Basic properties
| Modulus: | \(967\) | |
| Conductor: | \(967\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(69\) | 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 967.k
\(\chi_{967}(15,\cdot)\) \(\chi_{967}(39,\cdot)\) \(\chi_{967}(53,\cdot)\) \(\chi_{967}(61,\cdot)\) \(\chi_{967}(68,\cdot)\) \(\chi_{967}(73,\cdot)\) \(\chi_{967}(113,\cdot)\) \(\chi_{967}(124,\cdot)\) \(\chi_{967}(128,\cdot)\) \(\chi_{967}(129,\cdot)\) \(\chi_{967}(145,\cdot)\) \(\chi_{967}(190,\cdot)\) \(\chi_{967}(198,\cdot)\) \(\chi_{967}(202,\cdot)\) \(\chi_{967}(225,\cdot)\) \(\chi_{967}(241,\cdot)\) \(\chi_{967}(280,\cdot)\) \(\chi_{967}(321,\cdot)\) \(\chi_{967}(335,\cdot)\) \(\chi_{967}(341,\cdot)\) \(\chi_{967}(352,\cdot)\) \(\chi_{967}(377,\cdot)\) \(\chi_{967}(400,\cdot)\) \(\chi_{967}(421,\cdot)\) \(\chi_{967}(445,\cdot)\) \(\chi_{967}(494,\cdot)\) \(\chi_{967}(513,\cdot)\) \(\chi_{967}(524,\cdot)\) \(\chi_{967}(539,\cdot)\) \(\chi_{967}(554,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{69})$ |
| Fixed field: | Number field defined by a degree 69 polynomial |
Values on generators
\(5\) → \(e\left(\frac{25}{69}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 967 }(513, a) \) | \(1\) | \(1\) | \(e\left(\frac{35}{69}\right)\) | \(e\left(\frac{20}{23}\right)\) | \(e\left(\frac{1}{69}\right)\) | \(e\left(\frac{25}{69}\right)\) | \(e\left(\frac{26}{69}\right)\) | \(e\left(\frac{19}{69}\right)\) | \(e\left(\frac{12}{23}\right)\) | \(e\left(\frac{17}{23}\right)\) | \(e\left(\frac{20}{23}\right)\) | \(e\left(\frac{17}{23}\right)\) |