Basic properties
Modulus: | \(8005\) | |
Conductor: | \(1601\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(1600\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{1601}(11,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8005.cw
\(\chi_{8005}(6,\cdot)\) \(\chi_{8005}(11,\cdot)\) \(\chi_{8005}(26,\cdot)\) \(\chi_{8005}(46,\cdot)\) \(\chi_{8005}(56,\cdot)\) \(\chi_{8005}(71,\cdot)\) \(\chi_{8005}(96,\cdot)\) \(\chi_{8005}(101,\cdot)\) \(\chi_{8005}(111,\cdot)\) \(\chi_{8005}(126,\cdot)\) \(\chi_{8005}(131,\cdot)\) \(\chi_{8005}(136,\cdot)\) \(\chi_{8005}(141,\cdot)\) \(\chi_{8005}(146,\cdot)\) \(\chi_{8005}(166,\cdot)\) \(\chi_{8005}(176,\cdot)\) \(\chi_{8005}(181,\cdot)\) \(\chi_{8005}(186,\cdot)\) \(\chi_{8005}(191,\cdot)\) \(\chi_{8005}(201,\cdot)\) \(\chi_{8005}(211,\cdot)\) \(\chi_{8005}(216,\cdot)\) \(\chi_{8005}(231,\cdot)\) \(\chi_{8005}(236,\cdot)\) \(\chi_{8005}(246,\cdot)\) \(\chi_{8005}(251,\cdot)\) \(\chi_{8005}(266,\cdot)\) \(\chi_{8005}(291,\cdot)\) \(\chi_{8005}(301,\cdot)\) \(\chi_{8005}(306,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{1600})$ |
Fixed field: | Number field defined by a degree 1600 polynomial (not computed) |
Values on generators
\((1602,4806)\) → \((1,e\left(\frac{633}{1600}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
\( \chi_{ 8005 }(11, a) \) | \(-1\) | \(1\) | \(e\left(\frac{229}{400}\right)\) | \(e\left(\frac{633}{1600}\right)\) | \(e\left(\frac{29}{200}\right)\) | \(e\left(\frac{1549}{1600}\right)\) | \(e\left(\frac{371}{1600}\right)\) | \(e\left(\frac{287}{400}\right)\) | \(e\left(\frac{633}{800}\right)\) | \(e\left(\frac{689}{1600}\right)\) | \(e\left(\frac{173}{320}\right)\) | \(e\left(\frac{1}{64}\right)\) |