Basic properties
Modulus: | \(4025\) | |
Conductor: | \(575\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(220\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{575}(533,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4025.dg
\(\chi_{4025}(8,\cdot)\) \(\chi_{4025}(78,\cdot)\) \(\chi_{4025}(127,\cdot)\) \(\chi_{4025}(197,\cdot)\) \(\chi_{4025}(288,\cdot)\) \(\chi_{4025}(302,\cdot)\) \(\chi_{4025}(358,\cdot)\) \(\chi_{4025}(372,\cdot)\) \(\chi_{4025}(463,\cdot)\) \(\chi_{4025}(512,\cdot)\) \(\chi_{4025}(533,\cdot)\) \(\chi_{4025}(547,\cdot)\) \(\chi_{4025}(652,\cdot)\) \(\chi_{4025}(673,\cdot)\) \(\chi_{4025}(708,\cdot)\) \(\chi_{4025}(722,\cdot)\) \(\chi_{4025}(813,\cdot)\) \(\chi_{4025}(883,\cdot)\) \(\chi_{4025}(1002,\cdot)\) \(\chi_{4025}(1037,\cdot)\) \(\chi_{4025}(1163,\cdot)\) \(\chi_{4025}(1177,\cdot)\) \(\chi_{4025}(1198,\cdot)\) \(\chi_{4025}(1212,\cdot)\) \(\chi_{4025}(1317,\cdot)\) \(\chi_{4025}(1338,\cdot)\) \(\chi_{4025}(1352,\cdot)\) \(\chi_{4025}(1373,\cdot)\) \(\chi_{4025}(1478,\cdot)\) \(\chi_{4025}(1513,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{220})$ |
Fixed field: | Number field defined by a degree 220 polynomial (not computed) |
Values on generators
\((2577,1151,3501)\) → \((e\left(\frac{3}{20}\right),1,e\left(\frac{2}{11}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
\( \chi_{ 4025 }(533, a) \) | \(-1\) | \(1\) | \(e\left(\frac{113}{220}\right)\) | \(e\left(\frac{211}{220}\right)\) | \(e\left(\frac{3}{110}\right)\) | \(e\left(\frac{26}{55}\right)\) | \(e\left(\frac{119}{220}\right)\) | \(e\left(\frac{101}{110}\right)\) | \(e\left(\frac{2}{55}\right)\) | \(e\left(\frac{217}{220}\right)\) | \(e\left(\frac{87}{220}\right)\) | \(e\left(\frac{3}{55}\right)\) |