LMFDB - Embedded newform 51.6.h.a.25.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [51,6,Mod(19,51)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(51, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([0, 7])) N = Newforms(chi, 6, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("51.19"); S:= CuspForms(chi, 6); N := Newforms(S);

Level:	$ N $	$=$	$ 51 = 3 \cdot 17 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	51.h (of order $8$, degree $4$, 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:	$8.17957481046$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			25.3
Character	$\chi$	$=$	51.25
Dual form			51.6.h.a.49.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-5.30075 + 5.30075i) q^{2} +(3.44415 - 8.31492i) q^{3} -24.1960i q^{4} +(28.6013 + 11.8471i) q^{5} +(25.8187 + 62.3319i) q^{6} +(-117.456 + 48.6520i) q^{7} +(-41.3672 - 41.3672i) q^{8} +(-57.2756 - 57.2756i) q^{9} +(-214.407 + 88.8103i) q^{10} +(-154.528 - 373.064i) q^{11} +(-201.187 - 83.3346i) q^{12} +25.4893i q^{13} +(364.715 - 880.499i) q^{14} +(197.015 - 197.015i) q^{15} +1212.83 q^{16} +(291.056 - 1155.48i) q^{17} +607.208 q^{18} +(439.251 - 439.251i) q^{19} +(286.651 - 692.037i) q^{20} +1144.20i q^{21} +(2796.64 + 1158.40i) q^{22} +(-1740.28 - 4201.42i) q^{23} +(-486.440 + 201.490i) q^{24} +(-1532.03 - 1532.03i) q^{25} +(-135.112 - 135.112i) q^{26} +(-673.508 + 278.976i) q^{27} +(1177.18 + 2841.97i) q^{28} +(-1542.51 - 638.927i) q^{29} +2088.65i q^{30} +(-59.7005 + 144.130i) q^{31} +(-5105.14 + 5105.14i) q^{32} -3634.21 q^{33} +(4582.12 + 7667.75i) q^{34} -3935.79 q^{35} +(-1385.84 + 1385.84i) q^{36} +(-4737.39 + 11437.1i) q^{37} +4656.72i q^{38} +(211.941 + 87.7889i) q^{39} +(-693.078 - 1673.24i) q^{40} +(7374.91 - 3054.79i) q^{41} +(-6065.14 - 6065.14i) q^{42} +(-2570.48 - 2570.48i) q^{43} +(-9026.64 + 3738.96i) q^{44} +(-959.612 - 2316.71i) q^{45} +(31495.5 + 13045.9i) q^{46} -6356.70i q^{47} +(4177.16 - 10084.5i) q^{48} +(-455.378 + 455.378i) q^{49} +16241.8 q^{50} +(-8605.31 - 6399.77i) q^{51} +616.737 q^{52} +(-8318.65 + 8318.65i) q^{53} +(2091.32 - 5048.88i) q^{54} -12500.8i q^{55} +(6871.44 + 2846.24i) q^{56} +(-2139.49 - 5165.18i) q^{57} +(11563.2 - 4789.65i) q^{58} +(-4108.49 - 4108.49i) q^{59} +(-4766.96 - 4766.96i) q^{60} +(4835.00 - 2002.72i) q^{61} +(-447.539 - 1080.45i) q^{62} +(9513.96 + 3940.81i) q^{63} -15311.7i q^{64} +(-301.973 + 729.027i) q^{65} +(19264.1 - 19264.1i) q^{66} -16702.6 q^{67} +(-27958.1 - 7042.39i) q^{68} -40928.2 q^{69} +(20862.7 - 20862.7i) q^{70} +(-30362.7 + 73302.1i) q^{71} +4738.67i q^{72} +(4100.27 + 1698.39i) q^{73} +(-35513.3 - 85736.8i) q^{74} +(-18015.2 + 7462.13i) q^{75} +(-10628.1 - 10628.1i) q^{76} +(36300.6 + 36300.6i) q^{77} +(-1588.79 + 658.100i) q^{78} +(-8040.19 - 19410.7i) q^{79} +(34688.4 + 14368.4i) q^{80} +6561.00i q^{81} +(-22899.9 + 55285.2i) q^{82} +(56928.1 - 56928.1i) q^{83} +27685.1 q^{84} +(22013.7 - 29600.2i) q^{85} +27251.0 q^{86} +(-10625.2 + 10625.2i) q^{87} +(-9040.22 + 21825.0i) q^{88} -53407.3i q^{89} +(17367.0 + 7193.63i) q^{90} +(-1240.10 - 2993.87i) q^{91} +(-101657. + 42107.9i) q^{92} +(992.810 + 992.810i) q^{93} +(33695.3 + 33695.3i) q^{94} +(17767.0 - 7359.32i) q^{95} +(24865.9 + 60031.7i) q^{96} +(105346. + 43635.9i) q^{97} -4827.69i q^{98} +(-12516.8 + 30218.2i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 88 q^{5} + 360 q^{6} + 1280 q^{10} - 632 q^{11} - 4256 q^{14} - 8192 q^{16} + 6248 q^{17} + 4152 q^{19} - 16384 q^{20} - 19592 q^{22} - 3608 q^{23} + 10440 q^{24} + 30384 q^{25} - 19936 q^{26} + 13624 q^{28}+ \cdots - 51192 q^{99}+O(q^{100}) $ 56 * q - 88 * q^5 + 360 * q^6 + 1280 * q^10 - 632 * q^11 - 4256 * q^14 - 8192 * q^16 + 6248 * q^17 + 4152 * q^19 - 16384 * q^20 - 19592 * q^22 - 3608 * q^23 + 10440 * q^24 + 30384 * q^25 - 19936 * q^26 + 13624 * q^28 - 23424 * q^29 + 2728 * q^31 + 67200 * q^32 + 20376 * q^33 + 11960 * q^34 + 26272 * q^35 + 3240 * q^36 + 32296 * q^37 - 22320 * q^39 - 100184 * q^40 + 6552 * q^41 - 21528 * q^42 - 38152 * q^43 - 26208 * q^44 + 31752 * q^45 + 106368 * q^46 + 9768 * q^49 + 96128 * q^50 - 62720 * q^52 + 65984 * q^53 + 29160 * q^54 - 268304 * q^56 - 28656 * q^57 - 139352 * q^58 - 67312 * q^59 - 109800 * q^60 - 307184 * q^61 + 150704 * q^62 - 696 * q^65 + 54720 * q^66 + 364272 * q^67 + 558960 * q^68 - 81864 * q^69 + 313960 * q^70 + 309808 * q^71 - 268752 * q^73 - 393712 * q^74 - 96624 * q^75 - 228552 * q^76 - 841536 * q^77 - 130824 * q^78 - 57216 * q^79 + 658528 * q^80 - 335992 * q^82 + 406240 * q^83 + 664848 * q^84 + 686840 * q^85 - 842560 * q^86 + 127224 * q^87 + 538248 * q^88 - 103680 * q^90 - 368592 * q^91 + 96752 * q^92 - 113472 * q^93 - 622576 * q^94 - 1143560 * q^95 - 375552 * q^96 - 40424 * q^97 - 51192 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/51\mathbb{Z}\right)^\times$.

$n$	$35$	$37$
$\chi(n)$	$1$	$e\left(\frac{5}{8}\right)$

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 $

$2$	−5.30075	+	5.30075i	−0.937050	+	0.937050i	−0.998133	−	0.0610830i	$-0.980545\pi$
$2$	−5.30075	+	5.30075i	−0.937050	+	0.937050i	0.0610830	+	0.998133i	$0.480545\pi$
$3$	3.44415	−	8.31492i	0.220942	−	0.533402i
$3$	3.44415	−	8.31492i	0.220942	−	0.533402i
$4$		−	24.1960i		−	0.756124i
$5$	28.6013	+	11.8471i	0.511636	+	0.211927i	0.623539	−	0.781793i	$-0.285694\pi$
$5$	28.6013	+	11.8471i	0.511636	+	0.211927i	−0.111902	+	0.993719i	$0.535694\pi$
$6$	25.8187	+	62.3319i	0.292790	+	0.706858i
$7$	−117.456	+	48.6520i	−0.906006	+	0.375280i	−0.786526	−	0.617557i	$-0.788123\pi$
$7$	−117.456	+	48.6520i	−0.906006	+	0.375280i	−0.119480	+	0.992837i	$0.538123\pi$
$8$	−41.3672	−	41.3672i	−0.228524	−	0.228524i
$9$	−57.2756	−	57.2756i	−0.235702	−	0.235702i
$10$	−214.407	+	88.8103i	−0.678014	+	0.280843i
$11$	−154.528	−	373.064i	−0.385058	−	0.929612i	−0.990970	−	0.134080i	$-0.957192\pi$
$11$	−154.528	−	373.064i	−0.385058	−	0.929612i	0.605913	−	0.795531i	$-0.292808\pi$
$12$	−201.187	−	83.3346i	−0.403318	−	0.167060i
$13$			25.4893i			0.0418311i	0.999781	+	0.0209155i	$0.00665810\pi$
$13$			25.4893i			0.0418311i	−0.999781	+	0.0209155i	$0.993342\pi$
$14$	364.715	−	880.499i	0.497317	−	1.20063i
$15$	197.015	−	197.015i	0.226084	−	0.226084i
$16$	1212.83			1.18440
$17$	291.056	−	1155.48i	0.244261	−	0.969709i
$17$	291.056	−	1155.48i	0.244261	−	0.969709i
$18$	607.208			0.441729
$19$	439.251	−	439.251i	0.279144	−	0.279144i	−0.553623	−	0.832767i	$-0.686755\pi$
$19$	439.251	−	439.251i	0.279144	−	0.279144i	0.832767	+	0.553623i	$0.186755\pi$
$20$	286.651	−	692.037i	0.160243	−	0.386861i
$21$			1144.20i			0.566181i
$22$	2796.64	+	1158.40i	1.23191	+	0.510274i
$23$	−1740.28	−	4201.42i	−0.685963	−	1.65606i	−0.752760	−	0.658295i	$-0.771278\pi$
$23$	−1740.28	−	4201.42i	−0.685963	−	1.65606i	0.0667972	−	0.997767i	$-0.478722\pi$
$24$	−486.440	+	201.490i	−0.172386	+	0.0714045i
$25$	−1532.03	−	1532.03i	−0.490248	−	0.490248i
$26$	−135.112	−	135.112i	−0.0391978	−	0.0391978i
$27$	−673.508	+	278.976i	−0.177801	+	0.0736475i
$28$	1177.18	+	2841.97i	0.283758	+	0.685053i
$29$	−1542.51	−	638.927i	−0.340590	−	0.141077i	0.205831	−	0.978588i	$-0.434010\pi$
$29$	−1542.51	−	638.927i	−0.340590	−	0.141077i	−0.546421	+	0.837511i	$0.684010\pi$
$30$			2088.65i			0.423704i
$31$	−59.7005	+	144.130i	−0.0111577	+	0.0269370i	−0.929360	−	0.369174i	$-0.879641\pi$
$31$	−59.7005	+	144.130i	−0.0111577	+	0.0269370i	0.918203	+	0.396111i	$0.129641\pi$
$32$	−5105.14	+	5105.14i	−0.881318	+	0.881318i
$33$	−3634.21			−0.580932
$34$	4582.12	+	7667.75i	0.679781	+	1.13755i
$35$	−3935.79			−0.543078
$36$	−1385.84	+	1385.84i	−0.178220	+	0.178220i
$37$	−4737.39	+	11437.1i	−0.568898	+	1.37344i	0.333586	+	0.942720i	$0.391741\pi$
$37$	−4737.39	+	11437.1i	−0.568898	+	1.37344i	−0.902484	+	0.430722i	$0.858259\pi$
$38$			4656.72i			0.523144i
$39$	211.941	+	87.7889i	0.0223128	+	0.00924225i
$40$	−693.078	−	1673.24i	−0.0684908	−	0.165351i
$41$	7374.91	−	3054.79i	0.685168	−	0.283806i	−0.0128176	−	0.999918i	$-0.504080\pi$
$41$	7374.91	−	3054.79i	0.685168	−	0.283806i	0.697985	+	0.716112i	$0.254080\pi$
$42$	−6065.14	−	6065.14i	−0.530540	−	0.530540i
$43$	−2570.48	−	2570.48i	−0.212004	−	0.212004i	0.593114	−	0.805118i	$-0.297898\pi$
$43$	−2570.48	−	2570.48i	−0.212004	−	0.212004i	−0.805118	+	0.593114i	$0.797898\pi$
$44$	−9026.64	+	3738.96i	−0.702902	+	0.291151i
$45$	−959.612	−	2316.71i	−0.0706422	−	0.170545i
$46$	31495.5	+	13045.9i	2.19459	+	0.909030i
$47$		−	6356.70i		−	0.419746i	−0.977729	−	0.209873i	$-0.932695\pi$
$47$		−	6356.70i		−	0.419746i	0.977729	−	0.209873i	$-0.0673051\pi$
$48$	4177.16	−	10084.5i	0.261684	−	0.631762i
$49$	−455.378	+	455.378i	−0.0270945	+	0.0270945i
$50$	16241.8			0.918773
$51$	−8605.31	−	6399.77i	−0.463277	−	0.344539i
$52$	616.737			0.0316295
$53$	−8318.65	+	8318.65i	−0.406783	+	0.406783i	−0.880615	−	0.473832i	$-0.842870\pi$
$53$	−8318.65	+	8318.65i	−0.406783	+	0.406783i	0.473832	+	0.880615i	$0.342870\pi$
$54$	2091.32	−	5048.88i	0.0975968	−	0.235619i
$55$		−	12500.8i		−	0.557227i
$56$	6871.44	+	2846.24i	0.292804	+	0.121284i
$57$	−2139.49	−	5165.18i	−0.0872213	−	0.210571i
$58$	11563.2	−	4789.65i	0.451346	−	0.186954i
$59$	−4108.49	−	4108.49i	−0.153657	−	0.153657i	0.626092	−	0.779749i	$-0.284653\pi$
$59$	−4108.49	−	4108.49i	−0.153657	−	0.153657i	−0.779749	+	0.626092i	$0.784653\pi$
