LMFDB - Embedded newform 152.2.o.c.27.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [152,2,Mod(27,152)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(152, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("152.27"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 152 = 2^{3} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	152.o (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [28,-3,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$1.21372611072$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			27.8
Character	$\chi$	$=$	152.27
Dual form			152.2.o.c.107.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.151949 + 1.40603i) q^{2} +(-1.05104 - 0.606818i) q^{3} +(-1.95382 - 0.427288i) q^{4} +(-2.45005 - 1.41453i) q^{5} +(1.01291 - 1.38558i) q^{6} +0.450769i q^{7} +(0.897660 - 2.68220i) q^{8} +(-0.763544 - 1.32250i) q^{9} +(2.36116 - 3.22989i) q^{10} -2.15933 q^{11} +(1.79426 + 1.63471i) q^{12} +(-1.86406 - 3.22864i) q^{13} +(-0.633793 - 0.0684938i) q^{14} +(1.71673 + 2.97346i) q^{15} +(3.63485 + 1.66969i) q^{16} +(-0.716566 + 1.24113i) q^{17} +(1.97549 - 0.872612i) q^{18} +(-0.0305680 + 4.35879i) q^{19} +(4.18254 + 3.81063i) q^{20} +(0.273535 - 0.473776i) q^{21} +(0.328108 - 3.03608i) q^{22} +(-1.12985 + 0.652319i) q^{23} +(-2.57108 + 2.27438i) q^{24} +(1.50182 + 2.60122i) q^{25} +(4.82280 - 2.13033i) q^{26} +5.49424i q^{27} +(0.192608 - 0.880723i) q^{28} +(-4.22992 - 7.32644i) q^{29} +(-4.44162 + 1.96195i) q^{30} -0.497284 q^{31} +(-2.89994 + 4.85699i) q^{32} +(2.26955 + 1.31032i) q^{33} +(-1.63618 - 1.19610i) q^{34} +(0.637628 - 1.10440i) q^{35} +(0.926743 + 2.91018i) q^{36} +6.72997 q^{37} +(-6.12393 - 0.705293i) q^{38} +4.52457i q^{39} +(-5.99338 + 5.30175i) q^{40} +(-7.30919 - 4.21996i) q^{41} +(0.624578 + 0.456587i) q^{42} +(2.90174 - 5.02595i) q^{43} +(4.21896 + 0.922659i) q^{44} +4.32024i q^{45} +(-0.745499 - 1.68772i) q^{46} +(-0.567335 + 0.327551i) q^{47} +(-2.80717 - 3.96060i) q^{48} +6.79681 q^{49} +(-3.88559 + 1.71634i) q^{50} +(1.50628 - 0.869651i) q^{51} +(2.26248 + 7.10468i) q^{52} +(3.86444 + 6.69340i) q^{53} +(-7.72504 - 0.834843i) q^{54} +(5.29047 + 3.05445i) q^{55} +(1.20905 + 0.404637i) q^{56} +(2.67712 - 4.56271i) q^{57} +(10.9439 - 4.83414i) q^{58} +(-12.1090 - 6.99113i) q^{59} +(-2.08366 - 6.54316i) q^{60} +(-2.13281 + 1.23138i) q^{61} +(0.0755618 - 0.699195i) q^{62} +(0.596141 - 0.344182i) q^{63} +(-6.38841 - 4.81541i) q^{64} +10.5471i q^{65} +(-2.18720 + 2.99194i) q^{66} +(2.16651 - 1.25083i) q^{67} +(1.93036 - 2.11877i) q^{68} +1.58336 q^{69} +(1.45594 + 1.06434i) q^{70} +(8.35311 - 14.4680i) q^{71} +(-4.23261 + 0.860827i) q^{72} +(8.25523 - 14.2985i) q^{73} +(-1.02261 + 9.46252i) q^{74} -3.64532i q^{75} +(1.92219 - 8.50325i) q^{76} -0.973361i q^{77} +(-6.36167 - 0.687504i) q^{78} +(-4.05535 + 7.02407i) q^{79} +(-6.54371 - 9.23244i) q^{80} +(1.04337 - 1.80717i) q^{81} +(7.04400 - 9.63570i) q^{82} +11.8333 q^{83} +(-0.736877 + 0.808796i) q^{84} +(3.51124 - 2.02722i) q^{85} +(6.62571 + 4.84361i) q^{86} +10.2672i q^{87} +(-1.93835 + 5.79177i) q^{88} +(-6.95256 + 4.01406i) q^{89} +(-6.07437 - 0.656455i) q^{90} +(1.45537 - 0.840259i) q^{91} +(2.48626 - 0.791744i) q^{92} +(0.522665 + 0.301761i) q^{93} +(-0.374340 - 0.847459i) q^{94} +(6.24056 - 10.6360i) q^{95} +(5.99526 - 3.34515i) q^{96} +(-5.47310 - 3.15990i) q^{97} +(-1.03277 + 9.55649i) q^{98} +(1.64875 + 2.85571i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 3 q^{2} - 6 q^{3} + q^{4} - 3 q^{6} + 8 q^{9} + 6 q^{10} - 16 q^{11} + 13 q^{16} - 22 q^{17} + 4 q^{19} - 40 q^{20} - 21 q^{22} - 11 q^{24} + 16 q^{25} + 36 q^{26} - 10 q^{28} + 4 q^{30} - 3 q^{32}+ \cdots - 28 q^{99}+O(q^{100}) $ 28 * q - 3 * q^2 - 6 * q^3 + q^4 - 3 * q^6 + 8 * q^9 + 6 * q^10 - 16 * q^11 + 13 * q^16 - 22 * q^17 + 4 * q^19 - 40 * q^20 - 21 * q^22 - 11 * q^24 + 16 * q^25 + 36 * q^26 - 10 * q^28 + 4 * q^30 - 3 * q^32 + 36 * q^33 - 12 * q^34 - 28 * q^35 - 8 * q^36 + 38 * q^38 - 48 * q^40 + 6 * q^41 + 14 * q^42 + 30 * q^43 + 5 * q^44 - 15 * q^48 - 68 * q^49 - 42 * q^51 + 36 * q^52 + 23 * q^54 - 26 * q^57 + 20 * q^58 - 18 * q^59 - 42 * q^60 + 22 * q^62 + 70 * q^64 - 27 * q^66 + 78 * q^67 + 4 * q^68 + 18 * q^70 - 24 * q^72 + 14 * q^73 + 4 * q^74 + 47 * q^76 - 30 * q^78 - 20 * q^80 + 6 * q^81 + 23 * q^82 - 32 * q^83 + 42 * q^86 - 18 * q^89 - 96 * q^90 - 12 * q^91 + 46 * q^92 + 50 * q^96 + 30 * q^97 + 15 * q^98 - 28 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/152\mathbb{Z}\right)^\times$.

$n$	$39$	$77$	$97$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.151949	+	1.40603i	−0.107444	+	0.994211i
$2$	−0.151949	+	1.40603i	−0.107444	+	0.994211i
$3$	−1.05104	−	0.606818i	−0.606818	−	0.350346i	0.164901	−	0.986310i	$-0.447269\pi$
$3$	−1.05104	−	0.606818i	−0.606818	−	0.350346i	−0.771719	+	0.635964i	$0.780603\pi$
$4$	−1.95382	−	0.427288i	−0.976912	−	0.213644i
$5$	−2.45005	−	1.41453i	−1.09569	−	0.632599i	−0.160607	−	0.987018i	$-0.551345\pi$
$5$	−2.45005	−	1.41453i	−1.09569	−	0.632599i	−0.935087	+	0.354419i	$0.884679\pi$
$6$	1.01291	−	1.38558i	0.413517	−	0.565662i
$7$			0.450769i			0.170375i	0.996365	+	0.0851873i	$0.0271489\pi$
$7$			0.450769i			0.170375i	−0.996365	+	0.0851873i	$0.972851\pi$
$8$	0.897660	−	2.68220i	0.317371	−	0.948302i
$9$	−0.763544	−	1.32250i	−0.254515	−	0.440832i
$10$	2.36116	−	3.22989i	0.746663	−	1.02138i
$11$	−2.15933			−0.651064			−0.325532	−	0.945531i	$-0.605543\pi$
$11$	−2.15933			−0.651064			−0.325532	+	0.945531i	$0.605543\pi$
$12$	1.79426	+	1.63471i	0.517958	+	0.471901i
$13$	−1.86406	−	3.22864i	−0.516996	−	0.895464i	−0.999805	−	0.0197382i	$-0.993717\pi$
$13$	−1.86406	−	3.22864i	−0.516996	−	0.895464i	0.482809	−	0.875726i	$-0.339617\pi$
$14$	−0.633793	−	0.0684938i	−0.169388	−	0.0183057i
$15$	1.71673	+	2.97346i	0.443258	+	0.767745i
$16$	3.63485	+	1.66969i	0.908712	+	0.417423i
$17$	−0.716566	+	1.24113i	−0.173793	+	0.301018i	−0.939743	−	0.341882i	$-0.888936\pi$
$17$	−0.716566	+	1.24113i	−0.173793	+	0.301018i	0.765950	+	0.642900i	$0.222269\pi$
$18$	1.97549	−	0.872612i	0.465627	−	0.205677i
$19$	−0.0305680	+	4.35879i	−0.00701278	+	0.999975i
$19$	−0.0305680	+	4.35879i	−0.00701278	+	0.999975i
$20$	4.18254	+	3.81063i	0.935245	+	0.852082i
$21$	0.273535	−	0.473776i	0.0596901	−	0.103386i
$22$	0.328108	−	3.03608i	0.0699530	−	0.647295i
$23$	−1.12985	+	0.652319i	−0.235590	+	0.136018i	−0.613148	−	0.789968i	$-0.710097\pi$
$23$	−1.12985	+	0.652319i	−0.235590	+	0.136018i	0.377558	+	0.925986i	$0.376764\pi$
$24$	−2.57108	+	2.27438i	−0.524820	+	0.464257i
$25$	1.50182	+	2.60122i	0.300363	+	0.520245i
$26$	4.82280	−	2.13033i	0.945828	−	0.417791i
$27$			5.49424i			1.05737i
$28$	0.192608	−	0.880723i	0.0363995	−	0.166441i
$29$	−4.22992	−	7.32644i	−0.785477	−	1.36049i	−0.928714	−	0.370797i	$-0.879085\pi$
$29$	−4.22992	−	7.32644i	−0.785477	−	1.36049i	0.143237	−	0.989688i	$-0.454249\pi$
$30$	−4.44162	+	1.96195i	−0.810926	+	0.358202i
$31$	−0.497284			−0.0893149			−0.0446575	−	0.999002i	$-0.514220\pi$
$31$	−0.497284			−0.0893149			−0.0446575	+	0.999002i	$0.514220\pi$
$32$	−2.89994	+	4.85699i	−0.512642	+	0.858602i
$33$	2.26955	+	1.31032i	0.395077	+	0.228098i
$34$	−1.63618	−	1.19610i	−0.280603	−	0.205129i
$35$	0.637628	−	1.10440i	0.107779	−	0.186678i
$36$	0.926743	+	2.91018i	0.154457	+	0.485030i
$37$	6.72997			1.10640			0.553200	−	0.833049i	$-0.313407\pi$
$37$	6.72997			1.10640			0.553200	+	0.833049i	$0.313407\pi$
$38$	−6.12393	−	0.705293i	−0.993433	−	0.114414i
$39$			4.52457i			0.724511i
$40$	−5.99338	+	5.30175i	−0.947636	+	0.838280i
$41$	−7.30919	−	4.21996i	−1.14150	−	0.659047i	−0.194701	−	0.980863i	$-0.562374\pi$
$41$	−7.30919	−	4.21996i	−1.14150	−	0.659047i	−0.946802	+	0.321815i	$0.895707\pi$
$42$	0.624578	+	0.456587i	0.0963745	+	0.0704529i
$43$	2.90174	−	5.02595i	0.442511	−	0.766451i	−0.555364	−	0.831607i	$-0.687421\pi$
$43$	2.90174	−	5.02595i	0.442511	−	0.766451i	0.997875	+	0.0651562i	$0.0207546\pi$
$44$	4.21896	+	0.922659i	0.636032	+	0.139096i
$45$			4.32024i			0.644023i
$46$	−0.745499	−	1.68772i	−0.109918	−	0.248841i
$47$	−0.567335	+	0.327551i	−0.0827543	+	0.0477782i	−0.540806	−	0.841147i	$-0.681881\pi$
$47$	−0.567335	+	0.327551i	−0.0827543	+	0.0477782i	0.458052	+	0.888925i	$0.348547\pi$
$48$	−2.80717	−	3.96060i	−0.405180	−	0.571664i
$49$	6.79681			0.970972
$50$	−3.88559	+	1.71634i	−0.549505	+	0.242727i
$51$	1.50628	−	0.869651i	0.210921	−	0.121775i
$52$	2.26248	+	7.10468i	0.313749	+	0.985242i
$53$	3.86444	+	6.69340i	0.530821	+	0.919409i	0.999353	+	0.0359626i	$0.0114497\pi$
$53$	3.86444	+	6.69340i	0.530821	+	0.919409i	−0.468532	+	0.883446i	$0.655217\pi$
$54$	−7.72504	−	0.834843i	−1.05125	−	0.113608i
$55$	5.29047	+	3.05445i	0.713367	+	0.411862i
$56$	1.20905	+	0.404637i	0.161567	+	0.0540719i
$57$	2.67712	−	4.56271i	0.354593	−	0.604346i
$58$	10.9439	−	4.83414i	1.43700	−	0.634753i
$59$	−12.1090	−	6.99113i	−1.57646	−	0.910168i	−0.995348	−	0.0963425i	$-0.969286\pi$
$59$	−12.1090	−	6.99113i	−1.57646	−	0.910168i	−0.581109	−	0.813826i	$-0.697381\pi$
$60$	−2.08366	−	6.54316i	−0.268999	−	0.844718i
$61$	−2.13281	+	1.23138i	−0.273078	+	0.157662i	−0.630286	−	0.776363i	$-0.717062\pi$
