Basic properties
Modulus: | \(1503\) | |
Conductor: | \(501\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(166\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{501}(377,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1503.k
\(\chi_{1503}(17,\cdot)\) \(\chi_{1503}(26,\cdot)\) \(\chi_{1503}(35,\cdot)\) \(\chi_{1503}(53,\cdot)\) \(\chi_{1503}(71,\cdot)\) \(\chi_{1503}(80,\cdot)\) \(\chi_{1503}(125,\cdot)\) \(\chi_{1503}(134,\cdot)\) \(\chi_{1503}(143,\cdot)\) \(\chi_{1503}(161,\cdot)\) \(\chi_{1503}(197,\cdot)\) \(\chi_{1503}(206,\cdot)\) \(\chi_{1503}(269,\cdot)\) \(\chi_{1503}(278,\cdot)\) \(\chi_{1503}(287,\cdot)\) \(\chi_{1503}(296,\cdot)\) \(\chi_{1503}(305,\cdot)\) \(\chi_{1503}(323,\cdot)\) \(\chi_{1503}(332,\cdot)\) \(\chi_{1503}(368,\cdot)\) \(\chi_{1503}(377,\cdot)\) \(\chi_{1503}(386,\cdot)\) \(\chi_{1503}(404,\cdot)\) \(\chi_{1503}(413,\cdot)\) \(\chi_{1503}(440,\cdot)\) \(\chi_{1503}(476,\cdot)\) \(\chi_{1503}(485,\cdot)\) \(\chi_{1503}(494,\cdot)\) \(\chi_{1503}(521,\cdot)\) \(\chi_{1503}(575,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{83})$ |
Fixed field: | Number field defined by a degree 166 polynomial (not computed) |
Values on generators
\((335,172)\) → \((-1,e\left(\frac{87}{166}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 1503 }(377, a) \) | \(1\) | \(1\) | \(e\left(\frac{77}{166}\right)\) | \(e\left(\frac{77}{83}\right)\) | \(e\left(\frac{2}{83}\right)\) | \(e\left(\frac{70}{83}\right)\) | \(e\left(\frac{65}{166}\right)\) | \(e\left(\frac{81}{166}\right)\) | \(e\left(\frac{29}{166}\right)\) | \(e\left(\frac{163}{166}\right)\) | \(e\left(\frac{51}{166}\right)\) | \(e\left(\frac{71}{83}\right)\) |