Basic properties
| Modulus: | \(8004\) | |
| Conductor: | \(667\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(154\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{667}(13,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8004.di
\(\chi_{8004}(13,\cdot)\) \(\chi_{8004}(121,\cdot)\) \(\chi_{8004}(265,\cdot)\) \(\chi_{8004}(325,\cdot)\) \(\chi_{8004}(361,\cdot)\) \(\chi_{8004}(469,\cdot)\) \(\chi_{8004}(673,\cdot)\) \(\chi_{8004}(817,\cdot)\) \(\chi_{8004}(961,\cdot)\) \(\chi_{8004}(1021,\cdot)\) \(\chi_{8004}(1153,\cdot)\) \(\chi_{8004}(1369,\cdot)\) \(\chi_{8004}(1405,\cdot)\) \(\chi_{8004}(1501,\cdot)\) \(\chi_{8004}(1513,\cdot)\) \(\chi_{8004}(1849,\cdot)\) \(\chi_{8004}(1981,\cdot)\) \(\chi_{8004}(2005,\cdot)\) \(\chi_{8004}(2065,\cdot)\) \(\chi_{8004}(2101,\cdot)\) \(\chi_{8004}(2197,\cdot)\) \(\chi_{8004}(2329,\cdot)\) \(\chi_{8004}(2557,\cdot)\) \(\chi_{8004}(2677,\cdot)\) \(\chi_{8004}(2893,\cdot)\) \(\chi_{8004}(3025,\cdot)\) \(\chi_{8004}(3049,\cdot)\) \(\chi_{8004}(3109,\cdot)\) \(\chi_{8004}(3397,\cdot)\) \(\chi_{8004}(3601,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{77})$ |
| Fixed field: | Number field defined by a degree 154 polynomial (not computed) |
Values on generators
\((4003,2669,3133,553)\) → \((1,1,e\left(\frac{7}{11}\right),e\left(\frac{9}{14}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(25\) | \(31\) | \(35\) | \(37\) |
| \( \chi_{ 8004 }(13, a) \) | \(1\) | \(1\) | \(e\left(\frac{60}{77}\right)\) | \(e\left(\frac{62}{77}\right)\) | \(e\left(\frac{123}{154}\right)\) | \(e\left(\frac{37}{77}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{51}{154}\right)\) | \(e\left(\frac{43}{77}\right)\) | \(e\left(\frac{71}{154}\right)\) | \(e\left(\frac{45}{77}\right)\) | \(e\left(\frac{45}{154}\right)\) |