LMFDB - Embedded newform 14.5.d.a.5.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [14,5,Mod(3,14)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("14.3"); S:= CuspForms(chi, 5); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(14, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 5, names="a")

Level:	$ N $	$=$	$ 14 = 2 \cdot 7 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	14.d (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.44717948317$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			5.1
Root			$-0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	14.5
Dual form			14.5.d.a.3.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.41421 + 2.44949i) q^{2} +(-12.9853 + 7.49706i) q^{3} +(-4.00000 - 6.92820i) q^{4} +(21.9853 + 12.6932i) q^{5} -42.4098i q^{6} +(-7.00000 + 48.4974i) q^{7} +22.6274 q^{8} +(71.9117 - 124.555i) q^{9} +(-62.1838 + 35.9018i) q^{10} +(-21.9853 - 38.0796i) q^{11} +(103.882 + 59.9764i) q^{12} +162.507i q^{13} +(-108.894 - 85.7321i) q^{14} -380.647 q^{15} +(-32.0000 + 55.4256i) q^{16} +(93.7355 - 54.1182i) q^{17} +(203.397 + 352.294i) q^{18} +(389.338 + 224.784i) q^{19} -203.091i q^{20} +(-272.691 - 682.232i) q^{21} +124.368 q^{22} +(217.911 - 377.433i) q^{23} +(-293.823 + 169.639i) q^{24} +(9.73506 + 16.8616i) q^{25} +(-398.059 - 229.819i) q^{26} +941.981i q^{27} +(364.000 - 145.492i) q^{28} +742.118 q^{29} +(538.316 - 932.390i) q^{30} +(-900.175 + 519.716i) q^{31} +(-90.5097 - 156.767i) q^{32} +(570.970 + 329.650i) q^{33} +306.139i q^{34} +(-769.485 + 977.377i) q^{35} -1150.59 q^{36} +(-493.338 + 854.486i) q^{37} +(-1101.21 + 635.786i) q^{38} +(-1218.32 - 2110.20i) q^{39} +(497.470 + 287.215i) q^{40} -1143.70i q^{41} +(2056.76 + 296.868i) q^{42} +2418.82 q^{43} +(-175.882 + 304.637i) q^{44} +(3162.00 - 1825.58i) q^{45} +(616.346 + 1067.54i) q^{46} +(-1165.17 - 672.714i) q^{47} -959.623i q^{48} +(-2303.00 - 678.964i) q^{49} -55.0698 q^{50} +(-811.455 + 1405.48i) q^{51} +(1125.88 - 650.027i) q^{52} +(1783.10 + 3088.42i) q^{53} +(-2307.37 - 1332.16i) q^{54} -1116.26i q^{55} +(-158.392 + 1097.37i) q^{56} -6740.88 q^{57} +(-1049.51 + 1817.81i) q^{58} +(3710.93 - 2142.50i) q^{59} +(1522.59 + 2637.20i) q^{60} +(-1209.57 - 698.345i) q^{61} -2939.96i q^{62} +(5537.20 + 4359.41i) q^{63} +512.000 q^{64} +(-2062.73 + 3572.76i) q^{65} +(-1614.95 + 932.390i) q^{66} +(-3632.89 - 6292.36i) q^{67} +(-749.884 - 432.946i) q^{68} +6534.77i q^{69} +(-1305.86 - 3267.07i) q^{70} +5987.76 q^{71} +(1627.18 - 2818.35i) q^{72} +(-500.123 + 288.746i) q^{73} +(-1395.37 - 2416.85i) q^{74} +(-252.825 - 145.969i) q^{75} -3596.55i q^{76} +(2000.66 - 799.672i) q^{77} +6891.88 q^{78} +(1573.12 - 2724.72i) q^{79} +(-1407.06 + 812.365i) q^{80} +(-1237.24 - 2142.95i) q^{81} +(2801.47 + 1617.43i) q^{82} -4729.96i q^{83} +(-3635.88 + 4618.19i) q^{84} +2747.74 q^{85} +(-3420.73 + 5924.88i) q^{86} +(-9636.61 + 5563.70i) q^{87} +(-497.470 - 861.644i) q^{88} +(-725.651 - 418.955i) q^{89} +10327.0i q^{90} +(-7881.16 - 1137.55i) q^{91} -3486.58 q^{92} +(7792.69 - 13497.3i) q^{93} +(3295.61 - 1902.72i) q^{94} +(5706.47 + 9883.89i) q^{95} +(2350.59 + 1357.11i) q^{96} +5622.23i q^{97} +(4920.05 - 4680.97i) q^{98} -6323.99 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 18 q^{3} - 16 q^{4} + 54 q^{5} - 28 q^{7} + 84 q^{9} - 96 q^{10} - 54 q^{11} + 144 q^{12} - 708 q^{15} - 128 q^{16} + 918 q^{17} + 576 q^{18} + 30 q^{19} - 378 q^{21} + 192 q^{22} - 486 q^{23} - 768 q^{24}+ \cdots - 11448 q^{99}+O(q^{100}) $ 4 * q - 18 * q^3 - 16 * q^4 + 54 * q^5 - 28 * q^7 + 84 * q^9 - 96 * q^10 - 54 * q^11 + 144 * q^12 - 708 * q^15 - 128 * q^16 + 918 * q^17 + 576 * q^18 + 30 * q^19 - 378 * q^21 + 192 * q^22 - 486 * q^23 - 768 * q^24 - 572 * q^25 - 1728 * q^26 + 1456 * q^28 + 3240 * q^29 + 1152 * q^30 - 546 * q^31 + 1062 * q^33 - 1890 * q^35 - 1344 * q^36 - 446 * q^37 - 4320 * q^38 - 3312 * q^39 + 768 * q^40 + 5376 * q^42 + 2344 * q^43 - 432 * q^44 + 5724 * q^45 + 3840 * q^46 + 702 * q^47 - 9212 * q^49 - 3456 * q^50 + 318 * q^51 - 384 * q^52 + 2754 * q^53 - 1440 * q^54 - 17460 * q^57 + 384 * q^58 + 12366 * q^59 + 2832 * q^60 + 7686 * q^61 + 6468 * q^63 + 2048 * q^64 - 3024 * q^65 - 3456 * q^66 - 5062 * q^67 - 7344 * q^68 - 2016 * q^70 + 18792 * q^71 + 4608 * q^72 - 17274 * q^73 - 4320 * q^74 - 5220 * q^75 + 4914 * q^77 + 8832 * q^78 + 794 * q^79 - 3456 * q^80 - 4338 * q^81 + 9984 * q^82 - 5040 * q^84 + 10380 * q^85 - 10368 * q^86 - 12276 * q^87 - 768 * q^88 - 12474 * q^89 + 2688 * q^91 + 7776 * q^92 + 18918 * q^93 + 15168 * q^94 + 8910 * q^95 + 6144 * q^96 - 11448 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/14\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−1.41421	+	2.44949i	−0.353553	+	0.612372i
$2$	−1.41421	+	2.44949i	−0.353553	+	0.612372i
$3$	−12.9853	+	7.49706i	−1.44281	+	0.833006i	−0.998036	−	0.0626373i	$-0.980049\pi$
$3$	−12.9853	+	7.49706i	−1.44281	+	0.833006i	−0.444773	+	0.895643i	$0.646716\pi$
$4$	−4.00000	−	6.92820i	−0.250000	−	0.433013i
$5$	21.9853	+	12.6932i	0.879411	+	0.507728i	0.870464	−	0.492232i	$-0.163819\pi$
$5$	21.9853	+	12.6932i	0.879411	+	0.507728i	0.00894701	+	0.999960i	$0.497152\pi$
$6$		−	42.4098i		−	1.17805i
$7$	−7.00000	+	48.4974i	−0.142857	+	0.989743i
$7$	−7.00000	+	48.4974i	−0.142857	+	0.989743i
$8$	22.6274			0.353553
$9$	71.9117	−	124.555i	0.887799	−	1.53771i
$10$	−62.1838	+	35.9018i	−0.621838	+	0.359018i
$11$	−21.9853	−	38.0796i	−0.181697	−	0.314708i	0.760762	−	0.649031i	$-0.224826\pi$
$11$	−21.9853	−	38.0796i	−0.181697	−	0.314708i	−0.942458	+	0.334324i	$0.891492\pi$
$12$	103.882	+	59.9764i	0.721405	+	0.416503i
$13$			162.507i			0.961579i	0.876836	+	0.480790i	$0.159650\pi$
$13$			162.507i			0.961579i	−0.876836	+	0.480790i	$0.840350\pi$
$14$	−108.894	−	85.7321i	−0.555584	−	0.437409i
$15$	−380.647			−1.69176
$16$	−32.0000	+	55.4256i	−0.125000	+	0.216506i
$17$	93.7355	−	54.1182i	0.324344	−	0.187260i	−0.328983	−	0.944336i	$-0.606706\pi$
$17$	93.7355	−	54.1182i	0.324344	−	0.187260i	0.653327	+	0.757076i	$0.273373\pi$
$18$	203.397	+	352.294i	0.627768	+	1.08733i
$19$	389.338	+	224.784i	1.07850	+	0.622671i	0.930491	−	0.366315i	$-0.119381\pi$
$19$	389.338	+	224.784i	1.07850	+	0.622671i	0.148007	+	0.988986i	$0.452714\pi$
$20$		−	203.091i		−	0.507728i
$21$	−272.691	−	682.232i	−0.618347	−	1.54701i
$22$	124.368			0.256958
$23$	217.911	−	377.433i	0.411931	−	0.713485i	−0.583170	−	0.812350i	$-0.698188\pi$
$23$	217.911	−	377.433i	0.411931	−	0.713485i	0.995101	+	0.0988653i	$0.0315213\pi$
$24$	−293.823	+	169.639i	−0.510110	+	0.294512i
$25$	9.73506	+	16.8616i	0.0155761	+	0.0269786i
$26$	−398.059	−	229.819i	−0.588844	−	0.339970i
$27$			941.981i			1.29215i
$28$	364.000	−	145.492i	0.464286	−	0.185577i
$29$	742.118			0.882423			0.441212	−	0.897403i	$-0.354549\pi$
$29$	742.118			0.882423			0.441212	+	0.897403i	$0.354549\pi$
$30$	538.316	−	932.390i	0.598129	−	1.03599i
$31$	−900.175	+	519.716i	−0.936707	+	0.540808i	−0.888926	−	0.458050i	$-0.848548\pi$
$31$	−900.175	+	519.716i	−0.936707	+	0.540808i	−0.0477804	+	0.998858i	$0.515215\pi$
$32$	−90.5097	−	156.767i	−0.0883883	−	0.153093i
$33$	570.970	+	329.650i	0.524307	+	0.302709i
$34$			306.139i			0.264826i
$35$	−769.485	+	977.377i	−0.628151	+	0.797859i
$36$	−1150.59			−0.887799
$37$	−493.338	+	854.486i	−0.360364	+	0.624168i	−0.988021	−	0.154322i	$-0.950681\pi$
$37$	−493.338	+	854.486i	−0.360364	+	0.624168i	0.627657	+	0.778490i	$0.284014\pi$
$38$	−1101.21	+	635.786i	−0.762613	+	0.440295i
$39$	−1218.32	−	2110.20i	−0.801001	−	1.38737i
$40$	497.470	+	287.215i	0.310919	+	0.179509i
$41$		−	1143.70i		−	0.680366i	−0.940359	−	0.340183i	$-0.889511\pi$
$41$		−	1143.70i		−	0.680366i	0.940359	−	0.340183i	$-0.110489\pi$
$42$	2056.76	+	296.868i	1.16597	+	0.168293i
$43$	2418.82			1.30818			0.654089	−	0.756418i	$-0.273052\pi$
$43$	2418.82			1.30818			0.654089	+	0.756418i	$0.273052\pi$
$44$	−175.882	+	304.637i	−0.0908483	+	0.157354i
$45$	3162.00	−	1825.58i	1.56148	−	0.901521i
$46$	616.346	+	1067.54i	0.291279	+	0.504510i
$47$	−1165.17	−	672.714i	−0.527467	−	0.304533i	0.212517	−	0.977157i	$-0.431834\pi$
$47$	−1165.17	−	672.714i	−0.527467	−	0.304533i	−0.739984	+	0.672624i	$0.765167\pi$
$48$		−	959.623i		−	0.416503i
$49$	−2303.00	−	678.964i	−0.959184	−	0.282784i
$50$	−55.0698			−0.0220279
$51$	−811.455	+	1405.48i	−0.311978	+	0.540362i
$52$	1125.88	−	650.027i	0.416376	−	0.240395i
$53$	1783.10	+	3088.42i	0.634782	+	1.09947i	0.986561	+	0.163391i	$0.0522432\pi$
$53$	1783.10	+	3088.42i	0.634782	+	1.09947i	−0.351780	+	0.936083i	$0.614423\pi$
$54$	−2307.37	−	1332.16i	−0.791280	−	0.456846i
$55$		−	1116.26i		−	0.369010i
$56$	−158.392	+	1097.37i	−0.0505076	+	0.349927i
$57$	−6740.88			−2.07475
$58$	−1049.51	+	1817.81i	−0.311984	+	0.540372i
$59$	3710.93	−	2142.50i	1.06605	−	0.615485i	0.138952	−	0.990299i	$-0.455627\pi$
$59$	3710.93	−	2142.50i	1.06605	−	0.615485i	0.927100	+	0.374814i	$0.122293\pi$
$60$	1522.59	+	2637.20i	0.422941	+	0.732555i
