LMFDB - Embedded newform 228.2.w.a.67.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [228,2,Mod(67,228)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(228, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 0, 17])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("228.67"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 228 = 2^{2} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	228.w (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [60,-3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$1.82058916609$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$10$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			67.10
Character	$\chi$	$=$	228.67
Dual form			228.2.w.a.211.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.36774 - 0.359580i) q^{2} +(-0.766044 + 0.642788i) q^{3} +(1.74140 - 0.983622i) q^{4} +(0.0388803 + 0.0141513i) q^{5} +(-0.816613 + 1.15462i) q^{6} +(1.39317 + 0.804345i) q^{7} +(2.02809 - 1.97151i) q^{8} +(0.173648 - 0.984808i) q^{9} +(0.0582665 + 0.00537462i) q^{10} +(3.14005 - 1.81291i) q^{11} +(-0.701733 + 1.87285i) q^{12} +(-2.36434 + 2.81771i) q^{13} +(2.19471 + 0.599176i) q^{14} +(-0.0388803 + 0.0141513i) q^{15} +(2.06498 - 3.42577i) q^{16} +(0.383315 + 2.17389i) q^{17} +(-0.116612 - 1.40940i) q^{18} +(-3.73568 + 2.24605i) q^{19} +(0.0816258 - 0.0136004i) q^{20} +(-1.58425 + 0.279346i) q^{21} +(3.64288 - 3.60868i) q^{22} +(-1.81312 - 4.98152i) q^{23} +(-0.286346 + 2.81390i) q^{24} +(-3.82891 - 3.21284i) q^{25} +(-2.22060 + 4.70406i) q^{26} +(0.500000 + 0.866025i) q^{27} +(3.21724 + 0.0303413i) q^{28} +(-6.31157 - 1.11290i) q^{29} +(-0.0480895 + 0.0333358i) q^{30} +(-1.55745 + 2.69759i) q^{31} +(1.59251 - 5.42807i) q^{32} +(-1.24010 + 3.40716i) q^{33} +(1.30596 + 2.83547i) q^{34} +(0.0427842 + 0.0509882i) q^{35} +(-0.666286 - 1.88575i) q^{36} +4.68757i q^{37} +(-4.30179 + 4.41527i) q^{38} -3.67826i q^{39} +(0.106752 - 0.0479528i) q^{40} +(1.14719 + 1.36717i) q^{41} +(-2.06639 + 0.951736i) q^{42} +(-1.47721 + 4.05860i) q^{43} +(3.68488 - 6.24563i) q^{44} +(0.0206878 - 0.0358323i) q^{45} +(-4.27113 - 6.16144i) q^{46} +(1.75144 + 0.308825i) q^{47} +(0.620175 + 3.95163i) q^{48} +(-2.20606 - 3.82101i) q^{49} +(-6.39221 - 3.01751i) q^{50} +(-1.69098 - 1.41890i) q^{51} +(-1.34571 + 7.23239i) q^{52} +(0.641725 + 1.76312i) q^{53} +(0.995274 + 1.00470i) q^{54} +(0.147741 - 0.0260508i) q^{55} +(4.41124 - 1.11536i) q^{56} +(1.41796 - 4.12182i) q^{57} +(-9.03275 + 0.747362i) q^{58} +(-2.50182 - 14.1885i) q^{59} +(-0.0537868 + 0.0628866i) q^{60} +(-2.28515 + 0.831725i) q^{61} +(-1.16019 + 4.24962i) q^{62} +(1.03405 - 1.23233i) q^{63} +(0.226303 - 7.99680i) q^{64} +(-0.131801 + 0.0760951i) q^{65} +(-0.470989 + 5.10601i) q^{66} +(-2.50601 + 14.2123i) q^{67} +(2.80579 + 3.40858i) q^{68} +(4.59099 + 2.65061i) q^{69} +(0.0768519 + 0.0543541i) q^{70} +(13.1840 + 4.79860i) q^{71} +(-1.58938 - 2.33963i) q^{72} +(6.09245 - 5.11217i) q^{73} +(1.68556 + 6.41136i) q^{74} +4.99829 q^{75} +(-4.29606 + 7.58577i) q^{76} +5.83282 q^{77} +(-1.32263 - 5.03089i) q^{78} +(-2.73538 + 2.29526i) q^{79} +(0.128766 - 0.103973i) q^{80} +(-0.939693 - 0.342020i) q^{81} +(2.06067 + 1.45742i) q^{82} +(-0.224975 - 0.129889i) q^{83} +(-2.48405 + 2.04476i) q^{84} +(-0.0158599 + 0.0899457i) q^{85} +(-0.561041 + 6.08227i) q^{86} +(5.55031 - 3.20447i) q^{87} +(2.79414 - 9.86739i) q^{88} +(4.77657 - 5.69250i) q^{89} +(0.0154108 - 0.0564480i) q^{90} +(-5.56033 + 2.02379i) q^{91} +(-8.05731 - 6.89141i) q^{92} +(-0.540898 - 3.06759i) q^{93} +(2.50655 - 0.207390i) q^{94} +(-0.177029 + 0.0344624i) q^{95} +(2.26916 + 5.18178i) q^{96} +(14.1948 - 2.50292i) q^{97} +(-4.39127 - 4.43287i) q^{98} +(-1.24010 - 3.40716i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 3 q^{2} - 3 q^{4} + 3 q^{6} + 3 q^{8} - 6 q^{10} - 6 q^{13} - 9 q^{14} - 27 q^{16} - 18 q^{19} + 30 q^{20} - 6 q^{21} + 12 q^{22} + 18 q^{24} + 30 q^{27} - 18 q^{28} + 12 q^{31} - 63 q^{32} - 39 q^{34}+ \cdots + 117 q^{98}+O(q^{100}) $ 60 * q - 3 * q^2 - 3 * q^4 + 3 * q^6 + 3 * q^8 - 6 * q^10 - 6 * q^13 - 9 * q^14 - 27 * q^16 - 18 * q^19 + 30 * q^20 - 6 * q^21 + 12 * q^22 + 18 * q^24 + 30 * q^27 - 18 * q^28 + 12 * q^31 - 63 * q^32 - 39 * q^34 - 3 * q^36 - 48 * q^38 + 33 * q^40 - 12 * q^41 - 9 * q^42 + 18 * q^43 - 9 * q^44 - 69 * q^46 + 6 * q^48 + 30 * q^49 - 27 * q^50 - 3 * q^52 + 12 * q^53 + 3 * q^54 - 42 * q^56 - 36 * q^58 - 3 * q^60 + 27 * q^62 + 12 * q^63 + 21 * q^64 - 36 * q^65 + 24 * q^66 - 42 * q^67 + 93 * q^68 - 72 * q^69 + 132 * q^70 - 24 * q^71 + 18 * q^72 + 18 * q^73 + 27 * q^74 - 60 * q^75 + 66 * q^76 - 72 * q^77 - 33 * q^78 - 12 * q^79 + 6 * q^80 - 9 * q^82 + 69 * q^84 - 60 * q^85 + 123 * q^86 + 36 * q^88 - 12 * q^89 + 15 * q^90 + 84 * q^91 - 99 * q^92 - 12 * q^93 + 24 * q^95 + 12 * q^97 + 117 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/228\mathbb{Z}\right)^\times$.

$n$	$77$	$97$	$115$
$\chi(n)$	$1$	$e\left(\frac{17}{18}\right)$	$-1$

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 $

$2$	1.36774	−	0.359580i	0.967135	−	0.254262i
$2$	1.36774	−	0.359580i	0.967135	−	0.254262i
$3$	−0.766044	+	0.642788i	−0.442276	+	0.371114i
$3$	−0.766044	+	0.642788i	−0.442276	+	0.371114i
$4$	1.74140	−	0.983622i	0.870702	−	0.491811i
$5$	0.0388803	+	0.0141513i	0.0173878	+	0.00632864i	0.350699	−	0.936488i	$-0.385944\pi$
$5$	0.0388803	+	0.0141513i	0.0173878	+	0.00632864i	−0.333312	+	0.942817i	$0.608166\pi$
$6$	−0.816613	+	1.15462i	−0.333381	+	0.471371i
$7$	1.39317	+	0.804345i	0.526567	+	0.304014i	0.739617	−	0.673028i	$-0.235006\pi$
$7$	1.39317	+	0.804345i	0.526567	+	0.304014i	−0.213050	+	0.977041i	$0.568340\pi$
$8$	2.02809	−	1.97151i	0.717038	−	0.697034i
$9$	0.173648	−	0.984808i	0.0578827	−	0.328269i
$10$	0.0582665	+	0.00537462i	0.0184255	+	0.00169960i
$11$	3.14005	−	1.81291i	0.946762	−	0.546613i	0.0546883	−	0.998503i	$-0.482583\pi$
$11$	3.14005	−	1.81291i	0.946762	−	0.546613i	0.892074	+	0.451890i	$0.149250\pi$
$12$	−0.701733	+	1.87285i	−0.202573	+	0.540645i
$13$	−2.36434	+	2.81771i	−0.655750	+	0.781493i	−0.986769	−	0.162132i	$-0.948163\pi$
$13$	−2.36434	+	2.81771i	−0.655750	+	0.781493i	0.331019	+	0.943624i	$0.392608\pi$
$14$	2.19471	+	0.599176i	0.586561	+	0.160137i
$15$	−0.0388803	+	0.0141513i	−0.0100389	+	0.00365384i
$16$	2.06498	−	3.42577i	0.516244	−	0.856441i
$17$	0.383315	+	2.17389i	0.0929674	+	0.527245i	0.995351	+	0.0963113i	$0.0307044\pi$
$17$	0.383315	+	2.17389i	0.0929674	+	0.527245i	−0.902384	+	0.430933i	$0.858184\pi$
$18$	−0.116612	−	1.40940i	−0.0274858	−	0.332198i
$19$	−3.73568	+	2.24605i	−0.857023	+	0.515278i
$19$	−3.73568	+	2.24605i	−0.857023	+	0.515278i
$20$	0.0816258	−	0.0136004i	0.0182521	−	0.00304115i
$21$	−1.58425	+	0.279346i	−0.345712	+	0.0609583i
$22$	3.64288	−	3.60868i	0.776664	−	0.769374i
$23$	−1.81312	−	4.98152i	−0.378062	−	1.03872i	−0.972159	−	0.234324i	$-0.924712\pi$
$23$	−1.81312	−	4.98152i	−0.378062	−	1.03872i	0.594096	−	0.804394i	$-0.297510\pi$
$24$	−0.286346	+	2.81390i	−0.0584501	+	0.574384i
$25$	−3.82891	−	3.21284i	−0.765782	−	0.642568i
$26$	−2.22060	+	4.70406i	−0.435496	+	0.922541i
$27$	0.500000	+	0.866025i	0.0962250	+	0.166667i
$28$	3.21724	+	0.0303413i	0.608000	+	0.00573396i
$29$	−6.31157	−	1.11290i	−1.17203	−	0.206661i	−0.446457	−	0.894805i	$-0.647314\pi$
$29$	−6.31157	−	1.11290i	−1.17203	−	0.206661i	−0.725573	+	0.688145i	$0.758425\pi$
$30$	−0.0480895	+	0.0333358i	−0.00877990	+	0.00608626i
$31$	−1.55745	+	2.69759i	−0.279727	+	0.484501i	−0.971317	−	0.237789i	$-0.923577\pi$
$31$	−1.55745	+	2.69759i	−0.279727	+	0.484501i	0.691590	+	0.722291i	$0.256911\pi$
$32$	1.59251	−	5.42807i	0.281518	−	0.959556i
$33$	−1.24010	+	3.40716i	−0.215874	+	0.593110i
$34$	1.30596	+	2.83547i	0.223970	+	0.486279i
$35$	0.0427842	+	0.0509882i	0.00723185	+	0.00861859i
$36$	−0.666286	−	1.88575i	−0.111048	−	0.314292i
$37$			4.68757i			0.770632i	0.922785	+	0.385316i	$0.125907\pi$
$37$			4.68757i			0.770632i	−0.922785	+	0.385316i	$0.874093\pi$
$38$	−4.30179	+	4.41527i	−0.697842	+	0.716252i
$39$		−	3.67826i		−	0.588993i
$40$	0.106752	−	0.0479528i	0.0168790	−	0.00758201i
$41$	1.14719	+	1.36717i	0.179162	+	0.213516i	0.848150	−	0.529757i	$-0.177717\pi$
$41$	1.14719	+	1.36717i	0.179162	+	0.213516i	−0.668988	+	0.743273i	$0.733272\pi$
$42$	−2.06639	+	0.951736i	−0.318851	+	0.146856i
$43$	−1.47721	+	4.05860i	−0.225272	+	0.618930i	−0.999909	−	0.0134758i	$-0.995710\pi$
$43$	−1.47721	+	4.05860i	−0.225272	+	0.618930i	0.774637	+	0.632406i	$0.217933\pi$
$44$	3.68488	−	6.24563i	0.555517	−	0.941565i
$45$	0.0206878	−	0.0358323i	0.00308395	−	0.00534156i
$46$	−4.27113	−	6.16144i	−0.629744	−	0.908454i
$47$	1.75144	+	0.308825i	0.255473	+	0.0450468i	0.299918	−	0.953965i	$-0.403041\pi$
$47$	1.75144	+	0.308825i	0.255473	+	0.0450468i	−0.0444447	+	0.999012i	$0.514152\pi$
$48$	0.620175	+	3.95163i	0.0895146	+	0.570369i
$49$	−2.20606	−	3.82101i	−0.315151	−	0.545858i
$50$	−6.39221	−	3.01751i	−0.903995	−	0.426741i
$51$	−1.69098	−	1.41890i	−0.236785	−	0.198686i
$52$	−1.34571	+	7.23239i	−0.186617	+	1.00295i
$53$	0.641725	+	1.76312i	0.0881477	+	0.242184i	0.975932	−	0.218077i	$-0.0699783\pi$
$53$	0.641725	+	1.76312i	0.0881477	+	0.242184i	−0.887784	+	0.460260i	$0.847756\pi$
$54$	0.995274	+	1.00470i	0.135440	+	0.136723i
$55$	0.147741	−	0.0260508i	0.0199214	−	0.00351269i
$56$	4.41124	−	1.11536i	0.589477	−	0.149046i
$57$	1.41796	−	4.12182i	0.187814	−	0.545948i
$58$	−9.03275	+	0.747362i	−1.18606	+	0.0981335i
$59$	−2.50182	−	14.1885i	−0.325710	−	1.84719i	−0.504640	−	0.863330i	$-0.668375\pi$
$59$	−2.50182	−	14.1885i	−0.325710	−	1.84719i	0.178931	−	0.983862i	$-0.442736\pi$
$60$	−0.0537868	+	0.0628866i	−0.00694385	+	0.00811863i
$61$	−2.28515	+	0.831725i	−0.292583	+	0.106491i	−0.484142	−	0.874990i	$-0.660868\pi$
