LMFDB - Embedded newform 168.4.t.a.115.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [168,4,Mod(19,168)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(168, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 0, 5])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("168.19"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 168 = 2^{3} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	168.t (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$9.91232088096$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$48$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			115.14
Character	$\chi$	$=$	168.115
Dual form			168.4.t.a.19.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.74973 + 2.22226i) q^{2} +(-2.59808 - 1.50000i) q^{3} +(-1.87689 - 7.77671i) q^{4} +(-5.68130 - 9.84030i) q^{5} +(7.87932 - 3.14901i) q^{6} +(1.38512 - 18.4684i) q^{7} +(20.5659 + 9.43622i) q^{8} +(4.50000 + 7.79423i) q^{9} +(31.8084 + 4.59254i) q^{10} +(-9.93039 + 17.1999i) q^{11} +(-6.78878 + 23.0198i) q^{12} -31.0152 q^{13} +(38.6180 + 35.3928i) q^{14} +34.0878i q^{15} +(-56.9546 + 29.1920i) q^{16} +(37.4442 + 21.6184i) q^{17} +(-25.1946 - 3.63762i) q^{18} +(-30.9280 + 17.8563i) q^{19} +(-65.8620 + 62.6510i) q^{20} +(-31.3012 + 45.9046i) q^{21} +(-20.8473 - 52.1632i) q^{22} +(-77.4445 + 44.7126i) q^{23} +(-39.2775 - 55.3649i) q^{24} +(-2.05428 + 3.55811i) q^{25} +(54.2682 - 68.9238i) q^{26} -27.0000i q^{27} +(-146.223 + 23.8914i) q^{28} +149.567i q^{29} +(-75.7519 - 59.6444i) q^{30} +(72.4769 - 125.534i) q^{31} +(34.7829 - 177.646i) q^{32} +(51.5998 - 29.7912i) q^{33} +(-113.559 + 45.3843i) q^{34} +(-189.604 + 91.2944i) q^{35} +(52.1675 - 49.6241i) q^{36} +(-255.281 + 147.387i) q^{37} +(14.4343 - 99.9739i) q^{38} +(80.5798 + 46.5228i) q^{39} +(-23.9860 - 255.985i) q^{40} +340.542i q^{41} +(-47.2433 - 149.880i) q^{42} -382.268 q^{43} +(152.397 + 44.9435i) q^{44} +(51.1317 - 88.5627i) q^{45} +(36.1439 - 250.337i) q^{46} +(46.6383 + 80.7798i) q^{47} +(191.760 + 9.58877i) q^{48} +(-339.163 - 51.1619i) q^{49} +(-4.31262 - 10.7909i) q^{50} +(-64.8552 - 112.333i) q^{51} +(58.2120 + 241.196i) q^{52} +(629.932 + 363.692i) q^{53} +(60.0010 + 47.2427i) q^{54} +225.670 q^{55} +(202.758 - 366.749i) q^{56} +107.138 q^{57} +(-332.376 - 261.701i) q^{58} +(-495.394 - 286.016i) q^{59} +(265.091 - 63.9789i) q^{60} +(7.77051 + 13.4589i) q^{61} +(152.153 + 380.712i) q^{62} +(150.180 - 72.3118i) q^{63} +(333.915 + 388.129i) q^{64} +(176.206 + 305.198i) q^{65} +(-24.0820 + 166.795i) q^{66} +(-55.2285 + 95.6585i) q^{67} +(97.8417 - 331.768i) q^{68} +268.276 q^{69} +(128.875 - 581.090i) q^{70} +518.920i q^{71} +(18.9986 + 202.759i) q^{72} +(948.097 + 547.384i) q^{73} +(119.142 - 825.189i) q^{74} +(10.6743 - 6.16283i) q^{75} +(196.912 + 207.004i) q^{76} +(303.901 + 207.222i) q^{77} +(-244.379 + 97.6670i) q^{78} +(-288.366 + 166.488i) q^{79} +(610.834 + 394.601i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(-756.773 - 595.856i) q^{82} -934.727i q^{83} +(415.736 + 157.263i) q^{84} -491.282i q^{85} +(668.867 - 849.500i) q^{86} +(224.350 - 388.586i) q^{87} +(-366.530 + 260.028i) q^{88} +(361.563 - 208.749i) q^{89} +(107.343 + 268.589i) q^{90} +(-42.9597 + 572.800i) q^{91} +(493.072 + 518.343i) q^{92} +(-376.601 + 217.431i) q^{93} +(-261.118 - 37.7005i) q^{94} +(351.423 + 202.894i) q^{95} +(-356.838 + 409.364i) q^{96} -477.327i q^{97} +(707.139 - 664.189i) q^{98} -178.747 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 2 q^{2} - 10 q^{4} - 16 q^{8} + 432 q^{9} + 18 q^{10} + 40 q^{11} + 274 q^{14} - 26 q^{16} - 18 q^{18} + 4 q^{22} + 270 q^{24} - 1200 q^{25} + 750 q^{26} + 922 q^{28} + 168 q^{30} - 108 q^{32} + 456 q^{35}+ \cdots + 720 q^{99}+O(q^{100}) $ 96 * q + 2 * q^2 - 10 * q^4 - 16 * q^8 + 432 * q^9 + 18 * q^10 + 40 * q^11 + 274 * q^14 - 26 * q^16 - 18 * q^18 + 4 * q^22 + 270 * q^24 - 1200 * q^25 + 750 * q^26 + 922 * q^28 + 168 * q^30 - 108 * q^32 + 456 * q^35 - 180 * q^36 - 1494 * q^38 + 1170 * q^40 - 564 * q^42 - 1616 * q^43 + 264 * q^44 + 808 * q^46 - 360 * q^49 - 1036 * q^50 - 3564 * q^52 + 176 * q^56 - 336 * q^57 - 394 * q^58 + 4128 * q^59 + 822 * q^60 - 2644 * q^64 + 2052 * q^66 - 1440 * q^67 - 1392 * q^68 + 3234 * q^70 - 72 * q^72 - 648 * q^73 + 850 * q^74 + 1692 * q^78 - 1548 * q^80 - 3888 * q^81 + 4596 * q^82 + 3120 * q^84 - 2522 * q^86 - 1454 * q^88 - 104 * q^91 + 5600 * q^92 - 2052 * q^94 + 3870 * q^96 + 852 * q^98 + 720 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/168\mathbb{Z}\right)^\times$.

$n$	$73$	$85$	$113$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$1$	$-1$

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 $

$2$	−1.74973	+	2.22226i	−0.618623	+	0.785688i
$2$	−1.74973	+	2.22226i	−0.618623	+	0.785688i
$3$	−2.59808	−	1.50000i	−0.500000	−	0.288675i
$3$	−2.59808	−	1.50000i	−0.500000	−	0.288675i
$4$	−1.87689	−	7.77671i	−0.234611	−	0.972089i
$5$	−5.68130	−	9.84030i	−0.508151	−	0.880143i	−0.999955	−	0.00943729i	$-0.996996\pi$
$5$	−5.68130	−	9.84030i	−0.508151	−	0.880143i	0.491805	−	0.870705i	$-0.336337\pi$
$6$	7.87932	−	3.14901i	0.536120	−	0.214263i
$7$	1.38512	−	18.4684i	0.0747894	−	0.997199i
$7$	1.38512	−	18.4684i	0.0747894	−	0.997199i
$8$	20.5659	+	9.43622i	0.908895	+	0.417026i
$9$	4.50000	+	7.79423i	0.166667	+	0.288675i
$10$	31.8084	+	4.59254i	1.00587	+	0.145229i
$11$	−9.93039	+	17.1999i	−0.272193	+	0.471453i	−0.969423	−	0.245395i	$-0.921082\pi$
$11$	−9.93039	+	17.1999i	−0.272193	+	0.471453i	0.697230	+	0.716848i	$0.254416\pi$
$12$	−6.78878	+	23.0198i	−0.163313	+	0.553771i
$13$	−31.0152			−0.661697			−0.330848	−	0.943684i	$-0.607335\pi$
$13$	−31.0152			−0.661697			−0.330848	+	0.943684i	$0.607335\pi$
$14$	38.6180	+	35.3928i	0.737221	+	0.675652i
$15$			34.0878i			0.586762i
$16$	−56.9546	+	29.1920i	−0.889915	+	0.456125i
$17$	37.4442	+	21.6184i	0.534209	+	0.308426i	0.742729	−	0.669593i	$-0.233531\pi$
$17$	37.4442	+	21.6184i	0.534209	+	0.308426i	−0.208520	+	0.978018i	$0.566865\pi$
$18$	−25.1946	−	3.63762i	−0.329912	−	0.0476331i
$19$	−30.9280	+	17.8563i	−0.373441	+	0.215606i	−0.674961	−	0.737854i	$-0.735839\pi$
$19$	−30.9280	+	17.8563i	−0.373441	+	0.215606i	0.301520	+	0.953460i	$0.402506\pi$
$20$	−65.8620	+	62.6510i	−0.736360	+	0.700459i
$21$	−31.3012	+	45.9046i	−0.325261	+	0.477010i
$22$	−20.8473	−	52.1632i	−0.202030	−	0.505510i
$23$	−77.4445	+	44.7126i	−0.702100	+	0.405357i	−0.808129	−	0.589006i	$-0.799520\pi$
$23$	−77.4445	+	44.7126i	−0.702100	+	0.405357i	0.106029	+	0.994363i	$0.466186\pi$
$24$	−39.2775	−	55.3649i	−0.334062	−	0.470888i
$25$	−2.05428	+	3.55811i	−0.0164342	+	0.0284649i
$26$	54.2682	−	68.9238i	0.409341	−	0.519887i
$27$		−	27.0000i		−	0.192450i
$28$	−146.223	+	23.8914i	−0.986913	+	0.161252i
$29$			149.567i			0.957718i	0.877892	+	0.478859i	$0.158950\pi$
$29$			149.567i			0.957718i	−0.877892	+	0.478859i	$0.841050\pi$
$30$	−75.7519	−	59.6444i	−0.461012	−	0.362984i
$31$	72.4769	−	125.534i	0.419911	−	0.727307i	−0.576019	−	0.817436i	$-0.695395\pi$
$31$	72.4769	−	125.534i	0.419911	−	0.727307i	0.995930	+	0.0901295i	$0.0287281\pi$
$32$	34.7829	−	177.646i	0.192150	−	0.981366i
$33$	51.5998	−	29.7912i	0.272193	−	0.157151i
$34$	−113.559	+	45.3843i	−0.572800	+	0.228922i
$35$	−189.604	+	91.2944i	−0.915682	+	0.440902i
$36$	52.1675	−	49.6241i	0.241516	−	0.229741i
$37$	−255.281	+	147.387i	−1.13427	+	0.654871i	−0.945005	−	0.327055i	$-0.893944\pi$
$37$	−255.281	+	147.387i	−1.13427	+	0.654871i	−0.189265	+	0.981926i	$0.560610\pi$
$38$	14.4343	−	99.9739i	0.0616200	−	0.426787i
$39$	80.5798	+	46.5228i	0.330848	+	0.191015i
$40$	−23.9860	−	255.985i	−0.0948129	−	1.01187i
$41$			340.542i			1.29716i	0.761145	+	0.648582i	$0.224638\pi$
$41$			340.542i			1.29716i	−0.761145	+	0.648582i	$0.775362\pi$
$42$	−47.2433	−	149.880i	−0.173567	−	0.550643i
$43$	−382.268			−1.35571			−0.677853	−	0.735197i	$-0.737090\pi$
$43$	−382.268			−1.35571			−0.677853	+	0.735197i	$0.737090\pi$
$44$	152.397	+	44.9435i	0.522154	+	0.153988i
$45$	51.1317	−	88.5627i	0.169384	−	0.293381i
$46$	36.1439	−	250.337i	0.115851	−	0.802395i
$47$	46.6383	+	80.7798i	0.144742	+	0.250701i	0.929277	−	0.369384i	$-0.120431\pi$
$47$	46.6383	+	80.7798i	0.144742	+	0.250701i	−0.784534	+	0.620085i	$0.787098\pi$
$48$	191.760	+	9.58877i	0.576630	+	0.0288337i
$49$	−339.163	−	51.1619i	−0.988813	−	0.149160i
$50$	−4.31262	−	10.7909i	−0.0121979	−	0.0305212i
$51$	−64.8552	−	112.333i	−0.178070	−	0.308426i
$52$	58.2120	+	241.196i	0.155241	+	0.643229i
$53$	629.932	+	363.692i	1.63260	+	0.942583i	0.983287	+	0.182062i	$0.0582772\pi$
$53$	629.932	+	363.692i	1.63260	+	0.942583i	0.649314	+	0.760520i	$0.275056\pi$
$54$	60.0010	+	47.2427i	0.151206	+	0.119054i
$55$	225.670			0.553261
$56$	202.758	−	366.749i	0.483834	−	0.875160i
$57$	107.138			0.248961
$58$	−332.376	−	261.701i	−0.752468	−	0.592467i
$59$	−495.394	−	286.016i	−1.09313	−	0.631121i	−0.158724	−	0.987323i	$-0.550738\pi$
$59$	−495.394	−	286.016i	−1.09313	−	0.631121i	−0.934409	+	0.356202i	$0.884071\pi$
$60$	265.091	−	63.9789i	0.570385	−	0.137661i
$61$	7.77051	+	13.4589i	0.0163100	+	0.0282498i	0.874065	−	0.485809i	$-0.161475\pi$
$61$	7.77051	+	13.4589i	0.0163100	+	0.0282498i	−0.857755	+	0.514058i	$0.828141\pi$
