LMFDB - Embedded newform 45.5.i.a.41.1

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			41.1
Character	$\chi$	$=$	45.41
Dual form			45.5.i.a.11.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-6.31571 + 3.64638i) q^{2} +(-7.77630 - 4.53091i) q^{3} +(18.5921 - 32.2025i) q^{4} +(9.68246 + 5.59017i) q^{5} +(65.6342 + 0.260606i) q^{6} +(-25.8824 - 44.8297i) q^{7} +154.491i q^{8} +(39.9417 + 70.4675i) q^{9} -81.5354 q^{10} +(-33.9762 + 19.6162i) q^{11} +(-290.484 + 166.177i) q^{12} +(-83.2911 + 144.264i) q^{13} +(326.932 + 188.754i) q^{14} +(-49.9651 - 87.3412i) q^{15} +(-265.860 - 460.482i) q^{16} +267.704i q^{17} +(-509.211 - 299.410i) q^{18} +662.379 q^{19} +(360.035 - 207.866i) q^{20} +(-1.84982 + 465.880i) q^{21} +(143.056 - 247.780i) q^{22} +(554.266 + 320.005i) q^{23} +(699.986 - 1201.37i) q^{24} +(62.5000 + 108.253i) q^{25} -1214.84i q^{26} +(8.68342 - 728.948i) q^{27} -1924.84 q^{28} +(-1091.79 + 630.344i) q^{29} +(634.044 + 369.430i) q^{30} +(-513.094 + 888.705i) q^{31} +(1217.49 + 702.917i) q^{32} +(353.088 + 1.40197i) q^{33} +(-976.150 - 1690.74i) q^{34} -578.749i q^{35} +(3011.83 + 23.9178i) q^{36} +1741.51 q^{37} +(-4183.39 + 2415.28i) q^{38} +(1301.35 - 744.459i) q^{39} +(-863.633 + 1495.86i) q^{40} +(-193.333 - 111.621i) q^{41} +(-1687.09 - 2949.11i) q^{42} +(821.707 + 1423.24i) q^{43} +1458.82i q^{44} +(-7.19147 + 905.579i) q^{45} -4667.44 q^{46} +(882.358 - 509.430i) q^{47} +(-19.0010 + 4785.43i) q^{48} +(-139.301 + 241.277i) q^{49} +(-789.464 - 455.797i) q^{50} +(1212.94 - 2081.75i) q^{51} +(3097.12 + 5364.36i) q^{52} -1082.66i q^{53} +(2603.18 + 4635.49i) q^{54} -438.631 q^{55} +(6925.80 - 3998.61i) q^{56} +(-5150.86 - 3001.18i) q^{57} +(4596.94 - 7962.14i) q^{58} +(-1556.31 - 898.538i) q^{59} +(-3741.56 - 14.8562i) q^{60} +(2253.85 + 3903.77i) q^{61} -7483.73i q^{62} +(2125.25 - 3614.44i) q^{63} -1744.90 q^{64} +(-1612.93 + 931.223i) q^{65} +(-2235.11 + 1278.64i) q^{66} +(-595.660 + 1031.71i) q^{67} +(8620.74 + 4977.19i) q^{68} +(-2860.22 - 4999.79i) q^{69} +(2110.34 + 3655.21i) q^{70} +7195.09i q^{71} +(-10886.6 + 6170.64i) q^{72} -3393.67 q^{73} +(-10998.9 + 6350.20i) q^{74} +(4.46687 - 1124.99i) q^{75} +(12315.0 - 21330.3i) q^{76} +(1758.77 + 1015.43i) q^{77} +(-5504.35 + 9446.98i) q^{78} +(-4052.63 - 7019.36i) q^{79} -5944.80i q^{80} +(-3370.33 + 5629.18i) q^{81} +1628.05 q^{82} +(-2362.82 + 1364.18i) q^{83} +(14968.1 + 8721.27i) q^{84} +(-1496.51 + 2592.03i) q^{85} +(-10379.3 - 5992.51i) q^{86} +(11346.1 + 45.0507i) q^{87} +(-3030.53 - 5249.03i) q^{88} -2910.83i q^{89} +(-3256.66 - 5745.60i) q^{90} +8623.11 q^{91} +(20609.9 - 11899.2i) q^{92} +(8016.62 - 4586.05i) q^{93} +(-3715.14 + 6434.82i) q^{94} +(6413.46 + 3702.81i) q^{95} +(-6282.70 - 10982.4i) q^{96} +(4342.24 + 7520.98i) q^{97} -2031.78i q^{98} +(-2739.37 - 1610.71i) 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 $\left(\mathbb{Z}/45\mathbb{Z}\right)^\times$.

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−6.31571	+	3.64638i	−1.57893	+	0.911594i	−0.583918	+	0.811813i	$0.698481\pi$
$2$	−6.31571	+	3.64638i	−1.57893	+	0.911594i	−0.995009	+	0.0997810i	$0.968186\pi$
$3$	−7.77630	−	4.53091i	−0.864033	−	0.503435i
$3$	−7.77630	−	4.53091i	−0.864033	−	0.503435i
$4$	18.5921	−	32.2025i	1.16201	−	2.01266i
$5$	9.68246	+	5.59017i	0.387298	+	0.223607i
$5$	9.68246	+	5.59017i	0.387298	+	0.223607i
$6$	65.6342	+	0.260606i	1.82317	+	0.00723907i
$7$	−25.8824	−	44.8297i	−0.528213	−	0.914892i	−0.999459	−	0.0328900i	$-0.989529\pi$
$7$	−25.8824	−	44.8297i	−0.528213	−	0.914892i	0.471246	−	0.882002i	$-0.343804\pi$
$8$			154.491i			2.41393i
$9$	39.9417	+	70.4675i	0.493107	+	0.869969i
$10$	−81.5354			−0.815354
$11$	−33.9762	+	19.6162i	−0.280795	+	0.162117i	−0.633783	−	0.773511i	$-0.718499\pi$
$11$	−33.9762	+	19.6162i	−0.280795	+	0.162117i	0.352988	+	0.935628i	$0.385166\pi$
$12$	−290.484	+	166.177i	−2.01725	+	1.15401i
$13$	−83.2911	+	144.264i	−0.492847	+	0.853636i	−0.999966	−	0.00824018i	$-0.997377\pi$
$13$	−83.2911	+	144.264i	−0.492847	+	0.853636i	0.507119	+	0.861876i	$0.330710\pi$
$14$	326.932	+	188.754i	1.66802	+	0.963032i
$15$	−49.9651	−	87.3412i	−0.222067	−	0.388183i
$16$	−265.860	−	460.482i	−1.03851	−	1.79876i
$17$			267.704i			0.926312i	0.886277	+	0.463156i	$0.153283\pi$
$17$			267.704i			0.926312i	−0.886277	+	0.463156i	$0.846717\pi$
$18$	−509.211	−	299.410i	−1.57164	−	0.924104i
$19$	662.379			1.83484			0.917422	−	0.397915i	$-0.130266\pi$
$19$	662.379			1.83484			0.917422	+	0.397915i	$0.130266\pi$
$20$	360.035	−	207.866i	0.900087	−	0.519665i
$21$	−1.84982	+	465.880i	−0.00419460	+	1.05642i
$22$	143.056	−	247.780i	0.295570	−	0.511942i
$23$	554.266	+	320.005i	1.04776	+	0.604925i	0.922022	−	0.387138i	$-0.126536\pi$
$23$	554.266	+	320.005i	1.04776	+	0.604925i	0.125739	+	0.992063i	$0.459870\pi$
$24$	699.986	−	1201.37i	1.21525	−	2.08571i
$25$	62.5000	+	108.253i	0.100000	+	0.173205i
$26$		−	1214.84i		−	1.79710i
$27$	8.68342	−	728.948i	0.0119114	−	0.999929i
$28$	−1924.84			−2.45515
$29$	−1091.79	+	630.344i	−1.29820	+	0.749518i	−0.980093	−	0.198537i	$-0.936381\pi$
$29$	−1091.79	+	630.344i	−1.29820	+	0.749518i	−0.318109	+	0.948054i	$0.603048\pi$
$30$	634.044	+	369.430i	0.704493	+	0.410478i
$31$	−513.094	+	888.705i	−0.533917	+	0.924771i	0.465298	+	0.885154i	$0.345947\pi$
$31$	−513.094	+	888.705i	−0.533917	+	0.924771i	−0.999215	+	0.0396170i	$0.987386\pi$
$32$	1217.49	+	702.917i	1.18895	+	0.686443i
$33$	353.088	+	1.40197i	0.324232	+	0.00128739i
$34$	−976.150	−	1690.74i	−0.844421	−	1.46258i
$35$		−	578.749i		−	0.472448i
$36$	3011.83	+	23.9178i	2.32394	+	0.0184551i
$37$	1741.51			1.27210			0.636052	−	0.771646i	$-0.280566\pi$
$37$	1741.51			1.27210			0.636052	+	0.771646i	$0.280566\pi$
$38$	−4183.39	+	2415.28i	−2.89709	+	1.67263i
$39$	1301.35	−	744.459i	0.855586	−	0.489454i
$40$	−863.633	+	1495.86i	−0.539770	+	0.934910i
$41$	−193.333	−	111.621i	−0.115011	−	0.0664016i	0.441391	−	0.897315i	$-0.354485\pi$
$41$	−193.333	−	111.621i	−0.115011	−	0.0664016i	−0.556402	+	0.830913i	$0.687819\pi$
$42$	−1687.09	−	2949.11i	−0.956401	−	1.67183i
$43$	821.707	+	1423.24i	0.444406	+	0.769734i	0.998011	−	0.0630454i	$-0.0200813\pi$
$43$	821.707	+	1423.24i	0.444406	+	0.769734i	−0.553604	+	0.832780i	$0.686748\pi$
$44$			1458.82i			0.753525i
$45$	−7.19147	+	905.579i	−0.00355134	+	0.447199i
$46$	−4667.44			−2.20578
$47$	882.358	−	509.430i	0.399438	−	0.230616i	−0.286804	−	0.957989i	$-0.592593\pi$
$47$	882.358	−	509.430i	0.399438	−	0.230616i	0.686241	+	0.727374i	$0.259259\pi$
$48$	−19.0010	+	4785.43i	−0.00824695	+	2.07701i
$49$	−139.301	+	241.277i	−0.0580181	+	0.100490i
$50$	−789.464	−	455.797i	−0.315785	−	0.182319i
$51$	1212.94	−	2081.75i	0.466338	−	0.800365i
$52$	3097.12	+	5364.36i	1.14538	+	1.98386i
$53$		−	1082.66i		−	0.385427i	−0.981255	−	0.192714i	$-0.938271\pi$
$53$		−	1082.66i		−	0.385427i	0.981255	−	0.192714i	$-0.0617288\pi$
$54$	2603.18	+	4635.49i	0.892722	+	1.58967i
$55$	−438.631			−0.145002
$56$	6925.80	−	3998.61i	2.20848	−	1.27507i
$57$	−5150.86	−	3001.18i	−1.58537	−	0.923725i
$58$	4596.94	−	7962.14i	1.36651	−	2.36687i
$59$	−1556.31	−	898.538i	−0.447088	−	0.258126i	0.259512	−	0.965740i	$-0.416438\pi$
$59$	−1556.31	−	898.538i	−0.447088	−	0.258126i	−0.706600	+	0.707614i	$0.749772\pi$
$60$	−3741.56	−	14.8562i	−1.03932	−	0.00412672i
$61$	2253.85	+	3903.77i	0.605709	+	1.04912i	0.991939	+	0.126717i	$0.0404440\pi$
$61$	2253.85	+	3903.77i	0.605709	+	1.04912i	−0.386229	+	0.922403i	$0.626223\pi$
$62$		−	7483.73i		−	1.94686i
$63$	2125.25	−	3614.44i	0.535462	−	0.910668i
$64$	−1744.90			−0.426000
$65$	−1612.93	+	931.223i	−0.381758	+	0.220408i
$66$	−2235.11	+	1278.64i	−0.513112	+	0.293535i
$67$	−595.660	+	1031.71i	−0.132693	+	0.229832i	−0.924714	−	0.380663i	$-0.875696\pi$
$67$	−595.660	+	1031.71i	−0.132693	+	0.229832i	0.792021	+	0.610494i	$0.209029\pi$
$68$	8620.74	+	4977.19i	1.86435	+	1.07638i
$69$	−2860.22	−	4999.79i	−0.600760	−	1.05015i
$70$	2110.34	+	3655.21i	0.430681	+	0.745961i
$71$			7195.09i			1.42731i	0.700496	+	0.713657i	$0.252962\pi$
$71$			7195.09i			1.42731i	−0.700496	+	0.713657i	$0.747038\pi$
$72$	−10886.6	+	6170.64i	−2.10004	+	1.19032i
$73$	−3393.67			−0.636831			−0.318415	−	0.947951i	$-0.603151\pi$
$73$	−3393.67			−0.636831			−0.318415	+	0.947951i	$0.603151\pi$
$74$	−10998.9	+	6350.20i	−2.00856	+	1.15964i
$75$	4.46687	−	1124.99i	0.000794111	−	0.199998i
$76$	12315.0	−	21330.3i	2.13210	−	3.69291i
$77$	1758.77	+	1015.43i	0.296639	+	0.171265i
$78$	−5504.35	+	9446.98i	−0.904725	+	1.55276i
$79$	−4052.63	−	7019.36i	−0.649356	−	1.12472i	−0.983277	−	0.182117i	$-0.941705\pi$
