LMFDB - Embedded newform 224.3.r.d.191.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [224,3,Mod(95,224)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(224, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("224.95");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 224 = 2^{5} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	224.r (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$6.10355792167$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			191.5
Root			$-0.385124 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	224.191
Dual form			224.3.r.d.95.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.53177 - 0.884367i) q^{3} +(4.10168 - 7.10432i) q^{5} +(5.46804 + 4.37041i) q^{7} +(-2.93579 + 5.08494i) q^{9} +O(q^{10})$	\(q+(1.53177 - 0.884367i) q^{3} +(4.10168 - 7.10432i) q^{5} +(5.46804 + 4.37041i) q^{7} +(-2.93579 + 5.08494i) q^{9} +(9.10155 - 5.25478i) q^{11} -5.87158 q^{13} -14.5096i q^{15} +(-13.5084 - 23.3972i) q^{17} +(-10.6595 - 6.15427i) q^{19} +(12.2408 + 1.85871i) q^{21} +(36.2985 + 20.9570i) q^{23} +(-21.1475 - 36.6286i) q^{25} +26.3039i q^{27} +36.4235 q^{29} +(-6.61671 + 3.82016i) q^{31} +(9.29431 - 16.0982i) q^{33} +(53.4770 - 20.9207i) q^{35} +(-3.62842 + 6.28461i) q^{37} +(-8.99390 + 5.19263i) q^{39} -48.1667 q^{41} +23.4863i q^{43} +(24.0833 + 41.7136i) q^{45} +(-51.1971 - 29.5587i) q^{47} +(10.7990 + 47.7952i) q^{49} +(-41.3835 - 23.8928i) q^{51} +(2.03281 + 3.52092i) q^{53} -86.2137i q^{55} -21.7705 q^{57} +(-23.2280 + 13.4107i) q^{59} +(-0.185012 + 0.320450i) q^{61} +(-38.2763 + 14.9740i) q^{63} +(-24.0833 + 41.7136i) q^{65} +(-1.80658 + 1.04303i) q^{67} +74.1346 q^{69} +121.781i q^{71} +(38.5726 + 66.8097i) q^{73} +(-64.7863 - 37.4044i) q^{75} +(72.7332 + 11.0442i) q^{77} +(31.8785 + 18.4050i) q^{79} +(-3.15983 - 5.47298i) q^{81} +98.2951i q^{83} -221.628 q^{85} +(55.7924 - 32.2118i) q^{87} +(15.1729 - 26.2802i) q^{89} +(-32.1060 - 25.6612i) q^{91} +(-6.75684 + 11.7032i) q^{93} +(-87.4437 + 50.4857i) q^{95} -5.87158 q^{97} +61.7077i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 18 q^{5}+O(q^{10}) $ 12 * q + 18 * q^5	$ 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

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/224\mathbb{Z}\right)^\times$.

