LMFDB - Embedded newform 75.3.h.a.14.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [75,3,Mod(14,75)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

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")

//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: f = N[0] # Warning: the index may be different

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			14.11
Character	$\chi$	$=$	75.14
Dual form			75.3.h.a.59.11

$q$-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} +(-2.98817 + 0.266209i) q^{3} +(-1.01773 + 3.13225i) q^{4} +(-4.99975 - 0.0496921i) q^{5} +(-1.90053 + 1.65741i) q^{6} +9.76040i q^{7} +(1.89447 + 5.83059i) q^{8} +(8.85827 - 1.59096i) q^{9} +(-3.42456 + 2.43645i) q^{10} +(-10.1778 - 14.0086i) q^{11} +(2.20731 - 9.63062i) q^{12} +(-1.60244 + 2.20557i) q^{13} +(4.82236 + 6.63741i) q^{14} +(14.9533 - 1.18249i) 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} +(-2.59831 - 29.1657i) 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} +(-26.0464 + 7.11219i) q^{27} +(-30.5720 - 9.93345i) q^{28} +(25.4429 + 8.26690i) q^{29} +(9.58453 - 8.19218i) q^{30} +(6.92473 + 21.3121i) q^{31} -31.2644 q^{32} +(34.1423 + 39.1505i) q^{33} +(15.1331 + 10.9948i) q^{34} +(0.485015 - 48.7996i) q^{35} +(-4.03205 + 29.3655i) q^{36} +(14.8003 - 20.3708i) q^{37} +(2.43974 + 1.77257i) q^{38} +(4.20122 - 7.01720i) q^{39} +(-9.18216 - 29.2456i) q^{40} +(-14.2504 + 19.6141i) q^{41} +(-16.1769 - 18.5499i) q^{42} +50.8068i q^{43} +(54.2367 - 17.6226i) q^{44} +(-44.3682 + 7.51420i) q^{45} +(0.291916 - 0.898424i) q^{46} +(-10.9874 + 33.8156i) q^{47} +(20.6445 + 12.3599i) 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} +(-14.1985 + 17.7054i) 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} +(-11.5146 + 48.0410i) q^{60} +(66.4241 - 48.2599i) q^{61} +(15.2388 + 11.0716i) q^{62} +(15.5284 + 86.4602i) q^{63} +(4.69420 - 3.41054i) q^{64} +(8.12141 - 10.9477i) q^{65} +(42.5612 + 9.75491i) q^{66} +(-68.7311 + 22.3321i) q^{67} -73.2904 q^{68} +(-2.54099 + 2.21594i) q^{69} +(-23.7808 - 33.4250i) q^{70} +(-44.5178 - 14.4647i) q^{71} +(26.0579 + 48.6349i) q^{72} +(-28.7539 - 39.5764i) q^{73} -21.1653i q^{74} +(-74.8217 + 5.16911i) q^{75} -11.8158 q^{76} +(136.729 - 99.3397i) q^{77} +(-0.610043 - 6.84765i) q^{78} +(44.9043 - 138.201i) q^{79} +(32.2080 + 23.8931i) q^{80} +(75.9377 - 28.1862i) q^{81} +20.3790i q^{82} +(-0.277581 - 0.854307i) q^{83} +(93.9987 + 21.5442i) q^{84} +(-33.3300 - 106.158i) q^{85} +(25.1023 + 34.5504i) q^{86} +(-78.2284 - 17.9297i) q^{87} +(62.3967 - 85.8816i) q^{88} +(20.9981 + 28.9013i) q^{89} +(-26.4593 + 27.0311i) 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} +(93.4232 - 8.32287i) 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	−0.404652	−	0.914471i	$-0.632607\pi$
$2$	0.680034	−	0.494074i	0.340017	−	0.247037i	0.744669	+	0.667434i	$0.232607\pi$
$3$	−2.98817	+	0.266209i	−0.996055	+	0.0887365i
$3$	−2.98817	+	0.266209i	−0.996055	+	0.0887365i
$4$	−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
$6$	−1.90053	+	1.65741i	−0.316755	+	0.276234i
$7$			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
$9$	8.85827	−	1.59096i	0.984252	−	0.176773i
$10$	−3.42456	+	2.43645i	−0.342456	+	0.243645i
$11$	−10.1778	−	14.0086i	−0.925258	−	1.27351i	−0.961681	−	0.274172i	$-0.911596\pi$
$11$	−10.1778	−	14.0086i	−0.925258	−	1.27351i	0.0364230	−	0.999336i	$-0.488404\pi$
$12$	2.20731	−	9.63062i	0.183943	−	0.802551i
$13$	−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
$15$	14.9533	−	1.18249i	0.996888	−	0.0788329i
$16$	−6.48876	−	4.71436i	−0.405548	−	0.294648i
$17$	6.87668	+	21.1642i	0.404511	+	1.24496i	0.921303	+	0.388845i	$0.127126\pi$
$17$	6.87668	+	21.1642i	0.404511	+	1.24496i	−0.516792	+	0.856111i	$0.672874\pi$
$18$	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
$21$	−2.59831	−	29.1657i	−0.123729	−	1.38884i
$22$	−13.8426	−	4.49772i	−0.629207	−	0.204442i
$23$	0.909200	−	0.660572i	0.0395304	−	0.0287205i	−0.567845	−	0.823136i	$-0.692223\pi$
$23$	0.909200	−	0.660572i	0.0395304	−	0.0287205i	0.607375	+	0.794415i	$0.292223\pi$
$24$	−7.21315	−	16.9184i	−0.300548	−	0.704934i
$25$	24.9951	+	0.496897i	0.999802	+	0.0198759i
$26$			2.29159i			0.0881381i
$27$	−26.0464	+	7.11219i	−0.964683	+	0.263414i
$28$	−30.5720	−	9.93345i	−1.09186	−	0.354766i
$29$	25.4429	+	8.26690i	0.877342	+	0.285066i	0.712853	−	0.701313i	$-0.247403\pi$
$29$	25.4429	+	8.26690i	0.877342	+	0.285066i	0.164489	+	0.986379i	$0.447403\pi$
$30$	9.58453	−	8.19218i	0.319484	−	0.273073i
$31$	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
$33$	34.1423	+	39.1505i	1.03461	+	1.18638i
$34$	15.1331	+	10.9948i	0.445091	+	0.323377i
$35$	0.485015	−	48.7996i	0.0138576	−	1.39427i
$36$	−4.03205	+	29.3655i	−0.112001	+	0.815708i
$37$	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
$39$	4.20122	−	7.01720i	0.107724	−	0.179928i
$40$	−9.18216	−	29.2456i	−0.229554	−	0.731141i
$41$	−14.2504	+	19.6141i	−0.347572	+	0.478391i	−0.946634	−	0.322311i	$-0.895540\pi$
$41$	−14.2504	+	19.6141i	−0.347572	+	0.478391i	0.599062	+	0.800703i	$0.295540\pi$
$42$	−16.1769	−	18.5499i	−0.385165	−	0.441665i
$43$			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
$45$	−44.3682	+	7.51420i	−0.985960	+	0.166982i
$46$	0.291916	−	0.898424i	0.00634599	−	0.0195310i
$47$	−10.9874	+	33.8156i	−0.233773	+	0.719481i	0.763508	+	0.645798i	$0.223475\pi$
$47$	−10.9874	+	33.8156i	−0.233773	+	0.719481i	−0.997282	+	0.0736826i	$0.976525\pi$
$48$	20.6445	+	12.3599i	0.430094	+	0.257498i
$49$	−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	−0.827949	−	0.560803i	$-0.810493\pi$
$53$	9.08989	−	27.9758i	0.171507	−	0.527845i	0.999457	+	0.0329575i	$0.0104926\pi$
$54$	−14.1985	+	17.7054i	−0.262936	+	0.327878i
$55$	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	$0.467590\pi$
$59$	−51.6779	+	71.1286i	−0.875897	+	1.20557i	−0.977540	+	0.210748i	$0.932410\pi$
$60$	−11.5146	+	48.0410i	−0.191910	+	0.800684i
$61$	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
$63$	15.5284	+	86.4602i	0.246482	+	1.37238i
$64$	4.69420	−	3.41054i	0.0733469	−	0.0532896i
$65$	8.12141	−	10.9477i	0.124945	−	0.168426i
$66$	42.5612	+	9.75491i	0.644866	+	0.147802i
$67$	−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
$69$	−2.54099	+	2.21594i	−0.0368259	+	0.0321150i
$70$	−23.7808	−	33.4250i	−0.339725	−	0.477500i
$71$	−44.5178	−	14.4647i	−0.627011	−	0.203728i	−0.0217603	−	0.999763i	$-0.506927\pi$
$71$	−44.5178	−	14.4647i	−0.627011	−	0.203728i	−0.605251	+	0.796035i	$0.706927\pi$
$72$	26.0579	+	48.6349i	0.361916	+	0.675484i
