LMFDB - Embedded newform 45.5.i.a.11.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [45,5,Mod(11,45)] 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("45.11"); 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([1, 0])) N = Newforms(chi, 5, names="a")

Level:	$ N $	$=$	$ 45 = 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	45.i (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:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.16
Character	$\chi$	$=$	45.11
Dual form			45.5.i.a.41.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(6.87716 + 3.97053i) q^{2} +(-1.96687 - 8.78245i) q^{3} +(23.5302 + 40.7555i) q^{4} +(9.68246 - 5.59017i) q^{5} +(21.3445 - 68.2078i) q^{6} +(10.1236 - 17.5346i) q^{7} +246.652i q^{8} +(-73.2629 + 34.5478i) q^{9} +88.7837 q^{10} +(-42.4341 - 24.4994i) q^{11} +(311.652 - 286.813i) q^{12} +(-87.2913 - 151.193i) q^{13} +(139.243 - 80.3920i) q^{14} +(-68.1395 - 74.0406i) q^{15} +(-602.856 + 1044.18i) q^{16} -237.493i q^{17} +(-641.013 - 53.3017i) q^{18} -177.596 q^{19} +(455.660 + 263.075i) q^{20} +(-173.908 - 54.4218i) q^{21} +(-194.551 - 336.972i) q^{22} +(57.7120 - 33.3200i) q^{23} +(2166.21 - 485.132i) q^{24} +(62.5000 - 108.253i) q^{25} -1386.37i q^{26} +(447.513 + 575.477i) q^{27} +952.840 q^{28} +(-110.189 - 63.6179i) q^{29} +(-174.626 - 779.739i) q^{30} +(326.291 + 565.152i) q^{31} +(-4874.16 + 2814.10i) q^{32} +(-131.702 + 420.863i) q^{33} +(942.972 - 1633.28i) q^{34} -226.370i q^{35} +(-3131.90 - 2172.95i) q^{36} +1552.24 q^{37} +(-1221.35 - 705.149i) q^{38} +(-1156.15 + 1064.01i) q^{39} +(1378.83 + 2388.20i) q^{40} +(501.340 - 289.449i) q^{41} +(-979.911 - 1064.77i) q^{42} +(-1117.07 + 1934.83i) q^{43} -2305.90i q^{44} +(-516.237 + 744.060i) q^{45} +529.192 q^{46} +(534.686 + 308.701i) q^{47} +(10356.2 + 3240.80i) q^{48} +(995.526 + 1724.30i) q^{49} +(859.645 - 496.316i) q^{50} +(-2085.77 + 467.117i) q^{51} +(4107.96 - 7115.20i) q^{52} -2087.62i q^{53} +(792.668 + 5734.50i) q^{54} -547.822 q^{55} +(4324.94 + 2497.00i) q^{56} +(349.307 + 1559.73i) q^{57} +(-505.193 - 875.021i) q^{58} +(-1542.38 + 890.492i) q^{59} +(1414.23 - 4519.25i) q^{60} +(-536.896 + 929.932i) q^{61} +5182.19i q^{62} +(-135.902 + 1634.38i) q^{63} -25402.4 q^{64} +(-1690.39 - 975.946i) q^{65} +(-2576.78 + 2371.41i) q^{66} +(3956.55 + 6852.95i) q^{67} +(9679.13 - 5588.25i) q^{68} +(-406.143 - 441.317i) q^{69} +(898.810 - 1556.78i) q^{70} -7444.34i q^{71} +(-8521.29 - 18070.4i) q^{72} +4925.00 q^{73} +(10675.0 + 6163.23i) q^{74} +(-1073.66 - 335.984i) q^{75} +(-4178.86 - 7238.00i) q^{76} +(-859.172 + 496.043i) q^{77} +(-12175.7 + 2726.80i) q^{78} +(-430.602 + 745.825i) q^{79} +13480.3i q^{80} +(4173.90 - 5062.14i) q^{81} +4597.06 q^{82} +(1269.78 + 733.110i) q^{83} +(-1874.11 - 8368.27i) q^{84} +(-1327.63 - 2299.51i) q^{85} +(-15364.6 + 8870.76i) q^{86} +(-341.993 + 1092.86i) q^{87} +(6042.82 - 10466.5i) q^{88} -13657.3i q^{89} +(-6504.55 + 3067.28i) q^{90} -3534.80 q^{91} +(2715.95 + 1568.05i) q^{92} +(4321.65 - 3977.21i) q^{93} +(2451.41 + 4245.97i) q^{94} +(-1719.56 + 992.791i) q^{95} +(34301.5 + 37272.1i) q^{96} +(-5265.88 + 9120.77i) q^{97} +15811.1i q^{98} +(3955.25 + 328.888i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 8 q^{3} + 128 q^{4} + 98 q^{6} - 26 q^{7} - 220 q^{9} - 738 q^{11} - 214 q^{12} + 10 q^{13} + 1998 q^{14} - 50 q^{15} - 1024 q^{16} - 2504 q^{18} + 508 q^{19} - 1620 q^{21} + 672 q^{22} + 1998 q^{23}+ \cdots + 53512 q^{99}+O(q^{100}) $ 32 * q - 8 * q^3 + 128 * q^4 + 98 * q^6 - 26 * q^7 - 220 * q^9 - 738 * q^11 - 214 * q^12 + 10 * q^13 + 1998 * q^14 - 50 * q^15 - 1024 * q^16 - 2504 * q^18 + 508 * q^19 - 1620 * q^21 + 672 * q^22 + 1998 * q^23 + 4164 * q^24 + 2000 * q^25 + 2158 * q^27 - 1664 * q^28 - 270 * q^29 + 2000 * q^30 - 1472 * q^31 - 6048 * q^32 - 1354 * q^33 - 594 * q^34 + 4498 * q^36 + 2068 * q^37 - 7164 * q^38 - 4616 * q^39 + 1650 * q^40 - 13428 * q^41 - 10230 * q^42 + 568 * q^43 - 100 * q^45 + 5724 * q^46 + 12528 * q^47 + 25844 * q^48 - 1674 * q^49 + 1454 * q^51 + 1534 * q^52 + 8456 * q^54 + 21294 * q^56 - 12512 * q^57 - 8190 * q^58 - 4374 * q^59 - 5050 * q^60 - 4478 * q^61 + 5604 * q^63 - 37216 * q^64 - 8550 * q^65 - 19472 * q^66 + 12838 * q^67 + 65736 * q^68 + 8706 * q^69 + 2400 * q^70 - 36372 * q^72 + 29236 * q^73 - 20628 * q^74 + 1000 * q^75 + 6190 * q^76 - 31806 * q^77 - 42430 * q^78 - 3512 * q^79 - 3088 * q^81 + 34692 * q^82 - 43074 * q^83 - 19350 * q^84 - 4350 * q^85 - 10746 * q^86 + 69622 * q^87 - 16128 * q^88 - 26750 * q^90 - 48904 * q^91 + 27036 * q^92 + 27030 * q^93 + 5118 * q^94 + 6300 * q^95 + 53566 * q^96 + 23266 * q^97 + 53512 * 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 $

$2$	6.87716	+	3.97053i	1.71929	+	0.992632i	0.920229	+	0.391381i	$0.128003\pi$
$2$	6.87716	+	3.97053i	1.71929	+	0.992632i	0.799060	+	0.601251i	$0.205331\pi$
$3$	−1.96687	−	8.78245i	−0.218541	−	0.975828i
$3$	−1.96687	−	8.78245i	−0.218541	−	0.975828i
$4$	23.5302	+	40.7555i	1.47064	+	2.54722i
$5$	9.68246	−	5.59017i	0.387298	−	0.223607i
$5$	9.68246	−	5.59017i	0.387298	−	0.223607i
$6$	21.3445	−	68.2078i	0.592903	−	1.89466i
$7$	10.1236	−	17.5346i	0.206604	−	0.357848i	−0.744039	−	0.668137i	$-0.767092\pi$
$7$	10.1236	−	17.5346i	0.206604	−	0.357848i	0.950643	+	0.310288i	$0.100426\pi$
$8$			246.652i			3.85394i
$9$	−73.2629	+	34.5478i	−0.904480	+	0.426516i
$10$	88.7837			0.887837
$11$	−42.4341	−	24.4994i	−0.350695	−	0.202474i	0.314296	−	0.949325i	$-0.398232\pi$
$11$	−42.4341	−	24.4994i	−0.350695	−	0.202474i	−0.664992	+	0.746851i	$0.731565\pi$
$12$	311.652	−	286.813i	2.16425	−	1.99176i
$13$	−87.2913	−	151.193i	−0.516517	−	0.894633i	−0.999816	−	0.0191778i	$-0.993895\pi$
$13$	−87.2913	−	151.193i	−0.516517	−	0.894633i	0.483300	−	0.875455i	$-0.339438\pi$
$14$	139.243	−	80.3920i	0.710423	−	0.410163i
$15$	−68.1395	−	74.0406i	−0.302842	−	0.329069i
$16$	−602.856	+	1044.18i	−2.35491	+	4.07882i
$17$		−	237.493i		−	0.821775i	−0.911686	−	0.410887i	$-0.865219\pi$
$17$		−	237.493i		−	0.821775i	0.911686	−	0.410887i	$-0.134781\pi$
$18$	−641.013	−	53.3017i	−1.97844	−	0.164511i
$19$	−177.596			−0.491955			−0.245978	−	0.969276i	$-0.579109\pi$
$19$	−177.596			−0.491955			−0.245978	+	0.969276i	$0.579109\pi$
$20$	455.660	+	263.075i	1.13915	+	0.657689i
$21$	−173.908	−	54.4218i	−0.394350	−	0.123405i
$22$	−194.551	−	336.972i	−0.401965	−	0.696223i
$23$	57.7120	−	33.3200i	0.109096	−	0.0629868i	−0.444459	−	0.895799i	$-0.646604\pi$
$23$	57.7120	−	33.3200i	0.109096	−	0.0629868i	0.553555	+	0.832812i	$0.313271\pi$
$24$	2166.21	−	485.132i	3.76078	−	0.842242i
$25$	62.5000	−	108.253i	0.100000	−	0.173205i
$26$		−	1386.37i		−	2.05084i
$27$	447.513	+	575.477i	0.613872	+	0.789406i
$28$	952.840			1.21536
$29$	−110.189	−	63.6179i	−0.131022	−	0.0756455i	0.433056	−	0.901367i	$-0.357435\pi$
$29$	−110.189	−	63.6179i	−0.131022	−	0.0756455i	−0.564078	+	0.825721i	$0.690768\pi$
$30$	−174.626	−	779.739i	−0.194028	−	0.866376i
$31$	326.291	+	565.152i	0.339533	+	0.588088i	0.984345	−	0.176253i	$-0.0563978\pi$
$31$	326.291	+	565.152i	0.339533	+	0.588088i	−0.644812	+	0.764341i	$0.723064\pi$
$32$	−4874.16	+	2814.10i	−4.75992	+	2.74814i
$33$	−131.702	+	420.863i	−0.120939	+	0.386467i
$34$	942.972	−	1633.28i	0.815720	−	1.41287i
$35$		−	226.370i		−	0.184792i
$36$	−3131.90	−	2172.95i	−2.41659	−	1.67666i
$37$	1552.24			1.13385			0.566926	−	0.823769i	$-0.308133\pi$
$37$	1552.24			1.13385			0.566926	+	0.823769i	$0.308133\pi$
$38$	−1221.35	−	705.149i	−0.845813	−	0.488331i
$39$	−1156.15	+	1064.01i	−0.760128	+	0.699545i
$40$	1378.83	+	2388.20i	0.861767	+	1.49262i
$41$	501.340	−	289.449i	0.298239	−	0.172189i	−0.343412	−	0.939185i	$-0.611583\pi$
$41$	501.340	−	289.449i	0.298239	−	0.172189i	0.641652	+	0.766996i	$0.278249\pi$
$42$	−979.911	−	1064.77i	−0.555505	−	0.603614i
$43$	−1117.07	+	1934.83i	−0.604151	+	1.04642i	0.388034	+	0.921645i	$0.373154\pi$
$43$	−1117.07	+	1934.83i	−0.604151	+	1.04642i	−0.992185	+	0.124775i	$0.960179\pi$
$44$		−	2305.90i		−	1.19106i
$45$	−516.237	+	744.060i	−0.254932	+	0.367437i
$46$	529.192			0.250091
$47$	534.686	+	308.701i	0.242049	+	0.139747i	0.616118	−	0.787654i	$-0.288704\pi$
$47$	534.686	+	308.701i	0.242049	+	0.139747i	−0.374069	+	0.927401i	$0.622038\pi$
$48$	10356.2	+	3240.80i	4.49487	+	1.40660i
$49$	995.526	+	1724.30i	0.414630	+	0.718160i
$50$	859.645	−	496.316i	0.343858	−	0.198526i
$51$	−2085.77	+	467.117i	−0.801911	+	0.179591i
$52$	4107.96	−	7115.20i	1.51922	−	2.63136i
$53$		−	2087.62i		−	0.743191i	−0.928395	−	0.371596i	$-0.878811\pi$
$53$		−	2087.62i		−	0.743191i	0.928395	−	0.371596i	$-0.121189\pi$
$54$	792.668	+	5734.50i	0.271834	+	1.96657i
$55$	−547.822			−0.181098
$56$	4324.94	+	2497.00i	1.37913	+	0.796239i
$57$	349.307	+	1559.73i	0.107512	+	0.480064i
$58$	−505.193	−	875.021i	−0.150176	−	0.260113i
$59$	−1542.38	+	890.492i	−0.443085	+	0.255815i	−0.704905	−	0.709302i	$-0.749010\pi$
$59$	−1542.38	+	890.492i	−0.443085	+	0.255815i	0.261821	+	0.965117i	$0.415677\pi$