$60$	−4766.96	−	4766.96i	−0.170948	−	0.170948i
$61$	4835.00	−	2002.72i	0.166369	−	0.0689122i	−0.297945	−	0.954583i	$-0.596301\pi$
$61$	4835.00	−	2002.72i	0.166369	−	0.0689122i	0.464314	+	0.885671i	$0.346301\pi$
$62$	−447.539	−	1080.45i	−0.0147860	−	0.0356966i
$63$	9513.96	+	3940.81i	0.302002	+	0.125093i
$64$		−	15311.7i		−	0.467277i
$65$	−301.973	+	729.027i	−0.00886512	+	0.0214023i
$66$	19264.1	−	19264.1i	0.544362	−	0.544362i
$67$	−16702.6			−0.454567			−0.227284	−	0.973829i	$-0.572984\pi$
$67$	−16702.6			−0.454567			−0.227284	+	0.973829i	$0.572984\pi$
$68$	−27958.1	−	7042.39i	−0.733221	−	0.184692i
$69$	−40928.2			−1.03490
$70$	20862.7	−	20862.7i	0.508891	−	0.508891i
$71$	−30362.7	+	73302.1i	−0.714817	+	1.72572i	−0.0272173	+	0.999630i	$0.508665\pi$
$71$	−30362.7	+	73302.1i	−0.714817	+	1.72572i	−0.687599	+	0.726090i	$0.741335\pi$
$72$			4738.67i			0.107727i
$73$	4100.27	+	1698.39i	0.0900545	+	0.0373018i	0.427256	−	0.904131i	$-0.359480\pi$
$73$	4100.27	+	1698.39i	0.0900545	+	0.0373018i	−0.337201	+	0.941433i	$0.609480\pi$
$74$	−35513.3	−	85736.8i	−0.753897	−	1.82007i
$75$	−18015.2	+	7462.13i	−0.369816	+	0.153183i
$76$	−10628.1	−	10628.1i	−0.211068	−	0.211068i
$77$	36300.6	+	36300.6i	0.697729	+	0.697729i
$78$	−1588.79	+	658.100i	−0.0295686	+	0.0122477i
$79$	−8040.19	−	19410.7i	−0.144943	−	0.349924i	0.834690	−	0.550721i	$-0.185647\pi$
$79$	−8040.19	−	19410.7i	−0.144943	−	0.349924i	−0.979633	+	0.200796i	$0.935647\pi$
$80$	34688.4	+	14368.4i	0.605982	+	0.251006i
$81$			6561.00i			0.111111i
$82$	−22899.9	+	55285.2i	−0.376096	+	0.907976i
$83$	56928.1	−	56928.1i	0.907050	−	0.907050i	−0.0889834	−	0.996033i	$-0.528362\pi$
$83$	56928.1	−	56928.1i	0.907050	−	0.907050i	0.996033	+	0.0889834i	$0.0283618\pi$
$84$	27685.1			0.428103
$85$	22013.7	−	29600.2i	0.330480	−	0.444373i
$86$	27251.0			0.397316
$87$	−10625.2	+	10625.2i	−0.150502	+	0.150502i
$88$	−9040.22	+	21825.0i	−0.124444	+	0.300433i
$89$		−	53407.3i		−	0.714703i	−0.933970	−	0.357351i	$-0.883680\pi$
$89$		−	53407.3i		−	0.714703i	0.933970	−	0.357351i	$-0.116320\pi$
$90$	17367.0	+	7193.63i	0.226005	+	0.0936143i
$91$	−1240.10	−	2993.87i	−0.0156984	−	0.0378992i
$92$	−101657.	+	42107.9i	−1.25219	+	0.518673i
$93$	992.810	+	992.810i	0.0119031	+	0.0119031i
$94$	33695.3	+	33695.3i	0.393323	+	0.393323i
$95$	17767.0	−	7359.32i	0.201978	−	0.0836621i
$96$	24865.9	+	60031.7i	0.275376	+	0.664818i
$97$	105346.	+	43635.9i	1.13682	+	0.470884i	0.870092	−	0.492889i	$-0.164059\pi$
$97$	105346.	+	43635.9i	1.13682	+	0.470884i	0.266723	+	0.963773i	$0.414059\pi$
$98$		−	4827.69i		−	0.0507778i
$99$	−12516.8	+	30218.2i	−0.128353	+	0.309871i
$100$	−37068.8	+	37068.8i	−0.370688	+	0.370688i
$101$	158332.			1.54442			0.772210	−	0.635368i	$-0.219151\pi$
$101$	158332.			1.54442			0.772210	+	0.635368i	$0.219151\pi$
$102$	79538.2	−	11691.0i	0.756964	−	0.111263i
$103$	−171642.			−1.59416			−0.797080	−	0.603874i	$-0.793623\pi$
$103$	−171642.			−1.59416			−0.797080	+	0.603874i	$0.793623\pi$
$104$	1054.42	−	1054.42i	0.00955939	−	0.00955939i
$105$	−13555.5	+	32725.8i	−0.119989	+	0.289679i
$106$		−	88190.2i		−	0.762352i
$107$	−173492.	−	71862.8i	−1.46494	−	0.606799i	−0.499242	−	0.866462i	$-0.666388\pi$
$107$	−173492.	−	71862.8i	−1.46494	−	0.606799i	−0.965699	+	0.259664i	$0.916388\pi$
$108$	6750.10	+	16296.2i	0.0556866	+	0.134439i
$109$	−190615.	+	78955.4i	−1.53671	+	0.636525i	−0.980852	−	0.194753i	$-0.937609\pi$
$109$	−190615.	+	78955.4i	−1.53671	+	0.636525i	−0.555856	+	0.831278i	$0.687609\pi$
$110$	66263.8	+	66263.8i	0.522149	+	0.522149i
$111$	78782.0	+	78782.0i	0.606903	+	0.606903i
$112$	−142454.	+	59006.4i	−1.07307	+	0.444482i
$113$	−9754.29	−	23548.9i	−0.0718621	−	0.173490i	0.883867	−	0.467738i	$-0.154931\pi$
$113$	−9754.29	−	23548.9i	−0.0718621	−	0.173490i	−0.955729	+	0.294248i	$0.904931\pi$
$114$	38720.2	+	16038.4i	0.279046	+	0.115585i
$115$		−	140783.i		−	0.992675i
$116$	−15459.5	+	37322.4i	−0.106672	+	0.257528i
$117$	1459.91	−	1459.91i	0.00985967	−	0.00985967i
$118$	43556.1			0.287968
$119$	22030.2	+	149879.i	0.142610	+	0.970229i
$120$	−16299.9			−0.103331
$121$	−1417.47	+	1417.47i	−0.00880137	+	0.00880137i
$122$	−15013.2	+	36245.1i	−0.0913217	+	0.220470i
$123$		−	71842.9i		−	0.428175i
$124$	3487.36	+	1444.51i	0.0203677	+	0.00843659i
$125$	−62690.0	−	151347.i	−0.358859	−	0.866362i
$126$	−71320.4	+	29541.9i	−0.400210	+	0.165772i
$127$	89248.0	+	89248.0i	0.491009	+	0.491009i	0.908624	−	0.417615i	$-0.137134\pi$
$127$	89248.0	+	89248.0i	0.491009	+	0.491009i	−0.417615	+	0.908624i	$0.637134\pi$
$128$	−82200.7	−	82200.7i	−0.443456	−	0.443456i
$129$	−30226.5	+	12520.2i	−0.159924	+	0.0662426i
$130$	−2263.71	−	5465.08i	−0.0117479	−	0.0283621i
$131$	287660.	+	119153.i	1.46454	+	0.606633i	0.965607	−	0.260006i	$-0.0837246\pi$
$131$	287660.	+	119153.i	1.46454	+	0.606633i	0.498935	+	0.866639i	$0.333725\pi$
$132$			87933.3i			0.439257i
$133$	−30222.3	+	72963.2i	−0.148149	+	0.357663i
$134$	88536.6	−	88536.6i	0.425952	−	0.425952i
$135$	−22568.3			−0.106577
$136$	−59839.4	+	35759.0i	−0.277421	+	0.165782i
$137$	−49988.2			−0.227544			−0.113772	−	0.993507i	$-0.536293\pi$
$137$	−49988.2			−0.227544			−0.113772	+	0.993507i	$0.536293\pi$
$138$	216951.	−	216951.i	0.969757	−	0.969757i
$139$	142550.	−	344146.i	0.625792	−	1.51080i	−0.219013	−	0.975722i	$-0.570284\pi$
$139$	142550.	−	344146.i	0.625792	−	1.51080i	0.844805	−	0.535074i	$-0.179716\pi$
$140$			95230.3i			0.410634i
$141$	−52855.4	−	21893.4i	−0.223893	−	0.0927397i
$142$	−227611.	−	549501.i	−0.947267	−	2.28690i
$143$	9509.12	−	3938.81i	0.0388866	−	0.0161074i
$144$	−69465.4	−	69465.4i	−0.279166	−	0.279166i
$145$	−36548.3	−	36548.3i	−0.144360	−	0.144360i
$146$	−30737.3	+	12731.8i	−0.119339	+	0.0494319i
$147$	2218.04	+	5354.82i	0.00846595	+	0.0204386i
$148$	276731.	+	114626.i	1.03849	+	0.430158i
$149$			172828.i			0.637747i	0.947797	+	0.318874i	$0.103305\pi$
$149$			172828.i			0.637747i	−0.947797	+	0.318874i	$0.896695\pi$
$150$	55939.1	−	135049.i	0.202996	−	0.490076i
$151$	392327.	−	392327.i	1.40025	−	1.40025i	0.601001	−	0.799248i	$-0.294769\pi$
$151$	392327.	−	392327.i	1.40025	−	1.40025i	0.799248	−	0.601001i	$-0.205231\pi$
$152$	−36341.2			−0.127582
$153$	−82851.5	+	49510.7i	−0.286136	+	0.170990i
$154$	−384841.			−1.30761
$155$	−3415.03	+	3415.03i	−0.0114173	+	0.0114173i
$156$	2124.14	−	5128.12i	0.00698829	−	0.0168712i
$157$		−	416630.i		−	1.34897i	−0.738290	−	0.674484i	$-0.764366\pi$
$157$		−	416630.i		−	1.34897i	0.738290	−	0.674484i	$-0.235634\pi$
$158$	145511.	+	60272.5i	0.463716	+	0.192077i
$159$	40518.2	+	97819.5i	0.127103	+	0.306855i
$160$	−206495.	+	85532.9i	−0.637689	+	0.264140i
$161$	408815.	+	408815.i	1.24297	+	1.24297i
$162$	−34778.2	−	34778.2i	−0.104117	−	0.104117i
$163$	−153472.	+	63570.3i	−0.452440	+	0.187407i	−0.597254	−	0.802052i	$-0.703742\pi$
$163$	−153472.	+	63570.3i	−0.452440	+	0.187407i	0.144814	+	0.989459i	$0.453742\pi$
$164$	−73913.5	−	178443.i	−0.214592	−	0.518072i
$165$	−103943.	−	43054.7i	−0.297226	−	0.123115i
$166$			603523.i			1.69990i
$167$	146162.	−	352867.i	0.405550	−	0.979084i	−0.580744	−	0.814086i	$-0.697238\pi$
$167$	146162.	−	352867.i	0.405550	−	0.979084i	0.986294	−	0.164998i	$-0.0527617\pi$
$168$	47332.5	−	47332.5i	0.129386	−	0.129386i
$169$	370643.			0.998250
$170$	40214.4	+	273593.i	0.106723	+	0.726076i
$171$	−50316.7			−0.131590
$172$	−62195.3	+	62195.3i	−0.160301	+	0.160301i
$173$	−173554.	+	418996.i	−0.440878	+	1.06437i	0.534763	+	0.845002i	$0.320401\pi$
$173$	−173554.	+	418996.i	−0.440878	+	1.06437i	−0.975641	+	0.219372i	$0.929599\pi$
$174$		−	112644.i		−	0.282055i
$175$	254482.	+	105410.i	0.628148	+	0.260187i
$176$	−187416.	−	452462.i	−0.456063	−	1.10103i
$177$	−48312.0	+	20011.5i	−0.115910	+	0.0480116i
$178$	283099.	+	283099.i	0.669712	+	0.669712i
$179$	−316565.	−	316565.i	−0.738466	−	0.738466i	0.233815	−	0.972281i	$-0.424879\pi$
$179$	−316565.	−	316565.i	−0.738466	−	0.738466i	−0.972281	+	0.233815i	$0.924879\pi$
$180$	−56055.0	+	23218.7i	−0.128954	+	0.0534143i
$181$	226100.	+	545854.i	0.512984	+	1.23845i	0.942139	+	0.335222i	$0.108811\pi$
$181$	226100.	+	545854.i	0.512984	+	1.23845i	−0.429155	+	0.903231i	$0.641189\pi$
$182$	22443.3	+	9296.31i	0.0502236	+	0.0208033i
$183$		−	47100.3i		−	0.103967i
$184$	−101810.	+	245792.i	−0.221691	+	0.535208i
$185$	−270991.	+	270991.i	−0.582138	+	0.582138i
$186$	−10525.3			−0.0223075
$187$	−476046.	+	69972.2i	−0.995508	+	0.146326i
$188$	−153806.			−0.317380
$189$	65535.0	−	65535.0i	0.133450	−	0.133450i
$190$	−55168.4	+	133188.i	−0.110868	+	0.267659i
$191$		−	275538.i		−	0.546510i	−0.961942	−	0.273255i	$-0.911900\pi$
$191$		−	275538.i		−	0.546510i	0.961942	−	0.273255i	$-0.0881002\pi$
$192$	−127316.	−	52736.0i	−0.249247	−	0.103241i
$193$	121840.	+	294147.i	0.235449	+	0.568423i	0.996802	−	0.0799142i	$-0.0254646\pi$
$193$	121840.	+	294147.i	0.235449	+	0.568423i	−0.761353	+	0.648337i	$0.775465\pi$
$194$	−789718.	+	327112.i	−1.50649	+	0.624010i
$195$	5021.76	+	5021.76i	0.00945734	+	0.00945734i
$196$	11018.3	+	11018.3i	0.0204868	+	0.0204868i
$197$	−840464.	+	348132.i	−1.54296	+	0.639113i	−0.982025	−	0.188749i	$-0.939557\pi$
$197$	−840464.	+	348132.i	−1.54296	+	0.639113i	−0.560931	+	0.827863i	$0.689557\pi$
$198$	−93830.7	−	226527.i	−0.170091	−	0.410637i
$199$	492011.	+	203798.i	0.880728	+	0.364810i	0.776779	−	0.629773i	$-0.216852\pi$
