LMFDB - Embedded newform 243.2.i.a.106.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [243,2,Mod(4,243)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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			106.8
Character	$\chi$	$=$	243.106
Dual form			243.2.i.a.94.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.536522 + 1.38963i) q^{2} +(1.34514 - 1.09115i) q^{3} +(-0.162116 - 0.147113i) q^{4} +(0.546288 + 0.390463i) q^{5} +(0.794597 + 2.45466i) q^{6} +(1.56166 + 1.21038i) q^{7} +(-2.37090 + 1.19071i) q^{8} +(0.618780 - 2.93549i) q^{9} +(-0.835693 + 0.549644i) q^{10} +(0.0684384 - 0.0997857i) q^{11} +(-0.378590 - 0.0209932i) q^{12} +(1.29377 - 0.254089i) q^{13} +(-2.51983 + 1.52073i) q^{14} +(1.16089 - 0.0708565i) q^{15} +(-0.424991 - 4.36929i) q^{16} +(0.0971116 + 0.225130i) q^{17} +(3.74725 + 2.43483i) q^{18} +(3.57456 + 4.80146i) q^{19} +(-0.0311200 - 0.143666i) q^{20} +(3.42135 - 0.0758838i) q^{21} +(0.101946 + 0.148641i) q^{22} +(-1.69637 - 0.693045i) q^{23} +(-1.88994 + 4.18868i) q^{24} +(-1.47270 - 4.30413i) q^{25} +(-0.341049 + 1.93418i) q^{26} +(-2.37072 - 4.62382i) q^{27} +(-0.0751084 - 0.425961i) q^{28} +(-6.40053 + 3.53166i) q^{29} +(-0.524376 + 1.65121i) q^{30} +(-0.486544 - 0.923680i) q^{31} +(1.18783 + 0.330656i) q^{32} +(-0.0168222 - 0.208902i) q^{33} +(-0.364949 + 0.0141617i) q^{34} +(0.380508 + 1.27098i) q^{35} +(-0.532162 + 0.384860i) q^{36} +(2.36708 + 2.50896i) q^{37} +(-8.59006 + 2.39121i) q^{38} +(1.46305 - 1.75349i) q^{39} +(-1.76013 - 0.275279i) q^{40} +(0.823942 - 1.02153i) q^{41} +(-1.73018 + 4.79510i) q^{42} +(-8.32258 - 8.16273i) q^{43} +(-0.0257747 + 0.00610871i) q^{44} +(1.48423 - 1.36201i) q^{45} +(1.87321 - 1.98549i) q^{46} +(0.209094 - 0.396955i) q^{47} +(-5.33922 - 5.41355i) q^{48} +(-0.772323 - 2.99834i) q^{49} +(6.77127 + 0.262756i) q^{50} +(0.376279 + 0.196867i) q^{51} +(-0.247121 - 0.149138i) q^{52} +(-2.74407 - 0.998759i) q^{53} +(7.69732 - 0.813636i) q^{54} +(0.0763497 - 0.0277890i) q^{55} +(-5.14375 - 1.01020i) q^{56} +(10.0474 + 2.55824i) q^{57} +(-1.47367 - 10.7892i) q^{58} +(11.3271 - 0.880415i) q^{59} +(-0.198622 - 0.159294i) q^{60} +(-1.40320 + 1.27333i) q^{61} +(1.54461 - 0.180539i) q^{62} +(4.51937 - 3.83528i) q^{63} +(4.14615 - 5.56925i) q^{64} +(0.805985 + 0.366365i) q^{65} +(0.299321 + 0.0887038i) q^{66} +(-1.32647 - 0.731913i) q^{67} +(0.0173761 - 0.0507835i) q^{68} +(-3.03807 + 0.918759i) q^{69} +(-1.97034 - 0.153147i) q^{70} +(-0.745627 - 12.8019i) q^{71} +(2.02826 + 7.69656i) q^{72} +(1.02878 + 0.676636i) q^{73} +(-4.75650 + 1.94324i) q^{74} +(-6.67744 - 4.18270i) q^{75} +(0.126862 - 1.30426i) q^{76} +(0.227656 - 0.0729949i) q^{77} +(1.65173 + 2.97388i) q^{78} +(-4.63724 + 0.725251i) q^{79} +(1.47388 - 2.55283i) q^{80} +(-8.23422 - 3.63285i) q^{81} +(0.977478 + 1.69304i) q^{82} +(-9.33520 - 11.5738i) q^{83} +(-0.565819 - 0.491021i) q^{84} +(-0.0348541 + 0.160904i) q^{85} +(15.8084 - 7.18579i) q^{86} +(-4.75601 + 11.7345i) q^{87} +(-0.0434449 + 0.318073i) q^{88} +(-0.127637 + 2.19144i) q^{89} +(1.09636 + 2.79328i) q^{90} +(2.32797 + 1.16915i) q^{91} +(0.173054 + 0.361911i) q^{92} +(-1.66234 - 0.711583i) q^{93} +(0.439436 + 0.503537i) q^{94} +(0.0779428 + 4.01871i) q^{95} +(1.95859 - 0.851328i) q^{96} +(-7.97787 + 5.70224i) q^{97} +(4.58094 + 0.535435i) q^{98} +(-0.250572 - 0.262646i) 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} - 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}+ \cdots + 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

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{50}{81}\right)$

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 $

$2$	−0.536522	+	1.38963i	−0.379378	+	0.982614i	0.603337	+	0.797487i	$0.293838\pi$
$2$	−0.536522	+	1.38963i	−0.379378	+	0.982614i	−0.982715	+	0.185127i	$0.940730\pi$
$3$	1.34514	−	1.09115i	0.776614	−	0.629976i
$3$	1.34514	−	1.09115i	0.776614	−	0.629976i
$4$	−0.162116	−	0.147113i	−0.0810580	−	0.0735563i
$5$	0.546288	+	0.390463i	0.244307	+	0.174620i	0.697054	−	0.717019i	$-0.254494\pi$
$5$	0.546288	+	0.390463i	0.244307	+	0.174620i	−0.452746	+	0.891639i	$0.649556\pi$
$6$	0.794597	+	2.45466i	0.324393	+	1.00211i
$7$	1.56166	+	1.21038i	0.590251	+	0.457479i	0.863419	−	0.504487i	$-0.168318\pi$
$7$	1.56166	+	1.21038i	0.590251	+	0.457479i	−0.273168	+	0.961966i	$0.588071\pi$
$8$	−2.37090	+	1.19071i	−0.838241	+	0.420981i
$9$	0.618780	−	2.93549i	0.206260	−	0.978497i
$10$	−0.835693	+	0.549644i	−0.264269	+	0.173813i
$11$	0.0684384	−	0.0997857i	0.0206350	−	0.0300865i	−0.814220	−	0.580556i	$-0.802835\pi$
$11$	0.0684384	−	0.0997857i	0.0206350	−	0.0300865i	0.834855	+	0.550470i	$0.185551\pi$
$12$	−0.378590	−	0.0209932i	−0.109290	−	0.00606022i
$13$	1.29377	−	0.254089i	0.358828	−	0.0704715i	−0.0100496	−	0.999950i	$-0.503199\pi$
$13$	1.29377	−	0.254089i	0.358828	−	0.0704715i	0.368878	+	0.929478i	$0.379742\pi$
$14$	−2.51983	+	1.52073i	−0.673454	+	0.406431i
$15$	1.16089	−	0.0708565i	0.299739	−	0.0182951i
$16$	−0.424991	−	4.36929i	−0.106248	−	1.09232i
$17$	0.0971116	+	0.225130i	0.0235530	+	0.0546020i	0.929587	−	0.368604i	$-0.120164\pi$
$17$	0.0971116	+	0.225130i	0.0235530	+	0.0546020i	−0.906034	+	0.423206i	$0.860905\pi$
$18$	3.74725	+	2.43483i	0.883234	+	0.573894i
$19$	3.57456	+	4.80146i	0.820059	+	1.10153i	0.993176	+	0.116629i	$0.0372090\pi$
$19$	3.57456	+	4.80146i	0.820059	+	1.10153i	−0.173116	+	0.984901i	$0.555384\pi$
$20$	−0.0311200	−	0.143666i	−0.00695865	−	0.0321247i
$21$	3.42135	−	0.0758838i	0.746599	−	0.0165592i
$22$	0.101946	+	0.148641i	0.0217350	+	0.0316904i
$23$	−1.69637	−	0.693045i	−0.353718	−	0.144510i	0.194374	−	0.980927i	$-0.437732\pi$
$23$	−1.69637	−	0.693045i	−0.353718	−	0.144510i	−0.548093	+	0.836418i	$0.684646\pi$
$24$	−1.88994	+	4.18868i	−0.385783	+	0.855012i
$25$	−1.47270	−	4.30413i	−0.294540	−	0.860826i
$26$	−0.341049	+	1.93418i	−0.0668852	+	0.379325i
$27$	−2.37072	−	4.62382i	−0.456245	−	0.889854i
$28$	−0.0751084	−	0.425961i	−0.0141942	−	0.0804991i
$29$	−6.40053	+	3.53166i	−1.18855	+	0.655814i	−0.949063	−	0.315086i	$-0.897967\pi$
$29$	−6.40053	+	3.53166i	−1.18855	+	0.655814i	−0.239486	+	0.970900i	$0.576979\pi$
$30$	−0.524376	+	1.65121i	−0.0957375	+	0.301469i
$31$	−0.486544	−	0.923680i	−0.0873858	−	0.165898i	0.837172	−	0.546940i	$-0.184207\pi$
$31$	−0.486544	−	0.923680i	−0.0873858	−	0.165898i	−0.924558	+	0.381042i	$0.875565\pi$
$32$	1.18783	+	0.330656i	0.209981	+	0.0584523i
$33$	−0.0168222	−	0.208902i	−0.00292837	−	0.0363652i
$34$	−0.364949	+	0.0141617i	−0.0625882	+	0.00242871i
$35$	0.380508	+	1.27098i	0.0643175	+	0.214835i
$36$	−0.532162	+	0.384860i	−0.0886936	+	0.0641433i
$37$	2.36708	+	2.50896i	0.389145	+	0.412470i	0.892097	−	0.451845i	$-0.149234\pi$
$37$	2.36708	+	2.50896i	0.389145	+	0.412470i	−0.502951	+	0.864315i	$0.667752\pi$
$38$	−8.59006	+	2.39121i	−1.39349	+	0.387905i
$39$	1.46305	−	1.75349i	0.234276	−	0.280782i
$40$	−1.76013	−	0.275279i	−0.278300	−	0.0435254i
$41$	0.823942	−	1.02153i	0.128678	−	0.159536i	−0.709928	−	0.704275i	$-0.751272\pi$
$41$	0.823942	−	1.02153i	0.128678	−	0.159536i	0.838606	+	0.544739i	$0.183371\pi$
$42$	−1.73018	+	4.79510i	−0.266972	+	0.739900i
$43$	−8.32258	−	8.16273i	−1.26918	−	1.24480i	−0.955402	−	0.295308i	$-0.904578\pi$
$43$	−8.32258	−	8.16273i	−1.26918	−	1.24480i	−0.313779	−	0.949496i	$-0.601595\pi$
$44$	−0.0257747	+	0.00610871i	−0.00388568	+	0.000920923i
$45$	1.48423	−	1.36201i	0.221256	−	0.203037i
$46$	1.87321	−	1.98549i	0.276190	−	0.292745i
$47$	0.209094	−	0.396955i	0.0304995	−	0.0579019i	−0.869038	−	0.494745i	$-0.835262\pi$
$47$	0.209094	−	0.396955i	0.0304995	−	0.0579019i	0.899538	+	0.436843i	$0.143903\pi$
$48$	−5.33922	−	5.41355i	−0.770650	−	0.781379i
$49$	−0.772323	−	2.99834i	−0.110332	−	0.428334i
$50$	6.77127	+	0.262756i	0.957602	+	0.0371593i
$51$	0.376279	+	0.196867i	0.0526896	+	0.0275669i
$52$	−0.247121	−	0.149138i	−0.0342695	−	0.0206818i
$53$	−2.74407	−	0.998759i	−0.376927	−	0.137190i	0.146607	−	0.989195i	$-0.453165\pi$
$53$	−2.74407	−	0.998759i	−0.376927	−	0.137190i	−0.523534	+	0.852005i	$0.675387\pi$
$54$	7.69732	−	0.813636i	1.04747	−	0.110722i
$55$	0.0763497	−	0.0277890i	0.0102950	−	0.00374707i
$56$	−5.14375	−	1.01020i	−0.687363	−	0.134994i
$57$	10.0474	+	2.55824i	1.33081	+	0.338847i
$58$	−1.47367	−	10.7892i	−0.193502	−	1.41669i
$59$	11.3271	−	0.880415i	1.47467	−	0.114620i	0.685174	−	0.728379i	$-0.259726\pi$
$59$	11.3271	−	0.880415i	1.47467	−	0.114620i	0.789494	+	0.613759i	$0.210343\pi$
$60$	−0.198622	−	0.159294i	−0.0256420	−	0.0205647i
$61$	−1.40320	+	1.27333i	−0.179661	+	0.163033i	−0.756876	−	0.653559i	$-0.773275\pi$
$61$	−1.40320	+	1.27333i	−0.179661	+	0.163033i	0.577215	+	0.816592i	$0.304139\pi$
$62$	1.54461	−	0.180539i	0.196166	−	0.0229285i
$63$	4.51937	−	3.83528i	0.569388	−	0.483200i
$64$	4.14615	−	5.56925i	0.518269	−	0.696156i
$65$	0.805985	+	0.366365i	0.0999701	+	0.0454420i
$66$	0.299321	+	0.0887038i	0.0368439	+	0.0109187i
$67$	−1.32647	−	0.731913i	−0.162054	−	0.0894174i	0.400013	−	0.916510i	$-0.369006\pi$
$67$	−1.32647	−	0.731913i	−0.162054	−	0.0894174i	−0.562066	+	0.827092i	$0.689993\pi$
$68$	0.0173761	−	0.0507835i	0.00210716	−	0.00615841i
$69$	−3.03807	+	0.918759i	−0.365740	+	0.110606i
$70$	−1.97034	−	0.153147i	−0.235501	−	0.0183046i
$71$	−0.745627	−	12.8019i	−0.0884897	−	1.51931i	−0.691967	−	0.721929i	$-0.743256\pi$
$71$	−0.745627	−	12.8019i	−0.0884897	−	1.51931i	0.603477	−	0.797380i	$-0.293781\pi$
$72$	2.02826	+	7.69656i	0.239033	+	0.907048i
$73$	1.02878	+	0.676636i	0.120409	+	0.0791943i	0.608285	−	0.793719i	$-0.291858\pi$
$73$	1.02878	+	0.676636i	0.120409	+	0.0791943i	−0.487876	+	0.872913i	$0.662228\pi$
