LMFDB - Embedded newform 135.2.p.a.4.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [135,2,Mod(4,135)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("135.4"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(135, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([2, 9])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 135 = 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	135.p (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:	$1.07798042729$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$16$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			4.5
Character	$\chi$	$=$	135.4
Dual form			135.2.p.a.34.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.557159 + 1.53078i) q^{2} +(-0.844941 - 1.51198i) q^{3} +(-0.500777 - 0.420202i) q^{4} +(-1.06369 + 1.96687i) q^{5} +(2.78527 - 0.451009i) q^{6} +(1.77805 + 2.11900i) q^{7} +(-1.89930 + 1.09656i) q^{8} +(-1.57215 + 2.55506i) q^{9} +(-2.41819 - 2.72414i) q^{10} +(0.0600421 + 0.340516i) q^{11} +(-0.212208 + 1.11221i) q^{12} +(1.40253 + 3.85342i) q^{13} +(-4.23438 + 1.54119i) q^{14} +(3.87261 - 0.0536071i) q^{15} +(-0.847418 - 4.80595i) q^{16} +(0.713284 + 0.411815i) q^{17} +(-3.03531 - 3.83019i) q^{18} +(-2.61103 - 4.52244i) q^{19} +(1.35915 - 0.537995i) q^{20} +(1.70153 - 4.47880i) q^{21} +(-0.554708 - 0.0978100i) q^{22} +(2.95144 - 3.51739i) q^{23} +(3.26278 + 1.94517i) q^{24} +(-2.73712 - 4.18428i) q^{25} -6.68017 q^{26} +(5.19157 + 0.218173i) q^{27} -1.80829i q^{28} +(6.53490 + 2.37851i) q^{29} +(-2.07560 + 5.95799i) q^{30} +(5.66883 + 4.75671i) q^{31} +(3.50939 + 0.618800i) q^{32} +(0.464120 - 0.378498i) q^{33} +(-1.02781 + 0.862436i) q^{34} +(-6.05909 + 1.24322i) q^{35} +(1.86094 - 0.618897i) q^{36} +(-4.91932 - 2.84017i) q^{37} +(8.37763 - 1.47720i) q^{38} +(4.64122 - 5.37651i) q^{39} +(-0.136517 - 4.90208i) q^{40} +(-2.88576 + 1.05033i) q^{41} +(5.90805 + 5.10007i) q^{42} +(2.26877 - 0.400046i) q^{43} +(0.113018 - 0.195752i) q^{44} +(-3.35318 - 5.81001i) q^{45} +(3.73993 + 6.47776i) q^{46} +(3.73422 + 4.45027i) q^{47} +(-6.55046 + 5.34202i) q^{48} +(-0.113154 + 0.641729i) q^{49} +(7.93023 - 1.85862i) q^{50} +(0.0199712 - 1.42643i) q^{51} +(0.916858 - 2.51905i) q^{52} -12.6853i q^{53} +(-3.22650 + 7.82560i) q^{54} +(-0.733615 - 0.244109i) q^{55} +(-5.70067 - 2.07488i) q^{56} +(-4.63166 + 7.76902i) q^{57} +(-7.28195 + 8.67829i) q^{58} +(1.74980 - 9.92363i) q^{59} +(-1.96184 - 1.60043i) q^{60} +(-9.63252 + 8.08265i) q^{61} +(-10.4399 + 6.02749i) q^{62} +(-8.20954 + 1.21165i) q^{63} +(1.97755 - 3.42522i) q^{64} +(-9.07102 - 1.34027i) q^{65} +(0.320809 + 0.921350i) q^{66} +(3.08859 + 8.48583i) q^{67} +(-0.184151 - 0.505951i) q^{68} +(-7.81201 - 1.49052i) q^{69} +(1.47277 - 9.96781i) q^{70} +(0.949232 - 1.64412i) q^{71} +(0.184197 - 6.57680i) q^{72} +(-0.359906 + 0.207792i) q^{73} +(7.08853 - 5.94798i) q^{74} +(-4.01383 + 7.67393i) q^{75} +(-0.592793 + 3.36190i) q^{76} +(-0.614795 + 0.732684i) q^{77} +(5.64436 + 10.1003i) q^{78} +(13.5502 + 4.93189i) q^{79} +(10.3540 + 3.44529i) q^{80} +(-4.05670 - 8.03388i) q^{81} -5.00267i q^{82} +(-2.03152 + 5.58154i) q^{83} +(-2.73409 + 1.52790i) q^{84} +(-1.56870 + 0.964890i) q^{85} +(-0.651684 + 3.69588i) q^{86} +(-1.92536 - 11.8903i) q^{87} +(-0.487435 - 0.580903i) q^{88} +(8.98648 + 15.5650i) q^{89} +(10.7621 - 1.89589i) q^{90} +(-5.67162 + 9.82354i) q^{91} +(-2.95603 + 0.521227i) q^{92} +(2.40221 - 12.5903i) q^{93} +(-8.89294 + 3.23677i) q^{94} +(11.6724 - 0.325062i) q^{95} +(-2.02962 - 5.82897i) q^{96} +(3.81769 - 0.673161i) q^{97} +(-0.919302 - 0.530759i) q^{98} +(-0.964435 - 0.381930i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 12 q^{4} - 9 q^{5} - 6 q^{6} - 18 q^{9} - 3 q^{10} - 6 q^{11} - 18 q^{14} - 21 q^{15} - 24 q^{16} - 6 q^{19} - 57 q^{20} + 24 q^{21} - 30 q^{24} + 3 q^{25} + 48 q^{26} - 30 q^{29} - 51 q^{30} - 30 q^{31}+ \cdots + 36 q^{99}+O(q^{100}) $ 96 * q - 12 * q^4 - 9 * q^5 - 6 * q^6 - 18 * q^9 - 3 * q^10 - 6 * q^11 - 18 * q^14 - 21 * q^15 - 24 * q^16 - 6 * q^19 - 57 * q^20 + 24 * q^21 - 30 * q^24 + 3 * q^25 + 48 * q^26 - 30 * q^29 - 51 * q^30 - 30 * q^31 - 24 * q^34 - 12 * q^35 + 54 * q^36 - 6 * q^39 - 9 * q^40 - 12 * q^41 + 78 * q^44 + 45 * q^45 - 6 * q^46 - 30 * q^49 + 84 * q^50 - 90 * q^51 + 108 * q^54 - 12 * q^55 - 96 * q^56 + 66 * q^59 + 84 * q^60 + 6 * q^61 + 45 * q^65 - 150 * q^66 + 24 * q^69 - 33 * q^70 - 90 * q^71 + 66 * q^74 + 39 * q^75 + 12 * q^76 + 24 * q^79 + 30 * q^80 - 54 * q^81 + 198 * q^84 - 21 * q^85 + 18 * q^86 + 96 * q^89 + 90 * q^90 - 6 * q^91 + 24 * q^94 + 87 * q^95 + 42 * q^96 + 36 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{1}{9}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.557159	+	1.53078i	−0.393971	+	1.08243i	0.571201	+	0.820810i	$0.306478\pi$
$2$	−0.557159	+	1.53078i	−0.393971	+	1.08243i	−0.965172	+	0.261616i	$0.915745\pi$
$3$	−0.844941	−	1.51198i	−0.487827	−	0.872940i
$3$	−0.844941	−	1.51198i	−0.487827	−	0.872940i
$4$	−0.500777	−	0.420202i	−0.250388	−	0.210101i
$5$	−1.06369	+	1.96687i	−0.475698	+	0.879609i
$5$	−1.06369	+	1.96687i	−0.475698	+	0.879609i
$6$	2.78527	−	0.451009i	1.13708	−	0.184124i
$7$	1.77805	+	2.11900i	0.672040	+	0.800907i	0.989060	−	0.147512i	$-0.0471266\pi$
$7$	1.77805	+	2.11900i	0.672040	+	0.800907i	−0.317020	+	0.948419i	$0.602682\pi$
$8$	−1.89930	+	1.09656i	−0.671505	+	0.387694i
$9$	−1.57215	+	2.55506i	−0.524049	+	0.851688i
$10$	−2.41819	−	2.72414i	−0.764700	−	0.861448i
$11$	0.0600421	+	0.340516i	0.0181034	+	0.102669i	0.992521	−	0.122077i	$-0.0389556\pi$
$11$	0.0600421	+	0.340516i	0.0181034	+	0.102669i	−0.974417	+	0.224747i	$0.927845\pi$
$12$	−0.212208	+	1.11221i	−0.0612592	+	0.321067i
$13$	1.40253	+	3.85342i	0.388992	+	1.06875i	0.967456	+	0.253039i	$0.0814299\pi$
$13$	1.40253	+	3.85342i	0.388992	+	1.06875i	−0.578464	+	0.815708i	$0.696348\pi$
$14$	−4.23438	+	1.54119i	−1.13169	+	0.411900i
$15$	3.87261	−	0.0536071i	0.999904	−	0.0138413i
$16$	−0.847418	−	4.80595i	−0.211855	−	1.20149i
$17$	0.713284	+	0.411815i	0.172997	+	0.0998798i	0.583998	−	0.811755i	$-0.301488\pi$
$17$	0.713284	+	0.411815i	0.172997	+	0.0998798i	−0.411001	+	0.911635i	$0.634821\pi$
$18$	−3.03531	−	3.83019i	−0.715429	−	0.902785i
$19$	−2.61103	−	4.52244i	−0.599012	−	1.03752i	−0.992967	−	0.118390i	$-0.962227\pi$
$19$	−2.61103	−	4.52244i	−0.599012	−	1.03752i	0.393955	−	0.919130i	$-0.371107\pi$
$20$	1.35915	−	0.537995i	0.303916	−	0.120299i
$21$	1.70153	−	4.47880i	0.371304	−	0.977355i
$22$	−0.554708	−	0.0978100i	−0.118264	−	0.0208532i
$23$	2.95144	−	3.51739i	0.615418	−	0.733427i	−0.364857	−	0.931063i	$-0.618882\pi$
$23$	2.95144	−	3.51739i	0.615418	−	0.733427i	0.980275	+	0.197637i	$0.0633267\pi$
$24$	3.26278	+	1.94517i	0.666012	+	0.397056i
$25$	−2.73712	−	4.18428i	−0.547423	−	0.836856i
$26$	−6.68017			−1.31009
$27$	5.19157	+	0.218173i	0.999118	+	0.0419873i
$28$		−	1.80829i		−	0.341734i
$29$	6.53490	+	2.37851i	1.21350	+	0.441678i	0.867916	−	0.496710i	$-0.165459\pi$
$29$	6.53490	+	2.37851i	1.21350	+	0.441678i	0.345583	+	0.938388i	$0.387681\pi$
$30$	−2.07560	+	5.95799i	−0.378951	+	1.08778i
$31$	5.66883	+	4.75671i	1.01815	+	0.854331i	0.989394	−	0.145256i	$-0.0464005\pi$
$31$	5.66883	+	4.75671i	1.01815	+	0.854331i	0.0287575	+	0.999586i	$0.490845\pi$
$32$	3.50939	+	0.618800i	0.620378	+	0.109389i
$33$	0.464120	−	0.378498i	0.0807929	−	0.0658881i
$34$	−1.02781	+	0.862436i	−0.176268	+	0.147907i
$35$	−6.05909	+	1.24322i	−1.02417	+	0.210143i
$36$	1.86094	−	0.618897i	0.310156	−	0.103150i
$37$	−4.91932	−	2.84017i	−0.808732	−	0.466921i	0.0377835	−	0.999286i	$-0.487970\pi$
$37$	−4.91932	−	2.84017i	−0.808732	−	0.466921i	−0.846515	+	0.532364i	$0.821304\pi$
$38$	8.37763	−	1.47720i	1.35903	−	0.239634i
$39$	4.64122	−	5.37651i	0.743191	−	0.860930i
$40$	−0.136517	−	4.90208i	−0.0215853	−	0.775087i
$41$	−2.88576	+	1.05033i	−0.450680	+	0.164034i	−0.557381	−	0.830257i	$-0.688194\pi$
$41$	−2.88576	+	1.05033i	−0.450680	+	0.164034i	0.106700	+	0.994291i	$0.465971\pi$
$42$	5.90805	+	5.10007i	0.911632	+	0.786959i
$43$	2.26877	−	0.400046i	0.345984	−	0.0610064i	0.00204410	−	0.999998i	$-0.499349\pi$
$43$	2.26877	−	0.400046i	0.345984	−	0.0610064i	0.343940	+	0.938992i	$0.388238\pi$
$44$	0.113018	−	0.195752i	0.0170380	−	0.0295108i
$45$	−3.35318	−	5.81001i	−0.499863	−	0.866104i
$46$	3.73993	+	6.47776i	0.551423	+	0.955093i
$47$	3.73422	+	4.45027i	0.544692	+	0.649139i	0.966233	−	0.257671i	$-0.0829550\pi$
$47$	3.73422	+	4.45027i	0.544692	+	0.649139i	−0.421541	+	0.906809i	$0.638511\pi$
$48$	−6.55046	+	5.34202i	−0.945478	+	0.771055i
$49$	−0.113154	+	0.641729i	−0.0161649	+	0.0916755i
$50$	7.93023	−	1.85862i	1.12150	−	0.262848i
$51$	0.0199712	−	1.42643i	0.00279652	−	0.199740i
$52$	0.916858	−	2.51905i	0.127145	−	0.349329i
$53$		−	12.6853i		−	1.74247i	−0.490869	−	0.871233i	$-0.663321\pi$
$53$		−	12.6853i		−	1.74247i	0.490869	−	0.871233i	$-0.336679\pi$
$54$	−3.22650	+	7.82560i	−0.439072	+	1.06493i
$55$	−0.733615	−	0.244109i	−0.0989206	−	0.0329157i
$56$	−5.70067	−	2.07488i	−0.761785	−	0.277267i
$57$	−4.63166	+	7.76902i	−0.613478	+	1.02903i
$58$	−7.28195	+	8.67829i	−0.956167	+	1.13952i
$59$	1.74980	−	9.92363i	0.227805	−	1.29195i	−0.629445	−	0.777045i	$-0.716718\pi$
$59$	1.74980	−	9.92363i	0.227805	−	1.29195i	0.857250	−	0.514901i	$-0.172171\pi$
$60$	−1.96184	−	1.60043i	−0.253272	−	0.206615i
$61$	−9.63252	+	8.08265i	−1.23332	+	1.03488i	−0.235302	+	0.971922i	$0.575608\pi$
$61$	−9.63252	+	8.08265i	−1.23332	+	1.03488i	−0.998016	+	0.0629545i	$0.979948\pi$
$62$	−10.4399	+	6.02749i	−1.32587	+	0.765492i
$63$	−8.20954	+	1.21165i	−1.03430	+	0.152654i
