LMFDB - Embedded newform 45.5.h.a.29.19

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [45,5,Mod(14,45)] 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("45.14"); S:= CuspForms(chi, 5); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(45, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 3])) N = Newforms(chi, 5, names="a")

Level:	$ N $	$=$	$ 45 = 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	45.h (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:	$4.65164833877$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			29.19
Character	$\chi$	$=$	45.29
Dual form			45.5.h.a.14.19

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.87361 - 4.97724i) q^{2} +(8.30470 + 3.46872i) q^{3} +(-8.51525 - 14.7488i) q^{4} +(24.3310 + 5.74467i) q^{5} +(41.1291 - 31.3667i) q^{6} +(-41.4151 - 23.9110i) q^{7} -5.92246 q^{8} +(56.9359 + 57.6134i) q^{9} +(98.5104 - 104.593i) q^{10} +(-73.2455 - 42.2883i) q^{11} +(-19.5569 - 152.022i) q^{12} +(-193.485 + 111.709i) q^{13} +(-238.021 + 137.422i) q^{14} +(182.135 + 132.105i) q^{15} +(119.225 - 206.504i) q^{16} -434.998 q^{17} +(450.367 - 117.825i) q^{18} +378.461 q^{19} +(-122.457 - 407.772i) q^{20} +(-260.999 - 342.231i) q^{21} +(-420.958 + 243.040i) q^{22} +(326.825 + 566.078i) q^{23} +(-49.1842 - 20.5434i) q^{24} +(558.998 + 279.547i) q^{25} +1284.03i q^{26} +(272.991 + 675.956i) q^{27} +814.433i q^{28} +(-430.201 - 248.377i) q^{29} +(1180.90 - 526.910i) q^{30} +(151.498 + 262.402i) q^{31} +(-732.592 - 1268.89i) q^{32} +(-461.595 - 605.260i) q^{33} +(-1250.01 + 2165.09i) q^{34} +(-870.311 - 819.695i) q^{35} +(364.907 - 1330.33i) q^{36} -55.6914i q^{37} +(1087.55 - 1883.69i) q^{38} +(-1994.32 + 256.560i) q^{39} +(-144.099 - 34.0226i) q^{40} +(411.405 - 237.525i) q^{41} +(-2453.37 + 315.616i) q^{42} +(-707.073 - 408.229i) q^{43} +1440.38i q^{44} +(1054.34 + 1728.87i) q^{45} +3756.67 q^{46} +(435.232 - 753.844i) q^{47} +(1706.43 - 1301.39i) q^{48} +(-57.0270 - 98.7737i) q^{49} +(2997.71 - 1978.95i) q^{50} +(-3612.52 - 1508.89i) q^{51} +(3295.14 + 1902.45i) q^{52} -2339.28 q^{53} +(4148.86 + 583.694i) q^{54} +(-1539.21 - 1449.69i) q^{55} +(245.279 + 141.612i) q^{56} +(3143.00 + 1312.77i) q^{57} +(-2472.46 + 1427.47i) q^{58} +(-1019.68 + 588.710i) q^{59} +(397.475 - 3811.19i) q^{60} +(3456.52 - 5986.86i) q^{61} +1741.38 q^{62} +(-980.413 - 3747.46i) q^{63} -4605.53 q^{64} +(-5349.42 + 1606.48i) q^{65} +(-4338.96 + 558.188i) q^{66} +(3356.29 - 1937.75i) q^{67} +(3704.11 + 6415.71i) q^{68} +(750.618 + 5834.77i) q^{69} +(-6580.75 + 1976.26i) q^{70} +5822.30i q^{71} +(-337.201 - 341.213i) q^{72} -6443.82i q^{73} +(-277.189 - 160.035i) q^{74} +(3672.63 + 4260.56i) q^{75} +(-3222.69 - 5581.85i) q^{76} +(2022.31 + 3502.75i) q^{77} +(-4453.93 + 10663.5i) q^{78} +(-2446.72 + 4237.84i) q^{79} +(4087.17 - 4339.54i) q^{80} +(-77.5982 + 6560.54i) q^{81} -2730.21i q^{82} +(-3257.36 + 5641.91i) q^{83} +(-2825.04 + 6763.61i) q^{84} +(-10583.9 - 2498.92i) q^{85} +(-4063.70 + 2346.18i) q^{86} +(-2711.14 - 3554.94i) q^{87} +(433.793 + 250.451i) q^{88} -13898.7i q^{89} +(11634.8 - 279.602i) q^{90} +10684.3 q^{91} +(5566.00 - 9640.59i) q^{92} +(347.944 + 2704.67i) q^{93} +(-2501.37 - 4332.50i) q^{94} +(9208.33 + 2174.13i) q^{95} +(-1682.54 - 13078.9i) q^{96} +(11681.7 + 6744.42i) q^{97} -655.493 q^{98} +(-1733.93 - 6627.64i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 162 q^{4} + 6 q^{5} - 36 q^{6} - 126 q^{9} + 28 q^{10} + 228 q^{11} + 282 q^{14} + 450 q^{15} - 1058 q^{16} - 8 q^{19} - 2196 q^{20} + 1056 q^{21} + 2970 q^{24} - 148 q^{25} + 2370 q^{29} + 1068 q^{30}+ \cdots + 44568 q^{99}+O(q^{100}) $ 44 * q - 162 * q^4 + 6 * q^5 - 36 * q^6 - 126 * q^9 + 28 * q^10 + 228 * q^11 + 282 * q^14 + 450 * q^15 - 1058 * q^16 - 8 * q^19 - 2196 * q^20 + 1056 * q^21 + 2970 * q^24 - 148 * q^25 + 2370 * q^29 + 1068 * q^30 - 1112 * q^31 - 436 * q^34 - 648 * q^36 - 6420 * q^39 - 850 * q^40 + 1830 * q^41 - 1944 * q^45 - 5668 * q^46 + 5396 * q^49 + 13524 * q^50 - 1500 * q^51 + 17766 * q^54 - 3072 * q^55 - 8250 * q^56 - 27348 * q^59 - 28722 * q^60 + 2782 * q^61 + 8348 * q^64 - 24906 * q^65 + 27240 * q^66 + 19662 * q^69 + 4782 * q^70 + 64728 * q^74 + 28446 * q^75 - 1776 * q^76 + 7900 * q^79 - 47754 * q^81 - 113166 * q^84 + 6766 * q^85 + 9192 * q^86 + 10674 * q^90 + 1560 * q^91 - 18826 * q^94 + 58746 * q^95 + 1902 * q^96 + 44568 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/45\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	2.87361	−	4.97724i	0.718402	−	1.24431i	−0.243231	−	0.969968i	$-0.578207\pi$
$2$	2.87361	−	4.97724i	0.718402	−	1.24431i	0.961633	−	0.274340i	$-0.0884595\pi$
$3$	8.30470	+	3.46872i	0.922744	+	0.385414i
$3$	8.30470	+	3.46872i	0.922744	+	0.385414i
$4$	−8.51525	−	14.7488i	−0.532203	−	0.921802i
$5$	24.3310	+	5.74467i	0.973241	+	0.229787i
$5$	24.3310	+	5.74467i	0.973241	+	0.229787i
$6$	41.1291	−	31.3667i	1.14247	−	0.871297i
$7$	−41.4151	−	23.9110i	−0.845206	−	0.487980i	0.0138245	−	0.999904i	$-0.495599\pi$
$7$	−41.4151	−	23.9110i	−0.845206	−	0.487980i	−0.859030	+	0.511925i	$0.828933\pi$
$8$	−5.92246			−0.0925384
$9$	56.9359	+	57.6134i	0.702913	+	0.711276i
$10$	98.5104	−	104.593i	0.985104	−	1.04593i
$11$	−73.2455	−	42.2883i	−0.605335	−	0.349490i	0.165803	−	0.986159i	$-0.446979\pi$
$11$	−73.2455	−	42.2883i	−0.605335	−	0.349490i	−0.771137	+	0.636669i	$0.780312\pi$
$12$	−19.5569	−	152.022i	−0.135812	−	1.05571i
$13$	−193.485	+	111.709i	−1.14488	+	0.660998i	−0.947635	−	0.319356i	$-0.896533\pi$
$13$	−193.485	+	111.709i	−1.14488	+	0.660998i	−0.197247	+	0.980354i	$0.563200\pi$
$14$	−238.021	+	137.422i	−1.21440	+	0.701131i
$15$	182.135	+	132.105i	0.809489	+	0.587135i
$16$	119.225	−	206.504i	0.465723	−	0.806656i
$17$	−434.998			−1.50518			−0.752591	−	0.658488i	$-0.771196\pi$
$17$	−434.998			−1.50518			−0.752591	+	0.658488i	$0.771196\pi$
$18$	450.367	−	117.825i	1.39002	−	0.363658i
$19$	378.461			1.04837			0.524184	−	0.851605i	$-0.324371\pi$
$19$	378.461			1.04837			0.524184	+	0.851605i	$0.324371\pi$
$20$	−122.457	−	407.772i	−0.306144	−	1.01943i
$21$	−260.999	−	342.231i	−0.591835	−	0.776034i
$22$	−420.958	+	243.040i	−0.869747	+	0.502149i
$23$	326.825	+	566.078i	0.617818	+	1.07009i	0.989883	+	0.141885i	$0.0453163\pi$
$23$	326.825	+	566.078i	0.617818	+	1.07009i	−0.372066	+	0.928206i	$0.621350\pi$
$24$	−49.1842	−	20.5434i	−0.0853893	−	0.0356656i
$25$	558.998	+	279.547i	0.894396	+	0.447276i
$26$			1284.03i			1.89945i
$27$	272.991	+	675.956i	0.374473	+	0.927238i
$28$			814.433i			1.03882i
$29$	−430.201	−	248.377i	−0.511535	−	0.295335i	0.221929	−	0.975063i	$-0.428765\pi$
$29$	−430.201	−	248.377i	−0.511535	−	0.295335i	−0.733464	+	0.679728i	$0.762098\pi$
$30$	1180.90	−	526.910i	1.31212	−	0.585456i
$31$	151.498	+	262.402i	0.157646	+	0.273051i	0.934019	−	0.357222i	$-0.116276\pi$
$31$	151.498	+	262.402i	0.157646	+	0.273051i	−0.776373	+	0.630273i	$0.782943\pi$
$32$	−732.592	−	1268.89i	−0.715422	−	1.23915i
$33$	−461.595	−	605.260i	−0.423871	−	0.555794i
$34$	−1250.01	+	2165.09i	−1.08133	+	1.87291i
$35$	−870.311	−	819.695i	−0.710458	−	0.669139i
$36$	364.907	−	1330.33i	0.281564	−	1.02649i
$37$		−	55.6914i		−	0.0406804i	−0.999793	−	0.0203402i	$-0.993525\pi$
$37$		−	55.6914i		−	0.0406804i	0.999793	−	0.0203402i	$-0.00647493\pi$
$38$	1087.55	−	1883.69i	0.753149	−	1.30449i
$39$	−1994.32	+	256.560i	−1.31119	+	0.168679i
$40$	−144.099	−	34.0226i	−0.0900622	−	0.0212641i
$41$	411.405	−	237.525i	0.244738	−	0.141300i	−0.372614	−	0.927986i	$-0.621539\pi$
$41$	411.405	−	237.525i	0.244738	−	0.141300i	0.617353	+	0.786687i	$0.288205\pi$
$42$	−2453.37	+	315.616i	−1.39080	+	0.178920i
$43$	−707.073	−	408.229i	−0.382409	−	0.220784i	0.296457	−	0.955046i	$-0.404195\pi$
$43$	−707.073	−	408.229i	−0.382409	−	0.220784i	−0.678866	+	0.734262i	$0.737528\pi$
$44$			1440.38i			0.743999i
$45$	1054.34	+	1728.87i	0.520662	+	0.853763i
$46$	3756.67			1.77537
$47$	435.232	−	753.844i	0.197027	−	0.341260i	−0.750536	−	0.660829i	$-0.770205\pi$
$47$	435.232	−	753.844i	0.197027	−	0.341260i	0.947563	+	0.319569i	$0.103538\pi$
$48$	1706.43	−	1301.39i	0.740639	−	0.564841i
$49$	−57.0270	−	98.7737i	−0.0237514	−	0.0411386i
$50$	2997.71	−	1978.95i	1.19909	−	0.791581i
$51$	−3612.52	−	1508.89i	−1.38890	−	0.580118i
$52$	3295.14	+	1902.45i	1.21862	+	0.703570i
$53$	−2339.28			−0.832780			−0.416390	−	0.909186i	$-0.636705\pi$
$53$	−2339.28			−0.832780			−0.416390	+	0.909186i	$0.636705\pi$
$54$	4148.86	+	583.694i	1.42279	+	0.200169i
$55$	−1539.21	−	1449.69i	−0.508828	−	0.479236i
$56$	245.279	+	141.612i	0.0782140	+	0.0451569i
$57$	3143.00	+	1312.77i	0.967375	+	0.404055i
$58$	−2472.46	+	1427.47i	−0.734976	+	0.424338i
$59$	−1019.68	+	588.710i	−0.292926	+	0.169121i	−0.639261	−	0.768990i	$-0.720760\pi$
$59$	−1019.68	+	588.710i	−0.292926	+	0.169121i	0.346335	+	0.938111i	$0.387426\pi$
$60$	397.475	−	3811.19i	0.110410	−	1.05866i
$61$	3456.52	−	5986.86i	0.928921	−	1.60894i	0.143792	−	0.989608i	$-0.454070\pi$
$61$	3456.52	−	5986.86i	0.928921	−	1.60894i	0.785130	−	0.619331i	$-0.212596\pi$
$62$	1741.38			0.453013
$63$	−980.413	−	3747.46i	−0.247018	−	0.944182i