$61$	−2.13281	+	1.23138i	−0.273078	+	0.157662i	0.357208	+	0.934025i	$0.383729\pi$
$62$	0.0755618	−	0.699195i	0.00959636	−	0.0887979i
$63$	0.596141	−	0.344182i	0.0751067	−	0.0433629i
$64$	−6.38841	−	4.81541i	−0.798552	−	0.601926i
$65$			10.5471i			1.30821i
$66$	−2.18720	+	2.99194i	−0.269226	+	0.368282i
$67$	2.16651	−	1.25083i	0.264681	−	0.152814i	−0.361787	−	0.932261i	$-0.617833\pi$
$67$	2.16651	−	1.25083i	0.264681	−	0.152814i	0.626468	+	0.779447i	$0.284500\pi$
$68$	1.93036	−	2.11877i	0.234091	−	0.256938i
$69$	1.58336			0.190614
$70$	1.45594	+	1.06434i	0.174018	+	0.127212i
$71$	8.35311	−	14.4680i	0.991332	−	1.71704i	0.381888	−	0.924209i	$-0.375274\pi$
$71$	8.35311	−	14.4680i	0.991332	−	1.71704i	0.609444	−	0.792829i	$-0.291393\pi$
$72$	−4.23261	+	0.860827i	−0.498818	+	0.101449i
$73$	8.25523	−	14.2985i	0.966202	−	1.67351i	0.259851	−	0.965649i	$-0.416327\pi$
$73$	8.25523	−	14.2985i	0.966202	−	1.67351i	0.706351	−	0.707862i	$-0.250340\pi$
$74$	−1.02261	+	9.46252i	−0.118876	+	1.10000i
$75$		−	3.64532i		−	0.420925i
$76$	1.92219	−	8.50325i	0.220490	−	0.975389i
$77$		−	0.973361i		−	0.110925i
$78$	−6.36167	−	0.687504i	−0.720317	−	0.0778445i
$79$	−4.05535	+	7.02407i	−0.456262	+	0.790269i	−0.998760	−	0.0497881i	$-0.984145\pi$
$79$	−4.05535	+	7.02407i	−0.456262	+	0.790269i	0.542498	+	0.840057i	$0.317479\pi$
$80$	−6.54371	−	9.23244i	−0.731609	−	1.03222i
$81$	1.04337	−	1.80717i	0.115930	−	0.200796i
$82$	7.04400	−	9.63570i	0.777880	−	1.06408i
$83$	11.8333			1.29887			0.649435	−	0.760417i	$-0.275006\pi$
$83$	11.8333			1.29887			0.649435	+	0.760417i	$0.275006\pi$
$84$	−0.736877	+	0.808796i	−0.0803999	+	0.0882469i
$85$	3.51124	−	2.02722i	0.380848	−	0.219882i
$86$	6.62571	+	4.84361i	0.714469	+	0.522300i
$87$			10.2672i			1.10076i
$88$	−1.93835	+	5.79177i	−0.206629	+	0.617405i
$89$	−6.95256	+	4.01406i	−0.736970	+	0.425490i	−0.820967	−	0.570976i	$-0.806565\pi$
$89$	−6.95256	+	4.01406i	−0.736970	+	0.425490i	0.0839965	+	0.996466i	$0.473232\pi$
$90$	−6.07437	−	0.656455i	−0.640295	−	0.0691965i
$91$	1.45537	−	0.840259i	0.152564	−	0.0880831i
$92$	2.48626	−	0.791744i	0.259210	−	0.0825451i
$93$	0.522665	+	0.301761i	0.0541979	+	0.0312912i
$94$	−0.374340	−	0.847459i	−0.0386102	−	0.0874088i
$95$	6.24056	−	10.6360i	0.640267	−	1.09123i
$96$	5.99526	−	3.34515i	0.611889	−	0.341413i
$97$	−5.47310	−	3.15990i	−0.555709	−	0.320839i	0.195712	−	0.980661i	$-0.437298\pi$
$97$	−5.47310	−	3.15990i	−0.555709	−	0.320839i	−0.751422	+	0.659822i	$0.770632\pi$
$98$	−1.03277	+	9.55649i	−0.104325	+	0.965352i
$99$	1.64875	+	2.85571i	0.165705	+	0.287010i
$100$	−1.82281	−	5.72404i	−0.182281	−	0.572404i
$101$	−4.61075	+	2.66202i	−0.458787	+	0.264881i	−0.711534	−	0.702652i	$-0.751999\pi$
$101$	−4.61075	+	2.66202i	−0.458787	+	0.264881i	0.252747	+	0.967532i	$0.418666\pi$
$102$	0.993875	+	2.25001i	0.0984083	+	0.222784i
$103$	−17.9095			−1.76468			−0.882340	−	0.470613i	$-0.844033\pi$
$103$	−17.9095			−1.76468			−0.882340	+	0.470613i	$0.844033\pi$
$104$	−10.3332	+	2.10155i	−1.01325	+	0.206074i
$105$	−1.34034	+	0.773848i	−0.130804	+	0.0755199i
$106$	−9.99830	+	4.41645i	−0.971120	+	0.428963i
$107$		−	0.909747i		−	0.0879485i	−0.999033	−	0.0439743i	$-0.985998\pi$
$107$		−	0.909747i		−	0.0879485i	0.999033	−	0.0439743i	$-0.0140020\pi$
$108$	2.34762	−	10.7348i	0.225900	−	1.03295i
$109$	−0.935166	+	1.61976i	−0.0895727	+	0.155144i	−0.907331	−	0.420418i	$-0.861883\pi$
$109$	−0.935166	+	1.61976i	−0.0895727	+	0.155144i	0.817758	+	0.575562i	$0.195217\pi$
$110$	−5.09853	+	6.97442i	−0.486125	+	0.664985i
$111$	−7.07346	−	4.08386i	−0.671383	−	0.387623i
$112$	−0.752645	+	1.63848i	−0.0711183	+	0.154822i
$113$			2.34200i			0.220317i	0.993914	+	0.110159i	$0.0351359\pi$
$113$			2.34200i			0.220317i	−0.993914	+	0.110159i	$0.964864\pi$
$114$	6.00851	+	4.45740i	0.562749	+	0.417474i
$115$	3.69091			0.344179
$116$	5.13402	+	16.1220i	0.476681	+	1.49689i
$117$	−2.84658	+	4.93042i	−0.263166	+	0.455818i
$118$	11.6697	−	15.9633i	1.07428	−	1.46954i
$119$	−0.559462	−	0.323006i	−0.0512858	−	0.0296099i
$120$	9.51647	−	1.93546i	0.868731	−	0.176682i
$121$	−6.33727			−0.576116
$122$	−1.40727	−	3.18589i	−0.127408	−	0.288437i
$123$	5.12150	+	8.87069i	0.461790	+	0.799843i
$124$	0.971606	+	0.212484i	0.0872528	+	0.0190816i
$125$			5.64786i			0.505160i
$126$	0.393346	+	0.890488i	0.0350421	+	0.0793310i
$127$	−1.06604	−	1.84643i	−0.0945955	−	0.163844i	0.814844	−	0.579680i	$-0.196822\pi$
$127$	−1.06604	−	1.84643i	−0.0945955	−	0.163844i	−0.909440	+	0.415836i	$0.863489\pi$
$128$	7.74131	−	8.25058i	0.684242	−	0.729255i
$129$	−6.09968	+	3.52165i	−0.537047	+	0.310064i
$130$	−14.8295	−	1.60262i	−1.30063	−	0.140559i
$131$	−8.72441	+	15.1111i	−0.762255	+	1.32026i	0.179430	+	0.983771i	$0.442575\pi$
$131$	−8.72441	+	15.1111i	−0.762255	+	1.32026i	−0.941686	+	0.336494i	$0.890759\pi$
$132$	−3.87441	−	3.52989i	−0.337224	−	0.307237i
$133$	−1.96481	−	0.0137791i	−0.170370	−	0.00119480i
$134$	1.42951	+	3.23623i	0.123491	+	0.279568i
$135$	7.77179	−	13.4611i	0.668889	−	1.15855i
$136$	2.68573	+	3.03609i	0.230299	+	0.260342i
$137$	−4.28881	−	7.42843i	−0.366417	−	0.634654i	0.622585	−	0.782552i	$-0.286082\pi$
$137$	−4.28881	−	7.42843i	−0.366417	−	0.634654i	−0.989003	+	0.147898i	$0.952749\pi$
$138$	−0.240589	+	2.22624i	−0.0204803	+	0.189510i
$139$	−2.38145	−	4.12479i	−0.201992	−	0.349860i	0.747178	−	0.664624i	$-0.231408\pi$
$139$	−2.38145	−	4.12479i	−0.201992	−	0.349860i	−0.949170	+	0.314763i	$0.898075\pi$
$140$	−1.71771	+	1.88536i	−0.145173	+	0.159342i
$141$	0.795055			0.0669557
$142$	19.0732	+	13.9431i	1.60059	+	1.17008i
$143$	4.02512	+	6.97172i	0.336598	+	0.583004i
$144$	−0.567205	−	6.08196i	−0.0472671	−	0.506830i
$145$			23.9335i			1.98757i
$146$	18.8497	+	13.7797i	1.56001	+	1.14042i
$147$	−7.14371	−	4.12442i	−0.589203	−	0.340177i
$148$	−13.1492	−	2.87564i	−1.08085	−	0.236376i
$149$	9.33207	+	5.38787i	0.764513	+	0.441392i	0.830914	−	0.556401i	$-0.187818\pi$
$149$	9.33207	+	5.38787i	0.764513	+	0.441392i	−0.0664008	+	0.997793i	$0.521152\pi$
$150$	5.12541	+	0.553902i	0.418488	+	0.0452259i
$151$	−5.40642			−0.439968			−0.219984	−	0.975503i	$-0.570601\pi$
$151$	−5.40642			−0.439968			−0.219984	+	0.975503i	$0.570601\pi$
$152$	11.6637	+	3.99470i	0.946053	+	0.324013i
$153$	2.18852			0.176931
$154$	1.36857	+	0.147901i	0.110283	+	0.0119182i
$155$	1.21837	+	0.703426i	0.0978618	+	0.0565005i
$156$	1.93330	−	8.84021i	0.154788	−	0.707784i
$157$	13.3288	+	7.69539i	1.06375	+	0.614159i	0.926468	−	0.376373i	$-0.122829\pi$
$157$	13.3288	+	7.69539i	1.06375	+	0.614159i	0.137286	+	0.990531i	$0.456162\pi$
$158$	−9.25982	−	6.76922i	−0.736672	−	0.538531i
$159$		−	9.38003i		−	0.743885i
$160$	13.9754	−	7.79777i	1.10485	−	0.616468i
$161$	−0.294045	−	0.509301i	−0.0231740	−	0.0401386i
$162$	2.38239	+	1.74160i	0.187178	+	0.136833i
$163$	0.534048			0.0418298			0.0209149	−	0.999781i	$-0.493342\pi$
$163$	0.534048			0.0418298			0.0209149	+	0.999781i	$0.493342\pi$
$164$	12.4777	+	11.3682i	0.974346	+	0.887706i
$165$	−3.70699	−	6.42070i	−0.288589	−	0.499851i
$166$	−1.79805	+	16.6379i	−0.139556	+	1.29135i
$167$	−6.81811	−	11.8093i	−0.527601	−	0.913832i	−0.999482	−	0.0321697i	$-0.989758\pi$
$167$	−6.81811	−	11.8093i	−0.527601	−	0.913832i	0.471881	−	0.881662i	$-0.343575\pi$
$168$	−1.02522	−	1.15896i	−0.0790975	−	0.0894161i
$169$	−0.449417	+	0.778413i	−0.0345705	+	0.0598779i
$170$	2.31679	+	5.24493i	0.177690	+	0.402268i
$171$	5.78783	−	3.28770i	0.442606	−	0.251417i
$172$	−7.81701	+	8.57995i	−0.596041	+	0.654215i
$173$	0.822987	−	1.42546i	0.0625706	−	0.108375i	−0.833043	−	0.553208i	$-0.813403\pi$
$173$	0.822987	−	1.42546i	0.0625706	−	0.108375i	0.895614	+	0.444833i	$0.146737\pi$
$174$	−14.4359	−	1.56008i	−1.09438	−	0.118270i
$175$	−1.17255	+	0.676972i	−0.0886365	+	0.0511743i
$176$	−7.84886	−	3.60542i	−0.591630	−	0.271769i
$177$	8.48469	+	14.6959i	0.637748	+	1.10461i
$178$	−4.58745	−	10.3854i	−0.343844	−	0.778420i
$179$			7.67159i			0.573402i	0.958020	+	0.286701i	$0.0925586\pi$
$179$			7.67159i			0.573402i	−0.958020	+	0.286701i	$0.907441\pi$
$180$	1.84599	−	8.44098i	0.137592	−	0.629154i
$181$	−11.7649	−	20.3774i	−0.874479	−	1.51464i	−0.857316	−	0.514790i	$-0.827870\pi$
$181$	−11.7649	−	20.3774i	−0.874479	−	1.51464i	−0.0171632	−	0.999853i	$-0.505463\pi$
$182$	0.960285	+	2.17397i	0.0711810	+	0.161145i
$183$	2.98889			0.220945
$184$	0.735430	+	3.61605i	0.0542166	+	0.266578i
$185$	−16.4887	−	9.51977i	−1.21228	−	0.699908i
$186$	−0.503703	+	0.689029i	−0.0369333	+	0.0505221i
$187$	1.54731	−	2.68001i	0.113150	−	0.195982i
$188$	1.24843	−	0.397561i	0.0910512	−	0.0289951i
$189$	−2.47663			−0.180148
$190$	14.0063	+	10.3905i	1.01612	+	0.753807i
$191$		−	23.8645i		−	1.72678i	−0.504540	−	0.863388i	$-0.668338\pi$
$191$		−	23.8645i		−	1.72678i	0.504540	−	0.863388i	$-0.331662\pi$
$192$	3.79240	+	8.93779i	0.273693	+	0.645029i
$193$	16.5463	+	9.55301i	1.19103	+	0.687641i	0.958540	−	0.284958i	$-0.0919798\pi$
$193$	16.5463	+	9.55301i	1.19103	+	0.687641i	0.232489	+	0.972599i	$0.425313\pi$
$194$	5.27453	−	7.21519i	0.378689	−	0.518020i
$195$	6.40016	−	11.0854i	0.458325	−	0.793843i
$196$	−13.2798	−	2.90420i	−0.948554	−	0.207443i
$197$			11.2480i			0.801385i	0.916213	+	0.400693i	$0.131230\pi$
