LMFDB - Embedded newform 168.4.t.a.19.14

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			19.14
Character	$\chi$	$=$	168.19
Dual form			168.4.t.a.115.14

$q$-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 $\left(\mathbb{Z}/168\mathbb{Z}\right)^\times$.

$n$	$73$	$85$	$113$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$1$	$-1$

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	0.491805	+	0.870705i	$0.336337\pi$
$5$	−5.68130	+	9.84030i	−0.508151	+	0.880143i	−0.999955	+	0.00943729i	$0.996996\pi$
$6$	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	0.697230	−	0.716848i	$-0.254416\pi$
$11$	−9.93039	−	17.1999i	−0.272193	−	0.471453i	−0.969423	+	0.245395i	$0.921082\pi$
$12$	−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	−0.208520	−	0.978018i	$-0.566865\pi$
$17$	37.4442	−	21.6184i	0.534209	−	0.308426i	0.742729	+	0.669593i	$0.233531\pi$
$18$	−25.1946	+	3.63762i	−0.329912	+	0.0476331i
$19$	−30.9280	−	17.8563i	−0.373441	−	0.215606i	0.301520	−	0.953460i	$-0.402506\pi$
$19$	−30.9280	−	17.8563i	−0.373441	−	0.215606i	−0.674961	+	0.737854i	$0.735839\pi$
$20$	−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	0.106029	−	0.994363i	$-0.466186\pi$
$23$	−77.4445	−	44.7126i	−0.702100	−	0.405357i	−0.808129	+	0.589006i	$0.799520\pi$
$24$	−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	$-0.841050\pi$
$29$		−	149.567i		−	0.957718i	0.877892	−	0.478859i	$-0.158950\pi$
$30$	−75.7519	+	59.6444i	−0.461012	+	0.362984i
$31$	72.4769	+	125.534i	0.419911	+	0.727307i	0.995930	−	0.0901295i	$-0.0287281\pi$
$31$	72.4769	+	125.534i	0.419911	+	0.727307i	−0.576019	+	0.817436i	$0.695395\pi$
$32$	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	−0.189265	−	0.981926i	$-0.560610\pi$
$37$	−255.281	−	147.387i	−1.13427	−	0.654871i	−0.945005	+	0.327055i	$0.893944\pi$
$38$	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	$-0.775362\pi$
$41$		−	340.542i		−	1.29716i	0.761145	−	0.648582i	$-0.224638\pi$
$42$	−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	−0.784534	−	0.620085i	$-0.787098\pi$
$47$	46.6383	−	80.7798i	0.144742	−	0.250701i	0.929277	+	0.369384i	$0.120431\pi$
$48$	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	0.649314	−	0.760520i	$-0.275056\pi$
$53$	629.932	−	363.692i	1.63260	−	0.942583i	0.983287	−	0.182062i	$-0.0582772\pi$
$54$	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	−0.934409	−	0.356202i	$-0.884071\pi$
$59$	−495.394	+	286.016i	−1.09313	+	0.631121i	−0.158724	+	0.987323i	$0.550738\pi$
$60$	265.091	+	63.9789i	0.570385	+	0.137661i
$61$	7.77051	−	13.4589i	0.0163100	−	0.0282498i	−0.857755	−	0.514058i	$-0.828141\pi$
$61$	7.77051	−	13.4589i	0.0163100	−	0.0282498i	0.874065	+	0.485809i	$0.161475\pi$
$62$	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	0.811270	−	0.584671i	$-0.198776\pi$
$67$	−55.2285	−	95.6585i	−0.100705	−	0.174426i	−0.911975	+	0.410245i	$0.865443\pi$
$68$	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	$-0.857210\pi$
$71$		−	518.920i		−	0.867387i	0.901060	−	0.433693i	$-0.142790\pi$
$72$	18.9986	−	202.759i	0.0310974	−	0.331880i
$73$	948.097	−	547.384i	1.52009	−	0.877623i	0.520368	−	0.853942i	$-0.325795\pi$
$73$	948.097	−	547.384i	1.52009	−	0.877623i	0.999720	−	0.0236803i	$-0.00753837\pi$
