LMFDB - Embedded newform 153.3.t.a.7.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [153,3,Mod(7,153)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(153, base_ring=CyclotomicField(48)) chi = DirichletCharacter(H, H._module([32, 33])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("153.7"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 153 = 3^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	153.t (of order $48$, degree $16$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$4.16894804471$
Analytic rank:	$0$
Dimension:	$544$
Relative dimension:	$34$ over $\Q(\zeta_{48})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{48}]$

Embedding invariants

Embedding label			7.6
Character	$\chi$	$=$	153.7
Dual form			153.3.t.a.22.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.62741 - 2.12088i) q^{2} +(-0.107726 - 2.99807i) q^{3} +(-0.814394 + 3.03936i) q^{4} +(-4.22014 + 3.70097i) q^{5} +(-6.18322 + 5.10755i) q^{6} +(5.62018 + 4.92877i) q^{7} +(-2.10780 + 0.873079i) q^{8} +(-8.97679 + 0.645938i) q^{9} +(14.7172 + 2.92743i) q^{10} +(1.02596 + 15.6532i) q^{11} +(9.19993 + 2.11419i) q^{12} +(-12.9966 - 3.48242i) q^{13} +(1.30699 - 19.9408i) q^{14} +(11.5504 + 12.2536i) q^{15} +(16.1820 + 9.34268i) q^{16} +(-13.1079 - 10.8252i) q^{17} +(15.9788 + 17.9875i) q^{18} +(7.44374 - 17.9708i) q^{19} +(-7.81171 - 15.8406i) q^{20} +(14.1713 - 17.3806i) q^{21} +(31.5289 - 27.6501i) q^{22} +(-11.2723 + 22.8580i) q^{23} +(2.84461 + 6.22527i) q^{24} +(0.849305 - 6.45111i) q^{25} +(13.7649 + 33.2315i) q^{26} +(2.90360 + 26.8434i) q^{27} +(-19.5573 + 13.0678i) q^{28} +(6.33587 - 18.6649i) q^{29} +(7.19121 - 44.4385i) q^{30} +(-1.56473 + 23.8731i) q^{31} +(-5.32885 - 40.4766i) q^{32} +(46.8188 - 4.76216i) q^{33} +(-1.62700 + 45.4171i) q^{34} -41.9592 q^{35} +(5.34740 - 27.8097i) q^{36} +(-37.8938 + 56.7120i) q^{37} +(-50.2278 + 13.4585i) q^{38} +(-9.04046 + 39.3397i) q^{39} +(5.66398 - 11.4854i) q^{40} +(6.01941 - 2.04331i) q^{41} +(-59.9247 - 1.77030i) q^{42} +(-19.5930 - 2.57946i) q^{43} +(-48.4112 - 9.62959i) q^{44} +(35.4928 - 35.9488i) q^{45} +(66.8237 - 13.2921i) q^{46} +(-21.6496 - 80.7974i) q^{47} +(26.2667 - 49.5211i) q^{48} +(0.897911 + 6.82031i) q^{49} +(-15.0642 + 8.69731i) q^{50} +(-31.0425 + 40.4644i) q^{51} +(21.1687 - 36.6652i) q^{52} +(-31.2307 + 75.3976i) q^{53} +(52.2063 - 49.8433i) q^{54} +(-62.2617 - 62.2617i) q^{55} +(-16.1494 - 5.48199i) q^{56} +(-54.6794 - 20.3809i) q^{57} +(-49.8969 + 16.9377i) q^{58} +(18.0856 + 13.8776i) q^{59} +(-46.6496 + 25.1265i) q^{60} +(-40.9974 + 46.7485i) q^{61} +(53.1784 - 35.5327i) q^{62} +(-53.6349 - 40.6142i) q^{63} +(-24.3235 + 24.3235i) q^{64} +(67.7357 - 33.4036i) q^{65} +(-86.2932 - 91.5469i) q^{66} +(-25.1172 + 14.5014i) q^{67} +(43.5765 - 31.0236i) q^{68} +(69.7441 + 31.3327i) q^{69} +(68.2846 + 88.9903i) q^{70} +(7.89568 - 11.8167i) q^{71} +(18.3573 - 9.19895i) q^{72} +(-10.6359 - 53.4701i) q^{73} +(181.948 - 11.9255i) q^{74} +(-19.4323 - 1.85132i) q^{75} +(48.5575 + 37.2595i) q^{76} +(-71.3848 + 93.0305i) q^{77} +(98.1473 - 44.8480i) q^{78} +(6.55183 + 99.9616i) q^{79} +(-102.867 + 20.4616i) q^{80} +(80.1655 - 11.5969i) q^{81} +(-14.1296 - 9.44112i) q^{82} +(39.5807 - 30.3713i) q^{83} +(41.2849 + 57.2264i) q^{84} +(95.3806 - 2.82806i) q^{85} +(26.4150 + 45.7521i) q^{86} +(-56.6410 - 16.9847i) q^{87} +(-15.8290 - 32.0980i) q^{88} +(93.5945 + 93.5945i) q^{89} +(-134.004 - 16.7725i) q^{90} +(-55.8790 - 83.6289i) q^{91} +(-60.2936 - 52.8760i) q^{92} +(71.7417 + 2.11940i) q^{93} +(-136.129 + 177.406i) q^{94} +(35.0956 + 103.388i) q^{95} +(-120.777 + 20.3366i) q^{96} +(18.6085 - 54.8187i) q^{97} +(13.0038 - 13.0038i) q^{98} +(-19.3209 - 139.853i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 544 q - 8 q^{2} - 16 q^{3} - 8 q^{4} - 8 q^{5} - 16 q^{6} - 8 q^{7} - 32 q^{8} - 16 q^{9} - 32 q^{10} - 8 q^{11} + 176 q^{12} - 8 q^{13} - 8 q^{14} - 40 q^{15} - 32 q^{17} + 32 q^{18} - 32 q^{19} - 8 q^{20}+ \cdots + 448 q^{99}+O(q^{100}) $ 544 * q - 8 * q^2 - 16 * q^3 - 8 * q^4 - 8 * q^5 - 16 * q^6 - 8 * q^7 - 32 * q^8 - 16 * q^9 - 32 * q^10 - 8 * q^11 + 176 * q^12 - 8 * q^13 - 8 * q^14 - 40 * q^15 - 32 * q^17 + 32 * q^18 - 32 * q^19 - 8 * q^20 - 256 * q^21 - 8 * q^22 - 8 * q^23 + 176 * q^24 - 8 * q^25 - 32 * q^26 - 16 * q^27 - 32 * q^28 - 8 * q^29 - 16 * q^30 - 8 * q^31 - 72 * q^32 + 40 * q^34 - 64 * q^35 + 16 * q^36 - 32 * q^37 + 88 * q^38 - 192 * q^39 - 8 * q^40 - 440 * q^41 - 400 * q^42 - 248 * q^43 - 800 * q^44 - 176 * q^45 - 32 * q^46 + 112 * q^47 - 248 * q^48 - 8 * q^49 + 16 * q^51 - 16 * q^52 + 160 * q^53 - 312 * q^54 - 32 * q^55 - 488 * q^56 - 296 * q^57 - 8 * q^58 + 568 * q^59 + 2080 * q^60 - 8 * q^61 + 1120 * q^62 - 88 * q^63 - 288 * q^64 - 248 * q^65 - 24 * q^66 - 8 * q^68 - 416 * q^69 - 40 * q^70 - 32 * q^71 + 632 * q^72 - 32 * q^73 - 8 * q^74 + 752 * q^75 - 8 * q^76 - 8 * q^77 - 2304 * q^78 - 8 * q^79 - 432 * q^80 + 768 * q^81 + 352 * q^82 - 296 * q^83 - 8 * q^85 + 1184 * q^86 - 688 * q^87 - 8 * q^88 - 1184 * q^89 - 1136 * q^90 + 640 * q^91 - 2024 * q^92 - 528 * q^93 - 8 * q^94 + 472 * q^95 - 1064 * q^96 - 8 * q^97 - 848 * q^98 + 448 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/153\mathbb{Z}\right)^\times$.

$n$	$37$	$137$
$\chi(n)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.62741	−	2.12088i	−0.813703	−	1.06044i	−0.997002	−	0.0773816i	$-0.975344\pi$
$2$	−1.62741	−	2.12088i	−0.813703	−	1.06044i	0.183298	−	0.983057i	$-0.441323\pi$
$3$	−0.107726	−	2.99807i	−0.0359086	−	0.999355i
$3$	−0.107726	−	2.99807i	−0.0359086	−	0.999355i
$4$	−0.814394	+	3.03936i	−0.203598	+	0.759840i
$5$	−4.22014	+	3.70097i	−0.844029	+	0.740193i	−0.967693	−	0.252131i	$-0.918869\pi$
$5$	−4.22014	+	3.70097i	−0.844029	+	0.740193i	0.123664	+	0.992324i	$0.460535\pi$
$6$	−6.18322	+	5.10755i	−1.03054	+	0.851258i
$7$	5.62018	+	4.92877i	0.802883	+	0.704109i	0.958931	−	0.283640i	$-0.0915421\pi$
$7$	5.62018	+	4.92877i	0.802883	+	0.704109i	−0.156048	+	0.987749i	$0.549875\pi$
$8$	−2.10780	+	0.873079i	−0.263475	+	0.109135i
$9$	−8.97679	+	0.645938i	−0.997421	+	0.0717709i
$10$	14.7172	+	2.92743i	1.47172	+	0.292743i
$11$	1.02596	+	15.6532i	0.0932695	+	1.42302i	0.746261	+	0.665653i	$0.231847\pi$
$11$	1.02596	+	15.6532i	0.0932695	+	1.42302i	−0.652992	+	0.757365i	$0.726486\pi$
$12$	9.19993	+	2.11419i	0.766661	+	0.176182i
$13$	−12.9966	−	3.48242i	−0.999736	−	0.267879i	−0.278401	−	0.960465i	$-0.589805\pi$
$13$	−12.9966	−	3.48242i	−0.999736	−	0.267879i	−0.721335	+	0.692586i	$0.756471\pi$
$14$	1.30699	−	19.9408i	0.0933565	−	1.42434i
$15$	11.5504	+	12.2536i	0.770024	+	0.816905i
$16$	16.1820	+	9.34268i	1.01137	+	0.583918i
$17$	−13.1079	−	10.8252i	−0.771051	−	0.636774i
$17$	−13.1079	−	10.8252i	−0.771051	−	0.636774i
$18$	15.9788	+	17.9875i	0.887714	+	0.999304i
$19$	7.44374	−	17.9708i	0.391776	−	0.945830i	−0.597778	−	0.801662i	$-0.703949\pi$
$19$	7.44374	−	17.9708i	0.391776	−	0.945830i	0.989553	−	0.144168i	$-0.0460506\pi$
$20$	−7.81171	−	15.8406i	−0.390585	−	0.792029i
$21$	14.1713	−	17.3806i	0.674825	−	0.827649i
$22$	31.5289	−	27.6501i	1.43313	−	1.25682i
$23$	−11.2723	+	22.8580i	−0.490101	+	0.993826i	0.501581	+	0.865111i	$0.332752\pi$
$23$	−11.2723	+	22.8580i	−0.490101	+	0.993826i	−0.991682	+	0.128715i	$0.958915\pi$
$24$	2.84461	+	6.22527i	0.118525	+	0.259386i
$25$	0.849305	−	6.45111i	0.0339722	−	0.258044i
$26$	13.7649	+	33.2315i	0.529420	+	1.27813i
$27$	2.90360	+	26.8434i	0.107541	+	0.994201i
$28$	−19.5573	+	13.0678i	−0.698476	+	0.466707i
$29$	6.33587	−	18.6649i	0.218478	−	0.643616i	−0.781332	−	0.624116i	$-0.785459\pi$
$29$	6.33587	−	18.6649i	0.218478	−	0.643616i	0.999810	−	0.0195000i	$-0.00620743\pi$
$30$	7.19121	−	44.4385i	0.239707	−	1.48128i
$31$	−1.56473	+	23.8731i	−0.0504750	+	0.770100i	0.895338	+	0.445388i	$0.146934\pi$
$31$	−1.56473	+	23.8731i	−0.0504750	+	0.770100i	−0.945813	+	0.324712i	$0.894733\pi$
$32$	−5.32885	−	40.4766i	−0.166526	−	1.26489i
$33$	46.8188	−	4.76216i	1.41875	−	0.144308i
$34$	−1.62700	+	45.4171i	−0.0478530	+	1.33580i
$35$	−41.9592			−1.19883
$36$	5.34740	−	27.8097i	0.148539	−	0.772493i
$37$	−37.8938	+	56.7120i	−1.02416	+	1.53276i	−0.189580	+	0.981865i	$0.560713\pi$
$37$	−37.8938	+	56.7120i	−1.02416	+	1.53276i	−0.834576	+	0.550893i	$0.814287\pi$
$38$	−50.2278	+	13.4585i	−1.32178	+	0.354171i
$39$	−9.04046	+	39.3397i	−0.231807	+	1.00871i
$40$	5.66398	−	11.4854i	0.141599	−	0.287135i
$41$	6.01941	−	2.04331i	0.146815	−	0.0498369i	−0.247065	−	0.968999i	$-0.579466\pi$
$41$	6.01941	−	2.04331i	0.146815	−	0.0498369i	0.393880	+	0.919162i	$0.371133\pi$
$42$	−59.9247	−	1.77030i	−1.42678	−	0.0421500i
$43$	−19.5930	−	2.57946i	−0.455651	−	0.0599875i	−0.100792	−	0.994908i	$-0.532138\pi$
$43$	−19.5930	−	2.57946i	−0.455651	−	0.0599875i	−0.354859	+	0.934920i	$0.615471\pi$
$44$	−48.4112	−	9.62959i	−1.10026	−	0.218854i
$45$	35.4928	−	35.9488i	0.788728	−	0.798861i
$46$	66.8237	−	13.2921i	1.45269	−	0.288958i
$47$	−21.6496	−	80.7974i	−0.460630	−	1.71909i	−0.670987	−	0.741469i	$-0.734129\pi$
$47$	−21.6496	−	80.7974i	−0.460630	−	1.71909i	0.210357	−	0.977625i	$-0.432537\pi$
$48$	26.2667	−	49.5211i	0.547224	−	1.03169i
$49$	0.897911	+	6.82031i	0.0183247	+	0.139190i
$50$	−15.0642	+	8.69731i	−0.301284	+	0.173946i
$51$	−31.0425	+	40.4644i	−0.608676	+	0.793419i
$52$	21.1687	−	36.6652i	0.407090	−	0.705100i
$53$	−31.2307	+	75.3976i	−0.589259	+	1.42260i	0.294954	+	0.955511i	$0.404696\pi$
$53$	−31.2307	+	75.3976i	−0.589259	+	1.42260i	−0.884213	+	0.467085i	$0.845304\pi$
$54$	52.2063	−	49.8433i	0.966783	−	0.923025i
$55$	−62.2617	−	62.2617i	−1.13203	−	1.13203i
$56$	−16.1494	−	5.48199i	−0.288382	−	0.0978926i
$57$	−54.6794	−	20.3809i	−0.959288	−	0.357559i
