LMFDB - Embedded newform 448.3.r.f.191.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [448,3,Mod(191,448)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(448, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 0, 2])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("448.191"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 448 = 2^{6} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	448.r (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,0,0,-18] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$12.2071158433$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.752609431977984.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 15x^{10} + 90x^{8} - 247x^{6} + 270x^{4} + 21x^{2} + 49 $ x^12 - 15x^10 + 90x^8 - 247x^6 + 270x^4 + 21*x^2 + 49
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{14} $
Twist minimal:	no (minimal twist has level 224)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			191.2
Root			$0.385124 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	448.191
Dual form			448.3.r.f.319.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.53177 + 0.884367i) q^{3} +(-4.10168 + 7.10432i) q^{5} +(5.46804 + 4.37041i) q^{7} +(-2.93579 + 5.08494i) q^{9} +(-9.10155 + 5.25478i) q^{11} +5.87158 q^{13} -14.5096i q^{15} +(-13.5084 - 23.3972i) q^{17} +(10.6595 + 6.15427i) q^{19} +(-12.2408 - 1.85871i) q^{21} +(36.2985 + 20.9570i) q^{23} +(-21.1475 - 36.6286i) q^{25} -26.3039i q^{27} -36.4235 q^{29} +(-6.61671 + 3.82016i) q^{31} +(9.29431 - 16.0982i) q^{33} +(-53.4770 + 20.9207i) q^{35} +(3.62842 - 6.28461i) q^{37} +(-8.99390 + 5.19263i) q^{39} -48.1667 q^{41} -23.4863i q^{43} +(-24.0833 - 41.7136i) q^{45} +(-51.1971 - 29.5587i) q^{47} +(10.7990 + 47.7952i) q^{49} +(41.3835 + 23.8928i) q^{51} +(-2.03281 - 3.52092i) q^{53} -86.2137i q^{55} -21.7705 q^{57} +(23.2280 - 13.4107i) q^{59} +(0.185012 - 0.320450i) q^{61} +(-38.2763 + 14.9740i) q^{63} +(-24.0833 + 41.7136i) q^{65} +(1.80658 - 1.04303i) q^{67} -74.1346 q^{69} +121.781i q^{71} +(38.5726 + 66.8097i) q^{73} +(64.7863 + 37.4044i) q^{75} +(-72.7332 - 11.0442i) q^{77} +(31.8785 + 18.4050i) q^{79} +(-3.15983 - 5.47298i) q^{81} -98.2951i q^{83} +221.628 q^{85} +(55.7924 - 32.2118i) q^{87} +(15.1729 - 26.2802i) q^{89} +(32.1060 + 25.6612i) q^{91} +(6.75684 - 11.7032i) q^{93} +(-87.4437 + 50.4857i) q^{95} -5.87158 q^{97} -61.7077i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 18 q^{5} - 6 q^{17} - 18 q^{21} + 186 q^{33} + 114 q^{37} + 180 q^{49} + 18 q^{53} - 684 q^{57} - 318 q^{61} + 228 q^{69} + 342 q^{73} - 318 q^{77} - 186 q^{81} + 996 q^{85} + 150 q^{89} + 222 q^{93}+O(q^{100}) $ 12 * q - 18 * q^5 - 6 * q^17 - 18 * q^21 + 186 * q^33 + 114 * q^37 + 180 * q^49 + 18 * q^53 - 684 * q^57 - 318 * q^61 + 228 * q^69 + 342 * q^73 - 318 * q^77 - 186 * q^81 + 996 * q^85 + 150 * q^89 + 222 * q^93

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/448\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.53177	+	0.884367i	−0.510590	+	0.294789i	−0.733076	−	0.680147i	$-0.761916\pi$
$3$	−1.53177	+	0.884367i	−0.510590	+	0.294789i	0.222486	+	0.974936i	$0.428583\pi$
$4$		0			0
$5$	−4.10168	+	7.10432i	−0.820336	+	1.42086i	0.0850965	+	0.996373i	$0.472880\pi$
$5$	−4.10168	+	7.10432i	−0.820336	+	1.42086i	−0.905432	+	0.424491i	$0.860453\pi$
$6$		0			0
$7$	5.46804	+	4.37041i	0.781149	+	0.624345i
$7$	5.46804	+	4.37041i	0.781149	+	0.624345i
$8$		0			0
$9$	−2.93579	+	5.08494i	−0.326199	+	0.564993i
$10$		0			0
$11$	−9.10155	+	5.25478i	−0.827413	+	0.477707i	−0.852966	−	0.521966i	$-0.825199\pi$
$11$	−9.10155	+	5.25478i	−0.827413	+	0.477707i	0.0255528	+	0.999673i	$0.491865\pi$
$12$		0			0
$13$	5.87158			0.451660			0.225830	−	0.974167i	$-0.427491\pi$
$13$	5.87158			0.451660			0.225830	+	0.974167i	$0.427491\pi$
$14$		0			0
$15$		−	14.5096i		−	0.967304i
$16$		0			0
$17$	−13.5084	−	23.3972i	−0.794612	−	1.37631i	−0.923086	−	0.384595i	$-0.874341\pi$
$17$	−13.5084	−	23.3972i	−0.794612	−	1.37631i	0.128474	−	0.991713i	$-0.458992\pi$
$18$		0			0
$19$	10.6595	+	6.15427i	0.561026	+	0.323909i	0.753557	−	0.657382i	$-0.228336\pi$
$19$	10.6595	+	6.15427i	0.561026	+	0.323909i	−0.192531	+	0.981291i	$0.561670\pi$
$20$		0			0
$21$	−12.2408	−	1.85871i	−0.582897	−	0.0885098i
$22$		0			0
$23$	36.2985	+	20.9570i	1.57820	+	0.911173i	0.995111	+	0.0987627i	$0.0314885\pi$
$23$	36.2985	+	20.9570i	1.57820	+	0.911173i	0.583086	+	0.812410i	$0.301845\pi$
$24$		0			0
$25$	−21.1475	−	36.6286i	−0.845902	−	1.46514i
$26$		0			0
$27$		−	26.3039i		−	0.974217i
$28$		0			0
$29$	−36.4235			−1.25598			−0.627992	−	0.778220i	$-0.716123\pi$
$29$	−36.4235			−1.25598			−0.627992	+	0.778220i	$0.716123\pi$
$30$		0			0
$31$	−6.61671	+	3.82016i	−0.213442	+	0.123231i	−0.602910	−	0.797809i	$-0.705992\pi$
$31$	−6.61671	+	3.82016i	−0.213442	+	0.123231i	0.389468	+	0.921040i	$0.372659\pi$
$32$		0			0
$33$	9.29431	−	16.0982i	0.281646	−	0.487825i
$34$		0			0
$35$	−53.4770	+	20.9207i	−1.52791	+	0.597733i
$36$		0			0
$37$	3.62842	−	6.28461i	0.0980654	−	0.169854i	−0.812818	−	0.582517i	$-0.802068\pi$
$37$	3.62842	−	6.28461i	0.0980654	−	0.169854i	0.910884	+	0.412663i	$0.135401\pi$
$38$		0			0
$39$	−8.99390	+	5.19263i	−0.230613	+	0.133144i
$40$		0			0
$41$	−48.1667			−1.17480			−0.587398	−	0.809298i	$-0.699848\pi$
$41$	−48.1667			−1.17480			−0.587398	+	0.809298i	$0.699848\pi$
$42$		0			0
$43$		−	23.4863i		−	0.546193i	−0.961987	−	0.273097i	$-0.911952\pi$
$43$		−	23.4863i		−	0.546193i	0.961987	−	0.273097i	$-0.0880479\pi$
$44$		0			0
$45$	−24.0833	−	41.7136i	−0.535185	−	0.926968i
$46$		0			0
$47$	−51.1971	−	29.5587i	−1.08930	−	0.628907i	−0.155910	−	0.987771i	$-0.549831\pi$
$47$	−51.1971	−	29.5587i	−1.08930	−	0.628907i	−0.933390	+	0.358864i	$0.883164\pi$
$48$		0			0
$49$	10.7990	+	47.7952i	0.220387	+	0.975412i
$50$		0			0
$51$	41.3835	+	23.8928i	0.811441	+	0.468486i
$52$		0			0
$53$	−2.03281	−	3.52092i	−0.0383548	−	0.0664325i	0.846211	−	0.532848i	$-0.178878\pi$
$53$	−2.03281	−	3.52092i	−0.0383548	−	0.0664325i	−0.884566	+	0.466416i	$0.845545\pi$
$54$		0			0
$55$		−	86.2137i		−	1.56752i
$56$		0			0
$57$	−21.7705			−0.381939
$58$		0			0
$59$	23.2280	−	13.4107i	0.393696	−	0.227300i	−0.290064	−	0.957007i	$-0.593677\pi$
$59$	23.2280	−	13.4107i	0.393696	−	0.227300i	0.683760	+	0.729707i	$0.260343\pi$
$60$		0			0
$61$	0.185012	−	0.320450i	0.00303298	−	0.00525328i	−0.864505	−	0.502624i	$-0.832368\pi$
$61$	0.185012	−	0.320450i	0.00303298	−	0.00525328i	0.867538	+	0.497371i	$0.165701\pi$
$62$		0			0
$63$	−38.2763	+	14.9740i	−0.607560	+	0.237683i
$64$		0			0