$64$	−4605.53			−1.12440
$65$	−5349.42	+	1606.48i	−1.26613	+	0.380231i
$66$	−4338.96	+	558.188i	−0.996089	+	0.128142i
$67$	3356.29	−	1937.75i	0.747669	−	0.431667i	−0.0771820	−	0.997017i	$-0.524592\pi$
$67$	3356.29	−	1937.75i	0.747669	−	0.431667i	0.824851	+	0.565350i	$0.191259\pi$
$68$	3704.11	+	6415.71i	0.801063	+	1.38748i
$69$	750.618	+	5834.77i	0.157660	+	1.22554i
$70$	−6580.75	+	1976.26i	−1.34301	+	0.403318i
$71$			5822.30i			1.15499i	0.816394	+	0.577495i	$0.195970\pi$
$71$			5822.30i			1.15499i	−0.816394	+	0.577495i	$0.804030\pi$
$72$	−337.201	−	341.213i	−0.0650464	−	0.0658204i
$73$		−	6443.82i		−	1.20920i	−0.796530	−	0.604599i	$-0.793333\pi$
$73$		−	6443.82i		−	1.20920i	0.796530	−	0.604599i	$-0.206667\pi$
$74$	−277.189	−	160.035i	−0.0506189	−	0.0292249i
$75$	3672.63	+	4260.56i	0.652912	+	0.757434i
$76$	−3222.69	−	5581.85i	−0.557944	−	0.966388i
$77$	2022.31	+	3502.75i	0.341088	+	0.590782i
$78$	−4453.93	+	10663.5i	−0.732073	+	1.75270i
$79$	−2446.72	+	4237.84i	−0.392039	+	0.679032i	−0.992718	−	0.120459i	$-0.961564\pi$
$79$	−2446.72	+	4237.84i	−0.392039	+	0.679032i	0.600679	+	0.799490i	$0.294897\pi$
$80$	4087.17	−	4339.54i	0.638620	−	0.678054i
$81$	−77.5982	+	6560.54i	−0.0118272	+	0.999930i
$82$		−	2730.21i		−	0.406040i
$83$	−3257.36	+	5641.91i	−0.472835	+	0.818974i	−0.999517	−	0.0310882i	$-0.990103\pi$
$83$	−3257.36	+	5641.91i	−0.472835	+	0.818974i	0.526682	+	0.850063i	$0.323436\pi$
$84$	−2825.04	+	6763.61i	−0.400374	+	0.958562i
$85$	−10583.9	−	2498.92i	−1.46491	−	0.345871i
$86$	−4063.70	+	2346.18i	−0.549446	+	0.317223i
$87$	−2711.14	−	3554.94i	−0.358190	−	0.469671i
$88$	433.793	+	250.451i	0.0560167	+	0.0323413i
$89$		−	13898.7i		−	1.75467i	−0.479881	−	0.877333i	$-0.659320\pi$
$89$		−	13898.7i		−	1.75467i	0.479881	−	0.877333i	$-0.340680\pi$
$90$	11634.8	−	279.602i	1.43639	−	0.0345187i
$91$	10684.3			1.29021
$92$	5566.00	−	9640.59i	0.657609	−	1.13901i
$93$	347.944	+	2704.67i	0.0402294	+	0.312715i
$94$	−2501.37	−	4332.50i	−0.283089	−	0.490324i
$95$	9208.33	+	2174.13i	1.02031	+	0.240901i
$96$	−1682.54	−	13078.9i	−0.182567	−	1.41915i
$97$	11681.7	+	6744.42i	1.24154	+	0.716805i	0.969408	−	0.245454i	$-0.0789372\pi$
$97$	11681.7	+	6744.42i	1.24154	+	0.716805i	0.272134	+	0.962259i	$0.412271\pi$
$98$	−655.493			−0.0682521
$99$	−1733.93	−	6627.64i	−0.176914	−	0.676221i
$100$	−637.001	−	10625.0i	−0.0637001	−	1.06250i
$101$	15773.9	+	9107.04i	1.54631	+	0.892760i	0.998419	+	0.0562073i	$0.0179008\pi$
$101$	15773.9	+	9107.04i	1.54631	+	0.892760i	0.547886	+	0.836553i	$0.315433\pi$
$102$	−17891.1	+	13644.4i	−1.71963	+	1.31146i
$103$	11205.3	−	6469.37i	1.05620	−	0.609800i	0.131825	−	0.991273i	$-0.457916\pi$
$103$	11205.3	−	6469.37i	1.05620	−	0.609800i	0.924380	+	0.381473i	$0.124583\pi$
$104$	1145.91	−	661.590i	0.105946	−	0.0611677i
$105$	−4384.37	−	9826.19i	−0.397675	−	0.891264i
$106$	−6722.17	+	11643.1i	−0.598271	+	1.03624i
$107$	−1372.35			−0.119867			−0.0599333	−	0.998202i	$-0.519089\pi$
$107$	−1372.35			−0.119867			−0.0599333	+	0.998202i	$0.519089\pi$
$108$	7644.99	−	9782.23i	0.655434	−	0.838669i
$109$	8324.99			0.700698			0.350349	−	0.936619i	$-0.386063\pi$
$109$	8324.99			0.700698			0.350349	+	0.936619i	$0.386063\pi$
$110$	−11638.5	+	3495.15i	−0.961861	+	0.288855i
$111$	193.178	−	462.500i	0.0156788	−	0.0375376i
$112$	−9875.44	+	5701.59i	−0.787264	+	0.454527i
$113$	−10406.4	−	18024.4i	−0.814972	−	1.41157i	−0.909348	−	0.416036i	$-0.863419\pi$
$113$	−10406.4	−	18024.4i	−0.814972	−	1.41157i	0.0943766	−	0.995537i	$-0.469914\pi$
$114$	15565.7	−	11871.1i	1.19773	−	0.913439i
$115$	4700.06	+	15650.8i	0.355392	+	1.18342i
$116$			8459.96i			0.628712i
$117$	−17452.2	−	4787.08i	−1.27490	−	0.349703i
$118$			6766.89i			0.485987i
$119$	18015.5	+	10401.2i	1.27219	+	0.734499i
$120$	−1078.69	−	782.388i	−0.0749089	−	0.0543325i
$121$	−3743.90	−	6484.62i	−0.255713	−	0.442908i
$122$	−19865.3	−	34407.8i	−1.33468	−	2.31173i
$123$	4240.50	−	545.522i	0.280290	−	0.0360580i
$124$	2580.08	−	4468.83i	0.167799	−	0.290637i
$125$	11995.1	+	10012.9i	0.767685	+	0.640828i
$126$	−21469.3	−	5888.98i	−1.35231	−	0.370936i
$127$			3442.90i			0.213460i	0.994288	+	0.106730i	$0.0340380\pi$
$127$			3442.90i			0.213460i	−0.994288	+	0.106730i	$0.965962\pi$
$128$	−1513.00	+	2620.60i	−0.0923465	+	0.159949i
$129$	−4456.00	−	5842.86i	−0.267772	−	0.351112i
$130$	−7376.31	+	31241.7i	−0.436468	+	1.84862i
$131$	−4773.97	+	2756.25i	−0.278187	+	0.160611i	−0.632602	−	0.774477i	$-0.718013\pi$
$131$	−4773.97	+	2756.25i	−0.278187	+	0.160611i	0.354415	+	0.935088i	$0.384680\pi$
$132$	−4996.28	+	11961.9i	−0.286747	+	0.686520i
$133$	−15674.0	−	9049.38i	−0.886086	−	0.511582i
$134$		−	22273.4i		−	1.24044i
$135$	2759.00	+	18015.0i	0.151386	+	0.988475i
$136$	2576.26			0.139287
$137$	−2167.08	+	3753.49i	−0.115460	+	0.199983i	−0.917964	−	0.396664i	$-0.870168\pi$
$137$	−2167.08	+	3753.49i	−0.115460	+	0.199983i	0.802503	+	0.596648i	$0.203501\pi$
$138$	31198.0	+	13030.9i	1.63821	+	0.684250i
$139$	−1687.03	−	2922.01i	−0.0873157	−	0.151235i	0.819060	−	0.573708i	$-0.194496\pi$
$139$	−1687.03	−	2922.01i	−0.0873157	−	0.151235i	−0.906376	+	0.422473i	$0.861162\pi$
$140$	−4678.65	+	19816.0i	−0.238707	+	1.01102i
$141$	6229.35	−	4750.75i	0.313332	−	0.238959i
$142$	28979.0	+	16731.0i	1.43716	+	0.829747i
$143$	18895.9			0.924048
$144$	18685.6	−	4888.54i	0.901118	−	0.235751i
$145$	−9040.39	−	8514.62i	−0.429983	−	0.404976i
$146$	−32072.4	−	18517.0i	−1.50462	−	0.868691i
$147$	−130.974	−	1018.10i	−0.00606107	−	0.0471145i
$148$	−821.384	+	474.226i	−0.0374993	+	0.0216502i
$149$	−29042.9	+	16768.0i	−1.30818	+	0.755279i	−0.981793	−	0.189956i	$-0.939165\pi$
$149$	−29042.9	+	16768.0i	−1.30818	+	0.755279i	−0.326389	+	0.945235i	$0.605832\pi$
$150$	31759.5	−	6036.36i	1.41153	−	0.268283i
$151$	−517.293	+	895.978i	−0.0226873	+	0.0392955i	−0.877146	−	0.480224i	$-0.840556\pi$
$151$	−517.293	+	895.978i	−0.0226873	+	0.0392955i	0.854459	+	0.519519i	$0.173889\pi$
$152$	−2241.42			−0.0970143
$153$	−24767.0	−	25061.7i	−1.05801	−	1.07060i
$154$	23245.3			0.980154
$155$	2178.68	+	7254.81i	0.0906840	+	0.301969i
$156$	20766.1	+	27229.2i	0.853307	+	1.11889i
$157$	−3936.83	+	2272.93i	−0.159716	+	0.0922119i	−0.577728	−	0.816230i	$-0.696060\pi$
$157$	−3936.83	+	2272.93i	−0.159716	+	0.0922119i	0.418012	+	0.908442i	$0.362727\pi$
$158$	14061.8	+	24355.8i	0.563283	+	0.975635i
$159$	−19427.0	−	8114.31i	−0.768443	−	0.320965i
$160$	−10535.4	−	35081.8i	−0.411538	−	1.37038i
$161$		−	31258.9i		−	1.20593i
$162$	32430.4	+	19238.6i	1.23573	+	0.733068i
$163$			35857.6i			1.34960i	0.737999	+	0.674802i	$0.235771\pi$
$163$			35857.6i			1.34960i	−0.737999	+	0.674802i	$0.764229\pi$
$164$	−7006.43	−	4045.17i	−0.260501	−	0.150400i
$165$	−7754.06	−	17378.3i	−0.284814	−	0.638321i
$166$	18720.8	+	32425.3i	0.679371	+	1.17671i
$167$	−11108.8	−	19241.0i	−0.398322	−	0.689914i	0.595197	−	0.803580i	$-0.297074\pi$
$167$	−11108.8	−	19241.0i	−0.398322	−	0.689914i	−0.993519	+	0.113666i	$0.963741\pi$
$168$	1545.76	+	2026.85i	0.0547674	+	0.0718130i
$169$	10677.1	−	18493.3i	0.373836	−	0.647502i
$170$	−42851.8	+	45497.9i	−1.48276	+	1.57432i
$171$	21548.0	+	21804.4i	0.736911	+	0.745679i
$172$			13904.7i			0.470007i
$173$	−17596.1	+	30477.3i	−0.587928	+	1.01832i	0.406575	+	0.913617i	$0.366723\pi$
$173$	−17596.1	+	30477.3i	−0.587928	+	1.01832i	−0.994503	+	0.104704i	$0.966610\pi$
$174$	−25484.5	+	3278.47i	−0.841740	+	0.108286i
$175$	−16466.7	−	24943.7i	−0.537687	−	0.814487i
$176$	−17465.4	+	10083.7i	−0.563837	+	0.325531i
$177$	−10510.2	+	1352.09i	−0.335477	+	0.0431577i
$178$	−69177.2	−	39939.5i	−2.18335	−	1.26056i
$179$			44189.5i			1.37915i	0.724213	+	0.689577i	$0.242203\pi$
$179$			44189.5i			1.37915i	−0.724213	+	0.689577i	$0.757797\pi$
$180$	16520.9	−	30272.0i	0.509903	−	0.934322i
$181$	−41327.3			−1.26148			−0.630740	−	0.775994i	$-0.717249\pi$
$181$	−41327.3			−1.26148			−0.630740	+	0.775994i	$0.717249\pi$
$182$	30702.4	−	53178.1i	0.926892	−	1.60542i
$183$	49472.1	−	37729.4i	1.47726	−	1.12662i
$184$	−1935.61	−	3352.58i	−0.0571719	−	0.0990246i
$185$	319.929	−	1355.03i	0.00934781	−	0.0395918i
$186$	14461.6	+	6040.36i	0.418015	+	0.174597i
$187$	31861.6	+	18395.3i	0.911139	+	0.526046i
$188$	−14824.4			−0.419433
$189$	4856.86	−	34522.3i	0.135966	−	0.966442i
$190$	37282.3	−	39584.4i	1.03275	−	1.09652i
$191$	20718.0	+	11961.5i	0.567912	+	0.327884i	0.756315	−	0.654208i	$-0.226998\pi$
$191$	20718.0	+	11961.5i	0.567912	+	0.327884i	−0.188403	+	0.982092i	$0.560331\pi$
$192$	−38247.5	−	15975.3i	−1.03753	−	0.433358i
$193$	−2034.57	+	1174.66i	−0.0546209	+	0.0315354i	−0.527062	−	0.849827i	$-0.676706\pi$
$193$	−2034.57	+	1174.66i	−0.0546209	+	0.0315354i	0.472441	+	0.881362i	$0.343373\pi$
$194$	67137.1	−	38761.6i	1.78385	−	1.02991i
$195$	−49997.7	−	5214.33i	−1.31486	−	0.137129i
$196$	−971.198	+	1682.16i	−0.0252811	+	0.0437881i
$197$	9314.30			0.240004			0.120002	−	0.992774i	$-0.461710\pi$
$197$	9314.30			0.240004			0.120002	+	0.992774i	$0.461710\pi$
$198$	−37970.0	−	10415.1i	−0.968523	−	0.265664i
$199$	−6189.82			−0.156305			−0.0781524	−	0.996941i	$-0.524902\pi$
