LMFDB - Embedded newform 55.3.c.a.21.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [55,3,Mod(21,55)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(55, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("55.21"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 55 = 5 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	55.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$1.49864145398$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 30x^{6} + 280x^{4} + 890x^{2} + 895 $ x^8 + 30x^6 + 280x^4 + 890*x^2 + 895
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			21.6
Root			$1.66769i$ of defining polynomial
Character	$\chi$	$=$	55.21
Dual form			55.3.c.a.21.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.66769i q^{2} +2.79505 q^{3} +1.21881 q^{4} -2.23607 q^{5} +4.66128i q^{6} -6.72266i q^{7} +8.70336i q^{8} -1.18769 q^{9} -3.72907i q^{10} +(-6.62122 + 8.78404i) q^{11} +3.40663 q^{12} -2.91291i q^{13} +11.2113 q^{14} -6.24993 q^{15} -9.63929 q^{16} -30.9615i q^{17} -1.98069i q^{18} -4.49991i q^{19} -2.72533 q^{20} -18.7902i q^{21} +(-14.6491 - 11.0422i) q^{22} +13.0410 q^{23} +24.3263i q^{24} +5.00000 q^{25} +4.85783 q^{26} -28.4751 q^{27} -8.19362i q^{28} +44.8359i q^{29} -10.4229i q^{30} +26.1730 q^{31} +18.7381i q^{32} +(-18.5067 + 24.5519i) q^{33} +51.6342 q^{34} +15.0323i q^{35} -1.44756 q^{36} -28.8149 q^{37} +7.50446 q^{38} -8.14172i q^{39} -19.4613i q^{40} +24.6573i q^{41} +31.3362 q^{42} -2.28690i q^{43} +(-8.06999 + 10.7060i) q^{44} +2.65575 q^{45} +21.7484i q^{46} -2.33270 q^{47} -26.9423 q^{48} +3.80580 q^{49} +8.33846i q^{50} -86.5390i q^{51} -3.55027i q^{52} +93.1057 q^{53} -47.4877i q^{54} +(14.8055 - 19.6417i) q^{55} +58.5097 q^{56} -12.5775i q^{57} -74.7724 q^{58} -108.616 q^{59} -7.61745 q^{60} +54.7958i q^{61} +43.6485i q^{62} +7.98441i q^{63} -69.8065 q^{64} +6.51346i q^{65} +(-40.9449 - 30.8634i) q^{66} +9.01793 q^{67} -37.7361i q^{68} +36.4504 q^{69} -25.0693 q^{70} -1.24936 q^{71} -10.3369i q^{72} +24.1060i q^{73} -48.0543i q^{74} +13.9753 q^{75} -5.48452i q^{76} +(59.0522 + 44.5123i) q^{77} +13.5779 q^{78} -108.479i q^{79} +21.5541 q^{80} -68.9002 q^{81} -41.1207 q^{82} +8.27453i q^{83} -22.9016i q^{84} +69.2320i q^{85} +3.81384 q^{86} +125.319i q^{87} +(-76.4507 - 57.6269i) q^{88} +84.8892 q^{89} +4.42897i q^{90} -19.5825 q^{91} +15.8945 q^{92} +73.1549 q^{93} -3.89022i q^{94} +10.0621i q^{95} +52.3739i q^{96} +160.450 q^{97} +6.34690i q^{98} +(7.86394 - 10.4327i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{3} - 28 q^{4} - 4 q^{9} + 8 q^{11} - 48 q^{12} + 20 q^{15} + 88 q^{16} - 20 q^{20} + 80 q^{22} + 8 q^{23} + 40 q^{25} - 100 q^{26} - 16 q^{27} + 36 q^{31} - 152 q^{33} + 80 q^{34} - 216 q^{36}+ \cdots - 184 q^{99}+O(q^{100}) $ 8 * q + 8 * q^3 - 28 * q^4 - 4 * q^9 + 8 * q^11 - 48 * q^12 + 20 * q^15 + 88 * q^16 - 20 * q^20 + 80 * q^22 + 8 * q^23 + 40 * q^25 - 100 * q^26 - 16 * q^27 + 36 * q^31 - 152 * q^33 + 80 * q^34 - 216 * q^36 - 88 * q^37 - 160 * q^38 + 280 * q^42 + 12 * q^44 - 8 * q^47 + 488 * q^48 + 172 * q^49 - 152 * q^53 - 20 * q^55 - 80 * q^56 + 160 * q^58 - 16 * q^59 - 300 * q^60 - 588 * q^64 + 180 * q^66 - 88 * q^67 + 8 * q^69 + 60 * q^70 + 276 * q^71 + 40 * q^75 + 160 * q^77 + 160 * q^78 + 320 * q^80 - 320 * q^81 - 520 * q^82 + 420 * q^86 - 520 * q^88 + 444 * q^89 - 40 * q^91 - 368 * q^92 - 104 * q^93 + 312 * q^97 - 184 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/55\mathbb{Z}\right)^\times$.

$n$	$12$	$46$
$\chi(n)$	$1$	$-1$

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 $

$2$			1.66769i			0.833846i	0.908942	+	0.416923i	$0.136891\pi$
$2$			1.66769i			0.833846i	−0.908942	+	0.416923i	$0.863109\pi$
$3$	2.79505			0.931684			0.465842	−	0.884868i	$-0.345752\pi$
$3$	2.79505			0.931684			0.465842	+	0.884868i	$0.345752\pi$
$4$	1.21881			0.304701
$5$	−2.23607			−0.447214
$5$	−2.23607			−0.447214
$6$			4.66128i			0.776881i
$7$		−	6.72266i		−	0.960380i	−0.877164	−	0.480190i	$-0.840568\pi$
$7$		−	6.72266i		−	0.960380i	0.877164	−	0.480190i	$-0.159432\pi$
$8$			8.70336i			1.08792i
$9$	−1.18769			−0.131965
$10$		−	3.72907i		−	0.372907i
$11$	−6.62122	+	8.78404i	−0.601929	+	0.798549i
$11$	−6.62122	+	8.78404i	−0.601929	+	0.798549i
$12$	3.40663			0.283885
$13$		−	2.91291i		−	0.224070i	−0.993704	−	0.112035i	$-0.964263\pi$
$13$		−	2.91291i		−	0.224070i	0.993704	−	0.112035i	$-0.0357368\pi$
$14$	11.2113			0.800809
$15$	−6.24993			−0.416662
$16$	−9.63929			−0.602456
$17$		−	30.9615i		−	1.82127i	−0.413217	−	0.910633i	$-0.635595\pi$
$17$		−	30.9615i		−	1.82127i	0.413217	−	0.910633i	$-0.364405\pi$
$18$		−	1.98069i		−	0.110039i
$19$		−	4.49991i		−	0.236837i	−0.992964	−	0.118419i	$-0.962217\pi$
$19$		−	4.49991i		−	0.236837i	0.992964	−	0.118419i	$-0.0377825\pi$
$20$	−2.72533			−0.136267
$21$		−	18.7902i		−	0.894771i
$22$	−14.6491	−	11.0422i	−0.665867	−	0.501916i
$23$	13.0410			0.567002			0.283501	−	0.958972i	$-0.408504\pi$
$23$	13.0410			0.567002			0.283501	+	0.958972i	$0.408504\pi$
$24$			24.3263i			1.01360i
$25$	5.00000			0.200000
$26$	4.85783			0.186840
$27$	−28.4751			−1.05463
$28$		−	8.19362i		−	0.292629i
$29$			44.8359i			1.54607i	0.634366	+	0.773033i	$0.281261\pi$
$29$			44.8359i			1.54607i	−0.634366	+	0.773033i	$0.718739\pi$
$30$		−	10.4229i		−	0.347432i
$31$	26.1730			0.844290			0.422145	−	0.906528i	$-0.361277\pi$
$31$	26.1730			0.844290			0.422145	+	0.906528i	$0.361277\pi$
$32$			18.7381i			0.585565i
$33$	−18.5067	+	24.5519i	−0.560808	+	0.743996i
$34$	51.6342			1.51865
$35$			15.0323i			0.429495i
$36$	−1.44756			−0.0402100
$37$	−28.8149			−0.778781			−0.389390	−	0.921073i	$-0.627314\pi$
$37$	−28.8149			−0.778781			−0.389390	+	0.921073i	$0.627314\pi$
$38$	7.50446			0.197486
$39$		−	8.14172i		−	0.208762i
$40$		−	19.4613i		−	0.486532i
$41$			24.6573i			0.601397i	0.953719	+	0.300698i	$0.0972197\pi$
$41$			24.6573i			0.601397i	−0.953719	+	0.300698i	$0.902780\pi$
$42$	31.3362			0.746101
$43$		−	2.28690i		−	0.0531837i	−0.999646	−	0.0265919i	$-0.991535\pi$
$43$		−	2.28690i		−	0.0531837i	0.999646	−	0.0265919i	$-0.00846545\pi$
$44$	−8.06999	+	10.7060i	−0.183409	+	0.243319i
$45$	2.65575			0.0590166
$46$			21.7484i			0.472792i
$47$	−2.33270			−0.0496319			−0.0248159	−	0.999692i	$-0.507900\pi$
$47$	−2.33270			−0.0496319			−0.0248159	+	0.999692i	$0.507900\pi$
$48$	−26.9423			−0.561298
$49$	3.80580			0.0776694
$50$			8.33846i			0.166769i
$51$		−	86.5390i		−	1.69684i
$52$		−	3.55027i		−	0.0682744i
$53$	93.1057			1.75671			0.878355	−	0.478009i	$-0.158641\pi$
$53$	93.1057			1.75671			0.878355	+	0.478009i	$0.158641\pi$
$54$		−	47.4877i		−	0.879402i
$55$	14.8055	−	19.6417i	0.269191	−	0.357122i
$56$	58.5097			1.04482
$57$		−	12.5775i		−	0.220658i
$58$	−74.7724			−1.28918
$59$	−108.616			−1.84095			−0.920473	−	0.390805i	$-0.872197\pi$
