LMFDB - Embedded newform 168.4.t.a.115.46

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			115.46
Character	$\chi$	$=$	168.115
Dual form			168.4.t.a.19.46

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.79940 - 0.404181i) q^{2} +(-2.59808 - 1.50000i) q^{3} +(7.67328 - 2.26293i) 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} +(19.8815 + 25.2506i) q^{10} +(-9.93039 + 17.1999i) q^{11} +(-23.3301 - 5.63066i) q^{12} +31.0152 q^{13} +(3.58706 + 52.2602i) q^{14} -34.0878i q^{15} +(53.7583 - 34.7281i) q^{16} +(37.4442 + 21.6184i) q^{17} +(15.7476 + 20.0003i) 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} +(-67.5862 - 6.33288i) q^{24} +(-2.05428 + 3.55811i) q^{25} +(86.8239 - 12.5357i) q^{26} -27.0000i q^{27} +(31.1642 + 144.847i) q^{28} -149.567i q^{29} +(-13.7776 - 95.4253i) q^{30} +(-72.4769 + 125.534i) q^{31} +(136.455 - 118.946i) 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} +(-79.3627 + 62.4874i) q^{38} +(-80.5798 - 46.5228i) q^{39} +(209.696 + 148.765i) q^{40} +340.542i q^{41} +(69.0709 - 141.157i) q^{42} -382.268 q^{43} +(-37.2764 + 154.452i) q^{44} +(-51.1317 + 88.5627i) q^{45} +(198.726 - 156.470i) 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} +(237.988 - 70.1850i) q^{52} +(-629.932 - 363.692i) q^{53} +(-10.9129 - 75.5838i) q^{54} -225.670 q^{55} +(145.786 + 392.890i) q^{56} +107.138 q^{57} +(-60.4519 - 418.697i) q^{58} +(-495.394 - 286.016i) q^{59} +(-77.1381 - 261.565i) 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} +(132.408 - 104.253i) q^{66} +(-55.2285 + 95.6585i) q^{67} +(336.240 + 81.1506i) q^{68} -268.276 q^{69} +(-493.877 + 332.204i) q^{70} -518.920i q^{71} +(166.095 + 117.833i) q^{72} +(948.097 + 547.384i) q^{73} +(655.063 - 515.774i) 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} +(647.152 + 331.697i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(137.640 + 953.313i) q^{82} -934.727i q^{83} +(136.304 - 423.071i) q^{84} +491.282i q^{85} +(-1070.12 + 154.505i) q^{86} +(-224.350 + 388.586i) q^{87} +(-41.9253 + 447.438i) 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} +(-163.209 - 207.285i) q^{94} +(-351.423 - 202.894i) q^{95} +(-532.938 + 104.349i) q^{96} -477.327i q^{97} +(-970.131 - 6.13945i) 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 $

$2$	2.79940	−	0.404181i	0.989737	−	0.142899i
$2$	2.79940	−	0.404181i	0.989737	−	0.142899i
$3$	−2.59808	−	1.50000i	−0.500000	−	0.288675i
$3$	−2.59808	−	1.50000i	−0.500000	−	0.288675i
$4$	7.67328	−	2.26293i	0.959160	−	0.282866i
$5$	5.68130	+	9.84030i	0.508151	+	0.880143i	0.999955	+	0.00943729i	$0.00300403\pi$
$5$	5.68130	+	9.84030i	0.508151	+	0.880143i	−0.491805	+	0.870705i	$0.663663\pi$
$6$	−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
$10$	19.8815	+	25.2506i	0.628708	+	0.798496i
$11$	−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	$0.254416\pi$
$12$	−23.3301	−	5.63066i	−0.561236	−	0.135453i
$13$	31.0152			0.661697			0.330848	−	0.943684i	$-0.392665\pi$
$13$	31.0152			0.661697			0.330848	+	0.943684i	$0.392665\pi$
$14$	3.58706	+	52.2602i	0.0684773	+	0.997653i
$15$		−	34.0878i		−	0.586762i
$16$	53.7583	−	34.7281i	0.839974	−	0.542627i
$17$	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	$0.566865\pi$
$18$	15.7476	+	20.0003i	0.206208	+	0.261896i
$19$	−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	−0.106029	−	0.994363i	$-0.533814\pi$
$23$	77.4445	−	44.7126i	0.702100	−	0.405357i	0.808129	+	0.589006i	$0.200480\pi$
$24$	−67.5862	−	6.33288i	−0.574832	−	0.0538622i
$25$	−2.05428	+	3.55811i	−0.0164342	+	0.0284649i
$26$	86.8239	−	12.5357i	0.654906	−	0.0945561i
$27$		−	27.0000i		−	0.192450i
$28$	31.1642	+	144.847i	0.210339	+	0.977629i
$29$		−	149.567i		−	0.957718i	−0.877892	−	0.478859i	$-0.841050\pi$
$29$		−	149.567i		−	0.957718i	0.877892	−	0.478859i	$-0.158950\pi$
$30$	−13.7776	−	95.4253i	−0.0838479	−	0.580740i
$31$	−72.4769	+	125.534i	−0.419911	+	0.727307i	−0.995930	−	0.0901295i	$-0.971272\pi$
$31$	−72.4769	+	125.534i	−0.419911	+	0.727307i	0.576019	+	0.817436i	$0.304605\pi$
$32$	136.455	−	118.946i	0.753812	−	0.657090i
$33$	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	$-0.439390\pi$
$37$	255.281	−	147.387i	1.13427	−	0.654871i	0.945005	+	0.327055i	$0.106056\pi$
$38$	−79.3627	+	62.4874i	−0.338798	+	0.266758i
$39$	−80.5798	−	46.5228i	−0.330848	−	0.191015i
$40$	209.696	+	148.765i	0.828898	+	0.588045i
$41$			340.542i			1.29716i	0.761145	+	0.648582i	$0.224638\pi$
$41$			340.542i			1.29716i	−0.761145	+	0.648582i	$0.775362\pi$
$42$	69.0709	−	141.157i	0.253759	−	0.518594i
$43$	−382.268			−1.35571			−0.677853	−	0.735197i	$-0.737090\pi$
$43$	−382.268			−1.35571			−0.677853	+	0.735197i	$0.737090\pi$
$44$	−37.2764	+	154.452i	−0.127719	+	0.529192i
$45$	−51.1317	+	88.5627i	−0.169384	+	0.293381i
$46$	198.726	−	156.470i	0.636969	−	0.501527i
$47$	−46.6383	−	80.7798i	−0.144742	−	0.250701i	0.784534	−	0.620085i	$-0.212902\pi$
$47$	−46.6383	−	80.7798i	−0.144742	−	0.250701i	−0.929277	+	0.369384i	$0.879569\pi$
$48$	−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
$52$	237.988	−	70.1850i	0.634673	−	0.187171i
$53$	−629.932	−	363.692i	−1.63260	−	0.942583i	−0.983287	−	0.182062i	$-0.941723\pi$
$53$	−629.932	−	363.692i	−1.63260	−	0.942583i	−0.649314	−	0.760520i	$-0.724944\pi$
$54$	−10.9129	−	75.5838i	−0.0275010	−	0.190475i
$55$	−225.670			−0.553261
$56$	145.786	+	392.890i	0.347882	+	0.937538i
$57$	107.138			0.248961
$58$	−60.4519	−	418.697i	−0.136857	−	0.947890i
$59$	−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	$0.884071\pi$
$60$	−77.1381	−	261.565i	−0.165975	−	0.562798i
$61$	−7.77051	−	13.4589i	−0.0163100	−	0.0282498i	0.857755	−	0.514058i	$-0.171859\pi$
$61$	−7.77051	−	13.4589i	−0.0163100	−	0.0282498i	−0.874065	+	0.485809i	$0.838525\pi$
$62$	−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
$66$	132.408	−	104.253i	0.246943	−	0.194434i
$67$	−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	$0.198776\pi$
$68$	336.240	+	81.1506i	0.599634	+	0.144720i
$69$	−268.276			−0.468066
$70$	−493.877	+	332.204i	−0.843280	+	0.567228i
$71$		−	518.920i		−	0.867387i	−0.901060	−	0.433693i	$-0.857210\pi$
$71$		−	518.920i		−	0.867387i	0.901060	−	0.433693i	$-0.142790\pi$
$72$	166.095	+	117.833i	0.271867	+	0.192871i
$73$	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	$0.325795\pi$
$74$	655.063	−	515.774i	1.02905	−	0.810237i
$75$	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	$-0.590468\pi$
