LMFDB - Embedded newform 125.2.g.a.11.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [125,2,Mod(6,125)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(125, base_ring=CyclotomicField(50))

chi = DirichletCharacter(H, H._module([4]))

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

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

chi := DirichletCharacter("125.6");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 125 = 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	125.g (of order $25$, degree $20$, 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:	$0.998130025266$
Analytic rank:	$0$
Dimension:	$220$
Relative dimension:	$11$ over $\Q(\zeta_{25})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{25}]$

Embedding invariants

Embedding label			11.6
Character	$\chi$	$=$	125.11
Dual form			125.2.g.a.91.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0548468 - 0.0515046i) q^{2} +(-0.203470 - 0.320618i) q^{3} +(-0.125226 + 1.99040i) q^{4} +(-0.553871 + 2.16639i) q^{5} +(-0.0276730 - 0.00710521i) q^{6} +(-1.02685 + 3.16032i) q^{7} +(0.191565 + 0.231562i) q^{8} +(1.21594 - 2.58401i) q^{9} +O(q^{10})$	\(q+(0.0548468 - 0.0515046i) q^{2} +(-0.203470 - 0.320618i) q^{3} +(-0.125226 + 1.99040i) q^{4} +(-0.553871 + 2.16639i) q^{5} +(-0.0276730 - 0.00710521i) q^{6} +(-1.02685 + 3.16032i) q^{7} +(0.191565 + 0.231562i) q^{8} +(1.21594 - 2.58401i) q^{9} +(0.0812007 + 0.147346i) q^{10} +(3.38861 - 3.18211i) q^{11} +(0.663639 - 0.364839i) q^{12} +(0.285576 - 0.606880i) q^{13} +(0.106452 + 0.226221i) q^{14} +(0.807279 - 0.263214i) q^{15} +(-3.93479 - 0.497080i) q^{16} +(0.233333 + 3.70872i) q^{17} +(-0.0663977 - 0.204351i) q^{18} +(0.358493 - 0.564895i) q^{19} +(-4.24262 - 1.37371i) q^{20} +(1.22219 - 0.313805i) q^{21} +(0.0219608 - 0.349057i) q^{22} +(0.904885 - 4.74358i) q^{23} +(0.0352652 - 0.108535i) q^{24} +(-4.38645 - 2.39980i) q^{25} +(-0.0155941 - 0.0479939i) q^{26} +(-2.20610 + 0.278695i) q^{27} +(-6.16173 - 2.43960i) q^{28} +(8.47614 + 3.35594i) q^{29} +(0.0307199 - 0.0560150i) q^{30} +(-0.133404 - 2.12040i) q^{31} +(-0.727680 + 0.528690i) q^{32} +(-1.70972 - 0.438982i) q^{33} +(0.203814 + 0.191394i) q^{34} +(-6.27773 - 3.97497i) q^{35} +(4.99095 + 2.74380i) q^{36} +(2.60134 + 0.328626i) q^{37} +(-0.00943246 - 0.0494467i) q^{38} +(-0.252683 + 0.0319213i) q^{39} +(-0.607755 + 0.286748i) q^{40} +(-0.486496 - 2.55030i) q^{41} +(0.0508708 - 0.0801595i) q^{42} +(-5.20385 - 3.78082i) q^{43} +(5.90935 + 7.14317i) q^{44} +(4.92448 + 4.06541i) q^{45} +(-0.194686 - 0.306776i) q^{46} +(4.74419 - 5.73474i) q^{47} +(0.641241 + 1.36271i) q^{48} +(-3.27009 - 2.37586i) q^{49} +(-0.364183 + 0.0943011i) q^{50} +(1.14161 - 0.829425i) q^{51} +(1.17217 + 0.644408i) q^{52} +(0.627649 - 0.161153i) q^{53} +(-0.106643 + 0.128910i) q^{54} +(5.01683 + 9.10351i) q^{55} +(-0.928519 + 0.367627i) q^{56} -0.254058 q^{57} +(0.637735 - 0.252497i) q^{58} +(-7.46982 + 4.10657i) q^{59} +(0.422810 + 1.63977i) q^{60} +(-0.857246 + 4.49384i) q^{61} +(-0.116527 - 0.109426i) q^{62} +(6.91771 + 6.49616i) q^{63} +(1.47365 - 7.72516i) q^{64} +(1.15656 + 0.954801i) q^{65} +(-0.116382 + 0.0639818i) q^{66} +(-14.2113 + 5.62666i) q^{67} -7.41107 q^{68} +(-1.70499 + 0.675054i) q^{69} +(-0.549042 + 0.105318i) q^{70} +(2.91281 - 3.52098i) q^{71} +(0.831290 - 0.213439i) q^{72} +(13.4740 + 7.40740i) q^{73} +(0.159601 - 0.115957i) q^{74} +(0.123095 + 1.89466i) q^{75} +(1.07948 + 0.784285i) q^{76} +(6.57691 + 13.9766i) q^{77} +(-0.0122147 + 0.0147651i) q^{78} +(-2.54046 - 4.00312i) q^{79} +(3.25624 - 8.24896i) q^{80} +(-4.92284 - 5.95070i) q^{81} +(-0.158035 - 0.114819i) q^{82} +(6.30486 - 9.93486i) q^{83} +(0.471549 + 2.47195i) q^{84} +(-8.16376 - 1.54866i) q^{85} +(-0.480143 + 0.0606562i) q^{86} +(-0.648668 - 3.40044i) q^{87} +(1.38599 + 0.175092i) q^{88} +(7.79608 + 4.28593i) q^{89} +(0.479479 - 0.0306588i) q^{90} +(1.62469 + 1.52569i) q^{91} +(9.32832 + 2.39510i) q^{92} +(-0.652695 + 0.474211i) q^{93} +(-0.0351617 - 0.558880i) q^{94} +(1.02522 + 1.08951i) q^{95} +(0.317569 + 0.125734i) q^{96} +(-14.2841 - 5.65548i) q^{97} +(-0.301722 + 0.0381163i) q^{98} +(-4.10226 - 12.6254i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 220 q - 20 q^{2} - 20 q^{3} - 20 q^{4} - 15 q^{5} - 20 q^{6} - 15 q^{7} - 5 q^{8} - 20 q^{9}+O(q^{10}) $ 220 * q - 20 * q^2 - 20 * q^3 - 20 * q^4 - 15 * q^5 - 20 * q^6 - 15 * q^7 - 5 * q^8 - 20 * q^9	\( 220 q - 20 q^{2} - 20 q^{3} - 20 q^{4} - 15 q^{5} - 20 q^{6} - 15 q^{7} - 5 q^{8} - 20 q^{9} - 20 q^{10} - 15 q^{11} - 100 q^{12} - 20 q^{13} - 10 q^{14} - 15 q^{17} + 10 q^{18} - 10 q^{19} + 5 q^{20} - 5 q^{21} + 25 q^{22} - 90 q^{23} + 15 q^{24} - 45 q^{25} + 15 q^{26} + 10 q^{27} + 30 q^{28} - 10 q^{29} + 40 q^{30} - 10 q^{31} + 20 q^{32} + 15 q^{33} + 5 q^{34} + 10 q^{35} - 210 q^{36} + 20 q^{37} + 30 q^{38} + 45 q^{40} - 5 q^{41} + 70 q^{42} + 25 q^{43} + 15 q^{44} - 100 q^{45} - 100 q^{47} + 105 q^{48} - 20 q^{49} + 60 q^{50} + 25 q^{51} + 85 q^{52} + 20 q^{53} + 60 q^{54} + 15 q^{55} - 105 q^{56} + 40 q^{57} - 225 q^{58} + 5 q^{59} - 35 q^{60} + 65 q^{62} + 85 q^{63} + 45 q^{64} + 45 q^{65} + 55 q^{66} - 105 q^{67} + 80 q^{68} + 40 q^{69} + 95 q^{70} - 85 q^{71} + 160 q^{72} + 40 q^{73} + 35 q^{74} + 55 q^{75} + 35 q^{76} + 75 q^{77} - 10 q^{78} - 330 q^{80} + 55 q^{81} - 95 q^{82} + 50 q^{83} + 115 q^{84} + 85 q^{85} + 40 q^{86} + 95 q^{87} + 165 q^{88} + 55 q^{89} + 170 q^{90} - 105 q^{91} + 155 q^{92} - 185 q^{93} + 60 q^{94} + 30 q^{95} + 135 q^{96} + 65 q^{97} + 135 q^{98} + 45 q^{99}+O(q^{100}) \) 220 * q - 20 * q^2 - 20 * q^3 - 20 * q^4 - 15 * q^5 - 20 * q^6 - 15 * q^7 - 5 * q^8 - 20 * q^9 - 20 * q^10 - 15 * q^11 - 100 * q^12 - 20 * q^13 - 10 * q^14 - 15 * q^17 + 10 * q^18 - 10 * q^19 + 5 * q^20 - 5 * q^21 + 25 * q^22 - 90 * q^23 + 15 * q^24 - 45 * q^25 + 15 * q^26 + 10 * q^27 + 30 * q^28 - 10 * q^29 + 40 * q^30 - 10 * q^31 + 20 * q^32 + 15 * q^33 + 5 * q^34 + 10 * q^35 - 210 * q^36 + 20 * q^37 + 30 * q^38 + 45 * q^40 - 5 * q^41 + 70 * q^42 + 25 * q^43 + 15 * q^44 - 100 * q^45 - 100 * q^47 + 105 * q^48 - 20 * q^49 + 60 * q^50 + 25 * q^51 + 85 * q^52 + 20 * q^53 + 60 * q^54 + 15 * q^55 - 105 * q^56 + 40 * q^57 - 225 * q^58 + 5 * q^59 - 35 * q^60 + 65 * q^62 + 85 * q^63 + 45 * q^64 + 45 * q^65 + 55 * q^66 - 105 * q^67 + 80 * q^68 + 40 * q^69 + 95 * q^70 - 85 * q^71 + 160 * q^72 + 40 * q^73 + 35 * q^74 + 55 * q^75 + 35 * q^76 + 75 * q^77 - 10 * q^78 - 330 * q^80 + 55 * q^81 - 95 * q^82 + 50 * q^83 + 115 * q^84 + 85 * q^85 + 40 * q^86 + 95 * q^87 + 165 * q^88 + 55 * q^89 + 170 * q^90 - 105 * q^91 + 155 * q^92 - 185 * q^93 + 60 * q^94 + 30 * q^95 + 135 * q^96 + 65 * q^97 + 135 * q^98 + 45 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/125\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{19}{25}\right)$

