LMFDB - Embedded newform 588.3.p.h.569.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [588,3,Mod(557,588)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [8,0,6,0,0,0,0,0,4,0,0,0,-56] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)

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			569.4
Root			$-1.68211 - 3.07604i$ of defining polynomial
Character	$\chi$	$=$	588.569
Dual form			588.3.p.h.557.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.68211 - 1.34399i) q^{3} +(-3.34957 - 1.93387i) q^{5} +(5.38739 - 7.20944i) q^{9} +(-12.2117 + 7.05043i) q^{11} -20.2288 q^{13} +(-11.5830 - 0.685072i) q^{15} +(-18.9108 + 10.9182i) q^{17} +(3.46863 - 6.00784i) q^{19} +(6.69914 + 3.86775i) q^{23} +(-5.02026 - 8.69534i) q^{25} +(4.76013 - 26.5771i) q^{27} +37.3073i q^{29} +(7.64575 + 13.2428i) q^{31} +(-23.2774 + 35.3224i) q^{33} +(6.06275 - 10.5010i) q^{37} +(-54.2557 + 27.1872i) q^{39} -42.3026i q^{41} +16.1255 q^{43} +(-31.9876 + 13.7300i) q^{45} +(-62.2451 - 35.9372i) q^{47} +(-36.0470 + 54.6997i) q^{51} +(-87.8550 + 50.7231i) q^{53} +54.5385 q^{55} +(1.22876 - 20.7755i) q^{57} +(-22.2604 + 12.8520i) q^{59} +(39.0516 - 67.6394i) q^{61} +(67.7576 + 39.1199i) q^{65} +(61.5830 + 106.665i) q^{67} +(23.1660 + 1.37014i) q^{69} +34.5671i q^{71} +(-50.2693 - 87.0689i) q^{73} +(-25.1513 - 16.5747i) q^{75} +(21.2915 - 36.8780i) q^{79} +(-22.9521 - 77.6801i) q^{81} -82.1075i q^{83} +84.4575 q^{85} +(50.1407 + 100.062i) q^{87} +(36.6351 + 21.1513i) q^{89} +(38.3049 + 25.2429i) q^{93} +(-23.2368 + 13.4158i) q^{95} -48.3320 q^{97} +(-14.9595 + 126.023i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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}+ \cdots - 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

Character values

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

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

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
$3$	2.68211	−	1.34399i	0.894035	−	0.447996i
$3$	2.68211	−	1.34399i	0.894035	−	0.447996i
$4$		0			0
$5$	−3.34957	−	1.93387i	−0.669914	−	0.386775i	0.126130	−	0.992014i	$-0.459744\pi$
$5$	−3.34957	−	1.93387i	−0.669914	−	0.386775i	−0.796044	+	0.605239i	$0.793078\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	5.38739	−	7.20944i	0.598599	−	0.801049i
$10$		0			0
$11$	−12.2117	+	7.05043i	−1.11015	+	0.640948i	−0.938869	−	0.344274i	$-0.888125\pi$
$11$	−12.2117	+	7.05043i	−1.11015	+	0.640948i	−0.171285	+	0.985222i	$0.554792\pi$
$12$		0			0
$13$	−20.2288			−1.55606			−0.778029	−	0.628228i	$-0.783780\pi$
$13$	−20.2288			−1.55606			−0.778029	+	0.628228i	$0.783780\pi$
$14$		0			0
$15$	−11.5830	−	0.685072i	−0.772200	−	0.0456715i
$16$		0			0
$17$	−18.9108	+	10.9182i	−1.11240	+	0.642246i	−0.939450	−	0.342685i	$-0.888664\pi$
$17$	−18.9108	+	10.9182i	−1.11240	+	0.642246i	−0.172951	+	0.984930i	$0.555330\pi$
$18$		0			0
$19$	3.46863	−	6.00784i	0.182559	−	0.316202i	−0.760192	−	0.649698i	$-0.774895\pi$
$19$	3.46863	−	6.00784i	0.182559	−	0.316202i	0.942751	+	0.333496i	$0.108229\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	6.69914	+	3.86775i	0.291267	+	0.168163i	0.638513	−	0.769611i	$-0.279550\pi$
$23$	6.69914	+	3.86775i	0.291267	+	0.168163i	−0.347246	+	0.937774i	$0.612883\pi$
$24$		0			0
$25$	−5.02026	−	8.69534i	−0.200810	−	0.347814i
$26$		0			0
$27$	4.76013	−	26.5771i	0.176301	−	0.984336i
$28$		0			0
$29$			37.3073i			1.28646i	0.765673	+	0.643230i	$0.222406\pi$
$29$			37.3073i			1.28646i	−0.765673	+	0.643230i	$0.777594\pi$
$30$		0			0
$31$	7.64575	+	13.2428i	0.246637	+	0.427188i	0.962591	−	0.270960i	$-0.0873411\pi$
$31$	7.64575	+	13.2428i	0.246637	+	0.427188i	−0.715953	+	0.698148i	$0.754008\pi$
$32$		0			0
$33$	−23.2774	+	35.3224i	−0.705375	+	1.07037i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	6.06275	−	10.5010i	0.163858	−	0.283810i	−0.772391	−	0.635147i	$-0.780939\pi$
$37$	6.06275	−	10.5010i	0.163858	−	0.283810i	0.936249	+	0.351337i	$0.114273\pi$
$38$		0			0
$39$	−54.2557	+	27.1872i	−1.39117	+	0.697108i
$40$		0			0
$41$		−	42.3026i		−	1.03177i	−0.856658	−	0.515885i	$-0.827463\pi$
$41$		−	42.3026i		−	1.03177i	0.856658	−	0.515885i	$-0.172537\pi$
$42$		0			0
$43$	16.1255			0.375011			0.187506	−	0.982264i	$-0.439960\pi$
$43$	16.1255			0.375011			0.187506	+	0.982264i	$0.439960\pi$
$44$		0			0
$45$	−31.9876	+	13.7300i	−0.710835	+	0.305111i
$46$		0			0
$47$	−62.2451	−	35.9372i	−1.32436	−	0.764621i	−0.339941	−	0.940447i	$-0.610407\pi$
$47$	−62.2451	−	35.9372i	−1.32436	−	0.764621i	−0.984421	+	0.175825i	$0.943741\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−36.0470	+	54.6997i	−0.706803	+	1.07254i
$52$		0			0
$53$	−87.8550	+	50.7231i	−1.65764	+	0.957040i	−0.683843	+	0.729629i	$0.739693\pi$
$53$	−87.8550	+	50.7231i	−1.65764	+	0.957040i	−0.973799	+	0.227411i	$0.926974\pi$
$54$		0			0
$55$	54.5385			0.991610
$56$		0			0
$57$	1.22876	−	20.7755i	0.0215571	−	0.364482i
$58$		0			0
$59$	−22.2604	+	12.8520i	−0.377295	+	0.217831i	−0.676641	−	0.736313i	$-0.736565\pi$
$59$	−22.2604	+	12.8520i	−0.377295	+	0.217831i	0.299346	+	0.954145i	$0.403232\pi$
$60$		0			0
$61$	39.0516	−	67.6394i	0.640191	−	1.10884i	−0.345199	−	0.938529i	$-0.612189\pi$
$61$	39.0516	−	67.6394i	0.640191	−	1.10884i	0.985390	−	0.170313i	$-0.0544780\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	67.7576	+	39.1199i	1.04242	+	0.601844i
$66$		0			0
$67$	61.5830	+	106.665i	0.919149	+	1.59201i	0.800710	+	0.599052i	$0.204456\pi$
$67$	61.5830	+	106.665i	0.919149	+	1.59201i	0.118439	+	0.992961i	$0.462211\pi$
$68$		0			0
$69$	23.1660	+	1.37014i	0.335739	+	0.0198572i
$70$		0			0
$71$			34.5671i			0.486860i	0.969918	+	0.243430i	$0.0782726\pi$
$71$			34.5671i			0.486860i	−0.969918	+	0.243430i	$0.921727\pi$
$72$		0			0
$73$	−50.2693	−	87.0689i	−0.688620	−	1.19273i	−0.972284	−	0.233801i	$-0.924883\pi$
$73$	−50.2693	−	87.0689i	−0.688620	−	1.19273i	0.283664	−	0.958924i	$-0.408450\pi$
$74$		0			0
$75$	−25.1513	−	16.5747i	−0.335351	−	0.220995i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	21.2915	−	36.8780i	0.269513	−	0.466810i	−0.699223	−	0.714903i	$-0.746471\pi$
$79$	21.2915	−	36.8780i	0.269513	−	0.466810i	0.968736	+	0.248094i	$0.0798040\pi$
$80$		0			0
$81$	−22.9521	−	77.6801i	−0.283360	−	0.959014i
$82$		0			0
$83$		−	82.1075i		−	0.989247i	−0.869107	−	0.494623i	$-0.835306\pi$
$83$		−	82.1075i		−	0.989247i	0.869107	−	0.494623i	$-0.164694\pi$
