Basic properties
| Modulus: | \(9196\) | |
| Conductor: | \(9196\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(330\) | 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.dh
\(\chi_{9196}(31,\cdot)\) \(\chi_{9196}(103,\cdot)\) \(\chi_{9196}(179,\cdot)\) \(\chi_{9196}(335,\cdot)\) \(\chi_{9196}(411,\cdot)\) \(\chi_{9196}(559,\cdot)\) \(\chi_{9196}(863,\cdot)\) \(\chi_{9196}(867,\cdot)\) \(\chi_{9196}(939,\cdot)\) \(\chi_{9196}(1015,\cdot)\) \(\chi_{9196}(1171,\cdot)\) \(\chi_{9196}(1247,\cdot)\) \(\chi_{9196}(1323,\cdot)\) \(\chi_{9196}(1395,\cdot)\) \(\chi_{9196}(1699,\cdot)\) \(\chi_{9196}(1851,\cdot)\) \(\chi_{9196}(2007,\cdot)\) \(\chi_{9196}(2083,\cdot)\) \(\chi_{9196}(2159,\cdot)\) \(\chi_{9196}(2231,\cdot)\) \(\chi_{9196}(2535,\cdot)\) \(\chi_{9196}(2539,\cdot)\) \(\chi_{9196}(2611,\cdot)\) \(\chi_{9196}(2687,\cdot)\) \(\chi_{9196}(2843,\cdot)\) \(\chi_{9196}(2919,\cdot)\) \(\chi_{9196}(2995,\cdot)\) \(\chi_{9196}(3067,\cdot)\) \(\chi_{9196}(3371,\cdot)\) \(\chi_{9196}(3375,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{165})$ |
| Fixed field: | Number field defined by a degree 330 polynomial (not computed) |
Values on generators
\((4599,3269,8229)\) → \((-1,e\left(\frac{43}{55}\right),e\left(\frac{5}{6}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) | \(25\) |
| \( \chi_{ 9196 }(31, a) \) | \(1\) | \(1\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{31}{165}\right)\) | \(e\left(\frac{107}{110}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{43}{330}\right)\) | \(e\left(\frac{53}{165}\right)\) | \(e\left(\frac{106}{165}\right)\) | \(e\left(\frac{7}{66}\right)\) | \(e\left(\frac{59}{66}\right)\) | \(e\left(\frac{62}{165}\right)\) |