LMFDB - Embedded newform 224.2.be.a.115.17

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [224,2,Mod(3,224)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(224, base_ring=CyclotomicField(24)) chi = DirichletCharacter(H, H._module([12, 9, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("224.3"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$N$	$=$	$224 = 2^{5} \cdot 7$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	224.be (of order $24$ , degree $8$ , 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:	$1.78864900528$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			115.17
Character	$\chi$	$=$	224.115
Dual form			224.2.be.a.187.17

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.286901 + 1.38481i) q^{2} +(-0.360299 - 0.469551i) q^{3} +(-1.83538 + 0.794605i) q^{4} +(2.24363 - 2.92396i) q^{5} +(0.546866 - 0.633659i) q^{6} +(2.53705 + 0.750581i) q^{7} +(-1.62695 - 2.31367i) q^{8} +(0.685795 - 2.55942i) q^{9} +(4.69281 + 2.26811i) q^{10} +(0.0254955 - 0.193658i) q^{11} +(1.03439 + 0.575506i) q^{12} +(-1.79545 + 4.33461i) q^{13} +(-0.311526 + 3.72867i) q^{14} -2.18132 q^{15} +(2.73720 - 2.91680i) q^{16} +(1.63000 - 2.82324i) q^{17} +(3.74106 + 0.215391i) q^{18} +(0.981731 + 7.45699i) q^{19} +(-1.79451 + 7.14936i) q^{20} +(-0.561661 - 1.46171i) q^{21} +(0.275493 - 0.0202543i) q^{22} +(-0.849490 - 0.227620i) q^{23} +(-0.500196 + 1.59754i) q^{24} +(-2.22155 - 8.29094i) q^{25} +(-6.51771 - 1.24275i) q^{26} +(-3.08928 + 1.27962i) q^{27} +(-5.25286 + 0.638357i) q^{28} +(-0.793041 + 1.91457i) q^{29} +(-0.625825 - 3.02071i) q^{30} +(1.85113 - 3.20626i) q^{31} +(4.82451 + 2.95366i) q^{32} +(-0.100118 + 0.0578032i) q^{33} +(4.37729 + 1.44724i) q^{34} +(7.88688 - 5.73420i) q^{35} +(0.775039 + 5.24243i) q^{36} +(-8.19504 - 6.28828i) q^{37} +(-10.0448 + 3.49893i) q^{38} +(2.68222 - 0.718698i) q^{39} +(-10.4153 - 0.433891i) q^{40} +(-3.81582 + 3.81582i) q^{41} +(1.86304 - 1.19716i) q^{42} +(-2.28159 + 0.945065i) q^{43} +(0.107088 + 0.375693i) q^{44} +(-5.94497 - 7.74763i) q^{45} +(0.0714899 - 1.24168i) q^{46} +(-1.58163 + 0.913157i) q^{47} +(-2.35580 - 0.234337i) q^{48} +(5.87326 + 3.80853i) q^{49} +(10.8440 - 5.45510i) q^{50} +(-1.91294 + 0.251843i) q^{51} +(-0.148972 - 9.38231i) q^{52} +(8.93961 + 1.17692i) q^{53} +(-2.65834 - 3.91093i) q^{54} +(-0.509044 - 0.509044i) q^{55} +(-2.39105 - 7.09104i) q^{56} +(3.14772 - 3.14772i) q^{57} +(-2.87883 - 0.548915i) q^{58} +(-1.11273 + 8.45206i) q^{59} +(4.00355 - 1.73329i) q^{60} +(-0.828697 - 6.29458i) q^{61} +(4.97114 + 1.64358i) q^{62} +(3.66095 - 5.97864i) q^{63} +(-2.70609 + 7.52842i) q^{64} +(8.64588 + 14.9751i) q^{65} +(-0.108770 - 0.122060i) q^{66} +(-9.50532 + 7.29369i) q^{67} +(-0.748297 + 6.47691i) q^{68} +(0.199191 + 0.480890i) q^{69} +(10.2035 + 9.27664i) q^{70} +(-4.95899 - 4.95899i) q^{71} +(-7.03739 + 2.57734i) q^{72} +(2.03722 + 7.60300i) q^{73} +(6.35688 - 13.1527i) q^{74} +(-3.09259 + 4.03035i) q^{75} +(-7.72721 - 12.9063i) q^{76} +(0.210039 - 0.472183i) q^{77} +(1.76479 + 3.50816i) q^{78} +(2.39290 + 4.14462i) q^{79} +(-2.38732 - 14.5477i) q^{80} +(-5.17023 - 2.98503i) q^{81} +(-6.37893 - 4.18940i) q^{82} +(-5.02518 - 2.08150i) q^{83} +(2.19234 + 2.23648i) q^{84} +(-4.59792 - 11.1004i) q^{85} +(-1.96332 - 2.88842i) q^{86} +(1.18472 - 0.317445i) q^{87} +(-0.489538 + 0.256082i) q^{88} +(0.0259571 - 0.0968732i) q^{89} +(9.02335 - 10.4554i) q^{90} +(-7.80863 + 9.64949i) q^{91} +(1.74000 - 0.257241i) q^{92} +(-2.17246 + 0.286010i) q^{93} +(-1.71832 - 1.92827i) q^{94} +(24.0066 + 13.8602i) q^{95} +(-0.351370 - 3.32955i) q^{96} +9.39885i q^{97} +(-3.58902 + 9.22599i) q^{98} +(-0.478166 - 0.198063i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$240 q - 4 q^{2} - 12 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{7} - 16 q^{8} - 4 q^{9} - 12 q^{10} - 4 q^{11} - 12 q^{12} - 40 q^{14} - 32 q^{15} - 24 q^{16} + 16 q^{18} - 12 q^{19} - 8 q^{21} - 8 q^{22} + 4 q^{23}+ \cdots - 40 q^{99}+O(q^{100})$ 240 * q - 4 * q^2 - 12 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^7 - 16 * q^8 - 4 * q^9 - 12 * q^10 - 4 * q^11 - 12 * q^12 - 40 * q^14 - 32 * q^15 - 24 * q^16 + 16 * q^18 - 12 * q^19 - 8 * q^21 - 8 * q^22 + 4 * q^23 - 12 * q^24 - 4 * q^25 - 12 * q^26 + 12 * q^28 - 16 * q^29 - 52 * q^30 - 4 * q^32 - 24 * q^33 - 32 * q^35 + 64 * q^36 - 4 * q^37 - 12 * q^38 - 4 * q^39 - 12 * q^40 - 28 * q^42 - 32 * q^43 - 52 * q^44 - 48 * q^45 - 4 * q^46 - 24 * q^47 - 40 * q^50 + 20 * q^51 + 60 * q^52 - 20 * q^53 - 12 * q^54 - 48 * q^56 - 16 * q^57 - 36 * q^58 + 84 * q^59 + 28 * q^60 - 12 * q^61 - 136 * q^64 - 8 * q^65 + 132 * q^66 + 36 * q^67 - 12 * q^68 + 28 * q^70 - 80 * q^71 - 4 * q^72 - 12 * q^73 - 20 * q^74 - 72 * q^75 - 8 * q^77 - 216 * q^78 - 8 * q^79 + 24 * q^80 + 108 * q^82 + 12 * q^84 + 24 * q^85 - 4 * q^86 - 12 * q^87 - 48 * q^88 - 12 * q^89 + 40 * q^91 - 80 * q^92 + 20 * q^93 + 60 * q^94 + 312 * q^96 - 16 * q^98 - 40 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/224\mathbb{Z}\right)^\times$ .

