LMFDB - Artin representation search results

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Dimension	Conductor	Group	Root number	Parity

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Results (49 matches)

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Galois conjugate representations are grouped into single lines.

Label	Dimension	Conductor	Ramified prime count	Artin stem field	$G$	Projective image	Container	Ind	$\chi(c)$
1.11.5t1.a.a 1.11.5t1.a.b 1.11.5t1.a.c 1.11.5t1.a.d	$1$	$ 11 $	$1$	$\Q(\zeta_{11})^+$	$C_5$	$C_1$	$C_5$	$0$	$1$
1.25.5t1.a.a 1.25.5t1.a.b 1.25.5t1.a.c 1.25.5t1.a.d	$1$	$ 5^{2}$	$1$	5.5.390625.1	$C_5$	$C_1$	$C_5$	$0$	$1$
1.31.5t1.a.a 1.31.5t1.a.b 1.31.5t1.a.c 1.31.5t1.a.d	$1$	$ 31 $	$1$	5.5.923521.1	$C_5$	$C_1$	$C_5$	$0$	$1$
1.41.5t1.a.a 1.41.5t1.a.b 1.41.5t1.a.c 1.41.5t1.a.d	$1$	$ 41 $	$1$	5.5.2825761.1	$C_5$	$C_1$	$C_5$	$0$	$1$
1.61.5t1.a.a 1.61.5t1.a.b 1.61.5t1.a.c 1.61.5t1.a.d	$1$	$ 61 $	$1$	5.5.13845841.1	$C_5$	$C_1$	$C_5$	$0$	$1$
1.71.5t1.a.a 1.71.5t1.a.b 1.71.5t1.a.c 1.71.5t1.a.d	$1$	$ 71 $	$1$	5.5.25411681.1	$C_5$	$C_1$	$C_5$	$0$	$1$
1.101.5t1.a.a 1.101.5t1.a.b 1.101.5t1.a.c 1.101.5t1.a.d	$1$	$ 101 $	$1$	5.5.104060401.1	$C_5$	$C_1$	$C_5$	$0$	$1$
1.131.5t1.a.a 1.131.5t1.a.b 1.131.5t1.a.c 1.131.5t1.a.d	$1$	$ 131 $	$1$	5.5.294499921.1	$C_5$	$C_1$	$C_5$	$0$	$1$
1.151.5t1.a.a 1.151.5t1.a.b 1.151.5t1.a.c 1.151.5t1.a.d	$1$	$ 151 $	$1$	5.5.519885601.1	$C_5$	$C_1$	$C_5$	$0$	$1$
1.181.5t1.a.a 1.181.5t1.a.b 1.181.5t1.a.c 1.181.5t1.a.d	$1$	$ 181 $	$1$	5.5.1073283121.1	$C_5$	$C_1$	$C_5$	$0$	$1$
1.191.5t1.a.a 1.191.5t1.a.b 1.191.5t1.a.c 1.191.5t1.a.d	$1$	$ 191 $	$1$	5.5.1330863361.1	$C_5$	$C_1$	$C_5$	$0$	$1$
1.211.5t1.a.a 1.211.5t1.a.b 1.211.5t1.a.c 1.211.5t1.a.d	$1$	$ 211 $	$1$	5.5.1982119441.1	$C_5$	$C_1$	$C_5$	$0$	$1$
1.241.5t1.a.a 1.241.5t1.a.b 1.241.5t1.a.c 1.241.5t1.a.d	$1$	$ 241 $	$1$	5.5.3373402561.1	$C_5$	$C_1$	$C_5$	$0$	$1$
1.251.5t1.a.a 1.251.5t1.a.b 1.251.5t1.a.c 1.251.5t1.a.d	$1$	$ 251 $	$1$	5.5.3969126001.1	$C_5$	$C_1$	$C_5$	$0$	$1$