$58$	−49.8969	+	16.9377i	−0.860292	+	0.292030i
$59$	18.0856	+	13.8776i	0.306536	+	0.235213i	0.750561	−	0.660801i	$-0.229783\pi$
$59$	18.0856	+	13.8776i	0.306536	+	0.235213i	−0.444025	+	0.896014i	$0.646450\pi$
$60$	−46.6496	+	25.1265i	−0.777493	+	0.418774i
$61$	−40.9974	+	46.7485i	−0.672088	+	0.766369i	−0.982908	−	0.184100i	$-0.941063\pi$
$61$	−40.9974	+	46.7485i	−0.672088	+	0.766369i	0.310820	+	0.950469i	$0.399396\pi$
$62$	53.1784	−	35.5327i	0.857716	−	0.573107i
$63$	−53.6349	−	40.6142i	−0.851347	−	0.644670i
$64$	−24.3235	+	24.3235i	−0.380055	+	0.380055i
$65$	67.7357	−	33.4036i	1.04209	−	0.513901i
$66$	−86.2932	−	91.5469i	−1.30747	−	1.38707i
$67$	−25.1172	+	14.5014i	−0.374883	+	0.216439i	−0.675590	−	0.737278i	$-0.736111\pi$
$67$	−25.1172	+	14.5014i	−0.374883	+	0.216439i	0.300706	+	0.953717i	$0.402778\pi$
$68$	43.5765	−	31.0236i	0.640831	−	0.456229i
$69$	69.7441	+	31.3327i	1.01078	+	0.454098i
$70$	68.2846	+	88.9903i	0.975495	+	1.27129i
$71$	7.89568	−	11.8167i	0.111207	−	0.166433i	−0.771691	−	0.635997i	$-0.780589\pi$
$71$	7.89568	−	11.8167i	0.111207	−	0.166433i	0.882898	+	0.469564i	$0.155589\pi$
$72$	18.3573	−	9.19895i	0.254963	−	0.127763i
$73$	−10.6359	−	53.4701i	−0.145697	−	0.732467i	−0.982691	−	0.185255i	$-0.940689\pi$
$73$	−10.6359	−	53.4701i	−0.145697	−	0.732467i	0.836994	−	0.547212i	$-0.184311\pi$
$74$	181.948	−	11.9255i	2.45876	−	0.161155i
$75$	−19.4323	−	1.85132i	−0.259098	−	0.0246843i
$76$	48.5575	+	37.2595i	0.638914	+	0.490256i
$77$	−71.3848	+	93.0305i	−0.927076	+	1.20819i
$78$	98.1473	−	44.8480i	1.25830	−	0.574975i
$79$	6.55183	+	99.9616i	0.0829346	+	1.26534i	0.813123	+	0.582092i	$0.197765\pi$
$79$	6.55183	+	99.9616i	0.0829346	+	1.26534i	−0.730189	+	0.683246i	$0.760568\pi$
$80$	−102.867	+	20.4616i	−1.28584	+	0.255770i
$81$	80.1655	−	11.5969i	0.989698	−	0.143172i
$82$	−14.1296	−	9.44112i	−0.172313	−	0.115136i
$83$	39.5807	−	30.3713i	0.476876	−	0.365920i	−0.342179	−	0.939635i	$-0.611165\pi$
$83$	39.5807	−	30.3713i	0.476876	−	0.365920i	0.819055	+	0.573715i	$0.194498\pi$
$84$	41.2849	+	57.2264i	0.491487	+	0.681267i
$85$	95.3806	−	2.82806i	1.12212	−	0.0332713i
$86$	26.4150	+	45.7521i	0.307151	+	0.532002i
$87$	−56.6410	−	16.9847i	−0.651046	−	0.195226i
$88$	−15.8290	−	32.0980i	−0.179875	−	0.364750i
$89$	93.5945	+	93.5945i	1.05162	+	1.05162i	0.998593	+	0.0530313i	$0.0168883\pi$
$89$	93.5945	+	93.5945i	1.05162	+	1.05162i	0.0530313	+	0.998593i	$0.483112\pi$
$90$	−134.004	−	16.7725i	−1.48893	−	0.186362i
$91$	−55.8790	−	83.6289i	−0.614055	−	0.918999i
$92$	−60.2936	−	52.8760i	−0.655365	−	0.574740i
$93$	71.7417	+	2.11940i	0.771416	+	0.0227893i
$94$	−136.129	+	177.406i	−1.44818	+	1.88730i
$95$	35.0956	+	103.388i	0.369427	+	1.08830i
$96$	−120.777	+	20.3366i	−1.25810	+	0.211840i
$97$	18.6085	−	54.8187i	0.191840	−	0.565142i	−0.807867	−	0.589365i	$-0.799378\pi$
$97$	18.6085	−	54.8187i	0.191840	−	0.565142i	0.999707	+	0.0242234i	$0.00771129\pi$
$98$	13.0038	−	13.0038i	0.132692	−	0.132692i
$99$	−19.3209	−	139.853i	−0.195160	−	1.41265i
$100$	18.9156	+	7.83509i	0.189156	+	0.0783509i
$101$	−62.3178	−	35.9792i	−0.617008	−	0.356229i	0.158695	−	0.987328i	$-0.449271\pi$
$101$	−62.3178	−	35.9792i	−0.617008	−	0.356229i	−0.775703	+	0.631098i	$0.782605\pi$
$102$	136.339	−	0.0147321i	1.33665	−	0.000144432i
$103$	−17.3611	−	30.0704i	−0.168555	−	0.291945i	0.769357	−	0.638819i	$-0.220577\pi$
$103$	−17.3611	−	30.0704i	−0.168555	−	0.291945i	−0.937912	+	0.346874i	$0.887243\pi$
$104$	30.4346	−	4.00679i	0.292640	−	0.0385268i
$105$	4.52009	+	125.796i	0.0430484	+	1.19806i
$106$	210.734	−	56.4660i	1.98806	−	0.532699i
$107$	−3.31627	−	16.6720i	−0.0309932	−	0.155813i	0.962190	−	0.272381i	$-0.0878110\pi$
$107$	−3.31627	−	16.6720i	−0.0309932	−	0.155813i	−0.993183	+	0.116567i	$0.962811\pi$
$108$	−83.9515	−	13.0360i	−0.777328	−	0.120704i
$109$	29.2816	−	147.209i	0.268639	−	1.35054i	−0.576984	−	0.816756i	$-0.695770\pi$
$109$	29.2816	−	147.209i	0.268639	−	1.35054i	0.845622	−	0.533782i	$-0.179230\pi$
$110$	−30.7243	+	233.375i	−0.279312	+	2.12159i
$111$	174.109	+	107.499i	1.56855	+	0.968456i
$112$	44.8979	+	132.265i	0.400874	+	1.18094i
$113$	31.0764	+	15.3252i	0.275012	+	0.135621i	0.574566	−	0.818459i	$-0.305171\pi$
$113$	31.0764	+	15.3252i	0.275012	+	0.135621i	−0.299554	+	0.954079i	$0.596838\pi$
$114$	45.7603	+	149.136i	0.401406	+	1.30821i
$115$	−37.0259	−	138.183i	−0.321964	−	1.20159i
$116$	51.5693	+	34.4575i	0.444563	+	0.297048i
$117$	118.917	+	22.8660i	1.01638	+	0.195436i
$118$		−	60.9418i		−	0.516456i
$119$	−20.3139	−	125.445i	−0.170705	−	1.05416i
$120$	−35.0442	−	15.7437i	−0.292035	−	0.131198i
$121$	−124.005	+	16.3256i	−1.02484	+	0.134922i
$122$	165.867	+	10.8715i	1.35957	+	0.0891108i
$123$	−6.77443	−	17.8265i	−0.0550767	−	0.144931i
$124$	−71.2846	−	24.1979i	−0.574876	−	0.195144i
$125$	−57.6705	−	86.3100i	−0.461364	−	0.690480i
$126$	1.14796	+	179.849i	0.00911077	+	1.42737i
$127$	17.7455	−	7.35042i	0.139728	−	0.0578773i	−0.311724	−	0.950173i	$-0.600906\pi$
$127$	17.7455	−	7.35042i	0.139728	−	0.0578773i	0.451452	+	0.892296i	$0.350906\pi$
$128$	−70.7348	−	9.31242i	−0.552616	−	0.0727533i
$129$	−5.62273	+	59.0189i	−0.0435871	+	0.457511i
$130$	−181.079	−	89.2980i	−1.39291	−	0.686908i
$131$	53.2703	+	60.7432i	0.406644	+	0.463688i	0.918522	−	0.395370i	$-0.129383\pi$
$131$	53.2703	+	60.7432i	0.406644	+	0.463688i	−0.511878	+	0.859058i	$0.671050\pi$
$132$	−23.6550	+	146.177i	−0.179205	+	1.10740i
$133$	130.409	−	64.3105i	0.980518	−	0.483538i
$134$	71.6316	+	29.6708i	0.534564	+	0.221424i
$135$	−111.600	−	102.537i	−0.826668	−	0.759533i
$136$	37.0799	+	11.3730i	0.272647	+	0.0836254i
$137$	−0.0415519	+	0.0719701i	−0.000303299	+	0.000525329i	−0.866177	−	0.499737i	$-0.833430\pi$
$137$	−0.0415519	+	0.0719701i	−0.000303299	+	0.000525329i	0.865874	+	0.500263i	$0.166763\pi$
$138$	−47.0491	−	198.910i	−0.340935	−	1.44138i
$139$	13.7239	+	0.899510i	0.0987329	+	0.00647129i	0.114689	−	0.993401i	$-0.463413\pi$
$139$	13.7239	+	0.899510i	0.0987329	+	0.00647129i	−0.0159566	+	0.999873i	$0.505079\pi$
$140$	34.1713	−	127.529i	0.244081	−	0.910921i
$141$	−239.904	+	73.6109i	−1.70144	+	0.522063i
$142$	−37.9113	+	2.48484i	−0.266981	+	0.0174989i
$143$	41.1770	−	207.011i	0.287951	−	1.44763i
$144$	−151.297	−	73.4147i	−1.05068	−	0.509824i
$145$	42.3398	+	102.217i	0.291998	+	0.704947i
$146$	−96.0947	+	109.575i	−0.658183	+	0.750513i
$147$	20.3510	−	3.42672i	0.138442	−	0.0233110i
$148$	−141.508	−	161.359i	−0.956134	−	1.09026i
$149$	−180.788	−	48.4419i	−1.21334	−	0.325113i	−0.405268	−	0.914198i	$-0.632822\pi$
$149$	−180.788	−	48.4419i	−1.21334	−	0.325113i	−0.808072	+	0.589084i	$0.799489\pi$
$150$	27.6979	+	44.2265i	0.184653	+	0.294843i
$151$	−128.355	+	98.4902i	−0.850033	+	0.652253i	−0.939051	−	0.343777i	$-0.888294\pi$
$151$	−128.355	+	98.4902i	−0.850033	+	0.652253i	0.0890188	+	0.996030i	$0.471627\pi$
$152$			44.3777i			0.291959i
$153$	124.659	+	88.7083i	0.814764	+	0.579793i
$154$	313.479			2.03557
$155$	−81.7502	−	106.539i	−0.527421	−	0.687348i
$156$	−112.205	−	59.5152i	−0.719263	−	0.381508i
$157$	7.92603	−	29.5803i	0.0504843	−	0.188410i	−0.936079	−	0.351790i	$-0.885573\pi$
$157$	7.92603	−	29.5803i	0.0504843	−	0.188410i	0.986563	+	0.163380i	$0.0522397\pi$
$158$	201.344	−	176.574i	1.27433	−	1.11756i
$159$	229.411	+	85.5094i	1.44284	+	0.537795i
$160$	172.291	+	151.095i	1.07682	+	0.944345i
$161$	−176.014	+	72.9075i	−1.09326	+	0.452841i
$162$	−155.058	−	151.148i	−0.957145	−	0.933015i
$163$	−122.629	−	24.3924i	−0.752323	−	0.149646i	−0.195990	−	0.980606i	$-0.562792\pi$
$163$	−122.629	−	24.3924i	−0.752323	−	0.149646i	−0.556333	+	0.830960i	$0.687792\pi$
$164$	1.30820	+	19.9592i	0.00797680	+	0.121702i
$165$	−179.957	+	193.372i	−1.09065	+	1.17195i
$166$	−128.828	−	34.5193i	−0.776071	−	0.207948i
$167$	7.01385	−	107.011i	0.0419991	−	0.640782i	−0.924025	−	0.382331i	$-0.875121\pi$
$167$	7.01385	−	107.011i	0.0419991	−	0.640782i	0.966024	−	0.258451i	$-0.0832120\pi$
$168$	−14.6956	+	49.0075i	−0.0874741	+	0.291712i
$169$	10.4254	+	6.01909i	0.0616885	+	0.0356159i
$170$	−161.221	−	197.688i	−0.948359	−	1.16287i
$171$	−55.2129	+	166.128i	−0.322882	+	0.971509i
$172$	23.7963	−	57.4494i	0.138351	−	0.334008i
$173$	149.349	+	302.851i	0.863292	+	1.75058i	0.627212	+	0.778849i	$0.284196\pi$
$173$	149.349	+	302.851i	0.863292	+	1.75058i	0.236080	+	0.971734i	$0.424137\pi$
$174$	56.1556	+	147.770i	0.322733	+	0.849251i
$175$	36.5693	−	32.0704i	0.208967	−	0.183259i
$176$	−129.641	+	262.885i	−0.736595	+	1.49367i
$177$	39.6576	−	55.7168i	0.224054	−	0.314784i
$178$	46.1862	−	350.819i	0.259473	−	1.97089i
$179$	−55.9322	−	135.032i	−0.312471	−	0.754371i	−0.999612	−	0.0278472i	$-0.991135\pi$
$179$	−55.9322	−	135.032i	−0.312471	−	0.754371i	0.687142	−	0.726523i	$-0.258865\pi$
$180$	80.3561	+	137.152i	0.446423	+	0.761954i
$181$	−200.358	+	133.875i	−1.10695	+	0.739640i	−0.968073	−	0.250669i	$-0.919349\pi$
$181$	−200.358	+	133.875i	−1.10695	+	0.739640i	−0.138877	+	0.990310i	$0.544349\pi$
$182$	−86.4287	+	254.611i	−0.474883	+	1.39896i
$183$	144.572	+	117.877i	0.790009	+	0.644135i
$184$	3.80294	−	58.0217i	0.0206682	−	0.315335i
$185$	−49.9722	−	379.577i	−0.270120	−	2.05177i
$186$	−112.258	−	155.604i	−0.603537	−	0.836583i
$187$	156.000	−	216.286i	0.834225	−	1.15661i
$188$	263.204			1.40002
$189$	−115.986	+	165.176i	−0.613684	+	0.873947i
$190$	162.159	−	242.688i	0.853469	−	1.27731i
$191$	297.726	−	79.7755i	1.55878	−	0.417673i	0.626500	−	0.779422i	$-0.284487\pi$
$191$	297.726	−	79.7755i	1.55878	−	0.417673i	0.932275	+	0.361749i	$0.117820\pi$
$192$	75.5438	+	70.3033i	0.393457	+	0.366163i
$193$	138.026	−	279.888i	0.715158	−	1.45020i	−0.170258	−	0.985400i	$-0.554460\pi$
