LMFDB - Embedded newform 540.2.be.a.11.34

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [540,2,Mod(11,540)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(540, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 13, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("540.11"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 540 = 2^{2} \cdot 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	540.be (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:	$4.31192170915$
Analytic rank:	$0$
Dimension:	$432$
Relative dimension:	$72$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			11.34
Character	$\chi$	$=$	540.11
Dual form			540.2.be.a.491.34

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.207894 + 1.39885i) q^{2} +(-1.63820 + 0.562416i) q^{3} +(-1.91356 - 0.581624i) q^{4} +(-0.342020 + 0.939693i) q^{5} +(-0.446166 - 2.40851i) q^{6} +(3.58594 + 0.632299i) q^{7} +(1.21142 - 2.55587i) q^{8} +(2.36738 - 1.84270i) q^{9} +(-1.24338 - 0.673791i) q^{10} +(5.64449 - 2.05443i) q^{11} +(3.46190 - 0.123404i) q^{12} +(-3.21163 + 2.69488i) q^{13} +(-1.62999 + 4.88475i) q^{14} +(0.0317976 - 1.73176i) q^{15} +(3.32343 + 2.22594i) q^{16} +(-1.97007 + 1.13742i) q^{17} +(2.08549 + 3.69469i) q^{18} +(6.70166 + 3.86920i) q^{19} +(1.20102 - 1.59923i) q^{20} +(-6.23010 + 0.980964i) q^{21} +(1.70038 + 8.32289i) q^{22} +(-1.02230 - 5.79773i) q^{23} +(-0.547083 + 4.86834i) q^{24} +(-0.766044 - 0.642788i) q^{25} +(-3.10205 - 5.05283i) q^{26} +(-2.84186 + 4.35015i) q^{27} +(-6.49416 - 3.29561i) q^{28} +(1.26653 - 1.50939i) q^{29} +(2.41586 + 0.404502i) q^{30} +(-7.49112 + 1.32089i) q^{31} +(-3.80468 + 4.18622i) q^{32} +(-8.09134 + 6.54011i) q^{33} +(-1.18152 - 2.99230i) q^{34} +(-1.82063 + 3.15343i) q^{35} +(-5.60187 + 2.14919i) q^{36} +(2.70576 + 4.68652i) q^{37} +(-6.80566 + 8.57023i) q^{38} +(3.74564 - 6.22101i) q^{39} +(1.98740 + 2.01252i) q^{40} +(2.78986 + 3.32482i) q^{41} +(-0.0770250 - 8.91890i) q^{42} +(1.67347 + 4.59783i) q^{43} +(-11.9960 + 0.648301i) q^{44} +(0.921879 + 2.85484i) q^{45} +(8.32268 - 0.224728i) q^{46} +(0.129968 - 0.737083i) q^{47} +(-6.69634 - 1.77738i) q^{48} +(5.88135 + 2.14063i) q^{49} +(1.05842 - 0.937950i) q^{50} +(2.58766 - 2.97132i) q^{51} +(7.71305 - 3.28885i) q^{52} -1.52004i q^{53} +(-5.49440 - 4.87971i) q^{54} +6.00674i q^{55} +(5.96016 - 8.39922i) q^{56} +(-13.1547 - 2.56939i) q^{57} +(1.84810 + 2.08547i) q^{58} +(3.24272 + 1.18025i) q^{59} +(-1.06808 + 3.29533i) q^{60} +(0.266750 - 1.51282i) q^{61} +(-0.290366 - 10.7535i) q^{62} +(9.65441 - 5.11092i) q^{63} +(-5.06492 - 6.19246i) q^{64} +(-1.43391 - 3.93965i) q^{65} +(-7.46649 - 12.6782i) q^{66} +(8.49402 + 10.1228i) q^{67} +(4.43140 - 1.03069i) q^{68} +(4.93546 + 8.92287i) q^{69} +(-4.03267 - 3.20237i) q^{70} +(1.22816 + 2.12724i) q^{71} +(-1.84180 - 8.28298i) q^{72} +(-4.32175 + 7.48548i) q^{73} +(-7.11824 + 2.81066i) q^{74} +(1.61645 + 0.622176i) q^{75} +(-10.5736 - 11.3018i) q^{76} +(21.5398 - 3.79805i) q^{77} +(7.92357 + 6.53289i) q^{78} +(2.99597 - 3.57046i) q^{79} +(-3.22838 + 2.36168i) q^{80} +(2.20893 - 8.72471i) q^{81} +(-5.23092 + 3.21138i) q^{82} +(0.175465 + 0.147233i) q^{83} +(12.4922 + 1.74644i) q^{84} +(-0.395022 - 2.24028i) q^{85} +(-6.77957 + 1.38508i) q^{86} +(-1.22592 + 3.18499i) q^{87} +(1.58701 - 16.9153i) q^{88} +(-8.63210 - 4.98374i) q^{89} +(-4.18515 + 0.696066i) q^{90} +(-13.2207 + 7.63297i) q^{91} +(-1.41587 + 11.6889i) q^{92} +(11.5290 - 6.37700i) q^{93} +(1.00405 + 0.335040i) q^{94} +(-5.92796 + 4.97415i) q^{95} +(3.87842 - 8.99766i) q^{96} +(0.147263 - 0.0535994i) q^{97} +(-4.21712 + 7.78209i) q^{98} +(9.57694 - 15.2647i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 432 q + 18 q^{12} + 30 q^{14} + 30 q^{24} + 12 q^{29} - 24 q^{30} + 60 q^{33} - 60 q^{36} - 60 q^{38} + 60 q^{41} - 60 q^{42} - 72 q^{44} + 12 q^{45} - 150 q^{48} + 54 q^{52} - 84 q^{54} - 84 q^{56} - 12 q^{57}+ \cdots + 36 q^{97}+O(q^{100}) $ 432 * q + 18 * q^12 + 30 * q^14 + 30 * q^24 + 12 * q^29 - 24 * q^30 + 60 * q^33 - 60 * q^36 - 60 * q^38 + 60 * q^41 - 60 * q^42 - 72 * q^44 + 12 * q^45 - 150 * q^48 + 54 * q^52 - 84 * q^54 - 84 * q^56 - 12 * q^57 + 54 * q^58 - 198 * q^62 - 48 * q^66 - 138 * q^68 - 48 * q^69 - 84 * q^72 - 84 * q^74 - 48 * q^77 - 78 * q^78 - 66 * q^84 + 54 * q^86 - 36 * q^89 + 120 * q^92 - 54 * q^94 + 210 * q^96 + 36 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/540\mathbb{Z}\right)^\times$.

$n$	$217$	$271$	$461$
$\chi(n)$	$1$	$-1$	$e\left(\frac{13}{18}\right)$

Coefficient data

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

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

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

$2$	−0.207894	+	1.39885i	−0.147003	+	0.989136i
$2$	−0.207894	+	1.39885i	−0.147003	+	0.989136i
$3$	−1.63820	+	0.562416i	−0.945813	+	0.324711i
$3$	−1.63820	+	0.562416i	−0.945813	+	0.324711i
$4$	−1.91356	−	0.581624i	−0.956780	−	0.290812i
$5$	−0.342020	+	0.939693i	−0.152956	+	0.420243i
$5$	−0.342020	+	0.939693i	−0.152956	+	0.420243i
$6$	−0.446166	−	2.40851i	−0.182146	−	0.983271i
$7$	3.58594	+	0.632299i	1.35536	+	0.238986i	0.803676	−	0.595067i	$-0.202875\pi$
$7$	3.58594	+	0.632299i	1.35536	+	0.238986i	0.551683	+	0.834054i	$0.313986\pi$
$8$	1.21142	−	2.55587i	0.428302	−	0.903636i
$9$	2.36738	−	1.84270i	0.789125	−	0.614232i
$10$	−1.24338	−	0.673791i	−0.393193	−	0.213071i
$11$	5.64449	−	2.05443i	1.70188	−	0.619433i	0.705841	−	0.708371i	$-0.250569\pi$
$11$	5.64449	−	2.05443i	1.70188	−	0.619433i	0.996037	+	0.0889379i	$0.0283473\pi$
$12$	3.46190	−	0.123404i	0.999365	−	0.0356237i
$13$	−3.21163	+	2.69488i	−0.890746	+	0.747424i	−0.968360	−	0.249559i	$-0.919714\pi$
$13$	−3.21163	+	2.69488i	−0.890746	+	0.747424i	0.0776138	+	0.996983i	$0.475270\pi$
$14$	−1.62999	+	4.88475i	−0.435632	+	1.30550i
$15$	0.0317976	−	1.73176i	0.00821011	−	0.447138i
$16$	3.32343	+	2.22594i	0.830857	+	0.556486i
$17$	−1.97007	+	1.13742i	−0.477813	+	0.275865i	−0.719505	−	0.694488i	$-0.755631\pi$
$17$	−1.97007	+	1.13742i	−0.477813	+	0.275865i	0.241692	+	0.970353i	$0.422298\pi$
$18$	2.08549	+	3.69469i	0.491556	+	0.870846i
$19$	6.70166	+	3.86920i	1.53747	+	0.887656i	0.998986	+	0.0450173i	$0.0143343\pi$
$19$	6.70166	+	3.86920i	1.53747	+	0.887656i	0.538479	+	0.842639i	$0.318999\pi$
$20$	1.20102	−	1.59923i	0.268557	−	0.357599i
$21$	−6.23010	+	0.980964i	−1.35952	+	0.214064i
$22$	1.70038	+	8.32289i	0.362522	+	1.77445i
$23$	−1.02230	−	5.79773i	−0.213164	−	1.20891i	−0.884065	−	0.467364i	$-0.845204\pi$
$23$	−1.02230	−	5.79773i	−0.213164	−	1.20891i	0.670901	−	0.741546i	$-0.265907\pi$
$24$	−0.547083	+	4.86834i	−0.111673	+	0.993745i
$25$	−0.766044	−	0.642788i	−0.153209	−	0.128558i
$26$	−3.10205	−	5.05283i	−0.608362	−	0.990942i
$27$	−2.84186	+	4.35015i	−0.546917	+	0.837187i
$28$	−6.49416	−	3.29561i	−1.22728	−	0.622812i
$29$	1.26653	−	1.50939i	0.235188	−	0.280286i	−0.635522	−	0.772083i	$-0.719215\pi$
$29$	1.26653	−	1.50939i	0.235188	−	0.280286i	0.870710	+	0.491796i	$0.163660\pi$
$30$	2.41586	+	0.404502i	0.441074	+	0.0738515i
$31$	−7.49112	+	1.32089i	−1.34544	+	0.237238i	−0.799542	−	0.600611i	$-0.794924\pi$
$31$	−7.49112	+	1.32089i	−1.34544	+	0.237238i	−0.545902	+	0.837849i	$0.683813\pi$
$32$	−3.80468	+	4.18622i	−0.672579	+	0.740026i
$33$	−8.09134	+	6.54011i	−1.40852	+	1.13849i
$34$	−1.18152	−	2.99230i	−0.202628	−	0.513175i
$35$	−1.82063	+	3.15343i	−0.307743	+	0.533026i
$36$	−5.60187	+	2.14919i	−0.933645	+	0.358199i
$37$	2.70576	+	4.68652i	0.444824	+	0.770458i	0.998040	−	0.0625797i	$-0.0199327\pi$
$37$	2.70576	+	4.68652i	0.444824	+	0.770458i	−0.553216	+	0.833038i	$0.686599\pi$
$38$	−6.80566	+	8.57023i	−1.10402	+	1.39027i
$39$	3.74564	−	6.22101i	0.599782	−	0.996159i
$40$	1.98740	+	2.01252i	0.314235	+	0.318208i
$41$	2.78986	+	3.32482i	0.435702	+	0.519250i	0.938558	−	0.345120i	$-0.112162\pi$
$41$	2.78986	+	3.32482i	0.435702	+	0.519250i	−0.502856	+	0.864370i	$0.667717\pi$
$42$	−0.0770250	−	8.91890i	−0.0118852	−	1.37622i
$43$	1.67347	+	4.59783i	0.255202	+	0.701162i	0.999447	+	0.0332551i	$0.0105874\pi$
$43$	1.67347	+	4.59783i	0.255202	+	0.701162i	−0.744245	+	0.667907i	$0.767190\pi$
$44$	−11.9960	+	0.648301i	−1.80846	+	0.0977350i
$45$	0.921879	+	2.85484i	0.137426	+	0.425575i
$46$	8.32268	−	0.224728i	1.22711	−	0.0331344i
$47$	0.129968	−	0.737083i	0.0189577	−	0.107515i	−0.973861	−	0.227147i	$-0.927060\pi$
$47$	0.129968	−	0.737083i	0.0189577	−	0.107515i	0.992818	+	0.119632i	$0.0381715\pi$
$48$	−6.69634	−	1.77738i	−0.966533	−	0.256543i
$49$	5.88135	+	2.14063i	0.840192	+	0.305805i
$50$	1.05842	−	0.937950i	0.149683	−	0.132646i
$51$	2.58766	−	2.97132i	0.362345	−	0.416068i
$52$	7.71305	−	3.28885i	1.06961	−	0.456082i
$53$		−	1.52004i		−	0.208794i	−0.994536	−	0.104397i	$-0.966709\pi$
$53$		−	1.52004i		−	0.208794i	0.994536	−	0.104397i	$-0.0332912\pi$
$54$	−5.49440	−	4.87971i	−0.747693	−	0.664044i
$55$			6.00674i			0.809949i
$56$	5.96016	−	8.39922i	0.796460	−	1.12239i
$57$	−13.1547	−	2.56939i	−1.74239	−	0.340324i
$58$	1.84810	+	2.08547i	0.242668	+	0.273836i
$59$	3.24272	+	1.18025i	0.422166	+	0.153656i	0.544363	−	0.838850i	$-0.316772\pi$
$59$	3.24272	+	1.18025i	0.422166	+	0.153656i	−0.122196	+	0.992506i	$0.538994\pi$
$60$	−1.06808	+	3.29533i	−0.137888	+	0.425425i
$61$	0.266750	−	1.51282i	0.0341539	−	0.193696i	−0.962957	−	0.269655i	$-0.913090\pi$
$61$	0.266750	−	1.51282i	0.0341539	−	0.193696i	0.997111	+	0.0759583i	$0.0242016\pi$
$62$	−0.290366	−	10.7535i	−0.0368765	−	1.36570i
$63$	9.65441	−	5.11092i	1.21634	−	0.643916i
