Basic properties
Modulus: | \(100315\) | |
Conductor: | \(100315\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(20062\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
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 100315.u
\(\chi_{100315}(9,\cdot)\) \(\chi_{100315}(19,\cdot)\) \(\chi_{100315}(24,\cdot)\) \(\chi_{100315}(29,\cdot)\) \(\chi_{100315}(39,\cdot)\) \(\chi_{100315}(44,\cdot)\) \(\chi_{100315}(49,\cdot)\) \(\chi_{100315}(54,\cdot)\) \(\chi_{100315}(69,\cdot)\) \(\chi_{100315}(74,\cdot)\) \(\chi_{100315}(99,\cdot)\) \(\chi_{100315}(104,\cdot)\) \(\chi_{100315}(109,\cdot)\) \(\chi_{100315}(114,\cdot)\) \(\chi_{100315}(119,\cdot)\) \(\chi_{100315}(124,\cdot)\) \(\chi_{100315}(134,\cdot)\) \(\chi_{100315}(144,\cdot)\) \(\chi_{100315}(159,\cdot)\) \(\chi_{100315}(169,\cdot)\) \(\chi_{100315}(184,\cdot)\) \(\chi_{100315}(194,\cdot)\) \(\chi_{100315}(209,\cdot)\) \(\chi_{100315}(214,\cdot)\) \(\chi_{100315}(219,\cdot)\) \(\chi_{100315}(234,\cdot)\) \(\chi_{100315}(249,\cdot)\) \(\chi_{100315}(264,\cdot)\) \(\chi_{100315}(279,\cdot)\) \(\chi_{100315}(284,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{10031})$ |
Fixed field: | Number field defined by a degree 20062 polynomial (not computed) |
Values on generators
\((40127,40131)\) → \((-1,e\left(\frac{738}{10031}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
\( \chi_{ 100315 }(24, a) \) | \(1\) | \(1\) | \(e\left(\frac{1855}{2866}\right)\) | \(e\left(\frac{13049}{20062}\right)\) | \(e\left(\frac{422}{1433}\right)\) | \(e\left(\frac{2986}{10031}\right)\) | \(e\left(\frac{4607}{20062}\right)\) | \(e\left(\frac{2699}{2866}\right)\) | \(e\left(\frac{3018}{10031}\right)\) | \(e\left(\frac{1279}{10031}\right)\) | \(e\left(\frac{18957}{20062}\right)\) | \(e\left(\frac{1681}{20062}\right)\) |