LMFDB - Embedded newform 45.5.h.a.14.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [45,5,Mod(14,45)] 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("45.14"); 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([5, 3])) N = Newforms(chi, 5, names="a")

Level:	$ N $	$=$	$ 45 = 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	45.h (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:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			14.5
Character	$\chi$	$=$	45.14
Dual form			45.5.h.a.29.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.61690 - 4.53261i) q^{2} +(8.42379 - 3.16855i) q^{3} +(-5.69638 + 9.86641i) q^{4} +(-19.7616 - 15.3127i) q^{5} +(-36.4061 - 29.8900i) q^{6} +(50.0684 - 28.9070i) q^{7} -24.1135 q^{8} +(60.9206 - 53.3825i) q^{9} +(-17.6925 + 129.644i) q^{10} +(-146.496 + 84.5798i) q^{11} +(-16.7228 + 101.162i) q^{12} +(-99.1268 - 57.2309i) q^{13} +(-262.048 - 151.294i) q^{14} +(-214.987 - 66.3757i) q^{15} +(154.245 + 267.160i) q^{16} +209.860 q^{17} +(-401.385 - 136.432i) q^{18} +26.9887 q^{19} +(263.651 - 107.749i) q^{20} +(330.173 - 402.151i) q^{21} +(766.735 + 442.674i) q^{22} +(458.642 - 794.390i) q^{23} +(-203.127 + 76.4047i) q^{24} +(156.040 + 605.208i) q^{25} +599.071i q^{26} +(344.037 - 642.713i) q^{27} +658.661i q^{28} +(308.888 - 178.337i) q^{29} +(261.744 + 1148.15i) q^{30} +(629.269 - 1089.93i) q^{31} +(614.379 - 1064.14i) q^{32} +(-966.061 + 1176.66i) q^{33} +(-549.182 - 951.212i) q^{34} +(-1432.08 - 195.436i) q^{35} +(179.667 + 905.154i) q^{36} +368.530i q^{37} +(-70.6268 - 122.329i) q^{38} +(-1016.36 - 168.013i) q^{39} +(476.520 + 369.243i) q^{40} +(1591.16 + 918.657i) q^{41} +(-2686.82 - 444.153i) q^{42} +(-277.639 + 160.295i) q^{43} -1927.19i q^{44} +(-2021.32 + 122.062i) q^{45} -4800.88 q^{46} +(1224.29 + 2120.54i) q^{47} +(2145.83 + 1761.76i) q^{48} +(470.730 - 815.329i) q^{49} +(2334.83 - 2291.04i) q^{50} +(1767.81 - 664.951i) q^{51} +(1129.33 - 652.018i) q^{52} +1898.83 q^{53} +(-3813.48 + 122.531i) q^{54} +(4190.15 + 571.831i) q^{55} +(-1207.32 + 697.048i) q^{56} +(227.347 - 85.5151i) q^{57} +(-1616.66 - 933.380i) q^{58} +(-4208.65 - 2429.87i) q^{59} +(1879.53 - 1743.05i) q^{60} +(-473.839 - 820.714i) q^{61} -6586.95 q^{62} +(1507.07 - 4433.81i) q^{63} -1495.26 q^{64} +(1082.54 + 2648.88i) q^{65} +(7861.45 + 1299.56i) q^{66} +(-1877.97 - 1084.25i) q^{67} +(-1195.44 + 2070.56i) q^{68} +(1346.43 - 8145.01i) q^{69} +(2861.77 + 7002.48i) q^{70} +9078.87i q^{71} +(-1469.00 + 1287.24i) q^{72} -984.836i q^{73} +(1670.40 - 964.407i) q^{74} +(3232.08 + 4603.72i) q^{75} +(-153.738 + 266.282i) q^{76} +(-4889.90 + 8469.55i) q^{77} +(1898.19 + 5046.45i) q^{78} +(5125.48 + 8877.60i) q^{79} +(1042.82 - 7641.40i) q^{80} +(861.628 - 6504.18i) q^{81} -9616.15i q^{82} +(-2390.39 - 4140.27i) q^{83} +(2087.00 + 5548.42i) q^{84} +(-4147.16 - 3213.52i) q^{85} +(1453.11 + 838.954i) q^{86} +(2036.94 - 2481.00i) q^{87} +(3532.54 - 2039.51i) q^{88} +858.461i q^{89} +(5842.85 + 8842.42i) q^{90} -6617.50 q^{91} +(5225.19 + 9050.29i) q^{92} +(1847.35 - 11175.2i) q^{93} +(6407.71 - 11098.5i) q^{94} +(-533.339 - 413.271i) q^{95} +(1803.63 - 10910.8i) q^{96} +(3694.13 - 2132.80i) q^{97} -4927.43 q^{98} +(-4409.57 + 12973.0i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 162 q^{4} + 6 q^{5} - 36 q^{6} - 126 q^{9} + 28 q^{10} + 228 q^{11} + 282 q^{14} + 450 q^{15} - 1058 q^{16} - 8 q^{19} - 2196 q^{20} + 1056 q^{21} + 2970 q^{24} - 148 q^{25} + 2370 q^{29} + 1068 q^{30}+ \cdots + 44568 q^{99}+O(q^{100}) $ 44 * q - 162 * q^4 + 6 * q^5 - 36 * q^6 - 126 * q^9 + 28 * q^10 + 228 * q^11 + 282 * q^14 + 450 * q^15 - 1058 * q^16 - 8 * q^19 - 2196 * q^20 + 1056 * q^21 + 2970 * q^24 - 148 * q^25 + 2370 * q^29 + 1068 * q^30 - 1112 * q^31 - 436 * q^34 - 648 * q^36 - 6420 * q^39 - 850 * q^40 + 1830 * q^41 - 1944 * q^45 - 5668 * q^46 + 5396 * q^49 + 13524 * q^50 - 1500 * q^51 + 17766 * q^54 - 3072 * q^55 - 8250 * q^56 - 27348 * q^59 - 28722 * q^60 + 2782 * q^61 + 8348 * q^64 - 24906 * q^65 + 27240 * q^66 + 19662 * q^69 + 4782 * q^70 + 64728 * q^74 + 28446 * q^75 - 1776 * q^76 + 7900 * q^79 - 47754 * q^81 - 113166 * q^84 + 6766 * q^85 + 9192 * q^86 + 10674 * q^90 + 1560 * q^91 - 18826 * q^94 + 58746 * q^95 + 1902 * q^96 + 44568 * 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 $

$2$	−2.61690	−	4.53261i	−0.654226	−	1.13315i	−0.982087	−	0.188427i	$-0.939661\pi$
$2$	−2.61690	−	4.53261i	−0.654226	−	1.13315i	0.327861	−	0.944726i	$-0.393672\pi$
$3$	8.42379	−	3.16855i	0.935977	−	0.352061i
$3$	8.42379	−	3.16855i	0.935977	−	0.352061i
$4$	−5.69638	+	9.86641i	−0.356024	+	0.616651i
$5$	−19.7616	−	15.3127i	−0.790463	−	0.612509i
$5$	−19.7616	−	15.3127i	−0.790463	−	0.612509i
$6$	−36.4061	−	29.8900i	−1.01128	−	0.830277i
$7$	50.0684	−	28.9070i	1.02180	−	0.589939i	0.107178	−	0.994240i	$-0.465818\pi$
$7$	50.0684	−	28.9070i	1.02180	−	0.589939i	0.914626	+	0.404301i	$0.132485\pi$
$8$	−24.1135			−0.376773
$9$	60.9206	−	53.3825i	0.752106	−	0.659043i
$10$	−17.6925	+	129.644i	−0.176925	+	1.29644i
$11$	−146.496	+	84.5798i	−1.21071	+	0.699007i	−0.962915	−	0.269805i	$-0.913041\pi$
$11$	−146.496	+	84.5798i	−1.21071	+	0.699007i	−0.247800	+	0.968811i	$0.579708\pi$
$12$	−16.7228	+	101.162i	−0.116131	+	0.702513i
$13$	−99.1268	−	57.2309i	−0.586549	−	0.338644i	0.177183	−	0.984178i	$-0.443302\pi$
$13$	−99.1268	−	57.2309i	−0.586549	−	0.338644i	−0.763732	+	0.645534i	$0.776635\pi$
$14$	−262.048	−	151.294i	−1.33698	−	0.771907i
$15$	−214.987	−	66.3757i	−0.955496	−	0.295003i
$16$	154.245	+	267.160i	0.602518	+	1.04359i
$17$	209.860			0.726158			0.363079	−	0.931758i	$-0.381726\pi$
$17$	209.860			0.726158			0.363079	+	0.931758i	$0.381726\pi$
$18$	−401.385	−	136.432i	−1.23884	−	0.421088i
$19$	26.9887			0.0747609			0.0373805	−	0.999301i	$-0.488099\pi$
$19$	26.9887			0.0747609			0.0373805	+	0.999301i	$0.488099\pi$
$20$	263.651	−	107.749i	0.659128	−	0.269372i
$21$	330.173	−	402.151i	0.748690	−	0.911907i
$22$	766.735	+	442.674i	1.58416	+	0.914617i
$23$	458.642	−	794.390i	0.866997	−	1.50168i	0.00194692	−	0.999998i	$-0.499380\pi$
$23$	458.642	−	794.390i	0.866997	−	1.50168i	0.865050	−	0.501685i	$-0.167286\pi$
$24$	−203.127	+	76.4047i	−0.352651	+	0.132647i
$25$	156.040	+	605.208i	0.249665	+	0.968332i
$26$			599.071i			0.886200i
$27$	344.037	−	642.713i	0.471930	−	0.881636i
$28$			658.661i			0.840129i
$29$	308.888	−	178.337i	0.367287	−	0.212053i	−0.304986	−	0.952357i	$-0.598652\pi$
$29$	308.888	−	178.337i	0.367287	−	0.212053i	0.672272	+	0.740304i	$0.265318\pi$
$30$	261.744	+	1148.15i	0.290827	+	1.27572i
$31$	629.269	−	1089.93i	0.654807	−	1.13416i	−0.327135	−	0.944977i	$-0.606083\pi$
$31$	629.269	−	1089.93i	0.654807	−	1.13416i	0.981942	−	0.189181i	$-0.0605833\pi$
$32$	614.379	−	1064.14i	0.599980	−	1.03920i
$33$	−966.061	+	1176.66i	−0.887108	+	1.08050i
$34$	−549.182	−	951.212i	−0.475071	−	0.822848i
$35$	−1432.08	−	195.436i	−1.16904	−	0.159540i
$36$	179.667	+	905.154i	0.138632	+	0.698421i
$37$			368.530i			0.269196i	0.990900	+	0.134598i	$0.0429744\pi$
$37$			368.530i			0.269196i	−0.990900	+	0.134598i	$0.957026\pi$
$38$	−70.6268	−	122.329i	−0.0489105	−	0.0847155i
$39$	−1016.36	−	168.013i	−0.668220	−	0.110462i
$40$	476.520	+	369.243i	0.297825	+	0.230777i
$41$	1591.16	+	918.657i	0.946556	+	0.546494i	0.892009	−	0.452017i	$-0.149295\pi$
$41$	1591.16	+	918.657i	0.946556	+	0.546494i	0.0545466	+	0.998511i	$0.482629\pi$
$42$	−2686.82	−	444.153i	−1.52314	−	0.251787i
$43$	−277.639	+	160.295i	−0.150156	+	0.0866929i	−0.573196	−	0.819418i	$-0.694297\pi$
$43$	−277.639	+	160.295i	−0.150156	+	0.0866929i	0.423039	+	0.906111i	$0.360963\pi$
$44$		−	1927.19i		−	0.995451i
$45$	−2021.32	+	122.062i	−0.998182	+	0.0602773i
$46$	−4800.88			−2.26885
$47$	1224.29	+	2120.54i	0.554229	+	0.959953i	0.997963	+	0.0637941i	$0.0203201\pi$
$47$	1224.29	+	2120.54i	0.554229	+	0.959953i	−0.443734	+	0.896158i	$0.646347\pi$
$48$	2145.83	+	1761.76i	0.931351	+	0.764655i
$49$	470.730	−	815.329i	0.196056	−	0.339579i
$50$	2334.83	−	2291.04i	0.933931	−	0.916416i
$51$	1767.81	−	664.951i	0.679667	−	0.255652i
$52$	1129.33	−	652.018i	0.417651	−	0.241131i
$53$	1898.83			0.675981			0.337991	−	0.941149i	$-0.390253\pi$
$53$	1898.83			0.675981			0.337991	+	0.941149i	$0.390253\pi$
$54$	−3813.48	+	122.531i	−1.30778	+	0.0420204i
$55$	4190.15	+	571.831i	1.38517	+	0.189035i
$56$	−1207.32	+	697.048i	−0.384988	+	0.222273i
$57$	227.347	−	85.5151i	0.0699745	−	0.0263204i
$58$	−1616.66	−	933.380i	−0.480577	−	0.277461i
$59$	−4208.65	−	2429.87i	−1.20904	−	0.698037i	−0.246487	−	0.969146i	$-0.579276\pi$
$59$	−4208.65	−	2429.87i	−1.20904	−	0.698037i	−0.962549	+	0.271109i	$0.912609\pi$
$60$	1879.53	−	1743.05i	0.522093	−	0.484180i
$61$	−473.839	−	820.714i	−0.127342	−	0.220563i	0.795304	−	0.606211i	$-0.207311\pi$
$61$	−473.839	−	820.714i	−0.127342	−	0.220563i	−0.922646	+	0.385648i	$0.873978\pi$
$62$	−6586.95			−1.71357
$63$	1507.07	−	4433.81i	0.379710	−	1.11711i
$64$	−1495.26			−0.365053
$65$	1082.54	+	2648.88i	0.256223	+	0.626953i
$66$	7861.45	+	1299.56i	1.80474	+	0.298338i
