LMFDB - Embedded newform 168.4.i.c.125.71

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			125.71
Character	$\chi$	$=$	168.125
Dual form			168.4.i.c.125.69

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.60932 + 1.09154i) q^{2} +(-4.05635 + 3.24747i) q^{3} +(5.61708 + 5.69635i) q^{4} +13.2397i q^{5} +(-14.1290 + 4.04602i) q^{6} +(18.4748 + 1.29729i) q^{7} +(8.43895 + 20.9949i) q^{8} +(5.90788 - 26.3457i) q^{9} +(-14.4516 + 34.5465i) q^{10} -49.5250 q^{11} +(-41.2835 - 4.86507i) q^{12} +28.7924 q^{13} +(46.7905 + 23.5510i) q^{14} +(-42.9954 - 53.7046i) q^{15} +(-0.896814 + 63.9937i) q^{16} -69.2560 q^{17} +(44.1730 - 62.2957i) q^{18} -24.7890 q^{19} +(-75.4177 + 74.3682i) q^{20} +(-79.1529 + 54.7340i) q^{21} +(-129.227 - 54.0585i) q^{22} +85.5006i q^{23} +(-102.411 - 57.7572i) q^{24} -50.2885 q^{25} +(75.1286 + 31.4281i) q^{26} +(61.5925 + 126.053i) q^{27} +(96.3845 + 112.526i) q^{28} +111.594 q^{29} +(-53.5679 - 187.064i) q^{30} -236.812i q^{31} +(-72.1918 + 166.001i) q^{32} +(200.891 - 160.831i) q^{33} +(-180.711 - 75.5957i) q^{34} +(-17.1756 + 244.600i) q^{35} +(183.260 - 114.333i) q^{36} +261.434i q^{37} +(-64.6825 - 27.0582i) q^{38} +(-116.792 + 93.5026i) q^{39} +(-277.965 + 111.729i) q^{40} +471.089 q^{41} +(-266.280 + 56.4198i) q^{42} -261.133i q^{43} +(-278.186 - 282.112i) q^{44} +(348.808 + 78.2183i) q^{45} +(-93.3274 + 223.098i) q^{46} -217.418 q^{47} +(-204.180 - 262.493i) q^{48} +(339.634 + 47.9342i) q^{49} +(-131.219 - 54.8919i) q^{50} +(280.926 - 224.907i) q^{51} +(161.729 + 164.012i) q^{52} +11.8711 q^{53} +(23.1225 + 396.143i) q^{54} -655.694i q^{55} +(128.671 + 398.823i) q^{56} +(100.553 - 80.5016i) q^{57} +(291.184 + 121.809i) q^{58} -236.528i q^{59} +(64.4118 - 546.580i) q^{60} +754.519 q^{61} +(258.490 - 617.917i) q^{62} +(143.325 - 479.067i) q^{63} +(-369.568 + 354.349i) q^{64} +381.202i q^{65} +(699.741 - 200.379i) q^{66} +163.127i q^{67} +(-389.016 - 394.506i) q^{68} +(-277.661 - 346.820i) q^{69} +(-311.807 + 619.490i) q^{70} +478.338i q^{71} +(602.981 - 98.2952i) q^{72} +1038.37i q^{73} +(-285.366 + 682.164i) q^{74} +(203.988 - 163.310i) q^{75} +(-139.242 - 141.207i) q^{76} +(-914.963 - 64.2482i) q^{77} +(-406.810 + 116.495i) q^{78} -148.084 q^{79} +(-847.255 - 11.8735i) q^{80} +(-659.194 - 311.295i) q^{81} +(1229.22 + 514.213i) q^{82} +739.797i q^{83} +(-756.393 - 143.438i) q^{84} -916.925i q^{85} +(285.037 - 681.378i) q^{86} +(-452.664 + 362.398i) q^{87} +(-417.939 - 1039.77i) q^{88} +1347.82 q^{89} +(824.773 + 584.835i) q^{90} +(531.934 + 37.3521i) q^{91} +(-487.042 + 480.264i) q^{92} +(769.039 + 960.590i) q^{93} +(-567.311 - 237.320i) q^{94} -328.198i q^{95} +(-246.249 - 907.798i) q^{96} -183.115i q^{97} +(833.891 + 495.800i) q^{98} +(-292.588 + 1304.77i) 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 $

$2$	2.60932	+	1.09154i	0.922533	+	0.385918i
$2$	2.60932	+	1.09154i	0.922533	+	0.385918i
$3$	−4.05635	+	3.24747i	−0.780644	+	0.624976i
$3$	−4.05635	+	3.24747i	−0.780644	+	0.624976i
$4$	5.61708	+	5.69635i	0.702135	+	0.712044i
$5$			13.2397i			1.18419i	0.805868	+	0.592095i	$0.201699\pi$
$5$			13.2397i			1.18419i	−0.805868	+	0.592095i	$0.798301\pi$
$6$	−14.1290	+	4.04602i	−0.961359	+	0.275297i
$7$	18.4748	+	1.29729i	0.997544	+	0.0700470i
$7$	18.4748	+	1.29729i	0.997544	+	0.0700470i
$8$	8.43895	+	20.9949i	0.372953	+	0.927850i
$9$	5.90788	−	26.3457i	0.218810	−	0.975767i
$10$	−14.4516	+	34.5465i	−0.457000	+	1.09246i
$11$	−49.5250			−1.35749			−0.678743	−	0.734376i	$-0.737475\pi$
$11$	−49.5250			−1.35749			−0.678743	+	0.734376i	$0.737475\pi$
$12$	−41.2835	−	4.86507i	−0.993128	−	0.117035i
$13$	28.7924			0.614276			0.307138	−	0.951665i	$-0.400629\pi$
$13$	28.7924			0.614276			0.307138	+	0.951665i	$0.400629\pi$
$14$	46.7905	+	23.5510i	0.893235	+	0.449590i
$15$	−42.9954	−	53.7046i	−0.740091	−	0.924432i
$16$	−0.896814	+	63.9937i	−0.0140127	+	0.999902i
$17$	−69.2560			−0.988061			−0.494031	−	0.869445i	$-0.664477\pi$
$17$	−69.2560			−0.988061			−0.494031	+	0.869445i	$0.664477\pi$
$18$	44.1730	−	62.2957i	0.578426	−	0.815735i
$19$	−24.7890			−0.299315			−0.149658	−	0.988738i	$-0.547817\pi$
$19$	−24.7890			−0.299315			−0.149658	+	0.988738i	$0.547817\pi$
$20$	−75.4177	+	74.3682i	−0.843196	+	0.831462i
$21$	−79.1529	+	54.7340i	−0.822504	+	0.568759i
$22$	−129.227	−	54.0585i	−1.25233	−	0.523878i
$23$			85.5006i			0.775135i	0.921841	+	0.387568i	$0.126685\pi$
$23$			85.5006i			0.775135i	−0.921841	+	0.387568i	$0.873315\pi$
$24$	−102.411	−	57.7572i	−0.871027	−	0.491235i
$25$	−50.2885			−0.402308
$26$	75.1286	+	31.4281i	0.566690	+	0.237060i
$27$	61.5925	+	126.053i	0.439018	+	0.898478i
$28$	96.3845	+	112.526i	0.650534	+	0.759477i
$29$	111.594			0.714569			0.357284	−	0.933996i	$-0.383703\pi$
$29$	111.594			0.714569			0.357284	+	0.933996i	$0.383703\pi$
$30$	−53.5679	−	187.064i	−0.326004	−	1.13843i
$31$		−	236.812i		−	1.37202i	−0.727592	−	0.686010i	$-0.759360\pi$
$31$		−	236.812i		−	1.37202i	0.727592	−	0.686010i	$-0.240640\pi$
$32$	−72.1918	+	166.001i	−0.398807	+	0.917035i
$33$	200.891	−	160.831i	1.05971	−	0.848396i
$34$	−180.711	−	75.5957i	−0.911519	−	0.381310i
$35$	−17.1756	+	244.600i	−0.0829490	+	1.18128i
$36$	183.260	−	114.333i	0.848424	−	0.529318i
$37$			261.434i			1.16161i	0.814044	+	0.580804i	$0.197262\pi$
$37$			261.434i			1.16161i	−0.814044	+	0.580804i	$0.802738\pi$
$38$	−64.6825	−	27.0582i	−0.276128	−	0.115511i
$39$	−116.792	+	93.5026i	−0.479531	+	0.383908i
$40$	−277.965	+	111.729i	−1.09875	+	0.441647i
$41$	471.089			1.79443			0.897217	−	0.441590i	$-0.145585\pi$
$41$	471.089			1.79443			0.897217	+	0.441590i	$0.145585\pi$
$42$	−266.280	+	56.4198i	−0.978282	+	0.207280i
$43$		−	261.133i		−	0.926101i	−0.886332	−	0.463051i	$-0.846755\pi$
$43$		−	261.133i		−	0.926101i	0.886332	−	0.463051i	$-0.153245\pi$
$44$	−278.186	−	282.112i	−0.953139	−	0.966590i
$45$	348.808	+	78.2183i	1.15549	+	0.259113i
$46$	−93.3274	+	223.098i	−0.299138	+	0.715088i
$47$	−217.418			−0.674757			−0.337379	−	0.941369i	$-0.609540\pi$
$47$	−217.418			−0.674757			−0.337379	+	0.941369i	$0.609540\pi$
$48$	−204.180	−	262.493i	−0.613975	−	0.789325i
$49$	339.634	+	47.9342i	0.990187	+	0.139750i
$50$	−131.219	−	54.8919i	−0.371142	−	0.155258i
$51$	280.926	−	224.907i	0.771324	−	0.617514i
$52$	161.729	+	164.012i	0.431305	+	0.437391i
$53$	11.8711			0.0307665			0.0153832	−	0.999882i	$-0.495103\pi$
$53$	11.8711			0.0307665			0.0153832	+	0.999882i	$0.495103\pi$
$54$	23.1225	+	396.143i	0.0582699	+	0.998301i
$55$		−	655.694i		−	1.60752i
$56$	128.671	+	398.823i	0.307043	+	0.951696i
$57$	100.553	−	80.5016i	0.233659	−	0.187065i
$58$	291.184	+	121.809i	0.659213	+	0.275765i
$59$		−	236.528i		−	0.521921i	−0.965350	−	0.260960i	$-0.915961\pi$
$59$		−	236.528i		−	0.521921i	0.965350	−	0.260960i	$-0.0840392\pi$
$60$	64.4118	−	546.580i	0.138592	−	1.17605i
$61$	754.519			1.58371			0.791855	−	0.610709i	$-0.209116\pi$
$61$	754.519			1.58371			0.791855	+	0.610709i	$0.209116\pi$
$62$	258.490	−	617.917i	0.529487	−	1.26573i
$63$	143.325	−	479.067i	0.286623	−	0.958044i
$64$	−369.568	+	354.349i	−0.721813	+	0.692088i
$65$			381.202i			0.727420i
$66$	699.741	−	200.379i	1.30503	−	0.373711i
$67$			163.127i			0.297449i	0.988879	+	0.148725i	$0.0475168\pi$
$67$			163.127i			0.297449i	−0.988879	+	0.148725i	$0.952483\pi$
$68$	−389.016	−	394.506i	−0.693752	−	0.703543i
$69$	−277.661	−	346.820i	−0.484441	−	0.605105i
$70$	−311.807	+	619.490i	−0.532401	+	1.05776i
$71$			478.338i			0.799554i	0.916613	+	0.399777i	$0.130912\pi$
$71$			478.338i			0.799554i	−0.916613	+	0.399777i	$0.869088\pi$
$72$	602.981	−	98.2952i	0.986972	−	0.160892i
$73$			1038.37i			1.66482i	0.554157	+	0.832412i	$0.313041\pi$
$73$			1038.37i			1.66482i	−0.554157	+	0.832412i	$0.686959\pi$
$74$	−285.366	+	682.164i	−0.448285	+	1.07162i
$75$	203.988	−	163.310i	0.314059	−	0.251433i
$76$	−139.242	−	141.207i	−0.210160	−	0.213126i
$77$	−914.963	−	64.2482i	−1.35415	−	0.0950878i
$78$	−406.810	+	116.495i	−0.590540	+	0.169108i
$79$	−148.084			−0.210895			−0.105448	−	0.994425i	$-0.533628\pi$
$79$	−148.084			−0.210895			−0.105448	+	0.994425i	$0.533628\pi$
$80$	−847.255	−	11.8735i	−1.18407	−	0.0165937i
$81$	−659.194	−	311.295i	−0.904244	−	0.427016i
$82$	1229.22	+	514.213i	1.65542	+	0.692504i