$73$	−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
$75$	−74.8217	+	5.16911i	−0.997622	+	0.0689215i
$76$	−11.8158			−0.155471
$77$	136.729	−	99.3397i	1.77571	−	1.29013i
$78$	−0.610043	−	6.84765i	−0.00782106	−	0.0877904i
$79$	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
$81$	75.9377	−	28.1862i	0.937503	−	0.347978i
$82$			20.3790i			0.248524i
$83$	−0.277581	−	0.854307i	−0.00334435	−	0.0102929i	0.949370	−	0.314159i	$-0.101722\pi$
$83$	−0.277581	−	0.854307i	−0.00334435	−	0.0102929i	−0.952715	+	0.303866i	$0.901722\pi$
$84$	93.9987	+	21.5442i	1.11903	+	0.256479i
$85$	−33.3300	−	106.158i	−0.392118	−	1.24891i
$86$	25.1023	+	34.5504i	0.291887	+	0.401748i
$87$	−78.2284	−	17.9297i	−0.899176	−	0.206089i
$88$	62.3967	−	85.8816i	0.709053	−	0.975928i
$89$	20.9981	+	28.9013i	0.235933	+	0.324734i	0.910523	−	0.413459i	$-0.135679\pi$
$89$	20.9981	+	28.9013i	0.235933	+	0.324734i	−0.674590	+	0.738193i	$0.735679\pi$
$90$	−26.4593	+	27.0311i	−0.293993	+	0.300345i
$91$	−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
$96$	93.4232	−	8.32287i	0.973158	−	0.0866966i
$97$	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	$0.0455544\pi$
$101$			28.8103i			0.285251i	−0.989777	+	0.142625i	$0.954446\pi$
$102$	−48.1471	−	28.8258i	−0.472030	−	0.282606i
$103$	−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
$105$	11.5416	+	145.950i	0.109920	+	1.39000i
$106$	−7.64067	−	23.5156i	−0.0720818	−	0.221845i
$107$	117.493			1.09806			0.549031	−	0.835802i	$-0.314997\pi$
$107$	117.493			1.09806			0.549031	+	0.835802i	$0.314997\pi$
$108$	4.23107	−	88.8223i	0.0391766	−	0.822429i
$109$	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
$111$	−38.8027	+	64.8113i	−0.349574	+	0.583886i
$112$	46.0141	−	63.3329i	0.410840	−	0.565473i
$113$	−116.803	−	84.8623i	−1.03365	−	0.750994i	−0.0646176	−	0.997910i	$-0.520583\pi$
$113$	−116.803	−	84.8623i	−1.03365	−	0.750994i	−0.969037	+	0.246916i	$0.920583\pi$
$114$	−7.76221	−	4.64726i	−0.0680896	−	0.0407654i
$115$	−4.57860	+	3.25752i	−0.0398139	+	0.0283263i
$116$	−51.7880	+	71.2801i	−0.446449	+	0.614484i
$117$	−10.6859	+	22.0870i	−0.0913324	+	0.188777i
$118$			73.9026i			0.626293i
$119$	−206.572	+	67.1192i	−1.73590	+	0.564027i
$120$	35.2233	+	84.9464i	0.293527	+	0.707887i
$121$	−55.2612	+	170.076i	−0.456704	+	1.40559i
$122$	21.3267	−	65.6368i	0.174809	−	0.538006i
$123$	37.3612	−	62.4036i	0.303750	−	0.507347i
$124$	−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
$129$	−13.5252	−	151.819i	−0.104847	−	1.17689i
$130$	0.113874	−	11.4574i	0.000875953	−	0.0881337i
$131$	149.348	−	48.5260i	1.14006	−	0.370427i	0.322668	−	0.946512i	$-0.395420\pi$
$131$	149.348	−	48.5260i	1.14006	−	0.370427i	0.817390	+	0.576085i	$0.195420\pi$
$132$	−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
$135$	130.579	−	34.2649i	0.967253	−	0.253814i
$136$	−110.372	+	80.1902i	−0.811561	+	0.589634i
$137$	78.9672	+	57.3730i	0.576403	+	0.418781i	0.837425	−	0.546552i	$-0.184060\pi$
$137$	78.9672	+	57.3730i	0.576403	+	0.418781i	−0.261023	+	0.965333i	$0.584060\pi$
$138$	−0.633123	+	2.76235i	−0.00458785	+	0.0200170i
$139$	−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
$141$	23.8300	−	103.972i	0.169007	−	0.737387i
$142$	−37.4202	+	12.1586i	−0.263523	+	0.0856238i
$143$	47.2063			0.330114
$144$	−64.9795	−	31.4377i	−0.451247	−	0.218318i
$145$	−126.797	−	42.5968i	−0.874465	−	0.293771i
$146$	−39.1073	−	12.7067i	−0.267858	−	0.0870324i
$147$	138.249	−	12.3163i	0.940467	−	0.0837842i
$148$	48.7438	+	67.0901i	0.329350	+	0.453312i
$149$			138.880i			0.932082i	0.884763	+	0.466041i	$0.154320\pi$
$149$			138.880i			0.932082i	−0.884763	+	0.466041i	$0.845680\pi$
$150$	−48.3274	+	40.4826i	−0.322182	+	0.269884i
$151$	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
$153$	94.5868	+	176.538i	0.618215	+	1.15384i
$154$	43.8995	−	135.109i	0.285062	−	0.877330i
$155$	−33.5629	−	106.899i	−0.216535	−	0.689674i
$156$	17.7039	+	20.3009i	0.113487	+	0.130134i
$157$			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
$159$	−19.7147	+	86.0161i	−0.123992	+	0.540982i
$160$	156.314	+	1.55359i	0.976964	+	0.00970996i
$161$	6.44745	+	8.87415i	0.0400463	+	0.0551190i
$162$	37.7142	−	56.6864i	0.232804	−	0.349916i
$163$	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
$165$	−168.757	−	197.440i	−1.02277	−	1.19660i
$166$	−0.610855	−	0.443812i	−0.00367985	−	0.00267357i
$167$	−54.3150	−	167.164i	−0.325240	−	1.00098i	−0.971332	−	0.237726i	$-0.923598\pi$
$167$	−54.3150	−	167.164i	−0.325240	−	1.00098i	0.646093	−	0.763259i	$-0.276402\pi$
$168$	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
$171$	15.2492	+	28.4612i	0.0891764	+	0.166440i
$172$	−159.140	−	51.7076i	−0.925231	−	0.300626i
$173$	35.5781	−	25.8490i	0.205654	−	0.149416i	−0.480191	−	0.877164i	$-0.659433\pi$
$173$	35.5781	−	25.8490i	0.205654	−	0.149416i	0.685845	+	0.727748i	$0.259433\pi$
$174$	−62.0566	+	26.4577i	−0.356647	+	0.152056i
$175$	−4.84991	+	243.962i	−0.0277138	+	1.39407i
$176$			138.880i			0.789093i
$177$	135.487	−	226.301i	0.765464	−	1.27854i
$178$	28.5588	+	9.27931i	0.160443	+	0.0521310i
$179$	290.732	+	94.4646i	1.62420	+	0.527735i	0.972928	−	0.231107i	$-0.0742349\pi$
$179$	290.732	+	94.4646i	1.62420	+	0.527735i	0.651274	+	0.758843i	$0.274235\pi$
$180$	21.6185	−	146.620i	0.120103	−	0.814554i
$181$	−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
$183$	−185.639	+	161.891i	−1.01442	+	0.884652i
$184$	5.57398	+	4.04973i	0.0302934	+	0.0220094i
$185$	−75.0099	+	101.114i	−0.405459	+	0.546560i
$186$	−48.4835	−	29.0272i	−0.260664	−	0.156060i
$187$	226.492	−	311.739i	1.21118	−	1.66705i
$188$	−94.7368	−	68.8303i	−0.503919	−	0.366119i
$189$	−69.4178	−	254.224i	−0.367290	−	1.34510i
$190$	−12.1100	−	8.98366i	−0.0637368	−	0.0472824i
$191$	−1.85212	+	2.54922i	−0.00969695	+	0.0133467i	−0.813838	−	0.581092i	$-0.802626\pi$
$191$	−1.85212	+	2.54922i	−0.00969695	+	0.0133467i	0.804141	+	0.594439i	$0.202626\pi$
$192$	−13.1191	+	11.4409i	−0.0683288	+	0.0595880i
$193$		−	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
$195$	−21.3538	+	34.8755i	−0.109506	+	0.178849i
$196$	47.0857	−	144.915i	0.240233	−	0.739362i
$197$	−64.3443	+	198.031i	−0.326621	+	1.00524i	0.644083	+	0.764956i	$0.277239\pi$
$197$	−64.3443	+	198.031i	−0.326621	+	1.00524i	−0.970704	+	0.240280i	$0.922761\pi$
$198$	−129.777	−	17.8191i	−0.655438	−	0.0899954i
$199$	−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
$204$	219.004	−	19.5106i	1.07355	−	0.0956401i
$205$	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
$210$	79.9589	+	93.5488i	0.380757	+	0.445471i
$211$	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
