Basic properties
| Modulus: | \(1215\) | |
| Conductor: | \(243\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(162\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{243}(41,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1215.z
\(\chi_{1215}(11,\cdot)\) \(\chi_{1215}(41,\cdot)\) \(\chi_{1215}(56,\cdot)\) \(\chi_{1215}(86,\cdot)\) \(\chi_{1215}(101,\cdot)\) \(\chi_{1215}(131,\cdot)\) \(\chi_{1215}(146,\cdot)\) \(\chi_{1215}(176,\cdot)\) \(\chi_{1215}(191,\cdot)\) \(\chi_{1215}(221,\cdot)\) \(\chi_{1215}(236,\cdot)\) \(\chi_{1215}(266,\cdot)\) \(\chi_{1215}(281,\cdot)\) \(\chi_{1215}(311,\cdot)\) \(\chi_{1215}(326,\cdot)\) \(\chi_{1215}(356,\cdot)\) \(\chi_{1215}(371,\cdot)\) \(\chi_{1215}(401,\cdot)\) \(\chi_{1215}(416,\cdot)\) \(\chi_{1215}(446,\cdot)\) \(\chi_{1215}(461,\cdot)\) \(\chi_{1215}(491,\cdot)\) \(\chi_{1215}(506,\cdot)\) \(\chi_{1215}(536,\cdot)\) \(\chi_{1215}(551,\cdot)\) \(\chi_{1215}(581,\cdot)\) \(\chi_{1215}(596,\cdot)\) \(\chi_{1215}(626,\cdot)\) \(\chi_{1215}(641,\cdot)\) \(\chi_{1215}(671,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{81})$ |
| Fixed field: | Number field defined by a degree 162 polynomial (not computed) |
Values on generators
\((731,487)\) → \((e\left(\frac{53}{162}\right),1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 1215 }(41, a) \) | \(-1\) | \(1\) | \(e\left(\frac{53}{162}\right)\) | \(e\left(\frac{53}{81}\right)\) | \(e\left(\frac{73}{81}\right)\) | \(e\left(\frac{53}{54}\right)\) | \(e\left(\frac{95}{162}\right)\) | \(e\left(\frac{50}{81}\right)\) | \(e\left(\frac{37}{162}\right)\) | \(e\left(\frac{25}{81}\right)\) | \(e\left(\frac{43}{54}\right)\) | \(e\left(\frac{1}{27}\right)\) |