$61$	−1209.57	−	698.345i	−0.325066	−	0.187677i	0.328583	−	0.944475i	$-0.393429\pi$
$61$	−1209.57	−	698.345i	−0.325066	−	0.187677i	−0.653648	+	0.756799i	$0.726762\pi$
$62$		−	2939.96i		−	0.764818i
$63$	5537.20	+	4359.41i	1.39511	+	1.09837i
$64$	512.000			0.125000
$65$	−2062.73	+	3572.76i	−0.488221	+	0.845623i
$66$	−1614.95	+	932.390i	−0.370741	+	0.214047i
$67$	−3632.89	−	6292.36i	−0.809288	−	1.40173i	−0.913358	−	0.407158i	$-0.866520\pi$
$67$	−3632.89	−	6292.36i	−0.809288	−	1.40173i	0.104070	−	0.994570i	$-0.466813\pi$
$68$	−749.884	−	432.946i	−0.162172	−	0.0936301i
$69$			6534.77i			1.37256i
$70$	−1305.86	−	3267.07i	−0.266502	−	0.666748i
$71$	5987.76			1.18781			0.593906	−	0.804534i	$-0.297585\pi$
$71$	5987.76			1.18781			0.593906	+	0.804534i	$0.297585\pi$
$72$	1627.18	−	2818.35i	0.313884	−	0.543663i
$73$	−500.123	+	288.746i	−0.0938494	+	0.0541840i	−0.546190	−	0.837661i	$-0.683922\pi$
$73$	−500.123	+	288.746i	−0.0938494	+	0.0541840i	0.452341	+	0.891845i	$0.350589\pi$
$74$	−1395.37	−	2416.85i	−0.254815	−	0.441353i
$75$	−252.825	−	145.969i	−0.0449467	−	0.0259500i
$76$		−	3596.55i		−	0.622671i
$77$	2000.66	−	799.672i	0.337436	−	0.134875i
$78$	6891.88			1.13279
$79$	1573.12	−	2724.72i	0.252061	−	0.436583i	−0.712032	−	0.702147i	$-0.752225\pi$
$79$	1573.12	−	2724.72i	0.252061	−	0.436583i	0.964093	+	0.265564i	$0.0855582\pi$
$80$	−1407.06	+	812.365i	−0.219853	+	0.126932i
$81$	−1237.24	−	2142.95i	−0.188574	−	0.326620i
$82$	2801.47	+	1617.43i	0.416637	+	0.240546i
$83$		−	4729.96i		−	0.686596i	−0.939227	−	0.343298i	$-0.888456\pi$
$83$		−	4729.96i		−	0.686596i	0.939227	−	0.343298i	$-0.111544\pi$
$84$	−3635.88	+	4618.19i	−0.515289	+	0.654505i
$85$	2747.74			0.380309
$86$	−3420.73	+	5924.88i	−0.462511	+	0.801092i
$87$	−9636.61	+	5563.70i	−1.27317	+	0.735064i
$88$	−497.470	−	861.644i	−0.0642394	−	0.111266i
$89$	−725.651	−	418.955i	−0.0916110	−	0.0528916i	0.453495	−	0.891259i	$-0.350177\pi$
$89$	−725.651	−	418.955i	−0.0916110	−	0.0528916i	−0.545106	+	0.838367i	$0.683510\pi$
$90$			10327.0i			1.27494i
$91$	−7881.16	−	1137.55i	−0.951716	−	0.137368i
$92$	−3486.58			−0.411931
$93$	7792.69	−	13497.3i	0.900993	−	1.56057i
$94$	3295.61	−	1902.72i	0.372975	−	0.215337i
$95$	5706.47	+	9883.89i	0.632295	+	1.09517i
$96$	2350.59	+	1357.11i	0.255055	+	0.147256i
$97$			5622.23i			0.597537i	0.954326	+	0.298769i	$0.0965759\pi$
$97$			5622.23i			0.597537i	−0.954326	+	0.298769i	$0.903424\pi$
$98$	4920.05	−	4680.97i	0.512292	−	0.487398i
$99$	−6323.99			−0.645240
$100$	77.8805	−	134.893i	0.00778805	−	0.0134893i
$101$	−5703.21	+	3292.75i	−0.559083	+	0.322787i	−0.752778	−	0.658275i	$-0.771286\pi$
$101$	−5703.21	+	3292.75i	−0.559083	+	0.322787i	0.193694	+	0.981062i	$0.437953\pi$
$102$	−2295.14	−	3975.30i	−0.220602	−	0.382093i
$103$	1320.25	+	762.249i	0.124447	+	0.0718492i	0.560931	−	0.827863i	$-0.310443\pi$
$103$	1320.25	+	762.249i	0.124447	+	0.0718492i	−0.436484	+	0.899712i	$0.643777\pi$
$104$			3677.11i			0.339970i
$105$	2664.53	−	18460.4i	0.241680	−	1.67441i
$106$	−10086.7			−0.897717
$107$	−5303.31	+	9185.61i	−0.463212	+	0.802306i	−0.999119	−	0.0419706i	$-0.986636\pi$
$107$	−5303.31	+	9185.61i	−0.463212	+	0.802306i	0.535907	+	0.844277i	$0.319970\pi$
$108$	6526.23	−	3767.92i	0.559519	−	0.323039i
$109$	6976.13	+	12083.0i	0.587167	+	1.01700i	0.994601	+	0.103769i	$0.0330902\pi$
$109$	6976.13	+	12083.0i	0.587167	+	1.01700i	−0.407434	+	0.913235i	$0.633576\pi$
$110$	2734.26	+	1578.62i	0.225972	+	0.130465i
$111$		−	14794.3i		−	1.20074i
$112$	−2464.00	−	1939.90i	−0.196429	−	0.154647i
$113$	−8811.30			−0.690054			−0.345027	−	0.938593i	$-0.612130\pi$
$113$	−8811.30			−0.690054			−0.345027	+	0.938593i	$0.612130\pi$
$114$	9533.04	−	16511.7i	0.733537	−	1.27052i
$115$	9581.68	−	5531.99i	0.724513	−	0.418298i
$116$	−2968.47	−	5141.54i	−0.220606	−	0.382100i
$117$	20241.0	+	11686.1i	1.47863	+	0.853689i
$118$			12119.8i			0.870427i
$119$	1968.45	+	4924.76i	0.139005	+	0.347769i
$120$	−8613.05			−0.598129
$121$	6353.79	−	11005.1i	0.433973	−	0.751663i
$122$	3421.18	−	1975.22i	0.229856	−	0.132707i
$123$	8574.35	+	14851.2i	0.566749	+	0.981638i
$124$	7201.40	+	4157.73i	0.468353	+	0.270404i
$125$		−	15372.2i		−	0.983823i
$126$	−18509.1	+	7398.17i	−1.16586	+	0.465997i
$127$	3992.70			0.247548			0.123774	−	0.992310i	$-0.460500\pi$
$127$	3992.70			0.247548			0.123774	+	0.992310i	$0.460500\pi$
$128$	−724.077	+	1254.14i	−0.0441942	+	0.0765466i
$129$	−31409.1	+	18134.0i	−1.88745	+	1.08972i
$130$	−5834.29	−	10105.3i	−0.345224	−	0.597946i
$131$	−17515.4	−	10112.5i	−1.02065	−	0.589272i	−0.106357	−	0.994328i	$-0.533919\pi$
$131$	−17515.4	−	10112.5i	−1.02065	−	0.589272i	−0.914292	+	0.405056i	$0.867252\pi$
$132$		−	5274.40i		−	0.302709i
$133$	−13626.8	+	17308.4i	−0.770355	+	0.978483i
$134$	20550.7			1.14451
$135$	−11956.8	+	20709.7i	−0.656063	+	1.13634i
$136$	2120.99	−	1224.56i	0.114673	−	0.0662065i
$137$	−12528.9	−	21700.6i	−0.667530	−	1.15620i	−0.978593	−	0.205807i	$-0.934018\pi$
$137$	−12528.9	−	21700.6i	−0.667530	−	1.15620i	0.311062	−	0.950389i	$-0.399315\pi$
$138$	−16006.9	−	9241.56i	−0.840520	−	0.485274i
$139$			20070.1i			1.03877i	0.854541	+	0.519385i	$0.173839\pi$
$139$			20070.1i			1.03877i	−0.854541	+	0.519385i	$0.826161\pi$
$140$	9849.41	+	1421.64i	0.502521	+	0.0725326i
$141$	20173.5			1.01471
$142$	−8467.98	+	14667.0i	−0.419955	+	0.727384i
$143$	6188.20	−	3572.76i	0.302616	−	0.174716i
$144$	4602.35	+	7971.50i	0.221950	+	0.384428i
$145$	16315.7	+	9419.86i	0.776013	+	0.448031i
$146$		−	1633.40i		−	0.0766277i
$147$	34995.3	−	8449.18i	1.61948	−	0.391003i
$148$	7893.40			0.360364
$149$	21353.9	−	36986.1i	0.961846	−	1.66597i	0.243986	−	0.969779i	$-0.421545\pi$
$149$	21353.9	−	36986.1i	0.961846	−	1.66597i	0.717860	−	0.696188i	$-0.245122\pi$
$150$	715.097	−	412.862i	0.0317821	−	0.0183494i
$151$	−14803.7	−	25640.8i	−0.649258	−	1.12455i	−0.983301	−	0.181989i	$-0.941746\pi$
$151$	−14803.7	−	25640.8i	−0.649258	−	1.12455i	0.334043	−	0.942558i	$-0.391587\pi$
$152$	8809.71	+	5086.29i	0.381307	+	0.220147i
$153$		−	15566.9i		−	0.664998i
$154$	−870.573	+	6031.50i	−0.0367082	+	0.254322i
$155$	−26387.5			−1.09833
$156$	−9746.58	+	16881.6i	−0.400501	+	0.693687i
$157$	10597.6	−	6118.53i	0.429940	−	0.248226i	−0.269381	−	0.963034i	$-0.586819\pi$
$157$	10597.6	−	6118.53i	0.429940	−	0.248226i	0.699321	+	0.714808i	$0.253486\pi$
$158$	4449.44	+	7706.66i	0.178234	+	0.308711i
$159$	−46308.1	−	26736.0i	−1.83174	−	1.05755i
$160$		−	4595.43i		−	0.179509i
$161$	16779.2	+	13210.2i	0.647319	+	0.509632i
$162$	6998.86			0.266684
$163$	−10765.6	+	18646.5i	−0.405193	+	0.701814i	−0.994344	−	0.106209i	$-0.966129\pi$
$163$	−10765.6	+	18646.5i	−0.405193	+	0.701814i	0.589151	+	0.808023i	$0.299462\pi$
$164$	−7923.75	+	4574.78i	−0.294607	+	0.170092i
$165$	8368.63	+	14494.9i	0.307388	+	0.532411i
$166$	11586.0	+	6689.17i	0.420452	+	0.242748i
$167$			16578.9i			0.594461i	0.954806	+	0.297230i	$0.0960629\pi$
$167$			16578.9i			0.594461i	−0.954806	+	0.297230i	$0.903937\pi$
$168$	−6170.29	−	15437.1i	−0.218619	−	0.546951i
$169$	2152.52			0.0753658
$170$	−3885.88	+	6730.55i	−0.134460	+	0.232891i
$171$	55995.9	−	32329.2i	1.91498	−	1.10561i
$172$	−9675.28	−	16758.1i	−0.327044	−	0.566458i
$173$	−34972.8	−	20191.5i	−1.16852	−	0.674648i	−0.215192	−	0.976572i	$-0.569038\pi$
$173$	−34972.8	−	20191.5i	−1.16852	−	0.674648i	−0.953332	+	0.301924i	$0.902371\pi$
$174$		−	31473.0i		−	1.03954i
$175$	−885.891	+	354.094i	−0.0289270	+	0.0115623i
$176$	2814.12			0.0908483
$177$	−32124.9	+	55642.0i	−1.02541	+	1.77606i
$178$	2052.45	−	1184.98i	0.0647788	−	0.0374000i
$179$	26747.2	+	46327.5i	0.834780	+	1.44588i	0.894209	+	0.447649i	$0.147739\pi$
$179$	26747.2	+	46327.5i	0.834780	+	1.44588i	−0.0594290	+	0.998233i	$0.518928\pi$
$180$	−25296.0	−	14604.6i	−0.780740	−	0.450761i
$181$			54202.1i			1.65447i	0.561857	+	0.827235i	$0.310087\pi$
$181$			54202.1i			1.65447i	−0.561857	+	0.827235i	$0.689913\pi$
$182$	13932.1	−	17696.1i	0.420603	−	0.534238i
$183$	20942.1			0.625343
$184$	4930.77	−	8540.34i	0.145639	−	0.252255i
$185$	−21692.3	+	12524.1i	−0.633815	+	0.365934i
$186$	22041.0	+	38176.2i	0.637098	+	1.10349i
$187$	−4121.60	−	2379.61i	−0.117864	−	0.0680491i
$188$			10763.4i			0.304533i
$189$	−45683.6	−	6593.86i	−1.27890	−	0.184594i
$190$	−32280.6			−0.894201
$191$	601.936	−	1042.58i	0.0165000	−	0.0285788i	−0.857658	−	0.514221i	$-0.828081\pi$
$191$	601.936	−	1042.58i	0.0165000	−	0.0285788i	0.874158	+	0.485643i	$0.161414\pi$
$192$	−6648.46	+	3838.49i	−0.180351	+	0.104126i
$193$	−25656.5	−	44438.3i	−0.688783	−	1.19301i	−0.972232	−	0.234019i	$-0.924812\pi$
$193$	−25656.5	−	44438.3i	−0.688783	−	1.19301i	0.283449	−	0.958987i	$-0.408521\pi$
$194$	−13771.6	−	7951.03i	−0.365915	−	0.211261i
$195$		−	61857.7i		−	1.62676i
$196$	4508.00	+	18671.5i	0.117347	+	0.486035i
$197$	−1456.28			−0.0375242			−0.0187621	−	0.999824i	$-0.505973\pi$
$197$	−1456.28			−0.0375242			−0.0187621	+	0.999824i	$0.505973\pi$