$79$	288.366	−	166.488i	0.410680	−	0.237106i	0.691082	+	0.722777i	$0.257134\pi$
$80$	647.152	+	331.697i	0.904422	+	0.463561i
$81$	−40.5000	+	70.1481i	−0.0555556	+	0.0962250i
$82$	137.640	+	953.313i	0.185364	+	1.28385i
$83$		−	934.727i		−	1.23614i	−0.786123	−	0.618070i	$-0.787915\pi$
$83$		−	934.727i		−	1.23614i	0.786123	−	0.618070i	$-0.212085\pi$
$84$	136.304	−	423.071i	0.177048	−	0.549534i
$85$			491.282i			0.626907i
$86$	−1070.12	+	154.505i	−1.34179	+	0.193730i
$87$	−224.350	+	388.586i	−0.276469	+	0.478859i
$88$	−41.9253	+	447.438i	−0.0507870	+	0.542012i
$89$	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
$94$	−163.209	−	207.285i	−0.179082	−	0.227445i
$95$	−351.423	−	202.894i	−0.379528	−	0.219121i
$96$	−532.938	+	104.349i	−0.566592	+	0.110938i
$97$		−	477.327i		−	0.499642i	−0.968292	−	0.249821i	$-0.919628\pi$
$97$		−	477.327i		−	0.499642i	0.968292	−	0.249821i	$-0.0803717\pi$
$98$	−970.131	−	6.13945i	−0.999980	−	0.00632835i
$99$	−178.747			−0.181462
$100$	−7.71129	+	31.9510i	−0.00771129	+	0.0319510i
$101$	330.374	−	572.225i	0.325480	−	0.563748i	−0.656129	−	0.754648i	$-0.727807\pi$
$101$	330.374	−	572.225i	0.325480	−	0.563748i	0.981609	+	0.190901i	$0.0611408\pi$
$102$	−226.958	−	288.250i	−0.220316	−	0.279814i
$103$	452.718	+	784.131i	0.433084	+	0.750124i	0.997137	−	0.0756149i	$-0.0240920\pi$
$103$	452.718	+	784.131i	0.433084	+	0.750124i	−0.564053	+	0.825739i	$0.690759\pi$
$104$	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	$-0.377474\pi$
$108$	−61.0990	−	207.178i	−0.0544375	−	0.184590i
$109$	841.623	+	485.911i	0.739568	+	0.426990i	0.821912	−	0.569614i	$-0.192907\pi$
$109$	841.623	+	485.911i	0.739568	+	0.426990i	−0.0823444	+	0.996604i	$0.526241\pi$
$110$	−631.741	+	91.2114i	−0.547583	+	0.0790606i
$111$	−884.320			−0.756180
$112$	566.911	+	1040.93i	0.478286	+	0.878204i
$113$	−1694.16			−1.41038			−0.705189	−	0.709019i	$-0.749138\pi$
$113$	−1694.16			−1.41038			−0.705189	+	0.709019i	$0.749138\pi$
$114$	299.922	−	43.3030i	0.246406	−	0.0355763i
$115$	879.970	+	508.051i	0.713545	+	0.411965i
$116$	−338.458	−	1147.67i	−0.270906	−	0.918605i
$117$	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
$122$	−27.1926	−	34.5362i	−0.0201795	−	0.0256292i
$123$	510.813	−	884.754i	0.374459	−	0.648582i
$124$	−272.062	+	1127.26i	−0.197031	+	0.816381i
$125$	1373.64			0.982897
$126$	−391.187	+	263.129i	−0.276585	+	0.186043i
$127$			627.533i			0.438461i	0.975673	+	0.219231i	$0.0703547\pi$
$127$			627.533i			0.438461i	−0.975673	+	0.219231i	$0.929645\pi$
$128$	777.888	−	1221.49i	0.537158	−	0.843481i
$129$	993.162	+	573.403i	0.677853	+	0.391359i
$130$	616.627	+	783.153i	0.416014	+	0.528362i
$131$	−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
$136$	974.071	+	91.2712i	0.614161	+	0.0575473i
$137$	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	$0.0684509\pi$
$138$	−751.011	+	108.432i	−0.463263	+	0.0668864i
$139$		−	2556.40i		−	1.55994i	−0.625819	−	0.779969i	$-0.715235\pi$
$139$		−	2556.40i		−	1.55994i	0.625819	−	0.779969i	$-0.284765\pi$
$140$	−1248.29	+	1129.59i	−0.753569	+	0.681911i
$141$			279.830i			0.167134i
$142$	−209.737	−	1452.66i	−0.123949	−	0.858485i
$143$	−307.993	+	533.459i	−0.180109	+	0.311959i
$144$	512.591	+	262.728i	0.296638	+	0.152042i
$145$	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	$-0.379042\pi$
$149$	2474.68	−	1428.76i	1.36063	−	0.785559i	0.989707	+	0.143105i	$0.0457088\pi$
$150$	27.3908	−	21.5666i	0.0149097	−	0.0117394i
$151$	2143.73	+	1237.68i	1.15532	+	0.667027i	0.950179	−	0.311705i	$-0.100900\pi$
$151$	2143.73	+	1237.68i	1.15532	+	0.667027i	0.205145	+	0.978732i	$0.434233\pi$
$152$	−467.568	+	659.075i	−0.249505	+	0.351698i
$153$			389.131i			0.205617i
$154$	−934.494	−	457.267i	−0.488985	−	0.239271i
$155$	−1647.05			−0.853511
$156$	−723.588	−	174.636i	−0.371368	−	0.0896286i
$157$	−1225.00	+	2121.76i	−0.622709	+	1.07856i	0.366270	+	0.930509i	$0.380635\pi$
$157$	−1225.00	+	2121.76i	−0.622709	+	1.07856i	−0.988979	+	0.148056i	$0.952699\pi$
$158$	739.960	−	582.619i	0.372583	−	0.293359i
$159$	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	$0.552148\pi$
$164$	770.621	+	2613.07i	0.366923	+	1.24419i
$165$	586.308	+	338.505i	0.276630	+	0.159713i
$166$	−377.799	−	2616.68i	−0.176644	−	1.22345i
$167$	−882.107			−0.408739			−0.204370	−	0.978894i	$-0.565514\pi$
$167$	−882.107			−0.408739			−0.204370	+	0.978894i	$0.565514\pi$
$168$	210.573	−	1239.44i	0.0967028	−	0.569194i
$169$	−1235.06			−0.562157
$170$	198.567	+	1375.30i	0.0895846	+	0.620473i
$171$	−278.352	−	160.707i	−0.124480	−	0.0718687i
$172$	−2933.25	+	865.045i	−1.30034	+	0.383483i
$173$	−584.827	−	1012.95i	−0.257015	−	0.445163i	0.708426	−	0.705785i	$-0.249406\pi$
$173$	−584.827	−	1012.95i	−0.257015	−	0.445163i	−0.965441	+	0.260622i	$0.916072\pi$
$174$	−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
$178$	927.787	−	730.507i	0.390678	−	0.307606i
$179$	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	$0.137867\pi$
$180$	−191.937	+	795.273i	−0.0794784	+	0.329312i
$181$	−698.293			−0.286761			−0.143380	−	0.989668i	$-0.545797\pi$
$181$	−698.293			−0.286761			−0.143380	+	0.989668i	$0.545797\pi$
$182$	111.253	+	1620.86i	0.0453112	+	0.660144i
$183$			46.6231i			0.0188332i
$184$	1170.80	−	1650.34i	0.469090	−	0.661221i
$185$	2900.66	+	1674.70i	1.15276	+	0.665546i
$186$	966.375	−	760.890i	0.380957	−	0.299952i
$187$	−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	$-0.456690\pi$
$191$	2801.97	−	1617.72i	1.06148	−	0.612848i	0.925842	+	0.377910i	$0.123357\pi$
$192$	−1449.73	+	507.517i	−0.544924	+	0.190765i
$193$	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	$-0.0567270\pi$
$194$	−192.926	−	1336.23i	−0.0713985	−	0.494514i
$195$		−	1057.24i		−	0.388259i
$196$	−2718.27	+	374.921i	−0.990622	+	0.136633i
$197$			2199.91i			0.795618i	0.917468	+	0.397809i	$0.130229\pi$
$197$			2199.91i			0.795618i	−0.917468	+	0.397809i	$0.869771\pi$
$198$	−500.384	+	72.2461i	−0.179600	+	0.0259308i
$199$	1592.88	−	2758.94i	0.567417	−	0.982795i	−0.429404	−	0.903113i	$-0.641276\pi$
$199$	1592.88	−	2758.94i	0.567417	−	0.982795i	0.996820	−	0.0796820i	$-0.0253905\pi$
$200$	−8.67298	+	92.5605i	−0.00306636	+	0.0327251i
$201$	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
$206$	1584.27	+	2012.12i	0.535832	+	0.680538i
$207$	697.000	+	402.413i	0.234033	+	0.135119i
$208$	1667.32	−	1077.10i	0.555808	−	0.359054i
$209$		−	709.280i		−	0.234746i