$61$	−2.28515	+	0.831725i	−0.292583	+	0.106491i	0.191559	+	0.981481i	$0.438646\pi$
$62$	−1.16019	+	4.24962i	−0.147344	+	0.539702i
$63$	1.03405	−	1.23233i	0.130278	−	0.155259i
$64$	0.226303	−	7.99680i	0.0282879	−	0.999600i
$65$	−0.131801	+	0.0760951i	−0.0163478	+	0.00943843i
$66$	−0.470989	+	5.10601i	−0.0579747	+	0.628506i
$67$	−2.50601	+	14.2123i	−0.306157	+	1.73630i	0.311849	+	0.950132i	$0.399052\pi$
$67$	−2.50601	+	14.2123i	−0.306157	+	1.73630i	−0.618007	+	0.786173i	$0.712060\pi$
$68$	2.80579	+	3.40858i	0.340252	+	0.413351i
$69$	4.59099	+	2.65061i	0.552690	+	0.319096i
$70$	0.0768519	+	0.0543541i	0.00918556	+	0.00649656i
$71$	13.1840	+	4.79860i	1.56466	+	0.569489i	0.971798	−	0.235817i	$-0.0757765\pi$
$71$	13.1840	+	4.79860i	1.56466	+	0.569489i	0.592860	+	0.805306i	$0.297999\pi$
$72$	−1.58938	−	2.33963i	−0.187311	−	0.275728i
$73$	6.09245	−	5.11217i	0.713067	−	0.598334i	−0.212391	−	0.977185i	$-0.568125\pi$
$73$	6.09245	−	5.11217i	0.713067	−	0.598334i	0.925458	+	0.378851i	$0.123681\pi$
$74$	1.68556	+	6.41136i	0.195942	+	0.745305i
$75$	4.99829			0.577153
$76$	−4.29606	+	7.58577i	−0.492792	+	0.870147i
$77$	5.83282			0.664712
$78$	−1.32263	−	5.03089i	−0.149758	−	0.569636i
$79$	−2.73538	+	2.29526i	−0.307755	+	0.258237i	−0.783563	−	0.621312i	$-0.786600\pi$
$79$	−2.73538	+	2.29526i	−0.307755	+	0.258237i	0.475809	+	0.879549i	$0.342156\pi$
$80$	0.128766	−	0.103973i	0.0143965	−	0.0116245i
$81$	−0.939693	−	0.342020i	−0.104410	−	0.0380022i
$82$	2.06067	+	1.45742i	0.227563	+	0.160945i
$83$	−0.224975	−	0.129889i	−0.0246942	−	0.0142572i	0.487602	−	0.873066i	$-0.337872\pi$
$83$	−0.224975	−	0.129889i	−0.0246942	−	0.0142572i	−0.512296	+	0.858809i	$0.671205\pi$
$84$	−2.48405	+	2.04476i	−0.271032	+	0.223101i
$85$	−0.0158599	+	0.0899457i	−0.00172024	+	0.00975598i
$86$	−0.561041	+	6.08227i	−0.0604986	+	0.655868i
$87$	5.55031	−	3.20447i	0.595055	−	0.343555i
$88$	2.79414	−	9.86739i	0.297857	−	1.05187i
$89$	4.77657	−	5.69250i	0.506316	−	0.603404i	−0.450973	−	0.892538i	$-0.648923\pi$
$89$	4.77657	−	5.69250i	0.506316	−	0.603404i	0.957289	+	0.289134i	$0.0933673\pi$
$90$	0.0154108	−	0.0564480i	0.00162445	−	0.00595014i
$91$	−5.56033	+	2.02379i	−0.582881	+	0.212151i
$92$	−8.05731	−	6.89141i	−0.840032	−	0.718479i
$93$	−0.540898	−	3.06759i	−0.0560885	−	0.318094i
$94$	2.50655	−	0.207390i	0.258531	−	0.0213906i
$95$	−0.177029	+	0.0344624i	−0.0181628	+	0.00353576i
$96$	2.26916	+	5.18178i	0.231596	+	0.528864i
$97$	14.1948	−	2.50292i	1.44126	−	0.254133i	0.602275	−	0.798288i	$-0.294261\pi$
$97$	14.1948	−	2.50292i	1.44126	−	0.254133i	0.838984	+	0.544155i	$0.183150\pi$
$98$	−4.39127	−	4.43287i	−0.443585	−	0.447788i
$99$	−1.24010	−	3.40716i	−0.124635	−	0.342432i
$100$	−9.82790	−	1.82865i	−0.982790	−	0.182865i
$101$	4.24947	+	3.56573i	0.422838	+	0.354803i	0.829242	−	0.558890i	$-0.188773\pi$
$101$	4.24947	+	3.56573i	0.422838	+	0.354803i	−0.406403	+	0.913694i	$0.633217\pi$
$102$	−2.82303	−	1.33264i	−0.279521	−	0.131951i
$103$	2.59682	+	4.49783i	0.255873	+	0.443185i	0.965132	−	0.261763i	$-0.0843039\pi$
$103$	2.59682	+	4.49783i	0.255873	+	0.443185i	−0.709259	+	0.704947i	$0.750971\pi$
$104$	0.760047	+	10.3759i	0.0745287	+	1.01744i
$105$	−0.0655492	−	0.0115581i	−0.00639695	−	0.00112795i
$106$	1.51169	+	2.18074i	0.146829	+	0.211812i
$107$	−0.101896	+	0.176488i	−0.00985062	+	0.0170618i	−0.870909	−	0.491445i	$-0.836469\pi$
$107$	−0.101896	+	0.176488i	−0.00985062	+	0.0170618i	0.861058	+	0.508507i	$0.169802\pi$
$108$	1.72254	+	1.01629i	0.165752	+	0.0977925i
$109$	−0.545128	+	1.49773i	−0.0522138	+	0.143456i	−0.963058	−	0.269294i	$-0.913210\pi$
$109$	−0.545128	+	1.49773i	−0.0522138	+	0.143456i	0.910844	+	0.412750i	$0.135432\pi$
$110$	0.192704	−	0.0887554i	0.0183736	−	0.00846250i
$111$	−3.01311	−	3.59089i	−0.285992	−	0.340832i
$112$	5.63235	−	3.11171i	0.532207	−	0.294029i
$113$		−	9.50065i		−	0.893746i	−0.894597	−	0.446873i	$-0.852538\pi$
$113$		−	9.50065i		−	0.893746i	0.894597	−	0.446873i	$-0.147462\pi$
$114$	0.457276	−	6.14743i	0.0428279	−	0.575760i
$115$		−	0.219341i		−	0.0204536i
$116$	−12.0857	+	4.27019i	−1.12213	+	0.396477i
$117$	2.36434	+	2.81771i	0.218583	+	0.260498i
$118$	−8.52375	−	18.5066i	−0.784675	−	1.70367i
$119$	−1.21453	+	3.33690i	−0.111336	+	0.305893i
$120$	−0.0509534	+	0.105353i	−0.00465139	+	0.00961736i
$121$	1.07329	−	1.85899i	0.0975719	−	0.169000i
$122$	−2.82640	+	1.95927i	−0.255891	+	0.177384i
$123$	−1.75760	−	0.309913i	−0.158478	−	0.0279439i
$124$	−0.0587499	+	6.22954i	−0.00527589	+	0.559429i
$125$	−0.206842	−	0.358262i	−0.0185005	−	0.0320439i
$126$	0.971181	−	2.05732i	0.0865197	−	0.183281i
$127$	−10.3297	−	8.66762i	−0.916610	−	0.769127i	0.0567553	−	0.998388i	$-0.481925\pi$
$127$	−10.3297	−	8.66762i	−0.916610	−	0.769127i	−0.973365	+	0.229261i	$0.926369\pi$
$128$	−2.56597	−	11.0189i	−0.226802	−	0.973941i
$129$	−1.47721	−	4.05860i	−0.130061	−	0.357340i
$130$	−0.152906	+	0.151471i	−0.0134107	+	0.0132849i
$131$	−11.7699	+	2.07535i	−1.02834	+	0.181324i	−0.662271	−	0.749264i	$-0.730407\pi$
$131$	−11.7699	+	2.07535i	−1.02834	+	0.181324i	−0.366068	+	0.930588i	$0.619296\pi$
$132$	1.19183	+	7.15303i	0.103736	+	0.622592i
$133$	−7.01101	+	0.124343i	−0.607932	+	0.0107819i
$134$	1.68289	+	20.3397i	0.145380	+	1.75709i
$135$	0.00718479	+	0.0407470i	0.000618368	+	0.00350694i
$136$	5.06323	+	3.65313i	0.434168	+	0.313253i
$137$	16.0906	−	5.85651i	1.37472	−	0.500356i	0.454144	−	0.890928i	$-0.349945\pi$
$137$	16.0906	−	5.85651i	1.37472	−	0.500356i	0.920572	+	0.390573i	$0.127723\pi$
$138$	7.23237	+	1.97451i	0.615660	+	0.168081i
$139$	7.86226	−	9.36988i	0.666868	−	0.794743i	−0.321486	−	0.946914i	$-0.604182\pi$
$139$	7.86226	−	9.36988i	0.666868	−	0.794743i	0.988354	+	0.152172i	$0.0486267\pi$
$140$	0.124658	+	0.0467077i	0.0105355	+	0.00394752i
$141$	−1.54019	+	0.889227i	−0.129707	+	0.0748864i
$142$	19.7578	+	1.82250i	1.65804	+	0.152941i
$143$	−2.31590	+	13.1341i	−0.193665	+	1.09833i
$144$	−3.01514	−	2.62848i	−0.251262	−	0.219040i
$145$	−0.229647	−	0.132587i	−0.0190711	−	0.0110107i
$146$	6.49463	−	9.18282i	0.537499	−	0.759976i
$147$	4.14604	+	1.50903i	0.341959	+	0.124463i
$148$	4.61079	+	8.16295i	0.379005	+	0.670991i
$149$	−4.92009	+	4.12844i	−0.403069	+	0.338215i	−0.821679	−	0.569951i	$-0.806962\pi$
$149$	−4.92009	+	4.12844i	−0.403069	+	0.338215i	0.418609	+	0.908166i	$0.362518\pi$
$150$	6.83634	−	1.79729i	0.558185	−	0.146748i
$151$	14.8919			1.21189			0.605944	−	0.795507i	$-0.292795\pi$
$151$	14.8919			1.21189			0.605944	+	0.795507i	$0.292795\pi$
$152$	−3.14819	+	11.9201i	−0.255352	+	0.966848i
$153$	2.20742			0.178459
$154$	7.97776	−	2.09737i	0.642866	−	0.169011i
$155$	−0.0987286	+	0.0828432i	−0.00793008	+	0.00665412i
$156$	−3.61802	−	6.40534i	−0.289673	−	0.512838i
$157$	19.9665	+	7.26722i	1.59350	+	0.579988i	0.978084	−	0.208213i	$-0.0667646\pi$
$157$	19.9665	+	7.26722i	1.59350	+	0.579988i	0.615419	+	0.788200i	$0.288987\pi$
$158$	−2.91595	+	4.12290i	−0.231981	+	0.328000i
$159$	−1.62490	−	0.938139i	−0.128863	−	0.0743992i
$160$	0.138731	−	0.188509i	0.0109677	−	0.0149029i
$161$	1.48087	−	8.39846i	0.116709	−	0.661891i
$162$	−1.40824	−	0.129898i	−0.110641	−	0.0102058i
$163$	18.6904	−	10.7909i	1.46395	−	0.845209i	0.464755	−	0.885439i	$-0.346142\pi$
$163$	18.6904	−	10.7909i	1.46395	−	0.845209i	0.999190	+	0.0402299i	$0.0128090\pi$
$164$	3.34251	+	1.25239i	0.261006	+	0.0977956i
$165$	−0.0964313	+	0.114922i	−0.00750716	+	0.00894669i
$166$	−0.354412	−	0.0967577i	−0.0275077	−	0.00750986i
$167$	−21.5972	+	7.86073i	−1.67124	+	0.608281i	−0.992068	−	0.125699i	$-0.959883\pi$
$167$	−21.5972	+	7.86073i	−1.67124	+	0.608281i	−0.679171	+	0.733980i	$0.737660\pi$
$168$	−2.66227	+	3.68990i	−0.205399	+	0.284682i
$169$	−0.0919647	−	0.521558i	−0.00707421	−	0.0401198i
$170$	0.0106506	+	0.128725i	0.000816863	+	0.00987275i
$171$	1.56323	+	4.06894i	0.119543	+	0.311160i
$172$	1.41971	+	8.52067i	0.108252	+	0.649695i
$173$	−17.8399	+	3.14566i	−1.35634	+	0.239160i	−0.804086	−	0.594513i	$-0.797345\pi$
$173$	−17.8399	+	3.14566i	−1.35634	+	0.239160i	−0.552258	+	0.833673i	$0.686234\pi$
$174$	6.43909	−	6.37865i	0.488146	−	0.483564i
$175$	−2.75008	−	7.55578i	−0.207886	−	0.571163i
$176$	0.273532	−	14.5007i	0.0206183	−	1.09303i
$177$	11.0367	+	9.26092i	0.829571	+	0.696093i
$178$	4.48618	−	9.50340i	0.336254	−	0.712310i
$179$	7.00117	+	12.1264i	0.523292	+	0.906368i	0.999633	+	0.0271074i	$0.00862961\pi$
$179$	7.00117	+	12.1264i	0.523292	+	0.906368i	−0.476341	+	0.879261i	$0.658037\pi$
$180$	0.000780379	−	0.0827474i	5.81660e−5	−	0.00616763i
$181$	−10.5367	−	1.85791i	−0.783187	−	0.138097i	−0.232264	−	0.972653i	$-0.574613\pi$
$181$	−10.5367	−	1.85791i	−0.783187	−	0.138097i	−0.550923	+	0.834556i	$0.685724\pi$
$182$	−6.87735	+	4.76740i	−0.509783	+	0.353383i
$183$	1.21590	−	2.10600i	0.0898820	−	0.155680i
$184$	−13.4983	−	6.52838i	−0.995107	−	0.481278i
$185$	−0.0663351	+	0.182254i	−0.00487705	+	0.0133996i
$186$	−1.84285	−	4.00115i	−0.135124	−	0.293379i
$187$	5.14469	+	6.13120i	0.376217	+	0.448358i
$188$	3.35372	−	1.18496i	0.244595	−	0.0864221i
$189$			1.60869i			0.117015i
$190$	−0.229737	+	0.110791i	−0.0166668	+	0.00803765i
$191$			4.73008i			0.342257i	0.985249	+	0.171128i	$0.0547413\pi$
$191$			4.73008i			0.342257i	−0.985249	+	0.171128i	$0.945259\pi$
$192$	4.96688	+	6.27137i	0.358454	+	0.452597i
$193$	−3.60517	−	4.29648i	−0.259506	−	0.309267i	0.620522	−	0.784189i	$-0.286921\pi$
$193$	−3.60517	−	4.29648i	−0.259506	−	0.309267i	−0.880028	+	0.474922i	$0.842476\pi$
$194$	18.5147	−	8.52749i	1.32928	−	0.612238i
$195$	0.0520521	−	0.143012i	0.00372753	−	0.0102413i
$196$	−7.60007	−	4.48399i	−0.542862	−	0.320285i
$197$	−12.0327	+	20.8413i	−0.857295	+	1.48488i	0.0172047	+	0.999852i	$0.494523\pi$
