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 \(\chi_{4017}(1850,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8034.df
\(\chi_{8034}(101,\cdot)\) \(\chi_{8034}(173,\cdot)\) \(\chi_{8034}(251,\cdot)\) \(\chi_{8034}(569,\cdot)\) \(\chi_{8034}(875,\cdot)\) \(\chi_{8034}(1115,\cdot)\) \(\chi_{8034}(1271,\cdot)\) \(\chi_{8034}(2045,\cdot)\) \(\chi_{8034}(2207,\cdot)\) \(\chi_{8034}(2753,\cdot)\) \(\chi_{8034}(3065,\cdot)\) \(\chi_{8034}(3611,\cdot)\) \(\chi_{8034}(3689,\cdot)\) \(\chi_{8034}(3761,\cdot)\) \(\chi_{8034}(4001,\cdot)\) \(\chi_{8034}(4079,\cdot)\) \(\chi_{8034}(4781,\cdot)\) \(\chi_{8034}(4853,\cdot)\) \(\chi_{8034}(5009,\cdot)\) \(\chi_{8034}(5087,\cdot)\) \(\chi_{8034}(5327,\cdot)\) \(\chi_{8034}(5555,\cdot)\) \(\chi_{8034}(5633,\cdot)\) \(\chi_{8034}(5639,\cdot)\) \(\chi_{8034}(5789,\cdot)\) \(\chi_{8034}(5867,\cdot)\) \(\chi_{8034}(6803,\cdot)\) \(\chi_{8034}(7193,\cdot)\) \(\chi_{8034}(7427,\cdot)\) \(\chi_{8034}(7745,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{51})$ |
Fixed field: | Number field defined by a degree 102 polynomial (not computed) |
Values on generators
\((5357,1237,5773)\) → \((-1,e\left(\frac{1}{6}\right),e\left(\frac{37}{102}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
\( \chi_{ 8034 }(5867, a) \) | \(1\) | \(1\) | \(e\left(\frac{37}{102}\right)\) | \(e\left(\frac{29}{102}\right)\) | \(e\left(\frac{27}{34}\right)\) | \(e\left(\frac{23}{102}\right)\) | \(e\left(\frac{29}{34}\right)\) | \(e\left(\frac{89}{102}\right)\) | \(e\left(\frac{37}{51}\right)\) | \(e\left(\frac{37}{102}\right)\) | \(e\left(\frac{3}{17}\right)\) | \(e\left(\frac{11}{17}\right)\) |