Basic properties
Modulus: | \(7098\) | |
Conductor: | \(1183\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(52\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{1183}(356,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7098.cu
\(\chi_{7098}(265,\cdot)\) \(\chi_{7098}(307,\cdot)\) \(\chi_{7098}(811,\cdot)\) \(\chi_{7098}(853,\cdot)\) \(\chi_{7098}(1357,\cdot)\) \(\chi_{7098}(1399,\cdot)\) \(\chi_{7098}(1903,\cdot)\) \(\chi_{7098}(1945,\cdot)\) \(\chi_{7098}(2449,\cdot)\) \(\chi_{7098}(2491,\cdot)\) \(\chi_{7098}(2995,\cdot)\) \(\chi_{7098}(3037,\cdot)\) \(\chi_{7098}(3541,\cdot)\) \(\chi_{7098}(3583,\cdot)\) \(\chi_{7098}(4087,\cdot)\) \(\chi_{7098}(4129,\cdot)\) \(\chi_{7098}(4675,\cdot)\) \(\chi_{7098}(5179,\cdot)\) \(\chi_{7098}(5221,\cdot)\) \(\chi_{7098}(5725,\cdot)\) \(\chi_{7098}(5767,\cdot)\) \(\chi_{7098}(6271,\cdot)\) \(\chi_{7098}(6313,\cdot)\) \(\chi_{7098}(6817,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{52})$ |
Fixed field: | Number field defined by a degree 52 polynomial |
Values on generators
\((4733,5071,6931)\) → \((1,-1,e\left(\frac{31}{52}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
\( \chi_{ 7098 }(6271, a) \) | \(1\) | \(1\) | \(e\left(\frac{45}{52}\right)\) | \(e\left(\frac{21}{52}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(i\) | \(-1\) | \(e\left(\frac{19}{26}\right)\) | \(e\left(\frac{11}{13}\right)\) | \(e\left(\frac{1}{52}\right)\) | \(e\left(\frac{1}{52}\right)\) | \(e\left(\frac{9}{52}\right)\) |