$74$	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	0.280402	−	0.959883i	$-0.409532\pi$
$79$	−288.366	−	166.488i	−0.410680	−	0.237106i	−0.691082	+	0.722777i	$0.742866\pi$
$80$	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	$0.212085\pi$
$83$			934.727i			1.23614i	−0.786123	+	0.618070i	$0.787915\pi$
$84$	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	0.699613	−	0.714522i	$-0.253356\pi$
$89$	361.563	+	208.749i	0.430625	+	0.248621i	−0.268988	+	0.963144i	$0.586689\pi$
$90$	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	$0.0803717\pi$
$97$			477.327i			0.499642i	−0.968292	+	0.249821i	$0.919628\pi$
$98$	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	0.656129	−	0.754648i	$-0.272193\pi$
$101$	−330.374	−	572.225i	−0.325480	−	0.563748i	−0.981609	+	0.190901i	$0.938859\pi$
$102$	363.111	−	52.4264i	0.352484	−	0.0508921i
$103$	−452.718	+	784.131i	−0.433084	+	0.750124i	−0.997137	−	0.0756149i	$-0.975908\pi$
$103$	−452.718	+	784.131i	−0.433084	+	0.750124i	0.564053	+	0.825739i	$0.309241\pi$
$104$	−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	0.375491	+	0.926826i	$0.377474\pi$
$107$	−680.592	+	1178.82i	−0.614909	+	1.06505i	−0.990400	+	0.138228i	$0.955859\pi$
$108$	−209.971	−	50.6759i	−0.187079	−	0.0451509i
$109$	−841.623	+	485.911i	−0.739568	+	0.426990i	−0.821912	−	0.569614i	$-0.807093\pi$
$109$	−841.623	+	485.911i	−0.739568	+	0.426990i	0.0823444	+	0.996604i	$0.473759\pi$
$110$	−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	$0.0703547\pi$
$127$			627.533i			0.438461i	−0.975673	+	0.219231i	$0.929645\pi$
$128$	−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	−0.111067	−	0.993813i	$-0.535427\pi$
$131$	−1540.25	−	889.263i	−1.02727	−	0.593094i	−0.916201	+	0.400719i	$0.868760\pi$
$132$	−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	0.976967	−	0.213391i	$-0.0684509\pi$
$137$	486.966	+	843.450i	0.303681	+	0.525991i	−0.673286	+	0.739382i	$0.735118\pi$
$138$	−469.410	−	596.178i	−0.289557	−	0.367754i
$139$			2556.40i			1.55994i	0.625819	+	0.779969i	$0.284765\pi$
$139$			2556.40i			1.55994i	−0.625819	+	0.779969i	$0.715235\pi$
$140$	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	−0.370921	−	0.928664i	$-0.620958\pi$
$149$	−2474.68	−	1428.76i	−1.36063	−	0.785559i	−0.989707	+	0.143105i	$0.954291\pi$
$150$	−4.98179	−	34.5044i	−0.00271174	−	0.0187818i
$151$	−2143.73	+	1237.68i	−1.15532	+	0.667027i	−0.950179	−	0.311705i	$-0.899100\pi$
$151$	−2143.73	+	1237.68i	−1.15532	+	0.667027i	−0.205145	+	0.978732i	$0.565767\pi$
$152$	−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	0.988979	+	0.148056i	$0.0473015\pi$
$157$	1225.00	+	2121.76i	0.622709	+	1.07856i	−0.366270	+	0.930509i	$0.619365\pi$
$158$	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	−0.163095	−	0.986610i	$-0.552148\pi$
$163$	1608.40	−	2785.83i	0.772882	−	1.33867i	0.935977	−	0.352061i	$-0.114519\pi$
$164$	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	−0.708426	−	0.705785i	$-0.750594\pi$
$173$	584.827	−	1012.95i	0.257015	−	0.445163i	0.965441	+	0.260622i	$0.0839277\pi$
$174$	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	0.907660	−	0.419707i	$-0.137867\pi$
$179$	216.382	+	374.785i	0.0903528	+	0.156496i	−0.817307	+	0.576203i	$0.804534\pi$
