LMFDB - Embedded newform 168.4.t.a.19.1

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			19.1
Character	$\chi$	$=$	168.19
Dual form			168.4.t.a.115.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.82552 + 0.128292i) q^{2} +(-2.59808 + 1.50000i) q^{3} +(7.96708 - 0.724984i) q^{4} +(-8.82092 + 15.2783i) q^{5} +(7.14847 - 4.57159i) q^{6} +(-18.4632 - 1.45285i) q^{7} +(-22.4181 + 3.07057i) q^{8} +(4.50000 - 7.79423i) q^{9} +(22.9636 - 44.3007i) q^{10} +(24.2068 + 41.9275i) q^{11} +(-19.6116 + 13.8342i) q^{12} -47.7808 q^{13} +(52.3544 + 1.73636i) q^{14} -52.9255i q^{15} +(62.9488 - 11.5520i) q^{16} +(1.25446 - 0.724262i) q^{17} +(-11.7149 + 22.6000i) q^{18} +(19.1960 + 11.0828i) q^{19} +(-59.2005 + 128.118i) q^{20} +(50.1480 - 23.9202i) q^{21} +(-73.7758 - 115.361i) q^{22} +(58.0371 + 33.5077i) q^{23} +(53.6381 - 41.6047i) q^{24} +(-93.1171 - 161.284i) q^{25} +(135.006 - 6.12992i) q^{26} +27.0000i q^{27} +(-148.151 + 1.81056i) q^{28} -218.205i q^{29} +(6.78994 + 149.542i) q^{30} +(-151.856 - 263.021i) q^{31} +(-176.381 + 40.7163i) q^{32} +(-125.782 - 72.6205i) q^{33} +(-3.45158 + 2.20735i) q^{34} +(185.059 - 269.270i) q^{35} +(30.2012 - 65.3597i) q^{36} +(61.8777 + 35.7251i) q^{37} +(-55.6605 - 28.8520i) q^{38} +(124.138 - 71.6713i) q^{39} +(150.835 - 369.595i) q^{40} -419.167i q^{41} +(-138.625 + 74.0204i) q^{42} +258.857 q^{43} +(223.255 + 316.490i) q^{44} +(79.3882 + 137.504i) q^{45} +(-168.284 - 87.2309i) q^{46} +(-246.244 + 426.507i) q^{47} +(-146.218 + 124.436i) q^{48} +(338.778 + 53.6484i) q^{49} +(283.795 + 443.763i) q^{50} +(-2.17279 + 3.76338i) q^{51} +(-380.674 + 34.6404i) q^{52} +(-18.8500 + 10.8831i) q^{53} +(-3.46389 - 76.2889i) q^{54} -854.106 q^{55} +(418.371 - 24.1224i) q^{56} -66.4970 q^{57} +(27.9940 + 616.540i) q^{58} +(-371.955 + 214.748i) q^{59} +(-38.3701 - 421.662i) q^{60} +(206.442 - 357.568i) q^{61} +(462.814 + 723.690i) q^{62} +(-94.4082 + 137.368i) q^{63} +(493.143 - 137.673i) q^{64} +(421.471 - 730.009i) q^{65} +(364.717 + 189.054i) q^{66} +(-108.498 - 187.924i) q^{67} +(9.46930 - 6.67972i) q^{68} -201.046 q^{69} +(-488.343 + 784.569i) q^{70} +813.188i q^{71} +(-76.9488 + 188.549i) q^{72} +(-715.855 + 413.299i) q^{73} +(-179.420 - 93.0034i) q^{74} +(483.851 + 279.351i) q^{75} +(160.971 + 74.3810i) q^{76} +(-386.021 - 809.284i) q^{77} +(-341.560 + 218.434i) q^{78} +(614.797 + 354.953i) q^{79} +(-378.771 + 1063.65i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(53.7759 + 1184.36i) q^{82} +464.287i q^{83} +(382.192 - 226.930i) q^{84} +25.5546i q^{85} +(-731.404 + 33.2094i) q^{86} +(327.307 + 566.912i) q^{87} +(-671.413 - 865.606i) q^{88} +(-191.854 - 110.767i) q^{89} +(-241.954 - 378.336i) q^{90} +(882.187 + 69.4183i) q^{91} +(486.679 + 224.883i) q^{92} +(789.064 + 455.567i) q^{93} +(641.049 - 1236.69i) q^{94} +(-338.653 + 195.521i) q^{95} +(397.176 - 370.355i) q^{96} -1568.06i q^{97} +(-964.107 - 108.122i) q^{98} +435.723 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 $

$2$	−2.82552	+	0.128292i	−0.998971	+	0.0453582i
$2$	−2.82552	+	0.128292i	−0.998971	+	0.0453582i
$3$	−2.59808	+	1.50000i	−0.500000	+	0.288675i
$3$	−2.59808	+	1.50000i	−0.500000	+	0.288675i
$4$	7.96708	−	0.724984i	0.995885	−	0.0906230i
$5$	−8.82092	+	15.2783i	−0.788967	+	1.36653i	0.137634	+	0.990483i	$0.456050\pi$
$5$	−8.82092	+	15.2783i	−0.788967	+	1.36653i	−0.926600	+	0.376047i	$0.877283\pi$
$6$	7.14847	−	4.57159i	0.486392	−	0.311057i
$7$	−18.4632	−	1.45285i	−0.996918	−	0.0784464i
$7$	−18.4632	−	1.45285i	−0.996918	−	0.0784464i
$8$	−22.4181	+	3.07057i	−0.990750	+	0.135701i
$9$	4.50000	−	7.79423i	0.166667	−	0.288675i
$10$	22.9636	−	44.3007i	0.726171	−	1.40091i
$11$	24.2068	+	41.9275i	0.663513	+	1.14924i	0.979686	+	0.200536i	$0.0642684\pi$
$11$	24.2068	+	41.9275i	0.663513	+	1.14924i	−0.316174	+	0.948701i	$0.602398\pi$
$12$	−19.6116	+	13.8342i	−0.471782	+	0.332799i
$13$	−47.7808			−1.01939			−0.509693	−	0.860356i	$-0.670241\pi$
$13$	−47.7808			−1.01939			−0.509693	+	0.860356i	$0.670241\pi$
$14$	52.3544	+	1.73636i	0.999450	+	0.0331472i
$15$		−	52.9255i		−	0.911020i
$16$	62.9488	−	11.5520i	0.983575	−	0.180500i
$17$	1.25446	−	0.724262i	0.0178971	−	0.0103329i	−0.491025	−	0.871146i	$-0.663378\pi$
$17$	1.25446	−	0.724262i	0.0178971	−	0.0103329i	0.508922	+	0.860813i	$0.330044\pi$
$18$	−11.7149	+	22.6000i	−0.153401	+	0.295938i
$19$	19.1960	+	11.0828i	0.231783	+	0.133820i	0.611394	−	0.791326i	$-0.290609\pi$
$19$	19.1960	+	11.0828i	0.231783	+	0.133820i	−0.379612	+	0.925146i	$0.623942\pi$
$20$	−59.2005	+	128.118i	−0.661881	+	1.43241i
$21$	50.1480	−	23.9202i	0.521105	−	0.248562i
$22$	−73.7758	−	115.361i	−0.714957	−	1.11796i
$23$	58.0371	+	33.5077i	0.526155	+	0.303776i	0.739449	−	0.673212i	$-0.235086\pi$
$23$	58.0371	+	33.5077i	0.526155	+	0.303776i	−0.213294	+	0.976988i	$0.568419\pi$
$24$	53.6381	−	41.6047i	0.456201	−	0.353855i
$25$	−93.1171	−	161.284i	−0.744937	−	1.29027i
$26$	135.006	−	6.12992i	1.01834	−	0.0462375i
$27$			27.0000i			0.192450i
$28$	−148.151	+	1.81056i	−0.999925	+	0.0122201i
$29$		−	218.205i		−	1.39723i	−0.715500	−	0.698613i	$-0.753801\pi$
$29$		−	218.205i		−	1.39723i	0.715500	−	0.698613i	$-0.246199\pi$
$30$	6.78994	+	149.542i	0.0413222	+	0.910083i
$31$	−151.856	−	263.021i	−0.879808	−	1.52387i	−0.851551	−	0.524272i	$-0.824337\pi$
$31$	−151.856	−	263.021i	−0.879808	−	1.52387i	−0.0282575	−	0.999601i	$-0.508996\pi$
$32$	−176.381	+	40.7163i	−0.974375	+	0.224928i
$33$	−125.782	−	72.6205i	−0.663513	−	0.383079i
$34$	−3.45158	+	2.20735i	−0.0174100	+	0.0111341i
$35$	185.059	−	269.270i	0.893735	−	1.30043i
$36$	30.2012	−	65.3597i	0.139820	−	0.302591i
$37$	61.8777	+	35.7251i	0.274936	+	0.158734i	0.631129	−	0.775678i	$-0.282592\pi$
$37$	61.8777	+	35.7251i	0.274936	+	0.158734i	−0.356193	+	0.934413i	$0.615925\pi$
$38$	−55.6605	−	28.8520i	−0.237614	−	0.123169i
$39$	124.138	−	71.6713i	0.509693	−	0.294271i
$40$	150.835	−	369.595i	0.596229	−	1.46095i
$41$		−	419.167i		−	1.59666i	−0.602223	−	0.798328i	$-0.705718\pi$
$41$		−	419.167i		−	1.59666i	0.602223	−	0.798328i	$-0.294282\pi$
$42$	−138.625	+	74.0204i	−0.509294	+	0.271943i
$43$	258.857			0.918031			0.459015	−	0.888428i	$-0.348202\pi$
$43$	258.857			0.918031			0.459015	+	0.888428i	$0.348202\pi$
$44$	223.255	+	316.490i	0.764930	+	1.08438i
$45$	79.3882	+	137.504i	0.262989	+	0.455510i
$46$	−168.284	−	87.2309i	−0.539393	−	0.279598i
$47$	−246.244	+	426.507i	−0.764221	+	1.32367i	0.176437	+	0.984312i	$0.443543\pi$
$47$	−246.244	+	426.507i	−0.764221	+	1.32367i	−0.940658	+	0.339357i	$0.889791\pi$
$48$	−146.218	+	124.436i	−0.439682	+	0.374184i
$49$	338.778	+	53.6484i	0.987692	+	0.156409i
$50$	283.795	+	443.763i	0.802695	+	1.25515i
$51$	−2.17279	+	3.76338i	−0.00596571	+	0.0103329i
$52$	−380.674	+	34.6404i	−1.01519	+	0.0923799i
$53$	−18.8500	+	10.8831i	−0.0488538	+	0.0282058i	−0.524228	−	0.851578i	$-0.675646\pi$
$53$	−18.8500	+	10.8831i	−0.0488538	+	0.0282058i	0.475374	+	0.879784i	$0.342313\pi$
$54$	−3.46389	−	76.2889i	−0.00872919	−	0.192252i
$55$	−854.106			−2.09396
$56$	418.371	−	24.1224i	0.998342	−	0.0575624i
$57$	−66.4970			−0.154522
$58$	27.9940	+	616.540i	0.0633757	+	1.39579i
$59$	−371.955	+	214.748i	−0.820753	+	0.473862i	−0.850676	−	0.525690i	$-0.823807\pi$
$59$	−371.955	+	214.748i	−0.820753	+	0.473862i	0.0299227	+	0.999552i	$0.490474\pi$
$60$	−38.3701	−	421.662i	−0.0825594	−	0.907272i
$61$	206.442	−	357.568i	0.433315	−	0.750523i	−0.563842	−	0.825883i	$-0.690677\pi$
$61$	206.442	−	357.568i	0.433315	−	0.750523i	0.997156	+	0.0753596i	$0.0240105\pi$
$62$	462.814	+	723.690i	0.948023	+	1.48240i
$63$	−94.4082	+	137.368i	−0.188799	+	0.274711i
$64$	493.143	−	137.673i	0.963170	−	0.268892i
$65$	421.471	−	730.009i	0.804262	−	1.39302i
$66$	364.717	+	189.054i	0.680205	+	0.352589i
$67$	−108.498	−	187.924i	−0.197838	−	0.342665i	0.749989	−	0.661450i	$-0.230059\pi$
$67$	−108.498	−	187.924i	−0.197838	−	0.342665i	−0.947827	+	0.318785i	$0.896725\pi$
$68$	9.46930	−	6.67972i	0.0168871	−	0.0119123i
$69$	−201.046			−0.350770
$70$	−488.343	+	784.569i	−0.833830	+	1.33963i
$71$			813.188i			1.35926i	0.733553	+	0.679632i	$0.237860\pi$
$71$			813.188i			1.35926i	−0.733553	+	0.679632i	$0.762140\pi$
$72$	−76.9488	+	188.549i	−0.125951	+	0.308622i
$73$	−715.855	+	413.299i	−1.14773	+	0.662644i	−0.948334	−	0.317275i	$-0.897232\pi$
$73$	−715.855	+	413.299i	−1.14773	+	0.662644i	−0.199399	+	0.979918i	$0.563899\pi$
$74$	−179.420	−	93.0034i	−0.281853	−	0.146100i
$75$	483.851	+	279.351i	0.744937	+	0.430090i
$76$	160.971	+	74.3810i	0.242956	+	0.112264i
$77$	−386.021	−	809.284i	−0.571314	−	1.19775i
$78$	−341.560	+	218.434i	−0.495821	+	0.317087i
$79$	614.797	+	354.953i	0.875571	+	0.505511i	0.869195	−	0.494469i	$-0.164637\pi$
$79$	614.797	+	354.953i	0.875571	+	0.505511i	0.00637517	+	0.999980i	$0.497971\pi$
$80$	−378.771	+	1063.65i	−0.529349	+	1.48649i
