LMFDB - Embedded newform 168.4.i.c.125.62

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			125.62
Character	$\chi$	$=$	168.125
Dual form			168.4.i.c.125.64

$q$-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} +(17.7570 - 49.2817i) 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} +(-34.3765 - 89.8847i) 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} +(-45.2854 - 141.072i) 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} +(-232.184 - 142.051i) 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} +(-344.986 - 237.908i) 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} +(-493.494 + 80.6876i) 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} +(182.948 + 65.9192i) 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} +(-765.437 + 82.5256i) 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} +(-214.242 - 946.199i) 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	$-0.766194\pi$
$13$	−69.5724			−1.48430			−0.742150	+	0.670234i	$0.766194\pi$
$14$	17.7570	−	49.2817i	0.338984	−	0.940792i
$15$	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	$0.386524\pi$
$18$	−73.9931	+	18.8950i	−0.968908	+	0.247422i
$19$	−62.2883			−0.752100			−0.376050	−	0.926599i	$-0.622718\pi$
$19$	−62.2883			−0.752100			−0.376050	+	0.926599i	$0.622718\pi$
$20$	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	$0.0929301\pi$
$23$			63.4952i			0.575638i	−0.957685	+	0.287819i	$0.907070\pi$
$24$	−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
$28$	−45.2854	−	141.072i	−0.305648	−	0.952145i
$29$	−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	$0.109501\pi$
$37$			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	$0.317394\pi$
$42$	−232.184	−	142.051i	−0.853018	−	0.521881i
$43$		−	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	$0.0958594\pi$
$48$	−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
$56$	−344.986	−	237.908i	−0.823228	−	0.567711i
$57$	−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	$-0.293202\pi$
$61$	576.405			1.20985			0.604927	+	0.796281i	$0.293202\pi$
$62$	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
$66$	−309.642	−	635.746i	−0.577489	−	1.18568i
$67$			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
$70$	182.948	+	65.9192i	0.312378	+	0.112555i
$71$			129.482i			0.216432i	0.994127	+	0.108216i	$0.0345139\pi$
$71$			129.482i			0.216432i	−0.994127	+	0.108216i	$0.965486\pi$
$72$	−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	$0.831597\pi$
$84$	−765.437	+	82.5256i	−0.994238	+	0.107194i
$85$			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	$0.551324\pi$
$90$	−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	$-0.256717\pi$
$98$	−214.242	−	946.199i	−0.220833	−	0.975312i
$99$	−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
$105$	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	$-0.435851\pi$
$107$	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	$0.259253\pi$
$109$			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
$112$	−1183.65	+	62.4737i	−0.998610	+	0.0527073i
$113$		−	73.7875i		−	0.0614278i	−0.999528	−	0.0307139i	$-0.990222\pi$
$113$		−	73.7875i		−	0.0614278i	0.999528	−	0.0307139i	$-0.00977807\pi$
$114$	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
$126$	−966.423	+	1032.67i	−0.683300	+	0.730138i
$127$	−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	$-0.682395\pi$
$137$		−	2694.83i		−	1.68054i	0.542165	−	0.840272i	$-0.317605\pi$
$138$	838.966	−	408.621i	0.517518	−	0.252059i
$139$	−2581.98			−1.57554			−0.787771	−	0.615968i	$-0.788765\pi$
$139$	−2581.98			−1.57554			−0.787771	+	0.615968i	$0.788765\pi$
$140$	523.698	−	168.112i	0.316147	−	0.101486i
$141$	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
$147$	−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	$-0.852168\pi$
$149$	−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
$154$	854.380	−	2371.19i	0.447064	−	1.24075i
$155$	−287.271			−0.148865
$156$	2590.03	+	1286.79i	1.32928	+	0.660422i
$157$	706.105			0.358938			0.179469	−	0.983764i	$-0.442562\pi$
$157$	706.105			0.358938			0.179469	+	0.983764i	$0.442562\pi$
$158$	−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	$-0.880969\pi$
$163$		−	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	$0.649991\pi$
$168$	−1572.56	+	1506.22i	−0.722175	+	0.691711i
$169$	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	$-0.585986\pi$
