LMFDB - Embedded newform 45.5.h.a.14.4

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			14.4
Character	$\chi$	$=$	45.14
Dual form			45.5.h.a.29.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.87361 - 4.97724i) q^{2} +(-8.30470 + 3.46872i) q^{3} +(-8.51525 + 14.7488i) q^{4} +(7.19048 + 23.9436i) 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} +(-142.769 - 173.903i) q^{15} +(119.225 + 206.504i) q^{16} +434.998 q^{17} +(-450.367 - 117.825i) q^{18} +378.461 q^{19} +(-414.369 - 97.8346i) 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} +(-521.594 + 344.332i) q^{25} -1284.03i q^{26} +(-272.991 + 675.956i) q^{27} +814.433i q^{28} +(-430.201 + 248.377i) q^{29} +(-455.294 + 1210.32i) 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} +(42.5853 + 141.805i) q^{40} +(411.405 + 237.525i) q^{41} +(2453.37 + 315.616i) q^{42} +(707.073 - 408.229i) q^{43} -1440.38i q^{44} +(1788.87 + 948.985i) q^{45} +3756.67 q^{46} +(-435.232 - 753.844i) q^{47} +(-1706.43 - 1301.39i) q^{48} +(-57.0270 + 98.7737i) q^{49} +(3212.68 + 1606.62i) 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} +(3780.57 - 624.846i) q^{60} +(3456.52 + 5986.86i) q^{61} -1741.38 q^{62} +(980.413 - 3747.46i) q^{63} -4605.53 q^{64} +(-1283.46 + 5435.97i) 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} +(1578.89 - 6687.22i) q^{70} -5822.30i q^{71} +(337.201 - 341.213i) q^{72} -6443.82i q^{73} +(-277.189 + 160.035i) q^{74} +(3137.29 - 4668.84i) 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} +(3127.84 + 10415.4i) q^{85} +(-4063.70 - 2346.18i) q^{86} +(2711.14 - 3554.94i) q^{87} +(-433.793 + 250.451i) q^{88} +13898.7i q^{89} +(-417.189 - 11630.6i) q^{90} +10684.3 q^{91} +(-5566.00 - 9640.59i) q^{92} +(-347.944 + 2704.67i) q^{93} +(-2501.37 + 4332.50i) q^{94} +(2721.31 + 9061.72i) 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 $\left(\mathbb{Z}/45\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

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	−0.961633	−	0.274340i	$-0.911541\pi$
$2$	−2.87361	−	4.97724i	−0.718402	−	1.24431i	0.243231	−	0.969968i	$-0.421793\pi$
$3$	−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
$5$	7.19048	+	23.9436i	0.287619	+	0.957745i
$5$	7.19048	+	23.9436i	0.287619	+	0.957745i
$6$	41.1291	+	31.3667i	1.14247	+	0.871297i
$7$	41.4151	−	23.9110i	0.845206	−	0.487980i	−0.0138245	−	0.999904i	$-0.504401\pi$
$7$	41.4151	−	23.9110i	0.845206	−	0.487980i	0.859030	+	0.511925i	$0.171067\pi$
$8$	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	−0.771137	−	0.636669i	$-0.780312\pi$
$11$	−73.2455	+	42.2883i	−0.605335	+	0.349490i	0.165803	+	0.986159i	$0.446979\pi$
$12$	19.5569	−	152.022i	0.135812	−	1.05571i
$13$	193.485	+	111.709i	1.14488	+	0.660998i	0.947635	−	0.319356i	$-0.103467\pi$
$13$	193.485	+	111.709i	1.14488	+	0.660998i	0.197247	+	0.980354i	$0.436800\pi$
$14$	−238.021	−	137.422i	−1.21440	−	0.701131i
$15$	−142.769	−	173.903i	−0.634527	−	0.772901i
$16$	119.225	+	206.504i	0.465723	+	0.806656i
$17$	434.998			1.50518			0.752591	−	0.658488i	$-0.228804\pi$
$17$	434.998			1.50518			0.752591	+	0.658488i	$0.228804\pi$
$18$	−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	$0.324371\pi$
$20$	−414.369	−	97.8346i	−1.03592	−	0.244586i
$21$	−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	0.372066	+	0.928206i	$0.378650\pi$
$23$	−326.825	+	566.078i	−0.617818	+	1.07009i	−0.989883	+	0.141885i	$0.954684\pi$
$24$	−49.1842	+	20.5434i	−0.0853893	+	0.0356656i
$25$	−521.594	+	344.332i	−0.834550	+	0.550932i
$26$		−	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	−0.733464	−	0.679728i	$-0.762098\pi$
$29$	−430.201	+	248.377i	−0.511535	+	0.295335i	0.221929	+	0.975063i	$0.428765\pi$
$30$	−455.294	+	1210.32i	−0.505882	+	1.34480i
$31$	151.498	−	262.402i	0.157646	−	0.273051i	−0.776373	−	0.630273i	$-0.782943\pi$
$31$	151.498	−	262.402i	0.157646	−	0.273051i	0.934019	+	0.357222i	$0.116276\pi$
$32$	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
$40$	42.5853	+	141.805i	0.0266158	+	0.0886282i
$41$	411.405	+	237.525i	0.244738	+	0.141300i	0.617353	−	0.786687i	$-0.288205\pi$
$41$	411.405	+	237.525i	0.244738	+	0.141300i	−0.372614	+	0.927986i	$0.621539\pi$
$42$	2453.37	+	315.616i	1.39080	+	0.178920i
$43$	707.073	−	408.229i	0.382409	−	0.220784i	−0.296457	−	0.955046i	$-0.595805\pi$
$43$	707.073	−	408.229i	0.382409	−	0.220784i	0.678866	+	0.734262i	$0.262472\pi$
$44$		−	1440.38i		−	0.743999i
$45$	1788.87	+	948.985i	0.883392	+	0.468634i
$46$	3756.67			1.77537
$47$	−435.232	−	753.844i	−0.197027	−	0.341260i	0.750536	−	0.660829i	$-0.229795\pi$
$47$	−435.232	−	753.844i	−0.197027	−	0.341260i	−0.947563	+	0.319569i	$0.896462\pi$
$48$	−1706.43	−	1301.39i	−0.740639	−	0.564841i
$49$	−57.0270	+	98.7737i	−0.0237514	+	0.0411386i
$50$	3212.68	+	1606.62i	1.28507	+	0.642648i
$51$	−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	$-0.363295\pi$
$53$	2339.28			0.832780			0.416390	+	0.909186i	$0.363295\pi$
$54$	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	0.346335	−	0.938111i	$-0.387426\pi$
$59$	−1019.68	−	588.710i	−0.292926	−	0.169121i	−0.639261	+	0.768990i	$0.720760\pi$
$60$	3780.57	−	624.846i	1.05016	−	0.173568i
$61$	3456.52	+	5986.86i	0.928921	+	1.60894i	0.785130	+	0.619331i	$0.212596\pi$
$61$	3456.52	+	5986.86i	0.928921	+	1.60894i	0.143792	+	0.989608i	$0.454070\pi$
$62$	−1741.38			−0.453013
$63$	980.413	−	3747.46i	0.247018	−	0.944182i
$64$	−4605.53			−1.12440
$65$	−1283.46	+	5435.97i	−0.303777	+	1.28662i
$66$	−4338.96	−	558.188i	−0.996089	−	0.128142i
$67$	−3356.29	−	1937.75i	−0.747669	−	0.431667i	0.0771820	−	0.997017i	$-0.475408\pi$
$67$	−3356.29	−	1937.75i	−0.747669	−	0.431667i	−0.824851	+	0.565350i	$0.808741\pi$
$68$	−3704.11	+	6415.71i	−0.801063	+	1.38748i
$69$	750.618	−	5834.77i	0.157660	−	1.22554i
