LMFDB - Embedded newform 168.4.i.c.125.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [168,4,Mod(125,168)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

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")

//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: f = N[0] # Warning: the index may be different

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			125.10
Character	$\chi$	$=$	168.125
Dual form			168.4.i.c.125.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.60932 - 1.09154i) q^{2} +(4.05635 + 3.24747i) q^{3} +(5.61708 + 5.69635i) q^{4} +13.2397i q^{5} +(-7.03955 - 12.9013i) q^{6} +(18.4748 - 1.29729i) q^{7} +(-8.43895 - 20.9949i) q^{8} +(5.90788 + 26.3457i) q^{9} +O(q^{10})$	\(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} +(-49.6226 - 16.7809i) 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} +(79.1529 + 54.7340i) 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} +(111.164 + 97.9518i) 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} +(-146.791 - 229.217i) 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} +(-183.144 - 376.927i) 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} +(143.325 + 479.067i) 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} +(222.174 - 656.986i) 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} +(132.824 + 758.328i) 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} +(-938.535 - 245.649i) 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}+O(q^{10}) $ 80 * q + 28 * q^4 + 64 * q^7 + 104 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

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	$-0.599371\pi$
$13$	−28.7924			−0.614276			−0.307138	+	0.951665i	$0.599371\pi$
$14$	−49.6226	−	16.7809i	−0.947300	−	0.320349i
$15$	−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	$0.664477\pi$
$18$	13.3419	−	75.1930i	0.174706	−	0.984621i
$19$	24.7890			0.299315			0.149658	−	0.988738i	$-0.452183\pi$
$19$	24.7890			0.299315			0.149658	+	0.988738i	$0.452183\pi$
$20$	−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	$-0.873315\pi$
$23$		−	85.5006i		−	0.775135i	0.921841	−	0.387568i	$-0.126685\pi$
$24$	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
$28$	111.164	+	97.9518i	0.750287	+	0.661112i
$29$	−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	$0.197262\pi$
$37$			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	$0.145585\pi$
$42$	−146.791	−	229.217i	−0.539293	−	0.842118i
$43$		−	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	$0.609540\pi$
$48$	−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
$56$	−183.144	−	376.927i	−0.437030	−	0.899447i
$57$	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	$-0.790884\pi$
$61$	−754.519			−1.58371			−0.791855	+	0.610709i	$0.790884\pi$
$62$	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
$66$	−348.634	−	638.939i	−0.650210	−	1.19164i
$67$			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
$70$	222.174	−	656.986i	0.379354	−	1.12178i
$71$		−	478.338i		−	0.799554i	−0.916613	−	0.399777i	$-0.869088\pi$
$71$		−	478.338i		−	0.799554i	0.916613	−	0.399777i	$-0.130912\pi$
$72$	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	$0.837297\pi$
$84$	132.824	+	758.328i	0.172528	+	0.985005i
$85$		−	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	$0.203431\pi$
$90$	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	$0.969447\pi$
$98$	−938.535	−	245.649i	−0.967412	−	0.253207i
$99$	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
$105$	−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	$-0.584925\pi$
$107$	−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	$-0.696426\pi$
$109$		−	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
$112$	66.4498	+	1183.43i	0.0560618	+	0.998427i
$113$		−	951.492i		−	0.792114i	−0.918226	−	0.396057i	$-0.870378\pi$
$113$		−	951.492i		−	0.792114i	0.918226	−	0.396057i	$-0.129622\pi$
$114$	−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
$126$	148.941	−	1406.48i	0.105307	−	0.994440i
$127$	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	$0.114285\pi$
$137$			1126.88i			0.702745i	−0.936236	+	0.351373i	$0.885715\pi$
$138$	−1103.07	+	601.886i	−0.680434	+	0.371275i
$139$	2419.55			1.47643			0.738215	−	0.674565i	$-0.235669\pi$
$139$	2419.55			1.47643			0.738215	+	0.674565i	$0.235669\pi$
$140$	−1296.85	+	1471.77i	−0.782883	+	0.888483i
$141$	−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
$147$	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	$-0.309478\pi$
$149$	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
$154$	−2457.56	−	831.075i	−1.28595	−	0.434870i
$155$	−3135.31			−1.62473
$156$	−123.407	−	1190.50i	−0.0633364	−	0.611002i
$157$	2088.48			1.06165			0.530824	−	0.847482i	$-0.321883\pi$
$157$	2088.48			1.06165			0.530824	+	0.847482i	$0.321883\pi$
$158$	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	$-0.549556\pi$
$163$		−	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	$0.591595\pi$
$168$	481.164	−	2123.70i	0.220968	−	0.975281i
$169$	−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	$-0.442385\pi$
$181$	876.720			0.360034			0.180017	+	0.983664i	$0.442385\pi$
$182$	1428.76	+	483.163i	0.581903	+	0.196783i
$183$	−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
$189$	−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	$0.155423\pi$