$59$	−108.616			−1.84095			−0.920473	+	0.390805i	$0.872197\pi$
$60$	−7.61745			−0.126957
$61$			54.7958i			0.898292i	0.893458	+	0.449146i	$0.148272\pi$
$61$			54.7958i			0.898292i	−0.893458	+	0.449146i	$0.851728\pi$
$62$			43.6485i			0.704008i
$63$			7.98441i			0.126737i
$64$	−69.8065			−1.09073
$65$			6.51346i			0.100207i
$66$	−40.9449	−	30.8634i	−0.620377	−	0.467627i
$67$	9.01793			0.134596			0.0672980	−	0.997733i	$-0.478562\pi$
$67$	9.01793			0.134596			0.0672980	+	0.997733i	$0.478562\pi$
$68$		−	37.7361i		−	0.554942i
$69$	36.4504			0.528266
$70$	−25.0693			−0.358133
$71$	−1.24936			−0.0175966			−0.00879832	−	0.999961i	$-0.502801\pi$
$71$	−1.24936			−0.0175966			−0.00879832	+	0.999961i	$0.502801\pi$
$72$		−	10.3369i		−	0.143567i
$73$			24.1060i			0.330220i	0.986275	+	0.165110i	$0.0527979\pi$
$73$			24.1060i			0.330220i	−0.986275	+	0.165110i	$0.947202\pi$
$74$		−	48.0543i		−	0.649383i
$75$	13.9753			0.186337
$76$		−	5.48452i		−	0.0721647i
$77$	59.0522	+	44.5123i	0.766911	+	0.578081i
$78$	13.5779			0.174075
$79$		−	108.479i		−	1.37315i	−0.727060	−	0.686574i	$-0.759114\pi$
$79$		−	108.479i		−	1.37315i	0.727060	−	0.686574i	$-0.240886\pi$
$80$	21.5541			0.269426
$81$	−68.9002			−0.850620
$82$	−41.1207			−0.501472
$83$			8.27453i			0.0996931i	0.998757	+	0.0498466i	$0.0158732\pi$
$83$			8.27453i			0.0996931i	−0.998757	+	0.0498466i	$0.984127\pi$
$84$		−	22.9016i		−	0.272638i
$85$			69.2320i			0.814495i
$86$	3.81384			0.0443470
$87$			125.319i			1.44044i
$88$	−76.4507	−	57.6269i	−0.868757	−	0.654851i
$89$	84.8892			0.953811			0.476906	−	0.878954i	$-0.341758\pi$
$89$	84.8892			0.953811			0.476906	+	0.878954i	$0.341758\pi$
$90$			4.42897i			0.0492107i
$91$	−19.5825			−0.215192
$92$	15.8945			0.172766
$93$	73.1549			0.786611
$94$		−	3.89022i		−	0.0413853i
$95$			10.0621i			0.105917i
$96$			52.3739i			0.545561i
$97$	160.450			1.65413			0.827063	−	0.562109i	$-0.190010\pi$
$97$	160.450			1.65413			0.827063	+	0.562109i	$0.190010\pi$
$98$			6.34690i			0.0647643i
$99$	7.86394	−	10.4327i	0.0794337	−	0.105381i
$100$	6.09403			0.0609403
$101$		−	38.1687i		−	0.377908i	−0.981986	−	0.188954i	$-0.939490\pi$
$101$		−	38.1687i		−	0.377908i	0.981986	−	0.188954i	$-0.0605098\pi$
$102$	144.320			1.41491
$103$	34.4787			0.334744			0.167372	−	0.985894i	$-0.446472\pi$
$103$	34.4787			0.334744			0.167372	+	0.985894i	$0.446472\pi$
$104$	25.3521			0.243770
$105$			42.0161i			0.400154i
$106$			155.271i			1.46483i
$107$		−	132.298i		−	1.23643i	−0.786009	−	0.618214i	$-0.787856\pi$
$107$		−	132.298i		−	1.23643i	0.786009	−	0.618214i	$-0.212144\pi$
$108$	−34.7056			−0.321348
$109$			174.238i			1.59851i	0.600992	+	0.799255i	$0.294772\pi$
$109$			174.238i			1.59851i	−0.600992	+	0.799255i	$0.705228\pi$
$110$	32.7563	+	24.6910i	0.297785	+	0.224464i
$111$	−80.5391			−0.725577
$112$			64.8017i			0.578587i
$113$	−104.085			−0.921104			−0.460552	−	0.887633i	$-0.652349\pi$
$113$	−104.085			−0.921104			−0.460552	+	0.887633i	$0.652349\pi$
$114$	20.9754			0.183994
$115$	−29.1606			−0.253571
$116$			54.6462i			0.471088i
$117$			3.45962i			0.0295694i
$118$		−	181.138i		−	1.53507i
$119$	−208.144			−1.74911
$120$		−	54.3953i		−	0.453294i
$121$	−33.3188	−	116.322i	−0.275362	−	0.961341i
$122$	−91.3825			−0.749037
$123$			68.9183i			0.560312i
$124$	31.8998			0.257256
$125$	−11.1803			−0.0894427
$126$	−13.3155			−0.105679
$127$			32.2445i			0.253894i	0.991910	+	0.126947i	$0.0405178\pi$
$127$			32.2445i			0.253894i	−0.991910	+	0.126947i	$0.959482\pi$
$128$		−	41.4634i		−	0.323933i
$129$		−	6.39201i		−	0.0495504i
$130$	−10.8624			−0.0835572
$131$		−	253.053i		−	1.93170i	−0.259093	−	0.965852i	$-0.583423\pi$
$131$		−	253.053i		−	1.93170i	0.259093	−	0.965852i	$-0.416577\pi$
$132$	−22.5560	+	29.9239i	−0.170879	+	0.226697i
$133$	−30.2514			−0.227454
$134$			15.0391i			0.112232i
$135$	63.6723			0.471647
$136$	269.469			1.98139
$137$	−200.242			−1.46162			−0.730811	−	0.682580i	$-0.760858\pi$
$137$	−200.242			−1.46162			−0.730811	+	0.682580i	$0.760858\pi$
$138$			60.7880i			0.440492i
$139$		−	199.124i		−	1.43255i	−0.697821	−	0.716273i	$-0.745847\pi$
$139$		−	199.124i		−	1.43255i	0.697821	−	0.716273i	$-0.254153\pi$
$140$			18.3215i			0.130868i
$141$	−6.52001			−0.0462412
$142$		−	2.08355i		−	0.0146729i
$143$	25.5871	+	19.2870i	0.178931	+	0.134874i
$144$	11.4485			0.0795031
$145$		−	100.256i		−	0.691421i
$146$	−40.2014			−0.275352
$147$	10.6374			0.0723634
$148$	−35.1197			−0.237296
$149$		−	42.5232i		−	0.285391i	−0.989767	−	0.142695i	$-0.954423\pi$
$149$		−	42.5232i		−	0.285391i	0.989767	−	0.142695i	$-0.0455769\pi$
$150$			23.3064i			0.155376i
$151$			225.857i			1.49574i	0.663845	+	0.747870i	$0.268923\pi$
$151$			225.857i			1.49574i	−0.663845	+	0.747870i	$0.731077\pi$
$152$	39.1643			0.257660
$153$			36.7726i			0.240344i
$154$	−74.2327	+	98.4808i	−0.482030	+	0.639486i
$155$	−58.5246			−0.377578
$156$		−	9.92318i		−	0.0636101i
$157$	−121.955			−0.776782			−0.388391	−	0.921495i	$-0.626969\pi$
$157$	−121.955			−0.776782			−0.388391	+	0.921495i	$0.626969\pi$
$158$	180.909			1.14499
$159$	260.235			1.63670
$160$		−	41.8996i		−	0.261872i
$161$		−	87.6705i		−	0.544537i
$162$		−	114.904i		−	0.709286i
$163$	−88.1904			−0.541046			−0.270523	−	0.962714i	$-0.587197\pi$
$163$	−88.1904			−0.541046			−0.270523	+	0.962714i	$0.587197\pi$
$164$			30.0524i			0.183246i
$165$	41.3822	−	54.8996i	0.250801	−	0.332725i
$166$	−13.7994			−0.0831287
$167$		−	155.562i		−	0.931508i	−0.884914	−	0.465754i	$-0.845783\pi$
$167$		−	155.562i		−	0.931508i	0.884914	−	0.465754i	$-0.154217\pi$
$168$	163.538			0.973439
$169$	160.515			0.949793
$170$	−115.458			−0.679163
$171$			5.34448i			0.0312543i
$172$		−	2.78729i		−	0.0162052i
$173$			214.864i			1.24199i	0.783815	+	0.620995i	$0.213271\pi$
$173$			214.864i			1.24199i	−0.783815	+	0.620995i	$0.786729\pi$
$174$	−208.993			−1.20111
$175$		−	33.6133i		−	0.192076i
$176$	63.8239	−	84.6719i	0.362636	−	0.481090i
$177$	−303.587			−1.71518
$178$			141.569i			0.795331i
$179$	−155.650			−0.869555			−0.434778	−	0.900538i	$-0.643173\pi$
$179$	−155.650			−0.869555			−0.434778	+	0.900538i	$0.643173\pi$
$180$	3.23684			0.0179824
$181$	189.154			1.04505			0.522525	−	0.852624i	$-0.324990\pi$
$181$	189.154			1.04505			0.522525	+	0.852624i	$0.324990\pi$
$182$		−	32.6575i		−	0.179437i
$183$			153.157i			0.836924i
$184$			113.501i			0.616852i
$185$	64.4320			0.348281
$186$			122.000i			0.655913i
$187$	271.967	+	205.003i	1.45437	+	1.09627i
$188$	−2.84311			−0.0151229
$189$			191.429i			1.01285i
$190$	−16.7805			−0.0883184
$191$	−123.993			−0.649180			−0.324590	−	0.945855i	$-0.605226\pi$
$191$	−123.993			−0.649180			−0.324590	+	0.945855i	$0.605226\pi$
$192$	−195.113			−1.01621
$193$		−	234.124i		−	1.21308i	−0.795054	−	0.606538i	$-0.792558\pi$
$193$		−	234.124i		−	1.21308i	0.795054	−	0.606538i	$-0.207442\pi$