$199$	−6189.82			−0.156305			−0.0781524	+	0.996941i	$0.524902\pi$
$200$	−3310.64	−	1655.61i	−0.0827660	−	0.0413902i
$201$	34594.5	−	4450.42i	0.856277	−	0.110156i
$202$	90655.8	−	52340.2i	2.22174	−	1.28272i
$203$	11877.9	+	20573.1i	0.288235	+	0.499238i
$204$	8507.21	+	66129.1i	0.204422	+	1.58903i
$205$	11374.4	−	3415.84i	0.270658	−	0.0812811i
$206$		−	74361.7i		−	1.75233i
$207$	−14005.6	+	51059.7i	−0.326858	+	1.19162i
$208$			53273.9i			1.23137i
$209$	−27720.5	−	16004.5i	−0.634613	−	0.366394i
$210$	−61506.2	−	6414.57i	−1.39470	−	0.145455i
$211$	−716.811	−	1241.55i	−0.0161005	−	0.0278869i	0.857863	−	0.513879i	$-0.171792\pi$
$211$	−716.811	−	1241.55i	−0.0161005	−	0.0278869i	−0.873963	+	0.485992i	$0.838459\pi$
$212$	19919.5	+	34501.7i	0.443208	+	0.767659i
$213$	−20195.9	+	48352.4i	−0.445149	+	1.06576i
$214$	−3943.60	+	6830.52i	−0.0861124	+	0.149151i
$215$	−14858.7	−	13994.5i	−0.321442	−	0.302748i
$216$	−1616.78	−	4003.32i	−0.0346532	−	0.0858051i
$217$		−	14489.9i		−	0.307712i
$218$	23922.8	−	41435.4i	0.503383	−	0.871884i
$219$	22351.8	−	53514.0i	0.466042	−	1.11578i
$220$	−8274.52	+	35045.9i	−0.170961	+	0.724090i
$221$	84165.5	−	48593.0i	1.72326	−	0.994922i
$222$	−1746.85	−	2290.54i	−0.0354447	−	0.0464763i
$223$	−322.537	−	186.217i	−0.00648589	−	0.00374463i	0.496754	−	0.867892i	$-0.334525\pi$
$223$	−322.537	−	186.217i	−0.00648589	−	0.00374463i	−0.503239	+	0.864147i	$0.667859\pi$
$224$			70068.1i			1.39645i
$225$	15721.4	+	48122.0i	0.310546	+	0.950558i
$226$	−119615.			−2.34191
$227$	15116.7	−	26182.9i	0.293363	−	0.508119i	−0.681240	−	0.732060i	$-0.738559\pi$
$227$	15116.7	−	26182.9i	0.293363	−	0.508119i	0.974603	+	0.223941i	$0.0718922\pi$
$228$	−7401.52	−	57534.2i	−0.142381	−	1.10677i
$229$	22086.6	+	38255.1i	0.421171	+	0.729489i	0.996054	−	0.0887464i	$-0.0282861\pi$
$229$	22086.6	+	38255.1i	0.421171	+	0.729489i	−0.574884	+	0.818235i	$0.694953\pi$
$230$	91403.7	+	21580.9i	1.72786	+	0.407956i
$231$	4644.63	+	36104.1i	0.0870417	+	0.676601i
$232$	2547.85	+	1471.00i	0.0473367	+	0.0273298i
$233$	22978.1			0.423255			0.211628	−	0.977350i	$-0.432124\pi$
$233$	22978.1			0.423255			0.211628	+	0.977350i	$0.432124\pi$
$234$	−73977.1	+	73107.3i	−1.35103	+	1.33515i
$235$	14920.2	−	15841.5i	0.270172	−	0.286854i
$236$	17365.6	+	10026.0i	0.311792	+	0.180013i
$237$	−35019.1	+	26707.0i	−0.623460	+	0.475475i
$238$	103539.	−	59778.2i	1.82789	−	1.05533i
$239$	−58892.2	+	34001.4i	−1.03101	+	0.595253i	−0.917273	−	0.398258i	$-0.869615\pi$
$239$	−58892.2	+	34001.4i	−1.03101	+	0.595253i	−0.113735	+	0.993511i	$0.536281\pi$
$240$	48995.3	−	21861.3i	0.850614	−	0.379537i
$241$	−34731.9	+	60157.4i	−0.597991	+	1.03575i	0.395126	+	0.918627i	$0.370701\pi$
$241$	−34731.9	+	60157.4i	−0.597991	+	1.03575i	−0.993117	+	0.117124i	$0.962633\pi$
$242$	−43034.0			−0.734820
$243$	−23401.1	+	54214.1i	−0.396300	+	0.918121i
$244$	−117732.			−1.97750
$245$	−820.104	−	2730.87i	−0.0136627	−	0.0454955i
$246$	9470.35	−	22673.6i	0.156493	−	0.374671i
$247$	−73226.4	+	42277.3i	−1.20026	+	0.692968i
$248$	−897.239	−	1554.06i	−0.0145883	−	0.0252677i
$249$	−46621.6	+	35555.5i	−0.751950	+	0.573467i
$250$	84305.9	−	30929.1i	1.34889	−	0.494865i
$251$		−	44839.6i		−	0.711728i	−0.934538	−	0.355864i	$-0.884187\pi$
$251$		−	44839.6i		−	0.711728i	0.934538	−	0.355864i	$-0.115813\pi$
$252$	−46922.2	+	46370.5i	−0.738886	+	0.730198i
$253$		−	55283.6i		−	0.863684i
$254$	17136.1	+	9893.53i	0.265610	+	0.153350i
$255$	−79228.4	−	57465.5i	−1.21843	−	0.883745i
$256$	−28148.6	−	48754.9i	−0.429514	−	0.743941i
$257$	−256.172	−	443.703i	−0.00387852	−	0.00671779i	0.864080	−	0.503355i	$-0.167901\pi$
$257$	−256.172	−	443.703i	−0.00387852	−	0.00671779i	−0.867958	+	0.496637i	$0.834568\pi$
$258$	−41886.1	+	5388.46i	−0.629260	+	0.0809515i
$259$	−1331.64	+	2306.47i	−0.0198512	+	0.0343833i
$260$	69245.3	+	65218.1i	1.02434	+	0.964765i
$261$	−10184.1	−	38926.9i	−0.149500	−	0.571437i
$262$			31681.6i			0.461534i
$263$	−23457.5	+	40629.7i	−0.339134	+	0.587397i	−0.984270	−	0.176671i	$-0.943467\pi$
$263$	−23457.5	+	40629.7i	−0.339134	+	0.587397i	0.645136	+	0.764068i	$0.276801\pi$
$264$	2733.78	+	3584.63i	0.0392243	+	0.0514323i
$265$	−56917.1	−	13438.4i	−0.810496	−	0.191362i
$266$	−90081.7	+	52008.7i	−1.27313	+	0.735043i
$267$	48210.8	−	115425.i	0.676272	−	1.61911i
$268$	−57159.2	−	33000.9i	−0.795823	−	0.459469i
$269$			18619.3i			0.257311i	0.991689	+	0.128655i	$0.0410661\pi$
$269$			18619.3i			0.257311i	−0.991689	+	0.128655i	$0.958934\pi$
$270$	97592.9	+	38035.7i	1.33872	+	0.521752i
$271$	119151.			1.62240			0.811201	−	0.584767i	$-0.198814\pi$
$271$	119151.			1.62240			0.811201	+	0.584767i	$0.198814\pi$
$272$	−51862.7	+	89828.8i	−0.700998	+	1.21416i
$273$	88729.5	+	37060.7i	1.19054	+	0.497266i
$274$	12454.7	+	21572.1i	0.165894	+	0.287337i
$275$	−29122.5	−	44114.6i	−0.385090	−	0.583334i
$276$	79664.5	−	60755.3i	1.04579	−	0.797565i
$277$	−24078.5	−	13901.7i	−0.313812	−	0.181179i	0.334819	−	0.942282i	$-0.391325\pi$
$277$	−24078.5	−	13901.7i	−0.313812	−	0.181179i	−0.648631	+	0.761103i	$0.724658\pi$
$278$	−19391.4			−0.250911
$279$	−6492.18	+	23668.4i	−0.0834031	+	0.304061i
$280$	5154.38	+	4854.61i	0.0657446	+	0.0619211i
$281$	4746.39	+	2740.33i	0.0601106	+	0.0347049i	0.529754	−	0.848151i	$-0.322284\pi$
$281$	4746.39	+	2740.33i	0.0601106	+	0.0347049i	−0.469644	+	0.882856i	$0.655618\pi$
$282$	−5744.89	−	44656.7i	−0.0722409	−	0.561550i
$283$	104022.	−	60056.9i	1.29883	−	0.749877i	0.318624	−	0.947881i	$-0.396779\pi$
$283$	104022.	−	60056.9i	1.29883	−	0.749877i	0.980201	+	0.198004i	$0.0634460\pi$
$284$	85872.2	−	49578.3i	1.06467	−	0.614689i
$285$	68931.0	+	49996.7i	0.848642	+	0.615533i
$286$	54299.3	−	94049.2i	0.663838	−	1.14980i
$287$	−22717.8			−0.275806
$288$	31394.0	−	114452.i	0.378496	−	1.37987i
$289$	105702.			1.26558
$290$	−68357.8	+	20528.5i	−0.812816	+	0.244096i
$291$	73618.2	+	96530.8i	0.869359	+	1.13993i
$292$	−95038.8	+	54870.7i	−1.11464	+	0.643539i
$293$	−10131.5	−	17548.3i	−0.118016	−	0.204409i	0.800966	−	0.598710i	$-0.204320\pi$
$293$	−10131.5	−	17548.3i	−0.118016	−	0.204409i	−0.918981	+	0.394301i	$0.870987\pi$
$294$	−5443.67	−	2273.72i	−0.0629792	−	0.0263053i
$295$	−28191.7	+	8466.22i	−0.323949	+	0.0972849i
$296$			329.830i			0.00376450i
$297$	8589.69	−	61055.1i	0.0973789	−	0.692164i
$298$			192738.i			2.17038i
$299$	−126472.	−	73018.4i	−1.41466	−	0.816752i
$300$	31565.0	−	90446.8i	0.350722	−	1.00496i
$301$	19522.3	+	33813.7i	0.215476	+	0.373215i
$302$	2972.99	+	5149.38i	0.0325972	+	0.0564600i
$303$	99407.3	+	130346.i	1.08276	+	1.41976i
$304$	45122.0	−	78153.6i	0.488249	−	0.845672i
$305$	118493.	−	125810.i	1.27378	−	1.35243i
$306$	−195909.	+	51253.8i	−2.09224	+	0.547372i
$307$		−	132432.i		−	1.40512i	−0.711623	−	0.702562i	$-0.752039\pi$
$307$		−	132432.i		−	1.40512i	0.711623	−	0.702562i	$-0.247961\pi$
$308$	34441.0	−	59653.5i	0.363056	−	0.628832i
$309$	115497.	−	14858.2i	1.20963	−	0.155614i
$310$	42369.6	+	10003.7i	0.440890	+	0.104096i
$311$	−118174.	+	68227.6i	−1.22180	+	0.705406i	−0.965301	−	0.261139i	$-0.915902\pi$
$311$	−118174.	+	68227.6i	−1.22180	+	0.705406i	−0.256498	+	0.966545i	$0.582569\pi$
$312$	11811.3	−	1519.47i	0.121335	−	0.0156093i
$313$	−94500.3	−	54559.8i	−0.964594	−	0.556909i	−0.0670101	−	0.997752i	$-0.521346\pi$
$313$	−94500.3	−	54559.8i	−0.964594	−	0.556909i	−0.897584	+	0.440844i	$0.854679\pi$
$314$			26126.0i			0.264981i
$315$	−2326.54	−	96811.6i	−0.0234471	−	0.975678i
$316$	83337.5			0.834577
$317$	21419.5	−	37099.7i	0.213153	−	0.369191i	−0.739547	−	0.673105i	$-0.764960\pi$
$317$	21419.5	−	37099.7i	0.213153	−	0.369191i	0.952700	+	0.303914i	$0.0982935\pi$
$318$	−96212.4	+	73375.4i	−0.951430	+	0.725599i
$319$	21006.9	+	36384.9i	0.206433	+	0.357553i
$320$	−112057.	−	26457.2i	−1.09431	−	0.258371i
$321$	−11397.0	−	4760.31i	−0.110606	−	0.0461982i
$322$	−155583.	−	89825.9i	−1.50055	−	0.866343i
$323$	−164630.			−1.57798
$324$	97421.1	−	54720.1i	0.928032	−	0.521263i
$325$	−139385.	+	8356.59i	−1.31963	+	0.0791157i
$326$	178472.	+	103041.i	1.67932	+	0.969559i
$327$	69136.5	+	28877.1i	0.646565	+	0.270058i
$328$	−2436.53	+	1406.73i	−0.0226477	+	0.0130757i
$329$	−36050.3	+	20813.7i	−0.333056	+	0.192290i
$330$	−108778.	−	11344.6i	−0.998880	−	0.104175i
$331$	54784.8	−	94890.0i	0.500039	−	0.866093i	−0.499961	−	0.866048i	$-0.666652\pi$
$331$	54784.8	−	94890.0i	0.500039	−	0.866093i	1.00000		4.48028e-5i	$-1.42612e-5\pi$
$332$	110949.			1.00658
$333$	3208.57	−	3170.84i	0.0289350	−	0.0285948i
$334$	−127689.			−1.14462
$335$	92793.6	−	27866.7i	0.826854	−	0.248311i
$336$	−101790.	+	13094.8i	−0.901624	+	0.115990i
$337$	−7974.17	+	4603.89i	−0.0702143	+	0.0405383i	−0.534696	−	0.845044i	$-0.679574\pi$
$337$	−7974.17	+	4603.89i	−0.0702143	+	0.0405383i	0.464482	+	0.885583i	$0.346241\pi$
$338$	−61363.7	−	106285.i	−0.537128	−	0.930334i
$339$	−23900.2	−	185784.i	−0.207971	−	1.61662i
$340$	53268.7	+	177380.i	0.460802	+	1.53443i
$341$		−	25626.3i		−	0.220383i
$342$	170446.	−	44592.2i	1.45725	−	0.381248i
$343$			120275.i			1.02232i
$344$	4187.61	+	2417.72i	0.0353875	+	0.0204310i
