LMFDB - Embedded newform 168.4.i.c.125.11

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			125.11
Character	$\chi$	$=$	168.125
Dual form			168.4.i.c.125.9

$q$-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} +(7.03955 - 12.9013i) 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} +(-4.28610 + 41.3477i) 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} +(13.3419 + 75.1930i) q^{18} -24.7890 q^{19} +(75.4177 + 74.3682i) q^{20} +(-70.7271 + 65.2585i) q^{21} +(-129.227 + 54.0585i) q^{22} +85.5006i q^{23} +(-33.9488 - 112.568i) 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} +(170.809 + 93.2013i) 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} +(-116.889 - 181.639i) 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} +(113.317 - 247.482i) 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} +(211.455 + 256.668i) 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} +(-298.306 - 261.682i) 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} +(-547.429 - 56.7464i) q^{60} +754.519 q^{61} +(-258.490 - 617.917i) q^{62} +(74.9688 - 494.395i) q^{63} +(-369.568 - 354.349i) q^{64} +381.202i q^{65} +(348.634 - 638.939i) 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} +(503.268 + 346.365i) 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} +(202.686 - 371.461i) 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} +(-25.5448 + 769.449i) 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} +(-995.530 + 176.642i) 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} +(-831.918 - 438.917i) 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	$0.798301\pi$
$6$	7.03955	−	12.9013i	0.478981	−	0.877825i
$7$	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	$-0.262525\pi$
$11$	49.5250			1.35749			0.678743	+	0.734376i	$0.262525\pi$
$12$	−4.28610	+	41.3477i	−0.103107	+	0.994670i
$13$	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	$-0.335523\pi$
$17$	69.2560			0.988061			0.494031	+	0.869445i	$0.335523\pi$
$18$	13.3419	+	75.1930i	0.174706	+	0.984621i
$19$	−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
$21$	−70.7271	+	65.2585i	−0.734949	+	0.678122i
$22$	−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	$0.873315\pi$
$24$	−33.9488	−	112.568i	−0.288741	−	0.957407i
$25$	−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	$-0.616297\pi$
$29$	−111.594			−0.714569			−0.357284	+	0.933996i	$0.616297\pi$
$30$	170.809	+	93.2013i	1.03951	+	0.567205i
$31$			236.812i			1.37202i	0.727592	+	0.686010i	$0.240640\pi$
$31$			236.812i			1.37202i	−0.727592	+	0.686010i	$0.759360\pi$
$32$	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
$36$	−116.889	−	181.639i	−0.541155	−	0.840923i
$37$		−	261.434i		−	1.16161i	−0.814044	−	0.580804i	$-0.802738\pi$
$37$		−	261.434i		−	1.16161i	0.814044	−	0.580804i	$-0.197262\pi$
$38$	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	$-0.854415\pi$
$41$	−471.089			−1.79443			−0.897217	+	0.441590i	$0.854415\pi$
$42$	113.317	−	247.482i	0.416315	−	0.909220i
$43$			261.133i			0.926101i	0.886332	+	0.463051i	$0.153245\pi$
$43$			261.133i			0.926101i	−0.886332	+	0.463051i	$0.846755\pi$
$44$	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	$-0.390460\pi$
$47$	217.418			0.674757			0.337379	+	0.941369i	$0.390460\pi$
$48$	211.455	+	256.668i	0.635853	+	0.771810i
$49$	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	$-0.504897\pi$
$53$	−11.8711			−0.0307665			−0.0153832	+	0.999882i	$0.504897\pi$
$54$	−298.306	−	261.682i	−0.751747	−	0.659451i
$55$			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	$-0.0840392\pi$
$60$	−547.429	−	56.7464i	−1.17788	−	0.122099i
$61$	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
$63$	74.9688	−	494.395i	0.149923	−	0.988698i
$64$	−369.568	−	354.349i	−0.721813	−	0.692088i
$65$			381.202i			0.727420i
$66$	348.634	−	638.939i	0.650210	−	1.19164i
$67$		−	163.127i		−	0.297449i	−0.988879	−	0.148725i	$-0.952483\pi$
$67$		−	163.127i		−	0.297449i	0.988879	−	0.148725i	$-0.0475168\pi$
$68$	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	$0.869088\pi$
$72$	503.268	+	346.365i	0.823760	+	0.566938i
$73$		−	1038.37i		−	1.66482i	−0.554157	−	0.832412i	$-0.686959\pi$
$73$		−	1038.37i		−	1.66482i	0.554157	−	0.832412i	$-0.313041\pi$
$74$	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
$78$	202.686	−	371.461i	0.294226	−	0.539227i
