Basic properties
| Modulus: | \(9196\) | |
| Conductor: | \(2299\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(110\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2299}(189,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9196.cr
\(\chi_{9196}(189,\cdot)\) \(\chi_{9196}(569,\cdot)\) \(\chi_{9196}(721,\cdot)\) \(\chi_{9196}(1025,\cdot)\) \(\chi_{9196}(1405,\cdot)\) \(\chi_{9196}(1481,\cdot)\) \(\chi_{9196}(1557,\cdot)\) \(\chi_{9196}(1861,\cdot)\) \(\chi_{9196}(2241,\cdot)\) \(\chi_{9196}(2317,\cdot)\) \(\chi_{9196}(2697,\cdot)\) \(\chi_{9196}(3077,\cdot)\) \(\chi_{9196}(3153,\cdot)\) \(\chi_{9196}(3229,\cdot)\) \(\chi_{9196}(3533,\cdot)\) \(\chi_{9196}(3913,\cdot)\) \(\chi_{9196}(3989,\cdot)\) \(\chi_{9196}(4065,\cdot)\) \(\chi_{9196}(4369,\cdot)\) \(\chi_{9196}(4749,\cdot)\) \(\chi_{9196}(4825,\cdot)\) \(\chi_{9196}(4901,\cdot)\) \(\chi_{9196}(5205,\cdot)\) \(\chi_{9196}(5585,\cdot)\) \(\chi_{9196}(5661,\cdot)\) \(\chi_{9196}(5737,\cdot)\) \(\chi_{9196}(6421,\cdot)\) \(\chi_{9196}(6497,\cdot)\) \(\chi_{9196}(6573,\cdot)\) \(\chi_{9196}(6877,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((4599,3269,8229)\) → \((1,e\left(\frac{51}{110}\right),-1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) | \(25\) |
| \( \chi_{ 9196 }(189, a) \) | \(1\) | \(1\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{17}{55}\right)\) | \(e\left(\frac{27}{110}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{18}{55}\right)\) | \(e\left(\frac{67}{110}\right)\) | \(e\left(\frac{79}{110}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{34}{55}\right)\) |