Basic properties
Modulus: | \(1225\) | |
Conductor: | \(1225\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(140\) | 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
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1225.bp
\(\chi_{1225}(13,\cdot)\) \(\chi_{1225}(27,\cdot)\) \(\chi_{1225}(62,\cdot)\) \(\chi_{1225}(83,\cdot)\) \(\chi_{1225}(153,\cdot)\) \(\chi_{1225}(167,\cdot)\) \(\chi_{1225}(188,\cdot)\) \(\chi_{1225}(202,\cdot)\) \(\chi_{1225}(223,\cdot)\) \(\chi_{1225}(237,\cdot)\) \(\chi_{1225}(258,\cdot)\) \(\chi_{1225}(272,\cdot)\) \(\chi_{1225}(328,\cdot)\) \(\chi_{1225}(363,\cdot)\) \(\chi_{1225}(377,\cdot)\) \(\chi_{1225}(398,\cdot)\) \(\chi_{1225}(412,\cdot)\) \(\chi_{1225}(433,\cdot)\) \(\chi_{1225}(447,\cdot)\) \(\chi_{1225}(503,\cdot)\) \(\chi_{1225}(517,\cdot)\) \(\chi_{1225}(552,\cdot)\) \(\chi_{1225}(573,\cdot)\) \(\chi_{1225}(608,\cdot)\) \(\chi_{1225}(622,\cdot)\) \(\chi_{1225}(678,\cdot)\) \(\chi_{1225}(692,\cdot)\) \(\chi_{1225}(713,\cdot)\) \(\chi_{1225}(727,\cdot)\) \(\chi_{1225}(748,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{140})$ |
Fixed field: | Number field defined by a degree 140 polynomial (not computed) |
Values on generators
\((1177,101)\) → \((e\left(\frac{7}{20}\right),e\left(\frac{9}{14}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
\( \chi_{ 1225 }(153, a) \) | \(1\) | \(1\) | \(e\left(\frac{9}{140}\right)\) | \(e\left(\frac{13}{140}\right)\) | \(e\left(\frac{9}{70}\right)\) | \(e\left(\frac{11}{70}\right)\) | \(e\left(\frac{27}{140}\right)\) | \(e\left(\frac{13}{70}\right)\) | \(e\left(\frac{11}{35}\right)\) | \(e\left(\frac{31}{140}\right)\) | \(e\left(\frac{121}{140}\right)\) | \(e\left(\frac{9}{35}\right)\) |