LMFDB - Embedded newform 243.2.i.a.103.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [243,2,Mod(4,243)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(243, base_ring=CyclotomicField(162))

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

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

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

chi := DirichletCharacter("243.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 243 = 3^{5} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	243.i (of order $81$, degree $54$, 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:	$1.94036476912$
Analytic rank:	$0$
Dimension:	$1404$
Relative dimension:	$26$ over $\Q(\zeta_{81})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{81}]$

Embedding invariants

Embedding label			103.9
Character	$\chi$	$=$	243.103
Dual form			243.2.i.a.151.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.11059 - 0.309154i) q^{2} +(0.249684 - 1.71396i) q^{3} +(-0.574502 - 0.346714i) q^{4} +(2.97093 - 0.115286i) q^{5} +(-0.807174 + 1.82631i) q^{6} +(4.35689 + 0.681405i) q^{7} +(2.11307 + 2.23972i) q^{8} +(-2.87532 - 0.855898i) q^{9} +O(q^{10})$	\(q+(-1.11059 - 0.309154i) q^{2} +(0.249684 - 1.71396i) q^{3} +(-0.574502 - 0.346714i) q^{4} +(2.97093 - 0.115286i) q^{5} +(-0.807174 + 1.82631i) q^{6} +(4.35689 + 0.681405i) q^{7} +(2.11307 + 2.23972i) q^{8} +(-2.87532 - 0.855898i) q^{9} +(-3.33513 - 0.790440i) q^{10} +(0.228372 + 1.67198i) q^{11} +(-0.737697 + 0.898104i) q^{12} +(0.555061 - 0.809298i) q^{13} +(-4.62806 - 2.10371i) q^{14} +(0.544201 - 5.12085i) q^{15} +(-1.02889 - 1.95329i) q^{16} +(-0.733705 + 0.368480i) q^{17} +(2.92869 + 1.83946i) q^{18} +(-0.468654 - 8.04649i) q^{19} +(-1.74678 - 0.963831i) q^{20} +(2.25575 - 7.29740i) q^{21} +(0.263270 - 1.92748i) q^{22} +(-2.88972 + 7.48456i) q^{23} +(4.36639 - 3.06249i) q^{24} +(3.82820 - 0.297551i) q^{25} +(-0.866642 + 0.727199i) q^{26} +(-2.18490 + 4.71447i) q^{27} +(-2.26679 - 1.90206i) q^{28} +(-2.38271 - 1.70306i) q^{29} +(-2.18751 + 5.51891i) q^{30} +(-1.81668 + 2.08168i) q^{31} +(-0.764950 - 3.53140i) q^{32} +(2.92272 + 0.0260465i) q^{33} +(0.928762 - 0.182403i) q^{34} +(13.0226 + 1.52212i) q^{35} +(1.35512 + 1.48863i) q^{36} +(-1.78516 - 2.39789i) q^{37} +(-1.96712 + 9.08123i) q^{38} +(-1.24851 - 1.15342i) q^{39} +(6.53599 + 6.41046i) q^{40} +(-2.19104 + 8.50616i) q^{41} +(-4.76123 + 7.40704i) q^{42} +(-1.13031 - 1.02570i) q^{43} +(0.448497 - 1.03973i) q^{44} +(-8.64105 - 2.21133i) q^{45} +(5.52317 - 7.41890i) q^{46} +(-1.86632 - 2.13857i) q^{47} +(-3.60476 + 1.27576i) q^{48} +(11.8524 + 3.80033i) q^{49} +(-4.34354 - 0.853044i) q^{50} +(0.448366 + 1.34954i) q^{51} +(-0.599478 + 0.272496i) q^{52} +(1.22675 - 6.95726i) q^{53} +(3.88402 - 4.56037i) q^{54} +(0.871232 + 4.94100i) q^{55} +(7.68025 + 11.1981i) q^{56} +(-13.9084 - 1.20583i) q^{57} +(2.11971 + 2.62802i) q^{58} +(-2.23510 + 0.913139i) q^{59} +(-2.08811 + 2.75325i) q^{60} +(-1.90125 + 1.14741i) q^{61} +(2.66114 - 1.75026i) q^{62} +(-11.9442 - 5.68831i) q^{63} +(-0.498934 + 8.56636i) q^{64} +(1.55575 - 2.46836i) q^{65} +(-3.23789 - 0.932497i) q^{66} +(-7.25247 + 5.18375i) q^{67} +(0.549272 + 0.0426928i) q^{68} +(12.1067 + 6.82164i) q^{69} +(-13.9922 - 5.71643i) q^{70} +(2.04721 + 6.83814i) q^{71} +(-4.15876 - 8.24847i) q^{72} +(14.6670 - 3.47613i) q^{73} +(1.24126 + 3.21496i) q^{74} +(0.445850 - 6.63567i) q^{75} +(-2.52058 + 4.78521i) q^{76} +(-0.144303 + 7.44023i) q^{77} +(1.03000 + 1.66696i) q^{78} +(-10.8800 + 10.6710i) q^{79} +(-3.28194 - 5.68449i) q^{80} +(7.53488 + 4.92195i) q^{81} +(5.06306 - 8.76947i) q^{82} +(1.54587 + 6.00143i) q^{83} +(-3.82604 + 3.41027i) q^{84} +(-2.13731 + 1.17932i) q^{85} +(0.938213 + 1.48858i) q^{86} +(-3.51390 + 3.65864i) q^{87} +(-3.26220 + 4.04449i) q^{88} +(5.19714 - 17.3597i) q^{89} +(8.91301 + 5.12729i) q^{90} +(2.96980 - 3.14780i) q^{91} +(4.25515 - 3.29799i) q^{92} +(3.11432 + 3.63347i) q^{93} +(1.41157 + 2.95205i) q^{94} +(-2.31999 - 23.8516i) q^{95} +(-6.24368 + 0.429357i) q^{96} +(13.4534 + 0.522053i) q^{97} +(-11.9883 - 7.88483i) q^{98} +(0.774400 - 5.00292i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1404 q - 54 q^{2} - 54 q^{3} - 54 q^{4} - 54 q^{5} - 54 q^{6} - 54 q^{7} - 54 q^{8} - 54 q^{9}+O(q^{10}) $ 1404 * q - 54 * q^2 - 54 * q^3 - 54 * q^4 - 54 * q^5 - 54 * q^6 - 54 * q^7 - 54 * q^8 - 54 * q^9	\( 1404 q - 54 q^{2} - 54 q^{3} - 54 q^{4} - 54 q^{5} - 54 q^{6} - 54 q^{7} - 54 q^{8} - 54 q^{9} - 54 q^{10} - 54 q^{11} - 54 q^{12} - 54 q^{13} - 54 q^{14} - 54 q^{15} - 54 q^{16} - 54 q^{17} - 54 q^{18} - 54 q^{19} - 54 q^{20} - 54 q^{21} - 54 q^{22} - 54 q^{23} - 54 q^{24} - 54 q^{25} - 54 q^{26} - 54 q^{27} - 54 q^{28} - 54 q^{29} - 54 q^{30} - 54 q^{31} - 54 q^{32} - 54 q^{33} - 54 q^{34} - 54 q^{35} - 54 q^{36} - 54 q^{37} - 54 q^{38} - 54 q^{39} - 54 q^{40} - 54 q^{41} - 54 q^{42} - 54 q^{43} - 54 q^{44} - 54 q^{45} - 54 q^{46} - 54 q^{47} - 54 q^{48} - 54 q^{49} - 54 q^{50} - 54 q^{51} - 54 q^{52} - 54 q^{53} - 54 q^{54} - 54 q^{55} - 54 q^{56} - 54 q^{57} - 54 q^{58} - 54 q^{59} - 54 q^{60} - 54 q^{61} - 54 q^{62} - 54 q^{63} - 54 q^{64} + 54 q^{66} - 54 q^{67} + 135 q^{68} + 54 q^{69} - 54 q^{70} + 54 q^{71} + 270 q^{72} - 54 q^{73} + 162 q^{74} + 81 q^{75} - 54 q^{76} + 162 q^{77} + 162 q^{78} - 54 q^{79} + 351 q^{80} + 54 q^{81} - 27 q^{82} + 54 q^{83} + 324 q^{84} - 54 q^{85} + 162 q^{86} + 162 q^{87} - 54 q^{88} + 81 q^{89} + 162 q^{90} - 54 q^{91} + 270 q^{92} + 54 q^{93} - 54 q^{94} + 54 q^{95} + 135 q^{96} - 54 q^{97} + 54 q^{98}+O(q^{100}) \) 1404 * q - 54 * q^2 - 54 * q^3 - 54 * q^4 - 54 * q^5 - 54 * q^6 - 54 * q^7 - 54 * q^8 - 54 * q^9 - 54 * q^10 - 54 * q^11 - 54 * q^12 - 54 * q^13 - 54 * q^14 - 54 * q^15 - 54 * q^16 - 54 * q^17 - 54 * q^18 - 54 * q^19 - 54 * q^20 - 54 * q^21 - 54 * q^22 - 54 * q^23 - 54 * q^24 - 54 * q^25 - 54 * q^26 - 54 * q^27 - 54 * q^28 - 54 * q^29 - 54 * q^30 - 54 * q^31 - 54 * q^32 - 54 * q^33 - 54 * q^34 - 54 * q^35 - 54 * q^36 - 54 * q^37 - 54 * q^38 - 54 * q^39 - 54 * q^40 - 54 * q^41 - 54 * q^42 - 54 * q^43 - 54 * q^44 - 54 * q^45 - 54 * q^46 - 54 * q^47 - 54 * q^48 - 54 * q^49 - 54 * q^50 - 54 * q^51 - 54 * q^52 - 54 * q^53 - 54 * q^54 - 54 * q^55 - 54 * q^56 - 54 * q^57 - 54 * q^58 - 54 * q^59 - 54 * q^60 - 54 * q^61 - 54 * q^62 - 54 * q^63 - 54 * q^64 + 54 * q^66 - 54 * q^67 + 135 * q^68 + 54 * q^69 - 54 * q^70 + 54 * q^71 + 270 * q^72 - 54 * q^73 + 162 * q^74 + 81 * q^75 - 54 * q^76 + 162 * q^77 + 162 * q^78 - 54 * q^79 + 351 * q^80 + 54 * q^81 - 27 * q^82 + 54 * q^83 + 324 * q^84 - 54 * q^85 + 162 * q^86 + 162 * q^87 - 54 * q^88 + 81 * q^89 + 162 * q^90 - 54 * q^91 + 270 * q^92 + 54 * q^93 - 54 * q^94 + 54 * q^95 + 135 * q^96 - 54 * q^97 + 54 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/243\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{7}{81}\right)$

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 $

$2$	−1.11059	−	0.309154i	−0.785305	−	0.218605i	−0.147766	−	0.989022i	$-0.547208\pi$
$2$	−1.11059	−	0.309154i	−0.785305	−	0.218605i	−0.637539	+	0.770418i	$0.720048\pi$
$3$	0.249684	−	1.71396i	0.144155	−	0.989555i
$3$	0.249684	−	1.71396i	0.144155	−	0.989555i
$4$	−0.574502	−	0.346714i	−0.287251	−	0.173357i
$5$	2.97093	−	0.115286i	1.32864	−	0.0515574i	0.635356	−	0.772220i	$-0.280853\pi$
$5$	2.97093	−	0.115286i	1.32864	−	0.0515574i	0.693286	+	0.720662i	$0.256162\pi$
$6$	−0.807174	+	1.82631i	−0.329527	+	0.745590i
$7$	4.35689	+	0.681405i	1.64675	+	0.257547i	0.908777	−	0.417283i	$-0.137018\pi$
$7$	4.35689	+	0.681405i	1.64675	+	0.257547i	0.737973	+	0.674830i	$0.235783\pi$
$8$	2.11307	+	2.23972i	0.747082	+	0.791861i
$9$	−2.87532	−	0.855898i	−0.958438	−	0.285299i
$10$	−3.33513	−	0.790440i	−1.05466	−	0.249959i
$11$	0.228372	+	1.67198i	0.0688566	+	0.504120i	0.992630	+	0.121181i	$0.0386682\pi$
$11$	0.228372	+	1.67198i	0.0688566	+	0.504120i	−0.923774	+	0.382939i	$0.874912\pi$
$12$	−0.737697	+	0.898104i	−0.212955	+	0.259260i
$13$	0.555061	−	0.809298i	0.153946	−	0.224459i	−0.740030	−	0.672574i	$-0.765189\pi$
$13$	0.555061	−	0.809298i	0.153946	−	0.224459i	0.893976	+	0.448115i	$0.147905\pi$
$14$	−4.62806	−	2.10371i	−1.23690	−	0.562240i
$15$	0.544201	−	5.12085i	0.140512	−	1.32220i
$16$	−1.02889	−	1.95329i	−0.257222	−	0.488323i
$17$	−0.733705	+	0.368480i	−0.177950	+	0.0893696i	−0.535544	−	0.844507i	$-0.679893\pi$
$17$	−0.733705	+	0.368480i	−0.177950	+	0.0893696i	0.357594	+	0.933877i	$0.383597\pi$
$18$	2.92869	+	1.83946i	0.690299	+	0.433566i
$19$	−0.468654	−	8.04649i	−0.107517	−	1.84599i	−0.434151	−	0.900840i	$-0.642952\pi$
$19$	−0.468654	−	8.04649i	−0.107517	−	1.84599i	0.326635	−	0.945151i	$-0.394085\pi$
$20$	−1.74678	−	0.963831i	−0.390591	−	0.215519i
$21$	2.25575	−	7.29740i	0.492245	−	1.59242i
$22$	0.263270	−	1.92748i	0.0561294	−	0.410940i
$23$	−2.88972	+	7.48456i	−0.602548	+	1.56064i	0.209973	+	0.977707i	$0.432662\pi$
$23$	−2.88972	+	7.48456i	−0.602548	+	1.56064i	−0.812521	+	0.582932i	$0.801906\pi$
$24$	4.36639	−	3.06249i	0.891286	−	0.625128i
$25$	3.82820	−	0.297551i	0.765639	−	0.0595102i
$26$	−0.866642	+	0.727199i	−0.169962	+	0.142615i
$27$	−2.18490	+	4.71447i	−0.420483	+	0.907300i
$28$	−2.26679	−	1.90206i	−0.428383	−	0.359456i
$29$	−2.38271	−	1.70306i	−0.442458	−	0.316250i	0.338351	−	0.941020i	$-0.390131\pi$
$29$	−2.38271	−	1.70306i	−0.442458	−	0.316250i	−0.780809	+	0.624770i	$0.785193\pi$
$30$	−2.18751	+	5.51891i	−0.399383	+	1.00761i
$31$	−1.81668	+	2.08168i	−0.326285	+	0.373881i	−0.893018	−	0.450020i	$-0.851417\pi$
$31$	−1.81668	+	2.08168i	−0.326285	+	0.373881i	0.566734	+	0.823901i	$0.308207\pi$
$32$	−0.764950	−	3.53140i	−0.135225	−	0.624269i
$33$	2.92272	+	0.0260465i	0.508780	+	0.00453412i
$34$	0.928762	−	0.182403i	0.159281	−	0.0312818i
$35$	13.0226	+	1.52212i	2.20122	+	0.257286i
$36$	1.35512	+	1.48863i	0.225854	+	0.248104i
$37$	−1.78516	−	2.39789i	−0.293479	−	0.394210i	0.630790	−	0.775954i	$-0.282731\pi$
$37$	−1.78516	−	2.39789i	−0.293479	−	0.394210i	−0.924268	+	0.381744i	$0.875324\pi$
$38$	−1.96712	+	9.08123i	−0.319109	+	1.47317i
$39$	−1.24851	−	1.15342i	−0.199922	−	0.184695i
$40$	6.53599	+	6.41046i	1.03343	+	1.01358i