$199$	492011.	+	203798.i	0.880728	+	0.364810i	0.103949	+	0.994583i	$0.466852\pi$
$200$			126751.i			0.224067i
$201$	−57526.4	+	138881.i	−0.100433	+	0.242467i
$202$	−839279.	+	839279.i	−1.44720	+	1.44720i
$203$	212262.			0.361520
$204$	−154849.	+	208214.i	−0.260515	+	0.350295i
$205$	247122.			0.410703
$206$	909834.	−	909834.i	1.49381	−	1.49381i
$207$	−140963.	+	340315.i	−0.228654	+	0.552020i
$208$			30914.0i			0.0495447i
$209$	−231745.	−	95992.0i	−0.366982	−	0.152009i
$210$	−101617.	−	245325.i	−0.159008	−	0.383879i
$211$	381379.	−	157972.i	0.589727	−	0.244273i	−0.0678065	−	0.997698i	$-0.521600\pi$
$211$	381379.	−	157972.i	0.589727	−	0.244273i	0.657533	+	0.753426i	$0.271600\pi$
$212$	201278.	+	201278.i	0.307579	+	0.307579i
$213$	504927.	+	504927.i	0.762569	+	0.762569i
$214$	1.30057e6	−	538712.i	1.94132	−	0.804122i
$215$	−43066.6	−	103972.i	−0.0635396	−	0.153398i
$216$	39401.6	+	16320.7i	0.0574619	+	0.0238015i
$217$		−	19833.5i		−	0.0285924i
$218$	591881.	−	1.42893e6i	0.843516	−	2.03643i
$219$	28243.9	−	28243.9i	0.0397937	−	0.0397937i
$220$	−302470.			−0.421333
$221$	29452.4	+	7418.81i	0.0405640	+	0.0102177i
$222$	−835208.			−1.13740
$223$	496927.	−	496927.i	0.669161	−	0.669161i	−0.288361	−	0.957522i	$-0.593110\pi$
$223$	496927.	−	496927.i	0.669161	−	0.669161i	0.957522	+	0.288361i	$0.0931102\pi$
$224$	351256.	−	848006.i	0.467739	−	1.12922i
$225$			175495.i			0.231105i
$226$	176532.	+	73122.1i	0.229907	+	0.0952308i
$227$	−288854.	−	697355.i	−0.372061	−	0.898234i	−0.993401	−	0.114693i	$-0.963412\pi$
$227$	−288854.	−	697355.i	−0.372061	−	0.898234i	0.621340	−	0.783541i	$-0.286588\pi$
$228$	−124976.	+	51766.9i	−0.159218	+	0.0659501i
$229$	166050.	+	166050.i	0.209243	+	0.209243i	0.803946	−	0.594703i	$-0.202730\pi$
$229$	166050.	+	166050.i	0.209243	+	0.209243i	−0.594703	+	0.803946i	$0.702730\pi$
$230$	746258.	+	746258.i	0.930186	+	0.930186i
$231$	426861.	−	176812.i	0.526328	−	0.218012i
$232$	37378.6	+	90239.8i	0.0455935	+	0.110072i
$233$	−122914.	−	50912.8i	−0.148324	−	0.0614380i	0.307286	−	0.951617i	$-0.400579\pi$
$233$	−122914.	−	50912.8i	−0.148324	−	0.0614380i	−0.455611	+	0.890179i	$0.650579\pi$
$234$			15477.3i			0.0184780i
$235$	75308.2	−	181810.i	0.0889554	−	0.214757i
$236$	−99408.8	+	99408.8i	−0.116184	+	0.116184i
$237$	−189090.			−0.218675
$238$	−911250.	−	677697.i	−1.04279	−	0.775520i
$239$	−288279.			−0.326451			−0.163226	−	0.986589i	$-0.552190\pi$
$239$	−288279.			−0.326451			−0.163226	+	0.986589i	$0.552190\pi$
$240$	238944.	−	238944.i	0.267774	−	0.267774i
$241$	442358.	−	1.06795e6i	0.490604	−	1.18442i	−0.463809	−	0.885935i	$-0.653518\pi$
$241$	442358.	−	1.06795e6i	0.490604	−	1.18442i	0.954413	−	0.298488i	$-0.0964823\pi$
$242$		−	15027.3i		−	0.0164946i
$243$	54554.2	+	22597.1i	0.0592669	+	0.0245492i
$244$	−48457.8	−	116988.i	−0.0521062	−	0.125796i
$245$	−18419.3	+	7629.53i	−0.0196046	+	0.00812049i
$246$	380821.	+	380821.i	0.401221	+	0.401221i
$247$	11196.2	+	11196.2i	0.0116769	+	0.0116769i
$248$	8431.90	−	3492.61i	0.00870555	−	0.00360596i
$249$	−277283.	−	669421.i	−0.283416	−	0.684228i
$250$	1.13456e6	+	469949.i	1.14809	+	0.475555i
$251$			577525.i			0.578611i	0.957237	+	0.289305i	$0.0934243\pi$
$251$			577525.i			0.578611i	−0.957237	+	0.289305i	$0.906576\pi$
$252$	95351.8	−	230200.i	0.0945861	−	0.228351i
$253$	−1.29847e6	+	1.29847e6i	−1.27536	+	1.27536i
$254$	−946163.			−0.920199
$255$	−170305.	−	284990.i	−0.164012	−	0.274460i
$256$	1.36143e6			1.29836
$257$	−1.21456e6	+	1.21456e6i	−1.14706	+	1.14706i	−0.159930	+	0.987128i	$0.551127\pi$
$257$	−1.21456e6	+	1.21456e6i	−1.14706	+	1.14706i	−0.987128	+	0.159930i	$0.948873\pi$
$258$	93856.5	−	226590.i	0.0877840	−	0.211929i
$259$		−	1.57384e6i		−	1.45784i
$260$	17639.5	+	7306.53i	0.0161828	+	0.00670313i
$261$	51753.1	+	124943.i	0.0470257	+	0.113530i
$262$	−2.15642e6	+	893217.i	−1.94079	+	0.803903i
$263$	−248280.	−	248280.i	−0.221336	−	0.221336i	0.587725	−	0.809061i	$-0.300024\pi$
$263$	−248280.	−	248280.i	−0.221336	−	0.221336i	−0.809061	+	0.587725i	$0.800024\pi$
$264$	150337.	+	150337.i	0.132757	+	0.132757i
$265$	−336476.	+	139373.i	−0.294333	+	0.121917i
$266$	−226559.	−	546961.i	−0.196325	−	0.473971i
$267$	−444077.	−	183943.i	−0.381224	−	0.157908i
$268$			404137.i			0.343709i
$269$	475862.	−	1.14883e6i	0.400959	−	0.968000i	−0.586475	−	0.809967i	$-0.699485\pi$
$269$	475862.	−	1.14883e6i	0.400959	−	0.968000i	0.987434	−	0.158033i	$-0.0505153\pi$
$270$	119629.	−	119629.i	0.0998681	−	0.0998681i
$271$	−1.27119e6			−1.05145			−0.525724	−	0.850655i	$-0.676205\pi$
$271$	−1.27119e6			−1.05145			−0.525724	+	0.850655i	$0.676205\pi$
$272$	353001.	−	1.40140e6i	0.289303	−	1.14852i
$273$	−29164.9			−0.0236839
$274$	264975.	−	264975.i	0.213220	−	0.213220i
$275$	−334802.	+	808284.i	−0.266966	+	0.644514i
$276$			990299.i			0.782517i
$277$	−564133.	−	233672.i	−0.441756	−	0.182981i	0.150708	−	0.988578i	$-0.451845\pi$
$277$	−564133.	−	233672.i	−0.441756	−	0.182981i	−0.592464	+	0.805597i	$0.701845\pi$
$278$	1.06861e6	+	2.57985e6i	0.829292	+	2.00209i
$279$	11674.5	−	4835.74i	0.00897901	−	0.00371923i
$280$	162813.	+	162813.i	0.124106	+	0.124106i
$281$	868949.	+	868949.i	0.656490	+	0.656490i	0.954548	−	0.298057i	$-0.0963387\pi$
$281$	868949.	+	868949.i	0.656490	+	0.656490i	−0.298057	+	0.954548i	$0.596339\pi$
$282$	396225.	−	164122.i	0.296701	−	0.122898i
$283$	−410586.	−	991242.i	−0.304746	−	0.735722i	−0.999859	−	0.0168208i	$-0.994646\pi$
$283$	−410586.	−	991242.i	−0.304746	−	0.735722i	0.695113	−	0.718901i	$-0.255354\pi$
$284$	1.77361e6	+	734655.i	1.30486	+	0.540490i
$285$		−	173078.i		−	0.126220i
$286$	−29526.9	+	71284.2i	−0.0213453	+	0.0515321i
$287$	−717608.	+	717608.i	−0.514260	+	0.514260i
$288$	584800.			0.415457
$289$	−1.25043e6	−	672622.i	−0.880673	−	0.473725i
$290$	387467.			0.270545
$291$	725657.	−	725657.i	0.502341	−	0.502341i
$292$	41094.2	−	99210.1i	0.0282048	−	0.0680924i
$293$			935017.i			0.636283i	0.948043	+	0.318142i	$0.103059\pi$
$293$			935017.i			0.636283i	−0.948043	+	0.318142i	$0.896941\pi$
$294$	−40141.8	−	16627.3i	−0.0270850	−	0.0112190i
$295$	−68834.7	−	166182.i	−0.0460524	−	0.111180i
$296$	669092.	−	277147.i	0.443871	−	0.183857i
$297$	208152.	+	208152.i	0.136927	+	0.136927i
$298$	−916119.	−	916119.i	−0.597601	−	0.597601i
$299$	107091.	−	44358.6i	0.0692748	−	0.0286946i
$300$	180554.	+	435895.i	0.115825	+	0.279627i
$301$	426979.	+	176860.i	0.271638	+	0.112516i
$302$			4.15925e6i			2.62421i
$303$	545319.	−	1.31652e6i	0.341228	−	0.823797i
$304$	532734.	−	532734.i	0.330618	−	0.330618i
$305$	162014.			0.0997247
$306$	176732.	−	701619.i	0.107897	−	0.428349i
$307$	2.51962e6			1.52577			0.762885	−	0.646534i	$-0.223782\pi$
$307$	2.51962e6			1.52577			0.762885	+	0.646534i	$0.223782\pi$
$308$	878328.	−	878328.i	0.527570	−	0.527570i
$309$	−591163.	+	1.42719e6i	−0.352217	+	0.850328i
$310$		−	36204.5i		−	0.0213972i
$311$	−1.01753e6	−	421475.i	−0.596550	−	0.247099i	0.0639157	−	0.997955i	$-0.479641\pi$
$311$	−1.01753e6	−	421475.i	−0.596550	−	0.247099i	−0.660466	+	0.750856i	$0.729641\pi$
$312$	−5135.83	−	12399.0i	−0.00298692	−	0.00721107i
$313$	562802.	−	233120.i	0.324709	−	0.134499i	−0.214373	−	0.976752i	$-0.568771\pi$
$313$	562802.	−	233120.i	0.324709	−	0.134499i	0.539083	+	0.842253i	$0.318771\pi$
$314$	2.20845e6	+	2.20845e6i	1.26405	+	1.26405i
$315$	225425.	+	225425.i	0.128005	+	0.128005i
$316$	−469662.	+	194540.i	−0.264586	+	0.109595i
$317$	−998270.	−	2.41004e6i	−0.557956	−	1.34702i	−0.911382	−	0.411562i	$-0.864983\pi$
$317$	−998270.	−	2.41004e6i	−0.557956	−	1.34702i	0.353426	−	0.935462i	$-0.385017\pi$
$318$	−733294.	−	303740.i	−0.406640	−	0.168436i
$319$			674186.i			0.370939i
$320$	181399.	−	437936.i	0.0990286	−	0.239076i
$321$	−1.19507e6	+	1.19507e6i	−0.647335	+	0.647335i
$322$	−4.33405e6			−2.32946
$323$	−379700.	−	635394.i	−0.202504	−	0.338873i
$324$	158750.			0.0840138
$325$	39050.2	−	39050.2i	0.0205076	−	0.0205076i
$326$	476548.	−	1.15049e6i	0.248349	−	0.599568i
$327$			1.85688e6i			0.960319i
$328$	−431447.	−	178711.i	−0.221433	−	0.0917207i
$329$	309266.	+	746634.i	0.157522	+	0.380293i
$330$	779201.	−	322755.i	0.393880	−	0.163151i
$331$	−1.60933e6	−	1.60933e6i	−0.807373	−	0.807373i	0.176863	−	0.984236i	$-0.443405\pi$
$331$	−1.60933e6	−	1.60933e6i	−0.807373	−	0.807373i	−0.984236	+	0.176863i	$0.943405\pi$
$332$	−1.37743e6	−	1.37743e6i	−0.685842	−	0.685842i
$333$	926402.	−	383728.i	0.457814	−	0.189633i
$334$	1.09569e6	+	2.64523e6i	0.537430	+	1.29747i
$335$	−477718.	−	197877.i	−0.232573	−	0.0963350i
$336$			1.38772e6i			0.670585i
$337$	−266894.	+	644339.i	−0.128016	+	0.309058i	−0.974872	−	0.222764i	$-0.928492\pi$
$337$	−266894.	+	644339.i	−0.128016	+	0.309058i	0.846857	+	0.531821i	$0.178492\pi$
$338$	−1.96469e6	+	1.96469e6i	−0.935410	+	0.935410i
$339$	−229403.			−0.108418
$340$	−716206.	−	532643.i	−0.336001	−	0.249884i
$341$	62995.0			0.0293373
$342$	266717.	−	266717.i	0.123306	−	0.123306i
$343$	849026.	−	2.04973e6i	0.389660	−	0.940722i
$344$			212668.i			0.0968958i
$345$	−1.17060e6	−	484880.i	−0.529495	−	0.219324i
$346$	−1.30103e6	−	3.14096e6i	−0.584247	−	1.41050i
$347$	2.71112e6	−	1.12298e6i	1.20872	−	0.500667i	0.314910	−	0.949121i	$-0.398025\pi$
$347$	2.71112e6	−	1.12298e6i	1.20872	−	0.500667i	0.893806	+	0.448455i	$0.148025\pi$
$348$	257088.	+	257088.i	0.113798	+	0.113798i
