Basic properties
Modulus: | \(6001\) | |
Conductor: | \(6001\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(352\) | 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 6001.eo
\(\chi_{6001}(48,\cdot)\) \(\chi_{6001}(57,\cdot)\) \(\chi_{6001}(63,\cdot)\) \(\chi_{6001}(80,\cdot)\) \(\chi_{6001}(95,\cdot)\) \(\chi_{6001}(105,\cdot)\) \(\chi_{6001}(175,\cdot)\) \(\chi_{6001}(211,\cdot)\) \(\chi_{6001}(316,\cdot)\) \(\chi_{6001}(432,\cdot)\) \(\chi_{6001}(479,\cdot)\) \(\chi_{6001}(482,\cdot)\) \(\chi_{6001}(513,\cdot)\) \(\chi_{6001}(567,\cdot)\) \(\chi_{6001}(652,\cdot)\) \(\chi_{6001}(653,\cdot)\) \(\chi_{6001}(720,\cdot)\) \(\chi_{6001}(823,\cdot)\) \(\chi_{6001}(855,\cdot)\) \(\chi_{6001}(889,\cdot)\) \(\chi_{6001}(942,\cdot)\) \(\chi_{6001}(945,\cdot)\) \(\chi_{6001}(1112,\cdot)\) \(\chi_{6001}(1128,\cdot)\) \(\chi_{6001}(1133,\cdot)\) \(\chi_{6001}(1149,\cdot)\) \(\chi_{6001}(1184,\cdot)\) \(\chi_{6001}(1200,\cdot)\) \(\chi_{6001}(1204,\cdot)\) \(\chi_{6001}(1229,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{352})$ |
Fixed field: | Number field defined by a degree 352 polynomial (not computed) |
Values on generators
\((2825,3180)\) → \((e\left(\frac{3}{16}\right),e\left(\frac{123}{352}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 6001 }(1149, a) \) | \(1\) | \(1\) | \(e\left(\frac{41}{44}\right)\) | \(e\left(\frac{189}{352}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{321}{352}\right)\) | \(e\left(\frac{15}{32}\right)\) | \(e\left(\frac{21}{32}\right)\) | \(e\left(\frac{35}{44}\right)\) | \(e\left(\frac{13}{176}\right)\) | \(e\left(\frac{27}{32}\right)\) | \(e\left(\frac{49}{176}\right)\) |