$79$	−4052.63	−	7019.36i	−0.649356	−	1.12472i	0.333921	−	0.942601i	$-0.391628\pi$
$80$		−	5944.80i		−	0.928875i
$81$	−3370.33	+	5629.18i	−0.513691	+	0.857975i
$82$	1628.05			0.242125
$83$	−2362.82	+	1364.18i	−0.342985	+	0.198022i	−0.661591	−	0.749865i	$-0.730118\pi$
$83$	−2362.82	+	1364.18i	−0.342985	+	0.198022i	0.318606	+	0.947887i	$0.396785\pi$
$84$	14968.1	+	8721.27i	2.12133	+	1.23601i
$85$	−1496.51	+	2592.03i	−0.207130	+	0.358759i
$86$	−10379.3	−	5992.51i	−1.40337	−	0.810236i
$87$	11346.1	+	45.0507i	1.49902	+	0.00595200i
$88$	−3030.53	−	5249.03i	−0.391339	−	0.677819i
$89$		−	2910.83i		−	0.367482i	−0.982975	−	0.183741i	$-0.941179\pi$
$89$		−	2910.83i		−	0.367482i	0.982975	−	0.183741i	$-0.0588208\pi$
$90$	−3256.66	−	5745.60i	−0.402057	−	0.709333i
$91$	8623.11			1.04131
$92$	20609.9	−	11899.2i	2.43501	−	1.40585i
$93$	8016.62	−	4586.05i	0.926884	−	0.530241i
$94$	−3715.14	+	6434.82i	−0.420455	+	0.728250i
$95$	6413.46	+	3702.81i	0.710632	+	0.410284i
$96$	−6282.70	−	10982.4i	−0.681716	−	1.19167i
$97$	4342.24	+	7520.98i	0.461498	+	0.799339i	0.999036	−	0.0439012i	$-0.0139787\pi$
$97$	4342.24	+	7520.98i	0.461498	+	0.799339i	−0.537537	+	0.843240i	$0.680645\pi$
$98$		−	2031.78i		−	0.211556i
$99$	−2739.37	−	1610.71i	−0.279499	−	0.164342i
$100$	4648.03			0.464803
$101$	−6063.88	+	3500.98i	−0.594440	+	0.343200i	−0.766851	−	0.641825i	$-0.778178\pi$
$101$	−6063.88	+	3500.98i	−0.594440	+	0.343200i	0.172411	+	0.985025i	$0.444844\pi$
$102$	−69.7654	+	17570.6i	−0.00670563	+	1.68883i
$103$	−4431.99	+	7676.44i	−0.417758	+	0.723578i	−0.995714	−	0.0924901i	$-0.970517\pi$
$103$	−4431.99	+	7676.44i	−0.417758	+	0.723578i	0.577956	+	0.816068i	$0.303851\pi$
$104$	−22287.6	−	12867.8i	−2.06061	−	1.18970i
$105$	−2622.26	+	4500.53i	−0.237847	+	0.408211i
$106$	3947.80	+	6837.80i	0.351353	+	0.608561i
$107$		−	11167.1i		−	0.975382i	−0.873016	−	0.487691i	$-0.837839\pi$
$107$		−	11167.1i		−	0.975382i	0.873016	−	0.487691i	$-0.162161\pi$
$108$	−23312.5	−	13832.3i	−1.99867	−	1.18590i
$109$	−6742.91			−0.567537			−0.283768	−	0.958893i	$-0.591585\pi$
$109$	−6742.91			−0.567537			−0.283768	+	0.958893i	$0.591585\pi$
$110$	2770.26	−	1599.41i	0.228947	−	0.132183i
$111$	−13542.5	−	7890.63i	−1.09914	−	0.640421i
$112$	−13762.2	+	23836.8i	−1.09711	+	1.90026i
$113$	5984.05	+	3454.90i	0.468639	+	0.270569i	0.715670	−	0.698439i	$-0.246122\pi$
$113$	5984.05	+	3454.90i	0.468639	+	0.270569i	−0.247031	+	0.969008i	$0.579455\pi$
$114$	43474.7	+	172.620i	3.34524	+	0.0132826i
$115$	3577.77	+	6196.88i	0.270531	+	0.468573i
$116$			46877.7i			3.48378i
$117$	−13492.7	−	107.150i	−0.985663	−	0.00782744i
$118$	13105.6			0.941225
$119$	12001.1	−	6928.84i	0.847475	−	0.489290i
$120$	13493.5	−	7719.18i	0.937046	−	0.536054i
$121$	−6550.91	+	11346.5i	−0.447436	+	0.774982i
$122$	−28469.3	−	16436.7i	−1.91274	−	1.10432i
$123$	997.674	+	1743.98i	0.0659444	+	0.115274i
$124$	19079.0	+	33045.8i	1.24083	+	2.14918i
$125$			1397.54i			0.0894427i
$126$	−242.823	+	30577.2i	−0.0152950	+	1.92600i
$127$	−9600.31			−0.595221			−0.297610	−	0.954687i	$-0.596190\pi$
$127$	−9600.31			−0.595221			−0.297610	+	0.954687i	$0.596190\pi$
$128$	−8459.56	+	4884.13i	−0.516331	+	0.298104i
$129$	58.7274	−	14790.6i	0.00352908	−	0.888806i
$130$	6791.18	−	11762.7i	0.401845	−	0.696016i
$131$	4843.44	+	2796.36i	0.282235	+	0.162949i	0.634435	−	0.772976i	$-0.281233\pi$
$131$	4843.44	+	2796.36i	0.282235	+	0.162949i	−0.352200	+	0.935925i	$0.614566\pi$
$132$	6609.80	−	11344.3i	0.379351	−	0.651071i
$133$	−17144.0	−	29694.3i	−0.969189	−	1.67868i
$134$		−	8688.01i		−	0.483850i
$135$	4159.02	−	7009.47i	0.228204	−	0.384607i
$136$	−41358.0			−2.23605
$137$	10451.4	−	6034.14i	0.556846	−	0.321495i	−0.195033	−	0.980797i	$-0.562481\pi$
$137$	10451.4	−	6034.14i	0.556846	−	0.321495i	0.751878	+	0.659302i	$0.229148\pi$
$138$	36295.4	+	21147.8i	1.90587	+	1.11047i
$139$	3331.09	−	5769.62i	0.172408	−	0.298619i	−0.766853	−	0.641822i	$-0.778179\pi$
$139$	3331.09	−	5769.62i	0.172408	−	0.298619i	0.939261	+	0.343203i	$0.111512\pi$
$140$	−18637.2	−	10760.2i	−0.950875	−	0.548988i
$141$	−9169.66	−	36.4089i	−0.461227	−	0.00183134i
$142$	−26236.0	−	45442.1i	−1.30113	−	2.25362i
$143$		−	6535.41i		−	0.319596i
$144$	21830.1	−	37126.9i	1.05277	−	1.79046i
$145$	−14094.9			−0.670389
$146$	21433.4	−	12374.6i	1.00551	−	0.580531i
$147$	2176.45	−	1245.08i	0.100720	−	0.0576186i
$148$	32378.4	−	56081.0i	1.47819	−	2.56031i
$149$	17321.7	+	10000.7i	0.780224	+	0.450462i	0.836510	−	0.547952i	$-0.184592\pi$
$149$	17321.7	+	10000.7i	0.780224	+	0.450462i	−0.0562858	+	0.998415i	$0.517926\pi$
$150$	4073.93	+	7121.40i	0.181064	+	0.316507i
$151$	1006.89	+	1743.98i	0.0441599	+	0.0764872i	0.887261	−	0.461269i	$-0.152606\pi$
$151$	1006.89	+	1743.98i	0.0441599	+	0.0764872i	−0.843101	+	0.537756i	$0.819272\pi$
$152$			102332.i			4.42918i
$153$	−18864.4	+	10692.6i	−0.805862	+	0.456771i
$154$	−14810.5			−0.624496
$155$	−9936.02	+	5736.57i	−0.413570	+	0.238775i
$156$	221.351	−	55747.6i	0.00909561	−	2.29075i
$157$	5841.04	−	10117.0i	0.236969	−	0.410442i	−0.722874	−	0.690980i	$-0.757179\pi$
$157$	5841.04	−	10117.0i	0.236969	−	0.410442i	0.959843	+	0.280538i	$0.0905128\pi$
$158$	51190.5	+	29554.8i	2.05057	+	1.18390i
$159$	−4905.46	+	8419.13i	−0.194037	+	0.333022i
$160$	7858.85	+	13611.9i	0.306986	+	0.531716i
$161$		−	33130.1i		−	1.27812i
$162$	759.898	−	47841.7i	0.0289551	−	1.82296i
$163$	−7443.44			−0.280155			−0.140078	−	0.990141i	$-0.544735\pi$
$163$	−7443.44			−0.280155			−0.140078	+	0.990141i	$0.544735\pi$
$164$	−7188.96	+	4150.55i	−0.267287	+	0.154318i
$165$	3410.92	+	1987.40i	0.125286	+	0.0729990i
$166$	9948.59	−	17231.5i	0.361032	−	0.625325i
$167$	19331.4	+	11161.0i	0.693154	+	0.400192i	0.804792	−	0.593556i	$-0.202277\pi$
$167$	19331.4	+	11161.0i	0.693154	+	0.400192i	−0.111639	+	0.993749i	$0.535610\pi$
$168$	−71974.4	−	285.781i	−2.55011	−	0.0101254i
$169$	405.681	+	702.661i	0.0142040	+	0.0246021i
$170$		−	21827.4i		−	0.755273i
$171$	26456.5	+	46676.2i	0.904775	+	1.59626i
$172$	61109.1			2.06561
$173$	7734.25	−	4465.37i	0.258420	−	0.149199i	−0.365194	−	0.930932i	$-0.618997\pi$
$173$	7734.25	−	4465.37i	0.258420	−	0.149199i	0.623614	+	0.781733i	$0.285664\pi$
$174$	−71823.0	+	41087.6i	−2.37227	+	1.35710i
$175$	3235.30	−	5603.71i	0.105643	−	0.182978i
$176$	18065.8	+	10430.3i	0.583219	+	0.336722i
$177$	8031.16	+	14038.8i	0.256349	+	0.448109i
$178$	10614.0	+	18383.9i	0.334995	+	0.580228i
$179$		−	23701.2i		−	0.739716i	−0.929088	−	0.369858i	$-0.879406\pi$
$179$		−	23701.2i		−	0.739716i	0.929088	−	0.369858i	$-0.120594\pi$
$180$	29028.2	+	17068.2i	0.895932	+	0.526797i
$181$	−20635.9			−0.629891			−0.314945	−	0.949110i	$-0.601986\pi$
$181$	−20635.9			−0.629891			−0.314945	+	0.949110i	$0.601986\pi$
$182$	−54461.0	+	31443.1i	−1.64416	+	0.949254i
$183$	161.082	−	40568.9i	0.00481000	−	1.21141i
$184$	−49438.0	+	85629.2i	−1.46024	+	2.52922i
$185$	16862.1	+	9735.34i	0.492684	+	0.284451i
$186$	−33908.1	+	58195.8i	−0.980117	+	1.68215i
$187$	−5251.33	−	9095.57i	−0.150171	−	0.260104i
$188$		−	37885.5i		−	1.07191i
$189$	−32903.3	+	18477.7i	−0.921119	+	0.517278i
$190$	−54007.4			−1.49605
$191$	19710.3	−	11379.8i	0.540290	−	0.311937i	−0.204906	−	0.978782i	$-0.565689\pi$
$191$	19710.3	−	11379.8i	0.540290	−	0.311937i	0.745196	+	0.666845i	$0.232356\pi$
$192$	13568.8	+	7905.97i	0.368078	+	0.214463i
$193$	−30377.7	+	52615.7i	−0.815530	+	1.41254i	0.0934159	+	0.995627i	$0.470221\pi$
$193$	−30377.7	+	52615.7i	−0.815530	+	1.41254i	−0.908946	+	0.416913i	$0.863112\pi$
$194$	−54848.6	−	31666.9i	−1.45734	−	0.841398i
$195$	16761.9	+	66.5545i	0.440812	+	0.00175028i
$196$	5179.81	+	8971.70i	0.134835	+	0.233541i
$197$			20131.5i			0.518734i	0.965779	+	0.259367i	$0.0835139\pi$
$197$			20131.5i			0.518734i	−0.965779	+	0.259367i	$0.916486\pi$
$198$	23174.3	+	184.034i	0.591121	+	0.00469427i
$199$	29827.7			0.753205			0.376602	−	0.926375i	$-0.377092\pi$
$199$	29827.7			0.753205			0.376602	+	0.926375i	$0.377092\pi$
$200$	−16724.2	+	9655.71i	−0.418104	+	0.241393i
$201$	9306.64	−	5324.03i	0.230357	−	0.131780i
$202$	25531.8	−	44222.4i	0.625718	−	1.08378i
$203$	56516.3	+	32629.7i	1.37146	+	0.791810i
$204$	−44486.3	−	77763.9i	−1.06897	−	1.86861i
$205$	−1247.96	−	2161.53i	−0.0296957	−	0.0514345i
$206$		−	64642.9i		−	1.52330i
$207$	−411.671	+	51839.2i	−0.00960747	+	1.20981i
$208$	88574.9			2.04731
$209$	−22505.1	+	12993.3i	−0.515215	+	0.297460i
$210$	150.826	−	37985.8i	0.00342008	−	0.861355i
$211$	25655.9	−	44437.4i	0.576266	−	0.998122i	−0.419637	−	0.907692i	$-0.637842\pi$
