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Modulus Conductor Order Induced by
Parity Primitive Minimal Real
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Orbit label Conrey labels Modulus Conductor Order Value field Parity Real Primitive Minimal
17.d

\(\chi_{17}(2, \cdot)\)$, \cdots ,$\(\chi_{17}(15, \cdot)\)

$17$ $17$ $8$ \(\Q(\zeta_{8})\) even ✓ ✓
32.g

\(\chi_{32}(5, \cdot)\)$, \cdots ,$\(\chi_{32}(29, \cdot)\)

$32$ $32$ $8$ \(\Q(\zeta_{8})\) even ✓ ✓
32.h

\(\chi_{32}(3, \cdot)\)$, \cdots ,$\(\chi_{32}(27, \cdot)\)

$32$ $32$ $8$ \(\Q(\zeta_{8})\) odd ✓ ✓
34.d

\(\chi_{34}(9, \cdot)\)$, \cdots ,$\(\chi_{34}(25, \cdot)\)

$34$ $17$ $8$ \(\Q(\zeta_{8})\) even ✓
41.e

\(\chi_{41}(3, \cdot)\)$, \cdots ,$\(\chi_{41}(38, \cdot)\)

$41$ $41$ $8$ \(\Q(\zeta_{8})\) odd ✓ ✓
51.g

\(\chi_{51}(2, \cdot)\)$, \cdots ,$\(\chi_{51}(32, \cdot)\)

$51$ $51$ $8$ \(\Q(\zeta_{8})\) odd ✓ ✓
51.h

\(\chi_{51}(19, \cdot)\)$, \cdots ,$\(\chi_{51}(49, \cdot)\)

$51$ $17$ $8$ \(\Q(\zeta_{8})\) even ✓
64.g

\(\chi_{64}(9, \cdot)\)$, \cdots ,$\(\chi_{64}(57, \cdot)\)

$64$ $32$ $8$ \(\Q(\zeta_{8})\) even
64.h

\(\chi_{64}(7, \cdot)\)$, \cdots ,$\(\chi_{64}(55, \cdot)\)

$64$ $32$ $8$ \(\Q(\zeta_{8})\) odd
68.g

\(\chi_{68}(15, \cdot)\)$, \cdots ,$\(\chi_{68}(59, \cdot)\)

$68$ $68$ $8$ \(\Q(\zeta_{8})\) odd ✓ ✓
68.h

\(\chi_{68}(9, \cdot)\)$, \cdots ,$\(\chi_{68}(53, \cdot)\)

$68$ $17$ $8$ \(\Q(\zeta_{8})\) even ✓
73.f

\(\chi_{73}(10, \cdot)\)$, \cdots ,$\(\chi_{73}(63, \cdot)\)

$73$ $73$ $8$ \(\Q(\zeta_{8})\) odd ✓ ✓
82.e

\(\chi_{82}(3, \cdot)\)$, \cdots ,$\(\chi_{82}(79, \cdot)\)

$82$ $41$ $8$ \(\Q(\zeta_{8})\) odd ✓
85.k

\(\chi_{85}(2, \cdot)\)$, \cdots ,$\(\chi_{85}(43, \cdot)\)

$85$ $85$ $8$ \(\Q(\zeta_{8})\) odd ✓ ✓
85.l

\(\chi_{85}(26, \cdot)\)$, \cdots ,$\(\chi_{85}(76, \cdot)\)

$85$ $17$ $8$ \(\Q(\zeta_{8})\) even ✓
85.m

\(\chi_{85}(9, \cdot)\)$, \cdots ,$\(\chi_{85}(59, \cdot)\)

$85$ $85$ $8$ \(\Q(\zeta_{8})\) even ✓ ✓
85.n

\(\chi_{85}(42, \cdot)\)$, \cdots ,$\(\chi_{85}(83, \cdot)\)

$85$ $85$ $8$ \(\Q(\zeta_{8})\) odd ✓ ✓
89.d

\(\chi_{89}(12, \cdot)\)$, \cdots ,$\(\chi_{89}(77, \cdot)\)

$89$ $89$ $8$ \(\Q(\zeta_{8})\) odd ✓ ✓
96.m

\(\chi_{96}(19, \cdot)\)$, \cdots ,$\(\chi_{96}(91, \cdot)\)

$96$ $32$ $8$ \(\Q(\zeta_{8})\) odd ✓
96.n

\(\chi_{96}(13, \cdot)\)$, \cdots ,$\(\chi_{96}(85, \cdot)\)

$96$ $32$ $8$ \(\Q(\zeta_{8})\) even ✓
96.o

\(\chi_{96}(11, \cdot)\)$, \cdots ,$\(\chi_{96}(83, \cdot)\)

$96$ $96$ $8$ \(\Q(\zeta_{8})\) even ✓ ✓
96.p

\(\chi_{96}(5, \cdot)\)$, \cdots ,$\(\chi_{96}(77, \cdot)\)

$96$ $96$ $8$ \(\Q(\zeta_{8})\) odd ✓ ✓
97.f

\(\chi_{97}(33, \cdot)\)$, \cdots ,$\(\chi_{97}(64, \cdot)\)

$97$ $97$ $8$ \(\Q(\zeta_{8})\) even ✓ ✓
102.g

\(\chi_{102}(53, \cdot)\)$, \cdots ,$\(\chi_{102}(83, \cdot)\)

$102$ $51$ $8$ \(\Q(\zeta_{8})\) odd ✓
102.h

\(\chi_{102}(19, \cdot)\)$, \cdots ,$\(\chi_{102}(49, \cdot)\)