Coefficient data

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

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

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

$2$	0.0548468	−	0.0515046i	0.0387825	−	0.0364192i	−0.664914	−	0.746920i	$-0.731532\pi$
$2$	0.0548468	−	0.0515046i	0.0387825	−	0.0364192i	0.703696	+	0.710501i	$0.251532\pi$
$3$	−0.203470	−	0.320618i	−0.117474	−	0.185109i	0.780503	−	0.625152i	$-0.214963\pi$
$3$	−0.203470	−	0.320618i	−0.117474	−	0.185109i	−0.897977	+	0.440043i	$0.854963\pi$
$4$	−0.125226	+	1.99040i	−0.0626128	+	0.995202i
$5$	−0.553871	+	2.16639i	−0.247699	+	0.968837i
$5$	−0.553871	+	2.16639i	−0.247699	+	0.968837i
$6$	−0.0276730	−	0.00710521i	−0.0112974	−	0.00290069i
$7$	−1.02685	+	3.16032i	−0.388113	+	1.19449i	0.546083	+	0.837731i	$0.316118\pi$
$7$	−1.02685	+	3.16032i	−0.388113	+	1.19449i	−0.934197	+	0.356759i	$0.883882\pi$
$8$	0.191565	+	0.231562i	0.0677284	+	0.0818695i
$9$	1.21594	−	2.58401i	0.405314	−	0.861336i
$10$	0.0812007	+	0.147346i	0.0256779	+	0.0465950i
$11$	3.38861	−	3.18211i	1.02170	−	0.959443i	0.0225154	−	0.999746i	$-0.492833\pi$
$11$	3.38861	−	3.18211i	1.02170	−	0.959443i	0.999187	+	0.0403037i	$0.0128325\pi$
$12$	0.663639	−	0.364839i	0.191576	−	0.105320i
$13$	0.285576	−	0.606880i	0.0792045	−	0.168318i	−0.861302	−	0.508093i	$-0.830351\pi$
$13$	0.285576	−	0.606880i	0.0792045	−	0.168318i	0.940507	+	0.339774i	$0.110351\pi$
$14$	0.106452	+	0.226221i	0.0284504	+	0.0604601i
$15$	0.807279	−	0.263214i	0.208438	−	0.0679616i
$16$	−3.93479	−	0.497080i	−0.983698	−	0.124270i
$17$	0.233333	+	3.70872i	0.0565915	+	0.899497i	0.919241	+	0.393695i	$0.128803\pi$
$17$	0.233333	+	3.70872i	0.0565915	+	0.899497i	−0.862650	+	0.505802i	$0.831197\pi$
$18$	−0.0663977	−	0.204351i	−0.0156501	−	0.0481660i
$19$	0.358493	−	0.564895i	0.0822439	−	0.129596i	−0.800716	−	0.599044i	$-0.795547\pi$
$19$	0.358493	−	0.564895i	0.0822439	−	0.129596i	0.882960	+	0.469449i	$0.155547\pi$
$20$	−4.24262	−	1.37371i	−0.948679	−	0.307172i
$21$	1.22219	−	0.313805i	0.266704	−	0.0684779i
$22$	0.0219608	−	0.349057i	0.00468206	−	0.0744192i
$23$	0.904885	−	4.74358i	0.188682	−	0.989104i	−0.754368	−	0.656452i	$-0.772057\pi$
$23$	0.904885	−	4.74358i	0.188682	−	0.989104i	0.943050	−	0.332652i	$-0.107943\pi$
$24$	0.0352652	−	0.108535i	0.00719848	−	0.0221546i
$25$	−4.38645	−	2.39980i	−0.877291	−	0.479960i
$26$	−0.0155941	−	0.0479939i	−0.00305826	−	0.00941237i
$27$	−2.20610	+	0.278695i	−0.424564	+	0.0536349i
$28$	−6.16173	−	2.43960i	−1.16446	−	0.461041i
$29$	8.47614	+	3.35594i	1.57398	+	0.623182i	0.983017	−	0.183516i	$-0.0587481\pi$
$29$	8.47614	+	3.35594i	1.57398	+	0.623182i	0.590963	+	0.806699i	$0.298748\pi$
$30$	0.0307199	−	0.0560150i	0.00560866	−	0.0102269i
$31$	−0.133404	−	2.12040i	−0.0239601	−	0.380835i	−0.991673	−	0.128781i	$-0.958894\pi$
$31$	−0.133404	−	2.12040i	−0.0239601	−	0.380835i	0.967713	−	0.252055i	$-0.0811063\pi$
$32$	−0.727680	+	0.528690i	−0.128637	+	0.0934601i
$33$	−1.70972	−	0.438982i	−0.297625	−	0.0764170i
$34$	0.203814	+	0.191394i	0.0349537	+	0.0328237i
$35$	−6.27773	−	3.97497i	−1.06113	−	0.671892i
$36$	4.99095	+	2.74380i	0.831826	+	0.457300i
$37$	2.60134	+	0.328626i	0.427658	+	0.0540258i	0.336217	−	0.941785i	$-0.390853\pi$
$37$	2.60134	+	0.328626i	0.427658	+	0.0540258i	0.0914414	+	0.995810i	$0.470853\pi$
$38$	−0.00943246	−	0.0494467i	−0.00153015	−	0.00802131i
$39$	−0.252683	+	0.0319213i	−0.0404616	+	0.00511149i
$40$	−0.607755	+	0.286748i	−0.0960945	+	0.0453388i
$41$	−0.486496	−	2.55030i	−0.0759780	−	0.398290i	−0.999877	−	0.0156552i	$-0.995017\pi$
$41$	−0.486496	−	2.55030i	−0.0759780	−	0.398290i	0.923899	−	0.382635i	$-0.124983\pi$
$42$	0.0508708	−	0.0801595i	0.00784953	−	0.0123689i
$43$	−5.20385	−	3.78082i	−0.793579	−	0.576569i	0.115444	−	0.993314i	$-0.463171\pi$
$43$	−5.20385	−	3.78082i	−0.793579	−	0.576569i	−0.909023	+	0.416745i	$0.863171\pi$
$44$	5.90935	+	7.14317i	0.890868	+	1.07687i
$45$	4.92448	+	4.06541i	0.734099	+	0.606035i
$46$	−0.194686	−	0.306776i	−0.0287048	−	0.0452316i
$47$	4.74419	−	5.73474i	0.692011	−	0.836498i	−0.301110	−	0.953589i	$-0.597357\pi$
$47$	4.74419	−	5.73474i	0.692011	−	0.836498i	0.993121	+	0.117092i	$0.0373571\pi$
$48$	0.641241	+	1.36271i	0.0925552	+	0.196690i
$49$	−3.27009	−	2.37586i	−0.467156	−	0.339409i
$50$	−0.364183	+	0.0943011i	−0.0515033	+	0.0133362i
$51$	1.14161	−	0.829425i	0.159857	−	0.116143i
$52$	1.17217	+	0.644408i	0.162551	+	0.0893633i
$53$	0.627649	−	0.161153i	0.0862142	−	0.0221360i	−0.205336	−	0.978691i	$-0.565829\pi$
$53$	0.627649	−	0.161153i	0.0862142	−	0.0221360i	0.291551	+	0.956555i	$0.405829\pi$
$54$	−0.106643	+	0.128910i	−0.0145123	+	0.0175424i
$55$	5.01683	+	9.10351i	0.676469	+	1.22752i
$56$	−0.928519	+	0.367627i	−0.124079	+	0.0491262i
$57$	−0.254058			−0.0336508
$58$	0.637735	−	0.252497i	0.0837387	−	0.0331545i
$59$	−7.46982	+	4.10657i	−0.972488	+	0.534630i	−0.887030	−	0.461712i	$-0.847235\pi$
$59$	−7.46982	+	4.10657i	−0.972488	+	0.534630i	−0.0854579	+	0.996342i	$0.527235\pi$
$60$	0.422810	+	1.63977i	0.0545846	+	0.211694i
$61$	−0.857246	+	4.49384i	−0.109759	+	0.575377i	0.884335	+	0.466853i	$0.154612\pi$
$61$	−0.857246	+	4.49384i	−0.109759	+	0.575377i	−0.994094	+	0.108524i	$0.965388\pi$
$62$	−0.116527	−	0.109426i	−0.0147990	−	0.0138972i
$63$	6.91771	+	6.49616i	0.871549	+	0.818439i
$64$	1.47365	−	7.72516i	0.184207	−	0.965645i
$65$	1.15656	+	0.954801i	0.143454	+	0.118428i
$66$	−0.116382	+	0.0639818i	−0.0143257	+	0.00787561i
$67$	−14.2113	+	5.62666i	−1.73619	+	0.687406i	−0.736247	+	0.676713i	$0.763404\pi$
$67$	−14.2113	+	5.62666i	−1.73619	+	0.687406i	−0.999943	+	0.0106933i	$0.996596\pi$
$68$	−7.41107			−0.898724
$69$	−1.70499	+	0.675054i	−0.205257	+	0.0812670i
$70$	−0.549042	+	0.105318i	−0.0656231	+	0.0125879i
$71$	2.91281	−	3.52098i	0.345687	−	0.417864i	−0.568802	−	0.822475i	$-0.692593\pi$
$71$	2.91281	−	3.52098i	0.345687	−	0.417864i	0.914489	+	0.404611i	$0.132593\pi$
$72$	0.831290	−	0.213439i	0.0979685	−	0.0251540i
$73$	13.4740	+	7.40740i	1.57701	+	0.866971i	0.998690	+	0.0511640i	$0.0162931\pi$
$73$	13.4740	+	7.40740i	1.57701	+	0.866971i	0.578324	+	0.815807i	$0.303707\pi$
$74$	0.159601	−	0.115957i	0.0185532	−	0.0134797i
$75$	0.123095	+	1.89466i	0.0142138	+	0.218777i
$76$	1.07948	+	0.784285i	0.123824	+	0.0899637i
$77$	6.57691	+	13.9766i	0.749508	+	1.59279i
$78$	−0.0122147	+	0.0147651i	−0.00138305	+	0.00167182i
$79$	−2.54046	−	4.00312i	−0.285824	−	0.450387i	0.670831	−	0.741610i	$-0.265938\pi$
$79$	−2.54046	−	4.00312i	−0.285824	−	0.450387i	−0.956655	+	0.291224i	$0.905938\pi$
$80$	3.25624	−	8.24896i	0.364058	−	0.922262i
$81$	−4.92284	−	5.95070i	−0.546983	−	0.661188i
$82$	−0.158035	−	0.114819i	−0.0174520	−	0.0126797i
$83$	6.30486	−	9.93486i	0.692048	−	1.09049i	−0.298643	−	0.954365i	$-0.596534\pi$
$83$	6.30486	−	9.93486i	0.692048	−	1.09049i	0.990691	−	0.136128i	$-0.0434659\pi$
$84$	0.471549	+	2.47195i	0.0514502	+	0.269712i
$85$	−8.16376	−	1.54866i	−0.885484	−	0.167976i
$86$	−0.480143	+	0.0606562i	−0.0517752	+	0.00654073i
$87$	−0.648668	−	3.40044i	−0.0695445	−	0.364565i
$88$	1.38599	+	0.175092i	0.147747	+	0.0186648i
$89$	7.79608	+	4.28593i	0.826382	+	0.454308i	0.838030	−	0.545625i	$-0.183708\pi$
$89$	7.79608	+	4.28593i	0.826382	+	0.454308i	−0.0116473	+	0.999932i	$0.503708\pi$
$90$	0.479479	−	0.0306588i	0.0505415	−	0.00323172i
$91$	1.62469	+	1.52569i	0.170314	+	0.159935i
$92$	9.32832	+	2.39510i	0.972544	+	0.249707i
$93$	−0.652695	+	0.474211i	−0.0676813	+	0.0491734i
$94$	−0.0351617	−	0.558880i	−0.00362665	−	0.0576440i
$95$	1.02522	+	1.08951i	0.105185	+	0.111782i
$96$	0.317569	+	0.125734i	0.0324117	+	0.0128327i
$97$	−14.2841	−	5.65548i	−1.45033	−	0.574227i	−0.494772	−	0.869023i	$-0.664748\pi$
$97$	−14.2841	−	5.65548i	−1.45033	−	0.574227i	−0.955560	+	0.294796i	$0.904748\pi$
$98$	−0.301722	+	0.0381163i	−0.0304785	+	0.00385033i
$99$	−4.10226	−	12.6254i	−0.412292	−	1.26891i
$100$	5.32586	−	8.43030i	0.532586	−	0.843030i
$101$	−3.02868	+	9.32133i	−0.301365	+	0.927507i	0.679643	+	0.733543i	$0.262135\pi$
$101$	−3.02868	+	9.32133i	−0.301365	+	0.927507i	−0.981009	+	0.193964i	$0.937865\pi$
$102$	0.0198942	−	0.104289i	0.00196982	−	0.0103262i
$103$	−0.848861	+	13.4923i	−0.0836407	+	1.32943i	0.702633	+	0.711553i	$0.252008\pi$
$103$	−0.848861	+	13.4923i	−0.0836407	+	1.32943i	−0.786273	+	0.617879i	$0.787992\pi$
$104$	0.195237	−	0.0501282i	0.0191445	−	0.00491548i
$105$	0.00288680	+	2.82154i	0.000281723	+	0.275354i
$106$	0.0261244	−	0.0411655i	0.00253743	−	0.00399834i
$107$	−4.30824	−	13.2594i	−0.416493	−	1.28183i	−0.910909	−	0.412608i	$-0.864618\pi$
$107$	−4.30824	−	13.2594i	−0.416493	−	1.28183i	0.494416	−	0.869226i	$-0.335382\pi$
$108$	−0.278456	−	4.42593i	−0.0267944	−	0.425885i
$109$	−14.8520	−	1.87625i	−1.42256	−	0.179712i	−0.623907	−	0.781498i	$-0.714456\pi$
$109$	−14.8520	−	1.87625i	−1.42256	−	0.179712i	−0.798657	+	0.601787i	$0.794456\pi$
$110$	0.744029	+	0.240908i	0.0709404	+	0.0229697i
$111$	−0.423933	−	0.900903i	−0.0402379	−	0.0855099i
$112$	5.61138	−	11.9248i	0.530225	−	1.12679i
$113$	−10.5941	+	5.82414i	−0.996607	+	0.547889i	−0.894587	−	0.446893i	$-0.852530\pi$
$113$	−10.5941	+	5.82414i	−0.996607	+	0.547889i	−0.102020	+	0.994782i	$0.532530\pi$
$114$	−0.0139343	+	0.0130851i	−0.00130506	+	0.00122554i
$115$	9.77522	+	4.58766i	0.911544	+	0.427802i
$116$	−7.74111	+	16.4507i	−0.718744	+	1.52741i
$117$	−1.22094	−	1.47586i	−0.112876	−	0.136443i
$118$	−0.198189	+	0.609962i	−0.0182447	+	0.0561515i
$119$	−11.9603	−	3.07090i	−1.09640	−	0.281509i
$120$	0.215597	+	0.136512i	0.0196812	+	0.0124618i
$121$	0.666112	−	10.5875i	0.0605556	−	0.962504i
$122$	0.184436	+	0.290625i	0.0166981	+	0.0263119i
$123$	−0.718685	+	0.674891i	−0.0648017	+	0.0608528i
$124$	4.23716			0.380508
$125$	7.62842	−	8.17357i	0.682306	−	0.731066i
$126$	0.713996			0.0636078
$127$	13.7904	−	12.9501i	1.22370	−	1.14913i	0.239727	−	0.970840i	$-0.422942\pi$
$127$	13.7904	−	12.9501i	1.22370	−	1.14913i	0.983977	−	0.178295i	$-0.0570580\pi$
$128$	−1.28097	−	2.01848i	−0.113223	−	0.178410i
$129$	−0.153369	+	2.43773i	−0.0135034	+	0.214630i
$130$	0.112610	−	0.00720052i	0.00987658	−	0.000631527i
$131$	−10.8366	−	2.78236i	−0.946796	−	0.243096i	−0.256435	−	0.966561i	$-0.582548\pi$
$131$	−10.8366	−	2.78236i	−0.946796	−	0.243096i	−0.690360	+	0.723466i	$0.742548\pi$
$132$	1.08785	−	3.34807i	0.0946854	−	0.291412i
$133$	1.41713	+	1.71302i	0.122881	+	0.148537i
$134$	−0.489647	+	1.04055i	−0.0422990	+	0.0898900i
$135$	0.618134	−	4.93362i	0.0532005	−	0.424619i
$136$	−0.814100	+	0.764491i	−0.0698085	+	0.0655546i
$137$	2.66282	−	1.46390i	0.227500	−	0.125069i	−0.363928	−	0.931427i	$-0.618564\pi$
$137$	2.66282	−	1.46390i	0.227500	−	0.125069i	0.591428	+	0.806358i	$0.298564\pi$
$138$	−0.0587450	+	0.124839i	−0.00500071	+	0.0106270i
$139$	−3.57231	−	7.59154i	−0.302999	−	0.643906i	0.694111	−	0.719868i	$-0.255798\pi$
$139$	−3.57231	−	7.59154i	−0.302999	−	0.643906i	−0.997111	+	0.0759612i	$0.975798\pi$
$140$	8.69792	−	11.9975i	0.735109	−	1.01397i
$141$	−2.80396	−	0.354223i	−0.236136	−	0.0298309i
$142$	−0.0215884	−	0.343138i	−0.00181166	−	0.0287955i
$143$	−0.963455	−	2.96521i	−0.0805682	−	0.247963i
$144$	−6.06894	+	9.56312i	−0.505745	+	0.796927i
$145$	−11.9650	+	16.5038i	−0.993635	+	1.37057i
$146$	1.12052	−	0.287701i	0.0927350	−	0.0238103i
$147$	−0.0963770	+	1.53187i	−0.00794904	+	0.126346i
$148$	−0.979853	+	5.13657i	−0.0805434	+	0.422223i
$149$	0.834310	−	2.56774i	0.0683493	−	0.210358i	−0.911048	−	0.412300i	$-0.864725\pi$
$149$	0.834310	−	2.56774i	0.0683493	−	0.210358i	0.979397	+	0.201943i	$0.0647255\pi$
