Basic properties
Modulus: | \(8034\) | |
Conductor: | \(1339\) | 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 \(\chi_{1339}(84,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8034.eo
\(\chi_{8034}(67,\cdot)\) \(\chi_{8034}(85,\cdot)\) \(\chi_{8034}(115,\cdot)\) \(\chi_{8034}(241,\cdot)\) \(\chi_{8034}(271,\cdot)\) \(\chi_{8034}(349,\cdot)\) \(\chi_{8034}(379,\cdot)\) \(\chi_{8034}(457,\cdot)\) \(\chi_{8034}(487,\cdot)\) \(\chi_{8034}(799,\cdot)\) \(\chi_{8034}(817,\cdot)\) \(\chi_{8034}(895,\cdot)\) \(\chi_{8034}(1051,\cdot)\) \(\chi_{8034}(1081,\cdot)\) \(\chi_{8034}(1129,\cdot)\) \(\chi_{8034}(1177,\cdot)\) \(\chi_{8034}(1345,\cdot)\) \(\chi_{8034}(1423,\cdot)\) \(\chi_{8034}(1723,\cdot)\) \(\chi_{8034}(1735,\cdot)\) \(\chi_{8034}(1813,\cdot)\) \(\chi_{8034}(2035,\cdot)\) \(\chi_{8034}(2065,\cdot)\) \(\chi_{8034}(2251,\cdot)\) \(\chi_{8034}(2455,\cdot)\) \(\chi_{8034}(2515,\cdot)\) \(\chi_{8034}(2581,\cdot)\) \(\chi_{8034}(2659,\cdot)\) \(\chi_{8034}(2689,\cdot)\) \(\chi_{8034}(2971,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{204})$ |
Fixed field: | Number field defined by a degree 204 polynomial (not computed) |
Values on generators
\((5357,1237,5773)\) → \((1,e\left(\frac{5}{12}\right),e\left(\frac{29}{102}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
\( \chi_{ 8034 }(1423, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{204}\right)\) | \(e\left(\frac{49}{68}\right)\) | \(e\left(\frac{53}{204}\right)\) | \(e\left(\frac{25}{34}\right)\) | \(e\left(\frac{169}{204}\right)\) | \(e\left(\frac{101}{102}\right)\) | \(e\left(\frac{7}{102}\right)\) | \(e\left(\frac{2}{17}\right)\) | \(e\left(\frac{65}{68}\right)\) | \(e\left(\frac{77}{102}\right)\) |