$81$	−40.5000	−	70.1481i	−0.0555556	−	0.0962250i
$82$	53.7759	+	1184.36i	0.0724215	+	1.59501i
$83$			464.287i			0.614001i	0.951709	+	0.307001i	$0.0993254\pi$
$83$			464.287i			0.614001i	−0.951709	+	0.307001i	$0.900675\pi$
$84$	382.192	−	226.930i	0.496435	−	0.294764i
$85$			25.5546i			0.0326093i
$86$	−731.404	+	33.2094i	−0.917086	+	0.0416402i
$87$	327.307	+	566.912i	0.403344	+	0.698613i
$88$	−671.413	−	865.606i	−0.813328	−	1.04857i
$89$	−191.854	−	110.767i	−0.228500	−	0.131925i	0.381380	−	0.924418i	$-0.375449\pi$
$89$	−191.854	−	110.767i	−0.228500	−	0.131925i	−0.609880	+	0.792494i	$0.708782\pi$
$90$	−241.954	−	378.336i	−0.283379	−	0.443113i
$91$	882.187	+	69.4183i	1.01624	+	0.0799672i
$92$	486.679	+	224.883i	0.551519	+	0.254844i
$93$	789.064	+	455.567i	0.879808	+	0.507958i
$94$	641.049	−	1236.69i	0.703395	−	1.35697i
$95$	−338.653	+	195.521i	−0.365737	+	0.211159i
$96$	397.176	−	370.355i	0.422257	−	0.393742i
$97$		−	1568.06i		−	1.64136i	−0.571388	−	0.820680i	$-0.693595\pi$
$97$		−	1568.06i		−	1.64136i	0.571388	−	0.820680i	$-0.306405\pi$
$98$	−964.107	−	108.122i	−0.993770	−	0.111448i
$99$	435.723			0.442342
$100$	−858.800	−	1217.45i	−0.858800	−	1.21745i
$101$	501.221	+	868.140i	0.493795	+	0.855279i	0.999974	−	0.00714968i	$-0.00227583\pi$
$101$	501.221	+	868.140i	0.493795	+	0.855279i	−0.506179	+	0.862428i	$0.668943\pi$
$102$	5.65643	−	10.9122i	0.00549089	−	0.0105929i
$103$	754.415	−	1306.68i	0.721696	−	1.25001i	−0.238623	−	0.971112i	$-0.576696\pi$
$103$	754.415	−	1306.68i	0.721696	−	1.25001i	0.960319	−	0.278902i	$-0.0899706\pi$
$104$	1071.16	−	146.714i	1.00996	−	0.138332i
$105$	−76.8927	+	977.173i	−0.0714663	+	0.908213i
$106$	51.8649	−	33.1686i	0.0475242	−	0.0303927i
$107$	317.164	−	549.344i	0.286555	−	0.496328i	−0.686430	−	0.727196i	$-0.740823\pi$
$107$	317.164	−	549.344i	0.286555	−	0.496328i	0.972985	+	0.230868i	$0.0741565\pi$
$108$	19.5746	+	215.111i	0.0174404	+	0.191658i
$109$	−105.954	+	61.1723i	−0.0931056	+	0.0537546i	−0.545830	−	0.837896i	$-0.683786\pi$
$109$	−105.954	+	61.1723i	−0.0931056	+	0.0537546i	0.452724	+	0.891651i	$0.350452\pi$
$110$	2413.29	−	109.575i	2.09180	−	0.0949781i
$111$	−214.351			−0.183291
$112$	−1179.02	+	121.832i	−0.994703	+	0.102786i
$113$	−2269.62			−1.88945			−0.944726	−	0.327861i	$-0.893672\pi$
$113$	−2269.62			−1.88945			−0.944726	+	0.327861i	$0.893672\pi$
$114$	187.888	−	8.53105i	0.154363	−	0.00700883i
$115$	−1023.88	+	591.138i	−0.830238	+	0.479338i
$116$	−158.195	−	1738.45i	−0.126621	−	1.39148i
$117$	−215.014	+	372.415i	−0.169898	+	0.294271i
$118$	1023.42	−	654.494i	0.798415	−	0.510602i
$119$	−24.2136	+	11.5497i	−0.0186525	+	0.00889710i
$120$	162.511	+	1186.49i	0.123627	+	0.902593i
$121$	−506.442	+	877.184i	−0.380498	+	0.659041i
$122$	−537.432	+	1036.80i	−0.398826	+	0.769405i
$123$	628.751	+	1089.03i	0.460915	+	0.798328i
$124$	−1400.53	−	1985.42i	−1.01429	−	1.43787i
$125$	1080.28			0.772989
$126$	249.128	−	400.249i	0.176144	−	0.282992i
$127$		−	608.384i		−	0.425082i	−0.977152	−	0.212541i	$-0.931826\pi$
$127$		−	608.384i		−	0.425082i	0.977152	−	0.212541i	$-0.0681739\pi$
$128$	−1375.72	+	452.263i	−0.949983	+	0.312303i
$129$	−672.530	+	388.285i	−0.459015	+	0.265013i
$130$	−1097.22	+	2116.72i	−0.740249	+	1.42807i
$131$	−841.049	−	485.580i	−0.560938	−	0.323857i	0.192584	−	0.981280i	$-0.438313\pi$
$131$	−841.049	−	485.580i	−0.560938	−	0.323857i	−0.753522	+	0.657423i	$0.771646\pi$
$132$	−1054.77	−	487.383i	−0.695498	−	0.321373i
$133$	−338.318	−	232.513i	−0.220571	−	0.151590i
$134$	330.672	+	517.063i	0.213177	+	0.333339i
$135$	−412.513	−	238.165i	−0.262989	−	0.151837i
$136$	−25.8987	+	20.0885i	−0.0163294	+	0.0126660i
$137$	−878.430	−	1521.48i	−0.547805	−	0.948826i	−0.998425	−	0.0561101i	$-0.982130\pi$
$137$	−878.430	−	1521.48i	−0.547805	−	0.948826i	0.450619	−	0.892716i	$-0.351203\pi$
$138$	568.060	−	25.7927i	0.350409	−	0.0159103i
$139$			2535.81i			1.54737i	0.633569	+	0.773686i	$0.281589\pi$
$139$			2535.81i			1.54737i	−0.633569	+	0.773686i	$0.718411\pi$
$140$	1279.17	−	2279.46i	0.772209	−	1.37607i
$141$		−	1477.46i		−	0.882446i
$142$	−104.326	−	2297.68i	−0.0616537	−	1.35786i
$143$	−1156.62	−	2003.33i	−0.676376	−	1.17152i
$144$	193.231	−	542.621i	0.111823	−	0.314017i
$145$	3333.79	+	1924.76i	1.90935	+	1.10236i
$146$	1969.64	−	1259.62i	1.11650	−	0.714021i
$147$	−960.645	+	368.785i	−0.538998	+	0.206918i
$148$	518.885	+	239.765i	0.288190	+	0.133166i
$149$	−267.600	−	154.499i	−0.147132	−	0.0849467i	0.424627	−	0.905369i	$-0.360405\pi$
$149$	−267.600	−	154.499i	−0.147132	−	0.0849467i	−0.571759	+	0.820422i	$0.693739\pi$
$150$	−1402.97	−	727.238i	−0.763678	−	0.395858i
$151$	−449.367	+	259.442i	−0.242179	+	0.139822i	−0.616178	−	0.787607i	$-0.711320\pi$
$151$	−449.367	+	259.442i	−0.242179	+	0.139822i	0.373999	+	0.927429i	$0.377986\pi$
$152$	−464.369	−	189.513i	−0.247798	−	0.101129i
$153$		−	13.0367i		−	0.00688861i
$154$	1194.53	+	2237.12i	0.625054	+	1.17060i
$155$	5358.02			2.77656
$156$	937.059	−	661.009i	0.480928	−	0.339251i
$157$	−287.503	−	497.970i	−0.146148	−	0.253136i	0.783653	−	0.621199i	$-0.213354\pi$
$157$	−287.503	−	497.970i	−0.146148	−	0.253136i	−0.929801	+	0.368063i	$0.880021\pi$
$158$	−1782.66	−	924.052i	−0.897598	−	0.465276i
$159$	32.6492	−	56.5501i	0.0162846	−	0.0282058i
$160$	933.766	−	3053.95i	0.461379	−	1.50897i
$161$	−1022.87	−	702.979i	−0.500704	−	0.344115i
$162$	123.433	+	193.009i	0.0598630	+	0.0936061i
$163$	−1105.32	+	1914.47i	−0.531136	+	0.919954i	0.468204	+	0.883620i	$0.344901\pi$
$163$	−1105.32	+	1914.47i	−0.531136	+	0.919954i	−0.999340	+	0.0363336i	$0.988432\pi$
$164$	−303.890	−	3339.54i	−0.144694	−	1.59009i
$165$	2219.03	−	1281.16i	1.04698	−	0.604473i
$166$	−59.5644	−	1311.85i	−0.0278500	−	0.613369i
$167$	−1038.78			−0.481336			−0.240668	−	0.970607i	$-0.577367\pi$
$167$	−1038.78			−0.481336			−0.240668	+	0.970607i	$0.577367\pi$
$168$	−1050.78	+	690.228i	−0.482554	+	0.316978i
$169$	86.0088			0.0391483
$170$	−3.27846	−	72.2050i	−0.00147910	−	0.0325757i
$171$	172.764	−	99.7454i	0.0772609	−	0.0446066i
$172$	2062.33	−	187.667i	0.914253	−	0.0831947i
$173$	−402.318	+	696.835i	−0.176807	+	0.306239i	−0.940785	−	0.339003i	$-0.889910\pi$
$173$	−402.318	+	696.835i	−0.176807	+	0.306239i	0.763978	+	0.645242i	$0.223244\pi$
$174$	−997.541	−	1559.83i	−0.434617	−	0.679599i
$175$	1484.92	+	3113.09i	0.641424	+	1.34473i
$176$	2008.14	+	2359.65i	0.860052	+	1.01060i
$177$	644.245	−	1115.87i	0.273584	−	0.473862i
$178$	556.298	+	288.361i	0.234249	+	0.121425i
$179$	−2010.78	−	3482.78i	−0.839625	−	1.45427i	−0.890208	−	0.455554i	$-0.849441\pi$
$179$	−2010.78	−	3482.78i	−0.839625	−	1.45427i	0.0505832	−	0.998720i	$-0.483892\pi$
$180$	732.181	+	1037.95i	0.303186	+	0.429803i
$181$	−1552.28			−0.637461			−0.318730	−	0.947845i	$-0.603256\pi$
$181$	−1552.28			−0.637461			−0.318730	+	0.947845i	$0.603256\pi$
$182$	−2501.54	−	82.9647i	−1.01883	−	0.0337898i
$183$			1238.65i			0.500349i
$184$	−1403.97	−	572.973i	−0.562511	−	0.229566i
$185$	−1091.64	+	630.256i	−0.433831	+	0.250472i
$186$	−2287.96	−	1185.98i	−0.901943	−	0.467528i
$187$	60.7330	+	35.0642i	0.0237499	+	0.0137120i
$188$	−1652.63	+	3576.54i	−0.641121	+	1.38748i
$189$	39.2269	−	498.506i	0.0150970	−	0.191857i
$190$	931.785	−	595.895i	0.355783	−	0.227530i
$191$	1282.28	+	740.323i	0.485772	+	0.280460i	0.722819	−	0.691038i	$-0.242846\pi$
$191$	1282.28	+	740.323i	0.485772	+	0.280460i	−0.237047	+	0.971498i	$0.576180\pi$
$192$	−1074.71	+	1097.40i	−0.403963	+	0.412489i
$193$	−173.982	−	301.346i	−0.0648887	−	0.112391i	0.831756	−	0.555142i	$-0.187336\pi$
$193$	−173.982	−	301.346i	−0.0648887	−	0.112391i	−0.896645	+	0.442751i	$0.854003\pi$
$194$	201.169	+	4430.56i	0.0744491	+	1.63967i
$195$			2528.82i			0.928682i
$196$	2737.97	+	181.812i	0.997803	+	0.0662581i
$197$		−	3518.00i		−	1.27232i	−0.771558	−	0.636160i	$-0.780522\pi$
$197$		−	3518.00i		−	1.27232i	0.771558	−	0.636160i	$-0.219478\pi$
$198$	−1231.14	+	55.8999i	−0.441886	+	0.0200638i
$199$	228.161	+	395.187i	0.0812761	+	0.140774i	0.903798	−	0.427959i	$-0.140767\pi$
$199$	228.161	+	395.187i	0.0812761	+	0.140774i	−0.822522	+	0.568733i	$0.807434\pi$
$200$	2582.74	+	3329.75i	0.913137	+	1.17724i
$201$	563.772	+	325.494i	0.197838	+	0.114222i
$202$	−1527.58	−	2388.64i	−0.532081	−	0.832001i
$203$	−317.018	+	4028.75i	−0.109607	+	1.39292i
$204$	−14.5824	+	31.5584i	−0.00500476	+	0.0108310i
$205$	6404.15	+	3697.44i	2.18188	+	1.25971i
$206$	−1963.97	+	3788.85i	−0.664255	+	1.28146i
$207$	522.334	−	301.570i	0.175385	−	0.101259i
$208$	−3007.75	+	551.965i	−1.00264	+	0.183999i
$209$			1073.12i			0.355164i
$210$	91.8977	−	2770.88i	0.0301978	−	0.910520i
$211$	−4146.44			−1.35286			−0.676429	−	0.736508i	$-0.736473\pi$
$211$	−4146.44			−1.35286			−0.676429	+	0.736508i	$0.736473\pi$
$212$	−142.290	+	100.372i	−0.0460967	+	0.0325170i