$n$	$127$	$129$	$197$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{8}\right)$

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

)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$\alpha_n$			$\theta_n$
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$\alpha_p$			$\theta_p$

$2$	0.286901	+	1.38481i	0.202870	+	0.979206i
$2$	0.286901	+	1.38481i	0.202870	+	0.979206i
$3$	−0.360299	−	0.469551i	−0.208019	−	0.271095i	0.677679	−	0.735358i	$-0.262986\pi$
$3$	−0.360299	−	0.469551i	−0.208019	−	0.271095i	−0.885697	+	0.464263i	$0.846319\pi$
$4$	−1.83538	+	0.794605i	−0.917688	+	0.397303i
$5$	2.24363	−	2.92396i	1.00338	−	1.30763i	0.0523216	−	0.998630i	$-0.483338\pi$
$5$	2.24363	−	2.92396i	1.00338	−	1.30763i	0.951061	−	0.309003i	$-0.0999954\pi$
$6$	0.546866	−	0.633659i	0.223257	−	0.258690i
$7$	2.53705	+	0.750581i	0.958915	+	0.283693i
$7$	2.53705	+	0.750581i	0.958915	+	0.283693i
$8$	−1.62695	−	2.31367i	−0.575212	−	0.818004i
$9$	0.685795	−	2.55942i	0.228598	−	0.853140i
$10$	4.69281	+	2.26811i	1.48400	+	0.717238i
$11$	0.0254955	−	0.193658i	0.00768718	−	0.0583899i	−0.987171	−	0.159665i	$-0.948959\pi$
$11$	0.0254955	−	0.193658i	0.00768718	−	0.0583899i	0.994859	+	0.101275i	$0.0322921\pi$
$12$	1.03439	+	0.575506i	0.298603	+	0.166134i
$13$	−1.79545	+	4.33461i	−0.497969	+	1.20220i	0.452606	+	0.891711i	$0.350494\pi$
$13$	−1.79545	+	4.33461i	−0.497969	+	1.20220i	−0.950575	+	0.310494i	$0.899506\pi$
$14$	−0.311526	+	3.72867i	−0.0832588	+	0.996528i
$15$	−2.18132			−0.563215
$16$	2.73720	−	2.91680i	0.684301	−	0.729200i
$17$	1.63000	−	2.82324i	0.395333	−	0.684736i	−0.597811	−	0.801637i	$-0.703963\pi$
$17$	1.63000	−	2.82324i	0.395333	−	0.684736i	0.993144	+	0.116901i	$0.0372960\pi$
$18$	3.74106	+	0.215391i	0.881775	+	0.0507682i
$19$	0.981731	+	7.45699i	0.225225	+	1.71075i	0.613907	+	0.789378i	$0.289597\pi$
$19$	0.981731	+	7.45699i	0.225225	+	1.71075i	−0.388682	+	0.921372i	$0.627070\pi$
$20$	−1.79451	+	7.14936i	−0.401265	+	1.59865i
$21$	−0.561661	−	1.46171i	−0.122564	−	0.318971i
$22$	0.275493	−	0.0202543i	0.0587353	−	0.00431823i
$23$	−0.849490	−	0.227620i	−0.177131	−	0.0474621i	0.169163	−	0.985588i	$-0.445893\pi$
$23$	−0.849490	−	0.227620i	−0.177131	−	0.0474621i	−0.346294	+	0.938126i	$0.612560\pi$
$24$	−0.500196	+	1.59754i	−0.102102	+	0.326097i
$25$	−2.22155	−	8.29094i	−0.444310	−	1.65819i
$26$	−6.51771	−	1.24275i	−1.27823	−	0.243723i
$27$	−3.08928	+	1.27962i	−0.594532	+	0.246263i
$28$	−5.25286	+	0.638357i	−0.992697	+	0.120638i
$29$	−0.793041	+	1.91457i	−0.147264	+	0.355527i	−0.980249	−	0.197769i	$-0.936630\pi$
$29$	−0.793041	+	1.91457i	−0.147264	+	0.355527i	0.832985	+	0.553296i	$0.186630\pi$
$30$	−0.625825	−	3.02071i	−0.114259	−	0.551504i
$31$	1.85113	−	3.20626i	0.332473	−	0.575861i	−0.650523	−	0.759487i	$-0.725450\pi$
$31$	1.85113	−	3.20626i	0.332473	−	0.575861i	0.982996	+	0.183626i	$0.0587835\pi$
$32$	4.82451	+	2.95366i	0.852860	+	0.522139i
$33$	−0.100118	+	0.0578032i	−0.0174283	+	0.0100622i
$34$	4.37729	+	1.44724i	0.750699	+	0.248200i
$35$	7.88688	−	5.73420i	1.33313	−	0.969257i
$36$	0.775039	+	5.24243i	0.129173	+	0.873739i
$37$	−8.19504	−	6.28828i	−1.34726	−	1.03379i	−0.995206	−	0.0978057i	$-0.968818\pi$
$37$	−8.19504	−	6.28828i	−1.34726	−	1.03379i	−0.352051	−	0.935981i	$-0.614516\pi$
$38$	−10.0448	+	3.49893i	−1.62949	+	0.567601i
$39$	2.68222	−	0.718698i	0.429499	−	0.115084i
$40$	−10.4153	−	0.433891i	−1.64681	−	0.0686042i
$41$	−3.81582	+	3.81582i	−0.595930	+	0.595930i	−0.939227	−	0.343297i	$-0.888456\pi$
$41$	−3.81582	+	3.81582i	−0.595930	+	0.595930i	0.343297	+	0.939227i	$0.388456\pi$
$42$	1.86304	−	1.19716i	0.287473	−	0.184725i
$43$	−2.28159	+	0.945065i	−0.347939	+	0.144121i	−0.549807	−	0.835292i	$-0.685299\pi$
$43$	−2.28159	+	0.945065i	−0.347939	+	0.144121i	0.201868	+	0.979413i	$0.435299\pi$
$44$	0.107088	+	0.375693i	0.0161441	+	0.0566379i
$45$	−5.94497	−	7.74763i	−0.886223	−	1.15495i
$46$	0.0714899	−	1.24168i	0.0105406	−	0.183076i
$47$	−1.58163	+	0.913157i	−0.230705	+	0.133198i	−0.610897	−	0.791710i	$-0.709191\pi$
$47$	−1.58163	+	0.913157i	−0.230705	+	0.133198i	0.380192	+	0.924907i	$0.375858\pi$
$48$	−2.35580	−	0.234337i	−0.340030	−	0.0338236i
$49$	5.87326	+	3.80853i	0.839037	+	0.544075i
$50$	10.8440	−	5.45510i	1.53357	−	0.771467i
$51$	−1.91294	+	0.251843i	−0.267865	+	0.0352651i
$52$	−0.148972	−	9.38231i	−0.0206588	−	1.30109i
$53$	8.93961	+	1.17692i	1.22795	+	0.161663i	0.716461	−	0.697627i	$-0.245761\pi$
$53$	8.93961	+	1.17692i	1.22795	+	0.161663i	0.511489	+	0.859290i	$0.329094\pi$
$54$	−2.65834	−	3.91093i	−0.361755	−	0.532210i
$55$	−0.509044	−	0.509044i	−0.0686395	−	0.0686395i
$56$	−2.39105	−	7.09104i	−0.319518	−	0.947580i
$57$	3.14772	−	3.14772i	0.416925	−	0.416925i
$58$	−2.87883	−	0.548915i	−0.378009	−	0.0720761i
$59$	−1.11273	+	8.45206i	−0.144866	+	1.10036i	0.752347	+	0.658767i	$0.228921\pi$
$59$	−1.11273	+	8.45206i	−0.144866	+	1.10036i	−0.897213	+	0.441598i	$0.854412\pi$
$60$	4.00355	−	1.73329i	0.516856	−	0.223767i
$61$	−0.828697	−	6.29458i	−0.106104	−	0.805938i	−0.958910	−	0.283711i	$-0.908434\pi$
$61$	−0.828697	−	6.29458i	−0.106104	−	0.805938i	0.852806	−	0.522228i	$-0.174899\pi$
$62$	4.97114	+	1.64358i	0.631335	+	0.208735i
$63$	3.66095	−	5.97864i	0.461236	−	0.753237i
$64$	−2.70609	+	7.52842i	−0.338262	+	0.941052i
$65$	8.64588	+	14.9751i	1.07239	+	1.85743i
$66$	−0.108770	−	0.122060i	−0.0133887	−	0.0150246i
$67$	−9.50532	+	7.29369i	−1.16126	+	0.891066i	−0.995468	−	0.0950951i	$-0.969684\pi$
$67$	−9.50532	+	7.29369i	−1.16126	+	0.891066i	−0.165791	+	0.986161i	$0.553018\pi$
$68$	−0.748297	+	6.47691i	−0.0907443	+	0.785441i
$69$	0.199191	+	0.480890i	0.0239798	+	0.0578923i
$70$	10.2035	+	9.27664i	1.21955	+	1.10877i
$71$	−4.95899	−	4.95899i	−0.588524	−	0.588524i	0.348708	−	0.937231i	$-0.386621\pi$
$71$	−4.95899	−	4.95899i	−0.588524	−	0.588524i	−0.937231	+	0.348708i	$0.886621\pi$
$72$	−7.03739	+	2.57734i	−0.829365	+	0.303742i
$73$	2.03722	+	7.60300i	0.238438	+	0.889864i	0.976569	+	0.215206i	$0.0690422\pi$
$73$	2.03722	+	7.60300i	0.238438	+	0.889864i	−0.738130	+	0.674658i	$0.764291\pi$
$74$	6.35688	−	13.1527i	0.738972	−	1.52897i
$75$	−3.09259	+	4.03035i	−0.357102	+	0.465384i
$76$	−7.72721	−	12.9063i	−0.886372	−	1.48045i
$77$	0.210039	−	0.472183i	0.0239362	−	0.0538102i
$78$	1.76479	+	3.50816i	0.199823	+	0.397221i
$79$	2.39290	+	4.14462i	0.269222	+	0.466306i	0.968661	−	0.248386i	$-0.0799001\pi$
$79$	2.39290	+	4.14462i	0.269222	+	0.466306i	−0.699439	+	0.714692i	$0.746567\pi$
$80$	−2.38732	−	14.5477i	−0.266910	−	1.62648i
