LMFDB - Embedded newform 168.4.i.c.125.19

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [168,4,Mod(125,168)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(168, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 1, 1])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("168.125"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 168 = 2^{3} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	168.i (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [80] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$9.91232088096$
Analytic rank:	$0$
Dimension:	$80$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			125.19
Character	$\chi$	$=$	168.125
Dual form			168.4.i.c.125.17

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.24057 + 1.72622i) q^{2} +(-1.04870 - 5.08923i) q^{3} +(2.04030 - 7.73545i) q^{4} +3.71228i q^{5} +(11.1348 + 9.59247i) q^{6} +(15.6071 + 9.97081i) q^{7} +(8.78168 + 20.8538i) q^{8} +(-24.8005 + 10.6741i) q^{9} +(-6.40823 - 8.31763i) q^{10} -48.1150 q^{11} +(-41.5071 - 2.27139i) q^{12} +69.5724 q^{13} +(-52.1807 + 4.60114i) q^{14} +(18.8927 - 3.89307i) q^{15} +(-55.6743 - 31.5653i) q^{16} +48.9235 q^{17} +(37.1412 - 66.7273i) q^{18} +62.2883 q^{19} +(28.7162 + 7.57418i) q^{20} +(34.3765 - 89.8847i) q^{21} +(107.805 - 83.0572i) q^{22} -63.4952i q^{23} +(96.9205 - 66.5614i) q^{24} +111.219 q^{25} +(-155.882 + 120.098i) q^{26} +(80.3314 + 115.021i) q^{27} +(108.972 - 100.385i) q^{28} +20.2759 q^{29} +(-35.6100 + 41.3356i) q^{30} -77.3838i q^{31} +(179.231 - 25.3821i) q^{32} +(50.4582 + 244.868i) q^{33} +(-109.617 + 84.4529i) q^{34} +(-37.0145 + 57.9382i) q^{35} +(31.9689 + 213.621i) q^{36} +151.811i q^{37} +(-139.561 + 107.524i) q^{38} +(-72.9606 - 354.070i) q^{39} +(-77.4153 + 32.6001i) q^{40} +284.960 q^{41} +(78.1382 + 260.734i) q^{42} -441.143i q^{43} +(-98.1691 + 372.191i) q^{44} +(-39.6255 - 92.0663i) q^{45} +(109.607 + 142.265i) q^{46} +615.429 q^{47} +(-102.257 + 316.442i) q^{48} +(144.166 + 311.232i) q^{49} +(-249.194 + 191.989i) q^{50} +(-51.3061 - 248.983i) q^{51} +(141.949 - 538.174i) q^{52} +129.453 q^{53} +(-378.540 - 119.043i) q^{54} -178.616i q^{55} +(-70.8726 + 413.029i) q^{56} +(-65.3217 - 316.999i) q^{57} +(-45.4295 + 35.0007i) q^{58} -406.934i q^{59} +(8.43206 - 154.086i) q^{60} -576.405 q^{61} +(133.582 + 173.384i) q^{62} +(-493.494 - 80.6876i) q^{63} +(-357.764 + 366.263i) q^{64} +258.272i q^{65} +(-535.752 - 461.542i) q^{66} +665.046i q^{67} +(99.8187 - 378.445i) q^{68} +(-323.142 + 66.5875i) q^{69} +(-17.0807 - 193.710i) q^{70} -129.482i q^{71} +(-440.386 - 423.448i) q^{72} -290.352i q^{73} +(-262.059 - 340.142i) q^{74} +(-116.635 - 566.018i) q^{75} +(127.087 - 481.828i) q^{76} +(-750.938 - 479.745i) q^{77} +(774.677 + 667.371i) q^{78} -130.921 q^{79} +(117.179 - 206.679i) q^{80} +(501.125 - 529.447i) q^{81} +(-638.472 + 491.904i) q^{82} +763.300i q^{83} +(-625.160 - 449.309i) q^{84} +181.618i q^{85} +(761.511 + 988.411i) q^{86} +(-21.2633 - 103.189i) q^{87} +(-422.530 - 1003.38i) q^{88} -269.586 q^{89} +(247.711 + 137.879i) q^{90} +(1085.83 + 693.693i) q^{91} +(-491.164 - 129.549i) q^{92} +(-393.824 + 81.1524i) q^{93} +(-1378.91 + 1062.37i) q^{94} +231.232i q^{95} +(-317.135 - 885.529i) q^{96} +1379.26i q^{97} +(-860.269 - 448.473i) q^{98} +(1193.27 - 513.586i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 28 q^{4} + 64 q^{7} + 104 q^{9} - 8 q^{15} - 892 q^{16} + 692 q^{18} + 128 q^{22} - 976 q^{25} + 612 q^{28} - 332 q^{30} + 1544 q^{36} + 568 q^{39} + 780 q^{42} + 208 q^{46} - 4048 q^{49} - 1448 q^{57}+ \cdots - 2072 q^{88}+O(q^{100}) $ 80 * q + 28 * q^4 + 64 * q^7 + 104 * q^9 - 8 * q^15 - 892 * q^16 + 692 * q^18 + 128 * q^22 - 976 * q^25 + 612 * q^28 - 332 * q^30 + 1544 * q^36 + 568 * q^39 + 780 * q^42 + 208 * q^46 - 4048 * q^49 - 1448 * q^57 - 1760 * q^58 + 4156 * q^60 - 2152 * q^63 + 2764 * q^64 + 1968 * q^70 - 2740 * q^72 - 3620 * q^78 + 4992 * q^79 + 1568 * q^81 + 2484 * q^84 - 2072 * q^88

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/168\mathbb{Z}\right)^\times$.

$n$	$73$	$85$	$113$	$127$
$\chi(n)$	$-1$	$-1$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−2.24057	+	1.72622i	−0.792161	+	0.610312i
$2$	−2.24057	+	1.72622i	−0.792161	+	0.610312i
$3$	−1.04870	−	5.08923i	−0.201822	−	0.979422i
$3$	−1.04870	−	5.08923i	−0.201822	−	0.979422i
$4$	2.04030	−	7.73545i	0.255038	−	0.966931i
$5$			3.71228i			0.332037i	0.986123	+	0.166018i	$0.0530911\pi$
$5$			3.71228i			0.332037i	−0.986123	+	0.166018i	$0.946909\pi$
$6$	11.1348	+	9.59247i	0.757629	+	0.652685i
$7$	15.6071	+	9.97081i	0.842707	+	0.538373i
$7$	15.6071	+	9.97081i	0.842707	+	0.538373i
$8$	8.78168	+	20.8538i	0.388099	+	0.921618i
$9$	−24.8005	+	10.6741i	−0.918535	+	0.395339i
$10$	−6.40823	−	8.31763i	−0.202646	−	0.263027i
$11$	−48.1150			−1.31884			−0.659419	−	0.751776i	$-0.729198\pi$
$11$	−48.1150			−1.31884			−0.659419	+	0.751776i	$0.729198\pi$
$12$	−41.5071	−	2.27139i	−0.998506	−	0.0546413i
$13$	69.5724			1.48430			0.742150	−	0.670234i	$-0.233806\pi$
$13$	69.5724			1.48430			0.742150	+	0.670234i	$0.233806\pi$
$14$	−52.1807	+	4.60114i	−0.996135	+	0.0878362i
$15$	18.8927	−	3.89307i	0.325204	−	0.0670125i
$16$	−55.6743	−	31.5653i	−0.869911	−	0.493208i
$17$	48.9235			0.697982			0.348991	−	0.937126i	$-0.386524\pi$
$17$	48.9235			0.697982			0.348991	+	0.937126i	$0.386524\pi$
$18$	37.1412	−	66.7273i	0.486348	−	0.873765i
$19$	62.2883			0.752100			0.376050	−	0.926599i	$-0.377282\pi$
$19$	62.2883			0.752100			0.376050	+	0.926599i	$0.377282\pi$
$20$	28.7162	+	7.57418i	0.321057	+	0.0846819i
$21$	34.3765	−	89.8847i	0.357217	−	0.934021i
$22$	107.805	−	83.0572i	1.04473	−	0.804903i
$23$		−	63.4952i		−	0.575638i	−0.957685	−	0.287819i	$-0.907070\pi$
$23$		−	63.4952i		−	0.575638i	0.957685	−	0.287819i	$-0.0929301\pi$
$24$	96.9205	−	66.5614i	0.824326	−	0.566116i
$25$	111.219			0.889752
$26$	−155.882	+	120.098i	−1.17580	+	0.905887i
$27$	80.3314	+	115.021i	0.572585	+	0.819846i
$28$	108.972	−	100.385i	0.735492	−	0.677534i
$29$	20.2759			0.129832			0.0649161	−	0.997891i	$-0.479322\pi$
$29$	20.2759			0.129832			0.0649161	+	0.997891i	$0.479322\pi$
$30$	−35.6100	+	41.3356i	−0.216715	+	0.251561i
$31$		−	77.3838i		−	0.448340i	−0.974550	−	0.224170i	$-0.928033\pi$
$31$		−	77.3838i		−	0.448340i	0.974550	−	0.224170i	$-0.0719671\pi$
$32$	179.231	−	25.3821i	0.990121	−	0.140218i
$33$	50.4582	+	244.868i	0.266171	+	1.29170i
$34$	−109.617	+	84.4529i	−0.552914	+	0.425987i
$35$	−37.0145	+	57.9382i	−0.178760	+	0.279810i
$36$	31.9689	+	213.621i	0.148004	+	0.988987i
$37$			151.811i			0.674527i	0.941410	+	0.337263i	$0.109501\pi$
$37$			151.811i			0.674527i	−0.941410	+	0.337263i	$0.890499\pi$
$38$	−139.561	+	107.524i	−0.595785	+	0.459016i
$39$	−72.9606	−	354.070i	−0.299565	−	1.45376i
$40$	−77.4153	+	32.6001i	−0.306011	+	0.128863i
$41$	284.960			1.08544			0.542722	−	0.839912i	$-0.317394\pi$
$41$	284.960			1.08544			0.542722	+	0.839912i	$0.317394\pi$
$42$	78.1382	+	260.734i	0.287071	+	0.957909i
$43$		−	441.143i		−	1.56450i	−0.622963	−	0.782252i	$-0.714071\pi$
$43$		−	441.143i		−	1.56450i	0.622963	−	0.782252i	$-0.285929\pi$
$44$	−98.1691	+	372.191i	−0.336353	+	1.27523i
$45$	−39.6255	−	92.0663i	−0.131267	−	0.304988i
$46$	109.607	+	142.265i	0.351319	+	0.455998i
$47$	615.429			1.90999			0.954996	−	0.296620i	$-0.0958594\pi$
$47$	615.429			1.90999			0.954996	+	0.296620i	$0.0958594\pi$
$48$	−102.257	+	316.442i	−0.307491	+	0.951551i
$49$	144.166	+	311.232i	0.420309	+	0.907381i
$50$	−249.194	+	191.989i	−0.704826	+	0.543026i
$51$	−51.3061	−	248.983i	−0.140868	−	0.683619i
$52$	141.949	−	538.174i	0.378553	−	1.43522i
$53$	129.453			0.335504			0.167752	−	0.985829i	$-0.446349\pi$
$53$	129.453			0.335504			0.167752	+	0.985829i	$0.446349\pi$
$54$	−378.540	−	119.043i	−0.953941	−	0.299994i
$55$		−	178.616i		−	0.437903i
$56$	−70.8726	+	413.029i	−0.169121	+	0.985595i
$57$	−65.3217	−	316.999i	−0.151791	−	0.736624i
$58$	−45.4295	+	35.0007i	−0.102848	+	0.0792382i
$59$		−	406.934i		−	0.897938i	−0.893547	−	0.448969i	$-0.851791\pi$
$59$		−	406.934i		−	0.897938i	0.893547	−	0.448969i	$-0.148209\pi$
$60$	8.43206	−	154.086i	0.0181429	−	0.331541i
$61$	−576.405			−1.20985			−0.604927	−	0.796281i	$-0.706798\pi$
$61$	−576.405			−1.20985			−0.604927	+	0.796281i	$0.706798\pi$
$62$	133.582	+	173.384i	0.273627	+	0.355158i
$63$	−493.494	−	80.6876i	−0.986896	−	0.161360i
$64$	−357.764	+	366.263i	−0.698758	+	0.715358i
$65$			258.272i			0.492842i
$66$	−535.752	−	461.542i	−0.999190	−	0.860786i
