LMFDB - Embedded newform 798.2.cj.a.409.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [798,2,Mod(241,798)] 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("798.241"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(798, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 3, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 798 = 2 \cdot 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	798.cj (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [72] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$6.37206208130$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$12$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			409.9
Character	$\chi$	$=$	798.409
Dual form			798.2.cj.a.439.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.642788 + 0.766044i) q^{2} +(0.173648 + 0.984808i) q^{3} +(-0.173648 + 0.984808i) q^{4} +(0.161645 - 0.0285023i) q^{5} +(-0.642788 + 0.766044i) q^{6} +(-1.97551 + 1.75993i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-0.939693 + 0.342020i) q^{9} +(0.125737 + 0.105506i) q^{10} -4.25899 q^{11} -1.00000 q^{12} +(-4.34950 - 3.64966i) q^{13} +(-2.61802 - 0.382065i) q^{14} +(0.0561386 + 0.154239i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(0.0223450 - 0.0613923i) q^{17} +(-0.866025 - 0.500000i) q^{18} +(3.07743 + 3.08698i) q^{19} +0.164138i q^{20} +(-2.07624 - 1.63989i) q^{21} +(-2.73763 - 3.26258i) q^{22} +(-1.01569 - 0.852269i) q^{23} +(-0.642788 - 0.766044i) q^{24} +(-4.67315 + 1.70089i) q^{25} -5.67786i q^{26} +(-0.500000 - 0.866025i) q^{27} +(-1.39015 - 2.25111i) q^{28} +(4.11411 + 0.725429i) q^{29} +(-0.0820691 + 0.142148i) q^{30} +(3.07678 + 5.32914i) q^{31} +(-0.342020 - 0.939693i) q^{32} +(-0.739567 - 4.19429i) q^{33} +(0.0613923 - 0.0223450i) q^{34} +(-0.269168 + 0.340790i) q^{35} +(-0.173648 - 0.984808i) q^{36} +(0.0954391 - 0.0551018i) q^{37} +(-0.386631 + 4.34172i) q^{38} +(2.83893 - 4.91717i) q^{39} +(-0.125737 + 0.105506i) q^{40} +(-5.11725 + 4.29388i) q^{41} +(-0.0783542 - 2.64459i) q^{42} +(3.43339 + 1.24965i) q^{43} +(0.739567 - 4.19429i) q^{44} +(-0.142148 + 0.0820691i) q^{45} -1.32590i q^{46} +(1.89313 + 5.20134i) q^{47} +(0.173648 - 0.984808i) q^{48} +(0.805271 - 6.95353i) q^{49} +(-4.30680 - 2.48653i) q^{50} +(0.0643398 + 0.0113448i) q^{51} +(4.34950 - 3.64966i) q^{52} +(1.71412 + 0.302245i) q^{53} +(0.342020 - 0.939693i) q^{54} +(-0.688443 + 0.121391i) q^{55} +(0.830874 - 2.51190i) q^{56} +(-2.50569 + 3.56672i) q^{57} +(2.08879 + 3.61789i) q^{58} +(-2.07941 - 0.756843i) q^{59} +(-0.161645 + 0.0285023i) q^{60} +(-7.42587 + 8.84981i) q^{61} +(-2.10464 + 5.78246i) q^{62} +(1.25444 - 2.32946i) q^{63} +(0.500000 - 0.866025i) q^{64} +(-0.807096 - 0.465977i) q^{65} +(2.73763 - 3.26258i) q^{66} +(-5.50111 + 6.55597i) q^{67} +(0.0565794 + 0.0326662i) q^{68} +(0.662948 - 1.14826i) q^{69} +(-0.434078 + 0.0128609i) q^{70} +(3.15235 - 8.66100i) q^{71} +(0.642788 - 0.766044i) q^{72} +(-13.8307 + 2.43872i) q^{73} +(0.103558 + 0.0376919i) q^{74} +(-2.48653 - 4.30680i) q^{75} +(-3.57447 + 2.49463i) q^{76} +(8.41368 - 7.49554i) q^{77} +(5.59160 - 0.985951i) q^{78} +(0.821432 - 2.25687i) q^{79} +(-0.161645 - 0.0285023i) q^{80} +(0.766044 - 0.642788i) q^{81} +(-6.57861 - 1.15999i) q^{82} +(12.9977 + 7.50424i) q^{83} +(1.97551 - 1.75993i) q^{84} +(0.00186212 - 0.0105606i) q^{85} +(1.24965 + 3.43339i) q^{86} +4.17758i q^{87} +(3.68840 - 2.12950i) q^{88} +(2.71014 - 15.3699i) q^{89} +(-0.154239 - 0.0561386i) q^{90} +(15.0156 - 0.444885i) q^{91} +(1.01569 - 0.852269i) q^{92} +(-4.71390 + 3.95544i) q^{93} +(-2.76757 + 4.79358i) q^{94} +(0.585436 + 0.411280i) q^{95} +(0.866025 - 0.500000i) q^{96} +(0.229860 + 1.30360i) q^{97} +(5.84433 - 3.85277i) q^{98} +(4.00215 - 1.45666i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 12 q^{7} + 12 q^{10} - 12 q^{11} - 72 q^{12} - 30 q^{13} - 18 q^{14} + 36 q^{19} - 6 q^{21} + 12 q^{22} - 6 q^{23} - 30 q^{25} - 36 q^{27} - 12 q^{28} - 6 q^{31} - 12 q^{33} - 6 q^{34} - 6 q^{35}+ \cdots + 6 q^{99}+O(q^{100}) $ 72 * q + 12 * q^7 + 12 * q^10 - 12 * q^11 - 72 * q^12 - 30 * q^13 - 18 * q^14 + 36 * q^19 - 6 * q^21 + 12 * q^22 - 6 * q^23 - 30 * q^25 - 36 * q^27 - 12 * q^28 - 6 * q^31 - 12 * q^33 - 6 * q^34 - 6 * q^35 - 18 * q^37 - 12 * q^38 - 12 * q^40 - 6 * q^42 + 6 * q^43 + 12 * q^44 - 18 * q^45 - 18 * q^47 - 24 * q^49 - 18 * q^51 + 30 * q^52 - 48 * q^53 + 30 * q^55 - 18 * q^56 + 6 * q^57 - 48 * q^59 + 6 * q^61 + 12 * q^62 + 12 * q^63 + 36 * q^64 - 72 * q^65 - 12 * q^66 + 84 * q^67 - 6 * q^69 + 54 * q^70 + 6 * q^71 + 60 * q^73 - 18 * q^74 + 6 * q^75 + 18 * q^76 + 48 * q^77 - 12 * q^78 + 60 * q^79 + 6 * q^82 - 18 * q^83 - 12 * q^84 + 84 * q^85 - 12 * q^86 + 24 * q^89 - 6 * q^90 + 24 * q^91 + 6 * q^92 - 42 * q^93 + 18 * q^94 + 60 * q^95 - 30 * q^97 - 24 * q^98 + 6 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/798\mathbb{Z}\right)^\times$.

$n$	$115$	$211$	$533$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{17}{18}\right)$	$1$

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 $

$2$	0.642788	+	0.766044i	0.454519	+	0.541675i
$2$	0.642788	+	0.766044i	0.454519	+	0.541675i
$3$	0.173648	+	0.984808i	0.100256	+	0.568579i
$3$	0.173648	+	0.984808i	0.100256	+	0.568579i
$4$	−0.173648	+	0.984808i	−0.0868241	+	0.492404i
$5$	0.161645	−	0.0285023i	0.0722897	−	0.0127466i	−0.137386	−	0.990518i	$-0.543870\pi$
$5$	0.161645	−	0.0285023i	0.0722897	−	0.0127466i	0.209676	+	0.977771i	$0.432759\pi$
$6$	−0.642788	+	0.766044i	−0.262417	+	0.312736i
$7$	−1.97551	+	1.75993i	−0.746672	+	0.665192i
$7$	−1.97551	+	1.75993i	−0.746672	+	0.665192i
$8$	−0.866025	+	0.500000i	−0.306186	+	0.176777i
$9$	−0.939693	+	0.342020i	−0.313231	+	0.114007i
$10$	0.125737	+	0.105506i	0.0397616	+	0.0333639i
$11$	−4.25899			−1.28414			−0.642068	−	0.766648i	$-0.721923\pi$
$11$	−4.25899			−1.28414			−0.642068	+	0.766648i	$0.721923\pi$
$12$	−1.00000			−0.288675
$13$	−4.34950	−	3.64966i	−1.20633	−	1.01223i	−0.999426	−	0.0338732i	$-0.989216\pi$
$13$	−4.34950	−	3.64966i	−1.20633	−	1.01223i	−0.206907	−	0.978361i	$-0.566340\pi$
$14$	−2.61802	−	0.382065i	−0.699695	−	0.102111i
$15$	0.0561386	+	0.154239i	0.0144949	+	0.0398245i
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	0.0223450	−	0.0613923i	0.00541945	−	0.0148898i	−0.936953	−	0.349454i	$-0.886367\pi$
$17$	0.0223450	−	0.0613923i	0.00541945	−	0.0148898i	0.942373	+	0.334565i	$0.108589\pi$
$18$	−0.866025	−	0.500000i	−0.204124	−	0.117851i
$19$	3.07743	+	3.08698i	0.706010	+	0.708202i
$19$	3.07743	+	3.08698i	0.706010	+	0.708202i
$20$			0.164138i			0.0367024i
$21$	−2.07624	−	1.63989i	−0.453073	−	0.357853i
$22$	−2.73763	−	3.26258i	−0.583664	−	0.695584i
$23$	−1.01569	−	0.852269i	−0.211787	−	0.177710i	0.530723	−	0.847545i	$-0.321920\pi$
$23$	−1.01569	−	0.852269i	−0.211787	−	0.177710i	−0.742510	+	0.669835i	$0.766365\pi$
$24$	−0.642788	−	0.766044i	−0.131208	−	0.156368i
$25$	−4.67315	+	1.70089i	−0.934629	+	0.340177i
$26$		−	5.67786i		−	1.11352i
$27$	−0.500000	−	0.866025i	−0.0962250	−	0.166667i
$28$	−1.39015	−	2.25111i	−0.262714	−	0.425419i
$29$	4.11411	+	0.725429i	0.763972	+	0.134709i	0.542039	−	0.840353i	$-0.317652\pi$
$29$	4.11411	+	0.725429i	0.763972	+	0.134709i	0.221932	+	0.975062i	$0.428764\pi$
$30$	−0.0820691	+	0.142148i	−0.0149837	+	0.0259525i
$31$	3.07678	+	5.32914i	0.552607	+	0.957143i	0.998085	+	0.0618501i	$0.0197001\pi$
$31$	3.07678	+	5.32914i	0.552607	+	0.957143i	−0.445479	+	0.895292i	$0.646967\pi$
$32$	−0.342020	−	0.939693i	−0.0604612	−	0.166116i
$33$	−0.739567	−	4.19429i	−0.128742	−	0.730132i
$34$	0.0613923	−	0.0223450i	0.0105287	−	0.00383213i
$35$	−0.269168	+	0.340790i	−0.0454977	+	0.0576041i
$36$	−0.173648	−	0.984808i	−0.0289414	−	0.164135i
$37$	0.0954391	−	0.0551018i	0.0156901	−	0.00905868i	−0.492134	−	0.870519i	$-0.663783\pi$
$37$	0.0954391	−	0.0551018i	0.0156901	−	0.00905868i	0.507825	+	0.861461i	$0.330450\pi$
$38$	−0.386631	+	4.34172i	−0.0627198	+	0.704320i
$39$	2.83893	−	4.91717i	0.454593	−	0.787378i
$40$	−0.125737	+	0.105506i	−0.0198808	+	0.0166820i
$41$	−5.11725	+	4.29388i	−0.799180	+	0.670592i	−0.947999	−	0.318272i	$-0.896897\pi$
$41$	−5.11725	+	4.29388i	−0.799180	+	0.670592i	0.148819	+	0.988864i	$0.452453\pi$
$42$	−0.0783542	−	2.64459i	−0.0120903	−	0.408069i
$43$	3.43339	+	1.24965i	0.523587	+	0.190570i	0.590272	−	0.807204i	$-0.299020\pi$
$43$	3.43339	+	1.24965i	0.523587	+	0.190570i	−0.0666858	+	0.997774i	$0.521243\pi$
$44$	0.739567	−	4.19429i	0.111494	−	0.632313i
$45$	−0.142148	+	0.0820691i	−0.0211902	+	0.0122341i
$46$		−	1.32590i		−	0.195493i
$47$	1.89313	+	5.20134i	0.276142	+	0.758693i	0.997791	+	0.0664339i	$0.0211622\pi$
$47$	1.89313	+	5.20134i	0.276142	+	0.758693i	−0.721649	+	0.692259i	$0.756616\pi$
$48$	0.173648	−	0.984808i	0.0250640	−	0.142145i
$49$	0.805271	−	6.95353i	0.115039	−	0.993361i
$50$	−4.30680	−	2.48653i	−0.609073	−	0.351648i
$51$	0.0643398	+	0.0113448i	0.00900937	+	0.00158859i
$52$	4.34950	−	3.64966i	0.603167	−	0.506117i
$53$	1.71412	+	0.302245i	0.235452	+	0.0415165i	0.290129	−	0.956988i	$-0.406302\pi$
$53$	1.71412	+	0.302245i	0.235452	+	0.0415165i	−0.0546770	+	0.998504i	$0.517413\pi$
$54$	0.342020	−	0.939693i	0.0465430	−	0.127876i
$55$	−0.688443	+	0.121391i	−0.0928297	+	0.0163684i
$56$	0.830874	−	2.51190i	0.111030	−	0.335667i
$57$	−2.50569	+	3.56672i	−0.331887	+	0.472424i
$58$	2.08879	+	3.61789i	0.274272	+	0.475052i
$59$	−2.07941	−	0.756843i	−0.270716	−	0.0985325i	0.203095	−	0.979159i	$-0.434900\pi$
$59$	−2.07941	−	0.756843i	−0.270716	−	0.0985325i	−0.473811	+	0.880626i	$0.657122\pi$
$60$	−0.161645	+	0.0285023i	−0.0208682	+	0.00367963i
