LMFDB - Embedded newform 31.5.f.a.23.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [31,5,Mod(15,31)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(31, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([7])) N = Newforms(chi, 5, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("31.15"); S:= CuspForms(chi, 5); N := Newforms(S);

Level:	$ N $	$=$	$ 31 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	31.f (of order $10$, degree $4$, 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:	$3.20446885560$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$9$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			23.1
Character	$\chi$	$=$	31.23
Dual form			31.5.f.a.27.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.30154 + 7.08340i) q^{2} +(0.135338 - 0.0439738i) q^{3} +(-31.9333 - 23.2009i) q^{4} -18.1577 q^{5} +1.05986i q^{6} +(10.5920 + 7.69552i) q^{7} +(141.429 - 102.754i) q^{8} +(-65.5140 + 47.5987i) q^{9} +(41.7905 - 128.618i) q^{10} +(43.9751 - 60.5266i) q^{11} +(-5.34200 - 1.73572i) q^{12} +(-266.563 + 86.6115i) q^{13} +(-78.8883 + 57.3157i) q^{14} +(-2.45741 + 0.798462i) q^{15} +(207.186 + 637.653i) q^{16} +(56.3932 + 77.6185i) q^{17} +(-186.378 - 573.612i) q^{18} +(-160.347 + 493.498i) q^{19} +(579.833 + 421.274i) q^{20} +(1.77189 + 0.575723i) q^{21} +(327.524 + 450.798i) q^{22} +(-349.808 - 481.469i) q^{23} +(14.6221 - 20.1256i) q^{24} -295.299 q^{25} -2087.51i q^{26} +(-13.5485 + 18.6479i) q^{27} +(-159.694 - 491.486i) q^{28} +(1581.23 + 513.773i) q^{29} -19.2445i q^{30} +(518.624 + 809.043i) q^{31} -2196.55 q^{32} +(3.28990 - 10.1253i) q^{33} +(-679.594 + 220.814i) q^{34} +(-192.326 - 139.733i) q^{35} +3196.41 q^{36} -601.518i q^{37} +(-3126.60 - 2271.61i) q^{38} +(-32.2673 + 23.4436i) q^{39} +(-2568.02 + 1865.77i) q^{40} +(-547.973 + 1686.49i) q^{41} +(-8.15616 + 11.2260i) q^{42} +(705.813 + 229.333i) q^{43} +(-2808.54 + 912.550i) q^{44} +(1189.58 - 864.281i) q^{45} +(4215.54 - 1369.71i) q^{46} +(542.765 + 1670.46i) q^{47} +(56.0801 + 77.1876i) q^{48} +(-688.981 - 2120.47i) q^{49} +(679.643 - 2091.73i) q^{50} +(11.0453 + 8.02488i) q^{51} +(10521.7 + 3418.70i) q^{52} +(-651.590 - 896.837i) q^{53} +(-100.908 - 138.888i) q^{54} +(-798.485 + 1099.02i) q^{55} +2288.76 q^{56} +73.8399i q^{57} +(-7278.53 + 10018.0i) q^{58} +(-1011.96 - 3114.48i) q^{59} +(96.9983 + 31.5166i) q^{60} -2489.66i q^{61} +(-6924.41 + 1811.58i) q^{62} -1060.22 q^{63} +(1740.46 - 5356.59i) q^{64} +(4840.16 - 1572.66i) q^{65} +(64.1496 + 46.6074i) q^{66} -6649.82 q^{67} -3786.98i q^{68} +(-68.5142 - 49.7785i) q^{69} +(1432.43 - 1040.72i) q^{70} +(-5600.24 + 4068.81i) q^{71} +(-4374.61 + 13463.7i) q^{72} +(-1037.46 + 1427.94i) q^{73} +(4260.80 + 1384.42i) q^{74} +(-39.9651 + 12.9855i) q^{75} +(16570.0 - 12038.8i) q^{76} +(931.567 - 302.684i) q^{77} +(-91.7959 - 282.519i) q^{78} +(-350.123 - 481.902i) q^{79} +(-3762.01 - 11578.3i) q^{80} +(2025.94 - 6235.20i) q^{81} +(-10684.9 - 7763.03i) q^{82} +(8292.36 + 2694.35i) q^{83} +(-43.2251 - 59.4942i) q^{84} +(-1023.97 - 1409.37i) q^{85} +(-3248.91 + 4471.74i) q^{86} +236.593 q^{87} -13078.8i q^{88} +(1441.12 - 1983.54i) q^{89} +(3384.19 + 10415.5i) q^{90} +(-3489.95 - 1133.95i) q^{91} +23490.7i q^{92} +(105.766 + 86.6880i) q^{93} -13081.7 q^{94} +(2911.53 - 8960.76i) q^{95} +(-297.275 + 96.5906i) q^{96} +(3873.45 + 2814.23i) q^{97} +16605.8 q^{98} +6058.49i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 3 q^{2} - 5 q^{3} - 79 q^{4} - 2 q^{5} - 73 q^{7} + 173 q^{8} + 62 q^{9} + 84 q^{10} + 100 q^{11} + 150 q^{12} - 260 q^{13} + 488 q^{14} - 1075 q^{15} + 777 q^{16} - 725 q^{17} - 786 q^{18} - 1581 q^{19}+ \cdots + 74456 q^{98}+O(q^{100}) $ 36 * q - 3 * q^2 - 5 * q^3 - 79 * q^4 - 2 * q^5 - 73 * q^7 + 173 * q^8 + 62 * q^9 + 84 * q^10 + 100 * q^11 + 150 * q^12 - 260 * q^13 + 488 * q^14 - 1075 * q^15 + 777 * q^16 - 725 * q^17 - 786 * q^18 - 1581 * q^19 + 827 * q^20 + 2335 * q^21 - 1030 * q^22 + 1675 * q^23 - 165 * q^24 + 1294 * q^25 - 2855 * q^27 + 352 * q^28 - 575 * q^29 + 895 * q^31 - 5470 * q^32 + 4468 * q^33 + 1815 * q^34 - 3042 * q^35 + 7808 * q^36 - 6604 * q^38 + 595 * q^39 + 1482 * q^40 - 1740 * q^41 + 3840 * q^42 - 10055 * q^43 - 5780 * q^44 + 6774 * q^45 + 16515 * q^46 + 693 * q^47 + 4710 * q^48 - 944 * q^49 - 6240 * q^50 + 12641 * q^51 + 15885 * q^52 - 10835 * q^53 - 25960 * q^54 - 14010 * q^55 - 19976 * q^56 + 4755 * q^58 - 6021 * q^59 + 35 * q^60 - 11088 * q^62 - 15564 * q^63 + 6935 * q^64 + 26645 * q^65 + 23988 * q^66 + 28596 * q^67 - 4229 * q^69 + 8041 * q^70 + 31101 * q^71 + 20690 * q^72 + 6125 * q^73 - 47295 * q^74 - 27475 * q^75 + 12511 * q^76 + 35950 * q^77 + 29801 * q^78 - 29050 * q^79 - 47358 * q^80 - 1965 * q^81 + 9198 * q^82 + 21640 * q^83 - 35875 * q^84 - 55360 * q^85 - 27935 * q^86 - 2262 * q^87 - 11645 * q^89 - 14916 * q^90 + 670 * q^91 - 36224 * q^93 - 52442 * q^94 + 73983 * q^95 + 29810 * q^96 + 55059 * q^97 + 74456 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/31\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{9}{10}\right)$

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 $

$2$	−2.30154	+	7.08340i	−0.575384	+	1.77085i	0.0594822	+	0.998229i	$0.481055\pi$
$2$	−2.30154	+	7.08340i	−0.575384	+	1.77085i	−0.634867	+	0.772622i	$0.718945\pi$
$3$	0.135338	−	0.0439738i	0.0150375	−	0.00488598i	−0.301489	−	0.953470i	$-0.597484\pi$
$3$	0.135338	−	0.0439738i	0.0150375	−	0.00488598i	0.316526	+	0.948584i	$0.397484\pi$
$4$	−31.9333	−	23.2009i	−1.99583	−	1.45005i
$5$	−18.1577			−0.726306			−0.363153	−	0.931729i	$-0.618300\pi$
$5$	−18.1577			−0.726306			−0.363153	+	0.931729i	$0.618300\pi$
$6$			1.05986i			0.0294405i
$7$	10.5920	+	7.69552i	0.216163	+	0.157051i	0.690598	−	0.723239i	$-0.257348\pi$
$7$	10.5920	+	7.69552i	0.216163	+	0.157051i	−0.474435	+	0.880291i	$0.657348\pi$
$8$	141.429	−	102.754i	2.20982	−	1.60553i
$9$	−65.5140	+	47.5987i	−0.808815	+	0.587638i
$10$	41.7905	−	128.618i	0.417905	−	1.28618i
$11$	43.9751	−	60.5266i	0.363431	−	0.500219i	−0.587670	−	0.809101i	$-0.699955\pi$
$11$	43.9751	−	60.5266i	0.363431	−	0.500219i	0.951101	+	0.308881i	$0.0999546\pi$
$12$	−5.34200	−	1.73572i	−0.0370972	−	0.0120536i
$13$	−266.563	+	86.6115i	−1.57730	+	0.512494i	−0.961358	−	0.275301i	$-0.911222\pi$
$13$	−266.563	+	86.6115i	−1.57730	+	0.512494i	−0.615937	+	0.787795i	$0.711222\pi$
$14$	−78.8883	+	57.3157i	−0.402491	+	0.292427i
$15$	−2.45741	+	0.798462i	−0.0109218	+	0.00354872i
$16$	207.186	+	637.653i	0.809320	+	2.49083i
$17$	56.3932	+	77.6185i	0.195132	+	0.268576i	0.895360	−	0.445343i	$-0.146918\pi$
$17$	56.3932	+	77.6185i	0.195132	+	0.268576i	−0.700228	+	0.713919i	$0.746918\pi$
$18$	−186.378	−	573.612i	−0.575241	−	1.77041i
$19$	−160.347	+	493.498i	−0.444175	+	1.36703i	0.439211	+	0.898384i	$0.355258\pi$
$19$	−160.347	+	493.498i	−0.444175	+	1.36703i	−0.883386	+	0.468646i	$0.844742\pi$
$20$	579.833	+	421.274i	1.44958	+	1.05318i
$21$	1.77189	+	0.575723i	0.00401790	+	0.00130550i
$22$	327.524	+	450.798i	0.676702	+	0.931400i
$23$	−349.808	−	481.469i	−0.661263	−	0.910150i	0.338260	−	0.941053i	$-0.390162\pi$
$23$	−349.808	−	481.469i	−0.661263	−	0.910150i	−0.999522	+	0.0309029i	$0.990162\pi$
$24$	14.6221	−	20.1256i	0.0253857	−	0.0349404i
$25$	−295.299			−0.472479
$26$		−	2087.51i		−	3.08804i
$27$	−13.5485	+	18.6479i	−0.0185851	+	0.0255801i
$28$	−159.694	−	491.486i	−0.203691	−	0.626896i
$29$	1581.23	+	513.773i	1.88018	+	0.610908i	0.986882	+	0.161445i	$0.0516154\pi$
$29$	1581.23	+	513.773i	1.88018	+	0.610908i	0.893299	+	0.449463i	$0.148385\pi$
$30$		−	19.2445i		−	0.0213828i
$31$	518.624	+	809.043i	0.539671	+	0.841876i
$31$	518.624	+	809.043i	0.539671	+	0.841876i
$32$	−2196.55			−2.14507
$33$	3.28990	−	10.1253i	0.00302103	−	0.00929777i
$34$	−679.594	+	220.814i	−0.587884	+	0.191015i
$35$	−192.326	−	139.733i	−0.157000	−	0.114067i
$36$	3196.41			2.46636
$37$		−	601.518i		−	0.439385i	−0.975569	−	0.219692i	$-0.929495\pi$
$37$		−	601.518i		−	0.439385i	0.975569	−	0.219692i	$-0.0705054\pi$
$38$	−3126.60	−	2271.61i	−2.16523	−	1.57313i
$39$	−32.2673	+	23.4436i	−0.0212146	+	0.0154133i
$40$	−2568.02	+	1865.77i	−1.60501	+	1.16611i
$41$	−547.973	+	1686.49i	−0.325981	+	1.00327i	0.645015	+	0.764169i	$0.276851\pi$
$41$	−547.973	+	1686.49i	−0.325981	+	1.00327i	−0.970996	+	0.239096i	$0.923149\pi$
$42$	−8.15616	+	11.2260i	−0.00462368	+	0.00636394i
$43$	705.813	+	229.333i	0.381727	+	0.124031i	0.493594	−	0.869693i	$-0.335683\pi$
$43$	705.813	+	229.333i	0.381727	+	0.124031i	−0.111867	+	0.993723i	$0.535683\pi$
$44$	−2808.54	+	912.550i	−1.45069	+	0.471358i
$45$	1189.58	−	864.281i	0.587447	−	0.426805i
$46$	4215.54	−	1369.71i	1.99222	−	0.647312i
$47$	542.765	+	1670.46i	0.245706	+	0.756206i	0.995519	+	0.0945567i	$0.0301434\pi$
$47$	542.765	+	1670.46i	0.245706	+	0.756206i	−0.749813	+	0.661650i	$0.769857\pi$
$48$	56.0801	+	77.1876i	0.0243403	+	0.0335016i
$49$	−688.981	−	2120.47i	−0.286956	−	0.883159i
$50$	679.643	−	2091.73i	0.271857	−	0.836690i
$51$	11.0453	+	8.02488i	0.00424656	+	0.00308531i
$52$	10521.7	+	3418.70i	3.89116	+	1.26431i
$53$	−651.590	−	896.837i	−0.231965	−	0.319273i	0.677128	−	0.735865i	$-0.263224\pi$
$53$	−651.590	−	896.837i	−0.231965	−	0.319273i	−0.909093	+	0.416592i	$0.863224\pi$