$65$	−24.0833	+	41.7136i	−0.370513	+	0.641747i
$66$		0			0
$67$	1.80658	−	1.04303i	0.0269638	−	0.0155676i	−0.486458	−	0.873704i	$-0.661711\pi$
$67$	1.80658	−	1.04303i	0.0269638	−	0.0155676i	0.513421	+	0.858137i	$0.328378\pi$
$68$		0			0
$69$	−74.1346			−1.07442
$70$		0			0
$71$			121.781i			1.71523i	0.514291	+	0.857616i	$0.328055\pi$
$71$			121.781i			1.71523i	−0.514291	+	0.857616i	$0.671945\pi$
$72$		0			0
$73$	38.5726	+	66.8097i	0.528392	+	0.915202i	0.999452	+	0.0331005i	$0.0105381\pi$
$73$	38.5726	+	66.8097i	0.528392	+	0.915202i	−0.471060	+	0.882101i	$0.656129\pi$
$74$		0			0
$75$	64.7863	+	37.4044i	0.863817	+	0.498725i
$76$		0			0
$77$	−72.7332	−	11.0442i	−0.944587	−	0.143431i
$78$		0			0
$79$	31.8785	+	18.4050i	0.403525	+	0.232975i	0.688004	−	0.725707i	$-0.258487\pi$
$79$	31.8785	+	18.4050i	0.403525	+	0.232975i	−0.284479	+	0.958682i	$0.591821\pi$
$80$		0			0
$81$	−3.15983	−	5.47298i	−0.0390102	−	0.0675676i
$82$		0			0
$83$		−	98.2951i		−	1.18428i	−0.805836	−	0.592139i	$-0.798284\pi$
$83$		−	98.2951i		−	1.18428i	0.805836	−	0.592139i	$-0.201716\pi$
$84$		0			0
$85$	221.628			2.60739
$86$		0			0
$87$	55.7924	−	32.2118i	0.641292	−	0.370250i
$88$		0			0
$89$	15.1729	−	26.2802i	0.170482	−	0.295283i	−0.768107	−	0.640322i	$-0.778801\pi$
$89$	15.1729	−	26.2802i	0.170482	−	0.295283i	0.938588	+	0.345039i	$0.112134\pi$
$90$		0			0
$91$	32.1060	+	25.6612i	0.352814	+	0.281992i
$92$		0			0
$93$	6.75684	−	11.7032i	0.0726542	−	0.125841i
$94$		0			0
$95$	−87.4437	+	50.4857i	−0.920460	+	0.531428i
$96$		0			0
$97$	−5.87158			−0.0605317			−0.0302659	−	0.999542i	$-0.509635\pi$
$97$	−5.87158			−0.0605317			−0.0302659	+	0.999542i	$0.509635\pi$
$98$		0			0
$99$		−	61.7077i		−	0.623310i
$100$		0			0
$101$	−76.6583	−	132.776i	−0.758993	−	1.31461i	−0.943365	−	0.331757i	$-0.892358\pi$
$101$	−76.6583	−	132.776i	−0.758993	−	1.31461i	0.184372	−	0.982857i	$-0.440975\pi$
$102$		0			0
$103$	−67.3135	−	38.8635i	−0.653529	−	0.377315i	0.136278	−	0.990671i	$-0.456486\pi$
$103$	−67.3135	−	38.8635i	−0.653529	−	0.377315i	−0.789807	+	0.613356i	$0.789819\pi$
$104$		0			0
$105$	63.4128	−	79.3389i	0.603931	−	0.755609i
$106$		0			0
$107$	142.798	+	82.4447i	1.33456	+	0.770511i	0.985995	−	0.166772i	$-0.0533344\pi$
$107$	142.798	+	82.4447i	1.33456	+	0.770511i	0.348569	+	0.937283i	$0.386668\pi$
$108$		0			0
$109$	30.6298	+	53.0524i	0.281008	+	0.486719i	0.971633	−	0.236493i	$-0.0759981\pi$
$109$	30.6298	+	53.0524i	0.281008	+	0.486719i	−0.690626	+	0.723212i	$0.742665\pi$
$110$		0			0
$111$			12.8354i			0.115634i
$112$		0			0
$113$	−9.79509			−0.0866822			−0.0433411	−	0.999060i	$-0.513800\pi$
$113$	−9.79509			−0.0866822			−0.0433411	+	0.999060i	$0.513800\pi$
$114$		0			0
$115$	−297.770	+	171.918i	−2.58930	+	1.49494i
$116$		0			0
$117$	−17.2377	+	29.8566i	−0.147331	+	0.255185i
$118$		0			0
$119$	28.3911	−	186.974i	0.238580	−	1.57121i
$120$		0			0
$121$	−5.27456	+	9.13581i	−0.0435914	+	0.0755026i
$122$		0			0
$123$	73.7802	−	42.5970i	0.599839	−	0.346317i
$124$		0			0
$125$	141.878			1.13502
$126$		0			0
$127$			125.705i			0.989802i	0.868949	+	0.494901i	$0.164796\pi$
$127$			125.705i			0.989802i	−0.868949	+	0.494901i	$0.835204\pi$
$128$		0			0
$129$	20.7705	+	35.9756i	0.161012	+	0.278881i
$130$		0			0
$131$	−30.8455	−	17.8087i	−0.235462	−	0.135944i	0.377627	−	0.925958i	$-0.376740\pi$
$131$	−30.8455	−	17.8087i	−0.235462	−	0.135944i	−0.613089	+	0.790014i	$0.710073\pi$
$132$		0			0
$133$	31.3899	+	80.2382i	0.236014	+	0.603295i
$134$		0			0
$135$	186.871	+	107.890i	1.38423	+	0.799185i
$136$		0			0
$137$	59.7500	+	103.490i	0.436131	+	0.755402i	0.997387	−	0.0722407i	$-0.0230150\pi$
$137$	59.7500	+	103.490i	0.436131	+	0.755402i	−0.561256	+	0.827642i	$0.689682\pi$
$138$		0			0
$139$			47.3989i			0.341000i	0.985358	+	0.170500i	$0.0545382\pi$
$139$			47.3989i			0.341000i	−0.985358	+	0.170500i	$0.945462\pi$
$140$		0			0
$141$	104.563			0.741580
$142$		0			0
$143$	−53.4405	+	30.8539i	−0.373709	+	0.215761i
$144$		0			0
$145$	149.398	−	258.764i	1.03033	−	1.78458i
$146$		0			0
$147$	−58.8100	−	63.6610i	−0.400068	−	0.433068i
$148$		0			0
$149$	−94.6872	+	164.003i	−0.635485	+	1.10069i	0.350928	+	0.936403i	$0.385866\pi$
$149$	−94.6872	+	164.003i	−0.635485	+	1.10069i	−0.986412	+	0.164289i	$0.947467\pi$
$150$		0			0
$151$	212.442	−	122.654i	1.40690	−	0.812276i	0.411816	−	0.911267i	$-0.364895\pi$
$151$	212.442	−	122.654i	1.40690	−	0.812276i	0.995088	+	0.0989909i	$0.0315615\pi$
$152$		0			0
$153$	158.631			1.03681
$154$		0			0
$155$		−	62.6762i		−	0.404363i
$156$		0			0
$157$	110.359	+	191.148i	0.702924	+	1.21750i	0.967435	+	0.253118i	$0.0814562\pi$
$157$	110.359	+	191.148i	0.702924	+	1.21750i	−0.264511	+	0.964383i	$0.585211\pi$
$158$		0			0
$159$	6.22758	+	3.59549i	0.0391672	+	0.0226132i
$160$		0			0
$161$	106.891	+	273.233i	0.663921	+	1.69710i
$162$		0			0
$163$	−235.589	−	136.017i	−1.44533	−	0.834461i	−0.447131	−	0.894469i	$-0.647554\pi$
$163$	−235.589	−	136.017i	−1.44533	−	0.834461i	−0.998198	+	0.0600075i	$0.980888\pi$
$164$		0			0
$165$	76.2446	+	132.059i	0.462088	+	0.800360i
$166$		0			0
$167$			88.8674i			0.532140i	0.963954	+	0.266070i	$0.0857252\pi$
$167$			88.8674i			0.532140i	−0.963954	+	0.266070i	$0.914275\pi$
$168$		0			0
$169$	−134.525			−0.796003
$170$		0			0
$171$	−62.5881	+	36.1353i	−0.366012	+	0.211317i
$172$		0			0
$173$	−159.591	+	276.420i	−0.922491	+	1.59780i	−0.126944	+	0.991910i	$0.540517\pi$
$173$	−159.591	+	276.420i	−0.922491	+	1.59780i	−0.795547	+	0.605891i	$0.792817\pi$
$174$		0			0
$175$	44.4465	−	292.710i	0.253980	−	1.67263i
$176$		0			0
$177$	−23.7200	+	41.0842i	−0.134011	+	0.232114i
$178$		0			0
$179$	120.755	−	69.7179i	0.674608	−	0.389485i	−0.123212	−	0.992380i	$-0.539320\pi$
$179$	120.755	−	69.7179i	0.674608	−	0.389485i	0.797820	+	0.602895i	$0.205986\pi$
$180$		0			0
$181$	73.1328			0.404048			0.202024	−	0.979381i	$-0.435248\pi$
$181$	73.1328			0.404048			0.202024	+	0.979381i	$0.435248\pi$
$182$		0			0
$183$			0.654474i			0.00357636i
$184$		0			0
$185$	29.7652	+	51.5549i	0.160893	+	0.278675i
$186$		0			0
$187$	245.895	+	141.967i	1.31494	+	0.759183i
$188$		0			0
$189$	114.959	−	143.831i	0.608248	−	0.761009i
$190$		0			0
$191$	−111.101	−	64.1442i	−0.581680	−	0.335833i	0.180121	−	0.983645i	$-0.442351\pi$
$191$	−111.101	−	64.1442i	−0.581680	−	0.335833i	−0.761801	+	0.647811i	$0.775685\pi$
$192$		0			0
$193$	−139.769	−	242.087i	−0.724192	−	1.25434i	−0.959306	−	0.282370i	$-0.908879\pi$
$193$	−139.769	−	242.087i	−0.724192	−	1.25434i	0.235113	−	0.971968i	$-0.424454\pi$
$194$		0			0
$195$		−	85.1940i		−	0.436892i
$196$		0			0
