LMFDB - Embedded newform 153.3.t.a.7.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [153,3,Mod(7,153)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(153, base_ring=CyclotomicField(48)) chi = DirichletCharacter(H, H._module([32, 33])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("153.7"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 153 = 3^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	153.t (of order $48$, degree $16$, 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:	$4.16894804471$
Analytic rank:	$0$
Dimension:	$544$
Relative dimension:	$34$ over $\Q(\zeta_{48})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{48}]$

Embedding invariants

Embedding label			7.4
Character	$\chi$	$=$	153.7
Dual form			153.3.t.a.22.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.98557 - 2.58765i) q^{2} +(-2.23949 + 1.99617i) q^{3} +(-1.71816 + 6.41225i) q^{4} +(-3.06932 + 2.69172i) q^{5} +(9.61206 + 1.83148i) q^{6} +(1.95779 + 1.71694i) q^{7} +(7.95066 - 3.29327i) q^{8} +(1.03063 - 8.94079i) q^{9} +(13.0596 + 2.59771i) q^{10} +(-0.620087 - 9.46069i) q^{11} +(-8.95213 - 17.7899i) q^{12} +(4.92847 + 1.32058i) q^{13} +(0.555494 - 8.47520i) q^{14} +(1.50058 - 12.1549i) q^{15} +(-1.31220 - 0.757599i) q^{16} +(0.400214 - 16.9953i) q^{17} +(-25.1820 + 15.0857i) q^{18} +(3.49634 - 8.44091i) q^{19} +(-11.9864 - 24.3060i) q^{20} +(-7.81176 + 0.0630176i) q^{21} +(-23.2498 + 20.3895i) q^{22} +(2.19372 - 4.44843i) q^{23} +(-11.2315 + 23.2461i) q^{24} +(-1.08780 + 8.26266i) q^{25} +(-6.36864 - 15.3753i) q^{26} +(15.5392 + 22.0801i) q^{27} +(-14.3732 + 9.60389i) q^{28} +(3.93282 - 11.5857i) q^{29} +(-34.4323 + 20.2516i) q^{30} +(1.23680 - 18.8700i) q^{31} +(-3.84802 - 29.2286i) q^{32} +(20.2738 + 19.9493i) q^{33} +(-44.7725 + 32.7098i) q^{34} -10.6306 q^{35} +(55.5598 + 21.9703i) q^{36} +(30.6756 - 45.9092i) q^{37} +(-28.7844 + 7.71275i) q^{38} +(-13.6733 + 6.88062i) q^{39} +(-15.5385 + 31.5090i) q^{40} +(57.0422 - 19.3632i) q^{41} +(15.6739 + 20.0890i) q^{42} +(14.6101 + 1.92346i) q^{43} +(61.7297 + 12.2788i) q^{44} +(20.9028 + 30.2163i) q^{45} +(-15.8668 + 3.15610i) q^{46} +(-0.535006 - 1.99667i) q^{47} +(4.45095 - 0.922736i) q^{48} +(-5.51071 - 41.8580i) q^{49} +(23.5408 - 13.5913i) q^{50} +(33.0292 + 38.8597i) q^{51} +(-16.9358 + 29.3336i) q^{52} +(-24.7360 + 59.7181i) q^{53} +(26.2813 - 84.0519i) q^{54} +(27.3688 + 27.3688i) q^{55} +(21.2201 + 7.20325i) q^{56} +(9.01946 + 25.8826i) q^{57} +(-37.7887 + 12.8275i) q^{58} +(37.4123 + 28.7074i) q^{59} +(75.3623 + 30.5062i) q^{60} +(65.1776 - 74.3208i) q^{61} +(-51.2846 + 34.2673i) q^{62} +(17.3686 - 15.7347i) q^{63} +(-72.2786 + 72.2786i) q^{64} +(-18.6816 + 9.21277i) q^{65} +(11.3667 - 92.0725i) q^{66} +(-99.6003 + 57.5043i) q^{67} +(108.290 + 31.7668i) q^{68} +(3.96700 + 14.3413i) q^{69} +(21.1079 + 27.5083i) q^{70} +(-6.23767 + 9.33533i) q^{71} +(-21.2503 - 74.4793i) q^{72} +(14.2900 + 71.8409i) q^{73} +(-179.706 + 11.7785i) q^{74} +(-14.0575 - 20.6756i) q^{75} +(48.1179 + 36.9222i) q^{76} +(15.0294 - 19.5867i) q^{77} +(44.9541 + 21.7199i) q^{78} +(-10.1947 - 155.542i) q^{79} +(6.06680 - 1.20676i) q^{80} +(-78.8756 - 18.4293i) q^{81} +(-163.367 - 109.158i) q^{82} +(-47.6281 + 36.5464i) q^{83} +(13.0177 - 50.1992i) q^{84} +(44.5181 + 53.2412i) q^{85} +(-24.0323 - 41.6251i) q^{86} +(14.3195 + 33.7967i) q^{87} +(-36.0867 - 73.1766i) q^{88} +(-118.351 - 118.351i) q^{89} +(36.6852 - 114.086i) q^{90} +(7.38156 + 11.0473i) q^{91} +(24.7553 + 21.7098i) q^{92} +(34.8978 + 44.7279i) q^{93} +(-4.10439 + 5.34895i) q^{94} +(11.9892 + 35.3190i) q^{95} +(66.9629 + 57.7759i) q^{96} +(17.6964 - 52.1318i) q^{97} +(-97.3719 + 97.3719i) q^{98} +(-85.2252 - 4.20639i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 544 q - 8 q^{2} - 16 q^{3} - 8 q^{4} - 8 q^{5} - 16 q^{6} - 8 q^{7} - 32 q^{8} - 16 q^{9} - 32 q^{10} - 8 q^{11} + 176 q^{12} - 8 q^{13} - 8 q^{14} - 40 q^{15} - 32 q^{17} + 32 q^{18} - 32 q^{19} - 8 q^{20}+ \cdots + 448 q^{99}+O(q^{100}) $ 544 * q - 8 * q^2 - 16 * q^3 - 8 * q^4 - 8 * q^5 - 16 * q^6 - 8 * q^7 - 32 * q^8 - 16 * q^9 - 32 * q^10 - 8 * q^11 + 176 * q^12 - 8 * q^13 - 8 * q^14 - 40 * q^15 - 32 * q^17 + 32 * q^18 - 32 * q^19 - 8 * q^20 - 256 * q^21 - 8 * q^22 - 8 * q^23 + 176 * q^24 - 8 * q^25 - 32 * q^26 - 16 * q^27 - 32 * q^28 - 8 * q^29 - 16 * q^30 - 8 * q^31 - 72 * q^32 + 40 * q^34 - 64 * q^35 + 16 * q^36 - 32 * q^37 + 88 * q^38 - 192 * q^39 - 8 * q^40 - 440 * q^41 - 400 * q^42 - 248 * q^43 - 800 * q^44 - 176 * q^45 - 32 * q^46 + 112 * q^47 - 248 * q^48 - 8 * q^49 + 16 * q^51 - 16 * q^52 + 160 * q^53 - 312 * q^54 - 32 * q^55 - 488 * q^56 - 296 * q^57 - 8 * q^58 + 568 * q^59 + 2080 * q^60 - 8 * q^61 + 1120 * q^62 - 88 * q^63 - 288 * q^64 - 248 * q^65 - 24 * q^66 - 8 * q^68 - 416 * q^69 - 40 * q^70 - 32 * q^71 + 632 * q^72 - 32 * q^73 - 8 * q^74 + 752 * q^75 - 8 * q^76 - 8 * q^77 - 2304 * q^78 - 8 * q^79 - 432 * q^80 + 768 * q^81 + 352 * q^82 - 296 * q^83 - 8 * q^85 + 1184 * q^86 - 688 * q^87 - 8 * q^88 - 1184 * q^89 - 1136 * q^90 + 640 * q^91 - 2024 * q^92 - 528 * q^93 - 8 * q^94 + 472 * q^95 - 1064 * q^96 - 8 * q^97 - 848 * q^98 + 448 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/153\mathbb{Z}\right)^\times$.

$n$	$37$	$137$
$\chi(n)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.98557	−	2.58765i	−0.992787	−	1.29383i	−0.955647	−	0.294516i	$-0.904842\pi$
$2$	−1.98557	−	2.58765i	−0.992787	−	1.29383i	−0.0371408	−	0.999310i	$-0.511825\pi$
$3$	−2.23949	+	1.99617i	−0.746497	+	0.665389i
$3$	−2.23949	+	1.99617i	−0.746497	+	0.665389i
$4$	−1.71816	+	6.41225i	−0.429539	+	1.60306i
$5$	−3.06932	+	2.69172i	−0.613863	+	0.538344i	−0.908831	−	0.417163i	$-0.863024\pi$
$5$	−3.06932	+	2.69172i	−0.613863	+	0.538344i	0.294968	+	0.955507i	$0.404691\pi$
$6$	9.61206	+	1.83148i	1.60201	+	0.305246i
$7$	1.95779	+	1.71694i	0.279685	+	0.245277i	0.787682	−	0.616081i	$-0.211281\pi$
$7$	1.95779	+	1.71694i	0.279685	+	0.245277i	−0.507998	+	0.861358i	$0.669614\pi$
$8$	7.95066	−	3.29327i	0.993832	−	0.411659i
$9$	1.03063	−	8.94079i	0.114514	−	0.993422i
$10$	13.0596	+	2.59771i	1.30596	+	0.259771i
$11$	−0.620087	−	9.46069i	−0.0563715	−	0.860063i	−0.928627	−	0.371014i	$-0.879010\pi$
$11$	−0.620087	−	9.46069i	−0.0563715	−	0.860063i	0.872256	−	0.489050i	$-0.162656\pi$
$12$	−8.95213	−	17.7899i	−0.746011	−	1.48249i
$13$	4.92847	+	1.32058i	0.379113	+	0.101583i	0.443343	−	0.896352i	$-0.353792\pi$
$13$	4.92847	+	1.32058i	0.379113	+	0.101583i	−0.0642300	+	0.997935i	$0.520459\pi$
$14$	0.555494	−	8.47520i	0.0396781	−	0.605371i
$15$	1.50058	−	12.1549i	0.100039	−	0.810330i
$16$	−1.31220	−	0.757599i	−0.0820125	−	0.0473499i
$17$	0.400214	−	16.9953i	0.0235420	−	0.999723i
$17$	0.400214	−	16.9953i	0.0235420	−	0.999723i
$18$	−25.1820	+	15.0857i	−1.39900	+	0.838095i
$19$	3.49634	−	8.44091i	0.184018	−	0.444258i	−0.804770	−	0.593587i	$-0.797711\pi$
$19$	3.49634	−	8.44091i	0.184018	−	0.444258i	0.988788	+	0.149329i	$0.0477113\pi$
$20$	−11.9864	−	24.3060i	−0.599320	−	1.21530i
$21$	−7.81176	+	0.0630176i	−0.371988	+	0.00300084i
$22$	−23.2498	+	20.3895i	−1.05681	+	0.926795i
$23$	2.19372	−	4.44843i	0.0953793	−	0.193410i	−0.843954	−	0.536415i	$-0.819778\pi$
$23$	2.19372	−	4.44843i	0.0953793	−	0.193410i	0.939334	+	0.343005i	$0.111445\pi$
$24$	−11.2315	+	23.2461i	−0.467979	+	0.968587i
$25$	−1.08780	+	8.26266i	−0.0435120	+	0.330506i
$26$	−6.36864	−	15.3753i	−0.244948	−	0.591356i
$27$	15.5392	+	22.0801i	0.575528	+	0.817782i
$28$	−14.3732	+	9.60389i	−0.513330	+	0.342996i
$29$	3.93282	−	11.5857i	0.135615	−	0.399508i	−0.857814	−	0.513960i	$-0.828178\pi$
$29$	3.93282	−	11.5857i	0.135615	−	0.399508i	0.993429	+	0.114452i	$0.0365113\pi$
$30$	−34.4323	+	20.2516i	−1.14774	+	0.675052i
$31$	1.23680	−	18.8700i	0.0398968	−	0.608708i	−0.930363	−	0.366641i	$-0.880508\pi$
$31$	1.23680	−	18.8700i	0.0398968	−	0.608708i	0.970259	−	0.242067i	$-0.0778255\pi$
$32$	−3.84802	−	29.2286i	−0.120251	−	0.913395i
$33$	20.2738	+	19.9493i	0.614358	+	0.604525i
$34$	−44.7725	+	32.7098i	−1.31684	+	0.962053i
$35$	−10.6306			−0.303731
$36$	55.5598	+	21.9703i	1.54333	+	0.610287i
$37$	30.6756	−	45.9092i	0.829070	−	1.24079i	−0.139046	−	0.990286i	$-0.544403\pi$
$37$	30.6756	−	45.9092i	0.829070	−	1.24079i	0.968115	−	0.250505i	$-0.0805965\pi$
$38$	−28.7844	+	7.71275i	−0.757483	+	0.202967i
$39$	−13.6733	+	6.88062i	−0.350599	+	0.176426i
$40$	−15.5385	+	31.5090i	−0.388463	+	0.787725i
$41$	57.0422	−	19.3632i	1.39127	−	0.472274i	0.477548	−	0.878606i	$-0.341526\pi$
$41$	57.0422	−	19.3632i	1.39127	−	0.472274i	0.913726	+	0.406332i	$0.133192\pi$
$42$	15.6739	+	20.0890i	0.373188	+	0.478309i
$43$	14.6101	+	1.92346i	0.339771	+	0.0447317i	0.298481	−	0.954416i	$-0.403520\pi$
$43$	14.6101	+	1.92346i	0.339771	+	0.0447317i	0.0412896	+	0.999147i	$0.486853\pi$
$44$	61.7297	+	12.2788i	1.40295	+	0.279064i
$45$	20.9028	+	30.2163i	0.464506	+	0.671473i
$46$	−15.8668	+	3.15610i	−0.344930	+	0.0686109i
$47$	−0.535006	−	1.99667i	−0.0113831	−	0.0424824i	0.960001	−	0.279998i	$-0.0903337\pi$
$47$	−0.535006	−	1.99667i	−0.0113831	−	0.0424824i	−0.971384	+	0.237515i	$0.923667\pi$
$48$	4.45095	−	0.922736i	0.0927282	−	0.0192237i
$49$	−5.51071	−	41.8580i	−0.112463	−	0.854244i
$50$	23.5408	−	13.5913i	0.470816	−	0.271826i
$51$	33.0292	+	38.8597i	0.647631	+	0.761954i
$52$	−16.9358	+	29.3336i	−0.325688	+	0.564107i
$53$	−24.7360	+	59.7181i	−0.466718	+	1.12676i	0.498869	+	0.866677i	$0.333749\pi$
$53$	−24.7360	+	59.7181i	−0.466718	+	1.12676i	−0.965587	+	0.260079i	$0.916251\pi$
$54$	26.2813	−	84.0519i	0.486691	−	1.55652i
$55$	27.3688	+	27.3688i	0.497614	+	0.497614i
$56$	21.2201	+	7.20325i	0.378930	+	0.128629i
$57$	9.01946	+	25.8826i	0.158236	+	0.454081i