$60$	1414.23	−	4519.25i	0.392840	−	1.25535i
$61$	−536.896	+	929.932i	−0.144288	+	0.249915i	−0.929107	−	0.369811i	$-0.879423\pi$
$61$	−536.896	+	929.932i	−0.144288	+	0.249915i	0.784819	+	0.619725i	$0.212756\pi$
$62$			5182.19i			1.34812i
$63$	−135.902	+	1634.38i	−0.0342410	+	0.411787i
$64$	−25402.4			−6.20176
$65$	−1690.39	−	975.946i	−0.400092	−	0.230993i
$66$	−2576.78	+	2371.41i	−0.591548	+	0.544401i
$67$	3956.55	+	6852.95i	0.881389	+	1.52661i	0.849798	+	0.527109i	$0.176724\pi$
$67$	3956.55	+	6852.95i	0.881389	+	1.52661i	0.0315908	+	0.999501i	$0.489943\pi$
$68$	9679.13	−	5588.25i	2.09324	−	1.20853i
$69$	−406.143	−	441.317i	−0.0853063	−	0.0926941i
$70$	898.810	−	1556.78i	0.183431	−	0.317711i
$71$		−	7444.34i		−	1.47676i	−0.674385	−	0.738380i	$-0.735591\pi$
$71$		−	7444.34i		−	1.47676i	0.674385	−	0.738380i	$-0.264409\pi$
$72$	−8521.29	−	18070.4i	−1.64377	−	3.48581i
$73$	4925.00			0.924188			0.462094	−	0.886831i	$-0.347098\pi$
$73$	4925.00			0.924188			0.462094	+	0.886831i	$0.347098\pi$
$74$	10675.0	+	6163.23i	1.94942	+	1.12550i
$75$	−1073.66	−	335.984i	−0.190872	−	0.0597304i
$76$	−4178.86	−	7238.00i	−0.723487	−	1.25312i
$77$	−859.172	+	496.043i	−0.144910	+	0.0836638i
$78$	−12175.7	+	2726.80i	−2.00127	+	0.448193i
$79$	−430.602	+	745.825i	−0.0689957	+	0.119504i	−0.898459	−	0.439056i	$-0.855313\pi$
$79$	−430.602	+	745.825i	−0.0689957	+	0.119504i	0.829464	+	0.558561i	$0.188646\pi$
$80$			13480.3i			2.10629i
$81$	4173.90	−	5062.14i	0.636168	−	0.771551i
$82$	4597.06			0.683679
$83$	1269.78	+	733.110i	0.184320	+	0.106417i	0.589321	−	0.807899i	$-0.299395\pi$
$83$	1269.78	+	733.110i	0.184320	+	0.106417i	−0.405001	+	0.914316i	$0.632729\pi$
$84$	−1874.11	−	8368.27i	−0.265605	−	1.18598i
$85$	−1327.63	−	2299.51i	−0.183754	−	0.318272i
$86$	−15364.6	+	8870.76i	−2.07742	+	1.19940i
$87$	−341.993	+	1092.86i	−0.0451834	+	0.144386i
$88$	6042.82	−	10466.5i	0.780323	−	1.35156i
$89$		−	13657.3i		−	1.72419i	−0.506747	−	0.862095i	$-0.669152\pi$
$89$		−	13657.3i		−	1.72419i	0.506747	−	0.862095i	$-0.330848\pi$
$90$	−6504.55	+	3067.28i	−0.803031	+	0.378677i
$91$	−3534.80			−0.426857
$92$	2715.95	+	1568.05i	0.320882	+	0.185261i
$93$	4321.65	−	3977.21i	0.499671	−	0.459846i
$94$	2451.41	+	4245.97i	0.277435	+	0.480531i
$95$	−1719.56	+	992.791i	−0.190533	+	0.110005i
$96$	34301.5	+	37272.1i	3.72195	+	4.04428i
$97$	−5265.88	+	9120.77i	−0.559664	+	0.969366i	0.437860	+	0.899043i	$0.355736\pi$
$97$	−5265.88	+	9120.77i	−0.559664	+	0.969366i	−0.997524	+	0.0703234i	$0.977597\pi$
$98$			15811.1i			1.64630i
$99$	3955.25	+	328.888i	0.403555	+	0.0335565i
$100$	5882.55			0.588255
$101$	−9687.66	−	5593.17i	−0.949677	−	0.548296i	−0.0566967	−	0.998391i	$-0.518057\pi$
$101$	−9687.66	−	5593.17i	−0.949677	−	0.548296i	−0.892981	+	0.450095i	$0.851390\pi$
$102$	−16198.9	−	5069.17i	−1.55698	−	0.487233i
$103$	−5603.91	−	9706.26i	−0.528223	−	0.914908i	−0.999459	−	0.0329012i	$-0.989525\pi$
$103$	−5603.91	−	9706.26i	−0.528223	−	0.914908i	0.471236	−	0.882007i	$-0.343808\pi$
$104$	37292.1	−	21530.6i	3.44786	−	1.99062i
$105$	−1988.09	+	445.240i	−0.180325	+	0.0403846i
$106$	8288.97	−	14356.9i	0.737716	−	1.27776i
$107$		−	3207.26i		−	0.280134i	−0.990142	−	0.140067i	$-0.955268\pi$
$107$		−	3207.26i		−	0.280134i	0.990142	−	0.140067i	$-0.0447319\pi$
$108$	−12923.8	+	31779.7i	−1.10801	+	2.72459i
$109$	8014.71			0.674582			0.337291	−	0.941400i	$-0.390489\pi$
$109$	8014.71			0.674582			0.337291	+	0.941400i	$0.390489\pi$
$110$	−3767.46	−	2175.14i	−0.311360	−	0.179764i
$111$	−3053.05	−	13632.5i	−0.247793	−	1.10644i
$112$	12206.1	+	21141.7i	0.973066	+	1.68540i
$113$	10948.2	−	6320.95i	0.857405	−	0.495023i	−0.00573716	−	0.999984i	$-0.501826\pi$
$113$	10948.2	−	6320.95i	0.857405	−	0.495023i	0.863143	+	0.504960i	$0.168493\pi$
$114$	−3790.70	+	12113.4i	−0.291682	+	0.932088i
$115$	372.529	−	645.240i	0.0281686	−	0.0487894i
$116$		−	5987.76i		−	0.444988i
$117$	11618.6	+	8061.11i	0.848754	+	0.588875i
$118$	−14142.9			−1.01572
$119$	−4164.33	−	2404.28i	−0.294071	−	0.169782i
$120$	18262.3	−	16806.8i	1.26821	−	1.16714i
$121$	−6120.06	−	10600.3i	−0.418008	−	0.724012i
$122$	−7384.64	+	4263.53i	−0.496146	+	0.286450i
$123$	−3528.14	−	3833.69i	−0.233204	−	0.253400i
$124$	−15355.4	+	26596.3i	−0.998658	+	1.72973i
$125$		−	1397.54i		−	0.0894427i
$126$	−7423.98	+	10700.3i	−0.467623	+	0.673991i
$127$	73.9286			0.00458358			0.00229179	−	0.999997i	$-0.499270\pi$
$127$	73.9286			0.00458358			0.00229179	+	0.999997i	$0.499270\pi$
$128$	−96709.9	−	55835.5i	−5.90270	−	3.40793i
$129$	19189.7	+	6005.10i	1.15316	+	0.360862i
$130$	−7750.04	−	13423.5i	−0.458583	−	0.794288i
$131$	−18665.8	+	10776.7i	−1.08769	+	0.627978i	−0.932960	−	0.359979i	$-0.882784\pi$
$131$	−18665.8	+	10776.7i	−1.08769	+	0.627978i	−0.154729	+	0.987957i	$0.549450\pi$
$132$	−20251.4	+	4535.39i	−1.16227	+	0.260296i
$133$	−1797.91	+	3114.07i	−0.101640	+	0.176045i
$134$			62838.4i			3.49958i
$135$	7550.03	+	3070.36i	0.414268	+	0.168470i
$136$	58578.1			3.16707
$137$	26003.0	+	15012.8i	1.38542	+	0.799873i	0.992795	−	0.119825i	$-0.0382332\pi$
$137$	26003.0	+	15012.8i	1.38542	+	0.799873i	0.392626	+	0.919698i	$0.371567\pi$
$138$	−1040.85	−	4647.61i	−0.0546550	−	0.244046i
$139$	−6618.42	−	11463.4i	−0.342551	−	0.593315i	0.642355	−	0.766407i	$-0.277957\pi$
$139$	−6618.42	−	11463.4i	−0.342551	−	0.593315i	−0.984906	+	0.173092i	$0.944624\pi$
$140$	9225.83	−	5326.54i	0.470706	−	0.271762i
$141$	1659.50	−	5303.03i	0.0834715	−	0.266739i
$142$	29558.0	−	51195.9i	1.46588	−	2.53898i
$143$			8554.32i			0.418325i
$144$	8092.94	−	97326.8i	0.390285	−	4.69362i
$145$	−1422.54			−0.0676594
$146$	33870.0	+	19554.8i	1.58895	+	0.917378i
$147$	13185.5	−	12134.6i	0.610187	−	0.561554i
$148$	36524.6	+	63262.4i	1.66748	+	2.88817i
$149$	−15879.6	+	9168.12i	−0.715267	+	0.412960i	−0.813008	−	0.582252i	$-0.802172\pi$
$149$	−15879.6	+	9168.12i	−0.715267	+	0.412960i	0.0977412	+	0.995212i	$0.468838\pi$
$150$	−6049.68	−	6573.60i	−0.268874	−	0.292160i
$151$	−12392.5	+	21464.5i	−0.543508	+	0.941383i	0.455191	+	0.890394i	$0.349571\pi$
$151$	−12392.5	+	21464.5i	−0.543508	+	0.941383i	−0.998699	+	0.0509895i	$0.983762\pi$
$152$		−	43804.4i		−	1.89597i
$153$	8204.86	+	17399.4i	0.350500	+	0.743279i
$154$	−7878.21			−0.332190
$155$	6318.59	+	3648.04i	0.263001	+	0.151844i
$156$	−70568.7	−	22083.3i	−2.89976	−	0.907434i
$157$	9349.99	+	16194.7i	0.379325	+	0.657011i	0.990964	−	0.134126i	$-0.0428227\pi$
$157$	9349.99	+	16194.7i	0.379325	+	0.657011i	−0.611639	+	0.791137i	$0.709489\pi$
$158$	−5922.64	+	3419.44i	−0.237247	+	0.136975i
$159$	−18334.5	+	4106.08i	−0.725227	+	0.162418i
$160$	−31462.6	+	54494.8i	−1.22901	+	2.12870i
$161$		−	1349.27i		−	0.0520533i
$162$	48803.9	−	18240.6i	1.85962	−	0.695038i
$163$	−47870.0			−1.80173			−0.900863	−	0.434104i	$-0.857065\pi$
$163$	−47870.0			−1.80173			−0.900863	+	0.434104i	$0.857065\pi$
$164$	23593.3	+	13621.6i	0.877203	+	0.506454i
$165$	1077.49	+	4811.22i	0.0395773	+	0.176721i
$166$	5821.66	+	10083.4i	0.211267	+	0.365925i
$167$	−32191.9	+	18586.0i	−1.15429	+	0.666428i	−0.949928	−	0.312468i	$-0.898844\pi$
$167$	−32191.9	+	18586.0i	−1.15429	+	0.666428i	−0.204358	+	0.978896i	$0.565511\pi$
$168$	13423.2	−	42894.8i	0.475597	−	1.51980i
$169$	−959.040	+	1661.11i	−0.0335786	+	0.0581599i
$170$		−	21085.5i		−	0.729602i
$171$	13011.2	−	6135.55i	0.444964	−	0.209827i
$172$	−105140.			−3.55395
$173$	33147.6	+	19137.8i	1.10754	+	0.639439i	0.938191	−	0.346117i	$-0.112500\pi$
$173$	33147.6	+	19137.8i	1.10754	+	0.639439i	0.169349	+	0.985556i	$0.445833\pi$
$174$	−6691.18	+	6157.88i	−0.221006	+	0.203392i
$175$	−1265.45	−	2191.82i	−0.0413208	−	0.0715697i
$176$	51163.4	−	29539.2i	1.65171	−	0.953615i
$177$	10854.4	+	11794.4i	0.346463	+	0.376468i
$178$	54226.7	−	93923.5i	1.71149	−	2.96438i
$179$		−	20456.1i		−	0.638435i	−0.947681	−	0.319218i	$-0.896580\pi$
$179$		−	20456.1i		−	0.638435i	0.947681	−	0.319218i	$-0.103420\pi$
$180$	−42471.6	−	3531.61i	−1.31085	−	0.109000i
$181$	−16351.6			−0.499117			−0.249559	−	0.968360i	$-0.580286\pi$
$181$	−16351.6			−0.499117			−0.249559	+	0.968360i	$0.580286\pi$
$182$	−24309.4	−	14035.0i	−0.733891	−	0.423712i
$183$	9223.09	+	2886.22i	0.275406	+	0.0861840i
$184$	8218.46	+	14234.8i	0.242747	+	0.420451i
$185$	15029.5	−	8677.30i	0.439139	−	0.253537i
$186$	45512.3	−	10192.7i	1.31554	−	0.294620i
$187$	−5818.42	+	10077.8i	−0.166388	+	0.288193i
$188$			29055.2i			0.822069i
$189$	14621.2	−	2021.05i	0.409316	−	0.0565788i
$190$	−15767.6			−0.436776
$191$	1211.96	+	699.727i	0.0332218	+	0.0191806i	0.516519	−	0.856276i	$-0.327228\pi$
$191$	1211.96	+	699.727i	0.0332218	+	0.0191806i	−0.483297	+	0.875456i	$0.660561\pi$
$192$	49963.2	+	223096.i	1.35534	+	6.05185i
$193$	−20329.3	−	35211.5i	−0.545769	−	0.945300i	−0.998558	−	0.0536819i	$-0.982904\pi$
$193$	−20329.3	−	35211.5i	−0.545769	−	0.945300i	0.452789	−	0.891618i	$-0.350429\pi$
$194$	−72428.5	+	41816.6i	−1.92445	+	1.11108i
$195$	−5246.43	+	16765.3i	−0.137973	+	0.440902i
$196$	−46849.8	+	81146.3i	−1.21954	+	2.11230i