$84$		0			0
$85$	84.4575			0.993618
$86$		0			0
$87$	50.1407	+	100.062i	0.576329	+	1.15014i
$88$		0			0
$89$	36.6351	+	21.1513i	0.411630	+	0.237655i	0.691490	−	0.722386i	$-0.256955\pi$
$89$	36.6351	+	21.1513i	0.411630	+	0.237655i	−0.279860	+	0.960041i	$0.590288\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	38.3049	+	25.2429i	0.411881	+	0.271429i
$94$		0			0
$95$	−23.2368	+	13.4158i	−0.244598	+	0.141219i
$96$		0			0
$97$	−48.3320			−0.498268			−0.249134	−	0.968469i	$-0.580146\pi$
$97$	−48.3320			−0.498268			−0.249134	+	0.968469i	$0.580146\pi$
$98$		0			0
$99$	−14.9595	+	126.023i	−0.151106	+	1.27296i
$100$		0			0
$101$	−69.9206	+	40.3687i	−0.692283	+	0.399690i	−0.804467	−	0.593998i	$-0.797549\pi$
$101$	−69.9206	+	40.3687i	−0.692283	+	0.399690i	0.112184	+	0.993687i	$0.464216\pi$
$102$		0			0
$103$	24.1255	−	41.7866i	0.234228	−	0.405695i	−0.724820	−	0.688938i	$-0.758077\pi$
$103$	24.1255	−	41.7866i	0.234228	−	0.405695i	0.959048	+	0.283243i	$0.0914104\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−170.197	−	98.2636i	−1.59063	−	0.918351i	−0.993199	−	0.116432i	$-0.962854\pi$
$107$	−170.197	−	98.2636i	−1.59063	−	0.918351i	−0.597432	−	0.801920i	$-0.703812\pi$
$108$		0			0
$109$	26.6458	+	46.1518i	0.244456	+	0.423411i	0.961979	−	0.273125i	$-0.0880572\pi$
$109$	26.6458	+	46.1518i	0.244456	+	0.423411i	−0.717522	+	0.696536i	$0.754724\pi$
$110$		0			0
$111$	2.14772	−	36.3130i	0.0193488	−	0.327144i
$112$		0			0
$113$		−	140.124i		−	1.24003i	−0.784589	−	0.620017i	$-0.787126\pi$
$113$		−	140.124i		−	1.24003i	0.784589	−	0.620017i	$-0.212874\pi$
$114$		0			0
$115$	−14.9595	−	25.9106i	−0.130082	−	0.225309i
$116$		0			0
$117$	−108.980	+	145.838i	−0.931454	+	1.24648i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	38.9170	−	67.4062i	0.321628	−	0.557076i
$122$		0			0
$123$	−56.8542	−	113.460i	−0.462229	−	0.922438i
$124$		0			0
$125$			135.528i			1.08422i
$126$		0			0
$127$	−115.579			−0.910071			−0.455036	−	0.890473i	$-0.650374\pi$
$127$	−115.579			−0.910071			−0.455036	+	0.890473i	$0.650374\pi$
$128$		0			0
$129$	43.2503	−	21.6725i	0.335273	−	0.168004i
$130$		0			0
$131$	71.5275	+	41.2964i	0.546012	+	0.315240i	0.747512	−	0.664249i	$-0.231248\pi$
$131$	71.5275	+	41.2964i	0.546012	+	0.315240i	−0.201500	+	0.979488i	$0.564582\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−67.3411	+	79.8163i	−0.498823	+	0.591232i
$136$		0			0
$137$	133.142	−	76.8696i	0.971840	−	0.561092i	0.0720432	−	0.997402i	$-0.477048\pi$
$137$	133.142	−	76.8696i	0.971840	−	0.561092i	0.899797	+	0.436309i	$0.143715\pi$
$138$		0			0
$139$	−220.516			−1.58645			−0.793224	−	0.608930i	$-0.791599\pi$
$139$	−220.516			−1.58645			−0.793224	+	0.608930i	$0.791599\pi$
$140$		0			0
$141$	−215.247	−	12.7307i	−1.52657	−	0.0902887i
$142$		0			0
$143$	247.027	−	142.621i	1.72746	−	0.997352i
$144$		0			0
$145$	72.1477	−	124.964i	0.497570	−	0.861817i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	168.245	+	97.1361i	1.12916	+	0.651920i	0.943723	−	0.330736i	$-0.107297\pi$
$149$	168.245	+	97.1361i	1.12916	+	0.651920i	0.185436	+	0.982656i	$0.440630\pi$
$150$		0			0
$151$	−64.0405	−	110.921i	−0.424109	−	0.734579i	0.572227	−	0.820095i	$-0.306079\pi$
$151$	−64.0405	−	110.921i	−0.424109	−	0.734579i	−0.996337	+	0.0855160i	$0.972746\pi$
$152$		0			0
$153$	−23.1660	+	195.157i	−0.151412	+	1.27554i
$154$		0			0
$155$		−	59.1437i		−	0.381572i
$156$		0			0
$157$	73.8412	+	127.897i	0.470326	+	0.814628i	0.999424	−	0.0339322i	$-0.0108030\pi$
$157$	73.8412	+	127.897i	0.470326	+	0.814628i	−0.529098	+	0.848561i	$0.677470\pi$
$158$		0			0
$159$	−167.465	+	254.121i	−1.05324	+	1.59825i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	105.184	−	182.185i	0.645302	−	1.11770i	−0.338929	−	0.940812i	$-0.610065\pi$
$163$	105.184	−	182.185i	0.645302	−	1.11770i	0.984232	−	0.176885i	$-0.0566020\pi$
$164$		0			0
$165$	146.278	−	73.2992i	0.886534	−	0.444238i
$166$		0			0
$167$			85.0905i			0.509524i	0.967004	+	0.254762i	$0.0819971\pi$
$167$			85.0905i			0.509524i	−0.967004	+	0.254762i	$0.918003\pi$
$168$		0			0
$169$	240.203			1.42132
$170$		0			0
$171$	−24.6263	−	57.3734i	−0.144014	−	0.335517i
$172$		0			0
$173$	80.9457	+	46.7340i	0.467894	+	0.270139i	0.715358	−	0.698758i	$-0.246264\pi$
$173$	80.9457	+	46.7340i	0.467894	+	0.270139i	−0.247464	+	0.968897i	$0.579597\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−42.4317	+	64.3883i	−0.239727	+	0.363776i
$178$		0			0
$179$	170.197	−	98.2636i	0.950824	−	0.548958i	0.0574872	−	0.998346i	$-0.481691\pi$
$179$	170.197	−	98.2636i	0.950824	−	0.548958i	0.893337	+	0.449388i	$0.148358\pi$
$180$		0			0
$181$	164.022			0.906200			0.453100	−	0.891460i	$-0.350318\pi$
$181$	164.022			0.906200			0.453100	+	0.891460i	$0.350318\pi$
$182$		0			0
$183$	13.8340	−	233.901i	0.0755956	−	1.27815i
$184$		0			0
$185$	−40.6152	+	23.4492i	−0.219541	+	0.126752i
$186$		0			0
$187$	153.956	−	266.659i	0.823292	−	1.42598i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−199.367	−	115.105i	−1.04381	−	0.602642i	−0.122898	−	0.992419i	$-0.539219\pi$
$191$	−199.367	−	115.105i	−1.04381	−	0.602642i	−0.920909	+	0.389777i	$0.872552\pi$
$192$		0			0
$193$	92.3098	+	159.885i	0.478289	+	0.828421i	0.999690	−	0.0248907i	$-0.00792378\pi$
$193$	92.3098	+	159.885i	0.478289	+	0.828421i	−0.521401	+	0.853312i	$0.674590\pi$
$194$		0			0
$195$	234.310	+	13.8582i	1.20159	+	0.0710675i
$196$		0			0
$197$			91.4558i			0.464243i	0.972687	+	0.232121i	$0.0745667\pi$
$197$			91.4558i			0.464243i	−0.972687	+	0.232121i	$0.925433\pi$
$198$		0			0
$199$	−101.875	−	176.452i	−0.511932	−	0.886693i	−0.999904	−	0.0138334i	$-0.995597\pi$
$199$	−101.875	−	176.452i	−0.511932	−	0.886693i	0.487972	−	0.872859i	$-0.337737\pi$
$200$		0			0
$201$	308.529	+	203.320i	1.53497	+	1.01154i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−81.8078	+	141.695i	−0.399063	+	0.691197i
$206$		0			0
$207$	63.9752	−	27.4600i	0.309059	−	0.132657i
$208$		0			0
$209$			97.8212i			0.468044i
$210$		0			0
$211$	188.243			0.892147			0.446074	−	0.894996i	$-0.352822\pi$
$211$	188.243			0.892147			0.446074	+	0.894996i	$0.352822\pi$
$212$		0			0
$213$	46.4577	+	92.7125i	0.218111	+	0.435270i
$214$		0			0
$215$	−54.0134	−	31.1847i	−0.251225	−	0.145045i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−251.847	−	165.967i	−1.14999	−	0.757839i
$220$		0			0
$221$	382.543	−	220.861i	1.73096	−	0.999371i