$54$	−100.908	−	138.888i	−0.0346051	−	0.0476298i
$55$	−798.485	+	1099.02i	−0.263962	+	0.363313i
$56$	2288.76			0.729833
$57$			73.8399i			0.0227269i
$58$	−7278.53	+	10018.0i	−2.16365	+	2.97801i
$59$	−1011.96	−	3114.48i	−0.290708	−	0.894708i	−0.984629	−	0.174657i	$-0.944118\pi$
$59$	−1011.96	−	3114.48i	−0.290708	−	0.894708i	0.693921	−	0.720051i	$-0.255882\pi$
$60$	96.9983	+	31.5166i	0.0269440	+	0.00875462i
$61$		−	2489.66i		−	0.669085i	−0.942381	−	0.334542i	$-0.891418\pi$
$61$		−	2489.66i		−	0.669085i	0.942381	−	0.334542i	$-0.108582\pi$
$62$	−6924.41	+	1811.58i	−1.80136	+	0.471276i
$63$	−1060.22			−0.267125
$64$	1740.46	−	5356.59i	0.424918	−	1.30776i
$65$	4840.16	−	1572.66i	1.14560	−	0.372228i
$66$	64.1496	+	46.6074i	0.0147267	+	0.0106996i
$67$	−6649.82			−1.48136			−0.740679	−	0.671859i	$-0.765496\pi$
$67$	−6649.82			−1.48136			−0.740679	+	0.671859i	$0.765496\pi$
$68$		−	3786.98i		−	0.818984i
$69$	−68.5142	−	49.7785i	−0.0143907	−	0.0104555i
$70$	1432.43	−	1040.72i	0.292332	−	0.212392i
$71$	−5600.24	+	4068.81i	−1.11094	+	0.807144i	−0.982811	−	0.184614i	$-0.940896\pi$
$71$	−5600.24	+	4068.81i	−1.11094	+	0.807144i	−0.128127	+	0.991758i	$0.540896\pi$
$72$	−4374.61	+	13463.7i	−0.843867	+	2.59716i
$73$	−1037.46	+	1427.94i	−0.194682	+	0.267956i	−0.895187	−	0.445691i	$-0.852958\pi$
$73$	−1037.46	+	1427.94i	−0.194682	+	0.267956i	0.700505	+	0.713647i	$0.252958\pi$
$74$	4260.80	+	1384.42i	0.778085	+	0.252815i
$75$	−39.9651	+	12.9855i	−0.00710491	+	0.00230853i
$76$	16570.0	−	12038.8i	2.86876	−	2.08428i
$77$	931.567	−	302.684i	0.157120	−	0.0510515i
$78$	−91.7959	−	282.519i	−0.0150881	−	0.0464364i
$79$	−350.123	−	481.902i	−0.0561004	−	0.0772156i	0.780045	−	0.625723i	$-0.215196\pi$
$79$	−350.123	−	481.902i	−0.0561004	−	0.0772156i	−0.836145	+	0.548508i	$0.815196\pi$
$80$	−3762.01	−	11578.3i	−0.587814	−	1.80911i
$81$	2025.94	−	6235.20i	0.308785	−	0.950343i
$82$	−10684.9	−	7763.03i	−1.58907	−	1.15453i
$83$	8292.36	+	2694.35i	1.20371	+	0.391109i	0.841125	−	0.540841i	$-0.181894\pi$
$83$	8292.36	+	2694.35i	1.20371	+	0.391109i	0.362585	+	0.931951i	$0.381894\pi$
$84$	−43.2251	−	59.4942i	−0.00612601	−	0.00843172i
$85$	−1023.97	−	1409.37i	−0.141726	−	0.195069i
$86$	−3248.91	+	4471.74i	−0.439279	+	0.604616i
$87$	236.593			0.0312581
$88$		−	13078.8i		−	1.68890i
$89$	1441.12	−	1983.54i	0.181937	−	0.250415i	−0.708301	−	0.705911i	$-0.750538\pi$
$89$	1441.12	−	1983.54i	0.181937	−	0.250415i	0.890238	+	0.455496i	$0.150538\pi$
$90$	3384.19	+	10415.5i	0.417801	+	1.28586i
$91$	−3489.95	−	1133.95i	−0.421441	−	0.136934i
$92$			23490.7i			2.77537i
$93$	105.766	+	86.6880i	0.0122287	+	0.0100229i
$94$	−13081.7			−1.48050
$95$	2911.53	−	8960.76i	0.322607	−	0.992882i
$96$	−297.275	+	96.5906i	−0.0322564	+	0.0104808i
$97$	3873.45	+	2814.23i	0.411675	+	0.299099i	0.774280	−	0.632844i	$-0.218112\pi$
$97$	3873.45	+	2814.23i	0.411675	+	0.299099i	−0.362605	+	0.931943i	$0.618112\pi$
$98$	16605.8			1.72905
$99$			6058.49i			0.618151i
$100$	9429.88	+	6851.21i	0.942988	+	0.685121i
$101$	7621.88	−	5537.62i	0.747170	−	0.542851i	−0.147778	−	0.989020i	$-0.547212\pi$
$101$	7621.88	−	5537.62i	0.747170	−	0.542851i	0.894948	+	0.446170i	$0.147212\pi$
$102$	−82.2646	+	59.7688i	−0.00790702	+	0.00574479i
$103$	540.220	−	1662.62i	0.0509209	−	0.156718i	−0.922363	−	0.386326i	$-0.873744\pi$
$103$	540.220	−	1662.62i	0.0509209	−	0.156718i	0.973283	+	0.229607i	$0.0737441\pi$
$104$	−28800.0	+	39639.8i	−2.66272	+	3.66492i
$105$	−32.1735	−	10.4538i	−0.00291823	−	0.000948189i
$106$	7852.31	−	2551.37i	0.698853	−	0.227071i
$107$	−9064.10	+	6585.46i	−0.791694	+	0.575199i	−0.908466	−	0.417960i	$-0.862745\pi$
$107$	−9064.10	+	6585.46i	−0.791694	+	0.575199i	0.116772	+	0.993159i	$0.462745\pi$
$108$	865.296	−	281.152i	0.0741852	−	0.0241042i
$109$	3437.15	+	10578.5i	0.289298	+	0.890368i	0.985077	+	0.172112i	$0.0550592\pi$
$109$	3437.15	+	10578.5i	0.289298	+	0.890368i	−0.695779	+	0.718256i	$0.744941\pi$
$110$	−5947.06	−	8185.43i	−0.491493	−	0.676482i
$111$	−26.4511	−	81.4080i	−0.00214683	−	0.00660726i
$112$	−2712.56	+	8348.40i	−0.216244	+	0.665530i
$113$	−7732.40	−	5617.92i	−0.605560	−	0.439965i	0.242288	−	0.970204i	$-0.422102\pi$
$113$	−7732.40	−	5617.92i	−0.605560	−	0.439965i	−0.847848	+	0.530239i	$0.822102\pi$
$114$	−523.038	−	169.945i	−0.0402460	−	0.0130767i
$115$	6351.69	+	8742.35i	0.480279	+	0.661048i
$116$	−38573.9	−	53092.4i	−2.86667	−	3.94563i
$117$	13341.0	−	18362.3i	0.974578	−	1.34139i
$118$	24390.2			1.75166
$119$			1256.11i			0.0887020i
$120$	−265.504	+	365.435i	−0.0184378	+	0.0253774i
$121$	2794.66	+	8601.09i	0.190879	+	0.587466i
$122$	17635.3	+	5730.06i	1.18485	+	0.384981i
$123$			252.342i			0.0166793i
$124$	2209.13	−	37867.9i	0.143674	−	2.46279i
$125$	16710.5			1.06947
$126$	2440.14	−	7509.96i	0.153700	−	0.473039i
$127$	−17243.2	+	5602.65i	−1.06908	+	0.347365i	−0.790129	−	0.612941i	$-0.789986\pi$
$127$	−17243.2	+	5602.65i	−1.06908	+	0.347365i	−0.278950	+	0.960306i	$0.589986\pi$
$128$	5504.47	+	3999.23i	0.335966	+	0.244094i
$129$	105.608			0.00634623
$130$			37904.3i			2.24286i
$131$	12507.4	+	9087.14i	0.728826	+	0.529523i	0.889192	−	0.457535i	$-0.151268\pi$
$131$	12507.4	+	9087.14i	0.728826	+	0.529523i	−0.160366	+	0.987058i	$0.551268\pi$
$132$	−339.973	+	247.004i	−0.0195117	+	0.0141761i
$133$	−5496.11	+	3993.16i	−0.310708	+	0.225743i
$134$	15304.8	−	47103.4i	0.852351	−	2.62327i
$135$	246.009	−	338.603i	0.0134984	−	0.0185790i
$136$	15951.2	+	5182.87i	0.862415	+	0.280216i
$137$	−22529.4	+	7320.23i	−1.20035	+	0.390017i	−0.839889	−	0.542758i	$-0.817380\pi$
$137$	−22529.4	+	7320.23i	−1.20035	+	0.390017i	−0.360460	+	0.932775i	$0.617380\pi$
$138$	510.289	−	370.747i	0.0267953	−	0.0194679i
$139$	−18570.6	+	6033.97i	−0.961164	+	0.312301i	−0.747244	−	0.664550i	$-0.768623\pi$
$139$	−18570.6	+	6033.97i	−0.961164	+	0.312301i	−0.213920	+	0.976851i	$0.568623\pi$
$140$	2899.66	+	8924.24i	0.147942	+	0.455318i
$141$	146.913	+	202.209i	0.00738962	+	0.0101709i
$142$	−15931.9	−	49033.3i	−0.790115	−	2.43172i
$143$	−6479.84	+	19942.9i	−0.316878	+	0.975250i
$144$	−43925.0	−	31913.4i	−2.11830	−	1.53903i
$145$	−28711.5	−	9328.92i	−1.36559	−	0.443706i
$146$	−7726.93	−	10635.2i	−0.362494	−	0.498930i
$147$	−186.490	−	256.681i	−0.00863020	−	0.0118785i
$148$	−13955.7	+	19208.4i	−0.637132	+	0.876937i
$149$	27961.2			1.25946			0.629729	−	0.776815i	$-0.283166\pi$
$149$	27961.2			1.25946			0.629729	+	0.776815i	$0.283166\pi$
$150$		−	312.976i		−	0.0139100i
$151$	−9429.03	+	12977.9i	−0.413536	+	0.569183i	−0.964076	−	0.265625i	$-0.914422\pi$
$151$	−9429.03	+	12977.9i	−0.413536	+	0.569183i	0.550541	+	0.834808i	$0.314422\pi$
$152$	28031.2	+	86271.1i	1.21326	+	3.73403i
$153$	−7389.08	−	2400.86i	−0.315651	−	0.102561i
$154$			7295.30i			0.307611i
$155$	−9417.00	−	14690.3i	−0.391967	−	0.611460i
$156$	1574.31			0.0646907
$157$	−4579.00	+	14092.7i	−0.185768	+	0.571736i	−0.999961	−	0.00885891i	$-0.997180\pi$
$157$	−4579.00	+	14092.7i	−0.185768	+	0.571736i	0.814192	+	0.580595i	$0.197180\pi$
$158$	4219.33	−	1370.94i	0.169017	−	0.0549168i
$159$	−127.622	−	92.7228i	−0.00504814	−	0.00366769i
$160$	39884.2			1.55797
$161$		−	7791.67i		−	0.300593i
$162$	39503.7	+	28701.1i	1.50525	+	1.09363i
$163$	−9092.02	+	6605.74i	−0.342204	+	0.248626i	−0.745591	−	0.666404i	$-0.767833\pi$
$163$	−9092.02	+	6605.74i	−0.342204	+	0.248626i	0.403387	+	0.915029i	$0.367833\pi$
$164$	56626.6	−	41141.6i	2.10539	−	1.52966i
$165$	−59.7369	+	183.851i	−0.00219419	+	0.00675303i
$166$	−38170.3	+	52537.0i	−1.38519	+	1.90655i
$167$	14580.1	+	4737.37i	0.522791	+	0.169865i	0.558512	−	0.829497i	$-0.311373\pi$
$167$	14580.1	+	4737.37i	0.522791	+	0.169865i	−0.0357206	+	0.999362i	$0.511373\pi$
$168$	309.755	−	100.645i	0.0109749	−	0.00356595i
$169$	40447.9	−	29387.1i	1.41619	−	1.02892i
$170$	12339.8	−	4009.46i	0.426984	−	0.138736i
$171$	−12984.9	−	39963.3i	−0.444064	−	1.36669i
$172$	−17218.2	−	23698.8i	−0.582011	−	0.801069i
$173$	944.213	+	2905.99i	0.0315484	+	0.0970961i	0.965591	−	0.260066i	$-0.0837443\pi$
$173$	944.213	+	2905.99i	0.0315484	+	0.0970961i	−0.934042	+	0.357162i	$0.883744\pi$
$174$	−544.527	+	1675.88i	−0.0179854	+	0.0553535i
$175$	−3127.81	−	2272.48i	−0.102132	−	0.0742035i
$176$	47705.9	+	15500.6i	1.54009	+	0.500407i
$177$	−273.911	−	377.006i	−0.00874306	−	0.0120338i
$178$	10733.4	+	14773.2i	0.338764	+	0.466268i
$179$	−8742.76	+	12033.4i	−0.272862	+	0.375562i	−0.923353	−	0.383952i	$-0.874563\pi$
$179$	−8742.76	+	12033.4i	−0.272862	+	0.375562i	0.650492	+	0.759513i	$0.274563\pi$
$180$	−58039.3			−1.79134
$181$			22310.3i			0.681001i	0.940244	+	0.340500i	$0.110596\pi$
$181$			22310.3i			0.681001i	−0.940244	+	0.340500i	$0.889404\pi$
$182$	16064.5	−	22110.9i	0.484981	−	0.667519i
$183$	−109.480	−	336.945i	−0.00326914	−	0.0100614i
$184$	−98945.8	−	32149.4i	−2.92255	−	0.949594i
$185$			10922.2i			0.319128i
$186$	−857.470	+	549.668i	−0.0247852	+	0.0158882i
$187$	7177.88			0.205264
$188$	21423.9	−	65935.9i	0.606153	−	1.86555i
$189$	−287.011	+	93.2555i	−0.00803480	+	0.00261066i
$190$	56771.7	+	41247.1i	1.57262	+	1.14258i
$191$	−19815.2			−0.543165			−0.271583	−	0.962415i	$-0.587547\pi$
$191$	−19815.2			−0.543165			−0.271583	+	0.962415i	$0.587547\pi$
$192$		−	801.483i		−	0.0217416i