$81$	−5.17023	−	2.98503i	−0.574470	−	0.331670i
$82$	−6.37893	−	4.18940i	−0.704435	−	0.462642i
$83$	−5.02518	−	2.08150i	−0.551585	−	0.228474i	0.0894425	−	0.995992i	$-0.471491\pi$
$83$	−5.02518	−	2.08150i	−0.551585	−	0.228474i	−0.641027	+	0.767518i	$0.721491\pi$
$84$	2.19234	+	2.23648i	0.239204	+	0.244020i
$85$	−4.59792	−	11.1004i	−0.498714	−	1.20400i
$86$	−1.96332	−	2.88842i	−0.211710	−	0.311466i
$87$	1.18472	−	0.317445i	0.127015	−	0.0340336i
$88$	−0.489538	+	0.256082i	−0.0521850	+	0.0272985i
$89$	0.0259571	−	0.0968732i	0.00275145	−	0.0102685i	−0.964536	−	0.263950i	$-0.914975\pi$
$89$	0.0259571	−	0.0968732i	0.00275145	−	0.0102685i	0.967288	+	0.253681i	$0.0816414\pi$
$90$	9.02335	−	10.4554i	0.951144	−	1.10210i
$91$	−7.80863	+	9.64949i	−0.818567	+	1.01154i
$92$	1.74000	−	0.257241i	0.181408	−	0.0268192i
$93$	−2.17246	+	0.286010i	−0.225274	+	0.0296578i
$94$	−1.71832	−	1.92827i	−0.177231	−	0.198886i
$95$	24.0066	+	13.8602i	2.46302	+	1.42203i
$96$	−0.351370	−	3.32955i	−0.0358615	−	0.339821i
$97$			9.39885i			0.954309i	0.878819	+	0.477155i	$0.158332\pi$
$97$			9.39885i			0.954309i	−0.878819	+	0.477155i	$0.841668\pi$
$98$	−3.58902	+	9.22599i	−0.362546	+	0.931966i
$99$	−0.478166	−	0.198063i	−0.0480575	−	0.0199061i
$100$	10.6654	+	13.4517i	1.06654	+	1.34517i
$101$	1.36609	+	0.179849i	0.135931	+	0.0178956i	0.198184	−	0.980165i	$-0.436495\pi$
$101$	1.36609	+	0.179849i	0.135931	+	0.0178956i	−0.0622538	+	0.998060i	$0.519829\pi$
$102$	−0.897579	−	2.57680i	−0.0888736	−	0.255141i
$103$	−11.1523	−	2.98824i	−1.09887	−	0.294440i	−0.336563	−	0.941661i	$-0.609265\pi$
$103$	−11.1523	−	2.98824i	−1.09887	−	0.294440i	−0.762303	+	0.647221i	$0.775931\pi$
$104$	12.9499	−	2.89810i	1.26985	−	0.284182i
$105$	−5.53413	−	1.63726i	−0.540076	−	0.159780i
$106$	0.934978	+	12.7173i	0.0908130	+	1.23521i
$107$	−5.10252	−	3.91530i	−0.493279	−	0.378507i	0.331957	−	0.943295i	$-0.392291\pi$
$107$	−5.10252	−	3.91530i	−0.493279	−	0.378507i	−0.825236	+	0.564788i	$0.808958\pi$
$108$	4.65319	−	4.80334i	0.447753	−	0.462202i
$109$	−5.56613	+	4.27104i	−0.533139	+	0.409092i	−0.839938	−	0.542683i	$-0.817409\pi$
$109$	−5.56613	+	4.27104i	−0.533139	+	0.409092i	0.306799	+	0.951774i	$0.400742\pi$
$110$	0.558882	−	0.850972i	0.0532873	−	0.0811370i
$111$			6.11365i			0.580282i
$112$	9.13372	−	5.34557i	0.863055	−	0.505109i
$113$			1.27034i			0.119504i	0.998213	+	0.0597519i	$0.0190310\pi$
$113$			1.27034i			0.119504i	−0.998213	+	0.0597519i	$0.980969\pi$
$114$	5.26206	+	3.45589i	0.492837	+	0.323674i
$115$	−2.57149	+	1.97318i	−0.239793	+	0.184000i
$116$	−0.0658002	−	4.14411i	−0.00610940	−	0.384771i
$117$	9.86277	+	7.56797i	0.911814	+	0.699659i
$118$	−12.0237	+	0.883986i	−1.10687	+	0.0813775i
$119$	6.25446	−	5.93926i	0.573345	−	0.544451i
$120$	3.54890	+	5.04685i	0.323968	+	0.460713i
$121$	10.5883	+	2.83713i	0.962576	+	0.257921i
$122$	8.47902	−	2.95351i	0.767654	−	0.267398i
$123$	3.16655	+	0.416885i	0.285518	+	0.0375892i
$124$	−0.849815	+	7.35560i	−0.0763156	+	0.660553i
$125$	−12.2016	−	5.05406i	−1.09134	−	0.452049i
$126$	9.32958	+	3.35442i	0.831145	+	0.298836i
$127$		−	6.29532i		−	0.558619i	−0.960201	−	0.279310i	$-0.909894\pi$
$127$		−	6.29532i		−	0.558619i	0.960201	−	0.279310i	$-0.0901056\pi$
$128$	−11.2018	−	1.58750i	−0.990107	−	0.140317i
$129$	1.26581	+	0.730815i	0.111448	+	0.0643447i
$130$	−18.2571	+	16.2692i	−1.60125	+	1.42691i
$131$	20.1751	−	2.65611i	1.76271	−	0.232065i	0.821575	−	0.570100i	$-0.193095\pi$
$131$	20.1751	−	2.65611i	1.76271	−	0.232065i	0.941134	+	0.338035i	$0.109762\pi$
$132$	0.137823	−	0.185645i	0.0119960	−	0.0161583i
$133$	−3.10637	+	19.6556i	−0.269357	+	1.70436i
$134$	−12.8274	−	11.0705i	−1.10812	−	0.956342i
$135$	−3.18964	+	11.9039i	−0.274521	+	1.02453i
$136$	−9.18395	+	0.821989i	−0.787517	+	0.0704849i
$137$	21.1540	−	5.66819i	1.80731	−	0.484266i	0.812226	−	0.583342i	$-0.198255\pi$
$137$	21.1540	−	5.66819i	1.80731	−	0.484266i	0.995080	+	0.0990762i	$0.0315888\pi$
$138$	−0.608791	+	0.413809i	−0.0518237	+	0.0352257i
$139$	7.25213	+	17.5082i	0.615118	+	1.48503i	0.857311	+	0.514798i	$0.172133\pi$
$139$	7.25213	+	17.5082i	0.615118	+	1.48503i	−0.242194	+	0.970228i	$0.577867\pi$
$140$	−9.91895	+	16.7914i	−0.838304	+	1.41913i
$141$	0.998634	+	0.413648i	0.0841002	+	0.0348354i
$142$	5.44450	−	8.28998i	0.456892	−	0.695679i
$143$	0.793654	+	0.458216i	0.0663687	+	0.0383180i
$144$	−5.58815	−	9.00598i	−0.465679	−	0.750498i
$145$	3.81883	+	6.61441i	0.317137	+	0.549297i
$146$	−9.94420	+	5.00246i	−0.822988	+	0.414007i
$147$	−0.327832	−	4.13000i	−0.0270391	−	0.340636i
$148$	20.0377	+	5.02952i	1.64709	+	0.413424i
$149$	4.47610	−	5.83337i	0.366696	−	0.477888i	−0.573167	−	0.819439i	$-0.694285\pi$
$149$	4.47610	−	5.83337i	0.366696	−	0.477888i	0.939863	+	0.341551i	$0.110952\pi$
$150$	−6.46852	−	3.12633i	−0.528152	−	0.255264i
$151$	−5.48853	−	20.4835i	−0.446650	−	1.66692i	−0.711542	−	0.702643i	$-0.752003\pi$
$151$	−5.48853	−	20.4835i	−0.446650	−	1.66692i	0.264892	−	0.964278i	$-0.414664\pi$
$152$	15.6557	−	14.4035i	1.26985	−	1.16828i
$153$	−6.10801	−	6.10801i	−0.493804	−	0.493804i
$154$	0.714142	+	0.155394i	0.0575472	+	0.0125220i
$155$	−5.22170	−	12.6063i	−0.419417	−	1.01256i
$156$	−4.35180	+	3.45039i	−0.348422	+	0.276252i
$157$	−2.93506	+	2.25215i	−0.234244	+	0.179741i	−0.719213	−	0.694790i	$-0.755497\pi$
$157$	−2.93506	+	2.25215i	−0.234244	+	0.179741i	0.484969	+	0.874531i	$0.338831\pi$
$158$	−5.05297	+	4.50280i	−0.401993	+	0.358223i
$159$	−2.66831	−	4.62164i	−0.211610	−	0.366520i
$160$	19.4608	−	7.47972i	1.53851	−	0.591324i
$161$	−1.98435	−	1.21509i	−0.156389	−	0.0957629i
$162$	2.65035	−	8.01618i	0.208231	−	0.629810i
$163$	−1.88541	−	14.3211i	−0.147676	−	1.12171i	−0.891397	−	0.453223i	$-0.850274\pi$
$163$	−1.88541	−	14.3211i	−0.147676	−	1.12171i	0.743721	−	0.668491i	$-0.233059\pi$
$164$	3.97139	−	10.0355i	0.310113	−	0.783643i
$165$	−0.0556139	+	0.422430i	−0.00432954	+	0.0328861i
$166$	1.44074	−	7.55608i	0.111823	−	0.586465i
$167$	−8.50231	+	8.50231i	−0.657929	+	0.657929i	−0.954890	−	0.296961i	$-0.904027\pi$
$167$	−8.50231	+	8.50231i	−0.657929	+	0.657929i	0.296961	+	0.954890i	$0.404027\pi$
$168$	−2.46811	+	3.67761i	−0.190419	+	0.283734i
$169$	−6.37280	−	6.37280i	−0.490215	−	0.490215i
$170$	14.0527	−	9.55193i	1.07779	−	0.732600i
$171$	19.7588	+	2.60130i	1.51100	+	0.198926i
$172$	3.43662	−	3.54751i	0.262040	−	0.270495i
$173$	7.20683	−	0.948797i	0.547925	−	0.0721357i	0.148519	−	0.988910i	$-0.452550\pi$
$173$	7.20683	−	0.948797i	0.547925	−	0.0721357i	0.399407	+	0.916774i	$0.369216\pi$
$174$	0.779497	+	1.54953i	0.0590935	+	0.117470i