$213$	−1219.78	−	2112.73i	−0.392386	−	0.679632i
$214$	−825.675	+	1592.87i	−0.263748	+	0.508815i
$215$	−2283.36	+	3954.89i	−0.724296	+	1.25452i
$216$	−82.9054	−	605.289i	−0.0261157	−	0.190670i
$217$	2421.61	+	5076.84i	0.757555	+	1.58819i
$218$	291.526	−	186.436i	0.0905716	−	0.0579223i
$219$	1239.90	−	2147.57i	0.382578	−	0.662644i
$220$	−6804.73	+	619.213i	−2.08534	+	0.189761i
$221$	−59.9391	+	34.6059i	−0.0182441	+	0.0105332i
$222$	605.651	−	27.4995i	0.183102	−	0.00831373i
$223$	1005.79			0.302029			0.151014	−	0.988532i	$-0.451746\pi$
$223$	1005.79			0.302029			0.151014	+	0.988532i	$0.451746\pi$
$224$	3315.71	−	495.497i	0.989018	−	0.147798i
$225$	−1676.11			−0.496625
$226$	6412.85	−	291.175i	1.88751	−	0.0857021i
$227$	−462.963	+	267.292i	−0.135365	+	0.0781533i	−0.566153	−	0.824300i	$-0.691569\pi$
$227$	−462.963	+	267.292i	−0.135365	+	0.0781533i	0.430788	+	0.902453i	$0.358236\pi$
$228$	−529.787	+	48.2092i	−0.153886	+	0.0140032i
$229$	−1048.73	+	1816.45i	−0.302628	+	0.524167i	−0.976730	−	0.214471i	$-0.931197\pi$
$229$	−1048.73	+	1816.45i	−0.302628	+	0.524167i	0.674102	+	0.738638i	$0.264531\pi$
$230$	2817.15	−	1801.63i	0.807642	−	0.516503i
$231$	2216.84	+	1523.55i	0.631417	+	0.433949i
$232$	670.012	+	4891.73i	0.189605	+	1.38430i
$233$	2022.33	−	3502.79i	0.568616	−	0.984872i	−0.428087	−	0.903737i	$-0.640812\pi$
$233$	2022.33	−	3502.79i	0.568616	−	0.984872i	0.996703	−	0.0811344i	$-0.0258543\pi$
$234$	559.747	−	1079.85i	0.156375	−	0.301675i
$235$	−4344.19	−	7524.36i	−1.20589	−	2.08866i
$236$	−2807.71	+	1980.58i	−0.774433	+	0.546292i
$237$	−2129.72			−0.583714
$238$	66.9341	−	35.7401i	0.0182298	−	0.00973399i
$239$		−	7113.96i		−	1.92537i	−0.270622	−	0.962686i	$-0.587229\pi$
$239$		−	7113.96i		−	1.92537i	0.270622	−	0.962686i	$-0.412771\pi$
$240$	−611.396	−	3331.60i	−0.164439	−	0.896057i
$241$	4029.38	−	2326.37i	1.07699	−	0.621802i	0.146909	−	0.989150i	$-0.453067\pi$
$241$	4029.38	−	2326.37i	1.07699	−	0.621802i	0.930084	+	0.367348i	$0.119734\pi$
$242$	1318.43	−	2543.47i	0.350213	−	0.675622i
$243$	210.444	+	121.500i	0.0555556	+	0.0320750i
$244$	1385.51	−	2998.44i	0.363517	−	0.786703i
$245$	−3807.99	+	4702.72i	−0.992994	+	1.22631i
$246$	−1916.26	−	2996.40i	−0.496651	−	0.776600i
$247$	−917.202	−	529.547i	−0.236276	−	0.136414i
$248$	4211.94	+	5430.16i	1.07846	+	1.39039i
$249$	−696.430	−	1206.25i	−0.177247	−	0.307001i
$250$	−3052.36	+	138.592i	−0.772193	+	0.0350614i
$251$			1345.32i			0.338309i	0.985590	+	0.169155i	$0.0541037\pi$
$251$			1345.32i			0.338309i	−0.985590	+	0.169155i	$0.945896\pi$
$252$	−652.568	+	1162.87i	−0.163127	+	0.290690i
$253$			3244.47i			0.806237i
$254$	78.0511	+	1719.00i	0.0192809	+	0.424644i
$255$	−38.3320	−	66.3929i	−0.00941349	−	0.0163046i
$256$	3829.10	−	1454.37i	0.934839	−	0.355071i
$257$	−2512.75	−	1450.74i	−0.609887	−	0.352118i	0.163034	−	0.986620i	$-0.447872\pi$
$257$	−2512.75	−	1450.74i	−0.609887	−	0.352118i	−0.772921	+	0.634502i	$0.781205\pi$
$258$	1850.43	−	1183.39i	0.446522	−	0.285560i
$259$	−1090.56	−	749.498i	−0.261637	−	0.179813i
$260$	2828.65	−	6121.60i	0.674713	−	1.46018i
$261$	−1700.74	−	981.920i	−0.403344	−	0.232871i
$262$	2438.69	+	1264.11i	0.575050	+	0.298081i
$263$	1078.50	−	622.673i	0.252864	−	0.145991i	−0.368211	−	0.929742i	$-0.620030\pi$
$263$	1078.50	−	622.673i	0.252864	−	0.145991i	0.621075	+	0.783751i	$0.286696\pi$
$264$	3042.79	+	1241.79i	0.709359	+	0.289496i
$265$		−	383.995i		−	0.0890136i
$266$	985.753	+	613.566i	0.227219	+	0.141429i
$267$	664.603			0.152334
$268$	−1000.65	−	1418.55i	−0.228077	−	0.323326i
$269$	2283.53	+	3955.19i	0.517581	+	0.896477i	0.999791	+	0.0204214i	$0.00650078\pi$
$269$	2283.53	+	3955.19i	0.517581	+	0.896477i	−0.482210	+	0.876055i	$0.660166\pi$
$270$	1196.12	+	620.016i	0.269605	+	0.139752i
$271$	2456.80	−	4255.30i	0.550701	−	0.953842i	−0.447523	−	0.894272i	$-0.647694\pi$
$271$	2456.80	−	4255.30i	0.550701	−	0.953842i	0.998224	−	0.0595697i	$-0.0189728\pi$
$272$	70.6000	−	60.0830i	0.0157381	−	0.0133936i
$273$	−2396.12	+	1142.93i	−0.531207	+	0.253381i
$274$	2677.21	+	4186.28i	0.590278	+	0.923002i
$275$	4508.14	−	7808.33i	0.988550	−	1.71222i
$276$	−1601.75	+	145.755i	−0.349327	+	0.0317879i
$277$	−166.697	+	96.2428i	−0.0361584	+	0.0208761i	−0.517970	−	0.855399i	$-0.673312\pi$
$277$	−166.697	+	96.2428i	−0.0361584	+	0.0208761i	0.481812	+	0.876275i	$0.339979\pi$
$278$	−325.325	−	7164.98i	−0.0701860	−	1.54578i
$279$	−2733.40			−0.586539
$280$	−3321.86	+	6604.77i	−0.708998	+	1.40968i
$281$	1763.46			0.374375			0.187188	−	0.982324i	$-0.440063\pi$
$281$	1763.46			0.374375			0.187188	+	0.982324i	$0.440063\pi$
$282$	189.547	+	4174.60i	0.0400262	+	0.881538i
$283$	2239.75	−	1293.12i	0.470456	−	0.271618i	−0.245974	−	0.969276i	$-0.579108\pi$
$283$	2239.75	−	1293.12i	0.470456	−	0.271618i	0.716431	+	0.697658i	$0.245775\pi$
$284$	589.549	+	6478.74i	0.123181	+	1.35367i
$285$	586.564	−	1015.96i	0.121912	−	0.211159i
$286$	3525.07	+	5512.06i	0.728817	+	1.13963i
$287$	−608.986	+	7739.16i	−0.125252	+	1.59174i
$288$	−476.362	+	1557.98i	−0.0974649	+	0.318766i
$289$	−2455.45	+	4252.97i	−0.499786	+	0.865656i
$290$	−9666.61	−	5010.75i	−1.95739	−	1.01463i
$291$	2352.08	+	4073.93i	0.473820	+	0.820680i
$292$	−5403.64	+	3811.77i	−1.08296	+	0.763928i
$293$	−8390.64			−1.67299			−0.836496	−	0.547974i	$-0.815399\pi$
$293$	−8390.64			−1.67299			−0.836496	+	0.547974i	$0.815399\pi$
$294$	2667.01	−	1165.25i	0.529057	−	0.231153i
$295$		−	7577.11i		−	1.49545i
$296$	−1496.88	−	610.890i	−0.293933	−	0.119957i
$297$	−1132.04	+	653.585i	−0.221171	+	0.127693i
$298$	775.930	+	402.209i	0.150834	+	0.0781856i
$299$	−2773.06	−	1601.03i	−0.536356	−	0.309665i
$300$	4057.40	+	1874.83i	0.780848	+	0.360811i
$301$	−4779.32	−	376.080i	−0.915201	−	0.0720162i
$302$	1236.41	−	790.708i	0.235587	−	0.150663i
$303$	−2604.42	−	1503.66i	−0.493795	−	0.285093i
$304$	1336.40	+	475.898i	0.252130	+	0.0897849i
$305$	3642.02	+	6308.16i	0.683742	+	1.18428i
$306$	1.67251	+	36.8355i	0.000312455	+	0.00688152i
$307$		−	5923.17i		−	1.10115i	−0.834785	−	0.550575i	$-0.814408\pi$
$307$		−	5923.17i		−	1.10115i	0.834785	−	0.550575i	$-0.185592\pi$
$308$	−3662.18	−	6167.77i	−0.677507	−	1.14104i
$309$			4526.49i			0.833343i
$310$	−15139.2	+	687.393i	−2.77370	+	0.125940i
$311$	−1739.48	−	3012.86i	−0.317160	−	0.549336i	0.662735	−	0.748854i	$-0.269396\pi$
$311$	−1739.48	−	3012.86i	−0.317160	−	0.549336i	−0.979894	+	0.199518i	$0.936062\pi$
$312$	−2562.87	+	1987.91i	−0.465045	+	0.360715i
$313$	2191.22	+	1265.10i	0.395702	+	0.228459i	0.684628	−	0.728893i	$-0.259965\pi$
$313$	2191.22	+	1265.10i	0.395702	+	0.228459i	−0.288926	+	0.957352i	$0.593298\pi$
$314$	876.230	+	1370.14i	0.157479	+	0.246246i
$315$	−1265.99	−	2654.11i	−0.226445	−	0.474737i
$316$	5155.47	+	2382.22i	0.917779	+	0.424084i
$317$	493.130	+	284.709i	0.0873720	+	0.0504443i	0.543049	−	0.839701i	$-0.317270\pi$
$317$	493.130	+	284.709i	0.0873720	+	0.0504443i	−0.455677	+	0.890145i	$0.650603\pi$
$318$	−84.9960	+	163.972i	−0.0149885	+	0.0289154i
$319$	9148.77	−	5282.04i	1.60574	−	0.927077i
$320$	−2246.57	+	8748.78i	−0.392460	+	1.52835i
$321$			1902.98i			0.330885i
$322$	2980.32	+	1855.05i	0.515797	+	0.321050i
$323$	32.1075			0.00553099
$324$	−373.523	−	529.513i	−0.0640472	−	0.0907945i
$325$	4449.22	+	7706.27i	0.759379	+	1.31528i
$326$	2877.48	−	5551.16i	0.488862	−	0.943098i
$327$	183.517	−	317.861i	0.0310352	−	0.0537546i
$328$	1287.08	+	9396.94i	0.216668	+	1.58189i
$329$	5166.10	−	7516.92i	0.865703	−	1.25964i
$330$	−6105.55	+	3904.62i	−1.01848	+	0.651340i
$331$	1335.36	−	2312.92i	0.221747	−	0.384077i	−0.733592	−	0.679591i	$-0.762157\pi$
$331$	1335.36	−	2312.92i	0.221747	−	0.384077i	0.955338	+	0.295514i	$0.0954908\pi$
$332$	336.601	+	3699.01i	0.0556426	+	0.611475i
$333$	556.899	−	321.526i	0.0916453	−	0.0529115i
$334$	2935.09	−	133.267i	0.480841	−	0.0218325i
$335$	3828.20			0.624350
$336$	2880.43	−	2085.06i	0.467680	−	0.338539i
$337$	10365.2			1.67546			0.837731	−	0.546083i	$-0.183882\pi$
$337$	10365.2			1.67546			0.837731	+	0.546083i	$0.183882\pi$
$338$	−243.019	+	11.0343i	−0.0391080	+	0.00177570i
$339$	5896.65	−	3404.43i	0.944726	−	0.545438i
$340$	18.5267	+	203.596i	0.00295515	+	0.0324751i
$341$	7351.89	−	12733.8i	1.16753	−	2.02222i
$342$	−475.351	+	303.997i	−0.0751581	+	0.0480651i
$343$	−6176.99	−	1482.71i	−0.972379	−	0.233408i
$344$	−5803.08	+	794.838i	−0.909539	+	0.124578i
$345$	1773.41	−	3071.64i	0.276746	−	0.479338i
$346$	1047.36	−	2020.53i	0.162735	−	0.313944i
$347$	−273.002	−	472.854i	−0.0422350	−	0.0731531i	0.844135	−	0.536130i	$-0.180114\pi$
$347$	−273.002	−	472.854i	−0.0422350	−	0.0731531i	−0.886370	+	0.462977i	$0.846781\pi$
$348$	3018.68	+	4279.34i	0.464995	+	0.659186i
$349$	−11292.9			−1.73208			−0.866041	−	0.499974i	$-0.833343\pi$
$349$	−11292.9			−1.73208			−0.866041	+	0.499974i	$0.833343\pi$
$350$	−4595.05	−	8605.59i	−0.701759	−	1.31425i
