Basic properties
Modulus: | \(277\) | |
Conductor: | \(277\) | 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 277.i
\(\chi_{277}(3,\cdot)\) \(\chi_{277}(9,\cdot)\) \(\chi_{277}(10,\cdot)\) \(\chi_{277}(23,\cdot)\) \(\chi_{277}(28,\cdot)\) \(\chi_{277}(48,\cdot)\) \(\chi_{277}(49,\cdot)\) \(\chi_{277}(55,\cdot)\) \(\chi_{277}(57,\cdot)\) \(\chi_{277}(67,\cdot)\) \(\chi_{277}(71,\cdot)\) \(\chi_{277}(79,\cdot)\) \(\chi_{277}(81,\cdot)\) \(\chi_{277}(85,\cdot)\) \(\chi_{277}(88,\cdot)\) \(\chi_{277}(90,\cdot)\) \(\chi_{277}(91,\cdot)\) \(\chi_{277}(100,\cdot)\) \(\chi_{277}(136,\cdot)\) \(\chi_{277}(144,\cdot)\) \(\chi_{277}(147,\cdot)\) \(\chi_{277}(154,\cdot)\) \(\chi_{277}(156,\cdot)\) \(\chi_{277}(165,\cdot)\) \(\chi_{277}(171,\cdot)\) \(\chi_{277}(185,\cdot)\) \(\chi_{277}(188,\cdot)\) \(\chi_{277}(190,\cdot)\) \(\chi_{277}(191,\cdot)\) \(\chi_{277}(194,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{69})$ |
Fixed field: | Number field defined by a degree 69 polynomial |
Values on generators
\(5\) → \(e\left(\frac{37}{69}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 277 }(10, a) \) | \(1\) | \(1\) | \(e\left(\frac{19}{23}\right)\) | \(e\left(\frac{56}{69}\right)\) | \(e\left(\frac{15}{23}\right)\) | \(e\left(\frac{37}{69}\right)\) | \(e\left(\frac{44}{69}\right)\) | \(e\left(\frac{55}{69}\right)\) | \(e\left(\frac{11}{23}\right)\) | \(e\left(\frac{43}{69}\right)\) | \(e\left(\frac{25}{69}\right)\) | \(e\left(\frac{52}{69}\right)\) |