956	−	703.136i	−0.924728	−	1.60168i	−0.791998	−	0.610523i	$-0.790959\pi$
$439$	−405.956	−	703.136i	−0.924728	−	1.60168i	−0.132730	−	0.991152i	$-0.542374\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−14.4745	+	8.35684i	−0.0326738	+	0.0188642i	−0.516248	−	0.856439i	$-0.672672\pi$
$443$	−14.4745	+	8.35684i	−0.0326738	+	0.0188642i	0.483574	+	0.875303i	$0.339338\pi$
$444$		0			0
$445$	219.808	−	380.718i	0.493950	−	0.855547i
$446$		0			0
$447$	−227.800	+	633.195i	−0.509620	+	1.41654i
$448$		0			0
$449$			19.6369i			0.0437348i	0.999761	+	0.0218674i	$0.00696117\pi$
$449$			19.6369i			0.0437348i	−0.999761	+	0.0218674i	$0.993039\pi$
$450$		0			0
$451$	361.749	−	626.568i	0.802104	−	1.38929i
$452$		0			0
$453$	−10.6818	−	59.2886i	−0.0235800	−	0.130880i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−176.148	−	305.097i	−0.385444	−	0.667608i	0.606387	−	0.795170i	$-0.292618\pi$
$457$	−176.148	−	305.097i	−0.385444	−	0.667608i	−0.991831	+	0.127562i	$0.959285\pi$
$458$		0			0
$459$	−1.00731	−	90.2483i	−0.00219457	−	0.196619i
$460$		0			0
$461$		−	11.3850i		−	0.0246962i	−0.999924	−	0.0123481i	$-0.996069\pi$
$461$		−	11.3850i		−	0.0246962i	0.999924	−	0.0123481i	$-0.00393063\pi$
$462$		0			0
$463$	−482.081			−1.04121			−0.520606	−	0.853797i	$-0.674294\pi$
$463$	−482.081			−1.04121			−0.520606	+	0.853797i	$0.674294\pi$
$464$		0			0
$465$	−86.0564	−	101.787i	−0.185068	−	0.218896i
$466$		0			0
$467$	−652.878	+	376.939i	−1.39803	+	0.807151i	−0.994186	−	0.107679i	$-0.965658\pi$
$467$	−652.878	+	376.939i	−1.39803	+	0.807151i	−0.403840	+	0.914830i	$0.632325\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	98.7705	+	548.221i	0.209704	+	1.16395i
$472$		0			0
$473$	−643.862	−	371.734i	−1.36123	−	0.785907i
$474$		0			0
$475$	−572.346			−1.20494
$476$		0			0
$477$	−12.3765	+	14.9746i	−0.0259465	+	0.0313933i
$478$		0			0
$479$	−461.367	−	266.370i	−0.963187	−	0.556096i	−0.0660347	−	0.997817i	$-0.521035\pi$
$479$	−461.367	−	266.370i	−0.963187	−	0.556096i	−0.897153	+	0.441721i	$0.854368\pi$
$480$		0			0
$481$	136.642	+	236.671i	0.284079	+	0.492039i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	296.903	−	171.417i	0.612170	−	0.353437i
$486$		0			0
$487$	−164.373	+	284.702i	−0.337521	+	0.584603i	−0.983966	−	0.178358i	$-0.942922\pi$
$487$	−164.373	+	284.702i	−0.337521	+	0.584603i	0.646445	+	0.762960i	$0.276255\pi$
$488$		0			0
$489$	−571.261	−	205.519i	−1.16822	−	0.420283i
$490$		0			0
$491$			451.540i			0.919634i	0.888014	+	0.459817i	$0.152085\pi$
$491$			451.540i			0.919634i	−0.888014	+	0.459817i	$0.847915\pi$
$492$		0			0
$493$	−68.6719	+	118.943i	−0.139294	+	0.241264i
$494$		0			0
$495$	−219.345	+	1300.48i	−0.443121	+	2.62723i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	96.4091	+	166.985i	0.193205	+	0.334640i	0.946310	−	0.323259i	$-0.104779\pi$
$499$	96.4091	+	166.985i	0.193205	+	0.334640i	−0.753106	+	0.657899i	$0.771445\pi$
$500$		0			0
$501$	402.090	+	475.588i	0.802575	+	0.949277i
$502$		0			0
$503$			271.662i			0.540083i	0.962849	+	0.270041i	$0.0870374\pi$
$503$			271.662i			0.540083i	−0.962849	+	0.270041i	$0.912963\pi$
$504$		0			0
$505$	−968.272			−1.91737
$506$		0			0
$507$	−298.287	+	252.189i	−0.588337	+	0.497415i
$508$		0			0
$509$	−560.786	+	323.770i	−1.10174	+	0.636091i	−0.936678	−	0.350192i	$-0.886116\pi$
$509$	−560.786	+	323.770i	−1.10174	+	0.636091i	−0.165064	+	0.986283i	$0.552783\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−118.313	+	210.311i	−0.230630	+	0.409962i
$514$		0			0
$515$	913.205	+	527.239i	1.77321	+	1.02377i
$516$		0			0
$517$	378.510			0.732127
$518$		0			0
