Basic properties
Modulus: | \(799\) | |
Conductor: | \(799\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(368\) | 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 799.s
\(\chi_{799}(5,\cdot)\) \(\chi_{799}(10,\cdot)\) \(\chi_{799}(11,\cdot)\) \(\chi_{799}(20,\cdot)\) \(\chi_{799}(22,\cdot)\) \(\chi_{799}(23,\cdot)\) \(\chi_{799}(29,\cdot)\) \(\chi_{799}(31,\cdot)\) \(\chi_{799}(39,\cdot)\) \(\chi_{799}(40,\cdot)\) \(\chi_{799}(41,\cdot)\) \(\chi_{799}(44,\cdot)\) \(\chi_{799}(45,\cdot)\) \(\chi_{799}(57,\cdot)\) \(\chi_{799}(58,\cdot)\) \(\chi_{799}(62,\cdot)\) \(\chi_{799}(73,\cdot)\) \(\chi_{799}(78,\cdot)\) \(\chi_{799}(80,\cdot)\) \(\chi_{799}(82,\cdot)\) \(\chi_{799}(88,\cdot)\) \(\chi_{799}(90,\cdot)\) \(\chi_{799}(91,\cdot)\) \(\chi_{799}(92,\cdot)\) \(\chi_{799}(99,\cdot)\) \(\chi_{799}(105,\cdot)\) \(\chi_{799}(107,\cdot)\) \(\chi_{799}(109,\cdot)\) \(\chi_{799}(113,\cdot)\) \(\chi_{799}(114,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{368})$ |
Fixed field: | Number field defined by a degree 368 polynomial (not computed) |
Values on generators
\((377,52)\) → \((e\left(\frac{13}{16}\right),e\left(\frac{35}{46}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 799 }(29, a) \) | \(1\) | \(1\) | \(e\left(\frac{13}{184}\right)\) | \(e\left(\frac{11}{368}\right)\) | \(e\left(\frac{13}{92}\right)\) | \(e\left(\frac{303}{368}\right)\) | \(e\left(\frac{37}{368}\right)\) | \(e\left(\frac{105}{368}\right)\) | \(e\left(\frac{39}{184}\right)\) | \(e\left(\frac{11}{184}\right)\) | \(e\left(\frac{329}{368}\right)\) | \(e\left(\frac{5}{368}\right)\) |