LMFDB - Embedded newform 546.4.l.h.211.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [546,4,Mod(211,546)] 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("546.211"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(546, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 2])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	546.l (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [10,-10,15,-20,-18] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$32.2150428631$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 218 x^{8} - 1187 x^{7} + 37612 x^{6} - 176472 x^{5} + 2657151 x^{4} - 12165606 x^{3} + \cdots + 1979894016 $ x^10 - x^9 + 218x^8 - 1187x^7 + 37612x^6 - 176472x^5 + 2657151x^4 - 12165606x^3 + 134848233x^2 - 452924784x + 1979894016
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			211.1
Root			$-6.73237 - 11.6608i$ of defining polynomial
Character	$\chi$	$=$	546.211
Dual form			546.4.l.h.295.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.00000 - 1.73205i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-2.00000 + 3.46410i) q^{4} -15.4647 q^{5} +(3.00000 - 5.19615i) q^{6} +(3.50000 - 6.06218i) q^{7} +8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +(15.4647 + 26.7857i) q^{10} +(1.37235 + 2.37699i) q^{11} -12.0000 q^{12} +(-46.5597 + 5.40312i) q^{13} -14.0000 q^{14} +(-23.1971 - 40.1786i) q^{15} +(-8.00000 - 13.8564i) q^{16} +(30.5720 - 52.9522i) q^{17} +18.0000 q^{18} +(-47.3614 + 82.0323i) q^{19} +(30.9295 - 53.5714i) q^{20} +21.0000 q^{21} +(2.74471 - 4.75397i) q^{22} +(4.37157 + 7.57178i) q^{23} +(12.0000 + 20.7846i) q^{24} +114.158 q^{25} +(55.9182 + 75.2407i) q^{26} -27.0000 q^{27} +(14.0000 + 24.2487i) q^{28} +(8.67740 + 15.0297i) q^{29} +(-46.3942 + 80.3571i) q^{30} -116.289 q^{31} +(-16.0000 + 27.7128i) q^{32} +(-4.11706 + 7.13096i) q^{33} -122.288 q^{34} +(-54.1266 + 93.7500i) q^{35} +(-18.0000 - 31.1769i) q^{36} +(-12.4361 - 21.5399i) q^{37} +189.446 q^{38} +(-83.8773 - 112.861i) q^{39} -123.718 q^{40} +(23.6235 + 40.9171i) q^{41} +(-21.0000 - 36.3731i) q^{42} +(255.560 - 442.643i) q^{43} -10.9788 q^{44} +(69.5913 - 120.536i) q^{45} +(8.74314 - 15.1436i) q^{46} +605.950 q^{47} +(24.0000 - 41.5692i) q^{48} +(-24.5000 - 42.4352i) q^{49} +(-114.158 - 197.728i) q^{50} +183.432 q^{51} +(74.4025 - 172.094i) q^{52} +439.148 q^{53} +(27.0000 + 46.7654i) q^{54} +(-21.2231 - 36.7595i) q^{55} +(28.0000 - 48.4974i) q^{56} -284.168 q^{57} +(17.3548 - 30.0594i) q^{58} +(258.728 - 448.130i) q^{59} +185.577 q^{60} +(-136.521 + 236.461i) q^{61} +(116.289 + 201.418i) q^{62} +(31.5000 + 54.5596i) q^{63} +64.0000 q^{64} +(720.034 - 83.5578i) q^{65} +16.4682 q^{66} +(260.410 + 451.044i) q^{67} +(122.288 + 211.809i) q^{68} +(-13.1147 + 22.7153i) q^{69} +216.506 q^{70} +(163.637 - 283.427i) q^{71} +(-36.0000 + 62.3538i) q^{72} -230.359 q^{73} +(-24.8722 + 43.0799i) q^{74} +(171.237 + 296.591i) q^{75} +(-189.446 - 328.129i) q^{76} +19.2130 q^{77} +(-111.604 + 258.141i) q^{78} +1030.74 q^{79} +(123.718 + 214.286i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(47.2470 - 81.8343i) q^{82} +899.227 q^{83} +(-42.0000 + 72.7461i) q^{84} +(-472.787 + 818.892i) q^{85} -1022.24 q^{86} +(-26.0322 + 45.0891i) q^{87} +(10.9788 + 19.0159i) q^{88} +(459.231 + 795.411i) q^{89} -278.365 q^{90} +(-130.204 + 301.164i) q^{91} -34.9726 q^{92} +(-174.433 - 302.126i) q^{93} +(-605.950 - 1049.54i) q^{94} +(732.431 - 1268.61i) q^{95} -96.0000 q^{96} +(-607.492 + 1052.21i) q^{97} +(-49.0000 + 84.8705i) q^{98} -24.7024 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 10 q^{2} + 15 q^{3} - 20 q^{4} - 18 q^{5} + 30 q^{6} + 35 q^{7} + 80 q^{8} - 45 q^{9} + 18 q^{10} - 23 q^{11} - 120 q^{12} - 16 q^{13} - 140 q^{14} - 27 q^{15} - 80 q^{16} - 14 q^{17} + 180 q^{18}+ \cdots + 414 q^{99}+O(q^{100}) $ 10 * q - 10 * q^2 + 15 * q^3 - 20 * q^4 - 18 * q^5 + 30 * q^6 + 35 * q^7 + 80 * q^8 - 45 * q^9 + 18 * q^10 - 23 * q^11 - 120 * q^12 - 16 * q^13 - 140 * q^14 - 27 * q^15 - 80 * q^16 - 14 * q^17 + 180 * q^18 + 16 * q^19 + 36 * q^20 + 210 * q^21 - 46 * q^22 - 47 * q^23 + 120 * q^24 - 348 * q^25 - 50 * q^26 - 270 * q^27 + 140 * q^28 - 149 * q^29 - 54 * q^30 + 350 * q^31 - 160 * q^32 + 69 * q^33 + 56 * q^34 - 63 * q^35 - 180 * q^36 + 187 * q^37 - 64 * q^38 + 75 * q^39 - 144 * q^40 + 358 * q^41 - 210 * q^42 + 575 * q^43 + 184 * q^44 + 81 * q^45 - 94 * q^46 + 332 * q^47 + 240 * q^48 - 245 * q^49 + 348 * q^50 - 84 * q^51 + 164 * q^52 - 94 * q^53 + 270 * q^54 - 530 * q^55 + 280 * q^56 + 96 * q^57 - 298 * q^58 - 329 * q^59 + 216 * q^60 - 197 * q^61 - 350 * q^62 + 315 * q^63 + 640 * q^64 + 169 * q^65 - 276 * q^66 + 231 * q^67 - 56 * q^68 + 141 * q^69 + 252 * q^70 + 38 * q^71 - 360 * q^72 - 754 * q^73 + 374 * q^74 - 522 * q^75 + 64 * q^76 - 322 * q^77 - 246 * q^78 - 304 * q^79 + 144 * q^80 - 405 * q^81 + 716 * q^82 + 360 * q^83 - 420 * q^84 - 748 * q^85 - 2300 * q^86 + 447 * q^87 - 184 * q^88 + 1052 * q^89 - 324 * q^90 - 287 * q^91 + 376 * q^92 + 525 * q^93 - 332 * q^94 + 2272 * q^95 - 960 * q^96 - 1415 * q^97 - 490 * q^98 + 414 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.00000	−	1.73205i	−0.353553	−	0.612372i
$2$	−1.00000	−	1.73205i	−0.353553	−	0.612372i
$3$	1.50000	+	2.59808i	0.288675	+	0.500000i
$3$	1.50000	+	2.59808i	0.288675	+	0.500000i
$4$	−2.00000	+	3.46410i	−0.250000	+	0.433013i
$5$	−15.4647			−1.38321			−0.691604	−	0.722277i	$-0.743096\pi$
$5$	−15.4647			−1.38321			−0.691604	+	0.722277i	$0.743096\pi$
$6$	3.00000	−	5.19615i	0.204124	−	0.353553i
$7$	3.50000	−	6.06218i	0.188982	−	0.327327i
$7$	3.50000	−	6.06218i	0.188982	−	0.327327i
$8$	8.00000			0.353553
$9$	−4.50000	+	7.79423i	−0.166667	+	0.288675i
$10$	15.4647	+	26.7857i	0.489038	+	0.847039i
$11$	1.37235	+	2.37699i	0.0376164	+	0.0651535i	0.884221	−	0.467069i	$-0.154690\pi$
$11$	1.37235	+	2.37699i	0.0376164	+	0.0651535i	−0.846604	+	0.532223i	$0.821357\pi$
$12$	−12.0000			−0.288675
$13$	−46.5597	+	5.40312i	−0.993334	+	0.115274i
$13$	−46.5597	+	5.40312i	−0.993334	+	0.115274i
$14$	−14.0000			−0.267261
$15$	−23.1971	−	40.1786i	−0.399298	−	0.691604i
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	30.5720	−	52.9522i	0.436164	−	0.755459i	−0.561226	−	0.827663i	$-0.689670\pi$
$17$	30.5720	−	52.9522i	0.436164	−	0.755459i	0.997390	+	0.0722043i	$0.0230033\pi$
$18$	18.0000			0.235702
$19$	−47.3614	+	82.0323i	−0.571866	+	0.990500i	0.424509	+	0.905424i	$0.360447\pi$
$19$	−47.3614	+	82.0323i	−0.571866	+	0.990500i	−0.996374	+	0.0850765i	$0.972887\pi$
$20$	30.9295	−	53.5714i	0.345802	−	0.598947i
$21$	21.0000			0.218218
$22$	2.74471	−	4.75397i	0.0265988	−	0.0460705i
$23$	4.37157	+	7.57178i	0.0396320	+	0.0686446i	0.885161	−	0.465285i	$-0.154048\pi$
$23$	4.37157	+	7.57178i	0.0396320	+	0.0686446i	−0.845529	+	0.533929i	$0.820715\pi$
$24$	12.0000	+	20.7846i	0.102062	+	0.176777i
$25$	114.158			0.913265
$26$	55.9182	+	75.2407i	0.421787	+	0.567535i
$27$	−27.0000			−0.192450
$28$	14.0000	+	24.2487i	0.0944911	+	0.163663i
$29$	8.67740	+	15.0297i	0.0555639	+	0.0962394i	0.892469	−	0.451108i	$-0.148971\pi$
$29$	8.67740	+	15.0297i	0.0555639	+	0.0962394i	−0.836906	+	0.547347i	$0.815638\pi$
$30$	−46.3942	+	80.3571i	−0.282346	+	0.489038i
$31$	−116.289			−0.673743			−0.336872	−	0.941551i	$-0.609369\pi$
$31$	−116.289			−0.673743			−0.336872	+	0.941551i	$0.609369\pi$
$32$	−16.0000	+	27.7128i	−0.0883883	+	0.153093i
$33$	−4.11706	+	7.13096i	−0.0217178	+	0.0376164i
$34$	−122.288			−0.616829
$35$	−54.1266	+	93.7500i	−0.261402	+	0.452761i
$36$	−18.0000	−	31.1769i	−0.0833333	−	0.144338i
$37$	−12.4361	−	21.5399i	−0.0552562	−	0.0957066i	0.837074	−	0.547089i	$-0.184264\pi$
$37$	−12.4361	−	21.5399i	−0.0552562	−	0.0957066i	−0.892330	+	0.451383i	$0.850931\pi$
$38$	189.446			0.808740
$39$	−83.8773	−	112.861i	−0.344388	−	0.463390i
$40$	−123.718			−0.489038
$41$	23.6235	+	40.9171i	0.0899847	+	0.155858i	0.907504	−	0.420042i	$-0.137985\pi$
$41$	23.6235	+	40.9171i	0.0899847	+	0.155858i	−0.817520	+	0.575901i	$0.804652\pi$
$42$	−21.0000	−	36.3731i	−0.0771517	−	0.133631i
$43$	255.560	−	442.643i	0.906338	−	1.56982i	0.0872272	−	0.996188i	$-0.472199\pi$
$43$	255.560	−	442.643i	0.906338	−	1.56982i	0.819111	−	0.573635i	$-0.194467\pi$
$44$	−10.9788			−0.0376164
$45$	69.5913	−	120.536i	0.230535	−	0.399298i
$46$	8.74314	−	15.1436i	0.0280240	−	0.0485391i
$47$	605.950			1.88057			0.940285	−	0.340387i	$-0.110558\pi$
$47$	605.950			1.88057			0.940285	+	0.340387i	$0.110558\pi$
$48$	24.0000	−	41.5692i	0.0721688	−	0.125000i
$49$	−24.5000	−	42.4352i	−0.0714286	−	0.123718i
$50$	−114.158	−	197.728i	−0.322888	−	0.559258i
$51$	183.432			0.503639
$52$	74.4025	−	172.094i	0.198419	−	0.458945i
$53$	439.148			1.13815			0.569073	−	0.822287i	$-0.307302\pi$
$53$	439.148			1.13815			0.569073	+	0.822287i	$0.307302\pi$