$213$	136.877	+	31.3719i	0.642616	+	0.147286i
$214$	79.8990	−	58.0500i	0.373360	−	0.271262i
$215$	2.52470	−	254.021i	0.0117428	−	1.18150i
$216$	−90.8125	−	138.392i	−0.420428	−	0.640704i
$217$	−208.015	+	67.5881i	−0.958594	+	0.311466i
$218$	81.7107			0.374820
$219$	96.4571	+	110.606i	0.440443	+	0.505051i
$220$	−272.046	+	85.4134i	−1.23657	+	0.388243i
$221$	−57.6988	−	18.7475i	−0.261080	−	0.0848302i
$222$	5.63439	+	63.2453i	0.0253801	+	0.284889i
$223$	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
$225$	222.203	−	35.3644i	0.987571	−	0.157175i
$226$	−121.358			−0.536983
$227$	−244.647	+	177.746i	−1.07774	+	0.783023i	−0.977287	−	0.211919i	$-0.932029\pi$
$227$	−244.647	+	177.746i	−1.07774	+	0.783023i	−0.100451	+	0.994942i	$0.532029\pi$
$228$	35.3075	−	3.14547i	0.154857	−	0.0137959i
$229$	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
$231$	−382.125	+	333.242i	−1.65422	+	1.44261i
$232$			164.008i			0.706933i
$233$	−26.3563	−	81.1163i	−0.113117	−	0.348139i	0.878433	−	0.477866i	$-0.158590\pi$
$233$	−26.3563	−	81.1163i	−0.113117	−	0.348139i	−0.991550	+	0.129728i	$0.958590\pi$
$234$	3.64582	+	20.2995i	0.0155804	+	0.0867500i
$235$	56.6144	−	168.524i	0.240912	−	0.717122i
$236$	−170.198	−	234.258i	−0.721180	−	0.992619i
$237$	−97.3910	+	424.922i	−0.410932	+	1.79292i
$238$	−107.314	+	147.705i	−0.450899	+	0.620609i
$239$	34.7626	+	47.8466i	0.145450	+	0.200195i	0.875526	−	0.483171i	$-0.160515\pi$
$239$	34.7626	+	47.8466i	0.145450	+	0.200195i	−0.730076	+	0.683366i	$0.760515\pi$
$240$	−102.603	−	62.8225i	−0.427514	−	0.261760i
$241$	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
$246$	−5.42508	−	60.8958i	−0.0220532	−	0.247544i
$247$	−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	$-0.886954\pi$
$251$		−	174.558i		−	0.695449i	0.937597	−	0.347725i	$-0.113046\pi$
$252$	−286.619	−	39.3544i	−1.13738	−	0.156168i
$253$	−18.5074	−	6.01341i	−0.0731517	−	0.0237684i
$254$	2.64808	+	0.860414i	0.0104255	+	0.00338746i
$255$	127.856	+	308.344i	0.501395	+	1.20919i
$256$	−26.5785	−	81.8001i	−0.103822	−	0.319532i
$257$	−189.705			−0.738151			−0.369076	−	0.929399i	$-0.620326\pi$
$257$	−189.705			−0.738151			−0.369076	+	0.929399i	$0.620326\pi$
$258$	−84.2075	−	96.5597i	−0.326386	−	0.374263i
$259$	198.827	+	144.456i	0.767673	+	0.557747i
$260$	26.0255	+	36.5801i	0.100098	+	0.140693i
$261$	238.532	+	32.7519i	0.913917	+	0.125486i
$262$	77.5861	−	106.788i	0.296130	−	0.407588i
$263$	371.284	+	269.754i	1.41173	+	1.02568i	0.993069	+	0.117537i	$0.0374998\pi$
$263$	371.284	+	269.754i	1.41173	+	1.02568i	0.418659	+	0.908143i	$0.362500\pi$
$264$	−163.589	+	273.239i	−0.619655	+	1.03500i
$265$	−46.8374	+	139.420i	−0.176745	+	0.526115i
$266$	−17.3010	+	23.8128i	−0.0650414	+	0.0895218i
$267$	−70.4395	−	80.7721i	−0.263818	−	0.302517i
$268$		−	238.011i		−	0.888102i
$269$	53.7617	−	17.4682i	0.199858	−	0.0649377i	−0.207378	−	0.978261i	$-0.566493\pi$
$269$	53.7617	−	17.4682i	0.199858	−	0.0649377i	0.407235	+	0.913323i	$0.366493\pi$
$270$	71.8689	−	87.8170i	0.266181	−	0.325248i
$271$	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
$273$	68.4907	+	41.0056i	0.250882	+	0.150204i
$274$	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
$279$	95.2477	+	177.772i	0.341390	+	0.637174i
$280$	285.449	−	89.6215i	1.01946	−	0.320077i
$281$	11.6791	−	3.79478i	0.0415627	−	0.0135046i	−0.288162	−	0.957582i	$-0.593044\pi$
$281$	11.6791	−	3.79478i	0.0415627	−	0.0135046i	0.329725	+	0.944077i	$0.393044\pi$
$282$	−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
$285$	20.6127	+	49.7108i	0.0723254	+	0.174424i
$286$	32.1019	−	23.3234i	0.112245	−	0.0815504i
$287$	−191.441	−	139.090i	−0.667042	−	0.484634i
$288$	−276.948	+	49.7402i	−0.961626	+	0.172709i
$289$	−166.831	+	121.210i	−0.577269	+	0.419411i
$290$	−107.273	+	33.6800i	−0.369905	+	0.116138i
$291$	−356.946	−	81.8110i	−1.22662	−	0.281137i
$292$	153.227	−	49.7864i	0.524750	−	0.170502i
$293$	360.580			1.23065			0.615324	−	0.788274i	$-0.289025\pi$
$293$	360.580			1.23065			0.615324	+	0.788274i	$0.289025\pi$
$294$	87.9287	−	76.6805i	0.299077	−	0.260818i
$295$	261.912	−	353.057i	0.887836	−	1.19680i
$296$	146.812	+	47.7022i	0.495988	+	0.161156i
$297$	364.728	+	292.487i	1.22804	+	0.984805i
$298$	68.6171	+	94.4433i	0.230259	+	0.316924i
$299$			3.06384i			0.0102469i
$300$	59.9573	−	239.621i	0.199858	−	0.798737i
$301$	−495.895			−1.64749
$302$	42.3138	−	30.7428i	0.140112	−	0.101797i
$303$	−7.66958	−	86.0900i	−0.0253121	−	0.284125i
$304$	8.89198	−	27.3667i	0.0292499	−	0.0900221i
$305$	−334.502	+	237.987i	−1.09673	+	0.780285i
$306$	151.545	+	73.3190i	0.495246	+	0.239605i
$307$		−	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
$309$	19.9974	+	4.58336i	0.0647166	+	0.0148329i
$310$	−75.6402	−	56.1128i	−0.244001	−	0.181009i
$311$	−38.9964	−	53.6740i	−0.125390	−	0.172585i	0.741706	−	0.670725i	$-0.234017\pi$
$311$	−38.9964	−	53.6740i	−0.125390	−	0.172585i	−0.867097	+	0.498139i	$0.834017\pi$
$312$	48.8735	+	11.2017i	0.156646	+	0.0359028i
$313$	−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
$315$	−73.3416	−	433.051i	−0.232830	−	1.37477i
$316$	387.180	+	281.303i	1.22525	+	0.890199i
$317$	−13.0912	−	40.2905i	−0.0412971	−	0.127099i	0.928282	−	0.371876i	$-0.121285\pi$
$317$	−13.0912	−	40.2905i	−0.0412971	−	0.127099i	−0.969579	+	0.244777i	$0.921285\pi$
$318$	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
$321$	−351.087	+	31.2776i	−1.09373	+	0.0974381i
$322$	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
$327$	−250.211	−	149.802i	−0.765171	−	0.458110i
$328$	−141.358	−	45.9302i	−0.430971	−	0.140031i
$329$	−330.054	−	107.241i	−1.00320	−	0.325960i
$330$	−212.311	−	50.8871i	−0.643366	−	0.154203i
$331$	−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
$333$	98.6955	−	203.997i	0.296383	−	0.612602i
$334$	−119.528	−	86.8419i	−0.357867	−	0.260006i
$335$	344.748	−	108.240i	1.02910	−	0.323103i
$336$	−120.638	+	201.499i	−0.359041	+	0.599698i
$337$	−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
$339$	371.618	+	222.489i	1.09622	+	0.656309i
$340$	366.434	+	3.64195i	1.07775	+	0.0107116i
$341$	228.074	−	313.917i	0.668839	−	0.920578i
$342$	24.4319	+	11.8204i	0.0714383	+	0.0345626i
$343$			26.6908i			0.0778156i
$344$	−296.233	+	96.2521i	−0.861144	+	0.279803i
$345$	12.8144	−	10.9529i	0.0371433	−	0.0317475i
$346$	11.4230	−	35.1564i	0.0330145	−	0.101608i
$347$	−45.9693	+	141.479i	−0.132476	+	0.407721i	−0.995189	−	0.0979741i	$-0.968764\pi$
$347$	−45.9693	+	141.479i	−0.132476	+	0.407721i	0.862713	+	0.505695i	$0.168764\pi$
$348$	135.776	−	226.783i	0.390160	−	0.651676i