$197$			11.2480i			0.801385i	−0.916213	+	0.400693i	$0.868770\pi$
$198$	−4.26574	+	1.88426i	−0.303153	+	0.133909i
$199$	−9.91953	+	5.72704i	−0.703177	+	0.405979i	−0.808530	−	0.588456i	$-0.799736\pi$
$199$	−9.91953	+	5.72704i	−0.703177	+	0.405979i	0.105353	+	0.994435i	$0.466403\pi$
$200$	8.32513	−	1.69316i	0.588675	−	0.119725i
$201$	−3.03611			−0.214151
$202$	−3.04227	−	6.88733i	−0.214053	−	0.484591i
$203$	3.30253	−	1.90672i	0.231792	−	0.133825i
$204$	−3.31459	+	1.05553i	−0.232068	+	0.0739017i
$205$	11.9386	+	20.6782i	0.833825	+	1.44423i
$206$	2.72133	−	25.1813i	0.189604	−	1.75446i
$207$	1.72538	+	0.996149i	0.119922	+	0.0692371i
$208$	−1.38473	−	14.8480i	−0.0960138	−	1.02953i
$209$	0.0660065	−	9.41209i	0.00456577	−	0.651048i
$210$	−0.884388	−	2.00215i	−0.0610286	−	0.138161i
$211$	−13.8288	−	7.98406i	−0.952013	−	0.549645i	−0.0583076	−	0.998299i	$-0.518570\pi$
$211$	−13.8288	−	7.98406i	−0.952013	−	0.549645i	−0.893706	+	0.448653i	$0.851904\pi$
$212$	−4.69041	−	14.7289i	−0.322139	−	1.01159i
$213$	−17.5589	+	10.1376i	−1.20312	+	0.694619i
$214$	1.27913	+	0.138235i	0.0874394	+	0.00944955i
$215$	−14.2188	+	8.20921i	−0.969712	+	0.559864i
$216$	14.7366	+	4.93196i	1.00270	+	0.335577i
$217$		−	0.224160i		−	0.0152170i
$218$	−2.13532	−	1.56099i	−0.144622	−	0.105724i
$219$	−17.3531	+	10.0188i	−1.17262	+	0.677011i
$220$	−9.03151	−	8.22842i	−0.608904	−	0.554760i
$221$	5.34288			0.359401
$222$	6.81683	−	9.32494i	0.457516	−	0.625849i
$223$	−8.06323	+	13.9659i	−0.539954	+	0.935227i	0.458952	+	0.888461i	$0.348225\pi$
$223$	−8.06323	+	13.9659i	−0.539954	+	0.935227i	−0.998906	+	0.0467660i	$0.985108\pi$
$224$	−2.18938	−	1.30720i	−0.146284	−	0.0873412i
$225$	2.29341	−	3.97230i	0.152894	−	0.264820i
$226$	−3.29292	−	0.355865i	−0.219042	−	0.0236718i
$227$		−	13.0282i		−	0.864715i	−0.901702	−	0.432357i	$-0.857682\pi$
$227$		−	13.0282i		−	0.864715i	0.901702	−	0.432357i	$-0.142318\pi$
$228$	−7.18021	+	7.77083i	−0.475521	+	0.514636i
$229$		−	12.7253i		−	0.840914i	−0.907312	−	0.420457i	$-0.861870\pi$
$229$		−	12.7253i		−	0.840914i	0.907312	−	0.420457i	$-0.138130\pi$
$230$	−0.560830	+	5.18952i	−0.0369800	+	0.342187i
$231$	−0.590653	+	1.02304i	−0.0388621	+	0.0673111i
$232$	−23.4480	+	4.76885i	−1.53944	+	0.313090i
$233$	5.77758	−	10.0071i	0.378502	−	0.655585i	−0.612343	−	0.790593i	$-0.709773\pi$
$233$	5.77758	−	10.0071i	0.378502	−	0.655585i	0.990845	+	0.135008i	$0.0431060\pi$
$234$	−6.49977	−	4.75154i	−0.424903	−	0.310618i
$235$	1.85333			0.120898
$236$	20.6716	+	18.8335i	1.34561	+	1.22595i
$237$	8.52466	−	4.92171i	0.553736	−	0.319700i
$238$	0.539165	−	0.737539i	0.0349488	−	0.0478075i
$239$			18.8301i			1.21802i	0.793163	+	0.609010i	$0.208433\pi$
$239$			18.8301i			1.21802i	−0.793163	+	0.609010i	$0.791567\pi$
$240$	1.27529	+	13.6745i	0.0823194	+	0.882685i
$241$	−8.47571	+	4.89346i	−0.545969	+	0.315215i	−0.747494	−	0.664268i	$-0.768743\pi$
$241$	−8.47571	+	4.89346i	−0.545969	+	0.315215i	0.201526	+	0.979483i	$0.435410\pi$
$242$	0.962941	−	8.91038i	0.0619002	−	0.572781i
$243$	12.0812	−	6.97509i	0.775009	−	0.447452i
$244$	4.69328	−	1.49457i	0.300457	−	0.0956800i
$245$	−16.6525	−	9.61432i	−1.06389	−	0.614236i
$246$	−13.2506	+	5.85307i	−0.844830	+	0.373178i
$247$	14.1300	−	8.02634i	0.899068	−	0.510704i
$248$	−0.446392	+	1.33382i	−0.0283459	+	0.0846975i
$249$	−12.4372	−	7.18063i	−0.788177	−	0.455054i
$250$	−7.94104	−	0.858186i	−0.502235	−	0.0542764i
$251$	8.19032	+	14.1861i	0.516969	+	0.895416i	0.999806	+	0.0197059i	$0.00627298\pi$
$251$	8.19032	+	14.1861i	0.516969	+	0.895416i	−0.482837	+	0.875710i	$0.660394\pi$
$252$	−1.31182	+	0.417747i	−0.0826368	+	0.0263156i
$253$	2.43972	−	1.40858i	0.153384	−	0.0885564i
$254$	2.75812	−	1.21831i	0.173060	−	0.0764438i
$255$	−4.92060			−0.308140
$256$	10.4243	+	12.1382i	0.651516	+	0.758635i
$257$	7.56834	−	4.36958i	0.472100	−	0.272567i	−0.245019	−	0.969518i	$-0.578794\pi$
$257$	7.56834	−	4.36958i	0.472100	−	0.272567i	0.717118	+	0.696951i	$0.245461\pi$
$258$	−4.02470	−	9.11142i	−0.250567	−	0.567252i
$259$			3.03366i			0.188502i
$260$	4.50665	−	20.6072i	0.279491	−	1.27800i
$261$	−6.45946	+	11.1881i	−0.399831	+	0.692527i
$262$	−19.9210	−	14.5629i	−1.23072	−	0.899697i
$263$	24.1288	+	13.9308i	1.48785	+	0.859008i	0.999904	−	0.0138683i	$-0.00441455\pi$
$263$	24.1288	+	13.9308i	1.48785	+	0.859008i	0.487942	+	0.872876i	$0.337748\pi$
$264$	5.55183	−	4.91116i	0.341692	−	0.302261i
$265$		−	21.8655i		−	1.34319i
$266$	0.317924	−	2.76048i	0.0194932	−	0.169256i
$267$	9.74322			0.596276
$268$	−4.76744	+	1.51818i	−0.291218	+	0.0927379i
$269$	11.8357	−	20.5001i	0.721638	−	1.24991i	−0.238704	−	0.971092i	$-0.576723\pi$
$269$	11.8357	−	20.5001i	0.721638	−	1.24991i	0.960343	−	0.278822i	$-0.0899439\pi$
$270$	17.7458	+	12.9727i	1.07997	+	0.789496i
$271$	15.9524	+	9.21013i	0.969041	+	0.559476i	0.898944	−	0.438064i	$-0.144336\pi$
$271$	15.9524	+	9.21013i	0.969041	+	0.559476i	0.0700969	+	0.997540i	$0.477669\pi$
$272$	−4.67691	+	3.31487i	−0.283580	+	0.200994i
$273$	−2.03954			−0.123438
$274$	11.0963	−	4.90144i	0.670349	−	0.296107i
$275$	−3.24293	−	5.61691i	−0.195556	−	0.338713i
$276$	−3.09360	−	0.676549i	−0.186213	−	0.0407235i
$277$		−	26.0321i		−	1.56412i	−0.623203	−	0.782060i	$-0.714169\pi$
$277$		−	26.0321i		−	1.56412i	0.623203	−	0.782060i	$-0.285831\pi$
$278$	6.16143	−	2.72163i	0.369538	−	0.163232i
$279$	0.379699	+	0.657657i	0.0227320	+	0.0393729i
$280$	−2.38986	−	2.70163i	−0.142822	−	0.161453i
$281$	18.1670	−	10.4887i	1.08375	−	0.625706i	0.151848	−	0.988404i	$-0.451478\pi$
$281$	18.1670	−	10.4887i	1.08375	−	0.625706i	0.931907	+	0.362698i	$0.118144\pi$
$282$	−0.120808	+	1.11787i	−0.00719400	+	0.0665681i
$283$	−5.72882	+	9.92260i	−0.340543	+	0.589837i	−0.984534	−	0.175196i	$-0.943944\pi$
$283$	−5.72882	+	9.92260i	−0.340543	+	0.589837i	0.643991	+	0.765033i	$0.277277\pi$
$284$	−22.5025	+	24.6988i	−1.33528	+	1.46560i
$285$	−13.0132	+	7.39198i	−0.770835	+	0.437863i
$286$	−10.4140	+	4.60009i	−0.615795	+	0.272009i
$287$	1.90223	−	3.29475i	0.112285	−	0.194483i
$288$	8.63759	+	0.126641i	0.508975	+	0.00746241i
$289$	7.47307	+	12.9437i	0.439592	+	0.761396i
$290$	−33.6511	−	3.63666i	−1.97606	−	0.213552i
$291$	3.83496	+	6.64235i	0.224810	+	0.389382i
$292$	−22.2388	+	24.4093i	−1.30143	+	1.42845i
$293$	10.4003			0.607590			0.303795	−	0.952737i	$-0.401746\pi$
$293$	10.4003			0.607590			0.303795	+	0.952737i	$0.401746\pi$
$294$	6.88453	−	9.41755i	0.401514	−	0.549243i
$295$	19.7784	+	34.2572i	1.15154	+	1.99453i
$296$	6.04122	−	18.0511i	0.351139	−	1.04920i
$297$		−	11.8639i		−	0.688413i
$298$	−8.99349	+	12.3025i	−0.520979	+	0.712662i
$299$	4.21221	+	2.43192i	0.243598	+	0.140642i
$300$	−1.55760	+	7.12231i	−0.0899282	+	0.411206i
$301$	2.26554	+	1.30801i	0.130584	+	0.0753926i
$302$	0.821499	−	7.60157i	0.0472720	−	0.437421i
$303$	6.46144			0.371200
$304$	−7.38895	+	15.7925i	−0.423785	+	0.905763i
$305$	6.96731			0.398947
$306$	−0.332543	+	3.07712i	−0.0190102	+	0.175907i
$307$	−2.39992	−	1.38560i	−0.136971	−	0.0790801i	0.429949	−	0.902853i	$-0.358532\pi$
$307$	−2.39992	−	1.38560i	−0.136971	−	0.0790801i	−0.566920	+	0.823773i	$0.691865\pi$
$308$	−0.415906	+	1.90177i	−0.0236984	+	0.108364i
$309$	18.8236	+	10.8678i	1.07084	+	0.618249i
$310$	−1.17417	+	1.60618i	−0.0666881	+	0.0912246i
$311$		−	13.8001i		−	0.782530i	−0.920278	−	0.391265i	$-0.872038\pi$
$311$		−	13.8001i		−	0.782530i	0.920278	−	0.391265i	$-0.127962\pi$
$312$	12.1358	+	4.06153i	0.687055	+	0.229939i
$313$	5.89194	+	10.2051i	0.333032	+	0.576829i	0.983105	−	0.183043i	$-0.0585949\pi$
$313$	5.89194	+	10.2051i	0.333032	+	0.576829i	−0.650073	+	0.759872i	$0.725262\pi$
$314$	−12.8452	+	17.5714i	−0.724898	+	0.991609i
$315$	−1.94743			−0.109725
$316$	10.9247	−	11.9910i	0.614564	−	0.674545i
$317$	−8.86581	−	15.3560i	−0.497953	−	0.862480i	0.502044	−	0.864842i	$-0.332582\pi$
$317$	−8.86581	−	15.3560i	−0.497953	−	0.862480i	−0.999997	+	0.00236177i	$0.999248\pi$
$318$	13.1886	+	1.42529i	0.739579	+	0.0799260i
$319$	9.13381	+	15.8202i	0.511395	+	0.885763i
$320$	8.84034	+	20.8346i	0.494190	+	1.16469i
$321$	−0.552051	+	0.956180i	−0.0308125	+	0.0533687i
$322$	0.760771	−	0.336048i	0.0423961	−	0.0187272i
$323$	−5.38792	−	3.16130i	−0.299792	−	0.175900i
$324$	−2.81074	+	3.08506i	−0.156152	+	0.171392i
$325$	5.59894	−	9.69766i	0.310574	−	0.537929i
$326$	−0.0811479	+	0.750885i	−0.00449437	+	0.0415877i
$327$	1.96579	−	1.13495i	0.108709	−	0.0627630i
$328$	−17.8800	+	15.8166i	−0.987255	+	0.873327i
$329$	−0.147650	−	0.255737i	−0.00814020	−	0.0140992i
$330$	9.59095	−	4.23652i	0.527965	−	0.233212i
$331$		−	27.3712i		−	1.50445i	−0.658904	−	0.752227i	$-0.728980\pi$
$331$		−	27.3712i		−	1.50445i	0.658904	−	0.752227i	$-0.271020\pi$
$332$	−23.1201	−	5.05621i	−1.26888	−	0.277496i
$333$	−5.13863	−	8.90036i	−0.281595	−	0.487737i
$334$	17.6402	−	7.79203i	0.965229	−	0.426361i
$335$	−7.07739			−0.386679
$336$	1.78532	−	1.26539i	0.0973970	−	0.0690324i
$337$	10.7104	+	6.18363i	0.583430	+	0.336844i	0.762495	−	0.646994i	$-0.223974\pi$
$337$	10.7104	+	6.18363i	0.583430	+	0.336844i	−0.179065	+	0.983837i	$0.557307\pi$
$338$	−1.02618	−	0.750171i	−0.0558169	−	0.0408039i
$339$	1.42117	−	2.46154i	0.0771873	−	0.133692i
$340$	−7.72655	+	2.46051i	−0.419031	+	0.133440i
