Basic properties
Modulus: | \(8001\) | |
Conductor: | \(381\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(126\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{381}(134,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8001.nz
\(\chi_{8001}(134,\cdot)\) \(\chi_{8001}(260,\cdot)\) \(\chi_{8001}(575,\cdot)\) \(\chi_{8001}(638,\cdot)\) \(\chi_{8001}(827,\cdot)\) \(\chi_{8001}(1709,\cdot)\) \(\chi_{8001}(1835,\cdot)\) \(\chi_{8001}(1961,\cdot)\) \(\chi_{8001}(2087,\cdot)\) \(\chi_{8001}(2150,\cdot)\) \(\chi_{8001}(2339,\cdot)\) \(\chi_{8001}(2402,\cdot)\) \(\chi_{8001}(2654,\cdot)\) \(\chi_{8001}(2906,\cdot)\) \(\chi_{8001}(2969,\cdot)\) \(\chi_{8001}(3158,\cdot)\) \(\chi_{8001}(3221,\cdot)\) \(\chi_{8001}(3284,\cdot)\) \(\chi_{8001}(3347,\cdot)\) \(\chi_{8001}(3599,\cdot)\) \(\chi_{8001}(3662,\cdot)\) \(\chi_{8001}(4103,\cdot)\) \(\chi_{8001}(4292,\cdot)\) \(\chi_{8001}(4796,\cdot)\) \(\chi_{8001}(4922,\cdot)\) \(\chi_{8001}(5300,\cdot)\) \(\chi_{8001}(5363,\cdot)\) \(\chi_{8001}(5426,\cdot)\) \(\chi_{8001}(5552,\cdot)\) \(\chi_{8001}(6119,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{63})$ |
Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((3557,1144,7750)\) → \((-1,1,e\left(\frac{115}{126}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 8001 }(134, a) \) | \(1\) | \(1\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{19}{21}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{5}{42}\right)\) | \(e\left(\frac{71}{126}\right)\) | \(e\left(\frac{50}{63}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{23}{126}\right)\) | \(e\left(\frac{2}{3}\right)\) |