Basic properties
Modulus: | \(7098\) | |
Conductor: | \(3549\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(156\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{3549}(2333,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7098.ei
\(\chi_{7098}(11,\cdot)\) \(\chi_{7098}(149,\cdot)\) \(\chi_{7098}(431,\cdot)\) \(\chi_{7098}(527,\cdot)\) \(\chi_{7098}(557,\cdot)\) \(\chi_{7098}(977,\cdot)\) \(\chi_{7098}(1073,\cdot)\) \(\chi_{7098}(1241,\cdot)\) \(\chi_{7098}(1523,\cdot)\) \(\chi_{7098}(1619,\cdot)\) \(\chi_{7098}(1649,\cdot)\) \(\chi_{7098}(1787,\cdot)\) \(\chi_{7098}(2069,\cdot)\) \(\chi_{7098}(2165,\cdot)\) \(\chi_{7098}(2195,\cdot)\) \(\chi_{7098}(2333,\cdot)\) \(\chi_{7098}(2711,\cdot)\) \(\chi_{7098}(2741,\cdot)\) \(\chi_{7098}(2879,\cdot)\) \(\chi_{7098}(3161,\cdot)\) \(\chi_{7098}(3257,\cdot)\) \(\chi_{7098}(3287,\cdot)\) \(\chi_{7098}(3425,\cdot)\) \(\chi_{7098}(3707,\cdot)\) \(\chi_{7098}(3803,\cdot)\) \(\chi_{7098}(3833,\cdot)\) \(\chi_{7098}(3971,\cdot)\) \(\chi_{7098}(4253,\cdot)\) \(\chi_{7098}(4349,\cdot)\) \(\chi_{7098}(4379,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{156})$ |
Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((4733,5071,6931)\) → \((-1,e\left(\frac{1}{3}\right),e\left(\frac{149}{156}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
\( \chi_{ 7098 }(2333, a) \) | \(1\) | \(1\) | \(e\left(\frac{119}{156}\right)\) | \(e\left(\frac{11}{52}\right)\) | \(e\left(\frac{11}{39}\right)\) | \(-i\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{41}{78}\right)\) | \(e\left(\frac{55}{78}\right)\) | \(e\left(\frac{61}{156}\right)\) | \(e\left(\frac{139}{156}\right)\) | \(e\left(\frac{107}{156}\right)\) |