LMFDB - Embedded newform 273.2.bt.b.271.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [273,2,Mod(136,273)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(273, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 2, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("273.136"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.bt (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [40] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			271.7
Character	$\chi$	$=$	273.271
Dual form			273.2.bt.b.136.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.07562 + 1.07562i) q^{2} +(-0.866025 - 0.500000i) q^{3} +0.313900i q^{4} +(-0.962166 - 3.59085i) q^{5} +(-0.393703 - 1.46932i) q^{6} +(-2.21486 + 1.44721i) q^{7} +(1.81360 - 1.81360i) q^{8} +(0.500000 + 0.866025i) q^{9} +(2.82746 - 4.89730i) q^{10} +(-0.516435 - 1.92736i) q^{11} +(0.156950 - 0.271846i) q^{12} +(1.45921 - 3.29708i) q^{13} +(-3.93898 - 0.825695i) q^{14} +(-0.962166 + 3.59085i) q^{15} +4.52927 q^{16} +4.72149 q^{17} +(-0.393703 + 1.46932i) q^{18} +(-4.30650 - 1.15392i) q^{19} +(1.12717 - 0.302024i) q^{20} +(2.64173 - 0.145891i) q^{21} +(1.51761 - 2.62859i) q^{22} +2.08952i q^{23} +(-2.47742 + 0.663822i) q^{24} +(-7.63832 + 4.40999i) q^{25} +(5.11594 - 1.97684i) q^{26} -1.00000i q^{27} +(-0.454279 - 0.695244i) q^{28} +(5.10970 + 8.85026i) q^{29} +(-4.89730 + 2.82746i) q^{30} +(-2.20797 - 0.591623i) q^{31} +(1.24456 + 1.24456i) q^{32} +(-0.516435 + 1.92736i) q^{33} +(5.07852 + 5.07852i) q^{34} +(7.32777 + 6.56076i) q^{35} +(-0.271846 + 0.156950i) q^{36} +(0.455980 - 0.455980i) q^{37} +(-3.39097 - 5.87333i) q^{38} +(-2.91225 + 2.12575i) q^{39} +(-8.25733 - 4.76737i) q^{40} +(8.81239 + 2.36127i) q^{41} +(2.99841 + 2.68456i) q^{42} +(0.0966425 + 0.0557966i) q^{43} +(0.604999 - 0.162109i) q^{44} +(2.62869 - 2.62869i) q^{45} +(-2.24752 + 2.24752i) q^{46} +(-4.33009 + 1.16024i) q^{47} +(-3.92246 - 2.26463i) q^{48} +(2.81118 - 6.41072i) q^{49} +(-12.9594 - 3.47245i) q^{50} +(-4.08893 - 2.36075i) q^{51} +(1.03495 + 0.458046i) q^{52} +(-2.18989 - 3.79299i) q^{53} +(1.07562 - 1.07562i) q^{54} +(-6.42397 + 3.70888i) q^{55} +(-1.39220 + 6.64151i) q^{56} +(3.15258 + 3.15258i) q^{57} +(-4.02340 + 15.0156i) q^{58} +(-1.19927 - 1.19927i) q^{59} +(-1.12717 - 0.302024i) q^{60} +(5.84680 - 3.37565i) q^{61} +(-1.73857 - 3.01128i) q^{62} +(-2.36075 - 1.19452i) q^{63} -6.38120i q^{64} +(-13.2433 - 2.06746i) q^{65} +(-2.62859 + 1.51761i) q^{66} +(2.87850 - 0.771291i) q^{67} +1.48208i q^{68} +(1.04476 - 1.80957i) q^{69} +(0.825000 + 14.9387i) q^{70} +(14.4800 - 3.87990i) q^{71} +(2.47742 + 0.663822i) q^{72} +(-2.72063 + 10.1535i) q^{73} +0.980919 q^{74} +8.81997 q^{75} +(0.362217 - 1.35181i) q^{76} +(3.93312 + 3.52144i) q^{77} +(-5.41895 - 0.845973i) q^{78} +(-0.0273492 + 0.0473702i) q^{79} +(-4.35791 - 16.2639i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(6.93892 + 12.0186i) q^{82} +(9.05174 - 9.05174i) q^{83} +(0.0457952 + 0.829238i) q^{84} +(-4.54286 - 16.9542i) q^{85} +(0.0439346 + 0.163966i) q^{86} -10.2194i q^{87} +(-4.43206 - 2.55885i) q^{88} +(-5.06089 - 5.06089i) q^{89} +5.65491 q^{90} +(1.53962 + 9.41433i) q^{91} -0.655900 q^{92} +(1.61634 + 1.61634i) q^{93} +(-5.90549 - 3.40954i) q^{94} +16.5743i q^{95} +(-0.455541 - 1.70010i) q^{96} +(3.20050 + 11.9444i) q^{97} +(9.91922 - 3.87172i) q^{98} +(1.41093 - 1.41093i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 2 q^{7} + 20 q^{9} - 8 q^{11} + 24 q^{12} - 18 q^{14} - 64 q^{16} + 8 q^{17} - 14 q^{19} - 14 q^{20} - 8 q^{21} + 4 q^{22} + 18 q^{24} - 24 q^{25} - 10 q^{26} - 2 q^{28} + 8 q^{29} - 8 q^{31} + 10 q^{32}+ \cdots - 4 q^{99}+O(q^{100}) $ 40 * q - 2 * q^7 + 20 * q^9 - 8 * q^11 + 24 * q^12 - 18 * q^14 - 64 * q^16 + 8 * q^17 - 14 * q^19 - 14 * q^20 - 8 * q^21 + 4 * q^22 + 18 * q^24 - 24 * q^25 - 10 * q^26 - 2 * q^28 + 8 * q^29 - 8 * q^31 + 10 * q^32 - 8 * q^33 + 24 * q^34 - 22 * q^35 + 12 * q^37 + 8 * q^38 - 24 * q^39 - 30 * q^40 + 2 * q^41 + 6 * q^42 - 66 * q^43 + 28 * q^44 + 40 * q^46 + 10 * q^47 - 24 * q^48 + 38 * q^49 - 20 * q^50 + 40 * q^52 - 8 * q^53 + 42 * q^55 + 20 * q^56 - 14 * q^57 - 48 * q^58 - 26 * q^59 + 14 * q^60 - 12 * q^61 - 24 * q^62 - 4 * q^63 - 44 * q^65 - 18 * q^66 + 46 * q^67 - 4 * q^69 + 32 * q^70 - 6 * q^71 - 18 * q^72 + 10 * q^73 + 40 * q^74 + 48 * q^75 + 64 * q^76 - 24 * q^77 + 8 * q^78 + 34 * q^80 - 20 * q^81 + 24 * q^82 + 12 * q^83 + 20 * q^84 + 2 * q^85 + 12 * q^86 - 84 * q^88 - 16 * q^89 + 26 * q^91 + 236 * q^92 + 22 * q^93 + 30 * q^94 + 26 * q^96 + 62 * q^97 - 14 * q^98 - 4 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	1.07562	+	1.07562i	0.760575	+	0.760575i	0.976426	−	0.215851i	$-0.0692525\pi$
$2$	1.07562	+	1.07562i	0.760575	+	0.760575i	−0.215851	+	0.976426i	$0.569253\pi$
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$4$			0.313900i			0.156950i
$5$	−0.962166	−	3.59085i	−0.430294	−	1.60588i	−0.752085	−	0.659067i	$-0.770952\pi$
$5$	−0.962166	−	3.59085i	−0.430294	−	1.60588i	0.321791	−	0.946811i	$-0.395715\pi$
$6$	−0.393703	−	1.46932i	−0.160729	−	0.599847i
$7$	−2.21486	+	1.44721i	−0.837137	+	0.546993i
$7$	−2.21486	+	1.44721i	−0.837137	+	0.546993i
$8$	1.81360	−	1.81360i	0.641203	−	0.641203i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	2.82746	−	4.89730i	0.894120	−	1.54866i
$11$	−0.516435	−	1.92736i	−0.155711	−	0.581121i	−0.999043	−	0.0437290i	$-0.986076\pi$
$11$	−0.516435	−	1.92736i	−0.155711	−	0.581121i	0.843332	−	0.537392i	$-0.180590\pi$
$12$	0.156950	−	0.271846i	0.0453076	−	0.0784751i
$13$	1.45921	−	3.29708i	0.404711	−	0.914444i
$13$	1.45921	−	3.29708i	0.404711	−	0.914444i
$14$	−3.93898	−	0.825695i	−1.05274	−	0.220676i
$15$	−0.962166	+	3.59085i	−0.248430	+	0.927154i
$16$	4.52927			1.13232
$17$	4.72149			1.14513			0.572565	−	0.819859i	$-0.305948\pi$
$17$	4.72149			1.14513			0.572565	+	0.819859i	$0.305948\pi$
$18$	−0.393703	+	1.46932i	−0.0927966	+	0.346322i
$19$	−4.30650	−	1.15392i	−0.987980	−	0.264728i	−0.271578	−	0.962416i	$-0.587546\pi$
$19$	−4.30650	−	1.15392i	−0.987980	−	0.264728i	−0.716402	+	0.697688i	$0.754212\pi$
$20$	1.12717	−	0.302024i	0.252043	−	0.0675346i
$21$	2.64173	−	0.145891i	0.576472	−	0.0318360i
$22$	1.51761	−	2.62859i	0.323557	−	0.560416i
$23$			2.08952i			0.435694i	0.975983	+	0.217847i	$0.0699034\pi$
$23$			2.08952i			0.435694i	−0.975983	+	0.217847i	$0.930097\pi$
$24$	−2.47742	+	0.663822i	−0.505701	+	0.135502i
$25$	−7.63832	+	4.40999i	−1.52766	+	0.881997i
$26$	5.11594	−	1.97684i	1.00332	−	0.387691i
$27$		−	1.00000i		−	0.192450i
$28$	−0.454279	−	0.695244i	−0.0858507	−	0.131389i
$29$	5.10970	+	8.85026i	0.948847	+	1.64345i	0.747859	+	0.663858i	$0.231082\pi$
$29$	5.10970	+	8.85026i	0.948847	+	1.64345i	0.200988	+	0.979594i	$0.435585\pi$
$30$	−4.89730	+	2.82746i	−0.894120	+	0.516221i
$31$	−2.20797	−	0.591623i	−0.396563	−	0.106259i	0.0550260	−	0.998485i	$-0.482476\pi$
$31$	−2.20797	−	0.591623i	−0.396563	−	0.106259i	−0.451589	+	0.892226i	$0.649142\pi$
$32$	1.24456	+	1.24456i	0.220009	+	0.220009i
$33$	−0.516435	+	1.92736i	−0.0898998	+	0.335510i
$34$	5.07852	+	5.07852i	0.870958	+	0.870958i
$35$	7.32777	+	6.56076i	1.23862	+	1.10897i
$36$	−0.271846	+	0.156950i	−0.0453076	+	0.0261584i
$37$	0.455980	−	0.455980i	0.0749626	−	0.0749626i	−0.668631	−	0.743594i	$-0.733120\pi$
$37$	0.455980	−	0.455980i	0.0749626	−	0.0749626i	0.743594	+	0.668631i	$0.233120\pi$
$38$	−3.39097	−	5.87333i	−0.550087	−	0.952779i
$39$	−2.91225	+	2.12575i	−0.466333	+	0.340392i
$40$	−8.25733	−	4.76737i	−1.30560	−	0.753788i
$41$	8.81239	+	2.36127i	1.37626	+	0.368769i	0.869763	−	0.493471i	$-0.164272\pi$
$41$	8.81239	+	2.36127i	1.37626	+	0.368769i	0.506501	+	0.862239i	$0.330939\pi$
$42$	2.99841	+	2.68456i	0.462664	+	0.414237i
$43$	0.0966425	+	0.0557966i	0.0147378	+	0.00850890i	0.507351	−	0.861740i	$-0.330625\pi$
$43$	0.0966425	+	0.0557966i	0.0147378	+	0.00850890i	−0.492613	+	0.870249i	$0.663958\pi$
$44$	0.604999	−	0.162109i	0.0912071	−	0.0244389i
$45$	2.62869	−	2.62869i	0.391861	−	0.391861i
$46$	−2.24752	+	2.24752i	−0.331378	+	0.331378i
$47$	−4.33009	+	1.16024i	−0.631609	+	0.169239i	−0.560400	−	0.828222i	$-0.689352\pi$
$47$	−4.33009	+	1.16024i	−0.631609	+	0.169239i	−0.0712092	+	0.997461i	$0.522686\pi$
$48$	−3.92246	−	2.26463i	−0.566158	−	0.326872i
$49$	2.81118	−	6.41072i	0.401597	−	0.915817i
$50$	−12.9594	−	3.47245i	−1.83273	−	0.491078i
$51$	−4.08893	−	2.36075i	−0.572565	−	0.330571i
$52$	1.03495	+	0.458046i	0.143522	+	0.0635195i
$53$	−2.18989	−	3.79299i	−0.300804	−	0.521008i	0.675514	−	0.737347i	$-0.263922\pi$
$53$	−2.18989	−	3.79299i	−0.300804	−	0.521008i	−0.976318	+	0.216339i	$0.930588\pi$
$54$	1.07562	−	1.07562i	0.146373	−	0.146373i
$55$	−6.42397	+	3.70888i	−0.866208	+	0.500105i
$56$	−1.39220	+	6.64151i	−0.186041	+	0.887509i
$57$	3.15258	+	3.15258i	0.417569	+	0.417569i
$58$	−4.02340	+	15.0156i	−0.528299	+	1.97164i
$59$	−1.19927	−	1.19927i	−0.156131	−	0.156131i	0.624719	−	0.780850i	$-0.285214\pi$
$59$	−1.19927	−	1.19927i	−0.156131	−	0.156131i	−0.780850	+	0.624719i	$0.785214\pi$
$60$	−1.12717	−	0.302024i	−0.145517	−	0.0389911i
$61$	5.84680	−	3.37565i	0.748606	−	0.432208i	−0.0765837	−	0.997063i	$-0.524401\pi$
$61$	5.84680	−	3.37565i	0.748606	−	0.432208i	0.825190	+	0.564855i	$0.191068\pi$
$62$	−1.73857	−	3.01128i	−0.220798	−	0.382433i
$63$	−2.36075	−	1.19452i	−0.297426	−	0.150495i
