Basic properties
Modulus: | \(2450\) | |
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 \(\chi_{1225}(33,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2450.bv
\(\chi_{2450}(3,\cdot)\) \(\chi_{2450}(17,\cdot)\) \(\chi_{2450}(33,\cdot)\) \(\chi_{2450}(47,\cdot)\) \(\chi_{2450}(73,\cdot)\) \(\chi_{2450}(87,\cdot)\) \(\chi_{2450}(103,\cdot)\) \(\chi_{2450}(173,\cdot)\) \(\chi_{2450}(187,\cdot)\) \(\chi_{2450}(213,\cdot)\) \(\chi_{2450}(283,\cdot)\) \(\chi_{2450}(297,\cdot)\) \(\chi_{2450}(327,\cdot)\) \(\chi_{2450}(353,\cdot)\) \(\chi_{2450}(367,\cdot)\) \(\chi_{2450}(383,\cdot)\) \(\chi_{2450}(397,\cdot)\) \(\chi_{2450}(437,\cdot)\) \(\chi_{2450}(453,\cdot)\) \(\chi_{2450}(467,\cdot)\) \(\chi_{2450}(523,\cdot)\) \(\chi_{2450}(537,\cdot)\) \(\chi_{2450}(563,\cdot)\) \(\chi_{2450}(577,\cdot)\) \(\chi_{2450}(633,\cdot)\) \(\chi_{2450}(647,\cdot)\) \(\chi_{2450}(663,\cdot)\) \(\chi_{2450}(677,\cdot)\) \(\chi_{2450}(703,\cdot)\) \(\chi_{2450}(733,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{420})$ |
Fixed field: | Number field defined by a degree 420 polynomial (not computed) |
Values on generators
\((1177,101)\) → \((e\left(\frac{3}{20}\right),e\left(\frac{41}{42}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) |
\( \chi_{ 2450 }(33, a) \) | \(1\) | \(1\) | \(e\left(\frac{11}{420}\right)\) | \(e\left(\frac{11}{210}\right)\) | \(e\left(\frac{47}{105}\right)\) | \(e\left(\frac{9}{140}\right)\) | \(e\left(\frac{149}{420}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{313}{420}\right)\) | \(e\left(\frac{11}{140}\right)\) | \(e\left(\frac{61}{70}\right)\) | \(e\left(\frac{1}{30}\right)\) |