$102$ $17$ $8$ \(\Q(\zeta_{8})\) even ✓
113.e

\(\chi_{113}(18, \cdot)\)$, \cdots ,$\(\chi_{113}(95, \cdot)\)

$113$ $113$ $8$ \(\Q(\zeta_{8})\) even ✓ ✓
119.k

\(\chi_{119}(8, \cdot)\)$, \cdots ,$\(\chi_{119}(43, \cdot)\)

$119$ $17$ $8$ \(\Q(\zeta_{8})\) even ✓
119.l

\(\chi_{119}(76, \cdot)\)$, \cdots ,$\(\chi_{119}(111, \cdot)\)

$119$ $119$ $8$ \(\Q(\zeta_{8})\) odd ✓ ✓
123.h

\(\chi_{123}(55, \cdot)\)$, \cdots ,$\(\chi_{123}(109, \cdot)\)

$123$ $41$ $8$ \(\Q(\zeta_{8})\) odd ✓
123.i

\(\chi_{123}(14, \cdot)\)$, \cdots ,$\(\chi_{123}(68, \cdot)\)

$123$ $123$ $8$ \(\Q(\zeta_{8})\) even ✓ ✓
128.g

\(\chi_{128}(17, \cdot)\)$, \cdots ,$\(\chi_{128}(113, \cdot)\)

$128$ $32$ $8$ \(\Q(\zeta_{8})\) even
128.h

\(\chi_{128}(15, \cdot)\)$, \cdots ,$\(\chi_{128}(111, \cdot)\)

$128$ $32$ $8$ \(\Q(\zeta_{8})\) odd
136.m

\(\chi_{136}(15, \cdot)\)$, \cdots ,$\(\chi_{136}(127, \cdot)\)

$136$ $68$ $8$ \(\Q(\zeta_{8})\) odd
136.n

\(\chi_{136}(9, \cdot)\)$, \cdots ,$\(\chi_{136}(121, \cdot)\)

$136$ $17$ $8$ \(\Q(\zeta_{8})\) even ✓
136.o

\(\chi_{136}(53, \cdot)\)$, \cdots ,$\(\chi_{136}(117, \cdot)\)

$136$ $136$ $8$ \(\Q(\zeta_{8})\) even ✓ ✓
136.p

\(\chi_{136}(19, \cdot)\)$, \cdots ,$\(\chi_{136}(83, \cdot)\)

$136$ $136$ $8$ \(\Q(\zeta_{8})\) odd ✓ ✓
137.d

\(\chi_{137}(10, \cdot)\)$, \cdots ,$\(\chi_{137}(127, \cdot)\)

$137$ $137$ $8$ \(\Q(\zeta_{8})\) odd ✓ ✓
146.f

\(\chi_{146}(51, \cdot)\)$, \cdots ,$\(\chi_{146}(95, \cdot)\)

$146$ $73$ $8$ \(\Q(\zeta_{8})\) odd ✓
153.k

\(\chi_{153}(8, \cdot)\)$, \cdots ,$\(\chi_{153}(134, \cdot)\)

$153$ $51$ $8$ \(\Q(\zeta_{8})\) odd ✓
153.l

\(\chi_{153}(19, \cdot)\)$, \cdots ,$\(\chi_{153}(145, \cdot)\)

$153$ $17$ $8$ \(\Q(\zeta_{8})\) even ✓
160.u

\(\chi_{160}(43, \cdot)\)$, \cdots ,$\(\chi_{160}(147, \cdot)\)

$160$ $160$ $8$ \(\Q(\zeta_{8})\) even ✓ ✓
160.v

\(\chi_{160}(13, \cdot)\)$, \cdots ,$\(\chi_{160}(117, \cdot)\)

$160$ $160$ $8$ \(\Q(\zeta_{8})\) odd ✓ ✓
160.w

\(\chi_{160}(11, \cdot)\)$, \cdots ,$\(\chi_{160}(131, \cdot)\)

$160$ $32$ $8$ \(\Q(\zeta_{8})\) odd ✓
160.x

\(\chi_{160}(21, \cdot)\)$, \cdots ,$\(\chi_{160}(141, \cdot)\)

$160$ $32$ $8$ \(\Q(\zeta_{8})\) even ✓
160.y

\(\chi_{160}(19, \cdot)\)$, \cdots ,$\(\chi_{160}(139, \cdot)\)

$160$ $160$ $8$ \(\Q(\zeta_{8})\) odd ✓ ✓
160.z

\(\chi_{160}(29, \cdot)\)$, \cdots ,$\(\chi_{160}(149, \cdot)\)

$160$ $160$ $8$ \(\Q(\zeta_{8})\) even ✓ ✓
160.ba

\(\chi_{160}(3, \cdot)\)$, \cdots ,$\(\chi_{160}(107, \cdot)\)

$160$ $160$ $8$ \(\Q(\zeta_{8})\) even ✓ ✓
160.bb

\(\chi_{160}(53, \cdot)\)$, \cdots ,$\(\chi_{160}(157, \cdot)\)

$160$ $160$ $8$ \(\Q(\zeta_{8})\) odd ✓ ✓
164.h

\(\chi_{164}(85, \cdot)\)$, \cdots ,$\(\chi_{164}(161, \cdot)\)

$164$ $41$ $8$ \(\Q(\zeta_{8})\) odd ✓
164.i

\(\chi_{164}(3, \cdot)\)$, \cdots ,$\(\chi_{164}(79, \cdot)\)

$164$ $164$ $8$ \(\Q(\zeta_{8})\) even ✓ ✓
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