$41$	−2.19104	+	8.50616i	−0.342184	+	1.32844i	0.533601	+	0.845736i	$0.320838\pi$
$41$	−2.19104	+	8.50616i	−0.342184	+	1.32844i	−0.875785	+	0.482702i	$0.839655\pi$
$42$	−4.76123	+	7.40704i	−0.734673	+	1.14293i
$43$	−1.13031	−	1.02570i	−0.172371	−	0.156418i	0.581256	−	0.813721i	$-0.302562\pi$
$43$	−1.13031	−	1.02570i	−0.172371	−	0.156418i	−0.753627	+	0.657302i	$0.771697\pi$
$44$	0.448497	−	1.03973i	0.0676135	−	0.156746i
$45$	−8.64105	−	2.21133i	−1.28813	−	0.329646i
$46$	5.52317	−	7.41890i	0.814347	−	1.09386i
$47$	−1.86632	−	2.13857i	−0.272231	−	0.311942i	0.600999	−	0.799249i	$-0.294769\pi$
$47$	−1.86632	−	2.13857i	−0.272231	−	0.311942i	−0.873231	+	0.487307i	$0.837979\pi$
$48$	−3.60476	+	1.27576i	−0.520303	+	0.184141i
$49$	11.8524	+	3.80033i	1.69321	+	0.542905i
$50$	−4.34354	−	0.853044i	−0.614269	−	0.120639i
$51$	0.448366	+	1.34954i	0.0627838	+	0.188974i
$52$	−0.599478	+	0.272496i	−0.0831326	+	0.0377884i
$53$	1.22675	−	6.95726i	0.168507	−	0.955653i	−0.776867	−	0.629665i	$-0.783192\pi$
$53$	1.22675	−	6.95726i	0.168507	−	0.955653i	0.945374	−	0.325988i	$-0.105697\pi$
$54$	3.88402	−	4.56037i	0.528548	−	0.620588i
$55$	0.871232	+	4.94100i	0.117477	+	0.666245i
$56$	7.68025	+	11.1981i	1.02632	+	1.49641i
$57$	−13.9084	−	1.20583i	−1.84221	−	0.159716i
$58$	2.11971	+	2.62802i	0.278331	+	0.345076i
$59$	−2.23510	+	0.913139i	−0.290985	+	0.118881i	−0.518992	−	0.854779i	$-0.673693\pi$
$59$	−2.23510	+	0.913139i	−0.290985	+	0.118881i	0.228007	+	0.973659i	$0.426779\pi$
$60$	−2.08811	+	2.75325i	−0.269574	+	0.355443i
$61$	−1.90125	+	1.14741i	−0.243429	+	0.146910i	−0.633166	−	0.774016i	$-0.718245\pi$
$61$	−1.90125	+	1.14741i	−0.243429	+	0.146910i	0.389737	+	0.920926i	$0.372566\pi$
$62$	2.66114	−	1.75026i	0.337965	−	0.222283i
$63$	−11.9442	−	5.68831i	−1.50483	−	0.716659i
$64$	−0.498934	+	8.56636i	−0.0623667	+	1.07080i
$65$	1.55575	−	2.46836i	0.192967	−	0.306163i
$66$	−3.23789	−	0.932497i	−0.398557	−	0.114782i
$67$	−7.25247	+	5.18375i	−0.886030	+	0.633296i	−0.930731	−	0.365704i	$-0.880828\pi$
$67$	−7.25247	+	5.18375i	−0.886030	+	0.633296i	0.0447009	+	0.999000i	$0.485767\pi$
$68$	0.549272	+	0.0426928i	0.0666090	+	0.00517726i
$69$	12.1067	+	6.82164i	1.45748	+	0.821229i
$70$	−13.9922	−	5.71643i	−1.67238	−	0.683244i
$71$	2.04721	+	6.83814i	0.242959	+	0.811538i	0.989290	+	0.145964i	$0.0466283\pi$
$71$	2.04721	+	6.83814i	0.242959	+	0.811538i	−0.746331	+	0.665575i	$0.768187\pi$
$72$	−4.15876	−	8.24847i	−0.490115	−	0.972092i
$73$	14.6670	−	3.47613i	1.71664	−	0.406850i	0.749682	−	0.661798i	$-0.230206\pi$
$73$	14.6670	−	3.47613i	1.71664	−	0.406850i	0.966955	+	0.254947i	$0.0820582\pi$
$74$	1.24126	+	3.21496i	0.144294	+	0.373731i
$75$	0.445850	−	6.63567i	0.0514824	−	0.766221i
$76$	−2.52058	+	4.78521i	−0.289131	+	0.548901i
$77$	−0.144303	+	7.44023i	−0.0164449	+	0.847893i
$78$	1.03000	+	1.66696i	0.116625	+	0.188746i
$79$	−10.8800	+	10.6710i	−1.22410	+	1.20058i	−0.251556	+	0.967843i	$0.580942\pi$
$79$	−10.8800	+	10.6710i	−1.22410	+	1.20058i	−0.972539	+	0.232741i	$0.925230\pi$
$80$	−3.28194	−	5.68449i	−0.366932	−	0.635545i
$81$	7.53488	+	4.92195i	0.837209	+	0.546884i
$82$	5.06306	−	8.76947i	0.559121	−	0.968426i
$83$	1.54587	+	6.00143i	0.169681	+	0.658742i	0.995496	+	0.0948012i	$0.0302216\pi$
$83$	1.54587	+	6.00143i	0.169681	+	0.658742i	−0.825815	+	0.563941i	$0.809285\pi$
$84$	−3.82604	+	3.41027i	−0.417455	+	0.372091i
$85$	−2.13731	+	1.17932i	−0.231824	+	0.127915i
$86$	0.938213	+	1.48858i	0.101170	+	0.160517i
$87$	−3.51390	+	3.65864i	−0.376730	+	0.392248i
$88$	−3.26220	+	4.04449i	−0.347751	+	0.431144i
$89$	5.19714	−	17.3597i	0.550896	−	1.84012i	0.00855473	−	0.999963i	$-0.497277\pi$
$89$	5.19714	−	17.3597i	0.550896	−	1.84012i	0.542341	−	0.840158i	$-0.317538\pi$
$90$	8.91301	+	5.12729i	0.939514	+	0.540464i
$91$	2.96980	−	3.14780i	0.311319	−	0.329979i
$92$	4.25515	−	3.29799i	0.443630	−	0.343839i
$93$	3.11432	+	3.63347i	0.322940	+	0.376773i
$94$	1.41157	+	2.95205i	0.145593	+	0.304481i
$95$	−2.31999	−	23.8516i	−0.238026	−	2.44712i
$96$	−6.24368	+	0.429357i	−0.637242	+	0.0438211i
$97$	13.4534	+	0.522053i	1.36598	+	0.0530064i	0.711296	−	0.702893i	$-0.248109\pi$
$97$	13.4534	+	0.522053i	1.36598	+	0.0530064i	0.654688	+	0.755899i	$0.272800\pi$
$98$	−11.9883	−	7.88483i	−1.21100	−	0.796488i
$99$	0.774400	−	5.00292i	0.0778302	−	0.502813i
$100$	−2.30247	−	1.15634i	−0.230247	−	0.115634i
$101$	−0.121261	−	6.25220i	−0.0120659	−	0.622117i	−0.956226	−	0.292630i	$-0.905470\pi$
$101$	−0.121261	−	6.25220i	−0.0120659	−	0.622117i	0.944160	−	0.329488i	$-0.106876\pi$
$102$	−0.0807339	−	1.63740i	−0.00799384	−	0.162127i
$103$	−7.42474	−	5.75461i	−0.731581	−	0.567018i	0.177258	−	0.984164i	$-0.443277\pi$
$103$	−7.42474	−	5.75461i	−0.731581	−	0.567018i	−0.908839	+	0.417146i	$0.863030\pi$
$104$	2.98548	−	0.466921i	0.292751	−	0.0457854i
$105$	5.86039	−	21.9401i	0.571916	−	2.14114i
$106$	−3.51328	+	7.34740i	−0.341240	+	0.713643i
$107$	−2.30642	−	0.839467i	−0.222970	−	0.0811544i	0.228120	−	0.973633i	$-0.426742\pi$
$107$	−2.30642	−	0.839467i	−0.222970	−	0.0811544i	−0.451089	+	0.892479i	$0.648964\pi$
$108$	2.88980	−	1.95094i	0.278071	−	0.187729i
$109$	−12.4995	+	4.54943i	−1.19723	+	0.435756i	−0.862257	−	0.506471i	$-0.830950\pi$
$109$	−12.4995	+	4.54943i	−1.19723	+	0.435756i	−0.334974	+	0.942227i	$0.608728\pi$
$110$	0.559948	−	5.75677i	0.0533889	−	0.548886i
$111$	−4.55561	+	2.46098i	−0.432399	+	0.233586i
$112$	−3.15176	−	9.21137i	−0.297814	−	0.870393i
$113$	4.12654	−	3.74463i	0.388192	−	0.352266i	−0.454419	−	0.890788i	$-0.650153\pi$
$113$	4.12654	−	3.74463i	0.388192	−	0.352266i	0.842611	+	0.538523i	$0.181017\pi$
$114$	15.0737	+	5.63900i	1.41178	+	0.528141i
$115$	−7.72230	+	22.5693i	−0.720108	+	2.10460i
$116$	0.778398	+	1.80453i	0.0722724	+	0.167546i
$117$	−2.28865	+	1.85191i	−0.211586	+	0.171209i
$118$	2.76458	−	0.323133i	0.254500	−	0.0297468i
$119$	−3.44776	+	1.10548i	−0.316055	+	0.101339i
$120$	12.6192	−	9.60184i	1.15197	−	0.876524i
$121$	7.85373	−	2.18623i	0.713975	−	0.198749i
$122$	2.46623	−	0.686521i	0.223282	−	0.0621547i
$123$	14.0321	+	5.87922i	1.26524	+	0.530111i
$124$	1.76543	−	0.566062i	0.158540	−	0.0508339i
$125$	−3.42632	+	0.400479i	−0.306459	+	0.0358200i
$126$	11.5066	+	10.0100i	1.02509	+	0.891759i
$127$	3.77615	+	8.75410i	0.335079	+	0.776801i	0.999565	+	0.0294999i	$0.00939148\pi$
$127$	3.77615	+	8.75410i	0.335079	+	0.776801i	−0.664486	+	0.747301i	$0.731349\pi$
$128$	0.862936	−	2.52203i	0.0762735	−	0.222918i
$129$	−2.04024	+	1.68121i	−0.179633	+	0.148022i
$130$	−2.49090	+	2.26037i	−0.218466	+	0.198248i
$131$	−0.602632	−	1.76126i	−0.0526522	−	0.153882i	0.916688	−	0.399603i	$-0.130852\pi$
$131$	−0.602632	−	1.76126i	−0.0526522	−	0.153882i	−0.969341	+	0.245721i	$0.920975\pi$
$132$	−1.67008	−	1.02831i	−0.145362	−	0.0895030i
$133$	3.44104	−	35.3770i	0.298376	−	3.06757i
$134$	9.65709	−	3.51489i	0.834246	−	0.303641i
$135$	−5.94767	+	14.2583i	−0.511894	+	1.22716i
$136$	−2.37566	−	0.864670i	−0.203711	−	0.0741449i
$137$	−3.55080	+	7.42586i	−0.303365	+	0.634434i	−0.996241	−	0.0866224i	$-0.972393\pi$
$137$	−3.55080	+	7.42586i	−0.303365	+	0.634434i	0.692876	+	0.721057i	$0.256343\pi$
$138$	−11.3367	−	11.3189i	−0.965040	−	0.963527i
$139$	9.32341	−	1.45816i	0.790801	−	0.123679i	0.253796	−	0.967258i	$-0.418321\pi$
$139$	9.32341	−	1.45816i	0.790801	−	0.123679i	0.537006	+	0.843579i	$0.319555\pi$
$140$	−6.95376	−	5.38957i	−0.587700	−	0.455502i
$141$	−4.13141	+	2.66484i	−0.347928	+	0.224420i
$142$	−0.159568	−	8.22727i	−0.0133906	−	0.690417i
$143$	1.47989	+	0.743227i	0.123754	+	0.0621518i
$144$	1.28655	+	6.49696i	0.107213	+	0.541413i
$145$	−7.27521	−	4.78498i	−0.604174	−	0.397371i
$146$	−17.3636	−	0.673787i	−1.43702	−	0.0557630i
$147$	9.47299	−	19.3657i	0.781319	−	1.59726i
$148$	0.194198	+	1.99653i	0.0159630	+	0.164114i
$149$	1.06378	+	2.22470i	0.0871481	+	0.182255i	0.941127	−	0.338052i	$-0.109768\pi$
$149$	1.06378	+	2.22470i	0.0871481	+	0.182255i	−0.853979	+	0.520307i	$0.825817\pi$
$150$	−2.54660	+	7.23166i	−0.207929	+	0.590463i
$151$	1.15107	−	0.892146i	0.0936727	−	0.0726018i	−0.564688	−	0.825305i	$-0.691003\pi$
$151$	1.15107	−	0.892146i	0.0936727	−	0.0726018i	0.658360	+	0.752703i	$0.271250\pi$
$152$	17.0316	−	18.0524i	1.38144	−	1.46425i
$153$	2.42501	−	0.431521i	0.196051	−	0.0348864i
$154$	2.46044	−	8.21843i	0.198268	−	0.662260i
$155$	−5.15724	+	6.39397i	−0.414239	+	0.513576i
$156$	0.317367	+	1.09552i	0.0254097	+	0.0877117i
$157$	−1.92647	−	3.05655i	−0.153749	−	0.243939i	0.760273	−	0.649603i	$-0.225065\pi$
$157$	−1.92647	−	3.05655i	−0.153749	−	0.243939i	−0.914022	+	0.405664i	$0.867040\pi$
$158$	15.3822	−	8.48753i	1.22374	−	0.675232i
$159$	−11.6182	−	3.83972i	−0.921380	−	0.304510i
$160$	−2.67974	−	10.4034i	−0.211852	−	0.822459i
$161$	−17.6902	+	30.6403i	−1.39418	+	2.41480i
$162$	−6.84651	−	7.79570i	−0.537913	−	0.612488i
$163$	−8.79231	−	15.2287i	−0.688667	−	1.19281i	−0.972269	−	0.233864i	$-0.924863\pi$
$163$	−8.79231	−	15.2287i	−0.688667	−	1.19281i	0.283602	−	0.958942i	$-0.408470\pi$
$164$	4.20796	−	4.12714i	0.328586	−	0.322275i
$165$	8.68621	−	0.259566i	0.676221	−	0.0202072i
$166$	0.138539	−	7.14303i	0.0107527	−	0.554406i
$167$	−8.71802	+	16.5508i	−0.674621	+	1.28074i	0.273208	+	0.961955i	$0.411915\pi$
$167$	−8.71802	+	16.5508i	−0.674621	+	1.28074i	−0.947829	+	0.318781i	$0.896727\pi$
$168$	21.1107	−	10.3676i	1.62872	−	0.799881i
$169$	4.33544	+	11.2291i	0.333495	+	0.863775i
$170$	2.73826	−	0.648980i	0.210015	−	0.0497745i
$171$	−5.53944	+	23.5373i	−0.423612	+	1.79994i
$172$	0.293741	+	0.981164i	0.0223976	+	0.0748131i
$173$	3.68019	+	1.50352i	0.279800	+	0.114311i	0.513756	−	0.857936i	$-0.328254\pi$
$173$	3.68019	+	1.50352i	0.279800	+	0.114311i	−0.233956	+	0.972247i	$0.575167\pi$
$174$	5.03358	−	2.97691i	0.381595	−	0.225679i
$175$	16.8818	+	1.31216i	1.27614	+	0.0991896i
$176$	3.03089	−	2.16635i	0.228462	−	0.163295i
$177$	1.00701	+	4.05887i	0.0756918	+	0.305083i
$178$	−11.1387	+	17.6727i	−0.834881	+	1.32463i
$179$	−0.503733	+	8.64877i	−0.0376508	+	0.646439i	0.925711	+	0.378233i	$0.123468\pi$
$179$	−0.503733	+	8.64877i	−0.0376508	+	0.646439i	−0.963361	+	0.268207i	$0.913569\pi$
$180$	4.19760	+	4.26638i	0.312870	+	0.317997i
$181$	−1.31233	+	0.863134i	−0.0975448	+	0.0641562i	−0.597344	−	0.801985i	$-0.703777\pi$