$197$	99.0628			0.502857			0.251428	−	0.967876i	$-0.419100\pi$
$197$	99.0628			0.502857			0.251428	+	0.967876i	$0.419100\pi$
$198$		0			0
$199$	−204.657	+	118.159i	−1.02843	+	0.593763i	−0.916534	−	0.399957i	$-0.869025\pi$
$199$	−204.657	+	118.159i	−1.02843	+	0.593763i	−0.111894	+	0.993720i	$0.535692\pi$
$200$		0			0
$201$	−1.84484	+	3.19535i	−0.00917829	+	0.0158973i
$202$		0			0
$203$	−199.165	−	159.186i	−0.981110	−	0.784166i
$204$		0			0
$205$	197.564	−	342.191i	0.963728	−	1.66923i
$206$		0			0
$207$	−213.130	+	123.051i	−1.02961	+	0.594447i
$208$		0			0
$209$	−129.357			−0.618934
$210$		0			0
$211$			389.683i			1.84684i	0.383791	+	0.923420i	$0.374618\pi$
$211$			389.683i			1.84684i	−0.383791	+	0.923420i	$0.625382\pi$
$212$		0			0
$213$	−107.699	−	186.541i	−0.505631	−	0.875779i
$214$		0			0
$215$	166.854	+	96.3333i	0.776066	+	0.448062i
$216$		0			0
$217$	−52.8761	−	8.02896i	−0.243669	−	0.0369998i
$218$		0			0
$219$	−118.169	−	68.2247i	−0.539583	−	0.311528i
$220$		0			0
$221$	−79.3156	−	137.379i	−0.358894	−	0.621623i
$222$		0			0
$223$		−	102.219i		−	0.458379i	−0.973382	−	0.229190i	$-0.926392\pi$
$223$		−	102.219i		−	0.458379i	0.973382	−	0.229190i	$-0.0736076\pi$
$224$		0			0
$225$	248.339			1.10373
$226$		0			0
$227$	−200.037	+	115.491i	−0.881219	+	0.508772i	−0.871060	−	0.491176i	$-0.836567\pi$
$227$	−200.037	+	115.491i	−0.881219	+	0.508772i	−0.0101588	+	0.999948i	$0.503234\pi$
$228$		0			0
$229$	−8.40221	+	14.5530i	−0.0366909	+	0.0635504i	−0.883788	−	0.467888i	$-0.845015\pi$
$229$	−8.40221	+	14.5530i	−0.0366909	+	0.0635504i	0.847097	+	0.531439i	$0.178348\pi$
$230$		0			0
$231$	121.178	−	47.4058i	0.524578	−	0.205220i
$232$		0			0
$233$	60.3074	−	104.455i	0.258830	−	0.448307i	−0.707099	−	0.707115i	$-0.749996\pi$
$233$	60.3074	−	104.455i	0.258830	−	0.448307i	0.965929	+	0.258808i	$0.0833298\pi$
$234$		0			0
$235$	419.988	−	242.480i	1.78718	−	1.03183i
$236$		0			0
$237$	−65.1073			−0.274714
$238$		0			0
$239$			109.863i			0.459679i	0.973229	+	0.229840i	$0.0738202\pi$
$239$			109.863i			0.459679i	−0.973229	+	0.229840i	$0.926180\pi$
$240$		0			0
$241$	−92.4493	−	160.127i	−0.383607	−	0.664427i	0.607968	−	0.793962i	$-0.291985\pi$
$241$	−92.4493	−	160.127i	−0.383607	−	0.664427i	−0.991575	+	0.129535i	$0.958652\pi$
$242$		0			0
$243$	214.699	+	123.956i	0.883533	+	0.510108i
$244$		0			0
$245$	−383.846	−	119.321i	−1.56672	−	0.487026i
$246$		0			0
$247$	62.5881	+	36.1353i	0.253393	+	0.146297i
$248$		0			0
$249$	86.9289	+	150.565i	0.349112	+	0.604680i
$250$		0			0
$251$		−	224.827i		−	0.895724i	−0.894103	−	0.447862i	$-0.852186\pi$
$251$		−	224.827i		−	0.895724i	0.894103	−	0.447862i	$-0.147814\pi$
$252$		0			0
$253$	−440.497			−1.74110
$254$		0			0
$255$	−339.484	+	196.001i	−1.33131	+	0.768631i
$256$		0			0
$257$	−89.2071	+	154.511i	−0.347109	+	0.601211i	−0.985735	−	0.168307i	$-0.946170\pi$
$257$	−89.2071	+	154.511i	−0.347109	+	0.601211i	0.638625	+	0.769518i	$0.279503\pi$
$258$		0			0
$259$	47.3067	−	18.5068i	0.182651	−	0.0714549i
$260$		0			0
$261$	106.932	−	185.211i	0.409700	−	0.709622i
$262$		0			0
$263$	249.946	−	144.307i	0.950367	−	0.548694i	0.0571718	−	0.998364i	$-0.481792\pi$
$263$	249.946	−	144.307i	0.950367	−	0.548694i	0.893195	+	0.449670i	$0.148458\pi$
$264$		0			0
$265$	33.3517			0.125855
$266$		0			0
$267$			53.6736i			0.201025i
$268$		0			0
$269$	112.649	+	195.113i	0.418768	+	0.725328i	0.995816	−	0.0913828i	$-0.0291287\pi$
$269$	112.649	+	195.113i	0.418768	+	0.725328i	−0.577048	+	0.816710i	$0.695795\pi$
$270$		0			0
$271$	−169.467	−	97.8417i	−0.625339	−	0.361039i	0.153606	−	0.988132i	$-0.450911\pi$
$271$	−169.467	−	97.8417i	−0.625339	−	0.361039i	−0.778945	+	0.627093i	$0.784245\pi$
$272$		0			0
$273$	−71.8730	−	10.9135i	−0.263271	−	0.0399763i
$274$		0			0
$275$	384.951	+	222.251i	1.39982	+	0.808187i
$276$		0			0
$277$	−67.8142	−	117.458i	−0.244817	−	0.424035i	0.717263	−	0.696802i	$-0.245394\pi$
$277$	−67.8142	−	117.458i	−0.244817	−	0.424035i	−0.962080	+	0.272767i	$0.912061\pi$
$278$		0			0
$279$		−	44.8607i		−	0.160791i
$280$		0			0
$281$	−372.495			−1.32560			−0.662802	−	0.748795i	$-0.730633\pi$
$281$	−372.495			−1.32560			−0.662802	+	0.748795i	$0.730633\pi$
$282$		0			0
$283$	−248.903	+	143.704i	−0.879517	+	0.507789i	−0.870499	−	0.492170i	$-0.836204\pi$
$283$	−248.903	+	143.704i	−0.879517	+	0.507789i	−0.00901792	+	0.999959i	$0.502871\pi$
$284$		0			0
$285$	89.2957	−	154.665i	0.313318	−	0.542683i
$286$		0			0
$287$	−263.377	−	210.508i	−0.917691	−	0.733478i
$288$		0			0
$289$	−220.454	+	381.837i	−0.762815	+	1.32123i
$290$		0			0
$291$	8.99390	−	5.19263i	0.0309069	−	0.0178441i
$292$		0			0
$293$	−131.947			−0.450332			−0.225166	−	0.974320i	$-0.572292\pi$
$293$	−131.947			−0.450332			−0.225166	+	0.974320i	$0.572292\pi$
$294$		0			0
$295$			220.026i			0.745850i
$296$		0			0
$297$	138.221	+	239.406i	0.465391	+	0.806081i
$298$		0			0
$299$	213.130	+	123.051i	0.712809	+	0.411540i
$300$		0			0
$301$	102.645	−	128.424i	0.341013	−	0.426658i
$302$		0			0
$303$	234.845	+	135.588i	0.775068	+	0.447486i
$304$		0			0
$305$	1.51772	+	2.62877i	0.00497613	+	0.00861891i
$306$		0			0
$307$			47.8253i			0.155783i	0.996962	+	0.0778913i	$0.0248187\pi$
$307$			47.8253i			0.155783i	−0.996962	+	0.0778913i	$0.975181\pi$
$308$		0			0
$309$	137.478			0.444913
$310$		0			0
$311$	−197.020	+	113.749i	−0.633505	+	0.365754i	−0.782108	−	0.623143i	$-0.785856\pi$
$311$	−197.020	+	113.749i	−0.633505	+	0.365754i	0.148604	+	0.988897i	$0.452522\pi$
$312$		0			0
$313$	−61.5483	+	106.605i	−0.196640	+	0.340591i	−0.947437	−	0.319943i	$-0.896336\pi$
$313$	−61.5483	+	106.605i	−0.196640	+	0.340591i	0.750797	+	0.660533i	$0.229670\pi$
$314$		0			0
$315$	50.6168	−	333.346i	0.160688	−	1.05824i
$316$		0			0
$317$	−240.148	+	415.948i	−0.757563	+	1.31214i	0.186527	+	0.982450i	$0.440277\pi$
$317$	−240.148	+	415.948i	−0.757563	+	1.31214i	−0.944090	+	0.329688i	$0.893056\pi$
$318$		0			0
$319$	331.510	−	191.398i	1.03922	−	0.599992i
$320$		0			0
$321$	−291.646			−0.908553
$322$		0			0
$323$		−	332.537i		−	1.02953i
$324$		0			0
$325$	−124.169	−	215.068i	−0.382060	−	0.661747i
$326$		0			0
$327$	−93.8356	−	54.1760i	−0.286959	−	0.165676i
$328$		0			0
$329$	−150.764	−	385.380i	−0.458250	−	1.17137i
$330$		0			0
$331$	410.836	+	237.196i	1.24119	+	0.716604i	0.969337	−	0.245733i	$-0.0790287\pi$
$331$	410.836	+	237.196i	1.24119	+	0.716604i	0.271857	+	0.962338i	$0.412362\pi$
$332$		0			0
$333$	21.3046	+	36.9006i	0.0639777	+	0.110813i
$334$		0			0
$335$			17.1126i			0.0510825i
$336$		0			0
$337$	−305.861			−0.907599			−0.453799	−	0.891104i	$-0.649932\pi$