$345$	−15255.6	+	146278.i	−0.128171	+	1.22897i
$346$	101129.	+	175160.i	0.844737	+	1.46313i
$347$	11277.8	+	19533.8i	0.0936628	+	0.162229i	0.909050	−	0.416688i	$-0.136809\pi$
$347$	11277.8	+	19533.8i	0.0936628	+	0.162229i	−0.815387	+	0.578916i	$0.803476\pi$
$348$	−29345.2	+	70257.4i	−0.242314	+	0.580141i
$349$	−101902.	+	176500.i	−0.836629	+	1.44908i	0.0560687	+	0.998427i	$0.482143\pi$
$349$	−101902.	+	176500.i	−0.836629	+	1.44908i	−0.892697	+	0.450657i	$0.851190\pi$
$350$	−171469.	+	10280.1i	−1.39975	+	0.0839193i
$351$	−128330.	−	100292.i	−1.04163	−	0.814051i
$352$			123920.i			1.00013i
$353$	32305.1	−	55954.1i	0.259252	−	0.449038i	−0.706790	−	0.707424i	$-0.749857\pi$
$353$	32305.1	−	55954.1i	0.259252	−	0.449038i	0.966042	+	0.258386i	$0.0831906\pi$
$354$	−23472.5	+	56196.9i	−0.187306	+	0.448442i
$355$	−33447.2	+	141663.i	−0.265401	+	1.12408i
$356$	−204990.	+	118351.i	−1.61746	+	0.933839i
$357$	113534.	+	148870.i	0.890819	+	1.16807i
$358$	219941.	+	126983.i	1.71609	+	0.990787i
$359$			39569.8i			0.307026i	0.988147	+	0.153513i	$0.0490587\pi$
$359$			39569.8i			0.307026i	−0.988147	+	0.153513i	$0.950941\pi$
$360$	−6244.28	−	10239.2i	−0.0481812	−	0.0790059i
$361$	12911.4			0.0990741
$362$	−118759.	+	205696.i	−0.906250	+	1.56967i
$363$	−8598.59	−	66839.4i	−0.0652550	−	0.507247i
$364$	−90979.1	−	157580.i	−0.686656	−	1.18932i
$365$	37017.6	−	156785.i	0.277858	−	1.17684i
$366$	−45624.6	−	354654.i	−0.340594	−	2.64754i
$367$	168361.	+	97203.5i	1.25000	+	0.721688i	0.971109	−	0.238634i	$-0.0766998\pi$
$367$	168361.	+	97203.5i	1.25000	+	0.721688i	0.278891	+	0.960323i	$0.410033\pi$
$368$	155863.			1.15093
$369$	37108.3	+	10178.7i	0.272533	+	0.0747551i
$370$	−5824.95	−	5486.18i	−0.0425489	−	0.0400744i
$371$	96881.5	+	55934.5i	0.703871	+	0.406380i
$372$	36927.9	−	28162.7i	0.266851	−	0.203511i
$373$	−92982.6	+	53683.5i	−0.668319	+	0.385854i	−0.795439	−	0.606033i	$-0.792760\pi$
$373$	−92982.6	+	53683.5i	−0.668319	+	0.385854i	0.127120	+	0.991887i	$0.459427\pi$
$374$	183116.	−	105722.i	1.30913	−	0.755826i
$375$	64883.4	+	124762.i	0.461393	+	0.887196i
$376$	−2577.64	+	4464.61i	−0.0182325	+	0.0315797i
$377$	110983.			0.780863
$378$	−157869.	−	123377.i	−1.10487	−	0.863478i
$379$	231550.			1.61200			0.806002	−	0.591913i	$-0.201627\pi$
$379$	231550.			1.61200			0.806002	+	0.591913i	$0.201627\pi$
$380$	−46345.3	−	154326.i	−0.320951	−	1.06874i
$381$	−11942.4	+	28592.2i	−0.0822704	+	0.196969i
$382$	119071.	−	68745.5i	0.815978	−	0.471105i
$383$	23281.5	+	40324.7i	0.158713	+	0.274899i	0.934405	−	0.356213i	$-0.115932\pi$
$383$	23281.5	+	40324.7i	0.158713	+	0.274899i	−0.775692	+	0.631112i	$0.782599\pi$
$384$	−21655.2	+	16515.1i	−0.146859	+	0.112000i
$385$	29082.8	+	96843.0i	0.196207	+	0.653351i
$386$			13502.1i			0.0906204i
$387$	−16738.4	−	63979.8i	−0.111762	−	0.427190i
$388$		−	229721.i		−	1.52594i
$389$	−13106.7	−	7567.17i	−0.0866154	−	0.0500074i	0.456067	−	0.889946i	$-0.349258\pi$
$389$	−13106.7	−	7567.17i	−0.0866154	−	0.0500074i	−0.542682	+	0.839938i	$0.682591\pi$
$390$	−169627.	+	233866.i	−1.11523	+	1.53758i
$391$	−142168.	−	246243.i	−0.929928	−	1.61068i
$392$	337.740	+	584.983i	0.00219791	+	0.00380690i
$393$	−49207.0	+	6330.27i	−0.318597	+	0.0409861i
$394$	26765.7	−	46359.5i	0.172419	−	0.298639i
$395$	−83876.1	+	89055.3i	−0.537581	+	0.570776i
$396$	−82985.2	+	82009.5i	−0.529188	+	0.522966i
$397$		−	49119.2i		−	0.311652i	−0.987784	−	0.155826i	$-0.950196\pi$
$397$		−	49119.2i		−	0.311652i	0.987784	−	0.155826i	$-0.0498040\pi$
$398$	−17787.1	+	30808.2i	−0.112290	+	0.194491i
$399$	−98777.9	−	129521.i	−0.620460	−	0.813569i
$400$	124374.	−	82106.1i	0.777339	−	0.513163i
$401$	−116070.	+	67013.0i	−0.721823	+	0.416745i	−0.815423	−	0.578865i	$-0.803496\pi$
$401$	−116070.	+	67013.0i	−0.721823	+	0.416745i	0.0936000	+	0.995610i	$0.470163\pi$
$402$	77260.1	−	184974.i	0.478083	−	1.14461i
$403$	−58625.1	−	33847.2i	−0.360972	−	0.208407i
$404$		−	310195.i		−	1.90052i
$405$	−39576.2	+	159179.i	−0.241281	+	0.970455i
$406$	136529.			0.828274
$407$	−2355.10	+	4079.15i	−0.0142174	+	0.0246252i
$408$	21395.0	+	8936.32i	0.128526	+	0.0536832i
$409$	27109.9	+	46955.6i	0.162062	+	0.280699i	0.935608	−	0.353041i	$-0.114852\pi$
$409$	27109.9	+	46955.6i	0.162062	+	0.280699i	−0.773546	+	0.633740i	$0.781519\pi$
$410$	15684.2	−	66428.9i	0.0933027	−	0.395175i
$411$	−31016.7	+	23654.6i	−0.183617	+	0.140033i
$412$	−190831.	−	110177.i	−1.12423	−	0.649075i
$413$	56306.6			0.330110
$414$	213890.	+	216435.i	1.24793	+	1.26277i
$415$	−111666.	+	118561.i	−0.648372	+	0.688408i
$416$	283491.	+	163674.i	1.63815	+	0.945784i
$417$	−3874.58	−	30118.3i	−0.0222819	−	0.173204i
$418$	−159316.	+	91981.1i	−0.911815	+	0.526436i
$419$	152988.	−	88327.4i	0.871421	−	0.503115i	0.00360107	−	0.999994i	$-0.498854\pi$
$419$	152988.	−	88327.4i	0.871421	−	0.503115i	0.867820	+	0.496878i	$0.165520\pi$
$420$	−107591.	+	148337.i	−0.609926	+	0.840911i
$421$	−71752.2	+	124278.i	−0.404829	+	0.701184i	−0.994302	−	0.106605i	$-0.966002\pi$
$421$	−71752.2	+	124278.i	−0.404829	+	0.701184i	0.589473	+	0.807788i	$0.299335\pi$
$422$	−8239.33			−0.0462665
$423$	68211.8	−	17845.6i	0.381223	−	0.0997359i
$424$	13854.3			0.0770642
$425$	−243163.	−	121603.i	−1.34623	−	0.673232i
$426$	182626.	+	239466.i	1.00634	+	1.31955i
$427$	−286304.	+	165298.i	−1.57026	+	0.906590i
$428$	11685.9	+	20240.6i	0.0637933	+	0.110493i
$429$	156924.	+	65544.5i	0.852660	+	0.356141i
$430$	−112352.	+	33740.3i	−0.607637	+	0.182479i
$431$			96119.3i			0.517435i	0.965953	+	0.258718i	$0.0832999\pi$
$431$			96119.3i			0.517435i	−0.965953	+	0.258718i	$0.916700\pi$
$432$	172135.	+	24217.3i	0.922363	+	0.129765i
$433$		−	313068.i		−	1.66979i	−0.550406	−	0.834897i	$-0.685527\pi$
$433$		−	313068.i		−	1.66979i	0.550406	−	0.834897i	$-0.314473\pi$
$434$	−72119.4	−	41638.2i	−0.382889	−	0.221061i
$435$	−45542.8	−	102070.i	−0.240681	−	0.539411i
$436$	−70889.3	−	122784.i	−0.372913	−	0.645905i
$437$	123691.	+	214238.i	0.647700	+	1.12185i
$438$	−202121.	−	265028.i	−1.05357	−	1.38148i
$439$	52165.3	−	90353.0i	0.270678	−	0.468828i	−0.698358	−	0.715749i	$-0.746085\pi$
$439$	52165.3	−	90353.0i	0.270678	−	0.468828i	0.969036	+	0.246921i	$0.0794188\pi$
$440$	9115.88	+	8585.72i	0.0470862	+	0.0443477i
$441$	2443.80	−	8909.29i	0.0125657	−	0.0458106i
$442$		−	558549.i		−	2.85902i
$443$	15363.5	−	26610.4i	0.0782860	−	0.135595i	−0.824225	−	0.566263i	$-0.808389\pi$
$443$	15363.5	−	26610.4i	0.0782860	−	0.135595i	0.902511	+	0.430668i	$0.141722\pi$
$444$	−8466.30	+	1089.15i	−0.0429465	+	0.00552488i
$445$	79843.6	−	338170.i	0.403199	−	1.70771i
$446$	−1853.69	+	1070.23i	−0.00931896	+	0.00538030i
$447$	−299356.	+	38510.8i	−1.49821	+	0.192738i
$448$	190738.	+	110123.i	0.950346	+	0.548683i
$449$			47332.1i			0.234781i	0.993086	+	0.117391i	$0.0374529\pi$
$449$			47332.1i			0.234781i	−0.993086	+	0.117391i	$0.962547\pi$
$450$	284692.	+	60034.8i	1.40588	+	0.296468i
$451$	−40178.1			−0.197531
$452$	−177226.	+	306964.i	−0.867461	+	1.50249i
$453$	−7403.86	+	5646.48i	−0.0360796	+	0.0275157i
$454$	−86878.9	−	150479.i	−0.421505	−	0.730068i
$455$	259959.	+	61377.6i	1.25569	+	0.296474i
$456$	−18614.3	−	7774.85i	−0.0895193	−	0.0373906i
$457$	−101954.	−	58863.4i	−0.488173	−	0.281847i	0.235643	−	0.971840i	$-0.424280\pi$
$457$	−101954.	−	58863.4i	−0.488173	−	0.281847i	−0.723816	+	0.689993i	$0.757614\pi$
$458$	253873.			1.21028
$459$	−118750.	−	294040.i	−0.563650	−	1.39566i
$460$	190808.	−	202591.i	0.901741	−	0.957423i
$461$	−38057.7	−	21972.6i	−0.179077	−	0.103390i	0.407782	−	0.913079i	$-0.366302\pi$
$461$	−38057.7	−	21972.6i	−0.179077	−	0.103390i	−0.586859	+	0.809689i	$0.699636\pi$
$462$	193045.	+	80631.6i	0.904431	+	0.377765i
$463$	−32818.2	+	18947.6i	−0.153092	+	0.0883878i	−0.574589	−	0.818442i	$-0.694838\pi$
$463$	−32818.2	+	18947.6i	−0.153092	+	0.0883878i	0.421497	+	0.906830i	$0.361505\pi$
$464$	−102582.	+	59225.5i	−0.476467	+	0.275089i
$465$	−7071.61	+	67806.2i	−0.0327049	+	0.313591i
$466$	66030.0	−	114367.i	0.304067	−	0.526660i
$467$	−229722.			−1.05334			−0.526671	−	0.850069i	$-0.676560\pi$
$467$	−229722.			−1.05334			−0.526671	+	0.850069i	$0.676560\pi$
$468$	78005.4	+	298162.i	0.356150	+	1.36132i
$469$	−185335.			−0.842579
$470$	−35972.1	−	119784.i	−0.162844	−	0.542254i
$471$	−40578.3	+	5220.22i	−0.182916	+	0.0235314i
$472$	6038.99	−	3486.61i	0.0271069	−	0.0156502i
$473$	34526.6	+	59801.9i	0.154323	+	0.267296i
$474$	32295.6	+	251044.i	0.143743	+	1.11736i
$475$	211559.	+	105798.i	0.937656	+	0.468910i
$476$		−	354276.i		−	1.56361i
$477$	−133189.	−	134774.i	−0.585372	−	0.592337i
$478$			390827.i			1.71052i
$479$	−42607.9	−	24599.7i	−0.185703	−	0.107216i	0.404266	−	0.914641i	$-0.367527\pi$
$479$	−42607.9	−	24599.7i	−0.185703	−	0.107216i	−0.589969	+	0.807426i	$0.700860\pi$
$480$	34195.9	−	327888.i	0.148420	−	1.42313i
$481$	6221.21	+	10775.5i	0.0268896	+	0.0465742i
$482$	199612.	+	345738.i	0.859196	+	1.48817i
$483$	108428.	−	259596.i	0.464782	−	1.11276i
$484$	−63760.4	+	110436.i	−0.272183	+	0.471434i
$485$	245483.	+	231206.i	1.04361	+	0.982914i
$486$	202591.	+	272263.i	0.857723	+	1.15270i