$349$	1.21185e6	+	1.21185e6i	0.532580	+	0.532580i	0.921339	−	0.388759i	$-0.127096\pi$
$349$	1.21185e6	+	1.21185e6i	0.532580	+	0.532580i	−0.388759	+	0.921339i	$0.627096\pi$
$350$	−1.90770e6	+	790195.i	−0.832415	+	0.344797i
$351$	−7110.90	−	17167.2i	−0.00308075	−	0.00743759i
$352$	2.69343e6	+	1.11566e6i	1.15864	+	0.479925i
$353$			1.28175e6i			0.547477i	0.961804	+	0.273738i	$0.0882603\pi$
$353$			1.28175e6i			0.547477i	−0.961804	+	0.273738i	$0.911740\pi$
$354$	150014.	−	362166.i	0.0636243	−	0.153603i
$355$	−1.73683e6	+	1.73683e6i	−0.731452	+	0.731452i
$356$	−1.29224e6			−0.540404
$357$	1.32211e6	+	333028.i	0.549031	+	0.138296i
$358$	3.35607e6			1.38396
$359$	2.76124e6	−	2.76124e6i	1.13075	−	1.13075i	0.140699	−	0.990052i	$-0.455065\pi$
$359$	2.76124e6	−	2.76124e6i	1.13075	−	1.13075i	0.990052	−	0.140699i	$-0.0449351\pi$
$360$	−56139.3	+	135532.i	−0.0228303	+	0.0551171i
$361$			2.09022e6i			0.844157i
$362$	−4.09193e6	−	1.69493e6i	−1.64118	−	0.679801i
$363$	6904.16	+	16668.1i	0.00275007	+	0.00663927i
$364$	−72439.7	+	30005.5i	−0.0286565	+	0.0118699i
$365$	97152.4	+	97152.4i	0.0381699	+	0.0381699i
$366$	249667.	+	249667.i	0.0974224	+	0.0974224i
$367$	−3.43711e6	+	1.42370e6i	−1.33208	+	0.551764i	−0.931247	−	0.364390i	$-0.881278\pi$
$367$	−3.43711e6	+	1.42370e6i	−1.33208	+	0.551764i	−0.400829	+	0.916153i	$0.631278\pi$
$368$	−2.11066e6	−	5.09559e6i	−0.812455	−	1.96144i
$369$	−597367.	−	247438.i	−0.228389	−	0.0946019i
$370$		−	2.87292e6i		−	1.09098i
$371$	572359.	−	1.38180e6i	0.215891	−	0.521206i
$372$	24022.0	−	24022.0i	0.00900019	−	0.00900019i
$373$	1.75138e6			0.651792			0.325896	−	0.945406i	$-0.394334\pi$
$373$	1.75138e6			0.651792			0.325896	+	0.945406i	$0.394334\pi$
$374$	2.15250e6	−	2.89431e6i	0.795726	−	1.06995i
$375$	−1.47435e6			−0.541406
$376$	−262959.	+	262959.i	−0.0959220	+	0.0959220i
$377$	16285.8	−	39317.3i	0.00590140	−	0.0142472i
$378$			694770.i			0.250099i
$379$	2.45807e6	+	1.01817e6i	0.879016	+	0.364100i	0.776115	−	0.630591i	$-0.217188\pi$
$379$	2.45807e6	+	1.01817e6i	0.879016	+	0.364100i	0.102901	+	0.994692i	$0.467188\pi$
$380$	−178066.	−	429889.i	−0.0632590	−	0.152721i
$381$	1.04947e6	−	434706.i	0.370390	−	0.153420i
$382$	1.46056e6	+	1.46056e6i	0.512107	+	0.512107i
$383$	2.37938e6	+	2.37938e6i	0.828834	+	0.828834i	0.987355	−	0.158522i	$-0.0506728\pi$
$383$	2.37938e6	+	2.37938e6i	0.828834	+	0.828834i	−0.158522	+	0.987355i	$0.550673\pi$
$384$	−966603.	+	400380.i	−0.334519	+	0.138562i
$385$	608190.	+	1.46830e6i	0.209116	+	0.504851i
$386$	−2.20505e6	−	913360.i	−0.753268	−	0.312014i
$387$			294452.i			0.0999395i
$388$	1.05581e6	−	2.54896e6i	0.356047	−	0.859574i
$389$	1.55698e6	−	1.55698e6i	0.521686	−	0.521686i	−0.396395	−	0.918080i	$-0.629739\pi$
$389$	1.55698e6	−	1.55698e6i	0.521686	−	0.521686i	0.918080	+	0.396395i	$0.129739\pi$
$390$	−53238.2			−0.0177240
$391$	−5.36119e6	+	788022.i	−1.77345	+	0.260673i
$392$	37675.4			0.0123835
$393$	1.98149e6	−	1.98149e6i	0.647159	−	0.647159i
$394$	2.60973e6	−	6.30045e6i	0.846946	−	2.04471i
$395$		−	650426.i		−	0.209751i
$396$	731158.	+	302856.i	0.234301	+	0.0970505i
$397$	1.20603e6	+	2.91162e6i	0.384046	+	0.927169i	0.991174	+	0.132565i	$0.0423214\pi$
$397$	1.20603e6	+	2.91162e6i	0.384046	+	0.927169i	−0.607128	+	0.794604i	$0.707679\pi$
$398$	−3.68831e6	+	1.52775e6i	−1.16713	+	0.483441i
$399$	502592.	+	502592.i	0.158046	+	0.158046i
$400$	−1.85808e6	−	1.85808e6i	−0.580650	−	0.580650i
$401$	3.21479e6	−	1.33161e6i	0.998371	−	0.413539i	0.177172	−	0.984180i	$-0.443305\pi$
$401$	3.21479e6	−	1.33161e6i	0.998371	−	0.413539i	0.821200	+	0.570641i	$0.193305\pi$
$402$	−431241.	−	1.04111e6i	−0.133093	−	0.321315i
$403$	−3673.76	−	1521.72i	−0.00112680	−	0.000466738i
$404$		−	3.83100e6i		−	1.16777i
$405$	−77728.6	+	187653.i	−0.0235474	+	0.0568485i
$406$	−1.12515e6	+	1.12515e6i	−0.338762	+	0.338762i
$407$	4.99882e6			1.49583
$408$	91237.1	+	620719.i	0.0271345	+	0.184605i
$409$	5.31195e6			1.57017			0.785084	−	0.619389i	$-0.212620\pi$
$409$	5.31195e6			1.57017			0.785084	+	0.619389i	$0.212620\pi$
$410$	−1.30994e6	+	1.30994e6i	−0.384849	+	0.384849i
$411$	−172167.	+	415647.i	−0.0502742	+	0.121373i
$412$			4.15306e6i			1.20538i
$413$	682453.	+	282681.i	0.196878	+	0.0815497i
$414$	−1.05672e6	−	2.55114e6i	−0.303010	−	0.731531i
$415$	2.30265e6	−	953788.i	0.656308	−	0.271852i
$416$	−130126.	−	130126.i	−0.0368665	−	0.0368665i
$417$	−2.37058e6	−	2.37058e6i	−0.667597	−	0.667597i
$418$	1.73725e6	−	719594.i	0.486320	−	0.201440i
$419$	1.27320e6	+	3.07377e6i	0.354291	+	0.855334i	0.996080	+	0.0884531i	$0.0281923\pi$
$419$	1.27320e6	+	3.07377e6i	0.354291	+	0.855334i	−0.641789	+	0.766881i	$0.721808\pi$
$420$	791832.	+	327987.i	0.219033	+	0.0907265i
$421$			5.90421e6i			1.62352i	0.583993	+	0.811758i	$0.301489\pi$
$421$			5.90421e6i			1.62352i	−0.583993	+	0.811758i	$0.698511\pi$
$422$	−1.18422e6	+	2.85897e6i	−0.323707	+	0.781499i
$423$	−364084.	+	364084.i	−0.0989351	+	0.0989351i
$424$	688239.			0.185919
$425$	−2.21614e6	+	1.32432e6i	−0.595147	+	0.355650i
$426$	−5.35298e6			−1.42913
$427$	−470465.	+	470465.i	−0.124870	+	0.124870i
$428$	−1.73879e6	+	4.19781e6i	−0.458815	+	1.10768i
$429$		−	92633.4i		−	0.0243010i
$430$	779415.	+	322844.i	0.203281	+	0.0842019i
$431$	593430.	+	1.43267e6i	0.153878	+	0.371494i	0.981954	−	0.189122i	$-0.0605642\pi$
$431$	593430.	+	1.43267e6i	0.153878	+	0.371494i	−0.828076	+	0.560617i	$0.810564\pi$
$432$	−816848.	+	338350.i	−0.210587	+	0.0872281i
$433$	−4.11278e6	−	4.11278e6i	−1.05418	−	1.05418i	−0.998445	−	0.0557371i	$-0.982249\pi$
$433$	−4.11278e6	−	4.11278e6i	−1.05418	−	1.05418i	−0.0557371	−	0.998445i	$-0.517751\pi$
$434$	105133.	+	105133.i	0.0267925	+	0.0267925i
$435$	−429774.	+	178018.i	−0.108897	+	0.0451068i
$436$	1.91040e6	+	4.61212e6i	0.481292	+	1.16194i
$437$	−2.60990e6	−	1.08105e6i	−0.653762	−	0.270797i
$438$			299428.i			0.0745774i
$439$	−2.73327e6	+	6.59871e6i	−0.676896	+	1.63417i	0.0927415	+	0.995690i	$0.470437\pi$
$439$	−2.73327e6	+	6.59871e6i	−0.676896	+	1.63417i	−0.769637	+	0.638481i	$0.779563\pi$
$440$	−517125.	+	517125.i	−0.127340	+	0.127340i
$441$	52164.1			0.0127725
$442$	−195445.	+	116795.i	−0.0475850	+	0.0284360i
$443$	−2.28743e6			−0.553782			−0.276891	−	0.960901i	$-0.589304\pi$
$443$	−2.28743e6			−0.553782			−0.276891	+	0.960901i	$0.589304\pi$
$444$	1.90621e6	−	1.90621e6i	0.458894	−	0.458894i
$445$	632719.	−	1.52752e6i	0.151465	−	0.365668i
$446$			5.26818e6i			1.25407i
$447$	1.43705e6	+	595246.i	0.340176	+	0.140905i
$448$	744947.	+	1.79846e6i	0.175360	+	0.423356i
$449$	−7.15421e6	+	2.96337e6i	−1.67473	+	0.693697i	−0.999053	−	0.0434986i	$-0.986150\pi$
$449$	−7.15421e6	+	2.96337e6i	−1.67473	+	0.693697i	−0.675679	+	0.737196i	$0.736150\pi$
$450$	−930258.	−	930258.i	−0.216557	−	0.216557i
$451$	−2.27926e6	−	2.27926e6i	−0.527658	−	0.527658i
$452$	−569790.	+	236015.i	−0.131180	+	0.0543366i
$453$	−1.91093e6	−	4.61339e6i	−0.437521	−	1.05627i
$454$	5.22765e6	+	2.16536e6i	1.19033	+	0.493050i
$455$		−	100320.i		−	0.0227175i
$456$	−125164.	+	302174.i	−0.0281883	+	0.0680526i
$457$	1.78593e6	−	1.78593e6i	0.400014	−	0.400014i	−0.478224	−	0.878238i	$-0.658719\pi$
$457$	1.78593e6	−	1.78593e6i	0.400014	−	0.400014i	0.878238	+	0.478224i	$0.158719\pi$
$458$	−1.76038e6			−0.392141
$459$	126324.	+	859426.i	0.0279868	+	0.190404i
$460$	−3.40639e6			−0.750585
$461$	2.35862e6	−	2.35862e6i	0.516899	−	0.516899i	−0.399733	−	0.916632i	$-0.630897\pi$
$461$	2.35862e6	−	2.35862e6i	0.516899	−	0.516899i	0.916632	+	0.399733i	$0.130897\pi$
$462$	−1.32545e6	+	3.19992e6i	−0.288907	+	0.697484i
$463$		−	6.32126e6i		−	1.37041i	−0.728349	−	0.685206i	$-0.759712\pi$
$463$		−	6.32126e6i		−	1.37041i	0.728349	−	0.685206i	$-0.240288\pi$
$464$	−1.87079e6	−	774907.i	−0.403395	−	0.167092i
$465$	16633.8	+	40157.6i	0.00356746	+	0.00861261i
$466$	921415.	−	381662.i	0.196558	−	0.0814169i
$467$	1.87531e6	+	1.87531e6i	0.397906	+	0.397906i	0.877494	−	0.479588i	$-0.159214\pi$
$467$	1.87531e6	+	1.87531e6i	0.397906	+	0.397906i	−0.479588	+	0.877494i	$0.659214\pi$
$468$	−35324.0	−	35324.0i	−0.00745514	−	0.00745514i
$469$	1.96183e6	−	812617.i	0.411841	−	0.170590i
$470$	564540.	+	1.36292e6i	0.117883	+	0.284594i
$471$	−3.46424e6	−	1.43494e6i	−0.719542	−	0.298044i
$472$			339913.i			0.0702285i
$473$	−561743.	+	1.35617e6i	−0.115447	+	0.278715i
$474$	1.00232e6	−	1.00232e6i	0.204909	−	0.204909i
$475$	−1.34589e6			−0.273700
$476$	3.62648e6	−	533042.i	0.733614	−	0.107831i
$477$	952912.			0.191759
$478$	1.52810e6	−	1.52810e6i	0.305901	−	0.305901i
$479$	−626619.	+	1.51279e6i	−0.124786	+	0.301259i	−0.973910	−	0.226933i	$-0.927130\pi$
$479$	−626619.	+	1.51279e6i	−0.124786	+	0.301259i	0.849125	+	0.528193i	$0.177130\pi$
$480$			2.01157e6i			0.398504i
$481$	−291522.	−	120753.i	−0.0574525	−	0.0237976i
$482$	3.31609e6	+	8.00575e6i	0.650143	+	1.56958i
$483$	4.80728e6	−	1.99124e6i	0.937630	−	0.388379i
$484$	34297.1	+	34297.1i	0.00665493	+	0.00665493i
$485$	2.49609e6	+	2.49609e6i	0.481843	+	0.481843i
$486$	−408960.	+	169397.i	−0.0785398	+	0.0325323i
$487$	1.73540e6	+	4.18962e6i	0.331571	+	0.800483i	0.998468	+	0.0553333i	$0.0176221\pi$
$487$	1.73540e6	+	4.18962e6i	0.331571	+	0.800483i	−0.666897	+	0.745150i	$0.732378\pi$
$488$	−282858.	−	117164.i	−0.0537673	−	0.0222712i
$489$			1.49505e6i			0.282738i
$490$	57194.0	−	138078.i	0.0107612	−	0.0259798i