$79$	−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	$0.837297\pi$
$84$	−25.5448	+	769.449i	−0.0331806	+	0.999449i
$85$			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	$-0.796569\pi$
$89$	−1347.82			−1.60527			−0.802635	+	0.596470i	$0.796569\pi$
$90$	−995.530	+	176.642i	−1.16598	+	0.206885i
$91$	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
$96$	−831.918	−	438.917i	−0.884451	−	0.466633i
$97$			183.115i			0.191675i	0.995397	+	0.0958375i	$0.0305529\pi$
$97$			183.115i			0.191675i	−0.995397	+	0.0958375i	$0.969447\pi$
$98$	−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	$-0.138882\pi$
$102$	487.531	−	893.495i	0.473262	−	0.867345i
$103$			493.737i			0.472324i	0.971714	+	0.236162i	$0.0758896\pi$
$103$			493.737i			0.472324i	−0.971714	+	0.236162i	$0.924110\pi$
$104$	−242.978	+	604.493i	−0.229096	+	0.569956i
$105$	−864.000	−	936.403i	−0.803026	−	0.870320i
$106$	30.9755	−	12.9578i	0.0283831	−	0.0118733i
$107$	−583.614			−0.527290			−0.263645	−	0.964620i	$-0.584925\pi$
$107$	−583.614			−0.527290			−0.263645	+	0.964620i	$0.584925\pi$
$108$	1064.01	+	357.197i	0.948006	+	0.318253i
$109$			1856.22i			1.63113i	0.578665	+	0.815565i	$0.303574\pi$
$109$			1856.22i			1.63113i	−0.578665	+	0.815565i	$0.696426\pi$
$110$	−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	$0.870378\pi$
$114$	−174.504	+	319.812i	−0.143366	+	0.262747i
$115$	−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
$120$	1490.36	−	449.471i	1.13375	−	0.341924i
$121$	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
$126$	344.035	+	1371.87i	0.243247	+	0.969965i
$127$	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	$-0.0468391\pi$
$132$	−212.269	+	2047.74i	−0.139967	+	1.35025i
$133$	−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	$-0.114285\pi$
$138$	1103.07	+	601.886i	0.680434	+	0.371275i
$139$	−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
$144$	−1691.26	−	354.440i	−0.978738	−	0.205116i
$145$		−	1477.47i		−	0.846186i
$146$	1133.42	+	2709.44i	0.642485	+	1.53586i
$147$	−1222.01	+	1297.39i	−0.685643	+	0.727938i
$148$	−1489.22	−	1468.50i	−0.827115	−	0.815605i
$149$	2049.54			1.12688			0.563439	−	0.826158i	$-0.309478\pi$
$149$	2049.54			1.12688			0.563439	+	0.826158i	$0.309478\pi$
$150$	−354.008	+	648.789i	−0.192698	+	0.353156i
$151$	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
$156$	−123.407	+	1190.50i	−0.0633364	+	0.611002i
$157$	−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
$162$	2059.84	+	92.7308i	0.998988	+	0.0449729i
$163$			4111.75i			1.97581i	0.155057	+	0.987906i	$0.450444\pi$
$163$			4111.75i			1.97581i	−0.155057	+	0.987906i	$0.549556\pi$
$164$	−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	$-0.408405\pi$
$167$	1224.94			0.567598			0.283799	+	0.958884i	$0.408405\pi$
$168$	−773.230	−	2035.62i	−0.355095	−	0.934830i
$169$	−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	$-0.181079\pi$
$174$	−785.572	+	1439.71i	−0.342265	+	0.627267i
$175$	−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	$-0.438056\pi$
$179$	926.214			0.386751			0.193376	+	0.981125i	$0.438056\pi$
$180$	2404.84	−	1547.58i	0.995813	−	0.640830i
$181$	−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
$186$	3055.19	+	1667.05i	1.20439	+	0.657172i
$187$	3429.90			1.34128
$188$	1221.25	−	1238.49i	0.473771	−	0.480457i
$189$	1301.43	+	2248.90i	0.500875	+	0.865520i
$190$	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	$-0.155423\pi$
$192$	2649.83	+	237.202i	0.996017	+	0.0891593i
$193$	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	$-0.495081\pi$
$197$	85.4470			0.0309028			0.0154514	+	0.999881i	$0.495081\pi$
$198$	660.756	+	3723.94i	0.237161	+	1.33661i
$199$		−	3536.74i		−	1.25986i	−0.776650	−	0.629932i	$-0.783083\pi$
$199$		−	3536.74i		−	1.25986i	0.776650	−	0.629932i	$-0.216917\pi$
$200$	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
$204$	−296.838	+	2863.57i	−0.101876	+	0.982795i
$205$		−	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
$210$	3276.57	+	1500.28i	1.07669	+	0.492997i
$211$		−	1696.15i		−	0.553403i	−0.960956	−	0.276701i	$-0.910759\pi$
$211$		−	1696.15i		−	0.553403i	0.960956	−	0.276701i	$-0.0892413\pi$
$212$	−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
$216$	−3166.24	+	229.370i	−0.997386	+	0.0722531i
$217$	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
$222$	−3372.85	−	1840.38i	−1.01969	−	0.556388i
