LMFDB - Embedded newform 135.3.r.a.22.31

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [135,3,Mod(7,135)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("135.7"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(135, base_ring=CyclotomicField(36)) chi = DirichletCharacter(H, H._module([32, 9])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 135 = 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	135.r (of order $36$, degree $12$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$3.67848356886$
Analytic rank:	$0$
Dimension:	$408$
Relative dimension:	$34$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			22.31
Character	$\chi$	$=$	135.22
Dual form			135.3.r.a.43.31

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(3.11531 + 0.272554i) q^{2} +(-1.98048 + 2.25337i) q^{3} +(5.69163 + 1.00359i) q^{4} +(0.988365 + 4.90134i) q^{5} +(-6.78398 + 6.48016i) q^{6} +(-0.485519 + 0.693393i) q^{7} +(5.37504 + 1.44024i) q^{8} +(-1.15537 - 8.92553i) q^{9} +(1.74318 + 15.5386i) q^{10} +(9.25334 + 3.36794i) q^{11} +(-13.5336 + 10.8378i) q^{12} +(-2.77177 + 0.242499i) q^{13} +(-1.70153 + 2.02780i) q^{14} +(-13.0020 - 7.47987i) q^{15} +(-5.37118 - 1.95495i) q^{16} +(15.8329 - 4.24241i) q^{17} +(-1.16665 - 28.1207i) q^{18} +(22.9832 - 13.2694i) q^{19} +(0.706481 + 28.8885i) q^{20} +(-0.600910 - 2.46731i) q^{21} +(27.9091 + 13.0142i) q^{22} +(-10.8303 - 15.4673i) q^{23} +(-13.8906 + 9.25961i) q^{24} +(-23.0463 + 9.68862i) q^{25} -8.70102 q^{26} +(22.4007 + 15.0734i) q^{27} +(-3.45928 + 3.45928i) q^{28} +(3.76946 + 4.49226i) q^{29} +(-38.4665 - 26.8458i) q^{30} +(7.87682 - 44.6717i) q^{31} +(-36.3732 - 16.9611i) q^{32} +(-25.9153 + 14.1811i) q^{33} +(50.4807 - 8.90111i) q^{34} +(-3.87843 - 1.69437i) q^{35} +(2.38160 - 51.9603i) q^{36} +(-24.1614 + 6.47401i) q^{37} +(75.2164 - 35.0740i) q^{38} +(4.94301 - 6.72610i) q^{39} +(-1.74660 + 27.7684i) q^{40} +(-12.8693 - 10.7986i) q^{41} +(-1.19955 - 7.85021i) q^{42} +(-57.9753 + 27.0343i) q^{43} +(49.2866 + 28.4556i) q^{44} +(42.6051 - 14.4846i) q^{45} +(-29.5242 - 51.1374i) q^{46} +(14.6387 - 20.9063i) q^{47} +(15.0428 - 8.23153i) q^{48} +(16.5139 + 45.3716i) q^{49} +(-74.4369 + 23.9017i) q^{50} +(-21.7971 + 44.0795i) q^{51} +(-16.0193 - 1.40150i) q^{52} +(13.5777 - 13.5777i) q^{53} +(65.6769 + 53.0636i) q^{54} +(-7.36175 + 48.6825i) q^{55} +(-3.60834 + 3.02775i) q^{56} +(-15.6170 + 78.0695i) q^{57} +(10.5186 + 15.0222i) q^{58} +(2.57913 + 7.08611i) q^{59} +(-66.4958 - 55.6213i) q^{60} +(19.2546 + 109.198i) q^{61} +(36.7142 - 137.019i) q^{62} +(6.74986 + 3.53239i) q^{63} +(-88.8905 - 51.3210i) q^{64} +(-3.92809 - 13.3457i) q^{65} +(-84.5993 + 37.1151i) q^{66} +(9.70163 + 110.890i) q^{67} +(94.3727 - 8.25654i) q^{68} +(56.3030 + 6.22800i) q^{69} +(-11.6207 - 6.33556i) q^{70} +(68.3740 - 118.427i) q^{71} +(6.64471 - 49.6391i) q^{72} +(-25.7360 - 6.89594i) q^{73} +(-77.0346 + 13.5833i) q^{74} +(23.8107 - 71.1200i) q^{75} +(144.129 - 52.4586i) q^{76} +(-6.82798 + 4.78100i) q^{77} +(17.2322 - 19.6066i) q^{78} +(-88.3733 - 105.319i) q^{79} +(4.27319 - 28.2582i) q^{80} +(-78.3302 + 20.6246i) q^{81} +(-37.1486 - 37.1486i) q^{82} +(6.60880 - 75.5389i) q^{83} +(-0.943999 - 14.6461i) q^{84} +(36.4422 + 73.4094i) q^{85} +(-187.979 + 68.4189i) q^{86} +(-17.5881 - 0.402863i) q^{87} +(44.8865 + 31.4299i) q^{88} +(-63.7232 + 36.7906i) q^{89} +(136.676 - 33.5117i) q^{90} +(1.17760 - 2.03966i) q^{91} +(-46.1195 - 98.9035i) q^{92} +(85.0620 + 106.221i) q^{93} +(51.3023 - 61.1397i) q^{94} +(87.7534 + 99.5336i) q^{95} +(110.256 - 48.3712i) q^{96} +(22.8447 + 48.9905i) q^{97} +(39.0797 + 145.848i) q^{98} +(19.3696 - 86.4822i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 408 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 12 q^{7} - 6 q^{8} - 6 q^{10} - 60 q^{11} - 12 q^{12} - 12 q^{13} - 12 q^{15} - 24 q^{16} - 6 q^{17} - 54 q^{18} - 300 q^{20} - 24 q^{21} - 12 q^{22} - 156 q^{23}+ \cdots - 1032 q^{98}+O(q^{100}) $ 408 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 12 * q^7 - 6 * q^8 - 6 * q^10 - 60 * q^11 - 12 * q^12 - 12 * q^13 - 12 * q^15 - 24 * q^16 - 6 * q^17 - 54 * q^18 - 300 * q^20 - 24 * q^21 - 12 * q^22 - 156 * q^23 + 6 * q^25 - 48 * q^26 + 180 * q^27 - 24 * q^28 + 276 * q^30 - 24 * q^31 + 72 * q^32 - 78 * q^33 + 156 * q^35 - 312 * q^36 - 6 * q^37 - 252 * q^38 - 108 * q^40 - 384 * q^41 - 528 * q^42 - 12 * q^43 + 18 * q^45 - 12 * q^46 - 210 * q^47 + 444 * q^48 + 276 * q^50 - 144 * q^51 - 60 * q^52 + 516 * q^53 - 24 * q^55 + 912 * q^56 + 168 * q^57 - 12 * q^58 + 864 * q^60 - 312 * q^61 - 6 * q^62 - 54 * q^63 + 420 * q^65 + 1224 * q^66 - 480 * q^67 - 540 * q^68 - 12 * q^70 - 12 * q^71 - 1548 * q^72 - 6 * q^73 - 852 * q^75 - 216 * q^76 - 876 * q^77 - 1362 * q^78 - 1644 * q^80 - 204 * q^81 - 24 * q^82 - 372 * q^83 - 12 * q^85 + 516 * q^86 + 540 * q^87 + 348 * q^88 - 384 * q^90 - 12 * q^91 + 2082 * q^92 - 1404 * q^93 + 198 * q^95 + 924 * q^96 + 600 * q^97 - 1032 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	3.11531	+	0.272554i	1.55765	+	0.136277i	0.833171	−	0.553015i	$-0.186523\pi$
$2$	3.11531	+	0.272554i	1.55765	+	0.136277i	0.724483	+	0.689292i	$0.242078\pi$
$3$	−1.98048	+	2.25337i	−0.660161	+	0.751124i
$3$	−1.98048	+	2.25337i	−0.660161	+	0.751124i
$4$	5.69163	+	1.00359i	1.42291	+	0.250897i
$5$	0.988365	+	4.90134i	0.197673	+	0.980268i
$5$	0.988365	+	4.90134i	0.197673	+	0.980268i
$6$	−6.78398	+	6.48016i	−1.13066	+	1.08003i
$7$	−0.485519	+	0.693393i	−0.0693599	+	0.0990561i	−0.852333	−	0.522999i	$-0.824813\pi$
$7$	−0.485519	+	0.693393i	−0.0693599	+	0.0990561i	0.782973	+	0.622055i	$0.213702\pi$
$8$	5.37504	+	1.44024i	0.671881	+	0.180030i
$9$	−1.15537	−	8.92553i	−0.128375	−	0.991726i
$10$	1.74318	+	15.5386i	0.174318	+	1.55386i
$11$	9.25334	+	3.36794i	0.841213	+	0.306176i	0.726452	−	0.687217i	$-0.241168\pi$
$11$	9.25334	+	3.36794i	0.841213	+	0.306176i	0.114760	+	0.993393i	$0.463390\pi$
$12$	−13.5336	+	10.8378i	−1.12780	+	0.903148i
$13$	−2.77177	+	0.242499i	−0.213213	+	0.0186537i	−0.193262	−	0.981147i	$-0.561907\pi$
$13$	−2.77177	+	0.242499i	−0.213213	+	0.0186537i	−0.0199513	+	0.999801i	$0.506351\pi$
$14$	−1.70153	+	2.02780i	−0.121538	+	0.144843i
$15$	−13.0020	−	7.47987i	−0.866799	−	0.498658i
$16$	−5.37118	−	1.95495i	−0.335699	−	0.122184i
$17$	15.8329	−	4.24241i	0.931347	−	0.249554i	0.238918	−	0.971040i	$-0.423207\pi$
$17$	15.8329	−	4.24241i	0.931347	−	0.249554i	0.692429	+	0.721486i	$0.256541\pi$
$18$	−1.16665	−	28.1207i	−0.0648141	−	1.56226i
$19$	22.9832	−	13.2694i	1.20964	−	0.698387i	0.246961	−	0.969025i	$-0.420568\pi$
$19$	22.9832	−	13.2694i	1.20964	−	0.698387i	0.962681	+	0.270638i	$0.0872346\pi$
$20$	0.706481	+	28.8885i	0.0353240	+	1.44443i
$21$	−0.600910	−	2.46731i	−0.0286148	−	0.117491i
$22$	27.9091	+	13.0142i	1.26859	+	0.591555i
$23$	−10.8303	−	15.4673i	−0.470884	−	0.672493i	0.511517	−	0.859273i	$-0.329084\pi$
$23$	−10.8303	−	15.4673i	−0.470884	−	0.672493i	−0.982402	+	0.186780i	$0.940195\pi$
$24$	−13.8906	+	9.25961i	−0.578774	+	0.385817i
$25$	−23.0463	+	9.68862i	−0.921851	+	0.387545i
$26$	−8.70102			−0.334655
$27$	22.4007	+	15.0734i	0.829657	+	0.558273i
$28$	−3.45928	+	3.45928i	−0.123546	+	0.123546i
$29$	3.76946	+	4.49226i	0.129981	+	0.154906i	0.827109	−	0.562041i	$-0.189984\pi$
$29$	3.76946	+	4.49226i	0.129981	+	0.154906i	−0.697128	+	0.716946i	$0.745539\pi$
$30$	−38.4665	−	26.8458i	−1.28222	−	0.894861i
$31$	7.87682	−	44.6717i	0.254091	−	1.44102i	−0.544304	−	0.838888i	$-0.683206\pi$
$31$	7.87682	−	44.6717i	0.254091	−	1.44102i	0.798395	−	0.602134i	$-0.205683\pi$
$32$	−36.3732	−	16.9611i	−1.13666	−	0.530035i
$33$	−25.9153	+	14.1811i	−0.785312	+	0.429729i
$34$	50.4807	−	8.90111i	1.48473	−	0.261797i
$35$	−3.87843	−	1.69437i	−0.110812	−	0.0484105i
$36$	2.38160	−	51.9603i	0.0661555	−	1.44334i
$37$	−24.1614	+	6.47401i	−0.653009	+	0.174973i	−0.570089	−	0.821583i	$-0.693091\pi$
$37$	−24.1614	+	6.47401i	−0.653009	+	0.174973i	−0.0829203	+	0.996556i	$0.526425\pi$
$38$	75.2164	−	35.0740i	1.97938	−	0.923000i
$39$	4.94301	−	6.72610i	0.126744	−	0.172464i
$40$	−1.74660	+	27.7684i	−0.0436649	+	0.694210i
$41$	−12.8693	−	10.7986i	−0.313886	−	0.263381i	0.472210	−	0.881486i	$-0.343456\pi$
$41$	−12.8693	−	10.7986i	−0.313886	−	0.263381i	−0.786096	+	0.618105i	$0.787901\pi$
$42$	−1.19955	−	7.85021i	−0.0285606	−	0.186910i
$43$	−57.9753	+	27.0343i	−1.34826	+	0.628706i	−0.956600	−	0.291403i	$-0.905878\pi$
$43$	−57.9753	+	27.0343i	−1.34826	+	0.628706i	−0.391663	+	0.920109i	$0.628100\pi$
$44$	49.2866	+	28.4556i	1.12015	+	0.646718i
$45$	42.6051	−	14.4846i	0.946781	−	0.321879i
$46$	−29.5242	−	51.1374i	−0.641830	−	1.11168i
$47$	14.6387	−	20.9063i	0.311463	−	0.444815i	−0.632650	−	0.774438i	$-0.718033\pi$
$47$	14.6387	−	20.9063i	0.311463	−	0.444815i	0.944113	+	0.329623i	$0.106922\pi$
$48$	15.0428	−	8.23153i	0.313391	−	0.171490i
$49$	16.5139	+	45.3716i	0.337019	+	0.925952i
$50$	−74.4369	+	23.9017i	−1.48874	+	0.478034i
$51$	−21.7971	+	44.0795i	−0.427393	+	0.864303i
$52$	−16.0193	−	1.40150i	−0.308063	−	0.0269520i
$53$	13.5777	−	13.5777i	0.256183	−	0.256183i	−0.567317	−	0.823500i	$-0.692018\pi$
$53$	13.5777	−	13.5777i	0.256183	−	0.256183i	0.823500	+	0.567317i	$0.192018\pi$
$54$	65.6769	+	53.0636i	1.21624	+	0.982660i
$55$	−7.36175	+	48.6825i	−0.133850	+	0.885137i
$56$	−3.60834	+	3.02775i	−0.0644346	+	0.0540671i
$57$	−15.6170	+	78.0695i	−0.273983	+	1.36964i
$58$	10.5186	+	15.0222i	0.181356	+	0.259003i
$59$	2.57913	+	7.08611i	0.0437141	+	0.120104i	0.959629	−	0.281269i	$-0.0907554\pi$
$59$	2.57913	+	7.08611i	0.0437141	+	0.120104i	−0.915915	+	0.401373i	$0.868533\pi$
$60$	−66.4958	−	55.6213i	−1.10826	−	0.927021i