$67$	−1877.97	−	1084.25i	−0.418349	−	0.241534i	0.276022	−	0.961151i	$-0.410984\pi$
$67$	−1877.97	−	1084.25i	−0.418349	−	0.241534i	−0.694371	+	0.719617i	$0.744317\pi$
$68$	−1195.44	+	2070.56i	−0.258529	+	0.447786i
$69$	1346.43	−	8145.01i	0.282805	−	1.71078i
$70$	2861.77	+	7002.48i	0.584035	+	1.42908i
$71$			9078.87i			1.80101i	0.434850	+	0.900503i	$0.356801\pi$
$71$			9078.87i			1.80101i	−0.434850	+	0.900503i	$0.643199\pi$
$72$	−1469.00	+	1287.24i	−0.283373	+	0.248309i
$73$		−	984.836i		−	0.184807i	−0.995722	−	0.0924035i	$-0.970545\pi$
$73$		−	984.836i		−	0.184807i	0.995722	−	0.0924035i	$-0.0294550\pi$
$74$	1670.40	−	964.407i	0.305041	−	0.176115i
$75$	3232.08	+	4603.72i	0.574593	+	0.818440i
$76$	−153.738	+	266.282i	−0.0266166	+	0.0461014i
$77$	−4889.90	+	8469.55i	−0.824742	+	1.42850i
$78$	1898.19	+	5046.45i	0.311997	+	0.829463i
$79$	5125.48	+	8877.60i	0.821260	+	1.42246i	0.904745	+	0.425955i	$0.140062\pi$
$79$	5125.48	+	8877.60i	0.821260	+	1.42246i	−0.0834848	+	0.996509i	$0.526605\pi$
$80$	1042.82	−	7641.40i	0.162941	−	1.19397i
$81$	861.628	−	6504.18i	0.131326	−	0.991339i
$82$		−	9616.15i		−	1.43012i
$83$	−2390.39	−	4140.27i	−0.346986	−	0.600997i	0.638726	−	0.769434i	$-0.279462\pi$
$83$	−2390.39	−	4140.27i	−0.346986	−	0.600997i	−0.985713	+	0.168436i	$0.946128\pi$
$84$	2087.00	+	5548.42i	0.295777	+	0.786341i
$85$	−4147.16	−	3213.52i	−0.574001	−	0.444778i
$86$	1453.11	+	838.954i	0.196473	+	0.113433i
$87$	2036.94	−	2481.00i	0.269116	−	0.327784i
$88$	3532.54	−	2039.51i	0.456164	−	0.263367i
$89$			858.461i			0.108378i	0.998531	+	0.0541889i	$0.0172573\pi$
$89$			858.461i			0.108378i	−0.998531	+	0.0541889i	$0.982743\pi$
$90$	5842.85	+	8842.42i	0.721340	+	1.09166i
$91$	−6617.50			−0.799118
$92$	5225.19	+	9050.29i	0.617343	+	1.06927i
$93$	1847.35	−	11175.2i	0.213591	−	1.29208i
$94$	6407.71	−	11098.5i	0.725182	−	1.25605i
$95$	−533.339	−	413.271i	−0.0590958	−	0.0457918i
$96$	1803.63	−	10910.8i	0.195707	−	1.18389i
$97$	3694.13	−	2132.80i	0.392616	−	0.226677i	−0.290677	−	0.956821i	$-0.593880\pi$
$97$	3694.13	−	2132.80i	0.392616	−	0.226677i	0.683293	+	0.730144i	$0.260547\pi$
$98$	−4927.43			−0.513060
$99$	−4409.57	+	12973.0i	−0.449910	+	1.32364i
$100$	−6860.09	−	1907.93i	−0.686009	−	0.190793i
$101$	−3710.95	+	2142.52i	−0.363783	+	0.210030i	−0.670739	−	0.741693i	$-0.734023\pi$
$101$	−3710.95	+	2142.52i	−0.363783	+	0.210030i	0.306956	+	0.951724i	$0.400690\pi$
$102$	−7640.16	−	6272.70i	−0.734349	−	0.602912i
$103$	−9070.03	−	5236.58i	−0.854937	−	0.493598i	0.00737655	−	0.999973i	$-0.497652\pi$
$103$	−9070.03	−	5236.58i	−0.854937	−	0.493598i	−0.862314	+	0.506375i	$0.830985\pi$
$104$	2390.29	+	1380.03i	0.220996	+	0.127592i
$105$	−12682.8	+	2891.30i	−1.15036	+	0.262249i
$106$	−4969.06	−	8606.67i	−0.442245	−	0.765990i
$107$	17871.6			1.56097			0.780487	−	0.625171i	$-0.214971\pi$
$107$	17871.6			1.56097			0.780487	+	0.625171i	$0.214971\pi$
$108$	4381.50	+	7055.54i	0.375643	+	0.604899i
$109$	−14838.6			−1.24894			−0.624469	−	0.781049i	$-0.714685\pi$
$109$	−14838.6			−1.24894			−0.624469	+	0.781049i	$0.714685\pi$
$110$	−8373.33	−	20488.8i	−0.692011	−	1.69329i
$111$	1167.71	+	3104.42i	0.0947736	+	0.251962i
$112$	15445.6	+	8917.50i	1.23131	+	0.710898i
$113$	−4689.23	+	8121.99i	−0.367236	+	0.636071i	−0.989132	−	0.147028i	$-0.953029\pi$
$113$	−4689.23	+	8121.99i	−0.367236	+	0.636071i	0.621896	+	0.783099i	$0.286362\pi$
$114$	−982.552	−	806.691i	−0.0756042	−	0.0620723i
$115$	−21227.8	+	8675.36i	−1.60512	+	0.655982i
$116$			4063.49i			0.301984i
$117$	−9093.99	+	1805.10i	−0.664328	+	0.131865i
$118$			25434.9i			1.82670i
$119$	10507.3	−	6066.41i	0.741991	−	0.428389i
$120$	5184.07	+	1600.55i	0.360005	+	0.111149i
$121$	6986.98	−	12101.8i	0.477220	−	0.826570i
$122$	−2479.98	+	4295.46i	−0.166621	+	0.288596i
$123$	16314.4	+	2696.90i	1.07835	+	0.178260i
$124$	7169.11	+	12417.3i	0.466253	+	0.807574i
$125$	6183.78	−	14349.3i	0.395762	−	0.918353i
$126$	−24040.6	+	4771.89i	−1.51427	+	0.300573i
$127$		−	3644.02i		−	0.225929i	−0.993599	−	0.112965i	$-0.963965\pi$
$127$		−	3644.02i		−	0.225929i	0.993599	−	0.112965i	$-0.0360347\pi$
$128$	−5917.12	−	10248.8i	−0.361152	−	0.625534i
$129$	−1830.87	+	2230.01i	−0.110022	+	0.134007i
$130$	9173.42	−	11838.6i	0.542806	−	0.700509i
$131$	4646.98	+	2682.93i	0.270787	+	0.156339i	0.629245	−	0.777207i	$-0.283364\pi$
$131$	4646.98	+	2682.93i	0.270787	+	0.156339i	−0.358458	+	0.933546i	$0.616697\pi$
$132$	−6106.41	−	16234.3i	−0.350460	−	0.931719i
$133$	1351.28	−	780.162i	0.0763910	−	0.0441044i
$134$			11349.5i			0.632071i
$135$	−16640.4	+	7432.87i	−0.913054	+	0.407839i
$136$	−5060.44			−0.273596
$137$	−1222.29	−	2117.07i	−0.0651230	−	0.112796i	0.831626	−	0.555337i	$-0.187411\pi$
$137$	−1222.29	−	2117.07i	−0.0651230	−	0.112796i	−0.896749	+	0.442540i	$0.854077\pi$
$138$	−40441.6	+	15211.9i	−2.12359	+	0.798774i
$139$	−7504.01	+	12997.3i	−0.388386	+	0.672704i	−0.992233	−	0.124396i	$-0.960301\pi$
$139$	−7504.01	+	12997.3i	−0.388386	+	0.672704i	0.603847	+	0.797101i	$0.293634\pi$
$140$	10085.9	−	13016.2i	0.514587	−	0.664091i
$141$	17032.2	+	13983.7i	0.856708	+	0.703371i
$142$	41151.0	−	23758.5i	2.04081	−	1.17826i
$143$	19362.3			0.946859
$144$	23658.3	+	8041.55i	1.14093	+	0.387806i
$145$	−8834.94	−	1205.71i	−0.420211	−	0.0573464i
$146$	−4463.88	+	2577.22i	−0.209415	+	0.120906i
$147$	1381.92	−	8359.70i	0.0639513	−	0.386862i
$148$	−3636.07	−	2099.28i	−0.166000	−	0.0958402i
$149$	10932.2	+	6311.73i	0.492421	+	0.284299i	0.725578	−	0.688140i	$-0.241572\pi$
$149$	10932.2	+	6311.73i	0.492421	+	0.284299i	−0.233157	+	0.972439i	$0.574906\pi$
$150$	12408.8	−	26697.3i	0.551504	−	1.18655i
$151$	11641.2	+	20163.1i	0.510556	+	0.884309i	0.999925	+	0.0122322i	$0.00389373\pi$
$151$	11641.2	+	20163.1i	0.510556	+	0.884309i	−0.489369	+	0.872077i	$0.662773\pi$
$152$	−650.790			−0.0281679
$153$	12784.8	−	11202.8i	0.546147	−	0.478569i
$154$	51185.6			2.15827
$155$	−29125.1	+	11902.8i	−1.21228	+	0.495436i
$156$	7447.27	−	9070.79i	0.306019	−	0.372732i
$157$	14800.5	+	8545.07i	0.600450	+	0.346670i	0.769219	−	0.638986i	$-0.220646\pi$
$157$	14800.5	+	8545.07i	0.600450	+	0.346670i	−0.168768	+	0.985656i	$0.553979\pi$
$158$	26825.8	−	46463.6i	1.07458	−	1.86123i
$159$	15995.4	−	6016.55i	0.632703	−	0.237987i
$160$	−28435.9	+	11621.2i	−1.11078	+	0.453953i
$161$		−	53031.8i		−	2.04590i
$162$	−31735.7	+	13115.4i	−1.20926	+	0.499748i
$163$			26012.6i			0.979059i	0.871987	+	0.489530i	$0.162831\pi$
$163$			26012.6i			0.979059i	−0.871987	+	0.489530i	$0.837169\pi$
$164$	−18127.7	+	10466.0i	−0.673992	+	0.389130i
$165$	37108.8	−	8459.72i	1.36304	−	0.310734i
$166$	−12510.8	+	21669.4i	−0.454015	+	0.786376i
$167$	−22677.9	+	39279.2i	−0.813148	+	1.40841i	0.0975023	+	0.995235i	$0.468915\pi$
$167$	−22677.9	+	39279.2i	−0.813148	+	1.40841i	−0.910650	+	0.413178i	$0.864419\pi$
$168$	−7961.60	+	9697.25i	−0.282086	+	0.343582i
$169$	−7729.75	−	13388.3i	−0.270640	−	0.468762i
$170$	−3712.94	+	27206.9i	−0.128475	+	0.941417i
$171$	1644.17	−	1440.72i	0.0562281	−	0.0492706i
$172$		−	3652.41i		−	0.123459i
$173$	−2848.13	−	4933.11i	−0.0951630	−	0.164827i	0.814514	−	0.580144i	$-0.197004\pi$
$173$	−2848.13	−	4933.11i	−0.0951630	−	0.164827i	−0.909677	+	0.415317i	$0.863671\pi$
$174$	−16575.9	−	2740.12i	−0.547492	−	0.0905048i
$175$	25307.4	+	25791.1i	0.826365	+	0.842159i
$176$	−45192.6	−	26092.0i	−1.45896	−	0.842328i
$177$	−43152.0	−	7133.36i	−1.37738	−	0.227692i
$178$	3891.07	−	2246.51i	0.122809	−	0.0709036i
$179$			28582.7i			0.892066i	0.895017	+	0.446033i	$0.147164\pi$
$179$			28582.7i			0.892066i	−0.895017	+	0.446033i	$0.852836\pi$
$180$	10309.9	−	20638.5i	0.318206	−	0.636990i
$181$	34257.3			1.04567			0.522837	−	0.852433i	$-0.324874\pi$
$181$	34257.3			1.04567			0.522837	+	0.852433i	$0.324874\pi$
$182$	17317.4	+	29994.5i	0.522804	+	0.905523i
$183$	−6592.00	−	5412.14i	−0.196841	−	0.161609i
$184$	−11059.4	+	19155.5i	−0.326661	+	0.565793i
$185$	5643.20	−	7282.73i	0.164885	−	0.212790i
$186$	−55487.1	+	20871.1i	−1.60386	+	0.603281i
$187$	−30743.7	+	17749.9i	−0.879170	+	0.507589i
$188$	−27896.1			−0.789274
$189$	−1353.51	−	42124.7i	−0.0378913	−	1.17927i
$190$	−477.497	+	3498.91i	−0.0132271	+	0.0969227i
$191$	61661.0	−	35600.0i	1.69022	−	0.975850i	0.735889	−	0.677102i	$-0.236764\pi$
$191$	61661.0	−	35600.0i	1.69022	−	0.975850i	0.954332	−	0.298748i	$-0.0965690\pi$
$192$	−12595.7	+	4737.80i	−0.341681	+	0.128521i
$193$	−53250.9	−	30744.4i	−1.42959	−	0.825375i	−0.432504	−	0.901632i	$-0.642370\pi$
$193$	−53250.9	−	30744.4i	−1.42959	−	0.825375i	−0.997088	+	0.0762568i	$0.975703\pi$
$194$	−19334.3	−	11162.7i	−0.513720	−	0.296596i
$195$	17512.2	+	18883.5i	0.460545	+	0.496607i
$196$	5362.91	+	9288.84i	0.139601	+	0.241796i
$197$	−14233.7			−0.366763			−0.183382	−	0.983042i	$-0.558704\pi$
$197$	−14233.7			−0.366763			−0.183382	+	0.983042i	$0.558704\pi$
$198$	70340.9	−	13962.2i	1.79423	−	0.356142i
$199$	−58493.1			−1.47706			−0.738531	−	0.674220i	$-0.764480\pi$
$199$	−58493.1			−1.47706			−0.738531	+	0.674220i	$0.764480\pi$