$58$	−37.7887	+	12.8275i	−0.651530	+	0.221165i
$59$	37.4123	+	28.7074i	0.634106	+	0.486567i	0.875089	−	0.483963i	$-0.160803\pi$
$59$	37.4123	+	28.7074i	0.634106	+	0.486567i	−0.240982	+	0.970529i	$0.577470\pi$
$60$	75.3623	+	30.5062i	1.25604	+	0.508437i
$61$	65.1776	−	74.3208i	1.06849	−	1.21837i	0.0936137	−	0.995609i	$-0.470158\pi$
$61$	65.1776	−	74.3208i	1.06849	−	1.21837i	0.974872	−	0.222766i	$-0.0715085\pi$
$62$	−51.2846	+	34.2673i	−0.827171	+	0.552698i
$63$	17.3686	−	15.7347i	0.275691	−	0.249757i
$64$	−72.2786	+	72.2786i	−1.12935	+	1.12935i
$65$	−18.6816	+	9.21277i	−0.287410	+	0.141735i
$66$	11.3667	−	92.0725i	0.172223	−	1.39504i
$67$	−99.6003	+	57.5043i	−1.48657	+	0.858273i	−0.999883	−	0.0153028i	$-0.995129\pi$
$67$	−99.6003	+	57.5043i	−1.48657	+	0.858273i	−0.486689	+	0.873575i	$0.661795\pi$
$68$	108.290	+	31.7668i	1.59251	+	0.467159i
$69$	3.96700	+	14.3413i	0.0574927	+	0.207844i
$70$	21.1079	+	27.5083i	0.301541	+	0.392976i
$71$	−6.23767	+	9.33533i	−0.0878545	+	0.131484i	−0.872794	−	0.488089i	$-0.837694\pi$
$71$	−6.23767	+	9.33533i	−0.0878545	+	0.131484i	0.784939	+	0.619573i	$0.212694\pi$
$72$	−21.2503	−	74.4793i	−0.295143	−	1.03444i
$73$	14.2900	+	71.8409i	0.195754	+	0.984122i	0.946297	+	0.323300i	$0.104792\pi$
$73$	14.2900	+	71.8409i	0.195754	+	0.984122i	−0.750543	+	0.660822i	$0.770208\pi$
$74$	−179.706	+	11.7785i	−2.42846	+	0.159169i
$75$	−14.0575	−	20.6756i	−0.187434	−	0.275674i
$76$	48.1179	+	36.9222i	0.633131	+	0.485818i
$77$	15.0294	−	19.5867i	0.195187	−	0.254373i
$78$	44.9541	+	21.7199i	0.576335	+	0.278460i
$79$	−10.1947	−	155.542i	−0.129047	−	1.96888i	−0.227612	−	0.973752i	$-0.573092\pi$
$79$	−10.1947	−	155.542i	−0.129047	−	1.96888i	0.0985646	−	0.995131i	$-0.468575\pi$
$80$	6.06680	−	1.20676i	0.0758350	−	0.0150845i
$81$	−78.8756	−	18.4293i	−0.973773	−	0.227522i
$82$	−163.367	−	109.158i	−1.99228	−	1.33120i
$83$	−47.6281	+	36.5464i	−0.573833	+	0.440318i	−0.854473	−	0.519495i	$-0.826120\pi$
$83$	−47.6281	+	36.5464i	−0.573833	+	0.440318i	0.280640	+	0.959813i	$0.409453\pi$
$84$	13.0177	−	50.1992i	0.154973	−	0.597609i
$85$	44.5181	+	53.2412i	0.523743	+	0.626367i
$86$	−24.0323	−	41.6251i	−0.279445	−	0.484013i
$87$	14.3195	+	33.7967i	0.164592	+	0.388468i
$88$	−36.0867	−	73.1766i	−0.410076	−	0.831553i
$89$	−118.351	−	118.351i	−1.32979	−	1.32979i	−0.905551	−	0.424237i	$-0.860542\pi$
$89$	−118.351	−	118.351i	−1.32979	−	1.32979i	−0.424237	−	0.905551i	$-0.639458\pi$
$90$	36.6852	−	114.086i	0.407613	−	1.26762i
$91$	7.38156	+	11.0473i	0.0811161	+	0.121399i
$92$	24.7553	+	21.7098i	0.269079	+	0.235976i
$93$	34.8978	+	44.7279i	0.375245	+	0.480946i
$94$	−4.10439	+	5.34895i	−0.0436638	+	0.0569037i
$95$	11.9892	+	35.3190i	0.126202	+	0.371779i
$96$	66.9629	+	57.7759i	0.697530	+	0.601833i
$97$	17.6964	−	52.1318i	0.182437	−	0.537442i	−0.816783	−	0.576946i	$-0.804244\pi$
$97$	17.6964	−	52.1318i	0.182437	−	0.537442i	0.999219	+	0.0395039i	$0.0125778\pi$
$98$	−97.3719	+	97.3719i	−0.993591	+	0.993591i
$99$	−85.2252	−	4.20639i	−0.860861	−	0.0424888i
$100$	−51.1132	−	21.1718i	−0.511132	−	0.211718i
$101$	−33.5307	−	19.3590i	−0.331987	−	0.191673i	0.324736	−	0.945805i	$-0.394725\pi$
$101$	−33.5307	−	19.3590i	−0.331987	−	0.191673i	−0.656723	+	0.754132i	$0.728058\pi$
$102$	34.9734	−	162.627i	0.342876	−	1.59438i
$103$	−1.29977	−	2.25127i	−0.0126192	−	0.0218570i	0.859647	−	0.510889i	$-0.170684\pi$
$103$	−1.29977	−	2.25127i	−0.0126192	−	0.0218570i	−0.872266	+	0.489032i	$0.837350\pi$
$104$	43.5336	−	5.73130i	0.418592	−	0.0551087i
$105$	23.8071	−	21.2205i	0.226734	−	0.202100i
$106$	203.645	−	54.5665i	1.92118	−	0.514778i
$107$	40.4521	+	203.366i	0.378057	+	1.90062i	0.431619	+	0.902056i	$0.357943\pi$
$107$	40.4521	+	203.366i	0.378057	+	1.90062i	−0.0535618	+	0.998565i	$0.517057\pi$
$108$	−168.282	+	61.7044i	−1.55817	+	0.571337i
$109$	12.3646	−	62.1611i	0.113437	−	0.570285i	−0.881702	−	0.471806i	$-0.843602\pi$
$109$	12.3646	−	62.1611i	0.113437	−	0.570285i	0.995139	−	0.0984790i	$-0.0313977\pi$
$110$	16.4781	−	125.164i	0.149801	−	1.13785i
$111$	22.9449	+	164.047i	0.206711	+	1.47790i
$112$	−1.26827	−	3.73619i	−0.0113238	−	0.0333588i
$113$	35.3652	+	17.4402i	0.312967	+	0.154338i	0.591988	−	0.805947i	$-0.298343\pi$
$113$	35.3652	+	17.4402i	0.312967	+	0.154338i	−0.279021	+	0.960285i	$0.590010\pi$
$114$	49.0664	−	74.7311i	0.430407	−	0.655536i
$115$	5.24069	+	19.5585i	0.0455713	+	0.170074i
$116$	67.5333	+	45.1243i	0.582184	+	0.389003i
$117$	16.8864	−	42.7034i	0.144328	−	0.364986i
$118$		−	153.811i		−	1.30348i
$119$	29.9634	−	32.5861i	0.251793	−	0.273833i
$120$	−28.0989	−	101.582i	−0.234158	−	0.846513i
$121$	30.8446	−	4.06077i	0.254914	−	0.0335601i
$122$	−321.731	−	21.0874i	−2.63714	−	0.172848i
$123$	−89.0932	+	157.230i	−0.724335	+	1.27829i
$124$	118.874	+	40.3522i	0.958660	+	0.325421i
$125$	−75.6035	−	113.149i	−0.604828	−	0.905189i
$126$	−75.2025	−	13.7013i	−0.596845	−	0.108741i
$127$	−115.720	+	47.9329i	−0.911183	+	0.377425i	−0.788510	−	0.615023i	$-0.789147\pi$
$127$	−115.720	+	47.9329i	−0.911183	+	0.377425i	−0.122674	+	0.992447i	$0.539147\pi$
$128$	213.632	+	28.1252i	1.66900	+	0.219728i
$129$	−36.5588	+	24.8567i	−0.283402	+	0.192688i
$130$	60.9332	+	30.0489i	0.468717	+	0.231146i
$131$	−9.94795	−	11.3435i	−0.0759386	−	0.0865913i	0.712623	−	0.701547i	$-0.247507\pi$
$131$	−9.94795	−	11.3435i	−0.0759386	−	0.0865913i	−0.788561	+	0.614956i	$0.789174\pi$
$132$	−162.754	+	95.7246i	−1.23298	+	0.725187i
$133$	21.3376	−	10.5226i	0.160433	−	0.0791170i
$134$	346.565	+	143.552i	2.58630	+	1.07128i
$135$	−107.128	−	25.9436i	−0.793543	−	0.192175i
$136$	−52.7881	−	136.442i	−0.388148	−	1.00325i
$137$	92.2081	−	159.709i	0.673052	−	1.16576i	−0.303982	−	0.952678i	$-0.598316\pi$
$137$	92.2081	−	159.709i	0.673052	−	1.16576i	0.977034	−	0.213082i	$-0.0683502\pi$
$138$	29.2334	−	38.7409i	0.211836	−	0.280731i
$139$	87.1666	+	5.71320i	0.627098	+	0.0411022i	0.375639	−	0.926766i	$-0.377423\pi$
$139$	87.1666	+	5.71320i	0.627098	+	0.0411022i	0.251458	+	0.967868i	$0.419090\pi$
$140$	18.2650	−	68.1661i	0.130465	−	0.486900i
$141$	5.18383	+	3.40356i	0.0367648	+	0.0241387i
$142$	36.5419	−	2.39508i	0.257338	−	0.0168668i
$143$	9.43751	−	47.4456i	0.0659966	−	0.331787i
$144$	−8.12593	+	10.9513i	−0.0564301	+	0.0760508i
$145$	19.1144	+	46.1463i	0.131824	+	0.318250i
$146$	157.525	−	179.623i	1.07894	−	1.23030i
$147$	95.8967	+	82.7402i	0.652359	+	0.562859i
$148$	241.676	+	275.579i	1.63295	+	1.86202i
$149$	186.383	+	49.9412i	1.25089	+	0.335176i	0.822682	−	0.568502i	$-0.192477\pi$
$149$	186.383	+	49.9412i	1.25089	+	0.335176i	0.428213	+	0.903678i	$0.359143\pi$
$150$	−25.5889	+	77.4289i	−0.170592	+	0.516193i
$151$	−28.3730	+	21.7713i	−0.187900	+	0.144181i	−0.698428	−	0.715680i	$-0.746117\pi$
$151$	−28.3730	+	21.7713i	−0.187900	+	0.144181i	0.510528	+	0.859861i	$0.329450\pi$
$152$		−	78.6252i		−	0.517271i
$153$	−151.539	−	21.0941i	−0.990450	−	0.137870i
$154$	−80.5257			−0.522894
$155$	46.9965	+	61.2470i	0.303203	+	0.395142i
$156$	−20.6273	−	99.4989i	−0.132226	−	0.637813i
$157$	29.4760	−	110.006i	0.187745	−	0.700675i	−0.806281	−	0.591533i	$-0.798523\pi$
$157$	29.4760	−	110.006i	0.187745	−	0.700675i	0.994026	−	0.109142i	$-0.0348103\pi$
$158$	−382.245	+	335.220i	−2.41927	+	2.12165i
$159$	−63.8112	−	183.115i	−0.401328	−	1.15167i
$160$	90.4860	+	79.3541i	0.565538	+	0.495963i
$161$	11.9325	−	4.94262i	0.0741152	−	0.0306995i
$162$	108.925	+	240.695i	0.672376	+	1.48577i
$163$	83.0318	+	16.5160i	0.509397	+	0.101325i	0.443096	−	0.896474i	$-0.353880\pi$
$163$	83.0318	+	16.5160i	0.509397	+	0.101325i	0.0663015	+	0.997800i	$0.478880\pi$
$164$	26.1543	+	399.038i	0.159478	+	2.43316i
$165$	−115.925	−	6.65942i	−0.702574	−	0.0403601i
$166$	189.138	+	50.6795i	1.13939	+	0.305298i
$167$	16.8719	−	257.416i	0.101030	−	1.54141i	−0.583310	−	0.812250i	$-0.698243\pi$
$167$	16.8719	−	257.416i	0.101030	−	1.54141i	0.684339	−	0.729164i	$-0.260091\pi$
$168$	−61.9011	+	26.2273i	−0.368459	+	0.156115i
$169$	−123.812	−	71.4832i	−0.732618	−	0.422977i
$170$	49.3755	−	220.912i	0.290444	−	1.29948i
$171$	−71.8650	−	39.9595i	−0.420263	−	0.233681i
$172$	−37.4362	+	90.3790i	−0.217652	+	0.525459i
$173$	13.7526	+	27.8875i	0.0794946	+	0.161199i	0.932991	−	0.359900i	$-0.117189\pi$
$173$	13.7526	+	27.8875i	0.0794946	+	0.161199i	−0.853496	+	0.521099i	$0.825522\pi$
$174$	59.0215	−	104.160i	0.339204	−	0.598620i
$175$	−16.3162	+	14.3089i	−0.0932352	+	0.0817651i
$176$	−6.35374	+	12.8841i	−0.0361008	+	0.0732051i
$177$	−141.089	+	10.3911i	−0.797114	+	0.0587070i
$178$	−71.2565	+	541.247i	−0.400317	+	3.04071i
$179$	38.0939	+	91.9669i	0.212815	+	0.513782i	0.993854	−	0.110701i	$-0.0353097\pi$
$179$	38.0939	+	91.9669i	0.212815	+	0.513782i	−0.781038	+	0.624483i	$0.785310\pi$
$180$	−229.669	+	82.1175i	−1.27594	+	0.456208i
$181$	178.246	−	119.100i	0.984787	−	0.658013i	0.0447184	−	0.999000i	$-0.485761\pi$
$181$	178.246	−	119.100i	0.984787	−	0.658013i	0.940068	+	0.340986i	$0.110761\pi$
$182$	13.9299	−	41.0361i	0.0765379	−	0.225473i
$183$	2.39224	+	296.546i	0.0130724	+	1.62047i
$184$	2.79166	−	42.5925i	0.0151721	−	0.231481i
$185$	29.4217	+	223.480i	0.159036	+	1.20800i
$186$	46.4481	−	179.114i	0.249721	−	0.962978i
$187$	−161.035	+	6.75225i	−0.861152	+	0.0361083i
$188$	13.7224			0.0729914
$189$	−7.48759	+	69.9083i	−0.0396169	+	0.369885i
$190$	67.5878	−	101.152i	0.355725	−	0.532380i
$191$	−208.584	+	55.8900i	−1.09206	+	0.292618i	−0.759529	−	0.650473i	$-0.774571\pi$
$191$	−208.584	+	55.8900i	−1.09206	+	0.292618i	−0.332535	+	0.943091i	$0.607904\pi$
$192$	17.5870	−	306.147i	0.0915988	−	1.59452i
$193$	135.843	−	275.463i	0.703852	−	1.42727i	−0.191310	−	0.981530i	$-0.561274\pi$