$223$		−	3936.51i		−	1.18210i	−0.806635	−	0.591050i	$-0.798714\pi$
$223$		−	3936.51i		−	1.18210i	0.806635	−	0.591050i	$-0.201286\pi$
$224$	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	$-0.364512\pi$
$228$	106.248	−	1024.97i	0.0308617	−	0.297720i
$229$	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
$231$	−3502.76	+	3231.93i	−0.997683	+	0.920542i
$232$	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	$-0.158688\pi$
$234$	384.145	+	2164.99i	0.107318	+	0.604829i
$235$			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	$-0.207195\pi$
$240$	−3398.20	+	2799.60i	−0.913970	+	0.752972i
$241$			2312.70i			0.618151i	0.951037	+	0.309076i	$0.100020\pi$
$241$			2312.70i			0.618151i	−0.951037	+	0.309076i	$0.899980\pi$
$242$	−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
$246$	−3316.26	+	6077.69i	−0.859500	+	1.57520i
$247$	−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	$0.808892\pi$
$252$	−2395.14	−	3204.11i	−0.598729	−	0.800951i
$253$			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	$-0.555598\pi$
$257$	−1431.96			−0.347562			−0.173781	+	0.984784i	$0.555598\pi$
$258$	3368.96	+	1838.26i	0.812955	+	0.443585i
$259$	−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	$0.966255\pi$
$264$	−1681.32	−	5574.91i	−0.391962	−	1.29967i
$265$		−	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	$-0.0687015\pi$
$270$	3464.58	−	3949.47i	0.780916	−	0.890212i
$271$			7620.90i			1.70825i	0.520065	+	0.854127i	$0.325908\pi$
$271$			7620.90i			1.70825i	−0.520065	+	0.854127i	$0.674092\pi$
$272$	−62.1097	−	4431.95i	−0.0138454	−	0.987964i
$273$	−2036.41	+	1878.95i	−0.451461	+	0.416554i
$274$	1230.04	+	2940.40i	0.271202	+	0.648306i
$275$	−2490.54			−0.546128
$276$	−3535.25	−	366.464i	−0.771004	−	0.0799222i
$277$			2983.80i			0.647218i	0.946191	+	0.323609i	$0.104896\pi$
$277$			2983.80i			0.647218i	−0.946191	+	0.323609i	$0.895104\pi$
$278$	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	$-0.102761\pi$
$282$	1530.52	−	2804.98i	0.323196	−	0.592319i
$283$	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
$288$	4799.92	−	921.230i	0.982076	−	0.188486i
$289$	−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	$0.947852\pi$
$294$	1772.46	−	4719.17i	0.351605	−	0.936149i
$295$	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
$300$	215.541	−	2079.31i	0.0414810	−	0.400164i
$301$	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
$306$	924.004	+	5207.57i	0.172620	+	0.972865i
$307$	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	$-0.650603\pi$
$311$	−4998.37			−0.911356			−0.455678	+	0.890145i	$0.650603\pi$
$312$	−977.470	−	3241.10i	−0.177367	−	0.588112i
$313$			1152.65i			0.208152i	0.994569	+	0.104076i	$0.0331885\pi$
$313$			1152.65i			0.208152i	−0.994569	+	0.104076i	$0.966812\pi$
$314$	5449.50	−	2279.66i	0.979406	−	0.409709i
$315$	6545.62	+	992.561i	1.17081	+	0.177538i
$316$	−831.799	+	843.537i	−0.148077	+	0.150167i
$317$	−2738.80			−0.485256			−0.242628	−	0.970119i	$-0.578009\pi$
$317$	−2738.80			−0.485256			−0.242628	+	0.970119i	$0.578009\pi$
$318$	−83.5674	+	153.153i	−0.0147366	+	0.0270076i
$319$	−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
$324$	−5475.99	+	2006.43i	−0.938956	+	0.344038i
$325$	−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
$330$	8459.34	+	4615.79i	1.41112	+	0.769973i
$331$		−	5222.20i		−	0.867184i	−0.901109	−	0.433592i	$-0.857246\pi$
$331$		−	5222.20i		−	0.867184i	0.901109	−	0.433592i	$-0.142754\pi$
$332$	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
$336$	4239.56	+	4467.57i	0.688354	+	0.725374i
$337$	−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
$342$	−330.732	−	1863.96i	−0.0522922	−	0.294712i
$343$	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	$-0.804235\pi$
$347$	−10559.0			−1.63353			−0.816765	+	0.576970i	$0.804235\pi$
$348$	478.303	−	4614.15i	0.0736774	−	0.710760i
$349$	−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	$-0.234701\pi$
$353$	9819.24			1.48053			0.740263	+	0.672318i	$0.234701\pi$
$354$	−3051.53	−	1665.05i	−0.458155	−	0.249990i
$355$	−6333.03			−0.946824
$356$	−7570.83	+	7677.68i	−1.12712	+	1.14302i
$357$	−4898.28	+	4519.54i	−0.726175	+	0.670026i
$358$	−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	$-0.0170638\pi$
$360$	−4585.76	+	6663.10i	−0.671363	+	0.975489i
$361$	−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