$150$	0.104335	+	0.0975762i	0.00851893	+	0.00796707i
$151$	3.52636	+	10.8530i	0.286971	+	0.883206i	0.985801	+	0.167918i	$0.0537044\pi$
$151$	3.52636	+	10.8530i	0.286971	+	0.883206i	−0.698830	+	0.715288i	$0.746296\pi$
$152$	0.199483	−	0.0252005i	0.0161802	−	0.00204403i
$153$	9.86709	+	3.90666i	0.797707	+	0.315834i
$154$	1.08058	+	0.427833i	0.0870758	+	0.0344758i
$155$	4.66750	+	0.885424i	0.374902	+	0.0711190i
$156$	−0.0318938	−	0.506938i	−0.00255355	−	0.0405875i
$157$	−16.1364	+	11.7238i	−1.28782	+	0.935658i	−0.999759	−	0.0219538i	$-0.993011\pi$
$157$	−16.1364	+	11.7238i	−1.28782	+	0.935658i	−0.288063	+	0.957611i	$0.593011\pi$
$158$	−0.345515	−	0.0887132i	−0.0274877	−	0.00705764i
$159$	−0.179376	−	0.168446i	−0.0142255	−	0.0133586i
$160$	−0.742306	−	1.86926i	−0.0586844	−	0.147778i
$161$	14.0620	+	7.73067i	1.10824	+	0.609262i
$162$	−0.576490	−	0.0728276i	−0.0452933	−	0.00572188i
$163$	1.17525	+	6.16087i	0.0920526	+	0.482557i	0.998220	+	0.0596377i	$0.0189945\pi$
$163$	1.17525	+	6.16087i	0.0920526	+	0.482557i	−0.906167	+	0.422919i	$0.861005\pi$
$164$	5.13705	−	0.648961i	0.401137	−	0.0506753i
$165$	1.89797	−	3.46078i	0.147757	−	0.269421i
$166$	−0.165890	−	0.869624i	−0.0128755	−	0.0674959i
$167$	2.49967	−	3.93885i	0.193430	−	0.304797i	−0.733745	−	0.679425i	$-0.762229\pi$
$167$	2.49967	−	3.93885i	0.193430	−	0.304797i	0.927175	+	0.374628i	$0.122229\pi$
$168$	0.306794	+	0.222899i	0.0236697	+	0.0171970i
$169$	7.99976	+	9.67005i	0.615366	+	0.743850i
$170$	−0.527519	+	0.335531i	−0.0404589	+	0.0257341i
$171$	−1.02379	−	1.61323i	−0.0782909	−	0.123367i
$172$	8.17700	−	9.88430i	0.623491	−	0.753671i
$173$	−6.34435	−	13.4824i	−0.482352	−	1.02505i	−0.986850	−	0.161637i	$-0.948323\pi$
$173$	−6.34435	−	13.4824i	−0.482352	−	1.02505i	0.504498	−	0.863413i	$-0.331677\pi$
$174$	−0.210715	−	0.153094i	−0.0159743	−	0.0116060i
$175$	12.0884	−	11.3984i	0.913795	−	0.861636i
$176$	−14.9152	+	10.8365i	−1.12428	+	0.816835i
$177$	2.83653	+	1.55939i	0.213206	+	0.117211i
$178$	0.648335	−	0.166464i	0.0485947	−	0.0124770i
$179$	−0.860904	+	1.04065i	−0.0643470	+	0.0777822i	−0.801705	−	0.597720i	$-0.796073\pi$
$179$	−0.860904	+	1.04065i	−0.0643470	+	0.0777822i	0.737358	+	0.675503i	$0.236073\pi$
$180$	−8.70847	+	9.29262i	−0.649091	+	0.692631i
$181$	1.26318	−	0.500127i	0.0938911	−	0.0371741i	−0.320709	−	0.947178i	$-0.603921\pi$
$181$	1.26318	−	0.500127i	0.0938911	−	0.0371741i	0.414601	+	0.910003i	$0.363921\pi$
$182$	0.167689			0.0124299
$183$	1.61523	−	0.639515i	0.119401	−	0.0472743i
$184$	1.27178	−	0.699165i	0.0937566	−	0.0515431i
$185$	−2.15274	+	5.45349i	−0.158273	+	0.400949i
$186$	−0.0113742	+	0.0596257i	−0.000833998	+	0.00437197i
$187$	12.5922	+	11.8249i	0.920836	+	0.864722i
$188$	10.8204	+	10.1610i	0.789156	+	0.741066i
$189$	1.38457	−	7.25816i	0.100713	−	0.527954i
$190$	0.112345	+	0.00695275i	0.00815036	+	0.000504406i
$191$	−13.3363	+	7.33169i	−0.964980	+	0.530502i	−0.884645	−	0.466266i	$-0.845599\pi$
$191$	−13.3363	+	7.33169i	−0.964980	+	0.530502i	−0.0803353	+	0.996768i	$0.525599\pi$
$192$	−2.77667	+	1.09936i	−0.200389	+	0.0793395i
$193$	22.0390			1.58640			0.793200	−	0.608961i	$-0.208414\pi$
$193$	22.0390			1.58640			0.793200	+	0.608961i	$0.208414\pi$
$194$	−1.07472	+	0.425512i	−0.0771604	+	0.0305500i
$195$	0.0708000	−	0.565089i	0.00507009	−	0.0404668i
$196$	5.13842	−	6.21129i	0.367030	−	0.443663i
$197$	−8.48129	+	2.17763i	−0.604267	+	0.155149i	−0.538415	−	0.842680i	$-0.680977\pi$
$197$	−8.48129	+	2.17763i	−0.604267	+	0.155149i	−0.0658523	+	0.997829i	$0.520977\pi$
$198$	−0.875264	−	0.481180i	−0.0622023	−	0.0341960i
$199$	−8.56891	+	6.22567i	−0.607434	+	0.441326i	−0.848510	−	0.529180i	$-0.822500\pi$
$199$	−8.56891	+	6.22567i	−0.607434	+	0.441326i	0.241076	+	0.970506i	$0.422500\pi$
$200$	−0.284588	−	1.47545i	−0.0201234	−	0.104330i
$201$	4.69559	+	3.41155i	0.331202	+	0.240632i
$202$	0.313977	+	0.667236i	0.0220914	+	0.0469465i
$203$	−19.3096	+	23.3413i	−1.35527	+	1.63824i
$204$	1.50793	+	2.37612i	0.105576	+	0.166362i
$205$	5.79440	+	0.358601i	0.404698	+	0.0250458i
$206$	0.648355	+	0.783727i	0.0451731	+	0.0546048i
$207$	−11.1572	−	8.10615i	−0.775476	−	0.563416i
$208$	−1.42535	+	2.24599i	−0.0988302	+	0.155732i
$209$	−0.582767	−	3.05497i	−0.0403108	−	0.211317i
$210$	0.145481	+	0.154604i	0.0100391	+	0.0106687i
$211$	−9.50804	+	1.20114i	−0.654561	+	0.0826902i	−0.445598	−	0.895233i	$-0.647009\pi$
$211$	−9.50804	+	1.20114i	−0.654561	+	0.0826902i	−0.208963	+	0.977924i	$0.567009\pi$
$212$	0.242161	+	1.26945i	0.0166317	+	0.0871865i
$213$	−1.72156	−	0.217484i	−0.117959	−	0.0149017i
$214$	−0.919212	−	0.505341i	−0.0628360	−	0.0345444i
$215$	11.0730	−	9.17945i	0.755170	−	0.626034i
$216$	−0.487146	−	0.457461i	−0.0331461	−	0.0311263i
$217$	6.83814	+	1.75574i	0.464203	+	0.119187i
$218$	−0.911220	+	0.662040i	−0.0617156	+	0.0448390i
$219$	−0.366616	−	5.82720i	−0.0247736	−	0.393766i
$220$	−18.7479	+	8.84553i	−1.26398	+	0.596365i
$221$	2.31738	+	0.917516i	0.155884	+	0.0617188i
$222$	−0.0696519	−	0.0275771i	−0.00467473	−	0.00185086i
$223$	17.1026	−	2.16056i	1.14527	−	0.144682i	0.470289	−	0.882512i	$-0.344150\pi$
$223$	17.1026	−	2.16056i	1.14527	−	0.144682i	0.674986	+	0.737831i	$0.264150\pi$
$224$	−0.923613	−	2.84259i	−0.0617115	−	0.189928i
$225$	−11.5348	+	8.41662i	−0.768985	+	0.561108i
$226$	−0.281081	+	0.865079i	−0.0186972	+	0.0575442i
$227$	−0.525350	+	2.75398i	−0.0348687	+	0.182788i	−0.995461	−	0.0951745i	$-0.969659\pi$
$227$	−0.525350	+	2.75398i	−0.0348687	+	0.182788i	0.960592	+	0.277963i	$0.0896591\pi$
$228$	0.0318146	−	0.505678i	0.00210697	−	0.0334894i
$229$	18.9377	−	4.86238i	1.25144	−	0.321315i	0.435889	−	0.900001i	$-0.356434\pi$
$229$	18.9377	−	4.86238i	1.25144	−	0.321315i	0.815551	+	0.578686i	$0.196434\pi$
$230$	0.772425	−	0.251850i	0.0509322	−	0.0166065i
$231$	3.14296	−	4.95251i	0.206791	−	0.325851i
$232$	0.846621	+	2.60563i	0.0555834	+	0.171068i
$233$	−1.47519	−	23.4474i	−0.0966426	−	1.53609i	−0.685631	−	0.727949i	$-0.740474\pi$
$233$	−1.47519	−	23.4474i	−0.0966426	−	1.53609i	0.588989	−	0.808141i	$-0.299526\pi$
$234$	−0.142978	−	0.0180623i	−0.00934677	−	0.00118077i
$235$	9.79599	+	13.4541i	0.639020	+	0.877646i
$236$	−7.23832	−	15.3822i	−0.471174	−	1.00130i
$237$	−0.766565	+	1.62903i	−0.0497938	+	0.105817i
$238$	−0.814152	+	0.447584i	−0.0527736	+	0.0290125i
$239$	6.58202	−	6.18093i	0.425755	−	0.399811i	−0.441830	−	0.897099i	$-0.645671\pi$
$239$	6.58202	−	6.18093i	0.425755	−	0.399811i	0.867586	+	0.497288i	$0.165671\pi$
$240$	−3.30731	+	0.634411i	−0.213486	+	0.0409511i
$241$	9.41457	−	20.0070i	0.606446	−	1.28876i	−0.331982	−	0.943286i	$-0.607717\pi$
$241$	9.41457	−	20.0070i	0.606446	−	1.28876i	0.938427	−	0.345477i	$-0.112283\pi$
$242$	−0.508773	−	0.615001i	−0.0327052	−	0.0395337i
$243$	−2.96767	+	9.13355i	−0.190376	+	0.585917i
$244$	−8.83720	−	2.26901i	−0.565744	−	0.145258i
$245$	6.95824	−	5.76836i	0.444546	−	0.368527i
$246$	−0.00465764	+	0.0740311i	−0.000296961	+	0.00472005i
$247$	−0.240446	−	0.378882i	−0.0152992	−	0.0241077i
$248$	0.465449	−	0.437086i	0.0295560	−	0.0277550i
$249$	−4.46815			−0.283157
$250$	−0.00258195	−	0.841192i	−0.000163297	−	0.0532017i
$251$	2.22113			0.140197			0.0700984	−	0.997540i	$-0.477669\pi$
$251$	2.22113			0.140197			0.0700984	+	0.997540i	$0.477669\pi$
$252$	−13.7963	+	12.9555i	−0.869082	+	0.816123i
$253$	−12.0283	−	18.9536i	−0.756212	−	1.19160i
$254$	0.0893729	−	1.42054i	0.00560776	−	0.0891327i
$255$	1.16455	+	2.93255i	0.0729271	+	0.183644i
$256$	15.0605	+	3.86689i	0.941284	+	0.241681i
$257$	0.819924	−	2.52347i	0.0511455	−	0.157410i	−0.922222	−	0.386662i	$-0.873628\pi$
$257$	0.819924	−	2.52347i	0.0511455	−	0.157410i	0.973367	+	0.229252i	$0.0736281\pi$
$258$	0.117142	+	0.141601i	0.00729297	+	0.00881569i
$259$	−3.70975	+	7.88363i	−0.230513	+	0.489865i
$260$	−2.04527	+	2.18246i	−0.126842	+	0.135351i
$261$	18.9783	−	17.8218i	1.17473	−	1.10314i
$262$	−0.737655	+	0.405529i	−0.0455725	+	0.0250537i
$263$	0.364582	−	0.774777i	0.0224811	−	0.0477748i	−0.893271	−	0.449518i	$-0.851596\pi$
$263$	0.364582	−	0.774777i	0.0224811	−	0.0477748i	0.915752	+	0.401743i	$0.131596\pi$
$264$	−0.225871	−	0.480000i	−0.0139014	−	0.0295420i
$265$	0.00148250	+	1.44899i	9.10693e−5	+	0.0890105i
$266$	0.165953	+	0.0209648i	0.0101752	+	0.00128543i
$267$	−0.212124	−	3.37162i	−0.0129818	−	0.206340i
$268$	−9.41971	−	28.9909i	−0.575400	−	1.77090i
$269$	−13.2406	+	20.8639i	−0.807296	+	1.27209i	0.151630	+	0.988437i	$0.451548\pi$
$269$	−13.2406	+	20.8639i	−0.807296	+	1.27209i	−0.958926	+	0.283657i	$0.908452\pi$
$270$	−0.220201	−	0.302430i	−0.0134010	−	0.0184053i
$271$	−6.30509	+	1.61887i	−0.383007	+	0.0983394i	−0.435284	−	0.900293i	$-0.643352\pi$
$271$	−6.30509	+	1.61887i	−0.383007	+	0.0983394i	0.0522773	+	0.998633i	$0.483352\pi$
$272$	0.925414	−	14.7090i	0.0561115	−	0.891866i
$273$	0.158586	−	0.831337i	0.00959806	−	0.0503148i
$274$	0.0706498	−	0.217438i	0.00426811	−	0.0131359i
$275$	−22.5004	+	5.82622i	−1.35682	+	0.351334i
$276$	−1.13012	−	3.47816i	−0.0680254	−	0.209361i
$277$	0.204125	−	0.0257870i	0.0122647	−	0.00154939i	−0.119199	−	0.992870i	$-0.538032\pi$
$277$	0.204125	−	0.0257870i	0.0122647	−	0.00154939i	0.131463	+	0.991321i	$0.458032\pi$
$278$	−0.586929	−	0.232382i	−0.0352017	−	0.0139373i
$279$	−5.64135	−	2.23357i	−0.337739	−	0.133720i
$280$	−0.282141	−	2.21515i	−0.0168612	−	0.132380i
$281$	−0.623731	−	9.91393i	−0.0372087	−	0.591415i	−0.971817	−	0.235737i	$-0.924250\pi$
$281$	−0.623731	−	9.91393i	−0.0372087	−	0.591415i	0.934608	−	0.355679i	$-0.115750\pi$
$282$	−0.172032	+	0.124989i	−0.0102444	+	0.00744298i
$283$	11.9175	+	3.05990i	0.708423	+	0.181892i	0.585675	−	0.810546i	$-0.300829\pi$
$283$	11.9175	+	3.05990i	0.708423	+	0.181892i	0.122748	+	0.992438i	$0.460829\pi$
$284$	6.64342	+	6.23859i	0.394215	+	0.370192i
$285$	0.140715	−	0.550388i	0.00833527	−	0.0326022i
$286$	−0.205564	−	0.113010i	−0.0121553	−	0.00668242i
$287$	8.55934	+	1.08130i	0.505242	+	0.0638269i
$288$	0.481324	+	2.52319i	0.0283623	+	0.148680i
$289$	3.16579	−	0.399932i	0.186223	−	0.0235254i
$290$	0.193783	+	1.52143i	0.0113793	+	0.0893415i
$291$	1.09314	+	5.73047i	0.0640813	+	0.335926i
$292$	−16.4310	+	25.8911i	−0.961552	+	1.51516i
$293$	−16.6200	−	12.0751i	−0.970951	−	0.705437i	−0.0152827	−	0.999883i	$-0.504865\pi$
$293$	−16.6200	−	12.0751i	−0.970951	−	0.705437i	−0.955668	+	0.294446i	$0.904865\pi$
$294$	0.0736122	+	0.0889819i	0.00429315	+	0.00518953i
$295$	−4.75909	−	18.4570i	−0.277085	−	1.07461i
$296$	0.422228	+	0.665325i	0.0245415	+	0.0386712i
$297$	−6.58876	+	7.96444i	−0.382319	+	0.462144i
$298$	−0.0864912	−	0.183803i	−0.00501030	−	0.0106474i
$299$	−2.62037	−	1.90381i	−0.151540	−	0.110100i
$300$	−3.78656	+	0.00774829i	−0.218617	+	0.000447348i
$301$	17.2922	−	12.5635i	0.996704	−	0.724148i
$302$	0.752389	+	0.413630i	0.0432951	+	0.0238017i
$303$	3.60483	−	0.925563i	0.207092	−	0.0531722i
$304$	−1.69139	+	2.04454i	−0.0970081	+	0.117263i
$305$	−9.26058	−	4.34613i	−0.530260	−	0.248859i
$306$	0.742388	−	0.293932i	0.0424395	−	0.0168030i
$307$	−7.59754			−0.433615			−0.216807	−	0.976214i	$-0.569564\pi$
$307$	−7.59754			−0.433615			−0.216807	+	0.976214i	$0.569564\pi$
$308$	−28.6427	+	11.3405i	−1.63207	+	0.646183i
$309$	4.49858	−	2.47311i	0.255915	−	0.140691i
$310$	0.301601	−	0.191835i	0.0171298	−	0.0108955i
$311$	−3.98243	+	20.8766i	−0.225823	+	1.18381i	0.671014	+	0.741445i	$0.265859\pi$
$311$	−3.98243	+	20.8766i	−0.225823	+	1.18381i	−0.896837	+	0.442361i	$0.854141\pi$
$312$	−0.0557969	−	0.0523967i	−0.00315888	−	0.00296638i