$197$	−12.0327	+	20.8413i	−0.857295	+	1.48488i	−0.874500	+	0.485026i	$0.838810\pi$
$198$	−2.92128	−	4.21418i	−0.207606	−	0.299488i
$199$	−22.9889	−	4.05356i	−1.62964	−	0.287349i	−0.717293	−	0.696771i	$-0.754619\pi$
$199$	−22.9889	−	4.05356i	−1.62964	−	0.287349i	−0.912345	+	0.409422i	$0.865730\pi$
$200$	−14.0995	+	1.03281i	−0.996986	+	0.0730305i
$201$	−7.21576	−	12.4981i	−0.508960	−	0.881545i
$202$	7.09432	+	3.34895i	0.499155	+	0.235631i
$203$	−7.89791	−	6.62714i	−0.554325	−	0.465134i
$204$	−4.34035	−	0.807596i	−0.303885	−	0.0565431i
$205$	0.0252560	+	0.0693903i	0.00176396	+	0.00484643i
$206$	5.16910	+	5.21808i	0.360148	+	0.363561i
$207$	−5.22068	+	0.920547i	−0.362862	+	0.0639824i
$208$	4.77051	+	13.9182i	0.330775	+	0.965053i
$209$	−7.65834	+	13.8252i	−0.529739	+	0.956306i
$210$	−0.0938101	+	0.00776177i	−0.00647351	+	0.000535613i
$211$	−3.53720	−	20.0605i	−0.243511	−	1.38102i	−0.823925	−	0.566699i	$-0.808220\pi$
$211$	−3.53720	−	20.0605i	−0.243511	−	1.38102i	0.580414	−	0.814322i	$-0.302891\pi$
$212$	2.85175	+	2.43910i	0.195859	+	0.167518i
$213$	−13.1840	+	4.79860i	−0.903355	+	0.328795i
$214$	−0.0759046	+	0.278029i	−0.00518873	+	0.0190057i
$215$	−0.114869	+	0.136895i	−0.00783398	+	0.00933617i
$216$	2.72142	+	0.770623i	0.185169	+	0.0524343i
$217$	−4.33958	+	2.50546i	−0.294590	+	0.170082i
$218$	−0.207038	+	2.24451i	−0.0140224	+	0.152018i
$219$	−1.38105	+	7.83230i	−0.0933224	+	0.529258i
$220$	0.231653	−	0.190686i	0.0156181	−	0.0128561i
$221$	−7.03167	−	4.05973i	−0.473001	−	0.273087i
$222$	−5.41235	−	3.82793i	−0.363253	−	0.256914i
$223$	20.9007	+	7.60724i	1.39962	+	0.509419i	0.928064	−	0.372420i	$-0.121472\pi$
$223$	20.9007	+	7.60724i	1.39962	+	0.509419i	0.471552	+	0.881838i	$0.343694\pi$
$224$	6.58466	−	6.28127i	0.439956	−	0.419685i
$225$	−3.82891	+	3.21284i	−0.255261	+	0.214189i
$226$	−3.41624	−	12.9944i	−0.227245	−	0.864373i
$227$	14.2535			0.946041			0.473021	−	0.881051i	$-0.343164\pi$
$227$	14.2535			0.946041			0.473021	+	0.881051i	$0.343164\pi$
$228$	−1.58506	−	8.57249i	−0.104973	−	0.567727i
$229$	−18.8490			−1.24557			−0.622787	−	0.782391i	$-0.714000\pi$
$229$	−18.8490			−1.24557			−0.622787	+	0.782391i	$0.714000\pi$
$230$	−0.0788706	−	0.300000i	−0.00520058	−	0.0197814i
$231$	−4.46820	+	3.74926i	−0.293986	+	0.246684i
$232$	−14.9945	+	10.1863i	−0.984440	+	0.668761i
$233$	−16.9577	−	6.17211i	−1.11094	−	0.404348i	−0.279600	−	0.960116i	$-0.590202\pi$
$233$	−16.9577	−	6.17211i	−1.11094	−	0.404348i	−0.831337	+	0.555768i	$0.812424\pi$
$234$	4.24699	+	3.00372i	0.277634	+	0.196359i
$235$	0.0637261	+	0.0367923i	0.00415703	+	0.00240006i
$236$	−18.3128	−	22.2471i	−1.19206	−	1.44817i
$237$	0.620061	−	3.51654i	0.0402773	−	0.228424i
$238$	−0.461277	+	5.00072i	−0.0299001	+	0.324149i
$239$	11.8131	−	6.82032i	0.764129	−	0.441170i	−0.0666472	−	0.997777i	$-0.521230\pi$
$239$	11.8131	−	6.82032i	0.764129	−	0.441170i	0.830776	+	0.556606i	$0.187897\pi$
$240$	−0.0318080	+	0.162417i	−0.00205320	+	0.0104840i
$241$	−17.8835	+	21.3127i	−1.15198	+	1.37287i	−0.235946	+	0.971766i	$0.575819\pi$
$241$	−17.8835	+	21.3127i	−1.15198	+	1.37287i	−0.916031	+	0.401106i	$0.868626\pi$
$242$	0.799521	−	2.92855i	0.0513952	−	0.188254i
$243$	0.939693	−	0.342020i	0.0602813	−	0.0219406i
$244$	−3.16126	+	3.69609i	−0.202379	+	0.236618i
$245$	−0.0317001	−	0.179780i	−0.00202525	−	0.0114858i
$246$	−2.51538	+	0.208120i	−0.160374	+	0.0132693i
$247$	2.50370	−	15.8365i	0.159307	−	1.00765i
$248$	2.15966	+	8.54149i	0.137139	+	0.542385i
$249$	0.255832	−	0.0451101i	0.0162127	−	0.00285873i
$250$	−0.411730	−	0.415631i	−0.0260401	−	0.0262868i
$251$	−4.65063	−	12.7775i	−0.293545	−	0.806508i	−0.995541	−	0.0943275i	$-0.969930\pi$
$251$	−4.65063	−	12.7775i	−0.293545	−	0.806508i	0.701996	−	0.712181i	$-0.252292\pi$
$252$	0.588547	−	3.16309i	0.0370750	−	0.199256i
$253$	−14.7244	−	12.3552i	−0.925712	−	0.776765i
$254$	−17.2450	−	8.14067i	−1.08205	−	0.510791i
$255$	−0.0456666	−	0.0790969i	−0.00285976	−	0.00495324i
$256$	−7.47174	−	14.1483i	−0.466984	−	0.884266i
$257$	6.11746	+	1.07867i	0.381597	+	0.0672858i	0.361156	−	0.932505i	$-0.382382\pi$
$257$	6.11746	+	1.07867i	0.381597	+	0.0672858i	0.0204405	+	0.999791i	$0.493493\pi$
$258$	−3.47982	−	5.01992i	−0.216644	−	0.312526i
$259$	−3.77042	+	6.53056i	−0.234283	+	0.405789i
$260$	−0.154669	+	0.262154i	−0.00959218	+	0.0162581i
$261$	−2.19199	+	6.02243i	−0.135681	+	0.372779i
$262$	−15.3518	+	7.07074i	−0.948439	+	0.436832i
$263$	9.88399	+	11.7793i	0.609473	+	0.726341i	0.979222	−	0.202790i	$-0.0650009\pi$
$263$	9.88399	+	11.7793i	0.609473	+	0.726341i	−0.369749	+	0.929131i	$0.620556\pi$
$264$	4.20220	+	9.35490i	0.258627	+	0.575754i
$265$			0.0776320i			0.00476890i
$266$	−9.54450	+	2.69109i	−0.585211	+	0.165001i
$267$			7.43103i			0.454772i
$268$	9.61552	+	27.2143i	0.587361	+	1.66238i
$269$	9.68888	+	11.5468i	0.590742	+	0.704018i	0.975748	−	0.218895i	$-0.0702453\pi$
$269$	9.68888	+	11.5468i	0.590742	+	0.704018i	−0.385007	+	0.922914i	$0.625801\pi$
$270$	0.0244787	+	0.0531476i	0.00148973	+	0.00323446i
$271$	6.02894	−	16.5644i	0.366232	−	1.00621i	−0.610550	−	0.791978i	$-0.709052\pi$
$271$	6.02894	−	16.5644i	0.366232	−	1.00621i	0.976782	−	0.214236i	$-0.0687262\pi$
$272$	8.23876	+	3.17588i	0.499548	+	0.192566i
$273$	2.95859	−	5.12443i	0.179062	−	0.310144i
$274$	19.9019	−	13.7960i	1.20232	−	0.833449i
$275$	−17.8476	−	3.14701i	−1.07625	−	0.189772i
$276$	10.6020	+	0.0999856i	0.638163	+	0.00601842i
$277$	14.6706	+	25.4103i	0.881473	+	1.52676i	0.849703	+	0.527262i	$0.176781\pi$
$277$	14.6706	+	25.4103i	0.881473	+	1.52676i	0.0317704	+	0.999495i	$0.489885\pi$
$278$	7.38428	−	15.6426i	0.442880	−	0.938183i
$279$	2.38616	+	2.00222i	0.142856	+	0.119870i
$280$	0.187294	+	0.0190593i	0.0111930	+	0.00113901i
$281$	−5.40648	−	14.8542i	−0.322523	−	0.886126i	−0.989946	−	0.141446i	$-0.954825\pi$
$281$	−5.40648	−	14.8542i	−0.322523	−	0.886126i	0.667423	−	0.744679i	$-0.267398\pi$
$282$	−1.78682	+	1.77005i	−0.106404	+	0.105405i
$283$	−2.55553	+	0.450608i	−0.151910	+	0.0267859i	−0.249086	−	0.968481i	$-0.580130\pi$
$283$	−2.55553	+	0.450608i	−0.151910	+	0.0267859i	0.0971758	+	0.995267i	$0.469019\pi$
$284$	27.6787	−	4.61181i	1.64243	−	0.273660i
$285$	0.113460	−	0.140192i	0.00672078	−	0.00830423i
$286$	1.55523	+	18.7967i	0.0919625	+	1.11147i
$287$	0.498553	+	2.82744i	0.0294287	+	0.166898i
$288$	−5.06907	−	2.51089i	−0.298698	−	0.147955i
$289$	11.3959	−	4.14778i	0.670349	−	0.243987i
$290$	−0.361772	−	0.0987672i	−0.0212440	−	0.00579981i
$291$	−9.26497	+	11.0416i	−0.543122	+	0.647268i
$292$	5.58097	−	14.8950i	0.326602	−	0.871665i
$293$	5.57446	−	3.21842i	0.325664	−	0.188022i	−0.328251	−	0.944591i	$-0.606459\pi$
$293$	5.57446	−	3.21842i	0.325664	−	0.188022i	0.653914	+	0.756569i	$0.273126\pi$
$294$	6.21330	+	0.573127i	0.362367	+	0.0334255i
$295$	0.103514	−	0.587059i	0.00602684	−	0.0341799i
$296$	9.24159	+	9.50682i	0.537156	+	0.552572i
$297$	3.14005	+	1.81291i	0.182204	+	0.105196i
$298$	−5.24487	+	7.41579i	−0.303827	+	0.429585i
$299$	18.3233	+	6.66914i	1.05966	+	0.385686i
$300$	8.70404	−	4.91642i	0.502528	−	0.283850i
$301$	−5.32251	+	4.46611i	−0.306784	+	0.257423i
$302$	20.3682	−	5.35484i	1.17206	−	0.308137i
$303$	−5.54729			−0.318684
$304$	−0.0196608	+	17.4356i	−0.00112763	+	0.999999i
$305$	−0.100617			−0.00576132
$306$	3.01917	−	0.793745i	0.172594	−	0.0453754i
$307$	−8.38204	+	7.03337i	−0.478388	+	0.401416i	−0.849843	−	0.527035i	$-0.823304\pi$
$307$	−8.38204	+	7.03337i	−0.478388	+	0.401416i	0.371455	+	0.928451i	$0.378859\pi$
$308$	10.1573	−	5.73729i	0.578766	−	0.326912i
$309$	−4.88043	−	1.77633i	−0.277638	−	0.101052i
$310$	−0.105246	+	0.148808i	−0.00597757	+	0.00845175i
$311$	−5.40380	−	3.11989i	−0.306422	−	0.176913i	0.338903	−	0.940821i	$-0.389944\pi$
$311$	−5.40380	−	3.11989i	−0.306422	−	0.176913i	−0.645324	+	0.763909i	$0.723278\pi$
$312$	−7.25173	−	7.45985i	−0.410548	−	0.422331i
$313$	1.05721	−	5.99574i	0.0597571	−	0.338899i	−0.940242	−	0.340508i	$-0.889401\pi$
$313$	1.05721	−	5.99574i	0.0597571	−	0.338899i	0.999999	+	0.00160877i	$0.000512087\pi$
$314$	29.9221	+	2.76007i	1.68860	+	0.155760i
$315$	0.0576430	−	0.0332802i	0.00324782	−	0.00187513i
$316$	−2.50574	+	6.68756i	−0.140959	+	0.376205i
$317$	16.9074	−	20.1494i	0.949612	−	1.13170i	−0.0415621	−	0.999136i	$-0.513233\pi$
$317$	16.9074	−	20.1494i	0.949612	−	1.13170i	0.991174	−	0.132568i	$-0.0423221\pi$
$318$	−2.55978	−	0.698843i	−0.143545	−	0.0391892i
$319$	−21.8363	+	7.94775i	−1.22260	+	0.444989i
$320$	0.121964	−	0.307716i	0.00681798	−	0.0172018i
$321$	−0.0353880	−	0.200695i	−0.00197516	−	0.0112017i
$322$	−0.994473	−	12.0194i	−0.0554198	−	0.669813i
$323$	−6.31458	−	7.25999i	−0.351353	−	0.403957i
$324$	−1.97280	+	0.328707i	−0.109600	+	0.0182615i
$325$	18.1057	−	3.19252i	1.00432	−	0.177089i
$326$	21.6833	−	21.4798i	1.20093	−	1.18966i
$327$	−0.545128	−	1.49773i	−0.0301456	−	0.0828245i
$328$	5.02201	+	0.511046i	0.277294	+	0.0282178i
$329$	2.19164	+	1.83900i	0.120829	+	0.101387i
$330$	−0.0905687	+	0.191858i	−0.00498564	+	0.0105614i
$331$	14.1871	+	24.5728i	0.779793	+	1.35064i	0.932061	+	0.362302i	$0.118009\pi$
$331$	14.1871	+	24.5728i	0.779793	+	1.35064i	−0.152267	+	0.988339i	$0.548658\pi$
$332$	−0.519534	−	0.00489964i	−0.0285131	−	0.000268903i
$333$	4.61635	+	0.813988i	0.252975	+	0.0446063i
$334$	−26.7127	+	18.5173i	−1.46165	+	1.01322i
$335$	−0.298556	+	0.517114i	−0.0163119	+	0.0282530i
$336$	−2.31447	+	6.00411i	−0.126264	+	0.327551i
$337$	5.48229	−	15.0625i	0.298639	−	0.820505i	−0.696089	−	0.717956i	$-0.745078\pi$
$337$	5.48229	−	15.0625i	0.298639	−	0.820505i	0.994728	−	0.102549i	$-0.0326998\pi$
$338$	−0.313325	−	0.680285i	−0.0170426	−	0.0370026i
$339$	6.10690	+	7.27792i	0.331681	+	0.395282i