$193$	135.843	−	275.463i	0.703852	−	1.42727i	0.895162	−	0.445741i	$-0.147060\pi$
$194$	−170.037	+	57.7196i	−0.876477	+	0.297524i
$195$	23.4471	−	57.9236i	0.120242	−	0.297044i
$196$	277.872	+	36.5825i	1.41771	+	0.186646i
$197$	−209.143	−	41.6012i	−1.06164	−	0.211173i	−0.366772	−	0.930311i	$-0.619537\pi$
$197$	−209.143	−	41.6012i	−1.06164	−	0.211173i	−0.694868	+	0.719137i	$0.744537\pi$
$198$	158.336	+	228.885i	0.799679	+	1.15599i
$199$	−104.897	+	20.8654i	−0.527122	+	0.104851i	−0.451475	−	0.892284i	$-0.649102\pi$
$199$	−104.897	+	20.8654i	−0.527122	+	0.104851i	−0.0756468	+	0.997135i	$0.524102\pi$
$200$	18.5624	+	69.2760i	0.0928122	+	0.346380i
$201$	108.266	−	327.599i	0.538635	−	1.62985i
$202$	16.4835	+	125.205i	0.0816014	+	0.619824i
$203$	27.5916	−	15.9300i	0.135919	−	0.0784731i
$204$	−305.927	+	145.024i	−1.49964	+	0.710903i
$205$	−122.960	+	212.973i	−0.599806	+	1.03889i
$206$	−3.24471	+	7.83343i	−0.0157510	+	0.0380264i
$207$	−37.5116	−	24.1983i	−0.181216	−	0.116900i
$208$	−5.46666	−	5.46666i	−0.0262820	−	0.0262820i
$209$	−82.0249	−	27.8437i	−0.392464	−	0.133223i
$210$	−102.182	−	19.4697i	−0.486581	−	0.0927129i
$211$	−251.001	+	85.2034i	−1.18958	+	0.403808i	−0.844906	−	0.534915i	$-0.820344\pi$
$211$	−251.001	+	85.2034i	−1.18958	+	0.403808i	−0.344673	+	0.938723i	$0.612010\pi$
$212$	−340.427	−	261.219i	−1.60579	−	1.23216i
$213$	−4.66569	−	33.3578i	−0.0219047	−	0.156609i
$214$	445.921	−	508.475i	2.08374	−	2.37605i
$215$	−50.0205	+	33.4227i	−0.232654	+	0.155454i
$216$	196.263	+	124.377i	0.908625	+	0.575817i
$217$	34.8200	−	34.8200i	0.160461	−	0.160461i
$218$	−185.402	+	91.4302i	−0.850468	+	0.419404i
$219$	−175.409	−	132.362i	−0.800954	−	0.604391i
$220$	−222.519	+	128.471i	−1.01145	+	0.583961i
$221$	24.4160	−	83.2322i	0.110480	−	0.376616i
$222$	378.937	−	385.101i	1.70692	−	1.73469i
$223$	−87.3468	−	113.833i	−0.391690	−	0.510460i	0.555332	−	0.831629i	$-0.312591\pi$
$223$	−87.3468	−	113.833i	−0.391690	−	0.510460i	−0.947022	+	0.321168i	$0.895924\pi$
$224$	42.6501	−	63.8304i	0.190402	−	0.284957i
$225$	72.7536	+	18.2415i	0.323349	+	0.0810734i
$226$	−25.0911	−	126.142i	−0.111023	−	0.558149i
$227$	217.229	−	14.2380i	0.956958	−	0.0627223i	0.421085	−	0.907021i	$-0.361649\pi$
$227$	217.229	−	14.2380i	0.956958	−	0.0627223i	0.535873	+	0.844299i	$0.319983\pi$
$228$	−181.463	+	13.3646i	−0.795888	+	0.0586167i
$229$	−24.9734	−	19.1628i	−0.109054	−	0.0836802i	0.552795	−	0.833317i	$-0.313561\pi$
$229$	−24.9734	−	19.1628i	−0.109054	−	0.0836802i	−0.661849	+	0.749637i	$0.730228\pi$
$230$	40.2049	−	52.3960i	0.174804	−	0.227809i
$231$	5.44016	+	73.8656i	0.0235505	+	0.319764i
$232$	−6.88639	−	105.066i	−0.0296827	−	0.452871i
$233$	−94.1925	+	18.7361i	−0.404260	+	0.0804123i	−0.393032	−	0.919525i	$-0.628574\pi$
$233$	−94.1925	+	18.7361i	−0.404260	+	0.0804123i	−0.0112276	+	0.999937i	$0.503574\pi$
$234$	−144.031	+	41.0945i	−0.615516	+	0.175618i
$235$	7.01658	+	4.68833i	0.0298578	+	0.0199503i
$236$	−248.359	+	190.573i	−1.05237	+	0.807512i
$237$	333.318	+	327.984i	1.40641	+	1.38390i
$238$	−143.816	−	12.8327i	−0.604269	−	0.0539188i
$239$	203.361	+	352.232i	0.850884	+	1.47377i	0.880412	+	0.474210i	$0.157266\pi$
$239$	203.361	+	352.232i	0.850884	+	1.47377i	−0.0295277	+	0.999564i	$0.509400\pi$
$240$	−11.1776	+	14.8129i	−0.0465735	+	0.0617203i
$241$	−0.0579660	−	0.117543i	−0.000240523	−	0.000487732i	0.896752	−	0.442533i	$-0.145920\pi$
$241$	−0.0579660	−	0.117543i	−0.000240523	−	0.000487732i	−0.896993	+	0.442045i	$0.854253\pi$
$242$	−71.7521	−	71.7521i	−0.296496	−	0.296496i
$243$	213.429	−	116.177i	0.878309	−	0.478094i
$244$	364.578	+	545.630i	1.49417	+	2.23619i
$245$	129.584	+	113.642i	0.528914	+	0.463845i
$246$	583.757	−	81.6489i	2.37299	−	0.331906i
$247$	28.3785	−	36.9835i	0.114893	−	0.149731i
$248$	−52.3105	−	154.102i	−0.210929	−	0.621378i
$249$	33.7101	−	176.919i	0.135382	−	0.710518i
$250$	−142.673	+	420.301i	−0.570692	+	1.68120i
$251$	265.065	−	265.065i	1.05603	−	1.05603i	0.0577002	−	0.998334i	$-0.481623\pi$
$251$	265.065	−	265.065i	1.05603	−	1.05603i	0.998334	−	0.0577002i	$-0.0183768\pi$
$252$	71.0529	+	138.406i	0.281956	+	0.549231i
$253$	−43.4456	−	17.9957i	−0.171722	−	0.0711294i
$254$	353.805	+	204.269i	1.39293	+	0.804210i
$255$	−205.976	−	30.3674i	−0.807750	−	0.119088i
$256$	−146.969	−	254.558i	−0.574098	−	0.994368i
$257$	182.548	−	24.0329i	0.710305	−	0.0935134i	0.233288	−	0.972408i	$-0.425051\pi$
$257$	182.548	−	24.0329i	0.710305	−	0.0935134i	0.477017	+	0.878894i	$0.341718\pi$
$258$	136.911	+	45.2466i	0.530662	+	0.175374i
$259$	138.880	−	37.2127i	0.536215	−	0.143679i
$260$	−26.9766	−	135.620i	−0.103756	−	0.521617i
$261$	−99.5323	−	47.1031i	−0.381350	−	0.180472i
$262$	−9.60053	+	48.2651i	−0.0366432	+	0.184218i
$263$	15.2872	−	116.118i	0.0581261	−	0.441512i	−0.937493	−	0.348005i	$-0.886859\pi$
$263$	15.2872	−	116.118i	0.0581261	−	0.441512i	0.995619	−	0.0935064i	$-0.0298076\pi$
$264$	226.889	+	91.8431i	0.859427	+	0.347891i
$265$	−84.8215	−	249.876i	−0.320081	−	0.942929i
$266$	−69.5962	−	34.3210i	−0.261640	−	0.129026i
$267$	501.295	+	28.7974i	1.87751	+	0.107856i
$268$	−197.603	−	737.463i	−0.737323	−	2.75173i
$269$	102.410	+	68.4279i	0.380705	+	0.254379i	0.731168	−	0.682198i	$-0.238976\pi$
$269$	102.410	+	68.4279i	0.380705	+	0.254379i	−0.350463	+	0.936577i	$0.613976\pi$
$270$	145.578	+	328.724i	0.539179	+	1.21750i
$271$		−	57.0228i		−	0.210416i	−0.994450	−	0.105208i	$-0.966449\pi$
$271$		−	57.0228i		−	0.210416i	0.994450	−	0.105208i	$-0.0335509\pi$
$272$	−13.4008	+	21.9980i	−0.0492676	+	0.0808751i
$273$	−38.5832	−	10.0055i	−0.141330	−	0.0366500i
$274$	−596.358	+	78.5120i	−2.17649	+	0.286540i
$275$	78.8450	+	5.16777i	0.286709	+	0.0187919i
$276$	−98.7757	+	0.796825i	−0.357883	+	0.00288705i
$277$	−130.140	−	44.1764i	−0.469818	−	0.159482i	0.0764827	−	0.997071i	$-0.475631\pi$
$277$	−130.140	−	44.1764i	−0.469818	−	0.159482i	−0.546301	+	0.837589i	$0.683964\pi$
$278$	−158.292	−	236.901i	−0.569396	−	0.852161i
$279$	−167.438	−	30.5059i	−0.600135	−	0.109340i
$280$	−84.5203	+	35.0094i	−0.301858	+	0.125034i
$281$	159.777	+	21.0350i	0.568600	+	0.0748576i	0.409345	−	0.912380i	$-0.365757\pi$
$281$	159.777	+	21.0350i	0.568600	+	0.0748576i	0.159255	+	0.987237i	$0.449091\pi$
$282$	−1.48565	−	20.1720i	−0.00526828	−	0.0715318i
$283$	169.877	+	83.7740i	0.600272	+	0.296021i	0.716924	−	0.697152i	$-0.245550\pi$
$283$	169.877	+	83.7740i	0.600272	+	0.296021i	−0.116652	+	0.993173i	$0.537216\pi$
$284$	−49.1432	−	56.0370i	−0.173039	−	0.197313i
$285$	−97.3522	−	55.1641i	−0.341587	−	0.193558i
$286$	−141.512	+	69.7858i	−0.494795	+	0.244006i
$287$	144.922	+	60.0288i	0.504956	+	0.209160i
$288$	−265.293	+	4.28053i	−0.921157	+	0.0148629i
$289$	−288.680	−	13.6035i	−0.998892	−	0.0470710i
$290$	81.4574	−	141.088i	0.280888	−	0.486512i
$291$	64.4331	+	152.074i	0.221419	+	0.522590i
$292$	−485.214	−	31.8026i	−1.66169	−	0.108913i
$293$	−77.4400	+	289.010i	−0.264300	+	0.986383i	0.698377	+	0.715730i	$0.253906\pi$
$293$	−77.4400	+	289.010i	−0.264300	+	0.986383i	−0.962677	+	0.270652i	$0.912761\pi$
$294$	23.6927	−	412.434i	0.0805875	−	1.40284i
$295$	−192.102	+	12.5911i	−0.651195	+	0.0426815i
$296$	92.6995	−	466.032i	0.313174	−	1.57443i
$297$	199.258	−	160.704i	0.670901	−	0.541090i
$298$	−240.847	−	581.457i	−0.808213	−	1.95120i
$299$	16.6862	−	19.0270i	0.0558067	−	0.0636353i
$300$	156.730	−	54.6165i	0.522433	−	0.182055i
$301$	25.3012	+	28.8504i	0.0840570	+	0.0958487i
$302$	112.673	+	30.1907i	0.373090	+	0.0999693i
$303$	113.735	−	23.5787i	0.375365	−	0.0778176i
$304$	−10.9827	+	8.42734i	−0.0361274	+	0.0277215i
$305$			403.554i			1.32313i
$306$	246.308	+	434.014i	0.804927	+	1.41835i
$307$	−243.288			−0.792469			−0.396235	−	0.918149i	$-0.629683\pi$
$307$	−243.288			−0.792469			−0.396235	+	0.918149i	$0.629683\pi$
$308$	99.7721	+	130.026i	0.323935	+	0.422161i
$309$	7.40475	+	2.44714i	0.0239636	+	0.00791954i
$310$	65.1708	−	243.221i	0.210229	−	0.784584i
$311$	−386.412	+	338.874i	−1.24248	+	1.08963i	−0.249871	+	0.968279i	$0.580388\pi$
$311$	−386.412	+	338.874i	−1.24248	+	1.08963i	−0.992610	+	0.121347i	$0.961279\pi$
$312$	−86.0523	+	99.7355i	−0.275809	+	0.319665i
$313$	−103.181	−	90.4873i	−0.329652	−	0.289097i	0.478480	−	0.878098i	$-0.341188\pi$
$313$	−103.181	−	90.4873i	−0.329652	−	0.289097i	−0.808132	+	0.589002i	$0.799521\pi$
$314$	−343.184	+	142.151i	−1.09294	+	0.452712i
$315$	−10.9562	+	95.0460i	−0.0347816	+	0.301733i
$316$	1014.89	+	201.874i	3.21167	+	0.638841i
$317$	20.3435	+	310.382i	0.0641752	+	0.979124i	0.901600	+	0.432571i	$0.142394\pi$
$317$	20.3435	+	310.382i	0.0641752	+	0.979124i	−0.837425	+	0.546553i	$0.815940\pi$
$318$	−347.137	+	528.710i	−1.09162	+	1.66261i
$319$	−112.048	−	30.0231i	−0.351247	−	0.0941163i
$320$	27.2923	−	416.400i	0.0852883	−	1.30125i
$321$	−496.546	−	374.688i	−1.54687	−	1.16725i
$322$	−36.4828	−	21.0633i	−0.113300	−	0.0654141i
$323$	−142.056	−	62.7995i	−0.439803	−	0.194426i
$324$	253.694	−	474.106i	0.783005	−	1.46329i
$325$	−16.2727	+	39.2857i	−0.0500697	+	0.120879i
$326$	−122.128	−	247.651i	−0.374626	−	0.759666i
$327$	96.3935	+	163.891i	0.294781	+	0.501195i
$328$	389.755	−	341.806i	1.18828	−	1.04209i
$329$	2.38073	−	4.82764i	0.00723626	−	0.0146737i
$330$	212.945	+	313.196i	0.645288	+	0.949077i
$331$	−67.1185	+	509.815i	−0.202775	+	1.54023i	0.523023	+	0.852319i	$0.324804\pi$
$331$	−67.1185	+	509.815i	−0.202775	+	1.54023i	−0.725797	+	0.687909i	$0.758529\pi$
$332$	−152.512	−	368.196i	−0.459373	−	1.10902i
$333$	−378.850	−	321.579i	−1.13769	−	0.965704i
$334$	−699.603	+	467.460i	−2.09462	+	1.39958i
$335$	150.920	−	444.595i	0.450506	−	1.32715i
$336$	10.2983	+	5.83549i	0.0306498	+	0.0173675i
$337$	−32.6647	+	498.368i	−0.0969280	+	1.47884i	0.621598	+	0.783336i	$0.286484\pi$