$366$	5311.48	−	9734.31i	0.758567	−	1.39022i
$367$		−	8207.43i		−	1.16737i	−0.811981	−	0.583685i	$-0.801610\pi$
$367$		−	8207.43i		−	1.16737i	0.811981	−	0.583685i	$-0.198390\pi$
$368$	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
$372$	−9791.61	−	1015.00i	−1.36471	−	0.141466i
$373$		−	6620.48i		−	0.919023i	−0.888172	−	0.459511i	$-0.848025\pi$
$373$		−	6620.48i		−	0.919023i	0.888172	−	0.459511i	$-0.151975\pi$
$374$	−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
$378$	−5850.62	−	4447.52i	−0.796093	−	0.605174i
$379$			2808.73i			0.380672i	0.981719	+	0.190336i	$0.0609578\pi$
$379$			2808.73i			0.380672i	−0.981719	+	0.190336i	$0.939042\pi$
$380$	−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	$-0.448919\pi$
$383$	2395.34			0.319573			0.159786	+	0.987152i	$0.448919\pi$
$384$	−7173.18	+	2273.46i	−0.953267	+	0.302128i
$385$	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	$-0.211550\pi$
$389$	12078.7			1.57432			0.787162	+	0.616746i	$0.211550\pi$
$390$	4918.02	+	2683.49i	0.638548	+	0.348420i
$391$			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
$396$	−5788.95	−	8995.69i	−0.734610	−	1.14154i
$397$	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
$399$	1753.26	−	1617.69i	0.219982	−	0.202973i
$400$	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	$0.769230\pi$
$402$	−2104.55	−	1148.34i	−0.261109	−	0.142473i
$403$			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
$408$	−2351.16	−	7795.98i	−0.285294	−	0.945977i
$409$		−	10197.5i		−	1.23284i	−0.787416	−	0.616421i	$-0.788582\pi$
$409$		−	10197.5i		−	1.23284i	0.787416	−	0.616421i	$-0.211418\pi$
$410$	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
$414$	−6429.05	+	1140.74i	−0.763214	+	0.135421i
$415$	−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	$-0.184670\pi$
$420$	−10187.2	−	338.205i	−1.18354	−	0.0392921i
$421$		−	1525.15i		−	0.176559i	−0.996096	−	0.0882793i	$-0.971863\pi$
$421$		−	1525.15i		−	0.176559i	0.996096	−	0.0882793i	$-0.0281368\pi$
$422$	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
$426$	6171.21	+	3367.29i	0.701868	+	0.382971i
$427$	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	$0.856054\pi$
$432$	8011.36	−	4054.58i	0.892238	−	0.451565i
$433$		−	11246.6i		−	1.24821i	−0.781340	−	0.624106i	$-0.785464\pi$
$433$		−	11246.6i		−	1.24821i	0.781340	−	0.624106i	$-0.214536\pi$
$434$	−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
$438$	−13396.4	−	7309.67i	−1.46142	−	0.797419i
$439$			5899.62i			0.641397i	0.947181	+	0.320698i	$0.103918\pi$
$439$			5899.62i			0.641397i	−0.947181	+	0.320698i	$0.896082\pi$
$440$	−13766.2	−	5533.37i	−1.49154	−	0.599530i
$441$	743.658	−	9231.09i	0.0803000	−	0.996771i
$442$	−5203.11	+	2176.58i	−0.559924	+	0.234230i
$443$	991.808			0.106371			0.0531854	−	0.998585i	$-0.483063\pi$
$443$	991.808			0.106371			0.0531854	+	0.998585i	$0.483063\pi$
$444$	10809.7	+	1120.53i	1.15542	+	0.119770i
$445$		−	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	$-0.261438\pi$
$450$	−670.942	−	3781.34i	−0.0702856	−	0.396121i
$451$	−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
$456$	841.559	+	2790.44i	0.0864246	+	0.286567i
$457$	−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	$-0.288036\pi$
$462$	5612.04	−	12256.5i	0.565143	−	1.23425i
$463$	−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	$0.965489\pi$
$468$	−3365.53	−	5229.84i	−0.332418	−	0.516559i
$469$	−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
$474$	−1042.44	+	1910.48i	−0.101015	+	0.185129i
$475$	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	$-0.391191\pi$
$479$	7028.43			0.670433			0.335216	+	0.942141i	$0.391191\pi$
$480$	5811.11	−	11014.3i	0.552583	−	1.04736i
$481$		−	7527.32i		−	0.713547i
$482$	−2524.41	−	6034.58i	−0.238555	−	0.570265i
$483$	−5579.64	−	6047.22i	−0.525637	−	0.569685i
$484$	6300.83	−	6389.75i	0.591738	−	0.600089i
$485$	−2424.37			−0.226980
$486$	−8656.55	+	6313.11i	−0.807961	+	0.589236i
$487$	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	$-0.532704\pi$
$491$	−2231.72			−0.205124			−0.102562	+	0.994727i	$0.532704\pi$
$492$	2019.13	−	19478.4i	0.185020	−	1.78487i
$493$	−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
$498$	9544.38	+	5207.84i	0.858823	+	0.468612i
$499$		−	20669.1i		−	1.85426i	−0.374743	−	0.927129i	$-0.622269\pi$
$499$		−	20669.1i		−	1.85426i	0.374743	−	0.927129i	$-0.377731\pi$