$62$	152.153	+	380.712i	0.311669	+	0.779847i
$63$	150.180	−	72.3118i	0.300332	−	0.144610i
$64$	333.915	+	388.129i	0.652179	+	0.758065i
$65$	176.206	+	305.198i	0.336242	+	0.582388i
$66$	−24.0820	+	166.795i	−0.0449135	+	0.311076i
$67$	−55.2285	+	95.6585i	−0.100705	+	0.174426i	−0.911975	−	0.410245i	$-0.865443\pi$
$67$	−55.2285	+	95.6585i	−0.100705	+	0.174426i	0.811270	+	0.584671i	$0.198776\pi$
$68$	97.8417	−	331.768i	0.174486	−	0.591659i
$69$	268.276			0.468066
$70$	128.875	−	581.090i	0.220051	−	0.992193i
$71$			518.920i			0.867387i	0.901060	+	0.433693i	$0.142790\pi$
$71$			518.920i			0.867387i	−0.901060	+	0.433693i	$0.857210\pi$
$72$	18.9986	+	202.759i	0.0310974	+	0.331880i
$73$	948.097	+	547.384i	1.52009	+	0.877623i	0.999720	+	0.0236803i	$0.00753837\pi$
$73$	948.097	+	547.384i	1.52009	+	0.877623i	0.520368	+	0.853942i	$0.325795\pi$
$74$	119.142	−	825.189i	0.187161	−	1.29630i
$75$	10.6743	−	6.16283i	0.0164342	−	0.00948829i
$76$	196.912	+	207.004i	0.297202	+	0.312434i
$77$	303.901	+	207.222i	0.449775	+	0.306691i
$78$	−244.379	+	97.6670i	−0.354749	+	0.141777i
$79$	−288.366	+	166.488i	−0.410680	+	0.237106i	−0.691082	−	0.722777i	$-0.742866\pi$
$79$	−288.366	+	166.488i	−0.410680	+	0.237106i	0.280402	+	0.959883i	$0.409532\pi$
$80$	610.834	+	394.601i	0.853667	+	0.551472i
$81$	−40.5000	+	70.1481i	−0.0555556	+	0.0962250i
$82$	−756.773	−	595.856i	−1.01917	−	0.802455i
$83$		−	934.727i		−	1.23614i	−0.786123	−	0.618070i	$-0.787915\pi$
$83$		−	934.727i		−	1.23614i	0.786123	−	0.618070i	$-0.212085\pi$
$84$	415.736	+	157.263i	0.540006	+	0.204271i
$85$		−	491.282i		−	0.626907i
$86$	668.867	−	849.500i	0.838671	−	1.06516i
$87$	224.350	−	388.586i	0.276469	−	0.478859i
$88$	−366.530	+	260.028i	−0.444003	+	0.314989i
$89$	361.563	−	208.749i	0.430625	−	0.248621i	−0.268988	−	0.963144i	$-0.586689\pi$
$89$	361.563	−	208.749i	0.430625	−	0.248621i	0.699613	+	0.714522i	$0.253356\pi$
$90$	107.343	+	268.589i	0.125721	+	0.314575i
$91$	−42.9597	+	572.800i	−0.0494879	+	0.659844i
$92$	493.072	+	518.343i	0.558764	+	0.587402i
$93$	−376.601	+	217.431i	−0.419911	+	0.242436i
$94$	−261.118	−	37.7005i	−0.286514	−	0.0413672i
$95$	351.423	+	202.894i	0.379528	+	0.219121i
$96$	−356.838	+	409.364i	−0.379371	+	0.435214i
$97$		−	477.327i		−	0.499642i	−0.968292	−	0.249821i	$-0.919628\pi$
$97$		−	477.327i		−	0.499642i	0.968292	−	0.249821i	$-0.0803717\pi$
$98$	707.139	−	664.189i	0.728896	−	0.684625i
$99$	−178.747			−0.181462
$100$	31.5260	+	9.29735i	0.0315260	+	0.00929735i
$101$	−330.374	+	572.225i	−0.325480	+	0.563748i	−0.981609	−	0.190901i	$-0.938859\pi$
$101$	−330.374	+	572.225i	−0.325480	+	0.563748i	0.656129	+	0.754648i	$0.272193\pi$
$102$	363.111	+	52.4264i	0.352484	+	0.0508921i
$103$	−452.718	−	784.131i	−0.433084	−	0.750124i	0.564053	−	0.825739i	$-0.309241\pi$
$103$	−452.718	−	784.131i	−0.433084	−	0.750124i	−0.997137	+	0.0756149i	$0.975908\pi$
$104$	−637.856	−	292.666i	−0.601413	−	0.275945i
$105$	629.546	+	47.2157i	0.585119	+	0.0438836i
$106$	−1910.43	+	763.512i	−1.75054	+	0.699611i
$107$	−680.592	−	1178.82i	−0.614909	−	1.06505i	−0.990400	−	0.138228i	$-0.955859\pi$
$107$	−680.592	−	1178.82i	−0.614909	−	1.06505i	0.375491	−	0.926826i	$-0.377474\pi$
$108$	−209.971	+	50.6759i	−0.187079	+	0.0451509i
$109$	−841.623	−	485.911i	−0.739568	−	0.426990i	0.0823444	−	0.996604i	$-0.473759\pi$
$109$	−841.623	−	485.911i	−0.739568	−	0.426990i	−0.821912	+	0.569614i	$0.807093\pi$
$110$	−394.862	+	501.498i	−0.342260	+	0.434690i
$111$	884.320			0.756180
$112$	460.241	+	1092.29i	0.388292	+	0.921537i
$113$	−1694.16			−1.41038			−0.705189	−	0.709019i	$-0.749138\pi$
$113$	−1694.16			−1.41038			−0.705189	+	0.709019i	$0.749138\pi$
$114$	−187.462	+	238.088i	−0.154013	+	0.195605i
$115$	879.970	+	508.051i	0.713545	+	0.411965i
$116$	1163.14	−	280.720i	0.930988	−	0.224691i
$117$	−139.568	−	241.739i	−0.110283	−	0.191015i
$118$	1502.41	−	600.445i	1.17210	−	0.468436i
$119$	451.122	−	661.590i	0.347515	−	0.509646i
$120$	−321.660	+	701.047i	−0.244695	+	0.533305i
$121$	468.275	+	811.075i	0.351822	+	0.609373i
$122$	−43.5055	−	6.28138i	−0.0322853	−	0.00466139i
$123$	510.813	−	884.754i	0.374459	−	0.648582i
$124$	−1112.27	−	328.020i	−0.805523	−	0.237557i
$125$	−1373.64			−0.982897
$126$	−102.079	+	460.265i	−0.0721737	+	0.325426i
$127$		−	627.533i		−	0.438461i	−0.975673	−	0.219231i	$-0.929645\pi$
$127$		−	627.533i		−	0.438461i	0.975673	−	0.219231i	$-0.0703547\pi$
$128$	−1446.79	+	62.9252i	−0.999056	+	0.0434520i
$129$	993.162	+	573.403i	0.677853	+	0.391359i
$130$	−986.544	−	142.438i	−0.665582	−	0.0960975i
$131$	−1540.25	+	889.263i	−1.02727	+	0.593094i	−0.916201	−	0.400719i	$-0.868760\pi$
$131$	−1540.25	+	889.263i	−1.02727	+	0.593094i	−0.111067	+	0.993813i	$0.535427\pi$
$132$	−328.525	−	345.363i	−0.216624	−	0.227727i
$133$	286.938	+	595.924i	0.187073	+	0.388520i
$134$	−115.943	−	290.109i	−0.0747460	−	0.187027i
$135$	−265.688	+	153.395i	−0.169384	+	0.0977936i
$136$	566.078	+	797.934i	0.356918	+	0.503105i
$137$	486.966	−	843.450i	0.303681	−	0.525991i	−0.673286	−	0.739382i	$-0.735118\pi$
$137$	486.966	−	843.450i	0.303681	−	0.525991i	0.976967	+	0.213391i	$0.0684509\pi$
$138$	−469.410	+	596.178i	−0.289557	+	0.367754i
$139$		−	2556.40i		−	1.55994i	−0.625819	−	0.779969i	$-0.715235\pi$
$139$		−	2556.40i		−	1.55994i	0.625819	−	0.779969i	$-0.284765\pi$
$140$	1065.84	+	1303.14i	0.643425	+	0.786684i
$141$		−	279.830i		−	0.167134i
$142$	−1153.18	−	907.970i	−0.681495	−	0.536586i
$143$	307.993	−	533.459i	0.180109	−	0.311959i
$144$	−483.825	−	312.553i	−0.279991	−	0.180876i
$145$	1471.78	−	849.733i	0.842929	−	0.486665i
$146$	−2875.34	+	1149.14i	−1.62990	+	0.651396i
$147$	804.428	+	641.667i	0.451348	+	0.360026i
$148$	1625.32	+	1708.62i	0.902705	+	0.948972i
$149$	−2474.68	+	1428.76i	−1.36063	+	0.785559i	−0.989707	−	0.143105i	$-0.954291\pi$
$149$	−2474.68	+	1428.76i	−1.36063	+	0.785559i	−0.370921	+	0.928664i	$0.620958\pi$
$150$	−4.98179	+	34.5044i	−0.00271174	+	0.0187818i
$151$	−2143.73	−	1237.68i	−1.15532	−	0.667027i	−0.205145	−	0.978732i	$-0.565767\pi$
$151$	−2143.73	−	1237.68i	−1.15532	−	0.667027i	−0.950179	+	0.311705i	$0.899100\pi$
$152$	−804.560	+	75.3879i	−0.429332	+	0.0402287i
$153$			389.131i			0.205617i
$154$	−992.246	+	312.763i	−0.519204	+	0.163657i
$155$	−1647.05			−0.853511
$156$	210.555	−	713.964i	0.108063	−	0.366429i
$157$	1225.00	−	2121.76i	0.622709	−	1.07856i	−0.366270	−	0.930509i	$-0.619365\pi$
$157$	1225.00	−	2121.76i	0.622709	−	1.07856i	0.988979	−	0.148056i	$-0.0473015\pi$
$158$	134.583	−	932.134i	0.0677646	−	0.469345i
$159$	−1091.07	−	1889.80i	−0.544200	−	0.942583i
$160$	−1945.70	+	666.987i	−0.961383	+	0.329562i
$161$	718.500	+	1492.21i	0.351713	+	0.730450i
$162$	−85.0232	−	212.742i	−0.0412349	−	0.103176i
$163$	1608.40	+	2785.83i	0.772882	+	1.33867i	0.935977	+	0.352061i	$0.114519\pi$
$163$	1608.40	+	2785.83i	0.772882	+	1.33867i	−0.163095	+	0.986610i	$0.552148\pi$
$164$	2648.30	−	639.159i	1.26096	−	0.304329i
$165$	−586.308	−	338.505i	−0.276630	−	0.159713i
$166$	2077.21	+	1635.52i	0.971220	+	0.764705i
$167$	882.107			0.408739			0.204370	−	0.978894i	$-0.434486\pi$
$167$	882.107			0.408739			0.204370	+	0.978894i	$0.434486\pi$
$168$	−1076.91	+	648.706i	−0.494554	+	0.297909i
$169$	−1235.06			−0.562157
$170$	1091.76	+	859.612i	0.492553	+	0.387819i
$171$	−278.352	−	160.707i	−0.124480	−	0.0718687i
$172$	717.474	+	2972.79i	0.318063	+	1.31787i
$173$	584.827	+	1012.95i	0.257015	+	0.445163i	0.965441	−	0.260622i	$-0.0839277\pi$
$173$	584.827	+	1012.95i	0.257015	+	0.445163i	−0.708426	+	0.705785i	$0.750594\pi$
$174$	470.987	+	1178.48i	0.205203	+	0.513452i
$175$	62.8671	+	42.8676i	0.0271561	+	0.0185170i
$176$	63.4802	−	1269.50i	0.0271875	−	0.543707i
$177$	858.048	+	1486.18i	0.364378	+	0.631121i
$178$	−168.744	+	1168.74i	−0.0710557	+	0.492140i
$179$	216.382	−	374.785i	0.0903528	−	0.156496i	−0.817307	−	0.576203i	$-0.804534\pi$
$179$	216.382	−	374.785i	0.0903528	−	0.156496i	0.907660	+	0.419707i	$0.137867\pi$
$180$	−784.695	−	231.414i	−0.324932	−	0.0958256i
$181$	698.293			0.286761			0.143380	−	0.989668i	$-0.454203\pi$
$181$	698.293			0.286761			0.143380	+	0.989668i	$0.454203\pi$
$182$	−1197.74	−	1097.71i	−0.487817	−	0.447077i
$183$		−	46.6231i		−	0.0188332i
$184$	−2014.64	+	188.773i	−0.807179	+	0.0756333i
$185$	2900.66	+	1674.70i	1.15276	+	0.665546i
$186$	175.762	−	1217.35i	0.0692878	−	0.479895i
$187$	−743.671	+	429.359i	−0.290816	+	0.167903i
$188$	540.667	−	514.307i	0.209746	−	0.199520i
$189$	−498.647	−	37.3982i	−0.191911	−	0.0143932i
$190$	−1065.78	+	425.943i	−0.406946	+	0.162638i
$191$	−2801.97	+	1617.72i	−1.06148	+	0.612848i	−0.925842	−	0.377910i	$-0.876643\pi$
$191$	−2801.97	+	1617.72i	−1.06148	+	0.612848i	−0.135642	+	0.990758i	$0.543310\pi$
$192$	−285.343	−	1509.26i	−0.107255	−	0.567300i
$193$	1731.02	−	2998.21i	0.645603	−	1.11822i	−0.338559	−	0.940945i	$-0.609940\pi$
$193$	1731.02	−	2998.21i	0.645603	−	1.11822i	0.984162	−	0.177271i	$-0.0567270\pi$
$194$	1060.75	+	835.194i	0.392562	+	0.309090i
$195$		−	1057.24i		−	0.388259i
$196$	238.699	+	2733.60i	0.0869895	+	0.996209i
$197$		−	2199.91i		−	0.795618i	−0.917468	−	0.397809i	$-0.869771\pi$