$180$	−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	−0.135642	−	0.990758i	$-0.543310\pi$
$191$	−2801.97	−	1617.72i	−1.06148	−	0.612848i	−0.925842	+	0.377910i	$0.876643\pi$
$192$	−285.343	+	1509.26i	−0.107255	+	0.567300i
$193$	1731.02	+	2998.21i	0.645603	+	1.11822i	0.984162	+	0.177271i	$0.0567270\pi$
$193$	1731.02	+	2998.21i	0.645603	+	1.11822i	−0.338559	+	0.940945i	$0.609940\pi$
$194$	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	$0.130229\pi$
$197$			2199.91i			0.795618i	−0.917468	+	0.397809i	$0.869771\pi$
$198$	312.759	+	397.223i	0.112257	+	0.142573i
$199$	−1592.88	−	2758.94i	−0.567417	−	0.982795i	−0.996820	−	0.0796820i	$-0.974610\pi$
$199$	−1592.88	−	2758.94i	−0.567417	−	0.982795i	0.429404	−	0.903113i	$-0.358724\pi$
$200$	−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	−0.841574	−	0.540142i	$-0.818371\pi$
$227$	−2717.56	+	1568.98i	−0.794584	+	0.458753i	0.0469897	+	0.998895i	$0.485037\pi$
$228$	−201.086	+	833.180i	−0.0584088	+	0.242012i
$229$	2141.45	−	3709.10i	0.617952	−	1.07032i	−0.371907	−	0.928270i	$-0.621296\pi$
$229$	2141.45	−	3709.10i	0.617952	−	1.07032i	0.989859	−	0.142054i	$-0.0453706\pi$
$230$	−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	−0.886458	−	0.462810i	$-0.846841\pi$
$233$	−150.884	+	261.339i	−0.0424238	+	0.0734802i	0.844034	+	0.536290i	$0.180175\pi$
$234$	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	$0.152784\pi$
$239$			3412.31i			0.923530i	−0.887002	+	0.461765i	$0.847216\pi$
$240$	−995.092	+	1941.46i	−0.267637	+	0.522168i
$241$	−3873.71	+	2236.49i	−1.03538	+	0.597779i	−0.918522	−	0.395369i	$-0.870617\pi$
$241$	−3873.71	+	2236.49i	−1.03538	+	0.597779i	−0.116861	+	0.993148i	$0.537283\pi$
$242$	−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	$-0.901284\pi$
$251$		−	2427.14i		−	0.610358i	0.952295	−	0.305179i	$-0.0987164\pi$
$252$	−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	−0.344129	−	0.938922i	$-0.611826\pi$
$257$	−5476.85	−	3162.06i	−1.32932	−	0.767486i	−0.985195	+	0.171436i	$0.945159\pi$
$258$	−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	−0.693872	−	0.720098i	$-0.744097\pi$
$263$	−1779.35	+	1027.31i	−0.417184	+	0.240862i	0.276688	+	0.960960i	$0.410763\pi$
$264$	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	0.872908	−	0.487885i	$-0.162232\pi$
$269$	61.4698	+	106.469i	0.0139326	+	0.0241320i	−0.858975	+	0.512017i	$0.828898\pi$
$270$	123.999	+	858.828i	0.0279493	+	0.193580i
$271$	−206.365	+	357.435i	−0.0462576	+	0.0801204i	−0.888227	−	0.459405i	$-0.848063\pi$
$271$	−206.365	+	357.435i	−0.0462576	+	0.0801204i	0.841970	+	0.539525i	$0.181396\pi$
$272$	−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	−0.698340	−	0.715766i	$-0.746078\pi$
$277$	−1971.50	+	1138.25i	−0.427639	+	0.246897i	0.270701	+	0.962663i	$0.412744\pi$
$278$	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	0.414187	−	0.910192i	$-0.364066\pi$
$283$	6710.48	−	3874.30i	1.40953	−	0.813792i	0.995343	+	0.0963997i	$0.0307327\pi$
$284$	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	$-0.822282\pi$
$307$		−	5699.24i		−	1.05952i	0.848148	−	0.529760i	$-0.177718\pi$
$308$	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	0.577453	−	0.816424i	$-0.304047\pi$