$349$	−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	$-0.464796\pi$
$353$	213.661	−	657.582i	0.605273	−	1.86284i	0.494901	−	0.868949i	$-0.335204\pi$
$354$	−19.6736	−	220.833i	−0.0555750	−	0.623823i
$355$	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	−0.722673	−	0.691190i	$-0.757087\pi$
$359$	56.7241	−	78.0740i	0.158006	−	0.217476i	0.880679	+	0.473714i	$0.157087\pi$
$360$	−127.866	−	244.457i	−0.355185	−	0.679048i
$361$	281.642	−	204.625i	0.780172	−	0.566828i
$362$	−95.6723	−	69.5100i	−0.264288	−	0.192016i
$363$	119.854	−	522.927i	0.330175	−	1.44057i
$364$	70.8989	−	51.5110i	0.194777	−	0.141514i
$365$	141.796	+	199.301i	0.388482	+	0.546030i
$366$	−46.2545	+	201.811i	−0.126379	+	0.551396i
$367$	−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
$369$	−95.0291	+	196.418i	−0.257531	+	0.532299i
$370$	−1.05175	+	105.821i	−0.00284256	+	0.286003i
$371$	273.055	+	88.7209i	0.735997	+	0.239140i
$372$	220.534	−	19.6469i	0.592833	−	0.0528143i
$373$	−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
$375$	374.347	−	22.1262i	0.998258	−	0.0590033i
$376$	−217.980			−0.579734
$377$	−59.0040	+	42.8689i	−0.156509	+	0.113711i
$378$	−172.812	−	138.583i	−0.457174	−	0.366622i
$379$	−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
$381$	−6.53142	−	7.48951i	−0.0171428	−	0.0196575i
$382$			2.64864i			0.00693362i
$383$	74.5277	+	229.373i	0.194589	+	0.598884i	0.999981	+	0.00614145i	$0.00195490\pi$
$383$	74.5277	+	229.373i	0.194589	+	0.598884i	−0.805392	+	0.592743i	$0.798045\pi$
$384$	−87.0841	+	379.952i	−0.226782	+	0.989460i
$385$	−688.550	+	489.880i	−1.78844	+	1.27242i
$386$	−40.7512	−	56.0892i	−0.105573	−	0.145309i
$387$	80.8314	+	450.060i	0.208867	+	1.16295i
$388$	−236.302	+	325.242i	−0.609026	+	0.838252i
$389$	−366.878	−	504.964i	−0.943130	−	1.29811i	−0.954512	−	0.298172i	$-0.903623\pi$
$389$	−366.878	−	504.964i	−0.943130	−	1.29811i	0.0113819	−	0.999935i	$-0.496377\pi$
$390$	2.70979	+	34.2669i	0.00694818	+	0.0878638i
$391$	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
$396$	452.407	−	242.394i	1.14244	−	0.612105i
$397$	−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	$0.315825\pi$
$401$			671.456i			1.67445i	−0.546855	+	0.837227i	$0.684175\pi$
$402$	93.6121	−	156.358i	0.232866	−	0.388951i
$403$	−58.1019	−	18.8785i	−0.144173	−	0.0468448i
$404$	−90.2412	−	29.3211i	−0.223369	−	0.0725771i
$405$	−381.070	+	137.151i	−0.940915	+	0.338643i
$406$	67.8240	+	208.741i	0.167054	+	0.514140i
$407$	−436.001			−1.07126
$408$	308.463	−	269.004i	0.756037	−	0.659323i
$409$	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
$411$	−251.240	−	150.418i	−0.611290	−	0.365981i
$412$	13.2385	−	18.2213i	0.0321323	−	0.0442264i
$413$	−694.244	−	504.397i	−1.68098	−	1.22130i
$414$	1.15651	−	8.42290i	0.00279351	−	0.0203452i
$415$	1.34538	+	4.28512i	0.00324189	+	0.0103256i
$416$	50.0994	−	68.9559i	0.120431	−	0.165759i
$417$	441.978	−	385.439i	1.05990	−	0.924314i
$418$		−	52.2182i		−	0.124924i
$419$	523.183	−	169.993i	1.24865	−	0.405710i	0.391211	−	0.920301i	$-0.372056\pi$
$419$	523.183	−	169.993i	1.24865	−	0.405710i	0.857436	+	0.514591i	$0.172056\pi$
$420$	−468.900	−	112.387i	−1.11643	−	0.267588i
$421$	−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
$423$	−43.5298	+	317.028i	−0.102907	+	0.749475i
$424$	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
$429$	−141.060	+	12.5668i	−0.328812	+	0.0292932i
$430$	−123.788	−	173.991i	−0.287880	−	0.404630i
$431$	559.361	−	181.747i	1.29782	−	0.421687i	0.422998	−	0.906131i	$-0.360978\pi$
$431$	559.361	−	181.747i	1.29782	−	0.421687i	0.874823	+	0.484443i	$0.160978\pi$
$432$	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
$435$	390.231	+	93.5316i	0.897084	+	0.215015i
$436$	−259.008	+	188.181i	−0.594056	+	0.431607i
$437$	3.26191	+	2.36991i	0.00746431	+	0.00542314i
$438$	120.242	+	27.5591i	0.274525	+	0.0629203i
$439$	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
$441$	−409.831	+	73.6062i	−0.929322	+	0.166907i
$442$	−48.4998	+	15.7585i	−0.109728	+	0.0356528i
$443$	−600.844			−1.35631			−0.678153	−	0.734921i	$-0.737219\pi$
$443$	−600.844			−1.35631			−0.678153	+	0.734921i	$0.737219\pi$
$444$	−163.515	−	187.500i	−0.368276	−	0.422298i
$445$	−103.549	−	145.543i	−0.232694	−	0.327063i
$446$	45.9410	+	14.9271i	0.103007	+	0.0334689i
$447$	−36.9712	−	414.997i	−0.0827096	−	0.928405i
$448$	33.2882	+	45.8173i	0.0743040	+	0.102271i
$449$			160.308i			0.357034i	0.983937	+	0.178517i	$0.0571300\pi$
$449$			160.308i			0.357034i	−0.983937	+	0.178517i	$0.942870\pi$
$450$	133.633	−	133.834i	0.296963	−	0.297409i
$451$	419.804			0.930829
$452$	384.684	−	279.489i	0.851071	−	0.618339i
$453$	−185.933	+	16.5644i	−0.410448	+	0.0365659i
$454$	−78.5484	+	241.747i	−0.173014	+	0.532482i
$455$	106.854	+	79.2683i	0.234844	+	0.174216i
$456$	49.7301	−	43.3684i	0.109057	−	0.0951062i
$457$			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
$459$	−329.637	−	502.345i	−0.718164	−	1.09443i
$460$	−5.54359	−	17.6566i	−0.0120513	−	0.0383839i
$461$	421.360	+	579.953i	0.914014	+	1.25803i	0.965777	+	0.259373i	$0.0835158\pi$
$461$	421.360	+	579.953i	0.914014	+	1.25803i	−0.0517635	+	0.998659i	$0.516484\pi$
$462$	−95.2118	+	415.414i	−0.206086	+	0.899165i
$463$	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
$465$	128.749	+	310.499i	0.276880	+	0.667739i
$466$	−58.0006	−	42.1399i	−0.124465	−	0.0904290i
$467$	59.3052	+	182.523i	0.126992	+	0.390841i	0.994259	−	0.107003i	$-0.0341254\pi$
$467$	59.3052	+	182.523i	0.126992	+	0.390841i	−0.867267	+	0.497844i	$0.834125\pi$
$468$	−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
$471$	−50.2260	−	563.780i	−0.106637	−	1.19699i
$472$	−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
$477$	36.0124	−	262.279i	0.0754977	−	0.549850i
$478$	47.2795	+	15.3620i	0.0989111	+	0.0321382i
$479$	−275.957	−	89.6639i	−0.576111	−	0.187190i	0.00644656	−	0.999979i	$-0.497948\pi$
$479$	−275.957	−	89.6639i	−0.576111	−	0.187190i	−0.582558	+	0.812789i	$0.697948\pi$
$480$	−467.506	+	36.9699i	−0.973971	+	0.0770207i
$481$	21.2127	+	65.2861i	0.0441013	+	0.135730i
$482$	210.023			0.435731
$483$	−21.6284	−	24.8011i	−0.0447794	−	0.0513480i
$484$	−476.481	−	346.184i	−0.984465	−	0.715256i
$485$	−578.560	−	194.363i	−1.19291	−	0.400749i
$486$	−97.6058	+	179.428i	−0.200835	+	0.369194i
$487$	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
$489$	−44.2629	+	73.9312i	−0.0905171	+	0.151189i
$490$	158.438	−	112.724i	0.323344	−	0.230048i
$491$	105.426	−	145.107i	0.214717	−	0.295533i	−0.688049	−	0.725664i	$-0.741533\pi$
$491$	105.426	−	145.107i	0.214717	−	0.295533i	0.902766	+	0.430131i	$0.141533\pi$
