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 \(\chi_{4017}(1247,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8034.dd
\(\chi_{8034}(77,\cdot)\) \(\chi_{8034}(623,\cdot)\) \(\chi_{8034}(1013,\cdot)\) \(\chi_{8034}(1247,\cdot)\) \(\chi_{8034}(1715,\cdot)\) \(\chi_{8034}(2027,\cdot)\) \(\chi_{8034}(2105,\cdot)\) \(\chi_{8034}(2183,\cdot)\) \(\chi_{8034}(2417,\cdot)\) \(\chi_{8034}(2573,\cdot)\) \(\chi_{8034}(2729,\cdot)\) \(\chi_{8034}(3041,\cdot)\) \(\chi_{8034}(3587,\cdot)\) \(\chi_{8034}(3743,\cdot)\) \(\chi_{8034}(3899,\cdot)\) \(\chi_{8034}(4679,\cdot)\) \(\chi_{8034}(5225,\cdot)\) \(\chi_{8034}(5537,\cdot)\) \(\chi_{8034}(5615,\cdot)\) \(\chi_{8034}(6083,\cdot)\) \(\chi_{8034}(6161,\cdot)\) \(\chi_{8034}(6473,\cdot)\) \(\chi_{8034}(6551,\cdot)\) \(\chi_{8034}(6707,\cdot)\) \(\chi_{8034}(6863,\cdot)\) \(\chi_{8034}(6941,\cdot)\) \(\chi_{8034}(7253,\cdot)\) \(\chi_{8034}(7409,\cdot)\) \(\chi_{8034}(7487,\cdot)\) \(\chi_{8034}(7643,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{51})$ |
Fixed field: | Number field defined by a degree 102 polynomial (not computed) |
Values on generators
\((5357,1237,5773)\) → \((-1,-1,e\left(\frac{61}{102}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
\( \chi_{ 8034 }(1247, a) \) | \(1\) | \(1\) | \(e\left(\frac{61}{102}\right)\) | \(e\left(\frac{91}{102}\right)\) | \(e\left(\frac{49}{102}\right)\) | \(e\left(\frac{37}{102}\right)\) | \(e\left(\frac{35}{102}\right)\) | \(e\left(\frac{29}{34}\right)\) | \(e\left(\frac{10}{51}\right)\) | \(e\left(\frac{95}{102}\right)\) | \(e\left(\frac{10}{17}\right)\) | \(e\left(\frac{25}{51}\right)\) |