Properties

Label 2299.bq
Modulus 22992299
Conductor 22992299
Order 330330
Real no
Primitive yes
Minimal yes
Parity odd

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2299, base_ring=CyclotomicField(330)) M = H._module chi = DirichletCharacter(H, M([258,275])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(31,2299)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 22992299
Conductor: 22992299
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: 330330
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: yes
Copy content sage:chi.is_primitive()
 
Copy content pari:#znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: odd
Copy content sage:chi.is_odd()
 
Copy content pari:zncharisodd(g,chi)
 

Related number fields

Field of values: Q(ζ165)\Q(\zeta_{165})
Fixed field: Number field defined by a degree 330 polynomial (not computed)

First 31 of 80 characters in Galois orbit

Character 1-1 11 22 33 44 55 66 77 88 99 1010 1212
χ2299(31,)\chi_{2299}(31,\cdot) 1-1 11 e(203330)e\left(\frac{203}{330}\right) e(1930)e\left(\frac{19}{30}\right) e(38165)e\left(\frac{38}{165}\right) e(31165)e\left(\frac{31}{165}\right) e(41165)e\left(\frac{41}{165}\right) e(2655)e\left(\frac{26}{55}\right) e(93110)e\left(\frac{93}{110}\right) e(415)e\left(\frac{4}{15}\right) e(5366)e\left(\frac{53}{66}\right) e(1922)e\left(\frac{19}{22}\right)
χ2299(69,)\chi_{2299}(69,\cdot) 1-1 11 e(89330)e\left(\frac{89}{330}\right) e(730)e\left(\frac{7}{30}\right) e(89165)e\left(\frac{89}{165}\right) e(103165)e\left(\frac{103}{165}\right) e(83165)e\left(\frac{83}{165}\right) e(355)e\left(\frac{3}{55}\right) e(89110)e\left(\frac{89}{110}\right) e(715)e\left(\frac{7}{15}\right) e(5966)e\left(\frac{59}{66}\right) e(1722)e\left(\frac{17}{22}\right)
χ2299(103,)\chi_{2299}(103,\cdot) 1-1 11 e(91330)e\left(\frac{91}{330}\right) e(2330)e\left(\frac{23}{30}\right) e(91165)e\left(\frac{91}{165}\right) e(122165)e\left(\frac{122}{165}\right) e(7165)e\left(\frac{7}{165}\right) e(4255)e\left(\frac{42}{55}\right) e(91110)e\left(\frac{91}{110}\right) e(815)e\left(\frac{8}{15}\right) e(166)e\left(\frac{1}{66}\right) e(722)e\left(\frac{7}{22}\right)
χ2299(126,)\chi_{2299}(126,\cdot) 1-1 11 e(167330)e\left(\frac{167}{330}\right) e(130)e\left(\frac{1}{30}\right) e(2165)e\left(\frac{2}{165}\right) e(19165)e\left(\frac{19}{165}\right) e(89165)e\left(\frac{89}{165}\right) e(3955)e\left(\frac{39}{55}\right) e(57110)e\left(\frac{57}{110}\right) e(115)e\left(\frac{1}{15}\right) e(4166)e\left(\frac{41}{66}\right) e(122)e\left(\frac{1}{22}\right)