$351$		−	1290.08i		−	0.196181i
$352$	−5976.75	−	6409.59i	−0.905006	−	0.970546i
$353$	−1828.27	+	1055.55i	−0.275663	+	0.159154i	−0.631459	−	0.775410i	$-0.717543\pi$
$353$	−1828.27	+	1055.55i	−0.275663	+	0.159154i	0.355795	+	0.934564i	$0.384210\pi$
$354$	−1677.17	+	3235.55i	−0.251809	+	0.485784i
$355$	−12424.1	−	7173.07i	−1.85748	−	1.07241i
$356$	−1608.82	−	743.400i	−0.239516	−	0.110675i
$357$	45.5842	−	66.3272i	0.00675790	−	0.00983308i
$358$	6128.31	+	9582.67i	0.904724	+	1.41469i
$359$	5101.69	+	2945.46i	0.750019	+	0.433024i	0.825701	−	0.564108i	$-0.190780\pi$
$359$	5101.69	+	2945.46i	0.750019	+	0.433024i	−0.0756816	+	0.997132i	$0.524113\pi$
$360$	−2201.95	−	2838.82i	−0.322370	−	0.415609i
$361$	−3183.84	−	5514.58i	−0.464185	−	0.803991i
$362$	4386.01	−	199.146i	0.636805	−	0.0289141i
$363$		−	3038.65i		−	0.439361i
$364$	7078.78	−	86.5101i	1.01931	−	0.0124570i
$365$		−	14582.7i		−	2.09122i
$366$	−158.910	−	3499.83i	−0.0226949	−	0.499834i
$367$	1218.35	+	2110.24i	0.173290	+	0.300147i	0.939568	−	0.342362i	$-0.111227\pi$
$367$	1218.35	+	2110.24i	0.173290	+	0.300147i	−0.766278	+	0.642509i	$0.777894\pi$
$368$	4040.45	+	1438.83i	0.572345	+	0.203815i
$369$	−3267.08	−	1886.25i	−0.460915	−	0.266109i
$370$	3003.58	−	1920.85i	0.422023	−	0.269892i
$371$	363.843	−	173.550i	0.0509159	−	0.0242864i
$372$	6616.82	+	3057.48i	0.922221	+	0.426137i
$373$	−7425.37	−	4287.04i	−1.03075	−	0.595106i	−0.113553	−	0.993532i	$-0.536223\pi$
$373$	−7425.37	−	4287.04i	−1.03075	−	0.595106i	−0.917200	+	0.398426i	$0.869557\pi$
$374$	−176.101	−	91.2829i	−0.0243474	−	0.0126207i
$375$	−2806.66	+	1620.43i	−0.386494	+	0.223143i
$376$	4210.70	−	10317.6i	0.577528	−	1.41513i
$377$			10426.0i			1.42431i
$378$	−46.8817	+	1413.57i	−0.00637919	+	0.192344i
$379$	−11079.7			−1.50166			−0.750828	−	0.660498i	$-0.770345\pi$
$379$	−11079.7			−1.50166			−0.750828	+	0.660498i	$0.770345\pi$
$380$	−2556.33	+	1803.25i	−0.345097	+	0.243434i
$381$	912.577	+	1580.63i	0.122711	+	0.212541i
$382$	−3718.07	−	1927.29i	−0.497993	−	0.258138i
$383$	−1164.21	+	2016.47i	−0.155322	+	0.269026i	−0.933176	−	0.359419i	$-0.882975\pi$
$383$	−1164.21	+	2016.47i	−0.155322	+	0.269026i	0.777854	+	0.628445i	$0.216308\pi$
$384$	2895.84	−	3238.60i	0.384837	−	0.430388i
$385$	15769.5	+	1240.89i	2.08750	+	0.164263i
$386$	530.250	+	829.138i	0.0699197	+	0.109332i
$387$	1164.86	−	2017.59i	0.153005	−	0.265013i
$388$	−1136.82	−	12492.8i	−0.148745	−	1.63461i
$389$	−7770.44	+	4486.27i	−1.01279	+	0.584737i	−0.912009	−	0.410171i	$-0.865469\pi$
$389$	−7770.44	+	4486.27i	−1.01279	+	0.584737i	−0.100786	+	0.994908i	$0.532136\pi$
$390$	−324.429	−	7145.24i	−0.0421233	−	0.927726i
$391$	97.0736			0.0125556
$392$	−7759.50	−	162.452i	−0.999781	−	0.0209313i
$393$	2913.48			0.373958
$394$	451.332	+	9940.15i	0.0577101	+	1.27101i
$395$	−10846.1	+	6262.03i	−1.38159	+	0.797663i
$396$	3471.44	−	315.892i	0.440522	−	0.0400863i
$397$	1579.08	−	2735.04i	0.199626	−	0.345763i	−0.748781	−	0.662817i	$-0.769361\pi$
$397$	1579.08	−	2735.04i	0.199626	−	0.345763i	0.948407	+	0.317055i	$0.102694\pi$
$398$	−695.373	−	1087.34i	−0.0875777	−	0.136943i
$399$	1227.75	+	96.6099i	0.154046	+	0.0121217i
$400$	−7724.76	−	9076.92i	−0.965595	−	1.13461i
$401$	−5718.83	+	9905.31i	−0.712182	+	1.23354i	0.251855	+	0.967765i	$0.418960\pi$
$401$	−5718.83	+	9905.31i	−0.712182	+	1.23354i	−0.964036	+	0.265770i	$0.914374\pi$
$402$	−1634.70	−	847.360i	−0.202815	−	0.105131i
$403$	7255.79	+	12567.4i	0.896865	+	1.55341i
$404$	4622.66	+	6553.17i	0.569272	+	0.807010i
$405$	1428.99			0.175326
$406$	378.881	−	11424.0i	0.0463142	−	1.39646i
$407$			3459.17i			0.421289i
$408$	37.1541	−	91.0395i	0.00450833	−	0.0110469i
$409$	−2982.35	+	1721.86i	−0.360556	+	0.208167i	−0.669325	−	0.742970i	$-0.733417\pi$
$409$	−2982.35	+	1721.86i	−0.360556	+	0.208167i	0.308768	+	0.951137i	$0.400083\pi$
$410$	−18569.4	−	9625.57i	−2.23677	−	1.15945i
$411$	4564.45	+	2635.29i	0.547805	+	0.316275i
$412$	5063.16	−	10957.4i	0.605447	−	1.31027i
$413$	7179.48	−	3424.55i	0.855397	−	0.408017i
$414$	−1437.17	+	919.101i	−0.170612	+	0.109110i
$415$	−7093.50	−	4095.43i	−0.839051	−	0.484426i
$416$	8427.62	−	1945.46i	0.993265	−	0.229288i
$417$	−3803.72	−	6588.24i	−0.446688	−	0.773686i
$418$	−137.673	−	3032.12i	−0.0161096	−	0.354799i
$419$			4796.10i			0.559200i	0.960117	+	0.279600i	$0.0902018\pi$
$419$			4796.10i			0.559200i	−0.960117	+	0.279600i	$0.909798\pi$
$420$	95.8248	+	7840.97i	0.0111328	+	0.910952i
$421$			9193.37i			1.06427i	0.846660	+	0.532135i	$0.178610\pi$
$421$			9193.37i			1.06427i	−0.846660	+	0.532135i	$0.821390\pi$
$422$	11715.8	−	531.957i	1.35147	−	0.0613632i
$423$	2216.20	+	3838.56i	0.254740	+	0.441223i
$424$	389.165	−	301.858i	0.0445743	−	0.0345744i
$425$	−233.623	−	134.882i	−0.0266645	−	0.0153947i
$426$	3717.56	+	5813.05i	0.422809	+	0.661134i
$427$	−4331.07	+	6301.92i	−0.490855	+	0.714218i
$428$	2128.61	−	4606.61i	0.240397	−	0.520254i
$429$	6009.99	+	3469.87i	0.676376	+	0.390506i
$430$	5944.28	−	11467.5i	0.666647	−	1.28608i
$431$	13682.7	−	7899.69i	1.52917	−	0.882865i	0.529770	−	0.848141i	$-0.322278\pi$
$431$	13682.7	−	7899.69i	1.52917	−	0.882865i	0.999397	−	0.0347237i	$-0.0110551\pi$
$432$	311.904	+	1699.62i	0.0347373	+	0.189289i
$433$			2262.13i			0.251064i	0.992090	+	0.125532i	$0.0400638\pi$
$433$			2262.13i			0.251064i	−0.992090	+	0.125532i	$0.959936\pi$
$434$	−7493.61	−	14034.0i	−0.828813	−	1.55220i
$435$	−11548.6			−1.27290
$436$	−799.792	+	564.180i	−0.0878511	+	0.0619709i
$437$	742.721	+	1286.43i	0.0813024	+	0.140820i
$438$	−3227.83	+	6227.05i	−0.352128	+	0.679315i
$439$	−7381.62	+	12785.3i	−0.802519	+	1.39000i	0.115435	+	0.993315i	$0.463174\pi$
$439$	−7381.62	+	12785.3i	−0.802519	+	1.39000i	−0.917954	+	0.396688i	$0.870160\pi$
$440$	19147.4	−	2622.59i	2.07459	−	0.284153i
$441$	1942.65	−	2399.10i	0.209767	−	0.259054i
$442$	164.919	−	105.469i	0.0177475	−	0.0113499i
$443$	−278.837	+	482.959i	−0.0299050	+	0.0517971i	−0.880591	−	0.473878i	$-0.842854\pi$
$443$	−278.837	+	482.959i	−0.0299050	+	0.0517971i	0.850686	+	0.525675i	$0.176187\pi$
$444$	−1707.75	+	155.401i	−0.182536	+	0.0166104i
$445$	3384.66	−	1954.14i	0.360558	−	0.208168i
$446$	−2841.87	+	129.035i	−0.301718	+	0.0136995i
$447$	926.994			0.0980880
$448$	−9305.01	+	1825.42i	−0.981296	+	0.192506i
$449$	−15535.5			−1.63289			−0.816444	−	0.577424i	$-0.804058\pi$
$449$	−15535.5			−1.63289			−0.816444	+	0.577424i	$0.804058\pi$
$450$	4735.87	−	215.032i	0.496114	−	0.0225260i
$451$	17574.6	−	10146.7i	1.83494	−	1.05940i
$452$	−18082.3	+	1645.44i	−1.88168	+	0.171228i
$453$	778.326	−	1348.10i	0.0807262	−	0.139822i
$454$	1273.82	−	814.632i	0.131681	−	0.0842128i
$455$	−8842.29	+	12866.0i	−0.911061	+	1.32564i
$456$	1490.74	−	204.184i	0.153092	−	0.0209688i
$457$	−225.347	+	390.313i	−0.0230663	+	0.0399520i	−0.877328	−	0.479891i	$-0.840676\pi$
$457$	−225.347	+	390.313i	−0.0230663	+	0.0399520i	0.854262	+	0.519843i	$0.174010\pi$
$458$	2730.16	−	5266.95i	0.278541	−	0.537355i
$459$	19.5551	+	33.8704i	0.00198857	+	0.00344430i
$460$	−7728.78	+	5451.94i	−0.783383	+	0.552605i
$461$	10297.6			1.04037			0.520183	−	0.854055i	$-0.325864\pi$
$461$	10297.6			1.04037			0.520183	+	0.854055i	$0.325864\pi$
$462$	−6459.17	−	4020.41i	−0.650450	−	0.404862i
$463$		−	13595.9i		−	1.36470i	−0.731026	−	0.682349i	$-0.760958\pi$
$463$		−	13595.9i		−	1.36470i	0.731026	−	0.682349i	$-0.239042\pi$
$464$	−2520.70	−	13735.7i	−0.252200	−	1.37428i
$465$	−13920.5	+	8037.03i	−1.38828	+	0.801523i
$466$	−5264.76	+	10156.6i	−0.523359	+	1.00965i
$467$	15305.1	+	8836.40i	1.51656	+	0.875588i	0.999811	+	0.0194532i	$0.00619253\pi$
$467$	15305.1	+	8836.40i	1.51656	+	0.875588i	0.516752	+	0.856135i	$0.327141\pi$
$468$	−1443.04	+	3122.94i	−0.142531	+	0.308457i
$469$	1730.19	+	3627.30i	0.170347	+	0.357129i
$470$	13239.9	+	20702.9i	1.29939	+	2.03181i
$471$	1493.91	+	862.509i	0.146148	+	0.0843786i
$472$	7679.13	−	5956.37i	0.748858	−	0.580856i
$473$	6266.11	+	10853.2i	0.609125	+	1.05504i
$474$	6017.56	−	273.227i	0.583113	−	0.0264762i
$475$		−	4128.00i		−	0.398749i
$476$	−184.538	+	109.571i	−0.0177695	+	0.0105508i
$477$			195.895i			0.0188038i
$478$	912.667	+	20100.6i	0.0873314	+	1.92339i
$479$	−218.470	−	378.401i	−0.0208396	−	0.0360952i	0.855418	−	0.517939i	$-0.173301\pi$
$479$	−218.470	−	378.401i	−0.0208396	−	0.0360952i	−0.876257	+	0.481844i	$0.839967\pi$
$480$	2154.93	+	9335.04i	0.204914	+	0.887676i
$481$	−2956.57	−	1706.98i	−0.280266	−	0.161812i
$482$	−11086.6	+	7090.12i	−1.04768	+	0.670013i
$483$	3711.96	+	292.090i	0.349689	+	0.0275167i
$484$	−3398.92	+	7355.76i	−0.319208	+	0.690811i
$485$	23957.2	+	13831.7i	2.24297	+	1.29498i
$486$	−610.201	−	316.302i	−0.0569532	−	0.0295221i
$487$	−4871.56	+	2812.60i	−0.453289	+	0.261706i	−0.709218	−	0.704989i	$-0.750952\pi$
$487$	−4871.56	+	2812.60i	−0.453289	+	0.261706i	0.255929	+	0.966695i	$0.417619\pi$