$222$		0			0
$223$	−154.125			−0.691146			−0.345573	−	0.938392i	$-0.612315\pi$
$223$	−154.125			−0.691146			−0.345573	+	0.938392i	$0.612315\pi$
$224$		0			0
$225$	−89.7347	−	10.6519i	−0.398821	−	0.0473418i
$226$		0			0
$227$	202.296	−	116.796i	0.891174	−	0.514519i	0.0168475	−	0.999858i	$-0.494637\pi$
$227$	202.296	−	116.796i	0.891174	−	0.514519i	0.874326	+	0.485339i	$0.161304\pi$
$228$		0			0
$229$	137.635	−	238.390i	0.601025	−	1.04101i	−0.391642	−	0.920118i	$-0.628093\pi$
$229$	137.635	−	238.390i	0.601025	−	1.04101i	0.992666	−	0.120887i	$-0.0385740\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	30.7022	+	17.7259i	0.131769	+	0.0760769i	0.564435	−	0.825477i	$-0.309094\pi$
$233$	30.7022	+	17.7259i	0.131769	+	0.0760769i	−0.432666	+	0.901554i	$0.642427\pi$
$234$		0			0
$235$	138.996	+	240.748i	0.591473	+	1.02446i
$236$		0			0
$237$	7.54249	−	127.526i	0.0318248	−	0.538085i
$238$		0			0
$239$			56.8888i			0.238028i	0.992893	+	0.119014i	$0.0379734\pi$
$239$			56.8888i			0.238028i	−0.992893	+	0.119014i	$0.962027\pi$
$240$		0			0
$241$	−104.875	−	181.648i	−0.435164	−	0.753726i	0.562145	−	0.827039i	$-0.309976\pi$
$241$	−104.875	−	181.648i	−0.435164	−	0.753726i	−0.997309	+	0.0733126i	$0.976643\pi$
$242$		0			0
$243$	−165.961	−	177.499i	−0.682968	−	0.730448i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−70.1660	+	121.531i	−0.284073	+	0.492029i
$248$		0			0
$249$	−110.352	−	220.221i	−0.443179	−	0.884422i
$250$		0			0
$251$			77.1123i			0.307220i	0.988132	+	0.153610i	$0.0490900\pi$
$251$			77.1123i			0.307220i	−0.988132	+	0.153610i	$0.950910\pi$
$252$		0			0
$253$	−109.077			−0.431135
$254$		0			0
$255$	226.524	−	113.510i	0.888329	−	0.445137i
$256$		0			0
$257$	137.122	+	79.1675i	0.533549	+	0.308045i	0.742461	−	0.669890i	$-0.233659\pi$
$257$	137.122	+	79.1675i	0.533549	+	0.308045i	−0.208911	+	0.977935i	$0.566992\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	268.965	+	200.989i	1.03052	+	0.770073i
$262$		0			0
$263$	−130.003	+	75.0571i	−0.494307	+	0.285388i	−0.726359	−	0.687315i	$-0.758789\pi$
$263$	−130.003	+	75.0571i	−0.494307	+	0.285388i	0.232053	+	0.972703i	$0.425456\pi$
$264$		0			0
$265$	392.369			1.48064
$266$		0			0
$267$	126.686	+	7.49281i	0.474480	+	0.0280630i
$268$		0			0
$269$	−165.241	+	95.4019i	−0.614279	+	0.354654i	−0.774638	−	0.632405i	$-0.782068\pi$
$269$	−165.241	+	95.4019i	−0.614279	+	0.354654i	0.160359	+	0.987059i	$0.448735\pi$
$270$		0			0
$271$	−171.225	+	296.570i	−0.631826	+	1.09435i	0.355352	+	0.934732i	$0.384361\pi$
$271$	−171.225	+	296.570i	−0.631826	+	1.09435i	−0.987178	+	0.159622i	$0.948972\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	122.612	+	70.7899i	0.445861	+	0.257418i
$276$		0			0
$277$	46.6235	+	80.7543i	0.168316	+	0.291532i	0.937828	−	0.347101i	$-0.112834\pi$
$277$	46.6235	+	80.7543i	0.168316	+	0.291532i	−0.769512	+	0.638632i	$0.779500\pi$
$278$		0			0
$279$	136.664	+	16.2226i	0.489835	+	0.0581456i
$280$		0			0
$281$		−	251.075i		−	0.893505i	−0.894657	−	0.446753i	$-0.852580\pi$
$281$		−	251.075i		−	0.893505i	0.894657	−	0.446753i	$-0.147420\pi$
$282$		0			0
$283$	8.32484	+	14.4191i	0.0294164	+	0.0509507i	0.880359	−	0.474308i	$-0.157302\pi$
$283$	8.32484	+	14.4191i	0.0294164	+	0.0509507i	−0.850942	+	0.525259i	$0.823968\pi$
$284$		0			0
$285$	−44.2929	+	67.2126i	−0.155414	+	0.235834i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	93.9131	−	162.662i	0.324959	−	0.562845i
$290$		0			0
$291$	−129.632	+	64.9577i	−0.445469	+	0.223222i
$292$		0			0
$293$			307.322i			1.04888i	0.851448	+	0.524440i	$0.175725\pi$
$293$			307.322i			1.04888i	−0.851448	+	0.524440i	$0.824275\pi$
$294$		0			0
$295$	99.4170			0.337007
$296$		0			0
$297$	129.250	+	358.112i	0.435187	+	1.20576i
$298$		0			0
$299$	−135.515	−	78.2398i	−0.453228	−	0.261671i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−133.279	+	202.246i	−0.439866	+	0.667477i
$304$		0			0
$305$	−261.612	+	151.042i	−0.857745	+	0.495219i
$306$		0			0
$307$	−126.775			−0.412948			−0.206474	−	0.978452i	$-0.566199\pi$
$307$	−126.775			−0.412948			−0.206474	+	0.978452i	$0.566199\pi$
$308$		0			0
$309$	8.54642	−	144.500i	0.0276583	−	0.467639i
$310$		0			0
$311$	−284.849	+	164.458i	−0.915913	+	0.528803i	−0.882329	−	0.470633i	$-0.844026\pi$
$311$	−284.849	+	164.458i	−0.915913	+	0.528803i	−0.0335844	+	0.999436i	$0.510692\pi$
$312$		0			0
$313$	−129.642	+	224.546i	−0.414191	+	0.717400i	−0.995343	−	0.0963950i	$-0.969269\pi$
$313$	−129.642	+	224.546i	−0.414191	+	0.717400i	0.581152	+	0.813795i	$0.302602\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	7.46537	+	4.31014i	0.0235501	+	0.0135966i	0.511729	−	0.859147i	$-0.329005\pi$
$317$	7.46537	+	4.31014i	0.0235501	+	0.0135966i	−0.488179	+	0.872744i	$0.662339\pi$
$318$		0			0
$319$	−263.033	−	455.586i	−0.824554	−	1.42817i
$320$		0			0
$321$	−588.553	−	34.8097i	−1.83350	−	0.108442i
$322$		0			0
$323$			151.484i			0.468992i
$324$		0			0
$325$	101.554	+	175.896i	0.312473	+	0.541218i
$326$		0			0
$327$	133.494	+	87.9724i	0.408239	+	0.269029i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	237.184	−	410.815i	0.716569	−	1.24113i	−0.245782	−	0.969325i	$-0.579045\pi$
$331$	237.184	−	410.815i	0.716569	−	1.24113i	0.962351	−	0.271809i	$-0.0876218\pi$
$332$		0			0
$333$	−43.0439	−	100.282i	−0.129261	−	0.301147i
$334$		0			0
$335$		−	476.375i		−	1.42202i
$336$		0			0
$337$	−609.195			−1.80770			−0.903850	−	0.427850i	$-0.859271\pi$
$337$	−609.195			−1.80770			−0.903850	+	0.427850i	$0.859271\pi$
$338$		0			0
$339$	−188.325	−	375.827i	−0.555530	−	1.10863i
$340$		0			0
$341$	−186.735	−	107.812i	−0.547610	−	0.316163i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−74.9465	−	49.3896i	−0.217236	−	0.143158i
$346$		0			0
$347$	−369.911	+	213.568i	−1.06602	+	0.615470i	−0.927093	−	0.374832i	$-0.877700\pi$
$347$	−369.911	+	213.568i	−1.06602	+	0.615470i	−0.138932	+	0.990302i	$0.544367\pi$
$348$		0			0
$349$	−316.759			−0.907620			−0.453810	−	0.891098i	$-0.649936\pi$
$349$	−316.759			−0.907620			−0.453810	+	0.891098i	$0.649936\pi$
$350$		0			0
$351$	−96.2915	+	537.621i	−0.274335	+	1.53168i
$352$		0			0
$353$	74.8771	−	43.2303i	0.212116	−	0.122465i	−0.390178	−	0.920739i	$-0.627587\pi$
$353$	74.8771	−	43.2303i	0.212116	−	0.122465i	0.602295	+	0.798274i	$0.294253\pi$
$354$		0			0