$311$	−2294.28	−	3973.81i	−0.418317	−	0.724546i	−0.995770	+	0.0918773i	$0.970713\pi$
$312$	1218.20	−	1717.15i	0.221048	−	0.311585i
$313$	−5418.90	−	3128.61i	−0.978577	−	0.564982i	−0.0767366	−	0.997051i	$-0.524450\pi$
$313$	−5418.90	−	3128.61i	−0.978577	−	0.564982i	−0.901840	+	0.432070i	$0.857783\pi$
$314$	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	0.909915	−	0.414795i	$-0.136147\pi$
$317$	5675.91	+	3276.99i	1.00565	+	0.580612i	0.0957345	+	0.995407i	$0.469480\pi$
$318$	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	0.157704	−	0.987486i	$-0.449591\pi$
$331$	5624.81	−	9742.45i	0.934040	−	1.61781i	0.776336	−	0.630319i	$-0.217076\pi$
$332$	−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	0.623221	−	0.782046i	$-0.285824\pi$
$347$	−2363.60	−	4093.87i	−0.365662	−	0.633344i	−0.988882	+	0.148702i	$0.952491\pi$
$348$	−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	−0.0385409	−	0.999257i	$-0.512271\pi$
$353$	5356.02	−	3092.30i	0.807571	−	0.466251i	0.846112	+	0.533006i	$0.178938\pi$
$354$	−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	−0.495167	−	0.868798i	$-0.664893\pi$
$359$	−10170.1	−	5871.73i	−1.49515	−	0.863226i	−0.999984	+	0.00557116i	$0.998227\pi$
$360$	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	0.733279	−	0.679928i	$-0.237989\pi$
$367$	−1562.19	−	2705.80i	−0.222196	−	0.384855i	−0.955474	+	0.295074i	$0.904656\pi$
$368$	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	0.816172	−	0.577808i	$-0.196092\pi$
$373$	5214.58	+	3010.64i	0.723862	+	0.417922i	−0.0923105	+	0.995730i	$0.529425\pi$
$374$	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	−0.366254	+	0.930515i	$0.619360\pi$
$383$	−7412.83	+	12839.4i	−0.988977	+	1.71296i	−0.622722	+	0.782443i	$0.713973\pi$
$384$	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	−0.405377	−	0.914150i	$-0.632860\pi$
$389$	1408.72	−	813.323i	0.183611	−	0.106008i	0.588988	+	0.808142i	$0.299526\pi$
$390$	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	0.421465	+	0.906845i	$0.361516\pi$
$397$	−4545.33	+	7872.74i	−0.574618	+	0.995268i	−0.996083	+	0.0884234i	$0.971817\pi$
$398$	−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	−0.705982	−	0.708230i	$-0.749494\pi$
$401$	2090.65	−	3621.11i	0.260354	−	0.450947i	0.966336	+	0.257283i	$0.0828273\pi$
$402$	−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	−0.965664	−	0.259793i	$-0.916346\pi$
$409$	−10120.3	+	5842.94i	−1.22351	+	0.706393i	−0.257845	+	0.966186i	$0.583012\pi$
$410$	−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	$0.126328\pi$
$419$			6630.39i			0.773068i	−0.922275	+	0.386534i	$0.873672\pi$
$420$	−814.405	+	4984.42i	−0.0946164	+	0.579083i
$421$			8062.94i			0.933406i	0.884414	+	0.466703i	$0.154558\pi$
$421$			8062.94i			0.933406i	−0.884414	+	0.466703i	$0.845442\pi$
$422$	−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	0.280024	−	0.959993i	$-0.409657\pi$
$431$	11197.4	−	6464.82i	1.25141	−	0.722505i	0.971390	+	0.237488i	$0.0763242\pi$
$432$	788.185	−	1537.77i	0.0877814	−	0.171264i
$433$			15425.1i			1.71197i	0.516999	+	0.855986i	$0.327049\pi$
$433$			15425.1i			1.71197i	−0.516999	+	0.855986i	$0.672951\pi$
$434$	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	0.0576279	+	0.998338i	$0.481646\pi$