$341$	1.07380			0.0581497
$342$	3.74315	+	8.63741i	0.202406	+	0.467058i
$343$			6.21917i			0.335804i
$344$	−10.8759	−	12.2946i	−0.586387	−	0.662883i
$345$	−3.87929	−	2.23971i	−0.208854	−	0.120582i
$346$	1.87918	+	1.37374i	0.101025	+	0.0738527i
$347$	−5.69195	+	9.85874i	−0.305560	+	0.529245i	−0.977386	−	0.211464i	$-0.932177\pi$
$347$	−5.69195	+	9.85874i	−0.305560	+	0.529245i	0.671826	+	0.740709i	$0.265510\pi$
$348$	4.38704	−	20.0602i	0.235170	−	1.07534i
$349$		−	2.93676i		−	0.157201i	−0.996906	−	0.0786007i	$-0.974955\pi$
$349$		−	2.93676i		−	0.157201i	0.996906	−	0.0786007i	$-0.0250452\pi$
$350$	−0.773674	−	1.75150i	−0.0413546	−	0.0936218i
$351$	17.7389	−	10.2416i	0.946833	−	0.546655i
$352$	6.26195	−	10.4879i	0.333763	−	0.559005i
$353$	19.1919			1.02148			0.510740	−	0.859735i	$-0.329371\pi$
$353$	19.1919			1.02148			0.510740	+	0.859735i	$0.329371\pi$
$354$	−21.9521	+	9.69667i	−1.16674	+	0.515372i
$355$	−40.9310	+	23.6315i	−2.17239	+	1.25423i
$356$	15.2992	−	4.87202i	0.810858	−	0.258217i
$357$	0.392011	+	0.678984i	0.0207474	+	0.0359356i
$358$	−10.7865	−	1.16569i	−0.570082	−	0.0616086i
$359$	−3.85728	−	2.22700i	−0.203579	−	0.117537i	0.394745	−	0.918791i	$-0.370833\pi$
$359$	−3.85728	−	2.22700i	−0.203579	−	0.117537i	−0.598324	+	0.801254i	$0.704166\pi$
$360$	11.5878	+	3.87811i	0.610728	+	0.204394i
$361$	−18.9981	−	0.266479i	−0.999902	−	0.0140252i
$362$	30.4389	−	13.4455i	1.59983	−	0.706678i
$363$	6.66072	+	3.84557i	0.349597	+	0.201840i
$364$	−3.20257	+	1.01985i	−0.167860	+	0.0534549i
$365$	−40.4514	+	23.3546i	−2.11732	+	1.22244i
$366$	−0.454158	+	4.20246i	−0.0237392	+	0.219666i
$367$	−16.5629	+	9.56259i	−0.864576	+	0.499163i	−0.865542	−	0.500837i	$-0.833026\pi$
$367$	−16.5629	+	9.56259i	−0.864576	+	0.499163i	0.000966198		1.00000i	$0.499692\pi$
$368$	−5.19601	+	0.484581i	−0.270861	+	0.0252605i
$369$			12.8885i			0.670949i
$370$	15.8905	−	21.7371i	0.826108	−	1.13006i
$371$	−3.01718	+	1.74197i	−0.156644	+	0.0904384i
$372$	−0.892257	−	0.812917i	−0.0462614	−	0.0421478i
$373$	20.6810			1.07082			0.535411	−	0.844592i	$-0.320157\pi$
$373$	20.6810			1.07082			0.535411	+	0.844592i	$0.320157\pi$
$374$	3.53306	+	2.58278i	0.182690	+	0.133552i
$375$	3.42722	−	5.93612i	0.176981	−	0.306540i
$376$	0.369284	+	1.81574i	0.0190444	+	0.0936395i
$377$	−15.7696	+	27.3138i	−0.812177	+	1.40673i
$378$	0.376321	−	3.48221i	0.0193559	−	0.179106i
$379$			2.56021i			0.131509i	0.997836	+	0.0657546i	$0.0209454\pi$
$379$			2.56021i			0.131509i	−0.997836	+	0.0657546i	$0.979055\pi$
$380$	−16.7376	+	18.1143i	−0.858620	+	0.929246i
$381$			2.58756i			0.132565i
$382$	33.5542	+	3.62619i	1.71678	+	0.185532i
$383$	−9.13650	+	15.8249i	−0.466853	+	0.808613i	−0.999283	−	0.0378608i	$-0.987946\pi$
$383$	−9.13650	+	15.8249i	−0.466853	+	0.808613i	0.532430	+	0.846474i	$0.321279\pi$
$384$	−13.1430	+	3.97412i	−0.670702	+	0.202804i
$385$	−1.37685	+	2.38478i	−0.0701709	+	0.121540i
$386$	−15.9460	+	21.8130i	−0.811629	+	1.11025i
$387$	−8.86241			−0.450502
$388$	9.34329	+	8.51247i	0.474334	+	0.432155i
$389$	−12.4317	+	7.17743i	−0.630311	+	0.363910i	−0.780872	−	0.624690i	$-0.785225\pi$
$389$	−12.4317	+	7.17743i	−0.630311	+	0.363910i	0.150562	+	0.988601i	$0.451892\pi$
$390$	14.6139	+	10.6832i	0.740003	+	0.540966i
$391$		−	1.86972i		−	0.0945558i
$392$	6.10122	−	18.2304i	0.308158	−	0.920775i
$393$	18.3394	−	10.5883i	0.925100	−	0.534107i
$394$	−15.8150	−	1.70912i	−0.796746	−	0.0861041i
$395$	19.8716	−	11.4729i	0.999847	−	0.577262i
$396$	−2.00115	−	6.28405i	−0.100561	−	0.315785i
$397$	−22.8960	−	13.2190i	−1.14912	−	0.663444i	−0.200447	−	0.979705i	$-0.564239\pi$
$397$	−22.8960	−	13.2190i	−1.14912	−	0.663444i	−0.948673	+	0.316260i	$0.897573\pi$
$398$	−6.54512	−	14.8173i	−0.328077	−	0.742726i
$399$	2.05673	+	1.20676i	0.102965	+	0.0604137i
$400$	1.11564	+	11.9626i	0.0557819	+	0.598131i
$401$	−6.10144	−	3.52267i	−0.304691	−	0.175914i	0.339857	−	0.940477i	$-0.389621\pi$
$401$	−6.10144	−	3.52267i	−0.304691	−	0.175914i	−0.644549	+	0.764563i	$0.722955\pi$
$402$	0.461334	−	4.26886i	0.0230092	−	0.212911i
$403$	0.926966	+	1.60555i	0.0461755	+	0.0799783i
$404$	10.1460	−	3.23099i	0.504784	−	0.160748i
$405$	−5.11260	+	2.95176i	−0.254047	+	0.146674i
$406$	2.17908	+	4.93317i	0.108146	+	0.244829i
$407$	−14.5323			−0.720337
$408$	−0.980452	−	4.82079i	−0.0485396	−	0.238665i
$409$	17.6696	−	10.2015i	0.873705	−	0.504434i	0.00512749	−	0.999987i	$-0.498368\pi$
$409$	17.6696	−	10.2015i	0.873705	−	0.504434i	0.868578	+	0.495553i	$0.165035\pi$
$410$	−30.8882	+	13.6439i	−1.52546	+	0.673825i
$411$			10.4101i			0.513492i
$412$	34.9921	+	7.65254i	1.72394	+	0.377014i
$413$	3.15139	−	5.45836i	0.155070	−	0.268588i
$414$	−1.66278	+	2.27457i	−0.0817213	+	0.111789i
$415$	−28.9920	−	16.7386i	−1.42316	−	0.821664i
$416$	21.0871	+	0.309172i	1.03388	+	0.0151584i
$417$			5.78043i			0.283069i
$418$	13.2236	+	1.52296i	0.646788	+	0.0744906i
$419$	−7.69306			−0.375831			−0.187915	−	0.982185i	$-0.560173\pi$
$419$	−7.69306			−0.375831			−0.187915	+	0.982185i	$0.560173\pi$
$420$	2.94945	−	0.939249i	0.143919	−	0.0458307i
$421$	3.05025	−	5.28319i	0.148660	−	0.257487i	−0.782072	−	0.623188i	$-0.785837\pi$
$421$	3.05025	−	5.28319i	0.148660	−	0.257487i	0.930732	+	0.365701i	$0.119171\pi$
$422$	13.3271	−	18.2305i	0.648752	−	0.887446i
$423$	0.866371	+	0.500199i	0.0421244	+	0.0243205i
$424$	21.4220	−	4.35680i	1.04034	−	0.211585i
$425$	−4.30461			−0.208804
$426$	−11.5857	−	26.2287i	−0.561331	−	1.27078i
$427$	−0.555067	−	0.961404i	−0.0268616	−	0.0465256i
$428$	−0.388724	+	1.77748i	−0.0187897	+	0.0859179i
$429$		−	9.77007i		−	0.471703i
$430$	−9.38185	−	21.2394i	−0.452433	−	1.02425i
$431$	4.72335	+	8.18108i	0.227516	+	0.394069i	0.957071	−	0.289853i	$-0.0936063\pi$
$431$	4.72335	+	8.18108i	0.227516	+	0.394069i	−0.729555	+	0.683922i	$0.760273\pi$
$432$	−9.17368	+	19.9707i	−0.441369	+	0.960842i
$433$	−14.9419	+	8.62669i	−0.718061	+	0.414572i	−0.814038	−	0.580811i	$-0.802736\pi$
$433$	−14.9419	+	8.62669i	−0.718061	+	0.414572i	0.0959778	+	0.995383i	$0.469402\pi$
$434$	0.315175	+	0.0340609i	0.0151289	+	0.00163498i
$435$	14.5233	−	25.1550i	0.696337	−	1.20609i
$436$	2.51925	−	2.76513i	0.120650	−	0.132426i
$437$	−2.80879	−	4.94472i	−0.134362	−	0.236538i
$438$	−11.4500	−	25.9213i	−0.547101	−	1.23857i
$439$	4.84656	−	8.39450i	0.231314	−	0.400647i	−0.726881	−	0.686763i	$-0.759031\pi$
$439$	4.84656	−	8.39450i	0.231314	−	0.400647i	0.958195	+	0.286116i	$0.0923642\pi$
$440$	12.9417	−	11.4482i	0.616972	−	0.545774i
$441$	−5.18966	−	8.98876i	−0.247127	−	0.428036i
$442$	−0.811845	+	7.51224i	−0.0386155	+	0.357321i
$443$	8.03408	+	13.9154i	0.381711	+	0.661142i	0.991307	−	0.131570i	$-0.0420018\pi$
$443$	8.03408	+	13.9154i	0.381711	+	0.661142i	−0.609596	+	0.792712i	$0.708668\pi$
$444$	12.0753	+	11.0016i	0.573069	+	0.522111i
$445$	22.7121			1.07666
$446$	−18.4113	−	13.4592i	−0.871798	−	0.637312i
$447$	−6.53892	−	11.3257i	−0.309280	−	0.535689i
$448$	2.17064	−	2.87970i	0.102553	−	0.136053i
$449$		−	12.4409i		−	0.587123i	−0.955940	−	0.293562i	$-0.905159\pi$
$449$		−	12.4409i		−	0.587123i	0.955940	−	0.293562i	$-0.0948406\pi$
$450$	5.23668	+	3.82818i	0.246859	+	0.180462i
$451$	15.7830	+	9.11231i	0.743192	+	0.429082i
$452$	1.00071	−	4.57586i	0.0470695	−	0.215230i
$453$	5.68236	+	3.28071i	0.266981	+	0.154141i
$454$	18.3181	+	1.97963i	0.859709	+	0.0929084i
$455$	−4.75430			−0.222885
$456$	−9.83497	−	11.2763i	−0.460565	−	0.528063i
$457$	−23.5694			−1.10253			−0.551265	−	0.834330i	$-0.685855\pi$
$457$	−23.5694			−1.10253			−0.551265	+	0.834330i	$0.685855\pi$
$458$	17.8922	+	1.93360i	0.836046	+	0.0903513i
$459$	−6.81906	−	3.93698i	−0.318286	−	0.183763i
$460$	−7.21139	−	1.57708i	−0.336233	−	0.0735319i
$461$	0.956655	+	0.552325i	0.0445559	+	0.0257243i	0.522112	−	0.852877i	$-0.325144\pi$
$461$	0.956655	+	0.552325i	0.0445559	+	0.0257243i	−0.477557	+	0.878601i	$0.658477\pi$
$462$	−1.34867	−	0.985924i	−0.0627460	−	0.0458693i
$463$		−	26.1205i		−	1.21392i	−0.794731	−	0.606962i	$-0.792388\pi$
$463$		−	26.1205i		−	1.21392i	0.794731	−	0.606962i	$-0.207612\pi$
$464$	−3.14223	−	33.6932i	−0.145874	−	1.56417i
$465$	−0.853703	−	1.47866i	−0.0395895	−	0.0685711i
$466$	13.1923	+	9.64400i	0.611122	+	0.446749i
$467$	−18.4324			−0.852950			−0.426475	−	0.904499i	$-0.640245\pi$
$467$	−18.4324			−0.852950			−0.426475	+	0.904499i	$0.640245\pi$
$468$	7.66842	−	8.41686i	0.354473	−	0.389069i
$469$	0.563837	+	0.976594i	0.0260356	+	0.0450949i
$470$	−0.281611	+	2.60583i	−0.0129898	+	0.120198i
$471$	−9.33940	−	16.1763i	−0.430337	−	0.745365i
$472$	−29.6214	+	26.2031i	−1.36344	+	1.20610i
$473$	−6.26582	+	10.8527i	−0.288103	+	0.499008i
$474$	5.62475	+	12.7337i	0.258353	+	0.584880i
$475$	−11.3841	+	6.46659i	−0.522338	+	0.296708i
$476$	0.955074	+	0.870148i	0.0437758	+	0.0398832i
$477$	5.90133	−	10.2214i	0.270204	−	0.468006i
$478$	−26.4757	−	2.86121i	−1.21097	−	0.130869i
$479$	26.2671	−	15.1653i	1.20018	−	0.692922i	0.239581	−	0.970876i	$-0.422990\pi$
$479$	26.2671	−	15.1653i	1.20018	−	0.692922i	0.960594	+	0.277955i	$0.0896565\pi$
$480$	−19.4205	−	0.284736i	−0.886420	−	0.0129964i
$481$	−12.5450	−	21.7287i	−0.572005	−	0.990741i
$482$	−5.59245	−	12.6606i	−0.254729	−	0.576676i
