LMFDB - Embedded newform 171.2.x.a.14.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [171,2,Mod(14,171)] 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("171.14"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(171, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([15, 7])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 171 = 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	171.x (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:	$1.36544187456$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$18$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			14.11
Character	$\chi$	$=$	171.14
Dual form			171.2.x.a.110.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.353154 + 0.296331i) q^{2} +(0.726580 + 1.57229i) q^{3} +(-0.310391 - 1.76031i) q^{4} +(0.919654 + 2.52673i) q^{5} +(-0.209323 + 0.770567i) q^{6} +(2.00770 - 3.47744i) q^{7} +(0.873030 - 1.51213i) q^{8} +(-1.94416 + 2.28478i) q^{9} +(-0.423969 + 1.16485i) q^{10} +3.58291i q^{11} +(2.54219 - 1.76703i) q^{12} +(-1.68193 + 4.62107i) q^{13} +(1.73950 - 0.633126i) q^{14} +(-3.30454 + 3.28183i) q^{15} +(-2.60294 + 0.947393i) q^{16} +(-2.40209 - 6.59968i) q^{17} +(-1.36364 + 0.230763i) q^{18} +(-0.557476 - 4.32310i) q^{19} +(4.16239 - 2.40315i) q^{20} +(6.92628 + 0.630040i) q^{21} +(-1.06173 + 1.26532i) q^{22} +(2.11329 - 0.372629i) q^{23} +(3.01183 + 0.273967i) q^{24} +(-1.70837 + 1.43350i) q^{25} +(-1.96335 + 1.13354i) q^{26} +(-5.00492 - 1.39670i) q^{27} +(-6.74455 - 2.45482i) q^{28} +(-0.213376 - 1.21011i) q^{29} +(-2.13952 + 0.179753i) q^{30} -4.02416i q^{31} +(-4.48150 - 1.63113i) q^{32} +(-5.63336 + 2.60327i) q^{33} +(1.10738 - 3.04251i) q^{34} +(10.6329 + 1.87487i) q^{35} +(4.62539 + 2.71316i) q^{36} +0.477624i q^{37} +(1.08420 - 1.69192i) q^{38} +(-8.48770 + 0.713100i) q^{39} +(4.62363 + 0.815271i) q^{40} +(1.67493 + 1.40543i) q^{41} +(2.25934 + 2.27497i) q^{42} +(0.397937 - 2.25682i) q^{43} +(6.30705 - 1.11210i) q^{44} +(-7.56098 - 2.81116i) q^{45} +(0.856736 + 0.494637i) q^{46} +(-5.61172 + 0.989498i) q^{47} +(-3.38082 - 3.40421i) q^{48} +(-4.56171 - 7.90111i) q^{49} -1.02811 q^{50} +(8.63127 - 8.57196i) q^{51} +(8.65660 + 1.52639i) q^{52} +(-2.30385 + 1.93316i) q^{53} +(-1.35362 - 1.97636i) q^{54} +(-9.05304 + 3.29504i) q^{55} +(-3.50556 - 6.07181i) q^{56} +(6.39210 - 4.01759i) q^{57} +(0.283240 - 0.490586i) q^{58} +(-1.51577 + 8.59634i) q^{59} +(6.80275 + 4.79837i) q^{60} +(-7.98674 - 2.90694i) q^{61} +(1.19248 - 1.42115i) q^{62} +(4.04189 + 11.3479i) q^{63} +(1.67069 + 2.89372i) q^{64} -13.2230 q^{65} +(-2.76087 - 0.749985i) q^{66} +(6.88939 + 8.21046i) q^{67} +(-10.8719 + 6.27691i) q^{68} +(2.12135 + 3.05194i) q^{69} +(3.19948 + 3.81299i) q^{70} +(0.839138 + 0.704120i) q^{71} +(1.75758 + 4.93451i) q^{72} +(0.773620 - 4.38741i) q^{73} +(-0.141535 + 0.168675i) q^{74} +(-3.49513 - 1.64450i) q^{75} +(-7.43699 + 2.32319i) q^{76} +(12.4593 + 7.19341i) q^{77} +(-3.20878 - 2.26334i) q^{78} +(3.11236 + 8.55114i) q^{79} +(-4.78761 - 5.70565i) q^{80} +(-1.44046 - 8.88398i) q^{81} +(0.175034 + 0.992667i) q^{82} +(13.1641 + 7.60030i) q^{83} +(-1.04078 - 12.3880i) q^{84} +(14.4665 - 12.1388i) q^{85} +(0.809298 - 0.679082i) q^{86} +(1.74761 - 1.21473i) q^{87} +(5.41783 + 3.12799i) q^{88} +(-0.329717 - 1.86992i) q^{89} +(-1.83715 - 3.23333i) q^{90} +(12.6927 + 15.1265i) q^{91} +(-1.31189 - 3.60439i) q^{92} +(6.32713 - 2.92387i) q^{93} +(-2.27502 - 1.31348i) q^{94} +(10.4106 - 5.38435i) q^{95} +(-0.691561 - 8.23134i) q^{96} +(-6.65363 + 7.92948i) q^{97} +(0.730361 - 4.14209i) q^{98} +(-8.18617 - 6.96576i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 9 q^{2} - 3 q^{4} - 9 q^{5} + 3 q^{7} - 24 q^{9} - 12 q^{10} - 9 q^{12} - 6 q^{13} - 9 q^{14} - 36 q^{15} - 9 q^{16} + 27 q^{17} + 36 q^{18} - 15 q^{19} - 18 q^{20} + 3 q^{21} + 30 q^{22} - 45 q^{23}+ \cdots + 39 q^{99}+O(q^{100}) $ 108 * q - 9 * q^2 - 3 * q^4 - 9 * q^5 + 3 * q^7 - 24 * q^9 - 12 * q^10 - 9 * q^12 - 6 * q^13 - 9 * q^14 - 36 * q^15 - 9 * q^16 + 27 * q^17 + 36 * q^18 - 15 * q^19 - 18 * q^20 + 3 * q^21 + 30 * q^22 - 45 * q^23 - 21 * q^24 - 3 * q^25 - 72 * q^26 - 36 * q^28 - 9 * q^29 - 21 * q^30 - 9 * q^32 - 6 * q^33 + 33 * q^34 + 45 * q^35 + 18 * q^36 - 9 * q^38 - 18 * q^39 + 15 * q^40 - 9 * q^41 + 15 * q^42 + 9 * q^43 - 63 * q^44 + 33 * q^45 - 18 * q^46 - 9 * q^47 + 3 * q^48 - 15 * q^49 + 126 * q^50 + 39 * q^51 - 39 * q^52 - 51 * q^54 + 3 * q^55 + 63 * q^56 - 78 * q^57 - 6 * q^58 + 36 * q^59 - 75 * q^60 - 24 * q^61 + 18 * q^62 - 9 * q^63 - 18 * q^65 + 159 * q^66 - 63 * q^67 + 54 * q^68 - 9 * q^69 + 39 * q^70 + 141 * q^72 - 45 * q^73 - 117 * q^74 - 3 * q^76 - 18 * q^77 + 27 * q^78 + 3 * q^79 + 126 * q^80 - 60 * q^81 - 3 * q^82 + 27 * q^83 - 117 * q^84 - 3 * q^85 - 171 * q^86 + 15 * q^87 - 9 * q^88 + 54 * q^89 - 21 * q^90 - 9 * q^91 - 27 * q^92 + 42 * q^93 + 99 * q^95 + 207 * q^96 - 57 * q^97 - 27 * q^98 + 39 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/171\mathbb{Z}\right)^\times$.

$n$	$20$	$154$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{18}\right)$

Coefficient data

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

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

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

$2$	0.353154	+	0.296331i	0.249717	+	0.209538i	0.759051	−	0.651032i	$-0.225663\pi$
$2$	0.353154	+	0.296331i	0.249717	+	0.209538i	−0.509333	+	0.860569i	$0.670108\pi$
$3$	0.726580	+	1.57229i	0.419491	+	0.907759i
$3$	0.726580	+	1.57229i	0.419491	+	0.907759i
$4$	−0.310391	−	1.76031i	−0.155195	−	0.880157i
$5$	0.919654	+	2.52673i	0.411282	+	1.12999i	0.956510	+	0.291700i	$0.0942208\pi$
$5$	0.919654	+	2.52673i	0.411282	+	1.12999i	−0.545228	+	0.838288i	$0.683557\pi$
$6$	−0.209323	+	0.770567i	−0.0854557	+	0.314583i
$7$	2.00770	−	3.47744i	0.758839	−	1.31435i	−0.184604	−	0.982813i	$-0.559100\pi$
$7$	2.00770	−	3.47744i	0.758839	−	1.31435i	0.943443	−	0.331535i	$-0.107566\pi$
$8$	0.873030	−	1.51213i	0.308663	−	0.534619i
$9$	−1.94416	+	2.28478i	−0.648054	+	0.761594i
$10$	−0.423969	+	1.16485i	−0.134071	+	0.368357i
$11$			3.58291i			1.08029i	0.841573	+	0.540144i	$0.181630\pi$
$11$			3.58291i			1.08029i	−0.841573	+	0.540144i	$0.818370\pi$
$12$	2.54219	−	1.76703i	0.733868	−	0.510098i
$13$	−1.68193	+	4.62107i	−0.466484	+	1.28165i	0.454044	+	0.890979i	$0.349981\pi$
$13$	−1.68193	+	4.62107i	−0.466484	+	1.28165i	−0.920528	+	0.390676i	$0.872241\pi$
$14$	1.73950	−	0.633126i	0.464901	−	0.169210i
$15$	−3.30454	+	3.28183i	−0.853228	+	0.847365i
$16$	−2.60294	+	0.947393i	−0.650735	+	0.236848i
$17$	−2.40209	−	6.59968i	−0.582592	−	1.60066i	−0.783735	−	0.621095i	$-0.786688\pi$
$17$	−2.40209	−	6.59968i	−0.582592	−	1.60066i	0.201144	−	0.979562i	$-0.435534\pi$
$18$	−1.36364	+	0.230763i	−0.321413	+	0.0543914i
$19$	−0.557476	−	4.32310i	−0.127894	−	0.991788i
$19$	−0.557476	−	4.32310i	−0.127894	−	0.991788i
$20$	4.16239	−	2.40315i	0.930738	−	0.537362i
$21$	6.92628	+	0.630040i	1.51144	+	0.137486i
$22$	−1.06173	+	1.26532i	−0.226361	+	0.269767i
$23$	2.11329	−	0.372629i	0.440651	−	0.0776986i	0.0510786	−	0.998695i	$-0.483734\pi$
$23$	2.11329	−	0.372629i	0.440651	−	0.0776986i	0.389572	+	0.920996i	$0.372623\pi$
$24$	3.01183	+	0.273967i	0.614787	+	0.0559234i
$25$	−1.70837	+	1.43350i	−0.341675	+	0.286699i
$26$	−1.96335	+	1.13354i	−0.385044	+	0.222305i
$27$	−5.00492	−	1.39670i	−0.963197	−	0.268796i
$28$	−6.74455	−	2.45482i	−1.27460	−	0.463917i
$29$	−0.213376	−	1.21011i	−0.0396229	−	0.224712i	0.958566	−	0.284871i	$-0.0919506\pi$
$29$	−0.213376	−	1.21011i	−0.0396229	−	0.224712i	−0.998189	+	0.0601582i	$0.980839\pi$
$30$	−2.13952	+	0.179753i	−0.390621	+	0.0328182i
$31$		−	4.02416i		−	0.722760i	−0.932419	−	0.361380i	$-0.882306\pi$
$31$		−	4.02416i		−	0.722760i	0.932419	−	0.361380i	$-0.117694\pi$
$32$	−4.48150	−	1.63113i	−0.792224	−	0.288346i
$33$	−5.63336	+	2.60327i	−0.980642	+	0.453171i
$34$	1.10738	−	3.04251i	0.189915	−	0.521787i
$35$	10.6329	+	1.87487i	1.79729	+	0.316911i
$36$	4.62539	+	2.71316i	0.770898	+	0.452194i
$37$			0.477624i			0.0785210i	0.999229	+	0.0392605i	$0.0125002\pi$
$37$			0.477624i			0.0785210i	−0.999229	+	0.0392605i	$0.987500\pi$
$38$	1.08420	−	1.69192i	0.175880	−	0.274465i
$39$	−8.48770	+	0.713100i	−1.35912	+	0.114187i
$40$	4.62363	+	0.815271i	0.731061	+	0.128906i
$41$	1.67493	+	1.40543i	0.261580	+	0.219492i	0.764140	−	0.645051i	$-0.223164\pi$
$41$	1.67493	+	1.40543i	0.261580	+	0.219492i	−0.502560	+	0.864543i	$0.667608\pi$
$42$	2.25934	+	2.27497i	0.348624	+	0.351036i
$43$	0.397937	−	2.25682i	0.0606849	−	0.344161i	−0.939314	−	0.343057i	$-0.888538\pi$
$43$	0.397937	−	2.25682i	0.0606849	−	0.344161i	0.999999	−	0.00110390i	$-0.000351381\pi$
$44$	6.30705	−	1.11210i	0.950824	−	0.167656i
$45$	−7.56098	−	2.81116i	−1.12712	−	0.419064i
$46$	0.856736	+	0.494637i	0.126319	+	0.0729303i
$47$	−5.61172	+	0.989498i	−0.818554	+	0.144333i	−0.567219	−	0.823567i	$-0.691981\pi$
$47$	−5.61172	+	0.989498i	−0.818554	+	0.144333i	−0.251335	+	0.967900i	$0.580870\pi$
$48$	−3.38082	−	3.40421i	−0.487979	−	0.491355i
$49$	−4.56171	−	7.90111i	−0.651673	−	1.12873i
$50$	−1.02811			−0.145396
$51$	8.63127	−	8.57196i	1.20862	−	1.20031i
$52$	8.65660	+	1.52639i	1.20045	+	0.211672i
$53$	−2.30385	+	1.93316i	−0.316458	+	0.265540i	−0.787155	−	0.616755i	$-0.788447\pi$
$53$	−2.30385	+	1.93316i	−0.316458	+	0.265540i	0.470697	+	0.882295i	$0.344003\pi$
$54$	−1.35362	−	1.97636i	−0.184204	−	0.268949i
$55$	−9.05304	+	3.29504i	−1.22071	+	0.444303i
$56$	−3.50556	−	6.07181i	−0.468450	−	0.811380i
$57$	6.39210	−	4.01759i	0.846654	−	0.532143i
$58$	0.283240	−	0.490586i	0.0371912	−	0.0644171i