$198$	8943.48	−	15490.6i	0.228127	−	0.395127i
$199$	59546.3	−	34379.1i	1.50366	−	0.868137i	0.503667	−	0.863898i	$-0.331984\pi$
$199$	59546.3	−	34379.1i	1.50366	−	0.868137i	0.999991	−	0.00423890i	$-0.00134929\pi$
$200$	220.279	+	381.535i	0.00550698	+	0.00953838i
$201$	94348.3	+	54472.0i	2.33530	+	1.34828i
$202$		−	18626.6i		−	0.456490i
$203$	−5194.82	+	35990.8i	−0.126060	+	0.873372i
$204$	12983.3			0.311978
$205$	14517.2	−	25144.5i	0.345441	−	0.598322i
$206$	−3734.24	+	2155.96i	−0.0879970	+	0.0508051i
$207$	−31340.7	−	54283.7i	−0.731423	−	1.26686i
$208$	−9007.04	−	5200.22i	−0.208188	−	0.120197i
$209$		−	19767.8i		−	0.452549i
$210$	41450.3	+	32633.7i	0.939916	+	0.739992i
$211$	−622.821			−0.0139894			−0.00699469	−	0.999976i	$-0.502226\pi$
$211$	−622.821			−0.0139894			−0.00699469	+	0.999976i	$0.502226\pi$
$212$	14264.8	−	24707.4i	0.317391	−	0.549737i
$213$	−77752.8	+	44890.6i	−1.71379	+	0.989455i
$214$	−15000.0	−	25980.8i	−0.327540	−	0.567316i
$215$	53178.5	+	30702.6i	1.15043	+	0.664199i
$216$			21314.6i			0.456846i
$217$	−18903.7	−	47294.2i	−0.401446	−	1.00436i
$218$	−39463.0			−0.830380
$219$	4329.50	−	7498.91i	0.0902712	−	0.156354i
$220$	−7733.64	+	4465.02i	−0.159786	+	0.0922525i
$221$	8794.58	+	15232.7i	0.180066	+	0.311883i
$222$	36238.5	+	20922.3i	0.735300	+	0.424526i
$223$			11509.7i			0.231449i	0.993281	+	0.115725i	$0.0369190\pi$
$223$			11509.7i			0.231449i	−0.993281	+	0.115725i	$0.963081\pi$
$224$	8236.38	−	3292.11i	0.164150	−	0.0656113i
$225$	2800.26			0.0553138
$226$	12461.1	−	21583.2i	0.243971	−	0.422570i
$227$	−48815.4	+	28183.6i	−0.947339	+	0.546946i	−0.892253	−	0.451535i	$-0.850876\pi$
$227$	−48815.4	+	28183.6i	−0.947339	+	0.546946i	−0.0550855	+	0.998482i	$0.517543\pi$
$228$	26963.5	+	46702.2i	0.518689	+	0.898395i
$229$	−36484.4	−	21064.3i	−0.695722	−	0.401675i	0.110030	−	0.993928i	$-0.464905\pi$
$229$	−36484.4	−	21064.3i	−0.695722	−	0.401675i	−0.805752	+	0.592253i	$0.798239\pi$
$230$			31293.6i			0.591562i
$231$	−19984.0	+	25383.0i	−0.374505	+	0.475685i
$232$	16792.2			0.311984
$233$	27550.9	−	47719.6i	0.507486	−	0.878992i	−0.492476	−	0.870326i	$-0.663908\pi$
$233$	27550.9	−	47719.6i	0.507486	−	0.878992i	0.999962	−	0.00866633i	$-0.00275861\pi$
$234$	−57250.2	+	33053.4i	−1.04555	+	0.603649i
$235$	−17077.8	−	29579.6i	−0.309240	−	0.535620i
$236$	−29687.4	−	17140.0i	−0.533026	−	0.307743i
$237$			47174.9i			0.839875i
$238$	−14846.9	−	2142.97i	−0.262110	−	0.0378323i
$239$	23082.5			0.404098			0.202049	−	0.979375i	$-0.435240\pi$
$239$	23082.5			0.404098			0.202049	+	0.979375i	$0.435240\pi$
$240$	12180.7	−	21097.6i	0.211470	−	0.366278i
$241$	70643.9	−	40786.3i	1.21630	−	0.702231i	0.252175	−	0.967682i	$-0.418854\pi$
$241$	70643.9	−	40786.3i	1.21630	−	0.702231i	0.964124	+	0.265451i	$0.0855209\pi$
$242$	17971.2	+	31127.1i	0.306865	+	0.531506i
$243$	−33946.4	−	19599.0i	−0.574886	−	0.331910i
$244$			11173.5i			0.187677i
$245$	−42013.9	−	44159.7i	−0.699940	−	0.735688i
$246$	−48503.8			−0.801504
$247$	−36529.0	+	63270.0i	−0.598747	+	1.03706i
$248$	−20368.6	+	11759.8i	−0.331176	+	0.191204i
$249$	35460.8	+	61419.8i	0.571939	+	0.990627i
$250$	37654.1	+	21739.6i	0.602466	+	0.347834i
$251$		−	27207.6i		−	0.431859i	−0.976409	−	0.215930i	$-0.930722\pi$
$251$		−	27207.6i		−	0.431859i	0.976409	−	0.215930i	$-0.0692782\pi$
$252$	8054.11	−	55800.5i	0.126828	−	0.878693i
$253$	−19163.4			−0.299385
$254$	−5646.53	+	9780.08i	−0.0875214	+	0.151592i
$255$	−35680.1	+	20599.9i	−0.548714	+	0.316800i
$256$	−2048.00	−	3547.24i	−0.0312500	−	0.0541266i
$257$	93469.3	+	53964.5i	1.41515	+	0.817038i	0.995868	−	0.0908179i	$-0.0289481\pi$
$257$	93469.3	+	53964.5i	1.41515	+	0.817038i	0.419283	+	0.907856i	$0.362281\pi$
$258$		−	102582.i		−	1.54110i
$259$	−37987.0	−	29907.0i	−0.566286	−	0.445834i
$260$	33003.7			0.488221
$261$	53366.9	−	92434.3i	0.783414	−	1.35691i
$262$	49540.9	−	28602.5i	0.721708	−	0.416678i
$263$	20072.0	+	34765.8i	0.290188	+	0.502621i	0.973854	−	0.227174i	$-0.0729487\pi$
$263$	20072.0	+	34765.8i	0.290188	+	0.502621i	−0.683666	+	0.729795i	$0.739615\pi$
$264$	12919.6	+	7459.12i	0.185370	+	0.107024i
$265$			90533.1i			1.28919i
$266$	−23125.5	−	57856.5i	−0.326834	−	0.817690i
$267$	12563.7			0.176236
$268$	−29063.1	+	50338.8i	−0.404644	+	0.700864i
$269$	91239.0	−	52676.9i	1.26089	−	0.727973i	0.287641	−	0.957738i	$-0.407129\pi$
$269$	91239.0	−	52676.9i	1.26089	−	0.727973i	0.973246	+	0.229765i	$0.0737958\pi$
$270$	−33818.8	−	58575.9i	−0.463907	−	0.803510i
$271$	−13189.3	−	7614.84i	−0.179590	−	0.103687i	0.407510	−	0.913201i	$-0.366397\pi$
$271$	−13189.3	−	7614.84i	−0.179590	−	0.103687i	−0.587100	+	0.809514i	$0.699731\pi$
$272$			6927.13i			0.0936301i
$273$	110867.	−	44314.1i	1.48757	−	0.594589i
$274$	70874.0			0.944030
$275$	428.056	−	741.415i	0.00566025	−	0.00980384i
$276$	45274.2	−	26139.1i	0.594337	−	0.343141i
$277$	4935.81	+	8549.07i	0.0643278	+	0.111419i	0.896396	−	0.443255i	$-0.146176\pi$
$277$	4935.81	+	8549.07i	0.0643278	+	0.111419i	−0.832068	+	0.554674i	$0.812843\pi$
$278$	−49161.4	−	28383.4i	−0.636114	−	0.367260i
$279$			149495.i			1.92051i
$280$	−17411.5	+	22115.5i	−0.222085	+	0.282086i
$281$	−155117.			−1.96448			−0.982240	−	0.187631i	$-0.939919\pi$
$281$	−155117.			−1.96448			−0.982240	+	0.187631i	$0.939919\pi$
$282$	−28529.6	+	49414.8i	−0.358755	+	0.621382i
$283$	−94970.0	+	54831.0i	−1.18581	+	0.684626i	−0.957351	−	0.288929i	$-0.906701\pi$
$283$	−94970.0	+	54831.0i	−1.18581	+	0.684626i	−0.228456	+	0.973554i	$0.573368\pi$
$284$	−23951.1	−	41484.4i	−0.296953	−	0.514338i
$285$	−148200.	−	85563.4i	−1.82456	−	1.05341i
$286$			20210.6i			0.247085i
$287$	55466.3	+	8005.87i	0.673388	+	0.0971952i
$288$	−26034.8			−0.313884
$289$	−35902.9	+	62185.7i	−0.429867	+	0.744552i
$290$	−46147.7	+	26643.4i	−0.548724	+	0.316806i
$291$	−42150.2	−	73006.2i	−0.497752	−	0.862132i
$292$	4000.99	+	2309.97i	0.0469247	+	0.0270920i
$293$		−	89912.4i		−	1.04733i	−0.851924	−	0.523666i	$-0.824564\pi$
$293$		−	89912.4i		−	1.04733i	0.851924	−	0.523666i	$-0.175436\pi$
$294$	−28794.7	+	97669.7i	−0.333133	+	1.12997i
$295$	108781.			1.25000
$296$	−11163.0	+	19334.8i	−0.127408	+	0.220677i
$297$	35870.3	−	20709.7i	0.406651	−	0.234780i
$298$	60398.1	+	104613.i	0.680128	+	1.17802i
$299$	61335.5	+	35412.1i	0.686072	+	0.396104i
$300$			2335.50i			0.0259500i
$301$	−16931.7	+	117307.i	−0.186883	+	1.29476i
$302$	83742.5			0.918189
$303$	49371.9	−	85514.6i	0.537767	−	0.931440i
$304$	−24917.6	+	14386.2i	−0.269624	+	0.155668i
$305$	−17728.5	−	30706.6i	−0.190578	−	0.330090i
$306$	38131.0	+	22015.0i	0.407226	+	0.235112i
$307$		−	141681.i		−	1.50327i	−0.659582	−	0.751633i	$-0.729267\pi$
$307$		−	141681.i		−	1.50327i	0.659582	−	0.751633i	$-0.270733\pi$
$308$	−13542.9	−	10662.3i	−0.142762	−	0.112396i
$309$	−22858.5			−0.239403
$310$	37317.5	−	64635.9i	0.388320	−	0.672590i
$311$	−74171.3	+	42822.8i	−0.766858	+	0.442746i	−0.831753	−	0.555147i	$-0.812662\pi$
$311$	−74171.3	+	42822.8i	−0.766858	+	0.442746i	0.0648948	+	0.997892i	$0.479329\pi$
$312$	−27567.5	−	47748.3i	−0.283197	−	0.490511i
$313$	15442.6	+	8915.78i	0.157627	+	0.0910061i	0.576739	−	0.816929i	$-0.304325\pi$
$313$	15442.6	+	8915.78i	0.157627	+	0.0910061i	−0.419112	+	0.907935i	$0.637658\pi$
$314$			34611.6i			0.351045i
$315$	66401.9	+	166128.i	0.669206	+	1.67425i
$316$	−25169.8			−0.252061
$317$	−40402.6	+	69979.4i	−0.402060	+	0.696388i	−0.993974	−	0.109613i	$-0.965039\pi$
$317$	−40402.6	+	69979.4i	−0.402060	+	0.696388i	0.591914	+	0.806001i	$0.298372\pi$
$318$	130979.	−	75620.9i	1.29523	−	0.747804i
$319$	−16315.7	−	28259.6i	−0.160333	−	0.277705i
$320$	11256.5	+	6498.92i	0.109926	+	0.0634660i
$321$		−	159037.i		−	1.54343i
$322$	−56087.5	+	22418.4i	−0.540946	+	0.216218i
$323$	48659.7			0.466406
$324$	−9897.88	+	17143.6i	−0.0942871	+	0.163310i
$325$	−2740.13	+	1582.01i	−0.0259421	+	0.0149777i
$326$	−30449.6	−	52740.3i	−0.286514	−	0.496258i
$327$	−181174.	−	104601.i	−1.69434	−	0.978228i
$328$		−	25878.9i		−	0.240546i
$329$	40781.1	−	51799.0i	0.376762	−	0.478552i
$330$	−47340.1			−0.434712
$331$	−36402.1	+	63050.3i	−0.332254	+	0.575482i	−0.982954	−	0.183854i	$-0.941143\pi$
$331$	−36402.1	+	63050.3i	−0.332254	+	0.575482i	0.650699	+	0.759336i	$0.274476\pi$
$332$	−32770.1	+	18919.8i	−0.297305	+	0.171649i
$333$	70953.5	+	122895.i	0.639860	+	1.10827i
$334$	−40609.9	−	23446.1i	−0.364031	−	0.210174i
$335$		−	184452.i		−	1.64359i
$336$	46539.2	+	6717.36i	0.412231	+	0.0595004i
$337$	126538.			1.11419			0.557095	−	0.830449i	$-0.311916\pi$
$337$	126538.			1.11419			0.557095	+	0.830449i	$0.311916\pi$
$338$	−3044.13	+	5272.58i	−0.0266458	+	0.0461519i
$339$	114417.	−	66058.8i	0.995616	−	0.574819i
$340$	−10990.9	−	19036.9i	−0.0950773	−	0.164679i
$341$	39581.2	+	22852.2i	0.340393	+	0.196526i
$342$			182882.i			1.56357i
$343$	49049.0	−	106937.i	0.416910	−	0.908948i
$344$	54731.7			0.462511
$345$	−82947.2	+	143669.i	−0.696889	+	1.20705i
$346$	98917.9	−	57110.3i	0.826271	−	0.477048i