$54$	27.0000	+	46.7654i	0.0680414	+	0.117851i
$55$	−21.2231	−	36.7595i	−0.0520313	−	0.0901208i
$56$	28.0000	−	48.4974i	0.0668153	−	0.115728i
$57$	−284.168			−0.660334
$58$	17.3548	−	30.0594i	0.0392896	−	0.0680516i
$59$	258.728	−	448.130i	0.570907	−	0.988841i	−0.425566	−	0.904928i	$-0.639925\pi$
$59$	258.728	−	448.130i	0.570907	−	0.988841i	0.996473	−	0.0839131i	$-0.0267418\pi$
$60$	185.577			0.399298
$61$	−136.521	+	236.461i	−0.286553	+	0.496324i	−0.972985	−	0.230870i	$-0.925843\pi$
$61$	−136.521	+	236.461i	−0.286553	+	0.496324i	0.686432	+	0.727194i	$0.259176\pi$
$62$	116.289	+	201.418i	0.238204	+	0.412582i
$63$	31.5000	+	54.5596i	0.0629941	+	0.109109i
$64$	64.0000			0.125000
$65$	720.034	−	83.5578i	1.37399	−	0.159447i
$66$	16.4682			0.0307136
$67$	260.410	+	451.044i	0.474838	+	0.822444i	0.999585	−	0.0288144i	$-0.00917318\pi$
$67$	260.410	+	451.044i	0.474838	+	0.822444i	−0.524746	+	0.851259i	$0.675840\pi$
$68$	122.288	+	211.809i	0.218082	+	0.377729i
$69$	−13.1147	+	22.7153i	−0.0228815	+	0.0396320i
$70$	216.506			0.369678
$71$	163.637	−	283.427i	0.273523	−	0.473755i	−0.696239	−	0.717810i	$-0.745145\pi$
$71$	163.637	−	283.427i	0.273523	−	0.473755i	0.969761	+	0.244055i	$0.0784779\pi$
$72$	−36.0000	+	62.3538i	−0.0589256	+	0.102062i
$73$	−230.359			−0.369336			−0.184668	−	0.982801i	$-0.559121\pi$
$73$	−230.359			−0.369336			−0.184668	+	0.982801i	$0.559121\pi$
$74$	−24.8722	+	43.0799i	−0.0390721	+	0.0676748i
$75$	171.237	+	296.591i	0.263637	+	0.456632i
$76$	−189.446	−	328.129i	−0.285933	−	0.495250i
$77$	19.2130			0.0284353
$78$	−111.604	+	258.141i	−0.162008	+	0.374727i
$79$	1030.74			1.46795			0.733973	−	0.679179i	$-0.237664\pi$
$79$	1030.74			1.46795			0.733973	+	0.679179i	$0.237664\pi$
$80$	123.718	+	214.286i	0.172901	+	0.299473i
$81$	−40.5000	−	70.1481i	−0.0555556	−	0.0962250i
$82$	47.2470	−	81.8343i	0.0636288	−	0.110208i
$83$	899.227			1.18919			0.594596	−	0.804024i	$-0.297312\pi$
$83$	899.227			1.18919			0.594596	+	0.804024i	$0.297312\pi$
$84$	−42.0000	+	72.7461i	−0.0545545	+	0.0944911i
$85$	−472.787	+	818.892i	−0.603306	+	1.04496i
$86$	−1022.24			−1.28176
$87$	−26.0322	+	45.0891i	−0.0320798	+	0.0555639i
$88$	10.9788	+	19.0159i	0.0132994	+	0.0230352i
$89$	459.231	+	795.411i	0.546948	+	0.947341i	0.998482	+	0.0550873i	$0.0175437\pi$
$89$	459.231	+	795.411i	0.546948	+	0.947341i	−0.451534	+	0.892254i	$0.649123\pi$
$90$	−278.365			−0.326025
$91$	−130.204	+	301.164i	−0.149990	+	0.346929i
$92$	−34.9726			−0.0396320
$93$	−174.433	−	302.126i	−0.194493	−	0.336872i
$94$	−605.950	−	1049.54i	−0.664882	−	1.15161i
$95$	732.431	−	1268.61i	0.791009	−	1.37007i
$96$	−96.0000			−0.102062
$97$	−607.492	+	1052.21i	−0.635891	+	1.10140i	0.350435	+	0.936587i	$0.386034\pi$
$97$	−607.492	+	1052.21i	−0.635891	+	1.10140i	−0.986326	+	0.164808i	$0.947299\pi$
$98$	−49.0000	+	84.8705i	−0.0505076	+	0.0874818i
$99$	−24.7024			−0.0250776
$100$	−228.316	+	395.455i	−0.228316	+	0.395455i
$101$	−869.158	−	1505.43i	−0.856282	−	1.48312i	−0.875451	−	0.483307i	$-0.839436\pi$
$101$	−869.158	−	1505.43i	−0.856282	−	1.48312i	0.0191694	−	0.999816i	$-0.493898\pi$
$102$	−183.432	−	317.713i	−0.178063	−	0.308415i
$103$	1550.31			1.48307			0.741536	−	0.670913i	$-0.234098\pi$
$103$	1550.31			1.48307			0.741536	+	0.670913i	$0.234098\pi$
$104$	−372.478	+	43.2250i	−0.351197	+	0.0407553i
$105$	−324.759			−0.301841
$106$	−439.148	−	760.628i	−0.402395	−	0.696969i
$107$	−9.17842	−	15.8975i	−0.00829263	−	0.0143633i	0.861849	−	0.507164i	$-0.169306\pi$
$107$	−9.17842	−	15.8975i	−0.00829263	−	0.0143633i	−0.870142	+	0.492801i	$0.835973\pi$
$108$	54.0000	−	93.5307i	0.0481125	−	0.0833333i
$109$	−130.693			−0.114845			−0.0574227	−	0.998350i	$-0.518288\pi$
$109$	−130.693			−0.114845			−0.0574227	+	0.998350i	$0.518288\pi$
$110$	−42.4462	+	73.5189i	−0.0367917	+	0.0637251i
$111$	37.3083	−	64.6198i	0.0319022	−	0.0552562i
$112$	−112.000			−0.0944911
$113$	284.757	−	493.214i	0.237059	−	0.410599i	−0.722810	−	0.691047i	$-0.757150\pi$
$113$	284.757	−	493.214i	0.237059	−	0.410599i	0.959869	+	0.280448i	$0.0904831\pi$
$114$	284.168	+	492.194i	0.233463	+	0.404370i
$115$	−67.6052	−	117.096i	−0.0548193	−	0.0949498i
$116$	−69.4192			−0.0555639
$117$	167.406	−	387.211i	0.132279	−	0.305963i
$118$	−1034.91			−0.807385
$119$	−214.004	−	370.665i	−0.164855	−	0.285536i
$120$	−185.577	−	321.429i	−0.141173	−	0.244519i
$121$	661.733	−	1146.16i	0.497170	−	0.861124i
$122$	546.084			0.405247
$123$	−70.8706	+	122.751i	−0.0519527	+	0.0899847i
$124$	232.577	−	402.835i	0.168436	−	0.291739i
$125$	167.667			0.119973
$126$	63.0000	−	109.119i	0.0445435	−	0.0771517i
$127$	−1067.34	−	1848.69i	−0.745759	−	1.29169i	−0.949840	−	0.312738i	$-0.898754\pi$
$127$	−1067.34	−	1848.69i	−0.745759	−	1.29169i	0.204081	−	0.978954i	$-0.434579\pi$
$128$	−64.0000	−	110.851i	−0.0441942	−	0.0765466i
$129$	1533.36			1.04655
$130$	−864.760	−	1163.58i	−0.583419	−	0.785019i
$131$	630.680			0.420632			0.210316	−	0.977633i	$-0.432551\pi$
$131$	630.680			0.420632			0.210316	+	0.977633i	$0.432551\pi$
$132$	−16.4682	−	28.5238i	−0.0108589	−	0.0188082i
$133$	331.530	+	574.226i	0.216145	+	0.374374i
$134$	520.820	−	902.087i	0.335761	−	0.581556i
$135$	417.548			0.266199
$136$	244.576	−	423.618i	0.154207	−	0.267095i
$137$	784.316	−	1358.47i	0.489114	−	0.847170i	−0.510808	−	0.859695i	$-0.670654\pi$
$137$	784.316	−	1358.47i	0.489114	−	0.847170i	0.999922	+	0.0125249i	$0.00398690\pi$
$138$	52.4589			0.0323594
$139$	−106.519	+	184.496i	−0.0649987	+	0.112581i	−0.896693	−	0.442652i	$-0.854038\pi$
$139$	−106.519	+	184.496i	−0.0649987	+	0.112581i	0.831695	+	0.555233i	$0.187371\pi$
$140$	−216.506	−	375.000i	−0.130701	−	0.226381i
$141$	908.924	+	1574.30i	0.542874	+	0.940285i
$142$	−654.547			−0.386819
$143$	−76.7395	−	103.257i	−0.0448761	−	0.0603830i
$144$	144.000			0.0833333
$145$	−134.194	−	232.430i	−0.0768564	−	0.133119i
$146$	230.359	+	398.994i	0.130580	+	0.226171i
$147$	73.5000	−	127.306i	0.0412393	−	0.0714286i
$148$	99.4887			0.0552562
$149$	−919.265	+	1592.21i	−0.505430	+	0.875431i	0.494550	+	0.869149i	$0.335333\pi$
$149$	−919.265	+	1592.21i	−0.505430	+	0.875431i	−0.999980	+	0.00628186i	$0.998000\pi$
$150$	342.474	−	593.183i	0.186419	−	0.322888i
$151$	−1738.04			−0.936688			−0.468344	−	0.883546i	$-0.655149\pi$
$151$	−1738.04			−0.936688			−0.468344	+	0.883546i	$0.655149\pi$
$152$	−378.891	+	656.259i	−0.202185	+	0.350195i
$153$	275.148	+	476.570i	0.145388	+	0.251820i
$154$	−19.2130	−	33.2778i	−0.0100534	−	0.0174130i
$155$	1798.37			0.931927
$156$	558.716	−	64.8374i	0.286751	−	0.0332766i
$157$	−484.160			−0.246116			−0.123058	−	0.992399i	$-0.539270\pi$
$157$	−484.160			−0.246116			−0.123058	+	0.992399i	$0.539270\pi$
$158$	−1030.74	−	1785.30i	−0.518997	−	0.898929i
$159$	658.723	+	1140.94i	0.328554	+	0.569073i
$160$	247.436	−	428.571i	0.122259	−	0.211760i
$161$	61.2020			0.0299590
$162$	−81.0000	+	140.296i	−0.0392837	+	0.0680414i
$163$	−1509.25	+	2614.10i	−0.725238	+	1.25615i	0.233639	+	0.972324i	$0.424937\pi$
$163$	−1509.25	+	2614.10i	−0.725238	+	1.25615i	−0.958876	+	0.283825i	$0.908397\pi$
$164$	−188.988			−0.0899847
$165$	63.6693	−	110.278i	0.0300403	−	0.0520313i
$166$	−899.227	−	1557.51i	−0.420443	−	0.728229i
$167$	−1449.50	−	2510.60i	−0.671649	−	1.16333i	−0.977436	−	0.211231i	$-0.932253\pi$
$167$	−1449.50	−	2510.60i	−0.671649	−	1.16333i	0.305787	−	0.952100i	$-0.401080\pi$
$168$	168.000			0.0771517
$169$	2138.61	−	503.135i	0.973424	−	0.229010i
$170$	1891.15			0.853203
$171$	−426.252	−	738.291i	−0.190622	−	0.330167i
$172$	1022.24	+	1770.57i	0.453169	+	0.784912i
$173$	−412.439	+	714.365i	−0.181255	+	0.313943i	−0.942308	−	0.334747i	$-0.891349\pi$
$173$	−412.439	+	714.365i	−0.181255	+	0.313943i	0.761053	+	0.648690i	$0.224683\pi$
$174$	104.129			0.0453677
$175$	399.553	−	692.047i	0.172591	−	0.298936i
$176$	21.9577	−	38.0318i	0.00940410	−	0.0162884i
$177$	1552.37			0.659227
$178$	918.461	−	1590.82i	0.386750	−	0.669871i
$179$	224.407	+	388.684i	0.0937036	+	0.162299i	0.909067	−	0.416650i	$-0.136796\pi$
$179$	224.407	+	388.684i	0.0937036	+	0.162299i	−0.815363	+	0.578950i	$0.803463\pi$
$180$	278.365	+	482.143i	0.115267	+	0.199649i
$181$	−3507.15			−1.44024			−0.720122	−	0.693847i	$-0.755914\pi$
$181$	−3507.15			−1.44024			−0.720122	+	0.693847i	$0.755914\pi$
$182$	651.836	−	75.6437i	0.265480	−	0.0308081i
$183$	−819.127			−0.330883
$184$	34.9726	+	60.5743i	0.0140120	+	0.0242695i
$185$	192.321	+	333.110i	0.0764309	+	0.132382i
$186$	−348.866	+	604.253i	−0.137527	+	0.238204i
$187$	167.822			0.0656277
$188$	−1211.90	+	2099.07i	−0.470143	+	0.814311i
$189$	−94.5000	+	163.679i	−0.0363696	+	0.0629941i
$190$	−2929.73			−1.11866
$191$	1668.65	−	2890.18i	0.632141	−	1.09490i	−0.354972	−	0.934877i	$-0.615510\pi$
$191$	1668.65	−	2890.18i	0.632141	−	1.09490i	0.987113	−	0.160024i	$-0.0511571\pi$