$74$	−4.75650	+	1.94324i	−0.552932	+	0.225897i
$75$	−6.67744	−	4.18270i	−0.771044	−	0.482977i
$76$	0.126862	−	1.30426i	0.0145521	−	0.149608i
$77$	0.227656	−	0.0729949i	0.0259438	−	0.00831854i
$78$	1.65173	+	2.97388i	0.187022	+	0.336725i
$79$	−4.63724	+	0.725251i	−0.521730	+	0.0815971i	−0.409900	−	0.912130i	$-0.634437\pi$
$79$	−4.63724	+	0.725251i	−0.521730	+	0.0815971i	−0.111830	+	0.993727i	$0.535671\pi$
$80$	1.47388	−	2.55283i	0.164784	−	0.285415i
$81$	−8.23422	−	3.63285i	−0.914914	−	0.403650i
$82$	0.977478	+	1.69304i	0.107944	+	0.186965i
$83$	−9.33520	−	11.5738i	−1.02467	−	1.27039i	−0.962199	−	0.272346i	$-0.912200\pi$
$83$	−9.33520	−	11.5738i	−1.02467	−	1.27039i	−0.0624717	−	0.998047i	$-0.519898\pi$
$84$	−0.565819	−	0.491021i	−0.0617359	−	0.0535748i
$85$	−0.0348541	+	0.160904i	−0.00378045	+	0.0174525i
$86$	15.8084	−	7.18579i	1.70466	−	0.774863i
$87$	−4.75601	+	11.7345i	−0.509897	+	1.25807i
$88$	−0.0434449	+	0.318073i	−0.00463124	+	0.0339067i
$89$	−0.127637	+	2.19144i	−0.0135295	+	0.232292i	0.984764	+	0.173896i	$0.0556356\pi$
$89$	−0.127637	+	2.19144i	−0.0135295	+	0.232292i	−0.998294	+	0.0583959i	$0.981401\pi$
$90$	1.09636	+	2.79328i	0.115567	+	0.294437i
$91$	2.32797	+	1.16915i	0.244038	+	0.122561i
$92$	0.173054	+	0.361911i	0.0180421	+	0.0377319i
$93$	−1.66234	−	0.711583i	−0.172377	−	0.0737877i
$94$	0.439436	+	0.503537i	0.0453243	+	0.0519359i
$95$	0.0779428	+	4.01871i	0.00799676	+	0.412311i
$96$	1.95859	−	0.851328i	0.199898	−	0.0868883i
$97$	−7.97787	+	5.70224i	−0.810030	+	0.578975i	−0.909326	−	0.416083i	$-0.863402\pi$
$97$	−7.97787	+	5.70224i	−0.810030	+	0.578975i	0.0992966	+	0.995058i	$0.468341\pi$
$98$	4.58094	+	0.535435i	0.462745	+	0.0540871i
$99$	−0.250572	−	0.262646i	−0.0251834	−	0.0263969i
$100$	−0.394443	+	0.914422i	−0.0394443	+	0.0914422i
$101$	11.8881	+	3.81178i	1.18291	+	0.379286i	0.830746	−	0.556651i	$-0.187914\pi$
$101$	11.8881	+	3.81178i	1.18291	+	0.379286i	0.352167	+	0.935937i	$0.385445\pi$
$102$	−0.475453	+	0.417264i	−0.0470769	+	0.0413153i
$103$	−4.49131	+	9.39278i	−0.442542	+	0.925498i	0.553177	+	0.833064i	$0.313415\pi$
$103$	−4.49131	+	9.39278i	−0.442542	+	0.925498i	−0.995719	+	0.0924345i	$0.970535\pi$
$104$	−2.76487	+	2.14293i	−0.271117	+	0.210132i
$105$	1.89867	+	1.29445i	0.185291	+	0.126326i
$106$	2.86015	−	3.27737i	0.277803	−	0.318327i
$107$	7.23135	+	6.06782i	0.699081	+	0.586598i	0.921512	−	0.388350i	$-0.126955\pi$
$107$	7.23135	+	6.06782i	0.699081	+	0.586598i	−0.222431	+	0.974948i	$0.571399\pi$
$108$	−0.295889	+	1.09836i	−0.0284720	+	0.105690i
$109$	−12.5897	+	10.5640i	−1.20587	+	1.01185i	−0.206430	+	0.978461i	$0.566185\pi$
$109$	−12.5897	+	10.5640i	−1.20587	+	1.01185i	−0.999443	+	0.0333861i	$0.989371\pi$
$110$	−0.00234693	+	0.121007i	−0.000223771	+	0.0115376i
$111$	5.92169	+	0.792048i	0.562062	+	0.0751779i
$112$	4.62479	−	7.33773i	0.437002	−	0.693350i
$113$	−3.27186	+	3.20902i	−0.307791	+	0.301879i	−0.837651	−	0.546206i	$-0.816072\pi$
$113$	−3.27186	+	3.20902i	−0.307791	+	0.301879i	0.529860	+	0.848085i	$0.322244\pi$
$114$	−8.94563	+	12.5895i	−0.837835	+	1.17912i
$115$	−0.656099	−	1.04097i	−0.0611816	−	0.0970712i
$116$	1.55718	+	0.369059i	0.144581	+	0.0342662i
$117$	0.0546859	−	3.95508i	0.00505571	−	0.365648i
$118$	−4.85381	+	16.2128i	−0.446829	+	1.49251i
$119$	−0.120837	+	0.469118i	−0.0110771	+	0.0430040i
$120$	−2.66798	+	1.55027i	−0.243552	+	0.141520i
$121$	3.95668	+	10.2481i	0.359698	+	0.931642i
$122$	−1.01661	−	2.63309i	−0.0920396	−	0.238389i
$123$	−0.00632694	−	2.27314i	−0.000570481	−	0.204962i
$124$	−0.0570084	+	0.221320i	−0.00511950	+	0.0198751i
$125$	1.83901	−	6.14270i	0.164486	−	0.549420i
$126$	2.90486	+	8.33795i	0.258785	+	0.742803i
$127$	18.1585	+	4.30365i	1.61131	+	0.381887i	0.934977	−	0.354708i	$-0.115420\pi$
$127$	18.1585	+	4.30365i	1.61131	+	0.381887i	0.676333	+	0.736596i	$0.263568\pi$
$128$	6.82955	+	10.8358i	0.603653	+	0.957760i
$129$	−20.1018	−	1.89879i	−1.76986	−	0.167179i
$130$	−0.941538	+	0.923454i	−0.0825784	+	0.0809923i
$131$	−5.21495	+	8.27409i	−0.455633	+	0.722910i	−0.992697	−	0.120631i	$-0.961508\pi$
$131$	−5.21495	+	8.27409i	−0.455633	+	0.722910i	0.537065	+	0.843541i	$0.319533\pi$
$132$	−0.0280049	+	0.0363411i	−0.00243752	+	0.00316309i
$133$	−0.229342	+	11.8248i	−0.0198865	+	1.02534i
$134$	1.72876	−	1.45060i	0.149342	−	0.125313i
$135$	0.510334	−	3.45161i	0.0439226	−	0.297068i
$136$	−0.498308	−	0.418130i	−0.0427295	−	0.0358543i
$137$	−1.97760	+	2.26608i	−0.168958	+	0.193604i	−0.831670	−	0.555270i	$-0.812615\pi$
$137$	−1.97760	+	2.26608i	−0.168958	+	0.193604i	0.662712	+	0.748874i	$0.269405\pi$
$138$	0.353257	−	4.71471i	0.0300713	−	0.401343i
$139$	11.0109	−	8.53411i	0.933935	−	0.723854i	−0.0272880	−	0.999628i	$-0.508687\pi$
$139$	11.0109	−	8.53411i	0.933935	−	0.723854i	0.961223	+	0.275774i	$0.0889340\pi$
$140$	0.125291	−	0.262024i	0.0105890	−	0.0221451i
$141$	−0.151878	−	0.762112i	−0.0127904	−	0.0641814i
$142$	18.1899	+	5.83237i	1.52646	+	0.489441i
$143$	0.0631894	−	0.146489i	0.00528416	−	0.0122501i
$144$	−13.0890	−	1.45607i	−1.09075	−	0.121339i
$145$	−4.87552	−	0.569866i	−0.404890	−	0.0473248i
$146$	−1.49223	+	1.06658i	−0.123498	+	0.0882710i
$147$	−4.31052	−	3.19045i	−0.355526	−	0.263144i
$148$	−0.0146426	−	0.754969i	−0.00120361	−	0.0620581i
$149$	8.86790	+	10.1615i	0.726487	+	0.832461i	0.991270	−	0.131847i	$-0.0420906\pi$
$149$	8.86790	+	10.1615i	0.726487	+	0.832461i	−0.264784	+	0.964308i	$0.585301\pi$
$150$	9.39498	−	7.03503i	0.767097	−	0.574408i
$151$	−3.02464	−	6.32551i	−0.246142	−	0.514762i	0.741603	−	0.670839i	$-0.234066\pi$
$151$	−3.02464	−	6.32551i	−0.246142	−	0.514762i	−0.987745	+	0.156077i	$0.950115\pi$
$152$	−14.1921	−	7.12754i	−1.15113	−	0.578120i
$153$	0.720958	−	0.145764i	0.0582860	−	0.0117843i
$154$	−0.0207067	+	0.355520i	−0.00166859	+	0.0286486i
$155$	0.0948701	−	0.694572i	0.00762015	−	0.0557894i
$156$	−0.495144	+	0.0690350i	−0.0396432	+	0.00552723i
$157$	−8.68645	+	3.94848i	−0.693254	+	0.315123i	−0.729268	−	0.684229i	$-0.760139\pi$
$157$	−8.68645	+	3.94848i	−0.693254	+	0.315123i	0.0360132	+	0.999351i	$0.488534\pi$
$158$	1.48015	−	6.83314i	0.117755	−	0.543615i
$159$	−4.78094	+	1.65073i	−0.379153	+	0.130911i
$160$	0.519790	+	0.644438i	0.0410930	+	0.0509473i
$161$	−1.81031	−	3.13555i	−0.142672	−	0.247116i
$162$	9.46614	−	9.49338i	0.743730	−	0.745871i
$163$	−5.33409	+	9.23892i	−0.417798	+	0.723648i	−0.995718	−	0.0924458i	$-0.970532\pi$
$163$	−5.33409	+	9.23892i	−0.417798	+	0.723648i	0.577919	+	0.816094i	$0.303865\pi$
$164$	−0.283854	+	0.0443939i	−0.0221652	+	0.00346658i
$165$	0.0723787	−	0.120689i	0.00563467	−	0.00939563i
$166$	21.0918	−	6.76282i	1.63704	−	0.524897i
$167$	−0.0883082	+	0.907888i	−0.00683350	+	0.0702545i	−0.998099	−	0.0616233i	$-0.980372\pi$
$167$	−0.0883082	+	0.907888i	−0.00683350	+	0.0702545i	0.991266	+	0.131878i	$0.0421007\pi$
$168$	−8.02133	+	4.25375i	−0.618859	+	0.328184i
$169$	−10.4251	+	4.25913i	−0.801933	+	0.327626i
$170$	−0.204897	−	0.134763i	−0.0157149	−	0.0103358i
$171$	16.3065	−	7.52203i	1.24699	−	0.575224i
$172$	0.148385	+	2.54766i	0.0113142	+	0.194258i
$173$	8.27072	+	0.642851i	0.628811	+	0.0488751i	0.387944	−	0.921683i	$-0.373185\pi$
$173$	8.27072	+	0.642851i	0.628811	+	0.0488751i	0.240867	+	0.970558i	$0.422568\pi$
$174$	−13.7549	−	12.9049i	−1.04275	−	0.978317i
$175$	2.90976	−	8.50410i	0.219957	−	0.642850i
$176$	−0.465078	−	0.256619i	−0.0350566	−	0.0193434i
$177$	14.2759	−	13.5439i	1.07304	−	1.01802i
$178$	−2.97680	−	1.35312i	−0.223120	−	0.101421i
$179$	13.3767	−	17.9680i	0.999823	−	1.34299i	0.0611713	−	0.998127i	$-0.480516\pi$
$179$	13.3767	−	17.9680i	0.999823	−	1.34299i	0.938651	−	0.344868i	$-0.112076\pi$
$180$	−0.440987	+	0.00245486i	−0.0328692	+	0.000182975i
$181$	15.8290	−	1.85014i	1.17656	−	0.137520i	0.494740	−	0.869041i	$-0.335263\pi$
$181$	15.8290	−	1.85014i	1.17656	−	0.137520i	0.681819	+	0.731521i	$0.261189\pi$
$182$	−2.87369	+	2.60774i	−0.213012	+	0.193298i
$183$	−0.498091	+	3.24390i	−0.0368200	+	0.239796i
$184$	4.84715	−	0.376751i	0.357337	−	0.0277744i
$185$	0.313451	+	2.29487i	0.0230454	+	0.168722i
$186$	1.88072	−	1.92825i	0.137901	−	0.141386i
$187$	0.0291109	+	0.00571720i	0.00212880	+	0.000418083i
$188$	−0.0922946	+	0.0335925i	−0.00673127	+	0.00244998i
$189$	1.89430	−	10.0903i	0.137790	−	0.733960i
$190$	−5.62632	−	2.04781i	−0.408176	−	0.148564i
$191$	11.1246	+	6.71374i	0.804949	+	0.485789i	0.858523	−	0.512775i	$-0.171382\pi$
$191$	11.1246	+	6.71374i	0.804949	+	0.485789i	−0.0535744	+	0.998564i	$0.517061\pi$
$192$	−0.499753	−	12.0155i	−0.0360665	−	0.867142i
$193$	−9.29486	−	0.360683i	−0.669059	−	0.0259625i	−0.297992	−	0.954569i	$-0.596317\pi$
$193$	−9.29486	−	0.360683i	−0.669059	−	0.0259625i	−0.371067	+	0.928606i	$0.621008\pi$
$194$	−3.64368	−	14.1456i	−0.261601	−	1.01560i
$195$	1.48392	−	0.386640i	0.106266	−	0.0276879i
$196$	−0.315887	+	0.599698i	−0.0225634	+	0.0428355i
$197$	−6.44726	+	6.83369i	−0.459348	+	0.486880i	−0.915100	−	0.403226i	$-0.867889\pi$
$197$	−6.44726	+	6.83369i	−0.459348	+	0.486880i	0.455752	+	0.890107i	$0.349370\pi$
$198$	0.499417	−	0.207286i	0.0354920	−	0.0147312i
$199$	−6.43441	+	1.52498i	−0.456123	+	0.108103i	−0.452254	−	0.891889i	$-0.649380\pi$
$199$	−6.43441	+	1.52498i	−0.456123	+	0.108103i	−0.00386963	+	0.999993i	$0.501232\pi$
$200$	8.61662	+	8.45112i	0.609287	+	0.597584i
$201$	−2.58291	+	0.462852i	−0.182184	+	0.0326471i
$202$	−11.6752	+	14.4750i	−0.821463	+	1.01845i
$203$	−14.2701	−	2.23180i	−1.00156	−	0.156642i
$204$	−0.0320393	−	0.0872707i	−0.00224320	−	0.00611017i
$205$	0.848978	−	0.236329i	0.0592952	−	0.0165059i
$206$	−10.6428	−	11.2807i	−0.741517	−	0.785962i
