LMFDB - Embedded newform 108.3.j.a.103.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [108,3,Mod(7,108)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(108, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 16])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("108.7"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	108.j (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$2.94278685509$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$34$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			103.4
Character	$\chi$	$=$	108.103
Dual form			108.3.j.a.43.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.93570 + 0.503058i) q^{2} +(-2.40989 + 1.78674i) q^{3} +(3.49386 - 1.94754i) q^{4} +(3.67109 - 1.33617i) q^{5} +(3.76598 - 4.67091i) q^{6} +(2.42790 - 0.428104i) q^{7} +(-5.78335 + 5.52747i) q^{8} +(2.61510 - 8.61169i) q^{9} +(-6.43396 + 4.43320i) q^{10} +(-6.11759 + 16.8080i) q^{11} +(-4.94006 + 10.9360i) q^{12} +(15.7646 + 13.2281i) q^{13} +(-4.48432 + 2.05006i) q^{14} +(-6.45953 + 9.77932i) q^{15} +(8.41418 - 13.6089i) q^{16} +(-11.4681 + 19.8634i) q^{17} +(-0.729856 + 17.9852i) q^{18} +(6.65039 - 3.83960i) q^{19} +(10.2241 - 11.8180i) q^{20} +(-5.08605 + 5.36972i) q^{21} +(3.38644 - 35.6127i) q^{22} +(1.94638 + 0.343200i) q^{23} +(4.06103 - 23.6539i) q^{24} +(-7.45952 + 6.25928i) q^{25} +(-37.1701 - 17.6751i) q^{26} +(9.08480 + 25.4257i) q^{27} +(7.64900 - 6.22417i) q^{28} +(33.6153 - 28.2066i) q^{29} +(7.58413 - 22.1793i) q^{30} +(20.3189 + 3.58277i) q^{31} +(-9.44126 + 30.5755i) q^{32} +(-15.2888 - 51.4358i) q^{33} +(12.2064 - 44.2187i) q^{34} +(8.34103 - 4.81570i) q^{35} +(-7.63482 - 35.1811i) q^{36} +(-15.3854 + 26.6483i) q^{37} +(-10.9416 + 10.7778i) q^{38} +(-61.6262 - 3.71085i) q^{39} +(-13.8456 + 28.0194i) q^{40} +(-4.57109 - 3.83560i) q^{41} +(7.14378 - 12.9527i) q^{42} +(10.9148 - 29.9881i) q^{43} +(11.3601 + 70.6390i) q^{44} +(-1.90641 - 35.1086i) q^{45} +(-3.94026 + 0.314813i) q^{46} +(53.8769 - 9.49995i) q^{47} +(4.03837 + 47.8298i) q^{48} +(-40.3335 + 14.6802i) q^{49} +(11.2906 - 15.8687i) q^{50} +(-7.85390 - 68.3592i) q^{51} +(80.8418 + 15.5149i) q^{52} +19.4599 q^{53} +(-30.3761 - 44.6463i) q^{54} +69.8777i q^{55} +(-11.6751 + 15.8960i) q^{56} +(-9.16629 + 21.1355i) q^{57} +(-50.8796 + 71.5100i) q^{58} +(-19.2036 - 52.7614i) q^{59} +(-3.52310 + 46.7478i) q^{60} +(-2.78225 - 15.7789i) q^{61} +(-41.1336 + 3.28642i) q^{62} +(2.66249 - 22.0279i) q^{63} +(2.89417 - 63.9345i) q^{64} +(75.5485 + 27.4974i) q^{65} +(55.4697 + 91.8731i) q^{66} +(1.41276 - 1.68366i) q^{67} +(-1.38337 + 91.7347i) q^{68} +(-5.30377 + 2.65062i) q^{69} +(-13.7232 + 13.5178i) q^{70} +(-86.0838 - 49.7005i) q^{71} +(32.4769 + 64.2593i) q^{72} +(31.8044 + 55.0868i) q^{73} +(16.3759 - 59.3229i) q^{74} +(6.79286 - 28.4124i) q^{75} +(15.7578 - 26.3669i) q^{76} +(-7.65735 + 43.4270i) q^{77} +(121.157 - 23.8185i) q^{78} +(-12.9960 - 15.4880i) q^{79} +(12.7055 - 61.2023i) q^{80} +(-67.3225 - 45.0408i) q^{81} +(10.7778 + 5.12504i) q^{82} +(33.4876 + 39.9089i) q^{83} +(-7.31223 + 28.6663i) q^{84} +(-15.5598 + 88.2438i) q^{85} +(-6.04197 + 63.5388i) q^{86} +(-30.6111 + 128.037i) q^{87} +(-57.5253 - 131.021i) q^{88} +(-8.30808 - 14.3900i) q^{89} +(21.3519 + 67.0006i) q^{90} +(43.9380 + 25.3676i) q^{91} +(7.46880 - 2.59157i) q^{92} +(-55.3677 + 27.6706i) q^{93} +(-99.5105 + 45.4923i) q^{94} +(19.2838 - 22.9816i) q^{95} +(-31.8783 - 90.5526i) q^{96} +(-120.060 - 43.6982i) q^{97} +(70.6886 - 48.7066i) q^{98} +(128.747 + 96.6373i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q - 6 q^{2} - 6 q^{4} - 12 q^{5} - 6 q^{6} - 3 q^{8} - 12 q^{9} - 3 q^{10} + 39 q^{12} - 12 q^{13} + 39 q^{14} - 6 q^{16} - 6 q^{17} - 27 q^{18} - 69 q^{20} - 12 q^{21} - 6 q^{22} - 138 q^{24} - 12 q^{25}+ \cdots + 510 q^{98}+O(q^{100}) $ 204 * q - 6 * q^2 - 6 * q^4 - 12 * q^5 - 6 * q^6 - 3 * q^8 - 12 * q^9 - 3 * q^10 + 39 * q^12 - 12 * q^13 + 39 * q^14 - 6 * q^16 - 6 * q^17 - 27 * q^18 - 69 * q^20 - 12 * q^21 - 6 * q^22 - 138 * q^24 - 12 * q^25 - 174 * q^26 - 12 * q^28 + 60 * q^29 - 153 * q^30 - 96 * q^32 + 48 * q^33 + 6 * q^34 + 24 * q^36 - 6 * q^37 + 72 * q^38 + 69 * q^40 - 192 * q^41 - 126 * q^42 - 219 * q^44 - 132 * q^45 - 3 * q^46 - 219 * q^48 - 12 * q^49 - 165 * q^50 + 21 * q^52 - 24 * q^53 + 78 * q^54 + 99 * q^56 - 150 * q^57 - 141 * q^58 + 210 * q^60 - 12 * q^61 + 294 * q^62 - 3 * q^64 - 156 * q^65 + 393 * q^66 + 375 * q^68 - 60 * q^69 - 165 * q^70 + 228 * q^72 - 6 * q^73 + 447 * q^74 - 54 * q^76 + 132 * q^77 + 750 * q^78 + 798 * q^80 + 228 * q^81 - 12 * q^82 + 762 * q^84 + 138 * q^85 + 606 * q^86 - 198 * q^88 - 114 * q^89 + 894 * q^90 + 723 * q^92 - 1020 * q^93 - 357 * q^94 + 474 * q^96 + 168 * q^97 + 510 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.93570	+	0.503058i	−0.967850	+	0.251529i
$2$	−1.93570	+	0.503058i	−0.967850	+	0.251529i
$3$	−2.40989	+	1.78674i	−0.803295	+	0.595581i
$3$	−2.40989	+	1.78674i	−0.803295	+	0.595581i
$4$	3.49386	−	1.94754i	0.873466	−	0.486885i
$5$	3.67109	−	1.33617i	0.734219	−	0.267234i	0.0522694	−	0.998633i	$-0.483355\pi$
$5$	3.67109	−	1.33617i	0.734219	−	0.267234i	0.681950	+	0.731399i	$0.261132\pi$
$6$	3.76598	−	4.67091i	0.627663	−	0.778485i
$7$	2.42790	−	0.428104i	0.346843	−	0.0611577i	0.00248686	−	0.999997i	$-0.499208\pi$
$7$	2.42790	−	0.428104i	0.346843	−	0.0611577i	0.344356	+	0.938839i	$0.388097\pi$
$8$	−5.78335	+	5.52747i	−0.722918	+	0.690934i
$9$	2.61510	−	8.61169i	0.290566	−	0.956855i
$10$	−6.43396	+	4.43320i	−0.643396	+	0.443320i
$11$	−6.11759	+	16.8080i	−0.556145	+	1.52800i	0.269038	+	0.963130i	$0.413294\pi$
$11$	−6.11759	+	16.8080i	−0.556145	+	1.52800i	−0.825183	+	0.564866i	$0.808928\pi$
$12$	−4.94006	+	10.9360i	−0.411672	+	0.911332i
$13$	15.7646	+	13.2281i	1.21266	+	1.01755i	0.999175	+	0.0406014i	$0.0129274\pi$
$13$	15.7646	+	13.2281i	1.21266	+	1.01755i	0.213490	+	0.976945i	$0.431517\pi$
$14$	−4.48432	+	2.05006i	−0.320309	+	0.146433i
$15$	−6.45953	+	9.77932i	−0.430635	+	0.651955i
$16$	8.41418	−	13.6089i	0.525886	−	0.850555i
$17$	−11.4681	+	19.8634i	−0.674597	+	1.16844i	0.301990	+	0.953311i	$0.402349\pi$
$17$	−11.4681	+	19.8634i	−0.674597	+	1.16844i	−0.976587	+	0.215125i	$0.930984\pi$
$18$	−0.729856	+	17.9852i	−0.0405476	+	0.999178i
$19$	6.65039	−	3.83960i	0.350020	−	0.202084i	−0.314674	−	0.949200i	$-0.601895\pi$
$19$	6.65039	−	3.83960i	0.350020	−	0.202084i	0.664694	+	0.747116i	$0.268562\pi$
$20$	10.2241	−	11.8180i	0.511203	−	0.590900i
$21$	−5.08605	+	5.36972i	−0.242193	+	0.255701i
$22$	3.38644	−	35.6127i	0.153929	−	1.61876i
$23$	1.94638	+	0.343200i	0.0846254	+	0.0149217i	0.215801	−	0.976437i	$-0.430764\pi$
$23$	1.94638	+	0.343200i	0.0846254	+	0.0149217i	−0.131175	+	0.991359i	$0.541875\pi$
$24$	4.06103	−	23.6539i	0.169210	−	0.985580i
$25$	−7.45952	+	6.25928i	−0.298381	+	0.250371i
$26$	−37.1701	−	17.6751i	−1.42962	−	0.679812i
$27$	9.08480	+	25.4257i	0.336474	+	0.941693i
$28$	7.64900	−	6.22417i	0.273179	−	0.222292i
$29$	33.6153	−	28.2066i	1.15915	−	0.972641i	0.159255	−	0.987237i	$-0.449091\pi$
$29$	33.6153	−	28.2066i	1.15915	−	0.972641i	0.999893	+	0.0145960i	$0.00464622\pi$
$30$	7.58413	−	22.1793i	0.252804	−	0.739311i
$31$	20.3189	+	3.58277i	0.655448	+	0.115573i	0.491475	−	0.870892i	$-0.336458\pi$
$31$	20.3189	+	3.58277i	0.655448	+	0.115573i	0.163973	+	0.986465i	$0.447569\pi$
$32$	−9.44126	+	30.5755i	−0.295039	+	0.955485i
$33$	−15.2888	−	51.4358i	−0.463297	−	1.55866i
$34$	12.2064	−	44.2187i	0.359012	−	1.30055i
$35$	8.34103	−	4.81570i	0.238315	−	0.137591i
$36$	−7.63482	−	35.1811i	−0.212078	−	0.977253i
$37$	−15.3854	+	26.6483i	−0.415822	+	0.720225i	−0.995514	−	0.0946106i	$-0.969839\pi$
$37$	−15.3854	+	26.6483i	−0.415822	+	0.720225i	0.579692	+	0.814835i	$0.303173\pi$
$38$	−10.9416	+	10.7778i	−0.287937	+	0.283628i
$39$	−61.6262	−	3.71085i	−1.58016	−	0.0951500i
$40$	−13.8456	+	28.0194i	−0.346139	+	0.700485i
$41$	−4.57109	−	3.83560i	−0.111490	−	0.0935512i	0.585338	−	0.810789i	$-0.300962\pi$
$41$	−4.57109	−	3.83560i	−0.111490	−	0.0935512i	−0.696828	+	0.717238i	$0.745406\pi$
$42$	7.14378	−	12.9527i	0.170090	−	0.308398i
$43$	10.9148	−	29.9881i	0.253832	−	0.697399i	−0.745684	−	0.666300i	$-0.767877\pi$
$43$	10.9148	−	29.9881i	0.253832	−	0.697399i	0.999516	−	0.0310988i	$-0.00990066\pi$
$44$	11.3601	+	70.6390i	0.258184	+	1.60543i
$45$	−1.90641	−	35.1086i	−0.0423647	−	0.780190i
$46$	−3.94026	+	0.314813i	−0.0856579	+	0.00684375i
$47$	53.8769	−	9.49995i	1.14632	−	0.202127i	0.431950	−	0.901898i	$-0.357826\pi$
$47$	53.8769	−	9.49995i	1.14632	−	0.202127i	0.714367	+	0.699771i	$0.246715\pi$
$48$	4.03837	+	47.8298i	0.0841326	+	0.996455i
$49$	−40.3335	+	14.6802i	−0.823133	+	0.299596i
$50$	11.2906	−	15.8687i	0.225812	−	0.317373i
$51$	−7.85390	−	68.3592i	−0.153998	−	1.34038i
$52$	80.8418	+	15.5149i	1.55465	+	0.298364i
$53$	19.4599			0.367168			0.183584	−	0.983004i	$-0.441230\pi$
$53$	19.4599			0.367168			0.183584	+	0.983004i	$0.441230\pi$
$54$	−30.3761	−	44.6463i	−0.562520	−	0.826784i
$55$			69.8777i			1.27050i
$56$	−11.6751	+	15.8960i	−0.208483	+	0.283857i
$57$	−9.16629	+	21.1355i	−0.160812	+	0.370799i
$58$	−50.8796	+	71.5100i	−0.877234	+	1.23293i
$59$	−19.2036	−	52.7614i	−0.325484	−	0.894261i	−0.989239	−	0.146310i	$-0.953260\pi$
$59$	−19.2036	−	52.7614i	−0.325484	−	0.894261i	0.663754	−	0.747951i	$-0.268962\pi$
$60$	−3.52310	+	46.7478i	−0.0587183	+	0.779130i
$61$	−2.78225	−	15.7789i	−0.0456107	−	0.258671i	0.953473	−	0.301480i	$-0.0974806\pi$
$61$	−2.78225	−	15.7789i	−0.0456107	−	0.258671i	−0.999083	+	0.0428085i	$0.986369\pi$
$62$	−41.1336	+	3.28642i	−0.663445	+	0.0530068i