$64$	−5.06492	−	6.19246i	−0.633115	−	0.774058i
$65$	−1.43391	−	3.93965i	−0.177855	−	0.488653i
$66$	−7.46649	−	12.6782i	−0.919061	−	1.56058i
$67$	8.49402	+	10.1228i	1.03771	+	1.23669i	0.971040	+	0.238919i	$0.0767930\pi$
$67$	8.49402	+	10.1228i	1.03771	+	1.23669i	0.0666700	+	0.997775i	$0.478763\pi$
$68$	4.43140	−	1.03069i	0.537387	−	0.124989i
$69$	4.93546	+	8.92287i	0.594160	+	1.07419i
$70$	−4.03267	−	3.20237i	−0.481996	−	0.382756i
$71$	1.22816	+	2.12724i	0.145756	+	0.252457i	0.929655	−	0.368432i	$-0.120105\pi$
$71$	1.22816	+	2.12724i	0.145756	+	0.252457i	−0.783899	+	0.620889i	$0.786772\pi$
$72$	−1.84180	−	8.28298i	−0.217059	−	0.976159i
$73$	−4.32175	+	7.48548i	−0.505822	+	0.876110i	0.494155	+	0.869374i	$0.335477\pi$
$73$	−4.32175	+	7.48548i	−0.505822	+	0.876110i	−0.999977	+	0.00673584i	$0.997856\pi$
$74$	−7.11824	+	2.81066i	−0.827479	+	0.326732i
$75$	1.61645	+	0.622176i	0.186651	+	0.0718427i
$76$	−10.5736	−	11.3018i	−1.21288	−	1.29640i
$77$	21.5398	−	3.79805i	2.45469	−	0.432828i
$78$	7.92357	+	6.53289i	0.897167	+	0.739704i
$79$	2.99597	−	3.57046i	0.337073	−	0.401708i	−0.570708	−	0.821153i	$-0.693331\pi$
$79$	2.99597	−	3.57046i	0.337073	−	0.401708i	0.907780	+	0.419446i	$0.137776\pi$
$80$	−3.22838	+	2.36168i	−0.360944	+	0.264044i
$81$	2.20893	−	8.72471i	0.245437	−	0.969413i
$82$	−5.23092	+	3.21138i	−0.577658	+	0.354638i
$83$	0.175465	+	0.147233i	0.0192598	+	0.0161609i	0.652367	−	0.757903i	$-0.273776\pi$
$83$	0.175465	+	0.147233i	0.0192598	+	0.0161609i	−0.633107	+	0.774064i	$0.718221\pi$
$84$	12.4922	+	1.74644i	1.36301	+	0.190552i
$85$	−0.395022	−	2.24028i	−0.0428462	−	0.242993i
$86$	−6.77957	+	1.38508i	−0.731060	+	0.149357i
$87$	−1.22592	+	3.18499i	−0.131432	+	0.341467i
$88$	1.58701	−	16.9153i	0.169176	−	1.80318i
$89$	−8.63210	−	4.98374i	−0.915000	−	0.528276i	−0.0329637	−	0.999457i	$-0.510495\pi$
$89$	−8.63210	−	4.98374i	−0.915000	−	0.528276i	−0.882037	+	0.471181i	$0.843828\pi$
$90$	−4.18515	+	0.696066i	−0.441154	+	0.0733718i
$91$	−13.2207	+	7.63297i	−1.38590	+	0.800153i
$92$	−1.41587	+	11.6889i	−0.147615	+	1.21865i
$93$	11.5290	−	6.37700i	1.19550	−	0.661264i
$94$	1.00405	+	0.335040i	0.103560	+	0.0345567i
$95$	−5.92796	+	4.97415i	−0.608196	+	0.510337i
$96$	3.87842	−	8.99766i	0.395839	−	0.918320i
$97$	0.147263	−	0.0535994i	0.0149523	−	0.00544219i	−0.334533	−	0.942384i	$-0.608579\pi$
$97$	0.147263	−	0.0535994i	0.0149523	−	0.00544219i	0.349485	+	0.936942i	$0.386356\pi$
$98$	−4.21712	+	7.78209i	−0.425993	+	0.786110i
$99$	9.57694	−	15.2647i	0.962519	−	1.53416i
$100$	1.09201	+	1.67556i	0.109201	+	0.167556i
$101$	−12.3469	−	2.17709i	−1.22856	−	0.216629i	−0.478555	−	0.878058i	$-0.658839\pi$
$101$	−12.3469	−	2.17709i	−1.22856	−	0.216629i	−0.750008	+	0.661429i	$0.769950\pi$
$102$	3.61847	+	4.23747i	0.358282	+	0.419572i
$103$	4.96223	−	13.6336i	0.488943	−	1.34336i	−0.412695	−	0.910869i	$-0.635412\pi$
$103$	4.96223	−	13.6336i	0.488943	−	1.34336i	0.901638	−	0.432491i	$-0.142365\pi$
$104$	2.99711	+	11.4731i	0.293891	+	1.12503i
$105$	1.20901	−	6.18989i	0.117988	−	0.604071i
$106$	2.12631	+	0.316007i	0.206525	+	0.0306933i
$107$	6.23075			0.602350			0.301175	−	0.953569i	$-0.402621\pi$
$107$	6.23075			0.602350			0.301175	+	0.953569i	$0.402621\pi$
$108$	7.96823	−	6.67138i	0.766743	−	0.641954i
$109$	13.7678			1.31871			0.659357	−	0.751830i	$-0.270829\pi$
$109$	13.7678			1.31871			0.659357	+	0.751830i	$0.270829\pi$
$110$	−8.40253	−	1.24876i	−0.801150	−	0.119065i
$111$	−7.06834	−	6.15567i	−0.670897	−	0.584270i
$112$	10.5102	+	10.0835i	0.993117	+	0.952802i
$113$	−4.21681	+	11.5856i	−0.396684	+	1.08988i	0.567205	+	0.823577i	$0.308025\pi$
$113$	−4.21681	+	11.5856i	−0.396684	+	1.08988i	−0.963889	+	0.266304i	$0.914197\pi$
$114$	6.32898	−	17.8673i	0.592763	−	1.67343i
$115$	5.79773	+	1.02230i	0.540641	+	0.0953296i
$116$	−3.30147	+	2.15166i	−0.306534	+	0.199777i
$117$	−2.63729	+	12.2978i	−0.243818	+	1.13694i
$118$	−2.32514	+	4.29071i	−0.214046	+	0.394992i
$119$	−7.78376	+	2.83306i	−0.713536	+	0.259706i
$120$	−4.38763	−	2.17916i	−0.400534	−	0.198929i
$121$	19.2131	−	16.1217i	1.74665	−	1.46561i
$122$	2.06075	+	0.687648i	0.186571	+	0.0622567i
$123$	−6.44027	−	3.87765i	−0.580699	−	0.349636i
$124$	15.1030	+	1.82941i	1.35629	+	0.164286i
$125$	0.866025	−	0.500000i	0.0774597	−	0.0447214i
$126$	5.14232	+	14.5676i	0.458114	+	1.29778i
$127$	−6.48023	−	3.74136i	−0.575028	−	0.331992i	0.184127	−	0.982902i	$-0.441054\pi$
$127$	−6.48023	−	3.74136i	−0.575028	−	0.331992i	−0.759155	+	0.650910i	$0.774387\pi$
$128$	9.71529	−	5.79769i	0.858718	−	0.512448i
$129$	−5.32737	−	6.59096i	−0.469049	−	0.580301i
$130$	5.80907	−	1.18680i	0.509490	−	0.104090i
$131$	−1.04592	−	5.93173i	−0.0913828	−	0.518258i	−0.995796	−	0.0915997i	$-0.970802\pi$
$131$	−1.04592	−	5.93173i	−0.0913828	−	0.518258i	0.904413	−	0.426658i	$-0.140309\pi$
$132$	19.2872	−	7.80878i	1.67873	−	0.679667i
$133$	21.5853	+	18.1122i	1.87168	+	1.57053i
$134$	−15.9261	+	9.77739i	−1.37580	+	0.844638i
$135$	−3.11583	−	4.15832i	−0.268168	−	0.357891i
$136$	0.520513	+	6.41314i	0.0446336	+	0.549922i
$137$	−0.104174	+	0.124150i	−0.00890021	+	0.0106069i	−0.770476	−	0.637469i	$-0.779981\pi$
$137$	−0.104174	+	0.124150i	−0.00890021	+	0.0106069i	0.761576	+	0.648076i	$0.224426\pi$
$138$	−13.5078	+	5.04896i	−1.14986	+	0.429796i
$139$	−19.2018	+	3.38579i	−1.62868	+	0.287179i	−0.911988	−	0.410216i	$-0.865453\pi$
$139$	−19.2018	+	3.38579i	−1.62868	+	0.287179i	−0.716687	+	0.697395i	$0.754342\pi$
$140$	5.31800	−	4.97535i	0.449453	−	0.420494i
$141$	0.201635	+	1.28058i	0.0169807	+	0.107845i
$142$	−3.23102	+	1.27578i	−0.271141	+	0.107061i
$143$	−12.5916	+	21.8093i	−1.05296	+	1.82378i
$144$	11.9695	−	0.854427i	0.997462	−	0.0712022i
$145$	0.985183	+	1.70639i	0.0818150	+	0.141708i
$146$	−9.57260	−	7.60166i	−0.792234	−	0.629118i
$147$	−10.8387	−	0.199015i	−0.893963	−	0.0164145i
$148$	−2.45185	−	10.5417i	−0.201541	−	0.866520i
$149$	1.65752	+	1.97536i	0.135789	+	0.161828i	0.829654	−	0.558278i	$-0.188538\pi$
$149$	1.65752	+	1.97536i	0.135789	+	0.161828i	−0.693864	+	0.720106i	$0.744093\pi$
$150$	−1.20638	+	2.13182i	−0.0985005	+	0.174062i
$151$	−0.990244	−	2.72067i	−0.0805849	−	0.221405i	0.892857	−	0.450341i	$-0.148698\pi$
$151$	−0.990244	−	2.72067i	−0.0805849	−	0.221405i	−0.973442	+	0.228936i	$0.926475\pi$
$152$	18.0077	−	12.4413i	1.46062	−	1.00912i
$153$	−2.56798	+	6.32295i	−0.207609	+	0.511180i
$154$	0.834914	+	30.9206i	0.0672793	+	2.49165i
$155$	1.32089	−	7.49112i	0.106096	−	0.601701i
$156$	−10.7858	+	9.72573i	−0.863554	+	0.778682i
$157$	−0.575626	−	0.209511i	−0.0459399	−	0.0167208i	0.318948	−	0.947772i	$-0.396670\pi$
$157$	−0.575626	−	0.209511i	−0.0459399	−	0.0167208i	−0.364888	+	0.931051i	$0.618893\pi$
$158$	4.37169	+	4.93318i	0.347793	+	0.392463i
$159$	0.854896	+	2.49013i	0.0677977	+	0.197480i
$160$	−2.63248	−	5.00700i	−0.208116	−	0.395838i
$161$		−	21.4367i		−	1.68945i
$162$	11.7453	+	4.90378i	0.922801	+	0.385277i
$163$		−	14.9317i		−	1.16954i	−0.811199	−	0.584770i	$-0.801185\pi$
$163$		−	14.9317i		−	1.16954i	0.811199	−	0.584770i	$-0.198815\pi$
$164$	−3.40477	−	7.98490i	−0.265868	−	0.623516i
$165$	−3.37829	−	9.84022i	−0.263000	−	0.766060i
$166$	−0.242435	+	0.214841i	−0.0188166	+	0.0166749i
$167$	8.48836	+	3.08951i	0.656849	+	0.239073i	0.648875	−	0.760895i	$-0.275240\pi$
$167$	8.48836	+	3.08951i	0.656849	+	0.239073i	0.00797347	+	0.999968i	$0.497462\pi$
$168$	−5.04005	+	17.1117i	−0.388849	+	1.32019i
$169$	0.794775	−	4.50739i	0.0611365	−	0.346723i
$170$	3.21594	−	0.0868365i	0.246652	−	0.00666006i
$171$	22.9951	−	3.18927i	1.75848	−	0.243889i
$172$	−0.528086	−	9.77155i	−0.0402662	−	0.745074i
$173$	−3.40571	−	9.35712i	−0.258932	−	0.711409i	−0.999234	−	0.0391347i	$-0.987540\pi$
$173$	−3.40571	−	9.35712i	−0.258932	−	0.711409i	0.740302	−	0.672274i	$-0.234682\pi$
$174$	−4.20046	−	2.37701i	−0.318436	−	0.180201i
$175$	−2.34056	−	2.78937i	−0.176930	−	0.210857i
$176$	23.3321	+	5.73658i	1.75872	+	0.432411i
$177$	−5.97601	−	0.109728i	−0.449184	−	0.00824768i
$178$	8.76606	−	11.0389i	0.657044	−	0.827402i
$179$	2.36748	+	4.10059i	0.176954	+	0.306493i	0.940836	−	0.338863i	$-0.110042\pi$
$179$	2.36748	+	4.10059i	0.176954	+	0.306493i	−0.763882	+	0.645356i	$0.776709\pi$
$180$	−0.103626	−	5.99911i	−0.00772383	−	0.447147i
$181$	−6.26781	+	10.8562i	−0.465883	+	0.806932i	−0.999241	−	0.0389572i	$-0.987596\pi$
$181$	−6.26781	+	10.8562i	−0.465883	+	0.806932i	0.533358	+	0.845889i	$0.320930\pi$
$182$	−7.92888	−	20.0806i	−0.587728	−	1.48847i
$183$	0.413843	+	2.62831i	0.0305922	+	0.194291i
$184$	−16.0567	−	4.41064i	−1.18371	−	0.325157i
$185$	−5.32931	+	0.939701i	−0.391819	+	0.0690882i
$186$	6.52365	+	17.4531i	0.478337	+	1.27972i
$187$	−8.78331	+	10.4675i	−0.642299	+	0.765462i
$188$	−0.677406	+	1.33486i	−0.0494049	+	0.0973547i
$189$	−12.9414	+	13.8025i	−0.941345	+	1.00398i
$190$	−5.72571	−	9.32642i	−0.415386	−	0.676610i
$191$	8.36363	+	7.01792i	0.605171	+	0.507799i	0.893103	−	0.449852i	$-0.148523\pi$
$191$	8.36363	+	7.01792i	0.605171	+	0.507799i	−0.287932	+	0.957651i	$0.592968\pi$
$192$	11.7801	+	7.29588i	0.850154	+	0.526535i
$193$	−2.47340	−	14.0274i	−0.178039	−	1.00971i	−0.934577	−	0.355762i	$-0.884222\pi$
$193$	−2.47340	−	14.0274i	−0.178039	−	1.00971i	0.756537	−	0.653951i	$-0.226890\pi$
$194$	0.0443624	+	0.217142i	0.00318504	+	0.0155899i
$195$	4.56476	+	5.64746i	0.326889	+	0.404423i
$196$	−10.0093	−	7.51696i	−0.714948	−	0.536926i
$197$	−13.4996	−	7.79403i	−0.961810	−	0.555301i	−0.0650805	−	0.997880i	$-0.520730\pi$
