LMFDB - Embedded newform 45.5.i.a.11.14

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			11.14
Character	$\chi$	$=$	45.11
Dual form			45.5.i.a.41.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(5.22878 + 3.01884i) q^{2} +(8.75515 - 2.08503i) q^{3} +(10.2268 + 17.7133i) q^{4} +(-9.68246 + 5.59017i) q^{5} +(52.0731 + 15.5282i) q^{6} +(-8.13139 + 14.0840i) q^{7} +26.8889i q^{8} +(72.3053 - 36.5095i) q^{9} -67.5033 q^{10} +(-53.9512 - 31.1487i) q^{11} +(126.469 + 133.759i) q^{12} +(-63.3690 - 109.758i) q^{13} +(-85.0345 + 49.0947i) q^{14} +(-73.1157 + 69.1310i) q^{15} +(82.4550 - 142.816i) q^{16} +349.293i q^{17} +(488.285 + 27.3778i) q^{18} -545.481 q^{19} +(-198.040 - 114.339i) q^{20} +(-41.8260 + 140.262i) q^{21} +(-188.066 - 325.739i) q^{22} +(540.867 - 312.270i) q^{23} +(56.0641 + 235.416i) q^{24} +(62.5000 - 108.253i) q^{25} -765.202i q^{26} +(556.920 - 470.405i) q^{27} -332.631 q^{28} +(-683.122 - 394.401i) q^{29} +(-591.001 + 140.746i) q^{30} +(533.568 + 924.167i) q^{31} +(1234.86 - 712.947i) q^{32} +(-537.296 - 160.222i) q^{33} +(-1054.46 + 1826.38i) q^{34} -181.823i q^{35} +(1386.15 + 907.389i) q^{36} -1044.60 q^{37} +(-2852.20 - 1646.72i) q^{38} +(-783.654 - 828.824i) q^{39} +(-150.313 - 260.350i) q^{40} +(1317.17 - 760.469i) q^{41} +(-642.126 + 607.131i) q^{42} +(-1268.27 + 2196.70i) q^{43} -1274.20i q^{44} +(-495.999 + 757.701i) q^{45} +3770.77 q^{46} +(3084.58 + 1780.88i) q^{47} +(424.130 - 1422.30i) q^{48} +(1068.26 + 1850.28i) q^{49} +(653.597 - 377.355i) q^{50} +(728.287 + 3058.12i) q^{51} +(1296.12 - 2244.94i) q^{52} +2043.49i q^{53} +(4332.09 - 778.391i) q^{54} +696.506 q^{55} +(-378.702 - 218.644i) q^{56} +(-4775.77 + 1137.34i) q^{57} +(-2381.26 - 4124.47i) q^{58} +(2269.90 - 1310.53i) q^{59} +(-1972.27 - 588.132i) q^{60} +(-1478.31 + 2560.51i) q^{61} +6443.02i q^{62} +(-73.7436 + 1315.22i) q^{63} +5970.53 q^{64} +(1227.13 + 708.487i) q^{65} +(-2325.72 - 2459.78i) q^{66} +(-3511.86 - 6082.72i) q^{67} +(-6187.13 + 3572.14i) q^{68} +(4084.28 - 3861.69i) q^{69} +(548.895 - 950.714i) q^{70} +3791.96i q^{71} +(981.699 + 1944.21i) q^{72} -2842.71 q^{73} +(-5461.97 - 3153.47i) q^{74} +(321.486 - 1078.09i) q^{75} +(-5578.51 - 9662.26i) q^{76} +(877.395 - 506.565i) q^{77} +(-1595.47 - 6699.46i) q^{78} +(-2204.91 + 3819.02i) q^{79} +1843.75i q^{80} +(3895.11 - 5279.66i) q^{81} +9182.92 q^{82} +(-7467.39 - 4311.30i) q^{83} +(-2912.23 + 693.545i) q^{84} +(-1952.61 - 3382.02i) q^{85} +(-13263.0 + 7657.39i) q^{86} +(-6803.17 - 2028.71i) q^{87} +(837.554 - 1450.69i) q^{88} -5695.97i q^{89} +(-4880.84 + 2464.51i) q^{90} +2061.11 q^{91} +(11062.6 + 6387.02i) q^{92} +(6598.38 + 6978.71i) q^{93} +(10752.4 + 18623.7i) q^{94} +(5281.60 - 3049.33i) q^{95} +(9324.88 - 8816.68i) q^{96} +(8427.69 - 14597.2i) q^{97} +12899.6i q^{98} +(-5038.18 - 282.488i) 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 $

$2$	5.22878	+	3.01884i	1.30719	+	0.754709i	0.981627	−	0.190809i	$-0.0611112\pi$
$2$	5.22878	+	3.01884i	1.30719	+	0.754709i	0.325568	+	0.945519i	$0.394445\pi$
$3$	8.75515	−	2.08503i	0.972794	−	0.231670i
$3$	8.75515	−	2.08503i	0.972794	−	0.231670i
$4$	10.2268	+	17.7133i	0.639172	+	1.10708i
$5$	−9.68246	+	5.59017i	−0.387298	+	0.223607i
$5$	−9.68246	+	5.59017i	−0.387298	+	0.223607i
$6$	52.0731	+	15.5282i	1.44648	+	0.431339i
$7$	−8.13139	+	14.0840i	−0.165947	+	0.287428i	−0.936991	−	0.349353i	$-0.886401\pi$
$7$	−8.13139	+	14.0840i	−0.165947	+	0.287428i	0.771044	+	0.636781i	$0.219735\pi$
$8$			26.8889i			0.420139i
$9$	72.3053	−	36.5095i	0.892658	−	0.450734i
$10$	−67.5033			−0.675033
$11$	−53.9512	−	31.1487i	−0.445877	−	0.257427i	0.260210	−	0.965552i	$-0.416208\pi$
$11$	−53.9512	−	31.1487i	−0.445877	−	0.257427i	−0.706087	+	0.708125i	$0.749541\pi$
$12$	126.469	+	133.759i	0.878260	+	0.928883i
$13$	−63.3690	−	109.758i	−0.374964	−	0.649457i	0.615357	−	0.788248i	$-0.289012\pi$
$13$	−63.3690	−	109.758i	−0.374964	−	0.649457i	−0.990322	+	0.138791i	$0.955678\pi$
$14$	−85.0345	+	49.0947i	−0.433849	+	0.250483i
$15$	−73.1157	+	69.1310i	−0.324959	+	0.307249i
$16$	82.4550	−	142.816i	0.322090	−	0.557876i
$17$			349.293i			1.20863i	0.796746	+	0.604314i	$0.206553\pi$
$17$			349.293i			1.20863i	−0.796746	+	0.604314i	$0.793447\pi$
$18$	488.285	+	27.3778i	1.50705	+	0.0844995i
$19$	−545.481			−1.51103			−0.755514	−	0.655132i	$-0.772613\pi$
$19$	−545.481			−1.51103			−0.755514	+	0.655132i	$0.772613\pi$
$20$	−198.040	−	114.339i	−0.495101	−	0.285847i
$21$	−41.8260	+	140.262i	−0.0948436	+	0.318053i
$22$	−188.066	−	325.739i	−0.388566	−	0.673015i
$23$	540.867	−	312.270i	1.02243	−	0.590302i	0.107626	−	0.994191i	$-0.465675\pi$
$23$	540.867	−	312.270i	1.02243	−	0.590302i	0.914808	+	0.403889i	$0.132342\pi$
$24$	56.0641	+	235.416i	0.0973335	+	0.408709i
$25$	62.5000	−	108.253i	0.100000	−	0.173205i
$26$		−	765.202i		−	1.13196i
$27$	556.920	−	470.405i	0.763951	−	0.645274i
$28$	−332.631			−0.424274
$29$	−683.122	−	394.401i	−0.812274	−	0.468966i	0.0354713	−	0.999371i	$-0.488707\pi$
$29$	−683.122	−	394.401i	−0.812274	−	0.468966i	−0.847745	+	0.530404i	$0.822040\pi$
$30$	−591.001	+	140.746i	−0.656668	+	0.156385i
$31$	533.568	+	924.167i	0.555222	+	0.961672i	0.997886	+	0.0649848i	$0.0206999\pi$
$31$	533.568	+	924.167i	0.555222	+	0.961672i	−0.442665	+	0.896687i	$0.645967\pi$
$32$	1234.86	−	712.947i	1.20592	−	0.696238i
$33$	−537.296	−	160.222i	−0.493385	−	0.147128i
$34$	−1054.46	+	1826.38i	−0.912163	+	1.57991i
$35$		−	181.823i		−	0.148427i
$36$	1386.15	+	907.389i	1.06956	+	0.700146i
$37$	−1044.60			−0.763037			−0.381518	−	0.924361i	$-0.624599\pi$
$37$	−1044.60			−0.763037			−0.381518	+	0.924361i	$0.624599\pi$
$38$	−2852.20	−	1646.72i	−1.97521	−	1.14039i
$39$	−783.654	−	828.824i	−0.515223	−	0.544920i
$40$	−150.313	−	260.350i	−0.0939459	−	0.162719i
$41$	1317.17	−	760.469i	0.783564	−	0.452391i	−0.0541282	−	0.998534i	$-0.517238\pi$
$41$	1317.17	−	760.469i	0.783564	−	0.452391i	0.837692	+	0.546143i	$0.183905\pi$
$42$	−642.126	+	607.131i	−0.364017	+	0.344178i
$43$	−1268.27	+	2196.70i	−0.685921	+	1.18805i	0.287225	+	0.957863i	$0.407267\pi$
$43$	−1268.27	+	2196.70i	−0.685921	+	1.18805i	−0.973146	+	0.230187i	$0.926066\pi$
$44$		−	1274.20i		−	0.658162i
$45$	−495.999	+	757.701i	−0.244938	+	0.374173i
$46$	3770.77			1.78203
$47$	3084.58	+	1780.88i	1.39637	+	0.806193i	0.994010	−	0.109289i	$-0.0348574\pi$
$47$	3084.58	+	1780.88i	1.39637	+	0.806193i	0.402358	+	0.915482i	$0.368191\pi$
$48$	424.130	−	1422.30i	0.184084	−	0.617317i
$49$	1068.26	+	1850.28i	0.444923	+	0.770630i
$50$	653.597	−	377.355i	0.261439	−	0.150942i
$51$	728.287	+	3058.12i	0.280003	+	1.17575i
$52$	1296.12	−	2244.94i	0.479334	−	0.830230i
$53$			2043.49i			0.727479i	0.931501	+	0.363740i	$0.118500\pi$
$53$			2043.49i			0.727479i	−0.931501	+	0.363740i	$0.881500\pi$
$54$	4332.09	−	778.391i	1.48563	−	0.266938i
$55$	696.506			0.230250
$56$	−378.702	−	218.644i	−0.120760	−	0.0697206i
$57$	−4775.77	+	1137.34i	−1.46992	+	0.350060i
$58$	−2381.26	−	4124.47i	−0.707867	−	1.22606i
$59$	2269.90	−	1310.53i	0.652084	−	0.376481i	−0.137170	−	0.990547i	$-0.543801\pi$
$59$	2269.90	−	1310.53i	0.652084	−	0.376481i	0.789254	+	0.614067i	$0.210467\pi$
$60$	−1972.27	−	588.132i	−0.547853	−	0.163370i
$61$	−1478.31	+	2560.51i	−0.397288	+	0.688123i	−0.993390	−	0.114786i	$-0.963382\pi$
$61$	−1478.31	+	2560.51i	−0.397288	+	0.688123i	0.596102	+	0.802908i	$0.296715\pi$
$62$			6443.02i			1.67612i
$63$	−73.7436	+	1315.22i	−0.0185799	+	0.331373i
$64$	5970.53			1.45765
$65$	1227.13	+	708.487i	0.290446	+	0.167689i
$66$	−2325.72	−	2459.78i	−0.533912	−	0.564687i
$67$	−3511.86	−	6082.72i	−0.782325	−	1.35503i	−0.930584	−	0.366079i	$-0.880700\pi$
$67$	−3511.86	−	6082.72i	−0.782325	−	1.35503i	0.148258	−	0.988949i	$-0.452633\pi$
$68$	−6187.13	+	3572.14i	−1.33805	+	0.772522i
$69$	4084.28	−	3861.69i	0.857862	−	0.811110i
$70$	548.895	−	950.714i	0.112019	−	0.194023i
$71$			3791.96i			0.752225i	0.926574	+	0.376112i	$0.122739\pi$
$71$			3791.96i			0.752225i	−0.926574	+	0.376112i	$0.877261\pi$
$72$	981.699	+	1944.21i	0.189371	+	0.375040i
$73$	−2842.71			−0.533442			−0.266721	−	0.963774i	$-0.585940\pi$
$73$	−2842.71			−0.533442			−0.266721	+	0.963774i	$0.585940\pi$
$74$	−5461.97	−	3153.47i	−0.997438	−	0.575871i
$75$	321.486	−	1078.09i	0.0571530	−	0.191660i
$76$	−5578.51	−	9662.26i	−0.965808	−	1.67283i
$77$	877.395	−	506.565i	0.147984	−	0.0854384i
$78$	−1595.47	−	6699.46i	−0.262240	−	1.10116i
$79$	−2204.91	+	3819.02i	−0.353294	+	0.611924i	−0.986825	−	0.161794i	$-0.948272\pi$
$79$	−2204.91	+	3819.02i	−0.353294	+	0.611924i	0.633530	+	0.773718i	$0.281605\pi$