$64$		−	6.38120i		−	0.797649i
$65$	−13.2433	−	2.06746i	−1.64263	−	0.256437i
$66$	−2.62859	+	1.51761i	−0.323557	+	0.186805i
$67$	2.87850	−	0.771291i	0.351664	−	0.0942282i	−0.0786626	−	0.996901i	$-0.525065\pi$
$67$	2.87850	−	0.771291i	0.351664	−	0.0942282i	0.430327	+	0.902673i	$0.358398\pi$
$68$			1.48208i			0.179728i
$69$	1.04476	−	1.80957i	0.125774	−	0.217847i
$70$	0.825000	+	14.9387i	0.0986064	+	1.78552i
$71$	14.4800	−	3.87990i	1.71846	−	0.460459i	0.740985	−	0.671521i	$-0.234359\pi$
$71$	14.4800	−	3.87990i	1.71846	−	0.460459i	0.977473	+	0.211062i	$0.0676921\pi$
$72$	2.47742	+	0.663822i	0.291967	+	0.0782322i
$73$	−2.72063	+	10.1535i	−0.318426	+	1.18838i	0.602332	+	0.798246i	$0.294238\pi$
$73$	−2.72063	+	10.1535i	−0.318426	+	1.18838i	−0.920758	+	0.390135i	$0.872428\pi$
$74$	0.980919			0.114029
$75$	8.81997			1.01844
$76$	0.362217	−	1.35181i	0.0415492	−	0.155064i
$77$	3.93312	+	3.52144i	0.448221	+	0.401305i
$78$	−5.41895	−	0.845973i	−0.613575	−	0.0957876i
$79$	−0.0273492	+	0.0473702i	−0.00307703	+	0.00532957i	−0.867560	−	0.497333i	$-0.834313\pi$
$79$	−0.0273492	+	0.0473702i	−0.00307703	+	0.00532957i	0.864483	+	0.502662i	$0.167646\pi$
$80$	−4.35791	−	16.2639i	−0.487229	−	1.81836i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	6.93892	+	12.0186i	0.766276	+	1.32723i
$83$	9.05174	−	9.05174i	0.993558	−	0.993558i	−0.00642168	−	0.999979i	$-0.502044\pi$
$83$	9.05174	−	9.05174i	0.993558	−	0.993558i	0.999979	+	0.00642168i	$0.00204410\pi$
$84$	0.0457952	+	0.829238i	0.00499666	+	0.0904773i
$85$	−4.54286	−	16.9542i	−0.492742	−	1.83894i
$86$	0.0439346	+	0.163966i	0.00473759	+	0.0176809i
$87$		−	10.2194i		−	1.09563i
$88$	−4.43206	−	2.55885i	−0.472459	−	0.272774i
$89$	−5.06089	−	5.06089i	−0.536453	−	0.536453i	0.386032	−	0.922485i	$-0.373845\pi$
$89$	−5.06089	−	5.06089i	−0.536453	−	0.536453i	−0.922485	+	0.386032i	$0.873845\pi$
$90$	5.65491			0.596080
$91$	1.53962	+	9.41433i	0.161396	+	0.986890i
$92$	−0.655900			−0.0683823
$93$	1.61634	+	1.61634i	0.167607	+	0.167607i
$94$	−5.90549	−	3.40954i	−0.609105	−	0.351667i
$95$			16.5743i			1.70049i
$96$	−0.455541	−	1.70010i	−0.0464934	−	0.173516i
$97$	3.20050	+	11.9444i	0.324962	+	1.21277i	0.914350	+	0.404924i	$0.132702\pi$
$97$	3.20050	+	11.9444i	0.324962	+	1.21277i	−0.589388	+	0.807850i	$0.700631\pi$
$98$	9.91922	−	3.87172i	1.00199	−	0.391103i
$99$	1.41093	−	1.41093i	0.141803	−	0.141803i
$100$	−1.38430	−	2.39767i	−0.138430	−	0.239767i
$101$	−1.66871	+	2.89030i	−0.166043	+	0.287595i	−0.937025	−	0.349262i	$-0.886432\pi$
$101$	−1.66871	+	2.89030i	−0.166043	+	0.287595i	0.770982	+	0.636857i	$0.219766\pi$
$102$	−1.85887	−	6.93738i	−0.184055	−	0.686903i
$103$	−9.27777	+	16.0696i	−0.914166	+	1.58338i	−0.106048	+	0.994361i	$0.533820\pi$
$103$	−9.27777	+	16.0696i	−0.914166	+	1.58338i	−0.808118	+	0.589021i	$0.799514\pi$
$104$	−3.33315	−	8.62598i	−0.326842	−	0.845847i
$105$	−3.06565	−	9.34567i	−0.299177	−	0.912044i
$106$	1.72433	−	6.43528i	0.167482	−	0.625050i
$107$	5.32878			0.515153			0.257576	−	0.966258i	$-0.417076\pi$
$107$	5.32878			0.515153			0.257576	+	0.966258i	$0.417076\pi$
$108$	0.313900			0.0302051
$109$	2.89458	−	10.8027i	0.277251	−	1.03471i	−0.677067	−	0.735921i	$-0.736749\pi$
$109$	2.89458	−	10.8027i	0.277251	−	1.03471i	0.954318	−	0.298793i	$-0.0965840\pi$
$110$	−10.8991	−	2.92039i	−1.03918	−	0.278449i
$111$	−0.622880	+	0.166900i	−0.0591212	+	0.0158415i
$112$	−10.0317	+	6.55479i	−0.947904	+	0.619370i
$113$	1.28775	−	2.23045i	0.121142	−	0.209823i	−0.799077	−	0.601229i	$-0.794678\pi$
$113$	1.28775	−	2.23045i	0.121142	−	0.209823i	0.920218	+	0.391406i	$0.128011\pi$
$114$			6.78193i			0.635186i
$115$	7.50314	−	2.01046i	0.699672	−	0.187476i
$116$	−2.77810	+	1.60394i	−0.257940	+	0.148922i
$117$	3.58496	−	0.384827i	0.331429	−	0.0355773i
$118$		−	2.57990i		−	0.237499i
$119$	−10.4574	+	6.83299i	−0.958631	+	0.626379i
$120$	4.76737	+	8.25733i	0.435200	+	0.753788i
$121$	6.07826	−	3.50929i	0.552569	−	0.319026i
$122$	9.91982	+	2.65801i	0.898099	+	0.240645i
$123$	−6.45112	−	6.45112i	−0.581677	−	0.581677i
$124$	0.185711	−	0.693081i	0.0166773	−	0.0622405i
$125$	10.0415	+	10.0415i	0.898140	+	0.898140i
$126$	−1.25442	−	3.82410i	−0.111752	−	0.340678i
$127$	−15.9822	+	9.22735i	−1.41819	+	0.818795i	−0.996140	−	0.0877754i	$-0.972024\pi$
$127$	−15.9822	+	9.22735i	−1.41819	+	0.818795i	−0.422054	+	0.906570i	$0.638691\pi$
$128$	9.35284	−	9.35284i	0.826682	−	0.826682i
$129$	−0.0557966	−	0.0966425i	−0.00491262	−	0.00850890i
$130$	−12.0209	−	16.4685i	−1.05430	−	1.44438i
$131$	5.76722	+	3.32971i	0.503885	+	0.290918i	0.730316	−	0.683109i	$-0.239373\pi$
$131$	5.76722	+	3.32971i	0.503885	+	0.290918i	−0.226432	+	0.974027i	$0.572706\pi$
$132$	−0.604999	−	0.162109i	−0.0526584	−	0.0141098i
$133$	11.2083	−	3.67663i	0.971879	−	0.318804i
$134$	3.92577	+	2.26654i	0.339135	+	0.195800i
$135$	−3.59085	+	0.962166i	−0.309051	+	0.0828100i
$136$	8.56288	−	8.56288i	0.734261	−	0.734261i
$137$	−11.2909	+	11.2909i	−0.964647	+	0.964647i	−0.999396	−	0.0347494i	$-0.988937\pi$
$137$	−11.2909	+	11.2909i	−0.964647	+	0.964647i	0.0347494	+	0.999396i	$0.488937\pi$
$138$	3.07017	−	0.822648i	0.261350	−	0.0700285i
$139$	9.32621	+	5.38449i	0.791038	+	0.456706i	0.840328	−	0.542078i	$-0.182362\pi$
$139$	9.32621	+	5.38449i	0.791038	+	0.456706i	−0.0492896	+	0.998785i	$0.515696\pi$
$140$	−2.05943	+	2.30019i	−0.174053	+	0.194401i
$141$	4.33009	+	1.16024i	0.364660	+	0.0977102i
$142$	19.7482	+	11.4016i	1.65723	+	0.956803i
$143$	−7.10824	−	1.10969i	−0.594421	−	0.0927973i
$144$	2.26463	+	3.92246i	0.188719	+	0.326872i
$145$	26.8636	−	26.8636i	2.23090	−	2.23090i
$146$	−13.8476	+	7.99494i	−1.14604	+	0.661666i
$147$	−5.63991	+	4.14625i	−0.465172	+	0.341977i
$148$	0.143132	+	0.143132i	0.0117654	+	0.0117654i
$149$	0.686237	−	2.56107i	0.0562187	−	0.209811i	−0.932103	−	0.362194i	$-0.882028\pi$
$149$	0.686237	−	2.56107i	0.0562187	−	0.209811i	0.988322	+	0.152383i	$0.0486946\pi$
$150$	9.48691	+	9.48691i	0.774603	+	0.774603i
$151$	−3.46086	−	0.927335i	−0.281641	−	0.0754655i	0.115233	−	0.993338i	$-0.463238\pi$
$151$	−3.46086	−	0.927335i	−0.281641	−	0.0754655i	−0.396874	+	0.917873i	$0.629905\pi$
$152$	−9.90301	+	5.71751i	−0.803240	+	0.463751i
$153$	2.36075	+	4.08893i	0.190855	+	0.330571i
$154$	0.442812	+	8.01825i	0.0356828	+	0.646129i
$155$			8.49772i			0.682553i
$156$	−0.667273	−	0.914156i	−0.0534246	−	0.0731910i
$157$	−8.63943	+	4.98798i	−0.689502	+	0.398084i	−0.803425	−	0.595406i	$-0.796991\pi$
$157$	−8.63943	+	4.98798i	−0.689502	+	0.398084i	0.113924	+	0.993490i	$0.463658\pi$
$158$	−0.0803695	+	0.0215349i	−0.00639385	+	0.00171323i
$159$			4.37977i			0.347338i
$160$	3.27156	−	5.66651i	0.258639	−	0.447977i
$161$	−3.02396	−	4.62798i	−0.238322	−	0.364736i
$162$	−1.46932	+	0.393703i	−0.115441	+	0.0309322i
$163$	1.12311	+	0.300937i	0.0879688	+	0.0235712i	0.302535	−	0.953138i	$-0.402167\pi$
$163$	1.12311	+	0.300937i	0.0879688	+	0.0235712i	−0.214566	+	0.976709i	$0.568834\pi$
$164$	−0.741204	+	2.76621i	−0.0578783	+	0.216005i
$165$	7.41776			0.577472
$166$	19.4724			1.51135
$167$	−1.15161	+	4.29785i	−0.0891139	+	0.332578i	−0.996061	−	0.0886660i	$-0.971740\pi$
$167$	−1.15161	+	4.29785i	−0.0891139	+	0.332578i	0.906947	+	0.421244i	$0.138406\pi$
$168$	4.52644	−	5.05561i	0.349222	−	0.390049i
$169$	−8.74143	−	9.62224i	−0.672417	−	0.740172i
$170$	13.3498	−	23.1226i	1.02388	−	1.77342i
$171$	−1.15392	−	4.30650i	−0.0882428	−	0.329327i
$172$	−0.0175146	+	0.0303361i	−0.00133547	+	0.00231311i
$173$	−9.80425	−	16.9815i	−0.745403	−	1.29108i	−0.950006	−	0.312231i	$-0.898924\pi$
$173$	−9.80425	−	16.9815i	−0.745403	−	1.29108i	0.204603	−	0.978845i	$-0.434410\pi$
$174$	10.9921	−	10.9921i	0.833313	−	0.833313i
$175$	10.5356	−	20.8217i	0.796418	−	1.57397i
$176$	−2.33907	−	8.72953i	−0.176314	−	0.658013i
$177$	0.438963	+	1.63823i	0.0329945	+	0.123137i
$178$		−	10.8871i		−	0.816026i
$179$	19.9729	+	11.5314i	1.49284	+	0.861894i	0.999966	−	0.00820394i	$-0.00261142\pi$
$179$	19.9729	+	11.5314i	1.49284	+	0.861894i	0.492878	+	0.870098i	$0.335945\pi$
$180$	0.825145	+	0.825145i	0.0615027	+	0.0615027i
$181$	−20.5419			−1.52686			−0.763432	−	0.645888i	$-0.776487\pi$
$181$	−20.5419			−1.52686			−0.763432	+	0.645888i	$0.776487\pi$
$182$	−8.47016	+	11.7822i	−0.627850	+	0.873358i
$183$	−6.75131			−0.499071
$184$	3.78954	+	3.78954i	0.279368	+	0.279368i
$185$	−2.07608	−	1.19863i	−0.152637	−	0.0881249i
$186$			3.47713i			0.254956i
$187$	−2.43834	−	9.10002i	−0.178309	−	0.665460i
$188$	−0.364201	−	1.35922i	−0.0265621	−	0.0991311i
$189$	1.44721	+	2.21486i	0.105269	+	0.161107i
$190$	−17.8276	+	17.8276i	−1.29335	+	1.29335i
$191$	−11.4908	−	19.9026i	−0.831443	−	1.44010i	−0.896894	−	0.442246i	$-0.854182\pi$
$191$	−11.4908	−	19.9026i	−0.831443	−	1.44010i	0.0654501	−	0.997856i	$-0.479152\pi$
$192$	−3.19060	+	5.52628i	−0.230262	+	0.398825i
$193$	−2.01944	−	7.53664i	−0.145362	−	0.542500i	−0.999739	−	0.0228453i	$-0.992727\pi$
$193$	−2.01944	−	7.53664i	−0.145362	−	0.542500i	0.854377	−	0.519654i	$-0.173939\pi$
$194$	−9.40512	+	16.2901i	−0.675248	+	1.16956i
$195$	10.4353	+	8.41213i	0.747288	+	0.602405i
$196$	2.01233	+	0.882429i	0.143738	+	0.0630307i
$197$	−2.60698	+	9.72938i	−0.185740	+	0.693190i	0.808731	+	0.588178i	$0.200155\pi$
$197$	−2.60698	+	9.72938i	−0.185740	+	0.693190i	−0.994471	+	0.105012i	$0.966512\pi$
$198$	3.03523			0.215704
