LMFDB - Embedded newform 135.2.p.a.124.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [135,2,Mod(4,135)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(135, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([2, 9]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("135.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.07798042729$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$16$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			124.8
Character	$\chi$	$=$	135.124
Dual form			135.2.p.a.49.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.133405 + 0.158986i) q^{2} +(-1.17329 - 1.27412i) q^{3} +(0.339817 + 1.92720i) q^{4} +(-0.452543 + 2.18980i) q^{5} +(0.359090 - 0.0165625i) q^{6} +(2.83580 + 0.500029i) q^{7} +(-0.711201 - 0.410612i) q^{8} +(-0.246774 + 2.98983i) q^{9} +O(q^{10})$	\(q+(-0.133405 + 0.158986i) q^{2} +(-1.17329 - 1.27412i) q^{3} +(0.339817 + 1.92720i) q^{4} +(-0.452543 + 2.18980i) q^{5} +(0.359090 - 0.0165625i) q^{6} +(2.83580 + 0.500029i) q^{7} +(-0.711201 - 0.410612i) q^{8} +(-0.246774 + 2.98983i) q^{9} +(-0.287775 - 0.364077i) q^{10} +(1.38169 - 0.502894i) q^{11} +(2.05678 - 2.69413i) q^{12} +(1.55650 + 1.85496i) q^{13} +(-0.457807 + 0.384146i) q^{14} +(3.32103 - 1.99267i) q^{15} +(-3.51766 + 1.28032i) q^{16} +(-1.21975 + 0.704220i) q^{17} +(-0.442420 - 0.438091i) q^{18} +(2.34516 - 4.06194i) q^{19} +(-4.37395 - 0.128009i) q^{20} +(-2.69013 - 4.19984i) q^{21} +(-0.104371 + 0.286757i) q^{22} +(-2.36796 + 0.417535i) q^{23} +(0.311276 + 1.38792i) q^{24} +(-4.59041 - 1.98195i) q^{25} -0.502557 q^{26} +(4.09895 - 3.19353i) q^{27} +5.63507i q^{28} +(-6.73596 - 5.65214i) q^{29} +(-0.126235 + 0.793828i) q^{30} +(1.00865 + 5.72033i) q^{31} +(0.827470 - 2.27346i) q^{32} +(-2.26187 - 1.17040i) q^{33} +(0.0507589 - 0.287868i) q^{34} +(-2.37828 + 5.98355i) q^{35} +(-5.84585 + 0.540413i) q^{36} +(7.57034 - 4.37074i) q^{37} +(0.332934 + 0.914728i) q^{38} +(0.537223 - 4.15958i) q^{39} +(1.22101 - 1.37157i) q^{40} +(8.32538 - 6.98582i) q^{41} +(1.02659 + 0.132587i) q^{42} +(-2.63439 - 7.23793i) q^{43} +(1.43870 + 2.49190i) q^{44} +(-6.43545 - 1.89341i) q^{45} +(0.249515 - 0.432172i) q^{46} +(6.68918 + 1.17948i) q^{47} +(5.75853 + 2.97974i) q^{48} +(1.21391 + 0.441827i) q^{49} +(0.927484 - 0.465407i) q^{50} +(2.32838 + 0.727849i) q^{51} +(-3.04596 + 3.63003i) q^{52} +5.43934i q^{53} +(-0.0390949 + 1.07771i) q^{54} +(0.475961 + 3.25320i) q^{55} +(-1.81151 - 1.52004i) q^{56} +(-7.92696 + 1.77782i) q^{57} +(1.79722 - 0.316898i) q^{58} +(6.83272 + 2.48691i) q^{59} +(4.96882 + 5.72314i) q^{60} +(-1.03952 + 5.89541i) q^{61} +(-1.04401 - 0.602759i) q^{62} +(-2.19481 + 8.35519i) q^{63} +(-3.49236 - 6.04894i) q^{64} +(-4.76637 + 2.56897i) q^{65} +(0.487821 - 0.203468i) q^{66} +(-4.95280 - 5.90251i) q^{67} +(-1.77166 - 2.11138i) q^{68} +(3.31030 + 2.52718i) q^{69} +(-0.634024 - 1.17635i) q^{70} +(4.51802 + 7.82544i) q^{71} +(1.40317 - 2.02504i) q^{72} +(-10.8910 - 6.28791i) q^{73} +(-0.315035 + 1.78665i) q^{74} +(2.86064 + 8.17415i) q^{75} +(8.62507 + 3.13927i) q^{76} +(4.16966 - 0.735224i) q^{77} +(0.589646 + 0.640319i) q^{78} +(-1.14861 - 0.963795i) q^{79} +(-1.21176 - 8.28236i) q^{80} +(-8.87821 - 1.47563i) q^{81} +2.25556i q^{82} +(7.46590 - 8.89751i) q^{83} +(7.17977 - 6.61158i) q^{84} +(-0.990112 - 2.98968i) q^{85} +(1.50217 + 0.546744i) q^{86} +(0.701727 + 15.2140i) q^{87} +(-1.18915 - 0.209680i) q^{88} +(-5.96766 + 10.3363i) q^{89} +(1.15954 - 0.770553i) q^{90} +(3.48639 + 6.03861i) q^{91} +(-1.60934 - 4.42164i) q^{92} +(6.10496 - 7.99676i) q^{93} +(-1.07989 + 0.906134i) q^{94} +(7.83353 + 6.97362i) q^{95} +(-3.86752 + 1.61313i) q^{96} +(1.92260 + 5.28231i) q^{97} +(-0.232185 + 0.134052i) q^{98} +(1.16260 + 4.25512i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 12 q^{4} - 9 q^{5} - 6 q^{6} - 18 q^{9}+O(q^{10}) $ 96 * q - 12 * q^4 - 9 * q^5 - 6 * q^6 - 18 * q^9	$ 96 q - 12 q^{4} - 9 q^{5} - 6 q^{6} - 18 q^{9} - 3 q^{10} - 6 q^{11} - 18 q^{14} - 21 q^{15} - 24 q^{16} - 6 q^{19} - 57 q^{20} + 24 q^{21} - 30 q^{24} + 3 q^{25} + 48 q^{26} - 30 q^{29} - 51 q^{30} - 30 q^{31} - 24 q^{34} - 12 q^{35} + 54 q^{36} - 6 q^{39} - 9 q^{40} - 12 q^{41} + 78 q^{44} + 45 q^{45} - 6 q^{46} - 30 q^{49} + 84 q^{50} - 90 q^{51} + 108 q^{54} - 12 q^{55} - 96 q^{56} + 66 q^{59} + 84 q^{60} + 6 q^{61} + 45 q^{65} - 150 q^{66} + 24 q^{69} - 33 q^{70} - 90 q^{71} + 66 q^{74} + 39 q^{75} + 12 q^{76} + 24 q^{79} + 30 q^{80} - 54 q^{81} + 198 q^{84} - 21 q^{85} + 18 q^{86} + 96 q^{89} + 90 q^{90} - 6 q^{91} + 24 q^{94} + 87 q^{95} + 42 q^{96} + 36 q^{99}+O(q^{100}) $ 96 * q - 12 * q^4 - 9 * q^5 - 6 * q^6 - 18 * q^9 - 3 * q^10 - 6 * q^11 - 18 * q^14 - 21 * q^15 - 24 * q^16 - 6 * q^19 - 57 * q^20 + 24 * q^21 - 30 * q^24 + 3 * q^25 + 48 * q^26 - 30 * q^29 - 51 * q^30 - 30 * q^31 - 24 * q^34 - 12 * q^35 + 54 * q^36 - 6 * q^39 - 9 * q^40 - 12 * q^41 + 78 * q^44 + 45 * q^45 - 6 * q^46 - 30 * q^49 + 84 * q^50 - 90 * q^51 + 108 * q^54 - 12 * q^55 - 96 * q^56 + 66 * q^59 + 84 * q^60 + 6 * q^61 + 45 * q^65 - 150 * q^66 + 24 * q^69 - 33 * q^70 - 90 * q^71 + 66 * q^74 + 39 * q^75 + 12 * q^76 + 24 * q^79 + 30 * q^80 - 54 * q^81 + 198 * q^84 - 21 * q^85 + 18 * q^86 + 96 * q^89 + 90 * q^90 - 6 * q^91 + 24 * q^94 + 87 * q^95 + 42 * q^96 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{2}{9}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.133405	+	0.158986i	−0.0943314	+	0.112420i	−0.811145	−	0.584845i	$-0.801155\pi$
$2$	−0.133405	+	0.158986i	−0.0943314	+	0.112420i	0.716814	+	0.697265i	$0.245600\pi$
$3$	−1.17329	−	1.27412i	−0.677400	−	0.735615i
$3$	−1.17329	−	1.27412i	−0.677400	−	0.735615i
$4$	0.339817	+	1.92720i	0.169908	+	0.963598i
$5$	−0.452543	+	2.18980i	−0.202383	+	0.979306i
$5$	−0.452543	+	2.18980i	−0.202383	+	0.979306i
$6$	0.359090	−	0.0165625i	0.146598	−	0.00676162i
$7$	2.83580	+	0.500029i	1.07183	+	0.188993i	0.681602	−	0.731724i	$-0.261284\pi$
$7$	2.83580	+	0.500029i	1.07183	+	0.188993i	0.390232	+	0.920717i	$0.372395\pi$
$8$	−0.711201	−	0.410612i	−0.251448	−	0.145173i
$9$	−0.246774	+	2.98983i	−0.0822580	+	0.996611i
$10$	−0.287775	−	0.364077i	−0.0910023	−	0.115131i
$11$	1.38169	−	0.502894i	0.416595	−	0.151628i	−0.125214	−	0.992130i	$-0.539962\pi$
$11$	1.38169	−	0.502894i	0.416595	−	0.151628i	0.541809	+	0.840502i	$0.317740\pi$
$12$	2.05678	−	2.69413i	0.593741	−	0.777729i
$13$	1.55650	+	1.85496i	0.431695	+	0.514474i	0.937411	−	0.348226i	$-0.113216\pi$
$13$	1.55650	+	1.85496i	0.431695	+	0.514474i	−0.505715	+	0.862700i	$0.668771\pi$
$14$	−0.457807	+	0.384146i	−0.122354	+	0.102667i
$15$	3.32103	−	1.99267i	0.857487	−	0.514506i
$16$	−3.51766	+	1.28032i	−0.879415	+	0.320081i
$17$	−1.21975	+	0.704220i	−0.295832	+	0.170799i	−0.640569	−	0.767901i	$-0.721301\pi$
$17$	−1.21975	+	0.704220i	−0.295832	+	0.170799i	0.344737	+	0.938699i	$0.387968\pi$
$18$	−0.442420	−	0.438091i	−0.104279	−	0.103259i
$19$	2.34516	−	4.06194i	0.538017	−	0.931872i	−0.460994	−	0.887403i	$-0.652507\pi$
$19$	2.34516	−	4.06194i	0.538017	−	0.931872i	0.999011	−	0.0444689i	$-0.0141595\pi$
$20$	−4.37395	−	0.128009i	−0.978045	−	0.0286237i
$21$	−2.69013	−	4.19984i	−0.587034	−	0.916480i
$22$	−0.104371	+	0.286757i	−0.0222520	+	0.0611368i
$23$	−2.36796	+	0.417535i	−0.493753	+	0.0870620i	−0.414980	−	0.909831i	$-0.636211\pi$
$23$	−2.36796	+	0.417535i	−0.493753	+	0.0870620i	−0.0787733	+	0.996893i	$0.525100\pi$
$24$	0.311276	+	1.38792i	0.0635390	+	0.283309i
$25$	−4.59041	−	1.98195i	−0.918082	−	0.396390i
$26$	−0.502557			−0.0985595
$27$	4.09895	−	3.19353i	0.788843	−	0.614594i
$28$			5.63507i			1.06493i
$29$	−6.73596	−	5.65214i	−1.25084	−	1.04958i	−0.996596	−	0.0824353i	$-0.973730\pi$
$29$	−6.73596	−	5.65214i	−1.25084	−	1.04958i	−0.254240	−	0.967141i	$-0.581825\pi$
$30$	−0.126235	+	0.793828i	−0.0230472	+	0.144933i
$31$	1.00865	+	5.72033i	0.181159	+	1.02740i	0.930792	+	0.365549i	$0.119119\pi$
$31$	1.00865	+	5.72033i	0.181159	+	1.02740i	−0.749634	+	0.661853i	$0.769770\pi$
$32$	0.827470	−	2.27346i	0.146277	−	0.401894i
$33$	−2.26187	−	1.17040i	−0.393741	−	0.203740i
$34$	0.0507589	−	0.287868i	0.00870509	−	0.0493690i
$35$	−2.37828	+	5.98355i	−0.402003	+	1.01140i
$36$	−5.84585	+	0.540413i	−0.974309	+	0.0900689i
$37$	7.57034	−	4.37074i	1.24456	−	0.718545i	0.274538	−	0.961576i	$-0.411475\pi$
$37$	7.57034	−	4.37074i	1.24456	−	0.718545i	0.970019	+	0.243031i	$0.0781417\pi$
$38$	0.332934	+	0.914728i	0.0540090	+	0.148388i
$39$	0.537223	−	4.15958i	0.0860245	−	0.666066i
$40$	1.22101	−	1.37157i	0.193058	−	0.216864i
$41$	8.32538	−	6.98582i	1.30021	−	1.09100i	0.310096	−	0.950705i	$-0.399639\pi$
$41$	8.32538	−	6.98582i	1.30021	−	1.09100i	0.990110	−	0.140297i	$-0.0448056\pi$
$42$	1.02659	+	0.132587i	0.158406	+	0.0204586i
$43$	−2.63439	−	7.23793i	−0.401741	−	1.10377i	−0.961425	−	0.275068i	$-0.911300\pi$
$43$	−2.63439	−	7.23793i	−0.401741	−	1.10377i	0.559684	−	0.828706i	$-0.310923\pi$
$44$	1.43870	+	2.49190i	0.216892	+	0.375667i
$45$	−6.43545	−	1.89341i	−0.959340	−	0.282253i
$46$	0.249515	−	0.432172i	0.0367889	−	0.0637203i
$47$	6.68918	+	1.17948i	0.975717	+	0.172045i	0.638702	−	0.769454i	$-0.279472\pi$
$47$	6.68918	+	1.17948i	0.975717	+	0.172045i	0.337015	+	0.941499i	$0.390583\pi$
$48$	5.75853	+	2.97974i	0.831172	+	0.430088i
$49$	1.21391	+	0.441827i	0.173416	+	0.0631181i
$50$	0.927484	−	0.465407i	0.131166	−	0.0658185i
$51$	2.32838	+	0.727849i	0.326038	+	0.101919i
$52$	−3.04596	+	3.63003i	−0.422398	+	0.503394i
$53$			5.43934i			0.747151i	0.927600	+	0.373575i	$0.121868\pi$
$53$			5.43934i			0.747151i	−0.927600	+	0.373575i	$0.878132\pi$
$54$	−0.0390949	+	1.07771i	−0.00532014	+	0.146657i
$55$	0.475961	+	3.25320i	0.0641786	+	0.438661i
$56$	−1.81151	−	1.52004i	−0.242073	−	0.203123i
$57$	−7.92696	+	1.77782i	−1.04995	+	0.235477i