$80$			1843.75i			0.288086i
$81$	3895.11	−	5279.66i	0.593677	−	0.804704i
$82$	9182.92			1.36569
$83$	−7467.39	−	4311.30i	−1.08396	−	0.625824i	−0.151997	−	0.988381i	$-0.548570\pi$
$83$	−7467.39	−	4311.30i	−1.08396	−	0.625824i	−0.931962	+	0.362557i	$0.881904\pi$
$84$	−2912.23	+	693.545i	−0.412732	+	0.0982916i
$85$	−1952.61	−	3382.02i	−0.270257	−	0.468100i
$86$	−13263.0	+	7657.39i	−1.79326	+	1.03534i
$87$	−6803.17	−	2028.71i	−0.898821	−	0.268028i
$88$	837.554	−	1450.69i	0.108155	−	0.187330i
$89$		−	5695.97i		−	0.719097i	−0.933126	−	0.359549i	$-0.882931\pi$
$89$		−	5695.97i		−	0.719097i	0.933126	−	0.359549i	$-0.117069\pi$
$90$	−4880.84	+	2464.51i	−0.602573	+	0.304260i
$91$	2061.11			0.248896
$92$	11062.6	+	6387.02i	1.30702	+	0.754610i
$93$	6598.38	+	6978.71i	0.762907	+	0.806881i
$94$	10752.4	+	18623.7i	1.21688	+	2.10770i
$95$	5281.60	−	3049.33i	0.585219	−	0.337876i
$96$	9324.88	−	8816.68i	1.01181	−	0.956671i
$97$	8427.69	−	14597.2i	0.895705	−	1.55141i	0.0627748	−	0.998028i	$-0.480005\pi$
$97$	8427.69	−	14597.2i	0.895705	−	1.55141i	0.832930	−	0.553378i	$-0.186662\pi$
$98$			12899.6i			1.34315i
$99$	−5038.18	−	282.488i	−0.514047	−	0.0288223i
$100$	2556.69			0.255669
$101$	16818.7	+	9710.26i	1.64873	+	0.951893i	0.977579	+	0.210570i	$0.0675320\pi$
$101$	16818.7	+	9710.26i	1.64873	+	0.951893i	0.671148	+	0.741323i	$0.265801\pi$
$102$	−5423.90	+	18188.8i	−0.521329	+	1.74825i
$103$	878.619	+	1521.81i	0.0828182	+	0.143445i	0.904459	−	0.426560i	$-0.140275\pi$
$103$	878.619	+	1521.81i	0.0828182	+	0.143445i	−0.821641	+	0.570005i	$0.806941\pi$
$104$	2951.28	−	1703.92i	0.272862	−	0.157537i
$105$	−379.107	−	1591.89i	−0.0343861	−	0.144389i
$106$	−6168.96	+	10685.0i	−0.549035	+	0.950957i
$107$		−	16228.2i		−	1.41744i	−0.705492	−	0.708718i	$-0.749274\pi$
$107$		−	16228.2i		−	1.41744i	0.705492	−	0.708718i	$-0.250726\pi$
$108$	14027.9	+	5054.16i	1.20267	+	0.433313i
$109$	−2691.31			−0.226522			−0.113261	−	0.993565i	$-0.536130\pi$
$109$	−2691.31			−0.226522			−0.113261	+	0.993565i	$0.536130\pi$
$110$	3641.88	+	2102.64i	0.300982	+	0.173772i
$111$	−9145.60	+	2178.02i	−0.742278	+	0.176773i
$112$	1340.95	+	2322.59i	0.106899	+	0.185155i
$113$	14444.2	−	8339.34i	1.13119	−	0.653093i	0.186956	−	0.982368i	$-0.440138\pi$
$113$	14444.2	−	8339.34i	1.13119	−	0.653093i	0.944234	+	0.329276i	$0.106805\pi$
$114$	−28404.9	−	8470.35i	−2.18567	−	0.651766i
$115$	−3491.28	+	6047.08i	−0.263991	+	0.457246i
$116$		−	16133.8i		−	1.19900i
$117$	−8589.13	−	5622.54i	−0.627448	−	0.410734i
$118$	15825.1			1.13653
$119$	−4919.44	−	2840.24i	−0.347394	−	0.200568i
$120$	−1858.85	−	1966.00i	−0.129087	−	0.136528i
$121$	−5380.02	−	9318.46i	−0.367462	−	0.636463i
$122$	−15459.5	+	8925.55i	−1.03867	+	0.599674i
$123$	9946.42	−	9404.36i	0.657441	−	0.621611i
$124$	−10913.3	+	18902.5i	−0.709765	+	1.22935i
$125$			1397.54i			0.0894427i
$126$	−4356.02	+	6654.37i	−0.274378	+	0.419147i
$127$	−16025.5			−0.993585			−0.496792	−	0.867869i	$-0.665489\pi$
$127$	−16025.5			−0.993585			−0.496792	+	0.867869i	$0.665489\pi$
$128$	11460.8	+	6616.90i	0.699512	+	0.403863i
$129$	−6523.68	+	21876.9i	−0.392025	+	1.31464i
$130$	4277.61	+	7409.04i	0.253113	+	0.438405i
$131$	−7913.28	+	4568.73i	−0.461120	+	0.266228i	−0.712515	−	0.701657i	$-0.752444\pi$
$131$	−7913.28	+	4568.73i	−0.461120	+	0.266228i	0.251395	+	0.967885i	$0.419111\pi$
$132$	−2656.75	−	11155.8i	−0.152476	−	0.640256i
$133$	4435.52	−	7682.55i	0.250750	−	0.434312i
$134$		−	42406.9i		−	2.36171i
$135$	−2762.72	+	7667.95i	−0.151589	+	0.420738i
$136$	−9392.11			−0.507791
$137$	−9448.55	−	5455.12i	−0.503412	−	0.290645i	0.226709	−	0.973962i	$-0.427203\pi$
$137$	−9448.55	−	5455.12i	−0.503412	−	0.290645i	−0.730122	+	0.683317i	$0.760537\pi$
$138$	33013.6	−	7862.16i	1.73355	−	0.412842i
$139$	−1492.85	−	2585.69i	−0.0772656	−	0.133828i	0.824804	−	0.565419i	$-0.191286\pi$
$139$	−1492.85	−	2585.69i	−0.0772656	−	0.133828i	−0.902069	+	0.431591i	$0.857952\pi$
$140$	3220.69	−	1859.46i	0.164321	−	0.0948706i
$141$	30719.1	+	9160.45i	1.54515	+	0.460764i
$142$	−11447.3	+	19827.3i	−0.567711	+	0.983304i
$143$			7895.45i			0.386104i
$144$	747.784	−	13336.8i	0.0360621	−	0.643169i
$145$	8819.07			0.419456
$146$	−14863.9	−	8581.69i	−0.697313	−	0.402594i
$147$	13210.7	+	13972.1i	0.611351	+	0.646589i
$148$	−10682.8	−	18503.2i	−0.487712	−	0.844742i
$149$	7444.84	−	4298.28i	0.335338	−	0.193608i	−0.322870	−	0.946443i	$-0.604648\pi$
$149$	7444.84	−	4298.28i	0.335338	−	0.193608i	0.658209	+	0.752836i	$0.271314\pi$
$150$	4935.55	−	4666.57i	0.219358	−	0.207403i
$151$	1396.71	−	2419.18i	0.0612567	−	0.106100i	−0.833771	−	0.552111i	$-0.813823\pi$
$151$	1396.71	−	2419.18i	0.0612567	−	0.106100i	0.895027	+	0.446011i	$0.147156\pi$
$152$		−	14667.4i		−	0.634842i
$153$	12752.5	+	25255.8i	0.544770	+	1.07889i
$154$	6116.94			0.257925
$155$	−10332.5	−	5965.47i	−0.430073	−	0.248303i
$156$	6666.94	−	22357.3i	0.273954	−	0.918690i
$157$	1211.96	+	2099.17i	0.0491686	+	0.0851626i	0.889562	−	0.456814i	$-0.151009\pi$
$157$	1211.96	+	2099.17i	0.0491686	+	0.0851626i	−0.840394	+	0.541977i	$0.817676\pi$
$158$	−23058.0	+	13312.5i	−0.923649	+	0.533269i
$159$	4260.73	+	17891.1i	0.168535	+	0.707688i
$160$	−7970.99	+	13806.2i	−0.311367	+	0.539303i
$161$			10156.8i			0.391835i
$162$	36305.1	−	15847.5i	1.38337	−	0.603851i
$163$	−36203.9			−1.36264			−0.681319	−	0.731987i	$-0.738593\pi$
$163$	−36203.9			−1.36264			−0.681319	+	0.731987i	$0.738593\pi$
$164$	26940.8	+	15554.3i	1.00166	+	0.578311i
$165$	6098.02	−	1452.24i	0.223986	−	0.0533420i
$166$	−26030.2	−	45085.7i	−0.944630	−	1.63615i
$167$	−9987.09	+	5766.05i	−0.358102	+	0.206750i	−0.668248	−	0.743939i	$-0.732955\pi$
$167$	−9987.09	+	5766.05i	−0.358102	+	0.206750i	0.310146	+	0.950689i	$0.399622\pi$
$168$	−3771.47	−	1124.65i	−0.133627	−	0.0398475i
$169$	6249.25	−	10824.0i	0.218804	−	0.378979i
$170$		−	23578.4i		−	0.815863i
$171$	−39441.2	+	19915.3i	−1.34883	+	0.681073i
$172$	−51881.1			−1.75369
$173$	−12991.8	−	7500.81i	−0.434087	−	0.250620i	0.266999	−	0.963697i	$-0.413968\pi$
$173$	−12991.8	−	7500.81i	−0.434087	−	0.250620i	−0.701086	+	0.713077i	$0.747301\pi$
$174$	−29448.0	−	31145.3i	−0.972650	−	1.02871i
$175$	1016.42	+	1760.50i	0.0331893	+	0.0574856i
$176$	−8897.08	+	5136.73i	−0.287225	+	0.165829i
$177$	17140.9	−	16206.7i	0.547124	−	0.517307i
$178$	17195.2	−	29783.0i	0.542709	−	0.940000i
$179$			46584.0i			1.45389i	0.686698	+	0.726943i	$0.259060\pi$
$179$			46584.0i			1.45389i	−0.686698	+	0.726943i	$0.740940\pi$
$180$	−18493.8	−	1036.94i	−0.570797	−	0.0320042i
$181$	39784.3			1.21438			0.607190	−	0.794557i	$-0.292297\pi$
$181$	39784.3			1.21438			0.607190	+	0.794557i	$0.292297\pi$
$182$	10777.1	+	6222.16i	0.325356	+	0.187844i
$183$	−7604.08	+	25499.9i	−0.227062	+	0.761442i
$184$	8396.59	+	14543.3i	0.248009	+	0.429564i
$185$	10114.3	−	5839.48i	0.295523	−	0.170620i
$186$	13433.9	+	56409.6i	0.388308	+	1.63052i
$187$	10880.0	−	18844.8i	0.311134	−	0.538900i
$188$			72850.6i			2.06119i
$189$	2096.63	+	11668.7i	0.0586947	+	0.326662i
$190$	36821.8			1.01999
$191$	−40294.4	−	23264.0i	−1.10453	−	0.637702i	−0.167125	−	0.985936i	$-0.553448\pi$
$191$	−40294.4	−	23264.0i	−1.10453	−	0.637702i	−0.937408	+	0.348234i	$0.886782\pi$
$192$	52272.9	−	12448.7i	1.41799	−	0.337693i
$193$	−11908.7	−	20626.6i	−0.319707	−	0.553748i	0.660720	−	0.750632i	$-0.270251\pi$
$193$	−11908.7	−	20626.6i	−0.319707	−	0.553748i	−0.980427	+	0.196884i	$0.936918\pi$
$194$	88133.0	−	50883.6i	2.34172	−	1.35199i
$195$	12221.0	+	3644.29i	0.321393	+	0.0958394i
$196$	−21849.7	+	37844.8i	−0.568765	+	0.985131i
$197$			13917.2i			0.358608i	0.983794	+	0.179304i	$0.0573846\pi$
$197$			13917.2i			0.358608i	−0.983794	+	0.179304i	$0.942615\pi$
$198$	−25490.7	−	16686.5i	−0.650208	−	0.425633i
$199$	12235.9			0.308980			0.154490	−	0.987994i	$-0.450627\pi$
$199$	12235.9			0.308980			0.154490	+	0.987994i	$0.450627\pi$
$200$	2910.81	+	1680.55i	0.0727702	+	0.0420139i
$201$	−43429.5	−	45932.8i	−1.07496	−	1.13692i
$202$	58627.4	+	101546.i	1.43681	+	2.48862i
$203$	11109.5	−	6414.05i	0.269588	−	0.155647i
$204$	−46721.2	+	44175.0i	−1.12267	+	1.06149i
$205$	−8502.30	+	14726.4i	−0.202315	+	0.350420i
$206$			10609.6i			0.250015i
$207$	27706.8	−	42325.6i	0.646614	−	0.987784i
$208$	−20900.3			−0.483089
$209$	29429.4	+	16991.0i	0.673733	+	0.388980i
$210$	2823.39	−	9468.11i	0.0640225	−	0.214696i
$211$	2985.97	+	5171.85i	0.0670687	+	0.116166i	0.897610	−	0.440791i	$-0.145302\pi$
$211$	2985.97	+	5171.85i	0.0670687	+	0.116166i	−0.830541	+	0.556957i	$0.811969\pi$
$212$	−36196.9	+	20898.3i	−0.805377	+	0.464985i