$211$	25655.9	−	44437.4i	0.576266	−	0.998122i	0.995903	−	0.0904301i	$-0.0288242\pi$
$212$	−34864.5	−	20129.0i	−0.775732	−	0.447869i
$213$	32600.3	−	55951.2i	0.718559	−	1.23325i
$214$	40719.6	+	70528.5i	0.889152	+	1.54006i
$215$			18373.9i			0.397489i
$216$	112616.	+	1341.51i	2.41376	+	0.0287533i
$217$	53120.5			1.12809
$218$	42586.2	−	24587.2i	0.896099	−	0.517363i
$219$	26390.2	+	15376.4i	0.550243	+	0.320603i
$220$	−8155.07	+	14125.0i	−0.168493	+	0.291839i
$221$	−38620.2	−	22297.4i	−0.790733	−	0.456530i
$222$	114303.	+	453.849i	2.31927	+	0.00920884i
$223$	−17615.0	−	30510.1i	−0.354220	−	0.613527i	0.632764	−	0.774345i	$-0.281920\pi$
$223$	−17615.0	−	30510.1i	−0.354220	−	0.613527i	−0.986984	+	0.160817i	$0.948587\pi$
$224$		−	72772.8i		−	1.45035i
$225$	−5131.97	+	8728.03i	−0.101372	+	0.172406i
$226$	−50391.4			−0.986596
$227$	−48936.5	+	28253.5i	−0.949688	+	0.548303i	−0.892984	−	0.450088i	$-0.851392\pi$
$227$	−48936.5	+	28253.5i	−0.949688	+	0.548303i	−0.0567039	+	0.998391i	$0.518059\pi$
$228$	−192411.	+	110072.i	−3.70135	+	2.11742i
$229$	−16941.9	+	29344.2i	−0.323065	+	0.559566i	−0.981119	−	0.193406i	$-0.938047\pi$
$229$	−16941.9	+	29344.2i	−0.323065	+	0.559566i	0.658054	+	0.752971i	$0.271380\pi$
$230$	−45192.3	−	26091.8i	−0.854296	−	0.493228i
$231$	−9075.94	−	15865.1i	−0.170086	−	0.297317i
$232$	−97382.7	−	168672.i	−1.80928	−	3.13377i
$233$			57907.3i			1.06665i	0.845911	+	0.533324i	$0.179057\pi$
$233$			57907.3i			1.06665i	−0.845911	+	0.533324i	$0.820943\pi$
$234$	85606.9	−	48522.9i	1.56342	−	0.886165i
$235$	11391.2			0.206269
$236$	−57870.3	+	33411.4i	−1.03904	+	0.599889i
$237$	−289.641	+	72946.8i	−0.00515661	+	1.29870i
$238$	−50530.3	+	87521.0i	−0.892068	+	1.54511i
$239$	13932.7	+	8044.03i	0.243915	+	0.140824i	0.616975	−	0.786983i	$-0.288358\pi$
$239$	13932.7	+	8044.03i	0.243915	+	0.140824i	−0.373060	+	0.927807i	$0.621691\pi$
$240$	−26935.4	+	46228.5i	−0.467628	+	0.802579i
$241$	53785.7	+	93159.5i	0.926046	+	1.60396i	0.789871	+	0.613274i	$0.210148\pi$
$241$	53785.7	+	93159.5i	0.926046	+	1.60396i	0.136175	+	0.990685i	$0.456519\pi$
$242$		−	95548.3i		−	1.63152i
$243$	51714.0	−	28503.5i	0.875781	−	0.482710i
$244$	167615.			2.81535
$245$	−2697.56	+	1557.44i	−0.0449406	+	0.0259465i
$246$	−12660.2	−	7376.55i	−0.209204	−	0.121894i
$247$	−55170.3	+	95557.7i	−0.904298	+	1.56629i
$248$	−137297.	−	79268.6i	−2.23233	−	1.28884i
$249$	24555.0	+	97.4976i	0.396041	+	0.00157252i
$250$	−5095.97	−	8826.47i	−0.0815354	−	0.141224i
$251$		−	103855.i		−	1.64846i	−0.566255	−	0.824230i	$-0.691608\pi$
$251$		−	103855.i		−	1.64846i	0.566255	−	0.824230i	$-0.308392\pi$
$252$	−76881.2	−	135638.i	−1.21065	−	2.13590i
$253$	−25109.1			−0.392275
$254$	60632.8	−	35006.4i	0.939810	−	0.542600i
$255$	23381.6	−	13375.9i	0.359579	−	0.205704i
$256$	49577.9	−	85871.5i	0.756499	−	1.31029i
$257$	24343.3	+	14054.6i	0.368565	+	0.212791i	0.672831	−	0.739796i	$-0.265078\pi$
$257$	24343.3	+	14054.6i	0.368565	+	0.212791i	−0.304267	+	0.952587i	$0.598411\pi$
$258$	53561.2	+	93627.4i	0.804658	+	1.40658i
$259$	−45074.5	−	78071.4i	−0.671942	−	1.16384i
$260$			69253.6i			1.02446i
$261$	−88026.6	−	51758.5i	−1.29221	−	0.759803i
$262$	−40786.4			−0.594172
$263$	−72123.3	+	41640.4i	−1.04271	+	0.602009i	−0.920600	−	0.390507i	$-0.872300\pi$
$263$	−72123.3	+	41640.4i	−1.04271	+	0.602009i	−0.122111	+	0.992516i	$0.538966\pi$
$264$	−216.592	+	54549.1i	−0.00310766	+	0.782671i
$265$	6052.28	−	10482.9i	0.0861841	−	0.149275i
$266$	216553.	+	125027.i	3.06056	+	1.76701i
$267$	−13188.7	+	22635.5i	−0.185003	+	0.317517i
$268$	22149.2	+	38363.5i	0.308381	+	0.534132i
$269$		−	139224.i		−	1.92402i	−0.273023	−	0.962008i	$-0.588023\pi$
$269$		−	139224.i		−	1.92402i	0.273023	−	0.962008i	$-0.411977\pi$
$270$	−708.006	+	59435.1i	−0.00971202	+	0.815297i
$271$	121681.			1.65685			0.828425	−	0.560099i	$-0.189237\pi$
$271$	121681.			1.65685			0.828425	+	0.560099i	$0.189237\pi$
$272$	123273.	−	71171.7i	1.66621	−	0.961988i
$273$	−67055.9	−	39070.5i	−0.899729	−	0.524233i
$274$	−44005.5	+	76219.7i	−0.586146	+	1.01523i
$275$	−4247.02	−	2452.02i	−0.0561590	−	0.0324234i
$276$	−214183.	−	850.432i	−2.81169	−	0.0111640i
$277$	−2605.02	−	4512.03i	−0.0339509	−	0.0588048i	0.848551	−	0.529114i	$-0.177476\pi$
$277$	−2605.02	−	4512.03i	−0.0339509	−	0.0588048i	−0.882502	+	0.470309i	$0.844142\pi$
$278$			48585.7i			0.628664i
$279$	−83118.6	−	660.069i	−1.06780	−	0.00847971i
$280$	89411.7			1.14046
$281$	−80082.7	+	46235.7i	−1.01421	+	0.585552i	−0.912420	−	0.409255i	$-0.865789\pi$
$281$	−80082.7	+	46235.7i	−1.01421	+	0.585552i	−0.101785	+	0.994806i	$0.532455\pi$
$282$	58045.7	−	33206.1i	0.729914	−	0.417561i
$283$	54200.2	−	93877.5i	0.676749	−	1.17216i	−0.299205	−	0.954189i	$-0.596721\pi$
$283$	54200.2	−	93877.5i	0.676749	−	1.17216i	0.975954	−	0.217975i	$-0.0699452\pi$
$284$	231700.	+	133772.i	2.87269	+	1.65855i
$285$	−33095.9	−	57853.0i	−0.407459	−	0.712256i
$286$	23830.6	+	41275.7i	0.291341	+	0.504618i
$287$			11556.1i			0.140297i
$288$	−904.267	+	113869.i	−0.0109021	+	1.37284i
$289$	11855.5			0.141946
$290$	89019.4	−	51395.4i	1.05850	−	0.611122i
$291$	310.340	−	78159.7i	0.00366481	−	0.922990i
$292$	−63095.5	+	109285.i	−0.740002	+	1.28172i
$293$	−88942.9	−	51351.2i	−1.03604	−	0.598157i	−0.117330	−	0.993093i	$-0.537434\pi$
$293$	−88942.9	−	51351.2i	−1.03604	−	0.598157i	−0.918709	+	0.394935i	$0.870767\pi$
$294$	−9205.82	+	15799.7i	−0.106504	+	0.182791i
$295$	−10046.0	−	17400.1i	−0.115438	−	0.199944i
$296$			269048.i			3.07077i
$297$	14004.1	+	24937.2i	0.158761	+	0.282706i
$298$	−145865.			−1.64256
$299$	−92330.8	+	53307.2i	−1.03277	+	0.596271i
$300$	−36144.5	−	21059.8i	−0.401605	−	0.233998i
$301$	42535.6	−	73673.8i	0.469483	−	0.813168i
$302$	−12718.4	−	7343.00i	−0.139451	−	0.0805118i
$303$	63017.2	+	250.215i	0.686395	+	0.00272539i
$304$	−176100.	−	305014.i	−1.90551	−	3.30044i
$305$			50397.5i			0.541763i
$306$	80153.2	−	136318.i	0.856008	−	1.45583i
$307$	75941.7			0.805756			0.402878	−	0.915254i	$-0.368010\pi$
$307$	75941.7			0.805756			0.402878	+	0.915254i	$0.368010\pi$
$308$	65398.6	−	37757.9i	0.689394	−	0.398022i
$309$	69245.8	−	39613.3i	0.725231	−	0.414882i
$310$	41835.3	−	72460.9i	0.435331	−	0.754016i
$311$	−123487.	−	71295.3i	−1.27674	−	0.737124i	−0.300489	−	0.953785i	$-0.597150\pi$
$311$	−123487.	−	71295.3i	−1.27674	−	0.737124i	−0.976247	+	0.216662i	$0.930483\pi$
$312$	115012.	+	201047.i	1.18150	+	2.06532i
$313$	−18246.3	−	31603.6i	−0.186246	−	0.322587i	0.757750	−	0.652545i	$-0.226299\pi$
$313$	−18246.3	−	31603.6i	−0.186246	−	0.322587i	−0.943996	+	0.329958i	$0.892965\pi$
$314$			85194.5i			0.864077i
$315$	40783.0	−	23116.2i	0.411015	−	0.232968i
$316$	−301388.			−3.01823
$317$	88056.1	−	50839.2i	0.876276	−	0.505918i	0.00684707	−	0.999977i	$-0.497820\pi$
$317$	88056.1	−	50839.2i	0.876276	−	0.505918i	0.869429	+	0.494059i	$0.164487\pi$
$318$	282.149	−	71059.9i	0.00279013	−	0.702701i
$319$	24729.9	−	42833.4i	0.243019	−	0.420922i
$320$	−16894.9	−	9754.26i	−0.164989	−	0.0952564i
$321$	−50597.4	+	86839.1i	−0.491041	+	0.842763i
$322$	120805.	+	209240.i	1.16512	+	2.01805i
$323$			177322.i			1.69964i
$324$	118612.	+	213191.i	1.12990	+	2.03086i
$325$	−20822.8			−0.197139
$326$	47010.6	−	27141.6i	0.442344	−	0.255388i
$327$	52434.9	+	30551.5i	0.490371	+	0.285718i
$328$	17244.5	−	29868.3i	0.160289	−	0.277628i
$329$	−45675.2	−	26370.6i	−0.421977	−	0.243628i
$330$	−28789.2	−	114.310i	−0.264364	−	0.00104968i
$331$	−47740.6	−	82689.1i	−0.435744	−	0.754731i	0.561612	−	0.827401i	$-0.310181\pi$
$331$	−47740.6	−	82689.1i	−0.435744	−	0.754731i	−0.997356	+	0.0726696i	$0.976848\pi$
$332$			101452.i			0.920413i
$333$	69558.8	+	122720.i	0.627283	+	1.10669i
$334$	−162788.			−1.45925
$335$	−11534.9	+	6659.69i	−0.102784	+	0.0593423i
$336$	215021.	−	123007.i	1.90460	−	1.08956i
$337$	−13303.4	+	23042.2i	−0.117140	+	0.202892i	−0.918633	−	0.395112i	$-0.870706\pi$
$337$	−13303.4	+	23042.2i	−0.117140	+	0.202892i	0.801493	+	0.598004i	$0.204039\pi$
$338$	−5124.33	−	2958.53i	−0.0448543	−	0.0258966i
$339$	−30880.0	−	53979.5i	−0.268706	−	0.469710i
$340$	55646.6	+	96382.8i	0.481372	+	0.833761i
$341$		−	40259.8i		−	0.346228i
$342$	−337291.	−	198323.i	−2.88371	−	1.69559i
$343$	−109866.			−0.933843
$344$	−219878.	+	126947.i	−1.85808	+	1.07276i
$345$	255.703	−	64399.3i	0.00214831	−	0.541057i
$346$	−32564.8	+	56403.9i	−0.272017	+	0.471148i
$347$	−163631.	−	94472.2i	−1.35896	−	0.784595i	−0.369474	−	0.929241i	$-0.620462\pi$
$347$	−163631.	−	94472.2i	−1.35896	−	0.784595i	−0.989483	+	0.144646i	$0.953796\pi$
$348$	212399.	−	364535.i	1.75386	−	3.01010i