$58$	1.79722	−	0.316898i	0.235986	−	0.0416108i
$59$	6.83272	+	2.48691i	0.889545	+	0.323768i	0.746055	−	0.665884i	$-0.231945\pi$
$59$	6.83272	+	2.48691i	0.889545	+	0.323768i	0.143489	+	0.989652i	$0.454168\pi$
$60$	4.96882	+	5.72314i	0.641472	+	0.738854i
$61$	−1.03952	+	5.89541i	−0.133097	+	0.754830i	0.843069	+	0.537805i	$0.180746\pi$
$61$	−1.03952	+	5.89541i	−0.133097	+	0.754830i	−0.976166	+	0.217025i	$0.930365\pi$
$62$	−1.04401	−	0.602759i	−0.132589	−	0.0765504i
$63$	−2.19481	+	8.35519i	−0.276520	+	1.05265i
$64$	−3.49236	−	6.04894i	−0.436545	−	0.756118i
$65$	−4.76637	+	2.56897i	−0.591196	+	0.318641i
$66$	0.487821	−	0.203468i	0.0600466	−	0.0250452i
$67$	−4.95280	−	5.90251i	−0.605081	−	0.721107i	0.373348	−	0.927691i	$-0.378210\pi$
$67$	−4.95280	−	5.90251i	−0.605081	−	0.721107i	−0.978429	+	0.206584i	$0.933765\pi$
$68$	−1.77166	−	2.11138i	−0.214845	−	0.256043i
$69$	3.31030	+	2.52718i	0.398513	+	0.304236i
$70$	−0.634024	−	1.17635i	−0.0757803	−	0.140600i
$71$	4.51802	+	7.82544i	0.536190	+	0.928708i	0.999105	+	0.0423056i	$0.0134703\pi$
$71$	4.51802	+	7.82544i	0.536190	+	0.928708i	−0.462915	+	0.886403i	$0.653196\pi$
$72$	1.40317	−	2.02504i	0.165365	−	0.238654i
$73$	−10.8910	−	6.28791i	−1.27469	−	0.735944i	−0.298825	−	0.954308i	$-0.596595\pi$
$73$	−10.8910	−	6.28791i	−1.27469	−	0.735944i	−0.975867	+	0.218364i	$0.929928\pi$
$74$	−0.315035	+	1.78665i	−0.0366221	+	0.207694i
$75$	2.86064	+	8.17415i	0.330318	+	0.943870i
$76$	8.62507	+	3.13927i	0.989364	+	0.360099i
$77$	4.16966	−	0.735224i	0.475177	−	0.0837865i
$78$	0.589646	+	0.640319i	0.0667642	+	0.0725018i
$79$	−1.14861	−	0.963795i	−0.129228	−	0.108435i	0.575883	−	0.817532i	$-0.304658\pi$
$79$	−1.14861	−	0.963795i	−0.129228	−	0.108435i	−0.705111	+	0.709097i	$0.749103\pi$
$80$	−1.21176	−	8.28236i	−0.135478	−	0.925996i
$81$	−8.87821	−	1.47563i	−0.986467	−	0.163958i
$82$			2.25556i			0.249085i
$83$	7.46590	−	8.89751i	0.819489	−	0.976629i	−0.180487	−	0.983577i	$-0.557767\pi$
$83$	7.46590	−	8.89751i	0.819489	−	0.976629i	0.999976	+	0.00694857i	$0.00221182\pi$
$84$	7.17977	−	6.61158i	0.783377	−	0.721383i
$85$	−0.990112	−	2.98968i	−0.107393	−	0.324277i
$86$	1.50217	+	0.546744i	0.161983	+	0.0589569i
$87$	0.701727	+	15.2140i	0.0752330	+	1.63112i
$88$	−1.18915	−	0.209680i	−0.126764	−	0.0223519i
$89$	−5.96766	+	10.3363i	−0.632571	+	1.09564i	0.354454	+	0.935074i	$0.384667\pi$
$89$	−5.96766	+	10.3363i	−0.632571	+	1.09564i	−0.987024	+	0.160571i	$0.948666\pi$
$90$	1.15954	−	0.770553i	0.122227	−	0.0812235i
$91$	3.48639	+	6.03861i	0.365473	+	0.633018i
$92$	−1.60934	−	4.42164i	−0.167786	−	0.460987i
$93$	6.10496	−	7.99676i	0.633055	−	0.829225i
$94$	−1.07989	+	0.906134i	−0.111382	+	0.0934606i
$95$	7.83353	+	6.97362i	0.803703	+	0.715478i
$96$	−3.86752	+	1.61313i	−0.394727	+	0.164639i
$97$	1.92260	+	5.28231i	0.195211	+	0.536337i	0.998221	−	0.0596285i	$-0.0189916\pi$
$97$	1.92260	+	5.28231i	0.195211	+	0.536337i	−0.803010	+	0.595966i	$0.796769\pi$
$98$	−0.232185	+	0.134052i	−0.0234543	+	0.0135413i
$99$	1.16260	+	4.25512i	0.116846	+	0.427656i
$100$	2.25971	−	9.52012i	0.225971	−	0.952012i
$101$	1.86284	−	10.5647i	0.185360	−	1.05123i	−0.740133	−	0.672461i	$-0.765237\pi$
$101$	1.86284	−	10.5647i	0.185360	−	1.05123i	0.925492	−	0.378766i	$-0.123652\pi$
$102$	−0.426334	+	0.273080i	−0.0422134	+	0.0270390i
$103$	0.183395	−	0.503873i	0.0180704	−	0.0496480i	−0.930329	−	0.366725i	$-0.880479\pi$
$103$	0.183395	−	0.503873i	0.0180704	−	0.0496480i	0.948400	+	0.317077i	$0.102701\pi$
$104$	−0.345313	−	1.95837i	−0.0338608	−	0.192034i
$105$	10.4142	−	3.99022i	1.01632	−	0.389406i
$106$	−0.864777	−	0.725634i	−0.0839945	−	0.0704798i
$107$		−	2.82482i		−	0.273086i	−0.990634	−	0.136543i	$-0.956401\pi$
$107$		−	2.82482i		−	0.273086i	0.990634	−	0.136543i	$-0.0435992\pi$
$108$	7.54744	+	6.81427i	0.726253	+	0.655703i
$109$	−0.479801			−0.0459566			−0.0229783	−	0.999736i	$-0.507315\pi$
$109$	−0.479801			−0.0459566			−0.0229783	+	0.999736i	$0.507315\pi$
$110$	−0.580707	−	0.358321i	−0.0553682	−	0.0341646i
$111$	−14.4511	−	4.51739i	−1.37164	−	0.428772i
$112$	−10.6156	+	1.87182i	−1.00308	+	0.176870i
$113$	1.45557	−	3.99915i	0.136928	−	0.376208i	−0.852209	−	0.523202i	$-0.824737\pi$
$113$	1.45557	−	3.99915i	0.136928	−	0.376208i	0.989137	+	0.146994i	$0.0469597\pi$
$114$	0.774847	−	1.49744i	0.0725711	−	0.140248i
$115$	0.157286	−	5.37430i	0.0146670	−	0.501156i
$116$	8.60380	−	14.9022i	0.798843	−	1.38364i
$117$	−5.93014	+	4.19592i	−0.548241	+	0.387913i
$118$	−1.30690	+	0.754539i	−0.120310	+	0.0694609i
$119$	−3.81109	+	1.38712i	−0.349362	+	0.127157i
$120$	−3.18014	+	0.0535364i	−0.290305	+	0.00488718i
$121$	−6.77033	+	5.68098i	−0.615484	+	0.516453i
$122$	−0.798608	−	0.951744i	−0.0723026	−	0.0861669i
$123$	−18.6689	−	2.41114i	−1.68332	−	0.217405i
$124$	−10.6814	+	3.88773i	−0.959222	+	0.349128i
$125$	6.41742	−	9.15514i	0.573992	−	0.818861i
$126$	−1.03556	−	1.46356i	−0.0922547	−	0.130385i
$127$	−10.4667	−	6.04293i	−0.928765	−	0.536223i	−0.0423444	−	0.999103i	$-0.513483\pi$
$127$	−10.4667	−	6.04293i	−0.928765	−	0.536223i	−0.886421	+	0.462880i	$0.846816\pi$
$128$	6.19280	+	1.09196i	0.547371	+	0.0965164i
$129$	−6.13110	+	11.8487i	−0.539813	+	1.04322i
$130$	0.227428	−	1.10050i	0.0199468	−	0.0965200i
$131$	0.0451328	+	0.255961i	0.00394327	+	0.0223634i	0.986716	−	0.162455i	$-0.0519413\pi$
$131$	0.0451328	+	0.255961i	0.00394327	+	0.0223634i	−0.982773	+	0.184819i	$0.940830\pi$
$132$	1.48697	−	4.75679i	0.129424	−	0.414026i
$133$	8.68150	−	10.3462i	0.752781	−	0.897130i
$134$	1.59914			0.138145
$135$	5.13822	+	10.4211i	0.442228	+	0.896903i
$136$	1.15665			0.0991816
$137$	−12.0038	+	14.3056i	−1.02555	+	1.22221i	−0.0508517	+	0.998706i	$0.516194\pi$
$137$	−12.0038	+	14.3056i	−1.02555	+	1.22221i	−0.974703	+	0.223503i	$0.928251\pi$
$138$	−0.843394	+	0.189152i	−0.0717944	+	0.0161017i
$139$	−1.20743	−	6.84769i	−0.102413	−	0.580813i	−0.992222	−	0.124480i	$-0.960274\pi$
$139$	−1.20743	−	6.84769i	−0.102413	−	0.580813i	0.889809	−	0.456333i	$-0.150837\pi$
$140$	−12.3397	−	2.55011i	−1.04289	−	0.215524i
$141$	−6.34555	−	9.90671i	−0.534392	−	0.834295i
$142$	−1.84686	−	0.325651i	−0.154985	−	0.0273280i
$143$	3.08345	+	1.78023i	0.257851	+	0.148870i
$144$	−2.95989	−	10.8332i	−0.246657	−	0.902764i
$145$	15.4253	−	12.1925i	1.28101	−	1.01254i
$146$	2.45259	−	0.892671i	0.202978	−	0.0738780i
$147$	−0.861328	−	2.06506i	−0.0710411	−	0.170323i
$148$	10.9958	+	13.1043i	0.903850	+	1.07717i
$149$	−6.29367	+	5.28102i	−0.515598	+	0.432638i	−0.863094	−	0.505044i	$-0.831476\pi$
$149$	−6.29367	+	5.28102i	−0.515598	+	0.432638i	0.347496	+	0.937681i	$0.387032\pi$
$150$	−1.68120	−	0.635670i	−0.137269	−	0.0519022i
$151$	8.32039	−	3.02837i	0.677103	−	0.246445i	0.0195001	−	0.999810i	$-0.493793\pi$
$151$	8.32039	−	3.02837i	0.677103	−	0.246445i	0.657603	+	0.753364i	$0.271570\pi$
$152$	−3.33576	+	1.92590i	−0.270566	+	0.156211i
$153$	−1.80450	−	3.82062i	−0.145885	−	0.308879i
$154$	−0.439363	+	0.760998i	−0.0354049	+	0.0613230i
$155$	−12.9828	−	0.379958i	−1.04280	−	0.0305190i
$156$	8.19889	−	0.378162i	0.656437	−	0.0302772i
$157$	−2.12942	+	5.85053i	−0.169946	+	0.466923i	−0.995203	−	0.0978347i	$-0.968808\pi$
$157$	−2.12942	+	5.85053i	−0.169946	+	0.466923i	0.825256	+	0.564758i	$0.191031\pi$
$158$	0.306459	−	0.0540370i	0.0243806	−	0.00429895i
$159$	6.93038	−	6.38193i	0.549615	−	0.506120i
$160$	4.60394	+	2.84083i	0.363973	+	0.224587i
$161$	−6.92384			−0.545675
$162$	1.41900	−	1.21465i	0.111487	−	0.0954320i
$163$			20.6617i			1.61835i	0.587569	+	0.809174i	$0.300085\pi$
$163$			20.6617i			1.61835i	−0.587569	+	0.809174i	$0.699915\pi$
$164$	16.2922	+	13.6707i	1.27220	+	1.06751i
$165$	3.58653	−	4.42338i	0.279211	−	0.344360i
$166$	0.418590	+	2.37394i	0.0324889	+	0.184254i
$167$	−2.14444	+	5.89179i	−0.165942	+	0.455921i	−0.994594	−	0.103843i	$-0.966886\pi$
$167$	−2.14444	+	5.89179i	−0.165942	+	0.455921i	0.828652	+	0.559764i	$0.189108\pi$
$168$	0.188716	+	4.09153i	0.0145598	+	0.315668i
$169$	1.23923	−	7.02800i	0.0953251	−	0.540615i
$170$	0.607402	+	0.241424i	0.0465856	+	0.0185164i
$171$	11.5658	+	8.01402i	0.884458	+	0.612847i
$172$	13.0537	−	7.53656i	0.995336	−	0.574657i
$173$	1.35761	+	3.72999i	0.103217	+	0.283586i	0.980542	−	0.196311i	$-0.0628963\pi$
$173$	1.35761	+	3.72999i	0.103217	+	0.283586i	−0.877325	+	0.479897i	$0.840674\pi$
$174$	−2.51243	−	1.91806i	−0.190467	−	0.145408i
$175$	−12.0265	−	7.91576i	−0.909116	−	0.598376i
$176$	−4.21645	+	3.53802i	−0.317827	+	0.266688i
$177$	−4.84815	−	11.6236i	−0.364409	−	0.873682i
$178$	−0.847207	−	2.32768i	−0.0635008	−	0.174467i
$179$	−7.02005	−	12.1591i	−0.524703	−	0.908813i	−0.999586	−	0.0287637i	$-0.990843\pi$
$179$	−7.02005	−	12.1591i	−0.524703	−	0.908813i	0.474883	−	0.880049i	$-0.342490\pi$
$180$	1.46210	−	13.0458i	0.108979	−	0.972376i
$181$	−3.31514	+	5.74198i	−0.246412	+	0.426798i	−0.962528	−	0.271183i	$-0.912585\pi$
$181$	−3.31514	+	5.74198i	−0.246412	+	0.426798i	0.716116	+	0.697982i	$0.245918\pi$
$182$	−1.42515	−	0.251293i	−0.105639	−	0.0186271i
$183$	8.73113	−	5.59256i	0.645424	−	0.413414i
$184$	1.85554	+	0.675361i	0.136792	+	0.0497883i
$185$	6.14512	+	18.5555i	0.451799	+	1.36422i
$186$	0.456938	+	2.03741i	0.0335043	+	0.149390i
$187$	−1.33116	+	1.58642i	−0.0973441	+	0.116010i
$188$			13.2922i			0.969431i
$189$	13.2207	−	7.00662i	0.961663	−	0.509657i
$190$	−2.15373	+	0.315104i	−0.156248	+	0.0228600i
$191$	7.50310	+	6.29585i	0.542905	+	0.455552i	0.872530	−	0.488560i	$-0.162478\pi$
$191$	7.50310	+	6.29585i	0.542905	+	0.455552i	−0.329625	+	0.944112i	$0.606922\pi$
$192$	−3.60954	+	11.5469i	−0.260496	+	0.833323i
$193$	19.1316	−	3.37342i	1.37712	−	0.242824i	0.564414	−	0.825492i	$-0.309102\pi$
$193$	19.1316	−	3.37342i	1.37712	−	0.242824i	0.812710	+	0.582668i	$0.197991\pi$
$194$	−1.09630	−	0.399019i	−0.0787094	−	0.0286479i