$340$	0.0608541	+	0.172232i	0.00330028	+	0.00934059i
$341$			11.2941i			0.611610i
$342$	3.60120	+	5.00314i	0.194730	+	0.270539i
$343$		−	18.3586i		−	0.991269i
$344$	5.00565	+	11.1435i	0.269887	+	0.600819i
$345$	0.140990	+	0.168025i	0.00759063	+	0.00904616i
$346$	−23.2692	+	10.7173i	−1.25096	+	0.576166i
$347$	8.78378	−	24.1332i	0.471538	−	1.29554i	−0.444978	−	0.895542i	$-0.646788\pi$
$347$	8.78378	−	24.1332i	0.471538	−	1.29554i	0.916516	−	0.399998i	$-0.130989\pi$
$348$	6.51334	−	11.0397i	0.349152	−	0.591789i
$349$	5.00682	−	8.67206i	0.268009	−	0.464205i	−0.700339	−	0.713811i	$-0.746968\pi$
$349$	5.00682	−	8.67206i	0.268009	−	0.464205i	0.968348	+	0.249606i	$0.0803011\pi$
$350$	−6.47829	−	9.34544i	−0.346279	−	0.499535i
$351$	−3.62238	−	0.638723i	−0.193348	−	0.0340925i
$352$	−4.84005	−	19.9315i	−0.257975	−	1.06235i
$353$	10.8762	+	18.8382i	0.578883	+	1.00265i	0.995608	+	0.0936216i	$0.0298444\pi$
$353$	10.8762	+	18.8382i	0.578883	+	1.00265i	−0.416725	+	0.909032i	$0.636822\pi$
$354$	18.4254	+	8.69790i	0.979298	+	0.462288i
$355$	0.444693	+	0.373142i	0.0236019	+	0.0198043i
$356$	2.71868	−	14.6113i	0.144090	−	0.774397i
$357$	−1.21453	−	3.33690i	−0.0642799	−	0.176607i
$358$	13.9362	+	14.0682i	0.736549	+	0.743528i
$359$	7.80712	−	1.37661i	0.412044	−	0.0726545i	0.0362163	−	0.999344i	$-0.488469\pi$
$359$	7.80712	−	1.37661i	0.412044	−	0.0726545i	0.375828	+	0.926689i	$0.377358\pi$
$360$	−0.0286870	−	0.113457i	−0.00151194	−	0.00597972i
$361$	8.91056	−	16.7810i	0.468977	−	0.883211i
$362$	−15.0795	+	1.24767i	−0.792561	+	0.0655759i
$363$	0.372750	+	2.11397i	0.0195643	+	0.110955i
$364$	−7.69213	+	8.99350i	−0.403177	+	0.471388i
$365$	0.309220	−	0.112547i	0.0161853	−	0.00589097i
$366$	0.905755	−	3.31767i	0.0473446	−	0.173417i
$367$	3.06853	−	3.65693i	0.160176	−	0.190890i	−0.679987	−	0.733224i	$-0.738015\pi$
$367$	3.06853	−	3.65693i	0.160176	−	0.190890i	0.840163	+	0.542334i	$0.182459\pi$
$368$	−20.8096	−	4.07538i	−1.08477	−	0.212444i
$369$	1.54561	−	0.892358i	0.0804612	−	0.0464543i
$370$	−0.0251939	+	0.273128i	−0.00130977	+	0.0141993i
$371$	−0.524131	+	2.97249i	−0.0272115	+	0.154324i
$372$	−3.95927	−	4.80987i	−0.205278	−	0.249380i
$373$	13.8486	+	7.99548i	0.717052	+	0.413990i	0.813667	−	0.581331i	$-0.197468\pi$
$373$	13.8486	+	7.99548i	0.717052	+	0.413990i	−0.0966144	+	0.995322i	$0.530801\pi$
$374$	9.24123	+	6.53594i	0.477853	+	0.337965i
$375$	0.388737	+	0.141489i	0.0200743	+	0.00730644i
$376$	4.16092	−	2.82664i	0.214583	−	0.145773i
$377$	18.0585	−	15.1529i	0.930062	−	0.780415i
$378$	0.578453	+	2.20026i	0.0297524	+	0.113169i
$379$	−6.80529			−0.349564			−0.174782	−	0.984607i	$-0.555922\pi$
$379$	−6.80529			−0.349564			−0.174782	+	0.984607i	$0.555922\pi$
$380$	−0.274381	+	0.234142i	−0.0140754	+	0.0120112i
$381$	13.4844			0.690828
$382$	1.70084	+	6.46950i	0.0870227	+	0.331009i
$383$	−27.5079	+	23.0819i	−1.40559	+	1.17943i	−0.447036	+	0.894516i	$0.647520\pi$
$383$	−27.5079	+	23.0819i	−1.40559	+	1.17943i	−0.958553	+	0.284913i	$0.908035\pi$
$384$	9.04845	+	6.79158i	0.461752	+	0.346582i
$385$	0.226782	+	0.0825419i	0.0115579	+	0.00420672i
$386$	−6.47585	−	4.58010i	−0.329612	−	0.233121i
$387$	3.74042	+	2.15953i	0.190136	+	0.109775i
$388$	22.2569	−	18.3209i	1.12992	−	0.930101i
$389$	−1.90767	+	10.8190i	−0.0967229	+	0.548543i	0.897483	+	0.441049i	$0.145394\pi$
$389$	−1.90767	+	10.8190i	−0.0967229	+	0.548543i	−0.994206	+	0.107493i	$0.965718\pi$
$390$	0.0197693	−	0.214319i	0.00100106	−	0.0108525i
$391$	10.1342	−	5.85101i	0.512511	−	0.295898i
$392$	−12.0072	−	3.40008i	−0.606457	−	0.171730i
$393$	7.68224	−	9.15533i	0.387518	−	0.461826i
$394$	−8.96346	+	32.8321i	−0.451573	+	1.65406i
$395$	−0.138833	+	0.0505312i	−0.00698547	+	0.00254250i
$396$	−5.51088	−	4.71345i	−0.276932	−	0.236860i
$397$	−1.27505	−	7.23120i	−0.0639932	−	0.362923i	−0.999942	−	0.0107868i	$-0.996566\pi$
$397$	−1.27505	−	7.23120i	−0.0639932	−	0.362923i	0.935949	−	0.352137i	$-0.114545\pi$
$398$	−32.9003	+	2.72215i	−1.64914	+	0.136449i
$399$	5.29082	−	4.60184i	0.264872	−	0.230380i
$400$	−18.9130	+	6.48251i	−0.945652	+	0.324126i
$401$	−12.9816	+	2.28900i	−0.648268	+	0.114307i	−0.488107	−	0.872784i	$-0.662312\pi$
$401$	−12.9816	+	2.28900i	−0.648268	+	0.114307i	−0.160161	+	0.987091i	$0.551201\pi$
$402$	−14.3633	−	14.4994i	−0.716376	−	0.723164i
$403$	−3.91868	−	10.7665i	−0.195203	−	0.536316i
$404$	10.9074	+	2.02951i	0.542662	+	0.100972i
$405$	−0.0316955	−	0.0265957i	−0.00157496	−	0.00132155i
$406$	−13.1852	−	6.22424i	−0.654373	−	0.308904i
$407$	8.49815	+	14.7192i	0.421237	+	0.729605i
$408$	−6.22685	+	0.456124i	−0.308275	+	0.0225815i
$409$	8.84786	+	1.56012i	0.437499	+	0.0771428i	0.388059	−	0.921634i	$-0.373146\pi$
$409$	8.84786	+	1.56012i	0.437499	+	0.0771428i	0.0494391	+	0.998777i	$0.484257\pi$
$410$	0.0594949	+	0.0858261i	0.00293825	+	0.00423865i
$411$	−8.56165	+	14.8292i	−0.422315	+	0.731471i
$412$	8.94628	+	5.27825i	0.440752	+	0.260041i
$413$	7.92703	−	21.7793i	0.390063	−	1.07169i
$414$	−6.80950	+	3.13632i	−0.334669	+	0.154142i
$415$	−0.00690899	−	0.00823381i	−0.000339149	−	0.000404182i
$416$	11.5295	+	17.3210i	0.565280	+	0.849233i
$417$			12.2315i			0.598980i
$418$	−5.50334	+	21.6629i	−0.269177	+	1.05957i
$419$		−	33.9485i		−	1.65849i	−0.558885	−	0.829245i	$-0.688771\pi$
$419$		−	33.9485i		−	1.65849i	0.558885	−	0.829245i	$-0.311229\pi$
$420$	−0.125516	+	0.0443483i	−0.00612458	+	0.00216398i
$421$	−21.0539	−	25.0910i	−1.02610	−	1.22286i	−0.974545	−	0.224192i	$-0.928026\pi$
$421$	−21.0539	−	25.0910i	−1.02610	−	1.22286i	−0.0515585	−	0.998670i	$-0.516419\pi$
$422$	−12.0513	−	26.1655i	−0.586649	−	1.27372i
$423$	0.608267	−	1.67120i	0.0295750	−	0.0812565i
$424$	4.77749	+	2.31061i	0.232015	+	0.112213i
$425$	5.51666	−	9.55514i	0.267597	−	0.463492i
$426$	−16.3068	+	11.3039i	−0.790067	+	0.547677i
$427$	−3.85258	−	0.679314i	−0.186439	−	0.0328743i
$428$	−0.00384368	+	0.407564i	−0.000185791	+	0.0197004i
$429$	−6.66836	−	11.5499i	−0.321951	−	0.557636i
$430$	−0.107885	+	0.228541i	−0.00520269	+	0.0110212i
$431$	16.1580	+	13.5581i	0.778301	+	0.653072i	0.942820	−	0.333301i	$-0.108163\pi$
$431$	16.1580	+	13.5581i	0.778301	+	0.653072i	−0.164519	+	0.986374i	$0.552607\pi$
$432$	3.99929	+	0.0754401i	0.192416	+	0.00362961i
$433$	10.8926	+	29.9272i	0.523465	+	1.43821i	0.866639	+	0.498936i	$0.166276\pi$
$433$	10.8926	+	29.9272i	0.523465	+	1.43821i	−0.343174	+	0.939272i	$0.611502\pi$
$434$	−5.03449	+	4.98724i	−0.241663	+	0.239395i
$435$	0.261145	−	0.0460469i	0.0125209	−	0.00220778i
$436$	0.523908	+	3.14435i	0.0250907	+	0.150587i
$437$	17.9620	+	14.5370i	0.859237	+	0.695398i
$438$	0.927433	+	11.2091i	0.0443145	+	0.535592i
$439$	−0.990874	−	5.61953i	−0.0472918	−	0.268205i	0.951989	−	0.306133i	$-0.0990353\pi$
$439$	−0.990874	−	5.61953i	−0.0472918	−	0.268205i	−0.999280	+	0.0379280i	$0.987924\pi$
$440$	0.248273	−	0.344107i	0.0118360	−	0.0164046i
$441$	−4.14604	+	1.50903i	−0.197430	+	0.0718587i
$442$	−11.0773	−	3.02420i	−0.526892	−	0.143846i
$443$	2.44590	−	2.91491i	0.116208	−	0.138492i	−0.704804	−	0.709402i	$-0.748965\pi$
$443$	2.44590	−	2.91491i	0.116208	−	0.138492i	0.821013	+	0.570910i	$0.193410\pi$
$444$	−8.77912	−	3.28942i	−0.416639	−	0.156109i
$445$	0.266271	−	0.153732i	0.0126224	−	0.00728757i
$446$	31.3221	+	2.88921i	1.48314	+	0.136808i
$447$	1.11529	−	6.32514i	0.0527516	−	0.299169i
$448$	6.74746	−	10.9588i	0.318788	−	0.517757i
$449$	−23.9674	−	13.8376i	−1.13109	−	0.653035i	−0.186881	−	0.982382i	$-0.559838\pi$
$449$	−23.9674	−	13.8376i	−1.13109	−	0.653035i	−0.944209	+	0.329347i	$0.893171\pi$
$450$	−4.08167	+	5.77111i	−0.192412	+	0.272053i
$451$	6.08081	+	2.21323i	0.286334	+	0.104217i
$452$	−9.34504	−	16.5445i	−0.439554	−	0.778186i
$453$	−11.4079	+	9.57235i	−0.535989	+	0.449748i
$454$	19.4951	−	5.12529i	0.914950	−	0.240542i
$455$	−0.244827			−0.0114776
$456$	−5.25044	−	11.1549i	−0.245874	−	0.522378i
$457$	9.06829			0.424197			0.212098	−	0.977248i	$-0.431970\pi$
$457$	9.06829			0.424197			0.212098	+	0.977248i	$0.431970\pi$
$458$	−25.7804	+	6.77771i	−1.20464	+	0.316702i
$459$	−1.69098	+	1.41890i	−0.0789283	+	0.0662287i
$460$	−0.215748	−	0.381961i	−0.0100593	−	0.0178090i
$461$	−6.69914	−	2.43829i	−0.312010	−	0.113562i	0.181269	−	0.983434i	$-0.441980\pi$
$461$	−6.69914	−	2.43829i	−0.312010	−	0.113562i	−0.493279	+	0.869871i	$0.664202\pi$
$462$	−4.76316	+	6.73468i	−0.221602	+	0.313326i
$463$	6.34988	+	3.66611i	0.295104	+	0.170378i	0.640241	−	0.768174i	$-0.278834\pi$
$463$	6.34988	+	3.66611i	0.295104	+	0.170378i	−0.345137	+	0.938552i	$0.612168\pi$
$464$	−16.8458	+	19.3239i	−0.782046	+	0.897088i
$465$	0.0223800	−	0.126923i	0.00103785	−	0.00588592i
$466$	−25.4131	−	2.34415i	−1.17724	−	0.108591i
$467$	25.5106	−	14.7286i	1.18049	−	0.681557i	0.224364	−	0.974506i	$-0.427970\pi$
$467$	25.5106	−	14.7286i	1.18049	−	0.681557i	0.956128	+	0.292948i	$0.0946364\pi$
$468$	6.88883	+	2.58116i	0.318436	+	0.119314i
$469$	−14.9228	+	17.7843i	−0.689073	+	0.821205i
$470$	0.100390	+	0.0274075i	0.00463066	+	0.00126421i
$471$	−19.9665	+	7.26722i	−0.920009	+	0.334856i
$472$	−33.0468	−	23.8433i	−1.52110	−	1.09748i
$473$	2.71936	+	15.4223i	0.125036	+	0.709116i
$474$	−0.416399	−	5.03266i	−0.0191258	−	0.231158i
$475$	21.5198	+	3.40221i	0.987394	+	0.156104i
$476$	1.16725	+	7.00553i	0.0535010	+	0.321098i
$477$	1.84777	−	0.325812i	0.0846037	−	0.0149179i
$478$	13.7048	−	13.5762i	0.626844	−	0.620960i
$479$	10.9727	+	30.1473i	0.501357	+	1.37747i	0.889951	+	0.456057i	$0.150739\pi$
$479$	10.9727	+	30.1473i	0.501357	+	1.37747i	−0.388594	+	0.921409i	$0.627039\pi$
$480$	0.0148969	+	0.233581i	0.000679949	+	0.0106615i
$481$	−13.2082	−	11.0830i	−0.602243	−	0.505342i
$482$	−16.7963	+	35.5807i	−0.765049	+	1.62066i
$483$	4.26401	+	7.38548i	0.194019	+	0.336051i
