LMFDB - Embedded newform 75.3.h.a.14.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [75,3,Mod(14,75)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(75, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 3])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("75.14"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	75.h (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$2.04360198270$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			14.8
Character	$\chi$	$=$	75.14
Dual form			75.3.h.a.59.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.680034 + 0.494074i) q^{2} +(-2.26100 - 1.97177i) q^{3} +(-1.01773 + 3.13225i) q^{4} +(4.99975 + 0.0496921i) q^{5} +(2.51176 + 0.223767i) q^{6} +9.76040i q^{7} +(-1.89447 - 5.83059i) q^{8} +(1.22427 + 8.91634i) q^{9} +(-3.42456 + 2.43645i) q^{10} +(10.1778 + 14.0086i) q^{11} +(8.47716 - 5.07530i) q^{12} +(-1.60244 + 2.20557i) q^{13} +(-4.82236 - 6.63741i) q^{14} +(-11.2065 - 9.97070i) q^{15} +(-6.48876 - 4.71436i) q^{16} +(-6.87668 - 21.1642i) q^{17} +(-5.23787 - 5.45854i) q^{18} +(1.10865 + 3.41207i) q^{19} +(-5.24405 + 15.6099i) q^{20} +(19.2452 - 22.0683i) q^{21} +(-13.8426 - 4.49772i) q^{22} +(-0.909200 + 0.660572i) q^{23} +(-7.21315 + 16.9184i) q^{24} +(24.9951 + 0.496897i) q^{25} -2.29159i q^{26} +(14.8129 - 22.5738i) q^{27} +(-30.5720 - 9.93345i) q^{28} +(-25.4429 - 8.26690i) q^{29} +(12.5471 + 1.24360i) q^{30} +(6.92473 + 21.3121i) q^{31} +31.2644 q^{32} +(4.60957 - 51.7418i) q^{33} +(15.1331 + 10.9948i) q^{34} +(-0.485015 + 48.7996i) q^{35} +(-29.1742 - 5.23972i) q^{36} +(14.8003 - 20.3708i) q^{37} +(-2.43974 - 1.77257i) q^{38} +(7.97200 - 1.82716i) q^{39} +(-9.18216 - 29.2456i) q^{40} +(14.2504 - 19.6141i) q^{41} +(-2.18406 + 24.5158i) q^{42} +50.8068i q^{43} +(-54.2367 + 17.6226i) q^{44} +(5.67796 + 44.6403i) q^{45} +(0.291916 - 0.898424i) q^{46} +(10.9874 - 33.8156i) q^{47} +(5.37549 + 23.4535i) q^{48} -46.2654 q^{49} +(-17.2430 + 12.0115i) q^{50} +(-26.1828 + 61.4116i) q^{51} +(-5.27755 - 7.26393i) q^{52} +(-9.08989 + 27.9758i) q^{53} +(1.07987 + 22.6696i) q^{54} +(50.1905 + 70.5452i) q^{55} +(56.9088 - 18.4908i) q^{56} +(4.22115 - 9.90071i) q^{57} +(21.3865 - 6.94890i) q^{58} +(51.6779 - 71.1286i) q^{59} +(42.6359 - 24.9540i) q^{60} +(66.4241 - 48.2599i) q^{61} +(-15.2388 - 11.0716i) q^{62} +(-87.0271 + 11.9493i) q^{63} +(4.69420 - 3.41054i) q^{64} +(-8.12141 + 10.9477i) q^{65} +(22.4296 + 37.4637i) q^{66} +(-68.7311 + 22.3321i) q^{67} +73.2904 q^{68} +(3.35820 + 0.299175i) q^{69} +(-23.7808 - 33.4250i) q^{70} +(44.5178 + 14.4647i) q^{71} +(49.6682 - 24.0300i) q^{72} +(-28.7539 - 39.5764i) q^{73} +21.1653i q^{74} +(-55.5341 - 50.4079i) q^{75} -11.8158 q^{76} +(-136.729 + 99.3397i) q^{77} +(-4.51848 + 5.18129i) q^{78} +(44.9043 - 138.201i) q^{79} +(-32.2080 - 23.8931i) q^{80} +(-78.0023 + 21.8320i) q^{81} +20.3790i q^{82} +(0.277581 + 0.854307i) q^{83} +(49.5370 + 82.7405i) q^{84} +(-33.3300 - 106.158i) q^{85} +(-25.1023 - 34.5504i) q^{86} +(41.2261 + 68.8590i) q^{87} +(62.3967 - 85.8816i) q^{88} +(-20.9981 - 28.9013i) q^{89} +(-25.9168 - 27.5516i) q^{90} +(-21.5273 - 15.6405i) q^{91} +(-1.14376 - 3.52013i) q^{92} +(26.3657 - 61.8407i) q^{93} +(9.23562 + 28.4243i) q^{94} +(5.37342 + 17.1146i) q^{95} +(-70.6889 - 61.6461i) q^{96} +(116.093 + 37.7208i) q^{97} +(31.4621 - 22.8585i) q^{98} +(-112.445 + 107.899i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 5 q^{3} - 38 q^{4} + 5 q^{6} - 13 q^{9} - 20 q^{10} - 45 q^{12} - 10 q^{13} - 15 q^{15} + 22 q^{16} - 36 q^{19} + 54 q^{21} - 50 q^{22} - 20 q^{24} - 100 q^{25} + 100 q^{27} + 270 q^{28} - 5 q^{30}+ \cdots + 60 q^{99}+O(q^{100}) $ 72 * q - 5 * q^3 - 38 * q^4 + 5 * q^6 - 13 * q^9 - 20 * q^10 - 45 * q^12 - 10 * q^13 - 15 * q^15 + 22 * q^16 - 36 * q^19 + 54 * q^21 - 50 * q^22 - 20 * q^24 - 100 * q^25 + 100 * q^27 + 270 * q^28 - 5 * q^30 - 126 * q^31 + 20 * q^33 + 210 * q^34 - 213 * q^36 + 110 * q^37 - 191 * q^39 + 140 * q^40 - 175 * q^42 - 405 * q^45 - 210 * q^46 + 150 * q^48 - 224 * q^49 - 60 * q^51 - 320 * q^52 + 320 * q^54 - 10 * q^55 - 70 * q^58 + 1190 * q^60 + 294 * q^61 + 795 * q^63 + 362 * q^64 - 470 * q^66 - 260 * q^67 + 335 * q^69 + 1200 * q^70 + 215 * q^72 - 150 * q^73 + 200 * q^75 - 16 * q^76 - 1295 * q^78 - 346 * q^79 + 507 * q^81 - 456 * q^84 - 1450 * q^85 - 430 * q^87 - 1710 * q^88 - 820 * q^90 + 538 * q^91 - 560 * q^94 + 740 * q^96 - 150 * q^97 + 60 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/75\mathbb{Z}\right)^\times$.

$n$	$26$	$52$
$\chi(n)$	$-1$	$e\left(\frac{3}{10}\right)$

Coefficient data

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

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

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

$2$	−0.680034	+	0.494074i	−0.340017	+	0.247037i	−0.744669	−	0.667434i	$-0.767393\pi$
$2$	−0.680034	+	0.494074i	−0.340017	+	0.247037i	0.404652	+	0.914471i	$0.367393\pi$
$3$	−2.26100	−	1.97177i	−0.753668	−	0.657256i
$3$	−2.26100	−	1.97177i	−0.753668	−	0.657256i
$4$	−1.01773	+	3.13225i	−0.254433	+	0.783063i
$5$	4.99975	+	0.0496921i	0.999951	+	0.00993842i
$5$	4.99975	+	0.0496921i	0.999951	+	0.00993842i
$6$	2.51176	+	0.223767i	0.418626	+	0.0372945i
$7$			9.76040i			1.39434i	0.716904	+	0.697171i	$0.245558\pi$
$7$			9.76040i			1.39434i	−0.716904	+	0.697171i	$0.754442\pi$
$8$	−1.89447	−	5.83059i	−0.236809	−	0.728823i
$9$	1.22427	+	8.91634i	0.136030	+	0.990705i
$10$	−3.42456	+	2.43645i	−0.342456	+	0.243645i
$11$	10.1778	+	14.0086i	0.925258	+	1.27351i	0.961681	+	0.274172i	$0.0884036\pi$
$11$	10.1778	+	14.0086i	0.925258	+	1.27351i	−0.0364230	+	0.999336i	$0.511596\pi$
$12$	8.47716	−	5.07530i	0.706430	−	0.422942i
$13$	−1.60244	+	2.20557i	−0.123265	+	0.169659i	−0.866190	−	0.499715i	$-0.833438\pi$
$13$	−1.60244	+	2.20557i	−0.123265	+	0.169659i	0.742925	+	0.669375i	$0.233438\pi$
$14$	−4.82236	−	6.63741i	−0.344454	−	0.474100i
$15$	−11.2065	−	9.97070i	−0.747098	−	0.664714i
$16$	−6.48876	−	4.71436i	−0.405548	−	0.294648i
$17$	−6.87668	−	21.1642i	−0.404511	−	1.24496i	−0.921303	−	0.388845i	$-0.872874\pi$
$17$	−6.87668	−	21.1642i	−0.404511	−	1.24496i	0.516792	−	0.856111i	$-0.327126\pi$
$18$	−5.23787	−	5.45854i	−0.290993	−	0.303252i
$19$	1.10865	+	3.41207i	0.0583500	+	0.179583i	0.975983	−	0.217845i	$-0.0699028\pi$
$19$	1.10865	+	3.41207i	0.0583500	+	0.179583i	−0.917633	+	0.397428i	$0.869903\pi$
$20$	−5.24405	+	15.6099i	−0.262202	+	0.780496i
$21$	19.2452	−	22.0683i	0.916440	−	1.05087i
$22$	−13.8426	−	4.49772i	−0.629207	−	0.204442i
$23$	−0.909200	+	0.660572i	−0.0395304	+	0.0287205i	−0.607375	−	0.794415i	$-0.707777\pi$
$23$	−0.909200	+	0.660572i	−0.0395304	+	0.0287205i	0.567845	+	0.823136i	$0.307777\pi$
$24$	−7.21315	+	16.9184i	−0.300548	+	0.704934i
$25$	24.9951	+	0.496897i	0.999802	+	0.0198759i
$26$		−	2.29159i		−	0.0881381i
$27$	14.8129	−	22.5738i	0.548625	−	0.836068i
$28$	−30.5720	−	9.93345i	−1.09186	−	0.354766i
$29$	−25.4429	−	8.26690i	−0.877342	−	0.285066i	−0.164489	−	0.986379i	$-0.552597\pi$
$29$	−25.4429	−	8.26690i	−0.877342	−	0.285066i	−0.712853	+	0.701313i	$0.752597\pi$
$30$	12.5471	+	1.24360i	0.418235	+	0.0414532i
$31$	6.92473	+	21.3121i	0.223378	+	0.687488i	0.998452	+	0.0556172i	$0.0177127\pi$
$31$	6.92473	+	21.3121i	0.223378	+	0.687488i	−0.775074	+	0.631871i	$0.782287\pi$
$32$	31.2644			0.977012
$33$	4.60957	−	51.7418i	0.139684	−	1.56793i
$34$	15.1331	+	10.9948i	0.445091	+	0.323377i
$35$	−0.485015	+	48.7996i	−0.0138576	+	1.39427i
$36$	−29.1742	−	5.23972i	−0.810395	−	0.145548i
$37$	14.8003	−	20.3708i	0.400007	−	0.550562i	−0.560739	−	0.827993i	$-0.689483\pi$
$37$	14.8003	−	20.3708i	0.400007	−	0.550562i	0.960746	+	0.277430i	$0.0894828\pi$
$38$	−2.43974	−	1.77257i	−0.0642036	−	0.0466466i
$39$	7.97200	−	1.82716i	0.204410	−	0.0468503i
$40$	−9.18216	−	29.2456i	−0.229554	−	0.731141i
$41$	14.2504	−	19.6141i	0.347572	−	0.478391i	−0.599062	−	0.800703i	$-0.704460\pi$
$41$	14.2504	−	19.6141i	0.347572	−	0.478391i	0.946634	+	0.322311i	$0.104460\pi$
$42$	−2.18406	+	24.5158i	−0.0520014	+	0.583709i
$43$			50.8068i			1.18155i	0.806835	+	0.590777i	$0.201179\pi$
$43$			50.8068i			1.18155i	−0.806835	+	0.590777i	$0.798821\pi$
$44$	−54.2367	+	17.6226i	−1.23265	+	0.400513i
$45$	5.67796	+	44.6403i	0.126177	+	0.992008i
$46$	0.291916	−	0.898424i	0.00634599	−	0.0195310i
$47$	10.9874	−	33.8156i	0.233773	−	0.719481i	−0.763508	−	0.645798i	$-0.776525\pi$
$47$	10.9874	−	33.8156i	0.233773	−	0.719481i	0.997282	−	0.0736826i	$-0.0234752\pi$
$48$	5.37549	+	23.4535i	0.111989	+	0.488615i
$49$	−46.2654			−0.944192
$50$	−17.2430	+	12.0115i	−0.344860	+	0.240230i
$51$	−26.1828	+	61.4116i	−0.513388	+	1.20415i
$52$	−5.27755	−	7.26393i	−0.101491	−	0.139691i
$53$	−9.08989	+	27.9758i	−0.171507	+	0.527845i	−0.999457	−	0.0329575i	$-0.989507\pi$
$53$	−9.08989	+	27.9758i	−0.171507	+	0.527845i	0.827949	+	0.560803i	$0.189507\pi$
$54$	1.07987	+	22.6696i	0.0199977	+	0.419808i
$55$	50.1905	+	70.5452i	0.912555	+	1.28264i
$56$	56.9088	−	18.4908i	1.01623	−	0.330193i
$57$	4.22115	−	9.90071i	0.0740553	−	0.173697i
$58$	21.3865	−	6.94890i	0.368733	−	0.119809i
$59$	51.6779	−	71.1286i	0.875897	−	1.20557i	−0.101643	−	0.994821i	$-0.532410\pi$
$59$	51.6779	−	71.1286i	0.875897	−	1.20557i	0.977540	−	0.210748i	$-0.0675901\pi$
$60$	42.6359	−	24.9540i	0.710599	−	0.415900i
$61$	66.4241	−	48.2599i	1.08892	−	0.791146i	0.109703	−	0.993964i	$-0.465010\pi$
$61$	66.4241	−	48.2599i	1.08892	−	0.791146i	0.979216	+	0.202818i	$0.0650101\pi$