$355$	66.8483	−	115.785i	0.188305	−	0.326154i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−247.868	−	143.107i	−0.690440	−	0.398626i	0.113337	−	0.993557i	$-0.463846\pi$
$359$	−247.868	−	143.107i	−0.690440	−	0.398626i	−0.803777	+	0.594931i	$0.797179\pi$
$360$		0			0
$361$	156.437	+	270.957i	0.433344	+	0.750574i
$362$		0			0
$363$	13.7863	−	233.095i	0.0379788	−	0.642134i
$364$		0			0
$365$			388.858i			1.06536i
$366$		0			0
$367$	55.8078	+	96.6620i	0.152065	+	0.263384i	0.931986	−	0.362493i	$-0.118074\pi$
$367$	55.8078	+	96.6620i	0.152065	+	0.263384i	−0.779922	+	0.625877i	$0.784741\pi$
$368$		0			0
$369$	−304.978	−	227.900i	−0.826498	−	0.617616i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−42.5425	+	73.6857i	−0.114055	+	0.197549i	−0.917402	−	0.397963i	$-0.869717\pi$
$373$	−42.5425	+	73.6857i	−0.114055	+	0.197549i	0.803347	+	0.595512i	$0.203051\pi$
$374$		0			0
$375$	182.148	+	363.500i	0.485728	+	0.969334i
$376$		0			0
$377$		−	754.681i		−	2.00181i
$378$		0			0
$379$	−26.5464			−0.0700433			−0.0350217	−	0.999387i	$-0.511150\pi$
$379$	−26.5464			−0.0700433			−0.0350217	+	0.999387i	$0.511150\pi$
$380$		0			0
$381$	−309.995	+	155.337i	−0.813636	+	0.407709i
$382$		0			0
$383$	−100.067	−	57.7735i	−0.261271	−	0.150845i	0.363643	−	0.931538i	$-0.381533\pi$
$383$	−100.067	−	57.7735i	−0.261271	−	0.150845i	−0.624914	+	0.780693i	$0.714866\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	86.8743	−	116.256i	0.224481	−	0.300403i
$388$		0			0
$389$	−334.042	+	192.859i	−0.858719	+	0.495782i	−0.863583	−	0.504206i	$-0.831785\pi$
$389$	−334.042	+	192.859i	−0.858719	+	0.495782i	0.00486402	+	0.999988i	$0.498452\pi$
$390$		0			0
$391$	−168.915			−0.432008
$392$		0			0
$393$	247.346	+	14.6292i	0.629380	+	0.0372244i
$394$		0			0
$395$	−142.635	+	82.3502i	−0.361101	+	0.208481i
$396$		0			0
$397$	23.7967	−	41.2171i	0.0599413	−	0.103821i	−0.834498	−	0.551012i	$-0.814242\pi$
$397$	23.7967	−	41.2171i	0.0599413	−	0.103821i	0.894439	+	0.447190i	$0.147575\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	397.127	+	229.282i	0.990343	+	0.571775i	0.905377	−	0.424609i	$-0.139588\pi$
$401$	397.127	+	229.282i	0.990343	+	0.571775i	0.0849661	+	0.996384i	$0.472922\pi$
$402$		0			0
$403$	−154.664	−	267.886i	−0.383782	−	0.664729i
$404$		0			0
$405$	−73.3438	+	304.581i	−0.181096	+	0.752053i
$406$		0			0
$407$			170.980i			0.420098i
$408$		0			0
$409$	−28.9333	−	50.1140i	−0.0707416	−	0.122528i	0.828485	−	0.560011i	$-0.189203\pi$
$409$	−28.9333	−	50.1140i	−0.0707416	−	0.122528i	−0.899227	+	0.437483i	$0.855870\pi$
$410$		0			0
$411$	253.789	−	385.114i	0.617492	−	0.937017i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−158.786	+	275.025i	−0.382616	+	0.662710i
$416$		0			0
$417$	−591.448	+	296.372i	−1.41834	+	0.710723i
$418$		0			0
$419$		−	115.304i		−	0.275190i	−0.990489	−	0.137595i	$-0.956063\pi$
$419$		−	115.304i		−	0.275190i	0.990489	−	0.137595i	$-0.0439372\pi$
$420$		0			0
$421$	622.664			1.47901			0.739506	−	0.673150i	$-0.235059\pi$
$421$	622.664			1.47901			0.739506	+	0.673150i	$0.235059\pi$
$422$		0			0
$423$	−594.425	+	255.145i	−1.40526	+	0.603179i
$424$		0			0
$425$	189.875	+	109.624i	0.446764	+	0.257939i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	470.872	−	714.528i	1.09760	−	1.66557i
$430$		0			0
$431$	−147.801	+	85.3332i	−0.342927	+	0.197989i	−0.661565	−	0.749887i	$-0.730108\pi$
$431$	−147.801	+	85.3332i	−0.342927	+	0.197989i	0.318639	+	0.947876i	$0.396774\pi$
$432$		0			0
$433$	251.992			0.581968			0.290984	−	0.956728i	$-0.406017\pi$
$433$	251.992			0.581968			0.290984	+	0.956728i	$0.406017\pi$
$434$		0			0
$435$	25.5582	−	432.131i	0.0587546	−	0.993405i
$436$		0			0
$437$	46.4736	−	26.8316i	0.106347	−	0.0613994i
$438$		0			0
$439$	−226.044	+	391.520i	−0.514908	+	0.891846i	0.484943	+	0.874546i	$0.338840\pi$
$439$	−226.044	+	391.520i	−0.514908	+	0.891846i	−0.999850	+	0.0173003i	$0.994493\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	94.5542	+	54.5909i	0.213441	+	0.123230i	0.602909	−	0.797810i	$-0.294008\pi$
$443$	94.5542	+	54.5909i	0.213441	+	0.123230i	−0.389469	+	0.921040i	$0.627341\pi$
$444$		0			0
$445$	−81.8078	−	141.695i	−0.183838	−	0.318416i
$446$		0			0
$447$	581.800	+	34.4103i	1.30157	+	0.0769806i
$448$		0			0
$449$		−	565.005i		−	1.25836i	−0.777259	−	0.629181i	$-0.783390\pi$
$449$		−	565.005i		−	1.25836i	0.777259	−	0.629181i	$-0.216610\pi$
$450$		0			0
$451$	298.251	+	516.586i	0.661310	+	1.14542i
$452$		0			0
$453$	−320.841	−	211.433i	−0.708258	−	0.466740i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−297.852	+	515.895i	−0.651756	+	1.12887i	0.330941	+	0.943651i	$0.392634\pi$
$457$	−297.852	+	515.895i	−0.651756	+	1.12887i	−0.982697	+	0.185222i	$0.940699\pi$
$458$		0			0
$459$	200.155	+	554.567i	0.436068	+	1.20821i
$460$		0			0
$461$			445.590i			0.966573i	0.875462	+	0.483286i	$0.160557\pi$
$461$			445.590i			0.966573i	−0.875462	+	0.483286i	$0.839443\pi$
$462$		0			0
$463$	−333.919			−0.721207			−0.360604	−	0.932719i	$-0.617429\pi$
$463$	−333.919			−0.721207			−0.360604	+	0.932719i	$0.617429\pi$
$464$		0			0
$465$	−79.4885	−	158.630i	−0.170943	−	0.341139i
$466$		0			0
$467$	−388.191	−	224.122i	−0.831244	−	0.479919i	0.0230345	−	0.999735i	$-0.492667\pi$
$467$	−388.191	−	224.122i	−0.831244	−	0.479919i	−0.854278	+	0.519816i	$0.826001\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	369.942	+	243.791i	0.785439	+	0.517602i
$472$		0			0
$473$	−196.920	+	113.692i	−0.416320	+	0.240363i
$474$		0			0
$475$	−69.6536			−0.146639
$476$		0			0
$477$	−107.624	+	906.651i	−0.225626	+	1.90074i
$478$		0			0
$479$	11.8658	−	6.85072i	0.0247720	−	0.0143021i	−0.487563	−	0.873088i	$-0.662114\pi$
$479$	11.8658	−	6.85072i	0.0247720	−	0.0143021i	0.512335	+	0.858786i	$0.328781\pi$
$480$		0			0
$481$	−122.642	+	212.422i	−0.254973	+	0.441625i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	161.891	+	93.4681i	0.333797	+	0.192718i
$486$		0			0
$487$	−5.62746	−	9.74705i	−0.0115554	−	0.0200145i	0.860190	−	0.509974i	$-0.170345\pi$
$487$	−5.62746	−	9.74705i	−0.0115554	−	0.0200145i	−0.871745	+	0.489959i	$0.837012\pi$
$488$		0			0
$489$	37.2614	−	630.005i	0.0761992	−	1.28835i
$490$		0			0
$491$		−	285.642i		−	0.581756i	−0.956760	−	0.290878i	$-0.906053\pi$
$491$		−	285.642i		−	0.581756i	0.956760	−	0.290878i	$-0.0939473\pi$
$492$		0			0
$493$	−407.328	−	705.513i	−0.826223	−	1.43106i
$494$		0			0
