LMFDB - Embedded newform 168.4.i.c.125.63

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			125.63
Character	$\chi$	$=$	168.125
Dual form			168.4.i.c.125.61

$q$-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} +(6.43546 - 13.2131i) 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} +(37.2278 - 18.4957i) 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} +(-73.9931 - 18.8950i) q^{18} +62.2883 q^{19} +(-28.7162 + 7.57418i) q^{20} +(-67.1109 - 68.9719i) q^{21} +(107.805 + 83.0572i) q^{22} -63.4952i q^{23} +(115.339 + 22.8225i) 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} +(49.0506 + 23.8903i) 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} +(-133.170 - 170.064i) 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} +(-31.3057 - 270.385i) 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} +(219.029 + 250.237i) 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} +(-18.5642 + 396.383i) 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} +(68.6614 + 138.200i) q^{60} -576.405 q^{61} +(-133.582 + 173.384i) q^{62} +(-280.634 + 413.874i) q^{63} +(-357.764 - 366.263i) q^{64} +258.272i q^{65} +(309.642 - 635.746i) 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} +(-4.80718 - 610.921i) 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} +(447.730 - 919.264i) 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} +(396.602 - 659.857i) 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} +(70.1435 - 274.683i) 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} +(58.7843 + 938.765i) 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	$0.946909\pi$
$6$	6.43546	−	13.2131i	0.437878	−	0.899035i
$7$	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	$-0.270802\pi$
$11$	48.1150			1.31884			0.659419	+	0.751776i	$0.270802\pi$
$12$	37.2278	−	18.4957i	0.895561	−	0.444938i
$13$	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	$-0.613476\pi$
$17$	−48.9235			−0.697982			−0.348991	+	0.937126i	$0.613476\pi$
$18$	−73.9931	−	18.8950i	−0.968908	−	0.247422i
$19$	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
$21$	−67.1109	−	68.9719i	−0.697372	−	0.716710i
$22$	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	$-0.0929301\pi$
$24$	115.339	+	22.8225i	0.980980	+	0.194110i
$25$	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	$-0.520678\pi$
$29$	−20.2759			−0.129832			−0.0649161	+	0.997891i	$0.520678\pi$
$30$	49.0506	+	23.8903i	0.298513	+	0.145391i
$31$			77.3838i			0.448340i	0.974550	+	0.224170i	$0.0719671\pi$
$31$			77.3838i			0.448340i	−0.974550	+	0.224170i	$0.928033\pi$
$32$	−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
$36$	−133.170	−	170.064i	−0.616527	−	0.787334i
$37$		−	151.811i		−	0.674527i	−0.941410	−	0.337263i	$-0.890499\pi$
$37$		−	151.811i		−	0.674527i	0.941410	−	0.337263i	$-0.109501\pi$
$38$	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	$-0.682606\pi$
$41$	−284.960			−1.08544			−0.542722	+	0.839912i	$0.682606\pi$
$42$	−31.3057	−	270.385i	−0.115014	−	0.993364i
$43$			441.143i			1.56450i	0.622963	+	0.782252i	$0.285929\pi$
$43$			441.143i			1.56450i	−0.622963	+	0.782252i	$0.714071\pi$
$44$	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	$-0.904141\pi$
$47$	−615.429			−1.90999			−0.954996	+	0.296620i	$0.904141\pi$
$48$	219.029	+	250.237i	0.658626	+	0.752470i
$49$	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	$-0.553651\pi$
$53$	−129.453			−0.335504			−0.167752	+	0.985829i	$0.553651\pi$
$54$	−18.5642	+	396.383i	−0.0467828	+	0.998905i
$55$			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	$-0.148209\pi$
$60$	68.6614	+	138.200i	0.147736	+	0.297359i
$61$	−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
$63$	−280.634	+	413.874i	−0.561216	+	0.827669i
$64$	−357.764	−	366.263i	−0.698758	−	0.715358i
$65$			258.272i			0.492842i
$66$	309.642	−	635.746i	0.577489	−	1.18568i
$67$		−	665.046i		−	1.21266i	−0.795212	−	0.606331i	$-0.792641\pi$
$67$		−	665.046i		−	1.21266i	0.795212	−	0.606331i	$-0.207359\pi$
$68$	−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	$-0.0345139\pi$
$72$	−4.80718	−	610.921i	−0.00786849	−	0.999969i
$73$			290.352i			0.465523i	0.972534	+	0.232761i	$0.0747762\pi$
$73$			290.352i			0.465523i	−0.972534	+	0.232761i	$0.925224\pi$
$74$	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
$78$	447.730	−	919.264i	0.649942	−	1.33444i
