Basic properties
Modulus: | \(8041\) | |
Conductor: | \(473\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(70\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{473}(426,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8041.dt
\(\chi_{8041}(409,\cdot)\) \(\chi_{8041}(426,\cdot)\) \(\chi_{8041}(1140,\cdot)\) \(\chi_{8041}(1157,\cdot)\) \(\chi_{8041}(1888,\cdot)\) \(\chi_{8041}(2109,\cdot)\) \(\chi_{8041}(2483,\cdot)\) \(\chi_{8041}(2602,\cdot)\) \(\chi_{8041}(2840,\cdot)\) \(\chi_{8041}(3214,\cdot)\) \(\chi_{8041}(3350,\cdot)\) \(\chi_{8041}(3571,\cdot)\) \(\chi_{8041}(3792,\cdot)\) \(\chi_{8041}(3945,\cdot)\) \(\chi_{8041}(4523,\cdot)\) \(\chi_{8041}(5033,\cdot)\) \(\chi_{8041}(5101,\cdot)\) \(\chi_{8041}(5254,\cdot)\) \(\chi_{8041}(5407,\cdot)\) \(\chi_{8041}(5832,\cdot)\) \(\chi_{8041}(6563,\cdot)\) \(\chi_{8041}(6716,\cdot)\) \(\chi_{8041}(7719,\cdot)\) \(\chi_{8041}(8025,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{35})$ |
Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((6580,2366,562)\) → \((e\left(\frac{3}{10}\right),1,e\left(\frac{11}{14}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 8041 }(426, a) \) | \(1\) | \(1\) | \(e\left(\frac{18}{35}\right)\) | \(e\left(\frac{13}{70}\right)\) | \(e\left(\frac{1}{35}\right)\) | \(e\left(\frac{59}{70}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{19}{35}\right)\) | \(e\left(\frac{13}{35}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{3}{14}\right)\) |