LMFDB - Embedded newform 162.2.g.a.103.3

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			103.3
Character	$\chi$	$=$	162.103
Dual form			162.2.g.a.151.3

$q$-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 $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{7}{27}\right)$

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	0.129488	−	0.991581i	$-0.458667\pi$
$5$	1.08261	−	0.126540i	0.484160	−	0.0565902i	0.354672	+	0.934991i	$0.384593\pi$
$6$	1.69792	−	0.342169i	0.693172	−	0.139690i
$7$	−0.387485	−	0.194602i	−0.146456	−	0.0735528i	0.374062	−	0.927404i	$-0.377965\pi$
$7$	−0.387485	−	0.194602i	−0.146456	−	0.0735528i	−0.520518	+	0.853851i	$0.674261\pi$
$8$	−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	0.994157	−	0.107945i	$-0.0344270\pi$
$11$	0.774129	+	1.79463i	0.233409	+	0.541102i	−0.760748	+	0.649047i	$0.775168\pi$
$12$	1.41407	+	1.00021i	0.408206	+	0.288736i
$13$	−1.45186	−	0.344097i	−0.402674	−	0.0954354i	0.0242884	−	0.999705i	$-0.492268\pi$
$13$	−1.45186	−	0.344097i	−0.402674	−	0.0954354i	−0.426962	+	0.904270i	$0.640416\pi$
$14$	−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	0.677680	+	0.735357i	$0.262986\pi$
$17$	−0.868482	+	4.92541i	−0.210638	+	1.19459i	−0.888318	+	0.459230i	$0.848125\pi$
$18$	1.05287	−	2.80918i	0.248163	−	0.662129i
$19$	−0.565662	−	3.20803i	−0.129772	−	0.735972i	−0.978359	−	0.206916i	$-0.933657\pi$
$19$	−0.565662	−	3.20803i	−0.129772	−	0.735972i	0.848587	−	0.529056i	$-0.177454\pi$
$20$	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	−0.212685	−	0.977121i	$-0.568221\pi$
$23$	2.12973	−	1.06959i	0.444079	−	0.223025i	0.656764	+	0.754096i	$0.271925\pi$
$24$	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	0.358084	+	0.933689i	$0.383430\pi$
$29$	−2.44573	+	8.16932i	−0.454161	+	1.51700i	−0.812246	+	0.583315i	$0.801755\pi$
$30$	1.79489	−	0.585290i	0.327701	−	0.106859i
$31$	−5.16760	−	3.39878i	−0.928128	−	0.610439i	−0.00711652	−	0.999975i	$-0.502265\pi$
$31$	−5.16760	−	3.39878i	−0.928128	−	0.610439i	−0.921012	+	0.389535i	$0.872636\pi$
$32$	−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	−0.288645	−	0.957436i	$-0.593205\pi$
$37$	0.642752	−	0.233943i	0.105668	−	0.0384599i	0.394313	+	0.918976i	$0.370983\pi$
$38$	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	−0.470127	−	0.882599i	$-0.655792\pi$
$41$	2.80658	−	2.97480i	0.438315	−	0.464586i	0.908441	+	0.418013i	$0.137273\pi$
$42$	−0.724504	−	0.197833i	−0.111793	−	0.0305263i
$43$	3.51649	−	4.72346i	0.536259	−	0.720321i	−0.448589	−	0.893738i	$-0.648073\pi$
$43$	3.51649	−	4.72346i	0.536259	−	0.720321i	0.984849	+	0.173417i	$0.0554808\pi$
$44$	−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	−0.386511	−	0.922285i	$-0.626320\pi$
$47$	2.10644	−	1.38543i	0.307256	−	0.202086i	0.693767	+	0.720199i	$0.255950\pi$
$48$	−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	−0.933684	−	0.358099i	$-0.883425\pi$
$53$	−1.14093	+	1.97615i	−0.156719	+	0.271446i	0.776964	+	0.629544i	$0.216758\pi$
$54$	−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	−0.313175	−	0.949695i	$-0.601393\pi$
$59$	4.55125	−	10.5510i	0.592522	−	1.37362i	0.905697	−	0.423925i	$-0.139348\pi$
$60$	1.65745	+	0.903906i	0.213976	+	0.116694i
$61$	0.817619	+	14.0380i	0.104685	+	1.79738i	0.487058	+	0.873370i	$0.338070\pi$
$61$	0.817619	+	14.0380i	0.104685	+	1.79738i	−0.382372	+	0.924008i	$0.624893\pi$
$62$	−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	0.926198	−	0.377036i	$-0.123057\pi$
$67$	−0.448672	−	1.49867i	−0.0548140	−	0.183091i	−0.981012	+	0.193945i	$0.937872\pi$
$68$	−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	0.998884	+	0.0472262i	$0.0150382\pi$
$71$	10.2702	+	8.61771i	1.21885	+	1.02273i	0.219963	+	0.975508i	$0.429406\pi$
$72$	2.74321	+	1.21442i	0.323290	+	0.143121i
$73$	11.6826	−	9.80288i	1.36735	−	1.14734i	0.393710	−	0.919235i	$-0.371191\pi$