$197$	−13.4996	−	7.79403i	−0.961810	−	0.555301i	−0.896730	+	0.442579i	$0.854064\pi$
$198$	19.3620	+	16.5701i	1.37600	+	1.17759i
$199$	17.1841	−	9.92127i	1.21815	−	0.703300i	0.253629	−	0.967302i	$-0.418376\pi$
$199$	17.1841	−	9.92127i	1.21815	−	0.703300i	0.964522	+	0.264002i	$0.0850424\pi$
$200$	−2.57088	+	1.17922i	−0.181789	+	0.0833836i
$201$	−19.6081	−	11.8059i	−1.38305	−	0.832726i
$202$	5.61227	−	16.8189i	0.394878	−	1.18337i
$203$	5.49608	−	4.61176i	0.385749	−	0.323682i
$204$	−6.67984	+	4.18076i	−0.467682	+	0.292712i
$205$	−4.07850	+	1.48445i	−0.284855	+	0.103679i
$206$	18.0398	+	9.77576i	1.25689	+	0.681109i
$207$	−13.1036	−	11.8416i	−0.910765	−	0.823050i
$208$	−16.6723	+	1.80732i	−1.15601	+	0.125315i
$209$	45.7764	+	8.07162i	3.16642	+	0.558326i
$210$	8.40737	+	2.97806i	0.580164	+	0.205506i
$211$	−8.05932	+	22.1428i	−0.554826	+	1.52437i	0.272217	+	0.962236i	$0.412243\pi$
$211$	−8.05932	+	22.1428i	−0.554826	+	1.52437i	−0.827044	+	0.562137i	$0.809979\pi$
$212$	−0.884092	+	2.90869i	−0.0607197	+	0.199770i
$213$	−3.20837	−	2.79410i	−0.219834	−	0.191449i
$214$	−1.29533	+	8.71589i	−0.0885472	+	0.595806i
$215$	−4.89291			−0.333693
$216$	7.67572	+	12.5333i	0.522267	+	0.852782i
$217$	−27.6979			−1.88026
$218$	−2.86223	+	19.2590i	−0.193855	+	1.30439i
$219$	2.86991	−	14.6933i	0.193931	−	0.992882i
$220$	3.49366	−	11.4943i	0.235543	−	0.774943i
$221$	3.26193	−	8.96208i	0.219421	−	0.602855i
$222$	10.0803	−	8.60782i	0.676547	−	0.577719i
$223$	−4.29641	−	0.757574i	−0.287709	−	0.0507309i	0.0279310	−	0.999610i	$-0.491108\pi$
$223$	−4.29641	−	0.757574i	−0.287709	−	0.0507309i	−0.315640	+	0.948879i	$0.602219\pi$
$224$	−16.2903	+	12.6058i	−1.08844	+	0.842263i
$225$	−2.99798	−	0.110132i	−0.199865	−	0.00734211i
$226$	−15.3299	−	8.30726i	−1.01973	−	0.552590i
$227$	−7.70653	+	2.80495i	−0.511500	+	0.186171i	−0.584859	−	0.811135i	$-0.698850\pi$
$227$	−7.70653	+	2.80495i	−0.511500	+	0.186171i	0.0733591	+	0.997306i	$0.476628\pi$
$228$	23.6780	+	12.5678i	1.56811	+	0.832322i
$229$	−11.8639	+	9.95501i	−0.783990	+	0.657845i	−0.944250	−	0.329229i	$-0.893211\pi$
$229$	−11.8639	+	9.95501i	−0.783990	+	0.657845i	0.160260	+	0.987075i	$0.448767\pi$
$230$	−2.63535	+	7.89762i	−0.173770	+	0.520754i
$231$	−33.1504	+	18.3363i	−2.18114	+	1.20644i
$232$	−2.32350	−	5.06558i	−0.152545	−	0.332572i
$233$	2.40784	−	1.39017i	0.157743	−	0.0910728i	−0.419051	−	0.907963i	$-0.637637\pi$
$233$	2.40784	−	1.39017i	0.157743	−	0.0910728i	0.576793	+	0.816890i	$0.304304\pi$
$234$	−16.6546	−	6.24582i	−1.08874	−	0.408302i
$235$	0.648180	+	0.374227i	0.0422826	+	0.0244119i
$236$	−5.51868	−	4.14453i	−0.359235	−	0.269786i
$237$	−2.89990	+	7.53409i	−0.188369	+	0.489392i
$238$	−2.34483	−	11.4773i	−0.151993	−	0.743962i
$239$	−5.10894	−	28.9742i	−0.330470	−	1.87419i	−0.468057	−	0.883699i	$-0.655046\pi$
$239$	−5.10894	−	28.9742i	−0.330470	−	1.87419i	0.137587	−	0.990490i	$-0.456065\pi$
$240$	3.96048	−	5.68460i	0.255648	−	0.366939i
$241$	15.9925	+	13.4193i	1.03017	+	0.864416i	0.990871	−	0.134812i	$-0.0430430\pi$
$241$	15.9925	+	13.4193i	1.03017	+	0.864416i	0.0392993	+	0.999227i	$0.487487\pi$
$242$	18.5576	+	30.2279i	1.19293	+	1.94312i
$243$	1.28826	+	15.5351i	0.0826416	+	0.996579i
$244$	−1.39033	+	2.73972i	−0.0890069	+	0.175392i
$245$	−4.02308	+	4.79452i	−0.257025	+	0.306310i
$246$	6.76314	−	8.20283i	0.431202	−	0.522993i
$247$	−31.9503	+	5.63369i	−2.03295	+	0.358463i
$248$	−5.69888	+	20.7465i	−0.361880	+	1.31740i
$249$	−0.370253	−	0.142512i	−0.0234638	−	0.00903132i
$250$	0.519384	+	1.31539i	0.0328487	+	0.0831923i
$251$	10.3468	−	17.9212i	0.653085	−	1.13118i	−0.329285	−	0.944231i	$-0.606808\pi$
$251$	10.3468	−	17.9212i	0.653085	−	1.13118i	0.982370	−	0.186946i	$-0.0598590\pi$
$252$	−21.4469	+	4.16482i	−1.35103	+	0.262359i
$253$	−17.6814	−	30.6250i	−1.11162	−	1.92538i
$254$	6.58080	−	8.28706i	0.412916	−	0.519977i
$255$	1.90710	+	3.44786i	0.119427	+	0.215913i
$256$	6.09035	+	14.7955i	0.380647	+	0.924721i
$257$	−5.62594	−	6.70474i	−0.350937	−	0.418230i	0.561481	−	0.827489i	$-0.310232\pi$
$257$	−5.62594	−	6.70474i	−0.350937	−	0.418230i	−0.912418	+	0.409259i	$0.865787\pi$
$258$	10.3273	−	6.08197i	0.642948	−	0.378647i
$259$	6.73943	+	18.5164i	0.418768	+	1.15056i
$260$	0.452490	+	8.37275i	0.0280622	+	0.519256i
$261$	0.217000	−	5.90711i	0.0134319	−	0.365641i
$262$	8.51504	−	0.229922i	0.526061	−	0.0142046i
$263$	1.84046	−	10.4378i	0.113488	−	0.643620i	−0.874000	−	0.485925i	$-0.838483\pi$
$263$	1.84046	−	10.4378i	0.113488	−	0.643620i	0.987488	−	0.157695i	$-0.0504062\pi$
$264$	6.91363	+	28.6032i	0.425505	+	1.76041i
$265$	1.42837	+	0.519885i	0.0877442	+	0.0319363i
$266$	−29.8237	+	26.4291i	−1.82861	+	1.62047i
$267$	16.9440	+	3.30952i	1.03696	+	0.202539i
$268$	−10.3662	−	24.3109i	−0.633215	−	1.48502i
$269$		−	22.6197i		−	1.37915i	−0.724216	−	0.689574i	$-0.757798\pi$
$269$		−	22.6197i		−	1.37915i	0.724216	−	0.689574i	$-0.242202\pi$
$270$	6.46462	−	3.49409i	0.393424	−	0.212644i
$271$		−	13.9601i		−	0.848018i	−0.905658	−	0.424009i	$-0.860622\pi$
$271$		−	13.9601i		−	0.848018i	0.905658	−	0.424009i	$-0.139378\pi$
$272$	−9.07923	−	0.605131i	−0.550509	−	0.0366915i
$273$	17.3652	−	19.9398i	1.05099	−	1.20681i
$274$	−0.152010	−	0.171534i	−0.00918326	−	0.0103628i
$275$	−5.64449	−	2.05443i	−0.340376	−	0.123887i
$276$	−4.25456	−	19.9450i	−0.256094	−	1.20055i
$277$	−1.35936	+	7.70929i	−0.0816758	+	0.463207i	0.916349	+	0.400381i	$0.131122\pi$
$277$	−1.35936	+	7.70929i	−0.0816758	+	0.463207i	−0.998025	+	0.0628254i	$0.979989\pi$
$278$	−0.744288	−	27.5643i	−0.0446395	−	1.65320i
$279$	−15.3003	+	16.9309i	−0.916005	+	1.01363i
$280$	5.85419	+	8.47342i	0.349855	+	0.506384i
$281$	1.60795	+	4.41781i	0.0959223	+	0.263544i	0.978369	−	0.206869i	$-0.0663273\pi$
$281$	1.60795	+	4.41781i	0.0959223	+	0.263544i	−0.882446	+	0.470413i	$0.844105\pi$
$282$	−1.83326	+	0.0158323i	−0.109169	+	0.000942801i
$283$	−7.22664	−	8.61237i	−0.429579	−	0.511952i	0.507222	−	0.861816i	$-0.330673\pi$
$283$	−7.22664	−	8.61237i	−0.429579	−	0.511952i	−0.936801	+	0.349863i	$0.886228\pi$
$284$	−1.11291	−	4.78494i	−0.0660392	−	0.283934i
$285$	6.91362	−	11.4826i	0.409528	−	0.680172i
$286$	−27.8902	−	22.1477i	−1.64918	−	1.30962i
$287$	7.90199	+	13.6866i	0.466440	+	0.807897i
$288$	−1.29318	+	16.9212i	−0.0762011	+	0.997092i
$289$	−5.91254	+	10.2408i	−0.347797	+	0.602401i
$290$	−2.59179	+	1.02338i	−0.152195	+	0.0600947i
$291$	−0.211101	+	0.170629i	−0.0123749	+	0.0100025i
$292$	12.6237	−	11.8103i	0.738744	−	0.691145i
$293$	19.0430	−	3.35780i	1.11251	−	0.196165i	0.412958	−	0.910750i	$-0.364496\pi$
$293$	19.0430	−	3.35780i	1.11251	−	0.196165i	0.699548	+	0.714585i	$0.253385\pi$
$294$	2.53169	−	15.1204i	0.147651	−	0.881838i
$295$	−2.21815	+	2.64349i	−0.129146	+	0.153910i
$296$	15.2559	−	1.23822i	0.886733	−	0.0719704i
$297$	−7.10380	+	30.3928i	−0.412204	+	1.76357i
$298$	−3.10782	+	1.90796i	−0.180031	+	0.110525i
$299$	18.9074	+	15.8652i	1.09344	+	0.917508i
$300$	−2.73129	−	2.13074i	−0.157691	−	0.123018i
$301$	3.09378	+	17.5457i	0.178322	+	1.01132i
$302$	4.01168	−	0.819592i	0.230846	−	0.0471622i
$303$	21.4511	−	3.37760i	1.23233	−	0.194038i
$304$	13.6598	+	27.7765i	0.783446	+	1.59309i
$305$	1.33035	+	0.768077i	0.0761755	+	0.0439799i
$306$	−8.31099	−	4.90671i	−0.475108	−	0.280498i
$307$	9.27649	−	5.35578i	0.529437	−	0.305671i	−0.211350	−	0.977410i	$-0.567786\pi$
$307$	9.27649	−	5.35578i	0.529437	−	0.305671i	0.740787	+	0.671740i	$0.234453\pi$
$308$	−43.4268	−	5.26027i	−2.47447	−	0.299732i
$309$	−0.461339	+	25.1254i	−0.0262446	+	1.42933i
$310$	10.2043	+	3.40508i	0.579568	+	0.193395i
$311$	11.6128	−	9.74427i	0.658500	−	0.552547i	−0.251137	−	0.967952i	$-0.580805\pi$
$311$	11.6128	−	9.74427i	0.658500	−	0.552547i	0.909637	+	0.415405i	$0.136360\pi$
$312$	−11.3625	−	17.1096i	−0.643277	−	0.968641i
$313$	4.80755	−	1.74980i	0.271739	−	0.0989048i	−0.202557	−	0.979271i	$-0.564925\pi$
$313$	4.80755	−	1.74980i	0.271739	−	0.0989048i	0.474295	+	0.880366i	$0.342703\pi$
$314$	0.412743	−	0.761658i	0.0232924	−	0.0429828i
$315$	1.50069	+	10.8202i	0.0845544	+	0.609650i
$316$	−7.80963	+	5.08976i	−0.439326	+	0.286321i
$317$	−14.4856	−	2.55420i	−0.813592	−	0.143458i	−0.248655	−	0.968592i	$-0.579988\pi$
$317$	−14.4856	−	2.55420i	−0.813592	−	0.143458i	−0.564937	+	0.825134i	$0.691100\pi$
$318$	−3.66104	+	0.678190i	−0.205301	+	0.0380310i
$319$	4.04797	−	11.1217i	0.226643	−	0.622696i
$320$	7.55132	−	2.64152i	0.422131	−	0.147665i
$321$	−10.2072	+	3.50428i	−0.569710	+	0.195590i
$322$	29.9868	+	4.45656i	1.67110	+	0.248354i
$323$	−17.6037			−0.979494
$324$	−9.30143	+	15.4105i	−0.516746	+	0.856139i
$325$	4.19248			0.232557
$326$	20.8872	+	3.10420i	1.15683	+	0.171926i
$327$	−22.5543	+	7.74322i	−1.24726	+	0.428201i
$328$	11.8775	−	3.10275i	0.655825	−	0.171321i
$329$	0.932113	−	2.56096i	0.0513891	−	0.141190i
$330$	14.4673	−	2.68000i	0.796399	−	0.147529i
$331$	−2.18902	−	0.385984i	−0.120320	−	0.0212156i	0.113164	−	0.993576i	$-0.463901\pi$
$331$	−2.18902	−	0.385984i	−0.120320	−	0.0212156i	−0.233484	+	0.972361i	$0.575013\pi$
$332$	−0.250129	−	0.383794i	−0.0137276	−	0.0210634i
$333$	15.0414	+	6.10884i	0.824263	+	0.334763i
$334$	−6.08643	+	11.2316i	−0.333035	+	0.614568i
$335$	−12.4174	+	4.51957i	−0.678436	+	0.246931i
$336$	−22.8888	−	10.6077i	−1.24869	−	0.578696i
$337$	10.0769	−	8.45552i	0.548923	−	0.460601i	−0.325653	−	0.945489i	$-0.605584\pi$
$337$	10.0769	−	8.45552i	0.548923	−	0.460601i	0.874576	+	0.484888i	$0.161140\pi$
$338$	6.13994	+	2.04883i	0.333968	+	0.111442i