$59$	−1.51577	+	8.59634i	−0.197336	+	1.11915i	0.711717	+	0.702466i	$0.247918\pi$
$59$	−1.51577	+	8.59634i	−0.197336	+	1.11915i	−0.909053	+	0.416681i	$0.863193\pi$
$60$	6.80275	+	4.79837i	0.878231	+	0.619468i
$61$	−7.98674	−	2.90694i	−1.02260	−	0.372195i	−0.224340	−	0.974511i	$-0.572023\pi$
$61$	−7.98674	−	2.90694i	−1.02260	−	0.372195i	−0.798258	+	0.602316i	$0.794245\pi$
$62$	1.19248	−	1.42115i	0.151446	−	0.180486i
$63$	4.04189	+	11.3479i	0.509230	+	1.42970i
$64$	1.67069	+	2.89372i	0.208836	+	0.361715i
$65$	−13.2230			−1.64011
$66$	−2.76087	−	0.749985i	−0.339840	−	0.0923168i
$67$	6.88939	+	8.21046i	0.841673	+	1.00307i	0.999877	+	0.0156605i	$0.00498509\pi$
$67$	6.88939	+	8.21046i	0.841673	+	1.00307i	−0.158204	+	0.987406i	$0.550570\pi$
$68$	−10.8719	+	6.27691i	−1.31841	+	0.761187i
$69$	2.12135	+	3.05194i	0.255381	+	0.367411i
$70$	3.19948	+	3.81299i	0.382410	+	0.455739i
$71$	0.839138	+	0.704120i	0.0995873	+	0.0835637i	0.691222	−	0.722643i	$-0.257073\pi$
$71$	0.839138	+	0.704120i	0.0995873	+	0.0835637i	−0.591635	+	0.806206i	$0.701517\pi$
$72$	1.75758	+	4.93451i	0.207133	+	0.581538i
$73$	0.773620	−	4.38741i	0.0905453	−	0.513508i	−0.905476	−	0.424397i	$-0.860486\pi$
$73$	0.773620	−	4.38741i	0.0905453	−	0.513508i	0.996022	−	0.0891113i	$-0.0284027\pi$
$74$	−0.141535	+	0.168675i	−0.0164531	+	0.0196081i
$75$	−3.49513	−	1.64450i	−0.403583	−	0.189891i
$76$	−7.43699	+	2.32319i	−0.853081	+	0.266488i
$77$	12.4593	+	7.19341i	1.41987	+	0.819765i
$78$	−3.20878	−	2.26334i	−0.363323	−	0.256272i
$79$	3.11236	+	8.55114i	0.350168	+	0.962078i	0.982316	+	0.187230i	$0.0599511\pi$
$79$	3.11236	+	8.55114i	0.350168	+	0.962078i	−0.632148	+	0.774847i	$0.717827\pi$
$80$	−4.78761	−	5.70565i	−0.535271	−	0.637911i
$81$	−1.44046	−	8.88398i	−0.160051	−	0.987109i
$82$	0.175034	+	0.992667i	0.0193293	+	0.109622i
$83$	13.1641	+	7.60030i	1.44495	+	0.834241i	0.998174	−	0.0604058i	$-0.0192395\pi$
$83$	13.1641	+	7.60030i	1.44495	+	0.834241i	0.446774	+	0.894647i	$0.352573\pi$
$84$	−1.04078	−	12.3880i	−0.113559	−	1.35164i
$85$	14.4665	−	12.1388i	1.56911	−	1.31664i
$86$	0.809298	−	0.679082i	0.0872688	−	0.0732272i
$87$	1.74761	−	1.21473i	0.187363	−	0.130233i
$88$	5.41783	+	3.12799i	0.577543	+	0.333445i
$89$	−0.329717	−	1.86992i	−0.0349500	−	0.198211i	0.962333	−	0.271872i	$-0.0876428\pi$
$89$	−0.329717	−	1.86992i	−0.0349500	−	0.198211i	−0.997283	+	0.0736611i	$0.976532\pi$
$90$	−1.83715	−	3.23333i	−0.193653	−	0.340823i
$91$	12.6927	+	15.1265i	1.33055	+	1.58569i
$92$	−1.31189	−	3.60439i	−0.136774	−	0.375783i
$93$	6.32713	−	2.92387i	0.656092	−	0.303191i
$94$	−2.27502	−	1.31348i	−0.234650	−	0.135475i
$95$	10.4106	−	5.38435i	1.06811	−	0.552423i
$96$	−0.691561	−	8.23134i	−0.0705822	−	0.840108i
$97$	−6.65363	+	7.92948i	−0.675574	+	0.805117i	−0.989531	−	0.144320i	$-0.953901\pi$
$97$	−6.65363	+	7.92948i	−0.675574	+	0.805117i	0.313958	+	0.949437i	$0.398345\pi$
$98$	0.730361	−	4.14209i	0.0737776	−	0.418414i
$99$	−8.18617	−	6.96576i	−0.822741	−	0.700086i
$100$	3.05367	+	2.56233i	0.305367	+	0.256233i
$101$	−7.45770	−	8.88774i	−0.742068	−	0.884363i	0.254505	−	0.967071i	$-0.418087\pi$
$101$	−7.45770	−	8.88774i	−0.742068	−	0.884363i	−0.996574	+	0.0827086i	$0.973643\pi$
$102$	5.58830	−	0.469505i	0.553325	−	0.0464879i
$103$	−3.68495	+	2.12751i	−0.363089	+	0.209630i	−0.670435	−	0.741968i	$-0.733892\pi$
$103$	−3.68495	+	2.12751i	−0.363089	+	0.209630i	0.307346	+	0.951598i	$0.400559\pi$
$104$	5.51929	+	6.57764i	0.541211	+	0.644991i
$105$	4.77784	+	18.0802i	0.466269	+	1.76445i
$106$	−1.38647			−0.134666
$107$	5.10424	+	8.84081i	0.493446	+	0.854673i	0.999971	−	0.00755167i	$-0.00240379\pi$
$107$	5.10424	+	8.84081i	0.493446	+	0.854673i	−0.506526	+	0.862225i	$0.669070\pi$
$108$	−0.905155	+	9.24376i	−0.0870986	+	0.889481i
$109$	9.68120	−	11.5376i	0.927291	−	1.10510i	−0.0669312	−	0.997758i	$-0.521321\pi$
$109$	9.68120	−	11.5376i	0.927291	−	1.10510i	0.994222	−	0.107344i	$-0.0342347\pi$
$110$	−4.17354	−	1.51904i	−0.397931	−	0.144835i
$111$	−0.750962	+	0.347032i	−0.0712782	+	0.0329389i
$112$	−1.93142	+	10.9536i	−0.182502	+	1.03502i
$113$	−1.01676	+	1.76109i	−0.0956492	+	0.165669i	−0.909879	−	0.414873i	$-0.863826\pi$
$113$	−1.01676	+	1.76109i	−0.0956492	+	0.165669i	0.814230	+	0.580542i	$0.197159\pi$
$114$	3.44793	+	0.475351i	0.322928	+	0.0445207i
$115$	2.88503	+	4.99701i	0.269030	+	0.465974i
$116$	−2.06395	+	0.751216i	−0.191633	+	0.0697487i
$117$	−7.28819	−	12.8270i	−0.673794	−	1.18585i
$118$	−3.08266	+	2.58666i	−0.283782	+	0.238121i
$119$	−27.7726	−	4.89706i	−2.54591	−	0.448913i
$120$	2.07760	+	7.86203i	0.189658	+	0.717702i
$121$	−1.83725			−0.167023
$122$	−1.95913	−	3.39332i	−0.177371	−	0.307216i
$123$	−0.992771	+	3.65462i	−0.0895151	+	0.329526i
$124$	−7.08378	+	1.24906i	−0.636143	+	0.112169i
$125$	6.45006	+	3.72395i	0.576911	+	0.333080i
$126$	−1.93532	+	5.20528i	−0.172412	+	0.463723i
$127$	19.1239	−	3.37206i	1.69697	−	0.299222i	0.760338	−	0.649528i	$-0.225033\pi$
$127$	19.1239	−	3.37206i	1.69697	−	0.299222i	0.936636	+	0.350305i	$0.113922\pi$
$128$	−1.92378	+	10.9103i	−0.170040	+	0.964345i
$129$	3.83749	−	1.01409i	0.337872	−	0.0892852i
$130$	−4.66975	−	3.91839i	−0.409564	−	0.343665i
$131$	−8.60415	−	1.51714i	−0.751748	−	0.132553i	−0.215372	−	0.976532i	$-0.569096\pi$
$131$	−8.60415	−	1.51714i	−0.751748	−	0.132553i	−0.536377	+	0.843979i	$0.680207\pi$
$132$	6.33112	+	9.10845i	0.551053	+	0.792789i
$133$	−16.1526	−	6.74090i	−1.40060	−	0.584510i
$134$			4.94109i			0.426846i
$135$	−1.07370	−	13.9306i	−0.0924098	−	1.19895i
$136$	−12.0767	−	2.12944i	−1.03557	−	0.182598i
$137$	−3.49164	+	9.59321i	−0.298311	+	0.819604i	0.696471	+	0.717585i	$0.254752\pi$
$137$	−3.49164	+	9.59321i	−0.298311	+	0.819604i	−0.994782	+	0.102019i	$0.967470\pi$
$138$	−0.155223	+	1.70643i	−0.0132135	+	0.145261i
$139$	−0.991213	−	0.360772i	−0.0840736	−	0.0306003i	0.299641	−	0.954052i	$-0.403133\pi$
$139$	−0.991213	−	0.360772i	−0.0840736	−	0.0306003i	−0.383715	+	0.923452i	$0.625355\pi$
$140$		−	19.2992i		−	1.63108i
$141$	−5.63314	−	8.10428i	−0.474396	−	0.682503i
$142$	0.0876919	+	0.497325i	0.00735894	+	0.0417346i
$143$	−16.5569	−	6.02621i	−1.38456	−	0.503937i
$144$	2.89595	−	7.78904i	0.241330	−	0.649086i
$145$	2.86140	−	1.65203i	0.237626	−	0.137193i
$146$	1.57333	−	1.32018i	0.130210	−	0.109259i
$147$	9.10836	−	12.9131i	0.751245	−	1.06505i
$148$	0.840769	−	0.148250i	0.0691108	−	0.0121861i
$149$	−9.56694	+	11.4014i	−0.783755	+	0.934042i	−0.999097	−	0.0424963i	$-0.986469\pi$
$149$	−9.56694	+	11.4014i	−0.783755	+	0.934042i	0.215342	+	0.976539i	$0.430913\pi$
$150$	−0.747002	−	1.61648i	−0.0609925	−	0.131985i
$151$	11.9604	−	6.90536i	0.973326	−	0.561950i	0.0730776	−	0.997326i	$-0.476718\pi$
$151$	11.9604	−	6.90536i	0.973326	−	0.561950i	0.900249	+	0.435376i	$0.143385\pi$
$152$	−7.02380	−	2.93122i	−0.569705	−	0.237753i
$153$	19.7489	+	7.34261i	1.59660	+	0.593615i
$154$	2.26843	+	6.23247i	0.182796	+	0.502227i
$155$	10.1680	−	3.70083i	0.816710	−	0.297258i
$156$	3.88979	+	14.7197i	0.311432	+	1.17852i
$157$	2.97763	−	1.08377i	0.237640	−	0.0864941i	−0.220455	−	0.975397i	$-0.570754\pi$
$157$	2.97763	−	1.08377i	0.237640	−	0.0864941i	0.458095	+	0.888903i	$0.348532\pi$
$158$	−1.43483	+	3.94215i	−0.114149	+	0.313621i
$159$	−4.71341	−	2.21772i	−0.373798	−	0.175876i
$160$		−	12.8236i		−	1.01380i
$161$	2.94705	−	8.09695i	0.232260	−	0.638129i
$162$	2.12390	−	3.56426i	0.166869	−	0.280035i
$163$	−0.913014	+	1.58139i	−0.0715128	+	0.123864i	−0.899564	−	0.436788i	$-0.856116\pi$
$163$	−0.913014	+	1.58139i	−0.0715128	+	0.123864i	0.828052	+	0.560652i	$0.189449\pi$
$164$	1.95412	−	3.38463i	0.152591	−	0.264296i
$165$	−11.7585	−	11.8399i	−0.915398	−	0.921732i
$166$	2.39675	+	6.58501i	0.186024	+	0.511096i
$167$	−0.823788	−	4.67193i	−0.0637466	−	0.361525i	−0.999949	−	0.0100645i	$-0.996796\pi$
$167$	−0.823788	−	4.67193i	−0.0637466	−	0.361525i	0.936203	−	0.351460i	$-0.114315\pi$
$168$	6.99955	−	9.92340i	0.540027	−	0.765607i
$169$	−8.56683	−	7.18843i	−0.658987	−	0.552956i
$170$	8.70602			0.667721
$171$	10.9612	+	7.13111i	0.838222	+	0.545329i
$172$	−4.09622			−0.312334
$173$	−4.74859	−	3.98454i	−0.361029	−	0.302939i	0.444172	−	0.895942i	$-0.353498\pi$
$173$	−4.74859	−	3.98454i	−0.361029	−	0.302939i	−0.805201	+	0.593002i	$0.797942\pi$
$174$	0.977137	+	0.0888841i	0.0740766	+	0.00673829i
$175$	1.55499	+	8.81879i	0.117546	+	0.666638i
$176$	−3.39442	−	9.32610i	−0.255864	−	0.702981i
$177$	−14.6172	+	3.86271i	−1.09870	+	0.290339i
$178$	0.437675	−	0.758075i	0.0328051	−	0.0568201i
$179$	1.57339	−	2.72519i	0.117601	−	0.203690i	−0.801216	−	0.598376i	$-0.795813\pi$
$179$	1.57339	−	2.72519i	0.117601	−	0.203690i	0.918816	+	0.394685i	$0.129146\pi$
$180$	−2.60167	+	14.1823i	−0.193917	+	1.05708i
$181$	−1.17638	+	3.23207i	−0.0874394	+	0.240238i	−0.975703	−	0.219096i	$-0.929689\pi$
$181$	−1.17638	+	3.23207i	−0.0874394	+	0.240238i	0.888264	+	0.459333i	$0.151912\pi$
$182$			9.10323i			0.674776i
$183$	−1.23247	−	14.6696i	−0.0911070	−	1.08441i
$184$	1.28150	−	3.52088i	0.0944732	−	0.259563i
$185$	−1.20683	+	0.439249i	−0.0887277	+	0.0322943i
$186$	3.10088	+	0.842348i	0.227368	+	0.0617640i
$187$	23.6461	−	8.60646i	1.72917	−	0.629367i
$188$	3.48365	+	9.57126i	0.254072	+	0.698056i
$189$	−14.9053	+	14.6001i	−1.08420	+	1.06200i
$190$	5.27210	+	1.18349i	0.382478	+	0.0858593i
$191$	8.51271	−	4.91482i	0.615958	−	0.355624i	−0.159335	−	0.987225i	$-0.550935\pi$
$191$	8.51271	−	4.91482i	0.615958	−	0.355624i	0.775294	+	0.631601i	$0.217602\pi$
$192$	−3.33586	+	4.72931i	−0.240745	+	0.341309i
$193$	2.82149	−	3.36253i	0.203096	−	0.242040i	−0.654877	−	0.755736i	$-0.727280\pi$
