Basic properties
Modulus: | \(8624\) | |
Conductor: | \(4312\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(210\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{4312}(2229,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8624.gn
\(\chi_{8624}(73,\cdot)\) \(\chi_{8624}(409,\cdot)\) \(\chi_{8624}(425,\cdot)\) \(\chi_{8624}(633,\cdot)\) \(\chi_{8624}(745,\cdot)\) \(\chi_{8624}(761,\cdot)\) \(\chi_{8624}(985,\cdot)\) \(\chi_{8624}(1641,\cdot)\) \(\chi_{8624}(1657,\cdot)\) \(\chi_{8624}(1865,\cdot)\) \(\chi_{8624}(1977,\cdot)\) \(\chi_{8624}(1993,\cdot)\) \(\chi_{8624}(2217,\cdot)\) \(\chi_{8624}(2329,\cdot)\) \(\chi_{8624}(2537,\cdot)\) \(\chi_{8624}(2889,\cdot)\) \(\chi_{8624}(3097,\cdot)\) \(\chi_{8624}(3209,\cdot)\) \(\chi_{8624}(3225,\cdot)\) \(\chi_{8624}(3561,\cdot)\) \(\chi_{8624}(3769,\cdot)\) \(\chi_{8624}(4105,\cdot)\) \(\chi_{8624}(4121,\cdot)\) \(\chi_{8624}(4329,\cdot)\) \(\chi_{8624}(4457,\cdot)\) \(\chi_{8624}(4681,\cdot)\) \(\chi_{8624}(4793,\cdot)\) \(\chi_{8624}(5001,\cdot)\) \(\chi_{8624}(5337,\cdot)\) \(\chi_{8624}(5353,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{105})$ |
Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((5391,6469,7745,3137)\) → \((1,-1,e\left(\frac{37}{42}\right),e\left(\frac{7}{10}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
\( \chi_{ 8624 }(73, a) \) | \(1\) | \(1\) | \(e\left(\frac{103}{105}\right)\) | \(e\left(\frac{89}{105}\right)\) | \(e\left(\frac{101}{105}\right)\) | \(e\left(\frac{19}{70}\right)\) | \(e\left(\frac{29}{35}\right)\) | \(e\left(\frac{34}{105}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{73}{105}\right)\) | \(e\left(\frac{33}{35}\right)\) |