$64$	1.97755	−	3.42522i	0.247194	−	0.428153i
$65$	−9.07102	−	1.34027i	−1.12512	−	0.166240i
$66$	0.320809	+	0.921350i	0.0394889	+	0.113410i
$67$	3.08859	+	8.48583i	0.377331	+	1.03671i	0.972458	+	0.233078i	$0.0748797\pi$
$67$	3.08859	+	8.48583i	0.377331	+	1.03671i	−0.595127	+	0.803632i	$0.702898\pi$
$68$	−0.184151	−	0.505951i	−0.0223316	−	0.0613555i
$69$	−7.81201	−	1.49052i	−0.940455	−	0.179438i
$70$	1.47277	−	9.96781i	0.176030	−	1.19138i
$71$	0.949232	−	1.64412i	0.112653	−	0.195121i	−0.804186	−	0.594378i	$-0.797398\pi$
$71$	0.949232	−	1.64412i	0.112653	−	0.195121i	0.916839	+	0.399257i	$0.130732\pi$
$72$	0.184197	−	6.57680i	0.0217078	−	0.775083i
$73$	−0.359906	+	0.207792i	−0.0421238	+	0.0243202i	−0.520914	−	0.853609i	$-0.674409\pi$
$73$	−0.359906	+	0.207792i	−0.0421238	+	0.0243202i	0.478790	+	0.877929i	$0.341075\pi$
$74$	7.08853	−	5.94798i	0.824025	−	0.691439i
$75$	−4.01383	+	7.67393i	−0.463477	+	0.886109i
$76$	−0.592793	+	3.36190i	−0.0679980	+	0.385636i
$77$	−0.614795	+	0.732684i	−0.0700624	+	0.0834971i
$78$	5.64436	+	10.1003i	0.639097	+	1.14363i
$79$	13.5502	+	4.93189i	1.52452	+	0.554881i	0.962273	−	0.272087i	$-0.0877138\pi$
$79$	13.5502	+	4.93189i	1.52452	+	0.554881i	0.562250	+	0.826968i	$0.309936\pi$
$80$	10.3540	+	3.44529i	1.15762	+	0.385196i
$81$	−4.05670	−	8.03388i	−0.450744	−	0.892653i
$82$		−	5.00267i		−	0.552453i
$83$	−2.03152	+	5.58154i	−0.222988	+	0.612654i	−0.999855	−	0.0170101i	$-0.994585\pi$
$83$	−2.03152	+	5.58154i	−0.222988	+	0.612654i	0.776867	+	0.629664i	$0.216807\pi$
$84$	−2.73409	+	1.52790i	−0.298313	+	0.166707i
$85$	−1.56870	+	0.964890i	−0.170149	+	0.104657i
$86$	−0.651684	+	3.69588i	−0.0702729	+	0.398537i
$87$	−1.92536	−	11.8903i	−0.206420	−	1.27478i
$88$	−0.487435	−	0.580903i	−0.0519608	−	0.0619244i
$89$	8.98648	+	15.5650i	0.952565	+	1.64989i	0.739845	+	0.672777i	$0.234899\pi$
$89$	8.98648	+	15.5650i	0.952565	+	1.64989i	0.212720	+	0.977113i	$0.431768\pi$
$90$	10.7621	−	1.89589i	1.13443	−	0.199845i
$91$	−5.67162	+	9.82354i	−0.594548	+	1.02979i
$92$	−2.95603	+	0.521227i	−0.308187	+	0.0543417i
$93$	2.40221	−	12.5903i	0.249098	−	1.30555i
$94$	−8.89294	+	3.23677i	−0.917237	+	0.333847i
$95$	11.6724	−	0.325062i	1.19756	−	0.0333507i
$96$	−2.02962	−	5.82897i	−0.207147	−	0.594916i
$97$	3.81769	−	0.673161i	0.387627	−	0.0683492i	0.0235616	−	0.999722i	$-0.492499\pi$
$97$	3.81769	−	0.673161i	0.387627	−	0.0683492i	0.364066	+	0.931373i	$0.381388\pi$
$98$	−0.919302	−	0.530759i	−0.0928635	−	0.0536148i
$99$	−0.964435	−	0.381930i	−0.0969293	−	0.0383854i
$100$	−0.387557	+	3.24553i	−0.0387557	+	0.324553i
$101$	−3.66299	+	3.07362i	−0.364482	+	0.305836i	−0.806574	−	0.591133i	$-0.798681\pi$
$101$	−3.66299	+	3.07362i	−0.364482	+	0.305836i	0.442092	+	0.896970i	$0.354236\pi$
$102$	2.17242	+	0.825319i	0.215102	+	0.0817188i
$103$	4.73992	+	0.835776i	0.467038	+	0.0823514i	0.402215	−	0.915545i	$-0.368241\pi$
$103$	4.73992	+	0.835776i	0.467038	+	0.0823514i	0.0648233	+	0.997897i	$0.479352\pi$
$104$	−6.88934	−	5.78085i	−0.675556	−	0.566859i
$105$	6.99930	+	8.11075i	0.683062	+	0.791528i
$106$	19.4185	+	7.06775i	1.88609	+	0.686481i
$107$		−	8.59638i		−	0.831044i	−0.909583	−	0.415522i	$-0.863599\pi$
$107$		−	8.59638i		−	0.831044i	0.909583	−	0.415522i	$-0.136401\pi$
$108$	−2.50814	−	2.29076i	−0.241346	−	0.220429i
$109$	−4.48236			−0.429333			−0.214666	−	0.976687i	$-0.568866\pi$
$109$	−4.48236			−0.429333			−0.214666	+	0.976687i	$0.568866\pi$
$110$	0.782418	−	0.986996i	0.0746006	−	0.0941064i
$111$	−0.137736	+	9.83768i	−0.0130733	+	0.933751i
$112$	8.67705	−	10.3409i	0.819904	−	0.977124i
$113$	−8.00419	−	1.41135i	−0.752971	−	0.132769i	−0.216027	−	0.976387i	$-0.569310\pi$
$113$	−8.00419	−	1.41135i	−0.752971	−	0.132769i	−0.536943	+	0.843618i	$0.680421\pi$
$114$	−9.31211	−	11.4186i	−0.872159	−	1.06945i
$115$	3.77881	+	9.54651i	0.352375	+	0.890216i
$116$	−2.27307	−	3.93707i	−0.211049	−	0.365548i
$117$	−12.0507	−	2.47459i	−1.11409	−	0.228776i
$118$	14.2160	+	8.20760i	1.30869	+	0.755571i
$119$	0.395621	+	2.24368i	0.0362665	+	0.205678i
$120$	−7.29648	+	4.34838i	−0.666074	+	0.396951i
$121$	10.2243	−	3.72133i	0.929479	−	0.338303i
$122$	−7.00592	−	19.2486i	−0.634286	−	1.74269i
$123$	4.02638	+	3.47574i	0.363046	+	0.313397i
$124$	−0.840040	−	4.76410i	−0.0754378	−	0.427829i
$125$	11.1414	−	0.932751i	0.996514	−	0.0834278i
$126$	2.71924	−	13.2421i	0.242249	−	1.17970i
$127$	−6.37416	+	3.68012i	−0.565615	+	0.326558i	−0.755396	−	0.655268i	$-0.772556\pi$
$127$	−6.37416	+	3.68012i	−0.565615	+	0.326558i	0.189781	+	0.981826i	$0.439222\pi$
$128$	8.72264	+	10.3952i	0.770980	+	0.918818i
$129$	−2.52184	−	3.09231i	−0.222035	−	0.272263i
$130$	7.10565	−	13.1390i	0.623207	−	1.15237i
$131$	−6.66731	−	5.59453i	−0.582525	−	0.488797i	0.303250	−	0.952911i	$-0.401928\pi$
$131$	−6.66731	−	5.59453i	−0.582525	−	0.488797i	−0.885775	+	0.464114i	$0.846373\pi$
$132$	−0.391466	−	0.00548084i	−0.0340727	−	0.000477046i
$133$	4.94050	−	13.5739i	0.428396	−	1.17701i
$134$	−14.7108			−1.27082
$135$	−5.95135	+	9.97905i	−0.512211	+	0.858860i
$136$	−1.80632			−0.154891
$137$	1.04361	−	2.86731i	0.0891620	−	0.244970i	−0.887095	−	0.461587i	$-0.847280\pi$
$137$	1.04361	−	2.86731i	0.0891620	−	0.244970i	0.976257	+	0.216617i	$0.0695023\pi$
$138$	6.63419	−	11.1280i	0.564740	−	0.947280i
$139$	−7.41574	−	6.22255i	−0.628995	−	0.527789i	0.271621	−	0.962404i	$-0.412440\pi$
$139$	−7.41574	−	6.22255i	−0.628995	−	0.527789i	−0.900617	+	0.434615i	$0.856885\pi$
$140$	3.55665	+	1.92346i	0.300592	+	0.162562i
$141$	3.57351	−	9.40627i	0.300944	−	0.792151i
$142$	1.98791	+	2.36910i	0.166822	+	0.198811i
$143$	−1.22794	+	0.708951i	−0.102685	+	0.0592855i
$144$	13.6118	+	5.39046i	1.13431	+	0.449205i
$145$	−11.6293	+	10.3233i	−0.965763	+	0.857300i
$146$	−0.117559	−	0.666710i	−0.00972925	−	0.0551773i
$147$	1.06589	−	0.371137i	0.0879129	−	0.0306109i
$148$	1.27004	+	3.48940i	0.104396	+	0.286827i
$149$	9.84191	−	3.58216i	0.806280	−	0.293462i	0.0941940	−	0.995554i	$-0.469973\pi$
$149$	9.84191	−	3.58216i	0.806280	−	0.293462i	0.712086	+	0.702092i	$0.247750\pi$
$150$	−9.51076	−	10.4199i	−0.776551	−	0.850781i
$151$	−0.556200	−	3.15437i	−0.0452630	−	0.256699i	0.953777	−	0.300517i	$-0.0971591\pi$
$151$	−0.556200	−	3.15437i	−0.0452630	−	0.256699i	−0.999040	+	0.0438176i	$0.986048\pi$
$152$	9.91829	+	5.72633i	0.804479	+	0.464466i
$153$	−2.17360	+	1.17505i	−0.175725	+	0.0949974i
$154$	−0.779041	−	1.34934i	−0.0627769	−	0.108733i
$155$	−15.3857	+	6.09014i	−1.23581	+	0.489172i
$156$	−4.58343	+	0.742179i	−0.366968	+	0.0594219i
$157$	−19.2600	−	3.39606i	−1.53712	−	0.271035i	−0.659983	−	0.751280i	$-0.729437\pi$
$157$	−19.2600	−	3.39606i	−1.53712	−	0.271035i	−0.877134	+	0.480245i	$0.840548\pi$
$158$	−15.0993	+	17.9946i	−1.20123	+	1.43158i
$159$	−19.1800	+	10.7184i	−1.52107	+	0.850022i
$160$	−4.95001	+	6.24428i	−0.391332	+	0.493654i
$161$	12.7012			1.00099
$162$	14.5583	−	1.73378i	1.14381	−	0.136218i
$163$		−	15.6717i		−	1.22751i	−0.789498	−	0.613753i	$-0.789659\pi$
$163$		−	15.6717i		−	1.22751i	0.789498	−	0.613753i	$-0.210341\pi$
$164$	1.88647	+	0.686620i	0.147309	+	0.0536160i
$165$	0.250774	+	1.31547i	0.0195227	+	0.102409i
$166$	−7.41225	−	6.21961i	−0.575302	−	0.482736i
$167$	9.84537	+	1.73601i	0.761858	+	0.134336i	0.541061	−	0.840984i	$-0.318023\pi$
$167$	9.84537	+	1.73601i	0.761858	+	0.134336i	0.220797	+	0.975320i	$0.429134\pi$
$168$	1.67957	+	10.3724i	0.129582	+	0.800251i
$169$	−2.92317	+	2.45283i	−0.224859	+	0.188679i
$170$	−0.603020	−	2.93893i	−0.0462495	−	0.225406i
$171$	15.6601	+	0.438593i	1.19755	+	0.0335401i
$172$	−1.30425	−	0.753008i	−0.0994480	−	0.0574163i
$173$	3.18524	−	0.561643i	0.242169	−	0.0427010i	−0.0512461	−	0.998686i	$-0.516319\pi$
$173$	3.18524	−	0.561643i	0.242169	−	0.0427010i	0.293415	+	0.955985i	$0.405208\pi$
$174$	19.2742	+	3.67749i	1.46117	+	0.278790i
$175$	3.99975	−	13.2398i	0.302353	−	1.00084i
$176$	1.58562	−	0.577119i	0.119521	−	0.0435020i
$177$	−16.4828	+	5.73922i	−1.23892	+	0.431386i
$178$	−28.8336	+	5.08414i	−2.16117	+	0.381072i
$179$	−3.39398	+	5.87855i	−0.253678	+	0.439384i	−0.964536	−	0.263953i	$-0.914974\pi$
$179$	−3.39398	+	5.87855i	−0.253678	+	0.439384i	0.710857	+	0.703336i	$0.248307\pi$
$180$	−0.762177	+	4.31853i	−0.0568093	+	0.321884i
$181$	0.279124	+	0.483457i	0.0207471	+	0.0359351i	0.876213	−	0.481925i	$-0.160062\pi$
$181$	0.279124	+	0.483457i	0.0207471	+	0.0359351i	−0.855465	+	0.517860i	$0.826729\pi$
$182$	−11.8777	−	14.1553i	−0.880433	−	1.04926i
$183$	20.3597	+	7.73479i	1.50503	+	0.571772i
$184$	−1.74864	+	9.91703i	−0.128911	+	0.731093i
$185$	10.8189	−	6.65457i	0.795420	−	0.489254i
$186$	17.9346	+	10.6920i	1.31503	+	0.783979i
$187$	−0.0974024	+	0.267611i	−0.00712277	+	0.0195696i
$188$		−	3.79772i		−	0.276977i
$189$	8.76857	+	11.3889i	0.637820	+	0.828418i
$190$	−6.00577	+	18.0490i	−0.435704	+	1.30941i
$191$	−17.8115	−	6.48287i	−1.28880	−	0.469084i	−0.395466	−	0.918481i	$-0.629417\pi$
$191$	−17.8115	−	6.48287i	−1.28880	−	0.469084i	−0.893332	+	0.449396i	$0.851639\pi$
$192$	−6.84977	−	0.0959024i	−0.494340	−	0.00692116i
$193$	−7.49497	+	8.93215i	−0.539499	+	0.642950i	−0.965075	−	0.261972i	$-0.915627\pi$
$193$	−7.49497	+	8.93215i	−0.539499	+	0.642950i	0.425576	+	0.904923i	$0.360072\pi$
$194$	−1.09660	+	6.21910i	−0.0787310	+	0.446506i
$195$	5.63802	+	14.8476i	0.403747	+	1.06326i
$196$	0.326320	−	0.273815i	0.0233086	−	0.0195582i
$197$	14.0876	−	8.13346i	1.00370	−	0.579485i	0.0943576	−	0.995538i	$-0.469920\pi$
$197$	14.0876	−	8.13346i	1.00370	−	0.579485i	0.909340	+	0.416053i	$0.136587\pi$