$484$	0.0404864	−	4.29297i	0.00184029	−	0.195135i
$485$	0.587316	+	0.103560i	0.0266687	+	0.00470240i
$486$	1.16227	−	0.805688i	0.0527215	−	0.0365468i
$487$	−4.73272	+	8.19731i	−0.214460	+	0.371456i	−0.953105	−	0.302639i	$-0.902132\pi$
$487$	−4.73272	+	8.19731i	−0.214460	+	0.371456i	0.738645	+	0.674094i	$0.235466\pi$
$488$	−2.99473	+	6.19200i	−0.135565	+	0.280299i
$489$	−7.38142	+	20.2803i	−0.333799	+	0.917106i
$490$	−0.108003	−	0.234494i	−0.00487907	−	0.0105933i
$491$	−12.5048	−	14.9026i	−0.564332	−	0.672545i	0.406125	−	0.913817i	$-0.366880\pi$
$491$	−12.5048	−	14.9026i	−0.564332	−	0.672545i	−0.970457	+	0.241273i	$0.922435\pi$
$492$	−3.36553	+	1.18913i	−0.151730	+	0.0536102i
$493$		−	14.1472i		−	0.637159i
$494$	−2.27008	−	22.5604i	−0.102136	−	1.01504i
$495$		−	0.150020i		−	0.00674292i
$496$	6.02520	+	10.9059i	0.270540	+	0.489691i
$497$	14.5078	+	17.2898i	0.650765	+	0.775552i
$498$	0.333690	−	0.153691i	0.0149530	−	0.00688704i
$499$	−2.84774	+	7.82410i	−0.127482	+	0.350255i	−0.986971	−	0.160901i	$-0.948560\pi$
$499$	−2.84774	+	7.82410i	−0.127482	+	0.350255i	0.859488	+	0.511155i	$0.170782\pi$
$500$	−0.712590	−	0.420424i	−0.0318680	−	0.0188019i
$501$	11.4916	−	19.9041i	0.513407	−	0.889248i
$502$	−10.9554	−	15.8040i	−0.488962	−	0.705365i
$503$	−29.0019	−	5.11381i	−1.29313	−	0.228014i	−0.515584	−	0.856839i	$-0.672425\pi$
$503$	−29.0019	−	5.11381i	−1.29313	−	0.228014i	−0.777546	+	0.628826i	$0.783536\pi$
$504$	−0.332407	−	4.53790i	−0.0148066	−	0.202134i
$505$	0.114761	+	0.198772i	0.00510680	+	0.00884524i
$506$	−24.5817	−	11.6041i	−1.09279	−	0.515864i
$507$	0.405700	+	0.340423i	0.0180178	+	0.0151187i
$508$	−26.5138	−	4.93335i	−1.17636	−	0.218882i
$509$	−13.6299	−	37.4477i	−0.604133	−	1.65984i	−0.742808	−	0.669504i	$-0.766507\pi$
$509$	−13.6299	−	37.4477i	−0.604133	−	1.65984i	0.138675	−	0.990338i	$-0.455716\pi$
$510$	−0.0909016	−	0.0917629i	−0.00402519	−	0.00406333i
$511$	12.5997	−	2.22167i	0.557380	−	0.0982811i
$512$	−15.3068	−	16.6644i	−0.676471	−	0.736469i
$513$	−3.81297	−	2.11217i	−0.168347	−	0.0932545i
$514$	8.75495	−	0.724377i	0.386164	−	0.0319509i
$515$	0.0373153	+	0.211625i	0.00164431	+	0.00932533i
$516$	−6.56454	−	5.61464i	−0.288988	−	0.247171i
$517$	6.05947	−	2.20547i	0.266495	−	0.0969964i
$518$	−2.80868	+	10.2879i	−0.123406	+	0.452022i
$519$	11.6442	−	13.8770i	0.511123	−	0.609133i
$520$	−0.117281	+	0.414174i	−0.00514312	+	0.0181627i
$521$	−5.75966	+	3.32534i	−0.252335	+	0.145686i	−0.620833	−	0.783943i	$-0.713206\pi$
$521$	−5.75966	+	3.32534i	−0.252335	+	0.145686i	0.368498	+	0.929629i	$0.379872\pi$
$522$	−0.832512	+	9.02530i	−0.0364380	+	0.395026i
$523$	0.791261	−	4.48746i	0.0345994	−	0.196223i	−0.962609	−	0.270896i	$-0.912680\pi$
$523$	0.791261	−	4.48746i	0.0345994	−	0.196223i	0.997208	+	0.0746728i	$0.0237912\pi$
$524$	−18.4547	+	15.1911i	−0.806199	+	0.663627i
$525$	6.96344	+	4.02035i	0.303910	+	0.175462i
$526$	17.7543	+	12.5569i	0.774123	+	0.547505i
$527$	−6.46125	−	2.35170i	−0.281456	−	0.102442i
$528$	9.11134	+	11.2840i	0.396520	+	0.491073i
$529$	−3.90907	+	3.28010i	−0.169959	+	0.142613i
$530$	0.0279149	+	0.106180i	0.00121255	+	0.00461217i
$531$	−14.4074			−0.625229
$532$	−12.0867	+	7.11271i	−0.524025	+	0.308375i
$533$	−6.56465			−0.284347
$534$	2.67205	+	10.1637i	0.115631	+	0.439826i
$535$	−0.00645927	+	0.00541997i	−0.000279259	+	0.000234326i
$536$	22.9372	+	33.7644i	0.990736	+	1.45840i
$537$	−13.1579	−	4.78908i	−0.567805	−	0.206664i
$538$	17.4038	+	12.3090i	0.750332	+	0.530678i
$539$	−13.8543	−	7.99878i	−0.596746	−	0.344532i
$540$	0.0525912	+	0.0638898i	0.00226317	+	0.00274938i
$541$	−2.99495	+	16.9852i	−0.128763	+	0.730250i	0.850239	+	0.526397i	$0.176458\pi$
$541$	−2.99495	+	16.9852i	−0.128763	+	0.730250i	−0.979002	+	0.203853i	$0.934654\pi$
$542$	2.28978	−	24.8236i	0.0983543	−	1.06626i
$543$	9.26583	−	5.34963i	0.397635	−	0.229574i
$544$	12.4104	+	1.38127i	0.532093	+	0.0592214i
$545$	−0.0423895	+	0.0505178i	−0.00181577	+	0.00216395i
$546$	2.20393	−	8.07271i	0.0943194	−	0.345480i
$547$	−15.8887	+	5.78301i	−0.679351	+	0.247264i	−0.658569	−	0.752521i	$-0.728838\pi$
$547$	−15.8887	+	5.78301i	−0.679351	+	0.247264i	−0.0207821	+	0.999784i	$0.506616\pi$
$548$	22.2597	−	26.0257i	0.950888	−	1.11176i
$549$	0.422278	+	2.39486i	0.0180224	+	0.102210i
$550$	−25.5424	+	2.11336i	−1.08913	+	0.0901138i
$551$	26.0776	−	10.0186i	1.11094	−	0.426809i
$552$	14.5366	−	3.67550i	0.618721	−	0.156440i
$553$	−5.65702	+	0.997486i	−0.240561	+	0.0424174i
$554$	29.2026	+	29.4793i	1.24070	+	1.25246i
$555$	−0.0663351	−	0.182254i	−0.00281577	−	0.00773626i
$556$	4.47496	−	24.0502i	0.189781	−	1.01996i
$557$	25.8534	+	21.6936i	1.09544	+	0.919187i	0.997110	−	0.0759662i	$-0.0242041\pi$
$557$	25.8534	+	21.6936i	1.09544	+	0.919187i	0.0983343	+	0.995153i	$0.468649\pi$
$558$	3.98360	+	1.88050i	0.168639	+	0.0796079i
$559$	−7.94333	−	13.7583i	−0.335967	−	0.581912i
$560$	0.263022	−	0.0412791i	0.0111147	−	0.00174436i
$561$	−7.88212	−	1.38983i	−0.332783	−	0.0586787i
$562$	−12.7359	−	18.3725i	−0.537231	−	0.774998i
$563$	−12.4082	+	21.4917i	−0.522945	+	0.905767i	0.476699	+	0.879067i	$0.341833\pi$
$563$	−12.4082	+	21.4917i	−0.522945	+	0.905767i	−0.999643	+	0.0267000i	$0.991500\pi$
$564$	−1.80742	+	3.06346i	−0.0761063	+	0.128995i
$565$	0.134446	−	0.369388i	0.00565620	−	0.0155403i
$566$	−3.33326	+	1.53523i	−0.140107	+	0.0645305i
$567$	−1.03405	−	1.23233i	−0.0434258	−	0.0517529i
$568$	36.1989	−	16.2605i	1.51887	−	0.682274i
$569$		−	11.8870i		−	0.498327i	−0.968461	−	0.249164i	$-0.919844\pi$
$569$		−	11.8870i		−	0.498327i	0.968461	−	0.249164i	$-0.0801557\pi$
$570$	0.104773	−	0.232543i	0.00438846	−	0.00974015i
$571$		−	17.9272i		−	0.750230i	−0.926978	−	0.375115i	$-0.877603\pi$
$571$		−	17.9272i		−	0.750230i	0.926978	−	0.375115i	$-0.122397\pi$
$572$	8.88607	+	25.1497i	0.371545	+	1.05156i
$573$	−3.04044	−	3.62345i	−0.127016	−	0.151372i
$574$	1.69858	+	3.68792i	0.0708973	+	0.153931i
$575$	−9.06251	+	24.8991i	−0.377933	+	1.03836i
$576$	−7.83601	−	1.61149i	−0.326501	−	0.0671456i
$577$	−2.12586	+	3.68210i	−0.0885007	+	0.153288i	−0.906878	−	0.421394i	$-0.861541\pi$
$577$	−2.12586	+	3.68210i	−0.0885007	+	0.153288i	0.818377	+	0.574682i	$0.194874\pi$
$578$	14.0952	−	9.77082i	0.586282	−	0.406412i
$579$	5.52344	+	0.973932i	0.229547	+	0.0404752i
$580$	−0.530323	−	0.00500140i	−0.0220205	−	0.000207672i
$581$	−0.208951	−	0.361914i	−0.00866876	−	0.0150147i
$582$	−8.70171	+	18.4335i	−0.360698	+	0.764091i
$583$	5.21144	+	4.37291i	0.215836	+	0.181108i
$584$	2.27735	−	22.3793i	0.0942372	−	0.926060i
$585$	0.0520521	+	0.143012i	0.00215209	+	0.00591282i
$586$	6.46711	−	6.40641i	0.267154	−	0.264646i
$587$	−11.1032	+	1.95779i	−0.458277	+	0.0808065i	−0.398021	−	0.917376i	$-0.630303\pi$
$587$	−11.1032	+	1.95779i	−0.458277	+	0.0808065i	−0.0602559	+	0.998183i	$0.519192\pi$
$588$	8.70424	−	1.45029i	0.358957	−	0.0598091i
$589$	−0.240765	−	13.5754i	−0.00992057	−	0.559366i
$590$	−0.0695145	−	0.840164i	−0.00286187	−	0.0345890i
$591$	−4.17892	−	23.6998i	−0.171898	−	0.974880i
$592$	16.0585	+	9.67972i	0.660001	+	0.397834i
$593$	−23.0531	+	8.39064i	−0.946677	+	0.344562i	−0.768799	−	0.639490i	$-0.779145\pi$
$593$	−23.0531	+	8.39064i	−0.946677	+	0.344562i	−0.177878	+	0.984053i	$0.556923\pi$
$594$	4.94665	+	1.35048i	0.202964	+	0.0554110i
$595$	−0.0944428	+	0.112553i	−0.00387178	+	0.00461420i
$596$	−4.50703	+	12.0288i	−0.184615	+	0.492719i
$597$	20.2161	−	11.6718i	0.827389	−	0.477693i
$598$	27.4596	+	2.53293i	1.12290	+	0.103579i
$599$	−0.455333	+	2.58232i	−0.0186044	+	0.105511i	−0.992696	−	0.120643i	$-0.961504\pi$
$599$	−0.455333	+	2.58232i	−0.0186044	+	0.105511i	0.974091	+	0.226154i	$0.0726154\pi$
$600$	10.1370	−	9.85417i	0.413841	−	0.402295i
$601$	7.64110	+	4.41159i	0.311687	+	0.179953i	0.647681	−	0.761911i	$-0.275739\pi$
$601$	7.64110	+	4.41159i	0.311687	+	0.179953i	−0.335994	+	0.941864i	$0.609072\pi$
$602$	−5.67386	+	8.02233i	−0.231249	+	0.326966i
$603$	13.5612	+	4.93587i	0.552254	+	0.201004i
$604$	25.9329	−	14.6480i	1.05519	−	0.596020i
$605$	0.0680370	−	0.0570899i	0.00276610	−	0.00232103i
$606$	−7.58723	+	1.99470i	−0.308210	+	0.0810290i
$607$	−27.1964			−1.10387			−0.551933	−	0.833888i	$-0.686110\pi$
$607$	−27.1964			−1.10387			−0.551933	+	0.833888i	$0.686110\pi$
$608$	6.24260	+	23.8543i	0.253171	+	0.967422i
$609$	10.3100			0.417782
$610$	−0.137618	+	0.0361799i	−0.00557198	+	0.00146488i
$611$	−5.01117	+	4.20487i	−0.202730	+	0.170111i
$612$	3.84401	−	2.17127i	0.155385	−	0.0877683i
$613$	34.8590	+	12.6876i	1.40794	+	0.512449i	0.930525	−	0.366228i	$-0.119351\pi$
$613$	34.8590	+	12.6876i	1.40794	+	0.512449i	0.477417	+	0.878677i	$0.341573\pi$
$614$	−8.93536	+	12.6338i	−0.360602	+	0.509859i
$615$	−0.0639505	−	0.0369218i	−0.00257873	−	0.00148883i
$616$	11.8295	−	11.4995i	0.476624	−	0.463326i
$617$	2.09956	−	11.9072i	0.0845250	−	0.479365i	−0.912933	−	0.408109i	$-0.866188\pi$
$617$	2.09956	−	11.9072i	0.0845250	−	0.479365i	0.997458	−	0.0712559i	$-0.0227007\pi$
$618$	−7.31388	−	0.674647i	−0.294207	−	0.0271383i
$619$	−18.3411	+	10.5893i	−0.737193	+	0.425618i	−0.821048	−	0.570860i	$-0.806610\pi$
$619$	−18.3411	+	10.5893i	−0.737193	+	0.425618i	0.0838550	+	0.996478i	$0.473277\pi$
$620$	−0.0904402	+	0.241375i	−0.00363216	+	0.00969386i
$621$	3.40756	−	4.06097i	0.136741	−	0.162961i
$622$	−8.51283	−	2.32408i	−0.341333	−	0.0931872i
$623$	11.2333	−	4.08858i	0.450052	−	0.163806i
$624$	−12.6009	−	7.59553i	−0.504438	−	0.304064i
$625$	4.33675	+	24.5949i	0.173470	+	0.983796i
$626$	−0.709964	−	8.58074i	−0.0283759	−	0.342955i
$627$	−3.02001	−	15.5134i	−0.120607	−	0.619544i
$628$	41.9180	−	6.98434i	1.67271	−	0.278705i
$629$	−10.1902	+	1.79681i	−0.406311	+	0.0716437i
$630$	0.0668735	−	0.0662458i	0.00266431	−	0.00263930i