$67$			665.046i			1.21266i	0.795212	+	0.606331i	$0.207359\pi$
$67$			665.046i			1.21266i	−0.795212	+	0.606331i	$0.792641\pi$
$68$	99.8187	−	378.445i	0.178012	−	0.674901i
$69$	−323.142	+	66.5875i	−0.563792	+	0.116177i
$70$	−17.0807	−	193.710i	−0.0291648	−	0.330753i
$71$		−	129.482i		−	0.216432i	−0.994127	−	0.108216i	$-0.965486\pi$
$71$		−	129.482i		−	0.216432i	0.994127	−	0.108216i	$-0.0345139\pi$
$72$	−440.386	−	423.448i	−0.720834	−	0.693108i
$73$		−	290.352i		−	0.465523i	−0.972534	−	0.232761i	$-0.925224\pi$
$73$		−	290.352i		−	0.465523i	0.972534	−	0.232761i	$-0.0747762\pi$
$74$	−262.059	−	340.142i	−0.411672	−	0.534334i
$75$	−116.635	−	566.018i	−0.179572	−	0.871442i
$76$	127.087	−	481.828i	0.191814	−	0.727229i
$77$	−750.938	−	479.745i	−1.11139	−	0.710027i
$78$	774.677	+	667.371i	1.12455	+	0.968781i
$79$	−130.921			−0.186452			−0.0932261	−	0.995645i	$-0.529718\pi$
$79$	−130.921			−0.186452			−0.0932261	+	0.995645i	$0.529718\pi$
$80$	117.179	−	206.679i	0.163763	−	0.288843i
$81$	501.125	−	529.447i	0.687415	−	0.726265i
$82$	−638.472	+	491.904i	−0.859847	+	0.662460i
$83$			763.300i			1.00943i	0.863285	+	0.504717i	$0.168403\pi$
$83$			763.300i			1.00943i	−0.863285	+	0.504717i	$0.831597\pi$
$84$	−625.160	−	449.309i	−0.812030	−	0.583615i
$85$			181.618i			0.231756i
$86$	761.511	+	988.411i	0.954836	+	1.23934i
$87$	−21.2633	−	103.189i	−0.0262031	−	0.127161i
$88$	−422.530	−	1003.38i	−0.511840	−	1.21546i
$89$	−269.586			−0.321080			−0.160540	−	0.987029i	$-0.551324\pi$
$89$	−269.586			−0.321080			−0.160540	+	0.987029i	$0.551324\pi$
$90$	247.711	+	137.879i	0.290122	+	0.161485i
$91$	1085.83	+	693.693i	1.25083	+	0.799107i
$92$	−491.164	−	129.549i	−0.556602	−	0.146809i
$93$	−393.824	+	81.1524i	−0.439114	+	0.0904851i
$94$	−1378.91	+	1062.37i	−1.51302	+	1.16569i
$95$			231.232i			0.249725i
$96$	−317.135	−	885.529i	−0.337161	−	0.941447i
$97$			1379.26i			1.44374i	0.692030	+	0.721869i	$0.256717\pi$
$97$			1379.26i			1.44374i	−0.692030	+	0.721869i	$0.743283\pi$
$98$	−860.269	−	448.473i	−0.886738	−	0.462272i
$99$	1193.27	−	513.586i	1.21140	−	0.521388i
$100$	226.920	−	860.328i	0.226920	−	0.860328i
$101$			117.695i			0.115952i	0.998318	+	0.0579759i	$0.0184647\pi$
$101$			117.695i			0.115952i	−0.998318	+	0.0579759i	$0.981535\pi$
$102$	544.755	+	469.298i	0.528812	+	0.455563i
$103$		−	1590.34i		−	1.52137i	−0.649122	−	0.760684i	$-0.724863\pi$
$103$		−	1590.34i		−	1.52137i	0.649122	−	0.760684i	$-0.275137\pi$
$104$	610.962	+	1450.85i	0.576056	+	1.36796i
$105$	333.677	+	127.615i	0.310129	+	0.118609i
$106$	−290.048	+	223.465i	−0.265773	+	0.204762i
$107$	−443.102			−0.400339			−0.200169	−	0.979761i	$-0.564149\pi$
$107$	−443.102			−0.400339			−0.200169	+	0.979761i	$0.564149\pi$
$108$	1053.64	−	386.721i	0.938765	−	0.344558i
$109$			1655.46i			1.45472i	0.686256	+	0.727360i	$0.259253\pi$
$109$			1655.46i			1.45472i	−0.686256	+	0.727360i	$0.740747\pi$
$110$	308.332	+	400.203i	0.267257	+	0.346889i
$111$	772.598	−	159.204i	0.660647	−	0.136135i
$112$	−554.186	−	1047.76i	−0.467550	−	0.883966i
$113$			73.7875i			0.0614278i	0.999528	+	0.0307139i	$0.00977807\pi$
$113$			73.7875i			0.0614278i	−0.999528	+	0.0307139i	$0.990222\pi$
$114$	693.569	+	597.499i	0.569813	+	0.490885i
$115$	235.712			0.191133
$116$	41.3689	−	156.843i	0.0331121	−	0.125539i
$117$	−1725.43	+	742.626i	−1.36338	+	0.586801i
$118$	702.460	+	911.765i	0.548023	+	0.711312i
$119$	763.556	+	487.807i	0.588194	+	0.375775i
$120$	247.095	+	359.796i	0.187971	+	0.273706i
$121$	984.052			0.739332
$122$	1291.48	−	995.004i	0.958399	−	0.738389i
$123$	−298.837	−	1450.22i	−0.219067	−	1.06311i
$124$	−598.599	−	157.886i	−0.433514	−	0.114344i
$125$			876.912i			0.627467i
$126$	1244.99	−	671.095i	0.880260	−	0.474491i
$127$	−1960.00			−1.36947			−0.684733	−	0.728794i	$-0.740081\pi$
$127$	−1960.00			−1.36947			−0.684733	+	0.728794i	$0.740081\pi$
$128$	169.343	−	1438.22i	0.116937	−	0.993139i
$129$	−2245.08	+	462.626i	−1.53231	+	0.315752i
$130$	−445.836	−	578.677i	−0.300788	−	0.390410i
$131$			1179.46i			0.786642i	0.919401	+	0.393321i	$0.128674\pi$
$131$			1179.46i			0.786642i	−0.919401	+	0.393321i	$0.871326\pi$
$132$	1997.11	+	109.288i	1.31687	+	0.0720629i
$133$	972.142	+	621.064i	0.633800	+	0.404911i
$134$	−1148.02	−	1490.08i	−0.740102	−	0.960623i
$135$	−426.991	+	298.213i	−0.272219	+	0.190119i
$136$	429.630	+	1020.24i	0.270886	+	0.643273i
$137$			2694.83i			1.68054i	0.542165	+	0.840272i	$0.317605\pi$
$137$			2694.83i			1.68054i	−0.542165	+	0.840272i	$0.682395\pi$
$138$	609.076	−	707.009i	0.375710	−	0.436120i
$139$	2581.98			1.57554			0.787771	−	0.615968i	$-0.211235\pi$
$139$	2581.98			1.57554			0.787771	+	0.615968i	$0.211235\pi$
$140$	372.657	+	404.535i	0.224966	+	0.244210i
$141$	−645.401	−	3132.06i	−0.385479	−	1.87069i
$142$	223.515	+	290.114i	0.132091	+	0.171449i
$143$	−3347.47			−1.95755
$144$	1717.68	+	188.558i	0.994029	+	0.109119i
$145$			75.2698i			0.0431091i
$146$	501.213	+	650.555i	0.284114	+	0.368769i
$147$	1432.74	−	1060.08i	0.803881	−	0.594790i
$148$	1174.32	+	309.739i	0.652221	+	0.172030i
$149$	3252.26			1.78816			0.894079	−	0.447910i	$-0.147832\pi$
$149$	3252.26			1.78816			0.894079	+	0.447910i	$0.147832\pi$
$150$	1238.40	+	1066.86i	0.674102	+	0.580728i
$151$	74.9590			0.0403978			0.0201989	−	0.999796i	$-0.493570\pi$
$151$	74.9590			0.0403978			0.0201989	+	0.999796i	$0.493570\pi$
$152$	546.996	+	1298.95i	0.291889	+	0.693149i
$153$	−1213.33	+	522.217i	−0.641121	+	0.275939i
$154$	2510.68	−	221.384i	1.31374	−	0.115842i
$155$	287.271			0.148865
$156$	−2887.75	−	158.026i	−1.48208	−	0.0811041i
$157$	−706.105			−0.358938			−0.179469	−	0.983764i	$-0.557438\pi$
$157$	−706.105			−0.358938			−0.179469	+	0.983764i	$0.557438\pi$
$158$	293.337	−	225.998i	0.147700	−	0.113794i
$159$	−135.757	−	658.815i	−0.0677123	−	0.328600i
$160$	94.2256	+	665.356i	0.0465574	+	0.328756i
$161$	633.099	−	990.979i	0.309908	−	0.485094i
$162$	−208.861	+	2051.32i	−0.101294	+	0.994856i
$163$		−	1520.38i		−	0.730586i	−0.930893	−	0.365293i	$-0.880969\pi$
$163$		−	1520.38i		−	0.730586i	0.930893	−	0.365293i	$-0.119031\pi$
$164$	581.404	−	2204.29i	0.276829	−	1.04955i
$165$	−909.020	+	187.315i	−0.428891	+	0.0883786i
$166$	−1317.63	−	1710.23i	−0.616070	−	0.799634i
$167$	−1959.42			−0.907933			−0.453966	−	0.891019i	$-0.649991\pi$
$167$	−1959.42			−0.907933			−0.453966	+	0.891019i	$0.649991\pi$
$168$	2176.32	−	72.4570i	0.999446	−	0.0332749i
$169$	2643.32			1.20315
$170$	−313.513	−	406.928i	−0.141443	−	0.183588i
$171$	−1544.78	+	664.874i	−0.690831	+	0.297334i
$172$	−3412.44	−	900.065i	−1.51277	−	0.399007i
$173$		−	3842.54i		−	1.68869i	−0.535800	−	0.844345i	$-0.679990\pi$
$173$		−	3842.54i		−	1.68869i	0.535800	−	0.844345i	$-0.320010\pi$
$174$	225.768	+	194.496i	0.0983647	+	0.0847396i
$175$	1735.81	+	1108.94i	0.749800	+	0.479018i
$176$	2678.77	+	1518.76i	1.14727	+	0.650461i
$177$	−2070.98	+	426.752i	−0.879461	+	0.181224i
$178$	604.027	−	465.367i	0.254347	−	0.195959i
$179$	−2750.46			−1.14849			−0.574243	−	0.818685i	$-0.694704\pi$
$179$	−2750.46			−1.14849			−0.574243	+	0.818685i	$0.694704\pi$
$180$	−793.022	+	118.678i	−0.328380	+	0.0491428i
$181$	1299.66			0.533718			0.266859	−	0.963736i	$-0.414014\pi$
$181$	1299.66			0.533718			0.266859	+	0.963736i	$0.414014\pi$
$182$	−3630.34	+	320.112i	−1.47856	+	0.130375i
$183$	604.476	+	2933.45i	0.244176	+	1.18496i
$184$	1324.12	−	557.595i	0.530518	−	0.223404i
$185$	−563.564			−0.223968
$186$	742.302	−	861.656i	0.292625	−	0.339676i
$187$	−2353.95			−0.920525
$188$	1255.66	−	4760.62i	0.487120	−	1.84683i
$189$	106.890	+	2596.12i	0.0411380	+	0.999153i
$190$	−399.158	−	518.091i	−0.152410	−	0.197822i
$191$		−	3914.42i		−	1.48292i	−0.670998	−	0.741459i	$-0.734134\pi$
$191$		−	3914.42i		−	1.48292i	0.670998	−	0.741459i	$-0.265866\pi$
$192$	2239.18	+	1436.64i	0.841662	+	0.540004i
$193$	−3648.18			−1.36063			−0.680316	−	0.732919i	$-0.738157\pi$
$193$	−3648.18			−1.36063			−0.680316	+	0.732919i	$0.738157\pi$
$194$	−2380.91	−	3090.33i	−0.881131	−	1.14367i
$195$	1314.41	−	270.850i	0.482701	−	0.0994666i
$196$	2701.66	−	480.182i	0.984570	−	0.174993i
$197$	79.0843			0.0286016			0.0143008	−	0.999898i	$-0.495448\pi$
$197$	79.0843			0.0286016			0.0143008	+	0.999898i	$0.495448\pi$
$198$	−1787.05	+	3210.58i	−0.641414	+	1.15235i
$199$		−	710.675i		−	0.253158i	−0.991957	−	0.126579i	$-0.959600\pi$
$199$		−	710.675i		−	0.253158i	0.991957	−	0.126579i	$-0.0403997\pi$
$200$	976.689	+	2319.34i	0.345312	+	0.820011i
$201$	3384.57	−	697.434i	1.18771	−	0.244742i
