Basic properties
| Modulus: | \(750\) | |
| Conductor: | \(375\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(100\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{375}(83,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 750.r
\(\chi_{750}(17,\cdot)\) \(\chi_{750}(23,\cdot)\) \(\chi_{750}(47,\cdot)\) \(\chi_{750}(53,\cdot)\) \(\chi_{750}(77,\cdot)\) \(\chi_{750}(83,\cdot)\) \(\chi_{750}(113,\cdot)\) \(\chi_{750}(137,\cdot)\) \(\chi_{750}(167,\cdot)\) \(\chi_{750}(173,\cdot)\) \(\chi_{750}(197,\cdot)\) \(\chi_{750}(203,\cdot)\) \(\chi_{750}(227,\cdot)\) \(\chi_{750}(233,\cdot)\) \(\chi_{750}(263,\cdot)\) \(\chi_{750}(287,\cdot)\) \(\chi_{750}(317,\cdot)\) \(\chi_{750}(323,\cdot)\) \(\chi_{750}(347,\cdot)\) \(\chi_{750}(353,\cdot)\) \(\chi_{750}(377,\cdot)\) \(\chi_{750}(383,\cdot)\) \(\chi_{750}(413,\cdot)\) \(\chi_{750}(437,\cdot)\) \(\chi_{750}(467,\cdot)\) \(\chi_{750}(473,\cdot)\) \(\chi_{750}(497,\cdot)\) \(\chi_{750}(503,\cdot)\) \(\chi_{750}(527,\cdot)\) \(\chi_{750}(533,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{100})$ |
| Fixed field: | Number field defined by a degree 100 polynomial |
Values on generators
\((251,127)\) → \((-1,e\left(\frac{43}{100}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 750 }(83, a) \) | \(1\) | \(1\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{9}{50}\right)\) | \(e\left(\frac{77}{100}\right)\) | \(e\left(\frac{89}{100}\right)\) | \(e\left(\frac{37}{50}\right)\) | \(e\left(\frac{83}{100}\right)\) | \(e\left(\frac{4}{25}\right)\) | \(e\left(\frac{16}{25}\right)\) | \(e\left(\frac{47}{100}\right)\) | \(e\left(\frac{21}{50}\right)\) |