$207$	−3.08411	+	4.55085i	−0.214360	+	0.316306i
$208$	−1.66003	−	5.54488i	−0.115102	−	0.384468i
$209$	0.723754	−	0.0280850i	0.0500631	−	0.00194268i
$210$	−2.81748	+	1.94394i	−0.194425	+	0.134144i
$211$	25.8408	+	7.19328i	1.77895	+	0.495206i	0.992479	−	0.122417i	$-0.0390645\pi$
$211$	25.8408	+	7.19328i	1.77895	+	0.495206i	0.786475	+	0.617622i	$0.211904\pi$
$212$	0.297928	+	0.565602i	0.0204618	+	0.0388457i
$213$	−14.9718	−	16.4067i	−1.02585	−	1.12417i
$214$	−12.3118	+	6.79335i	−0.841615	+	0.464384i
$215$	−1.35928	−	7.70885i	−0.0927021	−	0.525740i
$216$	11.1264	+	8.13978i	0.757055	+	0.553842i
$217$	0.358186	−	2.03137i	0.0243152	−	0.137899i
$218$	−7.92537	−	23.1628i	−0.536774	−	1.56878i
$219$	2.12215	−	0.212381i	0.143402	−	0.0143514i
$220$	−0.0164656	−	0.00672695i	−0.00111011	−	0.000453531i
$221$	0.182843	+	0.266592i	0.0122994	+	0.0179329i
$222$	−4.27776	+	7.80398i	−0.287105	+	0.523769i
$223$	4.46624	+	20.6185i	0.299081	+	1.38071i	0.841342	+	0.540503i	$0.181766\pi$
$223$	4.46624	+	20.6185i	0.299081	+	1.38071i	−0.542261	+	0.840210i	$0.682431\pi$
$224$	1.45477	+	1.95410i	0.0972010	+	0.130564i
$225$	−13.5460	+	1.65979i	−0.903068	+	0.110653i
$226$	−2.70391	−	6.26837i	−0.179861	−	0.416966i
$227$	−2.47875	−	25.4838i	−0.164521	−	1.69142i	−0.607048	−	0.794665i	$-0.707646\pi$
$227$	−2.47875	−	25.4838i	−0.164521	−	1.69142i	0.442527	−	0.896755i	$-0.354082\pi$
$228$	−1.25249	−	1.89283i	−0.0829484	−	0.125356i
$229$	1.89804	−	1.14547i	0.125426	−	0.0756949i	−0.452598	−	0.891714i	$-0.649503\pi$
$229$	1.89804	−	1.14547i	0.125426	−	0.0756949i	0.578024	+	0.816020i	$0.303824\pi$
$230$	1.79857	−	0.353228i	0.118594	−	0.0232912i
$231$	0.226579	−	0.346595i	0.0149078	−	0.0228043i
$232$	10.9699	−	15.9944i	0.720206	−	1.05009i
$233$	8.03551	−	5.28504i	0.526424	−	0.346234i	−0.258315	−	0.966061i	$-0.583167\pi$
$233$	8.03551	−	5.28504i	0.526424	−	0.346234i	0.784739	+	0.619826i	$0.212797\pi$
$234$	5.46675	+	2.19798i	0.357372	+	0.143687i
$235$	0.269222	−	0.135208i	0.0175621	−	0.00882001i
$236$	−1.96583	−	1.52363i	−0.127965	−	0.0991801i
$237$	−5.44636	+	6.03549i	−0.353779	+	0.392047i
$238$	−0.587066	−	0.419610i	−0.0380539	−	0.0271993i
$239$	20.2867	+	18.4092i	1.31224	+	1.19079i	0.967725	+	0.252008i	$0.0810909\pi$
$239$	20.2867	+	18.4092i	1.31224	+	1.19079i	0.344511	+	0.938782i	$0.388045\pi$
$240$	−0.802958	−	5.04213i	−0.0518307	−	0.325468i
$241$	−3.10731	+	8.04814i	−0.200160	+	0.518426i	−0.996227	−	0.0867812i	$-0.972342\pi$
$241$	−3.10731	+	8.04814i	−0.200160	+	0.518426i	0.796068	+	0.605207i	$0.206910\pi$
$242$	−16.3638			−1.05191
$243$	−15.0401	+	4.09810i	−0.964825	+	0.262893i
$244$	0.414804			0.0265551
$245$	0.748831	−	1.93952i	0.0478410	−	0.123911i
$246$	3.16221	+	1.21080i	0.201615	+	0.0771975i
$247$	5.84466	+	5.30375i	0.371887	+	0.337469i
$248$	2.25339	+	1.61062i	0.143090	+	0.102275i
$249$	−25.1859	−	5.38226i	−1.59609	−	0.341087i
$250$	7.54939	+	5.85122i	0.477466	+	0.370064i
$251$	8.29562	−	4.16622i	0.523615	−	0.262969i	−0.167299	−	0.985906i	$-0.553505\pi$
$251$	8.29562	−	4.16622i	0.523615	−	0.262969i	0.690914	+	0.722937i	$0.257208\pi$
$252$	−1.29688	−	0.0430962i	−0.0816958	−	0.00271480i
$253$	−0.185253	+	0.121843i	−0.0116468	+	0.00766019i
$254$	−15.7229	+	22.9246i	−0.986544	+	1.43842i
$255$	0.128687	+	0.254469i	0.00805871	+	0.0159355i
$256$	−5.09596	+	1.00081i	−0.318497	+	0.0625509i
$257$	−25.3115	+	15.2756i	−1.57889	+	0.952864i	−0.589468	+	0.807792i	$0.700662\pi$
$257$	−25.3115	+	15.2756i	−1.57889	+	0.952864i	−0.989421	+	0.145072i	$0.953659\pi$
$258$	13.4236	−	26.9152i	0.835719	−	1.67567i
$259$	0.659786	+	6.78319i	0.0409971	+	0.421487i
$260$	−0.0767662	−	0.177964i	−0.00476084	−	0.0110369i
$261$	6.40665	+	20.9740i	0.396562	+	1.29826i
$262$	−8.69995	−	11.6861i	−0.537485	−	0.721967i
$263$	3.95131	+	18.2413i	0.243648	+	1.12481i	0.921126	+	0.389263i	$0.127270\pi$
$263$	3.95131	+	18.2413i	0.243648	+	1.12481i	−0.677478	+	0.735543i	$0.736927\pi$
$264$	0.288626	+	0.475256i	0.0177637	+	0.0292500i
$265$	−1.10907	−	1.61707i	−0.0681298	−	0.0993357i
$266$	−16.3090	−	6.66296i	−0.999969	−	0.408532i
$267$	2.21950	+	3.08705i	0.135831	+	0.188924i
$268$	0.107368	+	0.313795i	0.00655854	+	0.0191681i
$269$	−2.88011	+	16.3339i	−0.175603	+	0.995896i	0.761842	+	0.647763i	$0.224295\pi$
$269$	−2.88011	+	16.3339i	−0.175603	+	0.995896i	−0.937445	+	0.348133i	$0.886816\pi$
$270$	4.52264	+	2.56104i	0.275239	+	0.155860i
$271$	−2.96006	−	16.7873i	−0.179811	−	1.01976i	−0.932443	−	0.361317i	$-0.882327\pi$
$271$	−2.96006	−	16.7873i	−0.179811	−	1.01976i	0.752632	−	0.658441i	$-0.228784\pi$
$272$	0.942386	−	0.519987i	0.0571405	−	0.0315288i
$273$	4.40716	−	0.967502i	0.266734	−	0.0585559i
$274$	−2.08798	−	3.96393i	−0.126139	−	0.239470i
$275$	−0.530280	−	0.147614i	−0.0319771	−	0.00890143i
$276$	0.627681	+	0.297992i	0.0377819	+	0.0179370i
$277$	−26.0850	+	1.01222i	−1.56729	+	0.0608181i	−0.807706	−	0.589586i	$-0.799291\pi$
$277$	−26.0850	+	1.01222i	−1.56729	+	0.0608181i	−0.759588	+	0.650404i	$0.774600\pi$
$278$	5.95162	+	19.8798i	0.356955	+	1.19231i
$279$	−3.01252	+	0.856689i	−0.180355	+	0.0512887i
$280$	−2.41552	−	2.56031i	−0.144355	−	0.153008i
$281$	10.7649	−	2.99661i	0.642180	−	0.178763i	0.0682511	−	0.997668i	$-0.478258\pi$
$281$	10.7649	−	2.99661i	0.642180	−	0.178763i	0.573929	+	0.818905i	$0.305419\pi$
$282$	1.14054	+	0.197836i	0.0679179	+	0.0117809i
$283$	−0.402949	−	0.0630201i	−0.0239528	−	0.00374616i	0.142531	−	0.989790i	$-0.454476\pi$
$283$	−0.402949	−	0.0630201i	−0.0239528	−	0.00374616i	−0.166484	+	0.986044i	$0.553241\pi$
$284$	−1.76245	+	2.18509i	−0.104582	+	0.129661i
$285$	4.48986	+	5.32066i	0.265957	+	0.315169i
$286$	0.169663	+	0.166404i	0.0100324	+	0.00983970i
$287$	2.52315	−	0.597997i	0.148937	−	0.0352987i
$288$	1.70565	−	3.28227i	0.100506	−	0.193410i
$289$	11.6249	−	12.3216i	0.683815	−	0.724802i
$290$	3.40772	−	6.46940i	0.200108	−	0.379896i
$291$	−4.50932	+	16.3753i	−0.264341	+	0.959940i
$292$	−0.0672394	−	0.261039i	−0.00393489	−	0.0152762i
$293$	−6.78607	−	0.263330i	−0.396447	−	0.0153839i	−0.160218	−	0.987082i	$-0.551220\pi$
$293$	−6.78607	−	0.263330i	−0.396447	−	0.0153839i	−0.236228	+	0.971698i	$0.575911\pi$
$294$	6.74622	−	4.27826i	0.393448	−	0.249513i
$295$	6.53165	+	3.94187i	0.380287	+	0.229504i
$296$	−8.59956	−	3.12998i	−0.499839	−	0.181927i
$297$	−0.623639	−	0.0798829i	−0.0361872	−	0.00463528i
$298$	−18.8785	+	6.87120i	−1.09360	+	0.398038i
$299$	−2.37082	−	0.465613i	−0.137108	−	0.0269271i
$300$	0.467192	+	1.66042i	0.0269734	+	0.0958643i
$301$	−3.11705	−	22.8208i	−0.179664	−	1.31537i
$302$	10.4129	−	0.809353i	0.599194	−	0.0465730i
$303$	20.1504	−	7.84439i	1.15761	−	0.450648i
$304$	19.4598	−	17.6588i	1.11610	−	1.01280i
$305$	−1.26374	+	0.147710i	−0.0723614	+	0.00845784i
$306$	−0.184252	+	1.08007i	−0.0105330	+	0.0617433i
$307$	2.45902	−	3.30304i	0.140344	−	0.188514i	−0.726394	−	0.687278i	$-0.758805\pi$
$307$	2.45902	−	3.30304i	0.140344	−	0.188514i	0.866738	+	0.498764i	$0.166213\pi$
$308$	−0.0476451	−	0.0216574i	−0.00271483	−	0.00123404i
$309$	4.20752	+	17.5353i	0.239357	+	0.997547i
$310$	0.914296	+	0.504487i	0.0519285	+	0.0286529i
$311$	1.81160	−	5.29459i	0.102726	−	0.300229i	−0.882801	−	0.469748i	$-0.844345\pi$
$311$	1.81160	−	5.29459i	0.102726	−	0.300229i	0.985527	+	0.169519i	$0.0542214\pi$
$312$	−1.38086	+	5.89942i	−0.0781756	+	0.333989i
$313$	−25.3086	−	1.96714i	−1.43053	−	0.111189i	−0.661278	−	0.750141i	$-0.729986\pi$
$313$	−25.3086	−	1.96714i	−1.43053	−	0.111189i	−0.769247	+	0.638952i	$0.779368\pi$
$314$	−0.826436	−	14.1894i	−0.0466385	−	0.800752i
$315$	3.96641	−	0.330517i	0.223482	−	0.0186225i
$316$	0.858465	+	0.564621i	0.0482924	+	0.0317624i
$317$	26.0437	−	10.6400i	1.46276	−	0.597604i	0.499535	−	0.866294i	$-0.333504\pi$
$317$	26.0437	−	10.6400i	1.46276	−	0.597604i	0.963227	+	0.268689i	$0.0865905\pi$
$318$	0.271188	−	7.52937i	0.0152074	−	0.422226i
$319$	−0.0856329	+	0.880383i	−0.00479452	+	0.0492920i
$320$	4.43958	−	1.42349i	0.248180	−	0.0795757i
$321$	16.3480	+	0.271553i	0.912459	+	0.0151566i
$322$	5.32851	−	0.833364i	0.296946	−	0.0464415i
$323$	−0.733822	+	1.27102i	−0.0408310	+	0.0707213i
$324$	0.800462	+	1.80030i	0.0444701	+	0.100017i
$325$	−2.99897	−	5.19437i	−0.166353	−	0.288132i
$326$	−9.97679	−	12.3693i	−0.552563	−	0.685071i
$327$	−5.40792	+	27.9472i	−0.299059	+	1.54549i
$328$	−0.737141	+	3.40302i	−0.0407018	+	0.187900i
$329$	0.806999	−	0.366826i	0.0444913	−	0.0202238i
$330$	0.128880	+	0.165332i	0.00709460	+	0.00910120i
$331$	1.75442	−	12.8446i	0.0964318	−	0.706006i	−0.877567	−	0.479453i	$-0.840835\pi$
$331$	1.75442	−	12.8446i	0.0964318	−	0.706006i	0.973999	−	0.226552i	$-0.0727453\pi$
$332$	−0.189269	+	3.24963i	−0.0103875	+	0.178347i
$333$	8.82972	−	5.39605i	0.483866	−	0.295701i
$334$	−1.21425	−	0.609817i	−0.0664406	−	0.0333677i
$335$	−0.438847	−	0.917771i	−0.0239768	−	0.0501432i
$336$	−1.78560	−	14.9166i	−0.0974124	−	0.813767i
$337$	−13.7474	−	15.7528i	−0.748870	−	0.858109i	0.244902	−	0.969548i	$-0.421244\pi$
$337$	−13.7474	−	15.7528i	−0.748870	−	0.858109i	−0.993771	+	0.111439i	$0.964454\pi$
$338$	−0.325295	−	16.7721i	−0.0176937	−	0.912284i
$339$	−0.899574	+	7.88666i	−0.0488581	+	0.428344i
$340$	0.0293214	−	0.0209577i	0.00159018	−	0.00113659i
$341$	−0.125468	−	0.0146651i	−0.00679449	−	0.000794162i
$342$	1.70401	+	26.6957i	0.0921421	+	1.44354i
$343$	7.90104	−	18.3167i	0.426616	−	0.989007i
$344$	29.4515	+	9.44324i	1.58792	+	0.509145i
$345$	−2.01840	−	0.684346i	−0.108667	−	0.0368440i
$346$	−5.33074	+	11.1483i	−0.286582	+	0.599336i
$347$	−21.2679	+	16.4839i	−1.14172	+	0.884900i	−0.994555	−	0.104212i	$-0.966768\pi$