$194$			267.582i			1.37929i
$195$			18.2054i			0.0933613i
$196$	4.63853			0.0236660
$197$		−	218.949i		−	1.11142i	−0.831377	−	0.555709i	$-0.812447\pi$
$197$		−	218.949i		−	1.11142i	0.831377	−	0.555709i	$-0.187553\pi$
$198$	17.3985	+	13.1146i	0.0878712	+	0.0662354i
$199$	127.963			0.643028			0.321514	−	0.946905i	$-0.395808\pi$
$199$	127.963			0.643028			0.321514	+	0.946905i	$0.395808\pi$
$200$			43.5168i			0.217584i
$201$	25.2056			0.125401
$202$	63.6537			0.315117
$203$	301.417			1.48481
$204$		−	105.474i		−	0.517031i
$205$		−	55.1353i		−	0.268953i
$206$			57.4998i			0.279125i
$207$	−15.4887			−0.0748244
$208$			28.0783i			0.134992i
$209$	39.5274	+	29.7949i	0.189126	+	0.142559i
$210$	−70.0700			−0.333666
$211$			224.173i			1.06243i	0.847237	+	0.531215i	$0.178264\pi$
$211$			224.173i			1.06243i	−0.847237	+	0.531215i	$0.821736\pi$
$212$	113.478			0.535272
$213$	−3.49203			−0.0163945
$214$	220.632			1.03099
$215$			5.11367i			0.0237845i
$216$		−	247.829i		−	1.14736i
$217$		−	175.952i		−	0.810840i
$218$	−290.575			−1.33291
$219$			67.3776i			0.307660i
$220$	18.0450	−	23.9394i	0.0820229	−	0.108816i
$221$	−90.1880			−0.408090
$222$		−	134.314i		−	0.605020i
$223$	−267.394			−1.19908			−0.599538	−	0.800346i	$-0.704649\pi$
$223$	−267.394			−1.19908			−0.599538	+	0.800346i	$0.704649\pi$
$224$	125.970			0.562365
$225$	−5.93843			−0.0263930
$226$		−	173.581i		−	0.768059i
$227$			157.636i			0.694431i	0.937785	+	0.347216i	$0.112873\pi$
$227$			157.636i			0.694431i	−0.937785	+	0.347216i	$0.887127\pi$
$228$		−	15.3295i		−	0.0672347i
$229$	43.2374			0.188810			0.0944049	−	0.995534i	$-0.469905\pi$
$229$	43.2374			0.188810			0.0944049	+	0.995534i	$0.469905\pi$
$230$		−	48.6309i		−	0.211439i
$231$	165.054	+	124.414i	0.714519	+	0.538589i
$232$	−390.223			−1.68199
$233$		−	213.611i		−	0.916784i	−0.888750	−	0.458392i	$-0.848426\pi$
$233$		−	213.611i		−	0.916784i	0.888750	−	0.458392i	$-0.151574\pi$
$234$	−5.76958			−0.0246563
$235$	5.21607			0.0221960
$236$	−132.382			−0.560939
$237$		−	303.204i		−	1.27934i
$238$		−	347.120i		−	1.45849i
$239$		−	277.630i		−	1.16163i	−0.814035	−	0.580816i	$-0.802733\pi$
$239$		−	277.630i		−	1.16163i	0.814035	−	0.580816i	$-0.197267\pi$
$240$	60.2448			0.251020
$241$			39.3269i			0.163182i	0.996666	+	0.0815910i	$0.0260001\pi$
$241$			39.3269i			0.163182i	−0.996666	+	0.0815910i	$0.974000\pi$
$242$	193.990	−	55.5655i	0.801610	−	0.229609i
$243$	63.6963			0.262125
$244$			66.7855i			0.273711i
$245$	−8.51003			−0.0347348
$246$	−114.934			−0.467213
$247$	−13.1078			−0.0530681
$248$			227.793i			0.918520i
$249$			23.1277i			0.0928825i
$250$		−	18.6454i		−	0.0745814i
$251$	−348.287			−1.38760			−0.693800	−	0.720168i	$-0.744065\pi$
$251$	−348.287			−1.38760			−0.693800	+	0.720168i	$0.744065\pi$
$252$			9.73145i			0.0386169i
$253$	−86.3476	+	114.553i	−0.341295	+	0.452779i
$254$	−53.7739			−0.211708
$255$			193.507i			0.758852i
$256$	−210.078			−0.820616
$257$	−213.878			−0.832211			−0.416105	−	0.909316i	$-0.636605\pi$
$257$	−213.878			−0.832211			−0.416105	+	0.909316i	$0.636605\pi$
$258$	10.6599			0.0413174
$259$			193.713i			0.747926i
$260$			7.93864i			0.0305332i
$261$		−	53.2510i		−	0.204027i
$262$	422.015			1.61074
$263$		−	164.115i		−	0.624012i	−0.950080	−	0.312006i	$-0.898999\pi$
$263$		−	164.115i		−	0.624012i	0.950080	−	0.312006i	$-0.101001\pi$
$264$	−213.684	−	161.070i	−0.809407	−	0.610114i
$265$	−208.191			−0.785625
$266$		−	50.4500i		−	0.189662i
$267$	237.270			0.888651
$268$	10.9911			0.0410116
$269$	375.819			1.39710			0.698549	−	0.715562i	$-0.253829\pi$
$269$	375.819			1.39710			0.698549	+	0.715562i	$0.253829\pi$
$270$			106.186i			0.393280i
$271$			163.935i			0.604928i	0.953161	+	0.302464i	$0.0978092\pi$
$271$			163.935i			0.604928i	−0.953161	+	0.302464i	$0.902191\pi$
$272$			298.447i			1.09723i
$273$	−54.7341			−0.200491
$274$		−	333.942i		−	1.21877i
$275$	−33.1061	+	43.9202i	−0.120386	+	0.159710i
$276$	44.4259			0.160963
$277$			336.063i			1.21323i	0.794998	+	0.606613i	$0.207472\pi$
$277$			336.063i			1.21323i	−0.794998	+	0.606613i	$0.792528\pi$
$278$	332.077			1.19452
$279$	−31.0853			−0.111417
$280$	−130.832			−0.467256
$281$			383.397i			1.36440i	0.731164	+	0.682202i	$0.238977\pi$
$281$			383.397i			1.36440i	−0.731164	+	0.682202i	$0.761023\pi$
$282$		−	10.8734i		−	0.0385580i
$283$		−	31.1879i		−	0.110204i	−0.998481	−	0.0551022i	$-0.982452\pi$
$283$		−	31.1879i		−	0.110204i	0.998481	−	0.0551022i	$-0.0175485\pi$
$284$	−1.52273			−0.00536172
$285$			28.1241i			0.0986811i
$286$	−32.1648	+	42.6714i	−0.112464	+	0.149201i
$287$	165.762			0.577570
$288$		−	22.2549i		−	0.0772741i
$289$	−669.615			−2.31701
$290$	167.196			0.576539
$291$	448.467			1.54112
$292$			29.3806i			0.100618i
$293$			175.574i			0.599229i	0.954060	+	0.299614i	$0.0968580\pi$
$293$			175.574i			0.599229i	−0.954060	+	0.299614i	$0.903142\pi$
$294$			17.7399i			0.0603399i
$295$	242.872			0.823296
$296$		−	250.786i		−	0.847251i
$297$	188.540	−	250.127i	0.634815	−	0.842177i
$298$	70.9156			0.237972
$299$		−	37.9873i		−	0.127048i
$300$	17.0331			0.0567771
$301$	−15.3741			−0.0510766
$302$	−376.659			−1.24722
$303$		−	106.684i		−	0.352091i
$304$			43.3759i			0.142684i
$305$		−	122.527i		−	0.401728i
$306$	−61.3253			−0.200409
$307$			515.038i			1.67765i	0.544402	+	0.838825i	$0.316757\pi$
$307$			515.038i			1.67765i	−0.544402	+	0.838825i	$0.683243\pi$
$308$	71.9731	+	54.2518i	0.233679	+	0.176142i
$309$	96.3697			0.311876
$310$		−	97.6010i		−	0.314842i
$311$	419.087			1.34755			0.673774	−	0.738937i	$-0.264672\pi$
$311$	419.087			1.34755			0.673774	+	0.738937i	$0.264672\pi$
$312$	70.8603			0.227116
$313$	−82.3366			−0.263056			−0.131528	−	0.991312i	$-0.541988\pi$
$313$	−82.3366			−0.263056			−0.131528	+	0.991312i	$0.541988\pi$
$314$		−	203.383i		−	0.647716i
$315$		−	17.8537i		−	0.0566784i
$316$		−	132.215i		−	0.418400i
$317$	373.069			1.17687			0.588437	−	0.808543i	$-0.299743\pi$
$317$	373.069			1.17687			0.588437	+	0.808543i	$0.299743\pi$
$318$			433.992i			1.36475i
$319$	−393.840	−	296.868i	−1.23461	−	0.930622i
$320$	156.092			0.487788
$321$		−	369.779i		−	1.15196i
$322$	146.207			0.454060
$323$	−139.324			−0.431344
$324$	−83.9760			−0.259185
$325$		−	14.5645i		−	0.0448139i
$326$		−	147.074i		−	0.451149i
$327$			487.003i			1.48931i
$328$	−214.601			−0.654271
$329$			15.6819i			0.0476655i
$330$	91.5556	+	69.0127i	0.277441	+	0.209129i
$331$	179.066			0.540986			0.270493	−	0.962722i	$-0.412813\pi$
$331$	179.066			0.540986			0.270493	+	0.962722i	$0.412813\pi$
$332$			10.0850i			0.0303766i
$333$	34.2230			0.102772
$334$	259.429			0.776734
$335$	−20.1647			−0.0601931
$336$			181.124i			0.539060i
$337$		−	187.268i		−	0.555693i	−0.960626	−	0.277846i	$-0.910379\pi$
$337$		−	187.268i		−	0.555693i	0.960626	−	0.277846i	$-0.0896206\pi$
$338$			267.689i			0.791981i