$483$			0.713727i			0.0324757i
$484$	12.3819	+	2.70784i	0.562814	+	0.123084i
$485$	8.93957	+	15.4838i	0.405925	+	0.703083i
$486$	7.97143	+	18.0464i	0.361592	+	0.818599i
$487$	−41.6132			−1.88568			−0.942838	−	0.333253i	$-0.891854\pi$
$487$	−41.6132			−1.88568			−0.942838	+	0.333253i	$0.891854\pi$
$488$	1.38827	+	6.82598i	0.0628438	+	0.308998i
$489$	−0.561305	−	0.324070i	−0.0253831	−	0.0146549i
$490$	16.0483	−	21.9530i	0.724989	−	0.991734i
$491$	15.3752	−	26.6306i	0.693873	−	1.20182i	−0.276686	−	0.960960i	$-0.589236\pi$
$491$	15.3752	−	26.6306i	0.693873	−	1.20182i	0.970559	−	0.240863i	$-0.0774304\pi$
$492$	−6.21615	−	19.5201i	−0.280246	−	0.880035i
$493$	12.1241			0.546041
$494$	9.13822	+	21.0867i	0.411148	+	0.948735i
$495$		−	9.32884i		−	0.419300i
$496$	−1.80755	−	0.830312i	−0.0811616	−	0.0372821i
$497$	6.52173	+	3.76532i	0.292540	+	0.168898i
$498$	11.9860	−	16.3960i	0.537105	−	0.734721i
$499$	12.0566	−	20.8826i	0.539728	−	0.934835i	−0.459191	−	0.888338i	$-0.651861\pi$
$499$	12.0566	−	20.8826i	0.539728	−	0.934835i	0.998918	−	0.0464978i	$-0.0148061\pi$
$500$	2.41326	−	11.0349i	0.107924	−	0.493496i
$501$			16.5494i			0.739373i
$502$	−21.1905	+	9.36026i	−0.945778	+	0.417769i
$503$	−10.6337	+	6.13939i	−0.474135	+	0.273742i	−0.717969	−	0.696075i	$-0.754928\pi$
$503$	−10.6337	+	6.13939i	−0.474135	+	0.273742i	0.243834	+	0.969817i	$0.421595\pi$
$504$	−0.388034	−	1.90793i	−0.0172844	−	0.0849859i
$505$	15.0621			0.670253
$506$	1.60978	+	3.64435i	0.0715635	+	0.162011i
$507$	0.944710	−	0.545429i	0.0419560	−	0.0242233i
$508$	1.29389	+	4.06311i	0.0574071	+	0.180271i
$509$	−2.27630	−	3.94266i	−0.100895	−	0.174755i	0.811159	−	0.584826i	$-0.198837\pi$
$509$	−2.27630	−	3.94266i	−0.100895	−	0.174755i	−0.912054	+	0.410071i	$0.865504\pi$
$510$	0.747680	−	6.91850i	0.0331078	−	0.306356i
$511$	6.44531	+	3.72120i	0.285124	+	0.164616i
$512$	−18.6505	+	12.8124i	−0.824245	+	0.566234i
$513$	−23.9482	−	0.167948i	−1.05734	−	0.00741507i
$514$	4.99375	+	11.3052i	0.220265	+	0.498653i
$515$	43.8792	+	25.3337i	1.93355	+	1.11633i
$516$	13.4225	−	4.27436i	0.590890	−	0.188168i
$517$	1.22507	−	0.707292i	0.0538784	−	0.0311067i
$518$	−4.26541	−	0.460961i	−0.187411	−	0.0202535i
$519$	−1.72998	+	0.998807i	−0.0759379	+	0.0438428i
$520$	28.2894	+	9.46770i	1.24057	+	0.415186i
$521$			14.0347i			0.614871i	0.951569	+	0.307436i	$0.0994709\pi$
$521$			14.0347i			0.614871i	−0.951569	+	0.307436i	$0.900529\pi$
$522$	−14.7493	−	10.7822i	−0.645559	−	0.471924i
$523$	−5.94814	+	3.43416i	−0.260094	+	0.150165i	−0.624378	−	0.781123i	$-0.714647\pi$
$523$	−5.94814	+	3.43416i	−0.260094	+	0.150165i	0.364283	+	0.931288i	$0.381314\pi$
$524$	23.5028	−	25.7966i	1.02672	−	1.12693i
$525$	1.64320			0.0717149
$526$	−23.2534	+	31.8090i	−1.01390	+	1.38694i
$527$	0.356337	−	0.617194i	0.0155223	−	0.0268854i
$528$	6.06162	+	8.55227i	0.263798	+	0.372190i
$529$	−10.6490	+	18.4445i	−0.462998	+	0.801936i
$530$	30.7435	+	3.32244i	1.33541	+	0.144318i
$531$			21.3522i			0.926605i
$532$	3.83300	+	0.866461i	0.166182	+	0.0375659i
$533$			31.4650i			1.36290i
$534$	−1.48047	+	13.6992i	−0.0640663	+	0.592824i
$535$	−1.28687	+	2.22892i	−0.0556362	+	0.0963647i
$536$	−1.41020	−	6.93383i	−0.0609114	−	0.299496i
$537$	4.65526	−	8.06314i	0.200889	−	0.347950i
$538$	27.0253	+	19.7563i	1.16514	+	0.851757i
$539$	−14.6766			−0.632165
$540$	−20.9365	+	22.9799i	−0.900963	+	0.988896i
$541$	−34.4443	+	19.8865i	−1.48088	+	0.854985i	−0.999765	−	0.0216733i	$-0.993101\pi$
$541$	−34.4443	+	19.8865i	−1.48088	+	0.854985i	−0.481113	+	0.876659i	$0.659767\pi$
$542$	−15.3736	+	21.0301i	−0.660355	+	0.903319i
$543$			28.5566i			1.22548i
$544$	−3.95015	−	7.07956i	−0.169361	−	0.303534i
$545$	4.58240	−	2.64565i	0.196289	−	0.113327i
$546$	0.309905	−	2.86764i	0.0132627	−	0.122724i
$547$	−9.78439	+	5.64902i	−0.418350	+	0.241535i	−0.694371	−	0.719617i	$-0.744317\pi$
$547$	−9.78439	+	5.64902i	−0.418350	+	0.241535i	0.276021	+	0.961152i	$0.410984\pi$
$548$	5.20549	+	16.3464i	0.222367	+	0.698283i
$549$	3.25699	+	1.88042i	0.139005	+	0.0802545i
$550$	8.39029	−	3.70616i	0.357763	−	0.158031i
$551$	32.0637	−	18.2134i	1.36596	−	0.775916i
$552$	1.42132	−	4.24688i	0.0604952	−	0.180759i
$553$	−3.16623	−	1.82802i	−0.134642	−	0.0777355i
$554$	36.6019	+	3.95555i	1.55507	+	0.168055i
$555$	11.5535	+	20.0113i	0.490420	+	0.849433i
$556$	2.89046	+	9.07668i	0.122583	+	0.384937i
$557$	20.8369	−	12.0302i	0.882888	−	0.509735i	0.0112782	−	0.999936i	$-0.496410\pi$
$557$	20.8369	−	12.0302i	0.882888	−	0.509735i	0.871609	+	0.490201i	$0.163077\pi$
$558$	−0.982379	+	0.433936i	−0.0415874	+	0.0183700i
$559$	−21.6360			−0.915106
$560$	4.16170	−	2.94970i	0.175864	−	0.124648i
$561$	−3.25256	+	1.87787i	−0.137323	+	0.0792836i
$562$	11.9870	+	27.1371i	0.505641	+	1.14471i
$563$		−	30.2137i		−	1.27336i	−0.771130	−	0.636678i	$-0.780308\pi$
$563$		−	30.2137i		−	1.27336i	0.771130	−	0.636678i	$-0.219692\pi$
$564$	−1.55340	−	0.339718i	−0.0654098	−	0.0143047i
$565$	3.31284	−	5.73801i	0.139372	−	0.241400i
$566$	−13.0810	−	9.56260i	−0.549834	−	0.401946i
$567$	0.814614	+	0.470318i	0.0342106	+	0.0197515i
$568$	−31.3079	−	35.3921i	−1.31365	−	1.48502i
$569$			31.3114i			1.31264i	0.754482	+	0.656320i	$0.227888\pi$
$569$			31.3114i			1.31264i	−0.754482	+	0.656320i	$0.772112\pi$
$570$	−8.41598	−	19.4201i	−0.352506	−	0.813418i
$571$	−36.8938			−1.54396			−0.771978	−	0.635649i	$-0.780733\pi$
$571$	−36.8938			−1.54396			−0.771978	+	0.635649i	$0.780733\pi$
$572$	−4.88544	−	15.3414i	−0.204271	−	0.641456i
$573$	−14.4814	+	25.0826i	−0.604970	+	1.04784i
$574$	4.34347	+	3.17522i	0.181293	+	0.132531i
$575$	−3.39366	−	1.95933i	−0.141525	−	0.0817096i
$576$	−1.49053	+	12.1254i	−0.0621055	+	0.505227i
$577$	−1.16074			−0.0483220			−0.0241610	−	0.999708i	$-0.507691\pi$
$577$	−1.16074			−0.0483220			−0.0241610	+	0.999708i	$0.507691\pi$
$578$	−19.3348	+	8.54055i	−0.804220	+	0.355240i
$579$	−11.5939	−	20.0812i	−0.481825	−	0.834545i
$580$	10.2265	−	46.7618i	0.424632	−	1.94168i
$581$			5.33407i			0.221294i
$582$	−9.92205	+	4.38277i	−0.411282	+	0.181671i
$583$	−8.34461	−	14.4533i	−0.345598	−	0.598594i
$584$	−30.9410	−	34.9774i	−1.28035	−	1.44737i
$585$	13.9485	−	8.05317i	0.576700	−	0.332958i
$586$	−1.58031	+	14.6230i	−0.0652819	+	0.604072i
$587$	−0.751317	+	1.30132i	−0.0310102	+	0.0537112i	−0.881114	−	0.472904i	$-0.843206\pi$
$587$	−0.751317	+	1.30132i	−0.0310102	+	0.0537112i	0.850104	+	0.526615i	$0.176539\pi$
$588$	12.1952	+	11.1108i	0.502923	+	0.458202i
$589$	0.0152010	−	2.16756i	0.000626346	−	0.0893127i
$590$	−51.1718	+	22.6036i	−2.10671	+	0.930576i
$591$	6.82547	−	11.8221i	0.280763	−	0.486295i
$592$	24.4624	+	11.2370i	1.00540	+	0.461837i
$593$	9.24084	+	16.0056i	0.379476	+	0.657271i	0.990986	−	0.133965i	$-0.0427710\pi$
$593$	9.24084	+	16.0056i	0.379476	+	0.657271i	−0.611510	+	0.791237i	$0.709438\pi$
$594$	16.6810	+	1.80271i	0.684428	+	0.0739659i
$595$	0.913806	+	1.58276i	0.0374624	+	0.0648868i
$596$	−15.9310	−	14.5144i	−0.652561	−	0.594534i
$597$	13.9011			0.568934
$598$	−4.05939	+	5.55295i	−0.166001	+	0.227077i
$599$	16.6212	+	28.7888i	0.679124	+	1.17628i	0.975245	+	0.221127i	$0.0709734\pi$
$599$	16.6212	+	28.7888i	0.679124	+	1.17628i	−0.296121	+	0.955150i	$0.595693\pi$
$600$	−9.77748	−	3.27226i	−0.399164	−	0.133589i
$601$		−	11.1345i		−	0.454186i	−0.973873	−	0.227093i	$-0.927078\pi$
$601$		−	11.1345i		−	0.454186i	0.973873	−	0.227093i	$-0.0729221\pi$
$602$	−2.18335	+	2.98666i	−0.0889866	+	0.121727i
$603$	−3.30845	−	1.91013i	−0.134730	−	0.0777867i
$604$	10.5632	+	2.31010i	0.429810	+	0.0939967i
$605$	15.5266	+	8.96429i	0.631247	+	0.364450i
$606$	−0.981808	+	9.08495i	−0.0398832	+	0.369051i
$607$	11.2378			0.456127			0.228064	−	0.973646i	$-0.426761\pi$
$607$	11.2378			0.456127			0.228064	+	0.973646i	$0.426761\pi$
$608$	−21.0820	−	12.7887i	−0.854986	−	0.518651i
$609$	−4.62812			−0.187541
$610$	−1.05867	+	9.79622i	−0.0428645	+	0.396637i
$611$	2.11509	+	1.22115i	0.0855674	+	0.0494024i
$612$	−4.27598	−	0.935129i	−0.172846	−	0.0378004i
$613$	−20.5664	−	11.8740i	−0.830669	−	0.479587i	0.0234126	−	0.999726i	$-0.492547\pi$
$613$	−20.5664	−	11.8740i	−0.830669	−	0.479587i	−0.854082	+	0.520139i	$0.825880\pi$
$614$	2.31285	−	3.16381i	0.0933390	−	0.127681i
$615$		−	28.9781i		−	1.16851i
$616$	−2.61075	−	0.873747i	−0.105190	−	0.0352043i
$617$	−2.53920	−	4.39802i	−0.102224	−	0.177058i	0.810376	−	0.585910i	$-0.199263\pi$
$617$	−2.53920	−	4.39802i	−0.102224	−	0.177058i	−0.912601	+	0.408852i	$0.865929\pi$
$618$	−18.1407	+	24.8152i	−0.729726	+	0.998213i
$619$	45.0160			1.80935			0.904674	−	0.426105i	$-0.140115\pi$
$619$	45.0160			1.80935			0.904674	+	0.426105i	$0.140115\pi$
$620$	−2.07991	−	1.89497i	−0.0835313	−	0.0761036i
$621$	−3.58400	−	6.20766i	−0.143821	−	0.249105i
$622$	19.4033	+	2.09690i	0.778000	+	0.0840782i
$623$	−1.80941	−	3.13400i	−0.0724927	−	0.125561i
$624$	−7.55464	+	16.4461i	−0.302428	+	0.658372i
$625$	15.4982	−	26.8436i	0.619927	−	1.07375i
$626$	−15.2440	+	6.73357i	−0.609272	+	0.269127i
$627$	−5.78080	+	9.85242i	−0.230863	+	0.393468i
$628$	−22.7540	−	20.7307i	−0.907982	−	0.827244i
$629$	−4.82247	+	8.35276i	−0.192284	+	0.333046i
$630$	0.295910	−	2.73814i	0.0117893	−	0.109090i