$339$	0.392037	−	21.3511i	0.0212925	−	1.15963i
$340$	−0.547102	+	4.51667i	−0.0296708	+	0.244951i
$341$	−39.5699	+	22.8457i	−2.14283	+	1.23716i
$342$	−0.319228	+	32.8297i	−0.0172619	+	1.77523i
$343$	−2.33733	−	1.34946i	−0.126204	−	0.0728639i
$344$	13.7787	+	1.29273i	0.742899	+	0.0696993i
$345$	−10.0728	+	1.58602i	−0.542300	+	0.0853883i
$346$	13.7972	−	2.81880i	0.741744	−	0.151539i
$347$	2.74369	+	15.5602i	0.147289	+	0.835317i	0.965501	+	0.260400i	$0.0838546\pi$
$347$	2.74369	+	15.5602i	0.147289	+	0.835317i	−0.818212	+	0.574917i	$0.805034\pi$
$348$	4.19833	−	5.38165i	0.225054	−	0.288487i
$349$	−16.1039	−	13.5128i	−0.862023	−	0.723323i	0.100380	−	0.994949i	$-0.467994\pi$
$349$	−16.1039	−	13.5128i	−0.862023	−	0.723323i	−0.962403	+	0.271626i	$0.912439\pi$
$350$	4.38850	−	2.69420i	0.234575	−	0.144011i
$351$	−2.59611	−	21.6295i	−0.138570	−	1.15450i
$352$	−12.8752	+	31.4455i	−0.686251	+	1.67605i
$353$	5.27276	−	6.28383i	0.280641	−	0.334454i	−0.607249	−	0.794512i	$-0.707727\pi$
$353$	5.27276	−	6.28383i	0.280641	−	0.334454i	0.887889	+	0.460058i	$0.152171\pi$
$354$	1.39587	−	8.33672i	0.0741895	−	0.443092i
$355$	−2.41901	+	0.426537i	−0.128388	+	0.0226382i
$356$	13.6194	+	14.5573i	0.721825	+	0.771537i
$357$	11.1580	−	9.01882i	0.590542	−	0.477327i
$358$	−6.22829	+	2.45926i	−0.329176	+	0.129976i
$359$	−6.49584	+	11.2511i	−0.342837	+	0.593812i	−0.984958	−	0.172791i	$-0.944721\pi$
$359$	−6.49584	+	11.2511i	−0.342837	+	0.593812i	0.642121	+	0.766603i	$0.278055\pi$
$360$	8.41339	+	1.10222i	0.443425	+	0.0580920i
$361$	20.4415	+	35.4057i	1.07587	+	1.86346i
$362$	−13.8831	−	11.0246i	−0.729680	−	0.579443i
$363$	−22.4077	+	37.2163i	−1.17610	+	1.95335i
$364$	29.7381	−	6.91668i	1.55870	−	0.362533i
$365$	−5.55593	−	6.62130i	−0.290811	−	0.346575i
$366$	−3.76265	+	0.0324948i	−0.196677	+	0.00169853i
$367$	−2.55007	−	7.00627i	−0.133113	−	0.365724i	0.855172	−	0.518344i	$-0.173451\pi$
$367$	−2.55007	−	7.00627i	−0.133113	−	0.365724i	−0.988285	+	0.152620i	$0.951229\pi$
$368$	9.50790	−	21.5439i	0.495633	−	1.12305i
$369$	12.7313	+	2.73024i	0.662764	+	0.142131i
$370$	−0.206571	−	7.65026i	−0.0107391	−	0.397718i
$371$	0.961120	−	5.45078i	0.0498989	−	0.282991i
$372$	−25.7705	+	5.49721i	−1.33614	+	0.285017i
$373$	−25.4800	−	9.27395i	−1.31930	−	0.480187i	−0.416068	−	0.909334i	$-0.636592\pi$
$373$	−25.4800	−	9.27395i	−1.31930	−	0.480187i	−0.903235	+	0.429147i	$0.858814\pi$
$374$	−12.8165	−	14.4627i	−0.662726	−	0.747846i
$375$	−1.13751	+	1.30617i	−0.0587408	+	0.0674501i
$376$	−1.72644	−	1.22510i	−0.0890344	−	0.0631796i
$377$			8.26073i			0.425449i
$378$	−16.6172	−	20.9725i	−0.854696	−	1.07871i
$379$		−	12.7305i		−	0.653919i	−0.945038	−	0.326960i	$-0.893976\pi$
$379$		−	12.7305i		−	0.653919i	0.945038	−	0.326960i	$-0.106024\pi$
$380$	14.2366	−	6.07050i	0.730322	−	0.311410i
$381$	12.7201	+	2.48450i	0.651670	+	0.127285i
$382$	−11.5558	+	10.2405i	−0.591244	+	0.523948i
$383$	23.2618	+	8.46661i	1.18862	+	0.432623i	0.859240	−	0.511573i	$-0.170937\pi$
$383$	23.2618	+	8.46661i	1.18862	+	0.432623i	0.329383	+	0.944196i	$0.393159\pi$
$384$	−12.6548	+	14.9618i	−0.645789	+	0.763516i
$385$	−3.79805	+	21.5398i	−0.193567	+	1.09777i
$386$	20.1364	−	0.543720i	1.02491	−	0.0276746i
$387$	12.4341	+	7.80108i	0.632063	+	0.396551i
$388$	−0.312971	+	0.0169140i	−0.0158887	+	0.000858677i
$389$	3.12869	+	8.59601i	0.158631	+	0.435835i	0.993391	−	0.114779i	$-0.0366159\pi$
$389$	3.12869	+	8.59601i	0.158631	+	0.435835i	−0.834760	+	0.550614i	$0.814394\pi$
$390$	−8.84893	+	5.21134i	−0.448083	+	0.263886i
$391$	8.60846	+	10.2592i	0.435349	+	0.518828i
$392$	12.5960	−	12.4387i	0.636192	−	0.628251i
$393$	5.04953	+	9.12909i	0.254715	+	0.460502i
$394$	13.7092	−	17.2637i	0.690658	−	0.869730i
$395$	2.33045	+	4.03646i	0.117258	+	0.203096i
$396$	−27.2044	+	23.6397i	−1.36707	+	1.18794i
$397$	12.9430	−	22.4180i	0.649591	−	1.12512i	−0.333629	−	0.942704i	$-0.608273\pi$
$397$	12.9430	−	22.4180i	0.649591	−	1.12512i	0.983221	−	0.182421i	$-0.0583933\pi$
$398$	10.3059	+	26.1006i	0.516588	+	1.30830i
$399$	−45.5475	−	17.5314i	−2.28023	−	0.877669i
$400$	−1.11508	−	3.84143i	−0.0557542	−	0.192072i
$401$	−1.97679	+	0.348561i	−0.0987162	+	0.0174063i	−0.222788	−	0.974867i	$-0.571516\pi$
$401$	−1.97679	+	0.348561i	−0.0987162	+	0.0174063i	0.124072	+	0.992273i	$0.460405\pi$
$402$	20.5911	−	24.9744i	1.02699	−	1.24561i
$403$	20.4991	−	24.4298i	1.02113	−	1.21694i
$404$	22.3603	+	11.3473i	1.11247	+	0.564547i
$405$	7.44305	+	5.05975i	0.369848	+	0.251421i
$406$	5.30856	+	8.64694i	0.263459	+	0.429140i
$407$	24.9007	+	20.8942i	1.23428	+	1.03569i
$408$	−4.45956	−	10.2132i	−0.220781	−	0.505631i
$409$	−3.74191	−	21.2214i	−0.185026	−	1.04933i	−0.925922	−	0.377714i	$-0.876710\pi$
$409$	−3.74191	−	21.2214i	−0.185026	−	1.04933i	0.740897	−	0.671619i	$-0.234401\pi$
$410$	−1.22863	−	6.01381i	−0.0606778	−	0.297001i
$411$	0.100834	−	0.261971i	0.00497377	−	0.0129221i
$412$	−17.4252	+	23.2026i	−0.858477	+	1.14311i
$413$	10.8819	+	6.28269i	0.535465	+	0.309151i
$414$	19.2888	−	15.8682i	0.947993	−	0.779879i
$415$	−0.198366	+	0.114527i	−0.00973742	+	0.00562190i
$416$	0.937883	−	23.6977i	0.0459835	−	1.16188i
$417$	29.5521	−	16.3460i	1.44717	−	0.800467i
$418$	−20.8076	+	62.3563i	−1.01773	+	3.04995i
$419$	−8.66320	+	7.26929i	−0.423225	+	0.355128i	−0.829388	−	0.558672i	$-0.811311\pi$
$419$	−8.66320	+	7.26929i	−0.423225	+	0.355128i	0.406163	+	0.913801i	$0.366866\pi$
$420$	−5.91370	+	11.1415i	−0.288559	+	0.543651i
$421$	2.51549	−	0.915563i	0.122597	−	0.0446218i	−0.279993	−	0.960002i	$-0.590332\pi$
$421$	2.51549	−	0.915563i	0.122597	−	0.0446218i	0.402590	+	0.915380i	$0.368110\pi$
$422$	−29.2990	−	15.8771i	−1.42625	−	0.772886i
$423$	−1.05054	−	1.98444i	−0.0510789	−	0.0964869i
$424$	−3.88503	−	1.84141i	−0.188674	−	0.0894268i
$425$	2.24028	+	0.395022i	0.108670	+	0.0191614i
$426$	4.57553	−	3.90715i	0.221685	−	0.189302i
$427$	1.91310	−	5.25621i	0.0925815	−	0.254366i
$428$	−11.9229	−	3.62395i	−0.576316	−	0.175170i
$429$	8.36160	−	42.8096i	0.403702	−	2.06687i
$430$	1.01720	−	6.84444i	0.0490539	−	0.330068i
$431$	−5.46848			−0.263407			−0.131704	−	0.991289i	$-0.542045\pi$
$431$	−5.46848			−0.263407			−0.131704	+	0.991289i	$0.542045\pi$
$432$	−19.1279	+	8.13159i	−0.920292	+	0.391231i
$433$	10.7097			0.514675			0.257337	−	0.966322i	$-0.417155\pi$
$433$	10.7097			0.514675			0.257337	+	0.966322i	$0.417155\pi$
$434$	5.75822	−	38.7452i	0.276403	−	1.85983i
$435$	−2.57362	−	2.24131i	−0.123396	−	0.107463i
$436$	−26.3455	−	8.00766i	−1.26172	−	0.383498i
$437$	15.5815	−	42.8099i	0.745365	−	2.04787i
$438$	19.9571	+	7.06922i	0.953587	+	0.337780i
$439$	22.1001	+	3.89684i	1.05478	+	0.185986i	0.674039	−	0.738696i	$-0.264558\pi$
$439$	22.1001	+	3.89684i	1.05478	+	0.185986i	0.380740	+	0.924682i	$0.375669\pi$
$440$	15.3524	+	7.27669i	0.731899	+	0.346903i
$441$	17.8679	−	5.76985i	0.850852	−	0.274755i
$442$	11.8585	+	6.42611i	0.564050	+	0.305659i
$443$	35.0704	−	12.7646i	1.66625	−	0.606464i	0.674921	−	0.737890i	$-0.264178\pi$
$443$	35.0704	−	12.7646i	1.66625	−	0.606464i	0.991326	+	0.131425i	$0.0419554\pi$
$444$	9.94542	+	15.8904i	0.471989	+	0.754123i
$445$	7.63554	−	6.40698i	0.361959	−	0.303720i
$446$	1.95293	−	5.85254i	0.0924738	−	0.277126i
$447$	−3.82632	−	2.30381i	−0.180979	−	0.108966i
$448$	−14.2470	−	25.4084i	−0.673109	−	1.20043i
$449$	−31.8680	+	18.3990i	−1.50395	+	0.868303i	−0.503956	+	0.863729i	$0.668123\pi$
$449$	−31.8680	+	18.3990i	−1.50395	+	0.868303i	−0.999990	+	0.00457418i	$0.998544\pi$
$450$	0.777318	−	4.17082i	0.0366431	−	0.196615i
$451$	22.5779	+	13.0354i	1.06315	+	0.613812i
$452$	14.8076	−	19.7171i	0.696490	−	0.927416i
$453$	3.15237	+	3.90007i	0.148111	+	0.183241i
$454$	−2.32156	−	11.3634i	−0.108956	−	0.533311i
$455$	−2.65090	−	15.0340i	−0.124276	−	0.704805i
$456$	−22.5029	+	30.5091i	−1.05380	+	1.42872i
$457$	−20.2286	−	16.9738i	−0.946252	−	0.794000i	0.0324102	−	0.999475i	$-0.489682\pi$
$457$	−20.2286	−	16.9738i	−0.946252	−	0.794000i	−0.978662	+	0.205475i	$0.934126\pi$
$458$	−11.4591	−	18.6654i	−0.535450	−	0.872178i
$459$	0.650719	−	11.8025i	0.0303730	−	0.550894i
$460$	−10.4997	−	5.32832i	−0.489552	−	0.248434i
$461$	−2.17559	+	2.59276i	−0.101327	+	0.120757i	−0.814325	−	0.580409i	$-0.802893\pi$
$461$	−2.17559	+	2.59276i	−0.101327	+	0.120757i	0.712998	+	0.701166i	$0.247337\pi$
$462$	−18.7580	−	50.1844i	−0.872701	−	2.33479i
$463$	−23.3358	+	4.11472i	−1.08450	+	0.191227i	−0.687207	−	0.726462i	$-0.741163\pi$
$463$	−23.3358	+	4.11472i	−1.08450	+	0.191227i	−0.397298	+	0.917690i	$0.630052\pi$
$464$	7.56902	−	2.19712i	0.351383	−	0.101999i
$465$	2.04926	+	13.0148i	0.0950320	+	0.603547i
$466$	1.44406	+	3.65721i	0.0668947	+	0.169417i
$467$	−17.4218	+	30.1754i	−0.806183	+	1.39635i	0.109306	+	0.994008i	$0.465137\pi$
$467$	−17.4218	+	30.1754i	−0.806183	+	1.39635i	−0.915489	+	0.402343i	$0.868196\pi$
$468$	12.1993	−	21.9988i	0.563914	−	1.01689i
$469$	24.0585	+	41.6705i	1.11092	+	1.92416i
$470$	−0.658239	+	0.828907i	−0.0303623	+	0.0382346i
$471$	1.06082	+	0.0194782i	0.0488800	+	0.000897508i
$472$	6.94487	−	6.85818i	0.319664	−	0.315673i
$473$	18.8918	+	22.5144i	0.868646	+	1.03521i
$474$	−9.93619	−	5.62282i	−0.456384	−	0.258264i
$475$	−2.64669	−	7.27172i	−0.121439	−	0.333650i
$476$	16.5425	−	0.894008i	0.758223	−	0.0409768i
$477$	−2.80098	−	3.59851i	−0.128248	−	0.164764i
$478$	41.5927	−	1.12308i	1.90241	−	0.0513686i
$479$	5.73342	−	32.5158i	0.261966	−	1.48569i	−0.515570	−	0.856848i	$-0.672420\pi$
$479$	5.73342	−	32.5158i	0.261966	−	1.48569i	0.777536	−	0.628838i	$-0.216469\pi$
