Basic properties
Modulus: | \(8020\) | |
Conductor: | \(8020\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(100\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8020.dm
\(\chi_{8020}(183,\cdot)\) \(\chi_{8020}(703,\cdot)\) \(\chi_{8020}(1087,\cdot)\) \(\chi_{8020}(1103,\cdot)\) \(\chi_{8020}(1207,\cdot)\) \(\chi_{8020}(1407,\cdot)\) \(\chi_{8020}(1483,\cdot)\) \(\chi_{8020}(1523,\cdot)\) \(\chi_{8020}(1987,\cdot)\) \(\chi_{8020}(2023,\cdot)\) \(\chi_{8020}(2487,\cdot)\) \(\chi_{8020}(2527,\cdot)\) \(\chi_{8020}(2603,\cdot)\) \(\chi_{8020}(2803,\cdot)\) \(\chi_{8020}(2907,\cdot)\) \(\chi_{8020}(2923,\cdot)\) \(\chi_{8020}(3307,\cdot)\) \(\chi_{8020}(3827,\cdot)\) \(\chi_{8020}(4067,\cdot)\) \(\chi_{8020}(4103,\cdot)\) \(\chi_{8020}(4123,\cdot)\) \(\chi_{8020}(4347,\cdot)\) \(\chi_{8020}(4567,\cdot)\) \(\chi_{8020}(4743,\cdot)\) \(\chi_{8020}(5303,\cdot)\) \(\chi_{8020}(5307,\cdot)\) \(\chi_{8020}(5323,\cdot)\) \(\chi_{8020}(5663,\cdot)\) \(\chi_{8020}(5763,\cdot)\) \(\chi_{8020}(6267,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{100})$ |
Fixed field: | Number field defined by a degree 100 polynomial |
Values on generators
\((4011,6417,7221)\) → \((-1,-i,e\left(\frac{99}{100}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
\( \chi_{ 8020 }(703, a) \) | \(1\) | \(1\) | \(e\left(\frac{37}{50}\right)\) | \(e\left(\frac{63}{100}\right)\) | \(e\left(\frac{12}{25}\right)\) | \(e\left(\frac{14}{25}\right)\) | \(e\left(\frac{3}{50}\right)\) | \(e\left(\frac{23}{25}\right)\) | \(e\left(\frac{37}{100}\right)\) | \(e\left(\frac{37}{100}\right)\) | \(e\left(\frac{21}{25}\right)\) | \(e\left(\frac{11}{50}\right)\) |