$200$	−3762.67	−	14593.6i	−0.0940668	−	0.364841i
$201$	−19255.1	−	3183.02i	−0.476600	−	0.0787857i
$202$	19422.4	+	11213.5i	0.475993	+	0.274815i
$203$	10310.4	−	17858.1i	0.250197	−	0.433353i
$204$	−3509.45	+	21229.8i	−0.0843293	+	0.510135i
$205$	−17376.7	−	42519.1i	−0.413485	−	1.01176i
$206$			54814.5i			1.29170i
$207$	−14465.8	−	72878.1i	−0.337600	−	1.70081i
$208$		−	35310.2i		−	0.816158i
$209$	−3953.75	+	2282.70i	−0.0905141	+	0.0522584i
$210$	46294.7	+	49919.8i	1.04977	+	1.13197i
$211$	16666.2	−	28866.8i	0.374346	−	0.648386i	−0.615883	−	0.787838i	$-0.711201\pi$
$211$	16666.2	−	28866.8i	0.374346	−	0.648386i	0.990229	+	0.139452i	$0.0445340\pi$
$212$	−10816.5	+	18734.7i	−0.240665	+	0.416844i
$213$	28766.9	+	76478.5i	0.634065	+	1.68570i
$214$	−46768.3	−	81005.0i	−1.02123	−	1.76882i
$215$	7941.15	+	1083.73i	0.171793	+	0.0234447i
$216$	−8295.92	+	15498.0i	−0.177810	+	0.332176i
$217$		−	72761.2i		−	1.54518i
$218$	38831.3	+	67257.8i	0.817088	+	1.41524i
$219$	−3120.51	−	8296.06i	−0.0650634	−	0.172975i
$220$	−29510.6	+	38084.4i	−0.609723	+	0.786868i
$221$	−20802.7	−	12010.5i	−0.425927	−	0.245909i
$222$	11015.3	−	13416.7i	0.223508	−	0.272233i
$223$	40241.9	−	23233.7i	0.809223	−	0.467205i	−0.0374627	−	0.999298i	$-0.511928\pi$
$223$	40241.9	−	23233.7i	0.809223	−	0.467205i	0.846686	+	0.532093i	$0.178594\pi$
$224$		−	71039.5i		−	1.41581i
$225$	41813.5	+	28539.8i	0.825946	+	0.563749i
$226$	49085.1			0.961021
$227$	12971.6	+	22467.6i	0.251735	+	0.436018i	0.964004	−	0.265889i	$-0.0856656\pi$
$227$	12971.6	+	22467.6i	0.251735	+	0.436018i	−0.712269	+	0.701907i	$0.752332\pi$
$228$	−451.328	+	2730.23i	−0.00868205	+	0.0525205i
$229$	12098.4	−	20955.0i	0.230705	−	0.399593i	−0.727311	−	0.686308i	$-0.759230\pi$
$229$	12098.4	−	20955.0i	0.230705	−	0.399593i	0.958016	+	0.286716i	$0.0925635\pi$
$230$	94873.1	+	73514.7i	1.79344	+	1.38969i
$231$	−14355.3	+	86839.6i	−0.269022	+	1.62740i
$232$	−7448.36	+	4300.31i	−0.138384	+	0.0798958i
$233$	−59802.9			−1.10157			−0.550783	−	0.834648i	$-0.685671\pi$
$233$	−59802.9			−1.10157			−0.550783	+	0.834648i	$0.685671\pi$
$234$	31979.9	+	36495.8i	0.584044	+	0.666516i
$235$	8277.25	−	60652.4i	0.149882	−	1.09828i
$236$	47948.1	−	27682.9i	0.860890	−	0.497035i
$237$	71305.1	+	58542.7i	1.26947	+	1.04226i
$238$	−54993.4	−	31750.4i	−0.970860	−	0.560526i
$239$	64376.8	+	37168.0i	1.12703	+	0.650689i	0.943185	−	0.332267i	$-0.107814\pi$
$239$	64376.8	+	37168.0i	1.12703	+	0.650689i	0.183841	+	0.982956i	$0.441147\pi$
$240$	−15427.6	−	67673.8i	−0.267841	−	1.17489i
$241$	27807.6	+	48164.2i	0.478773	+	0.829259i	0.999704	−	0.0243398i	$-0.00774835\pi$
$241$	27807.6	+	48164.2i	0.478773	+	0.829259i	−0.520931	+	0.853599i	$0.674415\pi$
$242$	−73137.1			−1.24884
$243$	−13350.7	−	57519.9i	−0.226094	−	0.974105i
$244$	10796.7			0.181347
$245$	−21787.3	+	8904.02i	−0.362970	+	0.148339i
$246$	−30469.3	−	81004.5i	−0.503491	−	1.33856i
$247$	−2675.30	−	1544.59i	−0.0438510	−	0.0253174i
$248$	−15173.9	+	26281.9i	−0.246713	+	0.427320i
$249$	−33254.8	−	27302.7i	−0.536359	−	0.440359i
$250$	−81222.0	+	9521.99i	−1.29955	+	0.152352i
$251$			31731.5i			0.503666i	0.967771	+	0.251833i	$0.0810334\pi$
$251$			31731.5i			0.503666i	−0.967771	+	0.251833i	$0.918967\pi$
$252$	35160.9	+	40126.0i	0.553681	+	0.631865i
$253$			155167.i			2.42415i
$254$	−16516.9	+	9536.04i	−0.256013	+	0.147809i
$255$	−45117.0	−	13929.6i	−0.693841	−	0.214219i
$256$	−42931.1	+	74358.9i	−0.655077	+	1.13463i
$257$	21760.7	−	37690.7i	0.329463	−	0.570647i	−0.652942	−	0.757408i	$-0.726466\pi$
$257$	21760.7	−	37690.7i	0.329463	−	0.570647i	0.982405	+	0.186761i	$0.0597989\pi$
$258$	14899.0	+	2462.92i	0.223829	+	0.0370007i
$259$	10653.1	+	18451.7i	0.158809	+	0.275066i
$260$	−32301.5	−	4408.19i	−0.477832	−	0.0652100i
$261$	9297.59	−	27353.6i	0.136486	−	0.401544i
$262$		−	28083.9i		−	0.409124i
$263$	−20223.6	−	35028.3i	−0.292380	−	0.506417i	0.681992	−	0.731360i	$-0.261114\pi$
$263$	−20223.6	−	35028.3i	−0.292380	−	0.506417i	−0.974372	+	0.224943i	$0.927781\pi$
$264$	23295.1	−	28373.4i	0.334238	−	0.407103i
$265$	−37523.9	−	29076.3i	−0.534338	−	0.414045i
$266$	−7072.34	−	4083.22i	−0.0999540	−	0.0577085i
$267$	2720.08	+	7231.50i	0.0381557	+	0.101439i
$268$	21395.2	−	12352.5i	0.297884	−	0.171984i
$269$		−	16975.9i		−	0.234600i	−0.993097	−	0.117300i	$-0.962576\pi$
$269$		−	16975.9i		−	0.234600i	0.993097	−	0.117300i	$-0.0374239\pi$
$270$	77236.7	+	55973.4i	1.05949	+	0.767810i
$271$	79819.5			1.08685			0.543426	−	0.839457i	$-0.317127\pi$
$271$	79819.5			1.08685			0.543426	+	0.839457i	$0.317127\pi$
$272$	32369.7	+	56066.0i	0.437523	+	0.757812i
$273$	−55744.4	+	20967.9i	−0.747956	+	0.281339i
$274$	−6397.25	+	11080.4i	−0.0852103	+	0.147589i
$275$	−74047.7	−	75463.0i	−0.979143	−	0.997857i
$276$	72692.2	+	59681.5i	0.954267	+	0.783469i
$277$	76743.8	−	44308.0i	1.00019	−	0.577461i	0.0918873	−	0.995769i	$-0.470710\pi$
$277$	76743.8	−	44308.0i	1.00019	−	0.577461i	0.908305	+	0.418308i	$0.137377\pi$
$278$	78549.1			1.01637
$279$	−19847.5	−	99990.9i	−0.254975	−	1.28455i
$280$	34532.3	+	4712.64i	0.440463	+	0.0601101i
$281$	−63506.1	+	36665.3i	−0.804272	+	0.464346i	−0.844963	−	0.534825i	$-0.820377\pi$
$281$	−63506.1	+	36665.3i	−0.804272	+	0.464346i	0.0406910	+	0.999172i	$0.487044\pi$
$282$	18811.1	−	113794.i	0.236546	−	1.43094i
$283$	50958.4	+	29420.9i	0.636272	+	0.367352i	0.783177	−	0.621799i	$-0.213598\pi$
$283$	50958.4	+	29420.9i	0.636272	+	0.367352i	−0.146905	+	0.989151i	$0.546931\pi$
$284$	−89575.9	−	51716.7i	−1.11059	−	0.641200i
$285$	−5802.21	−	1791.39i	−0.0714338	−	0.0220547i
$286$	−50669.3	−	87761.8i	−0.619460	−	1.07294i
$287$	106223.			1.28959
$288$	−19377.9	−	97624.8i	−0.233626	−	1.17700i
$289$	−39479.9			−0.472695
$290$	17655.2	+	43200.6i	0.209931	+	0.513681i
$291$	24360.6	−	29671.3i	0.287675	−	0.350390i
$292$	9716.80	+	5610.00i	0.113961	+	0.0657956i
$293$	−50633.1	+	87699.2i	−0.589793	+	1.02155i	0.404466	+	0.914553i	$0.367457\pi$
$293$	−50633.1	+	87699.2i	−0.589793	+	1.02155i	−0.994259	+	0.106998i	$0.965876\pi$
$294$	−41507.6	+	15612.8i	−0.480212	+	0.180628i
$295$	45961.7	+	112464.i	0.528144	+	1.29232i
$296$		−	8886.52i		−	0.101426i
$297$	3960.29	+	123254.i	0.0448966	+	1.39729i
$298$		−	66068.8i		−	0.743984i
$299$	−90927.4	+	52496.9i	−1.01707	+	0.587208i
$300$	−63833.4	+	5664.54i	−0.709260	+	0.0629393i
$301$	−9267.31	+	16051.4i	−0.102287	+	0.177166i
$302$	60927.7	−	105530.i	0.668038	−	1.15708i
$303$	−24471.6	+	29806.5i	−0.266549	+	0.324658i
$304$	4162.86	+	7210.28i	0.0450448	+	0.0780199i
$305$	−3203.56	+	23474.4i	−0.0344376	+	0.252345i
$306$	−84234.5	−	28631.7i	−0.899596	−	0.305776i
$307$			43494.6i			0.461487i	0.973015	+	0.230743i	$0.0741158\pi$
$307$			43494.6i			0.461487i	−0.973015	+	0.230743i	$0.925884\pi$
$308$	−55709.4	−	96491.5i	−0.587255	−	1.01716i
$309$	−92996.4	−	15373.0i	−0.973978	−	0.161006i
$310$	130169.	+	100864.i	1.35451	+	1.04958i
$311$	−65710.8	−	37938.2i	−0.679385	−	0.392243i	0.120238	−	0.992745i	$-0.461634\pi$
$311$	−65710.8	−	37938.2i	−0.679385	−	0.392243i	−0.799623	+	0.600502i	$0.794967\pi$
$312$	24508.0	+	4051.37i	0.251767	+	0.0416191i
$313$	58416.4	−	33726.7i	0.596274	−	0.344259i	−0.171300	−	0.985219i	$-0.554797\pi$
$313$	58416.4	−	33726.7i	0.596274	−	0.344259i	0.767574	+	0.640960i	$0.221463\pi$
$314$		−	89446.5i		−	0.907202i
$315$	−97675.7	+	64541.7i	−0.984386	+	0.650458i
$316$	−116787.			−1.16955
$317$	−90575.3	−	156881.i	−0.901345	−	1.56118i	−0.825749	−	0.564037i	$-0.809248\pi$
$317$	−90575.3	−	156881.i	−0.901345	−	1.56118i	−0.0755957	−	0.997139i	$-0.524086\pi$
$318$	−69129.0	−	56756.0i	−0.683606	−	0.561252i
$319$	−30167.3	+	52251.4i	−0.296453	+	0.513472i
$320$	29548.7	+	22896.5i	0.288561	+	0.223599i
$321$	150547.	−	56627.1i	1.46104	−	0.549559i
$322$	−240373.	+	138779.i	−2.31832	+	1.33848i
$323$	5663.83			0.0542882
$324$	59264.7	+	45551.4i	0.564555	+	0.433922i
$325$	19168.8	−	68922.7i	0.181480	−	0.652522i
$326$	117905.	−	68072.5i	1.10942	−	0.640526i
$327$	−124998.	+	47017.0i	−1.16898	+	0.439703i
$328$	−38368.4	−	22152.0i	−0.356636	−	0.205904i
$329$	122597.	+	70781.2i	1.13263	+	0.653922i
$330$	−135455.	−	146062.i	−1.24385	−	1.34125i
$331$	−78059.4	−	135203.i	−0.712475	−	1.23404i	−0.963926	−	0.266172i	$-0.914241\pi$
$331$	−78059.4	−	135203.i	−0.712475	−	1.23404i	0.251451	−	0.967870i	$-0.419092\pi$
$332$	54466.2			0.494141
$333$	19673.0	+	22451.0i	0.177412	+	0.202464i
$334$	237383.			2.12793
$335$	20508.9	+	50183.3i	0.182748	+	0.447166i
$336$	158366.	+	26179.1i	1.40276	+	0.231887i
$337$	120915.	+	69810.3i	1.06468	+	0.614695i	0.926724	−	0.375743i	$-0.122612\pi$
$337$	120915.	+	69810.3i	1.06468	+	0.614695i	0.137959	+	0.990438i	$0.455946\pi$
$338$	−40456.0	+	70071.9i	−0.354119	+	0.613353i
$339$	−13766.2	+	83276.0i	−0.119788	+	0.724637i
$340$	55329.7	−	22612.1i	0.478631	−	0.195607i
$341$			212894.i			1.83086i
$342$	−10832.9	−	3682.13i	−0.0926170	−	0.0314809i
$343$			84381.8i			0.717234i
$344$	6694.84	−	3865.27i	0.0565749	−	0.0326635i
$345$	−151330.	+	140341.i	−1.27141	+	1.17909i
$346$	−14906.6	+	25819.0i	−0.124516	+	0.215668i