$70$	1578.89	−	6687.22i	0.322222	−	1.36474i
$71$		−	5822.30i		−	1.15499i	−0.816394	−	0.577495i	$-0.804030\pi$
$71$		−	5822.30i		−	1.15499i	0.816394	−	0.577495i	$-0.195970\pi$
$72$	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
$75$	3137.29	−	4668.84i	0.557740	−	0.830016i
$76$	−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	0.600679	−	0.799490i	$-0.294897\pi$
$79$	−2446.72	−	4237.84i	−0.392039	−	0.679032i	−0.992718	+	0.120459i	$0.961564\pi$
$80$	−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	$-0.00989729\pi$
$83$	3257.36	+	5641.91i	0.472835	+	0.818974i	−0.526682	+	0.850063i	$0.676564\pi$
$84$	−2825.04	−	6763.61i	−0.400374	−	0.958562i
$85$	3127.84	+	10415.4i	0.432920	+	1.44158i
$86$	−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	$0.340680\pi$
$89$			13898.7i			1.75467i	−0.479881	+	0.877333i	$0.659320\pi$
$90$	−417.189	−	11630.6i	−0.0515048	−	1.43588i
$91$	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
$95$	2721.31	+	9061.72i	0.301531	+	1.00407i
$96$	−1682.54	+	13078.9i	−0.182567	+	1.41915i
$97$	−11681.7	+	6744.42i	−1.24154	+	0.716805i	−0.969408	−	0.245454i	$-0.921063\pi$
$97$	−11681.7	+	6744.42i	−1.24154	+	0.716805i	−0.272134	+	0.962259i	$0.587729\pi$
$98$	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	0.547886	−	0.836553i	$-0.315433\pi$
$101$	15773.9	−	9107.04i	1.54631	−	0.892760i	0.998419	−	0.0562073i	$-0.0179008\pi$
$102$	17891.1	+	13644.4i	1.71963	+	1.31146i
$103$	−11205.3	−	6469.37i	−1.05620	−	0.609800i	−0.131825	−	0.991273i	$-0.542084\pi$
$103$	−11205.3	−	6469.37i	−1.05620	−	0.609800i	−0.924380	+	0.381473i	$0.875417\pi$
$104$	1145.91	+	661.590i	0.105946	+	0.0611677i
$105$	−10071.0	−	3788.46i	−0.913466	−	0.343624i
$106$	−6722.17	−	11643.1i	−0.598271	−	1.03624i
$107$	1372.35			0.119867			0.0599333	−	0.998202i	$-0.480911\pi$
$107$	1372.35			0.119867			0.0599333	+	0.998202i	$0.480911\pi$
$108$	−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	$0.386063\pi$
$110$	−2792.37	+	11826.8i	−0.230774	+	0.977424i
$111$	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	−0.0943766	−	0.995537i	$-0.530086\pi$
$113$	10406.4	−	18024.4i	0.814972	−	1.41157i	0.909348	−	0.416036i	$-0.136581\pi$
$114$	15565.7	+	11871.1i	1.19773	+	0.913439i
$115$	−15904.0	−	3755.01i	−1.20257	−	0.283933i
$116$		−	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
$120$	−845.541	−	1029.93i	−0.0587181	−	0.0715230i
$121$	−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
$130$	30744.2	−	9232.77i	1.81919	−	0.546318i
$131$	−4773.97	−	2756.25i	−0.278187	−	0.160611i	0.354415	−	0.935088i	$-0.384680\pi$
$131$	−4773.97	−	2756.25i	−0.278187	−	0.160611i	−0.632602	+	0.774477i	$0.718013\pi$
$132$	4996.28	+	11961.9i	0.286747	+	0.686520i
$133$	15674.0	−	9049.38i	0.886086	−	0.511582i
$134$			22273.4i			1.24044i
$135$	−18147.8	−	1675.94i	−0.995763	−	0.0919583i
$136$	2576.26			0.139287
$137$	2167.08	+	3753.49i	0.115460	+	0.199983i	0.917964	−	0.396664i	$-0.129832\pi$
$137$	2167.08	+	3753.49i	0.115460	+	0.199983i	−0.802503	+	0.596648i	$0.796499\pi$
$138$	−31198.0	+	13030.9i	−1.63821	+	0.684250i
$139$	−1687.03	+	2922.01i	−0.0873157	+	0.151235i	−0.906376	−	0.422473i	$-0.861162\pi$
$139$	−1687.03	+	2922.01i	−0.0873157	+	0.151235i	0.819060	+	0.573708i	$0.194496\pi$
$140$	−19500.5	+	5856.16i	−0.994922	+	0.298784i
$141$	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	−0.326389	−	0.945235i	$-0.605832\pi$
$149$	−29042.9	−	16768.0i	−1.30818	−	0.755279i	−0.981793	+	0.189956i	$0.939165\pi$
$150$	−32253.2	−	2198.60i	−1.43348	−	0.0977154i
$151$	−517.293	−	895.978i	−0.0226873	−	0.0392955i	0.854459	−	0.519519i	$-0.173889\pi$
$151$	−517.293	−	895.978i	−0.0226873	−	0.0392955i	−0.877146	+	0.480224i	$0.840556\pi$
$152$	2241.42			0.0970143
$153$	24767.0	−	25061.7i	1.05801	−	1.07060i
$154$	23245.3			0.980154
$155$	7372.19	+	1740.61i	0.306855	+	0.0724499i
$156$	20766.1	−	27229.2i	0.853307	−	1.11889i
$157$	3936.83	+	2272.93i	0.159716	+	0.0922119i	0.577728	−	0.816230i	$-0.303940\pi$
$157$	3936.83	+	2272.93i	0.159716	+	0.0922119i	−0.418012	+	0.908442i	$0.637273\pi$
$158$	−14061.8	+	24355.8i	−0.563283	+	0.975635i
$159$	−19427.0	+	8114.31i	−0.768443	+	0.320965i
$160$	35649.4	+	8417.00i	1.39256	+	0.328789i
$161$			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
$165$	17811.2	+	6700.15i	0.654222	+	0.246103i
$166$	18720.8	−	32425.3i	0.679371	−	1.17671i
$167$	11108.8	−	19241.0i	0.398322	−	0.689914i	−0.595197	−	0.803580i	$-0.702926\pi$
$167$	11108.8	−	19241.0i	0.398322	−	0.689914i	0.993519	+	0.113666i	$0.0362593\pi$
$168$	−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	0.994503	+	0.104704i	$0.0333896\pi$
$173$	17596.1	+	30477.3i	0.587928	+	1.01832i	−0.406575	+	0.913617i	$0.633277\pi$
$174$	−25484.5	−	3278.47i	−0.841740	−	0.108286i
$175$	−13368.5	+	26732.4i	−0.436523	+	0.872894i
$176$	−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	$-0.757797\pi$
$179$		−	44189.5i		−	1.37915i	0.724213	−	0.689577i	$-0.242203\pi$
$180$	−29229.1	+	18302.9i	−0.902132	+	0.564904i
$181$	−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
$185$	1333.45	−	400.448i	0.0389614	−	0.0117005i
$186$	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	−0.188403	−	0.982092i	$-0.560331\pi$
$191$	20718.0	−	11961.5i	0.567912	−	0.327884i	0.756315	+	0.654208i	$0.226998\pi$
$192$	38247.5	−	15975.3i	1.03753	−	0.433358i
$193$	2034.57	+	1174.66i	0.0546209	+	0.0315354i	0.527062	−	0.849827i	$-0.323294\pi$
$193$	2034.57	+	1174.66i	0.0546209	+	0.0315354i	−0.472441	+	0.881362i	$0.656627\pi$
$194$	67137.1	+	38761.6i	1.78385	+	1.02991i
$195$	−8197.13	−	49596.0i	−0.215572	−	1.30430i
$196$	−971.198	−	1682.16i	−0.0252811	−	0.0437881i
$197$	−9314.30			−0.240004			−0.120002	−	0.992774i	$-0.538290\pi$
