Basic properties
| Modulus: | \(187200\) | |
| Conductor: | \(187200\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(240\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| 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 187200.dri
\(\chi_{187200}(77,\cdot)\) \(\chi_{187200}(1013,\cdot)\) \(\chi_{187200}(3197,\cdot)\) \(\chi_{187200}(4133,\cdot)\) \(\chi_{187200}(9437,\cdot)\) \(\chi_{187200}(10373,\cdot)\) \(\chi_{187200}(18797,\cdot)\) \(\chi_{187200}(19733,\cdot)\) \(\chi_{187200}(21917,\cdot)\) \(\chi_{187200}(22853,\cdot)\) \(\chi_{187200}(31277,\cdot)\) \(\chi_{187200}(32213,\cdot)\) \(\chi_{187200}(37517,\cdot)\) \(\chi_{187200}(38453,\cdot)\) \(\chi_{187200}(40637,\cdot)\) \(\chi_{187200}(41573,\cdot)\) \(\chi_{187200}(46877,\cdot)\) \(\chi_{187200}(47813,\cdot)\) \(\chi_{187200}(49997,\cdot)\) \(\chi_{187200}(50933,\cdot)\) \(\chi_{187200}(56237,\cdot)\) \(\chi_{187200}(57173,\cdot)\) \(\chi_{187200}(65597,\cdot)\) \(\chi_{187200}(66533,\cdot)\) \(\chi_{187200}(68717,\cdot)\) \(\chi_{187200}(69653,\cdot)\) \(\chi_{187200}(78077,\cdot)\) \(\chi_{187200}(79013,\cdot)\) \(\chi_{187200}(84317,\cdot)\) \(\chi_{187200}(85253,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{240})$ |
| Fixed field: | Number field defined by a degree 240 polynomial (not computed) |
Values on generators
\((157951,58501,20801,14977,43201)\) → \((1,e\left(\frac{15}{16}\right),e\left(\frac{5}{6}\right),e\left(\frac{1}{20}\right),-1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 187200 }(77, a) \) | \(1\) | \(1\) | \(e\left(\frac{11}{24}\right)\) | \(e\left(\frac{197}{240}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{77}{80}\right)\) | \(e\left(\frac{101}{120}\right)\) | \(e\left(\frac{59}{240}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{31}{80}\right)\) | \(e\left(\frac{119}{120}\right)\) | \(e\left(\frac{13}{48}\right)\) |