$519$	174.085	−	483.888i	0.335424	−	0.932347i
$520$		0			0
$521$	−832.329	−	480.546i	−1.59756	−	0.922352i	−0.991955	−	0.126588i	$-0.959598\pi$
$521$	−832.329	−	480.546i	−1.59756	−	0.922352i	−0.605606	−	0.795765i	$-0.707069\pi$
$522$		0			0
$523$	−146.720	−	254.126i	−0.280535	−	0.485900i	0.690982	−	0.722872i	$-0.257178\pi$
$523$	−146.720	−	254.126i	−0.280535	−	0.485900i	−0.971517	+	0.236972i	$0.923845\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	13.6306	−	7.86963i	0.0258645	−	0.0149329i
$528$		0			0
$529$	−86.4190	+	149.682i	−0.163363	+	0.282953i
$530$		0			0
$531$	73.2693	−	88.6502i	0.137984	−	0.166950i
$532$		0			0
$533$			290.189i			0.544444i
$534$		0			0
$535$	141.941	−	245.849i	0.265311	−	0.459532i
$536$		0			0
$537$	−88.8238	+	16.0030i	−0.165407	+	0.0298007i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	10.4536	+	18.1061i	0.0193227	+	0.0334679i	0.875525	−	0.483173i	$-0.160516\pi$
$541$	10.4536	+	18.1061i	0.0193227	+	0.0334679i	−0.856202	+	0.516641i	$0.827182\pi$
$542$		0			0
$543$	581.849	−	491.929i	1.07154	−	0.905947i
$544$		0			0
$545$		−	403.003i		−	0.739455i
$546$		0			0
$547$	465.689			0.851351			0.425675	−	0.904876i	$-0.360037\pi$
$547$	465.689			0.851351			0.425675	+	0.904876i	$0.360037\pi$
$548$		0			0
$549$	167.811	−	62.4961i	0.305667	−	0.113836i
$550$		0			0
$551$	318.011	−	183.604i	0.577152	−	0.333219i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	1222.34	−	220.223i	2.20241	−	0.396798i
$556$		0			0
$557$	−217.416	−	125.525i	−0.390334	−	0.225359i	0.291971	−	0.956427i	$-0.405689\pi$
$557$	−217.416	−	125.525i	−0.390334	−	0.225359i	−0.682305	+	0.731068i	$0.739022\pi$
$558$		0			0
$559$	298.199			0.533450
$560$		0			0
$561$	−146.539	−	52.7191i	−0.261210	−	0.0939734i
$562$		0			0
$563$	384.262	+	221.854i	0.682526	+	0.394057i	0.800806	−	0.598924i	$-0.204405\pi$
$563$	384.262	+	221.854i	0.682526	+	0.394057i	−0.118280	+	0.992980i	$0.537738\pi$
$564$		0			0
$565$	−435.018	−	753.474i	−0.769944	−	1.33358i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−900.055	+	519.647i	−1.58182	+	0.913263i	−0.587224	+	0.809424i	$0.699779\pi$
$569$	−900.055	+	519.647i	−1.58182	+	0.913263i	−0.994594	+	0.103839i	$0.966887\pi$
$570$		0			0
$571$	−507.095	+	878.315i	−0.888083	+	1.53820i	−0.0459442	+	0.998944i	$0.514630\pi$
$571$	−507.095	+	878.315i	−0.888083	+	1.53820i	−0.842139	+	0.539261i	$0.818704\pi$
$572$		0			0
$573$	215.423	−	598.793i	0.375957	−	1.04501i
$574$		0			0
$575$			1208.59i			2.10189i
$576$		0			0
$577$	−479.280	+	830.137i	−0.830641	+	1.43871i	0.0668902	+	0.997760i	$0.478692\pi$
$577$	−479.280	+	830.137i	−0.830641	+	1.43871i	−0.897531	+	0.440952i	$0.854641\pi$
$578$		0			0
$579$	87.5665	+	486.034i	0.151237	+	0.839436i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	16.7608	+	29.0306i	0.0287493	+	0.0497952i
$584$		0			0
$585$	−184.615	−	495.717i	−0.315581	−	0.847379i
$586$		0			0
$587$			327.341i			0.557651i	0.960342	+	0.278826i	$0.0899451\pi$
$587$			327.341i			0.557651i	−0.960342	+	0.278826i	$0.910055\pi$
$588$		0			0
$589$	−42.0810			−0.0714449
$590$		0			0
$591$	335.457	+	396.775i	0.567610	+	0.671363i
$592$		0			0
$593$	671.604	−	387.751i	1.13255	−	0.653880i	0.187977	−	0.982173i	$-0.439807\pi$
$593$	671.604	−	387.751i	1.13255	−	0.653880i	0.944576	+	0.328293i	$0.106473\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	74.6040	+	414.086i	0.124965	+	0.693612i
$598$		0			0
$599$	−81.9009	−	47.2855i	−0.136729	−	0.0789408i	0.430075	−	0.902793i	$-0.358487\pi$
$599$	−81.9009	−	47.2855i	−0.136729	−	0.0789408i	−0.566804	+	0.823852i	$0.691820\pi$
$600$		0			0
