Basic properties
Modulus: | \(4508\) | |
Conductor: | \(1127\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(77\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{1127}(29,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4508.bw
\(\chi_{4508}(29,\cdot)\) \(\chi_{4508}(85,\cdot)\) \(\chi_{4508}(141,\cdot)\) \(\chi_{4508}(169,\cdot)\) \(\chi_{4508}(225,\cdot)\) \(\chi_{4508}(449,\cdot)\) \(\chi_{4508}(533,\cdot)\) \(\chi_{4508}(561,\cdot)\) \(\chi_{4508}(673,\cdot)\) \(\chi_{4508}(729,\cdot)\) \(\chi_{4508}(813,\cdot)\) \(\chi_{4508}(841,\cdot)\) \(\chi_{4508}(869,\cdot)\) \(\chi_{4508}(1037,\cdot)\) \(\chi_{4508}(1093,\cdot)\) \(\chi_{4508}(1205,\cdot)\) \(\chi_{4508}(1317,\cdot)\) \(\chi_{4508}(1429,\cdot)\) \(\chi_{4508}(1457,\cdot)\) \(\chi_{4508}(1485,\cdot)\) \(\chi_{4508}(1513,\cdot)\) \(\chi_{4508}(1681,\cdot)\) \(\chi_{4508}(1737,\cdot)\) \(\chi_{4508}(1821,\cdot)\) \(\chi_{4508}(1849,\cdot)\) \(\chi_{4508}(2017,\cdot)\) \(\chi_{4508}(2073,\cdot)\) \(\chi_{4508}(2101,\cdot)\) \(\chi_{4508}(2129,\cdot)\) \(\chi_{4508}(2325,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{77})$ |
Fixed field: | Number field defined by a degree 77 polynomial |
Values on generators
\((2255,1473,1569)\) → \((1,e\left(\frac{3}{7}\right),e\left(\frac{9}{11}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(25\) | \(27\) |
\( \chi_{ 4508 }(29, a) \) | \(1\) | \(1\) | \(e\left(\frac{40}{77}\right)\) | \(e\left(\frac{19}{77}\right)\) | \(e\left(\frac{3}{77}\right)\) | \(e\left(\frac{39}{77}\right)\) | \(e\left(\frac{46}{77}\right)\) | \(e\left(\frac{59}{77}\right)\) | \(e\left(\frac{34}{77}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{38}{77}\right)\) | \(e\left(\frac{43}{77}\right)\) |