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 \(\chi_{4017}(452,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8034.dm
\(\chi_{8034}(257,\cdot)\) \(\chi_{8034}(329,\cdot)\) \(\chi_{8034}(563,\cdot)\) \(\chi_{8034}(719,\cdot)\) \(\chi_{8034}(1187,\cdot)\) \(\chi_{8034}(1427,\cdot)\) \(\chi_{8034}(1733,\cdot)\) \(\chi_{8034}(1889,\cdot)\) \(\chi_{8034}(2825,\cdot)\) \(\chi_{8034}(3143,\cdot)\) \(\chi_{8034}(3371,\cdot)\) \(\chi_{8034}(3683,\cdot)\) \(\chi_{8034}(4229,\cdot)\) \(\chi_{8034}(4235,\cdot)\) \(\chi_{8034}(4307,\cdot)\) \(\chi_{8034}(4391,\cdot)\) \(\chi_{8034}(4469,\cdot)\) \(\chi_{8034}(4619,\cdot)\) \(\chi_{8034}(4697,\cdot)\) \(\chi_{8034}(4937,\cdot)\) \(\chi_{8034}(5015,\cdot)\) \(\chi_{8034}(5171,\cdot)\) \(\chi_{8034}(5249,\cdot)\) \(\chi_{8034}(5399,\cdot)\) \(\chi_{8034}(5945,\cdot)\) \(\chi_{8034}(6185,\cdot)\) \(\chi_{8034}(6257,\cdot)\) \(\chi_{8034}(6575,\cdot)\) \(\chi_{8034}(6809,\cdot)\) \(\chi_{8034}(7277,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{51})$ |
Fixed field: | Number field defined by a degree 102 polynomial (not computed) |
Values on generators
\((5357,1237,5773)\) → \((-1,e\left(\frac{5}{6}\right),e\left(\frac{31}{102}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
\( \chi_{ 8034 }(4469, a) \) | \(1\) | \(1\) | \(e\left(\frac{31}{102}\right)\) | \(e\left(\frac{13}{34}\right)\) | \(e\left(\frac{89}{102}\right)\) | \(e\left(\frac{15}{34}\right)\) | \(e\left(\frac{49}{102}\right)\) | \(e\left(\frac{13}{102}\right)\) | \(e\left(\frac{31}{51}\right)\) | \(e\left(\frac{33}{34}\right)\) | \(e\left(\frac{14}{17}\right)\) | \(e\left(\frac{35}{51}\right)\) |