1.271.5t1.a.a 1.271.5t1.a.b 1.271.5t1.a.c 1.271.5t1.a.d	$1$	$ 271 $	$1$	5.5.5393580481.1	$C_5$	$C_1$	$C_5$	$0$	$1$
1.275.5t1.a.a 1.275.5t1.a.b 1.275.5t1.a.c 1.275.5t1.a.d	$1$	$ 5^{2} \cdot 11 $	$2$	5.5.5719140625.1	$C_5$	$C_1$	$C_5$	$0$	$1$
1.275.5t1.b.a 1.275.5t1.b.b 1.275.5t1.b.c 1.275.5t1.b.d	$1$	$ 5^{2} \cdot 11 $	$2$	5.5.5719140625.2	$C_5$	$C_1$	$C_5$	$0$	$1$
1.275.5t1.c.a 1.275.5t1.c.b 1.275.5t1.c.c 1.275.5t1.c.d	$1$	$ 5^{2} \cdot 11 $	$2$	5.5.5719140625.3	$C_5$	$C_1$	$C_5$	$0$	$1$
1.275.5t1.d.a 1.275.5t1.d.b 1.275.5t1.d.c 1.275.5t1.d.d	$1$	$ 5^{2} \cdot 11 $	$2$	5.5.5719140625.4	$C_5$	$C_1$	$C_5$	$0$	$1$
1.281.5t1.a.a 1.281.5t1.a.b 1.281.5t1.a.c 1.281.5t1.a.d	$1$	$ 281 $	$1$	5.5.6234839521.1	$C_5$	$C_1$	$C_5$	$0$	$1$
1.311.5t1.a.a 1.311.5t1.a.b 1.311.5t1.a.c 1.311.5t1.a.d	$1$	$ 311 $	$1$	5.5.9354951841.1	$C_5$	$C_1$	$C_5$	$0$	$1$
1.331.5t1.a.a 1.331.5t1.a.b 1.331.5t1.a.c 1.331.5t1.a.d	$1$	$ 331 $	$1$	5.5.12003612721.1	$C_5$	$C_1$	$C_5$	$0$	$1$
1.341.5t1.a.a 1.341.5t1.a.b 1.341.5t1.a.c 1.341.5t1.a.d	$1$	$ 11 \cdot 31 $	$2$	5.5.13521270961.1	$C_5$	$C_1$	$C_5$	$0$	$1$
1.341.5t1.b.a 1.341.5t1.b.b 1.341.5t1.b.c 1.341.5t1.b.d	$1$	$ 11 \cdot 31 $	$2$	5.5.13521270961.2	$C_5$	$C_1$	$C_5$	$0$	$1$
1.341.5t1.c.a 1.341.5t1.c.b 1.341.5t1.c.c 1.341.5t1.c.d	$1$	$ 11 \cdot 31 $	$2$	5.5.13521270961.3	$C_5$	$C_1$	$C_5$	$0$	$1$
1.341.5t1.d.a 1.341.5t1.d.b 1.341.5t1.d.c 1.341.5t1.d.d	$1$	$ 11 \cdot 31 $	$2$	5.5.13521270961.4	$C_5$	$C_1$	$C_5$	$0$	$1$
1.401.5t1.a.a 1.401.5t1.a.b 1.401.5t1.a.c 1.401.5t1.a.d	$1$	$ 401 $	$1$	5.5.25856961601.1	$C_5$	$C_1$	$C_5$	$0$	$1$
1.421.5t1.a.a 1.421.5t1.a.b 1.421.5t1.a.c 1.421.5t1.a.d	$1$	$ 421 $	$1$	5.5.31414372081.1	$C_5$	$C_1$	$C_5$	$0$	$1$
1.431.5t1.a.a 1.431.5t1.a.b 1.431.5t1.a.c 1.431.5t1.a.d	$1$	$ 431 $	$1$	5.5.34507149121.1	$C_5$	$C_1$	$C_5$	$0$	$1$
1.451.5t1.a.a 1.451.5t1.a.b 1.451.5t1.a.c 1.451.5t1.a.d	$1$	$ 11 \cdot 41 $	$2$	5.5.41371966801.1	$C_5$	$C_1$	$C_5$	$0$	$1$
1.451.5t1.b.a 1.451.5t1.b.b 1.451.5t1.b.c 1.451.5t1.b.d	$1$	$ 11 \cdot 41 $	$2$	5.5.41371966801.2	$C_5$	$C_1$	$C_5$	$0$	$1$