$495$	293.820	−	393.193i	0.593576	−	0.794328i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−390.409	+	676.208i	−0.782383	+	1.35513i	0.148167	+	0.988962i	$0.452663\pi$
$499$	−390.409	+	676.208i	−0.782383	+	1.35513i	−0.930550	+	0.366165i	$0.880671\pi$
$500$		0			0
$501$	114.361	+	228.222i	0.228265	+	0.455532i
$502$		0			0
$503$		−	420.771i		−	0.836522i	−0.908327	−	0.418261i	$-0.862640\pi$
$503$		−	420.771i		−	0.836522i	0.908327	−	0.418261i	$-0.137360\pi$
$504$		0			0
$505$	312.272			0.618360
$506$		0			0
$507$	644.249	−	322.830i	1.27071	−	0.636745i
$508$		0			0
$509$	−89.1773	−	51.4866i	−0.175201	−	0.101152i	0.409835	−	0.912160i	$-0.365586\pi$
$509$	−89.1773	−	51.4866i	−0.175201	−	0.101152i	−0.585036	+	0.811007i	$0.698920\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−143.160	−	120.784i	−0.279064	−	0.235447i
$514$		0			0
$515$	−161.620	+	93.3113i	−0.313825	+	0.181187i
$516$		0			0
$517$	1013.49			1.96033
$518$		0			0
$519$	279.915	+	16.5555i	0.539335	+	0.0318988i
$520$		0			0
$521$	−66.4966	+	38.3918i	−0.127633	+	0.0736887i	−0.562457	−	0.826827i	$-0.690144\pi$
$521$	−66.4966	+	38.3918i	−0.127633	+	0.0736887i	0.434824	+	0.900515i	$0.356810\pi$
$522$		0			0
$523$	−202.280	+	350.360i	−0.386769	+	0.669904i	−0.992013	−	0.126136i	$-0.959742\pi$
$523$	−202.280	+	350.360i	−0.386769	+	0.669904i	0.605244	+	0.796040i	$0.293076\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−289.175	−	166.955i	−0.548719	−	0.316803i
$528$		0			0
$529$	−234.581	−	406.306i	−0.443442	−	0.768065i
$530$		0			0
$531$	−27.2693	+	229.724i	−0.0513546	+	0.432625i
$532$		0			0
$533$			855.728i			1.60549i
$534$		0			0
$535$	380.059	+	658.281i	0.710390	+	1.23043i
$536$		0			0
$537$	324.423	−	492.297i	0.604139	−	0.916754i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−296.454	+	513.473i	−0.547973	+	0.949118i	0.450440	+	0.892807i	$0.351267\pi$
$541$	−296.454	+	513.473i	−0.547973	+	0.949118i	−0.998413	+	0.0563109i	$0.982066\pi$
$542$		0			0
$543$	439.925	−	220.444i	0.810175	−	0.405974i
$544$		0			0
$545$		−	206.118i		−	0.378198i
$546$		0			0
$547$	−793.689			−1.45099			−0.725493	−	0.688230i	$-0.758388\pi$
$547$	−793.689			−1.45099			−0.725493	+	0.688230i	$0.758388\pi$
$548$		0			0
$549$	−277.256	−	645.940i	−0.505020	−	1.17658i
$550$		0			0
$551$	224.136	+	129.405i	0.406781	+	0.234855i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−77.4188	+	117.480i	−0.139493	+	0.211675i
$556$		0			0
$557$	319.531	−	184.482i	0.573665	−	0.331206i	−0.184947	−	0.982749i	$-0.559211\pi$
$557$	319.531	−	184.482i	0.573665	−	0.331206i	0.758612	+	0.651543i	$0.225878\pi$
$558$		0			0
$559$	−326.199			−0.583540
$560$		0			0
$561$	54.5385	−	922.122i	0.0972167	−	1.64371i
$562$		0			0
$563$	−458.816	+	264.898i	−0.814949	+	0.470511i	−0.848672	−	0.528920i	$-0.822597\pi$
$563$	−458.816	+	264.898i	−0.814949	+	0.470511i	0.0337223	+	0.999431i	$0.489264\pi$
$564$		0			0
$565$	−270.982	+	469.354i	−0.479614	+	0.830715i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−924.949	−	534.020i	−1.62557	−	0.938523i	−0.985393	−	0.170296i	$-0.945528\pi$
$569$	−924.949	−	534.020i	−1.62557	−	0.938523i	−0.640177	−	0.768227i	$-0.721139\pi$
$570$		0			0
$571$	59.0954	+	102.356i	0.103495	+	0.179258i	0.913122	−	0.407686i	$-0.133664\pi$
$571$	59.0954	+	102.356i	0.103495	+	0.179258i	−0.809628	+	0.586944i	$0.800331\pi$
$572$		0			0
$573$	−689.423	−	40.7757i	−1.20318	−	0.0711618i
$574$		0			0
$575$		−	77.6684i		−	0.135075i
$576$		0			0
$577$	293.280	+	507.975i	0.508284	+	0.880373i	0.999954	+	0.00959175i	$0.00305319\pi$
$577$	293.280	+	507.975i	0.508284	+	0.880373i	−0.491670	+	0.870781i	$0.663613\pi$
$578$		0			0
$579$	462.469	+	304.766i	0.798737	+	0.526366i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	715.239	−	1238.83i	1.22683	−	2.12492i
$584$		0			0
$585$	647.069	−	277.741i	1.10610	−	0.474771i
$586$		0			0
$587$			809.558i			1.37914i	0.724217	+	0.689572i	$0.242201\pi$
$587$			809.558i			1.37914i	−0.724217	+	0.689572i	$0.757799\pi$
$588$		0			0
$589$	106.081			0.180104
$590$		0			0
$591$	122.916	+	245.294i	0.207979	+	0.415049i
$592$		0			0
$593$	415.964	+	240.157i	0.701457	+	0.404986i	0.807890	−	0.589334i	$-0.200610\pi$
$593$	415.964	+	240.157i	0.701457	+	0.404986i	−0.106433	+	0.994320i	$0.533943\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−510.388	−	336.344i	−0.854921	−	0.563391i
$598$		0			0
$599$	334.882	−	193.344i	0.559069	−	0.322779i	−0.193703	−	0.981060i	$-0.562050\pi$
$599$	334.882	−	193.344i	0.559069	−	0.322779i	0.752772	+	0.658282i	$0.228716\pi$
$600$		0			0
$601$	474.369			0.789299			0.394649	−	0.918832i	$-0.370866\pi$
$601$	474.369			0.789299			0.394649	+	0.918832i	$0.370866\pi$
$602$		0			0
$603$	1100.77	+	130.666i	1.82548	+	0.216693i
$604$		0			0
$605$	−260.710	+	150.521i	−0.430926	+	0.248795i
$606$		0			0
$607$	−217.099	+	376.027i	−0.357660	+	0.619484i	−0.987569	−	0.157184i	$-0.949758\pi$
$607$	−217.099	+	376.027i	−0.357660	+	0.619484i	0.629910	+	0.776668i	$0.283092\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	1259.14	+	726.965i	2.06079	+	1.18980i
$612$		0			0
$613$	−307.391	−	532.417i	−0.501453	−	0.868542i	−0.999999	−	0.00167886i	$-0.999466\pi$
$613$	−307.391	−	532.417i	−0.501453	−	0.868542i	0.498545	−	0.866864i	$-0.333868\pi$
$614$		0			0
$615$	−28.9803	+	489.991i	−0.0471225	+	0.796733i
$616$		0			0
$617$		−	527.697i		−	0.855263i	−0.903953	−	0.427632i	$-0.859348\pi$
$617$		−	527.697i		−	0.855263i	0.903953	−	0.427632i	$-0.140652\pi$
$618$		0			0
$619$	−339.985	−	588.871i	−0.549249	−	0.951327i	−0.998326	−	0.0578339i	$-0.981581\pi$
$619$	−339.985	−	588.871i	−0.549249	−	0.951327i	0.449078	−	0.893493i	$-0.351753\pi$
$620$		0			0
$621$	134.682	−	159.633i	0.216880	−	0.257057i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	136.588	−	236.577i	0.218540	−	0.378522i
$626$		0			0
$627$	131.471	+	262.367i	0.209682	+	0.418448i
$628$		0			0
$629$			264.776i			0.420948i
$630$		0			0
$631$	−929.239			−1.47265			−0.736323	−	0.676631i	$-0.763439\pi$
$631$	−929.239			−1.47265			−0.736323	+	0.676631i	$0.763439\pi$
$632$		0			0
$633$	504.888	−	252.997i	0.797611	−	0.399679i
$634$		0			0
$635$	387.140	+	223.515i	0.609669	+	0.351993i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	249.209	+	186.226i	0.389999	+	0.291434i
$640$		0			0
$641$	691.890	−	399.463i	1.07939	−	0.623187i	0.148659	−	0.988889i	$-0.452504\pi$
$641$	691.890	−	399.463i	1.07939	−	0.623187i	0.930732	+	0.365702i	$0.119171\pi$
