Basic properties
Modulus: | \(8020\) | |
Conductor: | \(401\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(200\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{401}(181,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8020.do
\(\chi_{8020}(181,\cdot)\) \(\chi_{8020}(201,\cdot)\) \(\chi_{8020}(221,\cdot)\) \(\chi_{8020}(241,\cdot)\) \(\chi_{8020}(261,\cdot)\) \(\chi_{8020}(361,\cdot)\) \(\chi_{8020}(441,\cdot)\) \(\chi_{8020}(541,\cdot)\) \(\chi_{8020}(561,\cdot)\) \(\chi_{8020}(581,\cdot)\) \(\chi_{8020}(601,\cdot)\) \(\chi_{8020}(621,\cdot)\) \(\chi_{8020}(961,\cdot)\) \(\chi_{8020}(1121,\cdot)\) \(\chi_{8020}(1201,\cdot)\) \(\chi_{8020}(1261,\cdot)\) \(\chi_{8020}(1281,\cdot)\) \(\chi_{8020}(1341,\cdot)\) \(\chi_{8020}(1401,\cdot)\) \(\chi_{8020}(1501,\cdot)\) \(\chi_{8020}(1561,\cdot)\) \(\chi_{8020}(1861,\cdot)\) \(\chi_{8020}(1961,\cdot)\) \(\chi_{8020}(2041,\cdot)\) \(\chi_{8020}(2181,\cdot)\) \(\chi_{8020}(2461,\cdot)\) \(\chi_{8020}(2581,\cdot)\) \(\chi_{8020}(2621,\cdot)\) \(\chi_{8020}(2641,\cdot)\) \(\chi_{8020}(2961,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{200})$ |
Fixed field: | Number field defined by a degree 200 polynomial (not computed) |
Values on generators
\((4011,6417,7221)\) → \((1,1,e\left(\frac{47}{200}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
\( \chi_{ 8020 }(181, a) \) | \(1\) | \(1\) | \(e\left(\frac{47}{200}\right)\) | \(e\left(\frac{57}{100}\right)\) | \(e\left(\frac{47}{100}\right)\) | \(e\left(\frac{59}{100}\right)\) | \(e\left(\frac{193}{200}\right)\) | \(e\left(\frac{1}{200}\right)\) | \(e\left(\frac{61}{200}\right)\) | \(e\left(\frac{161}{200}\right)\) | \(e\left(\frac{77}{200}\right)\) | \(e\left(\frac{141}{200}\right)\) |