$491$	3.26303e6	−	3.26303e6i	0.610825	−	0.610825i	−0.332336	−	0.943161i	$-0.607837\pi$
$491$	3.26303e6	−	3.26303e6i	0.610825	−	0.610825i	0.943161	+	0.332336i	$0.107837\pi$
$492$	−1.73831e6			−0.323753
$493$	−1.18723e6	+	1.59638e6i	−0.219997	+	0.295814i
$494$	−118696.			−0.0218836
$495$	−715993.	+	715993.i	−0.131340	+	0.131340i
$496$	−72406.4	+	174804.i	−0.0132152	+	0.0319042i
$497$		−	1.00870e7i		−	1.83177i
$498$	5.01824e6	+	2.07862e6i	0.906731	+	0.375580i
$499$	−2.50293e6	−	6.04260e6i	−0.449984	−	1.08636i	−0.972328	−	0.233622i	$-0.924942\pi$
$499$	−2.50293e6	−	6.04260e6i	−0.449984	−	1.08636i	0.522344	−	0.852735i	$-0.325058\pi$
$500$	−3.66199e6	+	1.51685e6i	−0.655077	+	0.271342i
$501$	−2.43066e6	−	2.43066e6i	−0.432642	−	0.432642i
$502$	−3.06132e6	−	3.06132e6i	−0.542187	−	0.542187i
$503$	272332.	−	112804.i	0.0479932	−	0.0198794i	−0.358558	−	0.933508i	$-0.616731\pi$
$503$	272332.	−	112804.i	0.0479932	−	0.0198794i	0.406551	+	0.913628i	$0.366731\pi$
$504$	−230546.	−	556587.i	−0.0404279	−	0.0976015i
$505$	4.52851e6	+	1.87577e6i	0.790181	+	0.327304i
$506$		−	1.37658e7i		−	2.39015i
$507$	1.27655e6	−	3.08187e6i	0.220556	−	0.532469i
$508$	2.15944e6	−	2.15944e6i	0.371264	−	0.371264i
$509$	8.41470e6			1.43961			0.719804	−	0.694177i	$-0.244232\pi$
$509$	8.41470e6			1.43961			0.719804	+	0.694177i	$0.244232\pi$
$510$	2.41340e6	+	607915.i	0.410870	+	0.103495i
$511$	−564233.			−0.0955886
$512$	−4.58617e6	+	4.58617e6i	−0.773170	+	0.773170i
$513$	−173298.	+	418379.i	−0.0290738	+	0.0701902i
$514$		−	1.28761e7i		−	2.14970i
$515$	−4.90920e6	−	2.03346e6i	−0.815630	−	0.337845i
$516$	302939.	+	731359.i	0.0500877	+	0.120922i
$517$	−2.37145e6	+	982288.i	−0.390201	+	0.161627i
$518$	8.34253e6	+	8.34253e6i	1.36607	+	1.36607i
$519$	2.88617e6	+	2.88617e6i	0.470331	+	0.470331i
$520$	42649.6	−	17666.0i	0.00691682	−	0.00286504i
$521$	−4.54898e6	−	1.09822e7i	−0.734209	−	1.77254i	−0.628030	−	0.778189i	$-0.716138\pi$
$521$	−4.54898e6	−	1.09822e7i	−0.734209	−	1.77254i	−0.106179	−	0.994347i	$-0.533862\pi$
$522$	−936622.	−	387962.i	−0.150449	−	0.0623179i
$523$		−	4.53928e6i		−	0.725659i	−0.931856	−	0.362829i	$-0.881811\pi$
$523$		−	4.53928e6i		−	0.725659i	0.931856	−	0.362829i	$-0.118189\pi$
$524$	2.88302e6	−	6.96022e6i	0.458690	−	1.10738i
$525$	1.75295e6	−	1.75295e6i	0.277569	−	0.277569i
$526$	2.63214e6			0.414805
$527$	149163.	+	110933.i	0.0233957	+	0.0173994i
$528$	−4.40767e6			−0.688056
$529$	−1.00721e7	+	1.00721e7i	−1.56489	+	1.56489i
$530$	1.04479e6	−	2.52236e6i	0.161563	−	0.390047i
$531$			470632.i			0.0724345i
$532$	1.76541e6	+	731259.i	0.270438	+	0.112019i
$533$	77864.2	+	187981.i	0.0118719	+	0.0286613i
$534$	3.32898e6	−	1.37891e6i	0.505194	−	0.209258i
$535$	−4.11074e6	−	4.11074e6i	−0.620920	−	0.620920i
$536$	690942.	+	690942.i	0.103879	+	0.103879i
$537$	−3.72251e6	+	1.54192e6i	−0.557058	+	0.230741i
$538$	3.56725e6	+	8.61210e6i	0.531346	+	1.28278i
$539$	240254.	+	99516.3i	0.0356203	+	0.0147544i
$540$			546062.i			0.0805856i
$541$	741591.	−	1.79036e6i	0.108936	−	0.262995i	−0.860006	−	0.510285i	$-0.829540\pi$
$541$	741591.	−	1.79036e6i	0.108936	−	0.262995i	0.968942	+	0.247290i	$0.0795400\pi$
$542$	6.73827e6	−	6.73827e6i	0.985258	−	0.985258i
$543$	5.31745e6			0.773934
$544$	4.41302e6	+	7.38479e6i	0.639351	+	1.06989i
$545$	−6.38724e6			−0.921133
$546$	154596.	−	154596.i	0.0221930	−	0.0221930i
$547$	−2.18296e6	+	5.27012e6i	−0.311944	+	0.753100i	0.687689	+	0.726006i	$0.258625\pi$
$547$	−2.18296e6	+	5.27012e6i	−0.311944	+	0.753100i	−0.999633	+	0.0270941i	$0.991375\pi$
$548$			1.20951e6i			0.172052i
$549$	−391635.	−	162221.i	−0.0554563	−	0.0229707i
$550$	−2.50981e6	−	6.05922e6i	−0.353781	−	0.854102i
$551$	−958196.	+	396898.i	−0.134454	+	0.0556929i
$552$	1.69309e6	+	1.69309e6i	0.236500	+	0.236500i
$553$	1.88874e6	+	1.88874e6i	0.262639	+	0.262639i
$554$	4.22897e6	−	1.75170e6i	0.585410	−	0.242485i
$555$	1.31993e6	+	3.18660e6i	0.181895	+	0.439133i
$556$	−8.32695e6	−	3.44913e6i	−1.14235	−	0.473176i
$557$		−	5.97239e6i		−	0.815662i	−0.913058	−	0.407831i	$-0.866285\pi$
$557$		−	5.97239e6i		−	0.815662i	0.913058	−	0.407831i	$-0.133715\pi$
$558$	−36250.7	+	87516.8i	−0.00492868	+	0.0118989i
$559$	65519.7	−	65519.7i	0.00886834	−	0.00886834i
$560$	−4.77343e6			−0.643221
$561$	−1.05776e6	+	4.19927e6i	−0.141899	+	0.563336i
$562$	−9.21217e6			−1.23033
$563$	−8.79829e6	+	8.79829e6i	−1.16984	+	1.16984i	−0.187596	+	0.982246i	$0.560069\pi$
$563$	−8.79829e6	+	8.79829e6i	−1.16984	+	1.16984i	−0.982246	+	0.187596i	$0.939931\pi$
$564$	−529733.	+	1.27889e6i	−0.0701227	+	0.169291i
$565$		−	789091.i		−	0.103993i
$566$	7.43074e6	+	3.07791e6i	0.974970	+	0.403846i
$567$	−319206.	−	770631.i	−0.0416978	−	0.100667i
$568$	4.28832e6	−	1.77628e6i	0.557721	−	0.231015i
$569$	−3.33875e6	−	3.33875e6i	−0.432318	−	0.432318i	0.457098	−	0.889416i	$-0.348889\pi$
$569$	−3.33875e6	−	3.33875e6i	−0.432318	−	0.432318i	−0.889416	+	0.457098i	$0.848889\pi$
$570$	917442.	+	917442.i	0.118275	+	0.118275i
$571$	−9.78385e6	+	4.05260e6i	−1.25580	+	0.520168i	−0.908617	−	0.417631i	$-0.862861\pi$
$571$	−9.78385e6	+	4.05260e6i	−1.25580	+	0.520168i	−0.347180	+	0.937799i	$0.612861\pi$
$572$	−95303.3	−	230082.i	−0.0121792	−	0.0294031i
$573$	−2.29107e6	−	948994.i	−0.291509	−	0.120747i
$574$		−	7.60772e6i		−	0.963773i
$575$	−3.77052e6	+	9.10284e6i	−0.475589	+	1.14817i
$576$	−876990.	+	876990.i	−0.110138	+	0.110138i
$577$	7.37879e6			0.922668			0.461334	−	0.887227i	$-0.347371\pi$
$577$	7.37879e6			0.922668			0.461334	+	0.887227i	$0.347371\pi$
$578$	1.01936e7	−	3.06282e6i	1.26914	−	0.381330i
$579$	2.86545e6			0.355219
$580$	−884322.	+	884322.i	−0.109154	+	0.109154i
$581$	−3.91690e6	+	9.45622e6i	−0.481395	+	1.16219i
$582$			7.69306e6i			0.941438i
$583$	4.38885e6	+	1.81792e6i	0.534785	+	0.221515i
$584$	−99359.3	−	239875.i	−0.0120553	−	0.0291040i
$585$	59051.2	−	24459.8i	0.00713410	−	0.00295504i
$586$	−4.95629e6	−	4.95629e6i	−0.596229	−	0.596229i
$587$	4.52240e6	+	4.52240e6i	0.541718	+	0.541718i	0.924032	−	0.382314i	$-0.124873\pi$
$587$	4.52240e6	+	4.52240e6i	0.541718	+	0.541718i	−0.382314	+	0.924032i	$0.624873\pi$
$588$	129565.	−	53667.6i	0.0154541	−	0.00640131i
$589$	37085.6	+	89532.6i	0.00440471	+	0.0106339i
$590$	1.24576e6	+	516012.i	0.147335	+	0.0610281i
$591$			8.18741e6i			0.964223i
$592$	−5.74563e6	+	1.38712e7i	−0.673803	+	1.62671i
$593$	2.46890e6	−	2.46890e6i	0.288315	−	0.288315i	−0.548099	−	0.836414i	$-0.684648\pi$
$593$	2.46890e6	−	2.46890e6i	0.288315	−	0.288315i	0.836414	+	0.548099i	$0.184648\pi$
$594$	−2.20672e6			−0.256615
$595$	−1.14554e6	+	4.54774e6i	−0.132653	+	0.526627i
$596$	4.18174e6			0.482216
$597$	3.38912e6	−	3.38912e6i	0.389180	−	0.389180i
$598$	−332529.	+	802797.i	−0.0380257	+	0.0918021i
$599$		−	1.17174e7i		−	1.33434i	−0.744907	−	0.667169i	$-0.767506\pi$
$599$		−	1.17174e7i		−	1.33434i	0.744907	−	0.667169i	$-0.232494\pi$
$600$	1.05393e6	+	436550.i	0.119518	+	0.0495058i
$601$	−5.99743e6	−	1.44791e7i	−0.677297	−	1.63514i	−0.768919	−	0.639346i	$-0.779205\pi$
$601$	−5.99743e6	−	1.44791e7i	−0.677297	−	1.63514i	0.0916215	−	0.995794i	$-0.470795\pi$
$602$	−3.20080e6	+	1.32582e6i	−0.359971	+	0.149105i
$603$	956655.	+	956655.i	0.107143	+	0.107143i
$604$	−9.49272e6	−	9.49272e6i	−1.05876	−	1.05876i
$605$	−57334.4	+	23748.7i	−0.00636835	+	0.00263786i
$606$	4.08793e6	+	9.86914e6i	0.452191	+	1.09169i
$607$	1.85079e6	+	766622.i	0.203885	+	0.0844519i	0.482289	−	0.876012i	$-0.339805\pi$
$607$	1.85079e6	+	766622.i	0.203885	+	0.0844519i	−0.278404	+	0.960464i	$0.589805\pi$
$608$			4.48487e6i			0.492029i
$609$	731063.	−	1.76494e6i	0.0798751	−	0.192836i
$610$	−858796.	+	858796.i	−0.0934470	+	0.0934470i
$611$	162027.			0.0175584
$612$	1.19796e6	+	2.00467e6i	0.129289	+	0.216354i
$613$	1.13354e7			1.21838			0.609192	−	0.793023i	$-0.291494\pi$
$613$	1.13354e7			1.21838			0.609192	+	0.793023i	$0.291494\pi$
$614$	−1.33559e7	+	1.33559e7i	−1.42972	+	1.42972i
$615$	851127.	−	2.05480e6i	0.0907416	−	0.219070i
$616$		−	3.00331e6i		−	0.318896i
$617$	−7.99911e6	−	3.31334e6i	−0.845919	−	0.350391i	−0.0827347	−	0.996572i	$-0.526365\pi$
$617$	−7.99911e6	−	3.31334e6i	−0.845919	−	0.350391i	−0.763185	+	0.646180i	$0.776365\pi$
$618$	−4.43159e6	−	1.06988e7i	−0.466754	−	1.12684i
$619$	1.58525e6	−	656633.i	0.166292	−	0.0688805i	−0.297984	−	0.954571i	$-0.596314\pi$
$619$	1.58525e6	−	656633.i	0.166292	−	0.0688805i	0.464277	+	0.885690i	$0.346314\pi$
$620$	82630.0	+	82630.0i	0.00863293	+	0.00863293i
$621$	2.34419e6	+	2.34419e6i	0.243929	+	0.243929i
$622$	7.62782e6	−	3.15955e6i	0.790541	−	0.327453i
$623$	2.59837e6	+	6.27302e6i	0.268214	+	0.647525i
$624$	257048.	+	106473.i	0.0264273	+	0.0109465i
$625$			1.69923e6i			0.174002i
$626$	−1.74756e6	+	4.21899e6i	−0.178237	+	0.430301i
$627$	−1.59633e6	+	1.59633e6i	−0.162164	+	0.162164i
$628$	−1.00808e7			−1.01999
$629$	1.18365e7	+	8.80281e6i	1.19288	+	0.887145i
$630$	−2.38984e6			−0.239893
$631$	−2.62853e6	+	2.62853e6i	−0.262808	+	0.262808i	−0.826194	−	0.563386i	$-0.809498\pi$
$631$	−2.62853e6	+	2.62853e6i	−0.262808	+	0.262808i	0.563386	+	0.826194i	$0.309498\pi$
$632$	−470368.	+	1.13557e6i	−0.0468430	+	0.113089i
$633$		−	3.71522e6i		−	0.368532i
$634$	1.80666e7	+	7.48343e6i	1.78506	+	0.739397i
$635$	1.49529e6	+	3.60994e6i	0.147160	+	0.355276i
$636$	2.36684e6	−	980377.i	0.232020	−	0.0961059i
$637$	−11607.2	−	11607.2i	−0.00113339	−	0.00113339i
