Basic properties
Modulus: | \(8018\) | |
Conductor: | \(4009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(315\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{4009}(47,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8018.eo
\(\chi_{8018}(47,\cdot)\) \(\chi_{8018}(93,\cdot)\) \(\chi_{8018}(119,\cdot)\) \(\chi_{8018}(263,\cdot)\) \(\chi_{8018}(291,\cdot)\) \(\chi_{8018}(405,\cdot)\) \(\chi_{8018}(473,\cdot)\) \(\chi_{8018}(481,\cdot)\) \(\chi_{8018}(503,\cdot)\) \(\chi_{8018}(517,\cdot)\) \(\chi_{8018}(631,\cdot)\) \(\chi_{8018}(663,\cdot)\) \(\chi_{8018}(669,\cdot)\) \(\chi_{8018}(769,\cdot)\) \(\chi_{8018}(803,\cdot)\) \(\chi_{8018}(815,\cdot)\) \(\chi_{8018}(853,\cdot)\) \(\chi_{8018}(897,\cdot)\) \(\chi_{8018}(947,\cdot)\) \(\chi_{8018}(1061,\cdot)\) \(\chi_{8018}(1099,\cdot)\) \(\chi_{8018}(1107,\cdot)\) \(\chi_{8018}(1111,\cdot)\) \(\chi_{8018}(1263,\cdot)\) \(\chi_{8018}(1365,\cdot)\) \(\chi_{8018}(1385,\cdot)\) \(\chi_{8018}(1555,\cdot)\) \(\chi_{8018}(1631,\cdot)\) \(\chi_{8018}(1681,\cdot)\) \(\chi_{8018}(1735,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{315})$ |
Fixed field: | Number field defined by a degree 315 polynomial (not computed) |
Values on generators
\((2111,1901)\) → \((e\left(\frac{4}{9}\right),e\left(\frac{62}{105}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
\( \chi_{ 8018 }(47, a) \) | \(1\) | \(1\) | \(e\left(\frac{53}{315}\right)\) | \(e\left(\frac{17}{315}\right)\) | \(e\left(\frac{26}{35}\right)\) | \(e\left(\frac{106}{315}\right)\) | \(e\left(\frac{104}{105}\right)\) | \(e\left(\frac{79}{315}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{299}{315}\right)\) | \(e\left(\frac{41}{45}\right)\) | \(e\left(\frac{13}{45}\right)\) |