LMFDB - Embedded newform 152.2.t.a.101.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [152,2,Mod(5,152)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(152, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 9, 16])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("152.5"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 152 = 2^{3} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	152.t (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$1.21372611072$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$18$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			101.4
Character	$\chi$	$=$	152.101
Dual form			152.2.t.a.149.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.30663 + 0.541037i) q^{2} +(-0.467226 + 1.28369i) q^{3} +(1.41456 - 1.41387i) q^{4} +(1.73333 - 0.305632i) q^{5} +(-0.0840336 - 1.93009i) q^{6} +(1.91364 - 3.31452i) q^{7} +(-1.08335 + 2.61273i) q^{8} +(0.868569 + 0.728816i) q^{9} +(-2.09945 + 1.33714i) q^{10} +(-2.26499 + 1.30769i) q^{11} +(1.15405 + 2.47645i) q^{12} +(2.03996 + 5.60474i) q^{13} +(-0.707140 + 5.36619i) q^{14} +(-0.417517 + 2.36785i) q^{15} +(0.00195414 - 4.00000i) q^{16} +(2.13151 - 1.78855i) q^{17} +(-1.52921 - 0.482364i) q^{18} +(0.713969 - 4.30003i) q^{19} +(2.01977 - 2.88303i) q^{20} +(3.36072 + 4.00515i) q^{21} +(2.25199 - 2.93411i) q^{22} +(-1.10686 + 6.27729i) q^{23} +(-2.84777 - 2.61142i) q^{24} +(-1.78746 + 0.650581i) q^{25} +(-5.69783 - 6.21962i) q^{26} +(-4.89056 + 2.82357i) q^{27} +(-1.97934 - 7.39421i) q^{28} +(2.78015 - 3.31326i) q^{29} +(-0.735556 - 3.31980i) q^{30} +(2.41499 - 4.18289i) q^{31} +(2.16159 + 5.22757i) q^{32} +(-0.620412 - 3.51853i) q^{33} +(-1.81742 + 3.49020i) q^{34} +(2.30393 - 6.33001i) q^{35} +(2.25909 - 0.197089i) q^{36} -7.50278i q^{37} +(1.39358 + 6.00483i) q^{38} -8.14787 q^{39} +(-1.07926 + 4.85982i) q^{40} +(-6.78504 - 2.46955i) q^{41} +(-6.55815 - 3.41497i) q^{42} +(-3.24204 + 0.571659i) q^{43} +(-1.35505 + 5.05220i) q^{44} +(1.72826 + 0.997812i) q^{45} +(-1.95000 - 8.80095i) q^{46} +(3.73496 + 3.13400i) q^{47} +(5.13385 + 1.87141i) q^{48} +(-3.82402 - 6.62340i) q^{49} +(1.98356 - 1.81715i) q^{50} +(1.30005 + 3.57186i) q^{51} +(10.8100 + 5.04400i) q^{52} +(-1.49917 - 0.264344i) q^{53} +(4.86250 - 6.33533i) q^{54} +(-3.52629 + 2.95890i) q^{55} +(6.58680 + 8.59060i) q^{56} +(5.18633 + 2.92560i) q^{57} +(-1.84004 + 5.83336i) q^{58} +(-4.81703 - 5.74071i) q^{59} +(2.75723 + 3.93978i) q^{60} +(-5.64385 - 0.995163i) q^{61} +(-0.892404 + 6.77209i) q^{62} +(4.07780 - 1.48420i) q^{63} +(-5.65271 - 5.66100i) q^{64} +(5.24890 + 9.09135i) q^{65} +(2.71430 + 4.26175i) q^{66} +(-2.11430 + 2.51972i) q^{67} +(0.486374 - 5.54368i) q^{68} +(-7.54096 - 4.35377i) q^{69} +(0.414378 + 9.51748i) q^{70} +(0.236392 + 1.34065i) q^{71} +(-2.84516 + 1.47977i) q^{72} +(10.5450 + 3.83807i) q^{73} +(4.05928 + 9.80335i) q^{74} -2.59851i q^{75} +(-5.06972 - 7.09210i) q^{76} +10.0098i q^{77} +(10.6462 - 4.40830i) q^{78} +(-6.51619 - 2.37170i) q^{79} +(-1.21914 - 6.93390i) q^{80} +(-0.748928 - 4.24738i) q^{81} +(10.2016 - 0.444165i) q^{82} +(-5.89196 - 3.40173i) q^{83} +(10.4167 + 0.913906i) q^{84} +(3.14796 - 3.75160i) q^{85} +(3.92686 - 2.50101i) q^{86} +(2.95424 + 5.11690i) q^{87} +(-0.962869 - 7.33448i) q^{88} +(-6.91135 + 2.51553i) q^{89} +(-2.79805 - 0.368718i) q^{90} +(22.4807 + 3.96396i) q^{91} +(7.30955 + 10.4446i) q^{92} +(4.24120 + 5.05446i) q^{93} +(-6.57581 - 2.07423i) q^{94} +(-0.0766864 - 7.67156i) q^{95} +(-7.72054 + 0.332363i) q^{96} +(-9.33891 + 7.83628i) q^{97} +(8.58008 + 6.58539i) q^{98} +(-2.92036 - 0.514939i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 6 q^{2} - 12 q^{4} - 12 q^{6} - 6 q^{7} - 3 q^{8} - 12 q^{9} + 9 q^{10} - 3 q^{12} - 9 q^{14} - 12 q^{15} - 12 q^{17} - 12 q^{18} - 42 q^{20} - 12 q^{22} - 12 q^{23} - 36 q^{24} - 12 q^{25} + 21 q^{26}+ \cdots + 93 q^{98}+O(q^{100}) $ 108 * q - 6 * q^2 - 12 * q^4 - 12 * q^6 - 6 * q^7 - 3 * q^8 - 12 * q^9 + 9 * q^10 - 3 * q^12 - 9 * q^14 - 12 * q^15 - 12 * q^17 - 12 * q^18 - 42 * q^20 - 12 * q^22 - 12 * q^23 - 36 * q^24 - 12 * q^25 + 21 * q^26 + 24 * q^28 - 48 * q^30 + 30 * q^31 + 39 * q^32 - 30 * q^33 - 60 * q^34 + 69 * q^36 - 42 * q^38 - 24 * q^39 + 36 * q^40 - 24 * q^41 - 81 * q^42 + 45 * q^44 - 18 * q^46 - 48 * q^47 - 21 * q^48 - 24 * q^49 - 12 * q^50 + 3 * q^52 + 63 * q^54 - 42 * q^55 + 30 * q^56 - 12 * q^57 - 84 * q^58 + 30 * q^60 - 6 * q^62 + 30 * q^63 + 3 * q^64 - 6 * q^65 + 54 * q^66 + 36 * q^68 + 123 * q^70 - 12 * q^71 + 150 * q^72 + 12 * q^73 + 75 * q^74 + 42 * q^76 + 39 * q^78 - 12 * q^79 + 51 * q^80 - 18 * q^81 + 99 * q^82 + 75 * q^84 - 48 * q^86 - 6 * q^87 - 27 * q^88 - 12 * q^89 + 66 * q^90 - 48 * q^92 + 54 * q^94 - 72 * q^95 + 42 * q^96 - 12 * q^97 + 93 * q^98

Character values

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

$n$	$39$	$77$	$97$
$\chi(n)$	$1$	$-1$	$e\left(\frac{7}{9}\right)$

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 $

$2$	−1.30663	+	0.541037i	−0.923926	+	0.382571i
$2$	−1.30663	+	0.541037i	−0.923926	+	0.382571i
$3$	−0.467226	+	1.28369i	−0.269753	+	0.741140i	0.728663	+	0.684872i	$0.240142\pi$
$3$	−0.467226	+	1.28369i	−0.269753	+	0.741140i	−0.998416	+	0.0562672i	$0.982080\pi$
$4$	1.41456	−	1.41387i	0.707279	−	0.706934i
$5$	1.73333	−	0.305632i	0.775167	−	0.136683i	0.227949	−	0.973673i	$-0.426798\pi$
$5$	1.73333	−	0.305632i	0.775167	−	0.136683i	0.547218	+	0.836990i	$0.315687\pi$
$6$	−0.0840336	−	1.93009i	−0.0343066	−	0.787958i
$7$	1.91364	−	3.31452i	0.723287	−	1.25277i	−0.236388	−	0.971659i	$-0.575964\pi$
$7$	1.91364	−	3.31452i	0.723287	−	1.25277i	0.959675	−	0.281112i	$-0.0907031\pi$
$8$	−1.08335	+	2.61273i	−0.383022	+	0.923739i
$9$	0.868569	+	0.728816i	0.289523	+	0.242939i
$10$	−2.09945	+	1.33714i	−0.663906	+	0.422841i
$11$	−2.26499	+	1.30769i	−0.682919	+	0.394283i	−0.800954	−	0.598726i	$-0.795674\pi$
$11$	−2.26499	+	1.30769i	−0.682919	+	0.394283i	0.118035	+	0.993009i	$0.462341\pi$
$12$	1.15405	+	2.47645i	0.333146	+	0.714890i
$13$	2.03996	+	5.60474i	0.565782	+	1.55447i	0.811024	+	0.585012i	$0.198910\pi$
$13$	2.03996	+	5.60474i	0.565782	+	1.55447i	−0.245242	+	0.969462i	$0.578867\pi$
$14$	−0.707140	+	5.36619i	−0.188991	+	1.43418i
$15$	−0.417517	+	2.36785i	−0.107802	+	0.611377i
$16$	0.00195414	−	4.00000i	0.000488536	−	1.00000i
$17$	2.13151	−	1.78855i	0.516967	−	0.433787i	−0.346606	−	0.938011i	$-0.612666\pi$
$17$	2.13151	−	1.78855i	0.516967	−	0.433787i	0.863573	+	0.504224i	$0.168221\pi$
$18$	−1.52921	−	0.482364i	−0.360439	−	0.113694i
$19$	0.713969	−	4.30003i	0.163796	−	0.986494i
$19$	0.713969	−	4.30003i	0.163796	−	0.986494i
$20$	2.01977	−	2.88303i	0.451634	−	0.644665i
$21$	3.36072	+	4.00515i	0.733369	+	0.873995i
$22$	2.25199	−	2.93411i	0.480126	−	0.625554i
$23$	−1.10686	+	6.27729i	−0.230796	+	1.30891i	0.620494	+	0.784211i	$0.286932\pi$
$23$	−1.10686	+	6.27729i	−0.230796	+	1.30891i	−0.851290	+	0.524696i	$0.824179\pi$
$24$	−2.84777	−	2.61142i	−0.581299	−	0.533054i
$25$	−1.78746	+	0.650581i	−0.357492	+	0.130116i
$26$	−5.69783	−	6.21962i	−1.11744	−	1.21977i
$27$	−4.89056	+	2.82357i	−0.941189	+	0.543396i
$28$	−1.97934	−	7.39421i	−0.374060	−	1.39738i
$29$	2.78015	−	3.31326i	0.516261	−	0.615256i	−0.443431	−	0.896308i	$-0.646239\pi$
$29$	2.78015	−	3.31326i	0.516261	−	0.615256i	0.959693	+	0.281052i	$0.0906833\pi$
$30$	−0.735556	−	3.31980i	−0.134294	−	0.606110i
$31$	2.41499	−	4.18289i	0.433746	−	0.751270i	−0.563447	−	0.826153i	$-0.690525\pi$
$31$	2.41499	−	4.18289i	0.433746	−	0.751270i	0.997192	+	0.0748828i	$0.0238583\pi$
$32$	2.16159	+	5.22757i	0.382119	+	0.924113i
$33$	−0.620412	−	3.51853i	−0.108000	−	0.612497i
$34$	−1.81742	+	3.49020i	−0.311685	+	0.598564i
$35$	2.30393	−	6.33001i	0.389436	−	1.06997i
$36$	2.25909	−	0.197089i	0.376515	−	0.0328481i
$37$		−	7.50278i		−	1.23345i	−0.787179	−	0.616725i	$-0.788459\pi$
$37$		−	7.50278i		−	1.23345i	0.787179	−	0.616725i	$-0.211541\pi$
$38$	1.39358	+	6.00483i	0.226069	+	0.974111i
$39$	−8.14787			−1.30470
$40$	−1.07926	+	4.85982i	−0.170647	+	0.768404i
$41$	−6.78504	−	2.46955i	−1.05964	−	0.385679i	−0.247350	−	0.968926i	$-0.579560\pi$
$41$	−6.78504	−	2.46955i	−1.05964	−	0.385679i	−0.812295	+	0.583247i	$0.801782\pi$
$42$	−6.55815	−	3.41497i	−1.01194	−	0.526942i
$43$	−3.24204	+	0.571659i	−0.494407	+	0.0871772i	−0.415292	−	0.909688i	$-0.636321\pi$
$43$	−3.24204	+	0.571659i	−0.494407	+	0.0871772i	−0.0791149	+	0.996866i	$0.525209\pi$
$44$	−1.35505	+	5.05220i	−0.204282	+	0.761647i
$45$	1.72826	+	0.997812i	0.257634	+	0.148745i
$46$	−1.95000	−	8.80095i	−0.287511	−	1.29763i
$47$	3.73496	+	3.13400i	0.544800	+	0.457141i	0.873175	−	0.487406i	$-0.162057\pi$
$47$	3.73496	+	3.13400i	0.544800	+	0.457141i	−0.328376	+	0.944547i	$0.606501\pi$
$48$	5.13385	+	1.87141i	0.741008	+	0.270115i
$49$	−3.82402	−	6.62340i	−0.546289	−	0.946200i
$50$	1.98356	−	1.81715i	0.280517	−	0.256984i
$51$	1.30005	+	3.57186i	0.182043	+	0.500160i
$52$	10.8100	+	5.04400i	1.49908	+	0.699477i
$53$	−1.49917	−	0.264344i	−0.205927	−	0.0363104i	0.0697332	−	0.997566i	$-0.477785\pi$
$53$	−1.49917	−	0.264344i	−0.205927	−	0.0363104i	−0.275660	+	0.961255i	$0.588896\pi$
$54$	4.86250	−	6.33533i	0.661702	−	0.862129i
$55$	−3.52629	+	2.95890i	−0.475484	+	0.398979i
$56$	6.58680	+	8.59060i	0.880198	+	1.14797i
$57$	5.18633	+	2.92560i	0.686946	+	0.387505i
$58$	−1.84004	+	5.83336i	−0.241609	+	0.765958i
$59$	−4.81703	−	5.74071i	−0.627124	−	0.747377i	0.355154	−	0.934808i	$-0.384428\pi$
$59$	−4.81703	−	5.74071i	−0.627124	−	0.747377i	−0.982278	+	0.187431i	$0.939984\pi$
$60$	2.75723	+	3.93978i	0.355957	+	0.508624i
