Basic properties
Modulus: | \(2450\) | |
Conductor: | \(1225\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(210\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{1225}(39,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2450.bt
\(\chi_{2450}(9,\cdot)\) \(\chi_{2450}(39,\cdot)\) \(\chi_{2450}(109,\cdot)\) \(\chi_{2450}(179,\cdot)\) \(\chi_{2450}(219,\cdot)\) \(\chi_{2450}(289,\cdot)\) \(\chi_{2450}(319,\cdot)\) \(\chi_{2450}(359,\cdot)\) \(\chi_{2450}(389,\cdot)\) \(\chi_{2450}(429,\cdot)\) \(\chi_{2450}(529,\cdot)\) \(\chi_{2450}(639,\cdot)\) \(\chi_{2450}(669,\cdot)\) \(\chi_{2450}(709,\cdot)\) \(\chi_{2450}(739,\cdot)\) \(\chi_{2450}(779,\cdot)\) \(\chi_{2450}(809,\cdot)\) \(\chi_{2450}(879,\cdot)\) \(\chi_{2450}(919,\cdot)\) \(\chi_{2450}(989,\cdot)\) \(\chi_{2450}(1019,\cdot)\) \(\chi_{2450}(1089,\cdot)\) \(\chi_{2450}(1129,\cdot)\) \(\chi_{2450}(1159,\cdot)\) \(\chi_{2450}(1229,\cdot)\) \(\chi_{2450}(1269,\cdot)\) \(\chi_{2450}(1339,\cdot)\) \(\chi_{2450}(1369,\cdot)\) \(\chi_{2450}(1409,\cdot)\) \(\chi_{2450}(1479,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{105})$ |
Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((1177,101)\) → \((e\left(\frac{3}{10}\right),e\left(\frac{17}{21}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) |
\( \chi_{ 2450 }(39, a) \) | \(1\) | \(1\) | \(e\left(\frac{191}{210}\right)\) | \(e\left(\frac{86}{105}\right)\) | \(e\left(\frac{19}{105}\right)\) | \(e\left(\frac{29}{70}\right)\) | \(e\left(\frac{29}{210}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{13}{210}\right)\) | \(e\left(\frac{51}{70}\right)\) | \(e\left(\frac{6}{35}\right)\) | \(e\left(\frac{1}{15}\right)\) |