$191$			2476.56i			0.938208i	−0.883143	+	0.469104i	$0.844577\pi$
$192$	−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
$196$	2180.80	+	1665.42i	0.794753	+	0.606933i
$197$	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
$210$	3034.75	−	1943.46i	0.997228	−	0.638626i
$211$			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
$216$	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	$-0.201286\pi$
$224$	1118.38	−	3160.48i	0.333592	−	0.942718i
$225$	−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	$-0.694360\pi$
$229$	−3973.83			−1.14672			−0.573359	+	0.819304i	$0.694360\pi$
$230$	−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	$0.158688\pi$
$233$			3401.07i			0.956273i	−0.878285	+	0.478137i	$0.841312\pi$
$234$	−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
$238$	3436.66	+	1162.18i	0.935990	+	0.316525i
$239$			4477.57i			1.21184i	0.795525	+	0.605920i	$0.207195\pi$
$239$			4477.57i			1.21184i	−0.795525	+	0.605920i	$0.792805\pi$
$240$	−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	$0.808892\pi$
$252$	−1923.87	+	3507.38i	−0.480921	+	0.876764i
$253$		−	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	$0.444402\pi$
$258$	−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	$-0.966255\pi$
$263$		−	902.626i		−	0.211629i	0.994386	−	0.105814i	$-0.0337449\pi$
$264$	1681.32	−	5574.91i	0.391962	−	1.29967i
$265$		−	157.170i		−	0.0364334i
$266$	−1230.10	−	415.983i	−0.283541	−	0.0958854i
$267$	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
$273$	−2279.01	−	1575.93i	−0.505245	−	0.349375i
$274$	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	$-0.895104\pi$
$277$		−	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
$280$	4990.39	−	2424.76i	1.06512	−	0.517526i
$281$			2988.80i			0.634508i	0.948341	+	0.317254i	$0.102761\pi$
$281$			2988.80i			0.634508i	−0.948341	+	0.317254i	$0.897239\pi$
$282$	1530.52	+	2804.98i	0.323196	+	0.592319i
$283$	−3150.99			−0.661861			−0.330930	−	0.943655i	$-0.607363\pi$
$283$	−3150.99			−0.661861			−0.330930	+	0.943655i	$0.607363\pi$
$284$	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	$0.947852\pi$
$294$	−3009.29	−	4044.30i	−0.596956	−	0.802274i
$295$	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	$-0.614550\pi$
$307$	−3788.51			−0.704305			−0.352152	+	0.935943i	$0.614550\pi$
$308$	5505.40	+	4851.06i	1.01850	+	0.897451i
$309$	−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	$0.349397\pi$
$312$	−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
$315$	−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	$-0.578009\pi$
$317$	−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
$322$	−1434.78	+	4242.76i	−0.248314	+	0.734285i
$323$	−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	$0.142754\pi$
$331$			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
$336$	−3573.62	+	5016.21i	−0.580229	+	0.814454i
$337$	−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	$-0.391871\pi$
$349$	4344.86			0.666404			0.333202	+	0.942855i	$0.391871\pi$
$350$	2495.44	+	843.887i	0.381106	+	0.128879i
$351$	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	$0.765299\pi$
$354$	−3051.53	+	1665.05i	−0.458155	+	0.249990i
$355$	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	$0.0170638\pi$
$359$			728.937i			0.107164i	−0.998563	+	0.0535820i	$0.982936\pi$
$360$	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
$364$	−3200.68	−	2820.27i	−0.460883	−	0.406105i
$365$	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	$0.151975\pi$
$373$			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
$378$	5171.66	−	5221.50i	0.703708	−	0.710489i
$379$		−	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	$0.551081\pi$
$384$	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
$392$	−3872.53	−	6726.06i	−0.498960	−	0.866625i
$393$	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	$-0.607465\pi$
$397$	−5240.22			−0.662466			−0.331233	+	0.943549i	$0.607465\pi$
$398$	−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	$-0.769230\pi$
$401$		−	10649.8i		−	1.32625i	0.748509	−	0.663125i	$-0.230770\pi$
$402$	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
$406$	5537.59	+	1872.65i	0.676911	+	0.228912i
$407$			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	$-0.184670\pi$
$420$	−10040.0	+	1758.55i	−1.16643	+	0.204306i
$421$			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
$426$	−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	$-0.856054\pi$
$431$		−	7819.69i		−	0.873924i	0.899480	−	0.436962i	$-0.143946\pi$
$432$	−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	$-0.214536\pi$
$434$	3973.92	−	11751.2i	0.439526	−	1.29971i
$435$	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
$441$	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	$-0.483063\pi$
$443$	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
$448$	−6367.99	+	7025.96i	−0.671561	+	0.740949i
$449$			13929.7i			1.46411i	0.681248	+	0.732053i	$0.261438\pi$
$449$			13929.7i			1.46411i	−0.681248	+	0.732053i	$0.738562\pi$
$450$	−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	$-0.288036\pi$
$462$	−7269.82	−	11352.0i	−0.732084	−	1.14316i
$463$	−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
$476$	−7698.78	−	6783.75i	−0.741329	−	0.653219i