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

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	−0.222486	−	0.974936i	$-0.571417\pi$
$3$	1.53177	−	0.884367i	0.510590	−	0.294789i	0.733076	+	0.680147i	$0.238084\pi$
$4$		0			0
$5$	4.10168	−	7.10432i	0.820336	−	1.42086i	−0.0850965	−	0.996373i	$-0.527120\pi$
$5$	4.10168	−	7.10432i	0.820336	−	1.42086i	0.905432	−	0.424491i	$-0.139547\pi$
$6$		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	−0.0255528	−	0.999673i	$-0.508135\pi$
$11$	9.10155	−	5.25478i	0.827413	−	0.477707i	0.852966	+	0.521966i	$0.174801\pi$
$12$		0			0
$13$	−5.87158			−0.451660			−0.225830	−	0.974167i	$-0.572509\pi$
$13$	−5.87158			−0.451660			−0.225830	+	0.974167i	$0.572509\pi$
$14$		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	0.192531	−	0.981291i	$-0.438330\pi$
$19$	−10.6595	−	6.15427i	−0.561026	−	0.323909i	−0.753557	+	0.657382i	$0.771664\pi$
$20$		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	$-0.283877\pi$
$29$	36.4235			1.25598			0.627992	+	0.778220i	$0.283877\pi$
$30$		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	−0.910884	−	0.412663i	$-0.864599\pi$
$37$	−3.62842	+	6.28461i	−0.0980654	+	0.169854i	0.812818	+	0.582517i	$0.197932\pi$
$38$		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	$0.0880479\pi$
$43$			23.4863i			0.546193i	−0.961987	+	0.273097i	$0.911952\pi$
$44$		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	0.884566	−	0.466416i	$-0.154455\pi$
$53$	2.03281	+	3.52092i	0.0383548	+	0.0664325i	−0.846211	+	0.532848i	$0.821122\pi$
$54$		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	−0.683760	−	0.729707i	$-0.739657\pi$
$59$	−23.2280	+	13.4107i	−0.393696	+	0.227300i	0.290064	+	0.957007i	$0.406323\pi$
$60$		0			0
$61$	−0.185012	+	0.320450i	−0.00303298	+	0.00525328i	−0.867538	−	0.497371i	$-0.834299\pi$
$61$	−0.185012	+	0.320450i	−0.00303298	+	0.00525328i	0.864505	+	0.502624i	$0.167632\pi$
$62$		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	−0.513421	−	0.858137i	$-0.671622\pi$
$67$	−1.80658	+	1.04303i	−0.0269638	+	0.0155676i	0.486458	+	0.873704i	$0.338289\pi$
$68$		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	$0.201716\pi$
$83$			98.2951i			1.18428i	−0.805836	+	0.592139i	$0.798284\pi$
$84$		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	$0.107642\pi$
$101$	76.6583	+	132.776i	0.758993	+	1.31461i	−0.184372	+	0.982857i	$0.559025\pi$
$102$		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	−0.348569	−	0.937283i	$-0.613332\pi$
$107$	−142.798	−	82.4447i	−1.33456	−	0.770511i	−0.985995	+	0.166772i	$0.946666\pi$
$108$		0			0
$109$	−30.6298	−	53.0524i	−0.281008	−	0.486719i	0.690626	−	0.723212i	$-0.257335\pi$
$109$	−30.6298	−	53.0524i	−0.281008	−	0.486719i	−0.971633	+	0.236493i	$0.924002\pi$
$110$		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	0.613089	−	0.790014i	$-0.289927\pi$
$131$	30.8455	+	17.8087i	0.235462	+	0.135944i	−0.377627	+	0.925958i	$0.623260\pi$
$132$		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	$-0.945462\pi$
$139$		−	47.3989i		−	0.341000i	0.985358	−	0.170500i	$-0.0545382\pi$
$140$		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	$-0.614134\pi$
$149$	94.6872	−	164.003i	0.635485	−	1.10069i	0.986412	−	0.164289i	$-0.0525329\pi$
$150$		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	$-0.918544\pi$
$157$	−110.359	−	191.148i	−0.702924	−	1.21750i	0.264511	−	0.964383i	$-0.414789\pi$
$158$		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	0.998198	−	0.0600075i	$-0.0191125\pi$
