LMFDB - Embedded newform 45.5.i.a.11.11

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			11.11
Character	$\chi$	$=$	45.11
Dual form			45.5.i.a.41.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.59623 + 1.49894i) q^{2} +(4.94975 - 7.51665i) q^{3} +(-3.50638 - 6.07323i) q^{4} +(9.68246 - 5.59017i) q^{5} +(24.1177 - 12.0956i) q^{6} +(-1.63719 + 2.83570i) q^{7} -68.9893i q^{8} +(-31.9999 - 74.4110i) q^{9} +33.5172 q^{10} +(81.9109 + 47.2913i) q^{11} +(-63.0060 - 3.70474i) q^{12} +(110.077 + 190.658i) q^{13} +(-8.50105 + 4.90809i) q^{14} +(5.90642 - 100.450i) q^{15} +(47.3086 - 81.9408i) q^{16} +169.411i q^{17} +(28.4581 - 241.154i) q^{18} +87.9803 q^{19} +(-67.9007 - 39.2025i) q^{20} +(13.2112 + 26.3422i) q^{21} +(141.773 + 245.558i) q^{22} +(-421.756 + 243.501i) q^{23} +(-518.568 - 341.480i) q^{24} +(62.5000 - 108.253i) q^{25} +659.991i q^{26} +(-717.713 - 127.784i) q^{27} +22.9624 q^{28} +(-403.964 - 233.229i) q^{29} +(165.902 - 251.937i) q^{30} +(470.420 + 814.791i) q^{31} +(-710.296 + 410.090i) q^{32} +(760.910 - 381.615i) q^{33} +(-253.936 + 439.830i) q^{34} +36.6087i q^{35} +(-339.711 + 455.256i) q^{36} +1347.72 q^{37} +(228.417 + 131.877i) q^{38} +(1977.96 + 116.304i) q^{39} +(-385.662 - 667.986i) q^{40} +(-2499.93 + 1443.34i) q^{41} +(-5.18575 + 88.1932i) q^{42} +(1704.82 - 2952.83i) q^{43} -663.285i q^{44} +(-725.808 - 541.597i) q^{45} -1459.97 q^{46} +(1197.53 + 691.394i) q^{47} +(-381.755 - 761.188i) q^{48} +(1195.14 + 2070.04i) q^{49} +(324.529 - 187.367i) q^{50} +(1273.40 + 838.541i) q^{51} +(771.940 - 1337.04i) q^{52} -4664.29i q^{53} +(-1671.81 - 1407.56i) q^{54} +1057.47 q^{55} +(195.633 + 112.949i) q^{56} +(435.481 - 661.317i) q^{57} +(-699.191 - 1211.03i) q^{58} +(2305.63 - 1331.16i) q^{59} +(-630.763 + 316.343i) q^{60} +(-534.899 + 926.473i) q^{61} +2820.52i q^{62} +(263.397 + 31.0829i) q^{63} -3972.67 q^{64} +(2131.62 + 1230.69i) q^{65} +(2547.52 + 149.794i) q^{66} +(859.963 + 1489.50i) q^{67} +(1028.87 - 594.018i) q^{68} +(-257.276 + 4375.46i) q^{69} +(-54.8741 + 95.0447i) q^{70} -96.5153i q^{71} +(-5133.57 + 2207.65i) q^{72} -6755.50 q^{73} +(3499.01 + 2020.15i) q^{74} +(-504.341 - 1005.62i) q^{75} +(-308.492 - 534.324i) q^{76} +(-268.207 + 154.850i) q^{77} +(4960.92 + 3266.79i) q^{78} +(-5660.74 + 9804.70i) q^{79} -1057.85i q^{80} +(-4513.01 + 4762.30i) q^{81} -8653.87 q^{82} +(-7241.08 - 4180.64i) q^{83} +(113.658 - 172.600i) q^{84} +(947.035 + 1640.31i) q^{85} +(8852.21 - 5110.83i) q^{86} +(-3752.62 + 1882.03i) q^{87} +(3262.59 - 5650.98i) q^{88} -7613.27i q^{89} +(-1072.55 - 2494.05i) q^{90} -720.865 q^{91} +(2957.67 + 1707.61i) q^{92} +(8452.96 + 497.033i) q^{93} +(2072.71 + 3590.04i) q^{94} +(851.866 - 491.825i) q^{95} +(-433.290 + 7368.88i) q^{96} +(8951.51 - 15504.5i) q^{97} +7165.75i q^{98} +(897.850 - 7608.39i) 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 $

$2$	2.59623	+	1.49894i	0.649059	+	0.374734i	0.788095	−	0.615553i	$-0.211067\pi$
$2$	2.59623	+	1.49894i	0.649059	+	0.374734i	−0.139037	+	0.990287i	$0.544401\pi$
$3$	4.94975	−	7.51665i	0.549972	−	0.835183i
$3$	4.94975	−	7.51665i	0.549972	−	0.835183i
$4$	−3.50638	−	6.07323i	−0.219149	−	0.379577i
$5$	9.68246	−	5.59017i	0.387298	−	0.223607i
$5$	9.68246	−	5.59017i	0.387298	−	0.223607i
$6$	24.1177	−	12.0956i	0.669936	−	0.335989i
$7$	−1.63719	+	2.83570i	−0.0334120	+	0.0578713i	−0.882248	−	0.470785i	$-0.843971\pi$
$7$	−1.63719	+	2.83570i	−0.0334120	+	0.0578713i	0.848836	+	0.528656i	$0.177304\pi$
$8$		−	68.9893i		−	1.07796i
$9$	−31.9999	−	74.4110i	−0.395061	−	0.918655i
$10$	33.5172			0.335172
$11$	81.9109	+	47.2913i	0.676950	+	0.390837i	0.798705	−	0.601723i	$-0.205519\pi$
$11$	81.9109	+	47.2913i	0.676950	+	0.390837i	−0.121755	+	0.992560i	$0.538852\pi$
$12$	−63.0060	−	3.70474i	−0.437542	−	0.0257274i
$13$	110.077	+	190.658i	0.651341	+	1.12815i	0.982798	+	0.184685i	$0.0591264\pi$
$13$	110.077	+	190.658i	0.651341	+	1.12815i	−0.331457	+	0.943470i	$0.607540\pi$
$14$	−8.50105	+	4.90809i	−0.0433727	+	0.0250413i
$15$	5.90642	−	100.450i	0.0262508	−	0.446442i
$16$	47.3086	−	81.9408i	0.184799	−	0.320081i
$17$			169.411i			0.586196i	0.956082	+	0.293098i	$0.0946863\pi$
$17$			169.411i			0.586196i	−0.956082	+	0.293098i	$0.905314\pi$
$18$	28.4581	−	241.154i	0.0878336	−	0.744304i
$19$	87.9803			0.243713			0.121856	−	0.992548i	$-0.461115\pi$
$19$	87.9803			0.243713			0.121856	+	0.992548i	$0.461115\pi$
$20$	−67.9007	−	39.2025i	−0.169752	−	0.0980063i
$21$	13.2112	+	26.3422i	0.0299575	+	0.0597328i
$22$	141.773	+	245.558i	0.292920	+	0.507352i
$23$	−421.756	+	243.501i	−0.797270	+	0.460304i	−0.842516	−	0.538672i	$-0.818926\pi$
$23$	−421.756	+	243.501i	−0.797270	+	0.460304i	0.0452457	+	0.998976i	$0.485593\pi$
$24$	−518.568	−	341.480i	−0.900292	−	0.592847i
$25$	62.5000	−	108.253i	0.100000	−	0.173205i
$26$			659.991i			0.976318i
$27$	−717.713	−	127.784i	−0.984517	−	0.175287i
$28$	22.9624			0.0292888
$29$	−403.964	−	233.229i	−0.480338	−	0.277323i	0.240219	−	0.970719i	$-0.422781\pi$
$29$	−403.964	−	233.229i	−0.480338	−	0.277323i	−0.720557	+	0.693395i	$0.756114\pi$
$30$	165.902	−	251.937i	0.184336	−	0.279930i
$31$	470.420	+	814.791i	0.489511	+	0.847857i	0.999927	−	0.0120700i	$-0.00384208\pi$
$31$	470.420	+	814.791i	0.489511	+	0.847857i	−0.510416	+	0.859927i	$0.670509\pi$
$32$	−710.296	+	410.090i	−0.693648	+	0.400478i
$33$	760.910	−	381.615i	0.698724	−	0.350427i
$34$	−253.936	+	439.830i	−0.219668	+	0.380476i
$35$			36.6087i			0.0298846i
$36$	−339.711	+	455.256i	−0.262123	+	0.351278i
$37$	1347.72			0.984459			0.492229	−	0.870466i	$-0.336182\pi$
$37$	1347.72			0.984459			0.492229	+	0.870466i	$0.336182\pi$
$38$	228.417	+	131.877i	0.158184	+	0.0913275i
$39$	1977.96	+	116.304i	1.30043	+	0.0764654i
$40$	−385.662	−	667.986i	−0.241039	−	0.417491i
$41$	−2499.93	+	1443.34i	−1.48717	+	0.858617i	−0.999893	−	0.0146313i	$-0.995343\pi$
$41$	−2499.93	+	1443.34i	−1.48717	+	0.858617i	−0.487275	+	0.873248i	$0.662009\pi$
$42$	−5.18575	+	88.1932i	−0.00293977	+	0.0499962i
$43$	1704.82	−	2952.83i	0.922021	−	1.59699i	0.125738	−	0.992063i	$-0.459870\pi$
$43$	1704.82	−	2952.83i	0.922021	−	1.59699i	0.796283	−	0.604924i	$-0.206797\pi$
$44$		−	663.285i		−	0.342606i
$45$	−725.808	−	541.597i	−0.358424	−	0.267455i
$46$	−1459.97			−0.689966
$47$	1197.53	+	691.394i	0.542114	+	0.312990i	0.745935	−	0.666018i	$-0.232003\pi$
$47$	1197.53	+	691.394i	0.542114	+	0.312990i	−0.203821	+	0.979008i	$0.565336\pi$
$48$	−381.755	−	761.188i	−0.165692	−	0.330377i
$49$	1195.14	+	2070.04i	0.497767	+	0.862158i
$50$	324.529	−	187.367i	0.129812	−	0.0749468i
$51$	1273.40	+	838.541i	0.489581	+	0.322392i
$52$	771.940	−	1337.04i	0.285481	−	0.494467i
$53$		−	4664.29i		−	1.66048i	−0.557406	−	0.830240i	$-0.688203\pi$
$53$		−	4664.29i		−	1.66048i	0.557406	−	0.830240i	$-0.311797\pi$
$54$	−1671.81	−	1407.56i	−0.573324	−	0.482703i
$55$	1057.47			0.349575
$56$	195.633	+	112.949i	0.0623829	+	0.0360168i
$57$	435.481	−	661.317i	0.134035	−	0.203545i
$58$	−699.191	−	1211.03i	−0.207845	−	0.359998i
$59$	2305.63	−	1331.16i	0.662347	−	0.382406i	−0.130824	−	0.991406i	$-0.541762\pi$
$59$	2305.63	−	1331.16i	0.662347	−	0.382406i	0.793171	+	0.608999i	$0.208429\pi$
$60$	−630.763	+	316.343i	−0.175212	+	0.0878731i
$61$	−534.899	+	926.473i	−0.143751	+	0.248985i	−0.928906	−	0.370314i	$-0.879250\pi$
$61$	−534.899	+	926.473i	−0.143751	+	0.248985i	0.785155	+	0.619299i	$0.212583\pi$
$62$			2820.52i			0.733745i
$63$	263.397	+	31.0829i	0.0663636	+	0.00783142i
$64$	−3972.67			−0.969889
$65$	2131.62	+	1230.69i	0.504526	+	0.291288i
$66$	2547.52	+	149.794i	0.584830	+	0.0343879i
$67$	859.963	+	1489.50i	0.191571	+	0.331811i	0.945771	−	0.324834i	$-0.105308\pi$
$67$	859.963	+	1489.50i	0.191571	+	0.331811i	−0.754200	+	0.656645i	$0.771975\pi$
$68$	1028.87	−	594.018i	0.222506	−	0.128464i
$69$	−257.276	+	4375.46i	−0.0540383	+	0.919021i
$70$	−54.8741	+	95.0447i	−0.0111988	+	0.0193969i
$71$		−	96.5153i		−	0.0191461i	−0.999954	−	0.00957303i	$-0.996953\pi$
$71$		−	96.5153i		−	0.0191461i	0.999954	−	0.00957303i	$-0.00304724\pi$
$72$	−5133.57	+	2207.65i	−0.990272	+	0.425859i
$73$	−6755.50			−1.26769			−0.633843	−	0.773462i	$-0.718523\pi$
$73$	−6755.50			−1.26769			−0.633843	+	0.773462i	$0.718523\pi$
$74$	3499.01	+	2020.15i	0.638971	+	0.368910i
$75$	−504.341	−	1005.62i	−0.0896607	−	0.178776i
$76$	−308.492	−	534.324i	−0.0534093	−	0.0925077i
$77$	−268.207	+	154.850i	−0.0452365	+	0.0261173i
$78$	4960.92	+	3266.79i	0.815404	+	0.536948i
$79$	−5660.74	+	9804.70i	−0.907025	+	1.57101i	−0.0888496	+	0.996045i	$0.528319\pi$
$79$	−5660.74	+	9804.70i	−0.907025	+	1.57101i	−0.818176	+	0.574969i	$0.805014\pi$