$63$	2.66249	−	22.0279i	0.0422617	−	0.349649i
$64$	2.89417	−	63.9345i	0.0452214	−	0.998977i
$65$	75.5485	+	27.4974i	1.16228	+	0.423037i
$66$	55.4697	+	91.8731i	0.840450	+	1.39202i
$67$	1.41276	−	1.68366i	0.0210859	−	0.0251292i	−0.755398	−	0.655266i	$-0.772557\pi$
$67$	1.41276	−	1.68366i	0.0210859	−	0.0251292i	0.776484	+	0.630137i	$0.217001\pi$
$68$	−1.38337	+	91.7347i	−0.0203436	+	1.34904i
$69$	−5.30377	+	2.65062i	−0.0768663	+	0.0384147i
$70$	−13.7232	+	13.5178i	−0.196045	+	0.193111i
$71$	−86.0838	−	49.7005i	−1.21245	−	0.700007i	−0.249156	−	0.968463i	$-0.580153\pi$
$71$	−86.0838	−	49.7005i	−1.21245	−	0.700007i	−0.963292	+	0.268456i	$0.913487\pi$
$72$	32.4769	+	64.2593i	0.451068	+	0.892490i
$73$	31.8044	+	55.0868i	0.435676	+	0.754614i	0.997351	−	0.0727449i	$-0.0231759\pi$
$73$	31.8044	+	55.0868i	0.435676	+	0.754614i	−0.561674	+	0.827358i	$0.689843\pi$
$74$	16.3759	−	59.3229i	0.221296	−	0.801661i
$75$	6.79286	−	28.4124i	0.0905715	−	0.378832i
$76$	15.7578	−	26.3669i	0.207339	−	0.346933i
$77$	−7.65735	+	43.4270i	−0.0994461	+	0.563987i
$78$	121.157	−	23.8185i	1.55329	−	0.305365i
$79$	−12.9960	−	15.4880i	−0.164506	−	0.196051i	0.677494	−	0.735529i	$-0.263066\pi$
$79$	−12.9960	−	15.4880i	−0.164506	−	0.196051i	−0.842000	+	0.539478i	$0.818622\pi$
$80$	12.7055	−	61.2023i	0.158819	−	0.765028i
$81$	−67.3225	−	45.0408i	−0.831142	−	0.556060i
$82$	10.7778	+	5.12504i	0.131436	+	0.0625005i
$83$	33.4876	+	39.9089i	0.403465	+	0.480830i	0.929073	−	0.369896i	$-0.120607\pi$
$83$	33.4876	+	39.9089i	0.403465	+	0.480830i	−0.525608	+	0.850727i	$0.676162\pi$
$84$	−7.31223	+	28.6663i	−0.0870503	+	0.341266i
$85$	−15.5598	+	88.2438i	−0.183056	+	1.03816i
$86$	−6.04197	+	63.5388i	−0.0702554	+	0.738823i
$87$	−30.6111	+	128.037i	−0.351852	+	1.47169i
$88$	−57.5253	−	131.021i	−0.653696	−	1.48888i
$89$	−8.30808	−	14.3900i	−0.0933492	−	0.161686i	0.815569	−	0.578659i	$-0.196424\pi$
$89$	−8.30808	−	14.3900i	−0.0933492	−	0.161686i	−0.908918	+	0.416974i	$0.863091\pi$
$90$	21.3519	+	67.0006i	0.237243	+	0.744451i
$91$	43.9380	+	25.3676i	0.482835	+	0.278765i
$92$	7.46880	−	2.59157i	0.0811826	−	0.0281692i
$93$	−55.3677	+	27.6706i	−0.595351	+	0.297533i
$94$	−99.5105	+	45.4923i	−1.05862	+	0.483960i
$95$	19.2838	−	22.9816i	0.202988	−	0.241911i
$96$	−31.8783	−	90.5526i	−0.332065	−	0.943256i
$97$	−120.060	−	43.6982i	−1.23773	−	0.450497i	−0.361492	−	0.932375i	$-0.617733\pi$
$97$	−120.060	−	43.6982i	−1.23773	−	0.450497i	−0.876238	+	0.481878i	$0.839955\pi$
$98$	70.6886	−	48.7066i	0.721312	−	0.497006i
$99$	128.747	+	96.6373i	1.30047	+	0.976134i
$100$	−13.8724	+	36.3968i	−0.138724	+	0.363968i
$101$	−19.5922	−	111.113i	−0.193982	−	1.10013i	−0.913861	−	0.406027i	$-0.866914\pi$
$101$	−19.5922	−	111.113i	−0.193982	−	1.10013i	0.719879	−	0.694100i	$-0.244197\pi$
$102$	49.5914	+	128.372i	0.486191	+	1.25855i
$103$	−47.3891	−	130.200i	−0.460088	−	1.26408i	−0.925419	−	0.378945i	$-0.876287\pi$
$103$	−47.3891	−	130.200i	−0.460088	−	1.26408i	0.465331	−	0.885137i	$-0.345935\pi$
$104$	−164.290	+	10.6359i	−1.57971	+	0.102268i
$105$	−11.4965	+	26.5086i	−0.109491	+	0.252462i
$106$	−37.6685	+	9.78947i	−0.355364	+	0.0923535i
$107$		−	151.616i		−	1.41697i	−0.705724	−	0.708487i	$-0.749378\pi$
$107$		−	151.616i		−	1.41697i	0.705724	−	0.708487i	$-0.250622\pi$
$108$	81.2586	+	71.1409i	0.752395	+	0.658712i
$109$	128.248			1.17659			0.588295	−	0.808646i	$-0.299799\pi$
$109$	128.248			1.17659			0.588295	+	0.808646i	$0.299799\pi$
$110$	−35.1526	−	135.262i	−0.319569	−	1.22966i
$111$	−10.5366	−	91.7092i	−0.0949245	−	0.826209i
$112$	14.6028	−	36.6431i	0.130382	−	0.327171i
$113$	135.610	−	49.3580i	1.20009	−	0.436797i	0.336833	−	0.941564i	$-0.390644\pi$
$113$	135.610	−	49.3580i	1.20009	−	0.436797i	0.863255	+	0.504768i	$0.168422\pi$
$114$	7.11077	−	45.5232i	0.0623751	−	0.399326i
$115$	7.60393	−	1.34078i	0.0661212	−	0.0116589i
$116$	62.5139	−	164.017i	0.538913	−	1.41394i
$117$	155.142	−	101.168i	1.32600	−	0.864680i
$118$	63.7144	+	92.4697i	0.539953	+	0.783641i
$119$	−19.3399	+	53.1359i	−0.162520	+	0.446520i
$120$	−16.6972	−	92.2620i	−0.139143	−	0.768850i
$121$	−152.391	−	127.871i	−1.25943	−	1.05679i
$122$	13.3233	+	29.1437i	0.109208	+	0.238882i
$123$	17.8690	+	1.07599i	0.145277	+	0.00874791i
$124$	77.9690	−	27.0541i	0.628782	−	0.218178i
$125$	−67.8549	+	117.528i	−0.542839	+	0.940225i
$126$	5.92752	+	43.9787i	0.0470438	+	0.349037i
$127$	−186.595	+	107.731i	−1.46925	+	0.848273i	−0.999406	−	0.0344751i	$-0.989024\pi$
$127$	−186.595	+	107.731i	−1.46925	+	0.848273i	−0.469847	+	0.882748i	$0.655691\pi$
$128$	26.5606	+	125.214i	0.207504	+	0.978234i
$129$	27.2777	+	91.7699i	0.211455	+	0.711395i
$130$	−160.072	−	15.2214i	−1.23132	−	0.117088i
$131$	37.7245	+	6.65185i	0.287974	+	0.0507775i	0.315769	−	0.948836i	$-0.397738\pi$
$131$	37.7245	+	6.65185i	0.287974	+	0.0507775i	−0.0277954	+	0.999614i	$0.508849\pi$
$132$	−153.590	−	149.934i	−1.16356	−	1.13587i
$133$	14.5027	−	12.1692i	0.109043	−	0.0914980i
$134$	−1.88769	+	3.96975i	−0.0140873	+	0.0296250i
$135$	67.3242	+	81.2013i	0.498698	+	0.601491i
$136$	−43.4701	−	178.267i	−0.319633	−	1.31078i
$137$	43.0492	−	36.1225i	0.314227	−	0.263668i	−0.472009	−	0.881594i	$-0.656471\pi$
$137$	43.0492	−	36.1225i	0.314227	−	0.263668i	0.786237	+	0.617925i	$0.212027\pi$
$138$	8.93310	−	7.79890i	0.0647326	−	0.0565138i
$139$	233.131	+	41.1073i	1.67720	+	0.295736i	0.929643	−	0.368461i	$-0.120115\pi$
$139$	233.131	+	41.1073i	1.67720	+	0.295736i	0.747558	+	0.664196i	$0.231226\pi$
$140$	19.7637	−	33.0699i	0.141169	−	0.236213i
$141$	−112.863	+	119.158i	−0.800448	+	0.845092i
$142$	191.635	+	52.9001i	1.34954	+	0.372536i
$143$	−318.779	+	184.047i	−2.22922	+	1.28704i
$144$	−95.1916	−	108.049i	−0.661053	−	0.750339i
$145$	85.7162	−	148.465i	0.591146	−	1.02390i
$146$	−89.2756	−	90.6320i	−0.611477	−	0.620767i
$147$	70.9694	−	107.443i	0.482785	−	0.730906i
$148$	−1.85590	+	123.069i	−0.0125398	+	0.831550i
$149$	−25.6459	−	21.5194i	−0.172120	−	0.144426i	0.552659	−	0.833408i	$-0.313613\pi$
$149$	−25.6459	−	21.5194i	−0.172120	−	0.144426i	−0.724778	+	0.688982i	$0.758058\pi$
$150$	1.14416	+	58.4151i	0.00762771	+	0.389434i
$151$	−12.5948	+	34.6040i	−0.0834093	+	0.229165i	−0.974385	−	0.224885i	$-0.927799\pi$
$151$	−12.5948	+	34.6040i	−0.0834093	+	0.229165i	0.890976	+	0.454051i	$0.150021\pi$
$152$	−17.2382	+	58.9656i	−0.113409	+	0.387931i
$153$	141.067	+	150.705i	0.922008	+	0.984999i
$154$	−7.02398	−	87.9137i	−0.0456103	−	0.570868i
$155$	79.3797	−	13.9968i	0.512127	−	0.0903018i
$156$	−222.541	+	107.054i	−1.42654	+	0.686246i
$157$	81.9630	−	29.8321i	0.522057	−	0.190013i	−0.0675312	−	0.997717i	$-0.521512\pi$
$157$	81.9630	−	29.8321i	0.522057	−	0.190013i	0.589588	+	0.807704i	$0.299290\pi$
$158$	32.9477	+	23.4424i	0.208530	+	0.148370i
$159$	−46.8962	+	34.7699i	−0.294944	+	0.218678i
$160$	6.19431	+	124.861i	0.0387145	+	0.780380i
$161$	4.87255			0.0302643
$162$	152.974	+	53.3183i	0.944286	+	0.329125i
$163$			265.936i			1.63151i	0.578398	+	0.815755i	$0.303678\pi$
$163$			265.936i			1.63151i	−0.578398	+	0.815755i	$0.696322\pi$
$164$	−23.4408	−	4.49869i	−0.142931	−	0.0274310i
$165$	−124.854	−	168.397i	−0.756688	−	1.02059i
$166$	−84.8984	−	60.4055i	−0.511436	−	0.363888i
$167$	−5.34309	−	14.6800i	−0.0319945	−	0.0879042i	0.922667	−	0.385598i	$-0.126005\pi$
$167$	−5.34309	−	14.6800i	−0.0319945	−	0.0879042i	−0.954661	+	0.297694i	$0.903783\pi$
$168$	−0.266566	−	59.1679i	−0.00158670	−	0.352190i
$169$	44.1947	+	250.640i	0.261507	+	1.48308i
$170$	−14.2728	−	178.641i	−0.0839574	−	1.05083i
$171$	−15.6741	−	67.3120i	−0.0916613	−	0.393638i
$172$	−20.2683	−	126.031i	−0.117839	−	0.732741i
$173$	−179.041	−	65.1656i	−1.03492	−	0.376680i	−0.231967	−	0.972724i	$-0.574516\pi$
$173$	−179.041	−	65.1656i	−1.03492	−	0.376680i	−0.802952	+	0.596044i	$0.796738\pi$
$174$	−5.15598	−	263.240i	−0.0296321	−	1.51287i
$175$	−15.4313	+	18.3904i	−0.0881791	+	0.105088i
$176$	177.263	+	224.679i	1.00718	+	1.27658i
$177$	140.549	+	92.8370i	0.794065	+	0.524503i
$178$	23.3210	+	23.6753i	0.131017	+	0.133007i
$179$	235.124	+	135.749i	1.31354	+	0.758374i	0.982681	−	0.185305i	$-0.0593272\pi$
$179$	235.124	+	135.749i	1.31354	+	0.758374i	0.330862	+	0.943679i	$0.392661\pi$
$180$	−75.0361	−	118.952i	−0.416867	−	0.660843i
$181$	6.50826	+	11.2726i	0.0359573	+	0.0622798i	0.883444	−	0.468537i	$-0.155219\pi$
$181$	6.50826	+	11.2726i	0.0359573	+	0.0622798i	−0.847487	+	0.530817i	$0.821885\pi$
$182$	−97.8121	−	27.0007i	−0.537429	−	0.148355i
$183$	34.8978	+	33.0543i	0.190699	+	0.180624i
$184$	−13.1536	+	8.77373i	−0.0714872	+	0.0476833i
$185$	−20.8747	+	118.386i	−0.112836	+	0.639924i
$186$	93.2552	−	81.4151i	0.501372	−	0.437715i
$187$	−263.706	−	314.272i	−1.41019	−	1.68060i
$188$	169.737	−	138.119i	0.902857	−	0.734675i
$189$	32.9418	+	57.8418i	0.174295	+	0.306041i
$190$	−25.7666	+	54.1863i	−0.135614	+	0.285191i
$191$	189.368	+	225.680i	0.991457	+	1.18157i	0.983372	+	0.181605i	$0.0581292\pi$
$191$	189.368	+	225.680i	0.991457	+	1.18157i	0.00808536	+	0.999967i	$0.497426\pi$
$192$	107.260	+	159.246i	0.558646	+	0.829406i
$193$	44.6187	−	253.045i	0.231185	−	1.31112i	−0.619316	−	0.785142i	$-0.712590\pi$
$193$	44.6187	−	253.045i	0.231185	−	1.31112i	0.850501	−	0.525974i	$-0.176299\pi$
$194$	254.382	+	24.1895i	1.31125	+	0.124688i
$195$	−231.194	+	68.7202i	−1.18561	+	0.352411i
$196$	−112.330	+	129.842i	−0.573110	+	0.662458i
$197$	−42.7613	−	74.0647i	−0.217062	−	0.375963i	0.736846	−	0.676060i	$-0.236314\pi$
$197$	−42.7613	−	74.0647i	−0.217062	−	0.375963i	−0.953909	+	0.300097i	$0.902981\pi$