$181$	−1.31233	+	0.863134i	−0.0975448	+	0.0641562i	0.499799	+	0.866141i	$0.333407\pi$
$182$	−4.27138	+	2.57779i	−0.316616	+	0.191079i
$183$	1.49190	+	3.54515i	0.110284	+	0.262065i
$184$	−22.8695	+	9.34322i	−1.68596	+	0.688791i
$185$	−5.58004	−	6.91816i	−0.410253	−	0.508633i
$186$	−2.33543	−	4.99810i	−0.171242	−	0.366478i
$187$	−0.783648	−	1.14259i	−0.0573060	−	0.0835542i
$188$	0.330735	+	1.87569i	0.0241213	+	0.136799i
$189$	−12.7318	+	19.0516i	−0.926103	+	1.38580i
$190$	−4.79724	+	27.2065i	−0.348028	+	1.97377i
$191$	−10.3239	+	4.69277i	−0.747008	+	0.339557i	−0.750883	−	0.660436i	$-0.770372\pi$
$191$	−10.3239	+	4.69277i	−0.747008	+	0.339557i	0.00387435	+	0.999992i	$0.498767\pi$
$192$	14.5578	+	2.99404i	1.05062	+	0.216076i
$193$	−11.6279	−	2.28365i	−0.836995	−	0.164381i	−0.244191	−	0.969727i	$-0.578522\pi$
$193$	−11.6279	−	2.28365i	−0.836995	−	0.164381i	−0.592804	+	0.805347i	$0.701979\pi$
$194$	−14.7798	−	4.73895i	−1.06113	−	0.340237i
$195$	−3.84223	−	3.28280i	−0.275148	−	0.235086i
$196$	−5.49162	−	6.29270i	−0.392259	−	0.449479i
$197$	−0.790673	+	1.06206i	−0.0563331	+	0.0756685i	−0.829397	−	0.558660i	$-0.811316\pi$
$197$	−0.790673	+	1.06206i	−0.0563331	+	0.0756685i	0.773064	+	0.634328i	$0.218723\pi$
$198$	−2.40671	+	5.31678i	−0.171038	+	0.377847i
$199$	5.77797	−	13.3948i	0.409590	−	0.949535i	−0.581155	−	0.813793i	$-0.697399\pi$
$199$	5.77797	−	13.3948i	0.409590	−	0.949535i	0.990744	−	0.135742i	$-0.0433419\pi$
$200$	8.75567	+	7.94534i	0.619119	+	0.561821i
$201$	7.07392	+	13.7247i	0.498956	+	0.968069i
$202$	−1.79822	+	6.98111i	−0.126522	+	0.491189i
$203$	−9.22073	−	9.04363i	−0.647169	−	0.634739i
$204$	0.210318	−	0.930770i	0.0147252	−	0.0651669i
$205$	−5.52881	+	25.5238i	−0.386149	+	1.78266i
$206$	6.46678	+	8.68639i	0.450562	+	0.605209i
$207$	14.7149	−	19.0472i	1.02275	−	1.32387i
$208$	−2.15189	−	0.251520i	−0.149207	−	0.0174398i
$209$	13.3465	−	2.62117i	0.923197	−	0.181310i
$210$	−13.2914	+	22.5547i	−0.917191	+	1.55642i
$211$	4.31652	+	19.9273i	0.297161	+	1.37185i	0.844777	+	0.535119i	$0.179733\pi$
$211$	4.31652	+	19.9273i	0.297161	+	1.37185i	−0.547615	+	0.836730i	$0.684464\pi$
$212$	−3.11695	+	3.57163i	−0.214073	+	0.245300i
$213$	12.2315	−	1.80145i	0.838086	−	0.123433i
$214$	2.30196	+	1.64534i	0.157359	+	0.112473i
$215$	−3.47634	−	2.91699i	−0.237084	−	0.198937i
$216$	−15.1759	+	5.06844i	−1.03259	+	0.344864i
$217$	−9.33352	+	7.83176i	−0.633601	+	0.531654i
$218$	15.2882	−	1.18830i	1.03545	−	0.0804815i
$219$	−2.29584	−	26.0065i	−0.155139	−	1.75736i
$220$	1.21259	−	3.14068i	0.0817527	−	0.211745i
$221$	−0.109040	+	0.798315i	−0.00733483	+	0.0537005i
$222$	5.82023	−	1.32475i	0.390628	−	0.0889116i
$223$	−2.94497	−	1.62497i	−0.197210	−	0.108816i	0.381434	−	0.924396i	$-0.375430\pi$
$223$	−2.94497	−	1.62497i	−0.197210	−	0.108816i	−0.578644	+	0.815580i	$0.696418\pi$
$224$	−0.926487	−	15.9072i	−0.0619035	−	1.06284i
$225$	−11.2619	−	2.42099i	−0.750796	−	0.161399i
$226$	−5.74055	+	2.88302i	−0.381856	+	0.191775i
$227$	−8.52335	−	16.1812i	−0.565714	−	1.07398i	−0.986024	−	0.166602i	$-0.946721\pi$
$227$	−8.52335	−	16.1812i	−0.565714	−	1.07398i	0.420310	−	0.907381i	$-0.361921\pi$
$228$	7.57231	+	5.51497i	0.501488	+	0.365238i
$229$	23.4060	+	10.6393i	1.54671	+	0.703068i	0.991676	−	0.128757i	$-0.0410989\pi$
$229$	23.4060	+	10.6393i	1.54671	+	0.703068i	0.555038	+	0.831825i	$0.312704\pi$
$230$	15.5537	−	22.6778i	1.02558	−	1.49533i
$231$	12.7162	+	2.10504i	0.836666	+	0.138501i
$232$	−1.22045	−	8.93529i	−0.0801266	−	0.586630i
$233$	−14.2513	−	3.37762i	−0.933635	−	0.221275i	−0.264474	−	0.964393i	$-0.585198\pi$
$233$	−14.2513	−	3.37762i	−0.933635	−	0.221275i	−0.669161	+	0.743117i	$0.733346\pi$
$234$	3.11428	−	1.34917i	0.203587	−	0.0881979i
$235$	−5.79127	−	6.13839i	−0.377781	−	0.400424i
$236$	1.60067	+	0.250340i	0.104194	+	0.0162957i
$237$	15.5731	+	21.3123i	1.01158	+	1.38438i
$238$	4.17080	−	0.161846i	0.270353	−	0.0104909i
$239$	−8.19155	−	4.94363i	−0.529868	−	0.319777i	0.226405	−	0.974033i	$-0.427303\pi$
$239$	−8.19155	−	4.94363i	−0.529868	−	0.319777i	−0.756273	+	0.654256i	$0.772982\pi$
$240$	−10.5624	+	4.20579i	−0.681802	+	0.271482i
$241$	−14.0512	−	3.91141i	−0.905114	−	0.251956i	−0.215817	−	0.976434i	$-0.569241\pi$
$241$	−14.0512	−	3.91141i	−0.905114	−	0.251956i	−0.689298	+	0.724478i	$0.742081\pi$
$242$	−9.39815			−0.604136
$243$	10.3174	−	11.6855i	0.661860	−	0.749628i
$244$	1.49009			0.0953932
$245$	35.6509	+	9.92412i	2.27766	+	0.634029i
$246$	−13.7664	−	10.8675i	−0.877711	−	0.692885i
$247$	−6.77214	−	4.08701i	−0.430901	−	0.260050i
$248$	−8.50114	+	0.329883i	−0.539823	+	0.0209476i
$249$	10.6722	−	1.15109i	0.676322	−	0.0729475i
$250$	3.92904	+	0.614491i	0.248495	+	0.0388638i
$251$	14.9722	+	15.8696i	0.945037	+	1.00168i	0.999995	+	0.00319193i	$0.00101603\pi$
$251$	14.9722	+	15.8696i	0.945037	+	1.00168i	−0.0549580	+	0.998489i	$0.517502\pi$
$252$	4.88976	+	7.40917i	0.308026	+	0.466734i
$253$	−13.1739	−	3.12228i	−0.828238	−	0.196296i
$254$	−1.48739	−	10.8896i	−0.0933272	−	0.683276i
$255$	1.48765	+	3.95772i	0.0931602	+	0.247842i
$256$	7.96875	−	11.6187i	0.498047	−	0.726170i
$257$	1.28488	+	0.584051i	0.0801488	+	0.0364321i	0.453484	−	0.891264i	$-0.350181\pi$
$257$	1.28488	+	0.584051i	0.0801488	+	0.0364321i	−0.373335	+	0.927697i	$0.621786\pi$
$258$	2.78562	−	1.23639i	0.173425	−	0.0769740i
$259$	−6.14382	−	11.6637i	−0.381758	−	0.724750i
$260$	−1.74959	+	0.878679i	−0.108505	+	0.0544934i
$261$	5.39340	+	6.93619i	0.333843	+	0.429339i
$262$	0.124777	+	2.14234i	0.00770876	+	0.132354i
$263$	−13.3099	−	7.34407i	−0.820722	−	0.452855i	0.0164042	−	0.999865i	$-0.494778\pi$
$263$	−13.3099	−	7.34407i	−0.820722	−	0.452855i	−0.837126	+	0.547010i	$0.815766\pi$
$264$	6.11757	+	6.60112i	0.376510	+	0.406271i
$265$	2.84253	−	20.8110i	0.174615	−	1.27841i
$266$	−14.7585	+	38.2255i	−0.904902	+	2.34376i
$267$	−28.4561	−	13.2421i	−1.74149	−	0.810405i
$268$	5.96383	−	0.463546i	0.364299	−	0.0283156i
$269$	21.6731	−	18.1859i	1.32143	−	1.10881i	0.335433	−	0.942064i	$-0.391117\pi$
$269$	21.6731	−	18.1859i	1.32143	−	1.10881i	0.985999	−	0.166749i	$-0.0533270\pi$
$270$	11.0134	−	13.9963i	0.670255	−	0.851790i
$271$	21.9323	+	18.4034i	1.33229	+	1.11793i	0.983536	+	0.180713i	$0.0578404\pi$
$271$	21.9323	+	18.4034i	1.33229	+	1.11793i	0.348756	+	0.937213i	$0.386604\pi$
$272$	1.47465	+	1.05402i	0.0894138	+	0.0639091i
$273$	−4.65369	−	5.87607i	−0.281654	−	0.355636i
$274$	6.23921	−	7.14934i	0.376924	−	0.431907i
$275$	1.37175	+	6.33270i	0.0827196	+	0.381876i
$276$	−4.59017	−	8.11661i	−0.276296	−	0.488562i
$277$	13.0784	−	2.56851i	0.785804	−	0.154327i	0.216313	−	0.976324i	$-0.430597\pi$
$277$	13.0784	−	2.56851i	0.785804	−	0.154327i	0.569491	+	0.821997i	$0.307140\pi$
$278$	−10.8053	−	1.26296i	−0.648057	−	0.0757470i
$279$	7.00522	−	4.43060i	0.419392	−	0.265253i
$280$	24.1085	+	32.3833i	1.44076	+	1.93527i
$281$	0.155606	−	0.718358i	0.00928269	−	0.0428536i	−0.972458	−	0.233080i	$-0.925120\pi$
$281$	0.155606	−	0.718358i	0.00928269	−	0.0428536i	0.981740	+	0.190226i	$0.0609221\pi$
$282$	5.41215	−	1.68230i	0.322289	−	0.100179i
$283$	7.06493	+	6.92923i	0.419966	+	0.411900i	0.879228	−	0.476401i	$-0.158059\pi$
$283$	7.06493	+	6.92923i	0.419966	+	0.411900i	−0.459262	+	0.888301i	$0.651886\pi$
$284$	1.19475	−	4.63832i	0.0708956	−	0.275234i
$285$	−41.4599	−	1.97900i	−2.45587	−	0.117226i
$286$	−1.41378	−	1.28293i	−0.0835983	−	0.0758614i
$287$	−15.3423	+	35.5674i	−0.905626	+	2.09948i
$288$	−0.823047	+	10.8086i	−0.0484985	+	0.636904i
$289$	−9.74915	+	13.0954i	−0.573479	+	0.770317i
$290$	6.60048	+	7.56331i	0.387593	+	0.444133i
$291$	4.25388	−	22.9282i	0.249367	−	1.34408i
$292$	−9.63141	−	3.08819i	−0.563636	−	0.180723i
$293$	−9.12136	−	1.79138i	−0.532875	−	0.104653i	−0.0809655	−	0.996717i	$-0.525800\pi$
$293$	−9.12136	−	1.79138i	−0.532875	−	0.104653i	−0.451910	+	0.892064i	$0.649257\pi$
$294$	−16.5076	+	18.5788i	−0.962741	+	1.08353i
$295$	−6.53506	+	2.97055i	−0.380486	+	0.172952i
$296$	1.59843	−	9.06516i	0.0929070	−	0.526902i
$297$	−8.38145	−	2.57644i	−0.486341	−	0.149500i
$298$	−0.493645	−	2.79960i	−0.0285961	−	0.162177i
$299$	4.45327	+	6.49303i	0.257539	+	0.375502i
$300$	−2.55682	+	3.65762i	−0.147618	+	0.211173i
$301$	−4.22573	−	5.23908i	−0.243567	−	0.301976i
$302$	−1.55417	+	0.634950i	−0.0894327	+	0.0365373i
$303$	−10.7463	−	1.35324i	−0.617359	−	0.0777416i
$304$	−15.2350	+	9.19434i	−0.873785	+	0.527332i
$305$	−5.51619	+	3.62806i	−0.315856	+	0.207742i
$306$	−2.82660	−	0.270459i	−0.161586	−	0.0154611i
$307$	1.86024	−	31.9390i	0.106169	−	1.82286i	−0.354245	−	0.935153i	$-0.615262\pi$
$307$	1.86024	−	31.9390i	0.106169	−	1.82286i	0.460415	−	0.887704i	$-0.347701\pi$
$308$	2.66253	−	4.22439i	0.151712	−	0.240707i
$309$	−11.7170	+	11.2889i	−0.666557	+	0.642201i
$310$	7.70429	−	5.50670i	0.437574	−	0.312759i
$311$	14.5698	+	1.13245i	0.826177	+	0.0642156i	0.483616	−	0.875280i	$-0.339323\pi$
$311$	14.5698	+	1.13245i	0.826177	+	0.0642156i	0.342561	+	0.939496i	$0.388706\pi$
$312$	−0.0548553	−	5.23358i	−0.00310557	−	0.296293i
$313$	5.16183	+	2.10884i	0.291764	+	0.119199i	0.519356	−	0.854558i	$-0.326172\pi$
$313$	5.16183	+	2.10884i	0.291764	+	0.119199i	−0.227592	+	0.973757i	$0.573085\pi$
$314$	1.19457	+	3.99014i	0.0674135	+	0.225177i
$315$	−36.1413	−	15.5226i	−2.03633	−	0.874599i
$316$	9.95036	−	2.35828i	0.559752	−	0.132664i
$317$	−9.21083	−	23.8566i	−0.517332	−	1.33992i	−0.907837	−	0.419322i	$-0.862268\pi$
$317$	−9.21083	−	23.8566i	−0.517332	−	1.33992i	0.390506	−	0.920601i	$-0.372300\pi$
$318$	11.7159	+	7.85615i	0.656997	+	0.440551i
$319$	2.30333	−	4.37277i	0.128962	−	0.244828i
$320$	−0.494720	+	25.5076i	−0.0276557	+	1.42592i
$321$	−2.01469	+	3.74350i	−0.112449	+	0.208942i
$322$	29.1191	−	28.5598i	1.62275	−	1.59158i
$323$	3.30883	+	5.73106i	0.184108	+	0.318885i
$324$	−2.62229	−	5.44011i	−0.145683	−	0.302229i
$325$	1.88407	−	3.26331i	0.104510	−	0.181016i
$326$	5.05663	+	19.6310i	0.280061	+	1.08726i
$327$	4.67662	+	22.5595i	0.258618	+	1.24754i
$328$	−23.6812	+	13.0668i	−1.30758	+	0.721491i
$329$	−6.67413	−	10.5892i	−0.367957	−	0.583803i
$330$	−9.72706	−	2.39710i	−0.535457	−	0.131956i
$331$	10.8568	−	13.4603i	0.596742	−	0.739844i	−0.386472	−	0.922301i	$-0.626306\pi$