$197$	−9314.30			−0.240004			−0.120002	+	0.992774i	$0.538290\pi$
$198$	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	$0.524902\pi$
$200$	−3089.12	+	2039.29i	−0.0772280	+	0.0509823i
$201$	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
$205$	−2729.00	+	11558.4i	−0.0649377	+	0.275037i
$206$			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
$210$	10084.0	+	61012.1i	0.228661	+	1.38349i
$211$	−716.811	+	1241.55i	−0.0161005	+	0.0278869i	−0.873963	−	0.485992i	$-0.838459\pi$
$211$	−716.811	+	1241.55i	−0.0161005	+	0.0278869i	0.857863	+	0.513879i	$0.171792\pi$
$212$	−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
$220$	34487.9	−	10357.0i	0.712561	−	0.213988i
$221$	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	$-0.665475\pi$
$223$	322.537	−	186.217i	0.00648589	−	0.00374463i	0.503239	+	0.864147i	$0.332141\pi$
$224$		−	70068.1i		−	1.39645i
$225$	−9859.30	+	49655.7i	−0.194752	+	0.980853i
$226$	−119615.			−2.34191
$227$	−15116.7	−	26182.9i	−0.293363	−	0.508119i	0.681240	−	0.732060i	$-0.261441\pi$
$227$	−15116.7	−	26182.9i	−0.293363	−	0.508119i	−0.974603	+	0.223941i	$0.928108\pi$
$228$	7401.52	−	57534.2i	0.142381	−	1.10677i
$229$	22086.6	−	38255.1i	0.421171	−	0.729489i	−0.574884	−	0.818235i	$-0.694953\pi$
$229$	22086.6	−	38255.1i	0.421171	−	0.729489i	0.996054	+	0.0887464i	$0.0282861\pi$
$230$	27012.3	+	89948.4i	0.510629	+	1.70035i
$231$	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	$-0.567876\pi$
$233$	−22978.1			−0.423255			−0.211628	+	0.977350i	$0.567876\pi$
$234$	−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	−0.113735	−	0.993511i	$-0.536281\pi$
$239$	−58892.2	−	34001.4i	−1.03101	−	0.595253i	−0.917273	+	0.398258i	$0.869615\pi$
$240$	18890.0	−	50215.8i	0.327951	−	0.871803i
$241$	−34731.9	−	60157.4i	−0.597991	−	1.03575i	−0.993117	−	0.117124i	$-0.962633\pi$
$241$	−34731.9	−	60157.4i	−0.597991	−	1.03575i	0.395126	−	0.918627i	$-0.370701\pi$
$242$	43034.0			0.734820
$243$	23401.1	+	54214.1i	0.396300	+	0.918121i
$244$	−117732.			−1.97750
$245$	−2775.05	−	655.203i	−0.0462316	−	0.0109155i
$246$	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
$250$	−15367.6	+	88475.5i	−0.245881	+	1.41561i
$251$			44839.6i			0.711728i	0.934538	+	0.355864i	$0.115813\pi$
$251$			44839.6i			0.711728i	−0.934538	+	0.355864i	$0.884187\pi$
$252$	46922.2	+	46370.5i	0.738886	+	0.730198i
$253$		−	55283.6i		−	0.863684i
$254$	17136.1	−	9893.53i	0.265610	−	0.153350i
$255$	−62104.0	−	75647.3i	−0.955079	−	1.16336i
$256$	−28148.6	+	48754.9i	−0.429514	+	0.743941i
$257$	256.172	−	443.703i	0.00387852	−	0.00671779i	−0.864080	−	0.503355i	$-0.832099\pi$
$257$	256.172	−	443.703i	0.00387852	−	0.00671779i	0.867958	+	0.496637i	$0.165432\pi$
$258$	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	$-0.0565327\pi$
$263$	23457.5	+	40629.7i	0.339134	+	0.587397i	−0.645136	+	0.764068i	$0.723199\pi$
$264$	2733.78	−	3584.63i	0.0392243	−	0.0514323i
$265$	16820.5	+	56010.8i	0.239524	+	0.797591i
$266$	−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	$-0.958934\pi$
$269$		−	18619.3i		−	0.257311i	0.991689	−	0.128655i	$-0.0410661\pi$
$270$	43808.1	+	95141.8i	0.600934	+	1.30510i
$271$	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
$275$	23643.2	−	47278.1i	0.312637	−	0.625165i
$276$	79664.5	+	60755.3i	1.04579	+	0.797565i
$277$	24078.5	−	13901.7i	0.313812	−	0.181179i	−0.334819	−	0.942282i	$-0.608675\pi$
$277$	24078.5	−	13901.7i	0.313812	−	0.181179i	0.648631	+	0.761103i	$0.275342\pi$
$278$	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	−0.469644	−	0.882856i	$-0.655618\pi$
$281$	4746.39	−	2740.33i	0.0601106	−	0.0347049i	0.529754	+	0.848151i	$0.322284\pi$
$282$	5744.89	−	44656.7i	0.0722409	−	0.561550i
$283$	−104022.	−	60056.9i	−1.29883	−	0.749877i	−0.318624	−	0.947881i	$-0.603221\pi$
$283$	−104022.	−	60056.9i	−1.29883	−	0.749877i	−0.980201	+	0.198004i	$0.936554\pi$
$284$	85872.2	+	49578.3i	1.06467	+	0.614689i
$285$	−54032.3	−	65815.3i	−0.665217	−	0.810284i
$286$	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
$290$	−16400.7	+	69463.8i	−0.195015	+	0.825967i
$291$	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	$-0.795680\pi$
$293$	10131.5	−	17548.3i	0.118016	−	0.204409i	0.918981	+	0.394301i	$0.129013\pi$
$294$	−5443.67	+	2273.72i	−0.0629792	+	0.0263053i
$295$	6763.89	−	28647.8i	0.0777235	−	0.329191i
$296$		−	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
$300$	42145.2	+	86027.6i	0.468280	+	0.955863i
$301$	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
$310$	−12521.4	−	41694.9i	−0.130295	−	0.433870i
$311$	−118174.	−	68227.6i	−1.22180	−	0.705406i	−0.256498	−	0.966545i	$-0.582569\pi$
$311$	−118174.	−	68227.6i	−1.22180	−	0.705406i	−0.965301	+	0.261139i	$0.915902\pi$
$312$	−11811.3	−	1519.47i	−0.121335	−	0.0156093i
$313$	94500.3	−	54559.8i	0.964594	−	0.556909i	0.0670101	−	0.997752i	$-0.478654\pi$
$313$	94500.3	−	54559.8i	0.964594	−	0.556909i	0.897584	+	0.440844i	$0.145321\pi$
$314$		−	26126.0i		−	0.264981i
$315$	96777.4	−	3471.39i	0.975332	−	0.0349850i
$316$	83337.5			0.834577
$317$	−21419.5	−	37099.7i	−0.213153	−	0.369191i	0.739547	−	0.673105i	$-0.235040\pi$
$317$	−21419.5	−	37099.7i	−0.213153	−	0.369191i	−0.952700	+	0.303914i	$0.901707\pi$
$318$	96212.4	+	73375.4i	0.951430	+	0.725599i
$319$	21006.9	−	36384.9i	0.206433	−	0.357553i
$320$	−33116.0	−	110273.i	−0.323398	−	1.07688i
$321$	−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
$330$	−17834.2	−	107904.i	−0.163767	−	0.990855i
$331$	54784.8	+	94890.0i	0.500039	+	0.866093i	1.00000		4.48028e-5i	$1.42612e-5\pi$
$331$	54784.8	+	94890.0i	0.500039	+	0.866093i	−0.499961	+	0.866048i	$0.666652\pi$
$332$	−110949.			−1.00658
$333$	−3208.57	−	3170.84i	−0.0289350	−	0.0285948i
$334$	−127689.			−1.14462
$335$	22263.5	−	94295.0i	0.198383	−	0.840232i