$195$	8.86552	+	3.05880i	0.634873	+	0.219045i
$196$	−0.438980	+	2.48958i	−0.0313557	+	0.177827i
$197$	−5.60720	−	3.23732i	−0.399497	−	0.230649i	0.286770	−	0.957999i	$-0.407418\pi$
$197$	−5.60720	−	3.23732i	−0.399497	−	0.230649i	−0.686267	+	0.727350i	$0.740752\pi$
$198$	−0.831600	−	0.382816i	−0.0590992	−	0.0272056i
$199$	8.61414	+	14.9201i	0.610640	+	1.05766i	0.991133	+	0.132875i	$0.0424210\pi$
$199$	8.61414	+	14.9201i	0.610640	+	1.05766i	−0.380493	+	0.924784i	$0.624246\pi$
$200$	2.45089	+	3.29444i	0.173304	+	0.232952i
$201$	−1.70945	+	13.2358i	−0.120575	+	0.933584i
$202$	1.43112	+	1.70555i	0.100693	+	0.120002i
$203$	−16.2756	−	19.3965i	−1.14233	−	1.36137i
$204$	−0.611485	+	4.73458i	−0.0428125	+	0.331487i
$205$	11.5299	+	21.3923i	0.805286	+	1.49410i
$206$	0.0556428	+	0.0963761i	0.00387681	+	0.00671484i
$207$	−0.664009	−	7.18284i	−0.0461518	−	0.499242i
$208$	−7.85019	−	4.53231i	−0.544313	−	0.314259i
$209$	1.19756	−	6.79170i	0.0828369	−	0.469792i
$210$	−0.754914	+	2.18802i	−0.0520940	+	0.150988i
$211$	−18.9632	−	6.90203i	−1.30548	−	0.475156i	−0.406702	−	0.913561i	$-0.633321\pi$
$211$	−18.9632	−	6.90203i	−1.30548	−	0.475156i	−0.898777	+	0.438405i	$0.855543\pi$
$212$	−10.4827	+	1.84838i	−0.719953	+	0.126947i
$213$	4.66961	−	14.9380i	0.319956	−	1.02354i
$214$	0.449106	+	0.376845i	0.0307003	+	0.0257606i
$215$	17.0418	−	2.49331i	1.16224	−	0.170042i
$216$	−4.22648	+	0.588160i	−0.287575	+	0.0400192i
$217$			16.7261i			1.13544i
$218$	0.0640078	−	0.0762815i	0.00433515	−	0.00516644i
$219$	4.76673	+	21.2540i	0.322105	+	1.43621i
$220$	−6.10781	+	2.02276i	−0.411789	+	0.136375i
$221$	−3.20484	−	1.16647i	−0.215581	−	0.0784649i
$222$	2.64604	−	1.69487i	0.177591	−	0.113752i
$223$	−9.20020	−	1.62224i	−0.616091	−	0.108633i	−0.143111	−	0.989707i	$-0.545711\pi$
$223$	−9.20020	−	1.62224i	−0.616091	−	0.108633i	−0.472980	+	0.881073i	$0.656822\pi$
$224$	3.48334	−	6.03332i	0.232740	−	0.403118i
$225$	7.05850	−	13.2355i	0.470567	−	0.882365i
$226$	0.441627	+	0.764920i	0.0293766	+	0.0508817i
$227$	−2.68962	−	7.38967i	−0.178516	−	0.490470i	0.817870	−	0.575403i	$-0.195155\pi$
$227$	−2.68962	−	7.38967i	−0.178516	−	0.490470i	−0.996387	+	0.0849329i	$0.972932\pi$
$228$	−6.11991	−	14.6727i	−0.405301	−	0.971722i
$229$	12.7733	−	10.7181i	0.844086	−	0.708272i	−0.114393	−	0.993436i	$-0.536492\pi$
$229$	12.7733	−	10.7181i	0.844086	−	0.708272i	0.958479	+	0.285163i	$0.0920478\pi$
$230$	0.833453	+	0.741963i	0.0549563	+	0.0489236i
$231$	−5.82899	−	4.45003i	−0.383520	−	0.292790i
$232$	2.46978	+	6.78568i	0.162149	+	0.445502i
$233$	−25.8565	+	14.9283i	−1.69391	+	0.977982i	−0.742613	+	0.669720i	$0.766414\pi$
$233$	−25.8565	+	14.9283i	−1.69391	+	0.977982i	−0.951302	+	0.308262i	$0.900253\pi$
$234$	0.124018	−	1.50256i	0.00810731	−	0.0982255i
$235$	−5.60996	+	14.1142i	−0.365954	+	0.920707i
$236$	−2.47089	+	14.0131i	−0.160841	+	0.912174i
$237$	0.119657	+	2.59428i	0.00777258	+	0.168516i
$238$	0.287885	−	0.790957i	0.0186608	−	0.0512701i
$239$	−4.19886	−	23.8129i	−0.271602	−	1.54033i	−0.749554	−	0.661943i	$-0.769732\pi$
$239$	−4.19886	−	23.8129i	−0.271602	−	1.54033i	0.477952	−	0.878386i	$-0.341379\pi$
$240$	−9.13099	+	11.2615i	−0.589403	+	0.726930i
$241$	11.3477	+	9.52183i	0.730968	+	0.613355i	0.930395	−	0.366558i	$-0.119464\pi$
$241$	11.3477	+	9.52183i	0.730968	+	0.613355i	−0.199427	+	0.979913i	$0.563908\pi$
$242$		−	1.83425i		−	0.117910i
$243$	8.53659	+	13.0433i	0.547623	+	0.836725i
$244$	−11.7149			−0.749967
$245$	−1.51686	+	2.45827i	−0.0969084	+	0.157053i
$246$	2.87385	−	2.64643i	0.183230	−	0.168730i
$247$	11.1850	−	1.97221i	0.711683	−	0.125489i
$248$	1.63149	−	4.48247i	0.103599	−	0.284637i
$249$	−20.0962	+	0.926909i	−1.27354	+	0.0587405i
$250$	0.599421	+	2.24162i	0.0379107	+	0.141772i
$251$	3.98405	−	6.90057i	0.251471	−	0.435560i	−0.712460	−	0.701712i	$-0.752419\pi$
$251$	3.98405	−	6.90057i	0.251471	−	0.435560i	0.963931	+	0.266152i	$0.0857525\pi$
$252$	−16.8479	−	1.39059i	−1.06132	−	0.0875989i
$253$	−3.06181	+	1.76773i	−0.192494	+	0.111137i
$254$	2.35704	−	0.857892i	0.147894	−	0.0538289i
$255$	−2.64753	+	4.76929i	−0.165795	+	0.298665i
$256$	9.70145	−	8.14048i	0.606341	−	0.508780i
$257$	13.0075	+	15.5017i	0.811386	+	0.966972i	0.999886	−	0.0151015i	$-0.00480713\pi$
$257$	13.0075	+	15.5017i	0.811386	+	0.966972i	−0.188500	+	0.982073i	$0.560363\pi$
$258$	−1.06586	−	2.55543i	−0.0663576	−	0.159094i
$259$	23.6535	−	8.60917i	1.46976	−	0.534948i
$260$	−6.57060	−	8.31276i	−0.407491	−	0.515536i
$261$	18.5612	−	18.7446i	1.14891	−	1.16026i
$262$	−0.0467150	−	0.0269709i	−0.00288606	−	0.00166627i
$263$	21.4662	+	3.78508i	1.32367	+	0.233398i	0.790421	−	0.612563i	$-0.209862\pi$
$263$	21.4662	+	3.78508i	1.32367	+	0.233398i	0.533244	+	0.845961i	$0.320973\pi$
$264$	1.12807	+	1.76114i	0.0694276	+	0.108391i
$265$	−11.9110	−	2.46153i	−0.731690	−	0.151211i
$266$	0.486745	+	2.76047i	0.0298442	+	0.169255i
$267$	20.1715	−	4.52395i	1.23448	−	0.276862i
$268$	9.69226	−	11.5508i	0.592049	−	0.705577i
$269$	−4.34109			−0.264681			−0.132341	−	0.991204i	$-0.542249\pi$
$269$	−4.34109			−0.264681			−0.132341	+	0.991204i	$0.542249\pi$
$270$	−2.34226	−	0.573317i	−0.142546	−	0.0348910i
$271$	−13.1672			−0.799852			−0.399926	−	0.916547i	$-0.630964\pi$
$271$	−13.1672			−0.799852			−0.399926	+	0.916547i	$0.630964\pi$
$272$	3.38902	−	4.03888i	0.205490	−	0.244893i
$273$	3.60337	−	11.5271i	0.218086	−	0.697654i
$274$	−0.673017	−	3.81687i	−0.0406584	−	0.230585i
$275$	−7.33923	−	0.429952i	−0.442572	−	0.0259271i
$276$	−3.74547	+	7.23837i	−0.225451	+	0.435699i
$277$	−0.500044	−	0.0881712i	−0.0300447	−	0.00529770i	0.158606	−	0.987342i	$-0.449300\pi$
$277$	−0.500044	−	0.0881712i	−0.0300447	−	0.00529770i	−0.188650	+	0.982044i	$0.560411\pi$
$278$	1.24976	+	0.721550i	0.0749557	+	0.0432757i
$279$	−17.3517	+	1.60406i	−1.03882	+	0.0960327i
$280$	4.14835	−	3.27895i	0.247912	−	0.195955i
$281$	−0.459552	+	0.167263i	−0.0274146	+	0.00997809i	−0.355691	−	0.934604i	$-0.615754\pi$
$281$	−0.459552	+	0.167263i	−0.0274146	+	0.00997809i	0.328276	+	0.944582i	$0.393532\pi$
$282$	2.42155	+	0.312751i	0.144201	+	0.0186240i
$283$	2.70977	+	3.22938i	0.161079	+	0.191967i	0.840547	−	0.541739i	$-0.182234\pi$
$283$	2.70977	+	3.22938i	0.161079	+	0.191967i	−0.679468	+	0.733705i	$0.737789\pi$
$284$	−13.5459	+	11.3663i	−0.803799	+	0.674467i
$285$	−0.305766	−	18.1630i	−0.0181120	−	1.07588i
$286$	−0.694377	+	0.252733i	−0.0410594	+	0.0149444i
$287$	27.1023	−	15.6475i	1.59980	−	0.923642i
$288$	6.59305	+	3.03503i	0.388499	+	0.178841i
$289$	−7.50815	+	13.0045i	−0.441656	+	0.764970i
$290$	−0.119376	+	4.07895i	−0.00700998	+	0.239524i
$291$	4.47453	−	8.64732i	0.262302	−	0.506915i
$292$	8.41710	−	23.1258i	0.492573	−	1.35333i
$293$	−22.7756	+	4.01595i	−1.33056	+	0.234614i	−0.793315	−	0.608811i	$-0.791647\pi$
$293$	−22.7756	+	4.01595i	−1.33056	+	0.234614i	−0.537247	+	0.843425i	$0.680536\pi$
$294$	0.443220	+	0.138550i	0.0258491	+	0.00808040i
$295$	−8.53792	+	13.8368i	−0.497097	+	0.805612i
$296$	−7.17872			−0.417254
$297$	4.05747	−	6.47380i	0.235438	−	0.375648i
$298$		−	1.70512i		−	0.0987747i
$299$	−4.46024	−	3.74258i	−0.257942	−	0.216439i
$300$	−14.7811	+	8.29073i	−0.853387	+	0.478666i
$301$	−3.85144	−	21.8426i	−0.221994	−	1.25899i
$302$	−0.628511	+	1.72682i	−0.0361668	+	0.0993674i
$303$	−15.6464	+	10.0220i	−0.898861	+	0.575748i
$304$	−3.04888	+	17.2911i	−0.174865	+	0.991711i
$305$	−12.4393	−	4.94426i	−0.712273	−	0.283107i
$306$	0.848152	+	0.222799i	0.0484856	+	0.0127366i
$307$	−2.88589	+	1.66617i	−0.164706	+	0.0950932i	−0.580087	−	0.814554i	$-0.696982\pi$
$307$	−2.88589	+	1.66617i	−0.164706	+	0.0950932i	0.415381	+	0.909648i	$0.363648\pi$
$308$	2.83384	+	7.78592i	0.161473	+	0.443644i
$309$	−0.857171	+	0.357522i	−0.0487627	+	0.0203387i
$310$	1.79238	−	2.01339i	0.101800	−	0.114353i
$311$	−8.46844	+	7.10587i	−0.480201	+	0.402937i	−0.850499	−	0.525976i	$-0.823700\pi$
$311$	−8.46844	+	7.10587i	−0.480201	+	0.402937i	0.370298	+	0.928913i	$0.379256\pi$
$312$	−2.09005	+	2.73771i	−0.118326	+	0.154992i
$313$	−3.19684	−	8.78326i	−0.180696	−	0.496459i	0.815965	−	0.578101i	$-0.196206\pi$
$313$	−3.19684	−	8.78326i	−0.180696	−	0.496459i	−0.996662	+	0.0816417i	$0.973984\pi$
$314$	−0.646076	−	1.11904i	−0.0364602	−	0.0631509i
$315$	−17.3029	−	8.58725i	−0.974909	−	0.483837i
$316$	1.46711	−	2.54110i	0.0825312	−	0.142948i
$317$	−26.8303	−	4.73090i	−1.50694	−	0.265714i	−0.641654	−	0.766994i	$-0.721752\pi$
$317$	−26.8303	−	4.73090i	−1.50694	−	0.265714i	−0.865285	+	0.501280i	$0.832863\pi$
$318$	0.0900891	+	1.95321i	0.00505195	+	0.109531i
$319$	−12.1494	−	4.42203i	−0.680238	−	0.247586i
$320$	14.8264	−	4.91015i	0.828820	−	0.274486i
$321$	−3.59917	+	3.31434i	−0.200886	+	0.184988i
$322$	0.923674	−	1.10079i	0.0514743	−	0.0613447i
$323$			6.60604i			0.367570i
$324$	−0.173141	−	17.6115i	−0.00961894	−	0.978416i
$325$	−3.46852	−	11.6000i	−0.192399	−	0.643450i
$326$	−3.28491	−	2.75637i	−0.181934	−	0.152661i
$327$	0.562947	+	0.611326i	0.0311310	+	0.0338064i
$328$	−8.78948	+	1.54982i	−0.485318	+	0.0855746i
$329$	18.3794	+	6.68956i	1.01329	+	0.368808i
$330$	0.224794	+	1.16031i	0.0123745	+	0.0638728i
$331$	4.40921	−	25.0059i	0.242352	−	1.37445i	−0.584210	−	0.811602i	$-0.698596\pi$
$331$	4.40921	−	25.0059i	0.242352	−	1.37445i	0.826562	−	0.562845i	$-0.190293\pi$
$332$	19.6843	+	11.3647i	1.08032	+	0.623721i
$333$	11.1996	+	23.7126i	0.613735	+	1.29945i
$334$	−0.650632	−	1.12693i	−0.0356010	−	0.0616628i
$335$	15.1667	−	8.17448i	0.828643	−	0.446619i
$336$	14.8401	+	11.3294i	0.809594	+	0.618068i
$337$	3.09214	+	3.68507i	0.168440	+	0.200739i	0.843661	−	0.536877i	$-0.180396\pi$
$337$	3.09214	+	3.68507i	0.168440	+	0.200739i	−0.675221	+	0.737616i	$0.735952\pi$
$338$	0.952032	+	1.13459i	0.0517837	+	0.0617134i
$339$	−6.80321	+	2.83759i	−0.369499	+	0.154117i