$83$			739.797i			0.978353i	0.872185	+	0.489176i	$0.162703\pi$
$83$			739.797i			0.978353i	−0.872185	+	0.489176i	$0.837297\pi$
$84$	−756.393	−	143.438i	−0.982490	−	0.186313i
$85$		−	916.925i		−	1.17005i
$86$	285.037	−	681.378i	0.357399	−	0.854359i
$87$	−452.664	+	362.398i	−0.557824	+	0.446588i
$88$	−417.939	−	1039.77i	−0.506278	−	1.25954i
$89$	1347.82			1.60527			0.802635	−	0.596470i	$-0.203431\pi$
$89$	1347.82			1.60527			0.802635	+	0.596470i	$0.203431\pi$
$90$	824.773	+	584.835i	0.965986	+	0.684967i
$91$	531.934	+	37.3521i	0.612767	+	0.0430282i
$92$	−487.042	+	480.264i	−0.551930	+	0.544250i
$93$	769.039	+	960.590i	0.857480	+	1.07106i
$94$	−567.311	−	237.320i	−0.622486	−	0.260401i
$95$		−	328.198i		−	0.354447i
$96$	−246.249	−	907.798i	−0.261798	−	0.965123i
$97$		−	183.115i		−	0.191675i	−0.995397	−	0.0958375i	$-0.969447\pi$
$97$		−	183.115i		−	0.191675i	0.995397	−	0.0958375i	$-0.0305529\pi$
$98$	833.891	+	495.800i	0.859548	+	0.511054i
$99$	−292.588	+	1304.77i	−0.297032	+	1.32459i
$100$	−282.475	−	286.461i	−0.282475	−	0.286461i
$101$		−	857.904i		−	0.845194i	−0.906318	−	0.422597i	$-0.861118\pi$
$101$		−	857.904i		−	0.845194i	0.906318	−	0.422597i	$-0.138882\pi$
$102$	978.520	−	280.211i	0.949882	−	0.272010i
$103$		−	493.737i		−	0.472324i	−0.971714	−	0.236162i	$-0.924110\pi$
$103$		−	493.737i		−	0.472324i	0.971714	−	0.236162i	$-0.0758896\pi$
$104$	242.978	+	604.493i	0.229096	+	0.569956i
$105$	−724.659	−	1047.96i	−0.673519	−	0.974002i
$106$	30.9755	+	12.9578i	0.0283831	+	0.0118733i
$107$	583.614			0.527290			0.263645	−	0.964620i	$-0.415075\pi$
$107$	583.614			0.527290			0.263645	+	0.964620i	$0.415075\pi$
$108$	−372.072	+	1058.90i	−0.331506	+	0.943453i
$109$		−	1856.22i		−	1.63113i	−0.578665	−	0.815565i	$-0.696426\pi$
$109$		−	1856.22i		−	1.63113i	0.578665	−	0.815565i	$-0.303574\pi$
$110$	715.716	−	1710.91i	0.620372	−	1.48299i
$111$	−848.999	−	1060.47i	−0.725976	−	0.906802i
$112$	−99.5867	+	1181.11i	−0.0840184	+	0.996464i
$113$			951.492i			0.792114i	0.918226	+	0.396057i	$0.129622\pi$
$113$			951.492i			0.792114i	−0.918226	+	0.396057i	$0.870378\pi$
$114$	350.245	−	100.297i	0.287750	−	0.0824005i
$115$	−1132.00			−0.917908
$116$	626.833	+	635.679i	0.501724	+	0.508804i
$117$	170.102	−	758.558i	0.134410	−	0.599390i
$118$	258.180	−	617.177i	0.201418	−	0.481489i
$119$	−1279.49	−	89.8449i	−0.985634	−	0.0692107i
$120$	764.685	−	1355.89i	0.581716	−	1.03146i
$121$	1121.73			0.842770
$122$	1968.78	+	823.588i	1.46102	+	0.611182i
$123$	−1910.90	+	1529.85i	−1.40081	+	1.12148i
$124$	1348.96	−	1330.19i	0.976939	−	0.963344i
$125$			989.155i			0.707781i
$126$	896.900	−	1093.59i	0.634145	−	0.773214i
$127$	2550.61			1.78213			0.891065	−	0.453876i	$-0.149959\pi$
$127$	2550.61			1.78213			0.891065	+	0.453876i	$0.149959\pi$
$128$	−1351.11	+	521.212i	−0.932985	+	0.359914i
$129$	848.020	+	1059.24i	0.578791	+	0.722956i
$130$	−416.097	+	994.677i	−0.280724	+	0.671069i
$131$		−	439.670i		−	0.293238i	−0.989193	−	0.146619i	$-0.953161\pi$
$131$		−	439.670i		−	0.293238i	0.989193	−	0.146619i	$-0.0468391\pi$
$132$	2044.57	+	240.943i	1.34816	+	0.158874i
$133$	−457.972	−	32.1585i	−0.298580	−	0.0209661i
$134$	−178.059	+	425.650i	−0.114791	+	0.274407i
$135$	−1668.90	+	815.464i	−1.06397	+	0.519881i
$136$	−584.448	−	1454.02i	−0.368500	−	0.916773i
$137$		−	1126.88i		−	0.702745i	−0.936236	−	0.351373i	$-0.885715\pi$
$137$		−	1126.88i		−	0.702745i	0.936236	−	0.351373i	$-0.114285\pi$
$138$	−345.937	−	1208.04i	−0.213392	−	0.745184i
$139$	−2419.55			−1.47643			−0.738215	−	0.674565i	$-0.764331\pi$
$139$	−2419.55			−1.47643			−0.738215	+	0.674565i	$0.764331\pi$
$140$	−1489.80	+	1276.10i	−0.899366	+	0.770356i
$141$	881.921	−	706.057i	0.526745	−	0.421707i
$142$	−522.125	+	1248.14i	−0.308562	+	0.737615i
$143$	−1425.95			−0.833871
$144$	1680.66	+	401.695i	0.972605	+	0.232462i
$145$			1477.47i			0.846186i
$146$	−1133.42	+	2709.44i	−0.642485	+	1.53586i
$147$	−1533.34	+	908.514i	−0.860324	+	0.509748i
$148$	−1489.22	+	1468.50i	−0.827115	+	0.815605i
$149$	−2049.54			−1.12688			−0.563439	−	0.826158i	$-0.690522\pi$
$149$	−2049.54			−1.12688			−0.563439	+	0.826158i	$0.690522\pi$
$150$	710.528	−	203.468i	0.386762	−	0.110754i
$151$	288.181			0.155310			0.0776551	−	0.996980i	$-0.475257\pi$
$151$	288.181			0.155310			0.0776551	+	0.996980i	$0.475257\pi$
$152$	−209.193	−	520.442i	−0.111630	−	0.277720i
$153$	−409.156	+	1824.60i	−0.216198	+	0.964118i
$154$	−2317.30	−	1166.36i	−1.21255	−	0.610313i
$155$	3135.31			1.62473
$156$	−1188.65	−	140.077i	−0.610054	−	0.0718920i
$157$	−2088.48			−1.06165			−0.530824	−	0.847482i	$-0.678117\pi$
$157$	−2088.48			−1.06165			−0.530824	+	0.847482i	$0.678117\pi$
$158$	−386.398	−	161.639i	−0.194558	−	0.0813883i
$159$	−48.1534	+	38.5511i	−0.0240177	+	0.0192283i
$160$	−2197.80	−	955.794i	−1.08594	−	0.472264i
$161$	−110.919	+	1579.60i	−0.0542959	+	0.773231i
$162$	−1380.26	−	1531.80i	−0.669402	−	0.742900i
$163$		−	4111.75i		−	1.97581i	−0.155057	−	0.987906i	$-0.549556\pi$
$163$		−	4111.75i		−	1.97581i	0.155057	−	0.987906i	$-0.450444\pi$
$164$	2646.15	+	2683.49i	1.25993	+	1.27772i
$165$	2129.35	+	2659.72i	1.00466	+	1.25490i
$166$	−807.518	+	1930.37i	−0.377564	+	0.902563i
$167$	−1224.94			−0.567598			−0.283799	−	0.958884i	$-0.591595\pi$
$167$	−1224.94			−0.567598			−0.283799	+	0.958884i	$0.591595\pi$
$168$	−1817.10	−	1199.91i	−0.834478	−	0.551041i
$169$	−1368.00			−0.622665
$170$	1000.86	−	2392.55i	0.451544	−	1.07941i
$171$	−146.451	+	653.085i	−0.0654934	+	0.292062i
$172$	1487.50	−	1466.80i	0.659425	−	0.650248i
$173$		−	2451.51i		−	1.07737i	−0.842508	−	0.538685i	$-0.818921\pi$
$173$		−	2451.51i		−	1.07737i	0.842508	−	0.538685i	$-0.181079\pi$
$174$	−1576.72	+	451.511i	−0.686957	+	0.196718i
$175$	−929.068	−	65.2386i	−0.401320	−	0.0281804i
$176$	44.4147	−	3169.29i	0.0190221	−	1.35735i
$177$	768.118	+	959.439i	0.326188	+	0.407434i
$178$	3516.90	+	1471.20i	1.48091	+	0.619502i
$179$	−926.214			−0.386751			−0.193376	−	0.981125i	$-0.561944\pi$
$179$	−926.214			−0.386751			−0.193376	+	0.981125i	$0.561944\pi$
$180$	1513.72	+	2426.29i	0.626813	+	1.00470i
$181$	−876.720			−0.360034			−0.180017	−	0.983664i	$-0.557615\pi$
$181$	−876.720			−0.360034			−0.180017	+	0.983664i	$0.557615\pi$
$182$	1347.21	+	678.090i	0.548693	+	0.276173i
$183$	−3060.59	+	2450.28i	−1.23631	+	0.989780i
$184$	−1795.07	+	721.536i	−0.719210	+	0.289089i
$185$	−3461.29			−1.37556
$186$	958.144	+	3345.92i	0.377713	+	1.31901i
$187$	3429.90			1.34128
$188$	−1221.25	−	1238.49i	−0.473771	−	0.480457i
$189$	974.380	+	2408.70i	0.375004	+	0.927023i
$190$	358.242	−	856.374i	0.136787	−	0.326989i
$191$		−	2476.56i		−	0.938208i	−0.883143	−	0.469104i	$-0.844577\pi$
$191$		−	2476.56i		−	0.938208i	0.883143	−	0.469104i	$-0.155423\pi$
$192$	348.358	−	2637.52i	0.130940	−	0.991390i
$193$	3130.49			1.16755			0.583776	−	0.811915i	$-0.301575\pi$
$193$	3130.49			1.16755			0.583776	+	0.811915i	$0.301575\pi$
$194$	199.877	−	477.804i	0.0739708	−	0.176827i
$195$	−1237.94	−	1546.29i	−0.454620	−	0.567856i
$196$	1634.70	+	2203.92i	0.595737	+	0.803180i
$197$	−85.4470			−0.0309028			−0.0154514	−	0.999881i	$-0.504919\pi$
$197$	−85.4470			−0.0309028			−0.0154514	+	0.999881i	$0.504919\pi$
$198$	−2187.67	+	3085.19i	−0.785205	+	1.10735i
$199$			3536.74i			1.25986i	0.776650	+	0.629932i	$0.216917\pi$
$199$			3536.74i			1.25986i	−0.776650	+	0.629932i	$0.783083\pi$
$200$	−424.382	−	1055.80i	−0.150042	−	0.373282i
$201$	−529.749	−	661.699i	−0.185899	−	0.232202i
$202$	936.437	−	2238.54i	0.326176	−	0.779720i
$203$	2061.67	+	144.770i	0.712814	+	0.0500534i
$204$	2859.13	+	336.935i	0.981271	+	0.115638i
$205$			6237.06i			2.12495i
$206$	538.934	−	1288.32i	0.182278	−	0.435735i
$207$	2252.58	+	505.128i	0.756352	+	0.169608i
$208$	−25.8215	+	1842.54i	−0.00860767	+	0.614216i
$209$	1227.68			0.406317
$210$	−746.979	−	3525.45i	−0.245459	−	1.15847i
$211$			1696.15i			0.553403i	0.960956	+	0.276701i	$0.0892413\pi$
$211$			1696.15i			0.553403i	−0.960956	+	0.276701i	$0.910759\pi$
$212$	66.6810	+	67.6221i	0.0216022	+	0.0219071i
$213$	−1553.39	−	1940.31i	−0.499702	−	0.624167i
$214$	1522.83	+	637.038i	0.486443	+	0.203491i
$215$	3457.31			1.09668
$216$	−2126.69	+	2356.88i	−0.669921	+	0.742433i