$638$	−3.57369e6	−	3.57369e6i	−0.347588	−	0.347588i
$639$	5.93747e6	−	2.45938e6i	0.575240	−	0.238272i
$640$	−1.37721e6	−	3.32489e6i	−0.132908	−	0.320868i
$641$	−9.22050e6	−	3.81926e6i	−0.886358	−	0.367142i	−0.107399	−	0.994216i	$-0.534252\pi$
$641$	−9.22050e6	−	3.81926e6i	−0.886358	−	0.367142i	−0.778959	+	0.627074i	$0.784252\pi$
$642$		−	1.26695e7i		−	1.21317i
$643$	1.15590e6	−	2.79059e6i	0.110254	−	0.266176i	−0.859117	−	0.511780i	$-0.828986\pi$
$643$	1.15590e6	−	2.79059e6i	0.110254	−	0.266176i	0.969370	+	0.245604i	$0.0789863\pi$
$644$	9.89167e6	−	9.89167e6i	0.939842	−	0.939842i
$645$	−1.01285e6			−0.0958615
$646$	5.38076e6	+	1.35537e6i	0.507297	+	0.127784i
$647$	4.36066e6			0.409536			0.204768	−	0.978811i	$-0.434356\pi$
$647$	4.36066e6			0.409536			0.204768	+	0.978811i	$0.434356\pi$
$648$	271410.	−	271410.i	0.0253915	−	0.0253915i
$649$	−897851.	+	2.16760e6i	−0.0836744	+	0.202008i
$650$			413991.i			0.0384333i
$651$	−164914.	−	68309.6i	−0.0152512	−	0.00631727i
$652$	1.53814e6	+	3.71341e6i	0.141703	+	0.342101i
$653$	−1.24552e6	+	515910.i	−0.114305	+	0.0473469i	−0.439103	−	0.898437i	$-0.644704\pi$
$653$	−1.24552e6	+	515910.i	−0.114305	+	0.0473469i	0.324798	+	0.945783i	$0.394704\pi$
$654$	−9.84289e6	−	9.84289e6i	−0.899867	−	0.899867i
$655$	6.81586e6	+	6.81586e6i	0.620751	+	0.620751i
$656$	8.94448e6	−	3.70492e6i	0.811513	−	0.336140i
$657$	−137569.	−	332122.i	−0.0124339	−	0.0300182i
$658$	−5.59706e6	−	2.31838e6i	−0.503959	−	0.208747i
$659$			1.27675e7i			1.14523i	0.819824	+	0.572616i	$0.194071\pi$
$659$			1.27675e7i			1.14523i	−0.819824	+	0.572616i	$0.805929\pi$
$660$	−1.04175e6	+	2.51501e6i	−0.0930903	+	0.224740i
$661$	6.22534e6	−	6.22534e6i	0.554191	−	0.554191i	−0.373457	−	0.927648i	$-0.621828\pi$
$661$	6.22534e6	−	6.22534e6i	0.554191	−	0.554191i	0.927648	+	0.373457i	$0.121828\pi$
$662$	1.70613e7			1.51310
$663$	163125.	−	219343.i	0.0144124	−	0.0193794i
$664$	−4.70991e6			−0.414565
$665$	−1.72880e6	+	1.72880e6i	−0.151597	+	0.151597i
$666$	−2.87658e6	+	6.94468e6i	−0.251299	+	0.606690i
$667$			7.59263e6i			0.660812i
$668$	−8.53796e6	−	3.53654e6i	−0.740309	−	0.306646i
$669$	−2.42042e6	−	5.84340e6i	−0.209086	−	0.504778i
$670$	3.58116e6	−	1.48337e6i	0.308203	−	0.127662i
$671$	−1.49429e6	−	1.49429e6i	−0.128123	−	0.128123i
$672$	−5.84132e6	−	5.84132e6i	−0.498986	−	0.498986i
$673$	5.46031e6	−	2.26174e6i	0.464708	−	0.192488i	−0.138029	−	0.990428i	$-0.544077\pi$
$673$	5.46031e6	−	2.26174e6i	0.464708	−	0.192488i	0.602737	+	0.797940i	$0.294077\pi$
$674$	−2.00074e6	−	4.83022e6i	−0.169645	−	0.409560i
$675$	1.45923e6	+	604433.i	0.123272	+	0.0510609i
$676$		−	8.96807e6i		−	0.754801i
$677$	2.65022e6	−	6.39821e6i	0.222234	−	0.536521i	−0.772959	−	0.634457i	$-0.781224\pi$
$677$	2.65022e6	−	6.39821e6i	0.222234	−	0.536521i	0.995193	+	0.0979357i	$0.0312239\pi$
$678$	1.21601e6	−	1.21601e6i	0.101593	−	0.101593i
$679$	−1.44966e7			−1.20668
$680$	−2.13512e6	+	313834.i	−0.177072	+	0.0260272i
$681$	−6.79331e6			−0.561324
$682$	−333921.	+	333921.i	−0.0274905	+	0.0274905i
$683$	−4.06138e6	+	9.80504e6i	−0.333136	+	0.804262i	0.665204	+	0.746662i	$0.268345\pi$
$683$	−4.06138e6	+	9.80504e6i	−0.333136	+	0.804262i	−0.998340	+	0.0575998i	$0.981655\pi$
$684$			1.21746e6i			0.0994982i
$685$	−1.42973e6	−	592213.i	−0.116420	−	0.0482227i
$686$	6.36464e6	+	1.53656e7i	0.516373	+	1.24663i
$687$	1.95259e6	−	808790.i	0.157841	−	0.0653799i
$688$	−3.11755e6	−	3.11755e6i	−0.251097	−	0.251097i
$689$	−212036.	−	212036.i	−0.0170162	−	0.0170162i
$690$	8.77530e6	−	3.63485e6i	0.701680	−	0.290646i
$691$	−1.99236e6	−	4.80998e6i	−0.158735	−	0.383220i	0.824424	−	0.565973i	$-0.191499\pi$
$691$	−1.99236e6	−	4.80998e6i	−0.158735	−	0.383220i	−0.983159	+	0.182753i	$0.941499\pi$
$692$	1.01380e7	+	4.19930e6i	0.804799	+	0.333359i
$693$		−	4.15828e6i		−	0.328913i
$694$	−8.41831e6	+	2.03236e7i	−0.663477	+	1.60178i
$695$	8.15424e6	−	8.15424e6i	0.640356	−	0.640356i
$696$	879074.			0.0687864
$697$	−1.38324e6	−	9.41070e6i	−0.107849	−	0.733736i
$698$	−1.28474e7			−0.998109
$699$	−846671.	+	846671.i	−0.0655423	+	0.0655423i
$700$	2.55050e6	−	6.15744e6i	0.196734	−	0.474958i
$701$		−	1.45297e7i		−	1.11677i	−0.829583	−	0.558384i	$-0.811422\pi$
$701$		−	1.45297e7i		−	1.11677i	0.829583	−	0.558384i	$-0.188578\pi$
$702$	128692.	+	53306.1i	0.00985621	+	0.00408258i
$703$	2.94284e6	+	7.10464e6i	0.224584	+	0.542193i
$704$	−5.71226e6	+	2.36610e6i	−0.434387	+	0.179929i
$705$	−1.25236e6	−	1.25236e6i	−0.0948980	−	0.0948980i
$706$	−6.79423e6	−	6.79423e6i	−0.513013	−	0.513013i
$707$	−1.85971e7	+	7.70317e6i	−1.39925	+	0.579590i
$708$	484197.	+	1.16895e6i	0.0363027	+	0.0876425i
$709$	−1.54917e7	−	6.41688e6i	−1.15740	−	0.479412i	−0.280393	−	0.959885i	$-0.590465\pi$
$709$	−1.54917e7	−	6.41688e6i	−1.15740	−	0.479412i	−0.877009	+	0.480474i	$0.840465\pi$
$710$		−	1.84130e7i		−	1.37081i
$711$	−651256.	+	1.57227e6i	−0.0483145	+	0.116641i
$712$	−2.20931e6	+	2.20931e6i	−0.163327	+	0.163327i
$713$	709446.			0.0522631
$714$	−8.77347e6	+	5.24288e6i	−0.644060	+	0.384879i
$715$	318637.			0.0233094
$716$	−7.65960e6	+	7.65960e6i	−0.558372	+	0.558372i
$717$	−992877.	+	2.39702e6i	−0.0721269	+	0.174130i
$718$			2.92733e7i			2.11914i
$719$	−1.13421e7	−	4.69804e6i	−0.818221	−	0.338918i	−0.0659920	−	0.997820i	$-0.521021\pi$
$719$	−1.13421e7	−	4.69804e6i	−0.818221	−	0.338918i	−0.752229	+	0.658902i	$0.771021\pi$
$720$	−1.16384e6	−	2.80976e6i	−0.0836687	−	0.201994i
$721$	2.01605e7	−	8.35075e6i	1.44432	−	0.598256i
$722$	−1.10797e7	−	1.10797e7i	−0.791017	−	0.791017i
$723$	−7.35634e6	−	7.35634e6i	−0.523379	−	0.523379i
$724$	1.32075e7	−	5.47071e6i	0.936425	−	0.387880i
$725$	1.38431e6	+	3.34201e6i	0.0978109	+	0.236136i
$726$	−124951.	−	51756.4i	−0.00879828	−	0.00364437i
$727$		−	2.08162e7i		−	1.46071i	−0.683067	−	0.730356i	$-0.739354\pi$
$727$		−	2.08162e7i		−	1.46071i	0.683067	−	0.730356i	$-0.260646\pi$
$728$	−72548.6	+	175148.i	−0.00507342	+	0.0122483i
$729$	375786.	−	375786.i	0.0261891	−	0.0261891i
$730$	−1.02996e6			−0.0715342
$731$	−3.71831e6	+	2.22200e6i	−0.257366	+	0.153798i
$732$	−1.13964e6			−0.0786121
$733$	1.83125e7	−	1.83125e7i	1.25889	−	1.25889i	0.307271	−	0.951622i	$-0.400584\pi$
$733$	1.83125e7	−	1.83125e7i	1.25889	−	1.25889i	0.951622	−	0.307271i	$-0.0994157\pi$
$734$	1.06726e7	−	2.57660e7i	0.731191	−	1.76525i
$735$			179432.i			0.0122513i
$736$	3.03332e7	+	1.25644e7i	2.06407	+	0.854965i
$737$	2.58103e6	+	6.23115e6i	0.175035	+	0.422571i
$738$	4.47810e6	−	1.85489e6i	0.302659	−	0.125365i
$739$	4.26126e6	+	4.26126e6i	0.287030	+	0.287030i	0.835905	−	0.548875i	$-0.184944\pi$
$739$	4.26126e6	+	4.26126e6i	0.287030	+	0.287030i	−0.548875	+	0.835905i	$0.684944\pi$
$740$	6.55690e6	+	6.55690e6i	0.440169	+	0.440169i
$741$	131657.	−	54533.9i	0.00880840	−	0.00364856i
$742$	4.29063e6	+	1.03585e7i	0.286096	+	0.690696i
$743$	−8.45193e6	−	3.50090e6i	−0.561673	−	0.232653i	0.0837382	−	0.996488i	$-0.473314\pi$
$743$	−8.45193e6	−	3.50090e6i	−0.561673	−	0.232653i	−0.645411	+	0.763835i	$0.723314\pi$
$744$		−	82139.6i		−	0.00544027i
$745$	−2.04750e6	+	4.94311e6i	−0.135156	+	0.326295i
$746$	−9.28365e6	+	9.28365e6i	−0.610762	+	0.610762i
$747$	−6.52118e6			−0.427587
$748$	1.69305e6	+	1.15184e7i	0.110641	+	0.752727i
$749$	2.38740e7			1.55497
$750$	7.81518e6	−	7.81518e6i	0.507324	−	0.507324i
$751$	−1.68343e6	+	4.06415e6i	−0.108917	+	0.262948i	−0.968935	−	0.247315i	$-0.920452\pi$
$751$	−1.68343e6	+	4.06415e6i	−0.108917	+	0.262948i	0.860019	+	0.510263i	$0.170452\pi$
$752$		−	7.70957e6i		−	0.497148i
$753$	4.80207e6	+	1.98908e6i	0.308632	+	0.127840i
$754$	122085.	+	294738.i	0.00782047	+	0.0188803i
$755$	1.58690e7	−	6.57315e6i	1.01317	−	0.419668i
$756$	−1.58568e6	−	1.58568e6i	−0.100905	−	0.100905i
$757$	1.29579e7	+	1.29579e7i	0.821852	+	0.821852i	0.986373	−	0.164522i	$-0.0526080\pi$
$757$	1.29579e7	+	1.29579e7i	0.821852	+	0.821852i	−0.164522	+	0.986373i	$0.552608\pi$
$758$	−1.84267e7	+	7.63258e6i	−1.16486	+	0.482501i
$759$	6.32457e6	+	1.52689e7i	0.398498	+	0.962060i
$760$	−1.03941e6	−	430536.i	−0.0652756	−	0.0270381i
$761$		−	3.33247e6i		−	0.208595i	−0.994546	−	0.104298i	$-0.966741\pi$
$761$		−	3.33247e6i		−	0.208595i	0.994546	−	0.104298i	$-0.0332595\pi$
$762$	−3.25873e6	+	7.86727e6i	−0.203311	+	0.490836i
$763$	1.85476e7	−	1.85476e7i	1.15339	−	1.15339i
$764$	−6.66690e6			−0.413229
$765$	−2.95622e6	+	434524.i	−0.182635	+	0.0268448i
$766$	−2.52250e7			−1.55332
$767$	104722.	−	104722.i	0.00642762	−	0.00642762i
$768$	4.68896e6	−	1.13202e7i	0.286862	−	0.692547i
$769$			2.50567e7i			1.52795i	0.645247	+	0.763974i	$0.276755\pi$
$769$			2.50567e7i			1.52795i	−0.645247	+	0.763974i	$0.723245\pi$
$770$	−1.10070e7	−	4.55924e6i	−0.669023	−	0.277118i
$771$	5.91583e6	+	1.42821e7i	0.358410	+	0.865277i
$772$	7.11718e6	−	2.94803e6i	0.429799	−	0.178028i
$773$	−1.63596e6	−	1.63596e6i	−0.0984748	−	0.0984748i	0.656153	−	0.754628i	$-0.272183\pi$
$773$	−1.63596e6	−	1.63596e6i	−0.0984748	−	0.0984748i	−0.754628	+	0.656153i	$0.772183\pi$
$774$	−1.56082e6	−	1.56082e6i	−0.0936483	−	0.0936483i
$775$	312273.	−	129348.i	0.0186759	−	0.00773579i
$776$	−2.55279e6	−	6.16298e6i	−0.152181	−	0.367398i
$777$	−1.30863e7	−	5.42054e6i	−0.777617	−	0.322099i
$778$			1.65063e7i			0.977691i
$779$	1.89761e6	−	4.58125e6i	0.112038	−	0.270483i
$780$	121506.	−	121506.i	0.00715093	−	0.00715093i