$62$	−15.2388	−	11.0716i	−0.245787	−	0.178575i
$63$	−87.0271	+	11.9493i	−1.38138	+	0.189672i
$64$	4.69420	−	3.41054i	0.0733469	−	0.0532896i
$65$	−8.12141	+	10.9477i	−0.124945	+	0.168426i
$66$	22.4296	+	37.4637i	0.339842	+	0.567631i
$67$	−68.7311	+	22.3321i	−1.02584	+	0.333315i	−0.773143	−	0.634231i	$-0.781317\pi$
$67$	−68.7311	+	22.3321i	−1.02584	+	0.333315i	−0.252694	+	0.967546i	$0.581317\pi$
$68$	73.2904			1.07780
$69$	3.35820	+	0.299175i	0.0486695	+	0.00433587i
$70$	−23.7808	−	33.4250i	−0.339725	−	0.477500i
$71$	44.5178	+	14.4647i	0.627011	+	0.203728i	0.605251	−	0.796035i	$-0.293073\pi$
$71$	44.5178	+	14.4647i	0.627011	+	0.203728i	0.0217603	+	0.999763i	$0.493073\pi$
$72$	49.6682	−	24.0300i	0.689836	−	0.333749i
$73$	−28.7539	−	39.5764i	−0.393889	−	0.542142i	0.565308	−	0.824880i	$-0.308757\pi$
$73$	−28.7539	−	39.5764i	−0.393889	−	0.542142i	−0.959197	+	0.282738i	$0.908757\pi$
$74$			21.1653i			0.286017i
$75$	−55.5341	−	50.4079i	−0.740455	−	0.672106i
$76$	−11.8158			−0.155471
$77$	−136.729	+	99.3397i	−1.77571	+	1.29013i
$78$	−4.51848	+	5.18129i	−0.0579293	+	0.0664268i
$79$	44.9043	−	138.201i	0.568409	−	1.74938i	−0.0891914	−	0.996015i	$-0.528428\pi$
$79$	44.9043	−	138.201i	0.568409	−	1.74938i	0.657600	−	0.753367i	$-0.271572\pi$
$80$	−32.2080	−	23.8931i	−0.402599	−	0.298664i
$81$	−78.0023	+	21.8320i	−0.962992	+	0.269530i
$82$			20.3790i			0.248524i
$83$	0.277581	+	0.854307i	0.00334435	+	0.0102929i	0.952715	−	0.303866i	$-0.0982775\pi$
$83$	0.277581	+	0.854307i	0.00334435	+	0.0102929i	−0.949370	+	0.314159i	$0.898278\pi$
$84$	49.5370	+	82.7405i	0.589726	+	0.985006i
$85$	−33.3300	−	106.158i	−0.392118	−	1.24891i
$86$	−25.1023	−	34.5504i	−0.291887	−	0.401748i
$87$	41.2261	+	68.8590i	0.473863	+	0.791483i
$88$	62.3967	−	85.8816i	0.709053	−	0.975928i
$89$	−20.9981	−	28.9013i	−0.235933	−	0.324734i	0.674590	−	0.738193i	$-0.264321\pi$
$89$	−20.9981	−	28.9013i	−0.235933	−	0.324734i	−0.910523	+	0.413459i	$0.864321\pi$
$90$	−25.9168	−	27.5516i	−0.287965	−	0.306129i
$91$	−21.5273	−	15.6405i	−0.236563	−	0.171873i
$92$	−1.14376	−	3.52013i	−0.0124322	−	0.0382623i
$93$	26.3657	−	61.8407i	0.283502	−	0.664954i
$94$	9.23562	+	28.4243i	0.0982513	+	0.302386i
$95$	5.37342	+	17.1146i	0.0565623	+	0.180154i
$96$	−70.6889	−	61.6461i	−0.736342	−	0.642147i
$97$	116.093	+	37.7208i	1.19683	+	0.388874i	0.838594	−	0.544757i	$-0.183378\pi$
$97$	116.093	+	37.7208i	1.19683	+	0.388874i	0.358237	+	0.933631i	$0.383378\pi$
$98$	31.4621	−	22.8585i	0.321041	−	0.233250i
$99$	−112.445	+	107.899i	−1.13581	+	1.08989i
$100$	−26.9946	+	77.7851i	−0.269946	+	0.777851i
$101$		−	28.8103i		−	0.285251i	−0.989777	−	0.142625i	$-0.954446\pi$
$101$		−	28.8103i		−	0.285251i	0.989777	−	0.142625i	$-0.0455544\pi$
$102$	−12.5367	−	54.6983i	−0.122909	−	0.536257i
$103$	−6.50394	−	2.11326i	−0.0631451	−	0.0205171i	0.277274	−	0.960791i	$-0.410569\pi$
$103$	−6.50394	−	2.11326i	−0.0631451	−	0.0205171i	−0.340419	+	0.940274i	$0.610569\pi$
$104$	15.8956	+	5.16478i	0.152842	+	0.0496614i
$105$	97.3181	−	109.380i	0.926839	−	1.04171i
$106$	−7.64067	−	23.5156i	−0.0720818	−	0.221845i
$107$	−117.493			−1.09806			−0.549031	−	0.835802i	$-0.685003\pi$
$107$	−117.493			−1.09806			−0.549031	+	0.835802i	$0.685003\pi$
$108$	55.6314	+	69.3718i	0.515106	+	0.642331i
$109$	78.6436	+	57.1379i	0.721501	+	0.524201i	0.886863	−	0.462032i	$-0.152879\pi$
$109$	78.6436	+	57.1379i	0.721501	+	0.524201i	−0.165362	+	0.986233i	$0.552879\pi$
$110$	−68.9859	−	23.1753i	−0.627144	−	0.210685i
$111$	−73.6299	+	16.8758i	−0.663332	+	0.152034i
$112$	46.0141	−	63.3329i	0.410840	−	0.565473i
$113$	116.803	+	84.8623i	1.03365	+	0.750994i	0.969037	−	0.246916i	$-0.0794172\pi$
$113$	116.803	+	84.8623i	1.03365	+	0.750994i	0.0646176	+	0.997910i	$0.479417\pi$
$114$	2.02115	+	8.81838i	0.0177294	+	0.0773542i
$115$	−4.57860	+	3.25752i	−0.0398139	+	0.0283263i
$116$	51.7880	−	71.2801i	0.446449	−	0.614484i
$117$	−21.6275	−	11.5877i	−0.184850	−	0.0990403i
$118$			73.9026i			0.626293i
$119$	206.572	−	67.1192i	1.73590	−	0.564027i
$120$	−36.9047	+	84.2295i	−0.307539	+	0.701913i
$121$	−55.2612	+	170.076i	−0.456704	+	1.40559i
$122$	−21.3267	+	65.6368i	−0.174809	+	0.538006i
$123$	−70.8946	+	16.2489i	−0.576379	+	0.132105i
$124$	−73.8025			−0.595181
$125$	124.944	+	3.72642i	0.999556	+	0.0298113i
$126$	53.2775	−	51.1238i	0.422838	−	0.405744i
$127$	1.94702	+	2.67985i	0.0153309	+	0.0211011i	0.816614	−	0.577185i	$-0.195849\pi$
$127$	1.94702	+	2.67985i	0.0153309	+	0.0211011i	−0.801283	+	0.598286i	$0.795849\pi$
$128$	−40.1521	+	123.575i	−0.313688	+	0.965433i
$129$	100.179	−	114.874i	0.776583	−	0.890499i
$130$	0.113874	−	11.4574i	0.000875953	−	0.0881337i
$131$	−149.348	+	48.5260i	−1.14006	+	0.370427i	−0.817390	−	0.576085i	$-0.804580\pi$
$131$	−149.348	+	48.5260i	−1.14006	+	0.370427i	−0.322668	+	0.946512i	$0.604580\pi$
$132$	157.377	+	67.0975i	1.19225	+	0.508314i
$133$	−33.3032	+	10.8209i	−0.250400	+	0.0813599i
$134$	35.7058	−	49.1448i	0.266461	−	0.366753i
$135$	75.1825	−	112.128i	0.556908	−	0.830575i
$136$	−110.372	+	80.1902i	−0.811561	+	0.589634i
$137$	−78.9672	−	57.3730i	−0.576403	−	0.418781i	0.261023	−	0.965333i	$-0.415940\pi$
$137$	−78.9672	−	57.3730i	−0.576403	−	0.418781i	−0.837425	+	0.546552i	$0.815940\pi$
$138$	−2.43150	+	1.45575i	−0.0176196	+	0.0105489i
$139$	−158.146	+	114.900i	−1.13774	+	0.826616i	−0.986803	−	0.161927i	$-0.948229\pi$
$139$	−158.146	+	114.900i	−1.13774	+	0.826616i	−0.150937	+	0.988543i	$0.548229\pi$
$140$	−152.359	−	51.1840i	−1.08828	−	0.365600i
$141$	−91.5189	+	54.7926i	−0.649070	+	0.388600i
$142$	−37.4202	+	12.1586i	−0.263523	+	0.0856238i
$143$	−47.2063			−0.330114
$144$	34.0909	−	63.6277i	0.236742	−	0.441859i
$145$	−126.797	−	42.5968i	−0.874465	−	0.293771i
$146$	39.1073	+	12.7067i	0.267858	+	0.0870324i
$147$	104.606	+	91.2246i	0.711607	+	0.620576i
$148$	48.7438	+	67.0901i	0.329350	+	0.453312i
$149$		−	138.880i		−	0.932082i	−0.884763	−	0.466041i	$-0.845680\pi$
$149$		−	138.880i		−	0.932082i	0.884763	−	0.466041i	$-0.154320\pi$
$150$	62.6704	+	6.84116i	0.417802	+	0.0456077i
$151$	62.2231			0.412073			0.206037	−	0.978544i	$-0.433943\pi$
$151$	62.2231			0.412073			0.206037	+	0.978544i	$0.433943\pi$
$152$	17.7941	−	12.9282i	0.117066	−	0.0850536i
$153$	180.289	−	87.2255i	1.17836	−	0.570101i
$154$	43.8995	−	135.109i	0.285062	−	0.877330i
$155$	33.5629	+	106.899i	0.216535	+	0.689674i
$156$	−2.39022	+	26.8299i	−0.0153219	+	0.171986i
$157$			188.671i			1.20173i	0.799352	+	0.600863i	$0.205176\pi$
$157$			188.671i			1.20173i	−0.799352	+	0.600863i	$0.794824\pi$
$158$	37.7451	+	116.168i	0.238893	+	0.735238i
$159$	75.7140	−	45.3302i	0.476189	−	0.285096i
$160$	156.314	+	1.55359i	0.976964	+	0.00970996i
$161$	−6.44745	−	8.87415i	−0.0400463	−	0.0551190i
$162$	42.2577	−	53.3854i	0.260850	−	0.329539i
$163$	16.8829	−	23.2373i	0.103576	−	0.142560i	−0.754083	−	0.656779i	$-0.771918\pi$
$163$	16.8829	−	23.2373i	0.103576	−	0.142560i	0.857659	+	0.514219i	$0.171918\pi$
$164$	46.9330	+	64.5978i	0.286177	+	0.393889i
$165$	25.6179	−	258.467i	0.155260	−	1.56647i
$166$	−0.610855	−	0.443812i	−0.00367985	−	0.00267357i
$167$	54.3150	+	167.164i	0.325240	+	1.00098i	0.971332	+	0.237726i	$0.0764020\pi$
$167$	54.3150	+	167.164i	0.325240	+	1.00098i	−0.646093	+	0.763259i	$0.723598\pi$
$168$	−165.131	−	70.4033i	−0.982920	−	0.419067i
$169$	49.9271	+	153.660i	0.295427	+	0.909230i
$170$	75.1153	+	55.7234i	0.441855	+	0.327785i
$171$	−29.0659	+	14.0624i	−0.169976	+	0.0822362i
$172$	−159.140	−	51.7076i	−0.925231	−	0.300626i
$173$	−35.5781	+	25.8490i	−0.205654	+	0.149416i	−0.685845	−	0.727748i	$-0.740567\pi$
$173$	−35.5781	+	25.8490i	−0.205654	+	0.149416i	0.480191	+	0.877164i	$0.340567\pi$
$174$	−62.0566	−	26.4577i	−0.356647	−	0.152056i
$175$	−4.84991	+	243.962i	−0.0277138	+	1.39407i
$176$		−	138.880i		−	0.789093i
$177$	−257.093	+	58.9250i	−1.45250	+	0.332910i
$178$	28.5588	+	9.27931i	0.160443	+	0.0521310i
$179$	−290.732	−	94.4646i	−1.62420	−	0.527735i	−0.651274	−	0.758843i	$-0.725765\pi$
$179$	−290.732	−	94.4646i	−1.62420	−	0.527735i	−0.972928	+	0.231107i	$0.925765\pi$
$180$	−145.603	−	27.6470i	−0.808908	−	0.153595i
$181$	−43.4748	−	133.802i	−0.240192	−	0.739236i	−0.996390	−	0.0848927i	$-0.972945\pi$
$181$	−43.4748	−	133.802i	−0.240192	−	0.739236i	0.756198	−	0.654343i	$-0.227055\pi$
$182$	22.3668			0.122895
$183$	−245.342	−	21.8570i	−1.34067	−	0.119437i
$184$	5.57398	+	4.04973i	0.0302934	+	0.0220094i
$185$	75.0099	−	101.114i	0.405459	−	0.546560i
$186$	12.6243	+	55.0804i	0.0678725	+	0.296131i
$187$	226.492	−	311.739i	1.21118	−	1.66705i
$188$	94.7368	+	68.8303i	0.503919	+	0.366119i
$189$	220.330	+	144.580i	1.16577	+	0.764972i
$190$	−12.1100	−	8.98366i	−0.0637368	−	0.0472824i
$191$	1.85212	−	2.54922i	0.00969695	−	0.0133467i	−0.804141	−	0.594439i	$-0.797374\pi$
$191$	1.85212	−	2.54922i	0.00969695	−	0.0133467i	0.813838	+	0.581092i	$0.197374\pi$
$192$	−17.3384	−	1.54464i	−0.0903041	−	0.00804500i
$193$		−	82.4800i		−	0.427357i	−0.976904	−	0.213679i	$-0.931455\pi$
$193$		−	82.4800i		−	0.427357i	0.976904	−	0.213679i	$-0.0685445\pi$
$194$	−97.5838	+	31.7069i	−0.503009	+	0.163438i
$195$	39.9488	−	8.73921i	0.204866	−	0.0448165i
$196$	47.0857	−	144.915i	0.240233	−	0.739362i
$197$	64.3443	−	198.031i	0.326621	−	1.00524i	−0.644083	−	0.764956i	$-0.722761\pi$
$197$	64.3443	−	198.031i	0.326621	−	1.00524i	0.970704	−	0.240280i	$-0.0772392\pi$
$198$	23.1562	−	128.931i	0.116951	−	0.651169i