$313$	−3.43568	−	3.22632i	−0.194196	−	0.182362i	0.581349	−	0.813654i	$-0.302525\pi$
$313$	−3.43568	−	3.22632i	−0.194196	−	0.182362i	−0.775545	+	0.631292i	$0.782525\pi$
$314$	−0.281201	+	1.47411i	−0.0158691	+	0.0831887i
$315$	−17.9047	+	11.3884i	−1.00882	+	0.641663i
$316$	8.28596	−	4.55525i	0.466122	−	0.256253i
$317$	12.0602	−	4.77497i	0.677368	−	0.268189i	−0.00414863	−	0.999991i	$-0.501321\pi$
$317$	12.0602	−	4.77497i	0.677368	−	0.268189i	0.681517	+	0.731802i	$0.261321\pi$
$318$	−0.0185139			−0.00103821
$319$	39.4013	−	15.6001i	2.20605	−	0.873436i
$320$	15.9195	+	7.47124i	0.889925	+	0.417655i
$321$	−3.37460	+	4.07919i	−0.188352	+	0.227678i
$322$	1.16942	−	0.300257i	0.0651694	−	0.0167327i
$323$	2.17868	+	1.19774i	0.121225	+	0.0666442i
$324$	12.4608	−	9.05327i	0.692264	−	0.502959i
$325$	−2.70905	+	1.97672i	−0.150271	+	0.109649i
$326$	0.381772	+	0.277373i	0.0211444	+	0.0153623i
$327$	2.42039	+	5.14358i	0.133848	+	0.284441i
$328$	0.497358	−	0.601202i	0.0274620	−	0.0331958i
$329$	13.2521	+	20.8819i	0.730609	+	1.15126i
$330$	−0.0741483	−	0.287567i	−0.00408173	−	0.0158300i
$331$	−6.55597	−	7.92480i	−0.360349	−	0.435587i	0.558918	−	0.829223i	$-0.311217\pi$
$331$	−6.55597	−	7.92480i	−0.360349	−	0.435587i	−0.919266	+	0.393637i	$0.871217\pi$
$332$	18.9849	+	13.7933i	1.04193	+	0.757006i
$333$	4.01225	−	6.32230i	0.219870	−	0.346460i
$334$	−0.0657698	−	0.344777i	−0.00359876	−	0.0188654i
$335$	−4.31827	−	33.9037i	−0.235933	−	1.85235i
$336$	−4.96505	+	0.627232i	−0.270866	+	0.0342183i
$337$	−1.53520	−	8.04779i	−0.0836275	−	0.438391i	−0.999332	−	0.0365390i	$-0.988367\pi$
$337$	−1.53520	−	8.04779i	−0.0836275	−	0.438391i	0.915705	−	0.401852i	$-0.131633\pi$
$338$	0.936813	+	0.118347i	0.0509559	+	0.00643723i
$339$	4.02291	+	2.21161i	0.218494	+	0.120118i
$340$	4.10478	−	16.0552i	0.222613	−	0.870717i
$341$	−7.19941	−	6.76070i	−0.389870	−	0.366112i
$342$	−0.139240	−	0.0357507i	−0.00752924	−	0.00193318i
$343$	−7.95193	+	5.77741i	−0.429364	+	0.311951i
$344$	−0.121380	−	1.92928i	−0.00654439	−	0.104020i
$345$	−0.518082	−	4.06757i	−0.0278926	−	0.218990i
$346$	−1.04237	−	0.412705i	−0.0560384	−	0.0221872i
$347$	19.0264	+	7.53309i	1.02139	+	0.404398i	0.818318	−	0.574766i	$-0.194907\pi$
$347$	19.0264	+	7.53309i	1.02139	+	0.404398i	0.203074	+	0.979163i	$0.434907\pi$
$348$	6.84947	−	0.865289i	0.367170	−	0.0463844i
$349$	5.59057	+	17.2060i	0.299256	+	0.921017i	0.981758	+	0.190133i	$0.0608919\pi$
$349$	5.59057	+	17.2060i	0.299256	+	0.921017i	−0.682502	+	0.730884i	$0.739108\pi$
$350$	0.0759400	−	1.24777i	0.00405916	−	0.0666961i
$351$	−0.460874	+	1.41843i	−0.0245997	+	0.0757100i
$352$	−0.783468	+	4.10708i	−0.0417590	+	0.218908i
$353$	0.851959	−	13.5415i	0.0453452	−	0.720741i	−0.908021	−	0.418925i	$-0.862407\pi$
$353$	0.851959	−	13.5415i	0.0453452	−	0.720741i	0.953366	−	0.301816i	$-0.0975929\pi$
$354$	0.235890	−	0.0605663i	0.0125374	−	0.00321906i
$355$	6.01449	+	8.26045i	0.319216	+	0.438419i
$356$	−9.50700	+	14.9806i	−0.503870	+	0.793972i
$357$	1.44899	+	4.45954i	0.0766888	+	0.236024i
$358$	0.00638062	+	0.101417i	0.000337226	+	0.00536006i
$359$	12.8379	+	1.62181i	0.677559	+	0.0855957i	0.456579	−	0.889683i	$-0.349074\pi$
$359$	12.8379	+	1.62181i	0.677559	+	0.0855957i	0.220980	+	0.975278i	$0.429074\pi$
$360$	0.00196350	+	1.91911i	0.000103486	+	0.101146i
$361$	7.89922	+	16.7867i	0.415748	+	0.883510i
$362$	0.0435223	−	0.0924896i	0.00228748	−	0.00486115i
$363$	−3.53009	+	1.94068i	−0.185282	+	0.101860i
$364$	−3.24019	+	3.04274i	−0.169832	+	0.159483i
$365$	−23.5102	+	25.0872i	−1.23058	+	1.31312i
$366$	0.0556522	−	0.118267i	0.00290899	−	0.00618191i
$367$	6.66844	+	8.06076i	0.348090	+	0.420768i	0.915280	−	0.402819i	$-0.131970\pi$
$367$	6.66844	+	8.06076i	0.348090	+	0.420768i	−0.567190	+	0.823587i	$0.691970\pi$
$368$	−5.91847	+	18.2152i	−0.308522	+	0.949532i
$369$	−7.18156	−	1.84391i	−0.373857	−	0.0959901i
$370$	0.162809	+	0.409982i	0.00846403	+	0.0213140i
$371$	−0.135207	+	2.14905i	−0.00701959	+	0.111573i
$372$	−0.862137	−	1.35851i	−0.0446997	−	0.0704355i
$373$	−18.6097	+	17.4757i	−0.963573	+	0.904855i	−0.995512	−	0.0946346i	$-0.969832\pi$
$373$	−18.6097	+	17.4757i	−0.963573	+	0.904855i	0.0319391	+	0.999490i	$0.489832\pi$
$374$	1.29968			0.0672048
$375$	−4.17275	−	0.782729i	−0.215480	−	0.0404199i
$376$	2.23677			0.115353
$377$	4.45723	−	4.18562i	0.229559	−	0.215570i
$378$	−0.297889	−	0.469398i	−0.0153218	−	0.0241433i
$379$	0.710325	−	11.2903i	0.0364870	−	0.579944i	−0.936730	−	0.350054i	$-0.886163\pi$
$379$	0.710325	−	11.2903i	0.0364870	−	0.579944i	0.973217	−	0.229890i	$-0.0738367\pi$
$380$	−2.29695	+	1.90417i	−0.117831	+	0.0976818i
$381$	−6.95798	−	1.78651i	−0.356468	−	0.0915255i
$382$	−0.353837	+	1.08900i	−0.0181039	+	0.0557180i
$383$	14.1160	+	17.0633i	0.721293	+	0.871893i	0.995974	−	0.0896420i	$-0.0285723\pi$
$383$	14.1160	+	17.0633i	0.721293	+	0.871893i	−0.274681	+	0.961535i	$0.588572\pi$
$384$	−0.386522	+	0.821402i	−0.0197246	+	0.0419170i
$385$	−33.9215	+	6.50686i	−1.72880	+	0.331620i
$386$	1.20877	−	1.13511i	0.0615246	−	0.0577754i
$387$	−16.0972	+	8.84953i	−0.818269	+	0.449847i
$388$	13.0454	−	27.7229i	0.662281	−	1.40742i
$389$	9.68711	+	20.5862i	0.491156	+	1.04376i	0.984735	+	0.174059i	$0.0556883\pi$
$389$	9.68711	+	20.5862i	0.491156	+	1.04376i	−0.493579	+	0.869701i	$0.664312\pi$
$390$	−0.0252215	−	0.0346398i	−0.00127714	−	0.00175405i
$391$	17.8037	+	2.24913i	0.900374	+	0.113744i
$392$	−0.0762753	−	1.21236i	−0.00385248	−	0.0612335i
$393$	1.31285	+	4.04053i	0.0662244	+	0.203818i
$394$	−0.353014	+	0.556261i	−0.0177846	+	0.0280240i
$395$	10.0794	−	3.28640i	0.507150	−	0.165357i
$396$	25.6434	−	6.58412i	1.28863	−	0.330864i
$397$	−1.09547	+	17.4119i	−0.0549798	+	0.873879i	0.869807	+	0.493393i	$0.164243\pi$
$397$	−1.09547	+	17.4119i	−0.0549798	+	0.873879i	−0.924786	+	0.380487i	$0.875757\pi$
$398$	−0.149326	+	0.782796i	−0.00748505	+	0.0392380i
$399$	0.260880	−	0.802905i	0.0130603	−	0.0401955i
$400$	16.0669	+	11.6231i	0.803345	+	0.581156i
$401$	−4.95067	−	15.2366i	−0.247225	−	0.760879i	−0.995263	−	0.0972233i	$-0.969004\pi$
$401$	−4.95067	−	15.2366i	−0.247225	−	0.760879i	0.748038	−	0.663656i	$-0.230996\pi$
$402$	0.433248	−	0.0547320i	0.0216085	−	0.00272978i
$403$	−1.32493	−	0.524575i	−0.0659993	−	0.0261310i
$404$	−18.1739	−	7.19557i	−0.904187	−	0.357993i
$405$	15.6181	−	7.36886i	0.776071	−	0.366161i
$406$	0.143114	+	2.27473i	0.00710261	+	0.112893i
$407$	9.86064	−	7.16418i	0.488774	−	0.355115i
$408$	0.410755	+	0.105464i	0.0203354	+	0.00522124i
$409$	−17.0780	−	16.0373i	−0.844454	−	0.792996i	0.135800	−	0.990736i	$-0.456640\pi$
$409$	−17.0780	−	16.0373i	−0.844454	−	0.792996i	−0.980254	+	0.197741i	$0.936640\pi$
$410$	0.336274	−	0.278770i	0.0166074	−	0.0137675i
$411$	−1.01116	−	0.555889i	−0.0498767	−	0.0274200i
$412$	−26.7487	−	3.37915i	−1.31782	−	0.166479i
$413$	−5.30769	−	27.8239i	−0.261174	−	1.36912i
$414$	−1.02944	+	0.130048i	−0.0505941	+	0.00639152i
$415$	18.0307	+	19.1614i	0.885091	+	0.940595i
$416$	0.113044	+	0.592595i	0.00554242	+	0.0290544i
$417$	−1.70713	+	2.69000i	−0.0835983	+	0.131730i
$418$	−0.189308	−	0.137540i	−0.00925934	−	0.00672731i
$419$	14.8563	+	17.9582i	0.725777	+	0.877313i	0.996348	−	0.0853867i	$-0.0272126\pi$
$419$	14.8563	+	17.9582i	0.725777	+	0.877313i	−0.270571	+	0.962700i	$0.587213\pi$
$420$	−5.61637	−	0.347583i	−0.274051	−	0.0169603i
$421$	1.56779	+	2.47045i	0.0764096	+	0.120402i	0.880384	−	0.474262i	$-0.157285\pi$
$421$	1.56779	+	2.47045i	0.0764096	+	0.120402i	−0.803974	+	0.594664i	$0.797285\pi$
$422$	−0.459621	+	0.555586i	−0.0223740	+	0.0270455i
$423$	−9.04996	−	19.2321i	−0.440024	−	0.935099i
$424$	0.157552	+	0.114468i	0.00765141	+	0.00555908i
$425$	7.87667	−	16.8281i	0.382075	−	0.816282i
$426$	−0.105624	+	0.0767400i	−0.00511748	+	0.00371806i
$427$	−13.3217	−	7.32367i	−0.644683	−	0.354417i
$428$	26.9310	−	6.91472i	1.30176	−	0.334235i
$429$	−0.754665	+	0.912233i	−0.0364356	+	0.0440430i
$430$	0.134533	−	1.07377i	0.00648775	−	0.0517819i
$431$	−9.08300	+	3.59621i	−0.437513	+	0.173224i	−0.576547	−	0.817064i	$-0.695600\pi$
$431$	−9.08300	+	3.59621i	−0.437513	+	0.173224i	0.139034	+	0.990288i	$0.455600\pi$
$432$	8.81908			0.424308
$433$	−15.7773	+	6.24669i	−0.758211	+	0.300197i	−0.715239	−	0.698879i	$-0.753682\pi$
$433$	−15.7773	+	6.24669i	−0.758211	+	0.300197i	−0.0429712	+	0.999076i	$0.513682\pi$
$434$	0.465478	−	0.255899i	0.0223437	−	0.0122835i
$435$	7.72593	+	0.478139i	0.370430	+	0.0229250i
$436$	5.59434	−	29.3265i	0.267920	−	1.40449i
$437$	−2.35523	−	2.21170i	−0.112666	−	0.105800i
$438$	−0.320235	−	0.300721i	−0.0153014	−	0.0143690i
$439$	−6.78443	+	35.5652i	−0.323803	+	1.69743i	0.332636	+	0.943055i	$0.392062\pi$
$439$	−6.78443	+	35.5652i	−0.323803	+	1.69743i	−0.656439	+	0.754379i	$0.727938\pi$
$440$	−1.14698	+	2.90562i	−0.0546800	+	0.138520i
$441$	−10.1155	+	5.56104i	−0.481690	+	0.264811i
$442$	0.174357	−	0.0690329i	0.00829333	−	0.00328356i
$443$	27.1141			1.28823			0.644114	−	0.764929i	$-0.277226\pi$
$443$	27.1141			1.28823			0.644114	+	0.764929i	$0.277226\pi$
$444$	1.84625	−	0.730981i	0.0876190	−	0.0346908i
$445$	−13.6030	+	14.5155i	−0.644844	+	0.688099i
$446$	0.826744	−	0.999362i	0.0391475	−	0.0473211i
$447$	−0.993021	+	0.254965i	−0.0469683	+	0.0120594i
$448$	22.9008	+	12.5898i	1.08196	+	0.594812i
$449$	5.37152	−	3.90264i	0.253498	−	0.184177i	−0.453778	−	0.891115i	$-0.649924\pi$
$449$	5.37152	−	3.90264i	0.253498	−	0.184177i	0.707276	+	0.706938i	$0.249924\pi$
$450$	−0.199151	+	1.05572i	−0.00938806	+	0.0497670i
$451$	−9.76389	−	7.09388i	−0.459764	−	0.334038i
$452$	−10.2657	−	21.8158i	−0.482860	−	1.02613i
$453$	2.76216	−	3.33888i	0.129778	−	0.156874i
$454$	0.113029	+	0.178105i	0.00530470	+	0.00835887i
$455$	−4.20510	+	2.67467i	−0.197138	+	0.125391i
$456$	−0.0486686	−	0.0588302i	−0.00227911	−	0.00275498i
$457$	14.1640	+	10.2907i	0.662563	+	0.481380i	0.867528	−	0.497389i	$-0.165708\pi$
$457$	14.1640	+	10.2907i	0.662563	+	0.481380i	−0.204964	+	0.978769i	$0.565708\pi$
$458$	0.788238	−	1.24206i	0.0368319	−	0.0580379i
$459$	−1.54836	−	8.11678i	−0.0722712	−	0.378859i
$460$	−10.3554	+	18.8821i	−0.482823	+	0.880385i
$461$	10.6931	−	1.35085i	0.498025	−	0.0629152i	0.127691	−	0.991814i	$-0.459243\pi$
$461$	10.6931	−	1.35085i	0.498025	−	0.0629152i	0.370334	+	0.928899i	$0.379243\pi$
$462$	−0.0826956	−	0.433506i	−0.00384735	−	0.0201685i
$463$	−13.1145	−	1.65675i	−0.609482	−	0.0769955i	−0.185467	−	0.982651i	$-0.559380\pi$
$463$	−13.1145	−	1.65675i	−0.609482	−	0.0769955i	−0.424015	+	0.905655i	$0.639380\pi$
$464$	−31.6837	−	17.4182i	−1.47088	−	0.808622i
$465$	−0.665814	−	1.67664i	−0.0308764	−	0.0777524i
$466$	−1.28856	−	1.21004i	−0.0596913	−	0.0560538i
$467$	−21.7203	−	5.57683i	−1.00510	−	0.258065i	−0.289952	−	0.957041i	$-0.593639\pi$
$467$	−21.7203	−	5.57683i	−1.00510	−	0.258065i	−0.715145	+	0.698976i	$0.753639\pi$
$468$	3.09045	−	2.24535i	0.142856	−	0.103791i
$469$	−3.18915	−	50.6901i	−0.147261	−	2.34065i
$470$	1.23022	+	0.233373i	0.0567460	+	0.0107647i
$471$	7.04212	+	2.78817i	0.324484	+	0.128472i
$472$	−2.38188	−	0.943053i	−0.109635	−	0.0434075i
$473$	−29.6648	+	3.74753i	−1.36399	+	0.172312i
$474$	0.0418590	+	0.128829i	0.00192265	+	0.00591731i
$475$	−2.92815	+	1.61757i	−0.134353	+	0.0742194i
$476$	7.61006	−	23.4214i	0.348807	−	1.07352i
$477$	0.346764	−	1.81780i	0.0158772	−	0.0832314i
$478$	0.0426566	−	0.678008i	0.00195107	−	0.0310114i
$479$	−21.3282	+	5.47614i	−0.974509	+	0.250211i	−0.702185	−	0.711994i	$-0.747792\pi$
$479$	−21.3282	+	5.47614i	−0.974509	+	0.250211i	−0.272324	+	0.962206i	$0.587792\pi$