$781$	3.20382e7			1.87949
$782$	2.42413e7	−	3.25955e7i	1.41755	−	1.90608i
$783$	1.21714e6			0.0709471
$784$	−552294.	+	552294.i	−0.0320908	+	0.0320908i
$785$	4.93584e6	−	1.19162e7i	0.285882	−	0.690181i
$786$			2.10068e7i			1.21284i
$787$	−1.97738e7	−	8.19057e6i	−1.13803	−	0.471387i	−0.267526	−	0.963551i	$-0.586206\pi$
$787$	−1.97738e7	−	8.19057e6i	−1.13803	−	0.471387i	−0.870503	+	0.492164i	$0.836206\pi$
$788$	8.42338e6	+	2.03358e7i	0.483249	+	1.16667i
$789$	−2.91954e6	+	1.20931e6i	−0.166963	+	0.0691585i
$790$	3.44775e6	+	3.44775e6i	0.196548	+	0.196548i
$791$	2.29141e6	+	2.29141e6i	0.130215	+	0.130215i
$792$	1.76783e6	−	732258.i	0.100144	−	0.0414812i
$793$	51047.9	+	123241.i	0.00288267	+	0.00695939i
$794$	−2.18267e7	−	9.04091e6i	−1.22867	−	0.508933i
$795$			3.27779e6i			0.183935i
$796$	4.93108e6	−	1.19047e7i	0.275841	−	0.665940i
$797$	−3.75499e6	+	3.75499e6i	−0.209393	+	0.209393i	−0.804010	−	0.594616i	$-0.797304\pi$
$797$	−3.75499e6	+	3.75499e6i	−0.209393	+	0.209393i	0.594616	+	0.804010i	$0.297304\pi$
$798$	−5.32823e6			−0.296194
$799$	−7.34506e6	−	1.85016e6i	−0.407032	−	0.102528i
$800$	1.56424e7			0.864129
$801$	−3.05894e6	+	3.05894e6i	−0.168457	+	0.168457i
$802$	−9.98228e6	+	2.40994e7i	−0.548017	+	1.32303i
$803$		−	1.79211e6i		−	0.0980791i
$804$	3.36036e6	+	1.39191e6i	0.183335	+	0.0759400i
$805$	6.84940e6	+	1.65359e7i	0.372531	+	0.899370i
$806$	27540.0	−	11407.4i	0.00149323	−	0.000618515i
$807$	−7.91350e6	−	7.91350e6i	−0.427745	−	0.427745i
$808$	−6.54976e6	−	6.54976e6i	−0.352937	−	0.352937i
$809$	−2.26847e7	+	9.39630e6i	−1.21860	+	0.504761i	−0.896964	−	0.442103i	$-0.854233\pi$
$809$	−2.26847e7	+	9.39630e6i	−1.21860	+	0.504761i	−0.321636	+	0.946864i	$0.604233\pi$
$810$	−582684.	−	1.40672e6i	−0.0312048	−	0.0753349i
$811$	−8.16513e6	−	3.38211e6i	−0.435924	−	0.180566i	0.153919	−	0.988083i	$-0.450811\pi$
$811$	−8.16513e6	−	3.38211e6i	−0.435924	−	0.180566i	−0.589843	+	0.807518i	$0.700811\pi$
$812$		−	5.13589e6i		−	0.273354i
$813$	−4.37817e6	+	1.05698e7i	−0.232309	+	0.560844i
$814$	−2.64975e7	+	2.64975e7i	−1.40166	+	1.40166i
$815$	−5.14263e6			−0.271201
$816$	−1.04367e7	−	7.76181e6i	−0.548706	−	0.408073i
$817$	−2.25817e6			−0.118359
$818$	−2.81574e7	+	2.81574e7i	−1.47133	+	1.47133i
$819$	−100448.	+	242504.i	−0.00523279	+	0.0126331i
$820$		−	5.97937e6i		−	0.310542i
$821$	643910.	+	266716.i	0.0333401	+	0.0138099i	0.399291	−	0.916824i	$-0.369256\pi$
$821$	643910.	+	266716.i	0.0333401	+	0.0138099i	−0.365951	+	0.930634i	$0.619256\pi$
$822$	−1.29063e6	−	3.11586e6i	−0.0666227	−	0.160842i
$823$	−1.32618e7	+	5.49321e6i	−0.682499	+	0.282700i	−0.696871	−	0.717196i	$-0.745425\pi$
$823$	−1.32618e7	+	5.49321e6i	−0.682499	+	0.282700i	0.0143719	+	0.999897i	$0.495425\pi$
$824$	7.10037e6	+	7.10037e6i	0.364303	+	0.364303i
$825$	5.56771e6	+	5.56771e6i	0.284801	+	0.284801i
$826$	−5.11594e6	+	2.11909e6i	−0.260901	+	0.108069i
$827$	−357776.	−	863748.i	−0.0181906	−	0.0439161i	0.914523	−	0.404533i	$-0.132566\pi$
$827$	−357776.	−	863748.i	−0.0181906	−	0.0439161i	−0.932714	+	0.360617i	$0.882566\pi$
$828$	8.23425e6	+	3.41074e6i	0.417396	+	0.172891i
$829$			2.12689e7i			1.07488i	0.843303	+	0.537439i	$0.180608\pi$
$829$			2.12689e7i			1.07488i	−0.843303	+	0.537439i	$0.819392\pi$
$830$	−7.14998e6	+	1.72616e7i	−0.360254	+	0.869731i
$831$	−3.88592e6	+	3.88592e6i	−0.195205	+	0.195205i
$832$	390285.			0.0195467
$833$	393641.	+	658722.i	0.0196557	+	0.0328920i
$834$	2.51317e7			1.25114
$835$	8.36088e6	−	8.36088e6i	0.414988	−	0.414988i
$836$	−2.32262e6	+	5.60730e6i	−0.114938	+	0.277484i
$837$		−	113728.i		−	0.00561116i
$838$	−2.30422e7	−	9.54438e6i	−1.13348	−	0.469502i
$839$	1.21762e7	+	2.93959e7i	0.597182	+	1.44172i	0.876441	+	0.481508i	$0.159911\pi$
$839$	1.21762e7	+	2.93959e7i	0.597182	+	1.44172i	−0.279260	+	0.960216i	$0.590089\pi$
$840$	1.91453e6	−	793023.i	0.0936188	−	0.0387782i
$841$	−1.25325e7	−	1.25325e7i	−0.611008	−	0.611008i
$842$	−3.12968e7	−	3.12968e7i	−1.52132	−	1.52132i
$843$	1.02180e7	−	4.23245e6i	0.495220	−	0.205127i
$844$	−3.82229e6	−	9.22784e6i	−0.184700	−	0.445906i
$845$	1.06009e7	+	4.39103e6i	0.510741	+	0.211556i
$846$		−	3.85984e6i		−	0.185414i
$847$	97528.0	−	235454.i	0.00467112	−	0.0112771i
$848$	−1.00891e7	+	1.00891e7i	−0.481794	+	0.481794i
$849$	−9.65621e6			−0.459767
$850$	4.72727e6	−	1.87671e7i	0.224421	−	0.890943i
$851$	5.62963e7			2.66475
$852$	1.22172e7	−	1.22172e7i	0.576597	−	0.576597i
$853$	18612.4	−	44934.2i	0.000875848	−	0.00211449i	−0.923441	−	0.383740i	$-0.874636\pi$
$853$	18612.4	−	44934.2i	0.000875848	−	0.00211449i	0.924317	+	0.381626i	$0.124636\pi$
$854$		−	4.98764e6i		−	0.234019i
$855$	−1.43913e6	−	596105.i	−0.0673261	−	0.0278874i
$856$	4.20412e6	+	1.01497e7i	0.196106	+	0.473442i
$857$	−1.25058e7	+	5.18007e6i	−0.581647	+	0.240926i	−0.654052	−	0.756449i	$-0.726932\pi$
$857$	−1.25058e7	+	5.18007e6i	−0.581647	+	0.240926i	0.0724054	+	0.997375i	$0.476932\pi$
$858$	491027.	+	491027.i	0.0227713	+	0.0227713i
$859$	−9.75152e6	−	9.75152e6i	−0.450910	−	0.450910i	0.444747	−	0.895656i	$-0.353294\pi$
$859$	−9.75152e6	−	9.75152e6i	−0.450910	−	0.450910i	−0.895656	+	0.444747i	$0.853294\pi$
$860$	−2.51570e6	+	1.04204e6i	−0.115988	+	0.0480438i
$861$	3.49530e6	+	8.43840e6i	0.160685	+	0.387929i
$862$	−1.07398e7	−	4.44859e6i	−0.492300	−	0.203917i
$863$			5.44154e6i			0.248711i	0.992238	+	0.124355i	$0.0396863\pi$
$863$			5.44154e6i			0.248711i	−0.992238	+	0.124355i	$0.960314\pi$
$864$	2.01414e6	−	4.86257e6i	0.0917921	−	0.221606i
$865$	−9.92774e6	+	9.92774e6i	−0.451139	+	0.451139i
$866$	4.36017e7			1.97564
$867$	−9.89946e6	+	8.08061e6i	−0.447264	+	0.365087i
$868$	−479891.			−0.0216194
$869$	−5.99901e6	+	5.99901e6i	−0.269482	+	0.269482i
$870$	1.33450e6	−	3.22176e6i	0.0597749	−	0.144309i
$871$		−	425738.i		−	0.0190150i
$872$	1.11514e7	+	4.61906e6i	0.496636	+	0.205713i
$873$	−3.53451e6	−	8.53305e6i	−0.156961	−	0.378938i
$874$	1.95648e7	−	8.10401e6i	0.866358	−	0.358857i
$875$	1.47267e7	+	1.47267e7i	0.650257	+	0.650257i
$876$	−683389.	−	683389.i	−0.0300890	−	0.0300890i
$877$	1.31262e7	−	5.43704e6i	0.576287	−	0.238706i	−0.0754516	−	0.997149i	$-0.524040\pi$
$877$	1.31262e7	−	5.43704e6i	0.576287	−	0.238706i	0.651739	+	0.758443i	$0.274040\pi$
$878$	−2.04897e7	−	4.94665e7i	−0.897015	−	2.16558i
$879$	7.77459e6	+	3.22034e6i	0.339395	+	0.140582i
$880$		−	1.51613e7i		−	0.659980i
$881$	7.65781e6	−	1.84876e7i	0.332403	−	0.802492i	−0.665998	−	0.745954i	$-0.731994\pi$
$881$	7.65781e6	−	1.84876e7i	0.332403	−	0.802492i	0.998400	−	0.0565376i	$-0.0180061\pi$
$882$	−276509.	+	276509.i	−0.0119685	+	0.0119685i
$883$	4.38429e6			0.189233			0.0946167	−	0.995514i	$-0.469837\pi$
$883$	4.38429e6			0.189233			0.0946167	+	0.995514i	$0.469837\pi$
$884$	179505.	−	712630.i	0.00772586	−	0.0306714i
$885$	−1.61886e6			−0.0694788
$886$	1.21251e7	−	1.21251e7i	0.518922	−	0.518922i
$887$	1.56446e7	−	3.77694e7i	0.667659	−	1.61187i	−0.117857	−	0.993031i	$-0.537602\pi$
$887$	1.56446e7	−	3.77694e7i	0.667659	−	1.61187i	0.785516	−	0.618841i	$-0.212398\pi$
$888$		−	6.51798e6i		−	0.277384i
$889$	−1.48248e7	−	6.14065e6i	−0.629123	−	0.260591i
$890$	4.74312e6	+	1.14509e7i	0.200719	+	0.484579i
$891$	2.44767e6	−	1.01386e6i	0.103290	−	0.0427842i
$892$	−1.20236e7	−	1.20236e7i	−0.505969	−	0.505969i
$893$	−2.79218e6	−	2.79218e6i	−0.117170	−	0.117170i
$894$	−1.07727e7	+	4.46220e6i	−0.450797	+	0.186726i
$895$	−5.30382e6	−	1.28046e7i	−0.221325	−	0.534327i
$896$	1.36542e7	+	5.65576e6i	0.568194	+	0.235354i
$897$		−	1.04323e6i		−	0.0432912i
$898$	2.22146e7	−	5.36308e7i	0.919279	−	2.21934i
$899$	184177.	−	184177.i	0.00760039	−	0.00760039i
$900$	4.24628e6			0.174744
$901$	7.19087e6	+	1.20333e7i	0.295100	+	0.493823i
$902$	2.41636e7			0.988884
$903$	2.94116e6	−	2.94116e6i	0.120033	−	0.120033i
$904$	−570647.	+	1.37766e6i	−0.0232245	+	0.0560689i
$905$			1.82908e7i			0.742353i
$906$	3.45838e7	+	1.43251e7i	1.39976	+	0.579798i
$907$	−3.34957e6	−	8.08659e6i	−0.135198	−	0.326398i	0.841752	−	0.539864i	$-0.181525\pi$
$907$	−3.34957e6	−	8.08659e6i	−0.135198	−	0.326398i	−0.976950	+	0.213467i	$0.931525\pi$
$908$	−1.68732e7	+	6.98910e6i	−0.679176	+	0.281324i
$909$	−9.06857e6	−	9.06857e6i	−0.364023	−	0.364023i
$910$	531774.	+	531774.i	0.0212874	+	0.0212874i
$911$	3.07877e6	−	1.27527e6i	0.122908	−	0.0509103i	−0.320382	−	0.947289i	$-0.603811\pi$
$911$	3.07877e6	−	1.27527e6i	0.122908	−	0.0509103i	0.443290	+	0.896378i	$0.353811\pi$
$912$	−2.59482e6	−	6.26446e6i	−0.103305	−	0.249400i
$913$	−3.00348e7	−	1.24408e7i	−1.19247	−	0.493937i
$914$			1.89336e7i			0.749666i
$915$	558000.	−	1.34713e6i	0.0220334	−	0.0531934i
$916$	4.01774e6	−	4.01774e6i	0.158213	−	0.158213i
$917$	−3.95846e7			−1.55454
$918$	−5.22521e6	−	3.88599e6i	−0.204643	−	0.152193i
$919$	−1.42966e7			−0.558397			−0.279199	−	0.960233i	$-0.590069\pi$
$919$	−1.42966e7			−0.558397			−0.279199	+	0.960233i	$0.590069\pi$
$920$	−5.82382e6	+	5.82382e6i	−0.226850	+	0.226850i
$921$	8.67796e6	−	2.09504e7i	0.337107	−	0.813849i
$922$			2.50049e7i			0.968720i
$923$	−1.86842e6	−	773923.i	−0.0721887	−	0.0299015i
$924$	−4.27813e6	−	1.03283e7i	−0.164844	−	0.397970i
$925$	2.47797e7	−	1.02641e7i	0.952229	−	0.394426i
$926$	3.35074e7	+	3.35074e7i	1.28414	+	1.28414i
$927$	9.83093e6	+	9.83093e6i	0.375747	+	0.375747i
$928$	1.11365e7	−	4.61290e6i	0.424502	−	0.175834i
