LMFDB - Embedded newform 162.2.g.a.151.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,2,Mod(7,162)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(162, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([16]))

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

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

chi := DirichletCharacter("162.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	162.g (of order $27$, degree $18$, 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:	$1.29357651274$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$4$ over $\Q(\zeta_{27})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			151.3
Character	$\chi$	$=$	162.151
Dual form			162.2.g.a.103.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.686242 - 0.727374i) q^{2} +(0.916297 + 1.46983i) q^{3} +(-0.0581448 - 0.998308i) q^{4} +(1.08261 + 0.126540i) q^{5} +(1.69792 + 0.342169i) q^{6} +(-0.387485 + 0.194602i) q^{7} +(-0.766044 - 0.642788i) q^{8} +(-1.32080 + 2.69360i) q^{9} +O(q^{10})$	\(q+(0.686242 - 0.727374i) q^{2} +(0.916297 + 1.46983i) q^{3} +(-0.0581448 - 0.998308i) q^{4} +(1.08261 + 0.126540i) q^{5} +(1.69792 + 0.342169i) q^{6} +(-0.387485 + 0.194602i) q^{7} +(-0.766044 - 0.642788i) q^{8} +(-1.32080 + 2.69360i) q^{9} +(0.834977 - 0.700629i) q^{10} +(0.774129 - 1.79463i) q^{11} +(1.41407 - 1.00021i) q^{12} +(-1.45186 + 0.344097i) q^{13} +(-0.124360 + 0.415391i) q^{14} +(0.806005 + 1.70721i) q^{15} +(-0.993238 + 0.116093i) q^{16} +(-0.868482 - 4.92541i) q^{17} +(1.05287 + 2.80918i) q^{18} +(-0.565662 + 3.20803i) q^{19} +(0.0633770 - 1.08814i) q^{20} +(-0.641084 - 0.391224i) q^{21} +(-0.774129 - 1.79463i) q^{22} +(2.12973 + 1.06959i) q^{23} +(0.242865 - 1.71494i) q^{24} +(-3.70918 - 0.879092i) q^{25} +(-0.746040 + 1.29218i) q^{26} +(-5.16938 + 0.526784i) q^{27} +(0.216803 + 0.375514i) q^{28} +(-2.44573 - 8.16932i) q^{29} +(1.79489 + 0.585290i) q^{30} +(-5.16760 + 3.39878i) q^{31} +(-0.597159 + 0.802123i) q^{32} +(3.34714 - 0.506578i) q^{33} +(-4.17860 - 2.74831i) q^{34} +(-0.444122 + 0.161647i) q^{35} +(2.76584 + 1.16195i) q^{36} +(0.642752 + 0.233943i) q^{37} +(1.94525 + 2.61293i) q^{38} +(-1.83610 - 1.81869i) q^{39} +(-0.747993 - 0.792826i) q^{40} +(2.80658 + 2.97480i) q^{41} +(-0.724504 + 0.197833i) q^{42} +(3.51649 + 4.72346i) q^{43} +(-1.83661 - 0.668471i) q^{44} +(-1.77077 + 2.74900i) q^{45} +(2.23950 - 0.815111i) q^{46} +(2.10644 + 1.38543i) q^{47} +(-1.08074 - 1.35352i) q^{48} +(-4.06784 + 5.46405i) q^{49} +(-3.18482 + 2.09469i) q^{50} +(6.44373 - 5.78966i) q^{51} +(0.427933 + 1.42940i) q^{52} +(-1.14093 - 1.97615i) q^{53} +(-3.16428 + 4.12157i) q^{54} +(1.06518 - 1.84494i) q^{55} +(0.421919 + 0.0999966i) q^{56} +(-5.23357 + 2.10808i) q^{57} +(-7.62051 - 3.82716i) q^{58} +(4.55125 + 10.5510i) q^{59} +(1.65745 - 0.903906i) q^{60} +(0.817619 - 14.0380i) q^{61} +(-1.07404 + 6.09116i) q^{62} +(-0.0123902 - 1.30076i) q^{63} +(0.173648 + 0.984808i) q^{64} +(-1.61535 + 0.188807i) q^{65} +(1.92847 - 2.78225i) q^{66} +(-0.448672 + 1.49867i) q^{67} +(-4.86658 + 1.15340i) q^{68} +(0.379348 + 4.11040i) q^{69} +(-0.187197 + 0.433972i) q^{70} +(10.2702 - 8.61771i) q^{71} +(2.74321 - 1.21442i) q^{72} +(11.6826 + 9.80288i) q^{73} +(0.611247 - 0.306980i) q^{74} +(-2.10659 - 6.25738i) q^{75} +(3.23549 + 0.378174i) q^{76} +(0.0492763 + 0.846041i) q^{77} +(-2.58288 + 0.0874673i) q^{78} +(4.78508 - 5.07189i) q^{79} -1.08998 q^{80} +(-5.51097 - 7.11542i) q^{81} +4.08979 q^{82} +(6.22295 - 6.59594i) q^{83} +(-0.353286 + 0.662747i) q^{84} +(-0.316973 - 5.44222i) q^{85} +(5.84888 + 0.683636i) q^{86} +(9.76649 - 11.0803i) q^{87} +(-1.74659 + 0.877168i) q^{88} +(-8.27201 - 6.94104i) q^{89} +(0.784376 + 3.17449i) q^{90} +(0.495612 - 0.415868i) q^{91} +(0.943948 - 2.18832i) q^{92} +(-9.73069 - 4.48120i) q^{93} +(2.45325 - 0.581432i) q^{94} +(-1.01834 + 3.40148i) q^{95} +(-1.72616 - 0.142739i) q^{96} +(14.2297 - 1.66321i) q^{97} +(1.18289 + 6.70850i) q^{98} +(3.81155 + 4.45555i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 9 q^{6}+O(q^{10}) $ 72 * q + 9 * q^6	$ 72 q + 9 q^{6} + 18 q^{13} - 9 q^{20} - 81 q^{23} + 18 q^{25} - 27 q^{26} - 27 q^{27} + 18 q^{28} - 27 q^{29} - 63 q^{30} - 54 q^{31} + 9 q^{33} - 27 q^{35} - 9 q^{36} + 9 q^{38} - 9 q^{41} + 9 q^{42} + 36 q^{43} - 117 q^{45} - 18 q^{46} - 27 q^{47} + 9 q^{48} - 27 q^{51} - 36 q^{52} - 27 q^{53} + 54 q^{55} + 27 q^{57} + 9 q^{58} - 18 q^{59} + 9 q^{63} + 9 q^{65} + 36 q^{66} - 135 q^{67} - 18 q^{68} + 108 q^{69} + 18 q^{70} + 72 q^{71} + 54 q^{72} + 36 q^{73} + 99 q^{74} - 36 q^{75} - 9 q^{76} + 144 q^{77} + 90 q^{78} - 9 q^{79} + 18 q^{80} - 72 q^{82} + 99 q^{83} + 18 q^{84} + 9 q^{85} + 72 q^{86} + 207 q^{87} - 9 q^{88} + 126 q^{89} - 18 q^{90} + 63 q^{91} + 36 q^{92} + 81 q^{93} + 18 q^{94} + 45 q^{95} - 171 q^{97} + 36 q^{98} + 99 q^{99}+O(q^{100}) $ 72 * q + 9 * q^6 + 18 * q^13 - 9 * q^20 - 81 * q^23 + 18 * q^25 - 27 * q^26 - 27 * q^27 + 18 * q^28 - 27 * q^29 - 63 * q^30 - 54 * q^31 + 9 * q^33 - 27 * q^35 - 9 * q^36 + 9 * q^38 - 9 * q^41 + 9 * q^42 + 36 * q^43 - 117 * q^45 - 18 * q^46 - 27 * q^47 + 9 * q^48 - 27 * q^51 - 36 * q^52 - 27 * q^53 + 54 * q^55 + 27 * q^57 + 9 * q^58 - 18 * q^59 + 9 * q^63 + 9 * q^65 + 36 * q^66 - 135 * q^67 - 18 * q^68 + 108 * q^69 + 18 * q^70 + 72 * q^71 + 54 * q^72 + 36 * q^73 + 99 * q^74 - 36 * q^75 - 9 * q^76 + 144 * q^77 + 90 * q^78 - 9 * q^79 + 18 * q^80 - 72 * q^82 + 99 * q^83 + 18 * q^84 + 9 * q^85 + 72 * q^86 + 207 * q^87 - 9 * q^88 + 126 * q^89 - 18 * q^90 + 63 * q^91 + 36 * q^92 + 81 * q^93 + 18 * q^94 + 45 * q^95 - 171 * q^97 + 36 * q^98 + 99 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{20}{27}\right)$

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 $

$2$	0.686242	−	0.727374i	0.485246	−	0.514331i
$2$	0.686242	−	0.727374i	0.485246	−	0.514331i
$3$	0.916297	+	1.46983i	0.529024	+	0.848607i
$3$	0.916297	+	1.46983i	0.529024	+	0.848607i
$4$	−0.0581448	−	0.998308i	−0.0290724	−	0.499154i
$5$	1.08261	+	0.126540i	0.484160	+	0.0565902i	0.354672	−	0.934991i	$-0.384593\pi$
$5$	1.08261	+	0.126540i	0.484160	+	0.0565902i	0.129488	+	0.991581i	$0.458667\pi$
$6$	1.69792	+	0.342169i	0.693172	+	0.139690i
$7$	−0.387485	+	0.194602i	−0.146456	+	0.0735528i	−0.520518	−	0.853851i	$-0.674261\pi$
$7$	−0.387485	+	0.194602i	−0.146456	+	0.0735528i	0.374062	+	0.927404i	$0.377965\pi$
$8$	−0.766044	−	0.642788i	−0.270838	−	0.227260i
$9$	−1.32080	+	2.69360i	−0.440267	+	0.897867i
$10$	0.834977	−	0.700629i	0.264043	−	0.221558i
$11$	0.774129	−	1.79463i	0.233409	−	0.541102i	−0.760748	−	0.649047i	$-0.775168\pi$
$11$	0.774129	−	1.79463i	0.233409	−	0.541102i	0.994157	+	0.107945i	$0.0344270\pi$
$12$	1.41407	−	1.00021i	0.408206	−	0.288736i
$13$	−1.45186	+	0.344097i	−0.402674	+	0.0954354i	−0.426962	−	0.904270i	$-0.640416\pi$
$13$	−1.45186	+	0.344097i	−0.402674	+	0.0954354i	0.0242884	+	0.999705i	$0.492268\pi$
$14$	−0.124360	+	0.415391i	−0.0332366	+	0.111018i
$15$	0.806005	+	1.70721i	0.208110	+	0.440799i
$16$	−0.993238	+	0.116093i	−0.248310	+	0.0290232i
$17$	−0.868482	−	4.92541i	−0.210638	−	1.19459i	−0.888318	−	0.459230i	$-0.848125\pi$
$17$	−0.868482	−	4.92541i	−0.210638	−	1.19459i	0.677680	−	0.735357i	$-0.262986\pi$
$18$	1.05287	+	2.80918i	0.248163	+	0.662129i
$19$	−0.565662	+	3.20803i	−0.129772	+	0.735972i	0.848587	+	0.529056i	$0.177454\pi$
$19$	−0.565662	+	3.20803i	−0.129772	+	0.735972i	−0.978359	+	0.206916i	$0.933657\pi$
$20$	0.0633770	−	1.08814i	0.0141715	−	0.243316i
$21$	−0.641084	−	0.391224i	−0.139896	−	0.0853720i
$22$	−0.774129	−	1.79463i	−0.165045	−	0.382617i
$23$	2.12973	+	1.06959i	0.444079	+	0.223025i	0.656764	−	0.754096i	$-0.271925\pi$
$23$	2.12973	+	1.06959i	0.444079	+	0.223025i	−0.212685	+	0.977121i	$0.568221\pi$
$24$	0.242865	−	1.71494i	0.0495745	−	0.350061i
$25$	−3.70918	−	0.879092i	−0.741836	−	0.175818i
$26$	−0.746040	+	1.29218i	−0.146310	+	0.253417i
$27$	−5.16938	+	0.526784i	−0.994848	+	0.101380i
$28$	0.216803	+	0.375514i	0.0409720	+	0.0709656i
$29$	−2.44573	−	8.16932i	−0.454161	−	1.51700i	−0.812246	−	0.583315i	$-0.801755\pi$
$29$	−2.44573	−	8.16932i	−0.454161	−	1.51700i	0.358084	−	0.933689i	$-0.383430\pi$
$30$	1.79489	+	0.585290i	0.327701	+	0.106859i
$31$	−5.16760	+	3.39878i	−0.928128	+	0.610439i	−0.921012	−	0.389535i	$-0.872636\pi$
$31$	−5.16760	+	3.39878i	−0.928128	+	0.610439i	−0.00711652	+	0.999975i	$0.502265\pi$
$32$	−0.597159	+	0.802123i	−0.105564	+	0.141797i
$33$	3.34714	−	0.506578i	0.582662	−	0.0881839i
$34$	−4.17860	−	2.74831i	−0.716624	−	0.471331i
$35$	−0.444122	+	0.161647i	−0.0750703	+	0.0273234i
$36$	2.76584	+	1.16195i	0.460974	+	0.193658i
$37$	0.642752	+	0.233943i	0.105668	+	0.0384599i	0.394313	−	0.918976i	$-0.370983\pi$
$37$	0.642752	+	0.233943i	0.105668	+	0.0384599i	−0.288645	+	0.957436i	$0.593205\pi$
$38$	1.94525	+	2.61293i	0.315562	+	0.423873i
$39$	−1.83610	−	1.81869i	−0.294011	−	0.291224i
$40$	−0.747993	−	0.792826i	−0.118268	−	0.125357i
$41$	2.80658	+	2.97480i	0.438315	+	0.464586i	0.908441	−	0.418013i	$-0.137273\pi$
$41$	2.80658	+	2.97480i	0.438315	+	0.464586i	−0.470127	+	0.882599i	$0.655792\pi$
$42$	−0.724504	+	0.197833i	−0.111793	+	0.0305263i
$43$	3.51649	+	4.72346i	0.536259	+	0.720321i	0.984849	−	0.173417i	$-0.0554808\pi$
$43$	3.51649	+	4.72346i	0.536259	+	0.720321i	−0.448589	+	0.893738i	$0.648073\pi$
$44$	−1.83661	−	0.668471i	−0.276879	−	0.100776i
$45$	−1.77077	+	2.74900i	−0.263970	+	0.409797i
$46$	2.23950	−	0.815111i	0.330196	−	0.120182i
$47$	2.10644	+	1.38543i	0.307256	+	0.202086i	0.693767	−	0.720199i	$-0.255950\pi$
$47$	2.10644	+	1.38543i	0.307256	+	0.202086i	−0.386511	+	0.922285i	$0.626320\pi$
$48$	−1.08074	−	1.35352i	−0.155991	−	0.195363i
$49$	−4.06784	+	5.46405i	−0.581119	+	0.780579i
$50$	−3.18482	+	2.09469i	−0.450402	+	0.296234i
$51$	6.44373	−	5.78966i	0.902302	−	0.810714i
$52$	0.427933	+	1.42940i	0.0593436	+	0.198222i
$53$	−1.14093	−	1.97615i	−0.156719	−	0.271446i	0.776964	−	0.629544i	$-0.216758\pi$
