Basic properties
Modulus: | \(8001\) | |
Conductor: | \(8001\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(126\) | 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
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Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
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Galois orbit 8001.ns
\(\chi_{8001}(416,\cdot)\) \(\chi_{8001}(920,\cdot)\) \(\chi_{8001}(1046,\cdot)\) \(\chi_{8001}(1550,\cdot)\) \(\chi_{8001}(2462,\cdot)\) \(\chi_{8001}(2621,\cdot)\) \(\chi_{8001}(2873,\cdot)\) \(\chi_{8001}(2936,\cdot)\) \(\chi_{8001}(3092,\cdot)\) \(\chi_{8001}(3188,\cdot)\) \(\chi_{8001}(3344,\cdot)\) \(\chi_{8001}(3470,\cdot)\) \(\chi_{8001}(3881,\cdot)\) \(\chi_{8001}(4007,\cdot)\) \(\chi_{8001}(4100,\cdot)\) \(\chi_{8001}(4289,\cdot)\) \(\chi_{8001}(4352,\cdot)\) \(\chi_{8001}(5015,\cdot)\) \(\chi_{8001}(5204,\cdot)\) \(\chi_{8001}(5267,\cdot)\) \(\chi_{8001}(5549,\cdot)\) \(\chi_{8001}(5582,\cdot)\) \(\chi_{8001}(5708,\cdot)\) \(\chi_{8001}(5990,\cdot)\) \(\chi_{8001}(6053,\cdot)\) \(\chi_{8001}(6305,\cdot)\) \(\chi_{8001}(6338,\cdot)\) \(\chi_{8001}(6368,\cdot)\) \(\chi_{8001}(6494,\cdot)\) \(\chi_{8001}(6590,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{63})$ |
Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((3557,1144,7750)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{1}{6}\right),e\left(\frac{38}{63}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 8001 }(416, a) \) | \(1\) | \(1\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{107}{126}\right)\) | \(e\left(\frac{67}{126}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{37}{63}\right)\) | \(-1\) |