$631$	20.6719	−	11.9349i	0.822936	−	0.475122i	−0.0284918	−	0.999594i	$-0.509070\pi$
$631$	20.6719	−	11.9349i	0.822936	−	0.475122i	0.851428	+	0.524472i	$0.175737\pi$
$632$	15.1996	+	17.1825i	0.604609	+	0.683482i
$633$	9.68974	+	16.7831i	0.385132	+	0.667069i
$634$	22.9381	−	10.1322i	0.910990	−	0.402402i
$635$			6.03179i			0.239364i
$636$	−4.00798	+	18.3269i	−0.158927	+	0.726710i
$637$	−12.6696	−	21.9445i	−0.501989	−	0.869471i
$638$	−23.6315	+	10.4385i	−0.935582	+	0.413265i
$639$	−25.5119			−1.00923
$640$	−30.6373	+	9.26396i	−1.21105	+	0.366190i
$641$	−0.303877	−	0.175444i	−0.0120024	−	0.00692960i	0.493987	−	0.869469i	$-0.335539\pi$
$641$	−0.303877	−	0.175444i	−0.0120024	−	0.00692960i	−0.505989	+	0.862540i	$0.668872\pi$
$642$	−1.26053	−	0.921488i	−0.0497492	−	0.0363682i
$643$	7.67194	−	13.2882i	0.302552	−	0.524035i	−0.674161	−	0.738584i	$-0.735495\pi$
$643$	7.67194	−	13.2882i	0.302552	−	0.524035i	0.976713	+	0.214549i	$0.0688281\pi$
$644$	0.356894	+	1.12073i	0.0140636	+	0.0441628i
$645$	19.9260			0.784585
$646$	5.26356	−	7.09520i	0.207092	−	0.279157i
$647$			12.4035i			0.487632i	0.969821	+	0.243816i	$0.0783994\pi$
$647$			12.4035i			0.487632i	−0.969821	+	0.243816i	$0.921601\pi$
$648$	−3.91060	−	4.42074i	−0.153623	−	0.173663i
$649$	26.1474	+	15.0962i	1.02637	+	0.592578i
$650$	12.7844	+	9.34581i	0.501446	+	0.366573i
$651$	−0.136024	+	0.235601i	−0.00533122	+	0.00923394i
$652$	−1.04343	−	0.228192i	−0.0408641	−	0.00893670i
$653$			38.6270i			1.51159i	0.654808	+	0.755795i	$0.272750\pi$
$653$			38.6270i			1.51159i	−0.654808	+	0.755795i	$0.727250\pi$
$654$	1.29707	+	2.93641i	0.0507195	+	0.114823i
$655$	42.7504	−	24.6820i	1.67040	−	0.964404i
$656$	−19.5218	−	27.5430i	−0.762197	−	1.07537i
$657$	−25.2129			−0.983650
$658$	0.382008	−	0.168741i	0.0148922	−	0.00657820i
$659$	0.427803	−	0.246992i	0.0166648	−	0.00962144i	−0.491644	−	0.870796i	$-0.663604\pi$
$659$	0.427803	−	0.246992i	0.0166648	−	0.00962144i	0.508309	+	0.861175i	$0.330271\pi$
$660$	4.49932	+	14.1289i	0.175136	+	0.549966i
$661$	12.5398	+	21.7195i	0.487740	+	0.844791i	0.999901	−	0.0140991i	$-0.00448802\pi$
$661$	12.5398	+	21.7195i	0.487740	+	0.844791i	−0.512160	+	0.858890i	$0.671155\pi$
$662$	38.4846	+	4.15902i	1.49575	+	0.161645i
$663$	−5.61558	−	3.24216i	−0.218091	−	0.125915i
$664$	10.6222	−	31.7392i	0.412223	−	1.23172i
$665$	4.79438	+	2.81305i	0.185918	+	0.109085i
$666$	13.2950	−	5.87265i	0.515169	−	0.227560i
$667$	9.55835	+	5.51852i	0.370101	+	0.213678i
$668$	8.27540	+	25.9866i	0.320185	+	1.00545i
$669$	16.9495	−	9.78582i	0.655307	−	0.378342i
$670$	1.07540	−	9.95100i	0.0415464	−	0.384441i
$671$	4.60545	−	2.65896i	0.177791	−	0.102648i
$672$	1.50789	+	2.70248i	0.0581681	+	0.104250i
$673$		−	12.2784i		−	0.473296i	−0.971595	−	0.236648i	$-0.923951\pi$
$673$		−	12.2784i		−	0.473296i	0.971595	−	0.236648i	$-0.0760489\pi$
$674$	−10.3218	+	14.1195i	−0.397580	+	0.543861i
$675$	−14.2917	+	8.25134i	−0.550089	+	0.317594i
$676$	1.21069	−	1.32885i	0.0465649	−	0.0511096i
$677$	6.28293			0.241473			0.120736	−	0.992685i	$-0.461474\pi$
$677$	6.28293			0.241473			0.120736	+	0.992685i	$0.461474\pi$
$678$	3.24504	+	2.37223i	0.124625	+	0.0911049i
$679$	1.42438	−	2.46710i	0.0546628	−	0.0946788i
$680$	−2.28550	−	11.2376i	−0.0876450	−	0.430943i
$681$	−7.90577	+	13.6932i	−0.302950	+	0.524724i
$682$	−0.163163	+	1.50980i	−0.00624784	+	0.0578131i
$683$		−	28.9958i		−	1.10949i	−0.832020	−	0.554746i	$-0.812815\pi$
$683$		−	28.9958i		−	1.10949i	0.832020	−	0.554746i	$-0.187185\pi$
$684$	−12.7132	+	3.95052i	−0.486101	+	0.151052i
$685$			24.2667i			0.927181i
$686$	−8.74432	−	0.944996i	−0.333860	−	0.0360801i
$687$	−7.72197	+	13.3748i	−0.294611	+	0.510282i
$688$	18.9392	−	13.4236i	0.722049	−	0.511769i
$689$	14.4071	−	24.9538i	0.548865	−	0.950662i
$690$	3.73855	−	5.11407i	0.142324	−	0.194689i
$691$	29.0538			1.10526			0.552629	−	0.833427i	$-0.313625\pi$
$691$	29.0538			1.10526			0.552629	+	0.833427i	$0.313625\pi$
$692$	−2.21705	+	2.43344i	−0.0842797	+	0.0925054i
$693$	−1.28727	+	0.743204i	−0.0488992	+	0.0282320i
$694$	−12.9968	−	9.50106i	−0.493351	−	0.360655i
$695$			13.4746i			0.511120i
$696$	27.5386	+	9.21642i	1.04385	+	0.349348i
$697$	10.4750	−	6.04776i	0.396770	−	0.229075i
$698$	4.12917	+	0.446238i	0.156291	+	0.0168903i
$699$	−12.1449	+	7.01188i	−0.459363	+	0.265214i
$700$	2.58022	−	0.821667i	0.0975231	−	0.0310561i
$701$	21.1436	+	12.2073i	0.798584	+	0.461063i	0.842976	−	0.537952i	$-0.180802\pi$
$701$	21.1436	+	12.2073i	0.798584	+	0.461063i	−0.0443920	+	0.999014i	$0.514135\pi$
$702$	11.7045	+	26.4976i	0.441758	+	1.00009i
$703$	−0.205722	+	29.3345i	−0.00775894	+	1.10637i
$704$	13.7947	+	10.3981i	0.519908	+	0.391893i
$705$	−1.94792	−	1.12463i	−0.0733630	−	0.0423561i
$706$	−2.91618	+	26.9843i	−0.109752	+	1.01557i
$707$	−1.19995	−	2.07838i	−0.0451289	−	0.0781656i
$708$	−10.2982	−	32.3386i	−0.387030	−	1.21536i
$709$	3.14824	−	1.81764i	0.118235	−	0.0682627i	−0.439716	−	0.898137i	$-0.644921\pi$
$709$	3.14824	−	1.81764i	0.118235	−	0.0682627i	0.557951	+	0.829874i	$0.311588\pi$
$710$	−27.0072	−	61.1409i	−1.01356	−	2.29458i
$711$	12.3857			0.464502
$712$	4.52549	+	22.2514i	0.169600	+	0.833908i
$713$	0.561857	−	0.324388i	0.0210417	−	0.0121484i
$714$	−1.01423	+	0.448008i	−0.0379568	+	0.0167663i
$715$		−	22.7747i		−	0.851726i
$716$	3.27798	−	14.9889i	0.122504	−	0.560163i
$717$	11.4265	−	19.7912i	0.426729	−	0.739116i
$718$	3.71733	−	5.08505i	0.138730	−	0.189772i
$719$	−34.9775	−	20.1943i	−1.30444	−	0.753120i	−0.323279	−	0.946304i	$-0.604785\pi$
$719$	−34.9775	−	20.1943i	−1.30444	−	0.753120i	−0.981163	+	0.193184i	$0.938119\pi$
$720$	−7.21347	+	15.7034i	−0.268830	+	0.585232i
$721$		−	8.07306i		−	0.300657i
$722$	3.26142	−	26.6714i	0.121378	−	0.992606i
$723$	11.8777			0.441738
$724$	14.2795	+	44.8409i	0.530694	+	1.66650i
$725$	12.7051	−	22.0059i	0.471857	−	0.817280i
$726$	−6.41907	+	8.78083i	−0.238234	+	0.325887i
$727$	4.07642	+	2.35352i	0.151186	+	0.0872873i	0.573685	−	0.819076i	$-0.305514\pi$
$727$	4.07642	+	2.35352i	0.151186	+	0.0872873i	−0.422499	+	0.906364i	$0.638847\pi$
$728$	−0.947315	−	4.65787i	−0.0351098	−	0.172632i
$729$	−23.1906			−0.858912
$730$	−26.6907	−	60.4245i	−0.987867	−	2.23641i
$731$	4.15857	+	7.20286i	0.153810	+	0.266407i
$732$	−5.83976	−	1.27712i	−0.215844	−	0.0472036i
$733$		−	23.9315i		−	0.883930i	−0.897032	−	0.441965i	$-0.854282\pi$
$733$		−	23.9315i		−	0.883930i	0.897032	−	0.441965i	$-0.145718\pi$
$734$	−10.9285	−	24.7409i	−0.403380	−	0.913203i
$735$	11.6683	+	20.2101i	0.430391	+	0.745459i
$736$	0.108194	−	7.37936i	0.00398807	−	0.272007i
$737$	−4.67821	+	2.70097i	−0.172324	+	0.0994915i
$738$	−18.1216	−	1.95839i	−0.667065	−	0.0720895i
$739$	1.44053	−	2.49507i	0.0529906	−	0.0917825i	−0.838313	−	0.545189i	$-0.816458\pi$
$739$	1.44053	−	2.49507i	0.0529906	−	0.0917825i	0.891304	+	0.453406i	$0.149791\pi$
$740$	28.1484	+	25.6454i	1.03475	+	0.942743i
$741$	−19.7217	−	0.138307i	−0.724494	−	0.00508084i
$742$	−1.99080	−	4.50692i	−0.0730844	−	0.165454i
$743$	−17.8747	+	30.9598i	−0.655758	+	1.13581i	0.325945	+	0.945389i	$0.394318\pi$
$743$	−17.8747	+	30.9598i	−0.655758	+	1.13581i	−0.981703	+	0.190418i	$0.939016\pi$
$744$	1.27856	−	1.13102i	0.0468743	−	0.0414650i
$745$	−15.2427	−	26.4011i	−0.558448	−	0.967261i
$746$	−3.14245	+	29.0780i	−0.115053	+	1.06462i
$747$	−9.03522	−	15.6495i	−0.330581	−	0.572584i
$748$	−4.16830	+	4.57513i	−0.152408	+	0.167283i
$749$	0.410086			0.0149842
$750$	7.82558	+	5.72075i	0.285750	+	0.208892i
$751$	−24.3250	−	42.1322i	−0.887632	−	1.53742i	−0.842667	−	0.538436i	$-0.819015\pi$
$751$	−24.3250	−	42.1322i	−0.887632	−	1.53742i	−0.0449656	−	0.998989i	$-0.514318\pi$
$752$	−2.60909	+	0.243324i	−0.0951436	+	0.00887312i
$753$		−	19.8801i		−	0.724473i
$754$	−36.0078	−	26.3228i	−1.31132	−	0.958621i
$755$	13.2460	+	7.64757i	0.482071	+	0.278324i
$756$	4.83890	+	1.05824i	0.175989	+	0.0384877i
$757$	29.4372	+	16.9956i	1.06991	+	0.617716i	0.928158	−	0.372186i	$-0.121392\pi$
$757$	29.4372	+	16.9956i	1.06991	+	0.617716i	0.141757	+	0.989902i	$0.454725\pi$
$758$	−3.59972	−	0.389021i	−0.130748	−	0.0141299i
$759$	−3.41899			−0.124102
$760$	−22.9260	−	26.2859i	−0.831614	−	0.953491i
$761$	−34.2969			−1.24326			−0.621631	−	0.783310i	$-0.713530\pi$
$761$	−34.2969			−1.24326			−0.621631	+	0.783310i	$0.713530\pi$
$762$	−3.63818	−	0.393177i	−0.131797	−	0.0142433i
$763$	−0.730135	−	0.421544i	−0.0264327	−	0.0152609i
$764$	−10.1970	+	46.6271i	−0.368916	+	1.68691i
$765$	−5.36198	−	3.09574i	−0.193863	−	0.111927i
$766$	−20.8619	−	15.2507i	−0.753772	−	0.551031i
$767$			52.1275i			1.88221i
$768$	−3.59066	−	19.0833i	−0.129567	−	0.688609i
$769$	−5.78344	−	10.0172i	−0.208556	−	0.361230i	0.742704	−	0.669620i	$-0.233543\pi$
$769$	−5.78344	−	10.0172i	−0.208556	−	0.361230i	−0.951260	+	0.308390i	$0.900210\pi$
$770$	−3.14385	−	2.29826i	−0.113297	−	0.0828234i
$771$	−10.6062			−0.381971
$772$	−28.2467	−	25.7349i	−1.01662	−	0.926220i
$773$	−11.6089	−	20.1073i	−0.417545	−	0.723209i	0.578147	−	0.815933i	$-0.303776\pi$
$773$	−11.6089	−	20.1073i	−0.417545	−	0.723209i	−0.995692	+	0.0927238i	$0.970443\pi$
$774$	1.34663	−	12.4608i	0.0484038	−	0.447894i
$775$	−0.746830	−	1.29355i	−0.0268269	−	0.0464656i