$61$	19.2546	+	109.198i	0.315649	+	1.79013i	0.568558	+	0.822643i	$0.307502\pi$
$61$	19.2546	+	109.198i	0.315649	+	1.79013i	−0.252909	+	0.967490i	$0.581387\pi$
$62$	36.7142	−	137.019i	0.592164	−	2.20999i
$63$	6.74986	+	3.53239i	0.107141	+	0.0560696i
$64$	−88.8905	−	51.3210i	−1.38891	−	0.801890i
$65$	−3.92809	−	13.3457i	−0.0604321	−	0.205319i
$66$	−84.5993	+	37.1151i	−1.28181	+	0.562350i
$67$	9.70163	+	110.890i	0.144800	+	1.65508i	0.627003	+	0.779017i	$0.284281\pi$
$67$	9.70163	+	110.890i	0.144800	+	1.65508i	−0.482203	+	0.876060i	$0.660163\pi$
$68$	94.3727	−	8.25654i	1.38783	−	0.121420i
$69$	56.3030	+	6.22800i	0.815985	+	0.0902608i
$70$	−11.6207	−	6.33556i	−0.166010	−	0.0905080i
$71$	68.3740	−	118.427i	0.963015	−	1.66799i	0.248158	−	0.968720i	$-0.420175\pi$
$71$	68.3740	−	118.427i	0.963015	−	1.66799i	0.714857	−	0.699271i	$-0.246492\pi$
$72$	6.64471	−	49.6391i	0.0922877	−	0.689432i
$73$	−25.7360	−	6.89594i	−0.352548	−	0.0944649i	0.0781989	−	0.996938i	$-0.475083\pi$
$73$	−25.7360	−	6.89594i	−0.352548	−	0.0944649i	−0.430747	+	0.902473i	$0.641750\pi$
$74$	−77.0346	+	13.5833i	−1.04101	+	0.183558i
$75$	23.8107	−	71.1200i	0.317476	−	0.948266i
$76$	144.129	−	52.4586i	1.89643	−	0.690245i
$77$	−6.82798	+	4.78100i	−0.0886751	+	0.0620910i
$78$	17.2322	−	19.6066i	0.220926	−	0.251367i
$79$	−88.3733	−	105.319i	−1.11865	−	1.33315i	−0.936815	−	0.349825i	$-0.886241\pi$
$79$	−88.3733	−	105.319i	−1.11865	−	1.33315i	−0.181835	−	0.983329i	$-0.558204\pi$
$80$	4.27319	−	28.2582i	0.0534149	−	0.353227i
$81$	−78.3302	+	20.6246i	−0.967040	+	0.254625i
$82$	−37.1486	−	37.1486i	−0.453032	−	0.453032i
$83$	6.60880	−	75.5389i	0.0796241	−	0.910107i	−0.846376	−	0.532585i	$-0.821221\pi$
$83$	6.60880	−	75.5389i	0.0796241	−	0.910107i	0.926001	−	0.377522i	$-0.123224\pi$
$84$	−0.943999	−	14.6461i	−0.0112381	−	0.174358i
$85$	36.4422	+	73.4094i	0.428732	+	0.863640i
$86$	−187.979	+	68.4189i	−2.18581	+	0.795569i
$87$	−17.5881	−	0.402863i	−0.202162	−	0.00463061i
$88$	44.8865	+	31.4299i	0.510074	+	0.357157i
$89$	−63.7232	+	36.7906i	−0.715991	+	0.413377i	−0.813275	−	0.581879i	$-0.802318\pi$
$89$	−63.7232	+	36.7906i	−0.715991	+	0.413377i	0.0972845	+	0.995257i	$0.468984\pi$
$90$	136.676	−	33.5117i	1.51862	−	0.372352i
$91$	1.17760	−	2.03966i	0.0129407	−	0.0224139i
$92$	−46.1195	−	98.9035i	−0.501298	−	1.07504i
$93$	85.0620	+	106.221i	0.914646	+	1.14216i
$94$	51.3023	−	61.1397i	0.545769	−	0.650422i
$95$	87.7534	+	99.5336i	0.923721	+	1.04772i
$96$	110.256	−	48.3712i	1.14850	−	0.503867i
$97$	22.8447	+	48.9905i	0.235512	+	0.505057i	0.988171	−	0.153353i	$-0.0490072\pi$
$97$	22.8447	+	48.9905i	0.235512	+	0.505057i	−0.752660	+	0.658410i	$0.771229\pi$
$98$	39.0797	+	145.848i	0.398773	+	1.48824i
$99$	19.3696	−	86.4822i	0.195653	−	0.873558i
$100$	−140.894	+	32.0151i	−1.40894	+	0.320151i
$101$	0.263161	+	1.49246i	0.00260555	+	0.0147768i	0.986083	−	0.166255i	$-0.0531674\pi$
$101$	0.263161	+	1.49246i	0.00260555	+	0.0147768i	−0.983477	+	0.181032i	$0.942056\pi$
$102$	−79.9186	+	131.380i	−0.783516	+	1.28804i
$103$	−74.8436	+	160.503i	−0.726637	+	1.55828i	0.0996460	+	0.995023i	$0.468229\pi$
$103$	−74.8436	+	160.503i	−0.726637	+	1.55828i	−0.826283	+	0.563255i	$0.809549\pi$
$104$	−15.2477	−	2.68857i	−0.146612	−	0.0258517i
$105$	11.4992	−	5.38387i	0.109516	−	0.0512749i
$106$	45.9994	−	38.5981i	0.433957	−	0.364133i
$107$	40.3904	+	40.3904i	0.377481	+	0.377481i	0.870192	−	0.492712i	$-0.163994\pi$
$107$	40.3904	+	40.3904i	0.377481	+	0.377481i	−0.492712	+	0.870192i	$0.663994\pi$
$108$	112.369	+	108.273i	1.04046	+	1.00253i
$109$		−	123.028i		−	1.12870i	−0.825536	−	0.564349i	$-0.809127\pi$
$109$		−	123.028i		−	1.12870i	0.825536	−	0.564349i	$-0.190873\pi$
$110$	−36.2027	+	149.655i	−0.329116	+	1.36050i
$111$	33.2628	−	67.2662i	0.299665	−	0.606002i
$112$	3.96336	−	2.77517i	0.0353871	−	0.0247783i
$113$	−74.8002	+	160.409i	−0.661948	+	1.41955i	0.232596	+	0.972573i	$0.425278\pi$
$113$	−74.8002	+	160.409i	−0.661948	+	1.41955i	−0.894544	+	0.446979i	$0.852500\pi$
$114$	−69.9301	+	238.954i	−0.613422	+	2.09609i
$115$	65.1063	−	68.3705i	0.566142	−	0.594526i
$116$	16.9460	+	29.3513i	0.146086	+	0.253028i
$117$	5.36686	+	24.4594i	0.0458706	+	0.209054i
$118$	6.10345	+	22.7784i	0.0517241	+	0.193037i
$119$	−4.74552	+	13.0382i	−0.0398783	+	0.109565i
$120$	−59.1134	−	58.9306i	−0.492612	−	0.491088i
$121$	−18.4101	−	15.4479i	−0.152149	−	0.127668i
$122$	30.2215	+	345.434i	0.247718	+	2.83142i
$123$	49.8208	−	7.61283i	0.405047	−	0.0618929i
$124$	89.6639	−	246.350i	0.723096	−	1.98669i
$125$	−70.2654	−	103.382i	−0.562123	−	0.827054i
$126$	20.0651	+	12.8442i	0.159247	+	0.101938i
$127$	20.2942	−	75.7390i	0.159797	−	0.596370i	−0.838850	−	0.544363i	$-0.816771\pi$
$127$	20.2942	−	75.7390i	0.159797	−	0.596370i	0.998647	−	0.0520071i	$-0.0165618\pi$
$128$	−131.432	−	92.0299i	−1.02681	−	0.718983i
$129$	53.9007	−	184.181i	0.417835	−	1.42776i
$130$	−8.59978	−	42.6466i	−0.0661521	−	0.328051i
$131$	32.9474	−	186.854i	0.251507	−	1.42637i	−0.553375	−	0.832932i	$-0.686660\pi$
$131$	32.9474	−	186.854i	0.251507	−	1.42637i	0.804882	−	0.593435i	$-0.202229\pi$
$132$	−161.732	+	54.7051i	−1.22524	+	0.414433i
$133$	−1.95790	+	22.3789i	−0.0147211	+	0.168263i
$134$			348.101i			2.59777i
$135$	−51.7397	+	124.692i	−0.383257	+	0.923642i
$136$	91.2127			0.670681
$137$	−36.9800	−	3.23533i	−0.269927	−	0.0236155i	−0.0486113	−	0.998818i	$-0.515480\pi$
$137$	−36.9800	−	3.23533i	−0.269927	−	0.0236155i	−0.221316	+	0.975202i	$0.571035\pi$
$138$	173.704	+	34.7477i	1.25872	+	0.251795i
$139$	−33.3525	−	5.88094i	−0.239946	−	0.0423089i	0.0523819	−	0.998627i	$-0.483319\pi$
$139$	−33.3525	−	5.88094i	−0.239946	−	0.0423089i	−0.292328	+	0.956318i	$0.594430\pi$
$140$	−20.3741	−	13.5361i	−0.145529	−	0.0966861i
$141$	18.1179	+	74.3911i	0.128496	+	0.527596i
$142$	245.284	−	350.302i	1.72735	−	2.46692i
$143$	−26.4649	−	7.09124i	−0.185069	−	0.0495891i
$144$	−11.2433	+	50.1994i	−0.0780781	+	0.348607i
$145$	−18.2925	+	22.9154i	−0.126155	+	0.158037i
$146$	−78.2960	−	28.4974i	−0.536274	−	0.195188i
$147$	−134.945	−	52.6457i	−0.917991	−	0.358134i
$148$	−144.015	+	12.5997i	−0.973072	+	0.0851328i
$149$	34.6021	−	41.2372i	0.232229	−	0.276760i	−0.637328	−	0.770593i	$-0.719960\pi$
$149$	34.6021	−	41.2372i	0.232229	−	0.276760i	0.869557	+	0.493833i	$0.164405\pi$
$150$	93.5616	−	215.071i	0.623744	−	1.43381i
$151$	7.70762	+	2.80535i	0.0510439	+	0.0185784i	0.367416	−	0.930057i	$-0.380243\pi$
$151$	7.70762	+	2.80535i	0.0510439	+	0.0185784i	−0.316372	+	0.948635i	$0.602465\pi$
$152$	142.647	−	38.2221i	0.938466	−	0.251461i
$153$	−56.1587	−	136.416i	−0.367050	−	0.891605i
$154$	−22.5743	+	13.0333i	−0.146587	+	0.0846318i
$155$	226.736	−	5.54493i	1.46282	−	0.0357738i
$156$	34.8840	−	33.3217i	0.223615	−	0.213601i
$157$	−57.9384	−	27.0171i	−0.369035	−	0.172084i	0.229250	−	0.973368i	$-0.426373\pi$
$157$	−57.9384	−	27.0171i	−0.369035	−	0.172084i	−0.598284	+	0.801284i	$0.704151\pi$
$158$	−246.605	−	352.188i	−1.56079	−	2.22904i
$159$	3.70521	+	57.4861i	0.0233032	+	0.361548i
$160$	47.1822	−	195.041i	0.294889	−	1.21901i
$161$	15.9833			0.0992750
$162$	−249.644	+	42.9029i	−1.54101	+	0.264833i
$163$	182.251	−	182.251i	1.11811	−	1.11811i	0.126087	−	0.992019i	$-0.459758\pi$
$163$	182.251	−	182.251i	1.11811	−	1.11811i	0.992019	−	0.126087i	$-0.0402419\pi$
$164$	−62.4099	−	74.3773i	−0.380548	−	0.453520i
$165$	−95.1200	−	113.004i	−0.576485	−	0.684871i
$166$	41.1769	−	233.526i	0.248054	−	1.40678i
$167$	185.063	+	86.2962i	1.10816	+	0.516744i	0.888520	−	0.458837i	$-0.151734\pi$
$167$	185.063	+	86.2962i	1.10816	+	0.516744i	0.219640	+	0.975581i	$0.429512\pi$
$168$	0.323593	−	14.1273i	0.00192615	−	0.0840913i
$169$	−158.809	+	28.0022i	−0.939696	+	0.165694i
$170$	93.5207	+	238.625i	0.550122	+	1.40368i
$171$	−144.990	−	189.806i	−0.847896	−	1.10998i
$172$	−357.105	+	95.6861i	−2.07619	+	0.556315i
$173$	−64.7550	+	30.1957i	−0.374306	+	0.174542i	−0.600662	−	0.799503i	$-0.705096\pi$
$173$	−64.7550	+	30.1957i	−0.374306	+	0.174542i	0.226356	+	0.974045i	$0.427319\pi$
$174$	−54.6825	−	6.04875i	−0.314267	−	0.0347629i
$175$	4.47138	−	20.6841i	0.0255507	−	0.118195i
$176$	−43.1172	−	36.1796i	−0.244984	−	0.205566i
$177$	−21.0756	−	8.22218i	−0.119071	−	0.0464530i
$178$	−208.545	+	97.2460i	−1.17160	+	0.546326i
$179$	−85.0074	−	49.0790i	−0.474902	−	0.274185i	0.243388	−	0.969929i	$-0.421741\pi$
$179$	−85.0074	−	49.0790i	−0.474902	−	0.274185i	−0.718289	+	0.695745i	$0.755075\pi$
$180$	257.029	−	39.6827i	1.42794	−	0.220460i
$181$	114.289	+	197.954i	0.631430	+	1.09367i	0.987260	+	0.159118i	$0.0508649\pi$
$181$	114.289	+	197.954i	0.631430	+	1.09367i	−0.355830	+	0.934551i	$0.615802\pi$
$182$	4.22451	−	6.03322i	0.0232116	−	0.0331496i
$183$	−284.197	−	172.877i	−1.55299	−	0.944685i
$184$	−35.9369	−	98.7359i	−0.195309	−	0.536608i
$185$	−55.6116	−	112.024i	−0.300603	−	0.605537i
$186$	236.044	+	354.095i	1.26905	+	1.90374i
$187$	160.795	+	14.0678i	0.859869	+	0.0752288i
$188$	104.300	−	104.300i	0.554785	−	0.554785i
$189$	−21.3278	+	8.21411i	−0.112845	+	0.0434609i
$190$	246.251	+	333.995i	1.29606	+	1.75787i
$191$	−61.5998	+	51.6883i	−0.322512	+	0.270620i	−0.789641	−	0.613570i	$-0.789733\pi$
$191$	−61.5998	+	51.6883i	−0.322512	+	0.270620i	0.467129	+	0.884189i	$0.345289\pi$
$192$	291.691	−	98.6632i	1.51923	−	0.513871i
$193$	23.1201	+	33.0189i	0.119793	+	0.171082i	0.874570	−	0.484899i	$-0.161144\pi$
$193$	23.1201	+	33.0189i	0.119793	+	0.171082i	−0.754777	+	0.655982i	$0.772255\pi$
$194$	57.8156	+	158.847i	0.298018	+	0.818799i
$195$	37.8524	+	17.5795i	0.194115	+	0.0901514i
$196$	48.4567	+	274.812i	0.247228	+	1.40210i
$197$	50.7562	−	189.425i	0.257646	−	0.961547i	−0.708954	−	0.705255i	$-0.750832\pi$