$80$		−	1057.85i		−	0.165289i
$81$	−4513.01	+	4762.30i	−0.687854	+	0.725849i
$82$	−8653.87			−1.28701
$83$	−7241.08	−	4180.64i	−1.05111	−	0.606857i	−0.128148	−	0.991755i	$-0.540903\pi$
$83$	−7241.08	−	4180.64i	−1.05111	−	0.606857i	−0.922959	+	0.384898i	$0.874237\pi$
$84$	113.658	−	172.600i	0.0161080	−	0.0244615i
$85$	947.035	+	1640.31i	0.131078	+	0.227033i
$86$	8852.21	−	5110.83i	1.19689	−	0.691026i
$87$	−3752.62	+	1882.03i	−0.495788	+	0.248650i
$88$	3262.59	−	5650.98i	0.421306	−	0.729723i
$89$		−	7613.27i		−	0.961150i	−0.876954	−	0.480575i	$-0.840428\pi$
$89$		−	7613.27i		−	0.961150i	0.876954	−	0.480575i	$-0.159572\pi$
$90$	−1072.55	−	2494.05i	−0.132414	−	0.307908i
$91$	−720.865			−0.0870504
$92$	2957.67	+	1707.61i	0.349441	+	0.201750i
$93$	8452.96	+	497.033i	0.977333	+	0.0574671i
$94$	2072.71	+	3590.04i	0.234576	+	0.406297i
$95$	851.866	−	491.825i	0.0943895	−	0.0544958i
$96$	−433.290	+	7368.88i	−0.0470149	+	0.799575i
$97$	8951.51	−	15504.5i	0.951377	−	1.64783i	0.208929	−	0.977931i	$-0.433002\pi$
$97$	8951.51	−	15504.5i	0.951377	−	1.64783i	0.742449	−	0.669903i	$-0.233664\pi$
$98$			7165.75i			0.746122i
$99$	897.850	−	7608.39i	0.0916080	−	0.776288i
$100$	−876.595			−0.0876595
$101$	−7680.93	−	4434.59i	−0.752959	−	0.434721i	0.0738031	−	0.997273i	$-0.476486\pi$
$101$	−7680.93	−	4434.59i	−0.752959	−	0.434721i	−0.826762	+	0.562552i	$0.809820\pi$
$102$	2049.13	+	4085.80i	0.196956	+	0.392714i
$103$	1576.45	+	2730.49i	0.148596	+	0.257375i	0.930709	−	0.365761i	$-0.119191\pi$
$103$	1576.45	+	2730.49i	0.148596	+	0.257375i	−0.782113	+	0.623137i	$0.785858\pi$
$104$	13153.4	−	7594.11i	1.21610	−	0.702118i
$105$	275.174	+	181.204i	0.0249591	+	0.0164357i
$106$	6991.47	−	12109.6i	0.622238	−	1.07775i
$107$			3557.60i			0.310734i	0.987857	+	0.155367i	$0.0496560\pi$
$107$			3557.60i			0.310734i	−0.987857	+	0.155367i	$0.950344\pi$
$108$	1740.51	+	4806.89i	0.149221	+	0.412114i
$109$	−12579.3			−1.05878			−0.529389	−	0.848379i	$-0.677579\pi$
$109$	−12579.3			−1.05878			−0.529389	+	0.848379i	$0.677579\pi$
$110$	2745.43	+	1585.07i	0.226895	+	0.130998i
$111$	6670.90	−	10130.4i	0.541425	−	0.822203i
$112$	154.906	+	268.305i	0.0123490	+	0.0213891i
$113$	−15897.9	+	9178.64i	−1.24504	+	0.718822i	−0.970115	−	0.242645i	$-0.921985\pi$
$113$	−15897.9	+	9178.64i	−1.24504	+	0.718822i	−0.274921	+	0.961467i	$0.588652\pi$
$114$	2121.88	−	1064.18i	0.163272	−	0.0818849i
$115$	−2722.42	+	4715.37i	−0.205854	+	0.356550i
$116$			3271.16i			0.243100i
$117$	10664.6	−	14292.0i	0.779066	−	1.04405i
$118$	7981.27			0.573203
$119$	−480.397	−	277.358i	−0.0339240	−	0.0195860i
$120$	−6929.95	−	407.480i	−0.481246	−	0.0282972i
$121$	−2847.57	−	4932.13i	−0.194493	−	0.336871i
$122$	−2777.45	+	1603.56i	−0.186606	+	0.107737i
$123$	−1524.99	+	25935.2i	−0.100799	+	1.71427i
$124$	3298.94	−	5713.93i	0.214551	−	0.371614i
$125$		−	1397.54i		−	0.0894427i
$126$	637.249	+	475.514i	0.0401391	+	0.0299517i
$127$	8767.67			0.543597			0.271798	−	0.962354i	$-0.412382\pi$
$127$	8767.67			0.543597			0.271798	+	0.962354i	$0.412382\pi$
$128$	1050.76	+	606.658i	0.0641334	+	0.0370275i
$129$	−13757.0	−	27430.3i	−0.826691	−	1.64836i
$130$	3689.46	+	6390.34i	0.218311	+	0.378126i
$131$	−15360.5	+	8868.41i	−0.895084	+	0.516777i	−0.875602	−	0.483033i	$-0.839535\pi$
$131$	−15360.5	+	8868.41i	−0.895084	+	0.516777i	−0.0194818	+	0.999810i	$0.506202\pi$
$132$	−4985.68	−	3283.09i	−0.286138	−	0.188424i
$133$	−144.040	+	249.485i	−0.00814294	+	0.0141040i
$134$			5156.12i			0.287153i
$135$	−7663.56	+	2774.88i	−0.420497	+	0.152257i
$136$	11687.5			0.631895
$137$	−8807.94	−	5085.27i	−0.469281	−	0.270940i	0.246657	−	0.969103i	$-0.420668\pi$
$137$	−8807.94	−	5085.27i	−0.469281	−	0.270940i	−0.715939	+	0.698163i	$0.754001\pi$
$138$	−7226.48	+	10974.1i	−0.379462	+	0.576248i
$139$	15316.9	+	26529.6i	0.792757	+	1.37310i	0.924254	+	0.381779i	$0.124689\pi$
$139$	15316.9	+	26529.6i	0.792757	+	1.37310i	−0.131496	+	0.991317i	$0.541978\pi$
$140$	222.333	−	128.364i	0.0113435	−	0.00654918i
$141$	11124.4	−	5579.18i	0.559551	−	0.280629i
$142$	144.670	−	250.576i	0.00717468	−	0.0124269i
$143$			20822.6i			1.01827i
$144$	−7611.17	−	898.178i	−0.367051	−	0.0433149i
$145$	−5215.16			−0.248046
$146$	−17538.8	−	10126.1i	−0.822802	−	0.475045i
$147$	21475.4	+	1262.75i	0.993818	+	0.0584364i
$148$	−4725.63	−	8185.03i	−0.215743	−	0.373678i
$149$	15268.6	−	8815.33i	0.687744	−	0.397069i	−0.115022	−	0.993363i	$-0.536694\pi$
$149$	15268.6	−	8815.33i	0.687744	−	0.397069i	0.802766	+	0.596294i	$0.203361\pi$
$150$	197.967	−	3366.79i	0.00879853	−	0.149635i
$151$	−6329.37	+	10962.8i	−0.277592	+	0.480803i	−0.970786	−	0.239948i	$-0.922870\pi$
$151$	−6329.37	+	10962.8i	−0.277592	+	0.480803i	0.693194	+	0.720751i	$0.256203\pi$
$152$		−	6069.70i		−	0.262712i
$153$	12606.0	−	5421.13i	0.538512	−	0.231583i
$154$	−928.439			−0.0391482
$155$	9109.64	+	5259.45i	0.379173	+	0.218916i
$156$	−6229.14	−	12420.4i	−0.255964	−	0.510372i
$157$	11302.1	+	19575.9i	0.458523	+	0.794185i	0.998883	−	0.0472490i	$-0.0150454\pi$
$157$	11302.1	+	19575.9i	0.458523	+	0.794185i	−0.540360	+	0.841434i	$0.681712\pi$
$158$	−29393.2	+	16970.2i	−1.17742	+	0.679787i
$159$	−35059.8	−	23087.1i	−1.38680	−	0.913218i
$160$	−4584.94	+	7941.35i	−0.179099	+	0.310209i
$161$		−	1594.63i		−	0.0615188i
$162$	−18855.2	+	5599.33i	−0.718458	+	0.213357i
$163$	14489.7			0.545362			0.272681	−	0.962105i	$-0.412090\pi$
$163$	14489.7			0.545362			0.272681	+	0.962105i	$0.412090\pi$
$164$	17531.4	+	10121.8i	0.651822	+	0.376330i
$165$	5234.19	−	7948.59i	0.192257	−	0.291959i
$166$	−12533.0	−	21707.8i	−0.454820	−	0.787771i
$167$	−2495.44	+	1440.74i	−0.0894776	+	0.0516599i	−0.544071	−	0.839039i	$-0.683118\pi$
$167$	−2495.44	+	1440.74i	−0.0894776	+	0.0516599i	0.454594	+	0.890699i	$0.349785\pi$
$168$	1817.33	−	911.435i	0.0643894	−	0.0322929i
$169$	−9953.20	+	17239.4i	−0.348489	+	0.603601i
$170$			5678.18i			0.196477i
$171$	−2815.36	−	6546.71i	−0.0962814	−	0.223888i
$172$	−23910.9			−0.808239
$173$	−9707.08	−	5604.39i	−0.324337	−	0.187256i	0.328987	−	0.944334i	$-0.393293\pi$
$173$	−9707.08	−	5604.39i	−0.324337	−	0.187256i	−0.653324	+	0.757078i	$0.726626\pi$
$174$	−12563.7	−	738.746i	−0.414973	−	0.0244004i
$175$	204.649	+	354.462i	0.00668241	+	0.0115743i
$176$	7750.17	−	4474.56i	0.250199	−	0.144453i
$177$	1406.46	−	23919.5i	0.0448933	−	0.763494i
$178$	11411.8	−	19765.8i	0.360176	−	0.623843i
$179$			33999.1i			1.06111i	0.847650	+	0.530555i	$0.178017\pi$
$179$			33999.1i			1.06111i	−0.847650	+	0.530555i	$0.821983\pi$
$180$	−744.280	+	6307.04i	−0.0229716	+	0.194662i
$181$	50443.3			1.53973			0.769867	−	0.638204i	$-0.220322\pi$
$181$	50443.3			1.53973			0.769867	+	0.638204i	$0.220322\pi$
$182$	−1871.53	−	1080.53i	−0.0565008	−	0.0326208i
$183$	4316.35	+	8606.46i	0.128889	+	0.256994i
$184$	16799.0	+	29096.6i	0.496188	+	0.859424i
$185$	13049.3	−	7534.01i	0.381279	−	0.220132i
$186$	21200.8	+	13960.9i	0.612812	+	0.403540i
$187$	−8011.65	+	13876.6i	−0.229107	+	0.396825i
$188$		−	9697.16i		−	0.274365i
$189$	1537.39	−	1826.01i	0.0430388	−	0.0511187i
$190$	2948.86			0.0816858
$191$	27846.2	+	16077.0i	0.763308	+	0.440696i	0.830482	−	0.557045i	$-0.188065\pi$
$191$	27846.2	+	16077.0i	0.763308	+	0.440696i	−0.0671741	+	0.997741i	$0.521398\pi$
$192$	−19663.7	+	29861.1i	−0.533412	+	0.810035i
$193$	−20382.2	−	35303.0i	−0.547188	−	0.947758i	−0.998466	−	0.0553742i	$-0.982365\pi$
$193$	−20382.2	−	35303.0i	−0.547188	−	0.947758i	0.451277	−	0.892384i	$-0.350968\pi$
$194$	46480.4	−	26835.5i	1.23500	−	0.713027i
$195$	19801.7	−	9931.03i	0.520754	−	0.261171i
$196$	8381.22	−	14516.7i	0.218170	−	0.377882i
$197$		−	69275.6i		−	1.78504i	−0.451007	−	0.892520i	$-0.648935\pi$
$197$		−	69275.6i		−	1.78504i	0.451007	−	0.892520i	$-0.351065\pi$
$198$	13735.5	−	18407.4i	0.350360	−	0.469527i
$199$	−2814.35			−0.0710678			−0.0355339	−	0.999368i	$-0.511313\pi$
$199$	−2814.35			−0.0710678			−0.0355339	+	0.999368i	$0.511313\pi$
$200$	−7468.31	−	4311.83i	−0.186708	−	0.107796i
$201$	15452.6	+	908.613i	0.382482	+	0.0224899i
$202$	−13294.3	−	23026.5i	−0.325810	−	0.564319i
$203$	1322.73	−	763.680i	0.0320982	−	0.0185319i
$204$	627.624	−	10673.9i	0.0150813	−	0.256485i
$205$	−16137.0	+	27950.1i	−0.383985	+	0.665082i
$206$			9452.00i			0.222735i
$207$	31615.3	+	23591.3i	0.737831	+	0.550568i
$208$	20830.3			0.481468
$209$	7206.55	+	4160.70i	0.164981	+	0.0952520i
$210$	442.804	+	882.916i	0.0100409	+	0.0200208i
$211$	−38115.4	−	66017.8i	−0.856122	−	1.48285i	−0.875600	−	0.483037i	$-0.839534\pi$
$211$	−38115.4	−	66017.8i	−0.856122	−	1.48285i	0.0194776	−	0.999810i	$-0.493800\pi$
$212$	−28327.3	+	16354.8i	−0.630279	+	0.363892i
