Basic properties
Modulus: | \(4011\) | |
Conductor: | \(1337\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(570\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{1337}(250,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4011.cg
\(\chi_{4011}(10,\cdot)\) \(\chi_{4011}(40,\cdot)\) \(\chi_{4011}(103,\cdot)\) \(\chi_{4011}(115,\cdot)\) \(\chi_{4011}(199,\cdot)\) \(\chi_{4011}(208,\cdot)\) \(\chi_{4011}(241,\cdot)\) \(\chi_{4011}(250,\cdot)\) \(\chi_{4011}(271,\cdot)\) \(\chi_{4011}(283,\cdot)\) \(\chi_{4011}(325,\cdot)\) \(\chi_{4011}(397,\cdot)\) \(\chi_{4011}(409,\cdot)\) \(\chi_{4011}(430,\cdot)\) \(\chi_{4011}(460,\cdot)\) \(\chi_{4011}(472,\cdot)\) \(\chi_{4011}(502,\cdot)\) \(\chi_{4011}(544,\cdot)\) \(\chi_{4011}(577,\cdot)\) \(\chi_{4011}(586,\cdot)\) \(\chi_{4011}(607,\cdot)\) \(\chi_{4011}(619,\cdot)\) \(\chi_{4011}(640,\cdot)\) \(\chi_{4011}(670,\cdot)\) \(\chi_{4011}(691,\cdot)\) \(\chi_{4011}(703,\cdot)\) \(\chi_{4011}(745,\cdot)\) \(\chi_{4011}(766,\cdot)\) \(\chi_{4011}(787,\cdot)\) \(\chi_{4011}(829,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{285})$ |
Fixed field: | Number field defined by a degree 570 polynomial (not computed) |
Values on generators
\((2675,2866,2311)\) → \((1,e\left(\frac{5}{6}\right),e\left(\frac{2}{95}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 4011 }(250, a) \) | \(-1\) | \(1\) | \(e\left(\frac{169}{285}\right)\) | \(e\left(\frac{53}{285}\right)\) | \(e\left(\frac{25}{114}\right)\) | \(e\left(\frac{74}{95}\right)\) | \(e\left(\frac{463}{570}\right)\) | \(e\left(\frac{7}{57}\right)\) | \(e\left(\frac{163}{190}\right)\) | \(e\left(\frac{106}{285}\right)\) | \(e\left(\frac{511}{570}\right)\) | \(e\left(\frac{107}{570}\right)\) |