Basic properties
Modulus: | \(4900\) | |
Conductor: | \(4900\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(210\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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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 4900.dn
\(\chi_{4900}(59,\cdot)\) \(\chi_{4900}(159,\cdot)\) \(\chi_{4900}(339,\cdot)\) \(\chi_{4900}(439,\cdot)\) \(\chi_{4900}(479,\cdot)\) \(\chi_{4900}(579,\cdot)\) \(\chi_{4900}(719,\cdot)\) \(\chi_{4900}(759,\cdot)\) \(\chi_{4900}(859,\cdot)\) \(\chi_{4900}(1039,\cdot)\) \(\chi_{4900}(1139,\cdot)\) \(\chi_{4900}(1179,\cdot)\) \(\chi_{4900}(1279,\cdot)\) \(\chi_{4900}(1319,\cdot)\) \(\chi_{4900}(1419,\cdot)\) \(\chi_{4900}(1459,\cdot)\) \(\chi_{4900}(1559,\cdot)\) \(\chi_{4900}(1739,\cdot)\) \(\chi_{4900}(1839,\cdot)\) \(\chi_{4900}(1879,\cdot)\) \(\chi_{4900}(2019,\cdot)\) \(\chi_{4900}(2119,\cdot)\) \(\chi_{4900}(2159,\cdot)\) \(\chi_{4900}(2259,\cdot)\) \(\chi_{4900}(2439,\cdot)\) \(\chi_{4900}(2539,\cdot)\) \(\chi_{4900}(2679,\cdot)\) \(\chi_{4900}(2719,\cdot)\) \(\chi_{4900}(2819,\cdot)\) \(\chi_{4900}(2859,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{105})$ |
Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((2451,1177,101)\) → \((-1,e\left(\frac{7}{10}\right),e\left(\frac{13}{42}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) |
\( \chi_{ 4900 }(59, a) \) | \(1\) | \(1\) | \(e\left(\frac{149}{210}\right)\) | \(e\left(\frac{44}{105}\right)\) | \(e\left(\frac{17}{210}\right)\) | \(e\left(\frac{18}{35}\right)\) | \(e\left(\frac{88}{105}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{101}{105}\right)\) | \(e\left(\frac{9}{70}\right)\) | \(e\left(\frac{34}{35}\right)\) | \(e\left(\frac{4}{15}\right)\) |