$198$	1.12199	−	1.26354i	0.0797367	−	0.0897961i
$199$	10.3331	−	17.8975i	0.732496	−	1.26872i	−0.223317	−	0.974746i	$-0.571688\pi$
$199$	10.3331	−	17.8975i	0.732496	−	1.26872i	0.955813	−	0.293975i	$-0.0949783\pi$
$200$	9.78694	+	4.94579i	0.692041	+	0.349720i
$201$	10.2207	−	11.8399i	0.720913	−	0.835123i
$202$	−2.66417	−	7.31974i	−0.187450	−	0.515015i
$203$	6.57933	+	18.0766i	0.461778	+	1.26873i
$204$	−0.609389	+	0.705930i	−0.0426657	+	0.0494250i
$205$	1.00370	−	6.79313i	0.0701017	−	0.474453i
$206$	−3.92028	+	6.79012i	−0.273139	+	0.473090i
$207$	4.34705	+	13.0710i	0.302141	+	0.908496i
$208$	17.3308	−	10.0059i	1.20168	−	0.693787i
$209$	1.38319	−	1.16064i	0.0956774	−	0.0802828i
$210$	−16.3155	+	6.19542i	−1.12588	+	0.427525i
$211$	1.06614	−	6.04636i	0.0733959	−	0.416249i	−0.925867	−	0.377850i	$-0.876663\pi$
$211$	1.06614	−	6.04636i	0.0733959	−	0.416249i	0.999263	−	0.0383983i	$-0.0122255\pi$
$212$	−5.33040	+	6.35253i	−0.366094	+	0.436293i
$213$	−3.28791	−	0.0460335i	−0.225284	−	0.00315416i
$214$	13.1592	+	4.78955i	0.899543	+	0.327407i
$215$	−1.62644	+	4.88789i	−0.110922	+	0.333351i
$216$	−10.0996	+	5.27851i	−0.687191	+	0.359157i
$217$			20.4699i			1.38959i
$218$	2.49739	−	6.86152i	0.169144	−	0.464721i
$219$	0.618276	+	0.368598i	0.0417792	+	0.0249075i
$220$	0.264802	+	0.430510i	0.0178530	+	0.0290250i
$221$	−0.586493	+	3.32617i	−0.0394518	+	0.223742i
$222$	−14.9826	−	5.69199i	−1.00557	−	0.382022i
$223$	−15.5057	−	18.4789i	−1.03834	−	1.23744i	−0.970842	−	0.239722i	$-0.922944\pi$
$223$	−15.5057	−	18.4789i	−1.03834	−	1.23744i	−0.0674952	−	0.997720i	$-0.521501\pi$
$224$	4.92864	+	8.53665i	0.329309	+	0.570379i
$225$	14.9943	−	0.415199i	0.999617	−	0.0276799i
$226$	6.62008	−	11.4663i	0.440361	−	0.762728i
$227$	−4.96505	+	0.875473i	−0.329542	+	0.0581072i	−0.335971	−	0.941872i	$-0.609065\pi$
$227$	−4.96505	+	0.875473i	−0.329542	+	0.0581072i	0.00642936	+	0.999979i	$0.497953\pi$
$228$	5.58398	−	1.94432i	0.369808	−	0.128765i
$229$	−8.20829	+	2.98757i	−0.542419	+	0.197424i	−0.598675	−	0.800992i	$-0.704306\pi$
$229$	−8.20829	+	2.98757i	−0.542419	+	0.197424i	0.0562561	+	0.998416i	$0.482084\pi$
$230$	−16.7190	+	0.465605i	−1.10242	+	0.0307011i
$231$	1.62727	+	0.310481i	0.107066	+	0.0204281i
$232$	−15.0199	+	2.64842i	−0.986107	+	0.173877i
$233$	−4.48642	−	2.59023i	−0.293915	−	0.169692i	0.345791	−	0.938312i	$-0.387611\pi$
$233$	−4.48642	−	2.59023i	−0.293915	−	0.169692i	−0.639706	+	0.768620i	$0.720944\pi$
$234$	10.5022	−	17.0683i	0.686552	−	1.11579i
$235$	−12.7251	+	2.61099i	−0.830097	+	0.170322i
$236$	−5.04619	+	4.23425i	−0.328479	+	0.275626i
$237$	−3.99227	−	24.6548i	−0.259326	−	1.60150i
$238$	−3.65500	−	0.644476i	−0.236919	−	0.0417752i
$239$	−3.90411	−	3.27594i	−0.252536	−	0.211903i	0.507727	−	0.861518i	$-0.330486\pi$
$239$	−3.90411	−	3.27594i	−0.252536	−	0.211903i	−0.760264	+	0.649615i	$0.774930\pi$
$240$	−3.53936	−	18.5661i	−0.228464	−	1.19844i
$241$	−14.5592	−	5.29911i	−0.937839	−	0.341345i	−0.172527	−	0.985005i	$-0.555193\pi$
$241$	−14.5592	−	5.29911i	−0.937839	−	0.341345i	−0.765312	+	0.643659i	$0.777415\pi$
$242$			17.7245i			1.13937i
$243$	−8.71936	+	12.9218i	−0.559347	+	0.828933i
$244$	8.22008			0.526237
$245$	−1.14183	−	0.905161i	−0.0729490	−	0.0578286i
$246$	−7.56392	+	4.22696i	−0.482258	+	0.269501i
$247$	13.7648	−	16.4043i	0.875834	−	1.04378i
$248$	−15.9829	−	2.81821i	−1.01491	−	0.178956i
$249$	10.1557	−	1.64447i	0.643590	−	0.104214i
$250$	−4.77967	+	17.5747i	−0.302293	+	1.11152i
$251$	−5.89984	−	10.2188i	−0.372395	−	0.645007i	0.617539	−	0.786541i	$-0.288130\pi$
$251$	−5.89984	−	10.2188i	−0.372395	−	0.645007i	−0.989933	+	0.141534i	$0.954797\pi$
$252$	4.62029	+	2.84289i	0.291051	+	0.179085i
$253$	1.37494	+	0.793821i	0.0864416	+	0.0499071i
$254$	−2.08204	−	11.8079i	−0.130639	−	0.740891i
$255$	2.78435	+	1.55656i	0.174363	+	0.0974757i
$256$	−13.3396	+	4.85520i	−0.833723	+	0.303450i
$257$	8.43069	+	23.1631i	0.525892	+	1.44488i	0.863866	+	0.503721i	$0.168036\pi$
$257$	8.43069	+	23.1631i	0.525892	+	1.44488i	−0.337974	+	0.941155i	$0.609742\pi$
$258$	6.13872	−	2.13747i	0.382180	−	0.133073i
$259$	−2.72849	−	15.4740i	−0.169540	−	0.961509i
$260$	3.97937	+	4.48283i	0.246790	+	0.278013i
$261$	−16.3511	+	12.9577i	−1.01211	+	0.802062i
$262$	12.2788	−	7.08914i	0.758584	−	0.437969i
$263$	−0.488486	−	0.582155i	−0.0301214	−	0.0358972i	0.750773	−	0.660560i	$-0.229681\pi$
$263$	−0.488486	−	0.582155i	−0.0301214	−	0.0358972i	−0.780895	+	0.624663i	$0.785237\pi$
$264$	−0.466457	+	1.22782i	−0.0287085	+	0.0755670i
$265$	24.9504	+	13.4933i	1.53269	+	0.828887i
$266$	18.0261	+	15.1257i	1.10525	+	0.927414i
$267$	15.9409	−	26.7389i	0.975569	−	1.63639i
$268$	2.01907	−	5.54734i	0.123334	−	0.338858i
$269$	−22.9672			−1.40034			−0.700169	−	0.713978i	$-0.746892\pi$
$269$	−22.9672			−1.40034			−0.700169	+	0.713978i	$0.746892\pi$
$270$	−11.9599	−	14.6701i	−0.727856	−	0.892796i
$271$	14.2192			0.863753			0.431877	−	0.901933i	$-0.357852\pi$
$271$	14.2192			0.863753			0.431877	+	0.901933i	$0.357852\pi$
$272$	1.37471	−	3.77699i	0.0833541	−	0.229014i
$273$	19.6452	+	0.275048i	1.18898	+	0.0166467i
$274$	3.80776	+	3.19509i	0.230035	+	0.193022i
$275$	1.26047	−	1.18326i	0.0760093	−	0.0713535i
$276$	3.28575	+	4.02904i	0.197779	+	0.242519i
$277$	9.37625	+	11.1742i	0.563364	+	0.671392i	0.970255	−	0.242085i	$-0.0778314\pi$
$277$	9.37625	+	11.1742i	0.563364	+	0.671392i	−0.406891	+	0.913477i	$0.633387\pi$
$278$	13.6571	−	7.88493i	0.819099	−	0.472907i
$279$	−21.0659	+	7.00596i	−1.26118	+	0.419436i
$280$	10.1448	−	9.00543i	0.606266	−	0.538177i
$281$	1.44710	+	8.20692i	0.0863268	+	0.489584i	0.997062	+	0.0765937i	$0.0244044\pi$
$281$	1.44710	+	8.20692i	0.0863268	+	0.489584i	−0.910736	+	0.412990i	$0.864484\pi$
$282$	12.4079	+	10.7110i	0.738882	+	0.637834i
$283$	−4.02395	−	11.0557i	−0.239199	−	0.657194i	−0.999967	−	0.00816979i	$-0.997399\pi$
$283$	−4.02395	−	11.0557i	−0.239199	−	0.657194i	0.760767	−	0.649025i	$-0.224823\pi$
$284$	−1.16621	+	0.424467i	−0.0692021	+	0.0251875i
$285$	−10.3540	−	17.3737i	−0.613316	−	1.02913i
$286$	−0.401092	−	2.27470i	−0.0237171	−	0.134506i
$287$	−7.35669	−	4.24739i	−0.434252	−	0.250715i
$288$	−7.09835	+	7.99387i	−0.418275	+	0.471043i
$289$	−8.16082	−	14.1349i	−0.480048	−	0.831468i
$290$	−9.32327	−	23.5536i	−0.547481	−	1.38312i
$291$	−4.24353	−	5.20347i	−0.248760	−	0.305033i
$292$	0.267547	+	0.0471758i	0.0156570	+	0.00276075i
$293$	−12.3681	+	14.7397i	−0.722551	+	0.861102i	−0.994876	−	0.101103i	$-0.967763\pi$
$293$	−12.3681	+	14.7397i	−0.722551	+	0.861102i	0.272325	+	0.962205i	$0.412207\pi$
$294$	−0.0257394	+	1.83842i	−0.00150115	+	0.107219i
$295$	17.6572	+	13.9973i	1.02804	+	0.814955i
$296$	12.4577			0.724090
$297$	0.237422	+	1.78091i	0.0137766	+	0.103339i
$298$			17.0616i			0.988354i
$299$	17.6935	+	6.43989i	1.02324	+	0.372429i
$300$	5.23463	−	2.15631i	0.302221	−	0.124494i
$301$	4.88169	+	4.09622i	0.281376	+	0.236102i
$302$	5.13854	+	0.906064i	0.295690	+	0.0521381i
$303$	7.74225	+	2.94134i	0.444781	+	0.168975i
$304$	−19.5220	+	16.3809i	−1.11966	+	0.939509i
$305$	−5.65143	−	27.5433i	−0.323600	−	1.57713i
$306$	−0.587707	−	3.98200i	−0.0335970	−	0.227636i
$307$	11.6318	+	6.71561i	0.663860	+	0.383280i	0.793746	−	0.608249i	$-0.208128\pi$
$307$	11.6318	+	6.71561i	0.663860	+	0.383280i	−0.129886	+	0.991529i	$0.541461\pi$
$308$	0.615750	−	0.108573i	0.0350856	−	0.00618654i
$309$	−2.74128	−	7.87283i	−0.155946	−	0.447870i
$310$	−0.750396	−	26.9453i	−0.0426196	−	1.53039i
$311$	−8.50951	+	3.09721i	−0.482530	+	0.175627i	−0.571820	−	0.820379i	$-0.693762\pi$
$311$	−8.50951	+	3.09721i	−0.482530	+	0.175627i	0.0892900	+	0.996006i	$0.471540\pi$
$312$	−2.91941	+	15.3010i	−0.165279	+	0.866249i
$313$	−3.46336	+	0.610683i	−0.195761	+	0.0345179i	−0.270669	−	0.962673i	$-0.587245\pi$
$313$	−3.46336	+	0.610683i	−0.195761	+	0.0345179i	0.0749081	+	0.997190i	$0.476134\pi$
$314$	15.9295	−	27.5907i	0.898955	−	1.55704i
$315$	6.34927	−	17.4359i	0.357741	−	0.982401i
$316$	−4.71326	−	8.16361i	−0.265142	−	0.459239i
$317$	−7.92050	−	9.43928i	−0.444860	−	0.530163i	0.496288	−	0.868158i	$-0.334696\pi$
$317$	−7.92050	−	9.43928i	−0.444860	−	0.530163i	−0.941148	+	0.337995i	$0.890251\pi$
$318$	−5.72121	−	35.3322i	−0.320829	−	1.98133i
$319$	−0.417550	+	2.36805i	−0.0233783	+	0.132585i
$320$	4.63344	+	7.53296i	0.259017	+	0.421106i
$321$	−12.9975	+	7.26344i	−0.725452	+	0.405406i
$322$	−7.07657	+	19.4427i	−0.394362	+	1.08350i
$323$		−	4.30105i		−	0.239317i
$324$	−1.34435	+	5.72781i	−0.0746859	+	0.318212i
$325$	12.2849	−	16.4158i	0.681443	−	0.910587i
$326$	23.9900	+	8.73165i	1.32868	+	0.483602i
$327$	3.78733	+	6.77723i	0.209440	+	0.374782i
$328$	4.32918	−	5.15932i	0.239039	−	0.284876i
$329$	−2.79048	+	15.8256i	−0.153844	+	0.872495i
$330$	−2.15341	−	0.349044i	−0.118541	−	0.0192142i
$331$	−1.81740	+	1.52498i	−0.0998935	+	0.0838206i	−0.691367	−	0.722504i	$-0.742991\pi$
$331$	−1.81740	+	1.52498i	−0.0998935	+	0.0838206i	0.591473	+	0.806325i	$0.298547\pi$
$332$	3.36271	−	1.94146i	0.184553	−	0.106552i
$333$	14.9907	−	8.10401i	0.821487	−	0.444097i
$334$	−8.14288	+	14.1039i	−0.445559	+	0.771730i
$335$	−19.9758	−	2.95148i	−1.09139	−	0.161256i
$336$	−22.9668	−	4.38204i	−1.25294	−	0.239060i
$337$	9.93294	+	27.2905i	0.541081	+	1.48661i	0.845450	+	0.534055i	$0.179332\pi$
$337$	9.93294	+	27.2905i	0.541081	+	1.48661i	−0.304368	+	0.952554i	$0.598445\pi$
$338$	−2.12608	−	5.84135i	−0.115643	−	0.317728i
$339$	4.62913	+	13.2947i	0.251420	+	0.722067i
$340$	1.19102	+	0.175976i	0.0645919	+	0.00954363i
$341$	−1.27937	+	2.21593i	−0.0692816	+	0.119999i
$342$	−9.39653	+	23.7278i	−0.508106	+	1.28305i