$163$	235.589	+	136.017i	1.44533	+	0.834461i	0.447131	+	0.894469i	$0.352446\pi$
$164$		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	$-0.459483\pi$
$173$	159.591	−	276.420i	0.922491	−	1.59780i	0.795547	−	0.605891i	$-0.207183\pi$
$174$		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	−0.797820	−	0.602895i	$-0.794014\pi$
$179$	−120.755	+	69.7179i	−0.674608	+	0.389485i	0.123212	+	0.992380i	$0.460680\pi$
$180$		0			0
$181$	−73.1328			−0.404048			−0.202024	−	0.979381i	$-0.564752\pi$
$181$	−73.1328			−0.404048			−0.202024	+	0.979381i	$0.564752\pi$
$182$		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	$-0.580900\pi$
$197$	−99.0628			−0.502857			−0.251428	+	0.967876i	$0.580900\pi$
$198$		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	$-0.625382\pi$
$211$		−	389.683i		−	1.84684i	0.383791	−	0.923420i	$-0.374618\pi$
$212$		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	0.0101588	−	0.999948i	$-0.496766\pi$
$227$	200.037	−	115.491i	0.881219	−	0.508772i	0.871060	+	0.491176i	$0.163433\pi$
$228$		0			0
$229$	8.40221	−	14.5530i	0.0366909	−	0.0635504i	−0.847097	−	0.531439i	$-0.821652\pi$
$229$	8.40221	−	14.5530i	0.0366909	−	0.0635504i	0.883788	+	0.467888i	$0.154985\pi$
$230$		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	$0.147814\pi$
$251$			224.827i			0.895724i	−0.894103	+	0.447862i	$0.852186\pi$
$252$		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	0.577048	−	0.816710i	$-0.304205\pi$
$269$	−112.649	−	195.113i	−0.418768	−	0.725328i	−0.995816	+	0.0913828i	$0.970871\pi$
$270$		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	0.962080	−	0.272767i	$-0.0879389\pi$
$277$	67.8142	+	117.458i	0.244817	+	0.424035i	−0.717263	+	0.696802i	$0.754606\pi$
$278$		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	0.00901792	−	0.999959i	$-0.497129\pi$
$283$	248.903	−	143.704i	0.879517	−	0.507789i	0.870499	+	0.492170i	$0.163796\pi$
$284$		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	$-0.427708\pi$
$293$	131.947			0.450332			0.225166	+	0.974320i	$0.427708\pi$
$294$		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	$-0.975181\pi$
$307$		−	47.8253i		−	0.155783i	0.996962	−	0.0778913i	$-0.0248187\pi$
$308$		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	$-0.559723\pi$
$317$	240.148	−	415.948i	0.757563	−	1.31214i	0.944090	−	0.329688i	$-0.106944\pi$
$318$		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	−0.271857	−	0.962338i	$-0.587638\pi$
$331$	−410.836	−	237.196i	−1.24119	−	0.716604i	−0.969337	+	0.245733i	$0.920971\pi$
$332$		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	$-0.206150\pi$
$347$	596.404	−	344.334i	1.71874	−	0.992317i	0.921233	−	0.389012i	$-0.127184\pi$
$348$		0			0
$349$	128.861			0.369228			0.184614	−	0.982811i	$-0.440896\pi$
$349$	128.861			0.369228			0.184614	+	0.982811i	$0.440896\pi$
$350$		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	−0.727999	−	0.685578i	$-0.759550\pi$
$373$	85.6886	−	148.417i	0.229728	−	0.397901i	0.957727	+	0.287677i	$0.0928830\pi$
$374$		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	$0.00960947\pi$
$379$			22.8798i			0.0603689i	−0.999544	+	0.0301845i	$0.990391\pi$
$380$		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	0.778931	−	0.627109i	$-0.215762\pi$
$389$	−59.7609	−	103.509i	−0.153627	−	0.266090i	−0.932558	+	0.361020i	$0.882429\pi$
$390$		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	$0.396874\pi$
