LMFDB - Embedded newform 45.5.i.a.11.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [45,5,Mod(11,45)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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			11.13
Character	$\chi$	$=$	45.11
Dual form			45.5.i.a.41.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(4.78725 + 2.76392i) q^{2} +(4.38356 + 7.86031i) q^{3} +(7.27848 + 12.6067i) q^{4} +(9.68246 - 5.59017i) q^{5} +(-0.740053 + 49.7450i) q^{6} +(-0.820328 + 1.42085i) q^{7} -7.97692i q^{8} +(-42.5688 + 68.9122i) q^{9} +61.8031 q^{10} +(-46.1525 - 26.6461i) q^{11} +(-67.1868 + 112.473i) q^{12} +(-30.4995 - 52.8267i) q^{13} +(-7.85422 + 4.53464i) q^{14} +(86.3841 + 51.6022i) q^{15} +(138.503 - 239.895i) q^{16} -106.725i q^{17} +(-394.255 + 212.243i) q^{18} +396.675 q^{19} +(140.947 + 81.3758i) q^{20} +(-14.7643 - 0.219647i) q^{21} +(-147.296 - 255.123i) q^{22} +(-213.343 + 123.173i) q^{23} +(62.7010 - 34.9673i) q^{24} +(62.5000 - 108.253i) q^{25} -337.192i q^{26} +(-728.274 - 32.5227i) q^{27} -23.8830 q^{28} +(999.692 + 577.172i) q^{29} +(270.918 + 485.791i) q^{30} +(-761.481 - 1318.92i) q^{31} +(1215.57 - 701.807i) q^{32} +(7.13465 - 479.578i) q^{33} +(294.979 - 510.919i) q^{34} +18.3431i q^{35} +(-1178.59 - 35.0754i) q^{36} -2718.12 q^{37} +(1898.98 + 1096.38i) q^{38} +(281.537 - 471.304i) q^{39} +(-44.5923 - 77.2362i) q^{40} +(-2005.22 + 1157.72i) q^{41} +(-70.0731 - 41.8587i) q^{42} +(-1.46928 + 2.54487i) q^{43} -775.774i q^{44} +(-26.9394 + 905.207i) q^{45} -1361.76 q^{46} +(2657.39 + 1534.24i) q^{47} +(2492.78 + 37.0849i) q^{48} +(1199.15 + 2077.00i) q^{49} +(598.406 - 345.490i) q^{50} +(838.892 - 467.836i) q^{51} +(443.980 - 768.996i) q^{52} +4000.85i q^{53} +(-3396.54 - 2168.58i) q^{54} -595.826 q^{55} +(11.3340 + 6.54369i) q^{56} +(1738.85 + 3117.99i) q^{57} +(3190.51 + 5526.13i) q^{58} +(-5835.85 + 3369.33i) q^{59} +(-21.7888 + 1464.60i) q^{60} +(1198.95 - 2076.65i) q^{61} -8418.68i q^{62} +(-62.9936 - 117.015i) q^{63} +3326.85 q^{64} +(-590.620 - 340.995i) q^{65} +(1359.67 - 2276.14i) q^{66} +(-586.022 - 1015.02i) q^{67} +(1345.45 - 776.796i) q^{68} +(-1903.38 - 1137.00i) q^{69} +(-50.6988 + 87.8129i) q^{70} -4266.36i q^{71} +(549.707 + 339.568i) q^{72} +1723.52 q^{73} +(-13012.3 - 7512.65i) q^{74} +(1124.88 + 16.7347i) q^{75} +(2887.19 + 5000.76i) q^{76} +(75.7204 - 43.7172i) q^{77} +(2650.43 - 1478.10i) q^{78} +(3763.71 - 6518.94i) q^{79} -3097.03i q^{80} +(-2936.80 - 5867.02i) q^{81} -12799.3 q^{82} +(-2939.41 - 1697.07i) q^{83} +(-104.692 - 187.727i) q^{84} +(-596.612 - 1033.36i) q^{85} +(-14.0676 + 8.12194i) q^{86} +(-154.541 + 10388.0i) q^{87} +(-212.554 + 368.155i) q^{88} +2313.92i q^{89} +(-2630.88 + 4258.99i) q^{90} +100.078 q^{91} +(-3105.62 - 1793.03i) q^{92} +(7029.15 - 11767.1i) q^{93} +(8481.04 + 14689.6i) q^{94} +(3840.79 - 2217.48i) q^{95} +(10844.9 + 6478.30i) q^{96} +(1576.49 - 2730.56i) q^{97} +13257.5i q^{98} +(3800.90 - 2046.18i) 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 $

$2$	4.78725	+	2.76392i	1.19681	+	0.690979i	0.959843	−	0.280538i	$-0.0905129\pi$
$2$	4.78725	+	2.76392i	1.19681	+	0.690979i	0.236968	+	0.971517i	$0.423846\pi$
$3$	4.38356	+	7.86031i	0.487062	+	0.873367i
$3$	4.38356	+	7.86031i	0.487062	+	0.873367i
$4$	7.27848	+	12.6067i	0.454905	+	0.787918i
$5$	9.68246	−	5.59017i	0.387298	−	0.223607i
$5$	9.68246	−	5.59017i	0.387298	−	0.223607i
$6$	−0.740053	+	49.7450i	−0.0205570	+	1.38181i
$7$	−0.820328	+	1.42085i	−0.0167414	+	0.0289969i	−0.874275	−	0.485431i	$-0.838663\pi$
$7$	−0.820328	+	1.42085i	−0.0167414	+	0.0289969i	0.857533	+	0.514428i	$0.171996\pi$
$8$		−	7.97692i		−	0.124639i
$9$	−42.5688	+	68.9122i	−0.525541	+	0.850769i
$10$	61.8031			0.618031
$11$	−46.1525	−	26.6461i	−0.381425	−	0.220216i	0.297013	−	0.954873i	$-0.404010\pi$
$11$	−46.1525	−	26.6461i	−0.381425	−	0.220216i	−0.678438	+	0.734657i	$0.737343\pi$
$12$	−67.1868	+	112.473i	−0.466575	+	0.781064i
$13$	−30.4995	−	52.8267i	−0.180470	−	0.312584i	0.761570	−	0.648082i	$-0.224429\pi$
$13$	−30.4995	−	52.8267i	−0.180470	−	0.312584i	−0.942041	+	0.335498i	$0.891095\pi$
$14$	−7.85422	+	4.53464i	−0.0400726	+	0.0231359i
$15$	86.3841	+	51.6022i	0.383929	+	0.229343i
$16$	138.503	−	239.895i	0.541028	−	0.937088i
$17$		−	106.725i		−	0.369291i	−0.982805	−	0.184646i	$-0.940886\pi$
$17$		−	106.725i		−	0.369291i	0.982805	−	0.184646i	$-0.0591137\pi$
$18$	−394.255	+	212.243i	−1.21684	+	0.655072i
$19$	396.675			1.09882			0.549411	−	0.835552i	$-0.314852\pi$
$19$	396.675			1.09882			0.549411	+	0.835552i	$0.314852\pi$
$20$	140.947	+	81.3758i	0.352368	+	0.203440i
$21$	−14.7643	−	0.219647i	−0.0334791	−	0.000498066i
$22$	−147.296	−	255.123i	−0.304330	−	0.527114i
$23$	−213.343	+	123.173i	−0.403294	+	0.232842i	−0.687904	−	0.725801i	$-0.741469\pi$
$23$	−213.343	+	123.173i	−0.403294	+	0.232842i	0.284610	+	0.958643i	$0.408136\pi$
$24$	62.7010	−	34.9673i	0.108856	−	0.0607071i
$25$	62.5000	−	108.253i	0.100000	−	0.173205i
$26$		−	337.192i		−	0.498805i
$27$	−728.274	−	32.5227i	−0.999004	−	0.0446127i
$28$	−23.8830			−0.0304630
$29$	999.692	+	577.172i	1.18869	+	0.686293i	0.958010	−	0.286735i	$-0.0925701\pi$
$29$	999.692	+	577.172i	1.18869	+	0.686293i	0.230685	+	0.973029i	$0.425903\pi$
$30$	270.918	+	485.791i	0.301019	+	0.539768i
$31$	−761.481	−	1318.92i	−0.792384	−	1.37245i	−0.924487	−	0.381214i	$-0.875506\pi$
$31$	−761.481	−	1318.92i	−0.792384	−	1.37245i	0.132103	−	0.991236i	$-0.457827\pi$
$32$	1215.57	−	701.807i	1.18708	−	0.685359i
$33$	7.13465	−	479.578i	0.00655156	−	0.440383i
$34$	294.979	−	510.919i	0.255172	−	0.441972i
$35$			18.3431i			0.0149740i
$36$	−1178.59	−	35.0754i	−0.909407	−	0.0270644i
$37$	−2718.12			−1.98548			−0.992739	−	0.120292i	$-0.961617\pi$
$37$	−2718.12			−1.98548			−0.992739	+	0.120292i	$0.961617\pi$
$38$	1898.98	+	1096.38i	1.31508	+	0.759264i
$39$	281.537	−	471.304i	0.185100	−	0.309865i
$40$	−44.5923	−	77.2362i	−0.0278702	−	0.0482726i
$41$	−2005.22	+	1157.72i	−1.19287	+	0.688706i	−0.958957	−	0.283550i	$-0.908488\pi$
$41$	−2005.22	+	1157.72i	−1.19287	+	0.688706i	−0.233917	+	0.972257i	$0.575154\pi$
$42$	−70.0731	−	41.8587i	−0.0397240	−	0.0237294i
$43$	−1.46928	+	2.54487i	−0.000794636	+	0.00137635i	−0.866422	−	0.499312i	$-0.833586\pi$
$43$	−1.46928	+	2.54487i	−0.000794636	+	0.00137635i	0.865628	+	0.500688i	$0.166920\pi$
$44$		−	775.774i		−	0.400709i
$45$	−26.9394	+	905.207i	−0.0133034	+	0.447016i
$46$	−1361.76			−0.643556
$47$	2657.39	+	1534.24i	1.20298	+	0.694542i	0.961217	−	0.275793i	$-0.0889404\pi$
$47$	2657.39	+	1534.24i	1.20298	+	0.694542i	0.241765	+	0.970335i	$0.422274\pi$
$48$	2492.78	+	37.0849i	1.08194	+	0.0160959i
$49$	1199.15	+	2077.00i	0.499439	+	0.865055i
$50$	598.406	−	345.490i	0.239362	−	0.138196i
$51$	838.892	−	467.836i	0.322527	−	0.179868i
$52$	443.980	−	768.996i	0.164194	−	0.284392i
$53$			4000.85i			1.42430i	0.702028	+	0.712149i	$0.252278\pi$
$53$			4000.85i			1.42430i	−0.702028	+	0.712149i	$0.747722\pi$
$54$	−3396.54	−	2168.58i	−1.16479	−	0.743684i
$55$	−595.826			−0.196967
$56$	11.3340	+	6.54369i	0.00361416	+	0.00208664i
$57$	1738.85	+	3117.99i	0.535195	+	0.959676i
$58$	3190.51	+	5526.13i	0.948429	+	1.64273i
$59$	−5835.85	+	3369.33i	−1.67649	+	0.967920i	−0.712613	+	0.701557i	$0.752489\pi$
$59$	−5835.85	+	3369.33i	−1.67649	+	0.967920i	−0.963873	+	0.266363i	$0.914178\pi$
$60$	−21.7888	+	1464.60i	−0.00605245	+	0.406834i
$61$	1198.95	−	2076.65i	0.322213	−	0.558088i	−0.658732	−	0.752378i	$-0.728907\pi$
$61$	1198.95	−	2076.65i	0.322213	−	0.558088i	0.980944	+	0.194289i	$0.0622401\pi$
$62$		−	8418.68i		−	2.19008i
$63$	−62.9936	−	117.015i	−0.0158714	−	0.0294821i
$64$	3326.85			0.812219
$65$	−590.620	−	340.995i	−0.139792	−	0.0807088i
$66$	1359.67	−	2276.14i	0.312137	−	0.522529i
$67$	−586.022	−	1015.02i	−0.130546	−	0.226113i	0.793341	−	0.608777i	$-0.208340\pi$
$67$	−586.022	−	1015.02i	−0.130546	−	0.226113i	−0.923887	+	0.382665i	$0.875006\pi$
$68$	1345.45	−	776.796i	0.290971	−	0.167992i
$69$	−1903.38	−	1137.00i	−0.399786	−	0.238815i
$70$	−50.6988	+	87.8129i	−0.0103467	+	0.0179210i
$71$		−	4266.36i		−	0.846332i	−0.906052	−	0.423166i	$-0.860919\pi$
$71$		−	4266.36i		−	0.846332i	0.906052	−	0.423166i	$-0.139081\pi$
$72$	549.707	+	339.568i	0.106039	+	0.0655030i
$73$	1723.52			0.323423			0.161712	−	0.986838i	$-0.448299\pi$
$73$	1723.52			0.323423			0.161712	+	0.986838i	$0.448299\pi$
$74$	−13012.3	−	7512.65i	−2.37624	−	1.37192i
$75$	1124.88	+	16.7347i	0.199978	+	0.00297506i
$76$	2887.19	+	5000.76i	0.499860	+	0.865783i
$77$	75.7204	−	43.7172i	0.0127712	−	0.00737345i
$78$	2650.43	−	1478.10i	0.435640	−	0.242949i
$79$	3763.71	−	6518.94i	0.603063	−	1.04454i	−0.389292	−	0.921115i	$-0.627280\pi$