$337$	−32.6647	+	498.368i	−0.0969280	+	1.47884i	−0.718527	+	0.695500i	$0.755183\pi$
$338$	60.8654	+	462.319i	0.180075	+	1.36781i
$339$	−114.014	+	31.5378i	−0.336323	+	0.0930318i
$340$	−417.885	+	193.985i	−1.22907	+	0.570543i
$341$	−179.290			−0.525777
$342$	39.2921	+	265.304i	0.114889	+	0.775743i
$343$	131.967	−	197.503i	0.384745	−	0.575811i
$344$	122.495	−	32.8223i	0.356089	−	0.0954138i
$345$	−50.7786	−	33.3398i	−0.147184	−	0.0966372i
$346$	44.8563	−	90.9595i	0.129642	−	0.262889i
$347$	52.0627	−	17.6729i	0.150037	−	0.0509306i	−0.245411	−	0.969419i	$-0.578923\pi$
$347$	52.0627	−	17.6729i	0.150037	−	0.0509306i	0.395448	+	0.918489i	$0.370590\pi$
$348$	−241.316	+	33.7524i	−0.693437	+	0.0969896i
$349$	−39.7919	−	5.23870i	−0.114017	−	0.0150106i	0.0733018	−	0.997310i	$-0.476646\pi$
$349$	−39.7919	−	5.23870i	−0.114017	−	0.0150106i	−0.187319	+	0.982299i	$0.559980\pi$
$350$	69.4234	+	13.8092i	0.198353	+	0.0394548i
$351$	47.4261	+	129.342i	0.135117	+	0.368495i
$352$	−274.137	+	54.5293i	−0.778799	+	0.154913i
$353$	−109.156	−	407.377i	−0.309225	−	1.15404i	−0.929247	−	0.369459i	$-0.879543\pi$
$353$	−109.156	−	407.377i	−0.309225	−	1.15404i	0.620022	−	0.784584i	$-0.287124\pi$
$354$	307.032	+	344.457i	0.867322	+	0.973044i
$355$	−5.98270	−	45.4431i	−0.0168527	−	0.128009i
$356$	962.243	−	555.551i	2.70293	−	1.56054i
$357$	−2.05537	+	132.788i	−0.00575735	+	0.371956i
$358$	162.340	−	281.181i	0.453463	−	0.785422i
$359$	175.216	−	423.009i	0.488067	−	1.17830i	−0.467625	−	0.883927i	$-0.654890\pi$
$359$	175.216	−	423.009i	0.488067	−	1.17830i	0.955692	−	0.294370i	$-0.0951098\pi$
$360$	265.701	+	171.401i	0.738059	+	0.476113i
$361$	196.241	+	196.241i	0.543604	+	0.543604i
$362$	−662.112	−	224.757i	−1.82904	−	0.620875i
$363$	−60.9702	+	70.6650i	−0.167962	+	0.194669i
$364$	−83.5207	+	28.3514i	−0.229452	+	0.0778886i
$365$	−237.236	−	182.038i	−0.649962	−	0.498733i
$366$	762.608	−	595.005i	2.08363	−	1.62570i
$367$	−117.717	+	134.230i	−0.320754	+	0.365750i	−0.889637	−	0.456669i	$-0.849042\pi$
$367$	−117.717	+	134.230i	−0.320754	+	0.365750i	0.568883	+	0.822419i	$0.307376\pi$
$368$	−6.24873	+	4.17527i	−0.0169803	+	0.0113458i
$369$	−114.333	−	529.959i	−0.309846	−	1.43620i
$370$	519.869	−	519.869i	1.40505	−	1.40505i
$371$	−150.960	+	74.4454i	−0.406901	+	0.200661i
$372$	−346.766	+	146.924i	−0.932168	+	0.394956i
$373$	−87.0849	+	50.2785i	−0.233472	+	0.134795i	−0.612173	−	0.790724i	$-0.709704\pi$
$373$	−87.0849	+	50.2785i	−0.233472	+	0.134795i	0.378701	+	0.925519i	$0.376371\pi$
$374$	337.220	+	403.296i	0.901659	+	1.07833i
$375$	395.177	+	102.478i	1.05381	+	0.273275i
$376$	−10.8292	−	14.1129i	−0.0288011	−	0.0375344i
$377$	34.6826	−	51.9062i	0.0919964	−	0.137682i
$378$	195.765	−	119.433i	0.517898	−	0.315960i
$379$	139.323	+	700.425i	0.367607	+	1.84809i	0.512565	+	0.858648i	$0.328695\pi$
$379$	139.323	+	700.425i	0.367607	+	1.84809i	−0.144958	+	0.989438i	$0.546305\pi$
$380$	−247.073	+	16.1940i	−0.650193	+	0.0426159i
$381$	163.472	−	338.342i	0.429061	−	0.888038i
$382$	558.783	+	428.770i	1.46278	+	1.12243i
$383$	312.125	−	406.770i	0.814948	−	1.06206i	−0.181946	−	0.983309i	$-0.558240\pi$
$383$	312.125	−	406.770i	0.814948	−	1.06206i	0.996894	−	0.0787530i	$-0.0250938\pi$
$384$	−534.569	+	363.459i	−1.39211	+	0.946508i
$385$	6.59189	+	100.573i	0.0171218	+	0.261228i
$386$	−982.530	+	195.437i	−2.54541	+	0.506314i
$387$	32.2549	−	128.644i	0.0833460	−	0.332413i
$388$	303.877	+	203.044i	0.783189	+	0.523310i
$389$	−456.782	+	350.501i	−1.17425	+	0.901031i	−0.996545	−	0.0830540i	$-0.973533\pi$
$389$	−456.782	+	350.501i	−1.17425	+	0.901031i	−0.177701	+	0.984085i	$0.556866\pi$
$390$	−196.442	+	54.3386i	−0.503698	+	0.139330i
$391$	−74.7245	−	39.0633i	−0.191111	−	0.0999062i
$392$	−181.663	−	314.650i	−0.463427	−	0.802679i
$393$	44.9218	+	5.54579i	0.114305	+	0.0141114i
$394$	307.620	+	623.792i	0.780762	+	1.58323i
$395$	449.965	+	449.965i	1.13915	+	1.13915i
$396$	173.403	−	539.258i	0.437886	−	1.36176i
$397$	343.362	+	513.877i	0.864891	+	1.29440i	0.954435	+	0.298418i	$0.0964590\pi$
$397$	343.362	+	513.877i	0.864891	+	1.29440i	−0.0895440	+	0.995983i	$0.528541\pi$
$398$	262.274	+	230.008i	0.658979	+	0.577909i
$399$	−26.7806	+	66.1586i	−0.0671193	+	0.165811i
$400$	7.68719	−	10.0181i	0.0192180	−	0.0250454i
$401$	44.8111	+	132.009i	0.111748	+	0.329200i	0.988389	−	0.151946i	$-0.0485540\pi$
$401$	44.8111	+	132.009i	0.111748	+	0.329200i	−0.876640	+	0.481146i	$0.840221\pi$
$402$	−1062.68	+	370.319i	−2.64349	+	0.921191i
$403$	31.0148	−	91.3666i	0.0769598	−	0.226716i
$404$	181.746	−	181.746i	0.449865	−	0.449865i
$405$	291.701	−	155.746i	0.720248	−	0.384557i
$406$	−96.0067	−	39.7673i	−0.236470	−	0.0979489i
$407$	−453.355	−	261.745i	−1.11389	−	0.643107i
$408$	390.579	+	200.186i	0.957301	+	0.490652i
$409$	231.664	+	401.253i	0.566414	+	0.981059i	0.996917	+	0.0784691i	$0.0250032\pi$
$409$	231.664	+	401.253i	0.566414	+	0.981059i	−0.430502	+	0.902590i	$0.641663\pi$
$410$	795.248	−	104.696i	1.93963	−	0.255357i
$411$	112.307	+	541.730i	0.273253	+	1.31808i
$412$	16.6689	−	4.46643i	0.0404586	−	0.0108408i
$413$	23.9566	+	120.438i	0.0580062	+	0.291617i
$414$	11.8653	+	145.115i	0.0286601	+	0.350518i
$415$	47.8133	−	240.374i	0.115213	−	0.579214i
$416$	19.6339	−	149.134i	0.0471968	−	0.358495i
$417$	−206.613	+	161.204i	−0.495475	+	0.386581i
$418$	90.8168	+	267.538i	0.217265	+	0.640042i
$419$	−107.894	−	53.2075i	−0.257504	−	0.126987i	0.308956	−	0.951076i	$-0.400021\pi$
$419$	−107.894	−	53.2075i	−0.257504	−	0.126987i	−0.566460	+	0.824090i	$0.691687\pi$
$420$	95.1665	+	189.117i	0.226587	+	0.450279i
$421$	−144.719	−	540.098i	−0.343750	−	1.28289i	−0.894065	−	0.447937i	$-0.852159\pi$
$421$	−144.719	−	540.098i	−0.343750	−	1.28289i	0.550315	−	0.834957i	$-0.314508\pi$
$422$	718.858	+	480.326i	1.70346	+	1.13821i
$423$	−18.4032	+	2.72556i	−0.0435064	+	0.00644340i
$424$			556.260i			1.31194i
$425$	139.991	+	21.7943i	0.329390	+	0.0512807i
$426$	−77.0543	+	78.3076i	−0.180879	+	0.183821i
$427$	255.209	−	33.5989i	0.597678	−	0.0786858i
$428$	−1373.54	−	90.0265i	−3.20920	−	0.210342i
$429$	73.5741	+	125.093i	0.171501	+	0.291591i
$430$	185.806	+	63.0725i	0.432106	+	0.146680i
$431$	405.058	+	606.212i	0.939810	+	1.40652i	0.913485	+	0.406871i	$0.133380\pi$
$431$	405.058	+	606.212i	0.939810	+	1.40652i	0.0263245	+	0.999653i	$0.491620\pi$
$432$	−3.66272	−	40.7461i	−0.00847851	−	0.0943196i
$433$	207.530	−	85.9619i	0.479285	−	0.198526i	−0.129943	−	0.991521i	$-0.541479\pi$
$433$	207.530	−	85.9619i	0.479285	−	0.198526i	0.609228	+	0.792995i	$0.291479\pi$
$434$	−159.240	−	20.9643i	−0.366911	−	0.0483048i
$435$	−134.922	−	65.1886i	−0.310166	−	0.149859i
$436$	377.348	+	186.087i	0.865477	+	0.426806i
$437$	−29.8788	−	34.0703i	−0.0683726	−	0.0779640i
$438$	5.78172	+	716.711i	0.0132003	+	1.63633i
$439$	−228.950	+	112.906i	−0.521526	+	0.257188i	−0.683945	−	0.729534i	$-0.739737\pi$
$439$	−228.950	+	112.906i	−0.521526	+	0.257188i	0.162419	+	0.986722i	$0.448070\pi$
$440$	307.732	+	127.467i	0.699392	+	0.289698i
$441$	−379.923	+	6.13009i	−0.861504	+	0.0139004i
$442$	−263.856	+	102.083i	−0.596959	+	0.230958i
$443$	362.873	−	628.515i	0.819127	−	1.41877i	−0.0871992	−	0.996191i	$-0.527792\pi$
$443$	362.873	−	628.515i	0.819127	−	1.41877i	0.906326	−	0.422579i	$-0.138875\pi$
$444$	−1091.33	−	134.730i	−2.45796	−	0.303445i
$445$	681.825	+	44.6892i	1.53219	+	0.100425i
$446$	−121.125	+	452.046i	−0.271582	+	1.01356i
$447$	−517.095	+	260.209i	−1.15681	+	0.582124i
$448$	−265.605	+	17.4086i	−0.592867	+	0.0388586i
$449$	63.1734	−	317.594i	0.140698	−	0.707336i	−0.844451	−	0.535633i	$-0.820073\pi$
$449$	63.1734	−	317.594i	0.140698	−	0.707336i	0.985149	−	0.171703i	$-0.0549270\pi$
$450$	−97.2550	−	224.481i	−0.216122	−	0.498846i
$451$	−218.561	−	527.652i	−0.484613	−	1.16996i
$452$	−172.594	+	196.806i	−0.381845	+	0.435411i
$453$	20.0817	−	105.394i	0.0443305	−	0.232658i
$454$	−468.168	−	533.844i	−1.03121	−	1.17587i
$455$	−52.3925	−	14.0385i	−0.115148	−	0.0308539i
$456$	156.949	+	176.080i	0.344186	+	0.386141i
$457$	681.350	−	522.818i	1.49092	−	1.14402i	0.537149	−	0.843488i	$-0.319501\pi$
$457$	681.350	−	522.818i	1.49092	−	1.14402i	0.953771	−	0.300535i	$-0.0971652\pi$
$458$			102.672i			0.224174i
$459$	381.477	−	255.257i	0.831105	−	0.556116i
$460$	−134.419			−0.292214
$461$	65.7185	+	85.6461i	0.142556	+	0.185783i	0.859175	−	0.511683i	$-0.170978\pi$
$461$	65.7185	+	85.6461i	0.142556	+	0.185783i	−0.716618	+	0.697466i	$0.754311\pi$
$462$	180.336	−	160.743i	0.390339	−	0.347928i
$463$	−18.5364	+	69.1787i	−0.0400354	+	0.149414i	−0.983050	−	0.183337i	$-0.941310\pi$
$463$	−18.5364	+	69.1787i	−0.0400354	+	0.149414i	0.943015	+	0.332751i	$0.107977\pi$
$464$	−13.9380	+	12.2233i	−0.0300388	+	0.0263433i
$465$	−227.507	−	43.3492i	−0.489263	−	0.0932240i
$466$	235.509	+	206.536i	0.505384	+	0.443209i
$467$	−205.200	+	84.9967i	−0.439401	+	0.182006i	−0.591406	−	0.806374i	$-0.701427\pi$
$467$	−205.200	+	84.9967i	−0.439401	+	0.182006i	0.152005	+	0.988380i	$0.451427\pi$
$468$	244.811	+	181.651i	0.523101	+	0.388143i
$469$	−293.728	−	58.4262i	−0.626286	−	0.124576i
$470$	−1.80018	−	27.4655i	−0.00383018	−	0.0584372i
$471$	153.579	+	305.196i	0.326070	+	0.647975i
$472$	391.993	+	105.034i	0.830495	+	0.222530i
$473$	9.13773	−	139.415i	0.0193187	−	0.294746i
$474$	186.879	−	1513.75i	0.394259	−	3.19356i
$475$	65.9410	+	38.0711i	0.138823	+	0.0801496i
$476$	157.468	+	248.121i	0.330816	+	0.521262i
$477$	508.433	+	282.707i	1.06590	+	0.592677i
$478$	507.665	−	1225.61i	1.06206	−	2.56404i
$479$	−5.15066	−	10.4445i	−0.0107529	−	0.0218048i	0.891430	−	0.453158i	$-0.149703\pi$
$479$	−5.15066	−	10.4445i	−0.0107529	−	0.0218048i	−0.902183	+	0.431354i	$0.858036\pi$