$198$	−297.829	−	122.294i	−1.50419	−	0.617644i
$199$	15.8969	+	9.17807i	0.0798839	+	0.0461210i	0.539410	−	0.842043i	$-0.318647\pi$
$199$	15.8969	+	9.17807i	0.0798839	+	0.0461210i	−0.459526	+	0.888164i	$0.651981\pi$
$200$	8.54300	−	77.4319i	0.0427150	−	0.387159i
$201$	−0.396317	+	6.58165i	−0.00197173	+	0.0327446i
$202$	93.8208	+	205.225i	0.464460	+	1.01597i
$203$	69.5393	−	82.8737i	0.342558	−	0.408245i
$204$	−160.573	−	223.542i	−0.787121	−	1.09579i
$205$	−21.9059	−	7.97310i	−0.106858	−	0.0388932i
$206$	157.229	+	228.189i	0.763250	+	1.10772i
$207$	8.04552	−	15.8642i	0.0388672	−	0.0766385i
$208$	312.666	−	103.235i	1.50320	−	0.496324i
$209$	23.8515	+	135.269i	0.114122	+	0.647218i
$210$	8.91845	−	57.0960i	0.0424688	−	0.271886i
$211$	−61.6793	−	169.463i	−0.292319	−	0.803140i	−0.995726	−	0.0923529i	$-0.970561\pi$
$211$	−61.6793	−	169.463i	−0.292319	−	0.803140i	0.703407	−	0.710787i	$-0.251661\pi$
$212$	67.9903	−	37.8990i	0.320709	−	0.178769i
$213$	296.254	−	34.0371i	1.39086	−	0.159799i
$214$	76.2718	+	293.483i	0.356410	+	1.37142i
$215$		−	124.673i		−	0.579876i
$216$	−193.080	−	96.8297i	−0.893890	−	0.448285i
$217$	50.8660			0.234406
$218$	−248.250	+	64.5164i	−1.13876	+	0.295947i
$219$	−175.071	−	75.9266i	−0.799410	−	0.346697i
$220$	136.090	+	244.143i	0.618589	+	1.10974i
$221$	−443.546	+	161.438i	−2.00700	+	0.730487i
$222$	66.5308	+	172.221i	0.299688	+	0.775770i
$223$	−51.7471	+	9.12442i	−0.232050	+	0.0409167i	−0.288464	−	0.957491i	$-0.593144\pi$
$223$	−51.7471	+	9.12442i	−0.232050	+	0.0409167i	0.0564138	+	0.998407i	$0.482033\pi$
$224$	−9.83292	+	78.2762i	−0.0438970	+	0.349447i
$225$	34.3957	+	80.6078i	0.152870	+	0.358257i
$226$	−237.670	+	163.762i	−1.05164	+	0.724611i
$227$	−27.9881	+	76.8966i	−0.123295	+	0.338752i	−0.985950	−	0.167043i	$-0.946578\pi$
$227$	−27.9881	+	76.8966i	−0.123295	+	0.338752i	0.862654	+	0.505794i	$0.168800\pi$
$228$	9.13653	+	91.6964i	0.0400725	+	0.402177i
$229$	18.8776	+	15.8402i	0.0824351	+	0.0691713i	0.683074	−	0.730349i	$-0.260643\pi$
$229$	18.8776	+	15.8402i	0.0824351	+	0.0691713i	−0.600639	+	0.799520i	$0.705087\pi$
$230$	−14.0444	+	6.42057i	−0.0610628	+	0.0279155i
$231$	−59.1396	−	118.336i	−0.256015	−	0.512276i
$232$	−38.4979	+	348.936i	−0.165939	+	1.50404i
$233$	−39.6338	+	68.6477i	−0.170102	+	0.294625i	−0.938455	−	0.345401i	$-0.887743\pi$
$233$	−39.6338	+	68.6477i	−0.170102	+	0.294625i	0.768353	+	0.640026i	$0.221076\pi$
$234$	−249.416	+	273.876i	−1.06588	+	1.17041i
$235$	185.094	−	106.864i	0.787633	−	0.454740i
$236$	−169.850	−	146.941i	−0.719702	−	0.622633i
$237$	58.9919	+	14.1038i	0.248911	+	0.0595099i
$238$	10.7058	−	112.584i	0.0449821	−	0.473043i
$239$	144.601	+	25.4971i	0.605027	+	0.106683i	0.467766	−	0.883852i	$-0.345059\pi$
$239$	144.601	+	25.4971i	0.605027	+	0.106683i	0.137261	+	0.990535i	$0.456170\pi$
$240$	78.7340	+	170.192i	0.328058	+	0.709133i
$241$	272.438	−	228.603i	1.13045	−	0.948559i	0.131364	−	0.991334i	$-0.458064\pi$
$241$	272.438	−	228.603i	1.13045	−	0.948559i	0.999085	+	0.0427750i	$0.0136199\pi$
$242$	359.310	+	170.859i	1.48475	+	0.706027i
$243$	242.716	−	11.7449i	0.998831	−	0.0483328i
$244$	−40.4509	−	49.7109i	−0.165783	−	0.203733i
$245$	−128.453	+	107.785i	−0.524298	+	0.439938i
$246$	−35.1304	+	6.90637i	−0.142806	+	0.0280747i
$247$	155.632	+	27.4421i	0.630088	+	0.111101i
$248$	−137.315	+	91.5916i	−0.553688	+	0.369321i
$249$	−152.008	−	36.3423i	−0.610475	−	0.145953i
$250$	72.2231	−	261.634i	0.288893	−	1.04654i
$251$	−206.394	+	119.161i	−0.822285	+	0.474747i	−0.851204	−	0.524835i	$-0.824127\pi$
$251$	−206.394	+	119.161i	−0.822285	+	0.474747i	0.0289186	+	0.999582i	$0.490794\pi$
$252$	−33.5978	−	82.1477i	−0.133324	−	0.325983i
$253$	−17.6757	+	30.6152i	−0.0698643	+	0.121009i
$254$	306.997	−	302.402i	1.20865	−	1.19056i
$255$	−120.172	−	240.459i	−0.471262	−	0.942976i
$256$	−114.403	−	229.015i	−0.446887	−	0.894590i
$257$	−278.987	−	234.098i	−1.08555	−	0.910887i	−0.0891830	−	0.996015i	$-0.528426\pi$
$257$	−278.987	−	234.098i	−1.08555	−	0.910887i	−0.996370	+	0.0851281i	$0.972870\pi$
$258$	−98.9671	−	163.917i	−0.383593	−	0.635336i
$259$	−25.9460	+	71.2860i	−0.100178	+	0.275236i
$260$	317.508	−	51.0615i	1.22119	−	0.196390i
$261$	−154.999	−	363.248i	−0.593867	−	1.39175i
$262$	−76.3696	+	6.10166i	−0.291487	+	0.0232888i
$263$	−320.879	+	56.5796i	−1.22007	+	0.215131i	−0.746356	−	0.665547i	$-0.768198\pi$
$263$	−320.879	+	56.5796i	−1.22007	+	0.215131i	−0.473715	+	0.880678i	$0.657087\pi$
$264$	372.730	+	212.963i	1.41186	+	0.806677i
$265$	71.4392	−	26.0017i	0.269582	−	0.0981198i
$266$	−21.9511	+	30.8517i	−0.0825228	+	0.115984i
$267$	45.7328	+	19.8339i	0.171284	+	0.0742842i
$268$	1.65699	−	8.63387i	0.00618280	−	0.0322159i
$269$	95.8215			0.356214			0.178107	−	0.984011i	$-0.443003\pi$
$269$	95.8215			0.356214			0.178107	+	0.984011i	$0.443003\pi$
$270$	−171.168	−	123.313i	−0.633957	−	0.456716i
$271$		−	494.220i		−	1.82369i	−0.410537	−	0.911844i	$-0.634659\pi$
$271$		−	494.220i		−	1.82369i	0.410537	−	0.911844i	$-0.365341\pi$
$272$	173.824	+	323.203i	0.639058	+	1.18825i
$273$	−151.211	+	17.3729i	−0.553886	+	0.0636369i
$274$	−65.1585	+	91.5786i	−0.237805	+	0.334229i
$275$	−59.5714	−	163.671i	−0.216623	−	0.595167i
$276$	−13.3685	+	19.5902i	−0.0484365	+	0.0709790i
$277$	48.7599	+	276.531i	0.176028	+	0.998307i	0.936950	+	0.349463i	$0.113636\pi$
$277$	48.7599	+	276.531i	0.176028	+	0.998307i	−0.760922	+	0.648844i	$0.775253\pi$
$278$	−471.951	+	37.7072i	−1.69767	+	0.135637i
$279$	83.9895	−	165.611i	0.301038	−	0.593587i
$280$	−21.6204	+	73.9556i	−0.0772159	+	0.264127i
$281$	106.961	+	38.9307i	0.380645	+	0.138543i	0.525254	−	0.850945i	$-0.323970\pi$
$281$	106.961	+	38.9307i	0.380645	+	0.138543i	−0.144609	+	0.989489i	$0.546192\pi$
$282$	158.526	−	287.431i	0.562148	−	1.01926i
$283$	198.767	−	236.881i	0.702356	−	0.837036i	−0.290435	−	0.956895i	$-0.593800\pi$
$283$	198.767	−	236.881i	0.702356	−	0.837036i	0.992791	+	0.119859i	$0.0382443\pi$
$284$	−397.559	−	5.99522i	−1.39986	−	0.0211099i
$285$	−5.40965	+	89.8383i	−0.0189812	+	0.315222i
$286$	524.474	−	516.625i	1.83383	−	1.80638i
$287$	−12.7402	−	7.35555i	−0.0443909	−	0.0256291i
$288$	238.617	+	161.263i	0.828532	+	0.559942i
$289$	−118.537	−	205.311i	−0.410161	−	0.710420i
$290$	−91.2344	+	330.504i	−0.314601	+	1.13967i
$291$	367.408	−	109.208i	1.26257	−	0.375287i
$292$	218.404	+	130.526i	0.747959	+	0.447005i
$293$	84.2825	−	477.990i	0.287654	−	1.63136i	−0.407996	−	0.912984i	$-0.633772\pi$
$293$	84.2825	−	477.990i	0.287654	−	1.63136i	0.695650	−	0.718381i	$-0.255116\pi$
$294$	−83.3252	+	243.680i	−0.283419	+	0.828842i
$295$	−140.996	−	168.033i	−0.477953	−	0.569603i
$296$	−58.3186	−	239.159i	−0.197022	−	0.807969i
$297$	−482.931	−	2.84721i	−1.62603	−	0.00958656i
$298$	60.4682	+	28.7538i	0.202913	+	0.0964892i
$299$	26.1442	+	31.1574i	0.0874387	+	0.104205i
$300$	−31.6009	−	112.498i	−0.105336	−	0.374995i
$301$	13.6620	−	77.4809i	0.0453886	−	0.257412i
$302$	6.97196	−	73.3188i	0.0230859	−	0.242777i
$303$	245.745	+	232.763i	0.811040	+	0.768195i
$304$	3.70485	−	122.811i	0.0121870	−	0.403985i
$305$	−31.2973	−	54.2084i	−0.102614	−	0.177733i
$306$	−348.877	−	220.754i	−1.14012	−	0.721419i
$307$	−70.4883	−	40.6964i	−0.229604	−	0.132562i	0.380786	−	0.924663i	$-0.375654\pi$
$307$	−70.4883	−	40.6964i	−0.229604	−	0.132562i	−0.610389	+	0.792102i	$0.708987\pi$
$308$	57.8220	+	166.641i	0.187734	+	0.541042i
$309$	346.837	+	229.096i	1.12245	+	0.741411i
$310$	−146.614	+	67.0262i	−0.472949	+	0.216214i
$311$	249.268	−	297.066i	0.801505	−	0.955196i	−0.198183	−	0.980165i	$-0.563504\pi$
$311$	249.268	−	297.066i	0.801505	−	0.955196i	0.999688	+	0.0249688i	$0.00794863\pi$
$312$	376.917	−	319.176i	1.20807	−	1.02300i
$313$	−479.995	−	174.704i	−1.53353	−	0.558160i	−0.569048	−	0.822304i	$-0.692688\pi$
$313$	−479.995	−	174.704i	−1.53353	−	0.558160i	−0.964483	+	0.264145i	$0.914910\pi$
$314$	−143.648	+	98.9781i	−0.457479	+	0.315217i
$315$	−19.6587	−	84.4239i	−0.0624086	−	0.268012i
$316$	−75.5697	−	28.8028i	−0.239145	−	0.0911481i
$317$	31.1223	+	176.503i	0.0981775	+	0.556792i	0.993727	+	0.111831i	$0.0356715\pi$
$317$	31.1223	+	176.503i	0.0981775	+	0.556792i	−0.895550	+	0.444961i	$0.853217\pi$
$318$	73.2856	−	90.8955i	0.230458	−	0.285835i
$319$	268.450	+	737.561i	0.841537	+	2.31210i
$320$	−74.8026	−	238.577i	−0.233758	−	0.745553i
$321$	270.899	+	365.378i	0.843923	+	1.13825i
$322$	−9.43179	+	2.45118i	−0.0292913	+	0.00761235i
$323$			176.132i			0.545302i
$324$	−322.935	−	26.2532i	−0.996712	−	0.0810285i
$325$	−200.395			−0.616601
$326$	−133.781	−	514.772i	−0.410372	−	1.57906i
$327$	−309.064	+	229.147i	−0.945149	+	0.700755i
$328$	47.6374	−	3.08396i	0.145236	−	0.00940232i
$329$	126.741	−	46.1299i	0.385230	−	0.140212i
$330$	326.393	+	263.158i	0.989069	+	0.797448i
$331$	−130.882	+	23.0781i	−0.395415	+	0.0697223i	−0.367820	−	0.929897i	$-0.619896\pi$
$331$	−130.882	+	23.0781i	−0.395415	+	0.0697223i	−0.0275947	+	0.999619i	$0.508785\pi$
$332$	194.725	+	74.2180i	0.586522	+	0.223548i
$333$	189.253	+	202.182i	0.568327	+	0.607154i
$334$	17.7275	+	25.7282i	0.0530764	+	0.0770305i
$335$	2.93671	−	8.06855i	0.00876630	−	0.0240852i
$336$	30.2809	+	114.397i	0.0901217	+	0.340468i
$337$	236.956	+	198.829i	0.703132	+	0.589998i	0.922663	−	0.385608i	$-0.126008\pi$
$337$	236.956	+	198.829i	0.703132	+	0.589998i	−0.219531	+	0.975606i	$0.570453\pi$
$338$	−211.634	−	462.932i	−0.626137	−	1.36962i
$339$	−238.615	+	361.247i	−0.703878	+	1.06563i
$340$	117.495	+	338.615i	0.345572	+	0.995927i
$341$	−184.522	+	319.601i	−0.541119	+	0.937246i
$342$	64.2022	+	122.411i	0.187726	+	0.357927i