$343$	15.2079	−	8.78030i	0.821151	−	0.474092i
$344$	−3.87041	+	3.24766i	−0.208678	+	0.175102i
$345$	11.2412	−	13.7797i	0.605207	−	0.741874i
$346$	−0.914930	+	5.18883i	−0.0491870	+	0.278953i
$347$	11.6896	−	13.9312i	0.627533	−	0.747864i	−0.354813	−	0.934937i	$-0.615456\pi$
$347$	11.6896	−	13.9312i	0.627533	−	0.747864i	0.982346	+	0.187073i	$0.0599000\pi$
$348$	−4.03215	+	6.76343i	−0.216146	+	0.362558i
$349$	−0.0893807	−	0.0325319i	−0.00478444	−	0.00174139i	0.339627	−	0.940560i	$-0.389699\pi$
$349$	−0.0893807	−	0.0325319i	−0.00478444	−	0.00174139i	−0.344411	+	0.938819i	$0.611921\pi$
$350$	18.0388	+	13.4994i	0.964213	+	0.721575i
$351$	6.44062	+	20.3113i	0.343775	+	1.08414i
$352$			1.23216i			0.0656742i
$353$	1.14869	−	3.15599i	0.0611384	−	0.167976i	−0.905363	−	0.424640i	$-0.860401\pi$
$353$	1.14869	−	3.15599i	0.0611384	−	0.167976i	0.966501	+	0.256663i	$0.0826231\pi$
$354$	0.398032	−	28.4292i	0.0211551	−	1.51099i
$355$	2.22407	+	3.61585i	0.118041	+	0.191909i
$356$	2.04023	−	11.5707i	0.108132	−	0.613248i
$357$	3.05811	−	2.49395i	0.161852	−	0.131994i
$358$	−7.10779	−	8.47073i	−0.375658	−	0.447692i
$359$	−3.29988	−	5.71556i	−0.174161	−	0.301656i	0.765710	−	0.643187i	$-0.222388\pi$
$359$	−3.29988	−	5.71556i	−0.174161	−	0.301656i	−0.939871	+	0.341531i	$0.889055\pi$
$360$	12.7397	+	7.35798i	0.671444	+	0.387800i
$361$	−4.13500	+	7.16203i	−0.217631	+	0.376949i
$362$	−0.895584	+	0.157916i	−0.0470708	+	0.00829986i
$363$	−14.2655	−	12.3146i	−0.748743	−	0.646347i
$364$	6.96808	−	2.53618i	0.365227	−	0.132932i
$365$	−0.0258691	−	0.928913i	−0.00135405	−	0.0486215i
$366$	−23.1839	+	26.8567i	−1.21184	+	1.40382i
$367$	9.36556	−	1.65140i	0.488878	−	0.0862025i	0.0762252	−	0.997091i	$-0.475713\pi$
$367$	9.36556	−	1.65140i	0.488878	−	0.0862025i	0.412653	+	0.910888i	$0.364602\pi$
$368$	−19.4055	−	11.2038i	−1.01158	−	0.584037i
$369$	1.85318	−	9.02458i	0.0964728	−	0.469801i
$370$	4.15886	+	20.2690i	0.216209	+	1.05374i
$371$	26.8803	−	22.5552i	1.39555	−	1.17101i
$372$	−6.49343	+	5.29551i	−0.336669	+	0.274559i
$373$	18.5053	+	3.26299i	0.958170	+	0.168951i	0.630800	−	0.775945i	$-0.282727\pi$
$373$	18.5053	+	3.26299i	0.958170	+	0.168951i	0.327370	+	0.944896i	$0.393838\pi$
$374$	−0.355385	−	0.298203i	−0.0183765	−	0.0154197i
$375$	−10.8241	−	16.0574i	−0.558954	−	0.829199i
$376$	−11.9724	−	4.35760i	−0.617430	−	0.224726i
$377$			28.5176i			1.46873i
$378$	−22.3193	+	7.07737i	−1.14798	+	0.364020i
$379$	17.6639			0.907335			0.453667	−	0.891171i	$-0.350115\pi$
$379$	17.6639			0.907335			0.453667	+	0.891171i	$0.350115\pi$
$380$	−5.98184	−	4.74197i	−0.306862	−	0.243258i
$381$	10.9501	+	6.52809i	0.560988	+	0.334444i
$382$	19.8477	−	23.6536i	1.01550	−	1.21022i
$383$	−12.6802	−	2.23586i	−0.647929	−	0.114247i	−0.159981	−	0.987120i	$-0.551143\pi$
$383$	−12.6802	−	2.23586i	−0.647929	−	0.114247i	−0.487948	+	0.872873i	$0.662254\pi$
$384$	8.34724	−	21.9718i	0.425968	−	1.12124i
$385$	−0.787138	−	1.98857i	−0.0401163	−	0.101347i
$386$	−9.49729	−	16.4498i	−0.483399	−	0.837272i
$387$	−2.54470	+	6.42579i	−0.129354	+	0.326641i
$388$	−2.19467	−	1.26709i	−0.111418	−	0.0643270i
$389$	1.45798	+	8.26860i	0.0739224	+	0.419235i	0.999202	+	0.0399485i	$0.0127194\pi$
$389$	1.45798	+	8.26860i	0.0739224	+	0.419235i	−0.925279	+	0.379286i	$0.876170\pi$
$390$	−25.8697	+	0.358105i	−1.30996	+	0.0181333i
$391$	3.55373	−	1.29345i	0.179720	−	0.0654127i
$392$	−0.488782	−	1.34292i	−0.0246872	−	0.0678276i
$393$	−2.82532	+	14.8079i	−0.142519	+	0.746958i
$394$	4.60154	+	26.0966i	0.231822	+	1.31473i
$395$	−24.1137	+	21.4055i	−1.21329	+	1.07703i
$396$	0.322479	+	0.596519i	0.0162052	+	0.0299762i
$397$	−25.7649	+	14.8754i	−1.29311	+	0.746575i	−0.979203	−	0.202881i	$-0.934970\pi$
$397$	−25.7649	+	14.8754i	−1.29311	+	0.746575i	−0.313902	+	0.949456i	$0.601636\pi$
$398$	21.6400	+	25.7895i	1.08471	+	1.29271i
$399$	−24.6979	+	3.99924i	−1.23644	+	0.200212i
$400$	−17.7900	+	16.7003i	−0.889498	+	0.835014i
$401$	5.32556	+	4.46867i	0.265946	+	0.223155i	0.766002	−	0.642838i	$-0.222243\pi$
$401$	5.32556	+	4.46867i	0.265946	+	0.223155i	−0.500057	+	0.865993i	$0.666688\pi$
$402$	12.4298	+	22.2424i	0.619940	+	1.10935i
$403$	−10.3789	+	28.5158i	−0.517010	+	1.42047i
$404$	3.12588			0.155518
$405$	20.1166	+	0.566593i	0.999604	+	0.0281542i
$406$	−31.3370			−1.55523
$407$	0.671757	−	1.84564i	0.0332978	−	0.0914848i
$408$	1.52624	+	2.73112i	0.0755600	+	0.135211i
$409$	7.61910	+	6.39318i	0.376740	+	0.316123i	0.811421	−	0.584462i	$-0.198694\pi$
$409$	7.61910	+	6.39318i	0.376740	+	0.316123i	−0.434681	+	0.900585i	$0.643139\pi$
$410$	9.83958	+	5.32131i	0.485942	+	0.262801i
$411$	−5.21709	+	0.844785i	−0.257340	+	0.0416702i
$412$	−2.02245	−	2.41026i	−0.0996388	−	0.118745i
$413$	24.1394	−	13.9369i	1.18782	−	0.685790i
$414$	−22.4308	−	0.628222i	−1.10241	−	0.0308754i
$415$	−8.81724	−	9.93277i	−0.432821	−	0.487580i
$416$	2.53753	+	14.3910i	0.124413	+	0.705579i
$417$	−3.14248	+	16.4701i	−0.153888	+	0.806545i
$418$	1.00602	+	2.76402i	0.0492061	+	0.135193i
$419$	−12.9063	+	4.69750i	−0.630513	+	0.229488i	−0.637454	−	0.770488i	$-0.720013\pi$
$419$	−12.9063	+	4.69750i	−0.630513	+	0.229488i	0.00694183	+	0.999976i	$0.497790\pi$
$420$	−0.0969370	−	7.00279i	−0.00473004	−	0.341701i
$421$	−2.00781	−	11.3869i	−0.0978547	−	0.554962i	−0.993835	−	0.110868i	$-0.964637\pi$
$421$	−2.00781	−	11.3869i	−0.0978547	−	0.554962i	0.895980	−	0.444094i	$-0.146474\pi$
$422$	8.66165	+	5.00081i	0.421643	+	0.243435i
$423$	−17.2415	+	2.54469i	−0.838309	+	0.123727i
$424$	13.9103	+	24.0933i	0.675543	+	1.17007i
$425$	−0.229194	−	4.11177i	−0.0111175	−	0.199450i
$426$	1.90236	−	5.00743i	0.0921695	−	0.242611i
$427$	−34.2543	−	6.03995i	−1.65768	−	0.292294i
$428$	−3.61221	+	4.30487i	−0.174603	+	0.208084i
$429$	2.10945	+	1.25759i	0.101845	+	0.0607172i
$430$	−6.57611	−	5.21306i	−0.317128	−	0.251396i
$431$	2.02098			0.0973474			0.0486737	−	0.998815i	$-0.484501\pi$
$431$	2.02098			0.0973474			0.0486737	+	0.998815i	$0.484501\pi$
$432$	−3.35091	−	25.1353i	−0.161221	−	1.20932i
$433$		−	7.13269i		−	0.342775i	−0.985204	−	0.171388i	$-0.945175\pi$
$433$		−	7.13269i		−	0.342775i	0.985204	−	0.171388i	$-0.0548251\pi$
$434$	−31.3350	−	11.4050i	−1.50413	−	0.547458i
$435$	25.4346	+	8.86072i	1.21950	+	0.424839i
$436$	2.24466	+	1.88350i	0.107500	+	0.0902031i
$437$	−23.6135	−	4.16370i	−1.12959	−	0.199177i
$438$	−0.908720	+	0.741078i	−0.0434203	+	0.0354101i
$439$	17.4314	−	14.6267i	0.831954	−	0.698092i	−0.123785	−	0.992309i	$-0.539503\pi$
$439$	17.4314	−	14.6267i	0.831954	−	0.698092i	0.955739	+	0.294217i	$0.0950587\pi$
$440$	1.66104	−	0.340817i	0.0791869	−	0.0162478i
$441$	−1.46176	−	1.29801i	−0.0696078	−	0.0618099i
$442$	−4.76486	−	2.75100i	−0.226641	−	0.130851i
$443$	2.31134	−	0.407552i	0.109815	−	0.0193634i	−0.118470	−	0.992958i	$-0.537799\pi$
$443$	2.31134	−	0.407552i	0.109815	−	0.0193634i	0.228286	+	0.973594i	$0.426688\pi$
$444$	4.20278	−	4.86861i	0.199455	−	0.231054i
$445$	−40.1732	+	1.11878i	−1.90439	+	0.0530351i
$446$	36.9263	−	13.4401i	1.74851	−	0.636407i
$447$	−13.7320	−	11.8540i	−0.649500	−	0.560676i
$448$	10.7742	−	1.89979i	0.509035	−	0.0897566i
$449$	13.1597	−	22.7932i	0.621043	−	1.07568i	−0.368249	−	0.929727i	$-0.620043\pi$
$449$	13.1597	−	22.7932i	0.621043	−	1.07568i	0.989292	−	0.145950i	$-0.0466239\pi$
$450$	−7.71860	+	23.1843i	−0.363858	+	1.09292i
$451$	−0.530922	−	0.919583i	−0.0250001	−	0.0433015i
$452$	3.41526	+	4.07015i	0.160640	+	0.191444i
$453$	−4.29938	+	3.50622i	−0.202002	+	0.164737i
$454$	1.42617	−	8.08819i	0.0669333	−	0.379597i
$455$	−13.2887	−	21.6045i	−0.622984	−	1.01284i
$456$	0.277701	−	19.8346i	0.0130045	−	0.928842i
$457$	14.0412	−	38.5779i	0.656820	−	1.80460i	0.0659625	−	0.997822i	$-0.478988\pi$
$457$	14.0412	−	38.5779i	0.656820	−	1.80460i	0.590857	−	0.806776i	$-0.298790\pi$
$458$		−	14.2296i		−	0.664908i
$459$	3.61322	+	2.29358i	0.168651	+	0.107055i
$460$	2.11912	−	6.36853i	0.0988044	−	0.296934i
$461$	15.5676	+	5.66615i	0.725057	+	0.263899i	0.678071	−	0.734996i	$-0.262816\pi$
$461$	15.5676	+	5.66615i	0.725057	+	0.263899i	0.0469859	+	0.998896i	$0.485038\pi$
$462$	−1.38192	+	2.31800i	−0.0642929	+	0.107843i
$463$	−27.5721	+	32.8591i	−1.28138	+	1.52709i	−0.578869	+	0.815421i	$0.696506\pi$
$463$	−27.5721	+	32.8591i	−1.28138	+	1.52709i	−0.702513	+	0.711671i	$0.747939\pi$
$464$	5.89319	−	33.4220i	0.273585	−	1.55158i
$465$	22.2082	+	18.1170i	1.02988	+	0.840156i
$466$	6.46473	−	5.42455i	0.299473	−	0.251287i
$467$	−2.06217	+	1.19059i	−0.0954257	+	0.0550941i	−0.546953	−	0.837163i	$-0.684213\pi$
$467$	−2.06217	+	1.19059i	−0.0954257	+	0.0550941i	0.451528	+	0.892257i	$0.350879\pi$
$468$	4.99489	+	6.30295i	0.230889	+	0.291354i
$469$	−12.4898	+	21.6330i	−0.576726	+	0.998918i
$470$	3.09307	−	20.9341i	0.142673	−	0.965620i
$471$	11.1388	+	31.9902i	0.513250	+	1.47403i
$472$	7.55848	+	20.7667i	0.347907	+	0.955867i
$473$	0.272444	+	0.748533i	0.0125270	+	0.0344176i
$474$	39.9655	+	7.62536i	1.83567	+	0.350245i
$475$	−11.7765	+	23.3037i	−0.540341	+	1.06925i
$476$	0.744679	−	1.28982i	0.0341323	−	0.0591189i
$477$	32.4119	+	19.9432i	1.48404	+	0.913139i
$478$	7.18996	−	4.15113i	0.328861	−	0.189868i
$479$	−16.1393	+	13.5425i	−0.737424	+	0.618772i	−0.932144	−	0.362087i	$-0.882064\pi$
$479$	−16.1393	+	13.5425i	−0.737424	+	0.618772i	0.194720	+	0.980859i	$0.437620\pi$
$480$	13.6237	+	2.20824i	0.621833	+	0.100792i
$481$	4.04488	−	22.9396i	0.184431	−	1.04596i
$482$	16.2235	−	19.3345i	0.738962	−	0.880661i
$483$	−10.7317	−	19.2039i	−0.488311	−	0.873806i
$484$	−6.68379	−	2.43270i	−0.303809	−	0.110577i
$485$	−2.73683	+	8.22491i	−0.124273	+	0.373474i