$193$	2.82149	−	3.36253i	0.203096	−	0.242040i	0.857972	+	0.513696i	$0.171724\pi$
$194$	−4.69951	+	0.828650i	−0.337405	+	0.0594936i
$195$	−9.60756	−	20.7903i	−0.688012	−	1.48883i
$196$	−12.4925	+	10.4825i	−0.892324	+	0.748749i
$197$	−5.16672	+	2.98300i	−0.368113	+	0.212530i	−0.672634	−	0.739975i	$-0.734837\pi$
$197$	−5.16672	+	2.98300i	−0.368113	+	0.212530i	0.304521	+	0.952506i	$0.401504\pi$
$198$	−0.826804	−	4.88580i	−0.0587584	−	0.347219i
$199$	−5.30760	−	1.93181i	−0.376246	−	0.136942i	0.146973	−	0.989140i	$-0.453047\pi$
$199$	−5.30760	−	1.93181i	−0.376246	−	0.136942i	−0.523219	+	0.852198i	$0.675269\pi$
$200$	0.676173	+	3.83477i	0.0478127	+	0.271159i
$201$	−7.90349	+	16.7976i	−0.557469	+	1.18481i
$202$		−	5.34868i		−	0.376332i
$203$	−4.63649	−	1.68754i	−0.325417	−	0.118442i
$204$	−17.7684	−	12.5331i	−1.24404	−	0.877492i
$205$	−2.01079	+	5.52460i	−0.140440	+	0.385855i
$206$	−1.93180	−	0.340629i	−0.134595	−	0.0237327i
$207$	−3.25720	+	5.55285i	−0.226391	+	0.385950i
$208$		−	13.6218i		−	0.944504i
$209$	15.4893	−	1.99739i	1.07142	−	0.138162i
$210$	−3.67043	+	7.80093i	−0.253284	+	0.538315i
$211$	−18.7120	−	3.29943i	−1.28819	−	0.227142i	−0.512734	−	0.858547i	$-0.671367\pi$
$211$	−18.7120	−	3.29943i	−1.28819	−	0.227142i	−0.775453	+	0.631405i	$0.782479\pi$
$212$	4.11807	+	3.45547i	0.282830	+	0.237322i
$213$	−0.497377	+	1.83096i	−0.0340797	+	0.125456i
$214$	−0.817225	+	4.63471i	−0.0558643	+	0.316822i
$215$	6.06833	−	1.07001i	0.413856	−	0.0729741i
$216$	−6.48144	+	6.34874i	−0.441006	+	0.431977i
$217$	−13.9938	−	8.07930i	−0.949958	−	0.548458i
$218$	6.83790	−	1.20571i	0.463121	−	0.0816608i
$219$	7.46036	−	1.97146i	0.504125	−	0.133219i
$220$	8.61029	+	14.9135i	0.580505	+	1.00546i
$221$	34.5377			2.32326
$222$	−0.368042	−	0.0999777i	−0.0247013	−	0.00671006i
$223$	3.50317	+	0.617704i	0.234590	+	0.0413645i	0.289707	−	0.957115i	$-0.406442\pi$
$223$	3.50317	+	0.617704i	0.234590	+	0.0413645i	−0.0551172	+	0.998480i	$0.517553\pi$
$224$	−14.6697	+	12.3093i	−0.980158	+	0.822450i
$225$	0.0461322	−	6.69021i	0.00307548	−	0.446014i
$226$	−0.880939	+	0.320636i	−0.0585992	+	0.0213284i
$227$	14.2517	+	24.6846i	0.945917	+	1.63838i	0.753905	+	0.656983i	$0.228168\pi$
$227$	14.2517	+	24.6846i	0.945917	+	1.63838i	0.192012	+	0.981393i	$0.438499\pi$
$228$	−9.05628	−	10.0051i	−0.599766	−	0.662603i
$229$	−3.73368	+	6.46693i	−0.246729	+	0.427347i	−0.962616	−	0.270869i	$-0.912689\pi$
$229$	−3.73368	+	6.46693i	−0.246729	+	0.427347i	0.715887	+	0.698216i	$0.246022\pi$
$230$	−0.461912	+	2.61964i	−0.0304576	+	0.172734i
$231$	−2.25738	+	24.8162i	−0.148525	+	1.63279i
$232$	−2.01613	−	0.733813i	−0.132366	−	0.0481772i
$233$	−3.34493	+	3.98634i	−0.219134	+	0.261154i	−0.864401	−	0.502804i	$-0.832302\pi$
$233$	−3.34493	+	3.98634i	−0.219134	+	0.261154i	0.645267	+	0.763957i	$0.276746\pi$
$234$	1.22718	−	6.68961i	0.0802232	−	0.437314i
$235$	−7.66104	−	13.2693i	−0.499751	−	0.865594i
$236$	15.6027			1.01565
$237$	−11.1834	+	11.1066i	−0.726443	+	0.721451i
$238$	−8.35685	−	9.95931i	−0.541694	−	0.645566i
$239$	−4.69171	+	2.70876i	−0.303481	+	0.175215i	−0.644006	−	0.765021i	$-0.722729\pi$
$239$	−4.69171	+	2.70876i	−0.303481	+	0.175215i	0.340524	+	0.940236i	$0.389395\pi$
$240$	5.49233	−	11.6731i	0.354528	−	0.753495i
$241$	−3.83553	−	4.57100i	−0.247068	−	0.294444i	0.628230	−	0.778027i	$-0.283780\pi$
$241$	−3.83553	−	4.57100i	−0.247068	−	0.294444i	−0.875298	+	0.483583i	$0.839335\pi$
$242$	−0.648831	−	0.544434i	−0.0417084	−	0.0349975i
$243$	12.9215	−	8.71973i	0.828917	−	0.559371i
$244$	−2.63811	+	14.9615i	−0.168888	+	0.957810i
$245$	15.7688	−	18.7925i	1.00743	−	1.20061i
$246$	−1.43358	+	0.996455i	−0.0914017	+	0.0635317i
$247$	20.9150	+	4.69503i	1.33079	+	0.298738i
$248$	−6.08506	−	3.51321i	−0.386402	−	0.223089i
$249$	−2.38507	+	26.2200i	−0.151147	+	1.66162i
$250$	1.17434	+	3.22648i	0.0742720	+	0.204061i
$251$	−3.69670	−	4.40555i	−0.233333	−	0.278076i	0.636654	−	0.771149i	$-0.280318\pi$
$251$	−3.69670	−	4.40555i	−0.233333	−	0.278076i	−0.869988	+	0.493073i	$0.835873\pi$
$252$	18.7212	−	10.6373i	1.17933	−	0.670085i
$253$	1.33510	+	7.57171i	0.0839369	+	0.476030i
$254$	7.75293	+	4.47616i	0.486462	+	0.280859i
$255$	29.5968	+	13.9256i	1.85342	+	0.872058i
$256$	1.20683	−	1.01265i	0.0754266	−	0.0632905i
$257$	10.2043	−	8.56245i	0.636529	−	0.534111i	−0.266421	−	0.963857i	$-0.585841\pi$
$257$	10.2043	−	8.56245i	0.636529	−	0.534111i	0.902950	+	0.429746i	$0.141397\pi$
$258$	1.65573	+	0.779040i	0.103081	+	0.0485009i
$259$	1.66091	+	0.958926i	0.103204	+	0.0595848i
$260$	4.10430	+	23.2766i	0.254538	+	1.44356i
$261$	3.17968	+	1.86514i	0.196817	+	0.115449i
$262$	−2.58901	−	3.08546i	−0.159950	−	0.190621i
$263$	−9.26200	−	25.4471i	−0.571119	−	1.56914i	−0.802739	−	0.596331i	$-0.796625\pi$
$263$	−9.26200	−	25.4471i	−0.571119	−	1.56914i	0.231620	−	0.972806i	$-0.425597\pi$
$264$	−0.981601	+	10.7911i	−0.0604134	+	0.664147i
$265$	−7.00332	−	4.04337i	−0.430210	−	0.248382i
$266$	−3.70680	−	7.16708i	−0.227278	−	0.439442i
$267$	2.70048	−	1.87706i	0.165267	−	0.114874i
$268$	12.3146	−	14.6759i	0.752233	−	0.896476i
$269$	2.43598	−	13.8151i	0.148524	−	0.842322i	−0.815946	−	0.578129i	$-0.803783\pi$
$269$	2.43598	−	13.8151i	0.148524	−	0.842322i	0.964470	−	0.264193i	$-0.0851057\pi$
$270$	3.74888	−	5.23780i	0.228149	−	0.318762i
$271$	7.78007	+	6.52825i	0.472605	+	0.396563i	0.847744	−	0.530406i	$-0.177960\pi$
$271$	7.78007	+	6.52825i	0.472605	+	0.396563i	−0.375138	+	0.926969i	$0.622405\pi$
$272$	12.5050	+	14.9028i	0.758225	+	0.903618i
$273$	−14.5610	+	30.9471i	−0.881272	+	1.87301i
$274$	−4.07586	+	2.35320i	−0.246231	+	0.142162i
$275$	−5.13609	−	6.12095i	−0.309718	−	0.369107i
$276$	4.71393	−	4.68154i	0.283745	−	0.281796i
$277$	5.68768			0.341740			0.170870	−	0.985294i	$-0.445342\pi$
$277$	5.68768			0.341740			0.170870	+	0.985294i	$0.445342\pi$
$278$	−0.243142	−	0.421135i	−0.0145827	−	0.0252580i
$279$	9.19432	+	7.82362i	0.550450	+	0.468388i
$280$	12.1179	−	14.4416i	0.724184	−	0.863049i
$281$	11.8182	+	4.30148i	0.705016	+	0.256605i	0.669551	−	0.742766i	$-0.266486\pi$
$281$	11.8182	+	4.30148i	0.705016	+	0.256605i	0.0354652	+	0.999371i	$0.488709\pi$
$282$	0.412187	−	4.53133i	0.0245454	−	0.269837i
$283$	0.409204	−	2.32071i	0.0243246	−	0.137952i	−0.970227	−	0.242198i	$-0.922132\pi$
$283$	0.409204	−	2.32071i	0.0243246	−	0.137952i	0.994552	+	0.104246i	$0.0332429\pi$
$284$	0.979012	−	1.69570i	0.0580937	−	0.100621i
$285$	16.0299	+	12.4563i	0.949529	+	0.737848i
$286$	−4.06137	−	7.03450i	−0.240154	−	0.415959i
$287$	8.25005	−	3.00277i	0.486985	−	0.177248i
$288$	12.4395	−	7.06806i	0.733007	−	0.416489i
$289$	−24.7630	+	20.7786i	−1.45665	+	1.22227i
$290$	1.50006	+	0.264501i	0.0880866	+	0.0155320i
$291$	−17.3018	−	4.70000i	−1.01425	−	0.275519i
$292$	−7.96335			−0.466020
$293$	−10.6813	−	18.5005i	−0.624006	−	1.08081i	−0.988732	−	0.149695i	$-0.952171\pi$
$293$	−10.6813	−	18.5005i	−0.624006	−	1.08081i	0.364726	−	0.931115i	$-0.381163\pi$
$294$	7.04321	−	1.86122i	0.410768	−	0.108549i
$295$	−23.1146	+	4.07573i	−1.34578	+	0.237298i
$296$	0.722231	+	0.416980i	0.0419788	+	0.0242365i
$297$	5.00426	−	17.9322i	0.290377	−	1.04053i
$298$	−6.75720	+	1.19148i	−0.391434	+	0.0690204i
$299$	−1.83246	+	10.3924i	−0.105974	+	0.601007i
$300$	−1.80998	+	6.66297i	−0.104499	+	0.384687i
$301$	−7.04899	−	5.91481i	−0.406297	−	0.340924i
$302$	6.27015	+	1.10560i	0.360806	+	0.0636199i
$303$	8.55545	−	18.1833i	0.491498	−	1.04460i
$304$	5.54675	+	10.7246i	0.318128	+	0.615100i
$305$		−	22.8537i		−	1.30860i
$306$	4.79854	+	8.44528i	0.274315	+	0.482784i
$307$	−10.8004	−	1.90439i	−0.616409	−	0.108689i	−0.143279	−	0.989682i	$-0.545765\pi$
$307$	−10.8004	−	1.90439i	−0.616409	−	0.108689i	−0.473130	+	0.880993i	$0.656876\pi$
$308$	8.79539	−	24.1651i	0.501164	−	1.37694i
$309$	−6.02246	−	4.24799i	−0.342606	−	0.241660i
$310$	4.68752	+	1.70612i	0.266233	+	0.0969011i
$311$		−	1.28709i		−	0.0729840i	−0.999334	−	0.0364920i	$-0.988382\pi$
$311$		−	1.28709i		−	0.0729840i	0.999334	−	0.0364920i	$-0.0116183\pi$
$312$	−6.33172	+	13.4571i	−0.358463	+	0.761857i
$313$	2.37807	+	13.4867i	0.134417	+	0.762315i	0.975264	+	0.221043i	$0.0709460\pi$
$313$	2.37807	+	13.4867i	0.134417	+	0.762315i	−0.840848	+	0.541272i	$0.817943\pi$
$314$	1.37271	+	0.499627i	0.0774667	+	0.0281956i
$315$	−24.9558	+	20.6489i	−1.40610	+	1.16343i
$316$	14.0866	−	8.13293i	0.792435	−	0.457513i
$317$	−23.4024	+	19.6369i	−1.31441	+	1.10292i	−0.326949	+	0.945042i	$0.606021\pi$
$317$	−23.4024	+	19.6369i	−1.31441	+	1.10292i	−0.987459	+	0.157877i	$0.949535\pi$
$318$	−1.00738	−	2.17993i	−0.0564911	−	0.122244i
$319$	4.33573	−	0.764506i	0.242754	−	0.0428041i
$320$	−5.77518	+	6.88259i	−0.322842	+	0.384749i
$321$	−10.1916	+	14.4489i	−0.568842	+	0.806458i
$322$	3.44014	−	1.98616i	0.191711	−	0.110685i
$323$	−27.1920	+	14.0636i	−1.51300	+	0.782521i
$324$	−15.1915	+	5.29317i	−0.843972	+	0.294065i
$325$	−3.75092	−	10.3056i	−0.208063	−	0.571650i
$326$	−0.791048	+	0.287918i	−0.0438121	+	0.0159463i
$327$	25.1746	+	6.83862i	1.39216	+	0.378176i
$328$	3.58746	−	1.30573i	0.198084	−	0.0720968i
$329$	−7.82573	+	21.5010i	−0.431447	+	1.18539i
$330$	−0.644039	−	7.66570i	−0.0354532	−	0.421983i
$331$			16.2936i			0.895576i	0.894140	+	0.447788i	$0.147788\pi$
$331$			16.2936i			0.895576i	−0.894140	+	0.447788i	$0.852212\pi$
$332$	9.29290	−	25.5320i	0.510014	−	1.40125i
$333$	−1.09127	−	0.928580i	−0.0598011	−	0.0508859i
$334$	1.09352	−	1.89402i	0.0598345	−	0.103636i
$335$	−14.4097	+	24.9584i	−0.787288	+	1.36362i
$336$	−18.6256	+	4.92195i	−1.01611	+	0.268514i
$337$	−2.12803	−	5.84672i	−0.115921	−	0.318491i	0.868140	−	0.496319i	$-0.165315\pi$