$331$	10.8568	−	13.4603i	0.596742	−	0.739844i	0.983214	+	0.182457i	$0.0584052\pi$
$332$	1.19267	−	3.98380i	0.0654564	−	0.218640i
$333$	3.08055	+	8.42260i	0.168813	+	0.461556i
$334$	14.7989	−	15.6859i	0.809758	−	0.858293i
$335$	−20.9490	+	16.2367i	−1.14457	+	0.887106i
$336$	−16.5749	+	3.10206i	−0.904233	+	0.169231i
$337$	−6.70257	−	14.0172i	−0.365112	−	0.763568i	0.634847	−	0.772638i	$-0.281063\pi$
$337$	−6.70257	−	14.0172i	−0.365112	−	0.763568i	−0.999959	+	0.00907068i	$0.997113\pi$
$338$	−1.34338	−	13.8112i	−0.0730705	−	0.751230i
$339$	−5.38782	−	8.00770i	−0.292626	−	0.434918i
$340$	1.63677	+	0.0635142i	0.0887665	+	0.00344454i
$341$	−3.89540	−	2.56204i	−0.210948	−	0.138742i
$342$	13.4287	−	24.4277i	0.726140	−	1.32090i
$343$	21.4647	+	10.7800i	1.15898	+	0.582064i
$344$	−0.0911364	−	4.69897i	−0.00491375	−	0.253351i
$345$	36.7547	+	18.8709i	1.97881	+	1.01598i
$346$	−3.62236	−	2.80754i	−0.194739	−	0.150934i
$347$	29.9331	−	4.68146i	1.60689	−	0.251314i	0.713523	−	0.700632i	$-0.247098\pi$
$347$	29.9331	−	4.68146i	1.60689	−	0.251314i	0.893372	+	0.449318i	$0.148333\pi$
$348$	3.28724	−	0.883579i	0.176215	−	0.0473648i
$349$	1.30803	−	2.73551i	0.0700172	−	0.146429i	−0.864183	−	0.503177i	$-0.832164\pi$
$349$	1.30803	−	2.73551i	0.0700172	−	0.146429i	0.934200	+	0.356749i	$0.116115\pi$
$350$	−18.3431	−	6.67633i	−0.980478	−	0.356865i
$351$	2.60266	+	4.38505i	0.138920	+	0.234057i
$352$	5.72973	−	2.08545i	0.305395	−	0.111155i
$353$	0.855468	−	8.79498i	0.0455320	−	0.468109i	−0.944625	−	0.328151i	$-0.893575\pi$
$353$	0.855468	−	8.79498i	0.0455320	−	0.468109i	0.990157	−	0.139959i	$-0.0446970\pi$
$354$	0.136435	−	4.81905i	0.00725145	−	0.256130i
$355$	6.87045	+	20.0797i	0.364646	+	1.06572i
$356$	−9.00460	+	8.17124i	−0.477243	+	0.433075i
$357$	1.03389	+	6.18534i	0.0547195	+	0.327363i
$358$	3.23324	−	9.44950i	0.170882	−	0.499421i
$359$	1.94357	+	4.50570i	0.102578	+	0.237802i	0.961774	−	0.273844i	$-0.0882952\pi$
$359$	1.94357	+	4.50570i	0.102578	+	0.237802i	−0.859196	+	0.511646i	$0.829036\pi$
$360$	−13.3063	−	24.0262i	−0.701306	−	1.26629i
$361$	−45.6548	+	5.33628i	−2.40288	+	0.280857i
$362$	1.72430	−	0.552875i	0.0906273	−	0.0290585i
$363$	−1.78617	−	14.0068i	−0.0937494	−	0.735169i
$364$	−2.79754	+	0.778748i	−0.146631	+	0.0408175i
$365$	43.1738	−	12.0183i	2.25982	−	0.629064i
$366$	−0.560891	−	4.39843i	−0.0293183	−	0.229909i
$367$	9.01293	−	2.88988i	0.470471	−	0.150850i	−0.0606276	−	0.998160i	$-0.519310\pi$
$367$	9.01293	−	2.88988i	0.470471	−	0.150850i	0.531099	+	0.847310i	$0.321779\pi$
$368$	17.5927	−	2.05630i	0.917085	−	0.107192i
$369$	13.5803	−	22.5826i	0.706964	−	1.17560i
$370$	4.05836	+	9.40832i	0.210984	+	0.489116i
$371$	10.0855	−	29.4761i	0.523615	−	1.53032i
$372$	−0.529408	−	3.16721i	−0.0274485	−	0.164212i
$373$	−1.11071	+	1.00791i	−0.0575102	+	0.0521877i	−0.700256	−	0.713892i	$-0.746931\pi$
$373$	−1.11071	+	1.00791i	−0.0575102	+	0.0521877i	0.642746	+	0.766079i	$0.277795\pi$
$374$	0.517076	+	1.51121i	0.0267374	+	0.0781429i
$375$	−0.169093	+	5.97257i	−0.00873193	+	0.308422i
$376$	0.846131	−	8.69899i	0.0436359	−	0.448616i
$377$	−2.70083	+	0.983022i	−0.139100	+	0.0506282i
$378$	20.0297	−	17.2224i	1.03022	−	0.885827i
$379$	5.26683	+	1.91697i	0.270539	+	0.0984681i	0.473727	−	0.880672i	$-0.342908\pi$
$379$	5.26683	+	1.91697i	0.270539	+	0.0984681i	−0.203189	+	0.979140i	$0.565130\pi$
$380$	−6.93682	+	14.5071i	−0.355851	+	0.744200i
$381$	15.9470	−	4.28641i	0.816991	−	0.219599i
$382$	12.9164	−	2.02008i	0.660858	−	0.103356i
$383$	−13.3540	−	10.3501i	−0.682359	−	0.528868i	0.211409	−	0.977398i	$-0.432195\pi$
$383$	−13.3540	−	10.3501i	−0.682359	−	0.528868i	−0.893768	+	0.448530i	$0.851948\pi$
$384$	−4.10719	−	2.10875i	−0.209594	−	0.107612i
$385$	0.429038	+	22.1211i	0.0218658	+	1.12739i
$386$	12.2078	+	6.13100i	0.621362	+	0.312060i
$387$	2.37211	+	3.91666i	0.120581	+	0.199095i
$388$	−7.54799	−	4.96439i	−0.383191	−	0.252029i
$389$	7.54227	+	0.292674i	0.382408	+	0.0148392i	0.229263	−	0.973365i	$-0.426368\pi$
$389$	7.54227	+	0.292674i	0.382408	+	0.0148392i	0.153145	+	0.988204i	$0.451060\pi$
$390$	3.25225	+	4.83368i	0.164684	+	0.244763i
$391$	−0.637713	−	6.55626i	−0.0322505	−	0.331565i
$392$	16.5333	+	34.5765i	0.835059	+	1.74638i
$393$	−3.16919	+	0.593128i	−0.159865	+	0.0299194i
$394$	1.20645	−	0.935071i	0.0607802	−	0.0471082i
$395$	−31.0935	+	32.9572i	−1.56449	+	1.65826i
$396$	−2.17948	+	2.60569i	−0.109523	+	0.130941i
$397$	1.08387	−	3.62038i	0.0543980	−	0.181702i	−0.926473	−	0.376362i	$-0.877175\pi$
$397$	1.08387	−	3.62038i	0.0543980	−	0.181702i	0.980871	+	0.194660i	$0.0623602\pi$
$398$	−10.5580	+	13.0899i	−0.529226	+	0.656137i
$399$	−59.7756	−	14.7309i	−2.99252	−	0.737467i
$400$	−4.51998	−	7.17144i	−0.225999	−	0.358572i
$401$	16.2467	−	8.96455i	0.811322	−	0.447668i	−0.0224700	−	0.999748i	$-0.507153\pi$
$401$	16.2467	−	8.96455i	0.811322	−	0.447668i	0.833792	+	0.552079i	$0.186165\pi$
$402$	−3.61316	−	17.4295i	−0.180208	−	0.869303i
$403$	0.676334	+	2.62569i	0.0336906	+	0.130795i
$404$	−2.09806	+	3.63394i	−0.104382	+	0.180795i
$405$	22.9531	+	13.7541i	1.14055	+	0.683448i
$406$	7.44457	+	12.8944i	0.369468	+	0.639937i
$407$	3.60153	−	3.53236i	0.178521	−	0.175092i
$408$	−2.07518	+	3.85589i	−0.102736	+	0.190895i
$409$	0.402162	−	20.7354i	0.0198857	−	1.02530i	−0.848436	−	0.529298i	$-0.822455\pi$
$409$	0.402162	−	20.7354i	0.0198857	−	1.02530i	0.868322	−	0.496001i	$-0.165199\pi$
$410$	14.0310	−	26.6372i	0.692943	−	1.31552i
$411$	11.8411	+	7.94005i	0.584076	+	0.391654i
$412$	2.27032	+	5.88029i	0.111851	+	0.289701i
$413$	−10.3603	+	2.45544i	−0.509797	+	0.120824i
$414$	−22.2307	+	16.6044i	−1.09258	+	0.816063i
$415$	5.28455	+	17.6516i	0.259408	+	0.866484i
$416$	−3.28255	−	1.34107i	−0.160940	−	0.0657513i
$417$	−0.171309	−	16.3440i	−0.00838902	−	0.800371i
$418$	−15.6328	−	1.21508i	−0.764627	−	0.0594315i
$419$	−27.7754	+	19.8527i	−1.35692	+	0.969867i	−0.357566	+	0.933888i	$0.616393\pi$
$419$	−27.7754	+	19.8527i	−1.35692	+	0.969867i	−0.999353	+	0.0359789i	$0.988545\pi$
$420$	−10.9738	+	10.5728i	−0.535464	+	0.515898i
$421$	2.44111	−	3.87308i	0.118972	−	0.188762i	−0.781219	−	0.624257i	$-0.785402\pi$
$421$	2.44111	−	3.87308i	0.118972	−	0.188762i	0.900191	+	0.435495i	$0.143427\pi$
$422$	1.36671	−	23.4655i	0.0665303	−	1.14228i
$423$	3.53587	+	7.74644i	0.171920	+	0.376645i
$424$	18.1745	−	11.9536i	0.882633	−	0.580517i
$425$	−2.69912	+	1.62893i	−0.130927	+	0.0790147i
$426$	−14.1410	−	1.78073i	−0.685136	−	0.0862765i
$427$	−9.06536	+	3.70361i	−0.438704	+	0.179230i
$428$	1.03399	+	1.28194i	0.0499796	+	0.0619650i
$429$	1.64337	−	2.35089i	0.0793425	−	0.113502i
$430$	2.95898	+	4.31430i	0.142695	+	0.208054i
$431$	−5.23573	−	29.6933i	−0.252196	−	1.43028i	−0.803169	−	0.595752i	$-0.796854\pi$
$431$	−5.23573	−	29.6933i	−0.252196	−	1.43028i	0.550972	−	0.834523i	$-0.314257\pi$
$432$	11.4568	−	0.582914i	0.551213	−	0.0280455i
$433$	−1.56645	+	8.88378i	−0.0752788	+	0.426927i	0.923755	+	0.382983i	$0.125103\pi$
$433$	−1.56645	+	8.88378i	−0.0752788	+	0.426927i	−0.999034	+	0.0439438i	$0.986008\pi$
$434$	12.7869	−	5.81237i	0.613792	−	0.279003i
$435$	−10.0178	+	11.2747i	−0.480316	+	0.540580i
$436$	8.75831	+	1.72008i	0.419447	+	0.0823767i
$437$	61.5787	+	19.7444i	2.94571	+	0.944503i
$438$	−5.49027	+	29.5923i	−0.262335	+	1.41398i
$439$	25.3462	+	29.0435i	1.20971	+	1.38617i	0.900316	+	0.435236i	$0.143335\pi$
$439$	25.3462	+	29.0435i	1.20971	+	1.38617i	0.309391	+	0.950935i	$0.399875\pi$
$440$	−9.22550	+	12.3920i	−0.439808	+	0.590765i
$441$	−30.8268	−	21.0716i	−1.46794	−	1.00341i
$442$	0.367901	−	0.852890i	0.0174993	−	0.0405678i
$443$	−5.92018	−	5.37228i	−0.281276	−	0.255245i	0.519140	−	0.854689i	$-0.326252\pi$
$443$	−5.92018	−	5.37228i	−0.281276	−	0.255245i	−0.800416	+	0.599445i	$0.795388\pi$
$444$	3.47046	+	0.165655i	0.164701	+	0.00786163i
$445$	13.4391	−	52.1736i	0.637072	−	2.47327i
$446$	2.76829	+	2.71512i	0.131082	+	0.128565i
$447$	4.07866	−	1.26780i	0.192914	−	0.0599648i
$448$	−8.01096	+	36.9827i	−0.378482	+	1.74727i
$449$	5.48268	+	7.36451i	0.258743	+	0.347553i	0.912445	−	0.409200i	$-0.134192\pi$
$449$	5.48268	+	7.36451i	0.258743	+	0.347553i	−0.653701	+	0.756753i	$0.726785\pi$
$450$	11.7589	+	6.17040i	0.554321	+	0.290875i
$451$	−14.7225	−	1.72081i	−0.693254	−	0.0810297i
$452$	−3.66902	+	0.720572i	−0.172576	+	0.0338928i
$453$	−1.24170	−	2.19564i	−0.0583401	−	0.103160i
$454$	4.46347	+	20.6057i	0.209481	+	0.967072i
$455$	8.46018	−	9.69429i	0.396619	−	0.454475i
$456$	−26.6886	−	33.6989i	−1.24981	−	1.57809i
$457$	15.9466	+	11.3980i	0.745952	+	0.533175i	0.889759	−	0.456431i	$-0.150873\pi$
$457$	15.9466	+	11.3980i	0.745952	+	0.533175i	−0.143806	+	0.989606i	$0.545934\pi$
$458$	−22.7053	−	19.0520i	−1.06095	−	0.890241i
$459$	−0.134121	−	4.26412i	−0.00626025	−	0.199032i
$460$	12.2616	−	10.2887i	0.571698	−	0.479711i
$461$	−9.85731	+	0.766171i	−0.459101	+	0.0356841i	−0.304961	−	0.952365i	$-0.598643\pi$
$461$	−9.85731	+	0.766171i	−0.459101	+	0.0356841i	−0.154140	+	0.988049i	$0.549261\pi$
$462$	−13.4717	−	6.26910i	−0.626761	−	0.291665i
$463$	0.120633	−	0.312446i	0.00560627	−	0.0145206i	−0.930052	−	0.367427i	$-0.880239\pi$
$463$	0.120633	−	0.312446i	0.00560627	−	0.0145206i	0.935659	+	0.352907i	$0.114807\pi$
$464$	−0.875035	+	6.40639i	−0.0406225	+	0.297409i
$465$	9.67133	+	10.4358i	0.448497	+	0.483947i
$466$	14.7831	+	8.15700i	0.684816	+	0.377866i
$467$	−1.25570	−	21.5595i	−0.0581069	−	0.997657i	−0.893802	−	0.448463i	$-0.851972\pi$
$467$	−1.25570	−	21.5595i	−0.0581069	−	0.997657i	0.835695	−	0.549194i	$-0.185065\pi$
$468$	1.95692	−	0.270420i	0.0904585	−	0.0125002i
$469$	−35.1305	+	17.6432i	−1.62217	+	0.814686i
$470$	4.53402	+	8.60762i	0.209139	+	0.397040i
$471$	−5.71981	+	2.53872i	−0.263555	+	0.116978i
$472$	−6.76809	−	3.07648i	−0.311527	−	0.141606i
$473$	1.45682	−	2.12410i	0.0669848	−	0.0976662i
$474$	−10.7066	−	28.4837i	−0.491770	−	1.30830i
$475$	−4.18834	−	30.6641i	−0.192174	−	1.40696i
$476$	2.36403	+	0.560285i	0.108355	+	0.0256806i
$477$	−9.48201	+	18.9543i	−0.434151	+	0.867860i
$478$	7.56911	+	8.02279i	0.346203	+	0.366954i
$479$	−35.9589	−	5.62387i	−1.64301	−	0.256961i	−0.735661	−	0.677350i	$-0.763128\pi$