$197$			4143.77i			0.106773i	0.998574	+	0.0533867i	$0.0170016\pi$
$197$			4143.77i			0.106773i	−0.998574	+	0.0533867i	$0.982998\pi$
$198$	25895.0	+	17966.2i	0.660519	+	0.458275i
$199$	21733.8			0.548819			0.274409	−	0.961613i	$-0.411518\pi$
$199$	21733.8			0.548819			0.274409	+	0.961613i	$0.411518\pi$
$200$	26700.9	+	15415.8i	0.667522	+	0.385394i
$201$	52403.7	−	48227.1i	1.29709	−	1.19371i
$202$	−44415.7	−	76930.2i	−1.08851	−	1.88536i
$203$	−2231.03	+	1288.08i	−0.0541393	+	0.0312573i
$204$	−68116.1	−	74015.2i	−1.63678	−	1.77853i
$205$	3236.14	−	5605.16i	0.0770051	−	0.133377i
$206$		−	89002.0i		−	2.09732i
$207$	−3077.01	+	4434.94i	−0.0718106	+	0.103502i
$208$	210496.			4.86539
$209$	7536.13	+	4350.99i	0.172526	+	0.0996082i
$210$	−15440.2	−	4831.77i	−0.350118	−	0.109564i
$211$	29775.4	+	51572.6i	0.668795	+	1.15839i	0.978241	+	0.207471i	$0.0665231\pi$
$211$	29775.4	+	51572.6i	0.668795	+	1.15839i	−0.309446	+	0.950917i	$0.600144\pi$
$212$	85082.1	−	49122.2i	1.89307	−	1.09296i
$213$	−65379.6	+	14642.0i	−1.44106	+	0.322732i
$214$	12734.5	−	22056.8i	0.278070	−	0.481632i
$215$			24978.6i			0.540369i
$216$	−141943.	+	110380.i	−3.04232	+	2.36583i
$217$	13212.9			0.280595
$218$	55118.4	+	31822.6i	1.15980	+	0.669612i
$219$	−9686.81	−	43253.5i	−0.201973	−	0.901848i
$220$	−12890.4	−	22326.8i	−0.266330	−	0.461297i
$221$	−35907.2	+	20731.1i	−0.735187	+	0.424460i
$222$	33131.9	−	105875.i	0.672265	−	2.14826i
$223$	13783.8	−	23874.2i	0.277178	−	0.480086i	−0.693505	−	0.720452i	$-0.743934\pi$
$223$	13783.8	−	23874.2i	0.277178	−	0.480086i	0.970682	+	0.240366i	$0.0772676\pi$
$224$			113955.i			2.27111i
$225$	−839.021	+	10090.2i	−0.0165732	+	0.199312i
$226$	100390.			1.96550
$227$	−64674.0	−	37339.5i	−1.25510	−	0.724632i	−0.282981	−	0.959125i	$-0.591323\pi$
$227$	−64674.0	−	37339.5i	−1.25510	−	0.724632i	−0.972118	+	0.234494i	$0.924657\pi$
$228$	−55348.1	+	50936.8i	−1.06472	+	0.979856i
$229$	−13802.9	−	23907.3i	−0.263208	−	0.455889i	0.703885	−	0.710314i	$-0.251447\pi$
$229$	−13802.9	−	23907.3i	−0.263208	−	0.455889i	−0.967093	+	0.254425i	$0.918114\pi$
$230$	5123.88	−	2958.28i	0.0968598	−	0.0559220i
$231$	6046.35	+	6569.98i	0.113310	+	0.123123i
$232$	15691.5	−	27178.5i	0.291533	−	0.504951i
$233$		−	72790.7i		−	1.34080i	−0.742000	−	0.670400i	$-0.766123\pi$
$233$		−	72790.7i		−	1.34080i	0.742000	−	0.670400i	$-0.233877\pi$
$234$	47896.0	+	101569.i	0.874718	+	1.85495i
$235$	6902.77			0.124994
$236$	−72584.8	−	41906.9i	−1.30323	−	0.752422i
$237$	7397.11	+	2314.80i	0.131694	+	0.0412114i
$238$	−19092.5	−	33069.2i	−0.337062	−	0.583808i
$239$	−20742.5	+	11975.7i	−0.363132	+	0.209654i	−0.670454	−	0.741951i	$-0.733901\pi$
$239$	−20742.5	+	11975.7i	−0.363132	+	0.209654i	0.307322	+	0.951606i	$0.400567\pi$
$240$	118390.	−	26513.9i	2.05538	−	0.460311i
$241$	−7281.19	+	12611.4i	−0.125363	+	0.217135i	−0.921875	−	0.387488i	$-0.873343\pi$
$241$	−7281.19	+	12611.4i	−0.125363	+	0.217135i	0.796512	+	0.604623i	$0.206676\pi$
$242$		−	97199.5i		−	1.65971i
$243$	−52667.5	−	26700.5i	−0.891929	−	0.452175i
$244$	−50533.1			−0.848782
$245$	19278.3	+	11130.3i	0.321171	+	0.185428i
$246$	−9041.80	−	40373.5i	−0.149412	−	0.667153i
$247$	15502.6	+	26851.2i	0.254103	+	0.440119i
$248$	−139396.	+	80480.3i	−2.26645	+	1.30854i
$249$	3941.01	−	12593.7i	0.0635636	−	0.203121i
$250$	5548.98	−	9611.12i	0.0887837	−	0.153778i
$251$			59554.3i			0.945292i	0.881252	+	0.472646i	$0.156701\pi$
$251$			59554.3i			0.945292i	−0.881252	+	0.472646i	$0.843299\pi$
$252$	−69807.8	+	32918.5i	−1.09927	+	0.518369i
$253$	−3265.28			−0.0510128
$254$	508.419	+	293.536i	0.00788051	+	0.00454981i
$255$	−17584.1	+	16182.6i	−0.270421	+	0.248868i
$256$	−240173.	−	415992.i	−3.66475	−	6.34754i
$257$	14251.4	−	8228.05i	0.215770	−	0.124575i	−0.388220	−	0.921567i	$-0.626910\pi$
$257$	14251.4	−	8228.05i	0.215770	−	0.124575i	0.603990	+	0.796992i	$0.293577\pi$
$258$	108127.	+	117491.i	1.62441	+	1.76509i
$259$	15714.3	−	27217.9i	0.234258	−	0.405747i
$260$		−	91856.8i		−	1.35883i
$261$	10270.7	+	854.028i	0.150771	+	0.0125369i
$262$	−171157.			−2.49340
$263$	70092.7	+	40468.0i	1.01335	+	0.585060i	0.912172	−	0.409808i	$-0.134404\pi$
$263$	70092.7	+	40468.0i	1.01335	+	0.585060i	0.101182	+	0.994868i	$0.467738\pi$
$264$	−103807.	−	32484.6i	−1.48942	−	0.466090i
$265$	−11670.2	−	20213.3i	−0.166183	−	0.287837i
$266$	−24729.0	+	14277.3i	−0.349497	+	0.201782i
$267$	−119945.	+	26862.1i	−1.68251	+	0.376806i
$268$	−186197.	+	322502.i	−2.59240	+	4.49018i
$269$		−	102974.i		−	1.42306i	−0.702657	−	0.711529i	$-0.748003\pi$
$269$		−	102974.i		−	1.42306i	0.702657	−	0.711529i	$-0.251997\pi$
$270$	39731.8	+	51093.0i	0.545018	+	0.700864i
$271$	132586.			1.80534			0.902669	−	0.430336i	$-0.141605\pi$
$271$	132586.			1.80534			0.902669	+	0.430336i	$0.141605\pi$
$272$	247985.	+	143174.i	3.35187	+	1.93520i
$273$	6952.49	+	31044.2i	0.0932856	+	0.416539i
$274$	119218.	+	206491.i	1.58796	+	2.75043i
$275$	−5304.27	+	3062.42i	−0.0701391	+	0.0404948i
$276$	8429.44	−	26936.8i	0.110657	−	0.353613i
$277$	−29094.5	+	50393.1i	−0.379185	+	0.656767i	−0.990944	−	0.134277i	$-0.957129\pi$
$277$	−29094.5	+	50393.1i	−0.379185	+	0.656767i	0.611759	+	0.791044i	$0.290462\pi$
$278$		−	105115.i		−	1.36011i
$279$	−43429.8	−	30132.0i	−0.557929	−	0.387097i
$280$	55834.7			0.712178
$281$	13479.1	+	7782.15i	0.170706	+	0.0985569i	0.582918	−	0.812531i	$-0.301911\pi$
$281$	13479.1	+	7782.15i	0.170706	+	0.0985569i	−0.412213	+	0.911088i	$0.635244\pi$
$282$	32468.5	−	29880.7i	0.408285	−	0.375744i
$283$	−33540.1	−	58093.2i	−0.418786	−	0.725358i	0.577032	−	0.816722i	$-0.304211\pi$
$283$	−33540.1	−	58093.2i	−0.418786	−	0.725358i	−0.995818	+	0.0913633i	$0.970878\pi$
$284$	303398.	−	175167.i	3.76163	−	2.17178i
$285$	12101.3	+	13149.3i	0.148985	+	0.161887i
$286$	−33965.2	+	58829.4i	−0.415243	+	0.719221i
$287$		−	11721.0i		−	0.142299i
$288$	259874.	−	374561.i	3.13313	−	4.51582i
$289$	27118.1			0.324687
$290$	−9783.03	−	5648.23i	−0.116326	−	0.0671609i
$291$	90460.0	+	28308.0i	1.06824	+	0.334290i
$292$	115886.	+	200721.i	1.35914	+	2.35411i
$293$	102469.	−	59160.7i	1.19360	−	0.689126i	0.234479	−	0.972121i	$-0.424661\pi$
$293$	102469.	−	59160.7i	1.19360	−	0.689126i	0.959121	+	0.282995i	$0.0913281\pi$
$294$	138860.	−	31098.2i	1.60650	−	0.359783i
$295$	−9956.00	+	17244.3i	−0.114404	+	0.198153i
$296$			382864.i			4.36980i
$297$	−4891.00	−	35383.6i	−0.0554479	−	0.401134i
$298$	−145609.			−1.63967
$299$	−10075.5	−	5817.10i	−0.112700	−	0.0650675i
$300$	−11570.2	−	51663.2i	−0.128558	−	0.574035i
$301$	22617.6	+	39174.9i	0.249640	+	0.432389i
$302$	−170451.	+	98409.7i	−1.86889	+	1.07901i
$303$	−30067.4	+	96082.4i	−0.327500	+	1.04655i
$304$	107065.	−	185442.i	1.15851	−	2.00660i
$305$			12005.4i			0.129055i
$306$	−12658.8	+	152236.i	−0.135191	+	1.62583i
$307$	119696.			1.26999			0.634997	−	0.772515i	$-0.281001\pi$
$307$	119696.			1.26999			0.634997	+	0.772515i	$0.281001\pi$
$308$	−40432.9	−	23344.0i	−0.426220	−	0.246078i
$309$	−74222.6	+	68307.0i	−0.777355	+	0.715399i
$310$	28969.3	+	50176.3i	0.301450	+	0.522126i
$311$	−42422.5	+	24492.7i	−0.438607	+	0.253230i	−0.703007	−	0.711183i	$-0.748160\pi$
$311$	−42422.5	+	24492.7i	−0.438607	+	0.253230i	0.264399	+	0.964413i	$0.414826\pi$
$312$	−262440.	−	285168.i	−2.69600	−	2.92949i
$313$	60212.0	−	104290.i	0.614603	−	1.06452i	−0.375851	−	0.926680i	$-0.622650\pi$
$313$	60212.0	−	104290.i	0.614603	−	1.06452i	0.990454	−	0.137843i	$-0.0440171\pi$
$314$			148498.i			1.50612i
$315$	7820.60	+	16584.5i	0.0788168	+	0.167141i
$316$	−40528.6			−0.405870
$317$	−62915.8	−	36324.4i	−0.626096	−	0.361477i	0.153142	−	0.988204i	$-0.451061\pi$
$317$	−62915.8	−	36324.4i	−0.626096	−	0.361477i	−0.779239	+	0.626727i	$0.784394\pi$
$318$	−142392.	−	44559.4i	−1.40810	−	0.440641i
$319$	3117.20	+	5399.14i	0.0306325	+	0.0530571i
$320$	−245958.	+	142004.i	−2.40193	+	1.38676i
$321$	−28167.6	+	6308.25i	−0.273363	+	0.0612208i
$322$	5357.33	−	9279.16i	0.0516698	−	0.0894946i
$323$			42177.7i			0.404276i
$324$	304523.	+	50996.1i	2.90088	+	0.485788i
$325$	−21822.8			−0.206607
$326$	−329210.	−	190069.i	−3.09769	−	1.78845i
$327$	−15763.9	−	70388.8i	−0.147424	−	0.658276i
$328$	71393.2	+	123657.i	0.663604	+	1.14940i
$329$	10825.9	−	6250.33i	0.100017	−	0.0577446i
$330$	−11693.0	+	37365.8i	−0.107374	+	0.343120i
$331$	15469.9	−	26794.6i	0.141199	−	0.244564i	−0.786749	−	0.617272i	$-0.788238\pi$
$331$	15469.9	−	26794.6i	0.141199	−	0.244564i	0.927948	+	0.372709i	$0.121571\pi$
$332$			69000.8i			0.626005i
$333$	−113722.	+	53626.6i	−1.02555	+	0.483606i
$334$	−295185.			−2.64607
$335$	76618.3	+	44235.6i	0.682721	+	0.394169i
$336$	161668.	−	148783.i	1.43201	−	1.31787i
$337$	15704.3	+	27200.6i	0.138280	+	0.239507i	0.926845	−	0.375443i	$-0.122509\pi$
$337$	15704.3	+	27200.6i	0.138280	+	0.239507i	−0.788566	+	0.614950i	$0.789176\pi$
$338$	−13190.9	+	7615.79i	−0.115463	+	0.0666625i
$339$	−77047.1	−	83719.6i	−0.670435	−	0.728497i
$340$	62478.5	−	108216.i	0.540472	−	0.936125i
$341$		−	31975.7i		−	0.274986i