$213$	7906.36	+	33199.2i	0.174268	+	0.731760i
$214$	48990.4	−	84853.8i	1.06975	−	1.85286i
$215$		−	28359.3i		−	0.613506i
$216$	12648.7	+	14975.0i	0.271105	+	0.320965i
$217$	−17354.6			−0.368549
$218$	−14072.3	−	8124.62i	−0.296108	−	0.170958i
$219$	−24888.4	+	5927.14i	−0.518930	+	0.123583i
$220$	7123.00	+	12337.4i	0.147169	+	0.254905i
$221$	38337.8	−	22134.4i	0.784952	−	0.453192i
$222$	−54395.4	−	16220.7i	−1.10371	−	0.329128i
$223$	−5834.69	+	10106.0i	−0.117330	+	0.203221i	−0.918709	−	0.394936i	$-0.870767\pi$
$223$	−5834.69	+	10106.0i	−0.117330	+	0.203221i	0.801379	+	0.598157i	$0.204100\pi$
$224$			23189.0i			0.462153i
$225$	566.813	−	10109.1i	0.0111963	−	0.199686i
$226$	100700.			1.97158
$227$	−55933.5	−	32293.2i	−1.08548	−	0.626700i	−0.153108	−	0.988209i	$-0.548928\pi$
$227$	−55933.5	−	32293.2i	−1.08548	−	0.626700i	−0.932369	+	0.361509i	$0.882262\pi$
$228$	−68986.8	−	72963.2i	−1.32708	−	1.40357i
$229$	38197.4	+	66159.8i	0.728387	+	1.26160i	0.957564	+	0.288219i	$0.0930632\pi$
$229$	38197.4	+	66159.8i	0.728387	+	1.26160i	−0.229177	+	0.973385i	$0.573603\pi$
$230$	−36510.3	+	21079.2i	−0.690176	+	0.398473i
$231$	6625.53	−	6264.44i	0.124164	−	0.117397i
$232$	10605.0	−	18368.4i	0.197031	−	0.341268i
$233$		−	22219.4i		−	0.409280i	−0.978837	−	0.204640i	$-0.934398\pi$
$233$		−	22219.4i		−	0.409280i	0.978837	−	0.204640i	$-0.0656024\pi$
$234$	−27937.2	−	55328.2i	−0.510212	−	1.01045i
$235$	−39821.7			−0.721081
$236$	46427.5	+	26804.9i	0.833588	+	0.481272i
$237$	−11341.6	+	38033.4i	−0.201918	+	0.677124i
$238$	−17148.4	−	29702.0i	−0.302741	−	0.524362i
$239$	29169.0	−	16840.7i	0.510653	−	0.294826i	−0.222449	−	0.974944i	$-0.571405\pi$
$239$	29169.0	−	16840.7i	0.510653	−	0.294826i	0.733102	+	0.680119i	$0.238072\pi$
$240$	3844.27	+	16142.3i	0.0667408	+	0.280248i
$241$	18651.1	−	32304.6i	0.321122	−	0.556199i	−0.659598	−	0.751619i	$-0.729273\pi$
$241$	18651.1	−	32304.6i	0.321122	−	0.556199i	0.980720	+	0.195419i	$0.0626068\pi$
$242$		−	64965.6i		−	1.10931i
$243$	23094.1	−	54345.6i	0.391100	−	0.920348i
$244$	−60473.2			−1.01574
$245$	−20686.8	−	11943.5i	−0.344636	−	0.198976i
$246$	80397.9	−	19146.7i	1.32854	−	0.316390i
$247$	34566.6	+	59871.1i	0.566582	+	0.981349i
$248$	−24849.8	+	14347.0i	−0.404036	+	0.233270i
$249$	−74367.3	−	22176.3i	−1.19945	−	0.357677i
$250$	−4218.95	+	7307.44i	−0.0675033	+	0.116919i
$251$			106662.i			1.69303i	0.532367	+	0.846513i	$0.321303\pi$
$251$			106662.i			1.69303i	−0.532367	+	0.846513i	$0.678697\pi$
$252$	−24051.0	+	12144.2i	−0.378732	+	0.191235i
$253$	−38907.2			−0.607840
$254$	−83794.0	−	48378.5i	−1.29881	−	0.749868i
$255$	−24147.0	−	25538.8i	−0.371350	−	0.392754i
$256$	−7813.55	−	13533.5i	−0.119225	−	0.206504i
$257$	−5856.75	+	3381.40i	−0.0886729	+	0.0511953i	−0.543681	−	0.839292i	$-0.682970\pi$
$257$	−5856.75	+	3381.40i	−0.0886729	+	0.0511953i	0.455008	+	0.890487i	$0.349636\pi$
$258$	−100154.	+	94695.3i	−1.50462	+	1.42262i
$259$	8494.02	−	14712.1i	0.126623	−	0.219318i
$260$			28982.1i			0.428729i
$261$	−63792.7	−	3576.82i	−0.936462	−	0.0525069i
$262$	−55169.1			−0.803698
$263$	15319.3	+	8844.61i	0.221476	+	0.127870i	0.606634	−	0.794981i	$-0.292519\pi$
$263$	15319.3	+	8844.61i	0.221476	+	0.127870i	−0.385157	+	0.922851i	$0.625853\pi$
$264$	4308.19	−	14447.3i	0.0618140	−	0.207290i
$265$	−11423.5	−	19786.0i	−0.162669	−	0.281751i
$266$	46384.7	−	26780.2i	0.655559	−	0.378487i
$267$	−11876.3	−	49869.1i	−0.166593	−	0.699534i
$268$	71829.9	−	124413.i	1.00008	−	1.73219i
$269$			72325.1i			0.999503i	0.866169	+	0.499752i	$0.166575\pi$
$269$			72325.1i			0.999503i	−0.866169	+	0.499752i	$0.833425\pi$
$270$	−37593.9	+	31753.9i	−0.515692	+	0.435581i
$271$	−47538.3			−0.647299			−0.323650	−	0.946177i	$-0.604910\pi$
$271$	−47538.3			−0.647299			−0.323650	+	0.946177i	$0.604910\pi$
$272$	49884.8	+	28801.0i	0.674264	+	0.389287i
$273$	18045.3	−	4297.48i	0.242125	−	0.0576618i
$274$	−32936.2	−	57047.2i	−0.438705	−	0.759860i
$275$	−6743.89	+	3893.59i	−0.0891755	+	0.0514855i
$276$	110172.	+	32853.4i	1.44628	+	0.431282i
$277$	62454.8	−	108175.i	0.813966	−	1.40983i	−0.0961016	−	0.995372i	$-0.530637\pi$
$277$	62454.8	−	108175.i	0.813966	−	1.40983i	0.910068	−	0.414459i	$-0.136029\pi$
$278$		−	18026.7i		−	0.233252i
$279$	72320.7	+	47341.9i	0.929082	+	0.608187i
$280$	4889.03			0.0623600
$281$	87208.4	+	50349.8i	1.10445	+	0.637654i	0.937386	−	0.348292i	$-0.113238\pi$
$281$	87208.4	+	50349.8i	1.10445	+	0.637654i	0.167063	+	0.985946i	$0.446572\pi$
$282$	132970.	+	140634.i	1.67207	+	1.76845i
$283$	56446.9	+	97768.9i	0.704802	+	1.22075i	0.966763	+	0.255675i	$0.0822976\pi$
$283$	56446.9	+	97768.9i	0.704802	+	1.22075i	−0.261961	+	0.965079i	$0.584369\pi$
$284$	−67168.1	+	38779.5i	−0.832772	+	0.480801i
$285$	39883.3	−	37709.7i	0.491022	−	0.464262i
$286$	−23835.1	+	41283.5i	−0.291396	+	0.504714i
$287$			24734.7i			0.300291i
$288$	63257.7	−	96634.0i	0.762655	−	1.16505i
$289$	−38484.9			−0.460781
$290$	46113.0	+	26623.3i	0.548311	+	0.316568i
$291$	43350.1	−	145372.i	0.511922	−	1.71671i
$292$	−29071.7	−	50353.7i	−0.340962	−	0.590563i
$293$	−22307.8	+	12879.4i	−0.259849	+	0.150024i	−0.624266	−	0.781212i	$-0.714602\pi$
$293$	−22307.8	+	12879.4i	−0.259849	+	0.150024i	0.364417	+	0.931236i	$0.381268\pi$
$294$	26896.1	+	112938.i	0.311168	+	1.30661i
$295$	−14652.2	+	25378.3i	−0.168367	+	0.291621i
$296$		−	28088.0i		−	0.320581i
$297$	−44699.0	+	8031.53i	−0.506740	+	0.0910511i
$298$	51903.3			0.584470
$299$	−68548.4	−	39576.4i	−0.766752	−	0.442685i
$300$	22384.2	−	5330.77i	0.248713	−	0.0592308i
$301$	−20625.6	−	35724.5i	−0.227653	−	0.394306i
$302$	14606.2	−	8432.91i	0.160149	−	0.0924620i
$303$	167496.	+	49947.4i	1.82440	+	0.544036i
$304$	−44977.7	+	77903.6i	−0.486687	+	0.842966i
$305$		−	33056.0i		−	0.355345i
$306$	−9562.90	+	170555.i	−0.102128	+	1.82146i
$307$	112735.			1.19614			0.598070	−	0.801444i	$-0.295934\pi$
$307$	112735.			1.19614			0.598070	+	0.801444i	$0.295934\pi$
$308$	17945.8	+	10361.0i	0.189174	+	0.109220i
$309$	10865.5	+	11491.7i	0.113797	+	0.120356i
$310$	−36017.6	−	62384.3i	−0.374793	−	0.649160i
$311$	−42334.4	+	24441.8i	−0.437696	+	0.252704i	−0.702620	−	0.711565i	$-0.747987\pi$
$311$	−42334.4	+	24441.8i	−0.437696	+	0.252704i	0.264924	+	0.964269i	$0.414653\pi$
$312$	22286.1	−	21071.6i	0.228942	−	0.216465i
$313$	−72030.4	+	124760.i	−0.735236	+	1.27347i	0.219383	+	0.975639i	$0.429595\pi$
$313$	−72030.4	+	124760.i	−0.735236	+	1.27347i	−0.954620	+	0.297828i	$0.903738\pi$
$314$			14634.8i			0.148432i
$315$	−6638.28	−	13146.8i	−0.0669013	−	0.132495i
$316$	−90196.3			−0.903264
$317$	70598.9	+	40760.3i	0.702553	+	0.405619i	0.808298	−	0.588774i	$-0.200389\pi$
$317$	70598.9	+	40760.3i	0.702553	+	0.405619i	−0.105744	+	0.994393i	$0.533722\pi$
$318$	−31731.7	+	106411.i	−0.313790	+	1.05228i
$319$	24570.1	+	42556.7i	0.241450	+	0.418203i
$320$	−57809.4	+	33376.3i	−0.564545	+	0.325940i
$321$	−33836.3	−	142081.i	−0.328377	−	1.37887i
$322$	−30661.6	+	53107.4i	−0.295721	+	0.512204i
$323$		−	190533.i		−	1.82627i
$324$	133354.	+	15001.4i	1.27033	+	0.142903i
$325$	−15842.2			−0.149986
$326$	−189302.	−	109294.i	−1.78123	−	1.02839i
$327$	−23562.8	+	5611.45i	−0.220359	+	0.0524783i
$328$	20448.1	+	35417.2i	0.190067	+	0.329205i
$329$	−50163.8	+	28962.1i	−0.463445	+	0.267570i
$330$	36269.3	+	10815.5i	0.333051	+	0.0993159i
$331$	−78040.0	+	135169.i	−0.712297	+	1.23373i	0.251696	+	0.967806i	$0.419012\pi$
$331$	−78040.0	+	135169.i	−0.712297	+	1.23373i	−0.963993	+	0.265928i	$0.914322\pi$
$332$		−	176363.i		−	1.60004i
$333$	−75529.9	+	38137.7i	−0.681131	+	0.343927i
$334$	−69627.1			−0.624145
$335$	68006.9	+	39263.8i	0.605987	+	0.349867i
$336$	16582.9	+	17538.7i	0.146886	+	0.155353i
$337$	16589.0	+	28733.1i	0.146070	+	0.253001i	0.929772	−	0.368137i	$-0.120004\pi$
$337$	16589.0	+	28733.1i	0.146070	+	0.253001i	−0.783702	+	0.621138i	$0.786671\pi$
$338$	65351.9	−	37730.9i	0.572038	−	0.330266i
$339$	109073.	−	103129.i	0.949113	−	0.897387i
$340$	39937.7	−	69174.2i	0.345482	−	0.598393i
$341$		−	66479.8i		−	0.571717i
$342$	−266350.	−	14934.1i	−2.27720	−	0.127681i
$343$	−73792.7			−0.627228
$344$	−59066.9	−	34102.3i	−0.499146	−	0.288182i
$345$	−17958.4	+	60222.5i	−0.150879	+	0.505965i
$346$	−45287.4	−	78440.1i	−0.378291	−	0.655219i
$347$	−5362.61	+	3096.10i	−0.0445366	+	0.0257132i	−0.522103	−	0.852882i	$-0.674852\pi$
$347$	−5362.61	+	3096.10i	−0.0445366	+	0.0257132i	0.477566	+	0.878596i	$0.341519\pi$
$348$	−33639.4	−	141253.i	−0.277773	−	1.16638i
$349$	61876.7	−	107174.i	0.508014	−	0.879907i	−0.491943	−	0.870628i	$-0.663713\pi$