$929$	4.84501e6	+	1.16969e7i	0.184185	+	0.444663i	0.988821	−	0.149106i	$-0.0476395\pi$
$929$	4.84501e6	+	1.16969e7i	0.184185	+	0.444663i	−0.804636	+	0.593768i	$0.797640\pi$
$930$	−301037.	−	124694.i	−0.0114133	−	0.00472756i
$931$			400050.i			0.0151266i
$932$	−1.23188e6	+	2.97403e6i	−0.0464548	+	0.112152i
$933$	−7.00906e6	+	7.00906e6i	−0.263606	+	0.263606i
$934$	−1.98811e7			−0.745715
$935$	−1.44445e7	−	3.63845e6i	−0.540348	−	0.136109i
$936$	−120785.			−0.00450634
$937$	2.71753e7	−	2.71753e7i	1.01117	−	1.01117i	0.0112356	−	0.999937i	$-0.496424\pi$
$937$	2.71753e7	−	2.71753e7i	1.01117	−	1.01117i	0.999937	−	0.0112356i	$-0.00357647\pi$
$938$	−6.09170e6	+	1.47067e7i	−0.226064	+	0.545767i
$939$		−	5.48255e6i		−	0.202917i
$940$	−4.39907e6	−	1.82215e6i	−0.162383	−	0.0672613i
$941$	−2.93197e6	−	7.07840e6i	−0.107941	−	0.260592i	0.860675	−	0.509155i	$-0.170042\pi$
$941$	−2.93197e6	−	7.07840e6i	−0.107941	−	0.260592i	−0.968616	+	0.248563i	$0.920042\pi$
$942$	2.59693e7	−	1.07569e7i	0.953529	−	0.394965i
$943$	−2.56689e7	−	2.56689e7i	−0.939999	−	0.939999i
$944$	−4.98288e6	−	4.98288e6i	−0.181991	−	0.181991i
$945$	2.65079e6	−	1.09799e6i	0.0965596	−	0.0399963i
$946$	−4.21105e6	−	1.01664e7i	−0.152990	−	0.369350i
$947$	3.58094e7	+	1.48327e7i	1.29754	+	0.537460i	0.921225	−	0.389030i	$-0.127190\pi$
$947$	3.58094e7	+	1.48327e7i	1.29754	+	0.537460i	0.376319	+	0.926490i	$0.377190\pi$
$948$			4.57522e6i			0.165345i
$949$	−43290.7	+	104513.i	−0.00156037	+	0.00376708i
$950$	7.13421e6	−	7.13421e6i	0.256470	−	0.256470i
$951$	−2.34774e7			−0.841782
$952$	5.28876e6	−	7.11142e6i	0.189131	−	0.254310i
$953$	−5.55761e6			−0.198224			−0.0991120	−	0.995076i	$-0.531600\pi$
$953$	−5.55761e6			−0.198224			−0.0991120	+	0.995076i	$0.531600\pi$
$954$	−5.05115e6	+	5.05115e6i	−0.179688	+	0.179688i
$955$	3.26431e6	−	7.88075e6i	0.115820	−	0.279614i
$956$			6.97519e6i			0.246838i
$957$	5.60580e6	+	2.32200e6i	0.197860	+	0.0819562i
$958$	−4.69739e6	−	1.13405e7i	−0.165365	−	0.399225i
$959$	5.87143e6	−	2.43202e6i	0.206157	−	0.0853928i
$960$	−3.01664e6	−	3.01664e6i	−0.105644	−	0.105644i
$961$	2.02267e7	+	2.02267e7i	0.706506	+	0.706506i
$962$	2.18537e6	−	905209.i	0.0761354	−	0.0315363i
$963$	5.82088e6	+	1.40529e7i	0.202266	+	0.488314i
$964$	−2.58400e7	−	1.07033e7i	−0.895571	−	0.370958i
$965$			9.85646e6i			0.340724i
$966$	−1.49271e7	+	3.60373e7i	−0.514676	+	1.24254i
$967$	4.28051e6	−	4.28051e6i	0.147207	−	0.147207i	−0.629662	−	0.776869i	$-0.716807\pi$
$967$	4.28051e6	−	4.28051e6i	0.147207	−	0.147207i	0.776869	+	0.629662i	$0.216807\pi$
$968$	117274.			0.00402265
$969$	−6.59099e6	+	968785.i	−0.225497	+	0.0331450i
$970$	−2.64623e7			−0.903022
$971$	−3.39538e7	+	3.39538e7i	−1.15569	+	1.15569i	−0.170295	+	0.985393i	$0.554472\pi$
$971$	−3.39538e7	+	3.39538e7i	−1.15569	+	1.15569i	−0.985393	+	0.170295i	$0.945528\pi$
$972$	546758.	−	1.31999e6i	0.0185622	−	0.0448131i
$973$			4.73574e7i			1.60364i
$974$	−3.14071e7	−	1.30092e7i	−1.06079	−	0.439394i
$975$	−190204.	−	459194.i	−0.00640780	−	0.0154698i
$976$	5.86402e6	−	2.42896e6i	0.197047	−	0.0816197i
$977$	−1.18015e7	−	1.18015e7i	−0.395549	−	0.395549i	0.481111	−	0.876660i	$-0.340234\pi$
$977$	−1.18015e7	−	1.18015e7i	−0.395549	−	0.395549i	−0.876660	+	0.481111i	$0.840234\pi$
$978$	−7.92491e6	−	7.92491e6i	−0.264940	−	0.264940i
$979$	−1.99243e7	+	8.25293e6i	−0.664396	+	0.275202i
$980$	184604.	+	445673.i	0.00614010	+	0.0148235i
$981$	1.54398e7	+	6.39539e6i	0.512236	+	0.212175i
$982$			3.45930e7i			1.14475i
$983$	1.34053e7	−	3.23634e7i	0.442480	−	1.06824i	−0.532595	−	0.846370i	$-0.678783\pi$
$983$	1.34053e7	−	3.23634e7i	0.442480	−	1.06824i	0.975076	−	0.221872i	$-0.0712168\pi$
$984$	−2.97194e6	+	2.97194e6i	−0.0978481	+	0.0978481i
$985$	−2.81627e7			−0.924878
$986$	−2.16881e6	−	1.47552e7i	−0.0710443	−	0.483340i
$987$	7.27336e6			0.237652
$988$	270902.	−	270902.i	0.00882918	−	0.00882918i
$989$	−6.32630e6	+	1.52731e7i	−0.205665	+	0.496518i
$990$		−	7.59061e6i		−	0.246144i
$991$	−5.16119e7	−	2.13784e7i	−1.66942	−	0.691497i	−0.670684	−	0.741743i	$-0.733999\pi$
$991$	−5.16119e7	−	2.13784e7i	−1.66942	−	0.691497i	−0.998737	+	0.0502462i	$0.983999\pi$
$992$	−431023.	−	1.04058e6i	−0.0139066	−	0.0335736i
$993$	−1.89242e7	+	7.83865e6i	−0.609037	+	0.252272i
$994$	5.34687e7	+	5.34687e7i	1.71646	+	1.71646i
$995$	1.16578e7	+	1.16578e7i	0.373300	+	0.373300i
$996$	−1.61973e7	+	6.70914e6i	−0.517361	+	0.214298i
$997$	−1.49376e6	−	3.60626e6i	−0.0475930	−	0.114900i	0.898295	−	0.439393i	$-0.144806\pi$
$997$	−1.49376e6	−	3.60626e6i	−0.0475930	−	0.114900i	−0.945888	+	0.324493i	$0.894806\pi$
$998$	4.52977e7	+	1.87629e7i	1.43963	+	0.596313i
$999$		−	9.02458e6i		−	0.286097i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	51.6.h.a.25.3	✓	56
17.7	odd	16		867.6.a.t.1.23		28
17.10	odd	16		867.6.a.u.1.23		28
17.15	even	8	inner	51.6.h.a.49.3	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.6.h.a.25.3	✓	56	1.1	even	1	trivial
51.6.h.a.49.3	yes	56	17.15	even	8	inner
867.6.a.t.1.23		28	17.7	odd	16
867.6.a.u.1.23		28	17.10	odd	16

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:	\( N \)	\(=\)	\( 51 = 3 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	51.h (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.30075 + 5.30075i) q^{2} +(3.44415 - 8.31492i) q^{3} -24.1960i q^{4} +(28.6013 + 11.8471i) q^{5} +(25.8187 + 62.3319i) q^{6} +(-117.456 + 48.6520i) q^{7} +(-41.3672 - 41.3672i) q^{8} +(-57.2756 - 57.2756i) q^{9} +(-214.407 + 88.8103i) q^{10} +(-154.528 - 373.064i) q^{11} +(-201.187 - 83.3346i) q^{12} +25.4893i q^{13} +(364.715 - 880.499i) q^{14} +(197.015 - 197.015i) q^{15} +1212.83 q^{16} +(291.056 - 1155.48i) q^{17} +607.208 q^{18} +(439.251 - 439.251i) q^{19} +(286.651 - 692.037i) q^{20} +1144.20i q^{21} +(2796.64 + 1158.40i) q^{22} +(-1740.28 - 4201.42i) q^{23} +(-486.440 + 201.490i) q^{24} +(-1532.03 - 1532.03i) q^{25} +(-135.112 - 135.112i) q^{26} +(-673.508 + 278.976i) q^{27} +(1177.18 + 2841.97i) q^{28} +(-1542.51 - 638.927i) q^{29} +2088.65i q^{30} +(-59.7005 + 144.130i) q^{31} +(-5105.14 + 5105.14i) q^{32} -3634.21 q^{33} +(4582.12 + 7667.75i) q^{34} -3935.79 q^{35} +(-1385.84 + 1385.84i) q^{36} +(-4737.39 + 11437.1i) q^{37} +4656.72i q^{38} +(211.941 + 87.7889i) q^{39} +(-693.078 - 1673.24i) q^{40} +(7374.91 - 3054.79i) q^{41} +(-6065.14 - 6065.14i) q^{42} +(-2570.48 - 2570.48i) q^{43} +(-9026.64 + 3738.96i) q^{44} +(-959.612 - 2316.71i) q^{45} +(31495.5 + 13045.9i) q^{46} -6356.70i q^{47} +(4177.16 - 10084.5i) q^{48} +(-455.378 + 455.378i) q^{49} +16241.8 q^{50} +(-8605.31 - 6399.77i) q^{51} +616.737 q^{52} +(-8318.65 + 8318.65i) q^{53} +(2091.32 - 5048.88i) q^{54} -12500.8i q^{55} +(6871.44 + 2846.24i) q^{56} +(-2139.49 - 5165.18i) q^{57} +(11563.2 - 4789.65i) q^{58} +(-4108.49 - 4108.49i) q^{59} +(-4766.96 - 4766.96i) q^{60} +(4835.00 - 2002.72i) q^{61} +(-447.539 - 1080.45i) q^{62} +(9513.96 + 3940.81i) q^{63} -15311.7i q^{64} +(-301.973 + 729.027i) q^{65} +(19264.1 - 19264.1i) q^{66} -16702.6 q^{67} +(-27958.1 - 7042.39i) q^{68} -40928.2 q^{69} +(20862.7 - 20862.7i) q^{70} +(-30362.7 + 73302.1i) q^{71} +4738.67i q^{72} +(4100.27 + 1698.39i) q^{73} +(-35513.3 - 85736.8i) q^{74} +(-18015.2 + 7462.13i) q^{75} +(-10628.1 - 10628.1i) q^{76} +(36300.6 + 36300.6i) q^{77} +(-1588.79 + 658.100i) q^{78} +(-8040.19 - 19410.7i) q^{79} +(34688.4 + 14368.4i) q^{80} +6561.00i q^{81} +(-22899.9 + 55285.2i) q^{82} +(56928.1 - 56928.1i) q^{83} +27685.1 q^{84} +(22013.7 - 29600.2i) q^{85} +27251.0 q^{86} +(-10625.2 + 10625.2i) q^{87} +(-9040.22 + 21825.0i) q^{88} -53407.3i q^{89} +(17367.0 + 7193.63i) q^{90} +(-1240.10 - 2993.87i) q^{91} +(-101657. + 42107.9i) q^{92} +(992.810 + 992.810i) q^{93} +(33695.3 + 33695.3i) q^{94} +(17767.0 - 7359.32i) q^{95} +(24865.9 + 60031.7i) q^{96} +(105346. + 43635.9i) q^{97} -4827.69i q^{98} +(-12516.8 + 30218.2i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 88 q^{5} + 360 q^{6} + 1280 q^{10} - 632 q^{11} - 4256 q^{14} - 8192 q^{16} + 6248 q^{17} + 4152 q^{19} - 16384 q^{20} - 19592 q^{22} - 3608 q^{23} + 10440 q^{24} + 30384 q^{25} - 19936 q^{26} + 13624 q^{28}+ \cdots - 51192 q^{99}+O(q^{100}) \) 56 * q - 88 * q^5 + 360 * q^6 + 1280 * q^10 - 632 * q^11 - 4256 * q^14 - 8192 * q^16 + 6248 * q^17 + 4152 * q^19 - 16384 * q^20 - 19592 * q^22 - 3608 * q^23 + 10440 * q^24 + 30384 * q^25 - 19936 * q^26 + 13624 * q^28 - 23424 * q^29 + 2728 * q^31 + 67200 * q^32 + 20376 * q^33 + 11960 * q^34 + 26272 * q^35 + 3240 * q^36 + 32296 * q^37 - 22320 * q^39 - 100184 * q^40 + 6552 * q^41 - 21528 * q^42 - 38152 * q^43 - 26208 * q^44 + 31752 * q^45 + 106368 * q^46 + 9768 * q^49 + 96128 * q^50 - 62720 * q^52 + 65984 * q^53 + 29160 * q^54 - 268304 * q^56 - 28656 * q^57 - 139352 * q^58 - 67312 * q^59 - 109800 * q^60 - 307184 * q^61 + 150704 * q^62 - 696 * q^65 + 54720 * q^66 + 364272 * q^67 + 558960 * q^68 - 81864 * q^69 + 313960 * q^70 + 309808 * q^71 - 268752 * q^73 - 393712 * q^74 - 96624 * q^75 - 228552 * q^76 - 841536 * q^77 - 130824 * q^78 - 57216 * q^79 + 658528 * q^80 - 335992 * q^82 + 406240 * q^83 + 664848 * q^84 + 686840 * q^85 - 842560 * q^86 + 127224 * q^87 + 538248 * q^88 - 103680 * q^90 - 368592 * q^91 + 96752 * q^92 - 113472 * q^93 - 622576 * q^94 - 1143560 * q^95 - 375552 * q^96 - 40424 * q^97 - 51192 * q^99

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