$347$	304.265	−	527.002i	0.00252693	−	0.00437677i	−0.864759	−	0.502187i	$-0.832529\pi$
$347$	304.265	−	527.002i	0.00252693	−	0.00437677i	0.867286	+	0.497810i	$0.165862\pi$
$348$	12875.4	+	34230.0i	0.106317	+	0.282650i
$349$	31381.4	+	54354.2i	0.257645	+	0.446254i	0.965611	−	0.259993i	$-0.0837202\pi$
$349$	31381.4	+	54354.2i	0.257645	+	0.446254i	−0.707966	+	0.706247i	$0.750387\pi$
$350$	50674.0	−	182202.i	0.413665	−	1.48736i
$351$	−70886.3	+	44020.5i	−0.575371	+	0.357307i
$352$			207856.i			1.67756i
$353$	−54482.8	−	94367.0i	−0.437230	−	0.757305i	0.560245	−	0.828327i	$-0.310707\pi$
$353$	−54482.8	−	94367.0i	−0.437230	−	0.757305i	−0.997475	+	0.0710225i	$0.977374\pi$
$354$	80591.8	+	214258.i	0.643109	+	1.70974i
$355$	139022.	−	179413.i	1.10313	−	1.42363i
$356$	−8469.93	−	4890.12i	−0.0668313	−	0.0385851i
$357$	69289.9	−	84395.3i	0.543667	−	0.662188i
$358$	129554.	−	74798.1i	1.01085	−	0.583613i
$359$			11414.0i			0.0885621i	0.999019	+	0.0442811i	$0.0140997\pi$
$359$			11414.0i			0.0885621i	−0.999019	+	0.0442811i	$0.985900\pi$
$360$	48741.0	−	2943.33i	0.376088	−	0.0227108i
$361$	−129593.			−0.994411
$362$	−89648.1	−	155275.i	−0.684107	−	1.18491i
$363$	20511.7	−	124082.i	0.155664	−	0.941661i
$364$	37695.8	−	65291.0i	0.284505	−	0.492777i
$365$	−15080.5	+	19461.9i	−0.113196	+	0.146083i
$366$	−7280.49	+	44042.0i	−0.0543499	+	0.328780i
$367$	−112351.	+	64865.6i	−0.834148	+	0.481595i	−0.855271	−	0.518182i	$-0.826609\pi$
$367$	−112351.	+	64865.6i	−0.834148	+	0.481595i	0.0211230	+	0.999777i	$0.493276\pi$
$368$	282972.			2.08953
$369$	145975.	−	28975.0i	1.07207	−	0.212799i
$370$	−47777.5	−	6520.21i	−0.348996	−	0.0476275i
$371$	95071.5	−	54889.5i	0.690721	−	0.398788i
$372$	99735.8	+	81884.7i	0.720718	+	0.591721i
$373$	49139.4	+	28370.6i	0.353193	+	0.203916i	0.666091	−	0.745871i	$-0.267966\pi$
$373$	49139.4	+	28370.6i	0.353193	+	0.203916i	−0.312898	+	0.949787i	$0.601300\pi$
$374$	160907.	+	92899.5i	1.15035	+	0.664156i
$375$	6624.48	−	140469.i	0.0471074	−	0.998890i
$376$	−29521.9	−	51133.4i	−0.208818	−	0.361684i
$377$	−40825.5			−0.287242
$378$	−187393.	+	116371.i	−1.31150	+	0.814445i
$379$	−98981.2			−0.689087			−0.344544	−	0.938770i	$-0.611966\pi$
$379$	−98981.2			−0.689087			−0.344544	+	0.938770i	$0.611966\pi$
$380$	7115.60	−	2908.00i	0.0492770	−	0.0201385i
$381$	−11546.3	−	30696.4i	−0.0795410	−	0.211465i
$382$	−322722.	−	186323.i	−2.21157	−	1.27685i
$383$	90868.5	−	157389.i	0.619464	−	1.07294i	−0.370120	−	0.928984i	$-0.620683\pi$
$383$	90868.5	−	157389.i	0.619464	−	1.07294i	0.989584	−	0.143959i	$-0.0459833\pi$
$384$	−82318.3	−	67584.6i	−0.558257	−	0.458338i
$385$	226324.	−	92494.0i	1.52690	−	0.624011i
$386$			321821.i			2.15993i
$387$	−8356.99	+	24586.3i	−0.0557992	+	0.164162i
$388$			48597.0i			0.322810i
$389$	141766.	−	81848.8i	0.936858	−	0.540895i	0.0478838	−	0.998853i	$-0.484752\pi$
$389$	141766.	−	81848.8i	0.936858	−	0.540895i	0.888974	+	0.457958i	$0.151419\pi$
$390$	39763.8	−	128792.i	0.261432	−	0.846761i
$391$	96250.3	−	166710.i	0.629577	−	1.09046i
$392$	−11350.9	+	19660.4i	−0.0738685	+	0.127944i
$393$	47646.2	+	7876.28i	0.308491	+	0.0509960i
$394$	37248.3	+	64515.9i	0.239946	+	0.415599i
$395$	34652.6	−	253920.i	0.222097	−	1.62743i
$396$	−102878.	−	117406.i	−0.656045	−	0.748684i
$397$		−	170885.i		−	1.08424i	−0.840302	−	0.542118i	$-0.817622\pi$
$397$		−	170885.i		−	1.08424i	0.840302	−	0.542118i	$-0.182378\pi$
$398$	153071.	+	265127.i	0.966332	+	1.67374i
$399$	8910.92	−	10853.5i	0.0559728	−	0.0681750i
$400$	−137619.	+	135038.i	−0.860116	+	0.843986i
$401$	−55371.9	−	31969.0i	−0.344350	−	0.198811i	0.317844	−	0.948143i	$-0.397041\pi$
$401$	−55371.9	−	31969.0i	−0.344350	−	0.198811i	−0.662194	+	0.749332i	$0.730375\pi$
$402$	35961.4	+	95605.6i	0.222528	+	0.591604i
$403$	−124755.	+	72027.3i	−0.768153	+	0.443493i
$404$		−	48818.4i		−	0.299103i
$405$	−116624.	+	115339.i	−0.711013	+	0.703179i
$406$	−107925.			−0.654741
$407$	−31170.2	−	53988.3i	−0.188170	−	0.325920i
$408$	−42628.1	+	16034.3i	−0.256080	+	0.0963227i
$409$	−22555.8	+	39067.7i	−0.134838	+	0.233546i	−0.925535	−	0.378661i	$-0.876385\pi$
$409$	−22555.8	+	39067.7i	−0.134838	+	0.233546i	0.790698	+	0.612207i	$0.209718\pi$
$410$	−147250.	+	190030.i	−0.875964	+	1.13046i
$411$	−17004.4	−	13960.9i	−0.100665	−	0.0826474i
$412$	103333.	−	59659.1i	0.608755	−	0.351465i
$413$	−280961.			−1.64720
$414$	−292473.	+	256283.i	−1.70641	+	1.49527i
$415$	−16161.0	+	118422.i	−0.0938368	+	0.687599i
$416$	−121803.	+	70323.0i	−0.703835	+	0.406360i
$417$	−22029.5	+	133264.i	−0.126687	+	0.766372i
$418$	20693.2	+	11947.2i	0.118433	+	0.0683776i
$419$	−107823.	−	62251.4i	−0.614160	−	0.354585i	0.160432	−	0.987047i	$-0.448711\pi$
$419$	−107823.	−	62251.4i	−0.614160	−	0.354585i	−0.774592	+	0.632461i	$0.782045\pi$
$420$	43719.1	−	141603.i	0.247840	−	0.802740i
$421$	91249.6	+	158049.i	0.514834	+	0.891718i	0.999852	+	0.0172140i	$0.00547966\pi$
$421$	91249.6	+	158049.i	0.514834	+	0.891718i	−0.485018	+	0.874504i	$0.661187\pi$
$422$	−174456.			−0.979627
$423$	187784.	+	63828.5i	1.04949	+	0.356725i
$424$	−45787.4			−0.254691
$425$	32746.6	+	127009.i	0.181296	+	0.703162i
$426$	271367.	−	330526.i	1.49533	−	1.82132i
$427$	−47448.8	−	27394.6i	−0.260237	−	0.150248i
$428$	−101803.	+	176329.i	−0.555744	+	0.962577i
$429$	163104.	−	61350.5i	0.886238	−	0.333352i
$430$	−15869.1	−	38830.2i	−0.0858253	−	0.210006i
$431$		−	52320.0i		−	0.281652i	−0.990034	−	0.140826i	$-0.955024\pi$
$431$		−	52320.0i		−	0.281652i	0.990034	−	0.140826i	$-0.0449758\pi$
$432$	224773.	−	7222.21i	1.20441	−	0.0386992i
$433$		−	342116.i		−	1.82473i	−0.409383	−	0.912363i	$-0.634256\pi$
$433$		−	342116.i		−	1.82473i	0.409383	−	0.912363i	$-0.365744\pi$
$434$	−329798.	+	190409.i	−1.75093	+	1.01090i
$435$	−78244.0	+	17837.3i	−0.413497	+	0.0942652i
$436$	84526.5	−	146404.i	0.444652	−	0.770159i
$437$	12378.1	−	21439.6i	0.0648175	−	0.112267i
$438$	−29436.7	+	35854.0i	−0.153441	+	0.186892i
$439$	130466.	+	225974.i	0.676970	+	1.17255i	0.975889	+	0.218268i	$0.0700406\pi$
$439$	130466.	+	225974.i	0.676970	+	1.17255i	−0.298919	+	0.954278i	$0.596626\pi$
$440$	−101039.	−	13788.8i	−0.521896	−	0.0712233i
$441$	−14847.1	−	74799.0i	−0.0763422	−	0.384608i
$442$			125721.i			0.643521i
$443$	93230.8	+	161480.i	0.475064	+	0.822835i	0.999592	−	0.0285583i	$-0.00909164\pi$
$443$	93230.8	+	161480.i	0.475064	+	0.822835i	−0.524528	+	0.851393i	$0.675758\pi$
$444$	−37281.2	−	6162.87i	−0.189114	−	0.0312620i
$445$	13145.4	−	16964.6i	0.0663825	−	0.0856688i
$446$	−210618.	−	121600.i	−1.05883	−	0.611316i
$447$	112090.	+	18529.3i	0.560986	+	0.0927353i
$448$	−74865.2	+	43223.4i	−0.373013	+	0.215359i
$449$		−	65910.0i		−	0.326933i	−0.986549	−	0.163466i	$-0.947732\pi$
$449$		−	65910.0i		−	0.326933i	0.986549	−	0.163466i	$-0.0522675\pi$
$450$	19937.7	−	264210.i	0.0984576	−	1.30474i
$451$	−310799.			−1.52801
$452$	−53423.3	−	92531.8i	−0.261489	−	0.452912i
$453$	161951.	+	132964.i	0.789200	+	0.647946i
$454$	67891.1	−	117591.i	0.329383	−	0.570508i
$455$	130772.	+	101332.i	0.631674	+	0.489467i
$456$	−5482.12	+	2062.06i	−0.0263645	+	0.00991682i
$457$	−143662.	+	82943.1i	−0.687874	+	0.397144i	−0.802815	−	0.596228i	$-0.796665\pi$
$457$	−143662.	+	82943.1i	−0.687874	+	0.397144i	0.114941	+	0.993372i	$0.463332\pi$
$458$	−126641.			−0.603733
$459$	72199.5	−	134879.i	0.342696	−	0.640207i
$460$	35326.7	−	258860.i	0.166950	−	1.22335i
$461$	−21859.7	+	12620.7i	−0.102859	+	0.0593857i	−0.550547	−	0.834804i	$-0.685581\pi$
$461$	−21859.7	+	12620.7i	−0.102859	+	0.0593857i	0.447688	+	0.894190i	$0.352248\pi$
$462$	431177.	−	162184.i	2.02009	−	0.759844i
$463$	−88939.9	−	51349.5i	−0.414892	−	0.239538i	0.277998	−	0.960582i	$-0.410329\pi$
$463$	−88939.9	−	51349.5i	−0.414892	−	0.239538i	−0.692889	+	0.721044i	$0.743663\pi$
$464$	95288.7	+	55014.9i	0.442594	+	0.255532i
$465$	−207629.	+	192551.i	−0.960246	+	0.890514i
$466$	156499.	+	271063.i	0.720673	+	1.24824i
$467$	88039.3			0.403685			0.201843	−	0.979418i	$-0.435307\pi$
$467$	88039.3			0.403685			0.201843	+	0.979418i	$0.435307\pi$
$468$	33993.0	−	100008.i	0.155202	−	0.456605i
$469$	−125369.			−0.569961
$470$	−296574.	+	121204.i	−1.34257	+	0.548682i
$471$	151752.	+	25085.8i	0.684057	+	0.113080i
$472$	101485.	+	58592.5i	0.455531	+	0.263001i
$473$	27115.5	−	46965.4i	0.121198	−	0.209921i
$474$	78752.4	−	476399.i	0.350516	−	2.12038i
$475$	4211.32	+	16333.8i	0.0186651	+	0.0723934i
$476$			138226.i			0.610066i
$477$	115678.	−	101364.i	0.508409	−	0.445501i
$478$		−	389060.i		−	1.70279i
$479$	241773.	−	139588.i	1.05375	−	0.608383i	0.130053	−	0.991507i	$-0.458485\pi$
$479$	241773.	−	139588.i	1.05375	−	0.608383i	0.923697	+	0.383124i	$0.125152\pi$
$480$	−202716.	+	187995.i	−0.879844	+	0.815951i
$481$	21091.3	−	36531.2i	0.0911618	−	0.157897i
$482$	145540.	−	252082.i	0.626452	−	1.08505i
$483$	−168034.	−	446729.i	−0.720283	−	1.91492i
$484$	79601.0	+	137873.i	0.339803	+	0.588557i
$485$	−105661.	−	14419.6i	−0.449191	−	0.0613012i
$486$	−225778.	+	211038.i	−0.955893	+	0.893485i
$487$			250438.i			1.05595i	0.849261	+	0.527974i	$0.177048\pi$