χ2299(141,)\chi_{2299}(141,\cdot) 1-1 11 e(283330)e\left(\frac{283}{330}\right) e(2930)e\left(\frac{29}{30}\right) e(118165)e\left(\frac{118}{165}\right) e(131165)e\left(\frac{131}{165}\right) e(136165)e\left(\frac{136}{165}\right) e(4655)e\left(\frac{46}{55}\right) e(63110)e\left(\frac{63}{110}\right) e(1415)e\left(\frac{14}{15}\right) e(4366)e\left(\frac{43}{66}\right) e(1522)e\left(\frac{15}{22}\right)
χ2299(179,)\chi_{2299}(179,\cdot) 1-1 11 e(109330)e\left(\frac{109}{330}\right) e(1730)e\left(\frac{17}{30}\right) e(109165)e\left(\frac{109}{165}\right) e(128165)e\left(\frac{128}{165}\right) e(148165)e\left(\frac{148}{165}\right) e(855)e\left(\frac{8}{55}\right) e(109110)e\left(\frac{109}{110}\right) e(215)e\left(\frac{2}{15}\right) e(766)e\left(\frac{7}{66}\right) e(522)e\left(\frac{5}{22}\right)
χ2299(236,)\chi_{2299}(236,\cdot) 1-1 11 e(157330)e\left(\frac{157}{330}\right) e(1130)e\left(\frac{11}{30}\right) e(157165)e\left(\frac{157}{165}\right) e(89165)e\left(\frac{89}{165}\right) e(139165)e\left(\frac{139}{165}\right) e(955)e\left(\frac{9}{55}\right) e(47110)e\left(\frac{47}{110}\right) e(1115)e\left(\frac{11}{15}\right) e(166)e\left(\frac{1}{66}\right) e(722)e\left(\frac{7}{22}\right)
χ2299(240,)\chi_{2299}(240,\cdot) 1-1 11 e(113330)e\left(\frac{113}{330}\right) e(1930)e\left(\frac{19}{30}\right) e(113165)e\left(\frac{113}{165}\right) e(1165)e\left(\frac{1}{165}\right) e(161165)e\left(\frac{161}{165}\right) e(3155)e\left(\frac{31}{55}\right) e(3110)e\left(\frac{3}{110}\right) e(415)e\left(\frac{4}{15}\right) e(2366)e\left(\frac{23}{66}\right) e(722)e\left(\frac{7}{22}\right)
χ2299(278,)\chi_{2299}(278,\cdot) 1-1 11 e(149330)e\left(\frac{149}{330}\right) e(730)e\left(\frac{7}{30}\right) e(149165)e\left(\frac{149}{165}\right) e(13165)e\left(\frac{13}{165}\right) e(113165)e\left(\frac{113}{165}\right) e(1855)e\left(\frac{18}{55}\right) e(39110)e\left(\frac{39}{110}\right) e(715)e\left(\frac{7}{15}\right) e(3566)e\left(\frac{35}{66}\right) e(322)e\left(\frac{3}{22}\right)
χ2299(312,)\chi_{2299}(312,\cdot) 1-1 11 e(301330)e\left(\frac{301}{330}\right) e(2330)e\left(\frac{23}{30}\right) e(136165)e\left(\frac{136}{165}\right) e(137165)e\left(\frac{137}{165}\right) e(112165)e\left(\frac{112}{165}\right) e(1255)e\left(\frac{12}{55}\right) e(81110)e\left(\frac{81}{110}\right) e(815)e\left(\frac{8}{15}\right) e(4966)e\left(\frac{49}{66}\right) e(1322)e\left(\frac{13}{22}\right)
χ2299(335,)\chi_{2299}(335,\cdot) 1-1 11 e(137330)e\left(\frac{137}{330}\right) e(130)e\left(\frac{1}{30}\right) e(137165)e\left(\frac{137}{165}\right) e(64165)e\left(\frac{64}{165}\right) e(74165)e\left(\frac{74}{165}\right) e(455)e\left(\frac{4}{55}\right) e(27110)e\left(\frac{27}{110}\right) e(115)e\left(\frac{1}{15}\right) e(5366)e\left(\frac{53}{66}\right) e(1922)e\left(\frac{19}{22}\right)