$487$			154002.i			0.649335i	0.945828	+	0.324668i	$0.105252\pi$
$487$			154002.i			0.649335i	−0.945828	+	0.324668i	$0.894748\pi$
$488$	−20471.1	+	35456.9i	−0.0859609	+	0.148889i
$489$	−124380.	+	297787.i	−0.520156	+	1.24534i
$490$	−15948.8	−	3765.59i	−0.0664258	−	0.0156834i
$491$	146133.	−	84370.0i	0.606158	−	0.349965i	−0.165302	−	0.986243i	$-0.552860\pi$
$491$	146133.	−	84370.0i	0.606158	−	0.349965i	0.771460	+	0.636278i	$0.219527\pi$
$492$	−44154.7	−	57897.2i	−0.182409	−	0.239182i
$493$	187137.	+	108043.i	0.769954	+	0.444533i
$494$			485954.i			1.99132i
$495$	−4114.65	−	171218.i	−0.0167928	−	0.698778i
$496$	72249.3			0.293677
$497$	139217.	−	241131.i	0.563612	−	0.976204i
$498$	42995.8	+	334219.i	0.173367	+	1.34764i
$499$	−87254.6	−	151129.i	−0.350419	−	0.606943i	0.635904	−	0.771768i	$-0.280627\pi$
$499$	−87254.6	−	151129.i	−0.350419	−	0.606943i	−0.986323	+	0.164825i	$0.947294\pi$
$500$	45538.1	−	262176.i	0.182153	−	1.04870i
$501$	−25513.5	−	198324.i	−0.101647	−	0.790133i
$502$	−223177.	−	128851.i	−0.885610	−	0.511307i
$503$	−384923.			−1.52138			−0.760691	−	0.649115i	$-0.775140\pi$
$503$	−384923.			−1.52138			−0.760691	+	0.649115i	$0.775140\pi$
$504$	5806.46	+	22194.2i	0.0228586	+	0.0873731i
$505$	331477.	+	312199.i	1.29978	+	1.22419i
$506$	−275159.	−	158863.i	−1.07469	−	0.620473i
$507$	152818.	−	116545.i	0.594511	−	0.453397i
$508$	50778.7	−	29317.1i	0.196768	−	0.113604i
$509$	−115913.	+	66922.3i	−0.447400	+	0.258306i	−0.706731	−	0.707482i	$-0.749831\pi$
$509$	−115913.	+	66922.3i	−0.447400	+	0.258306i	0.259332	+	0.965788i	$0.416498\pi$
$510$	−513691.	+	229205.i	−1.97497	+	0.881218i
$511$	−154078.	+	266871.i	−0.590065	+	1.02202i
$512$	−371969.			−1.41895
$513$	103316.	+	255823.i	0.392585	+	0.972086i
$514$	−2944.55			−0.0111453
$515$	309800.	−	93035.7i	1.16807	−	0.350780i
$516$	−48231.5	+	115474.i	−0.181147	+	0.433696i
$517$	−63757.6	+	36810.5i	−0.238534	+	0.137718i
$518$	7653.21	+	13255.8i	0.0285223	+	0.0494020i
$519$	−251848.	+	192069.i	−0.934982	+	0.713054i
$520$	31681.7	−	9514.29i	0.117166	−	0.0351860i
$521$		−	128028.i		−	0.471662i	−0.971794	−	0.235831i	$-0.924219\pi$
$521$		−	128028.i		−	0.471662i	0.971794	−	0.235831i	$-0.0757812\pi$
$522$	−223013.	−	61172.0i	−0.818446	−	0.224498i
$523$		−	396160.i		−	1.44833i	−0.689627	−	0.724165i	$-0.742225\pi$
$523$		−	396160.i		−	1.44833i	0.689627	−	0.724165i	$-0.257775\pi$
$524$	81303.1	+	46940.3i	0.296104	+	0.170956i
$525$	−50228.0	−	264268.i	−0.182233	−	0.958795i
$526$	134816.	+	233507.i	0.487269	+	0.843974i
$527$	−65901.2	−	114144.i	−0.237286	−	0.410991i
$528$	−180022.	+	23159.1i	−0.645741	+	0.0830717i
$529$	−73709.3	+	127668.i	−0.263397	+	0.456217i
$530$	−230443.	+	244673.i	−0.820375	+	0.871032i
$531$	−91973.8	−	25228.2i	−0.326193	−	0.0894740i
$532$			308231.i			1.08906i
$533$	−53067.1	+	91915.0i	−0.186798	+	0.323543i
$534$	−435957.	−	571641.i	−1.52884	−	2.00466i
$535$	−33390.7	−	7883.71i	−0.116659	−	0.0275438i
$536$	−19877.5	+	11476.3i	−0.0691881	+	0.0399458i
$537$	−153281.	+	366980.i	−0.531544	+	1.27261i
$538$	92672.5	+	53504.5i	0.320174	+	0.184853i
$539$			9646.31i			0.0332035i
$540$	242206.	−	194094.i	0.830611	−	0.665617i
$541$	−411433.			−1.40574			−0.702870	−	0.711318i	$-0.748098\pi$
$541$	−411433.			−1.40574			−0.702870	+	0.711318i	$0.748098\pi$
$542$	342393.	−	593042.i	1.16554	−	2.01877i
$543$	−343211.	−	143353.i	−1.16402	−	0.486191i
$544$	318676.	+	551963.i	1.07684	+	1.86514i
$545$	202556.	+	47824.3i	0.681948	+	0.161011i
$546$	439434.	−	335130.i	1.47404	−	1.12416i
$547$	224830.	+	129806.i	0.751414	+	0.433829i	0.826205	−	0.563370i	$-0.190495\pi$
$547$	224830.	+	129806.i	0.751414	+	0.433829i	−0.0747906	+	0.997199i	$0.523829\pi$
$548$	73812.8			0.245794
$549$	541723.	−	141726.i	1.79735	−	0.470224i
$550$	−303255.	+	18181.1i	−1.00250	+	0.0601028i
$551$	−162814.	−	94000.8i	−0.536277	−	0.309620i
$552$	−4445.50	−	34556.2i	−0.0145896	−	0.113409i
$553$	202662.	−	117007.i	0.662707	−	0.382614i
$554$	−138384.	+	79896.1i	−0.450886	+	0.260319i
$555$	7357.13	−	10143.4i	0.0238849	−	0.0329303i
$556$	−28730.9	+	49763.3i	−0.0929393	+	0.160976i
$557$	261444.			0.842691			0.421345	−	0.906900i	$-0.361558\pi$
$557$	261444.			0.842691			0.421345	+	0.906900i	$0.361558\pi$
$558$	99147.1	+	100327.i	0.318428	+	0.322217i
$559$	182411.			0.583750
$560$	−273033.	+	81994.3i	−0.870642	+	0.261461i
$561$	200793.	+	263287.i	0.638003	+	0.836572i
$562$	27278.5	−	15749.3i	0.0863671	−	0.0498641i
$563$	−185109.	−	320619.i	−0.583999	−	1.01152i	−0.994999	−	0.0998803i	$-0.968154\pi$
$563$	−185109.	−	320619.i	−0.583999	−	1.01152i	0.411001	−	0.911635i	$-0.365179\pi$
$564$	−123112.	−	51421.8i	−0.387029	−	0.161655i
$565$	−149654.	−	498333.i	−0.468803	−	1.56107i
$566$		−	690320.i		−	2.15485i
$567$	160083.	−	269850.i	0.497942	−	0.839375i
$568$		−	34482.3i		−	0.106881i
$569$	442601.	+	255536.i	1.36706	+	0.789273i	0.990552	−	0.137140i	$-0.0437910\pi$
$569$	442601.	+	255536.i	1.36706	+	0.789273i	0.376509	+	0.926413i	$0.377124\pi$
$570$	446926.	−	199415.i	1.37558	−	0.613773i
$571$	−9362.89	−	16217.0i	−0.0287169	−	0.0497391i	0.851310	−	0.524663i	$-0.175809\pi$
$571$	−9362.89	−	16217.0i	−0.0287169	−	0.0497391i	−0.880027	+	0.474924i	$0.842475\pi$
$572$	−160903.	−	278692.i	−0.491781	−	0.851790i
$573$	130565.	+	171202.i	0.397666	+	0.521434i
$574$	−65282.2	+	113072.i	−0.198139	+	0.343187i
$575$	24448.9	+	407800.i	0.0739474	+	1.23342i
$576$	−262220.	−	265340.i	−0.790352	−	0.799756i
$577$			165587.i			0.497364i	0.968585	+	0.248682i	$0.0799975\pi$
$577$			165587.i			0.497364i	−0.968585	+	0.248682i	$0.920003\pi$
$578$	303746.	−	526104.i	0.909192	−	1.57477i
$579$	−20971.1	+	2697.84i	−0.0625553	+	0.00804746i
$580$	−48599.7	+	205839.i	−0.144470	+	0.611889i
$581$	269808.	−	155774.i	0.799286	−	0.461468i
$582$	692006.	−	89023.5i	2.04298	−	0.262820i
$583$	171342.	+	98924.2i	0.504111	+	0.291048i
$584$			38163.3i			0.111897i
$585$	−397129.	−	216732.i	−1.16043	−	0.633301i
$586$	−116456.			−0.339131
$587$	−279639.	+	484350.i	−0.811563	+	1.40567i	0.100207	+	0.994967i	$0.468049\pi$
$587$	−279639.	+	484350.i	−0.811563	+	1.40567i	−0.911770	+	0.410701i	$0.865284\pi$
$588$	−13900.5	+	10601.1i	−0.0402045	+	0.0306616i
$589$	57335.9	+	99308.7i	0.165271	+	0.286257i
$590$	−38873.5	+	164645.i	−0.111673	+	0.472983i
$591$	77352.5	+	32308.7i	0.221462	+	0.0925007i
$592$	−11500.5	−	6639.82i	−0.0328151	−	0.0189458i
$593$	−398735.			−1.13390			−0.566950	−	0.823752i	$-0.691877\pi$
$593$	−398735.			−1.13390			−0.566950	+	0.823752i	$0.691877\pi$
$594$	−279202.	−	218201.i	−0.791308	−	0.618421i
$595$	378583.	+	356566.i	1.06937	+	1.00718i
$596$	494616.	+	285566.i	1.39244	+	0.803923i
$597$	−51404.6	−	21470.8i	−0.144229	−	0.0602420i
$598$	−726860.	+	419653.i	−2.03258	+	1.17351i
$599$	−203260.	+	117352.i	−0.566497	+	0.327067i	−0.755749	−	0.654861i	$-0.772727\pi$
$599$	−203260.	+	117352.i	−0.566497	+	0.327067i	0.189252	+	0.981929i	$0.439394\pi$
$600$	−21751.0	−	25233.0i	−0.0604195	−	0.0700917i
$601$	115910.	−	200763.i	0.320903	−	0.555820i	−0.659772	−	0.751466i	$-0.729347\pi$
$601$	115910.	−	200763.i	0.320903	−	0.555820i	0.980675	+	0.195646i	$0.0626805\pi$
$602$	224398.			0.619193
$603$	302734.	+	83039.2i	0.832580	+	0.228375i
$604$	17619.5			0.0482970
$605$	−53840.9	−	179285.i	−0.147096	−	0.489816i
$606$	934422.	−	120209.i	2.54447	−	0.327335i
$607$	459653.	−	265381.i	1.24753	−	0.720264i	0.276917	−	0.960894i	$-0.410687\pi$
$607$	459653.	−	265381.i	1.24753	−	0.720264i	0.970617	+	0.240630i	$0.0773539\pi$
$608$	−277257.	−	480224.i	−0.750025	−	1.29908i
$609$	27279.8	+	212054.i	0.0735541	+	0.571758i
$610$	−285683.	−	951297.i	−0.767758	−	2.55656i
$611$			194477.i			0.520937i
$612$	−158734.	+	578691.i	−0.423805	+	1.54505i
$613$		−	688057.i		−	1.83106i	−0.402247	−	0.915531i	$-0.631771\pi$
$613$		−	688057.i		−	1.83106i	0.402247	−	0.915531i	$-0.368229\pi$
$614$	−659143.	−	380556.i	−1.74841	−	1.00944i
$615$	106310.	+	11087.2i	0.281075	+	0.0293137i
$616$	−11977.1	−	20744.9i	−0.0315638	−	0.0546701i
$617$	70869.2	+	122749.i	0.186160	+	0.322439i	0.943967	−	0.330040i	$-0.107062\pi$
$617$	70869.2	+	122749.i	0.186160	+	0.322439i	−0.757807	+	0.652479i	$0.773729\pi$
$618$	257940.	−	617551.i	0.675370	−	1.61695i
$619$	276156.	−	478316.i	0.720731	−	1.24834i	−0.239977	−	0.970779i	$-0.577140\pi$
$619$	276156.	−	478316.i	0.720731	−	1.24834i	0.960707	−	0.277563i	$-0.0895268\pi$
$620$	88448.0	−	93909.5i	0.230094	−	0.244302i
$621$	−293424.	+	375454.i	−0.760873	+	0.973584i
$622$			784237.i			2.02706i
$623$	−332332.	+	575617.i	−0.856242	+	1.48305i
$624$	−184792.	+	442423.i	−0.474586	+	1.13624i
$625$	234331.	+	312533.i	0.599888	+	0.800084i
$626$	−543114.	+	313567.i	−1.38593	+	0.800168i
$627$	−174696.	−	229067.i	−0.444372	−	0.582676i
$628$	67046.2	+	38709.1i	0.170002	+	0.0981508i
$629$			24225.6i			0.0612314i
$630$	−488540.	−	266619.i	−1.23089	−	0.671754i
$631$	231361.			0.581073			0.290537	−	0.956864i	$-0.406166\pi$
$631$	231361.			0.581073			0.290537	+	0.956864i	$0.406166\pi$
$632$	14490.6	−	25098.4i	0.0362787	−	0.0628365i
$633$	−1646.29	−	12797.1i	−0.00410866	−	0.0319378i
