Basic properties
Modulus: | \(1856\) | |
Conductor: | \(1856\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
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Order: | \(112\) | 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
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Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
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Galois orbit 1856.cn
\(\chi_{1856}(37,\cdot)\) \(\chi_{1856}(61,\cdot)\) \(\chi_{1856}(77,\cdot)\) \(\chi_{1856}(85,\cdot)\) \(\chi_{1856}(205,\cdot)\) \(\chi_{1856}(213,\cdot)\) \(\chi_{1856}(229,\cdot)\) \(\chi_{1856}(253,\cdot)\) \(\chi_{1856}(301,\cdot)\) \(\chi_{1856}(333,\cdot)\) \(\chi_{1856}(421,\cdot)\) \(\chi_{1856}(453,\cdot)\) \(\chi_{1856}(501,\cdot)\) \(\chi_{1856}(525,\cdot)\) \(\chi_{1856}(541,\cdot)\) \(\chi_{1856}(549,\cdot)\) \(\chi_{1856}(669,\cdot)\) \(\chi_{1856}(677,\cdot)\) \(\chi_{1856}(693,\cdot)\) \(\chi_{1856}(717,\cdot)\) \(\chi_{1856}(765,\cdot)\) \(\chi_{1856}(797,\cdot)\) \(\chi_{1856}(885,\cdot)\) \(\chi_{1856}(917,\cdot)\) \(\chi_{1856}(965,\cdot)\) \(\chi_{1856}(989,\cdot)\) \(\chi_{1856}(1005,\cdot)\) \(\chi_{1856}(1013,\cdot)\) \(\chi_{1856}(1133,\cdot)\) \(\chi_{1856}(1141,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{112})$ |
Fixed field: | Number field defined by a degree 112 polynomial (not computed) |
Values on generators
\((639,581,321)\) → \((1,e\left(\frac{9}{16}\right),e\left(\frac{3}{28}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 1856 }(37, a) \) | \(-1\) | \(1\) | \(e\left(\frac{25}{112}\right)\) | \(e\left(\frac{103}{112}\right)\) | \(e\left(\frac{51}{56}\right)\) | \(e\left(\frac{25}{56}\right)\) | \(e\left(\frac{55}{112}\right)\) | \(e\left(\frac{41}{112}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(1\) | \(e\left(\frac{101}{112}\right)\) | \(e\left(\frac{15}{112}\right)\) |