$492$	157.440	+	180.535i	0.320000	+	0.366941i
$493$			595.329i			1.20756i
$494$	−7.81907	+	2.54057i	−0.0158281	+	0.00514285i
$495$	556.836	+	545.058i	1.12492	+	1.10113i
$496$	55.5402	−	170.935i	0.111976	−	0.344627i
$497$	141.181	−	434.511i	0.284067	−	0.874268i
$498$	1.94348	+	1.16357i	0.00390258	+	0.00233648i
$499$	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	$-0.774457\pi$
$503$	119.455	−	367.645i	0.237485	−	0.730905i	0.996782	−	0.0801602i	$-0.0255432\pi$
$504$	−474.696	+	254.336i	−0.941856	+	0.504635i
$505$	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	−0.961584	−	0.274512i	$-0.911484\pi$
$509$	−205.311	+	282.586i	−0.403361	+	0.555179i	0.558223	+	0.829691i	$0.311484\pi$
$510$	239.291	+	146.514i	0.469198	+	0.287283i
$511$	386.281	−	280.650i	0.755932	−	0.549217i
$512$	361.988	+	263.000i	0.707009	+	0.513672i
$513$	−53.1437	−	80.9874i	−0.103594	−	0.157870i
$514$	−129.006	+	93.7282i	−0.250984	+	0.182351i
$515$	32.4131	+	10.8890i	0.0629380	+	0.0211436i
$516$	489.301	+	112.146i	0.948257	+	0.217338i
$517$	585.536	−	190.252i	1.13257	−	0.367993i
$518$	206.581			0.398806
$519$	−99.4319	+	86.7123i	−0.191584	+	0.167076i
$520$	79.2172	+	26.6125i	0.152341	+	0.0511779i
$521$	255.878	+	83.1397i	0.491128	+	0.159577i	0.544103	−	0.839019i	$-0.316870\pi$
$521$	255.878	+	83.1397i	0.491128	+	0.159577i	−0.0529744	+	0.998596i	$0.516870\pi$
$522$	178.392	−	95.5802i	0.341747	−	0.183104i
$523$	−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
$525$	−50.4526	−	730.289i	−0.0961002	−	1.39103i
$526$	385.764			0.733392
$527$	−403.436	+	293.113i	−0.765533	+	0.556192i
$528$	−36.9713	−	414.998i	−0.0700214	−	0.785981i
$529$	−163.080	+	501.908i	−0.308279	+	0.948786i
$530$	37.0329	+	117.952i	0.0698735	+	0.222550i
$531$	−344.615	+	712.293i	−0.648992	+	1.34142i
$532$		−	115.327i		−	0.216780i
$533$	−20.4247	−	62.8608i	−0.0383203	−	0.117938i
$534$	−87.8086	−	20.1255i	−0.164436	−	0.0376882i
$535$	−587.434	−	5.83846i	−1.09801	−	0.0109130i
$536$	−260.418	−	358.435i	−0.485855	−	0.668722i
$537$	−893.903	−	204.880i	−1.66462	−	0.381527i
$538$	27.9292	−	38.4413i	0.0519130	−	0.0714522i
$539$	470.882	+	648.113i	0.873621	+	1.20244i
$540$	−25.5681	+	443.879i	−0.0473483	+	0.821999i
$541$	−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
$546$	66.8358	−	5.95426i	0.122410	−	0.0109052i
$547$	−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
$552$	−17.7340	−	10.6174i	−0.0321269	−	0.0192345i
$553$	1348.90	+	438.284i	2.43924	+	0.792556i
$554$	−221.969	−	72.1223i	−0.400667	−	0.130185i
$555$	197.225	−	322.112i	0.355360	−	0.580383i
$556$	−198.945	−	612.289i	−0.357815	−	1.10124i
$557$	202.807			0.364106			0.182053	−	0.983289i	$-0.441726\pi$
$557$	202.807			0.364106			0.182053	+	0.983289i	$0.441726\pi$
$558$	152.604	+	73.8313i	0.273484	+	0.132314i
$559$	−112.058	−	81.4150i	−0.200462	−	0.145644i
$560$	−233.206	+	314.362i	−0.416440	+	0.561362i
$561$	−593.806	+	991.821i	−1.05848	+	1.76795i
$562$	6.06731	−	8.35093i	0.0107959	−	0.0148593i
$563$	517.129	+	375.717i	0.918525	+	0.667347i	0.943156	−	0.332349i	$-0.107841\pi$
$563$	517.129	+	375.717i	0.918525	+	0.667347i	−0.0246316	+	0.999697i	$0.507841\pi$
$564$	301.412	+	180.456i	0.534419	+	0.319958i
$565$	579.769	+	430.095i	1.02614	+	0.761230i
$566$	−25.2626	+	34.7710i	−0.0446335	+	0.0614328i
$567$	275.109	+	741.183i	0.485200	+	1.30720i
$568$		−	286.968i		−	0.505225i
$569$	−122.002	+	39.6408i	−0.214415	+	0.0696676i	−0.414255	−	0.910161i	$-0.635958\pi$
$569$	−122.002	+	39.6408i	−0.214415	+	0.0696676i	0.199840	+	0.979829i	$0.435958\pi$
$570$	38.5782	+	23.6209i	0.0676810	+	0.0414401i
$571$	−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
$573$	4.85581	−	8.11055i	0.00847436	−	0.0141545i
$574$	−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
$579$	21.9569	+	246.464i	0.0379222	+	0.425671i
$580$	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
$585$	54.5244	−	109.898i	0.0932040	−	0.187860i
$586$	245.207	−	178.153i	0.418442	−	0.304016i
$587$	−760.672	−	552.661i	−1.29586	−	0.941501i	−0.295958	−	0.955201i	$-0.595639\pi$
$587$	−760.672	−	552.661i	−1.29586	−	0.941501i	−0.999906	+	0.0137003i	$0.995639\pi$
$588$	−102.122	+	445.564i	−0.173677	+	0.757762i
$589$	−65.0414	+	47.2554i	−0.110427	+	0.0802298i
$590$	3.67238	−	369.495i	0.00622437	−	0.626262i
$591$	139.554	−	608.880i	0.236131	−	1.03025i
$592$	−192.071	+	62.4076i	−0.324444	+	0.105418i
$593$	−413.092			−0.696615			−0.348307	−	0.937380i	$-0.613243\pi$
$593$	−413.092			−0.696615			−0.348307	+	0.937380i	$0.613243\pi$
$594$	392.538	+	18.6986i	0.660838	+	0.0314792i
$595$	1036.14	−	325.314i	1.74142	−	0.546747i
$596$	−435.008	−	141.343i	−0.729879	−	0.237152i
$597$	387.214	−	34.4961i	0.648600	−	0.0577824i
$598$	1.51376	+	2.08351i	0.00253137	+	0.00348414i
$599$		−	97.8025i		−	0.163276i	−0.996662	−	0.0816381i	$-0.973985\pi$
$599$		−	97.8025i		−	0.163276i	0.996662	−	0.0816381i	$-0.0260152\pi$
$600$	−171.886	−	426.461i	−0.286477	−	0.710769i
$601$	−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
$603$	−573.309	+	307.172i	−0.950761	+	0.509406i
$604$	−63.3263	+	194.898i	−0.104845	+	0.322679i
$605$	284.744	−	847.594i	0.470651	−	1.40098i
$606$	−47.7504	−	54.7548i	−0.0787960	−	0.0903545i
$607$		−	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
$609$	175.001	−	763.540i	0.287359	−	1.25376i
$610$	−109.890	+	327.108i	−0.180147	+	0.536243i
$611$	−56.9761	−	78.4209i	−0.0932506	−	0.128348i
$612$	−649.225	+	116.602i	−1.06083	+	0.190526i
$613$	−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
$615$	−189.898	+	310.146i	−0.308777	+	0.504303i
$616$	838.239	+	609.016i	1.36078	+	0.988663i
$617$	119.648	+	368.239i	0.193919	+	0.596821i	0.999988	+	0.00499907i	$0.00159126\pi$
$617$	119.648	+	368.239i	0.193919	+	0.596821i	−0.806069	+	0.591822i	$0.798409\pi$
$618$	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
$621$	−18.9833	+	23.6720i	−0.0305689	+	0.0381191i
$622$	−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
$627$	−95.7327	+	159.900i	−0.152684	+	0.255024i
$628$	−590.965	−	192.016i	−0.941027	−	0.305758i
$629$	532.909	+	173.153i	0.847233	+	0.275283i
$630$	−263.834	−	258.254i	−0.418784	−	0.409926i
$631$	−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
$633$	−334.794	+	291.966i	−0.528900	+	0.461242i
$634$	−28.8089	−	20.9309i	−0.0454400	−	0.0330141i
$635$	−9.60146	−	13.4953i	−0.0151204	−	0.0212525i
$636$	−249.360	−	149.293i	−0.392075	−	0.234737i
$637$	74.1376	−	102.042i	0.116386	−	0.160191i
$638$	−315.013	−	228.870i	−0.493750	−	0.358731i
$639$	−417.363	−	57.3064i	−0.653150	−	0.0896813i
$640$	−206.891	+	615.851i	−0.323267	+	0.962267i