$202$	−203.169	−	263.705i	−0.0707668	−	0.0918525i
$203$	316.449	+	202.167i	0.109411	+	0.0698982i
$204$	−2030.67	−	111.125i	−0.696939	−	0.0381386i
$205$			1057.85i			0.360408i
$206$	2745.29	+	3563.27i	0.928510	+	1.20517i
$207$	677.757	+	1574.71i	0.227572	+	0.528744i
$208$	−3873.40	−	2196.07i	−1.29121	−	0.732069i
$209$	−2997.00			−0.991898
$210$	−967.920	+	290.071i	−0.318061	+	0.0953182i
$211$			2273.94i			0.741915i	0.928650	+	0.370958i	$0.120971\pi$
$211$			2273.94i			0.741915i	−0.928650	+	0.370958i	$0.879029\pi$
$212$	264.123	−	1001.38i	0.0855663	−	0.324410i
$213$	−658.964	+	135.788i	−0.211979	+	0.0436809i
$214$	992.800	−	764.893i	0.317133	−	0.244332i
$215$	1637.65			0.519473
$216$	−1693.19	+	2685.30i	−0.533365	+	0.845885i
$217$	771.579	−	1207.74i	0.241374	−	0.377819i
$218$	−2857.70	−	3709.18i	−0.887833	−	1.15237i
$219$	−1477.67	+	304.493i	−0.455944	+	0.0939530i
$220$	−1381.68	−	364.432i	−0.423422	−	0.111682i
$221$	3403.72			1.03602
$222$	−1456.24	+	1690.38i	−0.440254	+	0.511041i
$223$		−	3196.79i		−	0.959968i	−0.877277	−	0.479984i	$-0.840642\pi$
$223$		−	3196.79i		−	0.959968i	0.877277	−	0.479984i	$-0.159358\pi$
$224$	3050.36	+	1390.94i	0.909871	+	0.414892i
$225$	−2758.28	+	1187.17i	−0.817268	+	0.351753i
$226$	−127.374	−	165.326i	−0.0374901	−	0.0486607i
$227$			3103.70i			0.907487i	0.891132	+	0.453744i	$0.149912\pi$
$227$			3103.70i			0.907487i	−0.891132	+	0.453744i	$0.850088\pi$
$228$	−2585.41	−	141.481i	−0.750977	−	0.0410957i
$229$	−693.650			−0.200165			−0.100082	−	0.994979i	$-0.531911\pi$
$229$	−693.650			−0.200165			−0.100082	+	0.994979i	$0.531911\pi$
$230$	−528.130	+	406.892i	−0.151408	+	0.116651i
$231$	−1654.02	+	4324.80i	−0.471112	+	1.23182i
$232$	178.056	+	422.830i	0.0503878	+	0.119656i
$233$			3188.80i			0.896589i	0.893886	+	0.448294i	$0.147968\pi$
$233$			3188.80i			0.896589i	−0.893886	+	0.448294i	$0.852032\pi$
$234$	2584.00	−	4642.38i	0.721886	−	1.29693i
$235$			2284.65i			0.634187i
$236$	−3147.82	−	830.269i	−0.868244	−	0.229008i
$237$	137.297	+	666.285i	0.0376302	+	0.182615i
$238$	−2552.86	+	225.104i	−0.695284	+	0.0613081i
$239$		−	1879.03i		−	0.508554i	−0.967131	−	0.254277i	$-0.918162\pi$
$239$		−	1879.03i		−	0.508554i	0.967131	−	0.254277i	$-0.0818375\pi$
$240$	−1174.72	−	379.608i	−0.315950	−	0.102098i
$241$		−	3281.84i		−	0.877187i	−0.898685	−	0.438594i	$-0.855477\pi$
$241$		−	3281.84i		−	0.877187i	0.898685	−	0.438594i	$-0.144523\pi$
$242$	−2204.84	+	1698.69i	−0.585670	+	0.451224i
$243$	−3220.01	−	1995.11i	−0.850056	−	0.526692i
$244$	−1176.04	+	4458.75i	−0.308558	+	1.16985i
$245$	−1155.38	+	535.185i	−0.301284	+	0.139558i
$246$	3172.98	+	2733.47i	0.822365	+	0.708454i
$247$	4333.54			1.11634
$248$	1613.75	−	679.560i	0.413198	−	0.174000i
$249$	3884.60	−	800.472i	0.988662	−	0.203726i
$250$	−1513.75	−	1964.78i	−0.382951	−	0.497055i
$251$		−	1680.42i		−	0.422578i	−0.977424	−	0.211289i	$-0.932234\pi$
$251$		−	1680.42i		−	0.422578i	0.977424	−	0.211289i	$-0.0677661\pi$
$252$	−1631.03	+	3652.77i	−0.407720	+	0.913107i
$253$			3055.07i			0.759173i
$254$	4391.53	−	3383.41i	1.08484	−	0.835803i
$255$	924.295	−	190.463i	0.226987	−	0.0467735i
$256$	2103.26	+	3514.75i	0.513492	+	0.858094i
$257$	6706.25			1.62772			0.813861	−	0.581059i	$-0.197362\pi$
$257$	6706.25			1.62772			0.813861	+	0.581059i	$0.197362\pi$
$258$	4231.65	−	4912.05i	1.02113	−	1.18531i
$259$	−1513.67	+	2369.33i	−0.363147	+	0.568428i
$260$	1997.85	+	526.954i	0.476545	+	0.125693i
$261$	−502.851	+	216.428i	−0.119256	+	0.0513277i
$262$	−2036.02	−	2642.67i	−0.480097	−	0.623147i
$263$		−	4758.38i		−	1.11564i	−0.829961	−	0.557822i	$-0.811637\pi$
$263$		−	4758.38i		−	1.11564i	0.829961	−	0.557822i	$-0.188363\pi$
$264$	−4663.33	+	3202.60i	−1.08715	+	0.746615i
$265$			480.566i			0.111400i
$266$	−3250.25	+	286.597i	−0.749194	+	0.0660616i
$267$	282.715	+	1371.99i	0.0648011	+	0.314473i
$268$	5144.43	+	1356.90i	1.17256	+	0.309275i
$269$			2644.09i			0.599306i	0.954048	+	0.299653i	$0.0968708\pi$
$269$			2644.09i			0.599306i	−0.954048	+	0.299653i	$0.903129\pi$
$270$	441.921	−	1405.25i	0.0996091	−	0.316743i
$271$			7621.80i			1.70846i	0.519899	+	0.854228i	$0.325970\pi$
$271$			7621.80i			1.70846i	−0.519899	+	0.854228i	$0.674030\pi$
$272$	−2723.78	−	1544.29i	−0.607183	−	0.344250i
$273$	2391.65	−	6253.49i	0.530218	−	1.38637i
$274$	−4651.87	−	6037.95i	−1.02566	−	1.33126i
$275$	−5351.30			−1.17344
$276$	−144.223	+	2635.50i	−0.0314536	+	0.574778i
$277$		−	3715.63i		−	0.805960i	−0.915209	−	0.402980i	$-0.867974\pi$
$277$		−	3715.63i		−	0.805960i	0.915209	−	0.402980i	$-0.132026\pi$
$278$	−5785.10	+	4457.07i	−1.24808	+	0.961573i
$279$	826.006	+	1919.15i	0.177246	+	0.411816i
$280$	−1533.28	−	263.099i	−0.327254	−	0.0561542i
$281$		−	7823.45i		−	1.66088i	−0.557106	−	0.830441i	$-0.688088\pi$
$281$		−	7823.45i		−	1.66088i	0.557106	−	0.830441i	$-0.311912\pi$
$282$	6852.70	+	5903.49i	1.44707	+	1.24662i
$283$	−4118.81			−0.865151			−0.432575	−	0.901598i	$-0.642395\pi$
$283$	−4118.81			−0.865151			−0.432575	+	0.901598i	$0.642395\pi$
$284$	−1001.60	−	264.183i	−0.209275	−	0.0551984i
$285$	1176.79	−	242.493i	0.244586	−	0.0504001i
$286$	7500.25	−	5778.49i	1.55070	−	1.19472i
$287$	4447.41	+	2841.28i	0.914711	+	0.584374i
$288$	−4174.08	+	2542.63i	−0.854027	+	0.520228i
$289$	−2519.49			−0.512821
$290$	−129.933	−	168.647i	−0.0263100	−	0.0341493i
$291$	7019.37	−	1446.43i	1.41403	−	0.291379i
$292$	−2246.01	−	592.407i	−0.450129	−	0.118726i
$293$		−	6032.10i		−	1.20273i	−0.798976	−	0.601363i	$-0.794624\pi$
$293$		−	6032.10i		−	1.20273i	0.798976	−	0.601363i	$-0.205376\pi$
$294$	−1380.22	+	4848.42i	−0.273796	+	0.961788i
$295$	1510.66			0.298148
$296$	−3165.83	+	1333.15i	−0.621656	+	0.261783i
$297$	−3865.14	−	5534.24i	−0.755146	−	1.08124i
$298$	−7286.91	+	5614.13i	−1.41651	+	1.09133i
$299$		−	4417.51i		−	0.854420i
$300$	−4616.38	−	252.622i	−0.888422	−	0.0486172i
$301$	4398.55	−	6884.98i	0.842286	−	1.31842i
$302$	−167.951	+	129.396i	−0.0320016	+	0.0246553i
$303$	598.979	−	123.427i	0.113566	−	0.0234017i
$304$	−3467.86	−	1966.15i	−0.654261	−	0.370942i
$305$		−	2139.78i		−	0.401716i
$306$	1817.08	−	3264.53i	0.339462	−	0.609872i
$307$	2031.61			0.377688			0.188844	−	0.982007i	$-0.439526\pi$
$307$	2031.61			0.377688			0.188844	+	0.982007i	$0.439526\pi$
$308$	−5243.18	+	4830.01i	−0.969994	+	0.893557i
$309$	−8093.61	+	1667.79i	−1.49006	+	0.307046i
$310$	−643.650	+	495.894i	−0.117925	+	0.0908544i
$311$	−6093.07			−1.11095			−0.555477	−	0.831532i	$-0.687464\pi$
$311$	−6093.07			−1.11095			−0.555477	+	0.831532i	$0.687464\pi$
$312$	6742.99	−	4630.83i	1.22355	−	0.840286i
$313$		−	2761.91i		−	0.498762i	−0.968405	−	0.249381i	$-0.919773\pi$
$313$		−	2761.91i		−	0.498762i	0.968405	−	0.249381i	$-0.0802271\pi$
$314$	1582.08	−	1218.89i	0.284337	−	0.219064i
$315$	299.535	−	1831.99i	0.0535775	−	0.327686i
$316$	−267.118	+	1012.73i	−0.0475524	+	0.180286i
$317$	3870.63			0.685792			0.342896	−	0.939373i	$-0.388592\pi$
$317$	3870.63			0.685792			0.342896	+	0.939373i	$0.388592\pi$
$318$	1441.44	+	1241.77i	0.254188	+	0.218979i
$319$	−975.573			−0.171228
$320$	−1359.67	−	1328.12i	−0.237525	−	0.232013i
$321$	464.681	+	2255.05i	0.0807974	+	0.392101i
$322$	292.151	+	3313.23i	0.0505618	+	0.573413i
$323$	3047.36			0.524953
$324$	−3073.07	−	4956.66i	−0.526932	−	0.849908i
$325$	7737.77			1.32066
$326$	2624.52	+	3406.52i	0.445885	+	0.578741i
$327$	8425.02	−	1736.08i	1.42478	−	0.293595i
$328$	2502.42	+	5942.50i	0.421260	+	1.00036i
$329$	9605.09	+	6136.33i	1.60956	+	1.02829i
$330$	1713.37	−	1988.86i	0.285813	−	0.331768i
$331$		−	4264.16i		−	0.708095i	−0.935227	−	0.354048i	$-0.884805\pi$
$331$		−	4264.16i		−	0.708095i	0.935227	−	0.354048i	$-0.115195\pi$
$332$	5904.47	+	1557.36i	0.976053	+	0.257444i
$333$	−1620.45	−	3764.97i	−0.266667	−	0.619577i
$334$	4390.22	−	3382.40i	0.719229	−	0.554123i
$335$	−2468.84			−0.402648
$336$	−4751.13	+	3919.17i	−0.771414	+	0.636333i
$337$	−3256.10			−0.526323			−0.263162	−	0.964752i	$-0.584765\pi$
$337$	−3256.10			−0.526323			−0.263162	+	0.964752i	$0.584765\pi$
$338$	−5922.53	+	4562.95i	−0.953087	+	0.734296i
$339$	375.521	−	77.3809i	0.0601637	−	0.0123975i
$340$	1404.90	+	370.556i	0.224092	+	0.0591065i
$341$			3723.32i			0.591288i
$342$	2313.46	−	4156.33i	0.365782	−	0.657159i
$343$	−853.212	+	6294.89i	−0.134312	+	0.990939i
$344$	9199.52	−	3873.97i	1.44187	−	0.607182i
$345$	−247.192	−	1199.59i	−0.0385749	−	0.187200i
$346$	6633.09	+	8609.49i	1.03063	+	1.33771i
$347$	−6076.58			−0.940081			−0.470041	−	0.882645i	$-0.655761\pi$