$217$	307.213	−	4375.04i	0.0961059	−	1.36865i
$218$	2026.13	−	4843.46i	0.629482	−	1.50477i
$219$	−3372.08	−	4211.99i	−1.04047	−	1.29964i
$220$	3735.06	−	3683.09i	1.14463	−	1.12870i
$221$	−1994.05			−0.606942
$222$	−1057.77	−	3693.81i	−0.319786	−	1.11672i
$223$			3936.51i			1.18210i	0.806635	+	0.591050i	$0.201286\pi$
$223$			3936.51i			1.18210i	−0.806635	+	0.591050i	$0.798714\pi$
$224$	−1549.08	+	2973.18i	−0.462063	+	0.886847i
$225$	−297.099	+	1324.89i	−0.0880292	+	0.392559i
$226$	−1038.59	+	2482.75i	−0.305691	+	0.730751i
$227$		−	6229.85i		−	1.82154i	−0.412912	−	0.910771i	$-0.635488\pi$
$227$		−	6229.85i		−	1.82154i	0.412912	−	0.910771i	$-0.364512\pi$
$228$	1023.38	+	120.600i	0.297258	+	0.0350305i
$229$	3973.83			1.14672			0.573359	−	0.819304i	$-0.305640\pi$
$229$	3973.83			1.14672			0.573359	+	0.819304i	$0.305640\pi$
$230$	−2953.75	−	1235.62i	−0.846801	−	0.354237i
$231$	3920.05	−	2710.70i	1.11654	−	0.772083i
$232$	941.737	+	2342.90i	0.266500	+	0.663013i
$233$		−	3401.07i		−	0.956273i	−0.878285	−	0.478137i	$-0.841312\pi$
$233$		−	3401.07i		−	0.956273i	0.878285	−	0.478137i	$-0.158688\pi$
$234$	1271.85	−	1793.64i	0.355313	−	0.501086i
$235$		−	2878.53i		−	0.799042i
$236$	1347.35	−	1328.60i	0.371630	−	0.366459i
$237$	600.679	−	480.898i	0.164634	−	0.131804i
$238$	−3240.52	−	1631.05i	−0.882571	−	0.444223i
$239$		−	4477.57i		−	1.21184i	−0.795525	−	0.605920i	$-0.792805\pi$
$239$		−	4477.57i		−	1.21184i	0.795525	−	0.605920i	$-0.207195\pi$
$240$	3475.32	−	2703.27i	0.934712	−	0.727064i
$241$		−	2312.70i		−	0.618151i	−0.951037	−	0.309076i	$-0.899980\pi$
$241$		−	2312.70i		−	0.618151i	0.951037	−	0.309076i	$-0.100020\pi$
$242$	2926.94	+	1224.41i	0.777483	+	0.325240i
$243$	3684.84	−	877.992i	0.972768	−	0.231783i
$244$	4238.20	+	4298.01i	1.11198	+	1.12767i
$245$	−634.632	+	4496.64i	−0.165490	+	1.17257i
$246$	−6656.04	+	1906.04i	−1.72510	+	0.494001i
$247$	−713.737			−0.183862
$248$	4971.83	−	1998.44i	1.27303	−	0.511699i
$249$	−2402.47	−	3000.87i	−0.611447	−	0.763745i
$250$	−1079.70	+	2581.02i	−0.273145	+	0.652952i
$251$			4493.21i			1.12992i	0.825119	+	0.564958i	$0.191108\pi$
$251$			4493.21i			1.12992i	−0.825119	+	0.564958i	$0.808892\pi$
$252$	3534.00	−	1874.53i	0.883417	−	0.468588i
$253$		−	4234.42i		−	1.05224i
$254$	6655.36	+	2784.10i	1.64407	+	0.687755i
$255$	2977.69	+	3719.37i	0.731255	+	0.913395i
$256$	−4094.39	−	114.781i	−0.999607	−	0.0280227i
$257$	1431.96			0.347562			0.173781	−	0.984784i	$-0.444402\pi$
$257$	1431.96			0.347562			0.173781	+	0.984784i	$0.444402\pi$
$258$	1056.55	+	3689.55i	0.254953	+	0.890316i
$259$	−339.155	+	4829.93i	−0.0813670	+	1.15875i
$260$	−2171.46	+	2141.24i	−0.517955	+	0.510747i
$261$	659.285	−	2940.03i	0.156355	−	0.697253i
$262$	479.917	−	1147.24i	0.113166	−	0.270521i
$263$			902.626i			0.211629i	0.994386	+	0.105814i	$0.0337449\pi$
$263$			902.626i			0.211629i	−0.994386	+	0.105814i	$0.966255\pi$
$264$	5071.93	+	2860.42i	1.18241	+	0.666844i
$265$			157.170i			0.0364334i
$266$	−1159.89	−	583.806i	−0.267359	−	0.134569i
$267$	−5467.24	+	4377.02i	−1.25314	+	1.00325i
$268$	−929.227	+	916.296i	−0.211797	+	0.208850i
$269$		−	1889.72i		−	0.428321i	−0.976798	−	0.214160i	$-0.931298\pi$
$269$		−	1889.72i		−	0.428321i	0.976798	−	0.214160i	$-0.0687015\pi$
$270$	−5244.80	+	306.134i	−1.18218	+	0.0690027i
$271$		−	7620.90i		−	1.70825i	−0.520065	−	0.854127i	$-0.674092\pi$
$271$		−	7620.90i		−	1.70825i	0.520065	−	0.854127i	$-0.325908\pi$
$272$	62.1097	−	4431.95i	0.0138454	−	0.987964i
$273$	−2279.01	+	1575.93i	−0.505245	+	0.349375i
$274$	1230.04	−	2940.40i	0.271202	−	0.648306i
$275$	2490.54			0.546128
$276$	415.967	−	3529.77i	0.0907183	−	0.769809i
$277$		−	2983.80i		−	0.647218i	−0.946191	−	0.323609i	$-0.895104\pi$
$277$		−	2983.80i		−	0.647218i	0.946191	−	0.323609i	$-0.104896\pi$
$278$	−6313.38	−	2641.04i	−1.36206	−	0.569781i
$279$	−6238.98	−	1399.06i	−1.33877	−	0.300213i
$280$	−5280.28	+	1703.56i	−1.12699	+	0.363598i
$281$		−	2988.80i		−	0.634508i	−0.948341	−	0.317254i	$-0.897239\pi$
$281$		−	2988.80i		−	0.634508i	0.948341	−	0.317254i	$-0.102761\pi$
$282$	3071.90	−	879.675i	0.648684	−	0.185758i
$283$	3150.99			0.661861			0.330930	−	0.943655i	$-0.392637\pi$
$283$	3150.99			0.661861			0.330930	+	0.943655i	$0.392637\pi$
$284$	−2724.78	+	2686.86i	−0.569317	+	0.561395i
$285$	1065.81	+	1331.29i	0.221521	+	0.276697i
$286$	−3720.75	−	1556.48i	−0.769274	−	0.321806i
$287$	8703.27	+	611.138i	1.79003	+	0.125695i
$288$	3946.92	+	2882.66i	0.807550	+	0.589800i
$289$	−116.610			−0.0237350
$290$	−1612.71	+	3855.18i	−0.326558	+	0.780635i
$291$	594.659	+	742.776i	0.119792	+	0.149630i
$292$	−5914.93	+	5832.62i	−1.18543	+	1.16893i
$293$			1635.98i			0.326194i	0.986610	+	0.163097i	$0.0521484\pi$
$293$			1635.98i			0.326194i	−0.986610	+	0.163097i	$0.947852\pi$
$294$	−4992.65	+	696.901i	−0.990398	+	0.138245i
$295$	3131.55			0.618054
$296$	−5488.77	+	2206.23i	−1.07780	+	0.433224i
$297$	−3050.37	−	6242.78i	−0.595961	−	1.21967i
$298$	−5347.90	−	2237.15i	−1.03958	−	0.434882i
$299$			2461.77i			0.476147i
$300$	2076.09	+	244.657i	0.399543	+	0.0470843i
$301$	338.764	−	4824.37i	0.0648706	−	0.923827i
$302$	751.956	+	314.561i	0.143279	+	0.0599369i
$303$	2786.02	+	3479.96i	0.528226	+	0.659796i
$304$	22.2311	−	1586.34i	0.00419422	−	0.299286i
$305$			9989.58i			1.87541i
$306$	−3059.24	+	4314.35i	−0.571520	+	0.805996i
$307$	3788.51			0.704305			0.352152	−	0.935943i	$-0.385450\pi$
$307$	3788.51			0.704305			0.352152	+	0.935943i	$0.385450\pi$
$308$	−4773.44	−	5572.84i	−0.883091	−	1.03098i
$309$	1603.40	+	2002.77i	0.295191	+	0.368717i
$310$	8181.01	+	3422.31i	1.49887	+	0.627014i
$311$	4998.37			0.911356			0.455678	−	0.890145i	$-0.349397\pi$
$311$	4998.37			0.911356			0.455678	+	0.890145i	$0.349397\pi$
$312$	−2948.68	−	1662.97i	−0.535051	−	0.301754i
$313$		−	1152.65i		−	0.208152i	−0.994569	−	0.104076i	$-0.966812\pi$
$313$		−	1152.65i		−	0.208152i	0.994569	−	0.104076i	$-0.0331885\pi$
$314$	−5449.50	−	2279.66i	−0.979406	−	0.409709i
$315$	6342.68	+	1897.57i	1.13451	+	0.339416i
$316$	−831.799	−	843.537i	−0.148077	−	0.150167i
$317$	2738.80			0.485256			0.242628	−	0.970119i	$-0.421991\pi$
$317$	2738.80			0.485256			0.242628	+	0.970119i	$0.421991\pi$
$318$	−167.728	+	48.0308i	−0.0295777	+	0.00846991i
$319$	−5526.70			−0.970018
$320$	−4691.46	−	4892.95i	−0.819565	−	0.854764i
$321$	−2367.34	+	1895.27i	−0.411626	+	0.329544i
$322$	−2013.62	+	4000.62i	−0.348493	+	0.692378i
$323$	1716.79			0.295742
$324$	−1929.50	−	5503.57i	−0.330847	−	0.943684i
$325$	−1447.93			−0.247128
$326$	4488.14	−	10728.9i	0.762500	−	1.82275i
$327$	6028.01	+	7529.46i	1.01942	+	1.27333i
$328$	3975.50	+	9890.45i	0.669239	+	1.66497i
$329$	−4016.74	−	282.053i	−0.673100	−	0.0472647i
$330$	2652.95	+	9264.33i	0.442546	+	1.54541i
$331$			5222.20i			0.867184i	0.901109	+	0.433592i	$0.142754\pi$
$331$			5222.20i			0.867184i	−0.901109	+	0.433592i	$0.857246\pi$
$332$	−4214.14	+	4155.50i	−0.696630	+	0.686936i
$333$	6887.66	+	1544.52i	1.13346	+	0.254172i
$334$	−3196.26	−	1337.07i	−0.523628	−	0.219046i
$335$	−2159.74			−0.352237
$336$	−3431.65	−	5114.38i	−0.557178	−	0.830393i
$337$	−2898.62			−0.468540			−0.234270	−	0.972172i	$-0.575270\pi$
$337$	−2898.62			−0.468540			−0.234270	+	0.972172i	$0.575270\pi$
$338$	−3569.53	−	1493.22i	−0.574429	−	0.240297i
$339$	−3089.94	−	3859.58i	−0.495052	−	0.618359i
$340$	5223.13	−	5150.44i	0.833129	−	0.821535i
$341$			11728.1i			1.86250i
$342$	−1095.00	+	1544.25i	−0.173132	+	0.244162i
$343$	6212.48	+	1326.18i	0.977966	+	0.208766i
$344$	5482.44	−	2203.69i	0.859284	−	0.345392i
$345$	4591.78	−	3676.13i	0.716560	−	0.573670i
$346$	2675.92	−	6396.77i	0.415776	−	0.993909i
$347$	10559.0			1.63353			0.816765	−	0.576970i	$-0.195765\pi$
$347$	10559.0			1.63353			0.816765	+	0.576970i	$0.195765\pi$
$348$	−4607.00	−	542.913i	−0.709658	−	0.0836298i
$349$	−4344.86			−0.666404			−0.333202	−	0.942855i	$-0.608129\pi$
$349$	−4344.86			−0.666404			−0.333202	+	0.942855i	$0.608129\pi$
$350$	−2353.02	−	1184.34i	−0.359355	−	0.180874i
$351$	1773.40	+	3629.37i	0.269678	+	0.551914i
$352$	3575.30	−	8221.20i	0.541375	−	1.24486i
$353$	−9819.24			−1.48053			−0.740263	−	0.672318i	$-0.765299\pi$
$353$	−9819.24			−1.48053			−0.740263	+	0.672318i	$0.765299\pi$
