Basic properties
Modulus: | \(38025\) | |
Conductor: | \(12675\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(260\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{12675}(1529,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 38025.me
\(\chi_{38025}(44,\cdot)\) \(\chi_{38025}(359,\cdot)\) \(\chi_{38025}(629,\cdot)\) \(\chi_{38025}(1214,\cdot)\) \(\chi_{38025}(1529,\cdot)\) \(\chi_{38025}(2114,\cdot)\) \(\chi_{38025}(2384,\cdot)\) \(\chi_{38025}(2969,\cdot)\) \(\chi_{38025}(3284,\cdot)\) \(\chi_{38025}(3554,\cdot)\) \(\chi_{38025}(3869,\cdot)\) \(\chi_{38025}(4139,\cdot)\) \(\chi_{38025}(4454,\cdot)\) \(\chi_{38025}(5039,\cdot)\) \(\chi_{38025}(5894,\cdot)\) \(\chi_{38025}(6209,\cdot)\) \(\chi_{38025}(6479,\cdot)\) \(\chi_{38025}(6794,\cdot)\) \(\chi_{38025}(7064,\cdot)\) \(\chi_{38025}(7379,\cdot)\) \(\chi_{38025}(7964,\cdot)\) \(\chi_{38025}(8234,\cdot)\) \(\chi_{38025}(8819,\cdot)\) \(\chi_{38025}(9134,\cdot)\) \(\chi_{38025}(9404,\cdot)\) \(\chi_{38025}(9719,\cdot)\) \(\chi_{38025}(9989,\cdot)\) \(\chi_{38025}(10304,\cdot)\) \(\chi_{38025}(10889,\cdot)\) \(\chi_{38025}(11159,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{260})$ |
Fixed field: | Number field defined by a degree 260 polynomial (not computed) |
Values on generators
\((29576,9127,37351)\) → \((-1,e\left(\frac{1}{10}\right),e\left(\frac{1}{52}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(14\) | \(16\) | \(17\) | \(19\) | \(22\) |
\( \chi_{ 38025 }(1529, a) \) | \(1\) | \(1\) | \(e\left(\frac{161}{260}\right)\) | \(e\left(\frac{31}{130}\right)\) | \(e\left(\frac{29}{52}\right)\) | \(e\left(\frac{223}{260}\right)\) | \(e\left(\frac{21}{260}\right)\) | \(e\left(\frac{23}{130}\right)\) | \(e\left(\frac{31}{65}\right)\) | \(e\left(\frac{79}{130}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{7}{10}\right)\) |