$479$	−35.9589	−	5.62387i	−1.64301	−	0.256961i	−0.907344	+	0.420389i	$0.861894\pi$
$480$	−18.5001	+	1.99540i	−0.844408	+	0.0910771i
$481$	−2.93148	+	0.113755i	−0.133664	+	0.00518677i
$482$	14.3958	+	8.68793i	0.655712	+	0.395724i
$483$	48.0993	+	37.9707i	2.18860	+	1.72773i
$484$	−5.26998	−	1.46700i	−0.239544	−	0.0666818i
$485$	40.0293			1.81764
$486$	−15.0710	+	9.78818i	−0.683634	+	0.444001i
$487$	8.30429			0.376303			0.188152	−	0.982140i	$-0.439750\pi$
$487$	8.30429			0.376303			0.188152	+	0.982140i	$0.439750\pi$
$488$	−6.58733	−	1.83371i	−0.298194	−	0.0830081i
$489$	−28.2967	+	11.2673i	−1.27962	+	0.509524i
$490$	−36.5255	−	22.0432i	−1.65005	−	0.995812i
$491$	−9.90733	+	0.384449i	−0.447111	+	0.0173500i	−0.261348	−	0.965245i	$-0.584167\pi$
$491$	−9.90733	+	0.384449i	−0.447111	+	0.0173500i	−0.185763	+	0.982595i	$0.559476\pi$
$492$	−6.02308	−	8.24275i	−0.271542	−	0.371612i
$493$	2.37575	+	0.371561i	0.106998	+	0.0167342i
$494$	6.25755	+	6.63261i	0.281540	+	0.298415i
$495$	1.72393	−	14.9526i	0.0774848	−	0.672071i
$496$	5.93528	+	1.40669i	0.266502	+	0.0631622i
$497$	4.25990	+	31.1880i	0.191083	+	1.39897i
$498$	−12.2083	−	2.02095i	−0.547066	−	0.0905610i
$499$	6.95378	−	10.1389i	0.311294	−	0.453878i	−0.637188	−	0.770708i	$-0.719903\pi$
$499$	6.95378	−	10.1389i	0.311294	−	0.453878i	0.948482	+	0.316830i	$0.102619\pi$
$500$	2.10728	+	0.957876i	0.0942404	+	0.0428375i
$501$	26.1906	+	19.0748i	1.17011	+	0.852199i
$502$	−11.7218	−	22.2533i	−0.523170	−	0.993214i
$503$	−10.2569	+	5.15119i	−0.457330	+	0.229680i	−0.662523	−	0.749042i	$-0.730514\pi$
$503$	−10.2569	+	5.15119i	−0.457330	+	0.229680i	0.205192	+	0.978722i	$0.434218\pi$
$504$	−12.4987	−	38.7715i	−0.556737	−	1.72702i
$505$	−1.08105	−	18.5609i	−0.0481061	−	0.825949i
$506$	13.6656	+	7.54034i	0.607509	+	0.335209i
$507$	20.3287	−	4.62704i	0.902828	−	0.205494i
$508$	0.865761	−	6.33849i	0.0384119	−	0.281225i
$509$	2.39693	−	6.20821i	0.106242	−	0.275174i	−0.869561	−	0.493826i	$-0.835598\pi$
$509$	2.39693	−	6.20821i	0.106242	−	0.275174i	0.975803	+	0.218652i	$0.0701659\pi$
$510$	−0.428624	−	4.85531i	−0.0189798	−	0.214997i
$511$	66.2710	−	5.15099i	2.93165	−	0.227866i
$512$	−16.5259	+	13.8669i	−0.730347	+	0.612834i
$513$	38.9589	+	15.3713i	1.72008	+	0.678658i
$514$	−1.24642	−	1.04587i	−0.0549770	−	0.0461312i
$515$	−22.7218	−	16.2406i	−1.00124	−	0.715646i
$516$	1.75502	−	0.258479i	0.0772604	−	0.0113789i
$517$	3.14942	−	3.60884i	0.138511	−	0.158716i
$518$	3.21737	+	14.8530i	0.141363	+	0.652604i
$519$	3.49586	−	5.93229i	0.153451	−	0.260399i
$520$	8.81584	−	1.73138i	0.386600	−	0.0759258i
$521$	−6.22438	−	0.727526i	−0.272695	−	0.0318735i	−0.0213537	−	0.999772i	$-0.506798\pi$
$521$	−6.22438	−	0.727526i	−0.272695	−	0.0318735i	−0.251341	+	0.967898i	$0.580872\pi$
$522$	−3.84550	−	9.37064i	−0.168313	−	0.410142i
$523$	−20.6587	−	27.7494i	−0.903341	−	1.21340i	−0.976378	−	0.216068i	$-0.930677\pi$
$523$	−20.6587	−	27.7494i	−0.903341	−	1.21340i	0.0730374	−	0.997329i	$-0.476731\pi$
$524$	−0.264439	+	1.22079i	−0.0115521	+	0.0533303i
$525$	6.46410	−	28.6071i	0.282116	−	1.24851i
$526$	12.5113	+	12.2710i	0.545521	+	0.535043i
$527$	0.565846	−	2.19675i	0.0246486	−	0.0956919i
$528$	−2.95627	−	5.73573i	−0.128655	−	0.249616i
$529$	−30.6357	−	27.8004i	−1.33199	−	1.20871i
$530$	−9.59067	+	22.2337i	−0.416592	+	0.965769i
$531$	7.20817	−	0.712545i	0.312808	−	0.0309218i
$532$	−14.2426	+	19.1311i	−0.617494	+	0.829438i
$533$	5.66785	+	6.49464i	0.245502	+	0.281314i
$534$	27.5092	+	23.5039i	1.19044	+	1.01711i
$535$	−6.94899	−	2.22811i	−0.300431	−	0.0963294i
$536$	−26.9351	−	5.28989i	−1.16342	−	0.228488i
$537$	14.6979	+	3.02284i	0.634260	+	0.130445i
$538$	−29.6921	+	13.4967i	−1.28012	+	0.581886i
$539$	−3.64730	+	20.6849i	−0.157100	+	0.890961i
$540$	8.36048	−	6.12926i	0.359778	−	0.263761i
$541$	2.06247	+	11.6969i	0.0886726	+	0.502888i	0.996504	+	0.0835510i	$0.0266261\pi$
$541$	2.06247	+	11.6969i	0.0886726	+	0.502888i	−0.907831	+	0.419337i	$0.862263\pi$
$542$	−18.6683	−	27.2190i	−0.801872	−	1.16916i
$543$	1.15171	+	2.46479i	0.0494245	+	0.105774i
$544$	1.86250	+	2.30914i	0.0798540	+	0.0990035i
$545$	−36.6106	+	14.9571i	−1.56823	+	0.640691i
$546$	3.35173	+	7.96460i	0.143441	+	0.340854i
$547$	−25.3996	+	15.3287i	−1.08601	+	0.655409i	−0.942488	−	0.334239i	$-0.891521\pi$
$547$	−25.3996	+	15.3287i	−1.08601	+	0.655409i	−0.143519	+	0.989648i	$0.545842\pi$
$548$	4.61459	−	3.03506i	0.197125	−	0.129651i
$549$	6.44874	−	1.67189i	0.275226	−	0.0713544i
$550$	0.434327	−	7.45711i	0.0185198	−	0.317972i
$551$	−12.5870	+	19.9706i	−0.536223	+	0.850776i
$552$	10.3037	+	41.5303i	0.438556	+	1.76765i
$553$	−54.6742	+	39.0788i	−2.32498	+	1.66180i
$554$	−15.3188	−	1.19067i	−0.650832	−	0.0505867i
$555$	−13.2507	+	7.83660i	−0.562461	+	0.332645i
$556$	−5.86188	−	2.39484i	−0.248599	−	0.101564i
$557$	7.35999	+	24.5841i	0.311853	+	1.04166i	0.959966	+	0.280116i	$0.0903731\pi$
$557$	7.35999	+	24.5841i	0.311853	+	1.04166i	−0.648113	+	0.761544i	$0.724442\pi$
$558$	−9.14966	+	2.75488i	−0.387336	+	0.116623i
$559$	−1.45749	+	0.345432i	−0.0616454	+	0.0146102i
$560$	−10.4256	−	27.0030i	−0.440563	−	1.14109i
$561$	−2.15401	+	1.05785i	−0.0909425	+	0.0446627i
$562$	−0.394897	+	0.749694i	−0.0166577	+	0.0316239i
$563$	−0.797749	+	41.1317i	−0.0336211	+	1.73350i	0.481559	+	0.876414i	$0.340071\pi$
$563$	−0.797749	+	41.1317i	−0.0336211	+	1.73350i	−0.515180	+	0.857082i	$0.672275\pi$
$564$	3.29744	−	0.0985356i	0.138847	−	0.00414910i
$565$	11.8280	−	11.6008i	0.497606	−	0.488049i
$566$	−5.70403	−	9.87967i	−0.239758	−	0.415274i
$567$	29.4748	+	26.5787i	1.23782	+	1.11620i
$568$	−10.9896	+	19.0346i	−0.461115	+	0.798675i
$569$	−4.17261	−	16.1991i	−0.174925	−	0.679100i	−0.994372	−	0.105945i	$-0.966213\pi$
$569$	−4.17261	−	16.1991i	−0.174925	−	0.679100i	0.819447	−	0.573155i	$-0.194281\pi$
$570$	45.4331	+	15.0153i	1.90298	+	0.628922i
$571$	2.02813	−	1.11907i	0.0848744	−	0.0468317i	−0.440108	−	0.897945i	$-0.645060\pi$
$571$	2.02813	−	1.11907i	0.0848744	−	0.0468317i	0.524982	+	0.851113i	$0.324072\pi$
$572$	−0.592511	−	0.940082i	−0.0247741	−	0.0393068i
$573$	5.46551	+	18.8664i	0.228325	+	0.788155i
$574$	28.0348	−	34.7576i	1.17015	−	1.45076i
$575$	−8.83537	+	29.5122i	−0.368460	+	1.23074i
$576$	8.76652	−	24.2040i	0.365272	−	1.00850i
$577$	−3.62204	+	3.83914i	−0.150788	+	0.159825i	−0.798364	−	0.602175i	$-0.794301\pi$
$577$	−3.62204	+	3.83914i	−0.150788	+	0.159825i	0.647577	+	0.762000i	$0.275783\pi$
$578$	14.8758	−	11.5296i	0.618751	−	0.479568i
$579$	−6.81739	+	19.3596i	−0.283321	+	0.804557i
$580$	2.52060	+	5.27140i	0.104662	+	0.218883i
$581$	2.64577	+	27.2009i	0.109765	+	1.12848i
$582$	−11.8126	+	24.1487i	−0.489650	+	1.00100i
$583$	11.9125	+	0.462260i	0.493367	+	0.0191449i
$584$	38.7778	+	25.5046i	1.60464	+	1.05539i
$585$	−6.58593	+	5.76576i	−0.272295	+	0.238385i
$586$	9.57627	+	4.80938i	0.395592	+	0.198674i
$587$	−0.697115	−	35.9431i	−0.0287730	−	1.48353i	−0.684766	−	0.728763i	$-0.740096\pi$
$587$	−0.697115	−	35.9431i	−0.0287730	−	1.48353i	0.655993	−	0.754767i	$-0.272250\pi$
$588$	−12.1566	+	7.84123i	−0.501330	+	0.323367i
$589$	17.6016	+	13.6423i	0.725261	+	0.562120i
$590$	8.17612	−	1.27872i	0.336606	−	0.0526442i
$591$	1.62291	+	1.62036i	0.0667574	+	0.0666527i
$592$	−2.84705	+	5.95410i	−0.117013	+	0.244712i
$593$	−13.2609	−	4.82656i	−0.544558	−	0.198203i	0.0550690	−	0.998483i	$-0.482462\pi$
$593$	−13.2609	−	4.82656i	−0.544558	−	0.198203i	−0.599627	+	0.800280i	$0.704684\pi$
$594$	8.51183	+	5.45252i	0.349245	+	0.223720i
$595$	−10.1156	+	3.68178i	−0.414700	+	0.150938i
$596$	0.160192	−	1.64692i	0.00656173	−	0.0674605i
$597$	−21.5156	−	13.2477i	−0.880573	−	0.542192i
$598$	−2.93841	−	8.58783i	−0.120161	−	0.351183i
$599$	17.9699	−	16.3068i	0.734229	−	0.666278i	−0.216506	−	0.976281i	$-0.569466\pi$
$599$	17.9699	−	16.3068i	0.734229	−	0.666278i	0.950735	+	0.310004i	$0.100330\pi$
$600$	15.8042	−	13.0230i	0.645202	−	0.531663i
$601$	11.8821	−	34.7269i	0.484683	−	1.41654i	−0.384995	−	0.922919i	$-0.625797\pi$
$601$	11.8821	−	34.7269i	0.484683	−	1.41654i	0.869678	−	0.493620i	$-0.164327\pi$
$602$	3.07337	+	7.12487i	0.125261	+	0.290388i
$603$	25.2899	−	8.69755i	1.02988	−	0.354192i
$604$	−0.970610	+	0.113448i	−0.0394936	+	0.00461614i
$605$	23.0809	−	7.40058i	0.938371	−	0.300877i
$606$	11.5164	+	4.82515i	0.467820	+	0.196008i
$607$	−25.7042	+	7.15526i	−1.04330	+	0.290423i	−0.747107	−	0.664704i	$-0.768558\pi$
$607$	−25.7042	+	7.15526i	−1.04330	+	0.290423i	−0.296196	+	0.955127i	$0.595718\pi$
$608$	−28.0569	+	7.81017i	−1.13786	+	0.316744i
$609$	−17.8027	+	13.5459i	−0.721402	+	0.548908i
$610$	7.24785	−	2.32393i	0.293457	−	0.0940932i
$611$	−2.76666	+	0.323377i	−0.111927	+	0.0130824i
$612$	−1.54279	−	0.592876i	−0.0623636	−	0.0239656i
$613$	3.53659	+	8.19873i	0.142841	+	0.331143i	0.974586	−	0.224016i	$-0.0719167\pi$
$613$	3.53659	+	8.19873i	0.142841	+	0.331143i	−0.831744	+	0.555159i	$0.812657\pi$
$614$	−11.9400	+	34.8960i	−0.481860	+	1.40829i
$615$	42.3664	+	15.8491i	1.70838	+	0.639096i
$616$	−16.9690	+	15.3985i	−0.683699	+	0.620424i
$617$	−9.41979	−	27.5304i	−0.379227	−	1.10833i	−0.956488	−	0.291772i	$-0.905755\pi$
$617$	−9.41979	−	27.5304i	−0.379227	−	1.10833i	0.577261	−	0.816559i	$-0.304121\pi$
$618$	16.5028	−	8.91494i	0.663839	−	0.358611i
$619$	−2.29438	+	23.5883i	−0.0922190	+	0.948094i	0.829052	+	0.559172i	$0.188881\pi$
$619$	−2.29438	+	23.5883i	−0.0922190	+	0.948094i	−0.921271	+	0.388922i	$0.872847\pi$
$620$	5.17972	−	1.88526i	0.208022	−	0.0757140i
$621$	−28.9720	−	29.9765i	−1.16261	−	1.20291i
$622$	−15.8310	−	5.76200i	−0.634763	−	0.231035i
$623$	34.4724	−	72.0928i	1.38111	−	2.88834i
$624$	−0.968389	+	3.62545i	−0.0387666	+	0.145134i
$625$	−29.1013	+	4.55137i	−1.16405	+	0.182055i
$626$	−5.08072	−	3.93786i	−0.203066	−	0.157388i
$627$	−1.16016	−	23.5298i	−0.0463324	−	0.939691i
$628$	0.0470120	+	2.42392i	0.00187598	+	0.0967251i
$629$	2.19336	+	1.10154i	0.0874548	+	0.0439215i
$630$	35.3392	+	28.4124i	1.40795	+	1.13198i
$631$	−6.16166	−	4.05258i	−0.245292	−	0.161331i	0.420910	−	0.907102i	$-0.361711\pi$
$631$	−6.16166	−	4.05258i	−0.245292	−	0.161331i	−0.666202	+	0.745771i	$0.732081\pi$
$632$	−46.8903	−	1.81956i	−1.86520	−	0.0723781i
$633$	35.2323	−	2.42281i	1.40036	−	0.0962981i