$337$	−2.12803	−	5.84672i	−0.115921	−	0.318491i	−0.984062	+	0.177828i	$0.943093\pi$
$338$	−0.895254	−	5.07724i	−0.0486954	−	0.276165i
$339$	−3.50769	−	0.319073i	−0.190512	−	0.0173297i
$340$	−25.8585	−	21.6978i	−1.40237	−	1.17673i
$341$	14.4182			0.780789
$342$	1.75781	+	5.76651i	0.0950515	+	0.311817i
$343$	−8.52638			−0.460381
$344$	−3.06519	−	2.57200i	−0.165264	−	0.138673i
$345$	−5.76053	+	8.16681i	−0.310136	+	0.439686i
$346$	−0.496239	−	2.81431i	−0.0266780	−	0.151298i
$347$	4.93948	+	13.5711i	0.265165	+	0.728535i	0.998799	+	0.0489907i	$0.0156005\pi$
$347$	4.93948	+	13.5711i	0.265165	+	0.728535i	−0.733634	+	0.679545i	$0.762177\pi$
$348$	−2.68075	−	2.69930i	−0.143703	−	0.144698i
$349$	17.0912	−	29.6028i	0.914870	−	1.58460i	0.107778	−	0.994175i	$-0.465626\pi$
$349$	17.0912	−	29.6028i	0.914870	−	1.58460i	0.807092	−	0.590426i	$-0.201040\pi$
$350$	−2.06413	+	3.57518i	−0.110332	+	0.191101i
$351$	14.8722	−	20.7789i	0.793820	−	1.10910i
$352$	5.84420	−	16.0568i	0.311497	−	0.855831i
$353$		−	10.0921i		−	0.537148i	−0.963259	−	0.268574i	$-0.913448\pi$
$353$		−	10.0921i		−	0.537148i	0.963259	−	0.268574i	$-0.0865525\pi$
$354$	−6.30677	−	2.96741i	−0.335201	−	0.157716i
$355$	−1.00740	+	2.76782i	−0.0534675	+	0.146901i
$356$	−3.18931	+	1.16081i	−0.169033	+	0.0615230i
$357$	−12.4795	−	47.2246i	−0.660483	−	2.49939i
$358$	1.36321	−	0.496167i	0.0720477	−	0.0262232i
$359$	1.69891	+	4.66772i	0.0896652	+	0.246353i	0.976417	−	0.215893i	$-0.0692661\pi$
$359$	1.69891	+	4.66772i	0.0896652	+	0.246353i	−0.886752	+	0.462246i	$0.847044\pi$
$360$	−10.8518	+	8.97897i	−0.571941	+	0.473233i
$361$	−18.3784	+	4.82005i	−0.967286	+	0.253687i
$362$	−1.37320	+	0.792820i	−0.0721740	+	0.0416697i
$363$	−1.33491	−	2.88868i	−0.0700645	−	0.151616i
$364$	22.6878	−	27.0382i	1.18916	−	1.41719i
$365$	11.7973	−	2.08018i	0.617497	−	0.108881i
$366$	3.91180	−	5.54583i	0.204473	−	0.289885i
$367$	24.8887	−	20.8841i	1.29918	−	1.09014i	0.308895	−	0.951096i	$-0.400041\pi$
$367$	24.8887	−	20.8841i	1.29918	−	1.09014i	0.990286	−	0.139046i	$-0.0444036\pi$
$368$	−5.14773	+	2.97204i	−0.268344	+	0.154928i
$369$	−6.46744	+	1.09446i	−0.336682	+	0.0569752i
$370$	−0.556359	−	0.202498i	−0.0289237	−	0.0105274i
$371$	2.09700	+	11.8927i	0.108871	+	0.617438i
$372$	−7.11082	−	10.2302i	−0.368679	−	0.530411i
$373$			20.4879i			1.06082i	0.847740	+	0.530412i	$0.177963\pi$
$373$			20.4879i			1.06082i	−0.847740	+	0.530412i	$0.822037\pi$
$374$	10.9011	+	3.96766i	0.563680	+	0.205163i
$375$	−1.16862	+	12.8471i	−0.0603473	+	0.663421i
$376$	−3.40295	+	9.34952i	−0.175494	+	0.482165i
$377$	5.95090	+	1.04930i	0.306487	+	0.0540419i
$378$	−9.59034	+	0.739180i	−0.493274	+	0.0380193i
$379$		−	32.7082i		−	1.68011i	−0.542504	−	0.840053i	$-0.682524\pi$
$379$		−	32.7082i		−	1.68011i	0.542504	−	0.840053i	$-0.317476\pi$
$380$	−12.7095	−	16.6547i	−0.651984	−	0.854369i
$381$	19.1969	+	27.6182i	0.983487	+	1.41492i
$382$	4.46271	+	0.786896i	0.228332	+	0.0402611i
$383$	−7.62881	−	6.40133i	−0.389814	−	0.327093i	0.426727	−	0.904381i	$-0.359667\pi$
$383$	−7.62881	−	6.40133i	−0.389814	−	0.327093i	−0.816541	+	0.577288i	$0.804111\pi$
$384$	−18.5519	+	4.90248i	−0.946724	+	0.250179i
$385$	−6.71750	+	38.0968i	−0.342355	+	1.94159i
$386$	1.99284	−	0.351392i	0.101433	−	0.0178854i
$387$	4.38268	+	5.29682i	0.222784	+	0.269252i
$388$	16.0236	+	9.25124i	0.813476	+	0.469660i
$389$	14.3615	−	2.53232i	0.728157	−	0.128394i	0.202733	−	0.979234i	$-0.435018\pi$
$389$	14.3615	−	2.53232i	0.728157	−	0.128394i	0.525424	+	0.850840i	$0.323907\pi$
$390$	2.76787	−	10.1892i	0.140157	−	0.515950i
$391$	−7.53553	−	13.0519i	−0.381088	−	0.660064i
$392$	−15.9300			−0.804588
$393$	−3.86622	−	14.6305i	−0.195025	−	0.738012i
$394$	−2.70860	−	0.477600i	−0.136457	−	0.0240611i
$395$	−18.7441	+	15.7282i	−0.943118	+	0.791370i
$396$	−9.72102	+	16.5723i	−0.488500	+	0.832792i
$397$	−9.05656	+	3.29632i	−0.454536	+	0.165437i	−0.559134	−	0.829077i	$-0.688866\pi$
$397$	−9.05656	+	3.29632i	−0.454536	+	0.165437i	0.104599	+	0.994515i	$0.466644\pi$
$398$	−1.30194	−	2.25503i	−0.0652605	−	0.113035i
$399$	−1.13750	−	30.2942i	−0.0569465	−	1.51661i
$400$	3.08871	−	5.34980i	0.154435	−	0.267490i
$401$	4.89142	−	27.7406i	0.244266	−	1.38530i	−0.577926	−	0.816089i	$-0.696138\pi$
$401$	4.89142	−	27.7406i	0.244266	−	1.38530i	0.822192	−	0.569211i	$-0.192751\pi$
$402$	−7.76881	+	3.59010i	−0.387473	+	0.179058i
$403$	18.5959	+	6.76836i	0.926329	+	0.337156i
$404$	−13.3304	+	15.8866i	−0.663213	+	0.790386i
$405$	21.1227	−	11.8098i	1.04959	−	0.586835i
$406$	−1.13732	−	1.96990i	−0.0564443	−	0.0977644i
$407$	−1.71129			−0.0848253
$408$	−5.42658	−	20.5352i	−0.268656	−	1.01664i
$409$	9.96645	+	11.8776i	0.492809	+	0.587307i	0.953930	−	0.300030i	$-0.0969968\pi$
$409$	9.96645	+	11.8776i	0.492809	+	0.587307i	−0.461120	+	0.887338i	$0.652552\pi$
$410$	−2.34723	+	1.35517i	−0.115921	+	0.0669273i
$411$	−17.6202	+	1.48037i	−0.869142	+	0.0730215i
$412$	4.88886	+	5.82632i	0.240857	+	0.287042i
$413$	26.8500	+	22.5298i	1.32120	+	1.10862i
$414$	−2.79577	+	0.995801i	−0.137405	+	0.0489409i
$415$	−7.09747	+	40.2518i	−0.348401	+	1.97588i
$416$	15.0752	−	17.9659i	0.739120	−	0.880849i
$417$	−0.152959	−	1.82060i	−0.00749042	−	0.0891551i
$418$	6.06199	+	3.88457i	0.296502	+	0.190001i
$419$	−31.9563	−	18.4500i	−1.56117	−	0.901341i	−0.997139	−	0.0755865i	$-0.975917\pi$
$419$	−31.9563	−	18.4500i	−1.56117	−	0.901341i	−0.564029	−	0.825755i	$-0.690750\pi$
$420$	30.3439	−	14.0224i	1.48063	−	0.684225i
$421$	−5.38378	−	14.7918i	−0.262389	−	0.720908i	−0.999005	−	0.0445970i	$-0.985800\pi$
$421$	−5.38378	−	14.7918i	−0.262389	−	0.720908i	0.736616	−	0.676311i	$-0.236423\pi$
$422$	−5.63049	−	6.71016i	−0.274088	−	0.326645i
$423$	8.64932	−	14.7453i	0.420544	−	0.716941i
$424$	0.911863	+	5.17143i	0.0442840	+	0.251147i
$425$	13.5643	+	7.83133i	0.657964	+	0.379876i
$426$	−0.718222	+	0.499223i	−0.0347980	+	0.0241874i
$427$	−26.1437	+	21.9371i	−1.26518	+	1.06161i
$428$	13.9783	−	11.7292i	0.675666	−	0.566951i
$429$	−2.55497	−	30.4107i	−0.123355	−	1.46824i
$430$	2.46013	+	1.42036i	0.118638	+	0.0684957i
$431$	−5.03464	−	28.5529i	−0.242510	−	1.37534i	−0.826204	−	0.563371i	$-0.809504\pi$
$431$	−5.03464	−	28.5529i	−0.242510	−	1.37534i	0.583694	−	0.811974i	$-0.301607\pi$
$432$	14.3507	−	1.10609i	0.690450	−	0.0532168i
$433$	18.4759	+	22.0187i	0.887894	+	1.05815i	0.997936	+	0.0642239i	$0.0204572\pi$
$433$	18.4759	+	22.0187i	0.887894	+	1.05815i	−0.110041	+	0.993927i	$0.535098\pi$
$434$	−2.54780	−	7.00002i	−0.122298	−	0.336012i
$435$	4.67649	+	3.29860i	0.224221	+	0.158156i
$436$	−23.3148	−	13.4608i	−1.11657	−	0.644655i
$437$	−2.78902	−	8.92822i	−0.133417	−	0.427095i
$438$	3.21886	+	1.51451i	0.153803	+	0.0723661i
$439$	−12.4493	+	14.8366i	−0.594175	+	0.708110i	−0.976403	−	0.215958i	$-0.930713\pi$
$439$	−12.4493	+	14.8366i	−0.594175	+	0.708110i	0.382228	+	0.924068i	$0.375157\pi$
$440$	−2.92104	+	16.5661i	−0.139255	+	0.789756i
$441$	26.9210	+	4.93854i	1.28195	+	0.235169i
$442$	12.1971	+	10.2346i	0.580158	+	0.486811i
$443$	12.0409	+	14.3497i	0.572079	+	0.681777i	0.972056	−	0.234748i	$-0.0754265\pi$
$443$	12.0409	+	14.3497i	0.572079	+	0.681777i	−0.399977	+	0.916525i	$0.630982\pi$
$444$	0.843978	+	1.21421i	0.0400534	+	0.0576240i
$445$	4.42156	−	2.55279i	0.209602	−	0.121014i
$446$	1.05411	+	1.25624i	0.0499137	+	0.0594848i
$447$	−24.8775	−	6.75791i	−1.17666	−	0.319638i
$448$	13.4170			0.633892
$449$	−4.73186	−	8.19582i	−0.223310	−	0.386785i	0.732501	−	0.680766i	$-0.238353\pi$
$449$	−4.73186	−	8.19582i	−0.223310	−	0.386785i	−0.955811	+	0.293981i	$0.905020\pi$
$450$	1.99881	−	2.34900i	0.0942248	−	0.110733i
$451$	−5.03554	+	6.00112i	−0.237114	+	0.282582i
$452$	3.41566	+	1.24320i	0.160659	+	0.0584752i
$453$	19.5474	+	13.7879i	0.918417	+	0.647813i
$454$	−2.28179	+	12.9407i	−0.107090	+	0.607336i
$455$	−26.5478	+	45.9821i	−1.24458	+	2.15568i
$456$	−0.494634	−	13.1732i	−0.0231633	−	0.616891i
$457$	−4.84785	−	8.39673i	−0.226773	−	0.392782i	0.730077	−	0.683365i	$-0.239484\pi$
$457$	−4.84785	−	8.39673i	−0.226773	−	0.392782i	−0.956850	+	0.290583i	$0.906151\pi$
$458$	−3.23492	+	1.17741i	−0.151158	+	0.0550169i
$459$	2.80446	+	36.3859i	0.130901	+	1.69835i
$460$	7.90082	−	6.62958i	0.368378	−	0.309106i
$461$	−36.1462	−	6.37354i	−1.68349	−	0.296846i	−0.751612	−	0.659605i	$-0.770723\pi$
$461$	−36.1462	−	6.37354i	−1.68349	−	0.296846i	−0.931883	+	0.362760i	$0.881835\pi$
$462$	−8.15102	+	8.09501i	−0.379220	+	0.376614i
$463$	−5.72670			−0.266142			−0.133071	−	0.991106i	$-0.542484\pi$
$463$	−5.72670			−0.266142			−0.133071	+	0.991106i	$0.542484\pi$
$464$	1.70186	+	2.94770i	0.0790067	+	0.136844i
$465$	13.2066	+	13.2980i	0.612441	+	0.616679i
$466$	−2.36255	+	0.416581i	−0.109443	+	0.0192978i
$467$	−17.8988	−	10.3339i	−0.828258	−	0.478195i	0.0249981	−	0.999687i	$-0.492042\pi$
$467$	−17.8988	−	10.3339i	−0.828258	−	0.478195i	−0.853256	+	0.521493i	$0.825375\pi$
$468$	−20.3173	+	16.8109i	−0.939168	+	0.777083i
$469$	42.3832	−	7.47330i	1.95707	−	0.345085i
$470$	1.22658	−	6.95631i	0.0565781	−	0.320871i
$471$	3.86748	+	3.89424i	0.178204	+	0.179437i
$472$	11.6755	+	9.79690i	0.537408	+	0.450939i
$473$	8.08597	+	1.42577i	0.371793	+	0.0655572i
$474$	−7.24071	+	0.608333i	−0.332577	+	0.0279416i
$475$	7.14953	+	6.58633i	0.328043	+	0.302202i
$476$			50.4086i			2.31047i
$477$	0.0622123	−	9.02218i	0.00284851	−	0.413097i
$478$	−2.45958	−	0.433691i	−0.112499	−	0.0198366i
$479$	3.98266	−	10.9423i	0.181973	−	0.499966i	−0.814845	−	0.579679i	$-0.803178\pi$
$479$	3.98266	−	10.9423i	0.181973	−	0.499966i	0.996818	+	0.0797130i	$0.0254004\pi$
$480$	20.1624	−	9.31738i	0.920282	−	0.425278i