$480$	7.12854	+	6.72190i	0.325372	+	0.306811i
$481$	−21.3195	−	7.75966i	−0.972085	−	0.353810i
$482$	−22.0964	+	19.5814i	−1.00646	+	0.891907i
$483$	12.0564	+	35.1176i	0.548584	+	1.59791i
$484$	−46.1422	+	19.6751i	−2.09737	+	0.894322i
$485$			0.156714i			0.00711602i
$486$	−21.9991	−	1.42758i	−0.997901	−	0.0647563i
$487$		−	6.38179i		−	0.289186i	−0.989491	−	0.144593i	$-0.953813\pi$
$487$		−	6.38179i		−	0.289186i	0.989491	−	0.144593i	$-0.0461873\pi$
$488$	−3.54341	−	2.51444i	−0.160403	−	0.113823i
$489$	8.39783	+	24.4610i	0.379763	+	1.10617i
$490$	−5.87044	−	6.62443i	−0.265199	−	0.299261i
$491$	−28.5883	−	10.4053i	−1.29017	−	0.469584i	−0.396387	−	0.918083i	$-0.629736\pi$
$491$	−28.5883	−	10.4053i	−1.29017	−	0.469584i	−0.893783	+	0.448500i	$0.851958\pi$
$492$	10.0685	+	11.1659i	0.453924	+	0.503399i
$493$	−0.778339	+	4.41418i	−0.0350546	+	0.198805i
$494$	−1.23844	−	45.8648i	−0.0557199	−	2.06356i
$495$	11.0686	+	14.2202i	0.497497	+	0.639151i
$496$	−27.8364	−	12.2849i	−1.24989	−	0.551610i
$497$	3.05907	+	8.40474i	0.137218	+	0.377004i
$498$	0.276326	−	0.488301i	0.0123825	−	0.0218813i
$499$	−9.76847	−	11.6416i	−0.437297	−	0.521150i	0.501716	−	0.865032i	$-0.332702\pi$
$499$	−9.76847	−	11.6416i	−0.437297	−	0.521150i	−0.939013	+	0.343882i	$0.888258\pi$
$500$	−1.94800	+	0.453079i	−0.0871174	+	0.0202623i
$501$	−15.6432	−	0.287232i	−0.698886	−	0.0128326i
$502$	22.9180	+	18.1993i	1.02288	+	0.812277i
$503$	−20.4158	−	35.3611i	−0.910294	−	1.57668i	−0.813649	−	0.581357i	$-0.802522\pi$
$503$	−20.4158	−	35.3611i	−0.910294	−	1.57668i	−0.0966452	−	0.995319i	$-0.530811\pi$
$504$	−1.36728	−	30.8669i	−0.0609036	−	1.37492i
$505$	6.26869	−	10.8577i	0.278953	−	0.483161i
$506$	46.5156	−	18.3668i	2.06787	−	0.816504i
$507$	1.23303	+	7.83099i	0.0547610	+	0.347786i
$508$	10.2242	+	10.9284i	0.453628	+	0.484868i
$509$	−15.0482	+	2.65341i	−0.667001	+	0.117610i	−0.496888	−	0.867814i	$-0.665524\pi$
$509$	−15.0482	+	2.65341i	−0.667001	+	0.117610i	−0.170112	+	0.985425i	$0.554413\pi$
$510$	−5.21951	+	1.95095i	−0.231124	+	0.0863897i
$511$	−20.2306	+	24.1099i	−0.894949	+	1.06656i
$512$	−21.9629	+	5.44359i	−0.970631	+	0.240575i
$513$	−35.8768	+	18.1575i	−1.58400	+	0.801672i
$514$	10.5485	−	6.47598i	0.465275	−	0.285643i
$515$	11.1142	+	9.32595i	0.489752	+	0.410950i
$516$	6.36079	+	15.7107i	0.280018	+	0.691626i
$517$	−0.780682	−	4.42747i	−0.0343343	−	0.194720i
$518$	−27.3028	+	5.57800i	−1.19962	+	0.245083i
$519$	10.8418	+	13.4134i	0.475903	+	0.588782i
$520$	−11.8063	−	1.10768i	−0.517740	−	0.0485748i
$521$	31.1297	+	17.9727i	1.36381	+	0.787399i	0.990129	−	0.140157i	$-0.0447606\pi$
$521$	31.1297	+	17.9727i	1.36381	+	0.787399i	0.373685	+	0.927555i	$0.378094\pi$
$522$	8.21805	+	1.53160i	0.359694	+	0.0670363i
$523$	16.3993	−	9.46811i	0.717089	−	0.414012i	−0.0965912	−	0.995324i	$-0.530794\pi$
$523$	16.3993	−	9.46811i	0.717089	−	0.414012i	0.813680	+	0.581312i	$0.197461\pi$
$524$	−1.44859	+	11.9591i	−0.0632822	+	0.522434i
$525$	5.40308	+	3.25317i	0.235810	+	0.141980i
$526$	14.2182	+	4.74447i	0.619945	+	0.206869i
$527$	13.2556	−	11.1228i	0.577425	−	0.484517i
$528$	−41.4489	+	3.72471i	−1.80383	+	0.162097i
$529$	−10.9557	+	3.98753i	−0.476333	+	0.173371i
$530$	−1.02419	+	1.89000i	−0.0444880	+	0.0820962i
$531$	9.85159	−	3.18125i	0.427522	−	0.138054i
$532$	−30.7702	−	47.2133i	−1.33406	−	2.04696i
$533$	−17.9200	−	3.15978i	−0.776200	−	0.136865i
$534$	−8.15207	+	23.0141i	−0.352774	+	0.995917i
$535$	−2.13104	+	5.85499i	−0.0921330	+	0.253133i
$536$	36.1623	−	9.44664i	1.56197	−	0.408033i
$537$	−6.18463	−	5.38607i	−0.266887	−	0.232426i
$538$	31.6416	+	4.70249i	1.36416	+	0.202739i
$539$	37.5950			1.61933
$540$	3.54376	+	9.76943i	0.152499	+	0.420409i
$541$	26.7122			1.14845			0.574223	−	0.818699i	$-0.305304\pi$
$541$	26.7122			1.14845			0.574223	+	0.818699i	$0.305304\pi$
$542$	19.5281	+	2.90222i	0.838806	+	0.124661i
$543$	4.16222	−	21.3096i	0.178618	−	0.914484i
$544$	2.73400	−	12.5747i	0.117219	−	0.539135i
$545$	−4.70886	+	12.9375i	−0.201705	+	0.554181i
$546$	24.2827	+	28.4366i	1.03920	+	1.21698i
$547$	28.7004	+	5.06065i	1.22714	+	0.216378i	0.749396	−	0.662122i	$-0.230344\pi$
$547$	28.7004	+	5.06065i	1.22714	+	0.216378i	0.477743	+	0.878500i	$0.341455\pi$
$548$	0.271552	−	0.176978i	0.0116001	−	0.00756014i
$549$	−2.15616	−	4.07294i	−0.0920228	−	0.173829i
$550$	4.04729	−	7.46869i	0.172577	−	0.318466i
$551$	14.3280	−	5.21495i	0.610391	−	0.222164i
$552$	28.7846	−	1.80504i	1.22515	−	0.0768276i
$553$	13.0010	−	10.9091i	0.552857	−	0.463903i
$554$	−10.5015	−	3.50425i	−0.446168	−	0.148881i
$555$	8.20195	−	4.53671i	0.348153	−	0.192572i
$556$	38.7131	+	4.68929i	1.64180	+	0.198870i
$557$	24.4659	−	14.1254i	1.03665	−	0.598513i	0.117771	−	0.993041i	$-0.462425\pi$
$557$	24.4659	−	14.1254i	1.03665	−	0.598513i	0.918884	+	0.394528i	$0.129092\pi$
$558$	−20.5029	−	24.9226i	−0.867959	−	1.05506i
$559$	−17.7652	−	10.2567i	−0.751386	−	0.433813i
$560$	−13.0701	+	6.42756i	−0.552312	+	0.271614i
$561$	8.50167	−	22.0878i	0.358941	−	0.932546i
$562$	−6.51413	+	1.33085i	−0.274782	+	0.0561384i
$563$	0.0568413	+	0.322363i	0.00239557	+	0.0135860i	0.985982	−	0.166851i	$-0.0533599\pi$
$563$	0.0568413	+	0.322363i	0.00239557	+	0.0135860i	−0.983587	+	0.180437i	$0.942249\pi$
$564$	0.358976	−	2.56775i	0.0151156	−	0.108122i
$565$	−9.44466	−	7.92501i	−0.397340	−	0.333408i
$566$	13.5498	−	8.31853i	0.569540	−	0.349654i
$567$	13.4377	−	29.8896i	0.564332	−	1.25525i
$568$	6.92477	−	0.562039i	0.290557	−	0.0235826i
$569$	7.68152	−	9.15448i	0.322026	−	0.383776i	−0.580609	−	0.814183i	$-0.697185\pi$
$569$	7.68152	−	9.15448i	0.322026	−	0.383776i	0.902635	+	0.430407i	$0.141630\pi$
$570$	14.6252	+	12.0583i	0.612581	+	0.505066i
$571$	23.0375	−	4.06213i	0.964088	−	0.169995i	0.330620	−	0.943764i	$-0.392742\pi$
$571$	23.0375	−	4.06213i	0.964088	−	0.169995i	0.633468	+	0.773769i	$0.281631\pi$
$572$	36.7795	−	34.4098i	1.53783	−	1.43875i
$573$	−17.6483	−	6.79288i	−0.737266	−	0.283777i
$574$	−20.7883	+	8.20833i	−0.867688	+	0.342609i
$575$	−2.94359	+	5.09844i	−0.122756	+	0.212620i
$576$	−23.4014	−	5.32677i	−0.975058	−	0.221949i
$577$	−19.9496	−	34.5537i	−0.830511	−	1.43849i	−0.897633	−	0.440743i	$-0.854715\pi$
$577$	−19.9496	−	34.5537i	−0.830511	−	1.43849i	0.0671223	−	0.997745i	$-0.478618\pi$
$578$	−13.0962	−	10.3998i	−0.544730	−	0.432573i
$579$	11.9411	+	21.5885i	0.496257	+	0.897188i
$580$	−0.892732	−	3.83828i	−0.0370687	−	0.159376i
$581$	0.536114	+	0.638916i	0.0222418	+	0.0265067i
$582$	−0.194798	−	0.330771i	−0.00807466	−	0.0137109i
$583$	−3.12281	−	8.57986i	−0.129334	−	0.355341i
$584$	13.8965	+	20.1139i	0.575039	+	0.832318i
$585$	−10.6542	−	6.68435i	−0.440497	−	0.276364i
$586$	0.738135	+	27.3364i	0.0304921	+	1.12926i
$587$	−1.44923	+	8.21900i	−0.0598162	+	0.339234i	−0.999999	−	0.00143595i	$-0.999543\pi$
$587$	−1.44923	+	8.21900i	−0.0598162	+	0.339234i	0.940183	+	0.340670i	$0.110654\pi$
$588$	20.6248	+	6.68489i	0.850553	+	0.275680i
$589$	−55.3137	−	20.1325i	−2.27916	−	0.829546i
$590$	−3.23671	−	3.65242i	−0.133253	−	0.150368i
$591$	26.4986	+	5.17572i	1.09001	+	0.212901i
$592$	−1.43952	+	21.5982i	−0.0591639	+	0.887679i
$593$		−	17.1461i		−	0.704104i	−0.935980	−	0.352052i	$-0.885484\pi$
$593$		−	17.1461i		−	0.704104i	0.935980	−	0.352052i	$-0.114516\pi$
$594$	−41.0381	−	16.2556i	−1.68381	−	0.666976i
$595$		−	8.28330i		−	0.339582i
$596$	−2.02285	−	4.74402i	−0.0828593	−	0.194323i
$597$	−22.5711	+	25.9176i	−0.923774	+	1.06074i
$598$	−26.1238	+	23.1503i	−1.06828	+	0.946688i
$599$	−25.4310	−	9.25612i	−1.03908	−	0.378195i	−0.234550	−	0.972104i	$-0.575362\pi$
$599$	−25.4310	−	9.25612i	−1.03908	−	0.378195i	−0.804532	+	0.593909i	$0.797584\pi$
$600$	3.54840	−	3.37770i	0.144863	−	0.137894i
$601$	−2.50943	+	14.2317i	−0.102362	+	0.580522i	0.889880	+	0.456196i	$0.150788\pi$
$601$	−2.50943	+	14.2317i	−0.102362	+	0.580522i	−0.992241	+	0.124327i	$0.960323\pi$
$602$	−25.1870	+	0.680095i	−1.02654	+	0.0277186i
$603$	38.7617	+	8.31251i	1.57850	+	0.338512i
$604$	0.312484	+	5.78212i	0.0127148	+	0.235271i
$605$	8.57818	+	23.5684i	0.348753	+	0.958190i
$606$	0.265208	+	30.7090i	0.0107733	+	1.24747i
$607$	11.0893	+	13.2157i	0.450101	+	0.536409i	0.942609	−	0.333899i	$-0.108364\pi$
$607$	11.0893	+	13.2157i	0.450101	+	0.536409i	−0.492508	+	0.870308i	$0.663920\pi$
$608$	−41.6950	+	13.3335i	−1.69095	+	0.540745i
$609$	−6.40993	+	10.6460i	−0.259743	+	0.431400i
$610$	−1.35099	+	1.70128i	−0.0547002	+	0.0688828i
$611$	1.56894	+	2.71748i	0.0634725	+	0.109938i
$612$	8.59156	−	10.6058i	0.347293	−	0.428712i
$613$	−8.43333	+	14.6070i	−0.340619	+	0.589969i	−0.984548	−	0.175116i	$-0.943970\pi$
$613$	−8.43333	+	14.6070i	−0.340619	+	0.589969i	0.643929	+	0.765085i	$0.277303\pi$
$614$	5.56341	+	14.0898i	0.224521	+	0.568620i
$615$	5.84650	−	4.72564i	0.235754	−	0.190556i
$616$	16.3865	−	59.6540i	0.660230	−	2.40353i
$617$	−15.0316	+	2.65048i	−0.605151	+	0.106704i	−0.467824	−	0.883822i	$-0.654962\pi$
$617$	−15.0316	+	2.65048i	−0.605151	+	0.106704i	−0.137326	+	0.990526i	$0.543851\pi$
$618$	−35.0507	−	5.86875i	−1.40995	−	0.236076i
$619$	7.81347	−	9.31173i	0.314050	−	0.374270i	−0.585811	−	0.810448i	$-0.699224\pi$
$619$	7.81347	−	9.31173i	0.314050	−	0.374270i	0.899860	+	0.436178i	$0.143668\pi$
$620$	−6.88461	+	13.5664i	−0.276492	+	0.544842i
$621$	28.1262	+	12.0292i	1.12867	+	0.482716i
$622$	11.2165	+	18.2703i	0.449743	+	0.732572i
$623$	−27.8030	−	23.3295i	−1.11390	−	0.934676i
$624$	26.2960	−	12.3375i	1.05268	−	0.493896i
$625$	0.173648	+	0.984808i	0.00694593	+	0.0393923i