$354$	956.996	+	3341.91i	0.143683	+	0.501753i
$355$	−6333.03			−0.946824
$356$	7570.83	+	7677.68i	1.12712	+	1.14302i
$357$	5481.81	−	3790.66i	0.812685	−	0.561969i
$358$	−2416.79	−	1011.00i	−0.356791	−	0.149254i
$359$		−	728.937i		−	0.107164i	−0.998563	−	0.0535820i	$-0.982936\pi$
$359$		−	728.937i		−	0.107164i	0.998563	−	0.0535820i	$-0.0170638\pi$
$360$	1301.39	+	7983.26i	0.190526	+	1.16876i
$361$	−6244.50			−0.910410
$362$	−2287.64	−	956.975i	−0.332143	−	0.138943i
$363$	−4550.11	+	3642.77i	−0.657903	+	0.526711i
$364$	2775.14	+	3239.89i	0.399607	+	0.466529i
$365$	−13747.7			−1.97147
$366$	−10660.6	+	3052.80i	−1.52251	+	0.435990i
$367$			8207.43i			1.16737i	0.811981	+	0.583685i	$0.198390\pi$
$367$			8207.43i			1.16737i	−0.811981	+	0.583685i	$0.801610\pi$
$368$	−5471.50	−	76.6782i	−0.775059	−	0.0108618i
$369$	2783.14	−	12411.2i	0.392641	−	1.75095i
$370$	−9031.62	−	3778.14i	−1.26900	−	0.530855i
$371$	219.316	+	15.4003i	0.0306909	+	0.00215510i
$372$	−1152.11	+	9776.43i	−0.160575	+	1.36259i
$373$			6620.48i			0.919023i	0.888172	+	0.459511i	$0.151975\pi$
$373$			6620.48i			0.919023i	−0.888172	+	0.459511i	$0.848025\pi$
$374$	8949.71	+	3743.88i	1.23738	+	0.517624i
$375$	−3212.25	−	4012.35i	−0.442346	−	0.552525i
$376$	−1834.78	−	4564.65i	−0.251653	−	0.626074i
$377$	3213.07			0.438942
$378$	−86.7287	+	7348.65i	−0.0118012	+	0.999930i
$379$		−	2808.73i		−	0.380672i	−0.981719	−	0.190336i	$-0.939042\pi$
$379$		−	2808.73i		−	0.380672i	0.981719	−	0.190336i	$-0.0609578\pi$
$380$	1869.53	−	1843.52i	0.252382	−	0.248869i
$381$	−10346.2	+	8283.04i	−1.39121	+	1.11379i
$382$	2703.27	−	6462.13i	0.362071	−	0.865528i
$383$	−2395.34			−0.319573			−0.159786	−	0.987152i	$-0.551081\pi$
$383$	−2395.34			−0.319573			−0.159786	+	0.987152i	$0.551081\pi$
$384$	3787.94	−	6501.89i	0.503392	−	0.864058i
$385$	850.624	−	12113.8i	0.112602	−	1.60357i
$386$	8168.44	+	3417.05i	1.07711	+	0.450579i
$387$	−6879.73	−	1542.74i	−0.903660	−	0.202641i
$388$	1043.09	−	1028.57i	0.136481	−	0.134582i
$389$	−12078.7			−1.57432			−0.787162	−	0.616746i	$-0.788450\pi$
$389$	−12078.7			−1.57432			−0.787162	+	0.616746i	$0.788450\pi$
$390$	−1542.35	−	5386.02i	−0.200256	−	0.699312i
$391$		−	5921.43i		−	0.765881i
$392$	1859.79	+	7535.08i	0.239626	+	0.970865i
$393$	1427.81	+	1783.45i	0.183266	+	0.228914i
$394$	−222.958	−	93.2688i	−0.0285088	−	0.0119259i
$395$		−	1960.58i		−	0.249740i
$396$	−9075.93	+	5662.33i	−1.15172	+	0.718542i
$397$	5240.22			0.662466			0.331233	−	0.943549i	$-0.392535\pi$
$397$	5240.22			0.662466			0.331233	+	0.943549i	$0.392535\pi$
$398$	−3860.50	+	9228.48i	−0.486204	+	1.16227i
$399$	1962.12	−	1356.80i	0.246188	−	0.170238i
$400$	45.0994	−	3218.15i	0.00563743	−	0.402268i
$401$			10649.8i			1.32625i	0.748509	+	0.663125i	$0.230770\pi$
$401$			10649.8i			1.32625i	−0.748509	+	0.663125i	$0.769230\pi$
$402$	−660.014	−	2304.82i	−0.0818868	−	0.285956i
$403$		−	6818.39i		−	0.842799i
$404$	4886.92	−	4818.92i	0.601815	−	0.593441i
$405$	4121.44	−	8727.50i	0.505669	−	1.07080i
$406$	5221.54	+	2628.15i	0.638278	+	0.321263i
$407$		−	12947.5i		−	1.57687i
$408$	7092.61	+	4000.03i	0.860628	+	0.485370i
$409$			10197.5i			1.23284i	0.787416	+	0.616421i	$0.211418\pi$
$409$			10197.5i			1.23284i	−0.787416	+	0.616421i	$0.788582\pi$
$410$	−6808.00	+	16274.5i	−0.820057	+	1.96034i
$411$	3659.52	+	4571.03i	0.439199	+	0.548594i
$412$	2812.50	−	2773.36i	0.336315	−	0.331635i
$413$	306.845	−	4369.80i	0.0365590	−	0.520639i
$414$	5326.32	+	3776.82i	0.632305	+	0.448358i
$415$	−9794.66			−1.15856
$416$	−2078.58	+	4779.58i	−0.244978	+	0.563312i
$417$	9814.54	−	7857.43i	1.15257	−	0.922733i
$418$	3203.40	+	1340.06i	0.374841	+	0.156805i
$419$		−	9402.75i		−	1.09631i	−0.836376	−	0.548155i	$-0.815330\pi$
$419$		−	9402.75i		−	1.09631i	0.836376	−	0.548155i	$-0.184670\pi$
$420$	1899.07	−	10014.4i	0.220631	−	1.16346i
$421$			1525.15i			0.176559i	0.996096	+	0.0882793i	$0.0281368\pi$
$421$			1525.15i			0.176559i	−0.996096	+	0.0882793i	$0.971863\pi$
$422$	−1851.42	+	4425.80i	−0.213568	+	0.510532i
$423$	−1284.48	+	5728.02i	−0.147644	+	0.658406i
$424$	100.180	+	249.233i	0.0114744	+	0.0285467i
$425$	3482.78			0.397505
$426$	−1935.36	−	6758.46i	−0.220114	−	0.768658i
$427$	13939.6	+	978.829i	1.57982	+	0.110934i
$428$	3278.20	+	3324.47i	0.370229	+	0.375454i
$429$	5784.13	−	4630.72i	0.650957	−	0.521149i
$430$	9021.21	+	3773.79i	1.01172	+	0.423229i
$431$			7819.69i			0.873924i	0.899480	+	0.436962i	$0.143946\pi$
$431$			7819.69i			0.873924i	−0.899480	+	0.436962i	$0.856054\pi$
$432$	−8121.84	+	3828.49i	−0.904542	+	0.426385i
$433$			11246.6i			1.24821i	0.781340	+	0.624106i	$0.214536\pi$
$433$			11246.6i			1.24821i	−0.781340	+	0.624106i	$0.785464\pi$
$434$	5577.15	−	11080.5i	0.616847	−	1.22554i
$435$	−4798.03	−	5993.12i	−0.528846	−	0.660570i
$436$	10573.7	−	10426.5i	1.16144	−	1.14527i
$437$		−	2119.48i		−	0.232010i
$438$	−4201.27	−	14671.2i	−0.458320	−	1.60049i
$439$		−	5899.62i		−	0.641397i	−0.947181	−	0.320698i	$-0.896082\pi$
$439$		−	5899.62i		−	0.641397i	0.947181	−	0.320698i	$-0.103918\pi$
$440$	13766.2	−	5533.37i	1.49154	−	0.599530i
$441$	3269.38	−	8664.71i	0.353027	−	0.935613i
$442$	−5203.11	−	2176.58i	−0.559924	−	0.234230i
$443$	−991.808			−0.106371			−0.0531854	−	0.998585i	$-0.516937\pi$
$443$	−991.808			−0.106371			−0.0531854	+	0.998585i	$0.516937\pi$
$444$	1271.89	−	10792.9i	0.135949	−	1.15362i
$445$			17844.7i			1.90095i
$446$	−4296.86	+	10271.6i	−0.456193	+	1.09053i
$447$	8313.64	−	6655.81i	0.879690	−	0.704271i
$448$	−7287.38	+	6067.08i	−0.768518	+	0.639828i
$449$		−	13929.7i		−	1.46411i	−0.681248	−	0.732053i	$-0.738562\pi$
$449$		−	13929.7i		−	1.46411i	0.681248	−	0.732053i	$-0.261438\pi$
$450$	−2221.39	+	3132.76i	−0.232705	+	0.328177i
$451$	−23330.7			−2.43592
$452$	−5420.03	+	5344.61i	−0.564020	+	0.556171i
$453$	−1168.96	+	935.859i	−0.121242	+	0.0970651i
$454$	6800.14	−	16255.7i	0.702965	−	1.68043i
$455$	−494.529	+	7042.62i	−0.0509535	+	0.725633i
$456$	2538.68	+	1431.74i	0.260712	+	0.147034i
$457$	−10005.2			−1.02412			−0.512060	−	0.858950i	$-0.671117\pi$
$457$	−10005.2			−1.02412			−0.512060	+	0.858950i	$0.671117\pi$
$458$	10369.0	+	4337.60i	1.05789	+	0.442539i
$459$	−4265.65	−	8729.92i	−0.433777	−	0.887752i
$460$	−6358.53	−	6448.26i	−0.644496	−	0.653591i
$461$		−	15566.9i		−	1.57272i	−0.617770	−	0.786359i	$-0.711964\pi$
$461$		−	15566.9i		−	1.57272i	0.617770	−	0.786359i	$-0.288036\pi$
$462$	13187.5	−	2794.19i	1.32800	−	0.281380i
$463$	−10866.3			−1.09071			−0.545357	−	0.838204i	$-0.683606\pi$
$463$	−10866.3			−1.09071			−0.545357	+	0.838204i	$0.683606\pi$
$464$	−100.079	+	7141.32i	−0.0100131	+	0.714499i
$465$	−12717.9	+	10181.8i	−1.26834	+	1.01542i
$466$	3712.41	−	8874.48i	0.369043	−	0.882194i
$467$			2184.04i			0.216414i	0.994128	+	0.108207i	$0.0345109\pi$
$467$			2184.04i			0.216414i	−0.994128	+	0.108207i	$0.965489\pi$
$468$	5276.49	−	3291.92i	0.521166	−	0.325147i
$469$	−211.622	+	3013.73i	−0.0208354	+	0.296719i
$470$	3142.03	−	7511.01i	0.308364	−	0.737142i
$471$	8471.59	−	6782.27i	0.828769	−	0.663504i
$472$	4965.87	−	1996.05i	0.484264	−	0.194652i
$473$			12932.6i			1.25717i
$474$	2092.28	−	599.150i	0.202746	−	0.0580588i
$475$	1246.60			0.120417
$476$	−6675.20	−	7793.08i	−0.642767	−	0.750410i
$477$	70.1332	−	312.753i	0.00673203	−	0.0300209i
$478$	4887.45	−	11683.4i	0.467671	−	1.11796i
$479$	−7028.43			−0.670433			−0.335216	−	0.942141i	$-0.608809\pi$
$479$	−7028.43			−0.670433			−0.335216	+	0.942141i	$0.608809\pi$
$480$	12018.9	−	3260.25i	1.14289	−	0.310019i
$481$			7527.32i			0.713547i
$482$	2524.41	−	6034.58i	0.238555	−	0.570265i
$483$	−4679.79	−	6767.63i	−0.440865	−	0.637552i
$484$	6300.83	+	6389.75i	0.591738	+	0.600089i
$485$	2424.37			0.226980
$486$	10573.3	+	1731.19i	0.986859	+	0.161581i
$487$	3566.36			0.331842			0.165921	−	0.986139i	$-0.446940\pi$
$487$	3566.36			0.331842			0.165921	+	0.986139i	$0.446940\pi$
$488$	6367.35	+	15841.0i	0.590649	+	1.46945i
$489$	13352.8	+	16678.7i	1.23483	+	1.54241i
$490$	−6564.22	+	11040.4i	−0.605186	+	1.01787i
$491$	2231.72			0.205124			0.102562	−	0.994727i	$-0.467296\pi$
$491$	2231.72			0.205124			0.102562	+	0.994727i	$0.467296\pi$
$492$	−19448.2	−	2291.88i	−1.78210	−	0.210012i
$493$	−7728.56			−0.706038
$494$	−1862.37	−	779.072i	−0.169619	−	0.0709557i