$175$	0.586835	−	22.7020i	0.0443606	−	1.71611i
$176$	−0.495074	−	0.604445i	−0.0373176	−	0.0455618i
$177$	4.36959	−	2.52278i	0.328438	−	0.189624i
$178$	0.141598	+	0.00815249i	0.0106132	+	0.000611055i
$179$	−10.2369	−	13.3410i	−0.765143	−	0.997154i	−0.999686	−	0.0250486i	$-0.992026\pi$
$179$	−10.2369	−	13.3410i	−0.765143	−	0.997154i	0.234543	−	0.972106i	$-0.424641\pi$
$180$	17.0676	+	9.49591i	1.27214	+	0.707783i
$181$	−1.48033	+	0.613171i	−0.110032	+	0.0455767i	−0.437020	−	0.899452i	$-0.643966\pi$
$181$	−1.48033	+	0.613171i	−0.110032	+	0.0455767i	0.326988	+	0.945028i	$0.393966\pi$
$182$	−15.6030	−	8.04499i	−1.15657	−	0.596334i
$183$	−2.65704	+	2.65704i	−0.196414	+	0.196414i
$184$	0.855437	+	2.33576i	0.0630637	+	0.172195i
$185$	−36.7733	+	9.85338i	−2.70363	+	0.724435i
$186$	−1.01935	−	2.92638i	−0.0747424	−	0.214573i
$187$	−0.505184	−	0.387641i	−0.0369427	−	0.0283471i
$188$	2.17729	−	2.93276i	0.158795	−	0.213894i
$189$	−8.79812	+	0.927710i	−0.639969	+	0.0674810i
$190$	−12.3062	+	37.2209i	−0.892783	+	2.70029i
$191$	7.04481	−	4.06732i	0.509745	−	0.294301i	−0.222984	−	0.974822i	$-0.571580\pi$
$191$	7.04481	−	4.06732i	0.509745	−	0.294301i	0.732729	+	0.680521i	$0.238246\pi$
$192$	4.50997	−	1.44183i	0.325479	−	0.104055i
$193$	1.59700	−	2.76608i	0.114954	−	0.199107i	−0.802807	−	0.596239i	$-0.796661\pi$
$193$	1.59700	−	2.76608i	0.114954	−	0.199107i	0.917761	+	0.397132i	$0.129995\pi$
$194$	−13.0156	+	2.69654i	−0.934465	+	0.193601i
$195$	3.91647	−	9.45519i	0.280464	−	0.677100i
$196$	−13.8059	−	2.32315i	−0.986136	−	0.165939i
$197$	−22.7704	+	9.43182i	−1.62233	+	0.671989i	−0.994341	−	0.106237i	$-0.966120\pi$
$197$	−22.7704	+	9.43182i	−1.62233	+	0.671989i	−0.627985	+	0.778226i	$0.716120\pi$
$198$	0.137092	−	0.718992i	0.00974272	−	0.0510965i
$199$	−3.74470	−	13.9754i	−0.265455	−	0.990690i	−0.961972	−	0.273150i	$-0.911935\pi$
$199$	−3.74470	−	13.9754i	−0.265455	−	0.990690i	0.696517	−	0.717540i	$-0.254732\pi$
$200$	−15.5681	+	18.6288i	−1.10083	+	1.31726i
$201$	6.84951	+	1.83532i	0.483127	+	0.129454i
$202$	0.142876	+	1.94336i	0.0100528	+	0.136735i
$203$	−3.44903	+	4.26212i	−0.242074	+	0.299142i
$204$	3.31085	−	1.98226i	0.231806	−	0.138786i
$205$	2.59600	+	19.7186i	0.181312	+	1.37720i
$206$	0.938534	−	16.3011i	0.0653908	−	1.13575i
$207$	−1.16515	+	2.01810i	−0.0809836	+	0.140268i
$208$	7.72866	+	17.1017i	0.535886	+	1.18579i
$209$	1.46913			0.101622
$210$	0.679539	−	8.13343i	0.0468926	−	0.561260i
$211$	6.84963	−	16.5365i	0.471548	−	1.13842i	−0.491931	−	0.870634i	$-0.663709\pi$
$211$	6.84963	−	16.5365i	0.471548	−	1.13842i	0.963479	−	0.267784i	$-0.0862913\pi$
$212$	−17.3427	+	4.94337i	−1.19110	+	0.339512i
$213$	−0.541778	+	4.11521i	−0.0371220	+	0.281970i
$214$	3.95801	−	8.18931i	0.270564	−	0.559810i
$215$	−2.35571	+	8.79164i	−0.160658	+	0.599585i
$216$	7.98670	+	5.06568i	0.543426	+	0.344676i
$217$	7.10297	−	6.74501i	0.482181	−	0.457881i
$218$	−7.51149	−	6.48264i	−0.508743	−	0.439060i
$219$	2.83599	−	3.69593i	0.191638	−	0.249748i
$220$	1.33878	+	0.529798i	0.0902602	+	0.0357189i
$221$	9.31105	+	12.1344i	0.626329	+	0.816248i
$222$	−8.46621	+	1.75401i	−0.568215	+	0.117722i
$223$	−2.20295			−0.147520			−0.0737601	−	0.997276i	$-0.523500\pi$
$223$	−2.20295			−0.147520			−0.0737601	+	0.997276i	$0.523500\pi$
$224$	10.0231	+	11.1148i	0.669694	+	0.742637i
$225$	−22.7435			−1.51623
$226$	−1.75918	+	0.364463i	−0.117019	+	0.0242437i
$227$	3.47455	+	4.52812i	0.230614	+	0.300542i	0.894299	−	0.447470i	$-0.147675\pi$
$227$	3.47455	+	4.52812i	0.230614	+	0.300542i	−0.663685	+	0.748012i	$0.731008\pi$
$228$	−3.27605	+	8.27843i	−0.216962	+	0.548253i
$229$	14.7391	−	19.2084i	0.973988	−	1.26933i	0.0109556	−	0.999940i	$-0.496513\pi$
$229$	14.7391	−	19.2084i	0.973988	−	1.26933i	0.963032	−	0.269386i	$-0.0868207\pi$
$230$	−3.47023	−	2.99491i	−0.228820	−	0.197479i
$231$	−0.297390	+	0.0715029i	−0.0195669	+	0.00470454i
$232$	5.71991	−	1.28007i	0.375531	−	0.0840408i
$233$	−4.59370	+	17.1439i	−0.300944	+	1.12314i	0.635438	+	0.772152i	$0.280820\pi$
$233$	−4.59370	+	17.1439i	−0.300944	+	1.12314i	−0.936381	+	0.350984i	$0.885847\pi$
$234$	−7.65053	+	15.8293i	−0.500131	+	1.03479i
$235$	−0.878572	+	6.67342i	−0.0573117	+	0.435326i
$236$	−4.67377	−	16.3969i	−0.304236	−	1.06735i
$237$	1.08395	−	2.61689i	0.0704102	−	0.169985i
$238$	10.0191	+	6.95723i	0.649444	+	0.450970i
$239$	12.6706			0.819591			0.409796	−	0.912177i	$-0.365600\pi$
$239$	12.6706			0.819591			0.409796	+	0.912177i	$0.365600\pi$
$240$	−5.97073	+	6.36248i	−0.385409	+	0.410696i
$241$	4.33725	−	7.51235i	0.279387	−	0.483913i	−0.691845	−	0.722046i	$-0.743202\pi$
$241$	4.33725	−	7.51235i	0.279387	−	0.483913i	0.971233	+	0.238133i	$0.0765354\pi$
$242$	−0.891075	+	15.4768i	−0.0572804	+	0.994884i
$243$	1.77057	+	13.4488i	0.113582	+	0.862741i
$244$	6.52268	+	10.8944i	0.417572	+	0.697444i
$245$	24.3134	−	8.62822i	1.55333	−	0.551237i
$246$	0.331184	+	4.50467i	0.0211155	+	0.287207i
$247$	−34.0858	−	9.13326i	−2.16883	−	0.581135i
$248$	−10.4299	+	0.933504i	−0.662299	+	0.0592776i
$249$	0.833197	+	3.10953i	0.0528017	+	0.197059i
$250$	3.49824	−	18.3469i	0.221248	−	1.16036i
$251$	4.22400	−	1.74964i	0.266617	−	0.110436i	−0.245370	−	0.969429i	$-0.578910\pi$
$251$	4.22400	−	1.74964i	0.266617	−	0.110436i	0.511987	+	0.858993i	$0.328910\pi$
$252$	−1.96856	+	13.8820i	−0.124007	+	0.874487i
$253$	−0.0657385	+	0.158707i	−0.00413294	+	0.00997781i
$254$	8.71779	−	1.80614i	0.547003	−	0.113327i
$255$	−3.55555	+	6.15840i	−0.222657	+	0.385654i
$256$	−1.01542	−	15.9677i	−0.0634640	−	0.997984i
$257$	−0.0444799	+	0.0256805i	−0.00277458	+	0.00160190i	−0.501387	−	0.865223i	$-0.667177\pi$
$257$	−0.0444799	+	0.0256805i	−0.00277458	+	0.00160190i	0.498612	+	0.866825i	$0.333843\pi$
$258$	−0.648875	+	1.96257i	−0.0403972	+	0.122184i
$259$	−16.0714	−	22.1047i	−0.998627	−	1.37352i
$260$	−27.7677	−	20.6149i	−1.72208	−	1.27848i
$261$	4.35633	+	3.34273i	0.269650	+	0.206910i
$262$	9.46646	+	27.1766i	0.584840	+	1.67898i
$263$	1.65899	−	0.444526i	0.102298	−	0.0274106i	−0.207307	−	0.978276i	$-0.566470\pi$
$263$	1.65899	−	0.444526i	0.102298	−	0.0274106i	0.309605	+	0.950865i	$0.399803\pi$
$264$	0.296624	+	0.137597i	0.0182559	+	0.00846851i
$265$	23.4985	−	23.4985i	1.44350	−	1.44350i
$266$	−28.1105	+	1.33750i	−1.72356	+	0.0820076i
$267$	−0.0548392	+	0.0227151i	−0.00335610	+	0.00139014i
$268$	11.6502	−	20.9396i	0.711651	−	1.27909i
$269$	−1.33922	−	1.74531i	−0.0816539	−	0.106413i	0.750740	−	0.660598i	$-0.229697\pi$
$269$	−1.33922	−	1.74531i	−0.0816539	−	0.106413i	−0.832394	+	0.554184i	$0.813030\pi$
