LMFDB - Embedded newform 936.2.cj.a.133.126

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [936,2,Mod(133,936)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(936, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 4, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("936.133"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 936 = 2^{3} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	936.cj (of order $6$, degree $2$, 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:	$7.47399762919$
Analytic rank:	$0$
Dimension:	$328$
Relative dimension:	$164$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			133.126
Character	$\chi$	$=$	936.133
Dual form			936.2.cj.a.373.125

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.07135 + 0.923151i) q^{2} +(-1.56623 + 0.739535i) q^{3} +(0.295586 + 1.97804i) q^{4} +(-0.715331 + 0.412997i) q^{5} +(-2.36069 - 0.653568i) q^{6} +(1.17877 + 2.04168i) q^{7} +(-1.50935 + 2.39204i) q^{8} +(1.90618 - 2.31657i) q^{9} +(-1.14763 - 0.217894i) q^{10} -0.713520i q^{11} +(-1.92578 - 2.87947i) q^{12} +(-1.89754 + 3.06584i) q^{13} +(-0.621909 + 3.27554i) q^{14} +(0.814950 - 1.17586i) q^{15} +(-3.82526 + 1.16936i) q^{16} +(-2.27932 + 3.94789i) q^{17} +(4.18073 - 0.722171i) q^{18} +(0.636605 + 0.367544i) q^{19} +(-1.02836 - 1.29288i) q^{20} +(-3.35612 - 2.32602i) q^{21} +(0.658686 - 0.764430i) q^{22} +(2.09174 - 3.62300i) q^{23} +(0.594995 - 4.86271i) q^{24} +(-2.15887 + 3.73927i) q^{25} +(-4.86316 + 1.53287i) q^{26} +(-1.27233 + 5.03797i) q^{27} +(-3.69010 + 2.93514i) q^{28} -7.31736i q^{29} +(1.95860 - 0.507439i) q^{30} +(-1.99094 - 3.44841i) q^{31} +(-5.17769 - 2.27849i) q^{32} +(0.527673 + 1.11754i) q^{33} +(-6.08645 + 2.12543i) q^{34} +(-1.68642 - 0.973654i) q^{35} +(5.14570 + 3.08574i) q^{36} +(-3.46950 + 2.00312i) q^{37} +(0.342729 + 0.981451i) q^{38} +(0.704695 - 6.20511i) q^{39} +(0.0917792 - 2.33446i) q^{40} +(-1.73954 + 3.01297i) q^{41} +(-1.44832 - 5.59019i) q^{42} +(2.23537 - 1.29059i) q^{43} +(1.41137 - 0.210906i) q^{44} +(-0.406812 + 2.44436i) q^{45} +(5.58556 - 1.95051i) q^{46} +(-0.0719052 + 0.124543i) q^{47} +(5.12646 - 4.66040i) q^{48} +(0.721015 - 1.24884i) q^{49} +(-5.76481 + 2.01311i) q^{50} +(0.650338 - 7.86896i) q^{51} +(-6.62522 - 2.84718i) q^{52} +4.60908i q^{53} +(-6.01392 + 4.22288i) q^{54} +(0.294681 + 0.510403i) q^{55} +(-6.66297 - 0.261954i) q^{56} +(-1.26888 - 0.104868i) q^{57} +(6.75502 - 7.83946i) q^{58} -15.0460i q^{59} +(2.56679 + 1.26443i) q^{60} +(-5.61990 + 3.24465i) q^{61} +(1.05040 - 5.53239i) q^{62} +(6.97664 + 1.16111i) q^{63} +(-3.44373 - 7.22085i) q^{64} +(0.0911879 - 2.97677i) q^{65} +(-0.466334 + 1.68440i) q^{66} +(6.94243 + 4.00821i) q^{67} +(-8.48281 - 3.34163i) q^{68} +(-0.596818 + 7.22137i) q^{69} +(-0.907917 - 2.59994i) q^{70} +(-1.19496 + 2.06973i) q^{71} +(2.66425 + 8.05617i) q^{72} -10.4588 q^{73} +(-5.56623 - 1.05683i) q^{74} +(0.615971 - 7.45313i) q^{75} +(-0.538844 + 1.36787i) q^{76} +(1.45678 - 0.841074i) q^{77} +(6.48323 - 5.99731i) q^{78} +(-6.92208 + 11.9894i) q^{79} +(2.25338 - 2.41630i) q^{80} +(-1.73299 - 8.83158i) q^{81} +(-4.64508 + 1.62209i) q^{82} +(8.70733 + 5.02718i) q^{83} +(3.60892 - 7.32607i) q^{84} -3.76540i q^{85} +(3.58627 + 0.680906i) q^{86} +(5.41144 + 11.4607i) q^{87} +(1.70677 + 1.07695i) q^{88} +(8.95021 + 15.5022i) q^{89} +(-2.69235 + 2.24322i) q^{90} +(-8.49623 - 0.260267i) q^{91} +(7.78471 + 3.06663i) q^{92} +(5.66849 + 3.92864i) q^{93} +(-0.192008 + 0.0670504i) q^{94} -0.607178 q^{95} +(9.79450 - 0.260429i) q^{96} +(6.90198 + 11.9546i) q^{97} +(1.92532 - 0.672335i) q^{98} +(-1.65292 - 1.36009i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 328 q - 2 q^{2} - 2 q^{4} + 4 q^{6} + 2 q^{7} - 2 q^{8} - 2 q^{9} - 4 q^{10} + 5 q^{12} - 6 q^{14} - 14 q^{15} - 2 q^{16} - 4 q^{17} - 12 q^{18} + 9 q^{20} + 14 q^{22} - 22 q^{23} + 18 q^{24} + 144 q^{25}+ \cdots + 39 q^{98}+O(q^{100}) $ 328 * q - 2 * q^2 - 2 * q^4 + 4 * q^6 + 2 * q^7 - 2 * q^8 - 2 * q^9 - 4 * q^10 + 5 * q^12 - 6 * q^14 - 14 * q^15 - 2 * q^16 - 4 * q^17 - 12 * q^18 + 9 * q^20 + 14 * q^22 - 22 * q^23 + 18 * q^24 + 144 * q^25 - 16 * q^26 - 10 * q^28 - 2 * q^30 - 4 * q^31 - 2 * q^32 + 22 * q^33 - 22 * q^36 + 6 * q^38 + 2 * q^39 + 8 * q^40 + 2 * q^41 + 17 * q^42 - 32 * q^44 - 6 * q^46 - 4 * q^47 + 41 * q^48 - 138 * q^49 - 34 * q^50 + 24 * q^52 - 41 * q^54 - 14 * q^55 + 28 * q^56 - 20 * q^57 + 50 * q^58 - 41 * q^60 + 3 * q^62 + 26 * q^63 - 26 * q^64 - 22 * q^65 - 6 * q^66 + 32 * q^68 - 17 * q^70 - 4 * q^71 + 32 * q^72 - 16 * q^73 + 19 * q^74 + 9 * q^76 + 2 * q^78 - 4 * q^79 - 42 * q^80 - 2 * q^81 + 3 * q^82 + 27 * q^84 + 36 * q^86 + 34 * q^87 - 10 * q^88 - 4 * q^89 + 33 * q^90 + 28 * q^92 + 3 * q^94 - 112 * q^95 - 113 * q^96 + 2 * q^97 + 39 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/936\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$469$	$703$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$1$

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 $

$2$	1.07135	+	0.923151i	0.757560	+	0.652766i
$2$	1.07135	+	0.923151i	0.757560	+	0.652766i
$3$	−1.56623	+	0.739535i	−0.904265	+	0.426971i
$3$	−1.56623	+	0.739535i	−0.904265	+	0.426971i
$4$	0.295586	+	1.97804i	0.147793	+	0.989018i
$5$	−0.715331	+	0.412997i	−0.319906	+	0.184698i	−0.651351	−	0.758777i	$-0.725797\pi$
$5$	−0.715331	+	0.412997i	−0.319906	+	0.184698i	0.331445	+	0.943475i	$0.392464\pi$
$6$	−2.36069	−	0.653568i	−0.963747	−	0.266818i
$7$	1.17877	+	2.04168i	0.445532	+	0.771684i	0.998089	−	0.0617908i	$-0.0196812\pi$
$7$	1.17877	+	2.04168i	0.445532	+	0.771684i	−0.552557	+	0.833475i	$0.686348\pi$
$8$	−1.50935	+	2.39204i	−0.533636	+	0.845715i
$9$	1.90618	−	2.31657i	0.635392	−	0.772190i
$10$	−1.14763	−	0.217894i	−0.362912	−	0.0689041i
$11$		−	0.713520i		−	0.215134i	−0.994198	−	0.107567i	$-0.965694\pi$
$11$		−	0.713520i		−	0.215134i	0.994198	−	0.107567i	$-0.0343061\pi$
$12$	−1.92578	−	2.87947i	−0.555926	−	0.831232i
$13$	−1.89754	+	3.06584i	−0.526282	+	0.850310i
$13$	−1.89754	+	3.06584i	−0.526282	+	0.850310i
$14$	−0.621909	+	3.27554i	−0.166212	+	0.875425i
$15$	0.814950	−	1.17586i	0.210419	−	0.303606i
$16$	−3.82526	+	1.16936i	−0.956314	+	0.292340i
$17$	−2.27932	+	3.94789i	−0.552816	+	0.957505i	0.445254	+	0.895404i	$0.353113\pi$
$17$	−2.27932	+	3.94789i	−0.552816	+	0.957505i	−0.998070	+	0.0621004i	$0.980220\pi$
$18$	4.18073	−	0.722171i	0.985407	−	0.170217i
$19$	0.636605	+	0.367544i	0.146047	+	0.0843204i	0.571243	−	0.820781i	$-0.306461\pi$
$19$	0.636605	+	0.367544i	0.146047	+	0.0843204i	−0.425196	+	0.905101i	$0.639795\pi$
$20$	−1.02836	−	1.29288i	−0.229949	−	0.289096i
$21$	−3.35612	−	2.32602i	−0.732366	−	0.507578i
$22$	0.658686	−	0.764430i	0.140432	−	0.162977i
$23$	2.09174	−	3.62300i	0.436157	−	0.755447i	−0.561232	−	0.827659i	$-0.689672\pi$
$23$	2.09174	−	3.62300i	0.436157	−	0.755447i	0.997389	+	0.0722117i	$0.0230057\pi$
$24$	0.594995	−	4.86271i	0.121453	−	0.992597i
$25$	−2.15887	+	3.73927i	−0.431773	+	0.747854i
$26$	−4.86316	+	1.53287i	−0.953744	+	0.300621i
$27$	−1.27233	+	5.03797i	−0.244861	+	0.969558i
$28$	−3.69010	+	2.93514i	−0.697363	+	0.554689i
$29$		−	7.31736i		−	1.35880i	−0.733769	−	0.679399i	$-0.762240\pi$
$29$		−	7.31736i		−	1.35880i	0.733769	−	0.679399i	$-0.237760\pi$
$30$	1.95860	−	0.507439i	0.357589	−	0.0926452i
$31$	−1.99094	−	3.44841i	−0.357583	−	0.619352i	0.629973	−	0.776617i	$-0.283066\pi$
$31$	−1.99094	−	3.44841i	−0.357583	−	0.619352i	−0.987556	+	0.157265i	$0.949732\pi$
$32$	−5.17769	−	2.27849i	−0.915295	−	0.402785i
$33$	0.527673	+	1.11754i	0.0918560	+	0.194538i
$34$	−6.08645	+	2.12543i	−1.04382	+	0.364508i
$35$	−1.68642	−	0.973654i	−0.285057	−	0.164578i
$36$	5.14570	+	3.08574i	0.857616	+	0.514290i
$37$	−3.46950	+	2.00312i	−0.570383	+	0.329311i	−0.757302	−	0.653065i	$-0.773483\pi$
$37$	−3.46950	+	2.00312i	−0.570383	+	0.329311i	0.186920	+	0.982375i	$0.440150\pi$
$38$	0.342729	+	0.981451i	0.0555980	+	0.159212i
$39$	0.704695	−	6.20511i	0.112841	−	0.993613i
$40$	0.0917792	−	2.33446i	0.0145116	−	0.369110i
$41$	−1.73954	+	3.01297i	−0.271670	+	0.470547i	−0.969290	−	0.245922i	$-0.920909\pi$
$41$	−1.73954	+	3.01297i	−0.271670	+	0.470547i	0.697619	+	0.716469i	$0.254243\pi$
$42$	−1.44832	−	5.59019i	−0.223481	−	0.862584i
$43$	2.23537	−	1.29059i	0.340890	−	0.196813i	−0.319775	−	0.947493i	$-0.603607\pi$
$43$	2.23537	−	1.29059i	0.340890	−	0.196813i	0.660666	+	0.750680i	$0.270274\pi$
$44$	1.41137	−	0.210906i	0.212772	−	0.0317953i
$45$	−0.406812	+	2.44436i	−0.0606439	+	0.364383i
$46$	5.58556	−	1.95051i	0.823545	−	0.287587i
$47$	−0.0719052	+	0.124543i	−0.0104884	+	0.0181665i	−0.871222	−	0.490889i	$-0.836672\pi$
$47$	−0.0719052	+	0.124543i	−0.0104884	+	0.0181665i	0.860734	+	0.509056i	$0.170005\pi$
$48$	5.12646	−	4.66040i	0.739941	−	0.672671i
$49$	0.721015	−	1.24884i	0.103002	−	0.178405i
$50$	−5.76481	+	2.01311i	−0.815268	+	0.284697i
$51$	0.650338	−	7.86896i	0.0910656	−	1.10187i
$52$	−6.62522	−	2.84718i	−0.918753	−	0.394833i
$53$			4.60908i			0.633106i	0.948575	+	0.316553i	$0.102525\pi$
$53$			4.60908i			0.633106i	−0.948575	+	0.316553i	$0.897475\pi$
$54$	−6.01392	+	4.22288i	−0.818391	+	0.574661i
$55$	0.294681	+	0.510403i	0.0397348	+	0.0688227i
$56$	−6.66297	−	0.261954i	−0.890376	−	0.0350051i
$57$	−1.26888	−	0.104868i	−0.168068	−	0.0138901i
$58$	6.75502	−	7.83946i	0.886978	−	1.02937i
$59$		−	15.0460i		−	1.95882i	−0.201875	−	0.979411i	$-0.564704\pi$