$79$	−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	$0.831597\pi$
$84$	396.602	−	659.857i	0.515153	−	0.857098i
$85$		−	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	$-0.448676\pi$
$89$	269.586			0.321080			0.160540	+	0.987029i	$0.448676\pi$
$90$	70.1435	−	274.683i	0.0821531	−	0.321713i
$91$	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
$96$	58.7843	+	938.765i	0.0624963	+	0.998045i
$97$		−	1379.26i		−	1.44374i	−0.692030	−	0.721869i	$-0.743283\pi$
$97$		−	1379.26i		−	1.44374i	0.692030	−	0.721869i	$-0.256717\pi$
$98$	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	$0.981535\pi$
$102$	−314.845	+	646.429i	−0.305631	+	0.627510i
$103$			1590.34i			1.52137i	0.649122	+	0.760684i	$0.275137\pi$
$103$			1590.34i			1.52137i	−0.649122	+	0.760684i	$0.724863\pi$
$104$	−610.962	+	1450.85i	−0.576056	+	1.36796i
$105$	256.043	−	249.135i	0.237974	−	0.231553i
$106$	−290.048	−	223.465i	−0.265773	−	0.204762i
$107$	443.102			0.400339			0.200169	−	0.979761i	$-0.435851\pi$
$107$	443.102			0.400339			0.200169	+	0.979761i	$0.435851\pi$
$108$	−725.840	+	856.077i	−0.646704	+	0.762741i
$109$		−	1655.46i		−	1.45472i	−0.686256	−	0.727360i	$-0.740747\pi$
$109$		−	1655.46i		−	1.45472i	0.686256	−	0.727360i	$-0.259253\pi$
$110$	−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	$0.990222\pi$
$114$	400.854	−	823.018i	0.329328	−	0.676164i
$115$	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
$120$	−84.7237	+	428.172i	−0.0644515	+	0.325721i
$121$	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
$126$	−1343.22	+	442.874i	−0.949710	+	0.313130i
$127$	−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	$0.871326\pi$
$132$	1791.21	−	889.922i	1.18110	−	0.586801i
$133$	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	$0.682395\pi$
$138$	−838.966	−	408.621i	−0.517518	−	0.252059i
$139$	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
$144$	1043.82	−	1377.11i	0.604060	−	0.796939i
$145$		−	75.2698i		−	0.0431091i
$146$	−501.213	+	650.555i	−0.284114	+	0.368769i
$147$	−1735.12	−	407.305i	−0.973537	−	0.228530i
$148$	1174.32	−	309.739i	0.652221	−	0.172030i
$149$	−3252.26			−1.78816			−0.894079	−	0.447910i	$-0.852168\pi$
$149$	−3252.26			−1.78816			−0.894079	+	0.447910i	$0.852168\pi$
$150$	715.745	−	1469.54i	0.389602	−	0.799917i
$151$	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
$156$	2590.03	−	1286.79i	1.32928	−	0.660422i
$157$	−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
$162$	2036.75	−	321.209i	0.987792	−	0.155781i
$163$			1520.38i			0.730586i	0.930893	+	0.365293i	$0.119031\pi$
$163$			1520.38i			0.730586i	−0.930893	+	0.365293i	$0.880969\pi$
$164$	−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	$-0.350009\pi$
$167$	1959.42			0.907933			0.453966	+	0.891019i	$0.350009\pi$
$168$	2027.67	−	793.830i	0.931182	−	0.364556i
$169$	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	$-0.320010\pi$
$174$	−130.485	+	267.906i	−0.0568506	+	0.116724i
$175$	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	$-0.305296\pi$
$179$	2750.46			1.14849			0.574243	+	0.818685i	$0.305296\pi$
$180$	631.326	−	494.364i	0.261424	−	0.204709i
$181$	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
$186$	1022.48	+	498.000i	0.403073	+	0.196318i
$187$	−2353.95			−0.920525
$188$	−1255.66	−	4760.62i	−0.487120	−	1.84683i
$189$	2400.60	+	994.183i	0.923904	+	0.382625i
$190$	−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	$-0.265866\pi$
$192$	−1488.81	+	2204.84i	−0.559612	+	0.828755i
$193$	−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	$-0.504552\pi$
$197$	−79.0843			−0.0286016			−0.0143008	+	0.999898i	$0.504552\pi$
$198$	−3560.18	−	909.131i	−1.27783	−	0.326309i
$199$			710.675i			0.253158i	0.991957	+	0.126579i	$0.0403997\pi$
$199$			710.675i			0.253158i	−0.991957	+	0.126579i	$0.959600\pi$
$200$	−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
$204$	−1821.31	+	904.876i	−0.625086	+	0.310559i
$205$		−	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
$210$	1003.75	−	116.216i	0.329833	−	0.0381888i
$211$		−	2273.94i		−	0.741915i	−0.928650	−	0.370958i	$-0.879029\pi$
$211$		−	2273.94i		−	0.741915i	0.928650	−	0.370958i	$-0.120971\pi$
$212$	−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
$216$	−3104.08	+	665.138i	−0.977804	+	0.209523i
$217$	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