$340$	5.42525	−	2.92409i	0.294226	−	0.158581i
$341$	4.27036	+	7.39648i	0.231253	+	0.400542i
$342$	−2.81704	+	0.769685i	−0.152328	+	0.0416198i
$343$	−14.2349	−	8.21851i	−0.768611	−	0.443758i
$344$	−1.09840	+	6.22934i	−0.0592218	+	0.335863i
$345$	−7.03205	+	6.10522i	−0.378593	+	0.328694i
$346$	−0.774126	−	0.281759i	−0.0416173	−	0.0151474i
$347$	23.4852	−	4.14108i	1.26075	−	0.222305i	0.496964	−	0.867771i	$-0.334448\pi$
$347$	23.4852	−	4.14108i	1.26075	−	0.222305i	0.763789	+	0.645466i	$0.223337\pi$
$348$	−29.0820	+	6.52235i	−1.55896	+	0.349635i
$349$	10.1403	+	8.50874i	0.542799	+	0.455462i	0.872494	−	0.488625i	$-0.162501\pi$
$349$	10.1403	+	8.50874i	0.542799	+	0.455462i	−0.329695	+	0.944087i	$0.606946\pi$
$350$	2.86288	−	0.856035i	0.153027	−	0.0457570i
$351$	12.3039	+	2.63268i	0.656733	+	0.140522i
$352$		−	3.55734i		−	0.189607i
$353$	12.6452	−	15.0700i	0.673036	−	0.802093i	−0.316158	−	0.948707i	$-0.602393\pi$
$353$	12.6452	−	15.0700i	0.673036	−	0.802093i	0.989194	+	0.146614i	$0.0468375\pi$
$354$	2.49475	+	0.779856i	0.132594	+	0.0414489i
$355$	−19.1807	+	6.35219i	−1.01801	+	0.337139i
$356$	−21.9480	−	7.98841i	−1.16324	−	0.423385i
$357$	6.23888	+	3.22829i	0.330197	+	0.170859i
$358$	2.86963	+	0.505993i	0.151665	+	0.0267425i
$359$	5.85683	−	10.1443i	0.309112	−	0.535397i	−0.669057	−	0.743211i	$-0.733302\pi$
$359$	5.85683	−	10.1443i	0.309112	−	0.535397i	0.978168	+	0.207814i	$0.0666350\pi$
$360$	3.79944	+	3.98907i	0.200248	+	0.210242i
$361$	−1.49955	−	2.59729i	−0.0789236	−	0.136700i
$362$	−0.470638	−	1.29307i	−0.0247362	−	0.0679621i
$363$	15.1818	+	1.96078i	0.796839	+	0.102914i
$364$	−10.4529	+	8.77098i	−0.547878	+	0.459724i
$365$	18.6979	−	21.0035i	0.978691	−	1.09937i
$366$	−0.275638	+	2.13420i	−0.0144078	+	0.111556i
$367$	−8.09527	−	22.2416i	−0.422569	−	1.16100i	−0.950231	−	0.311546i	$-0.899153\pi$
$367$	−8.09527	−	22.2416i	−0.422569	−	1.16100i	0.527662	−	0.849455i	$-0.323069\pi$
$368$	7.79509	−	4.50050i	0.406347	−	0.234605i
$369$	18.8320	+	26.6154i	0.980352	+	1.38554i
$370$	−3.76984	−	1.49840i	−0.195985	−	0.0778980i
$371$	−2.71983	+	15.4249i	−0.141206	+	0.800821i
$372$	17.4859	+	9.04803i	0.906601	+	0.469118i
$373$	−7.08072	+	19.4541i	−0.366626	+	1.00730i	0.610010	+	0.792394i	$0.291166\pi$
$373$	−7.08072	+	19.4541i	−0.366626	+	1.00730i	−0.976636	+	0.214902i	$0.931057\pi$
$374$	−0.0746341	−	0.423271i	−0.00385924	−	0.0218868i
$375$	−19.1943	+	2.56507i	−0.991188	+	0.132460i
$376$	−4.27304	−	3.58551i	−0.220365	−	0.184908i
$377$		−	21.2925i		−	1.09662i
$378$	−0.649749	+	3.03661i	−0.0334195	+	0.156187i
$379$	14.1618			0.727442			0.363721	−	0.931508i	$-0.381506\pi$
$379$	14.1618			0.727442			0.363721	+	0.931508i	$0.381506\pi$
$380$	−10.7776	+	17.4665i	−0.552878	+	0.896012i
$381$	4.58101	+	20.4259i	0.234692	+	1.04645i
$382$	−2.00190	+	0.352989i	−0.102426	+	0.0180605i
$383$	6.96733	−	19.1426i	0.356014	−	0.978140i	−0.624385	−	0.781117i	$-0.714650\pi$
$383$	6.96733	−	19.1426i	0.356014	−	0.978140i	0.980399	−	0.197023i	$-0.0631274\pi$
$384$	−5.87467	−	9.17157i	−0.299791	−	0.468035i
$385$	−0.276959	+	9.46343i	−0.0141151	+	0.482301i
$386$	−2.01592	+	3.49168i	−0.102608	+	0.177722i
$387$	22.2903	−	6.09026i	1.13308	−	0.309585i
$388$	−9.52672	+	5.50025i	−0.483646	+	0.279233i
$389$	10.7321	−	3.90618i	0.544141	−	0.198051i	−0.0553005	−	0.998470i	$-0.517612\pi$
$389$	10.7321	−	3.90618i	0.544141	−	0.198051i	0.599441	+	0.800419i	$0.295389\pi$
$390$	−1.66901	+	1.00143i	−0.0845135	+	0.0507095i
$391$	2.59427	−	2.17685i	0.131198	−	0.110088i
$392$	−0.681914	−	0.812674i	−0.0344419	−	0.0410462i
$393$	0.273171	−	0.357821i	0.0137797	−	0.0180497i
$394$	1.26271	−	0.459590i	0.0636146	−	0.0231538i
$395$	2.63031	−	2.07905i	0.132345	−	0.104609i
$396$	−7.80538	+	3.68653i	−0.392235	+	0.185255i
$397$	−2.93301	−	1.69337i	−0.147204	−	0.0849880i	0.424589	−	0.905386i	$-0.360419\pi$
$397$	−2.93301	−	1.69337i	−0.147204	−	0.0849880i	−0.571793	+	0.820398i	$0.693752\pi$
$398$	−3.52125	−	0.620891i	−0.176504	−	0.0311225i
$399$	−23.3683	+	1.07783i	−1.16988	+	0.0539589i
$400$	18.6850	+	1.09462i	0.934252	+	0.0547310i
$401$	3.73348	+	21.1736i	0.186441	+	1.05736i	0.924090	+	0.382175i	$0.124825\pi$
$401$	3.73348	+	21.1736i	0.186441	+	1.05736i	−0.737649	+	0.675184i	$0.764064\pi$
$402$	−1.87626	−	2.03750i	−0.0935793	−	0.101621i
$403$	−9.04105	+	10.7747i	−0.450367	+	0.536726i
$404$	20.9933			1.04445
$405$	7.24909	−	18.7737i	0.360210	−	0.932871i
$406$	5.25502			0.260802
$407$	8.26184	−	9.84608i	0.409524	−	0.488052i
$408$	−1.35708	−	1.47371i	−0.0671856	−	0.0729594i
$409$	2.13010	+	12.0804i	0.105327	+	0.597338i	0.991089	+	0.133199i	$0.0425250\pi$
$409$	2.13010	+	12.0804i	0.105327	+	0.597338i	−0.885762	+	0.464139i	$0.846364\pi$
$410$	−4.93921	−	1.02074i	−0.243930	−	0.0504105i
$411$	32.3110	−	1.49030i	1.59379	−	0.0735111i
$412$	1.03338	+	0.182213i	0.0509111	+	0.00897700i
$413$	18.1327	+	10.4689i	0.892254	+	0.515143i
$414$	1.23055	+	0.852656i	0.0604782	+	0.0419058i
$415$	16.1051	+	20.3753i	0.790568	+	1.00018i
$416$	5.50513	−	2.00370i	0.269911	−	0.0982397i
$417$	−7.30812	+	9.57275i	−0.357880	+	0.468779i
$418$	0.920022	+	1.09644i	0.0449998	+	0.0536286i
$419$	−23.2229	+	19.4864i	−1.13451	+	0.951971i	−0.999246	−	0.0388381i	$-0.987634\pi$
$419$	−23.2229	+	19.4864i	−1.13451	+	0.951971i	−0.135269	+	0.990809i	$0.543190\pi$
$420$	11.2289	+	18.7142i	0.547912	+	0.913162i
$421$	−8.53967	+	3.10819i	−0.416198	+	0.151484i	−0.541627	−	0.840619i	$-0.682191\pi$
$421$	−8.53967	+	3.10819i	−0.416198	+	0.151484i	0.125429	+	0.992103i	$0.459969\pi$
$422$	3.62710	−	2.09411i	0.176565	−	0.101940i
$423$	−5.17717	+	19.7085i	−0.251723	+	0.958258i
$424$	2.23346	−	3.86847i	0.108466	−	0.187869i
$425$	6.99486	−	0.815184i	0.339301	−	0.0395423i
$426$	1.75198	+	2.73520i	0.0848838	+	0.132521i
$427$	−5.89575	+	16.1984i	−0.285315	+	0.783897i
$428$	5.44399	−	0.959922i	0.263145	−	0.0463996i
$429$	−1.34955	−	6.01742i	−0.0651571	−	0.290524i
$430$	−1.87705	+	3.04201i	−0.0905195	+	0.146699i
$431$	−17.7056			−0.852847			−0.426424	−	0.904524i	$-0.640227\pi$
$431$	−17.7056			−0.852847			−0.426424	+	0.904524i	$0.640227\pi$
$432$	−10.3300	+	16.4817i	−0.497001	+	0.792977i
$433$			6.74677i			0.324229i	0.986772	+	0.162114i	$0.0518314\pi$
$433$			6.74677i			0.324229i	−0.986772	+	0.162114i	$0.948169\pi$
$434$	−2.65921	−	2.23134i	−0.127646	−	0.107108i
$435$	−33.6332	−	5.34837i	−1.61259	−	0.256434i
$436$	−0.163045	−	0.924672i	−0.00780842	−	0.0442837i
$437$	−3.85724	+	10.5977i	−0.184517	+	0.506956i
$438$	−4.01498	−	2.07754i	−0.191843	−	0.0992687i
$439$	0.774036	−	4.38977i	0.0369427	−	0.209512i	−0.960749	−	0.277419i	$-0.910521\pi$
$439$	0.774036	−	4.38977i	0.0369427	−	0.209512i	0.997692	+	0.0679067i	$0.0216320\pi$
$440$	0.997298	−	2.50911i	0.0475443	−	0.119617i
$441$	−1.62055	+	3.52035i	−0.0771690	+	0.167636i
$442$	0.612991	−	0.353911i	0.0291570	−	0.0168338i
$443$	−2.74386	−	7.53869i	−0.130365	−	0.358174i	0.857287	−	0.514838i	$-0.172148\pi$
$443$	−2.74386	−	7.53869i	−0.130365	−	0.358174i	−0.987652	+	0.156665i	$0.949926\pi$
$444$	3.79518	−	29.3851i	0.180111	−	1.39456i
$445$	−19.9337	−	17.7456i	−0.944950	−	0.841221i
$446$	1.48526	−	1.24628i	0.0703293	−	0.0590133i
$447$	14.1130	+	1.82273i	0.667521	+	0.0862123i
$448$	−6.87900	−	18.8999i	−0.325002	−	0.892936i
$449$	2.62606	+	4.54847i	0.123931	+	0.214655i	0.921315	−	0.388818i	$-0.127116\pi$
$449$	2.62606	+	4.54847i	0.123931	+	0.214655i	−0.797383	+	0.603473i	$0.793783\pi$
$450$	1.16261	+	2.88787i	0.0548060	+	0.136136i
$451$	7.98996	−	13.8390i	0.376232	−	0.651654i
$452$	8.20177	+	1.44619i	0.385779	+	0.0680232i
$453$	−13.6208	−	7.04802i	−0.639959	−	0.331145i
$454$	1.53366	+	0.558206i	0.0719782	+	0.0261979i
$455$	−14.8011	+	4.90176i	−0.693884	+	0.229798i
$456$	6.36765	+	1.99052i	0.298193	+	0.0932147i
$457$	−1.94777	+	2.32127i	−0.0911130	+	0.108584i	−0.809675	−	0.586879i	$-0.800356\pi$
$457$	−1.94777	+	2.32127i	−0.0911130	+	0.108584i	0.718562	+	0.695463i	$0.244801\pi$
$458$			3.46062i			0.161704i
$459$	−2.75073	+	6.78185i	−0.128393	+	0.316550i
$460$	10.4108	−	1.52316i	0.485405	−	0.0710175i
$461$	−2.25112	−	1.88892i	−0.104845	−	0.0879757i	0.588858	−	0.808236i	$-0.299578\pi$
$461$	−2.25112	−	1.88892i	−0.104845	−	0.0879757i	−0.693703	+	0.720261i	$0.744022\pi$
$462$	1.48511	−	0.333071i	0.0690934	−	0.0154959i
$463$	18.1798	−	3.20559i	0.844886	−	0.148976i	0.265583	−	0.964088i	$-0.414436\pi$
$463$	18.1798	−	3.20559i	0.844886	−	0.148976i	0.579304	+	0.815112i	$0.303325\pi$
$464$	30.9314	+	11.2581i	1.43595	+	0.522644i
$465$	14.7485	+	16.9875i	0.683946	+	0.787776i
$466$	1.07600	−	6.10231i	0.0498448	−	0.282684i
$467$	−18.7117	−	10.8032i	−0.865875	−	0.499913i	9.99457e−5	−	1.00000i	$-0.499968\pi$
$467$	−18.7117	−	10.8032i	−0.865875	−	0.499913i	−0.865975	+	0.500087i	$0.833302\pi$
$468$	−10.1015	−	10.0027i	−0.466943	−	0.462375i
$469$	−11.0937	−	19.2149i	−0.512261	−	0.887263i
$470$	−1.49555	−	2.77480i	−0.0689847	−	0.127992i
$471$	9.95272	−	4.15124i	0.458597	−	0.191279i
$472$	−3.83828	−	4.57429i	−0.176671	−	0.210549i
$473$	−7.27982	−	8.67575i	−0.334726	−	0.398911i
$474$	−0.428415	−	0.327065i	−0.0196778	−	0.0150226i
$475$	−18.8158	+	13.9980i	−0.863328	+	0.642270i
$476$	−3.96833	−	6.87335i	−0.181888	−	0.315040i
$477$	−16.2627	−	1.34229i	−0.744619	−	0.0614591i
$478$	4.34606	+	2.50920i	0.198784	+	0.114768i
$479$	0.173381	−	0.983295i	0.00792200	−	0.0449279i	−0.980591	−	0.196067i	$-0.937183\pi$
$479$	0.173381	−	0.983295i	0.00792200	−	0.0449279i	0.988513	+	0.151139i	$0.0482941\pi$
$480$	−1.78220	−	9.19909i	−0.0813460	−	0.419879i
$481$	19.8908	+	7.23966i	0.906942	+	0.330100i
$482$	−3.02767	+	0.533859i	−0.137906	+	0.0243166i
$483$	8.12369	+	8.82182i	0.369641	+	0.401407i
$484$	−13.2490	−	11.1173i	−0.602229	−	0.505330i
$485$	−12.4372	+	1.81964i	−0.564746	+	0.0826255i
