Basic properties
Modulus: | \(8034\) | |
Conductor: | \(4017\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(204\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{4017}(1253,\cdot)\) | 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.ei
\(\chi_{8034}(83,\cdot)\) \(\chi_{8034}(161,\cdot)\) \(\chi_{8034}(239,\cdot)\) \(\chi_{8034}(359,\cdot)\) \(\chi_{8034}(437,\cdot)\) \(\chi_{8034}(551,\cdot)\) \(\chi_{8034}(749,\cdot)\) \(\chi_{8034}(1019,\cdot)\) \(\chi_{8034}(1253,\cdot)\) \(\chi_{8034}(1295,\cdot)\) \(\chi_{8034}(1643,\cdot)\) \(\chi_{8034}(2075,\cdot)\) \(\chi_{8034}(2189,\cdot)\) \(\chi_{8034}(2231,\cdot)\) \(\chi_{8034}(2387,\cdot)\) \(\chi_{8034}(2501,\cdot)\) \(\chi_{8034}(2579,\cdot)\) \(\chi_{8034}(2657,\cdot)\) \(\chi_{8034}(2813,\cdot)\) \(\chi_{8034}(2891,\cdot)\) \(\chi_{8034}(2933,\cdot)\) \(\chi_{8034}(3047,\cdot)\) \(\chi_{8034}(3245,\cdot)\) \(\chi_{8034}(3359,\cdot)\) \(\chi_{8034}(3401,\cdot)\) \(\chi_{8034}(3437,\cdot)\) \(\chi_{8034}(3557,\cdot)\) \(\chi_{8034}(3593,\cdot)\) \(\chi_{8034}(3749,\cdot)\) \(\chi_{8034}(3791,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{204})$ |
Fixed field: | Number field defined by a degree 204 polynomial (not computed) |
Values on generators
\((5357,1237,5773)\) → \((-1,-i,e\left(\frac{35}{51}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
\( \chi_{ 8034 }(1253, a) \) | \(1\) | \(1\) | \(e\left(\frac{191}{204}\right)\) | \(e\left(\frac{203}{204}\right)\) | \(e\left(\frac{125}{204}\right)\) | \(e\left(\frac{2}{51}\right)\) | \(e\left(\frac{133}{204}\right)\) | \(e\left(\frac{8}{17}\right)\) | \(e\left(\frac{89}{102}\right)\) | \(e\left(\frac{53}{102}\right)\) | \(e\left(\frac{59}{68}\right)\) | \(e\left(\frac{95}{102}\right)\) |