$342$	113841.	+	9466.16i	0.973302	+	0.0809322i
$343$	88926.6			0.755864
$344$	−477230.	−	275529.i	−4.03284	−	2.32836i
$345$	−6399.50	−	2002.62i	−0.0537660	−	0.0168252i
$346$	151974.	+	263227.i	1.26945	+	2.19876i
$347$	93000.3	−	53693.8i	0.772370	−	0.445928i	−0.0613492	−	0.998116i	$-0.519540\pi$
$347$	93000.3	−	53693.8i	0.772370	−	0.445928i	0.833720	+	0.552188i	$0.186207\pi$
$348$	−52587.2	+	11777.1i	−0.434232	+	0.0972481i
$349$	−71323.1	+	123535.i	−0.585571	+	1.01424i	0.409233	+	0.912430i	$0.365796\pi$
$349$	−71323.1	+	123535.i	−0.585571	+	1.01424i	−0.994804	+	0.101808i	$0.967537\pi$
$350$		−	20098.0i		−	0.164065i
$351$	47944.1	−	117895.i	0.389153	−	0.956931i
$352$	275774.			2.22571
$353$	90090.8	+	52014.0i	0.722988	+	0.417417i	0.815852	−	0.578261i	$-0.196269\pi$
$353$	90090.8	+	52014.0i	0.722988	+	0.417417i	−0.0928634	+	0.995679i	$0.529602\pi$
$354$	27817.2	+	124209.i	0.221976	+	0.991168i
$355$	−41615.1	−	72079.5i	−0.330213	−	0.571946i
$356$	556610.	−	321359.i	4.39189	−	2.53566i
$357$	−12924.8	+	41302.0i	−0.101411	+	0.324067i
$358$	81221.6	−	140680.i	0.633731	−	1.09766i
$359$			27530.6i			0.213613i	0.994280	+	0.106806i	$0.0340625\pi$
$359$			27530.6i			0.213613i	−0.994280	+	0.106806i	$0.965938\pi$
$360$	−183524.	−	127331.i	−1.41608	−	0.982491i
$361$	−98780.7			−0.757980
$362$	−112452.	−	64924.4i	−0.858127	−	0.495440i
$363$	−81058.9	+	74598.4i	−0.615159	+	0.566130i
$364$	−83174.6	−	144063.i	−0.627752	−	1.08730i
$365$	47686.1	−	27531.6i	0.357936	−	0.206655i
$366$	51968.8	+	56469.5i	0.387954	+	0.421552i
$367$	60337.3	−	104507.i	0.447975	−	0.775916i	−0.550279	−	0.834981i	$-0.685479\pi$
$367$	60337.3	−	104507.i	0.447975	−	0.775916i	0.998254	+	0.0590650i	$0.0188119\pi$
$368$			80348.8i			0.593313i
$369$	−26729.8	+	38526.1i	−0.196310	+	0.282945i
$370$	137814.			1.00668
$371$	−36605.6	−	21134.3i	−0.265950	−	0.153546i
$372$	263782.	+	82546.4i	1.90616	+	0.596503i
$373$	−78112.5	−	135295.i	−0.561439	−	0.972441i	−0.997371	−	0.0724616i	$-0.976915\pi$
$373$	−78112.5	−	135295.i	−0.561439	−	0.972441i	0.435932	−	0.899980i	$-0.356419\pi$
$374$	−80028.4	+	46204.4i	−0.572138	+	0.330324i
$375$	−12273.8	+	2748.78i	−0.0872807	+	0.0195469i
$376$	−76141.8	+	131882.i	−0.538577	+	0.932842i
$377$			22213.2i			0.156289i
$378$	108577.	+	44154.7i	0.759894	+	0.309025i
$379$	73858.4			0.514187			0.257094	−	0.966386i	$-0.417235\pi$
$379$	73858.4			0.514187			0.257094	+	0.966386i	$0.417235\pi$
$380$	−80923.3	−	46721.1i	−0.560411	−	0.323553i
$381$	−145.408	−	649.274i	−0.00100170	−	0.00447279i
$382$	5556.57	+	9624.27i	0.0380785	+	0.0659540i
$383$	45085.2	−	26030.0i	0.307353	−	0.177450i	−0.338389	−	0.941006i	$-0.609882\pi$
$383$	45085.2	−	26030.0i	0.307353	−	0.177450i	0.645741	+	0.763556i	$0.276549\pi$
$384$	−300157.	+	959170.i	−2.03557	+	6.50479i
$385$	−5545.93	+	9605.83i	−0.0374156	+	0.0648057i
$386$		−	322873.i		−	2.16699i
$387$	14996.0	−	180344.i	0.100127	−	1.20415i
$388$	−495628.			−3.29225
$389$	−5075.20	−	2930.17i	−0.0335393	−	0.0193639i	0.483137	−	0.875545i	$-0.339497\pi$
$389$	−5075.20	−	2930.17i	−0.0335393	−	0.0193639i	−0.516676	+	0.856181i	$0.672831\pi$
$390$	−102648.	+	94466.5i	−0.674870	+	0.621082i
$391$	−7913.27	−	13706.2i	−0.0517610	−	0.0896526i
$392$	−425303.	+	245549.i	−2.76774	+	1.59796i
$393$	131359.	+	142735.i	0.850502	+	0.924159i
$394$	−16453.0	+	28497.4i	−0.105987	+	0.183574i
$395$			9628.56i			0.0617116i
$396$	79663.7	+	168937.i	0.508008	+	1.07729i
$397$	27523.4			0.174631			0.0873154	−	0.996181i	$-0.472171\pi$
$397$	27523.4			0.174631			0.0873154	+	0.996181i	$0.472171\pi$
$398$	149467.	+	86294.5i	0.943578	+	0.544775i
$399$	30885.4	+	9665.08i	0.194002	+	0.0607099i
$400$	75357.0	+	130522.i	0.470981	+	0.815764i
$401$	−167879.	+	96924.9i	−1.04402	+	0.602763i	−0.920968	−	0.389638i	$-0.872600\pi$
$401$	−167879.	+	96924.9i	−1.04402	+	0.602763i	−0.123048	+	0.992401i	$0.539267\pi$
$402$	551875.	−	123595.i	3.41499	−	0.764800i
$403$	56964.7	−	98665.7i	0.350748	−	0.607514i
$404$		−	526434.i		−	3.22538i
$405$	12115.4	−	72346.8i	0.0738629	−	0.441072i
$406$	−20457.5			−0.124108
$407$	−65868.1	−	38029.0i	−0.397637	−	0.229576i
$408$	−115215.	−	514459.i	−0.692133	−	3.09051i
$409$	−86638.9	−	150063.i	−0.517924	−	0.897071i	−0.999783	−	0.0208223i	$-0.993372\pi$
$409$	−86638.9	−	150063.i	−0.517924	−	0.897071i	0.481859	−	0.876249i	$-0.339962\pi$
$410$	44510.9	−	25698.4i	0.264788	−	0.152875i
$411$	80705.0	−	257898.i	0.477768	−	1.52674i
$412$	263722.	−	456780.i	1.55365	−	2.69100i
$413$			36059.9i			0.211409i
$414$	−38770.2	+	18282.4i	−0.226202	+	0.106668i
$415$	16392.8			0.0951826
$416$	850944.	+	491293.i	4.91716	+	2.83892i
$417$	−87659.6	+	80673.0i	−0.504112	+	0.463934i
$418$	34551.4	+	59844.8i	0.197749	+	0.342511i
$419$	−72723.7	+	41987.0i	−0.414236	+	0.239159i	−0.692608	−	0.721314i	$-0.743538\pi$
$419$	−72723.7	+	41987.0i	−0.414236	+	0.239159i	0.278372	+	0.960473i	$0.410205\pi$
$420$	−64926.0	−	70548.8i	−0.368061	−	0.399937i
$421$	−82514.3	+	142919.i	−0.465549	+	0.806354i	−0.999226	−	0.0393340i	$-0.987476\pi$
$421$	−82514.3	+	142919.i	−0.465549	+	0.806354i	0.533677	+	0.845688i	$0.320810\pi$
$422$			472897.i			2.65547i
$423$	−49837.6	−	4144.11i	−0.278533	−	0.0231606i
$424$	514917.			2.86422
$425$	−25709.4	−	14843.3i	−0.142336	−	0.0821775i
$426$	−507762.	−	158896.i	−2.79796	−	0.875575i
$427$	10870.6	+	18828.5i	0.0596210	+	0.103267i
$428$	130713.	−	75467.4i	0.713563	−	0.411976i
$429$	75127.9	−	16825.2i	0.408213	−	0.0914210i
$430$	−99178.1	+	171781.i	−0.536388	+	0.929050i
$431$			267599.i			1.44055i	0.693687	+	0.720277i	$0.255985\pi$
$431$			267599.i			1.44055i	−0.693687	+	0.720277i	$0.744015\pi$
$432$	−870686.	+	120353.i	−4.66545	+	0.644895i
$433$	−179474.			−0.957249			−0.478625	−	0.878020i	$-0.658865\pi$
$433$	−179474.			−0.957249			−0.478625	+	0.878020i	$0.658865\pi$
$434$	90867.4	+	52462.3i	0.482424	+	0.278528i
$435$	2797.94	+	12493.4i	0.0147863	+	0.0660240i
$436$	188588.	+	326643.i	0.992065	+	1.71831i
$437$	−10249.4	+	5917.50i	−0.0536705	+	0.0309867i
$438$	105122.	−	335923.i	0.547954	−	1.75102i
$439$	−94020.0	+	162847.i	−0.487855	+	0.844990i	−0.999902	−	0.0139671i	$-0.995554\pi$
$439$	−94020.0	+	162847.i	−0.487855	+	0.844990i	0.512047	+	0.858957i	$0.328887\pi$
$440$		−	135122.i		−	0.697942i
$441$	−132506.	−	91934.1i	−0.681331	−	0.472715i
$442$	−329253.			−1.68533
$443$	−150135.	−	86680.5i	−0.765023	−	0.441686i	0.0660732	−	0.997815i	$-0.478953\pi$
$443$	−150135.	−	86680.5i	−0.765023	−	0.441686i	−0.831096	+	0.556128i	$0.812286\pi$
$444$	483760.	−	445204.i	2.45394	−	2.25836i
$445$	−76346.7	−	132236.i	−0.385541	−	0.667776i
$446$	189586.	−	109458.i	0.953097	−	0.550271i
$447$	111752.	+	121430.i	0.559292	+	0.607729i
$448$	−257164.	+	445421.i	−1.28131	+	2.21929i
$449$			263401.i			1.30654i	0.757123	+	0.653272i	$0.226604\pi$
$449$			263401.i			1.30654i	−0.757123	+	0.653272i	$0.773396\pi$
$450$	−45833.4	+	66060.4i	−0.226338	+	0.326224i
$451$	−28365.3			−0.139455
$452$	515227.	+	297466.i	2.52186	+	1.45600i
$453$	212885.	+	66619.0i	1.03741	+	0.324640i
$454$	−296515.	−	513580.i	−1.43859	−	2.49170i
$455$	−34225.6	+	19760.2i	−0.165321	+	0.0954482i
$456$	−384710.	+	86157.4i	−1.85014	+	0.414346i
$457$	−163899.	+	283881.i	−0.784771	+	1.35926i	0.144365	+	0.989524i	$0.453886\pi$
$457$	−163899.	+	283881.i	−0.784771	+	1.35926i	−0.929136	+	0.369738i	$0.879447\pi$
$458$		−	219219.i		−	1.04507i
$459$	136672.	−	106281.i	0.648713	−	0.504464i
$460$	35062.7			0.165703
$461$	−162478.	−	93807.0i	−0.764529	−	0.441401i	0.0663904	−	0.997794i	$-0.478852\pi$
$461$	−162478.	−	93807.0i	−0.764529	−	0.441401i	−0.830920	+	0.556393i	$0.812185\pi$
$462$	15495.4	+	69190.0i	0.0725969	+	0.324160i
$463$	108481.	+	187895.i	0.506049	+	0.876502i	0.999976	+	0.00699856i	$0.00222773\pi$
$463$	108481.	+	187895.i	0.506049	+	0.876502i	−0.493927	+	0.869503i	$0.664439\pi$
$464$	132857.	−	76704.9i	0.617089	−	0.356277i
$465$	19610.9	−	62667.9i	0.0906968	−	0.289827i
$466$	289017.	−	500593.i	1.33092	−	2.30522i
$467$			120055.i			0.550488i	0.961374	+	0.275244i	$0.0887586\pi$
$467$			120055.i			0.550488i	−0.961374	+	0.275244i	$0.911241\pi$
$468$	−55146.6	+	663201.i	−0.251783	+	3.02798i
$469$	160218.			0.728393
$470$	47471.4	+	27407.6i	0.214900	+	0.124073i
$471$	123839.	−	113969.i	0.558232	−	0.513740i
$472$	−219642.	−	380431.i	−0.985896	−	1.70762i
$473$	94804.2	−	54735.3i	0.423746	−	0.244650i
$474$	41680.1	+	45289.7i	0.185512	+	0.201578i
$475$	−11099.7	+	19225.3i	−0.0491955	+	0.0852092i
$476$		−	226293.i		−	0.998749i
$477$	72122.8	+	152945.i	0.316983	+	0.672202i
$478$	−190199.			−0.832438
$479$	333777.	+	192706.i	1.45474	+	0.839895i	0.998745	−	0.0500867i	$-0.0159498\pi$
$479$	333777.	+	192706.i	1.45474	+	0.839895i	0.455996	+	0.889982i	$0.349283\pi$
$480$	540480.	+	169135.i	2.34584	+	0.734091i
$481$	−135497.	−	234688.i	−0.585653	−	1.01438i
$482$	−100148.	+	57820.4i	−0.431070	+	0.248878i
$483$	−11849.9	+	2653.84i	−0.0507950	+	0.0113758i
$484$	288012.	−	498852.i	1.22948	−	2.12952i