$193$	−16771.4	−	12185.1i	−0.450251	−	0.327127i	0.339444	−	0.940626i	$-0.389761\pi$
$193$	−16771.4	−	12185.1i	−0.450251	−	0.327127i	−0.789695	+	0.613500i	$0.789761\pi$
$194$	−28849.2	+	20960.2i	−0.766532	+	0.556918i
$195$	585.899	−	425.681i	0.0154083	−	0.0111948i
$196$	−27195.2	+	83698.3i	−0.707914	+	2.17874i
$197$	29919.7	−	41181.0i	0.770949	−	1.06112i	−0.225275	−	0.974295i	$-0.572328\pi$
$197$	29919.7	−	41181.0i	0.770949	−	1.06112i	0.996224	−	0.0868245i	$-0.0276719\pi$
$198$	−42914.8	−	13943.9i	−1.09465	−	0.355674i
$199$	46307.5	−	15046.2i	1.16935	−	0.379945i	0.340951	−	0.940081i	$-0.389251\pi$
$199$	46307.5	−	15046.2i	1.16935	−	0.379945i	0.828401	+	0.560136i	$0.189251\pi$
$200$	−41763.8	+	30343.2i	−1.04410	+	0.758580i
$201$	−899.971	+	292.418i	−0.0222759	+	0.00723789i
$202$	21683.2	+	66733.9i	0.531398	+	1.63547i
$203$	12794.6	+	17610.3i	0.310481	+	0.427341i
$204$	−166.528	−	512.521i	−0.00400154	−	0.0123155i
$205$	9949.91	−	30622.7i	0.236762	−	0.728678i
$206$	10533.7	+	7653.19i	0.248226	+	0.180347i
$207$	45834.6	+	14892.6i	1.06968	+	0.347559i
$208$	−110456.	−	152030.i	−2.55307	−	3.51400i
$209$	22818.4	+	31406.9i	0.522388	+	0.719005i
$210$	148.097	−	203.838i	0.00335820	−	0.00462217i
$211$	8163.63			0.183366			0.0916829	−	0.995788i	$-0.470775\pi$
$211$	8163.63			0.183366			0.0916829	+	0.995788i	$0.470775\pi$
$212$			43756.4i			0.973576i
$213$	−579.001	+	796.927i	−0.0127620	+	0.0175655i
$214$	−25786.1	−	79361.4i	−0.563064	−	1.73293i
$215$	−12815.9	−	4164.14i	−0.277251	−	0.0900842i
$216$			4029.52i			0.0863665i
$217$	−732.749	+	12560.4i	−0.0155609	+	0.266738i
$218$	−82842.3			−1.74317
$219$	−77.6152	+	238.875i	−0.00161830	+	0.00498061i
$220$	50996.5	−	16569.8i	1.05365	−	0.342350i
$221$	−21755.0	−	15805.9i	−0.445425	−	0.323620i
$222$	637.524			0.0129357
$223$		−	66877.0i		−	1.34483i	−0.740175	−	0.672414i	$-0.765257\pi$
$223$		−	66877.0i		−	1.34483i	0.740175	−	0.672414i	$-0.234743\pi$
$224$	−23265.8	−	16903.6i	−0.463683	−	0.336886i
$225$	19346.2	−	14055.9i	0.382148	−	0.277647i
$226$	57590.4	−	41841.9i	1.12754	−	0.819208i
$227$	−588.879	+	1812.38i	−0.0114281	+	0.0351721i	−0.956608	−	0.291378i	$-0.905886\pi$
$227$	−588.879	+	1812.38i	−0.0114281	+	0.0351721i	0.945180	+	0.326550i	$0.105886\pi$
$228$	1713.15	−	2357.95i	0.0329553	−	0.0453591i
$229$	−18002.8	−	5849.46i	−0.343296	−	0.111544i	0.132295	−	0.991210i	$-0.457766\pi$
$229$	−18002.8	−	5849.46i	−0.343296	−	0.111544i	−0.475590	+	0.879667i	$0.657766\pi$
$230$	−76544.3	+	24870.7i	−1.44696	+	0.470146i
$231$	112.766	−	81.9292i	0.00211326	−	0.00153538i
$232$	276424.	−	89815.6i	5.13570	−	1.66869i
$233$	−9708.26	−	29879.0i	−0.178826	−	0.550369i	0.820962	−	0.570983i	$-0.193438\pi$
$233$	−9708.26	−	29879.0i	−0.178826	−	0.550369i	−0.999788	+	0.0206144i	$0.993438\pi$
$234$	99362.9	+	136761.i	1.81465	+	2.49765i
$235$	−9855.35	−	30331.6i	−0.178458	−	0.549237i
$236$	−39943.6	+	122934.i	−0.717172	+	2.20723i
$237$	−68.5759	−	49.8233i	−0.00122088	−	0.000887024i
$238$	−8897.52	−	2890.98i	−0.157078	−	0.0510377i
$239$	36283.3	+	49939.7i	0.635200	+	0.874278i	0.998348	−	0.0574532i	$-0.0182980\pi$
$239$	36283.3	+	49939.7i	0.635200	+	0.874278i	−0.363148	+	0.931732i	$0.618298\pi$
$240$	−1018.28	−	1401.55i	−0.0176785	−	0.0243324i
$241$	−58735.9	+	80843.1i	−1.01128	+	1.39190i	−0.0931328	+	0.995654i	$0.529688\pi$
$241$	−58735.9	+	80843.1i	−1.01128	+	1.39190i	−0.918143	+	0.396248i	$0.870312\pi$
$242$	−67357.1			−1.15014
$243$		−	2800.00i		−	0.0474183i
$244$	−57762.4	+	79503.1i	−0.970210	+	1.33538i
$245$	12510.3	+	38502.7i	0.208418	+	0.641444i
$246$	−1787.44	−	580.774i	−0.0295366	−	0.00959703i
$247$		−	145436.i		−	2.38385i
$248$	156481.	+	61131.2i	2.54424	+	0.993938i
$249$	1240.75			0.0200118
$250$	−38459.8	+	118367.i	−0.615357	+	1.89387i
$251$	86042.2	−	27956.8i	1.36573	−	0.443752i	0.467776	−	0.883847i	$-0.345055\pi$
$251$	86042.2	−	27956.8i	1.36573	−	0.443752i	0.897951	+	0.440095i	$0.145055\pi$
$252$	33856.3	+	24598.0i	0.533136	+	0.387346i
$253$	−44524.5			−0.695598
$254$		−	135035.i		−	2.09305i
$255$	−200.557	−	145.713i	−0.00308430	−	0.00224088i
$256$	31908.5	−	23182.9i	0.486886	−	0.353743i
$257$	−51725.8	+	37581.0i	−0.783143	+	0.568987i	−0.905921	−	0.423448i	$-0.860820\pi$
$257$	−51725.8	+	37581.0i	−0.783143	+	0.568987i	0.122778	+	0.992434i	$0.460820\pi$
$258$	−243.060	+	748.062i	−0.00365152	+	0.0112382i
$259$	4629.00	−	6371.27i	0.0690061	−	0.0949787i
$260$	−191049.	−	62075.7i	−2.82617	−	0.918279i
$261$	−128048.	+	41605.2i	−1.87971	+	0.610755i
$262$	−93154.1	+	67680.4i	−1.35706	+	0.985962i
$263$	−87188.3	+	28329.2i	−1.26051	+	0.409565i	−0.861676	−	0.507458i	$-0.830585\pi$
$263$	−87188.3	+	28329.2i	−1.26051	+	0.409565i	−0.398835	+	0.917023i	$0.630585\pi$
$264$	−575.126	−	1770.06i	−0.00825192	−	0.0253968i
$265$	11831.3	+	16284.5i	0.168478	+	0.231890i
$266$	−15635.7	−	48121.6i	−0.220980	−	0.680106i
$267$	107.814	−	331.819i	0.00151236	−	0.00465456i
$268$	212351.	+	154282.i	2.95654	+	2.14805i
$269$	−5011.39	−	1628.30i	−0.0692554	−	0.0225025i	0.274184	−	0.961677i	$-0.411592\pi$
$269$	−5011.39	−	1628.30i	−0.0692554	−	0.0225025i	−0.343440	+	0.939175i	$0.611592\pi$
$270$	1832.26	+	2521.89i	0.0251339	+	0.0345938i
$271$	62856.5	+	86514.5i	0.855877	+	1.17801i	0.982537	+	0.186067i	$0.0595743\pi$
$271$	62856.5	+	86514.5i	0.855877	+	1.17801i	−0.126660	+	0.991946i	$0.540426\pi$
$272$	−37809.8	+	52040.7i	−0.511053	+	0.703405i
$273$	−522.186			−0.00700647
$274$		−	176432.i		−	2.35005i
$275$	−12985.8	+	17873.5i	−0.171713	+	0.236343i
$276$	1032.98	+	3179.18i	0.0135604	+	0.0417347i
$277$	35978.0	+	11690.0i	0.468897	+	0.152354i	0.533929	−	0.845529i	$-0.320715\pi$
$277$	35978.0	+	11690.0i	0.468897	+	0.152354i	−0.0650319	+	0.997883i	$0.520715\pi$
$278$		−	145431.i		−	1.88177i
$279$	−72486.5	−	28317.8i	−0.931213	−	0.363790i
$280$	−41558.5			−0.530082
$281$	−11086.1	+	34119.4i	−0.140399	+	0.432104i	−0.996391	−	0.0848856i	$-0.972948\pi$
$281$	−11086.1	+	34119.4i	−0.140399	+	0.432104i	0.855992	+	0.516990i	$0.172948\pi$
$282$	−1770.45	+	575.254i	−0.0222631	+	0.00723372i
$283$	−12316.8	−	8948.69i	−0.153789	−	0.111734i	0.508230	−	0.861222i	$-0.330300\pi$
$283$	−12316.8	−	8948.69i	−0.153789	−	0.111734i	−0.662019	+	0.749487i	$0.730300\pi$
$284$	273234.			3.38765
$285$		−	1340.76i		−	0.0165067i
$286$	−126350.	−	91798.6i	−1.54470	−	1.12229i
$287$	−18782.5	+	13646.3i	−0.228029	+	0.165673i
$288$	143905.	−	104553.i	1.73496	−	1.26052i
$289$	22965.0	−	70678.9i	0.274960	−	0.846241i
$290$	132161.	−	181904.i	1.57148	−	2.16295i
$291$	647.976	+	210.540i	0.00765196	+	0.00248627i
$292$	66258.9	−	21528.8i	0.777103	−	0.252496i
$293$	−7732.85	+	5618.24i	−0.0900750	+	0.0654433i	−0.631911	−	0.775041i	$-0.717729\pi$
$293$	−7732.85	+	5618.24i	−0.0900750	+	0.0654433i	0.541836	+	0.840484i	$0.317729\pi$
$294$	2247.39	−	730.222i	0.0260007	−	0.00844812i
$295$	18374.7	+	56551.6i	0.211143	+	0.649832i
$296$	−61808.4	−	85072.0i	−0.705446	−	0.970964i
$297$	532.897	+	1640.09i	0.00604130	+	0.0185932i
$298$	−64353.8	+	198061.i	−0.724672	+	2.23031i
$299$	134947.	+	98044.4i	1.50945	+	1.09668i
$300$	1577.49	+	512.558i	0.0175277	+	0.00569509i
$301$	5711.12	+	7860.69i	0.0630360	+	0.0867616i
$302$	−70226.8	−	96658.9i	−0.769997	−	1.05981i
$303$	788.016	−	1084.61i	0.00858322	−	0.0118138i
$304$	−347902.			−3.76452
$305$			45206.5i			0.485960i
$306$	34012.5	−	46814.2i	0.363242	−	0.499959i
$307$	−38626.5	−	118880.i	−0.409835	−	1.26134i	−0.916790	−	0.399369i	$-0.869229\pi$
$307$	−38626.5	−	118880.i	−0.409835	−	1.26134i	0.506956	−	0.861972i	$-0.330771\pi$
$308$	−36770.5	−	11947.5i	−0.387613	−	0.125943i
$309$		−	248.771i		−	0.00260545i
$310$	125731.	−	32894.1i	1.30834	−	0.342290i
$311$	−68459.8			−0.707807			−0.353903	−	0.935282i	$-0.615146\pi$
$311$	−68459.8			−0.707807			−0.353903	+	0.935282i	$0.615146\pi$
$312$	−2154.61	+	6631.20i	−0.0221339	+	0.0681213i
$313$	−68515.2	+	22261.9i	−0.699356	+	0.227235i	−0.637050	−	0.770823i	$-0.719846\pi$
$313$	−68515.2	+	22261.9i	−0.699356	+	0.227235i	−0.0623061	+	0.998057i	$0.519846\pi$
$314$	−89285.7	−	64869.9i	−0.905572	−	0.657936i
$315$	19251.1			0.194015
$316$			23511.9i			0.235458i
$317$	83860.2	+	60928.0i	0.834521	+	0.606315i	0.920835	−	0.389953i	$-0.127509\pi$
$317$	83860.2	+	60928.0i	0.834521	+	0.606315i	−0.0863138	+	0.996268i	$0.527509\pi$
$318$	950.520	−	690.593i	0.00939954	−	0.00682917i
$319$	100632.	−	73113.3i	0.988903	−	0.718480i
$320$	−31602.7	+	97263.2i	−0.308620	+	0.949836i
$321$	−937.126	+	1289.84i	−0.00909469	+	0.0125178i
$322$	55191.5	+	17932.8i	0.532305	+	0.172956i
$323$	−47347.0	+	15384.0i	−0.453824	+	0.147456i
$324$	−209357.	+	152107.i	−1.99433	+	1.44897i
$325$	78715.9	−	25576.3i	0.745239	−	0.242143i
$326$	−25865.5	−	79605.8i	−0.243380	−	0.749048i
$327$	930.351	+	1280.52i	0.00870065	+	0.0119754i
$328$	95794.3	+	294824.i	0.890414	+	2.74041i
$329$	−7106.10	+	21870.3i	−0.0656507	+	0.202052i
$330$	−1164.81	−	846.281i	−0.0106961	−	0.00777118i
$331$	−55957.8	−	18181.8i	−0.510745	−	0.165951i	0.0422960	−	0.999105i	$-0.486533\pi$
$331$	−55957.8	−	18181.8i	−0.510745	−	0.165951i	−0.553041	+	0.833154i	$0.686533\pi$
$332$	−202291.	−	278429.i	−1.83527	−	2.52603i
$333$	28631.5	+	39407.8i	0.258199	+	0.355381i