$61$	−7.42587	+	8.84981i	−0.950786	+	1.13310i	0.0402076	+	0.999191i	$0.487198\pi$
$61$	−7.42587	+	8.84981i	−0.950786	+	1.13310i	−0.990993	+	0.133911i	$0.957246\pi$
$62$	−2.10464	+	5.78246i	−0.267290	+	0.734373i
$63$	1.25444	−	2.32946i	0.158044	−	0.293484i
$64$	0.500000	−	0.866025i	0.0625000	−	0.108253i
$65$	−0.807096	−	0.465977i	−0.100108	−	0.0577974i
$66$	2.73763	−	3.26258i	0.336979	−	0.401596i
$67$	−5.50111	+	6.55597i	−0.672068	+	0.800939i	−0.989064	−	0.147488i	$-0.952881\pi$
$67$	−5.50111	+	6.55597i	−0.672068	+	0.800939i	0.316996	+	0.948427i	$0.397326\pi$
$68$	0.0565794	+	0.0326662i	0.00686126	+	0.00396135i
$69$	0.662948	−	1.14826i	0.0798095	−	0.138234i
$70$	−0.434078	+	0.0128609i	−0.0518823	+	0.00153717i
$71$	3.15235	−	8.66100i	0.374115	−	1.02787i	−0.599640	−	0.800270i	$-0.704689\pi$
$71$	3.15235	−	8.66100i	0.374115	−	1.02787i	0.973754	−	0.227602i	$-0.0730884\pi$
$72$	0.642788	−	0.766044i	0.0757532	−	0.0902792i
$73$	−13.8307	+	2.43872i	−1.61876	+	0.285431i	−0.908304	−	0.418310i	$-0.862623\pi$
$73$	−13.8307	+	2.43872i	−1.61876	+	0.285431i	−0.710456	+	0.703741i	$0.751511\pi$
$74$	0.103558	+	0.0376919i	0.0120383	+	0.00438159i
$75$	−2.48653	−	4.30680i	−0.287120	−	0.497306i
$76$	−3.57447	+	2.49463i	−0.410020	+	0.286153i
$77$	8.41368	−	7.49554i	0.958828	−	0.854197i
$78$	5.59160	−	0.985951i	0.633125	−	0.111637i
$79$	0.821432	−	2.25687i	0.0924183	−	0.253917i	−0.884867	−	0.465843i	$-0.845751\pi$
$79$	0.821432	−	2.25687i	0.0924183	−	0.253917i	0.977286	+	0.211926i	$0.0679734\pi$
$80$	−0.161645	−	0.0285023i	−0.0180724	−	0.00318665i
$81$	0.766044	−	0.642788i	0.0851160	−	0.0714208i
$82$	−6.57861	−	1.15999i	−0.726486	−	0.128099i
$83$	12.9977	+	7.50424i	1.42669	+	0.823697i	0.996858	−	0.0792140i	$-0.0252410\pi$
$83$	12.9977	+	7.50424i	1.42669	+	0.823697i	0.429827	+	0.902911i	$0.358574\pi$
$84$	1.97551	−	1.75993i	0.215546	−	0.192024i
$85$	0.00186212	−	0.0105606i	0.000201975	−	0.00114546i
$86$	1.24965	+	3.43339i	0.134753	+	0.370232i
$87$			4.17758i			0.447884i
$88$	3.68840	−	2.12950i	0.393184	−	0.227005i
$89$	2.71014	−	15.3699i	0.287274	−	1.62921i	−0.409775	−	0.912187i	$-0.634393\pi$
$89$	2.71014	−	15.3699i	0.287274	−	1.62921i	0.697049	−	0.717024i	$-0.254496\pi$
$90$	−0.154239	−	0.0561386i	−0.0162583	−	0.00591753i
$91$	15.0156	−	0.444885i	1.57407	−	0.0466366i
$92$	1.01569	−	0.852269i	0.105894	−	0.0888552i
$93$	−4.71390	+	3.95544i	−0.488809	+	0.410160i
$94$	−2.76757	+	4.79358i	−0.285453	+	0.494420i
$95$	0.585436	+	0.411280i	0.0600644	+	0.0421964i
$96$	0.866025	−	0.500000i	0.0883883	−	0.0510310i
$97$	0.229860	+	1.30360i	0.0233388	+	0.132361i	0.994251	−	0.107075i	$-0.0341486\pi$
$97$	0.229860	+	1.30360i	0.0233388	+	0.132361i	−0.970912	+	0.239436i	$0.923037\pi$
$98$	5.84433	−	3.85277i	0.590366	−	0.389188i
$99$	4.00215	−	1.45666i	0.402231	−	0.146400i
$100$	−0.863563	−	4.89751i	−0.0863563	−	0.489751i
$101$	4.88000	+	13.4077i	0.485578	+	1.33412i	0.904647	+	0.426161i	$0.140134\pi$
$101$	4.88000	+	13.4077i	0.485578	+	1.33412i	−0.419069	+	0.907954i	$0.637644\pi$
$102$	0.0326662	+	0.0565794i	0.00323443	+	0.00560220i
$103$	−3.11500	+	5.39533i	−0.306930	+	0.531618i	−0.977689	−	0.210057i	$-0.932635\pi$
$103$	−3.11500	+	5.39533i	−0.306930	+	0.531618i	0.670759	+	0.741675i	$0.265968\pi$
$104$	5.59160	+	0.985951i	0.548302	+	0.0966804i
$105$	−0.382353	−	0.205901i	−0.0373139	−	0.0200939i
$106$	0.870280	+	1.50737i	0.0845290	+	0.146409i
$107$		−	11.4318i		−	1.10516i	−0.833461	−	0.552578i	$-0.813644\pi$
$107$		−	11.4318i		−	1.10516i	0.833461	−	0.552578i	$-0.186356\pi$
$108$	0.939693	−	0.342020i	0.0904220	−	0.0329109i
$109$	6.90721	+	8.23170i	0.661591	+	0.788454i	0.987613	−	0.156909i	$-0.0501528\pi$
$109$	6.90721	+	8.23170i	0.661591	+	0.788454i	−0.326022	+	0.945362i	$0.605708\pi$
$110$	−0.535514	−	0.449350i	−0.0510592	−	0.0428438i
$111$	0.0708375	+	0.0844209i	0.00672360	+	0.00801287i
$112$	2.45830	−	0.978132i	0.232288	−	0.0924248i
$113$		−	9.10485i		−	0.856512i	−0.903658	−	0.428256i	$-0.859128\pi$
$113$		−	9.10485i		−	0.856512i	0.903658	−	0.428256i	$-0.140872\pi$
$114$	−4.34290	+	0.373174i	−0.406749	+	0.0349510i
$115$	−0.188473	−	0.108815i	−0.0175752	−	0.0101471i
$116$	−1.42882	+	3.92564i	−0.132662	+	0.364487i
$117$	5.33545	+	1.94194i	0.493262	+	0.179533i
$118$	−0.756843	−	2.07941i	−0.0696730	−	0.191425i
$119$	0.0639036	+	0.160607i	0.00585804	+	0.0147228i
$120$	−0.125737	−	0.105506i	−0.0114782	−	0.00963134i
$121$	7.13903			0.649003
$122$	−11.5526			−1.04592
$123$	−5.11725	−	4.29388i	−0.461407	−	0.387166i
$124$	−5.78246	+	2.10464i	−0.519280	+	0.189003i
$125$	−1.41765	+	0.818480i	−0.126798	+	0.0732071i
$126$	2.59081	−	0.536392i	0.230807	−	0.0477856i
$127$	−9.83437	+	11.7201i	−0.872659	+	1.03999i	0.126189	+	0.992006i	$0.459725\pi$
$127$	−9.83437	+	11.7201i	−0.872659	+	1.03999i	−0.998848	+	0.0479881i	$0.984719\pi$
$128$	0.984808	−	0.173648i	0.0870455	−	0.0153485i
$129$	−0.634464	+	3.59823i	−0.0558615	+	0.316806i
$130$	−0.161832	−	0.917796i	−0.0141936	−	0.0804960i
$131$	1.46394	+	1.74466i	0.127905	+	0.152431i	0.826196	−	0.563383i	$-0.190500\pi$
$131$	1.46394	+	1.74466i	0.127905	+	0.152431i	−0.698291	+	0.715814i	$0.746056\pi$
$132$	4.25899			0.370698
$133$	−11.5124	−	0.682289i	−0.998248	−	0.0591620i
$134$	−8.55821			−0.739317
$135$	−0.105506	−	0.125737i	−0.00908051	−	0.0108217i
$136$	0.0113448	+	0.0643398i	0.000972812	+	0.00551709i
$137$	−1.08123	+	6.13195i	−0.0923756	+	0.523888i	0.903144	+	0.429337i	$0.141253\pi$
$137$	−1.08123	+	6.13195i	−0.0923756	+	0.523888i	−0.995520	+	0.0945510i	$0.969858\pi$
$138$	1.30575	−	0.230239i	0.111153	−	0.0195993i
$139$	−11.7440	+	13.9960i	−0.996115	+	1.18712i	−0.0137968	+	0.999905i	$0.504392\pi$
$139$	−11.7440	+	13.9960i	−0.996115	+	1.18712i	−0.982318	+	0.187219i	$0.940053\pi$
$140$	−0.288872	−	0.324257i	−0.0244142	−	0.0274047i
$141$	−4.79358	+	2.76757i	−0.403692	+	0.233072i
$142$	8.66100	−	3.15235i	0.726815	−	0.264539i
$143$	18.5245	+	15.5439i	1.54909	+	1.29984i
$144$	1.00000			0.0833333
$145$	0.685701			0.0569443
$146$	−10.7584	−	9.02735i	−0.890369	−	0.747108i
$147$	6.98772	−	0.414430i	0.576338	−	0.0341816i
$148$	0.0376919	+	0.103558i	0.00309825	+	0.00851238i
$149$	−0.763915	−	0.278042i	−0.0625823	−	0.0227781i	0.310539	−	0.950561i	$-0.399490\pi$
$149$	−0.763915	−	0.278042i	−0.0625823	−	0.0227781i	−0.373122	+	0.927782i	$0.621713\pi$
$150$	1.70089	−	4.67315i	0.138877	−	0.381561i
$151$	2.54990	+	1.47219i	0.207508	+	0.119805i	0.600153	−	0.799885i	$-0.295106\pi$
$151$	2.54990	+	1.47219i	0.207508	+	0.119805i	−0.392645	+	0.919690i	$0.628440\pi$
$152$	−4.20862	−	1.13469i	−0.341364	−	0.0920354i
$153$			0.0653323i			0.00528180i
$154$	11.1501	+	1.62721i	0.898503	+	0.131124i
$155$	0.649238	+	0.773732i	0.0521481	+	0.0621476i
$156$	4.34950	+	3.64966i	0.348238	+	0.292207i
$157$	0.427376	+	0.509327i	0.0341083	+	0.0406487i	0.782829	−	0.622237i	$-0.213776\pi$
$157$	0.427376	+	0.509327i	0.0341083	+	0.0406487i	−0.748721	+	0.662886i	$0.769332\pi$
$158$	2.25687	−	0.821432i	0.179547	−	0.0653496i
$159$			1.74056i			0.138035i
$160$	−0.0820691	−	0.142148i	−0.00648813	−	0.0112378i
$161$	3.50645	−	0.103890i	0.276347	−	0.00818764i
$162$	0.984808	+	0.173648i	0.0773738	+	0.0136431i
$163$	9.62001	−	16.6624i	0.753498	−	1.30510i	−0.192620	−	0.981273i	$-0.561699\pi$
$163$	9.62001	−	16.6624i	0.753498	−	1.30510i	0.946118	−	0.323823i	$-0.104968\pi$
$164$	−3.34005	−	5.78513i	−0.260814	−	0.451743i
$165$	−0.239094	−	0.656905i	−0.0186134	−	0.0511400i
$166$	2.60619	+	14.7805i	0.202280	+	1.14719i
$167$	13.9373	−	5.07276i	1.07850	−	0.392542i	0.259151	−	0.965837i	$-0.416557\pi$
$167$	13.9373	−	5.07276i	1.07850	−	0.392542i	0.819349	+	0.573295i	$0.194335\pi$
$168$	2.61802	+	0.382065i	0.201985	+	0.0294769i
$169$	3.34067	+	18.9459i	0.256975	+	1.45737i
$170$	0.00928685	−	0.00536176i	0.000712269	−	0.000411229i
$171$	−3.94764	−	1.84827i	−0.301884	−	0.141341i
$172$	−1.82687	+	3.16423i	−0.139297	+	0.241270i
$173$	−1.54009	+	1.29229i	−0.117091	+	0.0982509i	−0.699453	−	0.714679i	$-0.746573\pi$
$173$	−1.54009	+	1.29229i	−0.117091	+	0.0982509i	0.582362	+	0.812929i	$0.302129\pi$
$174$	−3.20021	+	2.68530i	−0.242607	+	0.203572i
$175$	6.23840	−	11.5845i	0.471578	−	0.875709i
$176$	4.00215	+	1.45666i	0.301673	+	0.109800i
$177$	0.384259	−	2.17924i	0.0288827	−	0.163802i
$178$	13.5161	−	7.80352i	1.01307	−	0.584899i
$179$			10.6566i			0.796513i	0.917274	+	0.398257i	$0.130385\pi$
$179$			10.6566i			0.796513i	−0.917274	+	0.398257i	$0.869615\pi$
$180$	−0.0561386	−	0.154239i	−0.00418432	−	0.0114963i
$181$	−3.20443	+	18.1732i	−0.238183	+	1.35081i	0.597621	+	0.801778i	$0.296113\pi$
$181$	−3.20443	+	18.1732i	−0.238183	+	1.35081i	−0.835805	+	0.549027i	$0.814999\pi$
$182$	9.99266	+	11.2167i	0.740705	+	0.831435i
$183$	−10.0049	−	5.77630i	−0.739580	−	0.426997i
$184$	1.30575	+	0.230239i	0.0962613	+	0.0169735i
$185$	0.0138567	−	0.0116271i	0.00101876	−	0.000854845i
$186$	−6.06008	−	1.06856i	−0.444347	−	0.0783503i
$187$	−0.0951671	+	0.261469i	−0.00695931	+	0.0191205i
$188$	−5.45105	+	0.961168i	−0.397559	+	0.0701004i
$189$	2.51190	+	0.830874i	0.182714	+	0.0604372i
$190$	0.0612521	+	0.712835i	0.00444370	+	0.0517145i
$191$	−0.535178	−	0.926955i	−0.0387241	−	0.0670721i	0.846014	−	0.533161i	$-0.178996\pi$
$191$	−0.535178	−	0.926955i	−0.0387241	−	0.0670721i	−0.884738	+	0.466089i	$0.845663\pi$
$192$	0.939693	+	0.342020i	0.0678165	+	0.0246832i
$193$	13.3756	−	2.35848i	0.962798	−	0.169767i	0.329912	−	0.944012i	$-0.392981\pi$
$193$	13.3756	−	2.35848i	0.962798	−	0.169767i	0.632887	+	0.774244i	$0.281870\pi$
$194$	−0.850865	+	1.01402i	−0.0610886	+	0.0728025i
$195$	0.318747	−	0.875751i	0.0228260	−	0.0627138i