$349$	61876.7	−	107174.i	0.508014	−	0.879907i	0.999957	−	0.00927908i	$-0.00295367\pi$
$350$			12273.7i			0.100193i
$351$	−86922.3	−	31317.6i	−0.705532	−	0.254199i
$352$	−88829.6			−0.716922
$353$	5984.88	+	3455.37i	0.0480293	+	0.0277297i	0.523822	−	0.851828i	$-0.324506\pi$
$353$	5984.88	+	3455.37i	0.0480293	+	0.0277297i	−0.475793	+	0.879557i	$0.657839\pi$
$354$	138551.	−	32995.8i	1.10561	−	0.263301i
$355$	−21197.7	−	36715.5i	−0.168203	−	0.291335i
$356$	100894.	−	58251.3i	0.796097	−	0.459627i
$357$	−48992.4	−	14609.6i	−0.384408	−	0.114631i
$358$	−140629.	+	243577.i	−1.09726	+	1.90051i
$359$		−	135358.i		−	1.05026i	−0.851022	−	0.525129i	$-0.824017\pi$
$359$		−	135358.i		−	1.05026i	0.851022	−	0.525129i	$-0.175983\pi$
$360$	−20373.7	−	13336.9i	−0.157205	−	0.102908i
$361$	167229.			1.28321
$362$	208023.	+	120102.i	1.58743	+	0.916504i
$363$	−66532.1	−	70367.0i	−0.504915	−	0.534018i
$364$	21078.5	+	36509.0i	0.159088	+	0.275548i
$365$	27524.5	−	15891.3i	0.206601	−	0.119281i
$366$	−116740.	+	110378.i	−0.871482	+	0.823987i
$367$	56209.3	−	97357.4i	0.417327	−	0.722831i	−0.578343	−	0.815794i	$-0.696300\pi$
$367$	56209.3	−	97357.4i	0.417327	−	0.722831i	0.995670	+	0.0929626i	$0.0296337\pi$
$368$		−	102993.i		−	0.760521i
$369$	67474.1	−	103075.i	0.495546	−	0.757009i
$370$	70513.7			0.515075
$371$	−28780.5	−	16616.4i	−0.209098	−	0.120723i
$372$	−56135.7	+	188249.i	−0.405652	+	1.36033i
$373$	33609.0	+	58212.4i	0.241567	+	0.418406i	0.961161	−	0.275989i	$-0.0890054\pi$
$373$	33609.0	+	58212.4i	0.241567	+	0.418406i	−0.719594	+	0.694395i	$0.755672\pi$
$374$	113779.	−	65690.1i	0.813425	−	0.469631i
$375$	2913.92	+	12235.7i	0.0207212	+	0.0870094i
$376$	−47885.9	+	82940.8i	−0.338713	+	0.586668i
$377$			99971.1i			0.703382i
$378$	−24263.1	+	67342.4i	−0.169810	+	0.471309i
$379$	57143.2			0.397820			0.198910	−	0.980018i	$-0.436260\pi$
$379$	57143.2			0.397820			0.198910	+	0.980018i	$0.436260\pi$
$380$	108027.	+	62369.6i	0.748112	+	0.431922i
$381$	−140306.	+	33413.7i	−0.966554	+	0.230184i
$382$	−140460.	−	243285.i	−0.962559	−	1.66720i
$383$	−14086.6	+	8132.89i	−0.0960302	+	0.0554431i	−0.547246	−	0.836972i	$-0.684324\pi$
$383$	−14086.6	+	8132.89i	−0.0960302	+	0.0554431i	0.451216	+	0.892415i	$0.350990\pi$
$384$	114137.	+	34035.8i	0.774044	+	0.230820i
$385$	−5663.56	+	9809.58i	−0.0382092	+	0.0661803i
$386$		−	143802.i		−	0.965142i
$387$	−11501.9	+	205137.i	−0.0767978	+	1.36969i
$388$	344752.			2.29004
$389$	−91607.0	−	52889.3i	−0.605382	−	0.349517i	0.165774	−	0.986164i	$-0.446988\pi$
$389$	−91607.0	−	52889.3i	−0.605382	−	0.349517i	−0.771156	+	0.636646i	$0.780321\pi$
$390$	52899.2	+	55948.3i	0.347792	+	0.367839i
$391$	109074.	+	188921.i	0.713456	+	1.23574i
$392$	−49752.0	+	28724.3i	−0.323771	+	0.186930i
$393$	−59756.0	+	56499.4i	−0.386898	+	0.365813i
$394$	−42013.8	+	72770.1i	−0.270645	+	0.468771i
$395$		−	49303.3i		−	0.315996i
$396$	−46520.4	−	92131.5i	−0.296656	−	0.587513i
$397$	−214103.			−1.35845			−0.679223	−	0.733932i	$-0.737683\pi$
$397$	−214103.			−1.35845			−0.679223	+	0.733932i	$0.737683\pi$
$398$	63978.9	+	36938.2i	0.403897	+	0.233190i
$399$	22815.3	−	76510.1i	0.143311	−	0.480588i
$400$	−10306.9	−	17852.0i	−0.0644179	−	0.111575i
$401$	−47556.9	+	27457.0i	−0.295750	+	0.170751i	−0.640532	−	0.767932i	$-0.721286\pi$
$401$	−47556.9	+	27457.0i	−0.295750	+	0.170751i	0.344782	+	0.938683i	$0.387953\pi$
$402$	−88419.7	−	371279.i	−0.547138	−	2.29746i
$403$	67623.3	−	117127.i	0.416377	−	0.721185i
$404$			397218.i			2.43369i
$405$	−8200.08	+	72894.4i	−0.0499929	+	0.444411i
$406$	77451.9			0.469872
$407$	56357.2	+	32537.9i	0.340221	+	0.196427i
$408$	−82229.3	+	19582.8i	−0.493977	+	0.117640i
$409$	−91908.1	−	159189.i	−0.549423	−	0.951629i	−0.998314	−	0.0580425i	$-0.981514\pi$
$409$	−91908.1	−	159189.i	−0.549423	−	0.951629i	0.448891	−	0.893587i	$-0.351819\pi$
$410$	−88913.3	+	51334.1i	−0.528931	+	0.305378i
$411$	−94097.5	−	28059.9i	−0.557050	−	0.166113i
$412$	−17970.8	+	31126.4i	−0.105870	+	0.183373i
$413$			42625.7i			0.249903i
$414$	272647.	−	137669.i	1.59074	−	0.803221i
$415$	96403.6			0.559754
$416$	−156504.	−	90357.5i	−0.904353	−	0.522128i
$417$	−18461.3	−	19525.5i	−0.106167	−	0.112287i
$418$	102586.	+	177685.i	0.587134	+	1.01695i
$419$	−215753.	+	124565.i	−1.22893	+	0.709525i	−0.966807	−	0.255508i	$-0.917757\pi$
$419$	−215753.	+	124565.i	−1.22893	+	0.709525i	−0.262127	+	0.965033i	$0.584424\pi$
$420$	24320.5	−	22995.1i	0.137872	−	0.130358i
$421$	82342.8	−	142622.i	0.464581	−	0.804678i	−0.534602	−	0.845104i	$-0.679538\pi$
$421$	82342.8	−	142622.i	0.464581	−	0.804678i	0.999183	+	0.0404264i	$0.0128716\pi$
$422$			36056.6i			0.202470i
$423$	288050.	+	16150.8i	1.60986	+	0.0902639i
$424$	−54947.1			−0.305642
$425$	37812.1	+	21830.8i	0.209340	+	0.120863i
$426$	−58882.4	+	197459.i	−0.324464	+	1.08807i
$427$	−24041.4	−	41640.9i	−0.131857	−	0.228383i
$428$	287455.	−	165962.i	1.56921	−	0.905986i
$429$	16462.2	+	69125.8i	0.0894488	+	0.375600i
$430$	85612.2	−	148285.i	0.463019	−	0.801972i
$431$			124194.i			0.668568i	0.942472	+	0.334284i	$0.108494\pi$
$431$			124194.i			0.668568i	−0.942472	+	0.334284i	$0.891506\pi$
$432$	−21260.6	−	118324.i	−0.113922	−	0.634026i
$433$	−126928.			−0.676991			−0.338495	−	0.940968i	$-0.609918\pi$
$433$	−126928.			−0.676991			−0.338495	+	0.940968i	$0.609918\pi$
$434$	−90743.3	−	52390.7i	−0.481765	−	0.278147i
$435$	77212.3	−	18388.0i	0.408045	−	0.0971754i
$436$	−27523.3	−	47671.8i	−0.144787	−	0.250778i
$437$	−295033.	+	170337.i	−1.54493	+	0.891964i
$438$	−148029.	−	44142.3i	−0.771611	−	0.230095i
$439$	−124233.	+	215177.i	−0.644624	+	1.11652i	0.339764	+	0.940511i	$0.389653\pi$
$439$	−124233.	+	215177.i	−0.644624	+	1.11652i	−0.984388	+	0.176011i	$0.943680\pi$
$440$			18728.3i			0.0967370i
$441$	144794.	+	94783.6i	0.744514	+	0.487367i
$442$	267280.			1.36811
$443$	−204173.	−	117879.i	−1.04038	−	0.600661i	−0.120436	−	0.992721i	$-0.538429\pi$
$443$	−204173.	−	117879.i	−1.04038	−	0.600661i	−0.919940	+	0.392060i	$0.871763\pi$
$444$	−132110.	−	139724.i	−0.670145	−	0.708772i
$445$	31841.4	+	55151.0i	0.160795	+	0.278505i
$446$	−61016.6	+	35227.9i	−0.306746	+	0.177100i
$447$	56218.7	−	53154.8i	0.281362	−	0.266028i
$448$	−48548.7	+	84088.8i	−0.241892	+	0.418969i
$449$			185711.i			0.921183i	0.887612	+	0.460592i	$0.152363\pi$
$449$			185711.i			0.921183i	−0.887612	+	0.460592i	$0.847637\pi$
$450$	33481.5	−	51147.3i	0.165341	−	0.252579i
$451$	−94750.5			−0.465831
$452$	295434.	+	170569.i	1.44605	+	0.834877i
$453$	7184.38	−	24092.5i	0.0350101	−	0.117405i
$454$	−194976.	−	337708.i	−0.945953	−	1.63844i
$455$	−19956.6	+	11522.0i	−0.0963971	+	0.0556549i
$456$	−30581.9	−	128415.i	−0.147074	−	0.617571i
$457$	120748.	−	209142.i	0.578160	−	1.00140i	−0.417530	−	0.908663i	$-0.637104\pi$
$457$	120748.	−	209142.i	0.578160	−	1.00140i	0.995690	−	0.0927396i	$-0.0295624\pi$
$458$			461247.i			2.19888i
$459$	164309.	+	194529.i	0.779896	+	0.923333i
$460$	−142818.			−0.674943
$461$	300274.	+	173363.i	1.41292	+	0.815747i	0.995662	−	0.0930432i	$-0.0296595\pi$
$461$	300274.	+	173363.i	1.41292	+	0.815747i	0.417253	+	0.908790i	$0.362993\pi$
$462$	53554.8	−	12754.0i	0.250908	−	0.0597534i
$463$	47718.8	+	82651.4i	0.222601	+	0.385556i	0.955597	−	0.294677i	$-0.0952119\pi$
$463$	47718.8	+	82651.4i	0.222601	+	0.385556i	−0.732996	+	0.680233i	$0.761879\pi$
$464$	−112654.	+	65040.6i	−0.523250	+	0.302098i
$465$	−102901.	−	30685.0i	−0.475897	−	0.141912i
$466$	67076.8	−	116180.i	0.308888	−	0.535009i
$467$		−	144180.i		−	0.661104i	−0.943788	−	0.330552i	$-0.892765\pi$
$467$		−	144180.i		−	0.661104i	0.943788	−	0.330552i	$-0.107235\pi$
$468$	11754.5	−	209642.i	0.0536676	−	0.957164i
$469$	114225.			0.519297
$470$	−208219.	−	120215.i	−0.942594	−	0.544207i
$471$	14987.7	+	15851.6i	0.0675606	+	0.0714548i
$472$	35238.7	+	61035.2i	0.158174	+	0.273966i
$473$	136849.	−	79009.8i	0.611673	−	0.353150i
$474$	−174119.	+	164630.i	−0.774979	+	0.732743i
$475$	−34092.6	+	59050.1i	−0.151103	+	0.261718i
$476$		−	116186.i		−	0.512790i
$477$	74606.7	+	147755.i	0.327900	+	0.649390i
$478$	203358.			0.890031
$479$	−62513.4	−	36092.1i	−0.272459	−	0.157305i	0.357545	−	0.933896i	$-0.383614\pi$
$479$	−62513.4	−	36092.1i	−0.272459	−	0.157305i	−0.630005	+	0.776591i	$0.716947\pi$
$480$	−41001.0	+	137495.i	−0.177956	+	0.596766i
$481$	66195.0	+	114653.i	0.286111	+	0.495560i
$482$	195045.	−	112609.i	0.839538	−	0.484707i
$483$	21177.1	+	88923.9i	0.0907764	+	0.381175i
$484$	110040.	−	190595.i	0.469743	−	0.813620i
$485$			188449.i			0.801143i
$486$	284814.	−	214444.i	1.20584	−	0.907908i