$270$	−17.3997	−	1.00179i	−1.05891	−	0.0609670i
$271$	−3.98800	+	2.30247i	−0.242254	+	0.139865i	−0.616212	−	0.787580i	$-0.711334\pi$
$271$	−3.98800	+	2.30247i	−0.242254	+	0.139865i	0.373959	+	0.927445i	$0.378000\pi$
$272$	−3.77318	−	12.4822i	−0.228783	−	0.756842i
$273$	7.34437	+	0.189848i	0.444501	+	0.0114901i
$274$	13.9184	+	27.6679i	0.840844	+	1.67148i
$275$	−1.66224	+	0.218838i	−0.100237	+	0.0131964i
$276$	−0.747708	−	0.724335i	−0.0450067	−	0.0435998i
$277$	5.24024	+	0.689891i	0.314855	+	0.0414515i	0.286298	−	0.958141i	$-0.407575\pi$
$277$	5.24024	+	0.689891i	0.314855	+	0.0414515i	0.0285575	+	0.999592i	$0.490909\pi$
$278$	−22.1648	+	15.0659i	−1.32936	+	0.903594i
$279$	−6.93666	−	6.93666i	−0.415287	−	0.415287i
$280$	−26.0985	−	8.91835i	−1.55969	−	0.532973i
$281$	6.51561	−	6.51561i	0.388689	−	0.388689i	−0.485531	−	0.874220i	$-0.661374\pi$
$281$	6.51561	−	6.51561i	0.388689	−	0.388689i	0.874220	+	0.485531i	$0.161374\pi$
$282$	−0.286312	+	1.50159i	−0.0170497	+	0.0894184i
$283$	−1.59733	+	12.1329i	−0.0949514	+	0.721227i	0.876061	+	0.482200i	$0.160162\pi$
$283$	−1.59733	+	12.1329i	−0.0949514	+	0.721227i	−0.971013	+	0.239028i	$0.923171\pi$
$284$	13.0420	+	5.16117i	0.773903	+	0.306259i
$285$	−2.14147	−	16.2661i	−0.126850	−	0.963521i
$286$	−0.406840	+	1.23052i	−0.0240570	+	0.0727621i
$287$	−12.5450	+	6.81684i	−0.740508	+	0.402385i
$288$	10.8683	−	10.3223i	0.640420	−	0.608249i
$289$	3.18621	+	5.51868i	0.187424	+	0.324628i
$290$	−8.06405	+	7.18602i	−0.473537	+	0.421978i
$291$	4.41324	−	3.38640i	0.258709	−	0.198514i
$292$	−9.78044	−	12.3356i	−0.572357	−	0.721885i
$293$	−9.68853	−	23.3902i	−0.566010	−	1.36647i	−0.904892	−	0.425640i	$-0.860049\pi$
$293$	−9.68853	−	23.3902i	−0.566010	−	1.36647i	0.338883	−	0.940829i	$-0.389951\pi$
$294$	5.62519	−	1.63889i	0.328068	−	0.0955818i
$295$	22.2169	+	22.2169i	1.29352	+	1.29352i
$296$	−1.21608	+	29.1913i	−0.0706830	+	1.69671i
$297$	0.169046	+	0.630887i	0.00980902	+	0.0366078i
$298$	9.36228	+	4.52493i	0.542342	+	0.262122i
$299$	2.51186	−	3.27352i	0.145265	−	0.189313i
$300$	2.47353	−	9.85459i	0.142810	−	0.568955i
$301$	−6.49785	+	0.685161i	−0.374530	+	0.0394920i
$302$	26.7910	−	13.4773i	1.54165	−	0.775531i
$303$	−0.407751	−	0.706246i	−0.0234247	−	0.0405728i
$304$	24.4377	+	17.5478i	1.40160	+	1.00643i
$305$	−20.2644	−	11.6996i	−1.16033	−	0.669919i
$306$	6.70602	−	10.2108i	0.383357	−	0.583713i
$307$	−1.39053	−	0.575975i	−0.0793616	−	0.0328727i	0.342649	−	0.939463i	$-0.388676\pi$
$307$	−1.39053	−	0.575975i	−0.0793616	−	0.0328727i	−0.422011	+	0.906591i	$0.638676\pi$
$308$	−0.0103016	+	1.03353i	−0.000586989	+	0.0588909i
$309$	2.61502	+	6.31322i	0.148763	+	0.359146i
$310$	15.9592	−	10.8478i	0.906419	−	0.616114i
$311$	29.2400	−	7.83483i	1.65805	−	0.444273i	0.696198	−	0.717850i	$-0.254874\pi$
$311$	29.2400	−	7.83483i	1.65805	−	0.444273i	0.961850	+	0.273577i	$0.0882069\pi$
$312$	−6.02665	−	5.03647i	−0.341192	−	0.285134i
$313$	0.740609	−	2.76399i	0.0418617	−	0.156230i	−0.941831	−	0.336086i	$-0.890897\pi$
$313$	0.740609	−	2.76399i	0.0418617	−	0.156230i	0.983693	+	0.179856i	$0.0575633\pi$
$314$	−3.96087	−	3.41835i	−0.223525	−	0.192909i
$315$	−9.26746	−	24.1183i	−0.522162	−	1.35891i
$316$	−7.68521	−	5.70553i	−0.432327	−	0.320961i
$317$	5.28998	−	0.696439i	0.297115	−	0.0391159i	0.0195048	−	0.999810i	$-0.493791\pi$
$317$	5.28998	−	0.696439i	0.297115	−	0.0391159i	0.277610	+	0.960694i	$0.410458\pi$
$318$	5.63454	−	5.02104i	0.315969	−	0.281566i
$319$	0.350552	+	0.202391i	0.0196271	+	0.0113317i
$320$	15.9413	+	24.8035i	0.891146	+	1.38656i
$321$			3.80657i			0.212462i
$322$	1.11336	−	3.09655i	0.0620450	−	0.172564i
$323$	22.6531	+	9.38321i	1.26045	+	0.522096i
$324$	11.8612	+	1.37036i	0.658958	+	0.0761313i
$325$	39.9267	+	5.25645i	2.21473	+	0.291575i
$326$	19.2910	−	6.71966i	1.06843	−	0.372168i
$327$	4.01094	+	1.07473i	0.221805	+	0.0594326i
$328$	15.0366	+	2.62039i	0.830260	+	0.144687i
$329$	−4.69808	+	1.12958i	−0.259014	+	0.0622758i
$330$	−0.600939	+	0.0441812i	−0.0330806	+	0.00243209i
$331$	−12.7330	−	9.77040i	−0.699871	−	0.537030i	0.196407	−	0.980522i	$-0.437073\pi$
$331$	−12.7330	−	9.77040i	−0.699871	−	0.537030i	−0.896278	+	0.443493i	$0.853739\pi$
$332$	10.8771	−	0.172706i	0.596956	−	0.00947847i
$333$	−21.7145	+	16.6621i	−1.18995	+	0.913077i
$334$	−14.2134	−	9.33473i	−0.777721	−	0.510773i
$335$			44.1575i			2.41258i
$336$	−5.80089	−	2.36274i	−0.316464	−	0.128898i
$337$			25.9961i			1.41610i	0.706163	+	0.708049i	$0.250425\pi$
$337$			25.9961i			1.41610i	−0.706163	+	0.708049i	$0.749575\pi$
$338$	6.99672	−	10.6534i	0.380571	−	0.579471i
$339$	0.596490	−	0.457703i	0.0323969	−	0.0248590i
$340$	17.2593	+	16.7198i	0.936017	+	0.906758i
$341$	−0.573720	−	0.440231i	−0.0310687	−	0.0238398i
$342$	2.06654	+	28.1085i	0.111746	+	1.51993i
$343$	12.0421	+	14.0708i	0.650215	+	0.759751i
$344$	5.89858	+	3.74126i	0.318030	+	0.201715i
$345$	1.85301	+	0.496513i	0.0997628	+	0.0267314i
$346$	3.38155	+	9.70785i	0.181793	+	0.521897i
$347$	−25.7655	−	3.39209i	−1.38317	−	0.182097i	−0.598056	−	0.801454i	$-0.704060\pi$
$347$	−25.7655	−	3.39209i	−1.38317	−	0.182097i	−0.785109	+	0.619357i	$0.787393\pi$
$348$	−1.92216	+	1.52401i	−0.103039	+	0.0816958i
$349$	9.97430	+	4.13149i	0.533912	+	0.221154i	0.633316	−	0.773894i	$-0.281694\pi$
$349$	9.97430	+	4.13149i	0.533912	+	0.221154i	−0.0994037	+	0.995047i	$0.531694\pi$
$350$	31.6062	−	5.70058i	1.68942	−	0.304709i
$351$		−	15.6883i		−	0.837380i
$352$	0.695002	−	0.858997i	0.0370438	−	0.0457847i
$353$	−8.89552	−	5.13583i	−0.473461	−	0.273353i	0.244226	−	0.969718i	$-0.421466\pi$
$353$	−8.89552	−	5.13583i	−0.473461	−	0.273353i	−0.717687	+	0.696365i	$0.754799\pi$
$354$	4.74720	+	5.32724i	0.252311	+	0.283140i
$355$	−25.6260	+	3.37373i	−1.36009	+	0.179059i
$356$	0.0293350	+	0.198424i	0.00155475	+	0.0105165i
$357$	−5.04226	−	0.796877i	−0.266865	−	0.0421752i
$358$	15.5377	−	18.0037i	0.821195	−	0.951525i
$359$	8.49961	−	31.7210i	0.448592	−	1.67417i	−0.257682	−	0.966230i	$-0.582959\pi$
$359$	8.49961	−	31.7210i	0.448592	−	1.67417i	0.706274	−	0.707939i	$-0.250375\pi$
$360$	−8.25328	+	26.3596i	−0.434986	+	1.38927i
$361$	−36.2903	+	9.72395i	−1.91001	+	0.511787i
$362$	−1.27383	−	1.87405i	−0.0669511	−	0.0984976i
$363$	−2.48279	−	5.99397i	−0.130312	−	0.314602i
$364$	6.66424	−	23.9152i	0.349301	−	1.25350i
$365$	26.8016	+	11.1016i	1.40286	+	0.581084i
$366$	−4.44180	−	2.91718i	−0.232177	−	0.152484i
$367$	−4.93261	−	2.84784i	−0.257480	−	0.148656i	0.365704	−	0.930731i	$-0.380828\pi$