1.451.5t1.c.a 1.451.5t1.c.b 1.451.5t1.c.c 1.451.5t1.c.d	$1$	$ 11 \cdot 41 $	$2$	5.5.41371966801.3	$C_5$	$C_1$	$C_5$	$0$	$1$
1.451.5t1.d.a 1.451.5t1.d.b 1.451.5t1.d.c 1.451.5t1.d.d	$1$	$ 11 \cdot 41 $	$2$	5.5.41371966801.4	$C_5$	$C_1$	$C_5$	$0$	$1$
1.461.5t1.a.a 1.461.5t1.a.b 1.461.5t1.a.c 1.461.5t1.a.d	$1$	$ 461 $	$1$	5.5.45165175441.1	$C_5$	$C_1$	$C_5$	$0$	$1$
1.491.5t1.a.a 1.491.5t1.a.b 1.491.5t1.a.c 1.491.5t1.a.d	$1$	$ 491 $	$1$	5.5.58120048561.1	$C_5$	$C_1$	$C_5$	$0$	$1$
1.521.5t1.a.a 1.521.5t1.a.b 1.521.5t1.a.c 1.521.5t1.a.d	$1$	$ 521 $	$1$	5.5.73680216481.1	$C_5$	$C_1$	$C_5$	$0$	$1$
1.541.5t1.a.a 1.541.5t1.a.b 1.541.5t1.a.c 1.541.5t1.a.d	$1$	$ 541 $	$1$	5.5.85662167761.1	$C_5$	$C_1$	$C_5$	$0$	$1$
1.571.5t1.a.a 1.571.5t1.a.b 1.571.5t1.a.c 1.571.5t1.a.d	$1$	$ 571 $	$1$	5.5.106302733681.1	$C_5$	$C_1$	$C_5$	$0$	$1$
1.601.5t1.a.a 1.601.5t1.a.b 1.601.5t1.a.c 1.601.5t1.a.d	$1$	$ 601 $	$1$	5.5.130466162401.1	$C_5$	$C_1$	$C_5$	$0$	$1$
1.631.5t1.a.a 1.631.5t1.a.b 1.631.5t1.a.c 1.631.5t1.a.d	$1$	$ 631 $	$1$	5.5.158532181921.1	$C_5$	$C_1$	$C_5$	$0$	$1$
1.641.5t1.a.a 1.641.5t1.a.b 1.641.5t1.a.c 1.641.5t1.a.d	$1$	$ 641 $	$1$	5.5.168823196161.1	$C_5$	$C_1$	$C_5$	$0$	$1$
1.661.5t1.a.a 1.661.5t1.a.b 1.661.5t1.a.c 1.661.5t1.a.d	$1$	$ 661 $	$1$	5.5.190899960241.1	$C_5$	$C_1$	$C_5$	$0$	$1$
1.671.5t1.a.a 1.671.5t1.a.b 1.671.5t1.a.c 1.671.5t1.a.d	$1$	$ 11 \cdot 61 $	$2$	5.5.202716958081.1	$C_5$	$C_1$	$C_5$	$0$	$1$
1.671.5t1.b.a 1.671.5t1.b.b 1.671.5t1.b.c 1.671.5t1.b.d	$1$	$ 11 \cdot 61 $	$2$	5.5.202716958081.2	$C_5$	$C_1$	$C_5$	$0$	$1$
1.671.5t1.c.a 1.671.5t1.c.b 1.671.5t1.c.c 1.671.5t1.c.d	$1$	$ 11 \cdot 61 $	$2$	5.5.202716958081.3	$C_5$	$C_1$	$C_5$	$0$	$1$
1.671.5t1.d.a 1.671.5t1.d.b 1.671.5t1.d.c 1.671.5t1.d.d	$1$	$ 11 \cdot 61 $	$2$	5.5.202716958081.4	$C_5$	$C_1$	$C_5$	$0$	$1$
1.691.5t1.a.a 1.691.5t1.a.b 1.691.5t1.a.c 1.691.5t1.a.d	$1$	$ 691 $	$1$	5.5.227988105361.1	$C_5$	$C_1$	$C_5$	$0$	$1$
1.701.5t1.a.a 1.701.5t1.a.b 1.701.5t1.a.c 1.701.5t1.a.d	$1$	$ 701 $	$1$	5.5.241474942801.1	$C_5$	$C_1$	$C_5$	$0$	$1$