$339$	−290.922			−0.858178
$340$			84.3804i			0.248178i
$341$	−173.297	+	229.905i	−0.508203	+	0.674207i
$342$	−8.91295			−0.0260613
$343$		−	354.996i		−	1.03497i
$344$	19.9037			0.0578596
$345$	−81.5055			−0.236248
$346$	−358.327			−1.03563
$347$			388.617i			1.11993i	0.828515	+	0.559967i	$0.189186\pi$
$347$			388.617i			1.11993i	−0.828515	+	0.559967i	$0.810814\pi$
$348$			152.739i			0.438905i
$349$			73.9677i			0.211942i	0.994369	+	0.105971i	$0.0337950\pi$
$349$			73.9677i			0.211942i	−0.994369	+	0.105971i	$0.966205\pi$
$350$	56.0566			0.160162
$351$			82.9453i			0.236311i
$352$	−164.596	−	124.069i	−0.467602	−	0.352469i
$353$	208.797			0.591492			0.295746	−	0.955267i	$-0.404432\pi$
$353$	208.797			0.591492			0.295746	+	0.955267i	$0.404432\pi$
$354$		−	506.289i		−	1.43020i
$355$	2.79366			0.00786945
$356$	103.463			0.290628
$357$	−581.773			−1.62962
$358$		−	259.577i		−	0.725075i
$359$		−	32.9550i		−	0.0917967i	−0.998946	−	0.0458984i	$-0.985385\pi$
$359$		−	32.9550i		−	0.0917967i	0.998946	−	0.0458984i	$-0.0146150\pi$
$360$			23.1139i			0.0642053i
$361$	340.751			0.943908
$362$			315.450i			0.871410i
$363$	−93.1278	−	325.127i	−0.256550	−	0.895666i
$364$	−23.8672			−0.0655694
$365$		−	53.9028i		−	0.147679i
$366$	−255.419			−0.697866
$367$	−29.7192			−0.0809788			−0.0404894	−	0.999180i	$-0.512892\pi$
$367$	−29.7192			−0.0809788			−0.0404894	+	0.999180i	$0.512892\pi$
$368$	−125.706			−0.341593
$369$		−	29.2851i		−	0.0793634i
$370$			107.453i			0.290413i
$371$		−	625.918i		−	1.68711i
$372$	89.1616			0.239682
$373$		−	436.560i		−	1.17040i	−0.810889	−	0.585201i	$-0.801016\pi$
$373$		−	436.560i		−	1.17040i	0.810889	−	0.585201i	$-0.198984\pi$
$374$	−341.882	+	453.557i	−0.914123	+	1.21272i
$375$	−31.2496			−0.0833323
$376$		−	20.3023i		−	0.0539955i
$377$	130.603			0.346426
$378$	−319.244			−0.844560
$379$	74.5391			0.196673			0.0983366	−	0.995153i	$-0.468648\pi$
$379$	74.5391			0.196673			0.0983366	+	0.995153i	$0.468648\pi$
$380$			12.2638i			0.0322730i
$381$			90.1251i			0.236549i
$382$		−	206.783i		−	0.541316i
$383$	−496.956			−1.29754			−0.648768	−	0.760986i	$-0.724715\pi$
$383$	−496.956			−1.29754			−0.648768	+	0.760986i	$0.724715\pi$
$384$		−	115.892i		−	0.301803i
$385$	−132.045	−	99.5324i	−0.342973	−	0.258526i
$386$	390.446			1.01152
$387$			2.71612i			0.00701840i
$388$	195.558			0.504015
$389$	6.51617			0.0167511			0.00837554	−	0.999965i	$-0.497334\pi$
$389$	6.51617			0.0167511			0.00837554	+	0.999965i	$0.497334\pi$
$390$	−30.3611			−0.0778489
$391$		−	403.770i		−	1.03266i
$392$			33.1233i			0.0844981i
$393$		−	707.297i		−	1.79974i
$394$	365.140			0.926751
$395$			242.566i			0.614091i
$396$	9.58461	−	12.7154i	0.0242036	−	0.0321096i
$397$	−59.6577			−0.150271			−0.0751357	−	0.997173i	$-0.523939\pi$
$397$	−59.6577			−0.150271			−0.0751357	+	0.997173i	$0.523939\pi$
$398$			213.402i			0.536186i
$399$	−84.5542			−0.211915
$400$	−48.1964			−0.120491
$401$	−298.153			−0.743524			−0.371762	−	0.928328i	$-0.621246\pi$
$401$	−298.153			−0.743524			−0.371762	+	0.928328i	$0.621246\pi$
$402$			42.0351i			0.104565i
$403$		−	76.2395i		−	0.189180i
$404$		−	46.5203i		−	0.115149i
$405$	154.066			0.380409
$406$			502.670i			1.23810i
$407$	190.790	−	253.111i	0.468771	−	0.621895i
$408$	753.180			1.84603
$409$			170.539i			0.416967i	0.978026	+	0.208483i	$0.0668528\pi$
$409$			170.539i			0.416967i	−0.978026	+	0.208483i	$0.933147\pi$
$410$	91.9487			0.224265
$411$	−559.687			−1.36177
$412$	42.0228			0.101997
$413$			730.188i			1.76801i
$414$		−	25.8303i		−	0.0623920i
$415$		−	18.5024i		−	0.0445841i
$416$	54.5822			0.131207
$417$		−	556.561i		−	1.33468i
$418$	−49.6887	+	65.9195i	−0.118873	+	0.157702i
$419$	547.949			1.30775			0.653877	−	0.756601i	$-0.273141\pi$
$419$	547.949			1.30775			0.653877	+	0.756601i	$0.273141\pi$
$420$			51.2095i			0.121927i
$421$	375.189			0.891185			0.445593	−	0.895236i	$-0.352993\pi$
$421$	375.189			0.891185			0.445593	+	0.895236i	$0.352993\pi$
$422$	−373.851			−0.885902
$423$	2.77051			0.00654968
$424$			810.332i			1.91116i
$425$		−	154.808i		−	0.364253i
$426$		−	5.82363i		−	0.0136705i
$427$	368.374			0.862702
$428$		−	161.245i		−	0.376742i
$429$	71.5172	+	53.9082i	0.166707	+	0.125660i
$430$	−8.52802			−0.0198326
$431$			405.352i			0.940493i	0.882535	+	0.470246i	$0.155835\pi$
$431$			405.352i			0.940493i	−0.882535	+	0.470246i	$0.844165\pi$
$432$	274.480			0.635370
$433$	−122.182			−0.282175			−0.141088	−	0.989997i	$-0.545060\pi$
$433$	−122.182			−0.282175			−0.141088	+	0.989997i	$0.545060\pi$
$434$	293.434			0.676115
$435$		−	280.221i		−	0.644186i
$436$			212.362i			0.487068i
$437$		−	58.6835i		−	0.134287i
$438$	−112.365			−0.256541
$439$			125.331i			0.285492i	0.989759	+	0.142746i	$0.0455931\pi$
$439$			125.331i			0.285492i	−0.989759	+	0.142746i	$0.954407\pi$
$440$	170.949	+	128.858i	0.388520	+	0.292858i
$441$	−4.52010			−0.0102497
$442$		−	150.406i		−	0.340284i
$443$	−66.9517			−0.151133			−0.0755663	−	0.997141i	$-0.524076\pi$
$443$	−66.9517			−0.151133			−0.0755663	+	0.997141i	$0.524076\pi$
$444$	−98.1615			−0.221084
$445$	−189.818			−0.426557
$446$		−	445.931i		−	0.999845i
$447$		−	118.855i		−	0.265894i
$448$			469.285i			1.04751i
$449$	227.828			0.507413			0.253706	−	0.967281i	$-0.418350\pi$
$449$	227.828			0.507413			0.253706	+	0.967281i	$0.418350\pi$
$450$		−	9.90347i		−	0.0220077i
$451$	−216.590	−	163.261i	−0.480245	−	0.361998i
$452$	−126.859			−0.280662
$453$			631.281i			1.39356i
$454$	−262.888			−0.579049
$455$	43.7878			0.0962369
$456$	109.466			0.240058
$457$			328.089i			0.717919i	0.933353	+	0.358959i	$0.116868\pi$
$457$			328.089i			0.717919i	−0.933353	+	0.358959i	$0.883132\pi$
$458$			72.1067i			0.157438i
$459$			881.632i			1.92077i
$460$	−35.5412			−0.0772634
$461$			634.564i			1.37649i	0.725476	+	0.688247i	$0.241619\pi$
$461$			634.564i			1.37649i	−0.725476	+	0.688247i	$0.758381\pi$
$462$	−207.484	+	275.259i	−0.449100	+	0.595798i
$463$	−39.8190			−0.0860022			−0.0430011	−	0.999075i	$-0.513692\pi$
$463$	−39.8190			−0.0860022			−0.0430011	+	0.999075i	$0.513692\pi$
$464$		−	432.186i		−	0.931436i
$465$	−163.579			−0.351783
$466$	356.237			0.764456
$467$	−120.629			−0.258307			−0.129153	−	0.991625i	$-0.541226\pi$
$467$	−120.629			−0.258307			−0.129153	+	0.991625i	$0.541226\pi$
$468$			4.21660i			0.00900984i
$469$		−	60.6245i		−	0.129263i
$470$			8.69880i			0.0185081i
$471$	−340.870			−0.723715
$472$		−	945.323i		−	2.00280i
$473$	20.0882	+	15.1421i	0.0424698	+	0.0320129i
$474$	505.650			1.06677
$475$		−	22.4996i		−	0.0473675i
$476$	−253.687			−0.532956
$477$	−110.580			−0.231825
$478$	463.002			0.968623
$479$		−	611.310i		−	1.27622i	−0.769945	−	0.638110i	$-0.779716\pi$
$479$		−	611.310i		−	1.27622i	0.769945	−	0.638110i	$-0.220284\pi$
$480$		−	117.112i		−	0.243982i
$481$			83.9351i			0.174501i
