Basic properties
Modulus: | \(4025\) | |
Conductor: | \(4025\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
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
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4025.dm
\(\chi_{4025}(4,\cdot)\) \(\chi_{4025}(9,\cdot)\) \(\chi_{4025}(39,\cdot)\) \(\chi_{4025}(144,\cdot)\) \(\chi_{4025}(179,\cdot)\) \(\chi_{4025}(219,\cdot)\) \(\chi_{4025}(284,\cdot)\) \(\chi_{4025}(289,\cdot)\) \(\chi_{4025}(354,\cdot)\) \(\chi_{4025}(394,\cdot)\) \(\chi_{4025}(464,\cdot)\) \(\chi_{4025}(564,\cdot)\) \(\chi_{4025}(604,\cdot)\) \(\chi_{4025}(634,\cdot)\) \(\chi_{4025}(639,\cdot)\) \(\chi_{4025}(669,\cdot)\) \(\chi_{4025}(739,\cdot)\) \(\chi_{4025}(744,\cdot)\) \(\chi_{4025}(809,\cdot)\) \(\chi_{4025}(814,\cdot)\) \(\chi_{4025}(844,\cdot)\) \(\chi_{4025}(984,\cdot)\) \(\chi_{4025}(1089,\cdot)\) \(\chi_{4025}(1094,\cdot)\) \(\chi_{4025}(1129,\cdot)\) \(\chi_{4025}(1159,\cdot)\) \(\chi_{4025}(1269,\cdot)\) \(\chi_{4025}(1304,\cdot)\) \(\chi_{4025}(1369,\cdot)\) \(\chi_{4025}(1409,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{165})$ |
Fixed field: | Number field defined by a degree 330 polynomial (not computed) |
Values on generators
\((2577,1151,3501)\) → \((e\left(\frac{7}{10}\right),e\left(\frac{2}{3}\right),e\left(\frac{3}{11}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
\( \chi_{ 4025 }(284, a) \) | \(1\) | \(1\) | \(e\left(\frac{191}{330}\right)\) | \(e\left(\frac{307}{330}\right)\) | \(e\left(\frac{26}{165}\right)\) | \(e\left(\frac{28}{55}\right)\) | \(e\left(\frac{81}{110}\right)\) | \(e\left(\frac{142}{165}\right)\) | \(e\left(\frac{53}{165}\right)\) | \(e\left(\frac{29}{330}\right)\) | \(e\left(\frac{13}{110}\right)\) | \(e\left(\frac{52}{165}\right)\) |