$776$	−13.3885	+	11.8435i	−0.480618	+	0.425155i
$777$	1.84088	−	3.18850i	0.0660412	−	0.114387i
$778$	−8.20268	−	18.5699i	−0.294080	−	0.665762i
$779$	18.6174	−	31.7302i	0.667036	−	1.13685i
$780$	−17.2415	+	18.9242i	−0.617343	+	0.677596i
$781$	−18.0372	+	31.2413i	−0.645421	+	1.11790i
$782$	2.62888	+	0.284102i	0.0940084	+	0.0101595i
$783$	40.2532	−	23.2402i	1.43853	−	0.830536i
$784$	24.7054	+	11.3486i	0.882335	+	0.405306i
$785$	−21.7708	−	37.7081i	−0.777033	−	1.34586i
$786$	12.1007	+	27.3946i	0.431618	+	0.977132i
$787$		−	33.9207i		−	1.20914i	−0.796552	−	0.604571i	$-0.793345\pi$
$787$		−	33.9207i		−	1.20914i	0.796552	−	0.604571i	$-0.206655\pi$
$788$	4.80613	−	21.9766i	0.171211	−	0.782883i
$789$	−16.9069	−	29.2836i	−0.601901	−	1.04252i
$790$	13.1117	+	29.6833i	0.466493	+	1.05608i
$791$	−1.05570			−0.0375364
$792$	9.13962	−	1.85881i	0.324762	−	0.0660500i
$793$	7.95135	+	4.59072i	0.282361	+	0.163021i
$794$	22.0653	−	30.1838i	0.783070	−	1.07118i
$795$	−13.2684	+	22.9815i	−0.470581	+	0.815070i
$796$	21.8281	−	6.95113i	0.773677	−	0.246376i
$797$	−12.2630			−0.434378			−0.217189	−	0.976130i	$-0.569689\pi$
$797$	−12.2630			−0.434378			−0.217189	+	0.976130i	$0.569689\pi$
$798$	−2.00926	+	2.70845i	−0.0711270	+	0.0958781i
$799$		−	0.938848i		−	0.0332141i
$800$	−16.9893	−	0.249091i	−0.600662	−	0.00880670i
$801$	10.6172	+	6.12983i	0.375139	+	0.216587i
$802$	5.88007	−	8.04353i	0.207633	−	0.284027i
$803$	−17.8258	+	30.8752i	−0.629059	+	1.08956i
$804$	5.93203	+	1.29730i	0.209206	+	0.0457521i
$805$			1.66375i			0.0586394i
$806$	−2.39830	+	1.05938i	−0.0844766	+	0.0373150i
$807$	−24.8797	+	14.3643i	−0.875806	+	0.505647i
$808$	3.00118	+	14.7565i	0.105581	+	0.519133i
$809$	35.6199			1.25233			0.626164	−	0.779691i	$-0.284624\pi$
$809$	35.6199			1.25233			0.626164	+	0.779691i	$0.284624\pi$
$810$	−3.37340	−	7.63697i	−0.118529	−	0.268336i
$811$	16.4875	−	9.51908i	0.578956	−	0.334260i	−0.181763	−	0.983342i	$-0.558180\pi$
$811$	16.4875	−	9.51908i	0.578956	−	0.334260i	0.760718	+	0.649082i	$0.224847\pi$
$812$	−7.26728	+	2.31425i	−0.255031	+	0.0812144i
$813$	−11.1777	−	19.3604i	−0.392021	−	0.679000i
$814$	2.20816	−	20.4327i	0.0773959	−	0.716167i
$815$	−1.30844	−	0.755429i	−0.0458327	−	0.0264615i
$816$	6.92715	−	0.646027i	0.242499	−	0.0226155i
$817$	21.8184	+	12.8017i	0.763329	+	0.447875i
$818$	11.6588	+	26.3940i	0.407639	+	0.922846i
$819$	−2.22248	−	1.28315i	−0.0776597	−	0.0448369i
$820$	−14.4903	−	45.5028i	−0.506023	−	1.58903i
$821$	−34.7173	+	20.0441i	−1.21164	+	0.699543i	−0.963117	−	0.269082i	$-0.913280\pi$
$821$	−34.7173	+	20.0441i	−1.21164	+	0.699543i	−0.248526	+	0.968625i	$0.579946\pi$
$822$	−14.6369	−	1.58180i	−0.510520	−	0.0551717i
$823$	27.7423	−	16.0170i	0.967037	−	0.558319i	0.0687052	−	0.997637i	$-0.478113\pi$
$823$	27.7423	−	16.0170i	0.967037	−	0.558319i	0.898332	+	0.439318i	$0.144780\pi$
$824$	−16.0767	+	48.0370i	−0.560058	+	1.67345i
$825$			7.87146i			0.274049i
$826$	7.19575	+	5.26032i	0.250372	+	0.183030i
$827$	−13.4637	+	7.77329i	−0.468180	+	0.270304i	−0.715477	−	0.698636i	$-0.753791\pi$
$827$	−13.4637	+	7.77329i	−0.468180	+	0.270304i	0.247298	+	0.968940i	$0.420457\pi$
$828$	−2.94545	−	2.68353i	−0.102361	−	0.0932592i
$829$	5.94617			0.206519			0.103260	−	0.994654i	$-0.467073\pi$
$829$	5.94617			0.206519			0.103260	+	0.994654i	$0.467073\pi$
$830$	27.9402	−	38.2202i	0.969817	−	1.32664i
$831$	−15.7968	+	27.3608i	−0.547984	+	0.949136i
$832$	−3.63887	+	29.6021i	−0.126155	+	1.02627i
$833$	−4.87036	+	8.43572i	−0.168748	+	0.292280i
$834$	−8.12744	−	0.878329i	−0.281430	−	0.0304141i
$835$			38.5778i			1.33504i
$836$	−4.15064	+	18.3614i	−0.143553	+	0.635041i
$837$		−	2.73220i		−	0.0944386i
$838$	1.16895	−	10.8166i	0.0403808	−	0.373655i
$839$	6.06590	−	10.5064i	0.209418	−	0.362723i	−0.742113	−	0.670274i	$-0.766176\pi$
$839$	6.06590	−	10.5064i	0.209418	−	0.362723i	0.951531	+	0.307552i	$0.0995097\pi$
$840$	0.872444	+	4.28973i	0.0301022	+	0.148010i
$841$	−21.2845	+	36.8658i	−0.733947	+	1.27123i
$842$	6.96482	+	5.09151i	0.240024	+	0.175465i
$843$	−25.4590			−0.876855
$844$	23.6075	+	21.5083i	0.812604	+	0.740347i
$845$	2.20218	−	1.27143i	0.0757575	−	0.0437386i
$846$	−0.834938	+	1.14214i	−0.0287058	+	0.0392674i
$847$		−	2.85665i		−	0.0981555i
$848$	2.87073	+	30.7819i	0.0985812	+	1.05706i
$849$	12.0424	−	6.95270i	0.413295	−	0.238616i
$850$	0.654080	−	6.05239i	0.0224348	−	0.207595i
$851$	−7.60385	+	4.39009i	−0.260657	+	0.150490i
$852$	38.6387	−	12.3044i	1.32374	−	0.421543i
$853$	−13.8144	−	7.97575i	−0.472996	−	0.273085i	0.244497	−	0.969650i	$-0.421377\pi$
$853$	−13.8144	−	7.97575i	−0.472996	−	0.273085i	−0.717493	+	0.696565i	$0.754711\pi$
$854$	1.43610	−	0.634354i	0.0491424	−	0.0217072i
$855$	−18.8310	−	0.132061i	−0.644007	−	0.00451639i
$856$	−2.44012	−	0.816643i	−0.0834017	−	0.0279123i
$857$	46.8936	+	27.0741i	1.60186	+	0.924832i	0.991116	+	0.133001i	$0.0424614\pi$
$857$	46.8936	+	27.0741i	1.60186	+	0.924832i	0.610740	+	0.791831i	$0.290872\pi$
$858$	13.7370	+	1.48455i	0.468973	+	0.0506817i
$859$	10.3529	+	17.9317i	0.353236	+	0.611823i	0.986814	−	0.161856i	$-0.0517479\pi$
$859$	10.3529	+	17.9317i	0.353236	+	0.611823i	−0.633578	+	0.773678i	$0.718415\pi$
$860$	31.2887	−	9.96383i	1.06693	−	0.339764i
$861$	−3.99863	+	2.30861i	−0.136273	+	0.0786773i
$862$	−12.2205	+	5.39805i	−0.416233	+	0.183858i
$863$	−24.9184			−0.848231			−0.424115	−	0.905608i	$-0.639415\pi$
$863$	−24.9184			−0.848231			−0.424115	+	0.905608i	$0.639415\pi$
$864$	−26.6854	−	15.9330i	−0.907857	−	0.542051i
$865$	−4.03271	+	2.32829i	−0.137116	+	0.0791642i
$866$	−9.85896	−	22.3195i	−0.335021	−	0.758447i
$867$		−	18.1392i		−	0.616038i
$868$	−0.0957811	+	0.437970i	−0.00325102	+	0.0148657i
$869$	8.75685	−	15.1673i	0.297056	−	0.514516i
$870$	33.1619	+	24.2424i	1.12429	+	0.821893i
$871$	−8.07699	−	4.66325i	−0.273678	−	0.158008i
$872$	3.50505	+	3.96230i	0.118696	+	0.134180i
$873$			9.65089i			0.326633i
$874$	7.37920	−	3.19788i	0.249605	−	0.108170i
$875$	−2.54588			−0.0860664
$876$	38.1859	−	12.1603i	1.29018	−	0.410857i
$877$	19.0653	−	33.0221i	0.643790	−	1.11508i	−0.340790	−	0.940140i	$-0.610694\pi$
$877$	19.0653	−	33.0221i	0.643790	−	1.11508i	0.984580	−	0.174937i	$-0.0559723\pi$
$878$	11.0665	+	8.08993i	0.373475	+	0.273022i
$879$	−10.9311	−	6.31106i	−0.368696	−	0.212867i
$880$	14.1301	+	19.9359i	0.476324	+	0.672040i
$881$	16.6723			0.561702			0.280851	−	0.959751i	$-0.409383\pi$
$881$	16.6723			0.561702			0.280851	+	0.959751i	$0.409383\pi$
$882$	13.4270	−	5.93097i	0.452111	−	0.199706i
$883$	16.1610	+	27.9917i	0.543861	+	0.941994i	0.998678	+	0.0514093i	$0.0163713\pi$
$883$	16.1610	+	27.9917i	0.543861	+	0.941994i	−0.454817	+	0.890585i	$0.650295\pi$
$884$	−10.4390	−	2.28295i	−0.351103	−	0.0767840i
$885$		−	48.0076i		−	1.61376i
$886$	−20.7862	+	9.18170i	−0.698327	+	0.308465i
$887$	5.27663	+	9.13939i	0.177172	+	0.306871i	0.940911	−	0.338655i	$-0.109972\pi$
$887$	5.27663	+	9.13939i	0.177172	+	0.306871i	−0.763739	+	0.645525i	$0.776639\pi$
$888$	−17.3033	+	15.3065i	−0.580661	+	0.513653i
$889$	0.832314	−	0.480537i	0.0279149	−	0.0161167i
$890$	−3.45108	+	31.9339i	−0.115681	+	1.07043i
$891$	−2.25298	+	3.90228i	−0.0754777	+	0.130731i
$892$	21.7216	−	23.8416i	0.727293	−	0.798276i
$893$	−1.41038	−	2.48291i	−0.0471967	−	0.0830874i
$894$	16.9179	−	7.47296i	0.565818	−	0.249933i
$895$	10.8517	−	18.7958i	0.362733	−	0.628273i
$896$	3.71911	+	3.48954i	0.124247	+	0.116577i
$897$	−2.95147	−	5.11209i	−0.0985465	−	0.170688i
$898$	17.4923	+	1.89038i	0.583725	+	0.0630829i
$899$	2.10347	+	3.64332i	0.0701548	+	0.121512i
$900$	−6.17823	+	6.78122i	−0.205941	+	0.226041i
$901$	−11.0765			−0.369012
$902$	−15.2104	+	20.8067i	−0.506449	+	0.692787i
$903$	−1.58745	−	2.74954i	−0.0528270	−	0.0914991i
$904$	6.28172	+	2.10232i	0.208927	+	0.0699222i
$905$			66.5675i			2.21278i
$906$	−5.47620	+	7.49105i	−0.181935	+	0.248874i
$907$	−32.3892	−	18.6999i	−1.07546	−	0.620920i	−0.145795	−	0.989315i	$-0.546574\pi$
$907$	−32.3892	−	18.6999i	−1.07546	−	0.620920i	−0.929669	+	0.368395i	$0.879907\pi$
$908$	−5.56681	+	25.4549i	−0.184741	+	0.844750i
$909$	7.04102	+	4.06513i	0.233536	+	0.134832i
$910$	0.722411	−	6.68468i	0.0239477	−	0.221595i
$911$	40.7900			1.35143			0.675717	−	0.737162i	$-0.263834\pi$
$911$	40.7900			1.35143			0.675717	+	0.737162i	$0.263834\pi$
$912$	17.3493	−	12.1148i	0.574491	−	0.401161i
$913$	−25.5520			−0.845647
$914$	3.58134	−	33.1392i	0.118460	−	1.09615i
$915$	−7.32291	−	4.22789i	−0.242088	−	0.139770i
$916$	−5.43739	+	24.8631i	−0.179656	+	0.821499i
$917$	−6.81162	−	3.93269i	−0.224940	−	0.129869i
$918$	6.57165	−	8.98956i	0.216897	−	0.296700i
$919$		−	10.9991i		−	0.362826i	−0.983407	−	0.181413i	$-0.941933\pi$
$919$		−	10.9991i		−	0.362826i	0.983407	−	0.181413i	$-0.0580670\pi$
$920$	3.31318	−	9.89977i	0.109232	−	0.326386i
$921$	1.68161	+	2.91263i	0.0554109	+	0.0959744i
$922$	−0.921947	+	1.26116i	−0.0303627	+	0.0415340i
$923$	−62.2827			−2.05006
$924$	1.59116	−	1.74646i	0.0523455	−	0.0574544i
$925$	10.1072	+	17.5061i	0.332322	+	0.575599i
$926$	36.7261	+	3.96898i	1.20690	+	0.130429i
$927$	13.6747	+	23.6853i	0.449137	+	0.777928i
$928$	47.8509	+	0.701574i	1.57078	+	0.0230303i