$482$	−65.5851			−0.136069
$483$		−	245.044i		−	0.507337i
$484$	−40.6092	−	141.774i	−0.0839032	−	0.292922i
$485$	−358.778			−0.739748
$486$			106.226i			0.218572i
$487$	−386.421			−0.793472			−0.396736	−	0.917933i	$-0.629857\pi$
$487$	−386.421			−0.793472			−0.396736	+	0.917933i	$0.629857\pi$
$488$	−476.908			−0.977270
$489$	−246.497			−0.504083
$490$		−	14.1921i		−	0.0289635i
$491$			699.750i			1.42515i	0.701594	+	0.712577i	$0.252472\pi$
$491$			699.750i			1.42515i	−0.701594	+	0.712577i	$0.747528\pi$
$492$			83.9981i			0.170728i
$493$	1388.19			2.81580
$494$		−	21.8598i		−	0.0442506i
$495$	−17.5843	+	23.3282i	−0.0355238	+	0.0471277i
$496$	−252.289			−0.508647
$497$			8.39903i			0.0168995i
$498$	−38.5699			−0.0774496
$499$	−243.340			−0.487654			−0.243827	−	0.969819i	$-0.578403\pi$
$499$	−243.340			−0.487654			−0.243827	+	0.969819i	$0.578403\pi$
$500$	−13.6267			−0.0272533
$501$		−	434.803i		−	0.867871i
$502$		−	580.836i		−	1.15704i
$503$		−	90.1999i		−	0.179324i	−0.995972	−	0.0896620i	$-0.971421\pi$
$503$		−	90.1999i		−	0.179324i	0.995972	−	0.0896620i	$-0.0285787\pi$
$504$	−69.4912			−0.137879
$505$			85.3479i			0.169006i
$506$	−191.039	−	144.001i	−0.377548	−	0.284587i
$507$	448.648			0.884907
$508$			39.2998i			0.0773619i
$509$	629.870			1.23746			0.618732	−	0.785602i	$-0.287647\pi$
$509$	629.870			1.23746			0.618732	+	0.785602i	$0.287647\pi$
$510$	−322.710			−0.632765
$511$	162.057			0.317137
$512$		−	516.198i		−	1.00820i
$513$			128.135i			0.249777i
$514$		−	356.683i		−	0.693935i
$515$	−77.0967			−0.149702
$516$		−	7.79061i		−	0.0150981i
$517$	15.4453	−	20.4905i	0.0298749	−	0.0396335i
$518$	−323.053			−0.623655
$519$			600.556i			1.15714i
$520$	−56.6889			−0.109017
$521$	−355.136			−0.681643			−0.340822	−	0.940128i	$-0.610705\pi$
$521$	−355.136			−0.681643			−0.340822	+	0.940128i	$0.610705\pi$
$522$	88.8062			0.170127
$523$		−	107.213i		−	0.204996i	−0.994733	−	0.102498i	$-0.967317\pi$
$523$		−	107.213i		−	0.204996i	0.994733	−	0.102498i	$-0.0326835\pi$
$524$		−	308.423i		−	0.588593i
$525$		−	93.9510i		−	0.178954i
$526$	273.693			0.520330
$527$		−	810.355i		−	1.53768i
$528$	178.391	−	236.662i	0.337862	−	0.448224i
$529$	−358.931			−0.678509
$530$		−	347.198i		−	0.655090i
$531$	129.002			0.242941
$532$	−36.8706			−0.0693056
$533$	71.8243			0.134755
$534$			395.693i			0.740998i
$535$			295.827i			0.552948i
$536$			78.4862i			0.146430i
$537$	−435.051			−0.810151
$538$			626.750i			1.16496i
$539$	−25.1991	+	33.4303i	−0.0467515	+	0.0620229i
$540$	77.6041			0.143711
$541$		−	365.120i		−	0.674899i	−0.941344	−	0.337449i	$-0.890436\pi$
$541$		−	365.120i		−	0.674899i	0.941344	−	0.337449i	$-0.109564\pi$
$542$	−273.394			−0.504417
$543$	528.695			0.973656
$544$	580.159			1.06647
$545$		−	389.607i		−	0.714876i
$546$		−	91.2795i		−	0.167179i
$547$			384.034i			0.702074i	0.936362	+	0.351037i	$0.114171\pi$
$547$			384.034i			0.702074i	−0.936362	+	0.351037i	$0.885829\pi$
$548$	−244.056			−0.445358
$549$		−	65.0802i		−	0.118543i
$550$	−73.2454	−	55.2108i	−0.133173	−	0.100383i
$551$	201.758			0.366166
$552$			317.241i			0.574711i
$553$	−729.266			−1.31874
$554$	−560.450			−1.01164
$555$	180.091			0.324488
$556$		−	242.693i		−	0.436499i
$557$		−	93.3430i		−	0.167582i	−0.996483	−	0.0837908i	$-0.973297\pi$
$557$		−	93.3430i		−	0.167582i	0.996483	−	0.0837908i	$-0.0267028\pi$
$558$		−	51.8407i		−	0.0929045i
$559$	−6.66153			−0.0119169
$560$		−	144.901i		−	0.258752i
$561$	760.163	+	572.994i	1.35501	+	1.02138i
$562$	−639.388			−1.13770
$563$		−	325.624i		−	0.578373i	−0.957273	−	0.289187i	$-0.906615\pi$
$563$		−	325.624i		−	0.578373i	0.957273	−	0.289187i	$-0.0933848\pi$
$564$	−7.94663			−0.0140898
$565$	232.741			0.411930
$566$	52.0117			0.0918935
$567$			463.193i			0.816919i
$568$		−	10.8736i		−	0.0191437i
$569$			409.067i			0.718923i	0.933160	+	0.359461i	$0.117040\pi$
$569$			409.067i			0.718923i	−0.933160	+	0.359461i	$0.882960\pi$
$570$	−46.9023			−0.0822848
$571$		−	395.169i		−	0.692065i	−0.938223	−	0.346032i	$-0.887529\pi$
$571$		−	395.169i		−	0.692065i	0.938223	−	0.346032i	$-0.112471\pi$
$572$	31.1857	+	23.5071i	0.0545205	+	0.0410963i
$573$	−346.568			−0.604830
$574$			276.441i			0.481604i
$575$	65.2052			0.113400
$576$	82.9082			0.143938
$577$	−432.156			−0.748971			−0.374485	−	0.927233i	$-0.622181\pi$
$577$	−432.156			−0.748971			−0.374485	+	0.927233i	$0.622181\pi$
$578$		−	1116.71i		−	1.93203i
$579$		−	654.388i		−	1.13020i
$580$		−	122.193i		−	0.210677i
$581$	55.6269			0.0957433
$582$			747.904i			1.28506i
$583$	−616.473	+	817.844i	−1.05742	+	1.40282i
$584$	−209.804			−0.359253
$585$		−	7.73594i		−	0.0132238i
$586$	−292.803			−0.499664
$587$	−1.36709			−0.00232895			−0.00116447	−	0.999999i	$-0.500371\pi$
$587$	−1.36709			−0.00232895			−0.00116447	+	0.999999i	$0.500371\pi$
$588$	12.9649			0.0220492
$589$		−	117.776i		−	0.199960i
$590$			405.036i			0.686502i
$591$		−	611.974i		−	1.03549i
$592$	277.755			0.469181
$593$			232.591i			0.392228i	0.980581	+	0.196114i	$0.0628323\pi$
$593$			232.591i			0.392228i	−0.980581	+	0.196114i	$0.937168\pi$
$594$	417.134	+	314.427i	0.702246	+	0.529338i
$595$	465.424			0.782225
$596$		−	51.8275i		−	0.0869590i
$597$	357.662			0.599099
$598$	63.3511			0.105938
$599$	−291.349			−0.486392			−0.243196	−	0.969977i	$-0.578196\pi$
$599$	−291.349			−0.486392			−0.243196	+	0.969977i	$0.578196\pi$
$600$			121.632i			0.202719i
$601$			160.437i			0.266951i	0.991052	+	0.133475i	$0.0426137\pi$
$601$			160.437i			0.266951i	−0.991052	+	0.133475i	$0.957386\pi$
$602$		−	25.6392i		−	0.0425900i
$603$	−10.7105			−0.0177620
$604$			275.275i			0.455754i
$605$	74.5031	+	260.104i	0.123146	+	0.429925i
$606$	177.915			0.293590
$607$		−	107.785i		−	0.177571i	−0.996051	−	0.0887854i	$-0.971701\pi$
$607$		−	107.785i		−	0.177571i	0.996051	−	0.0887854i	$-0.0282985\pi$
$608$	84.3197			0.138684
$609$	842.475			1.38337
$610$	204.337			0.334979
$611$			6.79493i			0.0111210i
$612$			44.8186i			0.0732330i
$613$			552.780i			0.901761i	0.892584	+	0.450881i	$0.148890\pi$
$613$			552.780i			0.901761i	−0.892584	+	0.450881i	$0.851110\pi$
$614$	−858.925			−1.39890
$615$		−	154.106i		−	0.250579i
$616$	−387.406	+	513.952i	−0.628906	+	0.834338i
$617$	21.9153			0.0355192			0.0177596	−	0.999842i	$-0.494347\pi$
$617$	21.9153			0.0355192			0.0177596	+	0.999842i	$0.494347\pi$
$618$			160.715i			0.260056i
$619$	205.700			0.332310			0.166155	−	0.986100i	$-0.446865\pi$
$619$	205.700			0.332310			0.166155	+	0.986100i	$0.446865\pi$
$620$	−71.3301			−0.115049
$621$	−371.345			−0.597979
$622$			698.909i			1.12365i
$623$		−	570.682i		−	0.916022i
$624$			78.4804i			0.125770i
$625$	25.0000			0.0400000
$626$		−	137.312i		−	0.219348i
$627$	110.481	+	83.2783i	0.176206	+	0.132820i
$628$	−148.639			−0.236687
$629$			892.152i			1.41837i
$630$	29.7744			0.0472610