$486$	−14.9224	−	20.5469i	−0.676892	−	0.932028i
$487$		−	19.5413i		−	0.885501i	−0.896645	−	0.442750i	$-0.854003\pi$
$487$		−	19.5413i		−	0.885501i	0.896645	−	0.442750i	$-0.145997\pi$
$488$	9.43195	−	25.9141i	0.426964	−	1.17307i
$489$	−23.6953	+	13.2417i	−1.07154	+	0.598811i
$490$	2.02179	−	1.24358i	0.0913350	−	0.0561791i
$491$	0.0273807	−	0.155284i	0.00123567	−	0.00700785i	−0.984184	−	0.177151i	$-0.943312\pi$
$491$	0.0273807	−	0.155284i	0.00123567	−	0.00700785i	0.985419	+	0.170143i	$0.0544230\pi$
$492$	−0.555806	−	3.43246i	−0.0250577	−	0.154747i
$493$	3.68173	+	4.38772i	0.165817	+	0.197613i
$494$	17.4422	+	30.2107i	0.784760	+	1.35924i
$495$	1.77707	−	1.49066i	0.0798732	−	0.0670000i
$496$	18.0566	−	31.2750i	0.810767	−	1.40429i
$497$	5.17167	−	0.911905i	0.231981	−	0.0409045i
$498$	−3.14100	+	16.4624i	−0.140751	+	0.737696i
$499$	18.9250	−	6.88813i	0.847198	−	0.308355i	0.118301	−	0.992978i	$-0.462255\pi$
$499$	18.9250	−	6.88813i	0.847198	−	0.308355i	0.728897	+	0.684623i	$0.240033\pi$
$500$	−5.97128	−	4.21452i	−0.267044	−	0.188479i
$501$	−5.69396	−	16.3528i	−0.254388	−	0.730589i
$502$	18.9299	−	3.33786i	0.844885	−	0.148976i
$503$	−10.7950	−	6.23250i	−0.481325	−	0.277893i	0.239643	−	0.970861i	$-0.422969\pi$
$503$	−10.7950	−	6.23250i	−0.481325	−	0.277893i	−0.720969	+	0.692968i	$0.756303\pi$
$504$	14.2637	−	11.3036i	0.635358	−	0.503501i
$505$	−2.14909	−	10.4740i	−0.0956333	−	0.466087i
$506$	−1.98122	+	1.66244i	−0.0880762	+	0.0739047i
$507$	6.17853	+	2.34727i	0.274398	+	0.104246i
$508$	4.73842	+	0.835512i	0.210234	+	0.0370699i
$509$	21.7729	+	18.2697i	0.965068	+	0.809788i	0.981770	−	0.190072i	$-0.0608722\pi$
$509$	21.7729	+	18.2697i	0.965068	+	0.809788i	−0.0167021	+	0.999861i	$0.505317\pi$
$510$	−3.93408	+	3.39498i	−0.174204	+	0.150332i
$511$	−1.08024	−	0.393176i	−0.0477871	−	0.0173931i
$512$			4.01496i			0.177438i
$513$	−12.5687	−	24.0482i	−0.554921	−	1.06176i
$514$	−40.1549			−1.77116
$515$	−6.68567	+	8.43377i	−0.294606	+	0.371636i
$516$	−0.0365175	+	2.60824i	−0.00160759	+	0.114821i
$517$	−1.29118	+	1.53876i	−0.0567859	+	0.0676748i
$518$	25.2075	+	4.44477i	1.10756	+	0.195292i
$519$	−3.54053	−	4.34145i	−0.155412	−	0.190569i
$520$	18.6983	−	7.40137i	0.819974	−	0.324571i
$521$	16.9549	+	29.3668i	0.742810	+	1.28658i	0.951211	+	0.308541i	$0.0998407\pi$
$521$	16.9549	+	29.3668i	0.742810	+	1.28658i	−0.208401	+	0.978043i	$0.566826\pi$
$522$	−10.7253	−	32.2494i	−0.469433	−	1.41152i
$523$	17.0735	+	9.85740i	0.746573	+	0.431034i	0.824454	−	0.565928i	$-0.191482\pi$
$523$	17.0735	+	9.85740i	0.746573	+	0.431034i	−0.0778812	+	0.996963i	$0.524815\pi$
$524$	0.988000	+	5.60323i	0.0431610	+	0.244778i
$525$	−23.3978	+	5.13933i	−1.02117	+	0.224299i
$526$	1.16332	−	0.423413i	0.0507230	−	0.0184617i
$527$	2.08460	+	5.72740i	0.0908067	+	0.249489i
$528$	−2.21235	−	1.90979i	−0.0962800	−	0.0831130i
$529$	0.332877	+	1.88784i	0.0144729	+	0.0820801i
$530$	−34.5566	+	30.6756i	−1.50104	+	1.33246i
$531$	22.6046	+	20.0723i	0.980954	+	0.871063i
$532$	−8.17787	+	4.72150i	−0.354556	+	0.204703i
$533$	−8.09473	−	9.64693i	−0.350622	−	0.417855i
$534$	32.0498	+	39.2999i	1.38693	+	1.70067i
$535$	16.9079	+	9.14391i	0.730993	+	0.395326i
$536$	−15.1714	−	12.7303i	−0.655306	−	0.549867i
$537$	11.7560	+	0.164593i	0.507307	+	0.00710270i
$538$	12.7964	−	35.1578i	0.551692	−	1.51576i
$539$	−0.225313			−0.00970491
$540$	7.17351	−	2.49651i	0.308699	−	0.107433i
$541$	10.3965			0.446981			0.223490	−	0.974706i	$-0.428255\pi$
$541$	10.3965			0.446981			0.223490	+	0.974706i	$0.428255\pi$
$542$	−7.92234	+	21.7664i	−0.340294	+	0.934949i
$543$	0.495133	−	0.830522i	0.0212482	−	0.0356411i
$544$	2.24836	+	1.88660i	0.0963977	+	0.0808873i
$545$	4.76786	−	8.81620i	0.204233	−	0.377645i
$546$	−11.3665	+	29.9192i	−0.486442	+	1.28042i
$547$	−5.69005	−	6.78114i	−0.243289	−	0.289941i	0.630557	−	0.776143i	$-0.282826\pi$
$547$	−5.69005	−	6.78114i	−0.243289	−	0.289941i	−0.873846	+	0.486202i	$0.838382\pi$
$548$	−1.72746	+	0.997352i	−0.0737936	+	0.0426048i
$549$	−5.50792	−	37.3188i	−0.235072	−	1.59273i
$550$	1.10904	+	2.58877i	0.0472895	+	0.110386i
$551$	−6.30617	−	35.7641i	−0.268652	−	1.52360i
$552$	16.4718	−	5.73540i	0.701087	−	0.244115i
$553$	13.6424	+	37.4821i	0.580133	+	1.59390i
$554$	−22.3293	+	8.12720i	−0.948681	+	0.345292i
$555$	−19.2029	−	10.7352i	−0.815117	−	0.455683i
$556$	1.09891	+	6.23221i	0.0466041	+	0.264305i
$557$	−30.0694	−	17.3606i	−1.27408	−	0.735590i	−0.298327	−	0.954464i	$-0.596429\pi$
$557$	−30.0694	−	17.3606i	−1.27408	−	0.735590i	−0.975753	+	0.218873i	$0.929762\pi$
$558$	1.01248	−	36.1508i	0.0428617	−	1.53038i
$559$	4.72356	+	8.18145i	0.199785	+	0.346038i
$560$	11.1095	+	28.0661i	0.469460	+	1.18601i
$561$	0.486921	−	0.0788453i	0.0205578	−	0.00332885i
$562$	−13.3693	−	2.35736i	−0.563948	−	0.0994393i
$563$	19.0340	−	22.6838i	0.802186	−	0.956008i	−0.197519	−	0.980299i	$-0.563289\pi$
$563$	19.0340	−	22.6838i	0.802186	−	0.956008i	0.999705	+	0.0242914i	$0.00773295\pi$
$564$	−5.74206	+	3.20885i	−0.241784	+	0.135117i
$565$	11.2899	−	14.2419i	0.474971	−	0.599162i
$566$	19.1659			0.805602
$567$	9.81076	−	22.8808i	0.412013	−	0.960903i
$568$			4.16357i			0.174700i
$569$	−26.5073	−	9.64786i	−1.11124	−	0.404459i	−0.279794	−	0.960060i	$-0.590266\pi$
$569$	−26.5073	−	9.64786i	−1.11124	−	0.404459i	−0.831449	+	0.555601i	$0.812488\pi$
$570$	32.3641	−	6.16973i	1.35558	−	0.258422i
$571$	−32.9428	−	27.6423i	−1.37861	−	1.15679i	−0.969722	−	0.244210i	$-0.921471\pi$
$571$	−32.9428	−	27.6423i	−1.37861	−	1.15679i	−0.408890	−	0.912583i	$-0.634084\pi$
$572$	0.912826	+	0.160956i	0.0381672	+	0.00672990i
$573$	5.24776	+	32.4083i	0.219228	+	1.35388i
$574$	10.6007	−	8.89501i	0.442463	−	0.371271i
$575$	−22.7962	−	2.72215i	−0.950666	−	0.113521i
$576$	5.64266	+	10.4377i	0.235111	+	0.434906i
$577$	−3.00900	−	1.73725i	−0.125266	−	0.0723226i	0.436057	−	0.899919i	$-0.356374\pi$
$577$	−3.00900	−	1.73725i	−0.125266	−	0.0723226i	−0.561324	+	0.827596i	$0.689708\pi$
$578$	26.1844	−	4.61701i	1.08913	−	0.192042i
$579$	19.8380	+	3.78507i	0.824440	+	0.157302i
$580$	10.1615	−	0.282987i	0.421935	−	0.0117504i
$581$	−15.4394	+	5.61949i	−0.640536	+	0.233136i
$582$	10.3297	−	3.59675i	0.428180	−	0.149090i
$583$	4.31956	−	0.761655i	0.178898	−	0.0315445i
$584$	0.455714	−	0.789319i	0.0188576	−	0.0326623i
$585$	17.6854	−	21.0699i	0.731203	−	0.871134i
$586$	−15.6723	−	27.1452i	−0.647415	−	1.12136i
$587$	18.4958	+	22.0425i	0.763404	+	0.909790i	0.998058	−	0.0622891i	$-0.0198401\pi$
$587$	18.4958	+	22.0425i	0.763404	+	0.909790i	−0.234654	+	0.972079i	$0.575396\pi$
$588$	−0.689724	−	0.262031i	−0.0284437	−	0.0108060i
$589$	6.71046	−	38.0569i	0.276500	−	1.56811i
$590$	−31.2647	+	19.2306i	−1.28715	+	0.791710i
$591$	−24.2008	−	14.4278i	−0.995487	−	0.593480i
$592$	−9.48100	+	26.0488i	−0.389667	+	1.07060i
$593$			25.6792i			1.05452i	0.849705	+	0.527259i	$0.176780\pi$
$593$			25.6792i			1.05452i	−0.849705	+	0.527259i	$0.823220\pi$
$594$	−2.85847	−	0.628810i	−0.117284	−	0.0258004i
$595$	−4.83383	−	1.60845i	−0.198168	−	0.0659400i
$596$	−6.43383	−	2.34172i	−0.263540	−	0.0959207i
$597$	−35.7915	−	0.501110i	−1.46485	−	0.0205091i
$598$	−19.7161	+	23.4968i	−0.806253	+	0.960855i
$599$	−4.35478	+	24.6972i	−0.177931	+	1.00910i	0.756774	+	0.653676i	$0.226774\pi$
$599$	−4.35478	+	24.6972i	−0.177931	+	1.00910i	−0.934706	+	0.355423i	$0.884337\pi$
$600$	−0.791464	−	18.9765i	−0.0323114	−	0.774713i
$601$	18.6682	−	15.6645i	0.761492	−	0.638968i	−0.177023	−	0.984207i	$-0.556647\pi$
$601$	18.6682	−	15.6645i	0.761492	−	0.638968i	0.938515	+	0.345239i	$0.112202\pi$
$602$	−8.99030	+	5.19055i	−0.366417	+	0.211551i
$603$	−26.5376	−	5.44944i	−1.08069	−	0.221918i
$604$	−1.04694	+	1.81335i	−0.0425993	+	0.0737842i
$605$	−3.55613	+	24.0681i	−0.144577	+	0.978508i
$606$	−8.81621	+	10.2129i	−0.358134	+	0.414871i
$607$	−11.0715	−	30.4186i	−0.449377	−	1.23465i	−0.933159	−	0.359464i	$-0.882959\pi$
$607$	−11.0715	−	30.4186i	−0.449377	−	1.23465i	0.483782	−	0.875189i	$-0.339263\pi$
$608$	−6.36465	−	17.4867i	−0.258121	−	0.709180i
$609$	21.7722	−	25.2214i	0.882253	−	1.02202i
$610$	45.3116	+	6.69490i	1.83461	+	0.271069i
$611$	−11.9114	+	20.6312i	−0.481884	+	0.834647i
$612$	1.58225	+	0.324912i	0.0639586	+	0.0131338i
$613$	−11.9105	+	6.87651i	−0.481059	+	0.277740i	−0.720858	−	0.693083i	$-0.756252\pi$
$613$	−11.9105	+	6.87651i	−0.481059	+	0.277740i	0.239799	+	0.970823i	$0.422919\pi$
$614$	−16.7609	+	14.0640i	−0.676414	+	0.567578i
$615$	−11.1191	+	4.22222i	−0.448367	+	0.170257i
$616$	0.364247	−	2.06575i	0.0146759	−	0.0832314i
$617$	−7.71847	+	9.19852i	−0.310734	+	0.370318i	−0.898697	−	0.438569i	$-0.855485\pi$
$617$	−7.71847	+	9.19852i	−0.310734	+	0.370318i	0.587963	+	0.808888i	$0.299930\pi$
$618$	13.5789	+	0.190116i	0.546224	+	0.00764758i
$619$	−41.4672	−	15.0928i	−1.66671	−	0.606633i	−0.675313	−	0.737531i	$-0.735992\pi$
$619$	−41.4672	−	15.0928i	−1.66671	−	0.606633i	−0.991396	+	0.130898i	$0.958214\pi$
$620$	10.2639	+	3.41529i	0.412208	+	0.137162i
$621$	16.0900	−	17.6169i	0.645670	−	0.706940i
$622$		−	14.7518i		−	0.591495i
$623$	−17.0039	+	46.7178i	−0.681246	+	1.87171i
$624$	−29.7723	−	17.7493i	−1.19184	−	0.710542i
$625$	−10.0164	+	22.9057i	−0.400656	+	0.916229i
$626$	0.994818	−	5.64189i	0.0397609	−	0.225495i
$627$	−2.92357	−	1.11068i	−0.116756	−	0.0443565i
$628$	8.21794	+	9.79376i	0.327932	+	0.390814i
$629$	−2.33925	−	4.05170i	−0.0932720	−	0.161552i
$630$	23.1530	+	19.4339i	0.922437	+	0.774265i
$631$	−20.3931	+	35.3219i	−0.811837	+	1.40614i	0.0997402	+	0.995014i	$0.468199\pi$