$626$	1.44826	+	7.08881i	0.0578839	+	0.283326i
$627$	−79.5304	+	12.5225i	−3.17614	+	0.500101i
$628$	0.979638	+	0.735709i	0.0390918	+	0.0293580i
$629$	−10.6611	−	6.15518i	−0.425086	−	0.245423i
$630$	−15.4478	−	0.150211i	−0.615457	−	0.00598455i
$631$	−11.4975	+	6.63808i	−0.457708	+	0.264258i	−0.711080	−	0.703111i	$-0.751794\pi$
$631$	−11.4975	+	6.63808i	−0.457708	+	0.264258i	0.253372	+	0.967369i	$0.418460\pi$
$632$	−5.49623	−	11.9826i	−0.218628	−	0.476643i
$633$	0.749275	−	40.8069i	0.0297810	−	1.62193i
$634$	6.58440	−	19.7322i	0.261500	−	0.783664i
$635$	5.73210	−	4.80980i	0.227471	−	0.190871i
$636$	−0.187580	−	5.26224i	−0.00743801	−	0.208661i
$637$	−24.6574	+	8.97458i	−0.976964	+	0.355586i
$638$	14.7161	+	7.97463i	0.582614	+	0.315719i
$639$	6.82739	+	2.77285i	0.270087	+	0.109692i
$640$	2.12522	+	11.1123i	0.0840067	+	0.439253i
$641$	−37.6989	−	6.64733i	−1.48902	−	0.262554i	−0.630841	−	0.775912i	$-0.717290\pi$
$641$	−37.6989	−	6.64733i	−1.48902	−	0.262554i	−0.858174	+	0.513358i	$0.828401\pi$
$642$	−2.77995	−	15.0069i	−0.109716	−	0.592273i
$643$	8.21070	−	22.5587i	0.323798	−	0.889629i	−0.665846	−	0.746089i	$-0.731929\pi$
$643$	8.21070	−	22.5587i	0.323798	−	0.889629i	0.989645	−	0.143540i	$-0.0458485\pi$
$644$	−12.4681	+	41.0205i	−0.491312	+	1.61643i
$645$	8.01554	−	2.75185i	0.315612	−	0.108354i
$646$	3.65969	−	24.6249i	0.143989	−	0.968853i
$647$	1.49666			0.0588397			0.0294199	−	0.999567i	$-0.490634\pi$
$647$	1.49666			0.0588397			0.0294199	+	0.999567i	$0.490634\pi$
$648$	−19.6233	−	16.2150i	−0.770875	−	0.636987i
$649$	20.7282			0.813655
$650$	−0.871590	+	5.86466i	−0.0341866	+	0.230031i
$651$	45.3746	−	15.5778i	1.77837	−	0.610541i
$652$	−8.68462	+	28.5727i	−0.340116	+	1.11899i
$653$	−13.5777	+	37.3045i	−0.531338	+	1.45984i	0.326141	+	0.945321i	$0.394252\pi$
$653$	−13.5777	+	37.3045i	−0.531338	+	1.45984i	−0.857479	+	0.514518i	$0.827971\pi$
$654$	−6.14271	−	33.1599i	−0.240199	−	1.29665i
$655$	5.93173	+	1.04592i	0.231772	+	0.0408676i
$656$	1.87102	+	17.2599i	0.0730511	+	0.673885i
$657$	3.56228	+	25.6846i	0.138978	+	1.00205i
$658$	3.38862	+	1.83629i	0.132102	+	0.0715862i
$659$	−9.77049	+	3.55617i	−0.380604	+	0.138529i	−0.525235	−	0.850957i	$-0.676023\pi$
$659$	−9.77049	+	3.55617i	−0.380604	+	0.138529i	0.144631	+	0.989486i	$0.453800\pi$
$660$	0.741257	+	20.7948i	0.0288534	+	0.809435i
$661$	−14.5736	+	12.2287i	−0.566847	+	0.475641i	−0.880598	−	0.473864i	$-0.842859\pi$
$661$	−14.5736	+	12.2287i	−0.566847	+	0.475641i	0.313751	+	0.949505i	$0.398414\pi$
$662$	0.995017	−	2.98187i	0.0386724	−	0.115894i
$663$	−0.303262	+	16.5162i	−0.0117777	+	0.641437i
$664$	0.588870	−	0.270105i	0.0228526	−	0.0104821i
$665$	−24.4025	+	14.0888i	−0.946288	+	0.546340i
$666$	−11.6724	+	19.7706i	−0.452295	+	0.766097i
$667$	−10.0458	−	5.79994i	−0.388975	−	0.224575i
$668$	−14.4461	−	10.8490i	−0.558935	−	0.419760i
$669$	7.46444	−	1.17532i	0.288592	−	0.0454405i
$670$	−3.74070	−	18.3097i	−0.144516	−	0.707365i
$671$	−1.60230	−	9.08709i	−0.0618561	−	0.350803i
$672$	19.5970	−	29.8128i	0.755970	−	1.15005i
$673$	−6.83724	−	5.73713i	−0.263556	−	0.221150i	0.501427	−	0.865200i	$-0.332808\pi$
$673$	−6.83724	−	5.73713i	−0.263556	−	0.221150i	−0.764984	+	0.644050i	$0.777253\pi$
$674$	9.73308	+	15.8539i	0.374904	+	0.610670i
$675$	4.97322	−	1.50569i	0.191419	−	0.0579542i
$676$	−4.14246	+	8.16291i	−0.159325	+	0.313958i
$677$	−1.39192	+	1.65883i	−0.0534959	+	0.0637539i	−0.792129	−	0.610354i	$-0.791027\pi$
$677$	−1.39192	+	1.65883i	−0.0534959	+	0.0637539i	0.738633	+	0.674108i	$0.235472\pi$
$678$	29.7855	+	4.98715i	1.14390	+	0.191530i
$679$	0.561968	−	0.0990901i	0.0215663	−	0.00380273i
$680$	−6.20441	−	1.70430i	−0.237928	−	0.0653570i
$681$	11.0473	−	8.92933i	0.423332	−	0.342173i
$682$	−23.7313	−	60.1018i	−0.908720	−	2.30142i
$683$	−10.2871	+	17.8178i	−0.393625	+	0.681779i	−0.992925	−	0.118746i	$-0.962113\pi$
$683$	−10.2871	+	17.8178i	−0.393625	+	0.681779i	0.599299	+	0.800525i	$0.295446\pi$
$684$	−45.8575	−	7.27164i	−1.75340	−	0.278038i
$685$	−0.0810332	−	0.140354i	−0.00309612	−	0.00536263i
$686$	2.37360	−	2.98903i	0.0906246	−	0.114122i
$687$	13.8366	−	22.9807i	0.527898	−	0.876769i
$688$	−4.67284	+	19.0056i	−0.178150	+	0.724582i
$689$	4.09633	+	4.88181i	0.156058	+	0.185982i
$690$	−0.124534	−	14.4200i	−0.00474091	−	0.548961i
$691$	13.0566	+	35.8728i	0.496698	+	1.36467i	0.894448	+	0.447172i	$0.147569\pi$
$691$	13.0566	+	35.8728i	0.496698	+	1.36467i	−0.397750	+	0.917494i	$0.630209\pi$
$692$	1.07472	+	19.8863i	0.0408546	+	0.755962i
$693$	43.9942	−	48.6828i	1.67120	−	1.84931i
$694$	−22.3368	+	0.603137i	−0.847895	+	0.0228948i
$695$	3.38579	−	19.2018i	0.128431	−	0.728366i
$696$	6.65531	+	6.99164i	0.252269	+	0.265017i
$697$	−9.27795	−	3.37690i	−0.351427	−	0.127909i
$698$	22.2503	−	19.7177i	0.842185	−	0.746327i
$699$	−3.16266	+	3.63157i	−0.119623	+	0.137359i
$700$	2.85644	+	6.69895i	0.107963	+	0.253197i
$701$			9.81062i			0.370542i	0.982687	+	0.185271i	$0.0593163\pi$
$701$			9.81062i			0.370542i	−0.982687	+	0.185271i	$0.940684\pi$
$702$	30.7962	+	0.865072i	1.16233	+	0.0326500i
$703$			41.8766i			1.57940i
$704$	−41.3108	−	24.5478i	−1.55696	−	0.925180i
$705$	−1.27232	−	0.248510i	−0.0479182	−	0.00935943i
$706$	7.69396	+	8.68216i	0.289566	+	0.326757i
$707$	−42.8987	−	15.6139i	−1.61337	−	0.587220i
$708$	11.3716	+	3.68576i	0.427372	+	0.138519i
$709$	3.47390	−	19.7015i	0.130465	−	0.739905i	−0.847446	−	0.530882i	$-0.821861\pi$
$709$	3.47390	−	19.7015i	0.130465	−	0.739905i	0.977911	−	0.209023i	$-0.0670282\pi$
$710$	−0.0937642	−	3.47251i	−0.00351891	−	0.130321i
$711$	0.513312	−	13.9733i	0.0192507	−	0.524039i
$712$	−23.1949	+	16.0251i	−0.869265	+	0.600565i
$713$	15.3163	+	42.0811i	0.573599	+	1.57595i
$714$	10.2963	+	17.4833i	0.385329	+	0.654295i
$715$	−16.1874	−	19.2914i	−0.605375	−	0.721458i
$716$	−2.14531	−	9.22371i	−0.0801740	−	0.344706i
$717$	24.6650	+	44.5922i	0.921133	+	1.66532i
$718$	−14.3882	−	11.4257i	−0.536963	−	0.426405i
$719$	−1.58361	−	2.74289i	−0.0590587	−	0.102293i	0.834984	−	0.550274i	$-0.185477\pi$
$719$	−1.58361	−	2.74289i	−0.0590587	−	0.102293i	−0.894043	+	0.447981i	$0.852143\pi$
$720$	−3.29093	+	11.5399i	−0.122646	+	0.430068i
$721$	26.4148	−	45.7518i	0.983739	−	1.70389i
$722$	−53.7768	+	21.2339i	−2.00137	+	0.790245i
$723$	−33.7462	−	12.9890i	−1.25503	−	0.483068i
$724$	18.3080	−	17.1284i	0.680413	−	0.636573i
$725$	−1.94043	+	0.342150i	−0.0720658	+	0.0127071i
$726$	−47.4016	−	39.0821i	−1.75924	−	1.45047i
$727$	−6.53046	+	7.78269i	−0.242201	+	0.288644i	−0.873427	−	0.486955i	$-0.838108\pi$
$727$	−6.53046	+	7.78269i	−0.242201	+	0.288644i	0.631226	+	0.775599i	$0.282552\pi$
$728$	3.49304	+	43.0371i	0.129461	+	1.59506i
$729$	−10.8476	−	24.7251i	−0.401764	−	0.915743i
$730$	10.4172	−	6.39538i	0.385559	−	0.236704i
$731$	−8.52653	−	7.15461i	−0.315365	−	0.264623i
$732$	0.736776	−	5.27014i	0.0272320	−	0.194790i
$733$	3.62037	+	20.5321i	0.133721	+	0.758371i	0.975742	+	0.218925i	$0.0702551\pi$
$733$	3.62037	+	20.5321i	0.133721	+	0.758371i	−0.842020	+	0.539446i	$0.818634\pi$
$734$	10.3309	−	2.11061i	0.381319	−	0.0779041i
$735$	3.89408	−	10.1170i	0.143635	−	0.373171i
$736$	28.1601	+	17.7790i	1.03799	+	0.655341i
$737$	68.7409	+	39.6876i	2.53210	+	1.46191i
$738$	−6.46595	+	17.2415i	−0.238015	+	0.634670i
$739$	−9.05649	+	5.22877i	−0.333149	+	0.192343i	−0.657238	−	0.753683i	$-0.728275\pi$
$739$	−9.05649	+	5.22877i	−0.333149	+	0.192343i	0.324090	+	0.946026i	$0.394942\pi$
$740$	10.7445	+	1.30148i	0.394976	+	0.0478433i
$741$	49.1723	−	27.1985i	1.80639	−	0.999160i
$742$	7.42502	+	2.47765i	0.272581	+	0.0909572i
$743$	−37.2092	+	31.2222i	−1.36507	+	1.14543i	−0.390692	+	0.920521i	$0.627764\pi$
$743$	−37.2092	+	31.2222i	−1.36507	+	1.14543i	−0.974380	+	0.224910i	$0.927791\pi$
$744$	−2.33225	−	37.1919i	−0.0855045	−	1.36352i
$745$	−2.42314	+	0.881949i	−0.0887768	+	0.0323121i
$746$	18.2700	−	33.7146i	0.668911	−	1.23438i
$747$	0.686698	+	0.0252261i	0.0251250	+	0.000922973i
$748$	22.8956	−	14.9217i	0.837144	−	0.545591i
$749$	22.3431	+	3.93970i	0.816400	+	0.143953i
$750$	−1.59065	−	1.86275i	−0.0580822	−	0.0680180i
$751$	−3.61817	+	9.94084i	−0.132029	+	0.362746i	−0.988037	−	0.154216i	$-0.950715\pi$
$751$	−3.61817	+	9.94084i	−0.132029	+	0.362746i	0.856008	+	0.516962i	$0.172937\pi$
$752$	2.07264	−	2.16034i	0.0755815	−	0.0787795i
$753$	−6.87093	+	35.1777i	−0.250391	+	1.28195i
$754$	−11.5555	−	1.71735i	−0.420827	−	0.0625423i
$755$	2.89528			0.105370
$756$	32.7919	−	18.8849i	1.19263	−	0.686837i
$757$	−1.18943			−0.0432307			−0.0216154	−	0.999766i	$-0.506881\pi$
$757$	−1.18943			−0.0432307			−0.0216154	+	0.999766i	$0.506881\pi$
$758$	17.8080	+	2.64658i	0.646815	+	0.0961281i
$759$	46.1895	+	40.2255i	1.67657	+	1.46009i
$760$	5.53202	+	21.1769i	0.200667	+	0.768166i
$761$	−13.2111	+	36.2972i	−0.478901	+	1.31577i	0.431525	+	0.902101i	$0.357976\pi$
$761$	−13.2111	+	36.2972i	−0.478901	+	1.31577i	−0.910427	+	0.413670i	$0.864247\pi$
$762$	−6.11987	+	17.2770i	−0.221699	+	0.625879i
$763$	49.3705	+	8.70535i	1.78733	+	0.315155i
$764$	−11.9225	−	18.2937i	−0.431342	−	0.661842i
$765$	−5.06333	−	4.57569i	−0.183065	−	0.165434i
$766$	−16.6795	+	30.7796i	−0.602654	+	1.11211i
$767$	−13.5951	+	4.94820i	−0.490889	+	0.178669i
$768$	−18.2984	−	20.8127i	−0.660288	−	0.751013i
$769$	35.4858	−	29.7761i	1.27965	−	1.07375i	0.286359	−	0.958122i	$-0.407555\pi$
$769$	35.4858	−	29.7761i	1.27965	−	1.07375i	0.993292	−	0.115632i	$-0.0368894\pi$
$770$	−29.3414	−	9.79090i	−1.05739	−	0.352840i
$771$	12.9873	+	7.81955i	0.467724	+	0.281614i
