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 \(\chi_{836}(3,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9196.cj
\(\chi_{9196}(3,\cdot)\) \(\chi_{9196}(735,\cdot)\) \(\chi_{9196}(971,\cdot)\) \(\chi_{9196}(1219,\cdot)\) \(\chi_{9196}(2187,\cdot)\) \(\chi_{9196}(2423,\cdot)\) \(\chi_{9196}(2447,\cdot)\) \(\chi_{9196}(3415,\cdot)\) \(\chi_{9196}(3639,\cdot)\) \(\chi_{9196}(4195,\cdot)\) \(\chi_{9196}(4383,\cdot)\) \(\chi_{9196}(4867,\cdot)\) \(\chi_{9196}(5163,\cdot)\) \(\chi_{9196}(5835,\cdot)\) \(\chi_{9196}(6131,\cdot)\) \(\chi_{9196}(6615,\cdot)\) \(\chi_{9196}(6779,\cdot)\) \(\chi_{9196}(7287,\cdot)\) \(\chi_{9196}(7583,\cdot)\) \(\chi_{9196}(7747,\cdot)\) \(\chi_{9196}(7995,\cdot)\) \(\chi_{9196}(8715,\cdot)\) \(\chi_{9196}(8963,\cdot)\) \(\chi_{9196}(9035,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{45})$ |
Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((4599,3269,8229)\) → \((-1,e\left(\frac{4}{5}\right),e\left(\frac{13}{18}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) | \(25\) |
\( \chi_{ 9196 }(3, a) \) | \(1\) | \(1\) | \(e\left(\frac{13}{45}\right)\) | \(e\left(\frac{34}{45}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{26}{45}\right)\) | \(e\left(\frac{37}{90}\right)\) | \(e\left(\frac{2}{45}\right)\) | \(e\left(\frac{19}{45}\right)\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{23}{45}\right)\) |