$334$	−67113.4	+	92373.6i	−0.601612	+	0.828047i
$335$	120745.			1.07592
$336$			1249.13i			0.0110645i
$337$	−100964.	+	138965.i	−0.889013	+	1.22362i	0.0848290	+	0.996396i	$0.472966\pi$
$337$	−100964.	+	138965.i	−0.889013	+	1.22362i	−0.973842	+	0.227226i	$0.927034\pi$
$338$	115068.	+	354144.i	1.00722	+	3.09989i
$339$	−1293.53	−	420.292i	−0.0112558	−	0.00365722i
$340$			68762.8i			0.594834i
$341$	71775.1	+	4187.20i	0.617256	+	0.0360093i
$342$	312961.			2.67571
$343$	18734.3	−	57658.3i	0.159239	−	0.490088i
$344$	123387.	−	40090.9i	1.04268	−	0.338789i
$345$	1244.06	+	903.861i	0.0104521	+	0.00759387i
$346$	−22757.4			−0.190095
$347$			14567.7i			0.120985i	0.998169	+	0.0604925i	$0.0192671\pi$
$347$			14567.7i			0.120985i	−0.998169	+	0.0604925i	$0.980733\pi$
$348$	−7555.18	−	5489.16i	−0.0623859	−	0.0453260i
$349$	115225.	−	83715.9i	0.946010	−	0.687317i	−0.00384954	−	0.999993i	$-0.501225\pi$
$349$	115225.	−	83715.9i	0.946010	−	0.687317i	0.949860	+	0.312676i	$0.101225\pi$
$350$	23295.7	−	16925.3i	0.190169	−	0.138166i
$351$	1996.40	−	6144.30i	0.0162044	−	0.0498722i
$352$	−96593.4	+	132949.i	−0.779583	+	1.07300i
$353$	−64980.9	−	21113.6i	−0.521478	−	0.169439i	0.0364379	−	0.999336i	$-0.488399\pi$
$353$	−64980.9	−	21113.6i	−0.521478	−	0.169439i	−0.557916	+	0.829897i	$0.688399\pi$
$354$	3300.91	−	1072.53i	0.0263407	−	0.00855860i
$355$	101687.	−	73880.1i	0.806881	−	0.586234i
$356$	−92039.6	+	29905.5i	−0.726231	+	0.235967i
$357$	55.2359	+	169.999i	0.000433396	+	0.00133386i
$358$	−65115.5	−	89623.8i	−0.508064	−	0.699290i
$359$	−26434.0	−	81355.4i	−0.205104	−	0.631244i	−0.999709	−	0.0241180i	$-0.992322\pi$
$359$	−26434.0	−	81355.4i	−0.205104	−	0.631244i	0.794605	−	0.607126i	$-0.207678\pi$
$360$	79432.6	−	244468.i	0.612906	−	1.88633i
$361$	−112397.	−	81661.1i	−0.862461	−	0.626615i
$362$	−158033.	−	51347.9i	−1.20595	−	0.391837i
$363$	756.446	+	1041.16i	0.00574070	+	0.00790140i
$364$	85136.8	+	117181.i	0.642561	+	0.884409i
$365$	18837.8	−	25928.0i	0.141399	−	0.194618i
$366$	2638.69			0.0196982
$367$			253336.i			1.88090i	0.339937	+	0.940448i	$0.389594\pi$
$367$			253336.i			1.88090i	−0.339937	+	0.940448i	$0.610406\pi$
$368$	234535.	−	322810.i	1.73186	−	2.38370i
$369$	−44374.7	−	136571.i	−0.325899	−	1.00301i
$370$	−77366.1	−	25137.8i	−0.565128	−	0.183621i
$371$		−	14513.6i		−	0.105445i
$372$	−1366.22	−	5222.10i	−0.00987267	−	0.0377363i
$373$	196516.			1.41248			0.706238	−	0.707975i	$-0.250391\pi$
$373$	196516.			1.41248			0.706238	+	0.707975i	$0.250391\pi$
$374$	−16520.2	+	50843.8i	−0.118106	+	0.363492i
$375$	2261.56	−	734.824i	0.0160822	−	0.00522542i
$376$	248409.	+	180480.i	1.75708	+	1.27659i
$377$	−465996.			−3.27869
$378$		−	2247.65i		−	0.0157306i
$379$	160527.	+	116630.i	1.11756	+	0.811952i	0.983837	−	0.179068i	$-0.0573081\pi$
$379$	160527.	+	116630.i	1.11756	+	0.811952i	0.133719	+	0.991019i	$0.457308\pi$
$380$	−300872.	+	218596.i	−2.08360	+	1.51383i
$381$	−2087.28	+	1516.50i	−0.0143791	+	0.0104470i
$382$	45605.5	−	140359.i	0.312529	−	0.961865i
$383$	96327.7	−	132584.i	0.656680	−	0.903842i	−0.342686	−	0.939450i	$-0.611337\pi$
$383$	96327.7	−	132584.i	0.656680	−	0.903842i	0.999366	+	0.0356076i	$0.0113366\pi$
$384$	920.823	+	299.193i	0.00624473	+	0.00202904i
$385$	−16915.1	+	5496.04i	−0.114118	+	0.0370790i
$386$	124912.	−	90754.1i	0.838360	−	0.609104i
$387$	−57156.6	+	18571.3i	−0.381632	+	0.124000i
$388$	−58399.4	−	179735.i	−0.387922	−	1.19390i
$389$	144072.	+	198298.i	0.952096	+	1.31045i	0.950590	+	0.310449i	$0.100479\pi$
$389$	144072.	+	198298.i	0.952096	+	1.31045i	0.00150628	+	0.999999i	$0.499521\pi$
$390$	1666.80	+	5129.88i	0.0109586	+	0.0337270i
$391$	17644.2	−	54303.1i	0.115411	−	0.355199i
$392$	−315328.	−	229099.i	−2.05206	−	1.49091i
$393$	2092.31	+	679.834i	0.0135470	+	0.00440167i
$394$	222840.	+	306713.i	1.43549	+	1.97579i
$395$	6357.41	+	8750.22i	0.0407461	+	0.0560822i
$396$	140562.	−	193468.i	0.896352	−	1.23372i
$397$	169397.			1.07479			0.537395	−	0.843331i	$-0.319408\pi$
$397$	169397.			1.07479			0.537395	+	0.843331i	$0.319408\pi$
$398$			362644.i			2.28936i
$399$	−568.236	+	782.110i	−0.00356930	+	0.00491272i
$400$	−61181.9	−	188298.i	−0.382387	−	1.17687i
$401$	−210367.	−	68352.3i	−1.30824	−	0.425074i	−0.429801	−	0.902923i	$-0.641416\pi$
$401$	−210367.	−	68352.3i	−1.30824	−	0.425074i	−0.878442	+	0.477850i	$0.841416\pi$
$402$		−	7047.87i		−	0.0436120i
$403$	−208318.	−	170742.i	−1.28268	−	1.05131i
$404$	−371869.			−2.27839
$405$	−36786.3	+	113217.i	−0.224273	+	0.690240i
$406$	−154188.	+	50098.7i	−0.935403	+	0.303931i
$407$	−36407.8	−	26451.8i	−0.219789	−	0.159686i
$408$	2386.71			0.0143377
$409$			43089.1i			0.257585i	0.991672	+	0.128792i	$0.0411101\pi$
$409$			43089.1i			0.257585i	−0.991672	+	0.128792i	$0.958890\pi$
$410$	194013.	+	140959.i	1.15415	+	0.838540i
$411$	−2727.17	+	1981.40i	−0.0161446	+	0.0117298i
$412$	−55825.3	+	40559.5i	−0.328880	+	0.238945i
$413$	13248.9	−	40776.0i	0.0776749	−	0.239059i
$414$	−210980.	+	290389.i	−1.23095	+	1.69426i
$415$	−150570.	−	48923.1i	−0.874262	−	0.284065i
$416$	585518.	−	190246.i	3.38340	−	1.09933i
$417$	−2247.97	+	1633.25i	−0.0129276	+	0.00939246i
$418$	−274985.	+	89348.1i	−1.57383	+	0.511367i
$419$	−34113.9	−	104992.i	−0.194314	−	0.598036i	−0.999984	−	0.00567196i	$-0.998195\pi$
$419$	−34113.9	−	104992.i	−0.194314	−	0.598036i	0.805670	−	0.592365i	$-0.201805\pi$
$420$	784.866	+	1080.28i	0.00444936	+	0.00612401i
$421$	−88297.3	−	271751.i	−0.498176	−	1.53323i	−0.811947	−	0.583731i	$-0.801592\pi$
$421$	−88297.3	−	271751.i	−0.498176	−	1.53323i	0.313771	−	0.949499i	$-0.398408\pi$
$422$	−18788.9	+	57826.3i	−0.105506	+	0.324713i
$423$	−115070.	−	83603.6i	−0.643107	−	0.467244i
$424$	−184307.	−	59885.0i	−1.02520	−	0.333109i
$425$	−16652.9	−	22920.7i	−0.0921958	−	0.126897i
$426$	−4312.36	−	5935.46i	−0.0237627	−	0.0327066i
$427$	19159.3	−	26370.5i	0.105081	−	0.144631i
$428$	442235.			2.41416
$429$			2983.97i			0.0162136i
$430$	58992.6	−	81196.4i	0.319051	−	0.439137i
$431$	64866.4	+	199638.i	0.349193	+	1.07471i	0.959301	+	0.282387i	$0.0911261\pi$
$431$	64866.4	+	199638.i	0.349193	+	1.07471i	−0.610108	+	0.792318i	$0.708874\pi$
$432$	−14698.0	−	4775.65i	−0.0787570	−	0.0255897i
$433$		−	20972.4i		−	0.111859i	−0.998435	−	0.0559297i	$-0.982188\pi$
$433$		−	20972.4i		−	0.111859i	0.998435	−	0.0559297i	$-0.0178123\pi$
$434$	−87284.3	−	34098.7i	−0.463401	−	0.181033i
$435$	−4295.97			−0.0227030
$436$	135670.	−	417550.i	0.713693	−	2.19652i
$437$	293695.	−	95427.2i	1.53792	−	0.499700i
$438$	−1513.41	−	1099.56i	−0.00788877	−	0.00573153i
$439$	−38975.7			−0.202239			−0.101119	−	0.994874i	$-0.532242\pi$
$439$	−38975.7			−0.202239			−0.101119	+	0.994874i	$0.532242\pi$
$440$			237481.i			1.22666i
$441$	146069.	+	106126.i	0.751072	+	0.545686i
$442$	162030.	−	117721.i	0.829373	−	0.602575i
$443$	−111893.	+	81294.8i	−0.570157	+	0.414243i	−0.835162	−	0.550004i	$-0.814626\pi$
$443$	−111893.	+	81294.8i	−0.570157	+	0.414243i	0.265005	+	0.964247i	$0.414626\pi$
$444$	−1044.07	+	3213.31i	−0.00529618	+	0.0163000i
$445$	−26167.4	+	36016.4i	−0.132142	+	0.181878i
$446$	473717.	+	153920.i	2.38149	+	0.773794i
$447$	3784.20	−	1229.56i	0.0189391	−	0.00615369i
$448$	59656.7	−	43343.1i	0.297237	−	0.215956i
$449$	46703.0	−	15174.7i	0.231661	−	0.0752711i	−0.190886	−	0.981612i	$-0.561136\pi$
$449$	46703.0	−	15174.7i	0.231661	−	0.0752711i	0.422547	+	0.906341i	$0.361136\pi$
$450$	55037.3	+	169387.i	0.271789	+	0.836481i
$451$	77980.1	+	107330.i	0.383381	+	0.527679i
$452$	116580.	+	358797.i	0.570621	+	1.75619i
$453$	−705.412	+	2171.03i	−0.00343753	+	0.0105796i
$454$	−11482.5	−	8342.53i	−0.0557090	−	0.0404749i
$455$	63369.3	+	20589.9i	0.306095	+	0.0994563i
$456$	7587.34	+	10443.1i	0.0364888	+	0.0502226i
$457$	−66287.8	−	91237.3i	−0.317396	−	0.436858i	0.620274	−	0.784385i	$-0.287021\pi$
$457$	−66287.8	−	91237.3i	−0.317396	−	0.436858i	−0.937670	+	0.347527i	$0.887021\pi$
$458$	82868.1	−	114058.i	0.395054	−	0.543745i
$459$	−2211.47			−0.0104968
$460$		−	426537.i		−	2.01577i
$461$	72927.1	−	100376.i	0.343153	−	0.472309i	−0.602206	−	0.798341i	$-0.705712\pi$
$461$	72927.1	−	100376.i	0.343153	−	0.472309i	0.945359	+	0.326031i	$0.105712\pi$
$462$	320.803	+	987.329i	0.00150298	+	0.00462570i
$463$	−135833.	−	44134.9i	−0.633642	−	0.205883i	−0.0254541	−	0.999676i	$-0.508103\pi$
$463$	−135833.	−	44134.9i	−0.633642	−	0.205883i	−0.608188	+	0.793793i	$0.708103\pi$
$464$			1.11472e6i			5.17763i
$465$	−1920.46	−	1574.05i	−0.00888178	−	0.00727969i
$466$	233989.			1.07751
$467$	−53444.7	+	164486.i	−0.245059	+	0.754215i	0.750567	+	0.660794i	$0.229780\pi$
$467$	−53444.7	+	164486.i	−0.245059	+	0.754215i	−0.995627	+	0.0934212i	$0.970220\pi$
$468$	−852044.	+	276846.i	−3.89018	+	1.26400i
$469$	−70434.7	−	51173.8i	−0.320215	−	0.232650i
$470$	237534.			1.07530
$471$			2108.63i			0.00950515i
$472$	−463145.	−	336494.i	−2.07890	−	1.51041i
$473$	44918.9	−	32635.5i	0.200774	−	0.145871i
$474$	510.748	−	371.080i	0.00227327	−	0.00165162i
$475$	47350.4	−	145730.i	0.209863	−	0.645893i
$476$	29142.8	−	40111.7i	0.128623	−	0.177034i
$477$	85376.5	+	27740.5i	0.375234	+	0.121921i
$478$	−437250.	+	142071.i	−1.91370	+	0.621799i
$479$	80608.8	−	58565.8i	0.351327	−	0.255254i	−0.398098	−	0.917343i	$-0.630330\pi$