$79$	3763.71	−	6518.94i	0.603063	−	1.04454i	0.992354	−	0.123421i	$-0.0393865\pi$
$80$		−	3097.03i		−	0.483910i
$81$	−2936.80	−	5867.02i	−0.447614	−	0.894227i
$82$	−12799.3			−1.90353
$83$	−2939.41	−	1697.07i	−0.426682	−	0.246345i	0.271250	−	0.962509i	$-0.412563\pi$
$83$	−2939.41	−	1697.07i	−0.426682	−	0.246345i	−0.697932	+	0.716164i	$0.745896\pi$
$84$	−104.692	−	187.727i	−0.0148374	−	0.0266054i
$85$	−596.612	−	1033.36i	−0.0825760	−	0.143026i
$86$	−14.0676	+	8.12194i	−0.00190206	+	0.00109815i
$87$	−154.541	+	10388.0i	−0.0204176	+	1.37243i
$88$	−212.554	+	368.155i	−0.0274476	+	0.0475406i
$89$			2313.92i			0.292125i	0.989275	+	0.146063i	$0.0466601\pi$
$89$			2313.92i			0.292125i	−0.989275	+	0.146063i	$0.953340\pi$
$90$	−2630.88	+	4258.99i	−0.324800	+	0.525801i
$91$	100.078			0.0120853
$92$	−3105.62	−	1793.03i	−0.366921	−	0.211842i
$93$	7029.15	−	11767.1i	0.812712	−	1.36051i
$94$	8481.04	+	14689.6i	0.959828	+	1.66247i
$95$	3840.79	−	2217.48i	0.425572	−	0.245704i
$96$	10844.9	+	6478.30i	1.17675	+	0.702941i
$97$	1576.49	−	2730.56i	0.167551	−	0.290207i	−0.770007	−	0.638035i	$-0.779747\pi$
$97$	1576.49	−	2730.56i	0.167551	−	0.290207i	0.937558	+	0.347828i	$0.113081\pi$
$98$			13257.5i			1.38041i
$99$	3800.90	−	2046.18i	0.387808	−	0.208772i
$100$	1819.62			0.181962
$101$	10041.5	+	5797.47i	0.984365	+	0.568324i	0.903585	−	0.428408i	$-0.140926\pi$
$101$	10041.5	+	5797.47i	0.984365	+	0.568324i	0.0807801	+	0.996732i	$0.474259\pi$
$102$	5309.04	+	78.9823i	0.510288	+	0.00759153i
$103$	−818.425	−	1417.55i	−0.0771444	−	0.133618i	0.824872	−	0.565319i	$-0.191247\pi$
$103$	−818.425	−	1417.55i	−0.0771444	−	0.133618i	−0.902017	+	0.431701i	$0.857914\pi$
$104$	−421.394	+	243.292i	−0.0389603	+	0.0224937i
$105$	−144.182	+	80.4081i	−0.0130778	+	0.00729325i
$106$	−11058.0	+	19153.1i	−0.984161	+	1.70462i
$107$			8256.06i			0.721116i	0.932737	+	0.360558i	$0.117414\pi$
$107$			8256.06i			0.721116i	−0.932737	+	0.360558i	$0.882586\pi$
$108$	−4890.72	−	9417.84i	−0.419301	−	0.807428i
$109$	16715.8			1.40693			0.703466	−	0.710728i	$-0.251635\pi$
$109$	16715.8			1.40693			0.703466	+	0.710728i	$0.251635\pi$
$110$	−2852.37	−	1646.81i	−0.235733	−	0.136100i
$111$	−11915.0	−	21365.2i	−0.967051	−	1.73405i
$112$	227.236	+	393.585i	0.0181151	+	0.0313763i
$113$	−297.237	+	171.610i	−0.0232780	+	0.0134396i	−0.511594	−	0.859227i	$-0.670945\pi$
$113$	−297.237	+	171.610i	−0.0232780	+	0.0134396i	0.488316	+	0.872667i	$0.337611\pi$
$114$	−293.561	+	19732.6i	−0.0225885	+	1.51836i
$115$	−1377.12	+	2385.24i	−0.104130	+	0.180359i
$116$			16803.7i			1.24879i
$117$	4938.73	+	146.979i	0.360781	+	0.0107370i
$118$	−37250.2			−2.67525
$119$	151.640	+	87.5496i	0.0107083	+	0.00618245i
$120$	411.627	−	689.079i	0.0285852	−	0.0478527i
$121$	−5900.47	−	10219.9i	−0.403010	−	0.698033i
$122$	11479.4	−	6627.61i	0.771255	−	0.445284i
$123$	−17890.0	−	10686.7i	−1.18250	−	0.706374i
$124$	11084.8	−	19199.5i	0.720919	−	1.24867i
$125$		−	1397.54i		−	0.0894427i
$126$	21.8527	−	734.286i	0.00137646	−	0.0462513i
$127$	−4530.24			−0.280876			−0.140438	−	0.990090i	$-0.544851\pi$
$127$	−4530.24			−0.280876			−0.140438	+	0.990090i	$0.544851\pi$
$128$	−3522.62	−	2033.79i	−0.215004	−	0.124132i
$129$	−26.4441	−	0.393408i	−0.00158910	−	2.36409e-5i
$130$	−1884.96	−	3264.85i	−0.111536	−	0.193186i
$131$	7795.73	−	4500.86i	0.454270	−	0.262273i	−0.255362	−	0.966846i	$-0.582195\pi$
$131$	7795.73	−	4500.86i	0.454270	−	0.262273i	0.709632	+	0.704573i	$0.248861\pi$
$132$	6097.82	−	3400.65i	0.349967	−	0.195170i
$133$	−325.404	+	563.616i	−0.0183958	+	0.0318625i
$134$		−	6478.87i		−	0.360819i
$135$	−7233.29	+	3756.28i	−0.396888	+	0.206106i
$136$	−851.337			−0.0460282
$137$	18815.2	+	10863.0i	1.00246	+	0.578771i	0.908975	−	0.416850i	$-0.136866\pi$
$137$	18815.2	+	10863.0i	1.00246	+	0.578771i	0.0934854	+	0.995621i	$0.470199\pi$
$138$	−5969.38	−	10703.9i	−0.313452	−	0.562061i
$139$	1049.71	+	1818.15i	0.0543298	+	0.0941020i	0.891911	−	0.452211i	$-0.149364\pi$
$139$	1049.71	+	1818.15i	0.0543298	+	0.0941020i	−0.837581	+	0.546313i	$0.816031\pi$
$140$	−231.246	+	133.510i	−0.0117983	+	0.00681173i
$141$	−410.802	+	27613.3i	−0.0206630	+	1.38893i
$142$	11791.9	−	20424.1i	0.584798	−	1.01290i
$143$			3250.78i			0.158970i
$144$	10635.8	+	19756.6i	0.512913	+	0.952767i
$145$	12906.0			0.613839
$146$	8250.92	+	4763.67i	0.387077	+	0.223479i
$147$	−11069.3	+	18530.4i	−0.512252	+	0.857529i
$148$	−19783.8	−	34266.5i	−0.903203	−	1.56439i
$149$	13900.2	−	8025.31i	0.626109	−	0.361484i	−0.153135	−	0.988205i	$-0.548937\pi$
$149$	13900.2	−	8025.31i	0.626109	−	0.361484i	0.779244	+	0.626721i	$0.215604\pi$
$150$	5338.80	+	3189.18i	0.237280	+	0.141741i
$151$	2323.88	−	4025.08i	0.101920	−	0.176531i	−0.810556	−	0.585662i	$-0.800835\pi$
$151$	2323.88	−	4025.08i	0.101920	−	0.176531i	0.912476	+	0.409131i	$0.134168\pi$
$152$		−	3164.24i		−	0.136957i
$153$	7354.67	+	4543.16i	0.314181	+	0.194077i
$154$	483.323			0.0203796
$155$	−14746.0	−	8513.62i	−0.613778	−	0.354365i
$156$	7990.75	+	118.878i	0.328351	+	0.00488486i
$157$	16980.2	+	29410.5i	0.688879	+	1.19317i	0.972201	+	0.234149i	$0.0752303\pi$
$157$	16980.2	+	29410.5i	0.688879	+	1.19317i	−0.283322	+	0.959025i	$0.591436\pi$
$158$	36035.6	−	20805.2i	1.44350	−	0.833408i
$159$	−31447.9	+	17538.0i	−1.24394	+	0.693722i
$160$	7846.44	−	13590.4i	0.306502	−	0.530877i
$161$		−	404.170i		−	0.0155924i
$162$	2156.80	−	36203.9i	0.0821827	−	1.37951i
$163$	−4730.68			−0.178053			−0.0890263	−	0.996029i	$-0.528376\pi$
$163$	−4730.68			−0.178053			−0.0890263	+	0.996029i	$0.528376\pi$
$164$	−29189.9	−	16852.8i	−1.08529	−	0.626592i
$165$	−2611.84	−	4683.37i	−0.0959353	−	0.172025i
$166$	−9381.13	−	16248.6i	−0.340439	−	0.589657i
$167$	−37018.9	+	21372.9i	−1.32736	+	0.766354i	−0.984891	−	0.173173i	$-0.944598\pi$
$167$	−37018.9	+	21372.9i	−1.32736	+	0.766354i	−0.342473	+	0.939528i	$0.611265\pi$
$168$	−1.75211	+	117.773i	−6.20786e−5	+	0.00417281i
$169$	12420.1	−	21512.2i	0.434861	−	0.753201i
$170$		−	6595.94i		−	0.228233i
$171$	−16886.0	+	27335.8i	−0.577476	+	0.934844i
$172$	−42.7765			−0.00144593
$173$	9346.89	+	5396.43i	0.312302	+	0.180308i	0.647956	−	0.761678i	$-0.275624\pi$
$173$	9346.89	+	5396.43i	0.312302	+	0.180308i	−0.335654	+	0.941985i	$0.608957\pi$
$174$	−29451.3	+	49302.5i	−0.972760	+	1.62844i
$175$	102.541	+	177.606i	0.00334828	+	0.00579939i
$176$	−12784.5	+	7381.15i	−0.412724	+	0.238286i
$177$	−52065.7	−	31101.9i	−1.66190	−	0.992751i
$178$	−6395.49	+	11077.3i	−0.201852	+	0.349619i
$179$		−	52847.3i		−	1.64936i	−0.565597	−	0.824682i	$-0.691354\pi$
$179$		−	52847.3i		−	1.64936i	0.565597	−	0.824682i	$-0.308646\pi$
$180$	−11607.7	+	6248.91i	−0.358264	+	0.192868i
$181$	47183.7			1.44024			0.720119	−	0.693850i	$-0.244087\pi$
$181$	47183.7			1.44024			0.720119	+	0.693850i	$0.244087\pi$
$182$	479.100	+	276.608i	0.0144638	+	0.00835070i
$183$	21578.8	+	321.026i	0.644354	+	0.00958601i
$184$	982.544	+	1701.82i	0.0290213	+	0.0502663i
$185$	−26318.1	+	15194.7i	−0.768972	+	0.443966i
$186$	66173.4	−	36903.8i	1.91275	−	1.06671i
$187$	−2843.81	+	4925.63i	−0.0813238	+	0.140857i
$188$			44667.8i			1.26380i
$189$	643.634	−	1008.09i	0.0180184	−	0.0282212i
$190$	24515.7			0.679106
$191$	28642.0	+	16536.5i	0.785121	+	0.453290i	0.838242	−	0.545298i	$-0.183584\pi$
$191$	28642.0	+	16536.5i	0.785121	+	0.453290i	−0.0531211	+	0.998588i	$0.516917\pi$
$192$	14583.4	+	26150.0i	0.395601	+	0.709365i
$193$	16062.9	+	27821.7i	0.431229	+	0.746911i	0.996979	−	0.0776659i	$-0.0247468\pi$
$193$	16062.9	+	27821.7i	0.431229	+	0.746911i	−0.565750	+	0.824577i	$0.691413\pi$
$194$	15094.1	−	8714.58i	0.401055	−	0.231549i
$195$	91.3031	−	6137.23i	0.00240113	−	0.161400i
$196$	−17456.0	+	30234.7i	−0.454395	+	0.787035i
$197$			12747.9i			0.328477i	0.986421	+	0.164239i	$0.0525167\pi$
$197$			12747.9i			0.328477i	−0.986421	+	0.164239i	$0.947483\pi$
$198$	23851.3	+	709.826i	0.608390	+	0.0181060i
$199$	−39626.6			−1.00065			−0.500324	−	0.865838i	$-0.666786\pi$
$199$	−39626.6			−1.00065			−0.500324	+	0.865838i	$0.666786\pi$
$200$	−863.527	−	498.557i	−0.0215882	−	0.0124639i
$201$	5409.50	−	9055.72i	0.133895	−	0.224146i
$202$	32047.4	+	55507.8i	0.785400	+	1.36035i
$203$	−1640.15	+	946.942i	−0.0398008	+	0.0229790i
$204$	12003.7	+	7170.52i	0.288440	+	0.172302i
$205$	−12943.7	+	22419.1i	−0.307999	+	0.533470i
$206$		−	9048.24i		−	0.213221i
$207$	593.580	−	19945.3i	0.0138528	−	0.465478i
$208$	−16897.1			−0.390558
$209$	−18307.5	−	10569.9i	−0.419119	−	0.241978i
$210$	−912.477	−	13.5749i	−0.0206911	−	0.000307820i
$211$	−35433.2	−	61372.1i	−0.795877	−	1.37850i	−0.922281	−	0.386520i	$-0.873677\pi$
$211$	−35433.2	−	61372.1i	−0.795877	−	1.37850i	0.126405	−	0.991979i	$-0.459656\pi$