$347$	−21.2679	+	16.4839i	−1.14172	+	0.884900i	−0.147165	+	0.989112i	$0.547015\pi$
$348$	2.49732	−	1.20269i	0.133870	−	0.0644707i
$349$	8.49437	−	9.73347i	0.454693	−	0.521021i	−0.479619	−	0.877477i	$-0.659225\pi$
$349$	8.49437	−	9.73347i	0.454693	−	0.521021i	0.934312	+	0.356456i	$0.116015\pi$
$350$	10.2564	+	8.60612i	0.548226	+	0.460016i
$351$	−4.24203	−	5.37980i	−0.226423	−	0.287152i
$352$	0.114288	−	0.0958992i	0.00609158	−	0.00511144i
$353$	−0.166965	+	8.60865i	−0.00888662	+	0.458192i	0.968767	+	0.247971i	$0.0797639\pi$
$353$	−0.166965	+	8.60865i	−0.00888662	+	0.458192i	−0.977654	+	0.210221i	$0.932582\pi$
$354$	11.1616	+	27.1047i	0.593234	+	1.44060i
$355$	4.59135	−	7.28467i	0.243684	−	0.386630i
$356$	0.343080	−	0.336490i	0.0181832	−	0.0178339i
$357$	0.349336	+	0.762878i	0.0184888	+	0.0403758i
$358$	17.7920	+	28.2289i	0.940334	+	1.49194i
$359$	11.4898	+	2.72314i	0.606410	+	0.143722i	0.522339	−	0.852738i	$-0.325060\pi$
$359$	11.4898	+	2.72314i	0.606410	+	0.143722i	0.0840710	+	0.996460i	$0.473208\pi$
$360$	−1.89721	+	4.99650i	−0.0999917	+	0.263338i
$361$	−4.82732	+	16.1244i	−0.254070	+	0.848652i
$362$	−5.92159	+	22.9890i	−0.311232	+	1.20828i
$363$	16.5045	+	9.46770i	0.866259	+	0.496925i
$364$	−0.205405	−	0.532013i	−0.0107662	−	0.0278850i
$365$	0.297806	+	0.771337i	0.0155879	+	0.0403736i
$366$	−4.24057	−	2.43258i	−0.221658	−	0.127153i
$367$	2.59357	−	10.0688i	0.135383	−	0.525589i	−0.864359	−	0.502875i	$-0.832275\pi$
$367$	2.59357	−	10.0688i	0.135383	−	0.525589i	0.999742	−	0.0227140i	$-0.00723071\pi$
$368$	−2.30717	+	7.70647i	−0.120269	+	0.401728i
$369$	−2.48885	−	3.05078i	−0.129564	−	0.158817i
$370$	−3.35718	−	0.795667i	−0.174532	−	0.0413647i
$371$	−3.07642	−	4.88108i	−0.159720	−	0.253413i
$372$	0.164810	+	0.359910i	0.00854498	+	0.0186605i
$373$	0.716476	−	0.702715i	0.0370977	−	0.0363852i	−0.681432	−	0.731881i	$-0.738643\pi$
$373$	0.716476	−	0.702715i	0.0370977	−	0.0363852i	0.718530	+	0.695496i	$0.244815\pi$
$374$	−0.0235634	+	0.0373859i	−0.00121843	+	0.00193318i
$375$	−4.22891	−	10.2694i	−0.218380	−	0.530310i
$376$	−0.0230822	+	1.19011i	−0.00119038	+	0.0613754i
$377$	−7.38348	+	6.19548i	−0.380269	+	0.319083i
$378$	13.0054	+	8.04603i	0.668925	+	0.413843i
$379$	−11.1028	−	9.31634i	−0.570312	−	0.478548i	0.311438	−	0.950267i	$-0.399190\pi$
$379$	−11.1028	−	9.31634i	−0.570312	−	0.478548i	−0.881749	+	0.471718i	$0.843634\pi$
$380$	0.578567	−	0.662964i	0.0296799	−	0.0340093i
$381$	29.1216	−	14.0247i	1.49195	−	0.718508i
$382$	−15.2982	+	11.8570i	−0.782723	+	0.606656i
$383$	9.15795	−	19.1522i	0.467950	−	0.978633i	−0.523967	−	0.851739i	$-0.675548\pi$
$383$	9.15795	−	19.1522i	0.467950	−	0.978633i	0.991916	−	0.126895i	$-0.0405010\pi$
$384$	21.0102	+	7.12358i	1.07217	+	0.363524i
$385$	0.152867	+	0.0490149i	0.00779084	+	0.00249803i
$386$	5.48811	−	12.7229i	0.279337	−	0.647577i
$387$	−29.1115	+	19.3799i	−1.47982	+	0.985137i
$388$	2.13221	+	0.249220i	0.108247	+	0.0126522i
$389$	−9.26852	+	6.62474i	−0.469933	+	0.335888i	−0.791678	−	0.610939i	$-0.790792\pi$
$389$	−9.26852	+	6.62474i	−0.469933	+	0.335888i	0.321745	+	0.946826i	$0.395731\pi$
$390$	−0.258869	+	2.26953i	−0.0131083	+	0.114922i
$391$	−0.00871236	−	0.449207i	−0.000440603	−	0.0227174i
$392$	5.40127	+	6.18916i	0.272805	+	0.312600i
$393$	2.01346	+	16.8201i	0.101565	+	0.848460i
$394$	−6.03718	−	12.6257i	−0.304149	−	0.636073i
$395$	−2.81645	−	1.41447i	−0.141711	−	0.0711700i
$396$	0.00198321	+	0.0794414i	9.96599e−5	+	0.00399208i
$397$	−0.705712	+	12.1166i	−0.0354187	+	0.608115i	0.933168	+	0.359440i	$0.117032\pi$
$397$	−0.705712	+	12.1166i	−0.0354187	+	0.608115i	−0.968587	+	0.248675i	$0.920005\pi$
$398$	1.33304	−	9.75961i	0.0668195	−	0.489205i
$399$	12.5941	+	16.1562i	0.630496	+	0.808822i
$400$	−18.1801	+	8.26387i	−0.909005	+	0.413193i
$401$	−2.99695	+	13.8354i	−0.149660	+	0.690909i	0.839414	+	0.543492i	$0.182898\pi$
$401$	−2.99695	+	13.8354i	−0.149660	+	0.690909i	−0.989074	+	0.147417i	$0.952904\pi$
$402$	0.742593	−	3.83760i	0.0370372	−	0.191402i
$403$	−0.864174	−	1.07141i	−0.0430476	−	0.0533706i
$404$	−1.36650	−	2.36684i	−0.0679858	−	0.117755i
$405$	−3.07976	−	5.19974i	−0.153035	−	0.258377i
$406$	10.7576	−	18.6327i	0.533890	−	0.924724i
$407$	0.412357	−	0.0644915i	0.0204398	−	0.00319672i
$408$	−1.12653	−	0.0187125i	−0.0557717	−	0.000926409i
$409$	−7.88354	+	2.52776i	−0.389816	+	0.124989i	−0.493770	−	0.869593i	$-0.664381\pi$
$409$	−7.88354	+	2.52776i	−0.389816	+	0.124989i	0.103954	+	0.994582i	$0.466851\pi$
$410$	−0.127086	+	1.30656i	−0.00627632	+	0.0645263i
$411$	−0.187508	+	5.20605i	−0.00924908	+	0.256796i
$412$	2.10991	−	0.861993i	0.103948	−	0.0424674i
$413$	18.7548	+	12.3352i	0.922861	+	0.606975i
$414$	−4.66928	−	6.72738i	−0.229483	−	0.330633i
$415$	−0.580552	−	9.96769i	−0.0284982	−	0.489295i
$416$	1.62080	+	0.125979i	0.0794664	+	0.00617662i
$417$	5.49919	−	23.4941i	0.269296	−	1.15051i
$418$	−0.349282	+	1.02082i	−0.0170839	+	0.0499297i
$419$	−19.0400	−	10.5058i	−0.930166	−	0.513244i	−0.0557628	−	0.998444i	$-0.517759\pi$
$419$	−19.0400	−	10.5058i	−0.930166	−	0.513244i	−0.874403	+	0.485200i	$0.838747\pi$
$420$	−0.117374	−	0.489170i	−0.00572728	−	0.0238690i
$421$	25.9956	+	11.8164i	1.26695	+	0.575898i	0.930668	−	0.365865i	$-0.119227\pi$
$421$	25.9956	+	11.8164i	1.26695	+	0.575898i	0.336278	+	0.941763i	$0.390832\pi$
$422$	−23.8601	+	32.0497i	−1.16149	+	1.56015i
$423$	−1.03588	−	0.859422i	−0.0503660	−	0.0417865i
$424$	7.69516	−	0.899435i	0.373710	−	0.0436804i
$425$	0.825973	−	0.749530i	0.0400656	−	0.0363576i
$426$	30.8319	−	12.0026i	1.49381	−	0.581529i
$427$	−3.73252	+	0.290115i	−0.180629	+	0.0140396i
$428$	−0.279665	−	2.04751i	−0.0135181	−	0.0989703i
$429$	−0.0748438	−	0.265997i	−0.00361349	−	0.0128425i
$430$	11.4417	+	2.24708i	0.551768	+	0.108364i
$431$	−20.4030	+	7.42608i	−0.982777	+	0.357701i	−0.782919	−	0.622123i	$-0.786270\pi$
$431$	−20.4030	+	7.42608i	−0.982777	+	0.357701i	−0.199858	+	0.979825i	$0.564048\pi$
$432$	−19.1952	+	12.3234i	−0.923532	+	0.592911i
$433$	−25.6744	−	9.34472i	−1.23383	−	0.449079i	−0.358924	−	0.933367i	$-0.616856\pi$
$433$	−25.6744	−	9.34472i	−1.23383	−	0.449079i	−0.874909	+	0.484288i	$0.839079\pi$
$434$	2.63067	+	1.58762i	0.126276	+	0.0762082i
$435$	−7.18004	+	4.55338i	−0.344257	+	0.218318i
$436$	3.59509	+	0.139506i	0.172173	+	0.00668111i
$437$	−2.73615	−	10.6224i	−0.130888	−	0.508138i
$438$	−0.843451	+	3.06295i	−0.0403016	+	0.146353i
$439$	19.2882	−	36.6177i	0.920574	−	1.74767i	0.321652	−	0.946858i	$-0.395762\pi$
$439$	19.2882	−	36.6177i	0.920574	−	1.74767i	0.598921	−	0.800808i	$-0.295596\pi$
$440$	−0.147929	+	0.156796i	−0.00705224	+	0.00747494i
$441$	−9.27950	+	0.411833i	−0.441881	+	0.0196111i
$442$	−0.468563	+	0.111051i	−0.0222873	+	0.00528218i
$443$	3.74128	+	3.66943i	0.177754	+	0.174340i	0.783647	−	0.621206i	$-0.213357\pi$
$443$	3.74128	+	3.66943i	0.177754	+	0.174340i	−0.605893	+	0.795546i	$0.707184\pi$
$444$	−0.843481	−	0.999559i	−0.0400298	−	0.0474369i
$445$	−0.925401	+	1.14732i	−0.0438682	+	0.0543881i
$446$	−31.0482	−	4.85584i	−1.47017	−	0.229931i
$447$	23.0162	+	3.99236i	1.08863	+	0.188832i
$448$	13.2158	−	3.67886i	0.624386	−	0.173810i
$449$	26.3416	+	27.9205i	1.24314	+	1.31765i	0.929826	+	0.368001i	$0.119958\pi$
$449$	26.3416	+	27.9205i	1.24314	+	1.31765i	0.313314	+	0.949650i	$0.398561\pi$
$450$	4.96124	−	19.7144i	0.233875	−	0.929346i
$451$	−0.0455445	−	0.152129i	−0.00214461	−	0.00716349i
$452$	1.00251	−	0.0389019i	0.0471540	−	0.00182979i
$453$	−10.9706	−	5.20832i	−0.515446	−	0.244708i
$454$	36.7429	+	10.2281i	1.72443	+	0.480027i
$455$	0.815233	+	1.54768i	0.0382187	+	0.0725564i
$456$	−26.8675	+	5.89821i	−1.25819	+	0.276209i
$457$	−24.4341	+	13.4821i	−1.14298	+	0.630668i	−0.937497	−	0.347993i	$-0.886863\pi$
$457$	−24.4341	+	13.4821i	−1.14298	+	0.630668i	−0.205480	+	0.978661i	$0.565876\pi$
$458$	0.573439	+	3.25213i	0.0267950	+	0.151962i
$459$	0.810736	−	0.982747i	0.0378419	−	0.0458707i
$460$	−0.0467758	+	0.265279i	−0.00218093	+	0.0123687i
$461$	−7.24174	−	21.1648i	−0.337282	−	0.985743i	−0.976276	−	0.216531i	$-0.930526\pi$
$461$	−7.24174	−	21.1648i	−0.337282	−	0.985743i	0.638994	−	0.769212i	$-0.279351\pi$
$462$	0.360072	+	0.500816i	0.0167521	+	0.0233001i
$463$	−10.1034	−	4.12770i	−0.469546	−	0.191831i	0.131062	−	0.991374i	$-0.458161\pi$
$463$	−10.1034	−	4.12770i	−0.469546	−	0.191831i	−0.600608	+	0.799544i	$0.705075\pi$
$464$	18.1510	+	26.4648i	0.842640	+	1.22860i
$465$	−0.630270	−	1.03781i	−0.0292281	−	0.0481274i
$466$	3.03300	+	14.0019i	0.140501	+	0.648625i
$467$	−23.6585	−	31.7789i	−1.09479	−	1.47055i	−0.867970	−	0.496617i	$-0.834576\pi$
$467$	−23.6585	−	31.7789i	−1.09479	−	1.47055i	−0.226817	−	0.973937i	$-0.572832\pi$
$468$	−0.590708	+	0.633138i	−0.0273055	+	0.0292668i
$469$	−1.18560	−	2.74852i	−0.0547458	−	0.126915i
$470$	0.0434456	+	0.446660i	0.00200400	+	0.0206029i
$471$	−7.37607	+	14.7895i	−0.339872	+	0.681463i
$472$	−25.8072	+	15.5747i	−1.18787	+	0.716886i
$473$	−1.38411	+	0.271830i	−0.0636413	+	0.0124987i
$474$	−5.46498	−	10.8066i	−0.251015	−	0.496362i
$475$	15.4019	−	22.4565i	0.706686	−	1.03037i
$476$	0.0886027	−	0.0582749i	0.00406110	−	0.00267103i
$477$	−4.62983	+	7.43718i	−0.211985	+	0.340525i
$478$	−36.4661	+	18.3140i	−1.66792	+	0.837661i
$479$	−27.1193	−	21.0191i	−1.23911	−	0.960385i	−0.239170	−	0.970978i	$-0.576875\pi$
$479$	−27.1193	−	21.0191i	−1.23911	−	0.960385i	−0.999944	+	0.0105925i	$0.996628\pi$
$480$	1.40237	+	0.299688i	0.0640090	+	0.0136788i
$481$	3.69996	+	2.64457i	0.168704	+	0.120582i
$482$	−9.51676	−	8.63600i	−0.433477	−	0.393359i
$483$	−5.85647	−	2.24242i	−0.266479	−	0.102034i
$484$	0.866176	−	2.24345i	0.0393717	−	0.101975i