$59$		−	15.0460i		−	1.95882i	0.201875	−	0.979411i	$-0.435296\pi$
$60$	2.56679	+	1.26443i	0.331371	+	0.163238i
$61$	−5.61990	+	3.24465i	−0.719554	+	0.415435i	−0.814589	−	0.580039i	$-0.803037\pi$
$61$	−5.61990	+	3.24465i	−0.719554	+	0.415435i	0.0950342	+	0.995474i	$0.469704\pi$
$62$	1.05040	−	5.53239i	0.133401	−	0.702614i
$63$	6.97664	+	1.16111i	0.878974	+	0.146287i
$64$	−3.44373	−	7.22085i	−0.430466	−	0.902607i
$65$	0.0911879	−	2.97677i	0.0113105	−	0.369222i
$66$	−0.466334	+	1.68440i	−0.0574017	+	0.207335i
$67$	6.94243	+	4.00821i	0.848153	+	0.489681i	0.860027	−	0.510248i	$-0.170446\pi$
$67$	6.94243	+	4.00821i	0.848153	+	0.489681i	−0.0118743	+	0.999929i	$0.503780\pi$
$68$	−8.48281	−	3.34163i	−1.02869	−	0.405232i
$69$	−0.596818	+	7.22137i	−0.0718484	+	0.869351i
$70$	−0.907917	−	2.59994i	−0.108517	−	0.310753i
$71$	−1.19496	+	2.06973i	−0.141815	+	0.245632i	−0.928180	−	0.372131i	$-0.878627\pi$
$71$	−1.19496	+	2.06973i	−0.141815	+	0.245632i	0.786365	+	0.617762i	$0.211961\pi$
$72$	2.66425	+	8.05617i	0.313984	+	0.949428i
$73$	−10.4588			−1.22411			−0.612056	−	0.790815i	$-0.709657\pi$
$73$	−10.4588			−1.22411			−0.612056	+	0.790815i	$0.709657\pi$
$74$	−5.56623	−	1.05683i	−0.647062	−	0.122854i
$75$	0.615971	−	7.45313i	0.0711263	−	0.860613i
$76$	−0.538844	+	1.36787i	−0.0618096	+	0.156905i
$77$	1.45678	−	0.841074i	0.166016	−	0.0958492i
$78$	6.48323	−	5.99731i	0.734081	−	0.679062i
$79$	−6.92208	+	11.9894i	−0.778795	+	1.34891i	0.153841	+	0.988096i	$0.450835\pi$
$79$	−6.92208	+	11.9894i	−0.778795	+	1.34891i	−0.932637	+	0.360817i	$0.882498\pi$
$80$	2.25338	−	2.41630i	0.251936	−	0.270150i
$81$	−1.73299	−	8.83158i	−0.192554	−	0.981286i
$82$	−4.64508	+	1.62209i	−0.512963	+	0.179130i
$83$	8.70733	+	5.02718i	0.955753	+	0.551804i	0.894863	−	0.446340i	$-0.147273\pi$
$83$	8.70733	+	5.02718i	0.955753	+	0.551804i	0.0608899	+	0.998144i	$0.480606\pi$
$84$	3.60892	−	7.32607i	0.393766	−	0.799340i
$85$		−	3.76540i		−	0.408415i
$86$	3.58627	+	0.680906i	0.386718	+	0.0734240i
$87$	5.41144	+	11.4607i	0.580167	+	1.22871i
$88$	1.70677	+	1.07695i	0.181942	+	0.114803i
$89$	8.95021	+	15.5022i	0.948720	+	1.64323i	0.748125	+	0.663557i	$0.230954\pi$
$89$	8.95021	+	15.5022i	0.948720	+	1.64323i	0.200595	+	0.979674i	$0.435712\pi$
$90$	−2.69235	+	2.24322i	−0.283799	+	0.236456i
$91$	−8.49623	−	0.260267i	−0.890647	−	0.0272834i
$92$	7.78471	+	3.06663i	0.811612	+	0.319718i
$93$	5.66849	+	3.92864i	0.587795	+	0.407381i
$94$	−0.192008	+	0.0670504i	−0.0198041	+	0.00691572i
$95$	−0.607178			−0.0622951
$96$	9.79450	−	0.260429i	0.999647	−	0.0265799i
$97$	6.90198	+	11.9546i	0.700790	+	1.21380i	0.968190	+	0.250218i	$0.0805022\pi$
$97$	6.90198	+	11.9546i	0.700790	+	1.21380i	−0.267400	+	0.963586i	$0.586164\pi$
$98$	1.92532	−	0.672335i	0.194487	−	0.0679161i
$99$	−1.65292	−	1.36009i	−0.166124	−	0.136695i
$100$	−8.03454	−	3.16504i	−0.803454	−	0.316504i
$101$			12.1826i			1.21221i	0.795384	+	0.606106i	$0.207269\pi$
$101$			12.1826i			1.21221i	−0.795384	+	0.606106i	$0.792731\pi$
$102$	7.96097	−	7.83005i	0.788254	−	0.775291i
$103$	−3.15465	−	5.46402i	−0.310837	−	0.538386i	0.667707	−	0.744424i	$-0.267276\pi$
$103$	−3.15465	−	5.46402i	−0.310837	−	0.538386i	−0.978544	+	0.206039i	$0.933943\pi$
$104$	−4.46956	−	9.16641i	−0.438277	−	0.898840i
$105$	3.36138	+	0.277804i	0.328037	+	0.0271109i
$106$	−4.25487	+	4.93794i	−0.413270	+	0.479615i
$107$	−5.20611	+	3.00575i	−0.503293	+	0.290577i	−0.730073	−	0.683370i	$-0.760514\pi$
$107$	−5.20611	+	3.00575i	−0.503293	+	0.290577i	0.226779	+	0.973946i	$0.427180\pi$
$108$	−10.3414	−	1.02757i	−0.995100	−	0.0988777i
$109$			5.73467i			0.549282i	0.961547	+	0.274641i	$0.0885590\pi$
$109$			5.73467i			0.549282i	−0.961547	+	0.274641i	$0.911441\pi$
$110$	−0.155472	+	0.818856i	−0.0148236	+	0.0780748i
$111$	3.95268	−	5.70317i	0.375171	−	0.541321i
$112$	−6.89655	−	6.43157i	−0.651663	−	0.607726i
$113$	11.6994			1.10058			0.550292	−	0.834972i	$-0.314516\pi$
$113$	11.6994			1.10058			0.550292	+	0.834972i	$0.314516\pi$
$114$	−1.26261	−	1.28372i	−0.118254	−	0.120232i
$115$			3.45552i			0.322229i
$116$	14.4740	−	2.16291i	1.34388	−	0.200821i
$117$	3.48518	+	10.2398i	0.322205	+	0.946670i
$118$	13.8897	−	16.1195i	1.27865	−	1.48392i
$119$	−10.7471			−0.985188
$120$	1.58267	+	3.72418i	0.144477	+	0.339970i
$121$	10.4909			0.953717
$122$	−9.01619	−	1.71185i	−0.816287	−	0.154984i
$123$	0.496328	−	6.00546i	0.0447524	−	0.541494i
$124$	6.23258	−	4.95745i	0.559702	−	0.445192i
$125$		−	7.69639i		−	0.688386i
$126$	6.40255	+	7.68445i	0.570384	+	0.684585i
$127$	6.96220	+	12.0589i	0.617796	+	1.07005i	0.989887	+	0.141857i	$0.0453074\pi$
$127$	6.96220	+	12.0589i	0.617796	+	1.07005i	−0.372092	+	0.928196i	$0.621359\pi$
$128$	2.97649	−	10.9152i	0.263087	−	0.964772i
$129$	−2.54667	+	3.67450i	−0.224222	+	0.323521i
$130$	2.84570	−	3.10498i	0.249584	−	0.272325i
$131$	10.8350	−	6.25559i	0.946658	−	0.546553i	0.0546171	−	0.998507i	$-0.482606\pi$
$131$	10.8350	−	6.25559i	0.946658	−	0.546553i	0.892041	+	0.451954i	$0.149273\pi$
$132$	−2.05456	+	1.37408i	−0.178826	+	0.119599i
$133$			1.73300i			0.150270i
$134$	3.73760	+	10.7031i	0.322879	+	0.924608i
$135$	−1.17053	−	4.12929i	−0.100743	−	0.355393i
$136$	−6.00324	−	11.4110i	−0.514774	−	0.978483i
$137$	1.39508	+	2.41635i	0.119190	+	0.206443i	0.919447	−	0.393214i	$-0.128637\pi$
$137$	1.39508	+	2.41635i	0.119190	+	0.206443i	−0.800257	+	0.599657i	$0.795304\pi$
$138$	−7.30581	+	7.18567i	−0.621912	+	0.611685i
$139$			7.74528i			0.656946i	0.944513	+	0.328473i	$0.106534\pi$
$139$			7.74528i			0.656946i	−0.944513	+	0.328473i	$0.893466\pi$
$140$	1.42744	−	3.62360i	0.120641	−	0.306250i
$141$	0.0205161	−	0.248241i	0.00172777	−	0.0209056i
$142$	−3.19089	+	1.11428i	−0.267774	+	0.0935083i
$143$	2.18753	+	1.35393i	0.182931	+	0.113221i
$144$	−4.58271	+	11.0905i	−0.381893	+	0.924207i
$145$	3.02204	+	5.23433i	0.250967	+	0.434688i
$146$	−11.2051	−	9.65506i	−0.927337	−	0.799058i
$147$	−0.205721	+	2.48918i	−0.0169676	+	0.205304i
$148$	−4.98778	−	6.27071i	−0.409993	−	0.515449i
$149$		−	8.16204i		−	0.668660i	−0.942456	−	0.334330i	$-0.891490\pi$
$149$		−	8.16204i		−	0.668660i	0.942456	−	0.334330i	$-0.108510\pi$
$150$	7.54028	−	7.41628i	0.615661	−	0.605537i
$151$	7.60177	−	13.1667i	0.618623	−	1.07149i	−0.371114	−	0.928587i	$-0.621024\pi$
$151$	7.60177	−	13.1667i	0.618623	−	1.07149i	0.989737	−	0.142900i	$-0.0456426\pi$
$152$	−1.84004	+	0.968033i	−0.149247	+	0.0785179i
$153$	4.80079	+	12.8056i	0.388121	+	1.03527i
$154$	2.33716	+	0.443744i	0.188334	+	0.0357579i
$155$	2.84836	+	1.64450i	0.228786	+	0.132090i
$156$	12.4822	−	0.440233i	0.999379	−	0.0352468i
$157$	−19.0653	+	11.0073i	−1.52157	+	0.878481i	−0.521898	+	0.853008i	$0.674776\pi$
$157$	−19.0653	+	11.0073i	−1.52157	+	0.878481i	−0.999676	+	0.0254729i	$0.991891\pi$
$158$	−18.4840	+	6.45473i	−1.47051	+	0.513511i
$159$	−3.40858	−	7.21890i	−0.270318	−	0.572496i
$160$	4.64477	−	0.508491i	0.367202	−	0.0401997i
$161$	9.86269			0.777289
$162$	6.29624	−	11.0615i	0.494679	−	0.869076i
$163$	1.95082	+	1.12630i	0.152800	+	0.0882189i	0.574450	−	0.818539i	$-0.305216\pi$
$163$	1.95082	+	1.12630i	0.152800	+	0.0882189i	−0.421651	+	0.906758i	$0.638549\pi$
$164$	−6.47395	−	2.55028i	−0.505530	−	0.199143i
$165$	−0.839000	−	0.581483i	−0.0653161	−	0.0452684i
$166$	4.68776	+	13.4240i	0.363841	+	1.04191i
$167$	−5.91458	+	10.2443i	−0.457684	+	0.792732i	−0.998838	−	0.0481917i	$-0.984654\pi$
$167$	−5.91458	+	10.2443i	−0.457684	+	0.792732i	0.541154	+	0.840923i	$0.317987\pi$
$168$	10.6295	−	4.51722i	0.820083	−	0.348511i
$169$	−5.79870	−	11.6351i	−0.446054	−	0.895006i
$170$	3.47603	−	4.03407i	0.266599	−	0.309399i
$171$	2.06492	−	0.774136i	0.157909	−	0.0591996i
$172$	3.21358	+	4.04016i	0.245033	+	0.308059i
$173$	8.62493	−	4.97961i	0.655741	−	0.378592i	−0.134911	−	0.990858i	$-0.543075\pi$
$173$	8.62493	−	4.97961i	0.655741	−	0.378592i	0.790652	+	0.612265i	$0.209742\pi$
$174$	−4.78239	+	17.2740i	−0.362552	+	1.30954i
$175$	−10.1792			−0.769476
$176$	0.834361	+	2.72940i	0.0628924	+	0.205736i
$177$	11.1270	+	23.5656i	0.836360	+	1.77130i
$178$	−4.72206	+	24.8707i	−0.353934	+	1.86414i
$179$	2.06025	−	1.18948i	0.153990	−	0.0889062i	−0.421025	−	0.907049i	$-0.638330\pi$
$179$	2.06025	−	1.18948i	0.153990	−	0.0889062i	0.575015	+	0.818143i	$0.304996\pi$
$180$	−4.95528	−	0.0821705i	−0.369345	−	0.00612463i
$181$			20.6555i			1.53531i	0.640861	+	0.767657i	$0.278577\pi$
$181$			20.6555i			1.53531i	−0.640861	+	0.767657i	$0.721423\pi$
$182$	−8.86218	−	8.12213i	−0.656908	−	0.602053i
$183$	6.40254	−	9.23799i	0.473290	−	0.682892i
$184$	5.50920	+	10.4719i	0.406143	+	0.771998i
$185$	1.65456	−	2.86579i	0.121646	−	0.210697i
$186$	2.44622	+	9.44182i	0.179365	+	0.692308i
$187$	2.81690	+	1.62634i	0.205992	+	0.118930i
$188$	−0.267606	−	0.105418i	−0.0195171	−	0.00768838i
$189$	−11.7857	+	3.34089i	−0.857286	+	0.243014i
$190$	−0.650501	−	0.560517i	−0.0471923	−	0.0406641i
$191$	1.65432	+	2.86537i	0.119702	+	0.207331i	0.919650	−	0.392740i	$-0.128473\pi$
$191$	1.65432	+	2.86537i	0.119702	+	0.207331i	−0.799947	+	0.600070i	$0.795139\pi$
$192$	10.7338	+	8.76279i	0.774642	+	0.632400i
$193$	−1.34779	+	2.33444i	−0.0970162	+	0.168037i	−0.910448	−	0.413623i	$-0.864263\pi$
$193$	−1.34779	+	2.33444i	−0.0970162	+	0.168037i	0.813432	+	0.581660i	$0.197597\pi$
$194$	−3.64143	+	19.1791i	−0.261440	+	1.37698i
$195$	2.05860	+	4.72975i	0.147419	+	0.338704i