1.751.5t1.a.a 1.751.5t1.a.b 1.751.5t1.a.c 1.751.5t1.a.d	$1$	$ 751 $	$1$	5.5.318097128001.1	$C_5$	$C_1$	$C_5$	$0$	$1$

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Elliptic curves over $\Q$
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Results (49 matches)

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	Dimension	Conductor	Ramified prime count	Artin stem field	$G$	Projective image	Container	Ind	$\chi(c)$
1.11.5t1.a.a 1.11.5t1.a.b 1.11.5t1.a.c 1.11.5t1.a.d	$1$	$ 11 $	$1$	\(\Q(\zeta_{11})^+\)	$C_5$	$C_1$	$C_5$	$0$	$1$
1.25.5t1.a.a 1.25.5t1.a.b 1.25.5t1.a.c 1.25.5t1.a.d	$1$	$ 5^{2}$	$1$	5.5.390625.1	$C_5$	$C_1$	$C_5$	$0$	$1$
1.31.5t1.a.a 1.31.5t1.a.b 1.31.5t1.a.c 1.31.5t1.a.d	$1$	$ 31 $	$1$	5.5.923521.1	$C_5$	$C_1$	$C_5$	$0$	$1$
1.41.5t1.a.a 1.41.5t1.a.b 1.41.5t1.a.c 1.41.5t1.a.d	$1$	$ 41 $	$1$	5.5.2825761.1	$C_5$	$C_1$	$C_5$	$0$	$1$
1.61.5t1.a.a 1.61.5t1.a.b 1.61.5t1.a.c 1.61.5t1.a.d	$1$	$ 61 $	$1$	5.5.13845841.1	$C_5$	$C_1$	$C_5$	$0$	$1$
1.71.5t1.a.a 1.71.5t1.a.b 1.71.5t1.a.c 1.71.5t1.a.d	$1$	$ 71 $	$1$	5.5.25411681.1	$C_5$	$C_1$	$C_5$	$0$	$1$
1.101.5t1.a.a 1.101.5t1.a.b 1.101.5t1.a.c 1.101.5t1.a.d	$1$	$ 101 $	$1$	5.5.104060401.1	$C_5$	$C_1$	$C_5$	$0$	$1$
1.131.5t1.a.a 1.131.5t1.a.b 1.131.5t1.a.c 1.131.5t1.a.d	$1$	$ 131 $	$1$	5.5.294499921.1	$C_5$	$C_1$	$C_5$	$0$	$1$
1.151.5t1.a.a 1.151.5t1.a.b 1.151.5t1.a.c 1.151.5t1.a.d	$1$	$ 151 $	$1$	5.5.519885601.1	$C_5$	$C_1$	$C_5$	$0$	$1$
1.181.5t1.a.a 1.181.5t1.a.b 1.181.5t1.a.c 1.181.5t1.a.d	$1$	$ 181 $	$1$	5.5.1073283121.1	$C_5$	$C_1$	$C_5$	$0$	$1$
1.191.5t1.a.a 1.191.5t1.a.b 1.191.5t1.a.c 1.191.5t1.a.d	$1$	$ 191 $	$1$	5.5.1330863361.1	$C_5$	$C_1$	$C_5$	$0$	$1$
1.211.5t1.a.a 1.211.5t1.a.b 1.211.5t1.a.c 1.211.5t1.a.d	$1$	$ 211 $	$1$	5.5.1982119441.1	$C_5$	$C_1$	$C_5$	$0$	$1$
1.241.5t1.a.a 1.241.5t1.a.b 1.241.5t1.a.c 1.241.5t1.a.d	$1$	$ 241 $	$1$	5.5.3373402561.1	$C_5$	$C_1$	$C_5$	$0$	$1$
1.251.5t1.a.a 1.251.5t1.a.b 1.251.5t1.a.c 1.251.5t1.a.d	$1$	$ 251 $	$1$	5.5.3969126001.1	$C_5$	$C_1$	$C_5$	$0$	$1$
1.271.5t1.a.a 1.271.5t1.a.b 1.271.5t1.a.c 1.271.5t1.a.d	$1$	$ 271 $	$1$	5.5.5393580481.1	$C_5$	$C_1$	$C_5$	$0$	$1$