$772$	−3.42564	+	28.2808i	−0.123292	+	1.01785i
$773$	−16.7524	+	9.67199i	−0.602541	+	0.347877i	−0.770041	−	0.637995i	$-0.779764\pi$
$773$	−16.7524	+	9.67199i	−0.602541	+	0.347877i	0.167500	+	0.985872i	$0.446431\pi$
$774$	−13.4975	+	15.7717i	−0.485158	+	0.566902i
$775$	6.58758	+	3.80334i	0.236633	+	0.136620i
$776$	0.0414046	−	0.441316i	0.00148634	−	0.0158423i
$777$	−21.4545	−	26.5432i	−0.769674	−	0.952232i
$778$	−12.6750	+	2.58951i	−0.454419	+	0.0928386i
$779$	5.83225	+	33.0763i	0.208962	+	1.18508i
$780$	−5.45024	−	13.4617i	−0.195150	−	0.482007i
$781$	11.3026	+	9.48403i	0.404440	+	0.339365i
$782$	−16.1407	+	9.90913i	−0.577189	+	0.354350i
$783$	2.96677	+	9.79906i	0.106024	+	0.350190i
$784$	14.7813	+	20.2058i	0.527903	+	0.721635i
$785$	0.393751	−	0.469254i	0.0140536	−	0.0167484i
$786$	−13.8200	+	5.16565i	−0.492943	+	0.184253i
$787$	10.8838	−	1.91911i	0.387967	−	0.0684090i	0.0237372	−	0.999718i	$-0.492443\pi$
$787$	10.8838	−	1.91911i	0.387967	−	0.0684090i	0.364229	+	0.931309i	$0.381332\pi$
$788$	21.2992	+	22.7661i	0.758753	+	0.811007i
$789$	2.85534	+	18.1342i	0.101653	+	0.645595i
$790$	−6.13088	+	2.42080i	−0.218127	+	0.0861280i
$791$	−22.4468	+	38.8790i	−0.798117	+	1.38238i
$792$	−27.4128	−	42.9694i	−0.974072	−	1.52685i
$793$	3.22015	+	5.57746i	0.114351	+	0.198062i
$794$	28.6686	+	22.7659i	1.01741	+	0.807931i
$795$	−2.63235	−	0.0483337i	−0.0933597	−	0.00171422i
$796$	−38.6533	+	8.99025i	−1.37003	+	0.318651i
$797$	−1.13686	−	1.35486i	−0.0402698	−	0.0479917i	0.745534	−	0.666468i	$-0.232195\pi$
$797$	−1.13686	−	1.35486i	−0.0402698	−	0.0479917i	−0.785803	+	0.618476i	$0.787750\pi$
$798$	33.9929	−	60.0695i	1.20333	−	2.12644i
$799$	0.582329	+	1.59993i	0.0206013	+	0.0566016i
$800$	5.60540	−	0.761227i	0.198181	−	0.0269134i
$801$	−29.6189	+	4.10795i	−1.04653	+	0.145147i
$802$	−0.0766231	−	2.83769i	−0.00270566	−	0.100202i
$803$	−9.01568	+	51.1304i	−0.318156	+	1.80435i
$804$	30.6547	+	33.9959i	1.08111	+	1.19894i
$805$	20.1439	+	7.33180i	0.709981	+	0.258412i
$806$	29.9120	+	33.7539i	1.05361	+	1.18893i
$807$	12.7217	+	37.0555i	0.447825	+	1.30442i
$808$	−20.5217	+	28.9197i	−0.721950	+	1.01739i
$809$			15.8027i			0.555594i	0.960640	+	0.277797i	$0.0896043\pi$
$809$			15.8027i			0.555594i	−0.960640	+	0.277797i	$0.910396\pi$
$810$	−8.62519	+	9.35982i	−0.303058	+	0.328870i
$811$		−	37.7701i		−	1.32629i	−0.748492	−	0.663144i	$-0.769222\pi$
$811$		−	37.7701i		−	1.32629i	0.748492	−	0.663144i	$-0.230778\pi$
$812$	−13.1994	+	5.62823i	−0.463208	+	0.197512i
$813$	7.85141	+	22.8695i	0.275361	+	0.802067i
$814$	−34.4046	+	30.4886i	−1.20588	+	1.06863i
$815$	14.0312	+	5.10694i	0.491491	+	0.178888i
$816$	15.2139	−	4.11499i	0.532593	−	0.144053i
$817$	−6.57489	+	37.2881i	−0.230026	+	1.30454i
$818$	30.4635	−	0.822572i	1.06513	−	0.0287606i
$819$	−17.2331	+	42.4318i	−0.602173	+	1.48269i
$820$	8.66785	−	0.468438i	0.302694	−	0.0163586i
$821$	−12.9219	−	35.5026i	−0.450977	−	1.23905i	−0.932038	−	0.362362i	$-0.881971\pi$
$821$	−12.9219	−	35.5026i	−0.450977	−	1.23905i	0.481061	−	0.876687i	$-0.340252\pi$
$822$	0.345496	+	0.195514i	0.0120506	+	0.00681932i
$823$	24.6964	+	29.4320i	0.860861	+	1.02593i	0.999367	+	0.0355731i	$0.0113257\pi$
$823$	24.6964	+	29.4320i	0.860861	+	1.02593i	−0.138506	+	0.990362i	$0.544230\pi$
$824$	−28.8344	−	29.1989i	−1.00449	−	1.01719i
$825$	10.4022	+	0.191000i	0.362159	+	0.00664977i
$826$	−11.0508	+	13.9161i	−0.384507	+	0.484202i
$827$	−28.3948	−	49.1812i	−0.987383	−	1.71020i	−0.630829	−	0.775922i	$-0.717285\pi$
$827$	−28.3948	−	49.1812i	−0.987383	−	1.71020i	−0.356554	−	0.934275i	$-0.616048\pi$
$828$	18.1872	+	30.2810i	0.632049	+	1.05234i
$829$	−3.15577	+	5.46595i	−0.109604	+	0.189840i	−0.915610	−	0.402067i	$-0.868292\pi$
$829$	−3.15577	+	5.46595i	−0.109604	+	0.189840i	0.806006	+	0.591908i	$0.201625\pi$
$830$	−0.118967	−	0.301294i	−0.00412940	−	0.0104581i
$831$	−2.10894	−	13.3939i	−0.0731583	−	0.464628i
$832$	32.9546	+	6.23856i	1.14249	+	0.216283i
$833$	−14.0215	+	2.47237i	−0.485816	+	0.0856624i
$834$	16.7219	+	44.7372i	0.579032	+	1.54912i
$835$	−5.80638	+	6.91977i	−0.200938	+	0.239469i
$836$	−82.9013	−	42.0702i	−2.86720	−	1.45503i
$837$	15.5427	−	36.3413i	0.537233	−	1.25614i
$838$	−8.36762	−	13.6298i	−0.289055	−	0.470832i
$839$	12.7376	+	10.6881i	0.439749	+	0.368993i	0.835616	−	0.549315i	$-0.185111\pi$
$839$	12.7376	+	10.6881i	0.439749	+	0.368993i	−0.395866	+	0.918308i	$0.629556\pi$
$840$	−14.3559	−	10.5886i	−0.495326	−	0.365343i
$841$	4.36164	+	24.7361i	0.150401	+	0.852968i
$842$	0.757782	+	3.70913i	0.0261149	+	0.127825i
$843$	−5.11878	−	6.33290i	−0.176300	−	0.218117i
$844$	28.3008	−	37.6841i	0.974153	−	1.29714i
$845$	3.96373	+	2.28846i	0.136357	+	0.0787255i
$846$	2.99434	−	1.05699i	0.102947	−	0.0363402i
$847$	79.0909	−	45.6631i	2.71759	−	1.56900i
$848$	3.38353	−	5.05175i	0.116191	−	0.173478i
$849$	16.6824	+	10.0444i	0.572538	+	0.344722i
$850$	−1.01832	+	3.05170i	−0.0349280	+	0.104672i
$851$	24.4051	−	20.4783i	0.836595	−	0.701987i
$852$	4.51430	+	7.21275i	0.154657	+	0.247105i
$853$	−31.7446	+	11.5541i	−1.08691	+	0.395605i	−0.822477	−	0.568798i	$-0.807409\pi$
$853$	−31.7446	+	11.5541i	−1.08691	+	0.395605i	−0.264438	+	0.964403i	$0.585186\pi$
$854$	6.95492	+	3.76887i	0.237993	+	0.128968i
$855$	−4.86786	+	22.6991i	−0.166477	+	0.776294i
$856$	7.54806	−	15.9250i	0.257988	−	0.544305i
$857$	−1.63431	−	0.288172i	−0.0558268	−	0.00984377i	0.145665	−	0.989334i	$-0.453468\pi$
$857$	−1.63431	−	0.288172i	−0.0558268	−	0.00984377i	−0.201492	+	0.979490i	$0.564579\pi$
$858$	58.1458	+	20.5965i	1.98507	+	0.703151i
$859$	−2.96498	+	8.14622i	−0.101164	+	0.277945i	−0.979941	−	0.199286i	$-0.936138\pi$
$859$	−2.96498	+	8.14622i	−0.101164	+	0.277945i	0.878777	+	0.477232i	$0.158360\pi$
$860$	9.36287	+	2.84583i	0.319271	+	0.0970420i
$861$	−20.6426	−	17.9772i	−0.703498	−	0.612662i
$862$	1.13686	−	7.64958i	0.0387216	−	0.260546i
$863$	−22.9752			−0.782087			−0.391043	−	0.920372i	$-0.627886\pi$
$863$	−22.9752			−0.782087			−0.391043	+	0.920372i	$0.627886\pi$
$864$	−7.39830	−	28.4476i	−0.251695	−	0.967807i
$865$	9.95764			0.338570
$866$	−2.22647	+	14.9812i	−0.0756587	+	0.509083i
$867$	3.92630	−	20.1018i	0.133344	−	0.682693i
$868$	53.0016	+	16.1098i	1.79899	+	0.546801i
$869$	9.57547	−	26.3084i	0.324826	−	0.892451i
$870$	3.67030	−	3.13416i	0.124435	−	0.106258i
$871$	−54.5593	−	9.62027i	−1.84867	−	0.325971i
$872$	16.6786	−	35.1886i	0.564808	−	1.19164i
$873$	0.249859	−	0.398251i	0.00845646	−	0.0134788i
$874$	56.6453	+	30.6961i	1.91606	+	1.03831i
$875$	3.42167	−	1.24539i	0.115673	−	0.0421017i
$876$	−14.0377	+	26.4473i	−0.474291	+	0.893573i
$877$	−7.04586	+	5.91218i	−0.237922	+	0.199640i	−0.753951	−	0.656931i	$-0.771854\pi$
$877$	−7.04586	+	5.91218i	−0.237922	+	0.199640i	0.516029	+	0.856571i	$0.327410\pi$
$878$	−10.0456	+	30.1046i	−0.339021	+	1.01598i
$879$	−29.3078	+	16.2109i	−0.988526	+	0.546779i
$880$	−13.3707	+	19.9630i	−0.450725	+	0.672952i
$881$	−2.48931	+	1.43720i	−0.0838668	+	0.0484205i	−0.541347	−	0.840799i	$-0.682085\pi$
$881$	−2.48931	+	1.43720i	−0.0838668	+	0.0484205i	0.457480	+	0.889220i	$0.348752\pi$
$882$	4.35654	+	26.1940i	0.146692	+	0.881998i
$883$	−41.1666	−	23.7675i	−1.38536	−	0.799841i	−0.392576	−	0.919719i	$-0.628416\pi$
$883$	−41.1666	−	23.7675i	−1.38536	−	0.799841i	−0.992789	+	0.119879i	$0.961749\pi$
$884$	−11.4545	+	15.2523i	−0.385255	+	0.512989i
$885$	2.14703	−	5.57808i	0.0721715	−	0.187505i
$886$	10.5648	+	51.7120i	0.354933	+	1.73730i
$887$	−5.58343	−	31.6652i	−0.187473	−	1.06321i	−0.922736	−	0.385431i	$-0.874053\pi$
$887$	−5.58343	−	31.6652i	−0.187473	−	1.06321i	0.735263	−	0.677782i	$-0.237058\pi$
$888$	−24.2958	+	10.6086i	−0.815314	+	0.356003i
$889$	−20.8721	−	17.5138i	−0.700027	−	0.587393i
$890$	7.37502	+	12.0129i	0.247211	+	0.402675i
$891$	−5.45598	−	53.7846i	−0.182782	−	1.80185i
$892$	7.78083	+	3.94856i	0.260521	+	0.132208i
$893$	3.72292	−	4.43681i	0.124583	−	0.148472i
$894$	4.01815	−	4.87350i	0.134387	−	0.162994i
$895$	−4.66302	+	0.822216i	−0.155868	+	0.0274837i
$896$	38.5043	−	14.6472i	1.28634	−	0.489329i
$897$	−39.8969	−	15.3565i	−1.33212	−	0.512738i
$898$	−19.1123	−	48.4036i	−0.637786	−	1.61525i
$899$	−7.49397	+	12.9799i	−0.249938	+	0.432905i
$900$	5.67276	+	1.95444i	0.189092	+	0.0651479i
$901$	1.72893	+	2.99459i	0.0575990	+	0.0997643i
$902$	−22.9283	+	28.8731i	−0.763430	+	0.961371i
$903$	−14.9362	−	27.0033i	−0.497046	−	0.898613i
$904$	24.5029	+	24.8126i	0.814955	+	0.825256i
$905$	−8.05774	−	9.60284i	−0.267848	−	0.319209i
$906$	−6.11097	+	3.59889i	−0.203023	+	0.119565i
$907$	−6.60369	−	18.1435i	−0.219272	−	0.602445i	0.780469	−	0.625194i	$-0.214980\pi$
$907$	−6.60369	−	18.1435i	−0.219272	−	0.602445i	−0.999741	+	0.0227494i	$0.992758\pi$
$908$	16.3783	−	0.885137i	0.543534	−	0.0293743i
$909$	−33.2415	+	17.5976i	−1.10255	+	0.583676i
$910$	21.5814	−	0.582739i	0.715418	−	0.0193176i
$911$	−5.82444	+	33.0320i	−0.192972	+	1.09440i	0.722305	+	0.691575i	$0.243083\pi$
$911$	−5.82444	+	33.0320i	−0.192972	+	1.09440i	−0.915277	+	0.402825i	$0.868028\pi$
$912$	−37.9995	−	37.8209i	−1.25829	−	1.25237i
$913$	1.29289	+	0.470574i	0.0427885	+	0.0155737i
$914$	27.9492	−	24.7680i	0.924476	−	0.819252i
$915$	−2.61135	−	0.510051i	−0.0863286	−	0.0168618i
$916$	28.4924	−	12.1492i	0.941415	−	0.401420i
$917$		−	21.9322i		−	0.724265i
$918$	16.3747	+	3.36392i	0.540444	+	0.111026i
$919$			4.59730i			0.151651i	0.997121	+	0.0758255i	$0.0241592\pi$
$919$			4.59730i			0.151651i	−0.997121	+	0.0758255i	$0.975841\pi$
