Basic properties
Modulus: | \(667\) | |
Conductor: | \(667\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(154\) | 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 667.u
\(\chi_{667}(4,\cdot)\) \(\chi_{667}(6,\cdot)\) \(\chi_{667}(9,\cdot)\) \(\chi_{667}(13,\cdot)\) \(\chi_{667}(35,\cdot)\) \(\chi_{667}(62,\cdot)\) \(\chi_{667}(64,\cdot)\) \(\chi_{667}(71,\cdot)\) \(\chi_{667}(96,\cdot)\) \(\chi_{667}(100,\cdot)\) \(\chi_{667}(121,\cdot)\) \(\chi_{667}(150,\cdot)\) \(\chi_{667}(151,\cdot)\) \(\chi_{667}(154,\cdot)\) \(\chi_{667}(167,\cdot)\) \(\chi_{667}(179,\cdot)\) \(\chi_{667}(187,\cdot)\) \(\chi_{667}(196,\cdot)\) \(\chi_{667}(209,\cdot)\) \(\chi_{667}(216,\cdot)\) \(\chi_{667}(225,\cdot)\) \(\chi_{667}(236,\cdot)\) \(\chi_{667}(238,\cdot)\) \(\chi_{667}(265,\cdot)\) \(\chi_{667}(266,\cdot)\) \(\chi_{667}(294,\cdot)\) \(\chi_{667}(303,\cdot)\) \(\chi_{667}(312,\cdot)\) \(\chi_{667}(324,\cdot)\) \(\chi_{667}(325,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{77})$ |
Fixed field: | Number field defined by a degree 154 polynomial (not computed) |
Values on generators
\((465,553)\) → \((e\left(\frac{4}{11}\right),e\left(\frac{1}{14}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 667 }(62, a) \) | \(1\) | \(1\) | \(e\left(\frac{123}{154}\right)\) | \(e\left(\frac{27}{154}\right)\) | \(e\left(\frac{46}{77}\right)\) | \(e\left(\frac{72}{77}\right)\) | \(e\left(\frac{75}{77}\right)\) | \(e\left(\frac{59}{77}\right)\) | \(e\left(\frac{61}{154}\right)\) | \(e\left(\frac{27}{77}\right)\) | \(e\left(\frac{113}{154}\right)\) | \(e\left(\frac{9}{154}\right)\) |