$485$	−6.58472			−0.298997
$486$	2.37453	−	23.0989i	0.107711	−	1.04779i
$487$	13.3522			0.605046			0.302523	−	0.953142i	$-0.402171\pi$
$487$	13.3522			0.605046			0.302523	+	0.953142i	$0.402171\pi$
$488$	1.81067	−	4.68975i	0.0819652	−	0.212295i
$489$	2.90598	+	18.2479i	0.131413	+	0.825199i
$490$	2.29344	+	2.08119i	0.103607	+	0.0940185i
$491$	−21.7848	−	15.5708i	−0.983135	−	0.702703i	−0.0282259	−	0.999602i	$-0.508986\pi$
$491$	−21.7848	−	15.5708i	−0.983135	−	0.702703i	−0.954909	+	0.296899i	$0.904048\pi$
$492$	−0.333381	+	0.369443i	−0.0150300	+	0.0166558i
$493$	−1.41665	−	1.09799i	−0.0638027	−	0.0494508i
$494$	−10.5060	+	5.27632i	−0.472688	+	0.237393i
$495$	−0.0343307	−	0.241319i	−0.00154305	−	0.0108465i
$496$	−3.82905	+	2.51840i	−0.171929	+	0.113080i
$497$	14.3307	−	20.8947i	0.642821	−	0.937256i
$498$	20.9921	−	32.1113i	0.940679	−	1.43894i
$499$	13.5544	−	2.66200i	0.606779	−	0.119167i	0.120120	−	0.992759i	$-0.461672\pi$
$499$	13.5544	−	2.66200i	0.606779	−	0.119167i	0.486659	+	0.873592i	$0.338215\pi$
$500$	−1.20180	+	0.725291i	−0.0537462	+	0.0324360i
$501$	0.871856	+	1.31759i	0.0389517	+	0.0588656i
$502$	1.33870	+	13.7631i	0.0597492	+	0.614276i
$503$	13.6888	+	31.7342i	0.610354	+	1.41496i	0.890492	+	0.455000i	$0.150361\pi$
$503$	13.6888	+	31.7342i	0.610354	+	1.41496i	−0.280138	+	0.959960i	$0.590380\pi$
$504$	−6.14829	+	14.4744i	−0.273866	+	0.644739i
$505$	5.00598	+	6.72420i	0.222763	+	0.299223i
$506$	−0.0699237	−	0.322804i	−0.00310849	−	0.0143504i
$507$	−9.37585	+	17.1045i	−0.416396	+	0.759637i
$508$	−2.31067	−	3.36904i	−0.102519	−	0.149477i
$509$	1.19802	+	0.489443i	0.0531011	+	0.0216942i	0.404595	−	0.914496i	$-0.367413\pi$
$509$	1.19802	+	0.489443i	0.0531011	+	0.0216942i	−0.351494	+	0.936190i	$0.614326\pi$
$510$	−0.422660	+	0.0422991i	−0.0187157	+	0.00187304i
$511$	0.787611	+	2.30188i	0.0348419	+	0.101829i
$512$	−3.10501	+	17.6094i	−0.137223	+	0.778233i
$513$	13.7268	−	27.9110i	0.606053	−	1.23230i
$514$	−7.64716	−	43.3692i	−0.337302	−	1.91293i
$515$	−6.12108	+	3.37747i	−0.269727	+	0.148829i
$516$	2.97948	+	3.26504i	0.131164	+	0.143736i
$517$	−0.0253004	−	0.0480316i	−0.00111271	−	0.00211243i
$518$	−9.78008	−	2.72247i	−0.429712	−	0.119619i
$519$	11.8267	−	8.15988i	0.519134	−	0.358179i
$520$	−2.34715	+	0.0910800i	−0.102929	+	0.00399412i
$521$	9.68931	+	32.3645i	0.424496	+	1.41792i	0.856548	+	0.516067i	$0.172605\pi$
$521$	9.68931	+	32.3645i	0.424496	+	1.41792i	−0.432052	+	0.901849i	$0.642210\pi$
$522$	−32.5834	−	2.35018i	−1.42613	−	0.102865i
$523$	26.7639	+	28.3681i	1.17030	+	1.24045i	0.965143	+	0.261722i	$0.0842904\pi$
$523$	26.7639	+	28.3681i	1.17030	+	1.24045i	0.205161	+	0.978728i	$0.434228\pi$
$524$	2.06265	−	0.574178i	0.0901072	−	0.0250831i
$525$	−5.36523	−	14.6142i	−0.234158	−	0.637814i
$526$	−27.4685	−	4.29600i	−1.19769	−	0.187315i
$527$	0.160699	−	0.199236i	0.00700016	−	0.00867884i
$528$	−0.905603	+	0.162282i	−0.0394113	+	0.00706244i
$529$	−14.0230	−	13.7537i	−0.609696	−	0.597986i
$530$	2.84216	−	0.673604i	0.123456	−	0.0292595i
$531$	4.42456	−	33.7955i	0.192010	−	1.46660i
$532$	1.77676	−	1.88325i	0.0770321	−	0.0816493i
$533$	0.806435	−	1.53098i	0.0349306	−	0.0663141i
$534$	−5.48065	+	1.42800i	−0.237171	+	0.0617957i
$535$	1.58114	+	6.13835i	0.0683585	+	0.265384i
$536$	4.01642	+	0.155856i	0.173483	+	0.00673193i
$537$	−1.61235	−	38.7655i	−0.0695780	−	1.67285i
$538$	−21.1528	−	12.7658i	−0.911961	−	0.550372i
$539$	−0.352048	−	0.128135i	−0.0151638	−	0.00551917i
$540$	−0.590509	+	0.484485i	−0.0254115	+	0.0208489i
$541$	36.8218	−	13.4020i	1.58309	−	0.576198i	0.607218	−	0.794535i	$-0.292285\pi$
$541$	36.8218	−	13.4020i	1.58309	−	0.576198i	0.975874	+	0.218337i	$0.0700631\pi$
$542$	24.9162	+	4.89339i	1.07024	+	0.210189i
$543$	19.2734	−	19.7605i	0.827099	−	0.848004i
$544$	0.0409118	+	0.299527i	0.00175408	+	0.0128421i
$545$	−11.0024	+	0.855177i	−0.471293	+	0.0366318i
$546$	−1.02007	+	6.64339i	−0.0436551	+	0.284311i
$547$	27.6418	−	25.0836i	1.18188	−	1.07250i	0.185931	−	0.982563i	$-0.440470\pi$
$547$	27.6418	−	25.0836i	1.18188	−	1.07250i	0.995948	−	0.0899349i	$-0.0286659\pi$
$548$	0.653970	−	0.0764381i	0.0279362	−	0.00326528i
$549$	2.86959	+	4.90698i	0.122471	+	0.209425i
$550$	0.489634	−	0.657693i	0.0208781	−	0.0280441i
$551$	−39.8362	−	18.1078i	−1.69708	−	0.771417i
$552$	6.10899	−	5.79576i	0.260016	−	0.246684i
$553$	−8.11961	−	4.48021i	−0.345281	−	0.190518i
$554$	12.5885	−	36.7914i	0.534836	−	1.56312i
$555$	2.92568	+	2.74489i	0.124188	+	0.116514i
$556$	−3.04052	−	0.236328i	−0.128947	−	0.0100225i
$557$	−1.01773	−	17.4738i	−0.0431228	−	0.740390i	−0.948694	−	0.316196i	$-0.897594\pi$
$557$	−1.01773	−	17.4738i	−0.0431228	−	0.740390i	0.905571	−	0.424194i	$-0.139443\pi$
$558$	0.425804	−	4.64591i	0.0180257	−	0.196677i
$559$	−12.8416	−	8.44604i	−0.543141	−	0.357229i
$560$	5.39158	−	2.20270i	0.227836	−	0.0930812i
$561$	0.0453965	−	0.0240740i	0.00191664	−	0.00101640i
$562$	−1.61143	+	16.5669i	−0.0679740	+	0.698834i
$563$	33.9039	−	10.8709i	1.42888	−	0.458152i	0.512579	−	0.858640i	$-0.328690\pi$
$563$	33.9039	−	10.8709i	1.42888	−	0.458152i	0.916302	+	0.400488i	$0.131159\pi$
$564$	−0.0874943	+	0.145894i	−0.00368417	+	0.00614323i
$565$	−3.04038	+	0.475507i	−0.127910	+	0.0200047i
$566$	0.303765	−	0.526137i	0.0127682	−	0.0221152i
$567$	−8.46193	−	15.6398i	−0.355367	−	0.656809i
$568$	17.0112	+	29.4643i	0.713775	+	1.23630i
$569$	1.15888	+	1.43679i	0.0485829	+	0.0602333i	0.802074	−	0.597225i	$-0.203730\pi$
$569$	1.15888	+	1.43679i	0.0485829	+	0.0602333i	−0.753491	+	0.657459i	$0.771631\pi$
$570$	−9.80264	+	3.38458i	−0.410587	+	0.141764i
$571$	−9.41099	+	43.4460i	−0.393838	+	1.81816i	0.161909	+	0.986806i	$0.448235\pi$
$571$	−9.41099	+	43.4460i	−0.393838	+	1.81816i	−0.555747	+	0.831352i	$0.687568\pi$
$572$	−0.0317944	+	0.0144523i	−0.00132939	+	0.000604283i
$573$	22.2898	−	3.10774i	0.931170	−	0.129828i
$574$	−0.522731	+	3.82707i	−0.0218184	+	0.159739i
$575$	−0.484705	+	8.32206i	−0.0202136	+	0.347054i
$576$	−13.7829	−	15.6171i	−0.574289	−	0.650714i
$577$	−2.37851	−	1.19453i	−0.0990186	−	0.0497290i	0.398601	−	0.917125i	$-0.369496\pi$
$577$	−2.37851	−	1.19453i	−0.0990186	−	0.0497290i	−0.497619	+	0.867396i	$0.665792\pi$
$578$	10.8855	+	22.7650i	0.452776	+	0.946900i
$579$	−12.8964	+	9.65693i	−0.535957	+	0.401328i
$580$	0.706565	+	0.809634i	0.0293385	+	0.0336182i
$581$	−0.569698	−	29.3735i	−0.0236350	−	1.21862i
$582$	−20.3362	−	15.0520i	−0.842965	−	0.623925i
$583$	−0.287462	+	0.205465i	−0.0119054	+	0.00850950i
$584$	−3.24481	−	0.379264i	−0.134271	−	0.0156940i
$585$	1.57419	−	2.13926i	0.0650847	−	0.0884476i
$586$	4.00680	−	9.28882i	0.165520	−	0.383717i
$587$	−22.3783	−	7.17531i	−0.923650	−	0.296157i	−0.194811	−	0.980841i	$-0.562409\pi$
$587$	−22.3783	−	7.17531i	−0.923650	−	0.296157i	−0.728840	+	0.684684i	$0.759940\pi$
$588$	0.229449	+	1.15136i	0.00946231	+	0.0474811i
$589$	2.69584	−	5.63787i	0.111080	−	0.232304i
$590$	−8.98209	+	6.96165i	−0.369787	+	0.286606i
$591$	−1.21585	+	16.2272i	−0.0500132	+	0.667497i
$592$	9.95636	−	11.4087i	0.409204	−	0.468896i
$593$	6.33997	+	5.31987i	0.260351	+	0.218461i	0.763614	−	0.645672i	$-0.223423\pi$
$593$	6.33997	+	5.31987i	0.260351	+	0.218461i	−0.503263	+	0.864133i	$0.667867\pi$
$594$	0.445603	−	0.823766i	0.0182833	−	0.0337995i
$595$	−0.249185	+	0.209091i	−0.0102156	+	0.00857189i
$596$	0.0572524	−	2.95192i	0.00234515	−	0.120915i
$597$	−6.99117	+	9.07223i	−0.286130	+	0.371301i
$598$	1.91902	−	3.04474i	0.0784746	−	0.124508i
$599$	−20.1963	+	19.8084i	−0.825199	+	0.809349i	−0.984039	−	0.177955i	$-0.943052\pi$
$599$	−20.1963	+	19.8084i	−0.825199	+	0.809349i	0.158840	+	0.987304i	$0.449225\pi$
$600$	20.8120	+	1.96587i	0.849645	+	0.0802565i
$601$	7.64037	+	12.1223i	0.311657	+	0.494478i	0.964881	−	0.262687i	$-0.0846087\pi$
$601$	7.64037	+	12.1223i	0.311657	+	0.494478i	−0.653224	+	0.757165i	$0.726584\pi$
$602$	33.3848	+	7.91234i	1.36066	+	0.322483i
$603$	−2.96932	+	3.44094i	−0.120920	+	0.140126i
$604$	−0.440218	+	1.47043i	−0.0179122	+	0.0598309i
$605$	−1.84000	+	7.14333i	−0.0748067	+	0.290418i
$606$	0.0896523	+	32.2102i	0.00364187	+	1.30845i
$607$	1.72831	+	4.47645i	0.0701501	+	0.181693i	0.963525	−	0.267619i	$-0.0862369\pi$
$607$	1.72831	+	4.47645i	0.0701501	+	0.181693i	−0.893375	+	0.449312i	$0.851669\pi$
$608$	2.65834	+	6.88528i	0.107810	+	0.279235i
$609$	−21.6304	+	12.5687i	−0.876510	+	0.509311i
$610$	0.472761	−	1.83537i	0.0191415	−	0.0743120i
$611$	0.169658	−	0.566698i	0.00686364	−	0.0229262i
$612$	−0.138323	−	0.0824312i	−0.00559136	−	0.00333208i
$613$	24.4115	+	5.78564i	0.985973	+	0.233680i	0.691813	−	0.722077i	$-0.256812\pi$
$613$	24.4115	+	5.78564i	0.985973	+	0.233680i	0.294159	+	0.955756i	$0.404960\pi$
$614$	3.27067	+	5.18927i	0.131993	+	0.209422i
$615$	0.884120	−	1.24426i	0.0356512	−	0.0501733i
$616$	−0.452834	+	0.444136i	−0.0182452	+	0.0178948i
$617$	9.47349	−	15.0307i	0.381388	−	0.605114i	−0.599339	−	0.800495i	$-0.704570\pi$
$617$	9.47349	−	15.0307i	0.381388	−	0.605114i	0.980727	+	0.195382i	$0.0625945\pi$
$618$	−26.6249	−	3.56118i	−1.07101	−	0.143251i
$619$	−0.709205	+	36.5664i	−0.0285054	+	1.46973i	0.663684	+	0.748013i	$0.268992\pi$
$619$	−0.709205	+	36.5664i	−0.0285054	+	1.46973i	−0.692189	+	0.721716i	$0.743354\pi$
$620$	−0.117560	+	0.0986448i	−0.00472133	+	0.00396167i
$621$	0.817114	+	9.48673i	0.0327897	+	0.380689i
$622$	6.38554	+	5.35810i	0.256037	+	0.214840i
$623$	−2.85179	+	3.26779i	−0.114254	+	0.130921i
$624$	−8.28326	−	5.64727i	−0.331596	−	0.226072i
$625$	−14.5748	+	11.2963i	−0.582991	+	0.451852i
$626$	16.3122	−	34.1140i	0.651966	−	1.36347i
$627$	0.942903	−	0.827503i	0.0376559	−	0.0330473i