$73$	11.6826	−	9.80288i	1.36735	−	1.14734i	0.973636	−	0.228106i	$-0.0732531\pi$
$74$	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	0.938261	−	0.345928i	$-0.112436\pi$
$79$	4.78508	+	5.07189i	0.538364	+	0.570632i	−0.399897	+	0.916560i	$0.630954\pi$
$80$	−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	0.972424	−	0.233220i	$-0.0749262\pi$
$83$	6.22295	+	6.59594i	0.683057	+	0.723998i	−0.289367	+	0.957218i	$0.593445\pi$
$84$	−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	−0.965525	−	0.260310i	$-0.916175\pi$
$89$	−8.27201	+	6.94104i	−0.876831	+	0.735749i	0.0886936	+	0.996059i	$0.471731\pi$
$90$	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	0.802078	−	0.597220i	$-0.203728\pi$
$97$	14.2297	+	1.66321i	1.44481	+	0.168874i	0.642729	+	0.766093i	$0.277802\pi$
$98$	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	−0.730277	−	0.683152i	$-0.760609\pi$
$101$	−0.846671	−	14.5368i	−0.0842469	−	1.44646i	0.646030	−	0.763312i	$-0.276428\pi$
$102$	0.210710	+	8.66010i	0.0208634	+	0.857478i
$103$	4.42196	−	10.2512i	0.435708	−	1.01009i	−0.548992	−	0.835828i	$-0.684988\pi$
$103$	4.42196	−	10.2512i	0.435708	−	1.01009i	0.984700	−	0.174258i	$-0.0557525\pi$
$104$	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	−0.877916	−	0.478815i	$-0.841066\pi$
$107$	−8.82995	−	15.2939i	−0.853624	−	1.47852i	0.0242921	−	0.999705i	$-0.492267\pi$
$108$	0.826465	−	5.13001i	0.0795267	−	0.493635i
$109$	−4.57987	+	7.93257i	−0.438672	+	0.759803i	−0.997587	−	0.0694222i	$-0.977884\pi$
$109$	−4.57987	+	7.93257i	−0.438672	+	0.759803i	0.558915	+	0.829225i	$0.311218\pi$
$110$	−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	0.876018	−	0.482279i	$-0.160191\pi$
$113$	1.73011	+	2.32394i	0.162755	+	0.218618i	−0.713263	+	0.700897i	$0.752783\pi$
$114$	−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	0.392323	−	0.919828i	$-0.371672\pi$
$127$	1.14503	+	0.416758i	0.101605	+	0.0369813i	−0.290717	+	0.956809i	$0.593894\pi$
$128$	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	0.573159	−	0.819444i	$-0.305718\pi$
$131$	0.546520	+	0.359452i	0.0477497	+	0.0314055i	−0.525410	+	0.850849i	$0.676088\pi$
$132$	−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	−0.616282	−	0.787526i	$-0.711362\pi$
$137$	−9.52260	+	2.25690i	−0.813571	+	0.192820i	−0.197289	+	0.980345i	$0.563214\pi$
$138$	3.25012	−	2.54480i	0.276669	−	0.216628i
$139$	−2.92471	+	1.46885i	−0.248071	+	0.124586i	−0.568491	−	0.822690i	$-0.692472\pi$
$139$	−2.92471	+	1.46885i	−0.248071	+	0.124586i	0.320420	+	0.947276i	$0.396176\pi$
$140$	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	−0.360623	−	0.932712i	$-0.617436\pi$
$149$	−13.4454	−	3.18661i	−1.10149	−	0.261057i	−0.740864	+	0.671655i	$0.765584\pi$
$150$	−5.99708	+	2.76179i	−0.489660	+	0.225499i
$151$	2.74008	+	6.35223i	0.222985	+	0.516937i	0.992580	−	0.121595i	$-0.0388011\pi$
$151$	2.74008	+	6.35223i	0.222985	+	0.516937i	−0.769595	+	0.638532i	$0.779542\pi$
$152$	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	0.254043	−	0.967193i	$-0.418240\pi$
$157$	9.07530	−	1.06075i	0.724288	−	0.0846571i	0.470245	+	0.882536i	$0.344165\pi$
$158$	−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	0.118968	−	0.992898i	$-0.462041\pi$
$167$	5.99241	−	0.700413i	0.463707	−	0.0541996i	0.344739	+	0.938699i	$0.387967\pi$
$168$	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	0.895341	−	0.445381i	$-0.146932\pi$
$173$	−0.566077	−	1.31231i	−0.0430380	−	0.0997733i	−0.938379	+	0.345608i	$0.887673\pi$
$174$	−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	−0.965166	−	0.261640i	$-0.915737\pi$
$179$	0.418491	−	2.37338i	0.0312795	−	0.177395i	0.996445	+	0.0842450i	$0.0268478\pi$
$180$	2.84731	−	1.60793i	0.212226	−	0.119848i
$181$	−1.46681	−	8.31867i	−0.109027	−	0.618322i	−0.989535	−	0.144292i	$-0.953910\pi$
$181$	−1.46681	−	8.31867i	−0.109027	−	0.618322i	0.880508	−	0.474031i	$-0.157201\pi$
