Basic properties
Modulus: | \(6012\) | |
Conductor: | \(1503\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
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Order: | \(249\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{1503}(61,\cdot)\) | 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 6012.y
\(\chi_{6012}(25,\cdot)\) \(\chi_{6012}(49,\cdot)\) \(\chi_{6012}(61,\cdot)\) \(\chi_{6012}(85,\cdot)\) \(\chi_{6012}(97,\cdot)\) \(\chi_{6012}(121,\cdot)\) \(\chi_{6012}(133,\cdot)\) \(\chi_{6012}(157,\cdot)\) \(\chi_{6012}(169,\cdot)\) \(\chi_{6012}(205,\cdot)\) \(\chi_{6012}(229,\cdot)\) \(\chi_{6012}(265,\cdot)\) \(\chi_{6012}(337,\cdot)\) \(\chi_{6012}(409,\cdot)\) \(\chi_{6012}(421,\cdot)\) \(\chi_{6012}(481,\cdot)\) \(\chi_{6012}(517,\cdot)\) \(\chi_{6012}(529,\cdot)\) \(\chi_{6012}(565,\cdot)\) \(\chi_{6012}(589,\cdot)\) \(\chi_{6012}(601,\cdot)\) \(\chi_{6012}(625,\cdot)\) \(\chi_{6012}(697,\cdot)\) \(\chi_{6012}(733,\cdot)\) \(\chi_{6012}(745,\cdot)\) \(\chi_{6012}(805,\cdot)\) \(\chi_{6012}(841,\cdot)\) \(\chi_{6012}(853,\cdot)\) \(\chi_{6012}(877,\cdot)\) \(\chi_{6012}(889,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{249})$ |
Fixed field: | Number field defined by a degree 249 polynomial (not computed) |
Values on generators
\((3007,3341,4681)\) → \((1,e\left(\frac{2}{3}\right),e\left(\frac{33}{83}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
\( \chi_{ 6012 }(61, a) \) | \(1\) | \(1\) | \(e\left(\frac{182}{249}\right)\) | \(e\left(\frac{145}{249}\right)\) | \(e\left(\frac{199}{249}\right)\) | \(e\left(\frac{71}{249}\right)\) | \(e\left(\frac{6}{83}\right)\) | \(e\left(\frac{5}{83}\right)\) | \(e\left(\frac{173}{249}\right)\) | \(e\left(\frac{115}{249}\right)\) | \(e\left(\frac{76}{249}\right)\) | \(e\left(\frac{29}{249}\right)\) |