Basic properties
Modulus: | \(2738\) | |
Conductor: | \(1369\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(333\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{1369}(7,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2738.o
\(\chi_{2738}(7,\cdot)\) \(\chi_{2738}(9,\cdot)\) \(\chi_{2738}(33,\cdot)\) \(\chi_{2738}(49,\cdot)\) \(\chi_{2738}(53,\cdot)\) \(\chi_{2738}(71,\cdot)\) \(\chi_{2738}(81,\cdot)\) \(\chi_{2738}(83,\cdot)\) \(\chi_{2738}(107,\cdot)\) \(\chi_{2738}(123,\cdot)\) \(\chi_{2738}(127,\cdot)\) \(\chi_{2738}(145,\cdot)\) \(\chi_{2738}(155,\cdot)\) \(\chi_{2738}(157,\cdot)\) \(\chi_{2738}(181,\cdot)\) \(\chi_{2738}(197,\cdot)\) \(\chi_{2738}(201,\cdot)\) \(\chi_{2738}(219,\cdot)\) \(\chi_{2738}(229,\cdot)\) \(\chi_{2738}(231,\cdot)\) \(\chi_{2738}(255,\cdot)\) \(\chi_{2738}(271,\cdot)\) \(\chi_{2738}(275,\cdot)\) \(\chi_{2738}(293,\cdot)\) \(\chi_{2738}(303,\cdot)\) \(\chi_{2738}(305,\cdot)\) \(\chi_{2738}(329,\cdot)\) \(\chi_{2738}(345,\cdot)\) \(\chi_{2738}(349,\cdot)\) \(\chi_{2738}(367,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{333})$ |
Fixed field: | Number field defined by a degree 333 polynomial (not computed) |
Values on generators
\(1371\) → \(e\left(\frac{26}{333}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 2738 }(7, a) \) | \(1\) | \(1\) | \(e\left(\frac{172}{333}\right)\) | \(e\left(\frac{184}{333}\right)\) | \(e\left(\frac{40}{333}\right)\) | \(e\left(\frac{11}{333}\right)\) | \(e\left(\frac{104}{111}\right)\) | \(e\left(\frac{322}{333}\right)\) | \(e\left(\frac{23}{333}\right)\) | \(e\left(\frac{56}{333}\right)\) | \(e\left(\frac{244}{333}\right)\) | \(e\left(\frac{212}{333}\right)\) |