$500$	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	$-0.225225\pi$
$503$	17146.1			1.51990			0.759948	+	0.649984i	$0.225225\pi$
$504$	9747.10	+	5746.14i	0.861449	+	0.507844i
$505$	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	$-0.0991223\pi$
$510$	11829.6	+	6454.74i	1.02710	+	0.560433i
$511$	−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
$516$	−10797.2	−	1119.24i	−0.921166	−	0.0954880i
$517$	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	$-0.424974\pi$
$521$	5554.16			0.467048			0.233524	+	0.972351i	$0.424974\pi$
$522$	−1488.87	−	8391.10i	−0.124839	−	0.703579i
$523$	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
$525$	3556.76	−	3281.75i	0.295676	−	0.272814i
$526$	−985.253	−	2355.24i	−0.0816712	−	0.195234i
$527$			16400.6i			1.35564i
$528$	10472.3	+	12711.5i	0.863162	+	1.04772i
$529$	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
$534$	−9488.08	+	17388.7i	−0.768894	+	1.40915i
$535$		−	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
$540$	−4729.17	+	14087.2i	−0.376872	+	1.12262i
$541$			13088.7i			1.04016i	0.854118	+	0.520079i	$0.174097\pi$
$541$			13088.7i			1.04016i	−0.854118	+	0.520079i	$0.825903\pi$
$542$	−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
$546$	3262.68	−	7125.60i	0.255733	−	0.558512i
$547$		−	134.806i		−	0.0105373i	−0.999986	−	0.00526863i	$-0.998323\pi$
$547$		−	134.806i		−	0.0105373i	0.999986	−	0.00526863i	$-0.00167706\pi$
$548$	−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
$552$	9624.61	−	2902.65i	0.742120	−	0.223813i
$553$	−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	$-0.488498\pi$
$557$	949.790			0.0722512			0.0361256	+	0.999347i	$0.488498\pi$
$558$	−17806.6	+	3159.51i	−1.35092	+	0.239700i
$559$			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	$-0.0372884\pi$
$564$	−931.872	+	8989.71i	−0.0695725	+	0.671161i
$565$	−12597.4			−0.938014
$566$	−8221.92	+	3439.43i	−0.610589	+	0.255424i
$567$	−12582.3	−	4895.94i	−0.931934	−	0.362628i
$568$	−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	$-0.193410\pi$
$570$	−4234.20	−	2310.37i	−0.311142	−	0.169773i
$571$		−	11912.4i		−	0.873063i	−0.899689	−	0.436531i	$-0.856207\pi$
$571$		−	11912.4i		−	0.873063i	0.899689	−	0.436531i	$-0.143793\pi$
$572$	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
$576$	−11519.0	+	7643.08i	−0.833258	+	0.552885i
$577$			5650.41i			0.407677i	0.979005	+	0.203838i	$0.0653417\pi$
$577$			5650.41i			0.407677i	−0.979005	+	0.203838i	$0.934658\pi$
$578$	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
$582$	2362.42	+	1289.05i	0.168257	+	0.0918087i
$583$	−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	$0.892837\pi$
$588$	526.262	+	14248.5i	0.0369093	+	0.999319i
$589$		−	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	$-0.563018\pi$
$593$	−5680.51			−0.393374			−0.196687	+	0.980466i	$0.563018\pi$
$594$	−14773.6	−	12959.8i	−1.02049	−	0.895196i
$595$	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	$-0.124914\pi$
$600$	1707.24	+	5660.86i	0.116163	+	0.385173i
$601$			4599.55i			0.312179i	0.987743	+	0.156089i	$0.0498888\pi$
$601$			4599.55i			0.312179i	−0.987743	+	0.156089i	$0.950111\pi$
$602$	−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
$606$	−11068.1	−	6039.26i	−0.741933	−	0.404832i
$607$			27115.8i			1.81318i	0.422017	+	0.906588i	$0.361322\pi$
$607$			27115.8i			1.81318i	−0.422017	+	0.906588i	$0.638678\pi$
$608$	−1789.56	−	4115.00i	−0.119369	−	0.274483i
$609$	7892.73	−	7282.46i	0.525172	−	0.484565i
$610$	−10904.0	−	26066.0i	−0.723756	−	1.73013i
$611$	6259.98			0.414487
$612$	−8095.29	−	12579.6i	−0.534694	−	0.830884i
$613$			2010.26i			0.132453i	0.997805	+	0.0662263i	$0.0210959\pi$
$613$			2010.26i			0.132453i	−0.997805	+	0.0662263i	$0.978904\pi$
$614$	−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	$0.829316\pi$
$618$	6369.87	+	3475.69i	0.414618	+	0.226234i
$619$	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
$624$	6088.32	+	7390.11i	0.390589	+	0.474104i
$625$	−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
$630$	−18163.0	+	4554.90i	−1.14862	+	0.288050i
$631$	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
$636$	50.8808	−	490.843i	0.00317225	−	0.0306025i
$637$	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	$-0.359296\pi$
$642$	−4108.38	+	7529.40i	−0.252562	+	0.462869i
$643$	−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	$-0.594280\pi$