$479$	80608.8	−	58565.8i	0.351327	−	0.255254i	0.749426	+	0.662089i	$0.230330\pi$
$480$	5397.82	−	1753.86i	0.0234281	−	0.00761224i
$481$	52098.4	+	160342.i	0.225182	+	0.693040i
$482$	−437461.	−	602114.i	−1.88298	−	2.59170i
$483$	−342.630	−	1054.51i	−0.00146869	−	0.00452017i
$484$	110310.	−	339500.i	0.470896	−	1.44927i
$485$	−70332.8	−	51099.7i	−0.299002	−	0.217238i
$486$	19833.6	+	6444.31i	0.0839708	+	0.0272838i
$487$	223739.	+	307951.i	0.943375	+	1.29844i	0.954408	+	0.298505i	$0.0964880\pi$
$487$	223739.	+	307951.i	0.943375	+	1.29844i	−0.0110332	+	0.999939i	$0.503512\pi$
$488$	−255823.	−	352110.i	−1.07424	−	1.47856i
$489$	−940.012	+	1293.82i	−0.00393111	+	0.00541072i
$490$	−301523.			−1.25582
$491$			63508.9i			0.263434i	0.991287	+	0.131717i	$0.0420490\pi$
$491$			63508.9i			0.263434i	−0.991287	+	0.131717i	$0.957951\pi$
$492$	5854.55	−	8058.10i	0.0241860	−	0.0332891i
$493$	49292.3	+	151706.i	0.202808	+	0.624179i
$494$	1.03018e6	+	334727.i	4.22144	+	1.37163i
$495$		−	110008.i		−	0.448967i
$496$	−408436.	+	498324.i	−1.66020	+	2.02558i
$497$	−90629.2			−0.366907
$498$	−2855.63	+	8788.72i	−0.0115144	+	0.0354378i
$499$	151270.	−	49150.5i	0.607506	−	0.197391i	0.0109206	−	0.999940i	$-0.496524\pi$
$499$	151270.	−	49150.5i	0.607506	−	0.197391i	0.596585	+	0.802550i	$0.296524\pi$
$500$	−533620.	−	387698.i	−2.13448	−	1.55079i
$501$	2181.56			0.00869143
$502$			673815.i			2.67383i
$503$	−120678.	−	87677.5i	−0.476970	−	0.346539i	0.323181	−	0.946337i	$-0.395248\pi$
$503$	−120678.	−	87677.5i	−0.476970	−	0.346539i	−0.800151	+	0.599798i	$0.795248\pi$
$504$	−149946.	+	108942.i	−0.590300	+	0.428878i
$505$	−138396.	+	100550.i	−0.542674	+	0.394276i
$506$	102475.	−	315385.i	0.400236	−	1.23180i
$507$	4181.85	−	5755.83i	0.0162687	−	0.0223919i
$508$	680617.	+	221146.i	2.63740	+	0.856942i
$509$	203601.	−	66153.8i	0.785857	−	0.255340i	0.111518	−	0.993762i	$-0.464429\pi$
$509$	203601.	−	66153.8i	0.785857	−	0.255340i	0.674339	+	0.738422i	$0.264429\pi$
$510$	1493.73	−	1085.26i	0.00574292	−	0.00417247i
$511$	−21977.5	+	7140.92i	−0.0841659	+	0.0273472i
$512$	124416.	+	382912.i	0.474608	+	1.46069i
$513$	−7030.24	−	9676.30i	−0.0267138	−	0.0367684i
$514$	−147153.	−	452889.i	−0.556982	−	1.71422i
$515$	−9809.12	+	30189.4i	−0.0369841	+	0.113826i
$516$	−3372.40	−	2450.19i	−0.0126660	−	0.00920239i
$517$	124975.	+	40607.0i	0.467566	+	0.151922i
$518$	34476.4	+	47452.8i	0.128488	+	0.176849i
$519$	255.575	+	351.769i	0.000948820	+	0.00130594i
$520$	522940.	−	719765.i	1.93395	−	2.66185i
$521$	424078.			1.56232			0.781161	−	0.624330i	$-0.214628\pi$
$521$	424078.			1.56232			0.781161	+	0.624330i	$0.214628\pi$
$522$		−	1.00277e6i		−	3.68011i
$523$	−268493.	+	369549.i	−0.981589	+	1.35104i	−0.0456203	+	0.998959i	$0.514526\pi$
$523$	−268493.	+	369549.i	−0.981589	+	1.35104i	−0.935969	+	0.352083i	$0.885474\pi$
$524$	−188572.	−	580364.i	−0.686774	−	2.11367i
$525$	−523.239	−	170.011i	−0.00189837	−	0.000616819i
$526$		−	682791.i		−	2.46783i
$527$	−33549.8	+	85879.3i	−0.120801	+	0.309220i
$528$	7138.03			0.0256041
$529$	−22971.5	+	70698.9i	−0.0820876	+	0.252640i
$530$	−142580.	+	46326.9i	−0.507581	+	0.164923i
$531$	214542.	+	155874.i	0.760894	+	0.552822i
$532$	268154.			0.947459
$533$		−	497016.i		−	1.74951i
$534$	2102.27	+	1527.39i	0.00737234	+	0.00535632i
$535$	164583.	−	119576.i	0.575012	−	0.417771i
$536$	−940476.	+	683296.i	−3.27354	+	2.37837i
$537$	−654.070	+	2013.02i	−0.00226817	+	0.00698071i
$538$	23067.8	−	31750.1i	0.0796970	−	0.109693i
$539$	−158642.	−	51546.1i	−0.546062	−	0.177426i
$540$	−15711.8	+	5105.06i	−0.0538812	+	0.0175071i
$541$	89728.6	−	65191.6i	0.306575	−	0.222740i	−0.423851	−	0.905732i	$-0.639322\pi$
$541$	89728.6	−	65191.6i	0.306575	−	0.222740i	0.730425	+	0.682993i	$0.239322\pi$
$542$	−757484.	+	246121.i	−2.57854	+	0.837820i
$543$	981.068	+	3019.42i	0.00332736	+	0.0102406i
$544$	−123870.	−	170493.i	−0.418571	−	0.576114i
$545$	−62410.6	−	192080.i	−0.210119	−	0.646680i
$546$	1201.83	−	3698.85i	0.00403142	−	0.0124074i
$547$	−539.656	−	392.083i	−0.00180361	−	0.00131040i	0.586883	−	0.809672i	$-0.300355\pi$
$547$	−539.656	−	392.083i	−0.00180361	−	0.00131040i	−0.588687	+	0.808361i	$0.700355\pi$
$548$	889272.	+	288942.i	2.96124	+	0.962165i
$549$	118505.	+	163108.i	0.393180	+	0.541166i
$550$	−96717.6	−	133120.i	−0.319728	−	0.440067i
$551$	−507092.	+	697952.i	−1.67026	+	2.29891i
$552$	−14804.8			−0.0485876
$553$		−	7798.68i		−	0.0255018i
$554$	−165609.	+	227942.i	−0.539592	+	0.742685i
$555$	480.289	+	1478.18i	0.00155925	+	0.00479889i
$556$	733015.	+	238171.i	2.37117	+	0.770441i
$557$		−	210793.i		−	0.679433i	−0.940528	−	0.339717i	$-0.889669\pi$
$557$		−	210793.i		−	0.679433i	0.940528	−	0.339717i	$-0.110331\pi$
$558$	367417.	−	448277.i	1.18002	−	1.43972i
$559$	−208006.			−0.665661
$560$	49253.8	−	151587.i	0.157059	−	0.483378i
$561$	971.437	−	315.639i	0.00308666	−	0.00100292i
$562$	−216166.	−	157054.i	−0.684409	−	0.497252i
$563$	−275165.			−0.868112			−0.434056	−	0.900886i	$-0.642918\pi$
$563$	−275165.			−0.868112			−0.434056	+	0.900886i	$0.642918\pi$
$564$		−	9865.69i		−	0.0310148i
$565$	140402.	+	102008.i	0.439822	+	0.319550i
$566$	91734.8	−	66649.2i	0.286353	−	0.208047i
$567$	69441.8	−	50452.5i	0.216001	−	0.156934i
$568$	−373948.	+	1.15089e6i	−1.15908	+	3.56729i
$569$	76702.2	−	105571.i	0.236910	−	0.326078i	−0.673963	−	0.738765i	$-0.735409\pi$
$569$	76702.2	−	105571.i	0.236910	−	0.326078i	0.910873	+	0.412686i	$0.135409\pi$
$570$	9497.14	+	3085.81i	0.0292310	+	0.00949771i
$571$	−572805.	+	186116.i	−1.75685	+	0.570835i	−0.996866	−	0.0791062i	$-0.974793\pi$
$571$	−572805.	+	186116.i	−1.75685	+	0.570835i	−0.759984	+	0.649941i	$0.774793\pi$
$572$	669615.	−	486504.i	2.04660	−	1.48694i
$573$	−2681.74	+	871.351i	−0.00816785	+	0.00265390i
$574$	−53433.6	−	164452.i	−0.162178	−	0.499131i
$575$	103298.	+	142178.i	0.312433	+	0.430027i
$576$	140942.	+	433776.i	0.424811	+	1.30743i
$577$	−6217.04	+	19134.1i	−0.0186738	+	0.0574720i	−0.959959	−	0.280140i	$-0.909619\pi$
$577$	−6217.04	+	19134.1i	−0.0186738	+	0.0574720i	0.941285	+	0.337612i	$0.109619\pi$
$578$	447792.	+	325340.i	1.34036	+	0.973828i
$579$	−2805.63	−	911.604i	−0.00836899	−	0.00271925i
$580$	700412.	+	964034.i	2.08208	+	2.86574i
$581$	67098.0	+	92352.5i	0.198773	+	0.273588i
$582$	−2982.68	+	4105.31i	−0.00880564	+	0.0121199i
$583$	−82936.2			−0.244010
$584$			308555.i			0.904705i
$585$	−242241.	+	333417.i	−0.707842	+	0.974261i
$586$	−21998.8	−	67705.5i	−0.0640626	−	0.197164i
$587$	−22358.3	−	7264.65i	−0.0648877	−	0.0210833i	0.276393	−	0.961045i	$-0.410861\pi$
$587$	−22358.3	−	7264.65i	−0.0648877	−	0.0210833i	−0.341281	+	0.939961i	$0.610861\pi$
$588$			12523.4i			0.0362216i
$589$	−482420.	+	126212.i	−1.39058	+	0.363807i
$590$	−442868.			−1.27224
$591$	2238.38	−	6889.02i	0.00640853	−	0.0197234i
$592$	383559.	−	124626.i	1.09443	−	0.355603i
$593$	88181.0	+	64067.3i	0.250764	+	0.182191i	0.706066	−	0.708147i	$-0.250468\pi$
$593$	88181.0	+	64067.3i	0.250764	+	0.182191i	−0.455301	+	0.890338i	$0.650468\pi$
$594$	−12843.9			−0.0364019
$595$		−	22808.0i		−	0.0644248i
$596$	−892893.	−	648725.i	−2.51366	−	1.82628i
$597$	5605.50	−	4072.64i	0.0157277	−	0.0114269i
$598$	−1.00507e6	+	730228.i	−2.81058	+	2.04200i
$599$	6078.50	−	18707.7i	0.0169412	−	0.0521395i	−0.942229	−	0.334971i	$-0.891274\pi$
$599$	6078.50	−	18707.7i	0.0169412	−	0.0521395i	0.959170	+	0.282831i	$0.0912736\pi$
$600$	−4317.91	+	5943.09i	−0.0119942	+	0.0165086i
$601$	−129135.	−	41958.7i	−0.357517	−	0.116164i	0.124751	−	0.992188i	$-0.460187\pi$
$601$	−129135.	−	41958.7i	−0.357517	−	0.116164i	−0.482268	+	0.876024i	$0.660187\pi$
$602$	−68824.8	+	22362.5i	−0.189912	+	0.0617061i
$603$	435656.	−	316523.i	1.19814	−	0.870503i
$604$	602199.	−	195666.i	1.65069	−	0.536343i
$605$	−50744.6	−	156176.i	−0.138637	−	0.426680i
$606$	5869.09	+	8078.11i	0.0159818	+	0.0219971i
$607$	−46583.8	−	143370.i	−0.126432	−	0.389118i	0.867727	−	0.497041i	$-0.165580\pi$
$607$	−46583.8	−	143370.i	−0.126432	−	0.389118i	−0.994159	+	0.107923i	$0.965580\pi$
$608$	352210.	−	1.08399e6i	0.952784	−	2.93237i
$609$	2505.98	+	1820.70i	0.00675684	+	0.00490913i
$610$	−320216.	−	104044.i	−0.860564	−	0.279614i
$611$	−289362.	−	398273.i	−0.775103	−	1.06684i
$612$	180256.	+	248100.i	0.481267	+	0.662407i
$613$	345889.	−	476075.i	0.920483	−	1.26694i	−0.0429754	−	0.999076i	$-0.513684\pi$
$613$	345889.	−	476075.i	0.920483	−	1.26694i	0.963458	−	0.267859i	$-0.0863163\pi$
$614$	930976.			2.46946
$615$		−	4581.94i		−	0.0121143i
$616$	100648.	−	138531.i	0.265244	−	0.365077i
$617$	−151577.	−	466505.i	−0.398164	−	1.22542i	−0.926470	−	0.376369i	$-0.877173\pi$
$617$	−151577.	−	466505.i	−0.398164	−	1.22542i	0.528306	−	0.849054i	$-0.322827\pi$
$618$	1762.15	+	572.556i	0.00461387	+	0.00149914i
$619$			538545.i			1.40553i	0.711422	+	0.702765i	$0.248052\pi$
$619$			538545.i			1.40553i	−0.711422	+	0.702765i	$0.751948\pi$
$620$	−40112.6	+	687593.i	−0.104351	+	1.78874i
$621$	13717.8			0.0355714
$622$	157563.	−	484928.i	0.407261	−	1.25342i
$623$	30528.7	−	9919.38i	0.0786561	−	0.0255569i
$624$	−21634.2	−	15718.2i	−0.0555612	−	0.0403676i
$625$	−118861.			−0.304284
$626$		−	536558.i		−	1.36920i
$627$	4469.27	+	3247.12i	0.0113685	+	0.00825967i
