Basic properties
Modulus: | \(8820\) | |
Conductor: | \(245\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(84\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{245}(73,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8820.iv
\(\chi_{8820}(73,\cdot)\) \(\chi_{8820}(397,\cdot)\) \(\chi_{8820}(577,\cdot)\) \(\chi_{8820}(1153,\cdot)\) \(\chi_{8820}(1333,\cdot)\) \(\chi_{8820}(1657,\cdot)\) \(\chi_{8820}(1837,\cdot)\) \(\chi_{8820}(2413,\cdot)\) \(\chi_{8820}(2593,\cdot)\) \(\chi_{8820}(2917,\cdot)\) \(\chi_{8820}(3097,\cdot)\) \(\chi_{8820}(3673,\cdot)\) \(\chi_{8820}(4177,\cdot)\) \(\chi_{8820}(4357,\cdot)\) \(\chi_{8820}(4933,\cdot)\) \(\chi_{8820}(5113,\cdot)\) \(\chi_{8820}(5437,\cdot)\) \(\chi_{8820}(6373,\cdot)\) \(\chi_{8820}(6697,\cdot)\) \(\chi_{8820}(6877,\cdot)\) \(\chi_{8820}(7453,\cdot)\) \(\chi_{8820}(7633,\cdot)\) \(\chi_{8820}(8137,\cdot)\) \(\chi_{8820}(8713,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((4411,7841,7057,1081)\) → \((1,1,-i,e\left(\frac{37}{42}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
\( \chi_{ 8820 }(73, a) \) | \(1\) | \(1\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{9}{28}\right)\) | \(e\left(\frac{65}{84}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{61}{84}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{79}{84}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{15}{28}\right)\) |