$212$	−50437.5	+	29120.1i	−1.12223	+	0.647920i
$213$	33534.9	−	18701.8i	0.739158	−	0.412216i
$214$	−22819.1	+	39523.8i	−0.498277	+	0.863040i
$215$			32.8541i			0.000710744i
$216$	−259.431	+	5809.38i	−0.00556050	+	0.124515i
$217$	2498.66			0.0530625
$218$	80022.5	+	46201.0i	1.68383	+	0.972162i
$219$	7555.17	+	13547.4i	0.157527	+	0.282467i
$220$	−4336.71	−	7511.40i	−0.0896014	−	0.155194i
$221$	−5637.93	+	3255.06i	−0.115434	+	0.0666461i
$222$	2011.55	−	135213.i	0.0408155	−	2.74354i
$223$	−29967.4	+	51905.1i	−0.602615	+	1.04376i	0.389809	+	0.920896i	$0.372541\pi$
$223$	−29967.4	+	51905.1i	−0.602615	+	1.04376i	−0.992424	+	0.122864i	$0.960792\pi$
$224$			2302.85i			0.0458954i
$225$	4799.42	+	8915.22i	0.0948034	+	0.176103i
$226$	−1897.26			−0.0371459
$227$	27434.5	+	15839.3i	0.532408	+	0.307386i	0.741997	−	0.670404i	$-0.233879\pi$
$227$	27434.5	+	15839.3i	0.532408	+	0.307386i	−0.209588	+	0.977790i	$0.567212\pi$
$228$	−26651.3	+	44615.3i	−0.512683	+	0.858251i
$229$	−35424.5	−	61357.0i	−0.675511	−	1.17002i	−0.976319	−	0.216335i	$-0.930590\pi$
$229$	−35424.5	−	61357.0i	−0.675511	−	1.17002i	0.300808	−	0.953685i	$-0.402744\pi$
$230$	−13185.2	+	7612.49i	−0.249248	+	0.143903i
$231$	675.555	+	403.548i	0.0126601	+	0.00756261i
$232$	4604.06	−	7974.46i	0.0855391	−	0.148158i
$233$		−	50930.5i		−	0.938138i	−0.883162	−	0.469069i	$-0.844590\pi$
$233$		−	50930.5i		−	0.938138i	0.883162	−	0.469069i	$-0.155410\pi$
$234$	23236.7	+	14353.9i	0.424368	+	0.262142i
$235$	34306.7			0.621217
$236$	−84952.2	−	49047.2i	−1.52528	−	0.880623i
$237$	67739.4	+	1007.75i	1.20599	+	0.0179415i
$238$	483.960	+	838.243i	0.00854388	+	0.0147984i
$239$	21579.6	−	12459.0i	0.377788	−	0.218116i	−0.299068	−	0.954232i	$-0.596676\pi$
$239$	21579.6	−	12459.0i	0.377788	−	0.218116i	0.676855	+	0.736116i	$0.263342\pi$
$240$	24343.6	−	13576.0i	0.422631	−	0.235694i
$241$	−56981.7	+	98695.2i	−0.981073	+	1.69927i	−0.322839	+	0.946454i	$0.604637\pi$
$241$	−56981.7	+	98695.2i	−0.981073	+	1.69927i	−0.658234	+	0.752814i	$0.728696\pi$
$242$		−	65233.6i		−	1.11389i
$243$	33243.0	−	48802.6i	0.562972	−	0.826476i
$244$	34906.2			0.586304
$245$	23221.5	+	13407.0i	0.386864	+	0.223356i
$246$	−56106.6	−	100607.i	−0.927136	−	1.66248i
$247$	−12098.4	−	20955.0i	−0.198305	−	0.343474i
$248$	−10520.9	+	6074.27i	−0.171061	+	0.0987622i
$249$	454.400	−	30543.9i	0.00732891	−	0.492636i
$250$	3862.69	−	6690.38i	0.0618031	−	0.107046i
$251$		−	18036.5i		−	0.286289i	−0.989702	−	0.143145i	$-0.954279\pi$
$251$		−	18036.5i		−	0.286289i	0.989702	−	0.143145i	$-0.0457214\pi$
$252$	1016.67	−	1645.83i	0.0160095	−	0.0259169i
$253$	13128.4			0.205102
$254$	−21687.4	−	12521.2i	−0.336155	−	0.194079i
$255$	5507.25	−	9219.35i	0.0846944	−	0.141782i
$256$	−37857.2	−	65570.6i	−0.577655	−	1.00053i
$257$	−60566.9	+	34968.3i	−0.917000	+	0.529430i	−0.882677	−	0.469981i	$-0.844261\pi$
$257$	−60566.9	+	34968.3i	−0.917000	+	0.529430i	−0.0343232	+	0.999411i	$0.510928\pi$
$258$	−125.507	−	74.9728i	−0.00188551	−	0.00112633i
$259$	2229.75	−	3862.04i	0.0332397	−	0.0575728i
$260$		−	9927.69i		−	0.146859i
$261$	−82329.9	+	44321.5i	−1.20858	+	0.650629i
$262$	49760.1			0.724900
$263$	−52155.5	−	30112.0i	−0.754029	−	0.435339i	0.0731187	−	0.997323i	$-0.476705\pi$
$263$	−52155.5	−	30112.0i	−0.754029	−	0.435339i	−0.827148	+	0.561984i	$0.810038\pi$
$264$	−3825.55	−	56.9125i	−0.0548891	−	0.000816582i
$265$	22365.5	+	38738.1i	0.318483	+	0.551628i
$266$	−3115.58	+	1798.78i	−0.0440327	+	0.0254223i
$267$	−18188.1	+	10143.2i	−0.255132	+	0.142283i
$268$	8530.70	−	14775.6i	0.118772	−	0.205720i
$269$			27875.7i			0.385230i	0.981274	+	0.192615i	$0.0616969\pi$
$269$			27875.7i			0.385230i	−0.981274	+	0.192615i	$0.938303\pi$
$270$	−45009.6	−	2010.00i	−0.617415	−	0.0275720i
$271$	34504.7			0.469829			0.234914	−	0.972016i	$-0.424519\pi$
$271$	34504.7			0.469829			0.234914	+	0.972016i	$0.424519\pi$
$272$	−25602.8	−	14781.8i	−0.346058	−	0.199797i
$273$	438.700	+	786.647i	0.00588630	+	0.0105549i
$274$	60048.6	+	104007.i	0.799838	+	1.38536i
$275$	−5769.06	+	3330.77i	−0.0762851	+	0.0440432i
$276$	480.093	−	32271.0i	0.00630242	−	0.423637i
$277$	41222.5	−	71399.4i	0.537248	−	0.930540i	−0.461803	−	0.886982i	$-0.652797\pi$
$277$	41222.5	−	71399.4i	0.537248	−	0.930540i	0.999051	−	0.0435578i	$-0.0138693\pi$
$278$			11605.2i			0.150163i
$279$	123305.	+	3669.62i	1.58407	+	0.0471426i
$280$	146.321			0.00186634
$281$	16162.8	+	9331.61i	0.204694	+	0.118180i	0.598843	−	0.800866i	$-0.295627\pi$
$281$	16162.8	+	9331.61i	0.204694	+	0.118180i	−0.394149	+	0.919046i	$0.628961\pi$
$282$	−78287.5	+	131056.i	−0.984452	+	1.64801i
$283$	−15003.3	−	25986.5i	−0.187333	−	0.324471i	0.757027	−	0.653384i	$-0.226651\pi$
$283$	−15003.3	−	25986.5i	−0.187333	−	0.324471i	−0.944360	+	0.328913i	$0.893318\pi$
$284$	53784.7	−	31052.6i	0.666840	−	0.385000i
$285$	34266.4	+	20469.3i	0.421870	+	0.252008i
$286$	−8984.88	+	15562.3i	−0.109845	+	0.190257i
$287$		−	3798.83i		−	0.0461196i
$288$	−3382.05	+	113642.i	−0.0407751	+	1.37011i
$289$	72130.8			0.863624
$290$	61784.0	+	35671.0i	0.734650	+	0.424150i
$291$	28373.7	+	422.114i	0.335066	+	0.00498475i
$292$	12544.6	+	21727.9i	0.147127	+	0.254831i
$293$	−87765.4	+	50671.4i	−1.02232	+	0.590238i	−0.914776	−	0.403962i	$-0.867633\pi$
$293$	−87765.4	+	50671.4i	−1.02232	+	0.590238i	−0.107547	+	0.994200i	$0.534300\pi$
$294$	−104208.	+	58114.8i	−1.20560	+	0.672345i
$295$	−37670.2	+	65246.8i	−0.432867	+	0.749747i
$296$			21682.2i			0.247469i
$297$	32745.1	+	20906.7i	0.371221	+	0.237013i
$298$	88725.1			0.999112
$299$	13013.7	+	7513.45i	0.145565	+	0.0840422i
$300$	7976.41	+	14302.8i	0.0886268	+	0.158920i
$301$	−2.41059	−	4.17526i	−2.66066e−5	−	4.60840e-5i
$302$	22250.0	−	12846.0i	0.243959	−	0.140850i
$303$	−1552.30	+	104343.i	−0.0169080	+	1.13652i
$304$	54940.8	−	95160.2i	0.594494	−	1.02969i
$305$		−	26809.4i		−	0.288196i
$306$	22651.7	+	42076.9i	0.241912	+	0.449367i
$307$	−159395.			−1.69121			−0.845603	−	0.533812i	$-0.820759\pi$
$307$	−159395.			−1.69121			−0.845603	+	0.533812i	$0.820759\pi$
$308$	1102.26	+	636.389i	0.0116193	+	0.00670843i
$309$	7554.79	−	12647.0i	0.0791235	−	0.132456i
$310$	−47061.9	−	81513.6i	−0.489718	−	0.848216i
$311$	154748.	−	89344.0i	1.59995	−	0.923729i	0.608450	−	0.793593i	$-0.291792\pi$
$311$	154748.	−	89344.0i	1.59995	−	0.923729i	0.991496	−	0.130137i	$-0.0415416\pi$
$312$	−3759.56	−	2245.80i	−0.0386213	−	0.0230708i
$313$	4902.05	−	8490.59i	0.0500367	−	0.0866661i	−0.839922	−	0.542707i	$-0.817400\pi$
$313$	4902.05	−	8490.59i	0.0500367	−	0.0866661i	0.889959	+	0.456041i	$0.150733\pi$
$314$			187727.i			1.90400i
$315$	−1264.06	−	780.843i	−0.0127394	−	0.00786942i
$316$	109576.			1.09734
$317$	−13873.8	−	8010.04i	−0.138063	−	0.0797106i	0.429378	−	0.903125i	$-0.358733\pi$
$317$	−13873.8	−	8010.04i	−0.138063	−	0.0797106i	−0.567440	+	0.823414i	$0.692066\pi$
$318$	−199023.	−	2960.85i	−1.96810	−	0.0292794i
$319$	−30758.8	−	53275.9i	−0.302266	−	0.523539i
$320$	32212.1	−	18597.6i	0.314571	−	0.181618i
$321$	−64895.2	+	36190.9i	−0.629799	+	0.351229i
$322$	1117.09	−	1934.86i	0.0107740	−	0.0186611i
$323$		−	42335.2i		−	0.405785i
$324$	52588.3	−	79726.3i	0.500956	−	0.759471i
$325$	−7624.88			−0.0721882
$326$	−22646.9	−	13075.2i	−0.213095	−	0.123031i
$327$	73274.6	+	131391.i	0.685264	+	1.22877i
$328$	9235.00	+	15995.5i	0.0858399	+	0.148679i
$329$	−4359.86	+	2517.17i	−0.0402792	+	0.0232552i
$330$	440.943	−	29639.4i	0.00404906	−	0.272171i
$331$	28154.5	−	48765.1i	0.256976	−	0.445095i	−0.708454	−	0.705757i	$-0.750607\pi$
$331$	28154.5	−	48765.1i	0.256976	−	0.445095i	0.965430	+	0.260661i	$0.0839406\pi$
$332$		−	49408.4i		−	0.448254i
$333$	115707.	−	187312.i	1.04345	−	1.68918i
$334$	−236291.			−2.11814
$335$	−11348.3	−	6551.93i	−0.101121	−	0.0583821i
$336$	−2097.59	+	3511.45i	−0.0185799	+	0.0311034i
$337$	−95472.2	−	165363.i	−0.840654	−	1.45606i	−0.889343	−	0.457242i	$-0.848837\pi$
$337$	−95472.2	−	165363.i	−0.840654	−	1.45606i	0.0486885	−	0.998814i	$-0.484496\pi$
$338$	118916.	−	68656.0i	1.04089	−	0.600960i
$339$	−2651.86	−	1584.11i	−0.0230755	−	0.0137844i
$340$	8684.85	−	15042.6i	0.0751284	−	0.130126i
$341$			81162.2i			0.697983i
$342$	−156391.	+	84191.6i	−1.33709	+	0.719808i
$343$	−7874.02			−0.0669280
$344$	20.3002	+	11.7203i	0.000171547	+	9.90429e-5i
$345$	−24785.4	−	368.731i	−0.208237	−	0.00309793i
$346$	29830.6	+	51668.1i	0.249178	+	0.431589i
$347$	140654.	−	81206.5i	1.16813	−	0.674423i	0.214894	−	0.976637i	$-0.431059\pi$
$347$	140654.	−	81206.5i	1.16813	−	0.674423i	0.953240	+	0.302215i	$0.0977260\pi$
$348$	−132083.	+	73660.2i	−1.09065	+	0.608240i
$349$	−56523.7	+	97901.9i	−0.464066	+	0.803786i	−0.999159	−	0.0410075i	$-0.986943\pi$