$199$	7.69033			0.545153			0.272576	−	0.962134i	$-0.412124\pi$
$199$	7.69033			0.545153			0.272576	+	0.962134i	$0.412124\pi$
$200$	−5.85489	+	21.8508i	−0.414004	+	1.54508i
$201$	−2.87850	−	0.771291i	−0.203033	−	0.0544027i
$202$	−4.90374	+	1.31395i	−0.345026	+	0.0924495i
$203$	−24.1254	−	12.2072i	−1.69327	−	0.856781i
$204$	0.741039	−	1.28352i	0.0518831	−	0.0898642i
$205$		−	33.9159i		−	2.36879i
$206$	−27.2640	+	7.30537i	−1.89957	+	0.508989i
$207$	−1.80957	+	1.04476i	−0.125774	+	0.0726157i
$208$	6.60914	−	14.9333i	0.458261	−	1.03544i
$209$			8.89611i			0.615357i
$210$	6.75489	−	13.3498i	0.466132	−	0.921225i
$211$	4.74990	+	8.22707i	0.326997	+	0.566375i	0.981914	−	0.189325i	$-0.0606301\pi$
$211$	4.74990	+	8.22707i	0.326997	+	0.566375i	−0.654918	+	0.755700i	$0.727297\pi$
$212$	1.19062	−	0.687406i	0.0817722	−	0.0472112i
$213$	−14.4800	−	3.87990i	−0.992152	−	0.265846i
$214$	5.73172	+	5.73172i	0.391812	+	0.391812i
$215$	0.107371	−	0.400715i	0.00732265	−	0.0273285i
$216$	−1.81360	−	1.81360i	−0.123400	−	0.123400i
$217$	5.74653	−	1.88503i	0.390100	−	0.127964i
$218$	14.7331	−	8.50613i	0.997848	−	0.576108i
$219$	7.43290	−	7.43290i	0.502269	−	0.502269i
$220$	−1.16422	−	2.01649i	−0.0784916	−	0.135951i
$221$	6.88964	−	15.5671i	0.463447	−	1.04716i
$222$	−0.849500	−	0.490459i	−0.0570147	−	0.0329175i
$223$	−16.5658	−	4.43878i	−1.10933	−	0.297243i	−0.342769	−	0.939420i	$-0.611365\pi$
$223$	−16.5658	−	4.43878i	−1.10933	−	0.297243i	−0.766556	+	0.642177i	$0.778031\pi$
$224$	−4.55766	−	0.955385i	−0.304522	−	0.0638343i
$225$	−7.63832	−	4.40999i	−0.509221	−	0.293999i
$226$	3.78424	−	1.01398i	0.251724	−	0.0674492i
$227$	4.39624	−	4.39624i	0.291789	−	0.291789i	−0.545998	−	0.837787i	$-0.683849\pi$
$227$	4.39624	−	4.39624i	0.291789	−	0.291789i	0.837787	+	0.545998i	$0.183849\pi$
$228$	−0.989596	+	0.989596i	−0.0655376	+	0.0655376i
$229$	−4.68814	+	1.25618i	−0.309801	+	0.0830110i	−0.410370	−	0.911919i	$-0.634600\pi$
$229$	−4.68814	+	1.25618i	−0.309801	+	0.0830110i	0.100569	+	0.994930i	$0.467934\pi$
$230$	10.2330	+	5.90802i	0.674743	+	0.389563i
$231$	−1.64546	−	5.01622i	−0.108264	−	0.330043i
$232$	25.3177	+	6.78386i	1.66219	+	0.445382i
$233$	11.3722	+	6.56573i	0.745016	+	0.430135i	0.823890	−	0.566749i	$-0.191799\pi$
$233$	11.3722	+	6.56573i	0.745016	+	0.430135i	−0.0788741	+	0.996885i	$0.525133\pi$
$234$	4.26996	+	3.44211i	0.279136	+	0.225018i
$235$	8.33253	+	14.4324i	0.543554	+	0.941464i
$236$	0.376451	−	0.376451i	0.0245048	−	0.0245048i
$237$	0.0473702	−	0.0273492i	0.00307703	−	0.00177652i
$238$	−18.5979	−	3.89851i	−1.20552	−	0.252703i
$239$	6.23607	+	6.23607i	0.403378	+	0.403378i	0.879422	−	0.476044i	$-0.157930\pi$
$239$	6.23607	+	6.23607i	0.403378	+	0.403378i	−0.476044	+	0.879422i	$0.657930\pi$
$240$	−4.35791	+	16.2639i	−0.281302	+	1.04983i
$241$	−6.46595	−	6.46595i	−0.416508	−	0.416508i	0.467490	−	0.883998i	$-0.345158\pi$
$241$	−6.46595	−	6.46595i	−0.416508	−	0.416508i	−0.883998	+	0.467490i	$0.845158\pi$
$242$	10.3125	+	2.76323i	0.662914	+	0.177627i
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$	1.05962	+	1.83531i	0.0678351	+	0.117494i
$245$	−25.7247	−	3.92635i	−1.64349	−	0.250845i
$246$		−	13.8778i		−	0.884819i
$247$	−10.0887	+	12.5151i	−0.641926	+	0.796314i
$248$	−5.07732	+	2.93139i	−0.322410	+	0.186144i
$249$	−12.3649	+	3.31317i	−0.783594	+	0.209963i
$250$			21.6016i			1.36621i
$251$	−6.74060	+	11.6751i	−0.425463	+	0.736924i	−0.996464	−	0.0840260i	$-0.973222\pi$
$251$	−6.74060	+	11.6751i	−0.425463	+	0.736924i	0.571000	+	0.820950i	$0.306555\pi$
$252$	0.374959	−	0.741039i	0.0236202	−	0.0466811i
$253$	4.02725	−	1.07910i	0.253191	−	0.0678424i
$254$	−27.1158	−	7.26567i	−1.70140	−	0.455889i
$255$	−4.54286	+	16.9542i	−0.284485	+	1.06171i
$256$	7.35774			0.459859
$257$	9.85058			0.614462			0.307231	−	0.951635i	$-0.400598\pi$
$257$	9.85058			0.614462			0.307231	+	0.951635i	$0.400598\pi$
$258$	0.0439346	−	0.163966i	0.00273525	−	0.0102081i
$259$	−0.350032	+	1.66983i	−0.0217499	+	0.103758i
$260$	0.648977	−	4.15708i	0.0402479	−	0.257811i
$261$	−5.10970	+	8.85026i	−0.316282	+	0.547817i
$262$	2.62183	+	9.78480i	0.161977	+	0.604507i
$263$	5.01903	−	8.69321i	0.309486	−	0.536046i	−0.668764	−	0.743475i	$-0.733176\pi$
$263$	5.01903	−	8.69321i	0.309486	−	0.536046i	0.978250	+	0.207429i	$0.0665095\pi$
$264$	2.55885	+	4.43206i	0.157486	+	0.272774i
$265$	−11.5130	+	11.5130i	−0.707240	+	0.707240i
$266$	16.0104	+	8.10114i	0.981662	+	0.496713i
$267$	1.85241	+	6.91330i	0.113366	+	0.423087i
$268$	0.242108	+	0.903561i	0.0147891	+	0.0551938i
$269$			30.2527i			1.84454i	0.386550	+	0.922268i	$0.373667\pi$
$269$			30.2527i			1.84454i	−0.386550	+	0.922268i	$0.626333\pi$
$270$	−4.89730	−	2.82746i	−0.298040	−	0.172074i
$271$	12.3851	+	12.3851i	0.752341	+	0.752341i	0.974916	−	0.222575i	$-0.0714461\pi$
$271$	12.3851	+	12.3851i	0.752341	+	0.752341i	−0.222575	+	0.974916i	$0.571446\pi$
$272$	21.3849			1.29665
$273$	3.37381	−	8.92286i	0.204192	−	0.540036i
$274$	−24.2893			−1.46737
$275$	12.4443	+	12.4443i	0.750421	+	0.750421i
$276$	0.568026	+	0.327950i	0.0341911	+	0.0197403i
$277$			17.8382i			1.07179i	0.844283	+	0.535897i	$0.180027\pi$
$277$			17.8382i			1.07179i	−0.844283	+	0.535897i	$0.819973\pi$
$278$	4.23978	+	15.8231i	0.254285	+	0.949004i
$279$	−0.591623	−	2.20797i	−0.0354195	−	0.132188i
$280$	25.1882	−	1.39103i	1.50528	−	0.0831301i
$281$	0.156351	−	0.156351i	0.00932711	−	0.00932711i	−0.702428	−	0.711755i	$-0.747901\pi$
$281$	0.156351	−	0.156351i	0.00932711	−	0.00932711i	0.711755	+	0.702428i	$0.247901\pi$
$282$	3.40954	+	5.90549i	0.203035	+	0.351667i
$283$	−12.8554	+	22.2662i	−0.764176	+	1.32359i	0.176506	+	0.984300i	$0.443521\pi$
$283$	−12.8554	+	22.2662i	−0.764176	+	1.32359i	−0.940681	+	0.339291i	$0.889813\pi$
$284$	1.21790	+	4.54527i	0.0722692	+	0.269712i
$285$	8.28714	−	14.3537i	0.490888	−	0.850243i
$286$	−6.45213	−	8.83935i	−0.381523	−	0.522681i
$287$	−22.9354	+	7.52348i	−1.35384	+	0.444097i
$288$	−0.455541	+	1.70010i	−0.0268430	+	0.100179i
$289$	5.29251			0.311324
$290$	57.7898			3.39353
$291$	3.20050	−	11.9444i	0.187617	−	0.700195i
$292$	−3.18719	−	0.854006i	−0.186516	−	0.0499769i
$293$	−15.5701	+	4.17200i	−0.909615	+	0.243731i	−0.683141	−	0.730286i	$-0.739387\pi$
$293$	−15.5701	+	4.17200i	−0.909615	+	0.243731i	−0.226474	+	0.974017i	$0.572720\pi$
$294$	−10.5262	−	1.60660i	−0.613898	−	0.0936987i
$295$	−3.15250	+	5.46029i	−0.183546	+	0.317910i
$296$		−	1.65393i		−	0.0961325i
$297$	−1.92736	+	0.516435i	−0.111837	+	0.0299666i
$298$	3.49286	−	2.01660i	0.202336	−	0.116819i
$299$	6.88929	+	3.04904i	0.398418	+	0.176330i
$300$			2.76859i			0.159845i
$301$	−0.294799	+	0.0162804i	−0.0169919	+	0.000938388i
$302$	−2.72510	−	4.72002i	−0.156812	−	0.271606i
$303$	2.89030	−	1.66871i	0.166043	−	0.0958651i
$304$	−19.5053	−	5.22643i	−1.11871	−	0.299756i
$305$	−17.7471	−	17.7471i	−1.01619	−	1.01619i
$306$	−1.85887	+	6.93738i	−0.106264	+	0.396584i
$307$	−21.2119	−	21.2119i	−1.21063	−	1.21063i	−0.970820	−	0.239809i	$-0.922915\pi$
$307$	−21.2119	−	21.2119i	−1.21063	−	1.21063i	−0.239809	−	0.970820i	$-0.577085\pi$
$308$	−1.10538	+	1.23461i	−0.0629849	+	0.0703483i
$309$	16.0696	−	9.27777i	0.914166	−	0.527794i
$310$	−9.14028	+	9.14028i	−0.519133	+	0.519133i
$311$	−12.0212	−	20.8214i	−0.681660	−	1.18067i	−0.974474	−	0.224501i	$-0.927925\pi$
$311$	−12.0212	−	20.8214i	−0.681660	−	1.18067i	0.292813	−	0.956170i	$-0.405409\pi$
$312$	−1.42640	+	9.13689i	−0.0807537	+	0.517275i
$313$	20.0578	+	11.5804i	1.13373	+	0.654562i	0.944872	−	0.327441i	$-0.106186\pi$
$313$	20.0578	+	11.5804i	1.13373	+	0.654562i	0.188863	+	0.982003i	$0.439520\pi$
$314$	−14.6579	−	3.92756i	−0.827191	−	0.221645i
$315$	−2.01791	+	9.62642i	−0.113696	+	0.542387i
$316$	−0.0148695	−	0.00858493i	−0.000836477	−	0.000482940i
$317$	−19.7590	+	5.29442i	−1.10978	+	0.297364i	−0.766740	−	0.641958i	$-0.778123\pi$
$317$	−19.7590	+	5.29442i	−1.10978	+	0.297364i	−0.343038	+	0.939322i	$0.611456\pi$
$318$	−4.71095	+	4.71095i	−0.264177	+	0.264177i
$319$	14.4188	−	14.4188i	0.807298	−	0.807298i
$320$	−22.9139	+	6.13977i	−1.28093	+	0.343223i
$321$	−4.61486	−	2.66439i	−0.257576	−	0.148712i
$322$	1.72530	−	8.23055i	0.0961474	−	0.458671i
$323$	−20.3331	−	5.44825i	−1.13137	−	0.303149i
$324$	−0.271846	−	0.156950i	−0.0151025	−	0.00871945i
$325$	3.39417	+	31.6192i	0.188275	+	1.75392i
$326$	0.884344	+	1.53173i	0.0489793	+	0.0848346i
$327$	−7.90815	+	7.90815i	−0.437322	+	0.437322i
$328$	20.2645	−	11.6997i	1.11892	−	0.646009i
$329$	7.91142	−	8.83632i	0.436170	−	0.487162i
$330$	7.97866	+	7.97866i	0.439211	+	0.439211i
$331$	−5.42874	+	20.2603i	−0.298390	+	1.11361i	0.640097	+	0.768294i	$0.278894\pi$
$331$	−5.42874	+	20.2603i	−0.298390	+	1.11361i	−0.938487	+	0.345314i	$0.887772\pi$
$332$	2.84134	+	2.84134i	0.155939	+	0.155939i
$333$	0.622880	+	0.166900i	0.0341336	+	0.00914608i
$334$	−5.86152	+	3.38415i	−0.320728	+	0.185173i
$335$	−5.53918	−	9.59414i	−0.302638	−	0.524184i
$336$	11.9651	−	0.660779i	0.652749	−	0.0360484i
$337$		−	30.0384i		−	1.63629i	−0.575009	−	0.818147i	$-0.695001\pi$
$337$		−	30.0384i		−	1.63629i	0.575009	−	0.818147i	$-0.304999\pi$
$338$	0.947415	−	19.7523i	0.0515326	−	1.07438i
$339$	−2.23045	+	1.28775i	−0.121142	+	0.0699411i
$340$	5.32192	−	1.42600i	0.288622	−	0.0773360i
$341$			4.56108i			0.246997i
$342$	3.39097	−	5.87333i	0.183362	−	0.317593i
$343$	3.05129	+	18.2672i	0.164754	+	0.986335i