$213$	−725.471	−	477.727i	−0.0159905	−	0.0105298i
$214$	−5332.61	+	9236.35i	−0.116443	+	0.201685i
$215$		−	38120.9i		−	0.824681i
$216$	−8815.72	+	49514.6i	−0.188952	+	1.06127i
$217$	−3080.67			−0.0654222
$218$	−32658.9	−	18855.6i	−0.687209	−	0.396760i
$219$	−33438.0	+	50778.7i	−0.697192	+	1.05875i
$220$	−3707.87	−	6422.23i	−0.0766090	−	0.132691i
$221$	−32299.6	+	18648.2i	−0.661320	+	0.381814i
$222$	32504.0	−	16301.5i	0.659524	−	0.330768i
$223$	22048.5	−	38189.1i	0.443373	−	0.767945i	−0.554564	−	0.832141i	$-0.687115\pi$
$223$	22048.5	−	38189.1i	0.443373	−	0.767945i	0.997937	+	0.0641960i	$0.0204483\pi$
$224$		−	2685.58i		−	0.0535231i
$225$	−10055.2	−	1186.60i	−0.198622	−	0.0234389i
$226$	−55032.8			−1.07747
$227$	46663.6	+	26941.2i	0.905579	+	0.522836i	0.879006	−	0.476811i	$-0.158207\pi$
$227$	46663.6	+	26941.2i	0.905579	+	0.522836i	0.0265729	+	0.999647i	$0.491541\pi$
$228$	−5543.29	−	325.945i	−0.106634	−	0.00627009i
$229$	−26016.5	−	45061.9i	−0.496110	−	0.859287i	0.503880	−	0.863774i	$-0.331905\pi$
$229$	−26016.5	−	45061.9i	−0.496110	−	0.859287i	−0.999990	+	0.00448635i	$0.998572\pi$
$230$	−14136.1	+	8161.48i	−0.267223	+	0.154281i
$231$	−163.610	+	2782.49i	−0.00306609	+	0.0521446i
$232$	−16090.3	+	27869.2i	−0.298943	+	0.517784i
$233$		−	37345.8i		−	0.687908i	−0.938987	−	0.343954i	$-0.888234\pi$
$233$		−	37345.8i		−	0.687908i	0.938987	−	0.343954i	$-0.111766\pi$
$234$	49110.6	−	21119.7i	0.896899	−	0.385705i
$235$	15460.0			0.279946
$236$	−16168.8	−	9335.07i	−0.290305	−	0.167608i
$237$	45679.2	+	91080.6i	0.813245	+	1.62155i
$238$	−831.483	−	1440.17i	−0.0146791	−	0.0254249i
$239$	−13246.2	+	7647.67i	−0.231897	+	0.133886i	−0.611447	−	0.791286i	$-0.709412\pi$
$239$	−13246.2	+	7647.67i	−0.231897	+	0.133886i	0.379550	+	0.925171i	$0.376079\pi$
$240$	−7951.50	−	5236.10i	−0.138047	−	0.0909045i
$241$	−50918.8	+	88193.9i	−0.876686	+	1.51846i	−0.0217301	+	0.999764i	$0.506917\pi$
$241$	−50918.8	+	88193.9i	−0.876686	+	1.51846i	−0.854956	+	0.518701i	$0.826416\pi$
$242$		−	17073.3i		−	0.291532i
$243$	13458.3	+	57494.9i	0.227917	+	0.973681i
$244$	7502.24			0.126012
$245$	23143.8	+	13362.1i	0.385569	+	0.222608i
$246$	−42834.5	+	65048.1i	−0.707821	+	1.07489i
$247$	9684.57	+	16774.2i	0.158740	+	0.274946i
$248$	56211.9	−	32453.9i	0.913955	−	0.527672i
$249$	−67265.9	+	33735.5i	−1.08492	+	0.544112i
$250$	2094.83	−	3628.35i	0.0335172	−	0.0580536i
$251$			42858.0i			0.680274i	0.940376	+	0.340137i	$0.110473\pi$
$251$			42858.0i			0.680274i	−0.940376	+	0.340137i	$0.889527\pi$
$252$	−734.796	−	1708.66i	−0.0115709	−	0.0269063i
$253$	−46061.9			−0.719615
$254$	22762.9	+	13142.2i	0.352826	+	0.203704i
$255$	17017.2	+	1000.61i	0.261703	+	0.0153881i
$256$	33600.0	+	58196.9i	0.512696	+	0.888015i
$257$	−16565.4	+	9564.06i	−0.250805	+	0.144803i	−0.620133	−	0.784497i	$-0.712921\pi$
$257$	−16565.4	+	9564.06i	−0.250805	+	0.144803i	0.369328	+	0.929299i	$0.379588\pi$
$258$	5399.96	−	91836.2i	0.0811243	−	1.37967i
$259$	−2206.48	+	3821.74i	−0.0328928	+	0.0569719i
$260$		−	17261.1i		−	0.255342i
$261$	−4427.97	+	37522.7i	−0.0650016	+	0.550825i
$262$	−53172.7			−0.774616
$263$	6020.90	+	3476.17i	0.0870462	+	0.0502562i	0.542891	−	0.839803i	$-0.317330\pi$
$263$	6020.90	+	3476.17i	0.0870462	+	0.0502562i	−0.455845	+	0.890059i	$0.650663\pi$
$264$	−26327.4	−	52494.7i	−0.377746	−	0.753195i
$265$	−26074.2	−	45161.8i	−0.371295	−	0.643101i
$266$	−747.925	+	431.815i	−0.0105705	+	0.00610287i
$267$	−57226.3	−	37683.8i	−0.802736	−	0.528606i
$268$	6030.71	−	10445.5i	0.0839651	−	0.145432i
$269$		−	11605.5i		−	0.160384i	−0.996779	−	0.0801919i	$-0.974447\pi$
$269$		−	11605.5i		−	0.160384i	0.996779	−	0.0801919i	$-0.0255533\pi$
$270$	−24055.8	−	4282.96i	−0.329983	−	0.0587512i
$271$	86730.7			1.18096			0.590479	−	0.807053i	$-0.298939\pi$
$271$	86730.7			1.18096			0.590479	+	0.807053i	$0.298939\pi$
$272$	13881.7	+	8014.58i	0.187631	+	0.108329i
$273$	−3568.10	+	5418.49i	−0.0478753	+	0.0727030i
$274$	−15245.0	−	26405.1i	−0.203061	−	0.351711i
$275$	10238.9	−	5911.41i	0.135390	−	0.0781674i
$276$	27475.3	−	13779.5i	0.360681	−	0.180890i
$277$	17061.8	−	29551.9i	0.222364	−	0.385146i	−0.733161	−	0.680055i	$-0.761956\pi$
$277$	17061.8	−	29551.9i	0.222364	−	0.385146i	0.955525	+	0.294909i	$0.0952892\pi$
$278$			91836.0i			1.18829i
$279$	45576.0	−	61077.7i	0.585502	−	0.784647i
$280$	2525.61			0.0322144
$281$	−494.925	−	285.745i	−0.00626797	−	0.00361881i	0.496863	−	0.867829i	$-0.334485\pi$
$281$	−494.925	−	285.745i	−0.00626797	−	0.00361881i	−0.503131	+	0.864210i	$0.667819\pi$
$282$	37244.5	+	2189.97i	0.468343	+	0.0275385i
$283$	−29903.5	−	51794.4i	−0.373378	−	0.646710i	0.616705	−	0.787195i	$-0.288467\pi$
$283$	−29903.5	−	51794.4i	−0.373378	−	0.646710i	−0.990083	+	0.140484i	$0.955134\pi$
$284$	−586.159	+	338.419i	−0.00726740	+	0.00419583i
$285$	519.649	−	8837.58i	0.00639765	−	0.108804i
$286$	−31211.8	+	54060.5i	−0.381581	+	0.660918i
$287$		−	9452.05i		−	0.114753i
$288$	53244.6	+	39731.0i	0.641935	+	0.479010i
$289$	54821.0			0.656374
$290$	−13539.8	−	7817.19i	−0.160996	−	0.0929511i
$291$	−72233.9	−	144029.i	−0.853012	−	1.70084i
$292$	23687.3	+	41027.7i	0.277812	+	0.481184i
$293$	83462.4	−	48187.1i	0.972200	−	0.561300i	0.0722941	−	0.997383i	$-0.476968\pi$
$293$	83462.4	−	48187.1i	0.972200	−	0.561300i	0.899906	+	0.436083i	$0.143635\pi$
$294$	53862.4	+	35468.7i	0.623148	+	0.410346i
$295$	14882.8	−	25777.7i	0.171017	−	0.296211i
$296$		−	92978.6i		−	1.06121i
$297$	−52745.5	−	44408.5i	−0.597960	−	0.503446i
$298$	52854.5			0.595181
$299$	−92850.8	−	53607.5i	−1.03859	−	0.599629i
$300$	−4338.92	+	6589.05i	−0.0482103	+	0.0732117i
$301$	5582.22	+	9668.69i	0.0616132	+	0.106717i
$302$	−32865.1	+	18974.7i	−0.360347	+	0.208046i
$303$	−71351.9	+	35784.8i	−0.777178	+	0.389774i
$304$	4162.22	−	7209.18i	0.0450379	−	0.0780079i
$305$			11960.7i			0.128575i
$306$	40854.2	+	4821.11i	0.436308	+	0.0514878i
$307$	79840.1			0.847118			0.423559	−	0.905868i	$-0.360781\pi$
$307$	79840.1			0.847118			0.423559	+	0.905868i	$0.360781\pi$
$308$	1880.87	+	1085.92i	0.0198270	+	0.0114472i
$309$	28327.2	+	1665.63i	0.296679	+	0.0174447i
$310$	15767.2	+	27309.5i	0.164070	+	0.284178i
$311$	60530.1	−	34947.0i	0.625821	−	0.361318i	−0.153311	−	0.988178i	$-0.548994\pi$
$311$	60530.1	−	34947.0i	0.625821	−	0.361318i	0.779132	+	0.626860i	$0.215660\pi$
$312$	8023.73	−	136458.i	0.0824265	−	1.40181i
$313$	−49941.1	+	86500.4i	−0.509764	+	0.882937i	0.490172	+	0.871626i	$0.336934\pi$
$313$	−49941.1	+	86500.4i	−0.509764	+	0.882937i	−0.999936	+	0.0113112i	$0.996399\pi$
$314$			67764.7i			0.687296i
$315$	2724.09	−	1171.48i	0.0274537	−	0.0118063i
$316$	79394.8			0.795093
$317$	35906.1	+	20730.4i	0.357314	+	0.206295i	0.667902	−	0.744249i	$-0.267193\pi$
$317$	35906.1	+	20730.4i	0.357314	+	0.206295i	−0.310588	+	0.950545i	$0.600526\pi$
$318$	−56417.4	−	112492.i	−0.557903	−	1.11241i
$319$	−22059.4	−	38208.0i	−0.216777	−	0.375468i
$320$	−38465.2	+	22207.9i	−0.375637	+	0.216874i
$321$	26741.2	+	17609.2i	0.259520	+	0.170895i
$322$	2390.25	−	4140.03i	0.0230532	−	0.0399293i
$323$			14904.8i			0.142864i
$324$	44746.8	+	10710.1i	0.426258	+	0.102024i
$325$	27519.1			0.260536
$326$	37618.7	+	21719.2i	0.353972	+	0.204366i
$327$	−62264.6	+	94554.4i	−0.582298	+	0.884273i
$328$	99574.7	+	172468.i	0.925553	+	1.60311i
$329$	−3921.17	+	2263.89i	−0.0362263	+	0.0209152i
$330$	25503.6	−	12790.7i	0.234193	−	0.117454i
$331$	33058.3	−	57258.6i	0.301734	−	0.522619i	−0.674795	−	0.738005i	$-0.735768\pi$
$331$	33058.3	−	57258.6i	0.301734	−	0.522619i	0.976529	+	0.215387i	$0.0691012\pi$
$332$			58635.6i			0.531968i
$333$	−43127.1	−	100286.i	−0.388921	−	0.904378i
$334$	−8638.33			−0.0774349
$335$	16653.1	+	9614.68i	0.148390	+	0.0856732i
$336$	2783.50	+	163.670i	0.0246555	+	0.00144974i
$337$	−25957.4	−	44959.6i	−0.228561	−	0.395879i	0.728821	−	0.684704i	$-0.240069\pi$
$337$	−25957.4	−	44959.6i	−0.228561	−	0.395879i	−0.957382	+	0.288825i	$0.906735\pi$
$338$	−51681.6	+	29838.4i	−0.452380	+	0.261181i
$339$	−9697.90	+	164931.i	−0.0843875	+	1.43516i
$340$	6641.33	−	11503.1i	0.0574509	−	0.0995079i
$341$			88987.0i			0.765276i
$342$	2503.75	−	21216.8i	0.0214062	−	0.181396i
$343$	−15688.5			−0.133350
$344$	−203714.	−	117614.i	−1.72149	−	0.993900i
$345$	21968.5	+	43803.4i	0.184570	+	0.368018i
$346$	−16801.2	−	29100.6i	−0.140342	−	0.243080i
$347$	−188478.	+	108818.i	−1.56532	+	0.903735i	−0.568612	+	0.822606i	$0.692519\pi$
$347$	−188478.	+	108818.i	−1.56532	+	0.903735i	−0.996704	+	0.0811298i	$0.974147\pi$
$348$	24588.1	+	16191.4i	0.203033	+	0.133698i
$349$	−4602.54	+	7971.84i	−0.0377874	+	0.0654497i	−0.884301	−	0.466918i	$-0.845364\pi$