$487$	253468.			1.06872			0.534361	−	0.845256i	$-0.320552\pi$
$487$	253468.			1.06872			0.534361	+	0.845256i	$0.320552\pi$
$488$	−68849.1	−	39750.1i	−0.289107	−	0.166916i
$489$	−316971.	+	75486.2i	−1.32557	+	0.315682i
$490$	−72111.1	−	124900.i	−0.300338	−	0.520200i
$491$	142419.	−	82225.5i	0.590751	−	0.341070i	−0.174644	−	0.984632i	$-0.555877\pi$
$491$	142419.	−	82225.5i	0.590751	−	0.341070i	0.765394	+	0.643562i	$0.222544\pi$
$492$	268302.	+	80007.6i	1.10839	+	0.330522i
$493$	137762.	−	238610.i	0.566806	−	0.981736i
$494$			417404.i			1.71042i
$495$	50361.1	−	25429.1i	0.205535	−	0.103782i
$496$	175981.			0.715325
$497$	−53405.9	−	30833.9i	−0.216211	−	0.124829i
$498$	−321904.	−	340458.i	−1.29798	−	1.37279i
$499$	−160672.	−	278293.i	−0.645268	−	1.11764i	−0.984240	−	0.176840i	$-0.943412\pi$
$499$	−160672.	−	278293.i	−0.645268	−	1.11764i	0.338972	−	0.940797i	$-0.389921\pi$
$500$	−24755.0	+	14292.3i	−0.0990202	+	0.0571693i
$501$	−75416.1	+	71306.0i	−0.300461	+	0.284087i
$502$	−321996.	+	557714.i	−1.27774	+	2.21312i
$503$		−	117404.i		−	0.464032i	−0.972712	−	0.232016i	$-0.925468\pi$
$503$		−	117404.i		−	0.464032i	0.972712	−	0.232016i	$-0.0745321\pi$
$504$	−35364.8	−	1982.88i	−0.139223	−	0.00780613i
$505$	−217128.			−0.851399
$506$	−203437.	−	117455.i	−0.794565	−	0.458742i
$507$	32144.7	−	107796.i	0.125053	−	0.419359i
$508$	−163889.	−	283864.i	−0.635072	−	1.09998i
$509$	213257.	−	123124.i	0.823130	−	0.475234i	−0.0283645	−	0.999598i	$-0.509030\pi$
$509$	213257.	−	123124.i	0.823130	−	0.475234i	0.851495	+	0.524363i	$0.175697\pi$
$510$	−49161.8	−	206433.i	−0.189011	−	0.793667i
$511$	23115.2	−	40036.7i	0.0885230	−	0.153326i
$512$		−	306092.i		−	1.16765i
$513$	−303790.	+	256597.i	−1.15435	+	0.975028i
$514$	−40831.6			−0.154550
$515$	−17014.4	−	9823.25i	−0.0641507	−	0.0370374i
$516$	−454227.	+	108174.i	−1.70598	+	0.406277i
$517$	−110944.	−	192161.i	−0.415073	−	0.718927i
$518$	88826.8	−	51284.2i	0.331043	−	0.191128i
$519$	−129384.	−	38582.5i	−0.480338	−	0.143237i
$520$	−19050.4	+	32996.3i	−0.0704527	+	0.122028i
$521$		−	80937.9i		−	0.298179i	−0.988824	−	0.149089i	$-0.952366\pi$
$521$		−	80937.9i		−	0.298179i	0.988824	−	0.149089i	$-0.0476342\pi$
$522$	−322760.	−	211282.i	−1.18451	−	0.775393i
$523$	−42919.8			−0.156911			−0.0784556	−	0.996918i	$-0.524999\pi$
$523$	−42919.8			−0.156911			−0.0784556	+	0.996918i	$0.524999\pi$
$524$	−161854.	−	93446.7i	−0.589470	−	0.340331i
$525$	12569.6	+	13294.1i	0.0456041	+	0.0482327i
$526$	53400.9	+	92493.0i	0.193009	+	0.334301i
$527$	−322805.	+	186372.i	−1.16230	+	0.671056i
$528$	−67185.0	+	63523.5i	−0.240993	+	0.227859i
$529$	55104.5	−	95443.7i	0.196913	−	0.341064i
$530$		−	137942.i		−	0.491072i
$531$	116279.	−	177631.i	0.412395	−	0.629985i
$532$	181444.			0.641091
$533$	−166935.	−	96380.2i	−0.587617	−	0.339261i
$534$	88448.2	−	296607.i	0.310175	−	1.04016i
$535$	90718.5	+	157129.i	0.316948	+	0.548971i
$536$	163557.	−	94429.9i	0.569299	−	0.328685i
$537$	97128.9	+	407850.i	0.336822	+	1.41433i
$538$	−218338.	+	378172.i	−0.754335	+	1.30655i
$539$		−	133100.i		−	0.458142i
$540$	−164078.	+	29481.6i	−0.562682	+	0.101103i
$541$	−496260.			−1.69557			−0.847783	−	0.530344i	$-0.822063\pi$
$541$	−496260.			−1.69557			−0.847783	+	0.530344i	$0.822063\pi$
$542$	−248567.	−	143510.i	−0.846146	−	0.488523i
$543$	348317.	−	82951.4i	1.18134	−	0.281335i
$544$	249028.	+	431329.i	0.841492	+	1.45751i
$545$	26058.5	−	15044.9i	0.0877316	−	0.0506518i
$546$	107328.	+	32005.4i	0.360022	+	0.107359i
$547$	−296435.	+	513441.i	−0.990730	+	1.71600i	−0.377722	+	0.925919i	$0.623292\pi$
$547$	−296435.	+	513441.i	−0.990730	+	1.71600i	−0.613009	+	0.790076i	$0.710041\pi$
$548$		−	223153.i		−	0.743090i
$549$	−13406.8	+	239110.i	−0.0444816	+	0.793330i
$550$	−47016.4			−0.155426
$551$	372630.	+	215138.i	1.22737	+	0.708622i
$552$	103837.	+	109822.i	0.340779	+	0.360421i
$553$	−35858.0	−	62107.8i	−0.117256	−	0.203094i
$554$	653125.	−	377082.i	2.12803	−	1.22862i
$555$	76376.5	−	72214.0i	0.247955	−	0.234442i
$556$	30534.0	−	52886.4i	0.0987720	−	0.171078i
$557$		−	533085.i		−	1.71825i	−0.511766	−	0.859125i	$-0.671008\pi$
$557$		−	533085.i		−	1.71825i	0.511766	−	0.859125i	$-0.328992\pi$
$558$	235231.	+	465864.i	0.755487	+	1.49621i
$559$	321475.			1.02878
$560$	−25967.3	−	14992.2i	−0.0828040	−	0.0478069i
$561$	55964.5	−	187674.i	0.177822	−	0.596319i
$562$	303996.	+	526536.i	0.962487	+	1.66708i
$563$	392722.	−	226738.i	1.23899	−	0.715332i	0.270104	−	0.962831i	$-0.412942\pi$
$563$	392722.	−	226738.i	1.23899	−	0.715332i	0.968888	+	0.247499i	$0.0796086\pi$
$564$	151896.	+	637818.i	0.477515	+	2.00511i
$565$	−93236.6	+	161491.i	−0.292072	+	0.505883i
$566$			681616.i			2.12768i
$567$	42685.9	+	97789.7i	0.132776	+	0.304177i
$568$	−101962.			−0.316039
$569$	87944.6	+	50774.8i	0.271634	+	0.156828i	0.629630	−	0.776895i	$-0.283206\pi$
$569$	87944.6	+	50774.8i	0.271634	+	0.156828i	−0.357996	+	0.933723i	$0.616540\pi$
$570$	322380.	−	76774.5i	0.992244	−	0.236302i
$571$	170078.	+	294583.i	0.521645	+	0.903516i	0.999683	+	0.0251767i	$0.00801485\pi$
$571$	170078.	+	294583.i	0.521645	+	0.903516i	−0.478038	+	0.878339i	$0.658652\pi$
$572$	−139854.	+	80744.8i	−0.427448	+	0.246787i
$573$	−401290.	−	119665.i	−1.22222	−	0.364466i
$574$	−74669.9	+	129332.i	−0.226632	+	0.392539i
$575$		−	78067.5i		−	0.236121i
$576$	431701.	−	217981.i	1.30118	−	0.657013i
$577$	436433.			1.31089			0.655444	−	0.755244i	$-0.272482\pi$
$577$	436433.			1.31089			0.655444	+	0.755244i	$0.272482\pi$
$578$	−201229.	−	116180.i	−0.602331	−	0.347756i
$579$	−147270.	−	155759.i	−0.439296	−	0.464617i
$580$	90190.5	+	156214.i	0.268105	+	0.464371i
$581$	121441.	−	70113.7i	0.359759	−	0.207707i
$582$	665524.	−	629254.i	1.96480	−	1.85772i
$583$	63652.0	−	110249.i	0.187273	−	0.324366i
$584$		−	76437.4i		−	0.224120i
$585$	114595.	+	6425.27i	0.334852	+	0.0187750i
$586$	−155523.			−0.452898
$587$	−266967.	−	154133.i	−0.774784	−	0.447322i	0.0597946	−	0.998211i	$-0.480955\pi$
$587$	−266967.	−	154133.i	−0.774784	−	0.447322i	−0.834579	+	0.550889i	$0.814289\pi$
$588$	−112390.	+	376894.i	−0.325067	+	1.09010i
$589$	−291051.	−	504116.i	−0.838956	−	1.45311i
$590$	−153226.	+	88465.0i	−0.440178	+	0.254137i
$591$	29017.8	+	121847.i	0.0830787	+	0.348852i
$592$	−86132.2	+	149185.i	−0.245766	+	0.425680i
$593$			394045.i			1.12056i	0.828302	+	0.560282i	$0.189307\pi$
$593$			394045.i			1.12056i	−0.828302	+	0.560282i	$0.810693\pi$
$594$	−257967.	−	92943.9i	−0.731125	−	0.263420i
$595$	63509.7			0.179393
$596$	152273.	+	87915.0i	0.428678	+	0.247497i
$597$	107127.	−	25512.2i	0.300574	−	0.0715813i
$598$	−238950.	−	413873.i	−0.668196	−	1.15735i
$599$	71867.4	−	41492.7i	0.200299	−	0.115643i	−0.396496	−	0.918036i	$-0.629774\pi$
$599$	71867.4	−	41492.7i	0.200299	−	0.115643i	0.596795	+	0.802394i	$0.296441\pi$
$600$	28988.6	+	8644.39i	0.0805238	+	0.0240122i
$601$	−37635.0	+	65185.7i	−0.104194	+	0.180469i	−0.913409	−	0.407044i	$-0.866560\pi$
$601$	−37635.0	+	65185.7i	−0.104194	+	0.180469i	0.809215	+	0.587513i	$0.199893\pi$
$602$		−	249061.i		−	0.687246i
$603$	−476003.	−	311597.i	−1.30911	−	0.856955i
$604$	57135.4			0.156614
$605$	104184.	+	60150.4i	0.284635	+	0.164334i
$606$	725017.	+	766807.i	1.97425	+	2.08805i
$607$	−31183.2	−	54010.9i	−0.0846337	−	0.146590i	0.820601	−	0.571501i	$-0.193639\pi$
$607$	−31183.2	−	54010.9i	−0.0846337	−	0.146590i	−0.905235	+	0.424911i	$0.860305\pi$
$608$	−673594.	+	388900.i	−1.82218	+	1.05204i
$609$	83891.5	−	79319.5i	0.226195	−	0.213868i
$610$	99790.6	−	172842.i	0.268182	−	0.464505i
$611$		−	451410.i		−	1.20918i
$612$	−316945.	+	484174.i	−0.846216	+	1.29270i
$613$	−473707.			−1.26063			−0.630317	−	0.776338i	$-0.717075\pi$
$613$	−473707.			−1.26063			−0.630317	+	0.776338i	$0.717075\pi$
$614$	589467.	+	340329.i	1.56359	+	0.902738i
$615$	−43733.9	+	146659.i	−0.115629	+	0.387757i
$616$	13621.0	+	23592.2i	0.0358960	+	0.0621737i
$617$	159744.	−	92228.3i	0.419618	−	0.242267i	−0.275296	−	0.961360i	$-0.588776\pi$
$617$	159744.	−	92228.3i	0.419618	−	0.242267i	0.694914	+	0.719093i	$0.255442\pi$
$618$	22121.4	+	92888.9i	0.0579209	+	0.243213i
$619$	181793.	−	314874.i	0.474455	−	0.821780i	−0.525117	−	0.851030i	$-0.675979\pi$
$619$	181793.	−	314874.i	0.474455	−	0.821780i	0.999572	+	0.0292498i	$0.00931184\pi$
$620$		−	244030.i		−	0.634833i
$621$	154327.	−	428336.i	0.400183	−	1.11071i
$622$	−295143.			−0.762872
$623$	80221.9	+	46316.1i	0.206689	+	0.119332i
$624$	−182986.	+	43577.8i	−0.469946	+	0.111917i
$625$	−7812.50	−	13531.6i	−0.0200000	−	0.0346410i
$626$	−753262.	+	434896.i	−1.92219	+	1.10978i
