Basic properties
Modulus: | \(38025\) | |
Conductor: | \(4225\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(780\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{4225}(28,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 38025.pf
\(\chi_{38025}(28,\cdot)\) \(\chi_{38025}(37,\cdot)\) \(\chi_{38025}(253,\cdot)\) \(\chi_{38025}(397,\cdot)\) \(\chi_{38025}(613,\cdot)\) \(\chi_{38025}(622,\cdot)\) \(\chi_{38025}(838,\cdot)\) \(\chi_{38025}(1198,\cdot)\) \(\chi_{38025}(1423,\cdot)\) \(\chi_{38025}(1567,\cdot)\) \(\chi_{38025}(1783,\cdot)\) \(\chi_{38025}(1792,\cdot)\) \(\chi_{38025}(2008,\cdot)\) \(\chi_{38025}(2152,\cdot)\) \(\chi_{38025}(2377,\cdot)\) \(\chi_{38025}(2737,\cdot)\) \(\chi_{38025}(3178,\cdot)\) \(\chi_{38025}(3322,\cdot)\) \(\chi_{38025}(3538,\cdot)\) \(\chi_{38025}(3547,\cdot)\) \(\chi_{38025}(3763,\cdot)\) \(\chi_{38025}(4123,\cdot)\) \(\chi_{38025}(4348,\cdot)\) \(\chi_{38025}(4492,\cdot)\) \(\chi_{38025}(4708,\cdot)\) \(\chi_{38025}(4717,\cdot)\) \(\chi_{38025}(4933,\cdot)\) \(\chi_{38025}(5077,\cdot)\) \(\chi_{38025}(5302,\cdot)\) \(\chi_{38025}(5662,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{780})$ |
Fixed field: | Number field defined by a degree 780 polynomial (not computed) |
Values on generators
\((29576,9127,37351)\) → \((1,e\left(\frac{7}{20}\right),e\left(\frac{109}{156}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(14\) | \(16\) | \(17\) | \(19\) | \(22\) |
\( \chi_{ 38025 }(28, a) \) | \(1\) | \(1\) | \(e\left(\frac{19}{390}\right)\) | \(e\left(\frac{19}{195}\right)\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{19}{130}\right)\) | \(e\left(\frac{443}{780}\right)\) | \(e\left(\frac{73}{130}\right)\) | \(e\left(\frac{38}{195}\right)\) | \(e\left(\frac{439}{780}\right)\) | \(e\left(\frac{43}{60}\right)\) | \(e\left(\frac{37}{60}\right)\) |