$61$	−5.64385	−	0.995163i	−0.722621	−	0.127418i	−0.199771	−	0.979843i	$-0.564020\pi$
$61$	−5.64385	−	0.995163i	−0.722621	−	0.127418i	−0.522850	+	0.852425i	$0.675131\pi$
$62$	−0.892404	+	6.77209i	−0.113335	+	0.860056i
$63$	4.07780	−	1.48420i	0.513755	−	0.186991i
$64$	−5.65271	−	5.66100i	−0.706588	−	0.707625i
$65$	5.24890	+	9.09135i	0.651045	+	1.12764i
$66$	2.71430	+	4.26175i	0.334107	+	0.524585i
$67$	−2.11430	+	2.51972i	−0.258302	+	0.307833i	−0.879574	−	0.475763i	$-0.842172\pi$
$67$	−2.11430	+	2.51972i	−0.258302	+	0.307833i	0.621271	+	0.783596i	$0.286617\pi$
$68$	0.486374	−	5.54368i	0.0589815	−	0.672270i
$69$	−7.54096	−	4.35377i	−0.907825	−	0.524133i
$70$	0.414378	+	9.51748i	0.0495276	+	1.13756i
$71$	0.236392	+	1.34065i	0.0280546	+	0.159106i	0.995617	−	0.0935279i	$-0.0298144\pi$
$71$	0.236392	+	1.34065i	0.0280546	+	0.159106i	−0.967562	+	0.252633i	$0.918703\pi$
$72$	−2.84516	+	1.47977i	−0.335306	+	0.174393i
$73$	10.5450	+	3.83807i	1.23420	+	0.449212i	0.875034	−	0.484062i	$-0.160839\pi$
$73$	10.5450	+	3.83807i	1.23420	+	0.449212i	0.359166	+	0.933274i	$0.383061\pi$
$74$	4.05928	+	9.80335i	0.471882	+	1.13962i
$75$		−	2.59851i		−	0.300050i
$76$	−5.06972	−	7.09210i	−0.581537	−	0.813520i
$77$			10.0098i			1.14072i
$78$	10.6462	−	4.40830i	1.20545	−	0.499141i
$79$	−6.51619	−	2.37170i	−0.733128	−	0.266837i	−0.0516399	−	0.998666i	$-0.516445\pi$
$79$	−6.51619	−	2.37170i	−0.733128	−	0.266837i	−0.681488	+	0.731829i	$0.738667\pi$
$80$	−1.21914	−	6.93390i	−0.136304	−	0.775233i
$81$	−0.748928	−	4.24738i	−0.0832143	−	0.471932i
$82$	10.2016	−	0.444165i	1.12658	−	0.0490498i
$83$	−5.89196	−	3.40173i	−0.646727	−	0.373388i	0.140474	−	0.990084i	$-0.455137\pi$
$83$	−5.89196	−	3.40173i	−0.646727	−	0.373388i	−0.787201	+	0.616696i	$0.788471\pi$
$84$	10.4167	+	0.913906i	1.13655	+	0.0997153i
$85$	3.14796	−	3.75160i	0.341444	−	0.406918i
$86$	3.92686	−	2.50101i	0.423444	−	0.269691i
$87$	2.95424	+	5.11690i	0.316728	+	0.548589i
$88$	−0.962869	−	7.33448i	−0.102642	−	0.781858i
$89$	−6.91135	+	2.51553i	−0.732602	+	0.266645i	−0.681266	−	0.732036i	$-0.738570\pi$
$89$	−6.91135	+	2.51553i	−0.732602	+	0.266645i	−0.0513361	+	0.998681i	$0.516348\pi$
$90$	−2.79805	−	0.368718i	−0.294940	−	0.0388663i
$91$	22.4807	+	3.96396i	2.35662	+	0.415536i
$92$	7.30955	+	10.4446i	0.762074	+	1.08892i
$93$	4.24120	+	5.05446i	0.439792	+	0.524123i
$94$	−6.57581	−	2.07423i	−0.678243	−	0.213940i
$95$	−0.0766864	−	7.67156i	−0.00786786	−	0.787085i
$96$	−7.72054	+	0.332363i	−0.787975	+	0.0339216i
$97$	−9.33891	+	7.83628i	−0.948223	+	0.795653i	−0.978997	−	0.203873i	$-0.934647\pi$
$97$	−9.33891	+	7.83628i	−0.948223	+	0.795653i	0.0307745	+	0.999526i	$0.490203\pi$
$98$	8.58008	+	6.58539i	0.866719	+	0.665225i
$99$	−2.92036	−	0.514939i	−0.293507	−	0.0517533i
$100$	−1.60863	+	3.44752i	−0.160863	+	0.344752i
$101$	−4.36652	−	11.9969i	−0.434485	−	1.19374i	−0.943031	−	0.332704i	$-0.892039\pi$
$101$	−4.36652	−	11.9969i	−0.434485	−	1.19374i	0.508546	−	0.861035i	$-0.330183\pi$
$102$	−3.63119	−	3.96372i	−0.359541	−	0.392467i
$103$	−2.02806	−	3.51270i	−0.199831	−	0.346117i	0.748643	−	0.662974i	$-0.230706\pi$
$103$	−2.02806	−	3.51270i	−0.199831	−	0.346117i	−0.948473	+	0.316857i	$0.897373\pi$
$104$	−16.8536	−	0.742033i	−1.65264	−	0.0727623i
$105$	7.04932	+	5.91508i	0.687943	+	0.577253i
$106$	2.10188	−	0.465705i	0.204152	−	0.0452333i
$107$	−1.10131	−	0.635844i	−0.106468	−	0.0614693i	0.445820	−	0.895122i	$-0.352912\pi$
$107$	−1.10131	−	0.635844i	−0.106468	−	0.0614693i	−0.552288	+	0.833653i	$0.686245\pi$
$108$	−2.92584	+	10.9087i	−0.281539	+	1.04969i
$109$	3.33109	−	0.587360i	0.319060	−	0.0562589i	−0.0118246	−	0.999930i	$-0.503764\pi$
$109$	3.33109	−	0.587360i	0.319060	−	0.0562589i	0.330885	+	0.943671i	$0.392653\pi$
$110$	3.00667	−	5.77404i	0.286675	−	0.550533i
$111$	9.63126	+	3.50549i	0.914159	+	0.332727i
$112$	−13.2543	−	7.66103i	−1.25242	−	0.723899i
$113$	−15.3010			−1.43939			−0.719697	−	0.694288i	$-0.755719\pi$
$113$	−15.3010			−1.43939			−0.719697	+	0.694288i	$0.755719\pi$
$114$	−8.35946	−	1.01668i	−0.782935	−	0.0952209i
$115$			11.2189i			1.04617i
$116$	−0.751818	−	8.61757i	−0.0698046	−	0.800121i
$117$	−2.31298	+	6.35485i	−0.213835	+	0.587506i
$118$	9.40000	+	4.89479i	0.865340	+	0.450602i
$119$	−1.84924	−	10.4876i	−0.169520	−	0.961394i
$120$	−5.73424	−	3.65607i	−0.523463	−	0.333752i
$121$	−2.07989	+	3.60248i	−0.189081	+	0.327498i
$122$	7.91284	−	1.75322i	0.716395	−	0.158729i
$123$	6.34028	−	7.55606i	0.571684	−	0.681307i
$124$	−2.49791	−	9.33143i	−0.224319	−	0.837987i
$125$	−10.5207	+	6.07413i	−0.941001	+	0.543287i
$126$	−4.52517	+	4.14554i	−0.403134	+	0.369314i
$127$	10.6056	−	3.86013i	0.941097	−	0.342531i	0.174498	−	0.984657i	$-0.444170\pi$
$127$	10.6056	−	3.86013i	0.941097	−	0.342531i	0.766599	+	0.642126i	$0.221947\pi$
$128$	10.4488	+	4.33850i	0.923552	+	0.383473i
$129$	0.780930	−	4.42887i	0.0687571	−	0.389941i
$130$	−11.7771	−	9.03918i	−1.03292	−	0.792789i
$131$	7.04562	+	8.39664i	0.615579	+	0.733618i	0.980303	−	0.197497i	$-0.0632813\pi$
$131$	7.04562	+	8.39664i	0.615579	+	0.733618i	−0.364725	+	0.931115i	$0.618837\pi$
$132$	−5.85235	−	4.09999i	−0.509381	−	0.356858i
$133$	−12.8862	−	10.5952i	−1.11738	−	0.918717i
$134$	1.39934	−	4.43625i	0.120885	−	0.383234i
$135$	−7.61396	+	6.38887i	−0.655305	+	0.549867i
$136$	2.36382	+	7.50668i	0.202696	+	0.643693i
$137$	3.48972	−	19.7912i	0.298147	−	1.69087i	−0.355984	−	0.934492i	$-0.615854\pi$
$137$	3.48972	−	19.7912i	0.298147	−	1.69087i	0.654130	−	0.756382i	$-0.273035\pi$
$138$	12.2088	+	1.60883i	1.03928	+	0.136953i
$139$	5.65104	+	15.5261i	0.479315	+	1.31691i	0.910076	+	0.414441i	$0.136023\pi$
$139$	5.65104	+	15.5261i	0.479315	+	1.31691i	−0.430761	+	0.902466i	$0.641755\pi$
$140$	−5.69074	−	12.2116i	−0.480956	−	1.03207i
$141$	−5.76816	+	3.33025i	−0.485767	+	0.280458i
$142$	−1.03422	−	1.62383i	−0.0867895	−	0.136269i
$143$	−11.9497	−	10.0270i	−0.999287	−	0.838501i
$144$	2.91696	−	3.47285i	0.243080	−	0.289404i
$145$	3.80627	−	6.59266i	0.316094	−	0.547490i
$146$	−15.8549	+	0.690302i	−1.31216	+	0.0571298i
$147$	10.2891	−	1.81424i	0.848630	−	0.149636i
$148$	−10.6079	−	10.6131i	−0.871968	−	0.872394i
$149$	6.28070	−	17.2561i	0.514535	−	1.41367i	−0.361929	−	0.932206i	$-0.617882\pi$
$149$	6.28070	−	17.2561i	0.514535	−	1.41367i	0.876464	−	0.481468i	$-0.159896\pi$
$150$	1.40589	+	3.39529i	0.114790	+	0.277224i
$151$	13.2947			1.08191			0.540954	−	0.841052i	$-0.318063\pi$
$151$	13.2947			1.08191			0.540954	+	0.841052i	$0.318063\pi$
$152$	10.4613	+	6.52384i	0.848526	+	0.529153i
$153$	3.15489			0.255057
$154$	−5.41566	−	13.0791i	−0.436406	−	1.05394i
$155$	2.90754	−	7.98841i	0.233540	−	0.641645i
$156$	−11.5256	+	11.5200i	−0.922790	+	0.922339i
$157$	0.992527	−	0.175009i	0.0792123	−	0.0139673i	−0.133902	−	0.990995i	$-0.542751\pi$
$157$	0.992527	−	0.175009i	0.0792123	−	0.0139673i	0.213114	+	0.977027i	$0.431639\pi$
$158$	9.79741	−	0.426565i	0.779440	−	0.0339357i
$159$	1.03979	−	1.80096i	0.0824604	−	0.142826i
$160$	5.34446	+	8.40043i	0.422516	+	0.664112i
$161$	18.6881	+	15.6812i	1.47283	+	1.23585i
$162$	3.27656	+	5.14456i	0.257431	+	0.404195i
$163$	−12.9858	+	7.49734i	−1.01712	+	0.587237i	−0.913270	−	0.407356i	$-0.866451\pi$
$163$	−12.9858	+	7.49734i	−1.01712	+	0.587237i	−0.103854	+	0.994593i	$0.533118\pi$
$164$	−13.0895	+	6.09982i	−1.02211	+	0.476316i
$165$	−2.15075	−	5.90914i	−0.167436	−	0.460026i
$166$	9.53907	+	1.25703i	0.740375	+	0.0975643i
$167$	−0.413879	+	2.34722i	−0.0320269	+	0.181634i	−0.996625	−	0.0820914i	$-0.973840\pi$
$167$	−0.413879	+	2.34722i	−0.0320269	+	0.181634i	0.964598	+	0.263725i	$0.0849512\pi$
$168$	−14.1052	+	4.44167i	−1.08824	+	0.342682i
$169$	−17.2931	+	14.5106i	−1.33024	+	1.11620i
$170$	−2.08347	+	6.60511i	−0.159795	+	0.506588i
$171$	3.75406	−	3.21452i	0.287080	−	0.245820i
$172$	−3.77781	+	5.39246i	−0.288055	+	0.411172i
$173$	11.5139	+	13.7218i	0.875388	+	1.04325i	0.998705	+	0.0508794i	$0.0162024\pi$
$173$	11.5139	+	13.7218i	0.875388	+	1.04325i	−0.123317	+	0.992367i	$0.539353\pi$
$174$	−6.62853	−	5.08753i	−0.502507	−	0.385685i
$175$	−1.26418	+	7.16954i	−0.0955633	+	0.541966i
$176$	5.22633	+	9.06250i	0.393950	+	0.683112i
$177$	9.61994	−	3.50137i	0.723079	−	0.263179i
$178$	7.66958	−	7.02615i	0.574860	−	0.526633i
$179$	19.7528	−	11.4043i	1.47639	−	0.852394i	0.476745	−	0.879042i	$-0.341816\pi$
$179$	19.7528	−	11.4043i	1.47639	−	0.852394i	0.999645	+	0.0266474i	$0.00848313\pi$
$180$	3.85550	−	1.03207i	0.287372	−	0.0769259i
$181$	−3.56113	+	4.24399i	−0.264696	+	0.315453i	−0.881979	−	0.471289i	$-0.843789\pi$
$181$	−3.56113	+	4.24399i	−0.264696	+	0.315453i	0.617283	+	0.786741i	$0.288233\pi$
$182$	−31.5186	+	6.98348i	−2.33632	+	0.517650i
$183$	3.91443	−	6.78000i	0.289363	−	0.501192i
$184$	−15.2018	−	9.69242i	−1.12069	−	0.714535i
$185$	−2.29309	−	13.0048i	−0.168591	−	0.956129i
$186$	−8.27632	−	4.30966i	−0.606849	−	0.316000i
$187$	−2.48897	+	6.83839i	−0.182012	+	0.500073i
$188$	9.71438	−	0.847507i	0.708494	−	0.0618108i
$189$			21.6131i			1.57213i
$190$	4.25079	+	9.98239i	0.308385	+	0.724199i
$191$	−1.52320			−0.110215			−0.0551073	−	0.998480i	$-0.517550\pi$
$191$	−1.52320			−0.110215			−0.0551073	+	0.998480i	$0.517550\pi$
$192$	9.90806	−	4.61137i	0.715053	−	0.332797i
$193$	9.17926	+	3.34098i	0.660738	+	0.240489i	0.650555	−	0.759459i	$-0.274536\pi$
$193$	9.17926	+	3.34098i	0.660738	+	0.240489i	0.0101828	+	0.999948i	$0.496759\pi$
$194$	7.96278	−	15.2918i	0.571694	−	1.09789i
$195$	−14.1229	+	2.49025i	−1.01136	+	0.178331i
$196$	−14.7739	−	3.96253i	−1.05528	−	0.283038i