$367$	−4.93261	−	2.84784i	−0.257480	−	0.148656i	−0.623185	+	0.782075i	$0.714161\pi$
$368$	−2.98915	+	1.85475i	−0.155820	+	0.0966854i
$369$	7.14941	+	12.3831i	0.372183	+	0.644641i
$370$	−24.1953	−	48.0970i	−1.25786	−	2.50044i
$371$	21.7969	+	9.69581i	1.13164	+	0.503381i
$372$	3.76002	−	2.25118i	0.194948	−	0.116718i
$373$	−1.55936	+	2.03219i	−0.0807404	+	0.105223i	−0.831977	−	0.554810i	$-0.812791\pi$
$373$	−1.55936	+	2.03219i	−0.0807404	+	0.105223i	0.751237	+	0.660033i	$0.229458\pi$
$374$	0.391870	−	0.810797i	0.0202631	−	0.0419253i
$375$	2.02308	+	7.55024i	0.104471	+	0.389893i
$376$	4.68597	+	2.17371i	0.241661	+	0.112101i
$377$	−6.87505	−	6.87505i	−0.354083	−	0.354083i
$378$	−3.80889	−	11.9175i	−0.195908	−	0.612971i
$379$	7.46656	+	18.0259i	0.383531	+	0.925926i	0.991277	+	0.131795i	$0.0420739\pi$
$379$	7.46656	+	18.0259i	0.383531	+	0.925926i	−0.607746	+	0.794132i	$0.707926\pi$
$380$	−55.0744	−	6.36291i	−2.82526	−	0.326411i
$381$	−2.95597	+	2.26820i	−0.151439	+	0.116203i
$382$	7.65362	+	8.58878i	0.391593	+	0.439440i
$383$	9.29771	+	16.1041i	0.475091	+	0.822882i	0.999593	−	0.0285276i	$-0.00908184\pi$
$383$	9.29771	+	16.1041i	0.475091	+	0.822882i	−0.524502	+	0.851409i	$0.675749\pi$
$384$	3.29058	+	5.83178i	0.167921	+	0.297602i
$385$	−0.909392	−	1.67355i	−0.0463469	−	0.0852920i
$386$	4.28866	+	1.41794i	0.218287	+	0.0721711i
$387$	0.854117	+	6.48766i	0.0434172	+	0.329786i
$388$	−7.46838	−	17.2504i	−0.379150	−	0.875758i
$389$	0.470226	−	3.57172i	0.0238414	−	0.181093i	−0.975381	−	0.220527i	$-0.929222\pi$
$389$	0.470226	−	3.57172i	0.0238414	−	0.181093i	0.999222	+	0.0394341i	$0.0125555\pi$
$390$	14.2172	+	2.71084i	0.719918	+	0.137269i
$391$	−2.02729	+	2.02729i	−0.102525	+	0.102525i
$392$	−0.743818	−	19.7850i	−0.0375685	−	0.999294i
$393$	−8.51625	−	8.51625i	−0.429588	−	0.429588i
$394$	−19.5941	−	28.8266i	−0.987137	−	1.45226i
$395$	17.4875	+	2.30227i	0.879891	+	0.115840i
$396$	1.03500	−	0.0164337i	0.0520105	−	0.000825824i
$397$	−13.9742	+	1.83974i	−0.701344	+	0.0923337i	−0.472761	−	0.881191i	$-0.656743\pi$
$397$	−13.9742	+	1.83974i	−0.701344	+	0.0923337i	−0.228583	+	0.973524i	$0.573409\pi$
$398$	18.2789	−	9.19524i	0.916237	−	0.460916i
$399$	10.3485	−	5.62330i	0.518075	−	0.281517i
$400$	−30.2638	−	16.2142i	−1.51319	−	0.810709i
$401$	9.96747	−	5.75472i	0.497752	−	0.287377i	−0.230033	−	0.973183i	$-0.573883\pi$
$401$	9.96747	−	5.75472i	0.497752	−	0.287377i	0.727785	+	0.685806i	$0.240550\pi$
$402$	−0.576429	+	10.0118i	−0.0287497	+	0.499343i
$403$	10.5742	+	13.7806i	0.526741	+	0.686462i
$404$	−2.65019	+	0.755410i	−0.131852	+	0.0375830i
$405$	−20.3282	+	8.42022i	−1.01012	+	0.418404i
$406$	−6.89174	−	3.55342i	−0.342031	−	0.176353i
$407$	−1.42671	+	1.42671i	−0.0707193	+	0.0707193i
$408$	3.69493	+	4.01617i	0.182926	+	0.198830i
$409$	−10.4818	+	2.80860i	−0.518294	+	0.138876i	−0.508477	−	0.861075i	$-0.669791\pi$
$409$	−10.4818	+	2.80860i	−0.518294	+	0.138876i	−0.00981657	+	0.999952i	$0.503125\pi$
$410$	−26.5616	+	9.25224i	−1.31178	+	0.456936i
$411$	−10.2833	−	7.89062i	−0.507236	−	0.389216i
$412$	22.8431	−	3.37711i	1.12540	−	0.166378i
$413$	−9.16702	+	20.6081i	−0.451080	+	1.01406i
$414$	−3.12896	−	1.03451i	−0.153780	−	0.0508435i
$415$	−17.3608	+	10.0233i	−0.852211	+	0.492024i
$416$	−21.4652	+	15.6092i	−1.05242	+	0.765303i
$417$	5.60805	−	9.71343i	0.274627	−	0.475669i
$418$	0.421496	+	2.03446i	0.0206160	+	0.0995088i
$419$	−1.14858	+	2.77292i	−0.0561119	+	0.135466i	−0.949449	−	0.313920i	$-0.898357\pi$
$419$	−1.14858	+	2.77292i	−0.0561119	+	0.135466i	0.893337	+	0.449387i	$0.148357\pi$
$420$	11.4582	−	1.39246i	0.559102	−	0.0679452i
$421$	18.6016	−	7.70504i	0.906587	−	0.375521i	0.119838	−	0.992793i	$-0.461762\pi$
$421$	18.6016	−	7.70504i	0.906587	−	0.375521i	0.786749	+	0.617273i	$0.211762\pi$
$422$	24.8650	+	4.74108i	1.21041	+	0.230792i
$423$	1.25248	+	4.67430i	0.0608975	+	0.227272i
$424$	−11.8213	−	22.5980i	−0.574091	−	1.09746i
$425$	−27.0284	−	7.24225i	−1.31107	−	0.351301i
$426$	−5.85421	+	0.430403i	−0.283637	+	0.0208531i
$427$	2.62215	−	16.5917i	0.126894	−	0.802927i
$428$	12.4762	+	3.13156i	0.603058	+	0.151370i
$429$	−0.0707968	−	0.537755i	−0.00341810	−	0.0259631i
$430$	−12.8506	−	0.739872i	−0.619710	−	0.0356798i
$431$	−0.410242	+	0.710561i	−0.0197607	+	0.0342265i	−0.875737	−	0.482789i	$-0.839624\pi$
$431$	−0.410242	+	0.710561i	−0.0197607	+	0.0342265i	0.855976	+	0.517016i	$0.172957\pi$
$432$	−4.72359	+	12.5134i	−0.227264	+	0.602051i
$433$	19.1887			0.922148			0.461074	−	0.887362i	$-0.347464\pi$
$433$	19.1887			0.922148			0.461074	+	0.887362i	$0.347464\pi$
$434$	11.3784	+	7.90109i	0.546180	+	0.379264i
$435$	1.72988	−	4.17630i	0.0829414	−	0.200238i
$436$	6.82214	−	12.2618i	0.326721	−	0.587236i
$437$	0.863390	−	6.55809i	0.0413015	−	0.313716i
$438$	5.93179	+	2.86692i	0.283432	+	0.136987i
$439$	−8.03114	+	29.9726i	−0.383305	+	1.43051i	0.457516	+	0.889201i	$0.348739\pi$
$439$	−8.03114	+	29.9726i	−0.383305	+	1.43051i	−0.840821	+	0.541313i	$0.817927\pi$
$440$	−0.349570	+	2.00594i	−0.0166651	+	0.0956296i
$441$	13.7755	−	12.4203i	0.655974	−	0.591441i
$442$	−14.1324	+	16.3754i	−0.672212	+	0.778897i
$443$	4.04691	−	5.27404i	0.192275	−	0.250577i	−0.687261	−	0.726411i	$-0.741187\pi$
$443$	4.04691	−	5.27404i	0.192275	−	0.250577i	0.879535	+	0.475834i	$0.157854\pi$
$444$	−4.85794	−	11.2208i	−0.230547	−	0.532517i
$445$	−0.225015	−	0.293245i	−0.0106667	−	0.0139012i
$446$	−0.632029	−	3.05066i	−0.0299274	−	0.144453i
$447$	−4.35179			−0.205833
$448$	−12.5162	+	17.0688i	−0.591334	+	0.806427i
$449$	−21.8843			−1.03278			−0.516392	−	0.856352i	$-0.672725\pi$
$449$	−21.8843			−1.03278			−0.516392	+	0.856352i	$0.672725\pi$
$450$	−6.52515	−	31.4954i	−0.307598	−	1.48471i
$451$	0.641675	+	0.836248i	0.0302153	+	0.0393774i
$452$	−1.00942	−	2.33156i	−0.0474792	−	0.109667i
$453$	−7.64051	+	9.95731i	−0.358983	+	0.467835i
$454$	−5.27372	+	6.11070i	−0.247508	+	0.286789i
$455$	10.6950	+	44.4820i	0.501390	+	2.08535i
$456$	−12.4039	−	2.16160i	−0.580867	−	0.101226i
$457$	5.04748	−	18.8375i	0.236111	−	0.881179i	−0.741534	−	0.670916i	$-0.765901\pi$
$457$	5.04748	−	18.8375i	0.236111	−	0.881179i	0.977645	−	0.210263i	$-0.0674321\pi$
$458$	30.8286	+	14.8999i	1.44052	+	0.696227i
$459$	−1.42284	+	10.8076i	−0.0664125	+	0.504453i
$460$	3.15176	−	5.66484i	0.146951	−	0.264125i
$461$	5.00740	−	12.0889i	0.233218	−	0.563038i	−0.763335	−	0.646003i	$-0.776439\pi$
$461$	5.00740	−	12.0889i	0.233218	−	0.563038i	0.996552	+	0.0829658i	$0.0264392\pi$
$462$	−0.184339	−	0.391314i	−0.00857624	−	0.0182056i
$463$	−37.5037			−1.74294			−0.871472	−	0.490445i	$-0.836834\pi$