$347$	33474.6	+	57979.8i	0.278008	+	0.481524i	0.970890	−	0.239528i	$-0.0769926\pi$
$347$	33474.6	+	57979.8i	0.278008	+	0.481524i	−0.692882	+	0.721051i	$0.743659\pi$
$348$	77092.9	+	44509.6i	0.636584	+	0.367532i
$349$			25527.5i			0.209583i	0.994494	+	0.104792i	$0.0334176\pi$
$349$			25527.5i			0.209583i	−0.994494	+	0.104792i	$0.966582\pi$
$350$	385.489	−	2670.75i	0.00314685	−	0.0218020i
$351$	−153078.			−1.24251
$352$	−3979.76	+	6893.15i	−0.0321197	+	0.0556330i
$353$	−48995.9	+	28287.8i	−0.393197	+	0.227013i	−0.683545	−	0.729909i	$-0.739563\pi$
$353$	−48995.9	+	28287.8i	−0.393197	+	0.227013i	0.290347	+	0.956921i	$0.406229\pi$
$354$	−90863.1	−	157379.i	−0.725071	−	1.25586i
$355$	131643.	+	76003.9i	1.04458	+	0.603086i
$356$			6703.27i			0.0528916i
$357$	−62482.0	−	49191.8i	−0.490251	−	0.385973i
$358$	−151305.			−1.18056
$359$	−18902.4	+	32739.9i	−0.146665	+	0.254032i	−0.929993	−	0.367577i	$-0.880187\pi$
$359$	−18902.4	+	32739.9i	−0.146665	+	0.254032i	0.783328	+	0.621609i	$0.213521\pi$
$360$	71547.8	−	41308.2i	0.552067	−	0.318736i
$361$	35895.4	+	62172.6i	0.275438	+	0.477073i
$362$	−132767.	−	76653.3i	−1.01315	−	0.584943i
$363$			190539.i			1.44601i
$364$	23643.5	+	59152.5i	0.178447	+	0.446447i
$365$	−14660.5			−0.110043
$366$	−29616.6	+	51297.5i	−0.221092	+	0.382943i
$367$	9367.27	−	5408.20i	0.0695474	−	0.0401532i	−0.464823	−	0.885404i	$-0.653882\pi$
$367$	9367.27	−	5408.20i	0.0695474	−	0.0401532i	0.534370	+	0.845250i	$0.320549\pi$
$368$	13946.3	+	24155.7i	0.102983	+	0.178371i
$369$	−142453.	−	82245.1i	−1.04621	−	0.604028i
$370$		−	70846.9i		−	0.517508i
$371$	−162262.	+	64856.9i	−1.17888	+	0.471203i
$372$	−124683.			−0.900993
$373$	15511.7	−	26867.0i	0.111491	−	0.193109i	−0.804880	−	0.593437i	$-0.797771\pi$
$373$	15511.7	−	26867.0i	0.111491	−	0.193109i	0.916372	+	0.400328i	$0.131104\pi$
$374$	11657.7	−	6730.55i	0.0833428	−	0.0481180i
$375$	115246.	+	199613.i	0.819531	+	1.41947i
$376$	−26364.9	−	15221.8i	−0.186488	−	0.107669i
$377$			120599.i			0.848519i
$378$	80758.0	−	102576.i	0.565200	−	0.717900i
$379$	−98527.5			−0.685929			−0.342964	−	0.939348i	$-0.611431\pi$
$379$	−98527.5			−0.685929			−0.342964	+	0.939348i	$0.611431\pi$
$380$	45651.7	−	79071.1i	0.316148	−	0.547584i
$381$	−51846.3	+	29933.5i	−0.357164	+	0.206209i
$382$	1702.53	+	2948.87i	0.0116673	+	0.0202083i
$383$	−4454.26	−	2571.67i	−0.0303653	−	0.0175314i	0.484741	−	0.874658i	$-0.338914\pi$
$383$	−4454.26	−	2571.67i	−0.0303653	−	0.0175314i	−0.515106	+	0.857127i	$0.672247\pi$
$384$		−	21713.8i		−	0.147256i
$385$	54135.5	+	7813.79i	0.365225	+	0.0527157i
$386$	145135.			0.974086
$387$	173941.	−	301275.i	1.16140	−	2.01160i
$388$	38951.9	−	22488.9i	0.258741	−	0.149384i
$389$	−43141.0	−	74722.4i	−0.285096	−	0.493801i	0.687537	−	0.726150i	$-0.258692\pi$
$389$	−43141.0	−	74722.4i	−0.285096	−	0.493801i	−0.972632	+	0.232349i	$0.925359\pi$
$390$	151520.	+	87480.0i	0.996186	+	0.575148i
$391$		−	47171.9i		−	0.308553i
$392$	−52110.9	−	15363.2i	−0.339123	−	0.0999792i
$393$	303256.			1.96347
$394$	2059.48	−	3567.13i	0.0132668	−	0.0229788i
$395$	69170.8	−	39935.8i	0.443331	−	0.255957i
$396$	25296.0	+	43813.9i	0.161310	+	0.279397i
$397$	−135036.	−	77963.1i	−0.856778	−	0.494661i	0.00615368	−	0.999981i	$-0.498041\pi$
$397$	−135036.	−	77963.1i	−0.856778	−	0.494661i	−0.862932	+	0.505320i	$0.831375\pi$
$398$			194478.i			1.22773i
$399$	47186.2	−	326915.i	0.296394	−	2.05347i
$400$	−1246.09			−0.00778805
$401$	−17307.2	+	29977.0i	−0.107631	+	0.186423i	−0.914810	−	0.403884i	$-0.867660\pi$
$401$	−17307.2	+	29977.0i	−0.107631	+	0.186423i	0.807179	+	0.590307i	$0.200993\pi$
$402$	−266857.	+	154070.i	−1.65130	+	0.953381i
$403$	−84457.5	−	146285.i	−0.520030	−	0.900718i
$404$	45625.7	+	26342.0i	0.279542	+	0.161393i
$405$		−	62817.9i		−	0.382978i
$406$	−80812.5	−	63623.3i	−0.490260	−	0.385980i
$407$	43384.7			0.261907
$408$	−18361.1	+	31802.4i	−0.110301	+	0.191047i
$409$	−271749.	+	156894.i	−1.62450	+	0.937907i	−0.638809	+	0.769366i	$0.720572\pi$
$409$	−271749.	+	156894.i	−1.62450	+	0.937907i	−0.985695	+	0.168542i	$0.946094\pi$
$410$	41060.7	+	71119.3i	0.244264	+	0.423077i
$411$	325382.	+	187859.i	1.92624	+	1.11211i
$412$		−	12196.0i		−	0.0718492i
$413$	77929.4	+	194968.i	0.456879	+	1.14304i
$414$	177290.			1.03439
$415$	60038.3	−	103989.i	0.348604	−	0.603800i
$416$	25475.8	−	14708.4i	0.147211	−	0.0849924i
$417$	−150466.	−	260615.i	−0.865301	−	1.49875i
$418$	48421.0	+	27955.9i	0.277128	+	0.160000i
$419$		−	7324.74i		−	0.0417219i	−0.999782	−	0.0208609i	$-0.993359\pi$
$419$		−	7324.74i		−	0.0417219i	0.999782	−	0.0208609i	$-0.00664073\pi$
$420$	−138555.	+	55381.2i	−0.785462	+	0.313952i
$421$	−25178.3			−0.142057			−0.0710285	−	0.997474i	$-0.522628\pi$
$421$	−25178.3			−0.142057			−0.0710285	+	0.997474i	$0.522628\pi$
$422$	880.802	−	1525.59i	0.00494599	−	0.00856671i
$423$	−167579.	+	96752.0i	−0.936569	+	0.540728i
$424$	40347.0	+	69883.0i	0.224429	+	0.388723i
$425$	1825.04	+	1053.69i	0.0101040	+	0.00583357i
$426$		−	253940.i		−	1.39930i
$427$	42334.9	−	53772.6i	0.232190	−	0.294920i
$428$	84853.0			0.463212
$429$	−53570.3	+	92786.6i	−0.291078	+	0.504162i
$430$	−150411.	+	86840.1i	−0.813474	+	0.469660i
$431$	−6913.59	−	11974.7i	−0.0372176	−	0.0644629i	0.846817	−	0.531885i	$-0.178516\pi$
$431$	−6913.59	−	11974.7i	−0.0372176	−	0.0644629i	−0.884034	+	0.467422i	$0.845183\pi$
$432$	−52209.9	−	30143.4i	−0.279760	−	0.161519i
$433$		−	47438.8i		−	0.253022i	−0.991965	−	0.126511i	$-0.959622\pi$
$433$		−	47438.8i		−	0.253022i	0.991965	−	0.126511i	$-0.0403779\pi$
$434$	142580.	+	20579.7i	0.756973	+	0.109260i
$435$	−282485.			−1.49285
$436$	55809.1	−	96664.1i	0.293584	−	0.508502i
$437$	169682.	−	97966.0i	0.888532	−	0.512994i
$438$	12245.7	+	21210.1i	0.0638314	+	0.110559i
$439$	95101.7	+	54907.0i	0.493469	+	0.284904i	0.726012	−	0.687682i	$-0.241372\pi$
$439$	95101.7	+	54907.0i	0.493469	+	0.284904i	−0.232544	+	0.972586i	$0.574705\pi$
$440$		−	25258.0i		−	0.130465i
$441$	−250181.	+	238024.i	−1.28640	+	1.22389i
$442$	−49749.7			−0.254651
$443$	41280.4	−	71499.7i	0.210347	−	0.364331i	−0.741476	−	0.670979i	$-0.765874\pi$
$443$	41280.4	−	71499.7i	0.210347	−	0.364331i	0.951823	+	0.306648i	$0.0992073\pi$
$444$	−102498.	+	59177.3i	−0.519936	+	0.300185i
$445$	−10635.8	−	18421.7i	−0.0537092	−	0.0930270i
$446$	−28193.0	−	16277.2i	−0.141733	−	0.0818297i
$447$			640367.i			3.20490i
$448$	−3584.00	+	24830.7i	−0.0178571	+	0.123718i
$449$	−330438.			−1.63907			−0.819534	−	0.573030i	$-0.805768\pi$
$449$	−330438.			−1.63907			−0.819534	+	0.573030i	$0.805768\pi$
$450$	−3960.17	+	6859.21i	−0.0195564	+	0.0338726i
$451$	−43551.5	+	25144.5i	−0.214116	+	0.123620i
$452$	35245.2	+	61046.4i	0.172513	+	0.298802i
$453$	384461.	+	221969.i	1.87351	+	1.08167i
$454$		−	159430.i		−	0.773499i
$455$	−158830.	−	125047.i	−0.767204	−	0.604017i
$456$	−152529.			−0.733537
$457$	186644.	−	323276.i	0.893677	−	1.54789i	0.0582431	−	0.998302i	$-0.481450\pi$
$457$	186644.	−	323276.i	0.893677	−	1.54789i	0.835434	−	0.549591i	$-0.185217\pi$
$458$	103193.	−	59578.7i	0.491950	−	0.284027i
$459$	50978.3	+	88297.0i	0.241969	+	0.419103i
$460$	−76653.4	−	44255.9i	−0.362256	−	0.209149i
$461$		−	20355.2i		−	0.0957798i	−0.998853	−	0.0478899i	$-0.984750\pi$
$461$		−	20355.2i		−	0.0957798i	0.998853	−	0.0478899i	$-0.0152497\pi$
$462$	−33913.9	−	84847.5i	−0.158889	−	0.397517i
$463$	−31552.7			−0.147189			−0.0735944	−	0.997288i	$-0.523447\pi$
$463$	−31552.7			−0.147189			−0.0735944	+	0.997288i	$0.523447\pi$
$464$	−23747.8	+	41132.3i	−0.110303	+	0.191050i
$465$	342649.	−	197828.i	1.58469	−	0.914919i
$466$	77925.8	+	134971.i	0.358847	+	0.621541i
$467$	−209452.	−	120927.i	−0.960397	−	0.554486i	−0.0641019	−	0.997943i	$-0.520418\pi$
$467$	−209452.	−	120927.i	−0.960397	−	0.554486i	−0.896295	+	0.443458i	$0.853752\pi$
$468$		−	186978.i		−	0.853689i
$469$	330593.	−	132139.i	1.50296	−	0.600740i
$470$	96606.6			0.437332
$471$	−91741.9	+	158902.i	−0.413548	+	0.716286i
$472$	83968.7	−	48479.3i	0.376906	−	0.217607i
$473$	−53178.5	−	92107.8i	−0.237691	−	0.411694i
$474$	−115555.	−	66715.4i	−0.514316	−	0.296941i
$475$			8753.16i			0.0387951i
$476$	26245.9	−	33336.8i	0.115837	−	0.147133i
$477$	512903.			2.25423
$478$	−32643.5	+	56540.3i	−0.142870	+	0.247458i
$479$	235631.	−	136042.i	1.02698	−	0.592926i	0.110861	−	0.993836i	$-0.464639\pi$
$479$	235631.	−	136042.i	1.02698	−	0.592926i	0.916117	+	0.400910i	$0.131306\pi$
$480$	34452.2	+	59673.0i	0.149532	+	0.258997i
$481$	−138860.	−	80170.8i	−0.600187	−	0.346518i
$482$			230722.i			0.993104i
$483$	−316920.	−	45743.4i	−1.35848	−	0.196080i
$484$	−101661.			−0.433973
$485$	−71364.1	+	123606.i	−0.303387	+	0.525481i
$486$	96015.0	−	55434.3i	0.406506	−	0.234696i
$487$	203873.	+	353119.i	0.859611	+	1.48889i	0.872300	+	0.488971i	$0.162628\pi$
$487$	203873.	+	353119.i	0.859611	+	1.48889i	−0.0126891	+	0.999919i	$0.504039\pi$
$488$	−27369.4	−	15801.7i	−0.114928	−	0.0663537i
$489$		−	322840.i		−	1.35011i