$197$	5.18292	+	2.99236i	0.369268	+	0.213197i	0.673138	−	0.739517i	$-0.264946\pi$
$197$	5.18292	+	2.99236i	0.369268	+	0.213197i	−0.303871	+	0.952713i	$0.598279\pi$
$198$	4.09443	−	0.907189i	0.290978	−	0.0644711i
$199$	3.61157	+	3.03047i	0.256017	+	0.214824i	0.761758	−	0.647861i	$-0.224336\pi$
$199$	3.61157	+	3.03047i	0.256017	+	0.214824i	−0.505741	+	0.862685i	$0.668781\pi$
$200$	0.236649	−	5.37495i	0.0167336	−	0.380066i
$201$	−2.24669	−	3.89138i	−0.158469	−	0.274477i
$202$	12.1962	+	13.3131i	0.858122	+	0.936705i
$203$	−5.66165	−	15.5552i	−0.397370	−	1.09176i
$204$	6.88913	+	3.21450i	0.482336	+	0.225060i
$205$	−12.5154	−	2.20681i	−0.874117	−	0.154130i
$206$	4.55042	+	3.49255i	0.317043	+	0.243337i
$207$	−5.53637	+	4.64557i	−0.384805	+	0.322889i
$208$	22.4229	−	8.14887i	1.55475	−	0.565023i
$209$	4.00598	+	10.6732i	0.277099	+	0.738278i
$210$	−12.4111	−	3.91488i	−0.856449	−	0.270152i
$211$	14.2288	+	16.9573i	0.979553	+	1.16739i	0.985888	+	0.167406i	$0.0535391\pi$
$211$	14.2288	+	16.9573i	0.979553	+	1.16739i	−0.00633485	+	0.999980i	$0.502016\pi$
$212$	−2.49441	+	1.74570i	−0.171317	+	0.119895i
$213$	−1.83143	−	0.322930i	−0.125487	−	0.0221268i
$214$	1.78302	+	0.234961i	0.121885	+	0.0160616i
$215$	−5.44479	+	1.98174i	−0.371332	+	0.135154i
$216$	−2.07903	−	15.8366i	−0.141460	−	1.07755i
$217$	−9.24285	−	16.0091i	−0.627446	−	1.08677i
$218$	−4.03471	+	2.56970i	−0.273265	+	0.174042i
$219$	−9.85379	+	11.7433i	−0.665857	+	0.793538i
$220$	−0.804638	+	9.17125i	−0.0542487	+	0.618325i
$221$	14.3725	+	8.29799i	0.966801	+	0.558183i
$222$	−14.4811	+	0.630486i	−0.971907	+	0.0423154i
$223$	4.15766	+	23.5792i	0.278417	+	1.57898i	0.727894	+	0.685690i	$0.240500\pi$
$223$	4.15766	+	23.5792i	0.278417	+	1.57898i	−0.449476	+	0.893292i	$0.648389\pi$
$224$	21.4634	+	2.83904i	1.43408	+	0.189692i
$225$	−2.02668	−	0.737653i	−0.135112	−	0.0491769i
$226$	19.9927	−	8.27838i	1.32989	−	0.550670i
$227$		−	1.68680i		−	0.111957i	−0.998432	−	0.0559784i	$-0.982172\pi$
$227$		−	1.68680i		−	0.111957i	0.998432	−	0.0559784i	$-0.0178278\pi$
$228$	11.4728	−	3.19435i	0.759803	−	0.211551i
$229$		−	3.60123i		−	0.237976i	−0.992896	−	0.118988i	$-0.962035\pi$
$229$		−	3.60123i		−	0.237976i	0.992896	−	0.118988i	$-0.0379650\pi$
$230$	−6.06983	−	14.6589i	−0.400232	−	0.966581i
$231$	−12.8495	−	4.67683i	−0.845433	−	0.307713i
$232$	5.64477	+	10.8532i	0.370597	+	0.712548i
$233$	−0.677514	−	3.84237i	−0.0443854	−	0.251722i	0.954539	−	0.298085i	$-0.0963480\pi$
$233$	−0.677514	−	3.84237i	−0.0443854	−	0.251722i	−0.998925	+	0.0463631i	$0.985237\pi$
$234$	−0.416004	−	9.55484i	−0.0271950	−	0.624619i
$235$	7.43175	+	4.29072i	0.484794	+	0.279896i
$236$	−14.9306	−	1.30993i	−0.971898	−	0.0852693i
$237$	6.08906	−	7.25666i	0.395527	−	0.471371i
$238$	8.09043	+	12.7029i	0.524425	+	0.823404i
$239$	−1.71193	−	2.96514i	−0.110735	−	0.191799i	0.805332	−	0.592825i	$-0.201987\pi$
$239$	−1.71193	−	2.96514i	−0.110735	−	0.191799i	−0.916067	+	0.401025i	$0.868654\pi$
$240$	9.47060	+	1.67469i	0.611325	+	0.108101i
$241$	8.46332	−	3.08040i	0.545171	−	0.198426i	−0.0547288	−	0.998501i	$-0.517429\pi$
$241$	8.46332	−	3.08040i	0.545171	−	0.198426i	0.599900	+	0.800075i	$0.295207\pi$
$242$	0.768575	−	5.83240i	0.0494059	−	0.374921i
$243$	−10.8818	−	1.91875i	−0.698066	−	0.123088i
$244$	−9.39059	+	6.57194i	−0.601171	+	0.420726i
$245$	−8.65260	−	10.3118i	−0.552794	−	0.658795i
$246$	−4.19630	+	13.3033i	−0.267546	+	0.848187i
$247$	25.5570	−	4.77027i	1.62615	−	0.303525i
$248$	8.31248	+	10.8413i	0.527843	+	0.688421i
$249$	7.11964	−	5.97409i	0.451189	−	0.378593i
$250$	10.4603	−	13.6287i	0.661570	−	0.861957i
$251$	5.43707	+	0.958702i	0.343185	+	0.0605127i	0.342584	−	0.939487i	$-0.388698\pi$
$251$	5.43707	+	0.958702i	0.343185	+	0.0605127i	0.000600364		1.00000i	$0.499809\pi$
$252$	3.66983	−	7.86496i	0.231178	−	0.495446i
$253$	−5.70174	−	15.6654i	−0.358466	−	0.984876i
$254$	−11.7691	+	10.7818i	−0.738462	+	0.676510i
$255$	3.34508	+	5.79385i	0.209477	+	0.362825i
$256$	−16.0000	−	0.0156332i	−1.00000	−	0.000977072i
$257$	−16.0217	−	13.4438i	−0.999404	−	0.838600i	−0.0125022	−	0.999922i	$-0.503980\pi$
$257$	−16.0217	−	13.4438i	−0.999404	−	0.838600i	−0.986902	+	0.161322i	$0.948424\pi$
$258$	1.37580	+	6.20941i	0.0856534	+	0.386581i
$259$	−24.8681	−	14.3576i	−1.54523	−	0.892139i
$260$	20.2788	+	5.43901i	1.25764	+	0.337313i
$261$	4.82951	−	0.851573i	0.298939	−	0.0527110i
$262$	−13.7489	−	7.15936i	−0.849410	−	0.442307i
$263$	−1.63905	−	0.596565i	−0.101068	−	0.0367857i	0.290991	−	0.956726i	$-0.406015\pi$
$263$	−1.63905	−	0.596565i	−0.101068	−	0.0367857i	−0.392059	+	0.919940i	$0.628237\pi$
$264$	9.86509	+	2.19083i	0.607154	+	0.134836i
$265$	−2.67934			−0.164590
$266$	22.5699	+	6.87202i	1.38385	+	0.421350i
$267$		−	10.0474i		−	0.614889i
$268$	0.571755	+	6.55363i	0.0349255	+	0.400327i
$269$	−3.49933	+	9.61432i	−0.213358	+	0.586195i	−0.999492	−	0.0318599i	$-0.989857\pi$
$269$	−3.49933	+	9.61432i	−0.213358	+	0.586195i	0.786135	+	0.618055i	$0.212079\pi$
$270$	6.49201	−	12.4673i	0.395091	−	0.758737i
$271$	−3.72486	−	21.1247i	−0.226269	−	1.28323i	−0.860244	−	0.509882i	$-0.829689\pi$
$271$	−3.72486	−	21.1247i	−0.226269	−	1.28323i	0.633976	−	0.773353i	$-0.281422\pi$
$272$	−7.15003	−	8.52953i	−0.433534	−	0.517179i
$273$	−15.5921	+	27.0063i	−0.943676	+	1.63449i
$274$	6.14798	+	27.7478i	0.371413	+	1.67631i
$275$	3.19781	−	3.81100i	0.192835	−	0.229812i
$276$	−16.8228	+	4.50325i	−1.01261	+	0.271064i
$277$	12.5634	−	7.25348i	0.754862	−	0.435820i	−0.0725863	−	0.997362i	$-0.523125\pi$
$277$	12.5634	−	7.25348i	0.754862	−	0.435820i	0.827448	+	0.561543i	$0.189792\pi$
$278$	−15.7840	−	17.2294i	−0.946662	−	1.03335i
$279$	5.14615	−	1.87304i	0.308092	−	0.112136i
$280$	14.0426	+	12.8772i	0.839208	+	0.769558i
$281$	−4.40069	+	24.9576i	−0.262523	+	1.48884i	0.513473	+	0.858106i	$0.328359\pi$
$281$	−4.40069	+	24.9576i	−0.262523	+	1.48884i	−0.775996	+	0.630738i	$0.782752\pi$
$282$	5.73506	−	7.47218i	0.341518	−	0.444962i
$283$	−7.08527	−	8.44390i	−0.421176	−	0.501938i	0.513179	−	0.858282i	$-0.328468\pi$
$283$	−7.08527	−	8.44390i	−0.421176	−	0.501938i	−0.934355	+	0.356344i	$0.884023\pi$
$284$	2.22989	+	1.56220i	0.132320	+	0.0926994i
$285$	9.88375	+	3.48591i	0.585463	+	0.206487i
$286$	21.0389	+	6.63635i	1.24405	+	0.392416i
$287$	−21.1695	+	17.7633i	−1.24959	+	1.04853i
$288$	−1.93245	+	6.11591i	−0.113870	+	0.360383i
$289$	−1.60759	+	9.11711i	−0.0945643	+	0.536301i
$290$	−1.40652	+	10.6735i	−0.0825936	+	0.626769i
$291$	−5.69599	−	15.6496i	−0.333905	−	0.917395i
$292$	20.3430	−	9.48007i	1.19049	−	0.554779i
$293$	9.23806	−	5.33360i	0.539693	−	0.311592i	−0.205261	−	0.978707i	$-0.565804\pi$
$293$	9.23806	−	5.33360i	0.539693	−	0.311592i	0.744955	+	0.667115i	$0.232471\pi$
$294$	−12.4624	+	7.93731i	−0.726825	+	0.462914i
$295$	−10.1040	−	8.47828i	−0.588279	−	0.493624i
$296$	19.6027	+	8.12814i	1.13939	+	0.472438i
$297$	7.38470	−	12.7907i	0.428504	−	0.742191i
$298$	1.12963	+	25.9454i	0.0654374	+	1.50298i
$299$	−37.4405	+	6.60177i	−2.16524	+	0.381790i
$300$	−3.67395	−	3.67575i	−0.212116	−	0.212220i
$301$	−4.30932	+	11.8398i	−0.248385	+	0.682432i
$302$	−17.3712	+	7.19292i	−0.999603	+	0.413906i
$303$	17.4405			1.00193
$304$	−17.1987	−	2.86428i	−0.986414	−	0.164278i
$305$	−10.0868			−0.577567
$306$	−4.12227	+	1.70691i	−0.235654	+	0.0975775i
$307$	−1.80674	+	4.96398i	−0.103116	+	0.283309i	−0.980512	−	0.196457i	$-0.937056\pi$
$307$	−1.80674	+	4.96398i	−0.103116	+	0.283309i	0.877396	+	0.479766i	$0.159279\pi$
$308$	14.1525	+	14.1594i	0.806414	+	0.806808i
$309$	5.45679	−	0.962179i	0.310426	−	0.0547365i
$310$	0.522941	+	12.0110i	0.0297011	+	0.682178i
$311$	−3.54816	+	6.14559i	−0.201197	+	0.348484i	−0.948915	−	0.315533i	$-0.897817\pi$
$311$	−3.54816	+	6.14559i	−0.201197	+	0.348484i	0.747717	+	0.664017i	$0.231150\pi$
$312$	8.82699	−	21.2882i	0.499730	−	1.20521i
$313$	19.4806	+	16.3462i	1.10111	+	0.923942i	0.997499	−	0.0706759i	$-0.0225156\pi$
$313$	19.4806	+	16.3462i	1.10111	+	0.923942i	0.103612	+	0.994618i	$0.466960\pi$
$314$	−1.20218	+	0.765666i	−0.0678429	+	0.0432090i
$315$	6.61454	−	3.81890i	0.372687	−	0.215171i
$316$	−12.5708	+	5.85812i	−0.707163	+	0.329545i
$317$	−0.393337	−	1.08068i	−0.0220920	−	0.0606973i	0.928156	−	0.372190i	$-0.121393\pi$
$317$	−0.393337	−	1.08068i	−0.0220920	−	0.0606973i	−0.950248	+	0.311493i	$0.899171\pi$
$318$	−0.384228	+	2.91575i	−0.0215464	+	0.163507i
$319$	−1.96429	+	11.1401i	−0.109979	+	0.623724i
$320$	−11.5282	−	8.08470i	−0.644444	−	0.451949i
$321$	1.33079	−	1.11666i	0.0742774	−	0.0623261i
$322$	−32.9025	−	10.3785i	−1.83358	−	0.578373i
$323$	−6.16898	−	10.4425i	−0.343251	−	0.581038i
$324$	−7.06464	−	4.94929i	−0.392480	−	0.274961i
$325$	−7.29267	−	8.69107i	−0.404525	−	0.482094i
$326$	12.9112	−	16.8220i	0.715088	−	0.931685i
$327$	−0.802379	+	4.55052i	−0.0443716	+	0.251644i
$328$	13.8028	−	15.0521i	0.762134	−	0.831112i
$329$	17.5351	−	6.38224i	0.966740	−	0.351864i
$330$	6.00729	+	6.55742i	0.330691	+	0.360974i
$331$	3.68736	−	2.12890i	0.202676	−	0.117015i	−0.395227	−	0.918583i	$-0.629334\pi$
$331$	3.68736	−	2.12890i	0.202676	−	0.117015i	0.597903	+	0.801568i	$0.296001\pi$
$332$	−13.1441	+	3.51852i	−0.721378	+	0.193104i
$333$	5.46815	−	6.51668i	0.299653	−	0.357112i
$334$	−0.729148	−	3.29087i	−0.0398972	−	0.180069i
$335$	−2.89466	+	5.01369i	−0.158152	+	0.273927i
$336$	16.0272	−	13.4350i	0.874353	−	0.732942i
$337$	−4.68326	−	26.5601i	−0.255114	−	1.44682i	−0.795781	−	0.605585i	$-0.792939\pi$
$337$	−4.68326	−	26.5601i	−0.255114	−	1.44682i	0.540667	−	0.841237i	$-0.318172\pi$
$338$	14.7449	−	28.3162i	0.802014	−	1.54020i
