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 \(\chi_{12675}(53,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 38025.md
\(\chi_{38025}(53,\cdot)\) \(\chi_{38025}(287,\cdot)\) \(\chi_{38025}(638,\cdot)\) \(\chi_{38025}(872,\cdot)\) \(\chi_{38025}(1223,\cdot)\) \(\chi_{38025}(1808,\cdot)\) \(\chi_{38025}(2042,\cdot)\) \(\chi_{38025}(2627,\cdot)\) \(\chi_{38025}(2978,\cdot)\) \(\chi_{38025}(3563,\cdot)\) \(\chi_{38025}(3797,\cdot)\) \(\chi_{38025}(4148,\cdot)\) \(\chi_{38025}(4967,\cdot)\) \(\chi_{38025}(5552,\cdot)\) \(\chi_{38025}(5903,\cdot)\) \(\chi_{38025}(6137,\cdot)\) \(\chi_{38025}(6488,\cdot)\) \(\chi_{38025}(6722,\cdot)\) \(\chi_{38025}(7073,\cdot)\) \(\chi_{38025}(7658,\cdot)\) \(\chi_{38025}(7892,\cdot)\) \(\chi_{38025}(8477,\cdot)\) \(\chi_{38025}(8828,\cdot)\) \(\chi_{38025}(9062,\cdot)\) \(\chi_{38025}(9413,\cdot)\) \(\chi_{38025}(9647,\cdot)\) \(\chi_{38025}(9998,\cdot)\) \(\chi_{38025}(10583,\cdot)\) \(\chi_{38025}(11402,\cdot)\) \(\chi_{38025}(11753,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{260})$ |
Fixed field: | Number field defined by a degree 260 polynomial (not computed) |
Values on generators
\((29576,9127,37351)\) → \((-1,e\left(\frac{7}{20}\right),e\left(\frac{10}{13}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(14\) | \(16\) | \(17\) | \(19\) | \(22\) |
\( \chi_{ 38025 }(53, a) \) | \(1\) | \(1\) | \(e\left(\frac{161}{260}\right)\) | \(e\left(\frac{31}{130}\right)\) | \(e\left(\frac{3}{52}\right)\) | \(e\left(\frac{223}{260}\right)\) | \(e\left(\frac{43}{130}\right)\) | \(e\left(\frac{44}{65}\right)\) | \(e\left(\frac{31}{65}\right)\) | \(e\left(\frac{93}{260}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{19}{20}\right)\) |