$628$	473186.	−	343790.i	1.19981	−	0.871714i
$629$	46688.9	−	33921.5i	0.118008	−	0.0857381i
$630$	−44307.1	+	136363.i	−0.111633	+	0.343571i
$631$	−112794.	+	155247.i	−0.283287	+	0.389911i	−0.926819	−	0.375508i	$-0.877468\pi$
$631$	−112794.	+	155247.i	−0.283287	+	0.389911i	0.643532	+	0.765419i	$0.277468\pi$
$632$	−99034.8	−	32178.4i	−0.247944	−	0.0805619i
$633$	1104.85	−	358.986i	0.00275736	−	0.000895922i
$634$	−624585.	+	453787.i	−1.55386	+	1.12895i
$635$	313096.	−	101731.i	0.776479	−	0.252293i
$636$	1924.14	+	5921.88i	0.00475687	+	0.0146402i
$637$	367313.	+	505564.i	0.905228	+	1.24594i
$638$	286283.	+	881089.i	0.703322	+	2.16460i
$639$	173224.	−	533128.i	0.424234	−	1.30566i
$640$	−99948.2	−	72616.6i	−0.244014	−	0.177287i
$641$	144348.	+	46901.4i	0.351312	+	0.114148i	0.479357	−	0.877620i	$-0.340870\pi$
$641$	144348.	+	46901.4i	0.351312	+	0.114148i	−0.128044	+	0.991768i	$0.540870\pi$
$642$	−6979.65	−	9606.66i	−0.0169342	−	0.0233079i
$643$	453504.	+	624195.i	1.09688	+	1.50973i	0.839455	+	0.543429i	$0.182874\pi$
$643$	453504.	+	624195.i	1.09688	+	1.50973i	0.257426	+	0.966298i	$0.417126\pi$
$644$	−180774.	+	248813.i	−0.435876	+	0.599932i
$645$	−1917.59			−0.00460931
$646$		−	370785.i		−	0.888499i
$647$	49883.1	−	68658.2i	0.119164	−	0.164015i	−0.745268	−	0.666765i	$-0.767678\pi$
$647$	49883.1	−	68658.2i	0.119164	−	0.164015i	0.864432	+	0.502750i	$0.167678\pi$
$648$	−354166.	−	1.09001e6i	−0.843445	−	2.59586i
$649$	−233010.	−	75709.4i	−0.553203	−	0.179746i
$650$			616441.i			1.45903i
$651$	453.163	+	1732.12i	0.00106928	+	0.00408711i
$652$	443597.			1.04350
$653$	170686.	−	525316.i	0.400286	−	1.23195i	−0.524482	−	0.851422i	$-0.675741\pi$
$653$	170686.	−	525316.i	0.400286	−	1.23195i	0.924768	−	0.380532i	$-0.124259\pi$
$654$	−11211.7	+	3642.89i	−0.0262129	+	0.00851708i
$655$	−227105.	−	165001.i	−0.529351	−	0.384596i
$656$	−1.18893e6			−2.76279
$657$		−	142932.i		−	0.331130i
$658$	−138561.	−	100671.i	−0.320030	−	0.232515i
$659$	−146475.	+	106421.i	−0.337282	+	0.245050i	−0.743514	−	0.668720i	$-0.766843\pi$
$659$	−146475.	+	106421.i	−0.337282	+	0.245050i	0.406232	+	0.913770i	$0.366843\pi$
$660$	6173.10	−	4485.02i	0.0141715	−	0.0102962i
$661$	−254068.	+	781939.i	−0.581495	+	1.78966i	0.0314154	+	0.999506i	$0.489999\pi$
$661$	−254068.	+	781939.i	−0.581495	+	1.78966i	−0.612911	+	0.790152i	$0.710001\pi$
$662$	257578.	−	354525.i	0.587750	−	0.808968i
$663$	−3639.31	−	1182.48i	−0.00827928	−	0.00269010i
$664$	1.44963e6	−	471014.i	3.28793	−	1.06831i
$665$	99796.6	−	72506.5i	0.225669	−	0.163958i
$666$	−345038.	+	112110.i	−0.777891	+	0.252752i
$667$	−305761.	−	941037.i	−0.687276	−	2.11522i
$668$	−355680.	−	489551.i	−0.797088	−	1.09710i
$669$	−2940.84	−	9050.97i	−0.00657081	−	0.0202229i
$670$	−277900.	+	855287.i	−0.619068	+	1.90529i
$671$	−150691.	−	109483.i	−0.334689	−	0.243166i
$672$	−3892.05	−	1264.60i	−0.00861866	−	0.00280037i
$673$	−163668.	−	225269.i	−0.361354	−	0.497361i	0.589171	−	0.808008i	$-0.299454\pi$
$673$	−163668.	−	225269.i	−0.361354	−	0.497361i	−0.950525	+	0.310647i	$0.899454\pi$
$674$	−751975.	−	1.03501e6i	−1.65533	−	2.27836i
$675$	4000.87	−	5506.72i	0.00878105	−	0.0120861i
$676$	−1.97344e6			−4.31848
$677$			577859.i			1.26079i	0.776273	+	0.630397i	$0.217108\pi$
$677$			577859.i			1.26079i	−0.776273	+	0.630397i	$0.782892\pi$
$678$	5954.19	−	8195.25i	0.0129528	−	0.0178280i
$679$	19370.6	+	59616.4i	0.0420148	+	0.129308i
$680$	−289637.	−	94108.8i	−0.626378	−	0.203522i
$681$			271.179i			0.000584738i
$682$	−194853.	+	498775.i	−0.418927	+	1.07235i
$683$	534355.			1.14548			0.572741	−	0.819736i	$-0.305880\pi$
$683$	534355.			1.14548			0.572741	+	0.819736i	$0.305880\pi$
$684$	−512535.	+	1.57742e6i	−1.09550	+	3.37159i
$685$	409080.	−	132918.i	0.871821	−	0.283272i
$686$	365299.	+	265406.i	0.776248	+	0.563978i
$687$	−2693.68			−0.00570731
$688$			497578.i			1.05120i
$689$	251366.	+	182628.i	0.529503	+	0.384706i
$690$	−9265.66	+	6731.89i	−0.0194616	+	0.0141397i
$691$	364729.	−	264991.i	0.763860	−	0.554977i	−0.136232	−	0.990677i	$-0.543499\pi$
$691$	364729.	−	264991.i	0.763860	−	0.554977i	0.900092	+	0.435700i	$0.143499\pi$
$692$	37269.7	−	114704.i	0.0778294	−	0.239534i
$693$	−46623.3	+	64171.4i	−0.0970815	+	0.133621i
$694$	−103189.	−	33528.1i	−0.214247	−	0.0696129i
$695$	337199.	−	109563.i	0.698099	−	0.226826i
$696$	33461.0	−	24310.9i	0.0690750	−	0.0501859i
$697$	−161805.	+	52573.5i	−0.333062	+	0.108219i
$698$	327799.	+	1.00886e6i	0.672816	+	2.07071i
$699$	−2627.79	−	3616.84i	−0.00537818	−	0.00740243i
$700$	47157.4	+	145136.i	0.0962397	+	0.296195i
$701$	51779.9	−	159362.i	0.105372	−	0.324302i	−0.884446	−	0.466643i	$-0.845463\pi$
$701$	51779.9	−	159362.i	0.105372	−	0.324302i	0.989818	+	0.142342i	$0.0454632\pi$
$702$	38927.8	+	28282.7i	0.0789924	+	0.0573913i
$703$	296848.	+	96451.7i	0.600652	+	0.195164i
$704$	−247679.	−	340901.i	−0.499740	−	0.687833i
$705$	−2667.60	−	3671.63i	−0.00536713	−	0.00738722i
$706$	299112.	−	411692.i	0.600101	−	0.825968i
$707$	123346.			0.246766
$708$			18394.0i			0.0366953i
$709$	275092.	−	378632.i	0.547250	−	0.753225i	−0.442386	−	0.896825i	$-0.645868\pi$
$709$	275092.	−	378632.i	0.547250	−	0.753225i	0.989636	+	0.143600i	$0.0458679\pi$
$710$	289286.	+	890329.i	0.573865	+	1.76618i
$711$	45875.9	+	14906.0i	0.0907497	+	0.0294864i
$712$		−	428610.i		−	0.845479i
$713$	208110.	−	532711.i	0.409369	−	1.04788i
$714$	−1331.30			−0.00261143
$715$	117659.	−	362116.i	0.230150	−	0.708330i
$716$	558370.	−	181425.i	1.08917	−	0.353893i
$717$	7106.53	+	5163.20i	0.0138235	+	0.0100434i
$718$	637112.			1.23585
$719$			125253.i			0.242288i	0.992635	+	0.121144i	$0.0386563\pi$
$719$			125253.i			0.242288i	−0.992635	+	0.121144i	$0.961344\pi$
$720$	797575.	+	579472.i	1.53853	+	1.11781i
$721$	18516.8	−	13453.2i	0.0356200	−	0.0258795i
$722$	837124.	−	608206.i	1.60589	−	1.16675i
$723$	−4394.20	+	13523.9i	−0.00840626	+	0.0258718i
$724$	517618.	−	712440.i	0.987489	−	1.35916i
$725$	−466937.	−	151717.i	−0.888346	−	0.288641i
$726$	−9115.94	+	2961.95i	−0.0172953	+	0.00561959i
$727$	−110199.	+	80064.3i	−0.208501	+	0.151485i	−0.687135	−	0.726529i	$-0.741132\pi$
$727$	−110199.	+	80064.3i	−0.208501	+	0.151485i	0.478634	+	0.878015i	$0.341132\pi$
$728$	−610097.	+	198233.i	−1.15116	+	0.374035i
$729$	163978.	+	504672.i	0.308554	+	0.949630i
$730$	140303.	+	193110.i	0.263282	+	0.362376i
$731$	22002.6	+	67717.0i	0.0411755	+	0.126725i
$732$	−4321.37	+	13299.8i	−0.00806490	+	0.0248212i
$733$	55787.6	+	40532.1i	0.103832	+	0.0754381i	0.638490	−	0.769630i	$-0.279560\pi$
$733$	55787.6	+	40532.1i	0.103832	+	0.0754381i	−0.534658	+	0.845069i	$0.679560\pi$
$734$	−1.79448e6	−	583063.i	−3.33079	−	1.08224i
$735$	3386.22	+	4660.73i	0.00626817	+	0.00862739i
$736$	768370.	+	1.05757e6i	1.41845	+	1.95233i
$737$	−292427.	+	402491.i	−0.538371	+	0.741005i
$738$	1.06952e6			1.96371
$739$			535106.i			0.979830i	0.871770	+	0.489915i	$0.162972\pi$
$739$			535106.i			0.979830i	−0.871770	+	0.489915i	$0.837028\pi$
$740$	253404.	−	348780.i	0.462753	−	0.636925i
$741$	−6395.38	−	19683.0i	−0.0116474	−	0.0358471i
$742$	102806.	+	33403.6i	0.186728	+	0.0606716i
$743$		−	450008.i		−	0.815160i	−0.913169	−	0.407580i	$-0.866373\pi$
$743$		−	450008.i		−	0.815160i	0.913169	−	0.407580i	$-0.133627\pi$
$744$	23865.9	+	1392.28i	0.0431154	+	0.00251526i
$745$	−507710.			−0.914752
$746$	−452290.	+	1.39200e6i	−0.812716	+	2.50128i
$747$	−671513.	+	218188.i	−1.20341	+	0.391011i
$748$	−229213.	−	166533.i	−0.409672	−	0.297644i
$749$	−146685.			−0.261471
$750$			17710.7i			0.0314858i
$751$	−4102.17	−	2980.40i	−0.00727333	−	0.00528439i	0.584143	−	0.811651i	$-0.301431\pi$
$751$	−4102.17	−	2980.40i	−0.00727333	−	0.00528439i	−0.591416	+	0.806367i	$0.701431\pi$
$752$	−952720.	+	692191.i	−1.68473	+	1.22403i
$753$	10415.4	−	7567.21i	0.0183690	−	0.0133458i
$754$	1.07251e6	−	3.30084e6i	1.88651	−	5.80607i
$755$	171209.	−	235649.i	0.300354	−	0.413401i
$756$	11328.8	+	3680.95i	0.0198217	+	0.00644046i
$757$	−50787.5	+	16501.8i	−0.0886268	+	0.0287966i	−0.352995	−	0.935625i	$-0.614837\pi$
$757$	−50787.5	+	16501.8i	−0.0886268	+	0.0287966i	0.264368	+	0.964422i	$0.414837\pi$
$758$	−1.19559e6	+	868649.i	−2.08087	+	1.51184i
$759$	−6025.84	+	1957.91i	−0.0104601	+	0.00339868i
$760$	−508980.	−	1.56648e6i	−0.881199	−	2.71205i
$761$	−264626.	−	364226.i	−0.456944	−	0.628929i	0.516928	−	0.856029i	$-0.327076\pi$
$761$	−264626.	−	364226.i	−0.456944	−	0.628929i	−0.973871	+	0.227100i	$0.927076\pi$
$762$	−5938.01	−	18275.3i	−0.0102266	−	0.0314742i
$763$	−45000.6	+	138498.i	−0.0772981	+	0.237899i
$764$	632765.	+	459730.i	1.08407	+	0.787620i
$765$	134168.	+	43594.0i	0.229260	+	0.0744909i
$766$	717442.	+	987475.i	1.22273	+	1.68294i
$767$	539500.	+	742558.i	0.917066	+	1.26223i
$768$	3298.98	−	4540.66i	0.00559316	−	0.00769833i
$769$	−395687.			−0.669112			−0.334556	−	0.942376i	$-0.608586\pi$
$769$	−395687.			−0.669112			−0.334556	+	0.942376i	$0.608586\pi$
$770$		−	132466.i		−	0.223420i
$771$	−5347.86	+	7360.70i	−0.00899646	+	0.0123826i
$772$	252860.	+	778223.i	0.424273	+	1.30578i
$773$	−588150.	−	191102.i	−0.984304	−	0.319820i	−0.227727	−	0.973725i	$-0.573129\pi$
$773$	−588150.	−	191102.i	−0.984304	−	0.319820i	−0.756576	+	0.653905i	$0.773129\pi$