$339$	7.14900	−	19.6417i	0.388281	−	1.06679i
$340$	−0.851283	−	9.75766i	−0.0461673	−	0.529183i
$341$			12.6323i			0.684075i
$342$	−3.16599	+	6.23127i	−0.171197	+	0.336948i
$343$	−2.48025			−0.133921
$344$	2.01867	−	9.08988i	0.108840	−	0.490094i
$345$	−14.4016	−	5.24175i	−0.775355	−	0.282206i
$346$	−22.4684	−	11.6998i	−1.20791	−	0.628985i
$347$	−17.6565	+	3.11331i	−0.947849	+	0.167131i	−0.626143	−	0.779708i	$-0.715367\pi$
$347$	−17.6565	+	3.11331i	−0.947849	+	0.167131i	−0.321706	+	0.946840i	$0.604256\pi$
$348$	11.4136	+	3.06124i	0.611831	+	0.164100i
$349$	17.4551	+	10.0777i	0.934352	+	0.539449i	0.888185	−	0.459485i	$-0.151966\pi$
$349$	17.4551	+	10.0777i	0.934352	+	0.539449i	0.0461670	+	0.998934i	$0.485299\pi$
$350$	−2.22716	−	10.0519i	−0.119047	−	0.537297i
$351$	−25.8019	−	21.6504i	−1.37720	−	1.15561i
$352$	−11.7320	−	9.01369i	−0.625319	−	0.480431i
$353$	−5.89589	−	10.2120i	−0.313806	−	0.543529i	0.665377	−	0.746508i	$-0.268271\pi$
$353$	−5.89589	−	10.2120i	−0.313806	−	0.543529i	−0.979183	+	0.202979i	$0.934938\pi$
$354$	−10.6753	+	9.77973i	−0.567387	+	0.519787i
$355$	0.819490	+	2.25153i	0.0434940	+	0.119499i
$356$	−6.21989	+	13.3301i	−0.329654	+	0.706494i
$357$	14.3268	+	2.52620i	0.758255	+	0.133701i
$358$	−19.6394	+	25.5881i	−1.03797	+	1.35237i
$359$	9.80756	−	8.22952i	0.517623	−	0.434338i	−0.346179	−	0.938169i	$-0.612521\pi$
$359$	9.80756	−	8.22952i	0.517623	−	0.434338i	0.863802	+	0.503831i	$0.168077\pi$
$360$	−4.47933	+	3.43450i	−0.236081	+	0.181014i
$361$	−17.9805	−	6.14017i	−0.946342	−	0.323167i
$362$	2.35692	−	7.47201i	0.123877	−	0.392720i
$363$	−3.65269	−	4.35311i	−0.191717	−	0.228479i
$364$	37.4049	−	26.1775i	1.96055	−	1.37208i
$365$	19.4510	+	3.42973i	1.01811	+	0.179520i
$366$	−1.44649	+	10.9768i	−0.0756090	+	0.573766i
$367$	−31.4886	+	11.4609i	−1.64369	+	0.598256i	−0.987679	−	0.156492i	$-0.949981\pi$
$367$	−31.4886	+	11.4609i	−1.64369	+	0.598256i	−0.656015	+	0.754748i	$0.727759\pi$
$368$	25.1070	+	4.43969i	1.30879	+	0.231435i
$369$	−4.09342	−	7.09002i	−0.213095	−	0.369092i
$370$	10.0323	+	15.7518i	0.521553	+	0.818895i
$371$	−3.74504	+	4.46316i	−0.194433	+	0.231716i
$372$	13.1458	+	1.15334i	0.681576	+	0.0597980i
$373$	−27.8103	−	16.0563i	−1.43996	−	0.831363i	−0.442117	−	0.896957i	$-0.645772\pi$
$373$	−27.8103	−	16.0563i	−1.43996	−	0.831363i	−0.997846	+	0.0655941i	$0.979106\pi$
$374$	−0.447658	−	10.2819i	−0.0231478	−	0.531663i
$375$	−2.88177	−	16.3433i	−0.148814	−	0.843966i
$376$	−12.2346	+	6.36321i	−0.630949	+	0.328158i
$377$	24.2413	+	8.82312i	1.24849	+	0.454414i
$378$	−11.6935	−	28.2404i	−0.601449	−	1.45253i
$379$		−	4.90569i		−	0.251989i	−0.992031	−	0.125994i	$-0.959788\pi$
$379$		−	4.90569i		−	0.251989i	0.992031	−	0.125994i	$-0.0402121\pi$
$380$	−10.9551	−	10.7434i	−0.561982	−	0.551127i
$381$			15.4179i			0.789883i
$382$	1.99025	−	0.824104i	0.101830	−	0.0421648i
$383$	−3.08105	−	1.12141i	−0.157434	−	0.0573015i	0.262101	−	0.965041i	$-0.415585\pi$
$383$	−3.08105	−	1.12141i	−0.157434	−	0.0573015i	−0.419535	+	0.907739i	$0.637807\pi$
$384$	−10.4512	+	11.3860i	−0.533338	+	0.581038i
$385$	3.05931	+	17.3502i	0.155917	+	0.884249i
$386$	−13.8015	+	0.600897i	−0.702477	+	0.0305848i
$387$	−3.23257	−	1.86633i	−0.164321	−	0.0948707i
$388$	−2.13098	+	24.2889i	−0.108184	+	1.23308i
$389$	11.9048	−	14.1876i	0.603598	−	0.719340i	−0.374560	−	0.927203i	$-0.622206\pi$
$389$	11.9048	−	14.1876i	0.603598	−	0.719340i	0.978158	+	0.207863i	$0.0666507\pi$
$390$	17.1061	−	10.8948i	0.866201	−	0.551682i
$391$	8.86798	+	15.3598i	0.448473	+	0.776778i
$392$	21.4479	−	2.81568i	1.08328	−	0.142213i
$393$	−14.0706	+	5.12128i	−0.709768	+	0.258334i
$394$	−8.39112	−	1.10576i	−0.422739	−	0.0557071i
$395$	−12.0195	−	2.11937i	−0.604769	−	0.106637i
$396$	−4.85908	+	3.40060i	−0.244178	+	0.170886i
$397$	8.96487	+	10.6839i	0.449934	+	0.536210i	0.942563	−	0.334029i	$-0.108408\pi$
$397$	8.96487	+	10.6839i	0.449934	+	0.536210i	−0.492629	+	0.870240i	$0.663964\pi$
$398$	−6.35858	−	2.00571i	−0.318727	−	0.100537i
$399$	19.6217	−	11.5916i	0.982314	−	0.580308i
$400$	2.59883	+	7.15110i	0.129942	+	0.357555i
$401$	18.4067	−	15.4451i	0.919188	−	0.771291i	−0.0546563	−	0.998505i	$-0.517406\pi$
$401$	18.4067	−	15.4451i	0.919188	−	0.771291i	0.973845	+	0.227215i	$0.0729619\pi$
$402$	5.04097	+	3.86905i	0.251421	+	0.192971i
$403$	28.3705	+	5.00248i	1.41323	+	0.249191i
$404$	−23.1388	−	10.7967i	−1.15120	−	0.537154i
$405$	−2.59627	−	7.13320i	−0.129010	−	0.354452i
$406$	15.8136	+	17.2618i	0.784817	+	0.856688i
$407$	9.81132	+	16.9937i	0.486329	+	0.842346i
$408$	−10.7407	−	0.472892i	−0.531744	−	0.0234117i
$409$	27.4590	+	23.0409i	1.35776	+	1.13930i	0.976667	+	0.214762i	$0.0688974\pi$
$409$	27.4590	+	23.0409i	1.35776	+	1.13930i	0.381095	+	0.924536i	$0.375547\pi$
$410$	17.5470	−	3.88783i	0.866585	−	0.192006i
$411$	23.7753	+	13.7267i	1.17275	+	0.677086i
$412$	−7.83531	−	2.10152i	−0.386018	−	0.103534i
$413$	−28.2457	+	4.98049i	−1.38988	+	0.245074i
$414$	4.72056	−	9.06542i	0.232003	−	0.445541i
$415$	−11.2524	−	4.09553i	−0.552357	−	0.201041i
$416$	−24.8896	+	22.7792i	−1.22031	+	1.11684i
$417$	−22.5710			−1.10531
$418$	−11.0089	−	11.7785i	−0.538463	−	0.576104i
$419$			16.1004i			0.786557i	0.919419	+	0.393279i	$0.128659\pi$
$419$			16.1004i			0.786557i	−0.919419	+	0.393279i	$0.871341\pi$
$420$	18.3348	−	1.59958i	0.894648	−	0.0780513i
$421$	−0.928735	+	2.55168i	−0.0452638	+	0.124361i	−0.960265	−	0.279090i	$-0.909967\pi$
$421$	−0.928735	+	2.55168i	−0.0452638	+	0.124361i	0.915001	+	0.403451i	$0.132189\pi$
$422$	−27.7663	−	14.4585i	−1.35164	−	0.703830i
$423$	0.959958	+	5.44419i	0.0466748	+	0.264706i
$424$	2.31478	−	3.63054i	0.112416	−	0.176315i
$425$	−2.64639	+	4.58368i	−0.128369	+	0.222341i
$426$	2.56771	−	0.568919i	0.124406	−	0.0275642i
$427$	−14.0988	+	16.8023i	−0.682288	+	0.813119i
$428$	−2.45687	+	0.657674i	−0.118757	+	0.0317899i
$429$	18.4548	−	10.6549i	0.891007	−	0.514423i
$430$	6.04213	−	5.53524i	0.291377	−	0.266933i
$431$	27.2647	−	9.92353i	1.31329	−	0.478000i	0.411990	−	0.911188i	$-0.364834\pi$
$431$	27.2647	−	9.92353i	1.31329	−	0.478000i	0.901303	+	0.433189i	$0.142612\pi$
$432$	11.2847	+	19.5678i	0.542936	+	0.941454i
$433$	4.76510	−	27.0242i	0.228996	−	1.29870i	−0.625901	−	0.779903i	$-0.715269\pi$
$433$	4.76510	−	27.0242i	0.228996	−	1.29870i	0.854897	−	0.518798i	$-0.173620\pi$
$434$	20.7385	+	15.9172i	0.995479	+	0.764051i
$435$	6.68455	+	7.96634i	0.320500	+	0.381957i
$436$	3.88157	−	5.54057i	0.185893	−	0.265345i
$437$	26.2023	+	9.24131i	1.25343	+	0.442072i
$438$	6.52170	−	20.6754i	0.311619	−	0.987908i
$439$	−2.72236	+	2.28433i	−0.129931	+	0.109025i	−0.705437	−	0.708772i	$-0.749249\pi$
$439$	−2.72236	+	2.28433i	−0.129931	+	0.109025i	0.575506	+	0.817797i	$0.304805\pi$
$440$	−3.91062	−	12.4188i	−0.186431	−	0.592041i
$441$	1.50581	−	8.53989i	0.0717054	−	0.406661i
$442$	−23.2691	−	3.06632i	−1.10680	−	0.145850i
$443$	11.4208	+	31.3785i	0.542620	+	1.49084i	0.843476	+	0.537167i	$0.180506\pi$
$443$	11.4208	+	31.3785i	0.542620	+	1.49084i	−0.300856	+	0.953670i	$0.597272\pi$
$444$	18.5803	−	8.65861i	0.881781	−	0.410919i
$445$	−11.2108	+	6.47256i	−0.531443	+	0.306829i
$446$	−18.1897	−	28.5599i	−0.861309	−	1.35235i
$447$	19.2170	+	16.1250i	0.908932	+	0.762685i
$448$	−29.5807	+	7.90290i	−1.39756	+	0.373377i
$449$	−5.75115	+	9.96129i	−0.271414	+	0.470102i	−0.969224	−	0.246180i	$-0.920825\pi$
$449$	−5.75115	+	9.96129i	−0.271414	+	0.470102i	0.697810	+	0.716283i	$0.254158\pi$
$450$	3.04722	−	0.132672i	0.143647	−	0.00625420i
$451$	18.5974	−	3.27923i	0.875718	−	0.154413i
$452$	−21.6441	+	21.6336i	−1.01805	+	1.01756i
$453$	−6.21162	+	17.0663i	−0.291847	+	0.801844i
$454$	0.912619	+	2.20402i	0.0428313	+	0.103440i
$455$	40.1779			1.88357
$456$	−13.2624	+	10.3810i	−0.621069	+	0.486136i
$457$	−10.9250			−0.511048			−0.255524	−	0.966803i	$-0.582248\pi$
$457$	−10.9250			−0.511048			−0.255524	+	0.966803i	$0.582248\pi$
$458$	1.94840	+	4.70547i	0.0910426	+	0.219872i
$459$	−5.37419	+	14.7655i	−0.250846	+	0.689193i
$460$	15.8620	+	15.8698i	0.739571	+	0.739932i
$461$	−40.6685	+	7.17095i	−1.89412	+	0.333985i	−0.994676	−	0.103050i	$-0.967140\pi$
$461$	−40.6685	+	7.17095i	−1.89412	+	0.333985i	−0.899445	+	0.437035i	$0.856029\pi$
$462$	19.3198	−	0.841158i	0.898840	−	0.0391342i
$463$	−5.45960	+	9.45631i	−0.253729	+	0.439472i	−0.964550	−	0.263902i	$-0.914991\pi$
$463$	−5.45960	+	9.45631i	−0.253729	+	0.439472i	0.710820	+	0.703374i	$0.248324\pi$
$464$	−13.2476	−	11.1271i	−0.615004	−	0.516562i
$465$	8.89618	+	7.46478i	0.412550	+	0.346171i
$466$	2.96412	+	4.65400i	0.137310	+	0.215592i
$467$	18.6654	−	10.7765i	0.863734	−	0.498677i	−0.00152700	−	0.999999i	$-0.500486\pi$
$467$	18.6654	−	10.7765i	0.863734	−	0.498677i	0.865261	+	0.501322i	$0.167153\pi$
$468$	5.71308	+	12.2596i	0.264087	+	0.566698i
$469$	4.30566	+	11.8297i	0.198817	+	0.546245i
$470$	−12.0320	−	1.58553i	−0.554994	−	0.0731353i
$471$	−0.239076	+	1.35587i	−0.0110160	+	0.0624751i
$472$	20.2174	−	6.36639i	0.930583	−	0.293037i
$473$	6.59562	−	5.53439i	0.303267	−	0.254471i
$474$	−4.03002	+	12.7762i	−0.185105	+	0.586829i
$475$	1.52133	+	8.15062i	0.0698034	+	0.373976i
$476$	−17.4439	−	12.2207i	−0.799540	−	0.560135i
$477$	−1.10947	−	1.32222i	−0.0507993	−	0.0605402i
$478$	3.84110	+	2.94813i	0.175688	+	0.134844i
$479$	−5.48301	+	31.0957i	−0.250525	+	1.42080i	0.556778	+	0.830661i	$0.312037\pi$
$479$	−5.48301	+	31.0957i	−0.250525	+	1.42080i	−0.807303	+	0.590137i	$0.799074\pi$
$480$	−13.2806	+	2.93574i	−0.606175	+	0.133997i
$481$	42.0511	−	15.3054i	1.91737	−	0.697864i
$482$	−9.39182	+	8.60391i	−0.427786	+	0.391897i
