Basic properties
Modulus: | \(8024\) | |
Conductor: | \(1003\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(464\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{1003}(345,\cdot)\) | 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 8024.cv
\(\chi_{8024}(65,\cdot)\) \(\chi_{8024}(73,\cdot)\) \(\chi_{8024}(97,\cdot)\) \(\chi_{8024}(113,\cdot)\) \(\chi_{8024}(129,\cdot)\) \(\chi_{8024}(201,\cdot)\) \(\chi_{8024}(209,\cdot)\) \(\chi_{8024}(233,\cdot)\) \(\chi_{8024}(249,\cdot)\) \(\chi_{8024}(313,\cdot)\) \(\chi_{8024}(329,\cdot)\) \(\chi_{8024}(337,\cdot)\) \(\chi_{8024}(345,\cdot)\) \(\chi_{8024}(377,\cdot)\) \(\chi_{8024}(385,\cdot)\) \(\chi_{8024}(401,\cdot)\) \(\chi_{8024}(465,\cdot)\) \(\chi_{8024}(505,\cdot)\) \(\chi_{8024}(537,\cdot)\) \(\chi_{8024}(585,\cdot)\) \(\chi_{8024}(601,\cdot)\) \(\chi_{8024}(657,\cdot)\) \(\chi_{8024}(673,\cdot)\) \(\chi_{8024}(721,\cdot)\) \(\chi_{8024}(745,\cdot)\) \(\chi_{8024}(777,\cdot)\) \(\chi_{8024}(785,\cdot)\) \(\chi_{8024}(809,\cdot)\) \(\chi_{8024}(857,\cdot)\) \(\chi_{8024}(873,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{464})$ |
Fixed field: | Number field defined by a degree 464 polynomial (not computed) |
Values on generators
\((2007,4013,3777,3129)\) → \((1,1,e\left(\frac{5}{16}\right),e\left(\frac{13}{58}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(19\) | \(21\) | \(23\) |
\( \chi_{ 8024 }(345, a) \) | \(1\) | \(1\) | \(e\left(\frac{241}{464}\right)\) | \(e\left(\frac{421}{464}\right)\) | \(e\left(\frac{219}{464}\right)\) | \(e\left(\frac{9}{232}\right)\) | \(e\left(\frac{367}{464}\right)\) | \(e\left(\frac{39}{116}\right)\) | \(e\left(\frac{99}{232}\right)\) | \(e\left(\frac{207}{232}\right)\) | \(e\left(\frac{115}{116}\right)\) | \(e\left(\frac{23}{464}\right)\) |