$336$	−101790.	−	13094.8i	−0.901624	−	0.115990i
$337$	7974.17	+	4603.89i	0.0702143	+	0.0405383i	0.534696	−	0.845044i	$-0.320426\pi$
$337$	7974.17	+	4603.89i	0.0702143	+	0.0405383i	−0.464482	+	0.885583i	$0.653759\pi$
$338$	61363.7	−	106285.i	0.537128	−	0.930334i
$339$	−23900.2	+	185784.i	−0.207971	+	1.61662i
$340$	−180250.	−	42557.8i	−1.55925	−	0.368147i
$341$			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
$345$	145103.	−	23982.3i	1.21910	−	0.201490i
$346$	101129.	−	175160.i	0.844737	−	1.46313i
$347$	−11277.8	+	19533.8i	−0.0936628	+	0.162229i	−0.909050	−	0.416688i	$-0.863191\pi$
$347$	−11277.8	+	19533.8i	−0.0936628	+	0.162229i	0.815387	+	0.578916i	$0.196524\pi$
$348$	29345.2	+	70257.4i	0.242314	+	0.580141i
$349$	−101902.	−	176500.i	−0.836629	−	1.44908i	−0.892697	−	0.450657i	$-0.851190\pi$
$349$	−101902.	−	176500.i	−0.836629	−	1.44908i	0.0560687	−	0.998427i	$-0.482143\pi$
$350$	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	$-0.250143\pi$
$353$	−32305.1	−	55954.1i	−0.259252	−	0.449038i	−0.966042	+	0.258386i	$0.916809\pi$
$354$	−23472.5	−	56196.9i	−0.187306	−	0.448442i
$355$	139407.	−	41865.1i	1.10619	−	0.332197i
$356$	−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	$-0.950941\pi$
$359$		−	39569.8i		−	0.307026i	0.988147	−	0.153513i	$-0.0490587\pi$
$360$	10594.5	+	5620.32i	0.0817477	+	0.0433667i
$361$	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
$365$	154288.	−	46334.2i	1.15810	−	0.347789i
$366$	−45624.6	+	354654.i	−0.340594	+	2.64754i
$367$	−168361.	+	97203.5i	−1.25000	+	0.721688i	−0.971109	−	0.238634i	$-0.923300\pi$
$367$	−168361.	+	97203.5i	−1.25000	+	0.721688i	−0.278891	+	0.960323i	$0.589967\pi$
$368$	−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	$-0.207240\pi$
$373$	92982.6	+	53683.5i	0.668319	+	0.385854i	−0.127120	+	0.991887i	$0.540573\pi$
$374$	183116.	+	105722.i	1.30913	+	0.755826i
$375$	134348.	+	41546.8i	0.955360	+	0.295444i
$376$	−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	$0.201627\pi$
$380$	−156822.	−	37026.5i	−1.08603	−	0.256416i
$381$	−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	$-0.884068\pi$
$383$	−23281.5	+	40324.7i	−0.158713	+	0.274899i	0.775692	+	0.631112i	$0.217401\pi$
$384$	−21655.2	−	16515.1i	−0.146859	−	0.112000i
$385$	−98409.9	−	23235.0i	−0.663922	−	0.156755i
$386$		−	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	−0.542682	−	0.839938i	$-0.682591\pi$
$389$	−13106.7	+	7567.17i	−0.0866154	+	0.0500074i	0.456067	+	0.889946i	$0.349258\pi$
$390$	−223296.	+	183319.i	−1.46808	+	1.20525i
$391$	−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
$400$	−133293.	−	66658.2i	−0.833082	−	0.416613i
$401$	−116070.	−	67013.0i	−0.721823	−	0.416745i	0.0936000	−	0.995610i	$-0.470163\pi$
$401$	−116070.	−	67013.0i	−0.721823	−	0.416745i	−0.815423	+	0.578865i	$0.803496\pi$
$402$	−77260.1	−	184974.i	−0.478083	−	1.14461i
$403$	58625.1	−	33847.2i	0.360972	−	0.208407i
$404$			310195.i			1.90052i
$405$	156525.	−	49031.4i	0.954276	−	0.298927i
$406$	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	−0.773546	−	0.633740i	$-0.781519\pi$
$409$	27109.9	−	46955.6i	0.162062	−	0.280699i	0.935608	+	0.353041i	$0.114852\pi$
$410$	65371.2	−	19631.5i	0.388883	−	0.116785i
$411$	−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	0.867820	−	0.496878i	$-0.165520\pi$
$419$	152988.	+	88327.4i	0.871421	+	0.503115i	0.00360107	+	0.999994i	$0.498854\pi$
$420$	141632.	−	116275.i	0.802903	−	0.659157i
$421$	−71752.2	−	124278.i	−0.404829	−	0.701184i	0.589473	−	0.807788i	$-0.299335\pi$
$421$	−71752.2	−	124278.i	−0.404829	−	0.701184i	−0.994302	+	0.106605i	$0.966002\pi$
$422$	8239.33			0.0462665
$423$	−68211.8	−	17845.6i	−0.381223	−	0.0997359i
$424$	13854.3			0.0770642
$425$	−226892.	+	149784.i	−1.25615	+	0.829253i
$426$	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
$430$	26956.1	−	114170.i	0.145787	−	0.617469i
$431$		−	96119.3i		−	0.517435i	−0.965953	−	0.258718i	$-0.916700\pi$
$431$		−	96119.3i		−	0.517435i	0.965953	−	0.258718i	$-0.0832999\pi$
$432$	−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
$435$	104613.	+	39352.8i	0.552847	+	0.207968i
$436$	−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	0.969036	−	0.246921i	$-0.0794188\pi$
$439$	52165.3	+	90353.0i	0.270678	+	0.468828i	−0.698358	+	0.715749i	$0.746085\pi$
$440$	−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	$-0.191611\pi$
$443$	−15363.5	−	26610.4i	−0.0782860	−	0.135595i	−0.902511	+	0.430668i	$0.858278\pi$
$444$	−8466.30	−	1089.15i	−0.0429465	−	0.00552488i
$445$	−332786.	+	99938.5i	−1.68052	+	0.504676i
$446$	−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	$-0.962547\pi$
$449$		−	47332.1i		−	0.234781i	0.993086	−	0.117391i	$-0.0374529\pi$
$450$	275480.	−	93618.9i	1.36039	−	0.462315i
$451$	−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
$455$	76825.0	+	255820.i	0.371090	+	1.23570i
$456$	−18614.3	+	7774.85i	−0.0895193	+	0.0373906i
$457$	101954.	−	58863.4i	0.488173	−	0.281847i	−0.235643	−	0.971840i	$-0.575720\pi$
$457$	101954.	−	58863.4i	0.488173	−	0.281847i	0.723816	+	0.689993i	$0.242386\pi$
$458$	−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	−0.586859	−	0.809689i	$-0.699636\pi$
$461$	−38057.7	+	21972.6i	−0.179077	+	0.103390i	0.407782	+	0.913079i	$0.366302\pi$
$462$	−193045.	+	80631.6i	−0.904431	+	0.377765i
$463$	32818.2	+	18947.6i	0.153092	+	0.0883878i	0.574589	−	0.818442i	$-0.305162\pi$
$463$	32818.2	+	18947.6i	0.153092	+	0.0883878i	−0.421497	+	0.906830i	$0.638495\pi$
$464$	−102582.	−	59225.5i	−0.476467	−	0.275089i
$465$	−67261.5	+	11116.8i	−0.311072	+	0.0514133i
$466$	66030.0	+	114367.i	0.304067	+	0.526660i
$467$	229722.			1.05334			0.526671	−	0.850069i	$-0.323440\pi$
$467$	229722.			1.05334			0.526671	+	0.850069i	$0.323440\pi$