$642$		0			0
$643$	−306.051			−0.475973			−0.237987	−	0.971268i	$-0.576487\pi$
$643$	−306.051			−0.475973			−0.237987	+	0.971268i	$0.576487\pi$
$644$		0			0
$645$	−186.782	−	11.0471i	−0.289584	−	0.0171273i
$646$		0			0
$647$	741.774	−	428.263i	1.14648	−	0.661922i	0.198455	−	0.980110i	$-0.436408\pi$
$647$	741.774	−	428.263i	1.14648	−	0.661922i	0.948028	+	0.318188i	$0.103074\pi$
$648$		0			0
$649$	181.225	−	313.891i	0.279237	−	0.483653i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−528.737	−	305.266i	−0.809705	−	0.467483i	0.0371487	−	0.999310i	$-0.488172\pi$
$653$	−528.737	−	305.266i	−0.809705	−	0.467483i	−0.846853	+	0.531827i	$0.821506\pi$
$654$		0			0
$655$	−159.724	−	276.651i	−0.243854	−	0.422367i
$656$		0			0
$657$	−898.539	−	106.661i	−1.36764	−	0.162345i
$658$		0			0
$659$			41.3318i			0.0627190i	0.999508	+	0.0313595i	$0.00998367\pi$
$659$			41.3318i			0.0627190i	−0.999508	+	0.0313595i	$0.990016\pi$
$660$		0			0
$661$	129.643	+	224.547i	0.196131	+	0.339709i	0.947271	−	0.320435i	$-0.103829\pi$
$661$	129.643	+	224.547i	0.196131	+	0.339709i	−0.751140	+	0.660143i	$0.770496\pi$
$662$		0			0
$663$	729.185	−	1106.51i	1.09983	−	1.66894i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−144.295	+	249.927i	−0.216335	+	0.374703i
$668$		0			0
$669$	−413.381	+	207.143i	−0.617909	+	0.309631i
$670$		0			0
$671$			1101.32i			1.64132i
$672$		0			0
$673$	113.498			0.168645			0.0843225	−	0.996439i	$-0.473127\pi$
$673$	113.498			0.168645			0.0843225	+	0.996439i	$0.473127\pi$
$674$		0			0
$675$	−254.994	+	92.0329i	−0.377769	+	0.136345i
$676$		0			0
$677$	−1073.38	−	619.717i	−1.58550	−	0.915387i	−0.994036	−	0.109053i	$-0.965218\pi$
$677$	−1073.38	−	619.717i	−1.58550	−	0.915387i	−0.591461	−	0.806334i	$-0.701449\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	385.608	−	585.143i	0.566238	−	0.859241i
$682$		0			0
$683$	1114.21	−	643.288i	1.63134	−	0.941856i	0.647662	−	0.761927i	$-0.275747\pi$
$683$	1114.21	−	643.288i	1.63134	−	0.941856i	0.983680	−	0.179928i	$-0.0575866\pi$
$684$		0			0
$685$	−594.625			−0.868065
$686$		0			0
$687$	48.7569	−	824.367i	0.0709707	−	1.19995i
$688$		0			0
$689$	1777.20	−	1026.07i	2.57939	−	1.48921i
$690$		0			0
$691$	−444.139	+	769.272i	−0.642748	+	1.11327i	0.342068	+	0.939675i	$0.388873\pi$
$691$	−444.139	+	769.272i	−0.642748	+	1.11327i	−0.984817	+	0.173598i	$0.944461\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	738.635	+	426.451i	1.06278	+	0.613598i
$696$		0			0
$697$	461.867	+	799.976i	0.662649	+	1.14774i
$698$		0			0
$699$	106.170	+	6.27938i	0.151888	+	0.00898338i
$700$		0			0
$701$			270.171i			0.385408i	0.981257	+	0.192704i	$0.0617257\pi$
$701$			270.171i			0.385408i	−0.981257	+	0.192704i	$0.938274\pi$
$702$		0			0
$703$	−42.0588	−	72.8480i	−0.0598276	−	0.103624i
$704$		0			0
$705$	696.365	+	458.903i	0.987752	+	0.650926i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−40.9412	+	70.9122i	−0.0577450	+	0.100017i	−0.893453	−	0.449157i	$-0.851724\pi$
$709$	−40.9412	+	70.9122i	−0.0577450	+	0.100017i	0.835708	+	0.549174i	$0.185058\pi$
$710$		0			0
$711$	−151.164	−	352.176i	−0.212608	−	0.495324i
$712$		0			0
$713$			118.287i			0.165901i
$714$		0			0
$715$	−1103.25			−1.54300
$716$		0			0
$717$	76.4579	+	152.582i	0.106636	+	0.212806i
$718$		0			0
$719$	589.375	+	340.276i	0.819715	+	0.473263i	0.850318	−	0.526269i	$-0.176409\pi$
$719$	589.375	+	340.276i	0.819715	+	0.473263i	−0.0306031	+	0.999532i	$0.509743\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−525.417	−	346.249i	−0.726718	−	0.478906i
$724$		0			0
$725$	324.400	−	187.293i	0.447449	−	0.258335i
$726$		0			0
$727$	−333.344			−0.458520			−0.229260	−	0.973365i	$-0.573631\pi$
$727$	−333.344			−0.458520			−0.229260	+	0.973365i	$0.573631\pi$
$728$		0			0
$729$	−683.682	−	253.021i	−0.937836	−	0.347079i
$730$		0			0
$731$	−304.946	+	176.061i	−0.417163	+	0.240849i
$732$		0			0
$733$	−412.631	+	714.697i	−0.562934	+	0.975030i	0.434304	+	0.900766i	$0.356994\pi$
$733$	−412.631	+	714.697i	−0.562934	+	0.975030i	−0.997239	+	0.0742643i	$0.976339\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−1504.07	−	868.373i	−2.04079	−	1.17825i
$738$		0			0
$739$	−537.383	−	930.775i	−0.727176	−	1.25951i	−0.958072	−	0.286527i	$-0.907499\pi$
$739$	−537.383	−	930.775i	−0.727176	−	1.25951i	0.230896	−	0.972978i	$-0.425834\pi$
$740$		0			0
$741$	−24.8562	+	420.262i	−0.0335442	+	0.567155i
$742$		0			0
$743$		−	171.465i		−	0.230774i	−0.993321	−	0.115387i	$-0.963189\pi$
$743$		−	171.465i		−	0.230774i	0.993321	−	0.115387i	$-0.0368108\pi$
$744$		0			0
$745$	−375.698	−	650.728i	−0.504293	−	0.873461i
$746$		0			0
$747$	−591.949	−	442.345i	−0.792436	−	0.592162i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−176.320	+	305.396i	−0.234781	+	0.406652i	−0.959209	−	0.282698i	$-0.908770\pi$
$751$	−176.320	+	305.396i	−0.234781	+	0.406652i	0.724428	+	0.689350i	$0.242104\pi$
$752$		0			0
$753$	103.638	+	206.823i	0.137634	+	0.274666i
$754$		0			0
$755$			495.385i			0.656139i
$756$		0			0
$757$	624.790			0.825349			0.412675	−	0.910878i	$-0.364595\pi$
$757$	624.790			0.825349			0.412675	+	0.910878i	$0.364595\pi$
$758$		0			0
$759$	−292.556	+	146.598i	−0.385450	+	0.193147i
$760$		0			0
$761$	466.912	+	269.572i	0.613551	+	0.354234i	0.774354	−	0.632753i	$-0.218075\pi$
$761$	466.912	+	269.572i	0.613551	+	0.354234i	−0.160803	+	0.986987i	$0.551408\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	455.005	−	608.892i	0.594778	−	0.795937i
$766$		0			0
$767$	450.300	−	259.981i	0.587093	−	0.338958i
$768$		0			0
$769$	357.409			0.464771			0.232386	−	0.972624i	$-0.425347\pi$
$769$	357.409			0.464771			0.232386	+	0.972624i	$0.425347\pi$
$770$		0			0
$771$	474.176	+	28.0450i	0.615015	+	0.0363748i
$772$		0			0
$773$	−201.530	+	116.354i	−0.260712	+	0.150522i	−0.624659	−	0.780897i	$-0.714762\pi$
$773$	−201.530	+	116.354i	−0.260712	+	0.150522i	0.363947	+	0.931419i	$0.381429\pi$
$774$		0			0
$775$	76.7673	−	132.965i	0.0990546	−	0.171568i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−254.147	−	146.732i	−0.326248	−	0.188359i
$780$		0			0
$781$	−243.712	−	422.122i	−0.312052	−	0.540490i
$782$		0			0
$783$	991.520	+	177.588i	1.26631	+	0.226804i
$784$		0			0
$785$		−	571.198i		−	0.727641i
$786$		0			0
$787$	601.357	+	1041.58i	0.764114	+	1.32348i	0.940714	+	0.339201i	$0.110157\pi$
$787$	601.357	+	1041.58i	0.764114	+	1.32348i	−0.176600	+	0.984283i	$0.556510\pi$
