Basic properties
| Modulus: | \(3021\) | |
| Conductor: | \(3021\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(234\) | 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 3021.co
\(\chi_{3021}(89,\cdot)\) \(\chi_{3021}(116,\cdot)\) \(\chi_{3021}(155,\cdot)\) \(\chi_{3021}(203,\cdot)\) \(\chi_{3021}(281,\cdot)\) \(\chi_{3021}(314,\cdot)\) \(\chi_{3021}(395,\cdot)\) \(\chi_{3021}(413,\cdot)\) \(\chi_{3021}(440,\cdot)\) \(\chi_{3021}(452,\cdot)\) \(\chi_{3021}(470,\cdot)\) \(\chi_{3021}(545,\cdot)\) \(\chi_{3021}(554,\cdot)\) \(\chi_{3021}(566,\cdot)\) \(\chi_{3021}(572,\cdot)\) \(\chi_{3021}(599,\cdot)\) \(\chi_{3021}(611,\cdot)\) \(\chi_{3021}(629,\cdot)\) \(\chi_{3021}(680,\cdot)\) \(\chi_{3021}(713,\cdot)\) \(\chi_{3021}(725,\cdot)\) \(\chi_{3021}(755,\cdot)\) \(\chi_{3021}(770,\cdot)\) \(\chi_{3021}(839,\cdot)\) \(\chi_{3021}(884,\cdot)\) \(\chi_{3021}(914,\cdot)\) \(\chi_{3021}(998,\cdot)\) \(\chi_{3021}(1001,\cdot)\) \(\chi_{3021}(1022,\cdot)\) \(\chi_{3021}(1181,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{117})$ |
| Fixed field: | Number field defined by a degree 234 polynomial (not computed) |
Values on generators
\((2015,1750,2281)\) → \((-1,e\left(\frac{5}{18}\right),e\left(\frac{9}{13}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 3021 }(89, a) \) | \(1\) | \(1\) | \(e\left(\frac{55}{117}\right)\) | \(e\left(\frac{110}{117}\right)\) | \(e\left(\frac{113}{234}\right)\) | \(e\left(\frac{14}{39}\right)\) | \(e\left(\frac{16}{39}\right)\) | \(e\left(\frac{223}{234}\right)\) | \(e\left(\frac{77}{78}\right)\) | \(e\left(\frac{1}{234}\right)\) | \(e\left(\frac{97}{117}\right)\) | \(e\left(\frac{103}{117}\right)\) |