$468$	−78005.4	+	298162.i	−0.356150	+	1.36132i
$469$	−185335.			−0.842579
$470$	−121722.	−	28739.1i	−0.551027	−	0.130100i
$471$	−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
$475$	−197403.	+	130316.i	−0.874915	+	0.577579i
$476$			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	−0.589969	−	0.807426i	$-0.700860\pi$
$479$	−42607.9	+	24599.7i	−0.185703	+	0.107216i	0.404266	+	0.914641i	$0.367527\pi$
$480$	−325254.	+	53757.3i	−1.41169	+	0.233322i
$481$	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
$490$	4713.31	+	15694.9i	0.0196306	+	0.0653681i
$491$	146133.	+	84370.0i	0.606158	+	0.349965i	0.771460	−	0.636278i	$-0.219527\pi$
$491$	146133.	+	84370.0i	0.606158	+	0.349965i	−0.165302	+	0.986243i	$0.552860\pi$
$492$	44154.7	−	57897.2i	0.182409	−	0.239182i
$493$	−187137.	+	108043.i	−0.769954	+	0.444533i
$494$		−	485954.i		−	1.99132i
$495$	−171158.	+	6139.39i	−0.698531	+	0.0250562i
$496$	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	−0.986323	−	0.164825i	$-0.947294\pi$
$499$	−87254.6	+	151129.i	−0.350419	+	0.606943i	0.635904	+	0.771768i	$0.280627\pi$
$500$	249820.	−	91650.8i	0.999281	−	0.366603i
$501$	−25513.5	+	198324.i	−0.101647	+	0.790133i
$502$	223177.	−	128851.i	0.885610	−	0.511307i
$503$	384923.			1.52138			0.760691	−	0.649115i	$-0.224860\pi$
$503$	384923.			1.52138			0.760691	+	0.649115i	$0.224860\pi$
$504$	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	0.259332	−	0.965788i	$-0.416498\pi$
$509$	−115913.	−	66922.3i	−0.447400	−	0.258306i	−0.706731	+	0.707482i	$0.749831\pi$
$510$	−198052.	+	526487.i	−0.761445	+	2.02417i
$511$	−154078.	−	266871.i	−0.590065	−	1.02202i
$512$	371969.			1.41895
$513$	−103316.	+	255823.i	−0.392585	+	0.972086i
$514$	−2944.55			−0.0111453
$515$	74328.8	−	314813.i	0.280248	−	1.18696i
$516$	−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
$520$	−7601.23	+	32194.3i	−0.0281111	+	0.119062i
$521$			128028.i			0.471662i	0.971794	+	0.235831i	$0.0757812\pi$
$521$			128028.i			0.471662i	−0.971794	+	0.235831i	$0.924219\pi$
$522$	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
$525$	18294.3	−	268376.i	0.0663739	−	0.973700i
$526$	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
$535$	9867.87	+	32859.1i	0.0344759	+	0.114802i
$536$	−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
$540$	179251.	−	253388.i	0.614715	−	0.868956i
$541$	−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
$545$	59860.7	+	199330.i	0.201534	+	0.671090i
$546$	439434.	+	335130.i	1.47404	+	1.12416i
$547$	−224830.	+	129806.i	−0.751414	+	0.433829i	−0.826205	−	0.563370i	$-0.809505\pi$
$547$	−224830.	+	129806.i	−0.751414	+	0.433829i	0.0747906	+	0.997199i	$0.476171\pi$
$548$	−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
$555$	−9684.89	+	7950.98i	−0.0314419	+	0.0258128i
$556$	−28730.9	−	49763.3i	−0.0929393	−	0.160976i
$557$	−261444.			−0.842691			−0.421345	−	0.906900i	$-0.638442\pi$
$557$	−261444.			−0.842691			−0.421345	+	0.906900i	$0.638442\pi$
$558$	−99147.1	+	100327.i	−0.318428	+	0.322217i
$559$	182411.			0.583750
$560$	−65507.5	+	277451.i	−0.208889	+	0.884728i
$561$	200793.	−	263287.i	0.638003	−	0.836572i
$562$	−27278.5	−	15749.3i	−0.0863671	−	0.0498641i
$563$	185109.	−	320619.i	0.583999	−	1.01152i	−0.411001	−	0.911635i	$-0.634821\pi$
$563$	185109.	−	320619.i	0.583999	−	1.01152i	0.994999	−	0.0998803i	$-0.0318460\pi$
$564$	−123112.	+	51421.8i	−0.387029	+	0.161655i
$565$	506395.	+	119562.i	1.58633	+	0.374540i
$566$			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	0.376509	−	0.926413i	$-0.377124\pi$
$569$	442601.	−	255536.i	1.36706	−	0.789273i	0.990552	+	0.137140i	$0.0437910\pi$
$570$	−172311.	+	458059.i	−0.530350	+	1.40985i
$571$	−9362.89	+	16217.0i	−0.0287169	+	0.0497391i	−0.880027	−	0.474924i	$-0.842475\pi$
$571$	−9362.89	+	16217.0i	−0.0287169	+	0.0497391i	0.851310	+	0.524663i	$0.175809\pi$
$572$	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
$580$	202562.	−	60831.1i	0.602146	−	0.180830i
$581$	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
$585$	240110.	+	383446.i	0.701613	+	1.12045i
$586$	−116456.			−0.339131
$587$	279639.	+	484350.i	0.811563	+	1.40567i	0.911770	+	0.410701i	$0.134716\pi$
$587$	279639.	+	484350.i	0.811563	+	1.40567i	−0.100207	+	0.994967i	$0.531951\pi$
$588$	13900.5	+	10601.1i	0.0402045	+	0.0306616i
$589$	57335.9	−	99308.7i	0.165271	−	0.286257i
$590$	−162024.	+	48657.2i	−0.465452	+	0.139779i
$591$	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	$-0.308123\pi$
$593$	398735.			1.13390			0.566950	+	0.823752i	$0.308123\pi$
$594$	−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	0.189252	−	0.981929i	$-0.439394\pi$
$599$	−203260.	−	117352.i	−0.566497	−	0.327067i	−0.755749	+	0.654861i	$0.772727\pi$
$600$	18580.4	−	27651.0i	0.0516124	−	0.0768084i
$601$	115910.	+	200763.i	0.320903	+	0.555820i	0.980675	−	0.195646i	$-0.0626805\pi$
$601$	115910.	+	200763.i	0.320903	+	0.555820i	−0.659772	+	0.751466i	$0.729347\pi$
$602$	−224398.			−0.619193
$603$	−302734.	+	83039.2i	−0.832580	+	0.228375i
$604$	17619.5			0.0482970
$605$	−182186.	−	43014.9i	−0.497741	−	0.117519i
$606$	934422.	+	120209.i	2.54447	+	0.327335i
$607$	−459653.	−	265381.i	−1.24753	−	0.720264i	−0.276917	−	0.960894i	$-0.589313\pi$
$607$	−459653.	−	265381.i	−1.24753	−	0.720264i	−0.970617	+	0.240630i	$0.922646\pi$
$608$	277257.	−	480224.i	0.750025	−	1.29908i
$609$	27279.8	−	212054.i	0.0735541	−	0.571758i
$610$	966689.	+	228240.i	2.59793	+	0.613383i
$611$		−	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
$615$	−17429.5	−	105456.i	−0.0460823	−	0.278817i
$616$	−11977.1	+	20744.9i	−0.0315638	+	0.0546701i
$617$	−70869.2	+	122749.i	−0.186160	+	0.322439i	−0.943967	−	0.330040i	$-0.892938\pi$
$617$	−70869.2	+	122749.i	−0.186160	+	0.322439i	0.757807	+	0.652479i	$0.226271\pi$