$631$	−20.3931	+	35.3219i	−0.811837	+	1.40614i	−0.911577	+	0.411129i	$0.865135\pi$
$632$	−31.1441	+	5.49155i	−1.23885	+	0.218442i
$633$	−10.0428	+	3.49685i	−0.399165	+	0.138987i
$634$	18.8625	−	6.86537i	0.749124	−	0.272659i
$635$	−0.458159	−	16.4516i	−0.0181815	−	0.652863i
$636$	14.1088	+	2.69193i	0.559448	+	0.106742i
$637$	−2.63155	+	0.464014i	−0.104266	+	0.0183849i
$638$	−3.39232	−	1.95856i	−0.134303	−	0.0775400i
$639$	2.70849	+	5.01015i	0.107146	+	0.198198i
$640$	−29.7242	+	6.09892i	−1.17495	+	0.241081i
$641$	−9.28107	+	7.78774i	−0.366580	+	0.307597i	−0.807407	−	0.589995i	$-0.799130\pi$
$641$	−9.28107	+	7.78774i	−0.366580	+	0.307597i	0.440827	+	0.897592i	$0.354685\pi$
$642$	−3.87705	−	23.9433i	−0.153015	−	0.944966i
$643$	3.62067	+	0.638422i	0.142785	+	0.0251769i	0.244584	−	0.969628i	$-0.421349\pi$
$643$	3.62067	+	0.638422i	0.142785	+	0.0251769i	−0.101799	+	0.994805i	$0.532460\pi$
$644$	−6.36045	−	5.33705i	−0.250637	−	0.210309i
$645$	8.76463	−	1.67084i	0.345107	−	0.0657894i
$646$	6.58397	+	2.39637i	0.259043	+	0.0942839i
$647$		−	43.1622i		−	1.69688i	−0.529292	−	0.848440i	$-0.677542\pi$
$647$		−	43.1622i		−	1.69688i	0.529292	−	0.848440i	$-0.322458\pi$
$648$	16.5146	+	10.8103i	0.648753	+	0.424670i
$649$	3.48421			0.136767
$650$	18.2844	+	27.9517i	0.717174	+	1.09636i
$651$	30.9501	−	17.2959i	1.21303	−	0.677879i
$652$	−6.58529	+	7.84805i	−0.257900	+	0.307353i
$653$	20.2657	+	3.57339i	0.793058	+	0.139837i	0.555479	−	0.831531i	$-0.312535\pi$
$653$	20.2657	+	3.57339i	0.793058	+	0.139837i	0.237579	+	0.971368i	$0.423646\pi$
$654$	−12.4846	+	2.02159i	−0.488187	+	0.0790503i
$655$	18.0957	−	7.16283i	0.707056	−	0.279875i
$656$	7.49329	+	12.9788i	0.292564	+	0.506735i
$657$	0.0349042	−	1.24626i	0.00136174	−	0.0486213i
$658$	−22.6708	−	13.0890i	−0.883801	−	0.510263i
$659$	2.82950	+	16.0469i	0.110222	+	0.625099i	0.989006	+	0.147879i	$0.0472445\pi$
$659$	2.82950	+	16.0469i	0.110222	+	0.625099i	−0.878784	+	0.477220i	$0.841644\pi$
$660$	0.427180	−	0.764131i	0.0166279	−	0.0297438i
$661$	−9.38752	+	3.41678i	−0.365132	+	0.132897i	−0.518069	−	0.855339i	$-0.673349\pi$
$661$	−9.38752	+	3.41678i	−0.365132	+	0.132897i	0.152937	+	0.988236i	$0.451127\pi$
$662$	−1.32183	−	3.63170i	−0.0513745	−	0.141150i
$663$	5.52464	−	1.92365i	0.214559	−	0.0747084i
$664$	−2.26205	−	12.8287i	−0.0877846	−	0.497851i
$665$	21.4429	+	24.1558i	0.831520	+	0.936721i
$666$	4.05325	+	27.4627i	0.157060	+	1.06416i
$667$	27.6535	−	15.9658i	1.07075	−	0.618196i
$668$	−4.20086	−	5.00639i	−0.162536	−	0.193703i
$669$	−14.8383	+	39.0578i	−0.573684	+	1.51006i
$670$	15.6478	−	28.9341i	0.604526	−	1.11782i
$671$	−3.33063	−	2.79473i	−0.128577	−	0.107889i
$672$	8.74281	−	14.6650i	0.337261	−	0.565713i
$673$	−8.31488	+	22.8449i	−0.320515	+	0.880608i	0.669896	+	0.742455i	$0.266339\pi$
$673$	−8.31488	+	22.8449i	−0.320515	+	0.880608i	−0.990411	+	0.138153i	$0.955884\pi$
$674$	−47.3100			−1.82231
$675$	−13.2970	−	22.3201i	−0.511803	−	0.859103i
$676$	2.49454			0.0959438
$677$	1.48495	−	4.07987i	0.0570713	−	0.156802i	−0.907881	−	0.419229i	$-0.862301\pi$
$677$	1.48495	−	4.07987i	0.0570713	−	0.156802i	0.964952	+	0.262427i	$0.0845228\pi$
$678$	−22.9304	−	0.321044i	−0.880636	−	0.0123296i
$679$	8.21448	+	6.89276i	0.315243	+	0.264520i
$680$	1.92137	−	3.55279i	0.0736813	−	0.136243i
$681$	5.51887	+	6.76732i	0.211484	+	0.259324i
$682$	−2.67929	−	3.19306i	−0.102595	−	0.122268i
$683$	−22.0653	+	12.7394i	−0.844305	+	0.487460i	−0.858725	−	0.512436i	$-0.828743\pi$
$683$	−22.0653	+	12.7394i	−0.844305	+	0.487460i	0.0144203	+	0.999896i	$0.495410\pi$
$684$	−7.65790	−	6.80002i	−0.292807	−	0.260005i
$685$	4.52952	+	5.10258i	0.173064	+	0.194960i
$686$	4.96749	+	28.1720i	0.189660	+	1.07561i
$687$	11.4527	+	9.88642i	0.436946	+	0.377190i
$688$	−3.84520	−	10.5646i	−0.146597	−	0.402771i
$689$	48.8820	−	17.7916i	1.86225	−	0.677805i
$690$	14.8306	+	24.8853i	0.564590	+	0.947369i
$691$	0.772020	+	4.37835i	0.0293690	+	0.166560i	0.995965	−	0.0897461i	$-0.0286056\pi$
$691$	0.772020	+	4.37835i	0.0293690	+	0.166560i	−0.966596	+	0.256306i	$0.917494\pi$
$692$	−1.83110	−	1.05718i	−0.0696078	−	0.0401881i
$693$	−0.905506	−	2.72273i	−0.0343973	−	0.103428i
$694$	14.8126	+	25.6562i	0.562278	+	0.973894i
$695$	20.1270	−	7.96689i	0.763460	−	0.302201i
$696$	16.6953	+	20.4720i	0.632834	+	0.775990i
$697$	−2.49091	−	0.439215i	−0.0943500	−	0.0166364i
$698$	0.0995985	−	0.118697i	0.00376986	−	0.00449274i
$699$	−0.125615	+	8.97195i	−0.00475118	+	0.339350i
$700$	−7.56637	+	4.94949i	−0.285982	+	0.187073i
$701$	2.41285			0.0911321			0.0455660	−	0.998961i	$-0.485491\pi$
$701$	2.41285			0.0911321			0.0455660	+	0.998961i	$0.485491\pi$
$702$	−34.6806	−	1.45743i	−1.30893	−	0.0550072i
$703$			29.6631i			1.11877i
$704$	1.28508	+	0.467730i	0.0484332	+	0.0176283i
$705$	14.6998	+	17.0340i	0.553625	+	0.641537i
$706$	4.19113	+	3.51678i	0.157735	+	0.132356i
$707$	−13.0260	−	2.29683i	−0.489893	−	0.0863813i
$708$	10.6658	+	4.05202i	0.400846	+	0.152284i
$709$	12.6783	−	10.6383i	0.476142	−	0.399530i	−0.372887	−	0.927877i	$-0.621632\pi$
$709$	12.6783	−	10.6383i	0.476142	−	0.399530i	0.849029	+	0.528346i	$0.177188\pi$
$710$	−6.77423	+	1.38996i	−0.254232	+	0.0521643i
$711$	−33.9043	+	26.8681i	−1.27151	+	1.00763i
$712$	−34.1361	−	19.7085i	−1.27930	−	0.738606i
$713$	33.4624	−	5.90033i	1.25318	−	0.220969i
$714$	2.11383	+	6.07082i	0.0791081	+	0.227195i
$715$	−0.0882612	−	3.16930i	−0.00330078	−	0.118525i
$716$	4.16980	−	1.51768i	0.155833	−	0.0567185i
$717$	−1.65440	+	8.67091i	−0.0617847	+	0.323821i
$718$	10.5878	−	1.86692i	0.395135	−	0.0696729i
$719$	25.9595	−	44.9633i	0.968128	−	1.67685i	0.267162	−	0.963652i	$-0.413914\pi$
$719$	25.9595	−	44.9633i	0.968128	−	1.67685i	0.700966	−	0.713195i	$-0.252753\pi$
$720$	−25.0810	+	21.0387i	−0.934715	+	0.784067i
$721$	6.65681	+	11.5299i	0.247913	+	0.429397i
$722$	−8.65964	−	10.3202i	−0.322279	−	0.384077i
$723$	4.28952	+	26.4906i	0.159529	+	0.985195i
$724$	0.0633706	−	0.359393i	0.00235515	−	0.0133567i
$725$	−7.93443	−	33.8541i	−0.294677	−	1.25731i
$726$	26.7990	−	14.9762i	0.994605	−	0.555818i
$727$	−0.812584	+	2.23256i	−0.0301371	+	0.0828009i	−0.953849	−	0.300288i	$-0.902917\pi$
$727$	−0.812584	+	2.23256i	−0.0301371	+	0.0828009i	0.923712	+	0.383088i	$0.125140\pi$
$728$		−	24.8772i		−	0.922009i
$729$	26.9048	+	2.26532i	0.996474	+	0.0839006i
$730$	1.43638	+	0.477952i	0.0531627	+	0.0176898i
$731$	1.78302	+	0.648968i	0.0659475	+	0.0240029i
$732$	−6.94549	−	12.4286i	−0.256713	−	0.459373i
$733$	28.5681	−	34.0461i	1.05519	−	1.25752i	0.0900041	−	0.995941i	$-0.471312\pi$
$733$	28.5681	−	34.0461i	1.05519	−	1.25752i	0.965182	−	0.261580i	$-0.0842436\pi$
$734$	−2.69017	+	15.2567i	−0.0992961	+	0.563136i
$735$	−0.403801	+	2.49123i	−0.0148944	+	0.0918905i
$736$	12.5343	−	10.5175i	0.462021	−	0.387682i
$737$	−2.70412	+	1.56122i	−0.0996074	+	0.0575083i
$738$	12.7821	+	7.86494i	0.470517	+	0.289513i
$739$	−14.1751	+	24.5520i	−0.521439	+	0.903159i	0.478250	+	0.878224i	$0.341271\pi$
$739$	−14.1751	+	24.5520i	−0.521439	+	0.903159i	−0.999689	+	0.0249353i	$0.992062\pi$
$740$	−8.21411	−	1.21366i	−0.301957	−	0.0446149i
$741$	−36.4333	−	6.95144i	−1.33841	−	0.255367i
$742$	19.5505	+	53.7146i	0.717722	+	1.97193i
$743$	−11.1870	−	30.7360i	−0.410410	−	1.12759i	−0.956974	−	0.290175i	$-0.906286\pi$
$743$	−11.1870	−	30.7360i	−0.410410	−	1.12759i	0.546563	−	0.837418i	$-0.315936\pi$
$744$	9.24351	+	26.5469i	0.338883	+	0.973258i
$745$	−3.42314	+	23.1680i	−0.125414	+	0.848811i
$746$	−15.3053	+	26.5096i	−0.560368	+	0.970586i
$747$	−11.0674	−	13.9657i	−0.404933	−	0.510977i
$748$	0.161227	−	0.0930846i	0.00589506	−	0.00340351i
$749$	18.2157	−	15.2848i	0.665588	−	0.558495i
$750$	30.6111	−	7.62282i	1.11776	−	0.278346i
$751$	−8.26550	+	46.8760i	−0.301613	+	1.71053i	0.337424	+	0.941353i	$0.390444\pi$
$751$	−8.26550	+	46.8760i	−0.301613	+	1.71053i	−0.639036	+	0.769177i	$0.720667\pi$
$752$	18.2233	−	21.7177i	0.664536	−	0.791963i
$753$	−10.4656	+	17.5547i	−0.381388	+	0.639730i
$754$	−43.6542	−	15.8888i	−1.58979	−	0.578638i
$755$	6.79585	+	2.26131i	0.247326	+	0.0822974i
$756$	0.394519	−	9.38784i	0.0143485	−	0.341433i
$757$		−	12.6135i		−	0.458445i	−0.973374	−	0.229222i	$-0.926382\pi$
$757$		−	12.6135i		−	0.458445i	0.973374	−	0.229222i	$-0.0736183\pi$
$758$	−9.84161	+	27.0396i	−0.357463	+	0.982123i
$759$	0.0384967	−	2.74961i	0.00139734	−	0.0998044i
$760$	−21.8129	+	13.4169i	−0.791238	+	0.486681i
$761$	−0.675417	+	3.83048i	−0.0244839	+	0.138855i	−0.994599	−	0.103789i	$-0.966903\pi$
$761$	−0.675417	+	3.83048i	−0.0244839	+	0.138855i	0.970116	+	0.242644i	$0.0780145\pi$
$762$	−16.0940	+	13.1249i	−0.583024	+	0.475467i
$763$	−7.96987	−	9.49813i	−0.288529	−	0.343855i
$764$	6.19550	+	10.7309i	0.224145	+	0.388231i
$765$	0.000873821	−	5.52508i	3.15931e−5	−	0.199760i
$766$	10.4875	−	18.1649i	0.378929	−	0.656325i
$767$	40.6941	−	7.17546i	1.46938	−	0.259091i
$768$	18.6121	+	16.0667i	0.671606	+	0.579759i
$769$	0.403174	−	0.146743i	0.0145388	−	0.00529170i	−0.334741	−	0.942310i	$-0.608649\pi$
$769$	0.403174	−	0.146743i	0.0145388	−	0.00529170i	0.349279	+	0.937019i	$0.386426\pi$
$770$	3.48263	−	0.0969870i	0.125505	−	0.00349517i
$771$	27.8987	−	32.3185i	1.00475	−	1.16392i
$772$	7.50661	−	1.32362i	0.270169	−	0.0476380i
$773$	32.7070	+	18.8834i	1.17639	+	0.679188i	0.955176	−	0.296038i	$-0.0956654\pi$
$773$	32.7070	+	18.8834i	1.17639	+	0.679188i	0.221212	+	0.975226i	$0.428999\pi$
$774$	−8.41867	−	7.47557i	−0.302603	−	0.268704i
$775$	4.38717	−	36.7396i	0.157592	−	1.31973i
$776$	−6.51278	+	5.46487i	−0.233795	+	0.196177i
$777$	−21.0909	+	17.2000i	−0.756633	+	0.617048i