$53$	−1.14093	−	1.97615i	−0.156719	−	0.271446i	−0.933684	+	0.358099i	$0.883425\pi$
$54$	−3.16428	+	4.12157i	−0.430603	+	0.560875i
$55$	1.06518	−	1.84494i	0.143628	−	0.248771i
$56$	0.421919	+	0.0999966i	0.0563813	+	0.0133626i
$57$	−5.23357	+	2.10808i	−0.693203	+	0.279222i
$58$	−7.62051	−	3.82716i	−1.00062	−	0.502531i
$59$	4.55125	+	10.5510i	0.592522	+	1.37362i	0.905697	+	0.423925i	$0.139348\pi$
$59$	4.55125	+	10.5510i	0.592522	+	1.37362i	−0.313175	+	0.949695i	$0.601393\pi$
$60$	1.65745	−	0.903906i	0.213976	−	0.116694i
$61$	0.817619	−	14.0380i	0.104685	−	1.79738i	−0.382372	−	0.924008i	$-0.624893\pi$
$61$	0.817619	−	14.0380i	0.104685	−	1.79738i	0.487058	−	0.873370i	$-0.338070\pi$
$62$	−1.07404	+	6.09116i	−0.136403	+	0.773578i
$63$	−0.0123902	−	1.30076i	−0.00156102	−	0.163880i
$64$	0.173648	+	0.984808i	0.0217060	+	0.123101i
$65$	−1.61535	+	0.188807i	−0.200359	+	0.0234186i
$66$	1.92847	−	2.78225i	0.237379	−	0.342472i
$67$	−0.448672	+	1.49867i	−0.0548140	+	0.183091i	−0.981012	−	0.193945i	$-0.937872\pi$
$67$	−0.448672	+	1.49867i	−0.0548140	+	0.183091i	0.926198	+	0.377036i	$0.123057\pi$
$68$	−4.86658	+	1.15340i	−0.590159	+	0.139870i
$69$	0.379348	+	4.11040i	0.0456681	+	0.494834i
$70$	−0.187197	+	0.433972i	−0.0223743	+	0.0518695i
$71$	10.2702	−	8.61771i	1.21885	−	1.02273i	0.219963	−	0.975508i	$-0.429406\pi$
$71$	10.2702	−	8.61771i	1.21885	−	1.02273i	0.998884	−	0.0472262i	$-0.0150382\pi$
$72$	2.74321	−	1.21442i	0.323290	−	0.143121i
$73$	11.6826	+	9.80288i	1.36735	+	1.14734i	0.973636	+	0.228106i	$0.0732531\pi$
$73$	11.6826	+	9.80288i	1.36735	+	1.14734i	0.393710	+	0.919235i	$0.371191\pi$
$74$	0.611247	−	0.306980i	0.0710560	−	0.0356857i
$75$	−2.10659	−	6.25738i	−0.243249	−	0.722540i
$76$	3.23549	+	0.378174i	0.371136	+	0.0433796i
$77$	0.0492763	+	0.846041i	0.00561555	+	0.0964153i
$78$	−2.58288	+	0.0874673i	−0.292453	+	0.00990372i
$79$	4.78508	−	5.07189i	0.538364	−	0.570632i	−0.399897	−	0.916560i	$-0.630954\pi$
$79$	4.78508	−	5.07189i	0.538364	−	0.570632i	0.938261	+	0.345928i	$0.112436\pi$
$80$	−1.08998			−0.121864
$81$	−5.51097	−	7.11542i	−0.612330	−	0.790602i
$82$	4.08979			0.451642
$83$	6.22295	−	6.59594i	0.683057	−	0.723998i	−0.289367	−	0.957218i	$-0.593445\pi$
$83$	6.22295	−	6.59594i	0.683057	−	0.723998i	0.972424	+	0.233220i	$0.0749262\pi$
$84$	−0.353286	+	0.662747i	−0.0385467	+	0.0723116i
$85$	−0.316973	−	5.44222i	−0.0343806	−	0.590291i
$86$	5.84888	+	0.683636i	0.630701	+	0.0737184i
$87$	9.76649	−	11.0803i	1.04708	−	1.18794i
$88$	−1.74659	+	0.877168i	−0.186187	+	0.0935064i
$89$	−8.27201	−	6.94104i	−0.876831	−	0.735749i	0.0886936	−	0.996059i	$-0.471731\pi$
$89$	−8.27201	−	6.94104i	−0.876831	−	0.735749i	−0.965525	+	0.260310i	$0.916175\pi$
$90$	0.784376	+	3.17449i	0.0826805	+	0.334620i
$91$	0.495612	−	0.415868i	0.0519543	−	0.0435948i
$92$	0.943948	−	2.18832i	0.0984133	−	0.228148i
$93$	−9.73069	−	4.48120i	−1.00903	−	0.464679i
$94$	2.45325	−	0.581432i	0.253034	−	0.0599701i
$95$	−1.01834	+	3.40148i	−0.104479	+	0.348984i
$96$	−1.72616	−	0.142739i	−0.176175	−	0.0145682i
$97$	14.2297	−	1.66321i	1.44481	−	0.168874i	0.642729	−	0.766093i	$-0.277802\pi$
$97$	14.2297	−	1.66321i	1.44481	−	0.168874i	0.802078	+	0.597220i	$0.203728\pi$
$98$	1.18289	+	6.70850i	0.119490	+	0.677660i
$99$	3.81155	+	4.45555i	0.383076	+	0.447799i
$100$	−0.661935	+	3.75402i	−0.0661935	+	0.375402i
$101$	−0.846671	+	14.5368i	−0.0842469	+	1.44646i	0.646030	+	0.763312i	$0.276428\pi$
$101$	−0.846671	+	14.5368i	−0.0842469	+	1.44646i	−0.730277	+	0.683152i	$0.760609\pi$
$102$	0.210710	−	8.66010i	0.0208634	−	0.857478i
$103$	4.42196	+	10.2512i	0.435708	+	1.01009i	0.984700	+	0.174258i	$0.0557525\pi$
$103$	4.42196	+	10.2512i	0.435708	+	1.01009i	−0.548992	+	0.835828i	$0.684988\pi$
$104$	1.33337	+	0.669644i	0.130748	+	0.0656640i
$105$	−0.644541	−	0.504667i	−0.0629008	−	0.0492505i
$106$	−2.22036	−	0.526235i	−0.215660	−	0.0511124i
$107$	−8.82995	+	15.2939i	−0.853624	+	1.47852i	0.0242921	+	0.999705i	$0.492267\pi$
$107$	−8.82995	+	15.2939i	−0.853624	+	1.47852i	−0.877916	+	0.478815i	$0.841066\pi$
$108$	0.826465	+	5.13001i	0.0795267	+	0.493635i
$109$	−4.57987	−	7.93257i	−0.438672	−	0.759803i	0.558915	−	0.829225i	$-0.311218\pi$
$109$	−4.57987	−	7.93257i	−0.438672	−	0.759803i	−0.997587	+	0.0694222i	$0.977884\pi$
$110$	−0.610992	−	2.04085i	−0.0582558	−	0.194588i
$111$	0.245095	+	1.15910i	0.0232634	+	0.110017i
$112$	0.362273	−	0.238271i	0.0342316	−	0.0225145i
$113$	1.73011	−	2.32394i	0.162755	−	0.218618i	−0.713263	−	0.700897i	$-0.752783\pi$
$113$	1.73011	−	2.32394i	0.162755	−	0.218618i	0.876018	+	0.482279i	$0.160191\pi$
$114$	−2.05813	+	5.25341i	−0.192762	+	0.492027i
$115$	2.17033	+	1.42745i	0.202384	+	0.133110i
$116$	−8.01329	+	2.91660i	−0.744015	+	0.270799i
$117$	0.990758	−	4.36521i	0.0915956	−	0.403564i
$118$	10.7978	+	3.93006i	0.994014	+	0.361792i
$119$	1.29502	+	1.73951i	0.118714	+	0.159461i
$120$	0.479937	−	1.82589i	0.0438120	−	0.166680i
$121$	4.92723	+	5.22255i	0.447930	+	0.474778i
$122$	−9.64977	−	10.2282i	−0.873649	−	0.926014i
$123$	−1.80079	+	6.85100i	−0.162372	+	0.617734i
$124$	3.69350	+	4.96123i	0.331686	+	0.445532i
$125$	−9.02563	−	3.28506i	−0.807277	−	0.293825i
$126$	−0.954642	−	0.883624i	−0.0850463	−	0.0787195i
$127$	1.14503	−	0.416758i	0.101605	−	0.0369813i	−0.290717	−	0.956809i	$-0.593894\pi$
$127$	1.14503	−	0.416758i	0.101605	−	0.0369813i	0.392323	+	0.919828i	$0.371672\pi$
$128$	0.835488	+	0.549509i	0.0738474	+	0.0485702i
$129$	−3.72054	+	9.49673i	−0.327575	+	0.836141i
$130$	−0.971185	+	1.30453i	−0.0851786	+	0.114415i
$131$	0.546520	−	0.359452i	0.0477497	−	0.0314055i	−0.525410	−	0.850849i	$-0.676088\pi$
$131$	0.546520	−	0.359452i	0.0477497	−	0.0314055i	0.573159	+	0.819444i	$0.305718\pi$
$132$	−0.700340	−	3.31202i	−0.0609567	−	0.288274i
$133$	−0.405104	−	1.35314i	−0.0351270	−	0.117332i
$134$	0.782194	+	1.35480i	0.0675713	+	0.117037i
$135$	−5.66311	−	0.0838272i	−0.487403	−	0.00721469i
$136$	−2.50070	+	4.33133i	−0.214433	+	0.371409i
$137$	−9.52260	−	2.25690i	−0.813571	−	0.192820i	−0.197289	−	0.980345i	$-0.563214\pi$
$137$	−9.52260	−	2.25690i	−0.813571	−	0.192820i	−0.616282	+	0.787526i	$0.711362\pi$
$138$	3.25012	+	2.54480i	0.276669	+	0.216628i
$139$	−2.92471	−	1.46885i	−0.248071	−	0.124586i	0.320420	−	0.947276i	$-0.396176\pi$
$139$	−2.92471	−	1.46885i	−0.248071	−	0.124586i	−0.568491	+	0.822690i	$0.692472\pi$
$140$	0.187197	+	0.433972i	0.0158210	+	0.0366773i
$141$	−0.106219	+	4.36558i	−0.00894527	+	0.367648i
$142$	0.779535	−	13.3841i	0.0654171	−	1.12317i
$143$	−0.506399	+	2.87193i	−0.0423472	+	0.240163i
$144$	0.999162	−	2.82872i	0.0832635	−	0.235727i
$145$	−1.61405	−	9.15371i	−0.134039	−	0.760174i
$146$	15.1475	−	1.77048i	1.25361	−	0.146526i
$147$	−11.7586	−	0.972336i	−0.969831	−	0.0801969i
$148$	0.196174	−	0.655267i	0.0161254	−	0.0538626i
$149$	−13.4454	+	3.18661i	−1.10149	+	0.261057i	−0.740864	−	0.671655i	$-0.765584\pi$
$149$	−13.4454	+	3.18661i	−1.10149	+	0.261057i	−0.360623	+	0.932712i	$0.617436\pi$
$150$	−5.99708	−	2.76179i	−0.489660	−	0.225499i
$151$	2.74008	−	6.35223i	0.222985	−	0.516937i	−0.769595	−	0.638532i	$-0.779542\pi$
$151$	2.74008	−	6.35223i	0.222985	−	0.516937i	0.992580	+	0.121595i	$0.0388011\pi$
$152$	2.49540	−	2.09389i	0.202404	−	0.169837i
$153$	14.4142	+	4.16614i	1.16532	+	0.336812i
$154$	0.649203	+	0.544746i	0.0523143	+	0.0438969i
$155$	−6.02460	+	3.02567i	−0.483907	+	0.243027i
$156$	−1.70886	+	1.93874i	−0.136818	+	0.155223i
$157$	9.07530	+	1.06075i	0.724288	+	0.0846571i	0.470245	−	0.882536i	$-0.344165\pi$
$157$	9.07530	+	1.06075i	0.724288	+	0.0846571i	0.254043	+	0.967193i	$0.418240\pi$
$158$	−0.405437	−	6.96109i	−0.0322548	−	0.553794i
$159$	1.85918	−	3.48772i	0.147442	−	0.276594i
$160$	−0.747993	+	0.792826i	−0.0591340	+	0.0626784i
$161$	−1.03338			−0.0814420
$162$	−8.95743	−	0.874365i	−0.703762	−	0.0686966i
$163$	−20.6768			−1.61953			−0.809765	−	0.586754i	$-0.800405\pi$
$163$	−20.6768			−1.61953			−0.809765	+	0.586754i	$0.800405\pi$
$164$	2.80658	−	2.97480i	0.219157	−	0.232293i
$165$	3.68776	−	0.124883i	0.287092	−	0.00972216i
$166$	−0.527267	−	9.05282i	−0.0409238	−	0.702635i
$167$	5.99241	+	0.700413i	0.463707	+	0.0541996i	0.344739	−	0.938699i	$-0.387967\pi$
$167$	5.99241	+	0.700413i	0.463707	+	0.0541996i	0.118968	+	0.992898i	$0.462041\pi$
$168$	0.239625	+	0.711775i	0.0184874	+	0.0549147i
$169$	−9.62773	+	4.83523i	−0.740595	+	0.371941i
$170$	−4.17605	−	3.50412i	−0.320288	−	0.268754i
$171$	−7.89401	−	5.76083i	−0.603670	−	0.440542i
$172$	4.51101	−	3.78518i	0.343961	−	0.288618i
$173$	−0.566077	+	1.31231i	−0.0430380	+	0.0997733i	−0.938379	−	0.345608i	$-0.887673\pi$
$173$	−0.566077	+	1.31231i	−0.0430380	+	0.0997733i	0.895341	+	0.445381i	$0.146932\pi$
$174$	−1.35737	−	14.7077i	−0.102902	−	1.11499i
$175$	1.60833	−	0.381180i	0.121578	−	0.0288145i
$176$	−0.560551	+	1.87237i	−0.0422531	+	0.141135i
$177$	−11.3379	+	16.3574i	−0.852205	+	1.22950i
$178$	−10.7253	+	1.25361i	−0.803897	+	0.0939621i
$179$	0.418491	+	2.37338i	0.0312795	+	0.177395i	0.996445	−	0.0842450i	$-0.0268478\pi$
$179$	0.418491	+	2.37338i	0.0312795	+	0.177395i	−0.965166	+	0.261640i	$0.915737\pi$
$180$	2.84731	+	1.60793i	0.212226	+	0.119848i
$181$	−1.46681	+	8.31867i	−0.109027	+	0.618322i	0.880508	+	0.474031i	$0.157201\pi$
$181$	−1.46681	+	8.31867i	−0.109027	+	0.618322i	−0.989535	+	0.144292i	$0.953910\pi$
$182$	0.0376183	−	0.645881i	0.00278845	−	0.0478759i
$183$	21.3826	−	11.6612i	1.58065	−	0.862020i
$184$	−0.943948	−	2.18832i	−0.0695887	−	0.161325i
$185$	0.666250	+	0.334603i	0.0489836	+	0.0246005i
$186$	−9.93711	+	4.00266i	−0.728624	+	0.293489i
$187$	−9.51162	−	2.25429i	−0.695558	−	0.164850i
$188$	1.26061	−	2.18343i	0.0919392	−	0.159243i
$189$	1.90054	−	1.21009i	0.138244	−	0.0880214i
$190$	1.77532	+	3.07495i	0.128795	+	0.223080i
$191$	−0.590982	−	1.97402i	−0.0427620	−	0.142835i	0.933943	−	0.357423i	$-0.116344\pi$