$196$	6.70805	+	2.00050i	0.479147	+	0.142893i
$197$	12.7512	−	22.0857i	0.908486	−	1.57354i	0.0923184	−	0.995730i	$-0.470572\pi$
$197$	12.7512	−	22.0857i	0.908486	−	1.57354i	0.816168	−	0.577815i	$-0.196094\pi$
$198$	3.68840	+	2.12950i	0.262123	+	0.151337i
$199$	−8.79522	+	10.4817i	−0.623477	+	0.743030i	−0.981664	−	0.190619i	$-0.938950\pi$
$199$	−8.79522	+	10.4817i	−0.623477	+	0.743030i	0.358187	+	0.933650i	$0.383395\pi$
$200$	3.19662	−	3.80958i	0.226035	−	0.269378i
$201$	−7.41163	−	4.27910i	−0.522776	−	0.301825i
$202$	−7.13408	+	12.3566i	−0.501952	+	0.869407i
$203$	−9.40417	+	5.80747i	−0.660044	+	0.407605i
$204$	−0.0223450	+	0.0613923i	−0.00156446	+	0.00429832i
$205$	−0.704790	+	0.839937i	−0.0492247	+	0.0586637i
$206$	−6.13535	+	1.08183i	−0.427470	+	0.0753745i
$207$	1.24593	+	0.453483i	0.0865984	+	0.0315192i
$208$	2.83893	+	4.91717i	0.196845	+	0.340945i
$209$	−13.1067	−	13.1474i	−0.906613	−	0.909427i
$210$	−0.0880425	−	0.425251i	−0.00607551	−	0.0293451i
$211$	−2.57372	+	0.453817i	−0.177182	+	0.0312421i	−0.261535	−	0.965194i	$-0.584229\pi$
$211$	−2.57372	+	0.453817i	−0.177182	+	0.0312421i	0.0843529	+	0.996436i	$0.473118\pi$
$212$	−0.595306	+	1.63559i	−0.0408858	+	0.112333i
$213$	9.07682	+	1.60049i	0.621933	+	0.109664i
$214$	8.75728	−	7.34823i	0.598635	−	0.502315i
$215$	0.590606	+	0.104140i	0.0402790	+	0.00710228i
$216$	0.866025	+	0.500000i	0.0589256	+	0.0340207i
$217$	−15.4571	−	5.11284i	−1.04930	−	0.347082i
$218$	−1.86597	+	10.5825i	−0.126380	+	0.716735i
$219$	−4.80335	−	13.1971i	−0.324580	−	0.891777i
$220$		−	0.699064i		−	0.0471309i
$221$	−0.321250	+	0.185474i	−0.0216096	+	0.0124763i
$222$	−0.0191367	+	0.108529i	−0.00128437	+	0.00728401i
$223$	4.59098	+	1.67098i	0.307435	+	0.111897i	0.491130	−	0.871086i	$-0.336584\pi$
$223$	4.59098	+	1.67098i	0.307435	+	0.111897i	−0.183696	+	0.982983i	$0.558806\pi$
$224$	2.32946	+	1.25444i	0.155644	+	0.0838157i
$225$	3.80958	−	3.19662i	0.253972	−	0.213108i
$226$	6.97472	−	5.85248i	0.463951	−	0.389301i
$227$	−9.99100	+	17.3049i	−0.663126	+	1.14857i	0.316664	+	0.948538i	$0.397437\pi$
$227$	−9.99100	+	17.3049i	−0.663126	+	1.14857i	−0.979790	+	0.200030i	$0.935896\pi$
$228$	−3.07743	−	3.08698i	−0.203808	−	0.204440i
$229$	−6.68916	+	3.86199i	−0.442032	+	0.255208i	−0.704459	−	0.709744i	$-0.748810\pi$
$229$	−6.68916	+	3.86199i	−0.442032	+	0.255208i	0.262427	+	0.964952i	$0.415477\pi$
$230$	−0.0377911	−	0.214324i	−0.00249187	−	0.0141321i
$231$	8.84269	+	6.98427i	0.581806	+	0.459531i
$232$	−3.92564	+	1.42882i	−0.257731	+	0.0938064i
$233$	−4.03630	−	22.8910i	−0.264427	−	1.49964i	−0.770662	−	0.637244i	$-0.780074\pi$
$233$	−4.03630	−	22.8910i	−0.264427	−	1.49964i	0.506235	−	0.862395i	$-0.331037\pi$
$234$	1.94194	+	5.33545i	0.126949	+	0.348789i
$235$	0.454264	+	0.786809i	0.0296329	+	0.0513258i
$236$	1.10643	−	1.91639i	0.0720225	−	0.124747i
$237$	2.36522	+	0.417052i	0.153638	+	0.0270904i
$238$	−0.0819554	+	0.152189i	−0.00531238	+	0.00986495i
$239$	5.93528	+	10.2802i	0.383921	+	0.664971i	0.991619	−	0.129198i	$-0.0412401\pi$
$239$	5.93528	+	10.2802i	0.383921	+	0.664971i	−0.607698	+	0.794168i	$0.707907\pi$
$240$		−	0.164138i		−	0.0105951i
$241$	17.4620	−	6.35565i	1.12483	−	0.409403i	0.288415	−	0.957506i	$-0.406872\pi$
$241$	17.4620	−	6.35565i	1.12483	−	0.409403i	0.836411	+	0.548102i	$0.184650\pi$
$242$	4.58888	+	5.46882i	0.294984	+	0.351549i
$243$	0.766044	+	0.642788i	0.0491418	+	0.0412348i
$244$	−7.42587	−	8.84981i	−0.475393	−	0.566551i
$245$	−0.0680238	−	1.14695i	−0.00434588	−	0.0732761i
$246$		−	6.68010i		−	0.425907i
$247$	−2.11883	−	24.6584i	−0.134818	−	1.56897i
$248$	−5.32914	−	3.07678i	−0.338401	−	0.195376i
$249$	−5.13320	+	14.1034i	−0.325303	+	0.893764i
$250$	−1.53824	−	0.559873i	−0.0972868	−	0.0354095i
$251$	2.56405	+	7.04467i	0.161841	+	0.444656i	0.993934	−	0.109982i	$-0.0350792\pi$
$251$	2.56405	+	7.04467i	0.161841	+	0.444656i	−0.832092	+	0.554637i	$0.812857\pi$
$252$	2.07624	+	1.63989i	0.130791	+	0.103303i
$253$	4.32584	+	3.62981i	0.271963	+	0.228204i
$254$	−15.2996			−0.959980
$255$	0.0107235			0.000671533
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	−6.96866	+	2.53639i	−0.434693	+	0.158215i	−0.550092	−	0.835104i	$-0.685408\pi$
$257$	−6.96866	+	2.53639i	−0.434693	+	0.158215i	0.115399	+	0.993319i	$0.463185\pi$
$258$	−3.16423	+	1.82687i	−0.196996	+	0.113736i
$259$	−0.0915654	+	0.276821i	−0.00568960	+	0.0172008i
$260$	0.599049	−	0.713919i	0.0371514	−	0.0442754i
$261$	−4.11411	+	0.725429i	−0.254657	+	0.0449029i
$262$	−0.395482	+	2.24289i	−0.0244329	+	0.138566i
$263$	−2.07587	−	11.7728i	−0.128004	−	0.725944i	−0.979478	−	0.201549i	$-0.935402\pi$
$263$	−2.07587	−	11.7728i	−0.128004	−	0.725944i	0.851475	−	0.524395i	$-0.175709\pi$
$264$	2.73763	+	3.26258i	0.168489	+	0.200798i
$265$	0.285692			0.0175499
$266$	−6.87734	−	9.25755i	−0.421677	−	0.567617i
$267$	15.6070			0.955136
$268$	−5.50111	−	6.55597i	−0.336034	−	0.400470i
$269$	0.799032	+	4.53154i	0.0487179	+	0.276293i	0.999429	−	0.0337848i	$-0.0107561\pi$
$269$	0.799032	+	4.53154i	0.0487179	+	0.276293i	−0.950711	+	0.310078i	$0.899645\pi$
$270$	0.0285023	−	0.161645i	0.00173459	−	0.00983738i
$271$	16.2702	−	2.86888i	0.988346	−	0.174272i	0.343970	−	0.938981i	$-0.388228\pi$
$271$	16.2702	−	2.86888i	0.988346	−	0.174272i	0.644376	+	0.764709i	$0.277117\pi$
$272$	−0.0419948	+	0.0500474i	−0.00254631	+	0.00303457i
$273$	3.04556	+	14.7103i	0.184326	+	0.890305i
$274$	−5.39235	+	3.11327i	−0.325764	+	0.188080i
$275$	19.9029	−	7.24406i	1.20019	−	0.436834i
$276$	1.01569	+	0.852269i	0.0611377	+	0.0513006i
$277$	−29.1191			−1.74960			−0.874800	−	0.484485i	$-0.839007\pi$
$277$	−29.1191			−1.74960			−0.874800	+	0.484485i	$0.839007\pi$
$278$	−18.2705			−1.09579
$279$	−4.71390	−	3.95544i	−0.282214	−	0.236806i
$280$	0.0627114	−	0.429717i	0.00374772	−	0.0256805i
$281$	−8.35435	−	22.9534i	−0.498379	−	1.36928i	−0.892841	−	0.450372i	$-0.851291\pi$
$281$	−8.35435	−	22.9534i	−0.498379	−	1.36928i	0.394462	−	0.918912i	$-0.370931\pi$
$282$	−5.20134	−	1.89313i	−0.309735	−	0.112734i
$283$	7.62781	−	20.9572i	0.453426	−	1.24578i	−0.476871	−	0.878973i	$-0.658229\pi$
$283$	7.62781	−	20.9572i	0.453426	−	1.24578i	0.930298	−	0.366806i	$-0.119549\pi$
$284$	7.98202	+	4.60842i	0.473646	+	0.273460i
$285$	−0.303372	+	0.647959i	−0.0179702	+	0.0383818i
$286$			24.1820i			1.42991i
$287$	2.55223	−	17.4886i	0.150653	−	1.03232i
$288$	0.642788	+	0.766044i	0.0378766	+	0.0451396i
$289$	13.0195	+	10.9246i	0.765852	+	0.642626i
$290$	0.440760	+	0.525277i	0.0258823	+	0.0308453i
$291$	−1.24388	+	0.452736i	−0.0729176	+	0.0265399i
$292$		−	14.0441i		−	0.821866i
$293$	8.12378	+	14.0708i	0.474596	+	0.822025i	0.999577	−	0.0290892i	$-0.00926070\pi$
$293$	8.12378	+	14.0708i	0.474596	+	0.822025i	−0.524980	+	0.851114i	$0.675927\pi$
$294$	4.80909	+	5.08651i	0.280472	+	0.296652i
$295$	−0.357697	−	0.0630716i	−0.0208259	−	0.00367217i
$296$	−0.0551018	+	0.0954391i	−0.00320273	+	0.00554729i
$297$	2.12950	+	3.68840i	0.123566	+	0.214023i
$298$	−0.278042	−	0.763915i	−0.0161066	−	0.0442524i
$299$	1.30727	+	7.41388i	0.0756013	+	0.428756i
$300$	4.67315	−	1.70089i	0.269804	−	0.0982007i
$301$	−8.98199	+	3.57384i	−0.517713	+	0.205992i
$302$	0.511285	+	2.89964i	0.0294212	+	0.166856i
$303$	−12.3566	+	7.13408i	−0.709868	+	0.409842i
$304$	−1.83603	−	3.95335i	−0.105303	−	0.226740i
$305$	−0.948112	+	1.64218i	−0.0542888	+	0.0940309i
$306$	−0.0500474	+	0.0419948i	−0.00286102	+	0.00240068i
$307$	5.07764	−	4.26064i	0.289796	−	0.243168i	−0.486286	−	0.873800i	$-0.661649\pi$
$307$	5.07764	−	4.26064i	0.289796	−	0.243168i	0.776082	+	0.630632i	$0.217204\pi$
$308$	5.92065	+	9.58745i	0.337360	+	0.546295i
$309$	−5.85428	−	2.13078i	−0.333038	−	0.121216i
$310$	−0.175391	+	0.994691i	−0.00996153	+	0.0564946i
$311$	17.0818	−	9.86217i	0.968619	−	0.559232i	0.0698041	−	0.997561i	$-0.477763\pi$
$311$	17.0818	−	9.86217i	0.968619	−	0.559232i	0.898815	+	0.438328i	$0.144429\pi$
$312$			5.67786i			0.321446i
$313$	−6.35346	−	17.4560i	−0.359119	−	0.986670i	−0.979336	−	0.202240i	$-0.935178\pi$
$313$	−6.35346	−	17.4560i	−0.359119	−	0.986670i	0.620217	−	0.784430i	$-0.287044\pi$
$314$	−0.115455	+	0.654779i	−0.00651551	+	0.0369513i
$315$	0.136378	−	0.412299i	0.00768404	−	0.0232304i
$316$	2.07994	+	1.20085i	0.117006	+	0.0675533i
$317$	−21.7808	−	3.84055i	−1.22333	−	0.215707i	−0.475573	−	0.879676i	$-0.657759\pi$
$317$	−21.7808	−	3.84055i	−1.22333	−	0.215707i	−0.747760	+	0.663970i	$0.768870\pi$
$318$	−1.33335	+	1.11881i	−0.0747703	+	0.0627397i
$319$	−17.5220	−	3.08960i	−0.981043	−	0.172984i
$320$	0.0561386	−	0.154239i	0.00313824	−	0.00862225i
$321$	11.2581	−	1.98511i	0.628368	−	0.110798i
$322$	2.33349	+	2.61932i	0.130040	+	0.145969i
$323$	0.258282	−	0.119952i	0.0143712	−	0.00667430i
$324$	0.500000	+	0.866025i	0.0277778	+	0.0481125i
$325$	26.5335	+	9.65740i	1.47181	+	0.535696i
$326$	18.9477	−	3.34100i	1.04942	−	0.185041i
$327$	−6.90721	+	8.23170i	−0.381970	+	0.455214i
$328$	2.28473	−	6.27724i	0.126153	−	0.346603i
$329$	−12.8939	−	6.94350i	−0.710864	−	0.382808i
$330$	0.349532	−	0.605407i	0.0192411	−	0.0333266i
$331$	−9.29590	−	5.36699i	−0.510949	−	0.294996i	0.222275	−	0.974984i	$-0.428652\pi$
$331$	−9.29590	−	5.36699i	−0.510949	−	0.294996i	−0.733224	+	0.679988i	$0.761985\pi$
$332$	−9.64726	+	11.4972i	−0.529462	+	0.630989i
$333$	−0.0708375	+	0.0844209i	−0.00388187	+	0.00462624i
$334$	12.8447	+	7.41588i	0.702829	+	0.405779i
$335$	−0.702365	+	1.21653i	−0.0383743	+	0.0664662i
$336$	1.39015	+	2.25111i	0.0758390	+	0.122808i
$337$	0.0529375	−	0.145444i	0.00288369	−	0.00792287i	−0.938242	−	0.345979i	$-0.887547\pi$
$337$	0.0529375	−	0.145444i	0.00288369	−	0.00792287i	0.941126	+	0.338056i	$0.109769\pi$