$631$	7.60167	+	20.8854i	0.302618	+	0.831435i	0.994043	+	0.108987i	$0.0347608\pi$
$631$	7.60167	+	20.8854i	0.302618	+	0.831435i	−0.691425	+	0.722448i	$0.743017\pi$
$632$	−1.02248	+	10.0478i	−0.0406721	+	0.399681i
$633$	15.6043	+	13.0935i	0.620214	+	0.520422i
$634$	15.8795	−	33.6386i	0.630655	−	1.33596i
$635$	−0.278963	−	0.483178i	−0.0110703	−	0.0191743i
$636$	−3.75239	−	0.0353882i	−0.148792	−	0.00140323i
$637$	15.9824	+	2.81812i	0.633245	+	0.111658i
$638$	−27.0084	+	18.7223i	−1.06927	+	0.741224i
$639$	7.01508	−	12.1505i	0.277512	−	0.480665i
$640$	0.0561657	−	0.464729i	0.00222014	−	0.0183700i
$641$	−11.6602	+	32.0361i	−0.460550	+	1.26535i	0.464522	+	0.885561i	$0.346226\pi$
$641$	−11.6602	+	32.0361i	−0.460550	+	1.26535i	−0.925073	+	0.379790i	$0.875996\pi$
$642$	−0.120567	−	0.261773i	−0.00475842	−	0.0103314i
$643$	16.6610	+	19.8558i	0.657047	+	0.783038i	0.986959	−	0.160974i	$-0.0514635\pi$
$643$	16.6610	+	19.8558i	0.657047	+	0.783038i	−0.329912	+	0.944012i	$0.607019\pi$
$644$	−5.68210	−	16.0817i	−0.223906	−	0.633709i
$645$		−	0.178704i		−	0.00703646i
$646$	−11.2472	−	7.65915i	−0.442516	−	0.301345i
$647$		−	22.6781i		−	0.891569i	−0.895140	−	0.445785i	$-0.852925\pi$
$647$		−	22.6781i		−	0.891569i	0.895140	−	0.445785i	$-0.147075\pi$
$648$	−2.58008	+	1.15896i	−0.101355	+	0.0455284i
$649$	−33.5784	−	40.0172i	−1.31807	−	1.57081i
$650$	23.6158	−	10.8770i	0.926290	−	0.426630i
$651$	1.71384	−	4.70873i	0.0671705	−	0.184549i
$652$	21.9334	−	37.1756i	0.858977	−	1.45591i
$653$	−4.59445	+	7.95783i	−0.179795	+	0.311414i	−0.941810	−	0.336145i	$-0.890877\pi$
$653$	−4.59445	+	7.95783i	−0.179795	+	0.311414i	0.762015	+	0.647559i	$0.224210\pi$
$654$	−1.28414	−	1.85248i	−0.0502140	−	0.0724376i
$655$	−0.486985	−	0.0858686i	−0.0190281	−	0.00335516i
$656$	7.05254	−	1.10684i	0.275355	−	0.0432147i
$657$	−3.97656	−	6.88761i	−0.155140	−	0.268711i
$658$	3.65885	+	1.72720i	0.142637	+	0.0673333i
$659$	3.81778	+	3.20350i	0.148720	+	0.124790i	0.714112	−	0.700032i	$-0.246831\pi$
$659$	3.81778	+	3.20350i	0.148720	+	0.124790i	−0.565392	+	0.824822i	$0.691275\pi$
$660$	−0.0548857	+	0.294978i	−0.00213642	+	0.0114820i
$661$	3.72500	+	10.2344i	0.144886	+	0.398070i	0.990815	−	0.135225i	$-0.0431757\pi$
$661$	3.72500	+	10.2344i	0.144886	+	0.398070i	−0.845929	+	0.533295i	$0.820953\pi$
$662$	28.2401	+	28.5077i	1.09758	+	1.10798i
$663$	7.99612	−	1.40993i	0.310543	−	0.0547572i
$664$	−0.712347	+	0.180113i	−0.0276444	+	0.00698972i
$665$	−0.274350	−	0.0943803i	−0.0106388	−	0.00365991i
$666$	6.60665	−	0.546629i	0.256002	−	0.0211814i
$667$	5.89973	+	33.4590i	0.228439	+	1.29554i
$668$	−29.8774	+	34.9321i	−1.15599	+	1.35157i
$669$	−20.9007	+	7.60724i	−0.808069	+	0.294113i
$670$	−0.222402	+	0.814630i	−0.00859213	+	0.0314719i
$671$	−5.66764	+	6.75443i	−0.218797	+	0.260752i
$672$	−1.00662	+	9.04428i	−0.0388312	+	0.348891i
$673$	−41.4052	+	23.9053i	−1.59605	+	0.921482i	−0.603815	+	0.797124i	$0.706354\pi$
$673$	−41.4052	+	23.9053i	−1.59605	+	0.921482i	−0.992237	+	0.124357i	$0.960313\pi$
$674$	2.08216	−	22.5728i	0.0802018	−	0.869472i
$675$	0.867944	−	4.92235i	0.0334072	−	0.189461i
$676$	−0.673163	−	0.817784i	−0.0258909	−	0.0314532i
$677$	−27.9704	−	16.1487i	−1.07499	−	0.620646i	−0.145449	−	0.989366i	$-0.546463\pi$
$677$	−27.9704	−	16.1487i	−1.07499	−	0.620646i	−0.929540	+	0.368720i	$0.879796\pi$
$678$	10.9696	+	7.75835i	0.421286	+	0.297958i
$679$	21.7889	+	7.93050i	0.836180	+	0.304345i
$680$	0.145164	+	0.213686i	0.00556677	+	0.00819448i
$681$	−10.9189	+	9.16200i	−0.418411	+	0.351089i
$682$	4.06114	+	15.4474i	0.155509	+	0.591510i
$683$	−16.4070			−0.627796			−0.313898	−	0.949457i	$-0.601635\pi$
$683$	−16.4070			−0.627796			−0.313898	+	0.949457i	$0.601635\pi$
$684$	6.72452	+	5.54805i	0.257118	+	0.212135i
$685$	0.708486			0.0270699
$686$	−6.60137	−	25.1097i	−0.252042	−	0.958691i
$687$	14.4391	−	12.1159i	0.550887	−	0.462249i
$688$	10.8534	+	13.4415i	0.413782	+	0.512452i
$689$	−6.48523	−	2.36043i	−0.247068	−	0.0899253i
$690$	0.253255	+	0.179117i	0.00964125	+	0.00681885i
$691$	−7.56790	−	4.36933i	−0.287896	−	0.166217i	0.349096	−	0.937087i	$-0.386489\pi$
$691$	−7.56790	−	4.36933i	−0.287896	−	0.166217i	−0.636993	+	0.770870i	$0.719822\pi$
$692$	−27.9724	+	23.0256i	−1.06335	+	0.875302i
$693$	1.01286	−	5.74421i	0.0384753	−	0.218204i
$694$	3.33606	−	36.1664i	0.126635	−	1.37286i
$695$	0.438283	−	0.253043i	0.0166250	−	0.00959846i
$696$	4.93888	−	17.4414i	0.187208	−	0.661116i
$697$	−2.53234	+	3.01792i	−0.0959192	+	0.114312i
$698$	3.72970	−	13.6614i	0.141171	−	0.517093i
$699$	16.9577	−	6.17211i	0.641400	−	0.233451i
$700$	−12.2210	−	10.4526i	−0.461911	−	0.395072i
$701$	−9.01254	−	51.1126i	−0.340399	−	1.93050i	−0.365496	−	0.930813i	$-0.619101\pi$
$701$	−9.01254	−	51.1126i	−0.340399	−	1.93050i	0.0250975	−	0.999685i	$-0.492010\pi$
$702$	−5.18413	+	0.428931i	−0.195662	+	0.0161890i
$703$	−10.5285	−	17.5112i	−0.397090	−	0.660449i
$704$	−13.7869	−	25.5206i	−0.519612	−	0.961845i
$705$	−0.0724666	+	0.0127778i	−0.00272925	+	0.000481241i
$706$	21.6496	+	21.8548i	0.814794	+	0.822515i
$707$	3.05214	+	8.38569i	0.114788	+	0.315376i
$708$	28.3286	+	5.27103i	1.06466	+	0.198098i
$709$	−28.1222	−	23.5974i	−1.05615	−	0.886217i	−0.0624256	−	0.998050i	$-0.519884\pi$
$709$	−28.1222	−	23.5974i	−1.05615	−	0.886217i	−0.993727	+	0.111832i	$0.964328\pi$
$710$	0.742397	+	0.350457i	0.0278617	+	0.0131524i
$711$	1.78540	+	3.09240i	0.0669576	+	0.115974i
$712$	−1.53549	−	20.9620i	−0.0575449	−	0.785583i
$713$	16.2619	+	2.86742i	0.609015	+	0.107386i
$714$	−2.86104	−	4.12728i	−0.107072	−	0.154459i
$715$	−0.275907	+	0.477885i	−0.0103183	+	0.0178719i
$716$	24.1196	+	14.2304i	0.901393	+	0.531816i
$717$	−4.66538	+	12.8180i	−0.174232	+	0.478698i
$718$	10.1831	−	4.69012i	0.380029	−	0.175034i
$719$	4.18795	+	4.99100i	0.156184	+	0.186133i	0.838462	−	0.544960i	$-0.183455\pi$
$719$	4.18795	+	4.99100i	0.156184	+	0.186133i	−0.682278	+	0.731093i	$0.739011\pi$
$720$	−0.0800332	−	0.144864i	−0.00298266	−	0.00539878i
$721$			8.35497i			0.311155i
$722$	6.15317	−	26.1560i	0.228997	−	0.973427i
$723$		−	27.8218i		−	1.03470i
$724$	−20.1761	+	7.12877i	−0.749840	+	0.264939i
$725$	20.5909	+	24.5393i	0.764726	+	0.911365i
$726$	1.26997	+	2.75732i	0.0471329	+	0.102334i
$727$	−8.42894	+	23.1583i	−0.312612	+	0.858894i	0.679515	+	0.733661i	$0.262190\pi$
$727$	−8.42894	+	23.1583i	−0.312612	+	0.858894i	−0.992127	+	0.125233i	$0.960032\pi$
$728$	−7.28692	+	15.0667i	−0.270071	+	0.558408i
$729$	−0.500000	+	0.866025i	−0.0185185	+	0.0320750i
$730$	0.382462	−	0.265124i	0.0141555	−	0.00981267i
$731$	−9.38916	−	1.65556i	−0.347271	−	0.0612332i
$732$	0.0458659	−	4.86339i	0.00169525	−	0.179756i
$733$	−18.9929	−	32.8967i	−0.701518	−	1.21507i	−0.967933	−	0.251207i	$-0.919172\pi$
$733$	−18.9929	−	32.8967i	−0.701518	−	1.21507i	0.266415	−	0.963858i	$-0.414161\pi$
$734$	2.88197	−	6.10509i	0.106376	−	0.225343i
$735$	0.139844	+	0.117343i	0.00515824	+	0.00432828i
$736$	−29.9274	+	1.90866i	−1.10314	+	0.0703541i
$737$	17.8966	+	49.1704i	0.659229	+	1.81122i
$738$	1.79311	−	1.77628i	0.0660054	−	0.0653858i
$739$	−50.1160	+	8.83681i	−1.84355	+	0.325067i	−0.982901	−	0.184135i	$-0.941052\pi$
$739$	−50.1160	+	8.83681i	−1.84355	+	0.325067i	−0.860647	+	0.509202i	$0.829941\pi$
$740$	0.0637529	+	0.382627i	0.00234360	+	0.0140656i
$741$	8.26154	+	13.7408i	0.303495	+	0.504781i
$742$	0.351977	+	4.25405i	0.0129215	+	0.156171i
$743$	−4.16062	−	23.5961i	−0.152638	−	0.865655i	−0.960913	−	0.276850i	$-0.910710\pi$
$743$	−4.16062	−	23.5961i	−0.152638	−	0.865655i	0.808275	−	0.588805i	$-0.200402\pi$
$744$	−7.14476	−	5.15496i	−0.261940	−	0.188990i
$745$	−0.249717	+	0.0908896i	−0.00914893	+	0.00332994i
$746$	21.8162	+	5.95604i	0.798749	+	0.218066i
$747$	−0.166982	+	0.199002i	−0.00610956	+	0.00728110i
$748$	14.9898	+	5.61647i	0.548080	+	0.205359i
$749$	−0.283915	+	0.163918i	−0.0103740	+	0.00598945i
$750$	0.582565	+	0.0537370i	0.0212723	+	0.00196220i
$751$	2.08600	−	11.8303i	0.0761191	−	0.431693i	−0.922803	−	0.385272i	$-0.874108\pi$
$751$	2.08600	−	11.8303i	0.0761191	−	0.431693i	0.998922	−	0.0464204i	$-0.0147814\pi$
$752$	4.67464	−	5.36229i	0.170466	−	0.195543i
$753$	11.7758	+	6.79876i	0.429134	+	0.247761i
$754$	19.2506	−	27.2187i	0.701067	−	0.991246i
$755$	0.579003	+	0.210740i	0.0210721	+	0.00766961i
$756$	1.58234	+	2.80138i	0.0575492	+	0.101885i
$757$	−1.69875	+	1.42542i	−0.0617421	+	0.0518078i	−0.673137	−	0.739518i	$-0.735053\pi$
$757$	−1.69875	+	1.42542i	−0.0617421	+	0.0518078i	0.611394	+	0.791326i	$0.290609\pi$
$758$	−9.30784	+	2.44705i	−0.338076	+	0.0888808i
$759$	19.2213			0.697688
$760$	−0.291087	+	0.418906i	−0.0105588	+	0.0151953i
$761$	−40.2788			−1.46011			−0.730053	−	0.683390i	$-0.760505\pi$
$761$	−40.2788			−1.46011			−0.730053	+	0.683390i	$0.760505\pi$
$762$	18.4431	−	4.84873i	0.668124	−	0.175651i
$763$	−1.96414	+	1.64811i	−0.0711067	+	0.0596656i
$764$	4.65261	+	8.23698i	0.168325	+	0.298004i
$765$	0.0858252	+	0.0312378i	0.00310302	+	0.00112941i
$766$	−29.3238	+	41.4612i	−1.05951	+	1.49806i
$767$	45.8944	+	26.4971i	1.65715	+	0.956756i
$768$	14.8180	+	6.03545i	0.534699	+	0.217786i
$769$	−8.32330	+	47.2038i	−0.300146	+	1.70221i	0.345372	+	0.938466i	$0.387753\pi$
$769$	−8.32330	+	47.2038i	−0.300146	+	1.70221i	−0.645518	+	0.763745i	$0.723358\pi$
$770$	0.339858	+	0.0313492i	0.0122476	+	0.00112975i
$771$	−5.37961	+	3.10592i	−0.193742	+	0.111857i
$772$	−10.5042	−	3.93578i	−0.378053	−	0.141652i
$773$	23.9044	−	28.4881i	0.859781	−	1.02465i	−0.139626	−	0.990204i	$-0.544590\pi$
$773$	23.9044	−	28.4881i	0.859781	−	1.02465i	0.999407	−	0.0344424i	$-0.0109655\pi$
$774$	5.89244	+	1.60869i	0.211799	+	0.0578232i
$775$	14.6303	−	5.32498i	0.525535	−	0.191279i
$776$	23.8537	−	33.0613i	0.856299	−	1.18683i