$490$	167585.	−	40461.3i	0.697981	−	0.168519i
$491$	−286772.			−1.18953			−0.594763	−	0.803901i	$-0.702754\pi$
$491$	−286772.			−1.18953			−0.594763	+	0.803901i	$0.702754\pi$
$492$	68594.8	−	118810.i	0.283375	−	0.490819i
$493$	69562.8	−	40162.1i	0.286209	−	0.165243i
$494$	−103320.	−	178955.i	−0.423378	−	0.733313i
$495$	−139035.	−	80271.8i	−0.567431	−	0.327606i
$496$		−	66523.7i		−	0.270404i
$497$	−41914.3	+	290391.i	−0.169687	+	1.17563i
$498$	−200596.			−0.808843
$499$	−175718.	+	304352.i	−0.705690	+	1.22229i	0.260751	+	0.965406i	$0.416030\pi$
$499$	−175718.	+	304352.i	−0.705690	+	1.22229i	−0.966442	+	0.256886i	$0.917304\pi$
$500$	−106502.	+	61488.9i	−0.426008	+	0.245956i
$501$	−124293.	−	215282.i	−0.495189	−	0.857693i
$502$	66644.7	+	38477.3i	0.264459	+	0.152685i
$503$		−	116045.i		−	0.458660i	−0.973349	−	0.229330i	$-0.926347\pi$
$503$		−	116045.i		−	0.458660i	0.973349	−	0.229330i	$-0.0736535\pi$
$504$	125293.	+	98642.3i	0.493247	+	0.388331i
$505$	−167182.			−0.655552
$506$	27101.1	−	46940.5i	0.105849	−	0.183335i
$507$	−27951.1	+	16137.6i	−0.108738	+	0.0627802i
$508$	−15970.8	−	27662.2i	−0.0618870	−	0.107191i
$509$	72030.7	+	41586.9i	0.278024	+	0.160517i	0.632528	−	0.774537i	$-0.282017\pi$
$509$	72030.7	+	41586.9i	0.278024	+	0.160517i	−0.354505	+	0.935054i	$0.615351\pi$
$510$		−	116531.i		−	0.448023i
$511$	−10502.6	−	26275.9i	−0.0402212	−	0.100627i
$512$	11585.2			0.0441942
$513$	−211742.	+	366749.i	−0.804587	+	1.39359i
$514$	−264371.	+	152635.i	−1.00066	+	0.577733i
$515$	19350.8	+	33516.5i	0.0729598	+	0.126370i
$516$	251273.	+	145072.i	0.943725	+	0.544860i
$517$			59159.2i			0.221330i
$518$	126979.	−	50753.9i	0.473229	−	0.189151i
$519$	605508.			2.24794
$520$	−46674.3	+	80842.3i	−0.172612	+	0.298973i
$521$	174948.	−	101006.i	0.644517	−	0.372112i	−0.141835	−	0.989890i	$-0.545300\pi$
$521$	174948.	−	101006.i	0.644517	−	0.372112i	0.786352	+	0.617778i	$0.211967\pi$
$522$	150945.	+	261444.i	0.553957	+	0.959482i
$523$	−24134.0	−	13933.8i	−0.0882321	−	0.0509408i	0.455235	−	0.890371i	$-0.349555\pi$
$523$	−24134.0	−	13933.8i	−0.0882321	−	0.0509408i	−0.543467	+	0.839431i	$0.682889\pi$
$524$			161800.i			0.589272i
$525$	8848.88	−	11239.6i	0.0321048	−	0.0407785i
$526$	−113545.			−0.410389
$527$	−56252.3	+	97431.8i	−0.202544	+	0.350816i
$528$	−36542.1	+	21097.6i	−0.131077	+	0.0756772i
$529$	44949.9	+	77855.5i	0.160626	+	0.278213i
$530$	−221760.	−	128033.i	−0.789462	−	0.455796i
$531$		−	616284.i		−	2.18571i
$532$	174423.	+	25175.8i	0.616284	+	0.0889530i
$533$	185858.			0.654226
$534$	−17767.8	+	30774.7i	−0.0623089	+	0.107922i
$535$	−233190.	+	134632.i	−0.814707	+	0.470372i
$536$	−82203.0	−	142380.i	−0.286126	−	0.495586i
$537$	−694640.	−	401050.i	−2.40886	−	1.39075i
$538$			297985.i			1.02951i
$539$	24777.4	+	102625.i	0.0852861	+	0.353243i
$540$	191308.			0.656063
$541$	18996.8	−	32903.4i	0.0649062	−	0.112421i	−0.831746	−	0.555156i	$-0.812659\pi$
$541$	18996.8	−	32903.4i	0.0649062	−	0.112421i	0.896652	+	0.442735i	$0.145992\pi$
$542$	37305.0	−	21538.0i	0.126990	−	0.0733175i
$543$	−406356.	−	703829.i	−1.37818	−	2.38708i
$544$	−16967.9	−	9796.44i	−0.0573365	−	0.0331032i
$545$			354198.i			1.19249i
$546$	−48243.1	+	334238.i	−0.161827	+	1.12117i
$547$	360160.			1.20371			0.601854	−	0.798606i	$-0.294429\pi$
$547$	360160.			1.20371			0.601854	+	0.798606i	$0.294429\pi$
$548$	−100231.	+	173605.i	−0.333765	+	0.578098i
$549$	−173964.	+	100438.i	−0.577185	+	0.333238i
$550$	1210.73	+	2097.04i	0.00400240	+	0.00693236i
$551$	288934.	+	166816.i	0.951691	+	0.549459i
$552$			147865.i			0.485274i
$553$	121130.	+	95365.1i	0.396097	+	0.311845i
$554$	−27921.1			−0.0909732
$555$	187787.	−	325257.i	0.609650	−	1.05594i
$556$	139049.	−	80280.2i	0.449800	−	0.259692i
$557$	−155272.	−	268938.i	−0.500474	−	0.866847i	−1.00000		0.000547960i	$-0.999826\pi$
$557$	−155272.	−	268938.i	−0.500474	−	0.866847i	0.499525	−	0.866299i	$-0.333508\pi$
$558$	−366186.	−	211418.i	−1.17607	−	0.679004i
$559$			393075.i			1.25792i
$560$	−29548.2	−	73925.2i	−0.0942226	−	0.235731i
$561$	71360.2			0.226741
$562$	219369.	−	379958.i	0.694548	−	1.20299i
$563$	14453.4	−	8344.68i	0.0455988	−	0.0263265i	−0.477027	−	0.878888i	$-0.658286\pi$
$563$	14453.4	−	8344.68i	0.0455988	−	0.0263265i	0.522626	+	0.852562i	$0.324952\pi$
$564$	−80694.0	−	139766.i	−0.253678	−	0.439383i
$565$	−193719.	−	111844.i	−0.606841	−	0.350360i
$566$		−	310171.i		−	0.968207i
$567$	112588.	−	45002.0i	0.350209	−	0.139980i
$568$	135488.			0.419955
$569$	65131.1	−	112810.i	0.201170	−	0.348437i	−0.747736	−	0.663997i	$-0.768859\pi$
$569$	65131.1	−	112810.i	0.201170	−	0.348437i	0.948906	+	0.315560i	$0.102192\pi$
$570$	419173.	−	242010.i	1.29016	−	0.744875i
$571$	249119.	+	431487.i	0.764073	+	1.32341i	0.940735	+	0.339142i	$0.110137\pi$
$571$	249119.	+	431487.i	0.764073	+	1.32341i	−0.176662	+	0.984272i	$0.556530\pi$
$572$	−49505.6	−	28582.1i	−0.151308	−	0.0873578i
$573$			18051.0i			0.0549784i
$574$	−98051.5	+	124542.i	−0.297598	+	0.378000i
$575$	8485.52			0.0256651
$576$	36818.8	−	63772.0i	0.110975	−	0.192214i
$577$	−29199.1	+	16858.1i	−0.0877035	+	0.0506357i	−0.543210	−	0.839597i	$-0.682791\pi$
$577$	−29199.1	+	16858.1i	−0.0877035	+	0.0506357i	0.455507	+	0.890232i	$0.349458\pi$
$578$	−101549.	−	175888.i	−0.303962	−	0.526478i
$579$	666313.	+	384696.i	1.98756	+	1.14752i
$580$		−	150718.i		−	0.448031i
$581$	229391.	+	33109.7i	0.679554	+	0.0980851i
$582$	238437.			0.703928
$583$	78404.0	−	135800.i	0.230675	−	0.399541i
$584$	−11316.5	+	6533.58i	−0.0331808	+	0.0191569i
$585$	296669.	+	513846.i	0.866884	+	1.50149i
$586$	220240.	+	127155.i	0.641357	+	0.370288i
$587$		−	356809.i		−	1.03552i	−0.855525	−	0.517762i	$-0.826765\pi$
$587$		−	356809.i		−	1.03552i	0.855525	−	0.517762i	$-0.173235\pi$
$588$	−198519.	−	208658.i	−0.574179	−	0.603504i
$589$	−467296.			−1.34698
$590$	−153840.	+	266458.i	−0.441941	+	0.765464i
$591$	18910.1	−	10917.8i	0.0541402	−	0.0312579i
$592$	−31573.6	−	54687.1i	−0.0900909	−	0.156042i
$593$	−28872.6	−	16669.6i	−0.0821063	−	0.0474041i	0.458385	−	0.888754i	$-0.348428\pi$
$593$	−28872.6	−	16669.6i	−0.0821063	−	0.0474041i	−0.540491	+	0.841350i	$0.681762\pi$
$594$			117152.i			0.332029i
$595$	−19234.1	+	133258.i	−0.0543299	+	0.376409i
$596$	−341663.			−0.961846
$597$	−515484.	+	892844.i	−1.44633	+	2.50511i
$598$	−173483.	+	100160.i	−0.485126	+	0.280088i
$599$	−162165.	−	280878.i	−0.451963	−	0.782824i	0.546545	−	0.837430i	$-0.315943\pi$
$599$	−162165.	−	280878.i	−0.451963	−	0.782824i	−0.998508	+	0.0546064i	$0.982610\pi$
$600$	−5720.78	−	3302.89i	−0.0158911	−	0.00917470i
$601$		−	66322.0i		−	0.183615i	−0.995777	−	0.0918076i	$-0.970736\pi$
$601$		−	66322.0i		−	0.183615i	0.995777	−	0.0918076i	$-0.0292645\pi$
$602$	−263396.	−	207371.i	−0.726803	−	0.572209i
$603$	−1.04499e6			−2.87394
$604$	−118430.	+	205126.i	−0.324629	+	0.562274i
$605$	279380.	−	161300.i	0.763281	−	0.440680i
$606$	139645.	+	241872.i	0.380259	+	0.658628i
$607$	−422322.	−	243828.i	−1.14622	−	0.661768i	−0.198253	−	0.980151i	$-0.563527\pi$
$607$	−422322.	−	243828.i	−1.14622	−	0.661768i	−0.947962	+	0.318383i	$0.896860\pi$
$608$		−	81380.6i		−	0.220147i
$609$	−202369.	−	506297.i	−0.545643	−	1.36512i
$610$	100287.			0.269517
$611$	109321.	−	189349.i	0.292833	−	0.507201i
$612$	−107851.	+	62267.7i	−0.287952	+	0.166249i
$613$	170755.	+	295757.i	0.454415	+	0.787070i	0.998654	−	0.0518597i	$-0.0165149\pi$
$613$	170755.	+	295757.i	0.454415	+	0.787070i	−0.544239	+	0.838930i	$0.683182\pi$
$614$	347047.	+	200368.i	0.920558	+	0.531484i
$615$			435344.i			1.15102i
$616$	45269.8	−	18094.5i	0.119302	−	0.0476854i
$617$	240873.			0.632728			0.316364	−	0.948638i	$-0.397538\pi$
$617$	240873.			0.632728			0.316364	+	0.948638i	$0.397538\pi$
$618$	32326.8	−	55991.6i	0.0846419	−	0.146604i
$619$	−133658.	+	77167.4i	−0.348830	+	0.201397i	−0.664170	−	0.747582i	$-0.731215\pi$
$619$	−133658.	+	77167.4i	−0.348830	+	0.201397i	0.315340	+	0.948979i	$0.397881\pi$
$620$	105550.	+	182818.i	0.274584	+	0.475593i
$621$	355535.	+	205268.i	0.921932	+	0.532278i
$622$		−	242242.i		−	0.626137i
$623$	25397.8	−	32259.5i	0.0654364	−	0.0831154i
$624$	155945.			0.400501
$625$	201207.	−	348501.i	0.515091	−	0.892164i
$626$	−43678.2	+	25217.6i	−0.111459	+	0.0643510i
$627$	148200.	+	256690.i	0.376976	+	0.652941i
$628$	−84780.8	−	48948.2i	−0.214970	−	0.124113i
$629$			106794.i			0.269927i
$630$	−500835.	−	72289.3i	−1.26187	−	0.182135i
$631$	220248.			0.553164			0.276582	−	0.960990i	$-0.410798\pi$
$631$	220248.			0.553164			0.276582	+	0.960990i	$0.410798\pi$
$632$	35595.5	−	61653.3i	0.0891172	−	0.154355i
$633$	8087.50	−	4669.32i	0.0201840	−	0.0116532i
$634$	−114276.	−	197932.i	−0.284299	−	0.492421i
$635$	87780.7	+	50680.2i	0.217696	+	0.125687i
$636$			427776.i			1.05755i
$637$	110336.	−	374253.i	0.271919	−	0.922331i
$638$	92295.4			0.226745
$639$	430590.	−	745804.i	1.05454	−	1.82651i
$640$	−31838.1	+	18381.7i	−0.0777297	+	0.0448773i