$397$	−262.734	+	455.069i	−0.661799	+	1.14627i	−0.980143	+	0.198294i	$0.936460\pi$
$398$		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	$0.145795\pi$
$419$			370.547i			0.884360i	−0.896926	+	0.442180i	$0.854205\pi$
$420$		0			0
$421$	−248.779			−0.590924			−0.295462	−	0.955355i	$-0.595474\pi$
$421$	−248.779			−0.590924			−0.295462	+	0.955355i	$0.595474\pi$
$422$		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	−0.163111	−	0.986608i	$-0.552153\pi$
$443$	−486.899	−	281.111i	−1.09909	−	0.634562i	−0.935983	+	0.352045i	$0.885486\pi$
$444$		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	$-0.479597\pi$
$461$	59.0572			0.128107			0.0640534	+	0.997946i	$0.479597\pi$
$462$		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	0.126182	−	0.992007i	$-0.459728\pi$
$467$	−312.811	−	180.601i	−0.669830	−	0.386727i	−0.796012	+	0.605280i	$0.793061\pi$
$468$		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	$-0.806882\pi$
$491$		−	559.896i		−	1.14032i	0.821534	−	0.570159i	$-0.193118\pi$
$492$		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	0.140413	−	0.990093i	$-0.455157\pi$
$499$	−322.766	−	186.349i	−0.646826	−	0.373445i	−0.787239	+	0.616648i	$0.788490\pi$
$500$		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	−0.995230	−	0.0975601i	$-0.968896\pi$
$509$	−210.281	+	364.217i	−0.413125	+	0.715554i	0.582104	+	0.813114i	$0.302230\pi$
$510$		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	0.931255	−	0.364368i	$-0.118715\pi$
$523$	565.536	+	326.512i	1.08133	+	0.624307i	0.150076	+	0.988674i	$0.452048\pi$
$524$		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	−0.962442	−	0.271487i	$-0.912485\pi$
$541$	−133.144	+	230.612i	−0.246107	+	0.426269i	0.716336	+	0.697756i	$0.245818\pi$
$542$		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	$-0.914151\pi$
$547$		−	291.492i		−	0.532892i	0.963850	−	0.266446i	$-0.0858493\pi$
$548$		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	$0.00635170\pi$
$557$	288.069	+	498.951i	0.517180	+	0.895783i	−0.482621	+	0.875830i	$0.660315\pi$
$558$		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	−0.872210	−	0.489132i	$-0.837314\pi$
$563$	−498.094	+	287.575i	−0.884714	+	0.510790i	−0.0125043	+	0.999922i	$0.503980\pi$
$564$		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	−0.706747	−	0.707467i	$-0.749838\pi$
$571$	−255.486	+	147.505i	−0.447436	+	0.258327i	0.259311	+	0.965794i	$0.416505\pi$
$572$		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	$-0.729433\pi$
$587$		−	882.011i		−	1.50257i	0.659975	−	0.751287i	$-0.270567\pi$
$588$		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	$0.000384294\pi$
$613$	307.141	+	531.983i	0.501045	+	0.867836i	−0.498954	+	0.866628i	$0.666282\pi$
$614$		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	−0.801166	−	0.598442i	$-0.795787\pi$
$619$	−423.076	+	244.263i	−0.683483	+	0.394609i	0.117683	+	0.993051i	$0.462453\pi$
$620$		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	$0.235276\pi$
$643$			866.317i			1.34731i	−0.739048	+	0.673653i	$0.764724\pi$
$644$		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	$-0.516394\pi$
$653$	547.956	−	949.088i	0.839137	−	1.45343i	0.890617	−	0.454754i	$-0.150273\pi$
$654$		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	$-0.996642\pi$
$659$		−	13.9021i		−	0.0210957i	0.999944	−	0.0105479i	$-0.00335755\pi$
$660$		0			0
$661$	50.8103	+	88.0061i	0.0768689	+	0.133141i	0.901897	−	0.431950i	$-0.142174\pi$
$661$	50.8103	+	88.0061i	0.0768689	+	0.133141i	−0.825029	+	0.565091i	$0.808841\pi$