$347$	−6076.58			−0.940081			−0.470041	+	0.882645i	$0.655761\pi$
$348$	−841.593	−	46.0545i	−0.129638	−	0.00709420i
$349$	−6858.46			−1.05193			−0.525967	−	0.850505i	$-0.676296\pi$
$349$	−6858.46			−1.05193			−0.525967	+	0.850505i	$0.676296\pi$
$350$	−5803.49	+	511.734i	−0.886313	+	0.0781524i
$351$	5588.85	+	8002.30i	0.849887	+	1.21690i
$352$	−8623.70	+	1221.26i	−1.30581	+	0.184924i
$353$	−6340.22			−0.955965			−0.477983	−	0.878369i	$-0.658632\pi$
$353$	−6340.22			−0.955965			−0.477983	+	0.878369i	$0.658632\pi$
$354$	3903.51	−	4531.15i	0.586071	−	0.680304i
$355$	480.674			0.0718635
$356$	−550.038	+	2085.37i	−0.0818875	+	0.310462i
$357$	1681.82	−	4397.47i	0.249331	−	0.651930i
$358$	6162.60	−	4747.91i	0.909786	−	0.700935i
$359$			79.4813i			0.0116849i	0.999983	+	0.00584243i	$0.00185971\pi$
$359$			79.4813i			0.0116849i	−0.999983	+	0.00584243i	$0.998140\pi$
$360$	1571.96	−	1634.84i	0.230137	−	0.239343i
$361$	−2979.17			−0.434345
$362$	−2911.98	+	2243.50i	−0.422791	+	0.325735i
$363$	−1031.97	−	5008.06i	−0.149214	−	0.724119i
$364$	7581.44	−	6984.01i	1.09169	−	1.00566i
$365$	1077.87			0.154571
$366$	−6418.17	−	5529.15i	−0.916621	−	0.789654i
$367$			11025.8i			1.56824i	0.620610	+	0.784120i	$0.286885\pi$
$367$			11025.8i			1.56824i	−0.620610	+	0.784120i	$0.713115\pi$
$368$	−2004.25	+	3535.05i	−0.283909	+	0.500754i
$369$	−7067.13	+	3041.70i	−0.997019	+	0.429118i
$370$	1262.70	−	972.837i	0.177418	−	0.136690i
$371$	2020.39	+	1290.75i	0.282732	+	0.180626i
$372$	−175.769	+	3211.98i	−0.0244979	+	0.447670i
$373$		−	5947.81i		−	0.825646i	−0.910811	−	0.412823i	$-0.864543\pi$
$373$		−	5947.81i		−	0.825646i	0.910811	−	0.412823i	$-0.135457\pi$
$374$	5274.20	−	4063.45i	0.729204	−	0.561808i
$375$	4462.80	−	919.617i	0.614555	−	0.126637i
$376$	5404.50	+	12834.1i	0.741266	+	1.76028i
$377$	1410.64			0.192710
$378$	−4720.98	−	5632.27i	−0.642384	−	0.766383i
$379$			4855.67i			0.658098i	0.944313	+	0.329049i	$0.106728\pi$
$379$			4855.67i			0.658098i	−0.944313	+	0.329049i	$0.893272\pi$
$380$	1788.68	+	471.783i	0.241467	+	0.0636893i
$381$	2055.46	+	9974.91i	0.276389	+	1.34129i
$382$	6757.16	+	8770.53i	0.905043	+	1.17471i
$383$	4314.03			0.575553			0.287777	−	0.957698i	$-0.407084\pi$
$383$	4314.03			0.575553			0.287777	+	0.957698i	$0.407084\pi$
$384$	−7497.01	+	646.434i	−0.996303	+	0.0859067i
$385$	1780.95	−	2787.69i	0.235755	−	0.369023i
$386$	8174.00	−	6297.58i	1.07784	−	0.830410i
$387$	4708.82	+	10940.5i	0.618509	+	1.43705i
$388$	10669.2	+	2814.11i	1.39600	+	0.368208i
$389$	1492.00			0.194466			0.0972330	−	0.995262i	$-0.469001\pi$
$389$	1492.00			0.194466			0.0972330	+	0.995262i	$0.469001\pi$
$390$	−2477.47	+	2875.82i	−0.321671	+	0.373392i
$391$		−	3106.41i		−	0.401785i
$392$	−5224.35	+	5739.55i	−0.673137	+	0.739518i
$393$	6002.55	−	1236.90i	0.770454	−	0.158762i
$394$	−177.194	+	136.517i	−0.0226571	+	0.0174559i
$395$		−	486.015i		−	0.0619090i
$396$	−1538.18	−	10278.4i	−0.195193	−	1.30431i
$397$	2577.45			0.325840			0.162920	−	0.986639i	$-0.447909\pi$
$397$	2577.45			0.325840			0.162920	+	0.986639i	$0.447909\pi$
$398$	1226.78	+	1592.32i	0.154505	+	0.200542i
$399$	2141.25	−	5598.76i	0.268663	−	0.702478i
$400$	−6192.04	−	3510.66i	−0.774005	−	0.438833i
$401$			3185.37i			0.396682i	0.980133	+	0.198341i	$0.0635554\pi$
$401$			3185.37i			0.396682i	−0.980133	+	0.198341i	$0.936445\pi$
$402$	−6379.44	+	7405.18i	−0.791486	+	0.918748i
$403$		−	5383.78i		−	0.665471i
$404$	910.427	+	240.134i	0.112117	+	0.0295721i
$405$	1965.46	+	1860.32i	0.241147	+	0.228247i
$406$	−1058.01	+	93.2922i	−0.129330	+	0.0114040i
$407$		−	7304.36i		−	0.889592i
$408$	4741.69	−	3256.42i	0.575364	−	0.395139i
$409$		−	9157.04i		−	1.10706i	−0.832830	−	0.553529i	$-0.813281\pi$
$409$		−	9157.04i		−	1.10706i	0.832830	−	0.553529i	$-0.186719\pi$
$410$	−1826.09	−	2370.19i	−0.219961	−	0.285501i
$411$	13714.6	−	2826.06i	1.64596	−	0.339172i
$412$	−12302.0	−	3244.78i	−1.47106	−	0.388007i
$413$	4057.47	−	6351.09i	0.483426	−	0.756699i
$414$	−4236.87	−	2358.29i	−0.502972	−	0.279960i
$415$	−2833.58			−0.335169
$416$	12469.5	−	1765.89i	1.46964	−	0.208125i
$417$	−2707.72	−	13140.3i	−0.317980	−	1.54312i
$418$	6714.98	−	5173.49i	0.785743	−	0.605368i
$419$			16278.2i			1.89796i	0.315339	+	0.948979i	$0.397882\pi$
$419$			16278.2i			1.89796i	−0.315339	+	0.948979i	$0.602118\pi$
$420$	1667.96	−	2320.77i	0.193782	−	0.269624i
$421$		−	14.4956i		−	0.00167808i	−1.00000		0.000839038i	$-0.999733\pi$
$421$		−	14.4956i		−	0.00167808i	1.00000		0.000839038i	$-0.000267074\pi$
$422$	−3925.32	−	5094.91i	−0.452800	−	0.587716i
$423$	−15262.9	+	6569.18i	−1.75439	+	0.755093i
$424$	1136.81	+	2699.59i	0.130209	+	0.309207i
$425$	5441.22			0.621031
$426$	1242.05	−	1441.76i	0.141262	−	0.163975i
$427$	−8996.03	−	5747.22i	−1.01955	−	0.651353i
$428$	−904.062	+	3427.59i	−0.102102	+	0.387100i
$429$	3510.50	+	17036.1i	0.395078	+	1.91727i
$430$	−3669.26	+	2826.95i	−0.411506	+	0.317041i
$431$			6800.15i			0.759981i	0.924990	+	0.379991i	$0.124073\pi$
$431$			6800.15i			0.759981i	−0.924990	+	0.379991i	$0.875927\pi$
$432$	−841.718	−	8939.41i	−0.0937435	−	0.995596i
$433$			11155.5i			1.23811i	0.785349	+	0.619053i	$0.212483\pi$
$433$			11155.5i			1.23811i	−0.785349	+	0.619053i	$0.787517\pi$
$434$	356.054	+	4037.94i	0.0393805	+	0.446607i
$435$	383.065	−	78.9355i	0.0422220	−	0.00870038i
$436$	12805.7	+	3377.64i	1.40661	+	0.371009i
$437$		−	3955.01i		−	0.432938i
$438$	2785.20	−	3233.02i	0.303840	−	0.352694i
$439$		−	12426.7i		−	1.35101i	−0.737357	−	0.675504i	$-0.763926\pi$
$439$		−	12426.7i		−	1.35101i	0.737357	−	0.675504i	$-0.236074\pi$
$440$	3724.84	−	1568.55i	0.403579	−	0.169950i
$441$	−6897.51	−	6179.84i	−0.744792	−	0.667297i
$442$	−7626.28	+	5875.59i	−0.820691	+	0.632293i
$443$	−10870.0			−1.16580			−0.582900	−	0.812544i	$-0.698082\pi$
$443$	−10870.0			−1.16580			−0.582900	+	0.812544i	$0.698082\pi$
$444$	344.822	−	6301.22i	0.0368570	−	0.673519i
$445$		−	1000.78i		−	0.106610i
$446$	5518.38	+	7162.63i	0.585880	+	0.760449i
$447$	−3410.64	−	16551.5i	−0.360890	−	1.75136i
$448$	−9235.62	+	2149.12i	−0.973978	+	0.226644i
$449$			11786.4i			1.23883i	0.785063	+	0.619416i	$0.212631\pi$
$449$			11786.4i			1.23883i	−0.785063	+	0.619416i	$0.787369\pi$
$450$	4130.80	−	7421.34i	0.432729	−	0.777434i
$451$	−13710.8			−1.43153
$452$	570.779	+	150.549i	0.0593964	+	0.0156664i
$453$	−78.6095	−	381.483i	−0.00815319	−	0.0395665i
$454$	−5357.67	−	6954.05i	−0.553850	−	0.718876i
$455$	−2575.18	+	4030.90i	−0.265333	+	0.415321i
$456$	6037.01	−	4145.99i	0.619976	−	0.425776i
$457$	−1151.19			−0.117834			−0.0589171	−	0.998263i	$-0.518765\pi$
$457$	−1151.19			−0.117834			−0.0589171	+	0.998263i	$0.518765\pi$
$458$	1554.17	−	1197.40i	0.158563	−	0.122163i
$459$	3930.09	+	5627.24i	0.399654	+	0.572238i
$460$	480.924	−	1823.34i	0.0487461	−	0.184812i
$461$			1149.15i			0.116098i	0.998314	+	0.0580491i	$0.0184880\pi$
$461$			1149.15i			0.116098i	−0.998314	+	0.0580491i	$0.981512\pi$
$462$	−3759.62	−	12545.2i	−0.378600	−	1.26333i
$463$	511.258			0.0513179			0.0256590	−	0.999671i	$-0.491832\pi$
$463$	511.258			0.0513179			0.0256590	+	0.999671i	$0.491832\pi$
$464$	−1128.85	−	640.014i	−0.112943	−	0.0640343i
$465$	−301.261	−	1461.99i	−0.0300444	−	0.145802i
$466$	−5504.58	−	7144.73i	−0.547199	−	0.710243i
$467$			7738.29i			0.766779i	0.923587	+	0.383389i	$0.125243\pi$
$467$			7738.29i			0.766779i	−0.923587	+	0.383389i	$0.874757\pi$
$468$	2224.15	+	14862.1i	0.219682	+	1.46795i
$469$	−6631.05	+	10379.5i	−0.652864	+	1.02192i
$470$	−3943.81	−	5118.91i	−0.387052	−	0.502378i
$471$	740.492	+	3593.53i	0.0724418	+	0.351552i
$472$	8486.14	−	3573.57i	0.827556	−	0.348489i
$473$			21225.6i			2.06333i
$474$	−1457.78	−	1255.85i	−0.141262	−	0.121695i
$475$	6927.64			0.669183
$476$	5331.29	−	4911.18i	0.513360	−	0.472906i
$477$	−3210.49	+	1381.80i	−0.308173	+	0.132638i
$478$	3243.63	+	4210.10i	0.310377	+	0.402857i
$479$	−15169.4			−1.44699			−0.723493	−	0.690332i	$-0.757465\pi$
$479$	−15169.4			−1.44699			−0.723493	+	0.690332i	$0.757465\pi$
$480$	3287.33	−	1177.29i	0.312595	−	0.111950i
$481$			10561.8i			1.00120i
$482$	5665.20	+	7353.20i	0.535358	+	0.694874i
$483$	−5707.25	−	2182.74i	−0.537658	−	0.205628i
$484$	2007.76	−	7612.08i	0.188558	−	0.714884i
$485$	−5120.20			−0.479374
$486$	10658.7	−	1088.27i	0.994828	−	0.101574i
$487$	−7078.96			−0.658683			−0.329341	−	0.944211i	$-0.606827\pi$
$487$	−7078.96			−0.658683			−0.329341	+	0.944211i	$0.606827\pi$
$488$	−5061.80	−	12020.2i	−0.469543	−	1.11502i