$196$	2.68336	+	1.05706i	0.191669	+	0.0755040i
$197$	11.2217	−	6.47885i	0.799513	−	0.461599i	−0.0437880	−	0.999041i	$-0.513943\pi$
$197$	11.2217	−	6.47885i	0.799513	−	0.461599i	0.843301	+	0.537442i	$0.180609\pi$
$198$	−0.515283	−	2.98303i	−0.0366196	−	0.211995i
$199$	2.94021	−	5.09260i	0.208426	−	0.361005i	−0.742793	−	0.669521i	$-0.766499\pi$
$199$	2.94021	−	5.09260i	0.208426	−	0.361005i	0.951219	+	0.308517i	$0.0998326\pi$
$200$	−5.68600	−	10.8080i	−0.402061	−	0.764238i
$201$	−13.8377	−	1.14363i	−0.976035	−	0.0806654i
$202$	−11.2464	+	13.0518i	−0.791291	+	0.918323i
$203$	14.9397	−	8.62546i	1.04856	−	0.605389i
$204$	15.7573	−	1.03956i	1.10323	−	0.0727838i
$205$		−	2.87369i		−	0.200708i
$206$	1.66437	−	8.76610i	0.115962	−	0.610763i
$207$	−4.40570	−	11.7517i	−0.306217	−	0.816801i
$208$	3.67350	−	13.9465i	0.254712	−	0.967017i
$209$	0.262250	−	0.454230i	0.0181402	−	0.0314197i
$210$	3.34476	+	3.40068i	0.230810	+	0.234669i
$211$	4.43070	+	2.55806i	0.305022	+	0.176104i	0.644697	−	0.764439i	$-0.276984\pi$
$211$	4.43070	+	2.55806i	0.305022	+	0.176104i	−0.339675	+	0.940543i	$0.610317\pi$
$212$	−9.11693	+	1.36238i	−0.626153	+	0.0935686i
$213$	0.340947	−	4.12539i	0.0233613	−	0.282667i
$214$	−8.35232	−	1.58581i	−0.570953	−	0.108404i
$215$	−1.06602	+	1.84640i	−0.0727019	+	0.125923i
$216$	−10.1306	−	10.6475i	−0.689303	−	0.724473i
$217$	4.69370	−	8.12974i	0.318629	−	0.551882i
$218$	−5.29396	+	6.14384i	−0.358552	+	0.416114i
$219$	16.3809	−	7.73466i	1.10692	−	0.522660i
$220$	−0.922492	+	0.733758i	−0.0621944	+	0.0494700i
$221$	−7.77850	−	14.4793i	−0.523239	−	0.973982i
$222$	9.49959	−	2.46118i	0.637570	−	0.165184i
$223$	16.1367			1.08059			0.540296	−	0.841475i	$-0.318312\pi$
$223$	16.1367			1.08059			0.540296	+	0.841475i	$0.318312\pi$
$224$	−1.45132	−	13.2570i	−0.0969707	−	0.885772i
$225$	4.54709	+	12.1289i	0.303139	+	0.808591i
$226$	12.5341	+	10.8003i	0.833759	+	0.718424i
$227$	4.09658	−	2.36516i	0.271899	−	0.156981i	−0.357851	−	0.933779i	$-0.616490\pi$
$227$	4.09658	−	2.36516i	0.271899	−	0.156981i	0.629750	+	0.776798i	$0.283157\pi$
$228$	−0.167631	−	2.54090i	−0.0111016	−	0.168275i
$229$	−20.3569	+	11.7531i	−1.34522	+	0.776665i	−0.987568	−	0.157190i	$-0.949757\pi$
$229$	−20.3569	+	11.7531i	−1.34522	+	0.776665i	−0.357654	+	0.933854i	$0.616423\pi$
$230$	−3.18997	+	3.70208i	−0.210340	+	0.244108i
$231$	−1.65966	+	2.39466i	−0.109197	+	0.157557i
$232$	17.5034	+	11.0444i	1.14916	+	0.725103i
$233$	−9.63844			−0.631436			−0.315718	−	0.948853i	$-0.602245\pi$
$233$	−9.63844			−0.631436			−0.315718	+	0.948853i	$0.602245\pi$
$234$	−5.71903	+	14.1878i	−0.373864	+	0.927483i
$235$		−	0.118786i		−	0.00774877i
$236$	29.7615	−	4.44739i	1.93731	−	0.289500i
$237$	1.97502	−	23.8973i	0.128291	−	1.55230i
$238$	−11.5140	−	9.92122i	−0.746339	−	0.643097i
$239$	−7.85625	−	13.6074i	−0.508179	−	0.880191i	−0.999955	−	0.00946968i	$-0.996986\pi$
$239$	−7.85625	−	13.6074i	−0.508179	−	0.880191i	0.491777	−	0.870721i	$-0.336348\pi$
$240$	−1.74239	+	5.45095i	−0.112471	+	0.351857i
$241$	4.17739	+	7.23546i	0.269090	+	0.466077i	0.968627	−	0.248519i	$-0.0799439\pi$
$241$	4.17739	+	7.23546i	0.269090	+	0.466077i	−0.699537	+	0.714596i	$0.746611\pi$
$242$	11.2394	+	9.68467i	0.722498	+	0.622554i
$243$	9.24552	+	12.5507i	0.593100	+	0.805128i
$244$	−8.07920	−	10.1573i	−0.517218	−	0.650254i
$245$			1.19111i			0.0760971i
$246$	6.07569	−	5.97577i	0.387372	−	0.381001i
$247$	−2.33481	+	1.25430i	−0.148560	+	0.0798090i
$248$	11.2538	+	0.442441i	0.714614	+	0.0280950i
$249$	−17.3555	−	1.43436i	−1.09986	−	0.0908990i
$250$	7.10492	−	8.24553i	0.449355	−	0.521493i
$251$	1.45865	+	0.842153i	0.0920693	+	0.0531562i	0.545328	−	0.838223i	$-0.316405\pi$
$251$	1.45865	+	0.842153i	0.0920693	+	0.0531562i	−0.453258	+	0.891379i	$0.649739\pi$
$252$	−0.234530	+	14.1433i	−0.0147740	+	0.890942i
$253$	−2.58508	−	1.49250i	−0.162523	−	0.0938324i
$254$	−3.67321	+	19.3465i	−0.230478	+	1.21391i
$255$	2.78465	+	5.89750i	0.174381	+	0.369316i
$256$	13.2652	−	8.94621i	0.829075	−	0.559138i
$257$	8.78107	−	15.2093i	0.547748	−	0.948728i	−0.450680	−	0.892686i	$-0.648818\pi$
$257$	8.78107	−	15.2093i	0.547748	−	0.948728i	0.998428	−	0.0560423i	$-0.0178482\pi$
$258$	−6.12049	+	1.58572i	−0.381045	+	0.0987224i
$259$	−8.17947	−	4.72242i	−0.508248	−	0.293437i
$260$	5.91510	−	0.699517i	0.366839	−	0.0433822i
$261$	−16.9512	−	13.9482i	−1.04925	−	0.863370i
$262$	17.3829	+	3.30040i	1.07392	+	0.203900i
$263$	−27.5137			−1.69657			−0.848284	−	0.529541i	$-0.822364\pi$
$263$	−27.5137			−1.69657			−0.848284	+	0.529541i	$0.822364\pi$
$264$	−3.46964	−	0.424541i	−0.213542	−	0.0261287i
$265$	−1.90353	−	3.29702i	−0.116933	−	0.202534i
$266$	−1.59982	+	1.85665i	−0.0980910	+	0.113838i
$267$	−25.4826	−	17.6611i	−1.55951	−	1.08084i
$268$	−5.87631	+	14.9172i	−0.358953	+	0.911210i
$269$	5.91901	+	3.41734i	0.360888	+	0.208359i	0.669470	−	0.742839i	$-0.266521\pi$
$269$	5.91901	+	3.41734i	0.360888	+	0.208359i	−0.308582	+	0.951198i	$0.599854\pi$
$270$	2.55791	−	5.50449i	0.155669	−	0.334993i
$271$	10.7743	+	18.6616i	0.654490	+	1.13361i	0.982021	+	0.188769i	$0.0604498\pi$
$271$	10.7743	+	18.6616i	0.654490	+	1.13361i	−0.327532	+	0.944840i	$0.606217\pi$
$272$	4.10247	−	17.7670i	0.248749	−	1.07729i
$273$	13.4996	−	5.87562i	0.817030	−	0.355609i
$274$	−0.736035	+	3.87663i	−0.0444655	+	0.234196i
$275$	2.66804	+	1.54039i	0.160889	+	0.0928893i
$276$	−14.4605	+	0.954009i	−0.870423	+	0.0574246i
$277$	8.22223	−	4.74711i	0.494026	−	0.285226i	−0.232217	−	0.972664i	$-0.574598\pi$
$277$	8.22223	−	4.74711i	0.494026	−	0.285226i	0.726243	+	0.687438i	$0.241265\pi$
$278$	−7.15006	+	8.29791i	−0.428832	+	0.497676i
$279$	−11.7835	−	1.96112i	−0.705463	−	0.117409i
$280$	4.87442	−	2.56440i	0.291302	−	0.153252i
$281$	−5.35523	+	9.27554i	−0.319466	+	0.553332i	−0.980377	−	0.197133i	$-0.936837\pi$
$281$	−5.35523	+	9.27554i	−0.319466	+	0.553332i	0.660910	+	0.750465i	$0.270170\pi$
$282$	0.251143	−	0.247013i	0.0149554	−	0.0147094i
$283$	13.0520	+	7.53555i	0.775858	+	0.447942i	0.834960	−	0.550310i	$-0.185490\pi$
$283$	13.0520	+	7.53555i	0.775858	+	0.447942i	−0.0591022	+	0.998252i	$0.518824\pi$
$284$	−4.44721	−	1.75189i	−0.263893	−	0.103955i
$285$	0.950982	−	0.449029i	0.0563313	−	0.0265982i
$286$	1.09374	+	3.46996i	0.0646739	+	0.205183i
$287$	−8.20204			−0.484151
$288$	−15.1479	+	7.65127i	−0.892597	+	0.450855i
$289$	−1.89057	−	3.27456i	−0.111210	−	0.192621i
$290$	−1.59441	+	8.39761i	−0.0936269	+	0.493125i
$291$	−19.6509	−	13.6194i	−1.15196	−	0.798384i
$292$	−3.09148	−	20.6879i	−0.180915	−	1.21067i
$293$		−	9.91297i		−	0.579122i	−0.957160	−	0.289561i	$-0.906491\pi$
$293$		−	9.91297i		−	0.579122i	0.957160	−	0.289561i	$-0.0935093\pi$
$294$	−2.51829	+	2.47688i	−0.146870	+	0.144454i
$295$	6.21395	+	10.7629i	0.361790	+	0.626639i
$296$	0.445148	−	11.3226i	0.0258737	−	0.658113i
$297$	3.59469	+	0.907835i	0.208585	+	0.0526779i
$298$	7.53479	−	8.74441i	0.436479	−	0.506550i
$299$	7.13836	+	13.2877i	0.412822	+	0.768447i
$300$	14.9246	−	0.984626i	0.861674	−	0.0568474i
$301$	5.26996	+	3.04261i	0.303755	+	0.175373i
$302$	20.2990	−	7.08853i	1.16807	−	0.407899i
$303$	−9.00944	−	19.0808i	−0.517579	−	1.09616i
$304$	−2.86497	−	0.661530i	−0.164317	−	0.0379414i
$305$	2.68006	−	4.64200i	0.153460	−	0.265800i
$306$	−6.67814	+	18.1511i	−0.381764	+	1.03763i
$307$			11.6413i			0.664402i	0.943209	+	0.332201i	$0.107791\pi$
$307$			11.6413i			0.664402i	−0.943209	+	0.332201i	$0.892209\pi$
$308$	2.09428	+	2.63296i	0.119333	+	0.150027i
$309$	8.98176	+	6.22495i	0.510954	+	0.354125i
$310$	1.53347	+	4.39130i	0.0870953	+	0.249409i
$311$	−6.37253	−	11.0375i	−0.361353	−	0.625882i	0.626831	−	0.779156i	$-0.284352\pi$
$311$	−6.37253	−	11.0375i	−0.361353	−	0.625882i	−0.988184	+	0.153274i	$0.951018\pi$
$312$	13.7793	+	11.0513i	0.780097	+	0.625659i
$313$	−3.53945	+	6.13051i	−0.200062	+	0.346517i	−0.948548	−	0.316633i	$-0.897448\pi$
$313$	−3.53945	+	6.13051i	−0.200062	+	0.346517i	0.748486	+	0.663150i	$0.230781\pi$
$314$	−30.5870	−	5.80739i	−1.72613	−	0.327730i
$315$	−5.47015	+	2.05075i	−0.308208	+	0.115547i
$316$	−25.7615	−	10.1482i	−1.44920	−	0.570883i
$317$	−26.6192	−	15.3686i	−1.49508	−	0.863187i	−0.495099	−	0.868836i	$-0.664868\pi$
$317$	−26.6192	−	15.3686i	−1.49508	−	0.863187i	−0.999984	+	0.00564972i	$0.998202\pi$
$318$	3.01235	−	10.8806i	0.168924	−	0.610154i
$319$	−5.22108			−0.292324
$320$	5.44560	+	3.74305i	0.304418	+	0.209243i
$321$	5.93112	−	8.55780i	0.331043	−	0.477650i
$322$	10.5664	+	9.10475i	0.588842	+	0.507388i
$323$	−2.90205	+	1.67550i	−0.161474	+	0.0932272i
$324$	16.9569	−	6.03840i	0.942052	−	0.335467i
$325$	−7.36745	−	13.7141i	−0.408673	−	0.760723i
$326$	1.05026	+	3.00756i	0.0581685	+	0.166573i
$327$	−4.24099	−	8.98183i	−0.234527	−	0.496696i
$328$	−4.58158	−	8.70867i	−0.252975	−	0.480856i
$329$	−0.339038			−0.0186918
$330$	−0.362068	−	1.39750i	−0.0199312	−	0.0769296i
$331$	23.9649	−	13.8362i	1.31723	−	0.760505i	0.333950	−	0.942591i	$-0.391618\pi$
$331$	23.9649	−	13.8362i	1.31723	−	0.760505i	0.983283	+	0.182086i	$0.0582850\pi$
$332$	−7.37018	+	18.7094i	−0.404491	+	1.02681i
$333$	−1.97312	+	11.8556i	−0.108126	+	0.649685i
$334$	−15.7937	+	5.51525i	−0.864191	+	0.301781i
$335$	−6.62152			−0.361772
$336$	15.5580	+	4.97310i	0.848758	+	0.271305i
$337$	−7.69181	−	13.3226i	−0.419000	−	0.725729i	0.576839	−	0.816858i	$-0.304286\pi$
$337$	−7.69181	−	13.3226i	−0.419000	−	0.725729i	−0.995839	+	0.0911288i	$0.970953\pi$
