Basic properties
| Modulus: | \(5445\) | |
| Conductor: | \(605\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(110\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{605}(64,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5445.cs
\(\chi_{5445}(64,\cdot)\) \(\chi_{5445}(289,\cdot)\) \(\chi_{5445}(334,\cdot)\) \(\chi_{5445}(379,\cdot)\) \(\chi_{5445}(559,\cdot)\) \(\chi_{5445}(784,\cdot)\) \(\chi_{5445}(829,\cdot)\) \(\chi_{5445}(1054,\cdot)\) \(\chi_{5445}(1279,\cdot)\) \(\chi_{5445}(1324,\cdot)\) \(\chi_{5445}(1369,\cdot)\) \(\chi_{5445}(1549,\cdot)\) \(\chi_{5445}(1774,\cdot)\) \(\chi_{5445}(1819,\cdot)\) \(\chi_{5445}(1864,\cdot)\) \(\chi_{5445}(2044,\cdot)\) \(\chi_{5445}(2269,\cdot)\) \(\chi_{5445}(2314,\cdot)\) \(\chi_{5445}(2359,\cdot)\) \(\chi_{5445}(2539,\cdot)\) \(\chi_{5445}(2764,\cdot)\) \(\chi_{5445}(2809,\cdot)\) \(\chi_{5445}(2854,\cdot)\) \(\chi_{5445}(3259,\cdot)\) \(\chi_{5445}(3304,\cdot)\) \(\chi_{5445}(3349,\cdot)\) \(\chi_{5445}(3529,\cdot)\) \(\chi_{5445}(3799,\cdot)\) \(\chi_{5445}(3844,\cdot)\) \(\chi_{5445}(4024,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((3026,4357,3511)\) → \((1,-1,e\left(\frac{3}{55}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) | \(23\) |
| \( \chi_{ 5445 }(64, a) \) | \(1\) | \(1\) | \(e\left(\frac{61}{110}\right)\) | \(e\left(\frac{6}{55}\right)\) | \(e\left(\frac{97}{110}\right)\) | \(e\left(\frac{73}{110}\right)\) | \(e\left(\frac{1}{110}\right)\) | \(e\left(\frac{24}{55}\right)\) | \(e\left(\frac{12}{55}\right)\) | \(e\left(\frac{19}{110}\right)\) | \(e\left(\frac{29}{55}\right)\) | \(e\left(\frac{7}{22}\right)\) |