$182$	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	−0.976705	−	0.214588i	$-0.931159\pi$
$191$	−0.590982	+	1.97402i	−0.0427620	+	0.142835i	0.933943	+	0.357423i	$0.116344\pi$
$192$	−1.28839	−	1.15761i	−0.0929813	−	0.0835433i
$193$	6.81456	+	4.48201i	0.490523	+	0.322622i	0.770560	−	0.637367i	$-0.219977\pi$
$193$	6.81456	+	4.48201i	0.490523	+	0.322622i	−0.280037	+	0.959989i	$0.590347\pi$
$194$	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	0.336892	−	0.941543i	$-0.390624\pi$
$197$	−0.143804	−	0.0523405i	−0.0102456	−	0.00372910i	−0.347138	+	0.937814i	$0.612846\pi$
$198$	5.85650	−	0.285159i	0.416203	−	0.0202653i
$199$	−21.7193	+	7.90517i	−1.53964	+	0.560382i	−0.965958	−	0.258697i	$-0.916707\pi$
$199$	−21.7193	+	7.90517i	−1.53964	+	0.560382i	−0.573680	+	0.819080i	$0.694485\pi$
$200$	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	−0.775829	−	0.630943i	$-0.782668\pi$
$211$	−16.8174	−	22.5897i	−1.15776	−	1.55514i	−0.381926	−	0.924193i	$-0.624739\pi$
$212$	−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	0.896799	+	0.442438i	$0.145886\pi$
$223$	0.857579	+	14.7241i	0.0574278	+	0.985996i	−0.839371	+	0.543558i	$0.817077\pi$
$224$	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	0.266494	−	0.963837i	$-0.414135\pi$
$227$	4.57311	+	0.534520i	0.303528	+	0.0354774i	0.0370344	+	0.999314i	$0.488209\pi$
$228$	2.40882	−	5.10214i	0.159528	−	0.337897i
$229$	5.34042	+	17.8382i	0.352905	+	1.17878i	0.931675	+	0.363294i	$0.118348\pi$
$229$	5.34042	+	17.8382i	0.352905	+	1.17878i	−0.578770	+	0.815491i	$0.696467\pi$
$230$	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	0.987893	+	0.155136i	$0.0495815\pi$
$233$	20.0301	+	16.8073i	1.31222	+	1.10108i	0.324325	+	0.945946i	$0.394863\pi$
$234$	−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	0.430840	+	0.902428i	$0.358217\pi$
$239$	−1.57460	+	27.0348i	−0.101852	+	1.74874i	−0.532692	+	0.846309i	$0.678820\pi$
$240$	−0.998750	+	1.60209i	−0.0644690	+	0.103415i
$241$	−10.3975	−	11.0208i	−0.669765	−	0.709909i	0.300003	−	0.953938i	$-0.403012\pi$
$241$	−10.3975	−	11.0208i	−0.669765	−	0.709909i	−0.969768	+	0.244029i	$0.921531\pi$
$242$	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	−0.367505	−	0.930021i	$-0.619788\pi$
$251$	7.67704	−	6.44180i	0.484570	−	0.406603i	0.852076	+	0.523419i	$0.175344\pi$
$252$	−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	0.987549	−	0.157314i	$-0.0502835\pi$
$257$	1.21867	+	4.07063i	0.0760182	+	0.253919i	−0.911530	+	0.411233i	$0.865098\pi$
$258$	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	−0.997383	−	0.0722979i	$-0.976967\pi$
$263$	−0.245484	−	4.21481i	−0.0151372	−	0.259896i	0.982246	−	0.187598i	$-0.0600703\pi$
$264$	−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	0.837499	−	0.546439i	$-0.184017\pi$
$269$	−0.893553	−	1.54768i	−0.0544809	−	0.0943636i	−0.891980	+	0.452076i	$0.850684\pi$
$270$	−3.94723	−	4.06167i	−0.240221	−	0.247185i
$271$	−10.5130	+	18.2090i	−0.638619	+	1.10612i	0.347117	+	0.937822i	$0.387161\pi$
$271$	−10.5130	+	18.2090i	−0.638619	+	1.10612i	−0.985736	+	0.168299i	$0.946173\pi$
$272$	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	0.217643	−	0.976028i	$-0.430163\pi$
$277$	19.9728	−	13.1363i	1.20005	−	0.789287i	0.982409	+	0.186742i	$0.0597927\pi$
$278$	−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	−0.896422	−	0.443201i	$-0.853843\pi$
$281$	−3.59976	+	4.83531i	−0.214744	+	0.288451i	0.681679	+	0.731652i	$0.261250\pi$
$282$	3.10251	−	3.07310i	0.184752	−	0.183001i
$283$	−1.66727	+	1.76720i	−0.0991090	+	0.105049i	−0.775029	−	0.631925i	$-0.782265\pi$
$283$	−1.66727	+	1.76720i	−0.0991090	+	0.105049i	0.675920	+	0.736975i	$0.263746\pi$
$284$	−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	0.998727	+	0.0504432i	$0.0160634\pi$
$293$	24.6594	+	16.2188i	1.44062	+	0.947511i	0.441893	+	0.897068i	$0.354307\pi$