$480$	−361.047	+	2.91257i	−0.752181	+	0.00606785i
$481$	211.810	−	185.753i	0.440354	−	0.386180i
$482$	−0.189066	+	0.383387i	−0.000392252	+	0.000795409i
$483$	−16.8565	+	34.8883i	−0.0348996	+	0.0722325i
$484$	−26.9572	+	204.760i	−0.0556967	+	0.423058i
$485$	86.0084	+	207.643i	0.177337	+	0.428129i
$486$	−724.404	−	321.602i	−1.49054	−	0.661733i
$487$	−370.401	+	247.494i	−0.760577	+	0.508201i	−0.874344	−	0.485306i	$-0.838708\pi$
$487$	−370.401	+	247.494i	−0.760577	+	0.508201i	0.113767	+	0.993507i	$0.463708\pi$
$488$	273.446	−	805.547i	0.560341	−	1.65071i
$489$	−218.918	+	128.758i	−0.447684	+	0.263309i
$490$	36.7675	−	560.963i	0.0750356	−	1.14482i
$491$	−47.9650	−	364.330i	−0.0976884	−	0.742017i	−0.968255	−	0.249966i	$-0.919581\pi$
$491$	−47.9650	−	364.330i	−0.0976884	−	0.742017i	0.870566	−	0.492051i	$-0.163753\pi$
$492$	−855.119	−	841.433i	−1.73805	−	1.71023i
$493$	−195.329	−	71.4762i	−0.396204	−	0.144982i
$494$	−152.048			−0.307790
$495$	272.905	−	216.491i	0.551324	−	0.437356i
$496$	−15.9188	+	23.8242i	−0.0320943	+	0.0480326i
$497$	−28.2403	+	7.56695i	−0.0568214	+	0.0152253i
$498$	−524.739	+	264.056i	−1.05369	+	0.530233i
$499$	224.206	−	454.645i	0.449311	−	0.911112i	−0.547905	−	0.836540i	$-0.684575\pi$
$499$	224.206	−	454.645i	0.449311	−	0.911112i	0.997216	−	0.0745711i	$-0.0237588\pi$
$500$	855.436	−	290.381i	1.71087	−	0.580763i
$501$	476.061	+	610.160i	0.950222	+	1.21788i
$502$	−1212.20	−	159.589i	−2.41474	−	0.317907i
$503$	−634.027	−	126.116i	−1.26049	−	0.250727i	−0.480765	−	0.876849i	$-0.659641\pi$
$503$	−634.027	−	126.116i	−1.26049	−	0.250727i	−0.779725	+	0.626122i	$0.784641\pi$
$504$	86.2728	−	182.301i	0.171176	−	0.361707i
$505$	155.025	−	30.8364i	0.306981	−	0.0610623i
$506$	39.6977	+	148.154i	0.0784540	+	0.292794i
$507$	419.969	−	87.0646i	0.828341	−	0.171725i
$508$	−108.532	−	824.384i	−0.213646	−	1.62280i
$509$	803.637	−	463.980i	1.57885	−	0.911552i	0.583834	−	0.811873i	$-0.301552\pi$
$509$	803.637	−	463.980i	1.57885	−	0.911552i	0.995020	−	0.0996788i	$-0.0317815\pi$
$510$	330.401	+	593.291i	0.647845	+	1.16332i
$511$	−95.3695	+	165.185i	−0.186633	+	0.323258i
$512$	−37.0540	+	89.4564i	−0.0723712	+	0.174719i
$513$	240.707	−	53.9658i	0.469214	−	0.105196i
$514$	−424.652	−	424.652i	−0.826172	−	0.826172i
$515$	10.0492	+	3.41125i	0.0195130	+	0.00662378i
$516$	−96.5737	−	277.132i	−0.187158	−	0.537077i
$517$	−18.5581	+	6.29964i	−0.0358958	+	0.0121850i
$518$	−372.050	−	285.484i	−0.718243	−	0.551127i
$519$	−86.4668	−	35.0012i	−0.166603	−	0.0674397i
$520$	−118.191	+	134.771i	−0.227291	+	0.259175i
$521$	473.070	−	316.095i	0.908003	−	0.606708i	−0.0114386	−	0.999935i	$-0.503641\pi$
$521$	473.070	−	316.095i	0.908003	−	0.606708i	0.919442	+	0.393226i	$0.128641\pi$
$522$	75.7423	+	351.082i	0.145100	+	0.672570i
$523$	−317.313	+	317.313i	−0.606717	+	0.606717i	−0.942087	−	0.335369i	$-0.891139\pi$
$523$	−317.313	+	317.313i	−0.606717	+	0.606717i	0.335369	+	0.942087i	$0.391139\pi$
$524$	89.8293	−	44.2989i	0.171430	−	0.0845399i
$525$	7.97693	−	64.6144i	0.0151942	−	0.123075i
$526$	−330.826	+	191.002i	−0.628946	+	0.363122i
$527$	−320.205	−	28.5718i	−0.607600	−	0.0542160i
$528$	−11.4897	−	41.5369i	−0.0217608	−	0.0786684i
$529$	307.059	+	400.167i	0.580451	+	0.756459i
$530$	−478.173	+	715.636i	−0.902213	+	1.35026i
$531$	295.225	−	304.909i	0.555980	−	0.574216i
$532$	30.8118	+	154.902i	0.0579170	+	0.291168i
$533$	306.701	−	20.1023i	0.575424	−	0.0377153i
$534$	−920.841	−	1354.36i	−1.72442	−	2.53625i
$535$	−671.565	−	515.310i	−1.25526	−	0.963197i
$536$	−602.511	+	785.207i	−1.12409	+	1.46494i
$537$	−268.892	−	129.917i	−0.500731	−	0.241931i
$538$	−26.2743	−	400.869i	−0.0488371	−	0.745109i
$539$	−392.588	+	78.0907i	−0.728364	+	0.144881i
$540$	350.420	−	642.358i	0.648926	−	1.18955i
$541$	428.572	+	286.363i	0.792186	+	0.529322i	0.884573	−	0.466402i	$-0.154450\pi$
$541$	428.572	+	286.363i	0.792186	+	0.529322i	−0.0923874	+	0.995723i	$0.529450\pi$
$542$	−147.555	+	113.223i	−0.272242	+	0.208899i
$543$	−161.437	+	622.534i	−0.297305	+	1.14647i
$544$	−498.289	+	53.7005i	−0.915973	+	0.0987142i
$545$	129.369	+	224.074i	0.237375	+	0.411145i
$546$	50.7192	+	119.706i	0.0928923	+	0.219243i
$547$	98.1841	+	199.098i	0.179496	+	0.363981i	0.967962	−	0.251097i	$-0.0807913\pi$
$547$	98.1841	+	199.098i	0.179496	+	0.363981i	−0.788466	+	0.615078i	$0.789125\pi$
$548$	865.666	+	865.666i	1.57968	+	1.57968i
$549$	−597.313	−	659.337i	−1.08800	−	1.20098i
$550$	−143.180	−	214.284i	−0.260328	−	0.389608i
$551$	−84.0436	−	73.7042i	−0.152529	−	0.133764i
$552$	78.7699	+	100.958i	0.142699	+	0.182895i
$553$	247.096	−	322.022i	0.446829	−	0.582319i
$554$	144.089	+	424.471i	0.260088	+	0.766194i
$555$	−511.993	−	441.750i	−0.922510	−	0.795947i
$556$	−186.400	+	549.118i	−0.335252	+	0.987621i
$557$	−649.708	+	649.708i	−1.16644	+	1.16644i	−0.183405	+	0.983037i	$0.558712\pi$
$557$	−649.708	+	649.708i	−1.16644	+	1.16644i	−0.983037	+	0.183405i	$0.941288\pi$
$558$	253.521	+	493.842i	0.454339	+	0.885022i
$559$	69.4655	+	28.7735i	0.124267	+	0.0514732i
$560$	13.9495	+	8.05373i	0.0249098	+	0.0143817i
$561$	347.159	−	336.575i	0.618821	−	0.599956i
$562$	−262.817	−	455.213i	−0.467646	−	0.809987i
$563$	−110.856	+	14.5944i	−0.196902	+	0.0259226i	−0.228332	−	0.973583i	$-0.573327\pi$
$563$	−110.856	+	14.5944i	−0.196902	+	0.0259226i	0.0314301	+	0.999506i	$0.489994\pi$
$564$	−30.7311	+	27.3922i	−0.0544878	+	0.0485677i
$565$	−155.491	+	41.6637i	−0.275205	+	0.0737411i
$566$	−120.525	−	605.922i	−0.212942	−	1.07053i
$567$	−122.780	−	171.505i	−0.216544	−	0.302478i
$568$	−18.8498	+	94.7643i	−0.0331863	+	0.166839i
$569$	−56.2592	+	427.331i	−0.0988738	+	0.751021i	0.868144	+	0.496312i	$0.165313\pi$
$569$	−56.2592	+	427.331i	−0.0988738	+	0.751021i	−0.967018	+	0.254709i	$0.918020\pi$
$570$	50.5548	+	361.446i	0.0886926	+	0.634116i
$571$	−186.859	−	550.470i	−0.327250	−	0.964046i	−0.978689	−	0.205346i	$-0.934168\pi$
$571$	−186.859	−	550.470i	−0.327250	−	0.964046i	0.651440	−	0.758700i	$-0.274165\pi$
$572$	288.018	+	142.035i	0.503527	+	0.248312i
$573$	355.556	−	541.534i	0.620517	−	0.945086i
$574$	−132.421	−	494.200i	−0.230698	−	0.860976i
$575$	34.3695	+	22.9650i	0.0597731	+	0.0399391i
$576$	571.736	+	720.721i	0.992597	+	1.25125i
$577$			672.308i			1.16518i	0.812767	+	0.582589i	$0.197960\pi$
$577$			672.308i			1.16518i	−0.812767	+	0.582589i	$0.802040\pi$
$578$	537.994	+	774.013i	0.930785	+	1.33912i
$579$	245.651	+	888.063i	0.424267	+	1.53379i
$580$	−328.743	+	43.2799i	−0.566799	+	0.0746204i
$581$	−155.994	−	10.2244i	−0.268492	−	0.0175979i
$582$	265.577	−	468.684i	0.456318	−	0.805299i
$583$	580.313	+	196.990i	0.995391	+	0.337890i
$584$	350.207	+	524.121i	0.599669	+	0.897468i
$585$	63.1156	+	176.524i	0.107890	+	0.301750i
$586$	901.621	−	373.463i	1.53860	−	0.637310i
$587$	−203.682	−	26.8152i	−0.346988	−	0.0456818i	−0.0449819	−	0.998988i	$-0.514323\pi$
$587$	−203.682	−	26.8152i	−0.346988	−	0.0456818i	−0.302006	+	0.953306i	$0.597656\pi$
$588$	−695.316	+	472.753i	−1.18251	+	0.804002i
$589$	−154.955	−	76.4155i	−0.263082	−	0.129738i
$590$	414.015	+	472.094i	0.701720	+	0.800159i
$591$	551.417	−	324.319i	0.933023	−	0.548764i
$592$	−75.0333	+	37.0023i	−0.126745	+	0.0625039i
$593$	−682.597	−	282.741i	−1.15109	−	0.476798i	−0.276192	−	0.961102i	$-0.589073\pi$
$593$	−682.597	−	282.741i	−1.15109	−	0.476798i	−0.874899	+	0.484305i	$0.839073\pi$
$594$	−811.486	−	196.520i	−1.36614	−	0.330842i
$595$	−4.25452	+	180.670i	−0.00715045	+	0.303647i
$596$	−640.471	+	1109.33i	−1.07462	+	1.86129i
$597$	193.266	−	256.120i	0.323728	−	0.429012i
$598$	−82.3669	−	5.39861i	−0.137737	−	0.00902777i
$599$	−86.8460	+	324.114i	−0.144985	+	0.541091i	0.854771	+	0.519005i	$0.173697\pi$
$599$	−86.8460	+	324.114i	−0.144985	+	0.541091i	−0.999756	+	0.0220861i	$0.992969\pi$
$600$	−179.857	−	118.089i	−0.299761	−	0.196815i
$601$	−590.025	+	38.6723i	−0.981739	+	0.0643465i	−0.547812	−	0.836602i	$-0.684539\pi$
$601$	−590.025	+	38.6723i	−0.981739	+	0.0643465i	−0.433927	+	0.900948i	$0.642872\pi$
$602$	24.4176	−	122.755i	0.0405607	−	0.203912i
$603$	411.483	+	949.771i	0.682393	+	1.57508i
$604$	−90.8540	−	219.341i	−0.150421	−	0.363147i
$605$	−83.7414	+	95.4887i	−0.138415	+	0.157833i
$606$	−286.844	−	247.490i	−0.473340	−	0.408400i
$607$	367.114	+	418.613i	0.604800	+	0.689642i	0.970503	−	0.241089i	$-0.0775047\pi$
$607$	367.114	+	418.613i	0.604800	+	0.689642i	−0.365703	+	0.930732i	$0.619171\pi$
$608$	−260.170	−	69.7124i	−0.427912	−	0.114659i
$609$	−29.9922	+	90.7527i	−0.0492482	+	0.149019i
$610$	1044.26	−	801.287i	1.71190	−	1.31358i
$611$		−	10.5470i		−	0.0172619i
$612$	395.628	−	935.462i	0.646451	−	1.52853i
$613$	674.110			1.09969			0.549845	−	0.835267i	$-0.314687\pi$
$613$	674.110			1.09969			0.549845	+	0.835267i	$0.314687\pi$
$614$	483.067	+	629.545i	0.786754	+	1.02532i
$615$	−149.762	−	722.401i	−0.243516	−	1.17464i
$616$	54.9894	−	205.223i	0.0892686	−	0.333155i
$617$	−469.013	+	411.313i	−0.760151	+	0.666634i	−0.948966	−	0.315378i	$-0.897869\pi$
$617$	−469.013	+	411.313i	−0.760151	+	0.666634i	0.188815	+	0.982013i	$0.439535\pi$
$618$	−8.37034	−	24.0199i	−0.0135442	−	0.0388671i
$619$	−131.861	−	115.639i	−0.213023	−	0.186816i	0.546185	−	0.837665i	$-0.316080\pi$
$619$	−131.861	−	115.639i	−0.213023	−	0.186816i	−0.759207	+	0.650849i	$0.774413\pi$
$620$	−473.478	+	196.121i	−0.763674	+	0.316324i
$621$	132.311	−	20.6876i	0.213061	−	0.0333133i
$622$	1644.14	+	327.039i	2.64331	+	0.525786i
$623$	−28.5054	−	434.909i	−0.0457551	−	0.698088i
$624$	23.1549	+	1.33016i	0.0371072	+	0.00213166i
$625$	335.366	+	89.8610i	0.536585	+	0.143778i
$626$	−29.2760	+	446.666i	−0.0467668	+	0.713523i
$627$	239.275	−	101.380i	0.381618	−	0.161690i
$628$	654.741	+	378.015i	1.04258	+	0.601935i