χ2299(350,)\chi_{2299}(350,\cdot) 1-1 11 e(193330)e\left(\frac{193}{330}\right) e(2930)e\left(\frac{29}{30}\right) e(28165)e\left(\frac{28}{165}\right) e(101165)e\left(\frac{101}{165}\right) e(91165)e\left(\frac{91}{165}\right) e(5155)e\left(\frac{51}{55}\right) e(83110)e\left(\frac{83}{110}\right) e(1415)e\left(\frac{14}{15}\right) e(1366)e\left(\frac{13}{66}\right) e(322)e\left(\frac{3}{22}\right)
χ2299(388,)\chi_{2299}(388,\cdot) 1-1 11 e(169330)e\left(\frac{169}{330}\right) e(1730)e\left(\frac{17}{30}\right) e(4165)e\left(\frac{4}{165}\right) e(38165)e\left(\frac{38}{165}\right) e(13165)e\left(\frac{13}{165}\right) e(2355)e\left(\frac{23}{55}\right) e(59110)e\left(\frac{59}{110}\right) e(215)e\left(\frac{2}{15}\right) e(4966)e\left(\frac{49}{66}\right) e(1322)e\left(\frac{13}{22}\right)
χ2299(411,)\chi_{2299}(411,\cdot) 1-1 11 e(221330)e\left(\frac{221}{330}\right) e(1330)e\left(\frac{13}{30}\right) e(56165)e\left(\frac{56}{165}\right) e(37165)e\left(\frac{37}{165}\right) e(17165)e\left(\frac{17}{165}\right) e(4755)e\left(\frac{47}{55}\right) e(1110)e\left(\frac{1}{110}\right) e(1315)e\left(\frac{13}{15}\right) e(5966)e\left(\frac{59}{66}\right) e(1722)e\left(\frac{17}{22}\right)
χ2299(445,)\chi_{2299}(445,\cdot) 1-1 11 e(127330)e\left(\frac{127}{330}\right) e(1130)e\left(\frac{11}{30}\right) e(127165)e\left(\frac{127}{165}\right) e(134165)e\left(\frac{134}{165}\right) e(124165)e\left(\frac{124}{165}\right) e(2955)e\left(\frac{29}{55}\right) e(17110)e\left(\frac{17}{110}\right) e(1115)e\left(\frac{11}{15}\right) e(1366)e\left(\frac{13}{66}\right) e(322)e\left(\frac{3}{22}\right)
χ2299(449,)\chi_{2299}(449,\cdot) 1-1 11 e(23330)e\left(\frac{23}{330}\right) e(1930)e\left(\frac{19}{30}\right) e(23165)e\left(\frac{23}{165}\right) e(136165)e\left(\frac{136}{165}\right) e(116165)e\left(\frac{116}{165}\right) e(3655)e\left(\frac{36}{55}\right) e(23110)e\left(\frac{23}{110}\right) e(415)e\left(\frac{4}{15}\right) e(5966)e\left(\frac{59}{66}\right) e(1722)e\left(\frac{17}{22}\right)
χ2299(521,)\chi_{2299}(521,\cdot) 1-1 11 e(181330)e\left(\frac{181}{330}\right) e(2330)e\left(\frac{23}{30}\right) e(16165)e\left(\frac{16}{165}\right) e(152165)e\left(\frac{152}{165}\right) e(52165)e\left(\frac{52}{165}\right) e(3755)e\left(\frac{37}{55}\right) e(71110)e\left(\frac{71}{110}\right) e(815)e\left(\frac{8}{15}\right) e(3166)e\left(\frac{31}{66}\right) e(1922)e\left(\frac{19}{22}\right)
χ2299(544,)\chi_{2299}(544,\cdot) 1-1 11 e(107330)e\left(\frac{107}{330}\right) e(130)e\left(\frac{1}{30}\right) e(107165)e\left(\frac{107}{165}\right) e(109165)e\left(\frac{109}{165}\right) e(59165)e\left(\frac{59}{165}\right) e(2455)e\left(\frac{24}{55}\right) e(107110)e\left(\frac{107}{110}\right) e(115)e\left(\frac{1}{15}\right) e(6566)e\left(\frac{65}{66}\right) e(1522)e\left(\frac{15}{22}\right)