$349$	80550.3	+	139517.i	0.661327	+	1.14545i	0.980267	+	0.197677i	$0.0633398\pi$
$349$	80550.3	+	139517.i	0.661327	+	1.14545i	−0.318940	+	0.947775i	$0.603327\pi$
$350$			47188.6i			0.385213i
$351$	104438.	+	61967.6i	0.847705	+	0.502980i
$352$	−55154.2			−0.445136
$353$	141898.	−	81924.9i	1.13875	−	0.657456i	0.192627	−	0.981272i	$-0.438299\pi$
$353$	141898.	−	81924.9i	1.13875	−	0.657456i	0.946120	+	0.323816i	$0.104966\pi$
$354$	−101913.	−	59380.4i	−0.813250	−	0.473846i
$355$	−40221.8	+	69666.1i	−0.319157	+	0.552796i
$356$	−93735.9	−	54118.4i	−0.739615	−	0.427017i
$357$	−124718.	−	495.204i	−0.978573	−	0.00388551i
$358$	86423.6	+	149690.i	0.674321	+	1.16796i
$359$			224428.i			1.74136i	0.491853	+	0.870678i	$0.336320\pi$
$359$			224428.i			1.74136i	−0.491853	+	0.870678i	$0.663680\pi$
$360$	−139904.	−	1111.02i	−1.07951	−	0.00857268i
$361$	308425.			2.36666
$362$	130330.	−	75246.1i	0.994552	−	0.574205i
$363$	102352.	−	58552.3i	0.776753	−	0.444355i
$364$	160322.	−	277686.i	1.21001	−	2.09580i
$365$	−32859.1	−	18971.2i	−0.246644	−	0.142400i
$366$	146912.	+	256809.i	1.09672	+	1.91711i
$367$	−26611.7	−	46092.8i	−0.197579	−	0.342216i	0.750164	−	0.661252i	$-0.229974\pi$
$367$	−26611.7	−	46092.8i	−0.197579	−	0.342216i	−0.947743	+	0.319035i	$0.896641\pi$
$368$		−	340306.i		−	2.51289i
$369$	143.595	−	18082.1i	0.00105460	−	0.132799i
$370$	−141995.			−1.03722
$371$	−48535.5	+	28022.0i	−0.352624	+	0.203588i
$372$	1363.58	−	343419.i	0.00985357	−	2.48164i
$373$	−80370.4	+	139206.i	−0.577668	+	1.00055i	0.418078	+	0.908411i	$0.362704\pi$
$373$	−80370.4	+	139206.i	−0.577668	+	1.00055i	−0.995746	+	0.0921398i	$0.970629\pi$
$374$	66331.7	+	38296.6i	0.474218	+	0.273790i
$375$	6332.14	−	10867.7i	0.0450286	−	0.0772815i
$376$	78702.5	+	136317.i	0.556689	+	0.964213i
$377$		−	210008.i		−	1.47759i
$378$	140431.	−	236677.i	0.982832	−	1.65643i
$379$	−175474.			−1.22162			−0.610809	−	0.791778i	$-0.709156\pi$
$379$	−175474.			−1.22162			−0.610809	+	0.791778i	$0.709156\pi$
$380$	238479.	−	137686.i	1.65152	−	0.953505i
$381$	74654.9	+	43498.2i	0.514290	+	0.299655i
$382$	−82989.7	+	143742.i	−0.568719	+	0.985050i
$383$	142065.	+	82021.4i	0.968479	+	0.559151i	0.898772	−	0.438416i	$-0.144460\pi$
$383$	142065.	+	82021.4i	0.968479	+	0.559151i	0.0697066	+	0.997568i	$0.477794\pi$
$384$	87913.7	+	349.069i	0.596203	+	0.00236727i
$385$	11352.8	+	19663.7i	0.0765919	+	0.132661i
$386$		−	443074.i		−	2.97373i
$387$	−67471.7	+	114750.i	−0.450505	+	0.766181i
$388$	322926.			2.14506
$389$	132328.	−	76399.7i	0.874487	−	0.504885i	0.00565023	−	0.999984i	$-0.498201\pi$
$389$	132328.	−	76399.7i	0.874487	−	0.504885i	0.868837	+	0.495099i	$0.164868\pi$
$390$	−106106.	+	60699.8i	−0.697606	+	0.399078i
$391$	−85666.8	+	148379.i	−0.560349	+	0.970554i
$392$	−37275.2	−	21520.9i	−0.242576	−	0.140051i
$393$	−24994.0	−	43690.6i	−0.161827	−	0.282880i
$394$	−73407.2	−	127145.i	−0.472875	−	0.819043i
$395$		−	90619.6i		−	0.580802i
$396$	−102800.	+	58267.9i	−0.655543	+	0.371568i
$397$	123837.			0.785723			0.392862	−	0.919598i	$-0.371485\pi$
$397$	123837.			0.785723			0.392862	+	0.919598i	$0.371485\pi$
$398$	−188383.	+	108763.i	−1.18926	+	0.686617i
$399$	−1225.28	+	308589.i	−0.00769643	+	1.93836i
$400$	33232.4	−	57560.3i	0.207703	−	0.359752i
$401$	−67775.3	−	39130.1i	−0.421485	−	0.243345i	0.274227	−	0.961665i	$-0.411578\pi$
$401$	−67775.3	−	39130.1i	−0.421485	−	0.243345i	−0.695713	+	0.718320i	$0.744911\pi$
$402$	−39364.6	+	67560.5i	−0.243587	+	0.418062i
$403$	−85472.3	−	148042.i	−0.526278	−	0.911541i
$404$			260363.i			1.59520i
$405$	−64101.1	+	35663.6i	−0.390801	+	0.217428i
$406$	−475921.			−2.88724
$407$	−59169.9	+	34161.8i	−0.357200	+	0.206230i
$408$	321612.	+	187389.i	1.93202	+	1.12570i
$409$	81017.4	−	140326.i	0.484319	−	0.838866i	−0.515518	−	0.856879i	$-0.672401\pi$
$409$	81017.4	−	140326.i	0.484319	−	0.838866i	0.999838	+	0.0180127i	$0.00573391\pi$
$410$	15763.5	+	9101.08i	0.0937747	+	0.0541409i
$411$	−108614.	−	431.260i	−0.642985	−	0.00255303i
$412$	164800.	+	285442.i	0.970875	+	1.68161i
$413$			93025.4i			0.545383i
$414$	−186425.	−	328903.i	−1.08769	−	1.91896i
$415$	−30503.9			−0.177116
$416$	−202812.	+	117093.i	−1.17194	+	0.676622i
$417$	−52045.2	+	29773.4i	−0.299301	+	0.171221i
$418$	94757.2	−	164124.i	0.542325	−	0.939334i
$419$	−75491.1	−	43584.8i	−0.429999	−	0.248260i	0.269347	−	0.963043i	$-0.413192\pi$
$419$	−75491.1	−	43584.8i	−0.429999	−	0.248260i	−0.699346	+	0.714783i	$0.746525\pi$
$420$	96174.7	+	168118.i	0.545208	+	0.953048i
$421$	51786.1	+	89696.1i	0.292179	+	0.506069i	0.974325	−	0.225147i	$-0.0722864\pi$
$421$	51786.1	+	89696.1i	0.292179	+	0.506069i	−0.682146	+	0.731216i	$0.738953\pi$
$422$			374205.i			2.10128i
$423$	71141.1	+	41830.1i	0.397594	+	0.233780i
$424$	167262.			0.930393
$425$	−28979.8	+	16731.5i	−0.160442	+	0.0926312i
$426$	−1875.09	+	472244.i	−0.0103324	+	2.60224i
$427$	116670.	−	202078.i	0.639887	−	1.10832i
$428$	−359610.	−	207621.i	−1.96311	−	1.13340i
$429$	−29611.4	+	50821.3i	−0.160895	+	0.276141i
$430$	−66998.3	−	116044.i	−0.362349	−	0.627606i
$431$			328311.i			1.76738i	0.468070	+	0.883691i	$0.344950\pi$
$431$			328311.i			1.76738i	−0.468070	+	0.883691i	$0.655050\pi$
$432$	−337976.	+	189799.i	−1.81100	+	1.01701i
$433$	54957.7			0.293125			0.146562	−	0.989201i	$-0.453179\pi$
$433$	54957.7			0.293125			0.146562	+	0.989201i	$0.453179\pi$
$434$	−335494.	+	193697.i	−1.78117	+	1.02836i
$435$	109606.	+	63862.9i	0.579238	+	0.337497i
$436$	−125365.	+	217138.i	−0.659482	+	1.14226i
$437$	367134.	+	211965.i	1.92248	+	1.10994i
$438$	−222741.	−	884.413i	−1.16105	−	0.00461006i
$439$	−43708.3	−	75704.9i	−0.226796	−	0.392821i	0.730061	−	0.683382i	$-0.239492\pi$
$439$	−43708.3	−	75704.9i	−0.226796	−	0.392821i	−0.956857	+	0.290560i	$0.906158\pi$
$440$		−	67764.7i		−	0.350024i
$441$	−22566.1	−	179.204i	−0.116032	−	0.000921448i
$442$	325219.			1.66468
$443$	424.153	−	244.885i	0.00216130	−	0.00124783i	−0.498919	−	0.866649i	$-0.666269\pi$
$443$	424.153	−	244.885i	0.00216130	−	0.00124783i	0.501080	+	0.865401i	$0.332936\pi$
$444$	−505882.	+	289399.i	−2.56616	+	1.46802i
$445$	16272.0	−	28184.0i	0.0821715	−	0.142325i
$446$	222503.	+	128462.i	1.11858	+	0.645810i
$447$	−89386.7	−	156252.i	−0.447361	−	0.782006i
$448$	45162.1	+	78223.1i	0.225019	+	0.389744i
$449$		−	75725.3i		−	0.375620i	−0.982205	−	0.187810i	$-0.939861\pi$
$449$		−	75725.3i		−	0.375620i	0.982205	−	0.187810i	$-0.0601388\pi$
$450$	586.360	−	73836.8i	0.00289560	−	0.364626i
$451$	8758.32			0.0430594
$452$	222512.	−	128468.i	1.08912	−	0.628806i
$453$	71.9624	−	18123.9i	0.000350679	−	0.0883191i
$454$	206046.	−	356881.i	0.999659	−	1.73146i
$455$	83492.9	+	48204.6i	0.403299	+	0.232845i
$456$	463656.	−	795763.i	2.22980	−	3.82696i
$457$	−153143.	−	265252.i	−0.733273	−	1.27007i	−0.955477	−	0.295065i	$-0.904659\pi$
$457$	−153143.	−	265252.i	−0.733273	−	1.27007i	0.222205	−	0.975000i	$-0.428675\pi$
$458$		−	247106.i		−	1.17802i
$459$	195143.	+	2324.59i	0.926246	+	0.0110337i
$460$	266073.			1.25743
$461$	313878.	−	181218.i	1.47693	−	0.852705i	0.477267	−	0.878758i	$-0.341627\pi$
$461$	313878.	−	181218.i	1.47693	−	0.852705i	0.999661	+	0.0260535i	$0.00829403\pi$
$462$	115171.	+	67105.2i	0.539585	+	0.314393i
$463$	−87984.4	+	152393.i	−0.410434	+	0.710893i	−0.994937	−	0.100499i	$-0.967956\pi$
$463$	−87984.4	+	152393.i	−0.410434	+	0.710893i	0.584503	+	0.811392i	$0.301290\pi$
$464$	580525.	+	335166.i	2.69640	+	1.55677i
$465$	103257.	+	409.992i	0.477546	+	0.00189614i
$466$	−211152.	−	365725.i	−0.972350	−	1.68416i
$467$		−	99531.8i		−	0.456382i	−0.973616	−	0.228191i	$-0.926719\pi$
$467$		−	99531.8i		−	0.456382i	0.973616	−	0.228191i	$-0.0732810\pi$
$468$	−254309.	+	432507.i	−1.16110	+	1.97470i
$469$	61668.6			0.280361
$470$	−71943.5	+	41536.6i	−0.325683	+	0.188033i
$471$	−91260.9	+	52207.4i	−0.411380	+	0.235337i
$472$	138816.	−	240437.i	0.623098	−	1.07924i
$473$	−55837.0	−	32237.5i	−0.249574	−	0.144092i
$474$	−264162.	−	461767.i	−1.17575	−	2.05526i
$475$	41398.7	+	71704.6i	0.183484	+	0.317804i
$476$		−	515287.i		−	2.27423i
$477$	76292.6	−	43243.4i	0.335310	−	0.190057i
$478$	−117326.			−0.513498
$479$	207949.	−	120059.i	0.906328	−	0.523268i	0.0270798	−	0.999633i	$-0.491379\pi$
$479$	207949.	−	120059.i	0.906328	−	0.523268i	0.879248	+	0.476365i	$0.158046\pi$
$480$	561.672	−	141458.i	0.00243781	−	0.613968i
$481$	−145052.	+	251238.i	−0.626952	+	1.08591i
$482$	−679389.	−	392246.i	−2.92432	−	1.68836i
$483$	−150109.	+	257629.i	−0.643449	+	1.10434i
$484$	243591.	+	421911.i	1.03985	+	1.80107i
$485$			97095.4i			0.412777i
$486$	−222676.	+	368588.i	−0.942758	+	1.56052i