$481$	−2.20714	−	0.803332i	−0.100637	−	0.0366288i
$482$		−	2.75085i		−	0.125298i
$483$	14.8720	−	1.24948i	0.676698	−	0.0568532i
$484$	0.570265	+	3.23413i	0.0259211	+	0.147006i
$485$	−26.1547	−	9.51953i	−1.18762	−	0.432260i
$486$	7.14722	+	0.749650i	0.324204	+	0.0340048i
$487$	15.6688	−	9.04638i	0.710021	−	0.409931i	−0.101048	−	0.994882i	$-0.532220\pi$
$487$	15.6688	−	9.04638i	0.710021	−	0.409931i	0.811069	+	0.584951i	$0.198886\pi$
$488$	−11.3683	+	9.53917i	−0.514620	+	0.431818i
$489$	−3.14977	−	0.286515i	−0.142437	−	0.0129567i
$490$	11.1376	−	1.96386i	0.503146	−	0.0887182i
$491$	14.9636	−	17.8330i	0.675300	−	0.804791i	−0.314195	−	0.949358i	$-0.601735\pi$
$491$	14.9636	−	17.8330i	0.675300	−	0.804791i	0.989495	+	0.144567i	$0.0461791\pi$
$492$	6.74144	+	0.613227i	0.303927	+	0.0276464i
$493$	−7.47381	+	4.31501i	−0.336603	+	0.194338i
$494$	5.99493	+	7.85584i	0.269725	+	0.353451i
$495$	10.0722	−	27.0903i	0.452710	−	1.21762i
$496$	3.81246	+	10.4746i	0.171184	+	0.470325i
$497$	4.13327	−	1.50439i	0.185402	−	0.0674810i
$498$	−8.61208	+	8.55290i	−0.385917	+	0.383265i
$499$	6.66620	−	2.42630i	0.298420	−	0.108616i	−0.188471	−	0.982079i	$-0.560353\pi$
$499$	6.66620	−	2.42630i	0.298420	−	0.108616i	0.486891	+	0.873463i	$0.338131\pi$
$500$	4.55327	−	12.5100i	0.203629	−	0.559465i
$501$	6.74706	−	4.68976i	0.301437	−	0.209523i
$502$		−	2.65128i		−	0.118333i
$503$	−6.92989	+	19.0397i	−0.308989	+	0.848939i	0.683866	+	0.729608i	$0.260297\pi$
$503$	−6.92989	+	19.0397i	−0.308989	+	0.848939i	−0.992854	+	0.119331i	$0.961925\pi$
$504$	20.6882	+	3.79515i	0.921524	+	0.169049i
$505$	15.5984	−	27.0172i	0.694120	−	1.20225i
$506$	−1.77224	+	3.06961i	−0.0787857	+	0.136461i
$507$	5.07777	−	18.6925i	0.225512	−	0.830162i
$508$	−11.8718	−	32.6175i	−0.526725	−	1.44717i
$509$	−7.10496	−	40.2942i	−0.314922	−	1.78601i	−0.572657	−	0.819795i	$-0.694087\pi$
$509$	−7.10496	−	40.2942i	−0.314922	−	1.78601i	0.257735	−	0.966216i	$-0.417024\pi$
$510$	6.32562	+	13.6883i	0.280103	+	0.606130i
$511$	−13.7038	−	11.4988i	−0.606219	−	0.508678i
$512$	22.8835			1.01132
$513$	−3.24797	+	22.4154i	−0.143401	+	0.989665i
$514$	6.14102			0.270869
$515$	−8.76452	−	7.35430i	−0.386211	−	0.324069i
$516$	−2.97623	−	6.44043i	−0.131021	−	0.283524i
$517$	−3.54528	−	20.1063i	−0.155921	−	0.884274i
$518$	0.302396	+	0.830827i	0.0132865	+	0.0365045i
$519$	2.81461	−	10.3612i	0.123548	−	0.454808i
$520$	−11.5441	+	19.9949i	−0.506241	+	0.876835i
$521$	−11.7351	+	20.3257i	−0.514122	+	0.890486i	0.485744	+	0.874101i	$0.338549\pi$
$521$	−11.7351	+	20.3257i	−0.514122	+	0.890486i	−0.999866	+	0.0163842i	$0.994785\pi$
$522$	0.570217	+	1.60092i	0.0249577	+	0.0700704i
$523$	−11.1640	+	30.6728i	−0.488168	+	1.34123i	0.414170	+	0.910200i	$0.364072\pi$
$523$	−11.1640	+	30.6728i	−0.488168	+	1.34123i	−0.902338	+	0.431030i	$0.858150\pi$
$524$			15.6169i			0.682228i
$525$	−12.7358	+	8.85244i	−0.555837	+	0.386352i
$526$	4.26987	−	11.7314i	0.186175	−	0.511512i
$527$	−26.5581	+	9.66638i	−1.15689	+	0.421074i
$528$	12.1970	−	12.1132i	0.530805	−	0.527158i
$529$	−17.2858	+	6.29152i	−0.751557	+	0.273544i
$530$	−1.27507	−	3.50323i	−0.0553856	−	0.152171i
$531$	−16.6939	−	20.1759i	−0.724452	−	0.875558i
$532$	−6.85250	+	30.5259i	−0.297093	+	1.32347i
$533$	−9.31172	+	5.37612i	−0.403335	+	0.232866i
$534$	1.50992	+	0.137348i	0.0653405	+	0.00594362i
$535$	−17.6442	+	21.0275i	−0.762825	+	0.909099i
$536$	18.4299	−	3.24970i	0.796052	−	0.140365i
$537$	5.42797	+	0.493749i	0.234234	+	0.0213068i
$538$	4.95412	−	4.15700i	0.213587	−	0.179221i
$539$	28.3090	−	16.3442i	1.21935	−	0.703995i
$540$	−24.1889	+	6.21398i	−1.04092	+	0.267407i
$541$	−12.0005	−	4.36782i	−0.515941	−	0.187787i	0.0709091	−	0.997483i	$-0.477410\pi$
$541$	−12.0005	−	4.36782i	−0.515941	−	0.187787i	−0.586850	+	0.809696i	$0.699632\pi$
$542$	0.813035	+	4.61095i	0.0349229	+	0.198057i
$543$	−5.93646	+	0.498756i	−0.254758	+	0.0214037i
$544$			33.4946i			1.43607i
$545$	38.0558	+	13.8512i	1.63013	+	0.593319i
$546$	−14.3129	+	6.61422i	−0.612534	+	0.283063i
$547$	−11.1278	+	30.5733i	−0.475789	+	1.30722i	0.437248	+	0.899341i	$0.355953\pi$
$547$	−11.1278	+	30.5733i	−0.475789	+	1.30722i	−0.913037	+	0.407878i	$0.866269\pi$
$548$	17.9708	+	3.16875i	0.767677	+	0.135362i
$549$	22.1692	−	12.5964i	0.946160	−	0.537601i
$550$		−	3.68362i		−	0.157070i
$551$	−5.11249	+	1.59705i	−0.217799	+	0.0680368i
$552$	6.46694	−	0.543324i	0.275251	−	0.0231254i
$553$	35.9847	+	6.34508i	1.53023	+	0.269820i
$554$	2.00863	+	1.68544i	0.0853384	+	0.0716074i
$555$	−1.56748	−	1.57833i	−0.0665359	−	0.0669963i
$556$	−0.327409	+	1.85683i	−0.0138852	+	0.0787470i
$557$	−30.4300	+	5.36562i	−1.28936	+	0.227349i	−0.775949	−	0.630795i	$-0.782729\pi$
$557$	−30.4300	+	5.36562i	−1.28936	+	0.227349i	−0.513409	+	0.858144i	$0.671618\pi$
$558$	0.928627	+	5.48751i	0.0393119	+	0.232305i
$559$	9.75960	+	5.63471i	0.412787	+	0.238323i
$560$	−29.4531	+	5.19338i	−1.24462	+	0.219460i
$561$	30.7126	+	30.9251i	1.29669	+	1.30566i
$562$	2.89899	+	5.02119i	0.122286	+	0.211806i
$563$	−23.5131			−0.990960			−0.495480	−	0.868619i	$-0.665008\pi$
$563$	−23.5131			−0.990960			−0.495480	+	0.868619i	$0.665008\pi$
$564$	−12.5176	+	12.4316i	−0.527086	+	0.523464i
$565$	−5.38486	−	0.949497i	−0.226543	−	0.0399456i
$566$	0.832210	−	0.698307i	0.0349804	−	0.0293521i
$567$	−33.7855	−	12.8273i	−1.41886	−	0.538694i
$568$	1.79732	−	0.654169i	0.0754137	−	0.0274483i
$569$	1.32667	+	2.29785i	0.0556167	+	0.0963310i	0.892493	−	0.451061i	$-0.148954\pi$
$569$	1.32667	+	2.29785i	0.0556167	+	0.0963310i	−0.836877	+	0.547392i	$0.815621\pi$
$570$	1.96982	+	9.14915i	0.0825067	+	0.383216i
$571$	16.1864	−	28.0356i	0.677379	−	1.17326i	−0.298388	−	0.954445i	$-0.596449\pi$
$571$	16.1864	−	28.0356i	0.677379	−	1.17326i	0.975767	−	0.218811i	$-0.0702177\pi$
$572$	−5.46893	+	31.0158i	−0.228667	+	1.29684i
$573$	13.9127	+	9.81341i	0.581210	+	0.409961i
$574$	3.80335	+	1.38431i	0.158749	+	0.0577799i
$575$	−3.07612	+	3.66598i	−0.128283	+	0.152882i
$576$	−9.85960	−	1.80870i	−0.410817	−	0.0753625i
$577$	16.7591	+	29.0276i	0.697691	+	1.20844i	0.969265	+	0.246019i	$0.0791226\pi$
$577$	16.7591	+	29.0276i	0.697691	+	1.20844i	−0.271574	+	0.962418i	$0.587544\pi$
$578$	−14.9025			−0.619862
$579$	7.33689	+	1.99305i	0.304911	+	0.0828284i
$580$	−3.79624	−	4.52418i	−0.157630	−	0.187856i
$581$	52.8591	−	30.5182i	2.19297	−	1.26611i
$582$	−4.71744	−	6.78689i	−0.195544	−	0.281325i
$583$	−6.92634	−	8.25449i	−0.286860	−	0.341866i
$584$	−5.95896	−	5.00016i	−0.246583	−	0.206908i
$585$	25.7077	−	30.2117i	1.06288	−	1.24910i
$586$	1.71014	−	9.69871i	0.0706454	−	0.400650i
$587$	28.0469	−	33.4250i	1.15762	−	1.37960i	0.245640	−	0.969361i	$-0.421002\pi$
$587$	28.0469	−	33.4250i	1.15762	−	1.37960i	0.911979	−	0.410236i	$-0.134554\pi$
$588$	−25.5583	−	12.0255i	−1.05401	−	0.495922i
$589$	−17.3968	+	2.24337i	−0.716825	+	0.0924365i
$590$	−9.37077	−	5.41022i	−0.385788	−	0.222735i
$591$	−8.44417	−	5.95616i	−0.347347	−	0.245004i
$592$	−0.452498	−	1.24323i	−0.0185975	−	0.0510963i
$593$	14.5287	+	17.3146i	0.596621	+	0.711025i	0.976864	−	0.213861i	$-0.0686040\pi$
$593$	14.5287	+	17.3146i	0.596621	+	0.711025i	−0.380243	+	0.924887i	$0.624160\pi$
$594$	7.08114	−	4.84990i	0.290543	−	0.198994i
$595$	−13.1677	−	74.6775i	−0.539821	−	3.06148i
$596$	23.0396	+	13.3019i	0.943739	+	0.544868i
$597$	−0.819041	−	9.74868i	−0.0335211	−	0.398987i
$598$	−3.72673	+	3.12710i	−0.152397	+	0.127876i
$599$	−10.4777	+	8.79184i	−0.428108	+	0.359225i	−0.831237	−	0.555918i	$-0.812367\pi$
$599$	−10.4777	+	8.79184i	−0.428108	+	0.359225i	0.403130	+	0.915143i	$0.367922\pi$
$600$	−5.53806	+	3.84940i	−0.226090	+	0.157151i
$601$	−2.81916	−	1.62764i	−0.114996	−	0.0663928i	0.441399	−	0.897311i	$-0.354482\pi$
$601$	−2.81916	−	1.62764i	−0.114996	−	0.0663928i	−0.556395	+	0.830918i	$0.687816\pi$
$602$	−0.736637	−	4.17767i	−0.0300231	−	0.170269i
$603$	−32.1532	−	0.221712i	−1.30938	−	0.00902881i
$604$	−15.8680	−	18.9108i	−0.645660	−	0.769468i
$605$	−1.68963	−	4.64223i	−0.0686933	−	0.188733i
$606$	8.40966	−	3.88625i	0.341619	−	0.157868i
$607$	34.5135	+	19.9264i	1.40086	+	0.808787i	0.994481	−	0.104918i	$-0.0334580\pi$
$607$	34.5135	+	19.9264i	1.40086	+	0.808787i	0.406379	+	0.913705i	$0.366791\pi$
$608$	−4.55322	+	20.2833i	−0.184658	+	0.822596i
$609$	−0.715478	−	8.51601i	−0.0289926	−	0.345086i
$610$	6.77227	−	8.07087i	0.274201	−	0.326780i
$611$	4.86600	−	27.5964i	0.196857	−	1.11643i
$612$	6.79543	−	37.0433i	0.274689	−	1.49739i
$613$	14.7663	+	12.3904i	0.596405	+	0.500443i	0.890288	−	0.455398i	$-0.150503\pi$
$613$	14.7663	+	12.3904i	0.596405	+	0.500443i	−0.293883	+	0.955841i	$0.594948\pi$
$614$	−3.24985	−	3.87302i	−0.131153	−	0.156303i
$615$	−10.1473	+	0.852528i	−0.409177	+	0.0343772i
$616$	21.7548	−	12.5601i	0.876524	−	0.506061i
$617$	10.5837	+	12.6132i	0.426084	+	0.507788i	0.935788	−	0.352562i	$-0.114690\pi$
$617$	10.5837	+	12.6132i	0.426084	+	0.507788i	−0.509704	+	0.860350i	$0.670245\pi$
$618$	−0.868042	−	3.28484i	−0.0349178	−	0.132136i
$619$	25.6956			1.03279			0.516397	−	0.856350i	$-0.327273\pi$
$619$	25.6956			1.03279			0.516397	+	0.856350i	$0.327273\pi$
$620$	−9.67067	−	16.7501i	−0.388384	−	0.672700i
$621$	−11.0973	−	1.08665i	−0.445318	−	0.0436059i
$622$	0.381404	−	0.454540i	0.0152929	−	0.0182254i
$623$	−7.16450	−	2.60767i	−0.287040	−	0.104474i
$624$	21.4174	−	9.89734i	0.857382	−	0.396211i
$625$	−5.41386	+	30.7035i	−0.216554	+	1.22814i
$626$	−3.15671	+	5.46758i	−0.126168	+	0.218529i
$627$	14.3947	+	22.9023i	0.574868	+	0.914631i
$628$	−2.83200	−	4.90517i	−0.113009	−	0.195738i
$629$	3.15217	−	1.14730i	0.125685	−	0.0457457i
$630$	−14.9321	−	0.102964i	−0.594911	−	0.00410220i