$601$	61.6314			0.102548			0.0512740	−	0.998685i	$-0.483672\pi$
$601$	61.6314			0.102548			0.0512740	+	0.998685i	$0.483672\pi$
$602$		0			0
$603$	−560.766	−	463.472i	−0.929960	−	0.768611i
$604$		0			0
$605$	981.988	+	566.951i	1.62312	+	0.937109i
$606$		0			0
$607$	95.0993	+	164.717i	0.156671	+	0.271362i	0.933666	−	0.358144i	$-0.116590\pi$
$607$	95.0993	+	164.717i	0.156671	+	0.271362i	−0.776995	+	0.629507i	$0.783257\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−131.477	+	75.9085i	−0.215184	+	0.124237i
$612$		0			0
$613$	15.3908	−	26.6577i	0.0251074	−	0.0434873i	−0.853199	−	0.521586i	$-0.825341\pi$
$613$	15.3908	−	26.6577i	0.0251074	−	0.0434873i	0.878306	+	0.478099i	$0.158674\pi$
$614$		0			0
$615$	1240.98	+	446.458i	2.01785	+	0.725949i
$616$		0			0
$617$			60.7242i			0.0984184i	0.998788	+	0.0492092i	$0.0156701\pi$
$617$			60.7242i			0.0984184i	−0.998788	+	0.0492092i	$0.984330\pi$
$618$		0			0
$619$	−41.0151	+	71.0402i	−0.0662602	+	0.114766i	−0.897252	−	0.441518i	$-0.854440\pi$
$619$	−41.0151	+	71.0402i	−0.0662602	+	0.114766i	0.830992	+	0.556284i	$0.187773\pi$
$620$		0			0
$621$	444.100	+	249.834i	0.715137	+	0.402310i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−937.588	−	1623.95i	−1.50014	−	2.59832i
$626$		0			0
$627$	268.825	+	317.963i	0.428748	+	0.507118i
$628$		0			0
$629$			146.661i			0.233165i
$630$		0			0
$631$	−230.761			−0.365707			−0.182853	−	0.983140i	$-0.558533\pi$
$631$	−230.761			−0.365707			−0.182853	+	0.983140i	$0.558533\pi$
$632$		0			0
$633$	−587.038	+	496.317i	−0.927391	+	0.784071i
$634$		0			0
$635$	1304.07	−	752.904i	2.05365	−	1.18568i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−580.942	−	97.9845i	−0.909142	−	0.153340i
$640$		0			0
$641$	−779.922	−	450.288i	−1.21673	−	0.702478i	−0.252511	−	0.967594i	$-0.581256\pi$
$641$	−779.922	−	450.288i	−1.21673	−	0.702478i	−0.964217	+	0.265116i	$0.914590\pi$
$642$		0			0
$643$	440.051			0.684372			0.342186	−	0.939632i	$-0.388833\pi$
$643$	440.051			0.684372			0.342186	+	0.939632i	$0.388833\pi$
$644$		0			0
$645$	458.782	−	1275.23i	0.711289	−	1.97711i
$646$		0			0
$647$	698.320	+	403.175i	1.07932	+	0.623146i	0.930713	−	0.365750i	$-0.119188\pi$
$647$	698.320	+	403.175i	1.07932	+	0.623146i	0.148607	+	0.988896i	$0.452521\pi$
$648$		0			0
$649$	−99.2248	−	171.862i	−0.152889	−	0.264811i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	295.397	−	170.547i	0.452368	−	0.261175i	−0.256462	−	0.966554i	$-0.582557\pi$
$653$	295.397	−	170.547i	0.452368	−	0.261175i	0.708830	+	0.705379i	$0.249223\pi$
$654$		0			0
$655$	−1186.28	+	2054.69i	−1.81111	+	3.13693i
$656$		0			0
$657$	−697.461	−	576.451i	−1.06159	−	0.877398i
$658$		0			0
$659$		−	648.132i		−	0.983509i	−0.870734	−	0.491755i	$-0.836356\pi$
$659$		−	648.132i		−	0.983509i	0.870734	−	0.491755i	$-0.163644\pi$
$660$		0			0
$661$	587.357	−	1017.33i	0.888589	−	1.53908i	0.0470455	−	0.998893i	$-0.485019\pi$
$661$	587.357	−	1017.33i	0.888589	−	1.53908i	0.841544	−	0.540189i	$-0.181647\pi$
$662$		0			0
$663$	61.4735	−	11.0754i	0.0927203	−	0.0167050i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−387.705	−	671.524i	−0.581266	−	1.00678i
$668$		0			0
$669$	−425.828	+	360.020i	−0.636514	+	0.538147i
$670$		0			0
$671$		−	308.987i		−	0.460487i
$672$		0			0
$673$	−13.4980			−0.0200565			−0.0100283	−	0.999950i	$-0.503192\pi$
$673$	−13.4980			−0.0200565			−0.0100283	+	0.999950i	$0.503192\pi$
$674$		0			0
$675$	−1728.99	+	19.2981i	−2.56146	+	0.0285898i
$676$		0			0
$677$	110.700	−	63.9129i	0.163516	−	0.0944061i	−0.416009	−	0.909361i	$-0.636571\pi$