$192$	96.0000	+	166.277i	0.0360844	+	0.0625000i
$193$	738.573	+	1279.25i	0.275459	+	0.477110i	0.970251	−	0.242101i	$-0.0778367\pi$
$193$	738.573	+	1279.25i	0.275459	+	0.477110i	−0.694791	+	0.719211i	$0.744503\pi$
$194$	2429.97			0.899286
$195$	1297.14	+	1745.37i	0.476360	+	0.640965i
$196$	196.000			0.0714286
$197$	130.996	+	226.891i	0.0473759	+	0.0820575i	0.888741	−	0.458410i	$-0.151581\pi$
$197$	130.996	+	226.891i	0.0473759	+	0.0820575i	−0.841365	+	0.540467i	$0.818247\pi$
$198$	24.7024	+	42.7858i	0.00886627	+	0.0153568i
$199$	1337.48	−	2316.58i	0.476440	−	0.825218i	−0.523196	−	0.852212i	$-0.675260\pi$
$199$	1337.48	−	2316.58i	0.476440	−	0.825218i	0.999636	+	0.0269947i	$0.00859373\pi$
$200$	913.265			0.322888
$201$	−781.231	+	1353.13i	−0.274148	+	0.474838i
$202$	−1738.32	+	3010.85i	−0.605482	+	1.04873i
$203$	121.484			0.0420023
$204$	−366.864	+	635.426i	−0.125910	+	0.218082i
$205$	−365.332	−	632.773i	−0.124468	−	0.215584i
$206$	−1550.31	−	2685.21i	−0.524345	−	0.908192i
$207$	−78.6883			−0.0264213
$208$	447.345	+	601.925i	0.149124	+	0.200654i
$209$	−259.986			−0.0860461
$210$	324.759	+	562.500i	0.106717	+	0.184839i
$211$	989.327	+	1713.56i	0.322787	+	0.559084i	0.981062	−	0.193694i	$-0.0620469\pi$
$211$	989.327	+	1713.56i	0.322787	+	0.559084i	−0.658275	+	0.752778i	$0.728714\pi$
$212$	−878.297	+	1521.26i	−0.284536	+	0.492831i
$213$	981.820			0.315837
$214$	−18.3568	+	31.7950i	−0.00586377	+	0.0101564i
$215$	−3952.17	+	6845.36i	−1.25365	+	2.17139i
$216$	−216.000			−0.0680414
$217$	−407.010	+	704.962i	−0.127325	+	0.220534i
$218$	130.693	+	226.367i	0.0406039	+	0.0703281i
$219$	−345.539	−	598.491i	−0.106618	−	0.184668i
$220$	169.785			0.0520313
$221$	−1137.31	+	2630.62i	−0.346172	+	0.800701i
$222$	−149.233			−0.0451165
$223$	−2108.21	−	3651.52i	−0.633077	−	1.09652i	−0.986919	−	0.161216i	$-0.948459\pi$
$223$	−2108.21	−	3651.52i	−0.633077	−	1.09652i	0.353843	−	0.935305i	$-0.384875\pi$
$224$	112.000	+	193.990i	0.0334077	+	0.0578638i
$225$	−513.712	+	889.774i	−0.152211	+	0.263637i
$226$	−1139.03			−0.335253
$227$	−3021.40	+	5233.22i	−0.883425	+	1.53014i	−0.0359165	+	0.999355i	$0.511435\pi$
$227$	−3021.40	+	5233.22i	−0.883425	+	1.53014i	−0.847508	+	0.530782i	$0.821898\pi$
$228$	568.337	−	984.388i	0.165083	−	0.285933i
$229$	−2221.09			−0.640935			−0.320467	−	0.947260i	$-0.603840\pi$
$229$	−2221.09			−0.640935			−0.320467	+	0.947260i	$0.603840\pi$
$230$	−135.210	+	234.191i	−0.0387631	+	0.0671396i
$231$	28.8194	+	49.9167i	0.00820857	+	0.0142177i
$232$	69.4192	+	120.238i	0.0196448	+	0.0340258i
$233$	4975.20			1.39887			0.699434	−	0.714697i	$-0.253435\pi$
$233$	4975.20			1.39887			0.699434	+	0.714697i	$0.253435\pi$
$234$	−838.075	+	97.2562i	−0.234131	+	0.0271702i
$235$	−9370.85			−2.60122
$236$	1034.91	+	1792.52i	0.285454	+	0.494420i
$237$	1546.12	+	2677.95i	0.423759	+	0.733973i
$238$	−428.008	+	741.331i	−0.116570	+	0.201905i
$239$	1052.97			0.284982			0.142491	−	0.989796i	$-0.454489\pi$
$239$	1052.97			0.284982			0.142491	+	0.989796i	$0.454489\pi$
$240$	−371.154	+	642.857i	−0.0998245	+	0.172901i
$241$	−1977.35	+	3424.88i	−0.528517	+	0.915418i	0.470930	+	0.882171i	$0.343918\pi$
$241$	−1977.35	+	3424.88i	−0.528517	+	0.915418i	−0.999447	+	0.0332478i	$0.989415\pi$
$242$	−2646.93			−0.703105
$243$	121.500	−	210.444i	0.0320750	−	0.0555556i
$244$	−546.084	−	945.846i	−0.143277	−	0.248162i
$245$	378.886	+	656.250i	0.0988006	+	0.171128i
$246$	283.482			0.0734722
$247$	1761.90	−	4075.30i	0.453875	−	1.04982i
$248$	−930.308			−0.238204
$249$	1348.84	+	2336.26i	0.343290	+	0.594596i
$250$	−167.667	−	290.408i	−0.0424167	−	0.0734679i
$251$	461.957	−	800.133i	0.116169	−	0.201211i	−0.802077	−	0.597220i	$-0.796272\pi$
$251$	461.957	−	800.133i	0.116169	−	0.201211i	0.918247	+	0.396009i	$0.129605\pi$
$252$	−252.000			−0.0629941
$253$	−11.9987	+	20.7823i	−0.00298162	+	0.00516432i
$254$	−2134.69	+	3697.38i	−0.527331	+	0.913364i
$255$	−2836.72			−0.696638
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	214.030	+	370.712i	0.0519489	+	0.0899781i	0.890830	−	0.454336i	$-0.150123\pi$
$257$	214.030	+	370.712i	0.0519489	+	0.0899781i	−0.838882	+	0.544314i	$0.816790\pi$
$258$	−1533.36	−	2655.86i	−0.370011	−	0.640878i
$259$	−174.105			−0.0417698
$260$	−1150.61	+	2661.39i	−0.274454	+	0.634816i
$261$	−156.193			−0.0370426
$262$	−630.680	−	1092.37i	−0.148716	−	0.257583i
$263$	3175.07	+	5499.38i	0.744423	+	1.28938i	0.950464	+	0.310835i	$0.100609\pi$
$263$	3175.07	+	5499.38i	0.744423	+	1.28938i	−0.206041	+	0.978543i	$0.566058\pi$
$264$	−32.9365	+	57.0477i	−0.00767841	+	0.0132994i
$265$	−6791.32			−1.57429
$266$	663.059	−	1148.45i	0.152838	−	0.264722i
$267$	−1377.69	+	2386.23i	−0.315780	+	0.546948i
$268$	−2083.28			−0.474838
$269$	−2282.74	+	3953.82i	−0.517402	+	0.896166i	0.482394	+	0.875954i	$0.339767\pi$
$269$	−2282.74	+	3953.82i	−0.517402	+	0.896166i	−0.999796	+	0.0202115i	$0.993566\pi$
$270$	−417.548	−	723.214i	−0.0941154	−	0.163013i
$271$	2041.99	+	3536.84i	0.457720	+	0.792795i	0.998840	−	0.0481506i	$-0.0153328\pi$
$271$	2041.99	+	3536.84i	0.457720	+	0.792795i	−0.541120	+	0.840946i	$0.681999\pi$
$272$	−978.303			−0.218082
$273$	−977.754	+	113.466i	−0.216763	+	0.0251547i
$274$	−3137.26			−0.691712
$275$	156.665	+	271.352i	0.0343537	+	0.0595024i
$276$	−52.4589	−	90.8614i	−0.0114408	−	0.0198160i
$277$	2969.47	−	5143.27i	0.644109	−	1.11563i	−0.340398	−	0.940281i	$-0.610562\pi$
$277$	2969.47	−	5143.27i	0.644109	−	1.11563i	0.984507	−	0.175348i	$-0.0561049\pi$
$278$	426.076			0.0919221
$279$	523.298	−	906.379i	0.112291	−	0.194493i
$280$	−433.013	+	750.000i	−0.0924195	+	0.160075i
$281$	4237.99			0.899706			0.449853	−	0.893103i	$-0.351476\pi$
$281$	4237.99			0.899706			0.449853	+	0.893103i	$0.351476\pi$
$282$	1817.85	−	3148.61i	0.383870	−	0.664882i
$283$	2950.43	+	5110.29i	0.619735	+	1.07341i	0.989534	+	0.144300i	$0.0460931\pi$
$283$	2950.43	+	5110.29i	0.619735	+	1.07341i	−0.369799	+	0.929112i	$0.620574\pi$
$284$	654.547	+	1133.71i	0.136761	+	0.236877i
$285$	4394.59			0.913379
$286$	−102.106	+	236.174i	−0.0211108	+	0.0488295i
$287$	330.729			0.0680221
$288$	−144.000	−	249.415i	−0.0294628	−	0.0510310i
$289$	587.209	+	1017.08i	0.119522	+	0.207017i
$290$	−268.387	+	464.861i	−0.0543457	+	0.0941295i
$291$	−3644.95			−0.734264
$292$	460.718	−	797.987i	0.0923339	−	0.159927i
$293$	2775.71	−	4807.67i	0.553443	−	0.958591i	−0.444580	−	0.895739i	$-0.646647\pi$
$293$	2775.71	−	4807.67i	0.553443	−	0.958591i	0.998023	−	0.0628517i	$-0.0200195\pi$
$294$	−294.000			−0.0583212
$295$	−4001.16	+	6930.22i	−0.789684	+	1.36777i
$296$	−99.4887	−	172.320i	−0.0195360	−	0.0338374i
$297$	−37.0536	−	64.1786i	−0.00723928	−	0.0125388i
$298$	3677.06			0.714787
$299$	−244.450	−	328.920i	−0.0472807	−	0.0636185i
$300$	−1369.90			−0.263637
$301$	−1788.92	−	3098.50i	−0.342564	−	0.593338i
$302$	1738.04	+	3010.38i	0.331169	+	0.573602i
$303$	2607.47	−	4516.28i	0.494374	−	0.856282i
$304$	1515.56			0.285933
$305$	2111.26	−	3656.82i	0.396363	−	0.686520i
$306$	550.295	−	953.140i	0.102805	−	0.178063i
$307$	−648.228			−0.120509			−0.0602546	−	0.998183i	$-0.519191\pi$
$307$	−648.228			−0.120509			−0.0602546	+	0.998183i	$0.519191\pi$
$308$	−38.4259	+	66.5556i	−0.00710883	+	0.0123129i
$309$	2325.46	+	4027.82i	0.428126	+	0.741536i
$310$	−1798.37	−	3114.87i	−0.329486	−	0.570686i
$311$	−3768.61			−0.687132			−0.343566	−	0.939129i	$-0.611635\pi$
$311$	−3768.61			−0.687132			−0.343566	+	0.939129i	$0.611635\pi$
$312$	−671.018	−	902.888i	−0.121759	−	0.163833i
$313$	2777.95			0.501659			0.250829	−	0.968031i	$-0.419297\pi$
$313$	2777.95			0.501659			0.250829	+	0.968031i	$0.419297\pi$
$314$	484.160	+	838.591i	0.0870151	+	0.150715i
$315$	−487.139	−	843.750i	−0.0871339	−	0.150920i
$316$	−2061.49	+	3570.60i	−0.366986	+	0.635639i
$317$	4488.53			0.795271			0.397635	−	0.917543i	$-0.369831\pi$
$317$	4488.53			0.795271			0.397635	+	0.917543i	$0.369831\pi$
$318$	1317.45	−	2281.88i	0.232323	−	0.402395i
$319$	−23.8169	+	41.2521i	−0.00418022	+	0.00724036i
$320$	−989.743			−0.172901
$321$	27.5353	−	47.6925i	0.00478775	−	0.00829263i
$322$	−61.2020	−	106.005i	−0.0105921	−	0.0183460i
$323$	2895.86	+	5015.78i	0.498855	+	0.864042i
$324$	324.000			0.0555556
$325$	−5315.17	+	616.810i	−0.907177	+	0.105275i
$326$	6037.01			1.02564
$327$	−196.040	−	339.551i	−0.0331530	−	0.0574227i
$328$	188.988	+	327.337i	0.0318144	+	0.0551042i
$329$	2120.82	−	3673.37i	0.355394	−	0.615561i
$330$	−254.677			−0.0424834
$331$	5041.31	−	8731.80i	0.837146	−	1.44998i	−0.0551244	−	0.998479i	$-0.517556\pi$
$331$	5041.31	−	8731.80i	0.837146	−	1.44998i	0.892271	−	0.451501i	$-0.149111\pi$
$332$	−1798.45	+	3115.01i	−0.297298	+	0.514935i
$333$	223.850			0.0368375
$334$	−2898.99	+	5021.20i	−0.474928	+	0.822599i
$335$	−4027.18	−	6975.27i	−0.656800	−	1.13761i
