Basic properties
Modulus: | \(8023\) | |
Conductor: | \(71\) | 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 \(\chi_{71}(43,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8023.co
\(\chi_{8023}(114,\cdot)\) \(\chi_{8023}(453,\cdot)\) \(\chi_{8023}(679,\cdot)\) \(\chi_{8023}(1018,\cdot)\) \(\chi_{8023}(1357,\cdot)\) \(\chi_{8023}(1470,\cdot)\) \(\chi_{8023}(2148,\cdot)\) \(\chi_{8023}(2261,\cdot)\) \(\chi_{8023}(2487,\cdot)\) \(\chi_{8023}(2713,\cdot)\) \(\chi_{8023}(3278,\cdot)\) \(\chi_{8023}(3730,\cdot)\) \(\chi_{8023}(3843,\cdot)\) \(\chi_{8023}(4182,\cdot)\) \(\chi_{8023}(4408,\cdot)\) \(\chi_{8023}(4634,\cdot)\) \(\chi_{8023}(4973,\cdot)\) \(\chi_{8023}(5199,\cdot)\) \(\chi_{8023}(5312,\cdot)\) \(\chi_{8023}(5425,\cdot)\) \(\chi_{8023}(6329,\cdot)\) \(\chi_{8023}(6781,\cdot)\) \(\chi_{8023}(7007,\cdot)\) \(\chi_{8023}(7459,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{35})$ |
Fixed field: | Number field defined by a degree 35 polynomial |
Values on generators
\((6894,3054)\) → \((e\left(\frac{24}{35}\right),1)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 8023 }(114, a) \) | \(1\) | \(1\) | \(e\left(\frac{4}{35}\right)\) | \(e\left(\frac{29}{35}\right)\) | \(e\left(\frac{8}{35}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{33}{35}\right)\) | \(e\left(\frac{24}{35}\right)\) | \(e\left(\frac{12}{35}\right)\) | \(e\left(\frac{23}{35}\right)\) | \(e\left(\frac{11}{35}\right)\) | \(e\left(\frac{9}{35}\right)\) |