$480$	−0.448281	+	0.618336i	−0.0204612	+	0.0282230i
$481$	0.942317	−	1.48485i	0.0429660	−	0.0677035i
$482$	−0.514092	−	1.58221i	−0.0234162	−	0.0720677i
$483$	−0.382616	−	6.08151i	−0.0174096	−	0.276718i
$484$	20.9901	+	2.65166i	0.954094	+	0.120530i
$485$	20.1635	−	27.8125i	0.915578	−	1.26290i
$486$	0.307652	+	0.653794i	0.0139554	+	0.0296567i
$487$	9.44403	−	20.0696i	0.427950	−	0.909439i	−0.568292	−	0.822827i	$-0.692396\pi$
$487$	9.44403	−	20.0696i	0.427950	−	0.909439i	0.996242	−	0.0866127i	$-0.0276043\pi$
$488$	−1.20482	+	0.662356i	−0.0545397	+	0.0299834i
$489$	1.73616	−	1.63036i	0.0785118	−	0.0737275i
$490$	0.0845404	−	0.674757i	0.00381915	−	0.0304824i
$491$	1.73307	−	3.68295i	0.0782121	−	0.166209i	−0.861896	−	0.507084i	$-0.830723\pi$
$491$	1.73307	−	3.68295i	0.0782121	−	0.166209i	0.940109	+	0.340875i	$0.110723\pi$
$492$	−1.25331	−	1.51499i	−0.0565034	−	0.0683009i
$493$	−10.4685	+	32.2187i	−0.471477	+	1.45106i
$494$	−0.0327019	−	0.00839641i	−0.00147133	−	0.000377772i
$495$	29.6237	−	1.89420i	1.33149	−	0.0851378i
$496$	−0.529091	+	8.40965i	−0.0237569	+	0.377605i
$497$	8.13642	+	12.8209i	0.364968	+	0.575098i
$498$	−0.245063	+	0.230130i	−0.0109816	+	0.0103124i
$499$	−31.9559			−1.43054			−0.715270	−	0.698848i	$-0.753696\pi$
$499$	−31.9559			−1.43054			−0.715270	+	0.698848i	$0.753696\pi$
$500$	15.3134	+	16.2072i	0.684837	+	0.724807i
$501$	−1.77147			−0.0791436
$502$	0.121822	−	0.114399i	0.00543719	−	0.00510586i
$503$	−2.61423	−	4.11936i	−0.116563	−	0.183673i	0.781037	−	0.624484i	$-0.214691\pi$
$503$	−2.61423	−	4.11936i	−0.116563	−	0.183673i	−0.897600	+	0.440811i	$0.854691\pi$
$504$	−0.179075	+	2.84631i	−0.00797663	+	0.126785i
$505$	−18.5161	−	11.7241i	−0.823955	−	0.521716i
$506$	−1.63591	−	0.420030i	−0.0727249	−	0.0186726i
$507$	1.47268	−	4.53244i	0.0654039	−	0.201293i
$508$	24.0490	+	29.0702i	1.06700	+	1.28978i
$509$	3.40244	−	7.23056i	0.150811	−	0.320489i	−0.815119	−	0.579293i	$-0.803329\pi$
$509$	3.40244	−	7.23056i	0.150811	−	0.320489i	0.965930	+	0.258805i	$0.0833286\pi$
$510$	0.214912	+	0.100861i	0.00951646	+	0.00446622i
$511$	−37.2456	+	34.9759i	−1.64765	+	1.54724i
$512$	5.21505	−	2.86700i	0.230475	−	0.126705i
$513$	−0.633438	+	1.34612i	−0.0279670	+	0.0594328i
$514$	−0.0849999	−	0.180634i	−0.00374918	−	0.00796742i
$515$	−28.7593	−	9.31193i	−1.26728	−	0.410333i
$516$	−4.83286	−	0.610532i	−0.212755	−	0.0268772i
$517$	−2.17240	−	34.5293i	−0.0955421	−	1.51860i
$518$	0.202575	+	0.623461i	0.00890062	+	0.0273933i
$519$	−3.03182	+	4.77739i	−0.133082	+	0.209704i
$520$	0.000461147		0.450722i	2.02227e−5		0.0197655i
$521$	−41.6894	+	10.7040i	−1.82645	+	0.468952i	−0.996095	−	0.0882863i	$-0.971861\pi$
$521$	−41.6894	+	10.7040i	−1.82645	+	0.468952i	−0.830353	+	0.557238i	$0.811861\pi$
$522$	0.122994	−	1.95493i	0.00538330	−	0.0855652i
$523$	2.08788	−	10.9451i	0.0912966	−	0.478594i	−0.907045	−	0.421033i	$-0.861668\pi$
$523$	2.08788	−	10.9451i	0.0912966	−	0.478594i	0.998342	−	0.0575609i	$-0.0183323\pi$
$524$	6.89503	−	21.2207i	0.301211	−	0.927032i
$525$	−6.11415	−	1.55652i	−0.266843	−	0.0679320i
$526$	−0.0199084	−	0.0612717i	−0.000868046	−	0.00267157i
$527$	7.83285	−	0.989519i	0.341204	−	0.0431041i
$528$	6.50920	+	2.57717i	0.283276	+	0.112157i
$529$	−0.297832	−	0.117920i	−0.0129492	−	0.00512695i
$530$	0.0747107	+	0.0793959i	0.00324523	+	0.00344874i
$531$	1.52854	+	24.2954i	0.0663329	+	1.05433i
$532$	−3.58705	+	2.60615i	−0.155519	+	0.112991i
$533$	−1.68666	−	0.433060i	−0.0730573	−	0.0187579i
$534$	−0.185288	−	0.173997i	−0.00801821	−	0.00752960i
$535$	31.1112	−	1.98931i	1.34505	−	0.0860052i
$536$	−4.02531	−	2.21293i	−0.173867	−	0.0955842i
$537$	0.508821	+	0.0642790i	0.0219572	+	0.00277385i
$538$	0.348380	+	1.82627i	0.0150197	+	0.0787361i
$539$	−18.6413	+	2.35495i	−0.802938	+	0.101435i
$540$	9.74250	+	1.84815i	0.419250	+	0.0795318i
$541$	0.451385	+	2.36624i	0.0194066	+	0.101733i	0.990673	−	0.136264i	$-0.0435094\pi$
$541$	0.451385	+	2.36624i	0.0194066	+	0.101733i	−0.971266	+	0.237996i	$0.923509\pi$
$542$	−0.262434	+	0.413531i	−0.0112725	+	0.0177627i
$543$	−0.417368	−	0.303236i	−0.0179110	−	0.0130131i
$544$	−2.13056	−	2.57540i	−0.0913468	−	0.110419i
$545$	12.2908	−	31.1360i	0.526479	−	1.33372i
$546$	−0.0341197	−	0.0537641i	−0.00146019	−	0.00230089i
$547$	−3.06315	+	3.70271i	−0.130971	+	0.158317i	−0.831922	−	0.554893i	$-0.812759\pi$
$547$	−3.06315	+	3.70271i	−0.130971	+	0.158317i	0.700951	+	0.713210i	$0.252759\pi$
$548$	2.58030	+	5.48341i	0.110225	+	0.234240i
$549$	10.5698	+	7.67938i	0.451106	+	0.327748i
$550$	−0.933997	+	1.47842i	−0.0398258	+	0.0630401i
$551$	4.93439	−	3.58504i	0.210212	−	0.152728i
$552$	−0.482934	−	0.265495i	−0.0205550	−	0.0113002i
$553$	15.2598	−	3.91806i	0.648914	−	0.166613i
$554$	0.00986745	−	0.0119277i	0.000419228	−	0.000506759i
$555$	2.18651	−	0.419417i	0.0928120	−	0.0178033i
$556$	15.5576	−	6.15968i	0.659789	−	0.261229i
$557$	−2.00525			−0.0849651			−0.0424826	−	0.999097i	$-0.513527\pi$
$557$	−2.00525			−0.0849651			−0.0424826	+	0.999097i	$0.513527\pi$
$558$	−0.424449	+	0.168051i	−0.0179683	+	0.00711417i
$559$	−3.78059	+	2.07840i	−0.159902	+	0.0879069i
$560$	22.7257	+	18.7612i	0.960336	+	0.792806i
$561$	1.22913	−	6.44331i	0.0518938	−	0.272037i
$562$	−0.544822	−	0.511622i	−0.0229819	−	0.0215815i
$563$	18.0112	+	16.9136i	0.759082	+	0.712825i	0.963985	−	0.265957i	$-0.0856879\pi$
$563$	18.0112	+	16.9136i	0.759082	+	0.712825i	−0.204903	+	0.978782i	$0.565688\pi$
$564$	1.05617	−	5.53666i	0.0444730	−	0.233135i
$565$	−6.74958	−	26.1767i	−0.283957	−	1.10126i
$566$	0.811236	−	0.445981i	0.0340988	−	0.0187460i
$567$	23.8611	−	9.44729i	1.00207	−	0.396749i
$568$	1.37332			0.0576232
$569$	35.9222	−	14.2226i	1.50594	−	0.596242i	0.537006	−	0.843579i	$-0.319555\pi$
$569$	35.9222	−	14.2226i	1.50594	−	0.596242i	0.968930	+	0.247337i	$0.0795554\pi$
$570$	−0.0206297	−	0.0374345i	−0.000864082	−	0.00156796i
$571$	−22.4377	+	27.1226i	−0.938990	+	1.13504i	0.0516670	+	0.998664i	$0.483547\pi$
$571$	−22.4377	+	27.1226i	−0.938990	+	1.13504i	−0.990657	+	0.136379i	$0.956453\pi$
$572$	6.02261	−	1.54634i	0.251818	−	0.0646559i
$573$	5.06421	+	2.78407i	0.211560	+	0.116306i
$574$	0.525144	−	0.381539i	0.0219191	−	0.0159251i
$575$	−15.3529	+	18.6359i	−0.640258	+	0.777172i
$576$	−18.1700	−	13.2013i	−0.757083	−	0.550053i
$577$	−8.24978	−	17.5317i	−0.343443	−	0.729853i	0.656252	−	0.754542i	$-0.272141\pi$
$577$	−8.24978	−	17.5317i	−0.343443	−	0.729853i	−0.999695	+	0.0246883i	$0.992141\pi$
$578$	0.153035	−	0.184987i	0.00636541	−	0.00769446i
$579$	−4.48428	−	7.06609i	−0.186360	−	0.293657i
$580$	−31.3510	−	25.8818i	−1.30178	−	1.07468i
$581$	24.9232	+	30.1270i	1.03399	+	1.24988i
$582$	0.355101	+	0.257996i	0.0147194	+	0.0106943i
$583$	1.61405	−	2.54333i	0.0668470	−	0.105334i
$584$	0.865874	+	4.53907i	0.0358301	+	0.187828i
$585$	3.87353	−	1.82759i	0.160151	−	0.0755614i
$586$	−1.53348	+	0.193723i	−0.0633474	+	0.00800264i
$587$	3.81652	+	20.0069i	0.157525	+	0.825774i	0.970061	+	0.242863i	$0.0780864\pi$
$587$	3.81652	+	20.0069i	0.157525	+	0.825774i	−0.812536	+	0.582911i	$0.801914\pi$
$588$	−3.03697	−	0.383658i	−0.125242	−	0.0158218i
$589$	−1.24563	−	0.684790i	−0.0513252	−	0.0282163i
$590$	−1.21164	−	0.767193i	−0.0498825	−	0.0315848i
$591$	2.42388	+	2.27617i	0.0997050	+	0.0936292i
$592$	−10.0724	−	2.58615i	−0.413973	−	0.106290i
$593$	19.0792	−	13.8618i	0.783488	−	0.569237i	−0.122536	−	0.992464i	$-0.539103\pi$
$593$	19.0792	−	13.8618i	0.783488	−	0.569237i	0.906024	+	0.423227i	$0.139103\pi$
$594$	0.0488328	+	0.776175i	0.00200363	+	0.0318469i
$595$	13.2772	−	24.2098i	0.544314	−	0.992507i
$596$	5.00637	+	1.98216i	0.205069	+	0.0811924i
$597$	3.73958	+	1.48060i	0.153051	+	0.0605971i
$598$	−0.241773	+	0.0305431i	−0.00988685	+	0.00124900i
$599$	11.2693	+	34.6832i	0.460450	+	1.41712i	0.864616	+	0.502433i	$0.167562\pi$
$599$	11.2693	+	34.6832i	0.460450	+	1.41712i	−0.404166	+	0.914686i	$0.632438\pi$
$600$	−0.415151	+	0.391455i	−0.0169485	+	0.0159811i
$601$	−3.11301	+	9.58085i	−0.126982	+	0.390811i	−0.994257	−	0.107019i	$-0.965870\pi$
$601$	−3.11301	+	9.58085i	−0.126982	+	0.390811i	0.867275	+	0.497830i	$0.165870\pi$
$602$	0.301343	−	1.57969i	0.0122818	−	0.0643835i
$603$	−2.74081	+	43.5639i	−0.111614	+	1.77406i
$604$	−22.0435	+	5.65980i	−0.896936	+	0.230294i
$605$	22.5678	+	7.30719i	0.917510	+	0.297080i
$606$	0.150043	−	0.236429i	0.00609507	−	0.00960429i
$607$	2.53054	+	7.78821i	0.102712	+	0.316114i	0.989187	−	0.146663i	$-0.0468532\pi$
$607$	2.53054	+	7.78821i	0.102712	+	0.316114i	−0.886475	+	0.462777i	$0.846853\pi$
$608$	0.0377862	+	0.600594i	0.00153243	+	0.0243573i
$609$	11.4126	+	1.44174i	0.462460	+	0.0584223i
$610$	−0.731759	+	0.238591i	−0.0296281	+	0.00966026i
$611$	−2.12547	−	4.51686i	−0.0859874	−	0.182732i
$612$	−9.01143	+	19.1503i	−0.364266	+	0.774104i
$613$	−26.0067	+	14.2973i	−1.05040	+	0.577462i	−0.910843	−	0.412752i	$-0.864567\pi$
$613$	−26.0067	+	14.2973i	−1.05040	+	0.577462i	−0.139556	+	0.990214i	$0.544567\pi$
$614$	−0.416701	+	0.391308i	−0.0168167	+	0.0157919i
$615$	−1.06401	−	1.93075i	−0.0429052	−	0.0778554i
$616$	−1.97655	+	4.20039i	−0.0796377	+	0.169239i
$617$	−0.674372	−	0.815176i	−0.0271492	−	0.0328178i	0.756764	−	0.653688i	$-0.226779\pi$
$617$	−0.674372	−	0.815176i	−0.0271492	−	0.0328178i	−0.783913	+	0.620871i	$0.786779\pi$
$618$	0.119356	−	0.367340i	0.00480120	−	0.0147766i
$619$	−44.8842	−	11.5243i	−1.80405	−	0.463201i	−0.811426	−	0.584455i	$-0.801308\pi$
$619$	−44.8842	−	11.5243i	−1.80405	−	0.463201i	−0.992621	+	0.121255i	$0.961308\pi$
$620$	−2.34684	+	9.17933i	−0.0942514	+	0.368651i
$621$	−0.674256	+	10.7170i	−0.0270569	+	0.430058i
$622$	0.856819	+	1.35013i	0.0343553	+	0.0541353i
$623$	−21.5503	+	20.2371i	−0.863396	+	0.810782i
$624$	1.01012			0.0404372
$625$	13.4819	+	21.0532i	0.539278	+	0.842128i
$626$	−0.354606			−0.0141729
$627$	−0.860902	+	0.808441i	−0.0343811	+	0.0322860i
$628$	−21.3143	−	33.5860i	−0.850534	−	1.34023i
$629$	−0.611803	+	9.72433i	−0.0243942	+	0.387734i
$630$	−0.395462	+	1.54679i	−0.0157556	+	0.0616256i
$631$	16.5544	+	4.25045i	0.659021	+	0.169208i	0.563367	−	0.826207i	$-0.309506\pi$
$631$	16.5544	+	4.25045i	0.659021	+	0.169208i	0.0956538	+	0.995415i	$0.469506\pi$
$632$	0.440309	−	1.35513i	0.0175145	−	0.0539042i
$633$	2.31971	+	2.80405i	0.0922003	+	0.111451i
$634$	0.415530	−	0.883047i	0.0165028	−	0.0350703i
$635$	20.4168	+	37.0481i	0.810214	+	1.47021i
$636$	0.357737	−	0.335938i	0.0141852	−	0.0133208i
$637$	−2.37572	+	1.30606i	−0.0941296	+	0.0517482i
$638$	1.35756	−	2.88496i	0.0537462	−	0.114217i
$639$	−5.55644	−	11.8080i	−0.219810	−	0.467119i
$640$	5.08230	−	1.65709i	0.200896	−	0.0655022i
$641$	22.3243	+	2.82021i	0.881755	+	0.111392i	0.553156	−	0.833078i	$-0.313423\pi$
$641$	22.3243	+	2.82021i	0.881755	+	0.111392i	0.328599	+	0.944469i	$0.393423\pi$
$642$	0.0250110	+	0.397538i	0.000987104	+	0.0156896i
$643$	5.95414	+	18.3249i	0.234808	+	0.722665i	0.997147	+	0.0754869i	$0.0240511\pi$
$643$	5.95414	+	18.3249i	0.234808	+	0.722665i	−0.762339	+	0.647178i	$0.775949\pi$
$644$	−17.1481	+	27.0211i	−0.675729	+	1.06478i
$645$	−5.19612	−	1.68245i	−0.204597	−	0.0662462i
$646$	0.181183	−	0.0465199i	0.00712855	−	0.00183030i
$647$	0.935294	−	14.8661i	0.0367702	−	0.584445i	−0.935902	−	0.352261i	$-0.885413\pi$
$647$	0.935294	−	14.8661i	0.0367702	−	0.584445i	0.972672	−	0.232184i	$-0.0745872\pi$
$648$	0.434912	−	2.27989i	0.0170849	−	0.0895624i
$649$	−12.2447	+	37.6853i	−0.480647	+	1.47928i
$650$	−0.0467725	+	0.247946i	−0.00183457	+	0.00972523i
$651$	−0.828438	−	2.54967i	−0.0324690	−	0.0999295i