$336$	−168.000	−	290.985i	−0.0272772	−	0.0472456i
$337$	−2630.63			−0.425222			−0.212611	−	0.977137i	$-0.568197\pi$
$337$	−2630.63			−0.425222			−0.212611	+	0.977137i	$0.568197\pi$
$338$	−3010.07	−	3201.05i	−0.484397	−	0.515131i
$339$	1708.54			0.273733
$340$	−1891.15	−	3275.57i	−0.301653	−	0.522478i
$341$	−159.589	−	276.416i	−0.0253438	−	0.0438967i
$342$	−852.505	+	1476.58i	−0.134790	+	0.233463i
$343$	−343.000			−0.0539949
$344$	2044.48	−	3541.14i	0.320439	−	0.555016i
$345$	202.816	−	351.287i	0.0316499	−	0.0548193i
$346$	1649.75			0.256333
$347$	3983.99	−	6900.47i	0.616345	−	1.06754i	−0.373802	−	0.927509i	$-0.621946\pi$
$347$	3983.99	−	6900.47i	0.616345	−	1.06754i	0.990147	−	0.140033i	$-0.0447207\pi$
$348$	−104.129	−	180.356i	−0.0160399	−	0.0277819i
$349$	−1903.99	−	3297.81i	−0.292030	−	0.505811i	0.682260	−	0.731110i	$-0.260997\pi$
$349$	−1903.99	−	3297.81i	−0.292030	−	0.505811i	−0.974290	+	0.225299i	$0.927664\pi$
$350$	−1598.21			−0.244080
$351$	1257.11	−	145.884i	0.191167	−	0.0221844i
$352$	−87.8306			−0.0132994
$353$	−2407.64	−	4170.15i	−0.363019	−	0.628767i	0.625438	−	0.780274i	$-0.284921\pi$
$353$	−2407.64	−	4170.15i	−0.363019	−	0.628767i	−0.988456	+	0.151508i	$0.951587\pi$
$354$	−1552.37	−	2688.78i	−0.233072	−	0.403693i
$355$	−2530.60	+	4383.12i	−0.378339	+	0.655302i
$356$	−3673.85			−0.546948
$357$	642.011	−	1112.00i	0.0951788	−	0.164855i
$358$	448.814	−	777.368i	0.0662585	−	0.114763i
$359$	−7580.90			−1.11450			−0.557249	−	0.830346i	$-0.688143\pi$
$359$	−7580.90			−1.11450			−0.557249	+	0.830346i	$0.688143\pi$
$360$	556.731	−	964.286i	0.0815063	−	0.141173i
$361$	−1056.70	−	1830.26i	−0.154061	−	0.266841i
$362$	3507.15	+	6074.56i	0.509203	+	0.881966i
$363$	3970.40			0.574082
$364$	−782.855	−	1053.37i	−0.112727	−	0.151680i
$365$	3562.44			0.510868
$366$	819.127	+	1418.77i	0.116985	+	0.202624i
$367$	−2923.56	−	5063.76i	−0.415828	−	0.720235i	0.579687	−	0.814839i	$-0.303175\pi$
$367$	−2923.56	−	5063.76i	−0.415828	−	0.720235i	−0.995515	+	0.0946043i	$0.969841\pi$
$368$	69.9451	−	121.149i	0.00990800	−	0.0171612i
$369$	−425.223			−0.0599898
$370$	384.642	−	666.219i	0.0540448	−	0.0936083i
$371$	1537.02	−	2662.20i	0.215089	−	0.372545i
$372$	1395.46			0.194493
$373$	438.556	−	759.601i	0.0608782	−	0.105444i	−0.833980	−	0.551795i	$-0.813943\pi$
$373$	438.556	−	759.601i	0.0608782	−	0.105444i	0.894858	+	0.446351i	$0.147277\pi$
$374$	−167.822	−	290.677i	−0.0232029	−	0.0401886i
$375$	251.500	+	435.611i	0.0346331	+	0.0599863i
$376$	4847.60			0.664882
$377$	−485.224	−	652.893i	−0.0662873	−	0.0891928i
$378$	378.000			0.0514344
$379$	3616.68	+	6264.27i	0.490175	+	0.849008i	0.999936	−	0.0113083i	$-0.00359963\pi$
$379$	3616.68	+	6264.27i	0.490175	+	0.849008i	−0.509761	+	0.860316i	$0.670266\pi$
$380$	2929.73	+	5074.43i	0.395505	+	0.685034i
$381$	3202.03	−	5546.07i	0.430564	−	0.745759i
$382$	−6674.58			−0.893983
$383$	−2330.00	+	4035.68i	−0.310855	+	0.538416i	−0.978548	−	0.206021i	$-0.933949\pi$
$383$	−2330.00	+	4035.68i	−0.310855	+	0.538416i	0.667693	+	0.744437i	$0.267282\pi$
$384$	192.000	−	332.554i	0.0255155	−	0.0441942i
$385$	−297.123			−0.0393320
$386$	1477.15	−	2558.49i	0.194779	−	0.337368i
$387$	2300.04	+	3983.79i	0.302113	+	0.523275i
$388$	−2429.97	−	4208.82i	−0.317945	−	0.550698i
$389$	1723.57			0.224649			0.112325	−	0.993672i	$-0.464170\pi$
$389$	1723.57			0.224649			0.112325	+	0.993672i	$0.464170\pi$
$390$	1725.92	−	3992.08i	0.224091	−	0.518325i
$391$	534.590			0.0691442
$392$	−196.000	−	339.482i	−0.0252538	−	0.0437409i
$393$	946.020	+	1638.55i	0.121426	+	0.210316i
$394$	261.991	−	453.782i	0.0334998	−	0.0580234i
$395$	−15940.2			−2.03047
$396$	49.4047	−	85.5715i	0.00626940	−	0.0108589i
$397$	−1348.52	+	2335.70i	−0.170479	+	0.295278i	−0.938587	−	0.345041i	$-0.887865\pi$
$397$	−1348.52	+	2335.70i	−0.170479	+	0.295278i	0.768108	+	0.640320i	$0.221198\pi$
$398$	−5349.92			−0.673787
$399$	−994.589	+	1722.68i	−0.124791	+	0.216145i
$400$	−913.265	−	1581.82i	−0.114158	−	0.197728i
$401$	1023.85	+	1773.36i	0.127503	+	0.220841i	0.922708	−	0.385499i	$-0.125971\pi$
$401$	1023.85	+	1773.36i	0.127503	+	0.220841i	−0.795206	+	0.606340i	$0.792637\pi$
$402$	3124.92			0.387704
$403$	5414.36	−	628.321i	0.669252	−	0.0776647i
$404$	6953.26			0.856282
$405$	626.322	+	1084.82i	0.0768449	+	0.133099i
$406$	−121.484	−	210.416i	−0.0148501	−	0.0257211i
$407$	34.1334	−	59.1208i	0.00415708	−	0.00720027i
$408$	1467.45			0.178063
$409$	4821.83	−	8351.65i	0.582944	−	1.00969i	−0.412185	−	0.911100i	$-0.635234\pi$
$409$	4821.83	−	8351.65i	0.582944	−	1.00969i	0.995128	−	0.0985877i	$-0.0314325\pi$
$410$	−730.663	+	1265.55i	−0.0880119	+	0.152441i
$411$	4705.89			0.564780
$412$	−3100.62	+	5370.42i	−0.370768	+	0.642189i
$413$	−1811.10	−	3136.91i	−0.215783	−	0.373747i
$414$	78.6883	+	136.292i	0.00934135	+	0.0161797i
$415$	−13906.3			−1.64490
$416$	595.220	−	1376.75i	0.0701516	−	0.162261i
$417$	−639.114			−0.0750541
$418$	259.986	+	450.309i	0.0304219	+	0.0526922i
$419$	4711.03	+	8159.75i	0.549282	+	0.951383i	0.998324	+	0.0578730i	$0.0184319\pi$
$419$	4711.03	+	8159.75i	0.549282	+	0.951383i	−0.449042	+	0.893510i	$0.648235\pi$
$420$	649.519	−	1125.00i	0.0754602	−	0.130701i
$421$	6448.39			0.746497			0.373249	−	0.927731i	$-0.378244\pi$
$421$	6448.39			0.746497			0.373249	+	0.927731i	$0.378244\pi$
$422$	1978.65	−	3427.13i	0.228245	−	0.395332i
$423$	−2726.77	+	4722.91i	−0.313428	+	0.542874i
$424$	3513.19			0.402395
$425$	3490.04	−	6044.92i	0.398333	−	0.689934i
$426$	−981.820	−	1700.56i	−0.111665	−	0.193410i
$427$	955.648	+	1655.23i	0.108307	+	0.187593i
$428$	73.4274			0.00829263
$429$	153.160	−	354.260i	0.0172369	−	0.0398691i
$430$	15808.7			1.77293
$431$	−6302.96	−	10917.0i	−0.704415	−	1.22008i	−0.966902	−	0.255147i	$-0.917876\pi$
$431$	−6302.96	−	10917.0i	−0.704415	−	1.22008i	0.262487	−	0.964935i	$-0.415457\pi$
$432$	216.000	+	374.123i	0.0240563	+	0.0416667i
$433$	8166.28	−	14144.4i	0.906343	−	1.56983i	0.0872388	−	0.996187i	$-0.472196\pi$
$433$	8166.28	−	14144.4i	0.906343	−	1.56983i	0.819104	−	0.573645i	$-0.194471\pi$
$434$	1628.04			0.180065
$435$	402.581	−	697.291i	0.0443731	−	0.0768564i
$436$	261.386	−	452.735i	0.0287113	−	0.0497295i
$437$	−828.175			−0.0906567
$438$	−691.077	+	1196.98i	−0.0753903	+	0.130580i
$439$	4557.15	+	7893.21i	0.495446	+	0.858138i	0.999986	−	0.00525045i	$-0.00167128\pi$
$439$	4557.15	+	7893.21i	0.495446	+	0.858138i	−0.504540	+	0.863388i	$0.668338\pi$
$440$	−169.785	−	294.076i	−0.0183958	−	0.0318625i
$441$	441.000			0.0476190
$442$	5693.69	−	660.736i	0.612717	−	0.0711041i
$443$	−9877.95			−1.05940			−0.529701	−	0.848184i	$-0.677696\pi$
$443$	−9877.95			−1.05940			−0.529701	+	0.848184i	$0.677696\pi$
$444$	149.233	+	258.479i	0.0159511	+	0.0276281i
$445$	−7101.88	−	12300.8i	−0.756543	−	1.31037i
$446$	−4216.42	+	7303.05i	−0.447653	+	0.775357i
$447$	−5515.59			−0.583621
$448$	224.000	−	387.979i	0.0236228	−	0.0409159i
$449$	−2367.06	+	4099.87i	−0.248794	+	0.430924i	−0.963192	−	0.268816i	$-0.913368\pi$
$449$	−2367.06	+	4099.87i	−0.248794	+	0.430924i	0.714397	+	0.699740i	$0.246701\pi$
$450$	2054.85			0.215259
$451$	−64.8397	+	112.306i	−0.00676980	+	0.0117256i
$452$	1139.03	+	1972.86i	0.118530	+	0.205299i
$453$	−2607.06	−	4515.57i	−0.270398	−	0.468344i
$454$	12085.6			1.24935
$455$	2013.58	−	4657.42i	0.207468	−	0.479876i
$456$	−2273.35			−0.233463
$457$	−3069.35	−	5316.27i	−0.314175	−	0.544168i	0.665086	−	0.746766i	$-0.268395\pi$
$457$	−3069.35	−	5316.27i	−0.314175	−	0.544168i	−0.979262	+	0.202599i	$0.935061\pi$
$458$	2221.09	+	3847.05i	0.226605	+	0.392491i
$459$	−825.443	+	1429.71i	−0.0839398	+	0.145388i
$460$	540.842			0.0548193
$461$	1085.03	−	1879.32i	0.109620	−	0.189867i	−0.805996	−	0.591920i	$-0.798370\pi$
$461$	1085.03	−	1879.32i	0.109620	−	0.189867i	0.915616	+	0.402053i	$0.131703\pi$
$462$	57.6389	−	99.8334i	0.00580433	−	0.0100534i
$463$	−103.568			−0.0103957			−0.00519786	−	0.999986i	$-0.501655\pi$
$463$	−103.568			−0.0103957			−0.00519786	+	0.999986i	$0.501655\pi$
$464$	138.838	−	240.475i	0.0138910	−	0.0240599i
$465$	2697.56	+	4672.31i	0.269024	+	0.465963i
$466$	−4975.20	−	8617.30i	−0.494575	−	0.856628i
$467$	−19612.0			−1.94333			−0.971664	−	0.236367i	$-0.924043\pi$
$467$	−19612.0			−1.94333			−0.971664	+	0.236367i	$0.924043\pi$
$468$	1006.53	+	1354.33i	0.0994161	+	0.133769i
$469$	3645.74			0.358944
$470$	9370.85	+	16230.8i	0.919671	+	1.59292i
$471$	−726.241	−	1257.89i	−0.0710476	−	0.123058i
$472$	2069.83	−	3585.04i	0.201846	−	0.349608i
$473$	1402.88			0.136373
$474$	3092.23	−	5355.90i	0.299643	−	0.518997i
$475$	−5406.69	+	9364.66i	−0.522265	+	0.904589i
$476$	1712.03			0.164855
$477$	−1976.17	+	3422.82i	−0.189691	+	0.328554i
$478$	−1052.97	−	1823.79i	−0.100756	−	0.174515i
$479$	−4416.02	−	7648.77i	−0.421238	−	0.729606i	0.574823	−	0.818278i	$-0.305071\pi$