$489$	−7737.57	+	1594.42i	−0.715552	+	0.147449i
$490$	1664.86	−	3193.56i	0.153491	−	0.294430i
$491$	−8864.05			−0.814723			−0.407361	−	0.913267i	$-0.633551\pi$
$491$	−8864.05			−0.814723			−0.407361	+	0.913267i	$0.633551\pi$
$492$	−11827.9	−	647.256i	−1.08382	−	0.0593101i
$493$	991.967			0.0906206
$494$	−9709.60	+	7480.67i	−0.884323	+	0.681318i
$495$	1906.58	+	4429.77i	0.173120	+	0.402229i
$496$	−2442.64	+	4308.29i	−0.221125	+	0.390016i
$497$	1291.04	−	2020.85i	0.116521	−	0.182389i
$498$	−7321.93	+	8499.21i	−0.658843	+	0.764777i
$499$		−	9294.42i		−	0.833818i	−0.908948	−	0.416909i	$-0.863113\pi$
$499$		−	9294.42i		−	0.833818i	0.908948	−	0.416909i	$-0.136887\pi$
$500$	6783.31	+	1789.17i	0.606717	+	0.160028i
$501$	2054.85	+	9971.95i	0.183241	+	0.889249i
$502$	2900.78	+	3765.09i	0.257904	+	0.334749i
$503$	3930.02			0.348372			0.174186	−	0.984713i	$-0.444271\pi$
$503$	3930.02			0.348372			0.174186	+	0.984713i	$0.444271\pi$
$504$	−2651.06	−	10999.8i	−0.234301	−	0.972164i
$505$	−436.919			−0.0385003
$506$	−5273.74	−	6845.10i	−0.463333	−	0.601387i
$507$	−2772.05	−	13452.4i	−0.242822	−	1.17839i
$508$	−3999.00	+	15161.5i	−0.349266	+	1.32418i
$509$		−	4139.73i		−	0.360491i	−0.983622	−	0.180246i	$-0.942311\pi$
$509$		−	4139.73i		−	0.360491i	0.983622	−	0.180246i	$-0.0576893\pi$
$510$	−1742.17	+	2022.29i	−0.151264	+	0.175585i
$511$	2895.05	−	4531.57i	0.250625	−	0.392299i
$512$	−10779.8	−	4244.35i	−0.930474	−	0.366358i
$513$	5003.70	+	7164.47i	0.430641	+	0.616606i
$514$	−15025.8	+	11576.5i	−1.28942	+	0.993419i
$515$	5903.80			0.505150
$516$	−1002.01	+	18310.6i	−0.0854864	+	1.56217i
$517$	−29611.4			−2.51897
$518$	−698.502	−	7921.59i	−0.0592479	−	0.671920i
$519$	−19555.6	+	4029.68i	−1.65394	+	0.340815i
$520$	−5385.97	+	2268.07i	−0.454212	+	0.191272i
$521$	−15730.9			−1.32281			−0.661406	−	0.750028i	$-0.730040\pi$
$521$	−15730.9			−1.32281			−0.661406	+	0.750028i	$0.730040\pi$
$522$	753.070	−	1352.95i	0.0631436	−	0.113443i
$523$	12687.5			1.06078			0.530388	−	0.847755i	$-0.322046\pi$
$523$	12687.5			1.06078			0.530388	+	0.847755i	$0.322046\pi$
$524$	9123.67	+	2406.46i	0.760628	+	0.200623i
$525$	3823.32	−	9996.88i	0.317835	−	0.831047i
$526$	8214.03	+	10661.5i	0.680891	+	0.883769i
$527$		−	3785.89i		−	0.312933i
$528$	4920.11	−	15225.6i	0.405531	−	1.25494i
$529$	8135.36			0.668641
$530$	−829.565	−	1076.74i	−0.0679887	−	0.0882465i
$531$	4343.68	+	10092.2i	0.354990	+	0.824788i
$532$	6787.68	−	6252.80i	0.553164	−	0.509574i
$533$	19825.3			1.61113
$534$	−3001.80	−	2586.00i	−0.243260	−	0.209564i
$535$		−	1644.92i		−	0.132927i
$536$	−13868.8	+	5840.22i	−1.11761	+	0.470633i
$537$	2884.41	+	13997.7i	0.231790	+	1.12485i
$538$	−4564.30	−	5924.27i	−0.365764	−	0.474746i
$539$	−6936.54	−	14974.9i	−0.554319	−	1.19669i
$540$	1435.62	+	3911.41i	0.114406	+	0.311704i
$541$		−	16674.9i		−	1.32516i	−0.748991	−	0.662580i	$-0.769462\pi$
$541$		−	16674.9i		−	1.32516i	0.748991	−	0.662580i	$-0.230538\pi$
$542$	−13156.9	−	17077.2i	−1.04269	−	1.35337i
$543$	−1362.95	−	6614.26i	−0.107716	−	0.522735i
$544$	8768.61	−	1241.78i	0.691086	−	0.0978694i
$545$	−6145.54			−0.483020
$546$	5436.26	+	18139.9i	0.426100	+	1.42183i
$547$			3533.79i			0.276223i	0.990417	+	0.138111i	$0.0441032\pi$
$547$			3533.79i			0.276223i	−0.990417	+	0.138111i	$0.955897\pi$
$548$	20845.7	+	5498.26i	1.62497	+	0.428602i
$549$	14295.1	−	6152.63i	1.11129	−	0.478302i
$550$	11990.0	−	9237.54i	0.929552	−	0.716164i
$551$	1262.95			0.0976469
$552$	−4226.33	−	6153.99i	−0.325878	−	0.474513i
$553$	−2043.30	−	1305.39i	−0.157125	−	0.100381i
$554$	6414.02	+	8325.14i	0.491887	+	0.638450i
$555$	591.009	+	2868.10i	0.0452017	+	0.219359i
$556$	5268.01	−	19972.8i	0.401823	−	1.52344i
$557$	−8507.84			−0.647197			−0.323599	−	0.946194i	$-0.604893\pi$
$557$	−8507.84			−0.647197			−0.323599	+	0.946194i	$0.604893\pi$
$558$	−5163.61	−	2874.13i	−0.391744	−	0.218049i
$559$		−	30691.4i		−	2.32219i
$560$	3889.59	−	2057.30i	0.293509	−	0.155244i
$561$	2468.59	+	11979.8i	0.185783	+	0.901582i
$562$	13505.0	+	17529.0i	1.01366	+	1.31569i
$563$			12127.1i			0.907808i	0.891051	+	0.453904i	$0.149969\pi$
$563$			12127.1i			0.907808i	−0.891051	+	0.453904i	$0.850031\pi$
$564$	−25544.7	−	1397.88i	−1.90714	−	0.104364i
$565$	−273.920			−0.0203963
$566$	9228.47	−	7109.98i	0.685338	−	0.528012i
$567$	13100.2	−	3266.54i	0.970290	−	0.241943i
$568$	2700.20	−	1137.07i	0.199468	−	0.0839972i
$569$		−	16103.5i		−	1.18646i	−0.805034	−	0.593228i	$-0.797853\pi$
$569$		−	16103.5i		−	1.18646i	0.805034	−	0.593228i	$-0.202147\pi$
$570$	−2218.08	+	2574.73i	−0.162992	+	0.189199i
$571$		−	16824.4i		−	1.23307i	−0.787329	−	0.616533i	$-0.788537\pi$
$571$		−	16824.4i		−	1.23307i	0.787329	−	0.616533i	$-0.211463\pi$
$572$	−6829.86	+	25894.2i	−0.499250	+	1.89282i
$573$	−19921.4	+	4105.05i	−1.45240	+	0.299286i
$574$	−14869.4	+	1311.14i	−1.08125	+	0.0953413i
$575$		−	7061.87i		−	0.512175i
$576$	4963.17	−	12902.3i	0.359026	−	0.933328i
$577$		−	12917.3i		−	0.931986i	−0.884788	−	0.465993i	$-0.845697\pi$
$577$		−	12917.3i		−	0.931986i	0.884788	−	0.465993i	$-0.154303\pi$
$578$	5645.09	−	4349.20i	0.406237	−	0.312981i
$579$	3825.85	+	18566.4i	0.274606	+	1.33263i
$580$	582.246	+	153.573i	0.0416835	+	0.0109944i
$581$	−7610.71	+	11912.9i	−0.543452	+	0.850657i
$582$	−13230.5	+	15357.8i	−0.942307	+	1.09382i
$583$	−6228.63			−0.442476
$584$	6054.96	−	2549.78i	0.429034	−	0.180669i
$585$	−2756.84	−	6405.27i	−0.194840	−	0.452693i
$586$	10412.8	+	13515.3i	0.734039	+	0.952753i
$587$		−	15149.6i		−	1.06523i	−0.846357	−	0.532617i	$-0.821209\pi$
$587$		−	15149.6i		−	1.06523i	0.846357	−	0.532617i	$-0.178791\pi$
$588$	−5276.98	−	13245.8i	−0.370101	−	0.928992i
$589$		−	4820.10i		−	0.337197i
$590$	−3384.73	+	2607.73i	−0.236182	+	0.181964i
$591$	−82.9357	−	402.478i	−0.00577245	−	0.0280131i
$592$	4791.95	−	8451.95i	0.332682	−	0.586779i
$593$	5091.10			0.352558			0.176279	−	0.984340i	$-0.443594\pi$
$593$	5091.10			0.352558			0.176279	+	0.984340i	$0.443594\pi$
$594$	18213.5	+	5727.75i	1.25809	+	0.395644i
$595$	−1810.88	+	2834.54i	−0.124771	+	0.195302i
$596$	6635.59	−	25157.7i	0.456048	−	1.72902i
$597$	−3616.78	+	745.285i	−0.247948	+	0.0510929i
$598$	7625.62	+	9897.75i	0.521463	+	0.676838i
$599$			18901.6i			1.28931i	0.764472	+	0.644657i	$0.223000\pi$
$599$			18901.6i			1.28931i	−0.764472	+	0.644657i	$0.777000\pi$
$600$	10779.4	−	7402.88i	0.733445	−	0.503702i
$601$			28238.3i			1.91658i	0.285803	+	0.958288i	$0.407740\pi$
$601$			28238.3i			1.91658i	−0.285803	+	0.958288i	$0.592260\pi$
$602$	2029.76	+	23019.2i	0.137420	+	1.55846i
$603$	−7098.80	−	16493.5i	−0.479412	−	1.11387i
$604$	152.939	−	579.841i	0.0103030	−	0.0390619i
$605$			3653.08i			0.245486i
$606$	−1128.99	+	1310.52i	−0.0756801	+	0.0878485i
$607$			11435.7i			0.764683i	0.924021	+	0.382342i	$0.124882\pi$
$607$			11435.7i			0.764683i	−0.924021	+	0.382342i	$0.875118\pi$
$608$	11164.0	−	1581.01i	0.744670	−	0.105458i
$609$	697.013	−	1822.49i	0.0463783	−	0.121266i
$610$	3693.74	+	4794.32i	0.245172	+	0.318224i
$611$	42816.9			2.83500
$612$	1564.03	+	10451.1i	0.103304	+	0.690295i
$613$			577.455i			0.0380476i	0.999819	+	0.0190238i	$0.00605583\pi$
$613$			577.455i			0.0380476i	−0.999819	+	0.0190238i	$0.993944\pi$
$614$	−4551.97	+	3507.02i	−0.299190	+	0.230508i
$615$	5383.65	−	1109.37i	0.352991	−	0.0727383i
$616$	3410.03	−	19872.9i	0.223042	−	1.29984i
$617$		−	22282.8i		−	1.45393i	−0.686677	−	0.726963i	$-0.740931\pi$
$617$		−	22282.8i		−	1.45393i	0.686677	−	0.726963i	$-0.259069\pi$
$618$	15255.3	−	17708.2i	0.992975	−	1.15263i
$619$	16401.1			1.06497			0.532484	−	0.846440i	$-0.321259\pi$
$619$	16401.1			1.06497			0.532484	+	0.846440i	$0.321259\pi$
$620$	586.119	−	2222.17i	0.0379663	−	0.143943i
$621$	7303.30	−	5100.66i	0.471934	−	0.329601i
$622$	13652.0	−	10518.0i	0.880054	−	0.678028i
$623$	−4207.48	−	2688.00i	−0.270576	−	0.172861i
$624$	−7114.28	+	22015.6i	−0.456409	+	1.41239i
$625$	10647.0			0.681409
$626$	4767.68	+	6188.26i	0.304401	+	0.395100i
$627$	3142.95	+	15252.4i	0.200187	+	0.971487i
$628$	−1440.67	+	5462.04i	−0.0915428	+	0.347068i
$629$			7427.10i			0.470808i
$630$	2491.30	+	4621.77i	0.157549	+	0.292279i
$631$	6542.50			0.412762			0.206381	−	0.978472i	$-0.433831\pi$
$631$	6542.50			0.412762			0.206381	+	0.978472i	$0.433831\pi$
$632$	−1149.70	−	2730.20i	−0.0723619	−	0.171838i
$633$	11572.6	−	2384.68i	0.726648	−	0.149735i
$634$	−8672.40	+	6681.57i	−0.543257	+	0.418547i
$635$		−	7276.09i		−	0.454713i
$636$	−5373.22	−	294.039i	−0.335003	−	0.0183324i