$788$		0			0
$789$	−247.805	+	376.033i	−0.314075	+	0.476595i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−789.966	+	1368.26i	−0.996174	+	1.72542i
$794$		0			0
$795$	1052.37	−	527.339i	1.32374	−	0.663320i
$796$		0			0
$797$		−	1108.42i		−	1.39074i	−0.718654	−	0.695368i	$-0.755242\pi$
$797$		−	1108.42i		−	1.39074i	0.718654	−	0.695368i	$-0.244758\pi$
$798$		0			0
$799$	1569.47			1.96430
$800$		0			0
$801$	349.856	−	150.168i	0.436774	−	0.187476i
$802$		0			0
$803$	1227.75	+	708.840i	1.52895	+	0.882739i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−314.975	+	477.960i	−0.390303	+	0.592268i
$808$		0			0
$809$	−750.921	+	433.544i	−0.928209	+	0.535901i	−0.886245	−	0.463218i	$-0.846695\pi$
$809$	−750.921	+	433.544i	−0.928209	+	0.535901i	−0.0419640	+	0.999119i	$0.513361\pi$
$810$		0			0
$811$	1008.35			1.24335			0.621673	−	0.783277i	$-0.286453\pi$
$811$	1008.35			1.24335			0.621673	+	0.783277i	$0.286453\pi$
$812$		0			0
$813$	−60.6562	+	1025.56i	−0.0746078	+	1.26145i
$814$		0			0
$815$	−704.644	+	406.826i	−0.864594	+	0.499174i
$816$		0			0
$817$	55.9333	−	96.8793i	0.0684618	−	0.118579i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	1139.74	+	658.030i	1.38824	+	0.801499i	0.993116	−	0.117131i	$-0.0373697\pi$
$821$	1139.74	+	658.030i	1.38824	+	0.801499i	0.395120	+	0.918630i	$0.370703\pi$
$822$		0			0
$823$	496.073	+	859.224i	0.602762	+	1.04401i	0.992401	+	0.123047i	$0.0392665\pi$
$823$	496.073	+	859.224i	0.602762	+	1.04401i	−0.389639	+	0.920968i	$0.627400\pi$
$824$		0			0
$825$	423.999	+	25.0772i	0.513938	+	0.0303967i
$826$		0			0
$827$		−	39.2488i		−	0.0474593i	−0.999718	−	0.0237296i	$-0.992446\pi$
$827$		−	39.2488i		−	0.0474593i	0.999718	−	0.0237296i	$-0.00755409\pi$
$828$		0			0
$829$	541.870	+	938.546i	0.653643	+	1.13214i	0.982232	+	0.187670i	$0.0600934\pi$
$829$	541.870	+	938.546i	0.653643	+	1.13214i	−0.328589	+	0.944473i	$0.606573\pi$
$830$		0			0
$831$	233.582	+	153.930i	0.281086	+	0.185235i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	164.554	−	285.016i	0.197071	−	0.341337i
$836$		0			0
$837$	388.351	−	140.164i	0.463979	−	0.167460i
$838$		0			0
$839$		−	570.971i		−	0.680537i	−0.940328	−	0.340269i	$-0.889482\pi$
$839$		−	570.971i		−	0.680537i	0.940328	−	0.340269i	$-0.110518\pi$
$840$		0			0
$841$	−550.838			−0.654980
$842$		0			0
$843$	−337.442	−	673.410i	−0.400287	−	0.798825i
$844$		0			0
$845$	−804.575	−	464.522i	−0.952160	−	0.549730i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	41.7072	+	27.4849i	0.0491250	+	0.0323733i
$850$		0			0
$851$	81.2303	−	46.8984i	0.0954528	−	0.0551097i
$852$		0			0
$853$	381.290			0.446999			0.223499	−	0.974704i	$-0.428252\pi$
$853$	381.290			0.446999			0.223499	+	0.974704i	$0.428252\pi$
$854$		0			0
$855$	−28.4654	+	239.800i	−0.0332929	+	0.280468i
$856$		0			0
$857$	296.640	−	171.265i	0.346138	−	0.199843i	−0.316845	−	0.948477i	$-0.602623\pi$
$857$	296.640	−	171.265i	0.346138	−	0.199843i	0.662983	+	0.748634i	$0.269290\pi$
$858$		0			0
$859$	261.025	−	452.109i	0.303871	−	0.526321i	−0.673138	−	0.739517i	$-0.735054\pi$
$859$	261.025	−	452.109i	0.303871	−	0.526321i	0.977009	+	0.213196i	$0.0683874\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	102.514	+	59.1867i	0.118788	+	0.0685825i	0.558217	−	0.829695i	$-0.311486\pi$
$863$	102.514	+	59.1867i	0.118788	+	0.0685825i	−0.439429	+	0.898278i	$0.644819\pi$
$864$		0			0
$865$	−180.755	−	313.078i	−0.208966	−	0.361940i
$866$		0			0
$867$	33.2686	−	562.495i	0.0383721	−	0.648784i
$868$		0			0
$869$			600.457i			0.690974i
$870$		0			0
$871$	−1245.75	−	2157.70i	−1.43025	−	2.47727i
$872$		0			0
$873$	−260.383	+	348.447i	−0.298263	+	0.399137i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−30.3661	+	52.5956i	−0.0346249	+	0.0599721i	−0.882819	−	0.469714i	$-0.844357\pi$
$877$	−30.3661	+	52.5956i	−0.0346249	+	0.0599721i	0.848194	+	0.529686i	$0.177690\pi$
$878$		0			0
$879$	413.037	+	824.269i	0.469894	+	0.937735i
$880$		0			0
$881$			817.935i			0.928417i	0.885726	+	0.464208i	$0.153661\pi$
$881$			817.935i			0.928417i	−0.885726	+	0.464208i	$0.846339\pi$
$882$		0			0
$883$	19.9764			0.0226233			0.0113117	−	0.999936i	$-0.496399\pi$
$883$	19.9764			0.0226233			0.0113117	+	0.999936i	$0.496399\pi$
$884$		0			0
$885$	266.647	−	133.615i	0.301296	−	0.150978i
$886$		0			0
$887$	−590.636	−	341.004i	−0.665881	−	0.384446i	0.128633	−	0.991692i	$-0.458941\pi$
$887$	−590.636	−	341.004i	−0.665881	−	0.384446i	−0.794514	+	0.607246i	$0.792274\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	827.962	+	786.784i	0.929251	+	0.883034i
$892$		0			0
$893$	−431.810	+	249.305i	−0.483550	+	0.279177i
$894$		0			0
$895$	−760.118			−0.849293
$896$		0			0
$897$	−468.620	−	27.7163i	−0.522430	−	0.0308989i
$898$		0			0
$899$	−494.055	+	285.243i	−0.549560	+	0.317289i
$900$		0			0
$901$	1107.61	−	1918.43i	1.22931	−	2.12923i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−549.404	−	317.198i	−0.607076	−	0.350495i
$906$		0			0
$907$	−324.948	−	562.826i	−0.358266	−	0.620536i	0.629405	−	0.777078i	$-0.283299\pi$
$907$	−324.948	−	562.826i	−0.358266	−	0.620536i	−0.987671	+	0.156542i	$0.949965\pi$
$908$		0			0
$909$	−85.6536	+	721.570i	−0.0942284	+	0.793807i
$910$		0			0
$911$		−	1522.75i		−	1.67152i	−0.549099	−	0.835758i	$-0.685029\pi$
$911$		−	1522.75i		−	1.67152i	0.549099	−	0.835758i	$-0.314971\pi$
$912$		0			0
$913$	578.893	+	1002.67i	0.634056	+	1.09822i
$914$		0			0
$915$	−498.673	+	756.714i	−0.544998	+	0.827010i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	376.826	−	652.682i	0.410039	−	0.710209i	−0.584854	−	0.811138i	$-0.698848\pi$
$919$	376.826	−	652.682i	0.410039	−	0.710209i	0.994894	+	0.100929i	$0.0321816\pi$
$920$		0			0
$921$	−340.024	+	170.384i	−0.369191	+	0.184999i
$922$		0			0
$923$		−	699.249i		−	0.757582i
$924$		0			0
$925$	−121.746			−0.131618
$926$		0			0
$927$	−171.285	−	399.052i	−0.184773	−	0.430477i
$928$		0			0
$929$	−480.731	−	277.550i	−0.517471	−	0.298762i	0.218428	−	0.975853i	$-0.429907\pi$
$929$	−480.731	−	277.550i	−0.517471	−	0.298762i	−0.735900	+	0.677091i	$0.763240\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−542.966	+	823.927i	−0.581957	+	0.883094i
$934$		0			0
$935$	−1031.37	+	595.461i	−1.10307	+	0.636857i
$936$		0			0
$937$	231.357			0.246912			0.123456	−	0.992350i	$-0.460602\pi$
$937$	231.357			0.246912			0.123456	+	0.992350i	$0.460602\pi$