$191$	−0.590982	−	1.97402i	−0.0427620	−	0.142835i	−0.976705	+	0.214588i	$0.931159\pi$
$192$	−1.28839	+	1.15761i	−0.0929813	+	0.0835433i
$193$	6.81456	−	4.48201i	0.490523	−	0.322622i	−0.280037	−	0.959989i	$-0.590347\pi$
$193$	6.81456	−	4.48201i	0.490523	−	0.322622i	0.770560	+	0.637367i	$0.219977\pi$
$194$	8.55524	−	11.4917i	0.614230	−	0.825054i
$195$	−1.75765	−	2.20128i	−0.125868	−	0.157637i
$196$	5.69133	+	3.74325i	0.406524	+	0.267375i
$197$	−0.143804	+	0.0523405i	−0.0102456	+	0.00372910i	−0.347138	−	0.937814i	$-0.612846\pi$
$197$	−0.143804	+	0.0523405i	−0.0102456	+	0.00372910i	0.336892	+	0.941543i	$0.390624\pi$
$198$	5.85650	+	0.285159i	0.416203	+	0.0202653i
$199$	−21.7193	−	7.90517i	−1.53964	−	0.560382i	−0.573680	−	0.819080i	$-0.694485\pi$
$199$	−21.7193	−	7.90517i	−1.53964	−	0.560382i	−0.965958	+	0.258697i	$0.916707\pi$
$200$	2.27633	+	3.05764i	0.160961	+	0.216208i
$201$	−2.61390	+	0.713753i	−0.184370	+	0.0503442i
$202$	9.99265	+	10.5916i	0.703080	+	0.745222i
$203$	2.53745	+	2.68954i	0.178094	+	0.188769i
$204$	−6.15453	−	6.09619i	−0.430903	−	0.426818i
$205$	2.66202	+	3.57571i	0.185923	+	0.249739i
$206$	10.4910	+	3.81842i	0.730944	+	0.266042i
$207$	−5.69400	+	4.32392i	−0.395760	+	0.300533i
$208$	1.40210	−	0.510321i	0.0972179	−	0.0353844i
$209$	5.31933	+	3.49858i	0.367946	+	0.242002i
$210$	−0.809393	+	0.122499i	−0.0558534	+	0.00845322i
$211$	−16.8174	+	22.5897i	−1.15776	+	1.55514i	−0.381926	+	0.924193i	$0.624739\pi$
$211$	−16.8174	+	22.5897i	−1.15776	+	1.55514i	−0.775829	+	0.630943i	$0.782668\pi$
$212$	−1.90647	+	1.25391i	−0.130937	+	0.0861186i
$213$	22.0771	+	7.19905i	1.51270	+	0.493271i
$214$	5.06492	+	16.9180i	0.346231	+	1.15649i
$215$	3.20930	+	5.55867i	0.218872	+	0.379098i
$216$	4.29859	+	2.91927i	0.292482	+	0.198631i
$217$	1.34096	−	2.32260i	0.0910300	−	0.157669i
$218$	−8.91284	−	2.11238i	−0.603654	−	0.143069i
$219$	−3.70383	+	26.1538i	−0.250281	+	1.76731i
$220$	−1.90375	−	0.956100i	−0.128351	−	0.0644603i
$221$	2.95573	+	6.85216i	0.198824	+	0.460926i
$222$	1.01129	+	0.617144i	0.0678734	+	0.0414200i
$223$	0.857579	−	14.7241i	0.0574278	−	0.985996i	−0.839371	−	0.543558i	$-0.817077\pi$
$223$	0.857579	−	14.7241i	0.0574278	−	0.985996i	0.896799	−	0.442438i	$-0.145886\pi$
$224$	0.0752950	−	0.427019i	0.00503086	−	0.0285314i
$225$	7.26701	−	8.82995i	0.484468	−	0.588663i
$226$	−0.503100	−	2.85322i	−0.0334657	−	0.189794i
$227$	4.57311	−	0.534520i	0.303528	−	0.0354774i	0.0370344	−	0.999314i	$-0.488209\pi$
$227$	4.57311	−	0.534520i	0.303528	−	0.0354774i	0.266494	+	0.963837i	$0.414135\pi$
$228$	2.40882	+	5.10214i	0.159528	+	0.337897i
$229$	5.34042	−	17.8382i	0.352905	−	1.17878i	−0.578770	−	0.815491i	$-0.696467\pi$
$229$	5.34042	−	17.8382i	0.352905	−	1.17878i	0.931675	−	0.363294i	$-0.118348\pi$
$230$	2.52766	−	0.599066i	0.166669	−	0.0395013i
$231$	−1.19838	+	0.847652i	−0.0788479	+	0.0557714i
$232$	−3.37760	+	7.83015i	−0.221750	+	0.514074i
$233$	20.0301	−	16.8073i	1.31222	−	1.10108i	0.324325	−	0.945946i	$-0.394863\pi$
$233$	20.0301	−	16.8073i	1.31222	−	1.10108i	0.987893	−	0.155136i	$-0.0495815\pi$
$234$	−2.49524	−	3.71624i	−0.163119	−	0.242938i
$235$	2.10515	+	1.76643i	0.137325	+	0.115229i
$236$	10.2685	−	5.15703i	0.668422	−	0.335694i
$237$	11.8394	+	2.38590i	0.769050	+	0.154981i
$238$	2.15397	+	0.251763i	0.139621	+	0.0163194i
$239$	−1.57460	−	27.0348i	−0.101852	−	1.74874i	−0.532692	−	0.846309i	$-0.678820\pi$
$239$	−1.57460	−	27.0348i	−0.101852	−	1.74874i	0.430840	−	0.902428i	$-0.358217\pi$
$240$	−0.998750	−	1.60209i	−0.0644690	−	0.103415i
$241$	−10.3975	+	11.0208i	−0.669765	+	0.709909i	−0.969768	−	0.244029i	$-0.921531\pi$
$241$	−10.3975	+	11.0208i	−0.669765	+	0.709909i	0.300003	+	0.953938i	$0.403012\pi$
$242$	7.18002			0.461549
$243$	5.40878	−	14.6200i	0.346973	−	0.937875i
$244$	−14.0618			−0.900212
$245$	−5.09532	+	5.40072i	−0.325528	+	0.345039i
$246$	3.74746	+	6.01129i	0.238929	+	0.383266i
$247$	−0.282611	−	4.85225i	−0.0179821	−	0.308741i
$248$	6.14331	+	0.718049i	0.390100	+	0.0455962i
$249$	15.3970	+	3.10284i	0.975744	+	0.196634i
$250$	−8.58323	+	4.31066i	−0.542851	+	0.272630i
$251$	7.67704	+	6.44180i	0.484570	+	0.406603i	0.852076	−	0.523419i	$-0.175344\pi$
$251$	7.67704	+	6.44180i	0.484570	+	0.406603i	−0.367505	+	0.930021i	$0.619788\pi$
$252$	−1.29784	+	0.0880018i	−0.0817562	+	0.00554359i
$253$	3.56821	−	2.99408i	0.224331	−	0.188236i
$254$	0.482630	−	1.11886i	0.0302829	−	0.0702037i
$255$	7.70869	−	5.45258i	0.482737	−	0.341454i
$256$	0.973045	−	0.230616i	0.0608153	−	0.0144135i
$257$	1.21867	−	4.07063i	0.0760182	−	0.253919i	−0.911530	−	0.411233i	$-0.865098\pi$
$257$	1.21867	−	4.07063i	0.0760182	−	0.253919i	0.987549	+	0.157314i	$0.0502835\pi$
$258$	4.35448	+	9.22328i	0.271098	+	0.574216i
$259$	−0.294582	+	0.0344318i	−0.0183045	+	0.00213949i
$260$	0.282412	+	1.60164i	0.0175144	+	0.0993293i
$261$	25.2352	+	4.20222i	1.56202	+	0.260111i
$262$	0.113589	−	0.644195i	0.00701755	−	0.0397985i
$263$	−0.245484	+	4.21481i	−0.0151372	+	0.259896i	0.982246	+	0.187598i	$0.0600703\pi$
$263$	−0.245484	+	4.21481i	−0.0151372	+	0.259896i	−0.997383	+	0.0722979i	$0.976967\pi$
$264$	−2.88968	−	1.76344i	−0.177847	−	0.108532i
$265$	−0.985130	−	2.28379i	−0.0605160	−	0.140292i
$266$	−1.26224	−	0.633920i	−0.0773928	−	0.0388681i
$267$	2.62254	−	18.5185i	0.160497	−	1.13331i
$268$	1.52222	+	0.360773i	0.0929844	+	0.0220377i
$269$	−0.893553	+	1.54768i	−0.0544809	+	0.0943636i	−0.891980	−	0.452076i	$-0.850684\pi$
$269$	−0.893553	+	1.54768i	−0.0544809	+	0.0943636i	0.837499	+	0.546439i	$0.184017\pi$
$270$	−3.94723	+	4.06167i	−0.240221	+	0.247185i
$271$	−10.5130	−	18.2090i	−0.638619	−	1.10612i	−0.985736	−	0.168299i	$-0.946173\pi$
$271$	−10.5130	−	18.2090i	−0.638619	−	1.10612i	0.347117	−	0.937822i	$-0.387161\pi$
$272$	1.43441	+	4.79128i	0.0869742	+	0.290514i
$273$	1.06538	+	0.347407i	0.0644799	+	0.0210260i
$274$	−8.17641	+	5.37771i	−0.493955	+	0.324879i
$275$	−4.44903	+	5.97609i	−0.268287	+	0.360372i
$276$	4.08139	−	0.617704i	0.245671	−	0.0371814i
$277$	19.9728	+	13.1363i	1.20005	+	0.789287i	0.982409	−	0.186742i	$-0.0597927\pi$
$277$	19.9728	+	13.1363i	1.20005	+	0.789287i	0.217643	+	0.976028i	$0.430163\pi$
$278$	−3.07546	+	1.11938i	−0.184454	+	0.0671357i
$279$	−2.32959	−	18.4086i	−0.139469	−	1.10209i
$280$	0.444122	+	0.161647i	0.0265414	+	0.00966027i
$281$	−3.59976	−	4.83531i	−0.214744	−	0.288451i	0.681679	−	0.731652i	$-0.261250\pi$
$281$	−3.59976	−	4.83531i	−0.214744	−	0.288451i	−0.896422	+	0.443201i	$0.853843\pi$
$282$	3.10251	+	3.07310i	0.184752	+	0.183001i
$283$	−1.66727	−	1.76720i	−0.0991090	−	0.105049i	0.675920	−	0.736975i	$-0.263746\pi$
$283$	−1.66727	−	1.76720i	−0.0991090	−	0.105049i	−0.775029	+	0.631925i	$0.782265\pi$
$284$	−9.20029	−	9.75174i	−0.545937	−	0.578659i
$285$	−5.93269	+	1.61998i	−0.351422	+	0.0959595i
$286$	1.74146	+	2.33918i	0.102974	+	0.138319i
$287$	−1.66641	−	0.606525i	−0.0983653	−	0.0358020i
$288$	−1.37187	−	2.66795i	−0.0808383	−	0.157211i
$289$	−7.53061	+	2.74092i	−0.442977	+	0.161230i
$290$	−7.76579	−	5.10764i	−0.456023	−	0.299931i
$291$	15.4833	+	19.3912i	0.907645	+	1.13674i
$292$	9.10701	−	12.2328i	0.532947	−	0.715873i
$293$	24.6594	−	16.2188i	1.44062	−	0.947511i	0.441893	−	0.897068i	$-0.354307\pi$
$293$	24.6594	−	16.2188i	1.44062	−	0.947511i	0.998727	−	0.0504432i	$-0.0160634\pi$
$294$	−8.77647	+	7.88562i	−0.511854	+	0.459899i
$295$	3.59213	+	11.9986i	0.209142	+	0.698583i
$296$	−0.342001	−	0.592363i	−0.0198784	−	0.0344304i
$297$	−3.05639	+	9.68494i	−0.177349	+	0.561977i
$298$	−6.90891	+	11.9666i	−0.400223	+	0.693206i
$299$	−3.46011	−	0.820061i	−0.200103	−	0.0474254i
$300$	−6.12430	+	2.46686i	−0.353587	+	0.142424i
$301$	−2.28178	−	1.14595i	−0.131520	−	0.0660517i
$302$	−2.74008	−	6.35223i	−0.157674	−	0.365530i
$303$	−22.1424	+	12.0755i	−1.27205	+	0.693722i
$304$	0.189408	−	3.25200i	0.0108633	−	0.186515i
$305$	2.66152	−	15.0943i	0.152398	−	0.864295i
$306$	12.9219	−	7.62551i	0.738699	−	0.435921i
$307$	−0.355719	−	2.01738i	−0.0203020	−	0.115138i	0.972973	−	0.230920i	$-0.0741737\pi$
$307$	−0.355719	−	2.01738i	−0.0203020	−	0.115138i	−0.993275	+	0.115782i	$0.963063\pi$
$308$	0.841744	−	0.0983858i	0.0479628	−	0.00560605i
$309$	−11.0158	+	15.8927i	−0.626665	+	0.904104i
$310$	−1.93354	+	6.45847i	−0.109818	+	0.366817i
$311$	−14.8585	+	3.52154i	−0.842551	+	0.199688i	−0.629157	−	0.777278i	$-0.716600\pi$
$311$	−14.8585	+	3.52154i	−0.842551	+	0.199688i	−0.213394	+	0.976966i	$0.568452\pi$
$312$	0.237500	+	2.57342i	0.0134458	+	0.145691i
$313$	6.26007	−	14.5125i	0.353840	−	0.820293i	−0.644604	−	0.764517i	$-0.722978\pi$
$313$	6.26007	−	14.5125i	0.353840	−	0.820293i	0.998443	−	0.0557758i	$-0.0177632\pi$
$314$	6.99941	−	5.87321i	0.395000	−	0.331444i
$315$	0.151184	−	1.40979i	0.00851825	−	0.0794327i
$316$	−5.34154	−	4.48208i	−0.300485	−	0.252137i
$317$	−27.7693	+	13.9463i	−1.55968	+	0.783302i	−0.998999	−	0.0447290i	$-0.985758\pi$
$317$	−27.7693	+	13.9463i	−1.55968	+	0.783302i	−0.560683	+	0.828031i	$0.689461\pi$
$318$	−1.26103	−	3.74574i	−0.0707151	−	0.210050i
$319$	−16.5542	−	1.93491i	−0.926860	−	0.108334i
$320$	0.0633770	+	1.08814i	0.00354288	+	0.0608289i
$321$	−30.5703	+	1.03524i	−1.70627	+	0.0577816i
$322$	−0.709150	+	0.751655i	−0.0395194	+	0.0418881i
$323$	16.2921			0.906517
$324$	−6.78295	+	5.91537i	−0.376831	+	0.328632i
$325$	5.68771			0.315497
$326$	−14.1893	+	15.0397i	−0.785871	+	0.832974i
$327$	7.46301	−	14.0002i	0.412706	−	0.774214i
$328$	−0.237800	−	4.08287i	−0.0131303	−	0.225439i
$329$	−1.08582	−	0.126914i	−0.0598633	−	0.00699702i
$330$	2.43986	−	2.76808i	0.134310	−	0.152378i
$331$	−19.6234	+	9.85523i	−1.07860	+	0.541692i	−0.897158	−	0.441709i	$-0.854372\pi$
$331$	−19.6234	+	9.85523i	−1.07860	+	0.541692i	−0.181440	+	0.983402i	$0.558076\pi$
$332$	−6.94661	−	5.82890i	−0.381245	−	0.319902i
$333$	−1.47909	+	1.42232i	−0.0810539	+	0.0779429i
$334$	4.62171	−	3.87807i	0.252888	−	0.212199i
$335$	−0.675379	+	1.56571i	−0.0368999	+	0.0855436i
