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 \(\chi_{4017}(1577,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8034.do
\(\chi_{8034}(17,\cdot)\) \(\chi_{8034}(335,\cdot)\) \(\chi_{8034}(407,\cdot)\) \(\chi_{8034}(647,\cdot)\) \(\chi_{8034}(1193,\cdot)\) \(\chi_{8034}(1343,\cdot)\) \(\chi_{8034}(1421,\cdot)\) \(\chi_{8034}(1577,\cdot)\) \(\chi_{8034}(1655,\cdot)\) \(\chi_{8034}(1895,\cdot)\) \(\chi_{8034}(1973,\cdot)\) \(\chi_{8034}(2123,\cdot)\) \(\chi_{8034}(2201,\cdot)\) \(\chi_{8034}(2285,\cdot)\) \(\chi_{8034}(2357,\cdot)\) \(\chi_{8034}(2363,\cdot)\) \(\chi_{8034}(2909,\cdot)\) \(\chi_{8034}(3221,\cdot)\) \(\chi_{8034}(3449,\cdot)\) \(\chi_{8034}(3767,\cdot)\) \(\chi_{8034}(4703,\cdot)\) \(\chi_{8034}(4859,\cdot)\) \(\chi_{8034}(5165,\cdot)\) \(\chi_{8034}(5405,\cdot)\) \(\chi_{8034}(5873,\cdot)\) \(\chi_{8034}(6029,\cdot)\) \(\chi_{8034}(6263,\cdot)\) \(\chi_{8034}(6335,\cdot)\) \(\chi_{8034}(6959,\cdot)\) \(\chi_{8034}(7037,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{51})$ |
Fixed field: | Number field defined by a degree 102 polynomial (not computed) |
Values on generators
\((5357,1237,5773)\) → \((-1,e\left(\frac{1}{6}\right),e\left(\frac{8}{51}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
\( \chi_{ 8034 }(1577, a) \) | \(-1\) | \(1\) | \(e\left(\frac{8}{51}\right)\) | \(e\left(\frac{47}{102}\right)\) | \(e\left(\frac{4}{17}\right)\) | \(e\left(\frac{83}{102}\right)\) | \(e\left(\frac{13}{34}\right)\) | \(e\left(\frac{95}{102}\right)\) | \(e\left(\frac{16}{51}\right)\) | \(e\left(\frac{67}{102}\right)\) | \(e\left(\frac{15}{34}\right)\) | \(e\left(\frac{21}{34}\right)\) |