$486$	−3.21251	−	0.382837i	−0.145723	−	0.0173658i
$487$		−	18.3516i		−	0.831589i	−0.909459	−	0.415794i	$-0.863504\pi$
$487$		−	18.3516i		−	0.831589i	0.909459	−	0.415794i	$-0.136496\pi$
$488$	3.16003	−	3.76598i	0.143048	−	0.170478i
$489$	26.3255	−	24.2422i	1.19048	−	1.09627i
$490$	−0.188473	−	0.569103i	−0.00851436	−	0.0257094i
$491$	−10.2329	−	3.72447i	−0.461805	−	0.168083i	0.100632	−	0.994924i	$-0.467914\pi$
$491$	−10.2329	−	3.72447i	−0.461805	−	0.168083i	−0.562436	+	0.826841i	$0.690136\pi$
$492$	−1.69725	−	36.7980i	−0.0765181	−	1.65898i
$493$	12.1965	+	2.15057i	0.549303	+	0.0968570i
$494$	−1.17858	+	2.04135i	−0.0530266	+	0.0918449i
$495$	−9.84397	+	0.620241i	−0.442454	+	0.0278777i
$496$	−10.8720	−	18.8308i	−0.488165	−	0.845527i
$497$	8.89927	+	24.4505i	0.399187	+	1.09676i
$498$	2.53356	−	3.31866i	0.113532	−	0.148713i
$499$	−22.2753	+	18.6912i	−0.997180	+	0.836733i	−0.986591	−	0.163211i	$-0.947815\pi$
$499$	−22.2753	+	18.6912i	−0.997180	+	0.836733i	−0.0105884	+	0.999944i	$0.503370\pi$
$500$	19.8245	+	9.25657i	0.886579	+	0.413966i
$501$	10.0229	−	4.18052i	0.447791	−	0.186772i
$502$	0.565600	+	1.55397i	0.0252440	+	0.0693573i
$503$	−16.5027	+	9.52781i	−0.735817	+	0.424824i	−0.820546	−	0.571580i	$-0.806331\pi$
$503$	−16.5027	+	9.52781i	−0.735817	+	0.424824i	0.0847294	+	0.996404i	$0.472997\pi$
$504$	4.99169	−	5.04100i	0.222348	−	0.224544i
$505$	22.2915	+	8.86022i	0.991960	+	0.394275i
$506$	0.127415	−	0.722607i	0.00566429	−	0.0321238i
$507$	−10.4085	+	6.66697i	−0.462258	+	0.296090i
$508$	8.08916	−	22.2248i	0.358898	−	0.986065i
$509$	−6.00851	−	34.0759i	−0.266322	−	1.51039i	−0.765243	−	0.643741i	$-0.777381\pi$
$509$	−6.00851	−	34.0759i	−0.266322	−	1.51039i	0.498921	−	0.866648i	$-0.333730\pi$
$510$	−0.405056	−	1.05717i	−0.0179362	−	0.0468121i
$511$	−27.7405	−	23.2771i	−1.22717	−	1.02972i
$512$			15.2050i			0.671974i
$513$	−3.35920	−	24.1390i	−0.148312	−	1.06576i
$514$	−4.19981			−0.185246
$515$	1.02038	+	0.629621i	0.0449635	+	0.0277444i
$516$	−24.9183	−	7.78943i	−1.09697	−	0.342911i
$517$	9.83552	−	1.73427i	0.432566	−	0.0762730i
$518$	−1.78676	+	4.90907i	−0.0785055	+	0.215692i
$519$	3.15960	−	6.10612i	0.138691	−	0.268029i
$520$	4.44470	+	0.130080i	0.194913	+	0.00570437i
$521$	−10.0641	+	17.4315i	−0.440915	+	0.763686i	−0.997758	−	0.0669313i	$-0.978679\pi$
$521$	−10.0641	+	17.4315i	−0.440915	+	0.763686i	0.556843	+	0.830618i	$0.312012\pi$
$522$	0.503966	+	5.45158i	0.0220580	+	0.238609i
$523$	−15.9232	+	9.19327i	−0.696274	+	0.401994i	−0.805958	−	0.591973i	$-0.798349\pi$
$523$	−15.9232	+	9.19327i	−0.696274	+	0.401994i	0.109684	+	0.993966i	$0.465016\pi$
$524$	−0.477950	+	0.173960i	−0.0208793	+	0.00759946i
$525$	4.02491	+	24.6107i	0.175661	+	1.07410i
$526$	−3.46547	+	2.90788i	−0.151102	+	0.126789i
$527$	−5.25867	−	6.26704i	−0.229071	−	0.272996i
$528$	9.45499	+	1.22114i	0.411476	+	0.0531433i
$529$	−16.1800	+	5.88905i	−0.703480	+	0.256046i
$530$	1.98034	−	1.56530i	0.0860204	−	0.0679925i
$531$	−9.12158	+	19.8150i	−0.395843	+	0.859897i
$532$	22.8893	+	13.2151i	0.992377	+	0.572949i
$533$	25.9169	+	4.56985i	1.12259	+	0.197942i
$534$	−1.97173	+	3.81049i	−0.0853251	+	0.164896i
$535$	6.18579	+	1.27835i	0.267435	+	0.0552680i
$536$	1.09879	+	6.23155i	0.0474605	+	0.269162i
$537$	−7.25559	+	23.2106i	−0.313102	+	1.00161i
$538$	0.579122	−	0.690171i	0.0249677	−	0.0297554i
$539$	1.89944			0.0818146
$540$	−18.3374	+	13.4436i	−0.789116	+	0.578521i
$541$	4.17044			0.179301			0.0896506	−	0.995973i	$-0.471425\pi$
$541$	4.17044			0.179301			0.0896506	+	0.995973i	$0.471425\pi$
$542$	1.75657	−	2.09340i	0.0754512	−	0.0899192i
$543$	11.2056	−	2.51313i	0.480879	−	0.107849i
$544$	0.591711	+	3.35576i	0.0253694	+	0.143877i
$545$	0.217131	−	1.05067i	0.00930085	−	0.0450056i
$546$	1.35194	+	2.11066i	0.0578578	+	0.0903279i
$547$	23.2507	+	4.09973i	0.994128	+	0.175292i	0.646970	−	0.762515i	$-0.276036\pi$
$547$	23.2507	+	4.09973i	0.994128	+	0.175292i	0.347158	+	0.937807i	$0.387147\pi$
$548$	−31.6488	−	18.2724i	−1.35197	−	0.780560i
$549$	−17.3698	−	4.56283i	−0.741324	−	0.194737i
$550$	1.04744	−	1.10947i	0.0446632	−	0.0473081i
$551$	−38.7555	+	14.1059i	−1.65104	+	0.600930i
$552$	−1.31660	−	3.15658i	−0.0560380	−	0.134353i
$553$	−2.77530	−	3.30747i	−0.118018	−	0.140648i
$554$	0.0807262	−	0.0677373i	0.00342973	−	0.00287788i
$555$	16.4319	−	29.6006i	0.697495	−	1.25648i
$556$	12.7865	−	4.65392i	0.542270	−	0.197370i
$557$	−23.3763	+	13.4963i	−0.990484	+	0.571856i	−0.905419	−	0.424519i	$-0.860443\pi$
$557$	−23.3763	+	13.4963i	−0.990484	+	0.571856i	−0.0850648	+	0.996375i	$0.527110\pi$
$558$	2.05978	−	2.97267i	0.0871975	−	0.125843i
$559$	9.32567	−	16.1525i	0.394434	−	0.683179i
$560$	0.705114	−	24.0931i	0.0297965	−	1.01812i
$561$	3.58313	−	0.165267i	0.151280	−	0.00697757i
$562$	0.0347140	−	0.0953759i	0.00146432	−	0.00402319i
$563$	13.8182	−	2.43652i	0.582366	−	0.102687i	0.125299	−	0.992119i	$-0.460011\pi$
$563$	13.8182	−	2.43652i	0.582366	−	0.102687i	0.457067	+	0.889432i	$0.348900\pi$
$564$	16.9358	−	15.5956i	0.713128	−	0.656693i
$565$	8.09860	+	4.99718i	0.340711	+	0.210233i
$566$	−0.874921			−0.0367757
$567$	−24.4390	−	8.62395i	−1.02634	−	0.362172i
$568$		−	7.42061i		−	0.311362i
$569$	−17.5672	−	14.7406i	−0.736454	−	0.617958i	0.195429	−	0.980718i	$-0.437390\pi$
$569$	−17.5672	−	14.7406i	−0.736454	−	0.617958i	−0.931883	+	0.362760i	$0.881835\pi$
$570$	2.92844	+	2.37441i	0.122659	+	0.0994532i
$571$	0.200726	+	1.13838i	0.00840013	+	0.0476395i	0.988720	−	0.149778i	$-0.0478558\pi$
$571$	0.200726	+	1.13838i	0.00840013	+	0.0476395i	−0.980320	+	0.197417i	$0.936745\pi$
$572$	−2.38305	+	6.54736i	−0.0996401	+	0.273759i
$573$	−0.781644	−	16.9467i	−0.0326537	−	0.707960i
$574$	−1.12784	+	6.39632i	−0.0470753	+	0.266977i
$575$	11.6974	+	2.77652i	0.487817	+	0.115789i
$576$	18.9471	−	8.94885i	0.789464	−	0.372869i
$577$	−22.9770	+	13.2658i	−0.956544	+	0.552261i	−0.895108	−	0.445850i	$-0.852902\pi$
$577$	−22.9770	+	13.2658i	−0.956544	+	0.552261i	−0.0614366	+	0.998111i	$0.519568\pi$
$578$	−1.06590	−	2.92855i	−0.0443358	−	0.121812i
$579$	−26.7451	−	20.4180i	−1.11149	−	0.848544i
$580$	28.7392	+	25.5844i	1.19333	+	1.06234i
$581$	25.6208	−	21.4984i	1.06293	−	0.891906i
$582$	0.777875	+	1.86498i	0.0322440	+	0.0773059i
$583$	2.73541	+	7.51548i	0.113289	+	0.311259i
$584$	5.16378	+	8.94393i	0.213679	+	0.370102i
$585$	−6.50456	−	14.8846i	−0.268931	−	0.615403i
$586$	2.39989	−	4.15673i	0.0991385	−	0.171713i
$587$	−31.2941	−	5.51799i	−1.29165	−	0.227752i	−0.514728	−	0.857354i	$-0.672107\pi$
$587$	−31.2941	−	5.51799i	−1.29165	−	0.227752i	−0.776918	+	0.629602i	$0.783218\pi$
$588$	3.68708	−	2.36169i	0.152053	−	0.0973945i
$589$	25.6011	+	9.31802i	1.05487	+	0.383942i
$590$	−1.06086	−	3.20330i	−0.0436748	−	0.131878i
$591$	2.45414	+	10.9426i	0.100950	+	0.450118i
$592$	−21.0339	+	25.0673i	−0.864489	+	1.03026i
$593$			10.3324i			0.424303i	0.977237	+	0.212151i	$0.0680470\pi$
$593$			10.3324i			0.424303i	−0.977237	+	0.212151i	$0.931953\pi$
$594$	0.487954	+	1.50871i	0.0200210	+	0.0619033i
$595$	−1.31284	−	8.97324i	−0.0538210	−	0.367867i
$596$	−12.3163	−	10.3346i	−0.504494	−	0.423320i
$597$	8.90316	−	28.4811i	0.364382	−	1.16565i
$598$	1.19003	−	0.209835i	0.0486641	−	0.00858079i
$599$	30.6411	+	11.1524i	1.25196	+	0.455677i	0.881064	−	0.472997i	$-0.156828\pi$
$599$	30.6411	+	11.1524i	1.25196	+	0.455677i	0.370897	+	0.928674i	$0.379050\pi$
$600$	1.32191	−	6.98808i	0.0539669	−	0.285287i
$601$	−4.69496	+	26.6264i	−0.191511	+	1.08611i	0.725789	+	0.687918i	$0.241475\pi$
$601$	−4.69496	+	26.6264i	−0.191511	+	1.08611i	−0.917300	+	0.398197i	$0.869636\pi$
$602$	3.98646	+	2.30159i	0.162476	+	0.0938056i
$603$	18.8698	−	13.3515i	0.768436	−	0.543713i
$604$	8.66368	+	15.0059i	0.352520	+	0.610583i
$605$	−9.37632	−	17.3965i	−0.381202	−	0.707269i
$606$	0.493949	−	3.82453i	0.0200653	−	0.155361i
$607$	−4.08135	−	4.86396i	−0.165657	−	0.197422i	0.676830	−	0.736140i	$-0.263353\pi$
$607$	−4.08135	−	4.86396i	−0.165657	−	0.197422i	−0.842486	+	0.538718i	$0.818909\pi$
$608$	−7.29408	−	8.69275i	−0.295814	−	0.352537i
$609$	−5.61750	+	43.4949i	−0.227633	+	1.76250i
$610$	2.44553	−	1.31808i	0.0990166	−	0.0533677i
$611$	8.22381	+	14.2440i	0.332700	+	0.576253i
$612$	6.74988	−	4.77594i	0.272848	−	0.193056i
$613$	33.0811	+	19.0994i	1.33613	+	0.771416i	0.986231	−	0.165371i	$-0.0528823\pi$
$613$	33.0811	+	19.0994i	1.33613	+	0.771416i	0.349900	+	0.936787i	$0.386216\pi$
$614$	0.120094	−	0.681089i	0.00484661	−	0.0274865i
$615$	13.7284	−	39.7899i	0.553581	−	1.60448i
$616$	−3.26736	−	1.18922i	−0.131646	−	0.0479151i
$617$	−16.9692	+	2.99213i	−0.683155	+	0.120459i	−0.504446	−	0.863443i	$-0.668303\pi$
$617$	−16.9692	+	2.99213i	−0.683155	+	0.120459i	−0.178709	+	0.983902i	$0.557192\pi$
$618$	0.0575097	−	0.183973i	0.00231338	−	0.00740048i
$619$	3.05553	+	2.56390i	0.122812	+	0.103052i	0.702125	−	0.712053i	$-0.252235\pi$
$619$	3.05553	+	2.56390i	0.122812	+	0.103052i	−0.579313	+	0.815105i	$0.696679\pi$
$620$	−3.67952	−	25.1495i	−0.147773	−	1.01003i
$621$	−8.37273	+	9.27359i	−0.335986	+	0.372136i
$622$		−	2.29432i		−	0.0919937i
$623$	−22.0916	+	26.3277i	−0.885080	+	1.05480i
$624$	3.43585	+	15.3198i	0.137544	+	0.613284i
$625$	17.1437	+	18.1959i	0.685750	+	0.727838i
$626$	1.82289	+	0.663476i	0.0728571	+	0.0265178i
$627$	−10.0585	+	6.44281i	−0.401699	+	0.257301i
$628$	−11.9987	−	2.11570i	−0.478802	−	0.0844257i
$629$	−6.15593	+	10.6624i	−0.245453	+	0.425137i
$630$	3.67354	−	1.60533i	0.146357	−	0.0639580i
$631$	−3.17235	−	5.49468i	−0.126289	−	0.218740i	0.795947	−	0.605367i	$-0.206973\pi$
$631$	−3.17235	−	5.49468i	−0.126289	−	0.218740i	−0.922236	+	0.386627i	$0.873640\pi$
$632$	0.421144	+	1.15708i	0.0167522	+	0.0460263i
$633$	13.4553	+	32.2595i	0.534800	+	1.28220i
$634$	4.33143	−	3.63450i	0.172023	−	0.144345i
$635$	17.9694	−	20.1852i	0.713093	−	0.801023i