$197$	50.7562	−	189.425i	0.257646	−	0.961547i	0.966599	−	0.256292i	$-0.0825009\pi$
$198$	83.9134	−	264.140i	0.423805	−	1.33404i
$199$	2.18821	+	1.26336i	0.0109960	+	0.00634855i	0.505488	−	0.862834i	$-0.331313\pi$
$199$	2.18821	+	1.26336i	0.0109960	+	0.00634855i	−0.494492	+	0.869182i	$0.664646\pi$
$200$	−137.829	+	18.8847i	−0.689143	+	0.0944233i
$201$	−269.091	−	197.755i	−1.33876	−	0.983854i
$202$	0.413051	+	4.72120i	0.00204481	+	0.0233723i
$203$	−4.94505	+	0.432636i	−0.0243598	+	0.00213121i
$204$	−168.298	+	229.009i	−0.824992	+	1.12259i
$205$	40.2082	−	73.7498i	0.196138	−	0.359755i
$206$	−276.907	+	479.616i	−1.34421	+	2.32823i
$207$	−125.541	+	114.537i	−0.606478	+	0.553319i
$208$	15.3618	+	4.11617i	0.0738546	+	0.0197893i
$209$	257.362	−	45.3798i	1.23140	−	0.217128i
$210$	37.2909	−	13.6383i	0.177576	−	0.0649441i
$211$	−82.1384	+	29.8959i	−0.389281	+	0.141687i	−0.529243	−	0.848470i	$-0.677524\pi$
$211$	−82.1384	+	29.8959i	−0.389281	+	0.141687i	0.139962	+	0.990157i	$0.455302\pi$
$212$	90.9057	−	63.6529i	0.428801	−	0.300249i
$213$	131.447	+	388.615i	0.617123	+	1.82449i
$214$	114.820	+	136.837i	0.536542	+	0.639426i
$215$	−189.805	−	257.437i	−0.882815	−	1.19738i
$216$	98.6957	+	113.282i	0.456925	+	0.524456i
$217$	27.1507	+	27.1507i	0.125118	+	0.125118i
$218$	33.5318	−	383.270i	0.153816	−	1.75812i
$219$	66.5088	−	44.3355i	0.303693	−	0.202445i
$220$	−90.7575	+	269.695i	−0.412534	+	1.22589i
$221$	−42.8564	+	15.5985i	−0.193920	+	0.0705813i
$222$	121.958	−	200.489i	0.549358	−	0.903104i
$223$	−232.846	−	163.040i	−1.04415	−	0.731123i	−0.0800862	−	0.996788i	$-0.525520\pi$
$223$	−232.846	−	163.040i	−1.04415	−	0.731123i	−0.964065	+	0.265665i	$0.914408\pi$
$224$	29.4206	−	16.9860i	0.131342	−	0.0758303i
$225$	113.103	+	194.506i	0.502681	+	0.864472i
$226$	−276.746	+	479.338i	−1.22454	+	2.12096i
$227$	−56.8751	−	121.969i	−0.250551	−	0.537308i	0.740299	−	0.672278i	$-0.234684\pi$
$227$	−56.8751	−	121.969i	−0.250551	−	0.537308i	−0.990850	+	0.134970i	$0.956906\pi$
$228$	−167.236	+	428.669i	−0.733491	+	1.88013i
$229$	101.800	−	121.321i	0.444542	−	0.529784i	−0.496517	−	0.868027i	$-0.665388\pi$
$229$	101.800	−	121.321i	0.444542	−	0.529784i	0.941059	+	0.338243i	$0.109833\pi$
$230$	221.461	−	195.250i	0.962874	−	0.848915i
$231$	2.74932	−	24.8547i	0.0119018	−	0.107596i
$232$	13.7911	+	29.5750i	0.0594442	+	0.127479i
$233$	15.1789	+	56.6483i	0.0651453	+	0.243126i	0.990819	−	0.135198i	$-0.0431672\pi$
$233$	15.1789	+	56.6483i	0.0651453	+	0.243126i	−0.925673	+	0.378324i	$0.876501\pi$
$234$	10.0529	+	77.6612i	0.0429612	+	0.331885i
$235$	116.937	+	51.0864i	0.497605	+	0.217389i
$236$	7.56794	+	42.9199i	0.0320675	+	0.181864i
$237$	412.345	+	9.44495i	1.73985	+	0.0398521i
$238$	−18.3374	+	39.3246i	−0.0770477	+	0.165229i
$239$	158.120	+	27.8808i	0.661589	+	0.116656i	0.494353	−	0.869261i	$-0.335405\pi$
$239$	158.120	+	27.8808i	0.661589	+	0.116656i	0.167235	+	0.985917i	$0.446516\pi$
$240$	55.2133	+	65.5940i	0.230055	+	0.273308i
$241$	−52.7372	+	44.2517i	−0.218826	+	0.183617i	−0.745611	−	0.666382i	$-0.767842\pi$
$241$	−52.7372	+	44.2517i	−0.218826	+	0.183617i	0.526784	+	0.849999i	$0.323398\pi$
$242$	−53.1427	−	53.1427i	−0.219598	−	0.219598i
$243$	108.657	−	217.354i	0.447147	−	0.894461i
$244$			640.839i			2.62639i
$245$	−206.060	+	125.784i	−0.841061	+	0.513404i
$246$	157.282	−	10.1375i	0.639358	−	0.0412092i
$247$	−60.4864	+	42.3530i	−0.244884	+	0.171470i
$248$	106.676	−	228.768i	0.430146	−	0.922451i
$249$	157.129	+	164.496i	0.631039	+	0.660625i
$250$	−190.721	−	341.217i	−0.762885	−	1.36487i
$251$	169.418	+	293.440i	0.674971	+	1.16908i	0.976477	+	0.215621i	$0.0691774\pi$
$251$	169.418	+	293.440i	0.674971	+	1.16908i	−0.301506	+	0.953464i	$0.597489\pi$
$252$	34.8726	+	26.8791i	0.138383	+	0.106663i
$253$	−48.1238	−	179.600i	−0.190213	−	0.709883i
$254$	83.8657	−	230.419i	0.330180	−	0.907161i
$255$	−237.592	−	63.2682i	−0.931733	−	0.248111i
$256$	−69.8557	−	58.6159i	−0.272874	−	0.228968i
$257$	23.8546	+	272.659i	0.0928195	+	1.06093i	0.889624	+	0.456694i	$0.150967\pi$
$257$	23.8546	+	272.659i	0.0928195	+	1.06093i	−0.796804	+	0.604238i	$0.793478\pi$
$258$	218.117	−	559.090i	0.845414	−	2.16702i
$259$	7.24176	−	19.8966i	0.0279605	−	0.0768207i
$260$	−8.96363	−	79.9011i	−0.0344755	−	0.307312i
$261$	35.7407	−	38.8346i	0.136938	−	0.148792i
$262$	153.569	−	573.128i	0.586142	−	2.18751i
$263$	33.0696	+	23.1556i	0.125740	+	0.0880439i	0.634754	−	0.772714i	$-0.281101\pi$
$263$	33.0696	+	23.1556i	0.125740	+	0.0880439i	−0.509015	+	0.860758i	$0.669990\pi$
$264$	−159.720	+	38.8997i	−0.605000	+	0.147347i
$265$	79.9687	+	53.1292i	0.301769	+	0.200488i
$266$	−12.1989	+	69.1836i	−0.0458607	+	0.260089i
$267$	43.2998	−	216.455i	0.162171	−	0.810694i
$268$	−56.0699	+	640.882i	−0.209216	+	2.39135i
$269$			104.891i			0.389929i	0.980810	+	0.194964i	$0.0624592\pi$
$269$			104.891i			0.389929i	−0.980810	+	0.194964i	$0.937541\pi$
$270$	−195.170	+	374.351i	−0.722853	+	1.38649i
$271$	400.870			1.47923			0.739613	−	0.673032i	$-0.235008\pi$
$271$	400.870			1.47923			0.739613	+	0.673032i	$0.235008\pi$
$272$	−93.3351	−	8.16577i	−0.343144	−	0.0300212i
$273$	2.26391	+	6.69310i	0.00829269	+	0.0245168i
$274$	−114.322	−	20.1581i	−0.417235	−	0.0735697i
$275$	−245.886	+	12.0337i	−0.894130	+	0.0437588i
$276$	314.205	+	91.9524i	1.13842	+	0.333161i
$277$	−53.0009	+	75.6931i	−0.191339	+	0.273260i	−0.903347	−	0.428911i	$-0.858897\pi$
$277$	−53.0009	+	75.6931i	−0.191339	+	0.273260i	0.712008	+	0.702172i	$0.247786\pi$
$278$	−102.300	−	27.4113i	−0.367987	−	0.0986018i
$279$	−407.819	−	18.6924i	−1.46172	−	0.0669977i
$280$	−18.4064	−	14.6932i	−0.0657372	−	0.0524756i
$281$	436.140	+	158.742i	1.55210	+	0.564918i	0.968909	−	0.247418i	$-0.0795822\pi$
$281$	436.140	+	158.742i	1.55210	+	0.564918i	0.583190	+	0.812336i	$0.301804\pi$
$282$	36.1672	+	236.689i	0.128252	+	0.839324i
$283$	−520.808	+	45.5648i	−1.84031	+	0.161006i	−0.953552	−	0.301228i	$-0.902603\pi$
$283$	−520.808	+	45.5648i	−1.84031	+	0.161006i	−0.886758	+	0.462234i	$0.847048\pi$
$284$	508.012	−	605.425i	1.78877	−	2.13178i
$285$	−398.080	+	0.616668i	−1.39677	+	0.00216375i
$286$	−80.5135	−	29.3045i	−0.281516	−	0.102463i
$287$	13.7360	−	3.68055i	0.0478606	−	0.0128242i
$288$	−109.362	+	344.247i	−0.379730	+	1.19530i
$289$	−17.5985	+	10.1605i	−0.0608944	+	0.0351574i
$290$	−63.2325	+	66.4028i	−0.218043	+	0.228975i
$291$	−155.637	−	45.5474i	−0.534836	−	0.156520i
$292$	−139.559	−	65.0774i	−0.477942	−	0.222868i
$293$	135.833	+	193.989i	0.463593	+	0.662079i	0.981078	−	0.193613i	$-0.0620205\pi$
$293$	135.833	+	193.989i	0.463593	+	0.662079i	−0.517485	+	0.855692i	$0.673132\pi$
$294$	−406.046	−	200.787i	−1.38111	−	0.682950i
$295$	−32.1823	+	19.6449i	−0.109093	+	0.0665928i
$296$	−139.192			−0.470245
$297$	156.515	+	214.923i	0.526988	+	0.723648i
$298$	119.036	−	119.036i	0.399449	−	0.399449i
$299$	33.7700	+	40.2456i	0.112943	+	0.134601i
$300$	206.897	−	380.892i	0.689656	−	1.26964i
$301$	9.40270	−	53.3254i	0.0312382	−	0.177161i
$302$	23.2470	+	10.8403i	0.0769769	+	0.0358949i
$303$	−3.88425	−	2.36279i	−0.0128193	−	0.00779799i
$304$	−149.388	+	26.3411i	−0.491408	+	0.0866484i
$305$	−516.187	+	202.301i	−1.69242	+	0.663281i
$306$	−137.771	−	440.283i	−0.450232	−	1.43883i
$307$	−268.475	+	71.9376i	−0.874511	+	0.234324i	−0.668037	−	0.744128i	$-0.732865\pi$
$307$	−268.475	+	71.9376i	−0.874511	+	0.234324i	−0.206473	+	0.978452i	$0.566199\pi$
$308$	−43.6605	+	20.3592i	−0.141755	+	0.0661014i
$309$	−213.446	−	486.523i	−0.690763	−	1.57451i
$310$	707.865	+	44.5238i	2.28344	+	0.143625i
$311$	283.045	+	237.503i	0.910111	+	0.763674i	0.972140	−	0.234400i	$-0.0753126\pi$
$311$	283.045	+	237.503i	0.910111	+	0.763674i	−0.0620287	+	0.998074i	$0.519757\pi$
$312$	36.2561	−	29.0340i	0.116205	−	0.0930576i
$313$	488.323	−	227.709i	1.56014	−	0.727504i	0.564916	−	0.825149i	$-0.308909\pi$
$313$	488.323	−	227.709i	1.56014	−	0.727504i	0.995221	+	0.0976446i	$0.0311308\pi$
$314$	−173.132	−	99.9581i	−0.551377	−	0.318338i
$315$	−10.6421	+	36.5746i	−0.0337845	+	0.116110i
$316$	−397.291	−	688.128i	−1.25725	−	2.17762i
$317$	138.448	−	197.725i	0.436745	−	0.623737i	−0.539089	−	0.842249i	$-0.681231\pi$
$317$	138.448	−	197.725i	0.436745	−	0.623737i	0.975834	+	0.218512i	$0.0701203\pi$
$318$	−4.12519	+	180.097i	−0.0129723	+	0.566342i
$319$	19.7504	+	54.2638i	0.0619135	+	0.170106i
$320$	163.685	−	486.407i	0.511517	−	1.52002i
$321$	−171.007	+	11.0221i	−0.532733	+	0.0343368i
$322$	49.7928	+	4.35631i	0.154636	+	0.0135289i
$323$	307.597	−	307.597i	0.952312	−	0.952312i
$324$	−466.525	+	38.7765i	−1.43989	+	0.119681i
$325$	61.5295	−	32.4433i	0.189322	−	0.0998257i
$326$	617.442	−	518.096i	1.89400	−	1.58925i
$327$	277.228	+	243.655i	0.847792	+	0.745122i
$328$	−53.6205	−	76.5780i	−0.163477	−	0.233469i
$329$	7.38889	+	20.3008i	0.0224586	+	0.0617046i
$330$	−265.529	−	377.967i	−0.804632	−	1.14535i
$331$	86.5259	+	490.713i	0.261408	+	1.48252i	0.779073	+	0.626933i	$0.215690\pi$
$331$	86.5259	+	490.713i	0.261408	+	1.48252i	−0.517666	+	0.855583i	$0.673199\pi$
$332$	113.425	−	423.307i	0.341641	−	1.27502i
$333$	85.6994	+	208.173i	0.257356	+	0.625144i
$334$	553.007	+	319.279i	1.65571	+	0.955925i
$335$	−533.921	+	157.151i	−1.59380	+	0.469107i
$336$	−1.59587	+	14.4271i	−0.00474960	+	0.0429378i
$337$	5.23789	+	59.8694i	0.0155427	+	0.177654i	0.999998	+	0.00201838i	$0.000642470\pi$
$337$	5.23789	+	59.8694i	0.0155427	+	0.177654i	−0.984455	+	0.175636i	$0.943802\pi$
$338$	−502.370	+	43.9517i	−1.48630	+	0.130035i
$339$	−213.322	−	486.241i	−0.629268	−	1.43434i
$340$	133.743	+	454.392i	0.393361	+	1.33645i
$341$	223.339	−	386.834i	0.654952	−	1.13441i