$338$	−12.3660	+	14.7373i	−0.672624	+	0.801602i
$339$	8.96652	−	1.58104i	0.486995	−	0.0858703i
$340$	0.0100768	+	0.00366766i	0.000546492	+	0.000198907i
$341$	−13.1040	−	22.6968i	−0.709621	−	1.22910i
$342$	−1.12164	−	4.21212i	−0.0606514	−	0.227765i
$343$	10.6469	+	15.1540i	0.574880	+	0.818238i
$344$	−3.59823	+	0.634464i	−0.194003	+	0.0342080i
$345$	0.0744339	−	0.204505i	0.00400739	−	0.0110102i
$346$	−1.97990	−	0.349110i	−0.106440	−	0.0187683i
$347$	19.6872	−	16.5195i	1.05687	−	0.886816i	0.0630669	−	0.998009i	$-0.479912\pi$
$347$	19.6872	−	16.5195i	1.05687	−	0.886816i	0.993799	+	0.111194i	$0.0354674\pi$
$348$	−4.11411	−	0.725429i	−0.220540	−	0.0388871i
$349$	−31.0073	−	17.9020i	−1.65978	−	0.958274i	−0.972815	−	0.231584i	$-0.925609\pi$
$349$	−31.0073	−	17.9020i	−1.65978	−	0.958274i	−0.686965	−	0.726690i	$-0.741058\pi$
$350$	12.8842	−	2.66751i	0.688691	−	0.142584i
$351$	−0.985951	+	5.59160i	−0.0526262	+	0.298458i
$352$	1.45666	+	4.00215i	0.0776403	+	0.213315i
$353$			18.9839i			1.01041i	0.862999	+	0.505206i	$0.168583\pi$
$353$			18.9839i			1.01041i	−0.862999	+	0.505206i	$0.831417\pi$
$354$	1.91639	−	1.10643i	0.101855	−	0.0588061i
$355$	0.262701	−	1.48985i	0.0139427	−	0.0790732i
$356$	14.6658	+	5.33792i	0.777287	+	0.282909i
$357$	−0.147070	+	0.0908218i	−0.00778377	+	0.00480680i
$358$	−8.16344	+	6.84994i	−0.431451	+	0.362031i
$359$	15.2228	−	12.7734i	0.803426	−	0.674155i	−0.145603	−	0.989343i	$-0.546512\pi$
$359$	15.2228	−	12.7734i	0.803426	−	0.674155i	0.949029	+	0.315189i	$0.102068\pi$
$360$	0.0820691	−	0.142148i	0.00432542	−	0.00749185i
$361$	−0.0588814	+	18.9999i	−0.00309902	+	0.999995i
$362$	−15.9813	+	9.22679i	−0.839957	+	0.484949i
$363$	1.23968	+	7.03057i	0.0650663	+	0.369009i
$364$	−2.16931	+	14.8648i	−0.113703	+	0.779125i
$365$	−2.16615	+	0.788413i	−0.113381	+	0.0412674i
$366$	−2.00609	−	11.3771i	−0.104860	−	0.594691i
$367$	4.08190	+	11.2149i	0.213073	+	0.585415i	0.999478	−	0.0322969i	$-0.0102822\pi$
$367$	4.08190	+	11.2149i	0.213073	+	0.585415i	−0.786405	+	0.617711i	$0.788060\pi$
$368$	0.662948	+	1.14826i	0.0345585	+	0.0598572i
$369$	3.34005	−	5.78513i	0.173876	−	0.301162i
$370$	0.0178138	+	0.00314106i	0.000926096	+	0.000163296i
$371$	−3.91818	+	2.41964i	−0.203422	+	0.125622i
$372$	−3.07678	−	5.32914i	−0.159524	−	0.276303i
$373$			5.34168i			0.276582i	0.990392	+	0.138291i	$0.0441609\pi$
$373$			5.34168i			0.276582i	−0.990392	+	0.138291i	$0.955839\pi$
$374$	−0.261469	+	0.0951671i	−0.0135203	+	0.00492097i
$375$	−1.05222	−	1.25398i	−0.0543363	−	0.0647555i
$376$	−4.24017	−	3.55792i	−0.218670	−	0.183486i
$377$	−15.2468	−	18.1704i	−0.785248	−	0.935822i
$378$	0.978132	+	2.45830i	0.0503097	+	0.126442i
$379$			6.63479i			0.340806i	0.985374	+	0.170403i	$0.0545070\pi$
$379$			6.63479i			0.340806i	−0.985374	+	0.170403i	$0.945493\pi$
$380$	−0.506691	+	0.505123i	−0.0259927	+	0.0259123i
$381$	−13.2498	−	7.64978i	−0.678808	−	0.391910i
$382$	0.366083	−	1.00580i	0.0187304	−	0.0514615i
$383$	−21.4046	−	7.79062i	−1.09372	−	0.398082i	−0.268724	−	0.963217i	$-0.586602\pi$
$383$	−21.4046	−	7.79062i	−1.09372	−	0.398082i	−0.824998	+	0.565135i	$0.808824\pi$
$384$	0.342020	+	0.939693i	0.0174536	+	0.0479535i
$385$	1.14639	−	1.45142i	0.0584252	−	0.0739714i
$386$	10.4044	+	8.73032i	0.529569	+	0.444362i
$387$	−3.65373			−0.185730
$388$	−1.32371			−0.0672013
$389$	−20.5620	−	17.2536i	−1.04253	−	0.874790i	−0.0502454	−	0.998737i	$-0.516000\pi$
$389$	−20.5620	−	17.2536i	−1.04253	−	0.874790i	−0.992289	+	0.123947i	$0.960445\pi$
$390$	0.875751	−	0.318747i	0.0443454	−	0.0161404i
$391$	−0.0750184	+	0.0433119i	−0.00379384	+	0.00219038i
$392$	2.77938	+	6.42457i	0.140380	+	0.324490i
$393$	−1.46394	+	1.74466i	−0.0738461	+	0.0880063i
$394$	25.1150	−	4.42845i	1.26527	−	0.223102i
$395$	0.0684542	−	0.388223i	0.00344430	−	0.0195336i
$396$	0.739567	+	4.19429i	0.0371646	+	0.210771i
$397$	−13.8304	−	16.4825i	−0.694129	−	0.827231i	0.297720	−	0.954653i	$-0.403774\pi$
$397$	−13.8304	−	16.4825i	−0.694129	−	0.827231i	−0.991848	+	0.127423i	$0.959330\pi$
$398$	−13.6829			−0.685863
$399$	−1.32718	−	11.4559i	−0.0664420	−	0.573514i
$400$	4.97306			0.248653
$401$	16.4230	+	19.5721i	0.820124	+	0.977386i	0.999980	−	0.00630737i	$-0.00200771\pi$
$401$	16.4230	+	19.5721i	0.820124	+	0.977386i	−0.179856	+	0.983693i	$0.557563\pi$
$402$	−1.48612	−	8.42819i	−0.0741208	−	0.420360i
$403$	6.06711	−	34.4083i	0.302224	−	1.71400i
$404$	−14.0514	+	2.47764i	−0.699083	+	0.123267i
$405$	0.105506	−	0.125737i	0.00524264	−	0.00624793i
$406$	−10.4937	−	3.47104i	−0.520792	−	0.172265i
$407$	−0.406475	+	0.234678i	−0.0201482	+	0.0116326i
$408$	−0.0613923	+	0.0223450i	−0.00303937	+	0.00110624i
$409$	8.28602	+	6.95279i	0.409717	+	0.343794i	0.824235	−	0.566248i	$-0.191605\pi$
$409$	8.28602	+	6.95279i	0.409717	+	0.343794i	−0.414518	+	0.910041i	$0.636050\pi$
$410$	−1.09646			−0.0541503
$411$	−6.22654			−0.307133
$412$	−4.77245	−	4.00456i	−0.235122	−	0.197291i
$413$	5.43988	−	2.16447i	0.267679	−	0.106507i
$414$	0.453483	+	1.24593i	0.0222875	+	0.0612343i
$415$	2.31490	+	0.842554i	0.113634	+	0.0413594i
$416$	−1.94194	+	5.33545i	−0.0952116	+	0.261592i
$417$	−15.8227	−	9.13523i	−0.774840	−	0.447354i
$418$	1.64666	−	18.4914i	0.0805408	−	0.904442i
$419$		−	20.4427i		−	0.998692i	−0.866403	−	0.499346i	$-0.833574\pi$
$419$		−	20.4427i		−	0.998692i	0.866403	−	0.499346i	$-0.166426\pi$
$420$	0.269168	−	0.340790i	0.0131341	−	0.0166289i
$421$	9.52411	+	11.3504i	0.464177	+	0.553184i	0.946456	−	0.322833i	$-0.104635\pi$
$421$	9.52411	+	11.3504i	0.464177	+	0.553184i	−0.482279	+	0.876018i	$0.660191\pi$
$422$	−2.00200	−	1.67988i	−0.0974559	−	0.0817752i
$423$	−3.55792	−	4.24017i	−0.172992	−	0.206164i
$424$	−1.63559	+	0.595306i	−0.0794313	+	0.0289106i
$425$			0.324901i			0.0157600i
$426$	4.60842	+	7.98202i	0.223279	+	0.386730i
$427$	−0.905196	−	30.5519i	−0.0438055	−	1.47851i
$428$	11.2581	+	1.98511i	0.544183	+	0.0959541i
$429$	−12.0910	+	20.9422i	−0.583759	+	1.01110i
$430$	0.299859	+	0.519371i	0.0144605	+	0.0250463i
$431$	8.13807	+	22.3592i	0.391997	+	1.07700i	0.966088	+	0.258212i	$0.0831333\pi$
$431$	8.13807	+	22.3592i	0.391997	+	1.07700i	−0.574091	+	0.818791i	$0.694644\pi$
$432$	0.173648	+	0.984808i	0.00835465	+	0.0473816i
$433$	5.33810	−	1.94291i	0.256533	−	0.0933703i	−0.210553	−	0.977583i	$-0.567526\pi$
$433$	5.33810	−	1.94291i	0.256533	−	0.0933703i	0.467085	+	0.884212i	$0.345304\pi$
$434$	−6.01900	−	15.1273i	−0.288921	−	0.726135i
$435$	0.119071	+	0.675283i	0.00570900	+	0.0323774i
$436$	−9.30606	+	5.37286i	−0.445680	+	0.257313i
$437$	−0.494790	−	5.75823i	−0.0236690	−	0.275453i
$438$	7.02203	−	12.1625i	0.335525	−	0.581147i
$439$	−5.98491	+	5.02193i	−0.285644	+	0.239684i	−0.774339	−	0.632771i	$-0.781917\pi$
$439$	−5.98491	+	5.02193i	−0.285644	+	0.239684i	0.488695	+	0.872455i	$0.337473\pi$
$440$	0.535514	−	0.449350i	0.0255296	−	0.0214219i
$441$	1.62154	+	6.80960i	0.0772161	+	0.324267i
$442$	−0.348577	−	0.126872i	−0.0165801	−	0.00603467i
$443$	−4.78823	+	27.1554i	−0.227496	+	1.29019i	0.630361	+	0.776302i	$0.282907\pi$
$443$	−4.78823	+	27.1554i	−0.227496	+	1.29019i	−0.857856	+	0.513889i	$0.828204\pi$
$444$	−0.0954391	+	0.0551018i	−0.00452934	+	0.00261502i
$445$		−	2.56171i		−	0.121437i
$446$	1.67098	+	4.59098i	0.0791233	+	0.217389i
$447$	0.141166	−	0.800591i	0.00667691	−	0.0378666i
$448$	0.536392	+	2.59081i	0.0253422	+	0.122404i
$449$	−21.4033	−	12.3572i	−1.01009	−	0.583173i	−0.0988686	−	0.995100i	$-0.531522\pi$
$449$	−21.4033	−	12.3572i	−1.01009	−	0.583173i	−0.911217	+	0.411928i	$0.864856\pi$
$450$	4.89751	+	0.863563i	0.230871	+	0.0407087i
$451$	21.7943	−	18.2876i	1.02626	−	0.861131i
$452$	8.96652	+	1.58104i	0.421750	+	0.0743659i
$453$	−1.00704	+	2.76681i	−0.0473147	+	0.129996i
$454$	−19.6784	+	3.46984i	−0.923554	+	0.162848i
$455$	2.41451	−	0.499893i	0.113194	−	0.0234354i
$456$	0.386631	−	4.34172i	0.0181057	−	0.203320i
$457$	−10.9994	−	19.0515i	−0.514529	−	0.891191i	−0.999858	−	0.0168589i	$-0.994633\pi$
$457$	−10.9994	−	19.0515i	−0.514529	−	0.891191i	0.485329	−	0.874332i	$-0.338700\pi$
$458$	−7.25817	−	2.64176i	−0.339152	−	0.123441i
$459$	−0.0643398	+	0.0113448i	−0.00300312	+	0.000529532i
$460$	0.139890	−	0.166714i	0.00652240	−	0.00777310i
$461$	−9.19174	+	25.2541i	−0.428102	+	1.17620i	0.518861	+	0.854859i	$0.326356\pi$
$461$	−9.19174	+	25.2541i	−0.428102	+	1.17620i	−0.946963	+	0.321342i	$0.895866\pi$
$462$	0.333710	+	11.2633i	0.0155256	+	0.524016i
$463$	5.62625	−	9.74494i	0.261474	−	0.452886i	−0.705160	−	0.709048i	$-0.749125\pi$
$463$	5.62625	−	9.74494i	0.261474	−	0.452886i	0.966634	+	0.256162i	$0.0824582\pi$
$464$	−3.61789	−	2.08879i	−0.167956	−	0.0969696i
$465$	−0.649238	+	0.773732i	−0.0301077	+	0.0358810i
$466$	14.9410	−	17.8060i	0.692130	−	0.824849i
$467$	−33.2603	−	19.2028i	−1.53910	−	0.888600i	−0.998892	−	0.0470700i	$-0.985012\pi$
$467$	−33.2603	−	19.2028i	−1.53910	−	0.888600i	−0.540210	−	0.841530i	$-0.681655\pi$
$468$	−2.83893	+	4.91717i	−0.131230	+	0.227296i
$469$	−0.670572	−	22.6330i	−0.0309641	−	1.04509i
$470$	−0.310735	+	0.853738i	−0.0143331	+	0.0393800i
$471$	−0.427376	+	0.509327i	−0.0196925	+	0.0234686i
$472$	2.17924	−	0.384259i	0.100308	−	0.0176870i
$473$	−14.6228	−	5.32226i	−0.672356	−	0.244718i
$474$	1.20085	+	2.07994i	0.0551570	+	0.0955348i
$475$	−19.6319	−	9.19155i	−0.900772	−	0.421737i
$476$	−0.169263	+	0.0350437i	−0.00775818	+	0.00160623i
$477$	−1.71412	+	0.302245i	−0.0784840	+	0.0138388i
$478$	−4.05997	+	11.1547i	−0.185699	+	0.510203i
$479$	−0.962027	−	0.169631i	−0.0439561	−	0.00775065i	0.151627	−	0.988438i	$-0.451549\pi$