$487$	−364628.			−1.53742			−0.768709	−	0.639599i	$-0.779100\pi$
$487$	−364628.			−1.53742			−0.768709	+	0.639599i	$0.779100\pi$
$488$	−603099.	+	348199.i	−2.53250	+	1.46214i
$489$	57882.4	+	33725.6i	0.242063	+	0.141040i
$490$	11358.0	−	19672.6i	0.0473053	−	0.0819352i
$491$	−192398.	−	111081.i	−0.798063	−	0.460762i	0.0447303	−	0.998999i	$-0.485757\pi$
$491$	−192398.	−	111081.i	−0.798063	−	0.460762i	−0.842793	+	0.538237i	$0.819090\pi$
$492$	74709.2	+	296.639i	0.308634	+	0.00122546i
$493$	−168746.	−	292276.i	−0.694287	−	1.20254i
$494$		−	804686.i		−	3.29741i
$495$	−17519.7	−	30909.2i	−0.0715015	−	0.126147i
$496$	545644.			2.21792
$497$	322554.	−	186226.i	1.30584	−	0.753926i
$498$	−155437.	+	88920.9i	−0.626754	+	0.358546i
$499$	74588.1	−	129190.i	0.299549	−	0.518835i	−0.676483	−	0.736458i	$-0.736497\pi$
$499$	74588.1	−	129190.i	0.299549	−	0.518835i	0.976033	+	0.217623i	$0.0698303\pi$
$500$	45004.3	+	25983.3i	0.180017	+	0.103933i
$501$	−99757.1	−	174380.i	−0.397437	−	0.694737i
$502$	378693.	+	655915.i	1.50273	+	2.60280i
$503$		−	202331.i		−	0.799697i	−0.916581	−	0.399849i	$-0.869063\pi$
$503$		−	202331.i		−	0.799697i	0.916581	−	0.399849i	$-0.130937\pi$
$504$	558400.	+	328332.i	2.19829	+	1.29256i
$505$	−78284.4			−0.306967
$506$	158582.	−	91557.3i	0.619373	−	0.357595i
$507$	28.9940	−	7302.21i	0.000112796	−	0.0284078i
$508$	−178490.	+	309154.i	−0.691651	+	1.19797i
$509$	173370.	+	100095.i	0.669173	+	0.386347i	0.795763	−	0.605608i	$-0.207070\pi$
$509$	173370.	+	100095.i	0.669173	+	0.386347i	−0.126590	+	0.991955i	$0.540403\pi$
$510$	−98897.9	+	169736.i	−0.380230	+	0.652581i
$511$	87836.5	+	152137.i	0.336382	+	0.582631i
$512$			566827.i			2.16227i
$513$	5751.71	−	482840.i	0.0218556	−	1.83471i
$514$	−204994.			−0.775916
$515$	−85825.2	+	49551.2i	−0.323594	+	0.186827i
$516$	−475203.	−	276880.i	−1.78476	−	1.03990i
$517$	−19986.1	+	34617.0i	−0.0747734	+	0.129511i
$518$	569355.	+	328717.i	2.12189	+	1.22508i
$519$	−80376.0	−	319.140i	−0.298395	−	0.00118480i
$520$	−143866.	−	249183.i	−0.532048	−	0.921535i
$521$			191583.i			0.705801i	0.935661	+	0.352901i	$0.114805\pi$
$521$			191583.i			0.705801i	−0.935661	+	0.352901i	$0.885195\pi$
$522$	744681.	+	5913.74i	2.73294	+	0.0217031i
$523$	122186.			0.446702			0.223351	−	0.974738i	$-0.428300\pi$
$523$	122186.			0.446702			0.223351	+	0.974738i	$0.428300\pi$
$524$	180100.	−	103981.i	0.655919	−	0.378695i
$525$	−50548.6	+	28917.3i	−0.183396	+	0.104915i
$526$	303673.	−	525977.i	1.09758	−	1.90106i
$527$	−237910.	−	137357.i	−0.856627	−	0.494574i
$528$	−93226.3	−	162964.i	−0.334403	−	0.584551i
$529$	64886.3	+	112386.i	0.231869	+	0.401608i
$530$			88275.6i			0.314260i
$531$	1155.92	−	145558.i	0.00409958	−	0.516236i
$532$	−1.27497e6			−4.50482
$533$	32205.9	−	18594.1i	0.113366	−	0.0654517i
$534$	758.580	−	191050.i	0.00266023	−	0.669984i
$535$	62426.3	−	108125.i	0.218102	−	0.377764i
$536$	−159391.	−	92024.4i	−0.554797	−	0.320312i
$537$	−107388.	+	184308.i	−0.372399	+	0.639139i
$538$	507662.	+	879296.i	1.75392	+	3.03788i
$539$		−	10930.2i		−	0.0376229i
$540$	−148397.	−	264252.i	−0.508907	−	0.906213i
$541$	196875.			0.672660			0.336330	−	0.941744i	$-0.390814\pi$
$541$	196875.			0.672660			0.336330	+	0.941744i	$0.390814\pi$
$542$	−768500.	+	443694.i	−2.61605	+	1.51038i
$543$	160471.	+	93499.2i	0.544247	+	0.317109i
$544$	−188174.	+	325927.i	−0.635860	+	1.10134i
$545$	−65287.9	−	37694.0i	−0.219806	−	0.126905i
$546$	565971.	+	2247.24i	1.89849	+	0.00753813i
$547$	−145097.	−	251316.i	−0.484936	−	0.839934i	0.514914	−	0.857242i	$-0.327824\pi$
$547$	−145097.	−	251316.i	−0.484936	−	0.839934i	−0.999850	+	0.0173075i	$0.994491\pi$
$548$		−	448750.i		−	1.49432i
$549$	−185067.	+	314746.i	−0.614021	+	1.04428i
$550$	35764.0			0.118228
$551$	−723178.	+	417527.i	−2.38200	+	1.37525i
$552$	772423.	−	441879.i	2.53500	−	1.45019i
$553$	−209784.	+	363357.i	−0.685997	+	1.18818i
$554$	32905.1	+	18997.8i	0.107212	+	0.0618989i
$555$	−87014.8	−	152106.i	−0.282493	−	0.493809i
$556$	−123864.	−	214539.i	−0.400678	−	0.693995i
$557$		−	138499.i		−	0.446414i	−0.974771	−	0.223207i	$-0.928347\pi$
$557$		−	138499.i		−	0.446414i	0.974771	−	0.223207i	$-0.0716525\pi$
$558$	527360.	−	298913.i	1.69371	−	0.960011i
$559$	−273764.			−0.876097
$560$	−266504.	+	153866.i	−0.849820	+	0.490644i
$561$	−375.312	+	94523.2i	−0.00119252	+	0.300340i
$562$	337186.	−	584023.i	1.06757	−	1.84909i
$563$	327119.	+	188862.i	1.03202	+	0.595838i	0.917563	−	0.397590i	$-0.130153\pi$
$563$	327119.	+	188862.i	1.03202	+	0.595838i	0.114459	+	0.993428i	$0.463487\pi$
$564$	−171656.	+	294609.i	−0.539635	+	0.926164i
$565$	38626.9	+	66903.8i	0.121002	+	0.209582i
$566$			790537.i			2.46768i
$567$	339587.	+	5393.85i	1.05629	+	0.0167777i
$568$	−1.11158e6			−3.44543
$569$	96262.6	−	55577.2i	0.297326	−	0.171661i	−0.343915	−	0.939001i	$-0.611753\pi$
$569$	96262.6	−	55577.2i	0.297326	−	0.171661i	0.641241	+	0.767340i	$0.278420\pi$
$570$	419977.	+	244703.i	1.29264	+	0.753163i
$571$	57730.8	−	99992.7i	0.177066	−	0.306687i	−0.763808	−	0.645443i	$-0.776673\pi$
$571$	57730.8	−	99992.7i	0.177066	−	0.306687i	0.940874	+	0.338756i	$0.110006\pi$
$572$	−210456.	−	121507.i	−0.643236	−	0.371372i
$573$	−204834.	−	813.311i	−0.623868	−	0.00247712i
$574$	−42137.9	−	72985.0i	−0.127894	−	0.221518i
$575$			80001.3i			0.241970i
$576$	−69694.0	−	122958.i	−0.210064	−	0.370606i
$577$	−80342.3			−0.241320			−0.120660	−	0.992694i	$-0.538501\pi$
$577$	−80342.3			−0.241320			−0.120660	+	0.992694i	$0.538501\pi$
$578$	−74875.6	+	43229.5i	−0.224122	+	0.129397i
$579$	474623.	−	271517.i	1.41577	−	0.809915i
$580$	−262054.	+	453892.i	−0.778997	+	1.34926i
$581$	122311.	+	70616.4i	0.362338	+	0.209196i
$582$	283040.	+	494765.i	0.835605	+	1.46067i
$583$	21237.7	+	36784.8i	0.0624843	+	0.108226i
$584$		−	524293.i		−	1.53726i
$585$	−130044.	−	76464.2i	−0.379995	−	0.223432i
$586$	748983.			2.18111
$587$	449446.	−	259488.i	1.30437	−	0.753080i	0.323221	−	0.946323i	$-0.395234\pi$
$587$	449446.	−	259488.i	1.30437	−	0.753080i	0.981151	+	0.193244i	$0.0619008\pi$
$588$	370.201	−	93235.9i	0.00107074	−	0.269668i
$589$	−339863.	+	588659.i	−0.979654	+	1.69681i
$590$	126895.	+	73262.7i	0.364535	+	0.210464i
$591$	91214.2	−	156549.i	0.261149	−	0.448203i
$592$	−462997.	−	801935.i	−1.32110	−	2.28821i
$593$		−	214106.i		−	0.608863i	−0.952534	−	0.304431i	$-0.901534\pi$
$593$		−	214106.i		−	0.608863i	0.952534	−	0.304431i	$-0.0984664\pi$
$594$	−179377.	−	106432.i	−0.508385	−	0.301647i
$595$	154934.			0.437634
$596$	644096.	−	371869.i	1.81325	−	1.04688i
$597$	−231949.	−	135147.i	−0.650794	−	0.379189i
$598$	388756.	−	673345.i	1.08711	−	1.88294i
$599$	−80515.8	−	46485.8i	−0.224402	−	0.129559i	0.383585	−	0.923506i	$-0.374689\pi$
$599$	−80515.8	−	46485.8i	−0.224402	−	0.129559i	−0.607987	+	0.793947i	$0.708023\pi$
$600$	173801.	+	690.093i	0.482782	+	0.00191693i
$601$	82663.9	+	143178.i	0.228858	+	0.396394i	0.957470	−	0.288533i	$-0.0931674\pi$
$601$	82663.9	+	143178.i	0.228858	+	0.396394i	−0.728612	+	0.684927i	$0.759834\pi$
$602$			620403.i			1.71191i
$603$	−96493.9	−	766.287i	−0.265378	−	0.00210745i
$604$	74880.9			0.205256
$605$	−126858.	+	73241.4i	−0.346583	+	0.200100i
$606$	−398911.	+	228204.i	−1.08625	+	0.621410i
$607$	77697.7	−	134576.i	0.210878	−	0.365251i	−0.741112	−	0.671382i	$-0.765701\pi$
$607$	77697.7	−	134576.i	0.210878	−	0.365251i	0.951989	+	0.306131i	$0.0990345\pi$
$608$	806439.	+	465598.i	2.18155	+	1.25952i
$609$	−291645.	−	509809.i	−0.786358	−	1.37459i
$610$	−183768.	−	318296.i	−0.493868	−	0.855404i
$611$			169724.i			0.454632i
$612$	−6402.90	+	806279.i	−0.0170952	+	2.15269i
$613$	277176.			0.737623			0.368811	−	0.929504i	$-0.379765\pi$
$613$	277176.			0.737623			0.368811	+	0.929504i	$0.379765\pi$
$614$	−479626.	+	276912.i	−1.27223	+	0.734522i
$615$	−89.1918	+	22463.1i	−0.000235817	+	0.0593910i
$616$	−156875.	+	271715.i	−0.413420	+	0.716065i
$617$	−290211.	−	167553.i	−0.762331	−	0.440132i	0.0678012	−	0.997699i	$-0.478402\pi$
$617$	−290211.	−	167553.i	−0.762331	−	0.440132i	−0.830132	+	0.557567i	$0.811735\pi$
$618$	−292891.	+	502682.i	−0.766883	+	1.31618i
$619$	288674.	+	499997.i	0.753400	+	1.30493i	0.946166	+	0.323683i	$0.104921\pi$
$619$	288674.	+	499997.i	0.753400	+	1.30493i	−0.192765	+	0.981245i	$0.561746\pi$
$620$			426619.i			1.10983i
$621$	238080.	−	401252.i	0.617362	−	1.04048i
$622$	1.03988e6			2.68783
$623$	−130492.	+	75339.3i	−0.336207	+	0.194109i
$624$	−688785.	−	401325.i	−1.76895	−	1.03069i
$625$	−7812.50	+	13531.6i	−0.0200000	+	0.0346410i
$626$	230477.	+	133066.i	0.588138	+	0.339561i
$627$	233878.	+	928.633i	0.594915	+	0.00236216i