$294$	−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	−0.993275	−	0.115782i	$-0.963063\pi$
$307$	−0.355719	+	2.01738i	−0.0203020	+	0.115138i	0.972973	+	0.230920i	$0.0741737\pi$
$308$	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	−0.213394	−	0.976966i	$-0.568452\pi$
$311$	−14.8585	−	3.52154i	−0.842551	−	0.199688i	−0.629157	+	0.777278i	$0.716600\pi$
$312$	0.237500	−	2.57342i	0.0134458	−	0.145691i
$313$	6.26007	+	14.5125i	0.353840	+	0.820293i	0.998443	+	0.0557758i	$0.0177632\pi$
$313$	6.26007	+	14.5125i	0.353840	+	0.820293i	−0.644604	+	0.764517i	$0.722978\pi$
$314$	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	−0.560683	−	0.828031i	$-0.689461\pi$
$317$	−27.7693	−	13.9463i	−1.55968	−	0.783302i	−0.998999	+	0.0447290i	$0.985758\pi$
$318$	−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	−0.181440	−	0.983402i	$-0.558076\pi$
$331$	−19.6234	−	9.85523i	−1.07860	−	0.541692i	−0.897158	+	0.441709i	$0.854372\pi$
$332$	−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	0.717641	−	0.696413i	$-0.245222\pi$
$337$	19.2093	+	4.55270i	1.04640	+	0.248001i	0.328758	+	0.944414i	$0.393370\pi$
$338$	−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	−0.996283	−	0.0861361i	$-0.972548\pi$
$347$	−28.3542	+	14.2400i	−1.52213	+	0.764443i	−0.525847	+	0.850579i	$0.676252\pi$
$348$	−11.6295	+	9.10571i	−0.623404	+	0.488117i
$349$	−31.3103	+	7.42068i	−1.67600	+	0.397220i	−0.955210	−	0.295930i	$-0.904370\pi$
$349$	−31.3103	+	7.42068i	−1.67600	+	0.397220i	−0.720793	+	0.693150i	$0.756222\pi$
$350$	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	0.774132	+	0.633024i	$0.218187\pi$
$353$	−4.14279	+	13.8379i	−0.220498	+	0.736516i	−0.994630	+	0.103491i	$0.966999\pi$
$354$	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	0.739056	−	0.673643i	$-0.235272\pi$
$359$	16.5258	+	6.01489i	0.872197	+	0.317454i	0.133140	+	0.991097i	$0.457494\pi$
$360$	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	0.535624	−	0.844457i	$-0.320076\pi$
$367$	22.8160	−	30.6472i	1.19099	−	1.59977i	0.655362	−	0.755315i	$-0.272516\pi$
$368$	−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	0.971768	−	0.235939i	$-0.0758165\pi$
$373$	9.01994	+	12.1159i	0.467035	+	0.627337i	−0.504733	+	0.863275i	$0.668409\pi$
$374$	−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	0.827161	−	0.561965i	$-0.189955\pi$
$379$	−1.42303	−	2.46475i	−0.0730959	−	0.126606i	−0.900257	+	0.435360i	$0.856621\pi$
$380$	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	−0.958390	−	0.285462i	$-0.907853\pi$
$383$	−1.82133	+	4.22231i	−0.0930654	+	0.215750i	0.865325	+	0.501212i	$0.167112\pi$
$384$	−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	−0.291205	−	0.956661i	$-0.594056\pi$
$389$	−15.6834	−	1.83313i	−0.795182	−	0.0929435i	−0.503977	+	0.863717i	$0.668130\pi$
$390$	−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	−0.458267	−	0.888815i	$-0.651530\pi$
$397$	6.72400	−	5.64210i	0.337468	−	0.283169i	0.795734	+	0.605646i	$0.207085\pi$
$398$	−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	0.982979	+	0.183720i	$0.0588140\pi$
$401$	−0.294008	+	5.04791i	−0.0146820	+	0.252081i	−0.997661	+	0.0683609i	$0.978223\pi$
$402$	−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	−0.999485	−	0.0320792i	$-0.989787\pi$
$409$	−0.0613587	+	1.05349i	−0.00303399	+	0.0520917i	0.996451	+	0.0841709i	$0.0268242\pi$
$410$	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	0.995286	−	0.0969837i	$-0.0309195\pi$
$419$	2.26072	+	7.55132i	0.110443	+	0.368906i	−0.884843	+	0.465890i	$0.845734\pi$
$420$	−0.466337	−	0.672795i	−0.0227549	−	0.0328290i
$421$	−12.7902	−	1.49496i	−0.623355	−	0.0728597i	−0.201449	−	0.979499i	$-0.564565\pi$
$421$	−12.7902	−	1.49496i	−0.623355	−	0.0728597i	−0.421906	+	0.906639i	$0.638639\pi$
$422$	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	0.538126	−	0.842864i	$-0.319132\pi$