$343$	−196.259	+	113.310i	−0.572184	+	0.330350i
$344$	102.635	+	233.763i	0.298356	+	0.679543i
$345$	−15.9290	+	16.8174i	−0.0461710	+	0.0487461i
$346$	379.352	+	36.0729i	1.09639	+	0.104257i
$347$	−182.964	−	32.2614i	−0.527273	−	0.0929724i	−0.0963261	−	0.995350i	$-0.530709\pi$
$347$	−182.964	−	32.2614i	−0.527273	−	0.0929724i	−0.430947	+	0.902377i	$0.641820\pi$
$348$	142.405	+	506.959i	0.409211	+	1.45678i
$349$	−53.3290	+	44.7483i	−0.152805	+	0.128219i	−0.715985	−	0.698115i	$-0.754022\pi$
$349$	−53.3290	+	44.7483i	−0.152805	+	0.128219i	0.563180	+	0.826334i	$0.309578\pi$
$350$	20.6190	−	43.3611i	0.0589115	−	0.123889i
$351$	−193.115	+	521.002i	−0.550186	+	1.48434i
$352$	−456.154	−	345.737i	−1.29589	−	0.982207i
$353$	245.397	−	205.912i	0.695175	−	0.583321i	−0.225221	−	0.974308i	$-0.572311\pi$
$353$	245.397	−	205.912i	0.695175	−	0.583321i	0.920396	+	0.390987i	$0.127866\pi$
$354$	−318.764	−	109.000i	−0.900463	−	0.307910i
$355$	−382.430	−	67.4328i	−1.07727	−	0.189951i
$356$	−57.0524	−	34.0964i	−0.160260	−	0.0957765i
$357$	−48.3333	−	162.607i	−0.135387	−	0.455482i
$358$	−523.419	−	144.488i	−1.46207	−	0.403598i
$359$	117.892	−	68.0648i	0.328389	−	0.189596i	−0.326736	−	0.945115i	$-0.605949\pi$
$359$	117.892	−	68.0648i	0.328389	−	0.189596i	0.655126	+	0.755520i	$0.272616\pi$
$360$	205.087	+	192.507i	0.569686	+	0.534742i
$361$	−151.015	+	261.565i	−0.418324	+	0.724558i
$362$	−18.2688	−	18.5464i	−0.0504664	−	0.0512332i
$363$	595.718	+	35.8714i	1.64110	+	0.0988193i
$364$	202.918	+	3.06002i	0.557466	+	0.00840664i
$365$	190.362	+	159.733i	0.521540	+	0.437624i
$366$	−84.1799	−	46.4275i	−0.230000	−	0.126851i
$367$	−109.598	+	301.117i	−0.298631	+	0.820482i	0.696098	+	0.717947i	$0.254918\pi$
$367$	−109.598	+	301.117i	−0.298631	+	0.820482i	−0.994729	+	0.102536i	$0.967304\pi$
$368$	21.0478	−	23.6004i	0.0571951	−	0.0641314i
$369$	−44.9849	+	29.3344i	−0.121910	+	0.0794969i
$370$	−19.1480	−	239.661i	−0.0517514	−	0.647732i
$371$	47.2467	−	8.33087i	0.127350	−	0.0224552i
$372$	−139.558	+	204.508i	−0.375155	+	0.549752i
$373$	122.229	−	44.4878i	0.327692	−	0.119270i	−0.172935	−	0.984933i	$-0.555325\pi$
$373$	122.229	−	44.4878i	0.327692	−	0.119270i	0.500627	+	0.865663i	$0.333103\pi$
$374$	668.552	+	475.677i	1.78757	+	1.27186i
$375$	−46.4700	−	404.468i	−0.123920	−	1.07858i
$376$	−259.078	+	352.744i	−0.689037	+	0.938150i
$377$	903.053			2.39537
$378$	−92.8633	−	95.3927i	−0.245670	−	0.252362i
$379$			555.420i			1.46549i	0.680504	+	0.732745i	$0.261761\pi$
$379$			555.420i			1.46549i	−0.680504	+	0.732745i	$0.738239\pi$
$380$	22.6176	−	117.851i	0.0595199	−	0.310133i
$381$	257.186	−	593.016i	0.675028	−	1.55647i
$382$	−480.090	−	341.586i	−1.25678	−	0.894204i
$383$	13.6389	+	37.4725i	0.0356106	+	0.0978393i	0.956224	−	0.292637i	$-0.0945327\pi$
$383$	13.6389	+	37.4725i	0.0356106	+	0.0978393i	−0.920613	+	0.390476i	$0.872310\pi$
$384$	−287.733	−	254.294i	−0.749305	−	0.662225i
$385$	29.9150	+	169.656i	0.0777012	+	0.440665i
$386$	40.9282	+	512.266i	0.106032	+	1.32711i
$387$	−229.705	−	172.417i	−0.593554	−	0.445521i
$388$	−504.577	+	81.1457i	−1.30046	+	0.209138i
$389$	400.841	+	145.894i	1.03044	+	0.375049i	0.801248	−	0.598332i	$-0.204170\pi$
$389$	400.841	+	145.894i	1.03044	+	0.375049i	0.229191	+	0.973381i	$0.426392\pi$
$390$	412.952	−	249.326i	1.05885	−	0.639297i
$391$	−29.1385	+	34.7259i	−0.0745231	+	0.0888132i
$392$	152.118	−	307.843i	0.388057	−	0.785314i
$393$	−102.797	+	51.3739i	−0.261570	+	0.130722i
$394$	120.032	+	121.856i	0.304650	+	0.309278i
$395$	−68.4041	−	39.4931i	−0.173175	−	0.0999825i
$396$	638.029	+	86.8980i	1.61118	+	0.219439i
$397$	189.792	+	328.730i	0.478066	+	0.828035i	0.999684	−	0.0251445i	$-0.00800458\pi$
$397$	189.792	+	328.730i	0.478066	+	0.828035i	−0.521618	+	0.853179i	$0.674671\pi$
$398$	−35.3887	−	9.76893i	−0.0889163	−	0.0245450i
$399$	−13.2066	+	55.2391i	−0.0330993	+	0.138444i
$400$	22.4161	+	154.182i	0.0560402	+	0.385456i
$401$	20.0090	−	113.477i	0.0498977	−	0.282984i	−0.949641	−	0.313339i	$-0.898553\pi$
$401$	20.0090	−	113.477i	0.0498977	−	0.282984i	0.999539	+	0.0303545i	$0.00966363\pi$
$402$	−2.54381	−	12.9395i	−0.00632787	−	0.0321878i
$403$	272.927	+	325.261i	0.677237	+	0.807100i
$404$	−284.849	−	350.057i	−0.705072	−	0.866477i
$405$	−307.330	−	75.3948i	−0.758838	−	0.186160i
$406$	−92.9168	+	195.401i	−0.228859	+	0.481283i
$407$	−353.782	−	421.621i	−0.869243	−	1.03592i
$408$	423.275	+	351.932i	1.03744	+	0.862580i
$409$	37.7554	−	214.121i	0.0923114	−	0.523524i	−0.903227	−	0.429164i	$-0.858808\pi$
$409$	37.7554	−	214.121i	0.0923114	−	0.523524i	0.995538	−	0.0943603i	$-0.0300806\pi$
$410$	46.4142	+	4.41357i	0.113205	+	0.0107648i
$411$	−39.2019	+	163.969i	−0.0953816	+	0.398951i
$412$	−419.142	−	362.611i	−1.01733	−	0.880123i
$413$	−69.2117	−	119.878i	−0.167583	−	0.290262i
$414$	−7.59310	+	34.7556i	−0.0183408	+	0.0839508i
$415$	176.261	+	101.764i	0.424726	+	0.245215i
$416$	−553.294	+	357.122i	−1.33003	+	0.858467i
$417$	−635.267	+	317.481i	−1.52342	+	0.761346i
$418$	−114.217	−	249.840i	−0.273247	−	0.597705i
$419$	−83.3828	+	99.3717i	−0.199004	+	0.237164i	−0.856313	−	0.516458i	$-0.827250\pi$
$419$	−83.3828	+	99.3717i	−0.199004	+	0.237164i	0.657309	+	0.753622i	$0.271695\pi$
$420$	11.4592	+	115.007i	0.0272838	+	0.273827i
$421$	94.8522	+	34.5234i	0.225302	+	0.0820033i	0.452205	−	0.891914i	$-0.350638\pi$
$421$	94.8522	+	34.5234i	0.225302	+	0.0820033i	−0.226903	+	0.973917i	$0.572860\pi$
$422$	204.642	+	297.000i	0.484934	+	0.703792i
$423$	59.0826	−	488.815i	0.139675	−	1.15559i
$424$	−112.543	+	107.564i	−0.265433	+	0.253689i
$425$	−38.7838	−	219.954i	−0.0912560	−	0.517539i
$426$	−556.336	+	214.919i	−1.30595	+	0.504504i
$427$	−13.5101	−	37.1186i	−0.0316395	−	0.0869288i
$428$	−295.279	−	529.726i	−0.689903	−	1.23768i
$429$	439.376	−	1013.11i	1.02419	−	2.36156i
$430$	62.7180	+	241.330i	0.145856	+	0.561233i
$431$		−	17.3757i		−	0.0403148i	−0.999797	−	0.0201574i	$-0.993583\pi$
$431$		−	17.3757i		−	0.0403148i	0.999797	−	0.0201574i	$-0.00641674\pi$
$432$	422.456	+	90.3024i	0.977909	+	0.209033i
$433$	−737.761			−1.70384			−0.851918	−	0.523676i	$-0.824560\pi$
$433$	−737.761			−1.70384			−0.851918	+	0.523676i	$0.824560\pi$
$434$	−98.4613	+	25.5886i	−0.226869	+	0.0589598i
$435$	58.7023	+	510.936i	0.134948	+	1.17457i
$436$	448.082	−	249.769i	1.02771	−	0.572864i
$437$	14.2620	−	5.19093i	0.0326361	−	0.0118786i
$438$	377.080	+	58.9002i	0.860913	+	0.134475i
$439$	380.391	−	67.0733i	0.866495	−	0.152786i	0.277306	−	0.960782i	$-0.410558\pi$
$439$	380.391	−	67.0733i	0.866495	−	0.152786i	0.589189	+	0.807995i	$0.299447\pi$
$440$	−386.247	−	404.127i	−0.877834	−	0.918471i
$441$	20.9453	+	385.730i	0.0474951	+	0.874671i
$442$	777.360	−	535.625i	1.75873	−	1.21182i
$443$	71.4245	−	196.237i	0.161229	−	0.442973i	−0.832603	−	0.553871i	$-0.813150\pi$
$443$	71.4245	−	196.237i	0.161229	−	0.442973i	0.993832	+	0.110897i	$0.0353725\pi$
$444$	−215.421	−	299.899i	−0.485182	−	0.675448i
$445$	−49.7272	−	41.7261i	−0.111747	−	0.0937665i
$446$	95.5768	−	43.6940i	0.214298	−	0.0979685i
$447$	100.253	+	6.03680i	0.224280	+	0.0135051i
$448$	−20.3439	−	156.466i	−0.0454105	−	0.349254i
$449$	181.887	−	315.038i	0.405094	−	0.701644i	−0.589238	−	0.807959i	$-0.700572\pi$
$449$	181.887	−	315.038i	0.405094	−	0.701644i	0.994332	+	0.106316i	$0.0339054\pi$
$450$	−107.130	−	138.729i	−0.238067	−	0.308287i
$451$	92.4327	−	53.3660i	0.204950	−	0.118328i
$452$	377.676	−	436.556i	0.835567	−	0.965832i
$453$	−31.4763	−	105.895i	−0.0694842	−	0.233764i
$454$	15.4930	−	162.928i	0.0341256	−	0.358873i
$455$	195.196	+	34.4183i	0.429002	+	0.0756446i
$456$	−63.8142	−	172.900i	−0.139943	−	0.379168i
$457$	424.330	−	356.056i	0.928513	−	0.779115i	−0.0470369	−	0.998893i	$-0.514978\pi$
$457$	424.330	−	356.056i	0.928513	−	0.779115i	0.975550	+	0.219778i	$0.0705334\pi$
$458$	−44.5100	−	21.1654i	−0.0971834	−	0.0462126i
$459$	−609.227	−	111.130i	−1.32729	−	0.242114i
$460$	23.9559	−	19.4935i	0.0520780	−	0.0423771i
$461$	−362.858	+	304.474i	−0.787110	+	0.660463i	−0.945028	−	0.326989i	$-0.893966\pi$
$461$	−362.858	+	304.474i	−0.787110	+	0.660463i	0.157919	+	0.987452i	$0.449522\pi$
$462$	174.006	+	199.312i	0.376637	+	0.431411i
$463$	37.9817	+	6.69720i	0.0820339	+	0.0144648i	0.214514	−	0.976721i	$-0.431183\pi$
$463$	37.9817	+	6.69720i	0.0820339	+	0.0144648i	−0.132481	+	0.991186i	$0.542294\pi$
$464$	−101.015	−	694.802i	−0.217705	−	1.49742i
$465$	−166.287	+	175.562i	−0.357607	+	0.377552i
$466$	42.1853	−	152.819i	0.0905263	−	0.327939i
$467$	136.396	−	78.7483i	0.292069	−	0.168626i	−0.346806	−	0.937937i	$-0.612734\pi$
$467$	136.396	−	78.7483i	0.292069	−	0.168626i	0.638874	+	0.769311i	$0.279400\pi$
$468$	345.019	−	655.612i	0.737220	−	1.40088i
$469$	2.70925	−	4.69256i	0.00577665	−	0.0100055i
$470$	−304.527	+	299.969i	−0.647930	+	0.638233i
$471$	−144.219	+	218.339i	−0.306198	+	0.463564i
$472$	402.698	+	198.990i	0.853173	+	0.421589i
$473$	437.267	+	366.911i	0.924455	+	0.775709i
$474$	−121.286	+	2.37558i	−0.255877	+	0.00501177i
$475$	−25.5755	+	70.2682i	−0.0538433	+	0.147933i
$476$	35.9133	+	223.315i	0.0754482	+	0.469149i
$477$	50.8896	−	167.583i	0.106687	−	0.351327i
$478$	−292.732	+	23.3882i	−0.612409	+	0.0489292i
$479$	457.399	−	80.6517i	0.954903	−	0.168375i	0.325576	−	0.945516i	$-0.394442\pi$
$479$	457.399	−	80.6517i	0.954903	−	0.168375i	0.629327	+	0.777141i	$0.283331\pi$
$480$	−238.022	−	289.833i	−0.495879	−	0.603818i
$481$	−595.052	+	216.581i	−1.23712	+	0.450273i
$482$	−412.358	+	579.559i	−0.855514	+	1.20240i
$483$	−11.7423	+	8.70600i	−0.0243112	+	0.0180248i
$484$	−781.468	−	149.977i	−1.61460	−	0.309870i