$488$	−3530.10	+	8649.90i	−0.327460	+	0.802382i
$489$		−	6631.90i		−	0.613303i
$490$	10156.2	−	13776.2i	0.936349	−	1.27009i
$491$	−1704.19			−0.156638			−0.0783188	−	0.996928i	$-0.524955\pi$
$491$	−1704.19			−0.156638			−0.0783188	+	0.996928i	$0.524955\pi$
$492$	5798.84	+	8220.54i	0.531365	+	0.753274i
$493$	−158.037	−	273.729i	−0.0144374	−	0.0250063i
$494$	2659.51	+	1378.57i	0.242220	+	0.125557i
$495$	−3843.48	+	6657.10i	−0.348993	+	0.604473i
$496$	−12597.6	−	14802.6i	−1.14042	−	1.34004i
$497$	1181.44	−	15014.1i	0.106629	−	1.35507i
$498$	2122.53	+	3318.94i	0.190989	+	0.298645i
$499$	−9269.28	+	16054.9i	−0.831563	+	1.44031i	0.0652360	+	0.997870i	$0.479220\pi$
$499$	−9269.28	+	16054.9i	−0.831563	+	1.44031i	−0.896799	+	0.442439i	$0.854113\pi$
$500$	8606.72	−	783.189i	0.769808	−	0.0700506i
$501$	2698.83	−	1558.17i	0.240668	−	0.138950i
$502$	−172.594	−	3801.21i	−0.0153451	−	0.337961i
$503$	1979.86			0.175502			0.0877510	−	0.996142i	$-0.472032\pi$
$503$	1979.86			0.175502			0.0877510	+	0.996142i	$0.472032\pi$
$504$	1694.65	−	3369.43i	0.149773	−	0.297790i
$505$	−17684.9			−1.55835
$506$	−416.240	−	9167.29i	−0.0365694	−	0.805407i
$507$	−223.457	+	129.013i	−0.0195741	+	0.0113011i
$508$	−441.069	−	4847.05i	−0.0385222	−	0.423333i
$509$	−3252.55	+	5633.58i	−0.283235	+	0.490577i	−0.972180	−	0.234237i	$-0.924741\pi$
$509$	−3252.55	+	5633.58i	−0.283235	+	0.490577i	0.688945	+	0.724814i	$0.258074\pi$
$510$	116.825	+	182.676i	0.0101434	+	0.0158609i
$511$	13817.4	−	6590.79i	1.19618	−	0.570566i
$512$	−10632.6	+	4600.59i	−0.917772	+	0.397108i
$513$	−299.236	+	518.292i	−0.0257536	+	0.0446066i
$514$	7285.93	+	3776.71i	0.625230	+	0.324092i
$515$	13309.3	+	23052.3i	1.13879	+	1.97244i
$516$	−5076.60	+	3581.08i	−0.433110	+	0.305519i
$517$	−23843.2			−2.02828
$518$	3177.54	+	1977.81i	0.269523	+	0.167761i
$519$		−	2413.91i		−	0.204160i
$520$	−7207.04	+	17659.6i	−0.607787	+	1.48928i
$521$	9924.60	−	5729.97i	0.834558	−	0.481832i	−0.0208528	−	0.999783i	$-0.506638\pi$
$521$	9924.60	−	5729.97i	0.834558	−	0.481832i	0.855411	+	0.517950i	$0.173305\pi$
$522$	4931.43	+	2556.24i	0.413492	+	0.214336i
$523$	−15676.5	−	9050.84i	−1.31068	−	0.756722i	−0.328472	−	0.944514i	$-0.606534\pi$
$523$	−15676.5	−	9050.84i	−1.31068	−	0.756722i	−0.982209	+	0.187792i	$0.939867\pi$
$524$	−7052.75	−	3258.91i	−0.587978	−	0.271691i
$525$	−8527.57	−	5860.68i	−0.708902	−	0.487202i
$526$	−2967.44	+	1897.73i	−0.245982	+	0.157310i
$527$	−380.993	−	219.967i	−0.0314921	−	0.0181820i
$528$	−8756.77	−	3118.33i	−0.721760	−	0.257023i
$529$	−3837.96	−	6647.55i	−0.315440	−	0.546359i
$530$	49.2636	+	1084.98i	0.00403750	+	0.0889220i
$531$			3865.47i			0.315908i
$532$	−2863.98	−	1607.18i	−0.233401	−	0.130977i
$533$			20028.2i			1.62761i
$534$	−1877.85	+	85.2635i	−0.152177	+	0.00690958i
$535$	5595.36	+	9691.44i	0.452165	+	0.783173i
$536$	3009.35	+	3879.75i	0.242508	+	0.312648i
$537$	10448.3	+	6032.35i	0.839625	+	0.484758i
$538$	−6959.57	−	10882.5i	−0.557711	−	0.872078i
$539$	5951.42	+	15502.8i	0.475595	+	1.23887i
$540$	−3459.19	−	1598.41i	−0.275667	−	0.127379i
$541$	15840.4	+	9145.43i	1.25884	+	0.726789i	0.972848	−	0.231444i	$-0.0743451\pi$
$541$	15840.4	+	9145.43i	1.25884	+	0.726789i	0.285987	+	0.958233i	$0.407678\pi$
$542$	−6395.80	+	12338.6i	−0.506870	+	0.977839i
$543$	4032.95	−	2328.43i	0.318730	−	0.184019i
$544$	−191.773	+	178.823i	−0.0151144	+	0.0140937i
$545$		−	2158.38i		−	0.169642i
$546$	6623.63	−	3536.76i	0.519167	−	0.277215i
$547$	12201.9			0.953774			0.476887	−	0.878965i	$-0.341765\pi$
$547$	12201.9			0.953774			0.476887	+	0.878965i	$0.341765\pi$
$548$	−8101.57	−	11484.9i	−0.631537	−	0.895278i
$549$	−1857.98	−	3218.11i	−0.144438	−	0.250174i
$550$	−11736.1	+	22640.9i	−0.909870	+	1.75530i
$551$	2418.32	−	4188.66i	0.186976	−	0.323853i
$552$	4507.08	−	617.327i	0.347526	−	0.0476000i
$553$	−10835.4	−	7446.77i	−0.833217	−	0.572638i
$554$	458.659	−	293.322i	0.0351743	−	0.0224947i
$555$	1890.77	−	3274.91i	0.144610	−	0.250472i
$556$	1838.42	+	20203.0i	0.140228	+	1.54101i
$557$	−15422.0	+	8903.88i	−1.17316	+	0.677324i	−0.954422	−	0.298460i	$-0.903527\pi$
$557$	−15422.0	+	8903.88i	−1.17316	+	0.677324i	−0.218737	+	0.975784i	$0.570194\pi$
$558$	7723.26	−	350.674i	0.585935	−	0.0266043i
$559$	−12368.4			−0.935828
$560$	8538.64	−	19088.0i	0.644328	−	1.44039i
$561$	−210.385			−0.0158333
$562$	−4982.70	+	226.239i	−0.373990	+	0.0169810i
$563$	−71.1394	+	41.0724i	−0.00532534	+	0.00307459i	−0.502660	−	0.864484i	$-0.667645\pi$
$563$	−71.1394	+	41.0724i	−0.00532534	+	0.00307459i	0.497335	+	0.867559i	$0.334312\pi$
$564$	−1071.14	−	11771.1i	−0.0799699	−	0.878815i
$565$	20020.1	−	34675.9i	1.49071	−	2.58199i
$566$	−6162.54	+	3941.07i	−0.457652	+	0.292678i
$567$	645.845	+	1354.00i	0.0478358	+	0.100287i
$568$	−2496.95	−	18230.1i	−0.184454	−	1.34669i
$569$	−10075.8	+	17451.8i	−0.742353	+	1.28579i	0.209068	+	0.977901i	$0.432957\pi$
$569$	−10075.8	+	17451.8i	−0.742353	+	1.28579i	−0.951421	+	0.307892i	$0.900376\pi$
$570$	−1527.01	+	2945.86i	−0.112209	+	0.216471i
$571$	2236.85	+	3874.34i	0.163939	+	0.283951i	0.936278	−	0.351260i	$-0.114247\pi$
$571$	2236.85	+	3874.34i	0.163939	+	0.283951i	−0.772339	+	0.635211i	$0.780913\pi$
$572$	−10667.3	−	15122.2i	−0.779759	−	1.10540i
$573$	−4441.94			−0.323848
$574$	727.825	−	21945.3i	0.0529248	−	1.59578i
$575$		−	12480.6i		−	0.905176i
$576$	1146.09	−	4463.20i	0.0829059	−	0.322859i
$577$	18315.3	−	10574.3i	1.32145	−	0.762937i	0.337486	−	0.941330i	$-0.390423\pi$
$577$	18315.3	−	10574.3i	1.32145	−	0.762937i	0.983959	+	0.178394i	$0.0570900\pi$
$578$	6392.29	−	12331.8i	0.460008	−	0.887434i
$579$	904.038	+	521.947i	0.0648887	+	0.0374635i
$580$	27956.0	+	12917.8i	2.00140	+	0.924798i
$581$	674.538	−	8572.21i	0.0481662	−	0.612109i
$582$	−7168.50	−	11209.2i	−0.510557	−	0.798344i
$583$	−912.600	−	526.890i	−0.0648302	−	0.0374298i
$584$	14779.1	−	11463.5i	1.04719	−	0.812263i
$585$	−3793.24	−	6570.08i	−0.268087	−	0.464341i
$586$	23707.9	−	1076.45i	1.67127	−	0.0758839i
$587$		−	1439.95i		−	0.101249i	−0.998718	−	0.0506244i	$-0.983879\pi$
$587$		−	1439.95i		−	0.101249i	0.998718	−	0.0506244i	$-0.0161211\pi$
$588$	−7386.17	+	3634.59i	−0.518028	+	0.254912i
$589$		−	6731.95i		−	0.470943i
$590$	972.086	+	21409.3i	0.0678307	+	1.49391i
$591$	5276.99	+	9140.02i	0.367287	+	0.636160i
$592$	4307.82	+	1534.04i	0.299072	+	0.106501i
$593$	7668.69	+	4427.52i	0.531054	+	0.306604i	0.741446	−	0.671013i	$-0.234141\pi$
$593$	7668.69	+	4427.52i	0.531054	+	0.306604i	−0.210391	+	0.977617i	$0.567474\pi$
$594$	3114.75	−	1991.95i	0.215151	−	0.137594i
$595$	37.1270	−	471.820i	0.00255808	−	0.0325088i
$596$	−2244.00	−	1036.90i	−0.154225	−	0.0712636i
$597$	−1185.56	−	684.484i	−0.0812761	−	0.0469248i
$598$	8040.73	+	4167.97i	0.549849	+	0.285018i
$599$	−18738.6	+	10818.8i	−1.27820	+	0.737968i	−0.976517	−	0.215441i	$-0.930881\pi$
$599$	−18738.6	+	10818.8i	−1.27820	+	0.737968i	−0.301681	+	0.953409i	$0.597548\pi$
$600$	−11704.8	−	4776.83i	−0.796410	−	0.325022i
$601$			9365.01i			0.635618i	0.948155	+	0.317809i	$0.102947\pi$
$601$			9365.01i			0.635618i	−0.948155	+	0.317809i	$0.897053\pi$
$602$	13552.3	+	449.469i	0.917526	+	0.0304302i
$603$	−1952.96			−0.131892
$604$	−3392.05	+	2392.78i	−0.228511	+	0.161193i
$605$	−8934.57	−	15475.1i	−0.600400	−	1.03992i
$606$	7551.74	+	3914.50i	0.506218	+	0.262402i
$607$	−7324.84	+	12687.0i	−0.489796	+	0.848351i	−0.999931	−	0.0117431i	$-0.996262\pi$
$607$	−7324.84	+	12687.0i	−0.489796	+	0.848351i	0.510135	+	0.860094i	$0.329595\pi$
$608$	−3837.06	−	1173.21i	−0.255943	−	0.0782563i
$609$	−5219.49	−	10942.5i	−0.347298	−	0.728101i
$610$	−11099.9	−	17356.6i	−0.736755	−	1.15204i
$611$	11765.7	−	20378.9i	0.779036	−	1.34933i
$612$	−9.45142	−	103.865i	−0.000624266	−	0.00686026i
$613$	11506.9	−	6643.48i	0.758169	−	0.437729i	−0.0704693	−	0.997514i	$-0.522450\pi$
$613$	11506.9	−	6643.48i	0.758169	−	0.437729i	0.828638	+	0.559785i	$0.189116\pi$
$614$	759.898	+	16736.0i	0.0499462	+	1.10002i
$615$	−22184.6			−1.45459
$616$	11138.8	+	16957.3i	0.728565	+	1.10914i
$617$	−18139.5			−1.18358			−0.591790	−	0.806093i	$-0.701578\pi$
$617$	−18139.5			−1.18358			−0.591790	+	0.806093i	$0.701578\pi$
$618$	−580.714	−	12789.7i	−0.0377989	−	0.832485i
$619$	4782.49	−	2761.17i	0.310541	−	0.179291i	−0.336628	−	0.941638i	$-0.609286\pi$
$619$	4782.49	−	2761.17i	0.310541	−	0.179291i	0.647168	+	0.762347i	$0.275953\pi$
$620$	42687.8	−	3884.48i	2.76513	−	0.251620i
$621$	−904.709	+	1567.00i	−0.0584617	+	0.101259i
$622$	5301.44	+	8289.72i	0.341750	+	0.534385i
$623$	3381.32	+	2323.85i	0.217447	+	0.149443i
$624$	6986.41	−	5945.67i	0.448205	−	0.381438i
$625$	2110.54	−	3655.56i	0.135075	−	0.233956i
$626$	−6353.62	−	3293.44i	−0.405658	−	0.210275i
$627$	−1609.68	−	2788.05i	−0.102527	−	0.177582i
$628$	−2651.58	−	3758.93i	−0.168487	−	0.238850i