$431$	−9.56809	−	16.5724i	−0.460879	−	0.798265i	−0.999005	+	0.0445990i	$0.985799\pi$
$432$	5.07327	+	1.12335i	0.244088	+	0.0540472i
$433$	14.0876	−	24.4005i	0.677008	−	1.17261i	−0.298870	−	0.954294i	$-0.596610\pi$
$433$	14.0876	−	24.4005i	0.677008	−	1.17261i	0.975878	−	0.218318i	$-0.0700569\pi$
$434$	−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	0.226726	−	0.973958i	$-0.427198\pi$
$439$	25.3698	−	16.6860i	1.21083	−	0.796377i	0.984106	+	0.177581i	$0.0568273\pi$
$440$	−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	−0.864265	−	0.503037i	$-0.832216\pi$
$443$	−2.83061	+	3.80216i	−0.134486	+	0.180646i	0.729778	+	0.683684i	$0.239623\pi$
$444$	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	−0.861037	−	0.508542i	$-0.830185\pi$
$449$	−25.2950	+	9.20663i	−1.19375	+	0.434488i	−0.332708	+	0.943030i	$0.607962\pi$
$450$	−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	−0.474425	−	0.880296i	$-0.657344\pi$
$457$	8.67248	−	28.9681i	0.405682	−	1.35507i	0.880107	−	0.474775i	$-0.157471\pi$
$458$	−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	0.517222	−	0.855851i	$-0.326966\pi$
$461$	29.2763	−	6.93861i	1.36353	−	0.323163i	0.846312	+	0.532688i	$0.178818\pi$
$462$	−0.205822	−	1.45337i	−0.00957569	−	0.0676168i
$463$	14.5735	−	7.31906i	0.677286	−	0.340146i	−0.0766834	−	0.997055i	$-0.524433\pi$
$463$	14.5735	−	7.31906i	0.677286	−	0.340146i	0.753969	+	0.656910i	$0.228137\pi$
$464$	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	−0.930173	−	0.367121i	$-0.880344\pi$
$467$	−3.92568	−	22.2637i	−0.181659	−	1.03024i	0.748514	−	0.663119i	$-0.230768\pi$
$468$	−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	0.768809	−	0.639479i	$-0.220850\pi$
$479$	15.6479	+	7.85865i	0.714969	+	0.359071i	−0.0538397	+	0.998550i	$0.517146\pi$
$480$	−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	−0.822608	−	0.568608i	$-0.807482\pi$
$491$	−33.0586	+	3.86400i	−1.49191	+	0.174380i	−0.669305	+	0.742988i	$0.733408\pi$
$492$	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	0.668998	−	0.743264i	$-0.266723\pi$
$499$	20.8474	+	4.94094i	0.933260	+	0.221187i	0.264262	+	0.964451i	$0.414872\pi$
$500$	−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	−0.999960	−	0.00899840i	$-0.997136\pi$
$503$	−1.28347	+	7.27895i	−0.0572273	+	0.324552i	0.942732	+	0.333551i	$0.108247\pi$
$504$	−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	−0.464491	−	0.885578i	$-0.653763\pi$
$509$	−0.711178	+	0.357167i	−0.0315224	+	0.0158312i	0.432968	+	0.901409i	$0.357466\pi$
$510$	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	0.528147	−	0.849153i	$-0.322887\pi$
$521$	8.83131	+	3.21433i	0.386907	+	0.140823i	−0.141241	+	0.989975i	$0.545109\pi$
$522$	20.3740	+	15.4717i	0.891747	+	0.677178i
$523$	18.5496	−	6.75149i	0.811116	−	0.295222i	0.0970311	−	0.995281i	$-0.469065\pi$
$523$	18.5496	−	6.75149i	0.811116	−	0.295222i	0.714085	+	0.700059i	$0.246843\pi$
$524$	−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	0.998513	−	0.0545073i	$-0.0173588\pi$
$541$	10.5145	+	18.2116i	0.452052	+	0.782977i	−0.546461	+	0.837484i	$0.684025\pi$
$542$	−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	0.934528	+	0.355888i	$0.115822\pi$
$547$	1.11409	+	19.1282i	0.0476351	+	0.817863i	−0.886893	+	0.461974i	$0.847141\pi$
$548$	−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	−0.0370272	−	0.999314i	$-0.511789\pi$
$557$	−24.2520	−	20.3498i	−1.02759	−	0.862250i	−0.990562	+	0.137064i	$0.956233\pi$
$558$	−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	−0.918601	−	0.395185i	$-0.870680\pi$
$563$	0.941202	−	16.1598i	0.0396670	−	0.681055i	0.958268	−	0.285870i	$-0.0922826\pi$
$564$	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	0.929980	−	0.367611i	$-0.119824\pi$
$569$	12.1396	+	12.8672i	0.508917	+	0.539421i	−0.421063	+	0.907032i	$0.638343\pi$
$570$	−2.89293	−	5.42698i	−0.121171	−	0.227311i