$485$	−499.139			−1.02915
$486$	−463.917	+	144.835i	−0.954561	+	0.298014i
$487$		−	883.498i		−	1.81416i	−0.420954	−	0.907082i	$-0.638305\pi$
$487$		−	883.498i		−	1.81416i	0.420954	−	0.907082i	$-0.361695\pi$
$488$	103.308	+	75.8763i	0.211697	+	0.155484i
$489$	−475.159	−	640.875i	−0.971696	−	1.31058i
$490$	194.424	−	273.258i	0.396784	−	0.557670i
$491$	166.771	+	458.199i	0.339656	+	0.933196i	0.985492	+	0.169720i	$0.0542865\pi$
$491$	166.771	+	458.199i	0.339656	+	0.933196i	−0.645837	+	0.763476i	$0.723491\pi$
$492$	64.5275	−	31.0413i	0.131154	−	0.0630921i
$493$	174.774	+	991.192i	0.354511	+	2.01053i
$494$	−315.061	+	25.1722i	−0.637775	+	0.0509559i
$495$	601.766	+	182.737i	1.21569	+	0.369166i
$496$	219.724	−	246.371i	0.442992	−	0.496716i
$497$	−230.280	−	83.8150i	−0.463340	−	0.168642i
$498$	312.524	−	6.12131i	0.627559	−	0.0122918i
$499$	−166.489	+	198.413i	−0.333644	+	0.397622i	−0.906618	−	0.421952i	$-0.861345\pi$
$499$	−166.489	+	198.413i	−0.333644	+	0.397622i	0.572974	+	0.819574i	$0.305790\pi$
$500$	−8.18512	+	542.777i	−0.0163702	+	1.08555i
$501$	39.1056	+	25.8304i	0.0780552	+	0.0515577i
$502$	339.571	−	334.489i	0.676436	−	0.666312i
$503$	227.274	+	131.217i	0.451837	+	0.260868i	0.708606	−	0.705605i	$-0.249325\pi$
$503$	227.274	+	131.217i	0.451837	+	0.260868i	−0.256769	+	0.966473i	$0.582658\pi$
$504$	106.360	+	142.112i	0.211032	+	0.281967i
$505$	−220.390	−	381.727i	−0.436416	−	0.755896i
$506$	18.8136	−	68.1537i	0.0371810	−	0.134691i
$507$	−554.334	−	525.050i	−1.09336	−	1.03560i
$508$	−442.128	+	739.798i	−0.870331	+	1.45629i
$509$	−11.4399	+	64.8787i	−0.0224752	+	0.127463i	−0.993981	−	0.109553i	$-0.965058\pi$
$509$	−11.4399	+	64.8787i	−0.0224752	+	0.127463i	0.971506	+	0.237016i	$0.0761693\pi$
$510$	353.581	+	405.003i	0.693297	+	0.794123i
$511$	100.801	+	120.130i	0.197262	+	0.235087i
$512$	336.658	+	385.753i	0.657535	+	0.753424i
$513$	158.042	+	134.209i	0.308074	+	0.261615i
$514$	657.800	+	312.797i	1.27977	+	0.608554i
$515$	−347.940	−	414.658i	−0.675611	−	0.805162i
$516$	274.030	+	267.507i	0.531066	+	0.518425i
$517$	−169.922	+	963.677i	−0.328670	+	1.86398i
$518$	14.3626	−	151.041i	0.0277270	−	0.291584i
$519$	547.903	−	162.859i	1.05569	−	0.313793i
$520$	−588.914	+	258.565i	−1.13253	+	0.497240i
$521$	112.991	+	195.706i	0.216874	+	0.375636i	0.953851	−	0.300282i	$-0.0970807\pi$
$521$	112.991	+	195.706i	0.216874	+	0.375636i	−0.736977	+	0.675918i	$0.763747\pi$
$522$	482.767	+	625.165i	0.924841	+	1.19763i
$523$	−197.182	−	113.843i	−0.377021	−	0.217673i	0.299501	−	0.954096i	$-0.403180\pi$
$523$	−197.182	−	113.843i	−0.377021	−	0.217673i	−0.676521	+	0.736423i	$0.736513\pi$
$524$	144.759	−	50.2294i	0.276258	−	0.0958575i
$525$	4.32892	−	71.8905i	0.00824557	−	0.136934i
$526$	592.662	−	270.942i	1.12673	−	0.515098i
$527$	−304.186	+	362.514i	−0.577203	+	0.687883i
$528$	−828.626	−	224.727i	−1.56937	−	0.425619i
$529$	−493.427	−	179.593i	−0.932754	−	0.339495i
$530$	−125.204	+	86.2696i	−0.236235	+	0.162773i
$531$	−504.584	+	27.3992i	−0.950253	+	0.0515992i
$532$	26.9705	−	70.7623i	0.0506964	−	0.133012i
$533$	−21.3239	−	120.934i	−0.0400073	−	0.226893i
$534$	−98.5025	−	15.3862i	−0.184462	−	0.0288131i
$535$	−202.585	−	556.597i	−0.378663	−	1.04037i
$536$	1.13591	+	17.5461i	0.00211923	+	0.0327353i
$537$	−809.171	+	92.9670i	−1.50684	+	0.173123i
$538$	−185.482	+	48.2038i	−0.344761	+	0.0895981i
$539$		−	767.731i		−	1.42436i
$540$	393.364	+	152.590i	0.728453	+	0.282574i
$541$	786.104			1.45306			0.726529	−	0.687136i	$-0.241132\pi$
$541$	786.104			1.45306			0.726529	+	0.687136i	$0.241132\pi$
$542$	248.621	+	956.660i	0.458711	+	1.76506i
$543$	−35.8255	−	15.5372i	−0.0659770	−	0.0286136i
$544$	−499.060	−	538.180i	−0.917390	−	0.989302i
$545$	470.812	−	171.361i	0.863875	−	0.314425i
$546$	283.959	−	109.697i	0.520072	−	0.200909i
$547$	1054.07	−	185.862i	1.92701	−	0.339783i	0.927580	−	0.373624i	$-0.121885\pi$
$547$	1054.07	−	185.862i	1.92701	−	0.339783i	0.999427	+	0.0338407i	$0.0107739\pi$
$548$	80.0579	−	210.047i	0.146091	−	0.383298i
$549$	−143.159	−	17.3035i	−0.260764	−	0.0315183i
$550$	197.648	+	286.850i	0.359361	+	0.521546i
$551$	115.253	−	316.654i	0.209170	−	0.574690i
$552$	16.0224	−	44.6459i	0.0290260	−	0.0808802i
$553$	−38.1834	−	32.0397i	−0.0690478	−	0.0579380i
$554$	−233.496	−	510.752i	−0.421472	−	0.921935i
$555$	−161.220	−	322.594i	−0.290486	−	0.581251i
$556$	894.586	−	310.409i	1.60897	−	0.558289i
$557$	200.833	−	347.853i	0.360562	−	0.624512i	−0.627492	−	0.778623i	$-0.715918\pi$
$557$	200.833	−	347.853i	0.360562	−	0.624512i	0.988053	+	0.154112i	$0.0492516\pi$
$558$	−79.2666	+	362.824i	−0.142055	+	0.650222i
$559$	568.754	−	328.370i	1.01745	−	0.587425i
$560$	4.64669	−	154.032i	0.00829766	−	0.275058i
$561$	1197.02	+	286.186i	2.13373	+	0.510135i
$562$	−226.629	−	21.5504i	−0.403255	−	0.0383459i
$563$	−768.923	−	135.582i	−1.36576	−	0.240820i	−0.557760	−	0.830003i	$-0.688339\pi$
$563$	−768.923	−	135.582i	−1.36576	−	0.240820i	−0.808000	+	0.589182i	$0.799450\pi$
$564$	−162.264	+	636.128i	−0.287702	+	1.12789i
$565$	431.887	−	362.396i	0.764401	−	0.641409i
$566$	−265.588	+	558.522i	−0.469236	+	0.986788i
$567$	−182.735	−	80.5335i	−0.322283	−	0.142034i
$568$	772.571	−	188.390i	1.36016	−	0.331673i
$569$	108.765	−	91.2651i	0.191152	−	0.160396i	−0.542189	−	0.840257i	$-0.682404\pi$
$569$	108.765	−	91.2651i	0.191152	−	0.160396i	0.733341	+	0.679861i	$0.237960\pi$
$570$	−34.7224	−	176.621i	−0.0609165	−	0.309862i
$571$	−905.067	−	159.588i	−1.58506	−	0.279488i	−0.689449	−	0.724334i	$-0.742147\pi$
$571$	−905.067	−	159.588i	−1.58506	−	0.279488i	−0.895607	+	0.444846i	$0.853258\pi$
$572$	−755.332	+	1263.87i	−1.32051	+	2.20956i
$573$	−859.589	−	205.511i	−1.50015	−	0.358658i
$574$	28.3614	+	7.82908i	0.0494102	+	0.0136395i
$575$	−16.6673	+	9.62286i	−0.0289866	+	0.0167354i
$576$	−543.016	−	192.119i	−0.942736	−	0.333539i
$577$	33.2353	−	57.5652i	0.0576001	−	0.0997663i	−0.835788	−	0.549053i	$-0.814988\pi$
$577$	33.2353	−	57.5652i	0.0576001	−	0.0997663i	0.893388	+	0.449287i	$0.148322\pi$
$578$	332.735	+	337.790i	0.575666	+	0.584412i
$579$	344.601	+	689.533i	0.595166	+	1.19090i
$580$	10.3397	−	685.652i	0.0178270	−	1.18216i
$581$	98.3896	+	82.5587i	0.169345	+	0.142098i
$582$	−656.253	+	396.222i	−1.12758	+	0.680794i
$583$	−119.048	+	327.081i	−0.204199	+	0.561032i
$584$	−488.426	−	142.788i	−0.836346	−	0.244500i
$585$	434.366	−	578.692i	0.742506	−	0.989217i
$586$	77.3112	+	967.644i	0.131930	+	1.65127i
$587$	−522.614	+	92.1509i	−0.890313	+	0.156986i	−0.600052	−	0.799961i	$-0.704853\pi$
$587$	−522.614	+	92.1509i	−0.890313	+	0.156986i	−0.290262	+	0.956947i	$0.593742\pi$
$588$	38.7075	−	513.608i	0.0658291	−	0.873483i
$589$	148.885	−	54.1896i	0.252776	−	0.0920028i
$590$	357.457	+	254.332i	0.605859	+	0.431071i
$591$	235.385	+	102.084i	0.398282	+	0.172731i
$592$	233.198	+	433.602i	0.393916	+	0.732436i
$593$	−307.107			−0.517887			−0.258944	−	0.965892i	$-0.583374\pi$
$593$	−307.107			−0.517887			−0.258944	+	0.965892i	$0.583374\pi$
$594$	936.242	−	237.431i	1.57616	−	0.399716i
$595$			220.908i			0.371275i
$596$	−131.513	−	25.2396i	−0.220660	−	0.0423484i
$597$	−54.7085	+	6.28555i	−0.0916391	+	0.0105286i
$598$	−66.2812	−	47.1593i	−0.110838	−	0.0788617i
$599$	89.0609	+	244.693i	0.148683	+	0.408502i	0.991567	−	0.129592i	$-0.0413667\pi$
$599$	89.0609	+	244.693i	0.148683	+	0.408502i	−0.842885	+	0.538094i	$0.819144\pi$
$600$	117.763	+	201.866i	0.196272	+	0.336444i
$601$	−76.4196	−	433.397i	−0.127154	−	0.721126i	−0.980005	−	0.198972i	$-0.936240\pi$
$601$	−76.4196	−	433.397i	−0.127154	−	0.721126i	0.852851	−	0.522154i	$-0.174871\pi$
$602$	12.5319	+	156.852i	0.0208172	+	0.260552i
$603$	−10.8046	−	16.5692i	−0.0179182	−	0.0274779i
$604$	23.3880	+	145.430i	0.0387219	+	0.240779i
$605$	−730.299	−	265.807i	−1.20711	−	0.439351i
$606$	−592.782	−	326.935i	−0.978188	−	0.539497i
$607$	485.664	−	578.791i	0.800105	−	0.953528i	−0.199548	−	0.979888i	$-0.563947\pi$
$607$	485.664	−	578.791i	0.800105	−	0.953528i	0.999653	+	0.0263602i	$0.00839169\pi$
$608$	54.6098	+	239.590i	0.0898188	+	0.394062i
$609$	−19.5077	+	323.965i	−0.0320323	+	0.531962i
$610$	87.8521	+	89.1869i	0.144020	+	0.146208i
$611$	975.017	+	562.926i	1.59577	+	0.921319i
$612$	786.374	+	251.808i	1.28492	+	0.411451i
$613$	204.218	+	353.715i	0.333145	+	0.577024i	0.983127	−	0.182926i	$-0.0585569\pi$
$613$	204.218	+	353.715i	0.333145	+	0.577024i	−0.649982	+	0.759950i	$0.725224\pi$
$614$	156.917	+	43.3163i	0.255565	+	0.0705478i
$615$	67.0366	−	19.9260i	0.109003	−	0.0324000i
$616$	−195.756	−	293.479i	−0.317786	−	0.476427i
$617$	−158.965	+	901.535i	−0.257642	+	1.46116i	0.531558	+	0.847022i	$0.321607\pi$
$617$	−158.965	+	901.535i	−0.257642	+	1.46116i	−0.789200	+	0.614136i	$0.789504\pi$
$618$	−786.621	−	268.982i	−1.27285	−	0.435246i
$619$	−364.506	−	434.402i	−0.588863	−	0.701780i	0.386524	−	0.922279i	$-0.373676\pi$
$619$	−364.506	−	434.402i	−0.588863	−	0.701780i	−0.975387	+	0.220499i	$0.929231\pi$
$620$	250.083	−	203.498i	0.403359	−	0.328223i
$621$	8.95641	+	52.6061i	0.0144226	+	0.0847119i
$622$	−333.066	+	700.427i	−0.535476	+	1.12609i
$623$	−26.3316	−	31.3808i	−0.0422658	−	0.0503704i
$624$	−569.035	+	807.440i	−0.911914	+	1.29397i
$625$	−49.7908	+	282.378i	−0.0796653	+	0.451805i
$626$	1017.01	+	96.7087i	1.62462	+	0.154487i
$627$	−299.169	−	283.365i	−0.477144	−	0.451938i
$628$	228.268	−	263.855i	0.363485	−	0.420152i
$629$	−352.884	−	611.213i	−0.561024	−	0.971723i
$630$	80.5235	+	153.530i	0.127815	+	0.243698i
$631$	−276.842	−	159.835i	−0.438736	−	0.253304i	0.264326	−	0.964434i	$-0.414851\pi$