$197$		−	2199.91i		−	0.795618i	0.917468	−	0.397809i	$-0.130229\pi$
$198$	312.759	−	397.223i	0.112257	−	0.142573i
$199$	−1592.88	+	2758.94i	−0.567417	+	0.982795i	0.429404	+	0.903113i	$0.358724\pi$
$199$	−1592.88	+	2758.94i	−0.567417	+	0.982795i	−0.996820	+	0.0796820i	$0.974610\pi$
$200$	−75.8232	+	53.7913i	−0.0268076	+	0.0190181i
$201$	286.975	−	165.685i	0.100705	−	0.0581420i
$202$	−693.567	−	1735.42i	−0.241580	−	0.604473i
$203$	2762.26	+	207.168i	0.955036	+	0.0716272i
$204$	−751.852	+	715.196i	−0.258040	+	0.245459i
$205$	3351.03	−	1934.72i	1.14169	−	0.659154i
$206$	2534.68	+	365.960i	0.857279	+	0.123775i
$207$	−697.000	−	402.413i	−0.234033	−	0.135119i
$208$	1766.46	−	905.396i	0.588854	−	0.301817i
$209$		−	709.280i		−	0.234746i
$210$	−1206.46	+	1316.40i	−0.396447	+	0.432573i
$211$	683.474			0.222997			0.111498	−	0.993765i	$-0.464435\pi$
$211$	683.474			0.222997			0.111498	+	0.993765i	$0.464435\pi$
$212$	1646.01	−	5581.41i	0.533249	−	1.80817i
$213$	778.380	−	1348.19i	0.250393	−	0.433693i
$214$	3810.50	+	550.164i	1.21720	+	0.175740i
$215$	2171.78	+	3761.63i	0.688903	+	1.19322i
$216$	254.778	−	555.280i	0.0802567	−	0.174917i
$217$	−2218.01	−	1512.41i	−0.693865	−	0.473129i
$218$	2552.44	−	1020.09i	0.792994	−	0.316924i
$219$	−1642.15	−	2844.29i	−0.506696	−	0.877623i
$220$	−423.557	−	1754.97i	−0.129801	−	0.537819i
$221$	−1161.34	−	670.499i	−0.353484	−	0.204084i
$222$	−1547.32	+	1965.19i	−0.467790	+	0.594121i
$223$	4932.98			1.48133			0.740665	−	0.671874i	$-0.234510\pi$
$223$	4932.98			1.48133			0.740665	+	0.671874i	$0.234510\pi$
$224$	−3232.66	−	888.445i	−0.964246	−	0.265008i
$225$	−36.9770			−0.0109561
$226$	2964.32	−	3764.86i	0.872493	−	1.10812i
$227$	−2717.56	−	1568.98i	−0.794584	−	0.458753i	0.0469897	−	0.998895i	$-0.485037\pi$
$227$	−2717.56	−	1568.98i	−0.794584	−	0.458753i	−0.841574	+	0.540142i	$0.818371\pi$
$228$	−201.086	−	833.180i	−0.0584088	−	0.242012i
$229$	2141.45	+	3709.10i	0.617952	+	1.07032i	0.989859	+	0.142054i	$0.0453706\pi$
$229$	2141.45	+	3709.10i	0.617952	+	1.07032i	−0.371907	+	0.928270i	$0.621296\pi$
$230$	−2668.73	+	1066.57i	−0.765091	+	0.305772i
$231$	−478.723	−	994.230i	−0.136354	−	0.283184i
$232$	−1411.34	+	3075.98i	−0.399394	+	0.870465i
$233$	−150.884	−	261.339i	−0.0424238	−	0.0734802i	0.844034	−	0.536290i	$-0.180175\pi$
$233$	−150.884	−	261.339i	−0.0424238	−	0.0734802i	−0.886458	+	0.462810i	$0.846841\pi$
$234$	781.415	+	112.822i	0.218302	+	0.0315187i
$235$	529.932	−	917.868i	0.147102	−	0.254788i
$236$	−1294.47	+	4389.36i	−0.357045	+	1.21069i
$237$	998.929			0.273787
$238$	680.883	+	2160.11i	0.185442	+	0.588317i
$239$		−	3412.31i		−	0.923530i	−0.887002	−	0.461765i	$-0.847216\pi$
$239$		−	3412.31i		−	0.923530i	0.887002	−	0.461765i	$-0.152784\pi$
$240$	−995.092	−	1941.46i	−0.267637	−	0.522168i
$241$	−3873.71	−	2236.49i	−1.03538	−	0.597779i	−0.116861	−	0.993148i	$-0.537283\pi$
$241$	−3873.71	−	2236.49i	−1.03538	−	0.597779i	−0.918522	+	0.395369i	$0.870617\pi$
$242$	−2621.78	−	378.535i	−0.696422	−	0.100550i
$243$	210.444	−	121.500i	0.0555556	−	0.0320750i
$244$	90.0818	−	85.6899i	0.0236348	−	0.0224825i
$245$	1423.44	+	3628.13i	0.371184	+	0.946092i
$246$	1072.37	+	2683.24i	0.277934	+	0.695435i
$247$	959.238	−	553.816i	0.247105	−	0.142666i
$248$	2675.12	−	1897.81i	0.684960	−	0.485931i
$249$	−1402.09	+	2428.49i	−0.356843	+	0.618070i
$250$	2403.50	−	3052.59i	0.608043	−	0.772250i
$251$			2427.14i			0.610358i	0.952295	+	0.305179i	$0.0987164\pi$
$251$			2427.14i			0.610358i	−0.952295	+	0.305179i	$0.901284\pi$
$252$	−844.219	−	1032.19i	−0.211035	−	0.258022i
$253$		−	1776.05i		−	0.441342i
$254$	1394.54	+	1098.01i	0.344493	+	0.271242i
$255$	−736.924	+	1276.39i	−0.180972	+	0.313453i
$256$	2391.65	−	3325.24i	0.583899	−	0.811826i
$257$	−5476.85	+	3162.06i	−1.32932	+	0.767486i	−0.985195	−	0.171436i	$-0.945159\pi$
$257$	−5476.85	+	3162.06i	−1.32932	+	0.767486i	−0.344129	+	0.938922i	$0.611826\pi$
$258$	−3012.02	+	1203.77i	−0.726821	+	0.290477i
$259$	2368.40	+	4918.78i	0.568206	+	1.18007i
$260$	2042.72	−	1943.13i	0.487247	−	0.463492i
$261$	−1165.76	+	673.050i	−0.276469	+	0.159620i
$262$	718.846	−	4978.80i	0.169505	−	1.17401i
$263$	−1779.35	−	1027.31i	−0.417184	−	0.240862i	0.276688	−	0.960960i	$-0.410763\pi$
$263$	−1779.35	−	1027.31i	−0.417184	−	0.240862i	−0.693872	+	0.720098i	$0.744097\pi$
$264$	1342.32	−	125.776i	0.312931	−	0.0293219i
$265$		−	8264.96i		−	1.91590i
$266$	−1826.36	−	405.055i	−0.420983	−	0.0933666i
$267$	−1252.49			−0.287083
$268$	847.566	+	249.956i	0.193184	+	0.0569719i
$269$	61.4698	−	106.469i	0.0139326	−	0.0241320i	−0.858975	−	0.512017i	$-0.828898\pi$
$269$	61.4698	−	106.469i	0.0139326	−	0.0241320i	0.872908	+	0.487885i	$0.162232\pi$
$270$	123.999	−	858.828i	0.0279493	−	0.193580i
$271$	−206.365	−	357.435i	−0.0462576	−	0.0801204i	0.841970	−	0.539525i	$-0.181396\pi$
$271$	−206.365	−	357.435i	−0.0462576	−	0.0801204i	−0.888227	+	0.459405i	$0.848063\pi$
$272$	−2763.70	−	138.196i	−0.616081	−	0.0308065i
$273$	970.813	−	1423.74i	0.215224	−	0.315636i
$274$	1022.31	+	2557.98i	0.225401	+	0.563989i
$275$	−40.7995	−	70.6669i	−0.00894656	−	0.0154959i
$276$	−503.523	−	2086.30i	−0.109813	−	0.455002i
$277$	−1971.50	−	1138.25i	−0.427639	−	0.246897i	0.270701	−	0.962663i	$-0.412744\pi$
$277$	−1971.50	−	1138.25i	−0.427639	−	0.246897i	−0.698340	+	0.715766i	$0.746078\pi$
$278$	5680.99	+	4473.02i	1.22562	+	0.965013i
$279$	1304.58			0.279940
$280$	−4760.85	+	88.4127i	−1.01613	+	0.0188703i
$281$	−7937.53			−1.68510			−0.842551	−	0.538617i	$-0.818947\pi$
$281$	−7937.53			−1.68510			−0.842551	+	0.538617i	$0.818947\pi$
$282$	621.854	+	489.626i	0.131315	+	0.103393i
$283$	6710.48	+	3874.30i	1.40953	+	0.813792i	0.995343	−	0.0963997i	$-0.0307327\pi$
$283$	6710.48	+	3874.30i	1.40953	+	0.813792i	0.414187	+	0.910192i	$0.364066\pi$
$284$	4035.49	−	973.954i	0.843178	−	0.203498i
$285$	−608.682	−	1054.27i	−0.126509	−	0.219121i
$286$	646.581	+	1617.85i	0.133682	+	0.334495i
$287$	6289.26	+	471.691i	1.29353	+	0.0970141i
$288$	1541.14	−	528.302i	0.315321	−	0.108092i
$289$	−1521.79	−	2635.82i	−0.309747	−	0.536498i
$290$	−686.891	+	4757.48i	−0.139088	+	0.963341i
$291$	−715.991	+	1240.13i	−0.144234	+	0.249821i
$292$	2477.38	−	8400.46i	0.496499	−	1.68356i
$293$	−1805.31			−0.359957			−0.179978	−	0.983671i	$-0.557603\pi$
$293$	−1805.31			−0.359957			−0.179978	+	0.983671i	$0.557603\pi$
$294$	−2833.48	+	664.906i	−0.562082	+	0.131898i
$295$			6499.77i			1.28282i
$296$	−6640.87	+	622.255i	−1.30403	+	0.122189i
$297$	464.399	+	268.121i	0.0907311	+	0.0523836i
$298$	1154.95	−	7999.32i	0.224512	−	1.55499i
$299$	2401.95	−	1386.77i	0.464577	−	0.268224i
$300$	−67.9611	−	71.4443i	−0.0130791	−	0.0137495i
$301$	−529.487	+	7059.88i	−0.101393	+	1.35191i
$302$	6501.39	−	2598.31i	1.23878	−	0.495086i
$303$	1716.67	−	991.123i	0.325480	−	0.187916i
$304$	1240.23	−	1919.85i	0.233987	−	0.362207i
$305$	88.2932	−	152.928i	0.0165759	−	0.0287103i
$306$	−864.751	−	680.875i	−0.161551	−	0.127199i
$307$			5699.24i			1.05952i	0.848148	+	0.529760i	$0.177718\pi$
$307$			5699.24i			1.05952i	−0.848148	+	0.529760i	$0.822282\pi$
$308$	1041.12	−	2752.28i	0.192609	−	0.509174i
$309$			2716.31i			0.500082i
$310$	2881.89	−	3660.18i	0.528002	−	0.670594i
$311$	−2294.28	+	3973.81i	−0.418317	+	0.724546i	−0.995770	−	0.0918773i	$-0.970713\pi$
$311$	−2294.28	+	3973.81i	−0.418317	+	0.724546i	0.577453	+	0.816424i	$0.304047\pi$
$312$	1218.20	+	1717.15i	0.221048	+	0.311585i
$313$	−5418.90	+	3128.61i	−0.978577	+	0.564982i	−0.901840	−	0.432070i	$-0.857783\pi$
$313$	−5418.90	+	3128.61i	−0.978577	+	0.564982i	−0.0767366	+	0.997051i	$0.524450\pi$
$314$	2571.68	+	6434.76i	0.462193	+	1.15648i
$315$	−1564.79	−	1066.99i	−0.279891	−	0.190851i
$316$	1835.96	+	1930.06i	0.326838	+	0.343590i
$317$	5675.91	−	3276.99i	1.00565	−	0.580612i	0.0957345	−	0.995407i	$-0.469480\pi$
$317$	5675.91	−	3276.99i	1.00565	−	0.580612i	0.909915	+	0.414795i	$0.136147\pi$
$318$	6108.71	+	881.982i	1.07723	+	0.155532i
$319$	−2572.54	−	1485.26i	−0.451519	−	0.260685i
$320$	1922.24	−	5490.91i	0.335801	−	0.959222i
$321$			4083.55i			0.710036i
$322$	−4573.26	−	1014.27i	−0.791483	−	0.175537i
$323$	−1544.10			−0.265994
$324$	621.535	+	183.297i	0.106573	+	0.0314295i
$325$	63.7137	−	110.355i	0.0108745	−	0.0188351i
$326$	−9005.12	−	1300.17i	−1.52990	−	0.220889i
$327$	1457.73	+	2524.87i	0.246523	+	0.426990i
$328$	−3213.43	+	7003.56i	−0.540951	+	1.17898i
$329$	1556.47	−	749.444i	0.260824	−	0.125587i
$330$	1778.13	−	710.637i	0.296614	−	0.118543i
$331$	5624.81	+	9742.45i	0.934040	+	1.61781i	0.776336	+	0.630319i	$0.217076\pi$
$331$	5624.81	+	9742.45i	0.934040	+	1.61781i	0.157704	+	0.987486i	$0.449591\pi$
$332$	−7269.11	+	1754.38i	−1.20164	+	0.290012i
$333$	−2297.53	−	1326.48i	−0.378090	−	0.218290i
$334$	−1543.45	+	1960.27i	−0.252856	+	0.321141i
$335$	1255.08			0.204693
$336$	442.700	−	3528.22i	0.0718788	−	0.572858i
$337$	−4766.06			−0.770397			−0.385199	−	0.922834i	$-0.625867\pi$
$337$	−4766.06			−0.770397			−0.385199	+	0.922834i	$0.625867\pi$
$338$	2161.02	−	2744.62i	0.347763	−	0.441680i
$339$	4401.55	+	2541.23i	0.705189	+	0.407141i
$340$	−3820.56	+	922.081i	−0.609409	+	0.147079i
$341$	1439.45	+	2493.20i	0.228594	+	0.395936i
