Basic properties
Modulus: | \(1150\) | |
Conductor: | \(575\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(110\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{575}(144,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1150.u
\(\chi_{1150}(9,\cdot)\) \(\chi_{1150}(29,\cdot)\) \(\chi_{1150}(39,\cdot)\) \(\chi_{1150}(59,\cdot)\) \(\chi_{1150}(119,\cdot)\) \(\chi_{1150}(169,\cdot)\) \(\chi_{1150}(179,\cdot)\) \(\chi_{1150}(209,\cdot)\) \(\chi_{1150}(219,\cdot)\) \(\chi_{1150}(239,\cdot)\) \(\chi_{1150}(259,\cdot)\) \(\chi_{1150}(269,\cdot)\) \(\chi_{1150}(279,\cdot)\) \(\chi_{1150}(289,\cdot)\) \(\chi_{1150}(409,\cdot)\) \(\chi_{1150}(439,\cdot)\) \(\chi_{1150}(469,\cdot)\) \(\chi_{1150}(489,\cdot)\) \(\chi_{1150}(509,\cdot)\) \(\chi_{1150}(519,\cdot)\) \(\chi_{1150}(579,\cdot)\) \(\chi_{1150}(629,\cdot)\) \(\chi_{1150}(639,\cdot)\) \(\chi_{1150}(669,\cdot)\) \(\chi_{1150}(679,\cdot)\) \(\chi_{1150}(719,\cdot)\) \(\chi_{1150}(729,\cdot)\) \(\chi_{1150}(739,\cdot)\) \(\chi_{1150}(809,\cdot)\) \(\chi_{1150}(859,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{55})$ |
Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((277,51)\) → \((e\left(\frac{9}{10}\right),e\left(\frac{9}{11}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(27\) | \(29\) |
\( \chi_{ 1150 }(719, a) \) | \(1\) | \(1\) | \(e\left(\frac{43}{110}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{43}{55}\right)\) | \(e\left(\frac{42}{55}\right)\) | \(e\left(\frac{61}{110}\right)\) | \(e\left(\frac{47}{110}\right)\) | \(e\left(\frac{26}{55}\right)\) | \(e\left(\frac{24}{55}\right)\) | \(e\left(\frac{19}{110}\right)\) | \(e\left(\frac{29}{55}\right)\) |