Basic properties
Modulus: | \(8041\) | |
Conductor: | \(473\) | 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 \(\chi_{473}(184,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8041.fb
\(\chi_{8041}(18,\cdot)\) \(\chi_{8041}(205,\cdot)\) \(\chi_{8041}(392,\cdot)\) \(\chi_{8041}(545,\cdot)\) \(\chi_{8041}(579,\cdot)\) \(\chi_{8041}(800,\cdot)\) \(\chi_{8041}(1293,\cdot)\) \(\chi_{8041}(1361,\cdot)\) \(\chi_{8041}(1480,\cdot)\) \(\chi_{8041}(1531,\cdot)\) \(\chi_{8041}(1667,\cdot)\) \(\chi_{8041}(1854,\cdot)\) \(\chi_{8041}(1922,\cdot)\) \(\chi_{8041}(2041,\cdot)\) \(\chi_{8041}(2092,\cdot)\) \(\chi_{8041}(2262,\cdot)\) \(\chi_{8041}(2653,\cdot)\) \(\chi_{8041}(2823,\cdot)\) \(\chi_{8041}(2857,\cdot)\) \(\chi_{8041}(3044,\cdot)\) \(\chi_{8041}(3384,\cdot)\) \(\chi_{8041}(3588,\cdot)\) \(\chi_{8041}(3724,\cdot)\) \(\chi_{8041}(3775,\cdot)\) \(\chi_{8041}(4285,\cdot)\) \(\chi_{8041}(4319,\cdot)\) \(\chi_{8041}(4506,\cdot)\) \(\chi_{8041}(4846,\cdot)\) \(\chi_{8041}(4914,\cdot)\) \(\chi_{8041}(5645,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{105})$ |
Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((6580,2366,562)\) → \((e\left(\frac{3}{10}\right),1,e\left(\frac{13}{42}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 8041 }(4914, a) \) | \(1\) | \(1\) | \(e\left(\frac{23}{35}\right)\) | \(e\left(\frac{149}{210}\right)\) | \(e\left(\frac{11}{35}\right)\) | \(e\left(\frac{197}{210}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{34}{35}\right)\) | \(e\left(\frac{44}{105}\right)\) | \(e\left(\frac{25}{42}\right)\) | \(e\left(\frac{1}{42}\right)\) |