$637$	10030.0	+	21653.1i	0.623865	+	1.34683i
$638$	2185.84	−	1684.06i	0.135640	−	0.104502i
$639$	1382.11	+	3211.21i	0.0855641	+	0.198801i
$640$	5339.08	+	628.651i	0.329759	+	0.0388275i
$641$		−	634.500i		−	0.0390971i	−0.999809	−	0.0195486i	$-0.993777\pi$
$641$		−	634.500i		−	0.0390971i	0.999809	−	0.0195486i	$-0.00622290\pi$
$642$	−4933.86	−	4250.44i	−0.303309	−	0.261295i
$643$	4543.63			0.278668			0.139334	−	0.990245i	$-0.455504\pi$
$643$	4543.63			0.278668			0.139334	+	0.990245i	$0.455504\pi$
$644$	−6373.96	−	6919.20i	−0.390014	−	0.423377i
$645$	−1717.40	−	8334.36i	−0.104841	−	0.508783i
$646$	−6827.82	+	5260.43i	−0.415847	+	0.320385i
$647$	18802.6			1.14252			0.571258	−	0.820771i	$-0.306456\pi$
$647$	18802.6			1.14252			0.571258	+	0.820771i	$0.306456\pi$
$648$	15441.7	+	5800.94i	0.936124	+	0.351671i
$649$			19579.6i			1.18423i
$650$	−17337.0	+	13357.1i	−1.04617	+	0.806014i
$651$	−6955.62	−	2660.18i	−0.418759	−	0.160155i
$652$	−11760.8	−	3102.04i	−0.706426	−	0.186327i
$653$	−20232.4			−1.21249			−0.606243	−	0.795279i	$-0.707324\pi$
$653$	−20232.4			−1.21249			−0.606243	+	0.795279i	$0.707324\pi$
$654$	−15880.0	+	18433.3i	−0.949474	+	1.10214i
$655$	−4378.50			−0.261194
$656$	−15864.9	−	8994.84i	−0.944241	−	0.535350i
$657$	3099.26	+	7200.87i	0.184039	+	0.427599i
$658$	−32113.6	+	2831.68i	−1.90261	+	0.167766i
$659$	13420.3			0.793295			0.396648	−	0.917971i	$-0.370173\pi$
$659$	13420.3			0.793295			0.396648	+	0.917971i	$0.370173\pi$
$660$	−405.708	+	7413.85i	−0.0239275	+	0.437248i
$661$	8321.89			0.489689			0.244844	−	0.969562i	$-0.421263\pi$
$661$	8321.89			0.489689			0.244844	+	0.969562i	$0.421263\pi$
$662$	7360.90	+	9554.15i	0.432159	+	0.560925i
$663$	−3569.49	−	17322.3i	−0.209091	−	1.01470i
$664$	−15917.7	+	6703.05i	−0.930312	+	0.391760i
$665$	−2305.57	+	3608.87i	−0.134445	+	0.210445i
$666$	10129.9	+	5638.42i	0.589378	+	0.328055i
$667$		−	1287.42i		−	0.0747364i
$668$	−3997.82	+	15157.0i	−0.231557	+	0.877908i
$669$	−16269.2	+	3352.47i	−0.940214	+	0.193743i
$670$	5531.61	−	4261.77i	0.318962	−	0.245741i
$671$	27733.7			1.59560
$672$	3879.87	−	16982.7i	0.222722	−	0.974882i
$673$	2322.47			0.133023			0.0665117	−	0.997786i	$-0.478813\pi$
$673$	2322.47			0.133023			0.0665117	+	0.997786i	$0.478813\pi$
$674$	7295.51	−	5620.75i	0.416933	−	0.321221i
$675$	8934.37	+	12792.5i	0.509458	+	0.729459i
$676$	5393.16	−	20447.2i	0.306848	−	1.16336i
$677$		−	1313.39i		−	0.0745606i	−0.999305	−	0.0372803i	$-0.988131\pi$
$677$		−	1313.39i		−	0.0745606i	0.999305	−	0.0372803i	$-0.0118694\pi$
$678$	−707.804	+	821.611i	−0.0400930	+	0.0465395i
$679$	−13752.3	+	21526.3i	−0.777270	+	1.21665i
$680$	−3787.43	+	1594.91i	−0.213590	+	0.0899441i
$681$	15795.4	−	3254.85i	0.888813	−	0.183151i
$682$	−6427.29	−	8342.36i	−0.360870	−	0.468395i
$683$	−20367.6			−1.14106			−0.570532	−	0.821276i	$-0.693263\pi$
$683$	−20367.6			−1.14106			−0.570532	+	0.821276i	$0.693263\pi$
$684$	1991.29	+	13306.1i	0.111314	+	0.743817i
$685$	−10004.0			−0.558002
$686$	−8954.71	−	15577.0i	−0.498385	−	0.866956i
$687$	727.431	+	3530.14i	0.0403977	+	0.196046i
$688$	−13924.8	+	24560.3i	−0.771625	+	1.36098i
$689$	9006.35			0.497989
$690$	2624.62	+	2261.06i	0.144808	+	0.124750i
$691$	19327.1			1.06402			0.532010	−	0.846738i	$-0.321437\pi$
$691$	19327.1			1.06402			0.532010	+	0.846738i	$0.321437\pi$
$692$	−29723.8	−	7839.95i	−1.63285	−	0.430680i
$693$	23744.5	+	3882.28i	1.30155	+	0.212808i
$694$	13615.0	−	10489.5i	0.744696	−	0.573743i
$695$			9585.03i			0.523138i
$696$	1965.15	−	1349.59i	0.107024	−	0.0735001i
$697$	13941.2			0.757621
$698$	15366.9	−	11839.2i	0.833301	−	0.642008i
$699$	16228.5	−	3344.09i	0.878139	−	0.180952i
$700$	12119.7	−	11164.7i	0.654405	−	0.602837i
$701$	−7068.43			−0.380843			−0.190422	−	0.981702i	$-0.560985\pi$
$701$	−7068.43			−0.380843			−0.190422	+	0.981702i	$0.560985\pi$
$702$	−26336.0	−	8282.10i	−1.41594	−	0.445282i
$703$			9456.02i			0.507312i
$704$	17213.8	−	17622.7i	0.921549	−	0.943441i
$705$	11627.1	−	2395.91i	0.621137	−	0.127993i
$706$	14205.7	−	10944.6i	0.757278	−	0.583437i
$707$	−1173.52	+	1836.89i	−0.0624253	+	0.0977134i
$708$	−924.309	+	16890.7i	−0.0490645	+	0.896597i
$709$		−	5102.93i		−	0.270303i	−0.990825	−	0.135151i	$-0.956848\pi$
$709$		−	5102.93i		−	0.270303i	0.990825	−	0.135151i	$-0.0431520\pi$
$710$	−1076.98	+	829.751i	−0.0569274	+	0.0438592i
$711$	3246.89	−	1397.47i	0.171263	−	0.0737118i
$712$	−2367.42	−	5621.91i	−0.124611	−	0.295913i
$713$	−4913.50			−0.258082
$714$	3822.79	+	12756.0i	0.200370	+	0.668603i
$715$		−	12426.8i		−	0.649979i
$716$	−5611.77	+	21276.0i	−0.292907	+	1.11051i
$717$	−9562.82	+	1970.54i	−0.498089	+	0.102638i
$718$	−137.202	−	178.083i	−0.00713141	−	0.00925628i
$719$	−2163.33			−0.112209			−0.0561046	−	0.998425i	$-0.517868\pi$
$719$	−2163.33			−0.112209			−0.0561046	+	0.998425i	$0.517868\pi$
$720$	−699.981	+	6376.52i	−0.0362316	+	0.330054i
$721$	15857.0	−	24820.7i	0.819064	−	1.28207i
$722$	6675.04	−	5142.72i	0.344071	−	0.265086i
$723$	−16702.0	+	3441.67i	−0.859137	+	0.177036i
$724$	2651.70	−	10053.5i	0.136118	−	0.516068i
$725$	2255.06			0.115518
$726$	10957.2	+	9439.49i	0.560140	+	0.482551i
$727$		−	24985.1i		−	1.27462i	−0.770609	−	0.637309i	$-0.780048\pi$
$727$		−	24985.1i		−	1.27462i	0.770609	−	0.637309i	$-0.219952\pi$
$728$	−4930.77	+	28735.4i	−0.251026	+	1.46292i
$729$	−6776.74	+	18479.6i	−0.344294	+	0.938862i
$730$	−2415.04	+	1860.65i	−0.122445	+	0.0943364i
$731$		−	21582.3i		−	1.09200i
$732$	23924.9	+	1309.24i	1.20805	+	0.0661079i
$733$	2600.09			0.131018			0.0655092	−	0.997852i	$-0.479133\pi$
$733$	2600.09			0.131018			0.0655092	+	0.997852i	$0.479133\pi$
$734$	−19033.1	−	24704.1i	−0.957116	−	1.24230i
$735$	3935.33	+	5318.74i	0.197492	+	0.266918i
$736$	−1611.64	−	11380.3i	−0.0807146	−	0.569951i
$737$		−	31998.7i		−	1.59930i
$738$	10583.7	−	19014.6i	0.527904	−	0.948424i
$739$			17370.8i			0.864675i	0.901712	+	0.432338i	$0.142311\pi$
$739$			17370.8i			0.864675i	−0.901712	+	0.432338i	$0.857689\pi$
$740$	−1149.84	+	4359.42i	−0.0571202	+	0.216561i
$741$	−4544.59	−	22054.4i	−0.225303	−	1.09337i
$742$	−6754.95	+	595.631i	−0.334208	+	0.0294694i
$743$		−	28215.9i		−	1.39319i	−0.717463	−	0.696597i	$-0.754697\pi$
$743$		−	28215.9i		−	1.39319i	0.717463	−	0.696597i	$-0.245303\pi$
$744$	−5150.77	−	7500.08i	−0.253812	−	0.369578i
$745$			12073.3i			0.593734i
$746$	10267.3	+	13326.5i	0.503902	+	0.654045i
$747$	−8147.57	−	18930.2i	−0.399068	−	0.927201i
$748$	−4802.78	+	18208.9i	−0.234769	+	0.890084i
$749$	−6915.55	−	4418.08i	−0.337368	−	0.215532i
$750$	−8411.75	+	9764.26i	−0.409538	+	0.475387i
$751$	−33427.0			−1.62419			−0.812097	−	0.583522i	$-0.801674\pi$
$751$	−33427.0			−1.62419			−0.812097	+	0.583522i	$0.801674\pi$
$752$	−34263.6	−	19426.2i	−1.66152	−	0.942023i
$753$	−8552.02	+	1762.25i	−0.413882	+	0.0852856i
$754$	−3160.64	+	2435.08i	−0.152657	+	0.117613i
$755$			278.269i			0.0134136i
$756$	20300.2	+	4470.03i	0.976604	+	0.215044i
$757$			24841.4i			1.19270i	0.802723	+	0.596352i	$0.203384\pi$
$757$			24841.4i			1.19270i	−0.802723	+	0.596352i	$0.796616\pi$
$758$	−8381.97	−	10879.5i	−0.401645	−	0.521319i
$759$	15548.0	−	3203.85i	0.743551	−	0.153218i
$760$	−4822.07	+	2030.60i	−0.230151	+	0.0969180i
$761$	−20004.6			−0.952912			−0.476456	−	0.879198i	$-0.658079\pi$
$761$	−20004.6			−0.952912			−0.476456	+	0.879198i	$0.658079\pi$
$762$	−21824.3	−	18801.3i	−1.03755	−	0.893831i
$763$	−16506.3	+	25837.0i	−0.783182	+	1.22590i
$764$	−30279.8	−	7986.60i	−1.43388	−	0.378200i
$765$	−1938.62	−	4504.21i	−0.0916220	−	0.212876i
$766$	−9665.89	+	7446.99i	−0.455931	+	0.351267i
$767$		−	28311.4i		−	1.33281i
$768$	15681.7	−	14389.9i	0.736802	−	0.676108i
$769$			9604.90i			0.450405i	0.974312	+	0.225203i	$0.0723044\pi$
$769$			9604.90i			0.450405i	−0.974312	+	0.225203i	$0.927696\pi$
$770$	821.840	+	9320.34i	0.0384637	+	0.436210i
$771$	−7032.85	−	34129.6i	−0.328511	−	1.59423i
$772$	−7443.39	+	28220.3i	−0.347012	+	1.31564i
$773$		−	4885.24i		−	0.227309i	−0.993520	−	0.113655i	$-0.963744\pi$
$773$		−	4885.24i		−	0.227309i	0.993520	−	0.113655i	$-0.0362557\pi$
$774$	−29436.3	−	16384.6i	−1.36701	−	0.760893i
$775$		−	8606.55i		−	0.398911i
$776$	−28762.8	+	12112.2i	−1.33057	+	0.560313i
$777$	13645.4	+	5218.71i	0.630023	+	0.240953i
$778$	−3342.92	+	2575.52i	−0.154048	+	0.118685i
$779$	17749.6			0.816363
$780$	586.639	−	10720.1i	0.0269295	−	0.492106i
$781$			6230.03i			0.285439i
$782$	5362.36	+	6960.13i	0.245214	+	0.318278i
$783$	1628.79	+	2332.16i	0.0743400	+	0.106442i