$193$	138.026	−	279.888i	0.715158	−	1.45020i	0.885417	−	0.464798i	$-0.153873\pi$
$194$	−146.547	+	49.7461i	−0.755399	+	0.256423i
$195$	−107.443	−	199.478i	−0.550990	−	1.02296i
$196$	−21.4606	−	2.82534i	−0.109493	−	0.0144150i
$197$	157.278	+	31.2846i	0.798367	+	0.158805i	0.577384	−	0.816472i	$-0.304073\pi$
$197$	157.278	+	31.2846i	0.798367	+	0.158805i	0.220983	+	0.975278i	$0.429073\pi$
$198$	−265.168	+	268.575i	−1.33923	+	1.35644i
$199$	−56.1982	+	11.1785i	−0.282403	+	0.0561734i	−0.334259	−	0.942481i	$-0.608486\pi$
$199$	−56.1982	+	11.1785i	−0.282403	+	0.0561734i	0.0518565	+	0.998655i	$0.483486\pi$
$200$	3.84216	+	14.3392i	0.0192108	+	0.0716958i
$201$	46.1820	+	73.7408i	0.229761	+	0.366870i
$202$	25.1089	+	190.721i	0.124302	+	0.944164i
$203$	127.603	−	73.6719i	0.628589	−	0.362916i
$204$	−97.7050	−	127.303i	−0.478946	−	0.624035i
$205$	−17.8405	+	30.9007i	−0.0870270	+	0.150735i
$206$	−35.5219	+	85.7576i	−0.172437	+	0.416299i
$207$	86.4244	−	212.473i	0.417509	−	1.02644i
$208$	−177.775	−	177.775i	−0.854689	−	0.854689i
$209$	288.937	+	98.0809i	1.38247	+	0.469287i
$210$	259.443	−	214.308i	1.23544	−	1.02052i
$211$	−157.017	+	53.3000i	−0.744155	+	0.252607i	−0.667663	−	0.744463i	$-0.732705\pi$
$211$	−157.017	+	53.3000i	−0.744155	+	0.252607i	−0.0764922	+	0.997070i	$0.524372\pi$
$212$	−203.726	−	156.325i	−0.960973	−	0.737381i
$213$	−36.2779	−	22.3988i	−0.170319	−	0.105159i
$214$	−29.9624	+	34.1656i	−0.140011	+	0.159652i
$215$	92.2317	−	61.6272i	0.428985	−	0.286638i
$216$	−29.5566	−	54.0455i	−0.136836	−	0.250210i
$217$	−126.459	+	126.459i	−0.582760	+	0.582760i
$218$	−359.864	+	177.466i	−1.65075	+	0.814062i
$219$	−159.161	+	37.6471i	−0.726763	+	0.171905i
$220$	239.941	−	138.530i	1.09064	−	0.629682i
$221$	132.660	+	186.337i	0.600269	+	0.843154i
$222$	−55.3539	−	544.207i	−0.249342	−	2.45138i
$223$	141.930	+	184.967i	0.636458	+	0.829448i	0.994552	−	0.104237i	$-0.0332402\pi$
$223$	141.930	+	184.967i	0.636458	+	0.829448i	−0.358095	+	0.933685i	$0.616573\pi$
$224$	169.551	−	253.750i	0.756922	−	1.13281i
$225$	−3.45701	+	58.4589i	−0.0153645	+	0.259817i
$226$	−18.0711	−	90.8494i	−0.0799605	−	0.401989i
$227$	−145.065	+	9.50809i	−0.639055	+	0.0418859i	−0.381487	−	0.924374i	$-0.624588\pi$
$227$	−145.065	+	9.50809i	−0.639055	+	0.0418859i	−0.257568	+	0.966260i	$0.582921\pi$
$228$	106.475	−	149.592i	0.466997	−	0.656107i
$229$	287.497	+	220.604i	1.25544	+	0.963337i	0.999994	−	0.00348522i	$-0.00110938\pi$
$229$	287.497	+	220.604i	1.25544	+	0.963337i	0.255451	+	0.966822i	$0.417776\pi$
$230$	−232.812	+	303.407i	−1.01223	+	1.31916i
$231$	286.602	+	203.995i	1.24070	+	0.883093i
$232$	2.94116	+	44.8735i	0.0126774	+	0.193420i
$233$	188.480	−	37.4909i	0.808926	−	0.160905i	0.226734	−	0.973957i	$-0.427195\pi$
$233$	188.480	−	37.4909i	0.808926	−	0.160905i	0.582192	+	0.813051i	$0.302195\pi$
$234$	−145.030	−	289.421i	−0.619788	−	1.23684i
$235$	390.393	+	260.852i	1.66125	+	1.11001i
$236$	−56.9078	+	43.6669i	−0.241135	+	0.185029i
$237$	298.986	−	30.4113i	1.26154	−	0.128318i
$238$	−232.994	+	247.233i	−0.978968	+	1.03879i
$239$	−25.3782	−	43.9563i	−0.106185	−	0.183918i	0.808037	−	0.589132i	$-0.200530\pi$
$239$	−25.3782	−	43.9563i	−0.106185	−	0.183918i	−0.914222	+	0.405214i	$0.867197\pi$
$240$	72.4266	+	306.199i	0.301778	+	1.27583i
$241$	27.8323	+	56.4383i	0.115487	+	0.234184i	0.946940	−	0.321411i	$-0.104157\pi$
$241$	27.8323	+	56.4383i	0.115487	+	0.234184i	−0.831453	+	0.555595i	$0.812491\pi$
$242$	236.431	+	236.431i	0.976989	+	0.976989i
$243$	−43.4042	−	239.092i	−0.178618	−	0.983919i
$244$	−108.698	−	162.677i	−0.445482	−	0.666711i
$245$	−29.0311	−	25.4596i	−0.118494	−	0.103917i
$246$	−26.7830	+	43.3786i	−0.108874	+	0.176336i
$247$	−159.325	+	207.636i	−0.645040	+	0.840632i
$248$	−17.5450	−	51.6858i	−0.0707459	−	0.208411i
$249$	−95.3191	−	115.394i	−0.382808	−	0.463429i
$250$	−89.1996	+	262.773i	−0.356798	+	1.05109i
$251$	−180.293	+	180.293i	−0.718297	+	0.718297i	−0.968256	−	0.249959i	$-0.919583\pi$
$251$	−180.293	+	180.293i	−0.718297	+	0.718297i	0.249959	+	0.968256i	$0.419583\pi$
$252$	167.121	−	129.940i	0.663179	−	0.515633i
$253$	−369.366	−	152.996i	−1.45994	−	0.604728i
$254$	−44.4685	−	25.6739i	−0.175073	−	0.101078i
$255$	−18.7537	−	285.653i	−0.0735438	−	1.12021i
$256$	164.161	+	284.336i	0.641255	+	1.11069i
$257$	−319.842	+	42.1080i	−1.24452	+	0.163844i	−0.723876	−	0.689930i	$-0.757641\pi$
$257$	−319.842	+	42.1080i	−1.24452	+	0.163844i	−0.520644	+	0.853774i	$0.674308\pi$
$258$	134.322	−	84.1226i	0.520629	−	0.326057i
$259$	−492.490	+	131.962i	−1.90151	+	0.509507i
$260$	46.3619	+	233.077i	0.178315	+	0.896450i
$261$	−44.8194	+	171.643i	−0.171722	+	0.657637i
$262$	42.1363	−	211.834i	0.160826	−	0.808526i
$263$	−6.75540	+	51.3124i	−0.0256859	+	0.195104i	−0.999477	−	0.0323408i	$-0.989704\pi$
$263$	−6.75540	+	51.3124i	−0.0256859	+	0.195104i	0.973791	+	0.227445i	$0.0730371\pi$
$264$	−94.5268	+	50.9142i	−0.358056	+	0.192857i
$265$	−147.246	−	433.773i	−0.555645	−	1.63688i
$266$	−348.623	−	171.922i	−1.31061	−	0.646323i
$267$	270.520	−	290.685i	1.01318	−	1.08871i
$268$	−23.6197	−	88.1500i	−0.0881333	−	0.328918i
$269$	231.780	+	154.871i	0.861637	+	0.575727i	0.905995	−	0.423288i	$-0.139124\pi$
$269$	231.780	+	154.871i	0.861637	+	0.575727i	−0.0443582	+	0.999016i	$0.514124\pi$
$270$	−35.8495	+	403.560i	−0.132776	+	1.49467i
$271$			383.210i			1.41406i	0.707184	+	0.707029i	$0.249965\pi$
$271$			383.210i			1.41406i	−0.707184	+	0.707029i	$0.750035\pi$
$272$	−110.975	−	297.635i	−0.407998	−	1.09425i
$273$	−244.705	+	176.538i	−0.896356	+	0.646659i
$274$	0.220262	−	0.0289980i	0.000803875	−	0.000105832i
$275$	101.852	+	6.67572i	0.370370	+	0.0242754i
$276$	−152.031	+	186.460i	−0.550836	+	0.675580i
$277$	−134.096	−	45.5196i	−0.484102	−	0.164331i	0.0687094	−	0.997637i	$-0.478112\pi$
$277$	−134.096	−	45.5196i	−0.484102	−	0.164331i	−0.552812	+	0.833306i	$0.686445\pi$
$278$	−20.4266	−	30.5705i	−0.0734769	−	0.109966i
$279$	−1.37433	−	215.315i	−0.00492592	−	0.771737i
$280$	88.4415	−	36.6337i	0.315862	−	0.130835i
$281$	263.216	+	34.6531i	0.936713	+	0.123321i	0.583401	−	0.812185i	$-0.301722\pi$
$281$	263.216	+	34.6531i	0.936713	+	0.123321i	0.353313	+	0.935505i	$0.385055\pi$
$282$	546.541	+	389.012i	1.93809	+	1.37947i
$283$	141.442	+	69.7513i	0.499794	+	0.246471i	0.674670	−	0.738119i	$-0.264286\pi$
$283$	141.442	+	69.7513i	0.499794	+	0.246471i	−0.174876	+	0.984590i	$0.555953\pi$
$284$	29.4851	+	33.6213i	0.103821	+	0.118385i
$285$	306.184	−	116.356i	1.07433	−	0.408268i
$286$	−506.056	+	249.559i	−1.76943	+	0.872585i
$287$	43.9012	+	18.1845i	0.152966	+	0.0633605i
$288$	73.9813	+	359.908i	0.256880	+	1.24968i
$289$	54.6321	+	283.789i	0.189038	+	0.981970i
$290$	147.886	−	256.147i	0.509953	−	0.883264i
$291$	−166.355	−	49.8840i	−0.571666	−	0.171423i
$292$	171.177	+	11.2195i	0.586221	+	0.0384230i
$293$	−121.557	+	453.657i	−0.414870	+	1.54832i	0.370225	+	0.928942i	$0.379281\pi$
$293$	−121.557	+	453.657i	−0.414870	+	1.54832i	−0.785095	+	0.619375i	$0.787386\pi$
$294$	−40.3870	−	37.5853i	−0.137371	−	0.127841i
$295$	−127.684	+	8.36887i	−0.432828	+	0.0283691i
$296$	30.3584	−	152.622i	0.102562	−	0.515614i
$297$	−417.206	+	72.9910i	−1.40473	+	0.245761i
$298$	191.476	+	462.263i	0.642536	+	1.55122i
$299$	226.103	−	257.821i	0.756196	−	0.862277i
$300$	21.4524	−	57.5542i	0.0715080	−	0.191847i
$301$	−97.4025	−	111.066i	−0.323596	−	0.368991i
$302$	417.771	+	111.941i	1.38335	+	0.370667i
$303$	−101.155	+	190.709i	−0.333844	+	0.629401i
$304$	288.350	−	221.259i	0.948519	−	0.727824i
$305$		−	349.015i		−	1.14431i
$306$	−14.7314	−	408.751i	−0.0481417	−	1.33579i
$307$	142.891			0.465444			0.232722	−	0.972543i	$-0.425237\pi$
$307$	142.891			0.465444			0.232722	+	0.972543i	$0.425237\pi$
$308$	−224.618	−	292.728i	−0.729279	−	0.950414i
$309$	−88.2827	+	55.2892i	−0.285704	+	0.178929i
$310$	−92.9152	+	346.764i	−0.299727	+	1.11859i
$311$	171.670	−	150.551i	0.551995	−	0.484087i	−0.337315	−	0.941392i	$-0.609519\pi$
$311$	171.670	−	150.551i	0.551995	−	0.484087i	0.889310	+	0.457305i	$0.151185\pi$
$312$	−15.2912	−	90.8133i	−0.0490103	−	0.291068i
$313$	100.711	+	88.3215i	0.321762	+	0.282177i	0.804954	−	0.593337i	$-0.202190\pi$
$313$	100.711	+	88.3215i	0.321762	+	0.282177i	−0.483193	+	0.875514i	$0.660523\pi$
$314$	−75.6352	+	31.3291i	−0.240876	+	0.0997743i
$315$	376.659	−	27.1030i	1.19574	−	0.0860414i
$316$	−309.155	−	61.4948i	−0.978339	−	0.194604i
$317$	18.5377	+	282.830i	0.0584784	+	0.892208i	0.921827	+	0.387601i	$0.126696\pi$
$317$	18.5377	+	282.830i	0.0584784	+	0.892208i	−0.863349	+	0.504607i	$0.831637\pi$
$318$	−191.990	−	625.712i	−0.603743	−	1.96765i
$319$	298.665	+	80.0271i	0.936254	+	0.250869i
$320$	12.6282	−	192.669i	0.0394632	−	0.602092i
$321$	−49.6266	+	11.7384i	−0.154600	+	0.0365683i
$322$	441.075	+	254.654i	1.36980	+	0.790852i
$323$	−292.108	+	154.979i	−0.904358	+	0.479810i
$324$	−30.0392	+	253.096i	−0.0927135	+	0.781161i
$325$	−33.5035	+	80.8847i	−0.103088	+	0.248876i
$326$	147.833	+	299.777i	0.453477	+	0.919560i
$327$	−444.495	−	71.9300i	−1.35931	−	0.219969i
$328$	−10.9037	+	9.56231i	−0.0332431	+	0.0291534i
$329$	276.557	−	560.802i	0.840598	−	1.70456i
$330$	702.982	+	66.9731i	2.13025	+	0.202949i
$331$	−4.73239	+	35.9461i	−0.0142973	+	0.108598i	−0.997105	−	0.0760311i	$-0.975775\pi$
$331$	−4.73239	+	35.9461i	−0.0142973	+	0.108598i	0.982808	+	0.184629i	$0.0591085\pi$
$332$	60.0751	+	145.034i	0.180949	+	0.436850i
$333$	303.532	−	533.569i	0.911508	−	1.60231i
$334$	−238.371	+	159.274i	−0.713685	+	0.476869i
$335$	52.3289	−	154.156i	0.156206	−	0.460167i
$336$	391.702	−	148.855i	1.16578	−	0.443021i
$337$	−9.84114	+	150.147i	−0.0292022	+	0.445539i	0.958074	+	0.286522i	$0.0924992\pi$