$483$	−28.8613	+	16.6631i	−1.31324	+	0.758197i
$484$	2.15130	+	8.03661i	0.0977864	+	0.365301i
$485$	−13.7924	+	16.4371i	−0.626279	+	0.746370i
$486$	15.2566	−	3.38034i	0.692052	−	0.153335i
$487$	8.73788	−	15.1345i	0.395951	−	0.685808i	−0.597271	−	0.802040i	$-0.703748\pi$
$487$	8.73788	−	15.1345i	0.395951	−	0.685808i	0.993222	+	0.116232i	$0.0370816\pi$
$488$	8.71435	−	13.6677i	0.394480	−	0.618710i
$489$	−3.55699	−	20.1727i	−0.160852	−	0.912240i
$490$	16.8848	+	8.79228i	0.762777	+	0.397195i
$491$	3.77132	−	10.3616i	0.170197	−	0.467613i	−0.825042	−	0.565071i	$-0.808849\pi$
$491$	3.77132	−	10.3616i	0.170197	−	0.467613i	0.995240	+	0.0974577i	$0.0310711\pi$
$492$	−1.71456	−	19.6528i	−0.0772984	−	0.886017i
$493$		−	12.0347i		−	0.542015i
$494$	−30.8126	+	20.0602i	−1.38633	+	0.902553i
$495$	−5.21932			−0.234591
$496$	−16.7268	−	9.66815i	−0.751058	−	0.434113i
$497$	4.89597	+	1.78199i	0.219614	+	0.0799331i
$498$	−6.07053	+	11.6579i	−0.272027	+	0.522403i
$499$	27.4017	−	4.83166i	1.22667	−	0.216295i	0.477474	−	0.878646i	$-0.341552\pi$
$499$	27.4017	−	4.83166i	1.22667	−	0.216295i	0.749193	+	0.662351i	$0.230441\pi$
$500$	−6.29414	+	23.4671i	−0.281482	+	1.04948i
$501$	−2.81974	−	1.62798i	−0.125977	−	0.0727326i
$502$	−7.62292	+	1.68898i	−0.340228	+	0.0753831i
$503$	−5.06697	−	4.25169i	−0.225925	−	0.189573i	0.522798	−	0.852457i	$-0.324888\pi$
$503$	−5.06697	−	4.25169i	−0.225925	−	0.189573i	−0.748723	+	0.662883i	$0.769333\pi$
$504$	−0.539876	+	12.2621i	−0.0240480	+	0.546197i
$505$	−11.2352	−	19.4600i	−0.499962	−	0.865960i
$506$	15.9256	+	17.3840i	0.707980	+	0.772814i
$507$	−10.5474	−	28.9787i	−0.468425	−	1.28699i
$508$	9.54457	−	20.4553i	0.423472	−	0.907559i
$509$	12.0534	+	2.12533i	0.534256	+	0.0942038i	0.434266	−	0.900785i	$-0.357008\pi$
$509$	12.0534	+	2.12533i	0.534256	+	0.0942038i	0.0999901	+	0.994988i	$0.468119\pi$
$510$	−7.50547	−	5.76061i	−0.332348	−	0.255084i
$511$	32.9007	−	27.6069i	1.45544	−	1.22126i
$512$	20.9145	−	8.63615i	0.924300	−	0.381668i
$513$	8.64971	+	23.0455i	0.381894	+	1.01748i
$514$	28.2079	+	8.89772i	1.24420	+	0.392462i
$515$	−4.58888	−	5.46882i	−0.202210	−	0.240985i
$516$	−5.15717	−	7.36904i	−0.227032	−	0.324404i
$517$	−12.5579	−	2.21430i	−0.552297	−	0.0973849i
$518$	40.2614	+	5.30552i	1.76898	+	0.233111i
$519$	−22.9941	+	8.36918i	−1.00933	+	0.367366i
$520$	−29.4396	+	3.86483i	−1.29101	+	0.169484i
$521$	−6.12941	−	10.6165i	−0.268534	−	0.465115i	0.699949	−	0.714193i	$-0.253206\pi$
$521$	−6.12941	−	10.6165i	−0.268534	−	0.465115i	−0.968484	+	0.249077i	$0.919873\pi$
$522$	−5.84965	+	3.72563i	−0.256032	+	0.163066i
$523$	6.53118	−	7.78356i	0.285589	−	0.340351i	−0.604109	−	0.796902i	$-0.706471\pi$
$523$	6.53118	−	7.78356i	0.285589	−	0.340351i	0.889697	+	0.456551i	$0.150915\pi$
$524$	21.8382	+	1.91597i	0.954006	+	0.0836995i
$525$	−8.61282	−	4.97261i	−0.375894	−	0.217023i
$526$	2.46439	−	0.107296i	0.107453	−	0.00467833i
$527$	−2.33373	−	13.2352i	−0.101659	−	0.576535i
$528$	−14.0753	+	2.47477i	−0.612550	+	0.107701i
$529$	−16.5664	−	6.02967i	−0.720277	−	0.262159i
$530$	3.50090	−	1.44962i	0.152069	−	0.0629675i
$531$		−	8.49693i		−	0.368735i
$532$	−33.2085	+	3.23197i	−1.43977	+	0.140124i
$533$		−	43.0661i		−	1.86540i
$534$	5.43599	+	13.1282i	0.235238	+	0.568112i
$535$	−2.10327	−	0.765527i	−0.0909322	−	0.0330966i
$536$	−4.29282	−	8.25382i	−0.185422	−	0.356511i
$537$	5.41056	+	30.6848i	0.233483	+	1.32415i
$538$	−0.629377	−	14.4556i	−0.0271344	−	0.623226i
$539$	17.3227	+	10.0013i	0.746142	+	0.430785i
$540$	−1.73738	+	19.8026i	−0.0747647	+	0.852167i
$541$	14.8292	−	17.6728i	0.637557	−	0.759811i	−0.346425	−	0.938078i	$-0.612605\pi$
$541$	14.8292	−	17.6728i	0.637557	−	0.759811i	0.983982	+	0.178267i	$0.0570490\pi$
$542$	16.2962	+	25.5869i	0.699984	+	1.09905i
$543$	−3.78412	−	6.55429i	−0.162392	−	0.281271i
$544$	13.9572	+	7.27651i	0.598411	+	0.311978i
$545$	5.59434	−	2.03617i	0.239635	−	0.0872200i
$546$	5.76168	−	43.7231i	0.246577	−	1.87117i
$547$	−13.3611	−	2.35593i	−0.571281	−	0.100732i	−0.119457	−	0.992839i	$-0.538115\pi$
$547$	−13.3611	−	2.35593i	−0.571281	−	0.100732i	−0.451824	+	0.892107i	$0.649227\pi$
$548$	−23.0457	−	32.9298i	−0.984463	−	1.40669i
$549$	−4.17678	−	4.97770i	−0.178261	−	0.212443i
$550$	−2.11646	+	6.70969i	−0.0902461	+	0.286102i
$551$	−12.2622	−	14.3203i	−0.522386	−	0.610065i
$552$	19.5447	−	14.9858i	0.831879	−	0.637839i
$553$	−20.3307	+	17.0595i	−0.864548	+	0.725442i
$554$	−12.4913	+	16.2749i	−0.530705	+	0.691453i
$555$	17.7655	+	3.13254i	0.754103	+	0.132969i
$556$	29.9456	+	13.9728i	1.26998	+	0.592577i
$557$	12.9729	+	35.6427i	0.549679	+	1.51023i	0.834145	+	0.551545i	$0.185961\pi$
$557$	12.9729	+	35.6427i	0.549679	+	1.51023i	−0.284466	+	0.958686i	$0.591816\pi$
$558$	−5.71072	+	5.23163i	−0.241754	+	0.221472i
$559$	−9.81762	−	17.0046i	−0.415241	−	0.719219i
$560$	−25.3155	−	9.22811i	−1.06978	−	0.389959i
$561$	−7.61548	−	6.39014i	−0.321526	−	0.269792i
$562$	−7.75288	−	34.9912i	−0.327036	−	1.47602i
$563$	24.8787	+	14.3637i	1.04851	+	0.605360i	0.922233	−	0.386635i	$-0.126363\pi$
$563$	24.8787	+	14.3637i	1.04851	+	0.605360i	0.126281	+	0.991995i	$0.459696\pi$
$564$	−3.45087	+	12.8663i	−0.145308	+	0.541767i
$565$	−26.5216	+	4.67647i	−1.11577	+	0.196740i
$566$	13.8263	+	7.19965i	0.581162	+	0.302624i
$567$	−15.5112	−	5.64562i	−0.651410	−	0.237094i
$568$	−3.75884	−	0.834761i	−0.157718	−	0.0350258i
$569$	−14.4506			−0.605800			−0.302900	−	0.953022i	$-0.597955\pi$
$569$	−14.4506			−0.605800			−0.302900	+	0.953022i	$0.597955\pi$
$570$	−14.8004	+	0.792681i	−0.619920	+	0.0332017i
$571$		−	38.7437i		−	1.62137i	−0.585480	−	0.810687i	$-0.699094\pi$
$571$		−	38.7437i		−	1.62137i	0.585480	−	0.810687i	$-0.300906\pi$
$572$	−31.0805	+	2.71154i	−1.29954	+	0.113375i
$573$	0.711676	−	1.95531i	0.0297307	−	0.0816844i
$574$	18.0501	−	34.6635i	0.753395	−	1.44683i
$575$	−2.10543	−	11.9405i	−0.0878026	−	0.497953i
$576$	−0.783941	−	9.03675i	−0.0326642	−	0.376531i
$577$	−15.5793	+	26.9841i	−0.648575	+	1.12336i	0.334889	+	0.942258i	$0.391301\pi$
$577$	−15.5793	+	26.9841i	−0.648575	+	1.12336i	−0.983463	+	0.181107i	$0.942032\pi$
$578$	−2.83216	−	12.7824i	−0.117802	−	0.531680i
$579$	−8.57757	+	10.2223i	−0.356472	+	0.424826i
$580$	−3.93695	−	14.7073i	−0.163473	−	0.610686i
$581$	−22.5502	+	13.0194i	−0.935539	+	0.540134i
$582$	15.9095	+	17.3665i	0.659472	+	0.719864i
$583$	3.74127	−	1.36171i	0.154948	−	0.0563964i
$584$	−21.4518	+	23.3933i	−0.887680	+	0.968020i
$585$	−2.06690	+	11.7219i	−0.0854556	+	0.484643i
$586$	−9.18505	+	11.9672i	−0.379431	+	0.494359i
$587$	11.8358	+	14.1054i	0.488517	+	0.582192i	0.952840	−	0.303474i	$-0.0981467\pi$
$587$	11.8358	+	14.1054i	0.488517	+	0.582192i	−0.464323	+	0.885666i	$0.653702\pi$
$588$	11.9894	−	17.1138i	0.494435	−	0.705760i
$589$	−16.2623	−	13.3710i	−0.670078	−	0.550942i
$590$	17.7893	+	5.61132i	0.732372	+	0.231014i
$591$	−6.26286	+	5.25516i	−0.257619	+	0.216168i
$592$	−30.0111	−	0.0146615i	−1.23345	−	0.000602585i
$593$	1.95725	−	11.1001i	0.0803747	−	0.455828i	−0.917884	−	0.396848i	$-0.870104\pi$
$593$	1.95725	−	11.1001i	0.0803747	−	0.455828i	0.998259	−	0.0589799i	$-0.0187848\pi$
$594$	−2.72884	+	20.7081i	−0.111966	+	0.849662i
$595$	−6.41067	−	17.6132i	−0.262812	−	0.722070i
$596$	−15.5134	−	33.2898i	−0.635454	−	1.36360i
$597$	−5.57760	+	3.22023i	−0.228276	+	0.131795i
$598$	45.3491	−	28.8828i	1.85446	−	1.18110i
$599$	−23.7426	−	19.9224i	−0.970095	−	0.814007i	0.0124703	−	0.999922i	$-0.496030\pi$
$599$	−23.7426	−	19.9224i	−0.970095	−	0.814007i	−0.982566	+	0.185916i	$0.940475\pi$
$600$	6.78921	+	2.81510i	0.277168	+	0.114926i
$601$	−11.2846	+	19.5455i	−0.460307	+	0.797276i	−0.998976	−	0.0452420i	$-0.985594\pi$
$601$	−11.2846	+	19.5455i	−0.460307	+	0.797276i	0.538669	+	0.842518i	$0.318927\pi$
$602$	−0.775059	−	17.8017i	−0.0315891	−	0.725542i
$603$	−3.67282	+	0.647618i	−0.149569	+	0.0263730i
$604$	18.8061	−	18.7970i	0.765211	−	0.764837i
$605$	−2.50410	+	6.87995i	−0.101806	+	0.279710i
$606$	−22.7883	+	9.43595i	−0.925710	+	0.383309i
$607$	−15.7003			−0.637257			−0.318628	−	0.947880i	$-0.603222\pi$
$607$	−15.7003			−0.637257			−0.318628	+	0.947880i	$0.603222\pi$
$608$	24.0220	−	5.56259i	0.974222	−	0.225593i
$609$	22.6134			0.916341
$610$	13.1797	−	5.45732i	0.533630	−	0.220960i
$611$	−9.94610	+	27.3267i	−0.402376	+	1.10552i
$612$	4.46277	−	4.46059i	0.180397	−	0.180309i
$613$	27.8884	−	4.91748i	1.12640	−	0.198615i	0.420752	−	0.907176i	$-0.361766\pi$
$613$	27.8884	−	4.91748i	1.12640	−	0.198615i	0.705650	+	0.708561i	$0.250655\pi$
$614$	−0.324954	−	7.46359i	−0.0131141	−	0.301206i
$615$	8.68040	−	15.0349i	0.350028	−	0.606266i
$616$	−26.1529	−	10.8441i	−1.05373	−	0.436921i
$617$	20.1984	+	16.9484i	0.813155	+	0.682318i	0.951359	−	0.308086i	$-0.0996883\pi$
$617$	20.1984	+	16.9484i	0.813155	+	0.682318i	−0.138203	+	0.990404i	$0.544133\pi$
$618$	−6.60943	+	4.20953i	−0.265870	+	0.169332i
$619$	8.70164	−	5.02389i	0.349748	−	0.201927i	−0.314826	−	0.949149i	$-0.601946\pi$
$619$	8.70164	−	5.02389i	0.349748	−	0.201927i	0.664574	+	0.747222i	$0.268613\pi$
$620$	−7.18167	−	15.4110i	−0.288423	−	0.618919i
$621$	−12.3112	−	33.8248i	−0.494032	−	1.35734i
$622$	1.31114	−	9.94968i	0.0525718	−	0.398946i
$623$	−4.88807	+	27.7216i	−0.195836	+	1.11064i
$624$	−0.0159221	+	32.5915i	−0.000637395	+	1.30470i
$625$	−9.09362	+	7.63045i	−0.363745	+	0.305218i
$626$	−34.2979	−	10.8187i	−1.37082	−	0.432401i
$627$	−15.5727	+	0.155668i	−0.621915	+	0.00621679i
$628$	1.15655	−	1.65086i	0.0461513	−	0.0658766i
$629$	−13.4191	−	15.9923i	−0.535054	−	0.637653i
$630$	−6.57658	+	8.56860i	−0.262017	+	0.341381i