$349$	−4602.54	+	7971.84i	−0.0377874	+	0.0654497i	0.846513	+	0.532368i	$0.178698\pi$
$350$			1227.02i			0.0100165i
$351$	−54640.4	−	150904.i	−0.443506	−	1.22486i
$352$	−77574.6			−0.626087
$353$	−75387.6	−	43525.1i	−0.604994	−	0.349293i	0.166010	−	0.986124i	$-0.446912\pi$
$353$	−75387.6	−	43525.1i	−0.604994	−	0.349293i	−0.771004	+	0.636831i	$0.780245\pi$
$354$	39505.3	−	59992.4i	0.315246	−	0.478729i
$355$	−539.537	−	934.505i	−0.00428119	−	0.00741524i
$356$	−46237.1	+	26695.0i	−0.364830	+	0.210635i
$357$	−4462.65	+	2238.13i	−0.0350151	+	0.0175610i
$358$	−50962.4	+	88269.5i	−0.397634	+	0.688723i
$359$			150724.i			1.16948i	0.811220	+	0.584740i	$0.198804\pi$
$359$			150724.i			1.16948i	−0.811220	+	0.584740i	$0.801196\pi$
$360$	−37364.4	+	50073.0i	−0.288306	+	0.386366i
$361$	−122580.			−0.940604
$362$	130962.	+	75611.2i	0.999378	+	0.576991i
$363$	−51167.9	−	3008.66i	−0.388315	−	0.0228329i
$364$	2527.62	+	4377.97i	0.0190770	+	0.0330423i
$365$	−65409.8	+	37764.4i	−0.490972	+	0.283463i
$366$	−1694.28	+	28814.3i	−0.0126480	+	0.215103i
$367$	116337.	−	201502.i	0.863747	−	1.49605i	−0.00453814	−	0.999990i	$-0.501445\pi$
$367$	116337.	−	201502.i	0.863747	−	1.49605i	0.868286	−	0.496065i	$-0.165222\pi$
$368$			46078.7i			0.340255i
$369$	187398.	+	139836.i	1.37629	+	1.02699i
$370$	45172.0			0.329963
$371$	13226.5	+	7636.32i	0.0960942	+	0.0554800i
$372$	−26620.7	−	53079.5i	−0.192368	−	0.383567i
$373$	37030.9	+	64139.3i	0.266162	+	0.461006i	0.967867	−	0.251461i	$-0.0809111\pi$
$373$	37030.9	+	64139.3i	0.266162	+	0.461006i	−0.701705	+	0.712467i	$0.747578\pi$
$374$	−41600.3	+	24017.9i	−0.297408	+	0.171709i
$375$	−10504.8	−	6917.49i	−0.0747010	−	0.0491910i
$376$	47698.8	−	82616.8i	0.337390	−	0.584376i
$377$		−	102692.i		−	0.722528i
$378$	6728.49	−	2436.30i	0.0470906	−	0.0170509i
$379$	61553.8			0.428525			0.214263	−	0.976776i	$-0.431265\pi$
$379$	61553.8			0.428525			0.214263	+	0.976776i	$0.431265\pi$
$380$	−5973.93	−	3449.05i	−0.0413707	−	0.0238854i
$381$	43397.8	−	65903.5i	0.298963	−	0.454003i
$382$	48196.9	+	83479.5i	0.330288	+	0.572075i
$383$	148025.	−	85462.5i	1.00911	−	0.582610i	0.0981789	−	0.995169i	$-0.468698\pi$
$383$	148025.	−	85462.5i	1.00911	−	0.582610i	0.910931	+	0.412559i	$0.135365\pi$
$384$	9761.04	−	4895.40i	0.0661963	−	0.0331991i
$385$	−1731.27	+	2998.65i	−0.0116800	+	0.0202304i
$386$		−	122207.i		−	0.820200i
$387$	−274277.	−	32366.8i	−1.83134	−	0.216112i
$388$	−125550.			−0.833972
$389$	−146765.	−	84734.7i	−0.969890	−	0.559966i	−0.0706875	−	0.997499i	$-0.522519\pi$
$389$	−146765.	−	84734.7i	−0.969890	−	0.559966i	−0.899203	+	0.437532i	$0.855853\pi$
$390$	66295.8	+	3898.19i	0.435870	+	0.0256291i
$391$	−41251.7	−	71450.0i	−0.269829	−	0.467357i
$392$	142811.	−	82451.8i	0.929371	−	0.536572i
$393$	−9370.12	+	159356.i	−0.0606680	+	1.03177i
$394$	103840.	−	179856.i	0.668916	−	1.15860i
$395$			126578.i			0.811268i
$396$	−49355.7	+	21225.1i	−0.314736	+	0.135350i
$397$	160489.			1.01827			0.509137	−	0.860685i	$-0.329964\pi$
$397$	160489.			1.01827			0.509137	+	0.860685i	$0.329964\pi$
$398$	−7306.72	−	4218.54i	−0.0461271	−	0.0266315i
$399$	1162.33	+	2317.59i	0.00730101	+	0.0145576i
$400$	−5913.57	−	10242.6i	−0.0369598	−	0.0640163i
$401$	158816.	−	91692.5i	0.987656	−	0.570223i	0.0830831	−	0.996543i	$-0.473523\pi$
$401$	158816.	−	91692.5i	0.987656	−	0.570223i	0.904573	+	0.426319i	$0.140190\pi$
$402$	38756.7	+	25521.5i	0.239825	+	0.157926i
$403$	−103564.	+	179379.i	−0.637676	+	1.10449i
$404$			62197.4i			0.381074i
$405$	−17075.0	+	71339.2i	−0.104100	+	0.434929i
$406$	4578.83			0.0277781
$407$	110393.	+	63735.6i	0.666429	+	0.384763i
$408$	57850.4	−	87851.1i	0.347525	−	0.527748i
$409$	2346.29	+	4063.89i	0.0140260	+	0.0242938i	0.872953	−	0.487804i	$-0.162202\pi$
$409$	2346.29	+	4063.89i	0.0140260	+	0.0242938i	−0.858927	+	0.512098i	$0.828869\pi$
$410$	−83790.7	+	48376.6i	−0.498458	+	0.287785i
$411$	−81821.3	+	41035.4i	−0.484376	+	0.242926i
$412$	11055.3	−	19148.3i	0.0651290	−	0.112807i
$413$			8717.42i			0.0511079i
$414$	46718.9	+	108638.i	0.272579	+	0.633841i
$415$	−93481.9			−0.542789
$416$	−156374.	−	90282.5i	−0.903603	−	0.521695i
$417$	275228.	+	16183.4i	1.58278	+	0.0930673i
$418$	12473.3	+	21604.3i	0.0713883	+	0.123648i
$419$	167892.	−	96932.8i	0.956320	−	0.552132i	0.0612814	−	0.998121i	$-0.480481\pi$
$419$	167892.	−	96932.8i	0.956320	−	0.552132i	0.895038	+	0.445989i	$0.147148\pi$
$420$	135.626	−	2306.57i	0.000768854	−	0.0130758i
$421$	−90183.4	+	156202.i	−0.508818	+	0.881298i	0.491130	+	0.871086i	$0.336584\pi$
$421$	−90183.4	+	156202.i	−0.508818	+	0.881298i	−0.999948	+	0.0102120i	$0.996749\pi$
$422$		−	228530.i		−	1.28327i
$423$	13126.5	−	111234.i	0.0733614	−	0.621666i
$424$	−321786.			−1.78993
$425$	18339.3	+	10588.2i	0.101532	+	0.0586196i
$426$	−1167.41	−	2327.73i	−0.00643287	−	0.0128266i
$427$	−1751.46	−	3033.62i	−0.00960606	−	0.0166382i
$428$	21606.1	−	12474.3i	0.117947	−	0.0680970i
$429$	156516.	+	103067.i	0.850443	+	0.560021i
$430$	57140.8	−	98970.7i	0.309036	−	0.535266i
$431$		−	43119.1i		−	0.232121i	−0.993242	−	0.116061i	$-0.962973\pi$
$431$		−	43119.1i		−	0.232121i	0.993242	−	0.116061i	$-0.0370267\pi$
$432$	−44424.7	+	52764.7i	−0.238044	+	0.282733i
$433$	−137450.			−0.733108			−0.366554	−	0.930397i	$-0.619463\pi$
$433$	−137450.			−0.733108			−0.366554	+	0.930397i	$0.619463\pi$
$434$	−7998.13	−	4617.72i	−0.0424628	−	0.0245159i
$435$	−25813.7	+	39200.5i	−0.136418	+	0.207163i
$436$	44107.9	+	76397.2i	0.232030	+	0.401887i
$437$	−37106.2	+	21423.3i	−0.194305	+	0.112182i
$438$	−162927.	+	81711.9i	−0.849268	+	0.425929i
$439$	171773.	−	297519.i	0.891302	−	1.54378i	0.0529869	−	0.998595i	$-0.483126\pi$
$439$	171773.	−	297519.i	0.891302	−	1.54378i	0.838315	−	0.545186i	$-0.183541\pi$
$440$		−	72953.8i		−	0.376828i
$441$	115790.	−	155173.i	0.595377	−	0.797881i
$442$	−111810.			−0.572314
$443$	324839.	+	187546.i	1.65524	+	0.955652i	0.974868	+	0.222782i	$0.0715137\pi$
$443$	324839.	+	187546.i	1.65524	+	0.955652i	0.680369	+	0.732870i	$0.261820\pi$
$444$	−84914.7	−	4992.97i	−0.430742	−	0.0253276i
$445$	−42559.5	−	73715.2i	−0.214920	−	0.372252i
$446$	114486.	−	66098.6i	0.575550	−	0.332294i
$447$	9314.04	−	158402.i	0.0466147	−	0.792769i
$448$	6504.01	−	11265.3i	0.0324060	−	0.0561288i
$449$		−	104994.i		−	0.520803i	−0.965500	−	0.260402i	$-0.916145\pi$
$449$		−	104994.i		−	0.520803i	0.965500	−	0.260402i	$-0.0838550\pi$
$450$	−24327.1	−	18152.8i	−0.120134	−	0.0896436i
$451$	−273029.			−1.34232
$452$	111488.	+	64367.6i	0.545696	+	0.315058i
$453$	51074.7	+	101839.i	0.248891	+	0.496269i
$454$	80766.4	+	139891.i	0.391849	+	0.678703i
$455$	−6979.74	+	4029.76i	−0.0337145	+	0.0194651i
$456$	−45623.8	−	30043.5i	−0.219413	−	0.144484i
$457$	−131298.	+	227414.i	−0.628672	+	1.08889i	0.359146	+	0.933281i	$0.383068\pi$
$457$	−131298.	+	227414.i	−0.628672	+	1.08889i	−0.987818	+	0.155611i	$0.950265\pi$
$458$		−	155988.i		−	0.743637i
$459$	21648.0	−	121588.i	0.102752	−	0.577121i
$460$	38183.4			0.180451
$461$	292012.	+	168593.i	1.37404	+	0.793302i	0.991434	−	0.130610i	$-0.0416934\pi$
$461$	292012.	+	168593.i	1.37404	+	0.793302i	0.382606	+	0.923912i	$0.375027\pi$
$462$	−4595.54	+	6978.75i	−0.0215304	+	0.0326959i
$463$	41736.4	+	72289.5i	0.194694	+	0.337220i	0.946800	−	0.321822i	$-0.104295\pi$
$463$	41736.4	+	72289.5i	0.194694	+	0.337220i	−0.752106	+	0.659042i	$0.770962\pi$
$464$	−38221.9	+	22067.5i	−0.177532	+	0.102498i
$465$	84623.9	−	42441.0i	0.391370	−	0.196281i
$466$	55979.0	−	96958.5i	0.257783	−	0.446493i
$467$		−	208959.i		−	0.958138i	−0.877777	−	0.479069i	$-0.840974\pi$
$467$		−	208959.i		−	0.958138i	0.877777	−	0.479069i	$-0.159026\pi$
$468$	−124193.	−	14655.7i	−0.567027	−	0.0669136i
$469$	−5631.69			−0.0256031
$470$	40137.9	+	23173.6i	0.181702	+	0.104906i
$471$	203088.	+	11941.5i	0.915464	+	0.0538292i
$472$	−91835.5	−	159064.i	−0.412218	−	0.713982i
$473$	279286.	−	161246.i	1.24832	−	0.720720i
$474$	−17930.2	+	304937.i	−0.0798049	+	1.35723i
$475$	5498.77	−	9524.15i	0.0243713	−	0.0422123i
$476$			3890.08i			0.0171690i
$477$	−347075.	+	149257.i	−1.52541	+	0.655991i
$478$	−45853.5			−0.200686
$479$	−225538.	−	130214.i	−0.982990	−	0.567529i	−0.0798182	−	0.996809i	$-0.525434\pi$
$479$	−225538.	−	130214.i	−0.982990	−	0.567529i	−0.903171	+	0.429280i	$0.858767\pi$
$480$	36998.0	+	73771.1i	0.160582	+	0.320187i
$481$	148353.	+	256955.i	0.641218	+	1.11062i
$482$	−264394.	+	152648.i	−1.13804	+	0.657048i
$483$	−11986.3	−	7893.01i	−0.0513794	−	0.0338336i
$484$	−19969.3	+	34587.9i	−0.0852457	+	0.147650i
$485$		−	200162.i		−	0.850938i
$486$	−51240.4	+	169443.i	−0.216940	+	0.717384i