$485$			117749.i			0.500579i
$486$	−256188.	−	392741.i	−1.08464	−	1.66278i
$487$	253927.			1.07066			0.535329	−	0.844644i	$-0.320188\pi$
$487$	253927.			1.07066			0.535329	+	0.844644i	$0.320188\pi$
$488$	−229370.	−	132427.i	−0.963156	−	0.556078i
$489$	94153.9	+	420416.i	0.393750	+	1.75817i
$490$	88386.5	+	153090.i	0.368124	+	0.637609i
$491$	−43533.7	+	25134.2i	−0.180577	+	0.104256i	−0.587564	−	0.809178i	$-0.699913\pi$
$491$	−43533.7	+	25134.2i	−0.180577	+	0.104256i	0.406987	+	0.913434i	$0.366580\pi$
$492$	73226.0	−	233998.i	0.302507	−	0.966680i
$493$	−15108.8	+	26169.2i	−0.0621636	+	0.107670i
$494$			246214.i			1.00892i
$495$	40135.0	−	18926.1i	0.163800	−	0.0772413i
$496$	−786826.			−3.19827
$497$	−130533.	−	75363.5i	−0.528456	−	0.305104i
$498$	77106.7	−	70961.2i	0.310909	−	0.286129i
$499$	95793.7	+	165920.i	0.384712	+	0.666341i	0.991729	−	0.128348i	$-0.0409674\pi$
$499$	95793.7	+	165920.i	0.384712	+	0.666341i	−0.607017	+	0.794689i	$0.707634\pi$
$500$	56957.5	−	32884.4i	0.227830	−	0.131538i
$501$	226548.	+	246168.i	0.902577	+	0.980743i
$502$	−236462.	+	409564.i	−0.938327	+	1.62523i
$503$			385978.i			1.52555i	0.646665	+	0.762774i	$0.276163\pi$
$503$			385978.i			1.52555i	−0.646665	+	0.762774i	$0.723837\pi$
$504$	−403124.	−	33520.6i	−1.58700	−	0.131963i
$505$	−125067.			−0.490411
$506$	−22455.8	−	12964.9i	−0.0877057	−	0.0506369i
$507$	16474.9	+	5155.55i	0.0640924	+	0.0200567i
$508$	1739.55	+	3013.00i	0.00674079	+	0.0116754i
$509$	279085.	−	161130.i	1.07721	−	0.621928i	0.147068	−	0.989126i	$-0.453016\pi$
$509$	279085.	−	161130.i	1.07721	−	0.621928i	0.930143	+	0.367199i	$0.119683\pi$
$510$	−185182.	+	41472.3i	−0.711966	+	0.159448i
$511$	49858.6	−	86357.7i	0.190941	−	0.330719i
$512$		−	2.02772e6i		−	7.73515i
$513$	−79476.4	−	102202.i	−0.301998	−	0.388352i
$514$	130679.			0.494628
$515$	−108519.	−	62653.7i	−0.409159	−	0.236228i
$516$	206796.	+	923386.i	0.776682	+	3.46804i
$517$	−15126.0	−	26198.9i	−0.0565903	−	0.0980173i
$518$	216139.	−	124788.i	0.805515	−	0.465064i
$519$	102880.	−	328758.i	0.381940	−	1.22051i
$520$	240719.	−	416938.i	0.890234	−	1.54193i
$521$		−	79796.7i		−	0.293975i	−0.989138	−	0.146987i	$-0.953042\pi$
$521$		−	79796.7i		−	0.293975i	0.989138	−	0.146987i	$-0.0469576\pi$
$522$	67242.0	+	46653.2i	0.246774	+	0.171214i
$523$	−182234.			−0.666233			−0.333116	−	0.942886i	$-0.608100\pi$
$523$	−182234.			−0.666233			−0.333116	+	0.942886i	$0.608100\pi$
$524$	−878421.	−	507157.i	−3.19919	−	1.84705i
$525$	−16760.6	+	15424.8i	−0.0608094	+	0.0559628i
$526$	321359.	+	556610.i	1.16150	+	2.01177i
$527$	134220.	−	77491.7i	0.483275	−	0.279019i
$528$	−360058.	−	391240.i	−1.29153	−	1.40338i
$529$	−137700.	+	238503.i	−0.492065	+	0.852282i
$530$		−	185347.i		−	0.659833i
$531$	82234.5	−	118526.i	0.291652	−	0.420362i
$532$	−169220.			−0.597901
$533$	−87525.3	−	50532.7i	−0.308091	−	0.177876i
$534$	−931535.	−	291509.i	−3.26676	−	1.02228i
$535$	−17929.1	−	31054.2i	−0.0626400	−	0.108496i
$536$	−1.69030e6	+	975892.i	−5.88346	+	3.39682i
$537$	−179655.	+	40234.4i	−0.623003	+	0.139524i
$538$	408860.	−	708167.i	1.41257	−	2.44665i
$539$		−	97559.0i		−	0.335807i
$540$	52519.8	+	379951.i	0.180109	+	1.30299i
$541$	−457754.			−1.56400			−0.782002	−	0.623276i	$-0.785801\pi$
$541$	−457754.			−1.56400			−0.782002	+	0.623276i	$0.785801\pi$
$542$	911813.	+	526436.i	3.10390	+	1.79204i
$543$	32161.4	+	143607.i	0.109077	+	0.487053i
$544$	668328.	+	1.15758e6i	2.25835	+	3.91158i
$545$	77602.1	−	44803.6i	0.261265	−	0.150841i
$546$	−75448.7	+	241101.i	−0.253085	+	0.808750i
$547$	94306.1	−	163343.i	0.315185	−	0.545916i	−0.664292	−	0.747473i	$-0.731267\pi$
$547$	94306.1	−	163343.i	0.315185	−	0.545916i	0.979477	+	0.201557i	$0.0646002\pi$
$548$			1.41302e6i			4.70529i
$549$	7207.48	−	86678.1i	0.0239132	−	0.287584i
$550$	−48637.7			−0.160786
$551$	19569.2	+	11298.3i	0.0644569	+	0.0372142i
$552$	108852.	−	100176.i	0.357238	−	0.328765i
$553$	8718.48	+	15100.8i	0.0285096	+	0.0493800i
$554$	−400174.	+	231041.i	−1.30386	+	0.752781i
$555$	−105769.	−	114929.i	−0.343378	−	0.373116i
$556$	311465.	−	539474.i	1.00754	−	1.74510i
$557$		−	465876.i		−	1.50162i	−0.660519	−	0.750810i	$-0.729664\pi$
$557$		−	465876.i		−	1.50162i	0.660519	−	0.750810i	$-0.270336\pi$
$558$	−179033.	−	379662.i	−0.574996	−	1.21935i
$559$	390044.			1.24822
$560$	236371.	+	136469.i	0.753734	+	0.435168i
$561$	99951.9	+	31278.3i	0.317589	+	0.0993843i
$562$	61798.5	+	107038.i	0.195661	+	0.338895i
$563$	−152201.	+	87873.0i	−0.480175	+	0.277229i	−0.720489	−	0.693466i	$-0.756083\pi$
$563$	−152201.	+	87873.0i	−0.480175	+	0.277229i	0.240315	+	0.970695i	$0.422749\pi$
$564$	255176.	−	57147.7i	0.802197	−	0.179655i
$565$	70670.4	−	122405.i	0.221381	−	0.383443i
$566$		−	532688.i		−	1.66280i
$567$	−46507.7	−	124435.i	−0.144663	−	0.387057i
$568$	1.83616e6			5.69134
$569$	−290145.	−	167515.i	−0.896170	−	0.517404i	−0.0202144	−	0.999796i	$-0.506435\pi$
$569$	−290145.	−	167515.i	−0.896170	−	0.517404i	−0.875956	+	0.482392i	$0.839768\pi$
$570$	31012.8	+	138478.i	0.0954533	+	0.426218i
$571$	−238946.	−	413866.i	−0.732871	−	1.26937i	−0.955651	−	0.294501i	$-0.904847\pi$
$571$	−238946.	−	413866.i	−0.732871	−	1.26937i	0.222781	−	0.974869i	$-0.428487\pi$
$572$	−348636.	+	201285.i	−1.06556	+	0.615204i
$573$	3761.55	−	12020.3i	0.0114567	−	0.0366105i
$574$	46538.8	−	80607.5i	0.141251	−	0.244654i
$575$		−	8330.01i		−	0.0251947i
$576$	1.86105e6	−	877598.i	5.60937	−	2.64515i
$577$	−52345.6			−0.157227			−0.0786137	−	0.996905i	$-0.525049\pi$
$577$	−52345.6			−0.157227			−0.0786137	+	0.996905i	$0.525049\pi$
$578$	186496.	+	107673.i	0.558230	+	0.322294i
$579$	−269258.	+	247798.i	−0.803177	+	0.739163i
$580$	−33472.6	−	57976.3i	−0.0995024	−	0.172343i
$581$	25709.5	−	14843.4i	0.0761626	−	0.0439725i
$582$	509710.	+	553852.i	1.50479	+	1.63511i
$583$	−51145.5	+	88586.6i	−0.150477	+	0.260634i
$584$			1.21476e6i			3.56176i
$585$	157560.	+	13101.4i	0.460398	+	0.0382831i
$586$	939598.			2.73619
$587$	−217591.	−	125626.i	−0.631488	−	0.364590i	0.149840	−	0.988710i	$-0.452124\pi$
$587$	−217591.	−	125626.i	−0.631488	−	0.364590i	−0.781328	+	0.624120i	$0.785457\pi$
$588$	804810.	+	251852.i	2.32776	+	0.728436i
$589$	−57947.9	−	100369.i	−0.167035	−	0.289313i
$590$	−136938.	+	79061.2i	−0.393387	+	0.227122i
$591$	36392.5	−	8150.24i	0.104192	−	0.0233343i
$592$	−935780.	+	1.62082e6i	−2.67012	+	4.62478i
$593$		−	529036.i		−	1.50444i	−0.658910	−	0.752222i	$-0.728982\pi$
$593$		−	529036.i		−	1.50444i	0.658910	−	0.752222i	$-0.271018\pi$
$594$	106856.	−	262759.i	0.302848	−	0.744705i
$595$	−53761.3			−0.151857
$596$	−747302.	−	431455.i	−2.10380	−	1.21463i
$597$	−42747.4	−	190876.i	−0.119939	−	0.535553i
$598$	−46193.9	−	80010.2i	−0.129176	−	0.223740i
$599$	−18443.3	+	10648.2i	−0.0514025	+	0.0296773i	−0.525481	−	0.850805i	$-0.676115\pi$
$599$	−18443.3	+	10648.2i	−0.0514025	+	0.0296773i	0.474079	+	0.880483i	$0.342781\pi$
$600$	82871.1	−	264820.i	0.230198	−	0.735611i
$601$	−32788.2	+	56790.8i	−0.0907754	+	0.157228i	−0.907838	−	0.419322i	$-0.862268\pi$
$601$	−32788.2	+	56790.8i	−0.0907754	+	0.157228i	0.817062	+	0.576550i	$0.195601\pi$
$602$			359215.i			0.991202i
$603$	−526623.	−	365377.i	−1.44832	−	1.00486i
$604$	−1.16639e6			−3.19721
$605$	−118514.	−	68424.4i	−0.323788	−	0.186939i
$606$	−588276.	+	541390.i	−1.60190	+	1.47423i
$607$	204964.	+	355008.i	0.556288	+	0.963519i	0.997802	+	0.0662650i	$0.0211083\pi$
$607$	204964.	+	355008.i	0.556288	+	0.963519i	−0.441514	+	0.897254i	$0.645558\pi$
$608$	865631.	−	499772.i	2.34167	−	1.35196i
$609$	15700.7	+	17060.4i	0.0423334	+	0.0459996i
$610$	−47667.7	+	82562.8i	−0.128104	+	0.221883i
$611$		−	107788.i		−	0.288727i
$612$	−516059.	+	743804.i	−1.37783	+	1.98589i
$613$	215335.			0.573052			0.286526	−	0.958072i	$-0.407500\pi$
$613$	215335.			0.573052			0.286526	+	0.958072i	$0.407500\pi$
$614$	823165.	+	475255.i	2.18349	+	1.26064i
$615$	−55592.0	−	17396.6i	−0.146981	−	0.0459955i
$616$	−122350.	−	211917.i	−0.322435	−	0.558475i
$617$	603091.	−	348195.i	1.58421	−	0.914643i	0.589974	−	0.807422i	$-0.299138\pi$
$617$	603091.	−	348195.i	1.58421	−	0.914643i	0.994235	−	0.107221i	$-0.0341952\pi$
$618$	−781656.	+	175055.i	−2.04663	+	0.458350i
$619$	−56678.5	+	98170.1i	−0.147924	+	0.256211i	−0.930460	−	0.366394i	$-0.880592\pi$
$619$	−56678.5	+	98170.1i	−0.147924	+	0.256211i	0.782536	+	0.622605i	$0.213926\pi$
$620$			343356.i			0.893227i
$621$	45001.7	+	18300.8i	0.116693	+	0.0474555i
$622$	−388995.			−1.00546
$623$	−239475.	−	138261.i	−0.616999	−	0.356224i
$624$	−414018.	−	1.84867e6i	−1.06329	−	4.74779i
$625$	−7812.50	−	13531.6i	−0.0200000	−	0.0346410i
$626$	828175.	−	478147.i	2.11336	−	1.22015i
$627$	23389.8	−	74743.5i	0.0594964	−	0.190125i
$628$	−440014.	+	762127.i	−1.11570	+	1.93245i
$629$		−	368647.i		−	0.931771i
$630$	−12065.9	+	145106.i	−0.0304004	+	0.365599i
$631$	−79865.2			−0.200585			−0.100293	−	0.994958i	$-0.531978\pi$
$631$	−79865.2			−0.200585			−0.100293	+	0.994958i	$0.531978\pi$
$632$	−183959.	−	106209.i	−0.460561	−	0.265905i