$631$	1.03255	−	5.85590i	0.0411053	−	0.233120i	−0.957333	−	0.288987i	$-0.906681\pi$
$631$	1.03255	−	5.85590i	0.0411053	−	0.233120i	0.998438	+	0.0558677i	$0.0177925\pi$
$632$	13.2559	−	14.4557i	0.527292	−	0.575015i
$633$	−28.4160	+	10.3426i	−1.12943	+	0.411080i
$634$	1.09864	+	1.19924i	0.0436324	+	0.0476281i
$635$	17.2032	−	9.93228i	0.682689	−	0.394151i
$636$	−1.07548	−	4.01769i	−0.0426457	−	0.159312i
$637$	29.3216	−	34.9441i	1.16176	−	1.38454i
$638$	−3.46058	−	15.6187i	−0.137006	−	0.618350i
$639$	−0.771762	+	1.33673i	−0.0305304	+	0.0528803i
$640$	19.4372	+	4.32655i	0.768321	+	0.171022i
$641$	−1.53945	−	8.73067i	−0.0608047	−	0.344841i	−0.999999	−	0.00145435i	$-0.999537\pi$
$641$	−1.53945	−	8.73067i	−0.0608047	−	0.344841i	0.939194	−	0.343386i	$-0.111574\pi$
$642$	−1.13469	+	2.17907i	−0.0447827	+	0.0860011i
$643$	−11.2379	+	30.8759i	−0.443180	+	1.21763i	0.494209	+	0.869343i	$0.335458\pi$
$643$	−11.2379	+	30.8759i	−0.443180	+	1.21763i	−0.937389	+	0.348284i	$0.886765\pi$
$644$	48.6065	−	4.24055i	1.91536	−	0.167101i
$645$		−	7.91536i		−	0.311667i
$646$	13.7104	+	10.3069i	0.539427	+	0.405518i
$647$	−4.85643			−0.190926			−0.0954629	−	0.995433i	$-0.530433\pi$
$647$	−4.85643			−0.190926			−0.0954629	+	0.995433i	$0.530433\pi$
$648$	11.9086	+	2.64465i	0.467815	+	0.103892i
$649$	18.4176	+	6.70345i	0.722953	+	0.263133i
$650$	14.2310	+	7.41040i	0.558186	+	0.290660i
$651$	24.8692	−	4.38512i	0.974702	−	0.171866i
$652$	−7.76889	+	28.9656i	−0.304253	+	1.13438i
$653$	−22.9690	−	13.2611i	−0.898846	−	0.518949i	−0.0220202	−	0.999758i	$-0.507010\pi$
$653$	−22.9690	−	13.2611i	−0.898846	−	0.518949i	−0.876826	+	0.480809i	$0.840343\pi$
$654$	−1.41358	−	6.37995i	−0.0552755	−	0.249476i
$655$	14.7786	+	12.4007i	0.577449	+	0.484537i
$656$	−9.89146	+	27.1353i	−0.386197	+	1.05946i
$657$	6.36182	+	11.0190i	0.248198	+	0.429892i
$658$	−19.4588	+	17.8263i	−0.758583	+	0.694943i
$659$	1.53725	+	4.22355i	0.0598827	+	0.164526i	0.966026	−	0.258444i	$-0.0832097\pi$
$659$	1.53725	+	4.22355i	0.0598827	+	0.164526i	−0.906144	+	0.422970i	$0.860987\pi$
$660$	−11.3971	−	5.31795i	−0.443632	−	0.207001i
$661$	−14.3356	−	2.52775i	−0.557589	−	0.0983179i	−0.112250	−	0.993680i	$-0.535806\pi$
$661$	−14.3356	−	2.52775i	−0.557589	−	0.0983179i	−0.445339	+	0.895362i	$0.646917\pi$
$662$	−3.66620	+	4.77668i	−0.142491	+	0.185651i
$663$	−17.3673	+	14.5729i	−0.674489	+	0.565963i
$664$	15.2708	−	11.7088i	0.592624	−	0.454391i
$665$	−25.5743	−	14.4264i	−0.991728	−	0.559432i
$666$	−3.61908	+	11.4734i	−0.140236	+	0.444584i
$667$	17.7211	+	21.1191i	0.686162	+	0.817736i
$668$	2.73321	+	3.90546i	0.105751	+	0.151107i
$669$	−32.2110	−	5.67967i	−1.24535	−	0.219589i
$670$	1.06965	−	8.11715i	0.0413242	−	0.313593i
$671$	14.0846	−	5.12638i	0.543730	−	0.197902i
$672$	−13.6727	+	26.2259i	−0.527436	+	1.01169i
$673$	−1.27655	−	2.21106i	−0.0492076	−	0.0852300i	0.840372	−	0.542009i	$-0.182336\pi$
$673$	−1.27655	−	2.21106i	−0.0492076	−	0.0852300i	−0.889580	+	0.456779i	$0.849003\pi$
$674$	20.4893	+	32.1704i	0.789218	+	1.23916i
$675$	6.90471	−	8.22872i	0.265763	−	0.316723i
$676$	−3.94598	+	44.9762i	−0.151768	+	1.72985i
$677$	26.8658	+	15.5109i	1.03253	+	0.596134i	0.917710	−	0.397252i	$-0.130036\pi$
$677$	26.8658	+	15.5109i	1.03253	+	0.596134i	0.114825	+	0.993386i	$0.463369\pi$
$678$	1.28580	+	29.5323i	0.0493807	+	1.13418i
$679$	8.10219	+	45.9498i	0.310933	+	1.76339i
$680$	6.39156	+	12.2891i	0.245105	+	0.471264i
$681$	2.16533	+	0.788115i	0.0829756	+	0.0302006i
$682$	−6.83451	−	16.5057i	−0.261707	−	0.632035i
$683$		−	39.1949i		−	1.49975i	−0.661578	−	0.749876i	$-0.730113\pi$
$683$		−	39.1949i		−	1.49975i	0.661578	−	0.749876i	$-0.269887\pi$
$684$	0.765433	−	9.85487i	0.0292671	−	0.376811i
$685$		−	35.3711i		−	1.35146i
$686$	3.24077	−	1.34191i	0.123733	−	0.0512342i
$687$	4.62287	+	1.68259i	0.176374	+	0.0641947i
$688$	2.28030	+	12.9693i	0.0869357	+	0.494449i
$689$	−1.57666	−	8.94169i	−0.0600660	−	0.340651i
$690$	21.6535	−	0.942763i	0.824335	−	0.0358904i
$691$	−0.357391	−	0.206340i	−0.0135958	−	0.00784954i	0.493187	−	0.869923i	$-0.335832\pi$
$691$	−0.357391	−	0.206340i	−0.0135958	−	0.00784954i	−0.506782	+	0.862074i	$0.669165\pi$
$692$	35.6879	+	3.13107i	1.35665	+	0.119025i
$693$	−7.29529	+	8.69419i	−0.277125	+	0.330265i
$694$	21.3860	−	13.6207i	0.811803	−	0.517036i
$695$	14.5404	+	25.1847i	0.551548	+	0.955309i
$696$	−16.5695	+	2.17525i	−0.628067	+	0.0824525i
$697$	−18.8793	+	6.87150i	−0.715104	+	0.260277i
$698$	−28.2598	−	3.72399i	−1.06965	−	0.140955i
$699$	5.24897	+	0.925536i	0.198534	+	0.0350070i
$700$	8.34852	+	11.9291i	0.315544	+	0.450879i
$701$	−0.701629	−	0.836169i	−0.0265002	−	0.0315817i	0.752632	−	0.658442i	$-0.228784\pi$
$701$	−0.701629	−	0.836169i	−0.0265002	−	0.0315817i	−0.779132	+	0.626860i	$0.784340\pi$
$702$	45.4271	+	14.3292i	1.71454	+	0.540821i
$703$	−32.2622	−	5.35675i	−1.21679	−	0.202034i
$704$	20.2061	+	5.43009i	0.761547	+	0.204654i
$705$	−8.98027	+	7.53534i	−0.338216	+	0.283797i
$706$	13.2288	+	10.1534i	0.497872	+	0.382127i
$707$	−48.1200	−	8.48485i	−1.80974	−	0.319106i
$708$	8.65749	−	18.5542i	0.325369	−	0.697310i
$709$	15.5133	+	42.6225i	0.582615	+	1.60072i	0.783695	+	0.621146i	$0.213333\pi$
$709$	15.5133	+	42.6225i	0.582615	+	1.60072i	−0.201080	+	0.979575i	$0.564445\pi$
$710$	−2.28893	−	2.49854i	−0.0859020	−	0.0937685i
$711$	−3.93123	−	6.80908i	−0.147433	−	0.255361i
$712$	0.915021	−	20.7827i	0.0342919	−	0.778864i
$713$	23.5842	+	19.7895i	0.883235	+	0.741122i
$714$	−20.0866	+	4.45052i	−0.751722	+	0.166556i
$715$	−23.7773	−	13.7279i	−0.889222	−	0.513393i
$716$	11.8173	−	44.0598i	0.441634	−	1.64659i
$717$	4.60619	−	0.812195i	0.172021	−	0.0303320i
$718$	−8.36238	+	16.0592i	−0.312081	+	0.599323i
$719$	27.5011	+	10.0096i	1.02562	+	0.373295i	0.799411	−	0.600785i	$-0.205145\pi$
$719$	27.5011	+	10.0096i	1.02562	+	0.373295i	0.226207	+	0.974079i	$0.427367\pi$
$720$	3.99463	−	6.91110i	0.148871	−	0.257561i
$721$	−15.5239			−0.578140
$722$	26.8159	−	1.70518i	0.997984	−	0.0634602i
$723$			12.3035i			0.457574i
$724$	0.963012	+	11.0383i	0.0357901	+	0.410236i
$725$	−2.81386	+	7.73102i	−0.104504	+	0.287123i
$726$	7.12791	+	3.71166i	0.264541	+	0.137753i
$727$	−4.42851	−	25.1153i	−0.164244	−	0.931476i	−0.949840	−	0.312736i	$-0.898754\pi$
$727$	−4.42851	−	25.1153i	−0.164244	−	0.931476i	0.785596	−	0.618740i	$-0.212357\pi$
$728$	−34.7113	+	54.4417i	−1.28648	+	2.01774i
$729$	14.0167	−	24.2776i	0.519137	−	0.899171i
$730$	−27.2708	+	6.04229i	−1.00934	+	0.223635i
$731$	−5.88800	+	7.01705i	−0.217776	+	0.259535i
$732$	−4.04883	−	15.1252i	−0.149649	−	0.559043i
$733$	−24.3750	+	14.0729i	−0.900312	+	0.519795i	−0.877301	−	0.479940i	$-0.840658\pi$
$733$	−24.3750	+	14.0729i	−0.900312	+	0.519795i	−0.0230105	+	0.999735i	$0.507325\pi$
$734$	34.9432	−	32.0117i	1.28978	−	1.18157i
$735$	17.2798	−	6.28935i	0.637377	−	0.231986i
$736$	−35.2076	+	7.78278i	−1.29777	+	0.286877i
$737$	1.49384	−	8.47198i	0.0550262	−	0.312069i
$738$	9.18455	+	7.04933i	0.338088	+	0.259489i
$739$	−23.3977	−	27.8843i	−0.860699	−	1.02574i	−0.999373	−	0.0354033i	$-0.988728\pi$
$739$	−23.3977	−	27.8843i	−0.860699	−	1.02574i	0.138674	−	0.990338i	$-0.455716\pi$
$740$	−21.6307	−	15.1539i	−0.795161	−	0.557068i
$741$	−5.81733	+	35.0361i	−0.213705	+	1.28708i
$742$	2.47864	−	7.85790i	0.0909938	−	0.288473i
$743$	33.0844	−	27.7611i	1.21375	−	1.01845i	0.214619	−	0.976698i	$-0.431149\pi$
$743$	33.0844	−	27.7611i	1.21375	−	1.01845i	0.999128	−	0.0417571i	$-0.0132956\pi$
$744$	−17.8006	+	5.60535i	−0.652603	+	0.205502i
$745$	5.61248	−	31.8300i	0.205626	−	1.16616i
$746$	45.0248	+	5.93322i	1.64848	+	0.217231i
$747$	−2.63834	−	7.24879i	−0.0965320	−	0.265219i
$748$	6.14779	+	13.1924i	0.224785	+	0.482362i
$749$	−4.21503	+	2.43355i	−0.154014	+	0.0889199i
$750$	12.6077	+	19.7955i	0.460370	+	0.722831i
$751$	−21.9887	−	18.4507i	−0.802379	−	0.673276i	0.146397	−	0.989226i	$-0.453232\pi$
$751$	−21.9887	−	18.4507i	−0.802379	−	0.673276i	−0.948776	+	0.315950i	$0.897677\pi$
$752$	12.5433	−	14.9337i	0.457407	−	0.544576i
$753$	−3.77101	+	6.53159i	−0.137423	+	0.238024i
$754$	−36.4481	+	1.58690i	−1.32736	+	0.0577914i
$755$	23.0440	−	4.06329i	0.838658	−	0.147878i
$756$	30.5581	+	30.5731i	1.11139	+	1.11193i
$757$	9.23982	−	25.3862i	0.335827	−	0.922677i	−0.650737	−	0.759303i	$-0.725540\pi$
$757$	9.23982	−	25.3862i	0.335827	−	0.922677i	0.986564	−	0.163374i	$-0.0522378\pi$
$758$	2.65416	+	6.40992i	0.0964034	+	0.232819i
$759$	22.7736			0.826628
$760$	20.1268	+	8.11062i	0.730075	+	0.294203i
$761$	42.3246			1.53427			0.767133	−	0.641488i	$-0.221682\pi$
$761$	42.3246			1.53427			0.767133	+	0.641488i	$0.221682\pi$
$762$	−8.34165	−	20.1455i	−0.302186	−	0.729794i
$763$	4.42768	−	12.1649i	0.160293	−	0.440400i
$764$	−2.15465	+	2.15360i	−0.0779525	+	0.0779144i
$765$	5.46844	−	0.964234i	0.197712	−	0.0348620i
$766$	4.63252	−	0.201693i	0.167380	−	0.00728747i
$767$	22.3486	−	38.7090i	0.806962	−	1.39770i
$768$	7.49567	−	20.5318i	0.270477	−	0.740876i
$769$	−25.9294	−	21.7574i	−0.935038	−	0.784590i	0.0416766	−	0.999131i	$-0.486730\pi$
$769$	−25.9294	−	21.7574i	−0.935038	−	0.784590i	−0.976715	+	0.214541i	$0.931175\pi$
$770$	−13.3845	−	21.0151i	−0.482343	−	0.757331i
$771$	24.7434	−	14.2856i	0.891111	−	0.514483i
$772$	17.7083	−	8.25225i	0.637336	−	0.297005i
$773$	6.59542	+	18.1208i	0.237221	+	0.651759i	0.999987	+	0.00508474i	$0.00161853\pi$
$773$	6.59542	+	18.1208i	0.237221	+	0.651759i	−0.762766	+	0.646674i	$0.776159\pi$
$774$	5.23352	+	0.689656i	0.188115	+	0.0247892i
$775$	−1.59539	+	9.04790i	−0.0573080	+	0.325010i
$776$	−10.3568	−	32.8895i	−0.371786	−	1.18066i
