Basic properties
Modulus: | \(9196\) | |
Conductor: | \(121\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(55\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{121}(108,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9196.by
\(\chi_{9196}(229,\cdot)\) \(\chi_{9196}(533,\cdot)\) \(\chi_{9196}(609,\cdot)\) \(\chi_{9196}(685,\cdot)\) \(\chi_{9196}(1065,\cdot)\) \(\chi_{9196}(1369,\cdot)\) \(\chi_{9196}(1445,\cdot)\) \(\chi_{9196}(1521,\cdot)\) \(\chi_{9196}(1901,\cdot)\) \(\chi_{9196}(2281,\cdot)\) \(\chi_{9196}(2357,\cdot)\) \(\chi_{9196}(2737,\cdot)\) \(\chi_{9196}(3041,\cdot)\) \(\chi_{9196}(3117,\cdot)\) \(\chi_{9196}(3193,\cdot)\) \(\chi_{9196}(3573,\cdot)\) \(\chi_{9196}(3877,\cdot)\) \(\chi_{9196}(4029,\cdot)\) \(\chi_{9196}(4409,\cdot)\) \(\chi_{9196}(4713,\cdot)\) \(\chi_{9196}(4789,\cdot)\) \(\chi_{9196}(4865,\cdot)\) \(\chi_{9196}(5245,\cdot)\) \(\chi_{9196}(5549,\cdot)\) \(\chi_{9196}(5625,\cdot)\) \(\chi_{9196}(5701,\cdot)\) \(\chi_{9196}(6081,\cdot)\) \(\chi_{9196}(6385,\cdot)\) \(\chi_{9196}(6461,\cdot)\) \(\chi_{9196}(6917,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{55})$ |
Fixed field: | Number field defined by a degree 55 polynomial |
Values on generators
\((4599,3269,8229)\) → \((1,e\left(\frac{23}{55}\right),1)\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) | \(25\) |
\( \chi_{ 9196 }(229, a) \) | \(1\) | \(1\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{52}{55}\right)\) | \(e\left(\frac{51}{55}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{13}{55}\right)\) | \(e\left(\frac{41}{55}\right)\) | \(e\left(\frac{27}{55}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{49}{55}\right)\) |