1.275.5t1.a.a 1.275.5t1.a.b 1.275.5t1.a.c 1.275.5t1.a.d	$1$	$ 5^{2} \cdot 11 $	$2$	5.5.5719140625.1	$C_5$	$C_1$	$C_5$	$0$	$1$
1.275.5t1.b.a 1.275.5t1.b.b 1.275.5t1.b.c 1.275.5t1.b.d	$1$	$ 5^{2} \cdot 11 $	$2$	5.5.5719140625.2	$C_5$	$C_1$	$C_5$	$0$	$1$
1.275.5t1.c.a 1.275.5t1.c.b 1.275.5t1.c.c 1.275.5t1.c.d	$1$	$ 5^{2} \cdot 11 $	$2$	5.5.5719140625.3	$C_5$	$C_1$	$C_5$	$0$	$1$
1.275.5t1.d.a 1.275.5t1.d.b 1.275.5t1.d.c 1.275.5t1.d.d	$1$	$ 5^{2} \cdot 11 $	$2$	5.5.5719140625.4	$C_5$	$C_1$	$C_5$	$0$	$1$
1.281.5t1.a.a 1.281.5t1.a.b 1.281.5t1.a.c 1.281.5t1.a.d	$1$	$ 281 $	$1$	5.5.6234839521.1	$C_5$	$C_1$	$C_5$	$0$	$1$
1.311.5t1.a.a 1.311.5t1.a.b 1.311.5t1.a.c 1.311.5t1.a.d	$1$	$ 311 $	$1$	5.5.9354951841.1	$C_5$	$C_1$	$C_5$	$0$	$1$
1.331.5t1.a.a 1.331.5t1.a.b 1.331.5t1.a.c 1.331.5t1.a.d	$1$	$ 331 $	$1$	5.5.12003612721.1	$C_5$	$C_1$	$C_5$	$0$	$1$
1.341.5t1.a.a 1.341.5t1.a.b 1.341.5t1.a.c 1.341.5t1.a.d	$1$	$ 11 \cdot 31 $	$2$	5.5.13521270961.1	$C_5$	$C_1$	$C_5$	$0$	$1$
1.341.5t1.b.a 1.341.5t1.b.b 1.341.5t1.b.c 1.341.5t1.b.d	$1$	$ 11 \cdot 31 $	$2$	5.5.13521270961.2	$C_5$	$C_1$	$C_5$	$0$	$1$
1.341.5t1.c.a 1.341.5t1.c.b 1.341.5t1.c.c 1.341.5t1.c.d	$1$	$ 11 \cdot 31 $	$2$	5.5.13521270961.3	$C_5$	$C_1$	$C_5$	$0$	$1$
1.341.5t1.d.a 1.341.5t1.d.b 1.341.5t1.d.c 1.341.5t1.d.d	$1$	$ 11 \cdot 31 $	$2$	5.5.13521270961.4	$C_5$	$C_1$	$C_5$	$0$	$1$
1.401.5t1.a.a 1.401.5t1.a.b 1.401.5t1.a.c 1.401.5t1.a.d	$1$	$ 401 $	$1$	5.5.25856961601.1	$C_5$	$C_1$	$C_5$	$0$	$1$
1.421.5t1.a.a 1.421.5t1.a.b 1.421.5t1.a.c 1.421.5t1.a.d	$1$	$ 421 $	$1$	5.5.31414372081.1	$C_5$	$C_1$	$C_5$	$0$	$1$
1.431.5t1.a.a 1.431.5t1.a.b 1.431.5t1.a.c 1.431.5t1.a.d	$1$	$ 431 $	$1$	5.5.34507149121.1	$C_5$	$C_1$	$C_5$	$0$	$1$
1.451.5t1.a.a 1.451.5t1.a.b 1.451.5t1.a.c 1.451.5t1.a.d	$1$	$ 11 \cdot 41 $	$2$	5.5.41371966801.1	$C_5$	$C_1$	$C_5$	$0$	$1$
1.451.5t1.b.a 1.451.5t1.b.b 1.451.5t1.b.c 1.451.5t1.b.d	$1$	$ 11 \cdot 41 $	$2$	5.5.41371966801.2	$C_5$	$C_1$	$C_5$	$0$	$1$
1.451.5t1.c.a 1.451.5t1.c.b 1.451.5t1.c.c 1.451.5t1.c.d	$1$	$ 11 \cdot 41 $	$2$	5.5.41371966801.3	$C_5$	$C_1$	$C_5$	$0$	$1$