$337$	−305.861			−0.907599			−0.453799	+	0.891104i	$0.649932\pi$
$338$		0			0
$339$	15.0038	−	8.66246i	0.0442590	−	0.0255530i
$340$		0			0
$341$	40.1482	−	69.5387i	0.117737	−	0.203926i
$342$		0			0
$343$	−149.836	+	308.542i	−0.436838	+	0.899540i
$344$		0			0
$345$	304.076	−	526.676i	0.881381	−	1.52660i
$346$		0			0
$347$	−596.404	+	344.334i	−1.71874	+	0.992317i	−0.797511	+	0.603305i	$0.793850\pi$
$347$	−596.404	+	344.334i	−1.71874	+	0.992317i	−0.921233	+	0.389012i	$0.872816\pi$
$348$		0			0
$349$	−128.861			−0.369228			−0.184614	−	0.982811i	$-0.559104\pi$
$349$	−128.861			−0.369228			−0.184614	+	0.982811i	$0.559104\pi$
$350$		0			0
$351$		−	154.445i		−	0.440015i
$352$		0			0
$353$	47.5462	+	82.3524i	0.134692	+	0.233293i	0.925480	−	0.378797i	$-0.123662\pi$
$353$	47.5462	+	82.3524i	0.134692	+	0.233293i	−0.790788	+	0.612090i	$0.790329\pi$
$354$		0			0
$355$	−865.174	−	499.508i	−2.43711	−	1.40707i
$356$		0			0
$357$	121.865	+	311.510i	0.341360	+	0.872576i
$358$		0			0
$359$	31.3627	+	18.1072i	0.0873612	+	0.0504380i	0.543044	−	0.839704i	$-0.317272\pi$
$359$	31.3627	+	18.1072i	0.0873612	+	0.0504380i	−0.455683	+	0.890142i	$0.650605\pi$
$360$		0			0
$361$	−104.750	−	181.432i	−0.290166	−	0.502583i
$362$		0			0
$363$		−	18.6586i		−	0.0514011i
$364$		0			0
$365$	−632.850			−1.73384
$366$		0			0
$367$	−20.6725	+	11.9353i	−0.0563284	+	0.0325212i	−0.527900	−	0.849307i	$-0.677020\pi$
$367$	−20.6725	+	11.9353i	−0.0563284	+	0.0325212i	0.471571	+	0.881828i	$0.343687\pi$
$368$		0			0
$369$	141.407	−	244.924i	0.383217	−	0.663752i
$370$		0			0
$371$	4.27242	−	28.1368i	0.0115160	−	0.0758403i
$372$		0			0
$373$	−85.6886	+	148.417i	−0.229728	+	0.397901i	−0.957727	−	0.287677i	$-0.907117\pi$
$373$	−85.6886	+	148.417i	−0.229728	+	0.397901i	0.727999	+	0.685578i	$0.240450\pi$
$374$		0			0
$375$	−217.324	+	125.472i	−0.579531	+	0.334592i
$376$		0			0
$377$	−213.864			−0.567277
$378$		0			0
$379$		−	22.8798i		−	0.0603689i	−0.999544	−	0.0301845i	$-0.990391\pi$
$379$		−	22.8798i		−	0.0603689i	0.999544	−	0.0301845i	$-0.00960947\pi$
$380$		0			0
$381$	−111.169	−	192.551i	−0.291783	−	0.505383i
$382$		0			0
$383$	489.108	+	282.387i	1.27705	+	0.737302i	0.976304	−	0.216404i	$-0.0694327\pi$
$383$	489.108	+	282.387i	1.27705	+	0.737302i	0.300741	+	0.953706i	$0.402766\pi$
$384$		0			0
$385$	376.789	−	471.420i	0.978674	−	1.22447i
$386$		0			0
$387$	119.426	+	68.9509i	0.308595	+	0.178168i
$388$		0			0
$389$	59.7609	+	103.509i	0.153627	+	0.266090i	0.932558	−	0.361020i	$-0.117571\pi$
$389$	59.7609	+	103.509i	0.153627	+	0.266090i	−0.778931	+	0.627109i	$0.784238\pi$
$390$		0			0
$391$		−	1132.38i		−	2.89611i
$392$		0			0
$393$	62.9975			0.160299
$394$		0			0
$395$	−261.511	+	150.983i	−0.662052	+	0.382236i
$396$		0			0
$397$	262.734	−	455.069i	0.661799	−	1.14627i	−0.318343	−	0.947975i	$-0.603126\pi$
$397$	262.734	−	455.069i	0.661799	−	1.14627i	0.980143	−	0.198294i	$-0.0635402\pi$
$398$		0			0
$399$	−119.042	−	95.1462i	−0.298351	−	0.238462i
$400$		0			0
$401$	83.2528	−	144.198i	0.207613	−	0.359596i	−0.743349	−	0.668904i	$-0.766764\pi$
$401$	83.2528	−	144.198i	0.207613	−	0.359596i	0.950962	+	0.309307i	$0.100097\pi$
$402$		0			0
$403$	−38.8505	+	22.4304i	−0.0964032	+	0.0556584i
$404$		0			0
$405$	51.8424			0.128006
$406$		0			0
$407$			76.2662i			0.187386i
$408$		0			0
$409$	−237.672	−	411.660i	−0.581106	−	1.00650i	−0.995349	−	0.0963383i	$-0.969287\pi$
$409$	−237.672	−	411.660i	−0.581106	−	1.00650i	0.414243	−	0.910166i	$-0.364046\pi$
$410$		0			0
$411$	−183.046	−	105.682i	−0.445368	−	0.257134i
$412$		0			0
$413$	185.622	+	28.1858i	0.449449	+	0.0682465i
$414$		0			0
$415$	698.319	+	403.175i	1.68270	+	0.971506i
$416$		0			0
$417$	−41.9181	−	72.6042i	−0.100523	−	0.174111i
$418$		0			0
$419$		−	370.547i		−	0.884360i	−0.896926	−	0.442180i	$-0.854205\pi$
$419$		−	370.547i		−	0.884360i	0.896926	−	0.442180i	$-0.145795\pi$
$420$		0			0
$421$	248.779			0.590924			0.295462	−	0.955355i	$-0.404526\pi$
$421$	248.779			0.590924			0.295462	+	0.955355i	$0.404526\pi$
$422$		0			0
$423$	300.608	−	173.556i	0.710657	−	0.410298i
$424$		0			0
$425$	−571.339	+	989.588i	−1.34433	+	2.32844i
$426$		0			0
$427$	2.41215	−	0.943656i	0.00564907	−	0.00220997i
$428$		0			0
$429$	54.5723	−	94.5220i	0.127208	−	0.220331i
$430$		0			0
$431$	57.1732	−	33.0090i	0.132653	−	0.0765870i	−0.432205	−	0.901775i	$-0.642264\pi$
$431$	57.1732	−	33.0090i	0.132653	−	0.0765870i	0.564858	+	0.825188i	$0.308931\pi$
$432$		0			0
$433$	753.932			1.74118			0.870591	−	0.492007i	$-0.163737\pi$
$433$	753.932			1.74118			0.870591	+	0.492007i	$0.163737\pi$
$434$		0			0
$435$			528.489i			1.21492i
$436$		0			0
$437$	257.950	+	446.782i	0.590274	+	1.02238i
$438$		0			0
$439$	−32.2488	−	18.6188i	−0.0734596	−	0.0424119i	0.462820	−	0.886452i	$-0.346838\pi$
$439$	−32.2488	−	18.6188i	−0.0734596	−	0.0424119i	−0.536280	+	0.844040i	$0.680171\pi$
$440$		0			0
$441$	−274.739	−	85.4046i	−0.622991	−	0.193661i
$442$		0			0
$443$	486.899	+	281.111i	1.09909	+	0.634562i	0.935983	−	0.352045i	$-0.114514\pi$
$443$	486.899	+	281.111i	1.09909	+	0.634562i	0.163111	+	0.986608i	$0.447847\pi$
$444$		0			0
$445$	124.469	+	215.586i	0.279705	+	0.484463i
$446$		0			0
$447$		−	334.953i		−	0.749335i
$448$		0			0
$449$	265.855			0.592105			0.296052	−	0.955172i	$-0.404330\pi$
$449$	265.855			0.592105			0.296052	+	0.955172i	$0.404330\pi$
$450$		0			0
$451$	438.391	−	253.105i	0.972043	−	0.561209i
$452$		0			0
$453$	−216.942	+	375.754i	−0.478900	+	0.829480i
$454$		0			0
$455$	−313.994	+	122.837i	−0.690097	+	0.269972i
$456$		0			0
$457$	33.0409	−	57.2285i	0.0722995	−	0.125226i	−0.827609	−	0.561305i	$-0.810300\pi$
$457$	33.0409	−	57.2285i	0.0722995	−	0.125226i	0.899909	+	0.436078i	$0.143633\pi$
$458$		0			0
$459$	−615.438	+	355.323i	−1.34082	+	0.774124i
$460$		0			0
$461$	−59.0572			−0.128107			−0.0640534	−	0.997946i	$-0.520403\pi$
$461$	−59.0572			−0.128107			−0.0640534	+	0.997946i	$0.520403\pi$
$462$		0			0
$463$			390.109i			0.842569i	0.906929	+	0.421285i	$0.138421\pi$
$463$			390.109i			0.842569i	−0.906929	+	0.421285i	$0.861579\pi$
$464$		0			0
$465$	55.4288	+	96.0055i	0.119202	+	0.206463i
$466$		0			0
$467$	312.811	+	180.601i	0.669830	+	0.386727i	0.796012	−	0.605280i	$-0.206939\pi$
$467$	312.811	+	180.601i	0.669830	+	0.386727i	−0.126182	+	0.992007i	$0.540272\pi$
$468$		0			0
$469$	14.4369	+	2.19217i	0.0307823	+	0.00467413i
$470$		0			0
$471$	−338.089	−	195.196i	−0.717812	−	0.414429i
$472$		0			0
$473$	123.415	+	213.762i	0.260921	+	0.451928i
$474$		0			0
$475$		−	520.591i		−	1.09598i
$476$		0			0
$477$	23.8716			0.0500452
