Basic properties
Modulus: | \(4730\) | |
Conductor: | \(2365\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(420\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{2365}(1017,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4730.do
\(\chi_{4730}(3,\cdot)\) \(\chi_{4730}(147,\cdot)\) \(\chi_{4730}(157,\cdot)\) \(\chi_{4730}(163,\cdot)\) \(\chi_{4730}(313,\cdot)\) \(\chi_{4730}(377,\cdot)\) \(\chi_{4730}(433,\cdot)\) \(\chi_{4730}(493,\cdot)\) \(\chi_{4730}(577,\cdot)\) \(\chi_{4730}(587,\cdot)\) \(\chi_{4730}(663,\cdot)\) \(\chi_{4730}(707,\cdot)\) \(\chi_{4730}(757,\cdot)\) \(\chi_{4730}(807,\cdot)\) \(\chi_{4730}(863,\cdot)\) \(\chi_{4730}(933,\cdot)\) \(\chi_{4730}(1017,\cdot)\) \(\chi_{4730}(1037,\cdot)\) \(\chi_{4730}(1087,\cdot)\) \(\chi_{4730}(1093,\cdot)\) \(\chi_{4730}(1103,\cdot)\) \(\chi_{4730}(1137,\cdot)\) \(\chi_{4730}(1147,\cdot)\) \(\chi_{4730}(1237,\cdot)\) \(\chi_{4730}(1323,\cdot)\) \(\chi_{4730}(1367,\cdot)\) \(\chi_{4730}(1467,\cdot)\) \(\chi_{4730}(1523,\cdot)\) \(\chi_{4730}(1533,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{420})$ |
Fixed field: | Number field defined by a degree 420 polynomial (not computed) |
Values on generators
\((947,431,1981)\) → \((i,e\left(\frac{2}{5}\right),e\left(\frac{5}{42}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
\( \chi_{ 4730 }(1017, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{420}\right)\) | \(e\left(\frac{13}{60}\right)\) | \(e\left(\frac{29}{210}\right)\) | \(e\left(\frac{403}{420}\right)\) | \(e\left(\frac{157}{420}\right)\) | \(e\left(\frac{101}{105}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{55}{84}\right)\) | \(e\left(\frac{29}{140}\right)\) | \(e\left(\frac{19}{105}\right)\) |