$342$	844.174	−	337.378i	0.133473	−	0.0533430i
$343$	−1414.66	+	6192.93i	−0.222695	+	0.974888i
$344$	−7861.71	−	3607.17i	−1.23219	−	0.565365i
$345$	−1524.15	−	2639.91i	−0.237848	−	0.411965i
$346$	−3274.33	−	472.751i	−0.508754	−	0.0734546i
$347$	−2363.60	+	4093.87i	−0.365662	+	0.633344i	−0.988882	−	0.148702i	$-0.952491\pi$
$347$	−2363.60	+	4093.87i	−0.365662	+	0.633344i	0.623221	+	0.782046i	$0.285824\pi$
$348$	−3443.00	−	1015.37i	−0.530357	−	0.156407i
$349$	3269.10			0.501407			0.250703	−	0.968064i	$-0.419338\pi$
$349$	3269.10			0.501407			0.250703	+	0.968064i	$0.419338\pi$
$350$	−205.263	+	64.7005i	−0.0313480	+	0.00988111i
$351$			837.410i			0.127344i
$352$	2710.10	+	2362.36i	0.410365	+	0.357711i
$353$	5356.02	+	3092.30i	0.807571	+	0.466251i	0.846112	−	0.533006i	$-0.178938\pi$
$353$	5356.02	+	3092.30i	0.807571	+	0.466251i	−0.0385409	+	0.999257i	$0.512271\pi$
$354$	−4804.04	−	693.613i	−0.721276	−	0.104139i
$355$	5106.33	−	2948.14i	0.763424	−	0.440763i
$356$	−2301.99	−	2419.98i	−0.342711	−	0.360277i
$357$	−2164.43	+	1042.18i	−0.320879	+	0.154504i
$358$	454.259	+	1136.63i	0.0670624	+	0.167801i
$359$	−10170.1	+	5871.73i	−1.49515	+	0.863226i	−0.999984	−	0.00557116i	$-0.998227\pi$
$359$	−10170.1	+	5871.73i	−1.49515	+	0.863226i	−0.495167	+	0.868798i	$0.664893\pi$
$360$	1887.27	−	1338.88i	0.276299	−	0.196015i
$361$	−2791.80	+	4835.55i	−0.407028	+	0.704993i
$362$	−1221.82	+	1551.79i	−0.177397	+	0.225305i
$363$		−	2809.65i		−	0.406249i
$364$	4535.14	−	740.996i	0.653038	−	0.106700i
$365$		−	12439.4i		−	1.78386i
$366$	103.609	+	81.5778i	0.0147970	+	0.0116507i
$367$	−1562.19	+	2705.80i	−0.222196	+	0.384855i	−0.955474	−	0.295074i	$-0.904656\pi$
$367$	−1562.19	+	2705.80i	−0.222196	+	0.384855i	0.733279	+	0.679928i	$0.237989\pi$
$368$	3105.57	−	4807.35i	0.439916	−	0.680979i
$369$	−2654.26	+	1532.44i	−0.374459	+	0.216194i
$370$	−8796.98	+	3515.75i	−1.23604	+	0.493987i
$371$	7589.33	−	11130.1i	1.06204	−	1.55753i
$372$	2397.73	+	2520.62i	0.334185	+	0.351313i
$373$	5214.58	−	3010.64i	0.723862	−	0.417922i	−0.0923105	−	0.995730i	$-0.529425\pi$
$373$	5214.58	−	3010.64i	0.723862	−	0.417922i	0.816172	+	0.577808i	$0.196092\pi$
$374$	347.077	−	2403.89i	0.0479864	−	0.332359i
$375$	3568.82	+	2060.46i	0.491449	+	0.283738i
$376$	196.903	+	2101.40i	0.0270066	+	0.288222i
$377$		−	4638.84i		−	0.633719i
$378$	955.606	−	1042.69i	0.130029	−	0.141878i
$379$	−11131.0			−1.50860			−0.754300	−	0.656530i	$-0.772024\pi$
$379$	−11131.0			−1.50860			−0.754300	+	0.656530i	$0.772024\pi$
$380$	918.268	−	3113.72i	0.123964	−	0.420344i
$381$	−941.299	+	1630.38i	−0.126573	+	0.219231i
$382$	1307.70	−	9057.28i	0.175151	−	1.21312i
$383$	−7412.83	−	12839.4i	−0.988977	−	1.71296i	−0.622722	−	0.782443i	$-0.713973\pi$
$383$	−7412.83	−	12839.4i	−0.988977	−	1.71296i	−0.366254	−	0.930515i	$-0.619360\pi$
$384$	3853.25	+	2006.70i	0.512071	+	0.266676i
$385$	312.580	−	4167.76i	0.0413781	−	0.551711i
$386$	3633.99	+	9092.83i	0.479184	+	1.19900i
$387$	−1720.21	−	2979.49i	−0.225951	−	0.391359i
$388$	−3712.04	+	895.889i	−0.485696	+	0.117221i
$389$	1408.72	+	813.323i	0.183611	+	0.106008i	0.588988	−	0.808142i	$-0.299526\pi$
$389$	1408.72	+	813.323i	0.183611	+	0.106008i	−0.405377	+	0.914150i	$0.632860\pi$
$390$	2349.46	+	1849.88i	0.305050	+	0.240186i
$391$	−3866.46			−0.500090
$392$	−6492.43	−	4252.61i	−0.836523	−	0.547931i
$393$	5335.58			0.684845
$394$	4888.77	+	3849.24i	0.625108	+	0.492188i
$395$	3276.59	+	1891.74i	0.417374	+	0.240971i
$396$	335.488	+	1390.07i	0.0425730	+	0.176397i
$397$	−4545.33	−	7872.74i	−0.574618	−	0.995268i	−0.996083	−	0.0884234i	$-0.971817\pi$
$397$	−4545.33	−	7872.74i	−0.574618	−	0.995268i	0.421465	−	0.906845i	$-0.361516\pi$
$398$	−3343.98	−	8367.19i	−0.421153	−	1.05379i
$399$	148.399	−	1978.66i	0.0186196	−	0.248263i
$400$	13.1320	−	262.619i	0.00164150	−	0.0328274i
$401$	2090.65	+	3621.11i	0.260354	+	0.450947i	0.966336	−	0.257283i	$-0.0828273\pi$
$401$	2090.65	+	3621.11i	0.260354	+	0.450947i	−0.705982	+	0.708230i	$0.749494\pi$
$402$	−133.934	+	927.639i	−0.0166169	+	0.115091i
$403$	−2247.88	+	3893.45i	−0.277854	+	0.481257i
$404$	5070.11	+	1495.22i	0.624374	+	0.184134i
$405$	920.370			0.112922
$406$	−5293.58	+	5775.97i	−0.647084	+	0.706050i
$407$		−	5854.43i		−	0.713006i
$408$	−273.813	−	2922.21i	−0.0332250	−	0.354586i
$409$	−10120.3	−	5842.94i	−1.22351	−	0.706393i	−0.257845	−	0.966186i	$-0.583012\pi$
$409$	−10120.3	−	5842.94i	−1.22351	−	0.706393i	−0.965664	+	0.259793i	$0.916346\pi$
$410$	−1563.95	+	10832.1i	−0.188386	+	1.30478i
$411$	−2530.35	+	1460.90i	−0.303681	+	0.175330i
$412$	−5248.26	+	4992.39i	−0.627581	+	0.596984i
$413$	−5968.44	+	8752.97i	−0.711108	+	1.04287i
$414$	2113.83	−	844.802i	0.250940	−	0.100289i
$415$	−9197.99	+	5310.46i	−1.08798	+	0.628146i
$416$	−1078.80	+	5509.73i	−0.127145	+	0.649367i
$417$	−3834.60	+	6641.73i	−0.450315	+	0.779969i
$418$	1576.21	+	1241.05i	0.184437	+	0.145219i
$419$		−	6630.39i		−	0.773068i	−0.922275	−	0.386534i	$-0.873672\pi$
$419$		−	6630.39i		−	0.773068i	0.922275	−	0.386534i	$-0.126328\pi$
$420$	−814.405	−	4984.42i	−0.0946164	−	0.579083i
$421$		−	8062.94i		−	0.933406i	−0.884414	−	0.466703i	$-0.845442\pi$
$421$		−	8062.94i		−	0.933406i	0.884414	−	0.466703i	$-0.154558\pi$
$422$	−1195.89	+	1518.86i	−0.137951	+	0.175206i
$423$	−419.744	+	727.018i	−0.0482474	+	0.0835670i
$424$	9523.27	+	13423.8i	1.09078	+	1.53755i
$425$	−153.841	+	88.8203i	−0.0175586	+	0.0101375i
$426$	1634.08	+	4088.74i	0.185849	+	0.465024i
$427$	259.328	−	124.867i	0.0293905	−	0.0141516i
$428$	−7889.95	+	7505.28i	−0.891063	+	0.847620i
$429$	−1600.38	+	923.978i	−0.180109	+	0.103986i
$430$	−12159.4	−	1755.58i	−1.36367	−	0.196888i
$431$	11197.4	+	6464.82i	1.25141	+	0.722505i	0.971390	−	0.237488i	$-0.0763242\pi$
$431$	11197.4	+	6464.82i	1.25141	+	0.722505i	0.280024	+	0.959993i	$0.409657\pi$
$432$	788.185	+	1537.77i	0.0877814	+	0.171264i
$433$		−	15425.1i		−	1.71197i	−0.516999	−	0.855986i	$-0.672951\pi$
$433$		−	15425.1i		−	1.71197i	0.516999	−	0.855986i	$-0.327049\pi$
$434$	7241.90	−	2282.70i	0.800973	−	0.252472i
$435$	−5098.40			−0.561953
$436$	−2199.16	+	7457.06i	−0.241561	+	0.819102i
$437$	1596.80	−	2765.74i	0.174795	−	0.302754i
$438$	9194.08	+	1327.45i	1.00299	+	0.144813i
$439$	−7687.49	−	13315.1i	−0.835772	−	1.44760i	−0.893400	−	0.449262i	$-0.851687\pi$
$439$	−7687.49	−	13315.1i	−0.835772	−	1.44760i	0.0576279	−	0.998338i	$-0.481646\pi$
$440$	4641.12	+	2129.47i	0.502856	+	0.230724i
$441$	−1127.47	−	2873.74i	−0.121743	−	0.310306i
$442$	3522.05	−	1407.60i	0.379020	−	0.151477i
$443$	2141.57	+	3709.31i	0.229682	+	0.397820i	0.957714	−	0.287723i	$-0.0928981\pi$
$443$	2141.57	+	3709.31i	0.229682	+	0.397820i	−0.728032	+	0.685543i	$0.759565\pi$
$444$	−1659.77	−	6877.11i	−0.177408	−	0.735074i
$445$	−4108.29	−	2371.92i	−0.437645	−	0.252674i
$446$	−8631.38	+	10962.4i	−0.916385	+	1.16386i
$447$	8572.54			0.907086
$448$	7630.64	−	5629.27i	0.804718	−	0.593657i
$449$	14674.6			1.54240			0.771201	−	0.636592i	$-0.219656\pi$
$449$	14674.6			1.54240			0.771201	+	0.636592i	$0.219656\pi$
$450$	64.6997	−	82.1724i	0.00677772	−	0.00860810i
$451$	−5857.30	−	3381.71i	−0.611551	−	0.353079i
$452$	3179.74	+	13175.0i	0.330890	+	1.37101i
$453$	3713.04	+	6431.18i	0.385108	+	0.667027i
$454$	8241.68	−	3293.83i	0.851985	−	0.340500i
$455$	5880.59	−	2831.51i	0.605904	−	0.291744i
$456$	2203.39	+	1010.98i	0.226279	+	0.103823i
$457$	8662.00	+	15003.0i	0.886633	+	1.53569i	0.843831	+	0.536609i	$0.180295\pi$
$457$	8662.00	+	15003.0i	0.886633	+	1.53569i	0.0428020	+	0.999084i	$0.486372\pi$
$458$	−11989.5	−	1731.06i	−1.22322	−	0.176610i
$459$	583.697	−	1010.99i	0.0593565	−	0.102809i
$460$	2299.36	−	7796.83i	0.233062	−	0.790281i
$461$	6377.83			0.644349			0.322175	−	0.946680i	$-0.395586\pi$
$461$	6377.83			0.644349			0.322175	+	0.946680i	$0.395586\pi$
$462$	3047.08	+	675.787i	0.306846	+	0.0680529i
$463$		−	7592.70i		−	0.762123i	−0.924550	−	0.381061i	$-0.875559\pi$
$463$		−	7592.70i		−	0.762123i	0.924550	−	0.381061i	$-0.124441\pi$
$464$	−4366.15	−	8518.51i	−0.436840	−	0.852288i
$465$	4279.16	+	2470.58i	0.426756	+	0.246388i
$466$	844.770	+	121.969i	0.0839768	+	0.0121247i
$467$	4571.40	−	2639.30i	0.452975	−	0.261525i	−0.256111	−	0.966647i	$-0.582441\pi$
$467$	4571.40	−	2639.30i	0.452975	−	0.261525i	0.709086	+	0.705122i	$0.249108\pi$
$468$	−1617.98	+	1539.10i	−0.159811	+	0.152019i
$469$	1690.16	+	1152.48i	0.166406	+	0.113468i
$470$	1112.51	+	2783.67i	0.109183	+	0.273194i
$471$	−6365.27	+	3674.99i	−0.622709	+	0.359521i
$472$	−7489.34	−	10556.8i	−0.730349	−	1.02949i
$473$	3796.07	−	6574.99i	0.369014	−	0.639151i
$474$	−1747.86	+	2219.88i	−0.169371	+	0.215111i
$475$		−	146.727i		−	0.0141733i
$476$	−5991.70	−	2266.52i	−0.576952	−	0.218247i
$477$			6546.45i			0.628388i
$478$	7583.03	+	5970.62i	0.725607	+	0.571317i
$479$	7795.95	−	13503.0i	0.743645	−	1.28803i	−0.207180	−	0.978303i	$-0.566429\pi$
$479$	7795.95	−	13503.0i	0.743645	−	1.28803i	0.950825	−	0.309728i	$-0.100238\pi$
$480$	6055.56	+	1185.67i	0.575828	+	0.112746i
$481$	7917.59	−	4571.22i	0.750543	−	0.433326i
$482$	11748.0	−	4695.14i	1.11018	−	0.443688i
$483$	371.594	−	4954.62i	0.0350064	−	0.466756i