$571$	2.22221	−	38.1539i	0.0929967	−	1.59669i	−0.552887	−	0.833256i	$-0.686474\pi$
$571$	2.22221	−	38.1539i	0.0929967	−	1.59669i	0.645884	−	0.763436i	$-0.276489\pi$
$572$	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	0.258702	−	0.965957i	$-0.416705\pi$
$577$	−15.5573	−	13.0541i	−0.647657	−	0.543449i	−0.906359	+	0.422508i	$0.861150\pi$
$578$	−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	0.861165	+	0.508325i	$0.169735\pi$
$587$	1.57085	+	26.9704i	0.0648358	+	1.11319i	−0.796330	+	0.604863i	$0.793228\pi$
$588$	−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	0.918271	−	0.395952i	$-0.129585\pi$
$593$	2.83040	+	4.90240i	0.116231	+	0.201317i	−0.802040	+	0.597270i	$0.796252\pi$
$594$	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	0.728295	−	0.685263i	$-0.240313\pi$
$599$	−3.35440	−	4.50574i	−0.137057	−	0.184100i	−0.865352	+	0.501164i	$0.832905\pi$
$600$	−2.40842	−	6.14752i	−0.0983233	−	0.250971i
$601$	28.0761	−	18.4659i	1.14525	−	0.753241i	0.172477	−	0.985014i	$-0.444823\pi$
$601$	28.0761	−	18.4659i	1.14525	−	0.753241i	0.972770	+	0.231773i	$0.0744527\pi$
$602$	−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	−0.976928	−	0.213569i	$-0.931491\pi$
$607$	−17.4166	+	18.4605i	−0.706917	+	0.749288i	0.270011	+	0.962857i	$0.412973\pi$
$608$	−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	0.120434	−	0.992721i	$-0.461571\pi$
$613$	−10.5328	−	3.83363i	−0.425416	−	0.154839i	−0.545851	+	0.837882i	$0.683793\pi$
$614$	−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	0.971246	−	0.238079i	$-0.0765177\pi$
$617$	28.2507	+	18.5807i	1.13733	+	0.748033i	0.166083	+	0.986112i	$0.446888\pi$
$618$	4.00046	−	18.9188i	0.160922	−	0.761026i
$619$	−1.27718	+	4.26606i	−0.0513340	+	0.171468i	−0.979813	−	0.199919i	$-0.935932\pi$
$619$	−1.27718	+	4.26606i	−0.0513340	+	0.171468i	0.928478	+	0.371386i	$0.121117\pi$
$620$	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	−0.800940	−	0.598745i	$-0.795666\pi$
$631$	3.93074	−	22.2923i	0.156480	−	0.887444i	0.957420	−	0.288699i	$-0.0932226\pi$
$632$	−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	0.835500	−	0.549491i	$-0.185178\pi$
$641$	22.6258	+	11.3631i	0.893666	+	0.448816i	0.0581666	+	0.998307i	$0.481475\pi$
$642$	−20.2256	−	22.9465i	−0.798242	−	0.905625i
$643$	−21.0737	+	2.46316i	−0.831065	+	0.0971375i	−0.520977	−	0.853571i	$-0.674432\pi$
$643$	−21.0737	+	2.46316i	−0.831065	+	0.0971375i	−0.310087	+	0.950708i	$0.600358\pi$
$644$	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	−0.433245	−	0.901276i	$-0.642632\pi$
$653$	−16.5324	+	1.93236i	−0.646963	+	0.0756192i	−0.213718	+	0.976895i	$0.568557\pi$
$654$	−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	0.944967	+	0.327166i	$0.106094\pi$
$659$	13.7202	+	31.8070i	0.534463	+	1.23903i	−0.410503	+	0.911859i	$0.634647\pi$
$660$	−0.339097	+	3.67426i	−0.0131993	+	0.143020i
$661$	−35.9802	−	8.52747i	−1.39947	−	0.331680i	−0.539482	−	0.841997i	$-0.681380\pi$
$661$	−35.9802	−	8.52747i	−1.39947	−	0.331680i	−0.859986	+	0.510317i	$0.829528\pi$
$662$	−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	−0.826778	−	0.562529i	$-0.809829\pi$
$673$	−34.0661	+	8.07381i	−1.31315	+	0.311222i	−0.486373	+	0.873751i	$0.661680\pi$
$674$	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	−0.960721	−	0.277517i	$-0.910489\pi$
$677$	−0.144469	+	0.482558i	−0.00555238	+	0.0185462i	0.955168	+	0.296063i	$0.0956738\pi$
$678$	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	0.339178	−	0.940722i	$-0.389851\pi$
$683$	−0.148497	−	0.0540486i	−0.00568209	−	0.00206811i	−0.344860	+	0.938654i	$0.612073\pi$
$684$	−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	−0.921044	−	0.389459i	$-0.872662\pi$
$691$	−7.45991	+	10.0204i	−0.283788	+	0.381194i	0.637256	+	0.770653i	$0.280070\pi$
$692$	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	0.431325	+	0.902197i	$0.358046\pi$