$774$		−	447606.i		−	0.747160i
$775$	−153149.	−	238910.i	−0.254984	−	0.397769i
$776$	836990.			1.38994
$777$	346.308	−	1065.83i	0.000573615	−	0.00176541i
$778$	−1.73621e6	+	564130.i	−2.86843	+	0.932009i
$779$	−744412.	−	540847.i	−1.22670	−	0.891250i
$780$	−28585.8			−0.0469853
$781$			517890.i			0.849054i
$782$	344042.	+	249961.i	0.562598	+	0.408752i
$783$	−31004.1	+	22525.8i	−0.0505704	+	0.0367415i
$784$	1.20937e6	−	878661.i	1.96756	−	1.42952i
$785$	83144.0	−	255891.i	0.134925	−	0.415256i
$786$	−9631.08	+	13256.0i	−0.0155894	+	0.0214570i
$787$	783139.	+	254457.i	1.26441	+	0.410833i	0.863065	−	0.505092i	$-0.168542\pi$
$787$	783139.	+	254457.i	1.26441	+	0.410833i	0.401349	+	0.915925i	$0.368542\pi$
$788$	−1.91087e6	+	620880.i	−3.07736	+	0.999896i
$789$	−10554.1	+	7668.01i	−0.0169538	+	0.0123177i
$790$	−76613.2	+	24893.1i	−0.122758	+	0.0398864i
$791$	−38668.6	−	119010.i	−0.0618024	−	0.190208i
$792$	622535.	+	856846.i	0.992460	+	1.36600i
$793$	215634.	+	663652.i	0.342902	+	1.05534i
$794$	−389873.	+	1.19990e6i	−0.618418	+	1.90329i
$795$	2317.32	+	1683.63i	0.00366649	+	0.00266386i
$796$	−1.82783e6	−	593900.i	−2.88477	−	0.937318i
$797$	207634.	+	285784.i	0.326876	+	0.449906i	0.940551	−	0.339653i	$-0.110310\pi$
$797$	207634.	+	285784.i	0.326876	+	0.449906i	−0.613675	+	0.789559i	$0.710310\pi$
$798$	−4232.18	−	5825.10i	−0.00664598	−	0.00914740i
$799$	−99050.4	+	136331.i	−0.155154	+	0.213551i
$800$	648639.			1.01350
$801$			198545.i			0.309452i
$802$	968334.	−	1.33280e6i	1.50549	−	2.07212i
$803$	40805.9	+	125588.i	0.0632837	+	0.194767i
$804$	35523.4	+	11542.2i	0.0549543	+	0.0178557i
$805$			141478.i			0.218322i
$806$	1.68889e6	−	1.08263e6i	2.59974	−	1.66652i
$807$	−749.832			−0.00115138
$808$	508941.	−	1.56636e6i	0.779551	−	2.39921i
$809$	−144425.	+	46926.4i	−0.220670	+	0.0717001i	−0.417266	−	0.908785i	$-0.637012\pi$
$809$	−144425.	+	46926.4i	−0.220670	+	0.0717001i	0.196595	+	0.980485i	$0.437012\pi$
$810$	−717294.	−	521145.i	−1.09327	−	0.794307i
$811$	−229814.			−0.349410			−0.174705	−	0.984621i	$-0.555897\pi$
$811$	−229814.			−0.349410			−0.174705	+	0.984621i	$0.555897\pi$
$812$		−	859200.i		−	1.30311i
$813$	12311.2	+	8944.62i	0.0186260	+	0.0135326i
$814$	271163.	−	197011.i	0.409243	−	0.297333i
$815$	165090.	−	119945.i	0.248545	−	0.180578i
$816$	−2828.65	+	8705.70i	−0.00424815	+	0.0130745i
$817$	−226350.	+	311544.i	−0.339107	+	0.466741i
$818$	−305217.	−	99171.1i	−0.456145	−	0.148210i
$819$	282615.	−	91827.2i	0.421335	−	0.136900i
$820$	−1.02821e6	+	747036.i	−1.52916	+	1.11100i
$821$	−731061.	+	237536.i	−1.08459	+	0.352406i	−0.796156	−	0.605092i	$-0.793136\pi$
$821$	−731061.	+	237536.i	−1.08459	+	0.352406i	−0.288439	+	0.957498i	$0.593136\pi$
$822$	−7758.41	−	23877.9i	−0.0114823	−	0.0353389i
$823$	−464509.	−	639342.i	−0.685796	−	0.943917i	0.314189	−	0.949360i	$-0.398267\pi$
$823$	−464509.	−	639342.i	−0.685796	−	0.943917i	−0.999985	+	0.00544337i	$0.998267\pi$
$824$	−94438.8	−	290653.i	−0.139090	−	0.428075i
$825$	−971.506	+	2989.99i	−0.00142737	+	0.00439300i
$826$	258340.	+	187695.i	0.378645	+	0.275101i
$827$	−256394.	−	83307.4i	−0.374884	−	0.121807i	0.115514	−	0.993306i	$-0.463148\pi$
$827$	−256394.	−	83307.4i	−0.374884	−	0.121807i	−0.490398	+	0.871499i	$0.663148\pi$
$828$	−1.11813e6	−	1.53897e6i	−1.63091	−	2.24476i
$829$	−426131.	−	586519.i	−0.620060	−	0.853440i	0.377297	−	0.926092i	$-0.376854\pi$
$829$	−426131.	−	586519.i	−0.620060	−	0.853440i	−0.997357	+	0.0726525i	$0.976854\pi$
$830$	693084.	−	953948.i	1.00607	−	1.38474i
$831$	5383.23			0.00779544
$832$			1.57861e6i			2.28049i
$833$	125734.	−	173057.i	0.181201	−	0.249402i
$834$	−6395.15	−	19682.3i	−0.00919430	−	0.0282972i
$835$	−264741.	−	86019.5i	−0.379706	−	0.123374i
$836$		−	1.53233e6i		−	2.19250i
$837$	−22113.5	−	1290.06i	−0.0315651	−	0.00184144i
$838$	822214.			1.17084
$839$	−286181.	+	880775.i	−0.406553	+	1.25124i	0.513039	+	0.858365i	$0.328520\pi$
$839$	−286181.	+	880775.i	−0.406553	+	1.25124i	−0.919592	+	0.392876i	$0.871480\pi$
$840$	−5624.42	+	1827.49i	−0.00797112	+	0.00258997i
$841$	1.66413e6	+	1.20906e6i	2.35285	+	1.70945i
$842$	2.12814e6			3.00176
$843$			5105.13i			0.00718376i
$844$	−260691.	−	189403.i	−0.365967	−	0.265890i
$845$	−734439.	+	533601.i	−1.02859	+	0.747314i
$846$	857037.	−	622674.i	1.19745	−	0.870001i
$847$	−36588.9	+	112609.i	−0.0510014	+	0.156966i
$848$	436870.	−	601300.i	0.607520	−	0.836179i
$849$	−2060.44	−	669.476i	−0.00285854	−	0.000928795i
$850$	200684.	−	65206.1i	0.277763	−	0.0902507i
$851$	−289612.	+	210416.i	−0.399906	+	0.290549i
$852$	36978.8	−	12015.1i	0.0509417	−	0.0165520i
$853$	14244.8	+	43841.0i	0.0195775	+	0.0602535i	0.960368	−	0.278735i	$-0.0899152\pi$
$853$	14244.8	+	43841.0i	0.0195775	+	0.0602535i	−0.940790	+	0.338989i	$0.889915\pi$
$854$	142697.	+	196405.i	0.195659	+	0.269301i
$855$	235775.	+	725640.i	0.322526	+	0.992634i
$856$	−605243.	+	1.86275e6i	−0.826004	+	2.54218i
$857$	−162647.	−	118170.i	−0.221454	−	0.160896i	0.471527	−	0.881852i	$-0.343703\pi$
$857$	−162647.	−	118170.i	−0.221454	−	0.160896i	−0.692981	+	0.720956i	$0.743703\pi$
$858$	−21136.6	−	6867.71i	−0.0287119	−	0.00932905i
$859$	−765753.	−	1.05397e6i	−1.03777	−	1.42837i	−0.898949	−	0.438054i	$-0.855668\pi$
$859$	−765753.	−	1.05397e6i	−1.03777	−	1.42837i	−0.138824	−	0.990317i	$-0.544332\pi$
$860$	312642.	+	430315.i	0.422718	+	0.581821i
$861$	−1941.90	+	2672.80i	−0.00261952	+	0.00360545i
$862$	−1.56341e6			−2.10406
$863$			369261.i			0.495806i	0.968785	+	0.247903i	$0.0797415\pi$
$863$			369261.i			0.495806i	−0.968785	+	0.247903i	$0.920259\pi$
$864$	29759.9	−	40961.0i	0.0398662	−	0.0548711i
$865$	−17144.7	−	52766.0i	−0.0229138	−	0.0705215i
$866$	148556.	+	48268.8i	0.198086	+	0.0643622i
$867$		−	10575.4i		−	0.0140688i
$868$	314812.	−	384096.i	0.417842	−	0.509800i
$869$	−44564.6			−0.0590134
$870$	9887.34	−	30430.1i	0.0130629	−	0.0402036i
$871$	1.77260e6	−	575951.i	2.33654	−	0.759188i
$872$	1.57309e6	+	1.14292e6i	2.06881	+	1.50308i
$873$	−387719.			−0.508731
$874$			2.29999e6i			3.01094i
$875$	176997.	+	128596.i	0.231180	+	0.167962i
$876$	8020.62	−	5827.32i	0.0104520	−	0.00759383i
$877$	−120524.	+	87566.1i	−0.156702	+	0.113851i	−0.663373	−	0.748289i	$-0.730876\pi$
$877$	−120524.	+	87566.1i	−0.156702	+	0.113851i	0.506671	+	0.862139i	$0.330876\pi$
$878$	89703.9	−	276080.i	0.116365	−	0.358135i
$879$	−799.489	+	1100.40i	−0.00103475	+	0.00142421i
$880$	−866228.	−	281455.i	−1.11858	−	0.363449i
$881$	1.09118e6	−	354547.i	1.40587	−	0.456796i	0.494787	−	0.869014i	$-0.335246\pi$
$881$	1.09118e6	−	354547.i	1.40587	−	0.456796i	0.911085	+	0.412218i	$0.135246\pi$
$882$	−1.08791e6	+	790416.i	−1.39848	+	1.01606i
$883$	1.20451e6	−	391367.i	1.54485	−	0.501953i	0.592143	−	0.805833i	$-0.298282\pi$
$883$	1.20451e6	−	391367.i	1.54485	−	0.501953i	0.952710	+	0.303880i	$0.0982821\pi$
$884$	327996.	+	1.00947e6i	0.419725	+	1.29178i
$885$	4973.59	+	6845.55i	0.00635014	+	0.00874021i
$886$	−318319.	−	979685.i	−0.405504	−	1.24801i
$887$	239406.	−	736815.i	0.304290	−	0.936507i	−0.675652	−	0.737221i	$-0.736138\pi$
$887$	239406.	−	736815.i	0.304290	−	0.936507i	0.979941	−	0.199286i	$-0.0638623\pi$
$888$	−12105.9	−	8795.48i	−0.0153523	−	0.0111541i
$889$	−225755.	−	73352.1i	−0.285649	−	0.0928131i
$890$	−194893.	−	268248.i	−0.246046	−	0.338654i
$891$	−288304.	−	396817.i	−0.363158	−	0.499844i
$892$	−1.55161e6	+	2.13560e6i	−1.95008	+	2.68405i
$893$	−911399.			−1.14289
$894$			29634.9i			0.0370791i
$895$	158748.	−	218498.i	0.198181	−	0.272773i
$896$	27527.0	+	84719.5i	0.0342881	+	0.105528i
$897$	22574.7	+	7334.98i	0.0280568	+	0.00911620i
$898$			365742.i			0.453546i
$899$	404401.	+	1.54574e6i	0.500371	+	1.91257i
$900$	−943898.			−1.16531
$901$	32865.9	−	101151.i	0.0404852	−	0.124601i
$902$	−939739.	+	305340.i	−1.15503	+	0.375293i
$903$	1118.59	+	812.706i	0.00137182	+	0.000996685i
$904$	−1.67085e6			−2.04456
$905$		−	405102.i		−	0.494615i
$906$	−13754.8	−	9993.43i	−0.0167570	−	0.0121747i
$907$	−314219.	+	228293.i	−0.381959	+	0.277510i	−0.762153	−	0.647397i	$-0.775857\pi$
$907$	−314219.	+	228293.i	−0.381959	+	0.277510i	0.380193	+	0.924907i	$0.375857\pi$
$908$	60853.7	−	44212.8i	0.0738100	−	0.0536261i
$909$	−235756.	+	725583.i	−0.285322	+	0.878131i
$910$	−291694.	+	401482.i	−0.352244	+	0.484823i
$911$	−197674.	−	64228.0i	−0.238184	−	0.0773905i	0.187493	−	0.982266i	$-0.439964\pi$
$911$	−197674.	−	64228.0i	−0.238184	−	0.0773905i	−0.425676	+	0.904875i	$0.639964\pi$
$912$	−47084.2	+	15298.6i	−0.0566090	+	0.0183934i
$913$	527737.	−	383423.i	0.633106	−	0.459978i
$914$	798834.	−	259557.i	0.956234	−	0.310699i
$915$	1987.90	+	6118.13i	0.00237439	+	0.00730764i
$916$	439175.	+	604473.i	0.523416	+	0.720420i
$917$	62547.5	+	192502.i	0.0743826	+	0.228926i
$918$	5089.78	−	15664.7i	0.00603967	−	0.0185882i
$919$	−695922.	−	505617.i	−0.824005	−	0.598674i	0.0938521	−	0.995586i	$-0.470082\pi$
$919$	−695922.	−	505617.i	−0.824005	−	0.598674i	−0.917857	+	0.396912i	$0.870082\pi$
$920$	1.79662e6	+	583759.i	2.12267	+	0.689696i
$921$	−10455.2	−	14390.4i	−0.0123258	−	0.0169650i
$922$	543156.	+	747591.i	0.638944	+	0.879431i
$923$	1.14041e6	−	1.56964e6i	1.33862	−	1.84245i
$924$	−5501.81			−0.00644409
$925$			177628.i			0.207600i
$926$	625250.	−	860583.i	0.729175	−	1.00362i
