Basic properties
Modulus: | \(6025\) | |
Conductor: | \(6025\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(240\) | 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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6025.iw
\(\chi_{6025}(52,\cdot)\) \(\chi_{6025}(172,\cdot)\) \(\chi_{6025}(387,\cdot)\) \(\chi_{6025}(447,\cdot)\) \(\chi_{6025}(537,\cdot)\) \(\chi_{6025}(548,\cdot)\) \(\chi_{6025}(613,\cdot)\) \(\chi_{6025}(653,\cdot)\) \(\chi_{6025}(667,\cdot)\) \(\chi_{6025}(677,\cdot)\) \(\chi_{6025}(692,\cdot)\) \(\chi_{6025}(878,\cdot)\) \(\chi_{6025}(898,\cdot)\) \(\chi_{6025}(913,\cdot)\) \(\chi_{6025}(977,\cdot)\) \(\chi_{6025}(1003,\cdot)\) \(\chi_{6025}(1163,\cdot)\) \(\chi_{6025}(1362,\cdot)\) \(\chi_{6025}(1488,\cdot)\) \(\chi_{6025}(1508,\cdot)\) \(\chi_{6025}(1558,\cdot)\) \(\chi_{6025}(1573,\cdot)\) \(\chi_{6025}(1722,\cdot)\) \(\chi_{6025}(1738,\cdot)\) \(\chi_{6025}(1942,\cdot)\) \(\chi_{6025}(1997,\cdot)\) \(\chi_{6025}(2012,\cdot)\) \(\chi_{6025}(2038,\cdot)\) \(\chi_{6025}(2247,\cdot)\) \(\chi_{6025}(2273,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{240})$ |
Fixed field: | Number field defined by a degree 240 polynomial (not computed) |
Values on generators
\((2652,2176)\) → \((e\left(\frac{17}{20}\right),e\left(\frac{179}{240}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
\( \chi_{ 6025 }(2247, a) \) | \(1\) | \(1\) | \(e\left(\frac{67}{120}\right)\) | \(e\left(\frac{83}{120}\right)\) | \(e\left(\frac{7}{60}\right)\) | \(i\) | \(e\left(\frac{239}{240}\right)\) | \(e\left(\frac{27}{40}\right)\) | \(e\left(\frac{23}{60}\right)\) | \(e\left(\frac{59}{240}\right)\) | \(e\left(\frac{97}{120}\right)\) | \(e\left(\frac{49}{240}\right)\) |