$478$		0			0
$479$	83.4872	−	48.2014i	0.174295	−	0.100629i	−0.410315	−	0.911944i	$-0.634581\pi$
$479$	83.4872	−	48.2014i	0.174295	−	0.100629i	0.584609	+	0.811315i	$0.301248\pi$
$480$		0			0
$481$	21.3046	−	36.9006i	0.0442922	−	0.0767164i
$482$		0			0
$483$	−405.371	−	323.999i	−0.839278	−	0.670805i
$484$		0			0
$485$	24.0833	−	41.7136i	0.0496564	−	0.0860073i
$486$		0			0
$487$	−49.0925	+	28.3435i	−0.100806	+	0.0582003i	−0.549555	−	0.835457i	$-0.685203\pi$
$487$	−49.0925	+	28.3435i	−0.100806	+	0.0582003i	0.448750	+	0.893658i	$0.351870\pi$
$488$		0			0
$489$	481.156			0.983960
$490$		0			0
$491$			559.896i			1.14032i	0.821534	+	0.570159i	$0.193118\pi$
$491$			559.896i			1.14032i	−0.821534	+	0.570159i	$0.806882\pi$
$492$		0			0
$493$	492.023	+	852.209i	0.998019	+	1.72862i
$494$		0			0
$495$	438.391	+	253.105i	0.885639	+	0.511324i
$496$		0			0
$497$	−532.235	+	665.906i	−1.07090	+	1.33985i
$498$		0			0
$499$	322.766	+	186.349i	0.646826	+	0.373445i	0.787239	−	0.616648i	$-0.211510\pi$
$499$	322.766	+	186.349i	0.646826	+	0.373445i	−0.140413	+	0.990093i	$0.544843\pi$
$500$		0			0
$501$	−78.5914	−	136.124i	−0.156869	−	0.271705i
$502$		0			0
$503$			648.033i			1.28834i	0.764884	+	0.644168i	$0.222796\pi$
$503$			648.033i			1.28834i	−0.764884	+	0.644168i	$0.777204\pi$
$504$		0			0
$505$	1257.71			2.49052
$506$		0			0
$507$	206.061	−	118.969i	0.406431	−	0.234653i
$508$		0			0
$509$	210.281	−	364.217i	0.413125	−	0.715554i	−0.582104	−	0.813114i	$-0.697770\pi$
$509$	210.281	−	364.217i	0.413125	−	0.715554i	0.995230	+	0.0975601i	$0.0311038\pi$
$510$		0			0
$511$	−81.0694	+	533.897i	−0.158649	+	1.04481i
$512$		0			0
$513$	161.881	−	280.386i	0.315558	−	0.546562i
$514$		0			0
$515$	552.197	−	318.811i	1.07223	−	0.619050i
$516$		0			0
$517$	621.297			1.20173
$518$		0			0
$519$		−	564.548i		−	1.08776i
$520$		0			0
$521$	−138.832	−	240.464i	−0.266472	−	0.461543i	0.701476	−	0.712693i	$-0.252525\pi$
$521$	−138.832	−	240.464i	−0.266472	−	0.461543i	−0.967948	+	0.251150i	$0.919191\pi$
$522$		0			0
$523$	−565.536	−	326.512i	−1.08133	−	0.624307i	−0.150076	−	0.988674i	$-0.547952\pi$
$523$	−565.536	−	326.512i	−1.08133	−	0.624307i	−0.931255	+	0.364368i	$0.881285\pi$
$524$		0			0
$525$	190.782	+	487.672i	0.363393	+	0.928898i
$526$		0			0
$527$	178.762	+	103.208i	0.339207	+	0.195841i
$528$		0			0
$529$	613.889	+	1063.29i	1.16047	+	2.01000i
$530$		0			0
$531$			157.484i			0.296580i
$532$		0			0
$533$	−282.814			−0.530609
$534$		0			0
$535$	−1171.43	+	676.323i	−2.18958	+	1.26416i
$536$		0			0
$537$	−123.312	+	213.583i	−0.229632	+	0.397734i
$538$		0			0
$539$	−349.441	−	378.264i	−0.648313	−	0.701789i
$540$		0			0
$541$	133.144	−	230.612i	0.246107	−	0.426269i	−0.716336	−	0.697756i	$-0.754182\pi$
$541$	133.144	−	230.612i	0.246107	−	0.426269i	0.962442	+	0.271487i	$0.0875153\pi$
$542$		0			0
$543$	−112.023	+	64.6762i	−0.206303	+	0.119109i
$544$		0			0
$545$	−502.535			−0.922082
$546$		0			0
$547$			291.492i			0.532892i	0.963850	+	0.266446i	$0.0858493\pi$
$547$			291.492i			0.532892i	−0.963850	+	0.266446i	$0.914151\pi$
$548$		0			0
$549$	1.08631	+	1.88155i	0.00197871	+	0.00342723i
$550$		0			0
$551$	−388.256	−	224.160i	−0.704640	−	0.406824i
$552$		0			0
$553$	93.8752	+	239.962i	0.169756	+	0.433927i
$554$		0			0
$555$	−91.1869	−	52.6468i	−0.164301	−	0.0948591i
$556$		0			0
$557$	−288.069	−	498.951i	−0.517180	−	0.895783i	−0.999801	−	0.0199531i	$-0.993648\pi$
$557$	−288.069	−	498.951i	−0.517180	−	0.895783i	0.482621	−	0.875830i	$-0.339685\pi$
$558$		0			0
$559$		−	137.902i		−	0.246694i
$560$		0			0
$561$	−502.205			−0.895196
$562$		0			0
$563$	498.094	−	287.575i	0.884714	−	0.510790i	0.0125043	−	0.999922i	$-0.496020\pi$
$563$	498.094	−	287.575i	0.884714	−	0.510790i	0.872210	+	0.489132i	$0.162686\pi$
$564$		0			0
$565$	40.1763	−	69.5874i	0.0711085	−	0.123164i
$566$		0			0
$567$	6.64112	−	43.7362i	0.0117127	−	0.0771362i
$568$		0			0
$569$	−428.609	+	742.373i	−0.753268	+	1.30470i	0.192963	+	0.981206i	$0.438190\pi$
$569$	−428.609	+	742.373i	−0.753268	+	1.30470i	−0.946231	+	0.323492i	$0.895143\pi$
$570$		0			0
$571$	255.486	−	147.505i	0.447436	−	0.258327i	−0.259311	−	0.965794i	$-0.583495\pi$
$571$	255.486	−	147.505i	0.447436	−	0.258327i	0.706747	+	0.707467i	$0.250162\pi$
$572$		0			0
$573$	226.908			0.396000
$574$		0			0
$575$		−	1772.75i		−	3.08305i
$576$		0			0
$577$	283.201	+	490.519i	0.490817	+	0.850119i	0.999944	−	0.0105718i	$-0.00336517\pi$
$577$	283.201	+	490.519i	0.490817	+	0.850119i	−0.509127	+	0.860691i	$0.670032\pi$
$578$		0			0
$579$	428.188	+	247.214i	0.739530	+	0.426968i
$580$		0			0
$581$	429.590	−	537.482i	0.739398	−	0.925098i
$582$		0			0
$583$	37.0034	+	21.3639i	0.0634706	+	0.0366448i
$584$		0			0
$585$	−141.407	−	244.924i	−0.241722	−	0.418674i
$586$		0			0
$587$			882.011i			1.50257i	0.659975	+	0.751287i	$0.270567\pi$
$587$			882.011i			1.50257i	−0.659975	+	0.751287i	$0.729433\pi$
$588$		0			0
$589$	−94.0411			−0.159662
$590$		0			0
$591$	−151.741	+	87.6079i	−0.256754	+	0.148237i
$592$		0			0
$593$	462.541	−	801.145i	0.780003	−	1.35100i	−0.151937	−	0.988390i	$-0.548551\pi$
$593$	462.541	−	801.145i	0.780003	−	1.35100i	0.931939	−	0.362614i	$-0.118116\pi$
$594$		0			0
$595$	1211.87	+	968.608i	2.03676	+	1.62791i
$596$		0			0
$597$	208.992	−	361.984i	0.350070	−	0.606339i
$598$		0			0
$599$	131.504	−	75.9240i	0.219540	−	0.126751i	−0.386197	−	0.922416i	$-0.626212\pi$
$599$	131.504	−	75.9240i	0.219540	−	0.126751i	0.605737	+	0.795665i	$0.292878\pi$
$600$		0			0
$601$	485.178			0.807284			0.403642	−	0.914917i	$-0.367744\pi$
$601$	485.178			0.807284			0.403642	+	0.914917i	$0.367744\pi$
$602$		0			0
$603$			12.2484i			0.0203125i
$604$		0			0
$605$	−43.2691	−	74.9443i	−0.0715192	−	0.123875i
$606$		0			0
$607$	327.526	+	189.097i	0.539581	+	0.311527i	0.744909	−	0.667166i	$-0.232493\pi$
$607$	327.526	+	189.097i	0.539581	+	0.311527i	−0.205328	+	0.978693i	$0.565826\pi$
$608$		0			0
$609$	445.854	+	67.7006i	0.732108	+	0.111167i
$610$		0			0
$611$	−300.608	−	173.556i	−0.491993	−	0.284052i
$612$		0			0
$613$	−307.141	−	531.983i	−0.501045	−	0.867836i	−0.999999	−	0.00120729i	$-0.999616\pi$
$613$	−307.141	−	531.983i	−0.501045	−	0.867836i	0.498954	−	0.866628i	$-0.333718\pi$
$614$		0			0
$615$			698.877i			1.13639i
$616$		0			0
$617$	1193.13			1.93377			0.966883	−	0.255220i	$-0.0821479\pi$
$617$	1193.13			1.93377			0.966883	+	0.255220i	$0.0821479\pi$
$618$		0			0
$619$	423.076	−	244.263i	0.683483	−	0.394609i	−0.117683	−	0.993051i	$-0.537547\pi$
$619$	423.076	−	244.263i	0.683483	−	0.394609i	0.801166	+	0.598442i	$0.204213\pi$