$628$	−217195.	−	376192.i	−0.550719	−	0.953873i
$629$			466210.i			1.17837i
$630$	−173283.	+	294705.i	−0.436591	+	0.742518i
$631$	−102106.			−0.256444			−0.128222	−	0.991745i	$-0.540927\pi$
$631$	−102106.			−0.256444			−0.128222	+	0.991745i	$0.540927\pi$
$632$	1.08443e6	−	626096.i	2.71499	−	1.56750i
$633$	−400850.	+	229314.i	−1.00040	+	0.572299i
$634$	−370758.	+	642171.i	−0.922384	+	1.59762i
$635$	−92954.6	−	53667.4i	−0.230528	−	0.133095i
$636$	179914.	+	314497.i	0.444785	+	0.777504i
$637$	−23205.1	−	40192.5i	−0.0571880	−	0.0990526i
$638$			360698.i			0.886139i
$639$	−507020.	+	287384.i	−1.24172	+	0.703818i
$640$	−109212.			−0.266632
$641$	465013.	−	268475.i	1.13175	−	0.653414i	0.187373	−	0.982289i	$-0.440003\pi$
$641$	465013.	−	268475.i	1.13175	−	0.653414i	0.944374	+	0.328875i	$0.106669\pi$
$642$	2910.23	−	732947.i	0.00706085	−	1.77829i
$643$	223725.	−	387503.i	0.541118	−	0.937244i	−0.457722	−	0.889095i	$-0.651335\pi$
$643$	223725.	−	387503.i	0.541118	−	0.937244i	0.998840	−	0.0481488i	$-0.0153322\pi$
$644$	−1.06687e6	−	615958.i	−2.57241	−	1.48518i
$645$	83250.7	−	142881.i	0.200110	−	0.343444i
$646$	−646581.	−	1.11991e6i	−1.54938	−	2.68361i
$647$			568950.i			1.35914i	0.733609	+	0.679572i	$0.237834\pi$
$647$			568950.i			1.35914i	−0.733609	+	0.679572i	$0.762166\pi$
$648$	−869659.	−	520686.i	−2.07109	−	1.24001i
$649$	70503.5			0.167387
$650$	131511.	−	75927.7i	0.311268	−	0.179710i
$651$	−413081.	−	240684.i	−0.974705	−	0.567918i
$652$	−138389.	+	239697.i	−0.325542	+	0.563855i
$653$	−271005.	−	156465.i	−0.635553	−	0.366937i	0.147347	−	0.989085i	$-0.452927\pi$
$653$	−271005.	−	156465.i	−0.635553	−	0.366937i	−0.782899	+	0.622148i	$0.786260\pi$
$654$	−442566.	−	1757.24i	−1.03472	−	0.00410844i
$655$	31264.3	+	54151.3i	0.0728729	+	0.126220i
$656$			118702.i			0.275836i
$657$	−135549.	−	239143.i	−0.314026	−	0.554023i
$658$	384628.			0.888360
$659$	450141.	−	259889.i	1.03652	−	0.598436i	0.117675	−	0.993052i	$-0.462456\pi$
$659$	450141.	−	259889.i	1.03652	−	0.598436i	0.918846	+	0.394616i	$0.129123\pi$
$660$	127415.	−	72890.3i	0.292506	−	0.167333i
$661$	−349464.	+	605289.i	−0.799833	+	1.38535i	0.119891	+	0.992787i	$0.461746\pi$
$661$	−349464.	+	605289.i	−0.799833	+	1.38535i	−0.919724	+	0.392565i	$0.871588\pi$
$662$	603031.	+	348160.i	1.37602	+	0.794444i
$663$	199295.	+	348376.i	0.453387	+	0.792540i
$664$	−210753.	−	365035.i	−0.478011	−	0.827940i
$665$		−	383351.i		−	0.866869i
$666$	−886796.	−	521425.i	−1.99929	−	1.17556i
$667$	−806854.			−1.81361
$668$	718822.	−	415012.i	1.61090	−	0.930053i
$669$	−1258.94	+	317068.i	−0.00281290	+	0.708435i
$670$	48567.4	−	84121.3i	0.108192	−	0.187394i
$671$	−153154.	−	88423.6i	−0.340160	−	0.196392i
$672$	−329727.	+	565903.i	−0.730157	+	1.25315i
$673$	295247.	+	511383.i	0.651861	+	1.12906i	0.982671	+	0.185359i	$0.0593449\pi$
$673$	295247.	+	511383.i	0.651861	+	1.12906i	−0.330809	+	0.943698i	$0.607322\pi$
$674$		−	194037.i		−	0.427136i
$675$	79453.7	−	44619.3i	0.174384	−	0.0979298i
$676$	30169.9			0.0660207
$677$	−461706.	+	266566.i	−1.00737	+	0.581604i	−0.910420	−	0.413686i	$-0.864241\pi$
$677$	−461706.	+	266566.i	−1.00737	+	0.581604i	−0.0969476	+	0.995289i	$0.530908\pi$
$678$	391859.	+	228319.i	0.852452	+	0.496687i
$679$	224775.	−	389323.i	0.487539	−	0.844442i
$680$	−400447.	−	231198.i	−0.866018	−	0.499996i
$681$	508559.	+	2019.28i	1.09660	+	0.00435413i
$682$	146802.	+	254269.i	0.315619	+	0.546669i
$683$		−	91618.4i		−	0.196400i	−0.995167	−	0.0982000i	$-0.968692\pi$
$683$		−	91618.4i		−	0.196400i	0.995167	−	0.0982000i	$-0.0313085\pi$
$684$	1.99497e6	+	15842.7i	4.26407	+	0.0338622i
$685$	134927.			0.287554
$686$	693879.	−	400611.i	1.47447	−	0.851285i
$687$	264701.	−	151427.i	0.560844	−	0.320841i
$688$	436918.	−	756763.i	0.923044	−	1.59876i
$689$	156190.	+	90176.4i	0.329014	+	0.189957i
$690$	233209.	+	407660.i	0.489832	+	0.856248i
$691$	−222121.	−	384725.i	−0.465193	−	0.805738i	0.534017	−	0.845474i	$-0.320682\pi$
$691$	−222121.	−	384725.i	−0.465193	−	0.805738i	−0.999210	+	0.0397354i	$0.987349\pi$
$692$		−	332083.i		−	0.693480i
$693$	−1306.30	+	164494.i	−0.00272004	+	0.342519i
$694$	1.37793e6			2.86093
$695$	64506.3	−	37242.8i	0.133547	−	0.0771032i
$696$	−6959.94	+	1.75287e6i	−0.0143677	+	3.61853i
$697$	29881.4	−	51756.2i	0.0615086	−	0.106536i
$698$	−1.01746e6	−	587433.i	−2.08837	−	1.20572i
$699$	262373.	−	450304.i	0.536988	−	0.921619i
$700$	−120302.	−	208370.i	−0.245515	−	0.425244i
$701$		−	37065.4i		−	0.0754280i	−0.999289	−	0.0377140i	$-0.987992\pi$
$701$		−	37065.4i		−	0.0754280i	0.999289	−	0.0377140i	$-0.0120076\pi$
$702$	−885558.	−	10549.0i	−1.79698	−	0.0214061i
$703$	1.15354e6			2.33411
$704$	59284.9	−	34228.2i	0.119619	−	0.0690618i
$705$	−88581.3	−	51612.5i	−0.178223	−	0.103843i
$706$	−597458.	+	1.03483e6i	−1.19867	+	2.07615i
$707$	313896.	+	181228.i	0.627982	+	0.362565i
$708$	601401.	+	2387.91i	1.19977	+	0.00476378i
$709$	−205147.	−	355325.i	−0.408105	−	0.706859i	0.586572	−	0.809897i	$-0.300477\pi$
$709$	−205147.	−	355325.i	−0.408105	−	0.706859i	−0.994677	+	0.103038i	$0.967144\pi$
$710$		−	586655.i		−	1.16377i
$711$	332768.	−	565944.i	0.658267	−	1.11953i
$712$	449697.			0.887075
$713$	−568781.	+	328386.i	−1.11883	+	0.645959i
$714$	789489.	−	451642.i	1.54864	−	0.885926i
$715$	36534.1	−	63278.8i	0.0714637	−	0.123779i
$716$	−763239.	−	440656.i	−1.48879	−	0.859555i
$717$	−71897.8	−	125680.i	−0.139855	−	0.244472i
$718$	−818348.	−	1.41742e6i	−1.58741	−	2.74947i
$719$			428497.i			0.828876i	0.910077	+	0.414438i	$0.136022\pi$
$719$			428497.i			0.828876i	−0.910077	+	0.414438i	$0.863978\pi$
$720$	418915.	−	237445.i	0.808092	−	0.458035i
$721$	458843.			0.882661
$722$	−1.94792e6	+	1.12463e6i	−3.73678	+	2.15743i
$723$	3844.06	−	968134.i	0.00735383	−	1.85208i
$724$	−383664.	+	664526.i	−0.731938	+	1.26775i
$725$	−136474.	−	78793.0i	−0.259641	−	0.149904i
$726$	−432921.	+	743013.i	−0.821364	+	1.40969i
$727$	92789.3	+	160716.i	0.175561	+	0.304081i	0.940355	−	0.340194i	$-0.110493\pi$
$727$	92789.3	+	160716.i	0.175561	+	0.304081i	−0.764794	+	0.644275i	$0.777159\pi$
$728$			1.33220e6i			2.51365i
$729$	−531290.	−	12659.5i	−0.999716	−	0.0238211i
$730$	276705.			0.519243
$731$	−381007.	+	219975.i	−0.713014	+	0.411659i
$732$	−1.30342e6	−	759449.i	−2.43256	−	1.41735i
$733$	−91052.3	+	157707.i	−0.169466	+	0.293524i	−0.938232	−	0.346006i	$-0.887538\pi$
$733$	−91052.3	+	157707.i	−0.169466	+	0.293524i	0.768766	+	0.639530i	$0.220871\pi$
$734$	336143.	+	194072.i	0.623925	+	0.360223i
$735$	28033.6	+	111.310i	0.0518925	+	0.000206044i
$736$	449874.	+	779205.i	0.830493	+	1.43846i
$737$		−	46738.3i		−	0.0860474i
$738$	65027.1	+	114725.i	0.119394	+	0.210641i
$739$	−872310.			−1.59728			−0.798642	−	0.601806i	$-0.794448\pi$
$739$	−872310.			−1.59728			−0.798642	+	0.601806i	$0.794448\pi$
$740$	627004.	−	362001.i	1.14500	−	0.661068i
$741$	861984.	−	493114.i	1.56987	−	0.898071i
$742$	204358.	−	353958.i	0.371179	−	0.642900i
$743$	226965.	+	131038.i	0.411132	+	0.237367i	0.691276	−	0.722591i	$-0.257049\pi$
$743$	226965.	+	131038.i	0.411132	+	0.237367i	−0.280144	+	0.959958i	$0.590382\pi$
$744$	708505.	+	1.23850e6i	1.27996	+	2.23743i
$745$	111811.	+	193663.i	0.201453	+	0.348927i
$746$		−	1.17224e6i		−	2.10640i
$747$	−190505.	−	112015.i	−0.341401	−	0.200740i
$748$	−390533.			−0.697999
$749$	−500620.	+	289033.i	−0.892369	+	0.515210i
$750$	−364.208	+	91726.6i	−0.000647482	+	0.163070i
$751$	−88055.5	+	152517.i	−0.156126	+	0.270419i	−0.933469	−	0.358659i	$-0.883234\pi$
$751$	−88055.5	+	152517.i	−0.156126	+	0.270419i	0.777342	+	0.629078i	$0.216567\pi$
$752$	−469167.	−	270873.i	−0.829643	−	0.478995i
$753$	−470556.	+	807605.i	−0.829892	+	1.42432i
$754$	765769.	+	1.32635e6i	1.34696	+	2.33301i
$755$			22514.7i			0.0394978i
$756$	−16714.2	+	1.40311e6i	−0.0292443	+	2.45498i
$757$	880.005			0.00153565			0.000767827	−	1.00000i	$-0.499756\pi$
$757$	880.005			0.00153565			0.000767827		1.00000i	$0.499756\pi$
$758$	1.10824e6	−	639845.i	1.92884	−	1.11362i
$759$	195256.	+	113767.i	0.338938	+	0.197485i
$760$	−572052.	+	990823.i	−0.990395	+	1.71541i
$761$	−73054.4	−	42178.0i	−0.126147	−	0.0728310i	0.435599	−	0.900141i	$-0.356537\pi$
$761$	−73054.4	−	42178.0i	−0.126147	−	0.0728310i	−0.561746	+	0.827310i	$0.689870\pi$
$762$	−630109.	−	2501.90i	−1.08519	−	0.00430884i
$763$	174523.	+	302282.i	0.299780	+	0.519235i
$764$		−	846295.i		−	1.44989i
$765$	−242427.	−	1925.19i	−0.414246	−	0.00328965i
$766$	−1.19632e6			−2.03888
$767$	259254.	−	149680.i	0.440692	−	0.254433i
$768$	−774609.	+	443129.i	−1.31329	+	0.751290i
