Basic properties
Modulus: | \(8034\) | |
Conductor: | \(1339\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(102\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{1339}(641,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8034.dx
\(\chi_{8034}(751,\cdot)\) \(\chi_{8034}(1141,\cdot)\) \(\chi_{8034}(1297,\cdot)\) \(\chi_{8034}(1369,\cdot)\) \(\chi_{8034}(1609,\cdot)\) \(\chi_{8034}(1759,\cdot)\) \(\chi_{8034}(1765,\cdot)\) \(\chi_{8034}(1915,\cdot)\) \(\chi_{8034}(2227,\cdot)\) \(\chi_{8034}(2383,\cdot)\) \(\chi_{8034}(2701,\cdot)\) \(\chi_{8034}(2857,\cdot)\) \(\chi_{8034}(3169,\cdot)\) \(\chi_{8034}(3319,\cdot)\) \(\chi_{8034}(3475,\cdot)\) \(\chi_{8034}(3787,\cdot)\) \(\chi_{8034}(4339,\cdot)\) \(\chi_{8034}(4495,\cdot)\) \(\chi_{8034}(4957,\cdot)\) \(\chi_{8034}(5113,\cdot)\) \(\chi_{8034}(5119,\cdot)\) \(\chi_{8034}(5353,\cdot)\) \(\chi_{8034}(5737,\cdot)\) \(\chi_{8034}(5971,\cdot)\) \(\chi_{8034}(6055,\cdot)\) \(\chi_{8034}(6523,\cdot)\) \(\chi_{8034}(6601,\cdot)\) \(\chi_{8034}(6673,\cdot)\) \(\chi_{8034}(7141,\cdot)\) \(\chi_{8034}(7219,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{51})$ |
Fixed field: | Number field defined by a degree 102 polynomial (not computed) |
Values on generators
\((5357,1237,5773)\) → \((1,e\left(\frac{1}{6}\right),e\left(\frac{4}{17}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
\( \chi_{ 8034 }(3319, a) \) | \(1\) | \(1\) | \(e\left(\frac{25}{34}\right)\) | \(e\left(\frac{79}{102}\right)\) | \(e\left(\frac{53}{102}\right)\) | \(e\left(\frac{41}{51}\right)\) | \(e\left(\frac{67}{102}\right)\) | \(e\left(\frac{16}{51}\right)\) | \(e\left(\frac{8}{17}\right)\) | \(e\left(\frac{46}{51}\right)\) | \(e\left(\frac{31}{34}\right)\) | \(e\left(\frac{26}{51}\right)\) |