1.451.5t1.d.a 1.451.5t1.d.b 1.451.5t1.d.c 1.451.5t1.d.d	$1$	$ 11 \cdot 41 $	$2$	5.5.41371966801.4	$C_5$	$C_1$	$C_5$	$0$	$1$
1.461.5t1.a.a 1.461.5t1.a.b 1.461.5t1.a.c 1.461.5t1.a.d	$1$	$ 461 $	$1$	5.5.45165175441.1	$C_5$	$C_1$	$C_5$	$0$	$1$
1.491.5t1.a.a 1.491.5t1.a.b 1.491.5t1.a.c 1.491.5t1.a.d	$1$	$ 491 $	$1$	5.5.58120048561.1	$C_5$	$C_1$	$C_5$	$0$	$1$
1.521.5t1.a.a 1.521.5t1.a.b 1.521.5t1.a.c 1.521.5t1.a.d	$1$	$ 521 $	$1$	5.5.73680216481.1	$C_5$	$C_1$	$C_5$	$0$	$1$
1.541.5t1.a.a 1.541.5t1.a.b 1.541.5t1.a.c 1.541.5t1.a.d	$1$	$ 541 $	$1$	5.5.85662167761.1	$C_5$	$C_1$	$C_5$	$0$	$1$
1.571.5t1.a.a 1.571.5t1.a.b 1.571.5t1.a.c 1.571.5t1.a.d	$1$	$ 571 $	$1$	5.5.106302733681.1	$C_5$	$C_1$	$C_5$	$0$	$1$
1.601.5t1.a.a 1.601.5t1.a.b 1.601.5t1.a.c 1.601.5t1.a.d	$1$	$ 601 $	$1$	5.5.130466162401.1	$C_5$	$C_1$	$C_5$	$0$	$1$
1.631.5t1.a.a 1.631.5t1.a.b 1.631.5t1.a.c 1.631.5t1.a.d	$1$	$ 631 $	$1$	5.5.158532181921.1	$C_5$	$C_1$	$C_5$	$0$	$1$
1.641.5t1.a.a 1.641.5t1.a.b 1.641.5t1.a.c 1.641.5t1.a.d	$1$	$ 641 $	$1$	5.5.168823196161.1	$C_5$	$C_1$	$C_5$	$0$	$1$
1.661.5t1.a.a 1.661.5t1.a.b 1.661.5t1.a.c 1.661.5t1.a.d	$1$	$ 661 $	$1$	5.5.190899960241.1	$C_5$	$C_1$	$C_5$	$0$	$1$
1.671.5t1.a.a 1.671.5t1.a.b 1.671.5t1.a.c 1.671.5t1.a.d	$1$	$ 11 \cdot 61 $	$2$	5.5.202716958081.1	$C_5$	$C_1$	$C_5$	$0$	$1$
1.671.5t1.b.a 1.671.5t1.b.b 1.671.5t1.b.c 1.671.5t1.b.d	$1$	$ 11 \cdot 61 $	$2$	5.5.202716958081.2	$C_5$	$C_1$	$C_5$	$0$	$1$
1.671.5t1.c.a 1.671.5t1.c.b 1.671.5t1.c.c 1.671.5t1.c.d	$1$	$ 11 \cdot 61 $	$2$	5.5.202716958081.3	$C_5$	$C_1$	$C_5$	$0$	$1$
1.671.5t1.d.a 1.671.5t1.d.b 1.671.5t1.d.c 1.671.5t1.d.d	$1$	$ 11 \cdot 61 $	$2$	5.5.202716958081.4	$C_5$	$C_1$	$C_5$	$0$	$1$
1.691.5t1.a.a 1.691.5t1.a.b 1.691.5t1.a.c 1.691.5t1.a.d	$1$	$ 691 $	$1$	5.5.227988105361.1	$C_5$	$C_1$	$C_5$	$0$	$1$
1.701.5t1.a.a 1.701.5t1.a.b 1.701.5t1.a.c 1.701.5t1.a.d	$1$	$ 701 $	$1$	5.5.241474942801.1	$C_5$	$C_1$	$C_5$	$0$	$1$
1.751.5t1.a.a 1.751.5t1.a.b 1.751.5t1.a.c 1.751.5t1.a.d	$1$	$ 751 $	$1$	5.5.318097128001.1	$C_5$	$C_1$	$C_5$	$0$	$1$