$487$			250438.i			1.05595i	−0.849261	+	0.527974i	$0.822952\pi$
$488$	11425.9	+	19790.2i	0.0479790	+	0.0831020i
$489$	82422.3	+	219125.i	0.344689	+	0.916377i
$490$	97373.7	+	75452.4i	0.405555	+	0.314254i
$491$	−69322.6	−	40023.4i	−0.287549	−	0.166016i	0.349287	−	0.937016i	$-0.386424\pi$
$491$	−69322.6	−	40023.4i	−0.287549	−	0.166016i	−0.636836	+	0.770999i	$0.719757\pi$
$492$	−119542.	+	145602.i	−0.493844	+	0.601503i
$493$	64823.1	−	37425.7i	0.266708	−	0.153984i
$494$			16168.1i			0.0662531i
$495$	285792.	−	188844.i	1.16638	−	0.770714i
$496$	388246.			1.57813
$497$	262443.	+	454565.i	1.06248	+	1.84028i
$498$	−36728.0	+	222180.i	−0.148094	+	0.895871i
$499$	21430.3	−	37118.4i	0.0860652	−	0.149069i	−0.819779	−	0.572679i	$-0.805904\pi$
$499$	21430.3	−	37118.4i	0.0860652	−	0.149069i	0.905845	+	0.423610i	$0.139237\pi$
$500$	106351.	+	142751.i	0.425403	+	0.571002i
$501$	−66575.4	+	402736.i	−0.265240	+	1.60452i
$502$	143826.	−	83038.2i	0.570731	−	0.329512i
$503$	−189896.			−0.750549			−0.375274	−	0.926914i	$-0.622452\pi$
$503$	−189896.			−0.750549			−0.375274	+	0.926914i	$0.622452\pi$
$504$	−36340.6	+	106914.i	−0.143064	+	0.420896i
$505$	106142.	+	14485.3i	0.416203	+	0.0567993i
$506$	703313.	−	406058.i	2.74693	−	1.58594i
$507$	−107535.	−	88288.3i	−0.418346	−	0.343469i
$508$	35953.4	+	20757.7i	0.139320	+	0.0804362i
$509$	−18105.6	−	10453.2i	−0.0698838	−	0.0403474i	0.464651	−	0.885494i	$-0.346180\pi$
$509$	−18105.6	−	10453.2i	−0.0698838	−	0.0403474i	−0.534535	+	0.845147i	$0.679513\pi$
$510$	54929.6	+	240950.i	0.211186	+	0.926375i
$511$	−28468.7	−	49309.2i	−0.109025	−	0.188837i
$512$	260039.			0.991970
$513$	9285.11	−	17346.0i	0.0352819	−	0.0659119i
$514$	−227783.			−0.862174
$515$	99051.7	+	242370.i	0.373463	+	0.913828i
$516$	−11572.8	−	30767.1i	−0.0434651	−	0.115555i
$517$	−358709.	−	207101.i	−1.34203	−	0.774819i
$518$	55756.2	−	96572.7i	0.207794	−	0.359911i
$519$	−39622.9	−	32531.0i	−0.147100	−	0.120771i
$520$	−26103.8	−	63873.6i	−0.0965378	−	0.236219i
$521$		−	54650.3i		−	0.201334i	−0.994920	−	0.100667i	$-0.967902\pi$
$521$		−	54650.3i		−	0.201334i	0.994920	−	0.100667i	$-0.0320977\pi$
$522$	−148314.	+	29439.3i	−0.544304	+	0.108041i
$523$			543509.i			1.98703i	0.113723	+	0.993513i	$0.463722\pi$
$523$			543509.i			1.98703i	−0.113723	+	0.993513i	$0.536278\pi$
$524$	−52941.8	+	30566.0i	−0.192813	+	0.111321i
$525$	294905.	+	137071.i	1.06995	+	0.497310i
$526$	−105847.	+	183332.i	−0.382565	+	0.662622i
$527$	132058.	−	228732.i	0.475493	−	0.823578i
$528$	−463367.	−	76598.1i	−1.66210	−	0.274758i
$529$	−280784.	−	486331.i	−1.00337	−	1.73788i
$530$	−33595.1	+	246171.i	−0.119598	+	0.876366i
$531$	−386106.	+	76639.3i	−1.36936	+	0.271808i
$532$			17776.4i			0.0628088i
$533$	−105151.	−	182127.i	−0.370135	−	0.641092i
$534$	25659.4	−	31253.2i	0.0899837	−	0.109600i
$535$	−353171.	−	273663.i	−1.23389	−	0.956112i
$536$	45284.3	+	26144.9i	0.157623	+	0.0910034i
$537$	90565.7	+	240775.i	0.314062	+	0.834953i
$538$	−76945.1	+	44424.3i	−0.265838	+	0.153481i
$539$			159257.i			0.548178i
$540$	21454.2	−	206522.i	0.0735741	−	0.708236i
$541$	−17290.1			−0.0590748			−0.0295374	−	0.999564i	$-0.509403\pi$
$541$	−17290.1			−0.0590748			−0.0295374	+	0.999564i	$0.509403\pi$
$542$	−208880.	−	361791.i	−0.711047	−	1.23157i
$543$	288576.	−	108546.i	0.978726	−	0.368141i
$544$	128933.	−	223319.i	0.435680	−	0.754620i
$545$	293235.	+	227220.i	0.987240	+	0.764987i
$546$	240917.	+	197797.i	0.808132	+	0.663490i
$547$	70540.3	−	40726.4i	0.235756	−	0.136114i	−0.377469	−	0.926022i	$-0.623205\pi$
$547$	70540.3	−	40726.4i	0.235756	−	0.136114i	0.613225	+	0.789909i	$0.289872\pi$
$548$	27850.6			0.0927412
$549$	−72678.3	−	24703.6i	−0.241135	−	0.0819627i
$550$	−148268.	+	533109.i	−0.490144	+	1.76234i
$551$	8336.48	−	4813.07i	0.0274587	−	0.0158533i
$552$	−32467.2	+	196404.i	−0.106553	+	0.644574i
$553$	513249.	+	296325.i	1.67833	+	0.968986i
$554$	−401662.	−	231900.i	−1.30870	−	0.755581i
$555$	24461.4	−	79229.0i	0.0794137	−	0.257216i
$556$	−85491.3	−	148075.i	−0.276549	−	0.478997i
$557$	−449197.			−1.44786			−0.723930	−	0.689873i	$-0.757666\pi$
$557$	−449197.			−1.44786			−0.723930	+	0.689873i	$0.757666\pi$
$558$	−401281.	+	351628.i	−1.28878	+	1.12931i
$559$	36695.4			0.117432
$560$	−168677.	−	412738.i	−0.537875	−	1.31613i
$561$	−202737.	+	246934.i	−0.644180	+	0.784613i
$562$	332379.	+	191899.i	1.05235	+	0.607575i
$563$	122509.	−	212192.i	0.386501	−	0.669440i	−0.605475	−	0.795864i	$-0.707017\pi$
$563$	122509.	−	212192.i	0.386501	−	0.669440i	0.991976	+	0.126424i	$0.0403501\pi$
$564$	−234991.	+	88390.3i	−0.738742	+	0.277873i
$565$	217037.	−	88698.4i	0.679886	−	0.277855i
$566$		−	307966.i		−	0.961325i
$567$	−144876.	−	350561.i	−0.450641	−	1.09043i
$568$		−	218923.i		−	0.678570i
$569$	−92989.2	+	53687.3i	−0.287216	+	0.165824i	−0.636685	−	0.771124i	$-0.719695\pi$
$569$	−92989.2	+	53687.3i	−0.287216	+	0.165824i	0.349470	+	0.936948i	$0.386362\pi$
$570$	7064.14	+	30987.1i	0.0217425	+	0.0953741i
$571$	−153839.	+	266458.i	−0.471841	+	0.817252i	−0.999481	−	0.0322159i	$-0.989744\pi$
$571$	−153839.	+	266458.i	−0.471841	+	0.817252i	0.527640	+	0.849468i	$0.323077\pi$
$572$	−110295.	+	191037.i	−0.337104	+	0.583881i
$573$	406619.	−	495263.i	1.23845	−	1.50843i
$574$	−277974.	−	481465.i	−0.843686	−	1.46131i
$575$	552338.	+	153616.i	1.67059	+	0.464624i
$576$	−91092.0	+	79820.6i	−0.274559	+	0.240586i
$577$		−	310091.i		−	0.931404i	−0.884942	−	0.465702i	$-0.845802\pi$
$577$		−	310091.i		−	0.931404i	0.884942	−	0.465702i	$-0.154198\pi$
$578$	103315.	+	178947.i	0.309249	+	0.535636i
$579$	−545990.	−	90256.3i	−1.62865	−	0.269228i
$580$	62223.1	−	80301.0i	0.184968	−	0.238707i
$581$	−239366.	−	138198.i	−0.709104	−	0.409401i
$582$	−198238.	−	32770.3i	−0.585250	−	0.0967463i
$583$	−278172.	+	160603.i	−0.818421	+	0.472515i
$584$			23747.8i			0.0696302i
$585$	207353.	+	103582.i	0.605895	+	0.302673i
$586$	530008.			1.54343
$587$	33542.3	+	58097.0i	0.0973456	+	0.168608i	0.910585	−	0.413322i	$-0.135631\pi$
$587$	33542.3	+	58097.0i	0.0973456	+	0.168608i	−0.813240	+	0.581929i	$0.802298\pi$
$588$	74608.3	+	61254.6i	0.215790	+	0.177167i
$589$	16983.2	−	29415.7i	0.0489539	−	0.0847907i
$590$	389478.	−	502634.i	1.11887	−	1.44394i
$591$	−119902.	+	45100.2i	−0.343282	+	0.129123i
$592$	−98456.2	+	56843.7i	−0.280931	+	0.162196i
$593$	82855.9			0.235621			0.117810	−	0.993036i	$-0.462412\pi$
$593$	82855.9			0.235621			0.117810	+	0.993036i	$0.462412\pi$
$594$	548298.	−	340494.i	1.55397	−	0.965020i
$595$	−300535.	−	41014.1i	−0.848909	−	0.115851i
$596$	−124548.	+	71908.0i	−0.350627	+	0.202435i
$597$	−492734.	+	185338.i	−1.38250	+	0.520016i
$598$	475896.	+	274759.i	1.33079	+	0.768333i
$599$	−11075.7	−	6394.54i	−0.0308685	−	0.0178220i	0.484486	−	0.874799i	$-0.339007\pi$
$599$	−11075.7	−	6394.54i	−0.0308685	−	0.0178220i	−0.515355	+	0.856977i	$0.672340\pi$
$600$	−77936.7	−	111012.i	−0.216491	−	0.308366i
$601$	260678.	+	451507.i	0.721698	+	1.25002i	0.960319	+	0.278904i	$0.0899712\pi$
$601$	260678.	+	451507.i	0.721698	+	1.25002i	−0.238621	+	0.971113i	$0.576695\pi$
$602$	97006.6			0.267675
$603$	−172287.	+	34197.7i	−0.473824	+	0.0940508i
$604$	−265250.			−0.727080
$605$	−323386.	+	132161.i	−0.883507	+	0.361071i
$606$	199141.	+	32919.6i	0.542270	+	0.0896415i
$607$	125226.	+	72299.3i	0.339874	+	0.196226i	0.660216	−	0.751076i	$-0.270465\pi$
$607$	125226.	+	72299.3i	0.339874	+	0.196226i	−0.320343	+	0.947302i	$0.603798\pi$
$608$	16581.3	−	28719.6i	0.0448550	−	0.0776912i
$609$	30268.1	−	183102.i	0.0816114	−	0.493693i
$610$	114784.	−	46909.7i	0.308475	−	0.126068i
$611$		−	280269.i		−	0.750746i
$612$	37704.8	+	189955.i	0.100669	+	0.507164i
$613$			39623.7i			0.105447i	0.998609	+	0.0527235i	$0.0167902\pi$
$613$			39623.7i			0.105447i	−0.998609	+	0.0527235i	$0.983210\pi$
$614$	197144.	−	113821.i	0.522935	−	0.301917i
$615$	−281102.	−	303113.i	−0.743213	−	0.801410i
$616$	117912.	−	204230.i	0.310740	−	0.538218i
$617$	−81457.2	+	141088.i	−0.213973	+	0.370612i	−0.952954	−	0.303114i	$-0.901974\pi$
$617$	−81457.2	+	141088.i	−0.213973	+	0.370612i	0.738981	+	0.673726i	$0.235307\pi$
$618$	173683.	+	461746.i	0.454757	+	1.20900i
$619$	139987.	+	242465.i	0.365348	+	0.632801i	0.988832	−	0.149035i	$-0.0476168\pi$
$619$	139987.	+	242465.i	0.365348	+	0.632801i	−0.623484	+	0.781836i	$0.714283\pi$
$620$	48469.3	−	355163.i	0.126091	−	0.923942i
$621$	−352775.	−	568074.i	−0.914776	−	1.47307i
$622$			397122.i			1.02646i
$623$	24815.5	+	42981.8i	0.0639363	+	0.110741i
$624$	−111882.	−	297446.i	−0.287338	−	0.763905i
$625$	−341928.	+	188874.i	−0.875335	+	0.483517i
$626$	−305740.	−	176519.i	−0.780196	−	0.450447i
$627$	−26072.7	+	31756.6i	−0.0663210	+	0.0807791i
$628$	−168618.	+	97351.9i	−0.427549	+	0.246845i
$629$			77339.5i			0.195479i
$630$	548150.	+	273827.i	1.38108	+	0.689914i
$631$	521595.			1.31001			0.655005	−	0.755624i	$-0.272666\pi$
$631$	521595.			1.31001			0.655005	+	0.755624i	$0.272666\pi$
$632$	−123593.	−	214069.i	−0.309428	−	0.535945i
$633$	48927.1	−	295976.i	0.122107	−	0.738667i