$652$	−12.4098	+	1.56772i	−0.486005	+	0.0613967i
$653$	5.32301	+	2.10753i	0.208306	+	0.0824740i	0.469960	−	0.882688i	$-0.344268\pi$
$653$	5.32301	+	2.10753i	0.208306	+	0.0824740i	−0.261655	+	0.965162i	$0.584268\pi$
$654$	0.397668	+	0.157448i	0.0155501	+	0.00615670i
$655$	12.0297	−	21.9351i	0.470040	−	0.857076i
$656$	0.646558	+	10.2767i	0.0252438	+	0.401239i
$657$	35.5244	−	25.8100i	1.38594	−	1.00694i
$658$	1.80235	+	0.462764i	0.0702627	+	0.0180404i
$659$	1.70350	+	1.59969i	0.0663589	+	0.0623151i	0.717017	−	0.697056i	$-0.245507\pi$
$659$	1.70350	+	1.59969i	0.0663589	+	0.0623151i	−0.650658	+	0.759371i	$0.725507\pi$
$660$	6.65067	+	4.21111i	0.258877	+	0.163917i
$661$	−42.5560	−	23.3953i	−1.65523	−	0.909973i	−0.985965	−	0.166954i	$-0.946607\pi$
$661$	−42.5560	−	23.3953i	−1.65523	−	0.909973i	−0.669270	−	0.743019i	$-0.733393\pi$
$662$	−0.767737	−	0.0969877i	−0.0298389	−	0.00376954i
$663$	−0.177346	−	0.929681i	−0.00688756	−	0.0361058i
$664$	3.50833	−	0.443205i	0.136149	−	0.0171997i
$665$	−4.49596	+	2.12126i	−0.174346	+	0.0822589i
$666$	−0.105568	−	0.553407i	−0.00409068	−	0.0214441i
$667$	23.5891	−	37.1705i	0.913373	−	1.43925i
$668$	7.52687	+	5.46859i	0.291224	+	0.211586i
$669$	−4.17259	−	5.04379i	−0.161322	−	0.195004i
$670$	−1.98304	−	1.63710i	−0.0766114	−	0.0632465i
$671$	11.3950	+	17.9557i	0.439900	+	0.693172i
$672$	−0.723457	+	0.874509i	−0.0279080	+	0.0337349i
$673$	−16.2953	−	34.6292i	−0.628137	−	1.33486i	−0.925010	−	0.379942i	$-0.875944\pi$
$673$	−16.2953	−	34.6292i	−0.628137	−	1.33486i	0.296874	−	0.954917i	$-0.404056\pi$
$674$	−0.498698	−	0.362325i	−0.0192091	−	0.0139563i
$675$	10.3458	+	4.07171i	0.398209	+	0.156720i
$676$	−20.2491	+	14.7118i	−0.778811	+	0.565839i
$677$	−3.77613	−	2.07594i	−0.145128	−	0.0797850i	0.407535	−	0.913190i	$-0.366388\pi$
$677$	−3.77613	−	2.07594i	−0.145128	−	0.0797850i	−0.552663	+	0.833405i	$0.686388\pi$
$678$	0.334551	−	0.0858982i	0.0128484	−	0.00329890i
$679$	32.5408	−	39.3351i	1.24880	−	1.50954i
$680$	−1.20528	−	2.18709i	−0.0462202	−	0.0838709i
$681$	0.989868	−	0.391917i	0.0379318	−	0.0150183i
$682$	−0.743071			−0.0284537
$683$	−29.3030	+	11.6019i	−1.12125	+	0.443934i	−0.854301	−	0.519778i	$-0.826015\pi$
$683$	−29.3030	+	11.6019i	−1.12125	+	0.443934i	−0.266947	+	0.963711i	$0.586015\pi$
$684$	3.33918	−	1.83573i	0.127677	−	0.0701909i
$685$	1.69651	+	6.57951i	0.0648203	+	0.251390i
$686$	−0.138574	+	0.726433i	−0.00529080	+	0.0277353i
$687$	−5.41223	−	5.08242i	−0.206489	−	0.193906i
$688$	18.5967	+	17.4635i	0.708992	+	0.665788i
$689$	0.0814410	−	0.426928i	0.00310265	−	0.0162647i
$690$	−0.237913	−	0.196409i	−0.00905720	−	0.00747717i
$691$	33.1799	−	18.2408i	1.26222	−	0.693913i	0.296885	−	0.954913i	$-0.404052\pi$
$691$	33.1799	−	18.2408i	1.26222	−	0.693913i	0.965339	+	0.261000i	$0.0840522\pi$
$692$	27.6300	−	10.9395i	1.05033	−	0.415856i
$693$	44.1129			1.67571
$694$	1.43153	−	0.566782i	0.0543400	−	0.0215147i
$695$	18.4248	−	3.53426i	0.698893	−	0.134062i
$696$	0.663150	−	0.801611i	0.0251366	−	0.0303850i
$697$	9.34485	−	2.39935i	0.353961	−	0.0908818i
$698$	1.19281	+	0.655754i	0.0451486	+	0.0248207i
$699$	−7.21750	+	5.24382i	−0.272991	+	0.198340i
$700$	21.1736	+	25.4881i	0.800286	+	0.963360i
$701$	24.9087	+	18.0972i	0.940790	+	0.683524i	0.948611	−	0.316446i	$-0.102490\pi$
$701$	24.9087	+	18.0972i	0.940790	+	0.683524i	−0.00782097	+	0.999969i	$0.502490\pi$
$702$	0.0477779	+	0.101533i	0.00180326	+	0.00383212i
$703$	1.11820	−	1.35167i	0.0421738	−	0.0509794i
$704$	−19.5887	−	30.8668i	−0.738277	−	1.16334i
$705$	2.32042	−	5.87827i	0.0873920	−	0.221389i
$706$	−0.650722	−	0.786587i	−0.0244902	−	0.0296036i
$707$	−26.3484	−	19.1432i	−0.990933	−	0.719955i
$708$	−3.45903	+	5.45056i	−0.129998	+	0.204844i
$709$	1.12201	+	5.88178i	0.0421379	+	0.220895i	0.997127	−	0.0757456i	$-0.0241337\pi$
$709$	1.12201	+	5.88178i	0.0421379	+	0.220895i	−0.954989	+	0.296640i	$0.904134\pi$
$710$	0.755326	+	0.143285i	0.0283469	+	0.00537740i
$711$	−13.4332	+	1.69700i	−0.503783	+	0.0636426i
$712$	0.500995	+	2.62631i	0.0187756	+	0.0984251i
$713$	−10.1790	−	1.28591i	−0.381207	−	0.0481576i
$714$	0.309159	+	0.169962i	0.0115700	+	0.00636066i
$715$	6.95742	−	0.444871i	0.260193	−	0.0166372i
$716$	−1.96352	−	1.84386i	−0.0733800	−	0.0689084i
$717$	−3.32096	−	0.852678i	−0.124024	−	0.0318438i
$718$	0.787649	−	0.572260i	0.0293948	−	0.0213566i
$719$	−2.28106	−	36.2564i	−0.0850691	−	1.35213i	−0.776694	−	0.629878i	$-0.783105\pi$
$719$	−2.28106	−	36.2564i	−0.0850691	−	1.35213i	0.691625	−	0.722257i	$-0.256895\pi$
$720$	−17.3560	−	18.4444i	−0.646820	−	0.687382i
$721$	−41.7682	−	16.5372i	−1.55553	−	0.615878i
$722$	1.29784	+	0.513850i	0.0483005	+	0.0191235i
$723$	−8.33018	+	1.05235i	−0.309803	+	0.0391372i
$724$	0.837272	+	2.57686i	0.0311170	+	0.0957682i
$725$	−29.1266	−	35.0617i	−1.08173	−	1.30216i
$726$	−0.0936601	+	0.288256i	−0.00347605	+	0.0106982i
$727$	4.57861	−	24.0019i	0.169811	−	0.890181i	−0.790756	−	0.612132i	$-0.790312\pi$
$727$	4.57861	−	24.0019i	0.169811	−	0.890181i	0.960567	−	0.278049i	$-0.0896879\pi$
$728$	−0.0420575	+	0.668485i	−0.00155875	+	0.0247757i
$729$	−18.9090	+	4.85500i	−0.700332	+	0.179815i
$730$	0.00264666	+	2.58683i	9.79574e−5	+	0.0957429i
$731$	12.8078	−	20.1818i	0.473712	−	0.746451i
$732$	1.07062	+	3.29504i	0.0395714	+	0.121788i
$733$	1.67316	+	26.5941i	0.0617996	+	0.982277i	0.899715	+	0.436477i	$0.143774\pi$
$733$	1.67316	+	26.5941i	0.0617996	+	0.982277i	−0.837916	+	0.545800i	$0.816226\pi$
$734$	0.780908	+	0.0986516i	0.0288238	+	0.00364130i
$735$	−3.26524	−	1.05725i	−0.120440	−	0.0389972i
$736$	1.84942	+	3.93021i	0.0681704	+	0.144869i
$737$	−30.2519	+	64.2886i	−1.11434	+	2.36810i
$738$	−0.488855	+	0.268750i	−0.0179950	+	0.00989284i
$739$	−11.5018	+	10.8009i	−0.423102	+	0.397319i	−0.866638	−	0.498937i	$-0.833724\pi$
$739$	−11.5018	+	10.8009i	−0.423102	+	0.397319i	0.443536	+	0.896256i	$0.353724\pi$
$740$	−10.5851	−	4.96774i	−0.389115	−	0.182618i
$741$	−0.0725529	+	0.154183i	−0.00266530	+	0.00566404i
$742$	0.103270	+	0.124832i	0.00379117	+	0.00458274i
$743$	3.56070	−	10.9587i	0.130629	−	0.402036i	−0.864255	−	0.503054i	$-0.832210\pi$
$743$	3.56070	−	10.9587i	0.130629	−	0.402036i	0.994885	+	0.101017i	$0.0322098\pi$
$744$	−0.234843	−	0.0602973i	−0.00860975	−	0.00221061i
$745$	5.10062	+	3.22963i	0.186872	+	0.118325i
$746$	−0.120605	+	1.91697i	−0.00441568	+	0.0701851i
$747$	−18.0054	−	28.3720i	−0.658784	−	1.03808i
$748$	−25.1132	+	23.5829i	−0.918229	+	0.862275i
$749$	46.3279			1.69278
$750$	−0.269176	+	0.171985i	−0.00982892	+	0.00628002i
$751$	−19.7325			−0.720047			−0.360024	−	0.932943i	$-0.617231\pi$
$751$	−19.7325			−0.720047			−0.360024	+	0.932943i	$0.617231\pi$
$752$	−21.5180	+	20.2068i	−0.784682	+	0.736865i
$753$	−0.451935	−	0.712136i	−0.0164694	−	0.0259517i
$754$	0.0288864	−	0.459136i	0.00105198	−	0.0167207i
$755$	−25.4650	+	1.62828i	−0.926765	+	0.0592591i
$756$	14.2733	+	3.66476i	0.519115	+	0.133286i
$757$	−2.33614	+	7.18991i	−0.0849086	+	0.261322i	−0.984493	−	0.175426i	$-0.943870\pi$
$757$	−2.33614	+	7.18991i	−0.0849086	+	0.261322i	0.899584	+	0.436748i	$0.143870\pi$
$758$	−0.542543	−	0.655822i	−0.0197060	−	0.0238205i
$759$	−3.62945	+	7.71297i	−0.131741	+	0.279963i
$760$	−0.0558937	+	0.446115i	−0.00202748	+	0.0161823i
$761$	−4.56457	+	4.28642i	−0.165466	+	0.155383i	−0.762857	−	0.646567i	$-0.776204\pi$
$761$	−4.56457	+	4.28642i	−0.165466	+	0.155383i	0.597391	+	0.801950i	$0.296204\pi$
$762$	−0.473636	+	0.260384i	−0.0171580	+	0.00943270i
$763$	21.1803	−	45.0105i	0.766780	−	1.62949i
$764$	−12.9230	−	27.4627i	−0.467537	−	0.993566i
$765$	−13.9284	+	19.2121i	−0.503583	+	0.694616i
$766$	1.65305	+	0.208829i	0.0597272	+	0.00754530i
$767$	0.358992	+	5.70602i	0.0129625	+	0.206032i
$768$	−1.82458	−	5.61548i	−0.0658389	−	0.202631i
$769$	−8.42060	+	13.2687i	−0.303654	+	0.478483i	−0.961551	−	0.274625i	$-0.911446\pi$
$769$	−8.42060	+	13.2687i	−0.303654	+	0.478483i	0.657897	+	0.753108i	$0.271446\pi$
$770$	−1.52535	+	2.10399i	−0.0549700	+	0.0758227i
$771$	−0.975899	+	0.250568i	−0.0351461	+	0.00902400i
$772$	−2.75984	+	43.8665i	−0.0993289	+	1.57879i
$773$	6.82666	−	35.7866i	0.245538	−	1.28715i	−0.619320	−	0.785138i	$-0.712592\pi$
$773$	6.82666	−	35.7866i	0.245538	−	1.28715i	0.864858	−	0.502016i	$-0.167408\pi$
$774$	−0.427090	+	1.31445i	−0.0153515	+	0.0472469i
$775$	−4.50336	+	9.62119i	−0.161766	+	0.345603i
$776$	−1.42674	−	4.39105i	−0.0512169	−	0.157629i
$777$	3.28246	−	0.414671i	0.117758	−	0.0148762i
$778$	1.59159	+	0.630154i	0.0570612	+	0.0225921i
$779$	−1.61506	−	0.639447i	−0.0578655	−	0.0229106i
$780$	1.11589	+	0.211684i	0.0399552	+	0.00757951i
$781$	−1.33380	−	21.2001i	−0.0477271	−	0.758600i
$782$	1.09232	−	0.793616i	0.0390612	−	0.0283796i
$783$	−19.6345	−	5.04128i	−0.701679	−	0.180161i
$784$	11.6861	+	10.9740i	0.417362	+	0.391929i
$785$	−16.4607	−	41.4510i	−0.587508	−	1.47945i
$786$	0.280111	+	0.153992i	0.00999123	+	0.00549272i
$787$	27.8290	+	3.51562i	0.991997	+	0.125318i	0.604545	−	0.796571i	$-0.293355\pi$
$787$	27.8290	+	3.51562i	0.991997	+	0.125318i	0.387452	+	0.921890i	$0.373355\pi$
$788$	−3.27228	−	17.1539i	−0.116570	−	0.611082i
$789$	−0.322589	+	0.0407525i	−0.0114845	+	0.00145083i
$790$	0.383558	−	0.699383i	0.0136464	−	0.0248829i
$791$	−7.52763	−	39.4612i	−0.267652	−	1.40308i
$792$	2.13773	−	3.36852i	0.0759608	−	0.119695i
$793$	2.48241	+	1.80358i	0.0881530	+	0.0640469i
$794$	0.836711	+	1.01141i	0.0296937	+	0.0358936i
$795$	0.464269	−	0.295301i	0.0164659	−	0.0104733i
$796$	−11.3186	−	17.8352i	−0.401176	−	0.632152i
$797$	−33.8064	+	40.8649i	−1.19748	+	1.44751i	−0.334412	+	0.942427i	$0.608538\pi$
$797$	−33.8064	+	40.8649i	−1.19748	+	1.44751i	−0.863071	+	0.505082i	$0.831462\pi$
$798$	−0.0270449	−	0.0574733i	−0.000957378	−	0.00203453i
$799$	22.3755	+	16.2568i	0.791589	+	0.575123i
$800$	4.46068	−	0.572791i	0.157709	−	0.0202512i
$801$	20.5545	−	14.9337i	0.726256	−	0.527656i
$802$	−1.05628	−	0.580696i	−0.0372986	−	0.0205051i
$803$	69.2293	−	17.7751i	2.44305	−	0.627268i
$804$	−7.37837	+	8.91891i	−0.260215	+	0.314546i
$805$	−24.5362	+	26.1820i	−0.864787	+	0.922795i
$806$	−0.0996859	+	0.0394685i	−0.00351129	+	0.00139022i
$807$	9.38342			0.330312
$808$	−2.73865	+	1.08431i	−0.0963455	+	0.0381459i
$809$	36.7770	−	20.2184i	1.29301	−	0.710839i	0.321293	−	0.946980i	$-0.395883\pi$
$809$	36.7770	−	20.2184i	1.29301	−	0.710839i	0.971719	+	0.236140i	$0.0758825\pi$
$810$	0.477074	−	1.20856i	0.0167627	−	0.0424646i
$811$	0.0720394	−	0.377644i	0.00252964	−	0.0132609i	−0.981000	−	0.194007i	$-0.937851\pi$
$811$	0.0720394	−	0.377644i	0.00252964	−	0.0132609i	0.983530	+	0.180747i	$0.0578514\pi$
$812$	−44.0405	−	41.3568i	−1.54552	−	1.45134i
$813$	1.80194	+	1.69213i	0.0631967	+	0.0593457i
$814$	0.171837	−	0.900800i	0.00602288	−	0.0315730i
$815$	−13.9978	−	0.866287i	−0.490320	−	0.0303447i
$816$	−4.90427	+	2.69615i	−0.171684	+	0.0943840i
$817$	−4.00131	+	1.58423i	−0.139988	+	0.0554252i
$818$	−1.76267			−0.0616304
$819$	5.91792	−	2.34307i	0.206789	−	0.0818735i
$820$	−1.43937	+	11.4883i	−0.0502649	+	0.401188i
$821$	18.7390	−	22.6515i	0.653995	−	0.790544i	−0.334403	−	0.942430i	$-0.608535\pi$
$821$	18.7390	−	22.6515i	0.653995	−	0.790544i	0.988398	+	0.151886i	$0.0485347\pi$
$822$	−0.0840896	+	0.0215905i	−0.00293296	+	0.000753056i
$823$	−0.966082	−	0.531108i	−0.0336755	−	0.0185133i	0.464827	−	0.885402i	$-0.346117\pi$
$823$	−0.966082	−	0.531108i	−0.0336755	−	0.0185133i	−0.498502	+	0.866888i	$0.666117\pi$
$824$	−3.28691	+	2.38808i	−0.114505	+	0.0831926i
$825$	6.44615	+	6.02856i	0.224426	+	0.209888i