$342$	−399.957	−	630.823i	−1.16946	−	1.84451i
$343$	−79.5422	−	21.3133i	−0.231902	−	0.0621378i
$344$	−350.556	+	61.8125i	−1.01906	+	0.179687i
$345$	25.1223	+	282.115i	0.0728184	+	0.817726i
$346$	−209.962	+	76.4198i	−0.606826	+	0.220867i
$347$	−283.153	+	198.266i	−0.816001	+	0.571370i	−0.905368	−	0.424628i	$-0.860405\pi$
$347$	−283.153	+	198.266i	−0.816001	+	0.571370i	0.0893662	+	0.995999i	$0.471516\pi$
$348$	−99.7006	−	19.9441i	−0.286496	−	0.0573107i
$349$	179.830	+	214.313i	0.515272	+	0.614077i	0.959456	−	0.281858i	$-0.0909509\pi$
$349$	179.830	+	214.313i	0.515272	+	0.614077i	−0.444184	+	0.895935i	$0.646506\pi$
$350$	19.5673	−	63.2188i	0.0559065	−	0.180625i
$351$	−65.7450	−	36.3478i	−0.187308	−	0.103555i
$352$	−279.450	−	279.450i	−0.793891	−	0.793891i
$353$	−33.6777	+	384.937i	−0.0954041	+	1.09047i	0.786037	+	0.618180i	$0.212130\pi$
$353$	−33.6777	+	384.937i	−0.0954041	+	1.09047i	−0.881441	+	0.472294i	$0.843426\pi$
$354$	−63.4159	−	31.3589i	−0.179141	−	0.0885843i
$355$	648.031	+	218.075i	1.82544	+	0.614296i
$356$	−399.611	+	145.447i	−1.12250	+	0.408558i
$357$	−19.9815	−	36.5154i	−0.0559706	−	0.102284i
$358$	−251.448	−	176.065i	−0.702367	−	0.491803i
$359$	123.467	−	71.2834i	0.343918	−	0.198561i	−0.318085	−	0.948062i	$-0.603040\pi$
$359$	123.467	−	71.2834i	0.343918	−	0.198561i	0.662003	+	0.749501i	$0.269707\pi$
$360$	249.866	−	16.4936i	0.694071	−	0.0458155i
$361$	171.652	−	297.310i	0.475490	−	0.823573i
$362$	302.092	+	647.838i	0.834507	+	1.78961i
$363$	71.2707	−	10.8905i	0.196338	−	0.0300013i
$364$	8.74945	−	10.4272i	0.0240370	−	0.0286461i
$365$	8.36279	−	132.957i	0.0229118	−	0.364264i
$366$	−838.244	−	616.025i	−2.29028	−	1.68313i
$367$	155.552	+	333.582i	0.423847	+	0.908943i	0.996047	+	0.0888285i	$0.0283123\pi$
$367$	155.552	+	333.582i	0.423847	+	0.908943i	−0.572200	+	0.820114i	$0.693910\pi$
$368$	27.9339	+	104.251i	0.0759073	+	0.283290i
$369$	−81.5147	+	127.342i	−0.220907	+	0.345100i
$370$	−142.715	−	364.147i	−0.385715	−	0.984182i
$371$	2.82245	+	16.0069i	0.00760769	+	0.0431454i
$372$	377.540	+	689.938i	1.01489	+	1.85467i
$373$	131.466	−	281.931i	0.352457	−	0.755846i	−0.647524	−	0.762045i	$-0.724195\pi$
$373$	131.466	−	281.931i	0.352457	−	0.755846i	0.999981	+	0.00619915i	$0.00197326\pi$
$374$	497.093	+	87.6510i	1.32913	+	0.234361i
$375$	372.117	+	46.4117i	0.992312	+	0.123765i
$376$	108.794	−	91.2889i	0.289346	−	0.242790i
$377$	−11.5374	−	11.5374i	−0.0306033	−	0.0306033i
$378$	−68.6813	+	19.7765i	−0.181697	+	0.0523188i
$379$			251.208i			0.662819i	0.943487	+	0.331409i	$0.107524\pi$
$379$			251.208i			0.662819i	−0.943487	+	0.331409i	$0.892476\pi$
$380$	399.569	+	654.576i	1.05150	+	1.72257i
$381$	130.476	+	195.730i	0.342456	+	0.513727i
$382$	−205.990	+	144.236i	−0.539241	+	0.377581i
$383$	−29.9724	+	64.2760i	−0.0782569	+	0.167822i	−0.941543	−	0.336892i	$-0.890624\pi$
$383$	−29.9724	+	64.2760i	−0.0782569	+	0.167822i	0.863286	+	0.504714i	$0.168402\pi$
$384$	467.677	−	113.902i	1.21791	−	0.296620i
$385$	−30.1819	−	28.7409i	−0.0783944	−	0.0746516i
$386$	63.0267	+	109.165i	0.163282	+	0.282812i
$387$	308.279	+	486.226i	0.796587	+	1.25640i
$388$	80.8570	+	301.762i	0.208394	+	0.777738i
$389$	−218.115	+	599.267i	−0.560707	+	1.54053i	0.257897	+	0.966173i	$0.416971\pi$
$389$	−218.115	+	599.267i	−0.560707	+	1.54053i	−0.818604	+	0.574358i	$0.805252\pi$
$390$	113.130	+	65.0825i	0.290078	+	0.166878i
$391$	−237.095	−	198.946i	−0.606380	−	0.508813i
$392$	23.4171	+	267.658i	0.0597375	+	0.682802i
$393$	355.800	+	444.304i	0.905343	+	1.13054i
$394$	209.750	−	576.283i	0.532360	−	1.46265i
$395$	428.860	−	537.241i	1.08572	−	1.36010i
$396$	197.037	−	472.786i	0.497568	−	1.19390i
$397$	148.323	−	553.549i	0.373609	−	1.39433i	−0.481757	−	0.876305i	$-0.660001\pi$
$397$	148.323	−	553.549i	0.373609	−	1.39433i	0.855366	−	0.518024i	$-0.173332\pi$
$398$	6.47260	+	4.53217i	0.0162628	+	0.0113873i
$399$	−46.5505	−	48.7330i	−0.116668	−	0.122138i
$400$	142.726	−	6.98505i	0.356816	−	0.0174626i
$401$	−102.582	+	581.774i	−0.255817	+	1.45081i	0.538151	+	0.842848i	$0.319123\pi$
$401$	−102.582	+	581.774i	−0.255817	+	1.45081i	−0.793968	+	0.607960i	$0.791988\pi$
$402$	−784.401	−	689.408i	−1.95125	−	1.71495i
$403$	−10.9999	+	125.730i	−0.0272951	+	0.311985i
$404$			8.75864i			0.0216798i
$405$	−178.507	−	363.538i	−0.440759	−	0.897626i
$406$	−15.5233			−0.0382346
$407$	−245.377	−	21.4677i	−0.602893	−	0.0527463i
$408$	−180.645	+	205.536i	−0.442758	+	0.503765i
$409$	−135.633	−	23.9158i	−0.331622	−	0.0584739i	0.00535810	−	0.999986i	$-0.498294\pi$
$409$	−135.633	−	23.9158i	−0.331622	−	0.0584739i	−0.336980	+	0.941512i	$0.609406\pi$
$410$	145.362	−	218.795i	0.354541	−	0.533645i
$411$	80.5286	−	76.9222i	0.195933	−	0.187159i
$412$	−587.061	+	838.409i	−1.42490	+	2.03497i
$413$	−6.16568	−	1.65209i	−0.0149290	−	0.00400021i
$414$	−422.317	+	322.602i	−1.02009	+	0.779231i
$415$	376.774	−	42.2680i	0.907889	−	0.101851i
$416$	104.931	+	38.1919i	0.252239	+	0.0918074i
$417$	79.3059	−	63.5084i	0.190182	−	0.152298i
$418$	814.130	−	71.2272i	1.94768	−	0.170400i
$419$	65.2643	−	77.7789i	0.155762	−	0.185630i	−0.682520	−	0.730867i	$-0.739116\pi$
$419$	65.2643	−	77.7789i	0.155762	−	0.185630i	0.838282	+	0.545237i	$0.183560\pi$
$420$	70.8524	−	19.1025i	0.168696	−	0.0454822i
$421$	−494.486	−	179.978i	−1.17455	−	0.427501i	−0.320276	−	0.947324i	$-0.603776\pi$
$421$	−494.486	−	179.978i	−1.17455	−	0.427501i	−0.854274	+	0.519823i	$0.825998\pi$
$422$	−264.035	+	70.7479i	−0.625675	+	0.167649i
$423$	−203.513	−	106.504i	−0.481118	−	0.251782i
$424$	92.5359	−	53.4256i	0.218245	−	0.126004i
$425$	−323.786	+	251.171i	−0.761850	+	0.590990i
$426$	303.580	+	1246.48i	0.712629	+	2.92602i
$427$	−85.0657	−	39.6668i	−0.199217	−	0.0928965i
$428$	189.352	+	270.423i	0.442411	+	0.631829i
$429$	68.3924	−	45.5911i	0.159423	−	0.106273i
$430$	−521.136	−	853.728i	−1.21195	−	1.98541i
$431$	−357.212			−0.828799			−0.414399	−	0.910095i	$-0.636008\pi$
$431$	−357.212			−0.828799			−0.414399	+	0.910095i	$0.636008\pi$
$432$	−90.8508	−	124.754i	−0.210303	−	0.288783i
$433$	−50.9026	+	50.9026i	−0.117558	+	0.117558i	−0.763438	−	0.645881i	$-0.776490\pi$
$433$	−50.9026	+	50.9026i	−0.117558	+	0.117558i	0.645881	+	0.763438i	$0.276490\pi$
$434$	77.1827	+	91.9828i	0.177840	+	0.211942i
$435$	−15.4089	−	86.6034i	−0.0354227	−	0.199088i
$436$	123.469	−	700.230i	0.283187	−	1.60603i
$437$	−454.158	−	211.777i	−1.03926	−	0.484616i
$438$	219.279	−	119.991i	0.500638	−	0.273953i
$439$	66.9910	−	11.8123i	0.152599	−	0.0269074i	−0.0968266	−	0.995301i	$-0.530869\pi$
$439$	66.9910	−	11.8123i	0.152599	−	0.0269074i	0.249426	+	0.968394i	$0.419758\pi$
$440$	−109.684	+	251.068i	−0.249282	+	0.570609i
$441$	385.886	−	199.817i	0.875025	−	0.453099i
$442$	−137.762	+	36.9133i	−0.311680	+	0.0835143i
$443$	209.619	−	97.7472i	0.473182	−	0.220648i	−0.171373	−	0.985206i	$-0.554820\pi$
$443$	209.619	−	97.7472i	0.473182	−	0.220648i	0.644555	+	0.764558i	$0.277043\pi$
$444$	256.827	−	349.472i	0.578439	−	0.787099i
$445$	−243.305	−	275.966i	−0.546753	−	0.620149i
$446$	−680.949	−	571.384i	−1.52679	−	1.28113i
$447$	24.3939	+	159.641i	0.0545724	+	0.357139i
$448$	78.7437	−	36.7188i	0.175767	−	0.0819615i
$449$	−726.273	−	419.314i	−1.61753	−	0.933884i	−0.987556	−	0.157271i	$-0.949730\pi$
$449$	−726.273	−	419.314i	−1.61753	−	0.933884i	−0.629978	−	0.776613i	$-0.716936\pi$
$450$	299.338	+	636.774i	0.665195	+	1.41505i
$451$	−82.7149	−	143.266i	−0.183403	−	0.317664i
$452$	−586.720	+	837.923i	−1.29805	+	1.85381i
$453$	−21.5863	+	11.8122i	−0.0476519	+	0.0260755i
$454$	−143.940	−	395.473i	−0.317049	−	0.871085i
$455$	11.1610	+	3.75589i	0.0245296	+	0.00825470i
$456$	−196.381	+	397.135i	−0.430660	+	0.870909i
$457$	−287.799	−	25.1791i	−0.629756	−	0.0550965i	−0.232191	−	0.972670i	$-0.574589\pi$
$457$	−287.799	−	25.1791i	−0.629756	−	0.0550965i	−0.397566	+	0.917574i	$0.630145\pi$
$458$	350.205	−	350.205i	0.764639	−	0.764639i
$459$	418.616	+	143.622i	0.912018	+	0.312902i
$460$	439.177	−	323.800i	0.954732	−	0.703913i
$461$	291.254	−	244.391i	0.631787	−	0.530132i	−0.269697	−	0.962945i	$-0.586923\pi$
$461$	291.254	−	244.391i	0.631787	−	0.530132i	0.901484	+	0.432813i	$0.142479\pi$
$462$	15.3392	−	76.6806i	0.0332018	−	0.165975i
$463$	−119.897	−	171.231i	−0.258957	−	0.369829i	0.668529	−	0.743686i	$-0.266924\pi$
$463$	−119.897	−	171.231i	−0.258957	−	0.369829i	−0.927487	+	0.373856i	$0.878035\pi$
$464$	−11.4643	−	31.4979i	−0.0247075	−	0.0678833i
$465$	−436.553	+	521.903i	−0.938823	+	1.12237i
$466$	31.8471	+	180.614i	0.0683414	+	0.387584i
$467$	121.956	−	455.146i	0.261148	−	0.974616i	−0.703419	−	0.710776i	$-0.748344\pi$
$467$	121.956	−	455.146i	0.261148	−	0.974616i	0.964566	−	0.263841i	$-0.0849893\pi$
$468$	5.99906	+	144.600i	0.0128185	+	0.308974i
$469$	−81.6008	−	47.1122i	−0.173989	−	0.100452i
$470$	350.372	+	191.022i	0.745472	+	0.406429i
$471$	175.626	−	77.0499i	0.372879	−	0.163588i
$472$	3.65727	+	41.8027i	0.00774844	+	0.0885651i
$473$	−627.516	+	54.9005i	−1.32667	+	0.116069i
$474$	1282.01	+	141.810i	2.70466	+	0.299178i
$475$	−401.115	+	528.485i	−0.844453	+	1.11260i
$476$	−40.0947	+	69.4461i	−0.0842326	+	0.145895i
$477$	−136.876	−	105.501i	−0.286951	−	0.221176i
$478$	484.993	+	129.953i	1.01463	+	0.271869i
$479$	383.013	−	67.5355i	0.799609	−	0.140993i	0.241110	−	0.970498i	$-0.422489\pi$
$479$	383.013	−	67.5355i	0.799609	−	0.140993i	0.558499	+	0.829505i	$0.311377\pi$
$480$	346.057	+	492.595i	0.720952	+	1.02624i
$481$	65.3998	−	23.8036i	0.135966	−	0.0494877i
$482$	−176.354	+	123.484i	−0.365879	+	0.256191i
$483$	−31.6546	+	36.0163i	−0.0655375	+	0.0745678i
$484$	−89.2800	−	106.400i	−0.184463	−	0.219834i