$479$	−0.962027	−	0.169631i	−0.0439561	−	0.00775065i	−0.195583	+	0.980687i	$0.562660\pi$
$480$	0.125737	−	0.105506i	0.00573909	−	0.00481567i
$481$	−0.616215	−	0.108655i	−0.0280970	−	0.00495426i
$482$	16.0931	+	9.29133i	0.733019	+	0.423209i
$483$	0.711200	+	3.43514i	0.0323607	+	0.156304i
$484$	−1.23968	+	7.03057i	−0.0563491	+	0.319572i
$485$	0.0743113	+	0.204169i	0.00337430	+	0.00927082i
$486$			1.00000i			0.0453609i
$487$	−8.84901	+	5.10898i	−0.400987	+	0.231510i	−0.686910	−	0.726743i	$-0.741033\pi$
$487$	−8.84901	+	5.10898i	−0.400987	+	0.231510i	0.285923	+	0.958253i	$0.407700\pi$
$488$	2.00609	−	11.3771i	0.0908114	−	0.515017i
$489$	18.0797	+	6.58048i	0.817593	+	0.297579i
$490$	0.834891	−	0.789356i	0.0377166	−	0.0356595i
$491$	−15.5735	+	13.0677i	−0.702823	+	0.589739i	−0.922575	−	0.385817i	$-0.873920\pi$
$491$	−15.5735	+	13.0677i	−0.702823	+	0.589739i	0.219752	+	0.975556i	$0.429475\pi$
$492$	5.11725	−	4.29388i	0.230704	−	0.193583i
$493$	0.136465	−	0.236365i	0.00614610	−	0.0106453i
$494$	17.5274	−	17.4732i	0.788597	−	0.786157i
$495$	0.605407	−	0.349532i	0.0272110	−	0.0157103i
$496$	−1.06856	−	6.06008i	−0.0479796	−	0.272106i
$497$	9.01529	+	22.6578i	0.404391	+	1.01634i
$498$	−14.1034	+	5.13320i	−0.631986	+	0.230024i
$499$	−6.49650	−	36.8435i	−0.290823	−	1.64934i	−0.683710	−	0.729754i	$-0.739635\pi$
$499$	−6.49650	−	36.8435i	−0.290823	−	1.64934i	0.392887	−	0.919587i	$-0.371476\pi$
$500$	−0.559873	−	1.53824i	−0.0250383	−	0.0687922i
$501$	7.41588	+	12.8447i	0.331317	+	0.573858i
$502$	−3.74839	+	6.49240i	−0.167299	+	0.289770i
$503$	33.3885	+	5.88729i	1.48872	+	0.262501i	0.858056	−	0.513556i	$-0.171672\pi$
$503$	33.3885	+	5.88729i	1.48872	+	0.262501i	0.630662	+	0.776058i	$0.282783\pi$
$504$	0.0783542	+	2.64459i	0.00349017	+	0.117799i
$505$	1.17098	+	2.02819i	0.0521077	+	0.0902532i
$506$			5.64698i			0.251039i
$507$	−18.0779	+	6.57983i	−0.802870	+	0.292221i
$508$	−9.83437	−	11.7201i	−0.436329	−	0.519997i
$509$	27.9750	+	23.4738i	1.23997	+	1.04046i	0.997526	+	0.0702932i	$0.0223935\pi$
$509$	27.9750	+	23.4738i	1.23997	+	1.04046i	0.242444	+	0.970165i	$0.422051\pi$
$510$	0.00689295	+	0.00821470i	0.000305225	+	0.000363753i
$511$	23.0307	−	29.1588i	1.01882	−	1.28991i
$512$			1.00000i			0.0441942i
$513$	1.13469	−	4.20862i	0.0500977	−	0.185815i
$514$	−6.42235	−	3.70795i	−0.283278	−	0.163551i
$515$	−0.349743	+	0.960911i	−0.0154115	+	0.0423428i
$516$	−3.43339	−	1.24965i	−0.151146	−	0.0550128i
$517$	−8.06284	−	22.1525i	−0.354603	−	0.974264i
$518$	−0.270914	+	0.107794i	−0.0119033	+	0.00473618i
$519$	−1.54009	−	1.29229i	−0.0676024	−	0.0567252i
$520$	0.931955			0.0408689
$521$	−31.4406			−1.37744			−0.688718	−	0.725029i	$-0.741826\pi$
$521$	−31.4406			−1.37744			−0.688718	+	0.725029i	$0.741826\pi$
$522$	−3.20021	−	2.68530i	−0.140069	−	0.117532i
$523$	−12.4542	+	4.53294i	−0.544582	+	0.198212i	−0.599638	−	0.800272i	$-0.704689\pi$
$523$	−12.4542	+	4.53294i	−0.544582	+	0.198212i	0.0550554	+	0.998483i	$0.482466\pi$
$524$	−1.97236	+	1.13874i	−0.0861631	+	0.0497463i
$525$	12.4918	+	4.13199i	0.545188	+	0.180335i
$526$	7.68417	−	9.15764i	0.335046	−	0.399292i
$527$	0.395919	−	0.0698112i	0.0172465	−	0.00304102i
$528$	−0.739567	+	4.19429i	−0.0321855	+	0.182533i
$529$	−3.68863	−	20.9193i	−0.160375	−	0.909534i
$530$	0.183639	+	0.218853i	0.00797679	+	0.00950637i
$531$	2.21286			0.0960299
$532$	2.67102	−	11.2190i	0.115804	−	0.486405i
$533$	37.9287			1.64287
$534$	10.0320	+	11.9557i	0.434128	+	0.517373i
$535$	−0.325833	−	1.84789i	−0.0140870	−	0.0798913i
$536$	1.48612	−	8.42819i	0.0641905	−	0.364042i
$537$	−10.4947	+	1.85050i	−0.452881	+	0.0798551i
$538$	−2.95775	+	3.52491i	−0.127518	+	0.151970i
$539$	−3.42965	+	29.6150i	−0.147725	+	1.27561i
$540$	0.142148	−	0.0820691i	0.00611707	−	0.00353169i
$541$	−6.95037	+	2.52973i	−0.298820	+	0.108761i	−0.487079	−	0.873358i	$-0.661938\pi$
$541$	−6.95037	+	2.52973i	−0.298820	+	0.108761i	0.188259	+	0.982119i	$0.439715\pi$
$542$	12.6560	+	10.6196i	0.543621	+	0.456152i
$543$	−18.4536			−0.791919
$544$	−0.0653323			−0.00280110
$545$	1.35114	+	1.13374i	0.0578763	+	0.0485640i
$546$	−9.31106	+	11.7886i	−0.398477	+	0.504506i
$547$	15.0957	+	41.4750i	0.645443	+	1.77334i	0.633909	+	0.773408i	$0.281450\pi$
$547$	15.0957	+	41.4750i	0.645443	+	1.77334i	0.0115348	+	0.999933i	$0.496328\pi$
$548$	−5.85104	−	2.12960i	−0.249944	−	0.0909722i
$549$	3.95123	−	10.8559i	0.168634	−	0.463319i
$550$	18.3426	+	10.5901i	0.782132	+	0.451564i
$551$	10.4215	+	14.9326i	0.443971	+	0.636152i
$552$			1.32590i			0.0564339i
$553$	2.34919	+	5.90413i	0.0998976	+	0.251069i
$554$	−18.7174	−	22.3066i	−0.795227	−	0.947715i
$555$	0.0138567	+	0.0116271i	0.000588184	+	0.000493545i
$556$	−11.7440	−	13.9960i	−0.498058	−	0.593562i
$557$	−36.2164	+	13.1817i	−1.53454	+	0.558526i	−0.964727	−	0.263251i	$-0.915205\pi$
$557$	−36.2164	+	13.1817i	−1.53454	+	0.558526i	−0.569810	+	0.821777i	$0.692983\pi$
$558$		−	6.15357i		−	0.260501i
$559$	−10.3727	−	17.9661i	−0.438719	−	0.759883i
$560$	0.369492	−	0.228177i	0.0156139	−	0.00964224i
$561$	−0.274023	−	0.0483176i	−0.0115692	−	0.00203997i
$562$	12.2132	−	21.1540i	0.515185	−	0.892326i
$563$	10.7945	+	18.6966i	0.454933	+	0.787967i	0.998684	−	0.0512795i	$-0.0163299\pi$
$563$	10.7945	+	18.6966i	0.454933	+	0.787967i	−0.543752	+	0.839246i	$0.682997\pi$
$564$	−1.89313	−	5.20134i	−0.0797152	−	0.219016i
$565$	−0.259509	−	1.47175i	−0.0109176	−	0.0619169i
$566$	20.9572	−	7.62781i	0.880899	−	0.320621i
$567$	−0.382065	+	2.61802i	−0.0160452	+	0.109946i
$568$	1.60049	+	9.07682i	0.0671550	+	0.380855i
$569$	0.947563	−	0.547075i	0.0397239	−	0.0229346i	−0.480007	−	0.877265i	$-0.659366\pi$
$569$	0.947563	−	0.547075i	0.0397239	−	0.0229346i	0.519730	+	0.854330i	$0.326032\pi$
$570$	−0.691369	+	0.184104i	−0.0289583	+	0.00771127i
$571$	−9.66758	+	16.7447i	−0.404575	+	0.700745i	−0.994272	−	0.106880i	$-0.965914\pi$
$571$	−9.66758	+	16.7447i	−0.404575	+	0.700745i	0.589696	+	0.807625i	$0.299247\pi$
$572$	−18.5245	+	15.5439i	−0.774547	+	0.649922i
$573$	0.819940	−	0.688011i	0.0342535	−	0.0287421i
$574$	15.0376	−	9.28635i	0.627658	−	0.387605i
$575$	6.19610	+	2.25520i	0.258395	+	0.0940482i
$576$	−0.173648	+	0.984808i	−0.00723534	+	0.0410337i
$577$	−24.0810	+	13.9032i	−1.00251	+	0.578797i	−0.908989	−	0.416821i	$-0.863144\pi$
$577$	−24.0810	+	13.9032i	−1.00251	+	0.578797i	−0.0935169	+	0.995618i	$0.529811\pi$
$578$			16.9957i			0.706929i
$579$	4.64531	+	12.7629i	0.193052	+	0.530407i
$580$	−0.119071	+	0.675283i	−0.00494414	+	0.0280396i
$581$	−38.8841	+	8.05043i	−1.61318	+	0.333988i
$582$	−1.14637	−	0.661856i	−0.0475185	−	0.0274348i
$583$	−7.30041	−	1.28726i	−0.302352	−	0.0533128i
$584$	10.7584	−	9.02735i	0.445185	−	0.373554i
$585$	0.917796	+	0.161832i	0.0379462	+	0.00669094i
$586$	−5.55699	+	15.2677i	−0.229557	+	0.630704i
$587$	3.23231	−	0.569943i	0.133412	−	0.0235241i	−0.106544	−	0.994308i	$-0.533978\pi$
$587$	3.23231	−	0.569943i	0.133412	−	0.0235241i	0.239955	+	0.970784i	$0.422867\pi$
$588$	−0.805271	+	6.95353i	−0.0332088	+	0.286759i
$589$	−6.98238	+	25.8980i	−0.287704	+	1.06711i
$590$	−0.181607	−	0.314553i	−0.00747666	−	0.0129500i
$591$	23.9644	+	8.72234i	0.985765	+	0.358789i
$592$	−0.108529	+	0.0191367i	−0.00446053	+	0.000786512i
$593$	1.96963	−	2.34731i	0.0808830	−	0.0963926i	−0.724085	−	0.689710i	$-0.757738\pi$
$593$	1.96963	−	2.34731i	0.0808830	−	0.0963926i	0.804968	+	0.593318i	$0.202182\pi$
$594$	−1.45666	+	4.00215i	−0.0597676	+	0.164210i
$595$	0.0149073	+	0.0241398i	0.000611141	+	0.000989635i
$596$	0.406471	−	0.704028i	0.0166497	−	0.0288381i
$597$	−11.8498	−	6.84147i	−0.484979	−	0.280003i
$598$	−4.83907	+	5.76698i	−0.197884	+	0.235829i
$599$	−27.3486	+	32.5928i	−1.11744	+	1.33171i	−0.179953	+	0.983675i	$0.557594\pi$
$599$	−27.3486	+	32.5928i	−1.11744	+	1.33171i	−0.937483	+	0.348032i	$0.886850\pi$
$600$	4.30680	+	2.48653i	0.175824	+	0.101512i
$601$	4.45794	−	7.72138i	0.181843	−	0.314962i	−0.760665	−	0.649145i	$-0.775127\pi$
$601$	4.45794	−	7.72138i	0.181843	−	0.314962i	0.942508	+	0.334183i	$0.108460\pi$
$602$	−8.51123	−	4.58339i	−0.346892	−	0.186805i
$603$	2.92708	−	8.04209i	0.119200	−	0.327499i
$604$	−1.89261	+	2.25552i	−0.0770091	+	0.0917759i
$605$	1.15399	−	0.203479i	0.0469162	−	0.00827259i
$606$	−13.4077	−	4.88000i	−0.544650	−	0.198236i
$607$	−5.20264	−	9.01124i	−0.211169	−	0.365755i	0.740912	−	0.671602i	$-0.234394\pi$
$607$	−5.20264	−	9.01124i	−0.211169	−	0.365755i	−0.952081	+	0.305847i	$0.901060\pi$
$608$	1.84827	−	3.94764i	0.0749572	−	0.160098i
$609$	−7.35226	−	8.25285i	−0.297929	−	0.334422i
$610$	−1.86742	+	0.329276i	−0.0756095	+	0.0133320i
$611$	10.7489	−	29.5325i	0.434856	−	1.19476i
$612$	−0.0643398	−	0.0113448i	−0.00260078	−	0.000458588i
$613$	28.6836	−	24.0684i	1.15852	−	0.972112i	0.158634	−	0.987337i	$-0.449291\pi$
$613$	28.6836	−	24.0684i	1.15852	−	0.972112i	0.999884	+	0.0152252i	$0.00484652\pi$
$614$	6.52769	+	1.15101i	0.263436	+	0.0464509i
$615$	−0.949562	−	0.548230i	−0.0382900	−	0.0221068i
$616$	−3.53869	+	10.6982i	−0.142578	+	0.431042i
$617$	5.90793	−	33.5055i	0.237844	−	1.34888i	−0.598696	−	0.800976i	$-0.704314\pi$
$617$	5.90793	−	33.5055i	0.237844	−	1.34888i	0.836540	−	0.547906i	$-0.184575\pi$
$618$	−2.13078	−	5.85428i	−0.0857127	−	0.235494i
$619$			28.4973i			1.14540i	0.819763	+	0.572702i	$0.194105\pi$
$619$			28.4973i			1.14540i	−0.819763	+	0.572702i	$0.805895\pi$
$620$	−0.874716	+	0.505018i	−0.0351295	+	0.0202820i
$621$	−0.230239	+	1.30575i	−0.00923919	+	0.0523980i
$622$	18.5348	+	6.74612i	0.743179	+	0.270495i
$623$	21.6962	+	35.1331i	0.869239	+	1.40758i
$624$	−4.34950	+	3.64966i	−0.174119	+	0.146103i
$625$	18.8421	−	15.8104i	0.753684	−	0.632416i