$641$	−688.318	+	947.388i	−1.07382	+	1.47798i	−0.207669	+	0.978199i	$0.566588\pi$
$641$	−688.318	+	947.388i	−1.07382	+	1.47798i	−0.866150	+	0.499785i	$0.833412\pi$
$642$	−223.298	+	194.733i	−0.347816	+	0.303322i
$643$		−	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
$645$	60.0787	+	759.730i	0.0931452	+	1.17788i
$646$	−20.7379	+	63.8246i	−0.0321020	+	0.0987997i
$647$	−312.069	+	960.450i	−0.482332	+	1.48447i	0.353475	+	0.935444i	$0.385000\pi$
$647$	−312.069	+	960.450i	−0.482332	+	1.48447i	−0.835808	+	0.549022i	$0.815000\pi$
$648$	308.204	+	389.363i	0.475623	+	0.600869i
$649$	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	$0.255023\pi$
$653$	−188.871	+	581.286i	−0.289236	+	0.890177i	−0.985097	+	0.172000i	$0.944977\pi$
$654$	−244.165	+	21.7522i	−0.373341	+	0.0332602i
$655$	−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	$-0.542361\pi$
$659$	560.784	−	771.852i	0.850962	−	1.17125i	0.983650	−	0.180090i	$-0.0576390\pi$
$660$	790.180	−	327.651i	1.19724	−	0.496440i
$661$	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
$663$	177.404	+	40.6606i	0.267578	+	0.0613282i
$664$	4.45524	−	3.23692i	0.00670970	−	0.00487488i
$665$	167.045	−	52.4467i	0.251196	−	0.0788673i
$666$	−33.6730	−	187.488i	−0.0505600	−	0.281513i
$667$	28.5936	−	9.29062i	0.0428689	−	0.0139290i
$668$	578.879			0.866586
$669$	−113.312	−	129.934i	−0.169375	−	0.194221i
$670$	180.962	−	243.938i	0.270093	−	0.364086i
$671$	−1352.11	−	439.326i	−2.01506	−	0.654733i
$672$	81.2346	+	911.847i	0.120885	+	1.35692i
$673$	−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
$675$	−654.566	+	164.827i	−0.969728	+	0.244189i
$676$	−532.114			−0.787151
$677$	120.168	−	87.3073i	0.177501	−	0.128962i	−0.495487	−	0.868615i	$-0.665010\pi$
$677$	120.168	−	87.3073i	0.177501	−	0.128962i	0.672988	+	0.739653i	$0.265010\pi$
$678$	362.639	−	32.3067i	0.534865	−	0.0476500i
$679$	−368.170	+	1133.11i	−0.542224	+	1.66879i
$680$	555.819	−	395.446i	0.817381	−	0.581539i
$681$	683.727	−	596.262i	1.00400	−	0.875569i
$682$		−	326.160i		−	0.478240i
$683$	−157.437	−	484.540i	−0.230508	−	0.709430i	−0.997686	−	0.0679954i	$-0.978340\pi$
$683$	−157.437	−	484.540i	−0.230508	−	0.709430i	0.767178	−	0.641434i	$-0.221660\pi$
$684$	−104.667	+	18.7984i	−0.153022	+	0.0274830i
$685$	−391.965	−	290.775i	−0.572212	−	0.424489i
$686$	13.1872	+	18.1506i	0.0192233	+	0.0264586i
$687$	−175.432	+	765.418i	−0.255359	+	1.11415i
$688$	239.522	−	329.673i	0.348142	−	0.479176i
$689$	47.1366	+	64.8780i	0.0684131	+	0.0941626i
$690$	3.30273	−	13.7796i	0.00478656	−	0.0199704i
$691$	−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
$696$	−43.6606	−	490.084i	−0.0627307	−	0.704144i
$697$	−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	$-0.819307\pi$
$701$		−	753.805i		−	1.07533i	0.843159	−	0.537664i	$-0.180693\pi$
$702$	−16.2982	−	59.6877i	−0.0232168	−	0.0850253i
$703$	85.9150	+	27.9155i	0.122212	+	0.0397091i
$704$	−95.5536	−	31.0473i	−0.135730	−	0.0441012i
$705$	−124.311	+	518.648i	−0.176327	+	0.735670i
$706$	−179.597	−	552.743i	−0.254387	−	0.782922i
$707$	−281.200			−0.397737
$708$	570.943	+	654.693i	0.806416	+	0.924708i
$709$	−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
$711$	177.902	−	1295.66i	0.250214	−	1.82231i
$712$	−128.732	+	177.184i	−0.180803	+	0.248854i
$713$	20.3742	+	14.8027i	0.0285753	+	0.0207611i
$714$	281.351	−	469.935i	0.394049	−	0.658172i
$715$	−236.020	−	2.34578i	−0.330098	−	0.00328082i
$716$	−591.774	+	814.507i	−0.826500	+	1.13758i
$717$	−116.614	−	133.719i	−0.162641	−	0.186498i
$718$		−	81.1189i		−	0.112979i
$719$	1047.73	−	340.428i	1.45721	−	0.473475i	0.529991	−	0.848003i	$-0.322195\pi$
$719$	1047.73	−	340.428i	1.45721	−	0.473475i	0.927215	+	0.374529i	$0.122195\pi$
$720$	323.319	+	160.410i	0.449055	+	0.222792i
$721$	20.6263	−	63.4811i	0.0286078	−	0.0880459i
$722$	90.4264	−	278.304i	0.125244	−	0.385462i
$723$	−643.121	−	385.039i	−0.889518	−	0.532557i
$724$	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
$729$	627.833	−	370.494i	0.861226	−	0.508223i
$730$	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
$735$	−691.821	+	54.7085i	−0.941253	+	0.0744333i
$736$	−28.4256	+	20.6524i	−0.0386217	+	0.0280603i
$737$	1012.38	+	735.534i	1.37364	+	0.998010i
$738$	32.4221	+	180.523i	0.0439324	+	0.244611i
$739$	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
$741$	28.6009	+	6.55525i	0.0385977	+	0.00884649i
$742$	229.521	−	74.5760i	0.309328	−	0.100507i
$743$	168.513			0.226801			0.113401	−	0.993549i	$-0.463826\pi$
$743$	168.513			0.226801			0.113401	+	0.993549i	$0.463826\pi$
$744$	310.619	−	270.883i	0.417498	−	0.364090i
$745$	6.90125	−	694.367i	0.00926342	−	0.932036i
$746$	−154.480	−	50.1936i	−0.207078	−	0.0672836i
$747$	−3.81805	−	7.12606i	−0.00511118	−	0.00953957i
$748$	745.937	+	1026.69i	0.997242	+	1.37259i
$749$			1146.77i			1.53107i
$750$	243.637	−	200.001i	0.324849	−	0.266669i
$751$	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
$753$	46.4689	+	521.607i	0.0617117	+	0.692706i
$754$	−18.9443	+	58.3047i	−0.0251251	+	0.0773272i
$755$	−311.100	−	3.09200i	−0.412053	−	0.00409536i
$756$	866.941	+	41.2970i	1.14675	+	0.0546256i
$757$		−	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
$759$	56.9039	+	13.0422i	0.0749722	+	0.0171834i
$760$	89.6084	−	63.7534i	0.117906	−	0.0838860i
$761$	166.917	+	229.742i	0.219340	+	0.301895i	0.904480	−	0.426516i	$-0.140259\pi$
$761$	166.917	+	229.742i	0.219340	+	0.301895i	−0.685140	+	0.728411i	$0.740259\pi$
$762$	−8.14196	−	1.86612i	−0.0106850	−	0.00244897i
$763$	−557.689	+	767.593i	−0.730916	+	1.00602i
$764$	−6.09985	−	8.39572i	−0.00798409	−	0.0109892i
$765$	−464.138	−	887.347i	−0.606717	−	1.15993i
$766$	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
$771$	566.870	−	50.5012i	0.735239	−	0.0655009i
$772$	258.348	+	83.9423i	0.334648	+	0.108734i
$773$	195.091	−	141.742i	0.252382	−	0.183366i	−0.454400	−	0.890798i	$-0.650146\pi$
$773$	195.091	−	141.742i	0.252382	−	0.183366i	0.706782	+	0.707432i	$0.250146\pi$
$774$	277.331	+	266.120i	0.358309	+	0.343824i
$775$	162.494	+	536.139i	0.209670	+	0.691792i
$776$			748.349i			0.964367i
$777$	−632.584	−	378.730i	−0.814137	−	0.487426i
$778$	−498.979	−	162.128i	−0.641361	−	0.208391i
$779$	−82.7233	−	26.8784i	−0.106192	−	0.0345038i
$780$	−87.5065	−	102.379i	−0.112188	−	0.131255i
$781$	250.465	+	770.851i	0.320697	+	0.987005i
$782$	21.0219			0.0268822
$783$	−721.493	−	34.3685i	−0.921447	−	0.0438934i
$784$	300.205	+	218.112i	0.382915	+	0.278204i
$785$	9.37546	−	943.309i	0.0119433	−	1.20167i
$786$	−203.412	+	339.754i	−0.258794	+	0.432258i