$634$	−123103.	−	213220.i	−0.306259	−	0.530456i
$635$	−19778.3	+	83769.2i	−0.0490503	+	0.207748i
$636$	45749.1	+	355621.i	0.113101	+	0.879171i
$637$	22067.7	+	12740.8i	0.0543850	+	0.0313992i
$638$	241462.			0.593208
$639$	−335442.	+	331498.i	−0.821516	+	0.811857i
$640$	−51867.5	+	55070.2i	−0.126630	+	0.134449i
$641$	−390167.	−	225263.i	−0.949587	−	0.548244i	−0.0566340	−	0.998395i	$-0.518037\pi$
$641$	−390167.	−	225263.i	−0.949587	−	0.548244i	−0.892952	+	0.450151i	$0.851370\pi$
$642$	−56443.6	+	43046.1i	−0.136945	+	0.104439i
$643$	−265023.	+	153011.i	−0.641006	+	0.370085i	−0.785002	−	0.619493i	$-0.787338\pi$
$643$	−265023.	+	153011.i	−0.641006	+	0.370085i	0.143996	+	0.989578i	$0.454005\pi$
$644$	−461033.	+	266177.i	−1.11163	+	0.641799i
$645$	−74853.7	−	167761.i	−0.179926	−	0.403247i
$646$	−473081.	+	819400.i	−1.13363	+	1.96350i
$647$	200004.			0.477782			0.238891	−	0.971046i	$-0.423216\pi$
$647$	200004.			0.477782			0.238891	+	0.971046i	$0.423216\pi$
$648$	459.572	−	38854.5i	0.00109447	−	0.0925320i
$649$	99582.2			0.236424
$650$	−358946.	+	717768.i	−0.849577	+	1.69886i
$651$	50261.3	−	120334.i	0.118596	−	0.283939i
$652$	528859.	−	305337.i	1.24407	−	0.718263i
$653$	257809.	+	446538.i	0.604604	+	1.04721i	0.992114	+	0.125340i	$0.0400021\pi$
$653$	257809.	+	446538.i	0.604604	+	1.04721i	−0.387509	+	0.921866i	$0.626665\pi$
$654$	342399.	−	261127.i	0.800529	−	0.610516i
$655$	−131989.	+	39637.6i	−0.307650	+	0.0923899i
$656$		−	113276.i		−	0.263226i
$657$	371250.	−	366885.i	0.860074	−	0.849961i
$658$			239241.i			0.552567i
$659$	301526.	+	174086.i	0.694312	+	0.400861i	0.805225	−	0.592969i	$-0.202044\pi$
$659$	301526.	+	174086.i	0.694312	+	0.400861i	−0.110913	+	0.993830i	$0.535378\pi$
$660$	−190282.	+	262344.i	−0.436827	+	0.602259i
$661$	12324.1	+	21346.0i	0.0282068	+	0.0488556i	0.879784	−	0.475373i	$-0.157687\pi$
$661$	12324.1	+	21346.0i	0.0282068	+	0.0488556i	−0.851577	+	0.524229i	$0.824354\pi$
$662$	−314860.	−	545353.i	−0.718458	−	1.24441i
$663$	867525.	−	111603.i	1.97358	−	0.253892i
$664$	19291.6	−	33414.0i	0.0437554	−	0.0757866i
$665$	−329378.	−	310222.i	−0.744821	−	0.701504i
$666$	−6561.86	−	25081.6i	−0.0147938	−	0.0565466i
$667$		−	324703.i		−	0.729852i
$668$	−189188.	+	327684.i	−0.423976	+	0.734348i
$669$	−2032.64	−	2665.26i	−0.00454159	−	0.00595509i
$670$	127953.	−	541934.i	0.285037	−	1.20725i
$671$	−506349.	+	292340.i	−1.12462	+	0.649298i
$672$	−243047.	+	581894.i	−0.538209	+	1.28856i
$673$	−275390.	−	158997.i	−0.608020	−	0.351041i	0.164170	−	0.986432i	$-0.447505\pi$
$673$	−275390.	−	158997.i	−0.608020	−	0.351041i	−0.772190	+	0.635391i	$0.780839\pi$
$674$			52919.1i			0.116491i
$675$	−36360.7	+	454172.i	−0.0798039	+	0.996811i
$676$	−363673.			−0.795825
$677$	65955.5	−	114238.i	0.143904	−	0.249250i	−0.785059	−	0.619421i	$-0.787368\pi$
$677$	65955.5	−	114238.i	0.143904	−	0.249250i	0.928964	+	0.370171i	$0.120701\pi$
$678$	−993369.	−	414912.i	−2.16098	−	0.902603i
$679$	−322532.	−	558641.i	−0.699573	−	1.21170i
$680$	62683.0	+	14799.7i	0.135560	+	0.0320064i
$681$	216361.	−	165005.i	0.466535	−	0.355798i
$682$	−127548.	−	73640.0i	−0.274224	−	0.158323i
$683$	539667.			1.15687			0.578435	−	0.815729i	$-0.303664\pi$
$683$	539667.			1.15687			0.578435	+	0.815729i	$0.303664\pi$
$684$	138103.	−	503478.i	0.295182	−	1.07614i
$685$	−74289.8	+	78877.1i	−0.158324	+	0.168101i
$686$	598637.	+	345623.i	1.27208	+	0.734437i
$687$	50726.1	+	394309.i	0.107478	+	0.835456i
$688$	−168602.	+	97342.3i	−0.356193	+	0.205648i
$689$	452615.	−	261318.i	0.953435	−	0.550466i
$690$	684222.	+	496276.i	1.43714	+	1.04238i
$691$	194856.	−	337500.i	0.408091	−	0.706834i	−0.586585	−	0.809888i	$-0.699528\pi$
$691$	194856.	−	337500.i	0.408091	−	0.706834i	0.994676	+	0.103054i	$0.0328614\pi$
$692$	599341.			1.25159
$693$	−86662.8	+	315944.i	−0.180454	+	0.657876i
$694$	129632.			0.269150
$695$	−24261.1	−	80787.0i	−0.0502273	−	0.167252i
$696$	16056.6	+	21054.0i	0.0331463	+	0.0434626i
$697$	−178960.	+	103323.i	−0.368376	+	0.212682i
$698$	585654.	+	1.01438e6i	1.20207	+	2.08205i
$699$	190826.	+	79704.6i	0.390556	+	0.163128i
$700$	−227673.	+	455266.i	−0.464638	+	0.929114i
$701$		−	831525.i		−	1.69215i	−0.533063	−	0.846076i	$-0.678959\pi$
$701$		−	831525.i		−	1.69215i	0.533063	−	0.846076i	$-0.321041\pi$
$702$	−867946.	+	350528.i	−1.76124	+	0.711292i
$703$		−	21077.0i		−	0.0426480i
$704$	337334.	+	194760.i	0.680636	+	0.392965i
$705$	178858.	−	79805.0i	0.359857	−	0.160565i
$706$	−185665.	−	321580.i	−0.372494	−	0.645179i
$707$	−435517.	−	754338.i	−0.871298	−	1.50913i
$708$	109438.	+	143499.i	0.218325	+	0.286275i
$709$	−20819.3	+	36060.0i	−0.0414164	+	0.0717354i	−0.885991	−	0.463703i	$-0.846520\pi$
$709$	−20819.3	+	36060.0i	−0.0414164	+	0.0717354i	0.844574	+	0.535439i	$0.179854\pi$
$710$	608974.	+	573557.i	1.20804	+	1.13778i
$711$	−383462.	+	100322.i	−0.758548	+	0.198452i
$712$			82314.6i			0.162374i
$713$	−99026.6	+	171519.i	−0.194793	+	0.337391i
$714$	1.06721e6	−	137292.i	2.09341	−	0.269308i
$715$	459756.	+	108551.i	0.899322	+	0.212334i
$716$	651743.	−	376284.i	1.27131	−	0.733989i
$717$	−607024.	+	78090.9i	−1.18078	+	0.151901i
$718$	196948.	+	113708.i	0.382035	+	0.220568i
$719$		−	800950.i		−	1.54934i	−0.632364	−	0.774671i	$-0.717915\pi$
$719$		−	800950.i		−	1.54934i	0.632364	−	0.774671i	$-0.282085\pi$
$720$	482722.	−	11600.6i	0.931177	−	0.0223777i
$721$	−618757.			−1.19028
$722$	37102.4	−	64263.3i	0.0711750	−	0.123279i
$723$	−497107.	+	379114.i	−0.950985	+	0.725259i
$724$	351912.	+	609530.i	0.671363	+	1.16284i
$725$	−171048.	−	259104.i	−0.325419	−	0.492944i
$726$	−357384.	−	149273.i	−0.678051	−	0.283210i
$727$	722549.	+	417164.i	1.36709	+	0.789292i	0.990556	−	0.137109i	$-0.0437810\pi$
$727$	722549.	+	417164.i	1.36709	+	0.789292i	0.376538	+	0.926401i	$0.377114\pi$
$728$	−63277.1			−0.119394
$729$	−382393.	+	369060.i	−0.719540	+	0.694451i
$730$	−673980.	−	634783.i	−1.26474	−	1.19119i
$731$	307575.	+	177579.i	0.575595	+	0.332320i
$732$	−977731.	−	408381.i	−1.82472	−	0.762155i
$733$	359667.	−	207654.i	0.669411	−	0.386485i	−0.126442	−	0.991974i	$-0.540356\pi$
$733$	359667.	−	207654.i	0.669411	−	0.386485i	0.795854	+	0.605489i	$0.207022\pi$
$734$	967609.	−	558649.i	1.79601	−	1.03692i
$735$	2661.91	−	25523.7i	0.00492741	−	0.0472465i
$736$	478860.	−	829409.i	0.884000	−	1.53113i
$737$	−327777.			−0.603453
$738$	157297.	−	155447.i	0.288807	−	0.285411i
$739$	−862015.			−1.57843			−0.789216	−	0.614115i	$-0.789513\pi$
$739$	−862015.			−1.57843			−0.789216	+	0.614115i	$0.789513\pi$
$740$	−22709.4	+	6819.83i	−0.0414708	+	0.0124540i
$741$	−754771.	+	97098.0i	−1.37461	+	0.176837i
$742$	556799.	−	321468.i	1.01132	−	0.583888i
$743$	152108.	+	263459.i	0.275534	+	0.477239i	0.970270	−	0.242026i	$-0.0778120\pi$
$743$	152108.	+	263459.i	0.275534	+	0.477239i	−0.694736	+	0.719265i	$0.744479\pi$
$744$	−2060.68	−	16018.3i	−0.00372276	−	0.0289381i
$745$	−802971.	+	241139.i	−1.44673	+	0.434466i
$746$			617062.i			1.10879i
$747$	−510511.	+	133560.i	−0.914879	+	0.239351i
$748$		−	626563.i		−	1.11985i
$749$	56836.1	+	32814.3i	0.101312	+	0.0584925i
$750$	807419.	+	35577.2i	1.43541	+	0.0632484i
$751$	477638.	+	827293.i	0.846874	+	1.46683i	0.883984	+	0.467518i	$0.154852\pi$
$751$	477638.	+	827293.i	0.846874	+	1.46683i	−0.0371095	+	0.999311i	$0.511815\pi$
$752$	−103781.	−	179754.i	−0.183520	−	0.317866i
$753$	155536.	−	372379.i	0.274310	−	0.656743i
$754$	318922.	−	552390.i	0.560973	−	0.971634i
$755$	−17733.4	+	18828.4i	−0.0311098	+	0.0330308i
$756$	−550521.	+	222333.i	−0.963230	+	0.389009i
$757$		−	233252.i		−	0.407037i	−0.979071	−	0.203518i	$-0.934762\pi$
$757$		−	233252.i		−	0.407037i	0.979071	−	0.203518i	$-0.0652377\pi$
$758$	665383.	−	1.15248e6i	1.15807	−	2.00583i
$759$	191763.	−	459113.i	0.332876	−	0.796960i
$760$	−54536.0	−	12876.2i	−0.0944183	−	0.0222926i
$761$	−309676.	+	178791.i	−0.534734	+	0.308729i	−0.742942	−	0.669356i	$-0.766570\pi$
$761$	−309676.	+	178791.i	−0.534734	+	0.308729i	0.208208	+	0.978085i	$0.433237\pi$
$762$	107992.	+	141603.i	0.185987	+	0.243873i
$763$	−344780.	−	199059.i	−0.592234	−	0.341926i
$764$		−	407422.i		−	0.698003i
$765$	−458636.	−	752055.i	−0.783691	−	1.28507i
$766$	267607.			0.456079
$767$	131528.	−	227813.i	0.223577	−	0.387247i
$768$	−64648.8	−	502534.i	−0.109607	−	0.852007i
$769$	104137.	+	180371.i	0.176098	+	0.305010i	0.940541	−	0.339681i	$-0.110319\pi$
$769$	104137.	+	180371.i	0.176098	+	0.305010i	−0.764443	+	0.644692i	$0.776986\pi$
$770$	565583.	+	133537.i	0.953926	+	0.225226i
$771$	−588.349	−	4573.41i	−0.000989752	−	0.00769363i
$772$	34649.8	+	20005.1i	0.0581388	+	0.0335665i
$773$	−328500.			−0.549764			−0.274882	−	0.961478i	$-0.588639\pi$
$773$	−328500.			−0.549764			−0.274882	+	0.961478i	$0.588639\pi$
$774$	−366542.	−	100542.i	−0.611846	−	0.167828i
$775$	11333.1	+	189033.i	0.0188688	+	0.314727i
$776$	−69184.2	−	39943.5i	−0.114890	−	0.0663320i
$777$	−19059.3	+	14535.4i	−0.0315694	+	0.0240760i
$778$	−75327.2	+	43490.2i	−0.124449	+	0.0718509i
$779$	155701.	−	89893.8i	0.256576	−	0.148134i
$780$	348837.	+	781809.i	0.573368	+	1.28503i
