Basic properties
| Modulus: | \(9196\) | |
| Conductor: | \(9196\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(198\) | 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 9196.cx
\(\chi_{9196}(67,\cdot)\) \(\chi_{9196}(155,\cdot)\) \(\chi_{9196}(287,\cdot)\) \(\chi_{9196}(375,\cdot)\) \(\chi_{9196}(507,\cdot)\) \(\chi_{9196}(903,\cdot)\) \(\chi_{9196}(991,\cdot)\) \(\chi_{9196}(1079,\cdot)\) \(\chi_{9196}(1123,\cdot)\) \(\chi_{9196}(1343,\cdot)\) \(\chi_{9196}(1739,\cdot)\) \(\chi_{9196}(1827,\cdot)\) \(\chi_{9196}(1915,\cdot)\) \(\chi_{9196}(1959,\cdot)\) \(\chi_{9196}(2047,\cdot)\) \(\chi_{9196}(2575,\cdot)\) \(\chi_{9196}(2751,\cdot)\) \(\chi_{9196}(2795,\cdot)\) \(\chi_{9196}(2883,\cdot)\) \(\chi_{9196}(3015,\cdot)\) \(\chi_{9196}(3411,\cdot)\) \(\chi_{9196}(3499,\cdot)\) \(\chi_{9196}(3587,\cdot)\) \(\chi_{9196}(3719,\cdot)\) \(\chi_{9196}(3851,\cdot)\) \(\chi_{9196}(4247,\cdot)\) \(\chi_{9196}(4335,\cdot)\) \(\chi_{9196}(4423,\cdot)\) \(\chi_{9196}(4467,\cdot)\) \(\chi_{9196}(4555,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{99})$ |
| Fixed field: | Number field defined by a degree 198 polynomial (not computed) |
Values on generators
\((4599,3269,8229)\) → \((-1,e\left(\frac{10}{11}\right),e\left(\frac{17}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) | \(25\) |
| \( \chi_{ 9196 }(67, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{38}{99}\right)\) | \(e\left(\frac{35}{66}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{107}{198}\right)\) | \(e\left(\frac{16}{99}\right)\) | \(e\left(\frac{98}{99}\right)\) | \(e\left(\frac{61}{198}\right)\) | \(e\left(\frac{5}{198}\right)\) | \(e\left(\frac{76}{99}\right)\) |