$631$	−2.79689	+	2.34687i	−0.111342	+	0.0934274i	−0.696759	−	0.717305i	$-0.745375\pi$
$631$	−2.79689	+	2.34687i	−0.111342	+	0.0934274i	0.585417	+	0.810733i	$0.300931\pi$
$632$	15.6476	+	2.75910i	0.622429	+	0.109751i
$633$	−8.40812	−	31.8179i	−0.334193	−	1.26465i
$634$	−14.0837			−0.559334
$635$	26.1077	+	45.2198i	1.03605	+	1.79449i
$636$	−2.44088	+	8.98545i	−0.0967871	+	0.356296i
$637$	44.1841	−	7.79085i	1.75064	−	0.308685i
$638$	1.75772	+	1.01482i	0.0695890	+	0.0401772i
$639$	−3.24018	+	0.548322i	−0.128180	+	0.0216913i
$640$	−29.3366	+	5.17284i	−1.15963	+	0.204474i
$641$	−2.72716	+	15.4665i	−0.107717	+	0.610891i	0.882384	+	0.470530i	$0.155937\pi$
$641$	−2.72716	+	15.4665i	−0.107717	+	0.610891i	−0.990100	+	0.140361i	$0.955174\pi$
$642$	−7.88087	+	2.08258i	−0.311033	+	0.0821928i
$643$	−19.4965	−	16.3595i	−0.768869	−	0.645157i	0.171550	−	0.985175i	$-0.445122\pi$
$643$	−19.4965	−	16.3595i	−0.768869	−	0.645157i	−0.940419	+	0.340018i	$0.889567\pi$
$644$	−15.1679	−	2.67451i	−0.597699	−	0.105391i
$645$	6.09148	+	8.76369i	0.239852	+	0.345070i
$646$	−13.7704	−	3.09121i	−0.541791	−	0.121622i
$647$		−	44.6229i		−	1.75431i	−0.480211	−	0.877153i	$-0.659440\pi$
$647$		−	44.6229i		−	1.75431i	0.480211	−	0.877153i	$-0.340560\pi$
$648$	−14.6913	−	5.57782i	−0.577129	−	0.219117i
$649$	−30.7999	−	5.43085i	−1.20900	−	0.213180i
$650$	1.72921	−	4.75096i	0.0678251	−	0.186348i
$651$	2.53538	−	27.8724i	0.0993695	−	1.09241i
$652$	3.06713	+	1.11634i	0.120118	+	0.0437194i
$653$			16.0521i			0.628168i	0.949395	+	0.314084i	$0.101697\pi$
$653$			16.0521i			0.628168i	−0.949395	+	0.314084i	$0.898303\pi$
$654$	6.86400	+	9.87509i	0.268404	+	0.386147i
$655$	−4.07943	−	23.1356i	−0.159397	−	0.903983i
$656$	−5.69123	−	2.07144i	−0.222205	−	0.0808761i
$657$	8.52024	+	10.2974i	0.332406	+	0.401740i
$658$	−9.13511	+	5.27416i	−0.356124	+	0.205608i
$659$	1.86291	−	1.56317i	0.0725686	−	0.0608923i	−0.605782	−	0.795631i	$-0.707140\pi$
$659$	1.86291	−	1.56317i	0.0725686	−	0.0608923i	0.678350	+	0.734739i	$0.262695\pi$
$660$	−17.1921	+	24.3736i	−0.669203	+	0.948743i
$661$	−44.6104	+	7.86602i	−1.73514	+	0.305953i	−0.949742	−	0.313033i	$-0.898655\pi$
$661$	−44.6104	+	7.86602i	−1.73514	+	0.305953i	−0.785402	+	0.618985i	$0.787544\pi$
$662$	−4.82829	+	5.75413i	−0.187657	+	0.223641i
$663$	25.0944	+	54.3032i	0.974587	+	2.10896i
$664$	22.9853	−	13.2706i	0.892003	−	0.514998i
$665$	2.17766	−	47.0124i	0.0844461	−	1.82306i
$666$	−0.110218	−	0.651308i	−0.00427086	−	0.0252377i
$667$	−0.901847	−	2.47780i	−0.0349197	−	0.0959410i
$668$	−7.96837	+	2.90025i	−0.308306	+	0.112214i
$669$	1.57413	+	5.95680i	0.0608593	+	0.230303i
$670$	−12.4848	+	4.54410i	−0.482330	+	0.175554i
$671$	10.4153	−	28.6158i	0.402078	−	1.10470i
$672$	−30.0124	−	14.1212i	−1.15775	−	0.544737i
$673$			5.67199i			0.218639i	0.994007	+	0.109320i	$0.0348672\pi$
$673$			5.67199i			0.218639i	−0.994007	+	0.109320i	$0.965133\pi$
$674$	0.981043	−	2.69539i	0.0377884	−	0.103823i
$675$	10.5524	−	4.78844i	0.406164	−	0.184307i
$676$	−9.99483	+	17.3115i	−0.384416	+	0.665829i
$677$	−18.4733	+	31.9968i	−0.709988	+	1.22974i	0.254873	+	0.966975i	$0.417966\pi$
$677$	−18.4733	+	31.9968i	−0.709988	+	1.22974i	−0.964861	+	0.262761i	$0.915367\pi$
$678$	−1.14420	−	1.15212i	−0.0439429	−	0.0442469i
$679$	14.2158	+	39.0576i	0.545552	+	1.49889i
$680$	−5.72584	−	32.4728i	−0.219576	−	1.24528i
$681$	−28.4563	+	40.3431i	−1.09045	+	1.54595i
$682$	5.09184	+	4.27256i	0.194977	+	0.163605i
$683$	32.6619			1.24977			0.624886	−	0.780716i	$-0.285146\pi$
$683$	32.6619			1.24977			0.624886	+	0.780716i	$0.285146\pi$
$684$	9.15074	−	21.5085i	0.349887	−	0.822400i
$685$	−27.4506			−1.04883
$686$	−3.01112	−	2.52663i	−0.114965	−	0.0964673i
$687$	−12.8807	−	1.17168i	−0.491429	−	0.0447022i
$688$	1.10228	+	6.25136i	0.0420241	+	0.238331i
$689$	−5.05835	−	13.8977i	−0.192708	−	0.529461i
$690$	−4.45443	+	1.17712i	−0.169577	+	0.0448121i
$691$	−2.25801	+	3.91098i	−0.0858986	+	0.148781i	−0.905774	−	0.423762i	$-0.860709\pi$
$691$	−2.25801	+	3.91098i	−0.0858986	+	0.148781i	0.819875	+	0.572542i	$0.194043\pi$
$692$	−5.54013	+	9.59578i	−0.210604	+	0.364777i
$693$	−40.6584	+	14.4817i	−1.54448	+	0.550115i
$694$	−2.27715	+	6.25641i	−0.0864393	+	0.237490i
$695$		−	2.83631i		−	0.107587i
$696$	−0.311119	−	3.70311i	−0.0117929	−	0.140366i
$697$	5.25208	−	14.4300i	0.198937	−	0.546574i
$698$	14.8080	−	5.38969i	0.560493	−	0.204003i
$699$	−8.69802	−	2.36280i	−0.328989	−	0.0893692i
$700$	15.0412	−	5.47454i	0.568503	−	0.206918i
$701$	−8.52750	−	23.4291i	−0.322079	−	0.884906i	−0.990050	−	0.140718i	$-0.955059\pi$
$701$	−8.52750	−	23.4291i	−0.322079	−	0.884906i	0.667970	−	0.744188i	$-0.267163\pi$
$702$	11.4096	−	2.93106i	0.430628	−	0.110626i
$703$	2.06482	−	0.266264i	0.0778762	−	0.0100423i
$704$	−10.3679	+	5.98593i	−0.390756	+	0.225603i
$705$	15.2968	−	21.6865i	0.576110	−	0.816762i
$706$	2.99060	−	3.56406i	0.112553	−	0.134135i
$707$	−45.8793	+	8.08977i	−1.72547	+	0.304247i
$708$	11.3366	+	24.5320i	0.426057	+	0.921967i
$709$	−1.33119	+	1.11700i	−0.0499938	+	0.0419497i	−0.667442	−	0.744662i	$-0.732611\pi$
$709$	−1.33119	+	1.11700i	−0.0499938	+	0.0419497i	0.617448	+	0.786611i	$0.288166\pi$
$710$	−1.17596	+	0.678941i	−0.0441330	+	0.0254802i
$711$	−25.5884	−	9.51374i	−0.959641	−	0.356793i
$712$	−3.11542	−	1.13392i	−0.116755	−	0.0424955i
$713$	−1.49952	−	8.50420i	−0.0561574	−	0.318485i
$714$	9.58696	−	20.3756i	0.358783	−	0.762538i
$715$		−	47.3768i		−	1.77179i
$716$	−5.28556	−	1.92379i	−0.197531	−	0.0718953i
$717$	−7.66784	−	5.40857i	−0.286361	−	0.201987i
$718$	−0.783215	+	2.15186i	−0.0292293	+	0.0803069i
$719$	14.6076	+	2.57571i	0.544770	+	0.0960577i	0.439259	−	0.898360i	$-0.355241\pi$
$719$	14.6076	+	2.57571i	0.544770	+	0.0960577i	0.105511	+	0.994418i	$0.466352\pi$
$720$	22.3441	+	0.154073i	0.832714	+	0.00574197i
$721$			17.0856i			0.636300i
$722$	−7.91875	−	3.74388i	−0.294705	−	0.139333i
$723$	4.40010	−	9.35174i	0.163642	−	0.347795i
$724$	6.05459	+	1.06759i	0.225017	+	0.0396766i
$725$	2.09922	+	1.76145i	0.0779630	+	0.0654187i
$726$	0.384578	−	1.41572i	0.0142730	−	0.0525424i
$727$	−1.77358	+	10.0585i	−0.0657785	+	0.373049i	0.934093	+	0.357029i	$0.116210\pi$
$727$	−1.77358	+	10.0585i	−0.0657785	+	0.373049i	−0.999872	+	0.0160192i	$0.994901\pi$
$728$	33.9544	−	5.98708i	1.25843	−	0.221896i
$729$	23.0984	+	13.9808i	0.855498	+	0.517806i
$730$	4.78267	+	2.76128i	0.177015	+	0.102199i
$731$	−15.8501	+	2.79481i	−0.586238	+	0.103370i
$732$	−25.4405	+	6.72284i	−0.940308	+	0.248483i
$733$	−19.8194	−	34.3283i	−0.732048	−	1.26794i	−0.956007	−	0.293345i	$-0.905232\pi$
$733$	−19.8194	−	34.3283i	−0.732048	−	1.26794i	0.223959	−	0.974599i	$-0.428102\pi$
$734$	14.9782			0.552854
$735$	41.0045	+	11.1388i	1.51247	+	0.410860i
$736$	−10.0785	−	1.77711i	−0.371498	−	0.0655052i
$737$	−29.4173	+	24.6841i	−1.08360	+	0.909249i
$738$	−2.60832	−	1.52999i	−0.0960137	−	0.0563198i
$739$	14.3907	−	5.23779i	0.529371	−	0.192675i	−0.0634865	−	0.997983i	$-0.520222\pi$
$739$	14.3907	−	5.23779i	0.529371	−	0.192675i	0.592857	+	0.805307i	$0.298000\pi$
$740$	1.14781	+	1.98806i	0.0421942	+	0.0730824i
$741$	7.81450	+	36.2957i	0.287073	+	1.33336i
$742$	−2.78361	+	4.82136i	−0.102190	+	0.176998i
$743$	−5.33616	+	30.2629i	−0.195765	+	1.11024i	0.715561	+	0.698551i	$0.246171\pi$
$743$	−5.33616	+	30.2629i	−0.195765	+	1.11024i	−0.911325	+	0.411687i	$0.864940\pi$
$744$	1.10249	−	12.1201i	0.0404192	−	0.444344i
$745$	−37.6066	−	13.6877i	−1.37780	−	0.501478i
$746$	−6.07121	+	7.23539i	−0.222283	+	0.264906i
$747$	−42.9582	+	15.3009i	−1.57176	+	0.559830i
$748$	−22.4896	−	38.9531i	−0.822301	−	1.42427i
$749$	40.9911			1.49778
$750$	−4.21969	+	4.19070i	−0.154081	+	0.153023i
$751$	5.64578	+	6.72838i	0.206017	+	0.245522i	0.859153	−	0.511719i	$-0.170991\pi$
$751$	5.64578	+	6.72838i	0.206017	+	0.245522i	−0.653135	+	0.757241i	$0.726547\pi$
$752$	13.6695	−	7.89211i	0.498476	−	0.287795i
$753$	4.24084	−	9.01325i	0.154545	−	0.328461i
$754$	1.79064	+	2.13400i	0.0652113	+	0.0777158i
$755$	28.4474	+	23.8702i	1.03531	+	0.868727i
$756$	30.3273	+	21.7063i	1.10299	+	0.789451i
$757$	7.86615	−	44.6111i	0.285900	−	1.62142i	−0.416153	−	0.909295i	$-0.636622\pi$
$757$	7.86615	−	44.6111i	0.285900	−	1.62142i	0.702053	−	0.712125i	$-0.252267\pi$
$758$	9.69246	−	11.5510i	0.352046	−	0.419552i
$759$	−10.9348	+	7.60061i	−0.396910	+	0.275885i
$760$	0.946936	−	20.4429i	0.0343490	−	0.741543i
$761$	36.3567	+	20.9906i	1.31793	+	0.760908i	0.983395	−	0.181475i	$-0.0580873\pi$
$761$	36.3567	+	20.9906i	1.31793	+	0.760908i	0.334535	+	0.942383i	$0.391421\pi$
$762$	−1.40467	+	15.4421i	−0.0508859	+	0.559409i
$763$	−20.6844	−	56.8298i	−0.748824	−	2.05738i
$764$	−11.2939	−	13.4595i	−0.408599	−	0.486949i
$765$	−0.390648	+	56.6527i	−0.0141239	+	2.04828i
$766$	−0.797229	−	4.52131i	−0.0288051	−	0.163362i
$767$	−37.1749	−	21.4629i	−1.34231	−	0.774981i
$768$	2.46903	+	1.16171i	0.0890933	+	0.0419195i
$769$	18.5593	−	15.5731i	0.669267	−	0.561581i	−0.243582	−	0.969880i	$-0.578322\pi$
$769$	18.5593	−	15.5731i	0.669267	−	0.561581i	0.912848	+	0.408299i	$0.133878\pi$
$770$	−13.6616	+	11.4634i	−0.492329	+	0.413113i
$771$	20.8769	+	9.82282i	0.751863	+	0.353760i
$772$	−6.79487	−	3.92302i	−0.244553	−	0.141193i
$773$	−7.32708	−	41.5540i	−0.263537	−	1.49459i	−0.773169	−	0.634200i	$-0.781330\pi$
$773$	−7.32708	−	41.5540i	−0.263537	−	1.49459i	0.509632	−	0.860392i	$-0.329781\pi$
$774$	−0.0218540	+	3.16931i	−0.000785524	+	0.113919i
$775$	5.76861	+	6.87476i	0.207215	+	0.246949i
$776$	6.18161	+	16.9838i	0.221907	+	0.609684i
$777$	−0.300923	+	3.30816i	−0.0107955	+	0.118680i
$778$	5.82222	+	3.36146i	0.208737	+	0.120514i
