Basic properties
Modulus: | \(8041\) | |
Conductor: | \(473\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(35\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{473}(256,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8041.cr
\(\chi_{8041}(256,\cdot)\) \(\chi_{8041}(477,\cdot)\) \(\chi_{8041}(1208,\cdot)\) \(\chi_{8041}(1225,\cdot)\) \(\chi_{8041}(1939,\cdot)\) \(\chi_{8041}(1956,\cdot)\) \(\chi_{8041}(2381,\cdot)\) \(\chi_{8041}(2687,\cdot)\) \(\chi_{8041}(3690,\cdot)\) \(\chi_{8041}(3843,\cdot)\) \(\chi_{8041}(4574,\cdot)\) \(\chi_{8041}(4999,\cdot)\) \(\chi_{8041}(5152,\cdot)\) \(\chi_{8041}(5305,\cdot)\) \(\chi_{8041}(5373,\cdot)\) \(\chi_{8041}(5883,\cdot)\) \(\chi_{8041}(6461,\cdot)\) \(\chi_{8041}(6614,\cdot)\) \(\chi_{8041}(6835,\cdot)\) \(\chi_{8041}(7056,\cdot)\) \(\chi_{8041}(7192,\cdot)\) \(\chi_{8041}(7566,\cdot)\) \(\chi_{8041}(7804,\cdot)\) \(\chi_{8041}(7923,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{35})$ |
Fixed field: | Number field defined by a degree 35 polynomial |
Values on generators
\((6580,2366,562)\) → \((e\left(\frac{4}{5}\right),1,e\left(\frac{1}{7}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 8041 }(256, a) \) | \(1\) | \(1\) | \(e\left(\frac{23}{35}\right)\) | \(e\left(\frac{19}{35}\right)\) | \(e\left(\frac{11}{35}\right)\) | \(e\left(\frac{27}{35}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{34}{35}\right)\) | \(e\left(\frac{3}{35}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{6}{7}\right)\) |