$338$	4.52849	−	17.8183i	0.246317	−	0.969189i
$339$	−18.3240	+	8.65210i	−0.995221	+	0.469918i
$340$	7.44810	−	1.11300i	0.403930	−	0.0603609i
$341$	−2.46051	+	1.42057i	−0.133244	+	0.0769284i
$342$	2.92690	+	1.07686i	0.158269	+	0.0582301i
$343$	19.9024			1.07463
$344$	−0.286805	+	7.29504i	−0.0154635	+	0.393322i
$345$	−2.55548	−	5.41216i	−0.137582	−	0.291381i
$346$	13.8373	+	2.62720i	0.743895	+	0.141239i
$347$			4.55086i			0.244303i	0.992511	+	0.122151i	$0.0389794\pi$
$347$			4.55086i			0.244303i	−0.992511	+	0.122151i	$0.961021\pi$
$348$	−21.0701	+	14.0916i	−1.12948	+	0.755392i
$349$			27.2511i			1.45872i	0.684130	+	0.729360i	$0.260182\pi$
$349$			27.2511i			1.45872i	−0.684130	+	0.729360i	$0.739818\pi$
$350$	−10.9055	−	9.39694i	−0.582924	−	0.502288i
$351$	−13.0313	−	13.4605i	−0.695559	−	0.718469i
$352$	−1.62575	+	3.69438i	−0.0866528	+	0.196911i
$353$	−4.49293			−0.239135			−0.119567	−	0.992826i	$-0.538151\pi$
$353$	−4.49293			−0.239135			−0.119567	+	0.992826i	$0.538151\pi$
$354$	−9.83359	+	35.5189i	−0.522649	+	1.88781i
$355$		−	1.97406i		−	0.104772i
$356$	−28.0184	+	22.2861i	−1.48497	+	1.18116i
$357$	16.8325	−	7.94788i	0.890872	−	0.420647i
$358$	3.30532	+	0.627563i	0.174692	+	0.0331677i
$359$	4.92994			0.260192			0.130096	−	0.991501i	$-0.458471\pi$
$359$	4.92994			0.260192			0.130096	+	0.991501i	$0.458471\pi$
$360$	−5.23299	−	4.66250i	−0.275803	−	0.245735i
$361$	−9.22982	−	15.9865i	−0.485780	−	0.841396i
$362$	−19.0682	+	22.1293i	−1.00220	+	1.16309i
$363$	−16.4312	+	7.75838i	−0.862414	+	0.407209i
$364$	−1.99655	−	16.8828i	−0.104648	−	0.884898i
$365$	7.48152	−	4.31946i	0.391600	−	0.226091i
$366$	15.3874	−	3.98662i	0.804314	−	0.208384i
$367$	−19.5409			−1.02003			−0.510013	−	0.860167i	$-0.670360\pi$
$367$	−19.5409			−1.02003			−0.510013	+	0.860167i	$0.670360\pi$
$368$	−3.76485	+	16.3049i	−0.196256	+	0.849951i
$369$	3.66388	+	9.77301i	0.190734	+	0.508763i
$370$	4.41817	−	1.54285i	0.229690	−	0.0802091i
$371$	−9.41029	+	5.43303i	−0.488558	+	0.282069i
$372$	−6.09547	+	12.3737i	−0.316035	+	0.641548i
$373$		−	6.06322i		−	0.313942i	−0.987603	−	0.156971i	$-0.949827\pi$
$373$		−	6.06322i		−	0.313942i	0.987603	−	0.156971i	$-0.0501729\pi$
$374$	1.51653	+	4.34280i	0.0784181	+	0.224561i
$375$	5.69175	+	12.0543i	0.293921	+	0.622484i
$376$	−0.189383	−	0.359980i	−0.00976669	−	0.0185645i
$377$	22.4338	+	13.8850i	1.15540	+	0.715112i
$378$	−15.7108	−	7.30074i	−0.808077	−	0.375510i
$379$	21.0552	−	12.1562i	1.08153	−	0.624424i	0.150225	−	0.988652i	$-0.452000\pi$
$379$	21.0552	−	12.1562i	1.08153	−	0.624424i	0.931310	+	0.364228i	$0.118667\pi$
$380$	−0.179473	−	1.20102i	−0.00920679	−	0.0616110i
$381$	−19.8224	−	13.7382i	−1.01553	−	0.703832i
$382$	−0.872807	+	4.59700i	−0.0446567	+	0.235203i
$383$	4.59688			0.234889			0.117445	−	0.993079i	$-0.462530\pi$
$383$	4.59688			0.234889			0.117445	+	0.993079i	$0.462530\pi$
$384$	3.41025	+	19.2969i	0.174029	+	0.984741i
$385$	−0.694721	+	1.20329i	−0.0354063	+	0.0613255i
$386$	−3.59900	+	1.25679i	−0.183184	+	0.0639691i
$387$	1.27126	−	7.63847i	0.0646219	−	0.388285i
$388$	−21.6065	+	17.1860i	−1.09690	+	0.872486i
$389$	4.31934	+	2.49377i	0.218999	+	0.126439i	0.605487	−	0.795855i	$-0.292978\pi$
$389$	4.31934	+	2.49377i	0.218999	+	0.126439i	−0.386487	+	0.922295i	$0.626312\pi$
$390$	−2.16078	+	6.96762i	−0.109416	+	0.352819i
$391$	9.53547	+	16.5159i	0.482229	+	0.835246i
$392$	1.89900	+	3.60963i	0.0959141	+	0.182314i
$393$	−12.3439	+	17.8106i	−0.622668	+	0.898425i
$394$	18.0033	+	3.41819i	0.906995	+	0.172206i
$395$		−	11.4352i		−	0.575367i
$396$	2.20174	−	3.67156i	0.110641	−	0.184503i
$397$	13.3910	+	7.73131i	0.672076	+	0.388024i	0.796863	−	0.604160i	$-0.206491\pi$
$397$	13.3910	+	7.73131i	0.672076	+	0.388024i	−0.124786	+	0.992184i	$0.539825\pi$
$398$	7.85124	−	2.74170i	0.393547	−	0.137429i
$399$	−1.28161	−	2.71428i	−0.0641608	−	0.135884i
$400$	3.88567	−	16.8282i	0.194284	−	0.841408i
$401$	9.58243	−	16.5972i	0.478524	−	0.828827i	−0.521173	−	0.853451i	$-0.674505\pi$
$401$	9.58243	−	16.5972i	0.478524	−	0.828827i	0.999697	+	0.0246239i	$0.00783881\pi$
$402$	−13.7693	−	13.9995i	−0.686749	−	0.698231i
$403$	14.3501	+	0.439591i	0.714831	+	0.0218976i
$404$	−24.0976	+	3.60100i	−1.19890	+	0.179156i
$405$	4.88707	+	5.60179i	0.242841	+	0.278355i
$406$	23.9683	+	4.55073i	1.18953	+	0.225849i
$407$	1.42926	+	2.47556i	0.0708460	+	0.122709i
$408$	17.8413	+	13.4326i	0.883275	+	0.665015i
$409$	−12.6690			−0.626441			−0.313220	−	0.949680i	$-0.601408\pi$
$409$	−12.6690			−0.626441			−0.313220	+	0.949680i	$0.601408\pi$
$410$	2.65285	−	3.07874i	0.131015	−	0.152048i
$411$	−3.97200	−	2.75286i	−0.195924	−	0.135789i
$412$	9.87556	−	7.85511i	0.486534	−	0.386993i
$413$	30.7192	−	17.7357i	1.51159	−	0.872718i
$414$	6.12856	−	16.6573i	0.301202	−	0.818664i
$415$	−8.30483			−0.407668
$416$	16.8103	−	11.5504i	0.824195	−	0.566306i
$417$	−5.72790	−	12.1309i	−0.280497	−	0.594053i
$418$	0.700284	−	0.244544i	0.0342520	−	0.0119610i
$419$	−13.7547	−	7.94128i	−0.671961	−	0.387957i	0.124858	−	0.992175i	$-0.460152\pi$
$419$	−13.7547	−	7.94128i	−0.671961	−	0.387957i	−0.796819	+	0.604218i	$0.793486\pi$
$420$	0.444068	+	6.73104i	0.0216683	+	0.328441i
$421$	−1.19901	−	0.692247i	−0.0584361	−	0.0337381i	0.470497	−	0.882401i	$-0.344075\pi$
$421$	−1.19901	−	0.692247i	−0.0584361	−	0.0337381i	−0.528933	+	0.848663i	$0.677408\pi$
$422$	2.38535	+	6.83078i	0.116117	+	0.332517i
$423$	0.151450	+	0.403975i	0.00736373	+	0.0196419i
$424$	−11.0251	−	6.95671i	−0.535427	−	0.337848i
$425$	−9.84149	−	17.0460i	−0.477382	−	0.826850i
$426$	4.17363	−	4.10500i	0.202213	−	0.198888i
$427$	−13.2491	−	7.64938i	−0.641169	−	0.370179i
$428$	−7.48433	−	9.40941i	−0.361769	−	0.454821i
$429$	−4.42747	−	0.502813i	−0.213760	−	0.0242761i
$430$	−2.84658	+	0.994045i	−0.137274	+	0.0479371i
$431$	−14.6056	−	25.2976i	−0.703526	−	1.21854i	−0.967221	−	0.253937i	$-0.918274\pi$
$431$	−14.6056	−	25.2976i	−0.703526	−	1.21854i	0.263695	−	0.964606i	$-0.415059\pi$
$432$	−1.02420	−	20.7594i	−0.0492769	−	0.998785i
$433$	19.6108	−	33.9669i	0.942435	−	1.63235i	0.181628	−	0.983367i	$-0.441863\pi$
$433$	19.6108	−	33.9669i	0.942435	−	1.63235i	0.760807	−	0.648978i	$-0.224803\pi$
$434$	12.5336	−	4.37680i	0.601631	−	0.210093i
$435$	−8.60420	−	5.96328i	−0.412540	−	0.285917i
$436$	−11.3434	+	1.69509i	−0.543250	+	0.0811800i
$437$	2.66322	−	1.53761i	0.127399	−	0.0735539i
$438$	24.6900	+	6.83555i	1.17973	+	0.326615i
$439$	−23.9547			−1.14329			−0.571647	−	0.820500i	$-0.693695\pi$
$439$	−23.9547			−1.14329			−0.571647	+	0.820500i	$0.693695\pi$
$440$	−1.66568	−	0.0654863i	−0.0794083	−	0.00312194i
$441$	−1.51863	−	4.05078i	−0.0723158	−	0.192894i
$442$	5.03306	−	22.6931i	0.239398	−	1.07940i
$443$	30.7012	+	17.7254i	1.45866	+	0.842157i	0.998946	−	0.0459103i	$-0.0146188\pi$
$443$	30.7012	+	17.7254i	1.45866	+	0.842157i	0.459713	+	0.888067i	$0.347952\pi$
$444$	12.4494	+	6.13276i	0.590824	+	0.291048i
$445$	−12.8047	−	7.39281i	−0.607002	−	0.350453i
$446$	17.2880	+	14.8966i	0.818612	+	0.705373i
$447$	6.03611	+	12.7837i	0.285498	+	0.604647i
$448$	10.6834	−	15.5427i	0.504741	−	0.734324i
$449$	6.02963	−	10.4436i	0.284556	−	0.492865i	−0.687946	−	0.725762i	$-0.741487\pi$
$449$	6.02963	−	10.4436i	0.284556	−	0.492865i	0.972501	+	0.232897i	$0.0748206\pi$
$450$	−6.32524	+	17.1919i	−0.298175	+	0.810435i
$451$	2.14981	+	1.24119i	0.101231	+	0.0584456i
$452$	3.45817	+	23.1418i	0.162659	+	1.08850i
$453$	−2.16895	+	26.2438i	−0.101906	+	1.23304i
$454$	6.57227	+	1.24784i	0.308452	+	0.0585641i
$455$	6.18511	−	3.32274i	0.289962	−	0.155772i
$456$	2.16604	−	2.87694i	0.101434	−	0.134725i
$457$	4.12277			0.192855			0.0964275	−	0.995340i	$-0.469258\pi$
$457$	4.12277			0.192855			0.0964275	+	0.995340i	$0.469258\pi$
$458$	−32.6592	−	6.20083i	−1.52607	−	0.289746i
$459$	−16.9893	−	16.5062i	−0.792994	−	0.770442i
$460$	−6.83515	+	1.02140i	−0.318691	+	0.0476232i
$461$	19.6555	−	11.3481i	0.915449	−	0.528535i	0.0332690	−	0.999446i	$-0.489408\pi$
$461$	19.6555	−	11.3481i	0.915449	−	0.528535i	0.882180	+	0.470911i	$0.156075\pi$
$462$	−3.98871	+	1.03341i	−0.185571	+	0.0480784i
$463$	−5.25021	−	9.09363i	−0.243998	−	0.422617i	0.717852	−	0.696196i	$-0.245126\pi$
$463$	−5.25021	−	9.09363i	−0.243998	−	0.422617i	−0.961849	+	0.273580i	$0.911792\pi$
$464$	8.55662	+	27.9908i	0.397231	+	1.29944i
$465$	−5.67736	−	0.469212i	−0.263281	−	0.0217592i
$466$	−10.3262	−	8.89774i	−0.478350	−	0.412180i
$467$			28.5529i			1.32127i	0.750706	+	0.660636i	$0.229713\pi$
$467$			28.5529i			1.32127i	−0.750706	+	0.660636i	$0.770287\pi$
$468$	−19.2245	+	9.92056i	−0.888654	+	0.458578i
$469$			18.8990i			0.872675i
$470$	0.109658	−	0.127262i	0.00505813	−	0.00587016i
$471$	21.7203	−	31.3395i	1.00082	−	1.44405i
$472$	35.9907	+	22.7097i	1.65660	+	1.04530i
$473$	−0.920861	−	1.59498i	−0.0423412	−	0.0733372i
$474$	24.1768	−	23.7792i	1.11048	−	1.09221i
$475$	−2.74869	+	1.58696i	−0.126119	+	0.0728146i
$476$	−3.17670	−	21.2582i	−0.145604	−	0.974369i
$477$	10.6773	+	8.78572i	0.488878	+	0.402270i
$478$	4.14490	−	21.8308i	0.189583	−	0.998519i
$479$	−18.6786			−0.853449			−0.426724	−	0.904382i	$-0.640333\pi$
$479$	−18.6786			−0.853449			−0.426724	+	0.904382i	$0.640333\pi$
$480$	−6.89875	+	4.23139i	−0.314884	+	0.193136i
$481$	0.442280	−	14.4379i	0.0201662	−	0.658312i
$482$	−2.20396	+	11.6081i	−0.100388	+	0.528733i
$483$	−15.4473	+	7.29380i	−0.702875	+	0.331880i