$336$	0.682167	+	0.314153i	0.0372153	+	0.0171385i
$337$	19.2093	−	4.55270i	1.04640	−	0.248001i	0.328758	−	0.944414i	$-0.393370\pi$
$337$	19.2093	−	4.55270i	1.04640	−	0.248001i	0.717641	+	0.696413i	$0.245222\pi$
$338$	−3.08993	+	10.3211i	−0.168070	+	0.561393i
$339$	5.00109	+	0.413549i	0.271622	+	0.0224609i
$340$	−5.41458	+	0.632874i	−0.293647	+	0.0343224i
$341$	2.09918	+	11.9050i	0.113677	+	0.644694i
$342$	−9.60748	+	1.78858i	−0.519513	+	0.0967151i
$343$	1.03997	−	5.89798i	0.0561533	−	0.318461i
$344$	0.342397	−	5.87874i	0.0184608	−	0.316960i
$345$	−0.109441	+	4.49798i	−0.00589210	+	0.242163i
$346$	0.566077	+	1.31231i	0.0304325	+	0.0705504i
$347$	−28.3542	−	14.2400i	−1.52213	−	0.764443i	−0.525847	−	0.850579i	$-0.676252\pi$
$347$	−28.3542	−	14.2400i	−1.52213	−	0.764443i	−0.996283	+	0.0861361i	$0.972548\pi$
$348$	−11.6295	−	9.10571i	−0.623404	−	0.488117i
$349$	−31.3103	−	7.42068i	−1.67600	−	0.397220i	−0.720793	−	0.693150i	$-0.756222\pi$
$349$	−31.3103	−	7.42068i	−1.67600	−	0.397220i	−0.955210	+	0.295930i	$0.904370\pi$
$350$	0.826440	−	1.43144i	0.0441751	−	0.0765135i
$351$	7.32395	−	2.54359i	0.390924	−	0.135767i
$352$	0.977239	+	1.69263i	0.0520870	+	0.0902174i
$353$	−4.14279	−	13.8379i	−0.220498	−	0.736516i	−0.994630	−	0.103491i	$-0.966999\pi$
$353$	−4.14279	−	13.8379i	−0.220498	−	0.736516i	0.774132	−	0.633024i	$-0.218187\pi$
$354$	4.11742	+	19.4720i	0.218839	+	1.03492i
$355$	12.2091	−	8.03008i	0.647994	−	0.426192i
$356$	−6.44832	+	8.66160i	−0.341760	+	0.459064i
$357$	−1.37017	+	3.49737i	−0.0725169	+	0.185100i
$358$	2.01352	+	1.32431i	0.106418	+	0.0699922i
$359$	16.5258	−	6.01489i	0.872197	−	0.317454i	0.133140	−	0.991097i	$-0.457494\pi$
$359$	16.5258	−	6.01489i	0.872197	−	0.317454i	0.739056	+	0.673643i	$0.235272\pi$
$360$	3.12351	−	0.967629i	0.164623	−	0.0509985i
$361$	7.88270	+	2.86907i	0.414879	+	0.151004i
$362$	5.04420	+	6.77554i	0.265117	+	0.356114i
$363$	−3.16147	+	12.0276i	−0.165934	+	0.631285i
$364$	−0.443982	−	0.470593i	−0.0232710	−	0.0246658i
$365$	11.4073	+	12.0911i	0.597087	+	0.632875i
$366$	6.19160	−	23.5555i	0.323640	−	1.23127i
$367$	22.8160	+	30.6472i	1.19099	+	1.59977i	0.655362	+	0.755315i	$0.272516\pi$
$367$	22.8160	+	30.6472i	1.19099	+	1.59977i	0.535624	+	0.844457i	$0.320076\pi$
$368$	−2.23950	−	0.815111i	−0.116742	−	0.0424906i
$369$	−11.7199	+	3.63069i	−0.610112	+	0.189006i
$370$	0.700590	−	0.254994i	0.0364219	−	0.0132565i
$371$	0.826659	+	0.543702i	0.0429180	+	0.0282276i
$372$	−3.90783	+	9.97478i	−0.202611	+	0.517168i
$373$	9.01994	−	12.1159i	0.467035	−	0.627337i	−0.504733	−	0.863275i	$-0.668409\pi$
$373$	9.01994	−	12.1159i	0.467035	−	0.627337i	0.971768	+	0.235939i	$0.0758165\pi$
$374$	−8.16698	+	5.37151i	−0.422305	+	0.277754i
$375$	−3.44167	−	16.2762i	−0.177727	−	0.840501i
$376$	−0.723092	−	2.41530i	−0.0372906	−	0.124559i
$377$	6.36190	+	11.0191i	0.327655	+	0.567514i
$378$	0.424042	−	2.21282i	0.0218104	−	0.113815i
$379$	−1.42303	+	2.46475i	−0.0730959	+	0.126606i	−0.900257	−	0.435360i	$-0.856621\pi$
$379$	−1.42303	+	2.46475i	−0.0730959	+	0.126606i	0.827161	+	0.561965i	$0.189955\pi$
$380$	3.45493	+	0.818834i	0.177234	+	0.0420053i
$381$	1.66175	+	1.30113i	0.0851341	+	0.0666589i
$382$	−1.84141	−	0.924789i	−0.0942145	−	0.0473163i
$383$	−1.82133	−	4.22231i	−0.0930654	−	0.215750i	0.865325	−	0.501212i	$-0.167112\pi$
$383$	−1.82133	−	4.22231i	−0.0930654	−	0.215750i	−0.958390	+	0.285462i	$0.907853\pi$
$384$	−0.0421302	+	1.73154i	−0.00214995	+	0.0883622i
$385$	−0.0537104	+	0.922172i	−0.00273734	+	0.0469982i
$386$	1.41634	−	8.03247i	0.0720899	−	0.408842i
$387$	−17.3677	+	3.23326i	−0.882850	+	0.164356i
$388$	−2.48778	−	14.1089i	−0.126298	−	0.716272i
$389$	−15.6834	+	1.83313i	−0.795182	+	0.0929435i	−0.503977	−	0.863717i	$-0.668130\pi$
$389$	−15.6834	+	1.83313i	−0.795182	+	0.0929435i	−0.291205	+	0.956661i	$0.594056\pi$
$390$	−2.80733	−	0.232143i	−0.142155	−	0.0117550i
$391$	3.41853	−	11.4187i	0.172883	−	0.577469i
$392$	6.62837	−	1.57095i	0.334783	−	0.0793451i
$393$	1.02911	+	0.473927i	0.0519116	+	0.0239065i
$394$	−0.0606134	+	0.140518i	−0.00305366	+	0.00707917i
$395$	5.82220	−	4.88540i	0.292947	−	0.245811i
$396$	4.22639	−	4.06417i	0.212384	−	0.204232i
$397$	6.72400	+	5.64210i	0.337468	+	0.283169i	0.795734	−	0.605646i	$-0.207085\pi$
$397$	6.72400	+	5.64210i	0.337468	+	0.283169i	−0.458267	+	0.888815i	$0.651530\pi$
$398$	−20.6547	+	10.3732i	−1.03533	+	0.519960i
$399$	1.61769	−	1.83531i	0.0809859	−	0.0918806i
$400$	3.78616	+	0.442538i	0.189308	+	0.0221269i
$401$	−0.294008	−	5.04791i	−0.0146820	−	0.252081i	−0.997661	−	0.0683609i	$-0.978223\pi$
$401$	−0.294008	−	5.04791i	−0.0146820	−	0.252081i	0.982979	−	0.183720i	$-0.0588140\pi$
$402$	−1.27460	+	2.39109i	−0.0635715	+	0.119257i
$403$	6.33312	−	6.71271i	0.315475	−	0.334384i
$404$	14.5614			0.724458
$405$	−5.06587	−	8.40062i	−0.251725	−	0.417430i
$406$	3.69761			0.183509
$407$	0.917414	−	0.972402i	0.0454745	−	0.0482002i
$408$	−8.65770	+	0.293187i	−0.428620	+	0.0145149i
$409$	−0.0613587	−	1.05349i	−0.00303399	−	0.0520917i	0.996451	−	0.0841709i	$-0.0268242\pi$
$409$	−0.0613587	−	1.05349i	−0.00303399	−	0.0520917i	−0.999485	+	0.0320792i	$0.989787\pi$
$410$	4.42767	+	0.517520i	0.218667	+	0.0255585i
$411$	−5.40827	−	16.0646i	−0.266770	−	0.792408i
$412$	9.97679	−	5.01053i	0.491521	−	0.246851i
$413$	−3.81679	−	3.20266i	−0.187812	−	0.157593i
$414$	−0.762350	+	7.10892i	−0.0374674	+	0.349384i
$415$	7.57170	−	6.35341i	0.371680	−	0.311877i
$416$	0.590982	−	1.37005i	0.0289753	−	0.0671723i
$417$	−0.520951	−	5.64473i	−0.0255111	−	0.276424i
$418$	6.19512	−	1.46827i	0.303013	−	0.0718155i
$419$	2.26072	−	7.55132i	0.110443	−	0.368906i	−0.884843	−	0.465890i	$-0.845734\pi$
$419$	2.26072	−	7.55132i	0.110443	−	0.368906i	0.995286	+	0.0969837i	$0.0309195\pi$
$420$	−0.466337	+	0.672795i	−0.0227549	+	0.0328290i
$421$	−12.7902	+	1.49496i	−0.623355	+	0.0728597i	−0.421906	−	0.906639i	$-0.638639\pi$
$421$	−12.7902	+	1.49496i	−0.623355	+	0.0728597i	−0.201449	+	0.979499i	$0.564565\pi$
$422$	4.89034	+	27.7345i	0.238058	+	1.35009i
$423$	−6.51398	+	3.84404i	−0.316721	+	0.186904i
$424$	−0.396242	+	2.24720i	−0.0192432	+	0.109134i
$425$	−1.10853	+	19.0327i	−0.0537716	+	0.923222i
$426$	20.3866	−	11.1180i	0.987736	−	0.538670i
$427$	2.41501	+	5.59862i	0.116870	+	0.270936i
$428$	15.7815	+	7.92575i	0.762826	+	0.383106i
$429$	−4.68526	+	1.88722i	−0.226207	+	0.0911159i
$430$	6.24558	+	1.48023i	0.301189	+	0.0713830i
$431$	−9.56809	+	16.5724i	−0.460879	+	0.798265i	−0.999005	−	0.0445990i	$-0.985799\pi$
$431$	−9.56809	+	16.5724i	−0.460879	+	0.798265i	0.538126	+	0.842864i	$0.319132\pi$
$432$	5.07327	−	1.12335i	0.244088	−	0.0540472i
$433$	14.0876	+	24.4005i	0.677008	+	1.17261i	0.975878	+	0.218318i	$0.0700569\pi$
$433$	14.0876	+	24.4005i	0.677008	+	1.17261i	−0.298870	+	0.954294i	$0.596610\pi$
$434$	−0.769181	−	2.56924i	−0.0369219	−	0.123328i
$435$	11.9755	−	10.7599i	0.574179	−	0.515897i
$436$	−7.65286	+	5.03336i	−0.366505	+	0.241054i
$437$	−4.63598	+	6.22720i	−0.221769	+	0.297887i
$438$	16.4819	+	20.6419i	0.787534	+	0.986308i
$439$	25.3698	+	16.6860i	1.21083	+	0.796377i	0.984106	−	0.177581i	$-0.0568273\pi$
$439$	25.3698	+	16.6860i	1.21083	+	0.796377i	0.226726	+	0.973958i	$0.427198\pi$
$440$	−2.00188	+	0.728623i	−0.0954357	+	0.0347357i
$441$	−9.34517	−	18.1740i	−0.445008	−	0.865431i
$442$	7.01243	+	2.55232i	0.333547	+	0.121401i
$443$	−2.83061	−	3.80216i	−0.134486	−	0.180646i	0.729778	−	0.683684i	$-0.239623\pi$
$443$	−2.83061	−	3.80216i	−0.134486	−	0.180646i	−0.864265	+	0.503037i	$0.832216\pi$
$444$	1.14288	−	0.312076i	0.0542389	−	0.0148105i
$445$	−8.07709	−	8.56121i	−0.382891	−	0.405840i
$446$	−10.1214	−	10.7280i	−0.479262	−	0.507988i
$447$	−17.0037	−	16.8425i	−0.804248	−	0.796624i
$448$	−0.258932	−	0.347806i	−0.0122334	−	0.0164323i
$449$	−25.2950	−	9.20663i	−1.19375	−	0.434488i	−0.332708	−	0.943030i	$-0.607962\pi$
$449$	−25.2950	−	9.20663i	−1.19375	−	0.434488i	−0.861037	+	0.508542i	$0.830185\pi$
$450$	−1.43574	−	11.3453i	−0.0676816	−	0.534823i
$451$	7.51134	−	2.73390i	0.353695	−	0.128735i
$452$	−2.42061	−	1.59206i	−0.113856	−	0.0748841i
$453$	11.8474	−	1.79307i	0.556641	−	0.0842456i
$454$	2.74946	−	3.69317i	0.129039	−	0.173329i
$455$	0.589181	−	0.387510i	0.0276212	−	0.0181668i
$456$	5.36419	+	1.74919i	0.251201	+	0.0819134i
$457$	8.67248	+	28.9681i	0.405682	+	1.35507i	0.880107	+	0.474775i	$0.157471\pi$
$457$	8.67248	+	28.9681i	0.405682	+	1.35507i	−0.474425	+	0.880296i	$0.657344\pi$
$458$	−9.31025	−	16.1258i	−0.435039	−	0.753510i
$459$	7.08414	+	25.0038i	0.330659	+	1.16708i
$460$	1.29884	−	2.24966i	0.0605587	−	0.104891i
$461$	29.2763	+	6.93861i	1.36353	+	0.323163i	0.846312	−	0.532688i	$-0.178818\pi$
$461$	29.2763	+	6.93861i	1.36353	+	0.323163i	0.517222	+	0.855851i	$0.326966\pi$
$462$	−0.205822	+	1.45337i	−0.00957569	+	0.0676168i
$463$	14.5735	+	7.31906i	0.677286	+	0.340146i	0.753969	−	0.656910i	$-0.228137\pi$
$463$	14.5735	+	7.31906i	0.677286	+	0.340146i	−0.0766834	+	0.997055i	$0.524433\pi$
$464$	3.37760	+	7.83015i	0.156801	+	0.363506i
$465$	−9.96754	−	6.08273i	−0.462233	−	0.282080i
$466$	1.52034	−	26.1032i	0.0704284	−	1.20921i
$467$	−3.92568	+	22.2637i	−0.181659	+	1.03024i	0.748514	+	0.663119i	$0.230768\pi$
$467$	−3.92568	+	22.2637i	−0.181659	+	1.03024i	−0.930173	+	0.367121i	$0.880344\pi$
$468$	−4.41544	−	0.735267i	−0.204104	−	0.0339877i
$469$	−0.117791	−	0.668024i	−0.00543907	−	0.0308465i
$470$	2.72950	−	0.319033i	0.125903	−	0.0147159i
$471$	6.75655	+	14.3111i	0.311325	+	0.659421i
$472$	3.29558	−	11.0080i	0.151691	−	0.506684i
$473$	11.1991	−	2.65424i	0.514935	−	0.122042i
$474$	9.86012	−	6.97434i	0.452890	−	0.320342i
$475$	4.91829	−	11.4019i	0.225667	−	0.523154i
$476$	1.66127	−	1.39397i	0.0761443	−	0.0638926i
$477$	6.82992	−	0.463112i	0.312720	−	0.0212044i
$478$	−20.7450	−	17.4071i	−0.948853	−	0.796182i
$479$	15.6479	−	7.85865i	0.714969	−	0.359071i	−0.0538397	−	0.998550i	$-0.517146\pi$