$479$	−4416.02	−	7648.77i	−0.421238	−	0.729606i	−0.996061	+	0.0886723i	$0.971738\pi$
$480$	1484.61			0.141173
$481$	695.404	+	935.700i	0.0659203	+	0.0886990i
$482$	7909.42			0.747436
$483$	91.8030	+	159.007i	0.00864841	+	0.0149795i
$484$	2646.93	+	4584.62i	0.248585	+	0.430562i
$485$	9394.70	−	16272.1i	0.879570	−	1.52346i
$486$	−486.000			−0.0453609
$487$	4986.28	−	8636.49i	0.463963	−	0.803608i	−0.535191	−	0.844731i	$-0.679760\pi$
$487$	4986.28	−	8636.49i	0.463963	−	0.803608i	0.999154	+	0.0411234i	$0.0130937\pi$
$488$	−1092.17	+	1891.69i	−0.101312	+	0.175477i
$489$	−9055.51			−0.837432
$490$	757.772	−	1312.50i	0.0698626	−	0.121006i
$491$	−6388.79	−	11065.7i	−0.587214	−	1.01708i	−0.994595	−	0.103826i	$-0.966891\pi$
$491$	−6388.79	−	11065.7i	−0.587214	−	1.01708i	0.407382	−	0.913258i	$-0.366442\pi$
$492$	−283.482	−	491.006i	−0.0259764	−	0.0449924i
$493$	1061.14			0.0969399
$494$	−8820.53	+	1023.60i	−0.803349	+	0.0932263i
$495$	382.016			0.0346875
$496$	930.308	+	1611.34i	0.0842179	+	0.145870i
$497$	−1145.46	−	1983.99i	−0.103382	−	0.179063i
$498$	2697.68	−	4672.52i	0.242743	−	0.420443i
$499$	5539.87			0.496991			0.248496	−	0.968633i	$-0.420064\pi$
$499$	5539.87			0.496991			0.248496	+	0.968633i	$0.420064\pi$
$500$	−335.334	+	580.815i	−0.0299932	+	0.0519497i
$501$	4348.49	−	7531.80i	0.387777	−	0.671649i
$502$	−1847.83			−0.164288
$503$	7528.90	−	13040.4i	0.667389	−	1.15595i	−0.311242	−	0.950331i	$-0.600745\pi$
$503$	7528.90	−	13040.4i	0.667389	−	1.15595i	0.978632	−	0.205622i	$-0.0659216\pi$
$504$	252.000	+	436.477i	0.0222718	+	0.0385758i
$505$	13441.3	+	23281.0i	1.18442	+	2.05147i
$506$	47.9947			0.00421665
$507$	4515.10	+	4801.58i	0.395508	+	0.420602i
$508$	8538.74			0.745759
$509$	−1118.53	−	1937.36i	−0.0974030	−	0.168707i	0.813206	−	0.581976i	$-0.197720\pi$
$509$	−1118.53	−	1937.36i	−0.0974030	−	0.168707i	−0.910609	+	0.413269i	$0.864387\pi$
$510$	2836.72	+	4913.35i	0.246299	+	0.426602i
$511$	−806.257	+	1396.48i	−0.0697979	+	0.120893i
$512$	512.000			0.0441942
$513$	1278.76	−	2214.87i	0.110056	−	0.190622i
$514$	428.061	−	741.423i	0.0367334	−	0.0636241i
$515$	−23975.1			−2.05140
$516$	−3066.72	+	5311.72i	−0.261637	+	0.453169i
$517$	831.577	+	1440.33i	0.0707403	+	0.122526i
$518$	174.105	+	301.559i	0.0147679	+	0.0255787i
$519$	−2474.63			−0.209295
$520$	5760.27	−	668.463i	0.485778	−	0.0563731i
$521$	17534.8			1.47450			0.737248	−	0.675623i	$-0.236125\pi$
$521$	17534.8			1.47450			0.737248	+	0.675623i	$0.236125\pi$
$522$	156.193	+	270.534i	0.0130965	+	0.0226839i
$523$	8633.58	+	14953.8i	0.721836	+	1.25026i	0.960263	+	0.279096i	$0.0900348\pi$
$523$	8633.58	+	14953.8i	0.721836	+	1.25026i	−0.238427	+	0.971160i	$0.576632\pi$
$524$	−1261.36	+	2184.74i	−0.105158	+	0.182139i
$525$	2397.32			0.199291
$526$	6350.14	−	10998.8i	0.526387	−	0.911728i
$527$	−3555.17	+	6157.73i	−0.293863	+	0.508985i
$528$	131.746			0.0108589
$529$	6045.28	−	10470.7i	0.496859	−	0.860584i
$530$	6791.32	+	11762.9i	0.556596	+	0.964053i
$531$	2328.55	+	4033.17i	0.190302	+	0.329614i
$532$	−2652.24			−0.216145
$533$	−1320.98	−	1777.45i	−0.107351	−	0.144446i
$534$	5510.77			0.446581
$535$	141.942	+	245.850i	0.0114704	+	0.0198674i
$536$	2083.28	+	3608.35i	0.167881	+	0.290778i
$537$	−673.220	+	1166.05i	−0.0540998	+	0.0937036i
$538$	9130.95			0.731716
$539$	67.2453	−	116.472i	0.00537377	−	0.00930764i
$540$	−835.096	+	1446.43i	−0.0665496	+	0.115267i
$541$	−10987.3			−0.873164			−0.436582	−	0.899665i	$-0.643811\pi$
$541$	−10987.3			−0.873164			−0.436582	+	0.899665i	$0.643811\pi$
$542$	4083.99	−	7073.67i	0.323657	−	0.560591i
$543$	−5260.72	−	9111.84i	−0.415763	−	0.720122i
$544$	978.303	+	1694.47i	0.0771037	+	0.133547i
$545$	2021.14			0.158855
$546$	1174.28	+	1580.05i	0.0920414	+	0.123846i
$547$	5583.48			0.436439			0.218220	−	0.975900i	$-0.429975\pi$
$547$	5583.48			0.436439			0.218220	+	0.975900i	$0.429975\pi$
$548$	3137.26	+	5433.90i	0.244557	+	0.423585i
$549$	−1228.69	−	2128.15i	−0.0955177	−	0.165441i
$550$	313.331	−	542.705i	0.0242918	−	0.0420745i
$551$	−1643.89			−0.127100
$552$	−104.918	+	181.723i	−0.00808984	+	0.0140120i
$553$	3607.60	−	6248.55i	0.277416	−	0.480498i
$554$	−11877.9			−0.910907
$555$	−576.963	+	999.329i	−0.0441274	+	0.0764309i
$556$	−426.076	−	737.985i	−0.0324994	−	0.0562905i
$557$	2356.12	+	4080.91i	0.179231	+	0.310438i	0.941617	−	0.336685i	$-0.109306\pi$
$557$	2356.12	+	4080.91i	0.179231	+	0.310438i	−0.762386	+	0.647122i	$0.775972\pi$
$558$	−2093.19			−0.158803
$559$	−9507.15	+	21990.1i	−0.719337	+	1.66384i
$560$	1732.05			0.130701
$561$	251.733	+	436.015i	0.0189451	+	0.0328138i
$562$	−4237.99	−	7340.42i	−0.318094	−	0.550955i
$563$	390.077	−	675.632i	0.0292003	−	0.0505764i	−0.851056	−	0.525075i	$-0.824037\pi$
$563$	390.077	−	675.632i	0.0292003	−	0.0505764i	0.880256	+	0.474499i	$0.157371\pi$
$564$	−7271.39			−0.542874
$565$	−4403.70	+	7627.43i	−0.327903	+	0.567944i
$566$	5900.86	−	10220.6i	0.438218	−	0.759017i
$567$	−567.000			−0.0419961
$568$	1309.09	−	2267.42i	0.0967048	−	0.167498i
$569$	−984.578	−	1705.34i	−0.0725407	−	0.125644i	0.827473	−	0.561505i	$-0.189777\pi$
$569$	−984.578	−	1705.34i	−0.0725407	−	0.125644i	−0.900014	+	0.435861i	$0.856444\pi$
$570$	−4394.59	−	7611.65i	−0.322928	−	0.559328i
$571$	2958.63			0.216839			0.108419	−	0.994105i	$-0.465421\pi$
$571$	2958.63			0.216839			0.108419	+	0.994105i	$0.465421\pi$
$572$	511.171	−	59.3199i	0.0373656	−	0.00433617i
$573$	10011.9			0.729934
$574$	−330.729	−	572.840i	−0.0240494	−	0.0416548i
$575$	499.050	+	864.381i	0.0361945	+	0.0626907i
$576$	−288.000	+	498.831i	−0.0208333	+	0.0360844i
$577$	−10122.8			−0.730363			−0.365182	−	0.930936i	$-0.618993\pi$
$577$	−10122.8			−0.730363			−0.365182	+	0.930936i	$0.618993\pi$
$578$	1174.42	−	2034.15i	0.0845145	−	0.146383i
$579$	−2215.72	+	3837.74i	−0.159037	+	0.275459i
$580$	1073.55			0.0768564
$581$	3147.29	−	5451.27i	0.224736	−	0.389255i
$582$	3644.95	+	6313.24i	0.259601	+	0.449643i
$583$	602.667	+	1043.85i	0.0428129	+	0.0741541i
$584$	−1842.87			−0.130580
$585$	−2588.88	+	5988.12i	−0.182969	+	0.423211i
$586$	−11102.8			−0.782686
$587$	10683.8	+	18504.8i	0.751219	+	1.30115i	0.947232	+	0.320549i	$0.103867\pi$
$587$	10683.8	+	18504.8i	0.751219	+	1.30115i	−0.196013	+	0.980601i	$0.562799\pi$
$588$	294.000	+	509.223i	0.0206197	+	0.0357143i
$589$	5507.58	−	9539.42i	0.385290	−	0.667343i
$590$	16004.7			1.11678
$591$	−392.987	+	680.674i	−0.0273525	+	0.0473759i
$592$	−198.977	+	344.639i	−0.0138141	+	0.0239267i
$593$	12625.3			0.874300			0.437150	−	0.899389i	$-0.355988\pi$
$593$	12625.3			0.874300			0.437150	+	0.899389i	$0.355988\pi$
$594$	−74.1071	+	128.357i	−0.00511894	+	0.00886627i
$595$	3309.51	+	5732.24i	0.228028	+	0.394956i
$596$	−3677.06	−	6368.86i	−0.252715	−	0.437716i
$597$	8024.88			0.550145
$598$	−325.256	+	752.320i	−0.0222420	+	0.0514459i
$599$	15139.5			1.03269			0.516347	−	0.856380i	$-0.327292\pi$
$599$	15139.5			1.03269			0.516347	+	0.856380i	$0.327292\pi$
$600$	1369.90	+	2372.73i	0.0932097	+	0.161444i
$601$	−4040.47	−	6998.30i	−0.274233	−	0.474986i	0.695708	−	0.718325i	$-0.255091\pi$
$601$	−4040.47	−	6998.30i	−0.274233	−	0.474986i	−0.969941	+	0.243339i	$0.921757\pi$
$602$	−3577.84	+	6197.00i	−0.242229	+	0.419553i
$603$	−4687.38			−0.316559
$604$	3476.08	−	6020.75i	0.234172	−	0.405598i
$605$	−10233.5	+	17725.0i	−0.687690	+	1.19111i
$606$	−10429.9			−0.699151
$607$	−8201.64	+	14205.7i	−0.548425	+	0.949900i	0.449957	+	0.893050i	$0.351439\pi$
$607$	−8201.64	+	14205.7i	−0.548425	+	0.949900i	−0.998383	+	0.0568505i	$0.981894\pi$
$608$	−1515.56	−	2625.03i	−0.101093	−	0.175097i
$609$	182.225	+	315.624i	0.0121250	+	0.0210012i
$610$	−8445.05			−0.560541
$611$	−28212.8	+	3274.02i	−1.86803	+	0.216780i
$612$	−2201.18			−0.145388
$613$	443.002	+	767.301i	0.0291887	+	0.0505563i	0.880251	−	0.474509i	$-0.157374\pi$
$613$	443.002	+	767.301i	0.0291887	+	0.0505563i	−0.851062	+	0.525065i	$0.824041\pi$
$614$	648.228	+	1122.76i	0.0426064	+	0.0737965i
$615$	1095.99	−	1898.32i	0.0718614	−	0.124468i
$616$	153.704			0.0100534
$617$	7177.36	−	12431.6i	0.468314	−	0.811143i	−0.531030	−	0.847353i	$-0.678195\pi$
$617$	7177.36	−	12431.6i	0.468314	−	0.811143i	0.999344	+	0.0362095i	$0.0115284\pi$
$618$	4650.92	−	8055.64i	0.302731	−	0.524345i
$619$	25790.7			1.67466			0.837329	−	0.546699i	$-0.184116\pi$
$619$	25790.7			1.67466			0.837329	+	0.546699i	$0.184116\pi$
$620$	−3596.74	+	6229.74i	−0.232982	+	0.403536i
$621$	−118.032	−	204.438i	−0.00762718	−	0.0132107i
$622$	3768.61	+	6527.42i	0.242938	+	0.420781i
$623$	6429.23			0.413454
$624$	−892.829	+	2065.13i	−0.0572785	+	0.132486i
$625$	−16862.7			−1.07921
$626$	−2777.95	−	4811.56i	−0.177363	−	0.307202i
$627$	−389.979	−	675.464i	−0.0248394	−	0.0430230i
$628$	968.321	−	1677.18i	0.0615290	−	0.106571i