$627$	293085.	+	87398.1i	0.745519	+	0.222314i
$628$	−24788.8	+	42935.5i	−0.0628545	+	0.108867i
$629$		−	364871.i		−	0.922227i
$630$	4977.93	−	88781.6i	0.0125420	−	0.223688i
$631$	−765468.			−1.92251			−0.961255	−	0.275661i	$-0.911103\pi$
$631$	−765468.			−1.92251			−0.961255	+	0.275661i	$0.911103\pi$
$632$	−102689.	−	59287.6i	−0.257093	−	0.148433i
$633$	36926.0	+	39054.5i	0.0921564	+	0.0974683i
$634$	246097.	+	426253.i	0.612250	+	1.06045i
$635$	155167.	−	89585.4i	0.384814	−	0.222172i
$636$	−273335.	+	258439.i	−0.675743	+	0.638916i
$637$	135389.	−	234501.i	0.333661	−	0.577917i
$638$			296693.i			0.728897i
$639$	138443.	+	274179.i	0.339054	+	0.671479i
$640$	−147958.			−0.361226
$641$	304245.	+	175656.i	0.740470	+	0.427511i	0.822240	−	0.569140i	$-0.192724\pi$
$641$	304245.	+	175656.i	0.740470	+	0.427511i	−0.0817699	+	0.996651i	$0.526057\pi$
$642$	251995.	−	845054.i	0.611396	−	2.05029i
$643$	−180461.	−	312568.i	−0.436478	−	0.756003i	0.560937	−	0.827859i	$-0.310441\pi$
$643$	−180461.	−	312568.i	−0.436478	−	0.756003i	−0.997415	+	0.0718562i	$0.977108\pi$
$644$	−179909.	+	103871.i	−0.433792	+	0.250450i
$645$	−59130.0	−	248290.i	−0.142131	−	0.596816i
$646$	575188.	−	996256.i	1.37830	−	2.38729i
$647$			148451.i			0.354628i	0.984154	+	0.177314i	$0.0567409\pi$
$647$			148451.i			0.354628i	−0.984154	+	0.177314i	$0.943259\pi$
$648$	141964.	+	104735.i	0.338087	+	0.249427i
$649$	−163285.			−0.387666
$650$	−82835.6	−	47825.1i	−0.196061	−	0.113196i
$651$	−151942.	+	36184.8i	−0.358522	+	0.0853817i
$652$	−370249.	−	641289.i	−0.870960	−	1.50855i
$653$	−333185.	+	192364.i	−0.781374	+	0.451127i	−0.836917	−	0.547330i	$-0.815644\pi$
$653$	−333185.	+	192364.i	−0.781374	+	0.451127i	0.0555430	+	0.998456i	$0.482311\pi$
$654$	−140145.	−	41791.2i	−0.327658	−	0.0977078i
$655$	51080.0	−	88473.2i	0.119061	−	0.206219i
$656$		−	250818.i		−	0.582842i
$657$	−205543.	+	103786.i	−0.476182	+	0.240441i
$658$	−349727.			−0.807751
$659$	−12245.5	−	7069.97i	−0.0281973	−	0.0162797i	0.485835	−	0.874050i	$-0.338516\pi$
$659$	−12245.5	−	7069.97i	−0.0281973	−	0.0162797i	−0.514032	+	0.857771i	$0.671849\pi$
$660$	88086.8	+	93164.1i	0.202219	+	0.213875i
$661$	7485.52	+	12965.3i	0.0171324	+	0.0296743i	0.874465	−	0.485089i	$-0.161213\pi$
$661$	7485.52	+	12965.3i	0.0171324	+	0.0296743i	−0.857332	+	0.514764i	$0.827880\pi$
$662$	−816108.	+	471180.i	−1.86222	+	1.07515i
$663$	289503.	−	273725.i	0.658606	−	0.622713i
$664$	115926.	−	200790.i	0.262933	−	0.455413i
$665$			99181.3i			0.224278i
$666$	−510061.	−	28598.8i	−1.14994	−	0.0644762i
$667$	−492638.			−1.10733
$668$	−204271.	−	117936.i	−0.457777	−	0.264298i
$669$	−30012.3	+	100645.i	−0.0670575	+	0.224874i
$670$	237062.	+	410603.i	0.528095	+	0.914688i
$671$	159513.	−	92094.8i	0.354283	−	0.204546i
$672$	48349.8	+	203023.i	0.107067	+	0.449580i
$673$	236926.	−	410368.i	0.523098	−	0.906033i	−0.476540	−	0.879153i	$-0.658109\pi$
$673$	236926.	−	410368.i	0.523098	−	0.906033i	0.999639	−	0.0268801i	$-0.00855724\pi$
$674$			200318.i			0.440962i
$675$	−16115.3	−	89688.7i	−0.0353696	−	0.196848i
$676$	255638.			0.559413
$677$	583649.	+	336970.i	1.27343	+	0.735214i	0.975632	−	0.219415i	$-0.0704148\pi$
$677$	583649.	+	336970.i	1.27343	+	0.735214i	0.297797	+	0.954629i	$0.403748\pi$
$678$	881647.	−	209963.i	1.91794	−	0.456756i
$679$	137058.	+	237391.i	0.297278	+	0.514901i
$680$	90938.7	−	52503.5i	0.196667	−	0.113546i
$681$	−557039.	−	166109.i	−1.20113	−	0.358178i
$682$	200692.	−	347608.i	0.431480	−	0.747345i
$683$			477490.i			1.02358i	0.859110	+	0.511791i	$0.171018\pi$
$683$			477490.i			1.02358i	−0.859110	+	0.511791i	$0.828982\pi$
$684$	−756120.	−	494964.i	−1.61614	−	1.05794i
$685$	121980.			0.259961
$686$	−385846.	−	222768.i	−0.819909	−	0.473375i
$687$	472369.	+	499596.i	1.00085	+	1.05854i
$688$	209150.	+	362258.i	0.441856	+	0.765317i
$689$	224290.	−	129494.i	0.472467	−	0.272779i
$690$	−275702.	+	260677.i	−0.579085	+	0.547526i
$691$	−210533.	+	364655.i	−0.440925	+	0.763705i	−0.997758	−	0.0669195i	$-0.978683\pi$
$691$	−210533.	+	364655.i	−0.440925	+	0.763705i	0.556833	+	0.830624i	$0.312016\pi$
$692$		−	306836.i		−	0.640758i
$693$	44945.9	−	68660.6i	0.0935888	−	0.142969i
$694$	−37386.5			−0.0776241
$695$	28908.9	+	16690.5i	0.0598496	+	0.0345542i
$696$	54549.7	−	182930.i	0.112609	−	0.377629i
$697$	265627.	+	460079.i	0.546772	+	0.947037i
$698$	647079.	−	373591.i	1.32815	−	0.766806i
$699$	−46328.1	−	194534.i	−0.0948179	−	0.398145i
$700$	−20789.4	+	36008.4i	−0.0424274	+	0.0734864i
$701$		−	350619.i		−	0.713509i	−0.934198	−	0.356755i	$-0.883883\pi$
$701$		−	350619.i		−	0.713509i	0.934198	−	0.356755i	$-0.116117\pi$
$702$	−359955.	−	426157.i	−0.730422	−	0.864759i
$703$	569808.			1.15297
$704$	−322117.	−	185974.i	−0.649932	−	0.375239i
$705$	−348645.	+	83029.5i	−0.701464	+	0.167053i
$706$	20862.4	+	36134.7i	0.0418557	+	0.0724963i
$707$	−273518.	+	157916.i	−0.547202	+	0.315927i
$708$	462369.	+	137879.i	0.922406	+	0.275062i
$709$	−271948.	+	471027.i	−0.540995	+	0.937030i	0.457853	+	0.889028i	$0.348619\pi$
$709$	−271948.	+	471027.i	−0.540995	+	0.937030i	−0.998847	+	0.0480021i	$0.984715\pi$
$710$		−	255970.i		−	0.507776i
$711$	−19996.3	+	356635.i	−0.0395559	+	0.705481i
$712$	153158.			0.302121
$713$	577179.	+	333234.i	1.13535	+	0.655497i
$714$	−212067.	−	224290.i	−0.415984	−	0.439961i
$715$	−44136.9	−	76447.3i	−0.0863355	−	0.149538i
$716$	−825154.	+	476403.i	−1.60957	+	0.929284i
$717$	220266.	−	208261.i	0.428458	−	0.405108i
$718$	408625.	−	707759.i	0.792640	−	1.37289i
$719$		−	29250.5i		−	0.0565816i	−0.999600	−	0.0282908i	$-0.990994\pi$
$719$		−	29250.5i		−	0.0565816i	0.999600	−	0.0282908i	$-0.00900645\pi$
$720$	67314.4	+	133313.i	0.129850	+	0.257162i
$721$	−28577.6			−0.0549736
$722$	874404.	+	504837.i	1.67740	+	0.968449i
$723$	95936.9	−	321720.i	0.183531	−	0.615462i
$724$	406864.	+	704710.i	0.776198	+	1.34441i
$725$	−85390.3	+	49300.1i	−0.162455	+	0.0937933i
$726$	−135455.	−	568783.i	−0.256994	−	1.07913i
$727$	−404768.	+	701080.i	−0.765840	+	1.32647i	0.173962	+	0.984752i	$0.444343\pi$
$727$	−404768.	+	701080.i	−0.765840	+	1.32647i	−0.939802	+	0.341721i	$0.888990\pi$
$728$			55420.9i			0.104571i
$729$	88879.7	−	523956.i	0.167243	−	0.985916i
$730$	191892.			0.360091
$731$	−767294.	−	442998.i	−1.43591	−	0.829023i
$732$	−529452.	+	126088.i	−0.988108	+	0.235317i
$733$	443431.	+	768046.i	0.825313	+	1.42948i	0.901680	+	0.432404i	$0.142334\pi$
$733$	443431.	+	768046.i	0.825313	+	1.42948i	−0.0763676	+	0.997080i	$0.524332\pi$
$734$	587812.	−	339374.i	1.09106	−	0.629921i
$735$	−206019.	−	61434.8i	−0.381357	−	0.113721i
$736$	445264.	−	771220.i	0.821981	−	1.42371i
$737$			437559.i			0.805568i
$738$	663974.	−	335264.i	1.21910	−	0.615565i
$739$	−35945.0			−0.0658188			−0.0329094	−	0.999458i	$-0.510477\pi$
$739$	−35945.0			−0.0658188			−0.0329094	+	0.999458i	$0.510477\pi$
$740$	206872.	+	119438.i	0.377780	+	0.218111i
$741$	427469.	+	452108.i	0.778517	+	0.823390i
$742$	−100324.	−	173767.i	−0.182221	−	0.315616i
$743$	−259434.	+	149785.i	−0.469948	+	0.271325i	−0.716218	−	0.697877i	$-0.754128\pi$
$743$	−259434.	+	149785.i	−0.469948	+	0.271325i	0.246270	+	0.969201i	$0.420795\pi$
$744$	−187650.	+	177423.i	−0.339002	+	0.320527i
$745$	−48056.3	+	83235.9i	−0.0865840	+	0.149968i
$746$			405840.i			0.729251i
$747$	−697335.	−	39099.2i	−1.24968	−	0.0700691i
$748$	445070.			0.795473
$749$	228558.	+	131958.i	0.407411	+	0.235219i
$750$	−21701.3	+	72774.4i	−0.0385802	+	0.129377i
$751$	152670.	+	264432.i	0.270691	+	0.468851i	0.969039	−	0.246908i	$-0.0794145\pi$
$751$	152670.	+	264432.i	0.270691	+	0.468851i	−0.698348	+	0.715759i	$0.746081\pi$
$752$	508677.	−	293685.i	0.899512	−	0.519333i
$753$	222394.	+	933845.i	0.392223	+	1.64697i
$754$	−301796.	+	522727.i	−0.530849	+	0.919458i
$755$			31231.5i			0.0547897i
$756$	−185249.	+	156471.i	−0.324125	+	0.273773i
$757$	403292.			0.703765			0.351883	−	0.936044i	$-0.385542\pi$
$757$	403292.			0.703765			0.351883	+	0.936044i	$0.385542\pi$
$758$	298789.	+	172506.i	0.520028	+	0.300238i
$759$	−340639.	+	81122.7i	−0.591303	+	0.140818i
$760$	81993.2	+	142016.i	0.141955	+	0.245873i
$761$	575835.	−	332459.i	0.994326	−	0.574075i	0.0877617	−	0.996142i	$-0.472029\pi$
$761$	575835.	−	332459.i	0.994326	−	0.574075i	0.906565	+	0.422067i	$0.138695\pi$
$762$	−834499.	−	248848.i	−1.43720	−	0.428572i
$763$	21884.1	−	37904.3i	0.0375906	−	0.0651088i
$764$		−	951661.i		−	1.63041i
$765$	−264660.	−	173249.i	−0.452236	−	0.296039i
$766$	−98207.5			−0.167374
$767$	−287683.	−	166094.i	−0.489016	−	0.282334i
$768$	−96626.5	−	102196.i	−0.163823	−	0.173265i