$641$	340604.	+	589943.i	0.828960	+	1.43580i	0.898855	+	0.438247i	$0.144400\pi$
$641$	340604.	+	589943.i	0.828960	+	1.43580i	−0.0698947	+	0.997554i	$0.522266\pi$
$642$	389559.	+	224912.i	0.945156	+	0.545686i
$643$		−	572102.i		−	1.38373i	−0.722027	−	0.691865i	$-0.756789\pi$
$643$		−	572102.i		−	1.38373i	0.722027	−	0.691865i	$-0.243211\pi$
$644$	24406.1	−	169090.i	0.0588472	−	0.407705i
$645$	−920716.			−2.21313
$646$	−68815.2	+	119191.i	−0.164899	+	0.285614i
$647$	−525915.	+	303637.i	−1.25634	+	0.725348i	−0.972361	−	0.233482i	$-0.924988\pi$
$647$	−525915.	+	303637.i	−1.25634	+	0.725348i	−0.283979	+	0.958830i	$0.591655\pi$
$648$	−27995.4	−	48489.5i	−0.0666710	−	0.115478i
$649$	−163171.	−	94207.1i	−0.387396	−	0.223663i
$650$		−	8949.23i		−	0.0211816i
$651$	600037.	+	472407.i	1.41585	+	1.11469i
$652$	172249.			0.405193
$653$	242335.	−	419737.i	0.568316	−	0.984353i	−0.428416	−	0.903581i	$-0.640928\pi$
$653$	242335.	−	419737.i	0.568316	−	0.984353i	0.996733	−	0.0807713i	$-0.0257383\pi$
$654$	512438.	−	295856.i	1.19808	−	0.691711i
$655$	−256720.	−	444652.i	−0.598380	−	1.03642i
$656$	63390.0	+	36598.3i	0.147304	+	0.0850458i
$657$			83057.0i			0.192418i
$658$	69207.8	+	173148.i	0.159847	+	0.399912i
$659$	329627.			0.759017			0.379509	−	0.925188i	$-0.376093\pi$
$659$	329627.			0.759017			0.379509	+	0.925188i	$0.376093\pi$
$660$	66949.0	−	115959.i	0.153694	−	0.266205i
$661$	−182392.	+	105304.i	−0.417449	+	0.241014i	−0.693985	−	0.719989i	$-0.744147\pi$
$661$	−182392.	+	105304.i	−0.417449	+	0.241014i	0.276536	+	0.961003i	$0.410813\pi$
$662$	−102961.	−	178333.i	−0.234939	−	0.406927i
$663$	−228400.	−	131867.i	−0.519600	−	0.299991i
$664$		−	107027.i		−	0.242748i
$665$	−519288.	+	207562.i	−1.17426	+	0.469358i
$666$	−401374.			−0.904899
$667$	161716.	−	280100.i	0.363497	−	0.629595i
$668$	114862.	−	66315.7i	0.257409	−	0.148615i
$669$	−86289.2	−	149457.i	−0.192799	−	0.333937i
$670$	451814.	+	260855.i	1.00649	+	0.581098i
$671$			61413.2i			0.136401i
$672$	−82270.5	+	104498.i	−0.182182	+	0.231402i
$673$	94709.8			0.209105			0.104553	−	0.994519i	$-0.466659\pi$
$673$	94709.8			0.209105			0.104553	+	0.994519i	$0.466659\pi$
$674$	−178951.	+	309952.i	−0.393926	+	0.682300i
$675$	−15883.3	+	9170.24i	−0.0348605	+	0.0201267i
$676$	−8610.09	−	14913.1i	−0.0188414	−	0.0326343i
$677$	466400.	+	269276.i	1.01761	+	0.587517i	0.913411	−	0.407039i	$-0.133439\pi$
$677$	466400.	+	269276.i	1.01761	+	0.587517i	0.104199	+	0.994556i	$0.466772\pi$
$678$			373685.i			0.812917i
$679$	−272664.	−	39355.6i	−0.591408	−	0.0853625i
$680$	62174.1			0.134460
$681$	422588.	−	731944.i	0.911219	−	1.57828i
$682$	−111953.	+	64635.9i	−0.240694	+	0.138965i
$683$	64535.9	+	111779.i	0.138344	+	0.239618i	0.926870	−	0.375383i	$-0.122489\pi$
$683$	64535.9	+	111779.i	0.138344	+	0.239618i	−0.788526	+	0.615001i	$0.789155\pi$
$684$	−447967.	−	258634.i	−0.957489	−	0.552806i
$685$		−	636126.i		−	1.35570i
$686$	192575.	+	271377.i	0.409215	+	0.576666i
$687$	631680.			1.33839
$688$	−77402.3	+	134065.i	−0.163522	+	0.283229i
$689$	−501890.	+	289766.i	−1.05723	+	0.610393i
$690$	−234610.	−	406357.i	−0.492775	−	0.853511i
$691$	113201.	+	65356.6i	0.237079	+	0.136878i	0.613834	−	0.789435i	$-0.289627\pi$
$691$	113201.	+	65356.6i	0.237079	+	0.136878i	−0.376754	+	0.926313i	$0.622960\pi$
$692$			323064.i			0.674648i
$693$	44268.0	−	306697.i	0.0921771	−	0.638622i
$694$	−189361.			−0.393162
$695$	−254753.	+	441246.i	−0.527413	+	0.913505i
$696$	−218052.	+	125892.i	−0.450133	+	0.259884i
$697$	−61894.8	−	107205.i	−0.127406	−	0.220673i
$698$	−62529.3	−	36101.3i	−0.128343	−	0.0740989i
$699$			826204.i			1.69096i
$700$	5996.80	+	4721.26i	0.0122384	+	0.00963522i
$701$	−182501.			−0.371389			−0.185694	−	0.982608i	$-0.559453\pi$
$701$	−182501.			−0.371389			−0.185694	+	0.982608i	$0.559453\pi$
$702$	216485.	−	374964.i	0.439293	−	0.760878i
$703$	−384150.	+	221789.i	−0.777302	+	0.448776i
$704$	−11256.5	−	19496.8i	−0.0227121	−	0.0393385i
$705$	443520.	+	256066.i	0.892349	+	0.515198i
$706$		−	160020.i		−	0.321044i
$707$	−119767.	−	299640.i	−0.239607	−	0.599462i
$708$	513999.			1.02541
$709$	−406899.	+	704770.i	−0.809458	+	1.40202i	0.103783	+	0.994600i	$0.466905\pi$
$709$	−406899.	+	704770.i	−0.809458	+	1.40202i	−0.913240	+	0.407422i	$0.866428\pi$
$710$	−372342.	+	214972.i	−0.738627	+	0.426446i
$711$	−226251.	−	391878.i	−0.447560	−	0.775196i
$712$	−16419.6	−	9479.86i	−0.0323894	−	0.0187000i
$713$			453008.i			0.891101i
$714$	208858.	−	83481.3i	0.409689	−	0.163754i
$715$	181399.			0.354832
$716$	213978.	−	370620.i	0.417390	−	0.722941i
$717$	−299732.	+	173051.i	−0.583036	+	0.336616i
$718$	−53464.0	−	92602.4i	−0.103708	−	0.179628i
$719$	−364222.	−	210283.i	−0.704544	−	0.406769i	0.104494	−	0.994526i	$-0.466678\pi$
$719$	−364222.	−	210283.i	−0.704544	−	0.406769i	−0.809038	+	0.587757i	$0.800011\pi$
$720$			233674.i			0.450761i
$721$	−46208.9	+	58693.1i	−0.0888904	+	0.112906i
$722$	−203055.			−0.389528
$723$	−611554.	+	1.05924e6i	−1.16992	+	2.02637i
$724$	375523.	−	216808.i	0.716406	−	0.413617i
$725$	7224.56	+	12513.3i	0.0137447	+	0.0238065i
$726$	−466723.	−	269463.i	−0.885495	−	0.511241i
$727$		−	172948.i		−	0.327225i	−0.986525	−	0.163613i	$-0.947685\pi$
$727$		−	172948.i		−	0.327225i	0.986525	−	0.163613i	$-0.0523147\pi$
$728$	−178330.	−	25739.8i	−0.336483	−	0.0485671i
$729$	788171.			1.48308
$730$	20733.0	−	35910.7i	0.0389061	−	0.0673873i
$731$	226729.	−	130902.i	0.424300	−	0.244970i
$732$	−83768.5	−	145091.i	−0.156336	−	0.270782i
$733$	113936.	+	65780.9i	0.212057	+	0.122431i	0.602267	−	0.798295i	$-0.294264\pi$
$733$	113936.	+	65780.9i	0.212057	+	0.122431i	−0.390210	+	0.920726i	$0.627598\pi$
$734$			30593.4i			0.0567852i
$735$	876629.	+	258445.i	1.62271	+	0.478403i
$736$	−78892.3			−0.145639
$737$	−159740.	+	276678.i	−0.294090	+	0.509378i
$738$	402917.	−	232624.i	0.739780	−	0.427112i
$739$	244884.	+	424151.i	0.448406	+	0.776662i	0.998282	−	0.0585842i	$-0.0186586\pi$
$739$	244884.	+	424151.i	0.448406	+	0.776662i	−0.549877	+	0.835246i	$0.685325\pi$
$740$	173539.	+	100193.i	0.316908	+	0.182967i
$741$		−	1.09544e6i		−	1.99504i
$742$	70607.2	−	489181.i	0.128245	−	0.888509i
$743$	580258.			1.05110			0.525549	−	0.850763i	$-0.323860\pi$
$743$	580258.			1.05110			0.525549	+	0.850763i	$0.323860\pi$
$744$	176328.	−	305410.i	0.318549	−	0.551743i
$745$	938945.	−	542100.i	1.69172	−	0.976713i
$746$	43873.7	+	75991.5i	0.0788364	+	0.136549i
$747$	−589139.	−	340139.i	−1.05579	−	0.609559i
$748$			38073.7i			0.0680491i
$749$	−408355.	−	321496.i	−0.727904	−	0.573076i
$750$	−651933.			−1.15899
$751$	−218698.	+	378797.i	−0.387763	+	0.671624i	−0.992148	−	0.125067i	$-0.960085\pi$
$751$	−218698.	+	378797.i	−0.387763	+	0.671624i	0.604386	+	0.796692i	$0.293419\pi$
$752$	74571.2	−	43053.7i	0.131867	−	0.0761333i
$753$	203977.	+	353298.i	0.359742	+	0.623091i
$754$	−295407.	−	170553.i	−0.519610	−	0.299997i
$755$		−	751627.i		−	1.31859i
$756$	137051.	+	342881.i	0.239794	+	0.599929i
$757$	−24171.7			−0.0421809			−0.0210905	−	0.999778i	$-0.506714\pi$
$757$	−24171.7			−0.0421809			−0.0210905	+	0.999778i	$0.506714\pi$
$758$	139339.	−	241342.i	0.242512	−	0.420044i
$759$	248842.	−	143669.i	0.431956	−	0.249390i
$760$	129123.	+	223647.i	0.223550	+	0.387200i
$761$	−561376.	−	324111.i	−0.969359	−	0.559659i	−0.0703180	−	0.997525i	$-0.522401\pi$
$761$	−561376.	−	324111.i	−0.969359	−	0.559659i	−0.899041	+	0.437865i	$0.855735\pi$
$762$		−	169329.i		−	0.291624i
$763$	−634828.	+	253743.i	−1.09045	+	0.435859i
$764$	−9630.98			−0.0165000
$765$	197594.	−	342243.i	0.337638	−	0.584806i
$766$	12598.5	−	7273.77i	0.0214715	−	0.0123966i
$767$	348172.	+	603051.i	0.591838	+	1.02509i
$768$	53187.7	+	30707.9i	0.0901756	+	0.0520629i
$769$			179564.i			0.303646i	0.988408	+	0.151823i	$0.0485143\pi$
$769$			179564.i			0.303646i	−0.988408	+	0.151823i	$0.951486\pi$
$770$	−95698.9	+	121554.i	−0.161408	+	0.205016i
$771$	−1.61830e6			−2.72239
$772$	−205252.	+	355506.i	−0.344391	+	0.596503i
$773$	529068.	−	305457.i	0.885426	−	0.511201i	0.0129823	−	0.999916i	$-0.495867\pi$
$773$	529068.	−	305457.i	0.885426	−	0.511201i	0.872444	+	0.488715i	$0.162534\pi$
$774$	491981.	+	852136.i	0.821233	+	1.42242i
$775$	−17526.5	−	10118.9i	−0.0291805	−	0.0168474i
$776$			127216.i			0.211261i
$777$	717486.	+	103560.i	1.18842	+	0.171534i
$778$	244042.			0.403186
$779$	257085.	−	445284.i	0.423644	−	0.733773i
$780$	−428563.	+	247431.i	−0.704410	+	0.406691i
$781$	−131643.	−	228012.i	−0.215821	−	0.373814i
$782$	115547.	+	66711.1i	0.188949	+	0.109090i
$783$			699061.i			1.14023i
$784$	111328.	−	105918.i	0.181122	−	0.172321i
$785$	310655.			0.504126
$786$	−428868.	+	742822.i	−0.694191	+	1.20237i
$787$	1.03191e6	−	595774.i	1.66607	−	0.961905i	0.696342	−	0.717710i	$-0.254810\pi$
$787$	1.03191e6	−	595774.i	1.66607	−	0.961905i	0.969726	−	0.244195i	$-0.0785236\pi$
$788$	5825.10	+	10089.4i	0.00938104	+	0.0162484i
$789$	−521282.	−	300963.i	−0.837373	−	0.483458i
$790$			225911.i			0.361979i