$484$	3.10096	+	20.7514i	0.140953	+	0.943244i
$485$	−9.87440	−	5.70099i	−0.448374	−	0.258869i
$486$	−1.68100	+	21.9812i	−0.0762516	+	0.997089i
$487$	7.38624	−	12.7933i	0.334702	−	0.579722i	−0.648725	−	0.761023i	$-0.724698\pi$
$487$	7.38624	−	12.7933i	0.334702	−	0.579722i	0.983428	+	0.181301i	$0.0580309\pi$
$488$	0.721051	−	18.3403i	0.0326404	−	0.830229i
$489$	−3.88837	−	0.321359i	−0.175838	−	0.0145323i
$490$	−1.09957	+	1.27609i	−0.0496736	+	0.0576481i
$491$	30.0900	+	17.3725i	1.35794	+	0.784009i	0.989347	−	0.145580i	$-0.0465048\pi$
$491$	30.0900	+	17.3725i	1.35794	+	0.784009i	0.368597	+	0.929589i	$0.379838\pi$
$492$	12.0257	−	0.793376i	0.542162	−	0.0357682i
$493$	28.8881	+	16.6786i	1.30106	+	0.751165i
$494$	−3.65931	−	0.811589i	−0.164640	−	0.0365151i
$495$	1.74410	+	0.290268i	0.0783914	+	0.0130466i
$496$	11.6483	+	10.8629i	0.523023	+	0.487759i
$497$	−5.63431			−0.252733
$498$	−17.2697	−	17.5584i	−0.773873	−	0.786812i
$499$	−17.6854	+	10.2107i	−0.791707	+	0.457093i	−0.840563	−	0.541713i	$-0.817776\pi$
$499$	−17.6854	+	10.2107i	−0.791707	+	0.457093i	0.0488559	+	0.998806i	$0.484443\pi$
$500$	15.2237	−	2.27494i	0.680826	−	0.101739i
$501$	1.68756	−	20.4191i	0.0753945	−	0.912257i
$502$	0.785294	+	2.24880i	0.0350494	+	0.100369i
$503$	0.00569642	−	0.00986649i	0.000253991	−	0.000439925i	−0.865898	−	0.500220i	$-0.833252\pi$
$503$	0.00569642	−	0.00986649i	0.000253991	−	0.000439925i	0.866152	+	0.499780i	$0.166586\pi$
$504$	−13.3076	+	14.9359i	−0.592769	+	0.665298i
$505$	−5.03136	−	8.71458i	−0.223893	−	0.387794i
$506$	−1.39173	−	3.98540i	−0.0618699	−	0.177173i
$507$	17.6867	+	13.9349i	0.785493	+	0.618871i
$508$	−21.7950	+	17.3359i	−0.966996	+	0.769158i
$509$	−3.41032	−	1.96895i	−0.151160	−	0.0872721i	0.422512	−	0.906357i	$-0.361148\pi$
$509$	−3.41032	−	1.96895i	−0.151160	−	0.0872721i	−0.573672	+	0.819085i	$0.694482\pi$
$510$	−2.46095	+	8.88894i	−0.108973	+	0.393609i
$511$	−12.3285	−	21.3536i	−0.545381	−	0.944628i
$512$	22.4704	+	2.66124i	0.993060	+	0.117611i
$513$	−2.66165	+	2.73956i	−0.117515	+	0.120955i
$514$	23.4481	−	8.18821i	1.03425	−	0.361166i
$515$	4.51324	+	2.60572i	0.198877	+	0.114822i
$516$	−8.02105	−	3.95128i	−0.353107	−	0.173945i
$517$	0.0888642	+	0.0513058i	0.00390824	+	0.00225642i
$518$	−4.40358	−	12.6103i	−0.193482	−	0.554063i
$519$	−9.82606	+	14.1777i	−0.431316	+	0.622330i
$520$	6.98291	+	4.71110i	0.306221	+	0.206596i
$521$	19.6482			0.860804			0.430402	−	0.902637i	$-0.358372\pi$
$521$	19.6482			0.860804			0.430402	+	0.902637i	$0.358372\pi$
$522$	−5.28438	−	30.5919i	−0.231291	−	1.33897i
$523$	15.8740	−	9.16486i	0.694122	−	0.400751i	−0.111033	−	0.993817i	$-0.535416\pi$
$523$	15.8740	−	9.16486i	0.694122	−	0.400751i	0.805154	+	0.593065i	$0.202082\pi$
$524$	15.5765	+	19.5830i	0.680461	+	0.855486i
$525$	15.9430	−	7.52788i	0.695810	−	0.328544i
$526$	−29.4769	−	25.3993i	−1.28525	−	1.10746i
$527$	18.1519			0.790710
$528$	−3.32529	−	3.65783i	−0.144715	−	0.159187i
$529$	2.74927	+	4.76187i	0.119533	+	0.207038i
$530$	1.00429	−	5.28951i	0.0436236	−	0.229762i
$531$	−34.8551	−	28.6803i	−1.51258	−	1.24462i
$532$	−3.42793	+	0.512249i	−0.148620	+	0.0222088i
$533$	−5.93643	−	11.0504i	−0.257135	−	0.478644i
$534$	−10.9969	−	42.4455i	−0.475882	−	1.83680i
$535$	2.48273	−	4.30021i	0.107338	−	0.185914i
$536$	−20.0664	+	10.5568i	−0.866735	+	0.455984i
$537$	−2.34716	+	3.38663i	−0.101287	+	0.146144i
$538$	3.18661	+	9.12531i	0.137385	+	0.393420i
$539$	−0.891069	−	0.514459i	−0.0383810	−	0.0221593i
$540$	7.82189	−	3.53590i	0.336601	−	0.152161i
$541$			3.83563i			0.164907i	0.996595	+	0.0824534i	$0.0262756\pi$
$541$			3.83563i			0.164907i	−0.996595	+	0.0824534i	$0.973724\pi$
$542$	−5.68442	+	29.9394i	−0.244167	+	1.28601i
$543$	−15.2755	−	32.3514i	−0.655534	−	1.38833i
$544$	20.7968	−	15.2476i	0.891657	−	0.653733i
$545$	−2.36840	−	4.10219i	−0.101451	−	0.175718i
$546$	19.8868	+	6.16727i	0.851078	+	0.263935i
$547$	−27.6062	−	15.9385i	−1.18036	−	0.681479i	−0.224260	−	0.974529i	$-0.571996\pi$
$547$	−27.6062	−	15.9385i	−1.18036	−	0.681479i	−0.956097	+	0.293050i	$0.905330\pi$
$548$	−4.36727	+	3.47376i	−0.186561	+	0.148392i
$549$	−3.19606	+	19.2038i	−0.136405	+	0.819597i
$550$	1.43639	+	4.11331i	0.0612480	+	0.175392i
$551$	2.68945	−	4.65826i	0.114574	−	0.198449i
$552$	−16.3730	−	12.3272i	−0.696882	−	0.524680i
$553$	−32.6381			−1.38791
$554$	13.1912	+	2.50454i	0.560440	+	0.106408i
$555$	−0.472082	+	5.71210i	−0.0200388	+	0.242465i
$556$	−15.3204	+	2.28940i	−0.649731	+	0.0970920i
$557$	−25.3885	+	14.6580i	−1.07574	+	0.621081i	−0.929745	−	0.368203i	$-0.879973\pi$
$557$	−25.3885	+	14.6580i	−1.07574	+	0.621081i	−0.145999	+	0.989285i	$0.546640\pi$
$558$	−10.8139	−	12.9790i	−0.457789	−	0.549447i
$559$	−0.284957	+	9.30221i	−0.0120524	+	0.393442i
$560$	7.58954	+	1.75245i	0.320716	+	0.0740544i
$561$	−5.61465	−	0.464029i	−0.237051	−	0.0195913i
$562$	−14.3001	+	4.99367i	−0.603211	+	0.210645i
$563$			28.4113i			1.19739i	0.800976	+	0.598697i	$0.204314\pi$
$563$			28.4113i			1.19739i	−0.800976	+	0.598697i	$0.795686\pi$
$564$	0.497093	−	0.0327948i	0.0209314	−	0.00138091i
$565$	−8.36893	+	4.83180i	−0.352084	+	0.203276i
$566$	7.02678	+	20.1221i	0.295358	+	0.845797i
$567$	15.9885	−	13.9486i	0.671454	−	0.585785i
$568$	−3.14727	−	5.98233i	−0.132056	−	0.251013i
$569$	40.3323			1.69082			0.845408	−	0.534121i	$-0.179357\pi$
$569$	40.3323			1.69082			0.845408	+	0.534121i	$0.179357\pi$
$570$	1.43336	+	0.396832i	0.0600367	+	0.0166215i
$571$	6.34043	−	3.66065i	0.265339	−	0.153193i	−0.361429	−	0.932400i	$-0.617711\pi$
$571$	6.34043	−	3.66065i	0.265339	−	0.153193i	0.626767	+	0.779206i	$0.284378\pi$
$572$	−2.03152	+	4.72723i	−0.0849421	+	0.197655i
$573$	−4.71009	−	3.26441i	−0.196767	−	0.136373i
$574$	−8.78727	−	7.57172i	−0.366773	−	0.316038i
$575$	9.03157	+	15.6431i	0.376642	+	0.652364i
$576$	−23.2920	−	5.78658i	−0.970498	−	0.241107i
$577$	−23.2087			−0.966193			−0.483096	−	0.875567i	$-0.660488\pi$
$577$	−23.2087			−0.966193			−0.483096	+	0.875567i	$0.660488\pi$
$578$	0.997451	−	5.25349i	0.0414885	−	0.218516i
$579$	0.384554	−	4.65302i	0.0159815	−	0.193373i
$580$	−9.46043	+	7.52491i	−0.392823	+	0.312455i
$581$			23.7035i			0.983386i
$582$	−8.48029	−	32.7319i	−0.351519	−	1.35678i
$583$	3.28867			0.136203
$584$	15.7860	−	25.0179i	0.653229	−	1.03525i
$585$	−6.72206	−	5.88548i	−0.277923	−	0.243335i
$586$	9.15116	−	10.6203i	0.378031	−	0.438719i
$587$		−	14.4074i		−	0.594655i	−0.954775	−	0.297328i	$-0.903905\pi$
$587$		−	14.4074i		−	0.594655i	0.954775	−	0.297328i	$-0.0960954\pi$
$588$	−4.98451	+	0.328844i	−0.205558	+	0.0135613i
$589$		−	2.92703i		−	0.120606i
$590$	−3.27843	+	17.2672i	−0.134971	+	0.710881i
$591$	−12.7845	+	18.4462i	−0.525883	+	0.758776i
$592$	10.9294	−	11.7195i	0.449194	−	0.481670i
$593$	−16.2644			−0.667899			−0.333949	−	0.942591i	$-0.608381\pi$
$593$	−16.2644			−0.667899			−0.333949	+	0.942591i	$0.608381\pi$
$594$	3.01311	+	4.29105i	0.123629	+	0.176064i
$595$	7.68776	−	4.43853i	0.315168	−	0.181962i
$596$	16.1448	−	2.41259i	0.661317	−	0.0988233i
$597$	−0.838906	+	10.1506i	−0.0343342	+	0.415436i
$598$	−4.61885	+	20.8256i	−0.188879	+	0.851621i
$599$	5.90076	+	10.2204i	0.241098	+	0.417595i	0.961027	−	0.276453i	$-0.0891590\pi$
$599$	5.90076	+	10.2204i	0.241098	+	0.417595i	−0.719929	+	0.694048i	$0.755826\pi$
$600$	16.8985	+	12.7228i	0.689877	+	0.519406i
$601$	−35.7597			−1.45867			−0.729333	−	0.684158i	$-0.760170\pi$
$601$	−35.7597			−1.45867			−0.729333	+	0.684158i	$0.760170\pi$
$602$	2.83719	+	8.12467i	0.115635	+	0.331137i
$603$	22.5188	−	8.44226i	0.917036	−	0.343795i
$604$	28.2911	+	11.1447i	1.15115	+	0.453471i
$605$	−7.50446	+	4.33270i	−0.305100	+	0.176149i
$606$	7.96214	−	28.7593i	0.323440	−	1.16827i
$607$	26.7413			1.08540			0.542699	−	0.839927i	$-0.317403\pi$
$607$	26.7413			1.08540			0.542699	+	0.839927i	$0.317403\pi$
$608$	−2.45870	−	3.35353i	−0.0997133	−	0.136004i
$609$	−17.0203	+	24.5579i	−0.689697	+	0.995138i
$610$	7.15655	−	2.49911i	0.289760	−	0.101186i
$611$	−0.245387	−	0.456775i	−0.00992729	−	0.0184792i
$612$	−23.9108	+	13.2813i	−0.966539	+	0.536864i
$613$	−0.499668	+	0.288483i	−0.0201814	+	0.0116517i	−0.510057	−	0.860141i	$-0.670376\pi$
$613$	−0.499668	+	0.288483i	−0.0201814	+	0.0116517i	0.489875	+	0.871792i	$0.337042\pi$
$614$	−10.7466	+	12.4719i	−0.433699	+	0.503324i
$615$	2.12520	+	4.50088i	0.0856962	+	0.181493i
$616$	−0.186910	+	4.75416i	−0.00753080	+	0.191550i
$617$	−41.8576			−1.68512			−0.842562	−	0.538599i	$-0.818954\pi$
$617$	−41.8576			−1.68512			−0.842562	+	0.538599i	$0.818954\pi$
$618$	3.87604	+	14.9606i	0.155917	+	0.601805i
$619$	40.0034	+	23.0960i	1.60787	+	0.928305i	0.989846	+	0.142147i	$0.0454004\pi$
$619$	40.0034	+	23.0960i	1.60787	+	0.928305i	0.618025	+	0.786158i	$0.287933\pi$
$620$	−2.41095	+	6.12025i	−0.0968260	+	0.245795i
$621$	15.5912	+	15.1478i	0.625652	+	0.607859i
$622$	3.36210	−	17.7079i	0.134808	−	0.710022i
$623$	−21.1004	+	36.5470i	−0.845371	+	1.46423i
$624$	4.56037	+	24.5602i	0.182561	+	0.983195i
$625$	−7.61575	−	13.1909i	−0.304630	−	0.527635i
$626$	−9.45138	+	3.30048i	−0.377753	+	0.131914i
$627$	−0.0748255	+	0.905373i	−0.00298824	+	0.0361571i
$628$	−27.4083	−	34.4582i	−1.09371	−	1.37503i
$629$		−	18.2630i		−	0.728192i
$630$	−7.75360	−	2.85270i	−0.308911	−	0.113654i
$631$	−2.47356	+	4.28432i	−0.0984707	+	0.170556i	−0.911052	−	0.412292i	$-0.864728\pi$
$631$	−2.47356	+	4.28432i	−0.0984707	+	0.170556i	0.812581	+	0.582848i	$0.198062\pi$