$629$	−767.964	−	539.714i	−1.22093	−	0.858051i
$630$	267.700	−	160.370i	0.424921	−	0.254556i
$631$	−24.2118	+	58.4524i	−0.0383705	+	0.0926346i	−0.941903	−	0.335885i	$-0.890965\pi$
$631$	−24.2118	+	58.4524i	−0.0383705	+	0.0926346i	0.903533	+	0.428520i	$0.140965\pi$
$632$	−593.296	−	1203.08i	−0.938759	−	1.90362i
$633$	392.034	−	691.852i	0.619327	−	1.09297i
$634$	762.768	−	668.929i	1.20310	−	1.05509i
$635$	226.160	−	458.608i	0.356158	−	0.722217i
$636$	1283.82	−	94.5525i	2.01858	−	0.148667i
$637$	28.1174	−	213.573i	0.0441404	−	0.335279i
$638$	144.790	+	349.554i	0.226943	+	0.547890i
$639$	77.0365	+	65.3910i	0.120558	+	0.102333i
$640$	−731.409	+	488.712i	−1.14283	+	0.763612i
$641$	−42.6750	+	125.716i	−0.0665756	+	0.196125i	−0.975127	−	0.221649i	$-0.928856\pi$
$641$	−42.6750	+	125.716i	−0.0665756	+	0.196125i	0.908551	+	0.417774i	$0.137190\pi$
$642$	16.3668	+	2028.86i	0.0254935	+	3.16021i
$643$	82.1781	−	1253.79i	0.127804	−	1.94991i	−0.148656	−	0.988889i	$-0.547495\pi$
$643$	82.1781	−	1253.79i	0.127804	−	1.94991i	0.276460	−	0.961025i	$-0.410839\pi$
$644$	11.1913	+	85.0067i	0.0173779	+	0.131998i
$645$	45.3033	−	174.699i	0.0702376	−	0.270851i
$646$	119.560	+	492.285i	0.185078	+	0.762052i
$647$	198.274			0.306451			0.153226	−	0.988191i	$-0.451034\pi$
$647$	198.274			0.306451			0.153226	+	0.988191i	$0.451034\pi$
$648$	−687.805	+	113.234i	−1.06143	+	0.174744i
$649$	248.394	−	371.747i	0.382733	−	0.572800i
$650$	133.968	−	35.8967i	0.206105	−	0.0552257i
$651$	−8.47246	+	147.485i	−0.0130145	+	0.226552i
$652$	−248.567	+	504.043i	−0.381237	+	0.773073i
$653$	−605.619	+	205.580i	−0.927441	+	0.314824i	−0.743979	−	0.668203i	$-0.767064\pi$
$653$	−605.619	+	205.580i	−0.927441	+	0.314824i	−0.183462	+	0.983027i	$0.558730\pi$
$654$	232.696	−	574.850i	0.355804	−	0.878976i
$655$	61.0668	+	8.03960i	0.0932318	+	0.0122742i
$656$	−89.5204	−	17.8067i	−0.136464	−	0.0271444i
$657$	657.042	−	53.7231i	1.00006	−	0.0817703i
$658$	−17.2194	+	3.42515i	−0.0261693	+	0.00520539i
$659$	16.2694	+	60.7182i	0.0246880	+	0.0921368i	0.977171	−	0.212456i	$-0.0681463\pi$
$659$	16.2694	+	60.7182i	0.0246880	+	0.0921368i	−0.952483	+	0.304593i	$0.901480\pi$
$660$	241.879	−	731.896i	0.366483	−	1.10893i
$661$	129.515	+	983.764i	0.195938	+	1.48830i	0.753108	+	0.657897i	$0.228554\pi$
$661$	129.515	+	983.764i	0.195938	+	1.48830i	−0.557170	+	0.830399i	$0.688113\pi$
$662$	1452.49	−	838.597i	2.19410	−	1.26676i
$663$	111.466	+	235.136i	0.168124	+	0.354655i
$664$	−258.318	+	447.420i	−0.389033	+	0.673825i
$665$	−37.1682	+	89.7319i	−0.0558920	+	0.134935i
$666$	−79.9003	+	1618.85i	−0.119970	+	2.43071i
$667$	−42.9108	−	42.9108i	−0.0643340	−	0.0643340i
$668$	1621.63	+	550.468i	2.42759	+	0.824054i
$669$	422.841	+	80.5680i	0.632050	+	0.120431i
$670$	−1450.12	+	492.249i	−2.16436	+	0.734700i
$671$	−743.543	−	570.540i	−1.10811	−	0.850284i
$672$	31.9017	+	228.084i	0.0474728	+	0.339411i
$673$	43.4130	−	49.5030i	0.0645066	−	0.0735557i	−0.718686	−	0.695334i	$-0.755256\pi$
$673$	43.4130	−	49.5030i	0.0645066	−	0.0735557i	0.783193	+	0.621779i	$0.213590\pi$
$674$	1354.46	−	905.021i	2.00958	−	1.34276i
$675$	−199.344	+	104.377i	−0.295325	+	0.154632i
$676$	671.097	−	671.097i	0.992747	−	0.992747i
$677$	−767.439	+	378.459i	−1.13359	+	0.559024i	−0.909566	−	0.415560i	$-0.863586\pi$
$677$	−767.439	+	378.459i	−1.13359	+	0.559024i	−0.224023	+	0.974584i	$0.571919\pi$
$678$	307.991	+	232.407i	0.454264	+	0.342783i
$679$	124.153	−	71.6798i	0.182847	−	0.105567i
$680$	529.286	+	276.692i	0.778362	+	0.406900i
$681$	−458.062	+	465.512i	−0.672631	+	0.683572i
$682$	355.993	+	463.940i	0.521984	+	0.680263i
$683$	−31.2961	+	46.8379i	−0.0458215	+	0.0685767i	−0.853673	−	0.520809i	$-0.825630\pi$
$683$	−31.2961	+	46.8379i	−0.0458215	+	0.0685767i	0.807852	+	0.589386i	$0.200630\pi$
$684$	379.705	−	392.160i	0.555125	−	0.573333i
$685$	146.876	+	738.396i	0.214418	+	1.07795i
$686$	−773.100	+	50.6717i	−1.12697	+	0.0738654i
$687$	94.1798	−	6.93629i	0.137088	−	0.0100965i
$688$	−17.7142	−	13.5926i	−0.0257474	−	0.0197567i
$689$	−200.773	+	261.653i	−0.291398	+	0.379757i
$690$	14.5528	+	197.596i	0.0210911	+	0.286371i
$691$	65.8799	+	1005.13i	0.0953399	+	1.45461i	0.730863	+	0.682524i	$0.239118\pi$
$691$	65.8799	+	1005.13i	0.0953399	+	1.45461i	−0.635523	+	0.772082i	$0.719215\pi$
$692$	−202.450	+	40.2699i	−0.292558	+	0.0581935i
$693$	−159.631	−	154.562i	−0.230348	−	0.223033i
$694$	−149.106	−	99.6293i	−0.214850	−	0.143558i
$695$	−282.920	+	217.092i	−0.407079	+	0.312363i
$696$	225.151	+	221.548i	0.323493	+	0.318316i
$697$	−306.254	−	977.198i	−0.439390	−	1.40201i
$698$	65.4538	+	113.369i	0.0937734	+	0.162420i
$699$	173.543	−	229.983i	0.248273	−	0.329018i
$700$	−63.7184	−	129.208i	−0.0910263	−	0.184583i
$701$	−578.487	−	578.487i	−0.825230	−	0.825230i	0.161622	−	0.986853i	$-0.448327\pi$
$701$	−578.487	−	578.487i	−0.825230	−	0.825230i	−0.986853	+	0.161622i	$0.948327\pi$
$702$	240.524	−	379.540i	0.342626	−	0.540656i
$703$	−280.264	−	419.444i	−0.398668	−	0.596649i
$704$	728.625	+	638.987i	1.03498	+	0.907652i
$705$	−25.0722	+	3.50681i	−0.0355635	+	0.00497419i
$706$	−837.412	+	1091.34i	−1.18614	+	1.54580i
$707$	−32.4081	−	95.4711i	−0.0458388	−	0.135037i
$708$	175.783	−	922.553i	0.248281	−	1.30304i
$709$	28.6096	−	84.2812i	0.0403521	−	0.118873i	−0.924887	−	0.380242i	$-0.875841\pi$
$709$	28.6096	−	84.2812i	0.0403521	−	0.118873i	0.965239	+	0.261369i	$0.0841739\pi$
$710$	−105.712	+	105.712i	−0.148890	+	0.148890i
$711$	−1401.17	−	69.1566i	−1.97071	−	0.0972666i
$712$	−1330.73	−	551.207i	−1.86901	−	0.774167i
$713$	−81.2285	−	46.8973i	−0.113925	−	0.0657746i
$714$	347.691	−	258.342i	0.486962	−	0.361824i
$715$	98.7434	+	171.029i	0.138103	+	0.239201i
$716$	−655.166	+	86.2542i	−0.915036	+	0.120467i
$717$	−1158.54	−	382.877i	−1.61582	−	0.533998i
$718$	−1442.50	+	386.518i	−2.00906	+	0.538325i
$719$	−139.265	−	700.134i	−0.193693	−	0.973761i	−0.948250	−	0.317526i	$-0.897148\pi$
$719$	−139.265	−	700.134i	−0.193693	−	0.973761i	0.754557	−	0.656235i	$-0.227852\pi$
$720$	−4.53679	−	55.4857i	−0.00630110	−	0.0770635i
$721$	1.32061	−	6.63916i	0.00183164	−	0.00920827i
$722$	118.152	−	897.454i	0.163646	−	1.24301i
$723$	0.364451	+	0.147528i	0.000504081	+	0.000204049i
$724$	457.446	+	1347.59i	0.631832	+	1.86132i
$725$	91.4508	+	45.0985i	0.126139	+	0.0622049i
$726$	303.917	+	17.4589i	0.418619	+	0.0240480i
$727$	−220.395	−	822.525i	−0.303157	−	1.13140i	−0.934521	−	0.355909i	$-0.884171\pi$
$727$	−220.395	−	822.525i	−0.303157	−	1.13140i	0.631364	−	0.775487i	$-0.282495\pi$
$728$	95.0700	+	63.5237i	0.130591	+	0.0872579i
$729$	−246.064	+	686.217i	−0.337536	+	0.941313i
$730$			975.334i			1.33607i
$731$	38.5370	−	247.534i	0.0527181	−	0.338623i
$732$	−1905.64	−	494.173i	−2.60333	−	0.675100i
$733$	−45.3017	+	5.96408i	−0.0618031	+	0.00813654i	−0.161364	−	0.986895i	$-0.551589\pi$
$733$	−45.3017	+	5.96408i	−0.0618031	+	0.00813654i	0.0995612	+	0.995031i	$0.468256\pi$
$734$	581.076	+	38.0858i	0.791657	+	0.0518880i
$735$	−517.051	+	4.17106i	−0.703470	+	0.00567491i
$736$	−138.463	−	47.0019i	−0.188129	−	0.0638613i
$737$	605.791	+	906.630i	0.821969	+	1.23016i
$738$	−1144.33	+	1348.13i	−1.55059	+	1.82673i
$739$	−1191.31	+	493.457i	−1.61206	+	0.667736i	−0.993055	−	0.117653i	$-0.962463\pi$
$739$	−1191.31	+	493.457i	−1.61206	+	0.667736i	−0.619002	+	0.785389i	$0.712463\pi$
$740$	−1483.56	−	195.314i	−2.00481	−	0.263938i
$741$	10.2721	+	139.472i	0.0138624	+	0.188222i
$742$	492.382	+	242.816i	0.663587	+	0.327245i
$743$	−387.616	−	441.992i	−0.521691	−	0.594874i	0.429657	−	0.902992i	$-0.358634\pi$
$743$	−387.616	−	441.992i	−0.521691	−	0.594874i	−0.951348	+	0.308118i	$0.900301\pi$
$744$	424.761	+	240.689i	0.570916	+	0.323506i
$745$	−706.497	+	348.406i	−0.948318	+	0.467659i
$746$	303.017	+	125.514i	0.406189	+	0.168249i
$747$	277.667	+	463.499i	0.371709	+	0.620481i
$748$	233.387	−	1044.20i	0.312015	−	1.39599i
$749$	−269.971	+	467.603i	−0.360442	+	0.624303i
$750$	−519.476	−	1226.06i	−0.692635	−	1.63474i
$751$	323.622	+	21.2113i	0.430921	+	0.0282441i	0.279321	−	0.960198i	$-0.409891\pi$
$751$	323.622	+	21.2113i	0.430921	+	0.0282441i	0.151600	+	0.988442i	$0.451557\pi$
$752$	−0.810641	+	3.02535i	−0.00107798	+	0.00402307i
$753$	−64.4960	+	1122.72i	−0.0856521	+	1.49100i
$754$	−203.180	+	13.3171i	−0.269470	+	0.0176620i
$755$	28.4833	−	143.195i	0.0377262	−	0.189662i
$756$	−435.404	−	168.126i	−0.575931	−	0.222388i
$757$	−286.008	−	690.485i	−0.377818	−	0.912134i	−0.992374	−	0.123261i	$-0.960665\pi$
$757$	−286.008	−	690.485i	−0.377818	−	0.912134i	0.614556	−	0.788873i	$-0.289335\pi$
$758$	1535.82	−	1751.27i	2.02615	−	2.31038i
$759$	133.218	−	46.4234i	0.175518	−	0.0611639i
$760$	211.637	+	241.325i	0.278469	+	0.317533i
$761$	−339.837	−	91.0591i	−0.446566	−	0.119657i	0.0285260	−	0.999593i	$-0.490919\pi$
$761$	−339.837	−	91.0591i	−0.446566	−	0.119657i	−0.475092	+	0.879936i	$0.657585\pi$
$762$	−1200.10	+	248.795i	−1.57493	+	0.326502i
$763$	130.934	−	100.469i	0.171604	−	0.131677i
$764$		−	1433.52i		−	1.87634i
$765$	521.900	−	343.156i	0.682222	−	0.448569i
$766$	−1672.33			−2.18319
$767$	146.475	+	190.889i	0.190971	+	0.248878i
$768$	837.277	+	276.705i	1.09020	+	0.360293i
$769$	−142.269	+	530.956i	−0.185005	+	0.690450i	0.809624	+	0.586949i	$0.199671\pi$
$769$	−142.269	+	530.956i	−0.185005	+	0.690450i	−0.994629	+	0.103501i	$0.966996\pi$
$770$	247.159	−	216.752i	0.320986	−	0.281497i
$771$	−360.841	+	418.219i	−0.468017	+	0.542437i
$772$	1532.94	+	1344.35i	1.98567	+	1.74139i
$773$	906.080	−	375.310i	1.17216	−	0.485525i	0.290254	−	0.956950i	$-0.406260\pi$
$773$	906.080	−	375.310i	1.17216	−	0.485525i	0.881906	+	0.471425i	$0.156260\pi$
$774$	−396.930	+	171.968i	−0.512829	+	0.222180i