$222$	−2005.88	−	976.971i	−0.606423	−	0.295360i
$223$			3196.79i			0.959968i	0.877277	+	0.479984i	$0.159358\pi$
$223$			3196.79i			0.959968i	−0.877277	+	0.479984i	$0.840642\pi$
$224$	−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	$0.850088\pi$
$228$	2318.85	−	1152.07i	0.673552	−	0.334638i
$229$	−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
$231$	−3229.04	−	3318.58i	−0.919720	−	0.945224i
$232$	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	$0.852032\pi$
$234$	−5147.88	−	1314.57i	−1.43815	−	0.367248i
$235$		−	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	$-0.0818375\pi$
$240$	−928.950	+	813.097i	−0.249848	+	0.218688i
$241$			3281.84i			0.877187i	0.898685	+	0.438594i	$0.144523\pi$
$241$			3281.84i			0.877187i	−0.898685	+	0.438594i	$0.855477\pi$
$242$	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
$246$	−1833.85	+	3765.19i	−0.475292	+	0.975852i
$247$	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	$-0.0677661\pi$
$252$	−3774.08	−	1326.41i	−0.943430	−	0.331570i
$253$		−	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	$-0.802638\pi$
$257$	−6706.25			−1.62772			−0.813861	+	0.581059i	$0.802638\pi$
$258$	5828.84	+	2838.96i	1.40654	+	0.685061i
$259$	−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	$-0.188363\pi$
$264$	5549.54	+	1098.11i	1.29375	+	0.255999i
$265$		−	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	$0.903129\pi$
$270$	−1471.49	−	68.9157i	−0.331673	−	0.0155336i
$271$		−	7621.80i		−	1.70846i	−0.519899	−	0.854228i	$-0.674030\pi$
$271$		−	7621.80i		−	1.70846i	0.519899	−	0.854228i	$-0.325970\pi$
$272$	2723.78	−	1544.29i	0.607183	−	0.344250i
$273$	−4669.07	−	4798.54i	−1.03511	−	1.06381i
$274$	−4651.87	+	6037.95i	−1.02566	+	1.33126i
$275$	5351.30			1.17344
$276$	−1174.39	−	2363.79i	−0.256123	−	0.515519i
$277$			3715.63i			0.805960i	0.915209	+	0.402980i	$0.132026\pi$
$277$			3715.63i			0.805960i	−0.915209	+	0.402980i	$0.867974\pi$
$278$	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	$-0.311912\pi$
$282$	−3960.57	+	8131.70i	−0.836342	+	1.71715i
$283$	−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
$288$	4715.94	−	1283.65i	0.964894	−	0.262638i
$289$	−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	$-0.205376\pi$
$294$	−3184.55	−	3907.79i	−0.631723	−	0.775194i
$295$	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
$300$	4140.44	−	2057.08i	0.796827	−	0.395884i
$301$	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
$306$	3620.00	+	924.409i	0.676280	+	0.172696i
$307$	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	$-0.312536\pi$
$311$	6093.07			1.11095			0.555477	+	0.831532i	$0.312536\pi$
$312$	8024.42	+	1587.82i	1.45607	+	0.288117i
$313$			2761.91i			0.498762i	0.968405	+	0.249381i	$0.0802271\pi$
$313$			2761.91i			0.498762i	−0.968405	+	0.249381i	$0.919773\pi$
$314$	−1582.08	−	1218.89i	−0.284337	−	0.219064i
$315$	−1536.42	−	1041.79i	−0.274817	−	0.186344i
$316$	−267.118	−	1012.73i	−0.0475524	−	0.180286i
$317$	−3870.63			−0.685792			−0.342896	−	0.939373i	$-0.611408\pi$
$317$	−3870.63			−0.685792			−0.342896	+	0.939373i	$0.611408\pi$
$318$	−833.089	+	1710.47i	−0.146910	+	0.301630i
$319$	−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
$324$	5117.96	+	2796.20i	0.877565	+	0.479457i
$325$	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
$330$	2360.07	+	1149.48i	0.393690	+	0.191748i
$331$			4264.16i			0.708095i	0.935227	+	0.354048i	$0.115195\pi$
$331$			4264.16i			0.708095i	−0.935227	+	0.354048i	$0.884805\pi$
$332$	−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
$336$	5913.48	+	1721.59i	0.960138	+	0.279525i
$337$	−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
$342$	−4608.90	−	1176.94i	−0.728716	−	0.186086i
$343$	−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	$-0.344239\pi$
$347$	6076.58			0.940081			0.470041	+	0.882645i	$0.344239\pi$
$348$	−754.826	+	375.017i	−0.116273	+	0.0577673i
$349$	−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	$-0.341368\pi$
$353$	6340.22			0.955965			0.477983	+	0.878369i	$0.341368\pi$
$354$	−5376.85	−	2618.81i	−0.807278	−	0.393187i
$355$	480.674			0.0718635
$356$	550.038	+	2085.37i	0.0818875	+	0.310462i
$357$	3283.30	+	3374.35i	0.486753	+	0.500251i
$358$	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	$0.998140\pi$
$360$	2267.91	−	17.8456i	0.332026	−	0.00261263i
$361$	−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