$629$	−1520.78			−0.0964032
$630$	−974.278	+	1687.50i	−0.0616130	+	0.106717i
$631$	9343.81	−	16184.0i	0.589495	−	1.02103i	−0.404804	−	0.914404i	$-0.632660\pi$
$631$	9343.81	−	16184.0i	0.589495	−	1.02103i	0.994299	−	0.106631i	$-0.0340065\pi$
$632$	8245.95			0.518997
$633$	−2967.98	+	5140.69i	−0.186361	+	0.322787i
$634$	−4488.53	−	7774.36i	−0.281171	−	0.487002i
$635$	16506.2	+	28589.5i	1.03154	+	1.78668i
$636$	−5269.78			−0.328554
$637$	1370.00	+	1843.40i	0.0852138	+	0.114659i
$638$	95.2677			0.00591173
$639$	1472.73	+	2550.84i	0.0911742	+	0.157918i
$640$	989.743	+	1714.29i	0.0611297	+	0.105880i
$641$	6690.59	−	11588.4i	0.412266	−	0.714065i	−0.582871	−	0.812565i	$-0.698071\pi$
$641$	6690.59	−	11588.4i	0.412266	−	0.714065i	0.995137	+	0.0984990i	$0.0314041\pi$
$642$	−110.141			−0.00677090
$643$	−7759.54	+	13439.9i	−0.475904	+	0.824290i	−0.999619	−	0.0276036i	$-0.991212\pi$
$643$	−7759.54	+	13439.9i	−0.475904	+	0.824290i	0.523715	+	0.851894i	$0.324546\pi$
$644$	−122.404	+	212.010i	−0.00748974	+	0.0129726i
$645$	−23713.0			−1.44760
$646$	5791.72	−	10031.6i	0.352743	−	0.610970i
$647$	−2320.93	−	4019.97i	−0.141028	−	0.244268i	0.786856	−	0.617137i	$-0.211707\pi$
$647$	−2320.93	−	4019.97i	−0.141028	−	0.244268i	−0.927884	+	0.372869i	$0.878374\pi$
$648$	−324.000	−	561.184i	−0.0196419	−	0.0340207i
$649$	1420.27			0.0859019
$650$	6383.51	+	8589.33i	0.385203	+	0.518310i
$651$	−2442.06			−0.147023
$652$	−6037.01	−	10456.4i	−0.362619	−	0.628074i
$653$	−6013.12	−	10415.0i	−0.360355	−	0.624153i	0.627664	−	0.778484i	$-0.284011\pi$
$653$	−6013.12	−	10415.0i	−0.360355	−	0.624153i	−0.988019	+	0.154331i	$0.950678\pi$
$654$	−392.080	+	679.102i	−0.0234427	+	0.0406039i
$655$	−9753.30			−0.581821
$656$	377.976	−	654.674i	0.0224962	−	0.0389645i
$657$	1036.62	−	1795.47i	0.0615559	−	0.106618i
$658$	−8483.29			−0.502604
$659$	3227.27	−	5589.80i	0.190769	−	0.330421i	−0.754736	−	0.656028i	$-0.772235\pi$
$659$	3227.27	−	5589.80i	0.190769	−	0.330421i	0.945505	+	0.325607i	$0.105569\pi$
$660$	254.677	+	441.114i	0.0150201	+	0.0260156i
$661$	−2977.07	−	5156.43i	−0.175181	−	0.303422i	0.765043	−	0.643979i	$-0.222718\pi$
$661$	−2977.07	−	5156.43i	−0.175181	−	0.303422i	−0.940224	+	0.340557i	$0.889384\pi$
$662$	−20165.2			−1.18390
$663$	−8540.53	+	991.104i	−0.500282	+	0.0580562i
$664$	7193.82			0.420443
$665$	−5127.02	−	8880.26i	−0.298973	−	0.517837i
$666$	−223.850	−	387.719i	−0.0130240	−	0.0225583i
$667$	−75.8677	+	131.407i	−0.00440421	+	0.00762832i
$668$	11596.0			0.671649
$669$	6324.62	−	10954.6i	0.365507	−	0.633077i
$670$	−8054.35	+	13950.5i	−0.464428	+	0.804413i
$671$	−749.421			−0.0431164
$672$	−336.000	+	581.969i	−0.0192879	+	0.0334077i
$673$	13495.1	+	23374.1i	0.772951	+	1.33879i	0.935939	+	0.352163i	$0.114554\pi$
$673$	13495.1	+	23374.1i	0.772951	+	1.33879i	−0.162987	+	0.986628i	$0.552113\pi$
$674$	2630.63	+	4556.39i	0.150339	+	0.260394i
$675$	−3082.27			−0.175758
$676$	−2534.31	+	8414.64i	−0.144192	+	0.478758i
$677$	20690.6			1.17460			0.587300	−	0.809369i	$-0.300191\pi$
$677$	20690.6			1.17460			0.587300	+	0.809369i	$0.300191\pi$
$678$	−1708.54	−	2959.28i	−0.0967791	−	0.167626i
$679$	4252.44	+	7365.44i	0.240344	+	0.416288i
$680$	−3782.30	+	6551.14i	−0.213301	+	0.369448i
$681$	−18128.4			−1.02009
$682$	−319.178	+	552.832i	−0.0179208	+	0.0310397i
$683$	11529.7	−	19970.0i	0.645931	−	1.11879i	−0.338155	−	0.941090i	$-0.609803\pi$
$683$	11529.7	−	19970.0i	0.645931	−	1.11879i	0.984086	−	0.177695i	$-0.0568639\pi$
$684$	3410.02			0.190622
$685$	−12129.2	+	21008.5i	−0.676546	+	1.17181i
$686$	343.000	+	594.093i	0.0190901	+	0.0330650i
$687$	−3331.64	−	5770.57i	−0.185022	−	0.320467i
$688$	−8177.92			−0.453169
$689$	−20446.6	+	2372.77i	−1.13056	+	0.131198i
$690$	−811.262			−0.0447598
$691$	6702.69	+	11609.4i	0.369005	+	0.639135i	0.989410	−	0.145146i	$-0.0463653\pi$
$691$	6702.69	+	11609.4i	0.369005	+	0.639135i	−0.620405	+	0.784281i	$0.713032\pi$
$692$	−1649.75	−	2857.46i	−0.0906276	−	0.156972i
$693$	−86.4583	+	149.750i	−0.00473922	+	0.00820857i
$694$	−15936.0			−0.871644
$695$	1647.29	−	2853.19i	0.0899068	−	0.155723i
$696$	−208.258	+	360.713i	−0.0113419	+	0.0196448i
$697$	2888.87			0.156993
$698$	−3807.99	+	6595.63i	−0.206496	+	0.357662i
$699$	7462.80	+	12926.0i	0.403819	+	0.699434i
$700$	1598.21	+	2768.19i	0.0862954	+	0.149468i
$701$	−20876.7			−1.12483			−0.562413	−	0.826856i	$-0.690127\pi$
$701$	−20876.7			−1.12483			−0.562413	+	0.826856i	$0.690127\pi$
$702$	−1509.79	−	2031.50i	−0.0811729	−	0.109222i
$703$	2355.96			0.126397
$704$	87.8306	+	152.127i	0.00470205	+	0.00814419i
$705$	−14056.3	−	24346.2i	−0.750908	−	1.30061i
$706$	−4815.27	+	8340.30i	−0.256693	+	0.444605i
$707$	−12168.2			−0.647288
$708$	−3104.74	+	5377.56i	−0.164807	+	0.285454i
$709$	−4672.47	+	8092.95i	−0.247501	+	0.428684i	−0.962832	−	0.270102i	$-0.912943\pi$
$709$	−4672.47	+	8092.95i	−0.247501	+	0.428684i	0.715331	+	0.698786i	$0.246276\pi$
$710$	10122.4			0.535052
$711$	−4638.35	+	8033.85i	−0.244658	+	0.423759i
$712$	3673.85	+	6363.29i	0.193375	+	0.334936i
$713$	−508.364	−	880.511i	−0.0267018	−	0.0462488i
$714$	−2568.05			−0.134603
$715$	1186.76	+	1596.84i	0.0620730	+	0.0835222i
$716$	−1795.25			−0.0937036
$717$	1579.45	+	2735.69i	0.0822673	+	0.142491i
$718$	7580.90	+	13130.5i	0.394034	+	0.682487i
$719$	437.682	−	758.087i	0.0227020	−	0.0393211i	−0.854451	−	0.519532i	$-0.826106\pi$
$719$	437.682	−	758.087i	0.0227020	−	0.0393211i	0.877153	+	0.480211i	$0.159440\pi$
$720$	−2226.92			−0.115267
$721$	5426.08	−	9398.24i	0.280274	−	0.485449i
$722$	−2113.40	+	3660.52i	−0.108937	+	0.188685i
$723$	−11864.1			−0.610279
$724$	7014.30	−	12149.1i	0.360061	−	0.623644i
$725$	990.595	+	1715.76i	0.0507445	+	0.0878921i
$726$	−3970.40	−	6876.93i	−0.202969	−	0.351552i
$727$	−13584.9			−0.693036			−0.346518	−	0.938043i	$-0.612636\pi$
$727$	−13584.9			−0.693036			−0.346518	+	0.938043i	$0.612636\pi$
$728$	−1041.63	+	2409.31i	−0.0530296	+	0.122658i
$729$	729.000			0.0370370
$730$	−3562.44	−	6170.33i	−0.180619	−	0.312841i
$731$	−15625.9	−	27064.9i	−0.790624	−	1.36940i
$732$	1638.25	−	2837.54i	0.0827207	−	0.143277i
$733$	9652.07			0.486368			0.243184	−	0.969980i	$-0.421808\pi$
$733$	9652.07			0.486368			0.243184	+	0.969980i	$0.421808\pi$
$734$	−5847.13	+	10127.5i	−0.294035	+	0.509283i
$735$	−1136.66	+	1968.75i	−0.0570425	+	0.0988006i
$736$	−279.781			−0.0140120
$737$	−714.750	+	1237.98i	−0.0357234	+	0.0618748i
$738$	425.223	+	736.509i	0.0212096	+	0.0367361i
$739$	−11376.4	−	19704.6i	−0.566291	−	0.980845i	−0.996928	−	0.0783196i	$-0.975045\pi$
$739$	−11376.4	−	19704.6i	−0.566291	−	0.980845i	0.430637	−	0.902525i	$-0.358289\pi$
$740$	−1538.57			−0.0764309
$741$	13230.8	−	1535.40i	0.655932	−	0.0761190i
$742$	−6148.08			−0.304182
$743$	−1525.63	−	2642.47i	−0.0753297	−	0.130475i	0.825900	−	0.563817i	$-0.190668\pi$
$743$	−1525.63	−	2642.47i	−0.0753297	−	0.130475i	−0.901230	+	0.433342i	$0.857334\pi$
$744$	−1395.46	−	2417.01i	−0.0687636	−	0.119102i
$745$	14216.2	−	24623.2i	0.699115	−	1.21090i
$746$	−1754.22			−0.0860948
$747$	−4046.52	+	7008.78i	−0.198199	+	0.343290i
$748$	−335.644	+	581.353i	−0.0164069	+	0.0284176i
$749$	−128.498			−0.00626864
$750$	503.001	−	871.223i	0.0244893	−	0.0424167i
$751$	7586.24	+	13139.8i	0.368610	+	0.638451i	0.989348	−	0.145567i	$-0.0465005\pi$
$751$	7586.24	+	13139.8i	0.368610	+	0.638451i	−0.620739	+	0.784018i	$0.713167\pi$
$752$	−4847.60	−	8396.28i	−0.235071	−	0.407156i
$753$	2771.74			0.134141
$754$	−645.620	+	1493.33i	−0.0311831	+	0.0721270i
$755$	26878.4			1.29563
$756$	−378.000	−	654.715i	−0.0181848	−	0.0314970i
$757$	−3737.14	−	6472.92i	−0.179430	−	0.310782i	0.762255	−	0.647276i	$-0.224092\pi$
$757$	−3737.14	−	6472.92i	−0.179430	−	0.310782i	−0.941686	+	0.336494i	$0.890759\pi$
$758$	7233.35	−	12528.5i	0.346606	−	0.600339i
$759$	−71.9921			−0.00344288
$760$	5859.45	−	10148.9i	0.279664	−	0.484392i
$761$	−9152.76	+	15853.0i	−0.435988	+	0.755154i	−0.997376	−	0.0723992i	$-0.976934\pi$
$761$	−9152.76	+	15853.0i	−0.435988	+	0.755154i	0.561387	+	0.827553i	$0.310268\pi$
$762$	−12808.1			−0.608909
$763$	−457.426	+	792.285i	−0.0217037	+	0.0375920i
$764$	6674.58	+	11560.7i	0.316071	+	0.547450i
$765$	−4255.09	−	7370.03i	−0.201102	−	0.348319i
$766$	9319.99			0.439615
$767$	−9625.01	+	22262.8i	−0.453115	+	1.04806i
$768$	−768.000			−0.0360844
$769$	15480.0	+	26812.1i	0.725907	+	1.25731i	0.958599	+	0.284758i	$0.0919132\pi$
$769$	15480.0	+	26812.1i	0.725907	+	1.25731i	−0.232692	+	0.972550i	$0.574753\pi$
$770$	297.123	+	514.633i	0.0139059	+	0.0240858i
$771$	−642.091	+	1112.14i	−0.0299927	+	0.0519489i
$772$	−5908.59			−0.275459
$773$	5510.83	−	9545.03i	0.256417	−	0.444128i	−0.708862	−	0.705347i	$-0.750791\pi$
$773$	5510.83	−	9545.03i	0.256417	−	0.444128i	0.965280	+	0.261219i	$0.0841245\pi$