$778$	−13.4698	−	2.37508i	−0.482914	−	0.0851508i
$779$	12.2849	+	10.3082i	0.440152	+	0.369331i
$780$	3.41560	−	9.80445i	0.122298	−	0.351055i
$781$	0.616842	+	0.224512i	0.0220723	+	0.00803368i
$782$			6.16064i			0.220304i
$783$	33.4074	+	13.7739i	1.19388	+	0.492240i
$784$	3.18000			0.113572
$785$	27.1663	−	34.2695i	0.969608	−	1.22313i
$786$	−21.0935	−	12.5753i	−0.752379	−	0.448546i
$787$	17.1940	−	20.4911i	0.612902	−	0.730428i	−0.366931	−	0.930248i	$-0.619591\pi$
$787$	17.1940	−	20.4911i	0.612902	−	0.730428i	0.979833	+	0.199821i	$0.0640359\pi$
$788$	−10.4724	−	1.84657i	−0.373065	−	0.0657814i
$789$	−0.467463	+	1.23047i	−0.0166421	+	0.0438058i
$790$	−19.3320	−	48.8390i	−0.687802	−	1.73761i
$791$	−11.2412	−	19.4703i	−0.399691	−	0.692285i
$792$	2.25056	−	0.332163i	0.0799703	−	0.0118029i
$793$	−44.6557	−	25.7820i	−1.58577	−	0.915545i
$794$	−8.41581	−	47.7284i	−0.298666	−	1.69382i
$795$	−0.680025	−	49.1254i	−0.0241180	−	1.74230i
$796$	−12.6952	+	4.62066i	−0.449968	+	0.163775i
$797$	−0.415684	−	1.14208i	−0.0147243	−	0.0404547i	0.932113	−	0.362168i	$-0.117963\pi$
$797$	−0.415684	−	1.14208i	−0.0147243	−	0.0404547i	−0.946837	+	0.321714i	$0.895741\pi$
$798$	7.63868	−	40.0353i	0.270406	−	1.41723i
$799$	0.830873	+	4.71212i	0.0293942	+	0.166703i
$800$	−7.01638	−	16.3780i	−0.248066	−	0.579050i
$801$	−53.8977	−	1.50952i	−1.90438	−	0.0533363i
$802$	−9.80774	+	5.66250i	−0.346323	+	0.199950i
$803$	−0.0923659	−	0.110077i	−0.00325952	−	0.00388455i
$804$	−10.0934	+	1.63439i	−0.355968	+	0.0576407i
$805$	−13.5101	+	24.9815i	−0.476170	+	0.880481i
$806$	−37.8688	−	31.7757i	−1.33387	−	1.11925i
$807$	19.4060	+	34.7259i	0.683122	+	1.22241i
$808$	3.58672	−	9.85443i	0.126180	−	0.346678i
$809$	−5.52813			−0.194359			−0.0971794	−	0.995267i	$-0.530982\pi$
$809$	−5.52813			−0.194359			−0.0971794	+	0.995267i	$0.530982\pi$
$810$	−12.0755	+	30.4785i	−0.424289	+	1.07090i
$811$	6.32820			0.222213			0.111107	−	0.993808i	$-0.464560\pi$
$811$	6.32820			0.222213			0.111107	+	0.993808i	$0.464560\pi$
$812$	4.30102	−	11.8170i	0.150936	−	0.414694i
$813$	−12.0144	−	21.4991i	−0.421362	−	0.754005i
$814$	2.45099	+	2.05663i	0.0859072	+	0.0720847i
$815$	30.8242	+	16.6699i	1.07973	+	0.583922i
$816$	−6.87227	+	1.11280i	−0.240578	+	0.0389559i
$817$	−7.73302	−	9.21586i	−0.270544	−	0.322422i
$818$	−14.0316	+	8.10116i	−0.490604	+	0.283250i
$819$	−16.1831	−	29.9354i	−0.565485	−	1.04603i
$820$	−3.35712	+	2.98009i	−0.117236	+	0.104069i
$821$	−5.74162	−	32.5623i	−0.200384	−	1.13643i	−0.904540	−	0.426388i	$-0.859786\pi$
$821$	−5.74162	−	32.5623i	−0.200384	−	1.13643i	0.704156	−	0.710045i	$-0.251325\pi$
$822$	1.61357	−	8.45691i	0.0562796	−	0.294969i
$823$	−10.8073	−	29.6927i	−0.376717	−	1.03502i	−0.972708	−	0.232031i	$-0.925463\pi$
$823$	−10.8073	−	29.6927i	−0.376717	−	1.03502i	0.595991	−	0.802991i	$-0.296759\pi$
$824$	−9.91902	+	3.61023i	−0.345545	+	0.125768i
$825$	−2.85409	−	0.906014i	−0.0993667	−	0.0315434i
$826$	7.88485	+	44.7172i	0.274349	+	1.55591i
$827$	9.57560	+	5.52848i	0.332976	+	0.192244i	0.657162	−	0.753750i	$-0.271757\pi$
$827$	9.57560	+	5.52848i	0.332976	+	0.192244i	−0.324185	+	0.945994i	$0.605090\pi$
$828$	3.31554	−	8.37228i	0.115223	−	0.290957i
$829$	−5.02892	−	8.71034i	−0.174662	−	0.302523i	0.765383	−	0.643576i	$-0.222550\pi$
$829$	−5.02892	−	8.71034i	−0.174662	−	0.302523i	−0.940044	+	0.341053i	$0.889216\pi$
$830$	20.1175	−	7.96313i	0.698288	−	0.276404i
$831$	8.97272	−	23.6182i	0.311260	−	0.819306i
$832$	15.9724	+	2.81636i	0.553743	+	0.0976399i
$833$	−0.344985	+	0.411137i	−0.0119530	+	0.0142450i
$834$	−23.4613	−	13.9869i	−0.812398	−	0.484327i
$835$	−13.8869	+	17.5179i	−0.480577	+	0.606234i
$836$	−1.18037			−0.0408240
$837$	28.3923	+	25.9316i	0.981383	+	0.896327i
$838$		−	22.3739i		−	0.772895i
$839$	9.92391	+	3.61201i	0.342611	+	0.124700i	0.507595	−	0.861596i	$-0.330535\pi$
$839$	9.92391	+	3.61201i	0.342611	+	0.124700i	−0.164983	+	0.986296i	$0.552757\pi$
$840$	−22.1877	−	7.72959i	−0.765549	−	0.266696i
$841$	14.8323	+	12.4458i	0.511458	+	0.429164i
$842$	18.5495	+	3.27077i	0.639257	+	0.112718i
$843$	11.1860	−	9.12235i	0.385265	−	0.314190i
$844$	−3.07459	+	2.57989i	−0.105832	+	0.0888033i
$845$	−1.71503	−	8.35854i	−0.0589989	−	0.287543i
$846$	5.71088	−	27.8107i	0.196344	−	0.956152i
$847$	26.0648	+	15.0485i	0.895597	+	0.517073i
$848$	−60.9651	+	10.7498i	−2.09355	+	0.369150i
$849$	−13.3160	+	15.4256i	−0.457004	+	0.529404i
$850$	6.42191	+	1.94006i	0.220270	+	0.0665436i
$851$	−24.5091	+	8.92058i	−0.840161	+	0.305793i
$852$	1.62717	+	1.40464i	0.0557458	+	0.0481221i
$853$	37.2224	−	6.56332i	1.27447	−	0.224724i	0.504841	−	0.863213i	$-0.331551\pi$
$853$	37.2224	−	6.56332i	1.27447	−	0.224724i	0.769631	+	0.638489i	$0.220440\pi$
$854$	28.3309	−	49.0706i	0.969463	−	1.67916i
$855$	−17.5201	+	30.3347i	−0.599176	+	1.03742i
$856$	9.42647	+	16.3271i	0.322190	+	0.558050i
$857$	5.98027	+	7.12701i	0.204282	+	0.243454i	0.858452	−	0.512893i	$-0.171426\pi$
$857$	5.98027	+	7.12701i	0.204282	+	0.243454i	−0.654170	+	0.756347i	$0.726982\pi$
$858$	−3.10040	+	2.52843i	−0.105846	+	0.0863193i
$859$	−8.27362	+	46.9220i	−0.282292	+	1.60096i	0.432508	+	0.901630i	$0.357629\pi$
$859$	−8.27362	+	46.9220i	−0.282292	+	1.60096i	−0.714800	+	0.699328i	$0.753482\pi$
$860$	2.86838	−	1.76431i	0.0978111	−	0.0601625i
$861$	−0.205979	+	14.7119i	−0.00701974	+	0.501381i
$862$	−1.12601	+	3.09369i	−0.0383520	+	0.105371i
$863$			6.24140i			0.212460i	0.994342	+	0.106230i	$0.0338780\pi$
$863$			6.24140i			0.212460i	−0.994342	+	0.106230i	$0.966122\pi$
$864$	18.0842	+	3.97820i	0.615238	+	0.135341i
$865$	−2.28344	+	6.86235i	−0.0776392	+	0.233327i
$866$	10.9186	+	3.97404i	0.371029	+	0.135043i
$867$	−14.4763	+	24.2822i	−0.491641	+	0.824666i
$868$	8.60150	−	10.2509i	0.291954	−	0.347937i
$869$	−0.865800	+	4.91020i	−0.0293702	+	0.166567i
$870$	−27.7350	+	33.9980i	−0.940303	+	1.15264i
$871$	−28.3676	+	23.8033i	−0.961201	+	0.806543i
$872$	8.51336	−	4.91519i	0.288299	−	0.166449i
$873$	−4.28200	+	10.8127i	−0.144924	+	0.365956i
$874$	19.5302	−	33.8273i	0.660618	−	1.14422i
$875$	21.7864	+	21.9501i	0.736515	+	0.742048i
$876$	−0.154733	−	0.444386i	−0.00522794	−	0.0150144i
$877$	2.51999	+	6.92361i	0.0850940	+	0.233794i	0.974940	−	0.222467i	$-0.0714108\pi$
$877$	2.51999	+	6.92361i	0.0850940	+	0.233794i	−0.889846	+	0.456260i	$0.849189\pi$
$878$	12.6782	+	34.8330i	0.427868	+	1.17556i
$879$	32.7364	+	6.24606i	1.10417	+	0.210674i
$880$	−0.551498	+	3.73258i	−0.0185910	+	0.125825i
$881$	1.82592	−	3.16258i	0.0615168	−	0.106550i	−0.833627	−	0.552328i	$-0.813740\pi$
$881$	1.82592	−	3.16258i	0.0615168	−	0.106550i	0.895144	+	0.445778i	$0.147073\pi$
$882$	2.80140	−	1.51444i	0.0943281	−	0.0509939i
$883$	2.47127	−	1.42679i	0.0831649	−	0.0480153i	−0.457841	−	0.889034i	$-0.651377\pi$
$883$	2.47127	−	1.42679i	0.0831649	−	0.0480153i	0.541006	+	0.841019i	$0.318044\pi$
$884$	1.69136	−	1.41922i	0.0568867	−	0.0477336i
$885$	6.24433	−	38.5242i	0.209901	−	1.29498i
$886$	−0.663912	+	3.76523i	−0.0223045	+	0.126495i
$887$	−18.7921	+	22.3955i	−0.630976	+	0.751968i	−0.982916	−	0.184054i	$-0.941078\pi$
$887$	−18.7921	+	22.3955i	−0.630976	+	0.751968i	0.351940	+	0.936023i	$0.385522\pi$
$888$	−10.5260	−	18.8358i	−0.353231	−	0.632087i
$889$	−19.1318	−	6.96339i	−0.641659	−	0.233545i
$890$	20.6702	−	62.1197i	0.692868	−	2.08226i
$891$	2.49209	−	1.86374i	0.0834881	−	0.0624377i
$892$			15.7693i			0.527996i
$893$	10.3759	−	28.5076i	0.347217	−	0.953971i
$894$	25.7968	−	14.4161i	0.862774	−	0.482146i
$895$	−7.95216	−	12.9285i	−0.265811	−	0.432151i
$896$	−6.51820	+	36.9665i	−0.217758	+	1.23497i
$897$	−5.21297	−	32.1934i	−0.174056	−	1.07491i
$898$	27.5594	+	32.8440i	0.919668	+	1.09602i
$899$	25.7313	+	44.5680i	0.858188	+	1.48642i
$900$	−7.68324	−	6.09269i	−0.256108	−	0.203090i
$901$	5.22402	−	9.04826i	0.174037	−	0.301441i
$902$	1.70349	−	0.300371i	0.0567200	−	0.0100013i
$903$	2.06865	−	10.8421i	0.0688405	−	0.360802i
$904$	16.7500	−	6.09651i	0.557097	−	0.202767i
$905$	−1.24780	+	0.0347497i	−0.0414782	+	0.00115512i
$906$	−2.97182	−	8.53493i	−0.0987321	−	0.283554i
$907$	17.3288	−	3.05554i	0.575395	−	0.101458i	0.121624	−	0.992576i	$-0.461190\pi$
$907$	17.3288	−	3.05554i	0.575395	−	0.101458i	0.453770	+	0.891119i	$0.350079\pi$
$908$	2.85426	+	1.64791i	0.0947219	+	0.0546877i
$909$	−2.09452	−	14.1914i	−0.0694708	−	0.470698i
$910$	40.4758	−	8.30495i	1.34176	−	0.275306i
$911$	27.8200	−	23.3437i	0.921717	−	0.773412i	−0.0525947	−	0.998616i	$-0.516749\pi$
$911$	27.8200	−	23.3437i	0.921717	−	0.773412i	0.974312	+	0.225203i	$0.0723047\pi$
$912$	41.2625	+	15.6759i	1.36634	+	0.519081i
$913$	−2.02258	−	0.356636i	−0.0669376	−	0.0118029i
$914$	51.2311	+	42.9880i	1.69458	+	1.42192i
$915$	−36.8697	+	31.8173i	−1.21888	+	1.05185i
$916$	5.36590	+	1.95303i	0.177294	+	0.0645299i
$917$		−	24.0754i		−	0.795040i
$918$	−5.52411	+	4.25316i	−0.182323	+	0.140375i
$919$	42.5365			1.40315			0.701575	−	0.712596i	$-0.252481\pi$
$919$	42.5365			1.40315			0.701575	+	0.712596i	$0.252481\pi$
$920$	−17.6454	−	13.9880i	−0.581753	−	0.461171i
$921$	0.325677	−	23.2613i	0.0107314	−	0.766485i
$922$	−17.3473	+	20.6737i	−0.571302	+	0.680852i
$923$	7.66680	+	1.35186i	0.252356	+	0.0444972i
$924$	−0.684433	−	0.839262i	−0.0225162	−	0.0276097i
$925$	1.58068	+	28.3577i	0.0519726	+	0.932396i
$926$	−34.9381	−	60.5145i	−1.14814	−	1.98863i
$927$	−9.58732	+	10.7968i	−0.314889	+	0.354615i
$928$	21.4617	+	12.3909i	0.704514	+	0.406751i
$929$	0.516281	+	2.92797i	0.0169386	+	0.0960637i	0.992105	−	0.125410i	$-0.0400245\pi$
$929$	0.516281	+	2.92797i	0.0169386	+	0.0960637i	−0.975166	+	0.221473i	$0.928913\pi$