$210$	1781.44	−	122.275i	0.585385	−	0.0401799i
$211$	683.474			0.222997			0.111498	−	0.993765i	$-0.464435\pi$
$211$	683.474			0.222997			0.111498	+	0.993765i	$0.464435\pi$
$212$	−5656.65	−	1365.22i	−1.83255	−	0.442280i
$213$	−778.380	+	1348.19i	−0.250393	+	0.433693i
$214$	−2381.70	−	3024.90i	−0.760794	−	0.966253i
$215$	−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
$220$	−1731.63	+	510.675i	−0.530665	+	0.156499i
$221$	1161.34	+	670.499i	0.353484	+	0.204084i
$222$	−2475.57	+	357.425i	−0.748419	+	0.108058i
$223$	−4932.98			−1.48133			−0.740665	−	0.671874i	$-0.765490\pi$
$223$	−4932.98			−1.48133			−0.740665	+	0.671874i	$0.765490\pi$
$224$	2007.73	+	2684.85i	0.598872	+	0.800845i
$225$	−36.9770			−0.0109561
$226$	−4742.62	+	684.745i	−1.39590	+	0.201542i
$227$	−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	$0.818371\pi$
$228$	822.098	−	242.445i	0.238793	−	0.0704224i
$229$	−2141.45	−	3709.10i	−0.617952	−	1.07032i	−0.989859	−	0.142054i	$-0.954629\pi$
$229$	−2141.45	−	3709.10i	−0.617952	−	1.07032i	0.371907	−	0.928270i	$-0.378704\pi$
$230$	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	$0.846841\pi$
$234$	488.414	+	620.314i	0.136447	+	0.173296i
$235$	529.932	−	917.868i	0.147102	−	0.254788i
$236$	−4448.53	−	1073.64i	−1.22701	−	0.296136i
$237$	−998.929			−0.273787
$238$	−995.469	+	2034.39i	−0.271120	+	0.554075i
$239$			3412.31i			0.923530i	0.887002	+	0.461765i	$0.152784\pi$
$239$			3412.31i			0.923530i	−0.887002	+	0.461765i	$0.847216\pi$
$240$	−1183.80	−	1832.50i	−0.318393	−	0.492865i
$241$	−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	$0.870617\pi$
$242$	1638.71	+	2081.26i	0.435290	+	0.552844i
$243$	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
$248$	−305.991	+	3265.62i	−0.0783487	+	0.836159i
$249$	−1402.09	+	2428.49i	−0.356843	+	0.618070i
$250$	3845.37	−	555.199i	0.972810	−	0.140455i
$251$			2427.14i			0.610358i	0.952295	+	0.305179i	$0.0987164\pi$
$251$			2427.14i			0.610358i	−0.952295	+	0.305179i	$0.901284\pi$
$252$	−988.736	+	894.714i	−0.247161	+	0.223658i
$253$			1776.05i			0.441342i
$254$	253.637	+	1756.72i	0.0626558	+	0.433961i
$255$	736.924	−	1276.39i	0.180972	−	0.313453i
$256$	1683.92	−	3733.85i	0.411113	−	0.911585i
$257$	−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
$262$	−3952.35	+	3111.94i	−0.931973	+	0.733803i
$263$	1779.35	+	1027.31i	0.417184	+	0.240862i	0.693872	−	0.720098i	$-0.255903\pi$
$263$	1779.35	+	1027.31i	0.417184	+	0.240862i	−0.276688	+	0.960960i	$0.589237\pi$
$264$	780.083	−	1099.59i	0.181859	−	0.256345i
$265$		−	8264.96i		−	1.91590i
$266$	−1044.12	−	1552.25i	−0.240672	−	0.357800i
$267$	−1252.49			−0.287083
$268$	−207.315	+	858.992i	−0.0472529	+	0.195788i
$269$	−61.4698	+	106.469i	−0.0139326	+	0.0241320i	−0.872908	−	0.487885i	$-0.837768\pi$
$269$	−61.4698	+	106.469i	−0.0139326	+	0.0241320i	0.858975	+	0.512017i	$0.171102\pi$
$270$	681.768	−	536.800i	0.153671	−	0.120995i
$271$	206.365	+	357.435i	0.0462576	+	0.0801204i	0.888227	−	0.459405i	$-0.151937\pi$
$271$	206.365	+	357.435i	0.0462576	+	0.0801204i	−0.841970	+	0.539525i	$0.818604\pi$
$272$	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
$276$	−2058.55	+	607.088i	−0.448950	+	0.132400i
$277$	1971.50	+	1138.25i	0.427639	+	0.246897i	0.698340	−	0.715766i	$-0.253922\pi$
$277$	1971.50	+	1138.25i	0.427639	+	0.246897i	−0.270701	+	0.962663i	$0.587256\pi$
$278$	−1033.25	−	7156.39i	−0.222914	−	1.54393i
$279$	−1304.58			−0.279940
$280$	−3037.90	+	3666.70i	−0.648391	+	0.782597i
$281$	−7937.53			−1.68510			−0.842551	−	0.538617i	$-0.818947\pi$
$281$	−7937.53			−1.68510			−0.842551	+	0.538617i	$0.818947\pi$
$282$	113.102	+	783.355i	0.0238834	+	0.165419i
$283$	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	$0.364066\pi$
$284$	−1174.28	−	3981.82i	−0.245354	−	0.831962i
$285$	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
$290$	3776.66	−	2973.61i	0.764734	−	0.602125i
$291$	−715.991	+	1240.13i	−0.144234	+	0.249821i
$292$	8513.70	+	2054.76i	1.70626	+	0.411800i
$293$	1805.31			0.359957			0.179978	−	0.983671i	$-0.442397\pi$
$293$	1805.31			0.359957			0.179978	+	0.983671i	$0.442397\pi$
$294$	2511.27	+	1471.15i	0.498163	+	0.291834i
$295$		−	6499.77i		−	1.28282i
$296$	3859.32	−	5440.04i	0.757833	−	1.06823i
$297$	464.399	+	268.121i	0.0907311	+	0.0523836i
$298$	6350.14	−	4999.88i	1.23441	−	0.971930i
$299$	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
$304$	−1042.52	+	2034.00i	−0.196687	+	0.383743i
$305$	88.2932	−	152.928i	0.0165759	−	0.0287103i
$306$	157.279	+	1089.33i	0.0293825	+	0.203507i
$307$			5699.24i			1.05952i	0.848148	+	0.529760i	$0.177718\pi$
$307$			5699.24i			1.05952i	−0.848148	+	0.529760i	$0.822282\pi$
$308$	−2800.84	−	902.370i	−0.518158	−	0.166939i
$309$		−	2716.31i		−	0.500082i
$310$	−4610.75	+	665.706i	−0.844752	+	0.121966i
$311$	2294.28	−	3973.81i	0.418317	−	0.724546i	−0.577453	−	0.816424i	$-0.695953\pi$
$311$	2294.28	−	3973.81i	0.418317	−	0.724546i	0.995770	+	0.0918773i	$0.0292868\pi$
$312$	−2096.20	−	196.415i	−0.380365	−	0.0356405i
$313$	−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	−0.909915	−	0.414795i	$-0.863853\pi$
$317$	−5675.91	+	3276.99i	−1.00565	+	0.580612i	−0.0957345	+	0.995407i	$0.530520\pi$
$318$	3818.17	+	4849.31i	0.673310	+	0.855143i
$319$	2572.54	+	1485.26i	0.451519	+	0.260685i
$320$	5716.38	+	1080.75i	0.998611	+	0.188799i
$321$			4083.55i			0.710036i
$322$	2614.49	+	3886.88i	0.452484	+	0.672694i
$323$	−1544.10			−0.265994
$324$	−152.028	+	629.914i	−0.0260679	+	0.108010i
$325$	−63.7137	+	110.355i	−0.0108745	+	0.0188351i
$326$	5628.54	+	7148.58i	0.956245	+	1.21449i
$327$	−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	$0.449591\pi$
$332$	−2115.22	−	7172.42i	−0.349662	−	1.18566i
$333$	2297.53	+	1326.48i	0.378090	+	0.218290i
$334$	−2469.37	+	356.530i	−0.404544	+	0.0584086i
$335$	−1255.08			−0.204693
$336$	88.5220	−	3554.79i	0.0143728	−	0.577171i
$337$	−4766.06			−0.770397			−0.385199	−	0.922834i	$-0.625867\pi$
$337$	−4766.06			−0.770397			−0.385199	+	0.922834i	$0.625867\pi$
$338$	−3457.42	+	499.187i	−0.556388	+	0.0803319i
$339$	4401.55	+	2541.23i	0.705189	+	0.407141i
$340$	1111.74	+	3769.75i	0.177330	+	0.601303i
$341$	−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
$346$	−2046.58	−	2599.28i	−0.317991	−	0.403867i
$347$	−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	$0.285824\pi$
$348$	−842.159	+	3489.41i	−0.129725	+	0.537506i
$349$	−3269.10			−0.501407			−0.250703	−	0.968064i	$-0.580662\pi$