$647$	−9606.99			−0.583755			−0.291878	+	0.956456i	$0.594280\pi$
$648$	12098.5	−	11212.7i	0.733447	−	0.679746i
$649$		−	11714.1i		−	0.708500i
$650$	3778.11	−	1580.47i	0.227984	−	0.0953711i
$651$	−15454.0	−	16749.0i	−0.930398	−	1.00837i
$652$	23422.0	+	23096.0i	1.40686	+	1.38729i
$653$	5450.16			0.326618			0.163309	−	0.986575i	$-0.447783\pi$
$653$	5450.16			0.326618			0.163309	+	0.986575i	$0.447783\pi$
$654$	23947.7	+	13066.9i	1.43185	+	0.781281i
$655$	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	$-0.651844\pi$
$659$	−15534.8			−0.918287			−0.459144	+	0.888362i	$0.651844\pi$
$660$	−27111.4	−	2810.37i	−1.59896	−	0.165748i
$661$	−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
$666$	19658.0	−	3488.02i	1.14374	−	0.202940i
$667$		−	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
$672$	−15938.9	−	7029.65i	−0.914965	−	0.403534i
$673$	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	$0.937751\pi$
$678$	12275.5	+	6698.08i	0.695337	+	0.379407i
$679$	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	$-0.372677\pi$
$683$	13901.9			0.778833			0.389417	+	0.921062i	$0.372677\pi$
$684$	2897.57	+	4502.66i	0.161976	+	0.251701i
$685$	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
$690$	−7968.77	+	14604.3i	−0.439661	+	0.805763i
$691$	−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
$693$	3712.83	−	24484.9i	0.203519	−	1.34214i
$694$	27551.7	−	11525.5i	1.50699	−	0.630408i
$695$		−	32034.1i		−	1.74838i
$696$	3788.49	+	12561.9i	0.206325	+	0.684133i
$697$	−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	$-0.781559\pi$
$701$	−28716.9			−1.54725			−0.773626	+	0.633643i	$0.781559\pi$
$702$	−8588.97	−	7534.46i	−0.461780	−	0.405085i
$703$			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
$708$	9779.88	+	1013.78i	0.519139	+	0.0538139i
$709$			6971.08i			0.369259i	0.982808	+	0.184629i	$0.0591085\pi$
$709$			6971.08i			0.369259i	−0.982808	+	0.184629i	$0.940892\pi$
$710$	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
$714$	7847.90	−	17139.6i	0.411345	−	0.898365i
$715$			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	$-0.333205\pi$
$719$	19292.8			1.00070			0.500348	+	0.865825i	$0.333205\pi$
$720$	4692.67	−	22391.7i	0.242896	−	1.15901i
$721$	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
$726$	7896.45	−	14471.8i	0.403671	−	0.739805i
$727$			12461.6i			0.635732i	0.948136	+	0.317866i	$0.102966\pi$
$727$			12461.6i			0.635732i	−0.948136	+	0.317866i	$0.897034\pi$
$728$	−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
$732$	−3233.94	+	31197.6i	−0.163292	+	1.57527i
$733$	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
$735$	−17177.0	−	16179.0i	−0.862017	−	0.811933i
$736$	−14193.2	+	6172.44i	−0.710826	+	0.309129i
$737$		−	8078.86i		−	0.403784i
$738$	−6285.21	−	35422.6i	−0.313498	−	1.76684i
$739$		−	24642.5i		−	1.22664i	−0.789834	−	0.613321i	$-0.789833\pi$
$739$		−	24642.5i		−	1.22664i	0.789834	−	0.613321i	$-0.210167\pi$
$740$	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	$0.737591\pi$
$744$	26657.3	−	8039.49i	1.31358	−	0.396158i
$745$			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
$750$	12761.4	+	6963.21i	0.621308	+	0.339014i
$751$	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
$756$	20120.8	+	5218.81i	0.967970	+	0.251067i
$757$			10634.4i			0.510587i	0.966864	+	0.255293i	$0.0821720\pi$
$757$			10634.4i			0.510587i	−0.966864	+	0.255293i	$0.917828\pi$
$758$	−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	$-0.474984\pi$
$761$	3296.31			0.157019			0.0785094	+	0.996913i	$0.474984\pi$
$762$	17955.2	−	32906.4i	0.853606	−	1.56440i
$763$	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
$768$	16235.5	−	13762.0i	0.762824	−	0.646606i
$769$		−	29295.6i		−	1.37376i	−0.726769	−	0.686882i	$-0.758979\pi$
$769$		−	29295.6i		−	1.37376i	0.726769	−	0.686882i	$-0.241021\pi$
$770$	−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	$0.975263\pi$
$774$	−19635.4	+	3484.00i	−0.911859	+	0.161795i
$775$		−	11908.9i		−	0.551975i
$776$	−3844.47	−	1545.30i	−0.177846	−	0.0714857i
$777$	17060.8	+	18490.5i	0.787712	+	0.853722i
$778$	−31517.0	+	13184.3i	−1.45237	+	0.607559i
$779$	11677.8			0.537102
$780$	−15761.8	−	1633.87i	−0.723543	−	0.0750024i
$781$			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
$786$	−5672.33	−	3095.08i	−0.257411	−	0.140455i
$787$	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