$634$	−474054.	+	821085.i	−1.17937	+	2.04272i
$635$	−55799.8	+	72011.5i	−0.138384	+	0.178589i
$636$	−31753.9	+	192089.i	−0.0785023	+	0.474886i
$637$	−93324.0	+	53880.7i	−0.229993	+	0.132787i
$638$	315780.			0.775789
$639$	484652.	+	553090.i	1.18694	+	1.35455i
$640$	−40004.8	+	293139.i	−0.0976679	+	0.715671i
$641$	−69970.9	+	40397.7i	−0.170295	+	0.0983197i	−0.582725	−	0.812670i	$-0.698013\pi$
$641$	−69970.9	+	40397.7i	−0.170295	+	0.0983197i	0.412430	+	0.910989i	$0.364680\pi$
$642$	−650635.	−	534182.i	−1.57858	−	1.29604i
$643$	−163613.	−	94462.0i	−0.395727	−	0.228473i	0.288911	−	0.957356i	$-0.406707\pi$
$643$	−163613.	−	94462.0i	−0.395727	−	0.228473i	−0.684639	+	0.728883i	$0.740040\pi$
$644$	523234.	+	302089.i	1.26161	+	0.728389i
$645$	70328.5	−	16032.8i	0.169049	−	0.0385381i
$646$	−14821.7	−	25672.0i	−0.0355168	−	0.0615168i
$647$	315560.			0.753829			0.376915	−	0.926248i	$-0.376985\pi$
$647$	315560.			0.753829			0.376915	+	0.926248i	$0.376985\pi$
$648$	−20776.8	+	156838.i	−0.0494799	+	0.373510i
$649$	822070.			1.95173
$650$	−362563.	+	93479.3i	−0.858136	+	0.221253i
$651$	−230548.	−	612925.i	−0.544000	−	1.44626i
$652$	−256651.	−	148178.i	−0.603738	−	0.348568i
$653$	−252626.	+	437561.i	−0.592450	+	1.02615i	0.401452	+	0.915880i	$0.368506\pi$
$653$	−252626.	+	437561.i	−0.592450	+	1.02615i	−0.993901	+	0.110273i	$0.964828\pi$
$654$	540217.	+	443527.i	1.26303	+	1.03697i
$655$	−50748.6	−	124177.i	−0.118288	−	0.289440i
$656$			566792.i			1.31709i
$657$	−52573.0	−	59996.8i	−0.121796	−	0.138994i
$658$		−	740911.i		−	1.71125i
$659$	−667937.	+	385634.i	−1.53803	+	0.887982i	−0.539076	+	0.842257i	$0.681226\pi$
$659$	−667937.	+	385634.i	−1.53803	+	0.887982i	−0.998954	+	0.0457248i	$0.985440\pi$
$660$	−127919.	+	414321.i	−0.293661	+	0.951150i
$661$	28063.6	−	48607.6i	0.0642304	−	0.111250i	−0.832122	−	0.554593i	$-0.812874\pi$
$661$	28063.6	−	48607.6i	0.0642304	−	0.111250i	0.896352	+	0.443342i	$0.146207\pi$
$662$	−408548.	+	707626.i	−0.932239	+	1.61469i
$663$	−213294.	−	35259.1i	−0.485233	−	0.0802129i
$664$	57640.5	+	99836.2i	0.130735	+	0.226439i
$665$	−38649.9	−	5274.56i	−0.0873986	−	0.0119273i
$666$	50279.4	−	147922.i	0.113355	−	0.333492i
$667$		−	327170.i		−	0.735398i
$668$	−258363.	−	447499.i	−0.579000	−	1.00286i
$669$	265372.	−	323224.i	0.592929	−	0.722190i
$670$	173791.	−	224284.i	0.387150	−	0.499629i
$671$	138832.	+	80154.5i	0.308350	+	0.178026i
$672$	−225092.	−	598422.i	−0.498450	−	1.32516i
$673$	−457732.	+	264271.i	−1.01060	+	0.583472i	−0.911368	−	0.411592i	$-0.864973\pi$
$673$	−457732.	+	264271.i	−1.01060	+	0.583472i	−0.0992350	+	0.995064i	$0.531640\pi$
$674$		−	730747.i		−	1.60860i
$675$	442658.	+	107925.i	0.971541	+	0.236872i
$676$	176126.			0.385417
$677$	226733.	+	392712.i	0.494694	+	0.856835i	0.999981	−	0.00611624i	$-0.00194687\pi$
$677$	226733.	+	392712.i	0.494694	+	0.856835i	−0.505287	+	0.862951i	$0.668614\pi$
$678$	413483.	−	155529.i	0.899493	−	0.338338i
$679$	123306.	−	213572.i	0.267451	−	0.463239i
$680$	100002.	+	77489.2i	0.216268	+	0.167580i
$681$	180460.	+	148161.i	0.389123	+	0.319476i
$682$	964965.	−	557123.i	2.07464	−	1.19779i
$683$	210879.			0.452055			0.226027	−	0.974121i	$-0.427426\pi$
$683$	210879.			0.452055			0.226027	+	0.974121i	$0.427426\pi$
$684$	4848.97	+	24428.9i	0.0103642	+	0.0522146i
$685$	−8263.74	+	60553.4i	−0.0176115	+	0.129050i
$686$	382470.	−	220819.i	0.812735	−	0.469233i
$687$	35517.3	−	214855.i	0.0752534	−	0.455232i
$688$	−85648.8	−	49449.3i	−0.180944	−	0.104468i
$689$	−188225.	−	108672.i	−0.396496	−	0.228917i
$690$	1.03213e6	+	318662.i	2.16788	+	0.669317i
$691$	12289.0	+	21285.1i	0.0257371	+	0.0445780i	0.878607	−	0.477545i	$-0.158473\pi$
$691$	12289.0	+	21285.1i	0.0257371	+	0.0445780i	−0.852870	+	0.522123i	$0.825140\pi$
$692$	64896.2			0.135521
$693$	154230.	+	777004.i	0.321146	+	1.61792i
$694$	−3184.93			−0.00661273
$695$	347316.	−	141941.i	0.719043	−	0.293858i
$696$	−49117.7	+	59825.4i	−0.101396	+	0.123500i
$697$	333920.	+	192789.i	0.687349	+	0.396841i
$698$	164244.	−	284479.i	0.337116	−	0.583902i
$699$	−503767.	+	189489.i	−1.03104	+	0.387819i
$700$	−398627.	+	102778.i	−0.813524	+	0.209750i
$701$			349841.i			0.711925i	0.934500	+	0.355963i	$0.115847\pi$
$701$			349841.i			0.711925i	−0.934500	+	0.355963i	$0.884153\pi$
$702$	385031.	+	206103.i	0.781306	+	0.418224i
$703$			9946.13i			0.0201254i
$704$	219050.	−	126469.i	0.441975	−	0.255175i
$705$	−122454.	−	537150.i	−0.246375	−	1.08073i
$706$	−285153.	+	493899.i	−0.572095	+	0.990897i
$707$	−123868.	+	214545.i	−0.247810	+	0.429220i
$708$	316190.	−	385121.i	0.630786	−	0.768299i
$709$	−94271.7	−	163283.i	−0.187538	−	0.324825i	0.756891	−	0.653541i	$-0.226717\pi$
$709$	−94271.7	−	163283.i	−0.187538	−	0.324825i	−0.944429	+	0.328716i	$0.893384\pi$
$710$	−1.17702e6	−	160628.i	−2.33489	−	0.318643i
$711$	786155.	+	267217.i	1.55514	+	0.528598i
$712$		−	20700.5i		−	0.0408338i
$713$	−577218.	−	999771.i	−1.13543	−	1.96662i
$714$	−563856.	−	93209.8i	−1.10604	−	0.182837i
$715$	−382630.	−	296490.i	−0.748457	−	0.579960i
$716$	−282008.	−	162818.i	−0.550093	−	0.317596i
$717$	660066.	+	109114.i	1.28395	+	0.212247i
$718$	51735.1	−	29869.3i	0.100354	−	0.0579396i
$719$			570498.i			1.10356i	0.833989	+	0.551781i	$0.186051\pi$
$719$			570498.i			1.10356i	−0.833989	+	0.551781i	$0.813949\pi$
$720$	−344387.	−	521187.i	−0.664327	−	1.00538i
$721$	−605496.			−1.16477
$722$	339131.	+	587393.i	0.650569	+	1.12682i
$723$	386856.	+	317615.i	0.740071	+	0.607610i
$724$	−195143.	+	337997.i	−0.372284	+	0.644815i
$725$	156130.	+	159114.i	0.297036	+	0.302713i
$726$	−616091.	+	231739.i	−1.16889	+	0.439668i
$727$	309462.	−	178668.i	0.585515	−	0.338047i	−0.177807	−	0.984065i	$-0.556900\pi$
$727$	309462.	−	178668.i	0.585515	−	0.338047i	0.763322	+	0.646018i	$0.223567\pi$
$728$	159571.			0.301086
$729$	−294718.	−	442234.i	−0.554564	−	0.832141i
$730$	127678.	+	17424.2i	0.239590	+	0.0326970i
$731$	−58265.3	+	33639.5i	−0.109037	+	0.0629527i
$732$	90948.9	−	34209.8i	0.169737	−	0.0638452i
$733$	−310569.	−	179307.i	−0.578029	−	0.333725i	0.182321	−	0.983239i	$-0.441639\pi$
$733$	−310569.	−	179307.i	−0.578029	−	0.333725i	−0.760350	+	0.649514i	$0.774972\pi$
$734$	588021.	+	339494.i	1.09144	+	0.630144i
$735$	−155319.	+	144040.i	−0.287508	+	0.266629i
$736$	−563560.	−	976114.i	−1.04036	−	1.80196i
$737$	366821.			0.675335
$738$	−513334.	−	585821.i	−0.942512	−	1.07560i
$739$	−121677.			−0.222802			−0.111401	−	0.993776i	$-0.535534\pi$
$739$	−121677.			−0.222802			−0.111401	+	0.993776i	$0.535534\pi$
$740$	39708.7	+	97163.3i	0.0725140	+	0.177435i
$741$	−27430.3	−	4534.44i	−0.0499568	−	0.00825824i
$742$	−497586.	−	287281.i	−0.903775	−	0.521795i
$743$	−336425.	+	582705.i	−0.609411	+	1.05553i	0.381927	+	0.924193i	$0.375261\pi$
$743$	−336425.	+	582705.i	−0.609411	+	1.05553i	−0.991338	+	0.131338i	$0.958073\pi$
$744$	−44545.9	+	269472.i	−0.0804751	+	0.486820i
$745$	−119388.	−	292132.i	−0.215105	−	0.526341i
$746$		−	296973.i		−	0.533628i
$747$	−366642.	−	124623.i	−0.657053	−	0.223335i
$748$		−	404440.i		−	0.722855i
$749$	894803.	−	516615.i	1.59501	−	0.920880i
$750$	−654026.	+	337567.i	−1.16271	+	0.600120i
$751$	−75730.1	+	131168.i	−0.134273	+	0.232568i	−0.925319	−	0.379188i	$-0.876203\pi$
$751$	−75730.1	+	131168.i	−0.134273	+	0.232568i	0.791047	+	0.611756i	$0.209537\pi$
$752$	−377681.	+	654162.i	−0.667866	+	1.15678i
$753$	100543.	+	267299.i	0.177321	+	0.471420i
$754$	106836.	+	185046.i	0.187921	+	0.325489i
$755$	78704.3	−	576714.i	0.138072	−	1.01173i
$756$	423330.	+	226604.i	0.740688	+	0.396482i
$757$		−	667098.i		−	1.16412i	−0.813146	−	0.582060i	$-0.802247\pi$
$757$		−	667098.i		−	1.16412i	0.813146	−	0.582060i	$-0.197753\pi$
$758$	259024.	+	448643.i	0.450819	+	0.780841i
$759$	491655.	+	1.30710e6i	0.853448	+	2.26895i
$760$	12860.6	+	9965.38i	0.0222657	+	0.0172531i
$761$	93560.3	+	54017.1i	0.161556	+	0.0932742i	0.578598	−	0.815613i	$-0.303600\pi$
$761$	93560.3	+	54017.1i	0.161556	+	0.0932742i	−0.417042	+	0.908887i	$0.636933\pi$
$762$	−108920.	+	132664.i	−0.187584	+	0.228478i
$763$	−742947.	+	428941.i	−1.27617	+	0.736798i
$764$			811163.i			1.38970i
$765$	−424193.	+	25615.8i	−0.724837	+	0.0437708i
$766$	−951177.			−1.62108
$767$	278127.	+	481730.i	0.472773	+	0.818866i
$768$	−126033.	+	762414.i	−0.213679	+	1.29261i
$769$	341156.	−	590900.i	0.576900	−	0.999220i	−0.418932	−	0.908017i	$-0.637596\pi$
$769$	341156.	−	590900.i	0.576900	−	0.999220i	0.995832	−	0.0912025i	$-0.0290711\pi$
$770$	−1.01151e6	−	783791.i	−1.70603	−	1.32196i
$771$	63882.9	−	386448.i	0.107467	−	0.650104i
$772$	606674.	−	350263.i	1.01794	−	0.587706i
$773$	70204.3			0.117491			0.0587455	−	0.998273i	$-0.481290\pi$
$773$	70204.3			0.117491			0.0587455	+	0.998273i	$0.481290\pi$
$774$	133310.	−	26461.1i	0.222526	−	0.0441698i
$775$	757823.	+	210766.i	1.26172	+	0.350911i
$776$	−89078.1	+	51429.3i	−0.147927	+	0.0854057i
$777$	148205.	+	121678.i	0.245482	+	0.201545i
$778$	−741977.	−	428381.i	−1.22583	−	0.707735i
$779$	42943.3	+	24793.3i	0.0707654	+	0.0408564i
$780$	−286069.	+	65215.2i	−0.470198	+	0.107191i
