Basic properties
Modulus: | \(9464\) | |
Conductor: | \(1183\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(39\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{1183}(9,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9464.fg
\(\chi_{9464}(9,\cdot)\) \(\chi_{9464}(81,\cdot)\) \(\chi_{9464}(737,\cdot)\) \(\chi_{9464}(809,\cdot)\) \(\chi_{9464}(1465,\cdot)\) \(\chi_{9464}(1537,\cdot)\) \(\chi_{9464}(2193,\cdot)\) \(\chi_{9464}(2265,\cdot)\) \(\chi_{9464}(2921,\cdot)\) \(\chi_{9464}(2993,\cdot)\) \(\chi_{9464}(3649,\cdot)\) \(\chi_{9464}(3721,\cdot)\) \(\chi_{9464}(4377,\cdot)\) \(\chi_{9464}(4449,\cdot)\) \(\chi_{9464}(5105,\cdot)\) \(\chi_{9464}(5177,\cdot)\) \(\chi_{9464}(5833,\cdot)\) \(\chi_{9464}(5905,\cdot)\) \(\chi_{9464}(6561,\cdot)\) \(\chi_{9464}(6633,\cdot)\) \(\chi_{9464}(7361,\cdot)\) \(\chi_{9464}(8017,\cdot)\) \(\chi_{9464}(8745,\cdot)\) \(\chi_{9464}(8817,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | 39.39.253721406991290895924770503111827676888647505643788160579278763946491805765758913183386148271215912203961.1 |
Values on generators
\((2367,4733,2705,9297)\) → \((1,1,e\left(\frac{1}{3}\right),e\left(\frac{23}{39}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
\( \chi_{ 9464 }(9, a) \) | \(1\) | \(1\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{38}{39}\right)\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{17}{39}\right)\) | \(e\left(\frac{17}{39}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{37}{39}\right)\) | \(e\left(\frac{5}{13}\right)\) |