$677$	110.700	−	63.9129i	0.163516	−	0.0944061i	0.579525	+	0.814955i	$0.303238\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	233.877	−	42.1365i	0.343431	−	0.0618745i
$682$		0			0
$683$	−599.478	−	346.109i	−0.877713	−	0.506748i	−0.00780909	−	0.999970i	$-0.502486\pi$
$683$	−599.478	−	346.109i	−0.877713	−	0.506748i	−0.869904	+	0.493222i	$0.835819\pi$
$684$		0			0
$685$	2114.62			3.08704
$686$		0			0
$687$	493.243	+	177.450i	0.717967	+	0.258298i
$688$		0			0
$689$	−11.6439	−	6.72262i	−0.0168997	−	0.00975707i
$690$		0			0
$691$	659.139	+	1141.66i	0.953892	+	1.65219i	0.736884	+	0.676019i	$0.236296\pi$
$691$	659.139	+	1141.66i	0.953892	+	1.65219i	0.217007	+	0.976170i	$0.430370\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	576.254	−	332.701i	0.829143	−	0.478706i
$696$		0			0
$697$	−77.8666	+	134.869i	−0.111717	+	0.193499i
$698$		0			0
$699$	317.830	−	883.444i	0.454692	−	1.26387i
$700$		0			0
$701$		−	489.285i		−	0.697981i	−0.937126	−	0.348991i	$-0.886525\pi$
$701$		−	489.285i		−	0.697981i	0.937126	−	0.348991i	$-0.113475\pi$
$702$		0			0
$703$	196.059	−	339.584i	0.278889	−	0.483050i
$704$		0			0
$705$	122.340	+	679.044i	0.173532	+	0.963182i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−279.059	−	483.344i	−0.393595	−	0.681726i	0.599326	−	0.800505i	$-0.295435\pi$
$709$	−279.059	−	483.344i	−0.393595	−	0.681726i	−0.992921	+	0.118779i	$0.962102\pi$
$710$		0			0
$711$	180.633	−	67.2713i	0.254055	−	0.0946150i
$712$		0			0
$713$			88.8600i			0.124628i
$714$		0			0
$715$	−912.753			−1.27658
$716$		0			0
$717$	462.249	+	546.742i	0.644698	+	0.762542i
$718$		0			0
$719$	32.3244	−	18.6625i	0.0449575	−	0.0259562i	−0.477353	−	0.878712i	$-0.658404\pi$
$719$	32.3244	−	18.6625i	0.0449575	−	0.0259562i	0.522310	+	0.852756i	$0.325070\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	77.7956	+	431.801i	0.107601	+	0.597235i
$724$		0			0
$725$	2278.73	+	1315.62i	3.14307	+	1.81465i
$726$		0			0
$727$	−1010.66			−1.39017			−0.695087	−	0.718926i	$-0.744634\pi$
$727$	−1010.66			−1.39017			−0.695087	+	0.718926i	$0.744634\pi$
$728$		0			0
$729$	−350.318	+	639.311i	−0.480545	+	0.876970i
$730$		0			0
$731$	138.592	+	80.0159i	0.189592	+	0.109461i
$732$		0			0
$733$	−108.369	−	187.701i	−0.147844	−	0.256072i	0.782587	−	0.622542i	$-0.213900\pi$
$733$	−108.369	−	187.701i	−0.147844	−	0.256072i	−0.930430	+	0.366469i	$0.880567\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−1087.13	+	627.657i	−1.47508	+	0.851637i
$738$		0			0
$739$	293.383	−	508.154i	0.397000	−	0.687624i	−0.596354	−	0.802721i	$-0.703385\pi$
$739$	293.383	−	508.154i	0.397000	−	0.687624i	0.993354	+	0.115097i	$0.0367180\pi$
$740$		0			0
$741$	−157.144	−	56.5345i	−0.212070	−	0.0762948i
$742$		0			0
$743$			380.578i			0.512218i	0.966648	+	0.256109i	$0.0824406\pi$
$743$			380.578i			0.512218i	−0.966648	+	0.256109i	$0.917559\pi$
$744$		0			0
$745$	−1058.30	+	1833.03i	−1.42054	+	2.46045i
$746$		0			0
$747$	437.868	+	73.8530i	0.586169	+	0.0988661i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	670.320	+	1161.03i	0.892570	+	1.54598i	0.836783	+	0.547534i	$0.184433\pi$
$751$	670.320	+	1161.03i	0.892570	+	1.54598i	0.0557869	+	0.998443i	$0.482233\pi$
$752$		0			0
$753$	74.2541	+	87.8270i	0.0986111	+	0.116636i
$754$		0			0
$755$		−	189.487i		−	0.250976i
$756$		0			0
$757$	487.210			0.643607			0.321803	−	0.946806i	$-0.395711\pi$
$757$	487.210			0.643607			0.321803	+	0.946806i	$0.395711\pi$
$758$		0			0
$759$	671.423	−	567.661i	0.884615	−	0.747906i
$760$		0			0
$761$	−576.981	+	333.120i	−0.758188	+	0.437740i	−0.828645	−	0.559775i	$-0.810888\pi$