$463$	−37.5037			−1.74294			−0.871472	+	0.490445i	$0.836834\pi$
$464$	3.41370	+	7.55371i	0.158477	+	0.350672i
$465$	−4.03792	+	6.99388i	−0.187254	+	0.324334i
$466$	−25.0590	−	1.44277i	−1.16083	−	0.0668350i
$467$	2.46339	+	18.7113i	0.113992	+	0.865856i	0.948924	+	0.315504i	$0.102173\pi$
$467$	2.46339	+	18.7113i	0.113992	+	0.865856i	−0.834932	+	0.550353i	$0.814493\pi$
$468$	−24.1154	−	6.05306i	−1.11474	−	0.279803i
$469$	−29.5900	+	11.3699i	−1.36634	+	0.525015i
$470$	−9.49345	+	0.697961i	−0.437900	+	0.0321945i
$471$	2.11500	+	0.566713i	0.0974541	+	0.0261127i
$472$	21.3656	−	11.1765i	0.983431	−	0.514442i
$473$	0.124849	+	0.465942i	0.00574055	+	0.0214240i
$474$	3.93487	+	0.750273i	0.180735	+	0.0344612i
$475$	59.6445	−	24.7055i	2.73668	−	1.13357i
$476$	−6.75991	+	15.8706i	−0.309840	+	0.727427i
$477$	9.14297	−	22.0731i	0.418628	−	1.01066i
$478$	3.63521	+	17.5463i	0.166270	+	0.802549i
$479$	−9.26849	+	16.0535i	−0.423488	+	0.733503i	−0.996278	−	0.0861993i	$-0.972528\pi$
$479$	−9.26849	+	16.0535i	−0.423488	+	0.733503i	0.572790	+	0.819702i	$0.305861\pi$
$480$	−10.5238	−	6.44290i	−0.480344	−	0.294077i
$481$	41.9710	−	24.2320i	1.91372	−	1.10488i
$482$	11.6475	+	3.85095i	0.530529	+	0.175406i
$483$	0.144411	+	1.36955i	0.00657093	+	0.0623167i
$484$	−21.6880	+	3.20634i	−0.985816	+	0.145743i
$485$	27.4819	+	21.0876i	1.24789	+	0.957537i
$486$	−18.1160	+	6.31037i	−0.821758	+	0.286244i
$487$	−5.44957	+	1.46021i	−0.246944	+	0.0661684i	−0.380168	−	0.924918i	$-0.624134\pi$
$487$	−5.44957	+	1.46021i	−0.246944	+	0.0661684i	0.133224	+	0.991086i	$0.457467\pi$
$488$	−13.2153	+	12.1583i	−0.598229	+	0.550379i
$489$	−6.04516	+	6.04516i	−0.273372	+	0.273372i
$490$	18.9240	+	31.1939i	0.854897	+	1.40920i
$491$	−27.2761	+	11.2981i	−1.23095	+	0.509878i	−0.900877	−	0.434075i	$-0.857075\pi$
$491$	−27.2761	+	11.2981i	−1.23095	+	0.509878i	−0.330078	+	0.943954i	$0.607075\pi$
$492$	−6.14307	+	1.75102i	−0.276951	+	0.0789421i
$493$	4.11264	+	5.35969i	0.185224	+	0.241388i
$494$	2.86853	−	49.8225i	0.129061	−	2.24162i
$495$	−1.65196	+	0.953758i	−0.0742499	+	0.0428682i
$496$	−4.28507	−	14.1756i	−0.192405	−	0.636501i
$497$	−8.85908	−	16.3033i	−0.397384	−	0.731304i
$498$	−4.06706	+	2.04595i	−0.182249	+	0.0916811i
$499$	−11.2114	+	1.47600i	−0.501890	+	0.0660750i	−0.377221	−	0.926123i	$-0.623120\pi$
$499$	−11.2114	+	1.47600i	−0.501890	+	0.0660750i	−0.124669	+	0.992198i	$0.539787\pi$
$500$	26.4105	−	0.419346i	1.18111	−	0.0187537i
$501$	7.05564	+	0.928892i	0.315223	+	0.0414998i
$502$	3.63478	+	5.34745i	0.162228	+	0.238668i
$503$	−20.3957	−	20.3957i	−0.909400	−	0.909400i	0.0868238	−	0.996224i	$-0.472328\pi$
$503$	−20.3957	−	20.3957i	−0.909400	−	0.909400i	−0.996224	+	0.0868238i	$0.972328\pi$
$504$	−19.7887	+	1.25671i	−0.881460	+	0.0559782i
$505$	3.59086	−	3.59086i	0.159791	−	0.159791i
$506$	−0.238639	−	0.0455019i	−0.0106088	−	0.00202280i
$507$	−0.696239	+	5.28846i	−0.0309211	+	0.234869i
$508$	5.00229	+	11.5543i	0.221941	+	0.512638i
$509$	−3.36741	−	25.5780i	−0.149258	−	1.13372i	−0.888035	−	0.459775i	$-0.847930\pi$
$509$	−3.36741	−	25.5780i	−0.149258	−	1.13372i	0.738778	−	0.673949i	$-0.235403\pi$
$510$	−9.54828	−	3.15690i	−0.422805	−	0.139790i
$511$	−0.538143	+	20.8183i	−0.0238060	+	0.920947i
$512$	21.8209	−	5.98733i	0.964357	−	0.264605i
$513$	−12.5750	−	21.7805i	−0.555198	−	0.961631i
$514$	−0.0483238	−	0.0542283i	−0.00213147	−	0.00239191i
$515$	−33.7591	+	25.9043i	−1.48760	+	1.14148i
$516$	−2.90394	−	0.335501i	−0.127839	−	0.0147696i
$517$	0.136515	+	0.329577i	0.00600393	+	0.0144948i
$518$	25.9999	−	28.5976i	1.14237	−	1.25651i
$519$	−3.04212	−	3.04212i	−0.133534	−	0.133534i
$520$	20.5810	−	44.3673i	0.902536	−	1.94564i
$521$	−0.409945	−	1.52994i	−0.0179600	−	0.0670277i	0.956364	−	0.292177i	$-0.0943797\pi$
$521$	−0.409945	−	1.52994i	−0.0179600	−	0.0670277i	−0.974324	+	0.225149i	$0.927713\pi$
$522$	−3.37919	+	6.99170i	−0.147903	+	0.306019i
$523$	12.4581	−	16.2357i	0.544756	−	0.709939i	−0.437133	−	0.899397i	$-0.644006\pi$
$523$	12.4581	−	16.2357i	0.544756	−	0.709939i	0.981889	+	0.189457i	$0.0606729\pi$
$524$	−34.9184	+	20.9062i	−1.52542	+	0.913292i
$525$	−10.8712	+	7.90395i	−0.474457	+	0.344957i
$526$	1.09155	+	2.16985i	0.0475938	+	0.0946099i
$527$	−6.03469	−	10.4524i	−0.262875	−	0.455313i
$528$	−0.105443	+	0.450243i	−0.00458883	+	0.0195943i
$529$	−19.2488	−	11.1133i	−0.836903	−	0.483186i
$530$	39.2825	+	25.7991i	1.70632	+	1.12064i
$531$	20.8693	+	8.64433i	0.905649	+	0.375132i
$532$	−9.91711	−	38.5438i	−0.429961	−	1.67109i
$533$	−9.68895	−	23.3912i	−0.419675	−	1.01319i
$534$	−0.0471895	−	0.0694246i	−0.00204209	−	0.00300430i
$535$	−22.8964	+	6.13506i	−0.989896	+	0.265242i
$536$	32.3398	+	10.1257i	1.39687	+	0.437363i
$537$	−2.57593	+	9.61351i	−0.111160	+	0.414853i
$538$	2.03269	−	2.35530i	0.0876355	−	0.101544i
$539$	0.887291	−	1.04030i	0.0382183	−	0.0448089i
$540$	−3.60472	−	24.3827i	−0.155123	−	1.04926i
$541$	33.4196	−	4.39978i	1.43682	−	0.189161i	0.628458	−	0.777844i	$-0.283686\pi$
$541$	33.4196	−	4.39978i	1.43682	−	0.189161i	0.808365	+	0.588682i	$0.200353\pi$
$542$	−4.33264	−	4.86202i	−0.186103	−	0.208842i
$543$	0.821275	+	0.474163i	0.0352443	+	0.0203483i
$544$	16.2028	−	8.80627i	0.694691	−	0.377566i
$545$			25.8578i			1.10763i
$546$	1.84421	+	10.2250i	0.0789247	+	0.437589i
$547$	−1.87204	−	0.775425i	−0.0800427	−	0.0331548i	0.342303	−	0.939590i	$-0.388793\pi$
$547$	−1.87204	−	0.775425i	−0.0800427	−	0.0331548i	−0.422346	+	0.906435i	$0.638793\pi$
$548$	−34.3215	+	27.2123i	−1.46614	+	1.16245i
$549$	−16.6788	−	2.19580i	−0.711833	−	0.0937146i
$550$	−0.779948	−	2.23910i	−0.0332571	−	0.0954755i
$551$	−15.0555	−	4.03410i	−0.641385	−	0.171859i
$552$	0.788544	−	1.24324i	0.0335627	−	0.0529159i
$553$	2.96003	+	12.3112i	0.125873	+	0.523525i
$554$	0.548067	+	7.45464i	0.0232851	+	0.316718i
$555$	17.8760	+	13.7168i	0.758796	+	0.582244i
$556$	−27.2225	−	26.3715i	−1.15449	−	1.11840i
$557$	20.3854	−	15.6423i	0.863758	−	0.662785i	−0.0787771	−	0.996892i	$-0.525102\pi$
$557$	20.3854	−	15.6423i	0.863758	−	0.662785i	0.942535	+	0.334108i	$0.108435\pi$
$558$	7.61579	−	11.5961i	0.322402	−	0.490901i
$559$		−	11.5866i		−	0.490062i
$560$	4.86248	−	38.7001i	0.205477	−	1.63538i
$561$			0.376876i			0.0159117i
$562$	10.8922	+	7.15352i	0.459460	+	0.301753i
$563$	10.1022	−	7.75169i	0.425757	−	0.326695i	−0.373558	−	0.927607i	$-0.621862\pi$
$563$	10.1022	−	7.75169i	0.425757	−	0.326695i	0.799315	+	0.600912i	$0.205196\pi$
$564$	−2.16156	+	0.0343212i	−0.0910179	+	0.00144518i
$565$	3.71443	+	2.85018i	0.156267	+	0.119908i