$181$	−1299.66			−0.533718			−0.266859	+	0.963736i	$0.585986\pi$
$182$	−1235.40	+	3428.65i	−0.503153	+	1.39642i
$183$	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
$189$	−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	$0.265866\pi$
$191$			3914.42i			1.48292i	−0.670998	+	0.741459i	$0.734134\pi$
$192$	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
$196$	−2113.37	−	1750.20i	−0.770180	−	0.637826i
$197$	−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
$210$	527.335	−	861.933i	0.173284	−	0.283233i
$211$			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
$216$	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	$0.840642\pi$
$224$	−2544.20	+	2183.22i	−0.758892	+	0.651217i
$225$	−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	$-0.468089\pi$
$229$	693.650			0.200165			0.100082	+	0.994979i	$0.468089\pi$
$230$	−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	$-0.852032\pi$
$233$		−	3188.80i		−	0.896589i	0.893886	−	0.448294i	$-0.147968\pi$
$234$	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
$238$	868.737	−	2411.03i	0.236604	−	0.656656i
$239$			1879.03i			0.508554i	0.967131	+	0.254277i	$0.0818375\pi$
$239$			1879.03i			0.508554i	−0.967131	+	0.254277i	$0.918162\pi$
$240$	−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	$-0.0677661\pi$
$252$	−382.722	+	3982.03i	−0.0956715	+	0.995413i
$253$			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	$0.197362\pi$
$258$	−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	$0.188363\pi$
$263$			4758.38i			1.11564i	−0.829961	+	0.557822i	$0.811637\pi$
$264$	−5549.54	+	1098.11i	−1.29375	+	0.255999i
$265$		−	480.566i		−	0.111400i
$266$	−1106.06	+	3069.67i	−0.254950	+	0.707570i
$267$	−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
$273$	2391.65	+	6253.49i	0.530218	+	1.38637i
$274$	−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	$-0.867974\pi$
$277$		−	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
$280$	883.183	−	1280.69i	0.188501	−	0.273342i
$281$			7823.45i			1.66088i	0.557106	+	0.830441i	$0.311912\pi$
$281$			7823.45i			1.66088i	−0.557106	+	0.830441i	$0.688088\pi$
$282$	−3960.57	−	8131.70i	−0.836342	−	1.71715i
$283$	4118.81			0.865151			0.432575	−	0.901598i	$-0.357605\pi$
$283$	4118.81			0.865151			0.432575	+	0.901598i	$0.357605\pi$
$284$	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	$-0.205376\pi$
$294$	−5040.10	+	98.0456i	−0.999811	+	0.0194494i
$295$	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	$-0.560474\pi$
$307$	−2031.61			−0.377688			−0.188844	+	0.982007i	$0.560474\pi$
$308$	−2178.91	−	6787.66i	−0.403099	−	1.25572i
$309$	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	$0.687464\pi$
$312$	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
$315$	−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	$-0.611408\pi$
$317$	−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
$322$	3129.15	+	1127.49i	0.541556	+	0.195132i
$323$	−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	$-0.884805\pi$
$331$		−	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
$336$	−923.350	+	6089.37i	−0.149919	+	0.988698i
$337$	−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	$-0.323704\pi$
$349$	6858.46			1.05193			0.525967	+	0.850505i	$0.323704\pi$
$350$	1974.92	−	5481.06i	0.301611	−	0.837071i
$351$	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	$0.658632\pi$
$354$	−5376.85	+	2618.81i	−0.807278	+	0.393187i
$355$	−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	$-0.998140\pi$
$359$		−	79.4813i		−	0.0116849i	0.999983	−	0.00584243i	$-0.00185971\pi$
$360$	−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
$364$	3150.61	+	9814.70i	0.453673	+	1.41327i
$365$	−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	$-0.864543\pi$
$373$		−	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
$378$	4241.99	+	6001.30i	0.577208	+	0.816597i
$379$			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	$0.407084\pi$
$384$	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
$392$	−7756.39	−	273.276i	−0.999380	−	0.0352105i
$393$	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	$-0.552091\pi$
$397$	−2577.45			−0.325840			−0.162920	+	0.986639i	$0.552091\pi$
$398$	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	$-0.936445\pi$
$401$		−	3185.37i		−	0.396682i	0.980133	−	0.198341i	$-0.0635554\pi$
$402$	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
$406$	−360.040	+	999.230i	−0.0440110	+	0.122145i