$495$	−17274.7	−	3873.76i	−1.56857	−	0.351743i
$496$	15154.5	+	212.376i	1.37189	+	0.0192257i
$497$	−620.542	+	8837.19i	−0.0560063	+	0.797590i
$498$	−2993.23	−	10452.6i	−0.269337	−	0.940548i
$499$			20669.1i			1.85426i	0.374743	+	0.927129i	$0.377731\pi$
$499$			20669.1i			1.85426i	−0.374743	+	0.927129i	$0.622269\pi$
$500$	−5634.57	+	5556.16i	−0.503971	+	0.496958i
$501$	4968.79	−	3977.96i	0.443092	−	0.354735i
$502$	−4904.52	+	11724.2i	−0.436055	+	1.04239i
$503$	−17146.1			−1.51990			−0.759948	−	0.649984i	$-0.774775\pi$
$503$	−17146.1			−1.51990			−0.759948	+	0.649984i	$0.774775\pi$
$504$	11267.5	−	1033.74i	0.995818	−	0.0913620i
$505$	11358.4			1.00087
$506$	4622.04	−	11048.9i	0.406076	−	0.970723i
$507$	5549.06	−	4442.52i	0.486080	−	0.389151i
$508$	14327.0	+	14529.2i	1.25130	+	1.26895i
$509$		−	7036.98i		−	0.612787i	−0.951905	−	0.306393i	$-0.900878\pi$
$509$		−	7036.98i		−	0.612787i	0.951905	−	0.306393i	$-0.0991223\pi$
$510$	3709.89	+	12955.3i	0.322112	+	1.12484i
$511$	−1347.07	+	19183.7i	−0.116616	+	1.66074i
$512$	−10558.3	−	4768.69i	−0.911356	−	0.411618i
$513$	−1526.82	−	3124.73i	−0.131405	−	0.268928i
$514$	3736.44	+	1563.04i	0.320637	+	0.134130i
$515$	6536.91			0.559322
$516$	−1270.43	+	10780.5i	−0.108387	+	0.919737i
$517$	10767.6			0.915974
$518$	−6157.03	+	12232.6i	−0.522247	+	1.03759i
$519$	7961.20	+	9944.17i	0.673330	+	0.841042i
$520$	−8003.28	+	3216.95i	−0.674937	+	0.271293i
$521$	−5554.16			−0.467048			−0.233524	−	0.972351i	$-0.575026\pi$
$521$	−5554.16			−0.467048			−0.233524	+	0.972351i	$0.575026\pi$
$522$	4929.44	−	6951.83i	0.413325	−	0.582899i
$523$	1129.07			0.0943994			0.0471997	−	0.998885i	$-0.484970\pi$
$523$	1129.07			0.0943994			0.0471997	+	0.998885i	$0.484970\pi$
$524$	2504.51	−	2469.66i	0.208798	−	0.205892i
$525$	3980.48	−	2752.49i	0.330900	−	0.228816i
$526$	−985.253	+	2355.24i	−0.0816712	+	0.195234i
$527$			16400.6i			1.35564i
$528$	10112.0	+	13000.0i	0.833464	+	1.07150i
$529$	4856.64			0.399165
$530$	−171.557	+	410.105i	−0.0140603	+	0.0336110i
$531$	−6231.50	−	1397.38i	−0.509273	−	0.114202i
$532$	−2389.28	−	2789.40i	−0.194715	−	0.227323i
$533$	13563.8			1.10228
$534$	−19043.5	+	5453.32i	−1.54324	+	0.441925i
$535$			7726.84i			0.624412i
$536$	−3424.82	+	1376.62i	−0.275989	+	0.110935i
$537$	3757.04	−	3007.85i	0.301915	−	0.241710i
$538$	2062.71	−	4930.88i	0.165297	−	0.395140i
$539$	−16820.4	−	2373.94i	−1.34417	−	0.189708i
$540$	−14019.5	−	4926.11i	−1.11723	−	0.392566i
$541$		−	13088.7i		−	1.04016i	−0.854118	−	0.520079i	$-0.825903\pi$
$541$		−	13088.7i		−	1.04016i	0.854118	−	0.520079i	$-0.174097\pi$
$542$	8318.52	−	19885.4i	0.659245	−	1.57592i
$543$	3556.28	−	2847.12i	0.281058	−	0.225012i
$544$	4999.71	−	11496.6i	0.394046	−	0.906087i
$545$	24575.7			1.93157
$546$	−7666.84	+	1624.46i	−0.600935	+	0.127327i
$547$			134.806i			0.0105373i	0.999986	+	0.00526863i	$0.00167706\pi$
$547$			134.806i			0.0105373i	−0.999986	+	0.00526863i	$0.998323\pi$
$548$	6419.12	−	6329.79i	0.500385	−	0.493422i
$549$	4457.61	−	19878.4i	0.346532	−	1.54533i
$550$	6498.61	+	2718.52i	0.503821	+	0.210760i
$551$	−2766.31			−0.213881
$552$	4938.27	−	8756.25i	0.380773	−	0.675164i
$553$	−2735.81	−	192.107i	−0.210377	−	0.0147726i
$554$	3256.94	−	7785.69i	0.249773	−	0.597080i
$555$	14040.2	−	11240.4i	1.07383	−	0.859695i
$556$	−13590.8	−	13782.6i	−1.03665	−	1.05128i
$557$	−949.790			−0.0722512			−0.0361256	−	0.999347i	$-0.511502\pi$
$557$	−949.790			−0.0722512			−0.0361256	+	0.999347i	$0.511502\pi$
$558$	−14752.3	−	10460.7i	−1.11921	−	0.793612i
$559$		−	7518.65i		−	0.568882i
$560$	−15637.4	−	1318.49i	−1.18000	−	0.0994938i
$561$	−13912.9	+	11138.5i	−1.04706	+	0.838267i
$562$	3262.40	−	7798.73i	0.244868	−	0.585355i
$563$		−	3122.65i		−	0.233755i	−0.993146	−	0.116877i	$-0.962712\pi$
$563$		−	3122.65i		−	0.233755i	0.993146	−	0.116877i	$-0.0372884\pi$
$564$	8975.77	+	1057.75i	0.670120	+	0.0789705i
$565$	−12597.4			−0.938014
$566$	8221.92	+	3439.43i	0.610589	+	0.255424i
$567$	−11774.6	−	6606.26i	−0.872112	−	0.489307i
$568$	−10042.6	+	4036.67i	−0.741866	+	0.298196i
$569$		−	15497.7i		−	1.14182i	−0.821011	−	0.570912i	$-0.806590\pi$
$569$		−	15497.7i		−	1.14182i	0.821011	−	0.570912i	$-0.193410\pi$
$570$	1327.90	+	4637.13i	0.0975779	+	0.340751i
$571$			11912.4i			0.873063i	0.899689	+	0.436531i	$0.143793\pi$
$571$			11912.4i			0.873063i	−0.899689	+	0.436531i	$0.856207\pi$
$572$	−8009.65	−	8122.69i	−0.585490	−	0.593753i
$573$	8042.56	+	10045.8i	0.586357	+	0.732406i
$574$	22042.5	+	11094.6i	1.60285	+	0.806760i
$575$		−	4299.70i		−	0.311843i
$576$	7152.22	+	11830.0i	0.517377	+	0.855757i
$577$		−	5650.41i		−	0.407677i	−0.979005	−	0.203838i	$-0.934658\pi$
$577$		−	5650.41i		−	0.407677i	0.979005	−	0.203838i	$-0.0653417\pi$
$578$	−304.273	−	127.285i	−0.0218963	−	0.00915977i
$579$	−12698.3	+	10166.2i	−0.911443	+	0.729692i
$580$	−8416.17	+	8299.05i	−0.602521	+	0.594137i
$581$	−959.729	+	13667.6i	−0.0685306	+	0.975949i
$582$	740.885	+	2587.23i	0.0527675	+	0.184269i
$583$	−587.917			−0.0417651
$584$	−21800.5	+	8762.77i	−1.54471	+	0.620901i
$585$	10043.0	+	2252.10i	0.709793	+	0.159167i
$586$	−1785.74	+	4268.79i	−0.125884	+	0.300925i
$587$			9396.05i			0.660675i	0.943863	+	0.330338i	$0.107163\pi$
$587$			9396.05i			0.660675i	−0.943863	+	0.330338i	$0.892837\pi$
$588$	−13788.1	−	3631.24i	−0.967026	−	0.254676i
$589$			5870.33i			0.410667i
$590$	8171.21	+	3418.21i	0.570175	+	0.238518i
$591$	346.603	−	277.487i	0.0241241	−	0.0193135i
$592$	−16730.1	−	234.458i	−1.16149	−	0.0162773i
$593$	5680.51			0.393374			0.196687	−	0.980466i	$-0.436982\pi$
$593$	5680.51			0.393374			0.196687	+	0.980466i	$0.436982\pi$
$594$	−1145.14	−	19619.0i	−0.0791006	−	1.35518i
$595$	1189.52	−	16940.0i	0.0819587	−	1.16718i
$596$	−11512.4	−	11674.9i	−0.791220	−	0.802386i
$597$	−11485.5	−	14346.2i	−0.787385	−	0.983506i
$598$	−2687.12	+	6423.55i	−0.183754	+	0.439261i
$599$		−	11213.1i		−	0.764866i	−0.923983	−	0.382433i	$-0.875086\pi$
$599$		−	11213.1i		−	0.764866i	0.923983	−	0.382433i	$-0.124914\pi$
$600$	5150.12	+	2904.52i	0.350421	+	0.197628i
$601$		−	4599.55i		−	0.312179i	−0.987743	−	0.156089i	$-0.950111\pi$
$601$		−	4599.55i		−	0.312179i	0.987743	−	0.156089i	$-0.0498888\pi$
$602$	6149.93	−	12218.5i	0.416366	−	0.827226i
$603$	4297.69	+	963.734i	0.290241	+	0.0650850i
$604$	1618.74	+	1641.58i	0.109049	+	0.110588i
$605$			14851.3i			0.998000i
$606$	3471.09	+	12121.4i	0.232679	+	0.812536i
$607$		−	27115.8i		−	1.81318i	−0.422017	−	0.906588i	$-0.638678\pi$
$607$		−	27115.8i		−	1.81318i	0.422017	−	0.906588i	$-0.361322\pi$
$608$	1789.56	−	4115.00i	0.119369	−	0.274483i
$609$	−8833.00	+	6107.99i	−0.587736	+	0.406417i
$610$	−10904.0	+	26066.0i	−0.723756	+	1.73013i
$611$	−6259.98			−0.414487
$612$	−12691.8	+	7918.22i	−0.838294	+	0.522998i
$613$		−	2010.26i		−	0.132453i	−0.997805	−	0.0662263i	$-0.978904\pi$
$613$		−	2010.26i		−	0.132453i	0.997805	−	0.0662263i	$-0.0210959\pi$
$614$	9885.42	+	4135.31i	0.649745	+	0.271804i
$615$	−20254.7	−	25299.7i	−1.32804	−	1.65883i
$616$	−6372.45	−	19751.7i	−0.416807	−	1.29191i
$617$			15659.8i			1.02178i	0.859646	+	0.510891i	$0.170684\pi$
$617$			15659.8i			1.02178i	−0.859646	+	0.510891i	$0.829316\pi$
$618$	1997.67	+	6976.03i	0.130029	+	0.454073i
$619$	27135.8			1.76200			0.881001	−	0.473115i	$-0.156870\pi$
$619$	27135.8			1.76200			0.881001	+	0.473115i	$0.156870\pi$
$620$	17611.3	+	17859.8i	1.14078	+	1.15688i
$621$	−10777.6	+	5266.20i	−0.696442	+	0.340298i
$622$	13042.3	+	5455.92i	0.840756	+	0.351708i
$623$	24900.7	+	1748.52i	1.60133	+	0.112444i
$624$	−5878.84	−	7557.82i	−0.377150	−	0.484863i
$625$	−19382.1			−1.24046
$626$	1258.16	−	3007.62i	0.0803294	−	0.192027i
$627$	−4979.88	+	3986.84i	−0.317189	+	0.253938i
$628$	−11731.2	−	11896.7i	−0.745420	−	0.755940i
$629$		−	18105.9i		−	1.14774i
$630$	14478.8	+	11874.7i	0.915633	+	0.750948i
$631$	854.200			0.0538909			0.0269455	−	0.999637i	$-0.491422\pi$
$631$	854.200			0.0538909			0.0269455	+	0.999637i	$0.491422\pi$
$632$	−1249.67	−	3109.00i	−0.0786540	−	0.195679i
$633$	−5508.20	−	6880.18i	−0.345863	−	0.432011i
$634$	7146.39	+	2989.51i	0.447665	+	0.187269i
$635$			33769.3i			2.11038i
$636$	−490.082	−	57.7538i	−0.0305551	−	0.00360077i
$637$	9778.89	+	1380.14i	0.608248	+	0.0858449i