$626$	9.28813	−	16.0875i	0.371228	−	0.642987i
$627$	10.6717	−	15.1907i	0.426188	−	0.606656i
$628$	−0.575803	+	0.332440i	−0.0229770	+	0.0132658i
$629$	−0.00125024	−	0.00709047i	−4.98504e−5	−	0.000282716i
$630$	0.403502	−	0.160549i	0.0160759	−	0.00639642i
$631$	22.6940	−	8.25993i	0.903432	−	0.328822i	0.151805	−	0.988410i	$-0.451491\pi$
$631$	22.6940	−	8.25993i	0.903432	−	0.328822i	0.751627	+	0.659588i	$0.229269\pi$
$632$	0.417052	+	2.36522i	0.0165894	+	0.0940834i
$633$	−0.893845	−	2.45582i	−0.0355272	−	0.0976100i
$634$	−11.0584	−	19.1537i	−0.439186	−	0.760692i
$635$	−1.25562	+	2.17480i	−0.0498278	+	0.0863043i
$636$	−1.71412	−	0.302245i	−0.0679691	−	0.0119848i
$637$	−28.8805	+	27.3054i	−1.14429	+	1.08188i
$638$	−8.89614	−	15.4086i	−0.352202	−	0.610031i
$639$			9.21684i			0.364613i
$640$	0.154239	−	0.0561386i	0.00609685	−	0.00221907i
$641$	24.7248	+	29.4659i	0.976572	+	1.16383i	0.986480	+	0.163883i	$0.0524019\pi$
$641$	24.7248	+	29.4659i	0.976572	+	1.16383i	−0.00990746	+	0.999951i	$0.503154\pi$
$642$	8.75728	+	7.34823i	0.345622	+	0.290012i
$643$	−21.8575	−	26.0488i	−0.861978	−	1.02726i	−0.999325	−	0.0367419i	$-0.988302\pi$
$643$	−21.8575	−	26.0488i	−0.861978	−	1.02726i	0.137347	−	0.990523i	$-0.456142\pi$
$644$	−0.506578	+	3.47122i	−0.0199620	+	0.136785i
$645$			0.599718i			0.0236139i
$646$	0.257909	+	0.120752i	0.0101473	+	0.00475091i
$647$	13.7104	+	7.91570i	0.539011	+	0.311198i	0.744678	−	0.667424i	$-0.232603\pi$
$647$	13.7104	+	7.91570i	0.539011	+	0.311198i	−0.205667	+	0.978622i	$0.565936\pi$
$648$	−0.342020	+	0.939693i	−0.0134358	+	0.0369146i
$649$	8.85619	+	3.22339i	0.347636	+	0.126529i
$650$	9.65740	+	26.5335i	0.378794	+	1.04073i
$651$	2.35106	−	16.1102i	0.0921453	−	0.631407i
$652$	14.7387	+	12.3673i	0.577213	+	0.484339i
$653$	31.6409			1.23820			0.619102	−	0.785310i	$-0.287497\pi$
$653$	31.6409			1.23820			0.619102	+	0.785310i	$0.287497\pi$
$654$	−10.7457			−0.420191
$655$	0.286365	+	0.240289i	0.0111892	+	0.00938886i
$656$	6.27724	−	2.28473i	0.245085	−	0.0892036i
$657$	12.1625	−	7.02203i	0.474505	−	0.273955i
$658$	−2.96901	−	14.3405i	−0.115744	−	0.559051i
$659$	−11.7793	+	14.0381i	−0.458858	+	0.546845i	−0.945015	−	0.327026i	$-0.893954\pi$
$659$	−11.7793	+	14.0381i	−0.458858	+	0.546845i	0.486158	+	0.873871i	$0.338398\pi$
$660$	0.688443	−	0.121391i	0.0267976	−	0.00472514i
$661$	1.00060	−	5.67469i	0.0389189	−	0.220720i	−0.959145	−	0.282914i	$-0.908699\pi$
$661$	1.00060	−	5.67469i	0.0389189	−	0.220720i	0.998064	+	0.0621944i	$0.0198099\pi$
$662$	−1.86394	−	10.5709i	−0.0724439	−	0.410850i
$663$	−0.238441	−	0.284163i	−0.00926027	−	0.0110360i
$664$	−15.0085			−0.582442
$665$	−1.88036	+	0.217840i	−0.0729172	+	0.00844749i
$666$	−0.110204			−0.00427030
$667$	−3.56042	−	4.24315i	−0.137860	−	0.164295i
$668$	2.57551	+	14.6064i	0.0996493	+	0.565140i
$669$	−0.848379	+	4.81140i	−0.0328002	+	0.186019i
$670$	−1.38339	+	0.243929i	−0.0534450	+	0.00942379i
$671$	31.6268	−	37.6913i	1.22094	−	1.45506i
$672$	−0.830874	+	2.51190i	−0.0320517	+	0.0968987i
$673$	15.6103	−	9.01258i	0.601731	−	0.347410i	−0.167991	−	0.985788i	$-0.553728\pi$
$673$	15.6103	−	9.01258i	0.601731	−	0.347410i	0.769722	+	0.638379i	$0.220395\pi$
$674$	0.145444	−	0.0529375i	0.00560231	−	0.00203907i
$675$	3.80958	+	3.19662i	0.146631	+	0.123038i
$676$	−19.2381			−0.739929
$677$	25.6380			0.985349			0.492675	−	0.870214i	$-0.336019\pi$
$677$	25.6380			0.985349			0.492675	+	0.870214i	$0.336019\pi$
$678$	6.97472	+	5.85248i	0.267862	+	0.224763i
$679$	−2.74834	−	2.17074i	−0.105472	−	0.0833053i
$680$	0.00366766	+	0.0100768i	0.000140648	+	0.000386428i
$681$	−18.7769	−	6.83425i	−0.719534	−	0.261889i
$682$	8.96366	−	24.6275i	0.343236	−	0.943034i
$683$	−6.61340	−	3.81825i	−0.253055	−	0.146101i	0.368107	−	0.929783i	$-0.380006\pi$
$683$	−6.61340	−	3.81825i	−0.253055	−	0.146101i	−0.621162	+	0.783682i	$0.713339\pi$
$684$	2.50569	−	3.56672i	0.0958075	−	0.136377i
$685$			1.02201i			0.0390491i
$686$	−4.76491	+	17.8968i	−0.181925	+	0.683303i
$687$	−4.96488	−	5.91691i	−0.189422	−	0.225744i
$688$	−2.79892	−	2.34858i	−0.106708	−	0.0895386i
$689$	−6.35245	−	7.57056i	−0.242009	−	0.288415i
$690$	0.204505	−	0.0744339i	0.00778539	−	0.00283365i
$691$			15.9221i			0.605705i	0.953037	+	0.302853i	$0.0979390\pi$
$691$			15.9221i			0.605705i	−0.953037	+	0.302853i	$0.902061\pi$
$692$	−1.00522	−	1.74110i	−0.0382128	−	0.0661865i
$693$	−5.34265	+	9.92116i	−0.202950	+	0.376874i
$694$	25.3094	+	4.46273i	0.960732	+	0.169403i
$695$	−1.49944	+	2.59711i	−0.0568770	+	0.0985139i
$696$	−2.08879	−	3.61789i	−0.0791754	−	0.137136i
$697$	0.149267	+	0.410106i	0.00565387	+	0.0155339i
$698$	−6.21731	−	35.2601i	−0.235329	−	1.33462i
$699$	21.8423	−	7.94996i	0.826153	−	0.300695i
$700$	10.3253	+	8.15526i	0.390258	+	0.308240i
$701$	3.88837	+	22.0521i	0.146862	+	0.832895i	0.965853	+	0.259089i	$0.0834224\pi$
$701$	3.88837	+	22.0521i	0.146862	+	0.832895i	−0.818991	+	0.573806i	$0.805466\pi$
$702$	−4.91717	+	2.83893i	−0.185587	+	0.107149i
$703$	0.463805	+	0.125047i	0.0174927	+	0.00471623i
$704$	−2.12950	+	3.68840i	−0.0802584	+	0.139012i
$705$	−0.695974	+	0.583991i	−0.0262119	+	0.0219944i
$706$	−14.5425	+	12.2026i	−0.547315	+	0.459251i
$707$	−33.2371	−	17.8985i	−1.25001	−	0.673144i
$708$	2.07941	+	0.756843i	0.0781489	+	0.0284439i
$709$	−5.01763	+	28.4564i	−0.188441	+	1.06870i	0.733013	+	0.680215i	$0.238114\pi$
$709$	−5.01763	+	28.4564i	−0.188441	+	1.06870i	−0.921454	+	0.388488i	$0.872997\pi$
$710$	1.31015	−	0.756418i	0.0491692	−	0.0283879i
$711$			2.40171i			0.0900711i
$712$	5.33792	+	14.6658i	0.200047	+	0.549625i
$713$	1.41679	−	8.03503i	0.0530593	−	0.300914i
$714$	−0.164108	−	0.0542829i	−0.00614160	−	0.00203149i
$715$	3.43742	+	1.98459i	0.128552	+	0.0742196i
$716$	−10.4947	−	1.85050i	−0.392206	−	0.0691565i
$717$	−9.09337	+	7.63024i	−0.339598	+	0.284957i
$718$	19.5700	+	3.45072i	0.730346	+	0.128780i
$719$	−14.8401	+	40.7729i	−0.553443	+	1.52057i	0.275535	+	0.961291i	$0.411145\pi$
$719$	−14.8401	+	40.7729i	−0.553443	+	1.52057i	−0.828978	+	0.559281i	$0.811077\pi$
$720$	0.161645	−	0.0285023i	0.00602414	−	0.00106222i
$721$	−3.34172	−	16.1407i	−0.124452	−	0.601112i
$722$	−14.5926	+	12.1678i	−0.543081	+	0.452839i
$723$	9.29133	+	16.0931i	0.345548	+	0.598507i
$724$	−17.3407	−	6.31149i	−0.644462	−	0.234565i
$725$	−20.4597	+	3.60760i	−0.759855	+	0.133983i
$726$	−4.58888	+	5.46882i	−0.170309	+	0.202967i
$727$	−1.79653	+	4.93593i	−0.0666297	+	0.183064i	−0.968539	−	0.248862i	$-0.919943\pi$
$727$	−1.79653	+	4.93593i	−0.0666297	+	0.183064i	0.901909	+	0.431926i	$0.142166\pi$
$728$	−12.7815	+	7.89310i	−0.473713	+	0.292538i
$729$	−0.500000	+	0.866025i	−0.0185185	+	0.0320750i
$730$	−1.99633	−	1.15258i	−0.0738876	−	0.0426590i
$731$	0.153438	−	0.182860i	0.00567510	−	0.00676333i
$732$	7.42587	−	8.84981i	0.274468	−	0.327098i
$733$	41.0333	+	23.6906i	1.51560	+	0.875032i	0.999832	+	0.0183032i	$0.00582642\pi$
$733$	41.0333	+	23.6906i	1.51560	+	0.875032i	0.515767	+	0.856729i	$0.327507\pi$
$734$	−5.96734	+	10.3357i	−0.220259	+	0.381499i
$735$	1.11772	−	0.266156i	0.0412275	−	0.00981733i
$736$	−0.453483	+	1.24593i	−0.0167156	+	0.0459257i
$737$	23.4292	−	27.9218i	0.863026	−	1.02851i
$738$	6.57861	−	1.15999i	0.242162	−	0.0426997i
$739$	40.4163	+	14.7103i	1.48674	+	0.541128i	0.952588	−	0.304263i	$-0.0984103\pi$
$739$	40.4163	+	14.7103i	1.48674	+	0.541128i	0.534148	+	0.845391i	$0.320633\pi$
$740$	0.00904431	+	0.0156652i	0.000332476	+	0.000575865i
$741$	23.9158	−	6.36852i	0.878570	−	0.233954i
$742$	−4.37211	−	1.44619i	−0.160505	−	0.0530912i
$743$	9.12878	−	1.60965i	0.334902	−	0.0590523i	−0.00366831	−	0.999993i	$-0.501168\pi$
$743$	9.12878	−	1.60965i	0.334902	−	0.0590523i	0.338571	+	0.940941i	$0.390057\pi$
$744$	2.10464	−	5.78246i	0.0771600	−	0.211995i
$745$	−0.131408	−	0.0231707i	−0.00481440	−	0.000848909i
$746$	−4.09197	+	3.43357i	−0.149818	+	0.125712i
$747$	−14.7805	−	2.60619i	−0.540789	−	0.0953557i
$748$	−0.240971	−	0.139125i	−0.00881079	−	0.00508691i
$749$	20.1192	+	22.5837i	0.735141	+	0.825189i
$750$	0.284255	−	1.61209i	0.0103795	−	0.0588652i
$751$	7.33545	+	20.1540i	0.267674	+	0.735429i	0.998596	+	0.0529682i	$0.0168682\pi$
$751$	7.33545	+	20.1540i	0.267674	+	0.735429i	−0.730922	+	0.682461i	$0.760910\pi$
$752$		−	5.53515i		−	0.201846i
$753$	−6.49240	+	3.74839i	−0.236596	+	0.136599i
$754$	4.11889	−	23.3594i	0.150001	−	0.850698i
$755$	0.454139	+	0.165293i	0.0165278	+	0.00601563i
$756$	−1.25444	+	2.32946i	−0.0456235	+	0.0847216i
$757$	−13.6626	+	11.4643i	−0.496577	+	0.416678i	−0.856376	−	0.516352i	$-0.827290\pi$
$757$	−13.6626	+	11.4643i	−0.496577	+	0.416678i	0.359799	+	0.933030i	$0.382845\pi$
$758$	−5.08254	+	4.26476i	−0.184606	+	0.154903i
$759$	−2.82349	+	4.89043i	−0.102486	+	0.177511i
$760$	−0.712642	−	0.0634609i	−0.0258502	−	0.00230197i
$761$	34.3017	−	19.8041i	1.24344	−	0.717899i	0.273645	−	0.961831i	$-0.411771\pi$
$761$	34.3017	−	19.8041i	1.24344	−	0.717899i	0.969792	+	0.243932i	$0.0784375\pi$
$762$	−2.65674	−	15.0671i	−0.0962435	−	0.545824i
$763$	−28.1325	−	4.10556i	−1.01846	−	0.148631i
$764$	1.00580	−	0.366083i	0.0363887	−	0.0132444i
$765$	0.00186212	+	0.0105606i	6.73251e−5	+	0.000381820i
$766$	−7.79062	−	21.4046i	−0.281487	−	0.773378i
$767$	6.28216	+	10.8810i	0.226836	+	0.392891i
$768$	−0.500000	+	0.866025i	−0.0180422	+	0.0312500i
$769$	4.42279	+	0.779858i	0.159490	+	0.0281224i	0.252823	−	0.967513i	$-0.418641\pi$
$769$	4.42279	+	0.779858i	0.159490	+	0.0281224i	−0.0933329	+	0.995635i	$0.529752\pi$
$770$	1.84874	−	0.0547746i	0.0666239	−	0.00197394i
$771$	−3.70795	−	6.42235i	−0.133538	−	0.231295i
$772$			13.5820i			0.488826i