$366$	−3709.43	+	7616.07i	−0.529768	+	1.08770i
$367$		−	11025.8i		−	1.56824i	−0.620610	−	0.784120i	$-0.713115\pi$
$367$		−	11025.8i		−	1.56824i	0.620610	−	0.784120i	$-0.286885\pi$
$368$	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
$372$	1431.27	+	2880.83i	0.199484	+	0.401516i
$373$			5947.81i			0.825646i	0.910811	+	0.412823i	$0.135457\pi$
$373$			5947.81i			0.825646i	−0.910811	+	0.412823i	$0.864543\pi$
$374$	−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
$378$	3662.52	+	6371.51i	0.498359	+	0.866971i
$379$		−	4855.67i		−	0.658098i	−0.944313	−	0.329049i	$-0.893272\pi$
$379$		−	4855.67i		−	0.658098i	0.944313	−	0.329049i	$-0.106728\pi$
$380$	−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	$-0.592916\pi$
$383$	−4314.03			−0.575553			−0.287777	+	0.957698i	$0.592916\pi$
$384$	−7141.83	+	2370.09i	−0.949102	+	0.314969i
$385$	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	$-0.530999\pi$
$389$	−1492.00			−0.194466			−0.0972330	+	0.995262i	$0.530999\pi$
$390$	3412.57	+	1662.10i	0.443082	+	0.215805i
$391$			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
$396$	−6407.46	−	8182.63i	−0.813098	−	1.03837i
$397$	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
$399$	−4180.22	−	4296.14i	−0.524493	−	0.539038i
$400$	−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	$0.936445\pi$
$402$	−8787.29	−	4279.88i	−1.09022	−	0.530997i
$403$			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
$408$	−5642.80	−	1116.56i	−0.684706	−	0.135485i
$409$			9157.04i			1.10706i	0.832830	+	0.553529i	$0.186719\pi$
$409$			9157.04i			1.10706i	−0.832830	+	0.553529i	$0.813281\pi$
$410$	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
$414$	−1199.74	+	4698.21i	−0.142425	+	0.557740i
$415$	−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	$0.602118\pi$
$420$	2449.57	+	1472.30i	0.284588	+	0.171050i
$421$			14.4956i			0.00167808i	1.00000		0.000839038i	$0.000267074\pi$
$421$			14.4956i			0.00167808i	−1.00000		0.000839038i	$0.999733\pi$
$422$	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
$426$	−1710.85	−	833.276i	−0.194580	−	0.0947708i
$427$	−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	$0.875927\pi$
$432$	−8103.07	−	3868.04i	−0.902452	−	0.430790i
$433$		−	11155.5i		−	1.23811i	−0.785349	−	0.619053i	$-0.787517\pi$
$433$		−	11155.5i		−	1.23811i	0.785349	−	0.619053i	$-0.212483\pi$
$434$	−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
$438$	3836.44	+	1868.55i	0.418521	+	0.203842i
$439$			12426.7i			1.35101i	0.737357	+	0.675504i	$0.236074\pi$
$439$			12426.7i			1.35101i	−0.737357	+	0.675504i	$0.763926\pi$
$440$	−3724.84	−	1568.55i	−0.403579	−	0.169950i
$441$	−253.250	+	9257.54i	−0.0273458	+	0.999626i
$442$	−7626.28	−	5875.59i	−0.820691	−	0.632293i
$443$	10870.0			1.16580			0.582900	−	0.812544i	$-0.301918\pi$
$443$	10870.0			1.16580			0.582900	+	0.812544i	$0.301918\pi$
$444$	−2807.85	−	5651.57i	−0.300123	−	0.604080i
$445$			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	$0.787369\pi$
$450$	−8229.44	−	2101.48i	−0.862087	−	0.220144i
$451$	−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
$456$	7184.28	+	1421.58i	0.737795	+	0.145990i
$457$	−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	$0.981512\pi$
$462$	−1506.27	−	13009.6i	−0.151684	−	1.31009i
$463$	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	$0.874757\pi$
$468$	−9264.93	−	11831.8i	−0.915111	−	1.16864i
$469$	−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
$474$	−842.535	+	1729.86i	−0.0816433	+	0.167627i
$475$	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	$-0.242535\pi$
$479$	15169.4			1.44699			0.723493	+	0.690332i	$0.242535\pi$
$480$	−3484.96	+	218.224i	−0.331388	+	0.0207511i
$481$		−	10561.8i		−	1.00120i
$482$	−5665.20	+	7353.20i	−0.535358	+	0.694874i
$483$	−4379.39	+	4261.22i	−0.412565	+	0.401433i
$484$	2007.76	+	7612.08i	0.188558	+	0.714884i
$485$	5120.20			0.479374
$486$	−3770.65	−	10028.6i	−0.351934	−	0.936025i
$487$	−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	$-0.366449\pi$
$491$	8864.05			0.814723			0.407361	+	0.913267i	$0.366449\pi$
$492$	−10608.4	+	5270.54i	−0.972082	+	0.482956i
$493$	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
$498$	10085.5	+	4912.18i	0.907516	+	0.442008i
$499$			9294.42i			0.833818i	0.908948	+	0.416909i	$0.136887\pi$
$499$			9294.42i			0.833818i	−0.908948	+	0.416909i	$0.863113\pi$