$638$	−14420.9	−	6032.61i	−0.894873	−	0.374347i
$639$	12602.2	+	2825.97i	0.780178	+	0.174951i
$640$	−6900.66	−	17888.2i	−0.426207	−	1.10483i
$641$		−	29337.9i		−	1.80777i	−0.427779	−	0.903884i	$-0.640704\pi$
$641$		−	29337.9i		−	1.80777i	0.427779	−	0.903884i	$-0.359296\pi$
$642$	−8245.90	+	2361.31i	−0.506915	+	0.145161i
$643$	−24076.1			−1.47662			−0.738310	−	0.674461i	$-0.764376\pi$
$643$	−24076.1			−1.47662			−0.738310	+	0.674461i	$0.764376\pi$
$644$	−9621.02	+	8240.93i	−0.588698	+	0.504252i
$645$	−14024.0	+	11227.5i	−0.856117	+	0.685399i
$646$	4479.65	+	1873.94i	0.272832	+	0.114132i
$647$	9606.99			0.583755			0.291878	−	0.956456i	$-0.405720\pi$
$647$	9606.99			0.583755			0.291878	+	0.956456i	$0.405720\pi$
$648$	972.685	−	16466.7i	0.0589671	−	0.998260i
$649$			11714.1i			0.708500i
$650$	−3778.11	−	1580.47i	−0.227984	−	0.0953711i
$651$	12961.7	+	18744.3i	0.780349	+	1.12849i
$652$	23422.0	−	23096.0i	1.40686	−	1.38729i
$653$	−5450.16			−0.326618			−0.163309	−	0.986575i	$-0.552217\pi$
$653$	−5450.16			−0.326618			−0.163309	+	0.986575i	$0.552217\pi$
$654$	7510.28	+	26226.6i	0.449045	+	1.56810i
$655$	5821.08			0.347249
$656$	−422.479	+	30146.8i	−0.0251449	+	1.79426i
$657$	27356.6	+	6134.58i	1.62448	+	0.364281i
$658$	−10173.1	−	5120.40i	−0.602717	−	0.303364i
$659$	15534.8			0.918287			0.459144	−	0.888362i	$-0.348156\pi$
$659$	15534.8			0.918287			0.459144	+	0.888362i	$0.348156\pi$
$660$	−3190.00	+	27069.4i	−0.188137	+	1.59648i
$661$	−10381.1			−0.610858			−0.305429	−	0.952215i	$-0.598800\pi$
$661$	−10381.1			−0.610858			−0.305429	+	0.952215i	$0.598800\pi$
$662$	−5700.24	+	13626.4i	−0.334662	+	0.800006i
$663$	8088.55	−	6475.61i	0.473806	−	0.379324i
$664$	−15531.9	+	6243.11i	−0.907765	+	0.364879i
$665$	425.768	−	6063.39i	0.0248279	−	0.353576i
$666$	16286.2	+	11548.3i	0.947564	+	0.671904i
$667$			9541.36i			0.553888i
$668$	−6880.59	−	6977.69i	−0.398530	−	0.404154i
$669$	−12783.7	−	15967.9i	−0.738784	−	0.922799i
$670$	−5635.46	−	2357.45i	−0.324950	−	0.135934i
$671$	−37367.6			−2.14986
$672$	−3371.71	−	17090.8i	−0.193551	−	0.981090i
$673$	29748.6			1.70390			0.851948	−	0.523626i	$-0.175421\pi$
$673$	29748.6			1.70390			0.851948	+	0.523626i	$0.175421\pi$
$674$	−7563.42	−	3163.96i	−0.432244	−	0.180818i
$675$	−3097.39	−	6339.02i	−0.176620	−	0.361465i
$676$	−7684.14	−	7792.58i	−0.437195	−	0.443365i
$677$			6845.80i			0.388634i	0.980939	+	0.194317i	$0.0622491\pi$
$677$			6845.80i			0.388634i	−0.980939	+	0.194317i	$0.937751\pi$
$678$	−3849.75	−	13443.7i	−0.218066	−	0.761506i
$679$	237.552	−	3383.00i	0.0134262	−	0.191204i
$680$	19250.7	−	7737.89i	1.08563	−	0.436374i
$681$	20231.3	+	25270.4i	1.13842	+	1.42198i
$682$	−12801.7	+	30602.4i	−0.718772	+	1.71822i
$683$	−13901.9			−0.778833			−0.389417	−	0.921062i	$-0.627323\pi$
$683$	−13901.9			−0.778833			−0.389417	+	0.921062i	$0.627323\pi$
$684$	−4542.83	+	2834.20i	−0.253946	+	0.158433i
$685$	14919.5			0.832184
$686$	14762.8	+	10241.6i	0.821639	+	0.570008i
$687$	−16119.2	+	12904.9i	−0.895178	+	0.716671i
$688$	16710.9	+	234.187i	0.926011	+	0.0129772i
$689$	341.799			0.0188991
$690$	15994.1	−	4580.09i	0.882440	−	0.252697i
$691$	−7713.20			−0.424637			−0.212318	−	0.977201i	$-0.568101\pi$
$691$	−7713.20			−0.424637			−0.212318	+	0.977201i	$0.568101\pi$
$692$	13964.7	−	13770.3i	0.767134	−	0.756459i
$693$	−7098.16	+	23725.8i	−0.389086	+	1.30053i
$694$	27551.7	+	11525.5i	1.50699	+	0.630408i
$695$		−	32034.1i		−	1.74838i
$696$	−11428.5	−	6445.36i	−0.622409	−	0.351021i
$697$	−32625.7			−1.77301
$698$	−11337.1	−	4742.59i	−0.614780	−	0.257177i
$699$	11044.9	+	13795.9i	0.597648	+	0.746509i
$700$	−4847.03	−	5658.75i	−0.261715	−	0.305544i
$701$	28716.9			1.54725			0.773626	−	0.633643i	$-0.218441\pi$
$701$	28716.9			1.54725			0.773626	+	0.633643i	$0.218441\pi$
$702$	665.753	+	11405.9i	0.0357938	+	0.613232i
$703$		−	6480.69i		−	0.347687i
$704$	18302.9	−	17549.2i	0.979851	−	0.939501i
$705$	9347.95	+	11676.3i	0.499382	+	0.623767i
$706$	−25621.5	−	10718.1i	−1.36583	−	0.571361i
$707$	1112.95	−	15849.6i	0.0592033	−	0.843118i
$708$	−1150.73	+	9764.72i	−0.0610832	+	0.518334i
$709$		−	6971.08i		−	0.369259i	−0.982808	−	0.184629i	$-0.940892\pi$
$709$		−	6971.08i		−	0.369259i	0.982808	−	0.184629i	$-0.0591085\pi$
$710$	−16524.9	−	6912.76i	−0.873477	−	0.365396i
$711$	−874.862	+	3901.38i	−0.0461461	+	0.205785i
$712$	11374.2	+	28297.4i	0.598690	+	1.48945i
$713$	20247.6			1.06350
$714$	18441.5	−	3907.41i	0.966602	−	0.204805i
$715$		−	18879.0i		−	0.987463i
$716$	−5202.62	−	5276.04i	−0.271552	−	0.275384i
$717$	14540.8	+	18162.6i	0.757371	+	0.946016i
$718$	795.664	−	1902.03i	0.0413565	−	0.0988623i
$719$	−19292.8			−1.00070			−0.500348	−	0.865825i	$-0.666795\pi$
$719$	−19292.8			−1.00070			−0.500348	+	0.865825i	$0.666795\pi$
$720$	−5318.30	+	22251.4i	−0.275280	+	1.15175i
$721$	640.519	−	9121.68i	0.0330849	−	0.471164i
$722$	−16293.9	−	6816.13i	−0.839884	−	0.351343i
$723$	7510.44	+	9381.13i	0.386329	+	0.482556i
$724$	−4924.61	−	4994.10i	−0.252792	−	0.256360i
$725$	−5611.90			−0.287477
$726$	−15848.9	+	4538.53i	−0.810205	+	0.232012i
$727$		−	12461.6i		−	0.635732i	−0.948136	−	0.317866i	$-0.897034\pi$
$727$		−	12461.6i		−	0.635732i	0.948136	−	0.317866i	$-0.102966\pi$
$728$	3704.76	+	11483.1i	0.188609	+	0.584604i
$729$	−12095.7	+	15527.8i	−0.614527	+	0.788896i
$730$	−35872.1	−	15006.1i	−1.81875	−	0.760825i
$731$			18085.0i			0.915045i
$732$	−31149.2	−	3670.79i	−1.57283	−	0.185350i
$733$	26437.4			1.33218			0.666090	−	0.745872i	$-0.267967\pi$
$733$	26437.4			1.33218			0.666090	+	0.745872i	$0.267967\pi$
$734$	−8958.74	+	21415.8i	−0.450508	+	1.07694i
$735$	−12028.4	−	20300.9i	−0.603639	−	1.01879i
$736$	−14193.2	−	6172.44i	−0.710826	−	0.309129i
$737$		−	8078.86i		−	0.403784i
$738$	20809.4	−	29346.8i	1.03795	−	1.46378i
$739$			24642.5i			1.22664i	0.789834	+	0.613321i	$0.210167\pi$
$739$			24642.5i			1.22664i	−0.789834	+	0.613321i	$0.789833\pi$
$740$	−19442.4	−	19716.7i	−0.965832	−	0.979462i
$741$	2895.16	−	2317.84i	0.143531	−	0.114909i
$742$	555.456	+	279.577i	0.0274817	+	0.0138323i
$743$			29736.2i			1.46826i	0.679012	+	0.734128i	$0.262409\pi$
$743$			29736.2i			1.46826i	−0.679012	+	0.734128i	$0.737591\pi$
$744$	−13677.6	+	24252.2i	−0.673984	+	1.19507i
$745$		−	27135.2i		−	1.33444i
$746$	−7226.52	+	17274.9i	−0.354667	+	0.847829i
$747$	19490.5	+	4370.63i	0.954645	+	0.214074i
$748$	19266.0	+	19537.9i	0.941760	+	0.955050i
$749$	10782.1	+	757.115i	0.525995	+	0.0369351i
$750$	−4002.14	−	13975.8i	−0.194850	−	0.680432i
$751$	8068.95			0.392064			0.196032	−	0.980597i	$-0.437194\pi$
$751$	8068.95			0.392064			0.196032	+	0.980597i	$0.437194\pi$
$752$	194.983	−	13913.4i	0.00945519	−	0.674691i
$753$	−14591.6	−	18226.0i	−0.706171	−	0.882063i
$754$	8383.91	+	3507.19i	0.404939	+	0.169396i
$755$			3815.42i			0.183917i
$756$	−8247.65	+	19080.3i	−0.396778	+	0.917915i
$757$		−	10634.4i		−	0.510587i	−0.966864	−	0.255293i	$-0.917828\pi$
$757$		−	10634.4i		−	0.510587i	0.966864	−	0.255293i	$-0.0821720\pi$
$758$	3065.84	−	7328.87i	0.146908	−	0.351183i
$759$	13751.1	+	17176.3i	0.657622	+	0.821422i
$760$	6890.48	−	2769.65i	0.328873	−	0.132192i
$761$	−3296.31			−0.157019			−0.0785094	−	0.996913i	$-0.525016\pi$
$761$	−3296.31			−0.157019			−0.0785094	+	0.996913i	$0.525016\pi$
$762$	−36037.7	+	10319.8i	−1.71327	+	0.490614i
$763$	2408.05	−	34293.2i	0.114256	−	1.62712i
$764$	14107.4	−	13911.0i	0.668045	−	0.658748i
$765$	−24157.1	−	5417.09i	−1.14170	−	0.256020i
$766$	−6250.21	−	2614.61i	−0.294816	−	0.123329i
$767$		−	6810.22i		−	0.320603i
$768$	16981.0	−	12830.8i	0.797851	−	0.602855i
$769$			29295.6i			1.37376i	0.726769	+	0.686882i	$0.241021\pi$
$769$			29295.6i			1.37376i	−0.726769	+	0.686882i	$0.758979\pi$
$770$	15442.2	−	30680.3i	0.722727	−	1.43590i
$771$	−5808.53	+	4650.25i	−0.271322	+	0.217218i
$772$	17584.2	+	17832.4i	0.819779	+	0.831348i
$773$			3337.03i			0.155271i	0.996982	+	0.0776356i	$0.0247371\pi$
$773$			3337.03i			0.155271i	−0.996982	+	0.0776356i	$0.975263\pi$
$774$	−16267.4	−	11535.0i	−0.755453	−	0.535681i
$775$			11908.9i			0.551975i
$776$	3844.47	−	1545.30i	0.177846	−	0.0714857i
$777$	−14309.3	−	20693.3i	−0.660674	−	0.955427i
$778$	−31517.0	−	13184.3i	−1.45237	−	0.607559i
$779$	−11677.8			−0.537102