$631$	859.961			1.36285			0.681427	−	0.731886i	$-0.261360\pi$
$631$	859.961			1.36285			0.681427	+	0.731886i	$0.261360\pi$
$632$	944.129			1.49388
$633$			626.574i			0.989848i
$634$			622.164i			0.981331i
$635$		−	72.1010i		−	0.113545i
$636$	317.176			0.498705
$637$		−	11.0859i		−	0.0174034i
$638$	495.085	−	656.804i	0.775995	−	1.02947i
$639$	1.48385			0.00232214
$640$			92.7149i			0.144867i
$641$	794.780			1.23991			0.619953	−	0.784639i	$-0.287152\pi$
$641$	794.780			1.23991			0.619953	+	0.784639i	$0.287152\pi$
$642$	616.678			0.960558
$643$	−25.5239			−0.0396951			−0.0198475	−	0.999803i	$-0.506318\pi$
$643$	−25.5239			−0.0396951			−0.0198475	+	0.999803i	$0.506318\pi$
$644$		−	106.853i		−	0.165921i
$645$			14.2930i			0.0221596i
$646$		−	232.350i		−	0.359674i
$647$	−681.121			−1.05274			−0.526368	−	0.850257i	$-0.676447\pi$
$647$	−681.121			−1.05274			−0.526368	+	0.850257i	$0.676447\pi$
$648$		−	599.663i		−	0.925406i
$649$	719.170	−	954.086i	1.10812	−	1.47009i
$650$	24.2891			0.0373679
$651$		−	491.796i		−	0.755446i
$652$	−107.487			−0.164857
$653$	913.057			1.39825			0.699124	−	0.715000i	$-0.253573\pi$
$653$	913.057			1.39825			0.699124	+	0.715000i	$0.253573\pi$
$654$	−812.171			−1.24185
$655$			565.844i			0.863885i
$656$		−	237.678i		−	0.362315i
$657$		−	28.6304i		−	0.0435775i
$658$	−26.1526			−0.0397457
$659$		−	126.800i		−	0.192413i	−0.995361	−	0.0962065i	$-0.969329\pi$
$659$		−	126.800i		−	0.192413i	0.995361	−	0.0962065i	$-0.0306709\pi$
$660$	50.4368	−	66.9120i	0.0764194	−	0.101382i
$661$	−736.664			−1.11447			−0.557235	−	0.830355i	$-0.688138\pi$
$661$	−736.664			−1.11447			−0.557235	+	0.830355i	$0.688138\pi$
$662$			298.627i			0.451099i
$663$	−252.080			−0.380211
$664$	−72.0162			−0.108458
$665$	67.6442			0.101721
$666$			57.0735i			0.0856959i
$667$			584.706i			0.876621i
$668$		−	189.600i		−	0.283832i
$669$	−747.380			−1.11716
$670$		−	33.6285i		−	0.0501918i
$671$	−481.329	−	362.815i	−0.717331	−	0.540708i
$672$	352.092			0.523946
$673$		−	225.017i		−	0.334349i	−0.985927	−	0.167174i	$-0.946536\pi$
$673$		−	225.017i		−	0.334349i	0.985927	−	0.167174i	$-0.0534643\pi$
$674$	312.306			0.463362
$675$	−142.376			−0.210927
$676$	195.637			0.289403
$677$		−	109.258i		−	0.161386i	−0.996739	−	0.0806931i	$-0.974287\pi$
$677$		−	109.258i		−	0.161386i	0.996739	−	0.0806931i	$-0.0257134\pi$
$678$		−	485.169i		−	0.715588i
$679$		−	1078.65i		−	1.58859i
$680$	−602.551			−0.886105
$681$			440.601i			0.646991i
$682$	−383.410	−	289.006i	−0.562185	−	0.423763i
$683$	−1080.61			−1.58215			−0.791075	−	0.611719i	$-0.790478\pi$
$683$	−1080.61			−1.58215			−0.791075	+	0.611719i	$0.790478\pi$
$684$			6.51389i			0.00952323i
$685$	447.755			0.653657
$686$	592.023			0.863007
$687$	120.851			0.175911
$688$			22.0441i			0.0320408i
$689$		−	271.208i		−	0.393626i
$690$		−	135.926i		−	0.196994i
$691$	−1170.13			−1.69339			−0.846695	−	0.532078i	$-0.821411\pi$
$691$	−1170.13			−1.69339			−0.846695	+	0.532078i	$0.821411\pi$
$692$			261.878i			0.378436i
$693$	−70.1354	−	52.8666i	−0.101206	−	0.0762866i
$694$	−648.093			−0.933852
$695$			445.254i			0.640654i
$696$	−1090.69			−1.56709
$697$	763.426			1.09530
$698$	−123.355			−0.176727
$699$		−	597.053i		−	0.854153i
$700$		−	40.9681i		−	0.0585259i
$701$			328.408i			0.468485i	0.972178	+	0.234242i	$0.0752609\pi$
$701$			328.408i			0.468485i	−0.972178	+	0.234242i	$0.924739\pi$
$702$	−138.327			−0.197047
$703$			129.664i			0.184444i
$704$	462.204	−	613.183i	0.656540	−	0.870999i
$705$	14.5792			0.0206797
$706$			348.208i			0.493213i
$707$	−256.596			−0.362936
$708$	−370.014			−0.522618
$709$	−705.817			−0.995511			−0.497756	−	0.867317i	$-0.665842\pi$
$709$	−705.817			−0.995511			−0.497756	+	0.867317i	$0.665842\pi$
$710$			4.65896i			0.00656191i
$711$			128.839i			0.181208i
$712$			738.821i			1.03767i
$713$	341.323			0.478714
$714$		−	970.217i		−	1.35885i
$715$	−57.2145	−	43.1270i	−0.0800202	−	0.0603175i
$716$	−189.708			−0.264955
$717$		−	775.991i		−	1.08227i
$718$	54.9588			0.0765443
$719$	−584.645			−0.813137			−0.406568	−	0.913620i	$-0.633275\pi$
$719$	−584.645			−0.813137			−0.406568	+	0.913620i	$0.633275\pi$
$720$	−25.5995			−0.0355549
$721$		−	231.789i		−	0.321482i
$722$			568.267i			0.787074i
$723$			109.921i			0.152034i
$724$	230.542			0.318428
$725$			224.179i			0.309213i
$726$	542.211	−	155.308i	0.746847	−	0.213923i
$727$	370.464			0.509579			0.254790	−	0.966997i	$-0.417994\pi$
$727$	370.464			0.509579			0.254790	+	0.966997i	$0.417994\pi$
$728$		−	170.433i		−	0.234112i
$729$	798.136			1.09484
$730$	89.8932			0.123141
$731$	−70.8059			−0.0968617
$732$			186.669i			0.255012i
$733$			407.221i			0.555554i	0.960646	+	0.277777i	$0.0895977\pi$
$733$			407.221i			0.555554i	−0.960646	+	0.277777i	$0.910402\pi$
$734$		−	49.5625i		−	0.0675238i
$735$	−23.7860			−0.0323619
$736$			244.364i			0.332016i
$737$	−59.7097	+	79.2138i	−0.0810172	+	0.107481i
$738$	48.8385			0.0661768
$739$		−	1382.44i		−	1.87069i	−0.353731	−	0.935347i	$-0.615087\pi$
$739$		−	1382.44i		−	1.87069i	0.353731	−	0.935347i	$-0.384913\pi$
$740$	78.5301			0.106122
$741$	−36.6370			−0.0494427
$742$	1043.84			1.40679
$743$			748.989i			1.00806i	0.863686	+	0.504030i	$0.168150\pi$
$743$			748.989i			1.00806i	−0.863686	+	0.504030i	$0.831850\pi$
$744$			636.693i			0.855770i
$745$			95.0848i			0.127631i
$746$	728.047			0.975934
$747$		−	9.82754i		−	0.0131560i
$748$	331.475	+	249.859i	0.443149	+	0.334036i
$749$	−889.394			−1.18744
$750$		−	52.1147i		−	0.0694863i
$751$	−532.843			−0.709512			−0.354756	−	0.934959i	$-0.615436\pi$
$751$	−532.843			−0.709512			−0.354756	+	0.934959i	$0.615436\pi$
$752$	22.4856			0.0299010
$753$	−973.481			−1.29280
$754$			217.805i			0.288866i
$755$		−	505.031i		−	0.668915i
$756$			233.314i			0.308617i
$757$	−610.182			−0.806052			−0.403026	−	0.915188i	$-0.632042\pi$
$757$	−610.182			−0.806052			−0.403026	+	0.915188i	$0.632042\pi$
$758$			124.308i			0.163995i
$759$	−241.346	+	320.182i	−0.317979	+	0.421847i
$760$	−87.5741			−0.115229
$761$		−	180.435i		−	0.237102i	−0.992948	−	0.118551i	$-0.962175\pi$
$761$		−	180.435i		−	0.237102i	0.992948	−	0.118551i	$-0.0378249\pi$
$762$	−150.301			−0.197245
$763$	1171.34			1.53518
$764$	−151.124			−0.197806
$765$		−	82.2260i		−	0.107485i
$766$		−	828.769i		−	1.08194i
$767$			316.388i			0.412500i
$768$	−587.178			−0.764555
$769$			559.139i			0.727099i	0.931575	+	0.363550i	$0.118435\pi$
$769$			559.139i			0.727099i	−0.931575	+	0.363550i	$0.881565\pi$
$770$	165.989	−	220.210i	0.215571	−	0.285987i
$771$	−597.800			−0.775357
$772$		−	285.351i		−	0.369626i
$773$	272.373			0.352358			0.176179	−	0.984358i	$-0.443626\pi$
$773$	272.373			0.352358			0.176179	+	0.984358i	$0.443626\pi$
$774$	−4.52965			−0.00585226
$775$	130.865			0.168858
$776$			1396.46i			1.79956i
$777$			541.437i			0.696830i
$778$			10.8670i			0.0139678i