$662$		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	$-0.550843\pi$
$677$	524.998	−	909.323i	0.775477	−	1.34317i	0.934526	−	0.355895i	$-0.115824\pi$
$678$		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	−0.412637	−	0.910896i	$-0.635392\pi$
$683$	116.044	−	66.9981i	0.169904	−	0.0980939i	0.582540	+	0.812802i	$0.302059\pi$
$684$		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	0.190161	−	0.981753i	$-0.439099\pi$
$691$	−390.403	−	225.399i	−0.564982	−	0.326193i	−0.755143	+	0.655560i	$0.772432\pi$
$692$		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	$-0.622119\pi$
$701$	−524.776			−0.748611			−0.374305	+	0.927306i	$0.622119\pi$
$702$		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	−0.849931	−	0.526894i	$-0.823357\pi$
$709$	22.2186	−	38.4837i	0.0313379	−	0.0542789i	0.881269	+	0.472615i	$0.156690\pi$
$710$		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	−0.926580	−	0.376097i	$-0.877266\pi$
$733$	−100.846	+	174.671i	−0.137580	+	0.238296i	0.789000	+	0.614393i	$0.210599\pi$
$734$		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	−0.364383	−	0.931249i	$-0.618720\pi$
$739$	192.074	−	110.894i	0.259911	−	0.150059i	0.624294	+	0.781190i	$0.285387\pi$
$740$		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	$-0.676395\pi$
$757$	−796.713			−1.05246			−0.526230	+	0.850342i	$0.676395\pi$
$758$		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	$0.0568130\pi$
$773$	499.210	+	864.657i	0.645809	+	1.11857i	−0.338305	+	0.941036i	$0.609854\pi$
$774$		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	−0.853742	−	0.520696i	$-0.825673\pi$
$787$	−652.956	+	376.984i	−0.829677	+	0.479014i	0.0240648	+	0.999710i	$0.492339\pi$
$788$		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	$-0.432426\pi$
$797$	335.856			0.421400			0.210700	+	0.977551i	$0.432426\pi$
$798$		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	$-0.838008\pi$
$811$		−	790.284i		−	0.974456i	0.873275	−	0.487228i	$-0.161992\pi$
$812$		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	$0.355766\pi$
$821$	−459.548	+	795.961i	−0.559742	+	0.969501i	−0.997518	+	0.0704171i	$0.977567\pi$
$822$		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	$0.0212799\pi$
$827$			110.492i			0.133606i	−0.997766	+	0.0668029i	$0.978720\pi$
$828$		0			0
$829$	247.986	+	429.525i	0.299139	+	0.518124i	0.975939	−	0.218043i	$-0.0699673\pi$
$829$	247.986	+	429.525i	0.299139	+	0.518124i	−0.676800	+	0.736167i	$0.736634\pi$
$830$		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	$-0.271347\pi$
$853$	1122.77			1.31626			0.658132	+	0.752902i	$0.271347\pi$
$854$		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	0.377358	−	0.926067i	$-0.376833\pi$
$859$	−202.690	−	117.023i	−0.235961	−	0.136232i	−0.613319	+	0.789835i	$0.710166\pi$
$860$		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	−0.833493	−	0.552530i	$-0.813662\pi$
$877$	54.1626	−	93.8124i	0.0617590	−	0.106970i	0.895252	+	0.445561i	$0.146996\pi$
$878$		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	$0.0710731\pi$
$883$			391.049i			0.442864i	−0.975176	+	0.221432i	$0.928927\pi$
$884$		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	−0.263217	−	0.964737i	$-0.584784\pi$
$907$	399.679	−	230.755i	0.440660	−	0.254415i	0.703878	+	0.710321i	$0.251450\pi$
$908$		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	0.988786	−	0.149342i	$-0.0477154\pi$
$941$	343.521	+	594.995i	0.365059	+	0.632301i	−0.623726	+	0.781643i	$0.714382\pi$
