Basic properties
| Modulus: | \(1334\) | |
| Conductor: | \(667\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(154\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{667}(9,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1334.u
\(\chi_{1334}(9,\cdot)\) \(\chi_{1334}(13,\cdot)\) \(\chi_{1334}(35,\cdot)\) \(\chi_{1334}(71,\cdot)\) \(\chi_{1334}(121,\cdot)\) \(\chi_{1334}(151,\cdot)\) \(\chi_{1334}(167,\cdot)\) \(\chi_{1334}(179,\cdot)\) \(\chi_{1334}(187,\cdot)\) \(\chi_{1334}(209,\cdot)\) \(\chi_{1334}(225,\cdot)\) \(\chi_{1334}(265,\cdot)\) \(\chi_{1334}(303,\cdot)\) \(\chi_{1334}(325,\cdot)\) \(\chi_{1334}(353,\cdot)\) \(\chi_{1334}(357,\cdot)\) \(\chi_{1334}(361,\cdot)\) \(\chi_{1334}(381,\cdot)\) \(\chi_{1334}(399,\cdot)\) \(\chi_{1334}(439,\cdot)\) \(\chi_{1334}(441,\cdot)\) \(\chi_{1334}(469,\cdot)\) \(\chi_{1334}(473,\cdot)\) \(\chi_{1334}(499,\cdot)\) \(\chi_{1334}(515,\cdot)\) \(\chi_{1334}(531,\cdot)\) \(\chi_{1334}(535,\cdot)\) \(\chi_{1334}(555,\cdot)\) \(\chi_{1334}(593,\cdot)\) \(\chi_{1334}(647,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{77})$ |
| Fixed field: | Number field defined by a degree 154 polynomial (not computed) |
Values on generators
\((465,553)\) → \((e\left(\frac{5}{11}\right),e\left(\frac{5}{14}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 1334 }(9, a) \) | \(1\) | \(1\) | \(e\left(\frac{9}{154}\right)\) | \(e\left(\frac{24}{77}\right)\) | \(e\left(\frac{71}{77}\right)\) | \(e\left(\frac{9}{77}\right)\) | \(e\left(\frac{3}{154}\right)\) | \(e\left(\frac{61}{77}\right)\) | \(e\left(\frac{57}{154}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{5}{154}\right)\) | \(e\left(\frac{151}{154}\right)\) |