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.dg
\(\chi_{9196}(7,\cdot)\) \(\chi_{9196}(83,\cdot)\) \(\chi_{9196}(315,\cdot)\) \(\chi_{9196}(387,\cdot)\) \(\chi_{9196}(391,\cdot)\) \(\chi_{9196}(695,\cdot)\) \(\chi_{9196}(767,\cdot)\) \(\chi_{9196}(843,\cdot)\) \(\chi_{9196}(919,\cdot)\) \(\chi_{9196}(1075,\cdot)\) \(\chi_{9196}(1151,\cdot)\) \(\chi_{9196}(1223,\cdot)\) \(\chi_{9196}(1227,\cdot)\) \(\chi_{9196}(1531,\cdot)\) \(\chi_{9196}(1603,\cdot)\) \(\chi_{9196}(1679,\cdot)\) \(\chi_{9196}(1755,\cdot)\) \(\chi_{9196}(1911,\cdot)\) \(\chi_{9196}(1987,\cdot)\) \(\chi_{9196}(2059,\cdot)\) \(\chi_{9196}(2063,\cdot)\) \(\chi_{9196}(2367,\cdot)\) \(\chi_{9196}(2439,\cdot)\) \(\chi_{9196}(2515,\cdot)\) \(\chi_{9196}(2591,\cdot)\) \(\chi_{9196}(2747,\cdot)\) \(\chi_{9196}(2899,\cdot)\) \(\chi_{9196}(3203,\cdot)\) \(\chi_{9196}(3275,\cdot)\) \(\chi_{9196}(3351,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{165})$ |
| Fixed field: | Number field defined by a degree 330 polynomial (not computed) |
Values on generators
\((4599,3269,8229)\) → \((-1,e\left(\frac{7}{110}\right),e\left(\frac{1}{3}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) | \(25\) |
| \( \chi_{ 9196 }(7, a) \) | \(1\) | \(1\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{7}{165}\right)\) | \(e\left(\frac{52}{55}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{31}{330}\right)\) | \(e\left(\frac{157}{330}\right)\) | \(e\left(\frac{149}{330}\right)\) | \(e\left(\frac{25}{66}\right)\) | \(e\left(\frac{41}{66}\right)\) | \(e\left(\frac{14}{165}\right)\) |