$701$	−14.9767	+	25.9404i	−0.565663	+	0.979757i	−0.996988	+	0.0775602i	$0.975287\pi$
$702$	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	0.984765	+	0.173888i	$0.0556332\pi$
$709$	0.714825	+	12.2731i	0.0268458	+	0.460925i	−0.957920	+	0.287037i	$0.907330\pi$
$710$	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	0.312708	−	0.949849i	$-0.398764\pi$
$719$	−15.2414	−	12.7891i	−0.568410	−	0.476953i	−0.881118	+	0.472897i	$0.843208\pi$
$720$	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	0.948075	+	0.318046i	$0.103027\pi$
$727$	32.6375	+	34.5937i	1.21046	+	1.28301i	0.262382	+	0.964964i	$0.415492\pi$
$728$	−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	0.909950	+	0.414718i	$0.136120\pi$
$733$	−1.13692	+	19.5201i	−0.0419930	+	0.720993i	−0.951943	+	0.306275i	$0.900917\pi$
$734$	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	0.363850	−	0.931457i	$-0.381462\pi$
$739$	−13.3279	−	11.1834i	−0.490274	−	0.411389i	−0.854125	+	0.520068i	$0.825906\pi$
$740$	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	0.442510	+	0.896763i	$0.354088\pi$
$743$	15.4165	+	51.4948i	0.565578	+	1.88916i	0.123068	+	0.992398i	$0.460727\pi$
$744$	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	−0.536425	−	0.843948i	$-0.680225\pi$
$751$	12.2102	−	28.3065i	0.445558	−	1.03292i	0.981983	−	0.188971i	$-0.0605153\pi$
$752$	−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	−0.680657	−	0.732602i	$-0.738306\pi$
$757$	8.09241	−	14.0165i	0.294124	−	0.509437i	0.974781	+	0.223165i	$0.0716389\pi$
$758$	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	0.989869	−	0.141984i	$-0.0453483\pi$
$761$	15.7228	+	21.1194i	0.569952	+	0.765578i	−0.419917	+	0.907562i	$0.637941\pi$
$762$	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	−0.797418	−	0.603428i	$-0.793801\pi$
$769$	−4.12204	+	4.36911i	−0.148645	+	0.157554i	0.648773	+	0.760982i	$0.275283\pi$
$770$	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	−0.392648	−	0.919689i	$-0.628441\pi$
$773$	−2.84339	+	1.03491i	−0.102270	+	0.0372231i	0.290379	+	0.956912i	$0.406219\pi$
$774$	−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	−0.158938	−	0.987289i	$-0.550807\pi$
$787$	15.0950	−	7.58098i	0.538078	−	0.270233i	0.697016	+	0.717056i	$0.254511\pi$
$788$	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	0.120464	−	0.992718i	$-0.461562\pi$
$797$	−6.13793	−	1.45472i	−0.217417	−	0.0515287i	−0.337881	+	0.941189i	$0.609710\pi$
$798$	−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	0.816224	−	0.577735i	$-0.196063\pi$
$821$	−4.70289	−	10.9025i	−0.164132	−	0.380501i	−0.980356	+	0.197234i	$0.936804\pi$
$822$	−15.3963	+	7.09036i	−0.537009	+	0.247305i
$823$	−43.1132	−	10.2180i	−1.50283	−	0.356178i	−0.604896	−	0.796304i	$-0.706785\pi$
$823$	−43.1132	−	10.2180i	−1.50283	−	0.356178i	−0.897936	+	0.440127i	$0.854934\pi$
$824$	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	−0.840034	−	0.542534i	$-0.817465\pi$
$827$	3.87933	−	22.0007i	0.134897	−	0.765041i	0.974931	−	0.222507i	$-0.0714240\pi$
$828$	4.64768	−	5.43295i	0.161518	−	0.188808i
$829$	−3.12358	−	17.7147i	−0.108487	−	0.615258i	−0.989770	−	0.142670i	$-0.954431\pi$
$829$	−3.12358	−	17.7147i	−0.108487	−	0.615258i	0.881284	−	0.472588i	$-0.156680\pi$
$830$	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	−0.219483	−	0.975616i	$-0.570437\pi$
$839$	14.4828	−	48.3760i	0.500002	−	1.67012i	0.719485	−	0.694508i	$-0.244378\pi$
$840$	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	−0.983501	−	0.180903i	$-0.942098\pi$
$853$	−15.4245	+	20.7188i	−0.528126	+	0.709397i	0.455375	+	0.890300i	$0.349505\pi$
$854$	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	0.126881	−	0.991918i	$-0.459503\pi$
$857$	31.8487	−	20.9472i	1.08793	−	0.715544i	0.961050	+	0.276374i	$0.0891329\pi$
$858$	−1.84251	−	4.70303i	−0.0629022	−	0.160559i
$859$	34.7206	+	46.6379i	1.18465	+	1.59126i	0.694165	+	0.719816i	$0.255774\pi$