$618$	−257940.	−	617551.i	−0.675370	−	1.61695i
$619$	276156.	+	478316.i	0.720731	+	1.24834i	0.960707	+	0.277563i	$0.0895268\pi$
$619$	276156.	+	478316.i	0.720731	+	1.24834i	−0.239977	+	0.970779i	$0.577140\pi$
$620$	−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
$625$	153496.	−	359203.i	0.392949	−	0.919560i
$626$	−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
$630$	−295378.	−	471708.i	−0.744213	−	1.18848i
$631$	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
$635$	−82435.4	+	24756.1i	−0.204440	+	0.0613952i
$636$	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	−0.892952	−	0.450151i	$-0.851370\pi$
$641$	−390167.	+	225263.i	−0.949587	+	0.548244i	−0.0566340	+	0.998395i	$0.518037\pi$
$642$	56443.6	+	43046.1i	0.136945	+	0.104439i
$643$	265023.	+	153011.i	0.641006	+	0.370085i	0.785002	−	0.619493i	$-0.212662\pi$
$643$	265023.	+	153011.i	0.641006	+	0.370085i	−0.143996	+	0.989578i	$0.545995\pi$
$644$	−461033.	−	266177.i	−1.11163	−	0.641799i
$645$	−171940.	−	64679.7i	−0.413292	−	0.155471i
$646$	−473081.	−	819400.i	−1.13363	−	1.96350i
$647$	−200004.			−0.477782			−0.238891	−	0.971046i	$-0.576784\pi$
$647$	−200004.			−0.477782			−0.238891	+	0.971046i	$0.576784\pi$
$648$	−459.572	−	38854.5i	−0.00109447	−	0.0925320i
$649$	99582.2			0.236424
$650$	442132.	+	669741.i	1.04647	+	1.58518i
$651$	50261.3	+	120334.i	0.118596	+	0.283939i
$652$	−528859.	−	305337.i	−1.24407	−	0.718263i
$653$	−257809.	+	446538.i	−0.604604	+	1.04721i	0.387509	+	0.921866i	$0.373335\pi$
$653$	−257809.	+	446538.i	−0.604604	+	1.04721i	−0.992114	+	0.125340i	$0.959998\pi$
$654$	342399.	+	261127.i	0.800529	+	0.610516i
$655$	31667.5	−	134125.i	0.0738128	−	0.312627i
$656$			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	−0.110913	−	0.993830i	$-0.535378\pi$
$659$	301526.	−	174086.i	0.694312	−	0.400861i	0.805225	+	0.592969i	$0.202044\pi$
$660$	−250486.	+	205641.i	−0.575037	+	0.472087i
$661$	12324.1	−	21346.0i	0.0282068	−	0.0488556i	−0.851577	−	0.524229i	$-0.824354\pi$
$661$	12324.1	−	21346.0i	0.0282068	−	0.0488556i	0.879784	+	0.475373i	$0.157687\pi$
$662$	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
$670$	−533305.	+	160156.i	−1.18803	+	0.356775i
$671$	−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	$-0.552495\pi$
$673$	275390.	−	158997.i	0.608020	−	0.351041i	0.772190	+	0.635391i	$0.219161\pi$
$674$		−	52919.1i		−	0.116491i
$675$	−90363.2	−	446574.i	−0.198328	−	0.980136i
$676$	−363673.			−0.795825
$677$	−65955.5	−	114238.i	−0.143904	−	0.249250i	0.785059	−	0.619421i	$-0.212632\pi$
$677$	−65955.5	−	114238.i	−0.143904	−	0.249250i	−0.928964	+	0.370171i	$0.879299\pi$
$678$	993369.	−	414912.i	2.16098	−	0.902603i
$679$	−322532.	+	558641.i	−0.699573	+	1.21170i
$680$	18524.5	+	61684.9i	0.0400617	+	0.133402i
$681$	216361.	+	165005.i	0.466535	+	0.355798i
$682$	127548.	−	73640.0i	0.274224	−	0.158323i
$683$	−539667.			−1.15687			−0.578435	−	0.815729i	$-0.696336\pi$
$683$	−539667.			−1.15687			−0.578435	+	0.815729i	$0.696336\pi$
$684$	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
$690$	−536335.	−	653296.i	−1.12652	−	1.37218i
$691$	194856.	+	337500.i	0.408091	+	0.706834i	0.994676	−	0.103054i	$-0.0328614\pi$
$691$	194856.	+	337500.i	0.408091	+	0.706834i	−0.586585	+	0.809888i	$0.699528\pi$
$692$	−599341.			−1.25159
$693$	86662.8	+	315944.i	0.180454	+	0.657876i
$694$	129632.			0.269150
$695$	−82094.1	−	19382.8i	−0.169958	−	0.0401280i
$696$	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
$700$	−280435.	−	424803.i	−0.572317	−	0.866945i
$701$			831525.i			1.69215i	0.533063	+	0.846076i	$0.321041\pi$
$701$			831525.i			1.69215i	−0.533063	+	0.846076i	$0.678959\pi$
$702$	867946.	+	350528.i	1.76124	+	0.711292i
$703$		−	21077.0i		−	0.0426480i
$704$	337334.	−	194760.i	0.680636	−	0.392965i
$705$	−68958.1	+	183313.i	−0.138742	+	0.368821i
$706$	−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	0.844574	−	0.535439i	$-0.179854\pi$
$709$	−20819.3	−	36060.0i	−0.0414164	−	0.0717354i	−0.885991	+	0.463703i	$0.846520\pi$
$710$	−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
$715$	−135870.	−	452435.i	−0.265774	−	0.885003i
$716$	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	$0.282085\pi$
$719$			800950.i			1.54934i	−0.632364	+	0.774671i	$0.717915\pi$
$720$	17309.0	+	482551.i	0.0333893	+	0.930848i
$721$	−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
$725$	138866.	−	277684.i	0.264192	−	0.528293i
$726$	−357384.	+	149273.i	−0.678051	+	0.283210i
$727$	−722549.	+	417164.i	−1.36709	+	0.789292i	−0.990556	−	0.137109i	$-0.956219\pi$
$727$	−722549.	+	417164.i	−1.36709	+	0.789292i	−0.376538	+	0.926401i	$0.622886\pi$
$728$	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	$-0.459644\pi$
$733$	−359667.	−	207654.i	−0.669411	−	0.386485i	−0.795854	+	0.605489i	$0.792978\pi$
$734$	967609.	+	558649.i	1.79601	+	1.03692i
$735$	25318.7	−	4184.62i	0.0468669	−	0.00774607i
$736$	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	$0.789513\pi$
$740$	−5448.55	+	23076.8i	−0.00994987	+	0.0421417i
$741$	−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	$-0.922188\pi$
$743$	−152108.	+	263459.i	−0.275534	+	0.477239i	0.694736	+	0.719265i	$0.255521\pi$
$744$	−2060.68	+	16018.3i	−0.00372276	+	0.0289381i
$745$	192653.	−	815963.i	0.347106	−	1.47014i
$746$		−	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
$750$	−179274.	−	788068.i	−0.318709	−	1.40101i
$751$	477638.	−	827293.i	0.846874	−	1.46683i	−0.0371095	−	0.999311i	$-0.511815\pi$
$751$	477638.	−	827293.i	0.846874	−	1.46683i	0.883984	−	0.467518i	$-0.154852\pi$
$752$	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
$760$	16116.9	+	53667.7i	0.0279032	+	0.0929149i
$761$	−309676.	−	178791.i	−0.534734	−	0.308729i	0.208208	−	0.978085i	$-0.433237\pi$
