Basic properties
Modulus: | \(667\) | |
Conductor: | \(667\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(77\) | 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.s
\(\chi_{667}(16,\cdot)\) \(\chi_{667}(25,\cdot)\) \(\chi_{667}(36,\cdot)\) \(\chi_{667}(49,\cdot)\) \(\chi_{667}(52,\cdot)\) \(\chi_{667}(54,\cdot)\) \(\chi_{667}(78,\cdot)\) \(\chi_{667}(81,\cdot)\) \(\chi_{667}(82,\cdot)\) \(\chi_{667}(94,\cdot)\) \(\chi_{667}(110,\cdot)\) \(\chi_{667}(123,\cdot)\) \(\chi_{667}(140,\cdot)\) \(\chi_{667}(141,\cdot)\) \(\chi_{667}(165,\cdot)\) \(\chi_{667}(169,\cdot)\) \(\chi_{667}(170,\cdot)\) \(\chi_{667}(190,\cdot)\) \(\chi_{667}(197,\cdot)\) \(\chi_{667}(210,\cdot)\) \(\chi_{667}(219,\cdot)\) \(\chi_{667}(223,\cdot)\) \(\chi_{667}(239,\cdot)\) \(\chi_{667}(248,\cdot)\) \(\chi_{667}(255,\cdot)\) \(\chi_{667}(256,\cdot)\) \(\chi_{667}(257,\cdot)\) \(\chi_{667}(284,\cdot)\) \(\chi_{667}(285,\cdot)\) \(\chi_{667}(315,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{77})$ |
Fixed field: | Number field defined by a degree 77 polynomial |
Values on generators
\((465,553)\) → \((e\left(\frac{4}{11}\right),e\left(\frac{1}{7}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 667 }(16, a) \) | \(1\) | \(1\) | \(e\left(\frac{67}{77}\right)\) | \(e\left(\frac{41}{77}\right)\) | \(e\left(\frac{57}{77}\right)\) | \(e\left(\frac{39}{77}\right)\) | \(e\left(\frac{31}{77}\right)\) | \(e\left(\frac{48}{77}\right)\) | \(e\left(\frac{47}{77}\right)\) | \(e\left(\frac{5}{77}\right)\) | \(e\left(\frac{29}{77}\right)\) | \(e\left(\frac{65}{77}\right)\) |