$500$	−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	$-0.555729\pi$
$503$	−3930.02			−0.348372			−0.174186	+	0.984713i	$0.555729\pi$
$504$	−6166.41	−	9486.81i	−0.544987	−	0.838444i
$505$	−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	$-0.0576893\pi$
$510$	−2399.73	−	1168.79i	−0.208356	−	0.101481i
$511$	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
$516$	8159.26	+	16422.8i	0.696107	+	1.40111i
$517$	−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	$-0.269960\pi$
$521$	15730.9			1.32281			0.661406	+	0.750028i	$0.269960\pi$
$522$	1500.28	+	383.112i	0.125796	+	0.0321233i
$523$	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
$525$	−7464.01	−	7670.98i	−0.620487	−	0.637694i
$526$	8214.03	−	10661.5i	0.680891	−	0.883769i
$527$		−	3785.89i		−	0.312933i
$528$	10538.6	+	12040.1i	0.868621	+	0.992386i
$529$	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
$534$	1734.91	−	3562.06i	0.140594	−	0.288662i
$535$			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
$540$	−3178.00	−	2694.52i	−0.253258	−	0.214729i
$541$			16674.9i			1.32516i	0.748991	+	0.662580i	$0.230538\pi$
$541$			16674.9i			1.32516i	−0.748991	+	0.662580i	$0.769462\pi$
$542$	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
$546$	−2178.01	−	18811.3i	−0.170715	−	1.47445i
$547$		−	3533.79i		−	0.276223i	−0.990417	−	0.138111i	$-0.955897\pi$
$547$		−	3533.79i		−	0.276223i	0.990417	−	0.138111i	$-0.0441032\pi$
$548$	−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
$552$	1449.12	−	7323.49i	0.111737	−	0.564689i
$553$	−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	$-0.395107\pi$
$557$	8507.84			0.647197			0.323599	+	0.946194i	$0.395107\pi$
$558$	1462.17	−	5725.87i	0.110929	−	0.434400i
$559$			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	$0.850031\pi$
$564$	−22911.1	+	11382.8i	−1.71051	+	0.849828i
$565$	−273.920			−0.0203963
$566$	−9228.47	−	7109.98i	−0.685338	−	0.528012i
$567$	2542.12	−	13259.8i	0.188287	−	0.982114i
$568$	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	$-0.202147\pi$
$570$	3055.28	+	1488.08i	0.224511	+	0.109349i
$571$			16824.4i			1.23307i	0.787329	+	0.616533i	$0.211463\pi$
$571$			16824.4i			1.23307i	−0.787329	+	0.616533i	$0.788537\pi$
$572$	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
$576$	12782.3	+	5264.67i	0.924643	+	0.380835i
$577$			12917.3i			0.931986i	0.884788	+	0.465993i	$0.154303\pi$
$577$			12917.3i			0.931986i	−0.884788	+	0.465993i	$0.845697\pi$
$578$	−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
$582$	−18224.2	−	8876.17i	−1.29797	−	0.632181i
$583$	−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	$-0.178791\pi$
$588$	−389.476	−	14252.9i	−0.0273158	−	0.999627i
$589$			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	$-0.556406\pi$
$593$	−5091.10			−0.352558			−0.176279	+	0.984340i	$0.556406\pi$
$594$	−893.218	+	19072.0i	−0.0616990	+	1.31739i
$595$	−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	$0.777000\pi$
$600$	12827.9	+	2538.30i	0.872828	+	0.172709i
$601$		−	28238.3i		−	1.91658i	−0.285803	−	0.958288i	$-0.592260\pi$
$601$		−	28238.3i		−	1.91658i	0.285803	−	0.958288i	$-0.407740\pi$
$602$	−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
$606$	1555.12	+	757.424i	0.104245	+	0.0507727i
$607$		−	11435.7i		−	0.764683i	−0.924021	−	0.382342i	$-0.875118\pi$
$607$		−	11435.7i		−	0.764683i	0.924021	−	0.382342i	$-0.124882\pi$
$608$	−11164.0	−	1581.01i	−0.744670	−	0.105458i
$609$	1360.73	+	1398.47i	0.0905413	+	0.0930521i
$610$	3693.74	−	4794.32i	0.245172	−	0.318224i
$611$	−42816.9			−2.83500
$612$	6515.13	+	8320.14i	0.430324	+	0.549545i
$613$		−	577.455i		−	0.0380476i	−0.999819	−	0.0190238i	$-0.993944\pi$
$613$		−	577.455i		−	0.0380476i	0.999819	−	0.0190238i	$-0.00605583\pi$
$614$	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	$-0.259069\pi$
$618$	21013.3	+	10234.6i	1.36776	+	0.666173i
$619$	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
$624$	15238.3	+	17409.6i	0.977599	+	1.11689i
$625$	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
$630$	−1644.08	−	4986.41i	−0.103971	−	0.315339i
$631$	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
$636$	−4819.25	+	2394.33i	−0.300465	+	0.149279i
$637$	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	$-0.00622290\pi$
$642$	2851.56	−	5854.73i	0.175299	−	0.359919i