$942$		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	0.559827	−	0.828610i	$-0.310868\pi$
$947$	115.670	+	66.7819i	0.122143	+	0.0705194i	−0.437684	+	0.899129i	$0.644201\pi$
$948$		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	−0.497794	−	0.867295i	$-0.665857\pi$
$971$	−1454.36	−	839.672i	−1.49779	−	0.864750i	−0.999997	+	0.00254493i	$0.999190\pi$
$972$		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	$-0.848581\pi$
$997$	−838.567	−	1452.44i	−0.841090	−	1.45681i	0.0478838	−	0.998853i	$-0.484752\pi$
$998$		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	224.3.r.d.191.5	yes	12
4.3	odd	2	inner	224.3.r.d.191.2	yes	12
7.2	even	3		1568.3.d.i.1471.5		6
7.4	even	3	inner	224.3.r.d.95.2	✓	12
7.5	odd	6		1568.3.d.l.1471.2		6
8.3	odd	2		448.3.r.f.191.5		12
8.5	even	2		448.3.r.f.191.2		12
28.11	odd	6	inner	224.3.r.d.95.5	yes	12
28.19	even	6		1568.3.d.l.1471.5		6
28.23	odd	6		1568.3.d.i.1471.2		6
56.11	odd	6		448.3.r.f.319.2		12
56.53	even	6		448.3.r.f.319.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.3.r.d.95.2	✓	12	7.4	even	3	inner
224.3.r.d.95.5	yes	12	28.11	odd	6	inner
224.3.r.d.191.2	yes	12	4.3	odd	2	inner
224.3.r.d.191.5	yes	12	1.1	even	1	trivial
448.3.r.f.191.2		12	8.5	even	2
448.3.r.f.191.5		12	8.3	odd	2
448.3.r.f.319.2		12	56.11	odd	6
448.3.r.f.319.5		12	56.53	even	6
1568.3.d.i.1471.2		6	28.23	odd	6
1568.3.d.i.1471.5		6	7.2	even	3
1568.3.d.l.1471.2		6	7.5	odd	6
1568.3.d.l.1471.5		6	28.19	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 224 = 2^{5} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	224.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.53177 - 0.884367i) q^{3} +(4.10168 - 7.10432i) q^{5} +(5.46804 + 4.37041i) q^{7} +(-2.93579 + 5.08494i) q^{9} +O(q^{10})\)	\(q+(1.53177 - 0.884367i) q^{3} +(4.10168 - 7.10432i) q^{5} +(5.46804 + 4.37041i) q^{7} +(-2.93579 + 5.08494i) q^{9} +(9.10155 - 5.25478i) q^{11} -5.87158 q^{13} -14.5096i q^{15} +(-13.5084 - 23.3972i) q^{17} +(-10.6595 - 6.15427i) q^{19} +(12.2408 + 1.85871i) q^{21} +(36.2985 + 20.9570i) q^{23} +(-21.1475 - 36.6286i) q^{25} +26.3039i q^{27} +36.4235 q^{29} +(-6.61671 + 3.82016i) q^{31} +(9.29431 - 16.0982i) q^{33} +(53.4770 - 20.9207i) q^{35} +(-3.62842 + 6.28461i) q^{37} +(-8.99390 + 5.19263i) q^{39} -48.1667 q^{41} +23.4863i q^{43} +(24.0833 + 41.7136i) q^{45} +(-51.1971 - 29.5587i) q^{47} +(10.7990 + 47.7952i) q^{49} +(-41.3835 - 23.8928i) q^{51} +(2.03281 + 3.52092i) q^{53} -86.2137i q^{55} -21.7705 q^{57} +(-23.2280 + 13.4107i) q^{59} +(-0.185012 + 0.320450i) q^{61} +(-38.2763 + 14.9740i) q^{63} +(-24.0833 + 41.7136i) q^{65} +(-1.80658 + 1.04303i) q^{67} +74.1346 q^{69} +121.781i q^{71} +(38.5726 + 66.8097i) q^{73} +(-64.7863 - 37.4044i) q^{75} +(72.7332 + 11.0442i) q^{77} +(31.8785 + 18.4050i) q^{79} +(-3.15983 - 5.47298i) q^{81} +98.2951i q^{83} -221.628 q^{85} +(55.7924 - 32.2118i) q^{87} +(15.1729 - 26.2802i) q^{89} +(-32.1060 - 25.6612i) q^{91} +(-6.75684 + 11.7032i) q^{93} +(-87.4437 + 50.4857i) q^{95} -5.87158 q^{97} +61.7077i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 18 q^{5}+O(q^{10}) \) 12 * q + 18 * q^5	\( 12 q + 18 q^{5} - 6 q^{17} + 18 q^{21} + 186 q^{33} - 114 q^{37} + 180 q^{49} - 18 q^{53} - 684 q^{57} + 318 q^{61} - 228 q^{69} + 342 q^{73} + 318 q^{77} - 186 q^{81} - 996 q^{85} + 150 q^{89} - 222 q^{93}+O(q^{100}) \) 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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