$337$	−9.84114	+	150.147i	−0.0292022	+	0.445539i	−0.987276	+	0.159017i	$0.949167\pi$
$338$	−4.20056	−	31.9064i	−0.0124277	−	0.0943977i
$339$	42.5981	−	94.8199i	0.125658	−	0.279705i
$340$	−69.0819	+	292.199i	−0.203182	+	0.859409i
$341$	−375.296			−1.10057
$342$	442.191	−	153.258i	1.29296	−	0.448123i
$343$	174.929	−	261.799i	0.509996	−	0.763263i
$344$	43.5501	−	11.6692i	0.126599	−	0.0339222i
$345$	−410.292	+	125.892i	−1.18925	+	0.364904i
$346$	399.257	−	809.613i	1.15392	−	2.33992i
$347$	−254.312	+	86.3273i	−0.732888	+	0.248782i	−0.662839	−	0.748762i	$-0.730649\pi$
$347$	−254.312	+	86.3273i	−0.732888	+	0.248782i	−0.0700484	+	0.997544i	$0.522315\pi$
$348$	97.7506	−	158.320i	0.280892	−	0.454943i
$349$	210.404	+	27.7002i	0.602877	+	0.0793703i	0.425786	−	0.904824i	$-0.359998\pi$
$349$	210.404	+	27.7002i	0.602877	+	0.0793703i	0.177092	+	0.984194i	$0.443331\pi$
$350$	−127.530	−	25.3674i	−0.364373	−	0.0724782i
$351$	55.7433	−	358.984i	0.158813	−	1.02275i
$352$	628.121	−	124.941i	1.78443	−	0.354946i
$353$	−169.176	−	631.374i	−0.479253	−	1.78860i	−0.604653	−	0.796489i	$-0.706688\pi$
$353$	−169.176	−	631.374i	−0.479253	−	1.78860i	0.125400	−	0.992106i	$-0.459979\pi$
$354$	−182.708	+	6.56501i	−0.516123	+	0.0185452i
$355$	10.4124	+	79.0899i	0.0293307	+	0.222789i
$356$	−360.690	+	208.245i	−1.01317	+	0.584957i
$357$	−373.904	+	74.4161i	−1.04735	+	0.208448i
$358$	−195.363	+	338.378i	−0.545706	+	0.945190i
$359$	74.6994	−	180.340i	0.208076	−	0.502341i	−0.785044	−	0.619440i	$-0.787360\pi$
$359$	74.6994	−	180.340i	0.208076	−	0.502341i	0.993120	+	0.117100i	$0.0373596\pi$
$360$	−43.4255	+	106.761i	−0.120626	+	0.296558i
$361$	−12.2738	−	12.2738i	−0.0339993	−	0.0339993i
$362$	609.996	+	207.066i	1.68507	+	0.572005i
$363$	62.3037	+	370.017i	0.171636	+	1.01933i
$364$	299.686	−	101.730i	0.823313	−	0.279477i
$365$	242.776	+	186.289i	0.665140	+	0.510380i
$366$	14.7253	−	498.452i	0.0402331	−	1.36189i
$367$	−2.72639	+	3.10885i	−0.00742886	+	0.00847099i	−0.755542	−	0.655100i	$-0.772627\pi$
$367$	−2.72639	+	3.10885i	−0.00742886	+	0.00847099i	0.748113	+	0.663571i	$0.230960\pi$
$368$	−395.964	+	264.574i	−1.07599	+	0.718952i
$369$	−52.7151	+	22.2306i	−0.142859	+	0.0602454i
$370$	−723.711	+	723.711i	−1.95597	+	1.95597i
$371$	−547.139	+	269.819i	−1.47477	+	0.727276i
$372$	−64.8676	+	216.323i	−0.174375	+	0.581513i
$373$	176.684	−	102.008i	0.473683	−	0.273481i	−0.244097	−	0.969751i	$-0.578492\pi$
$373$	176.684	−	102.008i	0.473683	−	0.273481i	0.717780	+	0.696270i	$0.245158\pi$
$374$	−712.592	+	21.1285i	−1.90533	+	0.0564934i
$375$	−252.550	+	182.198i	−0.673468	+	0.485860i
$376$	116.176	+	151.403i	0.308977	+	0.402667i
$377$	−147.343	+	220.515i	−0.390832	+	0.584921i
$378$	539.075	−	22.8160i	1.42612	−	0.0603598i
$379$	−138.129	−	694.422i	−0.364457	−	1.83225i	−0.532453	−	0.846460i	$-0.678730\pi$
$379$	−138.129	−	694.422i	−0.364457	−	1.83225i	0.167996	−	0.985788i	$-0.446270\pi$
$380$	−342.816	+	22.4693i	−0.902147	+	0.0591298i
$381$	−23.9487	−	52.4103i	−0.0628574	−	0.137560i
$382$	−653.715	−	501.614i	−1.71130	−	1.31312i
$383$	123.339	−	160.738i	0.322034	−	0.419682i	−0.604082	−	0.796922i	$-0.706460\pi$
$383$	123.339	−	160.738i	0.322034	−	0.419682i	0.926116	+	0.377240i	$0.123127\pi$
$384$	−20.2993	+	213.071i	−0.0528627	+	0.554872i
$385$	−43.0486	−	656.795i	−0.111815	−	1.70596i
$386$	−818.232	+	162.757i	−2.11977	+	0.421649i
$387$	177.548	+	10.4995i	0.458781	+	0.0271304i
$388$	151.459	+	101.202i	0.390359	+	0.260829i
$389$	444.555	−	341.119i	1.14282	−	0.876913i	0.149097	−	0.988823i	$-0.452363\pi$
$389$	444.555	−	341.119i	1.14282	−	0.876913i	0.993718	+	0.111909i	$0.0356966\pi$
$390$	−248.215	+	552.505i	−0.636447	+	1.41668i
$391$	395.197	−	177.595i	1.01073	−	0.454207i
$392$	−7.84728	−	13.5919i	−0.0200186	−	0.0346732i
$393$	176.373	−	166.252i	0.448787	−	0.423032i
$394$	−189.605	−	384.481i	−0.481231	−	0.975840i
$395$	−397.604	−	397.604i	−1.00659	−	1.00659i
$396$	440.797	+	55.1722i	1.11312	+	0.139324i
$397$	320.873	+	480.220i	0.808244	+	1.20962i	0.974688	+	0.223571i	$0.0717716\pi$
$397$	320.873	+	480.220i	0.808244	+	1.20962i	−0.166444	+	0.986051i	$0.553228\pi$
$398$	115.166	+	100.997i	0.289361	+	0.253763i
$399$	−206.856	−	384.046i	−0.518435	−	0.962522i
$400$	74.0141	−	96.4571i	0.185035	−	0.241143i
$401$	130.739	+	385.144i	0.326032	+	0.960458i	0.979139	+	0.203192i	$0.0651317\pi$
$401$	130.739	+	385.144i	0.326032	+	0.960458i	−0.653107	+	0.757265i	$0.726535\pi$
$402$	81.2384	−	217.953i	0.202086	−	0.542171i
$403$	103.472	−	304.820i	0.256755	−	0.756376i
$404$	160.105	−	160.105i	0.396299	−	0.396299i
$405$	−295.390	+	345.631i	−0.729359	+	0.853409i
$406$	−363.912	−	150.737i	−0.896335	−	0.371274i
$407$	−926.602	−	534.974i	−2.27666	−	1.31443i
$408$	30.1027	−	112.393i	0.0737811	−	0.275474i
$409$	275.090	+	476.470i	0.672591	+	1.16496i	0.977167	+	0.212474i	$0.0681522\pi$
$409$	275.090	+	476.470i	0.672591	+	1.16496i	−0.304575	+	0.952488i	$0.598514\pi$
$410$	94.5704	−	12.4504i	0.230660	−	0.0303669i
$411$	0.220247	+	0.116822i	0.000535881	+	0.000284239i
$412$	105.533	−	28.2776i	0.256149	−	0.0686349i
$413$	33.2451	+	167.134i	0.0804965	+	0.404683i
$414$	−591.276	+	162.484i	−1.42820	+	0.392473i
$415$	−54.6329	+	274.658i	−0.131646	+	0.661827i
$416$	−71.6998	+	544.614i	−0.172355	+	1.30917i
$417$	1.21837	−	41.2420i	0.00292176	−	0.0989016i
$418$	−262.200	−	772.417i	−0.627274	−	1.84789i
$419$	−499.684	−	246.417i	−1.19256	−	0.588108i	−0.265901	−	0.964000i	$-0.585669\pi$
$419$	−499.684	−	246.417i	−1.19256	−	0.588108i	−0.926663	+	0.375893i	$0.877336\pi$
$420$	−386.021	−	88.7096i	−0.919099	−	0.211213i
$421$	20.9459	+	78.1712i	0.0497527	+	0.185680i	0.986330	−	0.164781i	$-0.0526917\pi$
$421$	20.9459	+	78.1712i	0.0497527	+	0.185680i	−0.936577	+	0.350461i	$0.886025\pi$
$422$	368.573	+	246.273i	0.873396	+	0.583584i
$423$	246.534	+	711.317i	0.582823	+	1.68160i
$424$		−	186.190i		−	0.439127i
$425$	−80.9668	+	75.3664i	−0.190510	+	0.177333i
$426$	11.5337	+	113.393i	0.0270745	+	0.266181i
$427$	−460.825	+	60.6688i	−1.07922	+	0.142081i
$428$	53.3731	+	3.49826i	0.124703	+	0.00817349i
$429$	−625.068	−	101.151i	−1.45703	−	0.235783i
$430$	−280.802	−	95.3196i	−0.653029	−	0.221673i
$431$	73.4781	+	109.968i	0.170483	+	0.255146i	0.906866	−	0.421419i	$-0.138468\pi$
$431$	73.4781	+	109.968i	0.170483	+	0.255146i	−0.736383	+	0.676565i	$0.763468\pi$
$432$	−203.804	+	461.508i	−0.471767	+	1.06830i
$433$	−28.0208	+	11.6066i	−0.0647133	+	0.0268051i	−0.414805	−	0.909910i	$-0.636150\pi$
$433$	−28.0208	+	11.6066i	−0.0647133	+	0.0268051i	0.350092	+	0.936715i	$0.386150\pi$
$434$	474.004	+	62.4038i	1.09218	+	0.143788i
$435$	301.893	−	137.949i	0.694007	−	0.317124i
$436$	423.573	+	208.883i	0.971498	+	0.479090i
$437$	326.868	+	372.721i	0.747981	+	0.852909i
$438$	338.865	+	276.294i	0.773664	+	0.630808i
$439$	308.752	−	152.259i	0.703306	−	0.346832i	−0.0552204	−	0.998474i	$-0.517586\pi$
$439$	308.752	−	152.259i	0.703306	−	0.346832i	0.758527	+	0.651642i	$0.225919\pi$
$440$	185.594	+	76.8757i	0.421806	+	0.174718i
$441$	−12.4659	−	60.6445i	−0.0282672	−	0.137516i
$442$	179.307	−	584.601i	0.405672	−	1.32263i
$443$	−301.343	+	521.942i	−0.680233	+	1.17820i	0.294676	+	0.955597i	$0.404788\pi$
$443$	−301.343	+	521.942i	−0.680233	+	1.17820i	−0.974910	+	0.222601i	$0.928545\pi$
$444$	−468.520	+	441.632i	−1.05523	+	0.994667i
$445$	−741.373	−	48.5921i	−1.66601	−	0.109196i
$446$	161.314	−	602.033i	0.361691	−	1.34985i
$447$	−125.756	+	547.232i	−0.281334	+	1.22423i
$448$	−256.588	+	16.8176i	−0.572740	+	0.0375394i
$449$	15.1247	−	76.0368i	0.0336852	−	0.169347i	−0.960281	−	0.279035i	$-0.909985\pi$
$449$	15.1247	−	76.0368i	0.0336852	−	0.169347i	0.993966	+	0.109688i	$0.0349853\pi$
$450$	129.610	−	87.8044i	0.288022	−	0.195121i
$451$	38.1601	+	92.1266i	0.0846121	+	0.204272i
$452$	−71.8871	+	81.9715i	−0.159042	+	0.181353i
$453$	309.107	+	374.206i	0.682356	+	0.826063i
$454$	256.246	+	292.193i	0.564418	+	0.643596i
$455$	545.325	+	146.120i	1.19852	+	0.321142i
$456$	133.047	−	4.78063i	0.291770	−	0.0104838i
$457$	131.379	−	100.810i	0.287480	−	0.220591i	−0.454946	−	0.890519i	$-0.650342\pi$
$457$	131.379	−	100.810i	0.287480	−	0.220591i	0.742427	+	0.669928i	$0.233675\pi$
$458$		−	968.758i		−	2.11519i
$459$	252.524	−	383.292i	0.550162	−	0.835058i
$460$	450.140			0.978565
$461$	1.45115	+	1.89117i	0.00314782	+	0.00410232i	0.794925	−	0.606708i	$-0.207510\pi$
$461$	1.45115	+	1.89117i	0.00314782	+	0.00410232i	−0.791777	+	0.610811i	$0.790844\pi$
$462$	−33.7697	−	939.829i	−0.0730947	−	2.03426i
$463$	−108.708	+	405.704i	−0.234790	+	0.876250i	0.743453	+	0.668788i	$0.233187\pi$
$463$	−108.708	+	405.704i	−0.234790	+	0.876250i	−0.978243	+	0.207461i	$0.933480\pi$
$464$	276.907	−	242.841i	0.596782	−	0.523364i
$465$	−310.604	+	256.569i	−0.667966	+	0.551762i
$466$	−386.247	−	338.729i	−0.828856	−	0.726887i
$467$	−375.030	+	155.342i	−0.803061	+	0.332639i	−0.746182	−	0.665742i	$-0.768115\pi$
$467$	−375.030	+	155.342i	−0.803061	+	0.332639i	−0.0568795	+	0.998381i	$0.518115\pi$
$468$	−166.343	+	342.809i	−0.355434	+	0.732499i
$469$	−212.637	−	42.2962i	−0.453384	−	0.0901837i
$470$	−82.0924	−	1252.49i	−0.174665	−	2.66487i
$471$	−89.5376	−	20.5762i	−0.190101	−	0.0436862i
$472$	−50.2370	−	13.4610i	−0.106434	−	0.0285190i
$473$	20.2752	−	309.339i	0.0428650	−	0.653994i
$474$	−551.070	−	584.621i	−1.16259	−	1.23338i
$475$	−109.609	−	63.2830i	−0.230757	−	0.133227i
$476$	397.816	+	40.4203i	0.835747	+	0.0849166i
$477$	231.649	−	697.002i	0.485638	−	1.46122i
$478$	−51.9254	+	125.359i	−0.108630	+	0.262257i
$479$	116.910	+	237.070i	0.244071	+	0.494926i	0.984093	−	0.177656i	$-0.0568516\pi$
$479$	116.910	+	237.070i	0.244071	+	0.494926i	−0.740022	+	0.672583i	$0.765185\pi$