$787$	−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
$789$	−1181.27	−	707.230i	−1.49717	−	0.896362i
$790$	182.944	+	582.685i	0.231574	+	0.737576i
$791$	828.290	−	1140.04i	1.04714	−	1.44127i
$792$	416.092	−	860.032i	0.525369	−	1.08590i
$793$			223.837i			0.282266i
$794$	−367.255	+	119.328i	−0.462537	+	0.150288i
$795$	102.843	−	429.080i	0.129362	−	0.539723i
$796$	131.880	−	405.885i	0.165678	−	0.509906i
$797$	347.475	−	1069.42i	0.435978	−	1.34180i	−0.456103	−	0.889927i	$-0.650755\pi$
$797$	347.475	−	1069.42i	0.435978	−	1.34180i	0.892081	−	0.451876i	$-0.149245\pi$
$798$	45.3591	−	75.7623i	0.0568410	−	0.0949402i
$799$	−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
$804$	63.3608	+	711.217i	0.0788070	+	0.884598i
$805$	−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	−0.858105	−	0.513474i	$-0.828358\pi$
$809$	−84.6156	+	116.463i	−0.104593	+	0.143960i	0.753512	+	0.657434i	$0.228358\pi$
$810$	−191.378	+	281.544i	−0.236270	+	0.347585i
$811$	−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
$813$	−34.8791	+	152.179i	−0.0429017	+	0.187182i
$814$	−296.495	+	215.417i	−0.364245	+	0.264640i
$815$	−85.5649	+	115.342i	−0.104988	+	0.141524i
$816$	−119.623	+	521.921i	−0.146597	+	0.639609i
$817$	−173.357	+	56.3269i	−0.212187	+	0.0689436i
$818$	188.200			0.230073
$819$	−215.578	−	104.299i	−0.263220	−	0.127349i
$820$	231.444	+	325.305i	0.282248	+	0.396714i
$821$	663.159	+	215.474i	0.807746	+	0.262453i	0.683643	−	0.729817i	$-0.260395\pi$
$821$	663.159	+	215.474i	0.807746	+	0.262453i	0.124103	+	0.992269i	$0.460395\pi$
$822$	−245.170	+	21.8416i	−0.298260	+	0.0265713i
$823$	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
$825$	833.934	+	995.535i	1.01083	+	1.20671i
$826$	−721.319			−0.873268
$827$	527.867	−	383.518i	0.638291	−	0.463746i	−0.220971	−	0.975280i	$-0.570923\pi$
$827$	527.867	−	383.518i	0.638291	−	0.463746i	0.859263	+	0.511535i	$0.170923\pi$
$828$	15.7321	+	29.3626i	0.0190001	+	0.0354620i
$829$	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
$831$	547.482	+	627.791i	0.658823	+	0.755464i
$832$			15.8186i			0.0190127i
$833$	−318.152	−	979.173i	−0.381936	−	1.17548i
$834$	110.125	−	480.482i	0.132045	−	0.576117i
$835$	263.255	+	838.480i	0.315275	+	1.00417i
$836$	120.259	+	165.522i	0.143851	+	0.197993i
$837$	−331.940	−	505.855i	−0.396584	−	0.604367i
$838$	271.794	−	374.092i	0.324336	−	0.446410i
$839$	420.161	+	578.302i	0.500788	+	0.689275i	0.982332	−	0.187147i	$-0.0599240\pi$
$839$	420.161	+	578.302i	0.500788	+	0.689275i	−0.481544	+	0.876422i	$0.659924\pi$
$840$	−829.111	+	343.793i	−0.987037	+	0.409278i
$841$	−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
$846$	127.033	+	237.097i	0.150158	+	0.280256i
$847$	−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
$852$	−237.569	+	396.805i	−0.278836	+	0.465734i
$853$	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
$855$	−74.8278	−	143.057i	−0.0875179	−	0.167318i
$856$	222.586	+	685.051i	0.260031	+	0.800293i
$857$	255.925			0.298629			0.149314	−	0.988790i	$-0.452293\pi$
$857$	255.925			0.298629			0.149314	+	0.988790i	$0.452293\pi$
$858$	−89.7170	+	78.2401i	−0.104565	+	0.0911889i
$859$	−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
$861$	609.084	+	364.661i	0.707415	+	0.423531i
$862$	290.588	−	399.960i	0.337109	−	0.463990i
$863$	−351.174	−	255.143i	−0.406923	−	0.295647i	0.365432	−	0.930838i	$-0.380921\pi$
$863$	−351.174	−	255.143i	−0.406923	−	0.295647i	−0.772355	+	0.635191i	$0.780921\pi$
$864$	814.326	−	222.358i	0.942507	−	0.257359i
$865$	−179.166	+	127.471i	−0.207128	+	0.147365i
$866$	−38.7397	+	53.3206i	−0.0447341	+	0.0615711i
$867$	466.251	−	406.606i	0.537775	−	0.468981i
$868$		−	720.342i		−	0.829887i
$869$	−2393.03	+	777.543i	−2.75378	+	0.894756i
$870$	311.582	−	129.198i	0.358141	−	0.148504i
$871$	60.8826	−	187.377i	0.0698996	−	0.215129i
$872$	−184.159	+	566.785i	−0.211192	+	0.649982i
$873$	1088.39	+	149.442i	1.24673	+	0.171183i
$874$	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
$879$	−1077.47	+	95.9898i	−1.22579	+	0.109203i
$880$	6.90126	−	694.368i	0.00784234	−	0.789054i
$881$	−1603.94	+	521.152i	−1.82059	+	0.591547i	−0.820800	+	0.571216i	$0.806472\pi$
$881$	−1603.94	+	521.152i	−1.82059	+	0.591547i	−0.999793	+	0.0203304i	$0.993528\pi$
$882$	−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
$885$	−688.648	+	1124.72i	−0.778133	+	1.27087i
$886$	−408.594	+	296.861i	−0.461167	+	0.335058i
$887$	−9.80606	−	7.12452i	−0.0110553	−	0.00803215i	0.582244	−	0.813014i	$-0.302175\pi$
$887$	−9.80606	−	7.12452i	−0.0110553	−	0.00803215i	−0.593299	+	0.804982i	$0.702175\pi$
$888$	−451.398	−	103.459i	−0.508332	−	0.116508i
$889$	−26.1564	+	19.0037i	−0.0294222	+	0.0213765i
$890$	−142.326	−	47.8134i	−0.159917	−	0.0537230i
$891$	−1167.73	−	776.906i	−1.31058	−	0.871948i
$892$	−180.002	+	58.4862i	−0.201796	+	0.0655675i
$893$	−127.562			−0.142847
$894$	−230.181	−	263.946i	−0.257473	−	0.295241i
$895$	−1448.89	−	486.747i	−1.61888	−	0.543851i
$896$	1206.14	+	391.900i	1.34614	+	0.437389i
$897$	−0.815622	−	9.15525i	−0.000909277	−	0.0102065i
$898$	79.2042	+	109.015i	0.0882007	+	0.121398i
$899$			599.489i			0.666839i
$900$	−115.373	+	731.988i	−0.128192	+	0.813321i
$901$	654.595			0.726521
$902$	285.481	−	207.414i	0.316498	−	0.229949i
$903$	1481.82	−	132.012i	1.64099	−	0.146192i
$904$	273.517	−	841.799i	0.302563	−	0.931193i
$905$	210.714	+	671.136i	0.232834	+	0.741586i
$906$	−118.257	+	103.129i	−0.130526	+	0.113829i
$907$			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
$909$	45.8359	+	255.209i	0.0504246	+	0.280758i
$910$	111.829	+	1.11146i	0.122889	+	0.00122138i
$911$	435.625	+	599.587i	0.478184	+	0.658164i	0.978155	−	0.207879i	$-0.0666559\pi$
$911$	435.625	+	599.587i	0.478184	+	0.658164i	−0.499971	+	0.866042i	$0.666656\pi$
$912$	−19.2854	+	84.1434i	−0.0211463	+	0.0922625i
$913$	−9.14246	+	12.5835i	−0.0100136	+	0.0137826i
$914$	259.700	+	357.447i	0.284136	+	0.391080i
$915$	936.193	−	800.192i	1.02316	−	0.874527i
$916$	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
$921$	37.8145	+	424.462i	0.0410580	+	0.460871i
$922$	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
$927$	−60.9757	−	8.37233i	−0.0657775	−	0.00903164i
$928$	−795.457	−	258.460i	−0.857173	−	0.278513i
$929$	−1427.52	−	463.830i	−1.53662	−	0.499279i	−0.586181	−	0.810180i	$-0.699369\pi$
$929$	−1427.52	−	463.830i	−1.53662	−	0.499279i	−0.950442	+	0.310901i	$0.899369\pi$
$930$	240.963	+	147.538i	0.259100	+	0.158643i
$931$	−51.2921	−	157.861i	−0.0550936	−	0.169561i
$932$	280.900			0.301395
$933$	130.816	+	150.005i	0.140210	+	0.160778i
$934$	130.509	+	94.8205i	0.139732	+	0.101521i