$761$	−576.981	+	333.120i	−0.758188	+	0.437740i	0.0704570	+	0.997515i	$0.477554\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	47.2141	−	279.929i	0.0617178	−	0.365920i
$766$		0			0
$767$	68.9325	+	39.7982i	0.0898729	+	0.0518882i
$768$		0			0
$769$	−129.409			−0.168282			−0.0841412	−	0.996454i	$-0.526815\pi$
$769$	−129.409			−0.168282			−0.0841412	+	0.996454i	$0.526815\pi$
$770$		0			0
$771$	−240.176	+	667.597i	−0.311513	+	0.865884i
$772$		0			0
$773$	145.738	+	84.1419i	0.188536	+	0.108851i	0.591297	−	0.806454i	$-0.298616\pi$
$773$	145.738	+	84.1419i	0.188536	+	0.108851i	−0.402761	+	0.915305i	$0.631949\pi$
$774$		0			0
$775$	−150.767	−	261.137i	−0.194538	−	0.336950i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	360.590	−	208.187i	0.462889	−	0.267249i
$780$		0			0
$781$	−508.288	+	880.380i	−0.650816	+	1.12725i
$782$		0			0
$783$	954.480	−	565.366i	1.21900	−	0.722051i
$784$		0			0
$785$			1752.12i			2.23200i
$786$		0			0
$787$	143.643	−	248.796i	0.182519	−	0.316132i	−0.760219	−	0.649667i	$-0.774908\pi$
$787$	143.643	−	248.796i	0.182519	−	0.316132i	0.942738	+	0.333535i	$0.108242\pi$
$788$		0			0
$789$	−245.494	+	44.2296i	−0.311146	+	0.0560578i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	61.9660	+	107.328i	0.0781412	+	0.135345i
$794$		0			0
$795$	−46.6633	+	39.4519i	−0.0586960	+	0.0496251i
$796$		0			0
$797$		−	107.769i		−	0.135219i	−0.997712	−	0.0676094i	$-0.978463\pi$
$797$		−	107.769i		−	0.135219i	0.997712	−	0.0676094i	$-0.0215372\pi$
$798$		0			0
$799$	−81.4744			−0.101970
$800$		0			0
$801$	−146.336	−	392.932i	−0.182691	−	0.490552i
$802$		0			0
$803$	−1352.14	+	780.658i	−1.68386	+	0.972177i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−984.344	+	177.345i	−1.21976	+	0.219758i
$808$		0			0
$809$	145.589	+	84.0556i	0.179961	+	0.103901i	0.587274	−	0.809388i	$-0.300201\pi$
$809$	145.589	+	84.0556i	0.179961	+	0.103901i	−0.407313	+	0.913289i	$0.633534\pi$
$810$		0			0
$811$	1013.65			1.24987			0.624936	−	0.780676i	$-0.285125\pi$
$811$	1013.65			1.24987			0.624936	+	0.780676i	$0.285125\pi$
$812$		0			0
$813$	616.656	+	221.850i	0.758495	+	0.272878i
$814$		0			0
$815$	−1653.74	−	954.788i	−2.02913	−	1.17152i
$816$		0			0
$817$	−213.933	−	370.543i	−0.261852	−	0.453541i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	116.575	−	67.3048i	0.141992	−	0.0819790i	−0.427321	−	0.904100i	$-0.640543\pi$
$821$	116.575	−	67.3048i	0.141992	−	0.0819790i	0.569313	+	0.822121i	$0.307209\pi$
$822$		0			0
$823$	−160.073	+	277.255i	−0.194500	+	0.336883i	−0.946736	−	0.322010i	$-0.895642\pi$
$823$	−160.073	+	277.255i	−0.194500	+	0.336883i	0.752237	+	0.658893i	$0.228975\pi$
$824$		0			0
$825$	−1010.00	+	2807.40i	−1.22424	+	3.40291i
$826$		0			0
$827$		−	1244.18i		−	1.50444i	−0.658910	−	0.752222i	$-0.728982\pi$
$827$		−	1244.18i		−	1.50444i	0.658910	−	0.752222i	$-0.271018\pi$
$828$		0			0
$829$	−460.870	+	798.250i	−0.555935	+	0.962907i	0.441895	+	0.897067i	$0.354306\pi$
$829$	−460.870	+	798.250i	−0.555935	+	0.962907i	−0.997830	+	0.0658406i	$0.979027\pi$
$830$		0			0
$831$	51.7289	+	287.118i	0.0622489	+	0.345510i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	979.446	+	1696.45i	1.17299	+	2.03168i
$836$		0			0
$837$	−127.122	+	1.41887i	−0.151878	+	0.00169519i
$838$		0			0
$839$		−	494.231i		−	0.589072i	−0.955640	−	0.294536i	$-0.904835\pi$
$839$		−	494.231i		−	0.589072i	0.955640	−	0.294536i	$-0.0951650\pi$
$840$		0			0
$841$	−847.162			−1.00733
$842$		0			0
$843$	747.797	+	884.486i	0.887066	+	1.04921i
$844$		0			0
$845$	−1064.01	+	614.304i	−1.25918	+	0.726987i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−141.148	−	783.437i	−0.166253	−	0.922777i