$779$	110.956			0.142433
$780$			22.1889i			0.0284473i
$781$	8.27230	−	10.9744i	0.0105919	−	0.0140518i
$782$	673.364			0.861079
$783$		−	1276.71i		−	1.63053i
$784$	−36.6852			−0.0467924
$785$	272.699			0.347387
$786$	1179.55			1.50070
$787$		−	1415.45i		−	1.79854i	−0.437398	−	0.899268i	$-0.644100\pi$
$787$		−	1415.45i		−	1.79854i	0.437398	−	0.899268i	$-0.355900\pi$
$788$		−	266.857i		−	0.338651i
$789$		−	458.710i		−	0.581382i
$790$	−404.525			−0.512057
$791$			699.727i			0.884610i
$792$	90.7994	+	68.4426i	0.114646	+	0.0864175i
$793$	159.615			0.201280
$794$		−	99.4906i		−	0.125303i
$795$	−581.903			−0.731954
$796$	155.961			0.195932
$797$	960.746			1.20545			0.602726	−	0.797948i	$-0.294081\pi$
$797$	960.746			1.20545			0.602726	+	0.797948i	$0.294081\pi$
$798$		−	141.010i		−	0.176705i
$799$			72.2239i			0.0903928i
$800$			93.6904i			0.117113i
$801$	−100.822			−0.125870
$802$		−	497.227i		−	0.619984i
$803$	−211.749	−	159.611i	−0.263697	−	0.198769i
$804$	30.7207			0.0382098
$805$			196.037i			0.243524i
$806$	127.144			0.157747
$807$	1050.43			1.30165
$808$	332.196			0.411134
$809$			850.203i			1.05093i	0.850815	+	0.525465i	$0.176109\pi$
$809$			850.203i			1.05093i	−0.850815	+	0.525465i	$0.823891\pi$
$810$			256.934i			0.317202i
$811$		−	316.974i		−	0.390843i	−0.980719	−	0.195422i	$-0.937392\pi$
$811$		−	316.974i		−	0.390843i	0.980719	−	0.195422i	$-0.0626075\pi$
$812$	367.368			0.452424
$813$			458.208i			0.563602i
$814$	422.111	+	318.178i	0.518564	+	0.390883i
$815$	197.200			0.241963
$816$			834.175i			1.02227i
$817$	−10.2909			−0.0125959
$818$	−284.407			−0.347686
$819$	23.2578			0.0283979
$820$		−	67.1993i		−	0.0819503i
$821$		−	1214.62i		−	1.47944i	−0.672915	−	0.739720i	$-0.734958\pi$
$821$		−	1214.62i		−	1.47944i	0.672915	−	0.739720i	$-0.265042\pi$
$822$		−	933.385i		−	1.13550i
$823$	1210.57			1.47093			0.735464	−	0.677564i	$-0.236964\pi$
$823$	1210.57			1.47093			0.735464	+	0.677564i	$0.236964\pi$
$824$			300.080i			0.364175i
$825$	−92.5333	+	122.759i	−0.112162	+	0.148799i
$826$	−1217.73			−1.47425
$827$			305.273i			0.369133i	0.982820	+	0.184566i	$0.0590881\pi$
$827$			305.273i			0.369133i	−0.982820	+	0.184566i	$0.940912\pi$
$828$	−18.8777			−0.0227991
$829$	−225.488			−0.272000			−0.136000	−	0.990709i	$-0.543425\pi$
$829$	−225.488			−0.272000			−0.136000	+	0.990709i	$0.543425\pi$
$830$	30.8563			0.0371763
$831$			939.315i			1.13034i
$832$			203.340i			0.244399i
$833$		−	117.833i		−	0.141457i
$834$	928.172			1.11292
$835$			347.847i			0.416583i
$836$	48.1762	+	36.3142i	0.0576271	+	0.0434381i
$837$	−745.279			−0.890417
$838$			913.810i			1.09047i
$839$	405.279			0.483050			0.241525	−	0.970395i	$-0.422352\pi$
$839$	405.279			0.483050			0.241525	+	0.970395i	$0.422352\pi$
$840$	−365.681			−0.435335
$841$	−1169.26			−1.39032
$842$			625.699i			0.743111i
$843$			1071.62i			1.27119i
$844$			273.223i			0.323724i
$845$	−358.922			−0.424760
$846$			4.62036i			0.00546142i
$847$	−781.995	+	223.991i	−0.923253	+	0.264452i
$848$	−897.472			−1.05834
$849$		−	87.1717i		−	0.102676i
$850$	258.171			0.303731
$851$	−375.776			−0.441570
$852$	−4.25610			−0.00499543
$853$		−	788.482i		−	0.924364i	−0.886785	−	0.462182i	$-0.847067\pi$
$853$		−	788.482i		−	0.924364i	0.886785	−	0.462182i	$-0.152933\pi$
$854$			614.334i			0.719360i
$855$		−	11.9506i		−	0.0139773i
$856$	1151.44			1.34514
$857$			1365.13i			1.59292i	0.604691	+	0.796460i	$0.293297\pi$
$857$			1365.13i			1.59292i	−0.604691	+	0.796460i	$0.706703\pi$
$858$	−89.9022	+	119.269i	−0.104781	+	0.139008i
$859$	519.889			0.605226			0.302613	−	0.953113i	$-0.402141\pi$
$859$	519.889			0.605226			0.302613	+	0.953113i	$0.402141\pi$
$860$			6.23257i			0.00724717i
$861$	463.315			0.538112
$862$	−676.003			−0.784226
$863$	1082.06			1.25384			0.626919	−	0.779085i	$-0.284316\pi$
$863$	1082.06			1.25384			0.626919	+	0.779085i	$0.284316\pi$
$864$		−	533.569i		−	0.617556i
$865$		−	480.451i		−	0.555434i
$866$		−	203.762i		−	0.235291i
$867$	−1871.61			−2.15872
$868$		−	214.452i		−	0.247064i
$869$	952.882	+	718.262i	1.09653	+	0.826538i
$870$	467.322			0.537152
$871$		−	26.2684i		−	0.0301589i
$872$	−1516.45			−1.73905
$873$	−190.565			−0.218287
$874$	97.8660			0.111975
$875$			75.1617i			0.0858990i
$876$			82.1203i			0.0937446i
$877$		−	819.535i		−	0.934475i	−0.884132	−	0.467238i	$-0.845249\pi$
$877$		−	819.535i		−	0.934475i	0.884132	−	0.467238i	$-0.154751\pi$
$878$	−209.013			−0.238056
$879$			490.738i			0.558292i
$880$	−142.715	+	189.332i	−0.162176	+	0.215150i
$881$	1482.75			1.68304			0.841518	−	0.540230i	$-0.181663\pi$
$881$	1482.75			1.68304			0.841518	+	0.540230i	$0.181663\pi$
$882$		−	7.53813i		−	0.00854663i
$883$	−503.758			−0.570508			−0.285254	−	0.958452i	$-0.592078\pi$
$883$	−503.758			−0.570508			−0.285254	+	0.958452i	$0.592078\pi$
$884$	−109.922			−0.124346
$885$	678.841			0.767052
$886$		−	111.655i		−	0.126021i
$887$		−	1653.39i		−	1.86402i	−0.362429	−	0.932011i	$-0.618053\pi$
$887$		−	1653.39i		−	1.86402i	0.362429	−	0.932011i	$-0.381947\pi$
$888$		−	700.960i		−	0.789370i
$889$	216.769			0.243835
$890$		−	316.558i		−	0.355683i
$891$	456.204	−	605.223i	0.512013	−	0.679262i
$892$	−325.901			−0.365360
$893$			10.4969i			0.0117547i
$894$	198.213			0.221714
$895$	348.045			0.388877
$896$	−278.744			−0.311098
$897$		−	106.176i		−	0.118368i
$898$			379.947i			0.423104i
$899$			1173.49i			1.30533i
$900$	−7.23779			−0.00804199
$901$		−	2882.69i		−	3.19944i
$902$	272.269	−	361.206i	0.301851	−	0.400450i
$903$	−42.9713			−0.0475873
$904$		−	905.887i		−	1.00209i
$905$	−422.961			−0.467360
$906$	−1052.78			−1.16201
$907$	1620.77			1.78695			0.893477	−	0.449109i	$-0.148258\pi$
$907$	1620.77			1.78695			0.893477	+	0.449109i	$0.148258\pi$
$908$			192.128i			0.211594i
$909$			45.3325i			0.0498707i
$910$			73.0245i			0.0802467i
$911$	−111.468			−0.122358			−0.0611791	−	0.998127i	$-0.519486\pi$
$911$	−111.468			−0.122358			−0.0611791	+	0.998127i	$0.519486\pi$
$912$			121.238i			0.132936i
$913$	−72.6838	−	54.7875i	−0.0796099	−	0.0600082i
$914$	−547.151			−0.598633
$915$		−	342.470i		−	0.374284i
$916$	52.6980			0.0575306
$917$	−1701.19			−1.85517
$918$	−1470.29			−1.60162
$919$			664.740i			0.723330i	0.932308	+	0.361665i	$0.117792\pi$
$919$			664.740i			0.723330i	−0.932308	+	0.361665i	$0.882208\pi$
$920$		−	253.795i		−	0.275865i
$921$			1439.56i			1.56304i
$922$	−1058.26			−1.14778
$923$			3.63927i			0.00394287i
$924$	201.169	+	151.637i	0.217715	+	0.164109i
$925$	−144.074			−0.155756
$926$		−	66.4058i		−	0.0717126i
$927$	−40.9499			−0.0441746
$928$	−840.138			−0.905321
$929$	−844.411			−0.908946			−0.454473	−	0.890760i	$-0.650172\pi$
$929$	−844.411			−0.908946			−0.454473	+	0.890760i	$0.650172\pi$
$930$		−	272.800i		−	0.293333i
$931$		−	17.1258i		−	0.0183950i
$932$		−	260.350i		−	0.279345i