$199$	−129.582			−0.651168			−0.325584	−	0.945513i	$-0.605561\pi$
$199$	−129.582			−0.651168			−0.325584	+	0.945513i	$0.605561\pi$
$200$	−44.4552	−	146.677i	−0.222276	−	0.733386i
$201$	199.435	+	85.0289i	0.992214	+	0.423029i
$202$	14.2344	+	19.5920i	0.0704675	+	0.0969901i
$203$	80.6883	−	248.333i	0.397479	−	1.22332i
$204$	−165.710	−	144.512i	−0.812303	−	0.708390i
$205$	72.2234	−	97.3573i	0.352309	−	0.474914i
$206$	5.46701	−	1.77634i	0.0265389	−	0.00862301i
$207$	−7.00299	−	7.29802i	−0.0338309	−	0.0352561i
$208$	20.7957	−	6.75694i	0.0999795	−	0.0324853i
$209$	−36.5147	+	50.2581i	−0.174711	+	0.240470i
$210$	−12.1380	+	122.464i	−0.0578000	+	0.583163i
$211$	119.794	−	87.0352i	0.567743	−	0.412489i	−0.266542	−	0.963823i	$-0.585881\pi$
$211$	119.794	−	87.0352i	0.567743	−	0.412489i	0.834285	+	0.551334i	$0.185881\pi$
$212$	−78.3762	−	56.9436i	−0.369699	−	0.268602i
$213$	−72.1338	−	120.483i	−0.338656	−	0.565650i
$214$	79.8990	−	58.0500i	0.373360	−	0.271262i
$215$	−2.52470	+	254.021i	−0.0117428	+	1.18150i
$216$	−159.681	−	43.6023i	−0.739265	−	0.201862i
$217$	−208.015	+	67.5881i	−0.958594	+	0.311466i
$218$	−81.7107			−0.374820
$219$	−13.0227	+	146.178i	−0.0594645	+	0.667481i
$220$	−272.046	+	85.4134i	−1.23657	+	0.388243i
$221$	57.6988	+	18.7475i	0.261080	+	0.0848302i
$222$	41.7330	−	47.8547i	0.187986	−	0.215562i
$223$	33.7784	+	46.4920i	0.151473	+	0.208484i	0.878009	−	0.478643i	$-0.158871\pi$
$223$	33.7784	+	46.4920i	0.151473	+	0.208484i	−0.726537	+	0.687128i	$0.758871\pi$
$224$			305.153i			1.36229i
$225$	26.1701	+	223.473i	0.116312	+	0.993213i
$226$	−121.358			−0.536983
$227$	244.647	−	177.746i	1.07774	−	0.783023i	0.100451	−	0.994942i	$-0.467971\pi$
$227$	244.647	−	177.746i	1.07774	−	0.783023i	0.977287	+	0.211919i	$0.0679714\pi$
$228$	26.7155	+	23.2980i	0.117173	+	0.102184i
$229$	80.8867	−	248.944i	0.353217	−	1.08709i	−0.603819	−	0.797122i	$-0.706355\pi$
$229$	80.8867	−	248.944i	0.353217	−	1.08709i	0.957036	−	0.289969i	$-0.0936451\pi$
$230$	1.50415	−	4.47739i	0.00653978	−	0.0194669i
$231$	505.020	+	44.9912i	2.18624	+	0.194767i
$232$			164.008i			0.706933i
$233$	26.3563	+	81.1163i	0.113117	+	0.348139i	0.991550	−	0.129728i	$-0.0414103\pi$
$233$	26.3563	+	81.1163i	0.113117	+	0.348139i	−0.878433	+	0.477866i	$0.841410\pi$
$234$	20.4326	−	2.80552i	0.0873188	−	0.0119894i
$235$	56.6144	−	168.524i	0.240912	−	0.717122i
$236$	170.198	+	234.258i	0.721180	+	0.992619i
$237$	−374.029	+	223.932i	−1.57818	+	0.944862i
$238$	−107.314	+	147.705i	−0.450899	+	0.620609i
$239$	−34.7626	−	47.8466i	−0.145450	−	0.200195i	0.730076	−	0.683366i	$-0.239485\pi$
$239$	−34.7626	−	47.8466i	−0.145450	−	0.200195i	−0.875526	+	0.483171i	$0.839485\pi$
$240$	25.7106	+	117.529i	0.107128	+	0.489704i
$241$	202.139	+	146.863i	0.838752	+	0.609389i	0.922022	−	0.387138i	$-0.126536\pi$
$241$	202.139	+	146.863i	0.838752	+	0.609389i	−0.0832701	+	0.996527i	$0.526536\pi$
$242$	−46.4508	−	142.961i	−0.191945	−	0.590747i
$243$	219.411	+	104.440i	0.902926	+	0.429796i
$244$	83.5604	+	257.172i	0.342461	+	1.05399i
$245$	−231.316	−	2.29903i	−0.944145	−	0.00938378i
$246$	40.1826	−	46.0770i	0.163344	−	0.187305i
$247$	−9.30212	−	3.02244i	−0.0376604	−	0.0122366i
$248$	111.143	−	80.7505i	0.448159	−	0.325607i
$249$	1.05688	−	2.47892i	0.00424451	−	0.00995548i
$250$	−86.8076	+	59.1977i	−0.347231	+	0.236791i
$251$			174.558i			0.695449i	0.937597	+	0.347725i	$0.113046\pi$
$251$			174.558i			0.695449i	−0.937597	+	0.347725i	$0.886954\pi$
$252$	51.1418	−	284.752i	0.202944	−	1.12997i
$253$	−18.5074	−	6.01341i	−0.0731517	−	0.0237684i
$254$	−2.64808	−	0.860414i	−0.0104255	−	0.00338746i
$255$	−133.959	+	305.742i	−0.525330	+	1.19899i
$256$	−26.5785	−	81.8001i	−0.103822	−	0.319532i
$257$	189.705			0.738151			0.369076	−	0.929399i	$-0.379674\pi$
$257$	189.705			0.738151			0.369076	+	0.929399i	$0.379674\pi$
$258$	−11.3689	+	127.614i	−0.0440655	+	0.494629i
$259$	198.827	+	144.456i	0.767673	+	0.557747i
$260$	−26.0255	−	36.5801i	−0.100098	−	0.140693i
$261$	42.5616	−	236.979i	0.163071	−	0.907964i
$262$	77.5861	−	106.788i	0.296130	−	0.407588i
$263$	−371.284	−	269.754i	−1.41173	−	1.02568i	−0.993069	−	0.117537i	$-0.962500\pi$
$263$	−371.284	−	269.754i	−1.41173	−	1.02568i	−0.418659	−	0.908143i	$-0.637500\pi$
$264$	−310.418	+	71.1469i	−1.17582	+	0.269496i
$265$	−46.8374	+	139.420i	−0.176745	+	0.526115i
$266$	17.3010	−	23.8128i	0.0650414	−	0.0895218i
$267$	−9.51007	+	106.749i	−0.0356182	+	0.399810i
$268$		−	238.011i		−	0.888102i
$269$	−53.7617	+	17.4682i	−0.199858	+	0.0649377i	−0.407235	−	0.913323i	$-0.633507\pi$
$269$	−53.7617	+	17.4682i	−0.199858	+	0.0649377i	0.207378	+	0.978261i	$0.433507\pi$
$270$	4.27260	+	113.396i	0.0158245	+	0.419986i
$271$	16.0818	−	49.4946i	0.0593423	−	0.182637i	−0.916991	−	0.398908i	$-0.869389\pi$
$271$	16.0818	−	49.4946i	0.0593423	−	0.182637i	0.976333	+	0.216271i	$0.0693894\pi$
$272$	−55.1548	+	169.749i	−0.202775	+	0.624077i
$273$	17.8338	+	77.8099i	0.0653254	+	0.285018i
$274$	82.0469			0.299441
$275$	247.435	+	355.203i	0.899763	+	1.29165i
$276$	−4.35483	+	10.2142i	−0.0157784	+	0.0370081i
$277$	−163.205	−	224.632i	−0.589186	−	0.810945i	0.405478	−	0.914105i	$-0.367105\pi$
$277$	−163.205	−	224.632i	−0.589186	−	0.810945i	−0.994665	+	0.103159i	$0.967105\pi$
$278$	50.7757	−	156.271i	0.182646	−	0.562127i
$279$	−181.549	+	87.8350i	−0.650712	+	0.314821i
$280$	285.449	−	89.6215i	1.01946	−	0.320077i
$281$	−11.6791	+	3.79478i	−0.0415627	+	0.0135046i	−0.329725	−	0.944077i	$-0.606956\pi$
$281$	−11.6791	+	3.79478i	−0.0415627	+	0.0135046i	0.288162	+	0.957582i	$0.406956\pi$
$282$	35.1644	−	82.4780i	0.124696	−	0.292475i
$283$	−48.6286	+	15.8004i	−0.171833	+	0.0558318i	−0.393670	−	0.919252i	$-0.628795\pi$
$283$	−48.6286	+	15.8004i	−0.171833	+	0.0558318i	0.221837	+	0.975084i	$0.428795\pi$
$284$	−90.6142	+	124.720i	−0.319064	+	0.439154i
$285$	21.5967	−	49.2913i	0.0757780	−	0.172952i
$286$	32.1019	−	23.3234i	0.112245	−	0.0815504i
$287$	191.441	+	139.090i	0.667042	+	0.484634i
$288$	38.2759	+	278.764i	0.132903	+	0.967931i
$289$	−166.831	+	121.210i	−0.577269	+	0.419411i
$290$	107.273	−	33.6800i	0.369905	−	0.116138i
$291$	−188.109	−	314.194i	−0.646423	−	1.07971i
$292$	153.227	−	49.7864i	0.524750	−	0.170502i
$293$	−360.580			−1.23065			−0.615324	−	0.788274i	$-0.710975\pi$
$293$	−360.580			−1.23065			−0.615324	+	0.788274i	$0.710975\pi$
$294$	−116.207	−	10.3527i	−0.395264	−	0.0352132i
$295$	261.912	−	353.057i	0.887836	−	1.19680i
$296$	−146.812	−	47.7022i	−0.495988	−	0.161156i
$297$	466.991	−	22.2452i	1.57236	−	0.0748998i
$298$	68.6171	+	94.4433i	0.230259	+	0.316924i
$299$		−	3.06384i		−	0.0102469i
$300$	214.409	−	122.645i	0.714697	−	0.408817i
$301$	−495.895			−1.64749
$302$	−42.3138	+	30.7428i	−0.140112	+	0.101797i
$303$	−56.8073	+	65.1402i	−0.187483	+	0.214984i
$304$	8.89198	−	27.3667i	0.0292499	−	0.0900221i
$305$	334.502	−	237.987i	1.09673	−	0.780285i
$306$	−79.5067	+	148.392i	−0.259826	+	0.484942i
$307$		−	142.048i		−	0.462696i	−0.972871	−	0.231348i	$-0.925686\pi$
$307$		−	142.048i		−	0.462696i	0.972871	−	0.231348i	$-0.0743137\pi$
$308$	−172.003	−	529.372i	−0.558453	−	1.71874i
$309$	10.5386	+	17.6023i	0.0341054	+	0.0569655i
$310$	−75.6402	−	56.1128i	−0.244001	−	0.181009i
$311$	38.9964	+	53.6740i	0.125390	+	0.172585i	0.867097	−	0.498139i	$-0.165983\pi$
$311$	38.9964	+	53.6740i	0.125390	+	0.172585i	−0.741706	+	0.670725i	$0.765983\pi$
$312$	−25.7562	−	43.0199i	−0.0825518	−	0.137884i
$313$	−23.9683	+	32.9895i	−0.0765759	+	0.105398i	−0.845587	−	0.533838i	$-0.820749\pi$
$313$	−23.9683	+	32.9895i	−0.0765759	+	0.105398i	0.769011	+	0.639236i	$0.220749\pi$
$314$	−93.2174	−	128.303i	−0.296871	−	0.408608i
$315$	−435.708	+	55.4191i	−1.38320	+	0.175934i
$316$	387.180	+	281.303i	1.22525	+	0.890199i
$317$	13.0912	+	40.2905i	0.0412971	+	0.127099i	0.969579	−	0.244777i	$-0.0787146\pi$
$317$	13.0912	+	40.2905i	0.0412971	+	0.127099i	−0.928282	+	0.371876i	$0.878715\pi$
$318$	−29.0917	+	68.2344i	−0.0914832	+	0.214574i
$319$	−143.146	−	440.558i	−0.448734	−	1.38106i
$320$	23.6393	−	16.8186i	0.0738729	−	0.0525581i
$321$	265.651	+	231.668i	0.827574	+	0.721707i
$322$	8.76898	+	2.84921i	0.0272328	+	0.00884849i
$323$	64.5901	−	46.9275i	0.199969	−	0.145286i
$324$	11.0022	−	266.542i	0.0339573	−	0.822661i
$325$	−41.1491	+	54.3322i	−0.126613	+	0.167176i
$326$			24.1435i			0.0740599i
$327$	−65.1507	−	284.256i	−0.199238	−	0.869284i
$328$	−141.358	−	45.9302i	−0.430971	−	0.140031i
$329$	330.054	+	107.241i	1.00320	+	0.325960i
$330$	110.281	+	188.424i	0.334184	+	0.570981i
$331$	−64.7347	−	199.233i	−0.195573	−	0.601912i	−0.999969	−	0.00781898i	$-0.997511\pi$
$331$	−64.7347	−	199.233i	−0.195573	−	0.601912i	0.804396	−	0.594093i	$-0.202489\pi$
$332$	−2.95841			−0.00891086
$333$	199.753	+	107.025i	0.599857	+	0.321396i
$334$	−119.528	−	86.8419i	−0.357867	−	0.260006i
$335$	−344.748	+	108.240i	−1.02910	+	0.323103i
$336$	−228.916	+	52.4669i	−0.681297	+	0.156151i
$337$	−43.6519	+	60.0817i	−0.129531	+	0.178284i	−0.868856	−	0.495064i	$-0.835145\pi$
$337$	−43.6519	+	60.0817i	−0.129531	+	0.178284i	0.739325	+	0.673348i	$0.235145\pi$
$338$	−109.872	−	79.8263i	−0.325064	−	0.236173i
$339$	−96.7630	−	422.182i	−0.285437	−	1.24538i
$340$	366.434	+	3.64195i	1.07775	+	0.0107116i
$341$	−228.074	+	313.917i	−0.668839	+	0.920578i
$342$	12.8180	−	23.9236i	0.0374795	−	0.0699521i
$343$			26.6908i			0.0778156i
$344$	296.233	−	96.2521i	0.861144	−	0.279803i
$345$	16.7753	+	1.66268i	0.0486241	+	0.00481935i