$349$	−3269.10			−0.501407			−0.250703	+	0.968064i	$0.580662\pi$
$350$	−193.316	−	94.5938i	−0.0295234	−	0.0144464i
$351$		−	837.410i		−	0.127344i
$352$	690.815	+	3528.19i	0.104604	+	0.534242i
$353$	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	$0.512271\pi$
$354$	3002.71	+	3813.61i	0.450825	+	0.572574i
$355$	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	$-0.335107\pi$
$359$	10170.1	−	5871.73i	1.49515	−	0.863226i	0.999984	+	0.00557116i	$0.00177336\pi$
$360$	−215.874	+	2303.86i	−0.0316043	+	0.337290i
$361$	−2791.80	+	4835.55i	−0.407028	+	0.704993i
$362$	−1954.80	+	282.237i	−0.283818	+	0.0409780i
$363$		−	2809.65i		−	0.406249i
$364$	966.563	+	4492.47i	0.139180	+	0.646894i
$365$			12439.4i			1.78386i
$366$	18.8441	+	130.517i	0.00269125	+	0.0186399i
$367$	1562.19	−	2705.80i	0.222196	−	0.384855i	−0.733279	−	0.679928i	$-0.762011\pi$
$367$	1562.19	−	2705.80i	0.222196	−	0.384855i	0.955474	+	0.295074i	$0.0953442\pi$
$368$	2610.50	−	5093.18i	0.369788	−	0.721468i
$369$	−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	$-0.803908\pi$
$373$	−5214.58	+	3010.64i	−0.723862	+	0.417922i	0.0923105	+	0.995730i	$0.470575\pi$
$374$	−1908.29	+	1502.52i	−0.263838	+	0.207737i
$375$	−3568.82	−	2060.46i	−0.491449	−	0.283738i
$376$	−1721.42	−	1221.22i	−0.236104	−	0.167499i
$377$		−	4638.84i		−	0.633719i
$378$	1411.03	−	96.8506i	0.191998	−	0.0131785i
$379$	−11131.0			−1.50860			−0.754300	−	0.656530i	$-0.772024\pi$
$379$	−11131.0			−1.50860			−0.754300	+	0.656530i	$0.772024\pi$
$380$	−3155.70	−	761.618i	−0.426010	−	0.102816i
$381$	941.299	−	1630.38i	0.126573	−	0.219231i
$382$	7189.99	−	5661.14i	0.963015	−	0.758244i
$383$	7412.83	+	12839.4i	0.988977	+	1.71296i	0.622722	+	0.782443i	$0.286027\pi$
$383$	7412.83	+	12839.4i	0.988977	+	1.71296i	0.366254	+	0.930515i	$0.380640\pi$
$384$	−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
$388$	−1080.16	−	3662.66i	−0.141331	−	0.479236i
$389$	−1408.72	−	813.323i	−0.183611	−	0.106008i	0.405377	−	0.914150i	$-0.367140\pi$
$389$	−1408.72	−	813.323i	−0.183611	−	0.106008i	−0.588988	+	0.808142i	$0.700474\pi$
$390$	−427.315	−	2959.63i	−0.0554819	−	0.384274i
$391$	3866.46			0.500090
$392$	−7457.98	+	2148.22i	−0.960930	+	0.276790i
$393$	5335.58			0.684845
$394$	889.159	+	6158.42i	0.113693	+	0.787453i
$395$	3276.59	+	1891.74i	0.417374	+	0.240971i
$396$	−1371.58	+	404.491i	−0.174051	+	0.0513294i
$397$	4545.33	+	7872.74i	0.574618	+	0.995268i	0.996083	+	0.0884234i	$0.0281828\pi$
$397$	4545.33	+	7872.74i	0.574618	+	0.995268i	−0.421465	+	0.906845i	$0.638484\pi$
$398$	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	$0.749494\pi$
$402$	736.392	−	579.809i	0.0913630	−	0.0719360i
$403$	−2247.88	+	3893.45i	−0.277854	+	0.481257i
$404$	1240.15	−	5138.45i	0.152722	−	0.632791i
$405$	−920.370			−0.112922
$406$	7816.39	−	536.505i	0.955470	−	0.0655820i
$407$			5854.43i			0.713006i
$408$	−2393.80	−	1698.24i	−0.290468	−	0.206067i
$409$	−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	$0.916346\pi$
$410$	−8598.90	+	6770.48i	−1.03578	+	0.815536i
$411$	−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
$416$	4232.16	−	3689.13i	0.498795	−	0.434794i
$417$	−3834.60	+	6641.73i	−0.450315	+	0.779969i
$418$	−286.677	−	1985.56i	−0.0335451	−	0.232337i
$419$		−	6630.39i		−	0.773068i	−0.922275	−	0.386534i	$-0.873672\pi$
$419$		−	6630.39i		−	0.773068i	0.922275	−	0.386534i	$-0.126328\pi$
$420$	4937.53	−	1062.32i	0.573635	−	0.123419i
$421$			8062.94i			0.933406i	0.884414	+	0.466703i	$0.154558\pi$
$421$			8062.94i			0.933406i	−0.884414	+	0.466703i	$0.845442\pi$
$422$	1913.32	−	276.247i	0.220708	−	0.0318661i
$423$	419.744	−	727.018i	0.0482474	−	0.0835670i
$424$	−16387.0	−	1535.48i	−1.87694	−	0.175871i
$425$	−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
$430$	−7600.06	−	9652.52i	−0.852343	−	1.08253i
$431$	−11197.4	−	6464.82i	−1.25141	−	0.722505i	−0.280024	−	0.959993i	$-0.590343\pi$
$431$	−11197.4	−	6464.82i	−1.25141	−	0.722505i	−0.971390	+	0.237488i	$0.923676\pi$
$432$	−937.659	−	1451.48i	−0.104429	−	0.161653i
$433$		−	15425.1i		−	1.71197i	−0.516999	−	0.855986i	$-0.672951\pi$
$433$		−	15425.1i		−	1.71197i	0.516999	−	0.855986i	$-0.327049\pi$
$434$	−6820.40	−	3337.36i	−0.754354	−	0.369121i
$435$	−5098.40			−0.561953
$436$	7557.59	+	1824.00i	0.830144	+	0.200353i
$437$	−1596.80	+	2765.74i	−0.174795	+	0.302754i
$438$	−5746.65	−	7298.58i	−0.626907	−	0.796209i
$439$	7687.49	+	13315.1i	0.835772	+	1.44760i	0.893400	+	0.449262i	$0.148313\pi$
$439$	7687.49	+	13315.1i	0.835772	+	1.44760i	−0.0576279	+	0.998338i	$0.518354\pi$
$440$	−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	$0.759565\pi$
$444$	−6785.63	+	2001.15i	−0.725297	+	0.213897i
$445$	4108.29	+	2371.92i	0.437645	+	0.252674i
$446$	−13809.4	+	1993.81i	−1.46613	+	0.211681i
$447$	−8572.54			−0.907086
$448$	6705.61	+	6704.49i	0.707166	+	0.707047i
$449$	14674.6			1.54240			0.771201	−	0.636592i	$-0.219656\pi$
$449$	14674.6			1.54240			0.771201	+	0.636592i	$0.219656\pi$
$450$	−103.513	+	14.9454i	−0.0108437	+	0.00156563i
$451$	−5857.30	−	3381.71i	−0.611551	−	0.353079i
$452$	−12999.7	+	3833.75i	−1.35278	+	0.398948i
$453$	−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	$0.486372\pi$
$458$	−7493.92	−	9517.71i	−0.764558	−	0.971034i
$459$	583.697	−	1010.99i	0.0593565	−	0.102809i
$460$	7901.94	+	1907.11i	0.800934	+	0.193303i
$461$	−6377.83			−0.644349			−0.322175	−	0.946680i	$-0.604414\pi$
$461$	−6377.83			−0.644349			−0.322175	+	0.946680i	$0.604414\pi$
$462$	1741.99	+	2589.76i	0.175421	+	0.260793i
$463$			7592.70i			0.762123i	0.924550	+	0.381061i	$0.124441\pi$
$463$			7592.70i			0.762123i	−0.924550	+	0.381061i	$0.875559\pi$
$464$	−5194.17	−	8040.46i	−0.519684	−	0.804459i
$465$	4279.16	+	2470.58i	0.426756	+	0.246388i
$466$	−528.013	−	670.608i	−0.0524887	−	0.0666637i
$467$	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
$472$	−12887.2	−	1207.54i	−1.25674	−	0.117757i
$473$	3796.07	−	6574.99i	0.369014	−	0.639151i
$474$	−2796.40	+	403.748i	−0.270977	+	0.0391239i
$475$		−	146.727i		−	0.0141733i
$476$	−1964.45	+	6097.41i	−0.189161	+	0.587131i
$477$		−	6546.45i		−	0.628388i
$478$	1379.19	+	9552.41i	0.131972	+	0.914052i
$479$	−7795.95	+	13503.0i	−0.743645	+	1.28803i	0.207180	+	0.978303i	$0.433571\pi$
$479$	−7795.95	+	13503.0i	−0.743645	+	1.28803i	−0.950825	+	0.309728i	$0.899762\pi$
$480$	−4054.60	−	4651.44i	−0.385555	−	0.442308i
$481$	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