$633$	394369.	−	362938.i	0.984228	−	0.905784i
$634$	−288454.	−	499618.i	−0.717627	−	1.24297i
$635$	715.811	−	413.274i	0.00177521	−	0.00102492i
$636$	−598758.	−	650613.i	−1.48026	−	1.60845i
$637$	173801.	−	301033.i	0.428326	−	0.741883i
$638$			49507.7i			0.121627i
$639$	257186.	+	545394.i	0.629861	+	1.33570i
$640$	−1.24852e6			−3.04814
$641$	501271.	+	289409.i	1.21999	+	0.704362i	0.964916	−	0.262560i	$-0.0845667\pi$
$641$	501271.	+	289409.i	1.21999	+	0.704362i	0.255074	+	0.966921i	$0.417900\pi$
$642$	−218760.	−	68457.4i	−0.530760	−	0.166093i
$643$	349236.	+	604895.i	0.844690	+	1.46305i	0.885890	+	0.463895i	$0.153549\pi$
$643$	349236.	+	604895.i	0.844690	+	1.46305i	−0.0411997	+	0.999151i	$0.513118\pi$
$644$	54990.3	−	31748.6i	0.132591	−	0.0765515i
$645$	219373.	−	49129.5i	0.527307	−	0.118093i
$646$	−167468.	+	290063.i	−0.401298	+	0.695068i
$647$		−	231853.i		−	0.553865i	−0.960889	−	0.276932i	$-0.910682\pi$
$647$		−	231853.i		−	0.553865i	0.960889	−	0.276932i	$-0.0893178\pi$
$648$	1.24859e6	+	1.02950e6i	2.97351	+	2.45175i
$649$	87265.9			0.207184
$650$	−150079.	−	86648.1i	−0.355216	−	0.205084i
$651$	−25988.1	−	116042.i	−0.0613214	−	0.273812i
$652$	−1.12639e6	−	1.95097e6i	−2.64968	−	4.58939i
$653$	238169.	−	137507.i	0.558546	−	0.322476i	−0.194016	−	0.980998i	$-0.562151\pi$
$653$	238169.	−	137507.i	0.558546	−	0.322476i	0.752562	+	0.658522i	$0.228818\pi$
$654$	171070.	−	546666.i	0.399962	−	1.27810i
$655$	−120487.	+	208690.i	−0.280840	+	0.486429i
$656$			697985.i			1.62195i
$657$	−360819.	+	170148.i	−0.835909	+	0.394181i
$658$	99268.4			0.229276
$659$	−330522.	−	190827.i	−0.761078	−	0.439409i	0.0686044	−	0.997644i	$-0.478145\pi$
$659$	−330522.	−	190827.i	−0.761078	−	0.439409i	−0.829683	+	0.558235i	$0.811479\pi$
$660$	−170730.	+	157123.i	−0.391942	+	0.360704i
$661$	214977.	+	372351.i	0.492027	+	0.852216i	0.999958	−	0.00918200i	$-0.00292276\pi$
$661$	214977.	+	372351.i	0.492027	+	0.852216i	−0.507931	+	0.861398i	$0.669589\pi$
$662$	212778.	−	122847.i	0.485523	−	0.280317i
$663$	252694.	+	274578.i	0.574868	+	0.624654i
$664$	−180823.	+	313195.i	−0.410126	+	0.710360i
$665$			40202.4i			0.0909095i
$666$	−995009.	−	82737.2i	−2.24325	−	0.186532i
$667$	−8479.00			−0.0190587
$668$	−1.51496e6	−	874664.i	−3.39507	−	1.96015i
$669$	−236785.	−	74097.9i	−0.529056	−	0.165559i
$670$	351277.	+	608430.i	0.782529	+	1.35538i
$671$	45565.5	−	26307.2i	0.101202	−	0.0584293i
$672$	1.00081e6	−	224134.i	2.21621	−	0.496329i
$673$	−62647.0	+	108508.i	−0.138315	+	0.239569i	−0.926859	−	0.375410i	$-0.877502\pi$
$673$	−62647.0	+	108508.i	−0.138315	+	0.239569i	0.788544	+	0.614979i	$0.210835\pi$
$674$			249417.i			0.549043i
$675$	90266.7	−	12477.4i	0.198116	−	0.0273852i
$676$	−90265.5			−0.197528
$677$	−91566.0	−	52865.7i	−0.199782	−	0.115344i	0.396772	−	0.917917i	$-0.370130\pi$
$677$	−91566.0	−	52865.7i	−0.199782	−	0.115344i	−0.596554	+	0.802573i	$0.703464\pi$
$678$	−197454.	−	881671.i	−0.429542	−	1.91799i
$679$	106619.	+	184670.i	0.231257	+	0.400550i
$680$	567180.	−	327462.i	1.22660	−	0.708178i
$681$	−200728.	+	641438.i	−0.432826	+	1.38312i
$682$	126960.	−	219902.i	0.272960	−	0.472781i
$683$			9196.24i			0.0197137i	0.999951	+	0.00985687i	$0.00313759\pi$
$683$			9196.24i			0.0197137i	−0.999951	+	0.00985687i	$0.996862\pi$
$684$	556213.	+	385906.i	1.18885	+	0.824840i
$685$	335697.			0.715429
$686$	611562.	+	353086.i	1.29955	+	0.750295i
$687$	−182816.	+	168246.i	−0.387348	+	0.356476i
$688$	−1.34687e6	−	2.33285e6i	−2.84544	−	4.92844i
$689$	−315634.	+	182231.i	−0.664884	+	0.383871i
$690$	−36058.9	−	39181.7i	−0.0757381	−	0.0822973i
$691$	368768.	−	638724.i	0.772319	−	1.33770i	−0.163970	−	0.986465i	$-0.552430\pi$
$691$	368768.	−	638724.i	0.772319	−	1.33770i	0.936289	−	0.351230i	$-0.114237\pi$
$692$			1.80126e6i			3.76153i
$693$	45808.2	−	66024.0i	0.0953842	−	0.137479i
$694$	852771.			1.77057
$695$	−128165.	−	73996.2i	−0.265339	−	0.153193i
$696$	−269557.	−	84353.4i	−0.556457	−	0.174134i
$697$	−68742.1	−	119065.i	−0.141500	−	0.245085i
$698$	−981000.	+	566381.i	−2.01353	+	1.16251i
$699$	−639280.	+	143169.i	−1.30839	+	0.293019i
$700$	59552.5	−	103148.i	0.121536	−	0.210506i
$701$			773845.i			1.57477i	0.616460	+	0.787386i	$0.288566\pi$
$701$			773845.i			1.57477i	−0.616460	+	0.787386i	$0.711434\pi$
$702$	797824.	−	620418.i	1.61895	−	1.25896i
$703$	−275672.			−0.557805
$704$	1.07793e6	+	622343.i	2.17493	+	1.25570i
$705$	−13576.8	−	60623.2i	−0.0273162	−	0.121972i
$706$	413046.	+	715416.i	0.828684	+	1.43532i
$707$	−196148.	+	113246.i	−0.392414	+	0.226560i
$708$	−225280.	+	719898.i	−0.449425	+	1.43617i
$709$	−113430.	+	196466.i	−0.225650	+	0.390837i	−0.956514	−	0.291686i	$-0.905784\pi$
$709$	−113430.	+	196466.i	−0.225650	+	0.390837i	0.730864	+	0.682523i	$0.239117\pi$
$710$		−	660936.i		−	1.31112i
$711$	5780.54	−	69517.6i	0.0114348	−	0.137517i
$712$	3.36860e6			6.64492
$713$	37661.8	+	21744.0i	0.0740835	+	0.0427722i
$714$	−252876.	+	232722.i	−0.496034	+	0.456500i
$715$	47820.1	+	82826.9i	0.0935403	+	0.162017i
$716$	833699.	−	481336.i	1.62623	−	0.938907i
$717$	145973.	+	158615.i	0.283946	+	0.308536i
$718$	−109311.	+	189332.i	−0.212039	+	0.367262i
$719$		−	371835.i		−	0.719270i	−0.933093	−	0.359635i	$-0.882901\pi$
$719$		−	371835.i		−	0.719270i	0.933093	−	0.359635i	$-0.117099\pi$
$720$	−465714.	−	987604.i	−0.898368	−	1.90510i
$721$	−226927.			−0.436531
$722$	−679330.	−	392212.i	−1.30319	−	0.752395i
$723$	125080.	+	39141.8i	0.239283	+	0.0748797i
$724$	−384756.	−	666417.i	−0.734020	−	1.27136i
$725$	−13773.7	+	7952.24i	−0.0262044	+	0.0151291i
$726$	−853650.	+	191178.i	−1.61960	+	0.362715i
$727$	−69493.5	+	120366.i	−0.131485	+	0.227738i	−0.924249	−	0.381790i	$-0.875308\pi$
$727$	−69493.5	+	120366.i	−0.131485	+	0.227738i	0.792764	+	0.609528i	$0.208641\pi$
$728$		−	871867.i		−	1.64508i
$729$	−130906.	+	515066.i	−0.246323	+	0.969188i
$730$	437259.			0.820528
$731$	459508.	+	265297.i	0.859921	+	0.496476i
$732$	99391.8	+	443804.i	0.185493	+	0.828265i
$733$	527416.	+	913511.i	0.981625	+	1.70022i	0.656070	+	0.754700i	$0.272218\pi$
$733$	527416.	+	913511.i	0.981625	+	1.70022i	0.325555	+	0.945523i	$0.394449\pi$
$734$	829899.	−	479142.i	1.54040	−	0.889349i
$735$	59833.7	−	191202.i	0.110757	−	0.353931i
$736$	−187532.	+	324814.i	−0.346194	+	0.599625i
$737$		−	387732.i		−	0.713833i
$738$	−336794.	+	158818.i	−0.618374	+	0.291600i
$739$	252899.			0.463082			0.231541	−	0.972825i	$-0.425623\pi$
$739$	252899.			0.463082			0.231541	+	0.972825i	$0.425623\pi$
$740$	707295.	+	408357.i	1.29163	+	0.745722i
$741$	205328.	−	188963.i	0.373949	−	0.344145i
$742$	−167828.	−	290687.i	−0.304830	−	0.527981i
$743$	−781617.	+	451267.i	−1.41585	+	0.817440i	−0.995931	−	0.0901223i	$-0.971274\pi$
$743$	−781617.	+	451267.i	−1.41585	+	0.817440i	−0.419917	+	0.907562i	$0.637941\pi$
$744$	980988.	+	1.06594e6i	1.77222	+	1.92570i
$745$	−102503.	+	177540.i	−0.184681	+	0.319877i
$746$		−	1.24059e6i		−	2.22921i
$747$	−118355.	−	9841.51i	−0.212103	−	0.0176368i
$748$	−547634.			−0.978785
$749$	−56237.9	−	32469.0i	−0.100246	−	0.0578769i
$750$	−95323.3	−	29829.9i	−0.169464	−	0.0530309i
$751$	103996.	+	180126.i	0.184390	+	0.319372i	0.943371	−	0.331740i	$-0.107636\pi$
$751$	103996.	+	180126.i	0.184390	+	0.319372i	−0.758981	+	0.651113i	$0.774302\pi$
$752$	−644678.	+	372205.i	−1.14001	+	0.658183i
$753$	523033.	−	117135.i	0.922442	−	0.206585i
$754$	−88198.0	+	152763.i	−0.155137	+	0.268705i
$755$			277105.i			0.486128i
$756$	426408.	+	548337.i	0.746073	+	0.959409i
$757$	−510491.			−0.890833			−0.445417	−	0.895323i	$-0.646944\pi$
$757$	−510491.			−0.890833			−0.445417	+	0.895323i	$0.646944\pi$
$758$	507936.	+	293257.i	0.884037	+	0.510399i
$759$	6422.36	+	28677.1i	0.0111484	+	0.0497797i
$760$	−244874.	−	424134.i	−0.423951	−	0.734305i
$761$	210978.	−	121808.i	0.364308	−	0.210333i	−0.306661	−	0.951819i	$-0.599212\pi$
$761$	210978.	−	121808.i	0.364308	−	0.210333i	0.670969	+	0.741486i	$0.265878\pi$
$762$	1577.97	−	5042.51i	0.00271762	−	0.00868433i
$763$	81137.6	−	140535.i	0.139371	−	0.241398i
$764$			65858.8i			0.112831i
$765$	176709.	+	122603.i	0.301950	+	0.209496i
$766$	413411.			0.704570
$767$	269272.	+	155464.i	0.457721	+	0.264265i
$768$	−3.18104e6	+	2.92751e6i	−5.39321	+	4.96336i
$769$	−377682.	−	654165.i	−0.638666	−	1.10620i	−0.985726	−	0.168359i	$-0.946153\pi$
$769$	−377682.	−	654165.i	−0.638666	−	1.10620i	0.347060	−	0.937843i	$-0.387180\pi$
$770$	−76280.4	+	44040.5i	−0.128656	+	0.0742799i
$771$	−100293.	−	108979.i	−0.168718	−	0.183330i
$772$	956707.	−	1.65706e6i	1.60526	−	2.78038i
$773$		−	80514.1i		−	0.134745i	−0.997728	−	0.0673726i	$-0.978538\pi$
$773$		−	80514.1i		−	0.134745i	0.997728	−	0.0673726i	$-0.0214616\pi$
$774$	819190.	−	1.18071e6i	1.36742	−	1.97089i
$775$	81572.7			0.135813
$776$	−2.24966e6	−	1.29884e6i	−3.73588	−	2.15691i
$777$	−269948.	−	84475.8i	−0.447134	−	0.139923i
$778$	−23268.6	−	40302.5i	−0.0384425	−	0.0665844i
$779$	−89036.0	+	51404.9i	−0.146720	+	0.0847091i
$780$	−806728.	+	180670.i	−1.32598	+	0.296959i