$929$	15.0117	−	26.0011i	0.492519	−	0.853067i	−0.507444	−	0.861685i	$-0.669410\pi$
$929$	15.0117	−	26.0011i	0.492519	−	0.853067i	0.999963	+	0.00861738i	$0.00274303\pi$
$930$	2.20875	−	0.975649i	0.0724278	−	0.0319928i
$931$	−0.207765	+	29.6259i	−0.00680921	+	0.970949i
$932$	−15.5643	+	17.0833i	−0.509825	+	0.559583i
$933$	−8.37412	+	14.5044i	−0.274156	+	0.474853i
$934$	2.80078	−	25.9165i	0.0916445	−	0.848013i
$935$	−7.58194	+	4.37744i	−0.247956	+	0.143158i
$936$	10.6691	+	12.0609i	0.348731	+	0.394224i
$937$	20.0689	+	34.7604i	0.655623	+	1.13557i	0.981737	+	0.190241i	$0.0609271\pi$
$937$	20.0689	+	34.7604i	0.655623	+	1.13557i	−0.326115	+	0.945330i	$0.605740\pi$
$938$	−1.45879	+	0.644377i	−0.0476312	+	0.0210397i
$939$		−	14.3013i		−	0.466706i
$940$	−3.62108	−	0.791906i	−0.118107	−	0.0258291i
$941$	0.433456	+	0.750768i	0.0141303	+	0.0244743i	0.873004	−	0.487713i	$-0.162169\pi$
$941$	0.433456	+	0.750768i	0.0141303	+	0.0244743i	−0.858874	+	0.512187i	$0.828835\pi$
$942$	24.1634	−	10.6735i	0.787287	−	0.347761i
$943$	11.0110			0.358569
$944$	−32.3413	−	45.6300i	−1.05262	−	1.48513i
$945$	6.06786	+	3.50328i	0.197387	+	0.113962i
$946$	−14.3071	−	10.4590i	−0.465165	−	0.340050i
$947$	−12.4598	+	21.5809i	−0.404888	+	0.701286i	−0.994308	−	0.106540i	$-0.966023\pi$
$947$	−12.4598	+	21.5809i	−0.404888	+	0.701286i	0.589421	+	0.807826i	$0.299356\pi$
$948$	−18.7587	+	5.97367i	−0.609253	+	0.194016i
$949$	−61.5529			−1.99809
$950$	−7.36240	−	16.9889i	−0.238868	−	0.551194i
$951$			21.5197i			0.697825i
$952$	−1.36857	+	1.21064i	−0.0443557	+	0.0392371i
$953$	−25.5317	−	14.7407i	−0.827053	−	0.477499i	0.0257895	−	0.999667i	$-0.491790\pi$
$953$	−25.5317	−	14.7407i	−0.827053	−	0.477499i	−0.852843	+	0.522168i	$0.825123\pi$
$954$	13.4749	+	9.85057i	0.436265	+	0.318924i
$955$	−33.7572	+	58.4692i	−1.09236	+	1.89202i
$956$	8.04589	−	36.7907i	0.260223	−	1.18990i
$957$		−	22.1702i		−	0.716662i
$958$	17.3316	+	39.2366i	0.559959	+	1.26768i
$959$	3.34851	−	1.93326i	0.108129	−	0.0624282i
$960$	3.35127	−	27.2625i	0.108162	−	0.879892i
$961$	−30.7527			−0.992023
$962$	32.4573	−	14.3370i	1.04646	−	0.462244i
$963$	−1.20314	+	0.694632i	−0.0387706	+	0.0223842i
$964$	18.6510	−	5.93937i	0.600707	−	0.191294i
$965$	−27.0261	−	46.8106i	−0.870002	−	1.50689i
$966$	−1.00352	−	0.108450i	−0.0322877	−	0.00348932i
$967$	50.5276	+	29.1722i	1.62486	+	0.938113i	0.985594	+	0.169127i	$0.0540948\pi$
$967$	50.5276	+	29.1722i	1.62486	+	0.938113i	0.639265	+	0.768986i	$0.279239\pi$
$968$	−5.68872	+	16.9978i	−0.182842	+	0.546331i
$969$	3.74458	+	6.59214i	0.120293	+	0.211770i
$970$	−23.1290	+	10.2165i	−0.742627	+	0.328033i
$971$	−0.791582	−	0.457020i	−0.0254031	−	0.0146665i	0.487245	−	0.873265i	$-0.338002\pi$
$971$	−0.791582	−	0.457020i	−0.0254031	−	0.0146665i	−0.512648	+	0.858599i	$0.671335\pi$
$972$	−26.5849	+	8.46593i	−0.852711	+	0.271545i
$973$	1.85933	−	1.07348i	0.0596073	−	0.0344143i
$974$	6.32308	−	58.5093i	0.202605	−	1.87476i
$975$	−11.7694	+	6.79508i	−0.376923	+	0.217617i
$976$	−9.80846	+	0.914739i	−0.313961	+	0.0292801i
$977$		−	19.2494i		−	0.615841i	−0.951412	−	0.307921i	$-0.900367\pi$
$977$		−	19.2494i		−	0.615841i	0.951412	−	0.307921i	$-0.0996331\pi$
$978$	0.540940	−	0.739968i	0.0172974	−	0.0236616i
$979$	15.0129	−	8.66771i	0.479815	−	0.277021i
$980$	28.4279	+	25.9001i	0.908097	+	0.827348i
$981$	2.85616			0.0911903
$982$	35.1071	+	25.6644i	1.12031	+	0.818985i
$983$	10.4028	−	18.0182i	0.331799	−	0.574693i	−0.651066	−	0.759021i	$-0.725678\pi$
$983$	10.4028	−	18.0182i	0.331799	−	0.574693i	0.982865	+	0.184329i	$0.0590111\pi$
$984$	28.3903	−	5.77402i	0.905051	−	0.184069i
$985$	15.9107	−	27.5581i	0.506956	−	0.878073i
$986$	−1.84224	+	17.0468i	−0.0586689	+	0.542880i
$987$			0.358386i			0.0114076i
$988$	−31.0370	+	9.64449i	−0.987418	+	0.306832i
$989$			7.57143i			0.240758i
$990$	13.1166	+	1.41751i	0.416873	+	0.0450513i
$991$	2.09378	−	3.62654i	0.0665113	−	0.115201i	−0.830852	−	0.556493i	$-0.812147\pi$
$991$	2.09378	−	3.62654i	0.0665113	−	0.115201i	0.897363	+	0.441292i	$0.145480\pi$
$992$	1.44210	−	2.41530i	0.0457866	−	0.0766860i
$993$	−16.6093	+	28.7682i	−0.527080	+	0.912930i
$994$	−6.28512	+	8.59759i	−0.199352	+	0.272699i
$995$	32.4044			1.02729
$996$	21.2319	+	19.3440i	0.672760	+	0.612937i
$997$	4.65708	−	2.68877i	0.147491	−	0.0851542i	−0.424438	−	0.905457i	$-0.639528\pi$
$997$	4.65708	−	2.68877i	0.147491	−	0.0851542i	0.571930	+	0.820303i	$0.306195\pi$
$998$	27.5296	+	20.1250i	0.871433	+	0.637046i
$999$			36.9760i			1.16987i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	152.2.o.c.27.8	✓	28
4.3	odd	2		608.2.s.c.559.9		28
8.3	odd	2	inner	152.2.o.c.27.12	yes	28
8.5	even	2		608.2.s.c.559.10		28
19.12	odd	6	inner	152.2.o.c.107.12	yes	28
76.31	even	6		608.2.s.c.335.10		28
152.69	odd	6		608.2.s.c.335.9		28
152.107	even	6	inner	152.2.o.c.107.8	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.2.o.c.27.8	✓	28	1.1	even	1	trivial
152.2.o.c.27.12	yes	28	8.3	odd	2	inner
152.2.o.c.107.8	yes	28	152.107	even	6	inner
152.2.o.c.107.12	yes	28	19.12	odd	6	inner
608.2.s.c.335.9		28	152.69	odd	6
608.2.s.c.335.10		28	76.31	even	6
608.2.s.c.559.9		28	4.3	odd	2
608.2.s.c.559.10		28	8.5	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 152 = 2^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	152.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.151949 + 1.40603i) q^{2} +(-1.05104 - 0.606818i) q^{3} +(-1.95382 - 0.427288i) q^{4} +(-2.45005 - 1.41453i) q^{5} +(1.01291 - 1.38558i) q^{6} +0.450769i q^{7} +(0.897660 - 2.68220i) q^{8} +(-0.763544 - 1.32250i) q^{9} +(2.36116 - 3.22989i) q^{10} -2.15933 q^{11} +(1.79426 + 1.63471i) q^{12} +(-1.86406 - 3.22864i) q^{13} +(-0.633793 - 0.0684938i) q^{14} +(1.71673 + 2.97346i) q^{15} +(3.63485 + 1.66969i) q^{16} +(-0.716566 + 1.24113i) q^{17} +(1.97549 - 0.872612i) q^{18} +(-0.0305680 + 4.35879i) q^{19} +(4.18254 + 3.81063i) q^{20} +(0.273535 - 0.473776i) q^{21} +(0.328108 - 3.03608i) q^{22} +(-1.12985 + 0.652319i) q^{23} +(-2.57108 + 2.27438i) q^{24} +(1.50182 + 2.60122i) q^{25} +(4.82280 - 2.13033i) q^{26} +5.49424i q^{27} +(0.192608 - 0.880723i) q^{28} +(-4.22992 - 7.32644i) q^{29} +(-4.44162 + 1.96195i) q^{30} -0.497284 q^{31} +(-2.89994 + 4.85699i) q^{32} +(2.26955 + 1.31032i) q^{33} +(-1.63618 - 1.19610i) q^{34} +(0.637628 - 1.10440i) q^{35} +(0.926743 + 2.91018i) q^{36} +6.72997 q^{37} +(-6.12393 - 0.705293i) q^{38} +4.52457i q^{39} +(-5.99338 + 5.30175i) q^{40} +(-7.30919 - 4.21996i) q^{41} +(0.624578 + 0.456587i) q^{42} +(2.90174 - 5.02595i) q^{43} +(4.21896 + 0.922659i) q^{44} +4.32024i q^{45} +(-0.745499 - 1.68772i) q^{46} +(-0.567335 + 0.327551i) q^{47} +(-2.80717 - 3.96060i) q^{48} +6.79681 q^{49} +(-3.88559 + 1.71634i) q^{50} +(1.50628 - 0.869651i) q^{51} +(2.26248 + 7.10468i) q^{52} +(3.86444 + 6.69340i) q^{53} +(-7.72504 - 0.834843i) q^{54} +(5.29047 + 3.05445i) q^{55} +(1.20905 + 0.404637i) q^{56} +(2.67712 - 4.56271i) q^{57} +(10.9439 - 4.83414i) q^{58} +(-12.1090 - 6.99113i) q^{59} +(-2.08366 - 6.54316i) q^{60} +(-2.13281 + 1.23138i) q^{61} +(0.0755618 - 0.699195i) q^{62} +(0.596141 - 0.344182i) q^{63} +(-6.38841 - 4.81541i) q^{64} +10.5471i q^{65} +(-2.18720 + 2.99194i) q^{66} +(2.16651 - 1.25083i) q^{67} +(1.93036 - 2.11877i) q^{68} +1.58336 q^{69} +(1.45594 + 1.06434i) q^{70} +(8.35311 - 14.4680i) q^{71} +(-4.23261 + 0.860827i) q^{72} +(8.25523 - 14.2985i) q^{73} +(-1.02261 + 9.46252i) q^{74} -3.64532i q^{75} +(1.92219 - 8.50325i) q^{76} -0.973361i q^{77} +(-6.36167 - 0.687504i) q^{78} +(-4.05535 + 7.02407i) q^{79} +(-6.54371 - 9.23244i) q^{80} +(1.04337 - 1.80717i) q^{81} +(7.04400 - 9.63570i) q^{82} +11.8333 q^{83} +(-0.736877 + 0.808796i) q^{84} +(3.51124 - 2.02722i) q^{85} +(6.62571 + 4.84361i) q^{86} +10.2672i q^{87} +(-1.93835 + 5.79177i) q^{88} +(-6.95256 + 4.01406i) q^{89} +(-6.07437 - 0.656455i) q^{90} +(1.45537 - 0.840259i) q^{91} +(2.48626 - 0.791744i) q^{92} +(0.522665 + 0.301761i) q^{93} +(-0.374340 - 0.847459i) q^{94} +(6.24056 - 10.6360i) q^{95} +(5.99526 - 3.34515i) q^{96} +(-5.47310 - 3.15990i) q^{97} +(-1.03277 + 9.55649i) q^{98} +(1.64875 + 2.85571i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 3 q^{2} - 6 q^{3} + q^{4} - 3 q^{6} + 8 q^{9} + 6 q^{10} - 16 q^{11} + 13 q^{16} - 22 q^{17} + 4 q^{19} - 40 q^{20} - 21 q^{22} - 11 q^{24} + 16 q^{25} + 36 q^{26} - 10 q^{28} + 4 q^{30} - 3 q^{32}+ \cdots - 28 q^{99}+O(q^{100}) \) 28 * q - 3 * q^2 - 6 * q^3 + q^4 - 3 * q^6 + 8 * q^9 + 6 * q^10 - 16 * q^11 + 13 * q^16 - 22 * q^17 + 4 * q^19 - 40 * q^20 - 21 * q^22 - 11 * q^24 + 16 * q^25 + 36 * q^26 - 10 * q^28 + 4 * q^30 - 3 * q^32 + 36 * q^33 - 12 * q^34 - 28 * q^35 - 8 * q^36 + 38 * q^38 - 48 * q^40 + 6 * q^41 + 14 * q^42 + 30 * q^43 + 5 * q^44 - 15 * q^48 - 68 * q^49 - 42 * q^51 + 36 * q^52 + 23 * q^54 - 26 * q^57 + 20 * q^58 - 18 * q^59 - 42 * q^60 + 22 * q^62 + 70 * q^64 - 27 * q^66 + 78 * q^67 + 4 * q^68 + 18 * q^70 - 24 * q^72 + 14 * q^73 + 4 * q^74 + 47 * q^76 - 30 * q^78 - 20 * q^80 + 6 * q^81 + 23 * q^82 - 32 * q^83 + 42 * q^86 - 18 * q^89 - 96 * q^90 - 12 * q^91 + 46 * q^92 + 50 * q^96 + 30 * q^97 + 15 * q^98 - 28 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more