Basic properties
| Modulus: | \(338130\) | |
| Conductor: | \(4335\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(136\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{4335}(53,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 338130.bfs
\(\chi_{338130}(53,\cdot)\) \(\chi_{338130}(2627,\cdot)\) \(\chi_{338130}(8243,\cdot)\) \(\chi_{338130}(19943,\cdot)\) \(\chi_{338130}(22517,\cdot)\) \(\chi_{338130}(28133,\cdot)\) \(\chi_{338130}(29537,\cdot)\) \(\chi_{338130}(39833,\cdot)\) \(\chi_{338130}(42407,\cdot)\) \(\chi_{338130}(48023,\cdot)\) \(\chi_{338130}(49427,\cdot)\) \(\chi_{338130}(59723,\cdot)\) \(\chi_{338130}(62297,\cdot)\) \(\chi_{338130}(67913,\cdot)\) \(\chi_{338130}(69317,\cdot)\) \(\chi_{338130}(79613,\cdot)\) \(\chi_{338130}(82187,\cdot)\) \(\chi_{338130}(87803,\cdot)\) \(\chi_{338130}(89207,\cdot)\) \(\chi_{338130}(99503,\cdot)\) \(\chi_{338130}(102077,\cdot)\) \(\chi_{338130}(107693,\cdot)\) \(\chi_{338130}(109097,\cdot)\) \(\chi_{338130}(119393,\cdot)\) \(\chi_{338130}(121967,\cdot)\) \(\chi_{338130}(128987,\cdot)\) \(\chi_{338130}(139283,\cdot)\) \(\chi_{338130}(141857,\cdot)\) \(\chi_{338130}(147473,\cdot)\) \(\chi_{338130}(148877,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{136})$ |
| Fixed field: | Number field defined by a degree 136 polynomial (not computed) |
Values on generators
\((262991,67627,104041,145081)\) → \((-1,-i,1,e\left(\frac{103}{136}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) | \(47\) |
| \( \chi_{ 338130 }(53, a) \) | \(1\) | \(1\) | \(e\left(\frac{19}{136}\right)\) | \(e\left(\frac{125}{136}\right)\) | \(e\left(\frac{7}{68}\right)\) | \(e\left(\frac{87}{136}\right)\) | \(e\left(\frac{91}{136}\right)\) | \(e\left(\frac{111}{136}\right)\) | \(e\left(\frac{61}{136}\right)\) | \(e\left(\frac{1}{136}\right)\) | \(e\left(\frac{7}{17}\right)\) | \(e\left(\frac{67}{68}\right)\) |