$485$	−217.540	+	160.390i	−0.448537	+	0.330701i
$486$	397.740	−	647.510i	0.818395	−	1.33232i
$487$	−489.085	−	489.085i	−1.00428	−	1.00428i	−0.999991	−	0.00429022i	$-0.998634\pi$
$487$	−489.085	−	489.085i	−1.00428	−	1.00428i	−0.00429022	−	0.999991i	$-0.501366\pi$
$488$	−53.7772	+	614.676i	−0.110199	+	1.25958i
$489$	49.7344	+	771.626i	0.101706	+	1.57797i
$490$	−676.223	+	335.694i	−1.38005	+	0.685089i
$491$	682.606	−	248.448i	1.39024	−	0.506005i	0.464971	−	0.885326i	$-0.346065\pi$
$491$	682.606	−	248.448i	1.39024	−	0.506005i	0.925265	+	0.379321i	$0.123842\pi$
$492$	291.202	+	6.67010i	0.591873	+	0.0135571i
$493$	78.7395	+	55.1340i	0.159715	+	0.111834i
$494$	−199.977	+	115.457i	−0.404812	+	0.233719i
$495$	443.023	+	9.46101i	0.894996	+	0.0191132i
$496$	−129.639	+	224.541i	−0.261369	+	0.452704i
$497$	48.9198	+	104.909i	0.0984301	+	0.211084i
$498$	444.670	+	555.281i	0.892912	+	1.11502i
$499$	−549.885	+	655.328i	−1.10197	+	1.31328i	−0.156467	+	0.987683i	$0.550010\pi$
$499$	−549.885	+	655.328i	−1.10197	+	1.31328i	−0.945508	+	0.325599i	$0.894434\pi$
$500$	−296.172	−	658.928i	−0.592344	−	1.31786i
$501$	−560.971	+	246.107i	−1.11970	+	0.491232i
$502$	447.810	+	960.333i	0.892053	+	1.91301i
$503$	197.631	+	737.569i	0.392904	+	1.46634i	0.825320	+	0.564665i	$0.190995\pi$
$503$	197.631	+	737.569i	0.392904	+	1.46634i	−0.432416	+	0.901674i	$0.642339\pi$
$504$	31.1933	+	28.7081i	0.0618915	+	0.0569606i
$505$	−7.05496	+	2.76494i	−0.0139702	+	0.00547512i
$506$	−100.970	−	572.627i	−0.199545	−	1.13167i
$507$	251.418	−	413.313i	0.495894	−	0.815213i
$508$	191.518	−	410.711i	0.377004	−	0.808487i
$509$	73.9537	+	13.0400i	0.145292	+	0.0256189i	0.245821	−	0.969315i	$-0.420942\pi$
$509$	73.9537	+	13.0400i	0.145292	+	0.0256189i	−0.100529	+	0.994934i	$0.532054\pi$
$510$	−722.928	−	261.857i	−1.41751	−	0.513445i
$511$	17.2769	−	14.4970i	0.0338100	−	0.0283700i
$512$	252.173	+	252.173i	0.492525	+	0.492525i
$513$	714.855	+	49.1911i	1.39348	+	0.0958890i
$514$			855.920i			1.66521i
$515$	−860.651	−	208.199i	−1.67117	−	0.404270i
$516$	491.625	−	994.196i	0.952761	−	1.92674i
$517$	205.868	−	144.151i	0.398198	−	0.278821i
$518$	27.9832	−	60.0102i	0.0540216	−	0.115850i
$519$	60.2039	−	205.719i	0.116000	−	0.396376i
$520$	−1.89263	−	77.3912i	−0.00363968	−	0.148829i
$521$	−341.445	−	591.399i	−0.655364	−	1.13512i	−0.981802	−	0.189905i	$-0.939182\pi$
$521$	−341.445	−	591.399i	−0.655364	−	1.13512i	0.326439	−	0.945218i	$-0.394151\pi$
$522$	121.928	−	111.241i	0.233578	−	0.213105i
$523$	−32.8676	−	122.664i	−0.0628444	−	0.234538i	0.927359	−	0.374174i	$-0.122074\pi$
$523$	−32.8676	−	122.664i	−0.0628444	−	0.234538i	−0.990203	+	0.139635i	$0.955407\pi$
$524$	375.049	−	1030.44i	0.715742	−	1.96649i
$525$	37.7536	+	51.0403i	0.0719116	+	0.0972195i
$526$	96.7107	+	81.1499i	0.183861	+	0.154277i
$527$	−64.8028	−	740.700i	−0.122965	−	1.40550i
$528$	166.919	−	25.5060i	0.316135	−	0.0483068i
$529$	58.9867	−	162.065i	0.111506	−	0.306360i
$530$	234.647	+	187.310i	0.442729	+	0.353415i
$531$	60.2675	−	31.2072i	0.113498	−	0.0587707i
$532$	−33.6029	+	125.408i	−0.0631633	+	0.235729i
$533$	38.2894	+	26.8105i	0.0718376	+	0.0503012i
$534$	193.888	−	662.523i	0.363086	−	1.24068i
$535$	−158.047	+	237.888i	−0.295414	+	0.444650i
$536$	−107.562	+	610.012i	−0.200675	+	1.13808i
$537$	278.949	−	94.3531i	0.519458	−	0.175704i
$538$	−28.5884	+	326.767i	−0.0531384	+	0.607374i
$539$			475.457i			0.882110i
$540$	−419.622	+	657.773i	−0.777078	+	1.21810i
$541$	557.644			1.03077			0.515383	−	0.856960i	$-0.327650\pi$
$541$	557.644			1.03077			0.515383	+	0.856960i	$0.327650\pi$
$542$	1248.83	+	109.259i	2.30412	+	0.201585i
$543$	−672.411	−	134.509i	−1.23833	−	0.247715i
$544$	−647.850	−	114.233i	−1.19090	−	0.209988i
$545$	603.002	−	121.597i	1.10643	−	0.223113i
$546$	5.22853	+	21.4681i	0.00957607	+	0.0393189i
$547$	304.370	−	434.686i	0.556436	−	0.794673i	−0.438116	−	0.898919i	$-0.644354\pi$
$547$	304.370	−	434.686i	0.556436	−	0.794673i	0.994552	+	0.104246i	$0.0332429\pi$
$548$	−207.229	−	55.5270i	−0.378156	−	0.101327i
$549$	952.405	−	298.022i	1.73480	−	0.542845i
$550$	−769.290	−	29.5286i	−1.39871	−	0.0536883i
$551$	146.244	+	53.2284i	0.265415	+	0.0966032i
$552$	293.661	+	114.565i	0.531995	+	0.207546i
$553$	115.935	−	10.1430i	0.209647	−	0.0183417i
$554$	−185.745	+	221.362i	−0.335279	+	0.399570i
$555$	362.570	+	96.5487i	0.653280	+	0.173962i
$556$	−183.928	−	66.9443i	−0.330805	−	0.120403i
$557$	−415.977	+	111.461i	−0.746817	+	0.200109i	−0.612106	−	0.790776i	$-0.709677\pi$
$557$	−415.977	+	111.461i	−0.746817	+	0.200109i	−0.134711	+	0.990885i	$0.543011\pi$
$558$	−1265.39	−	169.385i	−2.26772	−	0.303558i
$559$	154.139	−	88.9920i	0.275740	−	0.159198i
$560$	17.5193	+	16.6829i	0.0312845	+	0.0297909i
$561$	−350.153	+	334.471i	−0.624158	+	0.596205i
$562$	1315.44	+	613.402i	2.34065	+	1.09146i
$563$	−58.6661	−	83.7839i	−0.104203	−	0.148817i	0.763664	−	0.645614i	$-0.223398\pi$
$563$	−58.6661	−	83.7839i	−0.104203	−	0.148817i	−0.867867	+	0.496797i	$0.834509\pi$
$564$	28.4622	+	441.589i	0.0504649	+	0.782960i
$565$	−860.151	−	208.078i	−1.52239	−	0.368280i
$566$	−1634.90			−2.88851
$567$	23.7298	−	64.3273i	0.0418516	−	0.113452i
$568$	538.077	−	538.077i	0.947319	−	0.947319i
$569$	−93.1827	−	111.051i	−0.163766	−	0.195168i	0.677921	−	0.735135i	$-0.262881\pi$
$569$	−93.1827	−	111.051i	−0.163766	−	0.195168i	−0.841686	+	0.539967i	$0.818437\pi$
$570$	−1240.31	−	106.577i	−2.17598	−	0.186978i
$571$	−98.5739	+	559.041i	−0.172634	+	0.979055i	0.768206	+	0.640203i	$0.221150\pi$
$571$	−98.5739	+	559.041i	−0.172634	+	0.979055i	−0.940840	+	0.338852i	$0.889961\pi$
$572$	−143.512	−	66.9205i	−0.250894	−	0.116994i
$573$	5.52422	−	241.175i	0.00964088	−	0.420899i
$574$	43.7950	−	7.72224i	0.0762979	−	0.0134534i
$575$	399.456	+	251.533i	0.694706	+	0.437449i
$576$	−355.365	+	852.690i	−0.616954	+	1.48036i
$577$	−15.8762	+	4.25401i	−0.0275150	+	0.00737263i	−0.272550	−	0.962142i	$-0.587867\pi$
$577$	−15.8762	+	4.25401i	−0.0275150	+	0.00737263i	0.245035	+	0.969514i	$0.421200\pi$
$578$	−57.5940	+	26.8565i	−0.0996436	+	0.0464646i
$579$	−120.193	−	13.2952i	−0.207587	−	0.0229624i
$580$	−127.112	+	112.068i	−0.219158	+	0.193220i
$581$	49.1695	+	41.2581i	0.0846290	+	0.0710122i
$582$	−472.444	−	184.314i	−0.811760	−	0.316690i
$583$	171.368	−	79.9103i	0.293942	−	0.137067i
$584$	−128.400	−	74.1319i	−0.219863	−	0.126938i
$585$	−114.579	+	50.4796i	−0.195862	+	0.0862899i
$586$	370.288	+	641.358i	0.631891	+	1.09447i
$587$	115.966	−	165.617i	0.197558	−	0.282142i	−0.708134	−	0.706078i	$-0.750463\pi$
$587$	115.966	−	165.617i	0.197558	−	0.282142i	0.905692	+	0.423936i	$0.139352\pi$
$588$	−715.221	−	435.069i	−1.21636	−	0.739913i
$589$	−411.730	−	1131.22i	−0.699033	−	1.92058i
$590$	−105.612	+	52.4284i	−0.179004	+	0.0888617i
$591$	326.323	+	489.525i	0.552154	+	0.828300i
$592$	142.431	+	12.4611i	0.240594	+	0.0210492i
$593$	225.819	−	225.819i	0.380808	−	0.380808i	−0.490585	−	0.871393i	$-0.663217\pi$
$593$	225.819	−	225.819i	0.380808	−	0.380808i	0.871393	+	0.490585i	$0.163217\pi$
$594$	429.016	+	712.212i	0.722249	+	1.19901i
$595$	−68.5950	−	10.3729i	−0.115286	−	0.0174334i
$596$	238.328	−	199.981i	0.399879	−	0.335538i
$597$	−7.18053	+	2.42878i	−0.0120277	+	0.00406830i
$598$	94.2350	+	134.581i	0.157584	+	0.225053i
$599$	−141.436	−	388.592i	−0.236120	−	0.648734i	−0.999994	−	0.00336940i	$-0.998927\pi$
$599$	−141.436	−	388.592i	−0.236120	−	0.648734i	0.763874	−	0.645365i	$-0.223295\pi$
$600$	230.413	−	347.980i	0.384022	−	0.579967i
$601$	49.7481	+	282.135i	0.0827755	+	0.469443i	0.997814	+	0.0660779i	$0.0210486\pi$
$601$	49.7481	+	282.135i	0.0827755	+	0.469443i	−0.915039	+	0.403366i	$0.867840\pi$
$602$	43.8264	−	163.562i	0.0728013	−	0.271698i
$603$	978.544	−	214.712i	1.62279	−	0.356072i
$604$	41.0535	+	23.7023i	0.0679694	+	0.0392422i
$605$	57.5195	−	105.502i	0.0950735	−	0.174384i
$606$	−11.4567	−	8.41950i	−0.0189054	−	0.0138936i
$607$	−20.9461	−	239.415i	−0.0345075	−	0.394423i	−0.993733	−	0.111781i	$-0.964345\pi$
$607$	−20.9461	−	239.415i	−0.0345075	−	0.394423i	0.959225	−	0.282642i	$-0.0912109\pi$
$608$	−1061.04	+	92.8287i	−1.74513	+	0.152679i
$609$	8.81869	−	11.9999i	0.0144806	−	0.0197042i
$610$	−1663.22	+	489.541i	−2.72659	+	0.802526i
$611$	−35.5055	+	61.4973i	−0.0581105	+	0.100650i
$612$	−182.730	−	832.787i	−0.298578	−	1.36076i
$613$	−859.227	−	230.229i	−1.40168	−	0.375578i	−0.522730	−	0.852499i	$-0.675086\pi$
$613$	−859.227	−	230.229i	−1.40168	−	0.375578i	−0.878946	+	0.476921i	$0.841753\pi$
$614$	−855.989	+	150.934i	−1.39412	+	0.245821i
$615$	86.5542	+	236.664i	0.140739	+	0.384820i
$616$	−43.5865	+	15.8642i	−0.0707573	+	0.0257535i
$617$	613.325	−	429.455i	0.994043	−	0.696037i	0.0410907	−	0.999155i	$-0.486917\pi$
$617$	613.325	−	429.455i	0.994043	−	0.696037i	0.952953	+	0.303119i	$0.0980279\pi$
$618$	−532.345	−	1573.85i	−0.861400	−	2.54668i
$619$	380.849	+	453.879i	0.615265	+	0.733245i	0.980249	−	0.197769i	$-0.0633697\pi$
$619$	380.849	+	453.879i	0.615265	+	0.733245i	−0.364983	+	0.931014i	$0.618925\pi$
$620$	1296.06	+	195.990i	2.09043	+	0.316113i
$621$	−9.46276	−	509.729i	−0.0152379	−	0.820820i
$622$	817.039	+	817.039i	1.31357	+	1.31357i
$623$	5.42847	−	62.0477i	0.00871344	−	0.0995951i
$624$	−39.6990	+	26.4638i	−0.0636202	+	0.0424099i
$625$	437.261	−	446.573i	0.699618	−	0.714517i
$626$	1583.34	−	576.288i	2.52930	−	0.920589i
$627$	−407.443	+	669.806i	−0.649830	+	1.06827i
$628$	−302.650	−	211.918i	−0.481927	−	0.337449i
$629$	−355.079	+	205.005i	−0.564513	+	0.325922i
$630$	−43.1220	+	111.041i	−0.0684477	+	0.176255i
$631$	−166.669	+	288.679i	−0.264134	+	0.457494i	−0.967336	−	0.253496i	$-0.918420\pi$
