Basic properties
Modulus: | \(8034\) | |
Conductor: | \(1339\) | 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 \(\chi_{1339}(324,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8034.de
\(\chi_{8034}(25,\cdot)\) \(\chi_{8034}(337,\cdot)\) \(\chi_{8034}(883,\cdot)\) \(\chi_{8034}(1663,\cdot)\) \(\chi_{8034}(1819,\cdot)\) \(\chi_{8034}(1975,\cdot)\) \(\chi_{8034}(2521,\cdot)\) \(\chi_{8034}(2833,\cdot)\) \(\chi_{8034}(2989,\cdot)\) \(\chi_{8034}(3145,\cdot)\) \(\chi_{8034}(3379,\cdot)\) \(\chi_{8034}(3457,\cdot)\) \(\chi_{8034}(3535,\cdot)\) \(\chi_{8034}(3847,\cdot)\) \(\chi_{8034}(4315,\cdot)\) \(\chi_{8034}(4549,\cdot)\) \(\chi_{8034}(4939,\cdot)\) \(\chi_{8034}(5485,\cdot)\) \(\chi_{8034}(5797,\cdot)\) \(\chi_{8034}(5875,\cdot)\) \(\chi_{8034}(5953,\cdot)\) \(\chi_{8034}(6109,\cdot)\) \(\chi_{8034}(6187,\cdot)\) \(\chi_{8034}(6343,\cdot)\) \(\chi_{8034}(6655,\cdot)\) \(\chi_{8034}(6733,\cdot)\) \(\chi_{8034}(6889,\cdot)\) \(\chi_{8034}(7045,\cdot)\) \(\chi_{8034}(7123,\cdot)\) \(\chi_{8034}(7435,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{51})$ |
Fixed field: | Number field defined by a degree 102 polynomial (not computed) |
Values on generators
\((5357,1237,5773)\) → \((1,-1,e\left(\frac{20}{51}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
\( \chi_{ 8034 }(1663, a) \) | \(1\) | \(1\) | \(e\left(\frac{91}{102}\right)\) | \(e\left(\frac{7}{102}\right)\) | \(e\left(\frac{43}{102}\right)\) | \(e\left(\frac{23}{51}\right)\) | \(e\left(\frac{89}{102}\right)\) | \(e\left(\frac{7}{17}\right)\) | \(e\left(\frac{40}{51}\right)\) | \(e\left(\frac{37}{51}\right)\) | \(e\left(\frac{29}{34}\right)\) | \(e\left(\frac{49}{51}\right)\) |