Basic properties
Modulus: | \(7942\) | |
Conductor: | \(3971\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(570\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{3971}(107,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7942.bq
\(\chi_{7942}(107,\cdot)\) \(\chi_{7942}(145,\cdot)\) \(\chi_{7942}(183,\cdot)\) \(\chi_{7942}(217,\cdot)\) \(\chi_{7942}(255,\cdot)\) \(\chi_{7942}(259,\cdot)\) \(\chi_{7942}(369,\cdot)\) \(\chi_{7942}(525,\cdot)\) \(\chi_{7942}(563,\cdot)\) \(\chi_{7942}(601,\cdot)\) \(\chi_{7942}(635,\cdot)\) \(\chi_{7942}(673,\cdot)\) \(\chi_{7942}(677,\cdot)\) \(\chi_{7942}(711,\cdot)\) \(\chi_{7942}(787,\cdot)\) \(\chi_{7942}(943,\cdot)\) \(\chi_{7942}(981,\cdot)\) \(\chi_{7942}(1019,\cdot)\) \(\chi_{7942}(1053,\cdot)\) \(\chi_{7942}(1091,\cdot)\) \(\chi_{7942}(1095,\cdot)\) \(\chi_{7942}(1129,\cdot)\) \(\chi_{7942}(1205,\cdot)\) \(\chi_{7942}(1361,\cdot)\) \(\chi_{7942}(1399,\cdot)\) \(\chi_{7942}(1437,\cdot)\) \(\chi_{7942}(1471,\cdot)\) \(\chi_{7942}(1509,\cdot)\) \(\chi_{7942}(1547,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{285})$ |
Fixed field: | Number field defined by a degree 570 polynomial (not computed) |
Values on generators
\((5777,6139)\) → \((e\left(\frac{3}{10}\right),e\left(\frac{89}{114}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) | \(25\) |
\( \chi_{ 7942 }(107, a) \) | \(1\) | \(1\) | \(e\left(\frac{523}{570}\right)\) | \(e\left(\frac{92}{285}\right)\) | \(e\left(\frac{39}{190}\right)\) | \(e\left(\frac{238}{285}\right)\) | \(e\left(\frac{43}{285}\right)\) | \(e\left(\frac{137}{570}\right)\) | \(e\left(\frac{79}{570}\right)\) | \(e\left(\frac{7}{57}\right)\) | \(e\left(\frac{56}{57}\right)\) | \(e\left(\frac{184}{285}\right)\) |