$631$	−166.669	+	288.679i	−0.264134	+	0.457494i	0.703202	+	0.710990i	$0.251753\pi$
$632$	−323.326	−	693.374i	−0.511591	−	1.09711i
$633$	95.3070	−	244.297i	0.150564	−	0.385935i
$634$	485.200	−	578.238i	0.765299	−	0.912048i
$635$	391.281	+	24.6110i	0.616190	+	0.0387575i
$636$	−36.6036	+	330.908i	−0.0575529	+	0.520295i
$637$	−56.7754	−	121.755i	−0.0891293	−	0.191138i
$638$	46.7388	+	174.431i	0.0732582	+	0.273403i
$639$	−1136.02	−	473.447i	−1.77782	−	0.740919i
$640$	321.167	−	735.153i	0.501823	−	1.14868i
$641$	−136.519	−	774.240i	−0.212979	−	1.20786i	−0.884380	−	0.466769i	$-0.845418\pi$
$641$	−136.519	−	774.240i	−0.212979	−	1.20786i	0.671401	−	0.741095i	$-0.265693\pi$
$642$	−535.744	−	12.2715i	−0.834493	−	0.0191144i
$643$	−51.0814	+	109.544i	−0.0794423	+	0.170364i	−0.942017	−	0.335565i	$-0.891073\pi$
$643$	−51.0814	+	109.544i	−0.0794423	+	0.170364i	0.862575	+	0.505930i	$0.168850\pi$
$644$	90.9709	+	16.0406i	0.141259	+	0.0249078i
$645$	956.008	+	82.1477i	1.48218	+	0.127361i
$646$	1042.10	−	874.422i	1.61315	−	1.35359i
$647$	−213.559	−	213.559i	−0.330076	−	0.330076i	0.522539	−	0.852615i	$-0.324985\pi$
$647$	−213.559	−	213.559i	−0.330076	−	0.330076i	−0.852615	+	0.522539i	$0.824985\pi$
$648$	−450.733	−	1.95588i	−0.695575	−	0.00301833i
$649$			74.2566i			0.114417i
$650$	200.526	−	84.3009i	0.308502	−	0.129694i
$651$	−114.952	+	7.40913i	−0.176578	+	0.0113812i
$652$	1220.21	−	854.402i	1.87149	−	1.31043i
$653$	234.980	−	503.916i	0.359847	−	0.771694i	−0.640147	−	0.768252i	$-0.721127\pi$
$653$	234.980	−	503.916i	0.359847	−	0.771694i	0.999994	−	0.00344153i	$-0.00109548\pi$
$654$	797.241	+	834.620i	1.21902	+	1.27618i
$655$	948.399	−	23.1935i	1.44794	−	0.0354099i
$656$	48.0126	+	83.1603i	0.0731899	+	0.126769i
$657$	−31.8152	+	237.675i	−0.0484250	+	0.361758i
$658$	17.4856	+	65.2571i	0.0265739	+	0.0991750i
$659$	−193.126	+	530.609i	−0.293059	+	0.805174i	0.702556	+	0.711629i	$0.252042\pi$
$659$	−193.126	+	530.609i	−0.293059	+	0.805174i	−0.995615	+	0.0935450i	$0.970180\pi$
$660$	−427.979	−	738.636i	−0.648453	−	1.11915i
$661$	−404.684	−	339.571i	−0.612231	−	0.513722i	0.283120	−	0.959084i	$-0.408631\pi$
$661$	−404.684	−	339.571i	−0.612231	−	0.513722i	−0.895351	+	0.445362i	$0.853075\pi$
$662$	135.809	+	1552.30i	0.205150	+	2.34487i
$663$	49.7273	−	127.464i	0.0750034	−	0.192253i
$664$	144.317	−	396.507i	0.217344	−	0.597149i
$665$	−111.622	+	12.5222i	−0.167852	+	0.0188304i
$666$	210.242	+	671.881i	0.315678	+	1.00883i
$667$	28.6588	−	106.956i	0.0429667	−	0.160354i
$668$	966.703	+	676.893i	1.44716	+	1.01331i
$669$	828.538	−	201.790i	1.23847	−	0.301629i
$670$	−1706.16	+	344.051i	−2.54651	+	0.513509i
$671$	−189.604	+	1075.30i	−0.282569	+	1.60253i
$672$	−19.9912	+	99.9361i	−0.0297489	+	0.148714i
$673$	26.4882	−	302.762i	0.0393584	−	0.449869i	−0.950789	−	0.309840i	$-0.899725\pi$
$673$	26.4882	−	302.762i	0.0393584	−	0.449869i	0.990147	−	0.140030i	$-0.0447198\pi$
$674$			187.939i			0.278841i
$675$	−662.294	−	130.353i	−0.981176	−	0.193115i
$676$	−931.982			−1.37867
$677$	−827.836	−	72.4263i	−1.22280	−	0.106981i	−0.542590	−	0.839998i	$-0.682556\pi$
$677$	−827.836	−	72.4263i	−1.22280	−	0.106981i	−0.680211	+	0.733017i	$0.738112\pi$
$678$	−532.036	−	1572.93i	−0.784714	−	2.31996i
$679$	−45.0612	−	7.94550i	−0.0663641	−	0.0117018i
$680$	90.1514	+	447.064i	0.132576	+	0.657447i
$681$	387.482	+	113.397i	0.568989	+	0.166515i
$682$	801.202	−	1144.23i	1.17478	−	1.67776i
$683$	188.344	+	50.4667i	0.275761	+	0.0738898i	0.394049	−	0.919089i	$-0.371074\pi$
$683$	188.344	+	50.4667i	0.275761	+	0.0738898i	−0.118288	+	0.992979i	$0.537741\pi$
$684$	−634.744	−	1225.82i	−0.927988	−	1.79213i
$685$	−20.6923	−	184.449i	−0.0302077	−	0.269269i
$686$	−241.990	−	88.0770i	−0.352754	−	0.128392i
$687$	71.7671	+	469.667i	0.104465	+	0.683649i
$688$	364.247	−	31.8675i	0.529429	−	0.0463190i
$689$	−34.3417	+	40.9269i	−0.0498429	+	0.0594004i
$690$	1.37208	+	885.724i	0.00198852	+	1.28366i
$691$	−519.597	−	189.118i	−0.751950	−	0.273687i	−0.0625238	−	0.998043i	$-0.519915\pi$
$691$	−519.597	−	189.118i	−0.751950	−	0.273687i	−0.689426	+	0.724356i	$0.742137\pi$
$692$	−398.865	+	106.876i	−0.576395	+	0.154445i
$693$	50.5619	+	55.4195i	0.0729608	+	0.0799704i
$694$	−936.145	+	540.484i	−1.34891	+	0.778795i
$695$	−4.13992	−	169.284i	−0.00595672	−	0.243574i
$696$	−93.9565	−	27.4965i	−0.134995	−	0.0395064i
$697$	−249.571	−	116.377i	−0.358064	−	0.166968i
$698$	501.814	+	716.664i	0.718931	+	1.02674i
$699$	−157.711	−	77.9873i	−0.225624	−	0.111570i
$700$	46.2078	−	113.239i	0.0660111	−	0.161770i
$701$	624.400			0.890727			0.445364	−	0.895350i	$-0.353074\pi$
$701$	624.400			0.890727			0.445364	+	0.895350i	$0.353074\pi$
$702$	−194.909	−	131.154i	−0.277648	−	0.186829i
$703$	−469.399	+	469.399i	−0.667709	+	0.667709i
$704$	−649.689	−	774.269i	−0.922853	−	1.09981i
$705$	−346.709	+	162.327i	−0.491786	+	0.230252i
$706$	−209.833	+	1190.02i	−0.297213	+	1.68558i
$707$	−1.16263	−	0.542144i	−0.00164446	−	0.000766823i
$708$	−111.703	−	67.9488i	−0.157772	−	0.0959728i
$709$	1053.85	−	185.821i	1.48638	−	0.262090i	0.629258	−	0.777197i	$-0.283359\pi$
$709$	1053.85	−	185.821i	1.48638	−	0.262090i	0.857126	+	0.515107i	$0.172248\pi$
$710$	1959.38	+	855.995i	2.75969	+	1.20563i
$711$	−837.926	+	910.462i	−1.17852	+	1.28054i
$712$	−395.502	+	105.974i	−0.555481	+	0.148841i
$713$	−776.260	+	361.976i	−1.08872	+	0.507681i
$714$	−52.2961	−	119.203i	−0.0732439	−	0.166950i
$715$	8.59964	−	136.722i	0.0120275	−	0.191220i
$716$	−434.575	−	364.652i	−0.606949	−	0.509291i
$717$	−375.979	+	301.085i	−0.524378	+	0.419923i
$718$	404.065	−	188.419i	0.562764	−	0.262421i
$719$	480.338	+	277.323i	0.668064	+	0.385707i	0.795343	−	0.606160i	$-0.207291\pi$
$719$	480.338	+	277.323i	0.668064	+	0.385707i	−0.127278	+	0.991867i	$0.540624\pi$
$720$	−257.157	−	5.49173i	−0.357162	−	0.00762740i
$721$	−74.9534	−	129.823i	−0.103958	−	0.180060i
$722$	615.782	−	879.427i	0.852883	−	1.21804i
$723$	4.72943	−	206.476i	0.00654140	−	0.285583i
$724$	451.825	+	1241.38i	0.624068	+	1.71461i
$725$	−130.396	−	67.0091i	−0.179856	−	0.0924263i
$726$	224.998	−	14.5021i	0.309915	−	0.0199753i
$727$	214.320	+	18.7506i	0.294801	+	0.0257917i	0.233597	−	0.972334i	$-0.424950\pi$
$727$	214.320	+	18.7506i	0.294801	+	0.0257917i	0.0612041	+	0.998125i	$0.480506\pi$
$728$	9.26726	−	9.26726i	0.0127298	−	0.0127298i
$729$	274.587	+	675.310i	0.376662	+	0.926351i
$730$	62.2905	−	411.921i	0.0853295	−	0.564276i
$731$	−803.227	+	673.988i	−1.09881	+	0.922008i
$732$	−1444.05	−	1269.17i	−1.97274	−	1.73384i
$733$	359.198	+	512.988i	0.490038	+	0.699847i	0.985670	−	0.168686i	$-0.0539523\pi$
$733$	359.198	+	512.988i	0.490038	+	0.699847i	−0.495632	+	0.868533i	$0.665063\pi$
$734$	393.673	+	1081.61i	0.536339	+	1.47358i
$735$	124.660	−	713.443i	0.169605	−	0.970671i
$736$	131.591	+	746.291i	0.178792	+	1.01398i
$737$	−283.699	+	1058.78i	−0.384937	+	1.43661i
$738$	−288.651	+	374.492i	−0.391126	+	0.507442i
$739$	357.529	+	206.420i	0.483802	+	0.279323i	0.721999	−	0.691894i	$-0.243223\pi$
$739$	357.529	+	206.420i	0.483802	+	0.279323i	−0.238198	+	0.971217i	$0.576557\pi$
$740$	−204.094	−	693.412i	−0.275803	−	0.937043i
$741$	24.3551	−	220.178i	0.0328679	−	0.297136i
$742$	4.43006	+	50.6358i	0.00597043	+	0.0682423i
$743$	845.883	−	74.0052i	1.13847	−	0.0996032i	0.497709	−	0.867344i	$-0.334175\pi$
$743$	845.883	−	74.0052i	1.13847	−	0.0996032i	0.640761	+	0.767741i	$0.278619\pi$
$744$	304.229	+	693.452i	0.408909	+	0.932059i
$745$	236.317	+	128.839i	0.317204	+	0.172939i
$746$	486.400	−	842.469i	0.652010	−	1.12931i
$747$	−681.861	+	28.2886i	−0.912799	+	0.0378696i
$748$	901.070	+	241.441i	1.20464	+	0.322782i
$749$	−47.6168	+	8.39612i	−0.0635738	+	0.0112098i
$750$	1146.61	+	246.009i	1.52881	+	0.328012i
$751$	445.596	−	162.184i	0.593337	−	0.215957i	−0.0278595	−	0.999612i	$-0.508869\pi$
$751$	445.596	−	162.184i	0.593337	−	0.215957i	0.621196	+	0.783655i	$0.286647\pi$
$752$	−119.498	+	83.6735i	−0.158907	+	0.111268i
$753$	−996.759	−	199.392i	−1.32372	−	0.264797i
$754$	−32.7981	−	39.0873i	−0.0434988	−	0.0518399i
$755$	−6.13201	+	40.5504i	−0.00812187	+	0.0537091i
$756$	−129.633	+	25.3474i	−0.171473	+	0.0335283i
$757$	726.933	+	726.933i	0.960282	+	0.960282i	0.999241	−	0.0389592i	$-0.0124042\pi$
$757$	726.933	+	726.933i	0.960282	+	0.960282i	−0.0389592	+	0.999241i	$0.512404\pi$
$758$	−68.4679	+	782.591i	−0.0903270	+	1.03244i
$759$	500.015	+	247.255i	0.658781	+	0.325764i
$760$	328.327	+	661.383i	0.432009	+	0.870241i
$761$	336.528	−	122.486i	0.442218	−	0.160954i	−0.111308	−	0.993786i	$-0.535504\pi$
$761$	336.528	−	122.486i	0.442218	−	0.160954i	0.553526	+	0.832832i	$0.313282\pi$
$762$	353.125	+	645.322i	0.463419	+	0.846879i
$763$	85.3068	+	59.7325i	0.111804	+	0.0782863i
$764$	−402.477	+	232.370i	−0.526802	+	0.304149i
$765$	613.114	−	410.081i	0.801456	−	0.536054i
$766$	−110.892	+	192.071i	−0.144768	+	0.250745i
$767$	−8.86714	−	19.0156i	−0.0115608	−	0.0247922i
$768$	270.431	−	41.3231i	0.352124	−	0.0538061i
$769$	−584.717	+	696.838i	−0.760360	+	0.906162i	−0.997871	−	0.0652232i	$-0.979224\pi$
$769$	−584.717	+	696.838i	−0.760360	+	0.906162i	0.237511	+	0.971385i	$0.423668\pi$
$770$	−86.1923	−	97.7629i	−0.111938	−	0.126965i
$771$	−661.647	−	486.244i	−0.858167	−	0.630667i
$772$	98.4535	+	211.134i	0.127530	+	0.273490i
$773$	76.5537	+	285.702i	0.0990345	+	0.369602i	0.997600	−	0.0692371i	$-0.0220565\pi$
$773$	76.5537	+	285.702i	0.0990345	+	0.369602i	−0.898566	+	0.438839i	$0.855390\pi$
$774$	827.861	+	1598.77i	1.06959	+	2.06559i
$775$	251.276	+	1105.83i	0.324227	+	1.42688i
$776$	52.2330	+	296.228i	0.0673105	+	0.381737i
$777$	30.4922	+	55.7232i	0.0392435	+	0.0717158i
$778$	−842.829	+	1807.45i	−1.08333	+	2.32320i