$344$	0.276463	−	0.0740780i	0.0149059	−	0.00399402i
$345$	−7.50314	−	2.01046i	−0.403956	−	0.108240i
$346$	7.71992	−	28.8111i	0.415026	−	1.54890i
$347$	1.91000			0.102534			0.0512671	−	0.998685i	$-0.483674\pi$
$347$	1.91000			0.102534			0.0512671	+	0.998685i	$0.483674\pi$
$348$	3.20787			0.171960
$349$	0.864466	−	3.22623i	0.0462738	−	0.172696i	−0.938922	−	0.344131i	$-0.888174\pi$
$349$	0.864466	−	3.22623i	0.0462738	−	0.172696i	0.985195	+	0.171435i	$0.0548402\pi$
$350$	33.7285	−	11.0639i	1.80286	−	0.591391i
$351$	−3.29708	−	1.45921i	−0.175985	−	0.0778867i
$352$	1.75598	−	3.04145i	0.0935942	−	0.162110i
$353$	2.57961	+	9.62725i	0.137299	+	0.512407i	0.999978	+	0.00665464i	$0.00211825\pi$
$353$	2.57961	+	9.62725i	0.137299	+	0.512407i	−0.862679	+	0.505752i	$0.831215\pi$
$354$	−1.28995	+	2.23426i	−0.0685602	+	0.118750i
$355$	−27.8643	−	48.2624i	−1.47888	−	2.56150i
$356$	1.58861	−	1.58861i	0.0841963	−	0.0841963i
$357$	12.4729	−	0.688823i	0.660136	−	0.0364564i
$358$	9.07986	+	33.8865i	0.479885	+	1.79096i
$359$	−3.58279	−	13.3711i	−0.189092	−	0.705702i	−0.993717	−	0.111919i	$-0.964300\pi$
$359$	−3.58279	−	13.3711i	−0.189092	−	0.705702i	0.804625	−	0.593783i	$-0.202366\pi$
$360$		−	9.53475i		−	0.502525i
$361$	0.759955	+	0.438760i	0.0399976	+	0.0230927i
$362$	−22.0952	−	22.0952i	−1.16130	−	1.16130i
$363$	−7.01857			−0.368380
$364$	−2.95516	+	0.483287i	−0.154892	+	0.0253311i
$365$	39.0775			2.04541
$366$	−7.26181	−	7.26181i	−0.379581	−	0.379581i
$367$	22.7192	+	13.1169i	1.18593	+	0.684697i	0.957379	−	0.288834i	$-0.0932677\pi$
$367$	22.7192	+	13.1169i	1.18593	+	0.684697i	0.228552	+	0.973532i	$0.426601\pi$
$368$			9.46398i			0.493344i
$369$	2.36127	+	8.81239i	0.122923	+	0.458755i
$370$	−0.943806	−	3.52233i	−0.0490661	−	0.183117i
$371$	10.3395	+	5.23171i	0.536802	+	0.271617i
$372$	−0.507371	+	0.507371i	−0.0263059	+	0.0263059i
$373$	−7.19027	−	12.4539i	−0.372298	−	0.644839i	0.617621	−	0.786476i	$-0.288097\pi$
$373$	−7.19027	−	12.4539i	−0.372298	−	0.644839i	−0.989919	+	0.141637i	$0.954763\pi$
$374$	7.16541	−	12.4109i	0.370515	−	0.641750i
$375$	−3.67545	−	13.7170i	−0.189799	−	0.708340i
$376$	−5.74882	+	9.95725i	−0.296473	+	0.513506i
$377$	36.6361	−	3.93270i	1.88685	−	0.202545i
$378$	−0.825695	+	3.93898i	−0.0424692	+	0.202599i
$379$	0.297354	−	1.10974i	0.0152740	−	0.0570035i	−0.957868	−	0.287208i	$-0.907273\pi$
$379$	0.297354	−	1.10974i	0.0152740	−	0.0570035i	0.973142	+	0.230205i	$0.0739395\pi$
$380$	−5.20267			−0.266891
$381$	18.4547			0.945463
$382$	9.04790	−	33.7672i	0.462931	−	1.72768i
$383$	19.9438	+	5.34393i	1.01908	+	0.273062i	0.729419	−	0.684067i	$-0.239790\pi$
$383$	19.9438	+	5.34393i	1.01908	+	0.273062i	0.289662	+	0.957129i	$0.406457\pi$
$384$	−12.7762	+	3.42338i	−0.651983	+	0.174698i
$385$	8.86065	−	17.5115i	0.451580	−	0.892467i
$386$	5.93440	−	10.2787i	0.302053	−	0.523171i
$387$			0.111593i			0.00567260i
$388$	−3.74936	+	1.00464i	−0.190345	+	0.0510028i
$389$	25.6552	−	14.8121i	1.30077	−	0.751001i	0.320236	−	0.947338i	$-0.396238\pi$
$389$	25.6552	−	14.8121i	1.30077	−	0.751001i	0.980537	+	0.196337i	$0.0629046\pi$
$390$	2.17617	+	20.2726i	0.110194	+	1.02654i
$391$			9.86564i			0.498927i
$392$	−6.52811	−	16.7248i	−0.329719	−	0.844729i
$393$	−3.32971	−	5.76722i	−0.167962	−	0.290918i
$394$	−13.2692	+	7.66097i	−0.668492	+	0.385954i
$395$	0.196414	+	0.0526290i	0.00988266	+	0.00264805i
$396$	0.442890	+	0.442890i	0.0222561	+	0.0222561i
$397$	−4.88527	+	18.2321i	−0.245185	+	0.915042i	0.728106	+	0.685465i	$0.240401\pi$
$397$	−4.88527	+	18.2321i	−0.245185	+	0.915042i	−0.973290	+	0.229577i	$0.926266\pi$
$398$	8.27184	+	8.27184i	0.414630	+	0.414630i
$399$	−11.5450	−	2.42007i	−0.577970	−	0.121155i
$400$	−34.5960	+	19.9740i	−1.72980	+	0.998700i
$401$	−6.39233	+	6.39233i	−0.319218	+	0.319218i	−0.848467	−	0.529249i	$-0.822474\pi$
$401$	−6.39233	+	6.39233i	−0.319218	+	0.319218i	0.529249	+	0.848467i	$0.322474\pi$
$402$	−2.26654	−	3.92577i	−0.113045	−	0.195800i
$403$	−5.17251	+	6.41653i	−0.257661	+	0.319630i
$404$	−0.907265	−	0.523810i	−0.0451381	−	0.0260605i
$405$	3.59085	+	0.962166i	0.178431	+	0.0478104i
$406$	−12.8194	−	39.0800i	−0.636214	−	1.93951i
$407$	−1.11432	−	0.643354i	−0.0552349	−	0.0318899i
$408$	−11.6971	+	3.13423i	−0.579094	+	0.155168i
$409$	−6.11773	+	6.11773i	−0.302503	+	0.302503i	−0.841992	−	0.539490i	$-0.818617\pi$
$409$	−6.11773	+	6.11773i	−0.302503	+	0.302503i	0.539490	+	0.841992i	$0.318617\pi$
$410$	36.4805	−	36.4805i	1.80164	−	1.80164i
$411$	15.4237	−	4.13276i	0.760793	−	0.203854i
$412$	−5.04424	−	2.91229i	−0.248512	−	0.143478i
$413$	4.39180	+	0.920616i	0.216106	+	0.0453006i
$414$	−3.07017	−	0.822648i	−0.150890	−	0.0404310i
$415$	−41.2127	−	23.7942i	−2.02305	−	1.16801i
$416$	5.91948	−	2.28734i	0.290227	−	0.112146i
$417$	−5.38449	−	9.32621i	−0.263679	−	0.456706i
$418$	−9.56881	+	9.56881i	−0.468026	+	0.468026i
$419$	3.98045	−	2.29811i	0.194457	−	0.112270i	−0.399610	−	0.916685i	$-0.630854\pi$
$419$	3.98045	−	2.29811i	0.194457	−	0.112270i	0.594068	+	0.804415i	$0.297521\pi$
$420$	2.93361	−	0.962308i	0.143145	−	0.0469558i
$421$	16.2204	+	16.2204i	0.790532	+	0.790532i	0.981581	−	0.191049i	$-0.0611888\pi$
$421$	16.2204	+	16.2204i	0.790532	+	0.790532i	−0.191049	+	0.981581i	$0.561189\pi$
$422$	−3.74010	+	13.9582i	−0.182065	+	0.679476i
$423$	−3.16985	−	3.16985i	−0.154123	−	0.154123i
$424$	−10.8505	−	2.90739i	−0.526948	−	0.141195i
$425$	−36.0643	+	20.8217i	−1.74937	+	1.01000i
$426$	−11.4016	−	19.7482i	−0.552410	−	0.956803i
$427$	−8.06456	+	15.9381i	−0.390271	+	0.771300i
$428$			1.67271i			0.0808533i
$429$	5.60107	+	4.51514i	0.270422	+	0.217993i
$430$	0.546505	−	0.315525i	0.0263548	−	0.0152160i
$431$	11.2060	−	3.00263i	0.539772	−	0.144632i	0.0213750	−	0.999772i	$-0.493196\pi$
$431$	11.2060	−	3.00263i	0.539772	−	0.144632i	0.518397	+	0.855140i	$0.326529\pi$
$432$		−	4.52927i		−	0.217914i
$433$	0.155556	−	0.269431i	0.00747554	−	0.0129480i	−0.862263	−	0.506460i	$-0.830954\pi$
$433$	0.155556	−	0.269431i	0.00747554	−	0.0129480i	0.869739	+	0.493512i	$0.164287\pi$
$434$	8.20863	+	4.15349i	0.394027	+	0.199374i
$435$	−36.6963	+	9.83275i	−1.75945	+	0.471444i
$436$	3.39098	+	0.908611i	0.162399	+	0.0435146i
$437$	2.41114	−	8.99851i	0.115341	−	0.430457i
$438$	15.9899			0.764026
$439$	20.5750			0.981992			0.490996	−	0.871162i	$-0.336633\pi$
$439$	20.5750			0.981992			0.490996	+	0.871162i	$0.336633\pi$
$440$	−4.92408	+	18.3769i	−0.234746	+	0.876084i
$441$	6.95743	−	0.770807i	0.331306	−	0.0367051i
$442$	24.1549	−	9.33365i	1.14893	−	0.443956i
$443$	13.6460	−	23.6355i	0.648340	−	1.12296i	−0.335179	−	0.942154i	$-0.608797\pi$
$443$	13.6460	−	23.6355i	0.648340	−	1.12296i	0.983519	−	0.180804i	$-0.0578699\pi$
$444$	−0.0523900	−	0.195522i	−0.00248632	−	0.00927907i
$445$	−13.3035	+	23.0423i	−0.630645	+	1.09231i
$446$	−13.0440	−	22.5928i	−0.617650	−	1.06980i
$447$	−1.87483	+	1.87483i	−0.0886766	+	0.0886766i
$448$	9.23492	+	14.1334i	0.436309	+	0.667742i
$449$	−1.99206	−	7.43447i	−0.0940111	−	0.350854i	0.902857	−	0.429942i	$-0.141466\pi$
$449$	−1.99206	−	7.43447i	−0.0940111	−	0.350854i	−0.996868	+	0.0790877i	$0.974799\pi$
$450$	−3.47245	−	12.9594i	−0.163693	−	0.610910i
$451$		−	18.2041i		−	0.857197i
$452$	0.700140	+	0.404226i	0.0329318	+	0.0190132i
$453$	2.53353	+	2.53353i	0.119036	+	0.119036i
$454$	9.45734			0.443855
$455$	32.3241	−	14.5867i	1.51538	−	0.683835i
$456$	11.4350			0.535494
$457$	16.6443	+	16.6443i	0.778589	+	0.778589i	0.979591	−	0.201002i	$-0.0644197\pi$
$457$	16.6443	+	16.6443i	0.778589	+	0.778589i	−0.201002	+	0.979591i	$0.564420\pi$
$458$	−6.39382	−	3.69147i	−0.298763	−	0.172491i
$459$		−	4.72149i		−	0.220380i
$460$	0.631084	+	2.35524i	0.0294245	+	0.109814i
$461$	−8.59300	−	32.0695i	−0.400216	−	1.49363i	−0.812711	−	0.582666i	$-0.802009\pi$
$461$	−8.59300	−	32.0695i	−0.400216	−	1.49363i	0.412495	−	0.910960i	$-0.364657\pi$
$462$	3.62564	−	7.16541i	0.168680	−	0.333365i
$463$	−4.66625	+	4.66625i	−0.216859	+	0.216859i	−0.807173	−	0.590314i	$-0.799004\pi$
$463$	−4.66625	+	4.66625i	−0.216859	+	0.216859i	0.590314	+	0.807173i	$0.299004\pi$
$464$	23.1432	+	40.0852i	1.07440	+	1.86091i
$465$	4.24886	−	7.35924i	0.197036	−	0.341277i
$466$	5.16989	+	19.2943i	0.239491	+	0.893791i
$467$	−7.16204	+	12.4050i	−0.331420	+	0.574036i	−0.982790	−	0.184724i	$-0.940861\pi$
$467$	−7.16204	+	12.4050i	−0.331420	+	0.574036i	0.651371	+	0.758760i	$0.274194\pi$
$468$	0.120797	+	1.12532i	0.00558386	+	0.0520179i
$469$	−5.25924	+	5.87408i	−0.242849	+	0.271240i
$470$	−6.56108	+	24.4863i	−0.302640	+	1.12947i
$471$	9.97596			0.459668
$472$	−4.34998			−0.200224
$473$	0.0576306	−	0.215080i	0.00264986	−	0.00988941i
$474$	0.0803695	+	0.0215349i	0.00369149	+	0.000989132i
$475$	37.9833	−	10.1776i	1.74279	−	0.466979i
$476$	−2.14488	−	3.28259i	−0.0983102	−	0.150457i
$477$	2.18989	−	3.79299i	0.100268	−	0.173669i
$478$			13.4152i			0.613599i
$479$	14.2975	−	3.83101i	0.653271	−	0.175043i	0.0830635	−	0.996544i	$-0.473530\pi$
$479$	14.2975	−	3.83101i	0.653271	−	0.175043i	0.570207	+	0.821501i	$0.306863\pi$
$480$	−5.66651	+	3.27156i	−0.258639	+	0.149326i
$481$	−0.838031	−	2.16877i	−0.0382109	−	0.0988874i
$482$		−	13.9098i		−	0.633572i
$483$	0.304841	+	5.51993i	0.0138708	+	0.251165i
$484$	1.10157	+	1.90797i	0.0500712	+	0.0867259i
$485$	39.8113	−	22.9851i	1.80774	−	1.04370i