$631$	−276.842	−	159.835i	−0.438736	−	0.253304i	−0.703061	+	0.711129i	$0.748184\pi$
$632$	160.770	+	17.7376i	0.254382	+	0.0280658i
$633$	451.426	+	298.180i	0.713153	+	0.471059i
$634$	−149.035	−	326.001i	−0.235071	−	0.514197i
$635$	−541.062	+	644.812i	−0.852065	+	1.01545i
$636$	−96.1332	+	212.813i	−0.151153	+	0.334612i
$637$	−830.035	−	302.108i	−1.30304	−	0.474267i
$638$	−890.676	−	1292.65i	−1.39604	−	2.02610i
$639$	−653.123	+	611.356i	−1.02210	+	0.956738i
$640$	264.813	+	424.183i	0.413771	+	0.662786i
$641$	69.5108	+	394.215i	0.108441	+	0.615000i	0.989790	+	0.142534i	$0.0455250\pi$
$641$	69.5108	+	394.215i	0.108441	+	0.615000i	−0.881349	+	0.472466i	$0.843364\pi$
$642$	−708.186	−	570.983i	−1.10309	−	0.889382i
$643$	266.185	+	731.338i	0.413974	+	1.13738i	0.955059	+	0.296416i	$0.0957915\pi$
$643$	266.185	+	731.338i	0.413974	+	1.13738i	−0.541085	+	0.840968i	$0.681986\pi$
$644$	17.0240	−	9.48949i	0.0264348	−	0.0147352i
$645$	222.759	+	300.448i	0.345363	+	0.465811i
$646$	−88.6049	−	340.939i	−0.137159	−	0.527770i
$647$			429.893i			0.664440i	0.943202	+	0.332220i	$0.107798\pi$
$647$			429.893i			0.664440i	−0.943202	+	0.332220i	$0.892202\pi$
$648$	638.311	−	111.637i	0.985048	−	0.172279i
$649$	1004.29			1.54744
$650$	387.905	−	100.810i	0.596777	−	0.155093i
$651$	−122.581	+	90.8845i	−0.188297	+	0.139607i
$652$	517.921	+	929.144i	0.794357	+	1.42507i
$653$	−173.069	+	62.9920i	−0.265037	+	0.0964655i	−0.471120	−	0.882069i	$-0.656150\pi$
$653$	−173.069	+	62.9920i	−0.265037	+	0.0964655i	0.206084	+	0.978534i	$0.433928\pi$
$654$	482.980	−	599.036i	0.738502	−	0.915958i
$655$	147.378	−	25.9868i	0.225005	−	0.0396745i
$656$	−90.6602	+	29.9340i	−0.138202	+	0.0456311i
$657$	557.562	−	129.832i	0.848649	−	0.197614i
$658$	−222.126	+	153.052i	−0.337578	+	0.232601i
$659$	−275.221	+	756.165i	−0.417635	+	1.14744i	0.535404	+	0.844596i	$0.320159\pi$
$659$	−275.221	+	756.165i	−0.417635	+	1.14744i	−0.953039	+	0.302847i	$0.902063\pi$
$660$	−764.182	−	345.200i	−1.15785	−	0.523031i
$661$	−97.5532	−	81.8569i	−0.147584	−	0.123838i	0.566006	−	0.824401i	$-0.308488\pi$
$661$	−97.5532	−	81.8569i	−0.147584	−	0.123838i	−0.713591	+	0.700563i	$0.752932\pi$
$662$	241.739	−	110.514i	0.365165	−	0.166939i
$663$	780.448	−	1181.55i	1.17715	−	1.78213i
$664$	−414.266	−	45.7056i	−0.623894	−	0.0688338i
$665$	36.9807	−	64.0525i	0.0556101	−	0.0963195i
$666$	−468.046	−	296.159i	−0.702772	−	0.444683i
$667$	75.1088	−	43.3641i	0.112607	−	0.0650136i
$668$	−47.2579	−	40.8841i	−0.0707454	−	0.0612037i
$669$	108.402	−	114.448i	0.162035	−	0.171073i
$670$	−1.62564	+	17.0956i	−0.00242633	+	0.0255159i
$671$	282.232	+	49.7652i	0.420615	+	0.0741657i
$672$	−116.163	−	206.205i	−0.172862	−	0.306853i
$673$	385.770	−	323.700i	0.573210	−	0.480980i	−0.309500	−	0.950900i	$-0.600162\pi$
$673$	385.770	−	323.700i	0.573210	−	0.480980i	0.882709	+	0.469919i	$0.155717\pi$
$674$	−558.698	−	265.671i	−0.828928	−	0.394171i
$675$	−226.915	−	132.799i	−0.336170	−	0.196740i
$676$	642.542	+	789.633i	0.950506	+	1.16810i
$677$	−277.563	+	232.903i	−0.409990	+	0.344023i	−0.824340	−	0.566095i	$-0.808453\pi$
$677$	−277.563	+	232.903i	−0.409990	+	0.344023i	0.414350	+	0.910118i	$0.364009\pi$
$678$	280.157	−	819.304i	0.413212	−	1.20841i
$679$	−310.201	−	54.6967i	−0.456849	−	0.0805548i
$680$	−397.778	−	596.351i	−0.584967	−	0.876986i
$681$	−69.9464	−	235.320i	−0.102711	−	0.345550i
$682$	196.401	−	711.476i	0.287977	−	1.04322i
$683$	882.660	−	509.604i	1.29233	−	0.746126i	0.313262	−	0.949667i	$-0.398578\pi$
$683$	882.660	−	509.604i	1.29233	−	0.746126i	0.979067	+	0.203541i	$0.0652449\pi$
$684$	−185.856	−	204.653i	−0.271719	−	0.299201i
$685$	109.772	−	190.130i	0.160251	−	0.277562i
$686$	322.897	−	318.064i	0.470695	−	0.463650i
$687$	−73.7954	−	4.44362i	−0.107417	−	0.00646816i
$688$	−316.266	−	400.864i	−0.459689	−	0.582651i
$689$	306.779	+	257.418i	0.445252	+	0.373611i
$690$	22.3736	−	40.5666i	0.0324255	−	0.0587922i
$691$	22.0977	−	60.7129i	0.0319793	−	0.0878624i	−0.922676	−	0.385577i	$-0.874002\pi$
$691$	22.0977	−	60.7129i	0.0319793	−	0.0878624i	0.954655	+	0.297715i	$0.0962245\pi$
$692$	−752.458	+	121.010i	−1.08737	+	0.174870i
$693$	353.955	+	179.509i	0.510758	+	0.259031i
$694$	370.392	−	29.5930i	0.533706	−	0.0426412i
$695$	910.772	−	160.594i	1.31046	−	0.231070i
$696$	−530.684	−	909.682i	−0.762477	−	1.30701i
$697$	128.610	−	46.8102i	0.184519	−	0.0671596i
$698$	80.7179	−	113.447i	0.115642	−	0.162531i
$699$	−27.1430	−	236.248i	−0.0388311	−	0.337981i
$700$	−18.0991	+	94.3066i	−0.0258558	+	0.134724i
$701$	−847.120			−1.20845			−0.604223	−	0.796815i	$-0.706516\pi$
$701$	−847.120			−1.20845			−0.604223	+	0.796815i	$0.706516\pi$
$702$	111.719	−	1105.65i	0.159143	−	1.57500i
$703$			236.295i			0.336124i
$704$	1056.90	+	439.771i	1.50128	+	0.624674i
$705$	−255.116	+	588.245i	−0.361867	+	0.834390i
$706$	−371.428	+	522.033i	−0.526103	+	0.739424i
$707$	−95.1357	−	261.383i	−0.134563	−	0.369708i
$708$	671.865	+	50.6344i	0.948961	+	0.0715175i
$709$	34.9456	+	198.186i	0.0492885	+	0.279529i	0.999484	−	0.0321259i	$-0.0102278\pi$
$709$	34.9456	+	198.186i	0.0492885	+	0.279529i	−0.950195	+	0.311655i	$0.899117\pi$
$710$	774.192	−	61.8552i	1.09041	−	0.0871199i
$711$	−167.364	+	71.4148i	−0.235392	+	0.100443i
$712$	127.589	+	37.2998i	0.179198	+	0.0523873i
$713$	38.3187	+	13.9469i	0.0537430	+	0.0195608i
$714$	175.360	+	290.444i	0.245602	+	0.406784i
$715$	−924.350	+	1101.60i	−1.29280	+	1.54070i
$716$	1085.87	+	16.3750i	1.51658	+	0.0228701i
$717$	−394.030	+	196.921i	−0.549553	+	0.274645i
$718$	−193.962	+	191.059i	−0.270143	+	0.266100i
$719$	−513.183	−	296.286i	−0.713745	−	0.412081i	0.0987011	−	0.995117i	$-0.468531\pi$
$719$	−513.183	−	296.286i	−0.713745	−	0.412081i	−0.812446	+	0.583036i	$0.801865\pi$
$720$	−493.829	−	269.466i	−0.685874	−	0.374258i
$721$	−170.795	−	295.826i	−0.236887	−	0.410300i
$722$	160.737	−	582.281i	0.222627	−	0.806484i
$723$	−248.090	+	1037.68i	−0.343140	+	1.43525i
$724$	44.6929	+	26.7100i	0.0617305	+	0.0368922i
$725$	−74.2011	+	420.816i	−0.102346	+	0.580435i
$726$	−1171.18	+	230.245i	−1.61319	+	0.317141i
$727$	362.352	+	431.835i	0.498421	+	0.593995i	0.955338	−	0.295514i	$-0.0954909\pi$
$727$	362.352	+	431.835i	0.498421	+	0.593995i	−0.456917	+	0.889509i	$0.651046\pi$
$728$	−394.327	+	96.1562i	−0.541658	+	0.132083i
$729$	−563.933	+	461.975i	−0.773570	+	0.633711i
$730$	−448.839	−	213.431i	−0.614848	−	0.292372i
$731$	470.494	+	560.713i	0.643631	+	0.767049i
$732$	186.303	+	47.5222i	0.254512	+	0.0649211i
$733$	86.4998	−	490.565i	0.118008	−	0.669256i	−0.867209	−	0.497944i	$-0.834088\pi$
$733$	86.4998	−	490.565i	0.118008	−	0.669256i	0.985217	−	0.171312i	$-0.0548006\pi$
$734$	60.6686	−	638.006i	0.0826548	−	0.869218i
$735$	116.973	−	489.261i	0.159147	−	0.665662i
$736$	−28.8698	+	56.2715i	−0.0392253	+	0.0764558i
$737$	19.6562	+	34.0455i	0.0266705	+	0.0461947i
$738$	72.3203	−	79.4125i	0.0979949	−	0.107605i
$739$	64.8835	+	37.4605i	0.0877990	+	0.0506908i	0.543257	−	0.839567i	$-0.317191\pi$
$739$	64.8835	+	37.4605i	0.0877990	+	0.0506908i	−0.455458	+	0.890257i	$0.650524\pi$
$740$	157.628	+	454.279i	0.213011	+	0.613890i
$741$	−424.086	+	211.942i	−0.572316	+	0.286021i
$742$	−87.2645	+	39.8939i	−0.117607	+	0.0537654i
$743$	−393.521	+	468.979i	−0.529637	+	0.631197i	−0.962831	−	0.270104i	$-0.912942\pi$
$743$	−393.521	+	468.979i	−0.529637	+	0.631197i	0.433194	+	0.901301i	$0.357387\pi$
$744$	167.262	−	466.071i	0.224815	−	0.626440i
$745$	−122.902	−	44.7327i	−0.164969	−	0.0600438i
$746$	−214.219	+	147.604i	−0.287157	+	0.197860i
$747$	431.257	−	184.019i	0.577318	−	0.246344i
$748$	−1533.41	−	584.447i	−2.05001	−	0.781347i
$749$	−64.9075	−	368.109i	−0.0866589	−	0.491467i
$750$	293.423	+	759.552i	0.391231	+	1.01274i
$751$	−9.88829	−	27.1679i	−0.0131668	−	0.0361756i	0.932935	−	0.360045i	$-0.117239\pi$
$751$	−9.88829	−	27.1679i	−0.0131668	−	0.0361756i	−0.946102	+	0.323869i	$0.895016\pi$
$752$	324.046	−	813.139i	0.430913	−	1.08130i
$753$	284.474	−	655.938i	0.377788	−	0.871099i
$754$	−1748.04	+	454.289i	−2.31836	+	0.602505i
$755$			143.863i			0.190547i
$756$	227.744	+	137.936i	0.301248	+	0.182455i
$757$	−1216.32			−1.60676			−0.803380	−	0.595467i	$-0.796967\pi$
$757$	−1216.32			−1.60676			−0.803380	+	0.595467i	$0.796967\pi$
$758$	−279.409	−	1075.13i	−0.368613	−	1.41837i
$759$	−12.1051	−	105.361i	−0.0159487	−	0.138815i
$760$	15.5049	+	239.501i	0.0204012	+	0.315133i
$761$	132.675	−	48.2896i	0.174342	−	0.0634554i	−0.253374	−	0.967368i	$-0.581540\pi$
$761$	132.675	−	48.2896i	0.174342	−	0.0634554i	0.427717	+	0.903913i	$0.359318\pi$
$762$	−199.512	+	1277.28i	−0.261827	+	1.67622i
$763$	311.374	−	54.9036i	0.408092	−	0.0719576i
$764$	1101.15	+	419.694i	1.44129	+	0.549338i
$765$	719.239	+	364.762i	0.940181	+	0.476813i
$766$	−45.2516	−	65.6743i	−0.0590752	−	0.0857367i
$767$	395.196	−	1085.79i	0.515249	−	1.41563i
$768$	684.890	+	347.491i	0.891784	+	0.452462i
$769$	377.149	+	316.466i	0.490441	+	0.411529i	0.854184	−	0.519970i	$-0.174057\pi$
$769$	377.149	+	316.466i	0.490441	+	0.411529i	−0.363743	+	0.931499i	$0.618501\pi$
$770$	−143.253	−	313.354i	−0.186043	−	0.406954i
$771$	1090.60	+	65.6710i	1.41453	+	0.0851764i
$772$	−336.924	−	971.003i	−0.436430	−	1.25778i
$773$	139.762	−	242.074i	0.180804	−	0.313162i	−0.761350	−	0.648341i	$-0.775463\pi$
$773$	139.762	−	242.074i	0.180804	−	0.313162i	0.942155	+	0.335179i	$0.108797\pi$
$774$	531.376	+	218.192i	0.686533	+	0.281901i
$775$	−173.995	+	100.456i	−0.224509	+	0.129620i
$776$	935.888	−	410.905i	1.20604	−	0.529517i
$777$	−64.8429	−	218.150i	−0.0834530	−	0.280759i
$778$	−849.301	−	80.7609i	−1.09165	−	0.103806i