$643$	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	$-0.693544\pi$
$647$	−18802.6			−1.14252			−0.571258	+	0.820771i	$0.693544\pi$
$648$	6640.28	+	15099.8i	0.402554	+	0.915396i
$649$		−	19579.6i		−	1.18423i
$650$	17337.0	+	13357.1i	1.04617	+	0.806014i
$651$	5337.31	−	5193.30i	0.321330	−	0.312660i
$652$	−11760.8	+	3102.04i	−0.706426	+	0.186327i
$653$	20232.4			1.21249			0.606243	−	0.795279i	$-0.292676\pi$
$653$	20232.4			1.21249			0.606243	+	0.795279i	$0.292676\pi$
$654$	−21873.7	−	10653.7i	−1.30784	−	0.636989i
$655$	−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	$-0.629827\pi$
$659$	−13420.3			−0.793295			−0.396648	+	0.917971i	$0.629827\pi$
$660$	3303.64	+	6649.50i	0.194839	+	0.392169i
$661$	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
$666$	−2868.46	+	11232.9i	−0.166893	+	0.653555i
$667$			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
$672$	10277.7	+	14065.3i	0.589987	+	0.807413i
$673$	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	$-0.0118694\pi$
$678$	974.958	+	474.856i	0.0552257	+	0.0268979i
$679$	−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	$-0.306737\pi$
$683$	20367.6			1.14106			0.570532	+	0.821276i	$0.306737\pi$
$684$	−8294.91	−	10593.0i	−0.463690	−	0.592154i
$685$	−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
$690$	1516.92	−	3114.48i	0.0836928	−	0.171835i
$691$	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
$693$	−13502.7	+	19913.5i	−0.740153	+	1.09156i
$694$	13615.0	+	10489.5i	0.744696	+	0.573743i
$695$			9585.03i			0.523138i
$696$	−2338.60	−	462.747i	−0.127363	−	0.0252017i
$697$	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	$-0.439015\pi$
$701$	7068.43			0.380843			0.190422	+	0.981702i	$0.439015\pi$
$702$	−1291.56	+	27577.3i	−0.0694398	+	1.48268i
$703$		−	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
$708$	−7526.55	−	15149.3i	−0.399527	−	0.804159i
$709$			5102.93i			0.270303i	0.990825	+	0.135151i	$0.0431520\pi$
$709$			5102.93i			0.270303i	−0.990825	+	0.135151i	$0.956848\pi$
$710$	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
$714$	1531.58	+	13228.2i	0.0802775	+	0.693350i
$715$			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	$-0.482132\pi$
$719$	2163.33			0.112209			0.0561046	+	0.998425i	$0.482132\pi$
$720$	5112.22	+	3874.94i	0.264613	+	0.200570i
$721$	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
$726$	6332.82	−	13002.3i	0.323737	−	0.664685i
$727$			24985.1i			1.27462i	0.770609	+	0.637309i	$0.219952\pi$
$727$			24985.1i			1.27462i	−0.770609	+	0.637309i	$0.780048\pi$
$728$	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
$732$	−21458.3	+	10661.0i	−1.08350	+	0.538310i
$733$	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
$735$	1512.03	−	6441.24i	0.0758804	−	0.323250i
$736$	−1611.64	+	11380.3i	−0.0807146	+	0.569951i
$737$		−	31998.7i		−	1.59930i
$738$	21085.1	+	5384.31i	1.05170	+	0.268562i
$739$		−	17370.8i		−	0.864675i	−0.901712	−	0.432338i	$-0.857689\pi$
$739$		−	17370.8i		−	0.864675i	0.901712	−	0.432338i	$-0.142311\pi$
$740$	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	$-0.245303\pi$
$744$	−1766.09	+	8925.39i	−0.0870271	+	0.439813i
$745$		−	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
$750$	11586.7	+	5643.33i	0.564115	+	0.274754i
$751$	−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
$756$	−2792.51	+	20598.1i	−0.134342	+	0.990935i
$757$		−	24841.4i		−	1.19270i	−0.802723	−	0.596352i	$-0.796616\pi$
$757$		−	24841.4i		−	1.19270i	0.802723	−	0.596352i	$-0.203384\pi$
$758$	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	$-0.341921\pi$
$761$	20004.6			0.952912			0.476456	+	0.879198i	$0.341921\pi$
$762$	−12613.5	+	25897.7i	−0.599659	+	1.23120i
$763$	−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
$768$	−20093.1	−	7018.06i	−0.944071	−	0.329743i
$769$		−	9604.90i		−	0.450405i	−0.974312	−	0.225203i	$-0.927696\pi$
$769$		−	9604.90i		−	0.450405i	0.974312	−	0.225203i	$-0.0723044\pi$
$770$	−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	$-0.0362557\pi$
$774$	8335.38	−	32641.5i	0.387092	−	1.51586i
$775$			8606.55i			0.398911i
$776$	28762.8	+	12112.2i	1.33057	+	0.560313i
$777$	−10470.7	+	10188.1i	−0.483440	+	0.470396i
$778$	−3342.92	−	2575.52i	−0.154048	−	0.118685i
$779$	−17749.6			−0.816363
$780$	4776.94	+	9614.91i	0.219284	+	0.441371i
$781$		−	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