$480$	434.433	−	532.817i	0.905069	−	1.11003i
$481$	689.984	−	605.100i	1.43448	−	1.25800i
$482$	74.4043	−	150.877i	0.154366	−	0.313023i
$483$	237.543	+	519.848i	0.491807	+	1.07629i
$484$	51.3697	−	390.191i	0.106136	−	0.806181i
$485$	124.352	+	300.212i	0.256396	+	0.618994i
$486$	−436.449	+	481.155i	−0.898043	+	0.990031i
$487$	−267.408	+	178.677i	−0.549093	+	0.366892i	−0.798957	−	0.601389i	$-0.794614\pi$
$487$	−267.408	+	178.677i	−0.549093	+	0.366892i	0.249863	+	0.968281i	$0.419614\pi$
$488$	45.5990	−	134.330i	0.0934406	−	0.275267i
$489$	−59.9196	+	370.276i	−0.122535	+	0.757211i
$490$	−6.75126	+	103.004i	−0.0137781	+	0.210213i
$491$	9.36008	+	71.0969i	0.0190633	+	0.144800i	0.998329	−	0.0577776i	$-0.0184014\pi$
$491$	9.36008	+	71.0969i	0.0190633	+	0.144800i	−0.979266	+	0.202578i	$0.935068\pi$
$492$	59.6981	−	6.07218i	0.121338	−	0.0123418i
$493$	−285.100	+	176.070i	−0.578296	+	0.357139i
$494$	699.657			1.41631
$495$	599.127	+	518.693i	1.21036	+	1.04786i
$496$	−248.359	+	371.696i	−0.500724	+	0.749387i
$497$	102.617	−	27.4961i	0.206473	−	0.0553242i
$498$	−89.6130	+	389.953i	−0.179946	+	0.783038i
$499$	−391.971	+	794.839i	−0.785514	+	1.59286i	0.0196462	+	0.999807i	$0.493746\pi$
$499$	−391.971	+	794.839i	−0.785514	+	1.59286i	−0.805160	+	0.593058i	$0.797921\pi$
$500$	309.293	−	104.991i	0.618587	−	0.209982i
$501$	−321.580	−	9.50016i	−0.641877	−	0.0189624i
$502$	675.788	+	88.9692i	1.34619	+	0.177229i
$503$	−177.439	−	35.2948i	−0.352762	−	0.0701687i	0.0155288	−	0.999879i	$-0.495057\pi$
$503$	−177.439	−	35.2948i	−0.352762	−	0.0701687i	−0.368291	+	0.929711i	$0.620057\pi$
$504$	148.511	+	38.7791i	0.294664	+	0.0769427i
$505$	396.148	−	78.7987i	0.784451	−	0.156037i
$506$	276.622	+	1032.37i	0.546684	+	2.04025i
$507$	16.9225	−	31.9043i	0.0333778	−	0.0629277i
$508$	7.88875	+	59.9210i	0.0155290	+	0.117955i
$509$	−590.455	+	340.899i	−1.16003	+	0.669743i	−0.951311	−	0.308233i	$-0.900262\pi$
$509$	−590.455	+	340.899i	−1.16003	+	0.669743i	−0.208718	+	0.977976i	$0.566929\pi$
$510$	−575.315	+	504.647i	−1.12807	+	0.989504i
$511$	203.766	−	352.933i	0.398760	−	0.690672i
$512$	226.673	−	547.238i	0.442722	−	1.06882i
$513$	504.010	+	147.635i	0.982477	+	0.287788i
$514$	609.819	+	609.819i	1.18642	+	1.18642i
$515$	184.556	+	62.6483i	0.358361	+	0.121647i
$516$	−174.800	−	65.1541i	−0.338761	−	0.126268i
$517$	1242.53	−	421.781i	2.40334	−	0.815823i
$518$	1081.36	+	829.755i	2.08756	+	1.60184i
$519$	891.878	−	480.384i	1.71845	−	0.925596i
$520$	−113.609	+	129.547i	−0.218480	+	0.249128i
$521$	229.690	−	153.474i	0.440863	−	0.294575i	−0.315259	−	0.949006i	$-0.602091\pi$
$521$	229.690	−	153.474i	0.440863	−	0.294575i	0.756122	+	0.654430i	$0.227091\pi$
$522$	436.974	−	184.277i	0.837114	−	0.353021i
$523$	−450.940	+	450.940i	−0.862219	+	0.862219i	−0.991595	−	0.129377i	$-0.958702\pi$
$523$	−450.940	+	450.940i	−0.862219	+	0.862219i	0.129377	+	0.991595i	$0.458702\pi$
$524$	−228.003	+	112.439i	−0.435121	+	0.214578i
$525$	−100.089	−	106.182i	−0.190645	−	0.202252i
$526$	119.821	−	69.1787i	0.227797	−	0.131518i
$527$	278.940	−	295.987i	0.529298	−	0.561645i
$528$	802.113	+	360.352i	1.51915	+	0.682484i
$529$	−73.3882	−	95.6414i	−0.138730	−	0.180797i
$530$	−680.350	+	1018.22i	−1.28368	+	1.92116i
$531$	−171.315	−	112.894i	−0.322627	−	0.212606i
$532$	89.2586	+	448.733i	0.167779	+	0.843484i
$533$	−85.3473	+	5.59396i	−0.160126	+	0.0104952i
$534$	−1056.75	−	100.677i	−1.97894	−	0.188534i
$535$	75.6978	+	58.0850i	0.141491	+	0.108570i
$536$	40.2811	−	52.4954i	0.0751513	−	0.0979391i
$537$	−398.810	+	182.235i	−0.742664	+	0.339357i
$538$	−48.7391	−	743.615i	−0.0905932	−	1.38218i
$539$	−105.838	+	21.0526i	−0.196361	+	0.0390586i
$540$	402.533	−	255.688i	0.745432	−	0.473496i
$541$	−42.1798	−	28.1837i	−0.0779664	−	0.0520955i	0.515976	−	0.856603i	$-0.327429\pi$
$541$	−42.1798	−	28.1837i	−0.0779664	−	0.0520955i	−0.593942	+	0.804508i	$0.702429\pi$
$542$	812.741	−	623.638i	1.49952	−	1.15062i
$543$	422.949	+	586.264i	0.778912	+	1.07968i
$544$	−368.316	+	588.247i	−0.677051	+	1.08134i
$545$	421.241	+	729.612i	0.772920	+	1.33874i
$546$	772.651	+	231.691i	1.41511	+	0.424342i
$547$	−31.7196	−	64.3209i	−0.0579882	−	0.117589i	0.865949	−	0.500132i	$-0.166715\pi$
$547$	−31.7196	−	64.3209i	−0.0579882	−	0.117589i	−0.923938	+	0.382543i	$0.875048\pi$
$548$	−0.184903	−	0.184903i	−0.000337415	−	0.000337415i
$549$	337.828	−	446.133i	0.615352	−	0.812629i
$550$	−151.596	−	226.879i	−0.275629	−	0.412508i
$551$	−288.259	−	252.797i	−0.523157	−	0.458796i
$552$	−174.362	−	5.15103i	−0.315874	−	0.00933159i
$553$	−455.865	+	594.095i	−0.824349	+	1.07431i
$554$	121.688	+	358.481i	0.219653	+	0.647078i
$555$	−1132.61	+	190.710i	−2.04074	+	0.343622i
$556$	−13.9106	+	40.9792i	−0.0250190	+	0.0737036i
$557$	110.477	−	110.477i	0.198343	−	0.198343i	−0.600947	−	0.799289i	$-0.705210\pi$
$557$	110.477	−	110.477i	0.198343	−	0.198343i	0.799289	+	0.600947i	$0.205210\pi$
$558$	−454.419	+	353.319i	−0.814372	+	0.633188i
$559$	245.659	+	101.755i	0.439461	+	0.182031i
$560$	−678.983	−	392.011i	−1.21247	−	0.700020i
$561$	−665.245	−	444.399i	−1.18582	−	0.792155i
$562$	−354.865	−	614.645i	−0.631433	−	1.09367i
$563$	151.542	−	19.9509i	0.269169	−	0.0354368i	0.00526666	−	0.999986i	$-0.498324\pi$
$563$	151.542	−	19.9509i	0.269169	−	0.0354368i	0.263903	+	0.964549i	$0.414990\pi$
$564$	−28.3538	−	789.102i	−0.0502728	−	1.39912i
$565$	−187.865	+	50.3382i	−0.332504	+	0.0890941i
$566$	−82.2491	−	413.494i	−0.145316	−	0.730555i
$567$	507.703	+	329.940i	0.895420	+	0.581906i
$568$	−6.32558	+	31.8008i	−0.0111366	+	0.0559874i
$569$	−79.6465	+	604.975i	−0.139976	+	1.06323i	0.766882	+	0.641789i	$0.221807\pi$
$569$	−79.6465	+	604.975i	−0.139976	+	1.06323i	−0.906858	+	0.421437i	$0.861526\pi$
$570$	−745.064	−	460.020i	−1.30713	−	0.807052i
$571$	−216.728	−	638.461i	−0.379559	−	1.11815i	−0.954053	−	0.299637i	$-0.903135\pi$
$571$	−216.728	−	638.461i	−0.379559	−	1.11815i	0.574494	−	0.818509i	$-0.305199\pi$
$572$	595.646	+	293.740i	1.04134	+	0.513531i
$573$	−271.245	−	884.008i	−0.473377	−	1.54277i
$574$	−32.8780	−	122.703i	−0.0572788	−	0.213767i
$575$	137.886	+	92.1324i	0.239801	+	0.160230i
$576$	202.636	−	234.059i	0.351798	−	0.406352i
$577$		−	652.823i		−	1.13141i	−0.824608	−	0.565704i	$-0.808604\pi$
$577$		−	652.823i		−	1.13141i	0.824608	−	0.565704i	$-0.191396\pi$
$578$	512.974	−	577.709i	0.887498	−	0.999496i
$579$	−853.992	−	383.659i	−1.47494	−	0.662623i
$580$	−345.156	+	45.4407i	−0.595097	+	0.0783460i
$581$	372.144	+	24.3916i	0.640523	+	0.0419821i
$582$	164.929	+	434.000i	0.283383	+	0.745704i
$583$	−1212.25	−	411.505i	−2.07934	−	0.705841i
$584$	69.1019	+	103.418i	0.118325	+	0.177086i
$585$	−586.473	+	343.610i	−1.00252	+	0.587367i
$586$	1159.97	−	480.477i	1.97948	−	0.819927i
$587$	−317.918	−	41.8548i	−0.541599	−	0.0713028i	−0.145236	−	0.989397i	$-0.546394\pi$
$587$	−317.918	−	41.8548i	−0.541599	−	0.0713028i	−0.396362	+	0.918094i	$0.629728\pi$
$588$	−6.15870	+	64.6447i	−0.0104740	+	0.109940i
$589$	417.371	+	205.824i	0.708609	+	0.349447i
$590$	225.544	+	257.183i	0.382278	+	0.435904i
$591$	76.8504	−	474.901i	0.130034	−	0.803555i
$592$	−1143.04	+	563.685i	−1.93081	+	0.952170i
$593$	664.146	+	275.098i	1.11998	+	0.463909i	0.864362	−	0.502870i	$-0.167722\pi$
$593$	664.146	+	275.098i	1.11998	+	0.463909i	0.255614	+	0.966779i	$0.417722\pi$
$594$	833.769	+	766.058i	1.40365	+	1.28966i
$595$	549.995	+	454.214i	0.924361	+	0.763386i
$596$	294.465	−	510.028i	0.494068	−	0.855751i
$597$	39.5679	+	167.282i	0.0662779	+	0.280204i
$598$	−914.767	−	59.9570i	−1.52971	−	0.100263i
$599$	−111.906	+	417.641i	−0.186822	+	0.697230i	0.807411	+	0.589989i	$0.200868\pi$
$599$	−111.906	+	417.641i	−0.186822	+	0.697230i	−0.994233	+	0.107240i	$0.965799\pi$
$600$	42.5758	−	13.0638i	0.0709597	−	0.0217729i
$601$	−1104.58	+	72.3982i	−1.83791	+	0.120463i	−0.944444	−	0.328672i	$-0.893399\pi$
$601$	−1104.58	+	72.3982i	−1.83791	+	0.120463i	−0.893464	+	0.449135i	$0.851732\pi$
$602$	−77.0445	+	387.329i	−0.127981	+	0.643403i
$603$	216.105	−	146.400i	0.358383	−	0.242787i
$604$	−194.816	−	470.326i	−0.322542	−	0.778686i
$605$	462.899	−	527.835i	0.765122	−	0.872455i
$606$	569.089	−	95.8237i	0.939092	−	0.158125i
$607$	80.7531	+	92.0812i	0.133036	+	0.151699i	0.814522	−	0.580132i	$-0.196999\pi$
$607$	80.7531	+	92.0812i	0.133036	+	0.151699i	−0.681486	+	0.731831i	$0.738666\pi$
$608$	−767.062	−	205.534i	−1.26162	−	0.338049i
$609$	−234.619	−	374.627i	−0.385253	−	0.615151i
$610$	−740.219	+	567.990i	−1.21347	+	0.931131i
$611$			1125.48i			1.84203i
$612$	−371.138	+	306.640i	−0.606434	+	0.501045i
$613$	−811.715			−1.32417			−0.662084	−	0.749430i	$-0.730328\pi$
$613$	−811.715			−1.32417			−0.662084	+	0.749430i	$0.730328\pi$
$614$	−232.542	−	303.055i	−0.378733	−	0.493575i
$615$	94.5642	+	50.1583i	0.153763	+	0.0815582i
$616$	69.2419	−	258.414i	0.112406	−	0.419504i
$617$	−561.941	+	492.809i	−0.910764	+	0.798719i	−0.980024	−	0.198880i	$-0.936270\pi$
$617$	−561.941	+	492.809i	−0.910764	+	0.798719i	0.0692598	+	0.997599i	$0.477936\pi$
$618$	260.933	+	97.2588i	0.422222	+	0.157377i
$619$	569.070	+	499.061i	0.919338	+	0.806238i	0.981428	−	0.191833i	$-0.0614432\pi$
$619$	569.070	+	499.061i	0.919338	+	0.806238i	−0.0620898	+	0.998071i	$0.519777\pi$
$620$	390.387	−	161.704i	0.629656	−	0.260812i
$621$	−646.317	−	236.217i	−1.04077	−	0.380382i
$622$	−598.678	−	119.084i	−0.962505	−	0.191454i
$623$	64.7126	+	987.324i	0.103873	+	1.58479i
$624$	−513.831	+	552.133i	−0.823447	+	0.884829i
$625$	719.935	+	192.906i	1.15190	+	0.308649i
$626$	23.4207	−	357.332i	0.0374133	−	0.570817i
$627$	262.927	−	876.818i	0.419341	−	1.39843i
$628$	83.4504	+	48.1801i	0.132883	+	0.0767199i