$407$			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	$0.602118\pi$
$420$	−306.358	−	2841.52i	−0.0355923	−	0.330124i
$421$		−	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
$426$	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	$-0.875927\pi$
$431$		−	6800.15i		−	0.759981i	0.924990	−	0.379991i	$-0.124073\pi$
$432$	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	$-0.212483\pi$
$434$	3813.61	+	1374.11i	0.421795	+	0.151980i
$435$	−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
$441$	−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	$-0.301918\pi$
$443$	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
$448$	−1931.74	+	9283.52i	−0.203719	+	0.979029i
$449$		−	11786.4i		−	1.23883i	−0.785063	−	0.619416i	$-0.787369\pi$
$449$		−	11786.4i		−	1.23883i	0.785063	−	0.619416i	$-0.212631\pi$
$450$	−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	$0.981512\pi$
$462$	−11171.5	−	6834.80i	−1.12499	−	0.688276i
$463$	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
$476$	−2215.52	−	6901.72i	−0.213337	−	0.664580i
$477$	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	$0.757465\pi$
$480$	−3484.96	−	218.224i	−0.331388	−	0.0207511i
$481$		−	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
$486$	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
$490$	3512.56	−	795.326i	0.323839	−	0.0733248i
$491$	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	$-0.863113\pi$
$499$		−	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	$0.444271\pi$
$504$	6016.35	+	9582.67i	0.531726	+	0.846917i
$505$	−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
$518$	7481.48	+	2695.71i	0.634590	+	0.228654i
$519$	−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	$0.730040\pi$
$522$	1500.28	−	383.112i	0.125796	−	0.0321233i
$523$	−12687.5			−1.06078			−0.530388	−	0.847755i	$-0.677954\pi$
$523$	−12687.5			−1.06078			−0.530388	+	0.847755i	$0.677954\pi$
$524$	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
$528$	−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
$532$	2820.75	+	8787.11i	0.229878	+	0.716109i
$533$	−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	$-0.769462\pi$
$541$		−	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
$546$	16153.6	+	9882.85i	1.26614	+	0.774628i
$547$			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
$552$	−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
$560$	−231.920	−	4394.04i	−0.0175008	−	0.331575i
$561$	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
$567$	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	$0.202147\pi$
$569$			16103.5i			1.18646i	−0.805034	+	0.593228i	$0.797853\pi$
$570$	−3055.28	+	1488.08i	−0.224511	+	0.109349i
$571$		−	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
$574$	5060.04	−	14043.3i	0.367948	−	1.02118i
$575$			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	$-0.178791\pi$
$588$	−11123.4	+	8920.01i	−0.780141	+	0.625604i
$589$		−	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	$0.443594\pi$
$594$	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	$-0.777000\pi$
$599$		−	18901.6i		−	1.28931i	0.764472	−	0.644657i	$-0.223000\pi$
$600$	−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	$-0.407740\pi$
$602$	−21740.3	−	7833.39i	−1.47187	−	0.530341i
$603$	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
$609$	697.013	+	1822.49i	0.0463783	+	0.121266i
$610$	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	$0.00605583\pi$
$613$			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
$616$	−16599.0	−	11447.0i	−1.08570	−	0.748719i
$617$			22282.8i			1.45393i	0.686677	+	0.726963i	$0.259069\pi$
$617$			22282.8i			1.45393i	−0.686677	+	0.726963i	$0.740931\pi$
$618$	21013.3	−	10234.6i	1.36776	−	0.666173i
$619$	−16401.1			−1.06497			−0.532484	−	0.846440i	$-0.678741\pi$
$619$	−16401.1			−1.06497			−0.532484	+	0.846440i	$0.678741\pi$
$620$	−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
$630$	−3833.56	−	3587.64i	−0.242433	−	0.226881i
$631$	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	$0.00622290\pi$
$641$			634.500i			0.0390971i	−0.999809	+	0.0195486i	$0.993777\pi$
$642$	−2851.56	−	5854.73i	−0.175299	−	0.359919i
$643$	−4543.63			−0.278668			−0.139334	−	0.990245i	$-0.544496\pi$
$643$	−4543.63			−0.278668			−0.139334	+	0.990245i	$0.544496\pi$
$644$	8957.38	−	2875.41i	0.548091	−	0.175942i