$629$	103.497			0.00656075
$630$	3917.57	+	7336.81i	0.247745	+	0.463977i
$631$		−	1982.66i		−	0.125085i	−0.998042	−	0.0625424i	$-0.980079\pi$
$631$		−	1982.66i		−	0.125085i	0.998042	−	0.0625424i	$-0.0199209\pi$
$632$	−14872.5	−	6069.60i	−0.936070	−	0.382019i
$633$	10772.8	−	6219.67i	0.676429	−	0.390536i
$634$	−1429.87	−	741.184i	−0.0895702	−	0.0464293i
$635$	9295.06	+	5366.51i	0.580887	+	0.335375i
$636$	219.121	−	474.210i	0.0136615	−	0.0295655i
$637$	−16187.1	−	2563.37i	−1.00684	−	0.159441i
$638$	−25172.3	+	16098.2i	−1.56204	+	0.998957i
$639$	6338.18	+	3659.35i	0.392386	+	0.226544i
$640$	5225.33	−	25008.0i	0.322733	−	1.54458i
$641$	−9014.28	−	15613.2i	−0.555448	−	0.962065i	−0.997868	−	0.0652570i	$-0.979213\pi$
$641$	−9014.28	−	15613.2i	−0.555448	−	0.962065i	0.442420	−	0.896808i	$-0.354120\pi$
$642$	−244.138	−	5376.91i	−0.0150084	−	0.330545i
$643$			15597.4i			0.956610i	0.878194	+	0.478305i	$0.158749\pi$
$643$			15597.4i			0.956610i	−0.878194	+	0.478305i	$0.841251\pi$
$644$	−8658.92	−	4859.13i	−0.529828	−	0.297324i
$645$		−	13700.1i		−	0.836344i
$646$	−90.7203	+	4.11915i	−0.00552530	+	0.000250876i
$647$	−7017.02	−	12153.8i	−0.426380	−	0.738511i	0.570169	−	0.821528i	$-0.306878\pi$
$647$	−7017.02	−	12153.8i	−0.426380	−	0.738511i	−0.996548	+	0.0830166i	$0.973545\pi$
$648$	1123.33	+	1448.23i	0.0680995	+	0.0877960i
$649$	−18007.7	−	10396.8i	−1.08916	−	0.628827i
$650$	−13560.0	−	21203.4i	−0.818256	−	1.27948i
$651$	−13906.8	−	9557.60i	−0.837250	−	0.575410i
$652$	−7418.19	+	16054.0i	−0.445581	+	0.964302i
$653$	8110.72	+	4682.72i	0.486059	+	0.280627i	0.722938	−	0.690913i	$-0.242791\pi$
$653$	8110.72	+	4682.72i	0.486059	+	0.280627i	−0.236879	+	0.971539i	$0.576124\pi$
$654$	−477.751	+	921.664i	−0.0285651	+	0.0551069i
$655$	14837.7	−	8566.52i	0.885122	−	0.511026i
$656$	−4842.23	−	26386.1i	−0.288197	−	1.57043i
$657$			7439.38i			0.441763i
$658$	−13632.5	+	21902.0i	−0.807677	+	1.29761i
$659$	−16415.6			−0.970351			−0.485175	−	0.874417i	$-0.661244\pi$
$659$	−16415.6			−0.970351			−0.485175	+	0.874417i	$0.661244\pi$
$660$	16750.4	−	11815.9i	0.987891	−	0.696867i
$661$	−4574.55	−	7923.35i	−0.269182	−	0.466237i	0.699469	−	0.714663i	$-0.253420\pi$
$661$	−4574.55	−	7923.35i	−0.269182	−	0.466237i	−0.968651	+	0.248426i	$0.920087\pi$
$662$	−3476.36	+	6706.50i	−0.204098	+	0.393740i
$663$	103.818	−	179.817i	0.00608136	−	0.0105332i
$664$	−1425.63	−	10408.4i	−0.0833208	−	0.608322i
$665$	6536.67	−	3117.94i	0.381175	−	0.181817i
$666$	−1532.28	+	979.923i	−0.0891510	+	0.0570139i
$667$	7311.54	−	12664.0i	0.424444	−	0.735158i
$668$	−8276.04	+	753.099i	−0.479356	+	0.0436201i
$669$	−2613.11	+	1508.68i	−0.151014	+	0.0871882i
$670$	−10816.7	+	491.129i	−0.623707	+	0.0283194i
$671$	19989.2			1.15004
$672$	−7871.21	+	6260.90i	−0.451843	+	0.359404i
$673$	10129.6			0.580190			0.290095	−	0.956998i	$-0.406313\pi$
$673$	10129.6			0.580190			0.290095	+	0.956998i	$0.406313\pi$
$674$	−29287.2	+	1329.78i	−1.67374	+	0.0759959i
$675$	4354.66	−	2514.16i	0.248312	−	0.143363i
$676$	685.239	−	62.3550i	0.0389872	−	0.00354774i
$677$	15398.1	−	26670.4i	0.874149	−	1.51407i	0.0164817	−	0.999864i	$-0.494753\pi$
$677$	15398.1	−	26670.4i	0.874149	−	1.51407i	0.857667	−	0.514206i	$-0.171913\pi$
$678$	−16224.3	+	10375.8i	−0.919014	+	0.587727i
$679$	−2278.15	+	28951.3i	−0.128759	+	1.63630i
$680$	−78.4673	−	572.887i	−0.00442512	−	0.0323076i
$681$	801.876	−	1388.89i	0.0451218	−	0.0781533i
$682$	−19139.2	+	36922.9i	−1.07460	+	2.07309i
$683$	−9279.17	−	16072.0i	−0.519850	−	0.900406i	−0.999734	−	0.0230743i	$-0.992655\pi$
$683$	−9279.17	−	16072.0i	−0.519850	−	0.900406i	0.479884	−	0.877332i	$-0.340679\pi$
$684$	1304.11	−	919.931i	0.0729006	−	0.0514246i
$685$	30994.2			1.72880
$686$	17643.4	+	3396.97i	0.981965	+	0.189063i
$687$		−	6292.36i		−	0.349445i
$688$	16294.7	−	2990.32i	0.902952	−	0.165705i
$689$	900.671	−	520.002i	0.0498009	−	0.0287526i
$690$	−4616.74	+	8906.49i	−0.254719	+	0.491398i
$691$	−9239.53	−	5334.44i	−0.508666	−	0.293678i	0.223619	−	0.974677i	$-0.428213\pi$
$691$	−9239.53	−	5334.44i	−0.508666	−	0.293678i	−0.732285	+	0.680998i	$0.761546\pi$
$692$	−2700.11	+	5843.42i	−0.148328	+	0.321002i
$693$	−8044.84	−	633.039i	−0.440979	−	0.0347001i
$694$	832.036	+	1301.03i	0.0455096	+	0.0711621i
$695$	−38742.8	−	22368.2i	−2.11453	−	1.22083i
$696$	−9078.34	−	11704.1i	−0.494416	−	0.637416i
$697$	−303.587	−	525.828i	−0.0164981	−	0.0285756i
$698$	31908.3	−	1448.80i	1.73030	−	0.0785641i
$699$			12134.0i			0.656581i
$700$	14087.4	+	23725.7i	0.760649	+	1.28107i
$701$		−	26083.9i		−	1.40538i	−0.711494	−	0.702692i	$-0.751981\pi$
$701$		−	26083.9i		−	1.40538i	0.711494	−	0.702692i	$-0.248019\pi$
$702$	165.508	+	3645.15i	0.00889841	+	0.195979i
$703$	791.870	+	1371.56i	0.0424836	+	0.0735837i
$704$	17709.7	+	17343.6i	0.948096	+	0.928498i
$705$	22573.1	+	13032.6i	1.20589	+	0.696220i
$706$	5030.40	−	3217.04i	0.268161	−	0.171494i
$707$	−7992.86	−	16756.8i	−0.425180	−	0.891380i
$708$	4323.77	−	9357.26i	0.229516	−	0.496705i
$709$	11768.3	+	6794.45i	0.623370	+	0.359903i	0.778180	−	0.628042i	$-0.216143\pi$
$709$	11768.3	+	6794.45i	0.623370	+	0.359903i	−0.154810	+	0.987944i	$0.549477\pi$
$710$	36024.8	+	18673.7i	1.90421	+	0.987058i
$711$	5533.17	−	3194.58i	0.291857	−	0.168504i
$712$	4641.13	+	1894.09i	0.244289	+	0.0996966i
$713$		−	20353.3i		−	1.06906i
$714$	−120.290	+	193.257i	−0.00630494	+	0.0101295i
$715$	40809.9			2.13455
$716$	−18545.0	−	26289.8i	−0.967961	−	1.37220i
$717$	10670.9	+	18482.6i	0.555807	+	0.962686i
$718$	−14792.8	−	7667.94i	−0.768889	−	0.398559i
$719$	2183.96	−	3782.72i	0.113279	−	0.196206i	−0.803811	−	0.594884i	$-0.797198\pi$
$719$	2183.96	−	3782.72i	0.113279	−	0.196206i	0.917091	+	0.398679i	$0.130531\pi$
$720$	6585.85	+	7738.65i	0.340889	+	0.400559i
$721$	−15827.3	+	23029.5i	−0.817531	+	1.18955i
$722$	9703.47	+	15173.1i	0.500174	+	0.782109i
$723$	−6979.10	+	12088.1i	−0.358998	+	0.621802i
$724$	−12367.2	+	1125.38i	−0.634838	+	0.0577686i
$725$	−35192.8	+	20318.6i	−1.80280	+	1.04085i
$726$	389.836	+	8585.77i	0.0199286	+	0.438909i
$727$	5464.69			0.278782			0.139391	−	0.990237i	$-0.455486\pi$
$727$	5464.69			0.278782			0.139391	+	0.990237i	$0.455486\pi$
$728$	−19990.1	+	1152.59i	−1.01770	+	0.0586783i
$729$	−729.000			−0.0370370
$730$	1870.85	+	41203.7i	0.0948538	+	2.08906i
$731$	324.725	−	187.480i	0.0164301	−	0.00948593i
$732$	898.004	+	9868.45i	0.0453431	+	0.498290i
$733$	−12320.0	+	21338.9i	−0.620804	+	1.07526i	0.368532	+	0.929615i	$0.379861\pi$
$733$	−12320.0	+	21338.9i	−0.620804	+	1.07526i	−0.989336	+	0.145649i	$0.953473\pi$
$734$	−3713.20	−	5806.22i	−0.186726	−	0.291978i
$735$	2839.37	−	17930.0i	0.142492	−	0.899808i
$736$	−11600.9	−	3547.07i	−0.581000	−	0.177645i
$737$	5252.78	−	9098.09i	0.262536	−	0.454725i
$738$	9473.19	+	4910.49i	0.472511	+	0.244929i
$739$	4049.96	+	7014.74i	0.201597	+	0.349176i	0.949043	−	0.315146i	$-0.102054\pi$
$739$	4049.96	+	7014.74i	0.201597	+	0.349176i	−0.747446	+	0.664322i	$0.768720\pi$
$740$	−8240.23	+	5812.72i	−0.409347	+	0.288757i
$741$	3177.28			0.157517
$742$	−1005.78	+	537.047i	−0.0497619	+	0.0265709i
$743$			34330.6i			1.69511i	0.530708	+	0.847554i	$0.321926\pi$
$743$			34330.6i			1.69511i	−0.530708	+	0.847554i	$0.678074\pi$
$744$	−19088.2	−	7790.06i	−0.940600	−	0.383868i
$745$	4720.96	−	2725.65i	0.232165	−	0.134040i
$746$	21530.5	+	11160.5i	1.05669	+	0.547740i
$747$	3618.76	+	2089.29i	0.177247	+	0.102334i
$748$	509.286	+	235.329i	0.0248948	+	0.0115033i
$749$	−6653.97	+	9681.85i	−0.324607	+	0.472319i
$750$	7722.38	−	4938.62i	0.375975	−	0.240444i
$751$	−22038.7	−	12724.0i	−1.07084	−	0.618251i	−0.142431	−	0.989805i	$-0.545492\pi$
$751$	−22038.7	−	12724.0i	−1.07084	−	0.618251i	−0.928411	+	0.371554i	$0.878825\pi$
$752$	−10573.7	+	29692.7i	−0.512746	+	1.43987i
$753$	−2017.97	−	3495.23i	−0.0976614	−	0.169155i
$754$	−1337.58	−	29458.8i	−0.0646043	−	1.42285i
$755$		−	9154.07i		−	0.441259i
$756$	−48.8851	−	4000.08i	−0.00235177	−	0.192436i
$757$			18687.4i			0.897232i	0.893725	+	0.448616i	$0.148083\pi$
$757$			18687.4i			0.897232i	−0.893725	+	0.448616i	$0.851917\pi$
$758$	31306.0	−	1421.44i	1.50011	−	0.0681124i
$759$	−4866.70	−	8429.37i	−0.232740	−	0.403118i
$760$	6991.60	−	5423.08i	0.333700	−	0.258836i
$761$	8621.70	+	4977.74i	0.410692	+	0.237113i	0.691087	−	0.722772i	$-0.257132\pi$
$761$	8621.70	+	4977.74i	0.410692	+	0.237113i	−0.280395	+	0.959885i	$0.590465\pi$
$762$	−2781.28	−	4349.02i	−0.132225	−	0.206756i
$763$	2045.11	−	975.502i	0.0970356	−	0.0462851i
$764$	10752.7	+	4968.59i	0.509189	+	0.235284i
$765$	199.179	+	114.996i	0.00941349	+	0.00543488i
$766$	3030.80	−	5846.93i	0.142960	−	0.275794i
$767$	17772.3	−	10260.9i	0.836665	−	0.483049i
$768$	−7766.74	+	9522.22i	−0.364919	+	0.447400i
$769$		−	36286.2i		−	1.70158i	−0.525506	−	0.850790i	$-0.676124\pi$
$769$		−	36286.2i		−	1.70158i	0.525506	−	0.850790i	$-0.323876\pi$