$477$	−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	$0.608809\pi$
$480$	5811.11	+	11014.3i	0.552583	+	1.04736i
$481$		−	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
$486$	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
$490$	3252.30	−	12425.9i	0.299845	−	1.14560i
$491$	−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	$0.377731\pi$
$499$			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	$0.774775\pi$
$504$	8848.43	−	7051.91i	0.782024	−	0.623248i
$505$	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
$518$	4387.10	−	12973.0i	0.372120	−	1.10039i
$519$	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	$0.575026\pi$
$522$	−1488.87	+	8391.10i	−0.124839	+	0.703579i
$523$	−1129.07			−0.0943994			−0.0471997	−	0.998885i	$-0.515030\pi$
$523$	−1129.07			−0.0943994			−0.0471997	+	0.998885i	$0.515030\pi$
$524$	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
$528$	−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
$532$	2755.65	+	2428.13i	0.224572	+	0.197881i
$533$	−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	$-0.825903\pi$
$541$		−	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
$546$	4226.47	+	6599.72i	0.331275	+	0.517293i
$547$			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
$552$	−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
$560$	−15668.2	+	879.773i	−1.18233	+	0.0663878i
$561$	−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
$567$	−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	$0.193410\pi$
$569$			15497.7i			1.14182i	−0.821011	+	0.570912i	$0.806590\pi$
$570$	4234.20	−	2310.37i	0.311142	−	0.169773i
$571$			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
$574$	−23376.7	−	7905.31i	−1.69987	−	0.574845i
$575$			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	$0.892837\pi$
$588$	3437.67	+	13837.6i	0.241101	+	0.970500i
$589$			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	$0.436982\pi$
$594$	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	$0.124914\pi$
$599$			11213.1i			0.764866i	−0.923983	+	0.382433i	$0.875086\pi$
$600$	−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	$0.950111\pi$
$602$	−4382.05	+	12958.1i	−0.296676	+	0.877295i
$603$	−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
$609$	−8833.00	−	6107.99i	−0.587736	−	0.406417i
$610$	−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	$-0.978904\pi$
$613$		−	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
$616$	−9070.21	−	18667.3i	−0.593262	−	1.22099i
$617$		−	15659.8i		−	1.02178i	−0.859646	−	0.510891i	$-0.829316\pi$
$617$		−	15659.8i		−	1.02178i	0.859646	−	0.510891i	$-0.170684\pi$
$618$	6369.87	−	3475.69i	0.414618	−	0.226234i
$619$	−27135.8			−1.76200			−0.881001	−	0.473115i	$-0.843130\pi$
$619$	−27135.8			−1.76200			−0.881001	+	0.473115i	$0.843130\pi$
$620$	−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
$630$	18621.3	+	1971.92i	1.17761	+	0.124704i
$631$	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	$0.359296\pi$
$641$			29337.9i			1.80777i	−0.427779	+	0.903884i	$0.640704\pi$
$642$	4108.38	+	7529.40i	0.252562	+	0.462869i
$643$	24076.1			1.47662			0.738310	−	0.674461i	$-0.235624\pi$
$643$	24076.1			1.47662			0.738310	+	0.674461i	$0.235624\pi$
$644$	8374.94	−	9504.60i	0.512452	−	0.581574i
$645$	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	$0.405720\pi$
$648$	12098.5	+	11212.7i	0.733447	+	0.679746i
$649$		−	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	$-0.447783\pi$
$653$	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
$658$	10788.8	+	3648.46i	0.639197	+	0.216158i
$659$	−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	$-0.401200\pi$
$661$	10381.1			0.610858			0.305429	+	0.952215i	$0.401200\pi$
$662$	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
$672$	14800.1	−	9188.13i	0.849592	−	0.527440i
$673$	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
$686$	−17657.9	−	3320.75i	−0.982772	−	0.184821i
$687$	−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	$-0.431899\pi$
$691$	7713.20			0.424637			0.212318	+	0.977201i	$0.431899\pi$
$692$	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
$696$	−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
$700$	−5590.27	−	4925.85i	−0.301846	−	0.265971i
$701$	−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	$-0.940892\pi$
$709$		−	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
$714$	10166.1	+	15874.6i	0.532855	+	0.832064i
$715$		−	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	$0.666795\pi$
$720$	−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	$0.897034\pi$
$728$	5273.17	+	10852.7i	0.268457	+	0.552509i
$729$	−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	$-0.732033\pi$
$733$	−26437.4			−1.33218			−0.666090	+	0.745872i	$0.732033\pi$
$734$	−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
$738$	6285.21	−	35422.6i	0.313498	−	1.76684i
$739$			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
$742$	589.076	+	199.208i	0.0291451	+	0.00985602i
$743$		−	29736.2i		−	1.46826i	−0.679012	−	0.734128i	$-0.737591\pi$
$743$		−	29736.2i		−	1.46826i	0.679012	−	0.734128i	$-0.262409\pi$
$744$	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
$756$	−19194.0	+	7979.47i	−0.923385	+	0.383876i
$757$		−	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	$0.525016\pi$