$346$	11.4230	−	35.1564i	0.0330145	−	0.101608i
$347$	45.9693	−	141.479i	0.132476	−	0.407721i	−0.862713	−	0.505695i	$-0.831236\pi$
$347$	45.9693	−	141.479i	0.132476	−	0.407721i	0.995189	+	0.0979741i	$0.0312362\pi$
$348$	−257.641	+	59.0506i	−0.740347	+	0.169686i
$349$	−328.417			−0.941023			−0.470511	−	0.882394i	$-0.655931\pi$
$349$	−328.417			−0.941023			−0.470511	+	0.882394i	$0.655931\pi$
$350$	−117.237	−	168.299i	−0.334963	−	0.480853i
$351$	26.0515	+	68.8442i	0.0742207	+	0.196137i
$352$	318.204	+	437.970i	0.903988	+	1.24423i
$353$	−213.661	+	657.582i	−0.605273	+	1.86284i	−0.110372	+	0.993890i	$0.535204\pi$
$353$	−213.661	+	657.582i	−0.605273	+	1.86284i	−0.494901	+	0.868949i	$0.664796\pi$
$354$	145.719	−	167.094i	0.411635	−	0.472017i
$355$	221.859	+	74.5321i	0.624955	+	0.209950i
$356$	111.897	−	36.3574i	0.314316	−	0.102128i
$357$	−599.402	−	255.554i	−1.67900	−	0.715839i
$358$	244.380	−	79.4040i	0.682627	−	0.221799i
$359$	−56.7241	+	78.0740i	−0.158006	+	0.217476i	−0.880679	−	0.473714i	$-0.842913\pi$
$359$	−56.7241	+	78.0740i	−0.158006	+	0.217476i	0.722673	+	0.691190i	$0.242913\pi$
$360$	249.523	−	117.676i	0.693118	−	0.326877i
$361$	281.642	−	204.625i	0.780172	−	0.566828i
$362$	95.6723	+	69.5100i	0.264288	+	0.192016i
$363$	460.297	−	275.581i	1.26804	−	0.759176i
$364$	70.8989	−	51.5110i	0.194777	−	0.141514i
$365$	−141.796	−	199.301i	−0.388482	−	0.546030i
$366$	177.640	−	106.354i	0.485356	−	0.290584i
$367$	−203.965	+	66.2723i	−0.555764	+	0.180579i	−0.573414	−	0.819266i	$-0.694381\pi$
$367$	−203.965	+	66.2723i	−0.555764	+	0.180579i	0.0176504	+	0.999844i	$0.494381\pi$
$368$	9.01376			0.0244939
$369$	192.332	+	103.049i	0.521225	+	0.279266i
$370$	−1.05175	+	105.821i	−0.00284256	+	0.286003i
$371$	−273.055	−	88.7209i	−0.735997	−	0.239140i
$372$	166.868	+	145.521i	0.448569	+	0.391186i
$373$	−113.583	−	156.333i	−0.304511	−	0.419123i	0.629149	−	0.777285i	$-0.283404\pi$
$373$	−113.583	−	156.333i	−0.304511	−	0.419123i	−0.933660	+	0.358162i	$0.883404\pi$
$374$			323.897i			0.866034i
$375$	−275.152	−	254.787i	−0.733739	−	0.679432i
$376$	−217.980			−0.579734
$377$	59.0040	−	42.8689i	0.156509	−	0.113711i
$378$	−221.265	+	10.5400i	−0.585357	+	0.0278836i
$379$	−147.272	+	453.255i	−0.388579	+	1.19592i	0.545271	+	0.838260i	$0.316427\pi$
$379$	−147.272	+	453.255i	−0.388579	+	1.19592i	−0.933850	+	0.357664i	$0.883573\pi$
$380$	−59.0760	−	0.587151i	−0.155463	−	0.00154513i
$381$	0.881811	−	9.89821i	0.00231446	−	0.0259796i
$382$			2.64864i			0.00693362i
$383$	−74.5277	−	229.373i	−0.194589	−	0.598884i	−0.999981	−	0.00614145i	$-0.998045\pi$
$383$	−74.5277	−	229.373i	−0.194589	−	0.598884i	0.805392	−	0.592743i	$-0.201955\pi$
$384$	334.446	−	200.234i	0.870953	−	0.521442i
$385$	−688.550	+	489.880i	−1.78844	+	1.27242i
$386$	40.7512	+	56.0892i	0.105573	+	0.145309i
$387$	−453.011	+	62.2010i	−1.17057	+	0.160726i
$388$	−236.302	+	325.242i	−0.609026	+	0.838252i
$389$	366.878	+	504.964i	0.943130	+	1.29811i	0.954512	+	0.298172i	$0.0963770\pi$
$389$	366.878	+	504.964i	0.943130	+	1.29811i	−0.0113819	+	0.999935i	$0.503623\pi$
$390$	−22.8488	+	25.6806i	−0.0585866	+	0.0658478i
$391$	20.2328	+	14.7000i	0.0517463	+	0.0375959i
$392$	87.6485	+	269.754i	0.223593	+	0.688149i
$393$	433.357	+	184.761i	1.10269	+	0.470131i
$394$	54.0858	+	166.459i	0.137274	+	0.422485i
$395$	231.378	−	688.740i	0.585767	−	1.74365i
$396$	−223.529	−	462.018i	−0.564467	−	1.16671i
$397$	−436.912	−	141.961i	−1.10053	−	0.357585i	−0.298226	−	0.954495i	$-0.596395\pi$
$397$	−436.912	−	141.961i	−1.10053	−	0.357585i	−0.802308	+	0.596910i	$0.796395\pi$
$398$	88.1205	−	64.0233i	0.221408	−	0.160863i
$399$	96.6348	+	41.2002i	0.242193	+	0.103259i
$400$	−159.845	−	121.060i	−0.399611	−	0.302650i
$401$		−	671.456i		−	1.67445i	−0.546855	−	0.837227i	$-0.684175\pi$
$401$		−	671.456i		−	1.67445i	0.546855	−	0.837227i	$-0.315825\pi$
$402$	−177.633	+	40.7130i	−0.441873	+	0.101276i
$403$	−58.1019	−	18.8785i	−0.144173	−	0.0468448i
$404$	90.2412	+	29.3211i	0.223369	+	0.0725771i
$405$	−391.077	+	105.278i	−0.965623	+	0.259946i
$406$	67.8240	+	208.741i	0.167054	+	0.514140i
$407$	436.001			1.07126
$408$	407.668	+	36.3183i	0.999187	+	0.0890155i
$409$	181.136	+	131.603i	0.442875	+	0.321767i	0.786776	−	0.617238i	$-0.211749\pi$
$409$	181.136	+	131.603i	0.442875	+	0.321767i	−0.343901	+	0.939006i	$0.611749\pi$
$410$	−1.01268	+	101.890i	−0.00246994	+	0.248512i
$411$	65.4187	+	285.425i	0.159170	+	0.694466i
$412$	13.2385	−	18.2213i	0.0321323	−	0.0442264i
$413$	694.244	+	504.397i	1.68098	+	1.22130i
$414$	8.36804	+	1.50291i	0.0202126	+	0.00363022i
$415$	1.34538	+	4.28512i	0.00324189	+	0.0103256i
$416$	−50.0994	+	68.9559i	−0.120431	+	0.165759i
$417$	584.124	+	52.0383i	1.40078	+	0.124792i
$418$		−	52.2182i		−	0.124924i
$419$	−523.183	+	169.993i	−1.24865	+	0.405710i	−0.857436	−	0.514591i	$-0.827944\pi$
$419$	−523.183	+	169.993i	−1.24865	+	0.405710i	−0.391211	+	0.920301i	$0.627944\pi$
$420$	243.561	+	416.144i	0.579907	+	0.990818i
$421$	−245.390	+	755.232i	−0.582874	+	1.79390i	0.0247725	+	0.999693i	$0.492114\pi$
$421$	−245.390	+	755.232i	−0.582874	+	1.79390i	−0.607646	+	0.794208i	$0.707886\pi$
$422$	−38.4620	+	118.374i	−0.0911422	+	0.280507i
$423$	314.963	+	56.5677i	0.744593	+	0.133730i
$424$	180.336			0.425320
$425$	−161.367	−	532.419i	−0.379686	−	1.25275i
$426$	108.581	+	46.2935i	0.254885	+	0.108670i
$427$	471.036	+	648.325i	1.10313	+	1.51833i
$428$	119.576	−	368.016i	0.279383	−	0.859851i
$429$	106.734	+	93.0799i	0.248796	+	0.216970i
$430$	−123.788	−	173.991i	−0.287880	−	0.404630i
$431$	−559.361	+	181.747i	−1.29782	+	0.421687i	−0.874823	−	0.484443i	$-0.839022\pi$
$431$	−559.361	+	181.747i	−1.29782	+	0.421687i	−0.422998	+	0.906131i	$0.639022\pi$
$432$	−202.539	+	76.6430i	−0.468839	+	0.177414i
$433$	−74.5711	+	24.2296i	−0.172220	+	0.0559576i	−0.393858	−	0.919171i	$-0.628860\pi$
$433$	−74.5711	+	24.2296i	−0.172220	+	0.0559576i	0.221638	+	0.975129i	$0.428860\pi$
$434$	108.064	−	148.737i	0.248995	−	0.342712i
$435$	202.698	+	346.327i	0.465973	+	0.796153i
$436$	−259.008	+	188.181i	−0.594056	+	0.431607i
$437$	−3.26191	−	2.36991i	−0.00746431	−	0.00542314i
$438$	−63.3670	−	105.840i	−0.144674	−	0.241645i
$439$	651.540	−	473.372i	1.48415	−	1.07830i	0.507955	−	0.861384i	$-0.330402\pi$
$439$	651.540	−	473.372i	1.48415	−	1.07830i	0.976191	−	0.216912i	$-0.0695984\pi$
$440$	316.235	−	426.286i	0.718717	−	0.968832i
$441$	−56.6412	−	412.518i	−0.128438	−	0.935415i
$442$	−48.4998	+	15.7585i	−0.109728	+	0.0356528i
$443$	600.844			1.35631			0.678153	−	0.734921i	$-0.262781\pi$
$443$	600.844			1.35631			0.678153	+	0.734921i	$0.262781\pi$
$444$	22.0762	−	247.802i	0.0497212	−	0.558114i
$445$	−103.549	−	145.543i	−0.232694	−	0.327063i
$446$	−45.9410	−	14.9271i	−0.103007	−	0.0334689i
$447$	−273.839	+	314.009i	−0.612616	+	0.702480i
$448$	33.2882	+	45.8173i	0.0743040	+	0.102271i
$449$		−	160.308i		−	0.357034i	−0.983937	−	0.178517i	$-0.942870\pi$
$449$		−	160.308i		−	0.357034i	0.983937	−	0.178517i	$-0.0571300\pi$
$450$	−128.209	−	139.039i	−0.284908	−	0.308976i
$451$	419.804			0.930829
$452$	−384.684	+	279.489i	−0.851071	+	0.618339i
$453$	−140.686	−	122.689i	−0.310566	−	0.270838i
$454$	−78.5484	+	241.747i	−0.173014	+	0.532482i
$455$	−106.854	−	79.2683i	−0.234844	−	0.174216i
$456$	−65.7238	−	5.85519i	−0.144131	−	0.0128403i
$457$			525.631i			1.15018i	0.818091	+	0.575089i	$0.195032\pi$
$457$			525.631i			1.15018i	−0.818091	+	0.575089i	$0.804968\pi$
$458$	67.9909	+	209.254i	0.148452	+	0.456887i
$459$	−579.622	−	158.270i	−1.26279	−	0.344816i
$460$	−5.54359	−	17.6566i	−0.0120513	−	0.0383839i
$461$	−421.360	−	579.953i	−0.914014	−	1.25803i	−0.965777	−	0.259373i	$-0.916484\pi$
$461$	−421.360	−	579.953i	−0.914014	−	1.25803i	0.0517635	−	0.998659i	$-0.483516\pi$
$462$	−365.660	+	218.922i	−0.791472	+	0.473857i
$463$	348.693	−	479.934i	0.753116	−	1.03658i	−0.244640	−	0.969614i	$-0.578670\pi$
$463$	348.693	−	479.934i	0.753116	−	1.03658i	0.997756	−	0.0669612i	$-0.0213304\pi$
$464$	126.120	+	173.589i	0.271810	+	0.374114i
$465$	134.895	−	307.878i	0.290097	−	0.662104i
$466$	−58.0006	−	42.1399i	−0.124465	−	0.0904290i
$467$	−59.3052	−	182.523i	−0.126992	−	0.390841i	0.867267	−	0.497844i	$-0.165875\pi$
$467$	−59.3052	−	182.523i	−0.126992	−	0.390841i	−0.994259	+	0.107003i	$0.965875\pi$
$468$	58.3066	−	55.9495i	0.124587	−	0.119550i
$469$	−217.970	−	670.843i	−0.464755	−	1.43037i
$470$	44.7634	+	142.574i	0.0952412	+	0.303348i
$471$	372.015	−	426.586i	0.789842	−	0.905702i
$472$	−512.624	−	166.562i	−1.08607	−	0.352885i
$473$	−711.732	+	517.103i	−1.50472	+	1.09324i
$474$	143.714	−	337.080i	0.303193	−	0.711139i
$475$	26.0153	+	85.8359i	0.0547691	+	0.180707i
$476$			715.343i			1.50282i
$477$	−260.570	−	46.7987i	−0.546269	−	0.0981106i
$478$	47.2795	+	15.3620i	0.0989111	+	0.0321382i
$479$	275.957	+	89.6639i	0.576111	+	0.187190i	0.582558	−	0.812789i	$-0.302052\pi$
$479$	275.957	+	89.6639i	0.576111	+	0.187190i	−0.00644656	+	0.999979i	$0.502052\pi$
$480$	−350.364	−	311.728i	−0.729924	−	0.649433i
$481$	21.2127	+	65.2861i	0.0441013	+	0.135730i
$482$	−210.023			−0.435731
$483$	−2.92007	+	32.7774i	−0.00604569	+	0.0678620i
$484$	−476.481	−	346.184i	−0.984465	−	0.715256i
$485$	578.560	+	194.363i	1.19291	+	0.400749i
$486$	−200.808	+	37.3822i	−0.413186	+	0.0769181i
$487$	446.402	−	614.420i	0.916637	−	1.26164i	−0.0482116	−	0.998837i	$-0.515352\pi$
$487$	446.402	−	614.420i	0.916637	−	1.26164i	0.964849	−	0.262806i	$-0.0846478\pi$
