Basic properties
Modulus: | \(8034\) | |
Conductor: | \(4017\) | 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 \(\chi_{4017}(230,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8034.da
\(\chi_{8034}(113,\cdot)\) \(\chi_{8034}(731,\cdot)\) \(\chi_{8034}(815,\cdot)\) \(\chi_{8034}(893,\cdot)\) \(\chi_{8034}(1361,\cdot)\) \(\chi_{8034}(1433,\cdot)\) \(\chi_{8034}(1511,\cdot)\) \(\chi_{8034}(1979,\cdot)\) \(\chi_{8034}(2063,\cdot)\) \(\chi_{8034}(2297,\cdot)\) \(\chi_{8034}(2681,\cdot)\) \(\chi_{8034}(2915,\cdot)\) \(\chi_{8034}(2921,\cdot)\) \(\chi_{8034}(3077,\cdot)\) \(\chi_{8034}(3539,\cdot)\) \(\chi_{8034}(3695,\cdot)\) \(\chi_{8034}(4247,\cdot)\) \(\chi_{8034}(4559,\cdot)\) \(\chi_{8034}(4715,\cdot)\) \(\chi_{8034}(4865,\cdot)\) \(\chi_{8034}(5177,\cdot)\) \(\chi_{8034}(5333,\cdot)\) \(\chi_{8034}(5651,\cdot)\) \(\chi_{8034}(5807,\cdot)\) \(\chi_{8034}(6119,\cdot)\) \(\chi_{8034}(6269,\cdot)\) \(\chi_{8034}(6275,\cdot)\) \(\chi_{8034}(6425,\cdot)\) \(\chi_{8034}(6665,\cdot)\) \(\chi_{8034}(6737,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{51})$ |
Fixed field: | Number field defined by a degree 102 polynomial (not computed) |
Values on generators
\((5357,1237,5773)\) → \((-1,e\left(\frac{2}{3}\right),e\left(\frac{23}{34}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
\( \chi_{ 8034 }(4247, a) \) | \(1\) | \(1\) | \(e\left(\frac{3}{17}\right)\) | \(e\left(\frac{2}{51}\right)\) | \(e\left(\frac{22}{51}\right)\) | \(e\left(\frac{19}{102}\right)\) | \(e\left(\frac{23}{51}\right)\) | \(e\left(\frac{41}{102}\right)\) | \(e\left(\frac{6}{17}\right)\) | \(e\left(\frac{35}{102}\right)\) | \(e\left(\frac{19}{34}\right)\) | \(e\left(\frac{11}{51}\right)\) |