Basic properties
Modulus: | \(7581\) | |
Conductor: | \(2527\) | 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 \(\chi_{2527}(16,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
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Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7581.ea
\(\chi_{7581}(4,\cdot)\) \(\chi_{7581}(16,\cdot)\) \(\chi_{7581}(25,\cdot)\) \(\chi_{7581}(100,\cdot)\) \(\chi_{7581}(226,\cdot)\) \(\chi_{7581}(256,\cdot)\) \(\chi_{7581}(403,\cdot)\) \(\chi_{7581}(424,\cdot)\) \(\chi_{7581}(499,\cdot)\) \(\chi_{7581}(625,\cdot)\) \(\chi_{7581}(655,\cdot)\) \(\chi_{7581}(802,\cdot)\) \(\chi_{7581}(814,\cdot)\) \(\chi_{7581}(823,\cdot)\) \(\chi_{7581}(898,\cdot)\) \(\chi_{7581}(1024,\cdot)\) \(\chi_{7581}(1054,\cdot)\) \(\chi_{7581}(1201,\cdot)\) \(\chi_{7581}(1213,\cdot)\) \(\chi_{7581}(1222,\cdot)\) \(\chi_{7581}(1297,\cdot)\) \(\chi_{7581}(1423,\cdot)\) \(\chi_{7581}(1453,\cdot)\) \(\chi_{7581}(1600,\cdot)\) \(\chi_{7581}(1612,\cdot)\) \(\chi_{7581}(1621,\cdot)\) \(\chi_{7581}(1696,\cdot)\) \(\chi_{7581}(1822,\cdot)\) \(\chi_{7581}(1852,\cdot)\) \(\chi_{7581}(1999,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{171})$ |
Fixed field: | Number field defined by a degree 171 polynomial (not computed) |
Values on generators
\((2528,6499,1807)\) → \((1,e\left(\frac{1}{3}\right),e\left(\frac{2}{171}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(20\) |
\( \chi_{ 7581 }(16, a) \) | \(1\) | \(1\) | \(e\left(\frac{116}{171}\right)\) | \(e\left(\frac{61}{171}\right)\) | \(e\left(\frac{65}{171}\right)\) | \(e\left(\frac{2}{57}\right)\) | \(e\left(\frac{10}{171}\right)\) | \(e\left(\frac{10}{19}\right)\) | \(e\left(\frac{145}{171}\right)\) | \(e\left(\frac{122}{171}\right)\) | \(e\left(\frac{167}{171}\right)\) | \(e\left(\frac{14}{19}\right)\) |