$636$	14.6543	+	11.1875i	0.581081	+	0.443614i
$637$	1.06988	+	2.93946i	0.0423900	+	0.116466i
$638$	2.32383	−	1.34166i	0.0920014	−	0.0531170i
$639$	−24.5117	+	11.5770i	−0.969667	+	0.457979i
$640$	−5.19367	+	13.0668i	−0.205298	+	0.516511i
$641$	5.63430	−	31.9537i	0.222542	−	1.26210i	−0.644788	−	0.764362i	$-0.723054\pi$
$641$	5.63430	−	31.9537i	0.222542	−	1.26210i	0.867329	−	0.497734i	$-0.165835\pi$
$642$	−0.0467862	−	1.01436i	−0.00184650	−	0.0400338i
$643$	−5.98189	+	16.4351i	−0.235903	+	0.648137i	0.764093	+	0.645106i	$0.223187\pi$
$643$	−5.98189	+	16.4351i	−0.235903	+	0.648137i	−0.999995	+	0.00303079i	$0.999035\pi$
$644$	−2.35284	−	13.3436i	−0.0927148	−	0.525812i
$645$	−23.1717	−	18.7879i	−0.912386	−	0.739773i
$646$	−1.05026	−	0.881277i	−0.0413221	−	0.0346734i
$647$			3.69757i			0.145367i	0.997355	+	0.0726833i	$0.0231562\pi$
$647$			3.69757i			0.145367i	−0.997355	+	0.0726833i	$0.976844\pi$
$648$	5.70828	+	4.69497i	0.224242	+	0.184436i
$649$	10.6913			0.419672
$650$	2.30694	+	0.996043i	0.0904857	+	0.0390680i
$651$	21.3111	−	19.6246i	0.835247	−	0.769148i
$652$	−39.8191	+	7.02118i	−1.55944	+	0.274971i
$653$	−9.02248	+	24.7891i	−0.353077	+	0.970071i	0.628299	+	0.777972i	$0.283752\pi$
$653$	−9.02248	+	24.7891i	−0.353077	+	0.970071i	−0.981376	+	0.192099i	$0.938471\pi$
$654$	−0.172292	+	0.00794672i	−0.00673714	+	0.000310741i
$655$	−0.580927	−	0.0170015i	−0.0226987	−	0.000664305i
$656$	−20.3417	+	35.2329i	−0.794211	+	1.37561i
$657$	21.4874	−	31.0105i	0.838303	−	1.20983i
$658$	−3.51545	+	2.02964i	−0.137046	+	0.0791238i
$659$	−14.2209	+	5.17599i	−0.553968	+	0.201628i	−0.603809	−	0.797129i	$-0.706351\pi$
$659$	−14.2209	+	5.17599i	−0.553968	+	0.201628i	0.0498407	+	0.998757i	$0.484129\pi$
$660$	9.74349	+	5.40881i	0.379265	+	0.210538i
$661$	14.8757	−	12.4822i	0.578598	−	0.485501i	−0.305889	−	0.952067i	$-0.598953\pi$
$661$	14.8757	−	12.4822i	0.578598	−	0.485501i	0.884486	+	0.466566i	$0.154509\pi$
$662$	3.38736	+	4.03690i	0.131654	+	0.156899i
$663$	2.27399	+	5.45196i	0.0883144	+	0.211736i
$664$	−8.96318	+	3.26233i	−0.347839	+	0.126603i
$665$	18.7273	+	23.6928i	0.726215	+	0.918768i
$666$	−5.26405	−	1.38280i	−0.203978	−	0.0535825i
$667$	18.3104	+	10.5715i	0.708983	+	0.409332i
$668$	−12.0834	−	2.13062i	−0.467519	−	0.0824363i
$669$	8.72758	+	13.6255i	0.337428	+	0.526794i
$670$	−0.723680	+	3.50179i	−0.0279582	+	0.135286i
$671$	1.52847	+	8.66839i	0.0590060	+	0.334640i
$672$	−11.7741	+	2.64064i	−0.454198	+	0.101865i
$673$	15.8772	−	18.9217i	0.612021	−	0.729378i	−0.367656	−	0.929962i	$-0.619839\pi$
$673$	15.8772	−	18.9217i	0.612021	−	0.729378i	0.979677	+	0.200584i	$0.0642839\pi$
$674$	−0.998381			−0.0384562
$675$	−25.1453	+	6.53567i	−0.967842	+	0.251558i
$676$	13.9654			0.537133
$677$	−6.58819	+	7.85150i	−0.253205	+	0.301758i	−0.877641	−	0.479318i	$-0.840884\pi$
$677$	−6.58819	+	7.85150i	−0.253205	+	0.301758i	0.624437	+	0.781075i	$0.285329\pi$
$678$	0.456444	−	1.46016i	0.0175296	−	0.0560771i
$679$	2.81082	+	15.9410i	0.107869	+	0.611758i
$680$	−0.523431	+	2.53282i	−0.0200727	+	0.0971291i
$681$	−6.25964	+	12.0971i	−0.239870	+	0.463564i
$682$	−1.74562	−	0.307800i	−0.0668432	−	0.0117863i
$683$	12.1386	+	7.00820i	0.464469	+	0.268161i	0.713921	−	0.700226i	$-0.246917\pi$
$683$	12.1386	+	7.00820i	0.464469	+	0.268161i	−0.249453	+	0.968387i	$0.580251\pi$
$684$	−11.5143	+	25.0128i	−0.440262	+	0.956390i
$685$	−25.8941	−	32.7598i	−0.989362	−	1.25169i
$686$	3.20562	−	1.16675i	0.122391	−	0.0445468i
$687$	−28.6430	−	3.69933i	−1.09280	−	0.141138i
$688$	18.5338	+	22.0877i	0.706594	+	0.842086i
$689$	−10.0898	+	8.46633i	−0.384390	+	0.322542i
$690$	−0.0325322	−	1.93246i	−0.00123848	−	0.0735675i
$691$	−15.6160	+	5.68375i	−0.594060	+	0.216220i	−0.621514	−	0.783403i	$-0.713482\pi$
$691$	−15.6160	+	5.68375i	−0.594060	+	0.216220i	0.0274543	+	0.999623i	$0.491260\pi$
$692$	−6.72709	+	3.88389i	−0.255725	+	0.147643i
$693$	1.16923	+	12.6480i	0.0444155	+	0.480459i
$694$	−2.47467	+	4.28625i	−0.0939372	+	0.162704i
$695$	15.5414	+	0.454840i	0.589521	+	0.0172531i
$696$	5.74800	−	11.1084i	0.217878	−	0.421062i
$697$	−5.23528	+	14.3838i	−0.198301	+	0.544826i
$698$	−2.70553	+	0.477058i	−0.102406	+	0.0180569i
$699$	49.3576	+	15.4291i	1.86688	+	0.583583i
$700$	11.1684	−	25.8673i	0.422127	−	0.977692i
$701$	23.2471			0.878029			0.439015	−	0.898480i	$-0.355328\pi$
$701$	23.2471			0.878029			0.439015	+	0.898480i	$0.355328\pi$
$702$	−2.05996	+	1.60493i	−0.0777480	+	0.0605741i
$703$		−	41.0003i		−	1.54636i
$704$	−7.86733	−	6.60147i	−0.296511	−	0.248802i
$705$	24.5653	−	9.41226i	0.925183	−	0.354486i
$706$	0.708977	+	4.02081i	0.0266827	+	0.151325i
$707$	10.5653	−	29.0280i	0.397349	−	1.09171i
$708$	20.7535	−	13.2932i	0.779963	−	0.499590i
$709$	0.376750	−	2.13666i	0.0141492	−	0.0802438i	−0.976916	−	0.213626i	$-0.931473\pi$
$709$	0.376750	−	2.13666i	0.0141492	−	0.0802438i	0.991065	+	0.133382i	$0.0425837\pi$
$710$	1.54889	−	3.89687i	0.0581288	−	0.146247i
$711$	3.16503	−	3.19630i	0.118698	−	0.119871i
$712$	8.48841	−	4.90079i	0.318117	−	0.183665i
$713$	−4.77688	−	13.1244i	−0.178895	−	0.491511i
$714$	−1.34555	+	0.561223i	−0.0503559	+	0.0210032i
$715$	−5.29373	+	5.94649i	−0.197974	+	0.222386i
$716$	21.0474	−	17.6609i	0.786579	−	0.660018i
$717$	−25.4141	+	33.2893i	−0.949106	+	1.24321i
$718$	0.831472	+	2.28445i	0.0310303	+	0.0852550i
$719$	2.14999	+	3.72389i	0.0801810	+	0.138878i	0.903328	−	0.428951i	$-0.141117\pi$
$719$	2.14999	+	3.72389i	0.0801810	+	0.138878i	−0.823147	+	0.567829i	$0.807783\pi$
$720$	25.0619	−	1.57908i	0.934002	−	0.0588488i
$721$	0.772022	−	1.33718i	0.0287516	−	0.0497992i
$722$	0.612979	+	0.108085i	0.0228127	+	0.00402250i
$723$	−1.18216	−	25.6302i	−0.0439649	−	0.953197i
$724$	−12.1925	−	4.43770i	−0.453130	−	0.164926i
$725$	19.7186	+	39.2960i	0.732329	+	1.45942i
$726$	−2.33706	+	2.15211i	−0.0867365	+	0.0798724i
$727$	14.7760	−	17.6094i	0.548011	−	0.653095i	−0.418952	−	0.908008i	$-0.637603\pi$
$727$	14.7760	−	17.6094i	0.548011	−	0.653095i	0.966964	+	0.254914i	$0.0820470\pi$
$728$		−	5.72622i		−	0.212228i
$729$	6.60279	−	26.1802i	0.244548	−	0.969637i
$730$	0.844864	+	5.77465i	0.0312698	+	0.213729i
$731$	8.31038	+	6.97324i	0.307371	+	0.257915i
$732$	13.7449	+	14.9262i	0.508028	+	0.551687i
$733$	1.93062	−	0.340421i	0.0713092	−	0.0125737i	−0.137880	−	0.990449i	$-0.544029\pi$
$733$	1.93062	−	0.340421i	0.0713092	−	0.0125737i	0.209189	+	0.977875i	$0.432918\pi$
$734$	4.61603	+	1.68010i	0.170381	+	0.0620136i
$735$	4.91185	−	0.951605i	0.181176	−	0.0351005i
$736$	−1.01017	+	5.72894i	−0.0372353	+	0.211172i
$737$	−9.81157	−	5.66471i	−0.361414	−	0.208662i
$738$	−6.74374	−	0.556613i	−0.248240	−	0.0204892i
$739$	2.11839	+	3.66916i	0.0779263	+	0.134972i	0.902355	−	0.430993i	$-0.141837\pi$
$739$	2.11839	+	3.66916i	0.0779263	+	0.134972i	−0.824429	+	0.565966i	$0.808503\pi$
$740$	−33.6718	+	18.1483i	−1.23780	+	0.667145i
$741$	−15.6361	−	11.9371i	−0.574406	−	0.438519i
$742$	−2.08950	−	2.49017i	−0.0767080	−	0.0914170i
$743$	26.6003	+	31.7011i	0.975872	+	1.16300i	0.986617	+	0.163057i	$0.0521353\pi$
$743$	26.6003	+	31.7011i	0.975872	+	1.16300i	−0.0107448	+	0.999942i	$0.503420\pi$
$744$	−7.62542	+	3.18053i	−0.279561	+	0.116604i
$745$	−8.71620	−	16.1717i	−0.319337	−	0.592487i
$746$	−2.14832	−	3.72101i	−0.0786557	−	0.136236i
$747$	24.7597	+	24.5175i	0.905910	+	0.897047i
$748$	−3.50969	−	2.02632i	−0.128327	−	0.0740895i
$749$	1.41249	−	8.01065i	0.0516114	−	0.292703i
$750$	2.15280	−	3.39381i	0.0786091	−	0.123924i
$751$	−16.4803	−	5.99834i	−0.601375	−	0.218883i	0.0233500	−	0.999727i	$-0.492567\pi$
$751$	−16.4803	−	5.99834i	−0.601375	−	0.218883i	−0.624725	+	0.780845i	$0.714789\pi$
$752$	−25.0404	+	4.41529i	−0.913129	+	0.161009i
$753$	−13.4666	+	3.02022i	−0.490751	+	0.110063i
$754$	3.38520	+	2.84052i	0.123282	+	0.103446i
$755$	2.86619	+	19.5904i	0.104311	+	0.712968i
$756$	17.9957	+	23.0979i	0.654499	+	0.840062i
$757$		−	31.2786i		−	1.13684i	−0.822739	−	0.568420i	$-0.807555\pi$
$757$		−	31.2786i		−	1.13684i	0.822739	−	0.568420i	$-0.192445\pi$
$758$	−1.88925	+	2.25152i	−0.0686206	+	0.0817789i
$759$	5.84470	+	1.82705i	0.212149	+	0.0663176i
$760$	−2.70776	−	8.17619i	−0.0982207	−	0.296581i
$761$	12.3465	+	4.49377i	0.447561	+	0.162899i	0.555961	−	0.831208i	$-0.312350\pi$
$761$	12.3465	+	4.49377i	0.447561	+	0.162899i	−0.108400	+	0.994107i	$0.534573\pi$
$762$	−3.85855	−	1.99660i	−0.139781	−	0.0723291i
$763$	−1.36062	−	0.239915i	−0.0492579	−	0.00868549i
$764$	−9.58366	+	16.5994i	−0.346725	+	0.600545i
$765$	9.18299	−	2.22249i	0.332012	−	0.0803544i
$766$	2.11392	+	3.66141i	0.0763790	+	0.132292i
$767$	6.02200	+	16.5453i	0.217442	+	0.597417i
$768$	−21.7546	−	2.80967i	−0.785001	−	0.101385i
$769$	36.6235	−	30.7307i	1.32068	−	1.10818i	0.334514	−	0.942391i	$-0.391428\pi$
$769$	36.6235	−	30.7307i	1.32068	−	1.10818i	0.986161	−	0.165788i	$-0.0530166\pi$
$770$	−1.46760	−	1.30650i	−0.0528887	−	0.0470829i
$771$	4.48951	−	34.7612i	0.161686	−	1.25189i
$772$	13.0025	+	35.7240i	0.467970	+	1.28574i
$773$	45.6728	−	26.3692i	1.64274	−	0.948434i	0.662881	−	0.748725i	$-0.269333\pi$
$773$	45.6728	−	26.3692i	1.64274	−	0.948434i	0.979855	−	0.199710i	$-0.0639999\pi$
$774$	−2.00537	+	4.35631i	−0.0720815	+	0.156584i
$775$	6.70731	−	28.2578i	0.240934	−	1.01505i
$776$	0.801623	−	4.54623i	0.0287766	−	0.163200i
$777$	−38.7216	−	20.0364i	−1.38913	−	0.718801i
$778$	−0.810692	+	2.22736i	−0.0290647	+	0.0798546i
$779$	−8.85162	−	50.2000i	−0.317142	−	1.79860i
$780$	−2.88225	+	18.1250i	−0.103201	+	0.648980i
$781$	10.1779	+	8.54024i	0.364192	+	0.305594i
$782$			0.702854i			0.0251340i
$783$	−45.6606	−	1.65639i	−1.63178	−	0.0591944i
$784$	−4.83580			−0.172707
$785$	−11.8478	−	7.31061i	−0.422867	−	0.260927i
$786$	0.0204461	+	0.0911654i	0.000729288	+	0.00325176i
