Basic properties
Modulus: | \(8005\) | |
Conductor: | \(8005\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(400\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8005.cr
\(\chi_{8005}(2,\cdot)\) \(\chi_{8005}(8,\cdot)\) \(\chi_{8005}(58,\cdot)\) \(\chi_{8005}(62,\cdot)\) \(\chi_{8005}(128,\cdot)\) \(\chi_{8005}(187,\cdot)\) \(\chi_{8005}(232,\cdot)\) \(\chi_{8005}(308,\cdot)\) \(\chi_{8005}(438,\cdot)\) \(\chi_{8005}(488,\cdot)\) \(\chi_{8005}(512,\cdot)\) \(\chi_{8005}(573,\cdot)\) \(\chi_{8005}(673,\cdot)\) \(\chi_{8005}(717,\cdot)\) \(\chi_{8005}(722,\cdot)\) \(\chi_{8005}(928,\cdot)\) \(\chi_{8005}(992,\cdot)\) \(\chi_{8005}(1028,\cdot)\) \(\chi_{8005}(1113,\cdot)\) \(\chi_{8005}(1163,\cdot)\) \(\chi_{8005}(1232,\cdot)\) \(\chi_{8005}(1237,\cdot)\) \(\chi_{8005}(1293,\cdot)\) \(\chi_{8005}(1397,\cdot)\) \(\chi_{8005}(1473,\cdot)\) \(\chi_{8005}(1517,\cdot)\) \(\chi_{8005}(1543,\cdot)\) \(\chi_{8005}(1593,\cdot)\) \(\chi_{8005}(1682,\cdot)\) \(\chi_{8005}(1707,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{400})$ |
Fixed field: | Number field defined by a degree 400 polynomial (not computed) |
Values on generators
\((1602,4806)\) → \((i,e\left(\frac{117}{400}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
\( \chi_{ 8005 }(512, a) \) | \(-1\) | \(1\) | \(e\left(\frac{23}{50}\right)\) | \(e\left(\frac{17}{400}\right)\) | \(e\left(\frac{23}{25}\right)\) | \(e\left(\frac{201}{400}\right)\) | \(e\left(\frac{379}{400}\right)\) | \(e\left(\frac{19}{50}\right)\) | \(e\left(\frac{17}{200}\right)\) | \(e\left(\frac{61}{400}\right)\) | \(e\left(\frac{77}{80}\right)\) | \(e\left(\frac{9}{16}\right)\) |