$628$	1.98908	+	0.637774i	0.0793731	+	0.0254500i
$629$	−0.334971	+	0.776549i	−0.0133562	+	0.0309630i
$630$	−1.66877	+	5.68916i	−0.0664854	+	0.226661i
$631$	2.17446	+	0.254158i	0.0865639	+	0.0101179i	0.159265	−	0.987236i	$-0.449088\pi$
$631$	2.17446	+	0.254158i	0.0865639	+	0.0101179i	−0.0727007	+	0.997354i	$0.523162\pi$
$632$	10.1309	−	7.24112i	0.402985	−	0.288036i
$633$	42.6083	−	18.5203i	1.69353	−	0.736114i
$634$	0.812643	+	41.8997i	0.0322742	+	1.66405i
$635$	8.23937	+	9.44127i	0.326969	+	0.374665i
$636$	1.01791	+	0.435727i	0.0403628	+	0.0172777i
$637$	−1.76105	−	3.68293i	−0.0697755	−	0.145923i
$638$	−1.17746	−	0.591342i	−0.0466160	−	0.0234115i
$639$	−38.0413	−	5.73280i	−1.50489	−	0.226786i
$640$	−0.500087	+	8.58616i	−0.0197677	+	0.339398i
$641$	3.68769	−	26.9987i	0.145655	−	1.06638i	−0.762273	−	0.647256i	$-0.775917\pi$
$641$	3.68769	−	26.9987i	0.145655	−	1.06638i	0.907928	−	0.419127i	$-0.137664\pi$
$642$	−9.14844	+	22.5720i	−0.361060	+	0.890845i
$643$	1.94305	−	0.883224i	0.0766264	−	0.0348310i	−0.375131	−	0.926972i	$-0.622402\pi$
$643$	1.94305	−	0.883224i	0.0766264	−	0.0348310i	0.451757	+	0.892141i	$0.350797\pi$
$644$	−0.167798	+	0.774642i	−0.00661217	+	0.0305252i
$645$	−10.2399	−	8.88628i	−0.403197	−	0.349897i
$646$	−1.37253	−	1.70167i	−0.0540014	−	0.0669512i
$647$	−17.3724	−	30.0899i	−0.682980	−	1.18296i	−0.974067	−	0.226259i	$-0.927350\pi$
$647$	−17.3724	−	30.0899i	−0.682980	−	1.18296i	0.291087	−	0.956697i	$-0.405983\pi$
$648$	23.8482	−	1.19146i	0.936847	−	0.0468049i
$649$	0.687359	−	1.19054i	0.0269812	−	0.0467328i
$650$	8.82724	−	1.38056i	0.346233	−	0.0541499i
$651$	−1.73473	−	3.12331i	−0.0679893	−	0.122412i
$652$	2.22390	−	0.713066i	0.0870948	−	0.0279258i
$653$	0.827224	−	8.50460i	0.0323718	−	0.332811i	−0.965108	−	0.261854i	$-0.915666\pi$
$653$	0.827224	−	8.50460i	0.0323718	−	0.332811i	0.997479	−	0.0709572i	$-0.0226054\pi$
$654$	−35.9348	−	22.5093i	−1.40516	−	0.880183i
$655$	−6.07959	+	2.48379i	−0.237549	+	0.0970495i
$656$	−4.81351	−	3.16590i	−0.187936	−	0.123608i
$657$	2.62285	−	2.60127i	0.102327	−	0.101485i
$658$	0.0767785	+	1.31824i	0.00299314	+	0.0513902i
$659$	−37.4708	−	2.91246i	−1.45965	−	0.113453i	−0.677034	−	0.735952i	$-0.736735\pi$
$659$	−37.4708	−	2.91246i	−1.45965	−	0.113453i	−0.782621	+	0.622499i	$0.786118\pi$
$660$	−0.0294886	+	0.00891782i	−0.00114784	+	0.000347126i
$661$	13.5555	−	39.6174i	0.527247	−	1.54094i	−0.285534	−	0.958368i	$-0.592171\pi$
$661$	13.5555	−	39.6174i	0.527247	−	1.54094i	0.812781	−	0.582569i	$-0.197952\pi$
$662$	16.9080	+	9.32942i	0.657147	+	0.362598i
$663$	0.536841	+	0.159093i	0.0208492	+	0.00617866i
$664$	35.9140	+	16.3249i	1.39373	+	0.633529i
$665$	−4.74243	+	6.37019i	−0.183904	+	0.247026i
$666$	2.76115	+	15.1651i	0.106992	+	0.587636i
$667$	13.3053	−	1.55517i	0.515183	−	0.0602162i
$668$	0.147878	−	0.134192i	0.00572157	−	0.00519205i
$669$	28.5055	+	22.8613i	1.10209	+	0.883868i
$670$	1.51081	−	0.117429i	0.0583677	−	0.00453669i
$671$	0.0310278	+	0.227164i	0.00119782	+	0.00876956i
$672$	4.08908	+	1.04115i	0.157740	+	0.0401633i
$673$	13.0690	+	2.56666i	0.503772	+	0.0989376i	0.438141	−	0.898906i	$-0.355637\pi$
$673$	13.0690	+	2.56666i	0.503772	+	0.0989376i	0.0656312	+	0.997844i	$0.479094\pi$
$674$	29.2663	−	10.6521i	1.12729	−	0.410302i
$675$	−16.4102	+	17.0134i	−0.631627	+	0.654846i
$676$	2.31665	+	0.843192i	0.0891020	+	0.0324305i
$677$	19.6909	+	11.8835i	0.756781	+	0.456720i	0.841888	−	0.539652i	$-0.181444\pi$
$677$	19.6909	+	11.8835i	0.756781	+	0.456720i	−0.0851070	+	0.996372i	$0.527123\pi$
$678$	−10.4769	−	5.48143i	−0.402361	−	0.210513i
$679$	−19.3606	−	0.751278i	−0.742990	−	0.0288314i
$680$	−0.108955	−	0.422990i	−0.00417824	−	0.0162209i
$681$	−31.1409	−	31.5745i	−1.19332	−	1.20994i
$682$	0.0876955	−	0.166486i	0.00335804	−	0.00637507i
$683$	3.42972	−	3.63529i	0.131235	−	0.139101i	−0.658424	−	0.752648i	$-0.728776\pi$
$683$	3.42972	−	3.63529i	0.131235	−	0.139101i	0.789658	+	0.613547i	$0.210258\pi$
$684$	−3.75013	−	1.17945i	−0.143390	−	0.0450974i
$685$	−1.96516	+	0.465752i	−0.0750849	+	0.0177955i
$686$	21.2142	+	20.8068i	0.809963	+	0.794406i
$687$	1.30324	−	3.61186i	0.0497216	−	0.137801i
$688$	−32.1283	+	39.8328i	−1.22488	+	1.51861i
$689$	−3.80398	−	0.594931i	−0.144920	−	0.0226651i
$690$	2.03390	−	2.43765i	0.0774293	−	0.0927999i
$691$	12.0894	−	3.36531i	0.459901	−	0.128022i	−0.0304703	−	0.999536i	$-0.509701\pi$
$691$	12.0894	−	3.36531i	0.459901	−	0.128022i	0.490372	+	0.871513i	$0.336861\pi$
$692$	−1.24625	−	1.32094i	−0.0473751	−	0.0502147i
$693$	−0.0734069	−	0.713449i	−0.00278850	−	0.0271017i
$694$	−11.4957	−	38.3984i	−0.436371	−	1.45758i
$695$	9.34739	−	0.362721i	0.354567	−	0.0137588i
$696$	−2.69640	−	33.4844i	−0.102207	−	1.26922i
$697$	0.309991	+	0.0862918i	0.0117417	+	0.00326854i
$698$	8.96847	+	17.0262i	0.339461	+	0.644452i
$699$	5.04208	−	15.8770i	0.190709	−	0.600525i
$700$	−1.72278	+	0.950589i	−0.0651149	+	0.0359289i
$701$	2.68911	+	15.2507i	0.101566	+	0.576011i	0.992536	+	0.121949i	$0.0389144\pi$
$701$	2.68911	+	15.2507i	0.101566	+	0.576011i	−0.890970	+	0.454062i	$0.849974\pi$
$702$	9.75185	−	3.00846i	0.368060	−	0.113547i
$703$	−3.58540	+	20.3338i	−0.135226	+	0.766905i
$704$	−0.271975	−	0.794878i	−0.0102505	−	0.0299581i
$705$	0.214607	−	0.475635i	0.00808258	−	0.0179135i
$706$	−11.8732	−	4.85074i	−0.446854	−	0.182560i
$707$	13.9515	+	20.3418i	0.524701	+	0.765033i
$708$	−4.30682	+	0.0955233i	−0.161860	+	0.00358999i
$709$	−0.875430	−	4.04144i	−0.0328775	−	0.151779i	0.957944	−	0.286954i	$-0.0926428\pi$
$709$	−0.875430	−	4.04144i	−0.0328775	−	0.151779i	−0.990822	+	0.135175i	$0.956840\pi$
$710$	7.65961	+	10.2886i	0.287460	+	0.386126i
$711$	−0.740464	+	14.0614i	−0.0277696	+	0.527342i
$712$	−2.30676	−	5.34766i	−0.0864494	−	0.200412i
$713$	0.185208	+	1.90410i	0.00693609	+	0.0713092i
$714$	−1.24754	+	0.0761457i	−0.0466881	+	0.00284968i
$715$	0.0917183	−	0.0553523i	0.00343007	−	0.00207006i
$716$	−4.81191	+	0.945027i	−0.179829	+	0.0353173i
$717$	47.3755	+	2.62702i	1.76927	+	0.0981079i
$718$	−9.94868	+	14.5055i	−0.371282	+	0.541342i
$719$	6.71133	−	4.41411i	0.250290	−	0.164618i	−0.418164	−	0.908371i	$-0.637326\pi$
$719$	6.71133	−	4.41411i	0.250290	−	0.164618i	0.668455	+	0.743753i	$0.266956\pi$
$720$	−6.58181	−	5.90620i	−0.245289	−	0.220111i
$721$	−18.3827	+	9.23214i	−0.684608	+	0.343823i
$722$	−19.8169	−	15.3592i	−0.737508	−	0.571612i
$723$	4.60198	+	14.2164i	0.171149	+	0.528713i
$724$	−2.83831	−	2.02870i	−0.105485	−	0.0753962i
$725$	24.6268	+	22.3476i	0.914617	+	0.829971i
$726$	−22.0116	+	17.8554i	−0.816925	+	0.662676i
$727$	−7.63561	+	19.7767i	−0.283189	+	0.733478i	0.716178	+	0.697917i	$0.245890\pi$
$727$	−7.63561	+	19.7767i	−0.283189	+	0.733478i	−0.999368	+	0.0355609i	$0.988678\pi$
$728$	−6.91153			−0.256158
$729$	−15.7594	+	21.9236i	−0.583680	+	0.811983i
$730$	−1.23165			−0.0455854
$731$	1.02946	−	2.66636i	0.0380758	−	0.0986188i
$732$	0.557967	−	0.452613i	0.0206231	−	0.0167291i
$733$	28.2990	+	25.6800i	1.04525	+	0.948512i	0.998729	−	0.0504057i	$-0.0160514\pi$
$733$	28.2990	+	25.6800i	1.04525	+	0.948512i	0.0465189	+	0.998917i	$0.485187\pi$
$734$	12.6004	+	9.00624i	0.465090	+	0.332426i
$735$	−1.10903	−	3.42600i	−0.0409072	−	0.126370i
$736$	−1.78585	−	1.38414i	−0.0658273	−	0.0510200i
$737$	−0.163816	+	0.0822714i	−0.00603423	+	0.00303050i
$738$	5.57476	−	1.82176i	0.205210	−	0.0670598i
$739$	−12.7869	+	8.41005i	−0.470372	+	0.309369i	−0.762474	−	0.647019i	$-0.776016\pi$
$739$	−12.7869	+	8.41005i	−0.470372	+	0.309369i	0.292102	+	0.956387i	$0.405645\pi$
$740$	0.286788	−	0.418148i	0.0105426	−	0.0153714i
$741$	13.6490	+	0.756854i	0.501410	+	0.0278037i
$742$	8.43344	−	1.65627i	0.309601	−	0.0608037i
$743$	4.96023	−	2.99352i	0.181973	−	0.109821i	−0.422787	−	0.906229i	$-0.638948\pi$
$743$	4.96023	−	2.99352i	0.181973	−	0.109821i	0.604760	+	0.796408i	$0.293269\pi$
$744$	4.78854	−	0.292276i	0.175557	−	0.0107154i
$745$	0.876740	+	9.01368i	0.0321213	+	0.330236i
$746$	0.592105	+	1.37265i	0.0216785	+	0.0502565i
$747$	−39.7513	+	20.2417i	−1.45442	+	0.740606i
$748$	−0.00387828	−	0.00520943i	−0.000141804	−	0.000190476i
$749$	3.94855	+	18.2285i	0.144277	+	0.666055i
$750$	16.5395	−	0.366839i	0.603938	−	0.0133951i
$751$	−6.31508	−	9.20761i	−0.230441	−	0.335991i	0.692162	−	0.721742i	$-0.256658\pi$
$751$	−6.31508	−	9.20761i	−0.230441	−	0.335991i	−0.922603	+	0.385751i	$0.873942\pi$
$752$	−1.82327	−	0.744889i	−0.0664879	−	0.0271633i
$753$	6.61276	−	14.6559i	0.240982	−	0.534090i
$754$	−4.64800	−	13.5843i	−0.169270	−	0.494710i
$755$	0.817550	−	4.63656i	0.0297537	−	0.168742i
$756$	−1.79150	+	1.35712i	−0.0651564	+	0.0493580i
$757$	2.57293	+	14.5918i	0.0935148	+	0.530349i	0.995192	+	0.0979399i	$0.0312253\pi$
$757$	2.57293	+	14.5918i	0.0935148	+	0.530349i	−0.901677	+	0.432409i	$0.857664\pi$
$758$	18.9031	−	10.4303i	0.686592	−	0.378845i
$759$	−0.116242	+	0.366034i	−0.00421930	+	0.0132862i
$760$	−4.96993	−	9.43517i	−0.180278	−	0.342250i
$761$	−40.8971	−	11.3845i	−1.48252	−	0.412687i	−0.569973	−	0.821664i	$-0.693046\pi$
$761$	−40.8971	−	11.3845i	−1.48252	−	0.412687i	−0.912545	+	0.408977i	$0.865886\pi$
$762$	3.86471	+	47.9927i	0.140004	+	1.73859i
$763$	−32.4472	+	1.25910i	−1.17467	+	0.0455824i
$764$	−0.815804	−	2.72497i	−0.0295148	−	0.0985861i
$765$	0.450766	+	0.201878i	0.0162975	+	0.00729892i
$766$	21.7010	+	23.0017i	0.784089	+	0.831086i
$767$	14.4310	−	4.01716i	0.521075	−	0.145051i
$768$	−5.76272	+	6.90669i	−0.207944	+	0.249224i
$769$	4.44485	+	0.695161i	0.160285	+	0.0250682i	0.234152	−	0.972200i	$-0.424769\pi$
$769$	4.44485	+	0.695161i	0.160285	+	0.0250682i	−0.0738669	+	0.997268i	$0.523534\pi$
