Basic properties
| Modulus: | \(7623\) | |
| 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 \(\chi_{121}(26,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7623.do
\(\chi_{7623}(64,\cdot)\) \(\chi_{7623}(190,\cdot)\) \(\chi_{7623}(379,\cdot)\) \(\chi_{7623}(631,\cdot)\) \(\chi_{7623}(757,\cdot)\) \(\chi_{7623}(883,\cdot)\) \(\chi_{7623}(1072,\cdot)\) \(\chi_{7623}(1324,\cdot)\) \(\chi_{7623}(1450,\cdot)\) \(\chi_{7623}(1765,\cdot)\) \(\chi_{7623}(2143,\cdot)\) \(\chi_{7623}(2269,\cdot)\) \(\chi_{7623}(2458,\cdot)\) \(\chi_{7623}(2710,\cdot)\) \(\chi_{7623}(2836,\cdot)\) \(\chi_{7623}(2962,\cdot)\) \(\chi_{7623}(3151,\cdot)\) \(\chi_{7623}(3403,\cdot)\) \(\chi_{7623}(3529,\cdot)\) \(\chi_{7623}(3655,\cdot)\) \(\chi_{7623}(3844,\cdot)\) \(\chi_{7623}(4096,\cdot)\) \(\chi_{7623}(4222,\cdot)\) \(\chi_{7623}(4348,\cdot)\) \(\chi_{7623}(4537,\cdot)\) \(\chi_{7623}(4789,\cdot)\) \(\chi_{7623}(4915,\cdot)\) \(\chi_{7623}(5041,\cdot)\) \(\chi_{7623}(5482,\cdot)\) \(\chi_{7623}(5608,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 55 polynomial |
Values on generators
\((848,4357,4600)\) → \((1,1,e\left(\frac{51}{55}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(13\) | \(16\) | \(17\) | \(19\) | \(20\) |
| \( \chi_{ 7623 }(631, a) \) | \(1\) | \(1\) | \(e\left(\frac{51}{55}\right)\) | \(e\left(\frac{47}{55}\right)\) | \(e\left(\frac{34}{55}\right)\) | \(e\left(\frac{43}{55}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{36}{55}\right)\) | \(e\left(\frac{39}{55}\right)\) | \(e\left(\frac{24}{55}\right)\) | \(e\left(\frac{53}{55}\right)\) | \(e\left(\frac{26}{55}\right)\) |