$777$	30.0498	−	25.2147i	1.07803	−	0.904574i
$778$	−7.87916	+	24.9789i	−0.282482	+	0.895536i
$779$	−15.4634	+	27.4127i	−0.554035	+	0.982161i
$780$	−16.4568	+	23.4905i	−0.589248	+	0.841096i
$781$	−2.28858	−	2.72742i	−0.0818917	−	0.0975948i
$782$	−19.8974	−	15.2716i	−0.711528	−	0.546113i
$783$	−4.24131	+	24.0536i	−0.151572	+	0.859607i
$784$	−26.5011	+	15.2831i	−0.946467	+	0.545827i
$785$	1.66688	−	0.606696i	0.0594937	−	0.0216539i
$786$	15.6143	−	14.3043i	0.556942	−	0.510218i
$787$	−19.0253	+	10.9843i	−0.678179	+	0.391547i	−0.799169	−	0.601107i	$-0.794727\pi$
$787$	−19.0253	+	10.9843i	−0.678179	+	0.391547i	0.120990	+	0.992654i	$0.461393\pi$
$788$	11.5623	−	3.09509i	0.411891	−	0.110258i
$789$	1.53161	−	1.82530i	0.0545267	−	0.0649824i
$790$	16.8517	−	3.73378i	0.599558	−	0.132842i
$791$	−29.2805	+	50.7154i	−1.04110	+	1.80323i
$792$	4.50917	−	7.07226i	0.160226	−	0.251302i
$793$	−5.93559	−	33.6624i	−0.210779	−	1.19539i
$794$	−17.4941	−	9.10959i	−0.620844	−	0.323287i
$795$	1.25186	−	3.43944i	0.0443987	−	0.121984i
$796$	9.39346	−	0.819509i	0.332942	−	0.0290467i
$797$		−	0.710570i		−	0.0251697i	−0.999921	−	0.0125848i	$-0.995994\pi$
$797$		−	0.710570i		−	0.0251697i	0.999921	−	0.0125848i	$-0.00400599\pi$
$798$	−19.3668	+	25.7620i	−0.685577	+	0.911966i
$799$	13.5664			0.479945
$800$	−7.26472	−	7.93777i	−0.256847	−	0.280643i
$801$	−7.83634	−	2.85220i	−0.276884	−	0.100777i
$802$	−15.6944	+	30.1397i	−0.554189	+	1.06427i
$803$	−28.9033	+	5.09643i	−1.01997	+	0.179849i
$804$	−8.67998	−	2.32807i	−0.306119	−	0.0821045i
$805$	37.1852	+	21.4689i	1.31061	+	0.756679i
$806$	−39.7762	+	8.81308i	−1.40106	+	0.310428i
$807$	−10.7068	−	8.98411i	−0.376899	−	0.316256i
$808$	36.0752	+	1.58832i	1.26912	+	0.0558769i
$809$	7.13032	+	12.3501i	0.250689	+	0.434205i	0.963716	−	0.266931i	$-0.0860096\pi$
$809$	7.13032	+	12.3501i	0.250689	+	0.434205i	−0.713027	+	0.701137i	$0.752676\pi$
$810$	7.25169	+	7.91577i	0.254798	+	0.278132i
$811$	4.63202	+	12.7264i	0.162652	+	0.446883i	0.994067	−	0.108769i	$-0.0346909\pi$
$811$	4.63202	+	12.7264i	0.162652	+	0.446883i	−0.831415	+	0.555652i	$0.812469\pi$
$812$	−30.0018	−	13.9990i	−1.05286	−	0.491268i
$813$	28.8580	+	5.08844i	1.01209	+	0.178459i
$814$	−22.0140	−	16.8962i	−0.771589	−	0.592211i
$815$	−20.2171	+	16.9642i	−0.708175	+	0.594230i
$816$	14.2900	−	5.19322i	0.500249	−	0.181799i
$817$	0.143436	+	14.3490i	0.00501818	+	0.502009i
$818$	−48.3447	−	15.2495i	−1.69033	−	0.533187i
$819$	16.6371	+	19.8273i	0.581346	+	0.692822i
$820$	−20.8240	+	14.5735i	−0.727205	+	0.508930i
$821$	−21.6215	−	3.81246i	−0.754597	−	0.133056i	−0.216900	−	0.976194i	$-0.569594\pi$
$821$	−21.6215	−	3.81246i	−0.754597	−	0.133056i	−0.537697	+	0.843138i	$0.680706\pi$
$822$	−38.4921	−	5.07236i	−1.34257	−	0.176919i
$823$	−37.4025	+	13.6134i	−1.30377	+	0.474533i	−0.898222	−	0.439541i	$-0.855141\pi$
$823$	−37.4025	+	13.6134i	−1.30377	+	0.474533i	−0.405547	+	0.914074i	$0.632919\pi$
$824$	11.3748	−	1.49329i	0.396261	−	0.0520211i
$825$	3.39805	+	5.88560i	0.118305	+	0.204910i
$826$	34.2121	−	21.7896i	1.19039	−	0.758158i
$827$	8.15261	−	9.71590i	0.283494	−	0.337855i	−0.605439	−	0.795891i	$-0.707003\pi$
$827$	8.15261	−	9.71590i	0.283494	−	0.337855i	0.888933	+	0.458036i	$0.151447\pi$
$828$	−1.26331	+	14.3991i	−0.0439029	+	0.500404i
$829$	38.1089	+	22.0022i	1.32358	+	0.764168i	0.984297	−	0.176518i	$-0.0564834\pi$
$829$	38.1089	+	22.0022i	1.32358	+	0.764168i	0.339280	+	0.940686i	$0.389817\pi$
$830$	16.9185	−	0.736607i	0.587250	−	0.0255680i
$831$	3.44129	+	19.5165i	0.119377	+	0.677021i
$832$	20.1971	−	43.2301i	0.700209	−	1.49873i
$833$	−19.9972	−	7.27839i	−0.692863	−	0.252181i
$834$	29.4920	−	12.2118i	1.02122	−	0.422859i
$835$			4.19500i			0.145174i
$836$	20.7571	+	9.43388i	0.717900	+	0.326278i
$837$			27.2756i			0.942783i
$838$	−8.71092	−	21.0373i	−0.300914	−	0.726721i
$839$	18.6755	+	6.79733i	0.644750	+	0.234670i	0.643639	−	0.765330i	$-0.277424\pi$
$839$	18.6755	+	6.79733i	0.644750	+	0.234670i	0.00111150	+	0.999999i	$0.499646\pi$
$840$	−23.0914	+	12.0099i	−0.796729	+	0.414380i
$841$	1.78737	+	10.1367i	0.0616336	+	0.349541i
$842$	−0.167039	−	3.83658i	−0.00575654	−	0.132217i
$843$	−29.9817	−	17.3099i	−1.03262	−	0.596186i
$844$	44.1029	+	3.86936i	1.51808	+	0.133189i
$845$	−25.5396	+	30.4369i	−0.878589	+	1.04706i
$846$	−4.19982	−	6.59417i	−0.144393	−	0.226712i
$847$	7.96032	+	13.7877i	0.273520	+	0.473750i
$848$	−1.06030	+	5.99616i	−0.0364110	+	0.205909i
$849$	14.1498	−	5.15010i	0.485619	−	0.176751i
$850$	0.977910	−	7.42096i	0.0335420	−	0.254537i
$851$	47.0972	+	8.30450i	1.61447	+	0.284675i
$852$	−3.04724	+	2.13259i	−0.104397	+	0.0730614i
$853$	11.0526	+	13.1720i	0.378434	+	0.451000i	0.921319	−	0.388807i	$-0.127113\pi$
$853$	11.0526	+	13.1720i	0.378434	+	0.451000i	−0.542885	+	0.839807i	$0.682668\pi$
$854$	9.33123	−	29.5823i	0.319308	−	1.01228i
$855$	5.52455	−	6.71917i	0.188936	−	0.229791i
$856$	2.85439	−	2.18859i	0.0975612	−	0.0748046i
$857$	5.45272	−	4.57537i	0.186261	−	0.156292i	−0.544889	−	0.838508i	$-0.683428\pi$
$857$	5.45272	−	4.57537i	0.186261	−	0.156292i	0.731150	+	0.682216i	$0.238984\pi$
$858$	−18.3489	+	23.9067i	−0.626422	+	0.816162i
$859$	−20.8842	−	3.68245i	−0.712559	−	0.125643i	−0.194394	−	0.980924i	$-0.562274\pi$
$859$	−20.8842	−	3.68245i	−0.712559	−	0.125643i	−0.518166	+	0.855280i	$0.673385\pi$
$860$	−4.90006	+	10.5015i	−0.167091	+	0.358099i
$861$	−12.9117	−	35.4746i	−0.440029	−	1.20897i
$862$	−30.2558	+	27.7176i	−1.03052	+	0.944064i
$863$	2.52232	+	4.36878i	0.0858607	+	0.148715i	0.905758	−	0.423796i	$-0.139303\pi$
$863$	2.52232	+	4.36878i	0.0858607	+	0.148715i	−0.819897	+	0.572511i	$0.805969\pi$
$864$	−25.3318	−	19.4624i	−0.861806	−	0.662123i
$865$	24.1512	+	20.2653i	0.821165	+	0.689040i
$866$	8.39487	+	37.8887i	0.285269	+	1.28751i
$867$	−10.9524	−	6.32340i	−0.371965	−	0.214754i
$868$	−35.7093	−	9.57763i	−1.21205	−	0.325086i
$869$	17.8605	−	3.14929i	0.605877	−	0.106832i
$870$	−13.0443	−	6.79246i	−0.442243	−	0.230286i
$871$	−18.4354	−	6.70995i	−0.624661	−	0.227358i
$872$	−2.07412	+	9.33954i	−0.0702385	+	0.316277i
$873$	−13.8227			−0.467827
$874$	−39.2366	+	2.10143i	−1.32720	+	0.0710821i
$875$			46.4948i			1.57181i
$876$	2.66469	+	30.5435i	0.0900317	+	1.03197i
$877$	18.5385	−	50.9342i	0.626001	−	1.71992i	−0.0657963	−	0.997833i	$-0.520959\pi$
$877$	18.5385	−	50.9342i	0.626001	−	1.71992i	0.691798	−	0.722091i	$-0.256819\pi$
$878$	2.32121	−	4.45767i	0.0783369	−	0.150439i
$879$	2.53044	+	14.3508i	0.0853495	+	0.484041i
$880$	11.8287	+	14.1109i	0.398746	+	0.475679i
$881$	−21.6502	+	37.4992i	−0.729412	+	1.26338i	0.227719	+	0.973727i	$0.426873\pi$
$881$	−21.6502	+	37.4992i	−0.729412	+	1.26338i	−0.957132	+	0.289653i	$0.906460\pi$
$882$	2.65285	+	11.9732i	0.0893262	+	0.403158i
$883$	29.3322	−	34.9568i	0.987108	−	1.17639i	0.00278783	−	0.999996i	$-0.499113\pi$
$883$	29.3322	−	34.9568i	0.987108	−	1.17639i	0.984320	−	0.176393i	$-0.0564430\pi$
$884$	32.0631	−	8.58288i	1.07840	−	0.288673i
$885$	15.6044	−	9.00918i	0.524535	−	0.302840i
$886$	−31.8997	−	34.8209i	−1.07169	−	1.16983i
$887$	−9.47441	+	3.44840i	−0.318120	+	0.115786i	−0.496145	−	0.868240i	$-0.665251\pi$
$887$	−9.47441	+	3.44840i	−0.318120	+	0.115786i	0.178025	+	0.984026i	$0.443029\pi$
$888$	−19.5929	+	21.3662i	−0.657495	+	0.717003i
$889$	7.50085	−	42.5394i	0.251570	−	1.42673i
$890$	11.1465	−	14.5227i	0.373630	−	0.486801i
$891$	7.25057	+	8.64090i	0.242903	+	0.289481i
$892$	39.2192	+	27.4758i	1.31316	+	0.919959i
$893$	16.1429	−	13.8228i	0.540203	−	0.462564i
$894$	−33.8337	−	10.6723i	−1.13157	−	0.356934i
$895$	30.7524	−	25.8044i	1.02794	−	0.862545i
$896$	34.3753	−	26.3304i	1.14840	−	0.879637i
$897$	9.01853	−	51.1466i	0.301120	−	1.70774i
$898$	2.12520	−	16.1273i	0.0709189	−	0.538175i
$899$	−7.14495	−	19.6306i	−0.238297	−	0.654717i
$900$	−3.90981	+	1.82201i	−0.130327	+	0.0607337i
$901$	−3.66828	+	2.11788i	−0.122208	+	0.0705570i
$902$	−22.5257	+	14.3466i	−0.750025	+	0.477690i
$903$	−13.1852	−	11.0637i	−0.438775	−	0.368176i
$904$	16.5763	−	39.9773i	0.551320	−	1.32962i
$905$	−4.87549	+	8.44460i	−0.162067	+	0.280708i
$906$	−1.11720	−	25.6600i	−0.0371165	−	0.852497i
$907$	−10.1146	+	1.78348i	−0.335850	+	0.0592195i	−0.339030	−	0.940775i	$-0.610099\pi$
$907$	−10.1146	+	1.78348i	−0.335850	+	0.0592195i	0.00317994	+	0.999995i	$0.498988\pi$
$908$	−2.38491	−	2.38608i	−0.0791460	−	0.0791847i
$909$	4.95092	−	13.6025i	0.164212	−	0.451168i
$910$	−52.4977	+	21.7377i	−1.74028	+	0.720599i
$911$	18.0080			0.596631			0.298316	−	0.954467i	$-0.403575\pi$
$911$	18.0080			0.596631			0.298316	+	0.954467i	$0.403575\pi$
$912$	11.7125	−	20.7396i	0.387841	−	0.686756i
$913$	17.7936			0.588883
$914$	14.2749	−	5.91081i	0.472171	−	0.195512i
$915$	4.71280	−	12.9483i	0.155800	−	0.428058i
$916$	−5.09167	−	5.09415i	−0.168233	−	0.168316i
$917$	41.3136	−	7.28470i	1.36430	−	0.240562i
$918$	−0.966584	−	22.2006i	−0.0319020	−	0.732730i
$919$	3.23798	−	5.60834i	0.106811	−	0.185002i	−0.807666	−	0.589641i	$-0.799269\pi$
$919$	3.23798	−	5.60834i	0.106811	−	0.185002i	0.914477	+	0.404639i	$0.132603\pi$
$920$	−29.3119	−	12.1540i	−0.966385	−	0.400705i
$921$	−5.52806	−	4.63860i	−0.182156	−	0.152847i
$922$	49.2589	−	31.3729i	1.62226	−	1.03321i
$923$	−7.03175	+	4.05978i	−0.231453	+	0.133629i
$924$	−24.7888	+	11.5518i	−0.815490	+	0.380027i
$925$	4.88117	+	13.4109i	0.160492	+	0.440948i
$926$	2.01747	−	15.3097i	0.0662980	−	0.503109i
$927$	0.798604	−	4.52911i	0.0262296	−	0.148755i
$928$	23.3299	+	7.37154i	0.765840	+	0.241983i
$929$	−5.56288	+	4.66781i	−0.182512	+	0.153146i	−0.729466	−	0.684017i	$-0.760232\pi$