$484$	5428.60	−	5163.93i	0.509824	−	0.484968i
$485$	−4697.04	+	2711.84i	−0.439756	+	0.253893i
$486$	−98.2159	+	680.254i	−0.00916700	+	0.0634917i
$487$	9084.27	+	5244.80i	0.845272	+	0.488018i	0.859053	−	0.511887i	$-0.171053\pi$
$487$	9084.27	+	5244.80i	0.845272	+	0.488018i	−0.0137808	+	0.999905i	$0.504387\pi$
$488$	32.8065	+	350.120i	0.00304320	+	0.0324778i
$489$		−	9650.41i		−	0.892447i
$490$	−10553.3	−	3185.00i	−0.972956	−	0.293640i
$491$	7949.83			0.730694			0.365347	−	0.930871i	$-0.380950\pi$
$491$	7949.83			0.730694			0.365347	+	0.930871i	$0.380950\pi$
$492$	−7839.22	−	2311.86i	−0.718332	−	0.211843i
$493$	−3233.39	+	5600.40i	−0.295385	+	0.511621i
$494$	−447.684	+	3100.71i	−0.0407738	+	0.282404i
$495$	1015.52	+	1758.92i	0.0922101	+	0.159713i
$496$	−463.309	+	9265.46i	−0.0419419	+	0.838773i
$497$	9583.62	+	718.766i	0.864958	+	0.0648714i
$498$	−2943.46	−	7365.02i	−0.264859	−	0.662720i
$499$	−2422.80	−	4196.41i	−0.217353	−	0.376467i	0.736645	−	0.676280i	$-0.236409\pi$
$499$	−2422.80	−	4196.41i	−0.217353	−	0.376467i	−0.953998	+	0.299813i	$0.903076\pi$
$500$	2578.17	+	10682.4i	0.230598	+	0.955464i
$501$	−2291.78	−	1323.16i	−0.204370	−	0.117993i
$502$	−5393.75	−	4246.85i	−0.479551	−	0.377582i
$503$	−546.557			−0.0484488			−0.0242244	−	0.999707i	$-0.507712\pi$
$503$	−546.557			−0.0484488			−0.0242244	+	0.999707i	$0.507712\pi$
$504$	3770.94	−	70.0293i	0.333276	−	0.00618919i
$505$	7507.82			0.661571
$506$	3946.86	+	3107.62i	0.346757	+	0.273025i
$507$	3208.78	+	1852.59i	0.281079	+	0.162281i
$508$	−4880.15	+	1177.81i	−0.426223	+	0.102868i
$509$	−1123.03	−	1945.14i	−0.0977944	−	0.169385i	0.812977	−	0.582296i	$-0.197845\pi$
$509$	−1123.03	−	1945.14i	−0.0977944	−	0.169385i	−0.910771	+	0.412911i	$0.864512\pi$
$510$	−1547.05	−	3870.97i	−0.134323	−	0.336097i
$511$	11422.5	−	16751.6i	0.988851	−	1.45019i
$512$	3204.81	+	11133.1i	0.276628	+	0.960977i
$513$	482.120	+	835.057i	0.0414934	+	0.0718687i
$514$	2556.09	−	17703.7i	0.219347	−	1.51922i
$515$	−5144.05	+	8909.76i	−0.440144	+	0.762352i
$516$	2595.13	−	8799.75i	0.221404	−	0.750751i
$517$	−1852.54			−0.157592
$518$	−15074.9	−	3343.34i	−1.27867	−	0.283587i
$519$		−	3508.96i		−	0.296775i
$520$	743.929	+	7939.41i	0.0627374	+	0.669551i
$521$	6742.95	+	3893.04i	0.567013	+	0.327365i	0.755956	−	0.654623i	$-0.227173\pi$
$521$	6742.95	+	3893.04i	0.567013	+	0.327365i	−0.188942	+	0.981988i	$0.560506\pi$
$522$	544.067	−	3768.27i	0.0456191	−	0.315963i
$523$	10196.9	−	5887.21i	0.852545	−	0.492217i	−0.00896379	−	0.999960i	$-0.502853\pi$
$523$	10196.9	−	5887.21i	0.852545	−	0.492217i	0.861509	+	0.507743i	$0.169520\pi$
$524$	9806.42	+	10309.0i	0.817548	+	0.859450i
$525$	−99.0323	−	205.674i	−0.00823261	−	0.0170978i
$526$	5396.33	−	2156.67i	0.447322	−	0.178774i
$527$	5427.67	−	3133.67i	0.448640	−	0.259022i
$528$	−2069.18	+	3203.05i	−0.170549	+	0.264005i
$529$	−2085.07	+	3611.44i	−0.171371	+	0.296823i
$530$	18366.9	+	14461.5i	1.50530	+	1.18522i
$531$		−	5148.29i		−	0.420747i
$532$	4095.78	−	3349.92i	0.333787	−	0.273003i
$533$		−	10562.0i		−	0.858329i
$534$	2191.52	−	2783.36i	0.177596	−	0.225558i
$535$	−7733.29	+	13394.4i	−0.624933	+	1.08242i
$536$	−2038.48	+	1446.16i	−0.164270	+	0.116538i
$537$	−1124.35	+	649.146i	−0.0903528	+	0.0521652i
$538$	129.046	+	322.894i	0.0103412	+	0.0258754i
$539$	4248.00	−	5325.53i	0.339470	−	0.425578i
$540$	1691.58	+	1778.27i	0.134803	+	0.141713i
$541$	−5410.37	+	3123.68i	−0.429963	+	0.248239i	−0.699331	−	0.714798i	$-0.746519\pi$
$541$	−5410.37	+	3123.68i	−0.429963	+	0.248239i	0.269368	+	0.963037i	$0.413185\pi$
$542$	1155.40	+	166.818i	0.0915657	+	0.0132204i
$543$	−1814.22	−	1047.44i	−0.143380	−	0.0827807i
$544$	5142.84	−	5899.86i	0.405326	−	0.464990i
$545$			11042.4i			0.867900i
$546$	1465.26	+	4648.56i	0.114849	+	0.364359i
$547$	−3021.26			−0.236160			−0.118080	−	0.993004i	$-0.537674\pi$
$547$	−3021.26			−0.236160			−0.118080	+	0.993004i	$0.537674\pi$
$548$	−7473.25	−	2203.94i	−0.582557	−	0.171802i
$549$	−69.9346	+	121.130i	−0.00543668	+	0.00941660i
$550$	228.428	+	32.9807i	0.0177095	+	0.00255692i
$551$	−2670.71	−	4625.80i	−0.206490	−	0.357651i
$552$	5517.34	+	2531.51i	0.425423	+	0.195196i
$553$	2675.35	+	5556.26i	0.205728	+	0.427263i
$554$	5979.07	−	2389.56i	0.458532	−	0.183254i
$555$	−5024.09	−	8701.97i	−0.384253	−	0.665546i
$556$	−19880.4	+	4798.08i	−1.51640	+	0.365978i
$557$	−5016.95	−	2896.54i	−0.381643	−	0.220342i	0.296890	−	0.954912i	$-0.404051\pi$
$557$	−5016.95	−	2896.54i	−0.381643	−	0.220342i	−0.678533	+	0.734570i	$0.737384\pi$
$558$	−2282.67	+	2899.12i	−0.173178	+	0.219946i
$559$	11856.1			0.897067
$560$	8133.73	−	10734.6i	0.613773	−	0.810032i
$561$	2576.15			0.193877
$562$	13888.5	−	17639.3i	1.04244	−	1.32396i
$563$	−20719.3	−	11962.3i	−1.55100	−	0.895470i	−0.998061	−	0.0622488i	$-0.980173\pi$
$563$	−20719.3	−	11962.3i	−1.55100	−	0.895470i	−0.552939	−	0.833221i	$-0.686494\pi$
$564$	−2176.15	+	525.208i	−0.162469	+	0.0392115i
$565$	9625.01	+	16671.0i	0.716685	+	1.24133i
$566$	−20351.2	+	8133.47i	−1.51135	+	0.604020i
$567$	1239.42	+	845.133i	0.0918006	+	0.0625966i
$568$	−4896.64	+	10672.1i	−0.361723	+	0.788363i
$569$	4267.57	+	7391.65i	0.314422	+	0.544594i	0.979314	−	0.202345i	$-0.0648561\pi$
$569$	4267.57	+	7391.65i	0.314422	+	0.544594i	−0.664893	+	0.746939i	$0.731523\pi$
$570$	3407.89	+	492.035i	0.250422	+	0.0361563i
$571$	−4647.94	+	8050.46i	−0.340648	+	0.590020i	−0.984553	−	0.175086i	$-0.943980\pi$
$571$	−4647.94	+	8050.46i	−0.340648	+	0.590020i	0.643905	+	0.765105i	$0.277313\pi$
$572$	−4726.63	−	1393.93i	−0.345507	−	0.101894i
$573$	9706.31			0.707656
$574$	−12052.7	+	13151.0i	−0.876431	+	0.956296i
$575$		−	367.408i		−	0.0266469i
$576$	−1522.55	+	4349.20i	−0.110138	+	0.314612i
$577$	−8890.70	−	5133.05i	−0.641464	−	0.370349i	0.143714	−	0.989619i	$-0.454095\pi$
$577$	−8890.70	−	5133.05i	−0.641464	−	0.370349i	−0.785178	+	0.619270i	$0.787429\pi$
$578$	8520.19	+	1230.16i	0.613137	+	0.0885254i
$579$	−8994.63	+	5193.05i	−0.645603	+	0.372739i
$580$	−9370.49	−	9850.76i	−0.670842	−	0.705225i
$581$	−17262.9	−	1294.71i	−1.23268	−	0.0924502i
$582$	−1503.11	−	3761.02i	−0.107055	−	0.267868i
$583$	−12510.9	+	7223.20i	−0.888766	+	0.513129i
$584$	14333.3	+	20203.9i	1.01561	+	1.43158i
$585$	−1585.86	+	2746.79i	−0.112081	+	0.194129i
$586$	3158.81	−	4011.87i	0.222678	−	0.282814i
$587$			9195.89i			0.646601i	0.946296	+	0.323301i	$0.104792\pi$
$587$			9195.89i			0.646601i	−0.946296	+	0.323301i	$0.895208\pi$
$588$	3480.24	−	7460.15i	0.244086	−	0.523216i
$589$			5176.68i			0.362141i
$590$	−14444.2	−	11372.8i	−1.00789	−	0.793581i
$591$	−3299.86	+	5715.52i	−0.229675	+	0.397809i
$592$	10236.9	−	15846.5i	0.710701	−	1.10015i
$593$	−12551.0	+	7246.30i	−0.869150	+	0.501804i	−0.867066	−	0.498194i	$-0.833997\pi$
$593$	−12551.0	+	7246.30i	−0.869150	+	0.501804i	−0.00208435	+	0.999998i	$0.500663\pi$
$594$	−1408.41	+	562.876i	−0.0972855	+	0.0388806i
$595$	−9073.19	−	680.485i	−0.625151	−	0.0468860i
$596$	15755.7	+	16563.3i	1.08285	+	1.13835i
$597$	8276.82	−	4778.63i	0.567417	−	0.327598i
$598$	−1121.01	+	7764.24i	−0.0766580	+	0.530942i
$599$	8877.36	+	5125.35i	0.605541	+	0.349609i	0.771218	−	0.636571i	$-0.219648\pi$
$599$	8877.36	+	5125.35i	0.605541	+	0.349609i	−0.165677	+	0.986180i	$0.552981\pi$
$600$	277.681	−	26.0190i	0.0188938	−	0.00177037i
$601$			7735.54i			0.525024i	0.964929	+	0.262512i	$0.0845509\pi$
$601$			7735.54i			0.525024i	−0.964929	+	0.262512i	$0.915449\pi$
$602$	−14762.4	−	13529.5i	−0.999455	−	0.915985i
$603$	−994.112			−0.0671366
$604$	−5601.56	+	18994.1i	−0.377358	+	1.27957i
$605$	5320.81	−	9215.92i	0.357557	−	0.619307i
$606$	−801.185	+	5549.10i	−0.0537061	+	0.371975i
$607$	−11358.6	−	19673.6i	−0.759523	−	1.31553i	−0.943094	−	0.332525i	$-0.892099\pi$
$607$	−11358.6	−	19673.6i	−0.759523	−	1.31553i	0.183572	−	0.983006i	$-0.441234\pi$
$608$	2096.34	+	6115.34i	0.139832	+	0.407911i
$609$	−6865.80	−	4681.62i	−0.456841	−	0.311509i
$610$	185.357	+	463.794i	0.0123031	+	0.0307844i
$611$	−1446.49	−	2505.40i	−0.0957755	−	0.165888i
$612$	3026.16	−	730.355i	0.199878	−	0.0482400i
$613$	−11301.1	−	6524.70i	−0.744613	−	0.429902i	0.0791312	−	0.996864i	$-0.474785\pi$
$613$	−11301.1	−	6524.70i	−0.744613	−	0.429902i	−0.823744	+	0.566962i	$0.808119\pi$
$614$	−12665.2	−	9972.13i	−0.832452	−	0.655444i
$615$	−11608.3			−0.761126
$616$	4294.60	+	7129.39i	0.280900	+	0.466317i
$617$	3941.58			0.257183			0.128592	−	0.991698i	$-0.458954\pi$
$617$	3941.58			0.257183			0.128592	+	0.991698i	$0.458954\pi$
$618$	−6036.35	−	4752.81i	−0.392909	−	0.309363i
$619$	−11457.4	−	6614.93i	−0.743960	−	0.429526i	0.0795473	−	0.996831i	$-0.474653\pi$
$619$	−11457.4	−	6614.93i	−0.743960	−	0.429526i	−0.823507	+	0.567306i	$0.807986\pi$
$620$	3091.33	+	12808.6i	0.200243	+	0.829689i
$621$	1207.24	+	2091.00i	0.0780111	+	0.135119i
$622$	−4816.47	−	12051.6i	−0.310487	−	0.776888i
$623$	−3354.44	−	6966.63i	−0.215719	−	0.448013i
$624$	−5947.48	−	297.397i	−0.381554	−	0.0190792i
$625$	8060.84	+	13961.8i	0.515894	+	0.893555i
$626$	2529.04	−	17516.4i	0.161471	−	1.11837i
$627$	−1063.92	+	1842.76i	−0.0677654	+	0.117373i
$628$	−18799.5	−	5544.15i	−1.19456	−	0.352286i
$629$	−12745.1			−0.807916