$770$	−0.150129	+	0.186131i	−0.00541027	+	0.00670769i
$771$	−17.3795	+	48.1664i	−0.625906	+	1.73467i
$772$	1.45379	+	1.42586i	0.0523229	+	0.0513179i
$773$	31.9164	−	7.56432i	1.14795	−	0.272070i	0.387755	−	0.921762i	$-0.373251\pi$
$773$	31.9164	−	7.56432i	1.14795	−	0.272070i	0.760197	+	0.649693i	$0.225102\pi$
$774$	−11.3119	−	50.8518i	−0.406598	−	1.82783i
$775$	−3.25911	+	3.45445i	−0.117071	+	0.124088i
$776$	12.1250	−	23.0188i	0.435263	−	0.826327i
$777$	8.28898	+	8.40438i	0.297366	+	0.301506i
$778$	−4.23315	−	16.4341i	−0.151766	−	0.589191i
$779$	7.85005	+	0.304618i	0.281257	+	0.0109141i
$780$	−0.297447	−	0.155622i	−0.0106503	−	0.00557217i
$781$	−1.32848	−	0.801741i	−0.0475367	−	0.0286885i
$782$	0.628904	+	0.228902i	0.0224896	+	0.00818553i
$783$	31.5036	+	21.2223i	1.12585	+	0.758423i
$784$	−12.7724	+	4.64876i	−0.456156	+	0.166027i
$785$	−6.28704	−	1.23473i	−0.224394	−	0.0440695i
$786$	−24.4539	−	6.22638i	−0.872240	−	0.222088i
$787$	3.71210	+	27.1773i	0.132322	+	0.968768i	0.930486	+	0.366328i	$0.119385\pi$
$787$	3.71210	+	27.1773i	0.132322	+	0.968768i	−0.798164	+	0.602440i	$0.794195\pi$
$788$	2.05053	−	0.159379i	0.0730469	−	0.00567766i
$789$	25.2191	+	20.2255i	0.897822	+	0.720048i
$790$	3.47668	−	3.15492i	0.123695	−	0.112247i
$791$	−8.99365	+	1.05121i	−0.319777	+	0.0373766i
$792$	0.906817	+	0.324349i	0.0322224	+	0.0115253i
$793$	−1.49188	+	2.00394i	−0.0529781	+	0.0711620i
$794$	−16.4589	−	7.48150i	−0.584105	−	0.265508i
$795$	−3.25632	−	0.965010i	−0.115490	−	0.0342254i
$796$	1.26747	+	0.699358i	0.0449241	+	0.0247881i
$797$	13.1907	−	38.5514i	0.467240	−	1.36556i	−0.421366	−	0.906891i	$-0.638449\pi$
$797$	13.1907	−	38.5514i	0.467240	−	1.36556i	0.888606	−	0.458670i	$-0.151674\pi$
$798$	−29.2081	+	8.83299i	−1.03396	+	0.312684i
$799$	0.109672	+	0.00852438i	0.00387992	+	0.000301571i
$800$	−0.326136	−	5.59955i	−0.0115307	−	0.197974i
$801$	6.35396	+	1.73069i	0.224506	+	0.0611511i
$802$	−17.6182	−	11.5877i	−0.622119	−	0.409174i
$803$	0.137926	−	0.0563491i	0.00486732	−	0.00198852i
$804$	0.486822	+	0.304942i	0.0171689	+	0.0107545i
$805$	0.235366	−	2.41977i	0.00829555	−	0.0852857i
$806$	1.95250	−	0.626045i	0.0687740	−	0.0220515i
$807$	13.9486	+	25.1140i	0.491015	+	0.884054i
$808$	−32.7244	+	5.11800i	−1.15124	+	0.180051i
$809$	0.0400392	−	0.0693499i	0.00140770	−	0.00243821i	−0.865321	−	0.501219i	$-0.832885\pi$
$809$	0.0400392	−	0.0693499i	0.00140770	−	0.00243821i	0.866728	+	0.498780i	$0.166219\pi$
$810$	8.87805	−	1.48994i	0.311943	−	0.0523513i
$811$	5.63124	+	9.75359i	0.197740	+	0.342495i	0.947795	−	0.318880i	$-0.103307\pi$
$811$	5.63124	+	9.75359i	0.197740	+	0.342495i	−0.750056	+	0.661375i	$0.769973\pi$
$812$	1.98508	+	2.46112i	0.0696628	+	0.0863684i
$813$	−22.2992	−	19.3514i	−0.782067	−	0.678682i
$814$	−0.131619	+	0.607623i	−0.00461326	+	0.0212972i
$815$	−6.52141	+	2.96434i	−0.228435	+	0.103836i
$816$	0.700253	−	1.72774i	0.0245138	−	0.0604829i
$817$	9.44350	−	69.1386i	0.330386	−	2.41885i
$818$	0.717055	−	12.3114i	0.0250713	−	0.430457i
$819$	4.87254	−	6.11030i	0.170260	−	0.213511i
$820$	−0.172400	−	0.0865825i	−0.00602047	−	0.00302359i
$821$	14.7513	+	30.8496i	0.514822	+	1.07666i	0.981364	+	0.192160i	$0.0615493\pi$
$821$	14.7513	+	30.8496i	0.514822	+	1.07666i	−0.466541	+	0.884499i	$0.654500\pi$
$822$	−7.13386	−	3.05372i	−0.248822	−	0.106511i
$823$	−16.1701	−	18.5288i	−0.563653	−	0.645875i	0.398891	−	0.916998i	$-0.369395\pi$
$823$	−16.1701	−	18.5288i	−0.563653	−	0.645875i	−0.962545	+	0.271123i	$0.912605\pi$
$824$	−0.535636	−	27.6173i	−0.0186598	−	0.962093i
$825$	−0.874367	+	0.380055i	−0.0304416	+	0.0132318i
$826$	−27.2036	+	19.4440i	−0.946535	+	0.676543i
$827$	1.51484	+	0.177059i	0.0526761	+	0.00615695i	0.142390	−	0.989811i	$-0.454521\pi$
$827$	1.51484	+	0.177059i	0.0526761	+	0.00615695i	−0.0897140	+	0.995968i	$0.528595\pi$
$828$	1.16947	−	0.284054i	0.0406419	−	0.00987157i
$829$	−13.9446	+	32.3273i	−0.484317	+	1.12277i	0.484454	+	0.874816i	$0.339018\pi$
$829$	−13.9446	+	32.3273i	−0.484317	+	1.12277i	−0.968771	+	0.247956i	$0.920241\pi$
$830$	14.1628	+	4.54113i	0.491599	+	0.157625i
$831$	−33.9833	+	29.8242i	−1.17887	+	1.03459i
$832$	3.94910	−	8.25884i	0.136910	−	0.286324i
$833$	0.600015	−	0.465047i	0.0207893	−	0.0161129i
$834$	29.6976	+	20.2469i	1.02834	+	0.701093i
$835$	−0.402738	+	0.461487i	−0.0139373	+	0.0159704i
$836$	−0.121464	−	0.101920i	−0.00420091	−	0.00352499i
$837$	−3.11747	+	4.43948i	−0.107756	+	0.153451i
$838$	24.8146	−	20.8219i	0.857205	−	0.719280i
$839$	−0.384535	+	19.8265i	−0.0132756	+	0.684487i	0.932773	+	0.360463i	$0.117381\pi$
$839$	−0.384535	+	19.8265i	−0.0132756	+	0.684487i	−0.946049	+	0.324024i	$0.894964\pi$
$840$	−6.04289	−	0.808258i	−0.208499	−	0.0278876i
$841$	13.0312	−	20.6755i	0.449353	−	0.712947i
$842$	−30.3676	+	29.7843i	−1.04654	+	1.02644i
$843$	11.2105	−	15.7770i	0.386110	−	0.543388i
$844$	−3.13099	−	4.96765i	−0.107773	−	0.170994i
$845$	−7.35815	−	1.74391i	−0.253128	−	0.0599925i
$846$	1.75004	−	0.978381i	0.0601677	−	0.0336374i
$847$	−6.22503	+	20.7930i	−0.213895	+	0.714458i
$848$	−3.19766	+	12.4141i	−0.109808	+	0.426301i
$849$	−0.610786	+	0.354908i	−0.0209621	+	0.0121804i
$850$	0.598414	+	1.54993i	0.0205254	+	0.0531622i
$851$	−2.27663	−	5.89662i	−0.0780418	−	0.202133i
$852$	0.0135336	+	4.86233i	0.000463653	+	0.166581i
$853$	−13.6389	+	52.9496i	−0.466988	+	1.81296i	0.107203	+	0.994237i	$0.465811\pi$
$853$	−13.6389	+	52.9496i	−0.466988	+	1.81296i	−0.574191	+	0.818722i	$0.694683\pi$
$854$	1.59943	−	5.34246i	0.0547313	−	0.182815i
$855$	11.8451	+	2.25790i	0.405095	+	0.0772185i
$856$	−24.3699	−	5.77576i	−0.832945	−	0.197412i
$857$	−2.50827	−	3.97963i	−0.0856807	−	0.135942i	0.800411	−	0.599451i	$-0.204615\pi$
$857$	−2.50827	−	3.97963i	−0.0856807	−	0.135942i	−0.886092	+	0.463510i	$0.846590\pi$
$858$	0.409792	+	0.0387085i	0.0139901	+	0.00132149i
$859$	22.2009	−	21.7745i	0.757485	−	0.742937i	−0.214819	−	0.976654i	$-0.568916\pi$
$859$	22.2009	−	21.7745i	0.757485	−	0.742937i	0.972305	+	0.233717i	$0.0750890\pi$
$860$	−0.913708	+	1.44970i	−0.0311572	+	0.0494342i
$861$	2.74147	−	3.55752i	0.0934291	−	0.121240i
$862$	0.627171	−	32.3367i	0.0213615	−	1.10139i
$863$	5.11916	−	4.29548i	0.174258	−	0.146220i	−0.551487	−	0.834183i	$-0.685939\pi$
$863$	5.11916	−	4.29548i	0.174258	−	0.146220i	0.725745	+	0.687963i	$0.241495\pi$
$864$	−1.28713	−	6.27622i	−0.0437890	−	0.213521i
$865$	4.26718	+	3.58059i	0.145089	+	0.121744i
$866$	26.7605	−	30.6642i	0.909360	−	1.04201i
$867$	2.19226	−	29.2587i	0.0744529	−	0.993679i
$868$	−0.356908	+	0.276625i	−0.0121143	+	0.00938925i
$869$	−0.244996	+	0.512365i	−0.00831091	+	0.0173808i
$870$	−2.47524	−	12.4206i	−0.0839185	−	0.421096i
$871$	−1.90212	−	0.609889i	−0.0644508	−	0.0206653i
$872$	17.2702	−	40.0369i	0.584844	−	1.35582i
$873$	11.8023	+	26.9474i	0.399448	+	0.912031i
$874$	16.2292	+	1.89692i	0.548959	+	0.0641642i
$875$	10.3069	−	7.36692i	0.348436	−	0.249047i
$876$	−0.375279	−	0.277765i	−0.0126795	−	0.00938481i
$877$	−1.08547	−	55.9663i	−0.0366536	−	1.88985i	−0.345041	−	0.938588i	$-0.612135\pi$
$877$	−1.08547	−	55.9663i	−0.0366536	−	1.88985i	0.308387	−	0.951261i	$-0.400211\pi$
$878$	40.5363	+	46.4495i	1.36804	+	1.56759i
$879$	−9.41552	+	7.05041i	−0.317578	+	0.237804i
$880$	−0.153866	−	0.321784i	−0.00518682	−	0.0108473i
$881$	−32.1246	−	16.1336i	−1.08230	−	0.543553i	−0.183999	−	0.982926i	$-0.558904\pi$
$881$	−32.1246	−	16.1336i	−1.08230	−	0.543553i	−0.898305	+	0.439373i	$0.855201\pi$
$882$	4.40636	−	13.1160i	0.148370	−	0.441638i
$883$	1.56971	−	26.9508i	0.0528248	−	0.906967i	−0.862954	−	0.505283i	$-0.831388\pi$
$883$	1.56971	−	26.9508i	0.0528248	−	0.906967i	0.915778	−	0.401684i	$-0.131575\pi$
$884$	0.00957719	−	0.0701174i	0.000322116	−	0.00235830i
$885$	13.0871	−	1.82466i	0.439919	−	0.0613353i
$886$	−7.10641	+	3.23026i	−0.238744	+	0.108523i
$887$	−0.929105	+	4.28923i	−0.0311963	+	0.144018i	−0.990276	−	0.139119i	$-0.955573\pi$
$887$	−0.929105	+	4.28923i	−0.0311963	+	0.144018i	0.959079	+	0.283138i	$0.0913753\pi$
$888$	−14.9829	+	5.17316i	−0.502792	+	0.173600i
$889$	23.1484	+	28.6995i	0.776372	+	0.962551i
$890$	−1.09784	−	1.90152i	−0.0367998	−	0.0637391i
$891$	−0.926044	+	0.573031i	−0.0310236	+	0.0191973i
$892$	2.30918	−	3.99962i	0.0773172	−	0.133917i
$893$	2.65338	−	0.414982i	0.0887921	−	0.0138868i
$894$	−17.8966	+	29.8420i	−0.598552	+	0.998065i
$895$	14.3234	−	4.59261i	0.478778	−	0.153514i
$896$	−2.45000	+	25.1882i	−0.0818487	+	0.841478i
$897$	−3.69712	+	1.96060i	−0.123443	+	0.0654627i
$898$	−52.9319	+	21.6251i	−1.76636	+	0.721638i
$899$	6.37627	+	4.19374i	0.212660	+	0.139869i
$900$	2.44020	+	1.72371i	0.0813401	+	0.0574570i
$901$	−0.0416302	−	0.714763i	−0.00138690	−	0.0238122i
$902$	0.235838	+	0.0183308i	0.00785256	+	0.000610349i
$903$	−29.0938	−	27.2960i	−0.968182	−	0.908353i
$904$	3.93625	−	11.5041i	0.130918	−	0.382621i
$905$	9.36959	+	5.16992i	0.311456	+	0.171854i
$906$	13.1236	−	12.4507i	0.436003	−	0.413647i
$907$	28.3024	+	12.8650i	0.939765	+	0.427175i	0.824311	−	0.566137i	$-0.191563\pi$
$907$	28.3024	+	12.8650i	0.939765	+	0.427175i	0.115454	+	0.993313i	$0.463168\pi$
$908$	−3.34714	+	4.49599i	−0.111079	+	0.149205i
$909$	18.5456	−	32.5389i	0.615118	−	1.07925i
$910$	−2.58809	+	0.302504i	−0.0857943	+	0.0100279i
$911$	−37.4099	+	33.9477i	−1.23945	+	1.12474i	−0.251841	+	0.967769i	$0.581036\pi$
$911$	−37.4099	+	33.9477i	−1.23945	+	1.12474i	−0.987604	+	0.156968i	$0.949828\pi$
$912$	6.90763	−	44.9871i	0.228735	−	1.48967i
$913$	−1.79379	+	0.139424i	−0.0593657	+	0.00461427i
$914$	−5.62573	−	41.1877i	−0.186083	−	1.36237i
$915$	−1.53873	+	1.57762i	−0.0508687	+	0.0521544i