$779$	5.14209	−	8.02438i	0.184235	−	0.287503i
$780$	−33.6154	+	23.3655i	−1.20362	+	0.836618i
$781$	−2.52280	+	3.00656i	−0.0902729	+	0.107583i
$782$	1.20649	−	6.84235i	0.0431440	−	0.244682i
$783$	−0.622241	+	6.35454i	−0.0222371	+	0.227093i
$784$	19.3593	+	16.2444i	0.691404	+	0.580157i
$785$	5.47677	+	6.52696i	0.195474	+	0.232957i
$786$	2.97011	−	6.31250i	0.105940	−	0.225159i
$787$	1.26519	−	0.730460i	0.0450993	−	0.0260381i	−0.477281	−	0.878751i	$-0.658378\pi$
$787$	1.26519	−	0.730460i	0.0450993	−	0.0260381i	0.522380	+	0.852713i	$0.325044\pi$
$788$	6.85473	+	8.16915i	0.244190	+	0.291014i
$789$	33.2806	−	33.0519i	1.18482	−	1.17668i
$790$	−11.2803			−0.401335
$791$	4.08271	+	7.07147i	0.145165	+	0.251433i
$792$	−17.6799	+	6.29725i	−0.628229	+	0.223763i
$793$	26.8663	−	32.0180i	0.954051	−	1.13699i
$794$	−4.17516	−	1.51963i	−0.148171	−	0.0539298i
$795$	1.26886	−	13.9490i	0.0450018	−	0.494722i
$796$	−1.75316	+	9.94266i	−0.0621391	+	0.352408i
$797$	−5.43262	+	9.40958i	−0.192433	+	0.333304i	−0.946056	−	0.324003i	$-0.894971\pi$
$797$	−5.43262	+	9.40958i	−0.192433	+	0.333304i	0.753623	+	0.657307i	$0.228305\pi$
$798$	8.57541	−	11.0356i	0.303566	−	0.390656i
$799$	20.0102	+	34.6587i	0.707910	+	1.22614i
$800$	9.99429	−	3.63763i	0.353352	−	0.128609i
$801$	4.91339	+	2.88210i	0.173606	+	0.101834i
$802$	9.94783	−	8.34722i	0.351270	−	0.294751i
$803$	15.7197	+	2.77181i	0.554737	+	0.0978150i
$804$	32.0223	+	8.69879i	1.12934	+	0.306783i
$805$	23.1691			0.816602
$806$	4.56154	+	7.90083i	0.160674	+	0.278295i
$807$	23.4912	−	6.20773i	0.826930	−	0.218522i
$808$	−19.9502	+	3.51776i	−0.701846	+	0.123754i
$809$	44.4582	+	25.6680i	1.56307	+	0.902438i	0.996944	+	0.0781172i	$0.0248908\pi$
$809$	44.4582	+	25.6680i	1.56307	+	0.902438i	0.566124	+	0.824320i	$0.308442\pi$
$810$	10.9592	+	2.08862i	0.385066	+	0.0733867i
$811$	−34.1337	+	6.01869i	−1.19860	+	0.211345i	−0.737091	−	0.675793i	$-0.763801\pi$
$811$	−34.1337	+	6.01869i	−1.19860	+	0.211345i	−0.461504	+	0.887138i	$0.652690\pi$
$812$	−1.53148	+	8.68547i	−0.0537445	+	0.304800i
$813$	−4.61144	+	16.9758i	−0.161730	+	0.595367i
$814$	−0.604347	−	0.507107i	−0.0211823	−	0.0177741i
$815$	−4.83539	−	0.852610i	−0.169376	−	0.0298656i
$816$	−14.3457	+	30.4895i	−0.502199	+	1.06735i
$817$	−9.97829	−	0.462204i	−0.349096	−	0.0161705i
$818$			7.14797i			0.249923i
$819$	−59.2375	−	0.408471i	−2.06992	−	0.0142731i
$820$	10.3492	+	1.82484i	0.361409	+	0.0637261i
$821$	16.1971	−	44.5012i	0.565284	−	1.55310i	−0.246498	−	0.969143i	$-0.579280\pi$
$821$	16.1971	−	44.5012i	0.565284	−	1.55310i	0.811782	−	0.583961i	$-0.198498\pi$
$822$	−6.66133	−	4.69862i	−0.232341	−	0.163883i
$823$	−11.6809	−	4.25151i	−0.407172	−	0.148198i	0.130311	−	0.991473i	$-0.458402\pi$
$823$	−11.6809	−	4.25151i	−0.407172	−	0.148198i	−0.537483	+	0.843275i	$0.680625\pi$
$824$			7.42951i			0.258819i
$825$	5.89210	−	12.5228i	0.205137	−	0.435986i
$826$	2.80589	+	15.9130i	0.0976294	+	0.553684i
$827$	50.5536	+	18.4000i	1.75792	+	0.639831i	0.999923	−	0.0124266i	$-0.00395561\pi$
$827$	50.5536	+	18.4000i	1.75792	+	0.639831i	0.757998	+	0.652257i	$0.226178\pi$
$828$	10.7858	+	4.01014i	0.374831	+	0.139362i
$829$	−40.9272	+	23.6293i	−1.42146	+	0.820681i	−0.996424	−	0.0844946i	$-0.973072\pi$
$829$	−40.9272	+	23.6293i	−1.42146	+	0.820681i	−0.425037	+	0.905176i	$0.639739\pi$
$830$	−14.4344	+	12.1119i	−0.501024	+	0.420409i
$831$	4.13256	+	8.94266i	0.143357	+	0.310217i
$832$	−16.1821	+	2.85333i	−0.561012	+	0.0989215i
$833$	−41.1872	+	49.0850i	−1.42705	+	1.70069i
$834$	0.485482	−	0.688278i	0.0168109	−	0.0238331i
$835$	11.0471	−	6.37805i	0.382301	−	0.220722i
$836$	−8.32377	−	26.6461i	−0.287883	−	0.921573i
$837$	−5.62055	+	20.1406i	−0.194275	+	0.696161i
$838$	−5.81819	−	15.9853i	−0.200986	−	0.552204i
$839$	18.5447	−	6.74971i	0.640233	−	0.233026i	−0.00144595	−	0.999999i	$-0.500460\pi$
$839$	18.5447	−	6.74971i	0.640233	−	0.233026i	0.641679	+	0.766973i	$0.278238\pi$
$840$	31.5109	+	8.55987i	1.08723	+	0.295344i
$841$	25.8322	−	9.40217i	0.890767	−	0.324213i
$842$	2.48197	−	6.81916i	0.0855344	−	0.235004i
$843$	1.82373	+	21.7070i	0.0628125	+	0.747629i
$844$			33.9631i			1.16906i
$845$	10.2847	−	28.2569i	0.353804	−	0.972068i
$846$	7.42403	−	2.64430i	0.255243	−	0.0909128i
$847$	−3.68864	+	6.38891i	−0.126743	+	0.219526i
$848$	4.16532	−	7.21455i	0.143038	−	0.247749i
$849$	3.94614	−	1.04280i	0.135431	−	0.0357887i
$850$	2.46960	+	6.78518i	0.0847067	+	0.232730i
$851$	0.177977	+	1.00936i	0.00610097	+	0.0346003i
$852$	3.37745	+	0.307226i	0.115710	+	0.0105254i
$853$	25.3827	+	21.2986i	0.869087	+	0.729250i	0.963906	−	0.266244i	$-0.0857828\pi$
$853$	25.3827	+	21.2986i	0.869087	+	0.729250i	−0.0948190	+	0.995495i	$0.530227\pi$
$854$	−15.7334			−0.538385
$855$	−7.93789	+	34.2541i	−0.271470	+	1.17146i
$856$	17.8246			0.609233
$857$	−18.7672	−	15.7475i	−0.641075	−	0.537926i	0.263273	−	0.964721i	$-0.415198\pi$
$857$	−18.7672	−	15.7475i	−0.641075	−	0.537926i	−0.904348	+	0.426796i	$0.859642\pi$
$858$	8.10934	−	11.4968i	0.276848	−	0.392493i
$859$	2.29396	+	13.0097i	0.0782688	+	0.443885i	0.998607	+	0.0527613i	$0.0168023\pi$
$859$	2.29396	+	13.0097i	0.0782688	+	0.443885i	−0.920338	+	0.391123i	$0.872087\pi$
$860$	−3.76711	−	10.3500i	−0.128457	−	0.352934i
$861$	10.7155	+	10.7897i	0.365185	+	0.367711i
$862$	6.68311	−	11.5755i	0.227628	−	0.394262i
$863$	9.05208	−	15.6787i	0.308136	−	0.533708i	−0.669818	−	0.742525i	$-0.733628\pi$
$863$	9.05208	−	15.6787i	0.308136	−	0.533708i	0.977955	+	0.208817i	$0.0669613\pi$
$864$	20.1513	+	14.4230i	0.685562	+	0.490681i
$865$	5.70080	−	15.6628i	0.193833	−	0.532551i
$866$			13.2510i			0.450286i
$867$	−50.6622	−	23.8372i	−1.72058	−	0.809552i
$868$	−9.87857	+	27.1412i	−0.335301	+	0.921231i
$869$	−30.6380	+	11.1513i	−1.03932	+	0.378282i
$870$	0.674042	+	2.55070i	0.0228522	+	0.0864770i
$871$	−49.5286	+	18.0269i	−1.67821	+	0.610819i
$872$	−8.99440	−	24.7119i	−0.304589	−	0.836851i
$873$	−5.18141	−	30.6183i	−0.175364	−	1.03627i
$874$	1.66076	−	3.97951i	0.0561759	−	0.134609i
$875$	25.8996	−	14.9531i	0.875565	−	0.505508i
$876$	−5.78601	−	12.5207i	−0.195491	−	0.423034i
$877$	−34.3436	+	40.9291i	−1.15970	+	1.38208i	−0.249262	+	0.968436i	$0.580188\pi$
$877$	−34.3436	+	40.9291i	−1.15970	+	1.38208i	−0.910439	+	0.413643i	$0.864256\pi$
$878$	−8.79307	+	1.55046i	−0.296752	+	0.0523253i
$879$	21.3273	−	30.2361i	0.719351	−	1.01984i
$880$	20.4428	−	17.1536i	0.689128	−	0.578247i
$881$	−19.3893	+	11.1944i	−0.653243	+	0.377150i	−0.789698	−	0.613496i	$-0.789763\pi$
$881$	−19.3893	+	11.1944i	−0.653243	+	0.377150i	0.136454	+	0.990646i	$0.456429\pi$
$882$	8.04382	+	9.72161i	0.270850	+	0.327344i
$883$	43.5728	+	15.8592i	1.46634	+	0.533705i	0.947104	−	0.320926i	$-0.103994\pi$
$883$	43.5728	+	15.8592i	1.46634	+	0.533705i	0.519237	+	0.854630i	$0.326216\pi$
$884$	−10.7202	−	60.7973i	−0.360559	−	2.04483i
$885$	−23.2028	−	33.3814i	−0.779954	−	1.12210i
$886$			8.63575i			0.290124i
$887$	22.7637	+	8.28531i	0.764330	+	0.278193i	0.694623	−	0.719374i	$-0.255571\pi$
$887$	22.7637	+	8.28531i	0.764330	+	0.278193i	0.0697074	+	0.997567i	$0.477793\pi$
$888$	−0.130854	+	1.43852i	−0.00439116	+	0.0482737i
$889$	26.6689	−	73.2723i	0.894448	−	2.45747i
$890$	2.31796	+	0.408719i	0.0776982	+	0.0137003i
$891$	31.8305	−	5.16103i	1.06636	−	0.172901i
$892$		−	6.35841i		−	0.212895i
$893$	7.40610	+	23.7084i	0.247836	+	0.793372i
$894$	−6.78299	−	9.75855i	−0.226857	−	0.326375i
$895$	8.33279	+	1.46930i	0.278534	+	0.0491131i
$896$	34.0776	+	28.5945i	1.13845	+	0.955274i
$897$	−17.6712	+	4.66975i	−0.590025	+	0.155918i
$898$	0.757604	−	4.29658i	0.0252816	−	0.143379i
$899$	−4.86969	+	0.858657i	−0.162413	+	0.0286378i
$900$	−11.7912	+	1.99537i	−0.393040	+	0.0665124i
$901$	18.2923	+	10.5611i	0.609404	+	0.351840i
$902$	−3.55664	+	0.627131i	−0.118423	+	0.0208812i
$903$	4.17811	−	15.3806i	0.139039	−	0.511835i
$904$	1.77533	+	3.07496i	0.0590467	+	0.102272i
$905$	−9.24842			−0.307428
$906$	2.81745	+	10.6618i	0.0936035	+	0.354213i
$907$	9.61130	+	1.69473i	0.319138	+	0.0562727i	0.330923	−	0.943658i	$-0.392640\pi$
$907$	9.61130	+	1.69473i	0.319138	+	0.0562727i	−0.0117845	+	0.999931i	$0.503751\pi$
$908$	39.0291	−	32.7493i	1.29523	−	1.08682i
$909$	34.8055	+	0.240001i	1.15443	+	0.00796033i
$910$	−23.0014	+	8.37182i	−0.762489	+	0.277523i
$911$	−20.6596	−	35.7835i	−0.684483	−	1.18556i	−0.973599	−	0.228265i	$-0.926695\pi$
$911$	−20.6596	−	35.7835i	−0.684483	−	1.18556i	0.289116	−	0.957294i	$-0.406639\pi$
$912$	−12.8320	+	16.5134i	−0.424911	+	0.546813i
$913$	−27.2312	+	47.1658i	−0.901221	+	1.56096i
$914$	0.776175	−	4.40191i	0.0256736	−	0.145602i
$915$	35.9326	−	16.6050i	1.18789	−	0.548946i
$916$	12.5427	+	4.56518i	0.414424	+	0.150838i
$917$	−22.5503	+	26.8744i	−0.744677	+	0.887472i
$918$	−9.79186	+	13.6809i	−0.323180	+	0.451535i
$919$	−11.8172	−	20.4681i	−0.389815	−	0.675179i	0.602610	−	0.798036i	$-0.294128\pi$
$919$	−11.8172	−	20.4681i	−0.389815	−	0.675179i	−0.992424	+	0.122857i	$0.960794\pi$
$920$	10.0749			0.332158
$921$	−4.85307	−	18.3649i	−0.159914	−	0.605145i
$922$	−10.8765	−	12.9621i	−0.358198	−	0.426883i
$923$	−4.66516	+	2.69343i	−0.153556	+	0.0886554i
$924$	44.3850	−	3.72904i	1.46016	−	0.122676i
$925$	−0.684673	−	0.815961i	−0.0225119	−	0.0268286i
$926$	−2.02241	−	1.69700i	−0.0664604	−	0.0557669i
$927$	2.30326	−	12.5555i	0.0756489	−	0.412378i
$928$	−1.01761	+	5.77116i	−0.0334047	+	0.189448i
$929$	−30.4377	+	36.2742i	−0.998628	+	1.19012i	−0.0168943	+	0.999857i	$0.505378\pi$
$929$	−30.4377	+	36.2742i	−0.998628	+	1.19012i	−0.981734	+	0.190261i	$0.939067\pi$
$930$	0.723354	+	8.60976i	0.0237197	+	0.282325i