$775$	154.571	+	30.7460i	0.199446	+	0.0396723i
$776$	−30.9864	−	472.761i	−0.0399309	−	0.609229i
$777$	−236.737	+	360.565i	−0.304681	+	0.464048i
$778$	1813.95	+	486.046i	2.33155	+	0.624738i
$779$	35.9957	−	549.189i	0.0462076	−	0.704992i
$780$	331.135	+	249.871i	0.424532	+	0.320347i
$781$	92.1866	+	53.2240i	0.118037	+	0.0681485i
$782$	47.2888	+	270.924i	0.0604716	+	0.346450i
$783$	316.927	−	93.1962i	0.404760	−	0.119025i
$784$	−24.4804	+	59.1009i	−0.0312250	+	0.0753839i
$785$	205.634	+	416.984i	0.261954	+	0.531190i
$786$	−74.8450	−	127.254i	−0.0952227	−	0.161900i
$787$	310.070	−	271.924i	0.393990	−	0.345520i	−0.439315	−	0.898333i	$-0.644779\pi$
$787$	310.070	−	271.924i	0.393990	−	0.345520i	0.833306	+	0.552813i	$0.186446\pi$
$788$	626.098	−	1269.60i	0.794540	−	1.61117i
$789$	197.555	+	290.560i	0.250386	+	0.368264i
$790$	270.914	−	2057.79i	0.342929	−	2.60480i
$791$	39.2940	+	94.8642i	0.0496764	+	0.119929i
$792$	−691.449	+	247.226i	−0.873042	+	0.312154i
$793$	419.372	−	280.216i	0.528843	−	0.353361i
$794$	647.965	−	1908.84i	0.816076	−	2.40408i
$795$	688.752	+	390.277i	0.866354	+	0.490914i
$796$	46.4361	−	708.478i	0.0583368	−	0.890047i
$797$	38.3444	+	291.255i	0.0481109	+	0.365439i	0.998518	+	0.0544291i	$0.0173339\pi$
$797$	38.3444	+	291.255i	0.0481109	+	0.365439i	−0.950407	+	0.311010i	$0.899333\pi$
$798$	224.370	−	62.0640i	0.281166	−	0.0777745i
$799$	−34.1481	+	8.29349i	−0.0427386	+	0.0103798i
$800$	245.692			0.307115
$801$	−1180.13	+	936.177i	−1.47332	+	1.16876i
$802$	252.618	−	378.070i	0.314985	−	0.471409i
$803$	670.804	−	179.741i	0.835372	−	0.223837i
$804$	1914.63	+	1257.09i	2.38138	+	1.56355i
$805$	−23.3206	+	47.2895i	−0.0289697	+	0.0587447i
$806$	−298.007	+	101.160i	−0.369736	+	0.125508i
$807$	−365.939	+	51.1831i	−0.453456	+	0.0634239i
$808$	−330.346	−	43.4908i	−0.408844	−	0.0538253i
$809$	−384.942	−	76.5698i	−0.475825	−	0.0946475i	−0.0486489	−	0.998816i	$-0.515492\pi$
$809$	−384.942	−	76.5698i	−0.475825	−	0.0946475i	−0.427176	+	0.904168i	$0.640492\pi$
$810$	−982.209	−	445.575i	−1.21260	−	0.550092i
$811$	1155.23	−	229.790i	1.42446	−	0.283342i	0.578102	−	0.815964i	$-0.303793\pi$
$811$	1155.23	−	229.790i	1.42446	−	0.283342i	0.846353	+	0.532622i	$0.178793\pi$
$812$	54.7406	+	204.295i	0.0674145	+	0.251595i
$813$	113.827	+	127.702i	0.140009	+	0.157075i
$814$	222.866	+	1692.84i	0.273792	+	2.07965i
$815$	−299.307	+	172.805i	−0.367248	+	0.212031i
$816$	−13.9008	−	76.0145i	−0.0170353	−	0.0931551i
$817$	67.3177	−	116.598i	0.0823963	−	0.142715i
$818$	578.318	−	1396.18i	0.706990	−	1.70682i
$819$	106.379	−	54.6114i	0.129889	−	0.0666806i
$820$	−1154.37	−	1154.37i	−1.40777	−	1.40777i
$821$	−212.009	−	71.9673i	−0.258233	−	0.0876581i	0.189321	−	0.981915i	$-0.439371\pi$
$821$	−212.009	−	71.9673i	−0.258233	−	0.0876581i	−0.447554	+	0.894257i	$0.647705\pi$
$822$	1178.81	−	1366.26i	1.43408	−	1.66211i
$823$	−1068.68	+	362.769i	−1.29852	+	0.440789i	−0.883248	−	0.468907i	$-0.844648\pi$
$823$	−1068.68	+	362.769i	−1.29852	+	0.440789i	−0.415275	+	0.909696i	$0.636315\pi$
$824$	−17.7481	−	13.6186i	−0.0215390	−	0.0165274i
$825$	−186.888	+	145.815i	−0.226531	+	0.176745i
$826$	264.084	−	301.130i	0.319714	−	0.364564i
$827$	346.601	−	231.591i	0.419106	−	0.280038i	−0.328083	−	0.944649i	$-0.606403\pi$
$827$	346.601	−	231.591i	0.419106	−	0.280038i	0.747190	+	0.664611i	$0.231403\pi$
$828$	219.616	−	198.957i	0.265237	−	0.240287i
$829$	−1048.47	+	1048.47i	−1.26474	+	1.26474i	−0.315971	+	0.948769i	$0.602330\pi$
$829$	−1048.47	+	1048.47i	−1.26474	+	1.26474i	−0.948769	+	0.315971i	$0.897670\pi$
$830$	−716.941	+	353.556i	−0.863784	+	0.425971i
$831$	379.630	−	160.848i	0.456835	−	0.193559i
$832$	−451.672	+	260.773i	−0.542875	+	0.313429i
$833$	−713.594	+	76.9039i	−0.856655	+	0.0923216i
$834$	827.387	+	214.559i	0.992071	+	0.257265i
$835$	641.106	+	835.506i	0.767792	+	1.00061i
$836$	319.472	−	478.124i	0.382144	−	0.571919i
$837$	435.870	−	265.916i	0.520753	−	0.317701i
$838$	76.5494	+	384.840i	0.0913478	+	0.459236i
$839$	1084.53	−	71.0836i	1.29264	−	0.0847242i	0.596491	−	0.802620i	$-0.296561\pi$
$839$	1084.53	−	71.0836i	1.29264	−	0.0847242i	0.696151	+	0.717896i	$0.254895\pi$
$840$	119.398	−	247.120i	0.142140	−	0.294190i
$841$	548.448	+	420.839i	0.652138	+	0.500403i
$842$	−1110.24	+	1446.89i	−1.31857	+	1.71839i
$843$	−399.808	+	271.833i	−0.474268	+	0.322460i
$844$	−115.086	−	1755.87i	−0.136358	−	2.08042i
$845$	572.432	−	113.864i	0.677434	−	0.134750i
$846$	43.5938	+	42.2093i	0.0515293	+	0.0498928i
$847$	67.3594	+	45.0081i	0.0795271	+	0.0531383i
$848$	77.7010	−	59.6221i	0.0916285	−	0.0703091i
$849$	−547.664	+	151.492i	−0.645070	+	0.178435i
$850$	−221.566	−	405.522i	−0.260666	−	0.477085i
$851$	−136.930	−	237.171i	−0.160905	−	0.278696i
$852$	221.915	+	27.3964i	0.260463	+	0.0321554i
$853$	−614.969	−	1247.03i	−0.720948	−	1.46194i	−0.880152	−	0.474693i	$-0.842559\pi$
$853$	−614.969	−	1247.03i	−0.720948	−	1.46194i	0.159204	−	0.987246i	$-0.449107\pi$
$854$	−593.678	−	593.678i	−0.695173	−	0.695173i
$855$	328.136	−	70.7920i	0.383785	−	0.0827977i
$856$	991.361	+	1483.68i	1.15813	+	1.73327i
$857$	472.749	+	414.589i	0.551632	+	0.483768i	0.889191	−	0.457536i	$-0.151268\pi$
$857$	472.749	+	414.589i	0.551632	+	0.483768i	−0.337559	+	0.941304i	$0.609601\pi$
$858$	177.609	−	438.765i	0.207004	−	0.511381i
$859$	−197.232	+	257.038i	−0.229607	+	0.299229i	−0.893921	−	0.448224i	$-0.852057\pi$
$859$	−197.232	+	257.038i	−0.229607	+	0.299229i	0.664315	+	0.747453i	$0.268723\pi$
$860$	−128.371	−	378.169i	−0.149269	−	0.439732i
$861$	−444.380	+	154.855i	−0.516120	+	0.179855i
$862$	764.393	−	2251.83i	0.886767	−	2.61233i
$863$	332.721	−	332.721i	0.385539	−	0.385539i	−0.487554	−	0.873093i	$-0.662111\pi$
$863$	332.721	−	332.721i	0.385539	−	0.385539i	0.873093	+	0.487554i	$0.162111\pi$
$864$	585.577	−	539.156i	0.677751	−	0.624023i
$865$	−117.276	−	48.5774i	−0.135579	−	0.0561588i
$866$	−634.507	−	366.333i	−0.732687	−	0.423017i
$867$	673.650	−	545.788i	0.776990	−	0.629513i
$868$	163.448	+	283.100i	0.188304	+	0.326152i
$869$	−1465.21	+	192.899i	−1.68609	+	0.221978i
$870$	99.2131	+	478.569i	0.114038	+	0.550079i
$871$	−566.816	+	151.878i	−0.650764	+	0.174372i
$872$	−106.406	−	534.941i	−0.122026	−	0.613465i
$873$	−447.862	−	211.948i	−0.513015	−	0.242781i
$874$	−28.8353	+	144.965i	−0.0329924	+	0.165864i
$875$	46.2533	−	351.328i	0.0528609	−	0.401518i
$876$	1150.12	−	897.347i	1.31292	−	1.02437i
$877$	235.875	+	694.864i	0.268956	+	0.792319i	0.994556	+	0.104203i	$0.0332290\pi$
$877$	235.875	+	694.864i	0.268956	+	0.792319i	−0.725600	+	0.688117i	$0.758438\pi$
$878$	746.758	+	368.260i	0.850522	+	0.419431i
$879$	−403.487	−	801.819i	−0.459029	−	0.912194i
$880$	−15.1787	−	56.6478i	−0.0172486	−	0.0643725i
$881$	−462.261	−	308.873i	−0.524701	−	0.350594i	0.264840	−	0.964292i	$-0.414681\pi$
$881$	−462.261	−	308.873i	−0.524701	−	0.350594i	−0.789540	+	0.613699i	$0.789681\pi$
$882$	770.228	+	970.937i	0.873275	+	1.10084i
$883$		−	94.3963i		−	0.106904i	−0.998570	−	0.0534520i	$-0.982978\pi$
$883$		−	94.3963i		−	0.106904i	0.998570	−	0.0534520i	$-0.0170224\pi$
$884$	491.755	+	299.568i	0.556284	+	0.338877i
$885$	405.077	−	411.666i	0.457715	−	0.465160i
$886$	−2346.89	+	308.974i	−2.64886	+	0.348729i
$887$	979.699	+	64.2129i	1.10451	+	0.0723933i	0.606728	−	0.794910i	$-0.292482\pi$
$887$	979.699	+	64.2129i	1.10451	+	0.0723933i	0.497781	+	0.867303i	$0.334148\pi$
$888$	722.678	+	1228.72i	0.813826	+	1.38369i
$889$	−308.854	−	104.842i	−0.347418	−	0.117932i
$890$	−1238.17	−	1853.06i	−1.39121	−	2.08209i
$891$	−125.444	+	757.646i	−0.140790	+	0.850332i
$892$	879.998	−	364.507i	0.986545	−	0.408640i
$893$	−18.7243	−	2.46510i	−0.0209678	−	0.00276047i
$894$	1700.06	+	821.395i	1.90163	+	0.918787i
$895$	−364.471	−	179.737i	−0.407230	−	0.200824i
$896$	369.958	+	421.856i	0.412899	+	0.470822i
$897$	0.612441	+	75.9191i	0.000682766	+	0.0846367i
$898$	−947.258	+	467.136i	−1.05485	+	0.520196i
$899$	−213.758	−	88.5415i	−0.237773	−	0.0984888i
$900$	−241.971	+	435.172i	−0.268857	+	0.483525i
$901$	1005.03	+	444.296i	1.11546	+	0.493115i
$902$	−931.411	+	1613.25i	−1.03261	+	1.78853i
$903$	−114.252	−	14.1049i	−0.126525	−	0.0156201i
$904$	338.612	+	22.1938i	0.374571	+	0.0245507i
$905$	−226.510	+	845.346i	−0.250287	+	0.934084i
$906$	−312.596	+	157.303i	−0.345029	+	0.173624i
$907$	1320.68	−	86.5618i	1.45610	−	0.0954375i	0.683321	−	0.730118i	$-0.260535\pi$
$907$	1320.68	−	86.5618i	1.45610	−	0.0954375i	0.772774	+	0.634681i	$0.218868\pi$
$908$	−281.937	+	1417.39i	−0.310503	+	1.56100i
$909$	−207.642	+	279.839i	−0.228429	+	0.307854i
$910$	67.7025	+	163.448i	0.0743983	+	0.179613i
$911$	643.021	−	733.225i	0.705841	−	0.804857i	−0.282150	−	0.959370i	$-0.591048\pi$
$911$	643.021	−	733.225i	0.705841	−	0.804857i	0.987991	+	0.154513i	$0.0493810\pi$
$912$	7.77331	−	40.7963i	0.00852337	−	0.0447328i
$913$	375.288	+	427.933i	0.411049	+	0.468711i
$914$	−2705.74	−	725.002i	−2.96033	−	0.793219i
$915$	−805.561	−	903.755i	−0.880395	−	0.987710i
$916$	165.785	−	127.211i	0.180988	−	0.138877i
$917$		−	39.2882i		−	0.0428443i
$918$	−1417.97	−	480.298i	−1.54463	−	0.523200i
$919$	−1280.16			−1.39300			−0.696498	−	0.717559i	$-0.745259\pi$
$919$	−1280.16			−1.39300			−0.696498	+	0.717559i	$0.745259\pi$
$920$	106.078	+	138.244i	0.115303	+	0.150265i
$921$	544.841	−	485.644i	0.591576	−	0.527301i
$922$	91.1331	−	340.113i	0.0988428	−	0.368887i
$923$	−43.0702	+	37.7715i	−0.0466632	+	0.0409226i
$924$	−482.991	−	92.0290i	−0.522718	−	0.0995985i
$925$	345.963	+	303.402i	0.374015	+	0.328002i
$926$	215.816	−	89.3939i	0.233062	−	0.0965376i
$927$	−21.4678	+	9.30078i	−0.0231583	+	0.0100332i
$928$	−353.769	−	70.3689i	−0.381216	−	0.0758286i
$929$	42.0014	+	640.818i	0.0452114	+	0.689793i	0.958965	+	0.283524i	$0.0915037\pi$
