Basic properties
| Modulus: | \(309\) | |
| Conductor: | \(103\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(51\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{103}(4,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 309.m
\(\chi_{309}(4,\cdot)\) \(\chi_{309}(7,\cdot)\) \(\chi_{309}(16,\cdot)\) \(\chi_{309}(19,\cdot)\) \(\chi_{309}(25,\cdot)\) \(\chi_{309}(28,\cdot)\) \(\chi_{309}(49,\cdot)\) \(\chi_{309}(52,\cdot)\) \(\chi_{309}(55,\cdot)\) \(\chi_{309}(58,\cdot)\) \(\chi_{309}(82,\cdot)\) \(\chi_{309}(91,\cdot)\) \(\chi_{309}(97,\cdot)\) \(\chi_{309}(118,\cdot)\) \(\chi_{309}(121,\cdot)\) \(\chi_{309}(136,\cdot)\) \(\chi_{309}(139,\cdot)\) \(\chi_{309}(163,\cdot)\) \(\chi_{309}(166,\cdot)\) \(\chi_{309}(208,\cdot)\) \(\chi_{309}(223,\cdot)\) \(\chi_{309}(232,\cdot)\) \(\chi_{309}(235,\cdot)\) \(\chi_{309}(238,\cdot)\) \(\chi_{309}(244,\cdot)\) \(\chi_{309}(247,\cdot)\) \(\chi_{309}(256,\cdot)\) \(\chi_{309}(265,\cdot)\) \(\chi_{309}(274,\cdot)\) \(\chi_{309}(289,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{51})$ |
| Fixed field: | Number field defined by a degree 51 polynomial |
Values on generators
\((104,211)\) → \((1,e\left(\frac{44}{51}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 309 }(4, a) \) | \(1\) | \(1\) | \(e\left(\frac{49}{51}\right)\) | \(e\left(\frac{47}{51}\right)\) | \(e\left(\frac{44}{51}\right)\) | \(e\left(\frac{23}{51}\right)\) | \(e\left(\frac{15}{17}\right)\) | \(e\left(\frac{14}{17}\right)\) | \(e\left(\frac{32}{51}\right)\) | \(e\left(\frac{2}{17}\right)\) | \(e\left(\frac{7}{17}\right)\) | \(e\left(\frac{43}{51}\right)\) |