Basic properties
| Modulus: | \(9196\) | |
| Conductor: | \(836\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(90\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{836}(215,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9196.ck
\(\chi_{9196}(215,\cdot)\) \(\chi_{9196}(403,\cdot)\) \(\chi_{9196}(959,\cdot)\) \(\chi_{9196}(1183,\cdot)\) \(\chi_{9196}(2151,\cdot)\) \(\chi_{9196}(2175,\cdot)\) \(\chi_{9196}(2411,\cdot)\) \(\chi_{9196}(3379,\cdot)\) \(\chi_{9196}(3627,\cdot)\) \(\chi_{9196}(3863,\cdot)\) \(\chi_{9196}(4595,\cdot)\) \(\chi_{9196}(4759,\cdot)\) \(\chi_{9196}(4831,\cdot)\) \(\chi_{9196}(5079,\cdot)\) \(\chi_{9196}(5799,\cdot)\) \(\chi_{9196}(6047,\cdot)\) \(\chi_{9196}(6211,\cdot)\) \(\chi_{9196}(6507,\cdot)\) \(\chi_{9196}(7015,\cdot)\) \(\chi_{9196}(7179,\cdot)\) \(\chi_{9196}(7663,\cdot)\) \(\chi_{9196}(7959,\cdot)\) \(\chi_{9196}(8631,\cdot)\) \(\chi_{9196}(8927,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((4599,3269,8229)\) → \((-1,e\left(\frac{9}{10}\right),e\left(\frac{7}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) | \(25\) |
| \( \chi_{ 9196 }(215, a) \) | \(1\) | \(1\) | \(e\left(\frac{73}{90}\right)\) | \(e\left(\frac{2}{45}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{28}{45}\right)\) | \(e\left(\frac{71}{90}\right)\) | \(e\left(\frac{77}{90}\right)\) | \(e\left(\frac{79}{90}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{4}{45}\right)\) |