$439$	−7687.49	+	13315.1i	−0.835772	+	1.44760i	−0.893400	+	0.449262i	$0.851687\pi$
$440$	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	−0.728032	−	0.685543i	$-0.759565\pi$
$443$	2141.57	−	3709.31i	0.229682	−	0.397820i	0.957714	+	0.287723i	$0.0928981\pi$
$444$	−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	0.0428020	−	0.999084i	$-0.486372\pi$
$457$	8662.00	−	15003.0i	0.886633	−	1.53569i	0.843831	−	0.536609i	$-0.180295\pi$
$458$	−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	$0.124441\pi$
$463$			7592.70i			0.762123i	−0.924550	+	0.381061i	$0.875559\pi$
$464$	−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	0.709086	−	0.705122i	$-0.249108\pi$
$467$	4571.40	+	2639.30i	0.452975	+	0.261525i	−0.256111	+	0.966647i	$0.582441\pi$
$468$	−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	0.950825	+	0.309728i	$0.100238\pi$
$479$	7795.95	+	13503.0i	0.743645	+	1.28803i	−0.207180	+	0.978303i	$0.566429\pi$
$480$	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	−0.0137808	−	0.999905i	$-0.504387\pi$
$487$	9084.27	−	5244.80i	0.845272	−	0.488018i	0.859053	+	0.511887i	$0.171053\pi$
$488$	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	−0.953998	−	0.299813i	$-0.903076\pi$
$499$	−2422.80	+	4196.41i	−0.217353	+	0.376467i	0.736645	+	0.676280i	$0.236409\pi$
$500$	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	−0.910771	−	0.412911i	$-0.864512\pi$
$509$	−1123.03	+	1945.14i	−0.0977944	+	0.169385i	0.812977	+	0.582296i	$0.197845\pi$
$510$	−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	−0.188942	−	0.981988i	$-0.560506\pi$
$521$	6742.95	−	3893.04i	0.567013	−	0.327365i	0.755956	+	0.654623i	$0.227173\pi$
$522$	544.067	+	3768.27i	0.0456191	+	0.315963i
$523$	10196.9	+	5887.21i	0.852545	+	0.492217i	0.861509	−	0.507743i	$-0.169520\pi$
$523$	10196.9	+	5887.21i	0.852545	+	0.492217i	−0.00896379	+	0.999960i	$0.502853\pi$
$524$	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	0.269368	−	0.963037i	$-0.413185\pi$
$541$	−5410.37	−	3123.68i	−0.429963	−	0.248239i	−0.699331	+	0.714798i	$0.746519\pi$
$542$	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	−0.678533	−	0.734570i	$-0.737384\pi$
$557$	−5016.95	+	2896.54i	−0.381643	+	0.220342i	0.296890	+	0.954912i	$0.404051\pi$
$558$	−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	−0.552939	+	0.833221i	$0.686494\pi$
$563$	−20719.3	+	11962.3i	−1.55100	+	0.895470i	−0.998061	+	0.0622488i	$0.980173\pi$
$564$	−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	−0.664893	−	0.746939i	$-0.731523\pi$
$569$	4267.57	−	7391.65i	0.314422	−	0.544594i	0.979314	+	0.202345i	$0.0648561\pi$
$570$	3407.89	−	492.035i	0.250422	−	0.0361563i
$571$	−4647.94	−	8050.46i	−0.340648	−	0.590020i	0.643905	−	0.765105i	$-0.277313\pi$
$571$	−4647.94	−	8050.46i	−0.340648	−	0.590020i	−0.984553	+	0.175086i	$0.943980\pi$
$572$	−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	−0.785178	−	0.619270i	$-0.787429\pi$
$577$	−8890.70	+	5133.05i	−0.641464	+	0.370349i	0.143714	+	0.989619i	$0.454095\pi$
$578$	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	$-0.895208\pi$
$587$		−	9195.89i		−	0.646601i	0.946296	−	0.323301i	$-0.104792\pi$
$588$	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	−0.00208435	−	0.999998i	$-0.500663\pi$