χ2299(559,)\chi_{2299}(559,\cdot) 1-1 11 e(103330)e\left(\frac{103}{330}\right) e(2930)e\left(\frac{29}{30}\right) e(103165)e\left(\frac{103}{165}\right) e(71165)e\left(\frac{71}{165}\right) e(46165)e\left(\frac{46}{165}\right) e(155)e\left(\frac{1}{55}\right) e(103110)e\left(\frac{103}{110}\right) e(1415)e\left(\frac{14}{15}\right) e(4966)e\left(\frac{49}{66}\right) e(1322)e\left(\frac{13}{22}\right)
χ2299(597,)\chi_{2299}(597,\cdot) 1-1 11 e(229330)e\left(\frac{229}{330}\right) e(1730)e\left(\frac{17}{30}\right) e(64165)e\left(\frac{64}{165}\right) e(113165)e\left(\frac{113}{165}\right) e(43165)e\left(\frac{43}{165}\right) e(3855)e\left(\frac{38}{55}\right) e(9110)e\left(\frac{9}{110}\right) e(215)e\left(\frac{2}{15}\right) e(2566)e\left(\frac{25}{66}\right) e(2122)e\left(\frac{21}{22}\right)
χ2299(620,)\chi_{2299}(620,\cdot) 1-1 11 e(101330)e\left(\frac{101}{330}\right) e(1330)e\left(\frac{13}{30}\right) e(101165)e\left(\frac{101}{165}\right) e(52165)e\left(\frac{52}{165}\right) e(122165)e\left(\frac{122}{165}\right) e(1755)e\left(\frac{17}{55}\right) e(101110)e\left(\frac{101}{110}\right) e(1315)e\left(\frac{13}{15}\right) e(4166)e\left(\frac{41}{66}\right) e(122)e\left(\frac{1}{22}\right)
χ2299(654,)\chi_{2299}(654,\cdot) 1-1 11 e(97330)e\left(\frac{97}{330}\right) e(1130)e\left(\frac{11}{30}\right) e(97165)e\left(\frac{97}{165}\right) e(14165)e\left(\frac{14}{165}\right) e(109165)e\left(\frac{109}{165}\right) e(4955)e\left(\frac{49}{55}\right) e(97110)e\left(\frac{97}{110}\right) e(1115)e\left(\frac{11}{15}\right) e(2566)e\left(\frac{25}{66}\right) e(2122)e\left(\frac{21}{22}\right)
χ2299(658,)\chi_{2299}(658,\cdot) 1-1 11 e(263330)e\left(\frac{263}{330}\right) e(1930)e\left(\frac{19}{30}\right) e(98165)e\left(\frac{98}{165}\right) e(106165)e\left(\frac{106}{165}\right) e(71165)e\left(\frac{71}{165}\right) e(4155)e\left(\frac{41}{55}\right) e(43110)e\left(\frac{43}{110}\right) e(415)e\left(\frac{4}{15}\right) e(2966)e\left(\frac{29}{66}\right) e(522)e\left(\frac{5}{22}\right)
χ2299(696,)\chi_{2299}(696,\cdot) 1-1 11 e(269330)e\left(\frac{269}{330}\right) e(730)e\left(\frac{7}{30}\right) e(104165)e\left(\frac{104}{165}\right) e(163165)e\left(\frac{163}{165}\right) e(8165)e\left(\frac{8}{165}\right) e(4855)e\left(\frac{48}{55}\right) e(49110)e\left(\frac{49}{110}\right) e(715)e\left(\frac{7}{15}\right) e(5366)e\left(\frac{53}{66}\right) e(1922)e\left(\frac{19}{22}\right)