$486$	1.46932	+	0.393703i	0.0666497	+	0.0178587i
$487$	−23.4442	−	23.4442i	−1.06236	−	1.06236i	−0.997922	−	0.0644378i	$-0.979475\pi$
$487$	−23.4442	−	23.4442i	−1.06236	−	1.06236i	−0.0644378	−	0.997922i	$-0.520525\pi$
$488$	4.48167	−	16.7258i	0.202876	−	0.757142i
$489$	−0.822174	−	0.822174i	−0.0371800	−	0.0371800i
$490$	−23.4467	−	31.8932i	−1.05921	−	1.44079i
$491$	−17.1631	+	9.90909i	−0.774558	+	0.447191i	−0.834498	−	0.551011i	$-0.814242\pi$
$491$	−17.1631	+	9.90909i	−0.774558	+	0.447191i	0.0599403	+	0.998202i	$0.480909\pi$
$492$	2.02501	−	2.02501i	0.0912944	−	0.0912944i
$493$	24.1254	+	41.7864i	1.08655	+	1.88197i
$494$	−24.3129	+	2.60987i	−1.09389	+	0.117424i
$495$	−6.42397	−	3.70888i	−0.288736	−	0.166702i
$496$	−10.0005	−	2.67962i	−0.449034	−	0.120318i
$497$	−26.4561	+	29.5490i	−1.18672	+	1.32545i
$498$	−16.8636	−	9.73620i	−0.755676	−	0.436290i
$499$	22.4211	−	6.00770i	1.00370	−	0.268942i	0.280708	−	0.959793i	$-0.409431\pi$
$499$	22.4211	−	6.00770i	1.00370	−	0.268942i	0.722997	+	0.690852i	$0.242764\pi$
$500$	−3.15203	+	3.15203i	−0.140963	+	0.140963i
$501$	3.14625	−	3.14625i	0.140564	−	0.140564i
$502$	−19.8082	+	5.30759i	−0.884083	+	0.236889i
$503$	−24.2350	−	13.9921i	−1.08059	−	0.623877i	−0.149532	−	0.988757i	$-0.547777\pi$
$503$	−24.2350	−	13.9921i	−1.08059	−	0.623877i	−0.931055	+	0.364880i	$0.881110\pi$
$504$	−6.44781	+	2.11507i	−0.287208	+	0.0942127i
$505$	11.9842	+	3.21116i	0.533290	+	0.142895i
$506$	5.49247	+	3.17108i	0.244170	+	0.140972i
$507$	2.75918	+	12.7038i	0.122539	+	0.564196i
$508$	−2.89647	−	5.01683i	−0.128510	−	0.222586i
$509$	7.69978	−	7.69978i	0.341287	−	0.341287i	−0.515564	−	0.856851i	$-0.672418\pi$
$509$	7.69978	−	7.69978i	0.341287	−	0.341287i	0.856851	+	0.515564i	$0.172418\pi$
$510$	−23.1226	+	13.3498i	−1.02388	+	0.591140i
$511$	−8.66846	−	26.4259i	−0.383470	−	1.16901i
$512$	−10.7916	−	10.7916i	−0.476925	−	0.476925i
$513$	−1.15392	+	4.30650i	−0.0509470	+	0.190137i
$514$	10.5954	+	10.5954i	0.467345	+	0.467345i
$515$	66.6302	+	17.8535i	2.93608	+	0.786719i
$516$	0.0303361	−	0.0175146i	0.00133547	−	0.000771036i
$517$	4.47242	+	7.74646i	0.196697	+	0.340689i
$518$	−2.17259	+	1.41959i	−0.0954583	+	0.0623734i
$519$			19.6085i			0.860718i
$520$	−27.7676	+	20.2685i	−1.21769	+	0.888831i
$521$	−19.3656	+	11.1808i	−0.848424	+	0.489838i	−0.860119	−	0.510094i	$-0.829611\pi$
$521$	−19.3656	+	11.1808i	−0.848424	+	0.489838i	0.0116948	+	0.999932i	$0.496277\pi$
$522$	−15.0156	+	4.02340i	−0.657213	+	0.176100i
$523$			18.0863i			0.790857i	0.918497	+	0.395428i	$0.129404\pi$
$523$			18.0863i			0.790857i	−0.918497	+	0.395428i	$0.870596\pi$
$524$	−1.04520	+	1.81033i	−0.0456596	+	0.0790847i
$525$	−19.5350	+	12.7643i	−0.852576	+	0.557081i
$526$	14.7491	−	3.95201i	0.643091	−	0.172316i
$527$	−10.4249	−	2.79334i	−0.454116	−	0.121680i
$528$	−2.33907	+	8.72953i	−0.101795	+	0.379904i
$529$	18.6339			0.810171
$530$	−24.7672			−1.07582
$531$	0.438963	−	1.63823i	0.0190494	−	0.0710932i
$532$	1.15410	+	3.51827i	0.0500364	+	0.152537i
$533$	20.6444	−	25.6095i	0.894208	−	1.10927i
$534$	−5.44357	+	9.42854i	−0.235566	+	0.408013i
$535$	−5.12717	−	19.1349i	−0.221667	−	0.827272i
$536$	3.82162	−	6.61924i	0.165069	−	0.285908i
$537$	−11.5314	−	19.9729i	−0.497615	−	0.861894i
$538$	−32.5402	+	32.5402i	−1.40291	+	1.40291i
$539$	−13.8076	−	2.10744i	−0.594733	−	0.0907737i
$540$	−0.302024	−	1.12717i	−0.0129970	−	0.0485056i
$541$	2.69630	+	10.0627i	0.115923	+	0.432630i	0.999354	−	0.0359302i	$-0.0114394\pi$
$541$	2.69630	+	10.0627i	0.115923	+	0.432630i	−0.883431	+	0.468561i	$0.844773\pi$
$542$			26.6432i			1.14442i
$543$	17.7898	+	10.2709i	0.763432	+	0.440768i
$544$	5.87619	+	5.87619i	0.251939	+	0.251939i
$545$	−41.5761			−1.78092
$546$	13.2265	−	5.96864i	0.566042	−	0.255434i
$547$	22.4723			0.960845			0.480422	−	0.877037i	$-0.340483\pi$
$547$	22.4723			0.960845			0.480422	+	0.877037i	$0.340483\pi$
$548$	−3.54422	−	3.54422i	−0.151401	−	0.151401i
$549$	5.84680	+	3.37565i	0.249535	+	0.144069i
$550$			26.7706i			1.14150i
$551$	−11.7924	−	44.0099i	−0.502374	−	1.87488i
$552$	−1.38707	−	5.17661i	−0.0590375	−	0.220331i
$553$	−0.00798000	−	0.144498i	−0.000339344	−	0.00614469i
$554$	−19.1871	+	19.1871i	−0.815181	+	0.815181i
$555$	1.19863	+	2.07608i	0.0508789	+	0.0881249i
$556$	−1.69019	+	2.92750i	−0.0716801	+	0.124154i
$557$	5.57926	+	20.8221i	0.236401	+	0.882260i	0.977512	+	0.210878i	$0.0676323\pi$
$557$	5.57926	+	20.8221i	0.236401	+	0.882260i	−0.741112	+	0.671382i	$0.765701\pi$
$558$	1.73857	−	3.01128i	0.0735993	−	0.127478i
$559$	0.324987	−	0.237219i	0.0137455	−	0.0100333i
$560$	33.1894	+	29.7155i	1.40251	+	1.25571i
$561$	−2.43834	+	9.10002i	−0.102947	+	0.384203i
$562$	0.336347			0.0141879
$563$	3.93697			0.165924			0.0829618	−	0.996553i	$-0.473562\pi$
$563$	3.93697			0.165924			0.0829618	+	0.996553i	$0.473562\pi$
$564$	−0.364201	+	1.35922i	−0.0153356	+	0.0572334i
$565$	−9.24825	−	2.47806i	−0.389077	−	0.104253i
$566$	−37.7774	+	10.1224i	−1.58790	+	0.425478i
$567$	−0.145891	−	2.64173i	−0.00612684	−	0.110942i
$568$	19.2243	−	33.2974i	0.806633	−	1.39713i
$569$			32.0081i			1.34185i	0.741526	+	0.670924i	$0.234102\pi$
$569$			32.0081i			1.34185i	−0.741526	+	0.670924i	$0.765898\pi$
$570$	24.3529	−	6.52534i	1.02003	−	0.273316i
$571$	−7.22374	+	4.17063i	−0.302304	+	0.174535i	−0.643477	−	0.765465i	$-0.722509\pi$
$571$	−7.22374	+	4.17063i	−0.302304	+	0.174535i	0.341173	+	0.940000i	$0.389176\pi$
$572$	0.348333	−	2.23128i	0.0145646	−	0.0932945i
$573$			22.9816i			0.960068i
$574$	−32.7621	−	16.5773i	−1.36746	−	0.691925i
$575$	−9.21474	−	15.9604i	−0.384281	−	0.665594i
$576$	5.52628	−	3.19060i	0.230262	−	0.132942i
$577$	24.2355	+	6.49388i	1.00894	+	0.270344i	0.725185	−	0.688554i	$-0.241754\pi$
$577$	24.2355	+	6.49388i	1.00894	+	0.270344i	0.283752	+	0.958898i	$0.408421\pi$
$578$	5.69271	+	5.69271i	0.236785	+	0.236785i
$579$	−2.01944	+	7.53664i	−0.0839250	+	0.313212i
$580$	8.43248	+	8.43248i	0.350140	+	0.350140i
$581$	−6.94855	+	33.1481i	−0.288275	+	1.37521i
$582$	16.2901	−	9.40512i	0.675248	−	0.389855i
$583$	−6.17953	+	6.17953i	−0.255930	+	0.255930i
$584$	13.4803	+	23.3485i	0.557818	+	0.966169i
$585$	−4.83118	−	12.5028i	−0.199745	−	0.516926i
$586$	−21.2349	−	12.2600i	−0.877207	−	0.506456i
$587$	20.0251	+	5.36570i	0.826524	+	0.221466i	0.647197	−	0.762323i	$-0.275941\pi$
$587$	20.0251	+	5.36570i	0.826524	+	0.221466i	0.179327	+	0.983790i	$0.442608\pi$
$588$	−1.30151	−	1.77037i	−0.0536734	−	0.0730088i
$589$	8.82593	+	5.09565i	0.363666	+	0.209963i
$590$	−9.26405	+	2.48230i	−0.381395	+	0.102194i
$591$	7.12240	−	7.12240i	0.292976	−	0.292976i
$592$	2.06525	−	2.06525i	0.0848814	−	0.0848814i
$593$	−0.209425	+	0.0561154i	−0.00860007	+	0.00230438i	−0.263117	−	0.964764i	$-0.584750\pi$
$593$	−0.209425	+	0.0561154i	−0.00860007	+	0.00230438i	0.254516	+	0.967068i	$0.418084\pi$
$594$	−2.62859	−	1.51761i	−0.107852	−	0.0622685i
$595$	34.5980	+	30.9766i	1.41838	+	1.26992i
$596$	0.803921	+	0.215410i	0.0329299	+	0.00882354i
$597$	−6.66002	−	3.84516i	−0.272576	−	0.157372i
$598$	4.13064	+	10.6898i	0.168915	+	0.437140i
$599$	0.450193	+	0.779757i	0.0183944	+	0.0318600i	0.875076	−	0.483985i	$-0.160811\pi$
$599$	0.450193	+	0.779757i	0.0183944	+	0.0318600i	−0.856682	+	0.515845i	$0.827478\pi$
$600$	15.9959	−	15.9959i	0.653029	−	0.653029i
$601$	24.7998	−	14.3182i	1.01161	−	0.584051i	0.0999444	−	0.994993i	$-0.468134\pi$
$601$	24.7998	−	14.3182i	1.01161	−	0.584051i	0.911661	+	0.410942i	$0.134800\pi$
$602$	−0.334602	−	0.299579i	−0.0136373	−	0.0122099i
$603$	2.10721	+	2.10721i	0.0858121	+	0.0858121i
$604$	0.291091	−	1.08637i	0.0118443	−	0.0442036i
$605$	−18.4496	−	18.4496i	−0.750084	−	0.750084i
$606$	4.90374	+	1.31395i	0.199201	+	0.0533758i
$607$	−20.3907	+	11.7726i	−0.827635	+	0.477835i	−0.853042	−	0.521842i	$-0.825245\pi$
$607$	−20.3907	+	11.7726i	−0.827635	+	0.477835i	0.0254072	+	0.999677i	$0.491912\pi$
$608$	−3.92358	−	6.79584i	−0.159122	−	0.275608i
$609$	14.7896	+	22.6345i	0.599305	+	0.917196i
$610$		−	38.1781i		−	1.54578i
$611$	−2.49309	+	15.9697i	−0.100860	+	0.646064i
$612$	−1.28352	+	0.741039i	−0.0518831	+	0.0299547i
$613$	−27.9408	+	7.48670i	−1.12852	+	0.302385i	−0.774325	−	0.632788i	$-0.781911\pi$
$613$	−27.9408	+	7.48670i	−1.12852	+	0.302385i	−0.354191	+	0.935173i	$0.615244\pi$
$614$		−	45.6318i		−	1.84155i
$615$	−16.9580	+	29.3720i	−0.683811	+	1.18439i
$616$	13.5196	−	0.746626i	0.544719	−	0.0300824i
$617$	−17.9700	+	4.81504i	−0.723444	+	0.193846i	−0.601708	−	0.798716i	$-0.705513\pi$
$617$	−17.9700	+	4.81504i	−0.723444	+	0.193846i	−0.121736	+	0.992563i	$0.538846\pi$
$618$	27.2640	+	7.30537i	1.09672	+	0.293865i
$619$	10.9701	−	40.9411i	0.440927	−	1.64556i	−0.285543	−	0.958366i	$-0.592174\pi$
$619$	10.9701	−	40.9411i	0.440927	−	1.64556i	0.726471	−	0.687198i	$-0.241159\pi$
$620$	−2.66744			−0.107127
$621$	2.08952			0.0838494
$622$	9.46557	−	35.3260i	0.379535	−	1.41644i
$623$	18.5333	+	3.88498i	0.742521	+	0.155648i
$624$	−13.1904	+	9.62808i	−0.528037	+	0.385432i
$625$	4.34603	−	7.52754i	0.173841	−	0.301102i
$626$	9.11846	+	34.0306i	0.364447	+	1.36013i
$627$	4.44806	−	7.70426i	0.177638	−	0.307679i
$628$	−1.56573	−	2.71192i	−0.0624793	−	0.108217i
$629$	2.15291	−	2.15291i	0.0858420	−	0.0858420i
$630$	−12.5248	+	8.18384i	−0.499001	+	0.326052i
$631$	0.481180	+	1.79579i	0.0191555	+	0.0714893i	0.974842	−	0.222897i	$-0.0715514\pi$