$632$	−18.2313	−	34.6541i	−0.725202	−	1.37847i
$633$	−8.83128	−	0.729871i	−0.351012	−	0.0290098i
$634$	−14.3310	−	41.0387i	−0.569156	−	1.62985i
$635$	−9.96056	−	5.75073i	−0.395273	−	0.228211i
$636$	13.2717	−	8.87609i	0.526258	−	0.351960i
$637$	2.46057	+	4.58023i	0.0974914	+	0.181475i
$638$	−5.59361	−	4.81984i	−0.221453	−	0.190819i
$639$	2.51687	+	6.71347i	0.0995658	+	0.265581i
$640$	2.37874	+	9.03723i	0.0940281	+	0.357228i
$641$	7.05439	+	12.2186i	0.278631	+	0.482604i	0.971045	−	0.238897i	$-0.0767859\pi$
$641$	7.05439	+	12.2186i	0.278631	+	0.482604i	−0.692413	+	0.721501i	$0.743453\pi$
$642$	14.2545	−	3.69309i	0.562578	−	0.145755i
$643$			17.5061i			0.690373i	0.938534	+	0.345186i	$0.112184\pi$
$643$			17.5061i			0.690373i	−0.938534	+	0.345186i	$0.887816\pi$
$644$	2.91527	+	19.5088i	0.114878	+	0.768753i
$645$	0.304158	−	3.68025i	0.0119762	−	0.144910i
$646$	−4.65585	−	0.883981i	−0.183182	−	0.0347798i
$647$	3.13270	+	5.42600i	0.123159	+	0.213318i	0.921012	−	0.389534i	$-0.127364\pi$
$647$	3.13270	+	5.42600i	0.123159	+	0.213318i	−0.797853	+	0.602852i	$0.794031\pi$
$648$	23.7412	+	9.18456i	0.932642	+	0.360804i
$649$	−10.7356			−0.421410
$650$	4.76709	−	21.4939i	0.186981	−	0.843061i
$651$	−1.33922	+	16.2042i	−0.0524880	+	0.635094i
$652$	−1.65124	+	4.19170i	−0.0646674	+	0.164160i
$653$	9.82999	+	5.67534i	0.384677	+	0.222093i	0.679851	−	0.733350i	$-0.262044\pi$
$653$	9.82999	+	5.67534i	0.384677	+	0.222093i	−0.295174	+	0.955443i	$0.595378\pi$
$654$	3.74800	−	13.5378i	0.146558	−	0.529369i
$655$	−5.16708	+	8.94964i	−0.201894	+	0.349691i
$656$	3.13094	−	13.5595i	0.122243	−	0.529411i
$657$	−19.9363	+	24.2286i	−0.777791	+	0.945246i
$658$	−0.363229	−	0.312983i	−0.0141601	−	0.0122013i
$659$	−40.6818	+	23.4876i	−1.58474	+	0.914948i	−0.590582	+	0.806978i	$0.701102\pi$
$659$	−40.6818	+	23.4876i	−1.58474	+	0.914948i	−0.994154	+	0.107970i	$0.965565\pi$
$660$	0.902198	−	1.83145i	0.0351180	−	0.0712892i
$661$	−33.8988	−	19.5715i	−1.31851	−	0.761242i	−0.335021	−	0.942211i	$-0.608743\pi$
$661$	−33.8988	−	19.5715i	−1.31851	−	0.761242i	−0.983489	+	0.180968i	$0.942077\pi$
$662$	38.4477	+	7.29986i	1.49431	+	0.283717i
$663$	22.8909	+	16.9255i	0.889008	+	0.657331i
$664$	−25.1676	+	13.2405i	−0.976693	+	0.513832i
$665$	−0.715721	−	1.23967i	−0.0277545	−	0.0480722i
$666$	−13.0584	+	10.8801i	−0.506004	+	0.421594i
$667$	−26.5107	−	15.3060i	−1.02650	−	0.592650i
$668$	−22.0120	−	8.67116i	−0.851669	−	0.335497i
$669$	−25.2738	+	11.9336i	−0.977141	+	0.461381i
$670$	−7.09397	−	6.11266i	−0.274064	−	0.236153i
$671$	2.31512	+	4.00991i	0.0893743	+	0.154801i
$672$	12.0771	+	19.6903i	0.465886	+	0.759569i
$673$	22.9586			0.884990			0.442495	−	0.896771i	$-0.354093\pi$
$673$	22.9586			0.884990			0.442495	+	0.896771i	$0.354093\pi$
$674$	4.05814	−	21.3739i	0.156314	−	0.823292i
$675$	−16.0915	−	15.6339i	−0.619363	−	0.601750i
$676$	21.3006	−	14.9092i	0.819254	−	0.573431i
$677$	1.97526	+	1.14042i	0.0759155	+	0.0438298i	0.537477	−	0.843278i	$-0.319377\pi$
$677$	1.97526	+	1.14042i	0.0759155	+	0.0438298i	−0.461562	+	0.887108i	$0.652711\pi$
$678$	−27.6186	−	7.64634i	−1.06069	−	0.293656i
$679$	−16.2717	+	28.1833i	−0.624449	+	1.08158i
$680$	9.00700	+	5.68331i	0.345403	+	0.217945i
$681$	−4.66708	+	6.73395i	−0.178843	+	0.258046i
$682$	−3.94747	−	0.749484i	−0.151156	−	0.0286992i
$683$	−42.3096	−	24.4275i	−1.61893	−	0.934691i	−0.987197	−	0.159508i	$-0.949009\pi$
$683$	−42.3096	−	24.4275i	−1.61893	−	0.934691i	−0.631737	−	0.775183i	$-0.717658\pi$
$684$	2.14163	+	3.85567i	0.0818873	+	0.147425i
$685$	−1.99589	−	1.15233i	−0.0762591	−	0.0440282i
$686$	21.3224	+	18.3729i	0.814094	+	0.701480i
$687$	23.1919	−	33.4627i	0.884825	−	1.27668i
$688$	−7.04169	+	7.55079i	−0.268462	+	0.287871i
$689$	−14.1307	−	8.74590i	−0.538336	−	0.333192i
$690$	2.25842	−	8.15741i	0.0859766	−	0.310547i
$691$		−	34.8193i		−	1.32459i	−0.749243	−	0.662295i	$-0.769583\pi$
$691$		−	34.8193i		−	1.32459i	0.749243	−	0.662295i	$-0.230417\pi$
$692$	12.3993	+	15.5885i	0.471349	+	0.592587i
$693$	0.828478	−	4.97797i	0.0314713	−	0.189097i
$694$	−4.20113	+	4.87557i	−0.159473	+	0.185074i
$695$	−3.19877	−	5.54044i	−0.121336	−	0.210161i
$696$	−35.5822	−	4.35379i	−1.34874	−	0.165030i
$697$	−7.92992	−	13.7350i	−0.300367	−	0.520251i
$698$	−25.1569	+	29.1955i	−0.952203	+	1.10507i
$699$	15.0961	−	7.12797i	0.570985	−	0.269604i
$700$	−3.00883	−	20.1348i	−0.113723	−	0.761026i
$701$			28.3660i			1.07137i	0.844418	+	0.535685i	$0.179947\pi$
$701$			28.3660i			1.07137i	−0.844418	+	0.535685i	$0.820053\pi$
$702$	−1.53502	−	26.4508i	−0.0579355	−	0.998320i
$703$	−2.94494			−0.111070
$704$	−5.15222	+	2.45717i	−0.194182	+	0.0926080i
$705$	0.0878467	+	0.186047i	0.00330850	+	0.00700695i
$706$	−4.81351	−	4.14765i	−0.181159	−	0.156099i
$707$	−24.8730	+	14.3604i	−0.935445	+	0.540079i
$708$	−43.3245	+	28.9754i	−1.62824	+	1.08896i
$709$	17.1065	−	9.87642i	0.642447	−	0.370917i	−0.143110	−	0.989707i	$-0.545710\pi$
$709$	17.1065	−	9.87642i	0.642447	−	0.370917i	0.785556	+	0.618790i	$0.212377\pi$
$710$	1.82235	−	2.11491i	0.0683916	−	0.0793710i
$711$	14.5796	+	38.8894i	0.546776	+	1.45847i
$712$	−50.5909	−	1.98898i	−1.89598	−	0.0745403i
$713$	−16.6581			−0.623850
$714$	25.3706	+	7.02398i	0.949472	+	0.262866i
$715$	−2.12398	−	0.0650643i	−0.0794324	−	0.00243327i
$716$	2.96182	+	3.72365i	0.110688	+	0.139159i
$717$	22.3679	+	15.5024i	0.835344	+	0.578949i
$718$	5.28170	+	4.55108i	0.197111	+	0.169845i
$719$	19.0440	−	32.9853i	0.710223	−	1.23014i	−0.254550	−	0.967060i	$-0.581927\pi$
$719$	19.0440	−	32.9853i	0.710223	−	1.23014i	0.964773	−	0.263083i	$-0.0847393\pi$
$720$	−1.30218	−	9.82601i	−0.0485292	−	0.366194i
$721$	7.43720	−	12.8816i	0.276976	−	0.479736i
$722$	4.86959	−	25.6477i	0.181227	−	0.954508i
$723$	−11.8936	−	8.24309i	−0.442329	−	0.306564i
$724$	−40.8574	+	6.10549i	−1.51845	+	0.226909i
$725$	27.3616	+	15.7972i	1.01618	+	0.586693i
$726$	−24.7657	−	6.85651i	−0.919142	−	0.254469i
$727$	14.0533	−	24.3411i	0.521209	−	0.902760i	−0.478487	−	0.878094i	$-0.658815\pi$
$727$	14.0533	−	24.3411i	0.521209	−	0.902760i	0.999696	−	0.0246651i	$-0.00785195\pi$
$728$	13.4463	−	19.9305i	0.498355	−	0.738673i
$729$	−23.7623	−	12.8200i	−0.880087	−	0.474813i
$730$	12.0028	+	2.27891i	0.444245	+	0.0843464i
$731$			11.7667i			0.435205i
$732$	20.1656	+	9.93384i	0.745342	+	0.367165i
$733$	18.0106	−	10.3984i	0.665236	−	0.384074i	−0.129033	−	0.991640i	$-0.541187\pi$
$733$	18.0106	−	10.3984i	0.665236	−	0.384074i	0.794269	+	0.607566i	$0.207854\pi$
$734$	−20.9352	−	18.0392i	−0.772731	−	0.665839i
$735$	−0.880866	−	1.86555i	−0.0324912	−	0.0688120i
$736$	−19.0853	+	13.9927i	−0.703495	+	0.515779i
$737$	2.85994	−	4.95356i	0.105347	−	0.182467i
$738$	−5.09665	+	13.8526i	−0.187610	+	0.509923i
$739$	−1.23322	+	0.711998i	−0.0453646	+	0.0261913i	−0.522511	−	0.852633i	$-0.675005\pi$
$739$	−1.23322	+	0.711998i	−0.0453646	+	0.0261913i	0.477146	+	0.878824i	$0.341671\pi$
$740$	6.15769	+	2.42570i	0.226361	+	0.0891704i
$741$	2.72926	−	3.69120i	0.100262	−	0.135600i
$742$	−15.0972	−	2.86643i	−0.554237	−	0.105230i
$743$	1.74148	−	3.01633i	0.0638886	−	0.110658i	−0.832312	−	0.554308i	$-0.812983\pi$
$743$	1.74148	−	3.01633i	0.0638886	−	0.110658i	0.896200	+	0.443649i	$0.146316\pi$
$744$	−17.9532	+	7.62958i	−0.658196	+	0.279714i
$745$	3.37090	+	5.83856i	0.123500	+	0.213908i
$746$	5.59727	−	6.49584i	0.204930	−	0.237830i
$747$	28.2435	−	10.5884i	1.03338	−	0.387411i
$748$	−2.38432	+	6.05265i	−0.0871793	+	0.221307i
$749$	−12.2736	−	7.08615i	−0.448467	−	0.258922i
$750$	−5.03011	+	18.1688i	−0.183674	+	0.663430i
$751$	−5.51236	+	9.54769i	−0.201149	+	0.348400i	−0.948899	−	0.315580i	$-0.897801\pi$
$751$	−5.51236	+	9.54769i	−0.201149	+	0.348400i	0.747750	+	0.663980i	$0.231134\pi$
$752$	0.129420	−	0.560494i	0.00471945	−	0.0204391i
$753$	−2.90739	−	0.240284i	−0.105951	−	0.00875645i
$754$	11.2166	+	35.5854i	0.408484	+	1.29595i
$755$			12.5580i			0.457033i
$756$	−10.0921	−	22.3251i	−0.367046	−	0.811956i
$757$	38.9868	−	22.5090i	1.41700	−	0.818104i	0.420964	−	0.907077i	$-0.361692\pi$
$757$	38.9868	−	22.5090i	1.41700	−	0.818104i	0.996034	+	0.0889732i	$0.0283585\pi$
$758$	33.7796	+	6.41355i	1.22693	+	0.232950i
$759$	5.15259	+	0.425841i	0.187027	+	0.0154571i
$760$	0.916443	−	1.45239i	0.0332429	−	0.0526839i
$761$	45.4433			1.64732			0.823659	−	0.567085i	$-0.191929\pi$
$761$	45.4433			1.64732			0.823659	+	0.567085i	$0.191929\pi$
$762$	−8.55429	−	33.0175i	−0.309889	−	1.19610i
$763$	−11.7084	+	6.75984i	−0.423872	+	0.244723i
$764$	−5.17881	+	4.11927i	−0.187363	+	0.149030i
$765$	−8.72281	−	7.17752i	−0.315374	−	0.259504i
$766$	4.92487	+	4.24361i	0.177943	+	0.153328i
$767$	46.1286	+	28.5504i	1.66561	+	1.03089i
$768$	−14.1604	+	23.8219i	−0.510968	+	0.859600i
$769$	3.55382	−	6.15539i	0.128154	−	0.221969i	−0.794807	−	0.606862i	$-0.792428\pi$
$769$	3.55382	−	6.15539i	0.128154	−	0.221969i	0.922961	+	0.384893i	$0.125761\pi$
$770$	−1.85511	+	0.647816i	−0.0668535	+	0.0233457i
$771$	−2.50543	+	30.3152i	−0.0902308	+	1.09177i
$772$	−5.01600	−	1.97595i	−0.180530	−	0.0711161i
$773$	−13.4159	−	7.74567i	−0.482536	−	0.278592i	0.238937	−	0.971035i	$-0.423201\pi$
$773$	−13.4159	−	7.74567i	−0.482536	−	0.278592i	−0.721473	+	0.692443i	$0.756535\pi$
$774$	8.41343	−	7.00992i	0.302415	−	0.251966i
$775$	17.1927			0.617579
$776$	−39.0133	−	1.53381i	−1.40050	−	0.0550606i
$777$	16.3034	+	1.34741i	0.584880	+	0.0483380i