$930$	−40.1067	+	23.9018i	−1.31515	+	0.783771i
$931$	3.19763	−	1.16384i	0.104798	−	0.0381434i
$932$	1.15827	+	3.18233i	0.0379405	+	0.104241i
$933$	11.8729	+	10.2492i	0.388703	+	0.335544i
$934$	−0.673583	−	3.82008i	−0.0220403	−	0.124997i
$935$	−0.422748	−	0.476233i	−0.0138253	−	0.0155745i
$936$	25.6015	−	8.51437i	0.836811	−	0.278301i
$937$	−8.34878	+	4.82017i	−0.272743	+	0.157468i	−0.630133	−	0.776487i	$-0.717000\pi$
$937$	−8.34878	+	4.82017i	−0.272743	+	0.157468i	0.357391	+	0.933955i	$0.383666\pi$
$938$	−26.1566	−	31.1722i	−0.854042	−	1.01781i
$939$	3.84967	+	4.72052i	0.125629	+	0.154049i
$940$	7.46960	+	4.03960i	0.243631	+	0.131757i
$941$	28.1833	+	23.6486i	0.918749	+	0.770922i	0.973763	−	0.227564i	$-0.0730761\pi$
$941$	28.1833	+	23.6486i	0.918749	+	0.770922i	−0.0550146	+	0.998486i	$0.517521\pi$
$942$	−55.1761	−	0.772510i	−1.79773	−	0.0251697i
$943$	−4.82273	+	13.2503i	−0.157050	+	0.431491i
$944$	−49.1753			−1.60052
$945$	−31.7274	+	5.13236i	−1.03209	+	0.166956i
$946$	−1.29763			−0.0421897
$947$	6.07450	−	16.6896i	0.197395	−	0.542338i	−0.801019	−	0.598639i	$-0.795708\pi$
$947$	6.07450	−	16.6896i	0.197395	−	0.542338i	0.998414	+	0.0563011i	$0.0179307\pi$
$948$	−8.36076	+	14.0241i	−0.271545	+	0.455482i
$949$	−1.30549	−	1.09543i	−0.0423779	−	0.0355593i
$950$	−29.1116	−	31.0111i	−0.944505	−	1.00613i
$951$	−7.57962	+	19.9513i	−0.245786	+	0.646964i
$952$	−3.21174	−	3.82760i	−0.104093	−	0.124053i
$953$	−48.6703	+	28.0998i	−1.57658	+	0.910242i	−0.581254	+	0.813723i	$0.697438\pi$
$953$	−48.6703	+	28.0998i	−1.57658	+	0.910242i	−0.995331	+	0.0965191i	$0.969229\pi$
$954$	−48.5873	+	38.5039i	−1.57307	+	1.24661i
$955$	31.6970	−	28.1371i	1.02569	−	0.910496i
$956$	0.578534	+	3.28103i	0.0187111	+	0.106116i
$957$	3.93324	−	1.36953i	0.127143	−	0.0442707i
$958$	−11.7384	−	32.2511i	−0.379252	−	1.04199i
$959$	7.93142	−	2.88680i	0.256119	−	0.0932197i
$960$	7.47468	−	13.3706i	0.241244	−	0.431533i
$961$	4.12622	+	23.4009i	0.133104	+	0.754869i
$962$	32.8619	+	18.9728i	1.05951	+	0.611709i
$963$	21.9643	+	13.5148i	0.707790	+	0.435508i
$964$	5.06420	+	8.77146i	0.163107	+	0.282510i
$965$	−9.59600	−	24.2426i	−0.308906	−	0.780399i
$966$	35.3762	−	5.72834i	1.13821	−	0.184306i
$967$	−9.35163	−	1.64894i	−0.300728	−	0.0530265i	0.0212481	−	0.999774i	$-0.493236\pi$
$967$	−9.35163	−	1.64894i	−0.300728	−	0.0530265i	−0.321976	+	0.946748i	$0.604347\pi$
$968$	−15.3383	+	18.2795i	−0.492992	+	0.587525i
$969$	−6.50309	+	3.63414i	−0.208909	+	0.116745i
$970$	−11.0657	−	8.77207i	−0.355298	−	0.281654i
$971$	21.6905			0.696080			0.348040	−	0.937480i	$-0.386847\pi$
$971$	21.6905			0.696080			0.348040	+	0.937480i	$0.386847\pi$
$972$	9.79621	−	2.80704i	0.314214	−	0.0900360i
$973$		−	26.7780i		−	0.858462i
$974$	29.9135	+	10.8876i	0.958489	+	0.348861i
$975$	−35.2004	−	4.70406i	−1.12731	−	0.150651i
$976$	47.0076	+	39.4440i	1.50468	+	1.26257i
$977$	−31.7910	−	5.60561i	−1.01708	−	0.179339i	−0.359837	−	0.933015i	$-0.617168\pi$
$977$	−31.7910	−	5.60561i	−1.01708	−	0.179339i	−0.657246	+	0.753676i	$0.728279\pi$
$978$	−7.06810	−	43.6501i	−0.226013	−	1.39578i
$979$	−4.76057	+	3.99460i	−0.152149	+	0.127668i
$980$	0.191453	+	0.933084i	0.00611575	+	0.0298063i
$981$	7.04694	−	11.4527i	0.224991	−	0.365657i
$982$	0.222450	+	0.128431i	0.00709866	+	0.00409841i
$983$	−35.0455	+	6.17946i	−1.11778	+	0.197094i	−0.701864	−	0.712311i	$-0.747649\pi$
$983$	−35.0455	+	6.17946i	−1.11778	+	0.197094i	−0.415912	+	0.909405i	$0.636538\pi$
$984$	−11.4587	−	2.18630i	−0.365289	−	0.0696967i
$985$	1.01258	+	36.3599i	0.0322635	+	1.15852i
$986$	−8.76795	+	3.19127i	−0.279228	+	0.101631i
$987$	26.2858	−	9.15258i	0.836685	−	0.291330i
$988$	−13.7862	+	2.43088i	−0.438597	+	0.0773366i
$989$	5.28903	−	9.16086i	0.168181	−	0.291299i
$990$	1.29176	+	3.55083i	0.0410549	+	0.112853i
$991$	−9.65602	−	16.7247i	−0.306734	−	0.531278i	0.670912	−	0.741537i	$-0.265903\pi$
$991$	−9.65602	−	16.7247i	−0.306734	−	0.531278i	−0.977646	+	0.210259i	$0.932569\pi$
$992$	16.9507	+	20.2010i	0.538184	+	0.641383i
$993$	3.84134	+	1.45935i	0.121901	+	0.0463111i
$994$	−1.48551	+	8.42477i	−0.0471177	+	0.267218i
$995$	24.2107	+	39.3613i	0.767531	+	1.24784i
$996$	−5.77674	−	3.44392i	−0.183043	−	0.109125i
$997$	−3.52489	+	9.68456i	−0.111634	+	0.306713i	−0.982912	−	0.184078i	$-0.941070\pi$
$997$	−3.52489	+	9.68456i	−0.111634	+	0.306713i	0.871277	+	0.490791i	$0.163292\pi$
$998$			32.8078i			1.03851i
$999$	−24.9194	−	15.8182i	−0.788414	−	0.500466i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.2.p.a.4.5	✓	96
3.2	odd	2		405.2.p.a.64.12		96
5.2	odd	4		675.2.l.h.301.5		96
5.3	odd	4		675.2.l.h.301.12		96
5.4	even	2	inner	135.2.p.a.4.12	yes	96
15.14	odd	2		405.2.p.a.64.5		96
27.7	even	9	inner	135.2.p.a.34.12	yes	96
27.20	odd	18		405.2.p.a.19.5		96
135.7	odd	36		675.2.l.h.601.5		96
135.34	even	18	inner	135.2.p.a.34.5	yes	96
135.74	odd	18		405.2.p.a.19.12		96
135.88	odd	36		675.2.l.h.601.12		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.p.a.4.5	✓	96	1.1	even	1	trivial
135.2.p.a.4.12	yes	96	5.4	even	2	inner
135.2.p.a.34.5	yes	96	135.34	even	18	inner
135.2.p.a.34.12	yes	96	27.7	even	9	inner
405.2.p.a.19.5		96	27.20	odd	18
405.2.p.a.19.12		96	135.74	odd	18
405.2.p.a.64.5		96	15.14	odd	2
405.2.p.a.64.12		96	3.2	odd	2
675.2.l.h.301.5		96	5.2	odd	4
675.2.l.h.301.12		96	5.3	odd	4
675.2.l.h.601.5		96	135.7	odd	36
675.2.l.h.601.12		96	135.88	odd	36

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:	\( N \)	\(=\)	\( 135 = 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	135.p (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.557159 + 1.53078i) q^{2} +(-0.844941 - 1.51198i) q^{3} +(-0.500777 - 0.420202i) q^{4} +(-1.06369 + 1.96687i) q^{5} +(2.78527 - 0.451009i) q^{6} +(1.77805 + 2.11900i) q^{7} +(-1.89930 + 1.09656i) q^{8} +(-1.57215 + 2.55506i) q^{9} +(-2.41819 - 2.72414i) q^{10} +(0.0600421 + 0.340516i) q^{11} +(-0.212208 + 1.11221i) q^{12} +(1.40253 + 3.85342i) q^{13} +(-4.23438 + 1.54119i) q^{14} +(3.87261 - 0.0536071i) q^{15} +(-0.847418 - 4.80595i) q^{16} +(0.713284 + 0.411815i) q^{17} +(-3.03531 - 3.83019i) q^{18} +(-2.61103 - 4.52244i) q^{19} +(1.35915 - 0.537995i) q^{20} +(1.70153 - 4.47880i) q^{21} +(-0.554708 - 0.0978100i) q^{22} +(2.95144 - 3.51739i) q^{23} +(3.26278 + 1.94517i) q^{24} +(-2.73712 - 4.18428i) q^{25} -6.68017 q^{26} +(5.19157 + 0.218173i) q^{27} -1.80829i q^{28} +(6.53490 + 2.37851i) q^{29} +(-2.07560 + 5.95799i) q^{30} +(5.66883 + 4.75671i) q^{31} +(3.50939 + 0.618800i) q^{32} +(0.464120 - 0.378498i) q^{33} +(-1.02781 + 0.862436i) q^{34} +(-6.05909 + 1.24322i) q^{35} +(1.86094 - 0.618897i) q^{36} +(-4.91932 - 2.84017i) q^{37} +(8.37763 - 1.47720i) q^{38} +(4.64122 - 5.37651i) q^{39} +(-0.136517 - 4.90208i) q^{40} +(-2.88576 + 1.05033i) q^{41} +(5.90805 + 5.10007i) q^{42} +(2.26877 - 0.400046i) q^{43} +(0.113018 - 0.195752i) q^{44} +(-3.35318 - 5.81001i) q^{45} +(3.73993 + 6.47776i) q^{46} +(3.73422 + 4.45027i) q^{47} +(-6.55046 + 5.34202i) q^{48} +(-0.113154 + 0.641729i) q^{49} +(7.93023 - 1.85862i) q^{50} +(0.0199712 - 1.42643i) q^{51} +(0.916858 - 2.51905i) q^{52} -12.6853i q^{53} +(-3.22650 + 7.82560i) q^{54} +(-0.733615 - 0.244109i) q^{55} +(-5.70067 - 2.07488i) q^{56} +(-4.63166 + 7.76902i) q^{57} +(-7.28195 + 8.67829i) q^{58} +(1.74980 - 9.92363i) q^{59} +(-1.96184 - 1.60043i) q^{60} +(-9.63252 + 8.08265i) q^{61} +(-10.4399 + 6.02749i) q^{62} +(-8.20954 + 1.21165i) q^{63} +(1.97755 - 3.42522i) q^{64} +(-9.07102 - 1.34027i) q^{65} +(0.320809 + 0.921350i) q^{66} +(3.08859 + 8.48583i) q^{67} +(-0.184151 - 0.505951i) q^{68} +(-7.81201 - 1.49052i) q^{69} +(1.47277 - 9.96781i) q^{70} +(0.949232 - 1.64412i) q^{71} +(0.184197 - 6.57680i) q^{72} +(-0.359906 + 0.207792i) q^{73} +(7.08853 - 5.94798i) q^{74} +(-4.01383 + 7.67393i) q^{75} +(-0.592793 + 3.36190i) q^{76} +(-0.614795 + 0.732684i) q^{77} +(5.64436 + 10.1003i) q^{78} +(13.5502 + 4.93189i) q^{79} +(10.3540 + 3.44529i) q^{80} +(-4.05670 - 8.03388i) q^{81} -5.00267i q^{82} +(-2.03152 + 5.58154i) q^{83} +(-2.73409 + 1.52790i) q^{84} +(-1.56870 + 0.964890i) q^{85} +(-0.651684 + 3.69588i) q^{86} +(-1.92536 - 11.8903i) q^{87} +(-0.487435 - 0.580903i) q^{88} +(8.98648 + 15.5650i) q^{89} +(10.7621 - 1.89589i) q^{90} +(-5.67162 + 9.82354i) q^{91} +(-2.95603 + 0.521227i) q^{92} +(2.40221 - 12.5903i) q^{93} +(-8.89294 + 3.23677i) q^{94} +(11.6724 - 0.325062i) q^{95} +(-2.02962 - 5.82897i) q^{96} +(3.81769 - 0.673161i) q^{97} +(-0.919302 - 0.530759i) q^{98} +(-0.964435 - 0.381930i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 12 q^{4} - 9 q^{5} - 6 q^{6} - 18 q^{9} - 3 q^{10} - 6 q^{11} - 18 q^{14} - 21 q^{15} - 24 q^{16} - 6 q^{19} - 57 q^{20} + 24 q^{21} - 30 q^{24} + 3 q^{25} + 48 q^{26} - 30 q^{29} - 51 q^{30} - 30 q^{31}+ \cdots + 36 q^{99}+O(q^{100}) \) 96 * q - 12 * q^4 - 9 * q^5 - 6 * q^6 - 18 * q^9 - 3 * q^10 - 6 * q^11 - 18 * q^14 - 21 * q^15 - 24 * q^16 - 6 * q^19 - 57 * q^20 + 24 * q^21 - 30 * q^24 + 3 * q^25 + 48 * q^26 - 30 * q^29 - 51 * q^30 - 30 * q^31 - 24 * q^34 - 12 * q^35 + 54 * q^36 - 6 * q^39 - 9 * q^40 - 12 * q^41 + 78 * q^44 + 45 * q^45 - 6 * q^46 - 30 * q^49 + 84 * q^50 - 90 * q^51 + 108 * q^54 - 12 * q^55 - 96 * q^56 + 66 * q^59 + 84 * q^60 + 6 * q^61 + 45 * q^65 - 150 * q^66 + 24 * q^69 - 33 * q^70 - 90 * q^71 + 66 * q^74 + 39 * q^75 + 12 * q^76 + 24 * q^79 + 30 * q^80 - 54 * q^81 + 198 * q^84 - 21 * q^85 + 18 * q^86 + 96 * q^89 + 90 * q^90 - 6 * q^91 + 24 * q^94 + 87 * q^95 + 42 * q^96 + 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more