$826$	−1.72417	−	1.25268i	−0.0599914	−	0.0435863i
$827$	−2.44669	−	5.19948i	−0.0850797	−	0.180804i	0.857760	−	0.514051i	$-0.171856\pi$
$827$	−2.44669	−	5.19948i	−0.0850797	−	0.180804i	−0.942840	+	0.333247i	$0.891856\pi$
$828$	17.5317	−	21.1921i	0.609267	−	0.736478i
$829$	−7.02746	−	11.0735i	−0.244074	−	0.384599i	0.700101	−	0.714044i	$-0.253138\pi$
$829$	−7.02746	−	11.0735i	−0.244074	−	0.384599i	−0.944175	+	0.329445i	$0.893138\pi$
$830$	1.97582	+	0.122279i	0.0685818	+	0.00424436i
$831$	−0.0498011	−	0.0601992i	−0.00172758	−	0.00208829i
$832$	−4.26740	−	3.10045i	−0.147946	−	0.107489i
$833$	8.04839	−	12.6822i	0.278860	−	0.439413i
$834$	0.0449169	+	0.235463i	0.00155535	+	0.00815341i
$835$	7.14857	+	7.59686i	0.247386	+	0.262900i
$836$	6.15360	−	0.777381i	0.212827	−	0.0268863i
$837$	0.885249	+	4.64064i	0.0305987	+	0.160404i
$838$	1.73975	+	0.219781i	0.0600985	+	0.00759221i
$839$	15.4774	+	8.50876i	0.534339	+	0.293755i	0.725987	−	0.687709i	$-0.241383\pi$
$839$	15.4774	+	8.50876i	0.534339	+	0.293755i	−0.191648	+	0.981464i	$0.561383\pi$
$840$	−0.652809	+	0.541176i	−0.0225240	+	0.0186724i
$841$	39.4425	+	37.0390i	1.36009	+	1.27721i
$842$	0.213228	+	0.0547476i	0.00734831	+	0.00188673i
$843$	−3.05167	+	2.21717i	−0.105105	+	0.0763634i
$844$	−1.20011	−	19.0753i	−0.0413096	−	0.656597i
$845$	−25.3799	+	11.9746i	−0.873095	+	0.411939i
$846$	−1.48690	−	0.588707i	−0.0511208	−	0.0202402i
$847$	32.7761	+	12.9770i	1.12620	+	0.445894i
$848$	−2.54977	+	0.322111i	−0.0875596	+	0.0110613i
$849$	−1.44380	−	4.44357i	−0.0495512	−	0.152503i
$850$	−0.434713	−	1.32865i	−0.0149105	−	0.0455723i
$851$	3.91278	−	12.0423i	0.134128	−	0.412804i
$852$	0.648464	−	3.39937i	0.0222160	−	0.116460i
$853$	0.670597	−	10.6588i	0.0229608	−	0.364952i	−0.969723	−	0.244208i	$-0.921472\pi$
$853$	0.670597	−	10.6588i	0.0229608	−	0.364952i	0.992684	−	0.120744i	$-0.0385279\pi$
$854$	−1.10786	+	0.284449i	−0.0379100	+	0.00973365i
$855$	4.06192	−	1.32439i	0.138915	−	0.0452933i
$856$	2.24506	−	3.53766i	0.0767347	−	0.120915i
$857$	12.7066	+	39.1069i	0.434049	+	1.33587i	0.894058	+	0.447952i	$0.147846\pi$
$857$	12.7066	+	39.1069i	0.434049	+	1.33587i	−0.460008	+	0.887915i	$0.652154\pi$
$858$	0.00559322	+	0.0889017i	0.000190950	+	0.00303506i
$859$	−17.3200	−	2.18802i	−0.590951	−	0.0746544i	−0.175830	−	0.984421i	$-0.556261\pi$
$859$	−17.3200	−	2.18802i	−0.590951	−	0.0746544i	−0.415121	+	0.909766i	$0.636261\pi$
$860$	16.8842	+	23.1892i	0.575746	+	0.790744i
$861$	−1.39489	−	2.96429i	−0.0475377	−	0.101023i
$862$	−0.312952	+	0.665057i	−0.0106592	+	0.0226519i
$863$	−43.8089	+	24.0841i	−1.49127	+	0.819834i	−0.998726	−	0.0504526i	$-0.983934\pi$
$863$	−43.8089	+	24.0841i	−1.49127	+	0.819834i	−0.492546	+	0.870286i	$0.663934\pi$
$864$	1.45799	−	1.36914i	0.0496018	−	0.0465792i
$865$	32.7221	−	6.27678i	1.11258	−	0.213417i
$866$	−0.543603	+	1.15522i	−0.0184724	+	0.0392558i
$867$	−0.772369	−	0.933634i	−0.0262310	−	0.0317079i
$868$	−4.35093	+	13.3908i	−0.147680	+	0.454513i
$869$	−21.3470	−	5.48098i	−0.724147	−	0.185929i
$870$	0.448369	−	0.371696i	0.0152011	−	0.0126017i
$871$	−0.643705	+	10.2314i	−0.0218111	+	0.346678i
$872$	−2.41065	−	3.79858i	−0.0816351	−	0.128636i
$873$	−31.9825	+	30.0335i	−1.08244	+	1.01648i
$874$	−0.243089			−0.00822262
$875$	17.9979	+	32.5013i	0.608439	+	1.09874i
$876$	11.6444			0.393427
$877$	5.02856	−	4.72213i	0.169802	−	0.159455i	−0.594987	−	0.803735i	$-0.702843\pi$
$877$	5.02856	−	4.72213i	0.169802	−	0.159455i	0.764790	+	0.644280i	$0.222843\pi$
$878$	1.45967	+	2.30007i	0.0492613	+	0.0776235i
$879$	−0.489829	+	7.78560i	−0.0165215	+	0.262602i
$880$	−15.2150	−	38.3142i	−0.512898	−	1.29157i
$881$	−9.53275	−	2.44759i	−0.321166	−	0.0824615i	0.0846650	−	0.996409i	$-0.473018\pi$
$881$	−9.53275	−	2.44759i	−0.321166	−	0.0824615i	−0.405831	+	0.913948i	$0.633018\pi$
$882$	−0.268383	+	0.825999i	−0.00903694	+	0.0278128i
$883$	11.7308	+	14.1801i	0.394772	+	0.477198i	0.930026	−	0.367493i	$-0.119784\pi$
$883$	11.7308	+	14.1801i	0.394772	+	0.477198i	−0.535254	+	0.844691i	$0.679784\pi$
$884$	−2.11642	+	4.49763i	−0.0711830	+	0.151272i
$885$	−4.94932	+	5.28131i	−0.166370	+	0.177529i
$886$	1.48712	−	1.39650i	0.0499608	−	0.0469163i
$887$	−3.61137	+	1.98537i	−0.121258	+	0.0666621i	−0.541228	−	0.840876i	$-0.682040\pi$
$887$	−3.61137	+	1.98537i	−0.121258	+	0.0666621i	0.419970	+	0.907538i	$0.362040\pi$
$888$	0.127404	−	0.270748i	0.00427541	−	0.00908570i
$889$	26.7657	+	56.8801i	0.897694	+	1.90770i
$890$	0.00153136	+	1.49674i	5.13314e−5	+	0.0501709i
$891$	−35.6174	−	4.49952i	−1.19323	−	0.150740i
$892$	2.15871	+	34.3116i	0.0722788	+	1.14884i
$893$	−1.53877	−	4.73583i	−0.0514928	−	0.158479i
$894$	−0.0413322	+	0.0651291i	−0.00138236	+	0.00217824i
$895$	−1.77763	−	2.44144i	−0.0594196	−	0.0816083i
$896$	7.69441	−	1.97559i	0.257052	−	0.0659998i
$897$	−0.0772281	+	1.22750i	−0.00257857	+	0.0409852i
$898$	0.0936070	−	0.490705i	0.00312371	−	0.0163750i
$899$	5.98519	−	18.4205i	0.199617	−	0.614359i
$900$	−15.3080	−	24.0128i	−0.510267	−	0.800428i
$901$	0.744122	+	2.29017i	0.0247903	+	0.0762966i
$902$	−0.900885	+	0.113808i	−0.0299962	+	0.00378940i
$903$	−7.54653	−	2.98788i	−0.251133	−	0.0994305i
$904$	−3.37810	−	1.33749i	−0.112354	−	0.0444841i
$905$	0.383830	+	3.01353i	0.0127590	+	0.100173i
$906$	−0.0204719	−	0.325391i	−0.000680132	−	0.0108104i
$907$	5.51932	−	4.01002i	0.183266	−	0.133150i	−0.492370	−	0.870386i	$-0.663869\pi$
$907$	5.51932	−	4.01002i	0.183266	−	0.133150i	0.675636	+	0.737236i	$0.263869\pi$
$908$	−5.41574	−	1.39053i	−0.179728	−	0.0461462i
$909$	20.4037	+	19.1603i	0.676748	+	0.635508i
$910$	−0.0928781	+	0.363279i	−0.00307888	+	0.0120426i
$911$	−16.8398	−	9.25773i	−0.557926	−	0.306722i	0.177728	−	0.984080i	$-0.443125\pi$
$911$	−16.8398	−	9.25773i	−0.557926	−	0.306722i	−0.735654	+	0.677357i	$0.763125\pi$
$912$	0.999666	+	0.126287i	0.0331022	+	0.00418179i
$913$	−10.2492	−	53.7281i	−0.339198	−	1.77814i
$914$	1.30687	−	0.165096i	0.0432274	−	0.00546089i
$915$	0.490806	+	3.85342i	0.0162255	+	0.127390i
$916$	7.30661	+	38.3026i	0.241417	+	1.26555i
$917$	19.9207	−	31.3900i	0.657839	−	1.03659i
$918$	−0.502973	−	0.365432i	−0.0166006	−	0.0120610i
$919$	20.4175	+	24.6805i	0.673512	+	0.814136i	0.990963	−	0.134139i	$-0.0428268\pi$
$919$	20.4175	+	24.6805i	0.673512	+	0.814136i	−0.317451	+	0.948275i	$0.602827\pi$
$920$	0.810260	+	3.14240i	0.0267135	+	0.103602i
$921$	1.54587	+	2.43591i	0.0509383	+	0.0802659i
$922$	0.516905	−	0.624831i	0.0170234	−	0.0205777i
$923$	−1.30499	−	2.77323i	−0.0429541	−	0.0912821i
$924$	9.46391	+	6.87593i	0.311340	+	0.226202i
$925$	−10.6220	−	7.68420i	−0.349250	−	0.252655i
$926$	−0.804618	+	0.584589i	−0.0264414	+	0.0192108i
$927$	33.8319	+	18.5993i	1.11119	+	0.610880i
$928$	−7.94217	+	2.03920i	−0.260714	+	0.0669401i
$929$	−18.5489	+	22.4217i	−0.608569	+	0.735633i	−0.981338	−	0.192291i	$-0.938408\pi$
$929$	−18.5489	+	22.4217i	−0.608569	+	0.735633i	0.372769	+	0.927924i	$0.378408\pi$
$930$	−0.122872	−	0.0576659i	−0.00402914	−	0.00189094i
$931$	−2.51442	+	0.995528i	−0.0824067	+	0.0326271i
$932$	46.8545			1.53477
$933$	7.50373	−	2.97094i	0.245661	−	0.0972641i
$934$	−1.47852	+	0.812825i	−0.0483787	+	0.0265964i
$935$	−32.5918	+	20.7302i	−1.06586	+	0.677949i
$936$	0.107865	−	0.565446i	0.00352566	−	0.0184822i
$937$	3.08811	+	2.89993i	0.100884	+	0.0947366i	0.733348	−	0.679853i	$-0.237956\pi$
$937$	3.08811	+	2.89993i	0.100884	+	0.0947366i	−0.632464	+	0.774590i	$0.717956\pi$
$938$	−2.78569	−	2.61593i	−0.0909559	−	0.0854133i
$939$	−0.335356	+	1.75800i	−0.0109439	+	0.0573701i
$940$	−28.0057	+	17.8132i	−0.913445	+	0.581002i
$941$	32.2837	−	17.7481i	1.05242	−	0.578573i	0.140983	−	0.990012i	$-0.454974\pi$
$941$	32.2837	−	17.7481i	1.05242	−	0.578573i	0.911437	+	0.411439i	$0.134974\pi$
$942$	0.529841	−	0.209779i	0.0172632	−	0.00683497i
$943$	−12.5378			−0.408286
$944$	31.4335	−	12.4454i	1.02307	−	0.405063i
$945$	14.9571	+	7.01960i	0.486555	+	0.228348i
$946$	−1.43400	+	1.73341i	−0.0466234	+	0.0563580i
$947$	−39.7710	+	10.2114i	−1.29238	+	0.331828i	−0.831446	−	0.555605i	$-0.812487\pi$
$947$	−39.7710	+	10.2114i	−1.29238	+	0.331828i	−0.460937	+	0.887433i	$0.652487\pi$
$948$	−3.14644	−	1.72977i	−0.102192	−	0.0561804i
$949$	8.34326	−	6.06173i	0.270834	−	0.196772i
$950$	−0.0772870	+	0.239532i	−0.00250752	+	0.00777143i
$951$	−3.98483	−	2.89515i	−0.129217	−	0.0938817i
$952$	−1.58008	−	3.35784i	−0.0512106	−	0.108828i
$953$	−38.3778	+	46.3908i	−1.24318	+	1.50274i	−0.450912	+	0.892569i	$0.648901\pi$
$953$	−38.3778	+	46.3908i	−1.24318	+	1.50274i	−0.792266	+	0.610175i	$0.791099\pi$
$954$	−0.0746062	−	0.117561i	−0.00241546	−	0.00380616i
$955$	−8.49667	−	32.9524i	−0.274946	−	1.06631i
$956$	11.4783	+	13.8749i	0.371235	+	0.448746i
$957$	−13.0186	−	9.45860i	−0.420833	−	0.305753i
$958$	−0.887735	+	1.39885i	−0.0286814	+	0.0451947i
$959$	1.89207	+	9.91858i	0.0610982	+	0.320288i
$960$	−0.843723	−	6.62424i	−0.0272310	−	0.213796i
$961$	26.2772	−	3.31959i	0.847653	−	0.107084i
$962$	−0.0247937	−	0.129973i	−0.000799381	−	0.00419050i
$963$	−39.5009	−	4.99013i	−1.27290	−	0.160805i
$964$	38.6430	+	21.2442i	1.24461	+	0.684229i
$965$	−12.2068	+	47.7449i	−0.392949	+	1.53696i
$966$	−0.334211	−	0.313845i	−0.0107530	−	0.0100978i
$967$	−23.1506	−	5.94406i	−0.744473	−	0.191148i	−0.142645	−	0.989774i	$-0.545561\pi$
$967$	−23.1506	−	5.94406i	−0.744473	−	0.191148i	−0.601828	+	0.798626i	$0.705561\pi$
$968$	2.57928	−	1.87395i	0.0829011	−	0.0602312i
$969$	−0.0592801	−	0.942230i	−0.00190435	−	0.0302688i
$970$	−0.326566	−	2.56394i	−0.0104854	−	0.0823231i
$971$	44.1888	+	17.4956i	1.41809	+	0.561460i	0.947174	−	0.320719i	$-0.103925\pi$
$971$	44.1888	+	17.4956i	1.41809	+	0.561460i	0.470913	+	0.882180i	$0.343925\pi$
$972$	−17.8078	−	7.05061i	−0.571186	−	0.226149i
$973$	27.6600	−	3.49427i	0.886737	−	0.112021i
$974$	−0.515700	−	1.58716i	−0.0165241	−	0.0508560i
$975$	1.18499	+	0.466366i	0.0379499	+	0.0149357i
$976$	5.60688	−	17.2562i	0.179472	−	0.552358i
$977$	−3.93155	+	20.6099i	−0.125781	+	0.659369i	0.862418	+	0.506197i	$0.168949\pi$
$977$	−3.93155	+	20.6099i	−0.125781	+	0.659369i	−0.988199	+	0.153172i	$0.951051\pi$
$978$	0.0112517	−	0.178840i	0.000359789	−	0.00571867i
$979$	40.0561	−	10.2847i	1.28020	−	0.328699i
$980$	10.6100	+	14.5721i	0.338925	+	0.465487i
$981$	−22.9074	+	36.0963i	−0.731378	+	1.15247i
$982$	−0.0946357	−	0.291259i	−0.00301995	−	0.00929444i
$983$	−2.70597	−	43.0101i	−0.0863069	−	1.37181i	−0.768131	−	0.640293i	$-0.778813\pi$
$983$	−2.70597	−	43.0101i	−0.0863069	−	1.37181i	0.681824	−	0.731516i	$-0.261187\pi$
$984$	−0.293954	−	0.0371350i	−0.00937091	−	0.00118382i
$985$	−0.0200327	−	19.5799i	−0.000638296	−	0.623867i
$986$	1.08525	+	2.30627i	0.0345613	+	0.0734465i
$987$	3.99871	−	8.49769i	0.127280	−	0.270485i
$988$	0.784239	−	0.431139i	0.0249500	−	0.0137164i
$989$	−22.6435	+	21.2636i	−0.720020	+	0.676144i
$990$	1.52721	−	1.62965i	0.0485378	−	0.0517936i
$991$	8.90296	−	18.9197i	0.282812	−	0.601006i	−0.712064	−	0.702115i	$-0.752239\pi$
$991$	8.90296	−	18.9197i	0.282812	−	0.601006i	0.994875	+	0.101109i	$0.0322392\pi$
$992$	1.21811	+	1.47244i	0.0386751	+	0.0467501i
$993$	−1.20689	+	3.71442i	−0.0382995	+	0.117874i
$994$	1.10659	+	0.284125i	0.0350990	+	0.00901190i
$995$	−8.74114	−	22.0118i	−0.277113	−	0.697820i
$996$	0.559526	−	8.89342i	0.0177293	−	0.281799i
$997$	29.0304	+	45.7446i	0.919402	+	1.44875i	0.893490	+	0.449082i	$0.148249\pi$
$997$	29.0304	+	45.7446i	0.919402	+	1.44875i	0.0259120	+	0.999664i	$0.491751\pi$
$998$	−1.75268	+	1.64587i	−0.0554800	+	0.0520992i
$999$	−5.83041			−0.184466