$780$	1854.57	−	15737.4i	0.0851339	−	0.722421i
$781$		−	23689.7i		−	1.08538i
$782$	6463.48	−	15450.9i	0.295567	−	0.706551i
$783$	6873.36	+	14066.8i	0.313709	+	0.642025i
$784$	−3372.07	+	21691.5i	−0.153611	+	0.988131i
$785$		−	27650.7i		−	1.25719i
$786$	1778.91	+	6212.11i	0.0807273	+	0.281907i
$787$	643.131			0.0291298			0.0145649	−	0.999894i	$-0.495364\pi$
$787$	643.131			0.0291298			0.0145649	+	0.999894i	$0.495364\pi$
$788$	−479.963	−	486.736i	−0.0216979	−	0.0220041i
$789$	−2931.25	−	3661.37i	−0.132263	−	0.165207i
$790$	2140.05	−	5115.77i	0.0963792	−	0.230394i
$791$	−1234.36	+	17578.6i	−0.0554851	+	0.790168i
$792$	−29862.6	+	4868.07i	−1.33980	+	0.218408i
$793$	21724.5			0.972835
$794$	13673.4	+	5719.91i	0.611147	+	0.255657i
$795$	−510.403	−	637.534i	−0.0227700	−	0.0284415i
$796$	−20146.5	+	19866.2i	−0.897079	+	0.884595i
$797$		−	12470.7i		−	0.554248i	−0.960834	−	0.277124i	$-0.910619\pi$
$797$		−	12470.7i		−	0.554248i	0.960834	−	0.277124i	$-0.0893813\pi$
$798$	6600.81	−	1398.59i	0.292815	−	0.0620421i
$799$	15057.5			0.666702
$800$	3630.42	−	8347.94i	0.160443	−	0.368930i
$801$	7962.79	−	35509.4i	0.351250	−	1.56637i
$802$	−11624.7	+	27788.7i	−0.511823	+	1.22351i
$803$		−	51425.4i		−	2.25998i
$804$	793.623	−	6734.45i	0.0348121	−	0.295405i
$805$	−20913.4	−	1468.53i	−0.915654	−	0.0642967i
$806$	7442.54	−	17791.3i	0.325251	−	0.777510i
$807$	6136.81	+	7665.36i	0.267690	+	0.334366i
$808$	18011.6	−	7239.81i	0.784214	−	0.315217i
$809$			36823.8i			1.60032i	0.599789	+	0.800158i	$0.295251\pi$
$809$			36823.8i			1.60032i	−0.599789	+	0.800158i	$0.704749\pi$
$810$	20280.6	−	18274.1i	0.879736	−	0.792700i
$811$	28331.7			1.22671			0.613354	−	0.789808i	$-0.289820\pi$
$811$	28331.7			1.22671			0.613354	+	0.789808i	$0.289820\pi$
$812$	10755.9	+	12557.2i	0.464851	+	0.542699i
$813$	24748.6	+	30913.0i	1.06762	+	1.33354i
$814$	14132.7	−	33784.2i	0.608541	−	1.45471i
$815$	54438.2			2.33974
$816$	14140.7	+	18179.2i	0.606645	+	0.779902i
$817$			6473.23i			0.277196i
$818$	−11131.0	+	26608.5i	−0.475776	+	1.13734i
$819$	4126.67	−	13793.5i	0.176065	−	0.588503i
$820$	−35528.5	+	35034.1i	−1.51306	+	1.49200i
$821$	24314.1			1.03358			0.516789	−	0.856113i	$-0.327127\pi$
$821$	24314.1			1.03358			0.516789	+	0.856113i	$0.327127\pi$
$822$	4559.39	+	15921.8i	0.193463	+	0.675591i
$823$	−7780.71			−0.329549			−0.164774	−	0.986331i	$-0.552690\pi$
$823$	−7780.71			−0.329549			−0.164774	+	0.986331i	$0.552690\pi$
$824$	10365.9	−	4166.63i	0.438246	−	0.176154i
$825$	−10102.5	+	8087.95i	−0.426331	+	0.341317i
$826$	5570.47	−	11067.3i	0.234651	−	0.466198i
$827$	−9658.38			−0.406112			−0.203056	−	0.979167i	$-0.565087\pi$
$827$	−9658.38			−0.406112			−0.203056	+	0.979167i	$0.565087\pi$
$828$	9775.51	+	15668.8i	0.410293	+	0.657643i
$829$	−4178.46			−0.175059			−0.0875296	−	0.996162i	$-0.527897\pi$
$829$	−4178.46			−0.175059			−0.0875296	+	0.996162i	$0.527897\pi$
$830$	−25557.4	−	10691.3i	−1.06881	−	0.447107i
$831$	9689.81	+	12103.3i	0.404496	+	0.505247i
$832$	−10640.8	+	10202.6i	−0.443392	+	0.425133i
$833$	−23521.7	−	3319.73i	−0.978365	−	0.138081i
$834$	34186.0	−	9789.55i	1.41938	−	0.406456i
$835$		−	16217.8i		−	0.672144i
$836$	6895.96	+	6993.28i	0.285289	+	0.289315i
$837$	29850.8	−	14585.8i	1.23273	−	0.602342i
$838$	10263.5	−	24534.8i	0.423086	−	1.01138i
$839$	937.651			0.0385832			0.0192916	−	0.999814i	$-0.493859\pi$
$839$	937.651			0.0385832			0.0192916	+	0.999814i	$0.493859\pi$
$840$	15886.4	−	24057.8i	0.652537	−	0.988182i
$841$	−11935.8			−0.489391
$842$	−1664.76	+	3979.60i	−0.0681371	+	0.162881i
$843$	9706.04	+	12123.6i	0.396552	+	0.495325i
$844$	−9661.88	+	9527.43i	−0.394047	+	0.388563i
$845$		−	18111.8i		−	0.737354i
$846$	−9603.97	+	13544.2i	−0.390297	+	0.550423i
$847$	20723.6	+	1455.20i	0.840700	+	0.0590335i
$848$	−10.6462	+	759.677i	−0.000431122	+	0.0307635i
$849$	−12781.5	+	10232.7i	−0.516678	+	0.413647i
$850$	9087.68	+	3801.59i	0.366711	+	0.153404i
$851$	−22352.8			−0.900403
$852$	2327.15	−	19747.5i	0.0935761	−	0.794059i
$853$	5791.89			0.232486			0.116243	−	0.993221i	$-0.462915\pi$
$853$	5791.89			0.232486			0.116243	+	0.993221i	$0.462915\pi$
$854$	35304.3	+	17769.7i	1.41462	+	0.712021i
$855$	−8646.62	−	1938.96i	−0.345857	−	0.0775566i
$856$	4925.09	+	12252.9i	0.196654	+	0.489246i
$857$	−1880.84			−0.0749687			−0.0374843	−	0.999297i	$-0.511934\pi$
$857$	−1880.84			−0.0749687			−0.0374843	+	0.999297i	$0.511934\pi$
$858$	20147.2	−	5769.40i	0.801650	−	0.229562i
$859$	−9503.79			−0.377491			−0.188746	−	0.982026i	$-0.560442\pi$
$859$	−9503.79			−0.377491			−0.188746	+	0.982026i	$0.560442\pi$
$860$	19420.0	+	19694.0i	0.770018	+	0.780885i
$861$	−37288.1	+	25784.6i	−1.47593	+	1.02060i
$862$	−8535.51	+	20404.1i	−0.337263	+	0.806224i
$863$			5322.63i			0.209947i	0.994475	+	0.104974i	$0.0334758\pi$
$863$			5322.63i			0.209947i	−0.994475	+	0.104974i	$0.966524\pi$
$864$	−25371.4	+	1124.43i	−0.999019	+	0.0442753i
$865$	32457.2			1.27581
$866$	−12276.1	+	29345.9i	−0.481707	+	1.15152i
$867$	473.011	−	378.688i	0.0185286	−	0.0148338i
$868$	26647.4	−	22825.0i	1.04202	−	0.892546i
$869$	7333.85			0.286288
$870$	−5977.86	−	20875.2i	−0.232952	−	0.813489i
$871$			4696.82i			0.182716i
$872$	38971.0	−	15664.5i	1.51345	−	0.608335i
$873$	−4824.29	−	1081.82i	−0.187030	−	0.0419405i
$874$	2313.49	−	5530.39i	0.0895368	−	0.214037i
$875$	−1283.22	+	18274.4i	−0.0495779	+	0.706043i
$876$	5051.75	−	42867.7i	0.194843	−	1.65338i
$877$			15099.1i			0.581369i	0.956819	+	0.290684i	$0.0938829\pi$
$877$			15099.1i			0.581369i	−0.956819	+	0.290684i	$0.906117\pi$
$878$	6439.67	−	15394.0i	0.247526	−	0.591710i
$879$	−5312.79	−	6636.09i	−0.203863	−	0.254641i
$880$	41960.3	+	588.036i	1.60737	+	0.0225258i
$881$	−25460.6			−0.973654			−0.486827	−	0.873498i	$-0.661846\pi$
$881$	−25460.6			−0.973654			−0.486827	+	0.873498i	$0.661846\pi$
$882$	17988.7	−	19040.3i	0.686748	−	0.726895i
$883$		−	29492.7i		−	1.12402i	−0.827131	−	0.562009i	$-0.810028\pi$
$883$		−	29492.7i		−	1.12402i	0.827131	−	0.562009i	$-0.189972\pi$
$884$	−11200.7	−	11358.8i	−0.426155	−	0.432169i
$885$	−12702.6	+	10169.6i	−0.482480	+	0.386269i
$886$	−2587.94	−	1082.60i	−0.0981305	−	0.0410504i
$887$	11558.8			0.437550			0.218775	−	0.975775i	$-0.429794\pi$
$887$	11558.8			0.437550			0.218775	+	0.975775i	$0.429794\pi$
$888$	15099.7	−	26773.8i	0.570622	−	1.01179i
$889$	47122.0	+	3308.88i	1.77775	+	0.124833i
$890$	−19478.2	+	46562.6i	−0.733609	+	1.75369i
$891$	32646.6	+	15416.9i	1.22750	+	0.579669i
$892$	−22423.7	+	22111.7i	−0.841707	+	0.829994i
$893$	5389.57			0.201965
$894$	28958.0	−	8292.47i	1.08333	−	0.310225i
$895$		−	12262.8i		−	0.457987i
$896$	−25637.6	+	7876.49i	−0.955905	+	0.293677i
$897$	−7994.53	−	9985.80i	−0.297580	−	0.371701i
$898$	15204.8	−	36347.0i	0.565024	−	1.35069i
$899$		−	26426.8i		−	0.980403i
$900$	−9215.84	+	5749.62i	−0.341328	+	0.212949i
$901$	−822.146			−0.0303992
$902$	−60877.2	−	25466.4i	−2.24722	−	0.940065i
$903$	14292.8	+	20669.4i	0.526728	+	0.761722i
$904$	−19976.4	+	8029.60i	−0.734963	+	0.295421i
$905$		−	11607.5i		−	0.426348i
$906$	−4071.72	+	1165.98i	−0.149309	+	0.0427563i
$907$			10190.2i			0.373053i	0.982450	+	0.186527i	$0.0597231\pi$
$907$			10190.2i			0.373053i	−0.982450	+	0.186527i	$0.940277\pi$
$908$	35487.4	−	34993.6i	1.29702	−	1.27897i
$909$	−22602.1	−	5068.40i	−0.824713	−	0.184937i
$910$	−8977.68	+	17836.6i	−0.327041	+	0.649757i
$911$		−	33432.8i		−	1.21589i	−0.793978	−	0.607947i	$-0.791993\pi$
$911$		−	33432.8i		−	1.21589i	0.793978	−	0.607947i	$-0.208007\pi$
$912$	5061.42	+	6506.95i	0.183772	+	0.236257i
$913$		−	36638.5i		−	1.32810i
$914$	−26106.7	−	10921.1i	−0.944784	−	0.395226i
$915$	−32440.8	−	40521.2i	−1.17209	−	1.46403i
$916$	22321.3	+	22636.3i	0.805151	+	0.816513i
$917$	570.378	−	8122.80i	0.0205404	−	0.292517i
$918$	−1601.37	−	27435.3i	−0.0575742	−	0.986382i
$919$	−38879.2			−1.39554			−0.697772	−	0.716320i	$-0.745825\pi$
$919$	−38879.2			−1.39554			−0.697772	+	0.716320i	$0.745825\pi$
$920$	−9552.89	−	23766.2i	−0.342336	−	0.851682i
$921$	−15367.5	+	12303.1i	−0.549812	+	0.440174i
$922$	16991.9	−	40619.0i	0.606940	−	1.45088i
$923$			13772.5i			0.491146i
$924$	37460.3	+	7103.75i	1.33372	+	0.252918i
$925$		−	13147.1i		−	0.467324i