$778$	2.32540	+	6.65911i	0.0833698	+	0.238741i
$779$	−2.21480	+	1.27871i	−0.0793533	+	0.0458147i
$780$	−8.74712	+	5.47003i	−0.313197	+	0.195859i
$781$	1.47679	+	0.852626i	0.0528438	+	0.0305094i
$782$	−5.03084	+	26.4970i	−0.179903	+	0.947531i
$783$	36.8646	+	9.31011i	1.31743	+	0.332716i
$784$	−1.29773	+	5.62024i	−0.0463476	+	0.200723i
$785$	9.09198	−	15.7478i	0.324507	−	0.562062i
$786$	−29.6665	+	7.68609i	−1.05817	+	0.274154i
$787$			27.1591i			0.968118i	0.875035	+	0.484059i	$0.160838\pi$
$787$			27.1591i			0.968118i	−0.875035	+	0.484059i	$0.839162\pi$
$788$	16.1324	+	20.2819i	0.574692	+	0.722512i
$789$	43.0929	−	20.3474i	1.53415	−	0.724385i
$790$	10.5564	−	12.2511i	0.375580	−	0.435875i
$791$	13.7908	+	23.8864i	0.490346	+	0.849304i
$792$	5.74823	−	1.90099i	0.204255	−	0.0675488i
$793$	0.716405	−	23.3865i	0.0254403	−	0.830480i
$794$	7.20933	+	20.6449i	0.255849	+	0.732660i
$795$	5.41964	+	3.75617i	0.192215	+	0.133218i
$796$	10.9424	+	4.31055i	0.387844	+	0.152783i
$797$			20.7835i			0.736191i	0.929788	+	0.368095i	$0.119990\pi$
$797$			20.7835i			0.736191i	−0.929788	+	0.368095i	$0.880010\pi$
$798$	1.13263	−	4.09106i	0.0400947	−	0.144822i
$799$	−0.327789	−	0.567748i	−0.0115964	−	0.0200855i
$800$	19.6978	−	14.4418i	0.696424	−	0.510595i
$801$	52.9726	+	8.81618i	1.87170	+	0.311504i
$802$	25.5879	−	8.93546i	0.903540	−	0.315522i
$803$			7.46257i			0.263348i
$804$	−1.82808	−	27.7095i	−0.0644716	−	0.977238i
$805$	−7.05509	+	4.07326i	−0.248659	+	0.143563i
$806$	14.9682	+	13.7183i	0.527233	+	0.483206i
$807$	−11.7978	−	0.975041i	−0.415302	−	0.0343231i
$808$	−29.1412	−	18.3878i	−1.02519	−	0.646879i
$809$	21.2873	+	36.8706i	0.748420	+	1.29630i	0.948580	+	0.316538i	$0.102521\pi$
$809$	21.2873	+	36.8706i	0.748420	+	1.29630i	−0.200160	+	0.979763i	$0.564146\pi$
$810$	0.0644764	+	10.5130i	0.00226547	+	0.369389i
$811$		−	35.1214i		−	1.23328i	−0.787245	−	0.616640i	$-0.788493\pi$
$811$		−	35.1214i		−	1.23328i	0.787245	−	0.616640i	$-0.211507\pi$
$812$	21.4774	+	27.0018i	0.753711	+	0.947576i
$813$	−30.6759	−	21.2604i	−1.07585	−	0.745636i
$814$	−0.754069	+	3.97162i	−0.0264301	+	0.139205i
$815$	−1.86064			−0.0651753
$816$	6.71393	+	30.8613i	0.235035	+	1.08036i
$817$	1.89739			0.0663814
$818$	−13.5729	−	11.6954i	−0.474566	−	0.408919i
$819$	−16.7982	+	19.1860i	−0.586978	+	0.670412i
$820$	5.68427	−	0.849424i	0.198503	−	0.0296632i
$821$		−	15.4321i		−	0.538585i	−0.963058	−	0.269293i	$-0.913210\pi$
$821$		−	15.4321i		−	0.538585i	0.963058	−	0.269293i	$-0.0867899\pi$
$822$	−1.71410	−	6.61604i	−0.0597862	−	0.230761i
$823$	50.2387			1.75121			0.875606	−	0.483025i	$-0.160462\pi$
$823$	50.2387			1.75121			0.875606	+	0.483025i	$0.160462\pi$
$824$	17.8316	+	0.701051i	0.621194	+	0.0244223i
$825$	−5.31795	−	0.439508i	−0.185147	−	0.0153017i
$826$	49.2838	+	9.35724i	1.71480	+	0.325580i
$827$			24.1777i			0.840742i	0.907352	+	0.420371i	$0.138100\pi$
$827$			24.1777i			0.840742i	−0.907352	+	0.420371i	$0.861900\pi$
$828$	21.9431	−	12.1883i	0.762575	−	0.423572i
$829$	19.3485	−	11.1708i	0.672000	−	0.387979i	−0.124834	−	0.992178i	$-0.539840\pi$
$829$	19.3485	−	11.1708i	0.672000	−	0.387979i	0.796834	+	0.604198i	$0.206507\pi$
$830$	−8.89739	−	7.66661i	−0.308833	−	0.266112i
$831$	−9.36729	+	13.5157i	−0.324948	+	0.468855i
$832$	28.6726	+	3.14393i	0.994042	+	0.108996i
$833$	3.28685	+	5.69298i	0.113882	+	0.197250i
$834$	5.06206	−	18.2842i	0.175285	−	0.633129i
$835$		−	9.77080i		−	0.338133i
$836$	0.976001	+	0.384476i	0.0337557	+	0.0132974i
$837$	19.9061	−	5.64277i	0.688056	−	0.195043i
$838$	−7.40512	−	21.2056i	−0.255806	−	0.732534i
$839$	−27.4750	−	47.5881i	−0.948542	−	1.64292i	−0.748499	−	0.663136i	$-0.769225\pi$
$839$	−27.4750	−	47.5881i	−0.948542	−	1.64292i	−0.200043	−	0.979787i	$-0.564108\pi$
$840$	−5.73801	+	7.62125i	−0.197980	+	0.262958i
$841$	−24.5437			−0.846334
$842$	−0.645510	−	1.84850i	−0.0222457	−	0.0637037i
$843$	1.52796	−	18.4880i	0.0526259	−	0.636762i
$844$	−3.75029	+	9.52021i	−0.129090	+	0.327699i
$845$	8.95324	+	5.92809i	0.308001	+	0.203933i
$846$	−0.210674	+	0.572610i	−0.00724313	+	0.0196867i
$847$	12.3663	+	21.4191i	0.424912	+	0.735969i
$848$	−5.38967	−	17.6309i	−0.185082	−	0.605448i
$849$	−26.0152	−	2.15006i	−0.892840	−	0.0737897i
$850$	5.19230	−	27.3474i	0.178094	−	0.938007i
$851$			16.7600i			0.574525i
$852$	8.26096	−	0.545002i	0.283016	−	0.0186715i
$853$	−38.8568	−	22.4340i	−1.33043	−	0.768124i	−0.345065	−	0.938579i	$-0.612143\pi$
$853$	−38.8568	−	22.4340i	−1.33043	−	0.768124i	−0.985365	+	0.170455i	$0.945476\pi$
$854$	−7.13292	−	20.4261i	−0.244083	−	0.698966i
$855$	−1.15739	+	1.40657i	−0.0395818	+	0.0481037i
$856$	0.667960	−	16.9899i	0.0228304	−	0.580704i
$857$	3.85683	−	6.68022i	0.131747	−	0.228192i	−0.792603	−	0.609738i	$-0.791275\pi$
$857$	3.85683	−	6.68022i	0.131747	−	0.228192i	0.924350	+	0.381546i	$0.124608\pi$
$858$	−4.27920	−	4.62591i	−0.146089	−	0.157926i
$859$	−10.1480	+	5.85897i	−0.346246	+	0.199905i	−0.663031	−	0.748592i	$-0.730730\pi$
$859$	−10.1480	+	5.85897i	−0.346246	+	0.199905i	0.316784	+	0.948498i	$0.397397\pi$
$860$	−3.96734	−	1.56285i	−0.135285	−	0.0532929i
$861$	12.8463	−	6.06570i	0.437801	−	0.206718i
$862$	7.70580	−	40.5858i	0.262461	−	1.38236i
$863$	42.7208			1.45423			0.727117	−	0.686513i	$-0.240860\pi$
$863$	42.7208			1.45423			0.727117	+	0.686513i	$0.240860\pi$
$864$	18.0667	−	23.1861i	0.614643	−	0.788806i
$865$	−4.11312	+	7.12414i	−0.139850	+	0.242228i
$866$	52.3666	−	18.2868i	1.77949	−	0.621409i
$867$	5.38273	+	3.73059i	0.182807	+	0.126697i
$868$	17.4683	+	6.88128i	0.592913	+	0.233566i
$869$	8.55467	+	4.93904i	0.290197	+	0.167546i
$870$	−3.71311	−	14.3317i	−0.125886	−	0.485891i
$871$	−25.4621	+	13.6786i	−0.862749	+	0.463482i
$872$	−13.7176	−	8.65562i	−0.464536	−	0.293116i
$873$	40.8500	+	6.79862i	1.38256	+	0.230098i
$874$	4.27269	+	0.811232i	0.144526	+	0.0274403i
$875$	15.7136	−	9.07225i	0.531217	−	0.306698i
$876$	20.1414	+	30.1159i	0.680515	+	1.01752i
$877$		−	26.8232i		−	0.905754i	−0.891573	−	0.452877i	$-0.850398\pi$
$877$		−	26.8232i		−	0.905754i	0.891573	−	0.452877i	$-0.149602\pi$
$878$	−25.6639	−	22.1138i	−0.866113	−	0.746304i
$879$	7.33099	+	15.5260i	0.247268	+	0.523680i
$880$	−1.72408	−	1.60783i	−0.0581186	−	0.0542001i
$881$	29.1362	+	50.4654i	0.981624	+	1.70022i	0.656070	+	0.754700i	$0.272218\pi$
$881$	29.1362	+	50.4654i	0.981624	+	1.70022i	0.325555	+	0.945523i	$0.394449\pi$
$882$	2.11249	−	5.74174i	0.0711314	−	0.193334i
$883$			14.0915i			0.474216i	0.971483	+	0.237108i	$0.0761995\pi$
$883$			14.0915i			0.474216i	−0.971483	+	0.237108i	$0.923800\pi$
$884$	26.3413	−	19.6660i	0.885955	−	0.661440i
$885$	−17.6920	−	12.2617i	−0.594711	−	0.412174i
$886$	16.5286	+	47.3319i	0.555289	+	1.59015i
$887$	8.81424	−	15.2667i	0.295953	−	0.512606i	−0.679253	−	0.733904i	$-0.737696\pi$
$887$	8.81424	−	15.2667i	0.295953	−	0.512606i	0.975206	+	0.221298i	$0.0710294\pi$
$888$	7.67625	+	18.0630i	0.257598	+	0.606156i
$889$	−16.4136	+	28.4292i	−0.550496	+	0.953486i
$890$	−6.89368	−	19.7410i	−0.231077	−	0.661720i
$891$	−6.30150	+	1.23652i	−0.211108	+	0.0414249i
$892$	4.76977	+	31.9189i	0.159704	+	1.06872i
$893$	−0.0915504	+	0.0528566i	−0.00306362	+	0.00176878i
$894$	−5.33445	+	19.2680i	−0.178411	+	0.644419i
$895$	−0.982505	+	1.70175i	−0.0328415	+	0.0568832i
$896$	25.7939	−	6.78936i	0.861713	−	0.226817i
$897$	−21.0071	−	15.5326i	−0.701405	−	0.518617i
$898$	16.1009	−	5.62253i	0.537293	−	0.187626i
$899$	−25.2332	+	14.5684i	−0.841575	+	0.485883i
$900$	−22.6473	+	12.5794i	−0.754910	+	0.419315i
$901$	−18.1961	−	10.5056i	−0.606202	−	0.349991i
$902$	1.15739	+	3.31436i	0.0385370	+	0.110356i
$903$	−10.5041	−	0.868122i	−0.349555	−	0.0288893i
$904$	−17.6584	+	27.9854i	−0.587311	+	0.930781i
$905$	−8.53066	−	14.7755i	−0.283569	−	0.491156i
$906$	−26.5507	+	26.1141i	−0.882088	+	0.867582i
$907$		−	10.0797i		−	0.334690i	−0.985898	−	0.167345i	$-0.946481\pi$
$907$		−	10.0797i		−	0.334690i	0.985898	−	0.167345i	$-0.0535194\pi$
$908$	5.88926	+	7.40407i	0.195442	+	0.245713i
$909$	28.2218	+	23.2221i	0.936058	+	0.770230i
$910$	9.69381	+	2.14997i	0.321347	+	0.0712707i
$911$	−21.9031	+	37.9373i	−0.725682	+	1.25692i	0.233010	+	0.972474i	$0.425142\pi$
$911$	−21.9031	+	37.9373i	−0.725682	+	1.25692i	−0.958693	+	0.284444i	$0.908191\pi$
$912$	4.97644	−	1.08263i	0.164786	−	0.0358496i
$913$	3.58699	−	6.21285i	0.118712	−	0.205615i
$914$	4.41693	+	3.80593i	0.146099	+	0.125889i
$915$	−0.764679	+	9.25246i	−0.0252795	+	0.305877i
$916$	−29.2652	−	36.7927i	−0.966950	−	1.21566i
$917$	25.5439	+	14.7478i	0.843533	+	0.487014i
$918$	−2.96385	−	33.3676i	−0.0978216	−	1.10130i
$919$	−28.5730	+	49.4900i	−0.942538	+	1.63252i	−0.181930	+	0.983312i	$0.558234\pi$
$919$	−28.5730	+	49.4900i	−0.942538	+	1.63252i	−0.760608	+	0.649211i	$0.775099\pi$
$920$	−8.26576	−	5.21559i	−0.272514	−	0.171953i
$921$	−8.60912	−	18.2329i	−0.283680	−	0.600796i
$922$	31.5340	+	5.98719i	1.03852	+	0.197178i
$923$	−4.07797	−	7.59093i	−0.134228	−	0.249859i
$924$	−5.22730	−	2.57504i	−0.171965	−	0.0847125i
$925$		−	17.2979i		−	0.568750i
$926$	2.76997	−	14.5892i	0.0910269	−	0.479431i
$927$	−18.6711	−	3.10741i	−0.613239	−	0.102061i
$928$	−16.6725	+	37.8870i	−0.547303	+	1.24370i
$929$	8.01132	+	13.8760i	0.262843	+	0.455257i	0.966996	−	0.254791i	$-0.0820066\pi$
$929$	8.01132	+	13.8760i	0.262843	+	0.455257i	−0.704153	+	0.710048i	$0.748673\pi$
$930$	−5.64930	−	5.74375i	−0.185248	−	0.188345i