$859$	34.7206	+	46.6379i	1.18465	+	1.59126i	0.490487	+	0.871449i	$0.336819\pi$
$860$	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	−0.998865	−	0.0476316i	$-0.984833\pi$
$863$	−13.4600	+	23.3133i	−0.458182	+	0.793595i	0.540683	+	0.841227i	$0.318166\pi$
$864$	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	−0.998517	−	0.0544452i	$-0.982661\pi$
$877$	−5.75067	−	19.2086i	−0.194186	−	0.648627i	0.804330	−	0.594182i	$-0.202524\pi$
$878$	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	0.301024	−	0.953616i	$-0.402671\pi$
$881$	−17.3885	−	14.5907i	−0.585832	−	0.491572i	−0.886857	+	0.462045i	$0.847116\pi$
$882$	−19.6324	+	5.67436i	−0.661056	+	0.191066i
$883$	12.2003	−	10.2372i	0.410572	−	0.344511i	−0.413991	−	0.910281i	$-0.635866\pi$
$883$	12.2003	−	10.2372i	0.410572	−	0.344511i	0.824563	+	0.565770i	$0.191421\pi$
$884$	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	−0.876958	−	0.480567i	$-0.840431\pi$
$887$	1.48498	−	25.4961i	0.0498608	−	0.856077i	0.926819	−	0.375509i	$-0.122532\pi$
$888$	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	−0.125520	−	0.992091i	$-0.540060\pi$
$907$	−14.3489	−	1.67715i	−0.476448	−	0.0556888i	−0.350928	+	0.936402i	$0.614134\pi$
$908$	−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	0.988643	+	0.150286i	$0.0480193\pi$
$911$	0.728369	+	12.5056i	0.0241319	+	0.414329i	−0.964511	+	0.264044i	$0.914944\pi$
$912$	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	−0.962541	−	0.271136i	$-0.912601\pi$
$919$	−7.47142	+	12.9409i	−0.246460	+	0.426880i	0.716081	+	0.698017i	$0.245934\pi$
$920$	−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	−0.934335	−	0.356395i	$-0.884006\pi$
$929$	−9.90409	+	13.3035i	−0.324943	+	0.436474i	0.609393	+	0.792868i	$0.291413\pi$
$930$	−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	0.647732	−	0.761869i	$-0.275718\pi$
$937$	20.0254	+	7.28867i	0.654203	+	0.238110i	0.00647140	+	0.999979i	$0.497940\pi$
$938$	−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	−0.0268095	−	0.999641i	$-0.508535\pi$
$941$	−29.3050	−	19.2742i	−0.955314	−	0.628320i	−0.928505	+	0.371320i	$0.878905\pi$
$942$	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	−0.664584	−	0.747214i	$-0.731391\pi$
$947$	−28.4078	+	6.73276i	−0.923128	+	0.218785i	−0.258545	+	0.965999i	$0.583243\pi$
$948$	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	−0.984019	−	0.178064i	$-0.943017\pi$
$953$	−3.71205	−	21.0521i	−0.120245	−	0.681943i	0.863774	−	0.503879i	$-0.168094\pi$
$954$	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	−0.576870	−	0.816836i	$-0.695726\pi$
$967$	−29.5361	+	3.45227i	−0.949816	+	0.111018i	−0.372945	+	0.927853i	$0.621652\pi$
$968$	−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	0.0681316	−	0.997676i	$-0.478296\pi$
$977$	11.3934	−	1.33170i	0.364507	−	0.0426047i	0.296375	+	0.955072i	$0.404222\pi$
$978$	−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	−0.969118	−	0.246599i	$-0.920687\pi$
$983$	−15.1572	−	35.1382i	−0.483438	−	1.12074i	0.485680	−	0.874137i	$-0.338572\pi$
$984$	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	0.807194	+	0.590286i	$0.200985\pi$
$991$	7.88796	+	44.7349i	0.250569	+	1.42105i	−0.556625	+	0.830764i	$0.687904\pi$
$992$	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	0.189303	−	0.981919i	$-0.439377\pi$
$997$	25.2335	−	5.98046i	0.799154	−	0.189403i	0.609851	+	0.792516i	$0.291229\pi$
$998$	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.103.3	✓	72
3.2	odd	2		486.2.g.a.199.2		72
81.11	odd	54		486.2.g.a.127.2		72
81.70	even	27	inner	162.2.g.a.151.3	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
162.2.g.a.103.3	✓	72	1.1	even	1	trivial
162.2.g.a.151.3	yes	72	81.70	even	27	inner
486.2.g.a.127.2		72	81.11	odd	54
486.2.g.a.199.2		72	3.2	odd	2

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

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more