$631$	0.481180	+	1.79579i	0.0191555	+	0.0714893i	−0.955686	+	0.294386i	$0.904885\pi$
$632$	0.0363100	+	0.135511i	0.00144434	+	0.00539034i
$633$		−	9.49980i		−	0.377583i
$634$	−26.9479	−	15.5584i	−1.07024	−	0.617902i
$635$	48.5116	+	48.5116i	1.92512	+	1.92512i
$636$	−1.37481			−0.0545148
$637$	−17.0345	−	18.6232i	−0.674933	−	0.737879i
$638$	31.0182			1.22802
$639$	10.6001	+	10.6001i	0.419333	+	0.419333i
$640$	−42.5836	−	24.5857i	−1.68327	−	0.971834i
$641$			24.8855i			0.982916i	0.870901	+	0.491458i	$0.163536\pi$
$641$			24.8855i			0.982916i	−0.870901	+	0.491458i	$0.836464\pi$
$642$	−2.09796	−	7.82968i	−0.0827997	−	0.309013i
$643$	−2.77769	−	10.3665i	−0.109541	−	0.408814i	0.889279	−	0.457364i	$-0.151206\pi$
$643$	−2.77769	−	10.3665i	−0.109541	−	0.408814i	−0.998821	+	0.0485507i	$0.984540\pi$
$644$	1.45272	−	0.949223i	0.0572453	−	0.0374046i
$645$	−0.293343	+	0.293343i	−0.0115504	+	0.0115504i
$646$	−16.0104	−	27.7309i	−0.629922	−	1.09106i
$647$	−6.71722	+	11.6346i	−0.264081	+	0.457402i	−0.967323	−	0.253549i	$-0.918402\pi$
$647$	−6.71722	+	11.6346i	−0.264081	+	0.457402i	0.703241	+	0.710951i	$0.251735\pi$
$648$	0.663822	+	2.47742i	0.0260774	+	0.0973222i
$649$	−1.69208	+	2.93077i	−0.0664199	+	0.115043i
$650$	−30.3593	+	37.6610i	−1.19079	+	1.47718i
$651$	−5.91916	−	1.24078i	−0.231990	−	0.0486301i
$652$	−0.0944641	+	0.352545i	−0.00369950	+	0.0138067i
$653$	−21.6986			−0.849132			−0.424566	−	0.905397i	$-0.639573\pi$
$653$	−21.6986			−0.849132			−0.424566	+	0.905397i	$0.639573\pi$
$654$	−17.0123			−0.665232
$655$	6.40746	−	23.9130i	0.250360	−	0.934357i
$656$	39.9137	+	10.6948i	1.55837	+	0.417563i
$657$	−10.1535	+	2.72063i	−0.396127	+	0.106142i
$658$	18.0141	−	0.994841i	0.702264	−	0.0387829i
$659$	−6.28037	+	10.8779i	−0.244648	+	0.423744i	−0.962033	−	0.272934i	$-0.912006\pi$
$659$	−6.28037	+	10.8779i	−0.244648	+	0.423744i	0.717384	+	0.696678i	$0.245339\pi$
$660$			2.32844i			0.0906343i
$661$	−4.84489	+	1.29819i	−0.188445	+	0.0504936i	−0.351807	−	0.936073i	$-0.614433\pi$
$661$	−4.84489	+	1.29819i	−0.188445	+	0.0504936i	0.163362	+	0.986566i	$0.447766\pi$
$662$	−27.6316	+	15.9531i	−1.07393	+	0.620035i
$663$	−13.7502	+	10.0367i	−0.534012	+	0.389793i
$664$		−	32.8324i		−	1.27414i
$665$	−23.9864	−	36.7097i	−0.930154	−	1.42354i
$666$	0.490459	+	0.849500i	0.0190049	+	0.0329175i
$667$	−18.4928	+	10.6768i	−0.716042	+	0.413407i
$668$	−1.34910	−	0.361489i	−0.0521981	−	0.0139864i
$669$	12.1270	+	12.1270i	0.468856	+	0.468856i
$670$	4.36158	−	16.2776i	0.168503	−	0.628860i
$671$	−9.52560	−	9.52560i	−0.367732	−	0.367732i
$672$	3.46936	+	3.10622i	0.133833	+	0.119825i
$673$	−24.8578	+	14.3517i	−0.958198	+	0.553216i	−0.895618	−	0.444824i	$-0.853266\pi$
$673$	−24.8578	+	14.3517i	−0.958198	+	0.553216i	−0.0625799	+	0.998040i	$0.519933\pi$
$674$	32.3098	−	32.3098i	1.24453	−	1.24453i
$675$	4.40999	+	7.63832i	0.169740	+	0.293999i
$676$	3.02042	−	2.74394i	0.116170	−	0.105536i
$677$	−24.1896	−	13.9659i	−0.929683	−	0.536753i	−0.0429716	−	0.999076i	$-0.513682\pi$
$677$	−24.1896	−	13.9659i	−0.929683	−	0.536753i	−0.886711	+	0.462324i	$0.847016\pi$
$678$	−3.78424	−	1.01398i	−0.145333	−	0.0389418i
$679$	−24.3747	−	21.8234i	−0.935417	−	0.837506i
$680$	−38.9870	−	22.5091i	−1.49508	−	0.863186i
$681$	−6.00538	+	1.60914i	−0.230127	+	0.0616623i
$682$	−4.90598	+	4.90598i	−0.187859	+	0.187859i
$683$	−24.9210	+	24.9210i	−0.953575	+	0.953575i	−0.998969	−	0.0453944i	$-0.985546\pi$
$683$	−24.9210	+	24.9210i	−0.953575	+	0.953575i	0.0453944	+	0.998969i	$0.485546\pi$
$684$	1.35181	−	0.362217i	0.0516879	−	0.0138497i
$685$	51.4077	+	29.6802i	1.96419	+	1.13402i
$686$	−16.3665	+	22.9305i	−0.624874	+	0.875490i
$687$	4.68814	+	1.25618i	0.178864	+	0.0479264i
$688$	0.437720	+	0.252718i	0.0166879	+	0.00963477i
$689$	−15.7013	+	1.68546i	−0.598171	+	0.0642107i
$690$	−5.90802	−	10.2330i	−0.224914	−	0.389563i
$691$	6.36903	−	6.36903i	0.242289	−	0.242289i	−0.575507	−	0.817797i	$-0.695195\pi$
$691$	6.36903	−	6.36903i	0.242289	−	0.242289i	0.817797	+	0.575507i	$0.195195\pi$
$692$	5.33048	−	3.07756i	0.202635	−	0.116991i
$693$	−1.08309	+	5.16690i	−0.0411434	+	0.196274i
$694$	2.05443	+	2.05443i	0.0779849	+	0.0779849i
$695$	10.3615	−	38.6698i	0.393035	−	1.46683i
$696$	−18.5339	−	18.5339i	−0.702524	−	0.702524i
$697$	41.6076	+	11.1487i	1.57600	+	0.422288i
$698$	4.40002	−	2.54035i	0.166543	−	0.0961538i
$699$	−6.56573	−	11.3722i	−0.248339	−	0.430135i
$700$	6.53595	+	3.30713i	0.247036	+	0.124998i
$701$			10.4155i			0.393389i	0.980465	+	0.196695i	$0.0630207\pi$
$701$			10.4155i			0.393389i	−0.980465	+	0.196695i	$0.936979\pi$
$702$	−1.97684	−	5.11594i	−0.0746111	−	0.193089i
$703$	−2.48985	+	1.43751i	−0.0939063	+	0.0542168i
$704$	−12.2989	+	3.29547i	−0.463531	+	0.124203i
$705$		−	16.6651i		−	0.627643i
$706$	−7.58055	+	13.1299i	−0.285298	+	0.494150i
$707$	−0.486900	−	8.81657i	−0.0183118	−	0.331581i
$708$	−0.514241	+	0.137790i	−0.0193264	+	0.00517848i
$709$	−25.9362	−	6.94959i	−0.974055	−	0.260997i	−0.263516	−	0.964655i	$-0.584882\pi$
$709$	−25.9362	−	6.94959i	−0.974055	−	0.260997i	−0.710539	+	0.703658i	$0.751549\pi$
$710$	21.9405	−	81.8831i	0.823412	−	3.07302i
$711$	−0.0546985			−0.00205135
$712$	−18.3568			−0.687950
$713$	1.23621	−	4.61358i	0.0462963	−	0.172780i
$714$	14.1570	+	12.6751i	0.529811	+	0.474355i
$715$	2.85456	+	26.5923i	0.106754	+	0.994497i
$716$	−3.61970	+	6.26950i	−0.135274	+	0.234302i
$717$	−2.28256	−	8.51863i	−0.0852438	−	0.318134i
$718$	10.5285	−	18.2359i	0.392921	−	0.680559i
$719$	18.4889	+	32.0237i	0.689519	+	1.19428i	0.971993	+	0.235008i	$0.0755116\pi$
$719$	18.4889	+	32.0237i	0.689519	+	1.19428i	−0.282474	+	0.959275i	$0.591155\pi$
$720$	11.9060	−	11.9060i	0.443711	−	0.443711i
$721$	−2.70708	−	49.0187i	−0.100817	−	1.82555i
$722$	0.345482	+	1.28936i	0.0128575	+	0.0479849i
$723$	2.36670	+	8.83265i	0.0880186	+	0.328490i
$724$		−	6.44810i		−	0.239642i
$725$	−78.0590	−	45.0674i	−2.89904	−	1.67376i
$726$	−7.54929	−	7.54929i	−0.280181	−	0.280181i
$727$	32.7889			1.21607			0.608037	−	0.793909i	$-0.291957\pi$
$727$	32.7889			1.21607			0.608037	+	0.793909i	$0.291957\pi$
$728$	19.8660	+	14.2815i	0.736284	+	0.529309i
$729$	−1.00000			−0.0370370
$730$	42.0324	+	42.0324i	1.55569	+	1.55569i
$731$	0.456297	+	0.263443i	0.0168768	+	0.00974380i
$732$		−	2.11924i		−	0.0783293i
$733$	3.19209	+	11.9130i	0.117902	+	0.440018i	0.999488	−	0.0320071i	$-0.0101899\pi$
$733$	3.19209	+	11.9130i	0.117902	+	0.440018i	−0.881585	+	0.472025i	$0.843523\pi$
$734$	10.3283	+	38.5459i	0.381226	+	1.42275i
$735$	20.3151	+	16.2627i	0.749334	+	0.599858i
$736$	−2.60053	+	2.60053i	−0.0958568	+	0.0958568i
$737$	−2.97311	−	5.14958i	−0.109516	−	0.189687i
$738$	−6.93892	+	12.0186i	−0.255425	+	0.442410i
$739$	−1.22744	−	4.58088i	−0.0451522	−	0.168510i	0.939668	−	0.342088i	$-0.111134\pi$
$739$	−1.22744	−	4.58088i	−0.0451522	−	0.168510i	−0.984820	+	0.173577i	$0.944467\pi$
$740$	0.376250	−	0.651683i	0.0138312	−	0.0239564i
$741$	14.9946	−	5.79403i	0.550839	−	0.212849i
$742$	5.49405	+	16.7487i	0.201693	+	0.614863i
$743$	−6.39444	+	23.8644i	−0.234589	+	0.875499i	0.743745	+	0.668464i	$0.233048\pi$
$743$	−6.39444	+	23.8644i	−0.234589	+	0.875499i	−0.978334	+	0.207035i	$0.933619\pi$
$744$	5.86279			0.214940
$745$	−9.85670			−0.361121
$746$	5.66166	−	21.1296i	0.207288	−	0.773609i
$747$	12.3649	+	3.31317i	0.452408	+	0.121222i
$748$	2.85650	−	0.765397i	0.104444	−	0.0279857i
$749$	−11.8025	+	7.71185i	−0.431253	+	0.281785i
$750$	10.8008	−	18.7075i	0.394390	−	0.683103i
$751$		−	18.1111i		−	0.660885i	−0.943826	−	0.330443i	$-0.892802\pi$
$751$		−	18.1111i		−	0.660885i	0.943826	−	0.330443i	$-0.107198\pi$
$752$	−19.6121	+	5.25506i	−0.715181	+	0.191632i
$753$	11.6751	−	6.74060i	0.425463	−	0.245641i
$754$	43.6364	+	35.1763i	1.58915	+	1.28104i
$755$			13.3197i			0.484753i
$756$	−0.695244	+	0.454279i	−0.0252858	+	0.0165220i
$757$	−20.3244	−	35.2029i	−0.738704	−	1.27947i	−0.953079	−	0.302722i	$-0.902105\pi$
$757$	−20.3244	−	35.2029i	−0.738704	−	1.27947i	0.214375	−	0.976751i	$-0.431229\pi$
$758$	1.51349	−	0.873815i	0.0549725	−	0.0317384i
$759$	−4.02725	−	1.07910i	−0.146180	−	0.0391688i
$760$	30.0591	+	30.0591i	1.09036	+	1.09036i
$761$	6.69537	−	24.9874i	0.242707	−	0.905794i	−0.731815	−	0.681503i	$-0.761327\pi$
$761$	6.69537	−	24.9874i	0.242707	−	0.905794i	0.974522	−	0.224291i	$-0.0720067\pi$
$762$	19.8502	+	19.8502i	0.719096	+	0.719096i
$763$	9.22272	+	28.1156i	0.333885	+	1.01785i
$764$	6.24743	−	3.60696i	0.226024	−	0.130495i
$765$	12.4113	−	12.4113i	0.448732	−	0.448732i
$766$	15.7039	+	27.1999i	0.567404	+	0.982773i
$767$	−5.70406	+	2.20410i	−0.205962	+	0.0795854i
$768$	−6.37199	−	3.67887i	−0.229929	−	0.132750i
$769$	3.03465	+	0.813131i	0.109432	+	0.0293223i	0.313120	−	0.949714i	$-0.398626\pi$
$769$	3.03465	+	0.813131i	0.109432	+	0.0293223i	−0.203687	+	0.979036i	$0.565293\pi$
$770$	28.3663	−	9.30495i	1.02225	−	0.335327i
$771$	−8.53085	−	4.92529i	−0.307231	−	0.177380i
$772$	2.36575	−	0.633902i	0.0851454	−	0.0228146i
$773$	30.1200	−	30.1200i	1.08334	−	1.08334i	0.0871474	−	0.996195i	$-0.472225\pi$
$773$	30.1200	−	30.1200i	1.08334	−	1.08334i	0.996195	−	0.0871474i	$-0.0277751\pi$
$774$	−0.120031	+	0.120031i	−0.00431444	+	0.00431444i
$775$	19.4742	−	5.21810i	0.699534	−	0.187440i
$776$	27.4668	+	15.8580i	0.986001	+	0.569268i
$777$	1.13805	−	1.27110i	0.0408273	−	0.0456004i