$926$	−28353.7	−	11861.0i	−1.00622	−	0.420926i
$927$	−13007.9	−	2916.94i	−0.460878	−	0.103349i
$928$	−8056.17	+	18524.7i	−0.284975	+	0.655285i
$929$	−19916.3			−0.703370			−0.351685	−	0.936118i	$-0.614391\pi$
$929$	−19916.3			−0.703370			−0.351685	+	0.936118i	$0.614391\pi$
$930$	−44298.9	+	12685.5i	−1.56195	+	0.447284i
$931$	−8419.20	−	1188.24i	−0.296378	−	0.0418293i
$932$	19373.7	−	19104.1i	0.680908	−	0.671433i
$933$	−20275.1	+	16232.1i	−0.711444	+	0.569575i
$934$	−2383.97	+	5698.86i	−0.0835180	+	0.199649i
$935$			45410.7i			1.58833i
$936$	17361.3	−	2830.16i	0.606273	−	0.0988318i
$937$			27614.4i			0.962779i	0.876507	+	0.481390i	$0.159868\pi$
$937$			27614.4i			0.962779i	−0.876507	+	0.481390i	$0.840132\pi$
$938$	−3841.80	+	7632.78i	−0.133730	+	0.265692i
$939$	3743.19	+	4675.54i	0.130090	+	0.162492i
$940$	16397.1	−	16169.0i	0.568953	−	0.561035i
$941$			33189.4i			1.14978i	0.818231	+	0.574890i	$0.194955\pi$
$941$			33189.4i			1.14978i	−0.818231	+	0.574890i	$0.805045\pi$
$942$	29508.2	−	8450.02i	1.02063	−	0.292268i
$943$			40278.4i			1.39093i
$944$	15136.3	+	212.122i	0.521870	+	0.00731353i
$945$	−31890.4	+	12900.5i	−1.09777	+	0.444076i
$946$	−14116.5	+	33745.3i	−0.485164	+	1.15978i
$947$	6141.76			0.210750			0.105375	−	0.994433i	$-0.466396\pi$
$947$	6141.76			0.210750			0.105375	+	0.994433i	$0.466396\pi$
$948$	6113.43	+	720.438i	0.209446	+	0.0246822i
$949$			29897.2i			1.02266i
$950$	3252.78	+	1360.72i	0.111089	+	0.0464710i
$951$	−11109.5	+	8894.16i	−0.378812	+	0.303273i
$952$	−8911.26	−	27620.9i	−0.303378	−	0.940333i
$953$			7097.85i			0.241261i	0.992697	+	0.120631i	$0.0384916\pi$
$953$			7097.85i			0.241261i	−0.992697	+	0.120631i	$0.961508\pi$
$954$	524.383	−	739.519i	0.0177961	−	0.0250973i
$955$	32788.8			1.11102
$956$	25505.8	−	25150.9i	0.862883	−	0.850876i
$957$	22418.2	−	17947.8i	0.757239	−	0.606238i
$958$	−18339.4	−	7671.82i	−0.618497	−	0.258732i
$959$	1461.89	−	20818.9i	0.0492252	−	0.701019i
$960$	34919.9	+	4612.13i	1.17400	+	0.155058i
$961$	−26288.8			−0.882441
$962$	−8216.37	+	19641.2i	−0.275371	+	0.658271i
$963$	3447.92	−	15375.7i	0.115377	−	0.514513i
$964$	13174.0	−	12990.6i	0.440151	−	0.434026i
$965$			41446.6i			1.38260i
$966$	−4823.93	−	22767.1i	−0.160670	−	0.758301i
$967$	10526.5			0.350063			0.175031	−	0.984563i	$-0.443997\pi$
$967$	10526.5			0.350063			0.175031	+	0.984563i	$0.443997\pi$
$968$	9466.20	+	23550.5i	0.314313	+	0.781964i
$969$	−6963.89	+	5575.22i	−0.230869	+	0.184832i
$970$	6325.96	+	2646.30i	0.209396	+	0.0875955i
$971$		−	10918.3i		−	0.360848i	−0.983589	−	0.180424i	$-0.942253\pi$
$971$		−	10918.3i		−	0.360848i	0.983589	−	0.180424i	$-0.0577470\pi$
$972$	25699.4	+	16058.4i	0.848054	+	0.529910i
$973$	−44700.7	−	3138.86i	−1.47280	−	0.103419i
$974$	9305.75	+	3892.82i	0.306135	+	0.128064i
$975$	5873.30	−	4702.10i	0.192919	−	0.154449i
$976$	−676.663	+	48284.5i	−0.0221921	+	1.58355i
$977$		−	23312.8i		−	0.763400i	−0.924286	−	0.381700i	$-0.875339\pi$
$977$		−	23312.8i		−	0.763400i	0.924286	−	0.381700i	$-0.124661\pi$
$978$	16636.2	+	58095.1i	0.543934	+	1.89946i
$979$	−66751.0			−2.17913
$980$	−29179.2	+	21642.9i	−0.951118	+	0.705466i
$981$	−48903.4	−	10966.3i	−1.59160	−	0.356909i
$982$	5823.26	+	2436.01i	0.189234	+	0.0791611i
$983$	17319.7			0.561965			0.280982	−	0.959713i	$-0.409340\pi$
$983$	17319.7			0.561965			0.280982	+	0.959713i	$0.409340\pi$
$984$	−48245.0	−	27208.8i	−1.56300	−	0.881488i
$985$		−	1131.29i		−	0.0365948i
$986$	−20166.3	−	8436.03i	−0.651343	−	0.272472i
$987$	17209.2	−	11900.1i	0.554991	−	0.383774i
$988$	−4009.12	−	4065.69i	−0.129096	−	0.130918i
$989$	22327.0			0.717854
$990$	−40846.9	−	28963.9i	−1.31131	−	0.929833i
$991$	20423.3			0.654660			0.327330	−	0.944910i	$-0.393851\pi$
$991$	20423.3			0.654660			0.327330	+	0.944910i	$0.393851\pi$
$992$	39311.0	+	17095.9i	1.25819	+	0.547172i
$993$	−16958.9	−	21183.0i	−0.541969	−	0.676962i
$994$	−11265.3	+	22381.7i	−0.359472	+	0.714189i
$995$	−46825.2			−1.49192
$996$	3599.16	−	30541.4i	0.114502	−	0.971629i
$997$	47651.1			1.51367			0.756833	−	0.653608i	$-0.226745\pi$
$997$	47651.1			1.51367			0.756833	+	0.653608i	$0.226745\pi$
$998$	−22561.1	+	53932.2i	−0.715591	+	1.71061i
$999$	−32954.5	+	16102.4i	−1.04368	+	0.509966i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	168.4.i.c.125.71	yes	80
3.2	odd	2	inner	168.4.i.c.125.9	✓	80
4.3	odd	2		672.4.i.c.209.61		80
7.6	odd	2	inner	168.4.i.c.125.72	yes	80
8.3	odd	2		672.4.i.c.209.20		80
8.5	even	2	inner	168.4.i.c.125.12	yes	80
12.11	even	2		672.4.i.c.209.64		80
21.20	even	2	inner	168.4.i.c.125.10	yes	80
24.5	odd	2	inner	168.4.i.c.125.70	yes	80
24.11	even	2		672.4.i.c.209.17		80
28.27	even	2		672.4.i.c.209.19		80
56.13	odd	2	inner	168.4.i.c.125.11	yes	80
56.27	even	2		672.4.i.c.209.62		80
84.83	odd	2		672.4.i.c.209.18		80
168.83	odd	2		672.4.i.c.209.63		80
168.125	even	2	inner	168.4.i.c.125.69	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.4.i.c.125.9	✓	80	3.2	odd	2	inner
168.4.i.c.125.10	yes	80	21.20	even	2	inner
168.4.i.c.125.11	yes	80	56.13	odd	2	inner
168.4.i.c.125.12	yes	80	8.5	even	2	inner
168.4.i.c.125.69	yes	80	168.125	even	2	inner
168.4.i.c.125.70	yes	80	24.5	odd	2	inner
168.4.i.c.125.71	yes	80	1.1	even	1	trivial
168.4.i.c.125.72	yes	80	7.6	odd	2	inner
672.4.i.c.209.17		80	24.11	even	2
672.4.i.c.209.18		80	84.83	odd	2
672.4.i.c.209.19		80	28.27	even	2
672.4.i.c.209.20		80	8.3	odd	2
672.4.i.c.209.61		80	4.3	odd	2
672.4.i.c.209.62		80	56.27	even	2
672.4.i.c.209.63		80	168.83	odd	2
672.4.i.c.209.64		80	12.11	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+(2.60932 + 1.09154i) q^{2} +(-4.05635 + 3.24747i) q^{3} +(5.61708 + 5.69635i) q^{4} +13.2397i q^{5} +(-14.1290 + 4.04602i) q^{6} +(18.4748 + 1.29729i) q^{7} +(8.43895 + 20.9949i) q^{8} +(5.90788 - 26.3457i) q^{9} +(-14.4516 + 34.5465i) q^{10} -49.5250 q^{11} +(-41.2835 - 4.86507i) q^{12} +28.7924 q^{13} +(46.7905 + 23.5510i) q^{14} +(-42.9954 - 53.7046i) q^{15} +(-0.896814 + 63.9937i) q^{16} -69.2560 q^{17} +(44.1730 - 62.2957i) q^{18} -24.7890 q^{19} +(-75.4177 + 74.3682i) q^{20} +(-79.1529 + 54.7340i) q^{21} +(-129.227 - 54.0585i) q^{22} +85.5006i q^{23} +(-102.411 - 57.7572i) q^{24} -50.2885 q^{25} +(75.1286 + 31.4281i) q^{26} +(61.5925 + 126.053i) q^{27} +(96.3845 + 112.526i) q^{28} +111.594 q^{29} +(-53.5679 - 187.064i) q^{30} -236.812i q^{31} +(-72.1918 + 166.001i) q^{32} +(200.891 - 160.831i) q^{33} +(-180.711 - 75.5957i) q^{34} +(-17.1756 + 244.600i) q^{35} +(183.260 - 114.333i) q^{36} +261.434i q^{37} +(-64.6825 - 27.0582i) q^{38} +(-116.792 + 93.5026i) q^{39} +(-277.965 + 111.729i) q^{40} +471.089 q^{41} +(-266.280 + 56.4198i) q^{42} -261.133i q^{43} +(-278.186 - 282.112i) q^{44} +(348.808 + 78.2183i) q^{45} +(-93.3274 + 223.098i) q^{46} -217.418 q^{47} +(-204.180 - 262.493i) q^{48} +(339.634 + 47.9342i) q^{49} +(-131.219 - 54.8919i) q^{50} +(280.926 - 224.907i) q^{51} +(161.729 + 164.012i) q^{52} +11.8711 q^{53} +(23.1225 + 396.143i) q^{54} -655.694i q^{55} +(128.671 + 398.823i) q^{56} +(100.553 - 80.5016i) q^{57} +(291.184 + 121.809i) q^{58} -236.528i q^{59} +(64.4118 - 546.580i) q^{60} +754.519 q^{61} +(258.490 - 617.917i) q^{62} +(143.325 - 479.067i) q^{63} +(-369.568 + 354.349i) q^{64} +381.202i q^{65} +(699.741 - 200.379i) q^{66} +163.127i q^{67} +(-389.016 - 394.506i) q^{68} +(-277.661 - 346.820i) q^{69} +(-311.807 + 619.490i) q^{70} +478.338i q^{71} +(602.981 - 98.2952i) q^{72} +1038.37i q^{73} +(-285.366 + 682.164i) q^{74} +(203.988 - 163.310i) q^{75} +(-139.242 - 141.207i) q^{76} +(-914.963 - 64.2482i) q^{77} +(-406.810 + 116.495i) q^{78} -148.084 q^{79} +(-847.255 - 11.8735i) q^{80} +(-659.194 - 311.295i) q^{81} +(1229.22 + 514.213i) q^{82} +739.797i q^{83} +(-756.393 - 143.438i) q^{84} -916.925i q^{85} +(285.037 - 681.378i) q^{86} +(-452.664 + 362.398i) q^{87} +(-417.939 - 1039.77i) q^{88} +1347.82 q^{89} +(824.773 + 584.835i) q^{90} +(531.934 + 37.3521i) q^{91} +(-487.042 + 480.264i) q^{92} +(769.039 + 960.590i) q^{93} +(-567.311 - 237.320i) q^{94} -328.198i q^{95} +(-246.249 - 907.798i) q^{96} -183.115i q^{97} +(833.891 + 495.800i) q^{98} +(-292.588 + 1304.77i) 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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