Basic properties
Modulus: | \(8041\) | |
Conductor: | \(8041\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(210\) | 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 8041.ez
\(\chi_{8041}(288,\cdot)\) \(\chi_{8041}(458,\cdot)\) \(\chi_{8041}(492,\cdot)\) \(\chi_{8041}(679,\cdot)\) \(\chi_{8041}(1019,\cdot)\) \(\chi_{8041}(1223,\cdot)\) \(\chi_{8041}(1359,\cdot)\) \(\chi_{8041}(1410,\cdot)\) \(\chi_{8041}(1920,\cdot)\) \(\chi_{8041}(1954,\cdot)\) \(\chi_{8041}(2141,\cdot)\) \(\chi_{8041}(2481,\cdot)\) \(\chi_{8041}(2549,\cdot)\) \(\chi_{8041}(3280,\cdot)\) \(\chi_{8041}(3297,\cdot)\) \(\chi_{8041}(3416,\cdot)\) \(\chi_{8041}(3603,\cdot)\) \(\chi_{8041}(4011,\cdot)\) \(\chi_{8041}(4028,\cdot)\) \(\chi_{8041}(4045,\cdot)\) \(\chi_{8041}(4232,\cdot)\) \(\chi_{8041}(4419,\cdot)\) \(\chi_{8041}(4606,\cdot)\) \(\chi_{8041}(4759,\cdot)\) \(\chi_{8041}(4776,\cdot)\) \(\chi_{8041}(4793,\cdot)\) \(\chi_{8041}(4963,\cdot)\) \(\chi_{8041}(5150,\cdot)\) \(\chi_{8041}(5337,\cdot)\) \(\chi_{8041}(5473,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{105})$ |
Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((6580,2366,562)\) → \((e\left(\frac{3}{10}\right),-1,e\left(\frac{41}{42}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 8041 }(3297, a) \) | \(1\) | \(1\) | \(e\left(\frac{23}{35}\right)\) | \(e\left(\frac{92}{105}\right)\) | \(e\left(\frac{11}{35}\right)\) | \(e\left(\frac{11}{105}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{34}{35}\right)\) | \(e\left(\frac{79}{105}\right)\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{4}{21}\right)\) |