$778$	43.5273	+	11.6631i	1.56053	+	0.418142i
$779$	−35.2259	−	20.3377i	−1.26210	−	0.728672i
$780$	−2.64057	+	3.27565i	−0.0945476	+	0.117287i
$781$	−14.9559	−	25.9044i	−0.535166	−	0.926934i
$782$	−10.6116	+	10.6116i	−0.379472	+	0.379472i
$783$	8.85026	−	5.10970i	0.316282	−	0.182606i
$784$	12.7326	−	29.0358i	0.454735	−	1.03699i
$785$	26.2236	+	26.2236i	0.935962	+	0.935962i
$786$	2.62183	−	9.78480i	0.0935176	−	0.349012i
$787$	13.8798	+	13.8798i	0.494763	+	0.494763i	0.909803	−	0.415040i	$-0.136232\pi$
$787$	13.8798	+	13.8798i	0.494763	+	0.494763i	−0.415040	+	0.909803i	$0.636232\pi$
$788$	−3.05406	−	0.818332i	−0.108796	−	0.0291519i
$789$	−8.69321	+	5.01903i	−0.309486	+	0.178682i
$790$	0.154657	+	0.267875i	0.00550247	+	0.00953055i
$791$	0.375743	+	6.80378i	0.0133599	+	0.241915i
$792$		−	5.11770i		−	0.181850i
$793$	−2.59809	−	24.2031i	−0.0922608	−	0.859479i
$794$	−24.8654	+	14.3560i	−0.882440	+	0.509477i
$795$	15.7271	−	4.21406i	0.557783	−	0.149457i
$796$			2.41400i			0.0855618i
$797$	5.96514	−	10.3319i	0.211296	−	0.365976i	−0.740824	−	0.671699i	$-0.765565\pi$
$797$	5.96514	−	10.3319i	0.211296	−	0.365976i	0.952120	+	0.305723i	$0.0988982\pi$
$798$	−9.81487	−	15.0210i	−0.347443	−	0.531738i
$799$	−20.4445	+	5.47809i	−0.723275	+	0.193801i
$800$	−14.9949	−	4.01786i	−0.530148	−	0.142053i
$801$	1.85241	−	6.91330i	0.0654518	−	0.244269i
$802$	−13.7514			−0.485578
$803$	20.9745			0.740175
$804$	0.242108	−	0.903561i	0.00853851	−	0.0318661i
$805$	−13.7088	+	15.3115i	−0.483173	+	0.539659i
$806$	−12.4654	+	1.33810i	−0.439074	+	0.0471324i
$807$	15.1263	−	26.1996i	0.532472	−	0.922268i
$808$	2.21546	+	8.26820i	0.0779395	+	0.290874i
$809$	2.44784	−	4.23978i	0.0860614	−	0.149063i	−0.819782	−	0.572676i	$-0.805905\pi$
$809$	2.44784	−	4.23978i	0.0860614	−	0.149063i	0.905843	+	0.423614i	$0.139239\pi$
$810$	2.82746	+	4.89730i	0.0993467	+	0.172074i
$811$	−18.6293	+	18.6293i	−0.654164	+	0.654164i	−0.953993	−	0.299829i	$-0.903070\pi$
$811$	−18.6293	+	18.6293i	−0.654164	+	0.654164i	0.299829	+	0.953993i	$0.403070\pi$
$812$	3.83186	−	7.57297i	0.134472	−	0.265759i
$813$	−4.53326	−	16.9184i	−0.158988	−	0.593353i
$814$	−0.506581	−	1.89058i	−0.0177556	−	0.0662649i
$815$		−	4.32247i		−	0.151410i
$816$	−18.5199	−	10.6925i	−0.648325	−	0.374311i
$817$	−0.351806	−	0.351806i	−0.0123082	−	0.0123082i
$818$	−13.1607			−0.460152
$819$	−7.38324	+	6.04051i	−0.257991	+	0.211073i
$820$	10.6462			0.371782
$821$	−8.58396	−	8.58396i	−0.299582	−	0.299582i	0.541268	−	0.840850i	$-0.317945\pi$
$821$	−8.58396	−	8.58396i	−0.299582	−	0.299582i	−0.840850	+	0.541268i	$0.817945\pi$
$822$	21.0352	+	12.1447i	0.733687	+	0.423594i
$823$			15.7963i			0.550623i	0.961355	+	0.275312i	$0.0887810\pi$
$823$			15.7963i			0.550623i	−0.961355	+	0.275312i	$0.911219\pi$
$824$	12.3176	+	45.9698i	0.429103	+	1.60144i
$825$	−4.55494	−	16.9993i	−0.158583	−	0.591839i
$826$	3.73366	+	5.71412i	0.129911	+	0.198820i
$827$	25.0121	−	25.0121i	0.869756	−	0.869756i	−0.122689	−	0.992445i	$-0.539152\pi$
$827$	25.0121	−	25.0121i	0.869756	−	0.869756i	0.992445	+	0.122689i	$0.0391518\pi$
$828$	−0.327950	−	0.568026i	−0.0113970	−	0.0197403i
$829$	6.10233	−	10.5695i	0.211943	−	0.367095i	−0.740380	−	0.672189i	$-0.765354\pi$
$829$	6.10233	−	10.5695i	0.211943	−	0.367095i	0.952322	+	0.305093i	$0.0986877\pi$
$830$	−18.7357	−	69.9225i	−0.650325	−	2.42704i
$831$	8.91911	−	15.4484i	0.309401	−	0.535897i
$832$	−21.0393	−	9.31149i	−0.729406	−	0.322818i
$833$	13.2730	−	30.2682i	0.459881	−	1.04873i
$834$	4.23978	−	15.8231i	0.146811	−	0.547908i
$835$	16.5410			0.572424
$836$	−2.79249			−0.0965804
$837$	−0.591623	+	2.20797i	−0.0204495	+	0.0763185i
$838$	6.75332	+	1.80955i	0.233289	+	0.0625097i
$839$	31.9263	−	8.55462i	1.10222	−	0.295338i	0.338550	−	0.940948i	$-0.390064\pi$
$839$	31.9263	−	8.55462i	1.10222	−	0.295338i	0.763667	+	0.645610i	$0.223397\pi$
$840$	−22.5091	−	11.3894i	−0.776639	−	0.392972i
$841$	−37.7180	+	65.3295i	−1.30062	+	2.25274i
$842$			34.8938i			1.20252i
$843$	−0.213579	+	0.0572284i	−0.00735606	+	0.00197105i
$844$	−2.58248	+	1.49100i	−0.0888926	+	0.0513222i
$845$	−26.1413	+	40.6473i	−0.899289	+	1.39831i
$846$		−	6.81908i		−	0.234445i
$847$	−8.38381	+	16.5691i	−0.288071	+	0.569320i
$848$	−9.91858	−	17.1795i	−0.340605	−	0.589946i
$849$	22.2662	−	12.8554i	0.764176	−	0.441197i
$850$	−61.1875	−	16.3951i	−2.09871	−	0.562349i
$851$	0.952777	+	0.952777i	0.0326608	+	0.0326608i
$852$	1.21790	−	4.54527i	0.0417246	−	0.155718i
$853$	34.9288	+	34.9288i	1.19594	+	1.19594i	0.975372	+	0.220568i	$0.0707909\pi$
$853$	34.9288	+	34.9288i	1.19594	+	1.19594i	0.220568	+	0.975372i	$0.429209\pi$
$854$	−25.8177	+	8.46894i	−0.883463	+	0.289801i
$855$	−14.3537	+	8.28714i	−0.490888	+	0.283414i
$856$	9.66425	−	9.66425i	0.330317	−	0.330317i
$857$	15.4917	+	26.8324i	0.529186	+	0.916577i	0.999421	+	0.0340353i	$0.0108358\pi$
$857$	15.4917	+	26.8324i	0.529186	+	0.916577i	−0.470235	+	0.882541i	$0.655831\pi$
$858$	1.16804	+	10.8812i	0.0398762	+	0.371477i
$859$	3.82146	+	2.20632i	0.130387	+	0.0752788i	0.563775	−	0.825929i	$-0.309349\pi$
$859$	3.82146	+	2.20632i	0.130387	+	0.0752788i	−0.433388	+	0.901207i	$0.642682\pi$
$860$	0.125784	+	0.0337038i	0.00428921	+	0.00114929i
$861$	23.6244	+	4.95219i	0.805117	+	0.168770i
$862$	15.2830	+	8.82364i	0.520541	+	0.300534i
$863$	12.2961	−	3.29472i	0.418563	−	0.112154i	−0.0433897	−	0.999058i	$-0.513816\pi$
$863$	12.2961	−	3.29472i	0.418563	−	0.112154i	0.461953	+	0.886905i	$0.347149\pi$
$864$	1.24456	−	1.24456i	0.0423408	−	0.0423408i
$865$	−51.5446	+	51.5446i	−1.75257	+	1.75257i
$866$	0.457122	−	0.122486i	0.0155337	−	0.00416223i
$867$	−4.58345	−	2.64625i	−0.155662	−	0.0898715i
$868$	0.591711	+	1.80384i	0.0200840	+	0.0612262i
$869$	0.105424	+	0.0282482i	0.00357625	+	0.000958254i
$870$	−50.0474	−	28.8949i	−1.69677	−	0.979629i
$871$	1.65732	−	10.6161i	0.0561561	−	0.359713i
$872$	−14.3422	−	24.8414i	−0.485688	−	0.841236i
$873$	−8.74394	+	8.74394i	−0.295937	+	0.295937i
$874$	12.2724	−	7.08548i	0.415120	−	0.239670i
$875$	−36.7726	−	7.70834i	−1.24314	−	0.260590i
$876$	2.33319	+	2.33319i	0.0788311	+	0.0788311i
$877$	−6.59731	+	24.6215i	−0.222775	+	0.831409i	0.760508	+	0.649328i	$0.224950\pi$
$877$	−6.59731	+	24.6215i	−0.222775	+	0.831409i	−0.983284	+	0.182080i	$0.941717\pi$
$878$	22.1308	+	22.1308i	0.746879	+	0.746879i
$879$	15.5701	+	4.17200i	0.525167	+	0.140718i
$880$	−29.0959	+	16.7985i	−0.980822	+	0.566278i
$881$	−11.9538	−	20.7046i	−0.402735	−	0.697557i	0.591320	−	0.806437i	$-0.298607\pi$
$881$	−11.9538	−	20.7046i	−0.402735	−	0.697557i	−0.994055	+	0.108880i	$0.965274\pi$
$882$	8.31262	+	6.65443i	0.279900	+	0.224066i
$883$		−	43.3376i		−	1.45843i	−0.684287	−	0.729213i	$-0.739887\pi$
$883$		−	43.3376i		−	1.45843i	0.684287	−	0.729213i	$-0.260113\pi$
$884$	4.88653	+	2.16266i	0.164352	+	0.0727381i
$885$	5.46029	−	3.15250i	0.183546	−	0.105970i
$886$	40.1006	−	10.7449i	1.34721	−	0.360983i
$887$		−	25.9504i		−	0.871330i	−0.900109	−	0.435665i	$-0.856513\pi$
$887$		−	25.9504i		−	0.871330i	0.900109	−	0.435665i	$-0.143487\pi$
$888$	−0.826963	+	1.43234i	−0.0277511	+	0.0480663i
$889$	22.0445	−	43.5669i	0.739348	−	1.46119i
$890$	−39.0941	+	10.4752i	−1.31044	+	0.351131i
$891$	1.92736	+	0.516435i	0.0645690	+	0.0173012i
$892$	1.39333	−	5.20000i	0.0466523	−	0.174109i
$893$	19.9864			0.668819
$894$	−4.03320			−0.134891
$895$	22.1902	−	82.8148i	0.741735	−	2.76819i
$896$	−7.17969	+	34.2507i	−0.239857	+	1.14424i
$897$	−4.44179	−	6.08519i	−0.148307	−	0.203179i
$898$	5.85394	−	10.1393i	0.195349	−	0.338354i
$899$	−6.04603	−	22.5641i	−0.201646	−	0.752554i
$900$	1.38430	−	2.39767i	0.0461432	−	0.0799224i
$901$	−10.3395	−	17.9086i	−0.344460	−	0.596622i
$902$	19.5806	−	19.5806i	0.651963	−	0.651963i
$903$	0.263443	+	0.133300i	0.00876684	+	0.00443595i
$904$	−1.70968	−	6.38060i	−0.0568630	−	0.212216i
$905$	19.7647	+	73.7628i	0.657000	+	2.45196i
$906$			5.45021i			0.181071i
$907$	−8.29449	−	4.78882i	−0.275414	−	0.159010i	0.355931	−	0.934512i	$-0.384164\pi$
$907$	−8.29449	−	4.78882i	−0.275414	−	0.159010i	−0.631345	+	0.775502i	$0.717497\pi$
$908$	1.37998	+	1.37998i	0.0457963	+	0.0457963i
$909$	−3.33743			−0.110695
$910$	50.4580	+	19.0786i	1.67267	+	0.632450i
$911$	21.2966			0.705588			0.352794	−	0.935701i	$-0.385232\pi$
$911$	21.2966			0.705588			0.352794	+	0.935701i	$0.385232\pi$
$912$	14.2789	+	14.2789i	0.472821	+	0.472821i
$913$	−22.1206	−	12.7713i	−0.732085	−	0.422670i
$914$			35.8058i			1.18435i
$915$	6.49588	+	24.2429i	0.214747	+	0.801447i
$916$	−0.394317	−	1.47161i	−0.0130286	−	0.0486234i
$917$	−17.5923	+	0.971548i	−0.580950	+	0.0320833i
$918$	5.07852	−	5.07852i	0.167616	−	0.167616i
$919$	−3.06997	−	5.31734i	−0.101269	−	0.175403i	0.810939	−	0.585131i	$-0.198957\pi$
$919$	−3.06997	−	5.31734i	−0.101269	−	0.175403i	−0.912208	+	0.409728i	$0.865624\pi$
$920$	9.96150	−	17.2538i	0.328421	−	0.568842i
$921$	7.76411	+	28.9760i	0.255836	+	0.954793i
$922$	25.2517	−	43.7373i	0.831621	−	1.44041i
$923$	8.33698	−	53.4032i	0.274415	−	1.75779i
$924$	1.57459	−	0.516511i	0.0518003	−	0.0169920i
$925$	−1.47206	+	5.49379i	−0.0484009	+	0.180635i
$926$	−10.0382			−0.329875
$927$	−18.5555			−0.609444
$928$	−4.65535	+	17.3740i	−0.152819	+	0.570330i
$929$	25.1167	+	6.73001i	0.824053	+	0.220804i	0.646118	−	0.763238i	$-0.276391\pi$
$929$	25.1167	+	6.73001i	0.824053	+	0.220804i	0.177936	+	0.984042i	$0.443058\pi$