$787$	8.67001	−	1.52876i	0.309053	−	0.0544943i	−0.0169709	−	0.999856i	$-0.505402\pi$
$787$	8.67001	−	1.52876i	0.309053	−	0.0544943i	0.326023	+	0.945362i	$0.394291\pi$
$788$	4.33353	−	11.9063i	0.154376	−	0.424144i
$789$	−20.3635	−	31.7916i	−0.724960	−	1.13181i
$790$	−0.0203558	+	0.695537i	−0.000724225	+	0.0247461i
$791$	6.12740	−	10.6130i	0.217865	−	0.377354i
$792$	0.920360	−	3.50363i	0.0327036	−	0.124496i
$793$	−12.5538	+	7.24793i	−0.445798	+	0.257382i
$794$	0.660500	−	0.240402i	0.0234403	−	0.00853156i
$795$	10.8388	+	18.0642i	0.384414	+	0.640672i
$796$	−25.8268	+	21.6712i	−0.915406	+	0.768117i
$797$	5.59255	+	6.66494i	0.198098	+	0.236084i	0.855944	−	0.517068i	$-0.172977\pi$
$797$	5.59255	+	6.66494i	0.198098	+	0.236084i	−0.657846	+	0.753153i	$0.728532\pi$
$798$	2.94608	−	3.85900i	0.104290	−	0.136607i
$799$	−8.98971	+	3.27199i	−0.318033	+	0.115755i
$800$	−8.30431	+	8.79609i	−0.293602	+	0.310989i
$801$	−29.4311	−	20.3930i	−1.03990	−	0.720552i
$802$	−3.86436	−	2.23109i	−0.136455	−	0.0787825i
$803$	−18.2101	−	3.21093i	−0.642620	−	0.113311i
$804$	−26.0890	+	1.20332i	−0.920087	+	0.0424377i
$805$	3.13333	−	15.1618i	0.110436	−	0.534383i
$806$	−0.506903	−	2.87479i	−0.0178549	−	0.101260i
$807$	5.09337	+	5.53108i	0.179295	+	0.194703i
$808$	−5.66285	+	6.74872i	−0.199218	+	0.237419i
$809$	−37.8226			−1.32977			−0.664886	−	0.746945i	$-0.731520\pi$
$809$	−37.8226			−1.32977			−0.664886	+	0.746945i	$0.731520\pi$
$810$	2.01768	+	3.65700i	0.0708941	+	0.128494i
$811$	−0.322691			−0.0113312			−0.00566561	−	0.999984i	$-0.501803\pi$
$811$	−0.322691			−0.0113312			−0.00566561	+	0.999984i	$0.501803\pi$
$812$	31.8502	−	37.9576i	1.11772	−	1.33205i
$813$	15.4490	+	16.7767i	0.541820	+	0.588383i
$814$	0.463216	+	2.62703i	0.0162357	+	0.0920773i
$815$	−45.2449	−	9.35029i	−1.58486	−	0.327526i
$816$	−9.12233	+	0.420755i	−0.319345	+	0.0147294i
$817$	−35.5781	−	6.27337i	−1.24472	−	0.219478i
$818$	−2.20478	−	1.27293i	−0.0770883	−	0.0445069i
$819$	−18.9148	+	8.93356i	−0.660936	+	0.312164i
$820$	−37.3090	+	29.4899i	−1.30289	+	1.02983i
$821$	−0.715925	+	0.260575i	−0.0249859	+	0.00909414i	−0.354483	−	0.935063i	$-0.615343\pi$
$821$	−0.715925	+	0.260575i	−0.0249859	+	0.00909414i	0.329497	+	0.944157i	$0.393121\pi$
$822$	−4.07351	+	5.33580i	−0.142080	+	0.186107i
$823$	−34.5795	−	41.2102i	−1.20537	−	1.43650i	−0.869033	−	0.494755i	$-0.835258\pi$
$823$	−34.5795	−	41.2102i	−1.20537	−	1.43650i	−0.336332	−	0.941743i	$-0.609187\pi$
$824$	−0.337327	+	0.283051i	−0.0117513	+	0.00986054i
$825$	8.06325	+	9.85554i	0.280726	+	0.343126i
$826$	−4.08340	+	1.48624i	−0.142080	+	0.0517128i
$827$	−15.4598	+	8.92572i	−0.537590	+	0.310378i	−0.744102	−	0.668066i	$-0.767122\pi$
$827$	−15.4598	+	8.92572i	−0.537590	+	0.310378i	0.206512	+	0.978444i	$0.433789\pi$
$828$	13.6171	−	3.72052i	0.473227	−	0.129297i
$829$	3.49405	−	6.05188i	0.121354	−	0.210190i	−0.798948	−	0.601400i	$-0.794610\pi$
$829$	3.49405	−	6.05188i	0.121354	−	0.210190i	0.920302	+	0.391209i	$0.127943\pi$
$830$	−5.38787	−	0.157683i	−0.187016	−	0.00547326i
$831$	0.474356	+	0.740568i	0.0164552	+	0.0256900i
$832$	5.78471	−	15.8934i	0.200549	−	0.551003i
$833$	−1.79180	+	0.315943i	−0.0620823	+	0.0109468i
$834$	−0.546991	−	2.43894i	−0.0189408	−	0.0844534i
$835$	−11.9314	−	7.36217i	−0.412902	−	0.254778i
$836$	13.4959			0.466765
$837$	22.4024	+	20.2262i	0.774341	+	0.699120i
$838$		−	6.29168i		−	0.217343i
$839$	34.2020	+	28.6989i	1.18078	+	0.990795i	0.999974	+	0.00727705i	$0.00231638\pi$
$839$	34.2020	+	28.6989i	1.18078	+	0.990795i	0.180810	+	0.983518i	$0.442128\pi$
$840$	−9.04502	−	1.43834i	−0.312083	−	0.0496275i
$841$	8.39066	+	47.5858i	0.289333	+	1.64089i
$842$	0.645076	−	1.77233i	0.0222308	−	0.0610786i
$843$	0.752303	+	0.389277i	0.0259107	+	0.0134074i
$844$	6.85757	−	38.8912i	0.236047	−	1.33869i
$845$	14.8291	+	5.89412i	0.510136	+	0.202764i
$846$	−2.44270	−	3.45230i	−0.0839818	−	0.118692i
$847$	−22.0400	+	12.7248i	−0.757302	+	0.437229i
$848$	−6.96412	−	19.1338i	−0.239149	−	0.657056i
$849$	0.935272	−	7.24158i	0.0320984	−	0.248530i
$850$	−0.803545	+	1.22083i	−0.0275614	+	0.0418742i
$851$	−16.1013	+	13.5106i	−0.551946	+	0.463138i
$852$	30.3753	+	3.92306i	1.04064	+	0.134402i
$853$	6.47405	+	17.7873i	0.221667	+	0.609026i	0.999819	−	0.0190511i	$-0.00606451\pi$
$853$	6.47405	+	17.7873i	0.221667	+	0.609026i	−0.778151	+	0.628077i	$0.783842\pi$
$854$	−1.78880	−	3.09829i	−0.0612114	−	0.106021i
$855$	−22.7831	+	21.7000i	−0.779165	+	0.742125i
$856$	−1.15991	+	2.00902i	−0.0396448	+	0.0686668i
$857$	55.0204	+	9.70158i	1.87946	+	0.331400i	0.991665	−	0.128840i	$-0.0411252\pi$
$857$	55.0204	+	9.70158i	1.87946	+	0.331400i	0.887795	+	0.460239i	$0.152236\pi$
$858$	1.13672	+	0.588192i	0.0388070	+	0.0200806i
$859$	5.69311	+	2.07212i	0.194246	+	0.0706999i	0.437312	−	0.899310i	$-0.355931\pi$
$859$	5.69311	+	2.07212i	0.194246	+	0.0706999i	−0.243065	+	0.970010i	$0.578153\pi$
$860$	10.5962	+	31.9956i	0.361326	+	1.09104i
$861$	−51.7357	−	16.1725i	−1.76315	−	0.551158i
$862$	2.36201	−	2.81493i	0.0804503	−	0.0958769i
$863$		−	31.2067i		−	1.06229i	−0.847281	−	0.531145i	$-0.821762\pi$
$863$		−	31.2067i		−	1.06229i	0.847281	−	0.531145i	$-0.178238\pi$
$864$	−3.86858	−	11.9613i	−0.131612	−	0.406933i
$865$	−8.78229	+	1.28490i	−0.298607	+	0.0436879i
$866$	−1.07264	−	0.900051i	−0.0364497	−	0.0305850i
$867$	25.3786	−	5.69176i	0.861901	−	0.193302i
$868$	−32.2345	+	5.68381i	−1.09411	+	0.192921i
$869$	−2.07170	−	0.754038i	−0.0702777	−	0.0255790i
$870$	5.33714	−	4.63370i	0.180946	−	0.157097i
$871$	3.23992	−	18.3745i	0.109781	−	0.622597i
$872$	0.341235	+	0.197012i	0.0115557	+	0.00667168i
$873$	−16.2677	+	4.44473i	−0.550577	+	0.150431i
$874$	−1.17030	−	2.02703i	−0.0395861	−	0.0685652i
$875$	22.7764	−	22.7533i	0.769983	−	0.769202i
$876$	−39.3408	+	16.4089i	−1.32920	+	0.554404i
$877$	−0.574169	−	0.684268i	−0.0193883	−	0.0231061i	0.756263	−	0.654268i	$-0.227023\pi$
$877$	−0.574169	−	0.684268i	−0.0193883	−	0.0231061i	−0.775651	+	0.631161i	$0.782579\pi$
$878$	0.594651	+	0.708677i	0.0200685	+	0.0239167i
$879$	31.8392	+	24.3070i	1.07391	+	0.819854i
$880$	−5.83942	−	10.8343i	−0.196847	−	0.365223i
$881$	−28.2154	−	48.8706i	−0.950602	−	1.64649i	−0.744126	−	0.668039i	$-0.767134\pi$
$881$	−28.2154	−	48.8706i	−0.950602	−	1.64649i	−0.206476	−	0.978452i	$-0.566199\pi$
$882$	−0.343497	−	0.727276i	−0.0115661	−	0.0244887i
$883$	45.6611	+	26.3625i	1.53662	+	0.887168i	0.999033	+	0.0439585i	$0.0139969\pi$
$883$	45.6611	+	26.3625i	1.53662	+	0.887168i	0.537586	+	0.843209i	$0.319336\pi$
$884$	1.15895	−	6.57273i	0.0389797	−	0.221065i
$885$	27.6473	−	5.35629i	0.929353	−	0.180050i
$886$	1.56459	+	0.569463i	0.0525633	+	0.0191315i
$887$	51.5601	−	9.09144i	1.73122	−	0.305261i	0.782799	−	0.622275i	$-0.213792\pi$
$887$	51.5601	−	9.09144i	1.73122	−	0.305261i	0.948421	+	0.317015i	$0.102680\pi$
$888$	8.42273	+	9.14656i	0.282648	+	0.306938i
$889$	−26.6597	−	22.3702i	−0.894139	−	0.750272i
$890$	5.48055	−	0.801835i	0.183708	−	0.0268776i
$891$	−13.0090	+	2.42594i	−0.435818	+	0.0812719i
$892$		−	18.2819i		−	0.612122i
$893$	20.4782	−	24.4049i	0.685276	−	0.816680i
$894$	−2.17253	+	2.00060i	−0.0726601	+	0.0669100i
$895$	29.8028	−	9.86997i	0.996197	−	0.329917i
$896$	17.0156	+	6.19316i	0.568450	+	0.206899i
$897$	0.464650	+	10.0740i	0.0155142	+	0.336362i
$898$	−1.07347	−	0.189282i	−0.0358221	−	0.00631641i
$899$	25.5379	−	44.2330i	0.851737	−	1.47525i
$900$	27.9059	+	9.10548i	0.930198	+	0.303516i
$901$	−3.83049	−	6.63461i	−0.127612	−	0.221031i
$902$	1.13431	+	3.11648i	0.0377682	+	0.103767i
$903$	−23.3113	+	30.5350i	−0.775752	+	1.01614i
$904$	−2.67730	+	2.24652i	−0.0890457	+	0.0747182i
$905$	−11.0735	−	9.85796i	−0.368097	−	0.327690i
$906$	2.93761	−	1.22526i	0.0975955	−	0.0407067i
$907$	−6.80568	−	18.6984i	−0.225979	−	0.620872i	0.773945	−	0.633253i	$-0.218281\pi$
$907$	−6.80568	−	18.6984i	−0.225979	−	0.620872i	−0.999923	+	0.0123817i	$0.996059\pi$
$908$	13.3274	−	7.69456i	0.442284	−	0.255353i
$909$	31.1270	+	8.17668i	1.03242	+	0.271203i
$910$	1.19522	−	3.00707i	0.0396212	−	0.0996835i
$911$	−2.63013	+	14.9162i	−0.0871400	+	0.494195i	0.909734	+	0.415191i	$0.136285\pi$
$911$	−2.63013	+	14.9162i	−0.0871400	+	0.494195i	−0.996874	+	0.0790044i	$0.974826\pi$
$912$	25.6082	−	16.4028i	0.847971	−	0.543152i
$913$	5.84105	−	16.0482i	0.193311	−	0.531116i
$914$	−0.109206	−	0.619336i	−0.00361220	−	0.0204858i
$915$	8.29535	+	21.6503i	0.274236	+	0.715736i
$916$	24.9965	+	20.9746i	0.825907	+	0.693019i
$917$			0.748423i			0.0247151i
$918$	−0.711256	−	1.34206i	−0.0234750	−	0.0442945i
$919$	31.1704			1.02822			0.514109	−	0.857725i	$-0.328123\pi$
$919$	31.1704			1.02822			0.514109	+	0.857725i	$0.328123\pi$
$920$	−2.31861	+	3.75762i	−0.0764424	+	0.123885i
$921$	5.50889	+	1.72207i	0.181524	+	0.0567442i
$922$	0.600621	−	0.105906i	0.0197804	−	0.00348782i
$923$	−7.48361	+	20.5610i	−0.246326	+	0.676775i
$924$	6.59529	−	12.7458i	0.216969	−	0.419306i
$925$	−43.4136	+	5.05944i	−1.42743	+	0.166353i
$926$	−1.91563	+	3.31796i	−0.0629514	+	0.109035i
$927$	1.46124	+	0.672662i	0.0479934	+	0.0220931i
$928$	−18.4237	+	10.6369i	−0.604788	+	0.349174i
$929$	9.60870	−	3.49728i	0.315251	−	0.114742i	−0.179548	−	0.983749i	$-0.557464\pi$
$929$	9.60870	−	3.49728i	0.315251	−	0.114742i	0.494800	+	0.869007i	$0.335241\pi$
$930$	−4.66829	+	0.0785888i	−0.153079	+	0.00257703i
$931$	4.64148	−	3.89467i	0.152118	−	0.127643i
$932$	−37.5561	−	44.7577i	−1.23019	−	1.46609i
$933$	18.9897	+	2.45258i	0.621695	+	0.0802937i
$934$	4.21379	−	1.53369i	0.137879	−	0.0501840i
$935$	−2.87152	−	3.63289i	−0.0939088	−	0.118808i
$936$	5.94041	−	0.549155i	0.194168	−	0.0179497i
$937$	−0.758718	−	0.438046i	−0.0247862	−	0.0143103i	0.487556	−	0.873092i	$-0.337889\pi$
$937$	−0.758718	−	0.438046i	−0.0247862	−	0.0143103i	−0.512342	+	0.858782i	$0.671222\pi$