$792$	24924.4	+	17153.8i	1.11824	+	0.769611i
$793$	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	$-0.0893813\pi$
$798$	−2809.03	+	6134.83i	−0.124610	+	0.272144i
$799$	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
$804$	6744.91	+	699.177i	0.295864	+	0.0306693i
$805$	−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	$0.704749\pi$
$810$	−1227.72	+	27271.5i	−0.0532566	+	1.18299i
$811$	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
$816$	14644.6	+	17775.8i	0.628262	+	0.762595i
$817$		−	6473.23i		−	0.277196i
$818$	11131.0	+	26608.5i	0.475776	+	1.13734i
$819$	2158.53	−	14234.8i	0.0920944	−	0.607333i
$820$	−35528.5	−	35034.1i	−1.51306	−	1.49200i
$821$	−24314.1			−1.03358			−0.516789	−	0.856113i	$-0.672873\pi$
$821$	−24314.1			−1.03358			−0.516789	+	0.856113i	$0.672873\pi$
$822$	−14538.3	−	7932.75i	−0.616888	−	0.336602i
$823$	−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	$-0.434913\pi$
$827$	9658.38			0.406112			0.203056	+	0.979167i	$0.434913\pi$
$828$	15530.3	−	9994.12i	0.651829	−	0.419468i
$829$	−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
$834$	−17032.6	+	31215.5i	−0.707182	+	1.29605i
$835$			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	$-0.506141\pi$
$839$	−937.651			−0.0385832			−0.0192916	+	0.999814i	$0.506141\pi$
$840$	26950.9	−	10237.3i	1.10702	−	0.420500i
$841$	−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
$846$	2900.75	+	16348.3i	0.117884	+	0.664380i
$847$	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
$852$	−19778.2	−	2050.20i	−0.795292	−	0.0824399i
$853$	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	$-0.488066\pi$
$857$	1880.84			0.0749687			0.0374843	+	0.999297i	$0.488066\pi$
$858$	10038.0	−	18396.6i	0.399408	−	0.731993i
$859$	−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
$861$	33318.8	−	30742.6i	1.31882	−	1.21685i
$862$	−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	$0.966524\pi$
$864$	−16478.5	+	19324.4i	−0.648853	+	0.760914i
$865$	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
$870$	−19061.3	−	10400.7i	−0.742803	−	0.405307i
$871$		−	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
$876$	42934.2	+	4450.56i	1.65595	+	0.171656i
$877$		−	15099.1i		−	0.581369i	−0.956819	−	0.290684i	$-0.906117\pi$
$877$		−	15099.1i		−	0.581369i	0.956819	−	0.290684i	$-0.0938829\pi$
$878$	−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	$-0.338154\pi$
$881$	25460.6			0.973654			0.486827	+	0.873498i	$0.338154\pi$
$882$	8135.67	+	24898.6i	0.310592	+	0.950543i
$883$			29492.7i			1.12402i	0.827131	+	0.562009i	$0.189972\pi$
$883$			29492.7i			1.12402i	−0.827131	+	0.562009i	$0.810028\pi$
$884$	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	$-0.570206\pi$
$887$	−11558.8			−0.437550			−0.218775	+	0.975775i	$0.570206\pi$
$888$	−29429.0	+	8875.38i	−1.11213	+	0.335403i
$889$	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
$894$	14427.8	−	26441.8i	0.539753	−	0.989202i
$895$			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
$900$	5878.19	+	9134.37i	0.217711	+	0.338310i
$901$	−822.146			−0.0303992
$902$	60877.2	−	25466.4i	2.24722	−	0.940065i
$903$	−17041.1	−	18469.2i	−0.628010	−	0.680637i
$904$	−19976.4	−	8029.60i	−0.734963	−	0.295421i
$905$		−	11607.5i		−	0.426348i
$906$	2028.66	−	3717.92i	0.0743906	−	0.136335i
$907$		−	10190.2i		−	0.373053i	−0.982450	−	0.186527i	$-0.940277\pi$
$907$		−	10190.2i		−	0.373053i	0.982450	−	0.186527i	$-0.0597231\pi$
$908$	−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	$-0.208007\pi$
$912$	−5241.78	−	6362.56i	−0.190321	−	0.231015i
$913$			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
$918$	−20659.5	−	18123.0i	−0.742772	−	0.651578i
$919$	−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
$924$	−1265.11	+	38107.0i	−0.0450422	+	1.35674i
$925$			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	$-0.385609\pi$
$929$	19916.3			0.703370			0.351685	+	0.936118i	$0.385609\pi$
$930$	−22071.2	+	40449.7i	−0.778217	+	1.42623i
$931$	−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
$936$	14490.3	+	9972.71i	0.506016	+	0.348257i
$937$		−	27614.4i		−	0.962779i	−0.876507	−	0.481390i	$-0.840132\pi$
$937$		−	27614.4i		−	0.962779i	0.876507	−	0.481390i	$-0.159868\pi$
$938$	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	$0.805045\pi$
$942$	−14702.0	+	26944.2i	−0.508509	+	0.931942i