$487$	−58814.1			−0.247984			−0.123992	−	0.992283i	$-0.539570\pi$
$487$	−58814.1			−0.247984			−0.123992	+	0.992283i	$0.539570\pi$
$488$	63916.7	+	36902.3i	0.268395	+	0.154958i
$489$	71720.5	−	108914.i	0.299934	−	0.455477i
$490$	40057.8	+	69382.1i	0.166838	+	0.288972i
$491$	−178725.	+	103187.i	−0.741346	+	0.428017i	−0.822559	−	0.568680i	$-0.807454\pi$
$491$	−178725.	+	103187.i	−0.741346	+	0.428017i	0.0812123	+	0.996697i	$0.474121\pi$
$492$	162858.	−	81677.2i	0.672788	−	0.337420i
$493$	39511.5	−	68435.9i	0.162566	−	0.281573i
$494$			58066.2i			0.237941i
$495$	−33838.8	−	78687.1i	−0.138104	−	0.321139i
$496$	89019.5			0.361844
$497$	273.688	+	158.014i	0.00110801	+	0.000639709i
$498$	−225205.	−	13242.0i	−0.908072	−	0.0533945i
$499$	−153237.	−	265414.i	−0.615406	−	1.06592i	−0.990313	−	0.138853i	$-0.955659\pi$
$499$	−153237.	−	265414.i	−0.615406	−	1.06592i	0.374907	−	0.927063i	$-0.377675\pi$
$500$	−8487.59	+	4900.31i	−0.0339504	+	0.0196013i
$501$	−1522.25	+	25888.7i	−0.00606472	+	0.103142i
$502$	−64241.4	+	111269.i	−0.254922	+	0.441538i
$503$			148336.i			0.586286i	0.956069	+	0.293143i	$0.0947012\pi$
$503$			148336.i			0.586286i	−0.956069	+	0.293143i	$0.905299\pi$
$504$	2144.39	−	18171.6i	0.00844194	−	0.0715372i
$505$	−99160.4			−0.388826
$506$	−119587.	−	69043.8i	−0.467073	−	0.269664i
$507$	80316.9	+	160146.i	0.312458	+	0.623016i
$508$	−30742.8	−	53248.1i	−0.119128	−	0.206337i
$509$	−262221.	+	151393.i	−1.01212	+	0.584348i	−0.911812	−	0.410608i	$-0.865316\pi$
$509$	−262221.	+	151393.i	−1.01212	+	0.584348i	−0.100309	+	0.994956i	$0.531983\pi$
$510$	42680.9	+	28105.6i	0.164094	+	0.108057i
$511$	11060.0	−	19156.5i	0.0423559	−	0.0733627i
$512$			182044.i			0.694443i
$513$	−63144.6	−	11242.5i	−0.239939	−	0.0427196i
$514$	−57343.7			−0.217050
$515$	30527.8	+	17625.3i	0.115102	+	0.0664540i
$516$	−118353.	+	179730.i	−0.444509	+	0.675027i
$517$	65393.8	+	113265.i	0.244656	+	0.423757i
$518$	−11457.1	+	6614.75i	−0.0426987	+	0.0246521i
$519$	−90173.8	+	45224.4i	−0.334769	+	0.167895i
$520$	84904.7	−	147059.i	0.313997	−	0.543858i
$521$			390554.i			1.43882i	0.694588	+	0.719408i	$0.255587\pi$
$521$			390554.i			1.43882i	−0.694588	+	0.719408i	$0.744413\pi$
$522$	−67740.2	+	90780.5i	−0.248603	+	0.333159i
$523$	325321.			1.18935			0.594674	−	0.803967i	$-0.297281\pi$
$523$	325321.			1.18935			0.594674	+	0.803967i	$0.297281\pi$
$524$	107720.	+	62192.0i	0.392313	+	0.226502i
$525$	3677.32	+	216.226i	0.0133418	+	0.000784494i
$526$	10421.1	+	18049.9i	0.0376654	+	0.0652384i
$527$	−138034.	+	79694.2i	−0.497011	+	0.286949i
$528$	4727.70	−	80403.3i	0.0169583	−	0.288407i
$529$	−21335.2	+	36953.7i	−0.0762405	+	0.132052i
$530$		−	156334.i		−	0.556547i
$531$	−172833.	−	128967.i	−0.612967	−	0.457394i
$532$	2020.24			0.00713806
$533$	−550367.	−	317755.i	−1.93731	−	1.11850i
$534$	−92087.2	−	183614.i	−0.322936	−	0.643909i
$535$	19887.6	+	34446.3i	0.0694823	+	0.120347i
$536$	102760.	−	59328.2i	0.357678	−	0.206506i
$537$	255559.	+	168287.i	0.886222	+	0.583582i
$538$	17395.9	−	30130.7i	0.0601012	−	0.104098i
$539$			226079.i			0.778184i
$540$	43723.8	+	36812.8i	0.149944	+	0.126244i
$541$	−170586.			−0.582838			−0.291419	−	0.956596i	$-0.594127\pi$
$541$	−170586.			−0.582838			−0.291419	+	0.956596i	$0.594127\pi$
$542$	225173.	+	130004.i	0.766511	+	0.442545i
$543$	249682.	−	379164.i	0.846811	−	1.28596i
$544$	−69473.6	−	120332.i	−0.234759	−	0.406614i
$545$	−121799.	+	70320.6i	−0.410063	+	0.236750i
$546$	−17385.6	+	8719.30i	−0.0583182	+	0.0292480i
$547$	−45921.8	+	79538.9i	−0.153477	+	0.265830i	−0.932504	−	0.361161i	$-0.882381\pi$
$547$	−45921.8	+	79538.9i	−0.153477	+	0.265830i	0.779026	+	0.626991i	$0.215714\pi$
$548$			71323.5i			0.237504i
$549$	86056.6	+	10155.3i	0.285522	+	0.0336938i
$550$	35443.3			0.117168
$551$	−35540.9	−	20519.6i	−0.117065	−	0.0675872i
$552$	301860.	+	17749.3i	0.990666	+	0.0582510i
$553$	−18535.4	−	32104.3i	−0.0606111	−	0.104982i
$554$	88592.8	−	51149.1i	0.288655	−	0.166655i
$555$	7960.23	−	135378.i	0.0258428	−	0.439504i
$556$	107413.	−	186046.i	0.347463	−	0.601824i
$557$		−	283539.i		−	0.913908i	−0.889490	−	0.456954i	$-0.848940\pi$
$557$		−	283539.i		−	0.913908i	0.889490	−	0.456954i	$-0.151060\pi$
$558$	209878.	−	90256.4i	0.674059	−	0.289874i
$559$	750642.			2.40220
$560$	2999.74	+	1731.90i	0.00956551	+	0.00552265i
$561$	64649.7	+	128906.i	0.205419	+	0.409590i
$562$	−856.628	−	1483.72i	−0.00271219	−	0.00469764i
$563$	−210588.	+	121583.i	−0.664382	+	0.383581i	−0.793945	−	0.607990i	$-0.791976\pi$
$563$	−210588.	+	121583.i	−0.664382	+	0.383581i	0.129563	+	0.991571i	$0.458643\pi$
$564$	−72890.1	−	47998.5i	−0.229145	−	0.150893i
$565$	−102620.	+	177744.i	−0.321467	+	0.556797i
$566$		−	179294.i		−	0.559670i
$567$	−6115.78	−	20594.3i	−0.0190233	−	0.0640591i
$568$	−6658.53			−0.0206387
$569$	21866.5	+	12624.7i	0.0675391	+	0.0389937i	0.533389	−	0.845870i	$-0.320918\pi$
$569$	21866.5	+	12624.7i	0.0675391	+	0.0389937i	−0.465850	+	0.884864i	$0.654251\pi$
$570$	14596.1	−	22165.5i	0.0449249	−	0.0682226i
$571$	153290.	+	265507.i	0.470156	+	0.814335i	0.999418	−	0.0341241i	$-0.0108641\pi$
$571$	153290.	+	265507.i	0.470156	+	0.814335i	−0.529261	+	0.848459i	$0.677531\pi$
$572$	126461.	−	73012.1i	0.386512	−	0.223153i
$573$	258677.	−	129733.i	0.787860	−	0.395131i
$574$	14168.0	−	24539.7i	0.0430017	−	0.0744811i
$575$			60875.2i			0.184122i
$576$	127125.	+	295610.i	0.383165	+	0.890994i
$577$	1283.67			0.00385569			0.00192785	−	0.999998i	$-0.499386\pi$
$577$	1283.67			0.00385569			0.00192785	+	0.999998i	$0.499386\pi$
$578$	142328.	+	82173.2i	0.426025	+	0.245966i
$579$	−366247.	−	21535.3i	−1.09249	−	0.0642383i
$580$	18286.3	+	31672.8i	0.0543589	+	0.0941523i
$581$	23710.0	−	13689.0i	0.0702392	−	0.0405526i
$582$	28353.7	−	482206.i	0.0837072	−	1.42360i
$583$	220580.	−	382056.i	0.648977	−	1.12406i
$584$			466057.i			1.36651i
$585$	23365.4	−	197998.i	0.0682748	−	0.578562i
$586$	288917.			0.841353
$587$	−512103.	−	295663.i	−1.48621	−	0.858066i	−0.486337	−	0.873771i	$-0.661667\pi$
$587$	−512103.	−	295663.i	−1.48621	−	0.858066i	−0.999877	+	0.0157057i	$0.995001\pi$
$588$	−67632.0	−	134853.i	−0.195613	−	0.390036i
$589$	41387.7	+	71685.5i	0.119300	+	0.206634i
$590$	77278.3	−	44616.7i	0.222000	−	0.128172i
$591$	−520721.	−	342897.i	−1.49084	−	0.981723i
$592$	63758.9	−	110434.i	0.181927	−	0.315107i
$593$		−	229570.i		−	0.652839i	−0.945225	−	0.326420i	$-0.894158\pi$
$593$		−	229570.i		−	0.652839i	0.945225	−	0.326420i	$-0.105842\pi$
$594$	−70374.1	−	194357.i	−0.199453	−	0.550842i
$595$	−6201.90			−0.0175183
$596$	−107075.	−	61819.8i	−0.301436	−	0.174034i
$597$	−13930.4	+	21154.5i	−0.0390853	+	0.0593546i
$598$	−160708.	−	278355.i	−0.449403	−	0.778389i
$599$	344717.	−	199023.i	0.960748	−	0.554688i	0.0643446	−	0.997928i	$-0.479504\pi$
$599$	344717.	−	199023.i	0.960748	−	0.554688i	0.896403	+	0.443240i	$0.146171\pi$
$600$	−69376.8	+	34794.2i	−0.192713	+	0.0966505i
$601$	−63925.5	+	110722.i	−0.176980	+	0.306539i	−0.940845	−	0.338838i	$-0.889966\pi$
$601$	−63925.5	+	110722.i	−0.176980	+	0.306539i	0.763864	+	0.645377i	$0.223300\pi$
$602$			33469.6i			0.0923543i
$603$	83316.4	−	111655.i	0.229137	−	0.307073i
$604$	88772.7			0.243336
$605$	−55142.9	−	31836.8i	−0.150653	−	0.0869798i
$606$	−238885.	−	14046.4i	−0.650496	−	0.0382491i
$607$	−11626.2	−	20137.1i	−0.0315544	−	0.0546538i	0.849817	−	0.527078i	$-0.176712\pi$
$607$	−11626.2	−	20137.1i	−0.0315544	−	0.0546538i	−0.881371	+	0.472424i	$0.843379\pi$
$608$	−62492.0	+	36079.8i	−0.169051	+	0.0976016i
$609$	806.884	−	13722.5i	0.00217559	−	0.0369998i
$610$	−17928.3	+	31052.8i	−0.0481815	+	0.0834529i
$611$			304425.i			0.815452i
$612$	−77125.3	−	57550.7i	−0.205918	−	0.153655i
$613$	90508.8			0.240863			0.120431	−	0.992722i	$-0.461572\pi$
$613$	90508.8			0.240863			0.120431	+	0.992722i	$0.461572\pi$
$614$	207283.	+	119675.i	0.549829	+	0.317444i
$615$	130217.	+	259642.i	0.344284	+	0.686474i
$616$	10683.0	+	18503.4i	0.0281534	+	0.0487631i
$617$	−388972.	+	224573.i	−1.02176	+	0.589913i	−0.914613	−	0.404331i	$-0.867504\pi$
$617$	−388972.	+	224573.i	−1.02176	+	0.589913i	−0.107146	+	0.994243i	$0.534171\pi$
$618$	71047.3	+	46785.0i	0.186025	+	0.122498i
$619$	−260513.	+	451223.i	−0.679906	+	1.17763i	0.295103	+	0.955466i	$0.404646\pi$
$619$	−260513.	+	451223.i	−0.679906	+	1.17763i	−0.975009	+	0.222166i	$0.928687\pi$
$620$		−	73766.5i		−	0.191900i
$621$	333815.	−	120870.i	0.865611	−	0.313427i
$622$	209534.			0.541593
$623$	21588.9	+	12464.4i	0.0556230	+	0.0321140i
$624$	103105.	−	156574.i	0.264794	−	0.402114i
$625$	−7812.50	−	13531.6i	−0.0200000	−	0.0346410i
$626$	−259317.	+	149717.i	−0.661733	+	0.382052i