$634$	2.85408	+	29.3425i	0.113350	+	1.16534i
$635$	12.2279	+	25.5725i	0.485250	+	1.01481i
$636$	5.34337	+	6.23410i	0.211878	+	0.247198i
$637$	9.65442	−	7.48274i	0.382522	−	0.296477i
$638$	−3.90991	+	4.14426i	−0.154795	+	0.164073i
$639$	−0.0336099	−	21.4140i	−0.00132959	−	0.847125i
$640$	2.27297	−	7.59226i	0.0898471	−	0.300110i
$641$	21.3314	−	26.4468i	0.842540	−	1.04459i	−0.155845	−	0.987781i	$-0.549810\pi$
$641$	21.3314	−	26.4468i	0.842540	−	1.04459i	0.998385	−	0.0568044i	$-0.0180912\pi$
$642$	3.39481	−	3.53465i	0.133982	−	0.139501i
$643$	−1.41466	−	2.24451i	−0.0557888	−	0.0885149i	0.816934	−	0.576732i	$-0.195672\pi$
$643$	−1.41466	−	2.24451i	−0.0557888	−	0.0885149i	−0.872722	+	0.488217i	$0.837648\pi$
$644$	20.7865	−	11.4695i	0.819102	−	0.451961i
$645$	−5.86759	+	5.22997i	−0.231036	+	0.205930i
$646$	−1.90297	−	7.38778i	−0.0748714	−	0.290669i
$647$	0.427119	−	0.739791i	0.0167918	−	0.0290842i	−0.857507	−	0.514472i	$-0.827988\pi$
$647$	0.427119	−	0.739791i	0.0167918	−	0.0290842i	0.874299	+	0.485387i	$0.161321\pi$
$648$	4.89791	+	27.2764i	0.192408	+	1.07152i
$649$	−2.03718	−	3.52850i	−0.0799663	−	0.138506i
$650$	−3.10129	+	3.04173i	−0.121643	+	0.119306i
$651$	11.0929	+	17.9528i	0.434764	+	0.703624i
$652$	−0.228809	+	11.7973i	−0.00896086	+	0.462020i
$653$	3.05339	−	5.79673i	0.119489	−	0.226843i	−0.817717	−	0.575620i	$-0.804761\pi$
$653$	3.05339	−	5.79673i	0.119489	−	0.226843i	0.937206	+	0.348777i	$0.113403\pi$
$654$	1.78054	−	26.5001i	0.0696247	−	1.03624i
$655$	−1.99343	−	5.16311i	−0.0778897	−	0.201739i
$656$	18.8694	−	4.47212i	0.736725	−	0.174607i
$657$	−45.1473	−	2.55844i	−1.76137	−	0.0998142i
$658$	4.13852	+	13.8236i	0.161336	+	0.538901i
$659$	23.3914	+	9.55644i	0.911200	+	0.372266i	0.784826	−	0.619717i	$-0.212752\pi$
$659$	23.3914	+	9.55644i	0.911200	+	0.372266i	0.126374	+	0.991983i	$0.459666\pi$
$660$	−5.08024	−	2.86251i	−0.197748	−	0.111423i
$661$	−16.3929	−	1.27415i	−0.637609	−	0.0495589i	−0.245380	−	0.969427i	$-0.578913\pi$
$661$	−16.3929	−	1.27415i	−0.637609	−	0.0495589i	−0.392228	+	0.919868i	$0.628296\pi$
$662$	−16.2187	+	11.5924i	−0.630358	+	0.450552i
$663$	1.34105	+	0.386217i	0.0520822	+	0.0149994i
$664$	−10.1750	+	16.1437i	−0.394866	+	0.626498i
$665$	6.14464	−	105.499i	0.238279	−	4.09109i
$666$	−0.817353	−	10.3064i	−0.0316718	−	0.399365i
$667$	19.6320	−	12.9122i	0.760155	−	0.499962i
$668$	10.7469	−	6.48578i	0.415810	−	0.250942i
$669$	−3.52044	+	4.64184i	−0.136108	+	0.179464i
$670$	28.2854	−	11.5558i	1.09276	−	0.446441i
$671$	−2.35263	−	2.91680i	−0.0908222	−	0.112602i
$672$	−27.4956	−	2.38381i	−1.06066	−	0.0919575i
$673$	12.5074	+	18.2362i	0.482124	+	0.702954i	0.987087	−	0.160187i	$-0.0512099\pi$
$673$	12.5074	+	18.2362i	0.482124	+	0.702954i	−0.504963	+	0.863141i	$0.668494\pi$
$674$	3.11032	+	17.6395i	0.119805	+	0.679449i
$675$	−6.96141	+	18.6980i	−0.267945	+	0.719688i
$676$	1.40255	−	7.95428i	0.0539444	−	0.305934i
$677$	−5.62180	+	2.55542i	−0.216063	+	0.0982129i	−0.518918	−	0.854824i	$-0.673665\pi$
$677$	−5.62180	+	2.55542i	−0.216063	+	0.0982129i	0.302855	+	0.953037i	$0.402060\pi$
$678$	3.50804	+	10.5589i	0.134726	+	0.405513i
$679$	58.2592	+	11.4417i	2.23578	+	0.439093i
$680$	−7.15762	−	2.29500i	−0.274482	−	0.0880092i
$681$	−29.8620	+	10.5685i	−1.14432	+	0.404985i
$682$	3.53412	+	4.04965i	0.135328	+	0.155069i
$683$	3.83270	−	5.14821i	0.146654	−	0.196991i	−0.722726	−	0.691135i	$-0.757111\pi$
$683$	3.83270	−	5.14821i	0.146654	−	0.196991i	0.869380	+	0.494144i	$0.164518\pi$
$684$	11.3431	−	11.6016i	0.433715	−	0.443599i
$685$	−9.69309	+	22.4711i	−0.370354	+	0.858577i
$686$	−20.5058	−	18.6080i	−0.782915	−	0.710457i
$687$	24.0795	−	37.4605i	0.918691	−	1.42921i
$688$	−0.840538	+	3.26317i	−0.0320452	+	0.124407i
$689$	−4.94958	−	4.85451i	−0.188564	−	0.184942i
$690$	−34.9854	−	32.3207i	−1.33187	−	1.23043i
$691$	−4.72492	+	21.8127i	−0.179745	+	0.829793i	0.795024	+	0.606577i	$0.207458\pi$
$691$	−4.72492	+	21.8127i	−0.179745	+	0.829793i	−0.974769	+	0.223216i	$0.928345\pi$
$692$	−1.59298	−	2.13975i	−0.0605562	−	0.0813411i
$693$	6.78299	−	21.2695i	0.257665	−	0.807961i
$694$	−34.6907	−	4.05476i	−1.31684	−	0.153917i
$695$	27.5311	−	5.40694i	1.04432	−	0.205097i
$696$	−15.6194	−	0.139197i	−0.592054	−	0.00527623i
$697$	−1.52677	−	7.04837i	−0.0578306	−	0.266976i
$698$	−2.29838	+	2.63365i	−0.0869948	+	0.0996850i
$699$	−9.34744	+	23.5828i	−0.353553	+	0.891985i
$700$	−9.24367	−	6.60698i	−0.349378	−	0.249720i
$701$	−21.8028	−	18.2948i	−0.823482	−	0.690983i	0.130303	−	0.991474i	$-0.458405\pi$
$701$	−21.8028	−	18.2948i	−0.823482	−	0.690983i	−0.953785	+	0.300491i	$0.902849\pi$
$702$	−1.53483	−	5.67461i	−0.0579286	−	0.214174i
$703$	−18.4579	+	15.4881i	−0.696155	+	0.584143i
$704$	−14.4367	+	1.12211i	−0.544104	+	0.0422911i
$705$	−11.9669	+	8.39335i	−0.450701	+	0.316112i
$706$	−3.66907	+	9.50314i	−0.138087	+	0.357655i
$707$	3.73196	−	27.3228i	0.140355	−	1.02758i
$708$	0.828733	−	2.68097i	0.0311457	−	0.100757i
$709$	−39.7597	−	21.9385i	−1.49321	−	0.823916i	−0.494237	−	0.869327i	$-0.664553\pi$
$709$	−39.7597	−	21.9385i	−1.49321	−	0.823916i	−0.998968	+	0.0454110i	$0.985540\pi$
$710$	−1.42255	−	24.4243i	−0.0533874	−	0.916627i
$711$	40.4167	−	21.3704i	1.51575	−	0.801452i
$712$	49.8627	−	25.0420i	1.86869	−	0.938489i
$713$	−10.3308	−	19.6125i	−0.386891	−	0.734494i
$714$	0.763987	−	7.18900i	0.0285915	−	0.269041i
$715$	4.48233	+	2.03747i	0.167630	+	0.0761970i
$716$	3.28804	−	4.79408i	0.122880	−	0.179163i
$717$	−10.5185	+	12.8056i	−0.392820	+	0.478236i
$718$	−0.765553	−	5.60484i	−0.0285702	−	0.209171i
$719$	−15.4698	−	3.66641i	−0.576925	−	0.136734i	−0.0682137	−	0.997671i	$-0.521730\pi$
$719$	−15.4698	−	3.66641i	−0.576925	−	0.136734i	−0.508712	+	0.860937i	$0.669878\pi$
$720$	4.57128	+	19.1537i	0.170361	+	0.713817i
$721$	−28.4276	−	30.1314i	−1.05870	−	1.12215i
$722$	52.3534	+	8.18793i	1.94839	+	0.304723i
$723$	−10.2123	+	23.1065i	−0.379801	+	0.859340i
$724$	1.05320	−	0.0408688i	0.0391417	−	0.00151888i
$725$	−9.62823	−	5.81066i	−0.357583	−	0.215803i
$726$	−2.34657	+	16.1080i	−0.0870894	+	0.597826i
$727$	1.11230	+	0.309629i	0.0412528	+	0.0114835i	0.288738	−	0.957408i	$-0.406765\pi$
$727$	1.11230	+	0.309629i	0.0412528	+	0.0114835i	−0.247485	+	0.968892i	$0.579604\pi$
$728$	13.3256			0.493879
$729$	−17.4525	−	20.6013i	−0.646387	−	0.763009i
$730$	−51.6638			−1.91216
$731$	1.20727	+	0.336066i	0.0446524	+	0.0124299i
$732$	0.372052	−	2.55395i	0.0137514	−	0.0943969i
$733$	−10.6126	−	6.40472i	−0.391984	−	0.236564i	0.306987	−	0.951714i	$-0.400679\pi$
$733$	−10.6126	−	6.40472i	−0.391984	−	0.236564i	−0.698971	+	0.715150i	$0.746358\pi$
$734$	−10.9031	+	0.423089i	−0.402440	+	0.0156165i
$735$	25.9110	−	58.6264i	0.955743	−	2.16247i
$736$	28.6415	+	4.47945i	1.05574	+	0.165115i
$737$	−10.3234	−	10.9421i	−0.380266	−	0.403059i
$738$	−22.0637	+	20.8815i	−0.812175	+	0.768660i
$739$	35.1406	+	8.32848i	1.29267	+	0.306368i	0.818724	−	0.574187i	$-0.194682\pi$
$739$	35.1406	+	8.32848i	1.29267	+	0.306368i	0.473944	+	0.880555i	$0.342830\pi$
$740$	0.807121	+	5.90917i	0.0296704	+	0.217225i
$741$	−8.69586	+	10.5867i	−0.319450	+	0.388912i
$742$	−20.3135	+	29.6179i	−0.745733	+	1.08731i
$743$	−7.49504	−	3.40691i	−0.274966	−	0.124988i	0.271581	−	0.962415i	$-0.412453\pi$
$743$	−7.49504	−	3.40691i	−0.274966	−	0.124988i	−0.546548	+	0.837428i	$0.684058\pi$
$744$	−1.55720	+	14.6530i	−0.0570896	+	0.537204i
$745$	3.41689	+	6.48681i	0.125185	+	0.237658i
$746$	1.54514	−	0.775997i	0.0565715	−	0.0284113i
$747$	0.691751	−	18.5791i	0.0253098	−	0.679774i
$748$	0.0540568	+	0.928119i	0.00197651	+	0.0339354i
$749$	−9.47679	−	5.22907i	−0.346274	−	0.191066i
$750$	2.03423	−	6.58079i	0.0742797	−	0.240297i
$751$	−0.00706950	+	0.0517579i	−0.000257970	+	0.00188867i	−0.990929	−	0.134387i	$-0.957094\pi$
$751$	−0.00706950	+	0.0517579i	−0.000257970	+	0.00188867i	0.990671	+	0.136276i	$0.0435133\pi$
$752$	−2.25702	+	5.84582i	−0.0823050	+	0.213175i
$753$	30.9382	−	21.6994i	1.12745	−	0.790768i
$754$	3.30342	−	0.256762i	0.120303	−	0.00935072i
$755$	3.31690	−	2.78321i	0.120714	−	0.101291i
$756$	13.9199	−	6.53090i	0.506262	−	0.237527i
$757$	17.8487	+	14.9769i	0.648723	+	0.544343i	0.906683	−	0.421812i	$-0.138606\pi$
$757$	17.8487	+	14.9769i	0.648723	+	0.544343i	−0.257960	+	0.966156i	$0.583050\pi$
$758$	−5.25664	−	3.75722i	−0.190930	−	0.136468i
$759$	−8.64079	+	21.8000i	−0.313641	+	0.791290i
$760$	48.5185	−	55.5961i	1.75995	−	2.01668i
$761$	7.89204	+	36.4337i	0.286086	+	1.32072i	0.863533	+	0.504293i	$0.168247\pi$
$761$	7.89204	+	36.4337i	0.286086	+	1.32072i	−0.577446	+	0.816429i	$0.695951\pi$
$762$	−19.0358	−	0.169642i	−0.689593	−	0.00614547i
$763$	−57.5588	+	11.3042i	−2.08377	+	0.409239i
$764$	7.55812	+	0.883418i	0.273443	+	0.0319609i
$765$	7.15481	−	1.56159i	0.258683	−	0.0564594i
$766$	11.6310	+	15.6232i	0.420247	+	0.564489i
$767$	−0.501614	+	2.31571i	−0.0181122	+	0.0836154i
$768$	−17.9243	−	16.5591i	−0.646789	−	0.597526i
$769$	−11.1624	−	10.9480i	−0.402527	−	0.394796i	0.470553	−	0.882371i	$-0.344054\pi$
$769$	−11.1624	−	10.9480i	−0.402527	−	0.394796i	−0.873081	+	0.487575i	$0.837881\pi$
$770$	6.36232	−	24.7001i	0.229282	−	0.890128i
$771$	1.32185	−	2.05641i	0.0476054	−	0.0740597i
$772$	5.88848	+	5.34351i	0.211931	+	0.192317i
$773$	11.0914	−	25.7127i	0.398929	−	0.924822i	−0.593818	−	0.804600i	$-0.702380\pi$
$773$	11.0914	−	25.7127i	0.398929	−	0.924822i	0.992747	−	0.120222i	$-0.0383607\pi$
$774$	−1.42359	−	5.08314i	−0.0511699	−	0.182710i
$775$	−6.33518	+	8.50963i	−0.227567	+	0.305675i
$776$	27.2587	+	31.2350i	0.978529	+	1.12127i
$777$	−21.5252	+	7.61800i	−0.772213	+	0.273294i
$778$	−8.28588	−	2.65676i	−0.297063	−	0.0952495i
$779$	69.4715	+	13.6438i	2.48908	+	0.488838i
$780$	1.06917	+	3.21813i	0.0382826	+	0.115227i
$781$	−10.9657	+	4.98452i	−0.392383	+	0.178360i
$782$	−1.31866	+	7.47847i	−0.0471550	+	0.267429i
$783$	13.2350	−	7.51221i	0.472980	−	0.268465i
$784$	−4.77166	−	27.0614i	−0.170416	−	0.966479i
$785$	−6.07578	−	8.85871i	−0.216854	−	0.316181i
$786$	3.70304	+	0.321046i	0.132083	+	0.0114513i
$787$	−2.66680	−	3.30632i	−0.0950613	−	0.117857i	0.728600	−	0.684939i	$-0.240171\pi$
$787$	−2.66680	−	3.30632i	−0.0950613	−	0.117857i	−0.823662	+	0.567082i	$0.808072\pi$