$781$	−767889.	−	1.33002e6i	−1.25891	−	2.18050i
$782$	−1.00751e6			−1.64754
$783$	−8350.27	−	259881.i	−0.0136200	−	0.423887i
$784$	290431.			0.472509
$785$	−161633.	−	395500.i	−0.262295	−	0.641811i
$786$	−88985.3	−	236573.i	−0.144037	−	0.382931i
$787$	1.02067e6	+	589282.i	1.64791	+	0.951423i	0.977900	+	0.209072i	$0.0670444\pi$
$787$	1.02067e6	+	589282.i	1.64791	+	0.951423i	0.670012	+	0.742350i	$0.266289\pi$
$788$	81080.6	−	140436.i	0.130576	−	0.226165i
$789$	−281349.	−	230992.i	−0.451951	−	0.371059i
$790$	−1.24161e6	+	507419.i	−1.98943	+	0.813041i
$791$			542207.i			0.866587i
$792$	106330.	−	312824.i	0.169514	−	0.498711i
$793$			108473.i			0.172495i
$794$	−774557.	+	447191.i	−1.22861	+	0.709336i
$795$	−408223.	−	126036.i	−0.645898	−	0.199417i
$796$	333199.	−	577117.i	0.525869	−	0.910831i
$797$	259145.	−	448852.i	0.407968	−	0.706622i	−0.586694	−	0.809809i	$-0.699571\pi$
$797$	259145.	−	448852.i	0.407968	−	0.706622i	0.994662	+	0.103187i	$0.0329041\pi$
$798$	−72513.8	−	11987.1i	−0.113872	−	0.0188239i
$799$	256929.	+	445015.i	0.402458	+	0.697077i
$800$	739891.	+	205779.i	1.15608	+	0.321530i
$801$	45826.8	+	52297.9i	0.0714257	+	0.0815116i
$802$			334639.i			0.520269i
$803$	83297.2	+	144275.i	0.129181	+	0.223749i
$804$	141089.	−	171847.i	0.218264	−	0.265846i
$805$	−812062.	+	1.04799e6i	−1.25313	+	1.61721i
$806$	652944.	+	376977.i	1.00509	+	0.580290i
$807$	−53789.0	−	143001.i	−0.0825936	−	0.219580i
$808$	89483.9	−	51663.5i	0.137064	−	0.0791337i
$809$		−	1.25627e6i		−	1.91948i	−0.280881	−	0.959742i	$-0.590627\pi$
$809$		−	1.25627e6i		−	1.91948i	0.280881	−	0.959742i	$-0.409373\pi$
$810$	827980.	+	226780.i	1.26197	+	0.345648i
$811$	−28967.0			−0.0440415			−0.0220207	−	0.999758i	$-0.507010\pi$
$811$	−28967.0			−0.0440415			−0.0220207	+	0.999758i	$0.507010\pi$
$812$	117463.	+	203452.i	0.178152	+	0.308568i
$813$	672383.	−	252912.i	1.01727	−	0.382638i
$814$	−163139.	+	282565.i	−0.246211	+	0.426451i
$815$	398324.	−	514051.i	0.599683	−	0.773910i
$816$	450324.	+	369723.i	0.676308	+	0.555260i
$817$	−7493.12	+	4326.16i	−0.0112258	+	0.00648124i
$818$	236105.			0.352857
$819$	−403142.	+	353258.i	−0.601021	+	0.526653i
$820$	518496.	+	70759.3i	0.771112	+	0.105234i
$821$	318927.	−	184132.i	0.473156	−	0.273177i	−0.244404	−	0.969674i	$-0.578592\pi$
$821$	318927.	−	184132.i	0.473156	−	0.273177i	0.717560	+	0.696497i	$0.245259\pi$
$822$	−18780.4	+	113609.i	−0.0277946	+	0.168139i
$823$	547754.	+	316246.i	0.808697	+	0.466902i	0.846503	−	0.532383i	$-0.178704\pi$
$823$	547754.	+	316246.i	0.808697	+	0.466902i	−0.0378059	+	0.999285i	$0.512037\pi$
$824$	218710.	+	126272.i	0.322117	+	0.185974i
$825$	−862871.	−	401060.i	−1.26776	−	0.589253i
$826$	735247.	+	1.27349e6i	1.07764	+	1.86653i
$827$	−290970.			−0.425439			−0.212719	−	0.977113i	$-0.568232\pi$
$827$	−290970.			−0.425439			−0.212719	+	0.977113i	$0.568232\pi$
$828$	801448.	+	272415.i	1.16900	+	0.397348i
$829$	893630.			1.30032			0.650158	−	0.759799i	$-0.274703\pi$
$829$	893630.			1.30032			0.650158	+	0.759799i	$0.274703\pi$
$830$	579051.	−	236646.i	0.840545	−	0.343513i
$831$	506081.	−	616408.i	0.732855	−	0.892620i
$832$	148220.	+	85575.0i	0.214122	+	0.123623i
$833$	98787.3	−	171105.i	0.142368	−	0.246588i
$834$	661681.	−	248887.i	0.951298	−	0.357824i
$835$	1.04962e6	−	428960.i	1.50543	−	0.615238i
$836$		−	52012.4i		−	0.0744208i
$837$	−484018.	−	779414.i	−0.690892	−	1.11254i
$838$			651624.i			0.927916i
$839$	−120902.	+	69802.6i	−0.171755	+	0.0991625i	−0.583413	−	0.812176i	$-0.698283\pi$
$839$	−120902.	+	69802.6i	−0.171755	+	0.0991625i	0.411658	+	0.911338i	$0.364950\pi$
$840$	305825.	−	69719.1i	0.433426	−	0.0988083i
$841$	−290033.	+	502351.i	−0.410067	+	0.710257i
$842$	477583.	−	827198.i	0.673635	−	1.16677i
$843$	−418786.	+	510083.i	−0.589301	+	0.717771i
$844$	189874.	+	328872.i	0.266552	+	0.461681i
$845$	−52259.6	+	382938.i	−0.0731902	+	0.536309i
$846$	−202103.	−	1.01818e6i	−0.282378	−	1.42261i
$847$		−	807891.i		−	1.12612i
$848$	292885.	+	507291.i	0.407291	+	0.705449i
$849$	522485.	+	86370.8i	0.724867	+	0.119826i
$850$	489986.	−	480797.i	0.678182	−	0.665463i
$851$	292757.	+	169023.i	0.404248	+	0.233392i
$852$	−918436.	−	151825.i	−1.26523	−	0.209152i
$853$	702105.	−	405361.i	0.964948	−	0.557113i	0.0672558	−	0.997736i	$-0.478576\pi$
$853$	702105.	−	405361.i	0.964948	−	0.557113i	0.897692	+	0.440623i	$0.145242\pi$
$854$			286756.i			0.393185i
$855$	−54552.7	+	3294.28i	−0.0746250	+	0.00450639i
$856$	−430946.			−0.588133
$857$	−415009.	−	718817.i	−0.565062	−	0.978716i	−0.997044	−	0.0768340i	$-0.975519\pi$
$857$	−415009.	−	718817.i	−0.565062	−	0.978716i	0.431982	−	0.901882i	$-0.357814\pi$
$858$	−704906.	−	578739.i	−0.957539	−	0.786155i
$859$	−152784.	+	264629.i	−0.207057	+	0.358634i	−0.950786	−	0.309847i	$-0.899722\pi$
$859$	−152784.	+	264629.i	−0.207057	+	0.358634i	0.743729	+	0.668481i	$0.233055\pi$
$860$	−55928.3	+	72177.3i	−0.0756197	+	0.0975897i
$861$	894796.	−	336572.i	1.20703	−	0.454016i
$862$	−237146.	+	136916.i	−0.319155	+	0.184264i
$863$	−1.37893e6			−1.85149			−0.925746	−	0.378147i	$-0.876561\pi$
$863$	−1.37893e6			−1.85149			−0.925746	+	0.378147i	$0.876561\pi$
$864$	−472564.	−	760971.i	−0.633044	−	1.01939i
$865$	−19255.8	+	141099.i	−0.0257353	+	0.188578i
$866$	−1.55068e6	+	895285.i	−2.06769	+	1.19378i
$867$	−332571.	+	125094.i	−0.442431	+	0.166418i
$868$	717892.	+	414475.i	0.952839	+	0.550122i
$869$	−1.50173e6	−	867024.i	−1.98862	−	1.14813i
$870$	285607.	+	307971.i	0.377338	+	0.406885i
$871$	124105.	+	214956.i	0.163588	+	0.283343i
$872$	357811.			0.470566
$873$	111194.	−	327133.i	0.145899	−	0.429236i
$874$	−129570.			−0.169621
$875$	−105182.	−	897200.i	−0.137381	−	1.17185i
$876$	99627.9	+	16469.3i	0.129829	+	0.0214618i
$877$	−618881.	−	357311.i	−0.804652	−	0.464566i	0.0404430	−	0.999182i	$-0.487123\pi$
$877$	−618881.	−	357311.i	−0.804652	−	0.464566i	−0.845095	+	0.534616i	$0.820456\pi$
$878$	682836.	−	1.18271e6i	0.885783	−	1.53422i
$879$	−148644.	+	899193.i	−0.192384	+	1.16379i
$880$	493538.	+	1.20764e6i	0.637317	+	1.55945i
$881$			390992.i			0.503751i	0.967760	+	0.251875i	$0.0810473\pi$
$881$			390992.i			0.503751i	−0.967760	+	0.251875i	$0.918953\pi$
$882$	−300181.	+	263038.i	−0.385875	+	0.338128i
$883$			1.05235e6i			1.34971i	0.737950	+	0.674855i	$0.235794\pi$
$883$			1.05235e6i			1.34971i	−0.737950	+	0.674855i	$0.764206\pi$
$884$	237000.	−	136832.i	0.303280	−	0.175099i
$885$	743520.	+	801741.i	0.949306	+	1.02364i
$886$	487952.	−	845158.i	0.621598	−	1.07664i
$887$	−432865.	+	749744.i	−0.550181	+	0.952941i	0.448080	+	0.893993i	$0.352108\pi$
$887$	−432865.	+	749744.i	−0.550181	+	0.952941i	−0.998261	+	0.0589476i	$0.981225\pi$
$888$	−28157.4	−	74858.2i	−0.0357081	−	0.0949322i
$889$	−105338.	−	182450.i	−0.133285	−	0.230856i
$890$	−111294.	−	15188.3i	−0.140505	−	0.0191748i
$891$	423896.	+	1.02572e6i	0.533955	+	1.29203i
$892$			529391.i			0.665344i
$893$	33042.0	+	57230.5i	0.0414347	+	0.0717669i
$894$	−209342.	−	556550.i	−0.261928	−	0.696352i
$895$	437679.	−	564839.i	0.546399	−	0.705145i
$896$	−592521.	−	342092.i	−0.738054	−	0.426116i
$897$	−599614.	+	730332.i	−0.745224	+	0.907685i
$898$	−298744.	+	172480.i	−0.370465	+	0.213888i
$899$		−	448887.i		−	0.555415i
$900$	−519771.	+	249976.i	−0.641692	+	0.308613i
$901$	398488.			0.490869
$902$	813332.	+	1.40873e6i	0.999666	+	1.73147i
$903$	−27206.0	+	164578.i	−0.0333649	+	0.201835i
$904$	113074.	−	195849.i	0.138364	−	0.239654i
$905$	−676979.	−	524573.i	−0.826566	−	0.640485i
$906$	178866.	−	1.08202e6i	0.217907	−	1.31819i
$907$	−936179.	+	540503.i	−1.13800	+	0.657027i	−0.945936	−	0.324354i	$-0.894853\pi$
$907$	−936179.	+	540503.i	−1.13800	+	0.657027i	−0.192069	+	0.981381i	$0.561520\pi$
$908$	−295566.			−0.358494
$909$	−111700.	+	328623.i	−0.135184	+	0.397714i
$910$	117080.	−	857916.i	0.141384	−	1.03601i
$911$	−218106.	+	125923.i	−0.262803	+	0.151729i	−0.625613	−	0.780134i	$-0.715151\pi$
$911$	−218106.	+	125923.i	−0.262803	+	0.151729i	0.362809	+	0.931863i	$0.381818\pi$
$912$	57913.2	+	47547.7i	0.0696287	+	0.0571663i
$913$	700367.	+	404357.i	0.840202	+	0.485091i
$914$	751898.	+	434108.i	0.900050	+	0.519644i
$915$	47393.7	+	207894.i	0.0566081	+	0.248313i
$916$	137834.	+	238736.i	0.164273	+	0.284529i
$917$	310222.			0.368922
$918$	−800295.	+	25714.4i	−0.949653	+	0.0305134i
$919$	−1.32687e6			−1.57108			−0.785541	−	0.618809i	$-0.787615\pi$
$919$	−1.32687e6			−1.57108			−0.785541	+	0.618809i	$0.787615\pi$
$920$	511875.	−	209193.i	0.604767	−	0.247156i
$921$	137815.	+	366390.i	0.162472	+	0.431941i
$922$	114409.	+	66054.3i	0.134586	+	0.0777033i
$923$	519592.	−	899960.i	0.609901	−	1.05638i
$924$	−775023.	−	636306.i	−0.907759	−	0.745285i
$925$	−223037.	+	57505.5i	−0.260672	+	0.0672088i
$926$			537507.i			0.626847i
$927$	−832093.	+	165165.i	−0.968305	+	0.192202i
$928$		−	438265.i		−	0.508910i
$929$	−611138.	+	352841.i	−0.708122	+	0.408834i	−0.810365	−	0.585925i	$-0.800731\pi$
$929$	−611138.	+	352841.i	−0.708122	+	0.408834i	0.102243	+	0.994759i	$0.467398\pi$
$930$	1.41611e6	+	437213.i	1.63731	+	0.505507i