$770$	−44716.2	−	1483.03i	−2.09281	−	0.0694089i
$771$	8704.41			0.406591
$772$	−1604.60	−	2274.71i	−0.0748069	−	0.106048i
$773$	−6785.11	−	11752.1i	−0.315709	−	0.546825i	0.663879	−	0.747840i	$-0.268909\pi$
$773$	−6785.11	−	11752.1i	−0.315709	−	0.546825i	−0.979588	+	0.201016i	$0.935576\pi$
$774$	−3032.48	+	5850.18i	−0.140827	+	0.271680i
$775$	−28280.7	+	48983.6i	−1.31080	+	2.27038i
$776$	4814.82	+	35152.8i	0.222735	+	1.62618i
$777$	3957.60	+	311.419i	0.182726	+	0.0143785i
$778$	21380.0	−	13672.9i	0.985229	−	0.630074i
$779$	4645.56	−	8046.34i	0.213664	−	0.370077i
$780$	1833.36	+	20147.4i	0.0841599	+	0.924860i
$781$	−34094.9	+	19684.7i	−1.56212	+	0.901888i
$782$	−274.283	+	12.4538i	−0.0125426	+	0.000569497i
$783$	5891.52			0.268896
$784$	21945.4	−	536.473i	0.999701	−	0.0244384i
$785$	10144.2			0.461224
$786$	−8232.09	+	373.777i	−0.373574	+	0.0169621i
$787$	5979.45	−	3452.24i	0.270831	−	0.156365i	−0.358434	−	0.933555i	$-0.616689\pi$
$787$	5979.45	−	3452.24i	0.270831	−	0.156365i	0.629265	+	0.777190i	$0.283356\pi$
$788$	−2550.49	−	28028.2i	−0.115301	−	1.26708i
$789$	−1868.02	+	3235.50i	−0.0842880	+	0.145991i
$790$	29842.6	−	19084.9i	1.34399	−	0.859508i
$791$	41904.4	+	3297.41i	1.88363	+	0.148221i
$792$	−9768.09	+	1337.92i	−0.438250	+	0.0600263i
$793$	−9863.98	+	17084.9i	−0.441715	+	0.765073i
$794$	−4110.82	+	7930.49i	−0.183738	+	0.354462i
$795$	575.992	+	997.648i	0.0256960	+	0.0445068i
$796$	2104.29	+	2983.08i	0.0936990	+	0.132830i
$797$	8918.44			0.396370			0.198185	−	0.980165i	$-0.436495\pi$
$797$	8918.44			0.396370			0.198185	+	0.980165i	$0.436495\pi$
$798$	−3481.41	−	115.463i	−0.154437	−	0.00512197i
$799$			713.381i			0.0315865i
$800$	22990.9	+	24656.0i	1.01607	+	1.08965i
$801$	−1726.69	+	996.905i	−0.0761668	+	0.0439749i
$802$	14887.9	−	28721.3i	0.655498	−	1.26457i
$803$	−34657.2	−	20009.3i	−1.52307	−	0.879345i
$804$	4727.59	+	2184.51i	0.207375	+	0.0958230i
$805$	19762.9	−	9426.75i	0.865282	−	0.412732i
$806$	−22113.6	−	34578.5i	−0.966402	−	1.51114i
$807$	−11865.6	−	6850.59i	−0.517581	−	0.298826i
$808$	−13902.1	−	17923.0i	−0.605290	−	0.780359i
$809$	−3221.23	−	5579.33i	−0.139991	−	0.242471i	0.787502	−	0.616312i	$-0.211374\pi$
$809$	−3221.23	−	5579.33i	−0.139991	−	0.242471i	−0.927493	+	0.373841i	$0.878041\pi$
$810$	−4037.63	+	183.328i	−0.175145	+	0.00795247i
$811$			44844.6i			1.94169i	0.239718	+	0.970843i	$0.422945\pi$
$811$			44844.6i			1.94169i	−0.239718	+	0.970843i	$0.577055\pi$
$812$	395.073	+	32327.2i	0.0170743	+	1.39712i
$813$			14740.8i			0.635895i
$814$	−443.785	−	9773.94i	−0.0191089	−	0.420855i
$815$	−19499.8	−	33774.7i	−0.838097	−	1.45163i
$816$	−93.2997	+	262.000i	−0.00400263	+	0.0112400i
$817$	4969.02	+	2868.87i	0.212783	+	0.122851i
$818$	8205.77	−	5247.75i	0.350743	−	0.224307i
$819$	4510.90	−	6563.58i	0.192459	−	0.280037i
$820$	53703.0	+	24814.9i	2.28706	+	1.05680i
$821$	−10334.8	−	5966.82i	−0.439328	−	0.253646i	0.263984	−	0.964527i	$-0.414963\pi$
$821$	−10334.8	−	5966.82i	−0.439328	−	0.253646i	−0.703313	+	0.710881i	$0.748297\pi$
$822$	−13235.0	−	6860.47i	−0.561587	−	0.291102i
$823$	14766.2	−	8525.27i	0.625416	−	0.361084i	−0.153559	−	0.988140i	$-0.549073\pi$
$823$	14766.2	−	8525.27i	0.625416	−	0.361084i	0.778975	+	0.627056i	$0.215740\pi$
$824$	−12900.3	+	31609.9i	−0.545392	+	1.33639i
$825$			27048.9i			1.14148i
$826$	−19846.4	+	10597.2i	−0.836010	+	0.446396i
$827$	19496.7			0.819789			0.409894	−	0.912133i	$-0.365566\pi$
$827$	19496.7			0.819789			0.409894	+	0.912133i	$0.365566\pi$
$828$	3942.84	−	2781.31i	0.165487	−	0.116736i
$829$	2139.13	+	3705.08i	0.0896201	+	0.155227i	0.907351	−	0.420375i	$-0.138101\pi$
$829$	2139.13	+	3705.08i	0.0896201	+	0.155227i	−0.817730	+	0.575601i	$0.804768\pi$
$830$	20568.2	+	10661.7i	0.860160	+	0.445870i
$831$	288.728	−	500.092i	0.0120528	−	0.0208761i
$832$	−23562.8	+	6578.12i	−0.981843	+	0.274105i
$833$	463.839	−	178.065i	0.0192930	−	0.00740646i
$834$	11592.7	+	18127.2i	0.481321	+	0.752629i
$835$	9162.99	−	15870.8i	0.379758	−	0.657761i
$836$	777.996	+	8549.64i	0.0321861	+	0.353703i
$837$	7101.58	−	4100.10i	0.293269	−	0.169319i
$838$	−615.302	−	13551.4i	−0.0253643	−	0.558624i
$839$	−31281.0			−1.28717			−0.643587	−	0.765373i	$-0.722555\pi$
$839$	−31281.0			−1.28717			−0.643587	+	0.765373i	$0.722555\pi$
$840$	−1276.69	−	22142.5i	−0.0524405	−	0.909510i
$841$	−23224.2			−0.952241
$842$	−1179.44	−	25976.0i	−0.0482733	−	1.06317i
$843$	−4581.61	+	2645.20i	−0.187188	+	0.108073i
$844$	−33035.1	+	3006.11i	−1.34729	+	0.122600i
$845$	−758.676	+	1314.07i	−0.0308867	+	0.0534973i
$846$	−6754.35	−	10561.6i	−0.274491	−	0.429214i
$847$	10625.0	−	15459.8i	0.431025	−	0.627162i
$848$	−1060.87	+	902.832i	−0.0429602	+	0.0365606i
$849$	−3879.35	+	6719.24i	−0.156819	+	0.271618i
$850$	677.411	+	351.141i	0.0273353	+	0.0141694i
$851$	2394.14	+	4146.76i	0.0964394	+	0.167038i
$852$	−11249.8	−	15947.9i	−0.452361	−	0.641276i
$853$	683.576			0.0274387			0.0137193	−	0.999906i	$-0.495633\pi$
$853$	683.576			0.0274387			0.0137193	+	0.999906i	$0.495633\pi$
$854$	11429.0	−	18361.8i	0.457955	−	0.735748i
$855$			3519.38i			0.140772i
$856$	−5423.42	+	13289.1i	−0.216552	+	0.530623i
$857$	824.594	−	476.079i	0.0328677	−	0.0189762i	−0.483476	−	0.875358i	$-0.660626\pi$
$857$	824.594	−	476.079i	0.0328677	−	0.0189762i	0.516344	+	0.856381i	$0.327293\pi$
$858$	−17426.5	−	9033.14i	−0.693392	−	0.359425i
$859$	−9552.03	−	5514.87i	−0.379408	−	0.219051i	0.298153	−	0.954518i	$-0.403629\pi$
$859$	−9552.03	−	5514.87i	−0.379408	−	0.219051i	−0.677561	+	0.735467i	$0.736963\pi$
$860$	−15324.4	+	33164.3i	−0.607627	+	1.31499i
$861$	−10026.6	−	21020.4i	−0.396869	−	0.832025i
$862$	−37647.1	+	24076.1i	−1.48755	+	0.951317i
$863$	14467.8	+	8352.97i	0.570670	+	0.329477i	0.757417	−	0.652931i	$-0.226461\pi$
$863$	14467.8	+	8352.97i	0.570670	+	0.329477i	−0.186747	+	0.982408i	$0.559794\pi$
$864$	−1099.34	−	4762.28i	−0.0432874	−	0.187519i
$865$	−7097.63	−	12293.5i	−0.278990	−	0.483225i
$866$	−290.213	−	6391.67i	−0.0113878	−	0.250806i
$867$		−	14732.7i		−	0.577104i
$868$	22973.8	+	38692.0i	0.898365	+	1.51301i
$869$			34369.2i			1.34165i
$870$	32630.7	−	1481.59i	1.27159	−	0.0577365i
$871$	5184.12	+	8979.16i	0.201673	+	0.349308i
$872$	2187.45	−	1696.71i	0.0849498	−	0.0658919i
$873$	−12221.8	−	7056.25i	−0.473820	−	0.273560i
$874$	−2263.61	−	3539.54i	−0.0876061	−	0.136987i
$875$	−19945.5	−	1569.49i	−0.770607	−	0.0606382i
$876$	8321.41	−	18008.7i	0.320953	−	0.694588i
$877$	−18366.3	−	10603.8i	−0.707169	−	0.408284i	0.102843	−	0.994698i	$-0.467206\pi$
$877$	−18366.3	−	10603.8i	−0.707169	−	0.408284i	−0.810012	+	0.586413i	$0.800539\pi$
$878$	19216.6	−	37072.2i	0.738645	−	1.42497i
$879$	21799.5	−	12586.0i	0.836496	−	0.482951i
$880$	−53765.0	+	9866.65i	−2.05956	+	0.377960i
$881$		−	19650.0i		−	0.751447i	−0.926732	−	0.375724i	$-0.877394\pi$
$881$		−	19650.0i		−	0.751447i	0.926732	−	0.375724i	$-0.122606\pi$
$882$	−5181.21	+	7027.92i	−0.197801	+	0.268302i
$883$	16788.4			0.639836			0.319918	−	0.947445i	$-0.396345\pi$
$883$	16788.4			0.639836			0.319918	+	0.947445i	$0.396345\pi$
$884$	−452.451	+	319.163i	−0.0172145	+	0.0121432i
$885$	11365.7	+	19685.9i	0.431698	+	0.747723i
$886$	725.898	−	1400.38i	0.0275248	−	0.0531002i
$887$	−17393.4	+	30126.3i	−0.658415	+	1.14041i	0.322611	+	0.946532i	$0.395439\pi$
$887$	−17393.4	+	30126.3i	−0.658415	+	1.14041i	−0.981026	+	0.193876i	$0.937894\pi$
$888$	4805.34	−	658.179i	0.181595	−	0.0248728i
$889$	−883.890	+	11232.7i	−0.0333461	+	0.423772i
$890$	−9312.72	+	5955.67i	−0.350745	+	0.224309i
$891$	1960.75	−	3396.13i	0.0737236	−	0.127693i
$892$	8013.18	−	729.179i	0.300786	−	0.0273708i
$893$	−9453.80	+	5458.16i	−0.354266	+	0.204536i
$894$	−2619.24	+	118.926i	−0.0979870	+	0.00444909i
$895$	70947.8			2.64975
$896$	26057.3	−	6351.50i	0.971554	−	0.236818i
$897$	9606.17			0.357570
$898$	43895.9	−	1993.09i	1.63121	−	0.0740649i
$899$	−57392.5	+	33135.6i	−2.12919	+	1.22929i
$900$	−13353.7	+	1215.15i	−0.494581	+	0.0450056i
$901$	−15.7644	+	27.3047i	−0.000582895	+	0.00100960i
$902$	−48355.6	+	30924.4i	−1.78500	+	1.14154i
$903$	12981.2	−	6191.90i	0.478390	−	0.228188i
$904$	50880.6	−	6969.03i	1.87197	−	0.256401i
$905$	13692.6	−	23716.2i	0.502935	−	0.871110i
$906$	−2026.22	+	3908.93i	−0.0743010	+	0.143340i
$907$	18147.3	+	31432.0i	0.664355	+	1.15070i	0.979460	+	0.201639i	$0.0646269\pi$
$907$	18147.3	+	31432.0i	0.664355	+	1.15070i	−0.315105	+	0.949057i	$0.602040\pi$
$908$	−3494.68	+	2465.18i	−0.127726	+	0.0900989i
$909$	9021.97			0.329197
$910$	23333.4	−	37487.4i	0.849995	−	1.36560i
$911$			10328.8i			0.375639i	0.982204	+	0.187819i	$0.0601419\pi$
$911$			10328.8i			0.375639i	−0.982204	+	0.187819i	$0.939858\pi$
$912$	−4185.90	+	768.174i	−0.151984	+	0.0278912i
$913$	−19466.4	+	11238.9i	−0.705633	+	0.407397i
$914$	586.649	−	1131.75i	0.0212304	−	0.0409572i