$762$	−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	$-0.241021\pi$
$770$	11003.1	−	32537.2i	0.514969	−	1.52281i
$771$	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
$777$	−14309.3	+	20693.3i	−0.660674	+	0.955427i
$778$	−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
$784$	2762.90	+	21777.4i	0.125861	+	0.992048i
$785$			27650.7i			1.25719i
$786$	−5672.33	+	3095.08i	−0.257411	+	0.140455i
$787$	−643.131			−0.0291298			−0.0145649	−	0.999894i	$-0.504636\pi$
$787$	−643.131			−0.0291298			−0.0145649	+	0.999894i	$0.504636\pi$
$788$	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	$-0.0893813\pi$
$798$	−3638.80	−	5682.07i	−0.161419	−	0.252059i
$799$	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	$-0.704749\pi$
$809$		−	36823.8i		−	1.60032i	0.599789	−	0.800158i	$-0.295251\pi$
$810$	1227.72	+	27271.5i	0.0532566	+	1.18299i
$811$	−28331.7			−1.22671			−0.613354	−	0.789808i	$-0.710180\pi$
$811$	−28331.7			−1.22671			−0.613354	+	0.789808i	$0.710180\pi$
$812$	−12405.2	−	10930.8i	−0.536132	−	0.472410i
$813$	−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
$819$	−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	$-0.672873\pi$
$821$	−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
$826$	−3969.16	+	11737.1i	−0.167197	+	0.494415i
$827$	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	$-0.472103\pi$
$829$	4178.46			0.175059			0.0875296	+	0.996162i	$0.472103\pi$
$830$	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	$-0.493859\pi$
$839$	937.651			0.0385832			0.0192916	+	0.999814i	$0.493859\pi$
$840$	28117.1	+	6370.45i	1.15492	+	0.261668i
$841$	−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	$-0.537085\pi$
$853$	−5791.89			−0.232486			−0.116243	+	0.993221i	$0.537085\pi$
$854$	37441.2	+	12661.5i	1.50025	+	0.507340i
$855$	−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	$0.511934\pi$
$858$	10038.0	+	18396.6i	0.399408	+	0.731993i
$859$	9503.79			0.377491			0.188746	−	0.982026i	$-0.439558\pi$
$859$	9503.79			0.377491			0.188746	+	0.982026i	$0.439558\pi$
$860$	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	$-0.966524\pi$
$863$		−	5322.63i		−	0.209947i	0.994475	−	0.104974i	$-0.0334758\pi$
$864$	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
$868$	−23196.1	+	26325.0i	−0.907060	+	1.02941i
$869$	−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	$0.0938829\pi$
$877$			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	$0.661846\pi$
$882$	927.034	−	26177.7i	0.0353910	−	0.999374i
$883$		−	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	$0.429794\pi$
$888$	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
$896$	24285.2	−	11382.0i	0.905483	−	0.424383i
$897$	−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
$903$	14292.8	−	20669.4i	0.526728	−	0.761722i
$904$	−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	$0.0597231\pi$
$907$			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
$910$	−6396.92	+	18916.2i	−0.233028	+	0.689085i
$911$			33432.8i			1.21589i	0.793978	+	0.607947i	$0.208007\pi$
$911$			33432.8i			1.21589i	−0.793978	+	0.607947i	$0.791993\pi$
$912$	−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
$924$	6578.13	+	37556.2i	0.234204	+	1.33713i
$925$		−	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	$0.614391\pi$
$930$	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	$-0.159868\pi$
$938$	2737.42	−	8094.77i	0.0952877	−	0.281774i
$939$	−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
$945$	−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	$-0.533604\pi$
$947$	−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
$952$	12683.8	+	26104.5i	0.431812	+	0.888709i
$953$		−	7097.85i		−	0.241261i	−0.992697	−	0.120631i	$-0.961508\pi$
$953$		−	7097.85i		−	0.241261i	0.992697	−	0.120631i	$-0.0384916\pi$
$954$	−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
$966$	−19598.2	+	12550.7i	−0.652755	+	0.418025i
$967$	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	$0.124661\pi$
$977$			23312.8i			0.763400i	−0.924286	+	0.381700i	$0.875339\pi$
$978$	−53047.1	+	28944.9i	−1.73442	+	0.946376i
$979$	66751.0			2.17913
$980$	−22049.6	+	28873.1i	−0.718725	+	0.941139i
$981$	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	$0.409340\pi$
$984$	15992.9	−	53029.4i	0.518126	−	1.71800i
$985$			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
$990$	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
$994$	−8026.95	+	23736.4i	−0.256136	+	0.757417i
$995$	46825.2			1.49192
$996$	−30588.9	+	3170.84i	−0.973138	+	0.100875i
$997$	−47651.1			−1.51367			−0.756833	−	0.653608i	$-0.773255\pi$
$997$	−47651.1			−1.51367			−0.756833	+	0.653608i	$0.773255\pi$
$998$	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.125.10	yes	80
3.2	odd	2	inner	168.4.i.c.125.72	yes	80
4.3	odd	2		672.4.i.c.209.18		80
7.6	odd	2	inner	168.4.i.c.125.9	✓	80
8.3	odd	2		672.4.i.c.209.63		80
8.5	even	2	inner	168.4.i.c.125.69	yes	80
12.11	even	2		672.4.i.c.209.19		80
21.20	even	2	inner	168.4.i.c.125.71	yes	80
24.5	odd	2	inner	168.4.i.c.125.11	yes	80
24.11	even	2		672.4.i.c.209.62		80
28.27	even	2		672.4.i.c.209.64		80
56.13	odd	2	inner	168.4.i.c.125.70	yes	80
56.27	even	2		672.4.i.c.209.17		80
84.83	odd	2		672.4.i.c.209.61		80
168.83	odd	2		672.4.i.c.209.20		80
168.125	even	2	inner	168.4.i.c.125.12	yes	80