$777$	−1.30945	−	7.42628i	−0.0469764	−	0.266416i
$778$	1.28109	+	15.4834i	0.0459292	+	0.555108i
$779$	−7.35628	−	2.53066i	−0.263566	−	0.0906704i
$780$	−0.0500259	−	0.300241i	−0.00179121	−	0.0107504i
$781$	50.0980	−	8.83363i	1.79265	−	0.316092i
$782$	11.7571	−	11.6467i	0.420432	−	0.416486i
$783$	−2.19199	−	6.02243i	−0.0783352	−	0.215224i
$784$	−17.6453	−	0.332851i	−0.630191	−	0.0118875i
$785$	0.673464	+	0.565104i	0.0240370	+	0.0201694i
$786$	7.21520	−	15.2845i	0.257358	−	0.545179i
$787$	15.3008	+	26.5018i	0.545416	+	0.944688i	0.998581	+	0.0532610i	$0.0169615\pi$
$787$	15.3008	+	26.5018i	0.545416	+	0.944688i	−0.453165	+	0.891427i	$0.649705\pi$
$788$	−0.453894	+	48.1287i	−0.0161693	+	1.71451i
$789$	−15.1431	−	2.67015i	−0.539110	−	0.0950597i
$790$	−0.171717	+	0.119035i	−0.00610943	+	0.00423508i
$791$	7.64180	−	13.2360i	0.271711	−	0.470617i
$792$	−9.23229	−	4.46515i	−0.328055	−	0.158662i
$793$	3.05930	−	8.40536i	0.108639	−	0.298483i
$794$	−4.34413	−	9.43188i	−0.154168	−	0.334725i
$795$	−0.0499009	−	0.0594696i	−0.00176980	−	0.00210917i
$796$	−44.0201	+	15.5535i	−1.56025	+	0.551278i
$797$		−	10.7373i		−	0.380335i	−0.981752	−	0.190167i	$-0.939097\pi$
$797$		−	10.7373i		−	0.380335i	0.981752	−	0.190167i	$-0.0609031\pi$
$798$	5.58171	−	8.19658i	0.197591	−	0.290156i
$799$			3.92580i			0.138885i
$800$	−23.5371	+	15.6671i	−0.832161	+	0.553916i
$801$	−4.77657	−	5.69250i	−0.168772	−	0.201135i
$802$	−16.9323	+	7.79866i	−0.597899	+	0.275380i
$803$	9.86270	−	27.0976i	0.348047	−	0.956252i
$804$	−24.8589	−	14.6666i	−0.876706	−	0.517251i
$805$	0.176426	−	0.305578i	0.00621819	−	0.0107702i
$806$	−9.23113	−	13.3166i	−0.325153	−	0.469058i
$807$	−14.8442	−	2.61744i	−0.522542	−	0.0921382i
$808$	15.6482	−	1.14625i	0.550501	−	0.0403249i
$809$	13.6129	+	23.5782i	0.478603	+	0.828964i	0.999699	−	0.0245336i	$-0.00781008\pi$
$809$	13.6129	+	23.5782i	0.478603	+	0.828964i	−0.521096	+	0.853498i	$0.674477\pi$
$810$	−0.0529144	−	0.0249788i	−0.00185922	−	0.000877666i
$811$	15.5324	+	13.0332i	0.545416	+	0.457658i	0.873385	−	0.487030i	$-0.161920\pi$
$811$	15.5324	+	13.0332i	0.545416	+	0.457658i	−0.327969	+	0.944688i	$0.606364\pi$
$812$	−20.2721	−	3.77197i	−0.711410	−	0.132370i
$813$	6.02894	+	16.5644i	0.211444	+	0.580938i
$814$	16.9160	+	17.0762i	0.592904	+	0.598522i
$815$	0.879394	−	0.155061i	0.0308038	−	0.00543155i
$816$	−8.35267	+	2.86291i	−0.292402	+	0.100222i
$817$	−3.59742	−	18.4795i	−0.125858	−	0.646515i
$818$	12.6625	−	1.04769i	0.442735	−	0.0366315i
$819$	1.02751	+	5.82728i	0.0359040	+	0.203622i
$820$	0.112235	+	0.0959943i	0.00391941	+	0.00335226i
$821$	16.3339	−	5.94505i	0.570057	−	0.207484i	−0.0408788	−	0.999164i	$-0.513016\pi$
$821$	16.3339	−	5.94505i	0.570057	−	0.207484i	0.610935	+	0.791680i	$0.290794\pi$
$822$	−6.37779	+	23.3610i	−0.222451	+	0.814810i
$823$	−28.8056	+	34.3292i	−1.00410	+	1.19664i	−0.0236818	+	0.999720i	$0.507539\pi$
$823$	−28.8056	+	34.3292i	−1.00410	+	1.19664i	−0.980419	+	0.196922i	$0.936906\pi$
$824$	14.1341	+	4.00235i	0.492385	+	0.139428i
$825$	15.6949	−	9.06145i	0.546426	−	0.315479i
$826$	3.01067	−	32.6388i	0.104755	−	1.13565i
$827$	4.54986	−	25.8035i	0.158214	−	0.897277i	−0.797574	−	0.603221i	$-0.793884\pi$
$827$	4.54986	−	25.8035i	0.158214	−	0.897277i	0.955788	−	0.294056i	$-0.0950051\pi$
$828$	−8.18585	+	6.73822i	−0.284478	+	0.234169i
$829$	−17.2911	−	9.98301i	−0.600544	−	0.346724i	0.168712	−	0.985665i	$-0.446039\pi$
$829$	−17.2911	−	9.98301i	−0.600544	−	0.346724i	−0.769256	+	0.638941i	$0.779373\pi$
$830$	−0.0124104	−	0.00877735i	−0.000430771	−	0.000304666i
$831$	−27.5718	−	10.0353i	−0.956455	−	0.348121i
$832$	21.9976	+	19.5448i	0.762630	+	0.677594i
$833$	7.46081	−	6.26037i	0.258502	−	0.216909i
$834$	4.39821	+	16.7295i	0.152297	+	0.579294i
$835$	−0.950944			−0.0329088
$836$	0.262446	+	31.6081i	0.00907689	+	1.09319i
$837$	−3.11491			−0.107667
$838$	−12.2072	−	46.4325i	−0.421690	−	1.60399i
$839$	−8.96826	+	7.52526i	−0.309619	+	0.259801i	−0.784334	−	0.620338i	$-0.786995\pi$
$839$	−8.96826	+	7.52526i	−0.309619	+	0.259801i	0.474716	+	0.880139i	$0.342551\pi$
$840$	−0.155727	+	0.105790i	−0.00537308	+	0.00365010i
$841$	11.3463	+	4.12973i	0.391253	+	0.142404i
$842$	−37.8184	−	26.7474i	−1.30331	−	0.921775i
$843$	13.6897	+	7.90374i	0.471498	+	0.272219i
$844$	−25.8916	−	31.4541i	−0.891226	−	1.08270i
$845$	0.00380509	−	0.0215797i	0.000130899	−	0.000742366i
$846$	0.231018	−	2.50448i	0.00794258	−	0.0861058i
$847$	2.99055	−	1.72659i	0.102756	−	0.0593264i
$848$	7.36520	+	1.44241i	0.252922	+	0.0495327i
$849$	1.66800	−	1.98785i	0.0572457	−	0.0682227i
$850$	4.10950	−	15.0526i	0.140955	−	0.516300i
$851$	23.3512	−	8.49914i	0.800469	−	0.291347i
$852$	−18.2387	+	21.3244i	−0.624849	+	0.730562i
$853$	5.65724	+	32.0838i	0.193700	+	1.09853i	0.914258	+	0.405133i	$0.132775\pi$
$853$	5.65724	+	32.0838i	0.193700	+	1.09853i	−0.720557	+	0.693395i	$0.756114\pi$
$854$	−5.51358	+	0.456189i	−0.188671	+	0.0156105i
$855$	0.00319810	+	0.180324i	0.000109373	+	0.00616693i
$856$	0.141295	+	0.558823i	0.00482936	+	0.0191002i
$857$	−22.2559	+	3.92432i	−0.760248	+	0.134052i	−0.540315	−	0.841463i	$-0.681695\pi$
$857$	−22.2559	+	3.92432i	−0.760248	+	0.134052i	−0.219933	+	0.975515i	$0.570584\pi$
$858$	−13.2737	−	13.3995i	−0.453156	−	0.457450i
$859$	8.45388	+	23.2268i	0.288443	+	0.792490i	0.996285	+	0.0861191i	$0.0274466\pi$
$859$	8.45388	+	23.2268i	0.288443	+	0.792490i	−0.707842	+	0.706371i	$0.750331\pi$
$860$	−0.0653798	+	0.351377i	−0.00222943	+	0.0119819i
$861$	−2.19936	−	1.84548i	−0.0749538	−	0.0628937i
$862$	26.9751	+	12.7339i	0.918774	+	0.433717i
$863$	−2.99804	−	5.19276i	−0.102054	−	0.176764i	0.810476	−	0.585771i	$-0.199208\pi$
$863$	−2.99804	−	5.19276i	−0.102054	−	0.176764i	−0.912531	+	0.409008i	$0.865875\pi$
$864$	5.49710	−	1.33488i	0.187015	−	0.0454136i
$865$	−0.738137	−	0.130153i	−0.0250974	−	0.00442535i
$866$	25.6594	+	37.0157i	0.871942	+	1.25784i
$867$	−6.06365	+	10.5025i	−0.205932	+	0.356685i
$868$	−5.09255	+	8.63153i	−0.172852	+	0.292973i
$869$	−4.42815	+	12.1662i	−0.150215	+	0.412712i
$870$	0.340620	−	0.156883i	0.0115481	−	0.00531882i
$871$	−34.1210	−	40.6638i	−1.15615	−	1.37784i
$872$	1.84721	+	4.11225i	0.0625545	+	0.139258i
$873$		−	14.4137i		−	0.487831i
$874$	29.7944	+	13.4240i	1.00781	+	0.454073i
$875$		−	0.665490i		−	0.0224977i
$876$	5.29906	+	14.9976i	0.179039	+	0.506723i
$877$	−18.5453	−	22.1015i	−0.626231	−	0.746313i	0.355897	−	0.934525i	$-0.384175\pi$
$877$	−18.5453	−	22.1015i	−0.626231	−	0.746313i	−0.982128	+	0.188212i	$0.939731\pi$
$878$	−3.37592	−	7.32973i	−0.113932	−	0.247366i
$879$	−2.20153	+	6.04865i	−0.0742557	+	0.204016i
$880$	0.215839	−	0.559921i	0.00727591	−	0.0188749i
$881$	−5.64828	+	9.78311i	−0.190295	+	0.329601i	−0.945348	−	0.326063i	$-0.894278\pi$
$881$	−5.64828	+	9.78311i	−0.190295	+	0.329601i	0.755053	+	0.655664i	$0.227611\pi$
$882$	−5.12806	+	3.55479i	−0.172671	+	0.119696i
$883$	6.55374	+	1.15560i	0.220551	+	0.0388891i	0.282832	−	0.959170i	$-0.408726\pi$
$883$	6.55374	+	1.15560i	0.220551	+	0.0388891i	−0.0622806	+	0.998059i	$0.519837\pi$
$884$	−16.2382	−	0.153140i	−0.546150	−	0.00515066i
$885$	0.298058	+	0.516251i	0.0100191	+	0.0173536i
$886$	2.29721	−	4.86633i	0.0771761	−	0.163488i
$887$	−14.9772	−	12.5674i	−0.502886	−	0.421971i	0.355732	−	0.934588i	$-0.384232\pi$
$887$	−14.9772	−	12.5674i	−0.502886	−	0.421971i	−0.858617	+	0.512617i	$0.828676\pi$
$888$	−13.1903	−	1.34227i	−0.442638	−	0.0450435i
$889$	−7.41918	−	20.3840i	−0.248831	−	0.683659i
$890$	0.308909	−	0.306010i	0.0103547	−	0.0102575i
$891$	−3.57074	+	0.629617i	−0.119624	+	0.0210930i
$892$	43.8793	−	7.31112i	1.46919	−	0.244794i
$893$	−7.23643	+	2.78013i	−0.242158	+	0.0930336i
$894$	−0.748969	−	9.05216i	−0.0250493	−	0.302750i
$895$	0.100604	+	0.570553i	0.00336282	+	0.0190715i
$896$	5.28816	−	17.4151i	0.176665	−	0.581796i
$897$	−18.3233	+	6.66914i	−0.611798	+	0.222676i
$898$	−37.7568	−	10.3080i	−1.25996	−	0.343981i
$899$	12.8321	−	15.2927i	0.427976	−	0.510042i
$900$	−3.50747	+	9.36105i	−0.116916	+	0.312035i
$901$	−3.58685	+	2.07087i	−0.119495	+	0.0689906i
$902$	9.11278	+	0.840581i	0.303422	+	0.0279883i
$903$	1.20651	−	6.84248i	0.0401503	−	0.227704i
$904$	−18.7306	−	19.2682i	−0.622971	−	0.640850i
$905$	−0.383379	−	0.221344i	−0.0127439	−	0.00735772i
$906$	−12.1609	+	17.1945i	−0.404020	+	0.571249i
$907$	−48.2242	−	17.5522i	−1.60126	−	0.582811i	−0.621574	−	0.783355i	$-0.713507\pi$
$907$	−48.2242	−	17.5522i	−1.60126	−	0.582811i	−0.979685	+	0.200544i	$0.935729\pi$
$908$	24.8212	−	14.0201i	0.823720	−	0.465273i
$909$	4.24947	−	3.56573i	0.140946	−	0.118268i
$910$	−0.334858	+	0.0880348i	−0.0111004	+	0.00291832i
$911$	17.0961			0.566420			0.283210	−	0.959058i	$-0.408601\pi$
$911$	17.0961			0.566420			0.283210	+	0.959058i	$0.408601\pi$
$912$	−11.1923	−	13.3691i	−0.370615	−	0.442694i
$913$	−0.941910			−0.0311727
$914$	12.4030	−	3.26078i	0.410256	−	0.107857i
$915$	0.0770772	−	0.0646754i	0.00254809	−	0.00213810i
$916$	−32.8237	+	18.5402i	−1.08452	+	0.612587i
$917$	−18.0667	−	6.57573i	−0.596614	−	0.217150i
$918$	−1.80261	+	2.54873i	−0.0594949	+	0.0841206i
$919$	38.4585	+	22.2040i	1.26863	+	0.732444i	0.974729	−	0.223392i	$-0.0717130\pi$
$919$	38.4585	+	22.2040i	1.26863	+	0.732444i	0.293901	+	0.955836i	$0.405046\pi$
$920$	−0.432433	−	0.444843i	−0.0142569	−	0.0146660i
$921$	1.90005	−	10.7757i	0.0626089	−	0.355073i
$922$	−10.0394	−	0.926056i	−0.330630	−	0.0304980i
$923$	−44.6926	+	25.8033i	−1.47108	+	0.849326i
$924$	−4.09308	+	10.9240i	−0.134653	+	0.359373i
$925$	15.0604	−	17.9483i	0.495183	−	0.590136i
$926$	10.0032	+	2.73097i	0.328726	+	0.0897454i
$927$	4.88043	−	1.77633i	0.160294	−	0.0583424i
$928$	−16.0921	+	32.4874i	−0.528250	+	1.06645i
