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 \(\chi_{1339}(761,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8034.ed
\(\chi_{8034}(397,\cdot)\) \(\chi_{8034}(535,\cdot)\) \(\chi_{8034}(661,\cdot)\) \(\chi_{8034}(769,\cdot)\) \(\chi_{8034}(877,\cdot)\) \(\chi_{8034}(925,\cdot)\) \(\chi_{8034}(1207,\cdot)\) \(\chi_{8034}(1393,\cdot)\) \(\chi_{8034}(1519,\cdot)\) \(\chi_{8034}(1939,\cdot)\) \(\chi_{8034}(1969,\cdot)\) \(\chi_{8034}(2095,\cdot)\) \(\chi_{8034}(2113,\cdot)\) \(\chi_{8034}(2125,\cdot)\) \(\chi_{8034}(2203,\cdot)\) \(\chi_{8034}(2671,\cdot)\) \(\chi_{8034}(2749,\cdot)\) \(\chi_{8034}(2905,\cdot)\) \(\chi_{8034}(2983,\cdot)\) \(\chi_{8034}(3031,\cdot)\) \(\chi_{8034}(3205,\cdot)\) \(\chi_{8034}(3361,\cdot)\) \(\chi_{8034}(3439,\cdot)\) \(\chi_{8034}(3577,\cdot)\) \(\chi_{8034}(3625,\cdot)\) \(\chi_{8034}(3859,\cdot)\) \(\chi_{8034}(3889,\cdot)\) \(\chi_{8034}(3907,\cdot)\) \(\chi_{8034}(3919,\cdot)\) \(\chi_{8034}(3985,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{204})$ |
Fixed field: | Number field defined by a degree 204 polynomial (not computed) |
Values on generators
\((5357,1237,5773)\) → \((1,e\left(\frac{11}{12}\right),e\left(\frac{31}{102}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
\( \chi_{ 8034 }(3439, a) \) | \(1\) | \(1\) | \(e\left(\frac{113}{204}\right)\) | \(e\left(\frac{61}{204}\right)\) | \(e\left(\frac{65}{68}\right)\) | \(e\left(\frac{11}{102}\right)\) | \(e\left(\frac{61}{68}\right)\) | \(e\left(\frac{47}{102}\right)\) | \(e\left(\frac{11}{102}\right)\) | \(e\left(\frac{41}{51}\right)\) | \(e\left(\frac{39}{68}\right)\) | \(e\left(\frac{29}{34}\right)\) |