$769$	564685.	−	978063.i	0.954890	−	1.65392i	0.220272	−	0.975439i	$-0.429306\pi$
$769$	564685.	−	978063.i	0.954890	−	1.65392i	0.734619	−	0.678480i	$-0.237361\pi$
$770$	−143402.	−	82793.4i	−0.241866	−	0.139641i
$771$	−125621.	−	219590.i	−0.211326	−	0.369407i
$772$	1.12957e6	+	1.95647e6i	1.89530	+	3.28276i
$773$		−	956523.i		−	1.60080i	−0.599468	−	0.800399i	$-0.704621\pi$
$773$		−	956523.i		−	1.60080i	0.599468	−	0.800399i	$-0.295379\pi$
$774$	7709.06	−	970756.i	0.0128682	−	1.62042i
$775$	−128274.			−0.213567
$776$	−1.16193e6	+	670838.i	−1.92954	+	1.11402i
$777$	−3221.48	+	811335.i	−0.00533596	+	1.34387i
$778$	−557164.	+	965037.i	−0.920501	+	1.59435i
$779$	−128060.	−	73935.5i	−0.211027	−	0.121837i
$780$	313782.	−	538537.i	0.515750	−	0.885169i
$781$	−141140.	−	244462.i	−0.231392	−	0.400783i
$782$		−	1.24949e6i		−	2.04324i
$783$	450008.	+	801331.i	0.734001	+	1.30704i
$784$	148138.			0.241010
$785$	113111.	−	65304.8i	0.183555	−	0.105976i
$786$	317167.	+	184799.i	0.513385	+	0.299127i
$787$	−86337.1	+	149540.i	−0.139395	+	0.241440i	−0.927268	−	0.374399i	$-0.877849\pi$
$787$	−86337.1	+	149540.i	−0.139395	+	0.241440i	0.787873	+	0.615838i	$0.211183\pi$
$788$	648286.	+	374288.i	1.04403	+	0.602772i
$789$	749521.	+	2976.04i	1.20401	+	0.00478062i
$790$	330433.	+	572327.i	0.529455	+	0.917044i
$791$		−	357684.i		−	0.571672i
$792$	248841.	−	423208.i	0.396709	−	0.674690i
$793$	−750901.			−1.19409
$794$	−782119.	+	451556.i	−1.24060	+	0.716261i
$795$	−94561.3	+	54095.5i	−0.149616	+	0.0855907i
$796$	554559.	−	960525.i	0.875229	−	1.51594i
$797$	703379.	+	406096.i	1.10732	+	0.639311i	0.938134	−	0.346273i	$-0.112553\pi$
$797$	703379.	+	406096.i	1.10732	+	0.639311i	0.169185	+	0.985584i	$0.445886\pi$
$798$	−1.11749e6	−	1.95343e6i	−1.75485	−	3.06755i
$799$	136376.	+	236211.i	0.213622	+	0.370004i
$800$			175729.i			0.274577i
$801$	205119.	−	116263.i	0.319698	−	0.181208i
$802$	570732.			0.887326
$803$	115304.	−	66570.8i	0.178819	−	0.103241i
$804$	1583.00	−	398682.i	0.00244889	−	0.616758i
$805$	185203.	−	320781.i	0.285796	−	0.495013i
$806$	1.07964e6	+	623329.i	1.66191	+	0.959504i
$807$	−630810.	+	1.08264e6i	−0.968616	+	1.66241i
$808$	−540872.	−	936817.i	−0.828460	−	1.43493i
$809$		−	570214.i		−	0.871246i	−0.900129	−	0.435623i	$-0.856528\pi$
$809$		−	570214.i		−	0.871246i	0.900129	−	0.435623i	$-0.143472\pi$
$810$	274801.	−	458977.i	0.418840	−	0.699554i
$811$	−586982.			−0.892448			−0.446224	−	0.894921i	$-0.647232\pi$
$811$	−586982.			−0.892448			−0.446224	+	0.894921i	$0.647232\pi$
$812$	2.10151e6	−	1.21331e6i	3.18728	−	1.84018i
$813$	−946226.	−	551325.i	−1.43157	−	0.834116i
$814$	249133.	−	431511.i	0.375996	−	0.651244i
$815$	−72070.8	−	41610.1i	−0.108504	−	0.0626446i
$816$	−1.28108e6	−	5086.64i	−1.92396	−	0.00763925i
$817$	544282.	+	942724.i	0.815417	+	1.41234i
$818$			1.18168e6i			1.76601i
$819$	344421.	+	607649.i	0.513479	+	0.905909i
$820$	−92809.0			−0.138027
$821$	−358543.	+	207005.i	−0.531931	+	0.307110i	−0.741802	−	0.670619i	$-0.766029\pi$
$821$	−358543.	+	207005.i	−0.531931	+	0.307110i	0.209872	+	0.977729i	$0.432695\pi$
$822$	687545.	−	393322.i	1.01755	−	0.582110i
$823$	−119513.	+	207002.i	−0.176447	+	0.305615i	−0.940661	−	0.339348i	$-0.889794\pi$
$823$	−119513.	+	207002.i	−0.176447	+	0.305615i	0.764214	+	0.644963i	$0.223127\pi$
$824$	−1.18594e6	−	684705.i	−1.74666	−	1.00844i
$825$	21916.2	+	38310.5i	0.0322002	+	0.0562873i
$826$	−339205.	−	587521.i	−0.497168	−	0.861119i
$827$			307455.i			0.449542i	0.974412	+	0.224771i	$0.0721635\pi$
$827$			307455.i			0.449542i	−0.974412	+	0.224771i	$0.927837\pi$
$828$	1.66170e6	+	977058.i	2.42377	+	1.42515i
$829$	−593854.			−0.864113			−0.432057	−	0.901847i	$-0.642212\pi$
$829$	−593854.			−0.864113			−0.432057	+	0.901847i	$0.642212\pi$
$830$	192654.	−	111229.i	0.279654	−	0.161458i
$831$	−186.181	+	46890.0i	−0.000269608	+	0.0679014i
$832$	145334.	−	251726.i	0.209953	−	0.363649i
$833$	−64590.9	−	37291.6i	−0.0930853	−	0.0537428i
$834$	220137.	−	377817.i	0.316491	−	0.543187i
$835$	124783.	+	216131.i	0.178971	+	0.309988i
$836$			966294.i			1.38260i
$837$	643364.	+	381736.i	0.918346	+	0.544894i
$838$	635706.			0.905250
$839$	−192135.	+	110929.i	−0.272950	+	0.157587i	−0.630227	−	0.776411i	$-0.717038\pi$
$839$	−192135.	+	110929.i	−0.272950	+	0.157587i	0.357278	+	0.933998i	$0.383705\pi$
$840$	−695292.	−	405116.i	−0.985391	−	0.574145i
$841$	441027.	−	763882.i	0.623553	−	1.08003i
$842$	−654132.	−	377663.i	−0.922658	−	0.532697i
$843$	832237.	+	3304.47i	1.17109	+	0.00464993i
$844$	−953997.	−	1.65237e6i	−1.33925	−	2.31965i
$845$			9071.31i			0.0127045i
$846$	−601834.	−	4779.34i	−0.840884	−	0.00667771i
$847$	678214.			0.945366
$848$	−498548.	+	287837.i	−0.693290	+	0.400271i
$849$	−846827.	+	484443.i	−1.17484	+	0.672090i
$850$	122019.	−	211343.i	0.168884	−	0.292516i
$851$	965259.	+	557293.i	1.33286	+	0.769528i
$852$	−1.19566e6	−	2.09006e6i	−1.64713	−	2.87925i
$853$	−548740.	−	950446.i	−0.754169	−	1.30626i	−0.945786	−	0.324789i	$-0.894707\pi$
$853$	−548740.	−	950446.i	−0.754169	−	1.30626i	0.191617	−	0.981470i	$-0.438627\pi$
$854$			1.70169e6i			2.33327i
$855$	−4763.48	+	599837.i	−0.00651616	+	0.820542i
$856$	1.72523e6			2.35450
$857$	285695.	−	164946.i	0.388992	−	0.224585i	−0.292731	−	0.956195i	$-0.594564\pi$
$857$	285695.	−	164946.i	0.388992	−	0.224585i	0.681723	+	0.731610i	$0.261231\pi$
$858$	1703.17	−	428947.i	0.00231357	−	0.582678i
$859$	393404.	−	681395.i	0.533153	−	0.923448i	−0.466097	−	0.884734i	$-0.654340\pi$
$859$	393404.	−	681395.i	0.533153	−	0.923448i	0.999250	−	0.0387149i	$-0.0123264\pi$
$860$	591686.	+	341610.i	0.800009	+	0.461885i
$861$	52359.7	−	89863.8i	0.0706303	−	0.121221i
$862$	−1.19714e6	−	2.07352e6i	−1.61114	−	2.79057i
$863$		−	118902.i		−	0.159650i	−0.996809	−	0.0798248i	$-0.974564\pi$
$863$		−	118902.i		−	0.159650i	0.996809	−	0.0798248i	$-0.0254361\pi$
$864$	522962.	−	881382.i	0.700556	−	1.18069i
$865$	99848.7			0.133447
$866$	−347097.	+	200396.i	−0.462823	+	0.267211i
$867$	−92191.6	−	53716.0i	−0.122646	−	0.0714605i
$868$	987622.	−	1.71061e6i	1.31085	−	2.27045i
$869$	275386.	+	158994.i	0.364672	+	0.210543i
$870$	−925110.	−	3673.23i	−1.22224	−	0.00485299i
$871$	−99226.4	−	171865.i	−0.130795	−	0.226544i
$872$		−	1.04172e6i		−	1.36999i
$873$	−356548.	+	606387.i	−0.467831	+	0.795649i
$874$	−3.09161e6			−4.04727
$875$	62651.4	−	36171.8i	0.0818304	−	0.0472448i
$876$	985809.	−	563950.i	1.28465	−	0.734907i
$877$	−574391.	+	994875.i	−0.746808	+	1.29351i	0.202538	+	0.979274i	$0.435081\pi$
$877$	−574391.	+	994875.i	−0.746808	+	1.29351i	−0.949345	+	0.314234i	$0.898252\pi$
$878$	552097.	+	318754.i	0.716187	+	0.413491i
$879$	458979.	+	802315.i	0.594039	+	1.03841i
$880$	116614.	+	201982.i	0.150587	+	0.260823i
$881$			944737.i			1.21719i	0.793480	+	0.608596i	$0.208267\pi$
$881$			944737.i			1.21719i	−0.793480	+	0.608596i	$0.791733\pi$
$882$	143174.	−	81152.7i	0.184047	−	0.104320i
$883$	1.52306e6			1.95342			0.976712	−	0.214554i	$-0.0688297\pi$
$883$	1.52306e6			1.95342			0.976712	+	0.214554i	$0.0688297\pi$
$884$	−1.43606e6	+	829111.i	−1.83767	+	1.06098i
$885$	−717.984	+	180826.i	−0.000916702	+	0.230873i
$886$	−1785.88	+	3093.24i	−0.00227502	+	0.00394045i
$887$	766474.	+	442524.i	0.974205	+	0.562458i	0.900516	−	0.434824i	$-0.143189\pi$
$887$	766474.	+	442524.i	0.974205	+	0.562458i	0.0736894	+	0.997281i	$0.476523\pi$
$888$	1.21903e6	−	2.09220e6i	1.54593	−	2.65324i
$889$	248480.	+	430379.i	0.314403	+	0.544563i
$890$			237336.i			0.299628i
$891$	4087.97	−	257371.i	0.00514935	−	0.324193i
$892$	−1.31000e6			−1.64643
$893$	584455.	−	337436.i	0.732906	−	0.423144i
$894$	1.13429e6	+	660904.i	1.41922	+	0.826919i
$895$	132494.	−	229486.i	0.165406	−	0.286491i
$896$	437908.	+	252826.i	0.545465	+	0.314925i
$897$	959522.	+	3809.86i	1.19253	+	0.00473505i
$898$	276123.	+	478259.i	0.342413	+	0.593076i
$899$		−	1.29370e6i		−	1.60072i
$900$	185650.	+	327535.i	0.229198	+	0.404364i
$901$	289834.			0.357026
$902$	−55315.0	+	31936.1i	−0.0679876	+	0.0392526i
$903$	−664579.	+	380185.i	−0.815025	+	0.466250i
$904$	−533751.	+	924484.i	−0.653134	+	1.13126i
$905$	−199806.	−	115358.i	−0.243956	−	0.140848i
$906$	65632.0	+	114728.i	0.0799575	+	0.139769i
$907$	−745423.	−	1.29111e6i	−0.906125	−	1.56945i	−0.819400	−	0.573222i	$-0.805693\pi$
$907$	−745423.	−	1.29111e6i	−0.906125	−	1.56945i	−0.0867252	−	0.996232i	$-0.527640\pi$
$908$			2.10117e6i			2.54853i
$909$	−488907.	−	287471.i	−0.591696	−	0.347910i
$910$	−703089.			−0.849039
$911$	−473628.	+	273449.i	−0.570691	+	0.329489i	−0.757425	−	0.652922i	$-0.773543\pi$
$911$	−473628.	+	273449.i	−0.570691	+	0.329489i	0.186734	+	0.982410i	$0.440210\pi$
