Basic properties
Modulus: | \(8664\) | |
Conductor: | \(361\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(171\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{361}(25,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8664.dc
\(\chi_{8664}(25,\cdot)\) \(\chi_{8664}(73,\cdot)\) \(\chi_{8664}(169,\cdot)\) \(\chi_{8664}(289,\cdot)\) \(\chi_{8664}(313,\cdot)\) \(\chi_{8664}(385,\cdot)\) \(\chi_{8664}(481,\cdot)\) \(\chi_{8664}(529,\cdot)\) \(\chi_{8664}(625,\cdot)\) \(\chi_{8664}(745,\cdot)\) \(\chi_{8664}(769,\cdot)\) \(\chi_{8664}(841,\cdot)\) \(\chi_{8664}(937,\cdot)\) \(\chi_{8664}(985,\cdot)\) \(\chi_{8664}(1081,\cdot)\) \(\chi_{8664}(1201,\cdot)\) \(\chi_{8664}(1225,\cdot)\) \(\chi_{8664}(1297,\cdot)\) \(\chi_{8664}(1393,\cdot)\) \(\chi_{8664}(1441,\cdot)\) \(\chi_{8664}(1537,\cdot)\) \(\chi_{8664}(1657,\cdot)\) \(\chi_{8664}(1681,\cdot)\) \(\chi_{8664}(1753,\cdot)\) \(\chi_{8664}(1849,\cdot)\) \(\chi_{8664}(1897,\cdot)\) \(\chi_{8664}(1993,\cdot)\) \(\chi_{8664}(2113,\cdot)\) \(\chi_{8664}(2137,\cdot)\) \(\chi_{8664}(2209,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{171})$ |
Fixed field: | Number field defined by a degree 171 polynomial (not computed) |
Values on generators
\((2167,4333,5777,8305)\) → \((1,1,1,e\left(\frac{61}{171}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
\( \chi_{ 8664 }(25, a) \) | \(1\) | \(1\) | \(e\left(\frac{130}{171}\right)\) | \(e\left(\frac{29}{57}\right)\) | \(e\left(\frac{22}{57}\right)\) | \(e\left(\frac{62}{171}\right)\) | \(e\left(\frac{106}{171}\right)\) | \(e\left(\frac{14}{171}\right)\) | \(e\left(\frac{89}{171}\right)\) | \(e\left(\frac{11}{171}\right)\) | \(e\left(\frac{5}{57}\right)\) | \(e\left(\frac{46}{171}\right)\) |