$774$	4600.08	−	7967.57i	0.213626	−	0.370011i
$775$	−13275.3			−0.615306
$776$	−4859.93	+	8417.65i	−0.224821	+	0.389402i
$777$	−261.158	−	452.339i	−0.0120579	−	0.0208849i
$778$	−1723.57	−	2985.31i	−0.0794255	−	0.137569i
$779$	−4475.37			−0.205837
$780$	−8640.40	+	1002.69i	−0.396636	+	0.0460285i
$781$	898.269			0.0411557
$782$	−534.590	−	925.937i	−0.0244462	−	0.0423420i
$783$	−234.290	−	405.802i	−0.0106933	−	0.0185213i
$784$	−392.000	+	678.964i	−0.0178571	+	0.0309295i
$785$	7487.41			0.340430
$786$	1892.04	−	3277.11i	0.0858611	−	0.148716i
$787$	−8897.17	+	15410.3i	−0.402986	+	0.697992i	−0.994085	−	0.108607i	$-0.965361\pi$
$787$	−8897.17	+	15410.3i	−0.402986	+	0.697992i	0.591099	+	0.806599i	$0.298694\pi$
$788$	−1047.97			−0.0473759
$789$	−9525.21	+	16498.2i	−0.429793	+	0.744423i
$790$	15940.2	+	27609.2i	0.717881	+	1.24341i
$791$	−1993.30	−	3452.50i	−0.0896000	−	0.155192i
$792$	−197.619			−0.00886627
$793$	5078.75	−	11747.2i	0.227430	−	0.526048i
$794$	5394.07			0.241094
$795$	−10187.0	−	17644.4i	−0.454459	−	0.787146i
$796$	5349.92	+	9266.34i	0.238220	+	0.412609i
$797$	19479.8	−	33740.0i	0.865759	−	1.49954i	−0.000533246	−	1.00000i	$-0.500170\pi$
$797$	19479.8	−	33740.0i	0.865759	−	1.49954i	0.866292	−	0.499538i	$-0.166497\pi$
$798$	3978.36			0.176482
$799$	18525.1	−	32086.4i	0.820238	−	1.42069i
$800$	−1826.53	+	3163.64i	−0.0807220	+	0.139815i
$801$	−8266.15			−0.364632
$802$	2047.70	−	3546.72i	0.0901580	−	0.156158i
$803$	−316.134	−	547.561i	−0.0138931	−	0.0240635i
$804$	−3124.92	−	5412.52i	−0.137074	−	0.237419i
$805$	−946.473			−0.0414395
$806$	−6502.64	−	8749.62i	−0.284176	−	0.382373i
$807$	−13696.4			−0.597444
$808$	−6953.26	−	12043.4i	−0.302741	−	0.524363i
$809$	−5675.37	−	9830.03i	−0.246645	−	0.427201i	0.715948	−	0.698154i	$-0.245995\pi$
$809$	−5675.37	−	9830.03i	−0.246645	−	0.427201i	−0.962593	+	0.270952i	$0.912661\pi$
$810$	1252.64	−	2169.64i	0.0543376	−	0.0941154i
$811$	15489.5			0.670665			0.335333	−	0.942100i	$-0.391151\pi$
$811$	15489.5			0.670665			0.335333	+	0.942100i	$0.391151\pi$
$812$	−242.967	+	420.831i	−0.0105006	+	0.0181875i
$813$	−6125.98	+	10610.5i	−0.264265	+	0.457720i
$814$	−136.534			−0.00587900
$815$	23340.2	−	40426.4i	1.00315	−	1.73751i
$816$	−1467.45	−	2541.71i	−0.0629549	−	0.109041i
$817$	24207.4	+	41928.4i	1.03661	+	1.79546i
$818$	−19287.3			−0.824407
$819$	−1761.42	−	2370.08i	−0.0751515	−	0.101120i
$820$	2922.65			0.124468
$821$	−3408.93	−	5904.45i	−0.144912	−	0.250995i	0.784428	−	0.620220i	$-0.212957\pi$
$821$	−3408.93	−	5904.45i	−0.144912	−	0.250995i	−0.929340	+	0.369225i	$0.879623\pi$
$822$	−4705.89	−	8150.85i	−0.199680	−	0.345856i
$823$	15596.3	−	27013.5i	0.660573	−	1.14415i	−0.319893	−	0.947454i	$-0.603647\pi$
$823$	15596.3	−	27013.5i	0.660573	−	1.14415i	0.980465	−	0.196692i	$-0.0630198\pi$
$824$	12402.5			0.524345
$825$	−469.996	+	814.057i	−0.0198341	+	0.0343537i
$826$	−3622.19	+	6273.82i	−0.152581	+	0.264279i
$827$	−37235.9			−1.56568			−0.782841	−	0.622222i	$-0.786230\pi$
$827$	−37235.9			−1.56568			−0.782841	+	0.622222i	$0.786230\pi$
$828$	157.377	−	272.584i	0.00660533	−	0.0114408i
$829$	17481.5	+	30278.8i	0.732396	+	1.26855i	0.955856	+	0.293834i	$0.0949313\pi$
$829$	17481.5	+	30278.8i	0.732396	+	1.26855i	−0.223460	+	0.974713i	$0.571735\pi$
$830$	13906.3	+	24086.4i	0.581560	+	1.00729i
$831$	17816.8			0.743753
$832$	−2979.82	+	345.800i	−0.124167	+	0.0144092i
$833$	−2996.05			−0.124618
$834$	639.114	+	1106.98i	0.0265356	+	0.0459610i
$835$	22416.1	+	38825.8i	0.929031	+	1.60913i
$836$	519.973	−	900.619i	0.0215115	−	0.0372590i
$837$	3139.79			0.129662
$838$	9422.06	−	16319.5i	0.388401	−	0.672730i
$839$	2745.47	−	4755.30i	0.112973	−	0.195675i	−0.803995	−	0.594636i	$-0.797296\pi$
$839$	2745.47	−	4755.30i	0.112973	−	0.195675i	0.916968	+	0.398962i	$0.130629\pi$
$840$	−2598.08			−0.106717
$841$	12043.9	−	20860.7i	0.493825	−	0.855331i
$842$	−6448.39	−	11168.9i	−0.263927	−	0.457134i
$843$	6356.99	+	11010.6i	0.259723	+	0.449853i
$844$	−7914.62			−0.322787
$845$	−33073.1	+	7780.86i	−1.34645	+	0.316769i
$846$	10907.1			0.443255
$847$	−4632.13	−	8023.09i	−0.187913	−	0.325474i
$848$	−3513.19	−	6085.02i	−0.142268	−	0.246416i
$849$	−8851.29	+	15330.9i	−0.357804	+	0.619735i
$850$	−13960.2			−0.563329
$851$	108.731	−	188.327i	0.00437983	−	0.00758609i
$852$	−1963.64	+	3401.12i	−0.0789591	+	0.136761i
$853$	−36700.3			−1.47315			−0.736574	−	0.676357i	$-0.763558\pi$
$853$	−36700.3			−1.47315			−0.736574	+	0.676357i	$0.763558\pi$
$854$	1911.30	−	3310.46i	0.0765845	−	0.132648i
$855$	6591.88	+	11417.5i	0.263670	+	0.456689i
$856$	−73.4274	−	127.180i	−0.00293189	−	0.00507818i
$857$	−18241.6			−0.727097			−0.363548	−	0.931575i	$-0.618435\pi$
$857$	−18241.6			−0.727097			−0.363548	+	0.931575i	$0.618435\pi$
$858$	−766.757	+	88.9799i	−0.0305089	+	0.00354047i
$859$	−40313.2			−1.60125			−0.800623	−	0.599169i	$-0.795498\pi$
$859$	−40313.2			−1.60125			−0.800623	+	0.599169i	$0.795498\pi$
$860$	−15808.7	−	27381.4i	−0.626827	−	1.08570i
$861$	496.094	+	859.260i	0.0196363	+	0.0340110i
$862$	−12605.9	+	21834.1i	−0.498097	+	0.862729i
$863$	−30739.7			−1.21251			−0.606253	−	0.795272i	$-0.707328\pi$
$863$	−30739.7			−1.21251			−0.606253	+	0.795272i	$0.707328\pi$
$864$	432.000	−	748.246i	0.0170103	−	0.0294628i
$865$	6378.26	−	11047.5i	0.250714	−	0.434249i
$866$	−32665.1			−1.28176
$867$	−1761.63	+	3051.23i	−0.0690058	+	0.119522i
$868$	−1628.04	−	2819.85i	−0.0636627	−	0.110267i
$869$	1414.54	+	2450.06i	0.0552188	+	0.0956418i
$870$	−1610.32			−0.0627530
$871$	−14561.7	−	19593.4i	−0.566479	−	0.762225i
$872$	−1045.55			−0.0406039
$873$	−5467.42	−	9469.86i	−0.211964	−	0.367132i
$874$	828.175	+	1434.44i	0.0320520	+	0.0555156i
$875$	586.834	−	1016.43i	0.0226727	−	0.0392703i
$876$	2764.31			0.106618
$877$	−1113.28	+	1928.26i	−0.0428652	+	0.0742447i	−0.886662	−	0.462418i	$-0.846982\pi$
$877$	−1113.28	+	1928.26i	−0.0428652	+	0.0742447i	0.843797	+	0.536663i	$0.180315\pi$
$878$	9114.30	−	15786.4i	0.350333	−	0.606795i
$879$	16654.3			0.639060
$880$	−339.569	+	588.152i	−0.0130078	+	0.0225302i
$881$	3613.13	+	6258.12i	0.138172	+	0.239321i	0.926805	−	0.375544i	$-0.122544\pi$
$881$	3613.13	+	6258.12i	0.138172	+	0.239321i	−0.788633	+	0.614864i	$0.789211\pi$
$882$	−441.000	−	763.834i	−0.0168359	−	0.0291606i
$883$	627.851			0.0239285			0.0119643	−	0.999928i	$-0.496192\pi$
$883$	627.851			0.0239285			0.0119643	+	0.999928i	$0.496192\pi$
$884$	−6838.12	−	9201.02i	−0.260171	−	0.350072i
$885$	−24007.0			−0.911848
$886$	9877.95	+	17109.1i	0.374555	+	0.648749i
$887$	15769.6	+	27313.8i	0.596948	+	1.03394i	0.993269	+	0.115832i	$0.0369535\pi$
$887$	15769.6	+	27313.8i	0.596948	+	1.03394i	−0.396321	+	0.918112i	$0.629713\pi$
$888$	298.466	−	516.959i	0.0112791	−	0.0195360i
$889$	−14942.8			−0.563740
$890$	−14203.8	+	24601.6i	−0.534956	+	0.926572i
$891$	111.161	−	192.536i	0.00417960	−	0.00723928i
$892$	16865.7			0.633077
$893$	−28698.6	+	49707.5i	−1.07543	+	1.86271i
$894$	5515.59	+	9553.28i	0.206341	+	0.357393i
$895$	−3470.39	−	6010.90i	−0.129612	−	0.224494i
$896$	−896.000			−0.0334077
$897$	487.883	−	1128.48i	0.0181605	−	0.0420054i
$898$	9468.25			0.351848
$899$	−1009.08	−	1747.78i	−0.0374358	−	0.0648407i
$900$	−2054.85	−	3559.10i	−0.0761054	−	0.131818i
$901$	13425.6	−	23253.9i	0.496418	−	0.859821i
$902$	259.359			0.00957395
$903$	5366.76	−	9295.50i	0.197779	−	0.342564i
$904$	2278.06	−	3945.71i	0.0838132	−	0.145169i
$905$	54237.1			1.99216
$906$	−5214.13	+	9031.13i	−0.191201	+	0.331169i
$907$	13451.0	+	23297.8i	0.492429	+	0.852911i	0.999962	−	0.00872085i	$-0.00277597\pi$
$907$	13451.0	+	23297.8i	0.492429	+	0.852911i	−0.507533	+	0.861632i	$0.669443\pi$
$908$	−12085.6	−	20932.9i	−0.441712	−	0.765068i
$909$	15644.8			0.570854
$910$	−10080.5	+	1169.81i	−0.367214	+	0.0426141i
$911$	−5274.75			−0.191834			−0.0959168	−	0.995389i	$-0.530578\pi$
$911$	−5274.75			−0.191834			−0.0959168	+	0.995389i	$0.530578\pi$
$912$	2273.35	+	3937.55i	0.0825417	+	0.142966i
$913$	1234.06	+	2137.45i	0.0447331	+	0.0774800i
$914$	−6138.70	+	10632.5i	−0.222156	+	0.384785i
$915$	12667.6			0.457680
$916$	4442.19	−	7694.10i	0.160234	−	0.277533i
$917$	2207.38	−	3823.29i	0.0794919	−	0.137684i
$918$	3301.77			0.118709
$919$	−8168.41	+	14148.1i	−0.293200	+	0.507838i	−0.974565	−	0.224107i	$-0.928054\pi$
$919$	−8168.41	+	14148.1i	−0.293200	+	0.507838i	0.681364	+	0.731944i	$0.261387\pi$
$920$	−540.842	−	936.765i	−0.0193815	−	0.0335698i
$921$	−972.342	−	1684.15i	−0.0347880	−	0.0602546i
$922$	−4340.11			−0.155026
$923$	−6087.48	+	14080.4i	−0.217088	+	0.502127i
$924$	−230.555			−0.00820857
$925$	−1419.68	−	2458.96i	−0.0504636	−	0.0874055i
$926$	103.568	+	179.385i	0.00367544	+	0.00636605i
$927$	−6976.39	+	12083.5i	−0.247179	+	0.428126i
$928$	−555.353			−0.0196448
