Basic properties
| Modulus: | \(29645\) | |
| Conductor: | \(5929\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(770\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{5929}(6,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 29645.gm
\(\chi_{29645}(6,\cdot)\) \(\chi_{29645}(41,\cdot)\) \(\chi_{29645}(216,\cdot)\) \(\chi_{29645}(321,\cdot)\) \(\chi_{29645}(426,\cdot)\) \(\chi_{29645}(601,\cdot)\) \(\chi_{29645}(706,\cdot)\) \(\chi_{29645}(776,\cdot)\) \(\chi_{29645}(811,\cdot)\) \(\chi_{29645}(986,\cdot)\) \(\chi_{29645}(1091,\cdot)\) \(\chi_{29645}(1161,\cdot)\) \(\chi_{29645}(1196,\cdot)\) \(\chi_{29645}(1476,\cdot)\) \(\chi_{29645}(1581,\cdot)\) \(\chi_{29645}(1756,\cdot)\) \(\chi_{29645}(1931,\cdot)\) \(\chi_{29645}(1966,\cdot)\) \(\chi_{29645}(2141,\cdot)\) \(\chi_{29645}(2246,\cdot)\) \(\chi_{29645}(2316,\cdot)\) \(\chi_{29645}(2526,\cdot)\) \(\chi_{29645}(2631,\cdot)\) \(\chi_{29645}(2701,\cdot)\) \(\chi_{29645}(2736,\cdot)\) \(\chi_{29645}(2911,\cdot)\) \(\chi_{29645}(3121,\cdot)\) \(\chi_{29645}(3296,\cdot)\) \(\chi_{29645}(3401,\cdot)\) \(\chi_{29645}(3471,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{385})$ |
| Fixed field: | Number field defined by a degree 770 polynomial (not computed) |
Values on generators
\((23717,1816,19846)\) → \((1,e\left(\frac{9}{14}\right),e\left(\frac{89}{110}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(12\) | \(13\) | \(16\) | \(17\) |
| \( \chi_{ 29645 }(6, a) \) | \(1\) | \(1\) | \(e\left(\frac{403}{770}\right)\) | \(e\left(\frac{59}{70}\right)\) | \(e\left(\frac{18}{385}\right)\) | \(e\left(\frac{141}{385}\right)\) | \(e\left(\frac{439}{770}\right)\) | \(e\left(\frac{24}{35}\right)\) | \(e\left(\frac{137}{154}\right)\) | \(e\left(\frac{359}{385}\right)\) | \(e\left(\frac{36}{385}\right)\) | \(e\left(\frac{276}{385}\right)\) |