Basic properties
| Modulus: | \(9800\) | |
| Conductor: | \(9800\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(210\) | 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 9800.gn
\(\chi_{9800}(59,\cdot)\) \(\chi_{9800}(339,\cdot)\) \(\chi_{9800}(579,\cdot)\) \(\chi_{9800}(859,\cdot)\) \(\chi_{9800}(1139,\cdot)\) \(\chi_{9800}(1179,\cdot)\) \(\chi_{9800}(1419,\cdot)\) \(\chi_{9800}(1459,\cdot)\) \(\chi_{9800}(1739,\cdot)\) \(\chi_{9800}(2019,\cdot)\) \(\chi_{9800}(2259,\cdot)\) \(\chi_{9800}(2539,\cdot)\) \(\chi_{9800}(2819,\cdot)\) \(\chi_{9800}(2859,\cdot)\) \(\chi_{9800}(3139,\cdot)\) \(\chi_{9800}(3379,\cdot)\) \(\chi_{9800}(3419,\cdot)\) \(\chi_{9800}(3659,\cdot)\) \(\chi_{9800}(3979,\cdot)\) \(\chi_{9800}(4219,\cdot)\) \(\chi_{9800}(4259,\cdot)\) \(\chi_{9800}(4779,\cdot)\) \(\chi_{9800}(4819,\cdot)\) \(\chi_{9800}(5059,\cdot)\) \(\chi_{9800}(5339,\cdot)\) \(\chi_{9800}(5379,\cdot)\) \(\chi_{9800}(5619,\cdot)\) \(\chi_{9800}(5659,\cdot)\) \(\chi_{9800}(5939,\cdot)\) \(\chi_{9800}(6179,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((7351,4901,1177,5001)\) → \((-1,-1,e\left(\frac{7}{10}\right),e\left(\frac{13}{42}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) |
| \( \chi_{ 9800 }(59, a) \) | \(1\) | \(1\) | \(e\left(\frac{22}{105}\right)\) | \(e\left(\frac{44}{105}\right)\) | \(e\left(\frac{61}{105}\right)\) | \(e\left(\frac{1}{70}\right)\) | \(e\left(\frac{88}{105}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{101}{105}\right)\) | \(e\left(\frac{22}{35}\right)\) | \(e\left(\frac{33}{70}\right)\) | \(e\left(\frac{4}{15}\right)\) |