Basic properties
Modulus: | \(8034\) | |
Conductor: | \(1339\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(51\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{1339}(1231,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8034.cs
\(\chi_{8034}(55,\cdot)\) \(\chi_{8034}(139,\cdot)\) \(\chi_{8034}(289,\cdot)\) \(\chi_{8034}(607,\cdot)\) \(\chi_{8034}(841,\cdot)\) \(\chi_{8034}(1231,\cdot)\) \(\chi_{8034}(2167,\cdot)\) \(\chi_{8034}(2245,\cdot)\) \(\chi_{8034}(2395,\cdot)\) \(\chi_{8034}(2401,\cdot)\) \(\chi_{8034}(2479,\cdot)\) \(\chi_{8034}(2707,\cdot)\) \(\chi_{8034}(2947,\cdot)\) \(\chi_{8034}(3025,\cdot)\) \(\chi_{8034}(3181,\cdot)\) \(\chi_{8034}(3253,\cdot)\) \(\chi_{8034}(3955,\cdot)\) \(\chi_{8034}(4033,\cdot)\) \(\chi_{8034}(4273,\cdot)\) \(\chi_{8034}(4345,\cdot)\) \(\chi_{8034}(4423,\cdot)\) \(\chi_{8034}(4969,\cdot)\) \(\chi_{8034}(5281,\cdot)\) \(\chi_{8034}(5827,\cdot)\) \(\chi_{8034}(5989,\cdot)\) \(\chi_{8034}(6763,\cdot)\) \(\chi_{8034}(6919,\cdot)\) \(\chi_{8034}(7159,\cdot)\) \(\chi_{8034}(7465,\cdot)\) \(\chi_{8034}(7783,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{51})$ |
Fixed field: | Number field defined by a degree 51 polynomial |
Values on generators
\((5357,1237,5773)\) → \((1,e\left(\frac{2}{3}\right),e\left(\frac{26}{51}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
\( \chi_{ 8034 }(1231, a) \) | \(1\) | \(1\) | \(e\left(\frac{26}{51}\right)\) | \(e\left(\frac{19}{51}\right)\) | \(e\left(\frac{13}{17}\right)\) | \(e\left(\frac{1}{51}\right)\) | \(e\left(\frac{2}{17}\right)\) | \(e\left(\frac{46}{51}\right)\) | \(e\left(\frac{1}{51}\right)\) | \(e\left(\frac{26}{51}\right)\) | \(e\left(\frac{1}{17}\right)\) | \(e\left(\frac{15}{17}\right)\) |