$786$	15584.3	+	7590.38i	0.707218	+	0.344453i
$787$	−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
$792$	−231.297	−	29394.5i	−0.0103773	−	1.31880i
$793$	−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	$-0.152442\pi$
$798$	−1949.98	−	16841.8i	−0.0865018	−	0.747109i
$799$	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
$804$	−12300.5	−	24758.2i	−0.539559	−	1.08601i
$805$	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	$-0.107314\pi$
$810$	1192.42	+	7561.00i	0.0517251	+	0.327983i
$811$	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
$816$	−10715.7	−	12242.5i	−0.459709	−	0.525211i
$817$			27478.0i			1.17666i
$818$	−15807.1	+	20517.0i	−0.675651	+	0.876968i
$819$	−19524.4	+	28794.2i	−0.833013	+	1.22851i
$820$	8182.95	−	2158.34i	0.348489	−	0.0919175i
$821$	8486.07			0.360738			0.180369	−	0.983599i	$-0.442271\pi$
$821$	8486.07			0.360738			0.180369	+	0.983599i	$0.442271\pi$
$822$	35606.9	+	17342.4i	1.51087	+	0.735873i
$823$	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	$-0.422798\pi$
$827$	11423.5			0.480330			0.240165	+	0.970732i	$0.422798\pi$
$828$	−10798.3	+	8455.64i	−0.453219	+	0.354896i
$829$	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
$834$	16616.2	−	34115.8i	0.689895	−	1.41647i
$835$			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	$-0.291462\pi$
$839$	29613.1			1.21854			0.609272	+	0.792961i	$0.291462\pi$
$840$	2946.92	+	7527.30i	0.121046	+	0.309187i
$841$	−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
$846$	45537.5	+	11628.5i	1.85061	+	0.472573i
$847$	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
$852$	−2394.86	−	4820.33i	−0.0962990	−	0.193828i
$853$	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	$-0.762523\pi$
$857$	−36848.3			−1.46875			−0.734373	+	0.678747i	$0.762523\pi$
$858$	21542.5	−	44230.4i	0.857168	−	1.75991i
$859$	−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
$861$	19123.9	+	19654.2i	0.756958	+	0.777949i
$862$	−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	$0.601751\pi$
$864$	−11478.4	−	22654.3i	−0.451971	−	0.892033i
$865$	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
$870$	−994.544	−	484.396i	−0.0387566	−	0.0188765i
$871$		−	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
$876$	5370.28	+	10809.2i	0.207129	+	0.416904i
$877$			22331.1i			0.859825i	0.902871	+	0.429912i	$0.141456\pi$
$877$			22331.1i			0.859825i	−0.902871	+	0.429912i	$0.858544\pi$
$878$	−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	$-0.558404\pi$
$881$	−9542.16			−0.364908			−0.182454	+	0.983214i	$0.558404\pi$
$882$	−16548.0	+	20305.0i	−0.631746	+	0.775175i
$883$		−	31638.4i		−	1.20579i	−0.797819	−	0.602897i	$-0.794013\pi$
$883$		−	31638.4i		−	1.20579i	0.797819	−	0.602897i	$-0.205987\pi$
$884$	−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	$-0.497777\pi$
$887$	368.960			0.0139667			0.00698335	+	0.999976i	$0.497777\pi$
$888$	3464.70	−	17509.7i	0.130932	−	0.661697i
$889$	−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
$894$	−20929.8	+	42972.3i	−0.782994	+	1.60762i
$895$			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
$900$	−14811.0	−	18914.4i	−0.548555	−	0.700532i
$901$	6333.29			0.234176
$902$	−30720.1	−	23668.0i	−1.13400	−	0.873677i
$903$	30426.5	−	29605.5i	1.12129	−	1.09104i
$904$	−1538.75	−	647.978i	−0.0566129	−	0.0238401i
$905$			4824.71i			0.177214i
$906$	482.395	−	990.437i	0.0176893	−	0.0363191i
$907$		−	13767.1i		−	0.504003i	−0.967727	−	0.252001i	$-0.918911\pi$
$907$		−	13767.1i		−	0.504003i	0.967727	−	0.252001i	$-0.0810888\pi$
$908$	−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	$0.929896\pi$
$912$	13642.9	+	15586.8i	0.495353	+	0.565933i
$913$			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
$918$	908.228	−	19392.4i	0.0326536	−	0.697218i
$919$	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
$924$	19082.5	−	31749.0i	0.679403	−	1.13037i
$925$		−	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	$-0.197656\pi$
$929$	46059.3			1.62665			0.813324	+	0.581811i	$0.197656\pi$
$930$	−1848.72	+	3795.72i	−0.0651848	+	0.133835i
$931$	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
$936$	−334.447	−	42503.3i	−0.0116792	−	1.48425i
$937$		−	5647.59i		−	0.196904i	−0.995142	−	0.0984519i	$-0.968611\pi$
$937$		−	5647.59i		−	0.196904i	0.995142	−	0.0984519i	$-0.0313891\pi$
$938$	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	$0.745293\pi$