$620$		0			0
$621$	551.250	−	954.792i	0.887680	−	1.53751i
$622$		0			0
$623$	197.821	−	77.3895i	0.317530	−	0.124221i
$624$		0			0
$625$	−53.2486	+	92.2293i	−0.0851978	+	0.147567i
$626$		0			0
$627$	198.145	−	114.399i	0.316021	−	0.182455i
$628$		0			0
$629$	−196.057			−0.311696
$630$		0			0
$631$			384.907i			0.609995i	0.952353	+	0.304998i	$0.0986557\pi$
$631$			384.907i			0.609995i	−0.952353	+	0.304998i	$0.901344\pi$
$632$		0			0
$633$	−344.623	−	596.905i	−0.544428	−	0.942977i
$634$		0			0
$635$	−893.048	−	515.601i	−1.40637	−	0.811970i
$636$		0			0
$637$	63.4070	+	280.633i	0.0995401	+	0.440555i
$638$		0			0
$639$	−619.251	−	357.525i	−0.969093	−	0.559506i
$640$		0			0
$641$	−546.981	−	947.399i	−0.853325	−	1.47800i	−0.878191	−	0.478311i	$-0.841249\pi$
$641$	−546.981	−	947.399i	−0.853325	−	1.47800i	0.0248661	−	0.999691i	$-0.492084\pi$
$642$		0			0
$643$		−	866.317i		−	1.34731i	−0.739048	−	0.673653i	$-0.764724\pi$
$643$		−	866.317i		−	1.34731i	0.739048	−	0.673653i	$-0.235276\pi$
$644$		0			0
$645$	−340.776			−0.528335
$646$		0			0
$647$	32.2070	−	18.5947i	0.0497790	−	0.0287399i	−0.474904	−	0.880038i	$-0.657517\pi$
$647$	32.2070	−	18.5947i	0.0497790	−	0.0287399i	0.524683	+	0.851298i	$0.324184\pi$
$648$		0			0
$649$	−140.941	+	244.117i	−0.217166	+	0.376143i
$650$		0			0
$651$	88.0945	−	34.4634i	0.135322	−	0.0529391i
$652$		0			0
$653$	−547.956	+	949.088i	−0.839137	+	1.45343i	0.0514806	+	0.998674i	$0.483606\pi$
$653$	−547.956	+	949.088i	−0.839137	+	1.45343i	−0.890617	+	0.454754i	$0.849727\pi$
$654$		0			0
$655$	253.037	−	146.091i	0.386315	−	0.223039i
$656$		0			0
$657$	−452.964			−0.689443
$658$		0			0
$659$			13.9021i			0.0210957i	0.999944	+	0.0105479i	$0.00335755\pi$
$659$			13.9021i			0.0210957i	−0.999944	+	0.0105479i	$0.996642\pi$
$660$		0			0
$661$	−50.8103	−	88.0061i	−0.0768689	−	0.133141i	0.825029	−	0.565091i	$-0.191159\pi$
$661$	−50.8103	−	88.0061i	−0.0768689	−	0.133141i	−0.901897	+	0.431950i	$0.857826\pi$
$662$		0			0
$663$	242.986	+	140.288i	0.366495	+	0.211596i
$664$		0			0
$665$	−698.789	−	106.108i	−1.05081	−	0.159560i
$666$		0			0
$667$	−1322.12	−	763.326i	−1.98219	−	1.14442i
$668$		0			0
$669$	90.3988	+	156.575i	0.135125	+	0.234044i
$670$		0			0
$671$			3.88879i			0.00579551i
$672$		0			0
$673$	−71.7077			−0.106549			−0.0532747	−	0.998580i	$-0.516966\pi$
$673$	−71.7077			−0.106549			−0.0532747	+	0.998580i	$0.516966\pi$
$674$		0			0
$675$	−963.475	+	556.262i	−1.42737	+	0.824092i
$676$		0			0
$677$	−524.998	+	909.323i	−0.775477	+	1.34317i	0.159049	+	0.987271i	$0.449157\pi$
$677$	−524.998	+	909.323i	−0.775477	+	1.34317i	−0.934526	+	0.355895i	$0.884176\pi$
$678$		0			0
$679$	−32.1060	−	25.6612i	−0.0472843	−	0.0377927i
$680$		0			0
$681$	204.273	−	353.812i	0.299961	−	0.519547i
$682$		0			0
$683$	−116.044	+	66.9981i	−0.169904	+	0.0980939i	−0.582540	−	0.812802i	$-0.697941\pi$
$683$	−116.044	+	66.9981i	−0.169904	+	0.0980939i	0.412637	+	0.910896i	$0.364608\pi$
$684$		0			0
$685$	−980.301			−1.43110
$686$		0			0
$687$		−	29.7225i		−	0.0432643i
$688$		0			0
$689$	−11.9358	−	20.6734i	−0.0173233	−	0.0300049i
$690$		0			0
$691$	390.403	+	225.399i	0.564982	+	0.326193i	0.755143	−	0.655560i	$-0.227568\pi$
$691$	390.403	+	225.399i	0.564982	+	0.326193i	−0.190161	+	0.981753i	$0.560901\pi$
$692$		0			0
$693$	269.688	−	337.420i	0.389161	−	0.486898i
$694$		0			0
$695$	−336.737	−	194.415i	−0.484514	−	0.279734i
$696$		0			0
$697$	650.654	+	1126.97i	0.933507	+	1.61688i
$698$		0			0
$699$			213.335i			0.305201i
$700$		0			0
$701$	524.776			0.748611			0.374305	−	0.927306i	$-0.377881\pi$
$701$	524.776			0.748611			0.374305	+	0.927306i	$0.377881\pi$
$702$		0			0
$703$	77.3543	−	44.6605i	0.110035	−	0.0635285i
$704$		0			0
$705$	−428.883	+	742.847i	−0.608345	+	1.05368i
$706$		0			0
$707$	161.115	−	1061.05i	0.227886	−	1.50078i
$708$		0			0
$709$	−22.2186	+	38.4837i	−0.0313379	+	0.0542789i	−0.881269	−	0.472615i	$-0.843310\pi$
$709$	−22.2186	+	38.4837i	−0.0313379	+	0.0542789i	0.849931	+	0.526894i	$0.176643\pi$
$710$		0			0
$711$	−187.177	+	108.067i	−0.263259	+	0.151993i
$712$		0			0
$713$	−320.236			−0.449138
$714$		0			0
$715$		−	506.211i		−	0.707987i
$716$		0			0
$717$	−97.1595	−	168.285i	−0.135508	−	0.234707i
$718$		0			0
$719$	465.543	+	268.781i	0.647487	+	0.373827i	0.787493	−	0.616324i	$-0.211379\pi$
$719$	465.543	+	268.781i	0.647487	+	0.373827i	−0.140006	+	0.990151i	$0.544712\pi$
$720$		0			0
$721$	−198.224	−	506.695i	−0.274929	−	0.702767i
$722$		0			0
$723$	283.222	+	163.518i	0.391732	+	0.226166i
$724$		0			0
$725$	770.268	+	1334.14i	1.06244	+	1.84020i
$726$		0			0
$727$		−	168.754i		−	0.232124i	−0.993242	−	0.116062i	$-0.962973\pi$
$727$		−	168.754i		−	0.232124i	0.993242	−	0.116062i	$-0.0370271\pi$
$728$		0			0
$729$	−381.615			−0.523477
$730$		0			0
$731$	−549.515	+	317.262i	−0.751730	+	0.434012i
$732$		0			0
$733$	100.846	−	174.671i	0.137580	−	0.238296i	−0.789000	−	0.614393i	$-0.789401\pi$
$733$	100.846	−	174.671i	0.137580	−	0.238296i	0.926580	+	0.376097i	$0.122734\pi$
$734$		0			0
$735$	693.488	−	156.688i	0.943520	−	0.213181i
$736$		0			0
$737$	−10.9618	+	18.9863i	−0.0148735	+	0.0257616i
$738$		0			0
$739$	−192.074	+	110.894i	−0.259911	+	0.150059i	−0.624294	−	0.781190i	$-0.714613\pi$
$739$	−192.074	+	110.894i	−0.259911	+	0.150059i	0.364383	+	0.931249i	$0.381280\pi$
$740$		0			0
$741$	−127.827			−0.172507
$742$		0			0
$743$			344.416i			0.463547i	0.972770	+	0.231774i	$0.0744529\pi$
$743$			344.416i			0.463547i	−0.972770	+	0.231774i	$0.925547\pi$
$744$		0			0
$745$	−776.753	−	1345.38i	−1.04262	−	1.80587i
$746$		0			0
$747$	499.824	+	288.574i	0.669109	+	0.386310i
$748$		0			0
$749$	420.510	+	1074.90i	0.561429	+	1.43511i
$750$		0			0
$751$	−1167.06	−	673.805i	−1.55401	−	0.897211i	−0.997809	−	0.0661661i	$-0.978923\pi$
$751$	−1167.06	−	673.805i	−1.55401	−	0.897211i	−0.556206	−	0.831045i	$-0.687743\pi$
$752$		0			0
$753$	198.829	+	344.382i	0.264050	+	0.457347i
$754$		0			0
$755$			2012.34i			2.66536i
$756$		0			0
$757$	796.713			1.05246			0.526230	−	0.850342i	$-0.323605\pi$
$757$	796.713			1.05246			0.526230	+	0.850342i	$0.323605\pi$
$758$		0			0
$759$	674.740	−	389.561i	0.888985	−	0.513256i
$760$		0			0
$761$	407.280	−	705.429i	0.535190	−	0.926976i	−0.463964	−	0.885854i	$-0.653573\pi$
$761$	407.280	−	705.429i	0.535190	−	0.926976i	0.999154	−	0.0411222i	$-0.0130933\pi$
$762$		0			0
$763$	−64.3758	+	423.958i	−0.0843720	+	0.555646i
$764$		0			0
$765$	−650.654	+	1126.97i	−0.850529	+	1.47316i
$766$		0			0
$767$	136.385	−	78.7421i	0.177817	−	0.102662i
$768$		0			0