$627$	66945.1	−	33574.6i	0.170288	−	0.0854036i
$628$	79259.1	−	137281.i	0.200969	−	0.348089i
$629$			228319.i			0.577086i
$630$	8828.34	+	1041.81i	0.0222432	+	0.00262487i
$631$	−374837.			−0.941421			−0.470710	−	0.882288i	$-0.656002\pi$
$631$	−374837.			−0.941421			−0.470710	+	0.882288i	$0.656002\pi$
$632$	676419.	+	390531.i	1.69349	+	0.977735i
$633$	−684895.	−	40271.7i	−1.70929	−	0.100506i
$634$	62147.2	+	107642.i	0.154612	+	0.267796i
$635$	84892.6	−	49012.8i	0.210534	−	0.121552i
$636$	−17280.0	+	293878.i	−0.0427198	+	0.726529i
$637$	−263114.	+	455726.i	−0.648432	+	1.12312i
$638$		−	132263.i		−	0.324934i
$639$	−7181.81	+	3088.48i	−0.0175886	+	0.00756386i
$640$	13565.3			0.0331184
$641$	−205801.	−	118819.i	−0.500878	−	0.289182i	0.228198	−	0.973615i	$-0.426717\pi$
$641$	−205801.	−	118819.i	−0.500878	−	0.289182i	−0.729076	+	0.684433i	$0.760050\pi$
$642$	43031.3	+	85801.0i	0.104403	+	0.208172i
$643$	89135.0	+	154386.i	0.215589	+	0.373411i	0.953455	−	0.301537i	$-0.0974996\pi$
$643$	89135.0	+	154386.i	0.215589	+	0.373411i	−0.737866	+	0.674948i	$0.764166\pi$
$644$	−9684.54	+	5591.37i	−0.0233511	+	0.0134818i
$645$	−286541.	−	188689.i	−0.688759	−	0.453552i
$646$	−22341.4	+	38696.4i	−0.0535358	+	0.0927268i
$647$		−	451526.i		−	1.07864i	−0.842102	−	0.539318i	$-0.818682\pi$
$647$		−	451526.i		−	1.07864i	0.842102	−	0.539318i	$-0.181318\pi$
$648$	328548.	+	311349.i	0.782435	+	0.741477i
$649$	251808.			0.597834
$650$	71446.1	+	41249.4i	0.169103	+	0.0976318i
$651$	−15248.5	+	23156.3i	−0.0359804	+	0.0546395i
$652$	−50806.4	−	87999.3i	−0.119515	−	0.207007i
$653$	−117793.	+	68007.8i	−0.276244	+	0.159490i	−0.631722	−	0.775195i	$-0.717652\pi$
$653$	−117793.	+	68007.8i	−0.276244	+	0.159490i	0.355478	+	0.934685i	$0.384318\pi$
$654$	−303385.	+	152155.i	−0.709313	+	0.355738i
$655$	−99151.8	+	171736.i	−0.231110	+	0.400294i
$656$			273128.i			0.634686i
$657$	216175.	+	502684.i	0.500813	+	1.16457i
$658$	−13573.7			−0.0313506
$659$	12391.3	+	7154.09i	0.0285328	+	0.0164734i	0.514199	−	0.857671i	$-0.328089\pi$
$659$	12391.3	+	7154.09i	0.0285328	+	0.0164734i	−0.485666	+	0.874145i	$0.661423\pi$
$660$	−66626.6	−	3917.64i	−0.152954	−	0.00899366i
$661$	−147773.	−	255950.i	−0.338213	−	0.585803i	0.645883	−	0.763436i	$-0.276489\pi$
$661$	−147773.	−	255950.i	−0.338213	−	0.585803i	−0.984097	+	0.177633i	$0.943156\pi$
$662$	171654.	−	99104.5i	0.391686	−	0.226140i
$663$	−19703.1	+	335088.i	−0.0448238	+	0.762310i
$664$	−288419.	+	499557.i	−0.654166	+	1.13305i
$665$			3220.84i			0.00728326i
$666$	38353.7	−	325010.i	0.0864686	−	0.732736i
$667$	227166.			0.510612
$668$	17499.9	+	10103.6i	0.0392178	+	0.0226424i
$669$	−177920.	−	354758.i	−0.397532	−	0.792646i
$670$	28823.6	+	49923.9i	0.0642093	+	0.111214i
$671$	−87628.2	+	50592.1i	−0.194625	+	0.112367i
$672$	−20186.5	−	13292.9i	−0.0447016	−	0.0294362i
$673$	33425.5	−	57894.7i	0.0737985	−	0.127823i	−0.826765	−	0.562548i	$-0.809821\pi$
$673$	33425.5	−	57894.7i	0.0737985	−	0.127823i	0.900563	+	0.434725i	$0.143154\pi$
$674$		−	155634.i		−	0.342598i
$675$	−58690.1	+	69708.2i	−0.128812	+	0.152995i
$676$	139599.			0.305484
$677$	−323652.	−	186861.i	−0.706156	−	0.407700i	0.103480	−	0.994632i	$-0.467002\pi$
$677$	−323652.	−	186861.i	−0.706156	−	0.407700i	−0.809636	+	0.586932i	$0.800336\pi$
$678$	−272398.	+	413662.i	−0.592578	+	0.899883i
$679$	29310.6	+	50767.5i	0.0635749	+	0.110115i
$680$	113164.	−	65335.3i	0.244732	−	0.141296i
$681$	433481.	−	217401.i	0.934707	−	0.468779i
$682$	−133386.	+	231031.i	−0.286775	+	0.496709i
$683$			782942.i			1.67837i	0.543844	+	0.839186i	$0.316968\pi$
$683$			782942.i			1.67837i	−0.543844	+	0.839186i	$0.683032\pi$
$684$	−29887.9	+	40053.6i	−0.0638827	+	0.0856109i
$685$	−113710.			−0.242336
$686$	−40730.9	−	23516.0i	−0.0865518	−	0.0499707i
$687$	−467489.	−	27488.3i	−0.990509	−	0.0582418i
$688$	−161305.	−	279388.i	−0.340777	−	0.590244i
$689$	889285.	−	513429.i	1.87328	−	1.08154i
$690$	−8623.19	+	146653.i	−0.0181121	+	0.308030i
$691$	246770.	−	427418.i	0.516817	−	0.895153i	−0.482993	−	0.875624i	$-0.660450\pi$
$691$	246770.	−	427418.i	0.516817	−	0.895153i	0.999809	−	0.0195283i	$-0.00621643\pi$
$692$			78604.4i			0.164148i
$693$	20105.1	+	15002.4i	0.0418640	+	0.0312388i
$694$	−652444.			−1.35464
$695$	296610.	+	171248.i	0.614067	+	0.354532i
$696$	129840.	+	258891.i	0.268034	+	0.534439i
$697$	−244517.	−	423515.i	−0.503318	−	0.871773i
$698$	−23898.6	+	13797.8i	−0.0490525	+	0.0283205i
$699$	−280715.	−	184853.i	−0.574529	−	0.378330i
$700$	1435.15	−	2485.76i	0.00292888	−	0.00507297i
$701$		−	904304.i		−	1.84026i	−0.391616	−	0.920129i	$-0.628084\pi$
$701$		−	904304.i		−	1.84026i	0.391616	−	0.920129i	$-0.371916\pi$
$702$	84336.2	−	473684.i	0.171135	−	0.961202i
$703$	118573.			0.239925
$704$	−325405.	−	187873.i	−0.656566	−	0.379069i
$705$	76523.4	−	116208.i	0.153963	−	0.233807i
$706$	−130483.	−	226003.i	−0.261784	−	0.453423i
$707$	25150.3	−	14520.5i	0.0503158	−	0.0290498i
$708$	−150200.	+	75329.0i	−0.299643	+	0.150278i
$709$	−275075.	+	476444.i	−0.547216	+	0.947806i	0.451248	+	0.892399i	$0.350979\pi$
$709$	−275075.	+	476444.i	−0.547216	+	0.947806i	−0.998464	+	0.0554073i	$0.982354\pi$
$710$		−	3234.93i		−	0.00641723i
$711$	910721.	+	107472.i	1.80155	+	0.212597i
$712$	−525234.			−1.03608
$713$	−396805.	−	229095.i	−0.780544	−	0.450647i
$714$	−14940.9	−	878.522i	−0.0293076	−	0.00172328i
$715$	116402.	+	201614.i	0.227693	+	0.394375i
$716$	206484.	−	119214.i	0.402773	−	0.232541i
$717$	−8080.33	+	137421.i	−0.0157178	+	0.267309i
$718$	−225926.	+	391314.i	−0.438244	+	0.759062i
$719$		−	349893.i		−	0.676827i	−0.940998	−	0.338413i	$-0.890110\pi$
$719$		−	349893.i		−	0.676827i	0.940998	−	0.338413i	$-0.109890\pi$
$720$	−78715.8	+	33851.2i	−0.151844	+	0.0652994i
$721$	−10323.8			−0.0198595
$722$	−318248.	−	183740.i	−0.610507	−	0.352476i
$723$	410887.	+	819277.i	0.786043	+	1.56731i
$724$	−176873.	−	306353.i	−0.337431	−	0.584447i
$725$	−50495.6	+	29153.6i	−0.0960676	+	0.0554647i
$726$	−128334.	−	84508.6i	−0.243483	−	0.160335i
$727$	346890.	−	600831.i	0.656331	−	1.13680i	−0.325228	−	0.945636i	$-0.605441\pi$
$727$	346890.	−	600831.i	0.656331	−	1.13680i	0.981558	−	0.191163i	$-0.0612258\pi$
$728$			49732.0i			0.0938367i
$729$	498784.	+	183424.i	0.938549	+	0.345145i
$730$	−226426.			−0.424893
$731$	500241.	+	288814.i	0.936149	+	0.540486i
$732$	37134.2	−	56391.7i	0.0693030	−	0.105243i
$733$	−187413.	−	324609.i	−0.348812	−	0.604160i	0.637227	−	0.770676i	$-0.280082\pi$
$733$	−187413.	−	324609.i	−0.348812	−	0.604160i	−0.986039	+	0.166516i	$0.946748\pi$
$734$	604078.	−	348764.i	1.12125	−	0.647351i
$735$	214994.	−	107825.i	0.397971	−	0.199592i
$736$	199714.	−	345915.i	0.368683	−	0.638578i
$737$			162675.i			0.299492i
$738$	276923.	+	643944.i	0.508448	+	1.18232i
$739$	−178379.			−0.326630			−0.163315	−	0.986574i	$-0.552219\pi$
$739$	−178379.			−0.326630			−0.163315	+	0.986574i	$0.552219\pi$
$740$	−91511.5	−	52834.2i	−0.167114	−	0.0964831i
$741$	174022.	+	10232.5i	0.316933	+	0.0186356i
$742$	22892.7	+	39651.4i	0.0415805	+	0.0720195i
$743$	−299690.	+	173026.i	−0.542868	+	0.313425i	−0.746240	−	0.665677i	$-0.768143\pi$
$743$	−299690.	+	173026.i	−0.542868	+	0.313425i	0.203373	+	0.979101i	$0.434810\pi$
$744$	34290.0	−	583164.i	0.0619471	−	1.05352i
$745$	98558.4	−	170708.i	0.177575	−	0.307568i
$746$			222028.i			0.398960i
$747$	−79371.6	+	672596.i	−0.142241	+	1.20535i
$748$	112368.			0.200834
$749$	−10088.3	−	5824.46i	−0.0179826	−	0.0103823i
$750$	−16904.1	−	33705.5i	−0.0300518	−	0.0599209i
$751$	−242395.	−	419841.i	−0.429778	−	0.744397i	0.567075	−	0.823666i	$-0.308075\pi$
$751$	−242395.	−	419841.i	−0.429778	−	0.744397i	−0.996853	+	0.0792687i	$0.974741\pi$
$752$	113307.	−	65417.7i	0.200364	−	0.115680i
$753$	322148.	+	212136.i	0.568153	+	0.374132i
$754$	153929.	−	266613.i	0.270756	−	0.468963i
$755$			141529.i			0.248286i
$756$	−16480.4	−	2934.23i	−0.0288353	−	0.00513393i
$757$	855073.			1.49215			0.746073	−	0.665864i	$-0.231937\pi$
$757$	855073.			1.49215			0.746073	+	0.665864i	$0.231937\pi$
$758$	159808.	+	92265.2i	0.278138	+	0.160583i
$759$	−227995.	+	346231.i	−0.395769	+	0.601011i
$760$	−33930.7	−	58769.6i	−0.0587442	−	0.101748i
$761$	450394.	−	260035.i	0.777719	−	0.449016i	−0.0579021	−	0.998322i	$-0.518441\pi$
$761$	450394.	−	260035.i	0.777719	−	0.449016i	0.835621	+	0.549306i	$0.185108\pi$
$762$	211456.	−	106050.i	0.364175	−	0.182643i
$763$	20594.8	−	35671.2i	0.0353759	−	0.0612729i
$764$		−	225489.i		−	0.386312i
$765$	91752.3	−	122960.i	0.156781	−	0.210107i
$766$	512411.			0.873295
$767$	507592.	+	293058.i	0.862827	+	0.498153i
