Basic properties
Modulus: | \(8034\) | |
Conductor: | \(4017\) | 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 \(\chi_{4017}(11,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8034.eb
\(\chi_{8034}(11,\cdot)\) \(\chi_{8034}(293,\cdot)\) \(\chi_{8034}(371,\cdot)\) \(\chi_{8034}(383,\cdot)\) \(\chi_{8034}(479,\cdot)\) \(\chi_{8034}(695,\cdot)\) \(\chi_{8034}(791,\cdot)\) \(\chi_{8034}(869,\cdot)\) \(\chi_{8034}(1073,\cdot)\) \(\chi_{8034}(1289,\cdot)\) \(\chi_{8034}(1493,\cdot)\) \(\chi_{8034}(1619,\cdot)\) \(\chi_{8034}(1931,\cdot)\) \(\chi_{8034}(2381,\cdot)\) \(\chi_{8034}(2537,\cdot)\) \(\chi_{8034}(2615,\cdot)\) \(\chi_{8034}(2663,\cdot)\) \(\chi_{8034}(2801,\cdot)\) \(\chi_{8034}(3035,\cdot)\) \(\chi_{8034}(3083,\cdot)\) \(\chi_{8034}(3161,\cdot)\) \(\chi_{8034}(3191,\cdot)\) \(\chi_{8034}(3317,\cdot)\) \(\chi_{8034}(3395,\cdot)\) \(\chi_{8034}(3659,\cdot)\) \(\chi_{8034}(4037,\cdot)\) \(\chi_{8034}(4205,\cdot)\) \(\chi_{8034}(4271,\cdot)\) \(\chi_{8034}(4331,\cdot)\) \(\chi_{8034}(4361,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{204})$ |
Fixed field: | Number field defined by a degree 204 polynomial (not computed) |
Values on generators
\((5357,1237,5773)\) → \((-1,e\left(\frac{7}{12}\right),e\left(\frac{61}{102}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
\( \chi_{ 8034 }(11, a) \) | \(-1\) | \(1\) | \(e\left(\frac{71}{204}\right)\) | \(e\left(\frac{55}{68}\right)\) | \(e\left(\frac{13}{204}\right)\) | \(e\left(\frac{9}{17}\right)\) | \(e\left(\frac{155}{204}\right)\) | \(e\left(\frac{35}{51}\right)\) | \(e\left(\frac{71}{102}\right)\) | \(e\left(\frac{9}{34}\right)\) | \(e\left(\frac{23}{68}\right)\) | \(e\left(\frac{8}{51}\right)\) |