Basic properties
Modulus: | \(8035\) | |
Conductor: | \(1607\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(803\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{1607}(6,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8035.s
\(\chi_{8035}(6,\cdot)\) \(\chi_{8035}(16,\cdot)\) \(\chi_{8035}(31,\cdot)\) \(\chi_{8035}(36,\cdot)\) \(\chi_{8035}(41,\cdot)\) \(\chi_{8035}(46,\cdot)\) \(\chi_{8035}(51,\cdot)\) \(\chi_{8035}(81,\cdot)\) \(\chi_{8035}(91,\cdot)\) \(\chi_{8035}(101,\cdot)\) \(\chi_{8035}(106,\cdot)\) \(\chi_{8035}(111,\cdot)\) \(\chi_{8035}(121,\cdot)\) \(\chi_{8035}(136,\cdot)\) \(\chi_{8035}(146,\cdot)\) \(\chi_{8035}(186,\cdot)\) \(\chi_{8035}(196,\cdot)\) \(\chi_{8035}(201,\cdot)\) \(\chi_{8035}(206,\cdot)\) \(\chi_{8035}(211,\cdot)\) \(\chi_{8035}(216,\cdot)\) \(\chi_{8035}(226,\cdot)\) \(\chi_{8035}(231,\cdot)\) \(\chi_{8035}(236,\cdot)\) \(\chi_{8035}(241,\cdot)\) \(\chi_{8035}(246,\cdot)\) \(\chi_{8035}(256,\cdot)\) \(\chi_{8035}(266,\cdot)\) \(\chi_{8035}(276,\cdot)\) \(\chi_{8035}(281,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{803})$ |
Fixed field: | Number field defined by a degree 803 polynomial (not computed) |
Values on generators
\((4822,4826)\) → \((1,e\left(\frac{125}{803}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
\( \chi_{ 8035 }(6, a) \) | \(1\) | \(1\) | \(e\left(\frac{366}{803}\right)\) | \(e\left(\frac{370}{803}\right)\) | \(e\left(\frac{732}{803}\right)\) | \(e\left(\frac{736}{803}\right)\) | \(e\left(\frac{37}{803}\right)\) | \(e\left(\frac{295}{803}\right)\) | \(e\left(\frac{740}{803}\right)\) | \(e\left(\frac{47}{803}\right)\) | \(e\left(\frac{299}{803}\right)\) | \(e\left(\frac{731}{803}\right)\) |