$942$	−4544.11	+	9329.80i	−0.157171	+	0.322698i
$943$			18093.6i			0.624823i
$944$	12845.0	+	22655.8i	0.442870	+	0.781127i
$945$	−3690.69	+	8911.70i	−0.127046	+	0.306770i
$946$	−36640.1	+	47557.4i	−1.25927	+	1.63449i
$947$	−21290.6			−0.730571			−0.365285	−	0.930896i	$-0.619029\pi$
$947$	−21290.6			−0.730571			−0.365285	+	0.930896i	$0.619029\pi$
$948$	−4873.89	+	2421.47i	−0.166979	+	0.0829597i
$949$			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	$0.916626\pi$
$954$	9578.63	+	2446.01i	0.325073	+	0.0830110i
$955$	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
$960$	−8185.01	−	5526.88i	−0.275177	−	0.185812i
$961$	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
$966$	−17168.1	+	1987.76i	−0.571818	+	0.0662062i
$967$	−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	$-0.226633\pi$
$972$	8863.27	−	28978.8i	0.292479	−	0.956272i
$973$	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	$0.838517\pi$
$978$	20088.9	+	9784.35i	0.656822	+	0.319907i
$979$	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	$-0.522862\pi$
$983$	−4423.26			−0.143520			−0.0717599	+	0.997422i	$0.522862\pi$
$984$	−32867.0	−	6503.50i	−1.06480	−	0.210695i
$985$		−	293.583i		−	0.00949679i
$986$	2222.57	+	1712.36i	0.0717861	+	0.0553069i
$987$	41302.0	+	42447.3i	1.33197	+	1.36891i
$988$	8841.74	+	33521.9i	0.284710	+	1.07943i
$989$	28010.5			0.900587
$990$	3374.95	−	13216.4i	0.108347	−	0.424287i
$991$	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
$996$	14117.8	+	28416.0i	0.449136	+	0.904010i
$997$	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.125.63	yes	80
3.2	odd	2	inner	168.4.i.c.125.17	✓	80
4.3	odd	2		672.4.i.c.209.43		80
7.6	odd	2	inner	168.4.i.c.125.64	yes	80
8.3	odd	2		672.4.i.c.209.38		80
8.5	even	2	inner	168.4.i.c.125.20	yes	80
12.11	even	2		672.4.i.c.209.42		80
21.20	even	2	inner	168.4.i.c.125.18	yes	80
24.5	odd	2	inner	168.4.i.c.125.62	yes	80
24.11	even	2		672.4.i.c.209.39		80
28.27	even	2		672.4.i.c.209.37		80
56.13	odd	2	inner	168.4.i.c.125.19	yes	80
56.27	even	2		672.4.i.c.209.44		80
84.83	odd	2		672.4.i.c.209.40		80
168.83	odd	2		672.4.i.c.209.41		80
168.125	even	2	inner	168.4.i.c.125.61	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.4.i.c.125.17	✓	80	3.2	odd	2	inner
168.4.i.c.125.18	yes	80	21.20	even	2	inner
168.4.i.c.125.19	yes	80	56.13	odd	2	inner
168.4.i.c.125.20	yes	80	8.5	even	2	inner
168.4.i.c.125.61	yes	80	168.125	even	2	inner
168.4.i.c.125.62	yes	80	24.5	odd	2	inner
168.4.i.c.125.63	yes	80	1.1	even	1	trivial
168.4.i.c.125.64	yes	80	7.6	odd	2	inner
672.4.i.c.209.37		80	28.27	even	2
672.4.i.c.209.38		80	8.3	odd	2
672.4.i.c.209.39		80	24.11	even	2
672.4.i.c.209.40		80	84.83	odd	2
672.4.i.c.209.41		80	168.83	odd	2
672.4.i.c.209.42		80	12.11	even	2
672.4.i.c.209.43		80	4.3	odd	2
672.4.i.c.209.44		80	56.27	even	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} +(6.43546 - 13.2131i) 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} +(37.2278 - 18.4957i) 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} +(-73.9931 - 18.8950i) q^{18} +62.2883 q^{19} +(-28.7162 + 7.57418i) q^{20} +(-67.1109 - 68.9719i) q^{21} +(107.805 + 83.0572i) q^{22} -63.4952i q^{23} +(115.339 + 22.8225i) 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} +(49.0506 + 23.8903i) 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} +(-133.170 - 170.064i) 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} +(-31.3057 - 270.385i) 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} +(219.029 + 250.237i) 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} +(-18.5642 + 396.383i) 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} +(68.6614 + 138.200i) q^{60} -576.405 q^{61} +(-133.582 + 173.384i) q^{62} +(-280.634 + 413.874i) q^{63} +(-357.764 - 366.263i) q^{64} +258.272i q^{65} +(309.642 - 635.746i) 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} +(-4.80718 - 610.921i) 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} +(447.730 - 919.264i) 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} +(396.602 - 659.857i) 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} +(70.1435 - 274.683i) 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} +(58.7843 + 938.765i) 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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