$349$	−56523.7	+	97901.9i	−0.464066	+	0.803786i	0.535093	+	0.844793i	$0.320277\pi$
$350$			1133.66i			0.00925436i
$351$	20493.9	+	39464.2i	0.166346	+	0.320324i
$352$	−74801.8			−0.603708
$353$	−119690.	−	69102.8i	−0.960521	−	0.554557i	−0.0641878	−	0.997938i	$-0.520446\pi$
$353$	−119690.	−	69102.8i	−0.960521	−	0.554557i	−0.896333	+	0.443381i	$0.853779\pi$
$354$	−163288.	−	292798.i	−1.30301	−	2.33648i
$355$	−23849.7	−	41308.8i	−0.189246	−	0.327783i
$356$	−29170.9	+	16841.8i	−0.230171	+	0.132889i
$357$	−23.4419	+	1575.72i	−0.000183931	+	0.0123635i
$358$	146065.	−	252993.i	1.13968	−	1.97398i
$359$			180785.i			1.40272i	0.712805	+	0.701362i	$0.247425\pi$
$359$			180785.i			1.40272i	−0.712805	+	0.701362i	$0.752575\pi$
$360$	7220.76	+	214.893i	0.0557157	+	0.00165813i
$361$	27030.1			0.207412
$362$	225880.	+	130412.i	1.72369	+	0.995175i
$363$	54466.5	−	91179.0i	0.413349	−	0.691961i
$364$	728.418	+	1261.66i	0.00549766	+	0.00952223i
$365$	16687.9	−	9634.78i	0.125261	−	0.0723196i
$366$	102416.	+	61178.7i	0.764546	+	0.456708i
$367$	−13763.9	+	23839.9i	−0.102191	+	0.176999i	−0.912587	−	0.408883i	$-0.865918\pi$
$367$	−13763.9	+	23839.9i	−0.102191	+	0.176999i	0.810396	+	0.585882i	$0.199252\pi$
$368$			68239.6i			0.503896i
$369$	5579.10	−	187467.i	0.0409743	−	1.37680i
$370$	−167988.			−1.22709
$371$	−5684.61	−	3282.01i	−0.0413003	−	0.0238447i
$372$	199505.	+	2968.03i	1.44168	+	0.0214478i
$373$	72426.4	+	125446.i	0.520570	+	0.901654i	0.999714	+	0.0239175i	$0.00761390\pi$
$373$	72426.4	+	125446.i	0.520570	+	0.901654i	−0.479144	+	0.877736i	$0.659053\pi$
$374$	−27228.1	+	15720.1i	−0.194659	+	0.112386i
$375$	10985.1	−	6126.21i	0.0781163	−	0.0435642i
$376$	12238.5	−	21197.8i	0.0865672	−	0.149939i
$377$		−	70413.9i		−	0.495422i
$378$	5867.51	−	3047.02i	0.0410648	−	0.0213251i
$379$	−17111.5			−0.119127			−0.0595634	−	0.998225i	$-0.518971\pi$
$379$	−17111.5			−0.119127			−0.0595634	+	0.998225i	$0.518971\pi$
$380$	55910.2	+	32279.8i	0.387190	+	0.223544i
$381$	−19858.6	−	35609.1i	−0.136804	−	0.245308i
$382$	91410.8	+	158328.i	0.626428	+	1.08500i
$383$	−5056.85	+	2919.57i	−0.0344733	+	0.0199031i	−0.517138	−	0.855902i	$-0.673002\pi$
$383$	−5056.85	+	2919.57i	−0.0344733	+	0.0199031i	0.482664	+	0.875805i	$0.339669\pi$
$384$	544.557	−	36604.1i	0.00369301	−	0.248237i
$385$	488.773	−	846.579i	0.00329751	−	0.00571145i
$386$			177586.i			1.19188i
$387$	−112.827	−	209.584i	−0.000753341	−	0.00139938i
$388$	45897.8			0.304880
$389$	−71645.8	−	41364.7i	−0.473469	−	0.273358i	0.244222	−	0.969719i	$-0.421468\pi$
$389$	−71645.8	−	41364.7i	−0.473469	−	0.273358i	−0.717691	+	0.696362i	$0.754801\pi$
$390$	17399.9	−	29128.1i	0.114398	−	0.191506i
$391$	13145.7	+	22769.0i	0.0859864	+	0.148933i
$392$	16568.0	−	9565.55i	0.107820	−	0.0622498i
$393$	69551.2	+	41547.0i	0.450318	+	0.269001i
$394$	−35234.1	+	61027.2i	−0.226971	+	0.393126i
$395$		−	84159.2i		−	0.539396i
$396$	53460.3	+	33023.7i	0.340911	+	0.210589i
$397$	−31355.6			−0.198945			−0.0994727	−	0.995040i	$-0.531716\pi$
$397$	−31355.6			−0.198945			−0.0994727	+	0.995040i	$0.531716\pi$
$398$	−189702.	−	109525.i	−1.19759	−	0.691427i
$399$	−5856.62	−	87.1285i	−0.0367876	−	0.000547286i
$400$	−17312.9	−	29986.8i	−0.108206	−	0.187418i
$401$	−35460.8	+	20473.3i	−0.220526	+	0.127321i	−0.606194	−	0.795317i	$-0.707304\pi$
$401$	−35460.8	+	20473.3i	−0.220526	+	0.127321i	0.385668	+	0.922638i	$0.373971\pi$
$402$	50925.9	−	28400.5i	0.315128	−	0.175741i
$403$	−46449.6	+	80453.1i	−0.286004	+	0.495373i
$404$			168787.i			1.03413i
$405$	−61233.1	−	40390.0i	−0.373315	−	0.246243i
$406$	−10469.1			−0.0635121
$407$	125448.	+	72427.4i	0.757312	+	0.437234i
$408$	−3731.89	−	6691.77i	−0.0224186	−	0.0401995i
$409$	49618.3	+	85941.4i	0.296616	+	0.513755i	0.975360	−	0.220621i	$-0.0708084\pi$
$409$	49618.3	+	85941.4i	0.296616	+	0.513755i	−0.678743	+	0.734376i	$0.737475\pi$
$410$	−123929.	+	71550.4i	−0.737233	+	0.425642i
$411$	−2908.61	+	195512.i	−0.0172188	+	1.15741i
$412$	11913.8	−	20635.3i	0.0701867	−	0.121567i
$413$		−	11055.8i		−	0.0648173i
$414$	57968.6	−	93842.2i	0.338215	−	0.547517i
$415$	−37947.7			−0.220338
$416$	−74148.3	−	42809.5i	−0.428464	−	0.247374i
$417$	−9689.72	+	16221.0i	−0.0557236	+	0.0932834i
$418$	−58428.5	−	101201.i	−0.334404	−	0.579205i
$419$	63792.8	−	36830.8i	0.363366	−	0.209789i	−0.307190	−	0.951648i	$-0.599389\pi$
$419$	63792.8	−	36830.8i	0.363366	−	0.209789i	0.670556	+	0.741859i	$0.266056\pi$
$420$	−2063.11	−	1232.41i	−0.0116956	−	0.00698647i
$421$	45974.4	−	79629.9i	0.259389	−	0.449275i	−0.706689	−	0.707524i	$-0.749812\pi$
$421$	45974.4	−	79629.9i	0.259389	−	0.449275i	0.966078	+	0.258249i	$0.0831455\pi$
$422$		−	391738.i		−	2.19974i
$423$	−218850.	+	117816.i	−1.22311	+	0.658449i
$424$	31914.5			0.177524
$425$	−11553.3	−	6670.32i	−0.0639631	−	0.0369291i
$426$	212230.	+	3157.33i	1.16947	+	0.0173981i
$427$	1967.07	+	3407.06i	0.0107886	+	0.0186864i
$428$	−104082.	+	60091.6i	−0.568181	+	0.328039i
$429$	−25552.1	+	14250.0i	−0.138839	+	0.0774283i
$430$	−90.8061	+	157.281i	−0.000491109	+	0.000850626i
$431$		−	310504.i		−	1.67153i	−0.549091	−	0.835763i	$-0.685026\pi$
$431$		−	310504.i		−	1.67153i	0.549091	−	0.835763i	$-0.314974\pi$
$432$	−108670.	+	170205.i	−0.582295	+	0.912018i
$433$	169092.			0.901875			0.450937	−	0.892556i	$-0.351090\pi$
$433$	169092.			0.901875			0.450937	+	0.892556i	$0.351090\pi$
$434$	11961.7	+	6906.08i	0.0635058	+	0.0366651i
$435$	56574.1	+	101445.i	0.298978	+	0.536107i
$436$	121665.	+	210731.i	0.640021	+	1.10855i
$437$	−84627.7	+	48859.8i	−0.443149	+	0.255852i
$438$	−1275.50	+	85736.6i	−0.00664862	+	0.446908i
$439$	−78461.8	+	135900.i	−0.407126	+	0.705164i	−0.994566	−	0.104104i	$-0.966803\pi$
$439$	−78461.8	+	135900.i	−0.407126	+	0.705164i	0.587440	+	0.809268i	$0.300136\pi$
$440$			4752.85i			0.0245499i
$441$	−194177.	−	5778.80i	−0.998437	−	0.0297139i
$442$	−35986.9			−0.184204
$443$	−199655.	−	115271.i	−1.01736	−	0.587371i	−0.104019	−	0.994575i	$-0.533170\pi$
$443$	−199655.	−	115271.i	−1.01736	−	0.587371i	−0.913337	+	0.407204i	$0.866504\pi$
$444$	182622.	−	305716.i	0.926374	−	1.55079i
$445$	12935.2	+	22404.5i	0.0653211	+	0.113140i
$446$	−286923.	+	165655.i	−1.44243	+	0.832789i
$447$	124014.	+	74080.7i	0.620662	+	0.370758i
$448$	−2729.11	+	4726.95i	−0.0135977	+	0.0235519i
$449$			212213.i			1.05264i	0.850286	+	0.526320i	$0.176429\pi$
$449$			212213.i			1.05264i	−0.850286	+	0.526320i	$0.823571\pi$
$450$	−1664.94	+	55944.6i	−0.00822190	+	0.276269i
$451$	123395.			0.606657
$452$	−4326.87	−	2498.12i	−0.0211786	−	0.0122275i
$453$	41825.3	+	622.232i	0.203818	+	0.00303219i
$454$	87557.0	+	151653.i	0.424795	+	0.735766i
$455$	969.005	−	559.455i	0.00468062	−	0.00270236i
$456$	24871.9	−	13870.7i	0.119613	−	0.0667064i
$457$	−115663.	+	200334.i	−0.553810	+	0.959227i	0.444185	+	0.895935i	$0.353493\pi$
$457$	−115663.	+	200334.i	−0.553810	+	0.959227i	−0.997995	+	0.0632920i	$0.979840\pi$
$458$		−	391641.i		−	1.86706i
$459$	−3470.98	+	77725.1i	−0.0164751	+	0.368923i
$460$	−40093.4			−0.189477
$461$	−183131.	−	105731.i	−0.861709	−	0.497508i	0.00287540	−	0.999996i	$-0.499085\pi$
$461$	−183131.	−	105731.i	−0.861709	−	0.497508i	−0.864584	+	0.502488i	$0.832418\pi$
$462$	2118.67	+	3799.06i	0.00992614	+	0.0177989i
$463$	105778.	+	183213.i	0.493438	+	0.854660i	0.999971	−	0.00756049i	$-0.00240660\pi$
$463$	105778.	+	183213.i	0.493438	+	0.854660i	−0.506533	+	0.862220i	$0.669073\pi$
$464$	276921.	−	159880.i	1.28623	−	0.742608i
$465$	2279.57	−	153228.i	0.0105426	−	0.708652i
$466$	140768.	−	243817.i	0.648234	−	1.12277i
$467$			53825.6i			0.246806i	0.992357	+	0.123403i	$0.0393807\pi$
$467$			53825.6i			0.246806i	−0.992357	+	0.123403i	$0.960619\pi$
$468$	34093.5	+	63330.9i	0.155661	+	0.289150i
$469$	1922.92			0.00874210
$470$	164235.	+	94820.9i	0.743480	+	0.429248i
$471$	−156742.	+	262392.i	−0.706552	+	1.18279i
$472$	26876.9	+	46552.1i	0.120641	+	0.208956i
$473$	135.622	−	78.3014i	0.000606189	−	0.000349983i
$474$	321500.	+	192050.i	1.43095	+	0.854788i
$475$	24792.2	−	42941.3i	0.109882	−	0.190322i
$476$			2548.91i			0.0112497i
$477$	−275708.	−	170312.i	−1.21175	−	0.748527i
$478$	137743.			0.602854
$479$	102280.	+	59051.5i	0.445780	+	0.257371i	0.706046	−	0.708166i	$-0.250477\pi$
$479$	102280.	+	59051.5i	0.445780	+	0.257371i	−0.260266	+	0.965537i	$0.583810\pi$
$480$	141220.	+	2100.93i	0.612936	+	0.00911860i
$481$	82901.2	+	143589.i	0.358320	+	0.620628i
$482$	−545571.	+	314985.i	−2.34832	+	1.35580i
$483$	3176.90	−	1771.71i	0.0136179	−	0.00759447i
$484$	85892.8	−	148771.i	0.366662	−	0.635077i
$485$		−	35251.4i		−	0.149862i
$486$	294028.	−	141749.i	1.24485	−	0.600133i