$784$	1797.78	−	21878.3i	0.0818959	−	0.996641i
$785$		−	2621.26i		−	0.119181i
$786$	−11314.0	+	13133.1i	−0.513429	+	0.595983i
$787$	−34277.8			−1.55257			−0.776284	−	0.630384i	$-0.782897\pi$
$787$	−34277.8			−1.55257			−0.776284	+	0.630384i	$0.782897\pi$
$788$	161.356	−	611.752i	0.00729450	−	0.0276558i
$789$	−24216.5	+	4990.11i	−1.09269	+	0.225162i
$790$	838.970	+	1088.95i	0.0377838	+	0.0490419i
$791$	−735.721	+	1151.61i	−0.0330711	+	0.0517656i
$792$	21189.2	+	20374.2i	0.950663	+	0.914097i
$793$	−40101.9			−1.79579
$794$	−5774.95	+	4449.25i	−0.258117	+	0.198864i
$795$	2445.71	−	503.970i	0.109107	−	0.0224830i
$796$	−5497.39	−	1449.99i	−0.244786	−	0.0645648i
$797$		−	20736.8i		−	0.921624i	−0.887498	−	0.460812i	$-0.847558\pi$
$797$		−	20736.8i		−	0.921624i	0.887498	−	0.460812i	$-0.152442\pi$
$798$	4867.09	+	16240.7i	0.215906	+	0.720444i
$799$	30109.0			1.33314
$800$	19933.9	−	2822.97i	0.880961	−	0.124759i
$801$	6685.87	−	2877.61i	0.294923	−	0.126935i
$802$	−5498.66	−	7137.03i	−0.242100	−	0.314236i
$803$			13970.3i			0.613949i
$804$	1510.58	−	27604.2i	0.0662614	−	1.21085i
$805$	3678.80	+	2350.24i	0.161069	+	0.102901i
$806$	9293.60	+	12062.7i	0.406145	+	0.527160i
$807$	13456.4	−	2772.86i	0.586973	−	0.120953i
$808$	−2454.40	+	1033.56i	−0.106863	+	0.0450008i
$809$		−	15223.1i		−	0.661576i	−0.943705	−	0.330788i	$-0.892686\pi$
$809$		−	15223.1i		−	0.661576i	0.943705	−	0.330788i	$-0.107314\pi$
$810$	−7615.07	−	775.352i	−0.330329	−	0.0336335i
$811$	34460.7			1.49208			0.746042	−	0.665899i	$-0.231952\pi$
$811$	34460.7			1.49208			0.746042	+	0.665899i	$0.231952\pi$
$812$	2209.50	−	2035.39i	0.0954906	−	0.0879658i
$813$	38789.1	−	7992.98i	1.67330	−	0.344805i
$814$	12609.0	+	16365.9i	0.542929	+	0.704700i
$815$	5644.09			0.242581
$816$	−5002.79	+	15481.4i	−0.214623	+	0.664165i
$817$		−	27478.0i		−	1.17666i
$818$	15807.1	+	20517.0i	0.675651	+	0.876968i
$819$	−34333.6	−	5613.63i	−1.46485	−	0.239507i
$820$	8182.95	+	2158.34i	0.348489	+	0.0919175i
$821$	−8486.07			−0.360738			−0.180369	−	0.983599i	$-0.557729\pi$
$821$	−8486.07			−0.360738			−0.180369	+	0.983599i	$0.557729\pi$
$822$	−25850.1	+	30006.4i	−1.09687	+	1.27323i
$823$	21594.4			0.914622			0.457311	−	0.889307i	$-0.348813\pi$
$823$	21594.4			0.914622			0.457311	+	0.889307i	$0.348813\pi$
$824$	33164.7	−	13965.9i	1.40212	−	0.590442i
$825$	5611.91	+	27234.0i	0.236826	+	1.14929i
$826$	1872.36	+	21234.1i	0.0788715	+	0.894468i
$827$	−11423.5			−0.480330			−0.240165	−	0.970732i	$-0.577202\pi$
$827$	−11423.5			−0.480330			−0.240165	+	0.970732i	$0.577202\pi$
$828$	13563.9	−	2029.87i	0.569298	−	0.0851967i
$829$	6869.52			0.287802			0.143901	−	0.989592i	$-0.454035\pi$
$829$	6869.52			0.287802			0.143901	+	0.989592i	$0.454035\pi$
$830$	6348.84	−	4891.40i	0.265508	−	0.204558i
$831$	−18909.7	+	3896.59i	−0.789375	+	0.162661i
$832$	−24890.5	+	25481.8i	−1.03717	+	1.06181i
$833$	7053.11	+	15226.5i	0.293368	+	0.633336i
$834$	28749.9	+	24767.6i	1.19368	+	1.02833i
$835$		−	7273.94i		−	0.301467i
$836$	−6114.78	+	23183.1i	−0.252972	+	0.959097i
$837$	8900.78	−	6216.35i	0.367570	−	0.256713i
$838$	−28099.9	−	36472.5i	−1.15835	−	1.50349i
$839$	−29613.1			−1.21854			−0.609272	−	0.792961i	$-0.708538\pi$
$839$	−29613.1			−1.21854			−0.609272	+	0.792961i	$0.708538\pi$
$840$	268.981	+	8079.13i	0.0110485	+	0.331853i
$841$	−23977.9			−0.983144
$842$	25.0226	+	32.4783i	0.00102415	+	0.00132931i
$843$	−39815.3	+	8204.45i	−1.62670	+	0.335203i
$844$	17589.9	+	4639.51i	0.717381	+	0.189216i
$845$			9812.74i			0.399489i
$846$	22857.8	−	41065.9i	0.928920	−	1.66888i
$847$	15358.2	+	9811.79i	0.623040	+	0.398037i
$848$	−7207.21	−	4086.22i	−0.291859	−	0.165473i
$849$	4319.39	+	20961.5i	0.174607	+	0.847348i
$850$	−12191.4	+	9392.77i	−0.491956	+	0.379023i
$851$	9639.25			0.388283
$852$	−294.105	+	5374.43i	−0.0118261	+	0.216109i
$853$	15110.8			0.606545			0.303273	−	0.952904i	$-0.401921\pi$
$853$	15110.8			0.606545			0.303273	+	0.952904i	$0.401921\pi$
$854$	30077.2	−	2652.12i	1.20518	−	0.106269i
$855$	−2468.20	−	5734.65i	−0.0987260	−	0.229381i
$856$	−3891.18	−	9240.37i	−0.155371	−	0.368959i
$857$	36848.3			1.46875			0.734373	−	0.678747i	$-0.237477\pi$
$857$	36848.3			1.46875			0.734373	+	0.678747i	$0.237477\pi$
$858$	−37273.6	−	32110.6i	−1.48310	−	1.27766i
$859$	−35305.1			−1.40232			−0.701162	−	0.713002i	$-0.747335\pi$
$859$	−35305.1			−1.40232			−0.701162	+	0.713002i	$0.747335\pi$
$860$	3341.30	−	12667.9i	0.132485	−	0.502294i
$861$	9795.91	−	25613.5i	0.387740	−	1.01383i
$862$	−11738.6	−	15236.2i	−0.463826	−	0.602027i
$863$			48135.9i			1.89868i	0.314244	+	0.949342i	$0.398249\pi$
$863$			48135.9i			1.89868i	−0.314244	+	0.949342i	$0.601751\pi$
$864$	17317.4	+	18576.4i	0.681885	+	0.731460i
$865$	14264.6			0.560707
$866$	−19256.9	−	24994.7i	−0.755631	−	0.980779i
$867$	2642.19	+	12822.3i	0.103499	+	0.502268i
$868$	−7768.16	−	8432.67i	−0.303766	−	0.329750i
$869$	6299.25			0.245900
$870$	−722.024	+	838.117i	−0.0281367	+	0.0326607i
$871$			46268.9i			1.79995i
$872$	−34522.7	+	14537.7i	−1.34070	+	0.564575i
$873$	−14722.4	−	34206.3i	−0.570766	−	1.32612i
$874$	6827.23	+	8861.47i	0.264227	+	0.342956i
$875$	−8743.52	+	13686.1i	−0.337811	+	0.528771i
$876$	−659.505	+	12051.7i	−0.0254368	+	0.464828i
$877$		−	22331.1i		−	0.859825i	−0.902871	−	0.429912i	$-0.858544\pi$
$877$		−	22331.1i		−	0.859825i	0.902871	−	0.429912i	$-0.141456\pi$
$878$	21451.2	+	27842.8i	0.824537	+	1.07022i
$879$	−30698.7	+	6325.86i	−1.17798	+	0.242737i
$880$	−5638.08	+	9944.35i	−0.215977	+	0.380936i
$881$	9542.16			0.364908			0.182454	−	0.983214i	$-0.441596\pi$
$881$	9542.16			0.364908			0.182454	+	0.983214i	$0.441596\pi$
$882$	26122.1	+	1939.70i	0.997254	+	0.0740513i
$883$			31638.4i			1.20579i	0.797819	+	0.602897i	$0.205987\pi$
$883$			31638.4i			1.20579i	−0.797819	+	0.602897i	$0.794013\pi$
$884$	6944.63	−	26329.3i	0.264223	−	1.00176i
$885$	−1584.23	−	7688.07i	−0.0601731	−	0.292013i
$886$	24355.0	−	18764.0i	0.923501	−	0.711502i
$887$	−368.960			−0.0139667			−0.00698335	−	0.999976i	$-0.502223\pi$
$887$	−368.960			−0.0139667			−0.00698335	+	0.999976i	$0.502223\pi$
$888$	10104.7	+	14713.6i	0.381860	+	0.556030i
$889$	−30590.1	−	19542.8i	−1.15406	−	0.737284i
$890$	1727.57	+	2242.32i	0.0650656	+	0.0844525i
$891$	−24111.6	+	25474.3i	−0.906588	+	0.957826i
$892$	−24728.6	−	6522.42i	−0.928223	−	0.244828i
$893$	38334.0			1.43651
$894$	36213.4	+	31197.2i	1.35476	+	1.16710i
$895$		−	10210.5i		−	0.381340i
$896$	16983.2	−	20758.0i	0.633223	−	0.773969i
$897$	−22481.7	+	4632.65i	−0.836837	+	0.172441i
$898$	−20346.0	−	26408.3i	−0.756074	−	0.981354i
$899$		−	1569.02i		−	0.0582090i
$900$	3555.54	+	23758.7i	0.131687	+	0.879953i
$901$	6333.29			0.234176
$902$	30720.1	−	23668.0i	1.13400	−	0.873677i
$903$	−39652.0	−	15164.9i	−1.46128	−	0.558868i
$904$	−1538.75	+	647.978i	−0.0566129	+	0.0238401i
$905$			4824.71i			0.177214i
$906$	834.655	+	719.042i	0.0306066	+	0.0263671i
$907$			13767.1i			0.504003i	0.967727	+	0.252001i	$0.0810888\pi$
$907$			13767.1i			0.504003i	−0.967727	+	0.252001i	$0.918911\pi$
$908$	24008.5	+	6332.48i	0.877477	+	0.231443i
$909$	−1256.30	−	2918.90i	−0.0458403	−	0.106506i
$910$	−1188.35	−	13476.8i	−0.0432894	−	0.490937i
$911$			12013.8i			0.436921i	0.975846	+	0.218461i	$0.0701035\pi$
$911$			12013.8i			0.436921i	−0.975846	+	0.218461i	$0.929896\pi$
$912$	−6369.43	+	19710.6i	−0.231264	+	0.715662i
$913$		−	36726.1i		−	1.33128i
$914$	2579.31	−	1987.21i	0.0933436	−	0.0719157i
$915$	−10889.8	+	2243.99i	−0.393449	+	0.0810753i
$916$	−1415.26	+	5365.70i	−0.0510495	+	0.193545i
$917$	−11760.2	+	18408.0i	−0.423507	+	0.662908i
$918$	−18519.5	−	5824.00i	−0.665834	−	0.209391i
$919$	42760.2			1.53485			0.767425	−	0.641138i	$-0.221537\pi$
$919$	42760.2			1.53485			0.767425	+	0.641138i	$0.221537\pi$
$920$	2069.95	+	4915.50i	0.0741785	+	0.176152i
$921$	−2130.55	−	10339.3i	−0.0762259	−	0.369916i
$922$	−1983.69	−	2574.75i	−0.0708561	−	0.0919684i
$923$		−	9008.37i		−	0.321251i
$924$	30079.6	+	21618.5i	1.07094	+	0.769694i
$925$			16884.2i			0.600161i
$926$	−1145.51	+	882.546i	−0.0406520	+	0.0313200i
$927$	16975.5	+	39441.2i	0.601456	+	1.39743i
$928$	3634.07	−	514.644i	0.128550	−	0.0182048i
$929$	−46059.3			−1.62665			−0.813324	−	0.581811i	$-0.802344\pi$
$929$	−46059.3			−1.62665			−0.813324	+	0.581811i	$0.802344\pi$
$930$	3198.71	+	2755.64i	0.112785	+	0.0971622i
$931$	8979.85	+	19386.1i	0.316115	+	0.682442i
$932$	24666.8	+	6506.11i	0.866940	+	0.228664i
$933$	6389.81	+	31009.0i	0.224215	+	1.08809i