$916$	−0.476216	−	0.0935257i	−0.0157346	−	0.00309018i
$917$	−18.1587	+	6.60924i	−0.599654	+	0.218256i
$918$	0.930673	+	1.65388i	0.0307168	+	0.0545863i
$919$	−56.2857	−	20.4863i	−1.85669	−	0.675781i	−0.981335	−	0.192306i	$-0.938403\pi$
$919$	−56.2857	−	20.4863i	−1.85669	−	0.675781i	−0.875358	−	0.483475i	$-0.839374\pi$
$920$	2.79505	+	1.68682i	0.0921500	+	0.0556128i
$921$	−0.296396	−	7.12619i	−0.00976656	−	0.234816i
$922$	33.2965	+	1.29206i	1.09656	+	0.0425516i
$923$	−4.21750	−	16.3733i	−0.138821	−	0.538935i
$924$	−0.0877206	+	0.0228559i	−0.00288580	+	0.000751904i
$925$	7.31288	−	13.8832i	0.240446	−	0.456475i
$926$	11.1567	−	11.8254i	0.366631	−	0.388606i
$927$	24.7933	+	18.9963i	0.814319	+	0.623920i
$928$	−8.77053	+	2.07865i	−0.287907	+	0.0682352i
$929$	−4.27383	−	4.19174i	−0.140220	−	0.137527i	0.626723	−	0.779242i	$-0.284396\pi$
$929$	−4.27383	−	4.19174i	−0.140220	−	0.137527i	−0.766943	+	0.641716i	$0.778223\pi$
$930$	1.78032	−	0.319031i	0.0583791	−	0.0104614i
$931$	11.6357	−	14.4260i	0.381345	−	0.472793i
$932$	−2.08018	−	0.325334i	−0.0681386	−	0.0106567i
$933$	−3.34035	−	9.09867i	−0.109358	−	0.297877i
$934$	56.8542	−	15.8264i	1.86032	−	0.517857i
$935$	0.0136706	+	0.0144900i	0.000447076	+	0.000473873i
$936$	4.57972	+	9.44224i	0.149693	+	0.308629i
$937$	4.36692	+	14.5865i	0.142661	+	0.476522i	0.999218	−	0.0395306i	$-0.0125863\pi$
$937$	4.36692	+	14.5865i	0.142661	+	0.476522i	−0.856557	+	0.516052i	$0.827401\pi$
$938$	4.45552	−	0.172894i	0.145478	−	0.00564520i
$939$	−36.1899	+	24.9694i	−1.18101	+	0.814846i
$940$	−0.0635360	−	0.0176865i	−0.00207232	−	0.000576869i
$941$	9.94246	+	18.8753i	0.324115	+	0.615317i	0.991605	−	0.129301i	$-0.0412734\pi$
$941$	9.94246	+	18.8753i	0.324115	+	0.615317i	−0.667490	+	0.744618i	$0.732631\pi$
$942$	−16.5944	−	18.1849i	−0.540675	−	0.592494i
$943$	−2.10568	+	1.16186i	−0.0685703	+	0.0378355i
$944$	−8.66071	−	49.1173i	−0.281882	−	1.59863i
$945$	4.97472	−	4.77254i	0.161828	−	0.155251i
$946$	0.364862	−	2.06923i	0.0118627	−	0.0672766i
$947$	−4.72495	−	13.8092i	−0.153540	−	0.448738i	0.842390	−	0.538869i	$-0.181148\pi$
$947$	−4.72495	−	13.8092i	−0.153540	−	0.448738i	−0.995930	+	0.0901307i	$0.971272\pi$
$948$	1.77084	−	0.177222i	0.0575142	−	0.00575591i
$949$	1.50293	+	0.614013i	0.0487871	+	0.0199317i
$950$	22.9427	+	33.4512i	0.744358	+	1.08530i
$951$	23.4225	−	42.7299i	0.759526	−	1.38561i
$952$	−0.272092	−	1.25612i	−0.00881855	−	0.0407109i
$953$	−22.5987	−	30.3553i	−0.732044	−	0.983305i	−0.999804	−	0.0198196i	$-0.993691\pi$
$953$	−22.5987	−	30.3553i	−0.732044	−	0.983305i	0.267760	−	0.963486i	$-0.413717\pi$
$954$	−7.85089	−	10.4239i	−0.254182	−	0.337487i
$955$	3.45577	+	8.01138i	0.111826	+	0.259242i
$956$	−0.580576	−	5.96885i	−0.0187772	−	0.193046i
$957$	0.845443	+	1.27767i	0.0273293	+	0.0413013i
$958$	43.7587	−	26.4085i	1.41378	−	0.853221i
$959$	−5.83115	+	1.14520i	−0.188298	+	0.0369805i
$960$	4.41859	−	6.75904i	0.142609	−	0.218147i
$961$	16.9174	−	24.6661i	0.545721	−	0.795681i
$962$	−5.66007	+	3.72269i	−0.182488	+	0.120024i
$963$	22.2866	−	17.4729i	0.718177	−	0.563057i
$964$	1.68773	−	0.847608i	0.0543580	−	0.0272996i
$965$	−4.93684	−	3.82634i	−0.158922	−	0.123174i
$966$	6.25824	−	6.93519i	0.201356	−	0.223136i
$967$	−24.9064	−	17.8020i	−0.800935	−	0.572474i	0.105696	−	0.994398i	$-0.466293\pi$
$967$	−24.9064	−	17.8020i	−0.800935	−	0.572474i	−0.906631	+	0.421925i	$0.861355\pi$
$968$	−21.5834	−	19.5859i	−0.693717	−	0.629515i
$969$	0.399781	+	2.51040i	0.0128428	+	0.0806457i
$970$	3.53285	−	9.15030i	0.113433	−	0.293799i
$971$	11.7868			0.378255			0.189128	−	0.981953i	$-0.439434\pi$
$971$	11.7868			0.378255			0.189128	+	0.981953i	$0.439434\pi$
$972$	3.04113	+	1.54822i	0.0975443	+	0.0496593i
$973$	27.5248			0.882404
$974$	−7.16374	+	18.5546i	−0.229541	+	0.594526i
$975$	−9.70187	−	3.71480i	−0.310708	−	0.118969i
$976$	6.15990	+	5.58981i	0.197174	+	0.178925i
$977$	−26.4766	−	18.9243i	−0.847061	−	0.605443i	0.0729497	−	0.997336i	$-0.476759\pi$
$977$	−26.4766	−	18.9243i	−0.847061	−	0.605443i	−0.920011	+	0.391893i	$0.871820\pi$
$978$	−26.9169	−	5.75218i	−0.860707	−	0.183934i
$979$	0.209939	+	0.162715i	0.00670967	+	0.00520039i
$980$	−0.406725	+	0.204265i	−0.0129924	+	0.00652501i
$981$	23.2203	+	43.4937i	0.741366	+	1.38865i
$982$	33.3257	−	21.9186i	1.06346	−	0.699452i
$983$	−9.76909	+	14.2437i	−0.311585	+	0.454303i	−0.948567	−	0.316576i	$-0.897467\pi$
$983$	−9.76909	+	14.2437i	−0.311585	+	0.454303i	0.636982	+	0.770879i	$0.280183\pi$
$984$	2.72165	+	5.38186i	0.0867632	+	0.171567i
$985$	−6.19036	+	1.21575i	−0.197241	+	0.0387369i
$986$	2.28585	−	1.37952i	0.0727964	−	0.0439328i
$987$	0.685260	−	1.37399i	0.0218121	−	0.0437345i
$988$	−0.167266	−	1.71965i	−0.00532144	−	0.0547092i
$989$	8.46106	+	19.6149i	0.269046	+	0.623719i
$990$	0.353763	+	0.0817661i	0.0112433	+	0.00259870i
$991$	−0.966415	−	1.29812i	−0.0306992	−	0.0412362i	0.786509	−	0.617579i	$-0.211887\pi$
$991$	−0.966415	−	1.29812i	−0.0306992	−	0.0412362i	−0.817208	+	0.576343i	$0.804479\pi$
$992$	−0.272512	−	1.25806i	−0.00865227	−	0.0399433i
$993$	−11.6555	−	19.1921i	−0.369876	−	0.609044i
$994$	21.3471	+	31.1248i	0.677089	+	0.987220i
$995$	−4.11049	−	1.67932i	−0.130311	−	0.0532380i
$996$	3.29124	+	4.57771i	0.104287	+	0.145050i
$997$	−7.17911	−	20.9818i	−0.227365	−	0.664499i	−0.999576	−	0.0291323i	$-0.990726\pi$
$997$	−7.17911	−	20.9818i	−0.227365	−	0.664499i	0.772211	−	0.635366i	$-0.219151\pi$
$998$	−3.57305	+	20.2638i	−0.113103	+	0.641439i
$999$	5.98928	−	16.8930i	0.189492	−	0.534470i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	243.2.i.a.106.8	yes	1404
3.2	odd	2		729.2.i.a.559.19		1404
243.94	even	81	inner	243.2.i.a.94.8	✓	1404
243.149	odd	162		729.2.i.a.253.19		1404

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
243.2.i.a.94.8	✓	1404	243.94	even	81	inner
243.2.i.a.106.8	yes	1404	1.1	even	1	trivial
729.2.i.a.253.19		1404	243.149	odd	162
729.2.i.a.559.19		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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 243 = 3^{5} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	243.i (of order \(81\), degree \(54\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.536522 + 1.38963i) q^{2} +(1.34514 - 1.09115i) q^{3} +(-0.162116 - 0.147113i) q^{4} +(0.546288 + 0.390463i) q^{5} +(0.794597 + 2.45466i) q^{6} +(1.56166 + 1.21038i) q^{7} +(-2.37090 + 1.19071i) q^{8} +(0.618780 - 2.93549i) q^{9} +(-0.835693 + 0.549644i) q^{10} +(0.0684384 - 0.0997857i) q^{11} +(-0.378590 - 0.0209932i) q^{12} +(1.29377 - 0.254089i) q^{13} +(-2.51983 + 1.52073i) q^{14} +(1.16089 - 0.0708565i) q^{15} +(-0.424991 - 4.36929i) q^{16} +(0.0971116 + 0.225130i) q^{17} +(3.74725 + 2.43483i) q^{18} +(3.57456 + 4.80146i) q^{19} +(-0.0311200 - 0.143666i) q^{20} +(3.42135 - 0.0758838i) q^{21} +(0.101946 + 0.148641i) q^{22} +(-1.69637 - 0.693045i) q^{23} +(-1.88994 + 4.18868i) q^{24} +(-1.47270 - 4.30413i) q^{25} +(-0.341049 + 1.93418i) q^{26} +(-2.37072 - 4.62382i) q^{27} +(-0.0751084 - 0.425961i) q^{28} +(-6.40053 + 3.53166i) q^{29} +(-0.524376 + 1.65121i) q^{30} +(-0.486544 - 0.923680i) q^{31} +(1.18783 + 0.330656i) q^{32} +(-0.0168222 - 0.208902i) q^{33} +(-0.364949 + 0.0141617i) q^{34} +(0.380508 + 1.27098i) q^{35} +(-0.532162 + 0.384860i) q^{36} +(2.36708 + 2.50896i) q^{37} +(-8.59006 + 2.39121i) q^{38} +(1.46305 - 1.75349i) q^{39} +(-1.76013 - 0.275279i) q^{40} +(0.823942 - 1.02153i) q^{41} +(-1.73018 + 4.79510i) q^{42} +(-8.32258 - 8.16273i) q^{43} +(-0.0257747 + 0.00610871i) q^{44} +(1.48423 - 1.36201i) q^{45} +(1.87321 - 1.98549i) q^{46} +(0.209094 - 0.396955i) q^{47} +(-5.33922 - 5.41355i) q^{48} +(-0.772323 - 2.99834i) q^{49} +(6.77127 + 0.262756i) q^{50} +(0.376279 + 0.196867i) q^{51} +(-0.247121 - 0.149138i) q^{52} +(-2.74407 - 0.998759i) q^{53} +(7.69732 - 0.813636i) q^{54} +(0.0763497 - 0.0277890i) q^{55} +(-5.14375 - 1.01020i) q^{56} +(10.0474 + 2.55824i) q^{57} +(-1.47367 - 10.7892i) q^{58} +(11.3271 - 0.880415i) q^{59} +(-0.198622 - 0.159294i) q^{60} +(-1.40320 + 1.27333i) q^{61} +(1.54461 - 0.180539i) q^{62} +(4.51937 - 3.83528i) q^{63} +(4.14615 - 5.56925i) q^{64} +(0.805985 + 0.366365i) q^{65} +(0.299321 + 0.0887038i) q^{66} +(-1.32647 - 0.731913i) q^{67} +(0.0173761 - 0.0507835i) q^{68} +(-3.03807 + 0.918759i) q^{69} +(-1.97034 - 0.153147i) q^{70} +(-0.745627 - 12.8019i) q^{71} +(2.02826 + 7.69656i) q^{72} +(1.02878 + 0.676636i) q^{73} +(-4.75650 + 1.94324i) q^{74} +(-6.67744 - 4.18270i) q^{75} +(0.126862 - 1.30426i) q^{76} +(0.227656 - 0.0729949i) q^{77} +(1.65173 + 2.97388i) q^{78} +(-4.63724 + 0.725251i) q^{79} +(1.47388 - 2.55283i) q^{80} +(-8.23422 - 3.63285i) q^{81} +(0.977478 + 1.69304i) q^{82} +(-9.33520 - 11.5738i) q^{83} +(-0.565819 - 0.491021i) q^{84} +(-0.0348541 + 0.160904i) q^{85} +(15.8084 - 7.18579i) q^{86} +(-4.75601 + 11.7345i) q^{87} +(-0.0434449 + 0.318073i) q^{88} +(-0.127637 + 2.19144i) q^{89} +(1.09636 + 2.79328i) q^{90} +(2.32797 + 1.16915i) q^{91} +(0.173054 + 0.361911i) q^{92} +(-1.66234 - 0.711583i) q^{93} +(0.439436 + 0.503537i) q^{94} +(0.0779428 + 4.01871i) q^{95} +(1.95859 - 0.851328i) q^{96} +(-7.97787 + 5.70224i) q^{97} +(4.58094 + 0.535435i) q^{98} +(-0.250572 - 0.262646i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1404 q - 54 q^{2} - 54 q^{3} - 54 q^{4} - 54 q^{5} - 54 q^{6} - 54 q^{7} - 54 q^{8} - 54 q^{9} - 54 q^{10} - 54 q^{11} - 54 q^{12} - 54 q^{13} - 54 q^{14} - 54 q^{15} - 54 q^{16} - 54 q^{17} - 54 q^{18}+ \cdots + 54 q^{98}+O(q^{100}) \) 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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