Basic properties
| Modulus: | \(8004\) | |
| Conductor: | \(2001\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(154\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2001}(53,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8004.df
\(\chi_{8004}(53,\cdot)\) \(\chi_{8004}(65,\cdot)\) \(\chi_{8004}(281,\cdot)\) \(\chi_{8004}(401,\cdot)\) \(\chi_{8004}(605,\cdot)\) \(\chi_{8004}(893,\cdot)\) \(\chi_{8004}(953,\cdot)\) \(\chi_{8004}(977,\cdot)\) \(\chi_{8004}(1109,\cdot)\) \(\chi_{8004}(1325,\cdot)\) \(\chi_{8004}(1445,\cdot)\) \(\chi_{8004}(1673,\cdot)\) \(\chi_{8004}(1805,\cdot)\) \(\chi_{8004}(1901,\cdot)\) \(\chi_{8004}(1937,\cdot)\) \(\chi_{8004}(1997,\cdot)\) \(\chi_{8004}(2021,\cdot)\) \(\chi_{8004}(2153,\cdot)\) \(\chi_{8004}(2489,\cdot)\) \(\chi_{8004}(2501,\cdot)\) \(\chi_{8004}(2597,\cdot)\) \(\chi_{8004}(2633,\cdot)\) \(\chi_{8004}(2849,\cdot)\) \(\chi_{8004}(2981,\cdot)\) \(\chi_{8004}(3041,\cdot)\) \(\chi_{8004}(3185,\cdot)\) \(\chi_{8004}(3329,\cdot)\) \(\chi_{8004}(3533,\cdot)\) \(\chi_{8004}(3641,\cdot)\) \(\chi_{8004}(3677,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{77})$ |
| Fixed field: | Number field defined by a degree 154 polynomial (not computed) |
Values on generators
\((4003,2669,3133,553)\) → \((1,-1,e\left(\frac{19}{22}\right),e\left(\frac{2}{7}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(25\) | \(31\) | \(35\) | \(37\) |
| \( \chi_{ 8004 }(53, a) \) | \(1\) | \(1\) | \(e\left(\frac{50}{77}\right)\) | \(e\left(\frac{129}{154}\right)\) | \(e\left(\frac{32}{77}\right)\) | \(e\left(\frac{18}{77}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{81}{154}\right)\) | \(e\left(\frac{23}{77}\right)\) | \(e\left(\frac{36}{77}\right)\) | \(e\left(\frac{75}{154}\right)\) | \(e\left(\frac{153}{154}\right)\) |