$479$	15.6479	−	7.85865i	0.714969	−	0.359071i	0.768809	+	0.639479i	$0.220850\pi$
$480$	−1.85070	−	0.372959i	−0.0844727	−	0.0170232i
$481$	−1.01368	−	0.118483i	−0.0462200	−	0.00540235i
$482$	0.880978	+	15.1258i	0.0401274	+	0.688962i
$483$	−0.946885	−	1.51890i	−0.0430848	−	0.0691122i
$484$	4.92723	−	5.22255i	0.223965	−	0.237389i
$485$	15.6157			0.709075
$486$	−6.92249	−	13.9671i	−0.314011	−	0.633559i
$487$	1.65936			0.0751929			0.0375964	−	0.999293i	$-0.488030\pi$
$487$	1.65936			0.0751929			0.0375964	+	0.999293i	$0.488030\pi$
$488$	−9.64977	+	10.2282i	−0.436824	+	0.463007i
$489$	−18.9461	−	30.3914i	−0.856770	−	1.37434i
$490$	0.431723	+	7.41240i	0.0195033	+	0.334858i
$491$	−33.0586	−	3.86400i	−1.49191	−	0.174380i	−0.669305	−	0.742988i	$-0.733408\pi$
$491$	−33.0586	−	3.86400i	−1.49191	−	0.174380i	−0.822608	+	0.568608i	$0.807482\pi$
$492$	6.94412	+	1.39940i	0.313065	+	0.0630897i
$493$	−38.1132	+	19.1411i	−1.71653	+	0.862074i
$494$	−3.72334	−	3.12425i	−0.167521	−	0.140567i
$495$	3.56264	+	5.30596i	0.160129	+	0.238485i
$496$	4.73808	−	3.97572i	0.212746	−	0.178515i
$497$	−2.30252	+	5.33784i	−0.103282	+	0.239435i
$498$	12.8230	−	9.07006i	0.574611	−	0.406439i
$499$	20.8474	−	4.94094i	0.933260	−	0.221187i	0.264262	−	0.964451i	$-0.414872\pi$
$499$	20.8474	−	4.94094i	0.933260	−	0.221187i	0.668998	+	0.743264i	$0.266723\pi$
$500$	−2.75471	+	9.20137i	−0.123194	+	0.411498i
$501$	4.46134	+	9.44961i	0.199318	+	0.422178i
$502$	9.95390	−	1.16344i	0.444264	−	0.0519270i
$503$	−1.28347	−	7.27895i	−0.0572273	−	0.324552i	0.942732	−	0.333551i	$-0.108247\pi$
$503$	−1.28347	−	7.27895i	−0.0572273	−	0.324552i	−0.999960	+	0.00899840i	$0.997136\pi$
$504$	−0.826622	+	1.00441i	−0.0368207	+	0.0447398i
$505$	−2.75610	+	15.6306i	−0.122645	+	0.695553i
$506$	0.270836	−	4.65008i	0.0120401	−	0.206721i
$507$	−15.9288	−	9.72062i	−0.707424	−	0.431708i
$508$	−0.482630	−	1.11886i	−0.0214133	−	0.0496415i
$509$	−0.711178	−	0.357167i	−0.0315224	−	0.0158312i	0.432968	−	0.901409i	$-0.357466\pi$
$509$	−0.711178	−	0.357167i	−0.0315224	−	0.0158312i	−0.464491	+	0.885578i	$0.653763\pi$
$510$	1.32396	−	9.34889i	0.0586260	−	0.413976i
$511$	−6.43450	−	1.52501i	−0.284646	−	0.0674623i
$512$	0.500000	−	0.866025i	0.0220971	−	0.0382733i
$513$	1.23418	−	16.8815i	0.0544906	−	0.745336i
$514$	−2.12457	−	3.67986i	−0.0937106	−	0.162312i
$515$	3.49009	+	11.6577i	0.153792	+	0.513700i
$516$	9.69700	+	3.16206i	0.426886	+	0.139202i
$517$	4.11700	−	2.70779i	0.181065	−	0.119088i
$518$	−0.177110	+	0.237900i	−0.00778177	+	0.0104527i
$519$	−2.44757	+	0.370432i	−0.107436	+	0.0162601i
$520$	1.35879	+	0.893691i	0.0595869	+	0.0391909i
$521$	8.83131	−	3.21433i	0.386907	−	0.140823i	−0.141241	−	0.989975i	$-0.545109\pi$
$521$	8.83131	−	3.21433i	0.386907	−	0.140823i	0.528147	+	0.849153i	$0.322887\pi$
$522$	20.3740	−	15.4717i	0.891747	−	0.677178i
$523$	18.5496	+	6.75149i	0.811116	+	0.295222i	0.714085	−	0.700059i	$-0.246843\pi$
$523$	18.5496	+	6.75149i	0.811116	+	0.295222i	0.0970311	+	0.995281i	$0.469065\pi$
$524$	−0.390621	−	0.524695i	−0.0170644	−	0.0229214i
$525$	2.03397	+	2.01469i	0.0887699	+	0.0879284i
$526$	2.89728	+	3.07093i	0.126327	+	0.133899i
$527$	21.2284	+	22.5007i	0.924722	+	0.980148i
$528$	−3.26570	+	0.891732i	−0.142121	+	0.0388076i
$529$	−10.3429	−	13.8930i	−0.449692	−	0.604042i
$530$	−2.33720	−	0.850673i	−0.101522	−	0.0369509i
$531$	−34.4314	−	1.67650i	−1.49420	−	0.0727539i
$532$	−1.32730	+	0.483097i	−0.0575456	+	0.0209449i
$533$	−5.09839	−	3.35326i	−0.220836	−	0.145246i
$534$	−11.6702	−	14.6157i	−0.505018	−	0.632485i
$535$	−11.4947	+	15.4401i	−0.496960	+	0.667534i
$536$	1.30703	−	0.859645i	0.0564550	−	0.0371310i
$537$	−3.10501	+	2.78983i	−0.133991	+	0.120390i
$538$	0.512548	+	1.71203i	0.0220975	+	0.0738108i
$539$	6.65694	+	11.5302i	0.286735	+	0.496639i
$540$	0.245595	+	5.65840i	0.0105687	+	0.243499i
$541$	10.5145	−	18.2116i	0.452052	−	0.782977i	−0.546461	−	0.837484i	$-0.684025\pi$
$541$	10.5145	−	18.2116i	0.452052	−	0.782977i	0.998513	+	0.0545073i	$0.0173588\pi$
$542$	−20.4592	−	4.84893i	−0.878799	−	0.208279i
$543$	−13.5711	+	5.46642i	−0.582390	+	0.234586i
$544$	4.46941	+	2.24462i	0.191624	+	0.0962373i
$545$	−3.95446	−	9.16746i	−0.169390	−	0.392691i
$546$	0.983805	−	0.536526i	0.0421030	−	0.0229612i
$547$	1.11409	−	19.1282i	0.0476351	−	0.817863i	−0.886893	−	0.461974i	$-0.847141\pi$
$547$	1.11409	−	19.1282i	0.0476351	−	0.817863i	0.934528	−	0.355888i	$-0.115822\pi$
$548$	−1.69939	+	9.63772i	−0.0725943	+	0.411703i
$549$	36.7328	+	20.7437i	1.56772	+	0.885320i
$550$	1.29374	+	7.33715i	0.0551652	+	0.312857i
$551$	27.5908	−	3.22491i	1.17541	−	0.137386i
$552$	2.35152	−	3.39259i	0.100087	−	0.144398i
$553$	−0.867147	+	2.89647i	−0.0368748	+	0.123170i
$554$	23.2612	−	5.51301i	0.988275	−	0.234226i
$555$	0.118672	+	1.28587i	0.00503737	+	0.0545821i
$556$	−1.29630	+	3.00517i	−0.0549756	+	0.127448i
$557$	−24.2520	+	20.3498i	−1.02759	+	0.862250i	−0.990562	−	0.137064i	$-0.956233\pi$
$557$	−24.2520	+	20.3498i	−1.02759	+	0.862250i	−0.0370272	+	0.999314i	$0.511789\pi$
$558$	−14.9886	−	10.9382i	−0.634517	−	0.463053i
$559$	−6.73078	−	5.64779i	−0.284682	−	0.238876i
$560$	0.422353	−	0.212114i	0.0178477	−	0.00896344i
$561$	−5.40203	−	16.0461i	−0.228074	−	0.677465i
$562$	−5.98738	−	0.699825i	−0.252563	−	0.0295203i
$563$	0.941202	+	16.1598i	0.0396670	+	0.681055i	0.958268	+	0.285870i	$0.0922826\pi$
$563$	0.941202	+	16.1598i	0.0396670	+	0.681055i	−0.918601	+	0.395185i	$0.870680\pi$
$564$	4.36437	−	0.147796i	0.183773	−	0.00622334i
$565$	2.16711	−	2.29701i	0.0911712	−	0.0966358i
$566$	−2.42957			−0.102122
$567$	3.52010	+	1.68467i	0.147830	+	0.0707496i
$568$	−13.4068			−0.562536
$569$	12.1396	−	12.8672i	0.508917	−	0.539421i	−0.421063	−	0.907032i	$-0.638343\pi$
$569$	12.1396	−	12.8672i	0.508917	−	0.539421i	0.929980	+	0.367611i	$0.119824\pi$
$570$	−2.89293	+	5.42698i	−0.121171	+	0.227311i
$571$	2.22221	+	38.1539i	0.0929967	+	1.59669i	0.645884	+	0.763436i	$0.276489\pi$
$571$	2.22221	+	38.1539i	0.0929967	+	1.59669i	−0.552887	+	0.833256i	$0.686474\pi$
$572$	2.89652	+	0.338554i	0.121109	+	0.0141557i
$573$	2.35996	−	2.67743i	0.0985886	−	0.111851i
$574$	−1.58473	+	0.795882i	−0.0661454	+	0.0332195i
$575$	−6.95928	−	5.83953i	−0.290222	−	0.243525i
$576$	−2.88203	−	0.832996i	−0.120085	−	0.0347082i
$577$	−15.5573	+	13.0541i	−0.647657	+	0.543449i	−0.906359	−	0.422508i	$-0.861150\pi$
$577$	−15.5573	+	13.0541i	−0.647657	+	0.543449i	0.258702	+	0.965957i	$0.416705\pi$
$578$	−3.17415	+	7.35850i	−0.132027	+	0.306073i
$579$	12.8319	+	5.90940i	0.533277	+	0.245586i
$580$	−9.04437	+	2.14356i	−0.375547	+	0.0890063i
$581$	−1.12771	+	3.76683i	−0.0467855	+	0.156274i
$582$	24.7299	+	2.04496i	1.02509	+	0.0847663i
$583$	−4.42970	+	0.517758i	−0.183460	+	0.0214433i
$584$	−2.64823	−	15.0189i	−0.109585	−	0.621486i
$585$	1.62498	−	4.60048i	0.0671847	−	0.190206i
$586$	5.12523	−	29.0666i	0.211721	−	1.20073i
$587$	1.57085	−	26.9704i	0.0648358	−	1.11319i	−0.796330	−	0.604863i	$-0.793228\pi$
$587$	1.57085	−	26.9704i	0.0648358	−	1.11319i	0.861165	−	0.508325i	$-0.169735\pi$
$588$	−0.286990	+	11.7952i	−0.0118353	+	0.486426i
$589$	−7.98027	−	18.5004i	−0.328821	−	0.762294i
$590$	11.1925	+	5.62109i	0.460788	+	0.231417i
$591$	−0.208699	−	0.163408i	−0.00858473	−	0.00672172i
$592$	−0.665565	−	0.157742i	−0.0273545	−	0.00648315i
$593$	2.83040	−	4.90240i	0.116231	−	0.201317i	−0.802040	−	0.597270i	$-0.796252\pi$
$593$	2.83040	−	4.90240i	0.116231	−	0.201317i	0.918271	+	0.395952i	$0.129585\pi$
$594$	4.94715	+	8.86934i	0.202984	+	0.363914i
$595$	1.18189	+	2.04709i	0.0484528	+	0.0839227i
$596$	3.96300	+	13.2373i	0.162331	+	0.542222i
$597$	−8.28204	−	39.1671i	−0.338961	−	1.60300i
$598$	−2.97096	+	1.95403i	−0.121492	+	0.0799064i
$599$	−3.35440	+	4.50574i	−0.137057	+	0.184100i	−0.865352	−	0.501164i	$-0.832905\pi$
$599$	−3.35440	+	4.50574i	−0.137057	+	0.184100i	0.728295	+	0.685263i	$0.240313\pi$
$600$	−2.40842	+	6.14752i	−0.0983233	+	0.250971i
$601$	28.0761	+	18.4659i	1.14525	+	0.753241i	0.972770	−	0.231773i	$-0.0744527\pi$
$601$	28.0761	+	18.4659i	1.14525	+	0.753241i	0.172477	+	0.985014i	$0.444823\pi$
$602$	−2.39939	+	0.873307i	−0.0977919	+	0.0355933i
$603$	−3.44421	−	3.18798i	−0.140259	−	0.129825i
$604$	−6.50080	−	2.36610i	−0.264514	−	0.0962752i
$605$	4.67343	+	6.27750i	0.190002	+	0.255217i
$606$	−6.41161	+	24.3925i	−0.260454	+	0.990879i
$607$	−17.4166	−	18.4605i	−0.706917	−	0.749288i	0.270011	−	0.962857i	$-0.412973\pi$
$607$	−17.4166	−	18.4605i	−0.706917	−	0.749288i	−0.976928	+	0.213569i	$0.931491\pi$
$608$	−2.23544	−	2.36943i	−0.0906592	−	0.0960931i
$609$	−1.62811	+	6.19405i	−0.0659744	+	0.250995i
$610$	−9.15272	−	12.2942i	−0.370583	−	0.497779i
$611$	−3.53498	−	1.28663i	−0.143010	−	0.0520514i
$612$	3.32098	−	14.6320i	0.134243	−	0.591465i
$613$	−10.5328	+	3.83363i	−0.425416	+	0.154839i	−0.545851	−	0.837882i	$-0.683793\pi$
$613$	−10.5328	+	3.83363i	−0.425416	+	0.154839i	0.120434	+	0.992721i	$0.461571\pi$
$614$	−1.71150	−	1.12567i	−0.0690706	−	0.0454284i
$615$	−2.81649	+	7.18913i	−0.113572	+	0.289894i
$616$	0.506077	−	0.679779i	0.0203904	−	0.0273891i
$617$	28.2507	−	18.5807i	1.13733	−	0.748033i	0.166083	−	0.986112i	$-0.446888\pi$
$617$	28.2507	−	18.5807i	1.13733	−	0.748033i	0.971246	+	0.238079i	$0.0765177\pi$
$618$	4.00046	+	18.9188i	0.160922	+	0.761026i
$619$	−1.27718	−	4.26606i	−0.0513340	−	0.171468i	0.928478	−	0.371386i	$-0.121117\pi$
$619$	−1.27718	−	4.26606i	−0.0513340	−	0.171468i	−0.979813	+	0.199919i	$0.935932\pi$
$620$	3.37085	+	5.83848i	0.135377	+	0.234479i
$621$	−11.5728	−	4.40721i	−0.464401	−	0.176855i
$622$	−7.63508	+	13.2243i	−0.306139	+	0.530248i
$623$	4.55602	+	1.07980i	0.182533	+	0.0432612i
$624$	2.03482	+	1.59324i	0.0814580	+	0.0637805i
$625$	7.67675	+	3.85541i	0.307070	+	0.154216i
$626$	−6.26007	−	14.5125i	−0.250203	−	0.580035i
$627$	−0.268232	+	11.0243i	−0.0107122	+	0.440266i
$628$	0.531274	−	9.12163i	0.0212002	−	0.363993i
$629$	0.594044	−	3.36899i	0.0236861	−	0.134330i