$931$	−31.6143	+	24.1254i	−1.03612	+	0.790679i
$932$	8.05544	+	4.65081i	0.263865	+	0.152342i
$933$	2.02367	−	0.935171i	0.0662519	−	0.0306161i
$934$	−3.25878	−	8.95342i	−0.106630	−	0.292965i
$935$	43.4924	+	51.8322i	1.42235	+	1.69509i
$936$	−25.7589	−	0.177620i	−0.841955	−	0.00580569i
$937$	8.82002	+	50.0208i	0.288137	+	1.63411i	0.693858	+	0.720111i	$0.255909\pi$
$937$	8.82002	+	50.0208i	0.288137	+	1.63411i	−0.405721	+	0.913997i	$0.632980\pi$
$938$	17.1823	+	9.92023i	0.561023	+	0.323907i
$939$	−19.4771	+	13.5382i	−0.635612	+	0.441802i
$940$	−20.9802	+	17.6045i	−0.684300	+	0.574196i
$941$	5.51786	−	4.63003i	0.179877	−	0.150935i	−0.548404	−	0.836214i	$-0.684764\pi$
$941$	5.51786	−	4.63003i	0.179877	−	0.150935i	0.728281	+	0.685279i	$0.240320\pi$
$942$	0.211830	+	2.52132i	0.00690180	+	0.0821490i
$943$	4.06331	+	2.34595i	0.132320	+	0.0763947i
$944$	−4.19866	−	23.8118i	−0.136655	−	0.775007i
$945$	−50.5983	−	24.2346i	−1.64596	−	0.788353i
$946$	2.43309	+	2.89964i	0.0791065	+	0.0942755i
$947$	−7.29140	−	20.0330i	−0.236939	−	0.650984i	−0.999989	−	0.00464478i	$-0.998522\pi$
$947$	−7.29140	−	20.0330i	−0.236939	−	0.650984i	0.763051	−	0.646339i	$-0.223701\pi$
$948$	23.0224	+	16.2390i	0.747731	+	0.527418i
$949$	18.9734	+	10.9543i	0.615902	+	0.355591i
$950$	0.573146	+	4.44462i	0.0185953	+	0.144202i
$951$	−47.8785	−	22.5274i	−1.55257	−	0.730501i
$952$	−31.6513	+	37.7206i	−1.02583	+	1.22253i
$953$	−5.65230	+	32.0558i	−0.183096	+	1.03839i	0.745282	+	0.666750i	$0.232315\pi$
$953$	−5.65230	+	32.0558i	−0.183096	+	1.03839i	−0.928378	+	0.371638i	$0.878796\pi$
$954$	2.69552	−	3.16778i	0.0872708	−	0.102561i
$955$	20.2472	+	16.9894i	0.655183	+	0.549764i
$956$	6.22453	+	7.41811i	0.201316	+	0.239919i
$957$	4.35227	+	6.26153i	0.140689	+	0.202406i
$958$	4.64903	−	2.68412i	0.150203	−	0.0867200i
$959$	26.3496	+	31.4023i	0.850874	+	1.01403i
$960$	−15.0175	−	4.07948i	−0.484689	−	0.131665i
$961$	14.8062			0.477618
$962$	−0.541406	−	0.937743i	−0.0174556	−	0.0302341i
$963$	−30.1228	−	5.52589i	−0.970694	−	0.178069i
$964$	−6.85589	+	8.17053i	−0.220813	+	0.263155i
$965$	11.0910	+	4.03679i	0.357032	+	0.129949i
$966$	5.62235	+	3.96577i	0.180896	+	0.127597i
$967$	7.95703	−	45.1266i	0.255881	−	1.45117i	−0.537921	−	0.842996i	$-0.680790\pi$
$967$	7.95703	−	45.1266i	0.255881	−	1.45117i	0.793801	−	0.608177i	$-0.208099\pi$
$968$	−1.60397	+	2.77816i	−0.0515536	+	0.0892935i
$969$	−41.8692	−	32.5352i	−1.34503	−	1.04518i
$970$	−6.41569	−	11.1123i	−0.205996	−	0.356795i
$971$	−11.3013	+	4.11333i	−0.362675	+	0.132003i	−0.516929	−	0.856028i	$-0.672925\pi$
$971$	−11.3013	+	4.11333i	−0.362675	+	0.132003i	0.154254	+	0.988031i	$0.450703\pi$
$972$	−19.3602	−	20.0395i	−0.620979	−	0.642766i
$973$	−3.24462	+	2.72256i	−0.104018	+	0.0872812i
$974$	8.21422	+	1.44839i	0.263201	+	0.0464094i
$975$	13.4779	−	13.3853i	0.431640	−	0.428673i
$976$	23.5430			0.753594
$977$	−1.83199	−	3.17311i	−0.0586107	−	0.101517i	0.835231	−	0.549899i	$-0.185334\pi$
$977$	−1.83199	−	3.17311i	−0.0586107	−	0.101517i	−0.893842	+	0.448382i	$0.852000\pi$
$978$	−1.02745	−	1.03456i	−0.0328542	−	0.0330815i
$979$	6.69976	−	1.18135i	0.214125	−	0.0377560i
$980$	−37.9752	−	21.9250i	−1.21307	−	0.700368i
$981$	7.53908	+	44.5504i	0.240704	+	1.42239i
$982$	10.5689	−	1.86359i	0.337268	−	0.0594695i
$983$	7.43871	−	42.1870i	0.237258	−	1.34556i	−0.600548	−	0.799589i	$-0.705051\pi$
$983$	7.43871	−	42.1870i	0.237258	−	1.34556i	0.837806	−	0.545969i	$-0.183838\pi$
$984$	4.65956	+	4.69180i	0.148541	+	0.149569i
$985$	−12.2888	−	10.3116i	−0.391555	−	0.328554i
$986$	−3.91807	−	0.690862i	−0.124777	−	0.0220015i
$987$	−39.4918	+	3.31792i	−1.25704	+	0.105611i
$988$	1.77290	−	38.2743i	0.0564035	−	1.21767i
$989$		−	4.91758i		−	0.156370i
$990$	11.5847	−	6.58236i	0.368187	−	0.209201i
$991$	41.0477	+	7.23783i	1.30392	+	0.229917i	0.782109	−	0.623141i	$-0.214144\pi$
$991$	41.0477	+	7.23783i	1.30392	+	0.229917i	0.521815	+	0.853058i	$0.325255\pi$
$992$	−6.56393	+	18.0343i	−0.208405	+	0.572588i
$993$	−25.6181	+	11.8386i	−0.812967	+	0.375686i
$994$	1.90548	+	0.693537i	0.0604380	+	0.0219976i
$995$		−	15.1875i		−	0.481475i
$996$	46.8957	−	3.93997i	1.48595	−	0.124843i
$997$	−8.31011	−	47.1290i	−0.263184	−	1.49259i	−0.774158	−	0.632993i	$-0.781826\pi$
$997$	−8.31011	−	47.1290i	−0.263184	−	1.49259i	0.510974	−	0.859596i	$-0.329285\pi$
$998$	3.07318	+	1.11855i	0.0972799	+	0.0354070i
$999$	0.667100	−	2.39047i	0.0211061	−	0.0756312i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	171.2.x.a.14.11	✓	108
3.2	odd	2		513.2.bo.a.71.8		108
9.2	odd	6		171.2.bd.a.128.8	yes	108
9.7	even	3		513.2.cd.a.413.11		108
19.15	odd	18		171.2.bd.a.167.8	yes	108
57.53	even	18		513.2.cd.a.395.11		108
171.34	odd	18		513.2.bo.a.224.8		108
171.110	even	18	inner	171.2.x.a.110.11	yes	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
171.2.x.a.14.11	✓	108	1.1	even	1	trivial
171.2.x.a.110.11	yes	108	171.110	even	18	inner
171.2.bd.a.128.8	yes	108	9.2	odd	6
171.2.bd.a.167.8	yes	108	19.15	odd	18
513.2.bo.a.71.8		108	3.2	odd	2
513.2.bo.a.224.8		108	171.34	odd	18
513.2.cd.a.395.11		108	57.53	even	18
513.2.cd.a.413.11		108	9.7	even	3

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:	\( N \)	\(=\)	\( 171 = 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	171.x (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.353154 + 0.296331i) q^{2} +(0.726580 + 1.57229i) q^{3} +(-0.310391 - 1.76031i) q^{4} +(0.919654 + 2.52673i) q^{5} +(-0.209323 + 0.770567i) q^{6} +(2.00770 - 3.47744i) q^{7} +(0.873030 - 1.51213i) q^{8} +(-1.94416 + 2.28478i) q^{9} +(-0.423969 + 1.16485i) q^{10} +3.58291i q^{11} +(2.54219 - 1.76703i) q^{12} +(-1.68193 + 4.62107i) q^{13} +(1.73950 - 0.633126i) q^{14} +(-3.30454 + 3.28183i) q^{15} +(-2.60294 + 0.947393i) q^{16} +(-2.40209 - 6.59968i) q^{17} +(-1.36364 + 0.230763i) q^{18} +(-0.557476 - 4.32310i) q^{19} +(4.16239 - 2.40315i) q^{20} +(6.92628 + 0.630040i) q^{21} +(-1.06173 + 1.26532i) q^{22} +(2.11329 - 0.372629i) q^{23} +(3.01183 + 0.273967i) q^{24} +(-1.70837 + 1.43350i) q^{25} +(-1.96335 + 1.13354i) q^{26} +(-5.00492 - 1.39670i) q^{27} +(-6.74455 - 2.45482i) q^{28} +(-0.213376 - 1.21011i) q^{29} +(-2.13952 + 0.179753i) q^{30} -4.02416i q^{31} +(-4.48150 - 1.63113i) q^{32} +(-5.63336 + 2.60327i) q^{33} +(1.10738 - 3.04251i) q^{34} +(10.6329 + 1.87487i) q^{35} +(4.62539 + 2.71316i) q^{36} +0.477624i q^{37} +(1.08420 - 1.69192i) q^{38} +(-8.48770 + 0.713100i) q^{39} +(4.62363 + 0.815271i) q^{40} +(1.67493 + 1.40543i) q^{41} +(2.25934 + 2.27497i) q^{42} +(0.397937 - 2.25682i) q^{43} +(6.30705 - 1.11210i) q^{44} +(-7.56098 - 2.81116i) q^{45} +(0.856736 + 0.494637i) q^{46} +(-5.61172 + 0.989498i) q^{47} +(-3.38082 - 3.40421i) q^{48} +(-4.56171 - 7.90111i) q^{49} -1.02811 q^{50} +(8.63127 - 8.57196i) q^{51} +(8.65660 + 1.52639i) q^{52} +(-2.30385 + 1.93316i) q^{53} +(-1.35362 - 1.97636i) q^{54} +(-9.05304 + 3.29504i) q^{55} +(-3.50556 - 6.07181i) q^{56} +(6.39210 - 4.01759i) q^{57} +(0.283240 - 0.490586i) q^{58} +(-1.51577 + 8.59634i) q^{59} +(6.80275 + 4.79837i) q^{60} +(-7.98674 - 2.90694i) q^{61} +(1.19248 - 1.42115i) q^{62} +(4.04189 + 11.3479i) q^{63} +(1.67069 + 2.89372i) q^{64} -13.2230 q^{65} +(-2.76087 - 0.749985i) q^{66} +(6.88939 + 8.21046i) q^{67} +(-10.8719 + 6.27691i) q^{68} +(2.12135 + 3.05194i) q^{69} +(3.19948 + 3.81299i) q^{70} +(0.839138 + 0.704120i) q^{71} +(1.75758 + 4.93451i) q^{72} +(0.773620 - 4.38741i) q^{73} +(-0.141535 + 0.168675i) q^{74} +(-3.49513 - 1.64450i) q^{75} +(-7.43699 + 2.32319i) q^{76} +(12.4593 + 7.19341i) q^{77} +(-3.20878 - 2.26334i) q^{78} +(3.11236 + 8.55114i) q^{79} +(-4.78761 - 5.70565i) q^{80} +(-1.44046 - 8.88398i) q^{81} +(0.175034 + 0.992667i) q^{82} +(13.1641 + 7.60030i) q^{83} +(-1.04078 - 12.3880i) q^{84} +(14.4665 - 12.1388i) q^{85} +(0.809298 - 0.679082i) q^{86} +(1.74761 - 1.21473i) q^{87} +(5.41783 + 3.12799i) q^{88} +(-0.329717 - 1.86992i) q^{89} +(-1.83715 - 3.23333i) q^{90} +(12.6927 + 15.1265i) q^{91} +(-1.31189 - 3.60439i) q^{92} +(6.32713 - 2.92387i) q^{93} +(-2.27502 - 1.31348i) q^{94} +(10.4106 - 5.38435i) q^{95} +(-0.691561 - 8.23134i) q^{96} +(-6.65363 + 7.92948i) q^{97} +(0.730361 - 4.14209i) q^{98} +(-8.18617 - 6.96576i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 9 q^{2} - 3 q^{4} - 9 q^{5} + 3 q^{7} - 24 q^{9} - 12 q^{10} - 9 q^{12} - 6 q^{13} - 9 q^{14} - 36 q^{15} - 9 q^{16} + 27 q^{17} + 36 q^{18} - 15 q^{19} - 18 q^{20} + 3 q^{21} + 30 q^{22} - 45 q^{23}+ \cdots + 39 q^{99}+O(q^{100}) \) 108 * q - 9 * q^2 - 3 * q^4 - 9 * q^5 + 3 * q^7 - 24 * q^9 - 12 * q^10 - 9 * q^12 - 6 * q^13 - 9 * q^14 - 36 * q^15 - 9 * q^16 + 27 * q^17 + 36 * q^18 - 15 * q^19 - 18 * q^20 + 3 * q^21 + 30 * q^22 - 45 * q^23 - 21 * q^24 - 3 * q^25 - 72 * q^26 - 36 * q^28 - 9 * q^29 - 21 * q^30 - 9 * q^32 - 6 * q^33 + 33 * q^34 + 45 * q^35 + 18 * q^36 - 9 * q^38 - 18 * q^39 + 15 * q^40 - 9 * q^41 + 15 * q^42 + 9 * q^43 - 63 * q^44 + 33 * q^45 - 18 * q^46 - 9 * q^47 + 3 * q^48 - 15 * q^49 + 126 * q^50 + 39 * q^51 - 39 * q^52 - 51 * q^54 + 3 * q^55 + 63 * q^56 - 78 * q^57 - 6 * q^58 + 36 * q^59 - 75 * q^60 - 24 * q^61 + 18 * q^62 - 9 * q^63 - 18 * q^65 + 159 * q^66 - 63 * q^67 + 54 * q^68 - 9 * q^69 + 39 * q^70 + 141 * q^72 - 45 * q^73 - 117 * q^74 - 3 * q^76 - 18 * q^77 + 27 * q^78 + 3 * q^79 + 126 * q^80 - 60 * q^81 - 3 * q^82 + 27 * q^83 - 117 * q^84 - 3 * q^85 - 171 * q^86 + 15 * q^87 - 9 * q^88 + 54 * q^89 - 21 * q^90 - 9 * q^91 - 27 * q^92 + 42 * q^93 + 99 * q^95 + 207 * q^96 - 57 * q^97 - 27 * q^98 + 39 * q^99

Introduction

L-functions

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