$779$	−45.1267	−	7.95705i	−0.0579290	−	0.0102144i
$780$	−673.925	+	690.359i	−0.864007	+	0.885075i
$781$	1361.99	−	1142.85i	1.74391	−	1.46331i
$782$	38.9343	−	81.8774i	0.0497881	−	0.104703i
$783$	1022.56	+	598.442i	1.30595	+	0.764293i
$784$	−139.592	+	672.416i	−0.178051	+	0.857673i
$785$	261.033	−	219.033i	0.332526	−	0.279023i
$786$	173.140	−	151.157i	0.220280	−	0.192312i
$787$	−930.818	−	164.128i	−1.18274	−	0.208549i	−0.452517	−	0.891756i	$-0.649474\pi$
$787$	−930.818	−	164.128i	−1.18274	−	0.208549i	−0.730225	+	0.683207i	$0.760585\pi$
$788$	−293.646	−	175.493i	−0.372647	−	0.222707i
$789$	672.188	−	709.678i	0.851949	−	0.899465i
$790$	152.277	+	42.0355i	0.192756	+	0.0532095i
$791$	308.117	−	177.892i	0.389529	−	0.224894i
$792$	−1278.75	+	152.757i	−1.61458	+	0.192876i
$793$	164.864	−	285.553i	0.207900	−	0.360093i
$794$	−532.751	−	540.846i	−0.670971	−	0.681166i
$795$	−125.702	+	190.305i	−0.158116	+	0.239377i
$796$	73.4162	+	1.10712i	0.0922314	+	0.00139086i
$797$	−674.688	−	566.131i	−0.846535	−	0.710327i	0.112489	−	0.993653i	$-0.464118\pi$
$797$	−674.688	−	566.131i	−0.846535	−	0.710327i	−0.959024	+	0.283326i	$0.908562\pi$
$798$	−2.22446	−	113.570i	−0.00278754	−	0.142318i
$799$	−429.167	+	1179.13i	−0.537130	+	1.47575i
$800$	−120.954	−	287.174i	−0.151192	−	0.358968i
$801$	−145.649	+	33.9153i	−0.181834	+	0.0423412i
$802$	18.3540	+	229.722i	0.0228853	+	0.286437i
$803$	−1120.46	+	197.568i	−1.39535	+	0.246037i
$804$	11.4334	+	23.7673i	0.0142206	+	0.0295613i
$805$	17.8876	−	6.51055i	0.0222206	−	0.00808764i
$806$	−691.929	−	492.310i	−0.858473	−	0.610807i
$807$	−230.919	+	171.208i	−0.286145	+	0.212154i
$808$	727.481	+	534.309i	0.900348	+	0.661273i
$809$	−752.685			−0.930389			−0.465195	−	0.885208i	$-0.654016\pi$
$809$	−752.685			−0.930389			−0.465195	+	0.885208i	$0.654016\pi$
$810$	632.826	−	8.66300i	0.781266	−	0.0106951i
$811$		−	765.315i		−	0.943669i	−0.881687	−	0.471834i	$-0.843592\pi$
$811$		−	765.315i		−	0.943669i	0.881687	−	0.471834i	$-0.156408\pi$
$812$	81.5610	−	424.980i	0.100445	−	0.523374i
$813$	883.043	+	1191.01i	1.08615	+	1.46496i
$814$	896.916	+	638.158i	1.10186	+	0.783978i
$815$	355.335	+	976.276i	0.435994	+	1.19788i
$816$	−996.376	−	468.303i	−1.22105	−	0.573901i
$817$	−42.5550	−	241.341i	−0.0520869	−	0.295399i
$818$	34.6325	+	433.468i	0.0423380	+	0.529912i
$819$	333.360	−	312.042i	0.407033	−	0.381003i
$820$	−92.0642	+	14.8057i	−0.112273	+	0.0180557i
$821$	315.409	+	114.799i	0.384176	+	0.139829i	0.526886	−	0.849936i	$-0.323359\pi$
$821$	315.409	+	114.799i	0.384176	+	0.139829i	−0.142710	+	0.989765i	$0.545582\pi$
$822$	−6.60296	−	337.116i	−0.00803280	−	0.410116i
$823$	−334.820	+	399.023i	−0.406828	+	0.484839i	−0.930089	−	0.367333i	$-0.880271\pi$
$823$	−334.820	+	399.023i	−0.406828	+	0.484839i	0.523261	+	0.852173i	$0.324715\pi$
$824$	993.746	+	491.052i	1.20600	+	0.595937i
$825$	435.998	+	287.990i	0.528483	+	0.349078i
$826$	194.279	+	197.231i	0.235204	+	0.238778i
$827$	−546.337	−	315.428i	−0.660625	−	0.381412i	0.131890	−	0.991264i	$-0.457895\pi$
$827$	−546.337	−	315.428i	−0.660625	−	0.381412i	−0.792515	+	0.609852i	$0.791229\pi$
$828$	−2.78614	−	71.0962i	−0.00336491	−	0.0858650i
$829$	−225.729	−	390.973i	−0.272290	−	0.471620i	0.697158	−	0.716918i	$-0.254448\pi$
$829$	−225.729	−	390.973i	−0.272290	−	0.471620i	−0.969448	+	0.245297i	$0.921114\pi$
$830$	−392.382	−	108.316i	−0.472749	−	0.130501i
$831$	−611.596	−	579.287i	−0.735976	−	0.697096i
$832$	891.358	−	969.621i	1.07134	−	1.16541i
$833$	170.952	−	969.516i	0.205224	−	1.16388i
$834$	1069.97	−	934.125i	1.28294	−	1.12005i
$835$	−39.2300	−	46.7524i	−0.0469820	−	0.0559909i
$836$	346.775	+	426.158i	0.414802	+	0.509759i
$837$	93.4986	+	549.170i	0.111707	+	0.656118i
$838$	111.414	−	234.300i	0.132953	−	0.279595i
$839$	−637.673	−	759.949i	−0.760040	−	0.905780i	0.237811	−	0.971312i	$-0.423570\pi$
$839$	−637.673	−	759.949i	−0.760040	−	0.905780i	−0.997851	+	0.0655314i	$0.979126\pi$
$840$	−80.0369	−	216.855i	−0.0952820	−	0.258160i
$841$	188.339	−	1068.12i	0.223947	−	1.27006i
$842$	−200.973	−	19.1107i	−0.238685	−	0.0226968i
$843$	−327.324	+	97.2937i	−0.388284	+	0.115414i
$844$	−545.534	−	471.956i	−0.646367	−	0.559190i
$845$	497.141	+	861.073i	0.588332	+	1.01902i
$846$	131.536	+	975.920i	0.155480	+	1.15357i
$847$	−424.732	−	245.219i	−0.501455	−	0.289515i
$848$	163.739	−	264.828i	0.193089	−	0.312297i
$849$	−55.7596	+	926.002i	−0.0656768	+	1.09070i
$850$	185.723	+	406.254i	0.218498	+	0.477946i
$851$	−39.0916	+	46.5876i	−0.0459361	+	0.0547445i
$852$	968.783	−	695.888i	1.13707	−	0.816770i
$853$	−117.818	−	42.8824i	−0.138122	−	0.0502725i	0.272034	−	0.962288i	$-0.412304\pi$
$853$	−117.818	−	42.8824i	−0.138122	−	0.0502725i	−0.410156	+	0.912015i	$0.634526\pi$
$854$	44.8242	+	65.0541i	0.0524874	+	0.0761758i
$855$	−147.481	−	226.166i	−0.172493	−	0.264521i
$856$	838.054	+	876.849i	0.979035	+	1.02436i
$857$	−5.06668	−	28.7346i	−0.00591211	−	0.0335292i	0.981709	−	0.190388i	$-0.0609745\pi$
$857$	−5.06668	−	28.7346i	−0.00591211	−	0.0335292i	−0.987621	+	0.156858i	$0.949863\pi$
$858$	−340.847	+	2182.11i	−0.397258	+	2.54325i
$859$	−477.457	−	1311.80i	−0.555829	−	1.52713i	−0.825630	−	0.564211i	$-0.809180\pi$
$859$	−477.457	−	1311.80i	−0.555829	−	1.52713i	0.269802	−	0.962916i	$-0.413042\pi$
$860$	−242.806	−	435.592i	−0.282333	−	0.506502i
$861$	43.8449	−	5.03741i	0.0509232	−	0.00585065i
$862$	8.74099	+	33.6341i	0.0101404	+	0.0390187i
$863$			791.555i			0.917213i	0.888639	+	0.458606i	$0.151651\pi$
$863$			791.555i			0.917213i	−0.888639	+	0.458606i	$0.848349\pi$
$864$	−863.176	+	37.7219i	−0.999046	+	0.0436596i
$865$	−744.349			−0.860519
$866$	1428.08	−	371.137i	1.64906	−	0.428564i
$867$	652.498	+	282.983i	0.752593	+	0.326393i
$868$	177.719	−	99.0635i	0.204745	−	0.114129i
$869$	339.826	−	123.686i	0.391054	−	0.142332i
$870$	−370.661	−	959.488i	−0.426047	−	1.10286i
$871$	44.5432	−	7.85417i	0.0511403	−	0.00901742i
$872$	−741.704	+	708.888i	−0.850578	+	0.812945i
$873$	−690.284	+	919.643i	−0.790703	+	1.05343i
$874$	−24.9955	+	17.2227i	−0.0285990	+	0.0197056i
$875$	−114.431	+	314.395i	−0.130778	+	0.359309i
$876$	−759.544	+	75.6801i	−0.867059	+	0.0863929i
$877$	740.892	+	621.682i	0.844803	+	0.708874i	0.958639	−	0.284626i	$-0.0918693\pi$
$877$	740.892	+	621.682i	0.844803	+	0.708874i	−0.113836	+	0.993500i	$0.536314\pi$
$878$	−702.582	+	321.193i	−0.800207	+	0.365823i
$879$	650.934	+	1302.49i	0.740539	+	1.48179i
$880$	950.958	+	587.964i	1.08063	+	0.668141i
$881$	−176.281	+	305.328i	−0.200092	+	0.346570i	−0.948558	−	0.316604i	$-0.897458\pi$
$881$	−176.281	+	305.328i	−0.200092	+	0.346570i	0.748466	+	0.663174i	$0.230791\pi$
$882$	−234.589	−	736.121i	−0.265973	−	0.834604i
$883$	49.7450	−	28.7203i	0.0563364	−	0.0325258i	−0.471567	−	0.881830i	$-0.656312\pi$
$883$	49.7450	−	28.7203i	0.0563364	−	0.0325258i	0.527904	+	0.849304i	$0.322978\pi$
$884$	−1235.28	+	1427.87i	−1.39738	+	1.61523i
$885$	640.016	+	153.016i	0.723182	+	0.172899i
$886$	−39.5376	+	415.787i	−0.0446248	+	0.469285i
$887$	5.74429	+	1.01287i	0.00647609	+	0.00114191i	0.176885	−	0.984231i	$-0.443398\pi$
$887$	5.74429	+	1.01287i	0.00647609	+	0.00114191i	−0.170409	+	0.985373i	$0.554509\pi$
$888$	567.857	+	472.145i	0.639478	+	0.531695i
$889$	−406.914	+	341.441i	−0.457721	+	0.384074i
$890$	117.248	+	55.7535i	0.131739	+	0.0626444i
$891$	1168.90	−	856.013i	1.31189	−	0.960732i
$892$	−163.027	+	132.659i	−0.182766	+	0.148721i
$893$	321.826	−	270.044i	0.360388	−	0.302401i
$894$	−197.097	+	38.7478i	−0.220466	+	0.0433421i
$895$	1044.55	+	184.182i	1.16709	+	0.205790i
$896$	118.091	+	292.636i	0.131798	+	0.326603i
$897$	−118.675	−	28.3729i	−0.132302	−	0.0316308i
$898$	−193.597	+	701.319i	−0.215586	+	0.780979i
$899$	784.083	−	452.691i	0.872173	−	0.503549i
$900$	277.161	+	214.646i	0.307956	+	0.238495i
$901$	−223.169	+	386.540i	−0.247690	+	0.429012i
$902$	−152.076	+	149.800i	−0.168598	+	0.166075i
$903$	105.515	+	211.130i	0.116849	+	0.233810i
$904$	−511.455	+	1035.03i	−0.565768	+	1.14495i
$905$	38.9546	+	32.6868i	0.0430438	+	0.0361180i
$906$	114.200	+	189.147i	0.126049	+	0.208772i
$907$	358.801	−	985.799i	0.395591	−	1.08688i	−0.568818	−	0.822464i	$-0.692599\pi$
$907$	358.801	−	985.799i	0.395591	−	1.08688i	0.964409	−	0.264415i	$-0.0851788\pi$
$908$	51.9726	+	323.174i	0.0572386	+	0.355919i
$909$	−1008.11	−	121.849i	−1.10903	−	0.134047i
$910$	−395.155	+	31.5714i	−0.434236	+	0.0346939i
$911$	−1063.71	+	187.560i	−1.16763	+	0.205884i	−0.723658	−	0.690159i	$-0.757541\pi$
$911$	−1063.71	+	187.560i	−1.16763	+	0.205884i	−0.443968	+	0.896043i	$0.646430\pi$
$912$	210.504	+	302.581i	0.230816	+	0.331777i
$913$	−875.651	+	318.711i	−0.959092	+	0.349081i
$914$	−642.259	+	902.679i	−0.702691	+	0.987614i
$915$	172.279	+	74.7160i	0.188283	+	0.0816568i
$916$	96.8054	+	18.5786i	0.105683	+	0.0202824i
$917$	94.4391			0.102987
$918$	1235.19	−	91.3615i	1.34552	−	0.0995223i
$919$		−	64.6952i		−	0.0703974i	−0.999380	−	0.0351987i	$-0.988794\pi$
$919$		−	64.6952i		−	0.0703974i	0.999380	−	0.0351987i	$-0.0112064\pi$
$920$	−36.5651	+	49.7847i	−0.0397446	+	0.0541138i
$921$	242.583	−	27.8707i	0.263391	−	0.0302614i
$922$	549.215	−	771.908i	0.595678	−	0.837210i
$923$	−699.637	−	1922.24i	−0.758003	−	2.08260i
$924$	−437.089	−	298.273i	−0.473040	−	0.322806i
$925$	−52.0315	−	295.085i	−0.0562503	−	0.319011i
$926$	−76.8902	+	6.14325i	−0.0830348	+	0.00663418i
$927$	−1245.17	+	67.6135i	−1.34323	+	0.0729380i
$928$	545.061	+	1294.11i	0.587350	+	1.39452i
$929$	−90.3020	−	32.8673i	−0.0972035	−	0.0353792i	0.292961	−	0.956125i	$-0.405360\pi$
