Basic properties
Modulus: | \(4235\) | |
Conductor: | \(4235\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
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Order: | \(330\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
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Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4235.dk
\(\chi_{4235}(4,\cdot)\) \(\chi_{4235}(114,\cdot)\) \(\chi_{4235}(179,\cdot)\) \(\chi_{4235}(214,\cdot)\) \(\chi_{4235}(284,\cdot)\) \(\chi_{4235}(289,\cdot)\) \(\chi_{4235}(324,\cdot)\) \(\chi_{4235}(389,\cdot)\) \(\chi_{4235}(394,\cdot)\) \(\chi_{4235}(499,\cdot)\) \(\chi_{4235}(564,\cdot)\) \(\chi_{4235}(599,\cdot)\) \(\chi_{4235}(669,\cdot)\) \(\chi_{4235}(674,\cdot)\) \(\chi_{4235}(709,\cdot)\) \(\chi_{4235}(774,\cdot)\) \(\chi_{4235}(779,\cdot)\) \(\chi_{4235}(884,\cdot)\) \(\chi_{4235}(949,\cdot)\) \(\chi_{4235}(984,\cdot)\) \(\chi_{4235}(1054,\cdot)\) \(\chi_{4235}(1059,\cdot)\) \(\chi_{4235}(1094,\cdot)\) \(\chi_{4235}(1159,\cdot)\) \(\chi_{4235}(1164,\cdot)\) \(\chi_{4235}(1269,\cdot)\) \(\chi_{4235}(1369,\cdot)\) \(\chi_{4235}(1439,\cdot)\) \(\chi_{4235}(1444,\cdot)\) \(\chi_{4235}(1544,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{165})$ |
Fixed field: | Number field defined by a degree 330 polynomial (not computed) |
Values on generators
\((2542,1816,2906)\) → \((-1,e\left(\frac{1}{3}\right),e\left(\frac{49}{55}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(12\) | \(13\) | \(16\) | \(17\) |
\( \chi_{ 4235 }(289, a) \) | \(1\) | \(1\) | \(e\left(\frac{19}{330}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{19}{165}\right)\) | \(e\left(\frac{16}{55}\right)\) | \(e\left(\frac{19}{110}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{23}{66}\right)\) | \(e\left(\frac{53}{110}\right)\) | \(e\left(\frac{38}{165}\right)\) | \(e\left(\frac{161}{330}\right)\) |