$781$	−182382.	+	315894.i	−0.299005	+	0.517893i
$782$		−	125679.i		−	0.205518i
$783$	−12700.5	−	91881.3i	−0.0207157	−	0.149866i
$784$	−2.40064e6			−3.90566
$785$	181062.	+	104536.i	0.293824	+	0.169640i
$786$	336643.	+	1.50318e6i	0.544910	+	2.43313i
$787$	−47370.0	−	82047.2i	−0.0764810	−	0.132469i	0.825248	−	0.564770i	$-0.191035\pi$
$787$	−47370.0	−	82047.2i	−0.0764810	−	0.132469i	−0.901729	+	0.432301i	$0.857702\pi$
$788$	−168881.	+	97503.7i	−0.271975	+	0.157025i
$789$	217546.	−	695181.i	0.349459	−	1.11672i
$790$	−38230.5	+	66217.1i	−0.0612569	+	0.106100i
$791$		−	255963.i		−	0.409095i
$792$	−81120.8	+	975570.i	−0.129325	+	1.55528i
$793$	187466.			0.298109
$794$	189283.	+	109282.i	0.300241	+	0.173344i
$795$	−154569.	+	142250.i	−0.244562	+	0.225070i
$796$	511400.	+	885770.i	0.807113	+	1.39796i
$797$	−748212.	+	431980.i	−1.17790	+	0.680060i	−0.955528	−	0.294902i	$-0.904713\pi$
$797$	−748212.	+	431980.i	−1.17790	+	0.680060i	−0.222372	+	0.974962i	$0.571380\pi$
$798$	174028.	+	189100.i	0.273284	+	0.296951i
$799$	73314.3	−	126984.i	0.114841	−	0.198910i
$800$			703525.i			1.09926i
$801$	471830.	+	1.00057e6i	0.735395	+	1.55950i
$802$	−1.53937e6			−2.39329
$803$	−208988.	−	120659.i	−0.324108	−	0.187124i
$804$	3.19859e6	+	1.00095e6i	4.94818	+	1.54845i
$805$	−7542.67	−	13064.3i	−0.0116395	−	0.0201601i
$806$	783510.	−	452360.i	1.20608	−	0.696328i
$807$	−904363.	+	202536.i	−1.38866	+	0.310996i
$808$	1.37957e6	−	2.38948e6i	2.11310	−	3.66000i
$809$		−	6487.43i		−	0.00991233i	−0.999988	−	0.00495616i	$-0.998422\pi$
$809$		−	6487.43i		−	0.00991233i	0.999988	−	0.00495616i	$-0.00157760\pi$
$810$	370574.	−	449436.i	0.564814	−	0.685011i
$811$	−1.14309e6			−1.73795			−0.868976	−	0.494854i	$-0.835221\pi$
$811$	−1.14309e6			−1.73795			−0.868976	+	0.494854i	$0.835221\pi$
$812$	−104993.	−	60617.7i	−0.159238	−	0.0919363i
$813$	−260778.	−	1.16443e6i	−0.394540	−	1.76170i
$814$	−301990.	−	523062.i	−0.455768	−	0.789414i
$815$	−463500.	+	267602.i	−0.697805	+	0.402878i
$816$	769666.	−	2.45952e6i	1.15591	−	3.69377i
$817$	198388.	−	343618.i	0.297215	−	0.514792i
$818$		−	1.37601e6i		−	2.05643i
$819$	258970.	−	122120.i	0.386084	−	0.182061i
$820$	304588.			0.452986
$821$	656318.	+	378926.i	0.973707	+	0.562170i	0.900364	−	0.435137i	$-0.143300\pi$
$821$	656318.	+	378926.i	0.973707	+	0.562170i	0.0733425	+	0.997307i	$0.476633\pi$
$822$	1.57901e6	−	1.45316e6i	2.33691	−	2.15066i
$823$	198332.	+	343521.i	0.292815	+	0.507170i	0.974474	−	0.224500i	$-0.0720748\pi$
$823$	198332.	+	343521.i	0.292815	+	0.507170i	−0.681659	+	0.731670i	$0.738741\pi$
$824$	2.39407e6	−	1.38222e6i	3.52600	−	2.03574i
$825$	37328.3	+	40561.1i	0.0548442	+	0.0595939i
$826$	−143177.	+	247990.i	−0.209852	+	0.363474i
$827$		−	314626.i		−	0.460027i	−0.973187	−	0.230014i	$-0.926123\pi$
$827$		−	314626.i		−	0.460027i	0.973187	−	0.230014i	$-0.0738770\pi$
$828$	−253151.	−	21050.1i	−0.369249	−	0.0307038i
$829$	914606.			1.33084			0.665419	−	0.746470i	$-0.268253\pi$
$829$	914606.			1.33084			0.665419	+	0.746470i	$0.268253\pi$
$830$	112736.	+	65088.2i	0.163646	+	0.0944813i
$831$	499800.	+	156404.i	0.723759	+	0.226489i
$832$	2.21741e6	+	3.84067e6i	3.20331	+	5.54830i
$833$	409509.	−	236430.i	0.590165	−	0.340732i
$834$	−923163.	+	206746.i	−1.32723	+	0.297239i
$835$	−207798.	+	359916.i	−0.298036	+	0.516213i
$836$			409518.i			0.585950i
$837$	−179213.	+	440686.i	−0.255810	+	0.629039i
$838$	−666843.			−0.949589
$839$	320416.	+	184992.i	0.455187	+	0.262802i	0.710018	−	0.704183i	$-0.248687\pi$
$839$	320416.	+	184992.i	0.455187	+	0.262802i	−0.254831	+	0.966986i	$0.582020\pi$
$840$	−109819.	−	490366.i	−0.155640	−	0.694963i
$841$	−345546.	−	598503.i	−0.488556	−	0.846203i
$842$	−1.13493e6	+	655251.i	−1.60083	+	0.924237i
$843$	41834.8	−	133686.i	0.0588684	−	0.188118i
$844$	−1.40124e6	+	2.42702e6i	−1.96711	+	3.40713i
$845$			21444.8i			0.0300337i
$846$	−326287.	−	226381.i	−0.455889	−	0.316300i
$847$	−247828.			−0.345449
$848$	2.17985e6	+	1.25854e6i	3.03134	+	1.75015i
$849$	−444232.	+	408826.i	−0.616303	+	0.567183i
$850$	−117872.	−	204159.i	−0.163144	−	0.282574i
$851$	89583.1	−	51720.8i	0.123699	−	0.0714177i
$852$	−2.13514e6	−	2.32005e6i	−2.94135	−	3.19608i
$853$	227283.	−	393666.i	0.312370	−	0.541041i	−0.666505	−	0.745501i	$-0.732210\pi$
$853$	227283.	−	393666.i	0.312370	−	0.541041i	0.978875	+	0.204460i	$0.0655438\pi$
$854$			172649.i			0.236727i
$855$	91681.5	−	132142.i	0.125415	−	0.180762i
$856$	791077.			1.07962
$857$	519173.	+	299745.i	0.706888	+	0.408122i	0.809908	−	0.586557i	$-0.199517\pi$
$857$	519173.	+	299745.i	0.706888	+	0.408122i	−0.103020	+	0.994679i	$0.532850\pi$
$858$	583472.	+	182588.i	0.792584	+	0.248026i
$859$	−612694.	−	1.06122e6i	−0.830343	−	1.43820i	−0.897767	−	0.440471i	$-0.854811\pi$
$859$	−612694.	−	1.06122e6i	−0.830343	−	1.43820i	0.0674239	−	0.997724i	$-0.478522\pi$
$860$	−1.01801e6	+	587750.i	−1.37644	+	0.794686i
$861$	−102940.	+	23053.7i	−0.138860	+	0.0310982i
$862$	−1.06251e6	+	1.84032e6i	−1.42994	+	2.47673i
$863$			815945.i			1.09557i	0.836620	+	0.547784i	$0.184528\pi$
$863$			815945.i			1.09557i	−0.836620	+	0.547784i	$0.815472\pi$
$864$	−3.80070e6	−	1.54562e6i	−5.09138	−	2.07050i
$865$	427933.			0.571931
$866$	−1.23427e6	−	712605.i	−1.64579	−	0.950196i
$867$	−53337.8	−	238164.i	−0.0709572	−	0.316838i
$868$	310903.	+	538499.i	0.412653	+	0.714736i
$869$	36544.5	−	21099.0i	0.0483929	−	0.0279397i
$870$	−30363.4	+	97028.3i	−0.0401155	+	0.128192i
$871$	690745.	−	1.19641e6i	0.910504	−	1.57704i
$872$			1.97685e6i			2.59980i
$873$	70690.9	−	850138.i	0.0927545	−	1.11548i
$874$	−93982.4			−0.123034
$875$	−24505.3	−	14148.1i	−0.0320069	−	0.0184792i
$876$	1.53489e6	−	1.41255e6i	2.00017	−	1.84076i
$877$	30776.7	+	53306.8i	0.0400150	+	0.0693081i	0.885339	−	0.464946i	$-0.153926\pi$
$877$	30776.7	+	53306.8i	0.0400150	+	0.0693081i	−0.845324	+	0.534254i	$0.820593\pi$
$878$	−1.29318e6	+	746618.i	−1.67753	+	0.968522i
$879$	−721120.	−	783571.i	−0.933318	−	1.01415i
$880$	330258.	−	572024.i	0.426470	−	0.738667i
$881$			836575.i			1.07784i	0.842358	+	0.538919i	$0.181167\pi$
$881$			836575.i			1.07784i	−0.842358	+	0.538919i	$0.818833\pi$
$882$	−546237.	−	1.15836e6i	−0.702173	−	1.48904i
$883$	−912730.			−1.17063			−0.585317	−	0.810805i	$-0.699030\pi$
$883$	−912730.			−1.17063			−0.585317	+	0.810805i	$0.699030\pi$
$884$	−1.68981e6	−	975611.i	−2.16238	−	1.24845i
$885$	171029.	+	53520.9i	0.218366	+	0.0683340i
$886$	−688335.	−	1.19223e6i	−0.876864	−	1.51877i
$887$	366299.	−	211483.i	0.465573	−	0.268799i	−0.248811	−	0.968552i	$-0.580040\pi$
$887$	366299.	−	211483.i	0.465573	−	0.268799i	0.714385	+	0.699753i	$0.246707\pi$
$888$	3.36249e6	−	753042.i	4.26417	−	0.954978i
$889$	748.423	−	1296.31i	0.000946986	−	0.00164023i
$890$		−	1.21255e6i		−	1.53080i
$891$	−301135.	+	112550.i	−0.379320	+	0.141772i
$892$	1.29734e6			1.63051
$893$	−94958.1	−	54824.1i	−0.119077	−	0.0687493i
$894$	286393.	+	1.27880e6i	0.358334	+	1.60003i
$895$	−114353.	−	198065.i	−0.142759	−	0.247265i
$896$	−1.95810e6	+	1.13051e6i	−2.43904	+	1.40818i
$897$	−31271.2	+	99929.1i	−0.0388651	+	0.124196i
$898$	−1.04584e6	+	1.81145e6i	−1.29692	+	2.24633i
$899$		−	83031.7i		−	0.102737i
$900$	−430972.	+	203229.i	−0.532065	+	0.250900i
$901$	−495796.			−0.610736
$902$	−195072.	−	112625.i	−0.239763	−	0.138427i
$903$	299565.	−	275690.i	0.367381	−	0.338100i
$904$	1.55908e6	+	2.70040e6i	1.90779	+	3.30439i
$905$	−158324.	+	91408.1i	−0.193307	+	0.111606i
$906$	1.19953e6	+	1.30342e6i	1.46135	+	1.58791i
$907$	354817.	−	614562.i	0.431311	−	0.747052i	−0.565676	−	0.824628i	$-0.691385\pi$
$907$	354817.	−	614562.i	0.431311	−	0.747052i	0.996986	+	0.0775755i	$0.0247179\pi$
$908$		−	3.51443e6i		−	4.26268i
$909$	902978.	+	75084.6i	1.09282	+	0.0908705i
$910$	−313833.			−0.378980
$911$	1.13050e6	+	652696.i	1.36218	+	0.786455i	0.989914	−	0.141671i	$-0.0452474\pi$
$911$	1.13050e6	+	652696.i	1.36218	+	0.786455i	0.372267	+	0.928126i	$0.378581\pi$
$912$	−1.83921e6	−	575552.i	−2.21127	−	0.691983i
$913$	−35921.4	−	62217.8i	−0.0430935	−	0.0746402i
$914$	−2.25431e6	+	1.30153e6i	−2.69850	+	1.55798i
$915$	105437.	−	23613.0i	0.125936	−	0.0282038i
$916$	649569.	−	1.12509e6i	0.774166	−	1.34089i
$917$			436397.i			0.518970i
$918$	1.36190e6	−	188253.i	1.61607	−	0.223386i
$919$	−397330.			−0.470458			−0.235229	−	0.971940i	$-0.575584\pi$
$919$	−397330.			−0.470458			−0.235229	+	0.971940i	$0.575584\pi$
$920$	159150.	+	91885.1i	0.188031	+	0.108560i
$921$	−235425.	−	1.05122e6i	−0.277545	−	1.23929i
$922$	−744927.	−	1.29025e6i	−0.876298	−	1.51779i
$923$	−1.12553e6	+	649826.i	−1.32116	+	0.762770i
$924$	−125491.	+	401015.i	−0.146984	+	0.469695i
$925$	97015.2	−	168035.i	0.113385	−	0.196389i
$926$			1.72291e6i			2.00928i
$927$	745889.	+	517506.i	0.867990	+	0.602221i
$928$	716108.			0.831539
$929$	600385.	+	346633.i	0.695663	+	0.401641i	0.805730	−	0.592283i	$-0.201773\pi$
$929$	600385.	+	346633.i	0.695663	+	0.401641i	−0.110067	+	0.993924i	$0.535107\pi$
$930$	383692.	−	353112.i	0.443626	−	0.408269i