$630$	−0.921696	−	1.07742i	−0.0367213	−	0.0429256i
$631$	3.93074	+	22.2923i	0.156480	+	0.887444i	0.957420	+	0.288699i	$0.0932226\pi$
$631$	3.93074	+	22.2923i	0.156480	+	0.887444i	−0.800940	+	0.598745i	$0.795666\pi$
$632$	−6.92574	+	0.809502i	−0.275491	+	0.0322003i
$633$	−48.6126	−	4.01986i	−1.93218	−	0.159775i
$634$	−8.91232	+	29.7692i	−0.353953	+	1.18229i
$635$	1.29237	−	0.306296i	0.0512860	−	0.0121550i
$636$	−3.58992	−	1.65324i	−0.142350	−	0.0655552i
$637$	4.02576	−	9.33277i	0.159507	−	0.369778i
$638$	−12.7676	+	10.7133i	−0.505475	+	0.424144i
$639$	9.64780	+	39.0461i	0.381661	+	1.54464i
$640$	0.834977	+	0.700629i	0.0330054	+	0.0276948i
$641$	22.6258	−	11.3631i	0.893666	−	0.448816i	0.0581666	−	0.998307i	$-0.481475\pi$
$641$	22.6258	−	11.3631i	0.893666	−	0.448816i	0.835500	+	0.549491i	$0.185178\pi$
$642$	−20.2256	+	22.9465i	−0.798242	+	0.905625i
$643$	−21.0737	−	2.46316i	−0.831065	−	0.0971375i	−0.310087	−	0.950708i	$-0.600358\pi$
$643$	−21.0737	−	2.46316i	−0.831065	−	0.0971375i	−0.520977	+	0.853571i	$0.674432\pi$
$644$	0.0600859	+	1.03163i	0.00236771	+	0.0406521i
$645$	−5.22963	+	9.81051i	−0.205916	+	0.386288i
$646$	11.1803	−	11.8504i	0.439884	−	0.466250i
$647$	−35.7419			−1.40516			−0.702579	−	0.711605i	$-0.747968\pi$
$647$	−35.7419			−1.40516			−0.702579	+	0.711605i	$0.747968\pi$
$648$	−0.352058	+	8.99311i	−0.0138301	+	0.353283i
$649$	22.4584			0.881569
$650$	3.90314	−	4.13709i	0.153094	−	0.162270i
$651$	4.64255	−	0.157217i	0.181956	−	0.00616180i
$652$	1.20225	+	20.6418i	0.0470837	+	0.808395i
$653$	−16.5324	−	1.93236i	−0.646963	−	0.0756192i	−0.213718	−	0.976895i	$-0.568557\pi$
$653$	−16.5324	−	1.93236i	−0.646963	−	0.0756192i	−0.433245	+	0.901276i	$0.642632\pi$
$654$	−5.06196	−	15.0359i	−0.197938	−	0.587952i
$655$	0.637156	−	0.319992i	0.0248957	−	0.0125031i
$656$	−3.13296	−	2.62887i	−0.122322	−	0.102640i
$657$	−41.8355	+	18.5206i	−1.63216	+	0.722559i
$658$	−0.837451	+	0.702705i	−0.0326472	+	0.0273943i
$659$	13.7202	−	31.8070i	0.534463	−	1.23903i	−0.410503	−	0.911859i	$-0.634647\pi$
$659$	13.7202	−	31.8070i	0.534463	−	1.23903i	0.944967	−	0.327166i	$-0.106094\pi$
$660$	−0.339097	−	3.67426i	−0.0131993	−	0.143020i
$661$	−35.9802	+	8.52747i	−1.39947	+	0.331680i	−0.859986	−	0.510317i	$-0.829528\pi$
$661$	−35.9802	+	8.52747i	−1.39947	+	0.331680i	−0.539482	+	0.841997i	$0.681380\pi$
$662$	−6.29794	+	21.0366i	−0.244777	+	0.817611i
$663$	−7.36318	+	10.6230i	−0.285962	+	0.412565i
$664$	−9.00684	+	1.05275i	−0.349533	+	0.0408546i
$665$	−0.267346	−	1.51619i	−0.0103672	−	0.0587954i
$666$	0.0195452	+	2.05191i	0.000757360	+	0.0795100i
$667$	3.52907	−	20.0144i	0.136646	−	0.774959i
$668$	0.350800	−	6.02300i	0.0135729	−	0.233037i
$669$	22.4277	−	12.2311i	0.867104	−	0.472882i
$670$	0.675379	+	1.56571i	0.0260922	+	0.0604885i
$671$	−24.5601	−	12.3345i	−0.948131	−	0.476169i
$672$	0.696638	−	0.280605i	0.0268734	−	0.0108246i
$673$	−34.0661	−	8.07381i	−1.31315	−	0.311222i	−0.486373	−	0.873751i	$-0.661680\pi$
$673$	−34.0661	−	8.07381i	−1.31315	−	0.311222i	−0.826778	+	0.562529i	$0.809829\pi$
$674$	9.87074	−	17.0966i	0.380207	−	0.658537i
$675$	19.6373	+	2.59043i	0.755839	+	0.0997055i
$676$	5.38685	+	9.33030i	0.207187	+	0.358858i
$677$	−0.144469	−	0.482558i	−0.00555238	−	0.0185462i	0.955168	−	0.296063i	$-0.0956738\pi$
$677$	−0.144469	−	0.482558i	−0.00555238	−	0.0185462i	−0.960721	+	0.277517i	$0.910489\pi$
$678$	3.73276	−	3.35387i	0.143356	−	0.128805i
$679$	−5.19013	+	3.41360i	−0.199179	+	0.131002i
$680$	−3.25537	+	4.37273i	−0.124838	+	0.167686i
$681$	4.97598	+	6.23192i	0.190680	+	0.238808i
$682$	10.1000	+	6.64285i	0.386747	+	0.254368i
$683$	−0.148497	+	0.0540486i	−0.00568209	+	0.00206811i	−0.344860	−	0.938654i	$-0.612073\pi$
$683$	−0.148497	+	0.0540486i	−0.00568209	+	0.00206811i	0.339178	+	0.940722i	$0.389851\pi$
$684$	−5.29209	+	8.21562i	−0.202348	+	0.314132i
$685$	−10.0237	−	3.64834i	−0.382987	−	0.139396i
$686$	−3.57636	−	4.80389i	−0.136546	−	0.183413i
$687$	31.1126	−	8.49561i	1.18702	−	0.324128i
$688$	−4.04107	−	4.28328i	−0.154064	−	0.163299i
$689$	2.33646	+	2.47651i	0.0890122	+	0.0943474i
$690$	3.19661	+	3.16631i	0.121693	+	0.120539i
$691$	−7.45991	−	10.0204i	−0.283788	−	0.381194i	0.637256	−	0.770653i	$-0.280070\pi$
$691$	−7.45991	−	10.0204i	−0.283788	−	0.381194i	−0.921044	+	0.389459i	$0.872662\pi$
$692$	1.34301	+	0.488815i	0.0510535	+	0.0185819i
$693$	−2.34398	−	0.984721i	−0.0890405	−	0.0374065i
$694$	−29.8156	+	10.8520i	−1.13178	+	0.411936i
$695$	−2.98047	−	1.96029i	−0.113056	−	0.0743579i
$696$	−14.6039	+	2.21025i	−0.553558	+	0.0837791i
$697$	12.2147	−	16.4071i	0.462663	−	0.621464i
$698$	−26.8841	+	17.6819i	−1.01758	+	0.669270i
$699$	43.0574	+	14.0404i	1.62858	+	0.531058i
$700$	−0.474051	−	1.58344i	−0.0179175	−	0.0598485i
$701$	−14.9767	−	25.9404i	−0.565663	−	0.979757i	−0.996988	−	0.0775602i	$-0.975287\pi$
$701$	−14.9767	−	25.9404i	−0.565663	−	0.979757i	0.431325	−	0.902197i	$-0.358046\pi$
$702$	3.17586	−	7.07276i	0.119865	−	0.266944i
$703$	−1.11407	+	1.92963i	−0.0420181	+	0.0727774i
$704$	1.90179	+	0.450734i	0.0716766	+	0.0169877i
$705$	−0.667412	+	4.71280i	−0.0251362	+	0.177494i
$706$	−12.9083	−	6.48277i	−0.485809	−	0.243982i
$707$	−2.50082	−	5.79755i	−0.0940530	−	0.218039i
$708$	16.9889	+	10.3676i	0.638484	+	0.389637i
$709$	0.714825	−	12.2731i	0.0268458	−	0.460925i	−0.957920	−	0.287037i	$-0.907330\pi$
$709$	0.714825	−	12.2731i	0.0268458	−	0.460925i	0.984765	−	0.173888i	$-0.0556332\pi$
$710$	2.53755	−	14.3912i	0.0952327	−	0.540091i
$711$	7.34151	+	19.5881i	0.275328	+	0.734610i
$712$	1.87511	+	10.6343i	0.0702728	+	0.398537i
$713$	−14.6409	+	1.71127i	−0.548305	+	0.0640877i
$714$	1.60363	+	3.39666i	0.0600143	+	0.127117i
$715$	−0.911648	+	3.04512i	−0.0340937	+	0.113881i
$716$	2.34503	−	0.555783i	0.0876380	−	0.0207706i
$717$	38.2938	−	27.0863i	1.43011	−	1.01156i
$718$	6.96560	−	16.1481i	0.259954	−	0.602641i
$719$	−15.2414	+	12.7891i	−0.568410	+	0.476953i	−0.881118	−	0.472897i	$-0.843208\pi$
$719$	−15.2414	+	12.7891i	−0.568410	+	0.476953i	0.312708	+	0.949849i	$0.398764\pi$
$720$	1.43965	−	2.93598i	0.0536527	−	0.109418i
$721$	−3.70836	−	3.11168i	−0.138106	−	0.115885i
$722$	7.49632	−	3.76480i	0.278984	−	0.140111i
$723$	−25.7259	−	5.18435i	−0.956756	−	0.192808i
$724$	8.38989	+	0.980637i	0.311808	+	0.0364451i
$725$	1.89009	+	32.4515i	0.0701960	+	1.20522i
$726$	6.57902	+	10.5534i	0.244170	+	0.391674i
$727$	32.6375	−	34.5937i	1.21046	−	1.28301i	0.262382	−	0.964964i	$-0.415492\pi$
$727$	32.6375	−	34.5937i	1.21046	−	1.28301i	0.948075	−	0.318046i	$-0.103027\pi$
$728$	−0.646976			−0.0239785
$729$	26.4450	−	5.44629i	0.979444	−	0.201714i
$730$	16.6229			0.615241
$731$	20.2110	−	21.4224i	0.747530	−	0.792335i
$732$	−12.8847	−	20.6684i	−0.476234	−	0.763926i
$733$	−1.13692	−	19.5201i	−0.0419930	−	0.720993i	−0.951943	−	0.306275i	$-0.900917\pi$
$733$	−1.13692	−	19.5201i	−0.0419930	−	0.720993i	0.909950	−	0.414718i	$-0.136120\pi$
$734$	37.9493	+	4.43563i	1.40073	+	0.163722i
$735$	−12.6070	−	2.54059i	−0.465015	−	0.0937110i
$736$	−2.12973	+	1.06959i	−0.0785028	+	0.0394256i
$737$	2.34223	+	1.96536i	0.0862771	+	0.0723951i
$738$	−5.40180	+	11.0163i	−0.198843	+	0.405514i
$739$	−13.3279	+	11.1834i	−0.490274	+	0.411389i	−0.854125	−	0.520068i	$-0.825906\pi$
$739$	−13.3279	+	11.1834i	−0.490274	+	0.411389i	0.363850	+	0.931457i	$0.381462\pi$
$740$	0.295298	−	0.684578i	0.0108554	−	0.0251656i
$741$	6.87302	−	4.86149i	0.252487	−	0.178591i
$742$	0.962762	−	0.228179i	0.0353441	−	0.00837671i
$743$	15.4165	−	51.4948i	0.565578	−	1.88916i	0.123068	−	0.992398i	$-0.460727\pi$
$743$	15.4165	−	51.4948i	0.565578	−	1.88916i	0.442510	−	0.896763i	$-0.354088\pi$
$744$	4.57368	+	9.68756i	0.167679	+	0.355163i
$745$	−14.9594	+	1.74850i	−0.548069	+	0.0640601i
$746$	−2.62292	−	14.8753i	−0.0960318	−	0.544623i
$747$	9.54755	+	25.4741i	0.349327	+	0.932047i
$748$	−1.69743	+	9.62660i	−0.0620642	+	0.351983i
$749$	0.445241	−	7.64450i	0.0162688	−	0.279324i
$750$	−14.2007	−	8.66605i	−0.518537	−	0.316439i
$751$	12.2102	+	28.3065i	0.445558	+	1.03292i	0.981983	+	0.188971i	$0.0605153\pi$
$751$	12.2102	+	28.3065i	0.445558	+	1.03292i	−0.536425	+	0.843948i	$0.680225\pi$
$752$	−2.25304	−	1.13152i	−0.0821598	−	0.0412622i
$753$	−2.43391	+	17.1865i	−0.0886965	+	0.626312i
$754$	12.3808	+	2.93431i	0.450883	+	0.106861i
$755$	3.77026	−	6.53029i	0.137214	−	0.237661i
$756$	−1.31855	−	1.82697i	−0.0479553	−	0.0664462i
$757$	8.09241	+	14.0165i	0.294124	+	0.509437i	0.974781	−	0.223165i	$-0.0716389\pi$
$757$	8.09241	+	14.0165i	0.294124	+	0.509437i	−0.680657	+	0.732602i	$0.738306\pi$
$758$	0.816257	+	2.72649i	0.0296478	+	0.0990305i
$759$	7.67033	+	2.50119i	0.278415	+	0.0907875i
$760$	2.96652	−	1.95111i	0.107607	−	0.0707742i
$761$	15.7228	−	21.1194i	0.569952	−	0.765578i	−0.419917	−	0.907562i	$-0.637941\pi$
$761$	15.7228	−	21.1194i	0.569952	−	0.765578i	0.989869	+	0.141984i	$0.0453483\pi$
$762$	2.08677	−	0.315826i	0.0755957	−	0.0114412i
$763$	3.31833	+	2.18250i	0.120132	+	0.0790118i
$764$	−1.93632	+	0.704762i	−0.0700535	+	0.0254974i
$765$	15.0778	+	6.33429i	0.545140	+	0.229017i
$766$	−4.32107	−	1.57274i	−0.156126	−	0.0568254i
$767$	−10.2383	−	13.7525i	−0.369685	−	0.496573i
$768$	1.23056	+	1.21890i	0.0444041	+	0.0439832i
$769$	−4.12204	−	4.36911i	−0.148645	−	0.157554i	0.648773	−	0.760982i	$-0.275283\pi$
$769$	−4.12204	−	4.36911i	−0.148645	−	0.157554i	−0.797418	+	0.603428i	$0.793801\pi$
$770$	0.633905	+	0.671900i	0.0228444	+	0.0242136i
$771$	7.09979	−	1.93867i	0.255693	−	0.0698195i
$772$	−4.87066	−	6.54243i	−0.175299	−	0.235467i
$773$	−2.84339	−	1.03491i	−0.102270	−	0.0372231i	0.290379	−	0.956912i	$-0.406219\pi$
$773$	−2.84339	−	1.03491i	−0.102270	−	0.0372231i	−0.392648	+	0.919689i	$0.628441\pi$
$774$	−9.56665	+	14.8516i	−0.343866	+	0.533830i
$775$	22.1554	−	8.06391i	0.795846	−	0.289664i
$776$	−11.9697	−	7.87258i	−0.429686	−	0.282609i
$777$	−0.320534	−	0.401437i	−0.0114991	−	0.0144015i
$778$	−9.42926	+	12.6657i	−0.338055	+	0.454087i