$927$	43746.8	+	134639.i	0.0509081	+	0.156679i
$928$	−3.47325e6	−	1.12853e6i	−4.03311	−	1.31044i
$929$			737274.i			0.854275i	0.904187	+	0.427138i	$0.140478\pi$
$929$			737274.i			0.854275i	−0.904187	+	0.427138i	$0.859522\pi$
$930$	15569.7	−	9980.69i	0.0180017	−	0.0115397i
$931$	1.15692e6			1.33476
$932$	−383202.	+	1.17937e6i	−0.441159	+	1.35775i
$933$	−9265.18	+	3010.44i	−0.0106437	+	0.00345833i
$934$	−1.04212e6	−	757142.i	−1.19460	−	0.867927i
$935$	−130333.			−0.149085
$936$		−	3.96780e6i		−	4.52896i
$937$	−882249.	−	640991.i	−1.00487	−	0.730084i	−0.0417467	−	0.999128i	$-0.513292\pi$
$937$	−882249.	−	640991.i	−1.00487	−	0.730084i	−0.963128	+	0.269044i	$0.913292\pi$
$938$	524593.	−	381139.i	0.596234	−	0.433190i
$939$	−8293.74	+	6025.75i	−0.00940631	+	0.00683408i
$940$	−389007.	+	1.19724e6i	−0.440253	+	1.35496i
$941$	323305.	−	444991.i	0.365118	−	0.502542i	−0.586448	−	0.809987i	$-0.699474\pi$
$941$	323305.	−	444991.i	0.365118	−	0.502542i	0.951566	+	0.307445i	$0.0994741\pi$
$942$	−14936.3	−	4853.10i	−0.0168322	−	0.00546912i
$943$	1.00368e6	−	326115.i	1.12868	−	0.366730i
$944$	1.77629e6	−	1.29055e6i	1.99329	−	1.44821i
$945$	5211.45	−	1693.30i	0.00583572	−	0.00189614i
$946$	127788.	+	393291.i	0.142793	+	0.439472i
$947$	218263.	+	300413.i	0.243377	+	0.334980i	0.913178	−	0.407561i	$-0.133621\pi$
$947$	218263.	+	300413.i	0.243377	+	0.334980i	−0.669801	+	0.742541i	$0.733621\pi$
$948$	1033.91	+	3182.04i	0.00115044	+	0.00354070i
$949$	152872.	−	470492.i	0.169744	−	0.522420i
$950$	923283.	+	670804.i	1.02303	+	0.743273i
$951$	14028.7	+	4558.19i	0.0155116	+	0.00504001i
$952$	129070.	+	177650.i	0.142414	+	0.196016i
$953$	505612.	+	695916.i	0.556714	+	0.766251i	0.990904	−	0.134571i	$-0.0429655\pi$
$953$	505612.	+	695916.i	0.556714	+	0.766251i	−0.434190	+	0.900821i	$0.642965\pi$
$954$	−392994.	+	540911.i	−0.431807	+	0.594331i
$955$	359798.			0.394504
$956$		−	2.43654e6i		−	2.66599i
$957$	10404.2	−	14320.1i	0.0113602	−	0.0156359i
$958$	229321.	+	705776.i	0.249869	+	0.769017i
$959$	−294963.	−	95839.4i	−0.320724	−	0.104209i
$960$			14553.1i			0.0157911i
$961$	−385579.	+	839178.i	−0.417510	+	0.908673i
$962$	−1.25568e6			−1.35684
$963$	280366.	−	862879.i	0.302324	−	0.930459i
$964$	3.75126e6	−	1.21886e6i	4.03667	−	1.31159i
$965$	304530.	+	221254.i	0.327020	+	0.237594i
$966$	8258.06			0.00884961
$967$		−	883544.i		−	0.944877i	−0.881364	−	0.472438i	$-0.843374\pi$
$967$		−	883544.i		−	0.944877i	0.881364	−	0.472438i	$-0.156626\pi$
$968$	1.27904e6	+	929279.i	1.36501	+	0.991735i
$969$	−5731.34	+	4164.06i	−0.00610392	+	0.00443476i
$970$	523834.	−	380587.i	0.556737	−	0.404493i
$971$	−499424.	+	1.53707e6i	−0.529701	+	1.63025i	0.225126	+	0.974330i	$0.427721\pi$
$971$	−499424.	+	1.53707e6i	−0.529701	+	1.63025i	−0.754827	+	0.655924i	$0.772279\pi$
$972$	−64962.5	+	89413.3i	−0.0687592	+	0.0946389i
$973$	−243134.	−	78999.2i	−0.256815	−	0.0834443i
$974$	−2.69628e6	+	876076.i	−2.84215	+	0.923472i
$975$	9528.53	−	6922.88i	0.0100234	−	0.00728245i
$976$	1.58754e6	−	515823.i	1.66658	−	0.541504i
$977$	−351359.	−	1.08137e6i	−0.368097	−	1.13289i	−0.948019	−	0.318214i	$-0.896917\pi$
$977$	−351359.	−	1.08137e6i	−0.368097	−	1.13289i	0.579922	−	0.814672i	$-0.303083\pi$
$978$	−7001.15	−	9636.25i	−0.00731967	−	0.0100747i
$979$	−56683.1	−	174452.i	−0.0591409	−	0.182017i
$980$	493802.	−	1.51977e6i	0.514163	−	1.58243i
$981$	−728703.	−	529433.i	−0.757203	−	0.550140i
$982$	−449859.	−	146168.i	−0.466502	−	0.151576i
$983$	−482422.	−	663997.i	−0.499252	−	0.687162i	0.482808	−	0.875726i	$-0.339617\pi$
$983$	−482422.	−	663997.i	−0.499252	−	0.687162i	−0.982061	+	0.188564i	$0.939617\pi$
$984$	25929.1	+	35688.4i	0.0267792	+	0.0368584i
$985$	−543272.	+	747750.i	−0.559945	+	0.770698i
$986$	−1.18804e6			−1.22202
$987$			3272.36i			0.00335913i
$988$	−3.37424e6	+	4.64425e6i	−3.45671	+	4.75775i
$989$	−136482.	−	420050.i	−0.139535	−	0.429446i
$990$	779232.	+	253188.i	0.795053	+	0.258328i
$991$		−	157186.i		−	0.160054i	−0.996793	−	0.0800268i	$-0.974499\pi$
$991$		−	157186.i		−	0.160054i	0.996793	−	0.0800268i	$-0.0255006\pi$
$992$	−1.13918e6	−	1.77710e6i	−1.15763	−	1.80588i
$993$	−8372.71			−0.00849117
$994$	208587.	−	641963.i	0.211112	−	0.649737i
$995$	−840835.	+	273204.i	−0.849307	+	0.275957i
$996$	−39621.2	−	28786.5i	−0.0399400	−	0.0290181i
$997$	−211063.			−0.212335			−0.106167	−	0.994348i	$-0.533858\pi$
$997$	−211063.			−0.212335			−0.106167	+	0.994348i	$0.533858\pi$
$998$			1.18462e6i			1.18938i
$999$	11217.1	+	8149.67i	0.0112395	+	0.00816600i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	31.5.f.a.23.1	✓	36
31.27	odd	10	inner	31.5.f.a.27.1	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.5.f.a.23.1	✓	36	1.1	even	1	trivial
31.5.f.a.27.1	yes	36	31.27	odd	10	inner

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:	\( N \)	\(=\)	\( 31 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	31.f (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.30154 + 7.08340i) q^{2} +(0.135338 - 0.0439738i) q^{3} +(-31.9333 - 23.2009i) q^{4} -18.1577 q^{5} +1.05986i q^{6} +(10.5920 + 7.69552i) q^{7} +(141.429 - 102.754i) q^{8} +(-65.5140 + 47.5987i) q^{9} +(41.7905 - 128.618i) q^{10} +(43.9751 - 60.5266i) q^{11} +(-5.34200 - 1.73572i) q^{12} +(-266.563 + 86.6115i) q^{13} +(-78.8883 + 57.3157i) q^{14} +(-2.45741 + 0.798462i) q^{15} +(207.186 + 637.653i) q^{16} +(56.3932 + 77.6185i) q^{17} +(-186.378 - 573.612i) q^{18} +(-160.347 + 493.498i) q^{19} +(579.833 + 421.274i) q^{20} +(1.77189 + 0.575723i) q^{21} +(327.524 + 450.798i) q^{22} +(-349.808 - 481.469i) q^{23} +(14.6221 - 20.1256i) q^{24} -295.299 q^{25} -2087.51i q^{26} +(-13.5485 + 18.6479i) q^{27} +(-159.694 - 491.486i) q^{28} +(1581.23 + 513.773i) q^{29} -19.2445i q^{30} +(518.624 + 809.043i) q^{31} -2196.55 q^{32} +(3.28990 - 10.1253i) q^{33} +(-679.594 + 220.814i) q^{34} +(-192.326 - 139.733i) q^{35} +3196.41 q^{36} -601.518i q^{37} +(-3126.60 - 2271.61i) q^{38} +(-32.2673 + 23.4436i) q^{39} +(-2568.02 + 1865.77i) q^{40} +(-547.973 + 1686.49i) q^{41} +(-8.15616 + 11.2260i) q^{42} +(705.813 + 229.333i) q^{43} +(-2808.54 + 912.550i) q^{44} +(1189.58 - 864.281i) q^{45} +(4215.54 - 1369.71i) q^{46} +(542.765 + 1670.46i) q^{47} +(56.0801 + 77.1876i) q^{48} +(-688.981 - 2120.47i) q^{49} +(679.643 - 2091.73i) q^{50} +(11.0453 + 8.02488i) q^{51} +(10521.7 + 3418.70i) q^{52} +(-651.590 - 896.837i) q^{53} +(-100.908 - 138.888i) q^{54} +(-798.485 + 1099.02i) q^{55} +2288.76 q^{56} +73.8399i q^{57} +(-7278.53 + 10018.0i) q^{58} +(-1011.96 - 3114.48i) q^{59} +(96.9983 + 31.5166i) q^{60} -2489.66i q^{61} +(-6924.41 + 1811.58i) q^{62} -1060.22 q^{63} +(1740.46 - 5356.59i) q^{64} +(4840.16 - 1572.66i) q^{65} +(64.1496 + 46.6074i) q^{66} -6649.82 q^{67} -3786.98i q^{68} +(-68.5142 - 49.7785i) q^{69} +(1432.43 - 1040.72i) q^{70} +(-5600.24 + 4068.81i) q^{71} +(-4374.61 + 13463.7i) q^{72} +(-1037.46 + 1427.94i) q^{73} +(4260.80 + 1384.42i) q^{74} +(-39.9651 + 12.9855i) q^{75} +(16570.0 - 12038.8i) q^{76} +(931.567 - 302.684i) q^{77} +(-91.7959 - 282.519i) q^{78} +(-350.123 - 481.902i) q^{79} +(-3762.01 - 11578.3i) q^{80} +(2025.94 - 6235.20i) q^{81} +(-10684.9 - 7763.03i) q^{82} +(8292.36 + 2694.35i) q^{83} +(-43.2251 - 59.4942i) q^{84} +(-1023.97 - 1409.37i) q^{85} +(-3248.91 + 4471.74i) q^{86} +236.593 q^{87} -13078.8i q^{88} +(1441.12 - 1983.54i) q^{89} +(3384.19 + 10415.5i) q^{90} +(-3489.95 - 1133.95i) q^{91} +23490.7i q^{92} +(105.766 + 86.6880i) q^{93} -13081.7 q^{94} +(2911.53 - 8960.76i) q^{95} +(-297.275 + 96.5906i) q^{96} +(3873.45 + 2814.23i) q^{97} +16605.8 q^{98} +6058.49i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 3 q^{2} - 5 q^{3} - 79 q^{4} - 2 q^{5} - 73 q^{7} + 173 q^{8} + 62 q^{9} + 84 q^{10} + 100 q^{11} + 150 q^{12} - 260 q^{13} + 488 q^{14} - 1075 q^{15} + 777 q^{16} - 725 q^{17} - 786 q^{18} - 1581 q^{19}+ \cdots + 74456 q^{98}+O(q^{100}) \) 36 * q - 3 * q^2 - 5 * q^3 - 79 * q^4 - 2 * q^5 - 73 * q^7 + 173 * q^8 + 62 * q^9 + 84 * q^10 + 100 * q^11 + 150 * q^12 - 260 * q^13 + 488 * q^14 - 1075 * q^15 + 777 * q^16 - 725 * q^17 - 786 * q^18 - 1581 * q^19 + 827 * q^20 + 2335 * q^21 - 1030 * q^22 + 1675 * q^23 - 165 * q^24 + 1294 * q^25 - 2855 * q^27 + 352 * q^28 - 575 * q^29 + 895 * q^31 - 5470 * q^32 + 4468 * q^33 + 1815 * q^34 - 3042 * q^35 + 7808 * q^36 - 6604 * q^38 + 595 * q^39 + 1482 * q^40 - 1740 * q^41 + 3840 * q^42 - 10055 * q^43 - 5780 * q^44 + 6774 * q^45 + 16515 * q^46 + 693 * q^47 + 4710 * q^48 - 944 * q^49 - 6240 * q^50 + 12641 * q^51 + 15885 * q^52 - 10835 * q^53 - 25960 * q^54 - 14010 * q^55 - 19976 * q^56 + 4755 * q^58 - 6021 * q^59 + 35 * q^60 - 11088 * q^62 - 15564 * q^63 + 6935 * q^64 + 26645 * q^65 + 23988 * q^66 + 28596 * q^67 - 4229 * q^69 + 8041 * q^70 + 31101 * q^71 + 20690 * q^72 + 6125 * q^73 - 47295 * q^74 - 27475 * q^75 + 12511 * q^76 + 35950 * q^77 + 29801 * q^78 - 29050 * q^79 - 47358 * q^80 - 1965 * q^81 + 9198 * q^82 + 21640 * q^83 - 35875 * q^84 - 55360 * q^85 - 27935 * q^86 - 2262 * q^87 - 11645 * q^89 - 14916 * q^90 + 670 * q^91 - 36224 * q^93 - 52442 * q^94 + 73983 * q^95 + 29810 * q^96 + 55059 * q^97 + 74456 * q^98

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