$593$	−12551.0	−	7246.30i	−0.869150	−	0.501804i	−0.867066	+	0.498194i	$0.833997\pi$
$594$	−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	−0.165677	−	0.986180i	$-0.552981\pi$
$599$	8877.36	−	5125.35i	0.605541	−	0.349609i	0.771218	+	0.636571i	$0.219648\pi$
$600$	277.681	+	26.0190i	0.0188938	+	0.00177037i
$601$		−	7735.54i		−	0.525024i	−0.964929	−	0.262512i	$-0.915449\pi$
$601$		−	7735.54i		−	0.525024i	0.964929	−	0.262512i	$-0.0845509\pi$
$602$	−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	0.183572	+	0.983006i	$0.441234\pi$
$607$	−11358.6	+	19673.6i	−0.759523	+	1.31553i	−0.943094	+	0.332525i	$0.892099\pi$
$608$	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	−0.823744	−	0.566962i	$-0.808119\pi$
$613$	−11301.1	+	6524.70i	−0.744613	+	0.429902i	0.0791312	+	0.996864i	$0.474785\pi$
$614$	−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	−0.823507	−	0.567306i	$-0.807986\pi$
$619$	−11457.4	+	6614.93i	−0.743960	+	0.429526i	0.0795473	+	0.996831i	$0.474653\pi$
$620$	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	$-0.780320\pi$
$631$		−	20182.5i		−	1.27330i	0.771154	−	0.636649i	$-0.219680\pi$
$632$	−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	0.998442	+	0.0557977i	$0.0177702\pi$
$641$	8885.98	+	15391.0i	0.547543	+	0.948373i	−0.450899	+	0.892575i	$0.648896\pi$
$642$	−9074.71	+	7145.11i	−0.557867	+	0.439245i
$643$			7636.64i			0.468366i	0.972192	+	0.234183i	$0.0752416\pi$
$643$			7636.64i			0.468366i	−0.972192	+	0.234183i	$0.924758\pi$
$644$	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	0.762045	−	0.647524i	$-0.224195\pi$
$647$	−2958.17	−	5123.70i	−0.179749	−	0.311335i	−0.941795	+	0.336189i	$0.890862\pi$
$648$	−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	0.900608	−	0.434633i	$-0.143122\pi$
$653$	16261.3	+	9388.47i	0.974509	+	0.562633i	0.0739010	+	0.997266i	$0.476455\pi$
$654$	−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	−0.940612	−	0.339484i	$-0.889748\pi$
$661$	−12988.8	−	22497.3i	−0.764307	−	1.32382i	0.176305	−	0.984336i	$-0.443586\pi$
$662$	−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	−0.449634	−	0.893213i	$-0.648445\pi$
$677$	9665.86	−	16741.8i	0.548728	−	0.950425i	0.998362	−	0.0572123i	$-0.0182212\pi$
$678$	−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	0.904508	−	0.426456i	$-0.140238\pi$
$683$	1480.32	+	2563.99i	0.0829325	+	0.143643i	−0.821576	+	0.570099i	$0.806905\pi$
$684$	−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	0.933243	−	0.359246i	$-0.116966\pi$
$691$	19776.3	+	11417.8i	1.08875	+	0.628589i	0.155506	+	0.987835i	$0.450299\pi$
$692$	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	$-0.625902\pi$
$701$		−	34253.9i		−	1.84558i	0.385300	−	0.922791i	$-0.374098\pi$
$702$	−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	0.925550	−	0.378626i	$-0.123603\pi$
$709$	20019.3	+	11558.2i	1.06042	+	0.612237i	0.134875	+	0.990863i	$0.456937\pi$
$710$	−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	−0.972737	−	0.231910i	$-0.925502\pi$
$719$	−5504.81	+	9534.61i	−0.285528	+	0.494550i	0.687209	+	0.726460i	$0.258836\pi$
$720$	−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	−0.161896	−	0.986808i	$-0.551761\pi$