$850$		0			0
$851$	−717.079	−	414.005i	−0.842630	−	0.486493i
$852$		0			0
$853$	−1063.29			−1.24653			−0.623265	−	0.782011i	$-0.714194\pi$
$853$	−1063.29			−1.24653			−0.623265	+	0.782011i	$0.714194\pi$
$854$		0			0
$855$	−483.535	+	585.040i	−0.565538	+	0.684257i
$856$		0			0
$857$	184.365	+	106.443i	0.215128	+	0.124204i	0.603693	−	0.797217i	$-0.293695\pi$
$857$	184.365	+	106.443i	0.215128	+	0.124204i	−0.388564	+	0.921422i	$0.627029\pi$
$858$		0			0
$859$	−112.025	−	194.034i	−0.130414	−	0.225883i	0.793422	−	0.608672i	$-0.208297\pi$
$859$	−112.025	−	194.034i	−0.130414	−	0.225883i	−0.923836	+	0.382788i	$0.874964\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−812.247	+	468.951i	−0.941190	+	0.543396i	−0.890333	−	0.455310i	$-0.849529\pi$
$863$	−812.247	+	468.951i	−0.941190	+	0.543396i	−0.0508567	+	0.998706i	$0.516195\pi$
$864$		0			0
$865$	808.755	−	1400.81i	0.934977	−	1.61943i
$866$		0			0
$867$	−784.269	−	282.151i	−0.904577	−	0.325433i
$868$		0			0
$869$		−	332.596i		−	0.382734i
$870$		0			0
$871$	251.748	−	436.040i	0.289033	−	0.500620i
$872$		0			0
$873$	54.3833	−	322.434i	0.0622947	−	0.369340i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−797.634	−	1381.54i	−0.909503	−	1.57531i	−0.814756	−	0.579804i	$-0.803129\pi$
$877$	−797.634	−	1381.54i	−0.909503	−	1.57531i	−0.0947465	−	0.995501i	$-0.530204\pi$
$878$		0			0
$879$	485.113	+	573.786i	0.551891	+	0.652771i
$880$		0			0
$881$		−	51.6704i		−	0.0586497i	−0.999570	−	0.0293249i	$-0.990664\pi$
$881$		−	51.6704i		−	0.0586497i	0.999570	−	0.0293249i	$-0.00933573\pi$
$882$		0			0
$883$	−1503.98			−1.70326			−0.851629	−	0.524145i	$-0.824385\pi$
$883$	−1503.98			−1.70326			−0.851629	+	0.524145i	$0.824385\pi$
$884$		0			0
$885$	276.249	−	233.557i	0.312146	−	0.263906i
$886$		0			0
$887$	749.104	−	432.495i	0.844537	−	0.487593i	−0.0142671	−	0.999898i	$-0.504542\pi$
$887$	749.104	−	432.495i	0.844537	−	0.487593i	0.858804	+	0.512305i	$0.171208\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	822.807	+	951.462i	0.923464	+	1.06786i
$892$		0			0
$893$	188.649	+	108.916i	0.211253	+	0.121967i
$894$		0			0
$895$	−283.882			−0.317187
$896$		0			0
$897$	−119.380	+	331.831i	−0.133089	+	0.369934i
$898$		0			0
$899$	167.541	+	96.7296i	0.186363	+	0.107597i
$900$		0			0
$901$	−3.60778	−	6.24885i	−0.00400419	−	0.00693546i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	2075.49	−	1198.28i	2.29336	−	1.32407i
$906$		0			0
$907$	362.948	−	628.644i	0.400163	−	0.693102i	−0.593582	−	0.804773i	$-0.702287\pi$
$907$	362.948	−	628.644i	0.400163	−	0.693102i	0.993745	+	0.111671i	$0.0356202\pi$
$908$		0			0
$909$	−588.346	+	711.854i	−0.647246	+	0.783118i
$910$		0			0
$911$		−	1418.21i		−	1.55676i	−0.627794	−	0.778379i	$-0.716042\pi$
$911$		−	1418.21i		−	1.55676i	0.627794	−	0.778379i	$-0.283958\pi$
$912$		0			0
$913$	383.107	−	663.561i	0.419614	−	0.726792i
$914$		0			0
$915$	554.320	−	99.8693i	0.605814	−	0.109147i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−88.8261	−	153.851i	−0.0966552	−	0.167412i	0.813643	−	0.581365i	$-0.197481\pi$
$919$	−88.8261	−	153.851i	−0.0966552	−	0.167412i	−0.910298	+	0.413953i	$0.864148\pi$
$920$		0			0
$921$	−932.929	+	788.753i	−1.01295	+	0.856410i
$922$		0			0
$923$		−	407.740i		−	0.441755i
$924$		0			0
$925$	2809.75			3.03756
$926$		0			0
$927$	942.502	−	351.006i	1.01672	−	0.378648i
$928$		0			0
$929$	870.145	−	502.378i	0.936647	−	0.540773i	0.0477390	−	0.998860i	$-0.484798\pi$
$929$	870.145	−	502.378i	0.936647	−	0.540773i	0.888908	+	0.458087i	$0.151465\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	305.329	−	55.0098i	0.327255	−	0.0589602i
