Basic properties
| Modulus: | \(2151\) | |
| Conductor: | \(239\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(119\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{239}(55,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2151.y
\(\chi_{2151}(55,\cdot)\) \(\chi_{2151}(64,\cdot)\) \(\chi_{2151}(91,\cdot)\) \(\chi_{2151}(109,\cdot)\) \(\chi_{2151}(127,\cdot)\) \(\chi_{2151}(136,\cdot)\) \(\chi_{2151}(145,\cdot)\) \(\chi_{2151}(226,\cdot)\) \(\chi_{2151}(244,\cdot)\) \(\chi_{2151}(271,\cdot)\) \(\chi_{2151}(289,\cdot)\) \(\chi_{2151}(307,\cdot)\) \(\chi_{2151}(352,\cdot)\) \(\chi_{2151}(361,\cdot)\) \(\chi_{2151}(415,\cdot)\) \(\chi_{2151}(487,\cdot)\) \(\chi_{2151}(496,\cdot)\) \(\chi_{2151}(505,\cdot)\) \(\chi_{2151}(523,\cdot)\) \(\chi_{2151}(532,\cdot)\) \(\chi_{2151}(550,\cdot)\) \(\chi_{2151}(559,\cdot)\) \(\chi_{2151}(568,\cdot)\) \(\chi_{2151}(577,\cdot)\) \(\chi_{2151}(586,\cdot)\) \(\chi_{2151}(613,\cdot)\) \(\chi_{2151}(622,\cdot)\) \(\chi_{2151}(631,\cdot)\) \(\chi_{2151}(640,\cdot)\) \(\chi_{2151}(658,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{119})$ |
| Fixed field: | Number field defined by a degree 119 polynomial (not computed) |
Values on generators
\((479,1441)\) → \((1,e\left(\frac{71}{119}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 2151 }(55, a) \) | \(1\) | \(1\) | \(e\left(\frac{45}{119}\right)\) | \(e\left(\frac{90}{119}\right)\) | \(e\left(\frac{40}{119}\right)\) | \(e\left(\frac{71}{119}\right)\) | \(e\left(\frac{16}{119}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{46}{119}\right)\) | \(e\left(\frac{78}{119}\right)\) | \(e\left(\frac{116}{119}\right)\) | \(e\left(\frac{61}{119}\right)\) |