$931$	−176801.	−	306229.i	−0.203979	−	0.353302i
$932$	2.96662e6	−	1.71278e6i	3.41531	−	1.97183i
$933$	298545.	+	324400.i	0.342963	+	0.372664i
$934$	−476683.	+	825639.i	−0.546432	+	0.946447i
$935$			130104.i			0.148822i
$936$	−1.98829e6	+	2.86575e6i	−2.26949	+	3.27105i
$937$	595074.			0.677785			0.338892	−	0.940825i	$-0.389948\pi$
$937$	595074.			0.677785			0.338892	+	0.940825i	$0.389948\pi$
$938$	1.10184e6	+	636150.i	1.25232	+	0.723026i
$939$	−1.03435e6	−	323684.i	−1.17311	−	0.367105i
$940$	162423.	+	281326.i	0.183820	+	0.318386i
$941$	−493476.	+	284909.i	−0.557297	+	0.321756i	−0.752060	−	0.659095i	$-0.770940\pi$
$941$	−493476.	+	284909.i	−0.557297	+	0.321756i	0.194763	+	0.980850i	$0.437606\pi$
$942$	1.30417e6	−	292075.i	1.46972	−	0.329149i
$943$	19288.9	−	33409.3i	0.0216912	−	0.0375703i
$944$		−	2.14735e6i		−	2.40968i
$945$	130271.	−	101304.i	0.145876	−	0.113439i
$946$	869311.			0.971389
$947$	1.04595e6	+	603878.i	1.16630	+	0.673363i	0.952806	−	0.303581i	$-0.0981824\pi$
$947$	1.04595e6	+	603878.i	1.16630	+	0.673363i	0.213494	+	0.976944i	$0.431516\pi$
$948$	79714.3	+	355940.i	0.0886992	+	0.396060i
$949$	−429909.	−	744625.i	−0.477358	−	0.826809i
$950$	−152669.	+	88143.7i	−0.169163	+	0.0976661i
$951$	−195271.	+	624000.i	−0.215912	+	0.689959i
$952$	593021.	−	1.02714e6i	0.654329	−	1.13333i
$953$		−	709602.i		−	0.781321i	−0.920535	−	0.390660i	$-0.872247\pi$
$953$		−	709602.i		−	0.781321i	0.920535	−	0.390660i	$-0.127753\pi$
$954$	−111274.	+	1.33820e6i	−0.122263	+	1.47036i
$955$	15646.4			0.0171556
$956$	−976148.	−	563579.i	−1.06807	−	0.616650i
$957$	41286.6	−	37996.0i	0.0450801	−	0.0414872i
$958$	1.53029e6	+	2.65054e6i	1.66741	+	2.88804i
$959$	526487.	−	303967.i	0.572467	−	0.330514i
$960$	1.73091e6	+	1.88081e6i	1.87816	+	2.04081i
$961$	248829.	−	430985.i	0.269435	−	0.466676i
$962$		−	2.15198e6i		−	2.32535i
$963$	110804.	+	234973.i	0.119482	+	0.253376i
$964$	−685311.			−0.737452
$965$	−393676.	−	227289.i	−0.422751	−	0.244075i
$966$	−92030.9	−	28799.6i	−0.0986233	−	0.0308626i
$967$	119639.	+	207222.i	0.127944	+	0.221606i	0.922880	−	0.385088i	$-0.125829\pi$
$967$	119639.	+	207222.i	0.127944	+	0.221606i	−0.794936	+	0.606694i	$0.792495\pi$
$968$	2.61458e6	−	1.50953e6i	2.79030	−	1.61098i
$969$	370424.	−	82958.0i	0.394504	−	0.0883508i
$970$	−467524.	+	809776.i	−0.496890	+	0.860639i
$971$		−	908467.i		−	0.963542i	−0.876297	−	0.481771i	$-0.839994\pi$
$971$		−	908467.i		−	0.963542i	0.876297	−	0.481771i	$-0.160006\pi$
$972$	−151085.	−	2.77476e6i	−0.159915	−	2.93692i
$973$	−268009.			−0.283089
$974$	1.74629e6	+	1.00822e6i	1.84077	+	1.06277i
$975$	42922.6	+	191658.i	0.0451519	+	0.201612i
$976$	−647343.	−	1.12123e6i	−0.679571	−	1.17705i
$977$	86363.0	−	49861.7i	0.0904770	−	0.0522369i	−0.454079	−	0.890962i	$-0.650032\pi$
$977$	86363.0	−	49861.7i	0.0904770	−	0.0522369i	0.544556	+	0.838725i	$0.316698\pi$
$978$	−1.02176e6	+	3.26511e6i	−1.06825	+	3.41366i
$979$	−334595.	+	579536.i	−0.349104	+	0.604666i
$980$			1.04759e6i			1.09079i
$981$	−587181.	+	276891.i	−0.610146	+	0.287720i
$982$	−399184.			−0.413953
$983$	−904799.	−	522386.i	−0.936365	−	0.540611i	−0.0475459	−	0.998869i	$-0.515140\pi$
$983$	−904799.	−	522386.i	−0.936365	−	0.540611i	−0.888819	+	0.458259i	$0.848473\pi$
$984$	945588.	−	870223.i	0.976589	−	0.898753i
$985$	23164.4	+	40121.9i	0.0238753	+	0.0413532i
$986$	−207811.	+	119980.i	−0.213754	+	0.123411i
$987$	−76186.3	−	82784.3i	−0.0782064	−	0.0849794i
$988$	−729557.	+	1.26363e6i	−0.747386	+	1.29451i
$989$			148884.i			0.152214i
$990$	351161.	+	29199.9i	0.358291	+	0.0297927i
$991$	231947.			0.236179			0.118090	−	0.993003i	$-0.462323\pi$
$991$	231947.			0.236179			0.118090	+	0.993003i	$0.462323\pi$
$992$	−3.18079e6	−	1.83643e6i	−3.23230	−	1.86617i
$993$	−265750.	−	83162.1i	−0.269510	−	0.0843387i
$994$	−598465.	−	1.03657e6i	−0.605712	−	1.04912i
$995$	210436.	−	121495.i	0.212557	−	0.122720i
$996$	605996.	−	135715.i	0.610874	−	0.136808i
$997$	−486492.	+	842629.i	−0.489424	+	0.847708i	−0.999926	−	0.0121689i	$-0.996126\pi$
$997$	−486492.	+	842629.i	−0.489424	+	0.847708i	0.510502	+	0.859877i	$0.329460\pi$
$998$			1.52141e6i			1.52751i
$999$	694649.	+	893280.i	0.696040	+	0.895069i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.5.i.a.11.16	✓	32
3.2	odd	2		135.5.i.a.116.1		32
9.2	odd	6		405.5.c.b.161.32		32
9.4	even	3		135.5.i.a.71.1		32
9.5	odd	6	inner	45.5.i.a.41.16	yes	32
9.7	even	3		405.5.c.b.161.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.5.i.a.11.16	✓	32	1.1	even	1	trivial
45.5.i.a.41.16	yes	32	9.5	odd	6	inner
135.5.i.a.71.1		32	9.4	even	3
135.5.i.a.116.1		32	3.2	odd	2
405.5.c.b.161.1		32	9.7	even	3
405.5.c.b.161.32		32	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.i (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(6.87716 + 3.97053i) q^{2} +(-1.96687 - 8.78245i) q^{3} +(23.5302 + 40.7555i) q^{4} +(9.68246 - 5.59017i) q^{5} +(21.3445 - 68.2078i) q^{6} +(10.1236 - 17.5346i) q^{7} +246.652i q^{8} +(-73.2629 + 34.5478i) q^{9} +88.7837 q^{10} +(-42.4341 - 24.4994i) q^{11} +(311.652 - 286.813i) q^{12} +(-87.2913 - 151.193i) q^{13} +(139.243 - 80.3920i) q^{14} +(-68.1395 - 74.0406i) q^{15} +(-602.856 + 1044.18i) q^{16} -237.493i q^{17} +(-641.013 - 53.3017i) q^{18} -177.596 q^{19} +(455.660 + 263.075i) q^{20} +(-173.908 - 54.4218i) q^{21} +(-194.551 - 336.972i) q^{22} +(57.7120 - 33.3200i) q^{23} +(2166.21 - 485.132i) q^{24} +(62.5000 - 108.253i) q^{25} -1386.37i q^{26} +(447.513 + 575.477i) q^{27} +952.840 q^{28} +(-110.189 - 63.6179i) q^{29} +(-174.626 - 779.739i) q^{30} +(326.291 + 565.152i) q^{31} +(-4874.16 + 2814.10i) q^{32} +(-131.702 + 420.863i) q^{33} +(942.972 - 1633.28i) q^{34} -226.370i q^{35} +(-3131.90 - 2172.95i) q^{36} +1552.24 q^{37} +(-1221.35 - 705.149i) q^{38} +(-1156.15 + 1064.01i) q^{39} +(1378.83 + 2388.20i) q^{40} +(501.340 - 289.449i) q^{41} +(-979.911 - 1064.77i) q^{42} +(-1117.07 + 1934.83i) q^{43} -2305.90i q^{44} +(-516.237 + 744.060i) q^{45} +529.192 q^{46} +(534.686 + 308.701i) q^{47} +(10356.2 + 3240.80i) q^{48} +(995.526 + 1724.30i) q^{49} +(859.645 - 496.316i) q^{50} +(-2085.77 + 467.117i) q^{51} +(4107.96 - 7115.20i) q^{52} -2087.62i q^{53} +(792.668 + 5734.50i) q^{54} -547.822 q^{55} +(4324.94 + 2497.00i) q^{56} +(349.307 + 1559.73i) q^{57} +(-505.193 - 875.021i) q^{58} +(-1542.38 + 890.492i) q^{59} +(1414.23 - 4519.25i) q^{60} +(-536.896 + 929.932i) q^{61} +5182.19i q^{62} +(-135.902 + 1634.38i) q^{63} -25402.4 q^{64} +(-1690.39 - 975.946i) q^{65} +(-2576.78 + 2371.41i) q^{66} +(3956.55 + 6852.95i) q^{67} +(9679.13 - 5588.25i) q^{68} +(-406.143 - 441.317i) q^{69} +(898.810 - 1556.78i) q^{70} -7444.34i q^{71} +(-8521.29 - 18070.4i) q^{72} +4925.00 q^{73} +(10675.0 + 6163.23i) q^{74} +(-1073.66 - 335.984i) q^{75} +(-4178.86 - 7238.00i) q^{76} +(-859.172 + 496.043i) q^{77} +(-12175.7 + 2726.80i) q^{78} +(-430.602 + 745.825i) q^{79} +13480.3i q^{80} +(4173.90 - 5062.14i) q^{81} +4597.06 q^{82} +(1269.78 + 733.110i) q^{83} +(-1874.11 - 8368.27i) q^{84} +(-1327.63 - 2299.51i) q^{85} +(-15364.6 + 8870.76i) q^{86} +(-341.993 + 1092.86i) q^{87} +(6042.82 - 10466.5i) q^{88} -13657.3i q^{89} +(-6504.55 + 3067.28i) q^{90} -3534.80 q^{91} +(2715.95 + 1568.05i) q^{92} +(4321.65 - 3977.21i) q^{93} +(2451.41 + 4245.97i) q^{94} +(-1719.56 + 992.791i) q^{95} +(34301.5 + 37272.1i) q^{96} +(-5265.88 + 9120.77i) q^{97} +15811.1i q^{98} +(3955.25 + 328.888i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 8 q^{3} + 128 q^{4} + 98 q^{6} - 26 q^{7} - 220 q^{9} - 738 q^{11} - 214 q^{12} + 10 q^{13} + 1998 q^{14} - 50 q^{15} - 1024 q^{16} - 2504 q^{18} + 508 q^{19} - 1620 q^{21} + 672 q^{22} + 1998 q^{23}+ \cdots + 53512 q^{99}+O(q^{100}) \) 32 * q - 8 * q^3 + 128 * q^4 + 98 * q^6 - 26 * q^7 - 220 * q^9 - 738 * q^11 - 214 * q^12 + 10 * q^13 + 1998 * q^14 - 50 * q^15 - 1024 * q^16 - 2504 * q^18 + 508 * q^19 - 1620 * q^21 + 672 * q^22 + 1998 * q^23 + 4164 * q^24 + 2000 * q^25 + 2158 * q^27 - 1664 * q^28 - 270 * q^29 + 2000 * q^30 - 1472 * q^31 - 6048 * q^32 - 1354 * q^33 - 594 * q^34 + 4498 * q^36 + 2068 * q^37 - 7164 * q^38 - 4616 * q^39 + 1650 * q^40 - 13428 * q^41 - 10230 * q^42 + 568 * q^43 - 100 * q^45 + 5724 * q^46 + 12528 * q^47 + 25844 * q^48 - 1674 * q^49 + 1454 * q^51 + 1534 * q^52 + 8456 * q^54 + 21294 * q^56 - 12512 * q^57 - 8190 * q^58 - 4374 * q^59 - 5050 * q^60 - 4478 * q^61 + 5604 * q^63 - 37216 * q^64 - 8550 * q^65 - 19472 * q^66 + 12838 * q^67 + 65736 * q^68 + 8706 * q^69 + 2400 * q^70 - 36372 * q^72 + 29236 * q^73 - 20628 * q^74 + 1000 * q^75 + 6190 * q^76 - 31806 * q^77 - 42430 * q^78 - 3512 * q^79 - 3088 * q^81 + 34692 * q^82 - 43074 * q^83 - 19350 * q^84 - 4350 * q^85 - 10746 * q^86 + 69622 * q^87 - 16128 * q^88 - 26750 * q^90 - 48904 * q^91 + 27036 * q^92 + 27030 * q^93 + 5118 * q^94 + 6300 * q^95 + 53566 * q^96 + 23266 * q^97 + 53512 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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