$934$	−13358.0	−	17338.2i	−0.467974	−	0.607412i
$935$		−	8738.54i		−	0.305648i
$936$	−30638.7	−	29460.3i	−1.06993	−	1.02878i
$937$			5647.59i			0.196904i	0.995142	+	0.0984519i	$0.0313891\pi$
$937$			5647.59i			0.196904i	−0.995142	+	0.0984519i	$0.968611\pi$
$938$	−3059.97	−	34702.6i	−0.106516	−	1.20797i
$939$	−14056.0	+	2896.42i	−0.488499	+	0.100661i
$940$	17672.8	+	4661.37i	0.613215	+	0.161742i
$941$			41421.7i			1.43497i	0.696572	+	0.717486i	$0.254707\pi$
$941$			41421.7i			1.43497i	−0.696572	+	0.717486i	$0.745293\pi$
$942$	−7862.36	−	6773.29i	−0.271942	−	0.234274i
$943$		−	18093.6i		−	0.624823i
$944$	−12845.0	+	22655.8i	−0.442870	+	0.781127i
$945$	−9637.54	+	396.805i	−0.331756	+	0.0136593i
$946$	−36640.1	−	47557.4i	−1.25927	−	1.63449i
$947$	21290.6			0.730571			0.365285	−	0.930896i	$-0.380971\pi$
$947$	21290.6			0.730571			0.365285	+	0.930896i	$0.380971\pi$
$948$	5434.14	+	297.373i	0.186174	+	0.0101880i
$949$		−	20200.5i		−	0.690976i
$950$	−15521.8	+	11958.7i	−0.530100	+	0.408410i
$951$	−4059.13	−	19698.5i	−0.138408	−	0.671680i
$952$	−3467.34	+	20206.8i	−0.118043	+	0.687928i
$953$			15236.1i			0.517888i	0.965892	+	0.258944i	$0.0833745\pi$
$953$			15236.1i			0.517888i	−0.965892	+	0.258944i	$0.916626\pi$
$954$	4808.04	−	8638.05i	0.163172	−	0.293152i
$955$	14531.4			0.492383
$956$	−14535.2	−	3833.79i	−0.491737	−	0.129701i
$957$	1023.08	+	4964.91i	0.0345576	+	0.167704i
$958$	33988.0	−	26185.7i	1.14625	−	0.883113i
$959$	−26869.6	+	42058.6i	−0.904760	+	1.41621i
$960$	−5333.23	+	8312.49i	−0.179301	+	0.279463i
$961$	23802.7			0.798991
$962$	−18232.1	−	23664.5i	−0.611045	−	0.793112i
$963$	10989.1	−	4729.73i	0.367726	−	0.158269i
$964$	−25386.5	−	6695.95i	−0.848180	−	0.223716i
$965$		−	13543.1i		−	0.451780i
$966$	16555.4	−	4961.40i	0.551409	−	0.165249i
$967$	−29677.9			−0.986945			−0.493472	−	0.869761i	$-0.664273\pi$
$967$	−29677.9			−0.986945			−0.493472	+	0.869761i	$0.664273\pi$
$968$	8641.62	+	20521.2i	0.286934	+	0.681382i
$969$	−3195.77	−	15508.7i	−0.105947	−	0.514150i
$970$	11472.2	−	8838.62i	0.379741	−	0.292568i
$971$		−	39536.5i		−	1.30668i	−0.757065	−	0.653340i	$-0.773367\pi$
$971$		−	39536.5i		−	1.30668i	0.757065	−	0.653340i	$-0.226633\pi$
$972$	−22002.8	+	20837.6i	−0.726072	+	0.687619i
$973$	40297.3	+	25744.4i	1.32772	+	0.848230i
$974$	15860.9	−	12219.9i	0.521783	−	0.402002i
$975$	−8114.60	−	39379.2i	−0.266539	−	1.29348i
$976$	32091.0	+	18194.4i	1.05247	+	0.596709i
$977$			29672.8i			0.971665i	0.874052	+	0.485832i	$0.161483\pi$
$977$			29672.8i			0.971665i	−0.874052	+	0.485832i	$0.838517\pi$
$978$	14584.2	−	16929.2i	0.476842	−	0.553513i
$979$	12971.1			0.423452
$980$	1782.57	+	10029.3i	0.0581042	+	0.326913i
$981$	−17670.6	−	41056.2i	−0.575107	−	1.33621i
$982$	19860.5	−	15301.3i	0.645391	−	0.497235i
$983$	4423.26			0.143520			0.0717599	−	0.997422i	$-0.477138\pi$
$983$	4423.26			0.143520			0.0717599	+	0.997422i	$0.477138\pi$
$984$	27618.4	−	18967.3i	0.894760	−	0.614487i
$985$			293.583i			0.00949679i
$986$	−2222.57	+	1712.36i	−0.0717861	+	0.0553069i
$987$	21156.3	−	55317.7i	0.682282	−	1.78397i
$988$	8841.74	−	33521.9i	0.284710	−	1.07943i
$989$	−28010.5			−0.900587
$990$	−11918.6	−	6634.03i	−0.382624	−	0.212973i
$991$	38967.8			1.24910			0.624548	−	0.780986i	$-0.285283\pi$
$991$	38967.8			1.24910			0.624548	+	0.780986i	$0.285283\pi$
$992$	−1964.16	−	13869.6i	−0.0628652	−	0.443911i
$993$	−21701.3	+	4471.83i	−0.693524	+	0.142909i
$994$	595.765	+	6756.47i	0.0190106	+	0.215596i
$995$	2638.23			0.0840577
$996$	1733.75	−	31682.4i	0.0551567	−	1.00793i
$997$	43802.8			1.39142			0.695712	−	0.718321i	$-0.255089\pi$
$997$	43802.8			1.39142			0.695712	+	0.718321i	$0.255089\pi$
$998$	16044.3	+	20824.8i	0.508890	+	0.660518i
$999$	−17461.4	+	12195.2i	−0.553008	+	0.386224i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	168.4.i.c.125.19	yes	80
3.2	odd	2	inner	168.4.i.c.125.61	yes	80
4.3	odd	2		672.4.i.c.209.44		80
7.6	odd	2	inner	168.4.i.c.125.20	yes	80
8.3	odd	2		672.4.i.c.209.37		80
8.5	even	2	inner	168.4.i.c.125.64	yes	80
12.11	even	2		672.4.i.c.209.41		80
21.20	even	2	inner	168.4.i.c.125.62	yes	80
24.5	odd	2	inner	168.4.i.c.125.18	yes	80
24.11	even	2		672.4.i.c.209.40		80
28.27	even	2		672.4.i.c.209.38		80
56.13	odd	2	inner	168.4.i.c.125.63	yes	80
56.27	even	2		672.4.i.c.209.43		80
84.83	odd	2		672.4.i.c.209.39		80
168.83	odd	2		672.4.i.c.209.42		80
168.125	even	2	inner	168.4.i.c.125.17	✓	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.4.i.c.125.17	✓	80	168.125	even	2	inner
168.4.i.c.125.18	yes	80	24.5	odd	2	inner
168.4.i.c.125.19	yes	80	1.1	even	1	trivial
168.4.i.c.125.20	yes	80	7.6	odd	2	inner
168.4.i.c.125.61	yes	80	3.2	odd	2	inner
168.4.i.c.125.62	yes	80	21.20	even	2	inner
168.4.i.c.125.63	yes	80	56.13	odd	2	inner
168.4.i.c.125.64	yes	80	8.5	even	2	inner
672.4.i.c.209.37		80	8.3	odd	2
672.4.i.c.209.38		80	28.27	even	2
672.4.i.c.209.39		80	84.83	odd	2
672.4.i.c.209.40		80	24.11	even	2
672.4.i.c.209.41		80	12.11	even	2
672.4.i.c.209.42		80	168.83	odd	2
672.4.i.c.209.43		80	56.27	even	2
672.4.i.c.209.44		80	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	168.i (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.24057 + 1.72622i) q^{2} +(-1.04870 - 5.08923i) q^{3} +(2.04030 - 7.73545i) q^{4} +3.71228i q^{5} +(11.1348 + 9.59247i) q^{6} +(15.6071 + 9.97081i) q^{7} +(8.78168 + 20.8538i) q^{8} +(-24.8005 + 10.6741i) q^{9} +(-6.40823 - 8.31763i) q^{10} -48.1150 q^{11} +(-41.5071 - 2.27139i) q^{12} +69.5724 q^{13} +(-52.1807 + 4.60114i) q^{14} +(18.8927 - 3.89307i) q^{15} +(-55.6743 - 31.5653i) q^{16} +48.9235 q^{17} +(37.1412 - 66.7273i) q^{18} +62.2883 q^{19} +(28.7162 + 7.57418i) q^{20} +(34.3765 - 89.8847i) q^{21} +(107.805 - 83.0572i) q^{22} -63.4952i q^{23} +(96.9205 - 66.5614i) q^{24} +111.219 q^{25} +(-155.882 + 120.098i) q^{26} +(80.3314 + 115.021i) q^{27} +(108.972 - 100.385i) q^{28} +20.2759 q^{29} +(-35.6100 + 41.3356i) q^{30} -77.3838i q^{31} +(179.231 - 25.3821i) q^{32} +(50.4582 + 244.868i) q^{33} +(-109.617 + 84.4529i) q^{34} +(-37.0145 + 57.9382i) q^{35} +(31.9689 + 213.621i) q^{36} +151.811i q^{37} +(-139.561 + 107.524i) q^{38} +(-72.9606 - 354.070i) q^{39} +(-77.4153 + 32.6001i) q^{40} +284.960 q^{41} +(78.1382 + 260.734i) q^{42} -441.143i q^{43} +(-98.1691 + 372.191i) q^{44} +(-39.6255 - 92.0663i) q^{45} +(109.607 + 142.265i) q^{46} +615.429 q^{47} +(-102.257 + 316.442i) q^{48} +(144.166 + 311.232i) q^{49} +(-249.194 + 191.989i) q^{50} +(-51.3061 - 248.983i) q^{51} +(141.949 - 538.174i) q^{52} +129.453 q^{53} +(-378.540 - 119.043i) q^{54} -178.616i q^{55} +(-70.8726 + 413.029i) q^{56} +(-65.3217 - 316.999i) q^{57} +(-45.4295 + 35.0007i) q^{58} -406.934i q^{59} +(8.43206 - 154.086i) q^{60} -576.405 q^{61} +(133.582 + 173.384i) q^{62} +(-493.494 - 80.6876i) q^{63} +(-357.764 + 366.263i) q^{64} +258.272i q^{65} +(-535.752 - 461.542i) q^{66} +665.046i q^{67} +(99.8187 - 378.445i) q^{68} +(-323.142 + 66.5875i) q^{69} +(-17.0807 - 193.710i) q^{70} -129.482i q^{71} +(-440.386 - 423.448i) q^{72} -290.352i q^{73} +(-262.059 - 340.142i) q^{74} +(-116.635 - 566.018i) q^{75} +(127.087 - 481.828i) q^{76} +(-750.938 - 479.745i) q^{77} +(774.677 + 667.371i) q^{78} -130.921 q^{79} +(117.179 - 206.679i) q^{80} +(501.125 - 529.447i) q^{81} +(-638.472 + 491.904i) q^{82} +763.300i q^{83} +(-625.160 - 449.309i) q^{84} +181.618i q^{85} +(761.511 + 988.411i) q^{86} +(-21.2633 - 103.189i) q^{87} +(-422.530 - 1003.38i) q^{88} -269.586 q^{89} +(247.711 + 137.879i) q^{90} +(1085.83 + 693.693i) q^{91} +(-491.164 - 129.549i) q^{92} +(-393.824 + 81.1524i) q^{93} +(-1378.91 + 1062.37i) q^{94} +231.232i q^{95} +(-317.135 - 885.529i) q^{96} +1379.26i q^{97} +(-860.269 - 448.473i) q^{98} +(1193.27 - 513.586i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 28 q^{4} + 64 q^{7} + 104 q^{9} - 8 q^{15} - 892 q^{16} + 692 q^{18} + 128 q^{22} - 976 q^{25} + 612 q^{28} - 332 q^{30} + 1544 q^{36} + 568 q^{39} + 780 q^{42} + 208 q^{46} - 4048 q^{49} - 1448 q^{57}+ \cdots - 2072 q^{88}+O(q^{100}) \) 80 * q + 28 * q^4 + 64 * q^7 + 104 * q^9 - 8 * q^15 - 892 * q^16 + 692 * q^18 + 128 * q^22 - 976 * q^25 + 612 * q^28 - 332 * q^30 + 1544 * q^36 + 568 * q^39 + 780 * q^42 + 208 * q^46 - 4048 * q^49 - 1448 * q^57 - 1760 * q^58 + 4156 * q^60 - 2152 * q^63 + 2764 * q^64 + 1968 * q^70 - 2740 * q^72 - 3620 * q^78 + 4992 * q^79 + 1568 * q^81 + 2484 * q^84 - 2072 * q^88

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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