Basic properties
Modulus: | \(2667\) | |
Conductor: | \(381\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(126\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{381}(29,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2667.ew
\(\chi_{2667}(29,\cdot)\) \(\chi_{2667}(92,\cdot)\) \(\chi_{2667}(134,\cdot)\) \(\chi_{2667}(218,\cdot)\) \(\chi_{2667}(239,\cdot)\) \(\chi_{2667}(260,\cdot)\) \(\chi_{2667}(302,\cdot)\) \(\chi_{2667}(491,\cdot)\) \(\chi_{2667}(554,\cdot)\) \(\chi_{2667}(575,\cdot)\) \(\chi_{2667}(617,\cdot)\) \(\chi_{2667}(638,\cdot)\) \(\chi_{2667}(680,\cdot)\) \(\chi_{2667}(785,\cdot)\) \(\chi_{2667}(827,\cdot)\) \(\chi_{2667}(848,\cdot)\) \(\chi_{2667}(932,\cdot)\) \(\chi_{2667}(974,\cdot)\) \(\chi_{2667}(995,\cdot)\) \(\chi_{2667}(1226,\cdot)\) \(\chi_{2667}(1436,\cdot)\) \(\chi_{2667}(1625,\cdot)\) \(\chi_{2667}(1709,\cdot)\) \(\chi_{2667}(1835,\cdot)\) \(\chi_{2667}(1856,\cdot)\) \(\chi_{2667}(1919,\cdot)\) \(\chi_{2667}(1961,\cdot)\) \(\chi_{2667}(2087,\cdot)\) \(\chi_{2667}(2129,\cdot)\) \(\chi_{2667}(2150,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{63})$ |
Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((890,1144,2416)\) → \((-1,1,e\left(\frac{113}{126}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 2667 }(29, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{25}{42}\right)\) | \(e\left(\frac{61}{126}\right)\) | \(e\left(\frac{19}{63}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{73}{126}\right)\) | \(e\left(\frac{1}{3}\right)\) |