$934$		0			0
$935$	−424.214	−	244.920i	−0.453704	−	0.261946i
$936$		0			0
$937$	−943.357			−1.00678			−0.503392	−	0.864058i	$-0.667915\pi$
$937$	−943.357			−1.00678			−0.503392	+	0.864058i	$0.667915\pi$
$938$		0			0
$939$	731.925	+	263.319i	0.779473	+	0.280425i
$940$		0			0
$941$	−1224.73	−	707.099i	−1.30152	−	0.751434i	−0.320856	−	0.947128i	$-0.603971\pi$
$941$	−1224.73	−	707.099i	−1.30152	−	0.751434i	−0.980665	+	0.195694i	$0.937304\pi$
$942$		0			0
$943$	−439.616	−	761.437i	−0.466188	−	0.807462i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	213.677	−	123.367i	0.225636	−	0.130271i	−0.382921	−	0.923781i	$-0.625082\pi$
$947$	213.677	−	123.367i	0.225636	−	0.130271i	0.608557	+	0.793510i	$0.291749\pi$
$948$		0			0
$949$	313.115	−	542.331i	0.329942	−	0.571477i
$950$		0			0
$951$	232.184	−	645.382i	0.244148	−	0.678635i
$952$		0			0
$953$		−	1753.94i		−	1.84044i	−0.391406	−	0.920218i	$-0.628011\pi$
$953$		−	1753.94i		−	1.84044i	0.391406	−	0.920218i	$-0.371989\pi$
$954$		0			0
$955$	1000.80	−	1733.44i	1.04796	−	1.81512i
$956$		0			0
$957$	−339.408	−	1883.87i	−0.354658	−	1.96851i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	469.415	+	813.051i	0.488465	+	0.846046i
$962$		0			0
$963$	−94.4965	−	253.737i	−0.0981272	−	0.263486i
$964$		0			0
$965$			1553.37i			1.60971i
$966$		0			0
$967$	−3.97638			−0.00411208			−0.00205604	−	0.999998i	$-0.500654\pi$
$967$	−3.97638			−0.00411208			−0.00205604	+	0.999998i	$0.500654\pi$
$968$		0			0
$969$	−57.8646	−	68.4417i	−0.0597158	−	0.0706312i
$970$		0			0
$971$	707.336	−	408.381i	0.728462	−	0.420577i	−0.0893975	−	0.995996i	$-0.528494\pi$
$971$	707.336	−	408.381i	0.728462	−	0.420577i	0.817859	+	0.575419i	$0.195161\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−212.184	−	1177.72i	−0.217625	−	1.20791i
$976$		0			0
$977$	85.5224	+	49.3764i	0.0875357	+	0.0505388i	0.543129	−	0.839649i	$-0.317239\pi$
$977$	85.5224	+	49.3764i	0.0875357	+	0.0505388i	−0.455593	+	0.890188i	$0.650573\pi$
$978$		0			0
$979$	−723.498			−0.739017
$980$		0			0
$981$	−296.280	−	244.875i	−0.302018	−	0.249617i
$982$		0			0
$983$	−910.492	−	525.673i	−0.926238	−	0.534764i	−0.0406179	−	0.999175i	$-0.512933\pi$
$983$	−910.492	−	525.673i	−0.926238	−	0.534764i	−0.885620	+	0.464411i	$0.846266\pi$
$984$		0			0
$985$	817.136	+	1415.32i	0.829580	+	1.43687i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−782.454	+	451.750i	−0.791157	+	0.456775i
$990$		0			0
$991$	64.1255	−	111.069i	0.0647079	−	0.112077i	−0.831856	−	0.554991i	$-0.812722\pi$
$991$	64.1255	−	111.069i	0.0647079	−	0.112077i	0.896564	+	0.442913i	$0.146055\pi$
$992$		0			0
$993$	173.978	+	62.5907i	0.175204	+	0.0630319i
$994$		0			0
$995$			1323.43i			1.33008i
$996$		0			0
$997$	−656.222	+	1136.61i	−0.658196	+	1.14003i	0.322886	+	0.946438i	$0.395347\pi$
$997$	−656.222	+	1136.61i	−0.658196	+	1.14003i	−0.981082	+	0.193591i	$0.937986\pi$
$998$		0			0
$999$	580.819	−	1032.45i	0.581400	−	1.03348i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	588.3.p.h.557.3		8
3.2	odd	2	inner	588.3.p.h.557.2		8
7.2	even	3	inner	588.3.p.h.569.2		8
7.3	odd	6		84.3.c.a.29.4	yes	4
7.4	even	3		588.3.c.h.197.1		4
7.5	odd	6		588.3.p.f.569.3		8
7.6	odd	2		588.3.p.f.557.2		8
21.2	odd	6	inner	588.3.p.h.569.3		8
21.5	even	6		588.3.p.f.569.2		8
21.11	odd	6		588.3.c.h.197.2		4
21.17	even	6		84.3.c.a.29.3	✓	4
21.20	even	2		588.3.p.f.557.3		8
28.3	even	6		336.3.d.a.113.1		4
35.3	even	12		2100.3.e.a.449.4		8
35.17	even	12		2100.3.e.a.449.5		8
35.24	odd	6		2100.3.g.a.701.1		4
56.3	even	6		1344.3.d.g.449.4		4
56.45	odd	6		1344.3.d.a.449.1		4
