Basic properties
Modulus: | \(7350\) | |
Conductor: | \(1225\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(420\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{1225}(73,\cdot)\) | 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)
|
Galois orbit 7350.dp
\(\chi_{7350}(73,\cdot)\) \(\chi_{7350}(103,\cdot)\) \(\chi_{7350}(187,\cdot)\) \(\chi_{7350}(283,\cdot)\) \(\chi_{7350}(367,\cdot)\) \(\chi_{7350}(397,\cdot)\) \(\chi_{7350}(523,\cdot)\) \(\chi_{7350}(577,\cdot)\) \(\chi_{7350}(703,\cdot)\) \(\chi_{7350}(733,\cdot)\) \(\chi_{7350}(787,\cdot)\) \(\chi_{7350}(817,\cdot)\) \(\chi_{7350}(997,\cdot)\) \(\chi_{7350}(1027,\cdot)\) \(\chi_{7350}(1123,\cdot)\) \(\chi_{7350}(1153,\cdot)\) \(\chi_{7350}(1237,\cdot)\) \(\chi_{7350}(1333,\cdot)\) \(\chi_{7350}(1363,\cdot)\) \(\chi_{7350}(1417,\cdot)\) \(\chi_{7350}(1447,\cdot)\) \(\chi_{7350}(1573,\cdot)\) \(\chi_{7350}(1627,\cdot)\) \(\chi_{7350}(1753,\cdot)\) \(\chi_{7350}(1837,\cdot)\) \(\chi_{7350}(1867,\cdot)\) \(\chi_{7350}(1963,\cdot)\) \(\chi_{7350}(2047,\cdot)\) \(\chi_{7350}(2173,\cdot)\) \(\chi_{7350}(2203,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{420})$ |
Fixed field: | Number field defined by a degree 420 polynomial (not computed) |
Values on generators
\((4901,1177,2551)\) → \((1,e\left(\frac{11}{20}\right),e\left(\frac{37}{42}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
\( \chi_{ 7350 }(73, a) \) | \(1\) | \(1\) | \(e\left(\frac{4}{105}\right)\) | \(e\left(\frac{73}{140}\right)\) | \(e\left(\frac{73}{420}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{221}{420}\right)\) | \(e\left(\frac{67}{70}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{59}{420}\right)\) | \(e\left(\frac{29}{70}\right)\) | \(e\left(\frac{15}{28}\right)\) |