$779$	−439.069	−	77.4197i	−0.563631	−	0.0993834i
$780$	197.799	+	138.044i	0.253589	+	0.176980i
$781$	1031.54	−	865.569i	1.32080	−	1.10828i
$782$	−684.399	−	684.399i	−0.875191	−	0.875191i
$783$	16.7250	+	157.449i	0.0213602	+	0.201084i
$784$		−	275.983i		−	0.352019i
$785$	75.1559	−	310.679i	0.0957400	−	0.395769i
$786$	987.330	+	1481.12i	1.25614	+	1.88438i
$787$	−747.300	+	523.265i	−0.949555	+	0.664886i	−0.942187	−	0.335087i	$-0.891234\pi$
$787$	−747.300	+	523.265i	−0.949555	+	0.664886i	−0.00736798	+	0.999973i	$0.502345\pi$
$788$	478.990	−	1027.20i	0.607855	−	1.30355i
$789$	−117.672	+	28.6588i	−0.149140	+	0.0363230i
$790$	1482.46	−	1556.79i	1.87653	−	1.97061i
$791$	−74.9099	−	129.748i	−0.0947028	−	0.164030i
$792$	228.667	−	436.949i	0.288722	−	0.551703i
$793$	−79.8497	−	298.003i	−0.100693	−	0.375792i
$794$	612.944	−	1684.05i	0.771969	−	2.12097i
$795$	−278.097	+	74.9777i	−0.349807	+	0.0943116i
$796$	11.1866	+	9.38664i	0.0140535	+	0.0117923i
$797$	−49.5556	−	566.423i	−0.0621776	−	0.710694i	−0.961751	−	0.273924i	$-0.911678\pi$
$797$	−49.5556	−	566.423i	−0.0621776	−	0.710694i	0.899574	−	0.436769i	$-0.143877\pi$
$798$	−131.737	−	164.506i	−0.165084	−	0.206148i
$799$	143.081	−	393.111i	0.179075	−	0.492004i
$800$	1002.60	+	38.4839i	1.25325	+	0.0481049i
$801$	402.000	+	526.256i	0.501872	+	0.656999i
$802$	−478.141	+	1784.45i	−0.596186	+	2.22500i
$803$	−214.919	−	150.488i	−0.267645	−	0.187407i
$804$	−1333.10	−	1395.60i	−1.65808	−	1.73582i
$805$	15.7973	+	78.3395i	0.0196240	+	0.0973161i
$806$	−68.5364	+	388.689i	−0.0850327	+	0.482245i
$807$	−236.358	−	207.735i	−0.292885	−	0.257416i
$808$	−0.734997	+	8.40105i	−0.000909650	+	0.0103973i
$809$			906.509i			1.12053i	0.828313	+	0.560265i	$0.189301\pi$
$809$			906.509i			1.12053i	−0.828313	+	0.560265i	$0.810699\pi$
$810$	−457.021	−	1181.19i	−0.564224	−	1.45826i
$811$	−437.279			−0.539185			−0.269593	−	0.962974i	$-0.586889\pi$
$811$	−437.279			−0.539185			−0.269593	+	0.962974i	$0.586889\pi$
$812$	−28.5796	−	2.50039i	−0.0351965	−	0.00307930i
$813$	−793.917	+	903.310i	−0.976528	+	1.11108i
$814$	−758.575	−	133.757i	−0.931910	−	0.164321i
$815$	1073.41	+	713.145i	1.31706	+	0.875024i
$816$	203.249	−	194.147i	0.249080	−	0.237925i
$817$	−973.731	+	1390.63i	−1.19184	+	1.70212i
$818$	−416.022	−	111.473i	−0.508584	−	0.136275i
$819$	−19.5657	−	8.15414i	−0.0238897	−	0.00995622i
$820$	302.865	−	379.404i	0.369347	−	0.462688i
$821$	−1140.04	−	414.941i	−1.38860	−	0.505409i	−0.463826	−	0.885927i	$-0.653524\pi$
$821$	−1140.04	−	414.941i	−1.38860	−	0.505409i	−0.924774	+	0.380518i	$0.875746\pi$
$822$	271.837	−	217.688i	0.330702	−	0.264827i
$823$	−671.140	+	58.7171i	−0.815480	+	0.0713452i	−0.487261	−	0.873257i	$-0.662004\pi$
$823$	−671.140	+	58.7171i	−0.815480	+	0.0713452i	−0.328219	+	0.944602i	$0.606448\pi$
$824$	−633.450	+	754.916i	−0.768750	+	0.916160i
$825$	459.856	−	577.905i	0.557401	−	0.700490i
$826$	−18.7577	−	6.82725i	−0.0227091	−	0.00826543i
$827$	443.435	−	118.818i	0.536197	−	0.143674i	0.0194486	−	0.999811i	$-0.493809\pi$
$827$	443.435	−	118.818i	0.536197	−	0.143674i	0.516748	+	0.856137i	$0.327142\pi$
$828$	−829.481	+	525.911i	−1.00179	+	0.635158i
$829$	161.228	−	93.0850i	0.194485	−	0.112286i	−0.399596	−	0.916692i	$-0.630849\pi$
$829$	161.228	−	93.0850i	0.194485	−	0.112286i	0.594080	+	0.804406i	$0.297516\pi$
$830$	1185.29	−	28.9867i	1.42806	−	0.0349237i
$831$	−65.5974	−	269.340i	−0.0789379	−	0.324115i
$832$	258.830	+	120.694i	0.311093	+	0.145065i
$833$	453.949	+	648.306i	0.544956	+	0.778278i
$834$	264.372	−	176.233i	0.316993	−	0.211311i
$835$	−240.057	+	992.348i	−0.287494	+	1.18844i
$836$	1510.35			1.80664
$837$	849.800	−	881.949i	1.01529	−	1.05370i
$838$	224.517	−	224.517i	0.267920	−	0.267920i
$839$	−737.452	−	878.862i	−0.878966	−	1.04751i	−0.998504	−	0.0546812i	$-0.982586\pi$
$839$	−737.452	−	878.862i	−0.878966	−	1.04751i	0.119538	−	0.992830i	$-0.461859\pi$
$840$	69.5628	−	12.3769i	0.0828128	−	0.0147344i
$841$	140.066	−	794.357i	0.166548	−	0.944538i
$842$	−1491.42	−	695.461i	−1.77128	−	0.825963i
$843$	−1221.47	+	668.399i	−1.44896	+	0.792882i
$844$	−497.504	+	87.7235i	−0.589460	+	0.103938i
$845$	−294.209	−	750.699i	−0.348177	−	0.888401i
$846$	−604.978	−	387.261i	−0.715103	−	0.457755i
$847$	19.6499	−	5.26517i	0.0231994	−	0.00621626i
$848$	−99.4721	+	46.3846i	−0.117302	+	0.0546988i
$849$	928.777	−	1263.81i	1.09397	−	1.48859i
$850$	−1077.15	+	694.226i	−1.26724	+	0.816736i
$851$	361.811	+	303.596i	0.425160	+	0.356752i
$852$	358.139	+	2343.77i	0.420351	+	2.75091i
$853$	1072.09	−	499.924i	1.25685	−	0.586078i	0.323901	−	0.946091i	$-0.395006\pi$
$853$	1072.09	−	499.924i	1.25685	−	0.586078i	0.932947	+	0.360013i	$0.117228\pi$
$854$	−254.195	−	146.759i	−0.297652	−	0.171849i
$855$	787.002	−	898.245i	0.920470	−	1.05058i
$856$	158.928	+	275.272i	0.185664	+	0.321580i
$857$	845.206	−	1207.08i	0.986238	−	1.40849i	0.0747333	−	0.997204i	$-0.476189\pi$
$857$	845.206	−	1207.08i	0.986238	−	1.40849i	0.911505	−	0.411290i	$-0.134922\pi$
$858$	225.490	−	123.390i	0.262808	−	0.143811i
$859$	−153.807	−	422.581i	−0.179053	−	0.491945i	0.817402	−	0.576068i	$-0.195414\pi$
$859$	−153.807	−	422.581i	−0.179053	−	0.491945i	−0.996455	+	0.0841225i	$0.973191\pi$
$860$	−821.941	−	1655.72i	−0.955745	−	1.92526i
$861$	−18.9102	+	38.2416i	−0.0219631	+	0.0444153i
$862$	−1112.83	−	97.3597i	−1.29098	−	0.112946i
$863$	399.159	−	399.159i	0.462524	−	0.462524i	−0.436958	−	0.899482i	$-0.643944\pi$
$863$	399.159	−	399.159i	0.462524	−	0.462524i	0.899482	+	0.436958i	$0.143944\pi$
$864$	−559.126	−	928.209i	−0.647136	−	1.07432i
$865$	−212.001	−	287.542i	−0.245088	−	0.332418i
$866$	−172.451	+	144.704i	−0.199135	+	0.167094i
$867$	11.9581	−	59.7786i	0.0137925	−	0.0689488i
$868$	127.284	+	181.780i	0.146640	+	0.209424i
$869$	−463.040	−	1272.19i	−0.532842	−	1.46397i
$870$	−24.3993	−	273.996i	−0.0280452	−	0.314938i
$871$	−53.7814	−	305.009i	−0.0617467	−	0.350183i
$872$	177.190	−	661.281i	0.203199	−	0.758350i
$873$	410.872	−	260.503i	0.470644	−	0.298400i
$874$	−1357.12	−	783.534i	−1.55277	−	0.896492i
$875$	105.799	+	1.47228i	0.120914	+	0.00168260i
$876$	423.038	−	185.594i	0.482920	−	0.211865i
$877$	−48.8990	−	558.918i	−0.0557571	−	0.637307i	−0.971734	−	0.236077i	$-0.924138\pi$
$877$	−48.8990	−	558.918i	−0.0557571	−	0.637307i	0.915977	−	0.401230i	$-0.131417\pi$
$878$	211.917	−	18.5404i	0.241364	−	0.0211166i
$879$	−706.145	−	78.1107i	−0.803350	−	0.0888632i
$880$	134.713	−	247.091i	0.153083	−	0.280785i
$881$	−175.288	+	303.608i	−0.198965	+	0.344618i	−0.948193	−	0.317695i	$-0.897091\pi$
$881$	−175.288	+	303.608i	−0.198965	+	0.344618i	0.749228	+	0.662312i	$0.230425\pi$
$882$	1256.62	−	517.316i	1.42473	−	0.586526i
$883$	−671.771	−	180.000i	−0.760782	−	0.203851i	−0.142487	−	0.989797i	$-0.545510\pi$
$883$	−671.771	−	180.000i	−0.760782	−	0.203851i	−0.618295	+	0.785946i	$0.712176\pi$
$884$	−259.577	+	45.7705i	−0.293639	+	0.0517766i
$885$	19.4693	−	111.425i	0.0219992	−	0.125904i
$886$	679.671	−	247.380i	0.767123	−	0.279210i
$887$	112.472	−	78.7536i	0.126800	−	0.0887865i	−0.508456	−	0.861088i	$-0.669783\pi$
$887$	112.472	−	78.7536i	0.126800	−	0.0887865i	0.635256	+	0.772302i	$0.280895\pi$
$888$	275.668	−	313.652i	0.310437	−	0.353212i
$889$	42.6637	+	50.8446i	0.0479906	+	0.0571930i
$890$	−682.754	−	926.034i	−0.767140	−	1.04049i
$891$	−794.279	−	72.9647i	−0.891447	−	0.0818908i
$892$	−1161.65	−	1161.65i	−1.30229	−	1.30229i
$893$	59.0321	−	674.740i	0.0661054	−	0.755588i
$894$	32.4836	+	503.980i	0.0363351	+	0.563736i
$895$	156.535	−	465.158i	0.174899	−	0.519730i
$896$	127.626	−	46.4520i	0.142439	−	0.0518437i
$897$	−157.569	−	3.60919i	−0.175662	−	0.00402363i
$898$	−2148.28	−	1504.24i	−2.39229	−	1.67510i
$899$	230.368	−	133.003i	0.256250	−	0.147946i
$900$	448.537	+	1220.57i	0.498375	+	1.35618i
$901$	157.372	−	272.577i	0.174664	−	0.302527i
$902$	−218.635	−	468.864i	−0.242389	−	0.519804i
$903$	101.540	+	126.798i	0.112447	+	0.140418i
$904$	−633.082	+	754.478i	−0.700312	+	0.834599i
$905$	−857.281	+	755.819i	−0.947272	+	0.835159i
$906$	−70.4675	+	30.9152i	−0.0777787	+	0.0341228i
$907$	395.386	+	847.909i	0.435928	+	0.934850i	0.994435	+	0.105350i	$0.0335964\pi$
$907$	395.386	+	847.909i	0.435928	+	0.934850i	−0.558508	+	0.829499i	$0.688626\pi$
$908$	−201.305	−	751.282i	−0.221702	−	0.827403i
$909$	13.0170	−	4.07320i	0.0143201	−	0.00448097i
$910$	33.7462	+	14.7427i	0.0370838	+	0.0162008i
$911$	240.489	+	1363.88i	0.263984	+	1.49713i	0.771914	+	0.635727i	$0.219300\pi$
$911$	240.489	+	1363.88i	0.263984	+	1.49713i	−0.507930	+	0.861398i	$0.669589\pi$
$912$	236.504	−	388.795i	0.259324	−	0.426310i
$913$	315.564	−	676.729i	0.345634	−	0.741215i
$914$	−889.719	−	156.881i	−0.973434	−	0.171643i
$915$	566.440	−	1563.81i	0.619060	−	1.70909i
$916$	701.164	−	588.346i	0.765463	−	0.642299i
$917$	113.567	+	113.567i	0.123846	+	0.123846i
$918$	1264.97	+	561.523i	1.37797	+	0.611681i
$919$		−	389.728i		−	0.424078i	−0.977261	−	0.212039i	$-0.931990\pi$
$919$		−	389.728i		−	0.424078i	0.977261	−	0.212039i	$-0.0680104\pi$
$920$	448.419	−	273.726i	0.487412	−	0.297528i
$921$	369.608	−	747.445i	0.401311	−	0.811558i
$922$	973.955	−	681.971i	1.05635	−	0.739665i
$923$	−160.799	+	344.834i	−0.174213	+	0.373601i
$924$	40.5920	−	138.704i	0.0439307	−	0.150113i
$925$	494.105	−	383.292i	0.534167	−	0.414370i
$926$	−326.847	−	566.116i	−0.352967	−	0.611356i
$927$	1519.04	+	482.579i	1.63867	+	0.520581i
$928$	−60.9135	−	227.332i	−0.0656395	−	0.244970i
$929$	−482.475	+	1325.59i	−0.519348	+	1.42690i	0.351892	+	0.936041i	$0.385539\pi$
$929$	−482.475	+	1325.59i	−0.519348	+	1.42690i	−0.871240	+	0.490857i	$0.836684\pi$