$645$	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	$0.306456\pi$
$648$	6640.28	−	15099.8i	0.402554	−	0.915396i
$649$		−	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	$-0.292676\pi$
$653$	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
$658$	10928.2	−	30329.4i	0.647456	−	1.79691i
$659$	−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	$-0.578737\pi$
$661$	−8321.89			−0.489689			−0.244844	+	0.969562i	$0.578737\pi$
$662$	−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
$672$	8442.79	+	15237.6i	0.484655	+	0.874706i
$673$	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
$686$	−12778.1	−	12631.3i	−0.711179	−	0.703011i
$687$	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	$-0.678563\pi$
$691$	−19327.1			−1.06402			−0.532010	+	0.846738i	$0.678563\pi$
$692$	−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
$696$	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
$700$	−5036.59	−	15689.9i	−0.271950	−	0.847172i
$701$	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	$-0.956848\pi$
$709$		−	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
$714$	−11359.3	−	6949.65i	−0.595391	−	0.364264i
$715$		−	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	$0.517868\pi$
$720$	−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	$0.780048\pi$
$728$	24001.5	+	16551.8i	1.22192	+	0.842654i
$729$	−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	$-0.520867\pi$
$733$	−2600.09			−0.131018			−0.0655092	+	0.997852i	$0.520867\pi$
$734$	−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
$738$	−21085.1	+	5384.31i	−1.05170	+	0.268562i
$739$			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
$742$	−2298.70	+	6379.66i	−0.113730	+	0.315640i
$743$			28215.9i			1.39319i	0.717463	+	0.696597i	$0.245303\pi$
$743$			28215.9i			1.39319i	−0.717463	+	0.696597i	$0.754697\pi$
$744$	−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
$756$	19864.1	+	6123.71i	0.955621	+	0.294599i
$757$			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	$0.658079\pi$
$762$	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	$-0.0723044\pi$
$770$	8802.53	+	3171.70i	0.411975	+	0.148442i
$771$	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
$777$	13645.4	−	5218.71i	0.630023	−	0.240953i
$778$	−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
$784$	−17850.5	+	12777.0i	−0.813159	+	0.582041i
$785$			2621.26i			0.119181i
$786$	15584.3	−	7590.38i	0.707218	−	0.344453i
$787$	34277.8			1.55257			0.776284	−	0.630384i	$-0.217103\pi$
$787$	34277.8			1.55257			0.776284	+	0.630384i	$0.217103\pi$
$788$	−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	$-0.152442\pi$
$798$	14462.3	+	8848.13i	0.641555	+	0.392507i
$799$	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	$0.107314\pi$
$809$			15223.1i			0.661576i	−0.943705	+	0.330788i	$0.892686\pi$
$810$	−1192.42	+	7561.00i	−0.0517251	+	0.327983i
$811$	−34460.7			−1.49208			−0.746042	−	0.665899i	$-0.768048\pi$
$811$	−34460.7			−1.49208			−0.746042	+	0.665899i	$0.768048\pi$
$812$	918.201	+	2860.35i	0.0396829	+	0.123619i
$813$	−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
$819$	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	$-0.442271\pi$
$821$	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
$826$	−20054.4	−	7225.95i	−0.844773	−	0.304386i
$827$	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	$-0.545965\pi$
$829$	−6869.52			−0.287802			−0.143901	+	0.989592i	$0.545965\pi$
$830$	−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	$-0.708538\pi$
$839$	−29613.1			−1.21854			−0.609272	+	0.792961i	$0.708538\pi$
$840$	−5591.51	−	5837.78i	−0.229673	−	0.239789i
$841$	−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	$-0.598079\pi$
$853$	−15110.8			−0.606545			−0.303273	+	0.952904i	$0.598079\pi$
$854$	10235.2	−	28406.2i	0.410121	−	1.13822i
$855$	−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	$0.237477\pi$
$858$	21542.5	+	44230.4i	0.857168	+	1.75991i
$859$	35305.1			1.40232			0.701162	−	0.713002i	$-0.252665\pi$
$859$	35305.1			1.40232			0.701162	+	0.713002i	$0.252665\pi$
$860$	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	$-0.601751\pi$
$863$		−	48135.9i		−	1.89868i	0.314244	−	0.949342i	$-0.398249\pi$
$864$	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
$868$	10916.7	−	3504.36i	0.426885	−	0.137034i
$869$	−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	$-0.858544\pi$
$877$		−	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	$0.441596\pi$