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	125.2.g.a.11.6	✓	220
5.2	odd	4		625.2.h.b.199.12		440
5.3	odd	4		625.2.h.b.199.11		440
5.4	even	2		625.2.g.a.426.6		220
125.34	even	50		625.2.g.a.201.6		220
125.62	odd	100		625.2.h.b.424.11		440
125.63	odd	100		625.2.h.b.424.12		440
125.91	even	25	inner	125.2.g.a.91.6	yes	220

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
125.2.g.a.11.6	✓	220	1.1	even	1	trivial
125.2.g.a.91.6	yes	220	125.91	even	25	inner
625.2.g.a.201.6		220	125.34	even	50
625.2.g.a.426.6		220	5.4	even	2
625.2.h.b.199.11		440	5.3	odd	4
625.2.h.b.199.12		440	5.2	odd	4
625.2.h.b.424.11		440	125.62	odd	100
625.2.h.b.424.12		440	125.63	odd	100

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:	\( N \)	\(=\)	\( 125 = 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	125.g (of order \(25\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0548468 - 0.0515046i) q^{2} +(-0.203470 - 0.320618i) q^{3} +(-0.125226 + 1.99040i) q^{4} +(-0.553871 + 2.16639i) q^{5} +(-0.0276730 - 0.00710521i) q^{6} +(-1.02685 + 3.16032i) q^{7} +(0.191565 + 0.231562i) q^{8} +(1.21594 - 2.58401i) q^{9} +O(q^{10})\)	\(q+(0.0548468 - 0.0515046i) q^{2} +(-0.203470 - 0.320618i) q^{3} +(-0.125226 + 1.99040i) q^{4} +(-0.553871 + 2.16639i) q^{5} +(-0.0276730 - 0.00710521i) q^{6} +(-1.02685 + 3.16032i) q^{7} +(0.191565 + 0.231562i) q^{8} +(1.21594 - 2.58401i) q^{9} +(0.0812007 + 0.147346i) q^{10} +(3.38861 - 3.18211i) q^{11} +(0.663639 - 0.364839i) q^{12} +(0.285576 - 0.606880i) q^{13} +(0.106452 + 0.226221i) q^{14} +(0.807279 - 0.263214i) q^{15} +(-3.93479 - 0.497080i) q^{16} +(0.233333 + 3.70872i) q^{17} +(-0.0663977 - 0.204351i) q^{18} +(0.358493 - 0.564895i) q^{19} +(-4.24262 - 1.37371i) q^{20} +(1.22219 - 0.313805i) q^{21} +(0.0219608 - 0.349057i) q^{22} +(0.904885 - 4.74358i) q^{23} +(0.0352652 - 0.108535i) q^{24} +(-4.38645 - 2.39980i) q^{25} +(-0.0155941 - 0.0479939i) q^{26} +(-2.20610 + 0.278695i) q^{27} +(-6.16173 - 2.43960i) q^{28} +(8.47614 + 3.35594i) q^{29} +(0.0307199 - 0.0560150i) q^{30} +(-0.133404 - 2.12040i) q^{31} +(-0.727680 + 0.528690i) q^{32} +(-1.70972 - 0.438982i) q^{33} +(0.203814 + 0.191394i) q^{34} +(-6.27773 - 3.97497i) q^{35} +(4.99095 + 2.74380i) q^{36} +(2.60134 + 0.328626i) q^{37} +(-0.00943246 - 0.0494467i) q^{38} +(-0.252683 + 0.0319213i) q^{39} +(-0.607755 + 0.286748i) q^{40} +(-0.486496 - 2.55030i) q^{41} +(0.0508708 - 0.0801595i) q^{42} +(-5.20385 - 3.78082i) q^{43} +(5.90935 + 7.14317i) q^{44} +(4.92448 + 4.06541i) q^{45} +(-0.194686 - 0.306776i) q^{46} +(4.74419 - 5.73474i) q^{47} +(0.641241 + 1.36271i) q^{48} +(-3.27009 - 2.37586i) q^{49} +(-0.364183 + 0.0943011i) q^{50} +(1.14161 - 0.829425i) q^{51} +(1.17217 + 0.644408i) q^{52} +(0.627649 - 0.161153i) q^{53} +(-0.106643 + 0.128910i) q^{54} +(5.01683 + 9.10351i) q^{55} +(-0.928519 + 0.367627i) q^{56} -0.254058 q^{57} +(0.637735 - 0.252497i) q^{58} +(-7.46982 + 4.10657i) q^{59} +(0.422810 + 1.63977i) q^{60} +(-0.857246 + 4.49384i) q^{61} +(-0.116527 - 0.109426i) q^{62} +(6.91771 + 6.49616i) q^{63} +(1.47365 - 7.72516i) q^{64} +(1.15656 + 0.954801i) q^{65} +(-0.116382 + 0.0639818i) q^{66} +(-14.2113 + 5.62666i) q^{67} -7.41107 q^{68} +(-1.70499 + 0.675054i) q^{69} +(-0.549042 + 0.105318i) q^{70} +(2.91281 - 3.52098i) q^{71} +(0.831290 - 0.213439i) q^{72} +(13.4740 + 7.40740i) q^{73} +(0.159601 - 0.115957i) q^{74} +(0.123095 + 1.89466i) q^{75} +(1.07948 + 0.784285i) q^{76} +(6.57691 + 13.9766i) q^{77} +(-0.0122147 + 0.0147651i) q^{78} +(-2.54046 - 4.00312i) q^{79} +(3.25624 - 8.24896i) q^{80} +(-4.92284 - 5.95070i) q^{81} +(-0.158035 - 0.114819i) q^{82} +(6.30486 - 9.93486i) q^{83} +(0.471549 + 2.47195i) q^{84} +(-8.16376 - 1.54866i) q^{85} +(-0.480143 + 0.0606562i) q^{86} +(-0.648668 - 3.40044i) q^{87} +(1.38599 + 0.175092i) q^{88} +(7.79608 + 4.28593i) q^{89} +(0.479479 - 0.0306588i) q^{90} +(1.62469 + 1.52569i) q^{91} +(9.32832 + 2.39510i) q^{92} +(-0.652695 + 0.474211i) q^{93} +(-0.0351617 - 0.558880i) q^{94} +(1.02522 + 1.08951i) q^{95} +(0.317569 + 0.125734i) q^{96} +(-14.2841 - 5.65548i) q^{97} +(-0.301722 + 0.0381163i) q^{98} +(-4.10226 - 12.6254i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 220 q - 20 q^{2} - 20 q^{3} - 20 q^{4} - 15 q^{5} - 20 q^{6} - 15 q^{7} - 5 q^{8} - 20 q^{9}+O(q^{10}) \) 220 * q - 20 * q^2 - 20 * q^3 - 20 * q^4 - 15 * q^5 - 20 * q^6 - 15 * q^7 - 5 * q^8 - 20 * q^9	\( 220 q - 20 q^{2} - 20 q^{3} - 20 q^{4} - 15 q^{5} - 20 q^{6} - 15 q^{7} - 5 q^{8} - 20 q^{9} - 20 q^{10} - 15 q^{11} - 100 q^{12} - 20 q^{13} - 10 q^{14} - 15 q^{17} + 10 q^{18} - 10 q^{19} + 5 q^{20} - 5 q^{21} + 25 q^{22} - 90 q^{23} + 15 q^{24} - 45 q^{25} + 15 q^{26} + 10 q^{27} + 30 q^{28} - 10 q^{29} + 40 q^{30} - 10 q^{31} + 20 q^{32} + 15 q^{33} + 5 q^{34} + 10 q^{35} - 210 q^{36} + 20 q^{37} + 30 q^{38} + 45 q^{40} - 5 q^{41} + 70 q^{42} + 25 q^{43} + 15 q^{44} - 100 q^{45} - 100 q^{47} + 105 q^{48} - 20 q^{49} + 60 q^{50} + 25 q^{51} + 85 q^{52} + 20 q^{53} + 60 q^{54} + 15 q^{55} - 105 q^{56} + 40 q^{57} - 225 q^{58} + 5 q^{59} - 35 q^{60} + 65 q^{62} + 85 q^{63} + 45 q^{64} + 45 q^{65} + 55 q^{66} - 105 q^{67} + 80 q^{68} + 40 q^{69} + 95 q^{70} - 85 q^{71} + 160 q^{72} + 40 q^{73} + 35 q^{74} + 55 q^{75} + 35 q^{76} + 75 q^{77} - 10 q^{78} - 330 q^{80} + 55 q^{81} - 95 q^{82} + 50 q^{83} + 115 q^{84} + 85 q^{85} + 40 q^{86} + 95 q^{87} + 165 q^{88} + 55 q^{89} + 170 q^{90} - 105 q^{91} + 155 q^{92} - 185 q^{93} + 60 q^{94} + 30 q^{95} + 135 q^{96} + 65 q^{97} + 135 q^{98} + 45 q^{99}+O(q^{100}) \) 220 * q - 20 * q^2 - 20 * q^3 - 20 * q^4 - 15 * q^5 - 20 * q^6 - 15 * q^7 - 5 * q^8 - 20 * q^9 - 20 * q^10 - 15 * q^11 - 100 * q^12 - 20 * q^13 - 10 * q^14 - 15 * q^17 + 10 * q^18 - 10 * q^19 + 5 * q^20 - 5 * q^21 + 25 * q^22 - 90 * q^23 + 15 * q^24 - 45 * q^25 + 15 * q^26 + 10 * q^27 + 30 * q^28 - 10 * q^29 + 40 * q^30 - 10 * q^31 + 20 * q^32 + 15 * q^33 + 5 * q^34 + 10 * q^35 - 210 * q^36 + 20 * q^37 + 30 * q^38 + 45 * q^40 - 5 * q^41 + 70 * q^42 + 25 * q^43 + 15 * q^44 - 100 * q^45 - 100 * q^47 + 105 * q^48 - 20 * q^49 + 60 * q^50 + 25 * q^51 + 85 * q^52 + 20 * q^53 + 60 * q^54 + 15 * q^55 - 105 * q^56 + 40 * q^57 - 225 * q^58 + 5 * q^59 - 35 * q^60 + 65 * q^62 + 85 * q^63 + 45 * q^64 + 45 * q^65 + 55 * q^66 - 105 * q^67 + 80 * q^68 + 40 * q^69 + 95 * q^70 - 85 * q^71 + 160 * q^72 + 40 * q^73 + 35 * q^74 + 55 * q^75 + 35 * q^76 + 75 * q^77 - 10 * q^78 - 330 * q^80 + 55 * q^81 - 95 * q^82 + 50 * q^83 + 115 * q^84 + 85 * q^85 + 40 * q^86 + 95 * q^87 + 165 * q^88 + 55 * q^89 + 170 * q^90 - 105 * q^91 + 155 * q^92 - 185 * q^93 + 60 * q^94 + 30 * q^95 + 135 * q^96 + 65 * q^97 + 135 * q^98 + 45 * q^99

Introduction

L-functions

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