$733$	15353.3	−	26592.7i	0.773653	−	1.34001i	0.935549	−	0.353198i	$-0.114906\pi$
$734$	−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	0.805472	−	0.592634i	$-0.201912\pi$
$739$	−2219.89	−	3844.96i	−0.110501	−	0.191393i	−0.915972	+	0.401242i	$0.868579\pi$
$740$	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	$-0.830644\pi$
$743$		−	20548.4i		−	1.01460i	0.861770	−	0.507299i	$-0.169356\pi$
$744$	−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	0.882102	−	0.471058i	$-0.156128\pi$
$751$	18835.5	+	10874.7i	0.915205	+	0.528394i	0.0331028	+	0.999452i	$0.489461\pi$
$752$	−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	$0.248287\pi$
$757$			29296.1i			1.40658i	−0.710901	+	0.703292i	$0.751713\pi$
$758$	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	−0.199530	−	0.979892i	$-0.563942\pi$
$761$	−24098.1	−	13913.1i	−1.14791	−	0.662744i	−0.948376	+	0.317148i	$0.897275\pi$
$762$	−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	$-0.976014\pi$
$769$		−	3210.87i		−	0.150568i	0.997162	−	0.0752840i	$-0.0239863\pi$
$770$	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	0.955149	−	0.296125i	$-0.0956946\pi$
$773$	4752.28	+	8231.20i	0.221123	+	0.382996i	−0.734027	+	0.679121i	$0.762361\pi$
$774$	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	−0.597565	−	0.801821i	$-0.703865\pi$
$787$	−4458.68	+	2574.22i	−0.201950	+	0.116596i	0.395615	+	0.918417i	$0.370532\pi$
$788$	−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	0.933771	+	0.357870i	$0.116497\pi$
$809$	17874.7	+	30959.8i	0.776810	+	1.34547i	−0.156961	+	0.987605i	$0.550170\pi$
$810$	−1610.40	−	2045.30i	−0.0698564	−	0.0887217i
$811$			36313.3i			1.57230i	0.618037	+	0.786149i	$0.287928\pi$
$811$			36313.3i			1.57230i	−0.618037	+	0.786149i	$0.712072\pi$
$812$	−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	0.642952	−	0.765907i	$-0.277710\pi$
$821$	7083.90	+	4089.89i	0.301133	+	0.173859i	−0.341819	+	0.939766i	$0.611043\pi$
$822$	1180.93	+	8179.27i	0.0501092	+	0.347062i
$823$	6930.59	−	4001.38i	0.293542	−	0.169477i	−0.345996	−	0.938236i	$-0.612459\pi$
$823$	6930.59	−	4001.38i	0.293542	−	0.169477i	0.639538	+	0.768759i	$0.279126\pi$
$824$	−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	0.777186	−	0.629271i	$-0.216646\pi$
$829$	−3732.41	−	6464.72i	−0.156371	−	0.270843i	−0.933558	+	0.358428i	$0.883313\pi$
$830$	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	−0.868564	−	0.495578i	$-0.834956\pi$
$857$	−21918.7	+	12654.8i	−0.873662	+	0.504409i	−0.00509890	+	0.999987i	$0.501623\pi$
$858$	746.908	+	5173.17i	0.0297191	+	0.205838i
$859$	14459.6	+	8348.25i	0.574337	+	0.331593i	0.758880	−	0.651231i	$-0.225747\pi$
$859$	14459.6	+	8348.25i	0.574337	+	0.331593i	−0.184543	+	0.982824i	$0.559080\pi$
$860$	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	0.418765	−	0.908095i	$-0.362463\pi$
$863$	−4012.90	−	2316.85i	−0.158286	−	0.0913864i	−0.577051	+	0.816708i	$0.695797\pi$
$864$	−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	0.913956	−	0.405814i	$-0.133012\pi$
$877$	26477.8	+	15287.0i	1.01949	+	0.588602i	0.105533	+	0.994416i	$0.466345\pi$
$878$	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	$-0.914648\pi$
$881$		−	13856.1i		−	0.529881i	0.964265	−	0.264941i	$-0.0853524\pi$