$629$	1110.62	−	333.168i	1.76570	−	0.529678i
$630$	−670.459	−	754.739i	−1.06422	−	1.19800i
$631$	436.239	−	1053.17i	0.691345	−	1.66906i	−0.0507067	−	0.998714i	$-0.516147\pi$
$631$	436.239	−	1053.17i	0.691345	−	1.66906i	0.742052	−	0.670342i	$-0.233853\pi$
$632$	−101.084	−	204.979i	−0.159944	−	0.324333i
$633$	176.712	+	465.005i	0.279165	+	0.734605i
$634$	569.680	−	499.596i	0.898548	−	0.788006i
$635$	−47.6848	+	96.6953i	−0.0750942	+	0.152276i
$636$	−446.725	+	627.625i	−0.702398	+	0.986832i
$637$	12.0814	−	91.7676i	0.0189661	−	0.144062i
$638$	−316.322	−	763.669i	−0.495803	−	1.19697i
$639$	−63.2450	+	111.176i	−0.0989750	+	0.173985i
$640$	332.976	−	222.488i	0.520275	−	0.347637i
$641$	−233.173	+	686.906i	−0.363765	+	1.07162i	0.598878	+	0.800841i	$0.295614\pi$
$641$	−233.173	+	686.906i	−0.363765	+	1.07162i	−0.962642	+	0.270776i	$0.912720\pi$
$642$	105.658	+	86.1488i	0.164577	+	0.134188i
$643$	68.4383	−	1044.17i	0.106436	−	1.62390i	−0.526835	−	0.849968i	$-0.676621\pi$
$643$	68.4383	−	1044.17i	0.106436	−	1.62390i	0.633271	−	0.773930i	$-0.281712\pi$
$644$	−78.2471	−	594.346i	−0.121502	−	0.922897i
$645$	−194.698	−	269.878i	−0.301858	−	0.418415i
$646$	804.069	+	367.311i	1.24469	+	0.568594i
$647$	−626.323			−0.968042			−0.484021	−	0.875056i	$-0.660824\pi$
$647$	−626.323			−0.968042			−0.484021	+	0.875056i	$0.660824\pi$
$648$	−158.848	+	94.4348i	−0.245135	+	0.145733i
$649$	−198.673	+	297.336i	−0.306122	+	0.458144i
$650$	226.070	−	60.5754i	0.347801	−	0.0931929i
$651$	392.755	+	365.509i	0.603311	+	0.561458i
$652$	174.005	−	352.848i	0.266879	−	0.541177i
$653$	−774.414	+	262.878i	−1.18593	+	0.402570i	−0.843581	−	0.537002i	$-0.819557\pi$
$653$	−774.414	+	262.878i	−1.18593	+	0.402570i	−0.342352	+	0.939572i	$0.611223\pi$
$654$	570.820	+	1059.78i	0.872813	+	1.62046i
$655$	−449.617	−	59.1932i	−0.686438	−	0.0903713i
$656$	116.496	+	23.1725i	0.177585	+	0.0353239i
$657$	130.014	+	473.120i	0.197891	+	0.720121i
$658$	−1639.46	+	326.109i	−2.49158	+	0.495607i
$659$	282.060	+	1052.66i	0.428013	+	1.59736i	0.757255	+	0.653119i	$0.226540\pi$
$659$	282.060	+	1052.66i	0.428013	+	1.59736i	−0.329242	+	0.944245i	$0.606793\pi$
$660$	−441.170	−	704.436i	−0.668440	−	1.06733i
$661$	−86.4272	−	656.480i	−0.130752	−	0.993162i	−0.923496	−	0.383607i	$-0.874682\pi$
$661$	−86.4272	−	656.480i	−0.130752	−	0.993162i	0.792744	−	0.609554i	$-0.208652\pi$
$662$	83.9388	−	48.4621i	0.126796	−	0.0732055i
$663$	544.360	−	417.795i	0.821055	−	0.630159i
$664$	−56.9116	+	98.5737i	−0.0857102	+	0.148454i
$665$	−312.333	+	754.039i	−0.469674	+	1.13389i
$666$	−1625.61	+	224.580i	−2.44085	+	0.337207i
$667$	355.222	+	355.222i	0.532566	+	0.532566i
$668$	319.532	+	108.466i	0.478341	+	0.162375i
$669$	539.253	−	445.441i	0.806059	−	0.665832i
$670$	−412.106	+	139.891i	−0.615084	+	0.208793i
$671$	−773.826	−	593.777i	−1.15324	−	0.884914i
$672$	−779.025	−	480.988i	−1.15926	−	0.715756i
$673$	766.424	−	873.939i	1.13882	−	1.29857i	0.190343	−	0.981718i	$-0.439040\pi$
$673$	766.424	−	873.939i	1.13882	−	1.29857i	0.948474	−	0.316855i	$-0.102627\pi$
$674$	334.458	−	223.478i	0.496229	−	0.331570i
$675$	175.636	+	4.06682i	0.260201	+	0.00602492i
$676$	−26.7845	+	26.7845i	−0.0396221	+	0.0396221i
$677$	534.138	−	263.407i	0.788977	−	0.389080i	−0.00271839	−	0.999996i	$-0.500865\pi$
$677$	534.138	−	263.407i	0.788977	−	0.389080i	0.791696	+	0.610916i	$0.209199\pi$
$678$	−270.426	+	63.9651i	−0.398858	+	0.0943438i
$679$	374.772	−	216.375i	0.551946	−	0.318666i
$680$	−198.574	+	89.2358i	−0.292021	+	0.131229i
$681$	44.1332	+	433.891i	0.0648064	+	0.637139i
$682$	610.759	+	795.956i	0.895541	+	1.16709i
$683$	106.349	−	159.163i	0.155709	−	0.233035i	−0.745411	−	0.666605i	$-0.767747\pi$
$683$	106.349	−	159.163i	0.155709	−	0.233035i	0.901119	+	0.433571i	$0.142747\pi$
$684$	−459.958	−	303.105i	−0.672453	−	0.443136i
$685$	−0.0910037	−	0.457506i	−0.000132852	−	0.000667893i
$686$	−839.924	+	55.0515i	−1.22438	+	0.0802501i
$687$	630.415	−	885.699i	0.917634	−	1.28923i
$688$	−292.954	−	224.792i	−0.425806	−	0.326732i
$689$	668.458	−	871.152i	0.970186	−	1.26437i
$690$	934.713	+	665.301i	1.35466	+	0.964204i
$691$	58.5455	+	893.232i	0.0847258	+	1.29267i	0.802610	+	0.596504i	$0.203444\pi$
$691$	58.5455	+	893.232i	0.0847258	+	1.29267i	−0.717885	+	0.696162i	$0.754889\pi$
$692$	−1042.10	+	207.287i	−1.50593	+	0.299548i
$693$	580.715	−	881.226i	0.837972	−	1.27161i
$694$	596.959	+	398.875i	0.860171	+	0.574748i
$695$	−61.2458	+	46.9955i	−0.0881234	+	0.0676195i
$696$	134.217	−	13.6518i	0.192840	−	0.0196147i
$697$	−101.021	−	38.3775i	−0.144936	−	0.0550610i
$698$	−283.664	−	491.321i	−0.406396	−	0.703899i
$699$	−132.704	−	561.036i	−0.189849	−	0.802626i
$700$	67.6916	+	137.265i	0.0967023	+	0.196093i
$701$	−519.274	−	519.274i	−0.740761	−	0.740761i	0.231963	−	0.972725i	$-0.425485\pi$
$701$	−519.274	−	519.274i	−0.740761	−	0.740761i	−0.972725	+	0.231963i	$0.925485\pi$
$702$	−852.078	+	465.988i	−1.21379	+	0.663801i
$703$	737.088	+	1103.13i	1.04849	+	1.56917i
$704$	−405.696	−	355.786i	−0.576273	−	0.505378i
$705$	739.997	−	1198.52i	1.04964	−	1.70003i
$706$	−1063.75	+	1386.30i	−1.50673	+	1.96360i
$707$	−172.904	−	509.359i	−0.244560	−	0.720451i
$708$	137.047	+	165.909i	0.193569	+	0.234335i
$709$	313.477	−	923.474i	0.442140	−	1.30250i	−0.466352	−	0.884599i	$-0.654432\pi$
$709$	313.477	−	923.474i	0.442140	−	1.30250i	0.908492	−	0.417902i	$-0.137235\pi$
$710$	150.795	−	150.795i	0.212387	−	0.212387i
$711$	−123.383	−	893.103i	−0.173535	−	1.25612i
$712$	−278.994	−	115.563i	−0.391845	−	0.162308i
$713$	−528.053	−	304.872i	−0.740608	−	0.427590i
$714$	766.321	+	671.899i	1.07328	+	0.941035i
$715$	592.367	+	1026.01i	0.828485	+	1.43498i
$716$	455.963	−	60.0286i	0.636819	−	0.0838389i
$717$	−129.050	+	80.8207i	−0.179986	+	0.112721i
$718$	−504.046	+	135.059i	−0.702014	+	0.188104i
$719$	−169.818	−	853.733i	−0.236186	−	1.18739i	−0.898777	−	0.438407i	$-0.855543\pi$
$719$	−169.818	−	853.733i	−0.236186	−	1.18739i	0.662590	−	0.748982i	$-0.269457\pi$
$720$	910.202	−	250.125i	1.26417	−	0.347396i
$721$	50.6371	−	254.570i	0.0702317	−	0.353079i
$722$	−6.05674	+	46.0055i	−0.00838884	+	0.0637196i
$723$	166.207	−	89.5229i	0.229886	−	0.123821i
$724$	−243.724	−	717.986i	−0.336635	−	0.991694i
$725$	−115.028	−	56.7255i	−0.158659	−	0.0782421i
$726$	683.367	−	734.306i	0.941276	−	1.01144i
$727$	−313.390	−	1169.59i	−0.431073	−	1.60879i	−0.750292	−	0.661107i	$-0.770087\pi$
$727$	−313.390	−	1169.59i	−0.431073	−	1.60879i	0.319218	−	0.947681i	$-0.396580\pi$
$728$	190.796	+	127.486i	0.262083	+	0.175118i
$729$	−712.138	+	155.885i	−0.976870	+	0.213834i
$730$		−	818.065i		−	1.12064i
$731$	228.899	+	245.908i	0.313131	+	0.336400i
$732$	−476.008	+	343.407i	−0.650284	+	0.469135i
$733$	−74.9803	+	9.87135i	−0.102292	+	0.0134670i	−0.181499	−	0.983391i	$-0.558095\pi$
$733$	−74.9803	+	9.87135i	−0.102292	+	0.0134670i	0.0792062	+	0.996858i	$0.474761\pi$
$734$	11.0304	+	0.722974i	0.0150279	+	0.000984978i
$735$	−73.2020	+	89.7796i	−0.0995946	+	0.122149i
$736$	985.283	+	334.458i	1.33870	+	0.454427i
$737$	−252.763	−	378.286i	−0.342962	−	0.513279i
$738$	132.937	+	75.6241i	0.180132	+	0.102472i
$739$	−414.512	+	171.696i	−0.560909	+	0.232336i	−0.645080	−	0.764115i	$-0.723176\pi$
$739$	−414.512	+	171.696i	−0.560909	+	0.232336i	0.0841708	+	0.996451i	$0.473176\pi$
$740$	1194.37	+	157.241i	1.61401	+	0.212488i
$741$	639.670	+	455.298i	0.863253	+	0.614438i
$742$	1462.67	+	721.310i	1.97126	+	0.972116i
$743$	648.092	+	739.007i	0.872263	+	0.994626i	0.999996	+	0.00281700i	$0.000896681\pi$
$743$	648.092	+	739.007i	0.872263	+	0.994626i	−0.127733	+	0.991809i	$0.540770\pi$
$744$	−153.067	+	58.1689i	−0.205736	+	0.0781840i
$745$	942.232	−	464.657i	1.26474	−	0.623701i
$746$	−503.883	−	208.715i	−0.675447	−	0.279779i
$747$	−335.690	+	298.204i	−0.449384	+	0.399202i
$748$	530.326	+	650.282i	0.708992	+	0.869361i
$749$	63.5345	−	110.045i	0.0848258	−	0.146923i
$750$	797.421	+	239.119i	1.06323	+	0.318825i
$751$	107.078	+	7.01825i	0.142580	+	0.00934521i	0.136526	−	0.990636i	$-0.456406\pi$
$751$	107.078	+	7.01825i	0.142580	+	0.00934521i	0.00605415	+	0.999982i	$0.498073\pi$
$752$	404.531	−	1509.73i	0.537940	−	2.00762i
$753$	559.951	+	521.107i	0.743627	+	0.692041i
$754$	707.473	−	46.3703i	0.938294	−	0.0614990i
$755$	177.167	−	890.680i	0.234659	−	1.17971i
$756$	−407.571	−	487.042i	−0.539115	−	0.644235i
$757$	−245.045	−	591.591i	−0.323705	−	0.781494i	−0.999033	−	0.0439754i	$-0.985998\pi$
$757$	−245.045	−	591.591i	−0.323705	−	0.781494i	0.675327	−	0.737518i	$-0.264002\pi$
$758$	−1247.99	+	1423.06i	−1.64643	+	1.87739i
$759$	−418.903	+	1123.86i	−0.551914	+	1.48072i
$760$	−164.241	−	187.280i	−0.216106	−	0.246422i
$761$	−1169.52	−	313.373i	−1.53682	−	0.411791i	−0.611586	−	0.791178i	$-0.709468\pi$
$761$	−1169.52	−	313.373i	−1.53682	−	0.411791i	−0.925238	+	0.379387i	$0.876135\pi$
$762$	−72.1815	+	136.085i	−0.0947264	+	0.178589i
$763$	890.124	−	683.017i	1.16661	−	0.895172i
$764$			969.865i			1.26946i
$765$	−854.385	+	86.9969i	−1.11684	+	0.113721i
$766$	−541.629			−0.707087
$767$	−186.723	−	243.343i	−0.243446	−	0.317266i
$768$	834.772	−	522.796i	1.08694	−	0.680724i
$769$	138.740	−	517.785i	0.180416	−	0.673322i	−0.815149	−	0.579251i	$-0.803345\pi$
$769$	138.740	−	517.785i	0.180416	−	0.673322i	0.995565	−	0.0940712i	$-0.0299881\pi$
$770$	−1322.92	+	1160.17i	−1.71808	+	1.50672i
$771$	160.698	+	954.370i	0.208428	+	1.23783i
$772$	738.274	+	647.449i	0.956313	+	0.838664i
$773$	214.098	−	88.6825i	0.276971	−	0.114725i	−0.239874	−	0.970804i	$-0.577106\pi$
$773$	214.098	−	88.6825i	0.276971	−	0.114725i	0.516845	+	0.856079i	$0.327106\pi$
$774$	−266.675	−	393.645i	−0.344541	−	0.508585i