$779$	−11.1308	+	7.32086i	−0.398803	+	0.262297i
$780$	−2.09536	+	1.88267i	−0.0750259	+	0.0674104i
$781$	−7.51518	−	25.1024i	−0.268914	−	0.898236i
$782$	−5.95972	−	10.3225i	−0.213119	−	0.369133i
$783$	16.9464	+	40.9419i	0.605615	+	1.46315i
$784$	3.40599	−	5.89935i	0.121643	−	0.210691i
$785$	9.69083	+	2.29677i	0.345881	+	0.0819752i
$786$	1.05094	−	0.423317i	0.0374857	−	0.0150992i
$787$	15.0950	+	7.58098i	0.538078	+	0.270233i	0.697016	−	0.717056i	$-0.254511\pi$
$787$	15.0950	+	7.58098i	0.538078	+	0.270233i	−0.158938	+	0.987289i	$0.550807\pi$
$788$	0.0606134	+	0.140518i	0.00215926	+	0.00500573i
$789$	−6.41998	+	3.50119i	−0.228558	+	0.124646i
$790$	0.441920	−	7.58748i	0.0157228	−	0.269950i
$791$	−0.218148	+	1.23718i	−0.00775643	+	0.0439889i
$792$	−0.0558487	−	5.86317i	−0.00198450	−	0.208339i
$793$	3.64336	+	20.6625i	0.129379	+	0.733747i
$794$	8.71820	−	1.01901i	0.309398	−	0.0361634i
$795$	2.45411	−	3.54060i	0.0870383	−	0.125572i
$796$	−6.62893	+	22.1422i	−0.234956	+	0.784808i
$797$	−6.13793	+	1.45472i	−0.217417	+	0.0515287i	−0.337881	−	0.941189i	$-0.609710\pi$
$797$	−6.13793	+	1.45472i	−0.217417	+	0.0515287i	0.120464	+	0.992718i	$0.461562\pi$
$798$	−0.224830	−	2.43613i	−0.00795890	−	0.0862382i
$799$	4.99439	−	11.5783i	0.176689	−	0.409611i
$800$	2.92011	−	2.45026i	0.103241	−	0.0866299i
$801$	29.6221	−	13.1138i	1.04664	−	0.463352i
$802$	−3.87348	−	3.25024i	−0.136777	−	0.114770i
$803$	26.6364	−	13.3773i	0.939979	−	0.472075i
$804$	0.864530	+	2.56798i	0.0304896	+	0.0905657i
$805$	−1.11876	−	0.130764i	−0.0394310	−	0.00460882i
$806$	−0.536601	−	9.21309i	−0.0189010	−	0.324517i
$807$	−3.09358	+	0.104762i	−0.108899	+	0.00368780i
$808$	9.99265	−	10.5916i	0.351540	−	0.372611i
$809$	5.11611			0.179873			0.0899364	−	0.995948i	$-0.471334\pi$
$809$	5.11611			0.179873			0.0899364	+	0.995948i	$0.471334\pi$
$810$	−9.58680	−	2.08007i	−0.336846	−	0.0730862i
$811$	34.5108			1.21184			0.605919	−	0.795526i	$-0.292806\pi$
$811$	34.5108			1.21184			0.605919	+	0.795526i	$0.292806\pi$
$812$	2.53745	−	2.68954i	0.0890472	−	0.0943845i
$813$	17.1312	−	32.1372i	0.600817	−	1.12710i
$814$	−0.0777319	−	1.33461i	−0.00272450	−	0.0467779i
$815$	−22.3850	−	2.61643i	−0.784112	−	0.0916495i
$816$	−5.72802	+	6.49858i	−0.200521	+	0.227496i
$817$	−17.1421	+	8.60910i	−0.599727	+	0.301194i
$818$	−0.808387	−	0.678317i	−0.0282646	−	0.0237168i
$819$	0.465577	+	1.88426i	0.0162686	+	0.0658414i
$820$	3.41488	−	2.86542i	0.119253	−	0.100065i
$821$	−4.70289	+	10.9025i	−0.164132	+	0.380501i	−0.980356	−	0.197234i	$-0.936804\pi$
$821$	−4.70289	+	10.9025i	−0.164132	+	0.380501i	0.816224	+	0.577735i	$0.196063\pi$
$822$	−15.3963	−	7.09036i	−0.537009	−	0.247305i
$823$	−43.1132	+	10.2180i	−1.50283	+	0.356178i	−0.897936	−	0.440127i	$-0.854934\pi$
$823$	−43.1132	+	10.2180i	−1.50283	+	0.356178i	−0.604896	+	0.796304i	$0.706785\pi$
$824$	3.20196	−	10.6953i	0.111546	−	0.372588i
$825$	−12.8605	−	1.06345i	−0.447744	−	0.0370247i
$826$	−4.94877	+	0.578428i	−0.172190	+	0.0201261i
$827$	3.87933	+	22.0007i	0.134897	+	0.765041i	0.974931	+	0.222507i	$0.0714240\pi$
$827$	3.87933	+	22.0007i	0.134897	+	0.765041i	−0.840034	+	0.542534i	$0.817465\pi$
$828$	4.64768	+	5.43295i	0.161518	+	0.188808i
$829$	−3.12358	+	17.7147i	−0.108487	+	0.615258i	0.881284	+	0.472588i	$0.156680\pi$
$829$	−3.12358	+	17.7147i	−0.108487	+	0.615258i	−0.989770	+	0.142670i	$0.954431\pi$
$830$	0.574713	−	9.86743i	0.0199486	−	0.342504i
$831$	−1.00715	+	41.3935i	−0.0349376	+	1.43592i
$832$	−0.590982	−	1.37005i	−0.0204886	−	0.0474980i
$833$	30.4455	+	15.2903i	1.05487	+	0.529778i
$834$	−4.46333	−	3.49473i	−0.154552	−	0.121012i
$835$	6.39885	+	1.51655i	0.221441	+	0.0524825i
$836$	3.18337	−	5.51376i	0.110099	−	0.190697i
$837$	24.9229	−	20.2918i	0.861460	−	0.701388i
$838$	−3.94123	−	6.82642i	−0.136148	−	0.235815i
$839$	14.4828	+	48.3760i	0.500002	+	1.67012i	0.719485	+	0.694508i	$0.244378\pi$
$839$	14.4828	+	48.3760i	0.500002	+	1.67012i	−0.219483	+	0.975616i	$0.570437\pi$
$840$	0.169354	+	0.800901i	0.00584325	+	0.0276337i
$841$	−36.5270	+	24.0242i	−1.25955	+	0.828421i
$842$	−7.68976	+	10.3291i	−0.265007	+	0.355966i
$843$	3.80864	−	9.72161i	0.131177	−	0.334830i
$844$	23.5293	+	15.4754i	0.809911	+	0.532687i
$845$	−11.0350	+	4.01640i	−0.379615	+	0.138168i
$846$	−1.67411	+	7.37604i	−0.0575572	+	0.253593i
$847$	−2.92555	−	1.06481i	−0.100523	−	0.0365874i
$848$	1.36264	+	1.83034i	0.0467931	+	0.0628541i
$849$	1.06978	−	4.06989i	0.0367146	−	0.139678i
$850$	13.0832	+	13.8674i	0.448749	+	0.475646i
$851$	1.11866	+	1.18571i	0.0383473	+	0.0406458i
$852$	5.90320	−	22.4584i	0.202240	−	0.769410i
$853$	−15.4245	−	20.7188i	−0.528126	−	0.709397i	0.455375	−	0.890300i	$-0.349505\pi$
$853$	−15.4245	−	20.7188i	−0.528126	−	0.709397i	−0.983501	+	0.180903i	$0.942098\pi$
$854$	5.72956	+	2.08539i	0.196062	+	0.0713606i
$855$	−7.81720	−	7.23567i	−0.267343	−	0.247455i
$856$	16.5949	−	6.04004i	0.567201	−	0.206444i
$857$	31.8487	+	20.9472i	1.08793	+	0.715544i	0.961050	−	0.276374i	$-0.0891329\pi$
$857$	31.8487	+	20.9472i	1.08793	+	0.715544i	0.126881	+	0.991918i	$0.459503\pi$
$858$	−1.84251	+	4.70303i	−0.0629022	+	0.160559i
$859$	34.7206	−	46.6379i	1.18465	−	1.59126i	0.490487	−	0.871449i	$-0.336819\pi$
$859$	34.7206	−	46.6379i	1.18465	−	1.59126i	0.694165	−	0.719816i	$-0.255774\pi$
$860$	5.36266	−	3.52708i	0.182865	−	0.120272i
$861$	−0.635440	−	3.00510i	−0.0216557	−	0.102414i
$862$	5.48832	+	18.3323i	0.186933	+	0.624399i
$863$	−13.4600	−	23.3133i	−0.458182	−	0.793595i	0.540683	−	0.841227i	$-0.318166\pi$
$863$	−13.4600	−	23.3133i	−0.458182	−	0.793595i	−0.998865	+	0.0476316i	$0.984833\pi$
$864$	2.66439	−	4.46105i	0.0906446	−	0.151768i
$865$	−0.778903	+	1.34910i	−0.0264835	+	0.0458707i
$866$	27.4158	+	6.49766i	0.931626	+	0.220799i
$867$	−10.9290	−	8.55722i	−0.371167	−	0.290618i
$868$	−2.39664	−	1.20364i	−0.0813474	−	0.0408542i
$869$	−5.39791	−	12.5138i	−0.183112	−	0.424501i
$870$	0.391597	−	16.0945i	0.0132764	−	0.545655i
$871$	0.135721	−	2.33024i	0.00459874	−	0.0789572i
$872$	−1.59057	+	9.02059i	−0.0538636	+	0.305476i
$873$	−14.3146	+	40.5259i	−0.484475	+	1.37159i
$874$	1.34810	+	7.64545i	0.0456001	+	0.258611i
$875$	4.13658	−	0.483497i	0.139842	−	0.0163452i
$876$	26.3249	+	2.17685i	0.889436	+	0.0735490i
$877$	−5.75067	+	19.2086i	−0.194186	+	0.648627i	0.804330	+	0.594182i	$0.202524\pi$
$877$	−5.75067	+	19.2086i	−0.194186	+	0.648627i	−0.998517	+	0.0544452i	$0.982661\pi$
$878$	29.5467	−	7.00270i	0.997153	−	0.236330i
$879$	46.4342	+	21.3840i	1.56619	+	0.721264i
$880$	−0.843789	+	1.95612i	−0.0284441	+	0.0659409i
$881$	−17.3885	+	14.5907i	−0.585832	+	0.491572i	−0.886857	−	0.462045i	$-0.847116\pi$
$881$	−17.3885	+	14.5907i	−0.585832	+	0.491572i	0.301024	+	0.953616i	$0.402671\pi$
$882$	−19.6324	−	5.67436i	−0.661056	−	0.191066i
$883$	12.2003	+	10.2372i	0.410572	+	0.344511i	0.824563	−	0.565770i	$-0.191421\pi$
$883$	12.2003	+	10.2372i	0.410572	+	0.344511i	−0.413991	+	0.910281i	$0.635866\pi$
$884$	6.66871	−	3.34915i	0.224293	−	0.112644i
$885$	−14.3444	+	16.2741i	−0.482181	+	0.547047i
$886$	−4.70807	−	0.550295i	−0.158171	−	0.0184875i
$887$	1.48498	+	25.4961i	0.0498608	+	0.856077i	0.926819	+	0.375509i	$0.122532\pi$
$887$	1.48498	+	25.4961i	0.0498608	+	0.856077i	−0.876958	+	0.480567i	$0.840431\pi$
$888$	0.557299	−	1.04546i	0.0187017	−	0.0350835i
$889$	−0.362581	+	0.384313i	−0.0121606	+	0.0128895i
$890$	−11.7700			−0.394532
$891$	−17.0358	+	4.38191i	−0.570720	+	0.146800i
$892$	−14.7490			−0.493834
$893$	−5.63602	+	5.97384i	−0.188602	+	0.199907i
$894$	−23.9195	+	0.810015i	−0.799987	+	0.0270910i
$895$	0.152738	+	2.62241i	0.00510548	+	0.0876576i
$896$	−0.430675	−	0.0503387i	−0.0143878	−	0.00168170i
$897$	−1.96514	−	5.83719i	−0.0656140	−	0.194898i
$898$	−24.0551	+	12.0809i	−0.802731	+	0.403146i
$899$	40.4043	+	33.9032i	1.34756	+	1.13074i
$900$	−9.23755	−	6.74130i	−0.307918	−	0.224710i
$901$	−8.74249	+	7.33582i	−0.291254	+	0.244391i
$902$	3.16602	−	7.33967i	0.105417	−	0.244384i
$903$	−0.406432	−	4.40387i	−0.0135252	−	0.146552i
$904$	−2.81914	+	0.668149i	−0.0937633	+	0.0222223i
$905$	−2.64063	+	8.82031i	−0.0877774	+	0.293197i
$906$	6.82597	−	9.84798i	0.226778	−	0.327177i
$907$	−14.3489	+	1.67715i	−0.476448	+	0.0556888i	−0.350928	−	0.936402i	$-0.614134\pi$
$907$	−14.3489	+	1.67715i	−0.476448	+	0.0556888i	−0.125520	+	0.992091i	$0.540060\pi$
$908$	−0.799519	−	4.53430i	−0.0265330	−	0.150476i
$909$	−38.0380	−	21.4808i	−1.26164	−	0.712473i
$910$	0.122456	−	0.694480i	0.00405936	−	0.0230218i
$911$	0.728369	−	12.5056i	0.0241319	−	0.414329i	−0.964511	−	0.264044i	$-0.914944\pi$
$911$	0.728369	−	12.5056i	0.0241319	−	0.414329i	0.988643	−	0.150286i	$-0.0480193\pi$
$912$	4.95345	−	2.70140i	0.164025	−	0.0894524i
$913$	−7.01993	−	16.2740i	−0.232326	−	0.538591i
$914$	27.0221	+	13.5710i	0.893810	+	0.448888i
$915$	24.6247	−	9.91883i	0.814069	−	0.327906i
$916$	−18.1186	−	4.29418i	−0.598655	−	0.141884i
$917$	−0.141818	+	0.245636i	−0.00468325	+	0.00811163i
$918$	23.0485	+	12.0058i	0.760715	+	0.396252i
$919$	−7.47142	−	12.9409i	−0.246460	−	0.426880i	0.716081	−	0.698017i	$-0.245934\pi$
$919$	−7.47142	−	12.9409i	−0.246460	−	0.426880i	−0.962541	+	0.271136i	$0.912601\pi$
$920$	−0.745023	−	2.48855i	−0.0245627	−	0.0820451i
$921$	2.63927	−	2.37137i	0.0869668	−	0.0781393i
$922$	25.1376	−	16.5332i	0.827862	−	0.544493i
$923$	−11.9455	+	16.0457i	−0.393193	+	0.528149i
$924$	0.915898	+	1.14707i	0.0301308	+	0.0377359i
$925$	−2.17843	−	1.43277i	−0.0716262	−	0.0471093i
$926$	15.3246	−	5.57770i	0.503598	−	0.183295i
$927$	−33.4533	−	1.62887i	−1.09875	−	0.0534993i
$928$	8.01329	+	2.91660i	0.263049	+	0.0957421i
$929$	−9.90409	−	13.3035i	−0.324943	−	0.436474i	0.609393	−	0.792868i	$-0.291413\pi$
$929$	−9.90409	−	13.3035i	−0.324943	−	0.436474i	−0.934335	+	0.356395i	$0.884006\pi$
$930$	−11.2646	+	3.07590i	−0.369379	+	0.100863i
$931$	−15.2278	−	16.1405i	−0.499071	−	0.528984i
$932$	−17.9435	−	19.0190i	−0.587759	−	0.622988i