$768$	603757.	+	35500.9i	1.02362	+	0.0601889i
$769$	123522.	+	213946.i	0.208877	+	0.361785i	0.951361	−	0.308078i	$-0.0996859\pi$
$769$	123522.	+	213946.i	0.208877	+	0.361785i	−0.742484	+	0.669864i	$0.766353\pi$
$770$	−8989.57	+	5190.13i	−0.0151620	+	0.00875380i
$771$	−10105.1	+	171856.i	−0.0169994	+	0.289106i
$772$	−142936.	+	247572.i	−0.239831	+	0.415400i
$773$			96817.3i			0.162029i	0.996713	+	0.0810147i	$0.0258161\pi$
$773$			96817.3i			0.162029i	−0.996713	+	0.0810147i	$0.974184\pi$
$774$	−663572.	−	495156.i	−1.10766	−	0.826533i
$775$	117605.			0.195804
$776$	−1.06964e6	−	617559.i	−1.77630	−	1.02554i
$777$	17805.1	+	35502.0i	0.0294919	+	0.0588045i
$778$	−254024.	−	439982.i	−0.419677	−	0.726902i
$779$	−219945.	+	126985.i	−0.362442	+	0.209256i
$780$	−129746.	−	85438.2i	−0.213257	−	0.140431i
$781$	4564.33	−	7905.66i	0.00748299	−	0.0129609i
$782$		−	247334.i		−	0.404456i
$783$	260128.	+	219012.i	0.424290	+	0.357227i
$784$	226161.			0.367948
$785$	218865.	+	126362.i	0.355170	+	0.205058i
$786$	−263192.	+	399680.i	−0.426017	+	0.646946i
$787$	−168754.	−	292291.i	−0.272461	−	0.471917i	0.697030	−	0.717042i	$-0.254504\pi$
$787$	−168754.	−	292291.i	−0.272461	−	0.471917i	−0.969491	+	0.245125i	$0.921171\pi$
$788$	−420727.	+	242907.i	−0.677560	+	0.391189i
$789$	55931.1	−	28050.8i	0.0898461	−	0.0450600i
$790$	−189732.	+	328626.i	−0.304010	+	0.526560i
$791$		−	60108.7i		−	0.0960692i
$792$	−524898.	−	61942.0i	−0.836806	−	0.0987496i
$793$	−235519.			−0.374525
$794$	416668.	+	240563.i	0.660920	+	0.381582i
$795$	−468526.	−	27549.3i	−0.741309	−	0.0435889i
$796$	9868.19	+	17092.2i	0.0155744	+	0.0269757i
$797$	283598.	−	163735.i	0.446463	−	0.257766i	−0.259872	−	0.965643i	$-0.583680\pi$
$797$	283598.	−	163735.i	0.446463	−	0.257766i	0.706335	+	0.707877i	$0.250347\pi$
$798$	−456.244	+	7759.27i	−0.000716459	+	0.0121847i
$799$	−117130.	+	202874.i	−0.183473	+	0.317785i
$800$			102522.i			0.160191i
$801$	−566511.	+	243624.i	−0.882965	+	0.379713i
$802$	549765.			0.854729
$803$	−553349.	−	319476.i	−0.858159	−	0.495458i
$804$	−48664.6	−	97033.3i	−0.0752837	−	0.150110i
$805$	−8914.24	−	15439.9i	−0.0137560	−	0.0238261i
$806$	−537755.	+	310473.i	−0.827779	+	0.477918i
$807$	−87234.6	−	57444.5i	−0.133950	−	0.0882066i
$808$	−305939.	+	529902.i	−0.468611	+	0.811658i
$809$		−	809020.i		−	1.23613i	−0.786129	−	0.618063i	$-0.787918\pi$
$809$		−	809020.i		−	1.23613i	0.786129	−	0.618063i	$-0.212082\pi$
$810$	−151264.	+	159619.i	−0.230550	+	0.243285i
$811$	−973228.			−1.47970			−0.739849	−	0.672773i	$-0.765103\pi$
$811$	−973228.			−1.47970			−0.739849	+	0.672773i	$0.765103\pi$
$812$	−9276.00	−	5355.50i	−0.0140685	−	0.00812247i
$813$	429296.	−	651924.i	0.649494	−	0.986316i
$814$	191071.	+	330945.i	0.288368	+	0.499467i
$815$	140296.	−	81000.0i	0.211218	−	0.121947i
$816$	128954.	−	64673.3i	0.193666	−	0.0971281i
$817$	149990.	−	259791.i	0.224708	−	0.389206i
$818$			14067.8i			0.0210241i
$819$	23067.6	+	53640.3i	0.0343902	+	0.0799693i
$820$	226329.			0.336599
$821$	960456.	+	554519.i	1.42492	+	0.822679i	0.996714	−	0.0810011i	$-0.0258117\pi$
$821$	960456.	+	554519.i	1.42492	+	0.822679i	0.428208	+	0.903680i	$0.359145\pi$
$822$	−273937.	−	16107.4i	−0.405421	−	0.0238387i
$823$	568252.	+	984241.i	0.838960	+	1.45312i	0.890765	+	0.454463i	$0.150169\pi$
$823$	568252.	+	984241.i	0.838960	+	1.45312i	−0.0518058	+	0.998657i	$0.516498\pi$
$824$	188375.	−	108758.i	0.277440	−	0.160180i
$825$	6245.84	−	106222.i	0.00917662	−	0.156065i
$826$	−13066.9	+	22632.5i	−0.0191519	+	0.0331720i
$827$			440476.i			0.644038i	0.946733	+	0.322019i	$0.104361\pi$
$827$			440476.i			0.644038i	−0.946733	+	0.322019i	$0.895639\pi$
$828$	32419.9	−	274727.i	0.0472880	−	0.400720i
$829$	−713413.			−1.03808			−0.519041	−	0.854749i	$-0.673711\pi$
$829$	−713413.			−1.03808			−0.519041	+	0.854749i	$0.673711\pi$
$830$	−242701.	−	140123.i	−0.352302	−	0.203402i
$831$	−137679.	−	274522.i	−0.199373	−	0.397535i
$832$	−437297.	−	757421.i	−0.631728	−	1.09419i
$833$	−350687.	+	202469.i	−0.505394	+	0.291789i
$834$	690299.	+	454565.i	0.992442	+	0.653528i
$835$	−16108.0	+	27899.9i	−0.0231030	+	0.0400156i
$836$		−	58356.0i		−	0.0834974i
$837$	−233509.	−	644898.i	−0.333314	−	0.920535i
$838$	581184.			0.827610
$839$	794917.	+	458946.i	1.12927	+	0.651984i	0.943751	−	0.330656i	$-0.107270\pi$
$839$	794917.	+	458946.i	1.12927	+	0.651984i	0.185519	+	0.982641i	$0.440603\pi$
$840$	12501.1	−	18984.1i	0.0177170	−	0.0269049i
$841$	−244849.	−	424091.i	−0.346183	−	0.599607i
$842$	−468274.	+	270358.i	−0.660505	+	0.381343i
$843$	−4597.60	+	2305.81i	−0.00646958	+	0.00324465i
$844$	−267294.	+	462967.i	−0.375236	+	0.649928i
$845$			222560.i			0.311698i
$846$	200812.	−	269114.i	0.280575	−	0.376006i
$847$	18648.0			0.0259936
$848$	−382196.	−	220661.i	−0.531489	−	0.306855i
$849$	−537335.	−	31595.2i	−0.745469	−	0.0438335i
$850$	31742.0	+	54978.8i	0.0439336	+	0.0760952i
$851$	−568410.	+	328172.i	−0.784879	+	0.453150i
$852$	−357.565	+	6081.04i	−0.000492578	+	0.00837720i
$853$	277357.	−	480397.i	0.381190	−	0.660240i	−0.610043	−	0.792368i	$-0.708848\pi$
$853$	277357.	−	480397.i	0.381190	−	0.660240i	0.991233	+	0.132128i	$0.0421811\pi$
$854$		−	10501.3i		−	0.0143989i
$855$	−63856.8	−	47649.8i	−0.0873525	−	0.0651822i
$856$	245436.			0.334958
$857$	575338.	+	332171.i	0.783360	+	0.452273i	0.837620	−	0.546254i	$-0.183947\pi$
$857$	575338.	+	332171.i	0.783360	+	0.452273i	−0.0542598	+	0.998527i	$0.517280\pi$
$858$	251863.	+	502194.i	0.342128	+	0.682177i
$859$	462081.	+	800347.i	0.626227	+	1.08466i	0.988302	+	0.152508i	$0.0487349\pi$
$859$	462081.	+	800347.i	0.626227	+	1.08466i	−0.362076	+	0.932149i	$0.617932\pi$
$860$	−231517.	+	133666.i	−0.313030	+	0.180728i
$861$	−71047.7	−	46785.3i	−0.0958394	−	0.0631107i
$862$	64632.7	−	111947.i	0.0869837	−	0.150660i
$863$		−	35914.6i		−	0.0482224i	−0.999709	−	0.0241112i	$-0.992324\pi$
$863$		−	35914.6i		−	0.0482224i	0.999709	−	0.0241112i	$-0.00767558\pi$
$864$	562192.	−	203562.i	0.753107	−	0.272690i
$865$	−125318.			−0.167487
$866$	−356852.	−	206028.i	−0.475830	−	0.274721i
$867$	271350.	−	412070.i	0.360987	−	0.548192i
$868$	10802.0	+	18709.6i	0.0143372	+	0.0248327i
$869$	−927353.	+	535408.i	−1.22802	+	0.708998i
$870$	−125778.	+	63080.5i	−0.166175	+	0.0833406i
$871$	−189323.	+	327918.i	−0.249556	+	0.432244i
$872$			867840.i			1.14132i
$873$	−1.44015e6	−	169949.i	−1.88964	−	0.222993i
$874$	−128449.			−0.168154
$875$	3963.00	+	2288.04i	0.00517617	+	0.00298846i
$876$	425637.	+	25027.4i	0.554665	+	0.0326142i
$877$	412337.	+	714189.i	0.536109	+	0.928568i	0.999109	+	0.0422096i	$0.0134397\pi$
$877$	412337.	+	714189.i	0.536109	+	0.928568i	−0.463000	+	0.886358i	$0.653227\pi$
$878$	891924.	−	514953.i	1.15701	−	0.668003i
$879$	50913.1	−	865872.i	0.0658950	−	1.12066i
$880$	50027.2	−	86649.6i	0.0646012	−	0.111893i
$881$		−	71679.9i		−	0.0923518i	−0.998933	−	0.0461759i	$-0.985297\pi$
$881$		−	71679.9i		−	0.0923518i	0.998933	−	0.0461759i	$-0.0147035\pi$
$882$	533211.	−	229304.i	0.685428	−	0.294764i
$883$	−470173.			−0.603026			−0.301513	−	0.953462i	$-0.597492\pi$
$883$	−470173.			−0.603026			−0.301513	+	0.953462i	$0.597492\pi$
$884$	226509.	+	130775.i	0.289855	+	0.167348i
$885$	−120096.	−	239462.i	−0.153335	−	0.305738i
$886$	562238.	+	973825.i	0.716231	+	1.24055i
$887$	−250185.	+	144444.i	−0.317990	+	0.183592i	−0.650496	−	0.759509i	$-0.725439\pi$
$887$	−250185.	+	144444.i	−0.317990	+	0.183592i	0.332506	+	0.943101i	$0.392106\pi$
$888$	−698887.	−	460221.i	−0.886301	−	0.583634i
$889$	−14354.3	+	24862.4i	−0.0181627	+	0.0314587i
$890$		−	255176.i		−	0.322151i
$891$	−594880.	+	176658.i	−0.749331	+	0.222525i
$892$	−309242.			−0.388659
$893$	105359.	+	60829.1i	0.132120	+	0.0762796i
$894$	261617.	−	397289.i	0.327333	−	0.497085i
$895$	190060.	+	329194.i	0.237272	+	0.410966i
$896$	−3440.59	+	1986.43i	−0.00428566	+	0.00247433i
$897$	−862537.	+	432583.i	−1.07200	+	0.537632i
$898$	157380.	−	272590.i	0.195163	−	0.338032i
$899$		−	438862.i		−	0.543011i
$900$	28051.0	+	65228.3i	0.0346308	+	0.0805288i
$901$	790181.			0.973367
$902$	−708846.	−	409253.i	−0.871243	−	0.503012i
$903$	100307.	+	5898.02i	0.123014	+	0.00723321i
$904$	633228.	+	1.09678e6i	0.774860	+	1.34210i
$905$	488415.	−	281986.i	0.596337	−	0.344295i
$906$	−20048.1	+	340955.i	−0.0244240	+	0.415375i
$907$	300810.	−	521018.i	0.365660	−	0.633342i	−0.623222	−	0.782045i	$-0.714177\pi$
$907$	300810.	−	521018.i	0.365660	−	0.633342i	0.988882	+	0.148703i	$0.0475099\pi$
$908$		−	377865.i		−	0.458316i
$909$	−84193.0	+	713453.i	−0.101894	+	0.863451i
$910$	−24161.4			−0.0291769
$911$	86960.5	+	50206.7i	0.104782	+	0.0604957i	0.551475	−	0.834191i	$-0.314065\pi$