$488$	−407.222	−	295.864i	−0.834472	−	0.606279i
$489$	−83.9908	+	19.2505i	−0.171760	+	0.0393670i
$490$	158.438	−	112.724i	0.323344	−	0.230048i
$491$	−105.426	+	145.107i	−0.214717	+	0.295533i	−0.902766	−	0.430131i	$-0.858467\pi$
$491$	−105.426	+	145.107i	−0.214717	+	0.295533i	0.688049	+	0.725664i	$0.258467\pi$
$492$	21.2561	−	238.597i	0.0432034	−	0.484953i
$493$			595.329i			1.20756i
$494$	7.81907	−	2.54057i	0.0158281	−	0.00514285i
$495$	−567.559	+	533.882i	−1.14658	+	1.07855i
$496$	55.5402	−	170.935i	0.111976	−	0.344627i
$497$	−141.181	+	434.511i	−0.284067	+	0.874268i
$498$	0.506051	+	2.20793i	0.00101617	+	0.00443359i
$499$	379.268			0.760057			0.380028	−	0.924975i	$-0.375914\pi$
$499$	379.268			0.760057			0.380028	+	0.924975i	$0.375914\pi$
$500$	−138.832	+	387.565i	−0.277664	+	0.775130i
$501$	206.803	−	485.056i	0.412781	−	0.968176i
$502$	−86.2444	−	118.705i	−0.171802	−	0.236465i
$503$	−119.455	+	367.645i	−0.237485	+	0.730905i	0.759297	+	0.650745i	$0.225543\pi$
$503$	−119.455	+	367.645i	−0.237485	+	0.730905i	−0.996782	+	0.0801602i	$0.974457\pi$
$504$	234.542	+	484.781i	0.465361	+	0.961867i
$505$	1.43165	−	144.044i	0.00283494	−	0.285237i
$506$	15.5567	−	5.05468i	0.0307445	−	0.00998949i
$507$	190.096	−	445.870i	0.374943	−	0.879429i
$508$	−10.3755	+	3.37120i	−0.0204242	+	0.00663622i
$509$	205.311	−	282.586i	0.403361	−	0.555179i	−0.558223	−	0.829691i	$-0.688516\pi$
$509$	205.311	−	282.586i	0.403361	−	0.555179i	0.961584	+	0.274512i	$0.0885165\pi$
$510$	−59.9623	−	274.101i	−0.117573	−	0.537452i
$511$	386.281	−	280.650i	0.755932	−	0.549217i
$512$	−361.988	−	263.000i	−0.707009	−	0.513672i
$513$	93.4459	+	25.5162i	0.182156	+	0.0497391i
$514$	−129.006	+	93.7282i	−0.250984	+	0.182351i
$515$	−32.4131	−	10.8890i	−0.0629380	−	0.0211436i
$516$	257.860	+	430.698i	0.499728	+	0.834685i
$517$	585.536	−	190.252i	1.13257	−	0.367993i
$518$	−206.581			−0.398806
$519$	131.410	+	11.7071i	0.253199	+	0.0225570i
$520$	79.2172	+	26.6125i	0.152341	+	0.0511779i
$521$	−255.878	−	83.1397i	−0.491128	−	0.159577i	0.0529744	−	0.998596i	$-0.483130\pi$
$521$	−255.878	−	83.1397i	−0.491128	−	0.159577i	−0.544103	+	0.839019i	$0.683130\pi$
$522$	88.1415	+	182.182i	0.168854	+	0.349008i
$523$	−333.705	−	459.305i	−0.638059	−	0.878213i	0.360451	−	0.932778i	$-0.382623\pi$
$523$	−333.705	−	459.305i	−0.638059	−	0.878213i	−0.998510	+	0.0545650i	$0.982623\pi$
$524$		−	517.180i		−	0.986986i
$525$	492.002	−	542.035i	0.937146	−	1.03245i
$526$	385.764			0.733392
$527$	403.436	−	293.113i	0.765533	−	0.556192i
$528$	−273.840	+	314.009i	−0.518636	+	0.594714i
$529$	−163.080	+	501.908i	−0.308279	+	0.948786i
$530$	−37.0329	−	117.952i	−0.0698735	−	0.222550i
$531$	697.474	+	373.698i	1.31351	+	0.703763i
$532$		−	115.327i		−	0.216780i
$533$	20.4247	+	62.8608i	0.0383203	+	0.117938i
$534$	−46.2749	−	77.2919i	−0.0866570	−	0.144741i
$535$	−587.434	−	5.83846i	−1.09801	−	0.0109130i
$536$	260.418	+	358.435i	0.485855	+	0.668722i
$537$	471.084	+	786.841i	0.877251	+	1.46525i
$538$	27.9292	−	38.4413i	0.0519130	−	0.0714522i
$539$	−470.882	−	648.113i	−0.873621	−	1.20244i
$540$	274.696	+	349.606i	0.508697	+	0.647419i
$541$	−833.972	−	605.916i	−1.54154	−	1.11999i	−0.949362	−	0.314186i	$-0.898269\pi$
$541$	−833.972	−	605.916i	−1.54154	−	1.11999i	−0.592177	−	0.805808i	$-0.701731\pi$
$542$	13.5178	+	41.6036i	0.0249406	+	0.0767594i
$543$	−165.529	+	388.248i	−0.304842	+	0.715006i
$544$	−214.995	−	661.687i	−0.395212	−	1.21634i
$545$	390.359	+	289.584i	0.716256	+	0.531346i
$546$	−50.5715	−	44.1022i	−0.0926217	−	0.0807732i
$547$	−625.979	−	203.393i	−1.14439	−	0.371833i	−0.325360	−	0.945590i	$-0.605485\pi$
$547$	−625.979	−	203.393i	−1.14439	−	0.371833i	−0.819026	+	0.573757i	$0.805485\pi$
$548$	260.074	−	188.955i	0.474587	−	0.344808i
$549$	511.623	+	533.177i	0.931917	+	0.971178i
$550$	−343.761	−	119.299i	−0.625019	−	0.216907i
$551$		−	95.9782i		−	0.174189i
$552$	−4.61765	−	20.1470i	−0.00836531	−	0.0364983i
$553$	1348.90	+	438.284i	2.43924	+	0.792556i
$554$	221.969	+	72.1223i	0.400667	+	0.130185i
$555$	−368.970	+	80.7159i	−0.664811	+	0.145434i
$556$	−198.945	−	612.289i	−0.357815	−	1.10124i
$557$	−202.807			−0.364106			−0.182053	−	0.983289i	$-0.558274\pi$
$557$	−202.807			−0.364106			−0.182053	+	0.983289i	$0.558274\pi$
$558$	80.0623	−	149.429i	0.143481	−	0.267794i
$559$	−112.058	−	81.4150i	−0.200462	−	0.145644i
$560$	233.206	−	314.362i	0.416440	−	0.561362i
$561$	−1126.77	+	258.254i	−2.00851	+	0.460345i
$562$	6.06731	−	8.35093i	0.0107959	−	0.0148593i
$563$	−517.129	−	375.717i	−0.918525	−	0.667347i	0.0246316	−	0.999697i	$-0.492159\pi$
$563$	−517.129	−	375.717i	−0.918525	−	0.667347i	−0.943156	+	0.332349i	$0.892159\pi$
$564$	−78.4828	−	342.424i	−0.139154	−	0.607135i
$565$	579.769	+	430.095i	1.02614	+	0.761230i
$566$	25.2626	−	34.7710i	0.0446335	−	0.0614328i
$567$	−213.089	−	761.334i	−0.375818	−	1.34274i
$568$		−	286.968i		−	0.505225i
$569$	122.002	−	39.6408i	0.214415	−	0.0696676i	−0.199840	−	0.979829i	$-0.564042\pi$
$569$	122.002	−	39.6408i	0.214415	−	0.0696676i	0.414255	+	0.910161i	$0.364042\pi$
$570$	9.66705	+	44.1902i	0.0169597	+	0.0775266i
$571$	−247.161	+	760.684i	−0.432857	+	1.33220i	0.462410	+	0.886666i	$0.346985\pi$
$571$	−247.161	+	760.684i	−0.432857	+	1.33220i	−0.895267	+	0.445530i	$0.853015\pi$
$572$	48.0433	−	147.862i	0.0839918	−	0.258500i
$573$	−9.21412	+	2.11185i	−0.0160805	+	0.00368560i
$574$	−198.907			−0.346528
$575$	−23.0537	+	16.0593i	−0.0400935	+	0.0279292i
$576$	36.1565	+	37.6797i	0.0627717	+	0.0654162i
$577$	397.177	+	546.667i	0.688348	+	0.947430i	0.999996	−	0.00276735i	$-0.000880876\pi$
$577$	397.177	+	546.667i	0.688348	+	0.947430i	−0.311648	+	0.950198i	$0.600881\pi$
$578$	53.5641	−	164.853i	0.0926715	−	0.285214i
$579$	−162.631	+	186.487i	−0.280883	+	0.322085i
$580$	262.469	−	353.810i	0.452534	−	0.610016i
$581$	−8.33838	+	2.70930i	−0.0143518	+	0.00466317i
$582$	283.156	+	120.723i	0.486522	+	0.207428i
$583$	−484.417	+	157.397i	−0.830904	+	0.269977i
$584$	−176.280	+	242.629i	−0.301849	+	0.415460i
$585$	−107.556	−	59.0104i	−0.183857	−	0.100873i
$586$	245.207	−	178.153i	0.418442	−	0.304016i
$587$	760.672	+	552.661i	1.29586	+	0.941501i	0.999906	−	0.0137003i	$-0.00436107\pi$
$587$	760.672	+	552.661i	1.29586	+	0.941501i	0.295958	+	0.955201i	$0.404361\pi$
$588$	−392.199	+	234.811i	−0.667006	+	0.399338i
$589$	−65.0414	+	47.2554i	−0.110427	+	0.0802298i
$590$	−3.67238	+	369.495i	−0.00622437	+	0.626262i
$591$	−535.954	+	320.877i	−0.906860	+	0.542940i
$592$	−192.071	+	62.4076i	−0.324444	+	0.105418i
$593$	413.092			0.696615			0.348307	−	0.937380i	$-0.386757\pi$
$593$	413.092			0.696615			0.348307	+	0.937380i	$0.386757\pi$
$594$	−306.579	+	245.855i	−0.516126	+	0.413898i
$595$	1036.14	−	325.314i	1.74142	−	0.546747i
$596$	435.008	+	141.343i	0.729879	+	0.237152i
$597$	292.986	+	255.507i	0.490764	+	0.427984i
$598$	1.51376	+	2.08351i	0.00253137	+	0.00348414i
$599$			97.8025i			0.163276i	0.996662	+	0.0816381i	$0.0260152\pi$
$599$			97.8025i			0.163276i	−0.996662	+	0.0816381i	$0.973985\pi$
$600$	−188.700	+	419.293i	−0.314500	+	0.698822i
$601$	−477.154			−0.793933			−0.396967	−	0.917833i	$-0.629937\pi$
$601$	−477.154			−0.793933			−0.396967	+	0.917833i	$0.629937\pi$
$602$	337.225	−	245.009i	0.560175	−	0.406991i
$603$	−283.266	−	585.490i	−0.469761	−	0.970962i
$604$	−63.3263	+	194.898i	−0.104845	+	0.322679i
$605$	−284.744	+	847.594i	−0.470651	+	1.40098i
$606$	6.44681	−	72.3646i	0.0106383	−	0.119413i
$607$		−	726.229i		−	1.19642i	−0.801338	−	0.598211i	$-0.795878\pi$
$607$		−	726.229i		−	1.19642i	0.801338	−	0.598211i	$-0.204122\pi$
$608$	34.6613	+	106.676i	0.0570086	+	0.175455i
$609$	−672.091	+	402.383i	−1.10360	+	0.660727i
$610$	−109.890	+	327.108i	−0.180147	+	0.536243i
$611$	56.9761	+	78.4209i	0.0932506	+	0.128348i
$612$	89.7269	+	653.482i	0.146613	+	1.06778i
$613$	−135.315	+	186.245i	−0.220742	+	0.303825i	−0.904997	−	0.425417i	$-0.860127\pi$
$613$	−135.315	+	186.245i	−0.220742	+	0.303825i	0.684255	+	0.729243i	$0.260127\pi$
$614$	70.1821	+	96.5974i	0.114303	+	0.157325i
$615$	−355.263	+	77.7174i	−0.577664	+	0.126370i
$616$	838.239	+	609.016i	1.36078	+	0.988663i
$617$	−119.648	−	368.239i	−0.193919	−	0.596821i	−0.999988	−	0.00499907i	$-0.998409\pi$
$617$	−119.648	−	368.239i	−0.193919	−	0.596821i	0.806069	−	0.591822i	$-0.201591\pi$
$618$	−15.8635	−	6.76336i	−0.0256690	−	0.0109440i
$619$	350.417	+	1078.47i	0.566102	+	1.74228i	0.664655	+	0.747151i	$0.268579\pi$
$619$	350.417	+	1078.47i	0.566102	+	1.74228i	−0.0985527	+	0.995132i	$0.531421\pi$
$620$	−368.994	−	3.66740i	−0.595152	−	0.00591516i
$621$	1.44378	+	30.3091i	0.00232493	+	0.0488070i
$622$	−53.0378	−	17.2330i	−0.0852698	−	0.0277058i
$623$	282.089	−	204.949i	0.452791	−	0.328972i
$624$	−60.3423	−	25.7269i	−0.0967025	−	0.0412290i
$625$	624.506	+	24.8399i	0.999210	+	0.0397439i
$626$		−	34.2761i		−	0.0547541i
$627$	181.657	−	41.6353i	0.289724	−	0.0664040i
$628$	−590.965	−	192.016i	−0.941027	−	0.305758i
$629$	−532.909	−	173.153i	−0.847233	−	0.275283i
$630$	268.915	−	252.959i	0.426849	−	0.401522i
$631$	−121.844	−	374.998i	−0.193097	−	0.594292i	−0.999994	−	0.00359908i	$-0.998854\pi$
$631$	−121.844	−	374.998i	−0.193097	−	0.594292i	0.806896	−	0.590693i	$-0.201146\pi$
$632$	−890.864			−1.40959
$633$	−442.467	−	39.4185i	−0.699000	−	0.0622725i
$634$	−28.8089	−	20.9309i	−0.0454400	−	0.0330141i
$635$	9.60146	+	13.4953i	0.0151204	+	0.0212525i
$636$	64.9292	+	283.289i	0.102090	+	0.445423i