$912$	−12585.8	+	3.16977e6i	−0.0151319	+	3.81099i
$913$	53519.8	−	92699.0i	0.0642056	−	0.111207i
$914$	1.93442e6	+	1.11684e6i	2.31557	+	1.33689i
$915$	228347.	−	391906.i	0.272742	−	0.468101i
$916$	629970.	+	1.09114e6i	0.750808	+	1.30044i
$917$		−	289507.i		−	0.344287i
$918$	−1.24094e6	+	696882.i	−1.47253	+	0.826939i
$919$	−952352.			−1.12763			−0.563815	−	0.825901i	$-0.690667\pi$
$919$	−952352.			−1.12763			−0.563815	+	0.825901i	$0.690667\pi$
$920$	−957364.	+	552734.i	−1.13110	+	0.653041i
$921$	−590545.	−	344085.i	−0.696200	−	0.405645i
$922$	−1.32158e6	+	2.28904e6i	−1.55464	+	2.69272i
$923$	−1.03800e6	−	599287.i	−1.21841	−	0.703447i
$924$	−679637.	−	2698.56i	−0.796037	−	0.00316073i
$925$	108844.	+	188524.i	0.127210	+	0.220335i
$926$		−	1.28330e6i		−	1.49660i
$927$	−717960.	−	5701.54i	−0.835490	−	0.00663487i
$928$	−1.77232e6			−2.05800
$929$	−133472.	+	77060.0i	−0.154653	+	0.0892889i	−0.575329	−	0.817922i	$-0.695126\pi$
$929$	−133472.	+	77060.0i	−0.154653	+	0.0892889i	0.420676	+	0.907211i	$0.361793\pi$
$930$	−653638.	+	373926.i	−0.755739	+	0.432334i
$931$	−92270.3	+	159817.i	−0.106454	+	0.184384i
$932$	1.86476e6	+	1.07662e6i	2.14679	+	1.23945i
$933$	637240.	+	1.11392e6i	0.732049	+	1.27965i
$934$	362930.	+	628614.i	0.416035	+	0.720593i
$935$		−	117423.i		−	0.134317i
$936$	16553.7	−	2.08451e6i	0.0188949	−	2.37932i
$937$	−1.57033e6			−1.78860			−0.894299	−	0.447470i	$-0.852325\pi$
$937$	−1.57033e6			−1.78860			−0.894299	+	0.447470i	$0.852325\pi$
$938$	−389481.	+	224867.i	−0.442670	+	0.255576i
$939$	−1304.06	+	328431.i	−0.00147900	+	0.372489i
$940$	211786.	−	366825.i	0.239686	−	0.415148i
$941$	132092.	+	76263.1i	0.149175	+	0.0861262i	0.572730	−	0.819744i	$-0.305885\pi$
$941$	132092.	+	76263.1i	0.149175	+	0.0861262i	−0.423555	+	0.905871i	$0.639218\pi$
$942$	386009.	−	662498.i	0.435006	−	0.746591i
$943$	−71438.7	−	123735.i	−0.0803360	−	0.139146i
$944$			955539.i			1.07227i
$945$	−421878.	−	5025.52i	−0.472415	−	0.00562752i
$946$	470200.			0.525413
$947$	−257630.	+	148743.i	−0.287275	+	0.165858i	−0.636712	−	0.771102i	$-0.719706\pi$
$947$	−257630.	+	148743.i	−0.287275	+	0.165858i	0.349437	+	0.936960i	$0.386373\pi$
$948$	2.34368e6	+	1.36556e6i	2.60785	+	1.51948i
$949$	282663.	−	489586.i	0.313860	−	0.543622i
$950$	−522924.	−	301910.i	−0.579417	−	0.334527i
$951$	−915098.	−	3633.48i	−1.01183	−	0.00401755i
$952$	1.07045e6	+	1.85407e6i	1.18111	+	2.04574i
$953$		−	971057.i		−	1.06920i	−0.845105	−	0.534600i	$-0.820462\pi$
$953$		−	971057.i		−	1.06920i	0.845105	−	0.534600i	$-0.179538\pi$
$954$	−324160.	+	551305.i	−0.356175	+	0.605752i
$955$	254459.			0.279005
$956$	518075.	−	299111.i	0.566862	−	0.327278i
$957$	−386381.	+	221037.i	−0.421883	+	0.241346i
$958$	−875562.	+	1.51652e6i	−0.954017	+	1.65241i
$959$	−541017.	−	312356.i	−0.588266	−	0.339636i
$960$	87183.9	+	152401.i	0.0946006	+	0.165366i
$961$	−64770.4	−	112186.i	−0.0701342	−	0.121476i
$962$		−	2.11566e6i		−	2.28610i
$963$	786921.	−	446035.i	0.848552	−	0.480968i
$964$	3.99996e6			4.30429
$965$	−588262.	+	339633.i	−0.631707	+	0.364716i
$966$	8633.91	−	2.17447e6i	0.00925237	−	2.33023i
$967$	744399.	−	1.28934e6i	0.796073	−	1.37884i	−0.126083	−	0.992020i	$-0.540240\pi$
$967$	744399.	−	1.28934e6i	0.796073	−	1.37884i	0.922156	−	0.386819i	$-0.126426\pi$
$968$	−1.75294e6	−	1.01206e6i	−1.87075	−	1.08008i
$969$	803429.	−	1.37891e6i	0.855657	−	1.46854i
$970$	−354046.	−	613226.i	−0.376285	−	0.651744i
$971$		−	732461.i		−	0.776866i	−0.921477	−	0.388433i	$-0.873016\pi$
$971$		−	732461.i		−	0.776866i	0.921477	−	0.388433i	$-0.126984\pi$
$972$	43587.8	−	2.19526e6i	0.0461352	−	2.32356i
$973$	−344867.			−0.364272
$974$	2.30288e6	−	1.32957e6i	2.42747	−	1.40150i
$975$	161924.	+	94346.2i	0.170334	+	0.0992465i
$976$	1.19841e6	−	2.07571e6i	1.25808	−	2.17905i
$977$	−560348.	−	323517.i	−0.587042	−	0.338929i	0.176885	−	0.984231i	$-0.443398\pi$
$977$	−560348.	−	323517.i	−0.587042	−	0.338929i	−0.763927	+	0.645303i	$0.776731\pi$
$978$	−488544.	−	1939.81i	−0.510771	−	0.00202806i
$979$	57099.3	+	98898.8i	0.0595752	+	0.103187i
$980$			115824.i			0.120600i
$981$	−269323.	−	475155.i	−0.279857	−	0.493739i
$982$	1.62017e6			1.68011
$983$	425164.	−	245469.i	0.439997	−	0.254032i	−0.263599	−	0.964632i	$-0.584910\pi$
$983$	425164.	−	245469.i	0.439997	−	0.254032i	0.703596	+	0.710600i	$0.251576\pi$
$984$	−269429.	+	154132.i	−0.278262	+	0.159185i
$985$	−112539.	+	194923.i	−0.115992	+	0.200905i
$986$	2.13150e6	+	1.23062e6i	2.19246	+	1.26582i
$987$	235701.	+	412016.i	0.241951	+	0.422941i
$988$	2.05146e6	+	3.55324e6i	2.10160	+	3.64008i
$989$			1.05180e6i			1.07533i
$990$	223356.	+	131330.i	0.227891	+	0.133997i
$991$	−1.11475e6			−1.13509			−0.567543	−	0.823344i	$-0.692106\pi$
$991$	−1.11475e6			−1.13509			−0.567543	+	0.823344i	$0.692106\pi$
$992$	−1.24937e6	+	721325.i	−1.26960	+	0.733006i
$993$	−3412.02	+	859324.i	−0.00346029	+	0.871482i
$994$	−1.35810e6	+	2.35230e6i	−1.37455	+	2.38079i
$995$	288805.	+	166742.i	0.291715	+	0.168422i
$996$	459668.	−	788918.i	0.463368	−	0.795268i
$997$	−705865.	−	1.22259e6i	−0.710119	−	1.22996i	−0.964812	−	0.262941i	$-0.915308\pi$
$997$	−705865.	−	1.22259e6i	−0.710119	−	1.22996i	0.254693	−	0.967022i	$-0.418026\pi$
$998$			1.08791e6i			1.09227i
$999$	15122.3	−	1.26947e6i	0.0151526	−	1.27201i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.5.i.a.41.1	yes	32
3.2	odd	2		135.5.i.a.71.16		32
9.2	odd	6	inner	45.5.i.a.11.1	✓	32
9.4	even	3		405.5.c.b.161.2		32
9.5	odd	6		405.5.c.b.161.31		32
9.7	even	3		135.5.i.a.116.16		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.5.i.a.11.1	✓	32	9.2	odd	6	inner
45.5.i.a.41.1	yes	32	1.1	even	1	trivial
135.5.i.a.71.16		32	3.2	odd	2
135.5.i.a.116.16		32	9.7	even	3
405.5.c.b.161.2		32	9.4	even	3
405.5.c.b.161.31		32	9.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(-6.31571 + 3.64638i) q^{2} +(-7.77630 - 4.53091i) q^{3} +(18.5921 - 32.2025i) q^{4} +(9.68246 + 5.59017i) q^{5} +(65.6342 + 0.260606i) q^{6} +(-25.8824 - 44.8297i) q^{7} +154.491i q^{8} +(39.9417 + 70.4675i) q^{9} -81.5354 q^{10} +(-33.9762 + 19.6162i) q^{11} +(-290.484 + 166.177i) q^{12} +(-83.2911 + 144.264i) q^{13} +(326.932 + 188.754i) q^{14} +(-49.9651 - 87.3412i) q^{15} +(-265.860 - 460.482i) q^{16} +267.704i q^{17} +(-509.211 - 299.410i) q^{18} +662.379 q^{19} +(360.035 - 207.866i) q^{20} +(-1.84982 + 465.880i) q^{21} +(143.056 - 247.780i) q^{22} +(554.266 + 320.005i) q^{23} +(699.986 - 1201.37i) q^{24} +(62.5000 + 108.253i) q^{25} -1214.84i q^{26} +(8.68342 - 728.948i) q^{27} -1924.84 q^{28} +(-1091.79 + 630.344i) q^{29} +(634.044 + 369.430i) q^{30} +(-513.094 + 888.705i) q^{31} +(1217.49 + 702.917i) q^{32} +(353.088 + 1.40197i) q^{33} +(-976.150 - 1690.74i) q^{34} -578.749i q^{35} +(3011.83 + 23.9178i) q^{36} +1741.51 q^{37} +(-4183.39 + 2415.28i) q^{38} +(1301.35 - 744.459i) q^{39} +(-863.633 + 1495.86i) q^{40} +(-193.333 - 111.621i) q^{41} +(-1687.09 - 2949.11i) q^{42} +(821.707 + 1423.24i) q^{43} +1458.82i q^{44} +(-7.19147 + 905.579i) q^{45} -4667.44 q^{46} +(882.358 - 509.430i) q^{47} +(-19.0010 + 4785.43i) q^{48} +(-139.301 + 241.277i) q^{49} +(-789.464 - 455.797i) q^{50} +(1212.94 - 2081.75i) q^{51} +(3097.12 + 5364.36i) q^{52} -1082.66i q^{53} +(2603.18 + 4635.49i) q^{54} -438.631 q^{55} +(6925.80 - 3998.61i) q^{56} +(-5150.86 - 3001.18i) q^{57} +(4596.94 - 7962.14i) q^{58} +(-1556.31 - 898.538i) q^{59} +(-3741.56 - 14.8562i) q^{60} +(2253.85 + 3903.77i) q^{61} -7483.73i q^{62} +(2125.25 - 3614.44i) q^{63} -1744.90 q^{64} +(-1612.93 + 931.223i) q^{65} +(-2235.11 + 1278.64i) q^{66} +(-595.660 + 1031.71i) q^{67} +(8620.74 + 4977.19i) q^{68} +(-2860.22 - 4999.79i) q^{69} +(2110.34 + 3655.21i) q^{70} +7195.09i q^{71} +(-10886.6 + 6170.64i) q^{72} -3393.67 q^{73} +(-10998.9 + 6350.20i) q^{74} +(4.46687 - 1124.99i) q^{75} +(12315.0 - 21330.3i) q^{76} +(1758.77 + 1015.43i) q^{77} +(-5504.35 + 9446.98i) q^{78} +(-4052.63 - 7019.36i) q^{79} -5944.80i q^{80} +(-3370.33 + 5629.18i) q^{81} +1628.05 q^{82} +(-2362.82 + 1364.18i) q^{83} +(14968.1 + 8721.27i) q^{84} +(-1496.51 + 2592.03i) q^{85} +(-10379.3 - 5992.51i) q^{86} +(11346.1 + 45.0507i) q^{87} +(-3030.53 - 5249.03i) q^{88} -2910.83i q^{89} +(-3256.66 - 5745.60i) q^{90} +8623.11 q^{91} +(20609.9 - 11899.2i) q^{92} +(8016.62 - 4586.05i) q^{93} +(-3715.14 + 6434.82i) q^{94} +(6413.46 + 3702.81i) q^{95} +(-6282.70 - 10982.4i) q^{96} +(4342.24 + 7520.98i) q^{97} -2031.78i q^{98} +(-2739.37 - 1610.71i) 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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