$930$	12.4859	−	3.34558i	0.409427	−	0.109706i
$931$	−19.5038	+	24.3639i	−0.639212	+	0.798494i
$932$	−2.06098	+	3.56973i	−0.0675098	+	0.116930i
$933$			24.0424i			0.787114i
$934$	−21.0466	+	5.63943i	−0.688667	+	0.184528i
$935$	−30.3307	+	17.5115i	−0.991921	+	0.572686i
$936$	5.80374	−	7.19958i	0.189701	−	0.235326i
$937$			13.4306i			0.438759i	0.975640	+	0.219380i	$0.0704033\pi$
$937$			13.4306i			0.438759i	−0.975640	+	0.219380i	$0.929597\pi$
$938$	−11.9752	+	0.661336i	−0.391003	+	0.0215934i
$939$	−11.5804	−	20.0578i	−0.377912	−	0.654562i
$940$	−4.53032	+	2.61558i	−0.147763	+	0.0853109i
$941$	−36.6324	−	9.81563i	−1.19418	−	0.319981i	−0.393645	−	0.919262i	$-0.628786\pi$
$941$	−36.6324	−	9.81563i	−1.19418	−	0.319981i	−0.800538	+	0.599282i	$0.795453\pi$
$942$	10.7303	+	10.7303i	0.349612	+	0.349612i
$943$	−4.93392	+	18.4136i	−0.160670	+	0.599630i
$944$	−5.43181	−	5.43181i	−0.176790	−	0.176790i
$945$	6.56076	−	7.32777i	0.213422	−	0.238372i
$946$	0.293332	−	0.169356i	0.00953706	−	0.00550622i
$947$	−4.33229	+	4.33229i	−0.140780	+	0.140780i	−0.773985	−	0.633204i	$-0.781739\pi$
$947$	−4.33229	+	4.33229i	−0.140780	+	0.140780i	0.633204	+	0.773985i	$0.281739\pi$
$948$	0.00858493	+	0.0148695i	0.000278826	+	0.000482940i
$949$	29.5070	+	23.7862i	0.957837	+	0.772133i
$950$	51.8026	+	29.9082i	1.68070	+	0.970351i
$951$	19.7590	+	5.29442i	0.640731	+	0.171683i
$952$	−6.57328	+	31.3578i	−0.213041	+	1.01631i
$953$	16.2411	+	9.37683i	0.526102	+	0.303745i	0.739428	−	0.673236i	$-0.235096\pi$
$953$	16.2411	+	9.37683i	0.526102	+	0.303745i	−0.213326	+	0.976981i	$0.568430\pi$
$954$	6.43528	−	1.72433i	0.208350	−	0.0558272i
$955$	−60.4113	+	60.4113i	−1.95486	+	1.95486i
$956$	−1.95750	+	1.95750i	−0.0633102	+	0.0633102i
$957$	−19.6965	+	5.27765i	−0.636696	+	0.170602i
$958$	19.4994	+	11.2580i	0.629995	+	0.363728i
$959$	8.66744	−	41.3480i	0.279886	−	1.33520i
$960$	22.9139	+	6.13977i	0.739544	+	0.198160i
$961$	−22.3217	−	12.8874i	−0.720054	−	0.415724i
$962$	1.43136	−	3.23416i	0.0461490	−	0.104274i
$963$	2.66439	+	4.61486i	0.0858588	+	0.148712i
$964$	2.02966	−	2.02966i	0.0653710	−	0.0653710i
$965$	−25.1199	+	14.5030i	−0.808639	+	0.466868i
$966$	−5.60943	+	6.26522i	−0.180481	+	0.201580i
$967$	−37.6662	−	37.6662i	−1.21126	−	1.21126i	−0.970611	−	0.240652i	$-0.922639\pi$
$967$	−37.6662	−	37.6662i	−1.21126	−	1.21126i	−0.240652	−	0.970611i	$-0.577361\pi$
$968$	4.65909	−	17.3879i	0.149749	−	0.558870i
$969$	14.8849	+	14.8849i	0.478172	+	0.478172i
$970$	67.5448	+	18.0986i	2.16873	+	0.581110i
$971$	22.7279	−	13.1220i	0.729373	−	0.421104i	−0.0888197	−	0.996048i	$-0.528309\pi$
$971$	22.7279	−	13.1220i	0.729373	−	0.421104i	0.818193	+	0.574944i	$0.194976\pi$
$972$	0.156950	+	0.271846i	0.00503418	+	0.00871945i
$973$	−28.4487	+	1.57110i	−0.912023	+	0.0503670i
$974$		−	50.4340i		−	1.61601i
$975$	12.8702	−	29.0801i	0.412175	−	0.931309i
$976$	26.4817	−	15.2892i	0.847660	−	0.489397i
$977$	0.0867753	−	0.0232514i	0.00277619	−	0.000743877i	−0.257431	−	0.966297i	$-0.582876\pi$
$977$	0.0867753	−	0.0232514i	0.00277619	−	0.000743877i	0.260207	+	0.965553i	$0.416209\pi$
$978$		−	1.76869i		−	0.0565564i
$979$	−7.14054	+	12.3678i	−0.228213	+	0.395276i
$980$	1.23248	−	8.07500i	0.0393702	−	0.257947i
$981$	10.8027	−	2.89458i	0.344905	−	0.0924169i
$982$	−29.1192	−	7.80248i	−0.929232	−	0.248987i
$983$	5.38419	−	20.0941i	0.171729	−	0.640902i	−0.825357	−	0.564612i	$-0.809026\pi$
$983$	5.38419	−	20.0941i	0.171729	−	0.640902i	0.997086	−	0.0762899i	$-0.0243075\pi$
$984$	−23.3994			−0.745947
$985$	37.4451			1.19310
$986$	−18.9965	+	70.8958i	−0.604971	+	2.25778i
$987$	−11.2696	+	3.69677i	−0.358717	+	0.117669i
$988$	−3.92848	−	3.16683i	−0.124982	−	0.100750i
$989$	−0.116588	+	0.201936i	−0.00370728	+	0.00642120i
$990$	−2.92039	−	10.8991i	−0.0928162	−	0.346395i
$991$	−10.2654	+	17.7802i	−0.326090	+	0.564805i	−0.981732	−	0.190267i	$-0.939065\pi$
$991$	−10.2654	+	17.7802i	−0.326090	+	0.564805i	0.655642	+	0.755072i	$0.272398\pi$
$992$	−2.01164	−	3.48426i	−0.0638696	−	0.110625i
$993$	14.8316	−	14.8316i	0.470666	−	0.470666i
$994$	−60.2399	+	3.32679i	−1.91069	+	0.105519i
$995$	−7.39937	−	27.6148i	−0.234576	−	0.875449i
$996$	−1.04000	−	3.88135i	−0.0329538	−	0.122985i
$997$		−	56.8807i		−	1.80143i	−0.434412	−	0.900714i	$-0.643044\pi$
$997$		−	56.8807i		−	1.80143i	0.434412	−	0.900714i	$-0.356956\pi$
$998$	30.5784	+	17.6545i	0.967943	+	0.558842i
$999$	−0.455980	−	0.455980i	−0.0144266	−	0.0144266i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.bt.b.271.7	yes	40
3.2	odd	2		819.2.et.d.271.4		40
7.3	odd	6		273.2.cg.b.115.4	yes	40
13.6	odd	12		273.2.cg.b.19.4	yes	40
21.17	even	6		819.2.gh.d.388.7		40
39.32	even	12		819.2.gh.d.19.7		40
91.45	even	12	inner	273.2.bt.b.136.7	✓	40
273.227	odd	12		819.2.et.d.136.4		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bt.b.136.7	✓	40	91.45	even	12	inner
273.2.bt.b.271.7	yes	40	1.1	even	1	trivial
273.2.cg.b.19.4	yes	40	13.6	odd	12
273.2.cg.b.115.4	yes	40	7.3	odd	6
819.2.et.d.136.4		40	273.227	odd	12
819.2.et.d.271.4		40	3.2	odd	2
819.2.gh.d.19.7		40	39.32	even	12
819.2.gh.d.388.7		40	21.17	even	6

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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.bt (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.07562 + 1.07562i) q^{2} +(-0.866025 - 0.500000i) q^{3} +0.313900i q^{4} +(-0.962166 - 3.59085i) q^{5} +(-0.393703 - 1.46932i) q^{6} +(-2.21486 + 1.44721i) q^{7} +(1.81360 - 1.81360i) q^{8} +(0.500000 + 0.866025i) q^{9} +(2.82746 - 4.89730i) q^{10} +(-0.516435 - 1.92736i) q^{11} +(0.156950 - 0.271846i) q^{12} +(1.45921 - 3.29708i) q^{13} +(-3.93898 - 0.825695i) q^{14} +(-0.962166 + 3.59085i) q^{15} +4.52927 q^{16} +4.72149 q^{17} +(-0.393703 + 1.46932i) q^{18} +(-4.30650 - 1.15392i) q^{19} +(1.12717 - 0.302024i) q^{20} +(2.64173 - 0.145891i) q^{21} +(1.51761 - 2.62859i) q^{22} +2.08952i q^{23} +(-2.47742 + 0.663822i) q^{24} +(-7.63832 + 4.40999i) q^{25} +(5.11594 - 1.97684i) q^{26} -1.00000i q^{27} +(-0.454279 - 0.695244i) q^{28} +(5.10970 + 8.85026i) q^{29} +(-4.89730 + 2.82746i) q^{30} +(-2.20797 - 0.591623i) q^{31} +(1.24456 + 1.24456i) q^{32} +(-0.516435 + 1.92736i) q^{33} +(5.07852 + 5.07852i) q^{34} +(7.32777 + 6.56076i) q^{35} +(-0.271846 + 0.156950i) q^{36} +(0.455980 - 0.455980i) q^{37} +(-3.39097 - 5.87333i) q^{38} +(-2.91225 + 2.12575i) q^{39} +(-8.25733 - 4.76737i) q^{40} +(8.81239 + 2.36127i) q^{41} +(2.99841 + 2.68456i) q^{42} +(0.0966425 + 0.0557966i) q^{43} +(0.604999 - 0.162109i) q^{44} +(2.62869 - 2.62869i) q^{45} +(-2.24752 + 2.24752i) q^{46} +(-4.33009 + 1.16024i) q^{47} +(-3.92246 - 2.26463i) q^{48} +(2.81118 - 6.41072i) q^{49} +(-12.9594 - 3.47245i) q^{50} +(-4.08893 - 2.36075i) q^{51} +(1.03495 + 0.458046i) q^{52} +(-2.18989 - 3.79299i) q^{53} +(1.07562 - 1.07562i) q^{54} +(-6.42397 + 3.70888i) q^{55} +(-1.39220 + 6.64151i) q^{56} +(3.15258 + 3.15258i) q^{57} +(-4.02340 + 15.0156i) q^{58} +(-1.19927 - 1.19927i) q^{59} +(-1.12717 - 0.302024i) q^{60} +(5.84680 - 3.37565i) q^{61} +(-1.73857 - 3.01128i) q^{62} +(-2.36075 - 1.19452i) q^{63} -6.38120i q^{64} +(-13.2433 - 2.06746i) q^{65} +(-2.62859 + 1.51761i) q^{66} +(2.87850 - 0.771291i) q^{67} +1.48208i q^{68} +(1.04476 - 1.80957i) q^{69} +(0.825000 + 14.9387i) q^{70} +(14.4800 - 3.87990i) q^{71} +(2.47742 + 0.663822i) q^{72} +(-2.72063 + 10.1535i) q^{73} +0.980919 q^{74} +8.81997 q^{75} +(0.362217 - 1.35181i) q^{76} +(3.93312 + 3.52144i) q^{77} +(-5.41895 - 0.845973i) q^{78} +(-0.0273492 + 0.0473702i) q^{79} +(-4.35791 - 16.2639i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(6.93892 + 12.0186i) q^{82} +(9.05174 - 9.05174i) q^{83} +(0.0457952 + 0.829238i) q^{84} +(-4.54286 - 16.9542i) q^{85} +(0.0439346 + 0.163966i) q^{86} -10.2194i q^{87} +(-4.43206 - 2.55885i) q^{88} +(-5.06089 - 5.06089i) q^{89} +5.65491 q^{90} +(1.53962 + 9.41433i) q^{91} -0.655900 q^{92} +(1.61634 + 1.61634i) q^{93} +(-5.90549 - 3.40954i) q^{94} +16.5743i q^{95} +(-0.455541 - 1.70010i) q^{96} +(3.20050 + 11.9444i) q^{97} +(9.91922 - 3.87172i) q^{98} +(1.41093 - 1.41093i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 2 q^{7} + 20 q^{9} - 8 q^{11} + 24 q^{12} - 18 q^{14} - 64 q^{16} + 8 q^{17} - 14 q^{19} - 14 q^{20} - 8 q^{21} + 4 q^{22} + 18 q^{24} - 24 q^{25} - 10 q^{26} - 2 q^{28} + 8 q^{29} - 8 q^{31} + 10 q^{32}+ \cdots - 4 q^{99}+O(q^{100}) \) 40 * q - 2 * q^7 + 20 * q^9 - 8 * q^11 + 24 * q^12 - 18 * q^14 - 64 * q^16 + 8 * q^17 - 14 * q^19 - 14 * q^20 - 8 * q^21 + 4 * q^22 + 18 * q^24 - 24 * q^25 - 10 * q^26 - 2 * q^28 + 8 * q^29 - 8 * q^31 + 10 * q^32 - 8 * q^33 + 24 * q^34 - 22 * q^35 + 12 * q^37 + 8 * q^38 - 24 * q^39 - 30 * q^40 + 2 * q^41 + 6 * q^42 - 66 * q^43 + 28 * q^44 + 40 * q^46 + 10 * q^47 - 24 * q^48 + 38 * q^49 - 20 * q^50 + 40 * q^52 - 8 * q^53 + 42 * q^55 + 20 * q^56 - 14 * q^57 - 48 * q^58 - 26 * q^59 + 14 * q^60 - 12 * q^61 - 24 * q^62 - 4 * q^63 - 44 * q^65 - 18 * q^66 + 46 * q^67 - 4 * q^69 + 32 * q^70 - 6 * q^71 - 18 * q^72 + 10 * q^73 + 40 * q^74 + 48 * q^75 + 64 * q^76 - 24 * q^77 + 8 * q^78 + 34 * q^80 - 20 * q^81 + 24 * q^82 + 12 * q^83 + 20 * q^84 + 2 * q^85 + 12 * q^86 - 84 * q^88 - 16 * q^89 + 26 * q^91 + 236 * q^92 + 22 * q^93 + 30 * q^94 + 26 * q^96 + 62 * q^97 - 14 * q^98 - 4 * q^99

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