$769$	−50971.5	−	88285.2i	−0.0861935	−	0.149292i	0.819706	−	0.572785i	$-0.194137\pi$
$769$	−50971.5	−	88285.2i	−0.0861935	−	0.149292i	−0.905899	+	0.423493i	$0.860804\pi$
$770$	−59227.1	+	34194.8i	−0.0998938	+	0.0576737i
$771$	−44226.4	+	41816.2i	−0.0744001	+	0.0703454i
$772$	243576.	−	421886.i	0.408695	−	0.707881i
$773$			160450.i			0.268523i	0.990946	+	0.134262i	$0.0428663\pi$
$773$			160450.i			0.268523i	−0.990946	+	0.134262i	$0.957134\pi$
$774$	−679417.	+	1.03789e6i	−1.13411	+	1.73249i
$775$	133392.			0.222089
$776$	392502.	+	226611.i	0.651806	+	0.376320i
$777$	43691.3	−	146517.i	0.0723691	−	0.242686i
$778$	−319328.	−	553093.i	−0.527568	−	0.913775i
$779$	−718492.	+	414822.i	−1.18399	+	0.683575i
$780$	60428.5	+	253742.i	0.0993236	+	0.417065i
$781$	118115.	−	204581.i	0.193643	−	0.335400i
$782$			1.31710e6i			2.15381i
$783$	−565973.	+	101694.i	−0.923149	+	0.165872i
$784$	352334.			0.573221
$785$	−23469.5	−	13550.1i	−0.0380859	−	0.0219889i
$786$	−483013.	+	115029.i	−0.781833	+	0.186193i
$787$	−517548.	−	896419.i	−0.835605	−	1.44731i	−0.893537	−	0.448989i	$-0.851784\pi$
$787$	−517548.	−	896419.i	−0.835605	−	1.44731i	0.0579327	−	0.998320i	$-0.481549\pi$
$788$	−246519.	+	142328.i	−0.397007	+	0.229212i
$789$	152564.	+	45494.6i	0.245075	+	0.0730813i
$790$	148839.	−	257796.i	0.238485	−	0.413069i
$791$			271242.i			0.433514i
$792$	7595.78	−	135471.i	0.0121094	−	0.215971i
$793$	374716.			0.595875
$794$	−1.11950e6	−	646343.i	−1.77575	−	1.02523i
$795$	−141268.	−	149411.i	−0.223517	−	0.236401i
$796$	125134.	+	216738.i	0.197491	+	0.342065i
$797$	646947.	−	373515.i	1.01848	−	0.588019i	0.104815	−	0.994492i	$-0.466575\pi$
$797$	646947.	−	373515.i	1.01848	−	0.588019i	0.913663	+	0.406473i	$0.133241\pi$
$798$	350268.	−	331179.i	0.550040	−	0.520063i
$799$	−622050.	+	1.07742e6i	−0.974388	+	1.68769i
$800$		−	178237.i		−	0.278495i
$801$	−207957.	−	411849.i	−0.324122	−	0.641908i
$802$	−331552.			−0.515470
$803$	153368.	+	88546.9i	0.237850	+	0.137323i
$804$	369476.	−	1.23902e6i	0.571577	−	1.91676i
$805$	−56778.0	−	98342.3i	−0.0876169	−	0.151757i
$806$	707175.	−	408287.i	1.08857	−	0.628487i
$807$	150800.	+	633217.i	0.231555	+	0.972311i
$808$	−261098.	+	452235.i	−0.399927	+	0.692694i
$809$			272873.i			0.416930i	0.978030	+	0.208465i	$0.0668468\pi$
$809$			272873.i			0.416930i	−0.978030	+	0.208465i	$0.933153\pi$
$810$	−262933.	+	356394.i	−0.400751	+	0.543201i
$811$	−411812.			−0.626120			−0.313060	−	0.949733i	$-0.601354\pi$
$811$	−411812.			−0.626120			−0.313060	+	0.949733i	$0.601354\pi$
$812$	227228.	+	131190.i	0.344627	+	0.198970i
$813$	−416205.	+	99118.8i	−0.629689	+	0.149960i
$814$	196453.	+	340267.i	0.296490	+	0.513535i
$815$	350543.	−	202386.i	0.527747	−	0.304695i
$816$	496800.	+	148146.i	0.746107	+	0.222489i
$817$	691817.	−	1.19826e6i	1.03645	−	1.79518i
$818$		−	1.10982e6i		−	1.65862i
$819$	149029.	−	75250.1i	0.222179	−	0.112186i
$820$	−347804.			−0.517257
$821$	−482961.	−	278838.i	−0.716516	−	0.413681i	0.0969527	−	0.995289i	$-0.469090\pi$
$821$	−482961.	−	278838.i	−0.716516	−	0.413681i	−0.813469	+	0.581608i	$0.802424\pi$
$822$	−407307.	−	430784.i	−0.602807	−	0.637553i
$823$	−247052.	−	427907.i	−0.364745	−	0.631757i	0.623990	−	0.781432i	$-0.285510\pi$
$823$	−247052.	−	427907.i	−0.364745	−	0.631757i	−0.988735	+	0.149675i	$0.952177\pi$
$824$	−40919.8	+	23625.1i	−0.0602670	+	0.0347951i
$825$	−50925.6	+	48150.2i	−0.0748217	+	0.0707441i
$826$	−128680.	+	222880.i	−0.188604	+	0.326672i
$827$			203834.i			0.298034i	0.988835	+	0.149017i	$0.0476109\pi$
$827$			203834.i			0.298034i	−0.988835	+	0.149017i	$0.952389\pi$
$828$	1.03307e6	+	57923.9i	1.50685	+	0.0844884i
$829$	1.20555e6			1.75419			0.877093	−	0.480321i	$-0.159480\pi$
$829$	1.20555e6			1.75419			0.877093	+	0.480321i	$0.159480\pi$
$830$	504073.	+	291027.i	0.731707	+	0.422451i
$831$	321253.	−	1.07731e6i	0.465206	−	1.56005i
$832$	−378346.	−	655315.i	−0.546566	−	0.946680i
$833$	−646292.	+	373137.i	−0.931405	+	0.537747i
$834$	−37586.1	−	157826.i	−0.0540375	−	0.226906i
$835$	64466.4	−	111659.i	0.0924614	−	0.160148i
$836$			695053.i			0.994502i
$837$	731887.	+	263694.i	1.04470	+	0.376400i
$838$	−1.50417e6			−2.14194
$839$	−662852.	−	382698.i	−0.941657	−	0.543666i	−0.0511776	−	0.998690i	$-0.516297\pi$
$839$	−662852.	−	382698.i	−0.941657	−	0.543666i	−0.890479	+	0.455024i	$0.849631\pi$
$840$	42804.2	−	10193.8i	0.0606635	−	0.0144469i
$841$	−42536.7	−	73675.7i	−0.0601412	−	0.104168i
$842$	861105.	−	497159.i	1.21460	−	0.701247i
$843$	868503.	+	258988.i	1.22213	+	0.364439i
$844$	−61073.5	+	105782.i	−0.0857370	+	0.148501i
$845$			139737.i			0.195704i
$846$	1.45740e6	+	954026.i	2.03628	+	1.33297i
$847$	174988.			0.243917
$848$	291843.	+	168496.i	0.405843	+	0.234314i
$849$	698052.	+	738288.i	0.968440	+	1.02426i
$850$	131808.	+	228297.i	0.182433	+	0.315982i
$851$	−564988.	+	326196.i	−0.780154	+	0.450422i
$852$	−507210.	+	479568.i	−0.698729	+	0.660649i
$853$	−86973.3	+	150642.i	−0.119533	+	0.207037i	−0.919583	−	0.392896i	$-0.871473\pi$
$853$	−86973.3	+	150642.i	−0.119533	+	0.207037i	0.800050	+	0.599934i	$0.204806\pi$
$854$		−	290308.i		−	0.398056i
$855$	270558.	−	413312.i	0.370108	−	0.565386i
$856$	436359.			0.595520
$857$	−910870.	−	525891.i	−1.24021	−	0.716035i	−0.271072	−	0.962559i	$-0.587378\pi$
$857$	−910870.	−	525891.i	−1.24021	−	0.716035i	−0.969137	+	0.246525i	$0.920711\pi$
$858$	−122602.	+	411140.i	−0.166542	+	0.558490i
$859$	70628.1	+	122332.i	0.0957175	+	0.165788i	0.909908	−	0.414810i	$-0.136152\pi$
$859$	70628.1	+	122332.i	0.0957175	+	0.165788i	−0.814190	+	0.580598i	$0.802819\pi$
$860$	502336.	−	290024.i	0.679200	−	0.392136i
$861$	51572.5	+	216556.i	0.0695684	+	0.292121i
$862$	−374921.	+	649382.i	−0.504574	+	0.873948i
$863$			599750.i			0.805283i	0.915358	+	0.402642i	$0.131908\pi$
$863$			599750.i			0.805283i	−0.915358	+	0.402642i	$0.868092\pi$
$864$	352345.	−	977939.i	0.471999	−	1.31004i
$865$	167723.			0.224161
$866$	−663680.	−	383176.i	−0.884959	−	0.510931i
$867$	−336941.	+	80242.2i	−0.448245	+	0.106749i
$868$	−177481.	−	307406.i	−0.235566	−	0.408013i
$869$	237915.	−	137360.i	0.315052	−	0.181895i
$870$	459236.	+	136944.i	0.606733	+	0.180928i
$871$	−445086.	+	770911.i	−0.586688	+	1.01617i
$872$		−	72366.2i		−	0.0951706i
$873$	76430.7	−	1.36314e6i	0.100286	−	1.78860i
$874$	−2.05688e6			−2.69269
$875$	−19683.0	−	11364.0i	−0.0257084	−	0.0148427i
$876$	−359517.	−	380239.i	−0.468501	−	0.495506i
$877$	−266367.	−	461361.i	−0.346323	−	0.599849i	0.639270	−	0.768982i	$-0.279237\pi$
$877$	−266367.	−	461361.i	−0.346323	−	0.599849i	−0.985593	+	0.169133i	$0.945903\pi$
$878$	−1.29917e6	+	750076.i	−1.68530	+	0.973008i
$879$	−168454.	+	159274.i	−0.218024	+	0.206142i
$880$	57430.4	−	99472.4i	0.0741612	−	0.128451i
$881$			150366.i			0.193730i	0.995298	+	0.0968652i	$0.0308816\pi$
$881$			150366.i			0.193730i	−0.995298	+	0.0968652i	$0.969118\pi$
$882$	470959.	+	932711.i	0.605405	+	1.19897i
$883$	452108.			0.579857			0.289929	−	0.957048i	$-0.406368\pi$
$883$	452108.			0.579857			0.289929	+	0.957048i	$0.406368\pi$
$884$	784144.	+	452726.i	1.00344	+	0.579336i
$885$	−75367.4	+	252741.i	−0.0962270	+	0.322693i
$886$	−711716.	−	1.23273e6i	−0.906649	−	1.57036i
$887$	−269618.	+	155664.i	−0.342690	+	0.197852i	−0.661461	−	0.749980i	$-0.730063\pi$
$887$	−269618.	+	155664.i	−0.342690	+	0.197852i	0.318771	+	0.947832i	$0.396730\pi$
$888$	−58564.4	−	245915.i	−0.0742690	−	0.311860i
$889$	130310.	−	225703.i	0.164882	−	0.285584i
$890$			384496.i			0.485414i
$891$	−374600.	+	163516.i	−0.471860	+	0.205970i
$892$	−238680.			−0.299976
$893$	−1.68258e6	−	971438.i	−2.10995	−	1.21818i
$894$	454421.	−	108220.i	0.568569	−	0.135404i
$895$	−260412.	−	451047.i	−0.325099	−	0.563088i
$896$	−186384.	+	107609.i	−0.232163	+	0.134040i
$897$	−682670.	−	203572.i	−0.848449	−	0.253008i
$898$	−560633.	+	971044.i	−0.695226	+	1.20417i
$899$		−	841758.i		−	1.04152i
$900$	184862.	−	93343.4i	0.228225	−	0.115239i
$901$	−713777.			−0.879252
$902$	−495429.	−	286036.i	−0.608932	−	0.351567i
$903$	−255067.	−	269769.i	−0.312808	−	0.330838i
$904$	224235.	+	388387.i	0.274389	+	0.475257i
$905$	−385210.	+	222401.i	−0.470327	+	0.271544i
$906$	110297.	−	104286.i	0.134371	−	0.127048i
$907$	638499.	−	1.10591e6i	0.776150	−	1.34433i	−0.157996	−	0.987440i	$-0.550503\pi$
$907$	638499.	−	1.10591e6i	0.776150	−	1.34433i	0.934146	−	0.356891i	$-0.116163\pi$
$908$		−	1.32102e6i		−	1.60228i
$909$	1.57060e6	+	88062.4i	1.90080	+	0.106577i
$910$	−139132.			−0.168013
$911$	604824.	+	349196.i	0.728774	+	0.420758i	0.817973	−	0.575256i	$-0.195098\pi$