$933$	−18.7909	−	18.6128i	−0.615187	−	0.609355i
$934$	13.5000	+	18.1337i	0.441735	+	0.593352i
$935$	−10.0122	−	3.64413i	−0.327433	−	0.119176i
$936$	−3.56487	+	2.70710i	−0.116521	+	0.0884844i
$937$	20.0254	−	7.28867i	0.654203	−	0.238110i	0.00647140	−	0.999979i	$-0.497940\pi$
$937$	20.0254	−	7.28867i	0.654203	−	0.238110i	0.647732	+	0.761869i	$0.275718\pi$
$938$	−0.566736	−	0.372748i	−0.0185046	−	0.0121707i
$939$	27.0669	−	4.09649i	0.883296	−	0.133684i
$940$	1.64104	−	2.20430i	0.0535249	−	0.0718964i
$941$	−29.3050	+	19.2742i	−0.955314	+	0.628320i	−0.928505	−	0.371320i	$-0.878905\pi$
$941$	−29.3050	+	19.2742i	−0.955314	+	0.628320i	−0.0268095	+	0.999641i	$0.508535\pi$
$942$	15.0462	+	4.90635i	0.490230	+	0.159858i
$943$	2.79544	+	9.33742i	0.0910320	+	0.304068i
$944$	−5.74537	−	9.95127i	−0.186996	−	0.323886i
$945$	2.21068	−	1.06957i	0.0719135	−	0.0347932i
$946$	5.75467	−	9.96738i	0.187100	−	0.324067i
$947$	−28.4078	−	6.73276i	−0.923128	−	0.218785i	−0.258545	−	0.965999i	$-0.583243\pi$
$947$	−28.4078	−	6.73276i	−0.923128	−	0.218785i	−0.664584	+	0.747214i	$0.731391\pi$
$948$	1.69347	−	11.9581i	0.0550013	−	0.388380i
$949$	−20.3347	−	10.2125i	−0.660091	−	0.331510i
$950$	−4.91829	−	11.4019i	−0.159570	−	0.369926i
$951$	−45.9436	−	28.0373i	−1.48982	−	0.909171i
$952$	0.126095	−	2.16497i	0.00408676	−	0.0701670i
$953$	−3.71205	+	21.0521i	−0.120245	+	0.681943i	0.863774	+	0.503879i	$0.168094\pi$
$953$	−3.71205	+	21.0521i	−0.120245	+	0.681943i	−0.984019	+	0.178064i	$0.943017\pi$
$954$	4.35012	−	5.28571i	0.140840	−	0.171131i
$955$	−0.390015	−	2.21188i	−0.0126206	−	0.0715749i
$956$	−26.8975	+	3.14387i	−0.869928	+	0.101680i
$957$	−12.3246	−	26.1049i	−0.398398	−	0.843851i
$958$	5.02204	−	16.7748i	0.162255	−	0.541969i
$959$	4.12906	−	0.978606i	0.133334	−	0.0316008i
$960$	−1.54131	+	1.09021i	−0.0497456	+	0.0351865i
$961$	2.87388	−	6.66239i	0.0927057	−	0.214916i
$962$	−0.781814	+	0.656020i	−0.0252067	+	0.0211509i
$963$	−29.5331	−	43.9846i	−0.951692	−	1.41738i
$964$	11.6067	+	9.73916i	0.373826	+	0.313677i
$965$	7.94470	−	3.98998i	0.255749	−	0.128442i
$966$	−1.75460	−	0.353591i	−0.0564533	−	0.0113766i
$967$	−29.5361	−	3.45227i	−0.949816	−	0.111018i	−0.372945	−	0.927853i	$-0.621652\pi$
$967$	−29.5361	−	3.45227i	−0.949816	−	0.111018i	−0.576870	+	0.816836i	$0.695726\pi$
$968$	−0.417481	−	7.16787i	−0.0134183	−	0.230384i
$969$	14.9284	+	23.9466i	0.479569	+	0.769276i
$970$	10.7162	−	11.3585i	0.344076	−	0.364699i
$971$	−48.4558			−1.55502			−0.777511	−	0.628869i	$-0.783518\pi$
$971$	−48.4558			−1.55502			−0.777511	+	0.628869i	$0.783518\pi$
$972$	−14.9098	−	4.54955i	−0.478231	−	0.145927i
$973$	1.41912			0.0454950
$974$	1.13872	−	1.20698i	0.0364870	−	0.0386740i
$975$	5.21163	+	8.35996i	0.166906	+	0.267733i
$976$	0.817619	+	14.0380i	0.0261713	+	0.449345i
$977$	11.3934	+	1.33170i	0.364507	+	0.0426047i	0.296375	−	0.955072i	$-0.404222\pi$
$977$	11.3934	+	1.33170i	0.364507	+	0.0426047i	0.0681316	+	0.997676i	$0.478296\pi$
$978$	−35.1074	−	7.07495i	−1.12261	−	0.226232i
$979$	−18.8602	+	9.47196i	−0.602776	+	0.302725i
$980$	5.68785	+	4.77267i	0.181692	+	0.152457i
$981$	27.4163	−	1.85900i	0.875335	−	0.0593532i
$982$	−25.4967	+	21.3943i	−0.813634	+	0.682720i
$983$	−15.1572	+	35.1382i	−0.483438	+	1.12074i	0.485680	+	0.874137i	$0.338572\pi$
$983$	−15.1572	+	35.1382i	−0.483438	+	1.12074i	−0.969118	+	0.246599i	$0.920687\pi$
$984$	5.78323	−	4.09064i	0.184363	−	0.130405i
$985$	−0.162308	+	0.0384676i	−0.00517155	+	0.00122568i
$986$	−12.2321	+	40.8580i	−0.389548	+	1.30118i
$987$	−0.808393	−	1.71227i	−0.0257314	−	0.0545020i
$988$	−4.82761	+	0.564266i	−0.153587	+	0.0179517i
$989$	2.43700	+	13.8209i	0.0774920	+	0.439479i
$990$	6.30425	+	1.04980i	0.200362	+	0.0333647i
$991$	7.88796	−	44.7349i	0.250569	−	1.42105i	−0.556625	−	0.830764i	$-0.687904\pi$
$991$	7.88796	−	44.7349i	0.250569	−	1.42105i	0.807194	−	0.590286i	$-0.200985\pi$
$992$	0.359633	−	6.17466i	0.0114184	−	0.196046i
$993$	−32.4663	−	19.8127i	−1.03029	−	0.628738i
$994$	2.30252	+	5.33784i	0.0730315	+	0.169306i
$995$	−22.5133	−	11.3066i	−0.713719	−	0.358443i
$996$	2.20234	−	15.5513i	0.0697837	−	0.492763i
$997$	25.2335	+	5.98046i	0.799154	+	0.189403i	0.609851	−	0.792516i	$-0.291229\pi$
$997$	25.2335	+	5.98046i	0.799154	+	0.189403i	0.189303	+	0.981919i	$0.439377\pi$
$998$	10.7125	−	18.5546i	0.339098	−	0.587334i
$999$	−3.44587	−	0.870747i	−0.109022	−	0.0275492i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.2.g.a.151.3	yes	72
3.2	odd	2		486.2.g.a.127.2		72
81.22	even	27	inner	162.2.g.a.103.3	✓	72
81.59	odd	54		486.2.g.a.199.2		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
162.2.g.a.103.3	✓	72	81.22	even	27	inner
162.2.g.a.151.3	yes	72	1.1	even	1	trivial
486.2.g.a.127.2		72	3.2	odd	2
486.2.g.a.199.2		72	81.59	odd	54

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:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	162.g (of order \(27\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(0.686242 - 0.727374i) q^{2} +(0.916297 + 1.46983i) q^{3} +(-0.0581448 - 0.998308i) q^{4} +(1.08261 + 0.126540i) q^{5} +(1.69792 + 0.342169i) q^{6} +(-0.387485 + 0.194602i) q^{7} +(-0.766044 - 0.642788i) q^{8} +(-1.32080 + 2.69360i) q^{9} +O(q^{10})\)	\(q+(0.686242 - 0.727374i) q^{2} +(0.916297 + 1.46983i) q^{3} +(-0.0581448 - 0.998308i) q^{4} +(1.08261 + 0.126540i) q^{5} +(1.69792 + 0.342169i) q^{6} +(-0.387485 + 0.194602i) q^{7} +(-0.766044 - 0.642788i) q^{8} +(-1.32080 + 2.69360i) q^{9} +(0.834977 - 0.700629i) q^{10} +(0.774129 - 1.79463i) q^{11} +(1.41407 - 1.00021i) q^{12} +(-1.45186 + 0.344097i) q^{13} +(-0.124360 + 0.415391i) q^{14} +(0.806005 + 1.70721i) q^{15} +(-0.993238 + 0.116093i) q^{16} +(-0.868482 - 4.92541i) q^{17} +(1.05287 + 2.80918i) q^{18} +(-0.565662 + 3.20803i) q^{19} +(0.0633770 - 1.08814i) q^{20} +(-0.641084 - 0.391224i) q^{21} +(-0.774129 - 1.79463i) q^{22} +(2.12973 + 1.06959i) q^{23} +(0.242865 - 1.71494i) q^{24} +(-3.70918 - 0.879092i) q^{25} +(-0.746040 + 1.29218i) q^{26} +(-5.16938 + 0.526784i) q^{27} +(0.216803 + 0.375514i) q^{28} +(-2.44573 - 8.16932i) q^{29} +(1.79489 + 0.585290i) q^{30} +(-5.16760 + 3.39878i) q^{31} +(-0.597159 + 0.802123i) q^{32} +(3.34714 - 0.506578i) q^{33} +(-4.17860 - 2.74831i) q^{34} +(-0.444122 + 0.161647i) q^{35} +(2.76584 + 1.16195i) q^{36} +(0.642752 + 0.233943i) q^{37} +(1.94525 + 2.61293i) q^{38} +(-1.83610 - 1.81869i) q^{39} +(-0.747993 - 0.792826i) q^{40} +(2.80658 + 2.97480i) q^{41} +(-0.724504 + 0.197833i) q^{42} +(3.51649 + 4.72346i) q^{43} +(-1.83661 - 0.668471i) q^{44} +(-1.77077 + 2.74900i) q^{45} +(2.23950 - 0.815111i) q^{46} +(2.10644 + 1.38543i) q^{47} +(-1.08074 - 1.35352i) q^{48} +(-4.06784 + 5.46405i) q^{49} +(-3.18482 + 2.09469i) q^{50} +(6.44373 - 5.78966i) q^{51} +(0.427933 + 1.42940i) q^{52} +(-1.14093 - 1.97615i) q^{53} +(-3.16428 + 4.12157i) q^{54} +(1.06518 - 1.84494i) q^{55} +(0.421919 + 0.0999966i) q^{56} +(-5.23357 + 2.10808i) q^{57} +(-7.62051 - 3.82716i) q^{58} +(4.55125 + 10.5510i) q^{59} +(1.65745 - 0.903906i) q^{60} +(0.817619 - 14.0380i) q^{61} +(-1.07404 + 6.09116i) q^{62} +(-0.0123902 - 1.30076i) q^{63} +(0.173648 + 0.984808i) q^{64} +(-1.61535 + 0.188807i) q^{65} +(1.92847 - 2.78225i) q^{66} +(-0.448672 + 1.49867i) q^{67} +(-4.86658 + 1.15340i) q^{68} +(0.379348 + 4.11040i) q^{69} +(-0.187197 + 0.433972i) q^{70} +(10.2702 - 8.61771i) q^{71} +(2.74321 - 1.21442i) q^{72} +(11.6826 + 9.80288i) q^{73} +(0.611247 - 0.306980i) q^{74} +(-2.10659 - 6.25738i) q^{75} +(3.23549 + 0.378174i) q^{76} +(0.0492763 + 0.846041i) q^{77} +(-2.58288 + 0.0874673i) q^{78} +(4.78508 - 5.07189i) q^{79} -1.08998 q^{80} +(-5.51097 - 7.11542i) q^{81} +4.08979 q^{82} +(6.22295 - 6.59594i) q^{83} +(-0.353286 + 0.662747i) q^{84} +(-0.316973 - 5.44222i) q^{85} +(5.84888 + 0.683636i) q^{86} +(9.76649 - 11.0803i) q^{87} +(-1.74659 + 0.877168i) q^{88} +(-8.27201 - 6.94104i) q^{89} +(0.784376 + 3.17449i) q^{90} +(0.495612 - 0.415868i) q^{91} +(0.943948 - 2.18832i) q^{92} +(-9.73069 - 4.48120i) q^{93} +(2.45325 - 0.581432i) q^{94} +(-1.01834 + 3.40148i) q^{95} +(-1.72616 - 0.142739i) q^{96} +(14.2297 - 1.66321i) q^{97} +(1.18289 + 6.70850i) q^{98} +(3.81155 + 4.45555i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 9 q^{6}+O(q^{10}) \) 72 * q + 9 * q^6	\( 72 q + 9 q^{6} + 18 q^{13} - 9 q^{20} - 81 q^{23} + 18 q^{25} - 27 q^{26} - 27 q^{27} + 18 q^{28} - 27 q^{29} - 63 q^{30} - 54 q^{31} + 9 q^{33} - 27 q^{35} - 9 q^{36} + 9 q^{38} - 9 q^{41} + 9 q^{42} + 36 q^{43} - 117 q^{45} - 18 q^{46} - 27 q^{47} + 9 q^{48} - 27 q^{51} - 36 q^{52} - 27 q^{53} + 54 q^{55} + 27 q^{57} + 9 q^{58} - 18 q^{59} + 9 q^{63} + 9 q^{65} + 36 q^{66} - 135 q^{67} - 18 q^{68} + 108 q^{69} + 18 q^{70} + 72 q^{71} + 54 q^{72} + 36 q^{73} + 99 q^{74} - 36 q^{75} - 9 q^{76} + 144 q^{77} + 90 q^{78} - 9 q^{79} + 18 q^{80} - 72 q^{82} + 99 q^{83} + 18 q^{84} + 9 q^{85} + 72 q^{86} + 207 q^{87} - 9 q^{88} + 126 q^{89} - 18 q^{90} + 63 q^{91} + 36 q^{92} + 81 q^{93} + 18 q^{94} + 45 q^{95} - 171 q^{97} + 36 q^{98} + 99 q^{99}+O(q^{100}) \) 72 * q + 9 * q^6 + 18 * q^13 - 9 * q^20 - 81 * q^23 + 18 * q^25 - 27 * q^26 - 27 * q^27 + 18 * q^28 - 27 * q^29 - 63 * q^30 - 54 * q^31 + 9 * q^33 - 27 * q^35 - 9 * q^36 + 9 * q^38 - 9 * q^41 + 9 * q^42 + 36 * q^43 - 117 * q^45 - 18 * q^46 - 27 * q^47 + 9 * q^48 - 27 * q^51 - 36 * q^52 - 27 * q^53 + 54 * q^55 + 27 * q^57 + 9 * q^58 - 18 * q^59 + 9 * q^63 + 9 * q^65 + 36 * q^66 - 135 * q^67 - 18 * q^68 + 108 * q^69 + 18 * q^70 + 72 * q^71 + 54 * q^72 + 36 * q^73 + 99 * q^74 - 36 * q^75 - 9 * q^76 + 144 * q^77 + 90 * q^78 - 9 * q^79 + 18 * q^80 - 72 * q^82 + 99 * q^83 + 18 * q^84 + 9 * q^85 + 72 * q^86 + 207 * q^87 - 9 * q^88 + 126 * q^89 - 18 * q^90 + 63 * q^91 + 36 * q^92 + 81 * q^93 + 18 * q^94 + 45 * q^95 - 171 * q^97 + 36 * q^98 + 99 * q^99

Introduction

L-functions

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