Basic properties
| Modulus: | \(2000\) | |
| Conductor: | \(2000\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(100\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2000.bz
\(\chi_{2000}(13,\cdot)\) \(\chi_{2000}(37,\cdot)\) \(\chi_{2000}(117,\cdot)\) \(\chi_{2000}(173,\cdot)\) \(\chi_{2000}(197,\cdot)\) \(\chi_{2000}(253,\cdot)\) \(\chi_{2000}(277,\cdot)\) \(\chi_{2000}(333,\cdot)\) \(\chi_{2000}(413,\cdot)\) \(\chi_{2000}(437,\cdot)\) \(\chi_{2000}(517,\cdot)\) \(\chi_{2000}(573,\cdot)\) \(\chi_{2000}(597,\cdot)\) \(\chi_{2000}(653,\cdot)\) \(\chi_{2000}(677,\cdot)\) \(\chi_{2000}(733,\cdot)\) \(\chi_{2000}(813,\cdot)\) \(\chi_{2000}(837,\cdot)\) \(\chi_{2000}(917,\cdot)\) \(\chi_{2000}(973,\cdot)\) \(\chi_{2000}(997,\cdot)\) \(\chi_{2000}(1053,\cdot)\) \(\chi_{2000}(1077,\cdot)\) \(\chi_{2000}(1133,\cdot)\) \(\chi_{2000}(1213,\cdot)\) \(\chi_{2000}(1237,\cdot)\) \(\chi_{2000}(1317,\cdot)\) \(\chi_{2000}(1373,\cdot)\) \(\chi_{2000}(1397,\cdot)\) \(\chi_{2000}(1453,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{100})$ |
| Fixed field: | Number field defined by a degree 100 polynomial |
Values on generators
\((751,501,1377)\) → \((1,i,e\left(\frac{57}{100}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 2000 }(997, a) \) | \(-1\) | \(1\) | \(e\left(\frac{37}{50}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{12}{25}\right)\) | \(e\left(\frac{57}{100}\right)\) | \(e\left(\frac{49}{50}\right)\) | \(e\left(\frac{61}{100}\right)\) | \(e\left(\frac{1}{100}\right)\) | \(e\left(\frac{69}{100}\right)\) | \(e\left(\frac{17}{100}\right)\) | \(e\left(\frac{11}{50}\right)\) |