$769$	60.5653			0.0787585			0.0393792	−	0.999224i	$-0.487462\pi$
$769$	60.5653			0.0787585			0.0393792	+	0.999224i	$0.487462\pi$
$770$		0			0
$771$		−	315.567i		−	0.409296i
$772$		0			0
$773$	−499.210	−	864.657i	−0.645809	−	1.11857i	−0.984114	−	0.177537i	$-0.943187\pi$
$773$	−499.210	−	864.657i	−0.645809	−	1.11857i	0.338305	−	0.941036i	$-0.390146\pi$
$774$		0			0
$775$	279.854	+	161.574i	0.361102	+	0.208482i
$776$		0			0
$777$	−56.0961	+	70.1846i	−0.0721958	+	0.0903277i
$778$		0			0
$779$	−513.433	−	296.431i	−0.659092	−	0.380527i
$780$		0			0
$781$	−639.935	−	1108.40i	−0.819378	−	1.41921i
$782$		0			0
$783$			958.079i			1.22360i
$784$		0			0
$785$	−1810.63			−2.30654
$786$		0			0
$787$	652.956	−	376.984i	0.829677	−	0.479014i	−0.0240648	−	0.999710i	$-0.507661\pi$
$787$	652.956	−	376.984i	0.829677	−	0.479014i	0.853742	+	0.520696i	$0.174327\pi$
$788$		0			0
$789$	−255.240	+	442.089i	−0.323498	+	0.560315i
$790$		0			0
$791$	−53.5600	−	42.8086i	−0.0677117	−	0.0541196i
$792$		0			0
$793$	1.08631	−	1.88155i	0.00136988	−	0.00237270i
$794$		0			0
$795$	−51.0871	+	29.4951i	−0.0642605	+	0.0371008i
$796$		0			0
$797$	−335.856			−0.421400			−0.210700	−	0.977551i	$-0.567574\pi$
$797$	−335.856			−0.421400			−0.210700	+	0.977551i	$0.567574\pi$
$798$		0			0
$799$			1597.16i			1.99895i
$800$		0			0
$801$	89.0888	+	154.306i	0.111222	+	0.192642i
$802$		0			0
$803$	−702.141	−	405.381i	−0.874397	−	0.504833i
$804$		0			0
$805$	−2379.57	−	361.325i	−2.95599	−	0.448851i
$806$		0			0
$807$	−345.103	−	199.245i	−0.427637	−	0.246897i
$808$		0			0
$809$	−374.844	−	649.250i	−0.463343	−	0.802533i	0.535782	−	0.844356i	$-0.320017\pi$
$809$	−374.844	−	649.250i	−0.463343	−	0.802533i	−0.999125	+	0.0418229i	$0.986683\pi$
$810$		0			0
$811$			790.284i			0.974456i	0.873275	+	0.487228i	$0.161992\pi$
$811$			790.284i			0.974456i	−0.873275	+	0.487228i	$0.838008\pi$
$812$		0			0
$813$	346.112			0.425722
$814$		0			0
$815$	1932.62	−	1115.80i	2.37131	−	1.36908i
$816$		0			0
$817$	144.541	−	250.352i	0.176917	−	0.306429i
$818$		0			0
$819$	−224.742	+	87.9212i	−0.274411	+	0.107352i
$820$		0			0
$821$	459.548	−	795.961i	0.559742	−	0.969501i	−0.437776	−	0.899084i	$-0.644234\pi$
$821$	459.548	−	795.961i	0.559742	−	0.969501i	0.997518	−	0.0704171i	$-0.0224330\pi$
$822$		0			0
$823$	841.077	−	485.596i	1.02197	−	0.590032i	0.107293	−	0.994227i	$-0.465782\pi$
$823$	841.077	−	485.596i	1.02197	−	0.590032i	0.914673	+	0.404196i	$0.132448\pi$
$824$		0			0
$825$	−786.207			−0.952979
$826$		0			0
$827$		−	110.492i		−	0.133606i	−0.997766	−	0.0668029i	$-0.978720\pi$
$827$		−	110.492i		−	0.133606i	0.997766	−	0.0668029i	$-0.0212799\pi$
$828$		0			0
$829$	−247.986	−	429.525i	−0.299139	−	0.518124i	0.676800	−	0.736167i	$-0.263366\pi$
$829$	−247.986	−	429.525i	−0.299139	−	0.518124i	−0.975939	+	0.218043i	$0.930033\pi$
$830$		0			0
$831$	207.751	+	119.945i	0.250002	+	0.144339i
$832$		0			0
$833$	972.399	−	898.303i	1.16735	−	1.07839i
$834$		0			0
$835$	−631.342	−	364.506i	−0.756098	−	0.436534i
$836$		0			0
$837$	100.485	+	174.045i	0.120054	+	0.207939i
$838$		0			0
$839$			529.377i			0.630962i	0.948932	+	0.315481i	$0.102166\pi$
$839$			529.377i			0.630962i	−0.948932	+	0.315481i	$0.897834\pi$
$840$		0			0
$841$	485.672			0.577493
$842$		0			0
$843$	570.576	−	329.422i	0.676840	−	0.390774i
$844$		0			0
$845$	551.777	−	955.705i	0.652990	−	1.13101i
$846$		0			0
$847$	−68.7688	+	26.9030i	−0.0811910	+	0.0317627i
$848$		0			0
$849$	254.175	−	440.244i	0.299382	−	0.518544i
$850$		0			0
$851$	263.413	−	152.081i	0.309533	−	0.178709i
$852$		0			0
$853$	−1122.77			−1.31626			−0.658132	−	0.752902i	$-0.728653\pi$
$853$	−1122.77			−1.31626			−0.658132	+	0.752902i	$0.728653\pi$
$854$		0			0
$855$		−	592.861i		−	0.693405i
$856$		0			0
$857$	334.966	+	580.178i	0.390859	+	0.676987i	0.992563	−	0.121732i	$-0.0388448\pi$
$857$	334.966	+	580.178i	0.390859	+	0.676987i	−0.601704	+	0.798719i	$0.705511\pi$
$858$		0			0
$859$	202.690	+	117.023i	0.235961	+	0.136232i	0.613319	−	0.789835i	$-0.289834\pi$
$859$	202.690	+	117.023i	0.235961	+	0.136232i	−0.377358	+	0.926067i	$0.623167\pi$
$860$		0			0
$861$	589.600	+	89.5277i	0.684785	+	0.103981i
$862$		0			0
$863$	−44.7766	−	25.8518i	−0.0518849	−	0.0299557i	0.473833	−	0.880615i	$-0.342870\pi$
$863$	−44.7766	−	25.8518i	−0.0518849	−	0.0299557i	−0.525718	+	0.850659i	$0.676203\pi$
$864$		0			0
$865$	−1309.18	−	2267.57i	−1.51350	−	2.62147i
$866$		0			0
$867$		−	779.847i		−	0.899478i
$868$		0			0
$869$	−386.858			−0.445176
$870$		0			0
$871$	10.6074	−	6.12421i	0.0121785	−	0.00703124i
$872$		0			0
$873$	17.2377	−	29.8566i	0.0197454	−	0.0342000i
$874$		0			0
$875$	775.794	+	620.065i	0.886621	+	0.708645i
$876$		0			0
$877$	−54.1626	+	93.8124i	−0.0617590	+	0.106970i	−0.895252	−	0.445561i	$-0.853004\pi$
$877$	−54.1626	+	93.8124i	−0.0617590	+	0.106970i	0.833493	+	0.552530i	$0.186338\pi$
$878$		0			0
$879$	202.113	−	116.690i	0.229935	−	0.132753i
$880$		0			0
$881$	901.643			1.02343			0.511716	−	0.859155i	$-0.329010\pi$
$881$	901.643			1.02343			0.511716	+	0.859155i	$0.329010\pi$
$882$		0			0
$883$		−	391.049i		−	0.442864i	−0.975176	−	0.221432i	$-0.928927\pi$
$883$		−	391.049i		−	0.442864i	0.975176	−	0.221432i	$-0.0710731\pi$
$884$		0			0
$885$	−194.584	−	337.029i	−0.219869	−	0.380823i
$886$		0			0
$887$	−1123.13	−	648.438i	−1.26621	−	0.731047i	−0.291941	−	0.956436i	$-0.594301\pi$
$887$	−1123.13	−	648.438i	−1.26621	−	0.731047i	−0.974269	+	0.225390i	$0.927634\pi$
$888$		0			0
$889$	−549.382	+	687.360i	−0.617978	+	0.773183i
$890$		0			0
$891$	57.5186	+	33.2084i	0.0645551	+	0.0372709i
$892$		0			0
$893$	−363.824	−	630.161i	−0.407417	−	0.705668i
$894$		0			0
$895$			1143.84i			1.27803i
$896$		0			0
$897$	−435.287			−0.485270
$898$		0			0
$899$	241.004	−	139.144i	0.268080	−	0.154776i
$900$		0			0
$901$	−54.9199	+	95.1241i	−0.0609544	+	0.105576i
$902$		0			0
$903$	−43.6542	+	287.492i	−0.0483435	+	0.318374i
$904$		0			0
$905$	−299.967	+	519.558i	−0.331455	+	0.574098i
$906$		0			0
$907$	−399.679	+	230.755i	−0.440660	+	0.254415i	−0.703878	−	0.710321i	$-0.748550\pi$
$907$	−399.679	+	230.755i	−0.440660	+	0.254415i	0.263217	+	0.964737i	$0.415216\pi$
$908$		0			0
$909$	900.210			0.990330
$910$		0			0
$911$			119.595i			0.131279i	0.997843	+	0.0656395i	$0.0209087\pi$
$911$			119.595i			0.131279i	−0.997843	+	0.0656395i	$0.979091\pi$
$912$		0			0
$913$	516.519	+	894.637i	0.565738	+	0.979888i
$914$		0			0
$915$	−4.64959	−	2.68444i	−0.00508152	−	0.00293382i
$916$		0			0
$917$	−90.8333	−	232.186i	−0.0990548	−	0.253202i
$918$		0			0
$919$	−612.884	−	353.849i	−0.666903	−	0.385037i	0.127999	−	0.991774i	$-0.459145\pi$
