Basic properties
Modulus: | \(2450\) | |
Conductor: | \(1225\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(70\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{1225}(419,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2450.bl
\(\chi_{2450}(69,\cdot)\) \(\chi_{2450}(139,\cdot)\) \(\chi_{2450}(209,\cdot)\) \(\chi_{2450}(279,\cdot)\) \(\chi_{2450}(419,\cdot)\) \(\chi_{2450}(559,\cdot)\) \(\chi_{2450}(629,\cdot)\) \(\chi_{2450}(769,\cdot)\) \(\chi_{2450}(839,\cdot)\) \(\chi_{2450}(909,\cdot)\) \(\chi_{2450}(1119,\cdot)\) \(\chi_{2450}(1189,\cdot)\) \(\chi_{2450}(1259,\cdot)\) \(\chi_{2450}(1329,\cdot)\) \(\chi_{2450}(1539,\cdot)\) \(\chi_{2450}(1609,\cdot)\) \(\chi_{2450}(1679,\cdot)\) \(\chi_{2450}(1819,\cdot)\) \(\chi_{2450}(1889,\cdot)\) \(\chi_{2450}(2029,\cdot)\) \(\chi_{2450}(2169,\cdot)\) \(\chi_{2450}(2239,\cdot)\) \(\chi_{2450}(2309,\cdot)\) \(\chi_{2450}(2379,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{35})$ |
Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((1177,101)\) → \((e\left(\frac{9}{10}\right),e\left(\frac{1}{14}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) |
\( \chi_{ 2450 }(419, a) \) | \(-1\) | \(1\) | \(e\left(\frac{13}{35}\right)\) | \(e\left(\frac{26}{35}\right)\) | \(e\left(\frac{9}{35}\right)\) | \(e\left(\frac{16}{35}\right)\) | \(e\left(\frac{17}{35}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{43}{70}\right)\) | \(e\left(\frac{4}{35}\right)\) | \(e\left(\frac{3}{35}\right)\) | \(e\left(\frac{7}{10}\right)\) |