$775$	152.679	+	30.3698i	0.197005	+	0.0391868i
$776$	8.63821	+	131.794i	0.0111317	+	0.169837i
$777$	448.686	+	1462.30i	0.577459	+	1.88198i
$778$	−1446.94	−	387.708i	−1.85983	−	0.498339i
$779$	8.08697	−	123.383i	0.0103812	−	0.158387i
$780$	693.785	−	164.104i	0.889468	−	0.210390i
$781$	193.070	+	111.469i	0.247209	+	0.142726i
$782$	−1019.80	−	549.146i	−1.30410	−	0.702233i
$783$	519.426	+	115.881i	0.663379	+	0.147996i
$784$	−49.1900	+	118.755i	−0.0627423	+	0.151473i
$785$	76.0269	+	154.167i	0.0968496	+	0.196391i
$786$	−639.630	−	103.508i	−0.813779	−	0.131689i
$787$	−1052.47	+	922.987i	−1.33731	+	1.17279i	−0.367199	+	0.930142i	$0.619683\pi$
$787$	−1052.47	+	922.987i	−1.33731	+	1.17279i	−0.970114	+	0.242650i	$0.921983\pi$
$788$	−223.172	+	452.548i	−0.283213	+	0.574299i
$789$	154.566	+	14.7255i	0.195901	+	0.0186635i
$790$	−196.206	+	1490.33i	−0.248362	+	1.88650i
$791$	99.1206	+	239.298i	0.125310	+	0.302526i
$792$	162.827	+	277.913i	0.205590	+	0.350900i
$793$	695.623	−	464.801i	0.877205	−	0.586129i
$794$	496.298	−	1462.05i	0.625060	−	1.84137i
$795$	−1284.62	+	488.181i	−1.61587	+	0.614065i
$796$	11.7919	−	179.910i	0.0148140	−	0.226018i
$797$	150.933	+	1146.45i	0.189376	+	1.43846i	0.777091	+	0.629388i	$0.216695\pi$
$797$	150.933	+	1146.45i	0.189376	+	1.43846i	−0.587714	+	0.809068i	$0.699972\pi$
$798$	−477.877	+	1063.72i	−0.598844	+	1.33298i
$799$	−590.864	+	1293.44i	−0.739505	+	1.61883i
$800$	−265.645			−0.332056
$801$	−900.635	−	779.722i	−1.12439	−	0.973436i
$802$	604.078	−	904.066i	0.753214	−	1.12726i
$803$	826.066	−	221.344i	1.02872	−	0.275646i
$804$	−261.735	+	80.3095i	−0.325541	+	0.0998875i
$805$	472.977	−	959.103i	0.587549	−	1.19143i
$806$	−814.876	+	276.613i	−1.01101	+	0.343193i
$807$	439.344	−	711.576i	0.544416	−	0.881755i
$808$	162.766	+	21.4285i	0.201443	+	0.0265205i
$809$	−821.914	−	163.489i	−1.01596	−	0.202088i	−0.341097	−	0.940028i	$-0.610799\pi$
$809$	−821.914	−	163.489i	−1.01596	−	0.202088i	−0.674866	+	0.737940i	$0.735799\pi$
$810$	1213.76	+	64.0053i	1.49847	+	0.0790188i
$811$	12.0723	−	2.40134i	0.0148857	−	0.00296096i	−0.187642	−	0.982238i	$-0.560084\pi$
$811$	12.0723	−	2.40134i	0.0148857	−	0.00296096i	0.202528	+	0.979277i	$0.435084\pi$
$812$	119.996	+	447.831i	0.147778	+	0.551516i
$813$	1148.89	−	41.2816i	1.41315	−	0.0507769i
$814$	373.344	+	2835.83i	0.458654	+	3.48382i
$815$	607.786	−	350.905i	0.745750	−	0.430559i
$816$	−880.375	+	364.775i	−1.07889	+	0.447028i
$817$	−192.200	+	332.900i	−0.235251	+	0.407466i
$818$	562.851	−	1358.84i	0.688082	−	1.66118i
$819$	555.634	+	714.625i	0.678429	+	0.872558i
$820$	−79.3891	−	79.3891i	−0.0968160	−	0.0968160i
$821$	−319.630	−	108.500i	−0.389317	−	0.132155i	0.119916	−	0.992784i	$-0.461738\pi$
$821$	−319.630	−	108.500i	−0.389317	−	0.132155i	−0.509233	+	0.860629i	$0.670071\pi$
$822$	−0.110666	−	0.657235i	−0.000134630	−	0.000799556i
$823$	−1308.67	+	444.234i	−1.59012	+	0.539774i	−0.969659	−	0.244461i	$-0.921389\pi$
$823$	−1308.67	+	444.234i	−1.59012	+	0.539774i	−0.620464	+	0.784235i	$0.713056\pi$
$824$	62.8476	+	48.2246i	0.0762713	+	0.0585250i
$825$	9.04218	−	306.078i	0.0109602	−	0.371003i
$826$	300.368	−	342.504i	0.363642	−	0.414654i
$827$	501.331	−	334.979i	0.606205	−	0.405053i	−0.214238	−	0.976781i	$-0.568727\pi$
$827$	501.331	−	334.979i	0.606205	−	0.405053i	0.820443	+	0.571728i	$0.193727\pi$
$828$	575.397	+	435.711i	0.694924	+	0.526221i
$829$	−645.385	+	645.385i	−0.778510	+	0.778510i	−0.979577	−	0.201068i	$-0.935559\pi$
$829$	−645.385	+	645.385i	−0.778510	+	0.778510i	0.201068	+	0.979577i	$0.435559\pi$
$830$	671.427	−	331.111i	0.808948	−	0.398929i
$831$	−122.025	+	406.933i	−0.146841	+	0.489691i
$832$	400.828	−	231.418i	0.481764	−	0.278146i
$833$	62.0612	−	99.1197i	0.0745032	−	0.118991i
$834$	−89.4519	+	64.5334i	−0.107257	+	0.0773782i
$835$	366.443	+	477.558i	0.438854	+	0.571926i
$836$	−533.411	+	798.307i	−0.638052	+	0.954912i
$837$	−645.379	+	27.3153i	−0.771062	+	0.0326347i
$838$	290.569	+	1460.79i	0.346741	+	1.74319i
$839$	−508.928	+	33.3569i	−0.606589	+	0.0397580i	−0.365603	−	0.930771i	$-0.619137\pi$
$839$	−508.928	+	33.3569i	−0.606589	+	0.0397580i	−0.240986	+	0.970529i	$0.577471\pi$
$840$	−119.358	−	261.207i	−0.142092	−	0.310961i
$841$	358.976	+	275.452i	0.426844	+	0.327529i
$842$	131.704	−	171.640i	0.156418	−	0.203848i
$843$	75.5370	−	792.873i	0.0896050	−	0.940537i
$844$	−34.1244	−	520.638i	−0.0404317	−	0.616869i
$845$	−66.2730	+	13.1825i	−0.0784296	+	0.0156006i
$846$	1107.41	−	1680.47i	1.30899	−	1.98637i
$847$	−777.396	−	519.439i	−0.917823	−	0.613270i
$848$	−1209.79	+	928.305i	−1.42664	+	1.09470i
$849$	193.882	−	431.565i	0.228365	−	0.508322i
$850$	291.609	+	49.0689i	0.343069	+	0.0577282i
$851$	−869.173	−	1505.45i	−1.02136	−	1.76904i
$852$	97.6225	−	92.0200i	0.114580	−	0.108005i
$853$	168.231	+	341.139i	0.197223	+	0.399928i	0.972908	−	0.231191i	$-0.0742623\pi$
$853$	168.231	+	341.139i	0.197223	+	0.399928i	−0.775685	+	0.631120i	$0.782596\pi$
$854$	878.621	+	878.621i	1.02883	+	1.02883i
$855$	−381.828	−	905.425i	−0.446583	−	1.05898i
$856$	21.5460	+	32.2459i	0.0251706	+	0.0376705i
$857$	275.606	+	241.700i	0.321594	+	0.282030i	0.804887	−	0.593428i	$-0.202226\pi$
$857$	275.606	+	241.700i	0.321594	+	0.282030i	−0.483293	+	0.875459i	$0.660559\pi$
$858$	802.710	+	1490.31i	0.935560	+	1.73695i
$859$	63.9058	−	83.2837i	0.0743956	−	0.0969543i	−0.754673	−	0.656101i	$-0.772205\pi$
$859$	63.9058	−	83.2837i	0.0743956	−	0.0969543i	0.829069	+	0.559147i	$0.188871\pi$
$860$	112.194	+	330.514i	0.130459	+	0.384319i
$861$	49.7889	−	133.577i	0.0578268	−	0.155142i
$862$	113.649	−	334.800i	0.131844	−	0.388400i
$863$	299.211	−	299.211i	0.346710	−	0.346710i	−0.512172	−	0.858883i	$-0.671159\pi$
$863$	299.211	−	299.211i	0.346710	−	0.346710i	0.858883	+	0.512172i	$0.171159\pi$
$864$	1071.06	−	260.572i	1.23965	−	0.301588i
$865$	−1751.12	−	725.336i	−2.02441	−	0.838539i
$866$	70.2175	+	40.5401i	0.0810826	+	0.0468131i
$867$	844.933	−	194.362i	0.974548	−	0.224178i
$868$	−281.367	−	487.342i	−0.324155	−	0.561454i
$869$	−1558.00	+	205.114i	−1.79286	+	0.236035i
$870$	−783.875	−	415.779i	−0.901006	−	0.477907i
$871$	376.937	−	101.000i	0.432764	−	0.115959i
$872$	66.8050	+	335.851i	0.0766112	+	0.385150i
$873$	−131.635	+	504.116i	−0.150784	+	0.577453i
$874$	258.549	−	1299.82i	0.295823	−	1.48720i
$875$	101.283	−	769.322i	0.115752	−	0.879225i
$876$	15.1967	−	514.407i	0.0173478	−	0.587223i
$877$	−68.8535	−	202.836i	−0.0785102	−	0.231284i	0.900587	−	0.434675i	$-0.143137\pi$
$877$	−68.8535	−	202.836i	−0.0785102	−	0.231284i	−0.979097	+	0.203392i	$0.934804\pi$
$878$	−825.388	−	407.036i	−0.940077	−	0.463595i
$879$	1373.19	+	315.565i	1.56222	+	0.359005i
$880$	−425.827	−	1589.21i	−0.483895	−	1.80592i
$881$	827.823	+	553.134i	0.939641	+	0.627848i	0.928198	−	0.372087i	$-0.121358\pi$
$881$	827.823	+	553.134i	0.939641	+	0.627848i	0.0114427	+	0.999935i	$0.496358\pi$
$882$	−108.333	+	125.132i	−0.122826	+	0.141873i
$883$			273.833i			0.310117i	0.987905	+	0.155058i	$0.0495565\pi$
$883$			273.833i			0.310117i	−0.987905	+	0.155058i	$0.950443\pi$
$884$	−674.382	+	251.448i	−0.762876	+	0.284444i
$885$	38.8453	+	381.904i	0.0438930	+	0.431530i
$886$	1597.38	−	210.300i	1.80292	−	0.237358i
$887$	171.840	+	11.2630i	0.193732	+	0.0126978i	0.161960	−	0.986797i	$-0.448218\pi$
$887$	171.840	+	11.2630i	0.193732	+	0.0126978i	0.0317715	+	0.999495i	$0.489885\pi$
$888$	−460.841	−	74.5751i	−0.518965	−	0.0839809i
$889$	135.961	+	46.1526i	0.152937	+	0.0519152i
$890$	1103.46	+	1651.44i	1.23984	+	1.85555i
$891$	263.776	+	1242.95i	0.296044	+	1.39500i
$892$	−677.768	+	280.741i	−0.759829	+	0.314732i
$893$	−1613.15	−	212.375i	−1.80643	−	0.237822i
$894$	1365.27	−	623.854i	1.52715	−	0.697824i
$895$	735.792	+	362.853i	0.822114	+	0.405422i
$896$	−351.644	−	400.973i	−0.392460	−	0.447514i
$897$	−797.320	−	650.097i	−0.888874	−	0.724745i
$898$	−185.879	+	91.6652i	−0.206992	+	0.102077i
$899$	435.674	+	180.462i	0.484621	+	0.200737i
$900$	−174.862	−	58.1156i	−0.194291	−	0.0645729i
$901$	1225.56	−	650.224i	1.36022	−	0.721669i
$902$	133.287	−	230.860i	0.147769	−	0.255943i
$903$	−322.491	+	303.984i	−0.357133	+	0.336638i
$904$	−78.8828	−	5.17025i	−0.0872597	−	0.00571930i
$905$	350.073	−	1306.49i	0.386821	−	1.44363i
$906$	290.603	−	1264.56i	0.320754	−	1.39577i
$907$	266.371	−	17.4589i	0.293684	−	0.0192490i	0.0821507	−	0.996620i	$-0.473821\pi$
$907$	266.371	−	17.4589i	0.293684	−	0.0192490i	0.211533	+	0.977371i	$0.432154\pi$
$908$	89.2419	−	448.649i	0.0982840	−	0.494107i
$909$	582.654	+	282.724i	0.640983	+	0.311028i
$910$	−577.565	−	1394.36i	−0.634687	−	1.53227i
$911$	−941.341	+	1073.39i	−1.03331	+	1.17826i	−0.0495453	+	0.998772i	$0.515777\pi$
$911$	−941.341	+	1073.39i	−1.03331	+	1.17826i	−0.983760	+	0.179487i	$0.942556\pi$
$912$	−694.410	−	840.656i	−0.761415	−	0.921772i
$913$	516.017	+	588.404i	0.565188	+	0.644474i
$914$	−427.613	−	114.578i	−0.467847	−	0.125359i
$915$	−1046.37	+	37.5980i	−1.14357	+	0.0410907i
$916$	−904.631	+	694.148i	−0.987588	+	0.757803i
$917$			603.945i			0.658609i
$918$	−1223.87	+	88.1986i	−1.33320	+	0.0960769i
$919$	1261.75			1.37296			0.686482	−	0.727147i	$-0.259154\pi$
$919$	1261.75			1.37296			0.686482	+	0.727147i	$0.259154\pi$
$920$	198.687	+	258.934i	0.215965	+	0.281450i
$921$	−15.3931	−	428.397i	−0.0167134	−	0.465144i
$922$	1.64934	−	6.15540i	0.00178887	−	0.00667614i
$923$	−143.768	+	126.081i	−0.155761	+	0.136599i
$924$	−853.419	+	704.953i	−0.923614	+	0.762936i
$925$	333.672	+	292.623i	0.360727	+	0.316349i
$926$	1037.36	−	429.689i	1.12026	−	0.464027i
$927$	175.271	+	258.721i	0.189073	+	0.279095i
$928$	−789.253	−	156.992i	−0.850488	−	0.169173i
$929$	−64.8139	−	988.868i	−0.0697673	−	1.06444i	−0.878958	−	0.476898i	$-0.841761\pi$