$915$	−18924.5	−	10926.1i	−0.683742	−	0.394759i
$916$	−7038.40	+	15232.1i	−0.253881	+	0.549436i
$917$	14823.0	+	10187.3i	0.533804	+	0.366863i
$918$	−59.5985	−	93.1926i	−0.00214275	−	0.00335056i
$919$	−6954.88	−	4015.40i	−0.249641	−	0.144130i	0.369959	−	0.929048i	$-0.379372\pi$
$919$	−6954.88	−	4015.40i	−0.249641	−	0.144130i	−0.619600	+	0.784918i	$0.712705\pi$
$920$	21138.3	−	16396.1i	0.757511	−	0.587569i
$921$	8884.76	+	15388.9i	0.317875	+	0.550575i
$922$	−29096.1	+	1321.11i	−1.03929	+	0.0471891i
$923$		−	38854.8i		−	1.38561i
$924$	18766.3	+	10531.1i	0.668144	+	0.374942i
$925$		−	13306.5i		−	0.472988i
$926$	1744.25	+	38415.4i	0.0619002	+	1.36329i
$927$	−6789.73	−	11760.2i	−0.240565	−	0.416672i
$928$	8884.47	+	38487.1i	0.314275	+	1.36142i
$929$	48637.2	+	28080.7i	1.71769	+	0.991710i	0.923095	+	0.384572i	$0.125651\pi$
$929$	48637.2	+	28080.7i	1.71769	+	0.991710i	0.794597	+	0.607138i	$0.207682\pi$
$930$	38301.6	−	24494.7i	1.35049	−	0.863668i
$931$	5908.62	+	4784.46i	0.207999	+	0.168426i
$932$	13572.6	−	29373.1i	0.477024	−	1.03235i
$933$	9038.58	+	5218.43i	0.317160	+	0.183112i
$934$	−44378.4	−	23003.9i	−1.55472	−	0.805898i
$935$	−1071.44	+	618.597i	−0.0374758	+	0.0216367i
$936$	3676.68	−	9009.05i	0.128393	−	0.314605i
$937$		−	19380.1i		−	0.675689i	−0.941202	−	0.337844i	$-0.890302\pi$
$937$		−	19380.1i		−	0.675689i	0.941202	−	0.337844i	$-0.109698\pi$
$938$	−5354.04	−	10027.0i	−0.186371	−	0.349035i
$939$	−7590.59			−0.263802
$940$	−40065.6	−	56797.8i	−1.39021	−	1.97079i
$941$	−969.893	−	1679.90i	−0.0336000	−	0.0581969i	0.848736	−	0.528816i	$-0.177364\pi$
$941$	−969.893	−	1679.90i	−0.0336000	−	0.0581969i	−0.882336	+	0.470619i	$0.844031\pi$
$942$	−4331.72	−	2245.38i	−0.149825	−	0.0776628i
$943$	14045.3	−	24327.3i	0.485026	−	0.840089i
$944$	−20933.4	+	17815.0i	−0.721740	+	0.614225i
$945$	7270.30	+	4996.60i	0.250267	+	0.171999i
$946$	−19097.4	−	29862.1i	−0.656352	−	1.02632i
$947$	−1313.25	+	2274.62i	−0.0450633	+	0.0780519i	−0.887677	−	0.460466i	$-0.847682\pi$
$947$	−1313.25	+	2274.62i	−0.0450633	+	0.0780519i	0.842614	+	0.538518i	$0.181016\pi$
$948$	−16967.7	+	1544.01i	−0.581312	+	0.0528979i
$949$	34204.2	−	19747.8i	1.16998	−	0.675490i
$950$	529.591	+	11663.7i	0.0180865	+	0.398339i
$951$	−1708.25			−0.0582480
$952$	507.358	−	333.271i	0.0172727	−	0.0113460i
$953$	34296.0			1.16575			0.582873	−	0.812563i	$-0.301928\pi$
$953$	34296.0			1.16575			0.582873	+	0.812563i	$0.301928\pi$
$954$	−25.1319	−	553.505i	−0.000852908	−	0.0187845i
$955$	−22621.7	+	13060.7i	−0.766515	+	0.442548i
$956$	−5157.51	−	56677.5i	−0.174483	−	1.91745i
$957$	−15846.1	+	27446.3i	−0.535248	+	0.927077i
$958$	665.837	+	1041.15i	0.0224553	+	0.0351128i
$959$	14008.1	+	29367.7i	0.471685	+	0.988876i
$960$	−7286.40	−	26099.8i	−0.244966	−	0.877468i
$961$	−31224.7	+	54082.8i	−1.04813	+	1.81541i
$962$	8572.82	+	4443.78i	0.287317	+	0.148933i
$963$	−2854.48	−	4944.10i	−0.0955184	−	0.165443i
$964$	30415.8	−	21455.6i	1.01621	−	0.716844i
$965$	6138.73			0.204780
$966$	−10525.7	−	349.089i	−0.350577	−	0.0116271i
$967$			2430.56i			0.0808288i	0.999183	+	0.0404144i	$0.0128678\pi$
$967$			2430.56i			0.0808288i	−0.999183	+	0.0404144i	$0.987132\pi$
$968$	8660.03	−	21219.9i	0.287545	−	0.704579i
$969$	−83.4177	+	48.1612i	−0.00276549	+	0.00159666i
$970$	−69465.9	−	36008.1i	−2.29940	−	1.19191i
$971$	−36892.2	−	21299.7i	−1.21929	−	0.703955i	−0.254521	−	0.967067i	$-0.581918\pi$
$971$	−36892.2	−	21299.7i	−1.21929	−	0.703955i	−0.964765	+	0.263112i	$0.915251\pi$
$972$	1764.71	+	815.432i	0.0582337	+	0.0269084i
$973$	3684.15	−	46819.2i	0.121386	−	1.54260i
$974$	13403.8	−	8572.03i	0.440952	−	0.281997i
$975$	−23118.8	−	13347.6i	−0.759379	−	0.438427i
$976$	8864.65	−	24893.3i	0.290728	−	0.816409i
$977$	18762.1	+	32496.9i	0.614383	+	1.06414i	0.990492	+	0.137567i	$0.0439282\pi$
$977$	18762.1	+	32496.9i	0.614383	+	1.06414i	−0.376110	+	0.926575i	$0.622738\pi$
$978$	850.822	+	18738.5i	0.0278183	+	0.612671i
$979$		−	10725.3i		−	0.350135i
$980$	−26929.2	+	40227.7i	−0.877777	+	1.31125i
$981$			1101.10i			0.0358364i
$982$	4815.22	−	218.635i	0.156476	−	0.00710480i
$983$	−3021.63	−	5233.62i	−0.0980418	−	0.169813i	0.812832	−	0.582498i	$-0.197925\pi$
$983$	−3021.63	−	5233.62i	−0.0980418	−	0.169813i	−0.910874	+	0.412684i	$0.864591\pi$
$984$	−17439.3	−	22483.3i	−0.564986	−	0.728397i
$985$	53748.9	+	31032.0i	1.73866	+	1.00382i
$986$	481.654	+	753.150i	0.0155568	+	0.0243257i
$987$	−2146.53	+	27278.7i	−0.0692247	+	0.879726i
$988$	−7691.34	−	3553.99i	−0.247666	−	0.114441i
$989$	15023.3	+	8673.71i	0.483027	+	0.278876i
$990$	10005.8	−	19302.8i	0.321216	−	0.619681i
$991$	−822.652	+	474.958i	−0.0263697	+	0.0152246i	−0.513127	−	0.858313i	$-0.671513\pi$
$991$	−822.652	+	474.958i	−0.0263697	+	0.0152246i	0.486757	+	0.873537i	$0.338180\pi$
$992$	37493.7	+	40209.0i	1.20002	+	1.28693i
$993$			8012.18i			0.256051i
$994$	−1411.99	+	42574.0i	−0.0450558	+	1.35852i
$995$	−8050.37			−0.256496
$996$	−6423.03	−	9105.41i	−0.204339	−	0.289675i
$997$	−10097.8	−	17489.9i	−0.320762	−	0.555576i	0.659883	−	0.751368i	$-0.270606\pi$
$997$	−10097.8	−	17489.9i	−0.320762	−	0.555576i	−0.980645	+	0.195792i	$0.937272\pi$
$998$	24130.8	−	46552.4i	0.765377	−	1.47654i
$999$	−964.578	+	1670.70i	−0.0305484	+	0.0529115i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	168.4.t.a.19.1	✓	96
4.3	odd	2		672.4.bb.a.271.47		96
7.3	odd	6	inner	168.4.t.a.115.32	yes	96
8.3	odd	2	inner	168.4.t.a.19.32	yes	96
8.5	even	2		672.4.bb.a.271.48		96
28.3	even	6		672.4.bb.a.367.48		96
56.3	even	6	inner	168.4.t.a.115.1	yes	96
56.45	odd	6		672.4.bb.a.367.47		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.4.t.a.19.1	✓	96	1.1	even	1	trivial
168.4.t.a.19.32	yes	96	8.3	odd	2	inner
168.4.t.a.115.1	yes	96	56.3	even	6	inner
168.4.t.a.115.32	yes	96	7.3	odd	6	inner
672.4.bb.a.271.47		96	4.3	odd	2
672.4.bb.a.271.48		96	8.5	even	2
672.4.bb.a.367.47		96	56.45	odd	6
672.4.bb.a.367.48		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+(-2.82552 + 0.128292i) q^{2} +(-2.59808 + 1.50000i) q^{3} +(7.96708 - 0.724984i) q^{4} +(-8.82092 + 15.2783i) q^{5} +(7.14847 - 4.57159i) q^{6} +(-18.4632 - 1.45285i) q^{7} +(-22.4181 + 3.07057i) q^{8} +(4.50000 - 7.79423i) q^{9} +(22.9636 - 44.3007i) q^{10} +(24.2068 + 41.9275i) q^{11} +(-19.6116 + 13.8342i) q^{12} -47.7808 q^{13} +(52.3544 + 1.73636i) q^{14} -52.9255i q^{15} +(62.9488 - 11.5520i) q^{16} +(1.25446 - 0.724262i) q^{17} +(-11.7149 + 22.6000i) q^{18} +(19.1960 + 11.0828i) q^{19} +(-59.2005 + 128.118i) q^{20} +(50.1480 - 23.9202i) q^{21} +(-73.7758 - 115.361i) q^{22} +(58.0371 + 33.5077i) q^{23} +(53.6381 - 41.6047i) q^{24} +(-93.1171 - 161.284i) q^{25} +(135.006 - 6.12992i) q^{26} +27.0000i q^{27} +(-148.151 + 1.81056i) q^{28} -218.205i q^{29} +(6.78994 + 149.542i) q^{30} +(-151.856 - 263.021i) q^{31} +(-176.381 + 40.7163i) q^{32} +(-125.782 - 72.6205i) q^{33} +(-3.45158 + 2.20735i) q^{34} +(185.059 - 269.270i) q^{35} +(30.2012 - 65.3597i) q^{36} +(61.8777 + 35.7251i) q^{37} +(-55.6605 - 28.8520i) q^{38} +(124.138 - 71.6713i) q^{39} +(150.835 - 369.595i) q^{40} -419.167i q^{41} +(-138.625 + 74.0204i) q^{42} +258.857 q^{43} +(223.255 + 316.490i) q^{44} +(79.3882 + 137.504i) q^{45} +(-168.284 - 87.2309i) q^{46} +(-246.244 + 426.507i) q^{47} +(-146.218 + 124.436i) q^{48} +(338.778 + 53.6484i) q^{49} +(283.795 + 443.763i) q^{50} +(-2.17279 + 3.76338i) q^{51} +(-380.674 + 34.6404i) q^{52} +(-18.8500 + 10.8831i) q^{53} +(-3.46389 - 76.2889i) q^{54} -854.106 q^{55} +(418.371 - 24.1224i) q^{56} -66.4970 q^{57} +(27.9940 + 616.540i) q^{58} +(-371.955 + 214.748i) q^{59} +(-38.3701 - 421.662i) q^{60} +(206.442 - 357.568i) q^{61} +(462.814 + 723.690i) q^{62} +(-94.4082 + 137.368i) q^{63} +(493.143 - 137.673i) q^{64} +(421.471 - 730.009i) q^{65} +(364.717 + 189.054i) q^{66} +(-108.498 - 187.924i) q^{67} +(9.46930 - 6.67972i) q^{68} -201.046 q^{69} +(-488.343 + 784.569i) q^{70} +813.188i q^{71} +(-76.9488 + 188.549i) q^{72} +(-715.855 + 413.299i) q^{73} +(-179.420 - 93.0034i) q^{74} +(483.851 + 279.351i) q^{75} +(160.971 + 74.3810i) q^{76} +(-386.021 - 809.284i) q^{77} +(-341.560 + 218.434i) q^{78} +(614.797 + 354.953i) q^{79} +(-378.771 + 1063.65i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(53.7759 + 1184.36i) q^{82} +464.287i q^{83} +(382.192 - 226.930i) q^{84} +25.5546i q^{85} +(-731.404 + 33.2094i) q^{86} +(327.307 + 566.912i) q^{87} +(-671.413 - 865.606i) q^{88} +(-191.854 - 110.767i) q^{89} +(-241.954 - 378.336i) q^{90} +(882.187 + 69.4183i) q^{91} +(486.679 + 224.883i) q^{92} +(789.064 + 455.567i) q^{93} +(641.049 - 1236.69i) q^{94} +(-338.653 + 195.521i) q^{95} +(397.176 - 370.355i) q^{96} -1568.06i q^{97} +(-964.107 - 108.122i) q^{98} +435.723 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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