Basic properties
Modulus: | \(211\) | |
Conductor: | \(211\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(105\) | 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 211.o
\(\chi_{211}(4,\cdot)\) \(\chi_{211}(6,\cdot)\) \(\chi_{211}(9,\cdot)\) \(\chi_{211}(16,\cdot)\) \(\chi_{211}(20,\cdot)\) \(\chi_{211}(24,\cdot)\) \(\chi_{211}(30,\cdot)\) \(\chi_{211}(36,\cdot)\) \(\chi_{211}(37,\cdot)\) \(\chi_{211}(44,\cdot)\) \(\chi_{211}(45,\cdot)\) \(\chi_{211}(46,\cdot)\) \(\chi_{211}(47,\cdot)\) \(\chi_{211}(49,\cdot)\) \(\chi_{211}(51,\cdot)\) \(\chi_{211}(52,\cdot)\) \(\chi_{211}(53,\cdot)\) \(\chi_{211}(56,\cdot)\) \(\chi_{211}(59,\cdot)\) \(\chi_{211}(62,\cdot)\) \(\chi_{211}(66,\cdot)\) \(\chi_{211}(69,\cdot)\) \(\chi_{211}(70,\cdot)\) \(\chi_{211}(78,\cdot)\) \(\chi_{211}(80,\cdot)\) \(\chi_{211}(81,\cdot)\) \(\chi_{211}(84,\cdot)\) \(\chi_{211}(93,\cdot)\) \(\chi_{211}(95,\cdot)\) \(\chi_{211}(99,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{105})$ |
Fixed field: | Number field defined by a degree 105 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{1}{105}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 211 }(4, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{105}\right)\) | \(e\left(\frac{43}{105}\right)\) | \(e\left(\frac{2}{105}\right)\) | \(e\left(\frac{9}{35}\right)\) | \(e\left(\frac{44}{105}\right)\) | \(e\left(\frac{34}{105}\right)\) | \(e\left(\frac{1}{35}\right)\) | \(e\left(\frac{86}{105}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{19}{35}\right)\) |