Basic properties
| Modulus: | \(676\) | |
| Conductor: | \(676\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(52\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 676.s
\(\chi_{676}(31,\cdot)\) \(\chi_{676}(47,\cdot)\) \(\chi_{676}(83,\cdot)\) \(\chi_{676}(135,\cdot)\) \(\chi_{676}(151,\cdot)\) \(\chi_{676}(187,\cdot)\) \(\chi_{676}(203,\cdot)\) \(\chi_{676}(255,\cdot)\) \(\chi_{676}(291,\cdot)\) \(\chi_{676}(307,\cdot)\) \(\chi_{676}(343,\cdot)\) \(\chi_{676}(359,\cdot)\) \(\chi_{676}(395,\cdot)\) \(\chi_{676}(411,\cdot)\) \(\chi_{676}(447,\cdot)\) \(\chi_{676}(463,\cdot)\) \(\chi_{676}(499,\cdot)\) \(\chi_{676}(515,\cdot)\) \(\chi_{676}(551,\cdot)\) \(\chi_{676}(567,\cdot)\) \(\chi_{676}(603,\cdot)\) \(\chi_{676}(619,\cdot)\) \(\chi_{676}(655,\cdot)\) \(\chi_{676}(671,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{52})$ |
| Fixed field: | Number field defined by a degree 52 polynomial |
Values on generators
\((339,509)\) → \((-1,e\left(\frac{21}{52}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 676 }(47, a) \) | \(1\) | \(1\) | \(e\left(\frac{15}{26}\right)\) | \(e\left(\frac{33}{52}\right)\) | \(e\left(\frac{37}{52}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{5}{52}\right)\) | \(e\left(\frac{11}{52}\right)\) | \(e\left(\frac{25}{26}\right)\) | \(-i\) | \(e\left(\frac{15}{52}\right)\) | \(1\) |