$933$	1171.37			1.25549
$934$		−	201.172i		−	0.215388i
$935$	−608.137	−	458.401i	−0.650414	−	0.490268i
$936$	−30.1103			−0.0321691
$937$			175.541i			0.187343i	0.995603	+	0.0936716i	$0.0298604\pi$
$937$			175.541i			0.187343i	−0.995603	+	0.0936716i	$0.970140\pi$
$938$	101.103			0.107786
$939$	−230.135			−0.245085
$940$	6.35738			0.00676317
$941$		−	838.440i		−	0.891010i	−0.895279	−	0.445505i	$-0.853024\pi$
$941$		−	838.440i		−	0.891010i	0.895279	−	0.445505i	$-0.146976\pi$
$942$		−	568.466i		−	0.603467i
$943$			321.556i			0.340993i
$944$	1046.98			1.10909
$945$		−	428.047i		−	0.452960i
$946$	−25.2523	+	33.5010i	−0.0266938	+	0.0354133i
$947$	1483.34			1.56636			0.783179	−	0.621796i	$-0.213597\pi$
$947$	1483.34			1.56636			0.783179	+	0.621796i	$0.213597\pi$
$948$		−	369.546i		−	0.389817i
$949$	70.2186			0.0739922
$950$	37.5223			0.0394972
$951$	1042.75			1.09647
$952$		−	1811.55i		−	1.90289i
$953$		−	186.094i		−	0.195272i	−0.995222	−	0.0976359i	$-0.968872\pi$
$953$		−	186.094i		−	0.195272i	0.995222	−	0.0976359i	$-0.0311281\pi$
$954$		−	184.414i		−	0.193306i
$955$	277.258			0.290322
$956$		−	338.377i		−	0.353951i
$957$	−1100.80	−	829.763i	−1.15027	−	0.867046i
$958$	1019.48			1.06417
$959$			1346.16i			1.40371i
$960$	436.285			0.454464
$961$	−275.974			−0.287174
$962$	−139.978			−0.145507
$963$			157.128i			0.163166i
$964$			47.9318i			0.0497218i
$965$			523.517i			0.542504i
$966$	408.657			0.423040
$967$			948.621i			0.980994i	0.871443	+	0.490497i	$0.163185\pi$
$967$			948.621i			0.980994i	−0.871443	+	0.490497i	$0.836815\pi$
$968$	1012.39	−	289.986i	1.04586	−	0.299572i
$969$	−389.418			−0.401876
$970$		−	598.331i		−	0.616836i
$971$	685.460			0.705932			0.352966	−	0.935636i	$-0.385173\pi$
$971$	685.460			0.705932			0.352966	+	0.935636i	$0.385173\pi$
$972$	77.6334			0.0798698
$973$	−1338.64			−1.37579
$974$		−	644.430i		−	0.661633i
$975$		−	40.7086i		−	0.0417524i
$976$		−	528.193i		−	0.541181i
$977$	48.0051			0.0491352			0.0245676	−	0.999698i	$-0.492179\pi$
$977$	48.0051			0.0491352			0.0245676	+	0.999698i	$0.492179\pi$
$978$		−	411.081i		−	0.420328i
$979$	−562.070	+	745.670i	−0.574127	+	0.761665i
$980$	−10.3721			−0.0105838
$981$		−	206.940i		−	0.210948i
$982$	−1166.97			−1.18836
$983$	1453.38			1.47851			0.739257	−	0.673423i	$-0.235177\pi$
$983$	1453.38			1.47851			0.739257	+	0.673423i	$0.235177\pi$
$984$	−599.821			−0.609574
$985$			489.585i			0.497041i
$986$			2315.07i			2.34794i
$987$			43.8318i			0.0444092i
$988$	−15.9759			−0.0161699
$989$		−	29.8236i		−	0.0301553i
$990$	−38.9042	−	29.3252i	−0.0392972	−	0.0296214i
$991$	1112.63			1.12273			0.561366	−	0.827568i	$-0.310276\pi$
$991$	1112.63			1.12273			0.561366	+	0.827568i	$0.310276\pi$
$992$			490.431i			0.494386i
$993$	500.500			0.504028
$994$	−14.0070			−0.0140915
$995$	−286.133			−0.287571
$996$			28.1882i			0.0283014i
$997$			846.960i			0.849508i	0.905309	+	0.424754i	$0.139639\pi$
$997$			846.960i			0.849508i	−0.905309	+	0.424754i	$0.860361\pi$
$998$		−	405.815i		−	0.406629i
$999$	820.507			0.821328

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	55.3.c.a.21.6	yes	8
3.2	odd	2		495.3.b.a.406.3		8
4.3	odd	2		880.3.j.a.241.4		8
5.2	odd	4		275.3.d.c.274.5		16
5.3	odd	4		275.3.d.c.274.12		16
5.4	even	2		275.3.c.f.76.3		8
11.10	odd	2	inner	55.3.c.a.21.3	✓	8
33.32	even	2		495.3.b.a.406.6		8
44.43	even	2		880.3.j.a.241.3		8
55.32	even	4		275.3.d.c.274.11		16
55.43	even	4		275.3.d.c.274.6		16
55.54	odd	2		275.3.c.f.76.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.3.c.a.21.3	✓	8	11.10	odd	2	inner
55.3.c.a.21.6	yes	8	1.1	even	1	trivial
275.3.c.f.76.3		8	5.4	even	2
275.3.c.f.76.6		8	55.54	odd	2
275.3.d.c.274.5		16	5.2	odd	4
275.3.d.c.274.6		16	55.43	even	4
275.3.d.c.274.11		16	55.32	even	4
275.3.d.c.274.12		16	5.3	odd	4
495.3.b.a.406.3		8	3.2	odd	2
495.3.b.a.406.6		8	33.32	even	2
880.3.j.a.241.3		8	44.43	even	2
880.3.j.a.241.4		8	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 55 = 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	55.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.66769i q^{2} +2.79505 q^{3} +1.21881 q^{4} -2.23607 q^{5} +4.66128i q^{6} -6.72266i q^{7} +8.70336i q^{8} -1.18769 q^{9} -3.72907i q^{10} +(-6.62122 + 8.78404i) q^{11} +3.40663 q^{12} -2.91291i q^{13} +11.2113 q^{14} -6.24993 q^{15} -9.63929 q^{16} -30.9615i q^{17} -1.98069i q^{18} -4.49991i q^{19} -2.72533 q^{20} -18.7902i q^{21} +(-14.6491 - 11.0422i) q^{22} +13.0410 q^{23} +24.3263i q^{24} +5.00000 q^{25} +4.85783 q^{26} -28.4751 q^{27} -8.19362i q^{28} +44.8359i q^{29} -10.4229i q^{30} +26.1730 q^{31} +18.7381i q^{32} +(-18.5067 + 24.5519i) q^{33} +51.6342 q^{34} +15.0323i q^{35} -1.44756 q^{36} -28.8149 q^{37} +7.50446 q^{38} -8.14172i q^{39} -19.4613i q^{40} +24.6573i q^{41} +31.3362 q^{42} -2.28690i q^{43} +(-8.06999 + 10.7060i) q^{44} +2.65575 q^{45} +21.7484i q^{46} -2.33270 q^{47} -26.9423 q^{48} +3.80580 q^{49} +8.33846i q^{50} -86.5390i q^{51} -3.55027i q^{52} +93.1057 q^{53} -47.4877i q^{54} +(14.8055 - 19.6417i) q^{55} +58.5097 q^{56} -12.5775i q^{57} -74.7724 q^{58} -108.616 q^{59} -7.61745 q^{60} +54.7958i q^{61} +43.6485i q^{62} +7.98441i q^{63} -69.8065 q^{64} +6.51346i q^{65} +(-40.9449 - 30.8634i) q^{66} +9.01793 q^{67} -37.7361i q^{68} +36.4504 q^{69} -25.0693 q^{70} -1.24936 q^{71} -10.3369i q^{72} +24.1060i q^{73} -48.0543i q^{74} +13.9753 q^{75} -5.48452i q^{76} +(59.0522 + 44.5123i) q^{77} +13.5779 q^{78} -108.479i q^{79} +21.5541 q^{80} -68.9002 q^{81} -41.1207 q^{82} +8.27453i q^{83} -22.9016i q^{84} +69.2320i q^{85} +3.81384 q^{86} +125.319i q^{87} +(-76.4507 - 57.6269i) q^{88} +84.8892 q^{89} +4.42897i q^{90} -19.5825 q^{91} +15.8945 q^{92} +73.1549 q^{93} -3.89022i q^{94} +10.0621i q^{95} +52.3739i q^{96} +160.450 q^{97} +6.34690i q^{98} +(7.86394 - 10.4327i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{3} - 28 q^{4} - 4 q^{9} + 8 q^{11} - 48 q^{12} + 20 q^{15} + 88 q^{16} - 20 q^{20} + 80 q^{22} + 8 q^{23} + 40 q^{25} - 100 q^{26} - 16 q^{27} + 36 q^{31} - 152 q^{33} + 80 q^{34} - 216 q^{36}+ \cdots - 184 q^{99}+O(q^{100}) \) 8 * q + 8 * q^3 - 28 * q^4 - 4 * q^9 + 8 * q^11 - 48 * q^12 + 20 * q^15 + 88 * q^16 - 20 * q^20 + 80 * q^22 + 8 * q^23 + 40 * q^25 - 100 * q^26 - 16 * q^27 + 36 * q^31 - 152 * q^33 + 80 * q^34 - 216 * q^36 - 88 * q^37 - 160 * q^38 + 280 * q^42 + 12 * q^44 - 8 * q^47 + 488 * q^48 + 172 * q^49 - 152 * q^53 - 20 * q^55 - 80 * q^56 + 160 * q^58 - 16 * q^59 - 300 * q^60 - 588 * q^64 + 180 * q^66 - 88 * q^67 + 8 * q^69 + 60 * q^70 + 276 * q^71 + 40 * q^75 + 160 * q^77 + 160 * q^78 + 320 * q^80 - 320 * q^81 - 520 * q^82 + 420 * q^86 - 520 * q^88 + 444 * q^89 - 40 * q^91 - 368 * q^92 - 104 * q^93 + 312 * q^97 - 184 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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