Basic properties
Modulus: | \(8450\) | |
Conductor: | \(4225\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(780\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{4225}(37,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8450.da
\(\chi_{8450}(37,\cdot)\) \(\chi_{8450}(123,\cdot)\) \(\chi_{8450}(137,\cdot)\) \(\chi_{8450}(167,\cdot)\) \(\chi_{8450}(223,\cdot)\) \(\chi_{8450}(253,\cdot)\) \(\chi_{8450}(267,\cdot)\) \(\chi_{8450}(297,\cdot)\) \(\chi_{8450}(353,\cdot)\) \(\chi_{8450}(383,\cdot)\) \(\chi_{8450}(397,\cdot)\) \(\chi_{8450}(483,\cdot)\) \(\chi_{8450}(513,\cdot)\) \(\chi_{8450}(527,\cdot)\) \(\chi_{8450}(613,\cdot)\) \(\chi_{8450}(687,\cdot)\) \(\chi_{8450}(773,\cdot)\) \(\chi_{8450}(787,\cdot)\) \(\chi_{8450}(817,\cdot)\) \(\chi_{8450}(873,\cdot)\) \(\chi_{8450}(903,\cdot)\) \(\chi_{8450}(917,\cdot)\) \(\chi_{8450}(947,\cdot)\) \(\chi_{8450}(1003,\cdot)\) \(\chi_{8450}(1047,\cdot)\) \(\chi_{8450}(1077,\cdot)\) \(\chi_{8450}(1133,\cdot)\) \(\chi_{8450}(1163,\cdot)\) \(\chi_{8450}(1177,\cdot)\) \(\chi_{8450}(1337,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{780})$ |
Fixed field: | Number field defined by a degree 780 polynomial (not computed) |
Values on generators
\((677,3551)\) → \((e\left(\frac{9}{20}\right),e\left(\frac{151}{156}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
\( \chi_{ 8450 }(37, a) \) | \(1\) | \(1\) | \(e\left(\frac{137}{780}\right)\) | \(e\left(\frac{32}{39}\right)\) | \(e\left(\frac{137}{390}\right)\) | \(e\left(\frac{701}{780}\right)\) | \(e\left(\frac{133}{780}\right)\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{259}{260}\right)\) | \(e\left(\frac{47}{60}\right)\) | \(e\left(\frac{137}{260}\right)\) | \(e\left(\frac{241}{390}\right)\) |