Basic properties
Modulus: | \(8034\) | |
Conductor: | \(1339\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(204\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{1339}(463,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8034.eg
\(\chi_{8034}(109,\cdot)\) \(\chi_{8034}(151,\cdot)\) \(\chi_{8034}(187,\cdot)\) \(\chi_{8034}(307,\cdot)\) \(\chi_{8034}(463,\cdot)\) \(\chi_{8034}(499,\cdot)\) \(\chi_{8034}(577,\cdot)\) \(\chi_{8034}(733,\cdot)\) \(\chi_{8034}(775,\cdot)\) \(\chi_{8034}(889,\cdot)\) \(\chi_{8034}(967,\cdot)\) \(\chi_{8034}(1279,\cdot)\) \(\chi_{8034}(1321,\cdot)\) \(\chi_{8034}(1435,\cdot)\) \(\chi_{8034}(1477,\cdot)\) \(\chi_{8034}(1513,\cdot)\) \(\chi_{8034}(1633,\cdot)\) \(\chi_{8034}(1669,\cdot)\) \(\chi_{8034}(1747,\cdot)\) \(\chi_{8034}(1825,\cdot)\) \(\chi_{8034}(2137,\cdot)\) \(\chi_{8034}(2413,\cdot)\) \(\chi_{8034}(2683,\cdot)\) \(\chi_{8034}(2959,\cdot)\) \(\chi_{8034}(3073,\cdot)\) \(\chi_{8034}(3271,\cdot)\) \(\chi_{8034}(3307,\cdot)\) \(\chi_{8034}(3349,\cdot)\) \(\chi_{8034}(3775,\cdot)\) \(\chi_{8034}(3817,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{204})$ |
Fixed field: | Number field defined by a degree 204 polynomial (not computed) |
Values on generators
\((5357,1237,5773)\) → \((1,i,e\left(\frac{7}{102}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
\( \chi_{ 8034 }(463, a) \) | \(1\) | \(1\) | \(e\left(\frac{65}{204}\right)\) | \(e\left(\frac{5}{204}\right)\) | \(e\left(\frac{191}{204}\right)\) | \(e\left(\frac{31}{102}\right)\) | \(e\left(\frac{151}{204}\right)\) | \(e\left(\frac{5}{34}\right)\) | \(e\left(\frac{65}{102}\right)\) | \(e\left(\frac{46}{51}\right)\) | \(e\left(\frac{11}{68}\right)\) | \(e\left(\frac{35}{102}\right)\) |