Basic properties
Modulus: | \(1205\) | |
Conductor: | \(1205\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(80\) | 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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1205.cl
\(\chi_{1205}(17,\cdot)\) \(\chi_{1205}(23,\cdot)\) \(\chi_{1205}(28,\cdot)\) \(\chi_{1205}(57,\cdot)\) \(\chi_{1205}(73,\cdot)\) \(\chi_{1205}(93,\cdot)\) \(\chi_{1205}(102,\cdot)\) \(\chi_{1205}(103,\cdot)\) \(\chi_{1205}(117,\cdot)\) \(\chi_{1205}(138,\cdot)\) \(\chi_{1205}(148,\cdot)\) \(\chi_{1205}(168,\cdot)\) \(\chi_{1205}(213,\cdot)\) \(\chi_{1205}(218,\cdot)\) \(\chi_{1205}(262,\cdot)\) \(\chi_{1205}(342,\cdot)\) \(\chi_{1205}(508,\cdot)\) \(\chi_{1205}(618,\cdot)\) \(\chi_{1205}(622,\cdot)\) \(\chi_{1205}(638,\cdot)\) \(\chi_{1205}(702,\cdot)\) \(\chi_{1205}(808,\cdot)\) \(\chi_{1205}(828,\cdot)\) \(\chi_{1205}(847,\cdot)\) \(\chi_{1205}(862,\cdot)\) \(\chi_{1205}(907,\cdot)\) \(\chi_{1205}(938,\cdot)\) \(\chi_{1205}(947,\cdot)\) \(\chi_{1205}(997,\cdot)\) \(\chi_{1205}(1007,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{80})$ |
Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((242,971)\) → \((i,e\left(\frac{37}{80}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
\( \chi_{ 1205 }(17, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{37}{40}\right)\) | \(i\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{57}{80}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{7}{40}\right)\) | \(e\left(\frac{39}{80}\right)\) |