$929$	42.0014	+	640.818i	0.0452114	+	0.689793i	−0.913754	+	0.406269i	$0.866830\pi$
$930$	339.560	+	674.783i	0.365119	+	0.725573i
$931$	−372.587	−	99.8343i	−0.400200	−	0.107233i
$932$	41.6973	−	636.177i	0.0447396	−	0.682594i
$933$	188.916	−	1530.25i	0.202482	−	1.64014i
$934$	627.382	+	362.219i	0.671715	+	0.387815i
$935$	476.093	−	454.187i	0.509191	−	0.485761i
$936$	−6.37548	−	395.131i	−0.00681141	−	0.422149i
$937$	−605.654	+	1462.18i	−0.646376	+	1.56049i	0.171556	+	0.985174i	$0.445121\pi$
$937$	−605.654	+	1462.18i	−0.646376	+	1.56049i	−0.817932	+	0.575315i	$0.804879\pi$
$938$	432.033	+	876.076i	0.460589	+	0.933982i
$939$	411.701	−	3.32120i	0.438446	−	0.00353695i
$940$	−42.1183	+	36.9368i	−0.0448067	+	0.0392944i
$941$	160.941	−	326.357i	0.171032	−	0.346819i	−0.794433	−	0.607352i	$-0.792232\pi$
$941$	160.941	−	326.357i	0.171032	−	0.346819i	0.965465	+	0.260533i	$0.0838983\pi$
$942$	484.799	−	1003.40i	0.514648	−	1.06518i
$943$	38.9989	−	296.226i	0.0413562	−	0.314132i
$944$	−27.3436	−	66.0134i	−0.0289657	−	0.0699295i
$945$	−165.192	−	234.725i	−0.174806	−	0.248386i
$946$	−378.900	+	253.173i	−0.400529	+	0.267625i
$947$	−323.378	+	952.640i	−0.341476	+	1.00596i	0.631565	+	0.775323i	$0.282413\pi$
$947$	−323.378	+	952.640i	−0.341476	+	1.00596i	−0.973041	+	0.230633i	$0.925920\pi$
$948$	−2675.81	+	1573.79i	−2.82258	+	1.66012i
$949$	−24.4435	+	372.936i	−0.0257572	+	0.392978i
$950$	−32.4162	−	246.225i	−0.0341223	−	0.259185i
$951$	−665.134	−	654.489i	−0.699405	−	0.688211i
$952$	130.914	−	357.759i	0.137515	−	0.375797i
$953$	672.178			0.705328			0.352664	−	0.935750i	$-0.385276\pi$
$953$	672.178			0.705328			0.352664	+	0.935750i	$0.385276\pi$
$954$	−277.986	−	1876.98i	−0.291389	−	1.96749i
$955$	489.771	−	732.994i	0.512849	−	0.767533i
$956$	−2608.01	+	698.813i	−2.72804	+	0.730976i
$957$	310.861	−	156.430i	0.324828	−	0.163458i
$958$	−16.7997	+	34.0664i	−0.0175362	+	0.0355599i
$959$	454.735	−	154.362i	0.474176	−	0.160961i
$960$	770.083	+	987.002i	0.802169	+	1.02813i
$961$	598.233	+	78.7589i	0.622511	+	0.0819551i
$962$	−901.228	−	179.265i	−0.936828	−	0.186347i
$963$	1859.95	−	152.079i	1.93141	−	0.157922i
$964$	0.853313	−	0.169734i	0.000885179	−	0.000176073i
$965$	324.523	+	1211.14i	0.336293	+	1.25506i
$966$	123.749	−	25.6546i	0.128104	−	0.0265575i
$967$	17.7663	+	134.948i	0.0183726	+	0.139553i	0.998173	−	0.0604258i	$-0.0192458\pi$
$967$	17.7663	+	134.948i	0.0183726	+	0.139553i	−0.979800	+	0.199979i	$0.935913\pi$
$968$	231.862	−	133.865i	0.239526	−	0.138291i
$969$	443.492	−	142.930i	0.457680	−	0.147502i
$970$	366.531	−	634.850i	0.377867	−	0.654485i
$971$	348.888	−	842.289i	0.359307	−	0.867445i	−0.636090	−	0.771615i	$-0.719449\pi$
$971$	348.888	−	842.289i	0.359307	−	0.867445i	0.995398	−	0.0958302i	$-0.0305506\pi$
$972$	378.250	+	1568.17i	0.389146	+	1.61334i
$973$	160.845	+	160.845i	0.165308	+	0.165308i
$974$	1375.89	+	467.051i	1.41262	+	0.479518i
$975$	−41.9784	−	120.463i	−0.0430547	−	0.123552i
$976$	−141.831	+	48.1453i	−0.145319	+	0.0493292i
$977$	1511.36	+	1159.71i	1.54694	+	1.18701i	0.908908	+	0.416998i	$0.136918\pi$
$977$	1511.36	+	1159.71i	1.54694	+	1.18701i	0.638031	+	0.770010i	$0.279749\pi$
$978$	767.858	+	310.824i	0.785131	+	0.317816i
$979$	−1046.30	+	1193.07i	−1.06874	+	1.21866i
$980$	−951.347	+	635.670i	−0.970762	+	0.648642i
$981$	−543.026	−	174.614i	−0.553543	−	0.177996i
$982$	−847.522	+	847.522i	−0.863057	+	0.863057i
$983$	−853.114	+	420.709i	−0.867868	+	0.427985i	−0.821008	−	0.570916i	$-0.806588\pi$
$983$	−853.114	+	420.709i	−0.867868	+	0.427985i	−0.0468599	+	0.998901i	$0.514921\pi$
$984$	−190.550	+	1543.49i	−0.193649	+	1.56858i
$985$	753.905	−	435.267i	0.765386	−	0.441896i
$986$	202.884	+	647.364i	0.205765	+	0.656556i
$987$	4.30516	+	15.5638i	0.00436187	+	0.0157688i
$988$	188.389	+	245.513i	0.190677	+	0.248495i
$989$	40.6070	−	60.7727i	0.0410587	−	0.0614486i
$990$	−1102.08	−	276.324i	−1.11321	−	0.279115i
$991$	−116.094	−	583.646i	−0.117149	−	0.588947i	−0.994109	−	0.108384i	$-0.965432\pi$
$991$	−116.094	−	583.646i	−0.117149	−	0.588947i	0.876960	−	0.480563i	$-0.159568\pi$
$992$	−556.302	+	36.4620i	−0.560789	+	0.0367560i
$993$	−867.366	−	1275.71i	−0.873480	−	1.28470i
$994$	75.6538	+	58.0512i	0.0761104	+	0.0584016i
$995$	265.799	−	346.396i	0.267135	−	0.348137i
$996$	1076.53	+	520.132i	1.08085	+	0.522221i
$997$	−62.3623	−	951.465i	−0.0625500	−	0.954328i	−0.907652	−	0.419723i	$-0.862127\pi$
$997$	−62.3623	−	951.465i	−0.0625500	−	0.954328i	0.845102	−	0.534605i	$-0.179540\pi$
$998$	−1621.64	+	322.564i	−1.62489	+	0.323211i
$999$	1490.36	−	36.0745i	1.49185	−	0.0361106i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	153.3.t.a.7.4	✓	544
9.4	even	3	inner	153.3.t.a.58.31	yes	544
17.5	odd	16	inner	153.3.t.a.124.31	yes	544
153.22	odd	48	inner	153.3.t.a.22.4	yes	544

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
153.3.t.a.7.4	✓	544	1.1	even	1	trivial
153.3.t.a.22.4	yes	544	153.22	odd	48	inner
153.3.t.a.58.31	yes	544	9.4	even	3	inner
153.3.t.a.124.31	yes	544	17.5	odd	16	inner

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:	\( N \)	\(=\)	\( 153 = 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	153.t (of order \(48\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.98557 - 2.58765i) q^{2} +(-2.23949 + 1.99617i) q^{3} +(-1.71816 + 6.41225i) q^{4} +(-3.06932 + 2.69172i) q^{5} +(9.61206 + 1.83148i) q^{6} +(1.95779 + 1.71694i) q^{7} +(7.95066 - 3.29327i) q^{8} +(1.03063 - 8.94079i) q^{9} +(13.0596 + 2.59771i) q^{10} +(-0.620087 - 9.46069i) q^{11} +(-8.95213 - 17.7899i) q^{12} +(4.92847 + 1.32058i) q^{13} +(0.555494 - 8.47520i) q^{14} +(1.50058 - 12.1549i) q^{15} +(-1.31220 - 0.757599i) q^{16} +(0.400214 - 16.9953i) q^{17} +(-25.1820 + 15.0857i) q^{18} +(3.49634 - 8.44091i) q^{19} +(-11.9864 - 24.3060i) q^{20} +(-7.81176 + 0.0630176i) q^{21} +(-23.2498 + 20.3895i) q^{22} +(2.19372 - 4.44843i) q^{23} +(-11.2315 + 23.2461i) q^{24} +(-1.08780 + 8.26266i) q^{25} +(-6.36864 - 15.3753i) q^{26} +(15.5392 + 22.0801i) q^{27} +(-14.3732 + 9.60389i) q^{28} +(3.93282 - 11.5857i) q^{29} +(-34.4323 + 20.2516i) q^{30} +(1.23680 - 18.8700i) q^{31} +(-3.84802 - 29.2286i) q^{32} +(20.2738 + 19.9493i) q^{33} +(-44.7725 + 32.7098i) q^{34} -10.6306 q^{35} +(55.5598 + 21.9703i) q^{36} +(30.6756 - 45.9092i) q^{37} +(-28.7844 + 7.71275i) q^{38} +(-13.6733 + 6.88062i) q^{39} +(-15.5385 + 31.5090i) q^{40} +(57.0422 - 19.3632i) q^{41} +(15.6739 + 20.0890i) q^{42} +(14.6101 + 1.92346i) q^{43} +(61.7297 + 12.2788i) q^{44} +(20.9028 + 30.2163i) q^{45} +(-15.8668 + 3.15610i) q^{46} +(-0.535006 - 1.99667i) q^{47} +(4.45095 - 0.922736i) q^{48} +(-5.51071 - 41.8580i) q^{49} +(23.5408 - 13.5913i) q^{50} +(33.0292 + 38.8597i) q^{51} +(-16.9358 + 29.3336i) q^{52} +(-24.7360 + 59.7181i) q^{53} +(26.2813 - 84.0519i) q^{54} +(27.3688 + 27.3688i) q^{55} +(21.2201 + 7.20325i) q^{56} +(9.01946 + 25.8826i) q^{57} +(-37.7887 + 12.8275i) q^{58} +(37.4123 + 28.7074i) q^{59} +(75.3623 + 30.5062i) q^{60} +(65.1776 - 74.3208i) q^{61} +(-51.2846 + 34.2673i) q^{62} +(17.3686 - 15.7347i) q^{63} +(-72.2786 + 72.2786i) q^{64} +(-18.6816 + 9.21277i) q^{65} +(11.3667 - 92.0725i) q^{66} +(-99.6003 + 57.5043i) q^{67} +(108.290 + 31.7668i) q^{68} +(3.96700 + 14.3413i) q^{69} +(21.1079 + 27.5083i) q^{70} +(-6.23767 + 9.33533i) q^{71} +(-21.2503 - 74.4793i) q^{72} +(14.2900 + 71.8409i) q^{73} +(-179.706 + 11.7785i) q^{74} +(-14.0575 - 20.6756i) q^{75} +(48.1179 + 36.9222i) q^{76} +(15.0294 - 19.5867i) q^{77} +(44.9541 + 21.7199i) q^{78} +(-10.1947 - 155.542i) q^{79} +(6.06680 - 1.20676i) q^{80} +(-78.8756 - 18.4293i) q^{81} +(-163.367 - 109.158i) q^{82} +(-47.6281 + 36.5464i) q^{83} +(13.0177 - 50.1992i) q^{84} +(44.5181 + 53.2412i) q^{85} +(-24.0323 - 41.6251i) q^{86} +(14.3195 + 33.7967i) q^{87} +(-36.0867 - 73.1766i) q^{88} +(-118.351 - 118.351i) q^{89} +(36.6852 - 114.086i) q^{90} +(7.38156 + 11.0473i) q^{91} +(24.7553 + 21.7098i) q^{92} +(34.8978 + 44.7279i) q^{93} +(-4.10439 + 5.34895i) q^{94} +(11.9892 + 35.3190i) q^{95} +(66.9629 + 57.7759i) q^{96} +(17.6964 - 52.1318i) q^{97} +(-97.3719 + 97.3719i) q^{98} +(-85.2252 - 4.20639i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 544 q - 8 q^{2} - 16 q^{3} - 8 q^{4} - 8 q^{5} - 16 q^{6} - 8 q^{7} - 32 q^{8} - 16 q^{9} - 32 q^{10} - 8 q^{11} + 176 q^{12} - 8 q^{13} - 8 q^{14} - 40 q^{15} - 32 q^{17} + 32 q^{18} - 32 q^{19} - 8 q^{20}+ \cdots + 448 q^{99}+O(q^{100}) \) 544 * q - 8 * q^2 - 16 * q^3 - 8 * q^4 - 8 * q^5 - 16 * q^6 - 8 * q^7 - 32 * q^8 - 16 * q^9 - 32 * q^10 - 8 * q^11 + 176 * q^12 - 8 * q^13 - 8 * q^14 - 40 * q^15 - 32 * q^17 + 32 * q^18 - 32 * q^19 - 8 * q^20 - 256 * q^21 - 8 * q^22 - 8 * q^23 + 176 * q^24 - 8 * q^25 - 32 * q^26 - 16 * q^27 - 32 * q^28 - 8 * q^29 - 16 * q^30 - 8 * q^31 - 72 * q^32 + 40 * q^34 - 64 * q^35 + 16 * q^36 - 32 * q^37 + 88 * q^38 - 192 * q^39 - 8 * q^40 - 440 * q^41 - 400 * q^42 - 248 * q^43 - 800 * q^44 - 176 * q^45 - 32 * q^46 + 112 * q^47 - 248 * q^48 - 8 * q^49 + 16 * q^51 - 16 * q^52 + 160 * q^53 - 312 * q^54 - 32 * q^55 - 488 * q^56 - 296 * q^57 - 8 * q^58 + 568 * q^59 + 2080 * q^60 - 8 * q^61 + 1120 * q^62 - 88 * q^63 - 288 * q^64 - 248 * q^65 - 24 * q^66 - 8 * q^68 - 416 * q^69 - 40 * q^70 - 32 * q^71 + 632 * q^72 - 32 * q^73 - 8 * q^74 + 752 * q^75 - 8 * q^76 - 8 * q^77 - 2304 * q^78 - 8 * q^79 - 432 * q^80 + 768 * q^81 + 352 * q^82 - 296 * q^83 - 8 * q^85 + 1184 * q^86 - 688 * q^87 - 8 * q^88 - 1184 * q^89 - 1136 * q^90 + 640 * q^91 - 2024 * q^92 - 528 * q^93 - 8 * q^94 + 472 * q^95 - 1064 * q^96 - 8 * q^97 - 848 * q^98 + 448 * q^99

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