$911$	86960.5	+	50206.7i	0.104782	+	0.0604957i	−0.446693	+	0.894687i	$0.647399\pi$
$912$	−33586.9	−	66969.6i	−0.0403813	−	0.0805170i
$913$	−395415.	−	684880.i	−0.474364	−	0.821623i
$914$	−681759.	+	393614.i	−0.816090	+	0.471170i
$915$	89904.4	+	59202.5i	0.107384	+	0.0707128i
$916$	−182447.	+	316008.i	−0.217444	+	0.376623i
$917$		−	58077.1i		−	0.0690663i
$918$	238456.	−	283223.i	0.282959	−	0.336080i
$919$	−606532.			−0.718163			−0.359081	−	0.933306i	$-0.616910\pi$
$919$	−606532.			−0.718163			−0.359081	+	0.933306i	$0.616910\pi$
$920$	325310.	+	187818.i	0.384346	+	0.221902i
$921$	395188.	−	600129.i	0.465892	−	0.707499i
$922$	505421.	+	875416.i	0.594555	+	1.02980i
$923$	18401.4	−	10624.1i	0.0215997	−	0.0124706i
$924$	17472.3	−	8762.81i	0.0204648	−	0.0102636i
$925$	84232.8	−	145895.i	0.0984459	−	0.170513i
$926$			250241.i			0.291834i
$927$	152732.	−	204681.i	0.177735	−	0.238187i
$928$	382579.			0.444248
$929$	−144999.	−	83715.0i	−0.168009	−	0.0970000i	0.413638	−	0.910442i	$-0.364258\pi$
$929$	−144999.	−	83715.0i	−0.168009	−	0.0970000i	−0.581647	+	0.813442i	$0.697591\pi$
$930$	283320.	+	16659.2i	0.327575	+	0.0192614i
$931$	105149.	+	182123.i	0.121312	+	0.210119i
$932$	−226810.	+	130949.i	−0.261114	+	0.150754i
$933$	36924.1	−	627962.i	0.0424177	−	0.721390i
$934$	313217.	−	542507.i	0.359047	−	0.621887i
$935$			179146.i			0.204920i
$936$	−985993.	−	735746.i	−1.12544	−	0.839800i
$937$	−217290.			−0.247492			−0.123746	−	0.992314i	$-0.539491\pi$
$937$	−217290.			−0.247492			−0.123746	+	0.992314i	$0.539491\pi$
$938$	−14621.2	−	8441.54i	−0.0166179	−	0.00959436i
$939$	402997.	+	803545.i	0.457058	+	0.911337i
$940$	−54208.8	−	93892.3i	−0.0613499	−	0.106261i
$941$	−325363.	+	187848.i	−0.367442	+	0.212143i	−0.672340	−	0.740242i	$-0.734711\pi$
$941$	−325363.	+	187848.i	−0.367442	+	0.212143i	0.304899	+	0.952385i	$0.401377\pi$
$942$	509363.	+	335418.i	0.574018	+	0.377994i
$943$	702907.	−	1.21747e6i	0.790450	−	1.36910i
$944$		−	251900.i		−	0.282673i
$945$	4678.00	−	26274.5i	0.00523837	−	0.0294219i
$946$	966790.			1.08031
$947$	−8769.66	−	5063.16i	−0.00977874	−	0.00564576i	0.495103	−	0.868834i	$-0.335130\pi$
$947$	−8769.66	−	5063.16i	−0.00977874	−	0.00564576i	−0.504881	+	0.863189i	$0.668464\pi$
$948$	392985.	−	596783.i	0.437279	−	0.664048i
$949$	−743622.	−	1.28799e6i	−0.825695	−	1.43015i
$950$	28552.2	−	16484.6i	0.0316368	−	0.0182655i
$951$	333550.	−	167283.i	0.368807	−	0.184966i
$952$	−19134.7	+	33142.3i	−0.0211129	+	0.0365686i
$953$		−	230617.i		−	0.253925i	−0.991908	−	0.126962i	$-0.959477\pi$
$953$		−	230617.i		−	0.253925i	0.991908	−	0.126962i	$-0.0405228\pi$
$954$	−1.12481e6	−	132737.i	−1.23590	−	0.145846i
$955$	359494.			0.394171
$956$	92892.1	+	53631.3i	0.101640	+	0.0586817i
$957$	−396384.	−	23307.4i	−0.432805	−	0.0254489i
$958$	−390367.	−	676135.i	−0.425345	−	0.736720i
$959$	28840.5	−	16651.1i	0.0313593	−	0.0181053i
$960$	−23464.2	+	399053.i	−0.0254603	+	0.433000i
$961$	19171.0	−	33205.1i	0.0207586	−	0.0359549i
$962$			889486.i			0.961145i
$963$	264724.	−	113843.i	0.285457	−	0.122759i
$964$	714162.			0.768498
$965$	−394700.	−	227880.i	−0.423850	−	0.244710i
$966$	−19288.0	−	38458.7i	−0.0206696	−	0.0412136i
$967$	395716.	+	685400.i	0.423185	+	0.732979i	0.996249	−	0.0865323i	$-0.0275786\pi$
$967$	395716.	+	685400.i	0.423185	+	0.732979i	−0.573064	+	0.819511i	$0.694245\pi$
$968$	−340265.	+	196452.i	−0.363133	+	0.209655i
$969$	112034.	+	73775.1i	0.119317	+	0.0785710i
$970$	300030.	−	519667.i	0.318875	−	0.552308i
$971$		−	210031.i		−	0.222764i	−0.993778	−	0.111382i	$-0.964472\pi$
$971$		−	210031.i		−	0.222764i	0.993778	−	0.111382i	$-0.0355277\pi$
$972$	301990.	−	283334.i	0.319639	−	0.299893i
$973$	−100306.			−0.105951
$974$	−152695.	−	88158.5i	−0.160956	−	0.0929280i
$975$	136213.	−	206852.i	0.143288	−	0.217595i
$976$	50610.6	+	87660.2i	0.0531303	+	0.0920243i
$977$	402493.	−	232379.i	0.421666	−	0.243449i	−0.274124	−	0.961694i	$-0.588388\pi$
$977$	402493.	−	232379.i	0.421666	−	0.243449i	0.695790	+	0.718245i	$0.255054\pi$
$978$	349458.	−	175262.i	0.365357	−	0.183236i
$979$	360041.	−	623610.i	0.375653	−	0.650650i
$980$		−	187410.i		−	0.195137i
$981$	402538.	+	936042.i	0.418282	+	0.972651i
$982$	−618681.			−0.641570
$983$	1.18220e6	+	682541.i	1.22344	+	0.706353i	0.965649	−	0.259849i	$-0.0836727\pi$
$983$	1.18220e6	+	682541.i	1.22344	+	0.706353i	0.257789	+	0.966201i	$0.417006\pi$
$984$	1.78925e6	+	105208.i	1.84791	+	0.108657i
$985$	−387263.	−	670759.i	−0.399147	−	0.691343i
$986$	205162.	−	118450.i	0.211030	−	0.121838i
$987$	−2391.96	+	40679.7i	−0.00245539	+	0.0417584i
$988$	67915.5	−	117633.i	0.0695753	−	0.120508i
$989$			1.66050e6i			1.69764i
$990$	30093.4	−	255012.i	0.0307045	−	0.260190i
$991$	−1.28799e6			−1.31149			−0.655744	−	0.754983i	$-0.727645\pi$
$991$	−1.28799e6			−1.31149			−0.655744	+	0.754983i	$0.727645\pi$
$992$	−668275.	−	385828.i	−0.679097	−	0.392077i
$993$	−266763.	−	531903.i	−0.270537	−	0.539429i
$994$	473.705	+	820.482i	0.000479442	+	0.000830417i
$995$	−27249.9	+	15732.7i	−0.0275244	+	0.0158912i
$996$	440743.	+	290232.i	0.444290	+	0.292567i
$997$	564732.	−	978145.i	0.568136	−	0.984040i	−0.428614	−	0.903488i	$-0.640998\pi$
$997$	564732.	−	978145.i	0.568136	−	0.984040i	0.996750	−	0.0805528i	$-0.0256686\pi$
$998$		−	918769.i		−	0.922455i
$999$	−967279.	−	172217.i	−0.969217	−	0.172562i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.5.i.a.11.11	✓	32
3.2	odd	2		135.5.i.a.116.6		32
9.2	odd	6		405.5.c.b.161.21		32
9.4	even	3		135.5.i.a.71.6		32
9.5	odd	6	inner	45.5.i.a.41.11	yes	32
9.7	even	3		405.5.c.b.161.12		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.5.i.a.11.11	✓	32	1.1	even	1	trivial
45.5.i.a.41.11	yes	32	9.5	odd	6	inner
135.5.i.a.71.6		32	9.4	even	3
135.5.i.a.116.6		32	3.2	odd	2
405.5.c.b.161.12		32	9.7	even	3
405.5.c.b.161.21		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+(2.59623 + 1.49894i) q^{2} +(4.94975 - 7.51665i) q^{3} +(-3.50638 - 6.07323i) q^{4} +(9.68246 - 5.59017i) q^{5} +(24.1177 - 12.0956i) q^{6} +(-1.63719 + 2.83570i) q^{7} -68.9893i q^{8} +(-31.9999 - 74.4110i) q^{9} +33.5172 q^{10} +(81.9109 + 47.2913i) q^{11} +(-63.0060 - 3.70474i) q^{12} +(110.077 + 190.658i) q^{13} +(-8.50105 + 4.90809i) q^{14} +(5.90642 - 100.450i) q^{15} +(47.3086 - 81.9408i) q^{16} +169.411i q^{17} +(28.4581 - 241.154i) q^{18} +87.9803 q^{19} +(-67.9007 - 39.2025i) q^{20} +(13.2112 + 26.3422i) q^{21} +(141.773 + 245.558i) q^{22} +(-421.756 + 243.501i) q^{23} +(-518.568 - 341.480i) q^{24} +(62.5000 - 108.253i) q^{25} +659.991i q^{26} +(-717.713 - 127.784i) q^{27} +22.9624 q^{28} +(-403.964 - 233.229i) q^{29} +(165.902 - 251.937i) q^{30} +(470.420 + 814.791i) q^{31} +(-710.296 + 410.090i) q^{32} +(760.910 - 381.615i) q^{33} +(-253.936 + 439.830i) q^{34} +36.6087i q^{35} +(-339.711 + 455.256i) q^{36} +1347.72 q^{37} +(228.417 + 131.877i) q^{38} +(1977.96 + 116.304i) q^{39} +(-385.662 - 667.986i) q^{40} +(-2499.93 + 1443.34i) q^{41} +(-5.18575 + 88.1932i) q^{42} +(1704.82 - 2952.83i) q^{43} -663.285i q^{44} +(-725.808 - 541.597i) q^{45} -1459.97 q^{46} +(1197.53 + 691.394i) q^{47} +(-381.755 - 761.188i) q^{48} +(1195.14 + 2070.04i) q^{49} +(324.529 - 187.367i) q^{50} +(1273.40 + 838.541i) q^{51} +(771.940 - 1337.04i) q^{52} -4664.29i q^{53} +(-1671.81 - 1407.56i) q^{54} +1057.47 q^{55} +(195.633 + 112.949i) q^{56} +(435.481 - 661.317i) q^{57} +(-699.191 - 1211.03i) q^{58} +(2305.63 - 1331.16i) q^{59} +(-630.763 + 316.343i) q^{60} +(-534.899 + 926.473i) q^{61} +2820.52i q^{62} +(263.397 + 31.0829i) q^{63} -3972.67 q^{64} +(2131.62 + 1230.69i) q^{65} +(2547.52 + 149.794i) q^{66} +(859.963 + 1489.50i) q^{67} +(1028.87 - 594.018i) q^{68} +(-257.276 + 4375.46i) q^{69} +(-54.8741 + 95.0447i) q^{70} -96.5153i q^{71} +(-5133.57 + 2207.65i) q^{72} -6755.50 q^{73} +(3499.01 + 2020.15i) q^{74} +(-504.341 - 1005.62i) q^{75} +(-308.492 - 534.324i) q^{76} +(-268.207 + 154.850i) q^{77} +(4960.92 + 3266.79i) q^{78} +(-5660.74 + 9804.70i) q^{79} -1057.85i q^{80} +(-4513.01 + 4762.30i) q^{81} -8653.87 q^{82} +(-7241.08 - 4180.64i) q^{83} +(113.658 - 172.600i) q^{84} +(947.035 + 1640.31i) q^{85} +(8852.21 - 5110.83i) q^{86} +(-3752.62 + 1882.03i) q^{87} +(3262.59 - 5650.98i) q^{88} -7613.27i q^{89} +(-1072.55 - 2494.05i) q^{90} -720.865 q^{91} +(2957.67 + 1707.61i) q^{92} +(8452.96 + 497.033i) q^{93} +(2072.71 + 3590.04i) q^{94} +(851.866 - 491.825i) q^{95} +(-433.290 + 7368.88i) q^{96} +(8951.51 - 15504.5i) q^{97} +7165.75i q^{98} +(897.850 - 7608.39i) 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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