$938$		0			0
$939$	−45.9254	+	776.494i	−0.0489089	+	0.826937i
$940$		0			0
$941$	−455.108	+	262.757i	−0.483643	+	0.279231i	−0.721933	−	0.691963i	$-0.756746\pi$
$941$	−455.108	+	262.757i	−0.483643	+	0.279231i	0.238291	+	0.971194i	$0.423413\pi$
$942$		0			0
$943$	163.616	−	283.391i	0.173505	−	0.300520i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−495.241	−	285.928i	−0.522958	−	0.301930i	0.215186	−	0.976573i	$-0.430964\pi$
$947$	−495.241	−	285.928i	−0.522958	−	0.301930i	−0.738144	+	0.674643i	$0.764298\pi$
$948$		0			0
$949$	1016.88	+	1761.30i	1.07153	+	1.85595i
$950$		0			0
$951$	25.8157	+	1.52686i	0.0271458	+	0.00160553i
$952$		0			0
$953$		−	596.119i		−	0.625518i	−0.949833	−	0.312759i	$-0.898747\pi$
$953$		−	596.119i		−	0.625518i	0.949833	−	0.312759i	$-0.101253\pi$
$954$		0			0
$955$	445.196	+	771.102i	0.466174	+	0.807437i
$956$		0			0
$957$	−1317.78	−	868.417i	−1.37699	−	0.907437i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	363.585	−	629.748i	0.378340	−	0.655305i
$962$		0			0
$963$	−1625.35	+	697.645i	−1.68779	+	0.724450i
$964$		0			0
$965$		−	714.062i		−	0.739961i
$966$		0			0
$967$	1519.98			1.57185			0.785924	−	0.618324i	$-0.212188\pi$
$967$	1519.98			1.57185			0.785924	+	0.618324i	$0.212188\pi$
$968$		0			0
$969$	203.593	+	406.297i	0.210107	+	0.419295i
$970$		0			0
$971$	933.045	+	538.694i	0.960912	+	0.554783i	0.896454	−	0.443138i	$-0.146135\pi$
$971$	933.045	+	538.694i	0.960912	+	0.554783i	0.0644582	+	0.997920i	$0.479468\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	508.780	+	335.285i	0.521825	+	0.343882i
$976$		0			0
$977$	−1559.34	+	900.285i	−1.59605	+	0.921480i	−0.603811	+	0.797127i	$0.706352\pi$
$977$	−1559.34	+	900.285i	−1.59605	+	0.921480i	−0.992238	+	0.124352i	$0.960315\pi$
$978$		0			0
$979$	−596.502			−0.609297
$980$		0			0
$981$	476.280	+	56.5365i	0.485504	+	0.0576315i
$982$		0			0
$983$	444.096	−	256.399i	0.451776	−	0.260833i	−0.256804	−	0.966464i	$-0.582669\pi$
$983$	444.096	−	256.399i	0.451776	−	0.260833i	0.708580	+	0.705630i	$0.249336\pi$
$984$		0			0
$985$	176.864	−	306.338i	0.179557	−	0.311003i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	108.027	+	62.3694i	0.109228	+	0.0630630i
$990$		0			0
$991$	95.8745	+	166.060i	0.0967452	+	0.167568i	0.910336	−	0.413871i	$-0.135823\pi$
$991$	95.8745	+	166.060i	0.0967452	+	0.167568i	−0.813590	+	0.581438i	$0.802490\pi$
$992$		0			0
$993$	84.0222	−	1420.62i	0.0846145	−	1.43064i
$994$		0			0
$995$			788.050i			0.792010i
$996$		0			0
$997$	−838.778	−	1452.81i	−0.841302	−	1.45718i	−0.888794	−	0.458307i	$-0.848456\pi$
$997$	−838.778	−	1452.81i	−0.841302	−	1.45718i	0.0474918	−	0.998872i	$-0.484877\pi$
$998$		0			0
$999$	−250.226	−	211.116i	−0.250477	−	0.211327i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	588.3.p.h.569.4		8
3.2	odd	2	inner	588.3.p.h.569.1		8
7.2	even	3		588.3.c.h.197.4		4
7.3	odd	6		588.3.p.f.557.4		8
7.4	even	3	inner	588.3.p.h.557.1		8
7.5	odd	6		84.3.c.a.29.1	✓	4
7.6	odd	2		588.3.p.f.569.1		8
21.2	odd	6		588.3.c.h.197.3		4
21.5	even	6		84.3.c.a.29.2	yes	4
21.11	odd	6	inner	588.3.p.h.557.4		8
21.17	even	6		588.3.p.f.557.1		8
21.20	even	2		588.3.p.f.569.4		8
28.19	even	6		336.3.d.a.113.4		4
35.12	even	12		2100.3.e.a.449.1		8
35.19	odd	6		2100.3.g.a.701.4		4
35.33	even	12		2100.3.e.a.449.8		8
56.5	odd	6		1344.3.d.a.449.4		4
56.19	even	6		1344.3.d.g.449.1		4
63.5	even	6		2268.3.bg.a.2213.3		8
63.40	odd	6		2268.3.bg.a.2213.2		8
63.47	even	6		2268.3.bg.a.701.2		8
63.61	odd	6		2268.3.bg.a.701.3		8
84.47	odd	6		336.3.d.a.113.3		4
105.47	odd	12		2100.3.e.a.449.7		8
105.68	odd	12		2100.3.e.a.449.2		8
105.89	even	6		2100.3.g.a.701.3		4
168.5	even	6		1344.3.d.a.449.3		4
168.131	odd	6		1344.3.d.g.449.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.3.c.a.29.1	✓	4	7.5	odd	6
84.3.c.a.29.2	yes	4	21.5	even	6
336.3.d.a.113.3		4	84.47	odd	6
336.3.d.a.113.4		4	28.19	even	6
588.3.c.h.197.3		4	21.2	odd	6
588.3.c.h.197.4		4	7.2	even	3
588.3.p.f.557.1		8	21.17	even	6
588.3.p.f.557.4		8	7.3	odd	6
588.3.p.f.569.1		8	7.6	odd	2
588.3.p.f.569.4		8	21.20	even	2
588.3.p.h.557.1		8	7.4	even	3	inner
588.3.p.h.557.4		8	21.11	odd	6	inner
588.3.p.h.569.1		8	3.2	odd	2	inner
588.3.p.h.569.4		8	1.1	even	1	trivial
1344.3.d.a.449.3		4	168.5	even	6
1344.3.d.a.449.4		4	56.5	odd	6
1344.3.d.g.449.1		4	56.19	even	6
1344.3.d.g.449.2		4	168.131	odd	6
2100.3.e.a.449.1		8	35.12	even	12
2100.3.e.a.449.2		8	105.68	odd	12
2100.3.e.a.449.7		8	105.47	odd	12
2100.3.e.a.449.8		8	35.33	even	12
2100.3.g.a.701.3		4	105.89	even	6
2100.3.g.a.701.4		4	35.19	odd	6
2268.3.bg.a.701.2		8	63.47	even	6
2268.3.bg.a.701.3		8	63.61	odd	6
2268.3.bg.a.2213.2		8	63.40	odd	6
2268.3.bg.a.2213.3		8	63.5	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 $\F_{q}$
Belyi maps

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)

\(f(q)\)	\(=\)	\(q+(2.68211 - 1.34399i) q^{3} +(-3.34957 - 1.93387i) q^{5} +(5.38739 - 7.20944i) q^{9} +(-12.2117 + 7.05043i) q^{11} -20.2288 q^{13} +(-11.5830 - 0.685072i) q^{15} +(-18.9108 + 10.9182i) q^{17} +(3.46863 - 6.00784i) q^{19} +(6.69914 + 3.86775i) q^{23} +(-5.02026 - 8.69534i) q^{25} +(4.76013 - 26.5771i) q^{27} +37.3073i q^{29} +(7.64575 + 13.2428i) q^{31} +(-23.2774 + 35.3224i) q^{33} +(6.06275 - 10.5010i) q^{37} +(-54.2557 + 27.1872i) q^{39} -42.3026i q^{41} +16.1255 q^{43} +(-31.9876 + 13.7300i) q^{45} +(-62.2451 - 35.9372i) q^{47} +(-36.0470 + 54.6997i) q^{51} +(-87.8550 + 50.7231i) q^{53} +54.5385 q^{55} +(1.22876 - 20.7755i) q^{57} +(-22.2604 + 12.8520i) q^{59} +(39.0516 - 67.6394i) q^{61} +(67.7576 + 39.1199i) q^{65} +(61.5830 + 106.665i) q^{67} +(23.1660 + 1.37014i) q^{69} +34.5671i q^{71} +(-50.2693 - 87.0689i) q^{73} +(-25.1513 - 16.5747i) q^{75} +(21.2915 - 36.8780i) q^{79} +(-22.9521 - 77.6801i) q^{81} -82.1075i q^{83} +84.4575 q^{85} +(50.1407 + 100.062i) q^{87} +(36.6351 + 21.1513i) q^{89} +(38.3049 + 25.2429i) q^{93} +(-23.2368 + 13.4158i) q^{95} -48.3320 q^{97} +(-14.9595 + 126.023i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 6 q^{3} + 4 q^{9} - 56 q^{13} - 8 q^{15} - 4 q^{19} + 108 q^{25} - 36 q^{27} + 40 q^{31} - 116 q^{33} + 112 q^{37} + 28 q^{39} + 256 q^{43} + 100 q^{45} - 124 q^{51} - 368 q^{55} - 96 q^{57} + 196 q^{61}+ \cdots - 416 q^{99}+O(q^{100}) \) 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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