$637$	74.1376	−	102.042i	0.116386	−	0.160191i
$638$	315.013	+	228.870i	0.493750	+	0.358731i
$639$	−74.4706	+	414.644i	−0.116542	+	0.648896i
$640$	−206.891	+	615.851i	−0.323267	+	0.962267i
$641$	688.318	−	947.388i	1.07382	−	1.47798i	0.207669	−	0.978199i	$-0.433412\pi$
$641$	688.318	−	947.388i	1.07382	−	1.47798i	0.866150	−	0.499785i	$-0.166588\pi$
$642$	−295.113	−	26.2910i	−0.459678	−	0.0409517i
$643$		−	239.132i		−	0.371901i	−0.982559	−	0.185950i	$-0.940464\pi$
$643$		−	239.132i		−	0.371901i	0.982559	−	0.185950i	$-0.0595363\pi$
$644$	34.3579	−	11.1635i	0.0533507	−	0.0173347i
$645$	506.580	−	569.365i	0.785395	−	0.882737i
$646$	−20.7379	+	63.8246i	−0.0321020	+	0.0987997i
$647$	312.069	−	960.450i	0.482332	−	1.48447i	−0.353475	−	0.935444i	$-0.615000\pi$
$647$	312.069	−	960.450i	0.482332	−	1.48447i	0.835808	−	0.549022i	$-0.185000\pi$
$648$	275.066	+	413.439i	0.424485	+	0.638024i
$649$	1522.38			2.34573
$650$	1.13868	−	57.2784i	0.00175182	−	0.0881206i
$651$	603.590	+	257.340i	0.927174	+	0.395300i
$652$	55.6028	+	76.5307i	0.0852804	+	0.117378i
$653$	188.871	−	581.286i	0.289236	−	0.890177i	−0.695861	−	0.718177i	$-0.744977\pi$
$653$	188.871	−	581.286i	0.289236	−	0.890177i	0.985097	−	0.172000i	$-0.0550230\pi$
$654$	184.748	+	161.115i	0.282490	+	0.246352i
$655$	−749.112	+	235.196i	−1.14368	+	0.359079i
$656$	−184.936	+	60.0892i	−0.281914	+	0.0915994i
$657$	317.674	−	304.832i	0.483522	−	0.463975i
$658$	−277.433	+	90.1434i	−0.421630	+	0.136996i
$659$	−560.784	+	771.852i	−0.850962	+	1.17125i	0.132689	+	0.991158i	$0.457639\pi$
$659$	−560.784	+	771.852i	−0.850962	+	1.17125i	−0.983650	+	0.180090i	$0.942361\pi$
$660$	783.512	+	343.291i	1.18714	+	0.520138i
$661$	530.695	−	385.572i	0.802866	−	0.583317i	−0.108887	−	0.994054i	$-0.534729\pi$
$661$	530.695	−	385.572i	0.802866	−	0.583317i	0.911754	+	0.410738i	$0.134729\pi$
$662$	142.458	+	103.501i	0.215193	+	0.156347i
$663$	−93.4914	−	156.157i	−0.141013	−	0.235530i
$664$	4.45524	−	3.23692i	0.00670970	−	0.00487488i
$665$	−167.045	+	52.4467i	−0.251196	+	0.0788673i
$666$	−188.717	+	25.9119i	−0.283358	+	0.0389068i
$667$	28.5936	−	9.29062i	0.0428689	−	0.0139290i
$668$	−578.879			−0.866586
$669$	15.2983	−	171.722i	0.0228675	−	0.256684i
$670$	180.962	−	243.938i	0.270093	−	0.364086i
$671$	1352.11	+	439.326i	2.01506	+	0.654733i
$672$	601.691	−	689.952i	0.895373	−	1.02671i
$673$	−318.684	−	438.631i	−0.473527	−	0.651754i	0.503718	−	0.863868i	$-0.331965\pi$
$673$	−318.684	−	438.631i	−0.473527	−	0.651754i	−0.977245	+	0.212114i	$0.931965\pi$
$674$		−	62.4249i		−	0.0926185i
$675$	381.466	−	556.874i	0.565135	−	0.824999i
$676$	−532.114			−0.787151
$677$	−120.168	+	87.3073i	−0.177501	+	0.128962i	−0.672988	−	0.739653i	$-0.734990\pi$
$677$	−120.168	+	87.3073i	−0.177501	+	0.128962i	0.495487	+	0.868615i	$0.334990\pi$
$678$	274.391	+	239.290i	0.404707	+	0.352936i
$679$	−368.170	+	1133.11i	−0.542224	+	1.66879i
$680$	−555.819	+	395.446i	−0.817381	+	0.581539i
$681$	−903.621	−	80.5017i	−1.32690	−	0.118211i
$682$		−	326.160i		−	0.478240i
$683$	157.437	+	484.540i	0.230508	+	0.709430i	0.997686	+	0.0679954i	$0.0216603\pi$
$683$	157.437	+	484.540i	0.230508	+	0.709430i	−0.767178	+	0.641434i	$0.778340\pi$
$684$	−14.4657	−	105.354i	−0.0211486	−	0.154026i
$685$	−391.965	−	290.775i	−0.572212	−	0.424489i
$686$	−13.1872	−	18.1506i	−0.0192233	−	0.0264586i
$687$	−673.744	+	403.373i	−0.980705	+	0.587151i
$688$	239.522	−	329.673i	0.348142	−	0.479176i
$689$	−47.1366	−	64.8780i	−0.0684131	−	0.0941626i
$690$	−12.2293	+	7.15756i	−0.0177236	+	0.0103733i
$691$	−46.9769	−	34.1307i	−0.0679840	−	0.0493933i	0.553274	−	0.832999i	$-0.313378\pi$
$691$	−46.9769	−	34.1307i	−0.0679840	−	0.0493933i	−0.621258	+	0.783606i	$0.713378\pi$
$692$	−44.7566	−	137.747i	−0.0646772	−	0.199056i
$693$	−1053.14	−	1097.51i	−1.51968	−	1.58371i
$694$	38.6404	+	118.923i	0.0556778	+	0.171359i
$695$	−796.400	+	566.611i	−1.14590	+	0.815268i
$696$	323.387	−	370.824i	0.464636	−	0.532793i
$697$	−513.112	−	166.720i	−0.736173	−	0.239197i
$698$	223.335	−	162.262i	0.319964	−	0.232467i
$699$	100.351	−	235.373i	0.143563	−	0.336728i
$700$	−759.214	−	263.478i	−1.08459	−	0.376398i
$701$			753.805i			1.07533i	0.843159	+	0.537664i	$0.180693\pi$
$701$			753.805i			1.07533i	−0.843159	+	0.537664i	$0.819307\pi$
$702$	−51.7300	−	33.9451i	−0.0736894	−	0.0483548i
$703$	85.9150	+	27.9155i	0.122212	+	0.0397091i
$704$	95.5536	+	31.0473i	0.135730	+	0.0441012i
$705$	−460.295	+	269.402i	−0.652900	+	0.382130i
$706$	−179.597	−	552.743i	−0.254387	−	0.782922i
$707$	281.200			0.397737
$708$	77.0833	−	865.250i	0.108875	−	1.22210i
$709$	−875.929	−	636.400i	−1.23544	−	0.897602i	−0.238157	−	0.971227i	$-0.576543\pi$
$709$	−875.929	−	636.400i	−1.23544	−	0.897602i	−0.997286	+	0.0736243i	$0.976543\pi$
$710$	−187.696	+	58.9304i	−0.264361	+	0.0830005i
$711$	1287.22	+	231.187i	1.81044	+	0.325157i
$712$	−128.732	+	177.184i	−0.180803	+	0.248854i
$713$	−20.3742	−	14.8027i	−0.0285753	−	0.0207611i
$714$	533.877	−	122.363i	0.747727	−	0.171377i
$715$	−236.020	−	2.34578i	−0.330098	−	0.00328082i
$716$	591.774	−	814.507i	0.826500	−	1.13758i
$717$	−15.7441	+	176.725i	−0.0219582	+	0.246478i
$718$		−	81.1189i		−	0.112979i
$719$	−1047.73	+	340.428i	−1.45721	+	0.473475i	−0.927215	−	0.374529i	$-0.877805\pi$
$719$	−1047.73	+	340.428i	−1.45721	+	0.473475i	−0.529991	+	0.848003i	$0.677805\pi$
$720$	173.608	−	316.429i	0.241122	−	0.439484i
$721$	20.6263	−	63.4811i	0.0286078	−	0.0880459i
$722$	−90.4264	+	278.304i	−0.125244	+	0.385462i
$723$	−167.458	−	730.628i	−0.231616	−	1.01055i
$724$	463.346			0.639981
$725$	−631.839	−	219.274i	−0.871502	−	0.302447i
$726$	−176.860	+	414.825i	−0.243609	+	0.571384i
$727$	323.312	+	445.001i	0.444721	+	0.612106i	0.971253	−	0.238049i	$-0.0765079\pi$
$727$	323.312	+	445.001i	0.444721	+	0.612106i	−0.526532	+	0.850155i	$0.676508\pi$
$728$	−50.4103	+	155.147i	−0.0692449	+	0.213114i
$729$	−290.157	−	668.768i	−0.398020	−	0.917377i
$730$	194.895	+	65.4739i	0.266980	+	0.0896902i
$731$	1075.29	−	349.382i	1.47098	−	0.477951i
$732$	318.154	−	746.229i	0.434637	−	1.01944i
$733$	78.9194	−	25.6425i	0.107666	−	0.0349829i	−0.254688	−	0.967023i	$-0.581973\pi$
$733$	78.9194	−	25.6425i	0.107666	−	0.0349829i	0.362355	+	0.932040i	$0.381973\pi$
$734$	105.960	−	145.841i	0.144360	−	0.198694i
$735$	518.472	+	461.299i	0.705404	+	0.627617i
$736$	−28.4256	+	20.6524i	−0.0386217	+	0.0280603i
$737$	−1012.38	−	735.534i	−1.37364	−	0.998010i
$738$	−181.706	+	24.9493i	−0.246214	+	0.0338067i
$739$	8.53578	−	6.20160i	0.0115504	−	0.00839189i	−0.581995	−	0.813192i	$-0.697728\pi$
$739$	8.53578	−	6.20160i	0.0115504	−	0.00839189i	0.593545	+	0.804800i	$0.297728\pi$
$740$	240.373	+	337.856i	0.324829	+	0.456562i
$741$	15.0726	+	25.1754i	0.0203408	+	0.0339749i
$742$	229.521	−	74.5760i	0.309328	−	0.100507i
$743$	−168.513			−0.226801			−0.113401	−	0.993549i	$-0.536174\pi$
$743$	−168.513			−0.226801			−0.113401	+	0.993549i	$0.536174\pi$
$744$	−410.517	−	36.5721i	−0.551770	−	0.0491560i
$745$	6.90125	−	694.367i	0.00926342	−	0.932036i
$746$	154.480	+	50.1936i	0.207078	+	0.0672836i
$747$	−7.27746	+	3.52091i	−0.00974225	+	0.00471340i
$748$	745.937	+	1026.69i	0.997242	+	1.37259i
$749$		−	1146.77i		−	1.53107i
$750$	312.996	+	37.3183i	0.417328	+	0.0497578i
$751$	83.0662			0.110607			0.0553037	−	0.998470i	$-0.482387\pi$
$751$	83.0662			0.110607			0.0553037	+	0.998470i	$0.482387\pi$
$752$	−230.713	+	167.623i	−0.306800	+	0.222903i
$753$	344.187	−	394.676i	0.457088	−	0.524137i
$754$	−18.9443	+	58.3047i	−0.0251251	+	0.0773272i
$755$	311.100	+	3.09200i	0.412053	+	0.00409536i
$756$	−677.096	+	542.985i	−0.895630	+	0.718234i
$757$		−	124.740i		−	0.164782i	−0.996600	−	0.0823909i	$-0.973744\pi$
$757$		−	124.740i		−	0.164782i	0.996600	−	0.0823909i	$-0.0262556\pi$
$758$	−123.792	−	380.992i	−0.163314	−	0.502628i
$759$	29.9882	+	50.0886i	0.0395101	+	0.0659929i
$760$	89.6084	−	63.7534i	0.117906	−	0.0838860i
$761$	−166.917	−	229.742i	−0.219340	−	0.301895i	0.685140	−	0.728411i	$-0.259741\pi$
$761$	−166.917	−	229.742i	−0.219340	−	0.301895i	−0.904480	+	0.426516i	$0.859741\pi$
$762$	4.29079	+	7.16680i	0.00563095	+	0.00940525i
$763$	−557.689	+	767.593i	−0.730916	+	1.00602i
$764$	6.09985	+	8.39572i	0.00798409	+	0.0109892i
$765$	905.734	−	427.147i	1.18397	−	0.558362i
$766$	164.008	+	119.159i	0.214110	+	0.155560i
$767$	74.0683	+	227.959i	0.0965689	+	0.297208i
$768$	−101.197	+	237.357i	−0.131767	+	0.309058i
$769$	−168.931	−	519.916i	−0.219676	−	0.676093i	−0.998788	−	0.0492091i	$-0.984330\pi$
$769$	−168.931	−	519.916i	−0.219676	−	0.676093i	0.779112	−	0.626884i	$-0.215670\pi$
$770$	226.201	−	673.330i	0.293767	−	0.874454i
$771$	−428.923	−	374.054i	−0.556321	−	0.485154i
$772$	258.348	+	83.9423i	0.334648	+	0.108734i
$773$	−195.091	+	141.742i	−0.252382	+	0.183366i	−0.706782	−	0.707432i	$-0.749854\pi$
$773$	−195.091	+	141.742i	−0.252382	+	0.183366i	0.454400	+	0.890798i	$0.349854\pi$
$774$	277.331	−	266.120i	0.358309	−	0.343824i
$775$	162.494	+	536.139i	0.209670	+	0.691792i
$776$		−	748.349i		−	0.964367i
$777$	−164.714	−	718.657i	−0.211988	−	0.924913i
$778$	−498.979	−	162.128i	−0.641361	−	0.208391i
$779$	82.7233	+	26.8784i	0.106192	+	0.0345038i
$780$	−13.2837	+	134.024i	−0.0170304	+	0.171826i
$781$	250.465	+	770.851i	0.320697	+	0.987005i
$782$	−21.0219			−0.0268822
$783$	−563.499	+	451.888i	−0.719666	+	0.577123i
$784$	300.205	+	218.112i	0.382915	+	0.278204i
$785$	−9.37546	+	943.309i	−0.0119433	+	1.20167i