$882$	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	−0.948083	−	0.318022i	$-0.896981\pi$
$887$	−5247.14	+	9088.31i	−0.198626	+	0.344031i	0.749457	+	0.662053i	$0.230315\pi$
$888$	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	0.862636	−	0.505826i	$-0.168812\pi$
$907$	−184.106	−	318.881i	−0.00673995	−	0.0116739i	−0.869376	+	0.494152i	$0.835479\pi$
$908$	−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	$-0.912318\pi$
$911$		−	14957.6i		−	0.543980i	0.962300	−	0.271990i	$-0.0876818\pi$
$912$	−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	−0.152087	−	0.988367i	$-0.548599\pi$
$919$	−30202.0	−	17437.1i	−1.08408	−	0.625895i	−0.931995	+	0.362472i	$0.881933\pi$
$920$	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	0.922148	−	0.386837i	$-0.126432\pi$
$929$	29680.6	+	17136.1i	1.04821	+	0.605186i	0.126064	+	0.992022i	$0.459766\pi$
$930$	−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	$-0.955622\pi$
$937$		−	7971.69i		−	0.277933i	0.990297	−	0.138967i	$-0.0443781\pi$
$938$	−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	0.972388	+	0.233370i	$0.0749753\pi$
$941$	19868.3	+	34412.9i	0.688298	+	1.19217i	−0.284090	+	0.958798i	$0.591691\pi$
$942$	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	−0.554579	−	0.832131i	$-0.687121\pi$
$947$	12920.5	−	22378.9i	0.443357	−	0.767916i	0.997936	+	0.0642144i	$0.0204541\pi$
$948$	−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	$-0.807548\pi$
$967$		−	34186.3i		−	1.13687i	0.822727	−	0.568437i	$-0.192452\pi$
$968$	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	0.526028	−	0.850467i	$-0.323681\pi$
$971$	1588.97	+	917.394i	0.0525155	+	0.0303198i	−0.473512	+	0.880787i	$0.657014\pi$
$972$	−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	0.628276	−	0.777991i	$-0.283761\pi$
$977$	−10982.2	−	19021.7i	−0.359622	−	0.622884i	−0.987898	+	0.155107i	$0.950428\pi$
$978$	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	0.679604	−	0.733579i	$-0.262152\pi$
$983$	−9107.15	−	15774.0i	−0.295496	−	0.511815i	−0.975100	+	0.221765i	$0.928818\pi$
$984$	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	−0.989689	−	0.143234i	$-0.954250\pi$
$991$	−42443.0	+	24504.5i	−1.36049	+	0.785479i	−0.370801	+	0.928713i	$0.620917\pi$
$992$	−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	0.980333	−	0.197351i	$-0.0632339\pi$
$997$	10050.3	+	17407.7i	0.319255	+	0.552967i	−0.661077	+	0.750318i	$0.729901\pi$
$998$	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.19.14	✓	96
4.3	odd	2		672.4.bb.a.271.41		96
7.3	odd	6	inner	168.4.t.a.115.46	yes	96
8.3	odd	2	inner	168.4.t.a.19.46	yes	96
8.5	even	2		672.4.bb.a.271.42		96
28.3	even	6		672.4.bb.a.367.42		96
56.3	even	6	inner	168.4.t.a.115.14	yes	96
56.45	odd	6		672.4.bb.a.367.41		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.4.t.a.19.14	✓	96	1.1	even	1	trivial
168.4.t.a.19.46	yes	96	8.3	odd	2	inner
168.4.t.a.115.14	yes	96	56.3	even	6	inner
168.4.t.a.115.46	yes	96	7.3	odd	6	inner
672.4.bb.a.271.41		96	4.3	odd	2
672.4.bb.a.271.42		96	8.5	even	2
672.4.bb.a.367.41		96	56.45	odd	6
672.4.bb.a.367.42		96	28.3	even	6

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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more