$773$	−29.0418	+	10.5704i	−1.04456	+	0.380189i	−0.806608	−	0.591087i	$-0.798699\pi$
$773$	−29.0418	+	10.5704i	−1.04456	+	0.380189i	−0.237954	+	0.971276i	$0.576477\pi$
$774$	−2.34858	−	2.79892i	−0.0844178	−	0.100605i
$775$	−23.4425	−	19.6706i	−0.842080	−	0.706589i
$776$	−0.850865	−	1.01402i	−0.0305443	−	0.0364013i
$777$	−0.288515	−	0.0421049i	−0.0103504	−	0.00151050i
$778$		−	26.8418i		−	0.962324i
$779$	−29.0031	−	2.58273i	−1.03914	−	0.0925360i
$780$	0.807096	+	0.465977i	0.0288987	+	0.0166847i
$781$	−13.4258	+	36.8872i	−0.480414	+	1.31993i
$782$	−0.0813998	−	0.0296271i	−0.00291085	−	0.00105946i
$783$	−1.42882	−	3.92564i	−0.0510617	−	0.140291i
$784$	−3.13495	+	6.25876i	−0.111963	+	0.223527i
$785$	0.0836001	+	0.0701488i	0.00298381	+	0.00250372i
$786$	−2.27749			−0.0812353
$787$	34.8683			1.24292			0.621460	−	0.783446i	$-0.286540\pi$
$787$	34.8683			1.24292			0.621460	+	0.783446i	$0.286540\pi$
$788$	19.5360	+	16.3926i	0.695941	+	0.583964i
$789$	11.2335	−	4.08866i	0.399924	−	0.145560i
$790$	0.341398	−	0.197106i	0.0121464	−	0.00701272i
$791$	16.0239	+	17.9867i	0.569745	+	0.639534i
$792$	−2.73763	+	3.26258i	−0.0972774	+	0.115931i
$793$	64.5976	−	11.3903i	2.29393	−	0.404482i
$794$	3.73627	−	21.1894i	0.132595	−	0.751985i
$795$	0.0496099	+	0.281352i	0.00175948	+	0.00997853i
$796$	−8.79522	−	10.4817i	−0.311738	−	0.371515i
$797$	19.4982			0.690662			0.345331	−	0.938481i	$-0.387767\pi$
$797$	19.4982			0.690662			0.345331	+	0.938481i	$0.387767\pi$
$798$	7.92267	−	8.38041i	0.280459	−	0.296663i
$799$	0.361624			0.0127933
$800$	3.19662	+	3.80958i	0.113018	+	0.134689i
$801$	2.71014	+	15.3699i	0.0957579	+	0.543070i
$802$	−4.43664	+	25.1614i	−0.156663	+	0.888482i
$803$	58.9049	−	10.3865i	2.07871	−	0.366532i
$804$	5.50111	−	6.55597i	0.194009	−	0.231211i
$805$	0.563838	−	0.116735i	0.0198727	−	0.00411437i
$806$	30.2582	−	17.4696i	1.06580	−	0.615339i
$807$	−4.32394	+	1.57379i	−0.152210	+	0.0553999i
$808$	−10.9301	−	9.17140i	−0.384518	−	0.322649i
$809$	2.32888			0.0818789			0.0409394	−	0.999162i	$-0.486965\pi$
$809$	2.32888			0.0818789			0.0409394	+	0.999162i	$0.486965\pi$
$810$	0.164138			0.00576723
$811$	−15.2462	−	12.7931i	−0.535366	−	0.449225i	0.334584	−	0.942366i	$-0.391404\pi$
$811$	−15.2462	−	12.7931i	−0.535366	−	0.449225i	−0.869950	+	0.493141i	$0.835849\pi$
$812$	−4.08623	−	10.2698i	−0.143398	−	0.360398i
$813$	5.65059	+	15.5249i	0.198175	+	0.544481i
$814$	−0.441051	−	0.160529i	−0.0154588	−	0.00562655i
$815$	1.08011	−	2.96757i	0.0378345	−	0.103950i
$816$	−0.0565794	−	0.0326662i	−0.00198068	−	0.00114354i
$817$	6.70835	+	14.4445i	0.234696	+	0.505349i
$818$			10.8166i			0.378195i
$819$	−13.9579	+	5.55370i	−0.487729	+	0.194062i
$820$	−0.704790	−	0.839937i	−0.0246124	−	0.0293319i
$821$	28.0983	+	23.5773i	0.980637	+	0.822852i	0.984185	−	0.177142i	$-0.0566850\pi$
$821$	28.0983	+	23.5773i	0.980637	+	0.822852i	−0.00354840	+	0.999994i	$0.501129\pi$
$822$	−4.00235	−	4.76981i	−0.139598	−	0.166366i
$823$	3.41804	−	1.24407i	0.119145	−	0.0433654i	−0.281759	−	0.959485i	$-0.590918\pi$
$823$	3.41804	−	1.24407i	0.119145	−	0.0433654i	0.400905	+	0.916120i	$0.368696\pi$
$824$		−	6.22999i		−	0.217032i
$825$	10.5901	+	18.3426i	0.368700	+	0.638608i
$826$	5.15477	+	2.77590i	0.179357	+	0.0965858i
$827$	−38.7376	−	6.83048i	−1.34704	−	0.237519i	−0.546831	−	0.837243i	$-0.684166\pi$
$827$	−38.7376	−	6.83048i	−1.34704	−	0.237519i	−0.800207	+	0.599724i	$0.795277\pi$
$828$	−0.662948	+	1.14826i	−0.0230390	+	0.0399048i
$829$	−4.43232	−	7.67700i	−0.153941	−	0.266633i	0.778732	−	0.627357i	$-0.215863\pi$
$829$	−4.43232	−	7.67700i	−0.153941	−	0.266633i	−0.932673	+	0.360723i	$0.882530\pi$
$830$	0.842554	+	2.31490i	0.0292455	+	0.0803513i
$831$	−5.05648	−	28.6768i	−0.175408	−	0.994785i
$832$	−5.33545	+	1.94194i	−0.184973	+	0.0673248i
$833$	−0.408899	−	0.204814i	−0.0141675	−	0.00709638i
$834$	−3.17263	−	17.9929i	−0.109859	−	0.623043i
$835$	2.10830	−	1.21723i	0.0729608	−	0.0421239i
$836$	15.2237	−	10.6246i	0.526521	−	0.367459i
$837$	3.07678	−	5.32914i	0.106349	−	0.184202i
$838$	15.6600	−	13.1403i	0.540967	−	0.453925i
$839$	26.7016	−	22.4053i	0.921842	−	0.773517i	−0.0524929	−	0.998621i	$-0.516717\pi$
$839$	26.7016	−	22.4053i	0.921842	−	0.773517i	0.974335	+	0.225104i	$0.0722722\pi$
$840$	0.434078	−	0.0128609i	0.0149771	−	0.000443744i
$841$	−10.8514	−	3.94959i	−0.374186	−	0.136193i
$842$	−2.57292	+	14.5918i	−0.0886688	+	0.502866i
$843$	21.1540	−	12.2132i	0.728581	−	0.420647i
$844$		−	2.61343i		−	0.0899579i
$845$	1.08000	+	2.96728i	0.0371532	+	0.102078i
$846$	0.961168	−	5.45105i	0.0330456	−	0.187411i
$847$	−14.1032	+	12.5642i	−0.484592	+	0.431712i
$848$	−1.50737	−	0.870280i	−0.0517633	−	0.0298855i
$849$	21.9634	+	3.87274i	0.753782	+	0.132912i
$850$	−0.248889	+	0.208843i	−0.00853682	+	0.00716324i
$851$	−0.143899	−	0.0253732i	−0.00493278	−	0.000869782i
$852$	−3.15235	+	8.66100i	−0.107998	+	0.296721i
$853$	26.4899	−	4.67088i	0.906996	−	0.159928i	0.299357	−	0.954141i	$-0.403228\pi$
$853$	26.4899	−	4.67088i	0.906996	−	0.159928i	0.607639	+	0.794213i	$0.292117\pi$
$854$	22.8223	−	20.3318i	0.780962	−	0.695741i
$855$	−0.690795	−	0.186246i	−0.0236247	−	0.00636947i
$856$	5.71591	+	9.90024i	0.195366	+	0.338383i
$857$	−28.8363	−	10.4956i	−0.985030	−	0.358522i	−0.201236	−	0.979543i	$-0.564496\pi$
$857$	−28.8363	−	10.4956i	−0.985030	−	0.358522i	−0.783794	+	0.621021i	$0.786718\pi$
$858$	−23.8146	+	4.19916i	−0.813017	+	0.143357i
$859$	14.1040	−	16.8085i	0.481224	−	0.573500i	−0.469739	−	0.882805i	$-0.655652\pi$
$859$	14.1040	−	16.8085i	0.481224	−	0.573500i	0.950963	+	0.309305i	$0.100096\pi$
$860$	−0.205115	+	0.563550i	−0.00699438	+	0.0192169i
$861$	17.6661	−	0.523414i	0.602060	−	0.0178379i
$862$	−11.8971	+	20.6063i	−0.405216	+	0.701854i
$863$	−0.702724	−	0.405718i	−0.0239210	−	0.0138108i	0.487992	−	0.872848i	$-0.337730\pi$
$863$	−0.702724	−	0.405718i	−0.0239210	−	0.0138108i	−0.511913	+	0.859037i	$0.671063\pi$
$864$	−0.642788	+	0.766044i	−0.0218681	+	0.0260614i
$865$	−0.212114	+	0.252788i	−0.00721209	+	0.00859503i
$866$	4.91962	+	2.84034i	0.167175	+	0.0965188i
$867$	−8.49787	+	14.7187i	−0.288603	+	0.499874i
$868$	7.71927	−	14.3345i	0.262009	−	0.486544i
$869$	−3.49847	+	9.61198i	−0.118678	+	0.326064i
$870$	−0.440760	+	0.525277i	−0.0149432	+	0.0178086i
$871$	47.8541	−	8.43797i	1.62148	−	0.285910i
$872$	−10.0977	−	3.67525i	−0.341950	−	0.124460i
$873$	−0.661856	−	1.14637i	−0.0224004	−	0.0387987i
$874$	4.09301	−	4.08035i	0.138448	−	0.138020i
$875$	1.36011	−	4.11188i	0.0459801	−	0.139007i
$876$	13.8307	−	2.43872i	0.467296	−	0.0823969i
$877$	−16.9067	+	46.4507i	−0.570897	+	1.56853i	0.232192	+	0.972670i	$0.425410\pi$
$877$	−16.9067	+	46.4507i	−0.570897	+	1.56853i	−0.803090	+	0.595858i	$0.796812\pi$
$878$	−7.69405	−	1.35667i	−0.259661	−	0.0457853i
$879$	−12.4464	+	10.4437i	−0.419805	+	0.352258i
$880$	0.688443	+	0.121391i	0.0232074	+	0.00409209i
$881$	3.83984	+	2.21693i	0.129367	+	0.0746903i	0.563287	−	0.826261i	$-0.309537\pi$
$881$	3.83984	+	2.21693i	0.129367	+	0.0746903i	−0.433920	+	0.900952i	$0.642870\pi$
$882$	−4.17415	+	5.61930i	−0.140551	+	0.189212i
$883$	−6.68372	+	37.9053i	−0.224925	+	1.27561i	0.637903	+	0.770116i	$0.279802\pi$
$883$	−6.68372	+	37.9053i	−0.224925	+	1.27561i	−0.862828	+	0.505497i	$0.831309\pi$
$884$	−0.126872	−	0.348577i	−0.00426716	−	0.0117239i
$885$		−	0.363215i		−	0.0122093i
$886$	−23.8801	+	13.7872i	−0.802266	+	0.463189i
$887$	−4.39192	+	24.9078i	−0.147466	+	0.836323i	0.817888	+	0.575378i	$0.195145\pi$
$887$	−4.39192	+	24.9078i	−0.147466	+	0.836323i	−0.965354	+	0.260944i	$0.915966\pi$
$888$	−0.103558	−	0.0376919i	−0.00347516	−	0.00126486i
$889$	−1.19878	−	40.4611i	−0.0402060	−	1.35702i
$890$	1.96239	−	1.64664i	0.0657793	−	0.0551954i
$891$	−3.26258	+	2.73763i	−0.109301	+	0.0917140i
$892$	−2.44281	+	4.23107i	−0.0817914	+	0.141667i
$893$	−10.2304	+	21.8508i	−0.342349	+	0.731209i
$894$	0.704028	−	0.406471i	0.0235462	−	0.0135944i
$895$	0.303738	+	1.72258i	0.0101528	+	0.0575797i
$896$	−1.63989	+	2.07624i	−0.0547848	+	0.0693623i
$897$	−7.07425	+	2.57482i	−0.236202	+	0.0859706i
$898$	−4.29162	−	24.3390i	−0.143213	−	0.812202i
$899$	8.79232	+	24.1567i	0.293240	+	0.805671i
$900$	2.48653	+	4.30680i	0.0828843	+	0.143560i
$901$	0.0568574	−	0.0984799i	0.00189419	−	0.00328084i
$902$	28.0183	+	4.94038i	0.932906	+	0.164497i
$903$	−5.07925	−	8.22494i	−0.169027	−	0.273709i
$904$	4.55242	+	7.88503i	0.151411	+	0.262252i
$905$			3.02894i			0.100685i
$906$	−2.76681	+	1.00704i	−0.0919210	+	0.0334565i
$907$	23.0281	+	27.4438i	0.764634	+	0.911255i	0.998132	−	0.0611020i	$-0.0194615\pi$
$907$	23.0281	+	27.4438i	0.764634	+	0.911255i	−0.233497	+	0.972357i	$0.575017\pi$
$908$	−15.3071	−	12.8442i	−0.507984	−	0.426249i
$909$	−9.17140	−	10.9301i	−0.304196	−	0.362527i
$910$	1.93496	+	1.52830i	0.0641433	+	0.0506627i
$911$			13.1752i			0.436514i	0.975891	+	0.218257i	$0.0700371\pi$
$911$			13.1752i			0.436514i	−0.975891	+	0.218257i	$0.929963\pi$
$912$	3.57447	−	2.49463i	0.118363	−	0.0826053i
$913$	−55.3572	−	31.9605i	−1.83206	−	1.05774i
$914$	7.52402	−	20.6721i	0.248872	−	0.683771i
$915$	−1.78187	−	0.648547i	−0.0589068	−	0.0214403i
$916$	−2.64176	−	7.25817i	−0.0872861	−	0.239817i
$917$	−5.96251	−	0.870148i	−0.196899	−	0.0287348i
$918$	−0.0500474	−	0.0419948i	−0.00165181	−	0.00138603i
$919$	−20.1975			−0.666254			−0.333127	−	0.942882i	$-0.608104\pi$
$919$	−20.1975			−0.666254			−0.333127	+	0.942882i	$0.608104\pi$
$920$	0.217630			0.00717505
$921$	5.07764	+	4.26064i	0.167314	+	0.140393i
$922$	−25.2541	+	9.19174i	−0.831700	+	0.302714i
$923$	−45.3208	+	26.1660i	−1.49175	+	0.861264i
$924$	−8.41368	+	7.49554i	−0.276790	+	0.246585i