$929$	−4.11156	−	23.3178i	−0.134896	−	0.765032i	−0.974932	−	0.222502i	$-0.928578\pi$
$929$	−4.11156	−	23.3178i	−0.134896	−	0.765032i	0.840036	−	0.542530i	$-0.182534\pi$
$930$	−0.0150291	−	0.181645i	−0.000492825	−	0.00595636i
$931$	16.8233	+	9.31913i	0.551361	+	0.305422i
$932$	−35.6013	+	5.93185i	−1.16616	+	0.194304i
$933$	6.14498	−	1.08353i	0.201178	−	0.0354730i
$934$	29.5957	−	29.3179i	0.968402	−	0.959312i
$935$	0.113263	+	0.311187i	0.00370409	+	0.0101769i
$936$	10.3502	+	1.05326i	0.338308	+	0.0344267i
$937$	10.7950	+	9.05805i	0.352656	+	0.295913i	0.801856	−	0.597518i	$-0.203846\pi$
$937$	10.7950	+	9.05805i	0.352656	+	0.295913i	−0.449200	+	0.893431i	$0.648291\pi$
$938$	−14.0156	+	29.6903i	−0.457626	+	0.969421i
$939$	3.04412	+	5.27256i	0.0993410	+	0.172064i
$940$	0.147163	+	0.00138787i	0.00479991	+	4.52673e-5i
$941$	21.5103	+	3.79285i	0.701216	+	0.123643i	0.512879	−	0.858461i	$-0.328579\pi$
$941$	21.5103	+	3.79285i	0.701216	+	0.123643i	0.188338	+	0.982104i	$0.439690\pi$
$942$	−24.6958	+	17.1192i	−0.804633	+	0.557774i
$943$	4.73059	−	8.19362i	0.154049	−	0.266821i
$944$	−53.7728	−	20.7284i	−1.75016	−	0.674651i
$945$	−0.0227650	+	0.0625463i	−0.000740546	+	0.00203463i
$946$	9.26491	+	20.1158i	0.301228	+	0.654020i
$947$	15.6123	+	18.6060i	0.507332	+	0.604615i	0.957537	−	0.288311i	$-0.0930935\pi$
$947$	15.6123	+	18.6060i	0.507332	+	0.604615i	−0.450205	+	0.892925i	$0.648649\pi$
$948$	−2.37917	−	6.73363i	−0.0772718	−	0.218698i
$949$			29.2537i			0.949614i
$950$	30.6567	−	3.08475i	0.994635	−	0.100082i
$951$			26.3032i			0.852939i
$952$	4.11555	+	9.16200i	0.133386	+	0.296942i
$953$	11.2927	+	13.4581i	0.365807	+	0.435951i	0.917281	−	0.398240i	$-0.130379\pi$
$953$	11.2927	+	13.4581i	0.365807	+	0.435951i	−0.551474	+	0.834192i	$0.685935\pi$
$954$	2.41011	−	1.11005i	0.0780302	−	0.0359391i
$955$	−0.0669367	+	0.183907i	−0.00216602	+	0.00595109i
$956$	13.8628	−	23.4966i	0.448357	−	0.759935i
$957$	11.6188	−	20.1244i	0.375584	−	0.650530i
$958$	25.8482	+	37.2880i	0.835116	+	1.20472i
$959$	27.1276	+	4.78332i	0.875995	+	0.154462i
$960$	0.104366	+	0.314120i	0.00336840	+	0.0101382i
$961$	10.6487	+	18.4440i	0.343506	+	0.594969i
$962$	−22.0506	−	10.4092i	−0.710939	−	0.335607i
$963$	0.156113	+	0.130994i	0.00503068	+	0.00422124i
$964$	−10.1787	+	54.7046i	−0.327835	+	1.76192i
$965$	−0.0793696	−	0.218066i	−0.00255500	−	0.00701980i
$966$	8.48771	+	8.56813i	0.273088	+	0.275675i
$967$	−36.7741	+	6.48427i	−1.18258	+	0.208520i	−0.730153	−	0.683283i	$-0.760551\pi$
$967$	−36.7741	+	6.48427i	−1.18258	+	0.208520i	−0.452423	+	0.891803i	$0.649440\pi$
$968$	−1.48829	−	5.88621i	−0.0478356	−	0.189190i
$969$	9.50388	+	1.50254i	0.305309	+	0.0482685i
$970$	0.840532	−	0.0695449i	0.0269878	−	0.00223295i
$971$	−4.22797	−	23.9780i	−0.135682	−	0.769490i	−0.974382	−	0.224897i	$-0.927795\pi$
$971$	−4.22797	−	23.9780i	−0.135682	−	0.769490i	0.838701	−	0.544593i	$-0.183316\pi$
$972$	1.29997	−	1.51990i	0.0416964	−	0.0487507i
$973$	18.4900	−	6.72983i	0.592764	−	0.215748i
$974$	−3.52552	+	12.9135i	−0.112965	+	0.413777i
$975$	−11.8177	+	14.0837i	−0.378468	+	0.451040i
$976$	−1.86948	+	9.54587i	−0.0598406	+	0.305556i
$977$	25.8542	−	14.9269i	0.827149	−	0.477555i	−0.0257262	−	0.999669i	$-0.508190\pi$
$977$	25.8542	−	14.9269i	0.827149	−	0.477555i	0.852876	+	0.522114i	$0.174856\pi$
$978$	−2.80345	+	30.3923i	−0.0896443	+	0.971838i
$979$	4.67871	−	26.5343i	0.149532	−	0.848039i
$980$	−0.232039	−	0.281890i	−0.00741220	−	0.00900463i
$981$	1.38031	+	0.796924i	0.0440700	+	0.0254438i
$982$	−22.4619	−	15.8864i	−0.716788	−	0.506954i
$983$	−34.4009	−	12.5209i	−1.09722	−	0.399355i	−0.270928	−	0.962600i	$-0.587331\pi$
$983$	−34.4009	−	12.5209i	−1.09722	−	0.399355i	−0.826290	+	0.563245i	$0.809553\pi$
$984$	−4.17557	+	2.83660i	−0.133112	+	0.0904275i
$985$	−0.762766	+	0.640036i	−0.0243037	+	0.0203933i
$986$	−5.08706	−	19.3497i	−0.162005	−	0.616219i
$987$	−2.86098			−0.0910660
$988$	−11.2171	−	30.0404i	−0.356865	−	0.955712i
$989$	22.8963			0.728061
$990$	−0.0539444	−	0.205188i	−0.00171446	−	0.00652131i
$991$	4.65674	−	3.90746i	0.147926	−	0.124125i	−0.565821	−	0.824528i	$-0.691441\pi$
$991$	4.65674	−	3.90746i	0.147926	−	0.124125i	0.713748	+	0.700403i	$0.246996\pi$
$992$	12.1624	+	12.7499i	0.386158	+	0.404810i
$993$	−26.6630	−	9.70454i	−0.846125	−	0.307964i
$994$	26.0599	+	18.4311i	0.826571	+	0.584599i
$995$	−0.836452	−	0.482926i	−0.0265173	−	0.0153098i
$996$	0.401135	−	0.330197i	0.0127105	−	0.0104627i
$997$	−0.254414	+	1.44285i	−0.00805737	+	0.0456956i	−0.988571	−	0.150754i	$-0.951830\pi$
$997$	−0.254414	+	1.44285i	−0.00805737	+	0.0456956i	0.980514	+	0.196449i	$0.0629411\pi$
$998$	−1.08157	+	11.7253i	−0.0342363	+	0.371158i
$999$	−4.05955	+	2.34378i	−0.128439	+	0.0741541i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	228.2.w.a.67.10	✓	60
3.2	odd	2		684.2.cf.c.523.1		60
4.3	odd	2		228.2.w.b.67.10	yes	60
12.11	even	2		684.2.cf.b.523.1		60
19.2	odd	18		228.2.w.b.211.10	yes	60
57.2	even	18		684.2.cf.b.667.1		60
76.59	even	18	inner	228.2.w.a.211.10	yes	60
228.59	odd	18		684.2.cf.c.667.1		60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
228.2.w.a.67.10	✓	60	1.1	even	1	trivial
228.2.w.a.211.10	yes	60	76.59	even	18	inner
228.2.w.b.67.10	yes	60	4.3	odd	2
228.2.w.b.211.10	yes	60	19.2	odd	18
684.2.cf.b.523.1		60	12.11	even	2
684.2.cf.b.667.1		60	57.2	even	18
684.2.cf.c.523.1		60	3.2	odd	2
684.2.cf.c.667.1		60	228.59	odd	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 228 = 2^{2} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	228.w (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.36774 - 0.359580i) q^{2} +(-0.766044 + 0.642788i) q^{3} +(1.74140 - 0.983622i) q^{4} +(0.0388803 + 0.0141513i) q^{5} +(-0.816613 + 1.15462i) q^{6} +(1.39317 + 0.804345i) q^{7} +(2.02809 - 1.97151i) q^{8} +(0.173648 - 0.984808i) q^{9} +(0.0582665 + 0.00537462i) q^{10} +(3.14005 - 1.81291i) q^{11} +(-0.701733 + 1.87285i) q^{12} +(-2.36434 + 2.81771i) q^{13} +(2.19471 + 0.599176i) q^{14} +(-0.0388803 + 0.0141513i) q^{15} +(2.06498 - 3.42577i) q^{16} +(0.383315 + 2.17389i) q^{17} +(-0.116612 - 1.40940i) q^{18} +(-3.73568 + 2.24605i) q^{19} +(0.0816258 - 0.0136004i) q^{20} +(-1.58425 + 0.279346i) q^{21} +(3.64288 - 3.60868i) q^{22} +(-1.81312 - 4.98152i) q^{23} +(-0.286346 + 2.81390i) q^{24} +(-3.82891 - 3.21284i) q^{25} +(-2.22060 + 4.70406i) q^{26} +(0.500000 + 0.866025i) q^{27} +(3.21724 + 0.0303413i) q^{28} +(-6.31157 - 1.11290i) q^{29} +(-0.0480895 + 0.0333358i) q^{30} +(-1.55745 + 2.69759i) q^{31} +(1.59251 - 5.42807i) q^{32} +(-1.24010 + 3.40716i) q^{33} +(1.30596 + 2.83547i) q^{34} +(0.0427842 + 0.0509882i) q^{35} +(-0.666286 - 1.88575i) q^{36} +4.68757i q^{37} +(-4.30179 + 4.41527i) q^{38} -3.67826i q^{39} +(0.106752 - 0.0479528i) q^{40} +(1.14719 + 1.36717i) q^{41} +(-2.06639 + 0.951736i) q^{42} +(-1.47721 + 4.05860i) q^{43} +(3.68488 - 6.24563i) q^{44} +(0.0206878 - 0.0358323i) q^{45} +(-4.27113 - 6.16144i) q^{46} +(1.75144 + 0.308825i) q^{47} +(0.620175 + 3.95163i) q^{48} +(-2.20606 - 3.82101i) q^{49} +(-6.39221 - 3.01751i) q^{50} +(-1.69098 - 1.41890i) q^{51} +(-1.34571 + 7.23239i) q^{52} +(0.641725 + 1.76312i) q^{53} +(0.995274 + 1.00470i) q^{54} +(0.147741 - 0.0260508i) q^{55} +(4.41124 - 1.11536i) q^{56} +(1.41796 - 4.12182i) q^{57} +(-9.03275 + 0.747362i) q^{58} +(-2.50182 - 14.1885i) q^{59} +(-0.0537868 + 0.0628866i) q^{60} +(-2.28515 + 0.831725i) q^{61} +(-1.16019 + 4.24962i) q^{62} +(1.03405 - 1.23233i) q^{63} +(0.226303 - 7.99680i) q^{64} +(-0.131801 + 0.0760951i) q^{65} +(-0.470989 + 5.10601i) q^{66} +(-2.50601 + 14.2123i) q^{67} +(2.80579 + 3.40858i) q^{68} +(4.59099 + 2.65061i) q^{69} +(0.0768519 + 0.0543541i) q^{70} +(13.1840 + 4.79860i) q^{71} +(-1.58938 - 2.33963i) q^{72} +(6.09245 - 5.11217i) q^{73} +(1.68556 + 6.41136i) q^{74} +4.99829 q^{75} +(-4.29606 + 7.58577i) q^{76} +5.83282 q^{77} +(-1.32263 - 5.03089i) q^{78} +(-2.73538 + 2.29526i) q^{79} +(0.128766 - 0.103973i) q^{80} +(-0.939693 - 0.342020i) q^{81} +(2.06067 + 1.45742i) q^{82} +(-0.224975 - 0.129889i) q^{83} +(-2.48405 + 2.04476i) q^{84} +(-0.0158599 + 0.0899457i) q^{85} +(-0.561041 + 6.08227i) q^{86} +(5.55031 - 3.20447i) q^{87} +(2.79414 - 9.86739i) q^{88} +(4.77657 - 5.69250i) q^{89} +(0.0154108 - 0.0564480i) q^{90} +(-5.56033 + 2.02379i) q^{91} +(-8.05731 - 6.89141i) q^{92} +(-0.540898 - 3.06759i) q^{93} +(2.50655 - 0.207390i) q^{94} +(-0.177029 + 0.0344624i) q^{95} +(2.26916 + 5.18178i) q^{96} +(14.1948 - 2.50292i) q^{97} +(-4.39127 - 4.43287i) q^{98} +(-1.24010 - 3.40716i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 3 q^{2} - 3 q^{4} + 3 q^{6} + 3 q^{8} - 6 q^{10} - 6 q^{13} - 9 q^{14} - 27 q^{16} - 18 q^{19} + 30 q^{20} - 6 q^{21} + 12 q^{22} + 18 q^{24} + 30 q^{27} - 18 q^{28} + 12 q^{31} - 63 q^{32} - 39 q^{34}+ \cdots + 117 q^{98}+O(q^{100}) \) 60 * q - 3 * q^2 - 3 * q^4 + 3 * q^6 + 3 * q^8 - 6 * q^10 - 6 * q^13 - 9 * q^14 - 27 * q^16 - 18 * q^19 + 30 * q^20 - 6 * q^21 + 12 * q^22 + 18 * q^24 + 30 * q^27 - 18 * q^28 + 12 * q^31 - 63 * q^32 - 39 * q^34 - 3 * q^36 - 48 * q^38 + 33 * q^40 - 12 * q^41 - 9 * q^42 + 18 * q^43 - 9 * q^44 - 69 * q^46 + 6 * q^48 + 30 * q^49 - 27 * q^50 - 3 * q^52 + 12 * q^53 + 3 * q^54 - 42 * q^56 - 36 * q^58 - 3 * q^60 + 27 * q^62 + 12 * q^63 + 21 * q^64 - 36 * q^65 + 24 * q^66 - 42 * q^67 + 93 * q^68 - 72 * q^69 + 132 * q^70 - 24 * q^71 + 18 * q^72 + 18 * q^73 + 27 * q^74 - 60 * q^75 + 66 * q^76 - 72 * q^77 - 33 * q^78 - 12 * q^79 + 6 * q^80 - 9 * q^82 + 69 * q^84 - 60 * q^85 + 123 * q^86 + 36 * q^88 - 12 * q^89 + 15 * q^90 + 84 * q^91 - 99 * q^92 - 12 * q^93 + 24 * q^95 + 12 * q^97 + 117 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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