$487$	245730.			1.03610			0.518048	−	0.855352i	$-0.326659\pi$
$487$	245730.			1.03610			0.518048	+	0.855352i	$0.326659\pi$
$488$	−16565.2	−	9563.95i	−0.0695598	−	0.0401604i
$489$	−20737.2	−	37184.6i	−0.0867227	−	0.155505i
$490$	74111.4	+	128365.i	0.308669	+	0.534630i
$491$	210737.	−	121669.i	0.874134	−	0.504681i	0.00541403	−	0.999985i	$-0.498277\pi$
$491$	210737.	−	121669.i	0.874134	−	0.504681i	0.868720	+	0.495304i	$0.164943\pi$
$492$	4512.43	−	303317.i	0.0186415	−	1.25304i
$493$	61598.8	−	106692.i	0.253442	−	0.438974i
$494$		−	133756.i		−	0.548099i
$495$	25363.6	−	41059.7i	0.103514	−	0.167574i
$496$	−421870.			−1.71481
$497$	6061.86	+	3499.81i	0.0245410	+	0.0141688i
$498$	86596.2	−	144965.i	0.349172	−	0.584528i
$499$	−133235.	−	230770.i	−0.535078	−	0.926783i	−0.999160	−	0.0409900i	$-0.986949\pi$
$499$	−133235.	−	230770.i	−0.535078	−	0.926783i	0.464081	−	0.885793i	$-0.346385\pi$
$500$	17618.4	−	10172.0i	0.0704736	−	0.0406879i
$501$	−330272.	−	197290.i	−1.31582	−	0.786014i
$502$	49851.4	−	86345.2i	0.197820	−	0.342634i
$503$			245223.i			0.969225i	0.874729	+	0.484612i	$0.161039\pi$
$503$			245223.i			0.969225i	−0.874729	+	0.484612i	$0.838961\pi$
$504$	−933.415	+	502.495i	−0.00367463	+	0.00197820i
$505$	129635.			0.508324
$506$	62848.8	+	36285.8i	0.245469	+	0.141721i
$507$	223536.	+	3325.54i	0.869625	+	0.0129374i
$508$	−32973.3	−	57111.4i	−0.127772	−	0.221307i
$509$	−210530.	+	121549.i	−0.812601	+	0.469156i	−0.847858	−	0.530223i	$-0.822108\pi$
$509$	−210530.	+	121549.i	−0.812601	+	0.469156i	0.0352570	+	0.999378i	$0.488775\pi$
$510$	51846.1	−	28913.7i	0.199331	−	0.111164i
$511$	−1413.85	+	2448.87i	−0.00541456	+	0.00937828i
$512$		−	353456.i		−	1.34833i
$513$	−288888.	−	12900.9i	−1.09773	−	0.0490215i
$514$	−386598.			−1.46330
$515$	−15848.7	−	9150.27i	−0.0597558	−	0.0345000i
$516$	−187.514	−	336.237i	−0.000704260	−	0.00126283i
$517$	−81763.3	−	141618.i	−0.305899	−	0.529832i
$518$	21348.7	−	12325.7i	0.0795632	−	0.0459358i
$519$	−1444.92	+	97125.0i	−0.00536426	+	0.360576i
$520$	−2720.09	+	4711.33i	−0.0100595	+	0.0174236i
$521$		−	147869.i		−	0.544755i	−0.962190	−	0.272377i	$-0.912190\pi$
$521$		−	147869.i		−	0.544755i	0.962190	−	0.272377i	$-0.0878099\pi$
$522$	−516635.	−	15375.3i	−1.89602	−	0.0564264i
$523$	−460364.			−1.68305			−0.841526	−	0.540216i	$-0.818343\pi$
$523$	−460364.			−1.68305			−0.841526	+	0.540216i	$0.818343\pi$
$524$	113482.	+	65518.9i	0.413299	+	0.238618i
$525$	−946.545	+	1584.55i	−0.00343418	+	0.00574894i
$526$	−166454.	−	288307.i	−0.601620	−	1.04204i
$527$	−140762.	+	81269.2i	−0.506833	+	0.292620i
$528$	−114060.	−	68134.6i	−0.409134	−	0.244399i
$529$	−109577.	+	189793.i	−0.391569	+	0.678218i
$530$			247265.i			0.880260i
$531$	16237.0	−	545590.i	0.0575860	−	1.93498i
$532$	−9473.78			−0.0334734
$533$	122317.	+	70619.5i	0.430557	+	0.248582i
$534$	−115106.	−	1712.43i	−0.403660	−	0.00600522i
$535$	46152.8	+	79939.0i	0.161247	+	0.279287i
$536$	−8096.73	+	4674.65i	−0.0281825	+	0.0162712i
$537$	415396.	−	231659.i	1.44050	−	0.803343i
$538$	−77046.0	+	133448.i	−0.266186	+	0.461048i
$539$		−	127811.i		−	0.439938i
$540$	−100002.	−	63847.9i	−0.342941	−	0.218957i
$541$	−126467.			−0.432100			−0.216050	−	0.976382i	$-0.569317\pi$
$541$	−126467.			−0.432100			−0.216050	+	0.976382i	$0.569317\pi$
$542$	165182.	+	95368.1i	0.562296	+	0.324642i
$543$	206832.	+	370878.i	0.701486	+	1.25786i
$544$	−74900.5	−	129731.i	−0.253097	−	0.438377i
$545$	161850.	−	93444.0i	0.544903	−	0.314600i
$546$	−74.0633	+	4978.40i	−0.000248438	+	0.0166995i
$547$	227696.	−	394380.i	0.760992	−	1.31808i	−0.181348	−	0.983419i	$-0.558046\pi$
$547$	227696.	−	394380.i	0.760992	−	1.31808i	0.942340	−	0.334658i	$-0.108621\pi$
$548$			316263.i			1.05314i
$549$	92068.5	+	171023.i	0.305468	+	0.567426i
$550$	−36823.9			−0.121732
$551$	396553.	+	228950.i	1.30616	+	0.754115i
$552$	−9069.75	+	15183.1i	−0.0297658	+	0.0498290i
$553$	6174.96	+	10695.3i	0.0201922	+	0.0349739i
$554$	394684.	−	227871.i	1.28597	−	0.742454i
$555$	−234802.	−	140261.i	−0.762283	−	0.455356i
$556$	−15280.5	+	26466.7i	−0.0494298	+	0.0856149i
$557$			469409.i			1.51301i	0.653989	+	0.756504i	$0.273094\pi$
$557$			469409.i			1.51301i	−0.653989	+	0.756504i	$0.726906\pi$
$558$	580150.	+	358373.i	1.86325	+	1.15098i
$559$	179.249			0.000573633
$560$	4400.41	+	2540.58i	0.0140319	+	0.00810133i
$561$	−51183.0	−	761.446i	−0.162630	−	0.00241943i
$562$	51583.6	+	89345.4i	0.163320	+	0.282878i
$563$	420987.	−	243057.i	1.32816	−	0.766816i	0.343148	−	0.939281i	$-0.388507\pi$
$563$	420987.	−	243057.i	1.32816	−	0.766816i	0.985016	+	0.172466i	$0.0551734\pi$
$564$	−351103.	+	195804.i	−1.10376	+	0.615550i
$565$	−1918.66	+	3323.21i	−0.00601036	+	0.0104103i
$566$		−	165872.i		−	0.517773i
$567$	10745.3	+	640.137i	0.0334235	+	0.00199116i
$568$	−34032.4			−0.105486
$569$	66661.6	+	38487.1i	0.205897	+	0.118875i	0.599403	−	0.800447i	$-0.295405\pi$
$569$	66661.6	+	38487.1i	0.205897	+	0.118875i	−0.393506	+	0.919322i	$0.628738\pi$
$570$	107466.	+	192701.i	0.330767	+	0.593109i
$571$	173406.	+	300348.i	0.531854	+	0.921198i	0.999309	+	0.0371810i	$0.0118378\pi$
$571$	173406.	+	300348.i	0.531854	+	0.921198i	−0.467455	+	0.884017i	$0.654829\pi$
$572$	−40981.5	+	23660.7i	−0.125255	+	0.0723162i
$573$	−4427.72	+	297623.i	−0.0134856	+	0.906479i
$574$	10499.6	−	18185.9i	0.0318677	−	0.0551965i
$575$			30793.3i			0.0931368i
$576$	−141620.	+	229261.i	−0.426854	+	0.691010i
$577$	439490.			1.32007			0.660035	−	0.751234i	$-0.270541\pi$
$577$	439490.			1.32007			0.660035	+	0.751234i	$0.270541\pi$
$578$	345308.	+	199363.i	1.03360	+	0.596746i
$579$	−148274.	+	248217.i	−0.442292	+	0.740413i
$580$	93935.8	+	162702.i	0.279238	+	0.483655i
$581$	4822.57	−	2784.31i	0.0142865	−	0.00824832i
$582$	134665.	+	80443.3i	0.397566	+	0.237489i
$583$	106607.	−	184649.i	0.313653	−	0.543264i
$584$		−	13748.4i		−	0.0403113i
$585$	48640.7	−	26185.2i	0.142131	−	0.0765147i
$586$	−560206.			−1.63137
$587$	33478.2	+	19328.6i	0.0971596	+	0.0560951i	0.547792	−	0.836614i	$-0.315468\pi$
$587$	33478.2	+	19328.6i	0.0971596	+	0.0560951i	−0.450633	+	0.892709i	$0.648802\pi$
$588$	−314174.	−	4673.94i	−0.908689	−	0.0135185i
$589$	−302061.	−	523184.i	−0.870690	−	1.50808i
$590$	−360673.	+	208235.i	−1.03612	+	0.598204i
$591$	−100202.	+	55881.1i	−0.286881	+	0.159989i
$592$	−376468.	+	652062.i	−1.07420	+	1.86057i
$593$			533729.i			1.51779i	0.651213	+	0.758895i	$0.274260\pi$
$593$			533729.i			1.51779i	−0.651213	+	0.758895i	$0.725740\pi$
$594$	98974.2	+	190590.i	0.280511	+	0.540166i
$595$	1957.67			0.00552975
$596$	202345.	+	116824.i	0.569640	+	0.328882i
$597$	−173706.	−	311478.i	−0.487378	−	0.873933i
$598$	41533.1	+	71937.5i	0.116143	+	0.201165i
$599$	207901.	−	120032.i	0.579433	−	0.334536i	−0.181475	−	0.983396i	$-0.558087\pi$
$599$	207901.	−	120032.i	0.579433	−	0.334536i	0.760908	+	0.648860i	$0.224754\pi$
$600$	133.491	−	8973.04i	0.000370809	−	0.0249251i
$601$	125627.	−	217593.i	0.347805	−	0.602415i	−0.638054	−	0.769991i	$-0.720261\pi$
$601$	125627.	−	217593.i	0.347805	−	0.602415i	0.985859	+	0.167576i	$0.0535939\pi$
$602$		−	26.6506i		−	7.35385e-5i
$603$	94893.6	+	2824.08i	0.260977	+	0.00776679i
$604$	67657.3			0.185456
$605$	−114262.	−	65969.2i	−0.312170	−	0.180231i
$606$	−295826.	+	495225.i	−0.805548	+	1.34852i
$607$	−286713.	−	496601.i	−0.778161	−	1.34782i	−0.933000	−	0.359875i	$-0.882819\pi$
$607$	−286713.	−	496601.i	−0.778161	−	1.34782i	0.154839	−	0.987940i	$-0.450514\pi$
$608$	482185.	−	278389.i	1.30439	−	0.753088i
$609$	−14633.0	−	8741.11i	−0.0394546	−	0.0235685i
$610$	74099.0	−	128343.i	0.199137	−	0.344916i
$611$		−	187175.i		−	0.501377i
$612$	−3743.43	+	125785.i	−0.00999463	+	0.335836i
$613$	568610.			1.51319			0.756595	−	0.653884i	$-0.226862\pi$
$613$	568610.			1.51319			0.756595	+	0.653884i	$0.226862\pi$
$614$	−763061.	−	440553.i	−2.02405	−	1.16859i
$615$	−232960.	−	3465.73i	−0.615930	−	0.00916314i
$616$	−348.728	−	604.015i	−0.000919022	−	0.00159179i
$617$	−583219.	+	336722.i	−1.53201	+	0.884506i	−0.532740	+	0.846279i	$0.678837\pi$
$617$	−583219.	+	336722.i	−1.53201	+	0.884506i	−0.999269	+	0.0382263i	$0.987829\pi$
$618$	71121.9	−	39663.5i	0.186220	−	0.103852i
$619$	109102.	−	188971.i	0.284743	−	0.493189i	−0.687804	−	0.725897i	$-0.741425\pi$
$619$	109102.	−	188971.i	0.284743	−	0.493189i	0.972547	+	0.232707i	$0.0747584\pi$
$620$		−	247865.i		−	0.644809i
$621$	159378.	−	82765.5i	0.413280	−	0.214618i
$622$	987758.			2.55311
$623$	−3287.74	−	1898.18i	−0.00847073	−	0.00489058i
$624$	−74069.5	−	132816.i	−0.190226	−	0.341101i
$625$	−7812.50	−	13531.6i	−0.0200000	−	0.0346410i
$626$	46934.6	−	27097.7i	0.119769	−	0.0691487i
$627$	2830.14	−	190236.i	0.00719900	−	0.483903i