$791$	61679.1	−	427325.i	0.0985791	−	0.682976i
$792$	−143096.			−0.228127
$793$	113486.	−	196563.i	0.180466	−	0.312576i
$794$	381939.	−	220513.i	0.605834	−	0.349778i
$795$	−678732.	−	1.17560e6i	−1.07390	−	1.86005i
$796$	−476371.	−	275033.i	−0.751829	−	0.434069i
$797$			900495.i			1.41764i	0.705392	+	0.708818i	$0.250771\pi$
$797$			900495.i			1.41764i	−0.705392	+	0.708818i	$0.749229\pi$
$798$	734044.	+	577910.i	1.15270	+	0.907516i
$799$	−145624.			−0.228108
$800$	1762.23	−	3052.28i	0.00275349	−	0.00476919i
$801$	−104366.	+	60255.5i	−0.162664	+	0.0939142i
$802$	−48952.2	−	84787.8i	−0.0761069	−	0.131821i
$803$	21990.7	+	12696.3i	0.0341042	+	0.0196901i
$804$		−	871552.i		−	1.34828i
$805$	201215.	+	503411.i	0.310505	+	0.776838i
$806$	477764.			0.735433
$807$	−789843.	+	1.36805e6i	−1.21281	+	2.10065i
$808$	−129049.	+	74506.4i	−0.197666	+	0.114122i
$809$	−277882.	−	481306.i	−0.424584	−	0.735401i	0.571798	−	0.820395i	$-0.306246\pi$
$809$	−277882.	−	481306.i	−0.424584	−	0.735401i	−0.996381	+	0.0849939i	$0.972913\pi$
$810$	153872.	+	88838.0i	0.234525	+	0.135403i
$811$		−	70954.2i		−	0.107879i	−0.998544	−	0.0539395i	$-0.982822\pi$
$811$		−	70954.2i		−	0.107879i	0.998544	−	0.0539395i	$-0.0171778\pi$
$812$	270131.	−	107972.i	0.409696	−	0.163757i
$813$	228356.			0.345486
$814$	−61355.2	+	106270.i	−0.0925982	+	0.160385i
$815$	−473368.	+	273299.i	−0.712662	+	0.411455i
$816$	−51933.1	−	89950.8i	−0.0779945	−	0.135090i
$817$	941738.	+	543713.i	1.41087	+	0.814564i
$818$		−	887527.i		−	1.32640i
$819$	−708435.	+	899833.i	−1.05617	+	1.34151i
$820$	−232275.			−0.345441
$821$	312356.	−	541016.i	0.463408	−	0.802646i	−0.535720	−	0.844396i	$-0.679960\pi$
$821$	312356.	−	541016.i	0.463408	−	0.802646i	0.999128	+	0.0417495i	$0.0132931\pi$
$822$	−920319.	+	531346.i	−1.36206	+	0.786383i
$823$	105029.	+	181916.i	0.155064	+	0.268579i	0.933082	−	0.359663i	$-0.117108\pi$
$823$	105029.	+	181916.i	0.155064	+	0.268579i	−0.778018	+	0.628242i	$0.783775\pi$
$824$	29873.9	+	17247.7i	0.0439985	+	0.0254025i
$825$			12836.6i			0.0188601i
$826$	−587781.	−	84838.8i	−0.861500	−	0.124347i
$827$	−880910.			−1.28801			−0.644007	−	0.765020i	$-0.722729\pi$
$827$	−880910.			−1.28801			−0.644007	+	0.765020i	$0.722729\pi$
$828$	−250726.	+	434270.i	−0.365711	+	0.633431i
$829$	−1.11951e6	+	646349.i	−1.62899	+	0.940498i	−0.644595	+	0.764524i	$0.722974\pi$
$829$	−1.11951e6	+	646349.i	−1.62899	+	0.940498i	−0.984395	+	0.175974i	$0.943692\pi$
$830$	169814.	+	294127.i	0.246500	+	0.426951i
$831$	−128186.	−	74008.1i	−0.185625	−	0.107171i
$832$			83203.5i			0.120197i
$833$	−252617.	+	60991.2i	−0.364060	+	0.0878977i
$834$	851166.			1.22372
$835$	−210440.	+	364492.i	−0.301825	+	0.522775i
$836$	−136955.	+	79071.1i	−0.195959	+	0.113137i
$837$	−489563.	−	847948.i	−0.698808	−	1.21037i
$838$	17941.9	+	10358.7i	0.0255493	+	0.0147509i
$839$		−	1.11586e6i		−	1.58520i	−0.609741	−	0.792601i	$-0.708726\pi$
$839$		−	1.11586e6i		−	1.58520i	0.609741	−	0.792601i	$-0.291274\pi$
$840$	60291.4	−	417711.i	0.0854470	−	0.591994i
$841$	−156542.			−0.221330
$842$	35607.5	−	61674.1i	0.0502247	−	0.0869918i
$843$	2.01424e6	−	1.16292e6i	2.83437	−	1.63642i
$844$	2491.28	+	4315.03i	0.00349734	+	0.00605758i
$845$	47323.8	+	27322.4i	0.0662775	+	0.0382653i
$846$		−	547312.i		−	0.764705i
$847$	489242.	+	385178.i	0.681957	+	0.536902i
$848$	−228237.			−0.317391
$849$	822142.	−	1.42399e6i	1.14059	−	1.97557i
$850$	−5162.00	+	2980.28i	−0.00714464	+	0.00412496i
$851$	215008.	+	372404.i	0.296889	+	0.514228i
$852$	622022.	+	359125.i	0.856893	+	0.494728i
$853$			1.28959e6i			1.77236i	0.463341	+	0.886180i	$0.346650\pi$
$853$			1.28959e6i			1.77236i	−0.463341	+	0.886180i	$0.653350\pi$
$854$	71844.7	+	179745.i	0.0985097	+	0.246457i
$855$	1.64145e6			2.24540
$856$	−120000.	+	207847.i	−0.163770	+	0.283658i
$857$	−566854.	+	327273.i	−0.771809	+	0.445604i	−0.833519	−	0.552490i	$-0.813678\pi$
$857$	−566854.	+	327273.i	−0.771809	+	0.445604i	0.0617109	+	0.998094i	$0.480344\pi$
$858$	−151520.	−	262440.i	−0.205823	−	0.356497i
$859$	211796.	+	122281.i	0.287033	+	0.165718i	0.636603	−	0.771192i	$-0.280339\pi$
$859$	211796.	+	122281.i	0.287033	+	0.165718i	−0.349570	+	0.936910i	$0.613672\pi$
$860$		−	491242.i		−	0.664199i
$861$	−780266.	+	311875.i	−1.05253	+	0.420702i
$862$	39109.2			0.0526337
$863$	232638.	−	402942.i	0.312363	−	0.541029i	−0.666510	−	0.745496i	$-0.732213\pi$
$863$	232638.	−	402942.i	0.312363	−	0.541029i	0.978873	+	0.204467i	$0.0655461\pi$
$864$	147672.	−	85258.4i	0.197820	−	0.114211i
$865$	−512591.	−	887833.i	−0.685075	−	1.18659i
$866$	116201.	+	67088.6i	0.154944	+	0.0894567i
$867$		−	1.07667e6i		−	1.43233i
$868$	−252049.	+	320145.i	−0.334538	+	0.424921i
$869$	−138342.			−0.183195
$870$	399494.	−	691943.i	0.527802	−	0.914181i
$871$	1.02255e6	−	590370.i	1.34787	−	0.778194i
$872$	157852.	+	273407.i	0.207595	+	0.359565i
$873$	700275.	+	404304.i	0.918840	+	0.530493i
$874$			554179.i			0.725484i
$875$	745514.	+	107606.i	0.973732	+	0.140546i
$876$	−69271.9			−0.0902712
$877$	−152086.	+	263420.i	−0.197738	+	0.342492i	−0.947795	−	0.318882i	$-0.896693\pi$
$877$	−152086.	+	263420.i	−0.197738	+	0.342492i	0.750057	+	0.661373i	$0.230026\pi$
$878$	−268988.	+	155301.i	−0.348935	+	0.201458i
$879$	674078.	+	1.16754e6i	0.872434	+	1.51110i
$880$	61869.1	+	35720.2i	0.0798930	+	0.0461262i
$881$			697876.i			0.899138i	0.893246	+	0.449569i	$0.148422\pi$
$881$			697876.i			0.899138i	−0.893246	+	0.449569i	$0.851578\pi$
$882$	−229228.	−	949432.i	−0.294667	−	1.22047i
$883$	891773.			1.14375			0.571877	−	0.820339i	$-0.306215\pi$
$883$	891773.			1.14375			0.571877	+	0.820339i	$0.306215\pi$
$884$	70356.6	−	121861.i	0.0900328	−	0.155941i
$885$	−1.41255e6	+	815537.i	−1.80351	+	1.04126i
$886$	116758.	+	202232.i	0.148738	+	0.257621i
$887$	−1.09340e6	−	631278.i	−1.38974	−	0.802367i	−0.396455	−	0.918054i	$-0.629760\pi$
$887$	−1.09340e6	−	631278.i	−1.38974	−	0.802367i	−0.993286	+	0.115687i	$0.963093\pi$
$888$		−	334757.i		−	0.424526i
$889$	−27948.9	+	193636.i	−0.0353640	+	0.245009i
$890$	60164.9			0.0759562
$891$	−54401.9	+	94226.9i	−0.0685265	+	0.118691i
$892$	79741.8	−	46039.0i	0.100220	−	0.0578623i
$893$	−302431.	−	523826.i	−0.379248	−	0.656877i
$894$	−1.56857e6	−	905616.i	−1.96259	−	1.13310i
$895$			1.35803e6i			1.69537i
$896$	−55754.0	−	43894.9i	−0.0694480	−	0.0546761i
$897$	−1.06195e6			−1.31983
$898$	467310.	−	809404.i	0.579498	−	1.00372i
$899$	−668036.	+	385691.i	−0.826572	+	0.477221i
$900$	−11201.0	−	19400.8i	−0.0138284	−	0.0239516i
$901$	334280.	+	192997.i	0.411776	+	0.237739i
$902$		−	142239.i		−	0.174825i
$903$	−659590.	−	1.65020e6i	−0.808907	−	2.02377i
$904$	−199377.			−0.243971
$905$	−687998.	+	1.19165e6i	−0.840021	+	1.45496i
$906$	−1.08742e6	+	627822.i	−1.32477	+	0.764857i
$907$	−475990.	−	824439.i	−0.578607	−	1.00218i	−0.995639	−	0.0932848i	$-0.970263\pi$
$907$	−475990.	−	824439.i	−0.578607	−	1.00218i	0.417033	−	0.908891i	$-0.363070\pi$
$908$	390523.	+	225469.i	0.473669	+	0.273473i
$909$			947149.i			1.14628i
$910$	530920.	−	212211.i	0.641131	−	0.256263i
$911$	−743243.			−0.895559			−0.447779	−	0.894144i	$-0.647785\pi$
$911$	−743243.			−0.895559			−0.447779	+	0.894144i	$0.647785\pi$
$912$	215708.	−	373617.i	0.259344	−	0.449198i
$913$	−180115.	+	103989.i	−0.216077	+	0.124752i
$914$	527908.	+	914363.i	0.631925	+	1.09453i
$915$	460418.	+	265823.i	0.549934	+	0.317505i
$916$			337028.i			0.401675i
$917$	613038.	−	778662.i	0.729035	−	0.925999i
$918$	−288377.			−0.342196
$919$	262150.	−	454057.i	0.310398	−	0.537625i	−0.668050	−	0.744116i	$-0.732871\pi$
$919$	262150.	−	454057.i	0.310398	−	0.537625i	0.978449	+	0.206491i	$0.0662043\pi$
$920$	216809.	−	125175.i	0.256154	−	0.147891i
$921$	1.06219e6	+	1.83977e6i	1.25223	+	2.16892i
$922$	49859.9	+	28786.6i	0.0586529	+	0.0338633i
$923$			973052.i			1.14218i
$924$	255795.	+	36920.8i	0.299604	+	0.0432441i
$925$	−19210.7			−0.0224522
$926$	44622.3	−	77288.1i	0.0520391	−	0.0901344i
$927$	189883.	−	109629.i	0.220967	−	0.127575i
$928$	−67168.8	−	116340.i	−0.0779959	−	0.135093i
$929$	848178.	+	489696.i	0.982779	+	0.567408i	0.903108	−	0.429414i	$-0.141280\pi$
$929$	848178.	+	489696.i	0.982779	+	0.567408i	0.0796709	+	0.996821i	$0.474613\pi$
$930$			1.11909e6i			1.29389i
$931$	−744024.	−	782024.i	−0.858396	−	0.902237i
$932$	−440815.			−0.507486
$933$	642090.	−	1.11213e6i	0.737620	−	1.27759i
$934$	592420.	−	342034.i	0.679103	−	0.392081i
$935$	−60409.7	−	104633.i	−0.0691009	−	0.119686i
$936$	458001.	+	264427.i	0.522775	+	0.301824i
$937$		−	1.13988e6i		−	1.29831i	−0.760656	−	0.649155i	$-0.775123\pi$
$937$		−	1.13988e6i		−	1.29831i	0.760656	−	0.649155i	$-0.224877\pi$
$938$	−143855.	+	996658.i	−0.163501	+	1.13277i
$939$	−267368.			−0.303235
$940$	−136622.	+	236637.i	−0.154620	+	0.267810i
$941$	693791.	−	400561.i	0.783519	−	0.452365i	−0.0541569	−	0.998532i	$-0.517247\pi$
$941$	693791.	−	400561.i	0.783519	−	0.452365i	0.837676	+	0.546167i	$0.183914\pi$