$931$	12704.4	−	22004.7i	0.0146573	−	0.0253872i
$932$	340660.	−	590040.i	0.392183	−	0.679282i
$933$	−673743.	−	111375.i	−0.773982	−	0.127945i
$934$	−230390.	−	399048.i	−0.264101	−	0.457437i
$935$	879343.	+	120004.i	1.00585	+	0.137269i
$936$	219287.	−	43527.1i	0.250301	−	0.0496830i
$937$			1.20291e6i			1.37011i	0.728493	+	0.685053i	$0.240221\pi$
$937$			1.20291e6i			1.37011i	−0.728493	+	0.685053i	$0.759779\pi$
$938$	328079.	+	568250.i	0.372883	+	0.645853i
$939$	385223.	−	469202.i	0.436899	−	0.532144i
$940$	551271.	+	427166.i	0.623892	+	0.483438i
$941$	1.39400e6	+	804825.i	1.57428	+	0.908912i	0.995635	+	0.0933347i	$0.0297527\pi$
$941$	1.39400e6	+	804825.i	1.57428	+	0.908912i	0.578648	+	0.815578i	$0.303581\pi$
$942$	−283416.	−	753479.i	−0.319391	−	0.849120i
$943$	1.45954e6	−	842669.i	1.64132	−	0.947618i
$944$		−	1.49918e6i		−	1.68232i
$945$	−618296.	+	853176.i	−0.692362	+	0.955378i
$946$	−283834.			−0.317163
$947$	−584691.	−	1.01271e6i	−0.651968	−	1.12924i	−0.982645	−	0.185498i	$-0.940610\pi$
$947$	−584691.	−	1.01271e6i	−0.651968	−	1.12924i	0.330676	−	0.943744i	$-0.392723\pi$
$948$	−983787.	+	370045.i	−1.09467	+	0.411754i
$949$	−56363.1	+	97623.7i	−0.0625839	+	0.108398i
$950$	63014.0	−	61832.2i	0.0698216	−	0.0685121i
$951$	−1.26007e6	−	1.03454e6i	−1.39327	−	1.14390i
$952$	−253368.	+	146282.i	−0.279562	+	0.161405i
$953$	92982.8			0.102380			0.0511902	−	0.998689i	$-0.483699\pi$
$953$	92982.8			0.102380			0.0511902	+	0.998689i	$0.483699\pi$
$954$	−762163.	−	259062.i	−0.837435	−	0.284647i
$955$	−1.76365e6	−	240686.i	−1.93378	−	0.263903i
$956$	−733429.	+	423446.i	−0.802495	+	0.463321i
$957$	−88562.3	+	535742.i	−0.0966996	+	0.584967i
$958$	−1.26540e6	−	730577.i	−1.37878	−	0.796040i
$959$	−122397.	−	70665.7i	−0.133086	−	0.0768371i
$960$	321461.	+	99248.8i	0.348807	+	0.107692i
$961$	−330199.	−	571922.i	−0.357544	−	0.619284i
$962$	−220776.			−0.238562
$963$	1.08875e6	−	954030.i	1.17402	−	1.02875i
$964$	−633611.			−0.681818
$965$	581541.	+	1.42297e6i	0.624490	+	1.52807i
$966$	−1.58512e6	+	1.93068e6i	−1.69867	+	2.06898i
$967$	370274.	+	213778.i	0.395977	+	0.228618i	0.684747	−	0.728781i	$-0.259913\pi$
$967$	370274.	+	213778.i	0.395977	+	0.228618i	−0.288769	+	0.957399i	$0.593246\pi$
$968$	−168480.	+	291816.i	−0.179804	+	0.311429i
$969$	47711.0	−	17946.2i	0.0508125	−	0.0191128i
$970$	211146.	+	516654.i	0.224409	+	0.549106i
$971$		−	967416.i		−	1.02606i	−0.858369	−	0.513032i	$-0.828522\pi$
$971$		−	967416.i		−	1.02606i	0.858369	−	0.513032i	$-0.171478\pi$
$972$	643566.	+	195932.i	0.681178	+	0.207383i
$973$			867674.i			0.916496i
$974$	1.13514e6	−	655372.i	1.19655	−	0.690828i
$975$	−56911.1	−	641328.i	−0.0598670	−	0.674638i
$976$	146174.	−	253181.i	0.153452	−	0.265786i
$977$	267215.	−	462829.i	0.279944	−	0.484877i	−0.691427	−	0.722447i	$-0.743017\pi$
$977$	267215.	−	462829.i	0.279944	−	0.484877i	0.971370	+	0.237570i	$0.0763508\pi$
$978$	777517.	−	947017.i	0.812890	−	0.990103i
$979$	−72608.5	−	125762.i	−0.0757569	−	0.131215i
$980$	36257.9	−	265683.i	0.0377529	−	0.276638i
$981$	−903978.	+	792123.i	−0.939334	+	0.823104i
$982$			418950.i			0.434449i
$983$	−405897.	−	703034.i	−0.420057	−	0.727561i	0.575887	−	0.817529i	$-0.304657\pi$
$983$	−405897.	−	703034.i	−0.420057	−	0.727561i	−0.995945	+	0.0899684i	$0.971323\pi$
$984$	−393397.	−	65031.6i	−0.406294	−	0.0671636i
$985$	281281.	+	217957.i	0.289913	+	0.224646i
$986$	−339272.	−	195879.i	−0.348975	−	0.201481i
$987$	1.25700e6	+	207792.i	1.29033	+	0.213302i
$988$	30479.1	−	17597.1i	0.0312239	−	0.0180272i
$989$			294072.i			0.300650i
$990$	−1.60385e6	−	801197.i	−1.63641	−	0.817464i
$991$	−25780.3			−0.0262507			−0.0131254	−	0.999914i	$-0.504178\pi$
$991$	−25780.3			−0.0262507			−0.0131254	+	0.999914i	$0.504178\pi$
$992$	−773220.	−	1.33926e6i	−0.785742	−	1.36094i
$993$	−1.08595e6	−	891586.i	−1.10132	−	0.904200i
$994$	1.37358e6	−	2.37910e6i	1.39021	−	2.40791i
$995$	1.15592e6	+	895689.i	1.16756	+	0.904714i
$996$	458812.	−	172579.i	0.462504	−	0.173968i
$997$	696124.	−	401907.i	0.700319	−	0.404329i	−0.107147	−	0.994243i	$-0.534172\pi$
$997$	696124.	−	401907.i	0.700319	−	0.404329i	0.807466	+	0.589914i	$0.200838\pi$
$998$	−224324.			−0.225224
$999$	236859.	+	126788.i	0.237333	+	0.127042i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.5.h.a.14.5	✓	44
3.2	odd	2		135.5.h.a.44.18		44
5.4	even	2	inner	45.5.h.a.14.18	yes	44
9.2	odd	6	inner	45.5.h.a.29.18	yes	44
9.4	even	3		405.5.d.a.404.36		44
9.5	odd	6		405.5.d.a.404.10		44
9.7	even	3		135.5.h.a.89.5		44
15.14	odd	2		135.5.h.a.44.5		44
45.4	even	6		405.5.d.a.404.9		44
45.14	odd	6		405.5.d.a.404.35		44
45.29	odd	6	inner	45.5.h.a.29.5	yes	44
45.34	even	6		135.5.h.a.89.18		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.5.h.a.14.5	✓	44	1.1	even	1	trivial
45.5.h.a.14.18	yes	44	5.4	even	2	inner
45.5.h.a.29.5	yes	44	45.29	odd	6	inner
45.5.h.a.29.18	yes	44	9.2	odd	6	inner
135.5.h.a.44.5		44	15.14	odd	2
135.5.h.a.44.18		44	3.2	odd	2
135.5.h.a.89.5		44	9.7	even	3
135.5.h.a.89.18		44	45.34	even	6
405.5.d.a.404.9		44	45.4	even	6
405.5.d.a.404.10		44	9.5	odd	6
405.5.d.a.404.35		44	45.14	odd	6
405.5.d.a.404.36		44	9.4	even	3

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.h (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.61690 - 4.53261i) q^{2} +(8.42379 - 3.16855i) q^{3} +(-5.69638 + 9.86641i) q^{4} +(-19.7616 - 15.3127i) q^{5} +(-36.4061 - 29.8900i) q^{6} +(50.0684 - 28.9070i) q^{7} -24.1135 q^{8} +(60.9206 - 53.3825i) q^{9} +(-17.6925 + 129.644i) q^{10} +(-146.496 + 84.5798i) q^{11} +(-16.7228 + 101.162i) q^{12} +(-99.1268 - 57.2309i) q^{13} +(-262.048 - 151.294i) q^{14} +(-214.987 - 66.3757i) q^{15} +(154.245 + 267.160i) q^{16} +209.860 q^{17} +(-401.385 - 136.432i) q^{18} +26.9887 q^{19} +(263.651 - 107.749i) q^{20} +(330.173 - 402.151i) q^{21} +(766.735 + 442.674i) q^{22} +(458.642 - 794.390i) q^{23} +(-203.127 + 76.4047i) q^{24} +(156.040 + 605.208i) q^{25} +599.071i q^{26} +(344.037 - 642.713i) q^{27} +658.661i q^{28} +(308.888 - 178.337i) q^{29} +(261.744 + 1148.15i) q^{30} +(629.269 - 1089.93i) q^{31} +(614.379 - 1064.14i) q^{32} +(-966.061 + 1176.66i) q^{33} +(-549.182 - 951.212i) q^{34} +(-1432.08 - 195.436i) q^{35} +(179.667 + 905.154i) q^{36} +368.530i q^{37} +(-70.6268 - 122.329i) q^{38} +(-1016.36 - 168.013i) q^{39} +(476.520 + 369.243i) q^{40} +(1591.16 + 918.657i) q^{41} +(-2686.82 - 444.153i) q^{42} +(-277.639 + 160.295i) q^{43} -1927.19i q^{44} +(-2021.32 + 122.062i) q^{45} -4800.88 q^{46} +(1224.29 + 2120.54i) q^{47} +(2145.83 + 1761.76i) q^{48} +(470.730 - 815.329i) q^{49} +(2334.83 - 2291.04i) q^{50} +(1767.81 - 664.951i) q^{51} +(1129.33 - 652.018i) q^{52} +1898.83 q^{53} +(-3813.48 + 122.531i) q^{54} +(4190.15 + 571.831i) q^{55} +(-1207.32 + 697.048i) q^{56} +(227.347 - 85.5151i) q^{57} +(-1616.66 - 933.380i) q^{58} +(-4208.65 - 2429.87i) q^{59} +(1879.53 - 1743.05i) q^{60} +(-473.839 - 820.714i) q^{61} -6586.95 q^{62} +(1507.07 - 4433.81i) q^{63} -1495.26 q^{64} +(1082.54 + 2648.88i) q^{65} +(7861.45 + 1299.56i) q^{66} +(-1877.97 - 1084.25i) q^{67} +(-1195.44 + 2070.56i) q^{68} +(1346.43 - 8145.01i) q^{69} +(2861.77 + 7002.48i) q^{70} +9078.87i q^{71} +(-1469.00 + 1287.24i) q^{72} -984.836i q^{73} +(1670.40 - 964.407i) q^{74} +(3232.08 + 4603.72i) q^{75} +(-153.738 + 266.282i) q^{76} +(-4889.90 + 8469.55i) q^{77} +(1898.19 + 5046.45i) q^{78} +(5125.48 + 8877.60i) q^{79} +(1042.82 - 7641.40i) q^{80} +(861.628 - 6504.18i) q^{81} -9616.15i q^{82} +(-2390.39 - 4140.27i) q^{83} +(2087.00 + 5548.42i) q^{84} +(-4147.16 - 3213.52i) q^{85} +(1453.11 + 838.954i) q^{86} +(2036.94 - 2481.00i) q^{87} +(3532.54 - 2039.51i) q^{88} +858.461i q^{89} +(5842.85 + 8842.42i) q^{90} -6617.50 q^{91} +(5225.19 + 9050.29i) q^{92} +(1847.35 - 11175.2i) q^{93} +(6407.71 - 11098.5i) q^{94} +(-533.339 - 413.271i) q^{95} +(1803.63 - 10910.8i) q^{96} +(3694.13 - 2132.80i) q^{97} -4927.43 q^{98} +(-4409.57 + 12973.0i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 162 q^{4} + 6 q^{5} - 36 q^{6} - 126 q^{9} + 28 q^{10} + 228 q^{11} + 282 q^{14} + 450 q^{15} - 1058 q^{16} - 8 q^{19} - 2196 q^{20} + 1056 q^{21} + 2970 q^{24} - 148 q^{25} + 2370 q^{29} + 1068 q^{30}+ \cdots + 44568 q^{99}+O(q^{100}) \) 44 * q - 162 * q^4 + 6 * q^5 - 36 * q^6 - 126 * q^9 + 28 * q^10 + 228 * q^11 + 282 * q^14 + 450 * q^15 - 1058 * q^16 - 8 * q^19 - 2196 * q^20 + 1056 * q^21 + 2970 * q^24 - 148 * q^25 + 2370 * q^29 + 1068 * q^30 - 1112 * q^31 - 436 * q^34 - 648 * q^36 - 6420 * q^39 - 850 * q^40 + 1830 * q^41 - 1944 * q^45 - 5668 * q^46 + 5396 * q^49 + 13524 * q^50 - 1500 * q^51 + 17766 * q^54 - 3072 * q^55 - 8250 * q^56 - 27348 * q^59 - 28722 * q^60 + 2782 * q^61 + 8348 * q^64 - 24906 * q^65 + 27240 * q^66 + 19662 * q^69 + 4782 * q^70 + 64728 * q^74 + 28446 * q^75 - 1776 * q^76 + 7900 * q^79 - 47754 * q^81 - 113166 * q^84 + 6766 * q^85 + 9192 * q^86 + 10674 * q^90 + 1560 * q^91 - 18826 * q^94 + 58746 * q^95 + 1902 * q^96 + 44568 * q^99

Introduction

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