$628$	−247180.	+	428128.i	−0.626749	+	1.08556i
$629$			290091.i			0.733219i
$630$	−3893.20	−	7231.86i	−0.00980901	−	0.0182209i
$631$	−72841.4			−0.182944			−0.0914722	−	0.995808i	$-0.529157\pi$
$631$	−72841.4			−0.182944			−0.0914722	+	0.995808i	$0.529157\pi$
$632$	−52001.1	−	30022.8i	−0.130190	−	0.0751653i
$633$	327080.	−	547544.i	0.816294	−	1.36651i
$634$	−44278.2	−	76692.1i	−0.110157	−	0.190797i
$635$	−43863.9	+	25324.8i	−0.108783	+	0.0628057i
$636$	−449989.	−	268805.i	−1.11247	−	0.664542i
$637$	73147.2	−	126695.i	0.180268	−	0.312233i
$638$		−	340060.i		−	0.835437i
$639$	294004.	+	181614.i	0.720032	+	0.444782i
$640$	−45476.8			−0.111027
$641$	−393214.	−	227022.i	−0.957003	−	0.552526i	−0.0617537	−	0.998091i	$-0.519669\pi$
$641$	−393214.	−	227022.i	−0.957003	−	0.552526i	−0.895249	+	0.445565i	$0.853003\pi$
$642$	−410698.	−	6109.93i	−0.996443	−	0.0148240i
$643$	−279579.	−	484245.i	−0.676212	−	1.17123i	−0.976113	−	0.217263i	$-0.930287\pi$
$643$	−279579.	−	484245.i	−0.676212	−	1.17123i	0.299901	−	0.953970i	$-0.403046\pi$
$644$	5095.25	−	2941.74i	0.0122855	−	0.00709305i
$645$	−258.244	+	144.018i	−0.000620740	+	0.000346177i
$646$	117011.	−	202669.i	0.280389	−	0.485649i
$647$		−	369718.i		−	0.883205i	−0.897211	−	0.441602i	$-0.854410\pi$
$647$		−	369718.i		−	0.883205i	0.897211	−	0.441602i	$-0.145590\pi$
$648$	−46800.8	+	23426.6i	−0.111456	+	0.0557903i
$649$	359119.			0.852606
$650$	−36502.1	−	21074.5i	−0.0863956	−	0.0498805i
$651$	10953.0	+	19640.2i	0.0258447	+	0.0463430i
$652$	−34432.1	−	59638.2i	−0.0809970	−	0.140291i
$653$	228547.	−	131952.i	0.535981	−	0.309449i	−0.207468	−	0.978242i	$-0.566522\pi$
$653$	228547.	−	131952.i	0.535981	−	0.309449i	0.743449	+	0.668793i	$0.233189\pi$
$654$	−12370.6	+	831526.i	−0.0289224	+	1.94411i
$655$	50321.2	−	87158.9i	0.117292	−	0.203156i
$656$			641389.i			1.49044i
$657$	−73368.3	+	118772.i	−0.169972	+	0.275158i
$658$	−27829.0			−0.0642754
$659$	−322720.	−	186322.i	−0.743113	−	0.429037i	0.0800869	−	0.996788i	$-0.474480\pi$
$659$	−322720.	−	186322.i	−0.743113	−	0.429037i	−0.823200	+	0.567751i	$0.807814\pi$
$660$	40031.6	−	67014.5i	0.0919000	−	0.153844i
$661$	217857.	+	377340.i	0.498620	+	0.863634i	0.999999	−	0.00159331i	$-0.000507166\pi$
$661$	217857.	+	377340.i	0.498620	+	0.863634i	−0.501379	+	0.865228i	$0.667174\pi$
$662$	269565.	−	155634.i	0.615103	−	0.355130i
$663$	−50300.0	−	30047.1i	−0.114430	−	0.0683559i
$664$	−13537.4	+	23447.5i	−0.0307043	+	0.0531814i
$665$			7276.25i			0.0164537i
$666$	1.07163e6	−	576902.i	2.41600	−	1.30063i
$667$	−284369.			−0.639191
$668$	−538882.	−	311124.i	−1.20765	−	0.697236i
$669$	−539354.	−	8023.94i	−1.20510	−	0.0179281i
$670$	−36218.0	−	62731.4i	−0.0806816	−	0.139745i
$671$	−110669.	+	63895.0i	−0.245800	+	0.141913i
$672$	−18101.1	+	10094.7i	−0.0400836	+	0.0223539i
$673$	40353.9	−	69895.1i	0.0890955	−	0.154318i	−0.818034	−	0.575171i	$-0.804936\pi$
$673$	40353.9	−	69895.1i	0.0890955	−	0.154318i	0.907129	+	0.420853i	$0.138269\pi$
$674$		−	1.05551e6i		−	2.32350i
$675$	−49037.8	+	76805.3i	−0.107628	+	0.168571i
$676$	361597.			0.791281
$677$	60964.1	+	35197.6i	0.133014	+	0.0767955i	0.565030	−	0.825070i	$-0.308864\pi$
$677$	60964.1	+	35197.6i	0.133014	+	0.0767955i	−0.432017	+	0.901866i	$0.642198\pi$
$678$	−8316.77	−	14913.1i	−0.0180924	−	0.0324420i
$679$	2586.48	+	4479.91i	0.00561008	+	0.00971695i
$680$	−8243.04	+	4759.12i	−0.0178266	+	0.0102922i
$681$	−4241.05	+	285076.i	−0.00914491	+	0.614704i
$682$	−224326.	+	388543.i	−0.482292	+	0.835354i
$683$			450590.i			0.965919i	0.875643	+	0.482959i	$0.160438\pi$
$683$			450590.i			0.965919i	−0.875643	+	0.482959i	$0.839562\pi$
$684$	−467518.	−	13913.5i	−0.999277	−	0.0297389i
$685$	242903.			0.517669
$686$	−37694.8	−	21763.1i	−0.0801002	−	0.0462459i
$687$	326999.	−	547409.i	0.692841	−	1.15984i
$688$	407.000	+	704.945i	0.000859840	+	0.00148929i
$689$	211352.	−	122024.i	0.445213	−	0.257044i
$690$	−117635.	−	70270.1i	−0.247080	−	0.147595i
$691$	−35608.1	+	61675.0i	−0.0745749	+	0.129168i	−0.900901	−	0.434024i	$-0.857093\pi$
$691$	−35608.1	+	61675.0i	−0.0745749	+	0.129168i	0.826326	+	0.563191i	$0.190427\pi$
$692$			157111.i			0.328091i
$693$	−210.676	+	7079.05i	−0.000438680	+	0.0147404i
$694$	897793.			1.86405
$695$	20327.5	+	11736.1i	0.0420837	+	0.0242970i
$696$	82863.9	+	1232.76i	0.171059	+	0.00254484i
$697$	123557.	+	214008.i	0.254333	+	0.440518i
$698$	−541186.	+	312454.i	−1.11080	+	0.641320i
$699$	400330.	−	223257.i	0.819339	−	0.456931i
$700$	−1492.69	+	2585.41i	−0.00304630	+	0.00527634i
$701$			95870.0i			0.195095i	0.995231	+	0.0975476i	$0.0310998\pi$
$701$			95870.0i			0.195095i	−0.995231	+	0.0975476i	$0.968900\pi$
$702$	−10966.4	+	245569.i	−0.0222531	+	0.498309i
$703$	−1.07821e6			−2.18169
$704$	−153542.	−	88647.7i	−0.309801	−	0.178864i
$705$	150386.	+	269661.i	0.302571	+	0.542551i
$706$	−381989.	−	661624.i	−0.766375	−	1.32740i
$707$	−16474.7	+	9511.65i	−0.0329593	+	0.0190291i
$708$	13132.6	−	882751.i	0.0261990	−	1.76105i
$709$	−357702.	+	619558.i	−0.711589	+	1.23251i	0.252672	+	0.967552i	$0.418691\pi$
$709$	−357702.	+	619558.i	−0.711589	+	1.23251i	−0.964261	+	0.264956i	$0.914643\pi$
$710$		−	263674.i		−	0.523059i
$711$	289018.	+	536870.i	0.571724	+	1.06201i
$712$	18458.0			0.0364103
$713$	324913.	+	187588.i	0.639128	+	0.369001i
$714$	−4467.38	+	7478.56i	−0.00876307	+	0.0146697i
$715$	18172.4	+	31475.5i	0.0355468	+	0.0615688i
$716$	666229.	−	384648.i	1.29956	−	0.750304i
$717$	192527.	+	115008.i	0.374501	+	0.223711i
$718$	−499674.	+	865460.i	−0.969254	+	1.67880i
$719$			629906.i			1.21848i	0.792987	+	0.609239i	$0.208525\pi$
$719$			629906.i			1.21848i	−0.792987	+	0.609239i	$0.791475\pi$
$720$	213423.	+	131837.i	0.411696	+	0.254314i
$721$	2685.51			0.00516602
$722$	129400.	+	74709.0i	0.248233	+	0.143317i
$723$	−1.02556e6	−	15257.1i	−1.96193	−	0.0291875i
$724$	343425.	+	594830.i	0.655172	+	1.13479i
$725$	124962.	−	72146.6i	0.237739	−	0.137259i
$726$	512756.	−	285955.i	0.972831	−	0.542532i
$727$	−336355.	+	582583.i	−0.636397	+	1.10227i	0.349820	+	0.936817i	$0.386243\pi$
$727$	−336355.	+	582583.i	−0.636397	+	1.10227i	−0.986217	+	0.165456i	$0.947091\pi$
$728$		−	798.317i		−	0.00150630i
$729$	529326.	+	47370.8i	0.996019	+	0.0891366i
$730$	106519.			0.199885
$731$	271.602	+	156.809i	0.000508274	+	0.000293452i
$732$	153013.	+	274373.i	0.285567	+	0.512059i
$733$	−259653.	−	449732.i	−0.483265	−	0.837039i	0.516550	−	0.856257i	$-0.327216\pi$
$733$	−259653.	−	449732.i	−0.483265	−	0.837039i	−0.999815	+	0.0192174i	$0.993883\pi$
$734$	−131783.	+	76084.8i	−0.244606	+	0.141223i
$735$	−3589.78	+	241298.i	−0.00664497	+	0.446663i
$736$	−172888.	+	299451.i	−0.319160	+	0.552802i
$737$			62460.9i			0.114994i
$738$	544851.	−	882030.i	1.00038	−	1.61946i
$739$	349463.			0.639900			0.319950	−	0.947434i	$-0.396334\pi$
$739$	349463.			0.639900			0.319950	+	0.947434i	$0.396334\pi$
$740$	−383111.	−	221189.i	−0.699618	−	0.403925i
$741$	111679.	−	186955.i	0.203392	−	0.340487i
$742$	−18142.4	−	31423.6i	−0.0329524	−	0.0570753i
$743$	−437653.	+	252679.i	−0.792779	+	0.457711i	−0.840940	−	0.541128i	$-0.817997\pi$
$743$	−437653.	+	252679.i	−0.792779	+	0.457711i	0.0481610	+	0.998840i	$0.484664\pi$
$744$	−93864.9	−	56070.9i	−0.169573	−	0.101296i
$745$	89725.7	−	155409.i	0.161661	−	0.280004i
$746$			800722.i			1.43881i
$747$	242076.	−	130319.i	0.433822	−	0.233543i
$748$	−82794.5			−0.147978
$749$	−11730.6	−	6772.68i	−0.0209102	−	0.0120725i
$750$	69520.8	+	1034.26i	0.123592	+	0.00183868i
$751$	518613.	+	898264.i	0.919525	+	1.59266i	0.800138	+	0.599816i	$0.204760\pi$
$751$	518613.	+	898264.i	0.919525	+	1.59266i	0.119387	+	0.992848i	$0.461907\pi$
$752$	736113.	−	424995.i	1.30169	−	0.751533i
$753$	141773.	−	79064.2i	0.250036	−	0.139441i
$754$	194618.	−	337089.i	0.342327	−	0.592927i
$755$		−	51963.6i		−	0.0911602i
$756$	17393.3	+	776.737i	0.0304326	+	0.00135903i
$757$	−708017.			−1.23553			−0.617763	−	0.786365i	$-0.711961\pi$
$757$	−708017.			−1.23553			−0.617763	+	0.786365i	$0.711961\pi$
$758$	−81916.9	−	47294.8i	−0.142572	−	0.0823142i
$759$	57549.1	+	103193.i	0.0998975	+	0.179130i
$760$	−17688.7	−	30637.7i	−0.0306244	−	0.0530430i
$761$	−608190.	+	351139.i	−1.05019	+	0.606330i	−0.922704	−	0.385510i	$-0.874026\pi$
$761$	−608190.	+	351139.i	−1.05019	+	0.606330i	−0.127491	+	0.991840i	$0.540692\pi$
$762$	3352.62	−	225357.i	0.00577397	−	0.388116i
$763$	−13712.4	+	23750.6i	−0.0235540	+	0.0407968i
$764$			481441.i			0.824815i
$765$	96608.3	+	2875.11i	0.165079	+	0.00491282i
$766$	−32277.8			−0.0550106
$767$	355981.	+	205526.i	0.605112	+	0.349362i
$768$	349456.	−	585002.i	0.592474	−	0.991825i
