Basic properties
Modulus: | \(2075\) | |
Conductor: | \(2075\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(410\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
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Galois orbit 2075.t
\(\chi_{2075}(4,\cdot)\) \(\chi_{2075}(9,\cdot)\) \(\chi_{2075}(29,\cdot)\) \(\chi_{2075}(44,\cdot)\) \(\chi_{2075}(59,\cdot)\) \(\chi_{2075}(64,\cdot)\) \(\chi_{2075}(69,\cdot)\) \(\chi_{2075}(94,\cdot)\) \(\chi_{2075}(104,\cdot)\) \(\chi_{2075}(109,\cdot)\) \(\chi_{2075}(114,\cdot)\) \(\chi_{2075}(119,\cdot)\) \(\chi_{2075}(134,\cdot)\) \(\chi_{2075}(144,\cdot)\) \(\chi_{2075}(164,\cdot)\) \(\chi_{2075}(169,\cdot)\) \(\chi_{2075}(189,\cdot)\) \(\chi_{2075}(194,\cdot)\) \(\chi_{2075}(204,\cdot)\) \(\chi_{2075}(214,\cdot)\) \(\chi_{2075}(229,\cdot)\) \(\chi_{2075}(234,\cdot)\) \(\chi_{2075}(244,\cdot)\) \(\chi_{2075}(259,\cdot)\) \(\chi_{2075}(279,\cdot)\) \(\chi_{2075}(289,\cdot)\) \(\chi_{2075}(314,\cdot)\) \(\chi_{2075}(319,\cdot)\) \(\chi_{2075}(339,\cdot)\) \(\chi_{2075}(344,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{205})$ |
Fixed field: | Number field defined by a degree 410 polynomial (not computed) |
Values on generators
\((1827,251)\) → \((e\left(\frac{9}{10}\right),e\left(\frac{32}{41}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
\( \chi_{ 2075 }(119, a) \) | \(1\) | \(1\) | \(e\left(\frac{279}{410}\right)\) | \(e\left(\frac{203}{410}\right)\) | \(e\left(\frac{74}{205}\right)\) | \(e\left(\frac{36}{205}\right)\) | \(e\left(\frac{61}{82}\right)\) | \(e\left(\frac{17}{410}\right)\) | \(e\left(\frac{203}{205}\right)\) | \(e\left(\frac{27}{205}\right)\) | \(e\left(\frac{351}{410}\right)\) | \(e\left(\frac{81}{410}\right)\) |