$761$	−309676.	−	178791.i	−0.534734	−	0.308729i	−0.742942	+	0.669356i	$0.766570\pi$
$762$	−107992.	+	141603.i	−0.185987	+	0.243873i
$763$	344780.	−	199059.i	0.592234	−	0.341926i
$764$			407422.i			0.698003i
$765$	778154.	+	412806.i	1.32967	+	0.705380i
$766$	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	−0.764443	−	0.644692i	$-0.776986\pi$
$769$	104137.	−	180371.i	0.176098	−	0.305010i	0.940541	+	0.339681i	$0.110319\pi$
$770$	167145.	+	556577.i	0.281911	+	0.938737i
$771$	−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	$-0.411361\pi$
$773$	328500.			0.549764			0.274882	+	0.961478i	$0.411361\pi$
$774$	−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
$780$	801284.	+	301424.i	1.31704	+	0.495437i
$781$	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
$785$	−26114.5	+	110605.i	−0.0423781	+	0.179489i
$786$	−109895.	−	263106.i	−0.177882	−	0.425878i
$787$	184283.	+	106396.i	0.297533	+	0.171781i	0.641334	−	0.767262i	$-0.278381\pi$
$787$	184283.	+	106396.i	0.297533	+	0.171781i	−0.343801	+	0.939042i	$0.611715\pi$
$788$	79313.6	−	137375.i	0.127731	−	0.221236i
$789$	−335741.	−	256049.i	−0.539324	−	0.411310i
$790$	−684276.	−	161561.i	−1.09642	−	0.258870i
$791$		−	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
$795$	−333975.	−	406807.i	−0.528421	−	0.643657i
$796$	52707.9	−	91292.7i	0.0831858	−	0.144082i
$797$	75817.1	−	131319.i	0.119358	−	0.206734i	−0.800156	−	0.599792i	$-0.795250\pi$
$797$	75817.1	−	131319.i	0.119358	−	0.206734i	0.919513	+	0.393059i	$0.128583\pi$
$798$	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
$805$	−748452.	+	224767.i	−1.15497	+	0.346849i
$806$	−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	$0.0161768\pi$
$809$			66493.9i			0.101598i	−0.998709	+	0.0507989i	$0.983823\pi$
$810$	−693833.	−	638165.i	−1.05751	−	0.972665i
$811$	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
$815$	−858562.	+	257834.i	−1.29258	+	0.388172i
$816$	−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	−0.159325	−	0.987226i	$-0.550932\pi$
$821$	415193.	−	239712.i	0.615975	−	0.355634i	0.775300	+	0.631593i	$0.217598\pi$
$822$	−28604.5	+	222352.i	−0.0423342	+	0.329076i
$823$	−125938.	−	72710.6i	−0.185934	−	0.107349i	0.404144	−	0.914695i	$-0.367570\pi$
$823$	−125938.	−	72710.6i	−0.185934	−	0.107349i	−0.590078	+	0.807346i	$0.700903\pi$
$824$	−66362.8	−	38314.6i	−0.0977395	−	0.0564299i
$825$	−32354.8	+	474642.i	−0.0475368	+	0.697362i
$826$	161803.	+	280251.i	0.237152	+	0.410759i
$827$	−893602.			−1.30657			−0.653286	−	0.757111i	$-0.726610\pi$
$827$	−893602.			−1.30657			−0.653286	+	0.757111i	$0.726610\pi$
$828$	−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	$0.659359\pi$
$830$	910990.	+	215089.i	1.32238	+	0.312221i
$831$	−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
$835$	540577.	+	127633.i	0.775327	+	0.183058i
$836$		−	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	−0.944566	−	0.328322i	$-0.893517\pi$
$839$	−797201.	+	460264.i	−1.13251	+	0.653857i	−0.187948	+	0.982179i	$0.560184\pi$
$840$	−59644.8	−	22437.0i	−0.0845307	−	0.0317984i
$841$	−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
$850$	1.39751e6	+	698876.i	1.93427	+	0.967303i
$851$	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	$-0.500685\pi$
$853$	627776.	−	362447.i	0.862793	−	0.498134i	0.864947	+	0.501864i	$0.167352\pi$
$854$		−	1.90000e6i		−	2.60518i
$855$	677017.	+	359153.i	0.926120	+	0.491301i
$856$	8127.70			0.0110923
$857$	−492013.	−	852192.i	−0.669908	−	1.16032i	−0.977929	−	0.208936i	$-0.933000\pi$
$857$	−492013.	−	852192.i	−0.669908	−	1.16032i	0.308021	−	0.951380i	$-0.400333\pi$
$858$	−777170.	−	592700.i	−1.05570	−	0.805120i
$859$	−365776.	+	633542.i	−0.495711	+	0.858597i	−0.999988	−	0.00494530i	$-0.998426\pi$
$859$	−365776.	+	633542.i	−0.495711	+	0.858597i	0.504277	+	0.863542i	$0.331759\pi$
$860$	−332928.	+	99981.3i	−0.450147	+	0.135183i
$861$	−188665.	+	78801.9i	−0.254498	+	0.106299i
$862$	−478408.	+	276209.i	−0.643849	+	0.371727i
$863$	498062.			0.668747			0.334374	−	0.942441i	$-0.391475\pi$
$863$	498062.			0.668747			0.334374	+	0.942441i	$0.391475\pi$
$864$	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
$870$	−104748.	−	633766.i	−0.138390	−	0.837318i
$871$	−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
$875$	−736196.	−	127872.i	−0.961563	−	0.167017i
$876$	−979600.	−	126021.i	−1.27656	−	0.164223i
$877$	1.18504e6	+	684183.i	1.54076	+	0.889556i	0.998791	+	0.0491545i	$0.0156527\pi$
$877$	1.18504e6	+	684183.i	1.54076	+	0.889556i	0.541965	+	0.840401i	$0.317681\pi$
$878$	299805.	−	519278.i	0.388911	−	0.673614i
$879$	−23269.0	+	180877.i	−0.0301162	+	0.234102i
$880$	115855.	−	490691.i	0.149606	−	0.633641i
$881$		−	1.19744e6i		−	1.54277i	−0.636368	−	0.771386i	$-0.719564\pi$
$881$		−	1.19744e6i		−	1.54277i	0.636368	−	0.771386i	$-0.280436\pi$
$882$	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
$885$	43199.3	+	261374.i	0.0551557	+	0.333715i
$886$	−88297.6	+	152936.i	−0.112482	+	0.194824i
$887$	−427242.	+	740004.i	−0.543033	+	0.940561i	0.455695	+	0.890136i	$0.349391\pi$
$887$	−427242.	+	740004.i	−0.543033	+	0.940561i	−0.998728	+	0.0504250i	$0.983942\pi$
$888$	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
$895$	1.05806e6	−	317743.i	1.32088	−	0.396671i
$896$	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
$900$	−648409.	−	568243.i	−0.800505	−	0.701535i
$901$	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
$905$	−297163.	−	989526.i	−0.362826	−	1.20818i
$906$	6828.05	−	53076.5i	0.00831841	−	0.0646615i
$907$	−403158.	+	232764.i	−0.490073	+	0.282944i	−0.724605	−	0.689164i	$-0.757978\pi$
$907$	−403158.	+	232764.i	−0.490073	+	0.282944i	0.234531	+	0.972109i	$0.424644\pi$
$908$	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	−0.0957646	−	0.995404i	$-0.530530\pi$