$788$	0.822473	−	0.336017i	0.0292994	−	0.0119701i
$789$	−15.9107	+	20.9789i	−0.566436	+	0.746868i
$790$	44.7210	−	26.9892i	1.59110	−	0.960234i
$791$	20.5305	−	13.5031i	0.729980	−	0.480115i
$792$	12.8415	−	8.83707i	0.456303	−	0.314012i
$793$	−0.126712	+	2.17555i	−0.00449966	+	0.0772562i
$794$	−2.32299	+	3.68568i	−0.0824399	+	0.130800i
$795$	−34.9595	−	10.0682i	−1.23988	−	0.357081i
$796$	−7.96363	+	5.69206i	−0.282263	+	0.201750i
$797$	9.22985	+	0.717400i	0.326938	+	0.0254116i	0.239913	−	0.970794i	$-0.422881\pi$
$797$	9.22985	+	0.717400i	0.326938	+	0.0254116i	0.0870253	+	0.996206i	$0.472264\pi$
$798$	61.8320	+	34.8398i	2.18883	+	1.23332i
$799$	2.15735	+	0.881375i	0.0763216	+	0.0311808i
$800$	−3.97915	−	13.2913i	−0.140684	−	0.469918i
$801$	−29.8015	+	45.4663i	−1.05299	+	1.60647i
$802$	−20.8148	+	4.93321i	−0.734997	+	0.174198i
$803$	9.16153	+	23.7289i	0.323303	+	0.837376i
$804$	0.694577	−	10.3375i	0.0244959	−	0.364576i
$805$	−49.0240	+	93.0699i	−1.72787	+	3.28028i
$806$	0.0606123	−	3.12515i	0.00213498	−	0.110079i
$807$	−25.7584	−	41.6876i	−0.906740	−	1.46747i
$808$	13.7470	−	13.4829i	0.483616	−	0.474327i
$809$	−3.34882	−	5.80033i	−0.117738	−	0.203929i	0.801133	−	0.598487i	$-0.204231\pi$
$809$	−3.34882	−	5.80033i	−0.117738	−	0.203929i	−0.918871	+	0.394558i	$0.870898\pi$
$810$	−21.2393	−	22.3712i	−0.746272	−	0.786044i
$811$	15.5344	−	26.9063i	0.545485	−	0.944808i	−0.453091	−	0.891464i	$-0.649679\pi$
$811$	15.5344	−	26.9063i	0.545485	−	0.944808i	0.998576	−	0.0533441i	$-0.0169880\pi$
$812$	2.16178	+	8.39254i	0.0758635	+	0.294520i
$813$	37.0188	−	32.9960i	1.29831	−	1.15722i
$814$	−5.09186	+	2.80957i	−0.178470	+	0.0984754i
$815$	−27.8770	−	44.2299i	−0.976490	−	1.54931i
$816$	2.17474	−	2.26432i	0.0761311	−	0.0792670i
$817$	−7.72359	+	9.57575i	−0.270214	+	0.335013i
$818$	−6.85706	+	22.9042i	−0.239751	+	0.800825i
$819$	−11.2333	+	6.50908i	−0.392523	+	0.227446i
$820$	12.0258	−	12.7466i	0.419958	−	0.445129i
$821$	−22.9904	+	17.8189i	−0.802370	+	0.621884i	−0.929006	−	0.370066i	$-0.879335\pi$
$821$	−22.9904	+	17.8189i	−0.802370	+	0.621884i	0.126636	+	0.991949i	$0.459582\pi$
$822$	−10.6958	−	12.4788i	−0.373061	−	0.435249i
$823$	−6.98470	−	14.6073i	−0.243471	−	0.509177i	0.743765	−	0.668442i	$-0.233038\pi$
$823$	−6.98470	−	14.6073i	−0.243471	−	0.509177i	−0.987236	+	0.159265i	$0.949088\pi$
$824$	−2.80026	−	28.7892i	−0.0975518	−	1.00292i
$825$	11.1965	−	0.769947i	0.389812	−	0.0268061i
$826$	12.2651	+	0.475943i	0.426759	+	0.0165602i
$827$	11.2534	+	7.40149i	0.391320	+	0.257375i	0.729888	−	0.683567i	$-0.239572\pi$
$827$	11.2534	+	7.40149i	0.391320	+	0.257375i	−0.338568	+	0.940942i	$0.609943\pi$
$828$	−15.0576	+	5.84078i	−0.523289	+	0.202981i
$829$	24.6249	+	12.3671i	0.855258	+	0.429527i	0.821707	−	0.569910i	$-0.193022\pi$
$829$	24.6249	+	12.3671i	0.855258	+	0.429527i	0.0335510	+	0.999437i	$0.489318\pi$
$830$	−0.411900	−	21.2374i	−0.0142972	−	0.737162i
$831$	−1.13686	−	23.0571i	−0.0394371	−	0.799843i
$832$	6.65580	+	5.15864i	0.230748	+	0.178844i
$833$	−10.0965	+	1.57907i	−0.349824	+	0.0547116i
$834$	−4.86256	+	18.2045i	−0.168377	+	0.630369i
$835$	−23.9926	+	50.1763i	−0.830298	+	1.73642i
$836$	−8.57639	−	3.12155i	−0.296620	−	0.107961i
$837$	−5.84477	−	13.1129i	−0.202025	−	0.453249i
$838$	36.9846	−	13.4613i	1.27761	−	0.465013i
$839$	−5.04928	+	51.9111i	−0.174320	+	1.79217i	0.346036	+	0.938221i	$0.387527\pi$
$839$	−5.04928	+	51.9111i	−0.174320	+	1.79217i	−0.520356	+	0.853949i	$0.674201\pi$
$840$	61.5232	−	33.2354i	2.12275	−	1.14673i
$841$	−6.61139	−	19.3225i	−0.227979	−	0.666293i
$842$	−3.90844	+	3.54672i	−0.134694	+	0.122228i
$843$	−1.19238	−	0.446065i	−0.0410679	−	0.0153633i
$844$	4.42921	−	12.9448i	0.152460	−	0.445580i
$845$	14.1749	+	32.8610i	0.487630	+	1.13045i
$846$	−1.53206	−	9.69624i	−0.0526733	−	0.333364i
$847$	35.7075	−	4.17361i	1.22693	−	0.143407i
$848$	−14.8518	+	4.76203i	−0.510012	+	0.163529i
$849$	13.6404	−	10.3789i	0.468138	−	0.356202i
$850$	3.50121	−	0.974628i	0.120090	−	0.0334295i
$851$	23.1057	−	6.43192i	0.792055	−	0.220484i
$852$	−7.65158	−	3.20588i	−0.262139	−	0.109831i
$853$	−0.497552	+	0.159534i	−0.0170359	+	0.00546233i	−0.313832	−	0.949479i	$-0.601613\pi$
$853$	−0.497552	+	0.159534i	−0.0170359	+	0.00546233i	0.296796	+	0.954941i	$0.404082\pi$
$854$	11.2129	−	1.31060i	0.383697	−	0.0448477i
$855$	−13.7438	+	70.5664i	−0.470028	+	2.41332i
$856$	−2.99344	−	6.93958i	−0.102314	−	0.237190i
$857$	−12.7894	+	37.3785i	−0.436878	+	1.27683i	0.479863	+	0.877344i	$0.340686\pi$
$857$	−12.7894	+	37.3785i	−0.436878	+	1.27683i	−0.916741	+	0.399482i	$0.869190\pi$
$858$	−2.55189	+	2.10283i	−0.0871202	+	0.0717893i
$859$	33.8551	−	30.7219i	1.15512	−	1.04822i	0.156960	−	0.987605i	$-0.449831\pi$
$859$	33.8551	−	30.7219i	1.15512	−	1.04822i	0.998161	−	0.0606117i	$-0.0193051\pi$
$860$	0.985800	+	2.88111i	0.0336155	+	0.0982450i
$861$	57.1304	+	35.1767i	1.94700	+	1.19882i
$862$	−3.36504	+	34.5957i	−0.114614	+	1.17833i
$863$	37.4171	−	13.6187i	1.27369	−	0.463587i	0.385353	−	0.922769i	$-0.374080\pi$
$863$	37.4171	−	13.6187i	1.27369	−	0.463587i	0.888342	+	0.459183i	$0.151858\pi$
$864$	18.3200	+	4.10941i	0.623260	+	0.139805i
$865$	11.1069	+	4.04260i	0.377647	+	0.137452i
$866$	4.48613	−	9.38195i	0.152445	−	0.318812i
$867$	20.0107	+	19.9794i	0.679601	+	0.678535i
$868$	8.07750	−	1.26330i	0.274168	−	0.0428791i
$869$	−20.3264	−	15.7541i	−0.689525	−	0.534422i
$870$	14.6112	−	9.42451i	0.495368	−	0.319521i
$871$	0.169642	+	8.74671i	0.00574811	+	0.296371i
$872$	−36.6017	−	18.3820i	−1.23949	−	0.622495i
$873$	−38.2359	−	13.0158i	−1.29409	−	0.440518i
$874$	−62.2846	−	40.9652i	−2.10681	−	1.38567i
$875$	−15.2010	−	0.589868i	−0.513887	−	0.0199412i
$876$	−7.69784	+	15.7368i	−0.260086	+	0.531697i
$877$	−1.54354	−	15.8689i	−0.0521215	−	0.535856i	−0.984623	−	0.174691i	$-0.944107\pi$
$877$	−1.54354	−	15.8689i	−0.0521215	−	0.535856i	0.932502	−	0.361165i	$-0.117621\pi$
$878$	−19.1703	−	40.0913i	−0.646966	−	1.35301i
$879$	−5.34781	+	15.1864i	−0.180377	+	0.512223i
$880$	8.75483	−	6.78551i	0.295125	−	0.228739i
$881$	−3.74724	+	3.97184i	−0.126248	+	0.133815i	−0.787414	−	0.616425i	$-0.788580\pi$
$881$	−3.74724	+	3.97184i	−0.126248	+	0.133815i	0.661166	+	0.750240i	$0.270062\pi$
$882$	27.7215	+	32.9321i	0.933433	+	1.10888i
$883$	−13.8653	+	46.3132i	−0.466603	+	1.55856i	0.323892	+	0.946094i	$0.395009\pi$
$883$	−13.8653	+	46.3132i	−0.466603	+	1.55856i	−0.790495	+	0.612468i	$0.790177\pi$
$884$	0.339430	−	0.420828i	0.0114163	−	0.0141540i
$885$	3.45970	+	11.9425i	0.116297	+	0.401444i
$886$	4.91403	+	7.79663i	0.165090	+	0.261933i
$887$	16.9793	−	9.36875i	0.570107	−	0.314572i	−0.171738	−	0.985143i	$-0.554938\pi$
$887$	16.9793	−	9.36875i	0.570107	−	0.314572i	0.741846	+	0.670571i	$0.233951\pi$
$888$	−15.1382	−	5.00308i	−0.508005	−	0.167892i
$889$	10.4872	+	40.7138i	0.351729	+	1.36550i
$890$	−31.0549	+	53.7887i	−1.04096	+	1.80300i
$891$	−6.50864	+	13.7222i	−0.218047	+	0.459710i
$892$	1.12849	+	1.95461i	0.0377848	+	0.0654452i
$893$	−16.3333	+	16.0196i	−0.546573	+	0.536075i
$894$	−4.92166	+	0.147071i	−0.164605	+	0.00491880i
$895$	−0.499479	+	25.7530i	−0.0166957	+	0.860828i
$896$	5.47824	−	10.4002i	0.183015	−	0.347446i
$897$	12.2407	−	6.01152i	0.408705	−	0.200719i
$898$	−3.81223	−	9.87393i	−0.127216	−	0.329497i
$899$	7.87384	−	1.86613i	0.262607	−	0.0622390i
$900$	5.63061	+	5.29553i	0.187687	+	0.176518i
$901$	1.66354	+	5.55661i	0.0554206	+	0.185118i
$902$	15.8186	+	6.46261i	0.526702	+	0.215181i
$903$	−10.0347	+	5.93461i	−0.333933	+	0.197492i
$904$	17.1066	+	1.32963i	0.568957	+	0.0442228i
$905$	−3.79934	+	2.71561i	−0.126294	+	0.0902698i
$906$	0.700226	+	2.82233i	0.0232634	+	0.0937656i
$907$	−16.3008	+	25.8630i	−0.541260	+	0.858767i	−0.999549	−	0.0300362i	$-0.990438\pi$
$907$	−16.3008	+	25.8630i	−0.541260	+	0.858767i	0.458289	+	0.888803i	$0.348462\pi$
$908$	−0.713555	+	12.2513i	−0.0236802	+	0.406573i
$909$	−5.00258	+	18.0808i	−0.165925	+	0.599703i
$910$	−12.3928	+	8.15087i	−0.410817	+	0.270199i
$911$	−12.1991	+	7.36218i	−0.404174	+	0.243920i	−0.704186	−	0.710015i	$-0.748688\pi$
$911$	−12.1991	+	7.36218i	−0.404174	+	0.243920i	0.300013	+	0.953935i	$0.403009\pi$
$912$	11.9548	+	28.4078i	0.395863	+	0.940676i
$913$	−9.68121	+	3.95521i	−0.320401	+	0.130898i
$914$	−14.1864	−	17.5884i	−0.469246	−	0.581773i
$915$	4.84104	+	10.3604i	0.160040	+	0.342504i
$916$	−9.75800	−	14.2275i	−0.322413	−	0.470090i
$917$	−1.42547	−	8.08425i	−0.0470732	−	0.266965i
$918$	−1.16931	+	4.77715i	−0.0385931	+	0.157669i
$919$	−2.40352	+	13.6311i	−0.0792850	+	0.449647i	0.919159	+	0.393886i	$0.128870\pi$
$919$	−2.40352	+	13.6311i	−0.0792850	+	0.449647i	−0.998444	+	0.0557611i	$0.982241\pi$
$920$	−66.8666	+	30.3946i	−2.20453	+	1.00208i
$921$	−54.2777	−	11.1630i	−1.78851	−	0.367835i
$922$	11.1843	+	2.19652i	0.368335	+	0.0723386i
$923$	6.67042	+	2.13878i	0.219560	+	0.0703989i
$924$	−6.57565	−	5.61824i	−0.216323	−	0.184826i
$925$	−7.54744	−	8.64841i	−0.248158	−	0.284358i
$926$	−0.230567	+	0.309705i	−0.00757691	+	0.0101776i
$927$	16.4231	+	22.9011i	0.539406	+	0.752172i
$928$	−4.19153	+	9.71706i	−0.137594	+	0.318978i
$929$	21.4028	+	19.4220i	0.702203	+	0.637215i	0.942780	−	0.333415i	$-0.108201\pi$
$929$	21.4028	+	19.4220i	0.702203	+	0.637215i	−0.240577	+	0.970630i	$0.577337\pi$
$930$	−7.51461	−	14.5798i	−0.246414	−	0.478090i
$931$	25.0246	−	97.1516i	0.820149	−	3.18401i
$932$	7.01634	+	6.88157i	0.229828	+	0.225413i
$933$	5.57883	−	24.6893i	0.182643	−	0.808291i
$934$	−5.27064	+	24.3320i	−0.172461	+	0.796167i
$935$	−2.45989	−	3.30421i	−0.0804470	−	0.108059i
$936$	−8.98384	−	1.21272i	−0.293646	−	0.0396391i
$937$	−8.95854	−	1.04710i	−0.292663	−	0.0342074i	−0.0315053	−	0.999504i	$-0.510030\pi$
$937$	−8.95854	−	1.04710i	−0.292663	−	0.0342074i	−0.261157	+	0.965296i	$0.584104\pi$
$938$	44.4699	−	8.73361i	1.45200	−	0.285163i
$939$	4.90330	−	8.32063i	0.160013	−	0.271533i
$940$	1.19883	+	5.53443i	0.0391016	+	0.180513i
$941$	−7.61969	+	8.73119i	−0.248395	+	0.284629i	−0.864070	−	0.503371i	$-0.832093\pi$
$941$	−7.61969	+	8.73119i	−0.248395	+	0.284629i	0.615676	+	0.788000i	$0.288883\pi$
$942$	7.13721	−	1.05117i	0.232543	−	0.0342489i
$943$	−57.3333	−	40.9794i	−1.86703	−	1.33447i