$486$	540.009	−	425.184i	0.0504019	−	0.0396847i
$487$	−9084.27	−	5244.80i	−0.845272	−	0.488018i	0.0137808	−	0.999905i	$-0.495613\pi$
$487$	−9084.27	−	5244.80i	−0.845272	−	0.488018i	−0.859053	+	0.511887i	$0.828947\pi$
$488$	−286.809	−	203.471i	−0.0266050	−	0.0188744i
$489$		−	9650.41i		−	0.892447i
$490$	−5451.19	−	9581.26i	−0.502571	−	0.883341i
$491$	7949.83			0.730694			0.365347	−	0.930871i	$-0.380950\pi$
$491$	7949.83			0.730694			0.365347	+	0.930871i	$0.380950\pi$
$492$	1917.48	−	7944.89i	0.175704	−	0.728015i
$493$	3233.39	−	5600.40i	0.295385	−	0.511621i
$494$	−2461.45	+	1938.06i	−0.224182	+	0.176513i
$495$	−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	$0.903076\pi$
$500$	10540.3	−	3108.45i	0.942755	−	0.278028i
$501$	2291.78	+	1323.16i	0.204370	+	0.117993i
$502$	981.004	+	6794.55i	0.0872199	+	0.604094i
$503$	546.557			0.0484488			0.0242244	−	0.999707i	$-0.492288\pi$
$503$	546.557			0.0484488			0.0242244	+	0.999707i	$0.492288\pi$
$504$	−2406.24	+	2904.29i	−0.212664	+	0.256681i
$505$	7507.82			0.661571
$506$	717.847	+	4971.89i	0.0630675	+	0.436813i
$507$	3208.78	+	1852.59i	0.281079	+	0.162281i
$508$	1420.06	+	4815.23i	0.124026	+	0.420554i
$509$	1123.03	+	1945.14i	0.0977944	+	0.169385i	0.910771	−	0.412911i	$-0.135488\pi$
$509$	1123.03	+	1945.14i	0.0977944	+	0.169385i	−0.812977	+	0.582296i	$0.802155\pi$
$510$	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
$514$	−14053.8	+	11065.5i	−1.20601	+	0.949569i
$515$	−5144.05	+	8909.76i	−0.440144	+	0.762352i
$516$	8918.38	+	2152.42i	0.760871	+	0.183634i
$517$	1852.54			0.157592
$518$	8618.17	+	12812.4i	0.731006	+	1.08676i
$519$			3508.96i			0.296775i
$520$	6503.77	+	4613.97i	0.548479	+	0.389108i
$521$	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	$0.560506\pi$
$522$	2991.39	−	2355.31i	0.250823	−	0.197489i
$523$	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
$528$	1739.33	−	3393.49i	0.143361	−	0.279702i
$529$	−2085.07	+	3611.44i	−0.171371	+	0.296823i
$530$	−3340.54	−	23136.9i	−0.273780	−	1.89623i
$531$		−	5148.29i		−	0.420747i
$532$	−3550.29	−	3923.37i	−0.289332	−	0.319736i
$533$			10562.0i			0.858329i
$534$	−3506.22	+	506.233i	−0.284137	+	0.0410240i
$535$	7733.29	−	13394.4i	0.624933	−	1.08242i
$536$	−233.170	+	2488.45i	−0.0187900	+	0.200531i
$537$	−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	$-0.586815\pi$
$541$	5410.37	−	3123.68i	0.429963	−	0.248239i	0.699331	+	0.714798i	$0.253481\pi$
$542$	722.167	+	917.195i	0.0572320	+	0.0726880i
$543$	1814.22	+	1047.44i	0.143380	+	0.0827807i
$544$	7680.85	−	1503.90i	0.605356	−	0.118528i
$545$			11042.4i			0.867900i
$546$	2142.25	−	4378.00i	0.167911	−	0.343152i
$547$	−3021.26			−0.236160			−0.118080	−	0.993004i	$-0.537674\pi$
$547$	−3021.26			−0.236160			−0.118080	+	0.993004i	$0.537674\pi$
$548$	1827.96	−	7573.99i	0.142494	−	0.590410i
$549$	69.9346	−	121.130i	0.00543668	−	0.00941660i
$550$	−142.776	−	181.334i	−0.0110691	−	0.0140584i
$551$	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
$556$	−5784.95	−	19616.0i	−0.441253	−	1.49623i
$557$	5016.95	+	2896.54i	0.381643	+	0.220342i	0.678533	−	0.734570i	$-0.262616\pi$
$557$	5016.95	+	2896.54i	0.381643	+	0.220342i	−0.296890	+	0.954912i	$0.595949\pi$
$558$	−3652.05	+	527.287i	−0.277067	+	0.0400033i
$559$	−11856.1			−0.897067
$560$	−7022.30	+	11492.4i	−0.529904	+	0.867220i
$561$	2576.15			0.193877
$562$	−22220.3	+	3208.20i	−1.66781	+	0.240800i
$563$	−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	$-0.686494\pi$
$564$	633.233	+	2147.21i	0.0472765	+	0.160308i
$565$	−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	$0.731523\pi$
$570$	2130.06	+	2705.30i	0.156523	+	0.198794i
$571$	−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	$0.277313\pi$
$572$	−1156.14	+	4790.34i	−0.0845113	+	0.350165i
$573$	−9706.31			−0.707656
$574$	−17796.8	+	1221.54i	−1.29412	+	0.0888263i
$575$			367.408i			0.0266469i
$576$	4527.79	+	856.030i	0.327531	+	0.0619235i
$577$	−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	$0.787429\pi$
$578$	−5325.44	−	6763.62i	−0.383234	−	0.486730i
$579$	−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
$584$	24663.7	+	2311.01i	1.74759	+	0.163751i
$585$	−1585.86	+	2746.79i	−0.112081	+	0.194129i
$586$	5053.78	−	729.671i	0.356263	−	0.0514376i
$587$			9195.89i			0.646601i	0.946296	+	0.323301i	$0.104792\pi$
$587$			9195.89i			0.646601i	−0.946296	+	0.323301i	$0.895208\pi$
$588$	7624.64	+	3103.32i	0.534753	+	0.217651i
$589$		−	5176.68i		−	0.362141i
$590$	−2627.08	−	18195.5i	−0.183314	−	1.26965i
$591$	3299.86	−	5715.52i	0.229675	−	0.397809i
$592$	8605.03	−	16788.7i	0.597407	−	1.16556i
$593$	−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
$598$	6163.52	−	4852.94i	0.421480	−	0.331859i
$599$	−8877.36	−	5125.35i	−0.605541	−	0.349609i	0.165677	−	0.986180i	$-0.447019\pi$
$599$	−8877.36	−	5125.35i	−0.605541	−	0.349609i	−0.771218	+	0.636571i	$0.780352\pi$
$600$	161.374	−	227.470i	0.0109801	−	0.0154773i
$601$			7735.54i			0.525024i	0.964929	+	0.262512i	$0.0845509\pi$
$601$			7735.54i			0.525024i	−0.964929	+	0.262512i	$0.915449\pi$
$602$	−1371.22	−	19977.4i	−0.0928351	−	1.35252i
$603$	−994.112			−0.0671366
$604$	19250.2	+	4645.97i	1.29682	+	0.312983i
$605$	−5320.81	+	9215.92i	−0.357557	+	0.619307i
$606$	−4405.07	+	3468.40i	−0.295286	+	0.232498i
$607$	11358.6	+	19673.6i	0.759523	+	1.31553i	0.943094	+	0.332525i	$0.107901\pi$
$607$	11358.6	+	19673.6i	0.759523	+	1.31553i	−0.183572	+	0.983006i	$0.558766\pi$
$608$	−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
$612$	880.575	+	2985.91i	0.0581620	+	0.197220i
$613$	11301.1	+	6524.70i	0.744613	+	0.429902i	0.823744	−	0.566962i	$-0.191881\pi$
$613$	11301.1	+	6524.70i	0.744613	+	0.429902i	−0.0791312	+	0.996864i	$0.525215\pi$
$614$	2303.52	+	15954.4i	0.151405	+	1.04865i
$615$	11608.3			0.761126
$616$	−8205.39	−	1394.05i	−0.536696	−	0.0911815i
$617$	3941.58			0.257183			0.128592	−	0.991698i	$-0.458954\pi$
$617$	3941.58			0.257183			0.128592	+	0.991698i	$0.458954\pi$
$618$	−1097.88	−	7604.04i	−0.0714615	−	0.494950i
$619$	−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	$0.807986\pi$
$620$	−12638.3	+	3727.15i	−0.818654	+	0.241429i
$621$	−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
$626$	−13905.2	+	10948.4i	−0.887798	+	0.699021i
$627$	−1063.92	+	1842.76i	−0.0677654	+	0.117373i
$628$	−4598.36	+	19052.9i	−0.292189	+	1.21066i
$629$	12745.1			0.807916