$935$	−1147.89	+	1547.36i	−1.22769	+	1.65493i
$936$	−149.024	−	20.4619i	−0.159214	−	0.0218610i
$937$	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
$939$	62.8390	−	104.959i	0.0669212	−	0.111777i
$940$	470.240	+	348.842i	0.500255	+	0.371109i
$941$	746.258	−	1027.14i	0.793048	−	1.09154i	−0.200674	−	0.979658i	$-0.564313\pi$
$941$	746.258	−	1027.14i	0.793048	−	1.09154i	0.993722	−	0.111879i	$-0.0356868\pi$
$942$	−312.704	−	358.575i	−0.331958	−	0.380652i
$943$			27.2465i			0.0288935i
$944$	670.652	−	217.908i	0.710436	−	0.230835i
$945$	334.439	+	1274.50i	0.353904	+	1.34868i
$946$	228.515	−	703.296i	0.241559	−	0.743442i
$947$	422.962	−	1301.74i	0.446633	−	1.37460i	−0.434050	−	0.900889i	$-0.642916\pi$
$947$	422.962	−	1301.74i	0.446633	−	1.37460i	0.880683	−	0.473706i	$-0.157084\pi$
$948$	−1231.84	−	737.509i	−1.29941	−	0.777963i
$949$	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	$-0.775297\pi$
$953$	224.887	−	692.131i	0.235978	−	0.726265i	0.996990	−	0.0775277i	$-0.0247026\pi$
$954$	−105.095	−	196.151i	−0.110163	−	0.205609i
$955$	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
$960$	66.1610	−	56.5497i	0.0689177	−	0.0589059i
$961$	371.210	−	269.700i	0.386275	−	0.280645i
$962$	46.6815	+	33.9161i	0.0485255	+	0.0352558i
$963$	1040.78	−	186.925i	1.08077	−	0.194107i
$964$	−665.734	+	483.684i	−0.690595	+	0.501747i
$965$	−4.09860	+	412.379i	−0.00424726	+	0.427336i
$966$	−26.9616	−	6.17954i	−0.0279106	−	0.00639703i
$967$	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
$969$	180.513	−	157.422i	0.186288	−	0.162458i
$970$	−489.471	+	153.678i	−0.504609	+	0.158430i
$971$	671.700	+	218.249i	0.691762	+	0.224767i	0.633737	−	0.773548i	$-0.281520\pi$
$971$	671.700	+	218.249i	0.691762	+	0.224767i	0.0580241	+	0.998315i	$0.481520\pi$
$972$	−103.832	−	793.543i	−0.106823	−	0.816402i
$973$	−1121.47	−	1543.57i	−1.15259	−	1.58640i
$974$		−	638.382i		−	0.655423i
$975$	108.497	−	173.308i	0.111278	−	0.177752i
$976$	−658.525			−0.674718
$977$	518.731	−	376.880i	0.530942	−	0.385752i	−0.289768	−	0.957097i	$-0.593578\pi$
$977$	518.731	−	376.880i	0.530942	−	0.385752i	0.820710	+	0.571345i	$0.193578\pi$
$978$	6.42724	+	72.1449i	0.00657182	+	0.0737678i
$979$	191.152	−	588.306i	0.195253	−	0.600926i
$980$	−242.618	+	722.199i	−0.247569	+	0.736938i
$981$	787.550	+	381.024i	0.802803	+	0.388404i
$982$		−	150.766i		−	0.153529i
$983$	245.476	+	755.499i	0.249722	+	0.768564i	0.994824	+	0.101614i	$0.0324007\pi$
$983$	245.476	+	755.499i	0.249722	+	0.768564i	−0.745102	+	0.666950i	$0.767599\pi$
$984$	434.630	+	99.6159i	0.441697	+	0.101236i
$985$	331.546	−	986.911i	0.336595	−	1.00194i
$986$	294.136	+	404.844i	0.298313	+	0.410592i
$987$	1014.80	+	232.590i	1.02817	+	0.235654i
$988$	18.9341	−	26.0606i	0.0191641	−	0.0263771i
$989$	33.5616	+	46.1935i	0.0339349	+	0.0467073i
$990$	647.966	+	95.5400i	0.654511	+	0.0965050i
$991$	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
$996$	−8.84021	+	0.787556i	−0.00887571	+	0.000790718i
$997$	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.14.11	yes	72
3.2	odd	2	inner	75.3.h.a.14.8	✓	72
5.2	odd	4		375.3.j.b.176.21		144
5.3	odd	4		375.3.j.b.176.16		144
5.4	even	2		375.3.h.a.74.8		72
15.2	even	4		375.3.j.b.176.15		144
15.8	even	4		375.3.j.b.176.22		144
15.14	odd	2		375.3.h.a.74.11		72
25.9	even	10	inner	75.3.h.a.59.8	yes	72
25.12	odd	20		375.3.j.b.326.15		144
25.13	odd	20		375.3.j.b.326.22		144
25.16	even	5		375.3.h.a.299.11		72
75.38	even	20		375.3.j.b.326.16		144
75.41	odd	10		375.3.h.a.299.8		72
75.59	odd	10	inner	75.3.h.a.59.11	yes	72
75.62	even	20		375.3.j.b.326.21		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.3.h.a.14.8	✓	72	3.2	odd	2	inner
75.3.h.a.14.11	yes	72	1.1	even	1	trivial
75.3.h.a.59.8	yes	72	25.9	even	10	inner
75.3.h.a.59.11	yes	72	75.59	odd	10	inner
375.3.h.a.74.8		72	5.4	even	2
375.3.h.a.74.11		72	15.14	odd	2
375.3.h.a.299.8		72	75.41	odd	10
375.3.h.a.299.11		72	25.16	even	5
375.3.j.b.176.15		144	15.2	even	4
375.3.j.b.176.16		144	5.3	odd	4
375.3.j.b.176.21		144	5.2	odd	4
375.3.j.b.176.22		144	15.8	even	4
375.3.j.b.326.15		144	25.12	odd	20
375.3.j.b.326.16		144	75.38	even	20
375.3.j.b.326.21		144	75.62	even	20
375.3.j.b.326.22		144	25.13	odd	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} +(-2.98817 + 0.266209i) q^{3} +(-1.01773 + 3.13225i) q^{4} +(-4.99975 - 0.0496921i) q^{5} +(-1.90053 + 1.65741i) q^{6} +9.76040i q^{7} +(1.89447 + 5.83059i) q^{8} +(8.85827 - 1.59096i) q^{9} +(-3.42456 + 2.43645i) q^{10} +(-10.1778 - 14.0086i) q^{11} +(2.20731 - 9.63062i) q^{12} +(-1.60244 + 2.20557i) q^{13} +(4.82236 + 6.63741i) q^{14} +(14.9533 - 1.18249i) 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} +(-2.59831 - 29.1657i) 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} +(-26.0464 + 7.11219i) q^{27} +(-30.5720 - 9.93345i) q^{28} +(25.4429 + 8.26690i) q^{29} +(9.58453 - 8.19218i) q^{30} +(6.92473 + 21.3121i) q^{31} -31.2644 q^{32} +(34.1423 + 39.1505i) q^{33} +(15.1331 + 10.9948i) q^{34} +(0.485015 - 48.7996i) q^{35} +(-4.03205 + 29.3655i) q^{36} +(14.8003 - 20.3708i) q^{37} +(2.43974 + 1.77257i) q^{38} +(4.20122 - 7.01720i) q^{39} +(-9.18216 - 29.2456i) q^{40} +(-14.2504 + 19.6141i) q^{41} +(-16.1769 - 18.5499i) q^{42} +50.8068i q^{43} +(54.2367 - 17.6226i) q^{44} +(-44.3682 + 7.51420i) q^{45} +(0.291916 - 0.898424i) q^{46} +(-10.9874 + 33.8156i) q^{47} +(20.6445 + 12.3599i) 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} +(-14.1985 + 17.7054i) 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} +(-11.5146 + 48.0410i) q^{60} +(66.4241 - 48.2599i) q^{61} +(15.2388 + 11.0716i) q^{62} +(15.5284 + 86.4602i) q^{63} +(4.69420 - 3.41054i) q^{64} +(8.12141 - 10.9477i) q^{65} +(42.5612 + 9.75491i) q^{66} +(-68.7311 + 22.3321i) q^{67} -73.2904 q^{68} +(-2.54099 + 2.21594i) q^{69} +(-23.7808 - 33.4250i) q^{70} +(-44.5178 - 14.4647i) q^{71} +(26.0579 + 48.6349i) q^{72} +(-28.7539 - 39.5764i) q^{73} -21.1653i q^{74} +(-74.8217 + 5.16911i) q^{75} -11.8158 q^{76} +(136.729 - 99.3397i) q^{77} +(-0.610043 - 6.84765i) q^{78} +(44.9043 - 138.201i) q^{79} +(32.2080 + 23.8931i) q^{80} +(75.9377 - 28.1862i) q^{81} +20.3790i q^{82} +(-0.277581 - 0.854307i) q^{83} +(93.9987 + 21.5442i) q^{84} +(-33.3300 - 106.158i) q^{85} +(25.1023 + 34.5504i) q^{86} +(-78.2284 - 17.9297i) q^{87} +(62.3967 - 85.8816i) q^{88} +(20.9981 + 28.9013i) q^{89} +(-26.4593 + 27.0311i) 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} +(93.4232 - 8.32287i) 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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