$938$	4.53485	+	0.799617i	0.148068	+	0.0261084i
$939$	−7.44011	+	14.3785i	−0.242799	+	0.469224i
$940$	−29.1071	−	6.01527i	−0.949370	−	0.196197i
$941$	0.921099	+	5.22381i	0.0300270	+	0.170291i	0.996134	−	0.0878522i	$-0.0280003\pi$
$941$	0.921099	+	5.22381i	0.0300270	+	0.170291i	−0.966107	+	0.258144i	$0.916889\pi$
$942$	−0.667753	+	2.13613i	−0.0217566	+	0.0695990i
$943$	−16.7973	+	20.0183i	−0.546996	+	0.651884i
$944$	−27.2192			−0.885911
$945$	9.36015	+	32.1214i	0.304486	+	1.04491i
$946$	2.35048			0.0764208
$947$	−14.4581	+	17.2305i	−0.469825	+	0.559916i	−0.947968	−	0.318366i	$-0.896866\pi$
$947$	−14.4581	+	17.2305i	−0.469825	+	0.559916i	0.478143	+	0.878282i	$0.341310\pi$
$948$	−4.95902	+	1.11218i	−0.161061	+	0.0361220i
$949$	−5.28795	−	29.9895i	−0.171654	−	0.973500i
$950$	0.284644	−	4.85884i	0.00923506	−	0.157641i
$951$	25.4520	+	39.7358i	0.825338	+	1.28852i
$952$	3.28002	+	0.578356i	0.106306	+	0.0187446i
$953$	−3.69060	−	2.13077i	−0.119550	−	0.0690223i	0.439032	−	0.898471i	$-0.355321\pi$
$953$	−3.69060	−	2.13077i	−0.119550	−	0.0690223i	−0.558583	+	0.829449i	$0.688655\pi$
$954$	2.38293	−	2.40647i	0.0771502	−	0.0779124i
$955$	−17.1821	+	13.5811i	−0.556000	+	0.439475i
$956$	44.4653	−	16.1840i	1.43811	−	0.523430i
$957$	8.62062	+	20.6682i	0.278665	+	0.668108i
$958$	0.133200	+	0.158741i	0.00430349	+	0.00512870i
$959$	−41.1937	+	34.5656i	−1.33021	+	1.11618i
$960$	−23.6518	−	13.1296i	−0.763359	−	0.423756i
$961$	−2.57434	+	0.936985i	−0.0830434	+	0.0302253i
$962$	−3.80453	+	2.19655i	−0.122663	+	0.0708195i
$963$	8.44575	+	0.697093i	0.272161	+	0.0224635i
$964$	−14.4943	+	25.1049i	−0.466830	+	0.808573i
$965$	−1.27077	+	43.4210i	−0.0409075	+	1.39777i
$966$	−2.48628	+	0.114676i	−0.0799948	+	0.00368965i
$967$	1.30770	−	3.59289i	0.0420529	−	0.115539i	−0.916889	−	0.399143i	$-0.869308\pi$
$967$	1.30770	−	3.59289i	0.0420529	−	0.115539i	0.958942	+	0.283604i	$0.0915300\pi$
$968$	7.14774	−	1.26034i	0.229737	−	0.0405089i
$969$	8.41690	−	7.75081i	0.270390	−	0.248992i
$970$	1.36989	−	2.22009i	0.0439845	−	0.0712828i
$971$	57.0974			1.83234			0.916171	−	0.400787i	$-0.131263\pi$
$971$	57.0974			1.83234			0.916171	+	0.400787i	$0.131263\pi$
$972$	−22.2360	+	20.8840i	−0.713221	+	0.669855i
$973$		−	20.0225i		−	0.641890i
$974$	2.91763	+	2.44819i	0.0934870	+	0.0784449i
$975$	−10.7102	+	18.0294i	−0.343000	+	0.577404i
$976$	−3.89136	−	22.0690i	−0.124559	−	0.706411i
$977$	9.83942	−	27.0336i	0.314791	−	0.864881i	−0.676881	−	0.736092i	$-0.736669\pi$
$977$	9.83942	−	27.0336i	0.314791	−	0.864881i	0.991672	−	0.128789i	$-0.0411089\pi$
$978$	0.342209	+	7.41940i	0.0109426	+	0.237246i
$979$	−3.04740	+	17.2826i	−0.0973952	+	0.552356i
$980$	−5.25302	−	2.08792i	−0.167802	−	0.0666961i
$981$	0.118403	−	1.43453i	0.00378030	−	0.0458009i
$982$	1.95726	−	1.13002i	0.0624586	−	0.0360605i
$983$	14.8222	+	40.7237i	0.472756	+	1.29889i	0.915529	+	0.402252i	$0.131772\pi$
$983$	14.8222	+	40.7237i	0.472756	+	1.29889i	−0.442773	+	0.896634i	$0.646005\pi$
$984$	12.2873	+	9.38048i	0.391704	+	0.299039i
$985$	9.62657	−	10.8136i	0.306728	−	0.344550i
$986$	−1.96898	+	1.65217i	−0.0627052	+	0.0526159i
$987$	−13.0411	−	31.2664i	−0.415103	−	0.995222i
$988$	7.60169	+	20.8855i	0.241842	+	0.664455i
$989$	9.26022	+	16.0392i	0.294458	+	0.510016i
$990$	1.21462	−	1.64779i	0.0386033	−	0.0523703i
$991$	−23.9951	+	41.5607i	−0.762230	+	1.32022i	0.179469	+	0.983764i	$0.442562\pi$
$991$	−23.9951	+	41.5607i	−0.762230	+	1.32022i	−0.941699	+	0.336457i	$0.890771\pi$
$992$	13.8395	+	2.44028i	0.439406	+	0.0774791i
$993$	−37.0338	+	23.7213i	−1.17523	+	0.752773i
$994$	−5.07449	−	1.84696i	−0.160953	−	0.0585821i
$995$	−36.5703	+	12.1112i	−1.15936	+	0.383951i
$996$	−8.61536	−	38.4143i	−0.272988	−	1.21720i
$997$	21.4919	−	25.6130i	0.680655	−	0.811173i	−0.309537	−	0.950887i	$-0.600174\pi$
$997$	21.4919	−	25.6130i	0.680655	−	0.811173i	0.990192	+	0.139715i	$0.0446185\pi$
$998$		−	6.03495i		−	0.191033i
$999$	17.0724	−	42.0915i	0.540147	−	1.33172i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.2.p.a.124.8	yes	96
3.2	odd	2		405.2.p.a.289.9		96
5.2	odd	4		675.2.l.h.151.8		96
5.3	odd	4		675.2.l.h.151.9		96
5.4	even	2	inner	135.2.p.a.124.9	yes	96
15.14	odd	2		405.2.p.a.289.8		96
27.5	odd	18		405.2.p.a.199.8		96
27.22	even	9	inner	135.2.p.a.49.9	yes	96
135.22	odd	36		675.2.l.h.76.8		96
135.49	even	18	inner	135.2.p.a.49.8	✓	96
135.59	odd	18		405.2.p.a.199.9		96
135.103	odd	36		675.2.l.h.76.9		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.p.a.49.8	✓	96	135.49	even	18	inner
135.2.p.a.49.9	yes	96	27.22	even	9	inner
135.2.p.a.124.8	yes	96	1.1	even	1	trivial
135.2.p.a.124.9	yes	96	5.4	even	2	inner
405.2.p.a.199.8		96	27.5	odd	18
405.2.p.a.199.9		96	135.59	odd	18
405.2.p.a.289.8		96	15.14	odd	2
405.2.p.a.289.9		96	3.2	odd	2
675.2.l.h.76.8		96	135.22	odd	36
675.2.l.h.76.9		96	135.103	odd	36
675.2.l.h.151.8		96	5.2	odd	4
675.2.l.h.151.9		96	5.3	odd	4

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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.133405 + 0.158986i) q^{2} +(-1.17329 - 1.27412i) q^{3} +(0.339817 + 1.92720i) q^{4} +(-0.452543 + 2.18980i) q^{5} +(0.359090 - 0.0165625i) q^{6} +(2.83580 + 0.500029i) q^{7} +(-0.711201 - 0.410612i) q^{8} +(-0.246774 + 2.98983i) q^{9} +O(q^{10})\)	\(q+(-0.133405 + 0.158986i) q^{2} +(-1.17329 - 1.27412i) q^{3} +(0.339817 + 1.92720i) q^{4} +(-0.452543 + 2.18980i) q^{5} +(0.359090 - 0.0165625i) q^{6} +(2.83580 + 0.500029i) q^{7} +(-0.711201 - 0.410612i) q^{8} +(-0.246774 + 2.98983i) q^{9} +(-0.287775 - 0.364077i) q^{10} +(1.38169 - 0.502894i) q^{11} +(2.05678 - 2.69413i) q^{12} +(1.55650 + 1.85496i) q^{13} +(-0.457807 + 0.384146i) q^{14} +(3.32103 - 1.99267i) q^{15} +(-3.51766 + 1.28032i) q^{16} +(-1.21975 + 0.704220i) q^{17} +(-0.442420 - 0.438091i) q^{18} +(2.34516 - 4.06194i) q^{19} +(-4.37395 - 0.128009i) q^{20} +(-2.69013 - 4.19984i) q^{21} +(-0.104371 + 0.286757i) q^{22} +(-2.36796 + 0.417535i) q^{23} +(0.311276 + 1.38792i) q^{24} +(-4.59041 - 1.98195i) q^{25} -0.502557 q^{26} +(4.09895 - 3.19353i) q^{27} +5.63507i q^{28} +(-6.73596 - 5.65214i) q^{29} +(-0.126235 + 0.793828i) q^{30} +(1.00865 + 5.72033i) q^{31} +(0.827470 - 2.27346i) q^{32} +(-2.26187 - 1.17040i) q^{33} +(0.0507589 - 0.287868i) q^{34} +(-2.37828 + 5.98355i) q^{35} +(-5.84585 + 0.540413i) q^{36} +(7.57034 - 4.37074i) q^{37} +(0.332934 + 0.914728i) q^{38} +(0.537223 - 4.15958i) q^{39} +(1.22101 - 1.37157i) q^{40} +(8.32538 - 6.98582i) q^{41} +(1.02659 + 0.132587i) q^{42} +(-2.63439 - 7.23793i) q^{43} +(1.43870 + 2.49190i) q^{44} +(-6.43545 - 1.89341i) q^{45} +(0.249515 - 0.432172i) q^{46} +(6.68918 + 1.17948i) q^{47} +(5.75853 + 2.97974i) q^{48} +(1.21391 + 0.441827i) q^{49} +(0.927484 - 0.465407i) q^{50} +(2.32838 + 0.727849i) q^{51} +(-3.04596 + 3.63003i) q^{52} +5.43934i q^{53} +(-0.0390949 + 1.07771i) q^{54} +(0.475961 + 3.25320i) q^{55} +(-1.81151 - 1.52004i) q^{56} +(-7.92696 + 1.77782i) q^{57} +(1.79722 - 0.316898i) q^{58} +(6.83272 + 2.48691i) q^{59} +(4.96882 + 5.72314i) q^{60} +(-1.03952 + 5.89541i) q^{61} +(-1.04401 - 0.602759i) q^{62} +(-2.19481 + 8.35519i) q^{63} +(-3.49236 - 6.04894i) q^{64} +(-4.76637 + 2.56897i) q^{65} +(0.487821 - 0.203468i) q^{66} +(-4.95280 - 5.90251i) q^{67} +(-1.77166 - 2.11138i) q^{68} +(3.31030 + 2.52718i) q^{69} +(-0.634024 - 1.17635i) q^{70} +(4.51802 + 7.82544i) q^{71} +(1.40317 - 2.02504i) q^{72} +(-10.8910 - 6.28791i) q^{73} +(-0.315035 + 1.78665i) q^{74} +(2.86064 + 8.17415i) q^{75} +(8.62507 + 3.13927i) q^{76} +(4.16966 - 0.735224i) q^{77} +(0.589646 + 0.640319i) q^{78} +(-1.14861 - 0.963795i) q^{79} +(-1.21176 - 8.28236i) q^{80} +(-8.87821 - 1.47563i) q^{81} +2.25556i q^{82} +(7.46590 - 8.89751i) q^{83} +(7.17977 - 6.61158i) q^{84} +(-0.990112 - 2.98968i) q^{85} +(1.50217 + 0.546744i) q^{86} +(0.701727 + 15.2140i) q^{87} +(-1.18915 - 0.209680i) q^{88} +(-5.96766 + 10.3363i) q^{89} +(1.15954 - 0.770553i) q^{90} +(3.48639 + 6.03861i) q^{91} +(-1.60934 - 4.42164i) q^{92} +(6.10496 - 7.99676i) q^{93} +(-1.07989 + 0.906134i) q^{94} +(7.83353 + 6.97362i) q^{95} +(-3.86752 + 1.61313i) q^{96} +(1.92260 + 5.28231i) q^{97} +(-0.232185 + 0.134052i) q^{98} +(1.16260 + 4.25512i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 12 q^{4} - 9 q^{5} - 6 q^{6} - 18 q^{9}+O(q^{10}) \) 96 * q - 12 * q^4 - 9 * q^5 - 6 * q^6 - 18 * q^9	\( 96 q - 12 q^{4} - 9 q^{5} - 6 q^{6} - 18 q^{9} - 3 q^{10} - 6 q^{11} - 18 q^{14} - 21 q^{15} - 24 q^{16} - 6 q^{19} - 57 q^{20} + 24 q^{21} - 30 q^{24} + 3 q^{25} + 48 q^{26} - 30 q^{29} - 51 q^{30} - 30 q^{31} - 24 q^{34} - 12 q^{35} + 54 q^{36} - 6 q^{39} - 9 q^{40} - 12 q^{41} + 78 q^{44} + 45 q^{45} - 6 q^{46} - 30 q^{49} + 84 q^{50} - 90 q^{51} + 108 q^{54} - 12 q^{55} - 96 q^{56} + 66 q^{59} + 84 q^{60} + 6 q^{61} + 45 q^{65} - 150 q^{66} + 24 q^{69} - 33 q^{70} - 90 q^{71} + 66 q^{74} + 39 q^{75} + 12 q^{76} + 24 q^{79} + 30 q^{80} - 54 q^{81} + 198 q^{84} - 21 q^{85} + 18 q^{86} + 96 q^{89} + 90 q^{90} - 6 q^{91} + 24 q^{94} + 87 q^{95} + 42 q^{96} + 36 q^{99}+O(q^{100}) \) 96 * q - 12 * q^4 - 9 * q^5 - 6 * q^6 - 18 * q^9 - 3 * q^10 - 6 * q^11 - 18 * q^14 - 21 * q^15 - 24 * q^16 - 6 * q^19 - 57 * q^20 + 24 * q^21 - 30 * q^24 + 3 * q^25 + 48 * q^26 - 30 * q^29 - 51 * q^30 - 30 * q^31 - 24 * q^34 - 12 * q^35 + 54 * q^36 - 6 * q^39 - 9 * q^40 - 12 * q^41 + 78 * q^44 + 45 * q^45 - 6 * q^46 - 30 * q^49 + 84 * q^50 - 90 * q^51 + 108 * q^54 - 12 * q^55 - 96 * q^56 + 66 * q^59 + 84 * q^60 + 6 * q^61 + 45 * q^65 - 150 * q^66 + 24 * q^69 - 33 * q^70 - 90 * q^71 + 66 * q^74 + 39 * q^75 + 12 * q^76 + 24 * q^79 + 30 * q^80 - 54 * q^81 + 198 * q^84 - 21 * q^85 + 18 * q^86 + 96 * q^89 + 90 * q^90 - 6 * q^91 + 24 * q^94 + 87 * q^95 + 42 * q^96 + 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more