$911$	596214.	−	344224.i	0.718398	−	0.414767i	0.814163	+	0.580637i	$0.197196\pi$
$912$	−645818.	−	492526.i	−0.776462	−	0.592161i
$913$	−477174.	−	275497.i	−0.572447	−	0.330502i
$914$	−585954.	−	338301.i	−0.701409	−	0.404959i
$915$	547650.	−	1.45583e6i	0.654125	−	1.73888i
$916$	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	$0.634441\pi$
$920$	−94190.8	−	22238.9i	−0.111284	−	0.0262747i
$921$	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
$925$	19176.4	+	29048.3i	0.0224121	+	0.0339498i
$926$		−	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	−0.229436	−	0.973324i	$-0.573688\pi$
$929$	430458.	−	248525.i	0.498768	−	0.287964i	0.728205	+	0.685360i	$0.240355\pi$
$930$	248614.	+	302831.i	0.287449	+	0.350134i
$931$	−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
$940$	106595.	+	354951.i	0.120637	+	0.401710i
$941$	−222911.	−	128697.i	−0.251740	−	0.145342i	0.368821	−	0.929500i	$-0.379762\pi$
$941$	−222911.	−	128697.i	−0.251740	−	0.145342i	−0.620561	+	0.784159i	$0.713095\pi$
$942$	90624.0	+	216969.i	0.102127	+	0.244509i
$943$	−268915.	+	155258.i	−0.302407	+	0.174595i
$944$		−	280756.i		−	0.315054i
$945$	−791665.	+	364523.i	−0.886498	+	0.408189i
$946$	396864.			0.443465
$947$	−231511.	−	400990.i	−0.258150	−	0.447129i	0.707596	−	0.706617i	$-0.249780\pi$
$947$	−231511.	−	400990.i	−0.258150	−	0.447129i	−0.965746	+	0.259488i	$0.916446\pi$
$948$	−692093.	+	289075.i	−0.770101	+	0.321657i
$949$	719830.	−	1.24678e6i	0.799277	−	1.38439i
$950$	1.21587e6	+	608042.i	1.34723	+	0.673731i
$951$	306571.	+	233803.i	0.338977	+	0.258517i
$952$	106696.	−	61600.9i	0.117726	−	0.0679694i
$953$	−323955.			−0.356696			−0.178348	−	0.983967i	$-0.557075\pi$
$953$	−323955.			−0.356696			−0.178348	+	0.983967i	$0.557075\pi$
$954$	−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
$960$	657524.	+	800914.i	0.713459	+	0.869047i
$961$	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
$965$	−13496.1	+	57161.5i	−0.0144928	+	0.0613831i
$966$	−980488.	+	1.28565e6i	−1.05072	+	1.37774i
$967$	511790.	+	295482.i	0.547317	+	0.315994i	0.748039	−	0.663654i	$-0.230995\pi$
$967$	511790.	+	295482.i	0.547317	+	0.315994i	−0.200722	+	0.979648i	$0.564329\pi$
$968$	−22173.1	+	38404.9i	−0.0236633	+	0.0409861i
$969$	−1.36720e6	+	571054.i	−1.45608	+	0.608177i
$970$	−445346.	+	1.88622e6i	−0.473319	+	2.00470i
$971$			1.14727e6i			1.21682i	0.793622	+	0.608412i	$0.208193\pi$
$971$			1.14727e6i			1.21682i	−0.793622	+	0.608412i	$0.791807\pi$
$972$	−998862.	−	116507.i	−1.05724	−	0.123316i
$973$			161354.i			0.170433i
$974$	766505.	−	442542.i	0.807973	−	0.466484i
$975$	1.12857e6	−	552888.i	1.18718	−	0.581605i
$976$	−824207.	+	1.42757e6i	−0.865240	+	1.49864i
$977$	429287.	−	743546.i	0.449737	−	0.778967i	−0.548632	−	0.836064i	$-0.684851\pi$
$977$	429287.	−	743546.i	0.449737	−	0.778967i	0.998369	+	0.0570972i	$0.0181845\pi$
$978$	−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	−0.992735	−	0.120318i	$-0.961609\pi$
$983$	−580320.	−	1.00514e6i	−0.600566	−	1.04021i	0.392170	−	0.919893i	$-0.371725\pi$
$984$	−25114.2	−	3230.83i	−0.0259376	−	0.00333675i
$985$	−66974.3	−	223018.i	−0.0690297	−	0.229862i
$986$	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
$990$	522397.	+	834249.i	0.533004	+	0.851188i
$991$	−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
$995$	−44507.8	−	148207.i	−0.0449562	−	0.149700i
$996$	921397.	−	384851.i	0.928813	−	0.387948i
$997$	−1.12879e6	+	651705.i	−1.13559	+	0.655633i	−0.945334	−	0.326102i	$-0.894265\pi$
$997$	−1.12879e6	+	651705.i	−1.13559	+	0.655633i	−0.190254	+	0.981735i	$0.560931\pi$
$998$	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.14.4	✓	44
3.2	odd	2		135.5.h.a.44.19		44
5.4	even	2	inner	45.5.h.a.14.19	yes	44
9.2	odd	6	inner	45.5.h.a.29.19	yes	44
9.4	even	3		405.5.d.a.404.38		44
9.5	odd	6		405.5.d.a.404.8		44
9.7	even	3		135.5.h.a.89.4		44
15.14	odd	2		135.5.h.a.44.4		44
45.4	even	6		405.5.d.a.404.7		44
45.14	odd	6		405.5.d.a.404.37		44
45.29	odd	6	inner	45.5.h.a.29.4	yes	44
45.34	even	6		135.5.h.a.89.19		44

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

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} +(7.19048 + 23.9436i) 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} +(-142.769 - 173.903i) q^{15} +(119.225 + 206.504i) q^{16} +434.998 q^{17} +(-450.367 - 117.825i) q^{18} +378.461 q^{19} +(-414.369 - 97.8346i) 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} +(-521.594 + 344.332i) q^{25} -1284.03i q^{26} +(-272.991 + 675.956i) q^{27} +814.433i q^{28} +(-430.201 + 248.377i) q^{29} +(-455.294 + 1210.32i) 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} +(42.5853 + 141.805i) q^{40} +(411.405 + 237.525i) q^{41} +(2453.37 + 315.616i) q^{42} +(707.073 - 408.229i) q^{43} -1440.38i q^{44} +(1788.87 + 948.985i) q^{45} +3756.67 q^{46} +(-435.232 - 753.844i) q^{47} +(-1706.43 - 1301.39i) q^{48} +(-57.0270 + 98.7737i) q^{49} +(3212.68 + 1606.62i) 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} +(3780.57 - 624.846i) q^{60} +(3456.52 + 5986.86i) q^{61} -1741.38 q^{62} +(980.413 - 3747.46i) q^{63} -4605.53 q^{64} +(-1283.46 + 5435.97i) 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} +(1578.89 - 6687.22i) q^{70} -5822.30i q^{71} +(337.201 - 341.213i) q^{72} -6443.82i q^{73} +(-277.189 + 160.035i) q^{74} +(3137.29 - 4668.84i) 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} +(3127.84 + 10415.4i) q^{85} +(-4063.70 - 2346.18i) q^{86} +(2711.14 - 3554.94i) q^{87} +(-433.793 + 250.451i) q^{88} +13898.7i q^{89} +(-417.189 - 11630.6i) q^{90} +10684.3 q^{91} +(-5566.00 - 9640.59i) q^{92} +(-347.944 + 2704.67i) q^{93} +(-2501.37 + 4332.50i) q^{94} +(2721.31 + 9061.72i) 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more