χ2299(730,)\chi_{2299}(730,\cdot) 1-1 11 e(61330)e\left(\frac{61}{330}\right) e(2330)e\left(\frac{23}{30}\right) e(61165)e\left(\frac{61}{165}\right) e(2165)e\left(\frac{2}{165}\right) e(157165)e\left(\frac{157}{165}\right) e(755)e\left(\frac{7}{55}\right) e(61110)e\left(\frac{61}{110}\right) e(815)e\left(\frac{8}{15}\right) e(1366)e\left(\frac{13}{66}\right) e(322)e\left(\frac{3}{22}\right)
χ2299(768,)\chi_{2299}(768,\cdot) 1-1 11 e(13330)e\left(\frac{13}{330}\right) e(2930)e\left(\frac{29}{30}\right) e(13165)e\left(\frac{13}{165}\right) e(41165)e\left(\frac{41}{165}\right) e(1165)e\left(\frac{1}{165}\right) e(655)e\left(\frac{6}{55}\right) e(13110)e\left(\frac{13}{110}\right) e(1415)e\left(\frac{14}{15}\right) e(1966)e\left(\frac{19}{66}\right) e(122)e\left(\frac{1}{22}\right)
χ2299(806,)\chi_{2299}(806,\cdot) 1-1 11 e(289330)e\left(\frac{289}{330}\right) e(1730)e\left(\frac{17}{30}\right) e(124165)e\left(\frac{124}{165}\right) e(23165)e\left(\frac{23}{165}\right) e(73165)e\left(\frac{73}{165}\right) e(5355)e\left(\frac{53}{55}\right) e(69110)e\left(\frac{69}{110}\right) e(215)e\left(\frac{2}{15}\right) e(166)e\left(\frac{1}{66}\right) e(722)e\left(\frac{7}{22}\right)
χ2299(829,)\chi_{2299}(829,\cdot) 1-1 11 e(311330)e\left(\frac{311}{330}\right) e(1330)e\left(\frac{13}{30}\right) e(146165)e\left(\frac{146}{165}\right) e(67165)e\left(\frac{67}{165}\right) e(62165)e\left(\frac{62}{165}\right) e(4255)e\left(\frac{42}{55}\right) e(91110)e\left(\frac{91}{110}\right) e(1315)e\left(\frac{13}{15}\right) e(2366)e\left(\frac{23}{66}\right) e(722)e\left(\frac{7}{22}\right)
χ2299(863,)\chi_{2299}(863,\cdot) 1-1 11 e(67330)e\left(\frac{67}{330}\right) e(1130)e\left(\frac{11}{30}\right) e(67165)e\left(\frac{67}{165}\right) e(59165)e\left(\frac{59}{165}\right) e(94165)e\left(\frac{94}{165}\right) e(1455)e\left(\frac{14}{55}\right) e(67110)e\left(\frac{67}{110}\right) e(1115)e\left(\frac{11}{15}\right) e(3766)e\left(\frac{37}{66}\right) e(1722)e\left(\frac{17}{22}\right)
χ2299(867,)\chi_{2299}(867,\cdot) 1-1 11 e(173330)e\left(\frac{173}{330}\right) e(1930)e\left(\frac{19}{30}\right) e(8165)e\left(\frac{8}{165}\right) e(76165)e\left(\frac{76}{165}\right) e(26165)e\left(\frac{26}{165}\right) e(4655)e\left(\frac{46}{55}\right) e(63110)e\left(\frac{63}{110}\right) e(415)e\left(\frac{4}{15}\right) e(6566)e\left(\frac{65}{66}\right) e(1522)e\left(\frac{15}{22}\right)
χ2299(905,)\chi_{2299}(905,\cdot) 1-1 11 e(329330)e\left(\frac{329}{330}\right) e(730)e\left(\frac{7}{30}\right) e(164165)e\left(\frac{164}{165}\right) e(73165)e\left(\frac{73}{165}\right) e(38165)e\left(\frac{38}{165}\right) e(855)e\left(\frac{8}{55}\right) e(109110)e\left(\frac{109}{110}\right) e(715)e\left(\frac{7}{15}\right) e(2966)e\left(\frac{29}{66}\right) e(522)e\left(\frac{5}{22}\right)