$919$	−612.884	−	353.849i	−0.666903	−	0.385037i	−0.794902	+	0.606737i	$0.792478\pi$
$920$		0			0
$921$	−42.2951	−	73.2572i	−0.0459230	−	0.0795410i
$922$		0			0
$923$			715.049i			0.774701i
$924$		0			0
$925$	−306.929			−0.331815
$926$		0			0
$927$	395.236	−	228.190i	0.426361	−	0.246159i
$928$		0			0
$929$	198.528	−	343.860i	0.213701	−	0.370140i	−0.739169	−	0.673520i	$-0.764782\pi$
$929$	198.528	−	343.860i	0.213701	−	0.370140i	0.952870	+	0.303380i	$0.0981150\pi$
$930$		0			0
$931$	−179.033	+	575.933i	−0.192302	+	0.618618i
$932$		0			0
$933$	201.193	−	348.476i	0.215641	−	0.373500i
$934$		0			0
$935$	−2017.16	+	1164.61i	−2.15739	+	1.24557i
$936$		0			0
$937$	−1227.51			−1.31004			−0.655020	−	0.755612i	$-0.727340\pi$
$937$	−1227.51			−1.31004			−0.655020	+	0.755612i	$0.727340\pi$
$938$		0			0
$939$		−	217.725i		−	0.231869i
$940$		0			0
$941$	−343.521	−	594.995i	−0.365059	−	0.632301i	0.623726	−	0.781643i	$-0.285618\pi$
$941$	−343.521	−	594.995i	−0.365059	−	0.632301i	−0.988786	+	0.149342i	$0.952285\pi$
$942$		0			0
$943$	−1748.38	−	1009.43i	−1.85406	−	1.07044i
$944$		0			0
$945$	550.295	+	1406.65i	0.582322	+	1.48852i
$946$		0			0
$947$	−115.670	−	66.7819i	−0.122143	−	0.0705194i	0.437684	−	0.899129i	$-0.355799\pi$
$947$	−115.670	−	66.7819i	−0.122143	−	0.0705194i	−0.559827	+	0.828610i	$0.689132\pi$
$948$		0			0
$949$	226.482	+	392.279i	0.238653	+	0.413360i
$950$		0			0
$951$		−	849.514i		−	0.893285i
$952$		0			0
$953$	1030.34			1.08115			0.540575	−	0.841296i	$-0.318207\pi$
$953$	1030.34			1.08115			0.540575	+	0.841296i	$0.318207\pi$
$954$		0			0
$955$	911.401	−	526.198i	0.954346	−	0.550992i
$956$		0			0
$957$	−338.531	+	586.354i	−0.353742	+	0.612700i
$958$		0			0
$959$	−125.579	+	827.020i	−0.130948	+	0.862378i
$960$		0			0
$961$	−451.313	+	781.697i	−0.469628	+	0.813420i
$962$		0			0
$963$	−838.452	+	484.081i	−0.870667	+	0.502680i
$964$		0			0
$965$	2293.15			2.37632
$966$		0			0
$967$		−	337.880i		−	0.349410i	−0.984621	−	0.174705i	$-0.944103\pi$
$967$		−	337.880i		−	0.349410i	0.984621	−	0.174705i	$-0.0558972\pi$
$968$		0			0
$969$	294.085	+	509.370i	0.303493	+	0.525666i
$970$		0			0
$971$	1454.36	+	839.672i	1.49779	+	0.864750i	0.999997	−	0.00254493i	$-0.000810076\pi$
$971$	1454.36	+	839.672i	1.49779	+	0.864750i	0.497794	+	0.867295i	$0.334143\pi$
$972$		0			0
$973$	−207.153	+	259.179i	−0.212901	+	0.266371i
$974$		0			0
$975$	380.398	+	219.623i	0.390152	+	0.225254i
$976$		0			0
$977$	554.679	+	960.733i	0.567737	+	0.983350i	0.996789	+	0.0800700i	$0.0255144\pi$
$977$	554.679	+	960.733i	0.567737	+	0.983350i	−0.429052	+	0.903280i	$0.641152\pi$
$978$		0			0
$979$			318.921i			0.325762i
$980$		0			0
$981$	−359.691			−0.366657
$982$		0			0
$983$	360.616	−	208.202i	0.366852	−	0.211802i	−0.305230	−	0.952279i	$-0.598733\pi$
$983$	360.616	−	208.202i	0.366852	−	0.211802i	0.672082	+	0.740476i	$0.265400\pi$
$984$		0			0
$985$	−406.324	+	703.774i	−0.412512	+	0.714491i
$986$		0			0
$987$	571.754	+	456.983i	0.579285	+	0.463002i
$988$		0			0
$989$	492.202	−	852.519i	0.497677	−	0.862001i
$990$		0			0
$991$	−1034.76	+	597.420i	−1.04416	+	0.602846i	−0.921009	−	0.389542i	$-0.872633\pi$
$991$	−1034.76	+	597.420i	−1.04416	+	0.602846i	−0.123151	+	0.992388i	$0.539300\pi$
$992$		0			0
$993$	−839.073			−0.844988
$994$		0			0
$995$		−	1938.60i		−	1.94834i
$996$		0			0
$997$	838.567	+	1452.44i	0.841090	+	1.45681i	0.888974	+	0.457958i	$0.151419\pi$
$997$	838.567	+	1452.44i	0.841090	+	1.45681i	−0.0478838	+	0.998853i	$0.515248\pi$
$998$		0			0
$999$	−165.310	−	95.4415i	−0.165475	−	0.0955371i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	448.3.r.f.191.2		12
4.3	odd	2	inner	448.3.r.f.191.5		12
7.4	even	3	inner	448.3.r.f.319.5		12
8.3	odd	2		224.3.r.d.191.2	yes	12
8.5	even	2		224.3.r.d.191.5	yes	12
28.11	odd	6	inner	448.3.r.f.319.2		12
56.5	odd	6		1568.3.d.l.1471.2		6
56.11	odd	6		224.3.r.d.95.5	yes	12
56.19	even	6		1568.3.d.l.1471.5		6
56.37	even	6		1568.3.d.i.1471.5		6
56.51	odd	6		1568.3.d.i.1471.2		6
56.53	even	6		224.3.r.d.95.2	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.3.r.d.95.2	✓	12	56.53	even	6
224.3.r.d.95.5	yes	12	56.11	odd	6
224.3.r.d.191.2	yes	12	8.3	odd	2
224.3.r.d.191.5	yes	12	8.5	even	2
448.3.r.f.191.2		12	1.1	even	1	trivial
448.3.r.f.191.5		12	4.3	odd	2	inner
448.3.r.f.319.2		12	28.11	odd	6	inner
448.3.r.f.319.5		12	7.4	even	3	inner
1568.3.d.i.1471.2		6	56.51	odd	6
1568.3.d.i.1471.5		6	56.37	even	6
1568.3.d.l.1471.2		6	56.5	odd	6
1568.3.d.l.1471.5		6	56.19	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:	\( N \)	\(=\)	\( 448 = 2^{6} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	448.r (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.53177 + 0.884367i) q^{3} +(-4.10168 + 7.10432i) q^{5} +(5.46804 + 4.37041i) q^{7} +(-2.93579 + 5.08494i) q^{9} +(-9.10155 + 5.25478i) q^{11} +5.87158 q^{13} -14.5096i q^{15} +(-13.5084 - 23.3972i) q^{17} +(10.6595 + 6.15427i) q^{19} +(-12.2408 - 1.85871i) q^{21} +(36.2985 + 20.9570i) q^{23} +(-21.1475 - 36.6286i) q^{25} -26.3039i q^{27} -36.4235 q^{29} +(-6.61671 + 3.82016i) q^{31} +(9.29431 - 16.0982i) q^{33} +(-53.4770 + 20.9207i) q^{35} +(3.62842 - 6.28461i) q^{37} +(-8.99390 + 5.19263i) q^{39} -48.1667 q^{41} -23.4863i q^{43} +(-24.0833 - 41.7136i) q^{45} +(-51.1971 - 29.5587i) q^{47} +(10.7990 + 47.7952i) q^{49} +(41.3835 + 23.8928i) q^{51} +(-2.03281 - 3.52092i) q^{53} -86.2137i q^{55} -21.7705 q^{57} +(23.2280 - 13.4107i) q^{59} +(0.185012 - 0.320450i) q^{61} +(-38.2763 + 14.9740i) q^{63} +(-24.0833 + 41.7136i) q^{65} +(1.80658 - 1.04303i) q^{67} -74.1346 q^{69} +121.781i q^{71} +(38.5726 + 66.8097i) q^{73} +(64.7863 + 37.4044i) q^{75} +(-72.7332 - 11.0442i) q^{77} +(31.8785 + 18.4050i) q^{79} +(-3.15983 - 5.47298i) q^{81} -98.2951i q^{83} +221.628 q^{85} +(55.7924 - 32.2118i) q^{87} +(15.1729 - 26.2802i) q^{89} +(32.1060 + 25.6612i) q^{91} +(6.75684 - 11.7032i) q^{93} +(-87.4437 + 50.4857i) q^{95} -5.87158 q^{97} -61.7077i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 18 q^{5} - 6 q^{17} - 18 q^{21} + 186 q^{33} + 114 q^{37} + 180 q^{49} + 18 q^{53} - 684 q^{57} - 318 q^{61} + 228 q^{69} + 342 q^{73} - 318 q^{77} - 186 q^{81} + 996 q^{85} + 150 q^{89} + 222 q^{93}+O(q^{100}) \) 12 * q - 18 * q^5 - 6 * q^17 - 18 * q^21 + 186 * q^33 + 114 * q^37 + 180 * q^49 + 18 * q^53 - 684 * q^57 - 318 * q^61 + 228 * q^69 + 342 * q^73 - 318 * q^77 - 186 * q^81 + 996 * q^85 + 150 * q^89 + 222 * q^93

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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