$944$	4.08329	+	3.42629i	0.132900	+	0.111516i
$945$	−35.6290	+	58.0689i	−1.15901	+	1.88898i
$946$	−2.27460	+	1.90862i	−0.0739537	+	0.0620546i
$947$	30.3561	−	2.35946i	0.986441	−	0.0766722i	0.425875	−	0.904782i	$-0.359966\pi$
$947$	30.3561	−	2.35946i	0.986441	−	0.0766722i	0.560566	+	0.828110i	$0.310584\pi$
$948$	−1.55755	−	17.6433i	−0.0505867	−	0.573029i
$949$	5.32782	−	13.7994i	0.172948	−	0.447948i
$950$	−4.82838	+	35.3500i	−0.156653	+	1.14691i
$951$	−43.1891	+	9.83036i	−1.40050	+	0.318771i
$952$	−9.76131	−	5.38606i	−0.316366	−	0.174563i
$953$	−0.132636	−	2.27727i	−0.00429649	−	0.0737679i	0.995478	−	0.0949891i	$-0.0302816\pi$
$953$	−0.132636	−	2.27727i	−0.00429649	−	0.0737679i	−0.999775	+	0.0212212i	$0.993245\pi$
$954$	16.3904	−	18.1191i	0.530659	−	0.586627i
$955$	−30.1305	+	15.1321i	−0.975000	+	0.489664i
$956$	2.99204	+	5.68025i	0.0967695	+	0.183712i
$957$	−6.91964	−	5.03963i	−0.223680	−	0.162908i
$958$	38.1969	+	17.3626i	1.23409	+	0.560961i
$959$	−20.5305	+	29.9341i	−0.662963	+	0.966624i
$960$	43.5955	+	7.21678i	1.40704	+	0.232921i
$961$	3.16219	+	23.1513i	0.102006	+	0.746817i
$962$	3.29084	+	0.779942i	0.106101	+	0.0251463i
$963$	5.91318	+	4.38779i	0.190550	+	0.141395i
$964$	6.71628	+	7.11884i	0.216317	+	0.229282i
$965$	−34.8090	−	5.44403i	−1.12054	−	0.175250i
$966$	−41.6798	−	57.0399i	−1.34103	−	1.83523i
$967$	20.6369	−	0.800804i	0.663637	−	0.0257521i	0.295243	−	0.955422i	$-0.404599\pi$
$967$	20.6369	−	0.800804i	0.663637	−	0.0257521i	0.368393	+	0.929670i	$0.379908\pi$
$968$	21.4920	+	12.9705i	0.690780	+	0.416888i
$969$	10.6490	−	4.24024i	0.342094	−	0.136216i
$970$	−44.4561	−	12.3752i	−1.42740	−	0.397344i
$971$	33.1188			1.06283			0.531417	−	0.847110i	$-0.321660\pi$
$971$	33.1188			1.06283			0.531417	+	0.847110i	$0.321660\pi$
$972$	−9.97888	+	3.13619i	−0.320073	+	0.100593i
$973$	41.6147			1.33411
$974$	−9.22265	−	2.56730i	−0.295513	−	0.0822616i
$975$	−5.12276	−	4.04402i	−0.164060	−	0.129512i
$976$	4.19739	+	2.53314i	0.134355	+	0.0810837i
$977$	−3.98447	+	0.154616i	−0.127475	+	0.00494660i	−0.102434	−	0.994740i	$-0.532663\pi$
$977$	−3.98447	+	0.154616i	−0.127475	+	0.00494660i	−0.0250409	+	0.999686i	$0.507972\pi$
$978$	34.9094	−	3.76529i	1.11628	−	0.120401i
$979$	30.2118	+	4.72505i	0.965575	+	0.151013i
$980$	−17.0407	−	18.0621i	−0.544345	−	0.576972i
$981$	39.8337	−	2.38279i	1.27179	−	0.0760766i
$982$	11.1218	+	2.63592i	0.354912	+	0.0841156i
$983$	−5.64332	−	41.3164i	−0.179994	−	1.31779i	−0.829959	−	0.557824i	$-0.811636\pi$
$983$	−5.64332	−	41.3164i	−0.179994	−	1.31779i	0.649965	−	0.759964i	$-0.274783\pi$
$984$	16.4831	+	43.8513i	0.525461	+	1.39793i
$985$	−2.22660	+	3.24646i	−0.0709453	+	0.103441i
$986$	−2.52361	−	1.14712i	−0.0803682	−	0.0365318i
$987$	−19.8159	+	8.79523i	−0.630749	+	0.279955i
$988$	2.47358	+	4.69598i	0.0786952	+	0.149399i
$989$	10.9432	−	5.49590i	0.347975	−	0.174759i
$990$	−6.53723	+	16.0733i	−0.207767	+	0.510842i
$991$	−0.0522135	−	0.896471i	−0.00165862	−	0.0284773i	0.997377	−	0.0723776i	$-0.0230587\pi$
$991$	−0.0522135	−	0.896471i	−0.00165862	−	0.0284773i	−0.999036	+	0.0439003i	$0.986022\pi$
$992$	8.74091	+	4.82303i	0.277524	+	0.153131i
$993$	−20.3596	−	21.9689i	−0.646093	−	0.697161i
$994$	4.91088	−	35.9540i	0.155764	−	1.14039i
$995$	15.6217	−	40.4613i	0.495242	−	1.28271i
$996$	−6.53028	−	3.03888i	−0.206920	−	0.0962908i
$997$	−33.8048	+	2.62752i	−1.07061	+	0.0832144i	−0.600680	−	0.799489i	$-0.705103\pi$
$997$	−33.8048	+	2.62752i	−1.07061	+	0.0832144i	−0.469930	+	0.882704i	$0.655721\pi$
$998$	−10.8573	+	9.11033i	−0.343681	+	0.288382i
$999$	15.2052	−	3.17695i	0.481070	−	0.100514i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	243.2.i.a.103.9	✓	1404
3.2	odd	2		729.2.i.a.685.18		1404
243.92	odd	162		729.2.i.a.613.18		1404
243.151	even	81	inner	243.2.i.a.151.9	yes	1404

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
243.2.i.a.103.9	✓	1404	1.1	even	1	trivial
243.2.i.a.151.9	yes	1404	243.151	even	81	inner
729.2.i.a.613.18		1404	243.92	odd	162
729.2.i.a.685.18		1404	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:	\( N \)	\(=\)	\( 243 = 3^{5} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	243.i (of order \(81\), degree \(54\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.11059 - 0.309154i) q^{2} +(0.249684 - 1.71396i) q^{3} +(-0.574502 - 0.346714i) q^{4} +(2.97093 - 0.115286i) q^{5} +(-0.807174 + 1.82631i) q^{6} +(4.35689 + 0.681405i) q^{7} +(2.11307 + 2.23972i) q^{8} +(-2.87532 - 0.855898i) q^{9} +O(q^{10})\)	\(q+(-1.11059 - 0.309154i) q^{2} +(0.249684 - 1.71396i) q^{3} +(-0.574502 - 0.346714i) q^{4} +(2.97093 - 0.115286i) q^{5} +(-0.807174 + 1.82631i) q^{6} +(4.35689 + 0.681405i) q^{7} +(2.11307 + 2.23972i) q^{8} +(-2.87532 - 0.855898i) q^{9} +(-3.33513 - 0.790440i) q^{10} +(0.228372 + 1.67198i) q^{11} +(-0.737697 + 0.898104i) q^{12} +(0.555061 - 0.809298i) q^{13} +(-4.62806 - 2.10371i) q^{14} +(0.544201 - 5.12085i) q^{15} +(-1.02889 - 1.95329i) q^{16} +(-0.733705 + 0.368480i) q^{17} +(2.92869 + 1.83946i) q^{18} +(-0.468654 - 8.04649i) q^{19} +(-1.74678 - 0.963831i) q^{20} +(2.25575 - 7.29740i) q^{21} +(0.263270 - 1.92748i) q^{22} +(-2.88972 + 7.48456i) q^{23} +(4.36639 - 3.06249i) q^{24} +(3.82820 - 0.297551i) q^{25} +(-0.866642 + 0.727199i) q^{26} +(-2.18490 + 4.71447i) q^{27} +(-2.26679 - 1.90206i) q^{28} +(-2.38271 - 1.70306i) q^{29} +(-2.18751 + 5.51891i) q^{30} +(-1.81668 + 2.08168i) q^{31} +(-0.764950 - 3.53140i) q^{32} +(2.92272 + 0.0260465i) q^{33} +(0.928762 - 0.182403i) q^{34} +(13.0226 + 1.52212i) q^{35} +(1.35512 + 1.48863i) q^{36} +(-1.78516 - 2.39789i) q^{37} +(-1.96712 + 9.08123i) q^{38} +(-1.24851 - 1.15342i) q^{39} +(6.53599 + 6.41046i) q^{40} +(-2.19104 + 8.50616i) q^{41} +(-4.76123 + 7.40704i) q^{42} +(-1.13031 - 1.02570i) q^{43} +(0.448497 - 1.03973i) q^{44} +(-8.64105 - 2.21133i) q^{45} +(5.52317 - 7.41890i) q^{46} +(-1.86632 - 2.13857i) q^{47} +(-3.60476 + 1.27576i) q^{48} +(11.8524 + 3.80033i) q^{49} +(-4.34354 - 0.853044i) q^{50} +(0.448366 + 1.34954i) q^{51} +(-0.599478 + 0.272496i) q^{52} +(1.22675 - 6.95726i) q^{53} +(3.88402 - 4.56037i) q^{54} +(0.871232 + 4.94100i) q^{55} +(7.68025 + 11.1981i) q^{56} +(-13.9084 - 1.20583i) q^{57} +(2.11971 + 2.62802i) q^{58} +(-2.23510 + 0.913139i) q^{59} +(-2.08811 + 2.75325i) q^{60} +(-1.90125 + 1.14741i) q^{61} +(2.66114 - 1.75026i) q^{62} +(-11.9442 - 5.68831i) q^{63} +(-0.498934 + 8.56636i) q^{64} +(1.55575 - 2.46836i) q^{65} +(-3.23789 - 0.932497i) q^{66} +(-7.25247 + 5.18375i) q^{67} +(0.549272 + 0.0426928i) q^{68} +(12.1067 + 6.82164i) q^{69} +(-13.9922 - 5.71643i) q^{70} +(2.04721 + 6.83814i) q^{71} +(-4.15876 - 8.24847i) q^{72} +(14.6670 - 3.47613i) q^{73} +(1.24126 + 3.21496i) q^{74} +(0.445850 - 6.63567i) q^{75} +(-2.52058 + 4.78521i) q^{76} +(-0.144303 + 7.44023i) q^{77} +(1.03000 + 1.66696i) q^{78} +(-10.8800 + 10.6710i) q^{79} +(-3.28194 - 5.68449i) q^{80} +(7.53488 + 4.92195i) q^{81} +(5.06306 - 8.76947i) q^{82} +(1.54587 + 6.00143i) q^{83} +(-3.82604 + 3.41027i) q^{84} +(-2.13731 + 1.17932i) q^{85} +(0.938213 + 1.48858i) q^{86} +(-3.51390 + 3.65864i) q^{87} +(-3.26220 + 4.04449i) q^{88} +(5.19714 - 17.3597i) q^{89} +(8.91301 + 5.12729i) q^{90} +(2.96980 - 3.14780i) q^{91} +(4.25515 - 3.29799i) q^{92} +(3.11432 + 3.63347i) q^{93} +(1.41157 + 2.95205i) q^{94} +(-2.31999 - 23.8516i) q^{95} +(-6.24368 + 0.429357i) q^{96} +(13.4534 + 0.522053i) q^{97} +(-11.9883 - 7.88483i) q^{98} +(0.774400 - 5.00292i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1404 q - 54 q^{2} - 54 q^{3} - 54 q^{4} - 54 q^{5} - 54 q^{6} - 54 q^{7} - 54 q^{8} - 54 q^{9}+O(q^{10}) \) 1404 * q - 54 * q^2 - 54 * q^3 - 54 * q^4 - 54 * q^5 - 54 * q^6 - 54 * q^7 - 54 * q^8 - 54 * q^9	\( 1404 q - 54 q^{2} - 54 q^{3} - 54 q^{4} - 54 q^{5} - 54 q^{6} - 54 q^{7} - 54 q^{8} - 54 q^{9} - 54 q^{10} - 54 q^{11} - 54 q^{12} - 54 q^{13} - 54 q^{14} - 54 q^{15} - 54 q^{16} - 54 q^{17} - 54 q^{18} - 54 q^{19} - 54 q^{20} - 54 q^{21} - 54 q^{22} - 54 q^{23} - 54 q^{24} - 54 q^{25} - 54 q^{26} - 54 q^{27} - 54 q^{28} - 54 q^{29} - 54 q^{30} - 54 q^{31} - 54 q^{32} - 54 q^{33} - 54 q^{34} - 54 q^{35} - 54 q^{36} - 54 q^{37} - 54 q^{38} - 54 q^{39} - 54 q^{40} - 54 q^{41} - 54 q^{42} - 54 q^{43} - 54 q^{44} - 54 q^{45} - 54 q^{46} - 54 q^{47} - 54 q^{48} - 54 q^{49} - 54 q^{50} - 54 q^{51} - 54 q^{52} - 54 q^{53} - 54 q^{54} - 54 q^{55} - 54 q^{56} - 54 q^{57} - 54 q^{58} - 54 q^{59} - 54 q^{60} - 54 q^{61} - 54 q^{62} - 54 q^{63} - 54 q^{64} + 54 q^{66} - 54 q^{67} + 135 q^{68} + 54 q^{69} - 54 q^{70} + 54 q^{71} + 270 q^{72} - 54 q^{73} + 162 q^{74} + 81 q^{75} - 54 q^{76} + 162 q^{77} + 162 q^{78} - 54 q^{79} + 351 q^{80} + 54 q^{81} - 27 q^{82} + 54 q^{83} + 324 q^{84} - 54 q^{85} + 162 q^{86} + 162 q^{87} - 54 q^{88} + 81 q^{89} + 162 q^{90} - 54 q^{91} + 270 q^{92} + 54 q^{93} - 54 q^{94} + 54 q^{95} + 135 q^{96} - 54 q^{97} + 54 q^{98}+O(q^{100}) \) 1404 * q - 54 * q^2 - 54 * q^3 - 54 * q^4 - 54 * q^5 - 54 * q^6 - 54 * q^7 - 54 * q^8 - 54 * q^9 - 54 * q^10 - 54 * q^11 - 54 * q^12 - 54 * q^13 - 54 * q^14 - 54 * q^15 - 54 * q^16 - 54 * q^17 - 54 * q^18 - 54 * q^19 - 54 * q^20 - 54 * q^21 - 54 * q^22 - 54 * q^23 - 54 * q^24 - 54 * q^25 - 54 * q^26 - 54 * q^27 - 54 * q^28 - 54 * q^29 - 54 * q^30 - 54 * q^31 - 54 * q^32 - 54 * q^33 - 54 * q^34 - 54 * q^35 - 54 * q^36 - 54 * q^37 - 54 * q^38 - 54 * q^39 - 54 * q^40 - 54 * q^41 - 54 * q^42 - 54 * q^43 - 54 * q^44 - 54 * q^45 - 54 * q^46 - 54 * q^47 - 54 * q^48 - 54 * q^49 - 54 * q^50 - 54 * q^51 - 54 * q^52 - 54 * q^53 - 54 * q^54 - 54 * q^55 - 54 * q^56 - 54 * q^57 - 54 * q^58 - 54 * q^59 - 54 * q^60 - 54 * q^61 - 54 * q^62 - 54 * q^63 - 54 * q^64 + 54 * q^66 - 54 * q^67 + 135 * q^68 + 54 * q^69 - 54 * q^70 + 54 * q^71 + 270 * q^72 - 54 * q^73 + 162 * q^74 + 81 * q^75 - 54 * q^76 + 162 * q^77 + 162 * q^78 - 54 * q^79 + 351 * q^80 + 54 * q^81 - 27 * q^82 + 54 * q^83 + 324 * q^84 - 54 * q^85 + 162 * q^86 + 162 * q^87 - 54 * q^88 + 81 * q^89 + 162 * q^90 - 54 * q^91 + 270 * q^92 + 54 * q^93 - 54 * q^94 + 54 * q^95 + 135 * q^96 - 54 * q^97 + 54 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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