$931$	0.918004	−	0.530010i	0.0300864	−	0.0173704i
$932$	−2.84899	−	19.0652i	−0.0933218	−	0.624501i
$933$	18.1435	+	12.5747i	0.593992	+	0.411676i
$934$	−26.3586	+	30.5902i	−0.862481	+	1.00094i
$935$	−2.68669			−0.0878641
$936$	−29.7544	−	7.11874i	−0.972553	−	0.232683i
$937$	40.0275			1.30764			0.653822	−	0.756649i	$-0.273165\pi$
$937$	40.0275			1.30764			0.653822	+	0.756649i	$0.273165\pi$
$938$	−17.4466	+	20.2475i	−0.569653	+	0.661103i
$939$	1.00988	−	12.2194i	0.0329563	−	0.398764i
$940$	0.234964	−	0.0351116i	0.00766368	−	0.00114521i
$941$	−5.08240	+	2.93432i	−0.165681	+	0.0956562i	−0.580548	−	0.814226i	$-0.697162\pi$
$941$	−5.08240	+	2.93432i	−0.165681	+	0.0956562i	0.414867	+	0.909882i	$0.363828\pi$
$942$	52.2012	−	13.5244i	1.70081	−	0.440650i
$943$	7.27732	+	12.6047i	0.236982	+	0.410465i
$944$	17.5942	+	57.5548i	0.572642	+	1.87325i
$945$	7.05093	−	7.25732i	0.229367	−	0.236081i
$946$	0.485840	−	2.55888i	0.0157960	−	0.0831962i
$947$		−	36.9409i		−	1.20042i	−0.799844	−	0.600208i	$-0.795084\pi$
$947$		−	36.9409i		−	1.20042i	0.799844	−	0.600208i	$-0.204916\pi$
$948$	47.8536	−	3.15705i	1.55421	−	0.102536i
$949$	19.8460	−	32.0650i	0.644228	−	1.04087i
$950$	−4.40981	−	0.837267i	−0.143073	−	0.0271645i
$951$	53.0575	+	4.38499i	1.72051	+	0.142193i
$952$	16.2212	−	25.7076i	0.525731	−	0.833188i
$953$	−21.6575	+	37.5119i	−0.701556	+	1.21513i	0.266364	+	0.963872i	$0.414178\pi$
$953$	−21.6575	+	37.5119i	−0.701556	+	1.21513i	−0.967920	+	0.251258i	$0.919156\pi$
$954$	3.32854	+	19.2693i	0.107766	+	0.623867i
$955$	−2.36677	−	1.36646i	−0.0765870	−	0.0442175i
$956$	24.5938	−	19.5621i	0.795420	−	0.632684i
$957$	8.17743	−	3.86117i	0.264339	−	0.124814i
$958$	−20.0114	−	17.2432i	−0.646538	−	0.557102i
$959$	−3.28896	+	5.69664i	−0.106206	+	0.183954i
$960$	−11.2972	−	1.83529i	−0.364615	−	0.0592336i
$961$	7.57233	−	13.1157i	0.244269	−	0.423086i
$962$	13.8022	−	15.0598i	0.445001	−	0.485547i
$963$	−2.96073	+	17.7898i	−0.0954083	+	0.573268i
$964$	−13.0772	+	10.4017i	−0.421189	+	0.335017i
$965$		−	2.22653i		−	0.0716747i
$966$	−23.2827	−	6.44594i	−0.749110	−	0.207395i
$967$	−2.19892	−	3.80864i	−0.0707124	−	0.122478i	0.828501	−	0.559987i	$-0.189194\pi$
$967$	−2.19892	−	3.80864i	−0.0707124	−	0.122478i	−0.899214	+	0.437510i	$0.855861\pi$
$968$	−15.8344	+	25.0946i	−0.508937	+	0.806573i
$969$	3.30620	−	4.77039i	0.106210	−	0.153247i
$970$	−5.31608	−	15.2233i	−0.170689	−	0.488791i
$971$	31.2117	+	18.0201i	1.00163	+	0.578293i	0.908731	−	0.417383i	$-0.137052\pi$
$971$	31.2117	+	18.0201i	1.00163	+	0.578293i	0.0929015	+	0.995675i	$0.470386\pi$
$972$	−22.0929	+	21.9978i	−0.708631	+	0.705580i
$973$	−15.8134	+	9.12988i	−0.506955	+	0.292690i
$974$	19.7234	−	6.88755i	0.631980	−	0.220691i
$975$	21.6812	+	16.0311i	0.694355	+	0.513405i
$976$	17.7034	−	18.9833i	0.566672	−	0.607641i
$977$	18.1428	−	31.4243i	0.580440	−	1.00535i	−0.414987	−	0.909827i	$-0.636214\pi$
$977$	18.1428	−	31.4243i	0.580440	−	1.00535i	0.995427	−	0.0955238i	$-0.0304526\pi$
$978$	−3.86915	−	3.93384i	−0.123722	−	0.125790i
$979$	11.0611	−	6.38615i	0.353515	−	0.204102i
$980$	−2.35606	+	0.352075i	−0.0752614	+	0.0112466i
$981$	13.2848	+	10.9313i	0.424150	+	0.349009i
$982$	16.1996	+	46.3897i	0.516949	+	1.48035i
$983$	−28.0792	+	48.6346i	−0.895588	+	1.55120i	−0.0625117	+	0.998044i	$0.519911\pi$
$983$	−28.0792	+	48.6346i	−0.895588	+	1.55120i	−0.833076	+	0.553159i	$0.813422\pi$
$984$	13.6162	+	10.2516i	0.434068	+	0.326808i
$985$	−5.35149	+	9.26905i	−0.170513	+	0.295336i
$986$	15.5525	+	44.5367i	0.495292	+	1.41834i
$987$	0.531013	−	0.250730i	0.0169023	−	0.00798084i
$988$	−3.17118	−	4.24759i	−0.100889	−	0.135134i
$989$		−	10.7983i		−	0.343366i
$990$	1.60058	+	1.92104i	0.0508698	+	0.0610548i
$991$	30.5236	+	52.8684i	0.969613	+	1.67942i	0.696675	+	0.717387i	$0.254662\pi$
$991$	30.5236	+	52.8684i	0.969613	+	1.67942i	0.272938	+	0.962032i	$0.412005\pi$
$992$	2.45129	+	22.3911i	0.0778285	+	0.710919i
$993$	−27.3024	+	39.3936i	−0.866415	+	1.25012i
$994$	−6.03633	−	5.20132i	−0.191461	−	0.164976i
$995$			4.85719i			0.153983i
$996$	−2.29282	−	34.7538i	−0.0726507	−	1.10121i
$997$	−14.0471	+	8.11012i	−0.444877	+	0.256850i	−0.705664	−	0.708546i	$-0.749351\pi$
$997$	−14.0471	+	8.11012i	−0.444877	+	0.256850i	0.260787	+	0.965396i	$0.416018\pi$
$998$	−28.3733	−	5.38708i	−0.898140	−	0.170525i
$999$	−5.67729	−	20.0279i	−0.179622	−	0.633654i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	936.2.cj.a.133.126	yes	328
8.5	even	2	inner	936.2.cj.a.133.125	✓	328
9.4	even	3		936.2.db.a.445.17	yes	328
13.9	even	3		936.2.db.a.61.92	yes	328
72.13	even	6		936.2.db.a.445.92	yes	328
104.61	even	6		936.2.db.a.61.17	yes	328
117.22	even	3	inner	936.2.cj.a.373.126	yes	328
936.373	even	6	inner	936.2.cj.a.373.125	yes	328

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
936.2.cj.a.133.125	✓	328	8.5	even	2	inner
936.2.cj.a.133.126	yes	328	1.1	even	1	trivial
936.2.cj.a.373.125	yes	328	936.373	even	6	inner
936.2.cj.a.373.126	yes	328	117.22	even	3	inner
936.2.db.a.61.17	yes	328	104.61	even	6
936.2.db.a.61.92	yes	328	13.9	even	3
936.2.db.a.445.17	yes	328	9.4	even	3
936.2.db.a.445.92	yes	328	72.13	even	6

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:	\( N \)	\(=\)	\( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	936.cj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.07135 + 0.923151i) q^{2} +(-1.56623 + 0.739535i) q^{3} +(0.295586 + 1.97804i) q^{4} +(-0.715331 + 0.412997i) q^{5} +(-2.36069 - 0.653568i) q^{6} +(1.17877 + 2.04168i) q^{7} +(-1.50935 + 2.39204i) q^{8} +(1.90618 - 2.31657i) q^{9} +(-1.14763 - 0.217894i) q^{10} -0.713520i q^{11} +(-1.92578 - 2.87947i) q^{12} +(-1.89754 + 3.06584i) q^{13} +(-0.621909 + 3.27554i) q^{14} +(0.814950 - 1.17586i) q^{15} +(-3.82526 + 1.16936i) q^{16} +(-2.27932 + 3.94789i) q^{17} +(4.18073 - 0.722171i) q^{18} +(0.636605 + 0.367544i) q^{19} +(-1.02836 - 1.29288i) q^{20} +(-3.35612 - 2.32602i) q^{21} +(0.658686 - 0.764430i) q^{22} +(2.09174 - 3.62300i) q^{23} +(0.594995 - 4.86271i) q^{24} +(-2.15887 + 3.73927i) q^{25} +(-4.86316 + 1.53287i) q^{26} +(-1.27233 + 5.03797i) q^{27} +(-3.69010 + 2.93514i) q^{28} -7.31736i q^{29} +(1.95860 - 0.507439i) q^{30} +(-1.99094 - 3.44841i) q^{31} +(-5.17769 - 2.27849i) q^{32} +(0.527673 + 1.11754i) q^{33} +(-6.08645 + 2.12543i) q^{34} +(-1.68642 - 0.973654i) q^{35} +(5.14570 + 3.08574i) q^{36} +(-3.46950 + 2.00312i) q^{37} +(0.342729 + 0.981451i) q^{38} +(0.704695 - 6.20511i) q^{39} +(0.0917792 - 2.33446i) q^{40} +(-1.73954 + 3.01297i) q^{41} +(-1.44832 - 5.59019i) q^{42} +(2.23537 - 1.29059i) q^{43} +(1.41137 - 0.210906i) q^{44} +(-0.406812 + 2.44436i) q^{45} +(5.58556 - 1.95051i) q^{46} +(-0.0719052 + 0.124543i) q^{47} +(5.12646 - 4.66040i) q^{48} +(0.721015 - 1.24884i) q^{49} +(-5.76481 + 2.01311i) q^{50} +(0.650338 - 7.86896i) q^{51} +(-6.62522 - 2.84718i) q^{52} +4.60908i q^{53} +(-6.01392 + 4.22288i) q^{54} +(0.294681 + 0.510403i) q^{55} +(-6.66297 - 0.261954i) q^{56} +(-1.26888 - 0.104868i) q^{57} +(6.75502 - 7.83946i) q^{58} -15.0460i q^{59} +(2.56679 + 1.26443i) q^{60} +(-5.61990 + 3.24465i) q^{61} +(1.05040 - 5.53239i) q^{62} +(6.97664 + 1.16111i) q^{63} +(-3.44373 - 7.22085i) q^{64} +(0.0911879 - 2.97677i) q^{65} +(-0.466334 + 1.68440i) q^{66} +(6.94243 + 4.00821i) q^{67} +(-8.48281 - 3.34163i) q^{68} +(-0.596818 + 7.22137i) q^{69} +(-0.907917 - 2.59994i) q^{70} +(-1.19496 + 2.06973i) q^{71} +(2.66425 + 8.05617i) q^{72} -10.4588 q^{73} +(-5.56623 - 1.05683i) q^{74} +(0.615971 - 7.45313i) q^{75} +(-0.538844 + 1.36787i) q^{76} +(1.45678 - 0.841074i) q^{77} +(6.48323 - 5.99731i) q^{78} +(-6.92208 + 11.9894i) q^{79} +(2.25338 - 2.41630i) q^{80} +(-1.73299 - 8.83158i) q^{81} +(-4.64508 + 1.62209i) q^{82} +(8.70733 + 5.02718i) q^{83} +(3.60892 - 7.32607i) q^{84} -3.76540i q^{85} +(3.58627 + 0.680906i) q^{86} +(5.41144 + 11.4607i) q^{87} +(1.70677 + 1.07695i) q^{88} +(8.95021 + 15.5022i) q^{89} +(-2.69235 + 2.24322i) q^{90} +(-8.49623 - 0.260267i) q^{91} +(7.78471 + 3.06663i) q^{92} +(5.66849 + 3.92864i) q^{93} +(-0.192008 + 0.0670504i) q^{94} -0.607178 q^{95} +(9.79450 - 0.260429i) q^{96} +(6.90198 + 11.9546i) q^{97} +(1.92532 - 0.672335i) q^{98} +(-1.65292 - 1.36009i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 328 q - 2 q^{2} - 2 q^{4} + 4 q^{6} + 2 q^{7} - 2 q^{8} - 2 q^{9} - 4 q^{10} + 5 q^{12} - 6 q^{14} - 14 q^{15} - 2 q^{16} - 4 q^{17} - 12 q^{18} + 9 q^{20} + 14 q^{22} - 22 q^{23} + 18 q^{24} + 144 q^{25}+ \cdots + 39 q^{98}+O(q^{100}) \) 328 * q - 2 * q^2 - 2 * q^4 + 4 * q^6 + 2 * q^7 - 2 * q^8 - 2 * q^9 - 4 * q^10 + 5 * q^12 - 6 * q^14 - 14 * q^15 - 2 * q^16 - 4 * q^17 - 12 * q^18 + 9 * q^20 + 14 * q^22 - 22 * q^23 + 18 * q^24 + 144 * q^25 - 16 * q^26 - 10 * q^28 - 2 * q^30 - 4 * q^31 - 2 * q^32 + 22 * q^33 - 22 * q^36 + 6 * q^38 + 2 * q^39 + 8 * q^40 + 2 * q^41 + 17 * q^42 - 32 * q^44 - 6 * q^46 - 4 * q^47 + 41 * q^48 - 138 * q^49 - 34 * q^50 + 24 * q^52 - 41 * q^54 - 14 * q^55 + 28 * q^56 - 20 * q^57 + 50 * q^58 - 41 * q^60 + 3 * q^62 + 26 * q^63 - 26 * q^64 - 22 * q^65 - 6 * q^66 + 32 * q^68 - 17 * q^70 - 4 * q^71 + 32 * q^72 - 16 * q^73 + 19 * q^74 + 9 * q^76 + 2 * q^78 - 4 * q^79 - 42 * q^80 - 2 * q^81 + 3 * q^82 + 27 * q^84 + 36 * q^86 + 34 * q^87 - 10 * q^88 - 4 * q^89 + 33 * q^90 + 28 * q^92 + 3 * q^94 - 112 * q^95 - 113 * q^96 + 2 * q^97 + 39 * q^98

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