$630$	5109.08	−	1610.42i	0.323096	−	0.101842i
$631$			20182.5i			1.27330i	0.771154	+	0.636649i	$0.219680\pi$
$631$			20182.5i			1.27330i	−0.771154	+	0.636649i	$0.780320\pi$
$632$	−7501.53	+	702.900i	−0.472144	+	0.0442403i
$633$	−1775.72	−	1025.21i	−0.111498	−	0.0643736i
$634$	−2648.99	+	18347.2i	−0.165938	+	1.14931i
$635$	−6175.11	+	3565.20i	−0.385908	+	0.222804i
$636$	−12648.6	+	12031.9i	−0.788599	+	0.750151i
$637$	10519.2	+	1586.79i	0.654295	+	0.0986987i
$638$	7801.87	−	3118.05i	0.484137	−	0.193487i
$639$	−4044.58	+	2335.14i	−0.250393	+	0.144564i
$640$	8838.83	+	13879.3i	0.545915	+	0.857231i
$641$	8885.98	−	15391.0i	0.547543	−	0.948373i	−0.450899	−	0.892575i	$-0.648896\pi$
$641$	8885.98	−	15391.0i	0.547543	−	0.948373i	0.998442	−	0.0557977i	$-0.0177702\pi$
$642$	−9074.71	−	7145.11i	−0.557867	−	0.439245i
$643$		−	7636.64i		−	0.468366i	−0.972192	−	0.234183i	$-0.924758\pi$
$643$		−	7636.64i		−	0.468366i	0.972192	−	0.234183i	$-0.0752416\pi$
$644$	10255.9	−	8388.27i	0.627547	−	0.513267i
$645$		−	13030.7i		−	0.795477i
$646$	2701.76	−	3431.39i	0.164550	−	0.208988i
$647$	−2958.17	+	5123.70i	−0.179749	+	0.311335i	−0.941795	−	0.336189i	$-0.890862\pi$
$647$	−2958.17	+	5123.70i	−0.179749	+	0.311335i	0.762045	+	0.647524i	$0.224195\pi$
$648$	−1494.85	+	1060.49i	−0.0906225	+	0.0642903i
$649$	9838.92	−	5680.50i	0.595087	−	0.343574i
$650$	133.757	+	334.681i	0.00807133	+	0.0201958i
$651$	3493.96	+	7256.38i	0.210352	+	0.436866i
$652$	18645.8	−	17736.8i	1.11998	−	1.06538i
$653$	16261.3	−	9388.47i	0.974509	−	0.562633i	0.0739010	−	0.997266i	$-0.476455\pi$
$653$	16261.3	−	9388.47i	0.974509	−	0.562633i	0.900608	+	0.434633i	$0.143122\pi$
$654$	−8161.56	−	1178.38i	−0.487985	−	0.0704559i
$655$	17501.2	+	10104.3i	1.04401	+	0.602762i
$656$	−9941.11	−	19395.4i	−0.591669	−	1.15437i
$657$			9852.91i			0.585082i
$658$	−1057.95	+	4770.21i	−0.0626795	+	0.282617i
$659$	−1477.88			−0.0873594			−0.0436797	−	0.999046i	$-0.513908\pi$
$659$	−1477.88			−0.0873594			−0.0436797	+	0.999046i	$0.513908\pi$
$660$	−1532.02	+	5194.89i	−0.0903545	+	0.306380i
$661$	−12988.8	+	22497.3i	−0.764307	+	1.32382i	0.176305	+	0.984336i	$0.443586\pi$
$661$	−12988.8	+	22497.3i	−0.764307	+	1.32382i	−0.940612	+	0.339484i	$0.889748\pi$
$662$	−31492.2	−	4546.88i	−1.84891	−	0.266948i
$663$	2011.50	+	3484.01i	0.117828	+	0.204084i
$664$	8820.29	−	19223.5i	0.515503	−	1.12352i
$665$	4233.89	−	6209.18i	0.246892	−	0.362078i
$666$	6967.85	−	2784.73i	0.405403	−	0.162021i
$667$	−6687.51	−	11583.1i	−0.388218	−	0.672414i
$668$	−1655.61	−	6859.89i	−0.0958947	−	0.397331i
$669$	−12816.3	−	7399.47i	−0.740665	−	0.427623i
$670$	−2196.05	+	2789.11i	−0.126628	+	0.160825i
$671$	−308.657			−0.0177579
$672$	7066.03	+	7157.24i	0.405622	+	0.410858i
$673$	3291.08			0.188502			0.0942509	−	0.995548i	$-0.469954\pi$
$673$	3291.08			0.188502			0.0942509	+	0.995548i	$0.469954\pi$
$674$	8339.32	−	10591.4i	0.476585	−	0.605292i
$675$	96.0690	+	55.4654i	0.00547807	+	0.00316276i
$676$	2318.07	+	9604.70i	0.131888	+	0.546467i
$677$	9665.86	+	16741.8i	0.548728	+	0.950425i	0.998362	+	0.0572123i	$0.0182212\pi$
$677$	9665.86	+	16741.8i	0.548728	+	0.950425i	−0.449634	+	0.893213i	$0.648445\pi$
$678$	−13348.8	+	5334.91i	−0.756132	+	0.302192i
$679$	−8815.46	−	661.155i	−0.498242	−	0.0373679i
$680$	4635.85	−	10103.7i	0.261436	−	0.569792i
$681$	4706.95	+	8152.67i	0.264861	+	0.458753i
$682$	−8059.18	−	1163.59i	−0.452495	−	0.0653318i
$683$	1480.32	−	2563.99i	0.0829325	−	0.143643i	−0.821576	−	0.570099i	$-0.806905\pi$
$683$	1480.32	−	2563.99i	0.0829325	−	0.143643i	0.904508	+	0.426456i	$0.140238\pi$
$684$	−727.335	+	2466.29i	−0.0406584	+	0.137867i
$685$	−11066.4			−0.617263
$686$	−11287.0	−	13979.7i	−0.628194	−	0.778057i
$687$		−	12848.7i		−	0.713549i
$688$	21771.9	−	11159.2i	1.20646	−	0.618372i
$689$	−19537.5	−	11280.0i	−1.08029	−	0.623704i
$690$	8533.43	+	1232.07i	0.470815	+	0.0679768i
$691$	19776.3	−	11417.8i	1.08875	−	0.628589i	0.155506	−	0.987835i	$-0.450299\pi$
$691$	19776.3	−	11417.8i	1.08875	−	0.628589i	0.933243	+	0.359246i	$0.116966\pi$
$692$	6779.77	−	6449.23i	0.372440	−	0.354282i
$693$	−247.586	+	3301.17i	−0.0135715	+	0.180954i
$694$	−4961.99	−	12415.7i	−0.271404	−	0.679097i
$695$	−25155.8	+	14523.7i	−1.37297	+	0.792683i
$696$	8280.75	−	5874.61i	0.450978	−	0.319938i
$697$	−7361.97	+	12751.3i	−0.400078	+	0.692956i
$698$	−5720.05	+	7264.80i	−0.310182	+	0.393949i
$699$			905.304i			0.0489868i
$700$	215.374	−	569.357i	0.0116291	−	0.0307424i
$701$			34253.9i			1.84558i	0.385300	+	0.922791i	$0.374098\pi$
$701$			34253.9i			1.84558i	−0.385300	+	0.922791i	$0.625902\pi$
$702$	−1860.94	−	1465.24i	−0.100052	−	0.0787777i
$703$	5263.56	−	9116.76i	0.282388	−	0.489111i
$704$	−9991.72	+	1889.05i	−0.534911	+	0.101131i
$705$	−2753.60	+	1589.79i	−0.147102	+	0.0849293i
$706$	−16243.5	+	6491.79i	−0.865910	+	0.346065i
$707$	10110.5	+	6894.08i	0.537826	+	0.366731i
$708$	9947.16	−	9462.19i	0.528019	−	0.502275i
$709$	20019.3	−	11558.2i	1.06042	−	0.612237i	0.134875	−	0.990863i	$-0.456937\pi$
$709$	20019.3	−	11558.2i	1.06042	−	0.612237i	0.925550	+	0.378626i	$0.123603\pi$
$710$	−2383.16	+	16506.0i	−0.125970	+	0.872480i
$711$	−2595.29	−	1498.39i	−0.136893	−	0.0790354i
$712$	9405.68	−	881.319i	0.495074	−	0.0463888i
$713$			12962.5i			0.680856i
$714$	1471.18	−	6633.47i	0.0771116	−	0.347691i
$715$	−6999.20			−0.366091
$716$	−3320.72	−	979.313i	−0.173325	−	0.0511154i
$717$	−5118.46	+	8865.43i	−0.266600	+	0.461765i
$718$	4746.48	−	32874.7i	0.246709	−	1.70873i
$719$	−5504.81	−	9534.61i	−0.285528	−	0.494550i	0.687209	−	0.726460i	$-0.258836\pi$
$719$	−5504.81	−	9534.61i	−0.285528	−	0.494550i	−0.972737	+	0.231910i	$0.925502\pi$
$720$	−326.860	+	6536.69i	−0.0169185	+	0.338344i
$721$	−15108.7	+	7274.86i	−0.780413	+	0.375770i
$722$	−5860.94	−	14665.0i	−0.302108	−	0.755922i
$723$	6709.46	+	11621.1i	0.345128	+	0.597779i
$724$	−1310.62	−	5430.43i	−0.0672772	−	0.278757i
$725$	−532.175	−	307.251i	−0.0272613	−	0.0157393i
$726$	6243.77	+	4916.13i	0.319185	+	0.251315i
$727$	31122.9			1.58774			0.793869	−	0.608089i	$-0.208064\pi$
$727$	31122.9			1.58774			0.793869	+	0.608089i	$0.208064\pi$
$728$	−6288.58	+	11374.8i	−0.320151	+	0.579091i
$729$	−729.000			−0.0370370
$730$	27643.6	+	21765.6i	1.40156	+	1.10354i
$731$	−14313.7	−	8264.03i	−0.724230	−	0.418134i
$732$	−362.574	+	87.5062i	−0.0183076	+	0.00441847i
$733$	15353.3	+	26592.7i	0.773653	+	1.34001i	0.935549	+	0.353198i	$0.114906\pi$
$733$	15353.3	+	26592.7i	0.773653	+	1.34001i	−0.161896	+	0.986808i	$0.551761\pi$
$734$	−3279.57	−	8206.02i	−0.164920	−	0.412657i
$735$	1743.99	−	11561.3i	0.0875214	−	0.580198i
$736$	5249.28	+	15312.9i	0.262895	+	0.766906i
$737$	−1096.88	−	1899.85i	−0.0548224	−	0.0949552i
$738$	1238.76	−	8579.81i	0.0617880	−	0.427950i
$739$	−2219.89	+	3844.96i	−0.110501	+	0.191393i	−0.915972	−	0.401242i	$-0.868579\pi$
$739$	−2219.89	+	3844.96i	−0.110501	+	0.191393i	0.805472	+	0.592634i	$0.201912\pi$
$740$	7579.42	−	25700.8i	0.376520	−	1.27673i
$741$	−3322.90			−0.164736
$742$	11454.7	+	36340.1i	0.566730	+	1.79796i
$743$			20548.4i			1.01460i	0.861770	+	0.507299i	$0.169356\pi$
$743$			20548.4i			1.01460i	−0.861770	+	0.507299i	$0.830644\pi$
$744$	−9796.87	+	917.974i	−0.482756	+	0.0452346i
$745$	28118.8	+	16234.4i	1.38281	+	0.798365i
$746$	−2433.68	+	16856.0i	−0.119442	+	0.827266i
$747$	7285.48	−	4206.27i	0.356843	−	0.206023i
$748$	4734.78	+	4977.46i	0.231445	+	0.243307i
$749$	−22713.6	+	10936.6i	−1.10806	+	0.533532i
$750$	−10823.4	+	4325.60i	−0.526951	+	0.210598i
$751$	18835.5	−	10874.7i	0.915205	−	0.528394i	0.0331028	−	0.999452i	$-0.489461\pi$
$751$	18835.5	−	10874.7i	0.915205	−	0.528394i	0.882102	+	0.471058i	$0.156128\pi$
$752$	−5014.39	−	3239.32i	−0.243160	−	0.157082i
$753$	3640.72	−	6305.90i	0.176195	−	0.305179i
$754$	10308.7	+	8116.71i	0.497906	+	0.392033i
$755$			28126.5i			1.35580i
$756$	645.068	+	3948.02i	0.0310329	+	0.189932i
$757$		−	29296.1i		−	1.40658i	−0.710901	−	0.703292i	$-0.751713\pi$
$757$		−	29296.1i		−	1.40658i	0.710901	−	0.703292i	$-0.248287\pi$
$758$	19476.2	−	24735.9i	0.933255	−	1.18529i
$759$	−2664.08	+	4614.33i	−0.127405	+	0.220671i
$760$	5312.78	+	7488.81i	0.253572	+	0.357431i
$761$	−24098.1	+	13913.1i	−1.14791	+	0.662744i	−0.948376	−	0.317148i	$-0.897275\pi$
$761$	−24098.1	+	13913.1i	−1.14791	+	0.662744i	−0.199530	+	0.979892i	$0.563942\pi$
$762$	−1976.11	−	4944.54i	−0.0939459	−	0.235068i
$763$	−10139.8	+	14870.4i	−0.481106	+	0.705562i
$764$	17839.5	+	18753.9i	0.844779	+	0.888077i
$765$	3829.17	−	2210.77i	0.180972	−	0.104484i
$766$	41503.0	+	5992.25i	1.95765	+	0.282648i
$767$	15364.7	+	8870.84i	0.723323	+	0.417611i
$768$	−11201.6	+	5051.75i	−0.526304	+	0.237356i
$769$			3210.87i			0.150568i	0.997162	+	0.0752840i	$0.0239863\pi$
$769$			3210.87i			0.150568i	−0.997162	+	0.0752840i	$0.976014\pi$
$770$	8714.93	+	7987.10i	0.407875	+	0.373812i
$771$	18972.4			0.886216
$772$	−26565.1	−	7834.32i	−1.23847	−	0.365238i
$773$	4752.28	−	8231.20i	0.221123	−	0.382996i	−0.734027	−	0.679121i	$-0.762361\pi$
$773$	4752.28	−	8231.20i	0.221123	−	0.382996i	0.955149	+	0.296125i	$0.0956946\pi$
$774$	9631.10	+	1390.55i	0.447264	+	0.0645765i