$769$	209289.	+	362498.i	0.353910	+	0.612990i	0.986931	−	0.161145i	$-0.0515186\pi$
$769$	209289.	+	362498.i	0.353910	+	0.612990i	−0.633021	+	0.774135i	$0.718185\pi$
$770$	4679.75	−	2701.86i	0.00789299	−	0.00455702i
$771$	−540361.	−	322789.i	−0.909023	−	0.543012i
$772$	−233826.	+	404999.i	−0.392336	+	0.679546i
$773$		−	480664.i		−	0.804420i	−0.915547	−	0.402210i	$-0.868242\pi$
$773$		−	480664.i		−	0.804420i	0.915547	−	0.402210i	$-0.131758\pi$
$774$	39.1401	−	1315.17i	6.53342e−5	−	0.00219534i
$775$	−190370.			−0.316954
$776$	−21781.5	−	12575.5i	−0.0361713	−	0.0208835i
$777$	40131.0	+	597.027i	0.0664719	+	0.000988899i
$778$	−228657.	−	396046.i	−0.377769	−	0.654315i
$779$	−795421.	+	459237.i	−1.31076	+	0.756766i
$780$	78034.7	−	43518.6i	0.128262	−	0.0715296i
$781$	−113682.	+	196903.i	−0.186376	+	0.322813i
$782$			145334.i			0.237659i
$783$	−709279.	−	452852.i	−1.15689	−	0.738641i
$784$	664347.			1.08084
$785$	328820.	+	189844.i	0.533603	+	0.308076i
$786$	218126.	+	391129.i	0.353072	+	0.633104i
$787$	−316155.	−	547597.i	−0.510447	−	0.884121i	−0.999927	−	0.0121059i	$-0.996146\pi$
$787$	−316155.	−	547597.i	−0.510447	−	0.884121i	0.489479	−	0.872015i	$-0.337187\pi$
$788$	−160709.	+	92785.2i	−0.258813	+	0.149426i
$789$	8062.64	−	541955.i	0.0129516	−	0.870582i
$790$	232609.	−	402891.i	0.372711	−	0.645555i
$791$		−	563.106i		−	0.000899989i
$792$	−16322.2	−	30319.5i	−0.0260212	−	0.0483361i
$793$	−146270.			−0.232599
$794$	−150107.	−	86664.2i	−0.238100	−	0.137467i
$795$	−206453.	+	345610.i	−0.326653	+	0.546830i
$796$	−288422.	−	499561.i	−0.455199	−	0.788429i
$797$	321969.	−	185889.i	0.506871	−	0.292642i	−0.224675	−	0.974434i	$-0.572132\pi$
$797$	321969.	−	185889.i	0.506871	−	0.292642i	0.731547	+	0.681791i	$0.238799\pi$
$798$	−27796.3	−	16604.3i	−0.0436496	−	0.0260745i
$799$	163742.	−	283610.i	0.256488	−	0.444250i
$800$		−	175452.i		−	0.274143i
$801$	−159458.	−	98500.9i	−0.248531	−	0.153524i
$802$	−226346.			−0.351904
$803$	−79544.8	−	45925.2i	−0.123362	−	0.0712230i
$804$	153536.	+	2284.14i	0.237518	+	0.00353354i
$805$	−2259.38	−	3913.36i	−0.00348656	−	0.00603891i
$806$	−444731.	+	256766.i	−0.684585	+	0.395245i
$807$	−219111.	+	122195.i	−0.336448	+	0.187631i
$808$	46245.9	−	80100.3i	0.0708355	−	0.122691i
$809$		−	634644.i		−	0.969690i	−0.874600	−	0.484845i	$-0.838876\pi$
$809$		−	634644.i		−	0.969690i	0.874600	−	0.484845i	$-0.161124\pi$
$810$	−181503.	−	362600.i	−0.276639	−	0.552660i
$811$	−480986.			−0.731292			−0.365646	−	0.930754i	$-0.619152\pi$
$811$	−480986.			−0.731292			−0.365646	+	0.930754i	$0.619152\pi$
$812$	−23875.6	−	13784.6i	−0.0362112	−	0.0209065i
$813$	151253.	+	271217.i	0.228836	+	0.410333i
$814$	400367.	+	693455.i	0.604239	+	1.04657i
$815$	−45804.6	+	26445.3i	−0.0689595	+	0.0398138i
$816$	3957.90	−	266042.i	0.00594407	−	0.399549i
$817$	−582.827	+	1009.49i	−0.000873164	+	0.00151236i
$818$			548563.i			0.819823i
$819$	−4260.22	+	6896.63i	−0.00635132	+	0.0102818i
$820$	−376840.			−0.560441
$821$	165046.	+	95289.3i	0.244860	+	0.141370i	0.617409	−	0.786643i	$-0.288183\pi$
$821$	165046.	+	95289.3i	0.244860	+	0.141370i	−0.372548	+	0.928013i	$0.621516\pi$
$822$	−554302.	+	927923.i	−0.820357	+	1.37331i
$823$	443129.	+	767522.i	0.654230	+	1.13316i	0.982086	+	0.188432i	$0.0603405\pi$
$823$	443129.	+	767522.i	0.654230	+	1.13316i	−0.327856	+	0.944728i	$0.606326\pi$
$824$	−11307.7	+	6528.51i	−0.0166541	+	0.00961523i
$825$	−51469.9	−	30745.9i	−0.0756215	−	0.0451731i
$826$	30557.4	−	52926.9i	0.0447874	−	0.0775741i
$827$		−	721611.i		−	1.05510i	−0.849525	−	0.527548i	$-0.823111\pi$
$827$		−	721611.i		−	1.05510i	0.849525	−	0.527548i	$-0.176889\pi$
$828$	255764.	−	137688.i	0.373060	−	0.200833i
$829$	988071.			1.43774			0.718868	−	0.695147i	$-0.244661\pi$
$829$	988071.			1.43774			0.718868	+	0.695147i	$0.244661\pi$
$830$	−181665.	−	104884.i	−0.263703	−	0.152249i
$831$	741922.	+	11037.5i	1.07438	+	0.0159834i
$832$	−101467.	−	175746.i	−0.146581	−	0.253886i
$833$	221668.	−	127980.i	0.319457	−	0.184439i
$834$	−91220.5	+	50872.1i	−0.131148	+	0.0731388i
$835$	−238956.	+	413884.i	−0.342724	+	0.593615i
$836$		−	307730.i		−	0.440309i
$837$	511672.	+	985304.i	0.730367	+	1.40643i
$838$	407189.			0.579840
$839$	−225828.	−	130382.i	−0.320815	−	0.185223i	0.330941	−	0.943652i	$-0.392634\pi$
$839$	−225828.	−	130382.i	−0.320815	−	0.185223i	−0.651756	+	0.758429i	$0.725967\pi$
$840$	641.409	+	1150.13i	0.000909026	+	0.00163000i
$841$	312616.	+	541466.i	0.441996	+	0.765560i
$842$	440181.	−	254139.i	0.620879	−	0.358465i
$843$	−2498.59	+	167950.i	−0.00351592	+	0.236334i
$844$	515800.	−	893391.i	0.724096	−	1.25417i
$845$		−	277721.i		−	0.388951i
$846$	−1.37332e6	−	40870.7i	−1.91881	−	0.0571046i
$847$	19361.3			0.0269878
$848$	959783.	+	554131.i	1.33469	+	0.770585i
$849$	138494.	−	231844.i	0.192139	−	0.321648i
$850$	−36872.4	−	63864.9i	−0.0510345	−	0.0883943i
$851$	579890.	−	334800.i	0.800731	−	0.462302i
$852$	479851.	+	286643.i	0.661040	+	0.394877i
$853$	678993.	−	1.17605e6i	0.933184	−	1.61632i	0.155344	−	0.987860i	$-0.450351\pi$
$853$	678993.	−	1.17605e6i	0.933184	−	1.61632i	0.777840	−	0.628462i	$-0.216315\pi$
$854$			21747.3i			0.0298187i
$855$	−10686.2	+	359073.i	−0.0146181	+	0.491191i
$856$	65857.9			0.0898795
$857$	−526442.	−	303942.i	−0.716786	−	0.413836i	0.0967829	−	0.995306i	$-0.469145\pi$
$857$	−526442.	−	303942.i	−0.716786	−	0.413836i	−0.813568	+	0.581469i	$0.802478\pi$
$858$	−161710.	−	2405.75i	−0.219666	−	0.00326795i
$859$	−434193.	−	752044.i	−0.588432	−	1.01919i	−0.994438	−	0.105324i	$-0.966412\pi$
$859$	−434193.	−	752044.i	−0.588432	−	1.01919i	0.406006	−	0.913871i	$-0.366921\pi$
$860$	−414.182	+	239.128i	−0.000560008	+	0.000323321i
$861$	29859.9	−	16652.4i	0.0402794	−	0.0224631i
$862$	858208.	−	1.48646e6i	1.15499	−	2.00050i
$863$		−	950879.i		−	1.27674i	−0.769728	−	0.638371i	$-0.779608\pi$
$863$		−	950879.i		−	1.27674i	0.769728	−	0.638371i	$-0.220392\pi$
$864$	−908090.	+	471575.i	−1.21647	+	0.631718i
$865$	120668.			0.161272
$866$	809483.	+	467355.i	1.07937	+	0.623177i
$867$	316190.	+	566970.i	0.420639	+	0.754261i
$868$	18186.4	+	31499.8i	0.0241384	+	0.0418089i
$869$	−347410.	+	200577.i	−0.460047	+	0.265608i
$870$	−9551.10	+	642007.i	−0.0126187	+	0.848206i
$871$	−35746.8	+	61915.2i	−0.0471195	+	0.0816133i
$872$		−	133340.i		−	0.175359i
$873$	121060.	+	224876.i	0.158844	+	0.295063i
$874$	−540178.			−0.707154
$875$	1985.70	+	1146.44i	0.00259357	+	0.00149740i
$876$	−115798.	+	193850.i	−0.150901	+	0.252614i
$877$	158953.	+	275315.i	0.206667	+	0.357957i	0.950662	−	0.310227i	$-0.100405\pi$
$877$	158953.	+	275315.i	0.206667	+	0.357957i	−0.743996	+	0.668184i	$0.767072\pi$
$878$	−751232.	+	433724.i	−0.974507	+	0.562632i
$879$	−783017.	−	467742.i	−1.01343	−	0.605380i
$880$	−82523.8	+	142935.i	−0.106565	+	0.184576i
$881$		−	1.07868e6i		−	1.38977i	−0.719123	−	0.694883i	$-0.755456\pi$
$881$		−	1.07868e6i		−	1.38977i	0.719123	−	0.694883i	$-0.244544\pi$
$882$	−913601.	−	564354.i	−1.17441	−	0.725461i
$883$	−425808.			−0.546125			−0.273063	−	0.961996i	$-0.588037\pi$
$883$	−425808.			−0.546125			−0.273063	+	0.961996i	$0.588037\pi$
$884$	−82071.1	−	47383.8i	−0.105023	−	0.0606353i
$885$	−677989.	−	10086.4i	−0.865638	−	0.0128780i
$886$	−637199.	−	1.10366e6i	−0.811722	−	1.40594i
$887$	−151174.	+	87280.1i	−0.192145	+	0.110935i	−0.592986	−	0.805213i	$-0.702051\pi$
$887$	−151174.	+	87280.1i	−0.192145	+	0.110935i	0.400841	+	0.916147i	$0.368718\pi$
$888$	−170429.	+	95045.3i	−0.216131	+	0.120533i
$889$	3716.29	−	6436.80i	0.00470225	−	0.00814453i
$890$			143008.i			0.180542i
$891$	−20793.1	+	349032.i	−0.0261917	+	0.439653i
$892$	−872469.			−1.09653
$893$	1.05412e6	+	608596.i	1.32186	+	0.763179i
$894$	388932.	+	697407.i	0.486630	+	0.872592i
$895$	−295425.	−	511691.i	−0.368809	−	0.638796i
$896$	5779.41	−	3336.74i	0.00719892	−	0.00415630i
$897$	−2011.77	+	135227.i	−0.00250030	+	0.168066i
$898$	−586540.	+	1.01592e6i	−0.727353	+	1.25981i
$899$		−	1.75802e6i		−	2.17523i
$900$	−77459.0	+	125394.i	−0.0956284	+	0.154807i
$901$	426992.			0.525981
$902$	590720.	+	341053.i	0.726054	+	0.419187i
$903$	22.2518	−	37.2504i	2.72892e−5	−	4.56831e-5i
$904$	1368.92	+	2371.04i	0.00167510	+	0.00290136i
$905$	456854.	−	263765.i	0.557802	−	0.322047i
$906$	198508.	+	118580.i	0.241836	+	0.144463i
$907$	334047.	−	578587.i	0.406063	−	0.703322i	−0.588381	−	0.808583i	$-0.700235\pi$
$907$	334047.	−	578587.i	0.406063	−	0.703322i	0.994445	+	0.105262i	$0.0335680\pi$
$908$			461144.i			0.559325i
$909$	−826972.	+	445192.i	−1.00084	+	0.538790i
$910$	6185.15			0.00746909
$911$	−514011.	−	296764.i	−0.619349	−	0.357581i	0.157267	−	0.987556i	$-0.449732\pi$
$911$	−514011.	−	296764.i	−0.619349	−	0.357581i	−0.776615	+	0.629975i	$0.783065\pi$