$943$		−	40278.4i		−	1.39093i
$944$	−15136.3	+	212.122i	−0.521870	+	0.00731353i
$945$	−29774.6	+	17230.5i	−1.02494	+	0.593132i
$946$	−14116.5	−	33745.3i	−0.485164	−	1.15978i
$947$	−6141.76			−0.210750			−0.105375	−	0.994433i	$-0.533604\pi$
$947$	−6141.76			−0.210750			−0.105375	+	0.994433i	$0.533604\pi$
$948$	634.702	−	6122.92i	0.0217449	−	0.209771i
$949$		−	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	$0.961508\pi$
$954$	−158.383	−	892.626i	−0.00537509	−	0.0302933i
$955$	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
$960$	−3140.47	+	35082.9i	−0.105582	+	1.17947i
$961$	−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
$966$	21159.8	+	9688.71i	0.704769	+	0.322701i
$967$	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	$-0.0577470\pi$
$972$	15696.7	−	25921.9i	0.517975	−	0.855396i
$973$	−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	$-0.124661\pi$
$978$	53047.1	+	28944.9i	1.73442	+	0.946376i
$979$	−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	$-0.590660\pi$
$983$	−17319.7			−0.561965			−0.280982	+	0.959713i	$0.590660\pi$
$984$	15992.9	+	53029.4i	0.518126	+	1.71800i
$985$			1131.29i			0.0365948i
$986$	20166.3	−	8436.03i	0.651343	−	0.272472i
$987$	−15377.3	+	14188.3i	−0.495912	+	0.457568i
$988$	−4009.12	+	4065.69i	−0.129096	+	0.130918i
$989$	−22327.0			−0.717854
$990$	−49303.6	+	8748.18i	−1.58280	+	0.280844i
$991$	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
$996$	−30588.9	−	3170.84i	−0.973138	−	0.100875i
$997$	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.125.11	yes	80
3.2	odd	2	inner	168.4.i.c.125.69	yes	80
4.3	odd	2		672.4.i.c.209.62		80
7.6	odd	2	inner	168.4.i.c.125.12	yes	80
8.3	odd	2		672.4.i.c.209.19		80
8.5	even	2	inner	168.4.i.c.125.72	yes	80
12.11	even	2		672.4.i.c.209.63		80
21.20	even	2	inner	168.4.i.c.125.70	yes	80
24.5	odd	2	inner	168.4.i.c.125.10	yes	80
24.11	even	2		672.4.i.c.209.18		80
28.27	even	2		672.4.i.c.209.20		80
56.13	odd	2	inner	168.4.i.c.125.71	yes	80
56.27	even	2		672.4.i.c.209.61		80
84.83	odd	2		672.4.i.c.209.17		80
168.83	odd	2		672.4.i.c.209.64		80
168.125	even	2	inner	168.4.i.c.125.9	✓	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.4.i.c.125.9	✓	80	168.125	even	2	inner
168.4.i.c.125.10	yes	80	24.5	odd	2	inner
168.4.i.c.125.11	yes	80	1.1	even	1	trivial
168.4.i.c.125.12	yes	80	7.6	odd	2	inner
168.4.i.c.125.69	yes	80	3.2	odd	2	inner
168.4.i.c.125.70	yes	80	21.20	even	2	inner
168.4.i.c.125.71	yes	80	56.13	odd	2	inner
168.4.i.c.125.72	yes	80	8.5	even	2	inner
672.4.i.c.209.17		80	84.83	odd	2
672.4.i.c.209.18		80	24.11	even	2
672.4.i.c.209.19		80	8.3	odd	2
672.4.i.c.209.20		80	28.27	even	2
672.4.i.c.209.61		80	56.27	even	2
672.4.i.c.209.62		80	4.3	odd	2
672.4.i.c.209.63		80	12.11	even	2
672.4.i.c.209.64		80	168.83	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+(-2.60932 + 1.09154i) q^{2} +(-4.05635 + 3.24747i) q^{3} +(5.61708 - 5.69635i) q^{4} +13.2397i q^{5} +(7.03955 - 12.9013i) 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} +(-4.28610 + 41.3477i) 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} +(13.3419 + 75.1930i) q^{18} -24.7890 q^{19} +(75.4177 + 74.3682i) q^{20} +(-70.7271 + 65.2585i) q^{21} +(-129.227 + 54.0585i) q^{22} +85.5006i q^{23} +(-33.9488 - 112.568i) 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} +(170.809 + 93.2013i) 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} +(-116.889 - 181.639i) 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} +(113.317 - 247.482i) 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} +(211.455 + 256.668i) 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} +(-298.306 - 261.682i) 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} +(-547.429 - 56.7464i) q^{60} +754.519 q^{61} +(-258.490 - 617.917i) q^{62} +(74.9688 - 494.395i) q^{63} +(-369.568 - 354.349i) q^{64} +381.202i q^{65} +(348.634 - 638.939i) 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} +(503.268 + 346.365i) 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} +(202.686 - 371.461i) 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} +(-25.5448 + 769.449i) 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} +(-995.530 + 176.642i) 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} +(-831.918 - 438.917i) 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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