Basic properties
Modulus: | \(4011\) | |
Conductor: | \(1337\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
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Order: | \(285\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{1337}(16,\cdot)\) | 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)
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Galois orbit 4011.ce
\(\chi_{4011}(4,\cdot)\) \(\chi_{4011}(16,\cdot)\) \(\chi_{4011}(46,\cdot)\) \(\chi_{4011}(67,\cdot)\) \(\chi_{4011}(79,\cdot)\) \(\chi_{4011}(100,\cdot)\) \(\chi_{4011}(130,\cdot)\) \(\chi_{4011}(163,\cdot)\) \(\chi_{4011}(172,\cdot)\) \(\chi_{4011}(193,\cdot)\) \(\chi_{4011}(214,\cdot)\) \(\chi_{4011}(256,\cdot)\) \(\chi_{4011}(268,\cdot)\) \(\chi_{4011}(277,\cdot)\) \(\chi_{4011}(289,\cdot)\) \(\chi_{4011}(319,\cdot)\) \(\chi_{4011}(340,\cdot)\) \(\chi_{4011}(361,\cdot)\) \(\chi_{4011}(394,\cdot)\) \(\chi_{4011}(436,\cdot)\) \(\chi_{4011}(457,\cdot)\) \(\chi_{4011}(478,\cdot)\) \(\chi_{4011}(499,\cdot)\) \(\chi_{4011}(520,\cdot)\) \(\chi_{4011}(529,\cdot)\) \(\chi_{4011}(583,\cdot)\) \(\chi_{4011}(613,\cdot)\) \(\chi_{4011}(676,\cdot)\) \(\chi_{4011}(688,\cdot)\) \(\chi_{4011}(772,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{285})$ |
Fixed field: | Number field defined by a degree 285 polynomial (not computed) |
Values on generators
\((2675,2866,2311)\) → \((1,e\left(\frac{1}{3}\right),e\left(\frac{88}{95}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 4011 }(16, a) \) | \(1\) | \(1\) | \(e\left(\frac{121}{285}\right)\) | \(e\left(\frac{242}{285}\right)\) | \(e\left(\frac{56}{57}\right)\) | \(e\left(\frac{26}{95}\right)\) | \(e\left(\frac{116}{285}\right)\) | \(e\left(\frac{4}{57}\right)\) | \(e\left(\frac{71}{95}\right)\) | \(e\left(\frac{199}{285}\right)\) | \(e\left(\frac{32}{285}\right)\) | \(e\left(\frac{169}{285}\right)\) |