$929$	14702.9	−	25466.1i	0.519252	−	0.899371i	−0.480498	−	0.876996i	$-0.659544\pi$
$929$	14702.9	−	25466.1i	0.519252	−	0.899371i	0.999750	−	0.0223749i	$-0.00712276\pi$
$930$	5395.11	−	9344.61i	0.190229	−	0.329486i
$931$	4641.42			0.163390
$932$	−9950.40	+	17234.6i	−0.349717	+	0.605728i
$933$	−5652.91	−	9791.13i	−0.198358	−	0.343566i
$934$	19612.0	+	33968.9i	0.687070	+	1.19004i
$935$	−2595.33			−0.0907767
$936$	1339.24	−	3097.69i	0.0467677	−	0.108174i
$937$	38790.6			1.35244			0.676219	−	0.736700i	$-0.263617\pi$
$937$	38790.6			1.35244			0.676219	+	0.736700i	$0.263617\pi$
$938$	−3645.74	−	6314.61i	−0.126906	−	0.219807i
$939$	4166.93	+	7217.34i	0.144816	+	0.250829i
$940$	18741.7	−	32461.6i	0.650305	−	1.12636i
$941$	55567.8			1.92504			0.962518	−	0.271218i	$-0.0874265\pi$
$941$	55567.8			1.92504			0.962518	+	0.271218i	$0.0874265\pi$
$942$	−1452.48	+	2515.77i	−0.0502382	+	0.0870151i
$943$	−206.544	+	357.744i	−0.00713255	+	0.0123539i
$944$	−8279.30			−0.285454
$945$	1461.42	−	2531.25i	0.0503068	−	0.0871339i
$946$	−1402.88	−	2429.85i	−0.0482150	−	0.0835108i
$947$	3423.83	+	5930.24i	0.117486	+	0.203492i	0.918771	−	0.394791i	$-0.129183\pi$
$947$	3423.83	+	5930.24i	0.117486	+	0.203492i	−0.801285	+	0.598283i	$0.795850\pi$
$948$	−12368.9			−0.423759
$949$	10725.5	−	1244.66i	0.366874	−	0.0425746i
$950$	21626.7			0.738594
$951$	6732.79	+	11661.5i	0.229575	+	0.397635i
$952$	−1712.03	−	2965.32i	−0.0582849	−	0.100952i
$953$	−21955.9	+	38028.7i	−0.746296	+	1.29262i	0.203290	+	0.979119i	$0.434837\pi$
$953$	−21955.9	+	38028.7i	−0.746296	+	1.29262i	−0.949587	+	0.313505i	$0.898497\pi$
$954$	7904.67			0.268263
$955$	−25805.2	+	44695.9i	−0.874383	+	1.51448i
$956$	−2105.93	+	3647.58i	−0.0712455	+	0.123401i
$957$	−142.902			−0.00482691
$958$	−8832.04	+	15297.5i	−0.297860	+	0.515909i
$959$	−5490.21	−	9509.32i	−0.184868	−	0.320200i
$960$	−1484.61	−	2571.43i	−0.0499122	−	0.0864505i
$961$	−16268.0			−0.546070
$962$	925.276	−	2140.17i	0.0310105	−	0.0717276i
$963$	165.212			0.00552842
$964$	−7909.42	−	13699.5i	−0.264259	−	0.457709i
$965$	−11421.8	−	19783.2i	−0.381018	−	0.659942i
$966$	183.606	−	318.015i	0.00611535	−	0.0105921i
$967$	7546.27			0.250953			0.125477	−	0.992097i	$-0.459954\pi$
$967$	7546.27			0.250953			0.125477	+	0.992097i	$0.459954\pi$
$968$	5293.87	−	9169.25i	0.175776	−	0.304453i
$969$	−8687.58	+	15047.3i	−0.288014	+	0.498855i
$970$	−37578.8			−1.24390
$971$	−16006.4	+	27723.9i	−0.529011	+	0.916275i	0.470416	+	0.882445i	$0.344104\pi$
$971$	−16006.4	+	27723.9i	−0.529011	+	0.916275i	−0.999428	+	0.0338300i	$0.989230\pi$
$972$	486.000	+	841.777i	0.0160375	+	0.0277778i
$973$	745.633	+	1291.47i	0.0245672	+	0.0425517i
$974$	−19945.1			−0.656143
$975$	−9575.27	−	12884.0i	−0.314517	−	0.423198i
$976$	4368.68			0.143277
$977$	19774.4	+	34250.3i	0.647534	+	1.12156i	0.983710	+	0.179762i	$0.0575329\pi$
$977$	19774.4	+	34250.3i	0.647534	+	1.12156i	−0.336176	+	0.941799i	$0.609134\pi$
$978$	9055.51	+	15684.6i	0.296077	+	0.512820i
$979$	−1260.45	+	2183.17i	−0.0411484	+	0.0712711i
$980$	−3031.09			−0.0988006
$981$	588.119	−	1018.65i	0.0191409	−	0.0331530i
$982$	−12777.6	+	22131.4i	−0.415223	+	0.719187i
$983$	−39519.8			−1.28228			−0.641142	−	0.767422i	$-0.721539\pi$
$983$	−39519.8			−1.28228			−0.641142	+	0.767422i	$0.721539\pi$
$984$	−566.965	+	982.011i	−0.0183681	+	0.0318144i
$985$	−2025.81	−	3508.81i	−0.0655308	−	0.113503i
$986$	−1061.14	−	1837.95i	−0.0342734	−	0.0593633i
$987$	12724.9			0.410374
$988$	10593.5	+	14254.0i	0.341116	+	0.458988i
$989$	4468.80			0.143680
$990$	−382.016	−	661.670i	−0.0122639	−	0.0212417i
$991$	8641.92	+	14968.2i	0.277013	+	0.479800i	0.970641	−	0.240533i	$-0.0773222\pi$
$991$	8641.92	+	14968.2i	0.277013	+	0.479800i	−0.693628	+	0.720333i	$0.743989\pi$
$992$	1860.62	−	3222.68i	0.0595510	−	0.103145i
$993$	30247.9			0.966653
$994$	−2290.91	+	3967.98i	−0.0731020	+	0.126616i
$995$	−20683.8	+	35825.4i	−0.659015	+	1.14145i
$996$	−10790.7			−0.343290
$997$	−13719.2	+	23762.4i	−0.435799	+	0.754827i	−0.997361	−	0.0726086i	$-0.976868\pi$
$997$	−13719.2	+	23762.4i	−0.435799	+	0.754827i	0.561561	+	0.827435i	$0.310201\pi$
$998$	−5539.87	−	9595.33i	−0.175713	−	0.304344i
$999$	335.774	+	581.578i	0.0106341	+	0.0184187i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.4.l.h.211.1	✓	10
13.9	even	3	inner	546.4.l.h.295.1	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.4.l.h.211.1	✓	10	1.1	even	1	trivial
546.4.l.h.295.1	yes	10	13.9	even	3	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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	546.l (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.73205i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-2.00000 + 3.46410i) q^{4} -15.4647 q^{5} +(3.00000 - 5.19615i) q^{6} +(3.50000 - 6.06218i) q^{7} +8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +(15.4647 + 26.7857i) q^{10} +(1.37235 + 2.37699i) q^{11} -12.0000 q^{12} +(-46.5597 + 5.40312i) q^{13} -14.0000 q^{14} +(-23.1971 - 40.1786i) q^{15} +(-8.00000 - 13.8564i) q^{16} +(30.5720 - 52.9522i) q^{17} +18.0000 q^{18} +(-47.3614 + 82.0323i) q^{19} +(30.9295 - 53.5714i) q^{20} +21.0000 q^{21} +(2.74471 - 4.75397i) q^{22} +(4.37157 + 7.57178i) q^{23} +(12.0000 + 20.7846i) q^{24} +114.158 q^{25} +(55.9182 + 75.2407i) q^{26} -27.0000 q^{27} +(14.0000 + 24.2487i) q^{28} +(8.67740 + 15.0297i) q^{29} +(-46.3942 + 80.3571i) q^{30} -116.289 q^{31} +(-16.0000 + 27.7128i) q^{32} +(-4.11706 + 7.13096i) q^{33} -122.288 q^{34} +(-54.1266 + 93.7500i) q^{35} +(-18.0000 - 31.1769i) q^{36} +(-12.4361 - 21.5399i) q^{37} +189.446 q^{38} +(-83.8773 - 112.861i) q^{39} -123.718 q^{40} +(23.6235 + 40.9171i) q^{41} +(-21.0000 - 36.3731i) q^{42} +(255.560 - 442.643i) q^{43} -10.9788 q^{44} +(69.5913 - 120.536i) q^{45} +(8.74314 - 15.1436i) q^{46} +605.950 q^{47} +(24.0000 - 41.5692i) q^{48} +(-24.5000 - 42.4352i) q^{49} +(-114.158 - 197.728i) q^{50} +183.432 q^{51} +(74.4025 - 172.094i) q^{52} +439.148 q^{53} +(27.0000 + 46.7654i) q^{54} +(-21.2231 - 36.7595i) q^{55} +(28.0000 - 48.4974i) q^{56} -284.168 q^{57} +(17.3548 - 30.0594i) q^{58} +(258.728 - 448.130i) q^{59} +185.577 q^{60} +(-136.521 + 236.461i) q^{61} +(116.289 + 201.418i) q^{62} +(31.5000 + 54.5596i) q^{63} +64.0000 q^{64} +(720.034 - 83.5578i) q^{65} +16.4682 q^{66} +(260.410 + 451.044i) q^{67} +(122.288 + 211.809i) q^{68} +(-13.1147 + 22.7153i) q^{69} +216.506 q^{70} +(163.637 - 283.427i) q^{71} +(-36.0000 + 62.3538i) q^{72} -230.359 q^{73} +(-24.8722 + 43.0799i) q^{74} +(171.237 + 296.591i) q^{75} +(-189.446 - 328.129i) q^{76} +19.2130 q^{77} +(-111.604 + 258.141i) q^{78} +1030.74 q^{79} +(123.718 + 214.286i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(47.2470 - 81.8343i) q^{82} +899.227 q^{83} +(-42.0000 + 72.7461i) q^{84} +(-472.787 + 818.892i) q^{85} -1022.24 q^{86} +(-26.0322 + 45.0891i) q^{87} +(10.9788 + 19.0159i) q^{88} +(459.231 + 795.411i) q^{89} -278.365 q^{90} +(-130.204 + 301.164i) q^{91} -34.9726 q^{92} +(-174.433 - 302.126i) q^{93} +(-605.950 - 1049.54i) q^{94} +(732.431 - 1268.61i) q^{95} -96.0000 q^{96} +(-607.492 + 1052.21i) q^{97} +(-49.0000 + 84.8705i) q^{98} -24.7024 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 10 q^{2} + 15 q^{3} - 20 q^{4} - 18 q^{5} + 30 q^{6} + 35 q^{7} + 80 q^{8} - 45 q^{9} + 18 q^{10} - 23 q^{11} - 120 q^{12} - 16 q^{13} - 140 q^{14} - 27 q^{15} - 80 q^{16} - 14 q^{17} + 180 q^{18}+ \cdots + 414 q^{99}+O(q^{100}) \) 10 * q - 10 * q^2 + 15 * q^3 - 20 * q^4 - 18 * q^5 + 30 * q^6 + 35 * q^7 + 80 * q^8 - 45 * q^9 + 18 * q^10 - 23 * q^11 - 120 * q^12 - 16 * q^13 - 140 * q^14 - 27 * q^15 - 80 * q^16 - 14 * q^17 + 180 * q^18 + 16 * q^19 + 36 * q^20 + 210 * q^21 - 46 * q^22 - 47 * q^23 + 120 * q^24 - 348 * q^25 - 50 * q^26 - 270 * q^27 + 140 * q^28 - 149 * q^29 - 54 * q^30 + 350 * q^31 - 160 * q^32 + 69 * q^33 + 56 * q^34 - 63 * q^35 - 180 * q^36 + 187 * q^37 - 64 * q^38 + 75 * q^39 - 144 * q^40 + 358 * q^41 - 210 * q^42 + 575 * q^43 + 184 * q^44 + 81 * q^45 - 94 * q^46 + 332 * q^47 + 240 * q^48 - 245 * q^49 + 348 * q^50 - 84 * q^51 + 164 * q^52 - 94 * q^53 + 270 * q^54 - 530 * q^55 + 280 * q^56 + 96 * q^57 - 298 * q^58 - 329 * q^59 + 216 * q^60 - 197 * q^61 - 350 * q^62 + 315 * q^63 + 640 * q^64 + 169 * q^65 - 276 * q^66 + 231 * q^67 - 56 * q^68 + 141 * q^69 + 252 * q^70 + 38 * q^71 - 360 * q^72 - 754 * q^73 + 374 * q^74 - 522 * q^75 + 64 * q^76 - 322 * q^77 - 246 * q^78 - 304 * q^79 + 144 * q^80 - 405 * q^81 + 716 * q^82 + 360 * q^83 - 420 * q^84 - 748 * q^85 - 2300 * q^86 + 447 * q^87 - 184 * q^88 + 1052 * q^89 - 324 * q^90 - 287 * q^91 + 376 * q^92 + 525 * q^93 - 332 * q^94 + 2272 * q^95 - 960 * q^96 - 1415 * q^97 - 490 * q^98 + 414 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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