$786$	−385.983	+	88.4664i	−0.491073	+	0.112553i
$787$	−250.918	+	345.360i	−0.318829	+	0.438830i	−0.938109	−	0.346340i	$-0.887424\pi$
$787$	−250.918	+	345.360i	−0.318829	+	0.438830i	0.619280	+	0.785170i	$0.287424\pi$
$788$	554.799	+	403.085i	0.704060	+	0.511529i
$789$	307.583	+	1342.00i	0.389839	+	1.70089i
$790$	182.944	+	582.685i	0.231574	+	0.737576i
$791$	−828.290	+	1140.04i	−1.04714	+	1.44127i
$792$	842.140	+	451.208i	1.06331	+	0.569707i
$793$			223.837i			0.282266i
$794$	367.255	−	119.328i	0.462537	−	0.150288i
$795$	380.804	−	222.877i	0.478999	−	0.280349i
$796$	131.880	−	405.885i	0.165678	−	0.509906i
$797$	−347.475	+	1069.42i	−0.435978	+	1.34180i	0.456103	+	0.889927i	$0.349245\pi$
$797$	−347.475	+	1069.42i	−0.435978	+	1.34180i	−0.892081	+	0.451876i	$0.850755\pi$
$798$	−86.0709	+	19.7272i	−0.107858	+	0.0247208i
$799$	−791.238			−0.990285
$800$	781.455	+	15.5352i	0.976819	+	0.0194190i
$801$	231.987	−	222.609i	0.289622	−	0.277914i
$802$	331.749	+	456.613i	0.413652	+	0.569343i
$803$	261.757	−	805.604i	0.325973	−	1.00324i
$804$	−469.303	+	538.144i	−0.583710	+	0.669333i
$805$	−31.7947	−	44.6890i	−0.0394965	−	0.0555142i
$806$	48.8386	−	15.8686i	0.0605939	−	0.0196881i
$807$	155.999	+	66.5099i	0.193307	+	0.0824162i
$808$	−167.981	+	54.5803i	−0.207897	+	0.0675499i
$809$	84.6156	−	116.463i	0.104593	−	0.143960i	−0.753512	−	0.657434i	$-0.771642\pi$
$809$	84.6156	−	116.463i	0.104593	−	0.143960i	0.858105	+	0.513474i	$0.171642\pi$
$810$	213.931	−	264.814i	0.264112	−	0.326931i
$811$	−488.523	+	354.933i	−0.602371	+	0.437648i	−0.846720	−	0.532039i	$-0.821426\pi$
$811$	−488.523	+	354.933i	−0.602371	+	0.437648i	0.244349	+	0.969687i	$0.421426\pi$
$812$	695.722	+	505.472i	0.856801	+	0.622502i
$813$	−133.953	+	80.1979i	−0.164764	+	0.0986444i
$814$	−296.495	+	215.417i	−0.364245	+	0.264640i
$815$	85.5649	−	115.342i	0.104988	−	0.141524i
$816$	459.411	−	275.051i	0.563003	−	0.337072i
$817$	−173.357	+	56.3269i	−0.212187	+	0.0689436i
$818$	−188.200			−0.230073
$819$	113.101	−	211.093i	0.138096	−	0.257744i
$820$	231.444	+	325.305i	0.282248	+	0.396714i
$821$	−663.159	−	215.474i	−0.807746	−	0.262453i	−0.124103	−	0.992269i	$-0.539605\pi$
$821$	−663.159	−	215.474i	−0.807746	−	0.262453i	−0.683643	+	0.729817i	$0.739605\pi$
$822$	−185.508	−	161.777i	−0.225679	−	0.196809i
$823$	568.322	+	782.228i	0.690549	+	0.950459i	1.00000		0.000456023i	$-0.000145157\pi$
$823$	568.322	+	782.228i	0.690549	+	0.950459i	−0.309451	+	0.950915i	$0.600145\pi$
$824$			41.9253i			0.0508802i
$825$	140.927	−	1291.00i	0.170820	−	1.56485i
$826$	−721.319			−0.873268
$827$	−527.867	+	383.518i	−0.638291	+	0.463746i	−0.859263	−	0.511535i	$-0.829077\pi$
$827$	−527.867	+	383.518i	−0.638291	+	0.463746i	0.220971	+	0.975280i	$0.429077\pi$
$828$	29.9864	−	14.5077i	0.0362155	−	0.0175214i
$829$	288.910	−	889.173i	0.348504	−	1.07258i	−0.611177	−	0.791494i	$-0.709304\pi$
$829$	288.910	−	889.173i	0.348504	−	1.07258i	0.959681	−	0.281091i	$-0.0906962\pi$
$830$	−3.03207	−	2.24931i	−0.00365310	−	0.00271001i
$831$	−73.9158	+	829.695i	−0.0889480	+	0.998429i
$832$			15.8186i			0.0190127i
$833$	318.152	+	979.173i	0.381936	+	1.17548i
$834$	−422.935	+	253.212i	−0.507116	+	0.303612i
$835$	263.255	+	838.480i	0.315275	+	1.00417i
$836$	−120.259	−	165.522i	−0.143851	−	0.197993i
$837$	583.672	+	159.376i	0.697338	+	0.190414i
$838$	271.794	−	374.092i	0.324336	−	0.446410i
$839$	−420.161	−	578.302i	−0.500788	−	0.689275i	0.481544	−	0.876422i	$-0.340076\pi$
$839$	−420.161	−	578.302i	−0.500788	−	0.689275i	−0.982332	+	0.187147i	$0.940076\pi$
$840$	−822.114	−	360.205i	−0.978707	−	0.428815i
$841$	−101.383	−	73.6593i	−0.120551	−	0.0875854i
$842$	−206.267	−	634.825i	−0.244973	−	0.753948i
$843$	33.8890	+	14.4485i	0.0402004	+	0.0171394i
$844$	150.699	+	463.802i	0.178553	+	0.549529i
$845$	241.988	+	770.743i	0.286376	+	0.912122i
$846$	−242.134	+	117.147i	−0.286211	+	0.138472i
$847$	−1660.01	−	539.371i	−1.95987	−	0.636802i
$848$	190.870	−	138.675i	0.225083	−	0.163532i
$849$	141.104	+	60.1596i	0.166200	+	0.0708594i
$850$	372.789	+	282.336i	0.438575	+	0.332160i
$851$			28.2978i			0.0332524i
$852$	450.797	−	103.322i	0.529105	−	0.121269i
$853$	401.645	+	130.502i	0.470862	+	0.152992i	0.534830	−	0.844960i	$-0.320376\pi$
$853$	401.645	+	130.502i	0.470862	+	0.152992i	−0.0639683	+	0.997952i	$0.520376\pi$
$854$	−640.641	−	208.157i	−0.750165	−	0.243744i
$855$	−146.021	+	68.8641i	−0.170785	+	0.0805428i
$856$	222.586	+	685.051i	0.260031	+	0.800293i
$857$	−255.925			−0.298629			−0.149314	−	0.988790i	$-0.547707\pi$
$857$	−255.925			−0.298629			−0.149314	+	0.988790i	$0.547707\pi$
$858$	−118.571	−	10.5632i	−0.138195	−	0.0123115i
$859$	−311.375	−	226.227i	−0.362486	−	0.263361i	0.391603	−	0.920134i	$-0.371921\pi$
$859$	−311.375	−	226.227i	−0.362486	−	0.263361i	−0.754088	+	0.656773i	$0.771921\pi$
$860$	−793.090	−	266.433i	−0.922197	−	0.309806i
$861$	−158.595	−	691.960i	−0.184199	−	0.803670i
$862$	290.588	−	399.960i	0.337109	−	0.463990i
$863$	351.174	+	255.143i	0.406923	+	0.295647i	0.772355	−	0.635191i	$-0.219079\pi$
$863$	351.174	+	255.143i	0.406923	+	0.295647i	−0.365432	+	0.930838i	$0.619079\pi$
$864$	463.116	−	705.757i	0.536014	−	0.816849i
$865$	−179.166	+	127.471i	−0.207128	+	0.147365i
$866$	38.7397	−	53.3206i	0.0447341	−	0.0615711i
$867$	616.202	+	54.8962i	0.710729	+	0.0633174i
$868$		−	720.342i		−	0.829887i
$869$	2393.03	−	777.543i	2.75378	−	0.894756i
$870$	−308.953	−	135.366i	−0.355118	−	0.155593i
$871$	60.8826	−	187.377i	0.0698996	−	0.215129i
$872$	184.159	−	566.785i	0.211192	−	0.649982i
$873$	−194.203	+	1081.30i	−0.222455	+	1.23860i
$874$	3.38912			0.00387771
$875$	−36.3713	+	1219.51i	−0.0415672	+	1.39372i
$876$	−444.614	−	189.561i	−0.507550	−	0.216393i
$877$	167.096	+	229.987i	0.190531	+	0.262243i	0.893586	−	0.448892i	$-0.148181\pi$
$877$	167.096	+	229.987i	0.190531	+	0.262243i	−0.703055	+	0.711135i	$0.748181\pi$
$878$	−209.189	+	643.818i	−0.238256	+	0.733278i
$879$	815.273	+	710.980i	0.927500	+	0.808851i
$880$	6.90126	−	694.368i	0.00784234	−	0.789054i
$881$	1603.94	−	521.152i	1.82059	−	0.591547i	0.820800	−	0.571216i	$-0.193528\pi$
$881$	1603.94	−	521.152i	1.82059	−	0.591547i	0.999793	−	0.0203304i	$-0.00647180\pi$
$882$	242.332	+	252.542i	0.274753	+	0.286328i
$883$	1296.69	−	421.319i	1.46850	−	0.477145i	0.537846	−	0.843043i	$-0.319238\pi$
$883$	1296.69	−	421.319i	1.46850	−	0.477145i	0.930655	+	0.365898i	$0.119238\pi$
$884$	−117.444	+	161.647i	−0.132855	+	0.182859i
$885$	−1288.33	+	281.835i	−1.45574	+	0.318458i
$886$	−408.594	+	296.861i	−0.461167	+	0.335058i
$887$	9.80606	+	7.12452i	0.0110553	+	0.00803215i	0.593299	−	0.804982i	$-0.297825\pi$
$887$	9.80606	+	7.12452i	0.0110553	+	0.00803215i	−0.582244	+	0.813014i	$0.697825\pi$
$888$	237.885	+	397.335i	0.267889	+	0.447449i
$889$	−26.1564	+	19.0037i	−0.0294222	+	0.0213765i
$890$	142.326	+	47.8134i	0.159917	+	0.0537230i
$891$	−1099.73	−	870.501i	−1.23426	−	0.976993i
$892$	−180.002	+	58.4862i	−0.201796	+	0.0655675i
$893$	127.562			0.142847
$894$	31.0768	−	348.833i	0.0347616	−	0.390194i
$895$	−1448.89	−	486.747i	−1.61888	−	0.543851i
$896$	−1206.14	−	391.900i	−1.34614	−	0.437389i
$897$	−6.04117	+	6.92734i	−0.00673486	+	0.00772279i
$898$	79.2042	+	109.015i	0.0882007	+	0.121398i
$899$		−	599.489i		−	0.666839i
$900$	−726.607	−	145.464i	−0.807342	−	0.161626i
$901$	654.595			0.726521
$902$	−285.481	+	207.414i	−0.316498	+	0.229949i
$903$	1121.22	+	977.789i	1.24166	+	1.08282i
$904$	273.517	−	841.799i	0.302563	−	0.931193i
$905$	−210.714	−	671.136i	−0.232834	−	0.741586i
$906$	156.289	+	13.9235i	0.172505	+	0.0153681i
$907$			1370.88i			1.51144i	0.654895	+	0.755720i	$0.272713\pi$
$907$			1370.88i			1.51144i	−0.654895	+	0.755720i	$0.727287\pi$
$908$	307.761	+	947.192i	0.338944	+	1.04316i
$909$	256.883	−	35.2715i	0.282599	−	0.0388025i
$910$	111.829	+	1.11146i	0.122889	+	0.00122138i
$911$	−435.625	−	599.587i	−0.478184	−	0.658164i	0.499971	−	0.866042i	$-0.333344\pi$
$911$	−435.625	−	599.587i	−0.478184	−	0.658164i	−0.978155	+	0.207879i	$0.933344\pi$
$912$	−74.0656	+	44.3433i	−0.0812123	+	0.0486220i
$913$	−9.14246	+	12.5835i	−0.0100136	+	0.0137826i
$914$	−259.700	−	357.447i	−0.284136	−	0.391080i
$915$	−1225.56	−	121.471i	−1.33942	−	0.132756i
$916$	697.434	+	506.715i	0.761391	+	0.553183i
$917$	−473.633	−	1457.69i	−0.516503	−	1.58963i
$918$	472.360	−	178.747i	0.514553	−	0.194713i
$919$	−41.9839	−	129.213i	−0.0456843	−	0.140602i	0.925613	−	0.378473i	$-0.123551\pi$
$919$	−41.9839	−	129.213i	−0.0456843	−	0.140602i	−0.971297	+	0.237871i	$0.923551\pi$
$920$	27.6673	+	20.5246i	0.0300731	+	0.0223094i
$921$	−280.085	+	321.170i	−0.304110	+	0.348719i
$922$	573.079	+	186.205i	0.621561	+	0.201957i
$923$	−103.240	+	75.0083i	−0.111853	+	0.0812658i
$924$	−654.898	+	1536.06i	−0.708765	+	1.66241i
$925$	380.055	−	501.815i	0.410871	−	0.542503i
$926$			498.652i			0.538501i
$927$	10.8800	−	60.5786i	0.0117368	−	0.0653491i
$928$	−795.457	−	258.460i	−0.857173	−	0.278513i
$929$	1427.52	+	463.830i	1.53662	+	0.499279i	0.950442	−	0.310901i	$-0.100631\pi$
$929$	1427.52	+	463.830i	1.53662	+	0.499279i	0.586181	+	0.810180i	$0.300631\pi$
$930$	60.3813	+	276.016i	0.0649261	+	0.296791i
$931$	−51.2921	−	157.861i	−0.0550936	−	0.169561i
$932$	−280.900			−0.301395
$933$	17.6616	−	198.249i	0.0189299	−	0.212485i
$934$	130.509	+	94.8205i	0.139732	+	0.101521i
$935$	1147.89	−	1547.36i	1.22769	−	1.65493i
$936$	−26.5906	+	148.053i	−0.0284087	+	0.158177i