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-2.60932 - 1.09154i) q^{2} +(4.05635 + 3.24747i) q^{3} +(5.61708 + 5.69635i) q^{4} +13.2397i q^{5} +(-7.03955 - 12.9013i) q^{6} +(18.4748 - 1.29729i) q^{7} +(-8.43895 - 20.9949i) q^{8} +(5.90788 + 26.3457i) q^{9} +O(q^{10})\)	\(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} +(-49.6226 - 16.7809i) 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} +(79.1529 + 54.7340i) 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} +(111.164 + 97.9518i) 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} +(-146.791 - 229.217i) 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} +(-183.144 - 376.927i) 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} +(143.325 + 479.067i) 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} +(222.174 - 656.986i) 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} +(132.824 + 758.328i) 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} +(-938.535 - 245.649i) q^{98} +(292.588 + 1304.77i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 28 q^{4} + 64 q^{7} + 104 q^{9}+O(q^{10}) \) 80 * q + 28 * q^4 + 64 * q^7 + 104 * q^9	\( 80 q + 28 q^{4} + 64 q^{7} + 104 q^{9} - 8 q^{15} - 892 q^{16} + 692 q^{18} + 128 q^{22} - 976 q^{25} + 612 q^{28} - 332 q^{30} + 1544 q^{36} + 568 q^{39} + 780 q^{42} + 208 q^{46} - 4048 q^{49} - 1448 q^{57} - 1760 q^{58} + 4156 q^{60} - 2152 q^{63} + 2764 q^{64} + 1968 q^{70} - 2740 q^{72} - 3620 q^{78} + 4992 q^{79} + 1568 q^{81} + 2484 q^{84} - 2072 q^{88}+O(q^{100}) \) 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

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Representations

Groups

Database

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