$929$	−90.3020	−	32.8673i	−0.0972035	−	0.0353792i	−0.390164	+	0.920745i	$0.627582\pi$
$930$	233.564	−	423.487i	0.251145	−	0.455363i
$931$	−211.867	+	252.494i	−0.227570	+	0.271207i
$932$	−4.78090	+	317.034i	−0.00512972	+	0.340165i
$933$	−69.9266	+	1161.27i	−0.0749481	+	1.24467i
$934$	−224.407	+	221.048i	−0.240264	+	0.236668i
$935$	−1388.01	−	801.368i	−1.48450	−	0.857078i
$936$	−338.042	+	1442.63i	−0.361156	+	1.54127i
$937$	43.2795	+	74.9624i	0.0461895	+	0.0800025i	0.888196	−	0.459465i	$-0.151959\pi$
$937$	43.2795	+	74.9624i	0.0461895	+	0.0800025i	−0.842006	+	0.539468i	$0.818626\pi$
$938$	−2.88366	+	10.4463i	−0.00307427	+	0.0111368i
$939$	1468.88	−	436.612i	1.56431	−	0.464975i
$940$	438.571	−	733.845i	0.466565	−	0.780686i
$941$	−231.827	+	1314.76i	−0.246363	+	1.39719i	0.570944	+	0.820989i	$0.306577\pi$
$941$	−231.827	+	1314.76i	−0.246363	+	1.39719i	−0.817306	+	0.576203i	$0.804534\pi$
$942$	169.328	−	495.189i	0.179753	−	0.525678i
$943$	−7.58072	−	9.03435i	−0.00803894	−	0.00958043i
$944$	−879.606	−	182.605i	−0.931786	−	0.193437i
$945$	198.219	+	168.327i	0.209756	+	0.178124i
$946$	−1030.99	−	490.258i	−1.08985	−	0.518243i
$947$	1040.19	+	1239.65i	1.09840	+	1.30903i	0.947242	+	0.320519i	$0.103857\pi$
$947$	1040.19	+	1239.65i	1.09840	+	1.30903i	0.151162	+	0.988509i	$0.451698\pi$
$948$	233.578	−	65.6122i	0.246390	−	0.0692112i
$949$	−227.309	+	1289.14i	−0.239525	+	1.35841i
$950$	14.1575	−	148.884i	0.0149027	−	0.156720i
$951$	−390.367	−	369.745i	−0.410480	−	0.388796i
$952$	−181.858	−	414.204i	−0.191027	−	0.435088i
$953$	102.057	+	176.767i	0.107090	+	0.185485i	0.914590	−	0.404382i	$-0.132513\pi$
$953$	102.057	+	176.767i	0.107090	+	0.185485i	−0.807500	+	0.589867i	$0.799180\pi$
$954$	−14.2029	+	349.990i	−0.0148878	+	0.366866i
$955$	996.736	+	575.466i	1.04370	+	0.602582i
$956$	554.875	−	192.534i	0.580413	−	0.201395i
$957$	−1964.77	−	1297.79i	−2.05305	−	1.35610i
$958$	−844.814	+	386.216i	−0.881851	+	0.403148i
$959$	89.0548	−	106.131i	0.0928622	−	0.110669i
$960$	606.541	+	441.290i	0.631814	+	0.459677i
$961$	−503.024	−	183.086i	−0.523438	−	0.190516i
$962$	1042.89	−	718.583i	1.08408	−	0.746967i
$963$	−1305.67	−	396.491i	−1.35584	−	0.411725i
$964$	506.649	−	1329.29i	0.525570	−	1.37893i
$965$	−174.312	−	988.572i	−0.180634	−	1.02443i
$966$	18.3499	−	22.7593i	0.0189958	−	0.0235603i
$967$	−103.339	−	283.922i	−0.106866	−	0.293611i	0.874721	−	0.484626i	$-0.161044\pi$
$967$	−103.339	−	283.922i	−0.106866	−	0.293611i	−0.981587	+	0.191015i	$0.938822\pi$
$968$	1588.13	−	102.813i	1.64063	−	0.106212i
$969$	−314.703	−	424.459i	−0.324771	−	0.438038i
$970$	966.183	−	251.096i	0.996065	−	0.258862i
$971$			1000.22i			1.03010i	0.857161	+	0.515049i	$0.172226\pi$
$971$			1000.22i			1.03010i	−0.857161	+	0.515049i	$0.827774\pi$
$972$	825.143	−	513.734i	0.848913	−	0.528533i
$973$	583.617			0.599812
$974$	444.451	+	1710.19i	0.456315	+	1.75584i
$975$	482.929	−	358.055i	0.495312	−	0.367236i
$976$	−238.144	−	94.9035i	−0.244000	−	0.0972372i
$977$	−95.5668	+	34.7835i	−0.0978166	+	0.0356023i	−0.390465	−	0.920618i	$-0.627686\pi$
$977$	−95.5668	+	34.7835i	−0.0978166	+	0.0356023i	0.292648	+	0.956220i	$0.405463\pi$
$978$	1242.16	+	1001.51i	1.27011	+	1.02404i
$979$	292.692	−	51.6095i	0.298970	−	0.0527166i
$980$	−238.882	+	626.753i	−0.243757	+	0.639544i
$981$	335.382	−	1104.43i	0.341877	−	1.12583i
$982$	−553.319	−	803.040i	−0.563462	−	0.817760i
$983$	554.806	−	1524.32i	0.564400	−	1.55068i	−0.248716	−	0.968576i	$-0.580009\pi$
$983$	554.806	−	1524.32i	0.564400	−	1.55068i	0.813117	−	0.582101i	$-0.197769\pi$
$984$	−109.290	+	92.5477i	−0.111067	+	0.0940526i
$985$	−255.944	−	214.762i	−0.259841	−	0.218033i
$986$	−836.937	−	1830.73i	−0.848821	−	1.85672i
$987$	−223.009	+	337.621i	−0.225946	+	0.342068i
$988$	597.200	−	207.220i	0.604454	−	0.209737i
$989$	31.5363	−	54.6225i	0.0318871	−	0.0552300i
$990$	−1256.76	−	51.0007i	−1.26946	−	0.0515159i
$991$	−1135.19	+	655.405i	−1.14550	+	0.661357i	−0.947788	−	0.318902i	$-0.896686\pi$
$991$	−1135.19	+	655.405i	−1.14550	+	0.661357i	−0.197717	+	0.980259i	$0.563353\pi$
$992$	−301.381	+	587.434i	−0.303811	+	0.592172i
$993$	274.177	−	289.469i	0.276110	−	0.291509i
$994$	487.917	+	46.3965i	0.490862	+	0.0466765i
$995$	70.6224	+	12.4526i	0.0709773	+	0.0125152i
$996$	−601.874	+	169.067i	−0.604291	+	0.169746i
$997$	−170.842	+	143.354i	−0.171356	+	0.143785i	−0.724433	−	0.689346i	$-0.757898\pi$
$997$	−170.842	+	143.354i	−0.171356	+	0.143785i	0.553076	+	0.833131i	$0.313454\pi$
$998$	222.458	−	467.822i	0.222904	−	0.468760i
$999$	−817.326	−	149.090i	−0.818144	−	0.149240i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.3.j.a.103.4	yes	204
3.2	odd	2		324.3.j.a.199.31		204
4.3	odd	2	inner	108.3.j.a.103.13	yes	204
12.11	even	2		324.3.j.a.199.22		204
27.11	odd	18		324.3.j.a.127.22		204
27.16	even	9	inner	108.3.j.a.43.13	yes	204
108.11	even	18		324.3.j.a.127.31		204
108.43	odd	18	inner	108.3.j.a.43.4	✓	204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.3.j.a.43.4	✓	204	108.43	odd	18	inner
108.3.j.a.43.13	yes	204	27.16	even	9	inner
108.3.j.a.103.4	yes	204	1.1	even	1	trivial
108.3.j.a.103.13	yes	204	4.3	odd	2	inner
324.3.j.a.127.22		204	27.11	odd	18
324.3.j.a.127.31		204	108.11	even	18
324.3.j.a.199.22		204	12.11	even	2
324.3.j.a.199.31		204	3.2	odd	2

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:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	108.j (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.93570 + 0.503058i) q^{2} +(-2.40989 + 1.78674i) q^{3} +(3.49386 - 1.94754i) q^{4} +(3.67109 - 1.33617i) q^{5} +(3.76598 - 4.67091i) q^{6} +(2.42790 - 0.428104i) q^{7} +(-5.78335 + 5.52747i) q^{8} +(2.61510 - 8.61169i) q^{9} +(-6.43396 + 4.43320i) q^{10} +(-6.11759 + 16.8080i) q^{11} +(-4.94006 + 10.9360i) q^{12} +(15.7646 + 13.2281i) q^{13} +(-4.48432 + 2.05006i) q^{14} +(-6.45953 + 9.77932i) q^{15} +(8.41418 - 13.6089i) q^{16} +(-11.4681 + 19.8634i) q^{17} +(-0.729856 + 17.9852i) q^{18} +(6.65039 - 3.83960i) q^{19} +(10.2241 - 11.8180i) q^{20} +(-5.08605 + 5.36972i) q^{21} +(3.38644 - 35.6127i) q^{22} +(1.94638 + 0.343200i) q^{23} +(4.06103 - 23.6539i) q^{24} +(-7.45952 + 6.25928i) q^{25} +(-37.1701 - 17.6751i) q^{26} +(9.08480 + 25.4257i) q^{27} +(7.64900 - 6.22417i) q^{28} +(33.6153 - 28.2066i) q^{29} +(7.58413 - 22.1793i) q^{30} +(20.3189 + 3.58277i) q^{31} +(-9.44126 + 30.5755i) q^{32} +(-15.2888 - 51.4358i) q^{33} +(12.2064 - 44.2187i) q^{34} +(8.34103 - 4.81570i) q^{35} +(-7.63482 - 35.1811i) q^{36} +(-15.3854 + 26.6483i) q^{37} +(-10.9416 + 10.7778i) q^{38} +(-61.6262 - 3.71085i) q^{39} +(-13.8456 + 28.0194i) q^{40} +(-4.57109 - 3.83560i) q^{41} +(7.14378 - 12.9527i) q^{42} +(10.9148 - 29.9881i) q^{43} +(11.3601 + 70.6390i) q^{44} +(-1.90641 - 35.1086i) q^{45} +(-3.94026 + 0.314813i) q^{46} +(53.8769 - 9.49995i) q^{47} +(4.03837 + 47.8298i) q^{48} +(-40.3335 + 14.6802i) q^{49} +(11.2906 - 15.8687i) q^{50} +(-7.85390 - 68.3592i) q^{51} +(80.8418 + 15.5149i) q^{52} +19.4599 q^{53} +(-30.3761 - 44.6463i) q^{54} +69.8777i q^{55} +(-11.6751 + 15.8960i) q^{56} +(-9.16629 + 21.1355i) q^{57} +(-50.8796 + 71.5100i) q^{58} +(-19.2036 - 52.7614i) q^{59} +(-3.52310 + 46.7478i) q^{60} +(-2.78225 - 15.7789i) q^{61} +(-41.1336 + 3.28642i) q^{62} +(2.66249 - 22.0279i) q^{63} +(2.89417 - 63.9345i) q^{64} +(75.5485 + 27.4974i) q^{65} +(55.4697 + 91.8731i) q^{66} +(1.41276 - 1.68366i) q^{67} +(-1.38337 + 91.7347i) q^{68} +(-5.30377 + 2.65062i) q^{69} +(-13.7232 + 13.5178i) q^{70} +(-86.0838 - 49.7005i) q^{71} +(32.4769 + 64.2593i) q^{72} +(31.8044 + 55.0868i) q^{73} +(16.3759 - 59.3229i) q^{74} +(6.79286 - 28.4124i) q^{75} +(15.7578 - 26.3669i) q^{76} +(-7.65735 + 43.4270i) q^{77} +(121.157 - 23.8185i) q^{78} +(-12.9960 - 15.4880i) q^{79} +(12.7055 - 61.2023i) q^{80} +(-67.3225 - 45.0408i) q^{81} +(10.7778 + 5.12504i) q^{82} +(33.4876 + 39.9089i) q^{83} +(-7.31223 + 28.6663i) q^{84} +(-15.5598 + 88.2438i) q^{85} +(-6.04197 + 63.5388i) q^{86} +(-30.6111 + 128.037i) q^{87} +(-57.5253 - 131.021i) q^{88} +(-8.30808 - 14.3900i) q^{89} +(21.3519 + 67.0006i) q^{90} +(43.9380 + 25.3676i) q^{91} +(7.46880 - 2.59157i) q^{92} +(-55.3677 + 27.6706i) q^{93} +(-99.5105 + 45.4923i) q^{94} +(19.2838 - 22.9816i) q^{95} +(-31.8783 - 90.5526i) q^{96} +(-120.060 - 43.6982i) q^{97} +(70.6886 - 48.7066i) q^{98} +(128.747 + 96.6373i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q - 6 q^{2} - 6 q^{4} - 12 q^{5} - 6 q^{6} - 3 q^{8} - 12 q^{9} - 3 q^{10} + 39 q^{12} - 12 q^{13} + 39 q^{14} - 6 q^{16} - 6 q^{17} - 27 q^{18} - 69 q^{20} - 12 q^{21} - 6 q^{22} - 138 q^{24} - 12 q^{25}+ \cdots + 510 q^{98}+O(q^{100}) \) 204 * q - 6 * q^2 - 6 * q^4 - 12 * q^5 - 6 * q^6 - 3 * q^8 - 12 * q^9 - 3 * q^10 + 39 * q^12 - 12 * q^13 + 39 * q^14 - 6 * q^16 - 6 * q^17 - 27 * q^18 - 69 * q^20 - 12 * q^21 - 6 * q^22 - 138 * q^24 - 12 * q^25 - 174 * q^26 - 12 * q^28 + 60 * q^29 - 153 * q^30 - 96 * q^32 + 48 * q^33 + 6 * q^34 + 24 * q^36 - 6 * q^37 + 72 * q^38 + 69 * q^40 - 192 * q^41 - 126 * q^42 - 219 * q^44 - 132 * q^45 - 3 * q^46 - 219 * q^48 - 12 * q^49 - 165 * q^50 + 21 * q^52 - 24 * q^53 + 78 * q^54 + 99 * q^56 - 150 * q^57 - 141 * q^58 + 210 * q^60 - 12 * q^61 + 294 * q^62 - 3 * q^64 - 156 * q^65 + 393 * q^66 + 375 * q^68 - 60 * q^69 - 165 * q^70 + 228 * q^72 - 6 * q^73 + 447 * q^74 - 54 * q^76 + 132 * q^77 + 750 * q^78 + 798 * q^80 + 228 * q^81 - 12 * q^82 + 762 * q^84 + 138 * q^85 + 606 * q^86 - 198 * q^88 - 114 * q^89 + 894 * q^90 + 723 * q^92 - 1020 * q^93 - 357 * q^94 + 474 * q^96 + 168 * q^97 + 510 * q^98

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