$929$	−64.8139	−	988.868i	−0.0697673	−	1.06444i	0.809191	−	0.587546i	$-0.199906\pi$
$930$	1049.63	+	241.210i	1.12864	+	0.259366i
$931$	129.250	+	34.6324i	0.138829	+	0.0371992i
$932$	−39.5483	+	603.390i	−0.0424338	+	0.647414i
$933$	−469.855	−	498.461i	−0.503596	−	0.534256i
$934$	939.788	+	542.587i	1.00620	+	0.580928i
$935$	142.125	+	1490.11i	0.152006	+	1.59370i
$936$	−270.617	+	55.6270i	−0.289121	+	0.0594305i
$937$	302.614	−	730.575i	0.322961	−	0.779696i	−0.676119	−	0.736793i	$-0.736339\pi$
$937$	302.614	−	730.575i	0.322961	−	0.779696i	0.999079	−	0.0429032i	$-0.0136607\pi$
$938$	256.342	+	519.811i	0.273286	+	0.554169i
$939$	253.944	−	311.454i	0.270441	−	0.331687i
$940$	−1110.76	+	974.108i	−1.18166	+	1.03629i
$941$	164.409	−	333.388i	0.174717	−	0.354291i	−0.791846	−	0.610721i	$-0.790880\pi$
$941$	164.409	−	333.388i	0.174717	−	0.354291i	0.966563	+	0.256430i	$0.0825462\pi$
$942$	102.075	+	223.384i	0.108359	+	0.237138i
$943$	−21.1466	+	160.624i	−0.0224248	+	0.170333i
$944$	163.008	+	393.535i	0.172677	+	0.416880i
$945$	−121.833	−	1126.33i	−0.128923	−	1.19188i
$946$	−689.066	+	460.419i	−0.728400	+	0.486701i
$947$	−312.574	+	920.814i	−0.330068	+	0.972349i	0.647561	+	0.762013i	$0.275789\pi$
$947$	−312.574	+	920.814i	−0.330068	+	0.972349i	−0.977629	+	0.210336i	$0.932544\pi$
$948$	−151.061	+	933.492i	−0.159347	+	0.984696i
$949$	−47.9756	+	731.967i	−0.0505539	+	0.771303i
$950$	44.1635	+	335.455i	0.0464879	+	0.353111i
$951$	845.946	−	86.0452i	0.889533	−	0.0904787i
$952$	152.341	+	246.677i	0.160022	+	0.259114i
$953$	60.2023			0.0631714			0.0315857	−	0.999501i	$-0.489944\pi$
$953$	60.2023			0.0631714			0.0315857	+	0.999501i	$0.489944\pi$
$954$	−1855.24	+	643.005i	−1.94470	+	0.674010i
$955$	−961.201	+	1438.54i	−1.00649	+	1.50632i
$956$	154.267	−	41.3357i	0.161367	−	0.0432382i
$957$	207.752	−	904.039i	0.217087	−	0.944659i
$958$	312.536	−	633.760i	0.326238	−	0.661545i
$959$	−0.588253	+	0.199685i	−0.000613403	+	0.000208222i
$960$	−578.996	−	17.1048i	−0.603121	−	0.0178175i
$961$	385.302	+	50.7259i	0.400938	+	0.0527845i
$962$	−2406.23	−	478.629i	−2.50128	−	0.497535i
$963$	40.5386	+	147.519i	0.0420962	+	0.153187i
$964$	−194.203	+	38.6293i	−0.201455	+	0.0400719i
$965$	453.369	+	1692.00i	0.469813	+	1.75336i
$966$	715.956	−	1349.80i	0.741155	−	1.39731i
$967$	89.7860	+	681.992i	0.0928500	+	0.705266i	0.973039	+	0.230642i	$0.0740826\pi$
$967$	89.7860	+	681.992i	0.0928500	+	0.705266i	−0.880189	+	0.474624i	$0.842584\pi$
$968$	247.124	−	142.677i	0.255294	−	0.147394i
$969$	496.104	+	859.063i	0.511975	+	0.886546i
$970$	434.342	−	752.303i	0.447776	−	0.775570i
$971$	435.488	−	1051.36i	0.448494	−	1.08276i	−0.524393	−	0.851477i	$-0.675708\pi$
$971$	435.488	−	1051.36i	0.448494	−	1.08276i	0.972886	−	0.231283i	$-0.0742924\pi$
$972$	762.035	+	62.7944i	0.783987	+	0.0646033i
$973$	72.6971	+	72.6971i	0.0747144	+	0.0747144i
$974$	814.134	+	276.361i	0.835866	+	0.283738i
$975$	246.107	+	91.7324i	0.252417	+	0.0940845i
$976$	−1100.18	+	373.459i	−1.12723	+	0.382643i
$977$	426.225	+	327.054i	0.436259	+	0.334754i	0.803429	−	0.595400i	$-0.203007\pi$
$977$	426.225	+	327.054i	0.436259	+	0.334754i	−0.367170	+	0.930154i	$0.619673\pi$
$978$	882.825	−	475.508i	0.902684	−	0.486205i
$979$	−1369.03	+	1561.08i	−1.39840	+	1.59456i
$980$	101.023	−	67.5017i	0.103085	−	0.0688793i
$981$	−167.767	+	1340.37i	−0.171017	+	1.36633i
$982$	135.555	−	135.555i	0.138040	−	0.138040i
$983$	−54.7252	+	26.9875i	−0.0556716	+	0.0274542i	−0.469911	−	0.882714i	$-0.655714\pi$
$983$	−54.7252	+	26.9875i	−0.0556716	+	0.0274542i	0.414240	+	0.910168i	$0.364047\pi$
$984$	29.8430	+	31.6600i	0.0303283	+	0.0321748i
$985$	−779.521	+	450.057i	−0.791392	+	0.456910i
$986$	837.396	+	318.125i	0.849286	+	0.322642i
$987$	−1711.11	−	768.723i	−1.73365	−	0.778848i
$988$	−501.328	−	653.343i	−0.507417	−	0.661278i
$989$	279.820	−	418.780i	0.282932	−	0.423437i
$990$	125.060	−	2114.80i	0.126324	−	2.13616i
$991$	108.498	+	545.458i	0.109484	+	0.550412i	0.996125	+	0.0879534i	$0.0280327\pi$
$991$	108.498	+	545.458i	0.109484	+	0.550412i	−0.886641	+	0.462459i	$0.846967\pi$
$992$	974.640	−	63.8813i	0.982500	−	0.0643965i
$993$	108.278	+	10.3157i	0.109042	+	0.0103884i
$994$	−225.316	−	172.891i	−0.226676	−	0.173934i
$995$	195.793	−	255.163i	0.196777	−	0.256445i
$996$	428.350	−	195.733i	0.430071	−	0.196519i
$997$	−12.4224	−	189.530i	−0.0124598	−	0.190100i	−0.999552	−	0.0299442i	$-0.990467\pi$
$997$	−12.4224	−	189.530i	−0.0124598	−	0.190100i	0.987092	−	0.160156i	$-0.0511996\pi$
$998$	2323.65	−	462.204i	2.32831	−	0.463130i
$999$	−1632.37	−	852.530i	−1.63401	−	0.853383i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	153.3.t.a.7.6	✓	544
9.4	even	3	inner	153.3.t.a.58.29	yes	544
17.5	odd	16	inner	153.3.t.a.124.29	yes	544
153.22	odd	48	inner	153.3.t.a.22.6	yes	544

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
153.3.t.a.7.6	✓	544	1.1	even	1	trivial
153.3.t.a.22.6	yes	544	153.22	odd	48	inner
153.3.t.a.58.29	yes	544	9.4	even	3	inner
153.3.t.a.124.29	yes	544	17.5	odd	16	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:	\( N \)	\(=\)	\( 153 = 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	153.t (of order \(48\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.62741 - 2.12088i) q^{2} +(-0.107726 - 2.99807i) q^{3} +(-0.814394 + 3.03936i) q^{4} +(-4.22014 + 3.70097i) q^{5} +(-6.18322 + 5.10755i) q^{6} +(5.62018 + 4.92877i) q^{7} +(-2.10780 + 0.873079i) q^{8} +(-8.97679 + 0.645938i) q^{9} +(14.7172 + 2.92743i) q^{10} +(1.02596 + 15.6532i) q^{11} +(9.19993 + 2.11419i) q^{12} +(-12.9966 - 3.48242i) q^{13} +(1.30699 - 19.9408i) q^{14} +(11.5504 + 12.2536i) q^{15} +(16.1820 + 9.34268i) q^{16} +(-13.1079 - 10.8252i) q^{17} +(15.9788 + 17.9875i) q^{18} +(7.44374 - 17.9708i) q^{19} +(-7.81171 - 15.8406i) q^{20} +(14.1713 - 17.3806i) q^{21} +(31.5289 - 27.6501i) q^{22} +(-11.2723 + 22.8580i) q^{23} +(2.84461 + 6.22527i) q^{24} +(0.849305 - 6.45111i) q^{25} +(13.7649 + 33.2315i) q^{26} +(2.90360 + 26.8434i) q^{27} +(-19.5573 + 13.0678i) q^{28} +(6.33587 - 18.6649i) q^{29} +(7.19121 - 44.4385i) q^{30} +(-1.56473 + 23.8731i) q^{31} +(-5.32885 - 40.4766i) q^{32} +(46.8188 - 4.76216i) q^{33} +(-1.62700 + 45.4171i) q^{34} -41.9592 q^{35} +(5.34740 - 27.8097i) q^{36} +(-37.8938 + 56.7120i) q^{37} +(-50.2278 + 13.4585i) q^{38} +(-9.04046 + 39.3397i) q^{39} +(5.66398 - 11.4854i) q^{40} +(6.01941 - 2.04331i) q^{41} +(-59.9247 - 1.77030i) q^{42} +(-19.5930 - 2.57946i) q^{43} +(-48.4112 - 9.62959i) q^{44} +(35.4928 - 35.9488i) q^{45} +(66.8237 - 13.2921i) q^{46} +(-21.6496 - 80.7974i) q^{47} +(26.2667 - 49.5211i) q^{48} +(0.897911 + 6.82031i) q^{49} +(-15.0642 + 8.69731i) q^{50} +(-31.0425 + 40.4644i) q^{51} +(21.1687 - 36.6652i) q^{52} +(-31.2307 + 75.3976i) q^{53} +(52.2063 - 49.8433i) q^{54} +(-62.2617 - 62.2617i) q^{55} +(-16.1494 - 5.48199i) q^{56} +(-54.6794 - 20.3809i) q^{57} +(-49.8969 + 16.9377i) q^{58} +(18.0856 + 13.8776i) q^{59} +(-46.6496 + 25.1265i) q^{60} +(-40.9974 + 46.7485i) q^{61} +(53.1784 - 35.5327i) q^{62} +(-53.6349 - 40.6142i) q^{63} +(-24.3235 + 24.3235i) q^{64} +(67.7357 - 33.4036i) q^{65} +(-86.2932 - 91.5469i) q^{66} +(-25.1172 + 14.5014i) q^{67} +(43.5765 - 31.0236i) q^{68} +(69.7441 + 31.3327i) q^{69} +(68.2846 + 88.9903i) q^{70} +(7.89568 - 11.8167i) q^{71} +(18.3573 - 9.19895i) q^{72} +(-10.6359 - 53.4701i) q^{73} +(181.948 - 11.9255i) q^{74} +(-19.4323 - 1.85132i) q^{75} +(48.5575 + 37.2595i) q^{76} +(-71.3848 + 93.0305i) q^{77} +(98.1473 - 44.8480i) q^{78} +(6.55183 + 99.9616i) q^{79} +(-102.867 + 20.4616i) q^{80} +(80.1655 - 11.5969i) q^{81} +(-14.1296 - 9.44112i) q^{82} +(39.5807 - 30.3713i) q^{83} +(41.2849 + 57.2264i) q^{84} +(95.3806 - 2.82806i) q^{85} +(26.4150 + 45.7521i) q^{86} +(-56.6410 - 16.9847i) q^{87} +(-15.8290 - 32.0980i) q^{88} +(93.5945 + 93.5945i) q^{89} +(-134.004 - 16.7725i) q^{90} +(-55.8790 - 83.6289i) q^{91} +(-60.2936 - 52.8760i) q^{92} +(71.7417 + 2.11940i) q^{93} +(-136.129 + 177.406i) q^{94} +(35.0956 + 103.388i) q^{95} +(-120.777 + 20.3366i) q^{96} +(18.6085 - 54.8187i) q^{97} +(13.0038 - 13.0038i) q^{98} +(-19.3209 - 139.853i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 544 q - 8 q^{2} - 16 q^{3} - 8 q^{4} - 8 q^{5} - 16 q^{6} - 8 q^{7} - 32 q^{8} - 16 q^{9} - 32 q^{10} - 8 q^{11} + 176 q^{12} - 8 q^{13} - 8 q^{14} - 40 q^{15} - 32 q^{17} + 32 q^{18} - 32 q^{19} - 8 q^{20}+ \cdots + 448 q^{99}+O(q^{100}) \) 544 * q - 8 * q^2 - 16 * q^3 - 8 * q^4 - 8 * q^5 - 16 * q^6 - 8 * q^7 - 32 * q^8 - 16 * q^9 - 32 * q^10 - 8 * q^11 + 176 * q^12 - 8 * q^13 - 8 * q^14 - 40 * q^15 - 32 * q^17 + 32 * q^18 - 32 * q^19 - 8 * q^20 - 256 * q^21 - 8 * q^22 - 8 * q^23 + 176 * q^24 - 8 * q^25 - 32 * q^26 - 16 * q^27 - 32 * q^28 - 8 * q^29 - 16 * q^30 - 8 * q^31 - 72 * q^32 + 40 * q^34 - 64 * q^35 + 16 * q^36 - 32 * q^37 + 88 * q^38 - 192 * q^39 - 8 * q^40 - 440 * q^41 - 400 * q^42 - 248 * q^43 - 800 * q^44 - 176 * q^45 - 32 * q^46 + 112 * q^47 - 248 * q^48 - 8 * q^49 + 16 * q^51 - 16 * q^52 + 160 * q^53 - 312 * q^54 - 32 * q^55 - 488 * q^56 - 296 * q^57 - 8 * q^58 + 568 * q^59 + 2080 * q^60 - 8 * q^61 + 1120 * q^62 - 88 * q^63 - 288 * q^64 - 248 * q^65 - 24 * q^66 - 8 * q^68 - 416 * q^69 - 40 * q^70 - 32 * q^71 + 632 * q^72 - 32 * q^73 - 8 * q^74 + 752 * q^75 - 8 * q^76 - 8 * q^77 - 2304 * q^78 - 8 * q^79 - 432 * q^80 + 768 * q^81 + 352 * q^82 - 296 * q^83 - 8 * q^85 + 1184 * q^86 - 688 * q^87 - 8 * q^88 - 1184 * q^89 - 1136 * q^90 + 640 * q^91 - 2024 * q^92 - 528 * q^93 - 8 * q^94 + 472 * q^95 - 1064 * q^96 - 8 * q^97 - 848 * q^98 + 448 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more