$630$	−4811.72	−	2354.47i	−0.304291	−	0.148896i
$631$		−	20182.5i		−	1.27330i	−0.771154	−	0.636649i	$-0.780320\pi$
$631$		−	20182.5i		−	1.27330i	0.771154	−	0.636649i	$-0.219680\pi$
$632$	4359.50	−	6145.07i	0.274385	−	0.386769i
$633$	−1775.72	−	1025.21i	−0.111498	−	0.0643736i
$634$	−14564.6	+	11467.7i	−0.912360	+	0.718360i
$635$	−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
$640$	16439.3	+	714.994i	1.01534	+	0.0441603i
$641$	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	$-0.0177702\pi$
$642$	1650.49	+	11431.5i	0.101464	+	0.702749i
$643$		−	7636.64i		−	0.468366i	−0.972192	−	0.234183i	$-0.924758\pi$
$643$		−	7636.64i		−	0.468366i	0.972192	−	0.234183i	$-0.0752416\pi$
$644$	8890.00	+	9824.21i	0.543968	+	0.601130i
$645$			13030.7i			0.795477i
$646$	−4322.55	+	624.095i	−0.263264	+	0.0380103i
$647$	2958.17	−	5123.70i	0.179749	−	0.311335i	−0.762045	−	0.647524i	$-0.775805\pi$
$647$	2958.17	−	5123.70i	0.179749	−	0.311335i	0.941795	+	0.336189i	$0.109138\pi$
$648$	−170.988	+	1824.83i	−0.0103658	+	0.110627i
$649$	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	$-0.856878\pi$
$653$	−16261.3	+	9388.47i	−0.974509	+	0.562633i	−0.0739010	+	0.997266i	$0.523545\pi$
$654$	−5101.28	−	6478.93i	−0.305009	−	0.387380i
$655$	−17501.2	−	10104.3i	−1.04401	−	0.602762i
$656$	11826.4	+	18307.0i	0.703876	+	1.08958i
$657$			9852.91i			0.585082i
$658$	4054.28	−	2727.09i	0.240201	−	0.161570i
$659$	−1477.88			−0.0873594			−0.0436797	−	0.999046i	$-0.513908\pi$
$659$	−1477.88			−0.0873594			−0.0436797	+	0.999046i	$0.513908\pi$
$660$	5264.92	+	1270.67i	0.310510	+	0.0749406i
$661$	12988.8	−	22497.3i	0.764307	−	1.32382i	−0.176305	−	0.984336i	$-0.556414\pi$
$661$	12988.8	−	22497.3i	0.764307	−	1.32382i	0.940612	−	0.339484i	$-0.110252\pi$
$662$	19683.8	+	24999.6i	1.15564	+	1.46773i
$663$	−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
$668$	−6768.65	+	1996.14i	−0.392046	+	0.115618i
$669$	12816.3	+	7399.47i	0.740665	+	0.427623i
$670$	−3513.46	+	507.278i	−0.202592	+	0.0292505i
$671$	308.657			0.0177579
$672$	−1188.97	−	9987.05i	−0.0682521	−	0.573302i
$673$	3291.08			0.188502			0.0942509	−	0.995548i	$-0.469954\pi$
$673$	3291.08			0.188502			0.0942509	+	0.995548i	$0.469954\pi$
$674$	−13342.1	+	1926.35i	−0.762491	+	0.110089i
$675$	96.0690	+	55.4654i	0.00547807	+	0.00316276i
$676$	−9476.95	+	2794.85i	−0.539198	+	0.159015i
$677$	−9665.86	−	16741.8i	−0.548728	−	0.950425i	−0.998362	−	0.0572123i	$-0.981779\pi$
$677$	−9665.86	−	16741.8i	−0.548728	−	0.950425i	0.449634	−	0.893213i	$-0.351555\pi$
$678$	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
$682$	−5037.29	−	6397.66i	−0.282827	−	0.359207i
$683$	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	$0.140238\pi$
$684$	−2499.54	−	603.257i	−0.139726	−	0.0337224i
$685$	11066.4			0.617263
$686$	1457.13	−	17908.3i	0.0810986	−	0.996706i
$687$			12848.7i			0.713549i
$688$	−20550.1	+	13275.5i	−1.13876	+	0.735642i
$689$	−19537.5	−	11280.0i	−1.08029	−	0.623704i
$690$	−5333.71	−	6774.13i	−0.294277	−	0.373749i
$691$	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
$696$	−947.188	+	10108.6i	−0.0515848	+	0.550528i
$697$	−7361.97	+	12751.3i	−0.400078	+	0.692956i
$698$	−9151.52	+	1321.31i	−0.496261	+	0.0716507i
$699$			905.304i			0.0489868i
$700$	−579.403	−	186.671i	−0.0312848	−	0.0100793i
$701$		−	34253.9i		−	1.84558i	−0.385300	−	0.922791i	$-0.625902\pi$
$701$		−	34253.9i		−	1.84558i	0.385300	−	0.922791i	$-0.374098\pi$
$702$	−338.465	−	2344.24i	−0.0181973	−	0.126037i
$703$	−5263.56	+	9116.76i	−0.282388	+	0.489111i
$704$	3359.89	+	9597.61i	0.179873	+	0.513812i
$705$	−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	$-0.876397\pi$
$709$	−20019.3	+	11558.2i	−1.06042	+	0.612237i	−0.134875	+	0.990863i	$0.543063\pi$
$710$	13103.1	−	10316.9i	0.692605	−	0.545333i
$711$	2595.29	+	1498.39i	0.136893	+	0.0790354i
$712$	5466.08	−	7704.90i	0.287711	−	0.405552i
$713$			12962.5i			0.680856i
$714$	5637.89	−	3792.29i	0.295508	−	0.198772i
$715$	−6999.20			−0.366091
$716$	812.249	−	3365.48i	0.0423955	−	0.175662i
$717$	5118.46	−	8865.43i	0.266600	−	0.461765i
$718$	26097.1	−	20547.9i	1.35645	−	1.06802i
$719$	5504.81	+	9534.61i	0.285528	+	0.494550i	0.972737	−	0.231910i	$-0.0744976\pi$
$719$	5504.81	+	9534.61i	0.285528	+	0.494550i	−0.687209	+	0.726460i	$0.741164\pi$
$720$	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
$724$	−5358.20	+	1580.19i	−0.275049	+	0.0811148i
$725$	532.175	+	307.251i	0.0272613	+	0.0157393i
$726$	−1135.60	−	7865.33i	−0.0580527	−	0.402079i
$727$	−31122.9			−1.58774			−0.793869	−	0.608089i	$-0.791936\pi$
$727$	−31122.9			−1.58774			−0.793869	+	0.608089i	$0.791936\pi$
$728$	4521.56	+	12185.6i	0.230193	+	0.620366i
$729$	−729.000			−0.0370370
$730$	5027.77	+	34822.9i	0.254912	+	1.76555i
$731$	−14313.7	−	8264.03i	−0.724230	−	0.418134i
$732$	105.505	+	357.752i	0.00532727	+	0.0180640i
$733$	−15353.3	−	26592.7i	−0.773653	−	1.34001i	−0.935549	−	0.353198i	$-0.885094\pi$
$733$	−15353.3	−	26592.7i	−0.773653	−	1.34001i	0.161896	−	0.986808i	$-0.448239\pi$
$734$	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
$738$	−6810.96	+	5362.71i	−0.339722	+	0.267485i
$739$	−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	$0.201912\pi$
$740$	26047.3	+	6286.43i	1.29394	+	0.312289i
$741$	3322.90			0.164736
$742$	16747.0	−	34225.0i	0.828574	−	1.69331i
$743$		−	20548.4i		−	1.01460i	−0.861770	−	0.507299i	$-0.830644\pi$
$743$		−	20548.4i		−	1.01460i	0.861770	−	0.507299i	$-0.169356\pi$
$744$	5693.43	−	8025.35i	0.280553	−	0.395462i
$745$	28118.8	+	16234.4i	1.38281	+	0.798365i
$746$	−13380.8	+	10535.6i	−0.656712	+	0.517072i
$747$	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	$-0.843872\pi$
$751$	−18835.5	+	10874.7i	−0.915205	+	0.528394i	−0.0331028	+	0.999452i	$0.510539\pi$
$752$	−5312.52	−	2722.93i	−0.257617	−	0.132041i
$753$	3640.72	−	6305.90i	0.176195	−	0.305179i
$754$	−1874.93	−	12986.0i	−0.0905581	−	0.627216i
$755$			28126.5i			1.35580i
$756$	3910.88	−	841.433i	0.188145	−	0.0404797i
$757$			29296.1i			1.40658i	0.710901	+	0.703292i	$0.248287\pi$
$757$			29296.1i			1.40658i	−0.710901	+	0.703292i	$0.751713\pi$
$758$	−31160.0	+	4498.92i	−1.49312	+	0.215578i
$759$	2664.08	−	4614.33i	0.127405	−	0.220671i
$760$	−9141.89	−	856.602i	−0.436330	−	0.0408845i
$761$	−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
$766$	25940.9	+	32946.5i	1.22361	+	1.55405i
$767$	−15364.7	−	8870.84i	−0.723323	−	0.417611i