$781$	246215.	−	426457.i	0.403657	−	0.699155i
$782$	−1.63414e6			−2.67225
$783$	50450.8	−	358602.i	0.0822896	−	0.584910i
$784$	−27196.2			−0.0442462
$785$	−108844.	+	32686.9i	−0.176631	+	0.0530438i
$786$	−109895.	+	263106.i	−0.177882	+	0.425878i
$787$	−184283.	+	106396.i	−0.297533	+	0.171781i	−0.641334	−	0.767262i	$-0.721619\pi$
$787$	−184283.	+	106396.i	−0.297533	+	0.171781i	0.343801	+	0.939042i	$0.388285\pi$
$788$	−79313.6	−	137375.i	−0.127731	−	0.221236i
$789$	−335741.	+	256049.i	−0.539324	+	0.411310i
$790$	202222.	+	673381.i	0.324022	+	1.07896i
$791$			995308.i			1.59076i
$792$	10269.1	+	39251.9i	0.0163713	+	0.0625764i
$793$			1.54449e6i			2.45606i
$794$	−244478.	−	141149.i	−0.387792	−	0.223892i
$795$	−426065.	−	309031.i	−0.674127	−	0.488954i
$796$	52707.9	+	91292.7i	0.0831858	+	0.144082i
$797$	−75817.1	−	131319.i	−0.119358	−	0.206734i	0.800156	−	0.599792i	$-0.204750\pi$
$797$	−75817.1	−	131319.i	−0.119358	−	0.206734i	−0.919513	+	0.393059i	$0.871417\pi$
$798$	−928505.	+	119448.i	−1.45807	+	0.187574i
$799$	−189325.	+	327921.i	−0.296561	+	0.513659i
$800$	−54803.1	−	914099.i	−0.0856298	−	1.42828i
$801$	800752.	−	791336.i	1.24805	−	1.23338i
$802$			770276.i			1.19756i
$803$	−272498.	+	471981.i	−0.422603	+	0.731970i
$804$	−360219.	−	472332.i	−0.557256	−	0.730693i
$805$	179572.	−	760561.i	0.277107	−	1.17366i
$806$	−336931.	+	194527.i	−0.518646	+	0.299440i
$807$	−64585.1	+	154627.i	−0.0991711	+	0.237432i
$808$	−93420.1	−	53936.1i	−0.143093	−	0.0826146i
$809$		−	66493.9i		−	0.101598i	−0.998709	−	0.0507989i	$-0.983823\pi$
$809$		−	66493.9i		−	0.101598i	0.998709	−	0.0507989i	$-0.0161768\pi$
$810$	678544.	+	654398.i	1.03421	+	0.997406i
$811$	1.27019e6			1.93120			0.965602	−	0.260025i	$-0.0837307\pi$
$811$	1.27019e6			1.93120			0.965602	+	0.260025i	$0.0837307\pi$
$812$	202286.	−	350370.i	0.306799	−	0.531391i
$813$	989512.	+	413301.i	1.49706	+	0.625296i
$814$	13535.2	+	23443.7i	0.0204276	+	0.0353816i
$815$	−205990.	+	872453.i	−0.310121	+	1.31349i
$816$	−742295.	+	566103.i	−1.11480	+	0.850189i
$817$	−267599.	−	154499.i	−0.400905	−	0.231462i
$818$	311612.			0.465702
$819$	608318.	+	615556.i	0.906908	+	0.917698i
$820$	−147236.	−	138673.i	−0.218970	−	0.206235i
$821$	415193.	+	239712.i	0.615975	+	0.355634i	0.775300	−	0.631593i	$-0.217598\pi$
$821$	415193.	+	239712.i	0.615975	+	0.355634i	−0.159325	+	0.987226i	$0.550932\pi$
$822$	28604.5	+	222352.i	0.0423342	+	0.329076i
$823$	125938.	−	72710.6i	0.185934	−	0.107349i	−0.404144	−	0.914695i	$-0.632430\pi$
$823$	125938.	−	72710.6i	0.185934	−	0.107349i	0.590078	+	0.807346i	$0.299097\pi$
$824$	−66362.8	+	38314.6i	−0.0977395	+	0.0564299i
$825$	−88831.7	−	467376.i	−0.130515	−	0.686687i
$826$	161803.	−	280251.i	0.237152	−	0.410759i
$827$	893602.			1.30657			0.653286	−	0.757111i	$-0.273390\pi$
$827$	893602.			1.30657			0.653286	+	0.757111i	$0.273390\pi$
$828$	872332.	−	228220.i	1.27239	−	0.332884i
$829$	−659734.			−0.959975			−0.479988	−	0.877275i	$-0.659359\pi$
$829$	−659734.			−0.959975			−0.479988	+	0.877275i	$0.659359\pi$
$830$	269223.	+	896485.i	0.390801	+	1.30133i
$831$	−151743.	−	198971.i	−0.219739	−	0.288129i
$832$	891100.	−	514477.i	1.28730	−	0.743223i
$833$	24806.6	+	42966.4i	0.0357501	+	0.0619211i
$834$	−161040.	−	67263.4i	−0.231527	−	0.0967045i
$835$	−159755.	−	531970.i	−0.229130	−	0.762982i
$836$			545128.i			0.779984i
$837$	−136015.	+	174039.i	−0.194149	+	0.248425i
$838$		−	1.01527e6i		−	1.44576i
$839$	−797201.	−	460264.i	−1.13251	−	0.653857i	−0.187948	−	0.982179i	$-0.560184\pi$
$839$	−797201.	−	460264.i	−1.13251	−	0.653857i	−0.944566	+	0.328322i	$0.893517\pi$
$840$	25966.2	+	58195.2i	0.0368002	+	0.0824762i
$841$	−230259.	−	398819.i	−0.325555	−	0.563877i
$842$	412375.	+	714255.i	0.581659	+	1.00746i
$843$	29911.9	+	39221.5i	0.0420910	+	0.0551911i
$844$	−12207.6	+	21144.2i	−0.0171375	+	0.0296830i
$845$	366023.	−	388625.i	0.512620	−	0.544273i
$846$	107192.	−	390788.i	0.149769	−	0.546009i
$847$			358082.i			0.499132i
$848$	−278901.	+	483070.i	−0.387845	+	0.671767i
$849$	1.07219e6	−	137932.i	1.48750	−	0.191360i
$850$	−1.30400e6	+	860840.i	−1.80484	+	1.19147i
$851$	31525.7	−	18201.4i	0.0435317	−	0.0251330i
$852$	885116.	−	113866.i	1.21933	−	0.156861i
$853$	−627776.	−	362447.i	−0.862793	−	0.498134i	0.00215352	−	0.999998i	$-0.499315\pi$
$853$	−627776.	−	362447.i	−0.862793	−	0.498134i	−0.864947	+	0.501864i	$0.832648\pi$
$854$			1.90000e6i			2.60518i
$855$	399026.	+	654309.i	0.545845	+	0.895057i
$856$	8127.70			0.0110923
$857$	492013.	−	852192.i	0.669908	−	1.16032i	−0.308021	−	0.951380i	$-0.599667\pi$
$857$	492013.	−	852192.i	0.669908	−	1.16032i	0.977929	−	0.208936i	$-0.0669999\pi$
$858$	777170.	−	592700.i	1.05570	−	0.805120i
$859$	−365776.	−	633542.i	−0.495711	−	0.858597i	0.504277	−	0.863542i	$-0.331759\pi$
$859$	−365776.	−	633542.i	−0.495711	−	0.858597i	−0.999988	+	0.00494530i	$0.998426\pi$
$860$	−79877.8	+	338315.i	−0.108001	+	0.457430i
$861$	−188665.	−	78801.9i	−0.254498	−	0.106299i
$862$	478408.	+	276209.i	0.643849	+	0.371727i
$863$	−498062.			−0.668747			−0.334374	−	0.942441i	$-0.608525\pi$
$863$	−498062.			−0.668747			−0.334374	+	0.942441i	$0.608525\pi$
$864$	657721.	−	841595.i	0.881078	−	1.12739i
$865$	−603213.	+	640461.i	−0.806193	+	0.855974i
$866$	−1.55821e6	−	899635.i	−2.07774	−	1.19958i
$867$	877824.	+	366651.i	1.16780	+	0.487770i
$868$	−213709.	+	123385.i	−0.283650	+	0.163765i
$869$	358422.	−	206935.i	0.474630	−	0.274028i
$870$	−638898.	−	66631.7i	−0.844099	−	0.0880323i
$871$	−432927.	+	749852.i	−0.570662	+	0.988415i
$872$	−49304.4			−0.0648415
$873$	276538.	+	1.05702e6i	0.362850	+	1.38693i
$874$	1.42175e6			1.86124
$875$	−257358.	−	701501.i	−0.336141	−	0.916246i
$876$	−979600.	+	126021.i	−1.27656	+	0.164223i
$877$	−1.18504e6	+	684183.i	−1.54076	+	0.889556i	−0.541965	+	0.840401i	$0.682319\pi$
$877$	−1.18504e6	+	684183.i	−1.54076	+	0.889556i	−0.998791	+	0.0491545i	$0.984347\pi$
$878$	−299805.	−	519278.i	−0.388911	−	0.673614i
$879$	−23269.0	−	180877.i	−0.0301162	−	0.234102i
$880$	−482878.	+	145013.i	−0.623552	+	0.187258i
$881$			1.19744e6i			1.54277i	0.636368	+	0.771386i	$0.280436\pi$
$881$			1.19744e6i			1.54277i	−0.636368	+	0.771386i	$0.719564\pi$
$882$	−37321.1	−	37765.2i	−0.0479753	−	0.0485461i
$883$		−	461117.i		−	0.591412i	−0.955279	−	0.295706i	$-0.904445\pi$
$883$		−	461117.i		−	0.591412i	0.955279	−	0.295706i	$-0.0955548\pi$
$884$	−1.43338e6	−	827563.i	−1.83424	−	1.05900i
$885$	−263490.	−	27479.8i	−0.336417	−	0.0350855i
$886$	−88297.6	−	152936.i	−0.112482	−	0.194824i
$887$	427242.	+	740004.i	0.543033	+	0.940561i	0.998728	+	0.0504250i	$0.0160576\pi$
$887$	427242.	+	740004.i	0.543033	+	0.940561i	−0.455695	+	0.890136i	$0.650609\pi$
$888$	−1144.09	+	2739.14i	−0.00145089	+	0.00347367i
$889$	82323.1	−	142588.i	0.104164	−	0.180418i
$890$	−1.45371e6	−	1.36917e6i	−1.83526	−	1.72853i
$891$	283118.	−	477249.i	0.356625	−	0.601159i
$892$			6342.73i			0.00797162i
$893$	164718.	−	285300.i	0.206556	−	0.357766i
$894$	−668555.	+	1.60063e6i	−0.836492	+	2.00270i
$895$	−253854.	+	1.07517e6i	−0.316911	+	1.34225i
$896$	125322.	−	72355.0i	0.156104	−	0.0901265i
$897$	−797028.	−	1.04509e6i	−0.990578	−	1.29888i
$898$	235583.	+	136014.i	0.292140	+	0.168667i
$899$		−	150514.i		−	0.186233i
$900$	575873.	−	641643.i	0.710954	−	0.792152i
$901$	1.01758e6			1.25349
$902$	−115456.	+	199976.i	−0.141907	+	0.245790i
$903$	44836.8	+	348530.i	0.0549869	+	0.427430i
$904$	61631.3	+	106749.i	0.0754162	+	0.130625i
$905$	−1.00554e6	−	237412.i	−1.22772	−	0.289871i
$906$	6828.05	+	53076.5i	0.00831841	+	0.0646615i
$907$	403158.	+	232764.i	0.490073	+	0.282944i	0.724605	−	0.689164i	$-0.242022\pi$
$907$	403158.	+	232764.i	0.490073	+	0.282944i	−0.234531	+	0.972109i	$0.575356\pi$
$908$	−514890.			−0.624514
$909$	373412.	+	1.42730e6i	0.451919	+	1.72738i
$910$	1.05251e6	−	1.11750e6i	1.27099	−	1.34948i
$911$	596214.	+	344224.i	0.718398	+	0.414767i	0.814163	−	0.580637i	$-0.197196\pi$
$911$	596214.	+	344224.i	0.718398	+	0.414767i	−0.0957646	+	0.995404i	$0.530530\pi$
$912$	645818.	−	492526.i	0.776462	−	0.592161i
$913$	477174.	−	275497.i	0.572447	−	0.330502i
$914$	−585954.	+	338301.i	−0.701409	+	0.404959i
$915$	1.42045e6	−	633794.i	1.69662	−	0.757017i
$916$	376146.	−	651504.i	0.448296	−	0.776472i
$917$	263619.			0.313501
$918$	−1.80475e6	−	253905.i	−2.14156	−	0.301291i
$919$	−692392.			−0.819825			−0.409912	−	0.912125i	$-0.634441\pi$
$919$	−692392.			−0.819825			−0.409912	+	0.912125i	$0.634441\pi$
$920$	−27835.9	−	92691.0i	−0.0328875	−	0.109512i
$921$	459368.	−	1.09980e6i	0.541554	−	1.29657i
$922$	−218726.	+	126281.i	−0.257299	+	0.148552i
$923$	−650401.	−	1.12653e6i	−0.763445	−	1.32233i
$924$	492943.	−	375938.i	0.577368	−	0.440324i
$925$	15568.4	−	31131.4i	0.0181954	−	0.0363844i
$926$			217792.i			0.253992i
$927$	1.01070e6	+	277234.i	1.17616	+	0.322617i
$928$			727835.i			0.845157i
$929$	430458.	+	248525.i	0.498768	+	0.287964i	0.728205	−	0.685360i	$-0.240355\pi$
$929$	430458.	+	248525.i	0.498768	+	0.287964i	−0.229436	+	0.973324i	$0.573688\pi$
$930$	317166.	+	230046.i	0.366709	+	0.265979i
$931$	−21582.5	−	37382.0i	−0.0249002	−	0.0431283i