$775$	297.775	+	515.761i	0.0138018	+	0.0239054i
$776$	4504.16	−	9816.68i	0.208364	−	0.454121i
$777$	1224.89	−	16332.0i	0.0565543	−	0.754062i
$778$	−4272.29	+	1707.44i	−0.196875	+	0.0786821i
$779$	−6080.82	−	10532.3i	−0.279676	−	0.484414i
$780$	−8221.84	+	1984.32i	−0.377422	+	0.0910897i
$781$	−8925.40	−	5153.08i	−0.408932	−	0.236097i
$782$	6765.26	−	8592.28i	0.309367	−	0.392915i
$783$	4038.30			0.184313
$784$	20810.4	−	6986.95i	0.947996	−	0.318283i
$785$	−27838.3			−1.26572
$786$	−9335.82	+	11857.0i	−0.423661	+	0.538075i
$787$	−4458.68	−	2574.22i	−0.201950	−	0.116596i	0.395615	−	0.918417i	$-0.370532\pi$
$787$	−4458.68	−	2574.22i	−0.201950	−	0.116596i	−0.597565	+	0.801821i	$0.703865\pi$
$788$	−17108.0	+	4128.98i	−0.773412	+	0.186661i
$789$	3081.93	+	5338.05i	0.139061	+	0.240862i
$790$	−9937.07	+	3971.40i	−0.447526	+	0.178856i
$791$	−2346.61	+	31288.3i	−0.105481	+	1.40643i
$792$	−3676.10	−	1686.70i	−0.164930	−	0.0756745i
$793$	−241.004	−	417.431i	−0.0107923	−	0.0186928i
$794$	25448.4	+	3674.27i	1.13744	+	0.164225i
$795$	−12397.4	+	21473.0i	−0.553072	+	0.957948i
$796$	24445.1	+	7209.12i	1.08849	+	0.321006i
$797$	24018.5			1.06748			0.533738	−	0.845650i	$-0.320787\pi$
$797$	24018.5			1.06748			0.533738	+	0.845650i	$0.320787\pi$
$798$	4137.45	+	3791.91i	0.183539	+	0.168211i
$799$			4032.98i			0.178569i
$800$	560.631	+	488.695i	0.0247766	+	0.0215975i
$801$	3254.07	+	1878.74i	0.143542	+	0.0828738i
$802$	−11705.1	−	1690.00i	−0.515365	−	0.0744089i
$803$	−18830.0	+	10871.5i	−0.827515	+	0.477766i
$804$	−1827.11	−	1920.75i	−0.0801457	−	0.0842534i
$805$	10601.8	−	15547.9i	0.464177	−	0.680736i
$806$	−4719.07	−	11807.9i	−0.206231	−	0.516023i
$807$	−319.407	+	184.409i	−0.0139326	+	0.00804402i
$808$	−12194.1	+	8650.86i	−0.530924	+	0.376654i
$809$	17874.7	−	30959.8i	0.776810	−	1.34547i	−0.156961	−	0.987605i	$-0.550170\pi$
$809$	17874.7	−	30959.8i	0.776810	−	1.34547i	0.933771	−	0.357870i	$-0.116497\pi$
$810$	−1610.40	+	2045.30i	−0.0698564	+	0.0887217i
$811$		−	36313.3i		−	1.57230i	−0.618037	−	0.786149i	$-0.712072\pi$
$811$		−	36313.3i		−	1.57230i	0.618037	−	0.786149i	$-0.287928\pi$
$812$	−3573.36	−	21870.1i	−0.154434	−	0.945185i
$813$			1238.19i			0.0534136i
$814$	13010.1	+	10243.7i	0.560200	+	0.441082i
$815$	18275.6	−	31654.3i	0.785481	−	1.36049i
$816$	6973.02	+	4504.60i	0.299148	+	0.193251i
$817$	11822.8	−	6825.90i	0.506276	−	0.292299i
$818$	30692.3	−	12266.3i	1.31190	−	0.524305i
$819$	−4657.86	+	2242.76i	−0.198728	+	0.0956880i
$820$	−21335.3	−	22428.8i	−0.908610	−	0.955179i
$821$	7083.90	−	4089.89i	0.301133	−	0.173859i	−0.341819	−	0.939766i	$-0.611043\pi$
$821$	7083.90	−	4089.89i	0.301133	−	0.173859i	0.642952	+	0.765907i	$0.277710\pi$
$822$	1180.93	−	8179.27i	0.0501092	−	0.347062i
$823$	6930.59	+	4001.38i	0.293542	+	0.169477i	0.639538	−	0.768759i	$-0.279126\pi$
$823$	6930.59	+	4001.38i	0.293542	+	0.169477i	−0.345996	+	0.938236i	$0.612459\pi$
$824$	−1911.34	−	20398.3i	−0.0808067	−	0.862391i
$825$			244.797i			0.0103306i
$826$	−9008.23	−	28578.8i	−0.379463	−	1.20385i
$827$	−4176.53			−0.175613			−0.0878065	−	0.996138i	$-0.527986\pi$
$827$	−4176.53			−0.175613			−0.0878065	+	0.996138i	$0.527986\pi$
$828$	−1821.26	+	6175.66i	−0.0764411	+	0.259202i
$829$	−3732.41	+	6464.72i	−0.156371	+	0.270843i	−0.933558	−	0.358428i	$-0.883313\pi$
$829$	−3732.41	+	6464.72i	−0.156371	+	0.270843i	0.777186	+	0.629271i	$0.216646\pi$
$830$	4292.77	−	29732.2i	0.179523	−	1.24340i
$831$	3414.74	+	5914.50i	0.142546	+	0.246897i
$832$	−10356.4	−	12037.9i	−0.431545	−	0.501610i
$833$	−11593.6	−	9247.87i	−0.482228	−	0.384658i
$834$	−8050.13	−	20142.7i	−0.334237	−	0.836314i
$835$	−5011.51	−	8680.19i	−0.207701	−	0.359749i
$836$	−5515.87	+	1331.24i	−0.228194	+	0.0550740i
$837$	−3389.41	−	1956.88i	−0.139970	−	0.0808118i
$838$	14734.4	+	11601.4i	0.607390	+	0.478238i
$839$	−26786.2			−1.10222			−0.551110	−	0.834432i	$-0.685796\pi$
$839$	−26786.2			−1.10222			−0.551110	+	0.834432i	$0.685796\pi$
$840$	12501.7	+	6911.57i	0.513510	+	0.283895i
$841$	2018.81			0.0827754
$842$	17918.0	+	14108.0i	0.733366	+	0.577426i
$843$	20622.3	+	11906.3i	0.842551	+	0.486447i
$844$	−1282.80	−	5315.18i	−0.0523174	−	0.216773i
$845$	7016.74	+	12153.3i	0.285661	+	0.494779i
$846$	−881.185	−	2204.87i	−0.0358106	−	0.0896039i
$847$	15627.9	−	7524.84i	0.633979	−	0.305262i
$848$	−46494.4	−	2324.90i	−1.88281	−	0.0941480i
$849$	−11622.9	−	20131.5i	−0.469843	−	0.813792i
$850$	71.7989	−	497.287i	0.00289727	−	0.0200668i
$851$	13180.1	−	22828.6i	0.530914	−	0.919569i
$852$	−11945.4	−	3522.83i	−0.480334	−	0.141655i
$853$	−18794.9			−0.754425			−0.377212	−	0.926127i	$-0.623117\pi$
$853$	−18794.9			−0.754425			−0.377212	+	0.926127i	$0.623117\pi$
$854$	−176.267	+	794.777i	−0.00706293	+	0.0318463i
$855$			3652.09i			0.146081i
$856$	−2873.40	−	30665.7i	−0.114732	−	1.22445i
$857$	−21918.7	−	12654.8i	−0.873662	−	0.504409i	−0.00509890	−	0.999987i	$-0.501623\pi$
$857$	−21918.7	−	12654.8i	−0.873662	−	0.504409i	−0.868564	+	0.495578i	$0.834956\pi$
$858$	746.908	−	5173.17i	0.0297191	−	0.205838i
$859$	14459.6	−	8348.25i	0.574337	−	0.331593i	−0.184543	−	0.982824i	$-0.559080\pi$
$859$	14459.6	−	8348.25i	0.574337	−	0.331593i	0.758880	+	0.651231i	$0.225747\pi$
$860$	25177.0	−	23949.5i	0.998288	−	0.949617i
$861$	−15632.4	−	10659.4i	−0.618760	−	0.421917i
$862$	−33958.9	+	13571.8i	−1.34182	+	0.536263i
$863$	−4012.90	+	2316.85i	−0.158286	+	0.0913864i	−0.577051	−	0.816708i	$-0.695797\pi$
$863$	−4012.90	+	2316.85i	−0.158286	+	0.0913864i	0.418765	+	0.908095i	$0.362463\pi$
$864$	−4796.45	−	939.138i	−0.188864	−	0.0369793i
$865$	6645.15	−	11509.7i	0.261205	−	0.452420i
$866$	34278.6	+	26989.8i	1.34508	+	1.05907i
$867$			9130.73i			0.357666i
$868$	−7598.62	+	20087.5i	−0.297136	+	0.785500i
$869$		−	6613.17i		−	0.258155i
$870$	8920.82	−	11330.0i	0.347637	−	0.441519i
$871$	1712.92	−	2966.86i	0.0666361	−	0.115417i
$872$	−12723.6	−	17935.0i	−0.494123	−	0.696508i
$873$	3720.40	−	2147.97i	0.144234	−	0.0832736i
$874$	3352.23	+	8387.82i	0.129738	+	0.324625i
$875$	−1902.66	+	25368.9i	−0.0735103	+	0.980144i
$876$	−19037.1	+	18109.0i	−0.734251	+	0.698453i
$877$	26477.8	−	15287.0i	1.01949	−	0.588602i	0.105533	−	0.994416i	$-0.466345\pi$
$877$	26477.8	−	15287.0i	1.01949	−	0.588602i	0.913956	+	0.405814i	$0.133012\pi$
$878$	43040.7	+	6214.27i	1.65439	+	0.238863i
$879$	4690.33	+	2707.97i	0.179978	+	0.103911i
$880$	−12852.9	+	6587.77i	−0.492355	+	0.252356i
$881$			13856.1i			0.529881i	0.964265	+	0.264941i	$0.0853524\pi$
$881$			13856.1i			0.529881i	−0.964265	+	0.264941i	$0.914648\pi$
$882$	8358.96	+	2522.75i	0.319117	+	0.0963100i
$883$	−7762.38			−0.295838			−0.147919	−	0.988999i	$-0.547258\pi$
$883$	−7762.38			−0.295838			−0.147919	+	0.988999i	$0.547258\pi$
$884$	−3034.58	+	10289.8i	−0.115457	+	0.391499i
$885$	9749.65	−	16886.9i	0.370318	−	0.641409i
$886$	−11990.2	−	1731.16i	−0.454649	−	0.0656428i
$887$	−5247.14	−	9088.31i	−0.198626	−	0.344031i	0.749457	−	0.662053i	$-0.230315\pi$
$887$	−5247.14	−	9088.31i	−0.198626	−	0.344031i	−0.948083	+	0.318022i	$0.896981\pi$
$888$	18186.9	+	8344.64i	0.687288	+	0.315347i
$889$	−11589.5	−	869.208i	−0.437233	−	0.0327923i
$890$	12459.4	−	4979.47i	0.469260	−	0.187542i
$891$	−804.362	−	1393.20i	−0.0302437	−	0.0523836i
$892$	−9258.64	−	38362.4i	−0.347536	−	1.43999i
$893$	−2884.86	−	1665.57i	−0.108105	−	0.0624147i
$894$	−14999.6	+	19050.4i	−0.561144	+	0.712686i
$895$	−4917.32			−0.183651
$896$	−841.846	+	26807.0i	−0.0313885	+	0.999507i
$897$	−8320.61			−0.309718
$898$	−25676.6	+	32610.9i	−0.954166	+	1.21185i
$899$	18775.6	+	10840.1i	0.696555	+	0.402156i
$900$	69.4016	+	287.559i	0.00257043	+	0.0106503i
$901$	15724.9	+	27236.3i	0.581433	+	1.00707i
$902$	17763.7	−	7099.36i	0.655730	−	0.262065i
$903$	11965.5	−	17547.9i	0.440959	−	0.646685i
$904$	−34841.9	−	15986.4i	−1.28189	−	0.588165i
$905$	−3967.21	−	6871.41i	−0.145718	−	0.252391i
$906$	−20788.6	−	3001.48i	−0.762311	−	0.110063i
$907$	−184.106	+	318.881i	−0.00673995	+	0.0116739i	−0.869376	−	0.494152i	$-0.835479\pi$
$907$	−184.106	+	318.881i	−0.00673995	+	0.0116739i	0.862636	+	0.505826i	$0.168812\pi$
$908$	−7100.98	+	24078.5i	−0.259531	+	0.880035i
$909$	−5946.74			−0.216987
$910$	−3997.09	+	18022.6i	−0.145607	+	0.656531i
$911$			14957.6i			0.543980i	0.962300	+	0.271990i	$0.0876818\pi$
$911$			14957.6i			0.543980i	−0.962300	+	0.271990i	$0.912318\pi$
$912$	−6101.99	+	3127.57i	−0.221554	+	0.113557i
$913$	16077.3	+	9282.21i	0.582782	+	0.336469i
$914$	−48496.8	−	7002.02i	−1.75507	−	0.253399i
$915$	−458.785	+	264.880i	−0.0165759	+	0.00957011i
$916$	24825.3	−	23615.0i	0.895472	−	0.851814i
$917$	14289.8	+	29677.6i	0.514604	+	1.06875i
$918$	1225.38	+	3066.09i	0.0440561	+	0.110235i
$919$	−30202.0	+	17437.1i	−1.08408	+	0.625895i	−0.931995	−	0.362472i	$-0.881933\pi$
$919$	−30202.0	+	17437.1i	−1.08408	+	0.625895i	−0.152087	+	0.988367i	$0.548599\pi$
$920$	13303.3	+	18752.1i	0.476737	+	0.672000i
$921$	8548.86	−	14807.1i	0.305857	−	0.529760i
$922$	−11159.5	+	14173.2i	−0.398609	+	0.506257i
$923$		−	16094.4i		−	0.573947i
$924$	−6833.34	+	5588.95i	−0.243290	+	0.198986i
$925$		−	1211.09i		−	0.0430491i
$926$	16873.0	+	13285.2i	0.598790	+	0.471467i
