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 \(\chi_{4017}(3071,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
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Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8034.ds
\(\chi_{8034}(191,\cdot)\) \(\chi_{8034}(497,\cdot)\) \(\chi_{8034}(653,\cdot)\) \(\chi_{8034}(1589,\cdot)\) \(\chi_{8034}(1907,\cdot)\) \(\chi_{8034}(2135,\cdot)\) \(\chi_{8034}(2447,\cdot)\) \(\chi_{8034}(2993,\cdot)\) \(\chi_{8034}(2999,\cdot)\) \(\chi_{8034}(3071,\cdot)\) \(\chi_{8034}(3155,\cdot)\) \(\chi_{8034}(3233,\cdot)\) \(\chi_{8034}(3383,\cdot)\) \(\chi_{8034}(3461,\cdot)\) \(\chi_{8034}(3701,\cdot)\) \(\chi_{8034}(3779,\cdot)\) \(\chi_{8034}(3935,\cdot)\) \(\chi_{8034}(4013,\cdot)\) \(\chi_{8034}(4163,\cdot)\) \(\chi_{8034}(4709,\cdot)\) \(\chi_{8034}(4949,\cdot)\) \(\chi_{8034}(5021,\cdot)\) \(\chi_{8034}(5339,\cdot)\) \(\chi_{8034}(5573,\cdot)\) \(\chi_{8034}(6041,\cdot)\) \(\chi_{8034}(6353,\cdot)\) \(\chi_{8034}(6431,\cdot)\) \(\chi_{8034}(7055,\cdot)\) \(\chi_{8034}(7127,\cdot)\) \(\chi_{8034}(7361,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{51})$ |
Fixed field: | Number field defined by a degree 102 polynomial (not computed) |
Values on generators
\((5357,1237,5773)\) → \((-1,e\left(\frac{1}{3}\right),e\left(\frac{29}{102}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
\( \chi_{ 8034 }(3071, a) \) | \(1\) | \(1\) | \(e\left(\frac{40}{51}\right)\) | \(e\left(\frac{41}{51}\right)\) | \(e\left(\frac{3}{17}\right)\) | \(e\left(\frac{7}{102}\right)\) | \(e\left(\frac{7}{17}\right)\) | \(e\left(\frac{67}{102}\right)\) | \(e\left(\frac{29}{51}\right)\) | \(e\left(\frac{29}{102}\right)\) | \(e\left(\frac{7}{34}\right)\) | \(e\left(\frac{10}{17}\right)\) |