$768$	−9975.72	+	7174.95i	−0.468708	+	0.337114i
$769$			3210.87i			0.150568i	0.997162	+	0.0752840i	$0.0239863\pi$
$769$			3210.87i			0.150568i	−0.997162	+	0.0752840i	$0.976014\pi$
$770$	−809.492	−	11793.6i	−0.0378858	−	0.551962i
$771$	18972.4			0.886216
$772$	6497.84	−	26923.2i	0.302931	−	1.25517i
$773$	−4752.28	+	8231.20i	−0.221123	+	0.382996i	−0.955149	−	0.296125i	$-0.904305\pi$
$773$	−4752.28	+	8231.20i	−0.221123	+	0.382996i	0.734027	+	0.679121i	$0.237639\pi$
$774$	−6019.80	−	7645.50i	−0.279557	−	0.355054i
$775$	−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
$780$	−2392.45	−	8112.48i	−0.109825	−	0.372402i
$781$	8925.40	+	5153.08i	0.408932	+	0.236097i
$782$	10823.8	−	1562.75i	0.494958	−	0.0714626i
$783$	−4038.30			−0.184313
$784$	−20009.6	+	9028.11i	−0.911515	+	0.411266i
$785$	−27838.3			−1.26572
$786$	14936.4	−	2156.54i	0.677817	−	0.0978640i
$787$	−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	$0.703865\pi$
$788$	4978.22	+	16880.5i	0.225053	+	0.763125i
$789$	−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
$794$	15906.2	+	20201.8i	0.710944	+	0.902941i
$795$	−12397.4	+	21473.0i	−0.553072	+	0.957948i
$796$	5979.29	−	24774.7i	0.266244	−	1.10316i
$797$	−24018.5			−1.06748			−0.533738	−	0.845650i	$-0.679213\pi$
$797$	−24018.5			−1.06748			−0.533738	+	0.845650i	$0.679213\pi$
$798$	384.310	+	5599.05i	0.0170481	+	0.248376i
$799$		−	4032.98i		−	0.178569i
$800$	142.907	+	729.868i	0.00631567	+	0.0322559i
$801$	3254.07	+	1878.74i	0.143542	+	0.0828738i
$802$	7316.15	+	9291.94i	0.322122	+	0.409114i
$803$	−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
$808$	1394.81	−	14885.8i	0.0607294	−	0.648121i
$809$	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	$-0.116497\pi$
$810$	−2576.48	+	371.996i	−0.111763	+	0.0161365i
$811$		−	36313.3i		−	1.57230i	−0.618037	−	0.786149i	$-0.712072\pi$
$811$		−	36313.3i		−	1.57230i	0.618037	−	0.786149i	$-0.287928\pi$
$812$	21664.4	−	4661.12i	0.936293	−	0.201445i
$813$		−	1238.19i		−	0.0534136i
$814$	2366.25	+	16388.9i	0.101888	+	0.705689i
$815$	−18275.6	+	31654.3i	−0.785481	+	1.36049i
$816$	−7387.60	−	3786.51i	−0.316934	−	0.162444i
$817$	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	$-0.722290\pi$
$821$	−7083.90	+	4089.89i	−0.301133	+	0.173859i	0.341819	+	0.939766i	$0.388957\pi$
$822$	−6492.99	+	5112.36i	−0.275510	+	0.216927i
$823$	−6930.59	−	4001.38i	−0.293542	−	0.169477i	0.345996	−	0.938236i	$-0.387541\pi$
$823$	−6930.59	−	4001.38i	−0.293542	−	0.169477i	−0.639538	+	0.768759i	$0.720874\pi$
$824$	16709.8	+	11854.4i	0.706449	+	0.501176i
$825$			244.797i			0.0103306i
$826$	13170.3	−	26915.4i	0.554784	−	1.13378i
$827$	−4176.53			−0.175613			−0.0878065	−	0.996138i	$-0.527986\pi$
$827$	−4176.53			−0.175613			−0.0878065	+	0.996138i	$0.527986\pi$
$828$	6258.91	+	1510.57i	0.262696	+	0.0634008i
$829$	3732.41	−	6464.72i	0.156371	−	0.270843i	−0.777186	−	0.629271i	$-0.783354\pi$
$829$	3732.41	−	6464.72i	0.156371	−	0.270843i	0.933558	+	0.358428i	$0.116687\pi$
$830$	23602.5	−	18583.8i	0.987053	−	0.777171i
$831$	−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
$836$	−1605.05	−	5442.50i	−0.0664016	−	0.225159i
$837$	3389.41	+	1956.88i	0.139970	+	0.0808118i
$838$	−2679.87	−	18561.1i	−0.110471	−	0.765134i
$839$	26786.2			1.10222			0.551110	−	0.834432i	$-0.314204\pi$
$839$	26786.2			1.10222			0.551110	+	0.834432i	$0.314204\pi$
$840$	13392.7	−	4969.51i	0.550112	−	0.204124i
$841$	2018.81			0.0827754
$842$	3258.89	+	22571.4i	0.133383	+	0.923827i
$843$	20622.3	+	11906.3i	0.842551	+	0.486447i
$844$	5244.48	−	1546.65i	0.213889	−	0.0630781i
$845$	−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
$850$	−394.764	+	310.823i	−0.0159298	+	0.0125425i
$851$	13180.1	−	22828.6i	0.530914	−	0.919569i
$852$	−2921.86	+	12106.5i	−0.117490	+	0.486809i
$853$	18794.9			0.754425			0.377212	−	0.926127i	$-0.376883\pi$
$853$	18794.9			0.754425			0.377212	+	0.926127i	$0.376883\pi$
$854$	675.493	−	454.367i	0.0270666	−	0.0182062i
$855$		−	3652.09i		−	0.146081i
$856$	−25120.6	−	17821.3i	−1.00304	−	0.711588i
$857$	−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	$0.834956\pi$
$858$	4106.64	−	3233.43i	0.163401	−	0.128657i
$859$	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	−0.418765	−	0.908095i	$-0.637537\pi$
$863$	4012.90	−	2316.85i	0.158286	−	0.0913864i	0.577051	+	0.816708i	$0.304203\pi$
$864$	−3211.54	−	3684.28i	−0.126457	−	0.145071i
$865$	6645.15	−	11509.7i	0.261205	−	0.452420i
$866$	−6234.53	−	43181.1i	−0.244640	−	1.69440i
$867$			9130.73i			0.357666i
$868$	−20441.9	−	6585.94i	−0.799359	−	0.257536i
$869$			6613.17i			0.258155i
$870$	−14272.4	+	2060.67i	−0.556185	+	0.0803027i
$871$	−1712.92	+	2966.86i	−0.0666361	+	0.115417i
$872$	21893.9	+	2051.48i	0.850255	+	0.0796695i
$873$	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	$-0.866988\pi$
$877$	−26477.8	+	15287.0i	−1.01949	+	0.588602i	−0.105533	+	0.994416i	$0.533655\pi$
$878$	26902.1	+	34167.2i	1.03406	+	1.31331i
$879$	−4690.33	−	2707.97i	−0.179978	−	0.103911i
$880$	−12131.6	+	7837.09i	−0.464725	+	0.300214i
$881$			13856.1i			0.529881i	0.964265	+	0.264941i	$0.0853524\pi$
$881$			13856.1i			0.529881i	−0.964265	+	0.264941i	$0.914648\pi$
$882$	−4317.74	−	7589.05i	−0.164836	−	0.289724i
$883$	−7762.38			−0.295838			−0.147919	−	0.988999i	$-0.547258\pi$
$883$	−7762.38			−0.295838			−0.147919	+	0.988999i	$0.547258\pi$
$884$	10428.6	+	2516.90i	0.396776	+	0.0957608i
$885$	−9749.65	+	16886.9i	−0.370318	+	0.641409i
$886$	7494.34	+	9518.25i	0.284173	+	0.360916i
$887$	5247.14	+	9088.31i	0.198626	+	0.344031i	0.948083	−	0.318022i	$-0.103019\pi$
$887$	5247.14	+	9088.31i	0.198626	+	0.344031i	−0.749457	+	0.662053i	$0.769685\pi$
$888$	−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
$892$	−37852.1	+	11163.0i	−1.42083	+	0.419018i
$893$	2884.86	+	1665.57i	0.108105	+	0.0624147i
$894$	−23998.0	+	3464.85i	−0.897776	+	0.129622i
$895$	4917.32			0.183651
$896$	21481.5	+	16058.3i	0.800945	+	0.598737i
$897$	−8320.61			−0.309718
$898$	41080.2	−	5931.20i	1.52657	−	0.220408i
$899$	18775.6	+	10840.1i	0.696555	+	0.402156i
$900$	−283.734	+	83.6761i	−0.0105087	+	0.00309912i
$901$	−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
$906$	−12993.6	−	16502.7i	−0.476473	−	0.605149i
$907$	−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	$0.168812\pi$
$908$	−24403.1	−	5889.61i	−0.891899	−	0.215257i
$909$	5946.74			0.216987
$910$	−15317.7	+	10303.4i	−0.557996	+	0.375333i