$927$	4074.46	−	7057.18i	0.144361	−	0.250041i
$928$	26569.9	+	5202.36i	0.939872	+	0.184026i
$929$	29680.6	−	17136.1i	1.04821	−	0.605186i	0.126064	−	0.992022i	$-0.459766\pi$
$929$	29680.6	−	17136.1i	1.04821	−	0.605186i	0.922148	+	0.386837i	$0.126432\pi$
$930$	−12977.6	+	5186.57i	−0.457585	+	0.182876i
$931$	11403.2	−	4473.86i	0.401423	−	0.157492i
$932$	−1749.17	+	1663.89i	−0.0614762	+	0.0584790i
$933$	11921.4	−	6882.84i	0.418317	−	0.241515i
$934$	−2133.51	+	14776.9i	−0.0747436	+	0.517683i
$935$	8450.03	+	4878.63i	0.295557	+	0.170640i
$936$	−589.246	−	6288.59i	−0.0205770	−	0.219604i
$937$			7971.69i			0.277933i	0.990297	+	0.138967i	$0.0443781\pi$
$937$			7971.69i			0.277933i	−0.990297	+	0.138967i	$0.955622\pi$
$938$	−5518.43	+	1739.45i	−0.192093	+	0.0605491i
$939$	18771.6			0.652385
$940$	−8132.62	−	2398.39i	−0.282188	−	0.0832201i
$941$	19868.3	−	34412.9i	0.688298	−	1.19217i	−0.284090	−	0.958798i	$-0.591691\pi$
$941$	19868.3	−	34412.9i	0.688298	−	1.19217i	0.972388	−	0.233370i	$-0.0749753\pi$
$942$	2970.72	−	20575.5i	0.102751	−	0.711664i
$943$	−15226.5	−	26373.1i	−0.525815	−	0.910738i
$944$	36564.4	+	1828.36i	1.26067	+	0.0630382i
$945$	2464.95	+	5119.30i	0.0848517	+	0.176223i
$946$	7969.25	+	19940.3i	0.273893	+	0.685324i
$947$	12920.5	+	22378.9i	0.443357	+	0.767916i	0.997936	−	0.0642144i	$-0.0204541\pi$
$947$	12920.5	+	22378.9i	0.443357	+	0.767916i	−0.554579	+	0.832131i	$0.687121\pi$
$948$	−1874.88	−	7768.39i	−0.0642333	−	0.266145i
$949$	−29405.4	−	16977.2i	−1.00584	−	0.580720i
$950$	326.066	+	256.733i	0.0111358	+	0.00876791i
$951$	−19661.9			−0.670433
$952$	15520.6	−	9349.32i	0.528390	−	0.318291i
$953$	−28798.7			−0.978891			−0.489445	−	0.872034i	$-0.662801\pi$
$953$	−28798.7			−0.978891			−0.489445	+	0.872034i	$0.662801\pi$
$954$	−14547.9	−	11454.5i	−0.493717	−	0.388736i
$955$	31837.7	+	18381.5i	1.07879	+	0.622838i
$956$	−26536.5	+	6404.51i	−0.897754	+	0.216670i
$957$	4455.77	+	7717.62i	0.150506	+	0.260685i
$958$	16366.3	+	40951.2i	0.551954	+	1.38108i
$959$	−14902.7	−	10161.8i	−0.501806	−	0.342169i
$960$	−13230.5	+	11382.4i	−0.444804	+	0.382673i
$961$	4389.71	+	7603.20i	0.147350	+	0.255218i
$962$	−3695.20	+	25593.4i	−0.123844	+	0.857758i
$963$	6125.32	−	10609.4i	0.204970	−	0.355018i
$964$	−10122.0	+	34322.3i	−0.338182	+	1.14673i
$965$	−39337.7			−1.31225
$966$	10360.3	+	9495.02i	0.345068	+	0.316250i
$967$			34186.3i			1.13687i	0.822727	+	0.568437i	$0.192452\pi$
$967$			34186.3i			1.13687i	−0.822727	+	0.568437i	$0.807548\pi$
$968$	1977.02	+	21099.3i	0.0656444	+	0.700575i
$969$	4011.69	+	2316.15i	0.132997	+	0.0767858i
$970$	2192.14	−	15183.0i	0.0725624	−	0.502575i
$971$	1588.97	−	917.394i	0.0525155	−	0.0303198i	−0.473512	−	0.880787i	$-0.657014\pi$
$971$	1588.97	−	917.394i	0.0525155	−	0.0303198i	0.526028	+	0.850467i	$0.323681\pi$
$972$	−1339.85	−	1408.52i	−0.0442137	−	0.0464798i
$973$	−47212.7	−	3540.92i	−1.55557	−	0.116667i
$974$	−27550.3	+	11010.6i	−0.906335	+	0.362221i
$975$	−331.066	+	191.141i	−0.0108745	+	0.00627837i
$976$	−835.460	−	539.710i	−0.0274000	−	0.0177005i
$977$	−10982.2	+	19021.7i	−0.359622	+	0.622884i	−0.987898	−	0.155107i	$-0.950428\pi$
$977$	−10982.2	+	19021.7i	−0.359622	+	0.622884i	0.628276	+	0.777991i	$0.283761\pi$
$978$	21445.7	+	16885.6i	0.701185	+	0.552089i
$979$			8291.82i			0.270692i
$980$	25543.3	−	17879.3i	0.832603	−	0.582788i
$981$		−	8746.41i		−	0.284660i
$982$	−13910.1	+	17666.6i	−0.452024	+	0.574097i
$983$	−9107.15	+	15774.0i	−0.295496	+	0.511815i	−0.975100	−	0.221765i	$-0.928818\pi$
$983$	−9107.15	+	15774.0i	−0.295496	+	0.511815i	0.679604	+	0.733579i	$0.262152\pi$
$984$	18854.1	−	13375.6i	0.610819	−	0.433333i
$985$	−21647.7	+	12498.3i	−0.700258	+	0.404294i
$986$	−6787.99	−	16984.6i	−0.219243	−	0.548581i
$987$	−5168.00	−	387.597i	−0.166666	−	0.0124999i
$988$	−6107.25	−	6420.27i	−0.196657	−	0.206737i
$989$	29604.6	−	17092.2i	0.951841	−	0.549546i
$990$	−5685.67	−	820.903i	−0.182528	−	0.0263535i
$991$	−42443.0	−	24504.5i	−1.36049	−	0.785479i	−0.370801	−	0.928713i	$-0.620917\pi$
$991$	−42443.0	−	24504.5i	−1.36049	−	0.785479i	−0.989689	+	0.143234i	$0.954250\pi$
$992$	−19779.6	−	17241.7i	−0.633068	−	0.551838i
$993$		−	33748.8i		−	1.07854i
$994$	−18366.0	+	20039.7i	−0.586052	+	0.639456i
$995$	36198.4			1.15333
$996$	21517.3	+	6345.65i	0.684539	+	0.201877i
$997$	10050.3	−	17407.7i	0.319255	−	0.552967i	−0.661077	−	0.750318i	$-0.729901\pi$
$997$	10050.3	−	17407.7i	0.319255	−	0.552967i	0.980333	+	0.197351i	$0.0632339\pi$
$998$	13564.8	+	1958.50i	0.430246	+	0.0621194i
$999$	3979.44	+	6892.59i	0.126030	+	0.218290i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	168.4.t.a.115.14	yes	96
4.3	odd	2		672.4.bb.a.367.41		96
7.5	odd	6	inner	168.4.t.a.19.46	yes	96
8.3	odd	2	inner	168.4.t.a.115.46	yes	96
8.5	even	2		672.4.bb.a.367.42		96
28.19	even	6		672.4.bb.a.271.42		96
56.5	odd	6		672.4.bb.a.271.41		96
56.19	even	6	inner	168.4.t.a.19.14	✓	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.4.t.a.19.14	✓	96	56.19	even	6	inner
168.4.t.a.19.46	yes	96	7.5	odd	6	inner
168.4.t.a.115.14	yes	96	1.1	even	1	trivial
168.4.t.a.115.46	yes	96	8.3	odd	2	inner
672.4.bb.a.271.41		96	56.5	odd	6
672.4.bb.a.271.42		96	28.19	even	6
672.4.bb.a.367.41		96	4.3	odd	2
672.4.bb.a.367.42		96	8.5	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	168.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.74973 + 2.22226i) q^{2} +(-2.59808 - 1.50000i) q^{3} +(-1.87689 - 7.77671i) q^{4} +(-5.68130 - 9.84030i) q^{5} +(7.87932 - 3.14901i) q^{6} +(1.38512 - 18.4684i) q^{7} +(20.5659 + 9.43622i) q^{8} +(4.50000 + 7.79423i) q^{9} +(31.8084 + 4.59254i) q^{10} +(-9.93039 + 17.1999i) q^{11} +(-6.78878 + 23.0198i) q^{12} -31.0152 q^{13} +(38.6180 + 35.3928i) q^{14} +34.0878i q^{15} +(-56.9546 + 29.1920i) q^{16} +(37.4442 + 21.6184i) q^{17} +(-25.1946 - 3.63762i) q^{18} +(-30.9280 + 17.8563i) q^{19} +(-65.8620 + 62.6510i) q^{20} +(-31.3012 + 45.9046i) q^{21} +(-20.8473 - 52.1632i) q^{22} +(-77.4445 + 44.7126i) q^{23} +(-39.2775 - 55.3649i) q^{24} +(-2.05428 + 3.55811i) q^{25} +(54.2682 - 68.9238i) q^{26} -27.0000i q^{27} +(-146.223 + 23.8914i) q^{28} +149.567i q^{29} +(-75.7519 - 59.6444i) q^{30} +(72.4769 - 125.534i) q^{31} +(34.7829 - 177.646i) q^{32} +(51.5998 - 29.7912i) q^{33} +(-113.559 + 45.3843i) q^{34} +(-189.604 + 91.2944i) q^{35} +(52.1675 - 49.6241i) q^{36} +(-255.281 + 147.387i) q^{37} +(14.4343 - 99.9739i) q^{38} +(80.5798 + 46.5228i) q^{39} +(-23.9860 - 255.985i) q^{40} +340.542i q^{41} +(-47.2433 - 149.880i) q^{42} -382.268 q^{43} +(152.397 + 44.9435i) q^{44} +(51.1317 - 88.5627i) q^{45} +(36.1439 - 250.337i) q^{46} +(46.6383 + 80.7798i) q^{47} +(191.760 + 9.58877i) q^{48} +(-339.163 - 51.1619i) q^{49} +(-4.31262 - 10.7909i) q^{50} +(-64.8552 - 112.333i) q^{51} +(58.2120 + 241.196i) q^{52} +(629.932 + 363.692i) q^{53} +(60.0010 + 47.2427i) q^{54} +225.670 q^{55} +(202.758 - 366.749i) q^{56} +107.138 q^{57} +(-332.376 - 261.701i) q^{58} +(-495.394 - 286.016i) q^{59} +(265.091 - 63.9789i) q^{60} +(7.77051 + 13.4589i) q^{61} +(152.153 + 380.712i) q^{62} +(150.180 - 72.3118i) q^{63} +(333.915 + 388.129i) q^{64} +(176.206 + 305.198i) q^{65} +(-24.0820 + 166.795i) q^{66} +(-55.2285 + 95.6585i) q^{67} +(97.8417 - 331.768i) q^{68} +268.276 q^{69} +(128.875 - 581.090i) q^{70} +518.920i q^{71} +(18.9986 + 202.759i) q^{72} +(948.097 + 547.384i) q^{73} +(119.142 - 825.189i) q^{74} +(10.6743 - 6.16283i) q^{75} +(196.912 + 207.004i) q^{76} +(303.901 + 207.222i) q^{77} +(-244.379 + 97.6670i) q^{78} +(-288.366 + 166.488i) q^{79} +(610.834 + 394.601i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(-756.773 - 595.856i) q^{82} -934.727i q^{83} +(415.736 + 157.263i) q^{84} -491.282i q^{85} +(668.867 - 849.500i) q^{86} +(224.350 - 388.586i) q^{87} +(-366.530 + 260.028i) q^{88} +(361.563 - 208.749i) q^{89} +(107.343 + 268.589i) q^{90} +(-42.9597 + 572.800i) q^{91} +(493.072 + 518.343i) q^{92} +(-376.601 + 217.431i) q^{93} +(-261.118 - 37.7005i) q^{94} +(351.423 + 202.894i) q^{95} +(-356.838 + 409.364i) q^{96} -477.327i q^{97} +(707.139 - 664.189i) q^{98} -178.747 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 2 q^{2} - 10 q^{4} - 16 q^{8} + 432 q^{9} + 18 q^{10} + 40 q^{11} + 274 q^{14} - 26 q^{16} - 18 q^{18} + 4 q^{22} + 270 q^{24} - 1200 q^{25} + 750 q^{26} + 922 q^{28} + 168 q^{30} - 108 q^{32} + 456 q^{35}+ \cdots + 720 q^{99}+O(q^{100}) \) 96 * q + 2 * q^2 - 10 * q^4 - 16 * q^8 + 432 * q^9 + 18 * q^10 + 40 * q^11 + 274 * q^14 - 26 * q^16 - 18 * q^18 + 4 * q^22 + 270 * q^24 - 1200 * q^25 + 750 * q^26 + 922 * q^28 + 168 * q^30 - 108 * q^32 + 456 * q^35 - 180 * q^36 - 1494 * q^38 + 1170 * q^40 - 564 * q^42 - 1616 * q^43 + 264 * q^44 + 808 * q^46 - 360 * q^49 - 1036 * q^50 - 3564 * q^52 + 176 * q^56 - 336 * q^57 - 394 * q^58 + 4128 * q^59 + 822 * q^60 - 2644 * q^64 + 2052 * q^66 - 1440 * q^67 - 1392 * q^68 + 3234 * q^70 - 72 * q^72 - 648 * q^73 + 850 * q^74 + 1692 * q^78 - 1548 * q^80 - 3888 * q^81 + 4596 * q^82 + 3120 * q^84 - 2522 * q^86 - 1454 * q^88 - 104 * q^91 + 5600 * q^92 - 2052 * q^94 + 3870 * q^96 + 852 * q^98 + 720 * q^99

Introduction

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