$932$	−195664.	−	338900.i	−0.225258	−	0.390158i
$933$	−1.21806e6	+	156698.i	−1.39928	+	0.180011i
$934$	−660132.	+	1.14338e6i	−0.756723	+	1.31068i
$935$	669551.	+	630612.i	0.765879	+	0.721338i
$936$	103360.	+	28351.3i	0.117978	+	0.0323610i
$937$		−	761906.i		−	0.867805i	−0.900960	−	0.433903i	$-0.857136\pi$
$937$		−	761906.i		−	0.867805i	0.900960	−	0.433903i	$-0.142864\pi$
$938$	−532579.	+	922453.i	−0.605310	+	1.04843i
$939$	−595544.	−	780898.i	−0.675433	−	0.885652i
$940$	−360694.	−	85161.5i	−0.408209	−	0.0963801i
$941$	−222911.	+	128697.i	−0.251740	+	0.145342i	−0.620561	−	0.784159i	$-0.713095\pi$
$941$	−222911.	+	128697.i	−0.251740	+	0.145342i	0.368821	+	0.929500i	$0.379762\pi$
$942$	−90624.0	+	216969.i	−0.102127	+	0.244509i
$943$	268915.	+	155258.i	0.302407	+	0.174595i
$944$			280756.i			0.315054i
$945$	316491.	−	812061.i	0.354404	−	0.909338i
$946$	396864.			0.443465
$947$	231511.	−	400990.i	0.258150	−	0.447129i	−0.707596	−	0.706617i	$-0.750220\pi$
$947$	231511.	−	400990.i	0.258150	−	0.447129i	0.965746	+	0.259488i	$0.0835537\pi$
$948$	692093.	+	289075.i	0.770101	+	0.321657i
$949$	719830.	+	1.24678e6i	0.799277	+	1.38439i
$950$	1.13452e6	−	748955.i	1.25708	−	0.829868i
$951$	306571.	−	233803.i	0.338977	−	0.258517i
$952$	−106696.	−	61600.9i	−0.117726	−	0.0679694i
$953$	323955.			0.356696			0.178348	−	0.983967i	$-0.442925\pi$
$953$	323955.			0.356696			0.178348	+	0.983967i	$0.442925\pi$
$954$	−1.05353e6	+	275626.i	−1.15758	+	0.302848i
$955$	435375.	+	410054.i	0.477371	+	0.449609i
$956$	1.00296e6	+	579061.i	1.09741	+	0.633591i
$957$	48246.3	+	375033.i	0.0526793	+	0.409492i
$958$	−244877.	+	141380.i	−0.266819	+	0.154048i
$959$	179499.	−	103634.i	0.195176	−	0.112685i
$960$	−838828.	−	608415.i	−0.910187	−	0.660172i
$961$	415857.	−	720286.i	0.450296	−	0.779935i
$962$	71509.3			0.0772702
$963$	−78136.2	−	79065.8i	−0.0842557	−	0.0852582i
$964$	1.18300e6			1.27301
$965$	−56251.3	+	16892.8i	−0.0604057	+	0.0181404i
$966$	−980488.	−	1.28565e6i	−1.05072	−	1.37774i
$967$	−511790.	+	295482.i	−0.547317	+	0.315994i	−0.748039	−	0.663654i	$-0.769005\pi$
$967$	−511790.	+	295482.i	−0.547317	+	0.315994i	0.200722	+	0.979648i	$0.435671\pi$
$968$	22173.1	+	38404.9i	0.0236633	+	0.0409861i
$969$	−1.36720e6	−	571054.i	−1.45608	−	0.608177i
$970$	1.85619e6	−	557429.i	1.97278	−	0.592443i
$971$		−	1.14727e6i		−	1.21682i	−0.793622	−	0.608412i	$-0.791807\pi$
$971$		−	1.14727e6i		−	1.21682i	0.793622	−	0.608412i	$-0.208193\pi$
$972$	998862.	−	116507.i	1.05724	−	0.123316i
$973$			161354.i			0.170433i
$974$	766505.	+	442542.i	0.807973	+	0.466484i
$975$	−1.18654e6	−	414090.i	−1.24817	−	0.435598i
$976$	−824207.	−	1.42757e6i	−0.865240	−	1.49864i
$977$	−429287.	−	743546.i	−0.449737	−	0.778967i	0.548632	−	0.836064i	$-0.315149\pi$
$977$	−429287.	−	743546.i	−0.449737	−	0.778967i	−0.998369	+	0.0570972i	$0.981815\pi$
$978$	1.12473e6	+	1.47479e6i	1.17591	+	1.54189i
$979$	−587753.	+	1.01802e6i	−0.613239	+	1.06216i
$980$	−33293.7	+	35349.6i	−0.0346665	+	0.0368071i
$981$	473991.	+	479631.i	0.492529	+	0.498390i
$982$		−	969785.i		−	1.00566i
$983$	580320.	−	1.00514e6i	0.600566	−	1.04021i	−0.392170	−	0.919893i	$-0.628275\pi$
$983$	580320.	−	1.00514e6i	0.600566	−	1.04021i	0.992735	−	0.120318i	$-0.0383913\pi$
$984$	−25114.2	+	3230.83i	−0.0259376	+	0.00333675i
$985$	226627.	+	53507.6i	0.233581	+	0.0551497i
$986$	1.07551e6	−	620948.i	1.10627	−	0.638707i
$987$	−371584.	+	47802.6i	−0.381437	+	0.0490702i
$988$	1.24708e6	+	720003.i	1.27756	+	0.737599i
$989$		−	533679.i		−	0.545616i
$990$	−864017.	−	471534.i	−0.881560	−	0.481108i
$991$	−1.59778e6			−1.62693			−0.813467	−	0.581611i	$-0.802422\pi$
$991$	−1.59778e6			−1.62693			−0.813467	+	0.581611i	$0.802422\pi$
$992$	221972.	−	384467.i	0.225567	−	0.390693i
$993$	784118.	−	597999.i	0.795212	−	0.606460i
$994$	−800111.	−	1.38583e6i	−0.809799	−	1.40261i
$995$	−150605.	−	35558.5i	−0.152122	−	0.0359168i
$996$	921397.	+	384851.i	0.928813	+	0.387948i
$997$	1.12879e6	+	651705.i	1.13559	+	0.655633i	0.945334	−	0.326102i	$-0.105735\pi$
$997$	1.12879e6	+	651705.i	1.13559	+	0.655633i	0.190254	+	0.981735i	$0.439069\pi$
$998$	−1.00294e6			−1.00697
$999$	37645.0	−	15203.3i	0.0377204	−	0.0152337i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.5.h.a.29.19	yes	44
3.2	odd	2		135.5.h.a.89.4		44
5.4	even	2	inner	45.5.h.a.29.4	yes	44
9.2	odd	6		405.5.d.a.404.38		44
9.4	even	3		135.5.h.a.44.19		44
9.5	odd	6	inner	45.5.h.a.14.4	✓	44
9.7	even	3		405.5.d.a.404.8		44
15.14	odd	2		135.5.h.a.89.19		44
45.4	even	6		135.5.h.a.44.4		44
45.14	odd	6	inner	45.5.h.a.14.19	yes	44
45.29	odd	6		405.5.d.a.404.7		44
45.34	even	6		405.5.d.a.404.37		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.5.h.a.14.4	✓	44	9.5	odd	6	inner
45.5.h.a.14.19	yes	44	45.14	odd	6	inner
45.5.h.a.29.4	yes	44	5.4	even	2	inner
45.5.h.a.29.19	yes	44	1.1	even	1	trivial
135.5.h.a.44.4		44	45.4	even	6
135.5.h.a.44.19		44	9.4	even	3
135.5.h.a.89.4		44	3.2	odd	2
135.5.h.a.89.19		44	15.14	odd	2
405.5.d.a.404.7		44	45.29	odd	6
405.5.d.a.404.8		44	9.7	even	3
405.5.d.a.404.37		44	45.34	even	6
405.5.d.a.404.38		44	9.2	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:	\( N \)	\(=\)	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	45.h (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.87361 - 4.97724i) q^{2} +(8.30470 + 3.46872i) q^{3} +(-8.51525 - 14.7488i) q^{4} +(24.3310 + 5.74467i) q^{5} +(41.1291 - 31.3667i) q^{6} +(-41.4151 - 23.9110i) q^{7} -5.92246 q^{8} +(56.9359 + 57.6134i) q^{9} +(98.5104 - 104.593i) q^{10} +(-73.2455 - 42.2883i) q^{11} +(-19.5569 - 152.022i) q^{12} +(-193.485 + 111.709i) q^{13} +(-238.021 + 137.422i) q^{14} +(182.135 + 132.105i) q^{15} +(119.225 - 206.504i) q^{16} -434.998 q^{17} +(450.367 - 117.825i) q^{18} +378.461 q^{19} +(-122.457 - 407.772i) q^{20} +(-260.999 - 342.231i) q^{21} +(-420.958 + 243.040i) q^{22} +(326.825 + 566.078i) q^{23} +(-49.1842 - 20.5434i) q^{24} +(558.998 + 279.547i) q^{25} +1284.03i q^{26} +(272.991 + 675.956i) q^{27} +814.433i q^{28} +(-430.201 - 248.377i) q^{29} +(1180.90 - 526.910i) q^{30} +(151.498 + 262.402i) q^{31} +(-732.592 - 1268.89i) q^{32} +(-461.595 - 605.260i) q^{33} +(-1250.01 + 2165.09i) q^{34} +(-870.311 - 819.695i) q^{35} +(364.907 - 1330.33i) q^{36} -55.6914i q^{37} +(1087.55 - 1883.69i) q^{38} +(-1994.32 + 256.560i) q^{39} +(-144.099 - 34.0226i) q^{40} +(411.405 - 237.525i) q^{41} +(-2453.37 + 315.616i) q^{42} +(-707.073 - 408.229i) q^{43} +1440.38i q^{44} +(1054.34 + 1728.87i) q^{45} +3756.67 q^{46} +(435.232 - 753.844i) q^{47} +(1706.43 - 1301.39i) q^{48} +(-57.0270 - 98.7737i) q^{49} +(2997.71 - 1978.95i) q^{50} +(-3612.52 - 1508.89i) q^{51} +(3295.14 + 1902.45i) q^{52} -2339.28 q^{53} +(4148.86 + 583.694i) q^{54} +(-1539.21 - 1449.69i) q^{55} +(245.279 + 141.612i) q^{56} +(3143.00 + 1312.77i) q^{57} +(-2472.46 + 1427.47i) q^{58} +(-1019.68 + 588.710i) q^{59} +(397.475 - 3811.19i) q^{60} +(3456.52 - 5986.86i) q^{61} +1741.38 q^{62} +(-980.413 - 3747.46i) q^{63} -4605.53 q^{64} +(-5349.42 + 1606.48i) q^{65} +(-4338.96 + 558.188i) q^{66} +(3356.29 - 1937.75i) q^{67} +(3704.11 + 6415.71i) q^{68} +(750.618 + 5834.77i) q^{69} +(-6580.75 + 1976.26i) q^{70} +5822.30i q^{71} +(-337.201 - 341.213i) q^{72} -6443.82i q^{73} +(-277.189 - 160.035i) q^{74} +(3672.63 + 4260.56i) q^{75} +(-3222.69 - 5581.85i) q^{76} +(2022.31 + 3502.75i) q^{77} +(-4453.93 + 10663.5i) q^{78} +(-2446.72 + 4237.84i) q^{79} +(4087.17 - 4339.54i) q^{80} +(-77.5982 + 6560.54i) q^{81} -2730.21i q^{82} +(-3257.36 + 5641.91i) q^{83} +(-2825.04 + 6763.61i) q^{84} +(-10583.9 - 2498.92i) q^{85} +(-4063.70 + 2346.18i) q^{86} +(-2711.14 - 3554.94i) q^{87} +(433.793 + 250.451i) q^{88} -13898.7i q^{89} +(11634.8 - 279.602i) q^{90} +10684.3 q^{91} +(5566.00 - 9640.59i) q^{92} +(347.944 + 2704.67i) q^{93} +(-2501.37 - 4332.50i) q^{94} +(9208.33 + 2174.13i) q^{95} +(-1682.54 - 13078.9i) q^{96} +(11681.7 + 6744.42i) q^{97} -655.493 q^{98} +(-1733.93 - 6627.64i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 162 q^{4} + 6 q^{5} - 36 q^{6} - 126 q^{9} + 28 q^{10} + 228 q^{11} + 282 q^{14} + 450 q^{15} - 1058 q^{16} - 8 q^{19} - 2196 q^{20} + 1056 q^{21} + 2970 q^{24} - 148 q^{25} + 2370 q^{29} + 1068 q^{30}+ \cdots + 44568 q^{99}+O(q^{100}) \) 44 * q - 162 * q^4 + 6 * q^5 - 36 * q^6 - 126 * q^9 + 28 * q^10 + 228 * q^11 + 282 * q^14 + 450 * q^15 - 1058 * q^16 - 8 * q^19 - 2196 * q^20 + 1056 * q^21 + 2970 * q^24 - 148 * q^25 + 2370 * q^29 + 1068 * q^30 - 1112 * q^31 - 436 * q^34 - 648 * q^36 - 6420 * q^39 - 850 * q^40 + 1830 * q^41 - 1944 * q^45 - 5668 * q^46 + 5396 * q^49 + 13524 * q^50 - 1500 * q^51 + 17766 * q^54 - 3072 * q^55 - 8250 * q^56 - 27348 * q^59 - 28722 * q^60 + 2782 * q^61 + 8348 * q^64 - 24906 * q^65 + 27240 * q^66 + 19662 * q^69 + 4782 * q^70 + 64728 * q^74 + 28446 * q^75 - 1776 * q^76 + 7900 * q^79 - 47754 * q^81 - 113166 * q^84 + 6766 * q^85 + 9192 * q^86 + 10674 * q^90 + 1560 * q^91 - 18826 * q^94 + 58746 * q^95 + 1902 * q^96 + 44568 * q^99

Introduction

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