63.31	odd	6		2268.3.bg.a.2213.1		8
63.38	even	6		2268.3.bg.a.701.1		8
63.52	odd	6		2268.3.bg.a.701.4		8
63.59	even	6		2268.3.bg.a.2213.4		8
84.59	odd	6		336.3.d.a.113.2		4
105.17	odd	12		2100.3.e.a.449.3		8
105.38	odd	12		2100.3.e.a.449.6		8
105.59	even	6		2100.3.g.a.701.2		4
168.59	odd	6		1344.3.d.g.449.3		4
168.101	even	6		1344.3.d.a.449.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.3.c.a.29.3	✓	4	21.17	even	6
84.3.c.a.29.4	yes	4	7.3	odd	6
336.3.d.a.113.1		4	28.3	even	6
336.3.d.a.113.2		4	84.59	odd	6
588.3.c.h.197.1		4	7.4	even	3
588.3.c.h.197.2		4	21.11	odd	6
588.3.p.f.557.2		8	7.6	odd	2
588.3.p.f.557.3		8	21.20	even	2
588.3.p.f.569.2		8	21.5	even	6
588.3.p.f.569.3		8	7.5	odd	6
588.3.p.h.557.2		8	3.2	odd	2	inner
588.3.p.h.557.3		8	1.1	even	1	trivial
588.3.p.h.569.2		8	7.2	even	3	inner
588.3.p.h.569.3		8	21.2	odd	6	inner
1344.3.d.a.449.1		4	56.45	odd	6
1344.3.d.a.449.2		4	168.101	even	6
1344.3.d.g.449.3		4	168.59	odd	6
1344.3.d.g.449.4		4	56.3	even	6
2100.3.e.a.449.3		8	105.17	odd	12
2100.3.e.a.449.4		8	35.3	even	12
2100.3.e.a.449.5		8	35.17	even	12
2100.3.e.a.449.6		8	105.38	odd	12
2100.3.g.a.701.1		4	35.24	odd	6
2100.3.g.a.701.2		4	105.59	even	6
2268.3.bg.a.701.1		8	63.38	even	6
2268.3.bg.a.701.4		8	63.52	odd	6
2268.3.bg.a.2213.1		8	63.31	odd	6
2268.3.bg.a.2213.4		8	63.59	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:	\( N \)	\(=\)	\( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	588.p (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.29094 - 1.93690i) q^{3} +(8.17193 - 4.71806i) q^{5} +(1.49684 - 8.87465i) q^{9} +O(q^{10})\)	\(q+(2.29094 - 1.93690i) q^{3} +(8.17193 - 4.71806i) q^{5} +(1.49684 - 8.87465i) q^{9} +(-13.4490 - 7.76476i) q^{11} +6.22876 q^{13} +(9.58301 - 26.6370i) q^{15} +(2.89489 + 1.67137i) q^{17} +(-4.46863 - 7.73989i) q^{19} +(-16.3439 + 9.43613i) q^{23} +(32.0203 - 55.4607i) q^{25} +(-13.7601 - 23.2306i) q^{27} +41.0872i q^{29} +(2.35425 - 4.07768i) q^{31} +(-45.8504 + 8.26066i) q^{33} +(21.9373 + 37.9964i) q^{37} +(14.2697 - 12.0645i) q^{39} +46.5886i q^{41} +47.8745 q^{43} +(-29.6391 - 79.5852i) q^{45} +(-21.1081 + 12.1868i) q^{47} +(9.86931 - 1.77811i) q^{51} +(-1.86938 - 1.07929i) q^{53} -146.539 q^{55} +(-25.2288 - 9.07637i) q^{57} +(11.0668 + 6.38943i) q^{59} +(9.94837 + 17.2311i) q^{61} +(50.9009 - 29.3877i) q^{65} +(40.4170 - 70.0043i) q^{67} +(-19.1660 + 53.2740i) q^{69} -65.4608i q^{71} +(50.2693 - 87.0689i) q^{73} +(-34.0652 - 189.077i) q^{75} +(10.7085 + 18.5477i) q^{79} +(-76.5189 - 26.5679i) q^{81} +49.3392i q^{83} +31.5425 q^{85} +(79.5819 + 94.1286i) q^{87} +(40.3469 - 23.2943i) q^{89} +(-2.50460 - 13.9017i) q^{93} +(-73.0346 - 42.1665i) q^{95} +36.3320 q^{97} +(-89.0405 + 107.732i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 6 q^{3} + 4 q^{9}+O(q^{10}) \) 8 * q + 6 * q^3 + 4 * q^9	\( 8 q + 6 q^{3} + 4 q^{9} - 56 q^{13} - 8 q^{15} - 4 q^{19} + 108 q^{25} - 36 q^{27} + 40 q^{31} - 116 q^{33} + 112 q^{37} + 28 q^{39} + 256 q^{43} + 100 q^{45} - 124 q^{51} - 368 q^{55} - 96 q^{57} + 196 q^{61} + 408 q^{67} + 16 q^{69} - 358 q^{75} + 128 q^{79} - 188 q^{81} + 464 q^{85} + 140 q^{87} - 32 q^{93} - 48 q^{97} - 416 q^{99}+O(q^{100}) \) 8 * q + 6 * q^3 + 4 * q^9 - 56 * q^13 - 8 * q^15 - 4 * q^19 + 108 * q^25 - 36 * q^27 + 40 * q^31 - 116 * q^33 + 112 * q^37 + 28 * q^39 + 256 * q^43 + 100 * q^45 - 124 * q^51 - 368 * q^55 - 96 * q^57 + 196 * q^61 + 408 * q^67 + 16 * q^69 - 358 * q^75 + 128 * q^79 - 188 * q^81 + 464 * q^85 + 140 * q^87 - 32 * q^93 - 48 * q^97 - 416 * q^99

Introduction

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