$920$	9.63635	−	13.5798i	0.317701	−	0.447713i
$921$	−12.1845	+	13.9911i	−0.401494	+	0.461022i
$922$	−3.17460	−	3.58234i	−0.104550	−	0.117978i
$923$	−9.67706	−	3.52216i	−0.318524	−	0.115933i
$924$	74.1001	−	15.8066i	2.43772	−	0.519999i
$925$	0.939701	−	5.32931i	0.0308972	−	0.175227i
$926$	−0.904527	−	33.4987i	−0.0297246	−	1.10083i
$927$	−13.3752	−	41.4198i	−0.439298	−	1.36040i
$928$	1.49990	+	11.0447i	0.0492365	+	0.362560i
$929$	−3.45783	−	9.50031i	−0.113448	−	0.311695i	0.869955	−	0.493131i	$-0.164148\pi$
$929$	−3.45783	−	9.50031i	−0.113448	−	0.311695i	−0.983403	+	0.181436i	$0.941925\pi$
$930$	−18.6318	+	0.160907i	−0.610960	+	0.00527635i
$931$	31.1322	+	37.1019i	1.02032	+	1.21597i
$932$	−5.41609	+	1.25971i	−0.177410	+	0.0412632i
$933$	−13.5437	+	22.4942i	−0.443399	+	0.736428i
$934$	−38.5890	−	30.6437i	−1.26267	−	1.00269i
$935$	−6.83220	−	11.8337i	−0.223437	−	0.387004i
$936$	28.2368	+	21.6384i	0.922949	+	0.707274i
$937$	17.5432	−	30.3858i	0.573112	−	0.992659i	−0.423132	−	0.906068i	$-0.639069\pi$
$937$	17.5432	−	30.3858i	0.573112	−	0.992659i	0.996244	−	0.0865913i	$-0.0275974\pi$
$938$	−63.2923	+	24.9911i	−2.06657	+	0.815990i
$939$	−6.89159	+	5.57037i	−0.224899	+	0.181782i
$940$	−1.02267	−	1.09310i	−0.0333559	−	0.0356531i
$941$	−33.8851	+	5.97486i	−1.10462	+	0.194775i	−0.696080	−	0.717964i	$-0.745074\pi$
$941$	−33.8851	+	5.97486i	−1.10462	+	0.194775i	−0.408543	+	0.912739i	$0.633963\pi$
$942$	−0.247785	+	1.47988i	−0.00807326	+	0.0482170i
$943$	16.4244	−	19.5738i	0.534851	−	0.637410i
$944$	8.14977	+	11.1406i	0.265252	+	0.362596i
$945$	−8.54390	−	16.8816i	−0.277933	−	0.549159i
$946$	−35.4217	+	21.7462i	−1.15166	+	0.707030i
$947$	30.7779	+	25.8257i	1.00015	+	0.839223i	0.987005	−	0.160691i	$-0.0513722\pi$
$947$	30.7779	+	25.8257i	1.00015	+	0.839223i	0.0131421	+	0.999914i	$0.495817\pi$
$948$	9.93114	−	12.7303i	0.322549	−	0.413461i
$949$	−6.29261	−	35.6872i	−0.204267	−	1.15845i
$950$	10.7223	−	2.19058i	0.347877	−	0.0710717i
$951$	25.1668	−	3.96265i	0.816088	−	0.128498i
$952$	−2.18849	+	23.3263i	−0.0709294	+	0.756009i
$953$	−43.6691	−	25.2124i	−1.41458	−	0.816709i	−0.418766	−	0.908094i	$-0.637537\pi$
$953$	−43.6691	−	25.2124i	−1.41458	−	0.816709i	−0.995816	+	0.0913850i	$0.970871\pi$
$954$	5.61608	−	3.17004i	0.181827	−	0.102634i
$955$	−9.45521	+	5.45897i	−0.305963	+	0.176648i
$956$	−7.07584	+	58.4155i	−0.228849	+	1.88929i
$957$	−0.376340	+	20.4962i	−0.0121653	+	0.662548i
$958$	44.2928	+	14.7800i	1.43104	+	0.477521i
$959$	−0.452063	+	0.379326i	−0.0145979	+	0.0122491i
$960$	−10.8849	+	8.57431i	−0.351309	+	0.276735i
$961$	25.2416	−	9.18720i	0.814246	−	0.296361i
$962$	15.2868	−	28.2096i	0.492866	−	0.909513i
$963$	14.7505	−	11.4814i	0.475329	−	0.369983i
$964$	−22.7977	−	34.9804i	−0.734265	−	1.12664i
$965$	14.0274	+	2.47340i	0.451557	+	0.0796217i
$966$	−51.6307	+	9.56433i	−1.66119	+	0.307727i
$967$	12.1488	−	33.3786i	0.390679	−	1.07338i	−0.576013	−	0.817441i	$-0.695392\pi$
$967$	12.1488	−	33.3786i	0.390679	−	1.07338i	0.966692	−	0.255942i	$-0.0823856\pi$
$968$	−17.9298	−	68.6363i	−0.576286	−	2.20606i
$969$	28.8383	−	9.90059i	0.926419	−	0.318053i
$970$	−0.219219	−	0.0325798i	−0.00703871	−	0.00104608i
$971$	21.4422			0.688114			0.344057	−	0.938949i	$-0.388199\pi$
$971$	21.4422			0.688114			0.344057	+	0.938949i	$0.388199\pi$
$972$	6.57045	−	30.4767i	0.210747	−	0.977541i
$973$	−70.9974			−2.27607
$974$	8.92716	+	1.32673i	0.286045	+	0.0425112i
$975$	−6.86811	+	2.35792i	−0.219956	+	0.0755139i
$976$	4.25397	−	4.43396i	0.136166	−	0.141928i
$977$	3.82361	−	10.5053i	0.122328	−	0.336094i	−0.863380	−	0.504554i	$-0.831657\pi$
$977$	3.82361	−	10.5053i	0.122328	−	0.336094i	0.985709	+	0.168460i	$0.0538793\pi$
$978$	−35.9632	+	6.66200i	−1.14998	+	0.213027i
$979$	−58.9625	−	10.3967i	−1.88445	−	0.332279i
$980$	10.4870	−	6.83468i	0.334995	−	0.218326i
$981$	32.5935	−	25.3698i	1.04063	−	0.809997i
$982$	20.4987	−	37.8275i	0.654141	−	1.20712i
$983$	−14.2641	+	5.19170i	−0.454954	+	0.165590i	−0.559324	−	0.828949i	$-0.688939\pi$
$983$	−14.2641	+	5.19170i	−0.454954	+	0.165590i	0.104371	+	0.994538i	$0.466717\pi$
$984$	−17.7126	+	11.7630i	−0.564658	+	0.374991i
$985$	11.9411	−	10.0198i	0.380476	−	0.319258i
$986$	−6.01296	−	2.00646i	−0.191492	−	0.0638986i
$987$	−0.0866586	+	4.71959i	−0.00275837	+	0.150226i
$988$	64.4155	+	7.80261i	2.04933	+	0.248234i
$989$	24.9462	−	14.4027i	0.793242	−	0.457979i
$990$	−22.1930	+	12.5270i	−0.705341	+	0.398135i
$991$	−4.43436	−	2.56018i	−0.140862	−	0.0813268i	0.427913	−	0.903820i	$-0.359249\pi$
$991$	−4.43436	−	2.56018i	−0.140862	−	0.0813268i	−0.568775	+	0.822493i	$0.692582\pi$
$992$	22.9718	−	36.3850i	0.729355	−	1.15522i
$993$	3.80313	−	0.598825i	0.120689	−	0.0190031i
$994$	−12.3929	+	2.53189i	−0.393080	+	0.0803068i
$995$	3.44562	+	19.5411i	0.109234	+	0.619494i
$996$	0.625613	+	0.488053i	0.0198233	+	0.0154646i
$997$	−9.61861	−	8.07097i	−0.304624	−	0.255610i	0.477642	−	0.878555i	$-0.341492\pi$
$997$	−9.61861	−	8.07097i	−0.304624	−	0.255610i	−0.782266	+	0.622945i	$0.785936\pi$
$998$	18.3157	−	11.2444i	0.579772	−	0.355935i
$999$	−28.0765	−	1.54797i	−0.888300	−	0.0489755i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	540.2.be.a.11.34	yes	432
4.3	odd	2	inner	540.2.be.a.11.7	✓	432
27.5	odd	18	inner	540.2.be.a.491.7	yes	432
108.59	even	18	inner	540.2.be.a.491.34	yes	432

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
540.2.be.a.11.7	✓	432	4.3	odd	2	inner
540.2.be.a.11.34	yes	432	1.1	even	1	trivial
540.2.be.a.491.7	yes	432	27.5	odd	18	inner
540.2.be.a.491.34	yes	432	108.59	even	18	inner

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:	\( N \)	\(=\)	\( 540 = 2^{2} \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	540.be (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.207894 + 1.39885i) q^{2} +(-1.63820 + 0.562416i) q^{3} +(-1.91356 - 0.581624i) q^{4} +(-0.342020 + 0.939693i) q^{5} +(-0.446166 - 2.40851i) q^{6} +(3.58594 + 0.632299i) q^{7} +(1.21142 - 2.55587i) q^{8} +(2.36738 - 1.84270i) q^{9} +(-1.24338 - 0.673791i) q^{10} +(5.64449 - 2.05443i) q^{11} +(3.46190 - 0.123404i) q^{12} +(-3.21163 + 2.69488i) q^{13} +(-1.62999 + 4.88475i) q^{14} +(0.0317976 - 1.73176i) q^{15} +(3.32343 + 2.22594i) q^{16} +(-1.97007 + 1.13742i) q^{17} +(2.08549 + 3.69469i) q^{18} +(6.70166 + 3.86920i) q^{19} +(1.20102 - 1.59923i) q^{20} +(-6.23010 + 0.980964i) q^{21} +(1.70038 + 8.32289i) q^{22} +(-1.02230 - 5.79773i) q^{23} +(-0.547083 + 4.86834i) q^{24} +(-0.766044 - 0.642788i) q^{25} +(-3.10205 - 5.05283i) q^{26} +(-2.84186 + 4.35015i) q^{27} +(-6.49416 - 3.29561i) q^{28} +(1.26653 - 1.50939i) q^{29} +(2.41586 + 0.404502i) q^{30} +(-7.49112 + 1.32089i) q^{31} +(-3.80468 + 4.18622i) q^{32} +(-8.09134 + 6.54011i) q^{33} +(-1.18152 - 2.99230i) q^{34} +(-1.82063 + 3.15343i) q^{35} +(-5.60187 + 2.14919i) q^{36} +(2.70576 + 4.68652i) q^{37} +(-6.80566 + 8.57023i) q^{38} +(3.74564 - 6.22101i) q^{39} +(1.98740 + 2.01252i) q^{40} +(2.78986 + 3.32482i) q^{41} +(-0.0770250 - 8.91890i) q^{42} +(1.67347 + 4.59783i) q^{43} +(-11.9960 + 0.648301i) q^{44} +(0.921879 + 2.85484i) q^{45} +(8.32268 - 0.224728i) q^{46} +(0.129968 - 0.737083i) q^{47} +(-6.69634 - 1.77738i) q^{48} +(5.88135 + 2.14063i) q^{49} +(1.05842 - 0.937950i) q^{50} +(2.58766 - 2.97132i) q^{51} +(7.71305 - 3.28885i) q^{52} -1.52004i q^{53} +(-5.49440 - 4.87971i) q^{54} +6.00674i q^{55} +(5.96016 - 8.39922i) q^{56} +(-13.1547 - 2.56939i) q^{57} +(1.84810 + 2.08547i) q^{58} +(3.24272 + 1.18025i) q^{59} +(-1.06808 + 3.29533i) q^{60} +(0.266750 - 1.51282i) q^{61} +(-0.290366 - 10.7535i) q^{62} +(9.65441 - 5.11092i) q^{63} +(-5.06492 - 6.19246i) q^{64} +(-1.43391 - 3.93965i) q^{65} +(-7.46649 - 12.6782i) q^{66} +(8.49402 + 10.1228i) q^{67} +(4.43140 - 1.03069i) q^{68} +(4.93546 + 8.92287i) q^{69} +(-4.03267 - 3.20237i) q^{70} +(1.22816 + 2.12724i) q^{71} +(-1.84180 - 8.28298i) q^{72} +(-4.32175 + 7.48548i) q^{73} +(-7.11824 + 2.81066i) q^{74} +(1.61645 + 0.622176i) q^{75} +(-10.5736 - 11.3018i) q^{76} +(21.5398 - 3.79805i) q^{77} +(7.92357 + 6.53289i) q^{78} +(2.99597 - 3.57046i) q^{79} +(-3.22838 + 2.36168i) q^{80} +(2.20893 - 8.72471i) q^{81} +(-5.23092 + 3.21138i) q^{82} +(0.175465 + 0.147233i) q^{83} +(12.4922 + 1.74644i) q^{84} +(-0.395022 - 2.24028i) q^{85} +(-6.77957 + 1.38508i) q^{86} +(-1.22592 + 3.18499i) q^{87} +(1.58701 - 16.9153i) q^{88} +(-8.63210 - 4.98374i) q^{89} +(-4.18515 + 0.696066i) q^{90} +(-13.2207 + 7.63297i) q^{91} +(-1.41587 + 11.6889i) q^{92} +(11.5290 - 6.37700i) q^{93} +(1.00405 + 0.335040i) q^{94} +(-5.92796 + 4.97415i) q^{95} +(3.87842 - 8.99766i) q^{96} +(0.147263 - 0.0535994i) q^{97} +(-4.21712 + 7.78209i) q^{98} +(9.57694 - 15.2647i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 432 q + 18 q^{12} + 30 q^{14} + 30 q^{24} + 12 q^{29} - 24 q^{30} + 60 q^{33} - 60 q^{36} - 60 q^{38} + 60 q^{41} - 60 q^{42} - 72 q^{44} + 12 q^{45} - 150 q^{48} + 54 q^{52} - 84 q^{54} - 84 q^{56} - 12 q^{57}+ \cdots + 36 q^{97}+O(q^{100}) \) 432 * q + 18 * q^12 + 30 * q^14 + 30 * q^24 + 12 * q^29 - 24 * q^30 + 60 * q^33 - 60 * q^36 - 60 * q^38 + 60 * q^41 - 60 * q^42 - 72 * q^44 + 12 * q^45 - 150 * q^48 + 54 * q^52 - 84 * q^54 - 84 * q^56 - 12 * q^57 + 54 * q^58 - 198 * q^62 - 48 * q^66 - 138 * q^68 - 48 * q^69 - 84 * q^72 - 84 * q^74 - 48 * q^77 - 78 * q^78 - 66 * q^84 + 54 * q^86 - 36 * q^89 + 120 * q^92 - 54 * q^94 + 210 * q^96 + 36 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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