$911$	604824.	+	349196.i	0.728774	+	0.420758i	−0.0891998	+	0.996014i	$0.528431\pi$
$912$	−231355.	+	775837.i	−0.278156	+	0.932784i
$913$	268583.	+	465199.i	0.322208	+	0.558081i
$914$	1.26273e6	−	729038.i	1.51154	−	0.872686i
$915$	−68922.7	−	289410.i	−0.0823228	−	0.345678i
$916$	−781270.	+	1.35320e6i	−0.931130	+	1.61276i
$917$		−	148601.i		−	0.176718i
$918$	271887.	+	1.51317e6i	0.322629	+	1.79557i
$919$	1.34307e6			1.59025			0.795127	−	0.606442i	$-0.207404\pi$
$919$	1.34307e6			1.59025			0.795127	+	0.606442i	$0.207404\pi$
$920$	−162599.	−	93876.7i	−0.192107	−	0.110913i
$921$	987012.	−	235056.i	1.16360	−	0.277110i
$922$	1.04671e6	+	1.81296e6i	1.23130	+	2.13268i
$923$	416199.	−	240293.i	0.488538	−	0.282057i
$924$	178721.	+	53294.8i	0.209331	+	0.0624224i
$925$	−65287.3	+	113081.i	−0.0763037	+	0.132162i
$926$			576221.i			0.671997i
$927$	119089.	+	77957.2i	0.138584	+	0.0907186i
$928$	−1.12475e6			−1.30605
$929$	−623619.	−	360047.i	−0.722583	−	0.417184i	0.0931194	−	0.995655i	$-0.470316\pi$
$929$	−623619.	−	360047.i	−0.722583	−	0.417184i	−0.815703	+	0.578471i	$0.803650\pi$
$930$	−445412.	−	471086.i	−0.514987	−	0.544671i
$931$	−582717.	−	1.00929e6i	−0.672292	−	1.16444i
$932$	393578.	−	227233.i	0.453105	−	0.261601i
$933$	−319682.	+	302260.i	−0.367244	+	0.347230i
$934$	435255.	−	753883.i	0.498942	−	0.864192i
$935$			243285.i			0.278287i
$936$	151184.	−	230952.i	0.172565	−	0.263615i
$937$	−482883.			−0.550000			−0.275000	−	0.961444i	$-0.588678\pi$
$937$	−482883.			−0.550000			−0.275000	+	0.961444i	$0.588678\pi$
$938$	597258.	+	344827.i	0.678823	+	0.391918i
$939$	−370508.	+	1.24248e6i	−0.420210	+	1.40915i
$940$	−407247.	−	705373.i	−0.460895	−	0.798294i
$941$	986201.	−	569384.i	1.11375	−	0.643022i	0.173949	−	0.984755i	$-0.444347\pi$
$941$	986201.	−	569384.i	1.11375	−	0.643022i	0.939797	+	0.341733i	$0.111014\pi$
$942$	30514.0	+	128130.i	0.0343873	+	0.144394i
$943$	474943.	−	822625.i	0.534094	−	0.925079i
$944$		−	432239.i		−	0.485042i
$945$	−85530.6	−	101261.i	−0.0957762	−	0.113391i
$946$	954071.			1.06610
$947$	−162407.	−	93765.7i	−0.181094	−	0.104555i	0.406712	−	0.913556i	$-0.366675\pi$
$947$	−162407.	−	93765.7i	−0.181094	−	0.104555i	−0.587807	+	0.809001i	$0.700008\pi$
$948$	−789683.	+	188062.i	−0.878690	+	0.209259i
$949$	180140.	+	312011.i	0.200022	+	0.346448i
$950$	−356525.	+	205840.i	−0.395042	+	0.228078i
$951$	703090.	+	209662.i	0.777410	+	0.231824i
$952$	76370.9	−	132278.i	0.0842663	−	0.145954i
$953$			658389.i			0.724931i	0.931997	+	0.362466i	$0.118065\pi$
$953$			658389.i			0.724931i	−0.931997	+	0.362466i	$0.881935\pi$
$954$	−55946.3	+	997804.i	−0.0614716	+	1.09635i
$955$	520199.			0.570378
$956$	596609.	+	344452.i	0.652791	+	0.376889i
$957$	303847.	+	321361.i	0.331766	+	0.350889i
$958$	−217912.	−	377435.i	−0.237438	−	0.411255i
$959$	153660.	−	88715.4i	0.167079	−	0.0964632i
$960$	−436539.	+	412749.i	−0.473676	+	0.447861i
$961$	−107629.	+	186419.i	−0.116542	+	0.201857i
$962$			799328.i			0.863724i
$963$	−592484.	−	1.17339e6i	−0.638887	−	1.26529i
$964$	762960.			0.821009
$965$	230612.	+	133144.i	0.247644	+	0.142977i
$966$	−157716.	+	528894.i	−0.169014	+	0.566779i
$967$	607332.	+	1.05193e6i	0.649491	+	1.12495i	0.983245	+	0.182291i	$0.0583512\pi$
$967$	607332.	+	1.05193e6i	0.649491	+	1.12495i	−0.333754	+	0.942660i	$0.608315\pi$
$968$	250563.	−	144663.i	0.267403	−	0.154385i
$969$	−397267.	−	1.66815e6i	−0.423092	−	1.77659i
$970$	−568896.	+	985357.i	−0.604630	+	1.04725i
$971$			307344.i			0.325976i	0.986628	+	0.162988i	$0.0521133\pi$
$971$			307344.i			0.325976i	−0.986628	+	0.162988i	$0.947887\pi$
$972$	1.19882e6	−	146709.i	1.26888	−	0.155283i
$973$	48555.7			0.0512879
$974$	1.32533e6	+	765178.i	1.39703	+	0.806574i
$975$	−138701.	+	33031.5i	−0.145905	+	0.0347472i
$976$	243788.	+	422253.i	0.255925	+	0.443275i
$977$	464532.	−	268197.i	0.486661	−	0.280974i	−0.236527	−	0.971625i	$-0.576009\pi$
$977$	464532.	−	268197.i	0.486661	−	0.280974i	0.723188	+	0.690651i	$0.242676\pi$
$978$	−1.88525e6	−	562182.i	−1.97102	−	0.587759i
$979$	−177422.	+	307304.i	−0.185115	+	0.320629i
$980$		−	488574.i		−	0.508719i
$981$	−194596.	+	98258.2i	−0.202207	+	0.102101i
$982$	992901.			1.02963
$983$	152901.	+	88277.2i	0.158235	+	0.0913570i	0.577027	−	0.816725i	$-0.304213\pi$
$983$	152901.	+	88277.2i	0.158235	+	0.0913570i	−0.418792	+	0.908082i	$0.637546\pi$
$984$	252873.	+	267448.i	0.261163	+	0.276216i
$985$	−77799.6	−	134753.i	−0.0801872	−	0.138888i
$986$	1.44065e6	−	831760.i	1.48185	−	0.855547i
$987$	−378805.	+	358160.i	−0.388849	+	0.367657i
$988$	−707008.	+	1.22457e6i	−0.724287	+	1.25450i
$989$			1.58417e6i			1.61960i
$990$	340093.	+	19068.8i	0.346999	+	0.0194560i
$991$	1.03590e6			1.05481			0.527403	−	0.849615i	$-0.323166\pi$
$991$	1.03590e6			1.05481			0.527403	+	0.849615i	$0.323166\pi$
$992$	1.31776e6	+	760812.i	1.33910	+	0.773132i
$993$	−401420.	+	1.34614e6i	−0.407099	+	1.36519i
$994$	−186165.	−	322448.i	−0.188420	−	0.326352i
$995$	−118474.	+	68400.8i	−0.119667	+	0.0690900i
$996$	−367721.	−	1.54408e6i	−0.370681	−	1.55651i
$997$	−809745.	+	1.40252e6i	−0.814626	+	1.41097i	0.0949704	+	0.995480i	$0.469724\pi$
$997$	−809745.	+	1.40252e6i	−0.814626	+	1.41097i	−0.909596	+	0.415493i	$0.863609\pi$
$998$		−	1.94017e6i		−	1.94796i
$999$	−581757.	+	491384.i	−0.582923	+	0.492368i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.5.i.a.11.14	✓	32
3.2	odd	2		135.5.i.a.116.3		32
9.2	odd	6		405.5.c.b.161.28		32
9.4	even	3		135.5.i.a.71.3		32
9.5	odd	6	inner	45.5.i.a.41.14	yes	32
9.7	even	3		405.5.c.b.161.5		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.5.i.a.11.14	✓	32	1.1	even	1	trivial
45.5.i.a.41.14	yes	32	9.5	odd	6	inner
135.5.i.a.71.3		32	9.4	even	3
135.5.i.a.116.3		32	3.2	odd	2
405.5.c.b.161.5		32	9.7	even	3
405.5.c.b.161.28		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+(5.22878 + 3.01884i) q^{2} +(8.75515 - 2.08503i) q^{3} +(10.2268 + 17.7133i) q^{4} +(-9.68246 + 5.59017i) q^{5} +(52.0731 + 15.5282i) q^{6} +(-8.13139 + 14.0840i) q^{7} +26.8889i q^{8} +(72.3053 - 36.5095i) q^{9} -67.5033 q^{10} +(-53.9512 - 31.1487i) q^{11} +(126.469 + 133.759i) q^{12} +(-63.3690 - 109.758i) q^{13} +(-85.0345 + 49.0947i) q^{14} +(-73.1157 + 69.1310i) q^{15} +(82.4550 - 142.816i) q^{16} +349.293i q^{17} +(488.285 + 27.3778i) q^{18} -545.481 q^{19} +(-198.040 - 114.339i) q^{20} +(-41.8260 + 140.262i) q^{21} +(-188.066 - 325.739i) q^{22} +(540.867 - 312.270i) q^{23} +(56.0641 + 235.416i) q^{24} +(62.5000 - 108.253i) q^{25} -765.202i q^{26} +(556.920 - 470.405i) q^{27} -332.631 q^{28} +(-683.122 - 394.401i) q^{29} +(-591.001 + 140.746i) q^{30} +(533.568 + 924.167i) q^{31} +(1234.86 - 712.947i) q^{32} +(-537.296 - 160.222i) q^{33} +(-1054.46 + 1826.38i) q^{34} -181.823i q^{35} +(1386.15 + 907.389i) q^{36} -1044.60 q^{37} +(-2852.20 - 1646.72i) q^{38} +(-783.654 - 828.824i) q^{39} +(-150.313 - 260.350i) q^{40} +(1317.17 - 760.469i) q^{41} +(-642.126 + 607.131i) q^{42} +(-1268.27 + 2196.70i) q^{43} -1274.20i q^{44} +(-495.999 + 757.701i) q^{45} +3770.77 q^{46} +(3084.58 + 1780.88i) q^{47} +(424.130 - 1422.30i) q^{48} +(1068.26 + 1850.28i) q^{49} +(653.597 - 377.355i) q^{50} +(728.287 + 3058.12i) q^{51} +(1296.12 - 2244.94i) q^{52} +2043.49i q^{53} +(4332.09 - 778.391i) q^{54} +696.506 q^{55} +(-378.702 - 218.644i) q^{56} +(-4775.77 + 1137.34i) q^{57} +(-2381.26 - 4124.47i) q^{58} +(2269.90 - 1310.53i) q^{59} +(-1972.27 - 588.132i) q^{60} +(-1478.31 + 2560.51i) q^{61} +6443.02i q^{62} +(-73.7436 + 1315.22i) q^{63} +5970.53 q^{64} +(1227.13 + 708.487i) q^{65} +(-2325.72 - 2459.78i) q^{66} +(-3511.86 - 6082.72i) q^{67} +(-6187.13 + 3572.14i) q^{68} +(4084.28 - 3861.69i) q^{69} +(548.895 - 950.714i) q^{70} +3791.96i q^{71} +(981.699 + 1944.21i) q^{72} -2842.71 q^{73} +(-5461.97 - 3153.47i) q^{74} +(321.486 - 1078.09i) q^{75} +(-5578.51 - 9662.26i) q^{76} +(877.395 - 506.565i) q^{77} +(-1595.47 - 6699.46i) q^{78} +(-2204.91 + 3819.02i) q^{79} +1843.75i q^{80} +(3895.11 - 5279.66i) q^{81} +9182.92 q^{82} +(-7467.39 - 4311.30i) q^{83} +(-2912.23 + 693.545i) q^{84} +(-1952.61 - 3382.02i) q^{85} +(-13263.0 + 7657.39i) q^{86} +(-6803.17 - 2028.71i) q^{87} +(837.554 - 1450.69i) q^{88} -5695.97i q^{89} +(-4880.84 + 2464.51i) q^{90} +2061.11 q^{91} +(11062.6 + 6387.02i) q^{92} +(6598.38 + 6978.71i) q^{93} +(10752.4 + 18623.7i) q^{94} +(5281.60 - 3049.33i) q^{95} +(9324.88 - 8816.68i) q^{96} +(8427.69 - 14597.2i) q^{97} +12899.6i q^{98} +(-5038.18 - 282.488i) 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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