$882$	−4786.57	+	25753.0i	−0.182735	+	0.983162i
$883$			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	$0.502223\pi$
$888$	−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
$896$	11697.2	+	24135.0i	0.436135	+	0.899881i
$897$	−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
$903$	−39652.0	+	15164.9i	−1.46128	+	0.558868i
$904$	−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	$0.0810888\pi$
$907$			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
$910$	−12728.1	−	4586.16i	−0.463662	−	0.167065i
$911$		−	12013.8i		−	0.436921i	−0.975846	−	0.218461i	$-0.929896\pi$
$911$		−	12013.8i		−	0.436921i	0.975846	−	0.218461i	$-0.0701035\pi$
$912$	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
$924$	−36829.0	+	3970.72i	−1.31124	+	0.141371i
$925$			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	$0.802344\pi$
$930$	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	$-0.0313891\pi$
$938$	32774.6	+	11809.3i	1.14086	+	0.411072i
$939$	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
$945$	−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	$-0.619029\pi$
$947$	−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
$952$	−16877.9	−	11639.3i	−0.574598	−	0.396252i
$953$		−	15236.1i		−	0.517888i	−0.965892	−	0.258944i	$-0.916626\pi$
$953$		−	15236.1i		−	0.517888i	0.965892	−	0.258944i	$-0.0833745\pi$
$954$	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
$966$	9019.58	−	14742.6i	0.300414	−	0.491030i
$967$	−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	$-0.838517\pi$
$977$		−	29672.8i		−	0.971665i	0.874052	−	0.485832i	$-0.161483\pi$
$978$	−20088.9	+	9784.35i	−0.656822	+	0.319907i
$979$	−12971.1			−0.423452
$980$	6497.22	−	7845.45i	0.211782	−	0.255728i
$981$	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	$0.477138\pi$
$984$	−32867.0	+	6503.50i	−1.06480	+	0.210695i
$985$		−	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
$990$	−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
$994$	6381.10	+	2299.22i	0.203618	+	0.0733670i
$995$	−2638.23			−0.0840577
$996$	14117.8	−	28416.0i	0.449136	−	0.904010i
$997$	−43802.8			−1.39142			−0.695712	−	0.718321i	$-0.744911\pi$
$997$	−43802.8			−1.39142			−0.695712	+	0.718321i	$0.744911\pi$
$998$	−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.125.62	yes	80
3.2	odd	2	inner	168.4.i.c.125.20	yes	80
4.3	odd	2		672.4.i.c.209.39		80
7.6	odd	2	inner	168.4.i.c.125.61	yes	80
8.3	odd	2		672.4.i.c.209.42		80
8.5	even	2	inner	168.4.i.c.125.17	✓	80
12.11	even	2		672.4.i.c.209.38		80
21.20	even	2	inner	168.4.i.c.125.19	yes	80
24.5	odd	2	inner	168.4.i.c.125.63	yes	80
24.11	even	2		672.4.i.c.209.43		80
28.27	even	2		672.4.i.c.209.41		80
56.13	odd	2	inner	168.4.i.c.125.18	yes	80
56.27	even	2		672.4.i.c.209.40		80
84.83	odd	2		672.4.i.c.209.44		80
168.83	odd	2		672.4.i.c.209.37		80
168.125	even	2	inner	168.4.i.c.125.64	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.4.i.c.125.17	✓	80	8.5	even	2	inner
168.4.i.c.125.18	yes	80	56.13	odd	2	inner
168.4.i.c.125.19	yes	80	21.20	even	2	inner
168.4.i.c.125.20	yes	80	3.2	odd	2	inner
168.4.i.c.125.61	yes	80	7.6	odd	2	inner
168.4.i.c.125.62	yes	80	1.1	even	1	trivial
168.4.i.c.125.63	yes	80	24.5	odd	2	inner
168.4.i.c.125.64	yes	80	168.125	even	2	inner
672.4.i.c.209.37		80	168.83	odd	2
672.4.i.c.209.38		80	12.11	even	2
672.4.i.c.209.39		80	4.3	odd	2
672.4.i.c.209.40		80	56.27	even	2
672.4.i.c.209.41		80	28.27	even	2
672.4.i.c.209.42		80	8.3	odd	2
672.4.i.c.209.43		80	24.11	even	2
672.4.i.c.209.44		80	84.83	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} +(-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} +(17.7570 - 49.2817i) 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} +(-34.3765 - 89.8847i) 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} +(-45.2854 - 141.072i) 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} +(-232.184 - 142.051i) 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} +(-344.986 - 237.908i) 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} +(-493.494 + 80.6876i) 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} +(182.948 + 65.9192i) 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} +(-765.437 + 82.5256i) 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} +(-214.242 - 946.199i) 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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