$942$	−259485.	−	449441.i	−0.292422	−	0.506491i
$943$	−431669.	−	249224.i	−0.485431	−	0.280264i
$944$			274240.i			0.307743i
$945$	−920670.	−	724840.i	−1.03096	−	0.811668i
$946$	300823.			0.336146
$947$	−340143.	+	589145.i	−0.379282	+	0.656935i	−0.990958	−	0.134173i	$-0.957162\pi$
$947$	−340143.	+	589145.i	−0.379282	+	0.656935i	0.611676	+	0.791108i	$0.290496\pi$
$948$	326838.	−	188700.i	0.363677	−	0.209969i
$949$	−46923.3	−	81273.5i	−0.0521022	−	0.0902436i
$950$	−21440.8	−	12378.8i	−0.0237571	−	0.0137162i
$951$		−	1.21160e6i		−	1.33967i
$952$	44540.8	+	111435.i	0.0491456	+	0.122955i
$953$	−394774.			−0.434673			−0.217337	−	0.976097i	$-0.569737\pi$
$953$	−394774.			−0.434673			−0.217337	+	0.976097i	$0.569737\pi$
$954$	−725355.	+	1.25635e6i	−0.796992	+	1.38043i
$955$	26467.5	−	15281.0i	0.0290206	−	0.0167550i
$956$	−92329.9	−	159920.i	−0.101024	−	0.174979i
$957$	423727.	+	244639.i	0.462660	+	0.267117i
$958$			769567.i			0.838524i
$959$	1.14013e6	−	455714.i	1.23970	−	0.495513i
$960$	−194891.			−0.211470
$961$	78449.9	−	135879.i	0.0849465	−	0.147132i
$962$	392755.	−	226757.i	0.424396	−	0.245025i
$963$	762740.	+	1.32110e6i	0.822478	+	1.42457i
$964$	−565151.	−	326290.i	−0.608150	−	0.351115i
$965$		−	1.30265e6i		−	1.39886i
$966$	560240.	−	711600.i	0.600371	−	0.762574i
$967$	−604328.			−0.646279			−0.323140	−	0.946351i	$-0.604738\pi$
$967$	−604328.			−0.646279			−0.323140	+	0.946351i	$0.604738\pi$
$968$	143770.	−	249017.i	0.153433	−	0.265753i
$969$	−631860.	+	364804.i	−0.672935	+	0.388519i
$970$	−201848.	−	349611.i	−0.214527	−	0.371571i
$971$	657301.	+	379493.i	0.697149	+	0.402499i	0.806285	−	0.591528i	$-0.201475\pi$
$971$	657301.	+	379493.i	0.697149	+	0.402499i	−0.109136	+	0.994027i	$0.534808\pi$
$972$			313584.i			0.331910i
$973$	−973346.	−	140490.i	−1.02811	−	0.148396i
$974$	−1.15328e6			−1.21567
$975$	23720.9	−	41085.8i	0.0249530	−	0.0432198i
$976$	77412.4	−	44694.1i	0.0812664	−	0.0469192i
$977$	−612591.	−	1.06104e6i	−0.641773	−	1.11158i	−0.985037	−	0.172345i	$-0.944866\pi$
$977$	−612591.	−	1.06104e6i	−0.641773	−	1.11158i	0.343263	−	0.939239i	$-0.388468\pi$
$978$	790793.	+	456565.i	0.826771	+	0.477337i
$979$			36843.3i			0.0384409i
$980$	−137892.	+	467719.i	−0.143577	+	0.487005i
$981$	2.00666e6			2.08514
$982$	405557.	−	702446.i	0.420561	−	0.728434i
$983$	−1.03964e6	+	600236.i	−1.07591	+	0.621177i	−0.929790	−	0.368090i	$-0.880012\pi$
$983$	−1.03964e6	+	600236.i	−1.07591	+	0.621177i	−0.146120	+	0.989267i	$0.546678\pi$
$984$	194015.	+	336044.i	0.200376	+	0.347062i
$985$	−32016.6	−	18484.8i	−0.0329992	−	0.0190521i
$986$			227191.i			0.233689i
$987$	−141214.	+	978362.i	−0.144959	+	1.00430i
$988$	584464.			0.598747
$989$	527088.	−	912944.i	0.538878	−	0.933365i
$990$	393250.	−	227043.i	0.401234	−	0.231653i
$991$	−904963.	−	1.56744e6i	−0.921475	−	1.59604i	−0.797134	−	0.603802i	$-0.793652\pi$
$991$	−904963.	−	1.56744e6i	−0.921475	−	1.59604i	−0.124340	−	0.992240i	$-0.539682\pi$
$992$	162949.	+	94078.7i	0.165588	+	0.0956022i
$993$		−	1.09164e6i		−	1.10708i
$994$	−652034.	−	513344.i	−0.659929	−	0.519560i
$995$	1.74552e6			1.76311
$996$	283686.	−	491359.i	0.285969	−	0.495313i
$997$	648903.	−	374644.i	0.652814	−	0.376902i	−0.136719	−	0.990610i	$-0.543656\pi$
$997$	648903.	−	374644.i	0.652814	−	0.376902i	0.789534	+	0.613707i	$0.210323\pi$
$998$	−497004.	−	860837.i	−0.498998	−	0.864291i
$999$	−804909.	−	464715.i	−0.806521	−	0.465645i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	14.5.d.a.5.1	yes	4
3.2	odd	2		126.5.n.a.19.2		4
4.3	odd	2		112.5.s.b.33.2		4
5.2	odd	4		350.5.i.a.299.2		8
5.3	odd	4		350.5.i.a.299.3		8
5.4	even	2		350.5.k.a.201.2		4
7.2	even	3		98.5.b.b.97.3		4
7.3	odd	6	inner	14.5.d.a.3.1	✓	4
7.4	even	3		98.5.d.a.31.1		4
7.5	odd	6		98.5.b.b.97.4		4
7.6	odd	2		98.5.d.a.19.1		4
21.2	odd	6		882.5.c.b.685.2		4
21.5	even	6		882.5.c.b.685.1		4
21.17	even	6		126.5.n.a.73.2		4
28.3	even	6		112.5.s.b.17.2		4
28.19	even	6		784.5.c.b.97.1		4
28.23	odd	6		784.5.c.b.97.4		4
35.3	even	12		350.5.i.a.199.2		8
35.17	even	12		350.5.i.a.199.3		8
35.24	odd	6		350.5.k.a.101.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.5.d.a.3.1	✓	4	7.3	odd	6	inner
14.5.d.a.5.1	yes	4	1.1	even	1	trivial
98.5.b.b.97.3		4	7.2	even	3
98.5.b.b.97.4		4	7.5	odd	6
98.5.d.a.19.1		4	7.6	odd	2
98.5.d.a.31.1		4	7.4	even	3
112.5.s.b.17.2		4	28.3	even	6
112.5.s.b.33.2		4	4.3	odd	2
126.5.n.a.19.2		4	3.2	odd	2
126.5.n.a.73.2		4	21.17	even	6
350.5.i.a.199.2		8	35.3	even	12
350.5.i.a.199.3		8	35.17	even	12
350.5.i.a.299.2		8	5.2	odd	4
350.5.i.a.299.3		8	5.3	odd	4
350.5.k.a.101.2		4	35.24	odd	6
350.5.k.a.201.2		4	5.4	even	2
784.5.c.b.97.1		4	28.19	even	6
784.5.c.b.97.4		4	28.23	odd	6
882.5.c.b.685.1		4	21.5	even	6
882.5.c.b.685.2		4	21.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 14 = 2 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	14.d (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41421 + 2.44949i) q^{2} +(-12.9853 + 7.49706i) q^{3} +(-4.00000 - 6.92820i) q^{4} +(21.9853 + 12.6932i) q^{5} -42.4098i q^{6} +(-7.00000 + 48.4974i) q^{7} +22.6274 q^{8} +(71.9117 - 124.555i) q^{9} +(-62.1838 + 35.9018i) q^{10} +(-21.9853 - 38.0796i) q^{11} +(103.882 + 59.9764i) q^{12} +162.507i q^{13} +(-108.894 - 85.7321i) q^{14} -380.647 q^{15} +(-32.0000 + 55.4256i) q^{16} +(93.7355 - 54.1182i) q^{17} +(203.397 + 352.294i) q^{18} +(389.338 + 224.784i) q^{19} -203.091i q^{20} +(-272.691 - 682.232i) q^{21} +124.368 q^{22} +(217.911 - 377.433i) q^{23} +(-293.823 + 169.639i) q^{24} +(9.73506 + 16.8616i) q^{25} +(-398.059 - 229.819i) q^{26} +941.981i q^{27} +(364.000 - 145.492i) q^{28} +742.118 q^{29} +(538.316 - 932.390i) q^{30} +(-900.175 + 519.716i) q^{31} +(-90.5097 - 156.767i) q^{32} +(570.970 + 329.650i) q^{33} +306.139i q^{34} +(-769.485 + 977.377i) q^{35} -1150.59 q^{36} +(-493.338 + 854.486i) q^{37} +(-1101.21 + 635.786i) q^{38} +(-1218.32 - 2110.20i) q^{39} +(497.470 + 287.215i) q^{40} -1143.70i q^{41} +(2056.76 + 296.868i) q^{42} +2418.82 q^{43} +(-175.882 + 304.637i) q^{44} +(3162.00 - 1825.58i) q^{45} +(616.346 + 1067.54i) q^{46} +(-1165.17 - 672.714i) q^{47} -959.623i q^{48} +(-2303.00 - 678.964i) q^{49} -55.0698 q^{50} +(-811.455 + 1405.48i) q^{51} +(1125.88 - 650.027i) q^{52} +(1783.10 + 3088.42i) q^{53} +(-2307.37 - 1332.16i) q^{54} -1116.26i q^{55} +(-158.392 + 1097.37i) q^{56} -6740.88 q^{57} +(-1049.51 + 1817.81i) q^{58} +(3710.93 - 2142.50i) q^{59} +(1522.59 + 2637.20i) q^{60} +(-1209.57 - 698.345i) q^{61} -2939.96i q^{62} +(5537.20 + 4359.41i) q^{63} +512.000 q^{64} +(-2062.73 + 3572.76i) q^{65} +(-1614.95 + 932.390i) q^{66} +(-3632.89 - 6292.36i) q^{67} +(-749.884 - 432.946i) q^{68} +6534.77i q^{69} +(-1305.86 - 3267.07i) q^{70} +5987.76 q^{71} +(1627.18 - 2818.35i) q^{72} +(-500.123 + 288.746i) q^{73} +(-1395.37 - 2416.85i) q^{74} +(-252.825 - 145.969i) q^{75} -3596.55i q^{76} +(2000.66 - 799.672i) q^{77} +6891.88 q^{78} +(1573.12 - 2724.72i) q^{79} +(-1407.06 + 812.365i) q^{80} +(-1237.24 - 2142.95i) q^{81} +(2801.47 + 1617.43i) q^{82} -4729.96i q^{83} +(-3635.88 + 4618.19i) q^{84} +2747.74 q^{85} +(-3420.73 + 5924.88i) q^{86} +(-9636.61 + 5563.70i) q^{87} +(-497.470 - 861.644i) q^{88} +(-725.651 - 418.955i) q^{89} +10327.0i q^{90} +(-7881.16 - 1137.55i) q^{91} -3486.58 q^{92} +(7792.69 - 13497.3i) q^{93} +(3295.61 - 1902.72i) q^{94} +(5706.47 + 9883.89i) q^{95} +(2350.59 + 1357.11i) q^{96} +5622.23i q^{97} +(4920.05 - 4680.97i) q^{98} -6323.99 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 18 q^{3} - 16 q^{4} + 54 q^{5} - 28 q^{7} + 84 q^{9} - 96 q^{10} - 54 q^{11} + 144 q^{12} - 708 q^{15} - 128 q^{16} + 918 q^{17} + 576 q^{18} + 30 q^{19} - 378 q^{21} + 192 q^{22} - 486 q^{23} - 768 q^{24}+ \cdots - 11448 q^{99}+O(q^{100}) \) 4 * q - 18 * q^3 - 16 * q^4 + 54 * q^5 - 28 * q^7 + 84 * q^9 - 96 * q^10 - 54 * q^11 + 144 * q^12 - 708 * q^15 - 128 * q^16 + 918 * q^17 + 576 * q^18 + 30 * q^19 - 378 * q^21 + 192 * q^22 - 486 * q^23 - 768 * q^24 - 572 * q^25 - 1728 * q^26 + 1456 * q^28 + 3240 * q^29 + 1152 * q^30 - 546 * q^31 + 1062 * q^33 - 1890 * q^35 - 1344 * q^36 - 446 * q^37 - 4320 * q^38 - 3312 * q^39 + 768 * q^40 + 5376 * q^42 + 2344 * q^43 - 432 * q^44 + 5724 * q^45 + 3840 * q^46 + 702 * q^47 - 9212 * q^49 - 3456 * q^50 + 318 * q^51 - 384 * q^52 + 2754 * q^53 - 1440 * q^54 - 17460 * q^57 + 384 * q^58 + 12366 * q^59 + 2832 * q^60 + 7686 * q^61 + 6468 * q^63 + 2048 * q^64 - 3024 * q^65 - 3456 * q^66 - 5062 * q^67 - 7344 * q^68 - 2016 * q^70 + 18792 * q^71 + 4608 * q^72 - 17274 * q^73 - 4320 * q^74 - 5220 * q^75 + 4914 * q^77 + 8832 * q^78 + 794 * q^79 - 3456 * q^80 - 4338 * q^81 + 9984 * q^82 - 5040 * q^84 + 10380 * q^85 - 10368 * q^86 - 12276 * q^87 - 768 * q^88 - 12474 * q^89 + 2688 * q^91 + 7776 * q^92 + 18918 * q^93 + 15168 * q^94 + 8910 * q^95 + 6144 * q^96 - 11448 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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