$911$		−	14957.6i		−	0.543980i	−0.962300	−	0.271990i	$-0.912318\pi$
$911$		−	14957.6i		−	0.543980i	0.962300	−	0.271990i	$-0.0876818\pi$
$912$	5759.55	−	3720.69i	0.209120	−	0.135093i
$913$	16077.3	+	9282.21i	0.582782	+	0.336469i
$914$	30312.3	+	38498.4i	1.09698	+	1.39323i
$915$	−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	$-0.451401\pi$
$919$	30202.0	−	17437.1i	1.08408	−	0.625895i	0.931995	+	0.362472i	$0.118067\pi$
$920$	22891.5	+	2144.95i	0.820337	+	0.0768662i
$921$	8548.86	−	14807.1i	0.305857	−	0.529760i
$922$	−17854.1	+	2577.79i	−0.637736	+	0.0920771i
$923$		−	16094.4i		−	0.573947i
$924$	5923.24	+	6545.69i	0.210888	+	0.233049i
$925$			1211.09i			0.0430491i
$926$	3068.82	+	21255.0i	0.108907	+	0.754301i
$927$	−4074.46	+	7057.18i	−0.144361	+	0.250041i
$928$	−17790.3	−	20409.1i	−0.629307	−	0.721940i
$929$	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
$934$	11730.4	−	9236.13i	0.410954	−	0.323571i
$935$	−8450.03	−	4878.63i	−0.295557	−	0.170640i
$936$	5151.46	+	3654.60i	0.179894	+	0.127622i
$937$			7971.69i			0.277933i	0.990297	+	0.138967i	$0.0443781\pi$
$937$			7971.69i			0.277933i	−0.990297	+	0.138967i	$0.955622\pi$
$938$	−5197.24	−	2543.12i	−0.180913	−	0.0885243i
$939$	18771.6			0.652385
$940$	1989.24	−	8242.25i	0.0690234	−	0.285992i
$941$	−19868.3	+	34412.9i	−0.688298	+	1.19217i	0.284090	+	0.958798i	$0.408309\pi$
$941$	−19868.3	+	34412.9i	−0.688298	+	1.19217i	−0.972388	+	0.233370i	$0.925025\pi$
$942$	16333.6	−	12860.5i	0.564943	−	0.444817i
$943$	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	$0.687121\pi$
$948$	−7665.06	+	2260.50i	−0.262605	+	0.0774448i
$949$	29405.4	+	16977.2i	1.00584	+	0.580720i
$950$	−59.3042	−	410.748i	−0.00202535	−	0.0140278i
$951$	19661.9			0.670433
$952$	−3034.84	+	17863.1i	−0.103319	+	0.608137i
$953$	−28798.7			−0.978891			−0.489445	−	0.872034i	$-0.662801\pi$
$953$	−28798.7			−0.978891			−0.489445	+	0.872034i	$0.662801\pi$
$954$	−2645.95	−	18326.1i	−0.0897963	−	0.621939i
$955$	31837.7	+	18381.5i	1.07879	+	0.622838i
$956$	7721.80	+	26183.6i	0.261235	+	0.885813i
$957$	−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
$962$	20316.9	−	15996.8i	0.680918	−	0.536131i
$963$	6125.32	−	10609.4i	0.204970	−	0.355018i
$964$	−34785.0	−	8395.26i	−1.16219	−	0.280491i
$965$	39337.7			1.31225
$966$	−962.321	−	14020.1i	−0.0320519	−	0.466968i
$967$		−	34186.3i		−	1.13687i	−0.822727	−	0.568437i	$-0.807548\pi$
$967$		−	34186.3i		−	1.13687i	0.822727	−	0.568437i	$-0.192452\pi$
$968$	17284.0	+	12261.8i	0.573893	+	0.407137i
$969$	4011.69	+	2316.15i	0.132997	+	0.0767858i
$970$	12052.8	−	9489.97i	0.398962	−	0.314128i
$971$	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
$976$	−885.133	−	453.674i	−0.0290291	−	0.0148788i
$977$	−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	$0.283761\pi$
$978$	−3900.51	−	27015.4i	−0.127530	−	0.883288i
$979$			8291.82i			0.270692i
$980$	−19132.6	−	24618.5i	−0.623642	−	0.802458i
$981$			8746.41i			0.284660i
$982$	22254.7	−	3213.17i	0.723195	−	0.104416i
$983$	9107.15	−	15774.0i	0.295496	−	0.511815i	−0.679604	−	0.733579i	$-0.737848\pi$
$983$	9107.15	−	15774.0i	0.295496	−	0.511815i	0.975100	+	0.221765i	$0.0711816\pi$
$984$	2156.61	−	23015.9i	0.0698681	−	0.745651i
$985$	−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
$990$	−3553.76	−	4513.48i	−0.114087	−	0.144897i
$991$	42443.0	+	24504.5i	1.36049	+	0.785479i	0.989689	−	0.143234i	$-0.0457500\pi$
$991$	42443.0	+	24504.5i	1.36049	+	0.785479i	0.370801	+	0.928713i	$0.379083\pi$
$992$	5041.91	+	25750.5i	0.161372	+	0.824172i
$993$		−	33748.8i		−	1.07854i
$994$	27118.9	−	1861.40i	0.865351	−	0.0593963i
$995$	36198.4			1.15333
$996$	−5263.13	+	21807.3i	−0.167438	+	0.693767i
$997$	−10050.3	+	17407.7i	−0.319255	+	0.552967i	−0.980333	−	0.197351i	$-0.936766\pi$
$997$	−10050.3	+	17407.7i	−0.319255	+	0.552967i	0.661077	+	0.750318i	$0.270099\pi$
$998$	−8478.49	−	10768.2i	−0.268920	−	0.341544i
$999$	−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.115.46	yes	96
4.3	odd	2		672.4.bb.a.367.42		96
7.5	odd	6	inner	168.4.t.a.19.14	✓	96
8.3	odd	2	inner	168.4.t.a.115.14	yes	96
8.5	even	2		672.4.bb.a.367.41		96
28.19	even	6		672.4.bb.a.271.41		96
56.5	odd	6		672.4.bb.a.271.42		96
56.19	even	6	inner	168.4.t.a.19.46	yes	96

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(2.79940 - 0.404181i) q^{2} +(-2.59808 - 1.50000i) q^{3} +(7.67328 - 2.26293i) 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} +(19.8815 + 25.2506i) q^{10} +(-9.93039 + 17.1999i) q^{11} +(-23.3301 - 5.63066i) q^{12} +31.0152 q^{13} +(3.58706 + 52.2602i) q^{14} -34.0878i q^{15} +(53.7583 - 34.7281i) q^{16} +(37.4442 + 21.6184i) q^{17} +(15.7476 + 20.0003i) 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} +(-67.5862 - 6.33288i) q^{24} +(-2.05428 + 3.55811i) q^{25} +(86.8239 - 12.5357i) q^{26} -27.0000i q^{27} +(31.1642 + 144.847i) q^{28} -149.567i q^{29} +(-13.7776 - 95.4253i) q^{30} +(-72.4769 + 125.534i) q^{31} +(136.455 - 118.946i) 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} +(-79.3627 + 62.4874i) q^{38} +(-80.5798 - 46.5228i) q^{39} +(209.696 + 148.765i) q^{40} +340.542i q^{41} +(69.0709 - 141.157i) q^{42} -382.268 q^{43} +(-37.2764 + 154.452i) q^{44} +(-51.1317 + 88.5627i) q^{45} +(198.726 - 156.470i) 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} +(237.988 - 70.1850i) q^{52} +(-629.932 - 363.692i) q^{53} +(-10.9129 - 75.5838i) q^{54} -225.670 q^{55} +(145.786 + 392.890i) q^{56} +107.138 q^{57} +(-60.4519 - 418.697i) q^{58} +(-495.394 - 286.016i) q^{59} +(-77.1381 - 261.565i) 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} +(132.408 - 104.253i) q^{66} +(-55.2285 + 95.6585i) q^{67} +(336.240 + 81.1506i) q^{68} -268.276 q^{69} +(-493.877 + 332.204i) q^{70} -518.920i q^{71} +(166.095 + 117.833i) q^{72} +(948.097 + 547.384i) q^{73} +(655.063 - 515.774i) 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} +(647.152 + 331.697i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(137.640 + 953.313i) q^{82} -934.727i q^{83} +(136.304 - 423.071i) q^{84} +491.282i q^{85} +(-1070.12 + 154.505i) q^{86} +(-224.350 + 388.586i) q^{87} +(-41.9253 + 447.438i) 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} +(-163.209 - 207.285i) q^{94} +(-351.423 - 202.894i) q^{95} +(-532.938 + 104.349i) q^{96} -477.327i q^{97} +(-970.131 - 6.13945i) 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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