$912$	988824.	+	14710.7i	1.18886	+	0.0176865i
$913$	90440.8	+	156648.i	0.108498	+	0.187925i
$914$	−1.10741e6	+	639364.i	−1.32561	+	0.765342i
$915$	210730.	−	117521.i	0.251701	−	0.140369i
$916$	515672.	−	893171.i	0.614586	−	1.06449i
$917$			14768.7i			0.0175633i
$918$	−231442.	+	362496.i	−0.274636	+	0.430148i
$919$	−377757.			−0.447282			−0.223641	−	0.974672i	$-0.571794\pi$
$919$	−377757.			−0.447282			−0.223641	+	0.974672i	$0.571794\pi$
$920$	19026.9	+	10985.2i	0.0224798	+	0.0129787i
$921$	−698716.	−	1.25289e6i	−0.823723	−	1.47704i
$922$	−584463.	−	1.01232e6i	−0.687535	−	1.19085i
$923$	−225378.	+	130122.i	−0.264550	+	0.152738i
$924$	−170.396	+	11453.7i	−0.000199580	+	0.0134154i
$925$	−169882.	+	294245.i	−0.198548	+	0.343895i
$926$			1.16944e6i			1.36382i
$927$	132526.	+	3944.04i	0.154221	+	0.00458967i
$928$	1.62026e6			1.88143
$929$	34377.6	+	19847.9i	0.0398331	+	0.0229977i	0.519784	−	0.854298i	$-0.326012\pi$
$929$	34377.6	+	19847.9i	0.0398331	+	0.0229977i	−0.479951	+	0.877295i	$0.659346\pi$
$930$	434423.	−	727240.i	0.502281	−	0.840837i
$931$	475675.	+	823892.i	0.548796	+	0.950542i
$932$	642066.	−	370697.i	0.739176	−	0.426763i
$933$	1.38062e6	+	824724.i	1.58603	+	0.947427i
$934$	−148770.	+	257676.i	−0.170538	+	0.295380i
$935$			63589.6i			0.0727382i
$936$	1172.44	−	39395.9i	0.00133825	−	0.0449675i
$937$	−1.27172e6			−1.44847			−0.724237	−	0.689551i	$-0.757808\pi$
$937$	−1.27172e6			−1.44847			−0.724237	+	0.689551i	$0.757808\pi$
$938$	9205.50	+	5314.80i	0.0104626	+	0.00604061i
$939$	88227.1	+	1312.55i	0.100062	+	0.00148862i
$940$	249701.	+	432494.i	0.282595	+	0.489468i
$941$	402933.	−	232633.i	0.455044	−	0.262720i	−0.254914	−	0.966964i	$-0.582047\pi$
$941$	402933.	−	232633.i	0.455044	−	0.262720i	0.709958	+	0.704244i	$0.248714\pi$
$942$	−1.47559e6	+	822914.i	−1.66290	+	0.927369i
$943$	285199.	−	493980.i	0.320719	−	0.555502i
$944$			1.86665e6i			2.09469i
$945$	596.566	−	13358.8i	0.000668029	−	0.0149590i
$946$	865.674			0.000967325
$947$	−48783.5	−	28165.2i	−0.0543967	−	0.0314060i	0.472555	−	0.881301i	$-0.343332\pi$
$947$	−48783.5	−	28165.2i	−0.0543967	−	0.0314060i	−0.526952	+	0.849895i	$0.676665\pi$
$948$	480335.	+	861304.i	0.534475	+	0.958385i
$949$	−52566.6	−	91048.0i	−0.0583683	−	0.101097i
$950$	237373.	−	137047.i	0.263017	−	0.151853i
$951$	2144.73	−	144165.i	0.00237144	−	0.159404i
$952$	698.376	−	1209.62i	0.000770576	−	0.00133468i
$953$			688318.i			0.757885i	0.925420	+	0.378942i	$0.123712\pi$
$953$			688318.i			0.757885i	−0.925420	+	0.378942i	$0.876288\pi$
$954$	−849154.	−	1.57736e6i	−0.933018	−	1.73314i
$955$	369767.			0.405435
$956$	314133.	+	181365.i	0.343715	+	0.198444i
$957$	283931.	−	475312.i	0.310020	−	0.518985i
$958$	326427.	+	565388.i	0.355676	+	0.616049i
$959$	−30869.3	+	17822.4i	−0.0335652	+	0.0193789i
$960$	287387.	+	171673.i	0.311835	+	0.186277i
$961$	−697947.	+	1.20888e6i	−0.755745	+	1.30899i
$962$			916529.i			0.990367i
$963$	−568944.	−	351451.i	−0.613503	−	0.378976i
$964$	−1.65896e6			−1.78518
$965$	311056.	+	179588.i	0.334029	+	0.192851i
$966$	20105.5	+	299.108i	0.0215457	+	0.000320533i
$967$	820366.	+	1.42092e6i	0.877313	+	1.51955i	0.854278	+	0.519816i	$0.174000\pi$
$967$	820366.	+	1.42092e6i	0.877313	+	1.51955i	0.0230353	+	0.999735i	$0.492667\pi$
$968$	−81523.3	+	47067.5i	−0.0870024	+	0.0502309i
$969$	332768.	−	185579.i	0.354400	−	0.197643i
$970$	97431.9	−	168757.i	0.103552	−	0.179357i
$971$		−	317465.i		−	0.336711i	−0.985726	−	0.168355i	$-0.946154\pi$
$971$		−	317465.i		−	0.336711i	0.985726	−	0.168355i	$-0.0538456\pi$
$972$	857197.	+	63875.5i	0.907294	+	0.0676085i
$973$	−3444.42			−0.00363823
$974$	1.17637e6	+	679176.i	1.24001	+	0.715920i
$975$	−33424.1	−	59933.8i	−0.0351601	−	0.0630468i
$976$	−332118.	−	575244.i	−0.348652	−	0.603883i
$977$	−540123.	+	311840.i	−0.565853	+	0.326695i	−0.755491	−	0.655159i	$-0.772602\pi$
$977$	−540123.	+	311840.i	−0.565853	+	0.326695i	0.189639	+	0.981854i	$0.439268\pi$
$978$	3500.95	−	235328.i	0.00366023	−	0.246034i
$979$	61657.1	−	106793.i	0.0643306	−	0.111424i
$980$			390329.i			0.406423i
$981$	−711570.	+	1.15192e6i	−0.739400	+	1.19697i
$982$	1.34513e6			1.39490
$983$	983315.	+	567717.i	1.01762	+	0.587523i	0.913414	−	0.407032i	$-0.133436\pi$
$983$	983315.	+	567717.i	1.01762	+	0.587523i	0.104207	+	0.994556i	$0.466770\pi$
$984$	−85247.2	+	142707.i	−0.0880420	+	0.147386i
$985$	71262.8	+	123431.i	0.0734498	+	0.127219i
$986$	589777.	−	340508.i	0.606644	−	0.350246i
$987$	−38897.4	−	23235.7i	−0.0399288	−	0.0238518i
$988$	176116.	−	305041.i	0.180420	−	0.312496i
$989$		−	723.905i		−	0.000740098i
$990$	234907.	−	126460.i	0.239677	−	0.129028i
$991$	315849.			0.321612			0.160806	−	0.986986i	$-0.448591\pi$
$991$	315849.			0.321612			0.160806	+	0.986986i	$0.448591\pi$
$992$	−1.85126e6	−	1.06883e6i	−1.88124	−	1.08613i
$993$	506726.	+	7538.52i	0.513895	+	0.00764518i
$994$	19346.4	+	33508.9i	0.0195807	+	0.0339147i
$995$	−383683.	+	221520.i	−0.387549	+	0.223752i
$996$	388365.	−	216585.i	0.391491	−	0.218328i
$997$	−365263.	+	632654.i	−0.367464	+	0.636467i	−0.989168	−	0.146785i	$-0.953107\pi$
$997$	−365263.	+	632654.i	−0.367464	+	0.636467i	0.621704	+	0.783252i	$0.286441\pi$
$998$		−	1.47300e6i		−	1.47891i
$999$	1.97954e6	+	88400.4i	1.98350	+	0.0885775i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.5.i.a.11.13	✓	32
3.2	odd	2		135.5.i.a.116.4		32
9.2	odd	6		405.5.c.b.161.26		32
9.4	even	3		135.5.i.a.71.4		32
9.5	odd	6	inner	45.5.i.a.41.13	yes	32
9.7	even	3		405.5.c.b.161.7		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.5.i.a.11.13	✓	32	1.1	even	1	trivial
45.5.i.a.41.13	yes	32	9.5	odd	6	inner
135.5.i.a.71.4		32	9.4	even	3
135.5.i.a.116.4		32	3.2	odd	2
405.5.c.b.161.7		32	9.7	even	3
405.5.c.b.161.26		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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	45.i (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(4.78725 + 2.76392i) q^{2} +(4.38356 + 7.86031i) q^{3} +(7.27848 + 12.6067i) q^{4} +(9.68246 - 5.59017i) q^{5} +(-0.740053 + 49.7450i) q^{6} +(-0.820328 + 1.42085i) q^{7} -7.97692i q^{8} +(-42.5688 + 68.9122i) q^{9} +61.8031 q^{10} +(-46.1525 - 26.6461i) q^{11} +(-67.1868 + 112.473i) q^{12} +(-30.4995 - 52.8267i) q^{13} +(-7.85422 + 4.53464i) q^{14} +(86.3841 + 51.6022i) q^{15} +(138.503 - 239.895i) q^{16} -106.725i q^{17} +(-394.255 + 212.243i) q^{18} +396.675 q^{19} +(140.947 + 81.3758i) q^{20} +(-14.7643 - 0.219647i) q^{21} +(-147.296 - 255.123i) q^{22} +(-213.343 + 123.173i) q^{23} +(62.7010 - 34.9673i) q^{24} +(62.5000 - 108.253i) q^{25} -337.192i q^{26} +(-728.274 - 32.5227i) q^{27} -23.8830 q^{28} +(999.692 + 577.172i) q^{29} +(270.918 + 485.791i) q^{30} +(-761.481 - 1318.92i) q^{31} +(1215.57 - 701.807i) q^{32} +(7.13465 - 479.578i) q^{33} +(294.979 - 510.919i) q^{34} +18.3431i q^{35} +(-1178.59 - 35.0754i) q^{36} -2718.12 q^{37} +(1898.98 + 1096.38i) q^{38} +(281.537 - 471.304i) q^{39} +(-44.5923 - 77.2362i) q^{40} +(-2005.22 + 1157.72i) q^{41} +(-70.0731 - 41.8587i) q^{42} +(-1.46928 + 2.54487i) q^{43} -775.774i q^{44} +(-26.9394 + 905.207i) q^{45} -1361.76 q^{46} +(2657.39 + 1534.24i) q^{47} +(2492.78 + 37.0849i) q^{48} +(1199.15 + 2077.00i) q^{49} +(598.406 - 345.490i) q^{50} +(838.892 - 467.836i) q^{51} +(443.980 - 768.996i) q^{52} +4000.85i q^{53} +(-3396.54 - 2168.58i) q^{54} -595.826 q^{55} +(11.3340 + 6.54369i) q^{56} +(1738.85 + 3117.99i) q^{57} +(3190.51 + 5526.13i) q^{58} +(-5835.85 + 3369.33i) q^{59} +(-21.7888 + 1464.60i) q^{60} +(1198.95 - 2076.65i) q^{61} -8418.68i q^{62} +(-62.9936 - 117.015i) q^{63} +3326.85 q^{64} +(-590.620 - 340.995i) q^{65} +(1359.67 - 2276.14i) q^{66} +(-586.022 - 1015.02i) q^{67} +(1345.45 - 776.796i) q^{68} +(-1903.38 - 1137.00i) q^{69} +(-50.6988 + 87.8129i) q^{70} -4266.36i q^{71} +(549.707 + 339.568i) q^{72} +1723.52 q^{73} +(-13012.3 - 7512.65i) q^{74} +(1124.88 + 16.7347i) q^{75} +(2887.19 + 5000.76i) q^{76} +(75.7204 - 43.7172i) q^{77} +(2650.43 - 1478.10i) q^{78} +(3763.71 - 6518.94i) q^{79} -3097.03i q^{80} +(-2936.80 - 5867.02i) q^{81} -12799.3 q^{82} +(-2939.41 - 1697.07i) q^{83} +(-104.692 - 187.727i) q^{84} +(-596.612 - 1033.36i) q^{85} +(-14.0676 + 8.12194i) q^{86} +(-154.541 + 10388.0i) q^{87} +(-212.554 + 368.155i) q^{88} +2313.92i q^{89} +(-2630.88 + 4258.99i) q^{90} +100.078 q^{91} +(-3105.62 - 1793.03i) q^{92} +(7029.15 - 11767.1i) q^{93} +(8481.04 + 14689.6i) q^{94} +(3840.79 - 2217.48i) q^{95} +(10844.9 + 6478.30i) q^{96} +(1576.49 - 2730.56i) q^{97} +13257.5i q^{98} +(3800.90 - 2046.18i) 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

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