$930$	−1502.24	+	1506.90i	−1.61532	+	1.62033i
$931$	981.595	+	823.656i	1.05435	+	0.884701i
$932$	29.5409	+	337.654i	0.0316963	+	0.362290i
$933$	−1095.75	+	167.435i	−1.17443	+	0.179459i
$934$	503.982	−	1384.68i	0.539596	−	1.48253i
$935$	89.9736	+	802.018i	0.0962285	+	0.857773i
$936$	−6.38021	+	139.200i	−0.00681646	+	0.148718i
$937$	−442.445	+	1651.23i	−0.472193	+	1.76225i	0.159671	+	0.987170i	$0.448957\pi$
$937$	−442.445	+	1651.23i	−0.472193	+	1.76225i	−0.631864	+	0.775079i	$0.717710\pi$
$938$	−241.371	−	169.010i	−0.257325	−	0.180181i
$939$	−454.003	+	1551.35i	−0.483496	+	1.65213i
$940$	614.294	+	408.122i	0.653504	+	0.434172i
$941$	129.411	−	733.928i	0.137525	−	0.779945i	−0.835542	−	0.549426i	$-0.814846\pi$
$941$	129.411	−	733.928i	0.137525	−	0.779945i	0.973068	−	0.230519i	$-0.0740424\pi$
$942$	568.129	−	192.167i	0.603109	−	0.203999i
$943$	−27.6470	+	316.007i	−0.0293181	+	0.335108i
$944$		−	43.1029i		−	0.0456598i
$945$	−61.3397	−	96.4161i	−0.0649098	−	0.102028i
$946$	−1969.87			−2.08231
$947$	866.967	+	75.8498i	0.915488	+	0.0800948i	0.535154	−	0.844755i	$-0.320254\pi$
$947$	866.967	+	75.8498i	0.915488	+	0.0800948i	0.380334	+	0.924849i	$0.375809\pi$
$948$	2337.44	+	467.582i	2.46565	+	0.493230i
$949$	73.0065	+	12.8730i	0.0769300	+	0.0135648i
$950$	−1393.64	+	1537.07i	−1.46699	+	1.61797i
$951$	171.353	+	703.566i	0.180182	+	0.739817i
$952$	−44.2855	+	63.2462i	−0.0465184	+	0.0664351i
$953$	1106.30	+	296.432i	1.16086	+	0.311052i	0.787310	−	0.616558i	$-0.211473\pi$
$953$	1106.30	+	296.432i	1.16086	+	0.311052i	0.373551	+	0.927610i	$0.378140\pi$
$954$	−397.655	−	365.974i	−0.416829	−	0.383621i
$955$	−314.225	−	250.834i	−0.329032	−	0.262654i
$956$	871.978	+	317.374i	0.912111	+	0.331981i
$957$	−161.392	−	62.9635i	−0.168643	−	0.0657926i
$958$	1211.61	−	106.002i	1.26473	−	0.110649i
$959$	20.1978	−	24.0709i	0.0210614	−	0.0250999i
$960$	771.879	+	1332.16i	0.804041	+	1.38767i
$961$	−1030.47	−	375.061i	−1.07229	−	0.390282i
$962$	210.228	−	56.3305i	0.218533	−	0.0585556i
$963$	313.840	−	407.172i	0.325898	−	0.422816i
$964$	−344.571	+	198.938i	−0.357439	+	0.206367i
$965$	−138.986	+	145.954i	−0.144027	+	0.151248i
$966$	−108.430	+	103.574i	−0.112247	+	0.107220i
$967$	−146.755	−	68.4329i	−0.151763	−	0.0707682i	0.345253	−	0.938510i	$-0.387793\pi$
$967$	−146.755	−	68.4329i	−0.151763	−	0.0707682i	−0.497016	+	0.867741i	$0.665571\pi$
$968$	−76.7063	−	109.548i	−0.0792421	−	0.113169i
$969$	83.9398	+	1302.32i	0.0866252	+	1.34398i
$970$	−721.420	+	440.373i	−0.743732	+	0.453992i
$971$	−169.229			−0.174283			−0.0871414	−	0.996196i	$-0.527773\pi$
$971$	−169.229			−0.174283			−0.0871414	+	0.996196i	$0.527773\pi$
$972$	836.567	−	1128.05i	0.860666	−	1.16055i
$973$	20.2711	−	20.2711i	0.0208336	−	0.0208336i
$974$	−1390.35	−	1656.95i	−1.42746	−	1.70118i
$975$	−48.7512	+	202.902i	−0.0500013	+	0.208105i
$976$	110.057	−	624.165i	0.112763	−	0.639513i
$977$	−1310.27	−	610.988i	−1.34111	−	0.625371i	−0.386244	−	0.922397i	$-0.626228\pi$
$977$	−1310.27	−	610.988i	−1.34111	−	0.625371i	−0.954870	+	0.297025i	$0.904005\pi$
$978$	−55.3718	+	2417.41i	−0.0566174	+	2.47179i
$979$	−713.561	+	125.820i	−0.728867	+	0.128519i
$980$	−1299.05	+	509.117i	−1.32556	+	0.519507i
$981$	−1098.09	+	142.143i	−1.11936	+	0.144896i
$982$	2194.24	−	587.946i	2.23446	−	0.598723i
$983$	15.0317	−	7.00938i	0.0152916	−	0.00713060i	−0.414957	−	0.909841i	$-0.636204\pi$
$983$	15.0317	−	7.00938i	0.0152916	−	0.00713060i	0.430249	+	0.902710i	$0.358426\pi$
$984$	278.753	+	30.8345i	0.283286	+	0.0313359i
$985$	978.601	+	61.5527i	0.993504	+	0.0624901i
$986$	230.271	+	193.220i	0.233540	+	0.195964i
$987$	−60.3788	−	23.5555i	−0.0611741	−	0.0238657i
$988$	−386.771	+	180.354i	−0.391469	+	0.182545i
$989$	1046.04	+	603.932i	1.05768	+	0.610650i
$990$	1377.57	+	150.222i	1.39149	+	0.151739i
$991$	−449.290	−	778.193i	−0.453371	−	0.785261i	0.545222	−	0.838291i	$-0.316445\pi$
$991$	−449.290	−	778.193i	−0.453371	−	0.785261i	−0.998593	+	0.0530306i	$0.983112\pi$
$992$	−1044.19	+	1491.25i	−1.05261	+	1.50328i
$993$	−1277.12	−	776.873i	−1.28612	−	0.782350i
$994$	123.807	+	340.157i	0.124554	+	0.342210i
$995$	−4.02942	+	11.9738i	−0.00404967	+	0.0120340i
$996$	729.232	+	1093.94i	0.732161	+	1.09833i
$997$	−1057.35	−	92.5058i	−1.06053	−	0.0927841i	−0.456481	−	0.889733i	$-0.650890\pi$
$997$	−1057.35	−	92.5058i	−1.06053	−	0.0927841i	−0.604047	+	0.796949i	$0.706446\pi$
$998$	−1891.67	+	1891.67i	−1.89547	+	1.89547i
$999$	−638.817	−	219.170i	−0.639457	−	0.219390i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.3.r.a.22.31	✓	408
3.2	odd	2		405.3.s.a.37.4		408
5.3	odd	4	inner	135.3.r.a.103.31	yes	408
15.8	even	4		405.3.s.a.118.4		408
27.11	odd	18		405.3.s.a.127.4		408
27.16	even	9	inner	135.3.r.a.97.31	yes	408
135.38	even	36		405.3.s.a.208.4		408
135.43	odd	36	inner	135.3.r.a.43.31	yes	408

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.3.r.a.22.31	✓	408	1.1	even	1	trivial
135.3.r.a.43.31	yes	408	135.43	odd	36	inner
135.3.r.a.97.31	yes	408	27.16	even	9	inner
135.3.r.a.103.31	yes	408	5.3	odd	4	inner
405.3.s.a.37.4		408	3.2	odd	2
405.3.s.a.118.4		408	15.8	even	4
405.3.s.a.127.4		408	27.11	odd	18
405.3.s.a.208.4		408	135.38	even	36

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:	\( N \)	\(=\)	\( 135 = 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	135.r (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(3.11531 + 0.272554i) q^{2} +(-1.98048 + 2.25337i) q^{3} +(5.69163 + 1.00359i) q^{4} +(0.988365 + 4.90134i) q^{5} +(-6.78398 + 6.48016i) q^{6} +(-0.485519 + 0.693393i) q^{7} +(5.37504 + 1.44024i) q^{8} +(-1.15537 - 8.92553i) q^{9} +(1.74318 + 15.5386i) q^{10} +(9.25334 + 3.36794i) q^{11} +(-13.5336 + 10.8378i) q^{12} +(-2.77177 + 0.242499i) q^{13} +(-1.70153 + 2.02780i) q^{14} +(-13.0020 - 7.47987i) q^{15} +(-5.37118 - 1.95495i) q^{16} +(15.8329 - 4.24241i) q^{17} +(-1.16665 - 28.1207i) q^{18} +(22.9832 - 13.2694i) q^{19} +(0.706481 + 28.8885i) q^{20} +(-0.600910 - 2.46731i) q^{21} +(27.9091 + 13.0142i) q^{22} +(-10.8303 - 15.4673i) q^{23} +(-13.8906 + 9.25961i) q^{24} +(-23.0463 + 9.68862i) q^{25} -8.70102 q^{26} +(22.4007 + 15.0734i) q^{27} +(-3.45928 + 3.45928i) q^{28} +(3.76946 + 4.49226i) q^{29} +(-38.4665 - 26.8458i) q^{30} +(7.87682 - 44.6717i) q^{31} +(-36.3732 - 16.9611i) q^{32} +(-25.9153 + 14.1811i) q^{33} +(50.4807 - 8.90111i) q^{34} +(-3.87843 - 1.69437i) q^{35} +(2.38160 - 51.9603i) q^{36} +(-24.1614 + 6.47401i) q^{37} +(75.2164 - 35.0740i) q^{38} +(4.94301 - 6.72610i) q^{39} +(-1.74660 + 27.7684i) q^{40} +(-12.8693 - 10.7986i) q^{41} +(-1.19955 - 7.85021i) q^{42} +(-57.9753 + 27.0343i) q^{43} +(49.2866 + 28.4556i) q^{44} +(42.6051 - 14.4846i) q^{45} +(-29.5242 - 51.1374i) q^{46} +(14.6387 - 20.9063i) q^{47} +(15.0428 - 8.23153i) q^{48} +(16.5139 + 45.3716i) q^{49} +(-74.4369 + 23.9017i) q^{50} +(-21.7971 + 44.0795i) q^{51} +(-16.0193 - 1.40150i) q^{52} +(13.5777 - 13.5777i) q^{53} +(65.6769 + 53.0636i) q^{54} +(-7.36175 + 48.6825i) q^{55} +(-3.60834 + 3.02775i) q^{56} +(-15.6170 + 78.0695i) q^{57} +(10.5186 + 15.0222i) q^{58} +(2.57913 + 7.08611i) q^{59} +(-66.4958 - 55.6213i) q^{60} +(19.2546 + 109.198i) q^{61} +(36.7142 - 137.019i) q^{62} +(6.74986 + 3.53239i) q^{63} +(-88.8905 - 51.3210i) q^{64} +(-3.92809 - 13.3457i) q^{65} +(-84.5993 + 37.1151i) q^{66} +(9.70163 + 110.890i) q^{67} +(94.3727 - 8.25654i) q^{68} +(56.3030 + 6.22800i) q^{69} +(-11.6207 - 6.33556i) q^{70} +(68.3740 - 118.427i) q^{71} +(6.64471 - 49.6391i) q^{72} +(-25.7360 - 6.89594i) q^{73} +(-77.0346 + 13.5833i) q^{74} +(23.8107 - 71.1200i) q^{75} +(144.129 - 52.4586i) q^{76} +(-6.82798 + 4.78100i) q^{77} +(17.2322 - 19.6066i) q^{78} +(-88.3733 - 105.319i) q^{79} +(4.27319 - 28.2582i) q^{80} +(-78.3302 + 20.6246i) q^{81} +(-37.1486 - 37.1486i) q^{82} +(6.60880 - 75.5389i) q^{83} +(-0.943999 - 14.6461i) q^{84} +(36.4422 + 73.4094i) q^{85} +(-187.979 + 68.4189i) q^{86} +(-17.5881 - 0.402863i) q^{87} +(44.8865 + 31.4299i) q^{88} +(-63.7232 + 36.7906i) q^{89} +(136.676 - 33.5117i) q^{90} +(1.17760 - 2.03966i) q^{91} +(-46.1195 - 98.9035i) q^{92} +(85.0620 + 106.221i) q^{93} +(51.3023 - 61.1397i) q^{94} +(87.7534 + 99.5336i) q^{95} +(110.256 - 48.3712i) q^{96} +(22.8447 + 48.9905i) q^{97} +(39.0797 + 145.848i) q^{98} +(19.3696 - 86.4822i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 408 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 12 q^{7} - 6 q^{8} - 6 q^{10} - 60 q^{11} - 12 q^{12} - 12 q^{13} - 12 q^{15} - 24 q^{16} - 6 q^{17} - 54 q^{18} - 300 q^{20} - 24 q^{21} - 12 q^{22} - 156 q^{23}+ \cdots - 1032 q^{98}+O(q^{100}) \) 408 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 12 * q^7 - 6 * q^8 - 6 * q^10 - 60 * q^11 - 12 * q^12 - 12 * q^13 - 12 * q^15 - 24 * q^16 - 6 * q^17 - 54 * q^18 - 300 * q^20 - 24 * q^21 - 12 * q^22 - 156 * q^23 + 6 * q^25 - 48 * q^26 + 180 * q^27 - 24 * q^28 + 276 * q^30 - 24 * q^31 + 72 * q^32 - 78 * q^33 + 156 * q^35 - 312 * q^36 - 6 * q^37 - 252 * q^38 - 108 * q^40 - 384 * q^41 - 528 * q^42 - 12 * q^43 + 18 * q^45 - 12 * q^46 - 210 * q^47 + 444 * q^48 + 276 * q^50 - 144 * q^51 - 60 * q^52 + 516 * q^53 - 24 * q^55 + 912 * q^56 + 168 * q^57 - 12 * q^58 + 864 * q^60 - 312 * q^61 - 6 * q^62 - 54 * q^63 + 420 * q^65 + 1224 * q^66 - 480 * q^67 - 540 * q^68 - 12 * q^70 - 12 * q^71 - 1548 * q^72 - 6 * q^73 - 852 * q^75 - 216 * q^76 - 876 * q^77 - 1362 * q^78 - 1644 * q^80 - 204 * q^81 - 24 * q^82 - 372 * q^83 - 12 * q^85 + 516 * q^86 + 540 * q^87 + 348 * q^88 - 384 * q^90 - 12 * q^91 + 2082 * q^92 - 1404 * q^93 + 198 * q^95 + 924 * q^96 + 600 * q^97 - 1032 * q^98

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