$937$	828.513	−	1140.35i	0.884219	−	1.21702i	−0.0910157	−	0.995849i	$-0.529011\pi$
$937$	828.513	−	1140.35i	0.884219	−	1.21702i	0.975235	−	0.221173i	$-0.0709886\pi$
$938$	479.673	+	348.503i	0.511379	+	0.371538i
$939$	119.240	−	27.3295i	0.126986	−	0.0291049i
$940$	470.240	+	348.842i	0.500255	+	0.371109i
$941$	−746.258	+	1027.14i	−0.793048	+	1.09154i	0.200674	+	0.979658i	$0.435687\pi$
$941$	−746.258	+	1027.14i	−0.793048	+	1.09154i	−0.993722	+	0.111879i	$0.964313\pi$
$942$	−42.2184	+	473.896i	−0.0448178	+	0.503074i
$943$			27.2465i			0.0288935i
$944$	−670.652	+	217.908i	−0.710436	+	0.230835i
$945$	1094.41	+	733.811i	1.15811	+	0.776520i
$946$	228.515	−	703.296i	0.241559	−	0.743442i
$947$	−422.962	+	1301.74i	−0.446633	+	1.37460i	0.434050	+	0.900889i	$0.357084\pi$
$947$	−422.962	+	1301.74i	−0.446633	+	1.37460i	−0.880683	+	0.473706i	$0.842916\pi$
$948$	−320.752	−	1399.46i	−0.338346	−	1.47622i
$949$	133.365			0.140532
$950$	−60.1006	−	45.5178i	−0.0632637	−	0.0479135i
$951$	49.8443	−	116.910i	0.0524126	−	0.122933i
$952$	−782.688	−	1077.28i	−0.822151	−	1.13159i
$953$	−224.887	+	692.131i	−0.235978	+	0.726265i	0.761012	+	0.648737i	$0.224703\pi$
$953$	−224.887	+	692.131i	−0.235978	+	0.726265i	−0.996990	+	0.0775277i	$0.975297\pi$
$954$	200.319	−	96.9162i	0.209978	−	0.101589i
$955$	9.38681	−	12.6534i	0.00982912	−	0.0132497i
$956$	185.247	−	60.1902i	0.193772	−	0.0629605i
$957$	−545.025	+	1278.35i	−0.569514	+	1.33579i
$958$	−231.961	+	75.3687i	−0.242130	+	0.0786730i
$959$	559.983	−	770.751i	0.583924	−	0.803703i
$960$	−86.6109	−	8.58440i	−0.0902197	−	0.00894209i
$961$	371.210	−	269.700i	0.386275	−	0.280645i
$962$	−46.6815	−	33.9161i	−0.0485255	−	0.0352558i
$963$	−143.842	−	1047.60i	−0.149369	−	1.08786i
$964$	−665.734	+	483.684i	−0.690595	+	0.501747i
$965$	4.09860	−	412.379i	0.00424726	−	0.427336i
$966$	−14.2087	−	23.7325i	−0.0147088	−	0.0245678i
$967$	404.806	−	131.529i	0.418620	−	0.136018i	−0.0921302	−	0.995747i	$-0.529368\pi$
$967$	404.806	−	131.529i	0.418620	−	0.136018i	0.510750	+	0.859729i	$0.329368\pi$
$968$	1096.34			1.13258
$969$	−238.569	−	21.2536i	−0.246201	−	0.0219335i
$970$	−489.471	+	153.678i	−0.504609	+	0.158430i
$971$	−671.700	−	218.249i	−0.691762	−	0.224767i	−0.0580241	−	0.998315i	$-0.518480\pi$
$971$	−671.700	−	218.249i	−0.691762	−	0.224767i	−0.633737	+	0.773548i	$0.718480\pi$
$972$	−550.435	+	580.958i	−0.566291	+	0.597694i
$973$	−1121.47	−	1543.57i	−1.15259	−	1.58640i
$974$			638.382i			0.655423i
$975$	200.169	−	41.7088i	0.205301	−	0.0427782i
$976$	−658.525			−0.674718
$977$	−518.731	+	376.880i	−0.530942	+	0.385752i	−0.820710	−	0.571345i	$-0.806422\pi$
$977$	−518.731	+	376.880i	−0.530942	+	0.385752i	0.289768	+	0.957097i	$0.406422\pi$
$978$	47.6055	−	54.5886i	0.0486763	−	0.0558166i
$979$	191.152	−	588.306i	0.195253	−	0.600926i
$980$	242.618	−	722.199i	0.247569	−	0.736938i
$981$	−413.181	+	771.166i	−0.421183	+	0.786101i
$982$		−	150.766i		−	0.153529i
$983$	−245.476	−	755.499i	−0.249722	−	0.768564i	−0.994824	−	0.101614i	$-0.967599\pi$
$983$	−245.476	−	755.499i	−0.249722	−	0.768564i	0.745102	−	0.666950i	$-0.232401\pi$
$984$	229.048	+	382.574i	0.232773	+	0.388795i
$985$	331.546	−	986.911i	0.336595	−	1.00194i
$986$	−294.136	−	404.844i	−0.298313	−	0.410592i
$987$	−534.798	−	893.261i	−0.541842	−	0.905026i
$988$	18.9341	−	26.0606i	0.0191641	−	0.0263771i
$989$	−33.5616	−	46.1935i	−0.0339349	−	0.0467073i
$990$	122.182	−	643.474i	0.123416	−	0.649974i
$991$	369.744	+	268.634i	0.373101	+	0.271074i	0.758496	−	0.651678i	$-0.225935\pi$
$991$	369.744	+	268.634i	0.373101	+	0.271074i	−0.385394	+	0.922752i	$0.625935\pi$
$992$	216.497	+	666.311i	0.218243	+	0.671684i
$993$	−246.476	+	578.108i	−0.248213	+	0.582183i
$994$	−118.673	−	365.237i	−0.119389	−	0.367441i
$995$	−647.880	−	6.43923i	−0.651136	−	0.00647159i
$996$	6.68896	+	5.83329i	0.00671583	+	0.00585672i
$997$	1399.79	+	454.820i	1.40400	+	0.456188i	0.910483	−	0.413546i	$-0.135710\pi$
$997$	1399.79	+	454.820i	1.40400	+	0.456188i	0.493520	+	0.869735i	$0.335710\pi$
$998$	−257.916	+	187.387i	−0.258432	+	0.187762i
$999$	−240.613	−	635.849i	−0.240854	−	0.636486i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.3.h.a.14.8	✓	72
3.2	odd	2	inner	75.3.h.a.14.11	yes	72
5.2	odd	4		375.3.j.b.176.15		144
5.3	odd	4		375.3.j.b.176.22		144
5.4	even	2		375.3.h.a.74.11		72
15.2	even	4		375.3.j.b.176.21		144
15.8	even	4		375.3.j.b.176.16		144
15.14	odd	2		375.3.h.a.74.8		72
25.9	even	10	inner	75.3.h.a.59.11	yes	72
25.12	odd	20		375.3.j.b.326.21		144
25.13	odd	20		375.3.j.b.326.16		144
25.16	even	5		375.3.h.a.299.8		72
75.38	even	20		375.3.j.b.326.22		144
75.41	odd	10		375.3.h.a.299.11		72
75.59	odd	10	inner	75.3.h.a.59.8	yes	72
75.62	even	20		375.3.j.b.326.15		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.3.h.a.14.8	✓	72	1.1	even	1	trivial
75.3.h.a.14.11	yes	72	3.2	odd	2	inner
75.3.h.a.59.8	yes	72	75.59	odd	10	inner
75.3.h.a.59.11	yes	72	25.9	even	10	inner
375.3.h.a.74.8		72	15.14	odd	2
375.3.h.a.74.11		72	5.4	even	2
375.3.h.a.299.8		72	25.16	even	5
375.3.h.a.299.11		72	75.41	odd	10
375.3.j.b.176.15		144	5.2	odd	4
375.3.j.b.176.16		144	15.8	even	4
375.3.j.b.176.21		144	15.2	even	4
375.3.j.b.176.22		144	5.3	odd	4
375.3.j.b.326.15		144	75.62	even	20
375.3.j.b.326.16		144	25.13	odd	20
375.3.j.b.326.21		144	25.12	odd	20
375.3.j.b.326.22		144	75.38	even	20

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:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	75.h (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.680034 + 0.494074i) q^{2} +(-2.26100 - 1.97177i) q^{3} +(-1.01773 + 3.13225i) q^{4} +(4.99975 + 0.0496921i) q^{5} +(2.51176 + 0.223767i) q^{6} +9.76040i q^{7} +(-1.89447 - 5.83059i) q^{8} +(1.22427 + 8.91634i) q^{9} +(-3.42456 + 2.43645i) q^{10} +(10.1778 + 14.0086i) q^{11} +(8.47716 - 5.07530i) q^{12} +(-1.60244 + 2.20557i) q^{13} +(-4.82236 - 6.63741i) q^{14} +(-11.2065 - 9.97070i) q^{15} +(-6.48876 - 4.71436i) q^{16} +(-6.87668 - 21.1642i) q^{17} +(-5.23787 - 5.45854i) q^{18} +(1.10865 + 3.41207i) q^{19} +(-5.24405 + 15.6099i) q^{20} +(19.2452 - 22.0683i) q^{21} +(-13.8426 - 4.49772i) q^{22} +(-0.909200 + 0.660572i) q^{23} +(-7.21315 + 16.9184i) q^{24} +(24.9951 + 0.496897i) q^{25} -2.29159i q^{26} +(14.8129 - 22.5738i) q^{27} +(-30.5720 - 9.93345i) q^{28} +(-25.4429 - 8.26690i) q^{29} +(12.5471 + 1.24360i) q^{30} +(6.92473 + 21.3121i) q^{31} +31.2644 q^{32} +(4.60957 - 51.7418i) q^{33} +(15.1331 + 10.9948i) q^{34} +(-0.485015 + 48.7996i) q^{35} +(-29.1742 - 5.23972i) q^{36} +(14.8003 - 20.3708i) q^{37} +(-2.43974 - 1.77257i) q^{38} +(7.97200 - 1.82716i) q^{39} +(-9.18216 - 29.2456i) q^{40} +(14.2504 - 19.6141i) q^{41} +(-2.18406 + 24.5158i) q^{42} +50.8068i q^{43} +(-54.2367 + 17.6226i) q^{44} +(5.67796 + 44.6403i) q^{45} +(0.291916 - 0.898424i) q^{46} +(10.9874 - 33.8156i) q^{47} +(5.37549 + 23.4535i) q^{48} -46.2654 q^{49} +(-17.2430 + 12.0115i) q^{50} +(-26.1828 + 61.4116i) q^{51} +(-5.27755 - 7.26393i) q^{52} +(-9.08989 + 27.9758i) q^{53} +(1.07987 + 22.6696i) q^{54} +(50.1905 + 70.5452i) q^{55} +(56.9088 - 18.4908i) q^{56} +(4.22115 - 9.90071i) q^{57} +(21.3865 - 6.94890i) q^{58} +(51.6779 - 71.1286i) q^{59} +(42.6359 - 24.9540i) q^{60} +(66.4241 - 48.2599i) q^{61} +(-15.2388 - 11.0716i) q^{62} +(-87.0271 + 11.9493i) q^{63} +(4.69420 - 3.41054i) q^{64} +(-8.12141 + 10.9477i) q^{65} +(22.4296 + 37.4637i) q^{66} +(-68.7311 + 22.3321i) q^{67} +73.2904 q^{68} +(3.35820 + 0.299175i) q^{69} +(-23.7808 - 33.4250i) q^{70} +(44.5178 + 14.4647i) q^{71} +(49.6682 - 24.0300i) q^{72} +(-28.7539 - 39.5764i) q^{73} +21.1653i q^{74} +(-55.5341 - 50.4079i) q^{75} -11.8158 q^{76} +(-136.729 + 99.3397i) q^{77} +(-4.51848 + 5.18129i) q^{78} +(44.9043 - 138.201i) q^{79} +(-32.2080 - 23.8931i) q^{80} +(-78.0023 + 21.8320i) q^{81} +20.3790i q^{82} +(0.277581 + 0.854307i) q^{83} +(49.5370 + 82.7405i) q^{84} +(-33.3300 - 106.158i) q^{85} +(-25.1023 - 34.5504i) q^{86} +(41.2261 + 68.8590i) q^{87} +(62.3967 - 85.8816i) q^{88} +(-20.9981 - 28.9013i) q^{89} +(-25.9168 - 27.5516i) q^{90} +(-21.5273 - 15.6405i) q^{91} +(-1.14376 - 3.52013i) q^{92} +(26.3657 - 61.8407i) q^{93} +(9.23562 + 28.4243i) q^{94} +(5.37342 + 17.1146i) q^{95} +(-70.6889 - 61.6461i) q^{96} +(116.093 + 37.7208i) q^{97} +(31.4621 - 22.8585i) q^{98} +(-112.445 + 107.899i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 5 q^{3} - 38 q^{4} + 5 q^{6} - 13 q^{9} - 20 q^{10} - 45 q^{12} - 10 q^{13} - 15 q^{15} + 22 q^{16} - 36 q^{19} + 54 q^{21} - 50 q^{22} - 20 q^{24} - 100 q^{25} + 100 q^{27} + 270 q^{28} - 5 q^{30}+ \cdots + 60 q^{99}+O(q^{100}) \) 72 * q - 5 * q^3 - 38 * q^4 + 5 * q^6 - 13 * q^9 - 20 * q^10 - 45 * q^12 - 10 * q^13 - 15 * q^15 + 22 * q^16 - 36 * q^19 + 54 * q^21 - 50 * q^22 - 20 * q^24 - 100 * q^25 + 100 * q^27 + 270 * q^28 - 5 * q^30 - 126 * q^31 + 20 * q^33 + 210 * q^34 - 213 * q^36 + 110 * q^37 - 191 * q^39 + 140 * q^40 - 175 * q^42 - 405 * q^45 - 210 * q^46 + 150 * q^48 - 224 * q^49 - 60 * q^51 - 320 * q^52 + 320 * q^54 - 10 * q^55 - 70 * q^58 + 1190 * q^60 + 294 * q^61 + 795 * q^63 + 362 * q^64 - 470 * q^66 - 260 * q^67 + 335 * q^69 + 1200 * q^70 + 215 * q^72 - 150 * q^73 + 200 * q^75 - 16 * q^76 - 1295 * q^78 - 346 * q^79 + 507 * q^81 - 456 * q^84 - 1450 * q^85 - 430 * q^87 - 1710 * q^88 - 820 * q^90 + 538 * q^91 - 560 * q^94 + 740 * q^96 - 150 * q^97 + 60 * q^99

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