$929$	−5.56288	+	4.66781i	−0.182512	+	0.153146i	0.546954	+	0.837162i	$0.315787\pi$
$930$	−15.6627	−	4.94054i	−0.513601	−	0.162007i
$931$	−31.2111	+	11.7145i	−1.02290	+	0.383927i
$932$	−6.39099	−	4.47735i	−0.209344	−	0.146660i
$933$	−6.23125	−	7.42611i	−0.204002	−	0.243120i
$934$	−18.5583	+	24.1796i	−0.607247	+	0.791180i
$935$	−2.22417	+	12.6139i	−0.0727380	+	0.412518i
$936$	−14.0977	−	12.9277i	−0.460799	−	0.422555i
$937$	−10.5825	+	3.85173i	−0.345717	+	0.125831i	−0.509042	−	0.860742i	$-0.670000\pi$
$937$	−10.5825	+	3.85173i	−0.345717	+	0.125831i	0.163325	+	0.986572i	$0.447778\pi$
$938$	−12.0262	−	13.1275i	−0.392670	−	0.428629i
$939$	−30.0853	+	17.3698i	−0.981798	+	0.566841i
$940$	16.5792	−	4.43803i	0.540753	−	0.144753i
$941$	−11.4013	+	13.5876i	−0.371673	+	0.442942i	−0.919168	−	0.393867i	$-0.871137\pi$
$941$	−11.4013	+	13.5876i	−0.371673	+	0.442942i	0.547495	+	0.836809i	$0.315582\pi$
$942$	−0.421190	−	1.90097i	−0.0137231	−	0.0619368i
$943$	23.0122	−	39.8582i	0.749379	−	1.29796i
$944$	−22.9722	+	19.2569i	−0.747683	+	0.626758i
$945$	6.60567	+	37.4626i	0.214882	+	1.21866i
$946$	−5.62373	+	10.7999i	−0.182843	+	0.351134i
$947$	−19.3370	+	53.1281i	−0.628370	+	1.72643i	0.0571383	+	0.998366i	$0.481802\pi$
$947$	−19.3370	+	53.1281i	−0.628370	+	1.72643i	−0.685508	+	0.728065i	$0.740420\pi$
$948$	−1.64662	−	18.8741i	−0.0534799	−	0.613002i
$949$			66.9314i			2.17269i
$950$	−6.39759	−	9.82674i	−0.207565	−	0.318821i
$951$	1.57104			0.0509446
$952$	29.4045	+	6.53013i	0.953007	+	0.211643i
$953$	−14.6290	−	5.32453i	−0.473880	−	0.172478i	0.0940291	−	0.995569i	$-0.470025\pi$
$953$	−14.6290	−	5.32453i	−0.473880	−	0.172478i	−0.567909	+	0.823091i	$0.692248\pi$
$954$	2.16504	+	1.12738i	0.0700957	+	0.0365004i
$955$	−2.64019	+	0.465537i	−0.0854346	+	0.0150644i
$956$	−6.61394	−	1.77393i	−0.213910	−	0.0573731i
$957$	−13.3826	−	7.72647i	−0.432599	−	0.249761i
$958$	−9.65964	−	43.5970i	−0.312089	−	1.40856i
$959$	−58.9202	−	49.4399i	−1.90263	−	1.59650i
$960$	15.7645	−	11.0212i	0.508798	−	0.355709i
$961$	3.83561	+	6.64346i	0.123729	+	0.214305i
$962$	−46.6645	+	42.7496i	−1.50452	+	1.37830i
$963$	−0.493154	−	1.35493i	−0.0158917	−	0.0436620i
$964$	7.61659	−	16.3234i	0.245314	−	0.525742i
$965$	16.9318	+	2.98552i	0.545052	+	0.0961074i
$966$	28.6957	−	37.3875i	0.923269	−	1.20292i
$967$	−20.7509	+	17.4121i	−0.667304	+	0.559935i	−0.912266	−	0.409598i	$-0.865669\pi$
$967$	−20.7509	+	17.4121i	−0.667304	+	0.559935i	0.244962	+	0.969533i	$0.421225\pi$
$968$	−7.15905	−	9.33694i	−0.230101	−	0.300101i
$969$	16.2873	−	3.04006i	0.523223	−	0.0976607i
$970$	9.12843	−	28.9393i	0.293096	−	0.929186i
$971$	−26.6891	−	31.8069i	−0.856495	−	1.02073i	−0.999519	−	0.0310118i	$-0.990127\pi$
$971$	−26.6891	−	31.8069i	−0.856495	−	1.02073i	0.143024	−	0.989719i	$-0.454317\pi$
$972$	−18.1058	+	12.6712i	−0.580743	+	0.406429i
$973$	62.2756	+	10.9809i	1.99647	+	0.352031i
$974$	−3.22888	+	24.5026i	−0.103460	+	0.785115i
$975$	14.5640	−	5.30085i	0.466421	−	0.169763i
$976$	−3.99168	+	22.5735i	−0.127771	+	0.722559i
$977$	22.2421	+	38.5244i	0.711587	+	1.23251i	0.964261	+	0.264954i	$0.0853567\pi$
$977$	22.2421	+	38.5244i	0.711587	+	1.23251i	−0.252674	+	0.967551i	$0.581310\pi$
$978$	15.5618	+	24.4337i	0.497612	+	0.781305i
$979$	12.3646	−	14.7355i	0.395174	−	0.470950i
$980$	−26.8191	−	2.35297i	−0.856704	−	0.0751628i
$981$	3.32135	+	1.91759i	0.106043	+	0.0612238i
$982$	0.678296	+	15.5792i	0.0216453	+	0.497152i
$983$	−1.03224	−	5.85410i	−0.0329232	−	0.186717i	0.963911	−	0.266225i	$-0.0857763\pi$
$983$	−1.03224	−	5.85410i	−0.0329232	−	0.186717i	−0.996834	+	0.0795078i	$0.974665\pi$
$984$	12.8732	+	24.7513i	0.410382	+	0.789043i
$985$	9.89824	+	3.60266i	0.315384	+	0.114790i
$986$	6.51120	+	15.7249i	0.207359	+	0.500782i
$987$			25.4916i			0.811405i
$988$	29.4073	−	42.8820i	0.935572	−	1.36426i
$989$		−	20.9840i		−	0.667252i
$990$	6.81971	−	2.82384i	0.216745	−	0.0897476i
$991$	8.99995	+	3.27572i	0.285893	+	0.104057i	0.480986	−	0.876728i	$-0.340279\pi$
$991$	8.99995	+	3.27572i	0.285893	+	0.104057i	−0.195093	+	0.980785i	$0.562501\pi$
$992$	27.0866	+	3.58285i	0.860001	+	0.113756i
$993$	1.01002	+	5.72811i	0.0320520	+	0.181776i
$994$	−7.36134	+	0.320502i	−0.233487	+	0.0101657i
$995$	7.18623	+	4.14897i	0.227819	+	0.131531i
$996$	1.62458	−	18.5169i	0.0514768	−	0.586732i
$997$	−19.6721	+	23.4443i	−0.623021	+	0.742487i	−0.981587	−	0.191017i	$-0.938821\pi$
$997$	−19.6721	+	23.4443i	−0.623021	+	0.742487i	0.358566	+	0.933504i	$0.383266\pi$
$998$	−33.1897	+	21.1385i	−1.05060	+	0.669127i
$999$	21.1846	+	36.6928i	0.670252	+	1.16091i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	152.2.t.a.101.4	✓	108
4.3	odd	2		608.2.bf.a.177.13		108
8.3	odd	2		608.2.bf.a.177.6		108
8.5	even	2	inner	152.2.t.a.101.6	yes	108
19.16	even	9	inner	152.2.t.a.149.6	yes	108
76.35	odd	18		608.2.bf.a.529.6		108
152.35	odd	18		608.2.bf.a.529.13		108
152.149	even	18	inner	152.2.t.a.149.4	yes	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.2.t.a.101.4	✓	108	1.1	even	1	trivial
152.2.t.a.101.6	yes	108	8.5	even	2	inner
152.2.t.a.149.4	yes	108	152.149	even	18	inner
152.2.t.a.149.6	yes	108	19.16	even	9	inner
608.2.bf.a.177.6		108	8.3	odd	2
608.2.bf.a.177.13		108	4.3	odd	2
608.2.bf.a.529.6		108	76.35	odd	18
608.2.bf.a.529.13		108	152.35	odd	18

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.t (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.30663 + 0.541037i) q^{2} +(-0.467226 + 1.28369i) q^{3} +(1.41456 - 1.41387i) q^{4} +(1.73333 - 0.305632i) q^{5} +(-0.0840336 - 1.93009i) q^{6} +(1.91364 - 3.31452i) q^{7} +(-1.08335 + 2.61273i) q^{8} +(0.868569 + 0.728816i) q^{9} +(-2.09945 + 1.33714i) q^{10} +(-2.26499 + 1.30769i) q^{11} +(1.15405 + 2.47645i) q^{12} +(2.03996 + 5.60474i) q^{13} +(-0.707140 + 5.36619i) q^{14} +(-0.417517 + 2.36785i) q^{15} +(0.00195414 - 4.00000i) q^{16} +(2.13151 - 1.78855i) q^{17} +(-1.52921 - 0.482364i) q^{18} +(0.713969 - 4.30003i) q^{19} +(2.01977 - 2.88303i) q^{20} +(3.36072 + 4.00515i) q^{21} +(2.25199 - 2.93411i) q^{22} +(-1.10686 + 6.27729i) q^{23} +(-2.84777 - 2.61142i) q^{24} +(-1.78746 + 0.650581i) q^{25} +(-5.69783 - 6.21962i) q^{26} +(-4.89056 + 2.82357i) q^{27} +(-1.97934 - 7.39421i) q^{28} +(2.78015 - 3.31326i) q^{29} +(-0.735556 - 3.31980i) q^{30} +(2.41499 - 4.18289i) q^{31} +(2.16159 + 5.22757i) q^{32} +(-0.620412 - 3.51853i) q^{33} +(-1.81742 + 3.49020i) q^{34} +(2.30393 - 6.33001i) q^{35} +(2.25909 - 0.197089i) q^{36} -7.50278i q^{37} +(1.39358 + 6.00483i) q^{38} -8.14787 q^{39} +(-1.07926 + 4.85982i) q^{40} +(-6.78504 - 2.46955i) q^{41} +(-6.55815 - 3.41497i) q^{42} +(-3.24204 + 0.571659i) q^{43} +(-1.35505 + 5.05220i) q^{44} +(1.72826 + 0.997812i) q^{45} +(-1.95000 - 8.80095i) q^{46} +(3.73496 + 3.13400i) q^{47} +(5.13385 + 1.87141i) q^{48} +(-3.82402 - 6.62340i) q^{49} +(1.98356 - 1.81715i) q^{50} +(1.30005 + 3.57186i) q^{51} +(10.8100 + 5.04400i) q^{52} +(-1.49917 - 0.264344i) q^{53} +(4.86250 - 6.33533i) q^{54} +(-3.52629 + 2.95890i) q^{55} +(6.58680 + 8.59060i) q^{56} +(5.18633 + 2.92560i) q^{57} +(-1.84004 + 5.83336i) q^{58} +(-4.81703 - 5.74071i) q^{59} +(2.75723 + 3.93978i) q^{60} +(-5.64385 - 0.995163i) q^{61} +(-0.892404 + 6.77209i) q^{62} +(4.07780 - 1.48420i) q^{63} +(-5.65271 - 5.66100i) q^{64} +(5.24890 + 9.09135i) q^{65} +(2.71430 + 4.26175i) q^{66} +(-2.11430 + 2.51972i) q^{67} +(0.486374 - 5.54368i) q^{68} +(-7.54096 - 4.35377i) q^{69} +(0.414378 + 9.51748i) q^{70} +(0.236392 + 1.34065i) q^{71} +(-2.84516 + 1.47977i) q^{72} +(10.5450 + 3.83807i) q^{73} +(4.05928 + 9.80335i) q^{74} -2.59851i q^{75} +(-5.06972 - 7.09210i) q^{76} +10.0098i q^{77} +(10.6462 - 4.40830i) q^{78} +(-6.51619 - 2.37170i) q^{79} +(-1.21914 - 6.93390i) q^{80} +(-0.748928 - 4.24738i) q^{81} +(10.2016 - 0.444165i) q^{82} +(-5.89196 - 3.40173i) q^{83} +(10.4167 + 0.913906i) q^{84} +(3.14796 - 3.75160i) q^{85} +(3.92686 - 2.50101i) q^{86} +(2.95424 + 5.11690i) q^{87} +(-0.962869 - 7.33448i) q^{88} +(-6.91135 + 2.51553i) q^{89} +(-2.79805 - 0.368718i) q^{90} +(22.4807 + 3.96396i) q^{91} +(7.30955 + 10.4446i) q^{92} +(4.24120 + 5.05446i) q^{93} +(-6.57581 - 2.07423i) q^{94} +(-0.0766864 - 7.67156i) q^{95} +(-7.72054 + 0.332363i) q^{96} +(-9.33891 + 7.83628i) q^{97} +(8.58008 + 6.58539i) q^{98} +(-2.92036 - 0.514939i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 6 q^{2} - 12 q^{4} - 12 q^{6} - 6 q^{7} - 3 q^{8} - 12 q^{9} + 9 q^{10} - 3 q^{12} - 9 q^{14} - 12 q^{15} - 12 q^{17} - 12 q^{18} - 42 q^{20} - 12 q^{22} - 12 q^{23} - 36 q^{24} - 12 q^{25} + 21 q^{26}+ \cdots + 93 q^{98}+O(q^{100}) \) 108 * q - 6 * q^2 - 12 * q^4 - 12 * q^6 - 6 * q^7 - 3 * q^8 - 12 * q^9 + 9 * q^10 - 3 * q^12 - 9 * q^14 - 12 * q^15 - 12 * q^17 - 12 * q^18 - 42 * q^20 - 12 * q^22 - 12 * q^23 - 36 * q^24 - 12 * q^25 + 21 * q^26 + 24 * q^28 - 48 * q^30 + 30 * q^31 + 39 * q^32 - 30 * q^33 - 60 * q^34 + 69 * q^36 - 42 * q^38 - 24 * q^39 + 36 * q^40 - 24 * q^41 - 81 * q^42 + 45 * q^44 - 18 * q^46 - 48 * q^47 - 21 * q^48 - 24 * q^49 - 12 * q^50 + 3 * q^52 + 63 * q^54 - 42 * q^55 + 30 * q^56 - 12 * q^57 - 84 * q^58 + 30 * q^60 - 6 * q^62 + 30 * q^63 + 3 * q^64 - 6 * q^65 + 54 * q^66 + 36 * q^68 + 123 * q^70 - 12 * q^71 + 150 * q^72 + 12 * q^73 + 75 * q^74 + 42 * q^76 + 39 * q^78 - 12 * q^79 + 51 * q^80 - 18 * q^81 + 99 * q^82 + 75 * q^84 - 48 * q^86 - 6 * q^87 - 27 * q^88 - 12 * q^89 + 66 * q^90 - 48 * q^92 + 54 * q^94 - 72 * q^95 + 42 * q^96 - 12 * q^97 + 93 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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