$925$	−0.352279	+	0.419830i	−0.0115829	+	0.0138039i
$926$	11.0815	−	1.95397i	0.364162	−	0.0642116i
$927$	1.08183	−	6.13535i	0.0355319	−	0.201511i
$928$	−0.725429	−	4.11411i	−0.0238134	−	0.135052i
$929$	7.28828	+	8.68583i	0.239121	+	0.284973i	0.872237	−	0.489084i	$-0.162669\pi$
$929$	7.28828	+	8.68583i	0.239121	+	0.284973i	−0.633116	+	0.774057i	$0.718224\pi$
$930$	−1.01004			−0.0331204
$931$	23.9436	−	18.9131i	0.784718	−	0.619852i
$932$	23.2441			0.761387
$933$	12.6786	+	15.1097i	0.415078	+	0.494670i
$934$	−6.66907	−	37.8222i	−0.218219	−	1.23758i
$935$	−0.00793076	+	0.0449776i	−0.000259364	+	0.00147092i
$936$	−5.59160	+	0.985951i	−0.182767	+	0.0322268i
$937$	18.3517	−	21.8707i	0.599524	−	0.714484i	−0.377883	−	0.925853i	$-0.623348\pi$
$937$	18.3517	−	21.8707i	0.599524	−	0.714484i	0.977406	+	0.211369i	$0.0677922\pi$
$938$	16.9068	−	15.0619i	0.552027	−	0.491788i
$939$	16.0875	−	9.28813i	0.524996	−	0.303107i
$940$	−0.853738	+	0.310735i	−0.0278459	+	0.0101351i
$941$	−9.05166	−	7.59524i	−0.295076	−	0.247598i	0.483216	−	0.875501i	$-0.339469\pi$
$941$	−9.05166	−	7.59524i	−0.295076	−	0.247598i	−0.778291	+	0.627904i	$0.783913\pi$
$942$	−0.664880			−0.0216629
$943$	8.85711			0.288427
$944$	1.69515	+	1.42240i	0.0551724	+	0.0462951i
$945$	0.429717	+	0.0627114i	0.0139787	+	0.00204000i
$946$	−5.32226	−	14.6228i	−0.173041	−	0.475428i
$947$	−55.2763	−	20.1189i	−1.79624	−	0.653777i	−0.998725	−	0.0504737i	$-0.983927\pi$
$947$	−55.2763	−	20.1189i	−1.79624	−	0.653777i	−0.797512	−	0.603303i	$-0.793851\pi$
$948$	−0.821432	+	2.25687i	−0.0266789	+	0.0732996i
$949$	69.0571	+	39.8701i	2.24169	+	1.29424i
$950$	−5.57798	−	20.9471i	−0.180974	−	0.679614i
$951$		−	22.1168i		−	0.717187i
$952$	−0.135645	−	0.107138i	−0.00439630	−	0.00347235i
$953$	−3.22256	−	3.84050i	−0.104389	−	0.124406i	0.711320	−	0.702868i	$-0.248098\pi$
$953$	−3.22256	−	3.84050i	−0.104389	−	0.124406i	−0.815709	+	0.578462i	$0.803653\pi$
$954$	−1.33335	−	1.11881i	−0.0431687	−	0.0362228i
$955$	−0.112929	−	0.134583i	−0.00365429	−	0.00435502i
$956$	−11.1547	+	4.05997i	−0.360768	+	0.131309i
$957$		−	17.7923i		−	0.575143i
$958$	−0.488434	−	0.845992i	−0.0157806	−	0.0273328i
$959$	−8.65584	−	14.0166i	−0.279512	−	0.452620i
$960$	0.161645	+	0.0285023i	0.00521706	+	0.000919908i
$961$	−3.43319	+	5.94645i	−0.110748	+	0.191821i
$962$	−0.312861	−	0.541890i	−0.0100870	−	0.0174712i
$963$	3.90991	+	10.7424i	0.125995	+	0.346169i
$964$	3.22685	+	18.3004i	0.103930	+	0.589415i
$965$	2.09488	−	0.762472i	0.0674364	−	0.0245448i
$966$	−2.17432	+	2.75288i	−0.0699576	+	0.0885724i
$967$	6.95601	+	39.4495i	0.223690	+	1.26861i	0.865173	+	0.501473i	$0.167208\pi$
$967$	6.95601	+	39.4495i	0.223690	+	1.26861i	−0.641483	+	0.767137i	$0.721681\pi$
$968$	−6.18258	+	3.56952i	−0.198716	+	0.114729i
$969$	0.162980	+	0.233528i	0.00523566	+	0.00750201i
$970$	−0.108636	+	0.188163i	−0.00348809	+	0.00604154i
$971$	−6.57786	+	5.51948i	−0.211094	+	0.177129i	−0.742204	−	0.670174i	$-0.766219\pi$
$971$	−6.57786	+	5.51948i	−0.211094	+	0.177129i	0.531110	+	0.847303i	$0.321775\pi$
$972$	−0.766044	+	0.642788i	−0.0245709	+	0.0206174i
$973$	−1.43157	−	48.3179i	−0.0458939	−	1.54900i
$974$	−9.60174	−	3.49475i	−0.307660	−	0.111979i
$975$	−4.90319	+	27.8074i	−0.157028	+	0.890549i
$976$	10.0049	−	5.77630i	0.320248	−	0.184895i
$977$		−	45.4701i		−	1.45472i	−0.686258	−	0.727358i	$-0.740748\pi$
$977$		−	45.4701i		−	1.45472i	0.686258	−	0.727358i	$-0.259252\pi$
$978$	6.58048	+	18.0797i	0.210420	+	0.578125i
$979$	−11.5425	+	65.4605i	−0.368898	+	2.09213i
$980$	1.14134	+	0.132176i	0.0364588	+	0.00422220i
$981$	−9.30606	−	5.37286i	−0.297120	−	0.171542i
$982$	−20.0209	−	3.53023i	−0.638894	−	0.112654i
$983$	−18.7460	+	15.7298i	−0.597905	+	0.501702i	−0.890772	−	0.454451i	$-0.849835\pi$
$983$	−18.7460	+	15.7298i	−0.597905	+	0.501702i	0.292866	+	0.956153i	$0.405391\pi$
$984$	6.57861	+	1.15999i	0.209718	+	0.0369790i
$985$	1.43167	−	3.93348i	0.0456168	−	0.125331i
$986$	0.268784	−	0.0473940i	0.00855984	−	0.00150933i
$987$	4.59901	−	13.9037i	0.146388	−	0.442561i
$988$	24.6517	+	2.19524i	0.784275	+	0.0698399i
$989$	−2.42224	−	4.19543i	−0.0770226	−	0.133407i
$990$	0.656905	+	0.239094i	0.0208778	+	0.00759890i
$991$	47.4949	−	8.37463i	1.50872	−	0.266029i	0.642734	−	0.766089i	$-0.277800\pi$
$991$	47.4949	−	8.37463i	1.50872	−	0.266029i	0.865990	+	0.500060i	$0.166689\pi$
$992$	3.95544	−	4.71390i	0.125585	−	0.149667i
$993$	3.67124	−	10.0866i	0.116503	−	0.320090i
$994$	−11.5620	+	21.4703i	−0.366723	+	0.680996i
$995$	−1.12295	+	1.94500i	−0.0355998	+	0.0616606i
$996$	−12.9977	−	7.50424i	−0.411849	−	0.237781i
$997$	−3.94179	+	4.69765i	−0.124838	+	0.148776i	−0.824843	−	0.565362i	$-0.808737\pi$
$997$	−3.94179	+	4.69765i	−0.124838	+	0.148776i	0.700005	+	0.714138i	$0.253181\pi$
$998$	24.0479	−	28.6591i	0.761222	−	0.907189i
$999$	−0.0954391	−	0.0551018i	−0.00301956	−	0.00174334i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	798.2.cj.a.409.9	yes	72
7.5	odd	6		798.2.ca.a.523.9	yes	72
19.2	odd	18		798.2.ca.a.325.9	✓	72
133.40	even	18	inner	798.2.cj.a.439.9	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.ca.a.325.9	✓	72	19.2	odd	18
798.2.ca.a.523.9	yes	72	7.5	odd	6
798.2.cj.a.409.9	yes	72	1.1	even	1	trivial
798.2.cj.a.439.9	yes	72	133.40	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:	\( N \)	\(=\)	\( 798 = 2 \cdot 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	798.cj (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.642788 + 0.766044i) q^{2} +(0.173648 + 0.984808i) q^{3} +(-0.173648 + 0.984808i) q^{4} +(0.161645 - 0.0285023i) q^{5} +(-0.642788 + 0.766044i) q^{6} +(-1.97551 + 1.75993i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-0.939693 + 0.342020i) q^{9} +(0.125737 + 0.105506i) q^{10} -4.25899 q^{11} -1.00000 q^{12} +(-4.34950 - 3.64966i) q^{13} +(-2.61802 - 0.382065i) q^{14} +(0.0561386 + 0.154239i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(0.0223450 - 0.0613923i) q^{17} +(-0.866025 - 0.500000i) q^{18} +(3.07743 + 3.08698i) q^{19} +0.164138i q^{20} +(-2.07624 - 1.63989i) q^{21} +(-2.73763 - 3.26258i) q^{22} +(-1.01569 - 0.852269i) q^{23} +(-0.642788 - 0.766044i) q^{24} +(-4.67315 + 1.70089i) q^{25} -5.67786i q^{26} +(-0.500000 - 0.866025i) q^{27} +(-1.39015 - 2.25111i) q^{28} +(4.11411 + 0.725429i) q^{29} +(-0.0820691 + 0.142148i) q^{30} +(3.07678 + 5.32914i) q^{31} +(-0.342020 - 0.939693i) q^{32} +(-0.739567 - 4.19429i) q^{33} +(0.0613923 - 0.0223450i) q^{34} +(-0.269168 + 0.340790i) q^{35} +(-0.173648 - 0.984808i) q^{36} +(0.0954391 - 0.0551018i) q^{37} +(-0.386631 + 4.34172i) q^{38} +(2.83893 - 4.91717i) q^{39} +(-0.125737 + 0.105506i) q^{40} +(-5.11725 + 4.29388i) q^{41} +(-0.0783542 - 2.64459i) q^{42} +(3.43339 + 1.24965i) q^{43} +(0.739567 - 4.19429i) q^{44} +(-0.142148 + 0.0820691i) q^{45} -1.32590i q^{46} +(1.89313 + 5.20134i) q^{47} +(0.173648 - 0.984808i) q^{48} +(0.805271 - 6.95353i) q^{49} +(-4.30680 - 2.48653i) q^{50} +(0.0643398 + 0.0113448i) q^{51} +(4.34950 - 3.64966i) q^{52} +(1.71412 + 0.302245i) q^{53} +(0.342020 - 0.939693i) q^{54} +(-0.688443 + 0.121391i) q^{55} +(0.830874 - 2.51190i) q^{56} +(-2.50569 + 3.56672i) q^{57} +(2.08879 + 3.61789i) q^{58} +(-2.07941 - 0.756843i) q^{59} +(-0.161645 + 0.0285023i) q^{60} +(-7.42587 + 8.84981i) q^{61} +(-2.10464 + 5.78246i) q^{62} +(1.25444 - 2.32946i) q^{63} +(0.500000 - 0.866025i) q^{64} +(-0.807096 - 0.465977i) q^{65} +(2.73763 - 3.26258i) q^{66} +(-5.50111 + 6.55597i) q^{67} +(0.0565794 + 0.0326662i) q^{68} +(0.662948 - 1.14826i) q^{69} +(-0.434078 + 0.0128609i) q^{70} +(3.15235 - 8.66100i) q^{71} +(0.642788 - 0.766044i) q^{72} +(-13.8307 + 2.43872i) q^{73} +(0.103558 + 0.0376919i) q^{74} +(-2.48653 - 4.30680i) q^{75} +(-3.57447 + 2.49463i) q^{76} +(8.41368 - 7.49554i) q^{77} +(5.59160 - 0.985951i) q^{78} +(0.821432 - 2.25687i) q^{79} +(-0.161645 - 0.0285023i) q^{80} +(0.766044 - 0.642788i) q^{81} +(-6.57861 - 1.15999i) q^{82} +(12.9977 + 7.50424i) q^{83} +(1.97551 - 1.75993i) q^{84} +(0.00186212 - 0.0105606i) q^{85} +(1.24965 + 3.43339i) q^{86} +4.17758i q^{87} +(3.68840 - 2.12950i) q^{88} +(2.71014 - 15.3699i) q^{89} +(-0.154239 - 0.0561386i) q^{90} +(15.0156 - 0.444885i) q^{91} +(1.01569 - 0.852269i) q^{92} +(-4.71390 + 3.95544i) q^{93} +(-2.76757 + 4.79358i) q^{94} +(0.585436 + 0.411280i) q^{95} +(0.866025 - 0.500000i) q^{96} +(0.229860 + 1.30360i) q^{97} +(5.84433 - 3.85277i) q^{98} +(4.00215 - 1.45666i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 12 q^{7} + 12 q^{10} - 12 q^{11} - 72 q^{12} - 30 q^{13} - 18 q^{14} + 36 q^{19} - 6 q^{21} + 12 q^{22} - 6 q^{23} - 30 q^{25} - 36 q^{27} - 12 q^{28} - 6 q^{31} - 12 q^{33} - 6 q^{34} - 6 q^{35}+ \cdots + 6 q^{99}+O(q^{100}) \) 72 * q + 12 * q^7 + 12 * q^10 - 12 * q^11 - 72 * q^12 - 30 * q^13 - 18 * q^14 + 36 * q^19 - 6 * q^21 + 12 * q^22 - 6 * q^23 - 30 * q^25 - 36 * q^27 - 12 * q^28 - 6 * q^31 - 12 * q^33 - 6 * q^34 - 6 * q^35 - 18 * q^37 - 12 * q^38 - 12 * q^40 - 6 * q^42 + 6 * q^43 + 12 * q^44 - 18 * q^45 - 18 * q^47 - 24 * q^49 - 18 * q^51 + 30 * q^52 - 48 * q^53 + 30 * q^55 - 18 * q^56 + 6 * q^57 - 48 * q^59 + 6 * q^61 + 12 * q^62 + 12 * q^63 + 36 * q^64 - 72 * q^65 - 12 * q^66 + 84 * q^67 - 6 * q^69 + 54 * q^70 + 6 * q^71 + 60 * q^73 - 18 * q^74 + 6 * q^75 + 18 * q^76 + 48 * q^77 - 12 * q^78 + 60 * q^79 + 6 * q^82 - 18 * q^83 - 12 * q^84 + 84 * q^85 - 12 * q^86 + 24 * q^89 - 6 * q^90 + 24 * q^91 + 6 * q^92 - 42 * q^93 + 18 * q^94 + 60 * q^95 - 30 * q^97 - 24 * q^98 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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