$566$	−17.2600	+	1.26896i	−0.725493	+	0.0533384i
$567$	−10.8766	−	11.4539i	−0.456775	−	0.481017i
$568$	−3.40543	+	19.5414i	−0.142889	+	0.819941i
$569$	−29.9072	−	8.01362i	−1.25378	−	0.335948i	−0.429982	−	0.902837i	$-0.641480\pi$
$569$	−29.9072	−	8.01362i	−1.25378	−	0.335948i	−0.823794	+	0.566889i	$0.808147\pi$
$570$	21.9110	−	7.63229i	0.917751	−	0.319682i
$571$	16.4367	+	2.16393i	0.687853	+	0.0905576i	0.466348	−	0.884602i	$-0.345570\pi$
$571$	16.4367	+	2.16393i	0.687853	+	0.0905576i	0.221505	+	0.975159i	$0.428903\pi$
$572$	−1.82075	−	0.210357i	−0.0761295	−	0.00879547i
$573$	−4.44805	−	1.84244i	−0.185820	−	0.0769692i
$574$	−13.0392	−	15.4166i	−0.544245	−	0.643478i
$575$			7.54873i			0.314804i
$576$	17.4126	+	12.0890i	0.725523	+	0.503707i
$577$	−30.5815	−	17.6562i	−1.27312	−	0.735038i	−0.297549	−	0.954707i	$-0.596169\pi$
$577$	−30.5815	−	17.6562i	−1.27312	−	0.735038i	−0.975575	+	0.219668i	$0.929502\pi$
$578$	−6.72817	+	5.99560i	−0.279855	+	0.249384i
$579$	−1.87421	+	0.246744i	−0.0778894	+	0.0102543i
$580$	−12.2648	−	9.10546i	−0.509270	−	0.378084i
$581$	−11.1868	−	9.05266i	−0.464107	−	0.375568i
$582$	5.95567	+	5.13992i	0.246870	+	0.213056i
$583$	0.455840	−	1.70122i	0.0188789	−	0.0704572i
$584$	14.2764	−	17.0831i	0.590760	−	0.706904i
$585$	44.2569	−	11.8586i	1.82980	−	0.490292i
$586$	29.6112	−	20.1274i	1.22323	−	0.831456i
$587$	−5.67657	−	13.7044i	−0.234297	−	0.565643i	0.762377	−	0.647133i	$-0.224032\pi$
$587$	−5.67657	−	13.7044i	−0.234297	−	0.565643i	−0.996674	+	0.0814899i	$0.974032\pi$
$588$	3.88341	+	7.31960i	0.160149	+	0.301855i
$589$	25.7263	+	10.6562i	1.06003	+	0.439081i
$590$	−24.3920	+	37.1401i	−1.00420	+	1.52904i
$591$	12.6329	+	7.29359i	0.519647	+	0.300018i
$592$	−40.7731	+	6.69099i	−1.67577	+	0.274998i
$593$	−19.0770	−	33.0424i	−0.783400	−	1.35689i	−0.929950	−	0.367685i	$-0.880150\pi$
$593$	−19.0770	−	33.0424i	−0.783400	−	1.35689i	0.146550	−	0.989203i	$-0.453183\pi$
$594$	−0.825156	+	0.415097i	−0.0338566	+	0.0170317i
$595$	−3.33344	−	31.6133i	−0.136658	−	1.29602i
$596$	−3.58010	+	14.2631i	−0.146647	+	0.584241i
$597$	−5.21295	+	6.79365i	−0.213352	+	0.278045i
$598$	5.25385	+	2.53926i	0.214846	+	0.103838i
$599$	5.33450	+	19.9086i	0.217962	+	0.813444i	0.985103	+	0.171966i	$0.0550119\pi$
$599$	5.33450	+	19.9086i	0.217962	+	0.813444i	−0.767141	+	0.641478i	$0.778321\pi$
$600$	14.3564	+	0.598070i	0.586096	+	0.0244161i
$601$	11.0600	+	11.0600i	0.451146	+	0.451146i	0.895735	−	0.444589i	$-0.146650\pi$
$601$	11.0600	+	11.0600i	0.451146	+	0.451146i	−0.444589	+	0.895735i	$0.646650\pi$
$602$	−2.81306	−	8.80169i	−0.114652	−	0.358730i
$603$	12.1489	+	29.3301i	0.494742	+	1.19441i
$604$	26.3498	+	33.2336i	1.07216	+	1.35226i
$605$	32.0520	−	24.5943i	1.30310	−	0.999902i
$606$	0.861029	−	0.767279i	0.0349769	−	0.0311686i
$607$	−5.10135	−	8.83580i	−0.207057	−	0.358634i	0.743729	−	0.668481i	$-0.233055\pi$
$607$	−5.10135	−	8.83580i	−0.207057	−	0.358634i	−0.950786	+	0.309847i	$0.899722\pi$
$608$	−17.2891	+	38.8760i	−0.701164	+	1.57663i
$609$	3.24396	+	0.0838548i	0.131452	+	0.00339797i
$610$	10.3879	−	31.4189i	0.420592	−	1.27211i
$611$	−1.11843	−	8.49530i	−0.0452467	−	0.343683i
$612$	16.0640	+	6.35704i	0.649347	+	0.256968i
$613$	−2.74075	+	20.8180i	−0.110698	+	0.840832i	0.842545	+	0.538626i	$0.181056\pi$
$613$	−2.74075	+	20.8180i	−0.110698	+	0.840832i	−0.953243	+	0.302206i	$0.902277\pi$
$614$	0.398670	−	2.09086i	0.0160890	−	0.0843802i
$615$	8.32353	−	8.32353i	0.335637	−	0.335637i
$616$	−1.43419	+	0.282256i	−0.0577854	+	0.0113724i
$617$	24.2795	+	24.2795i	0.977456	+	0.977456i	0.999751	−	0.0222958i	$-0.00709757\pi$
$617$	24.2795	+	24.2795i	0.977456	+	0.977456i	−0.0222958	+	0.999751i	$0.507098\pi$
$618$	−7.99233	+	5.43257i	−0.321499	+	0.218530i
$619$	−5.89248	−	0.775760i	−0.236839	−	0.0311804i	0.0111723	−	0.999938i	$-0.496444\pi$
$619$	−5.89248	−	0.775760i	−0.236839	−	0.0311804i	−0.248011	+	0.968757i	$0.579777\pi$
$620$	19.6008	+	18.9881i	0.787187	+	0.762580i
$621$	2.91558	−	0.383843i	0.116998	−	0.0154031i
$622$	19.2387	+	38.2439i	0.771402	+	1.53344i
$623$	0.138566	−	0.226289i	0.00555152	−	0.00906609i
$624$	5.24548	−	9.79071i	0.209987	−	0.391942i
$625$	−4.98648	+	2.87894i	−0.199459	+	0.115158i
$626$	4.04007	+	0.232607i	0.161474	+	0.00929686i
$627$	−0.529326	−	0.689832i	−0.0211393	−	0.0275492i
$628$	3.59737	−	6.46577i	0.143551	−	0.258012i
$629$	−31.1112	+	12.8867i	−1.24049	+	0.513826i
$630$	30.7403	−	19.7532i	1.22472	−	0.786987i
$631$	−2.39818	+	2.39818i	−0.0954700	+	0.0954700i	−0.753229	−	0.657759i	$-0.771505\pi$
$631$	−2.39818	+	2.39818i	−0.0954700	+	0.0954700i	0.657759	+	0.753229i	$0.271505\pi$
$632$	5.69615	−	12.2794i	0.226581	−	0.488450i
$633$	−10.2326	+	2.74182i	−0.406711	+	0.108978i
$634$	2.48213	+	7.12578i	0.0985781	+	0.283001i
$635$	−18.4072	−	14.1244i	−0.730469	−	0.560509i
$636$	8.56973	+	6.36220i	0.339812	+	0.252278i
$637$	−27.0536	+	18.6202i	−1.07190	+	0.737761i
$638$	−0.179699	+	0.543513i	−0.00711435	+	0.0215179i
$639$	−16.0930	+	9.29129i	−0.636629	+	0.367558i
$640$	−29.7744	+	29.1918i	−1.17694	+	1.15391i
$641$	5.60572	−	9.70939i	0.221413	−	0.383498i	−0.733825	−	0.679339i	$-0.762267\pi$
$641$	5.60572	−	9.70939i	0.221413	−	0.383498i	0.955237	+	0.295841i	$0.0955999\pi$
$642$	−5.27136	+	1.09211i	−0.208044	+	0.0431022i
$643$	1.05264	−	2.54130i	0.0415121	−	0.100219i	−0.901764	−	0.432230i	$-0.857727\pi$
$643$	1.05264	−	2.54130i	0.0415121	−	0.100219i	0.943276	+	0.332011i	$0.107727\pi$
$644$	4.60755	+	0.653378i	0.181563	+	0.0257467i
$645$	4.97688	−	2.06149i	0.195965	−	0.0811712i
$646$	−6.49473	+	34.0622i	−0.255532	+	1.34016i
$647$	−7.76092	−	28.9642i	−0.305113	−	1.13870i	−0.932848	−	0.360271i	$-0.882684\pi$
$647$	−7.76092	−	28.9642i	−0.305113	−	1.13870i	0.627734	−	0.778428i	$-0.283982\pi$
$648$	1.50532	+	16.8187i	0.0591344	+	0.660700i
$649$	1.60844	+	0.430979i	0.0631366	+	0.0169174i
$650$	4.17586	+	56.7988i	0.163791	+	2.22783i
$651$	−5.72632	−	0.904986i	−0.224432	−	0.0354692i
$652$	14.8400	+	24.7864i	0.581181	+	0.970711i
$653$	−1.26276	−	9.59163i	−0.0494157	−	0.375349i	−0.998228	−	0.0595084i	$-0.981047\pi$
$653$	−1.26276	−	9.59163i	−0.0494157	−	0.375349i	0.948812	−	0.315841i	$-0.102287\pi$
$654$	−0.337546	+	5.86271i	−0.0131991	+	0.229250i
$655$	37.4992	−	64.9505i	1.46522	−	2.53783i
$656$	0.685297	+	21.5746i	0.0267564	+	0.842348i
$657$	20.8564			0.813685
$658$	−2.91214	−	6.18186i	−0.113527	−	0.240994i
$659$	8.00070	−	19.3154i	0.311663	−	0.752421i	−0.687981	−	0.725729i	$-0.741503\pi$
$659$	8.00070	−	19.3154i	0.311663	−	0.752421i	0.999644	−	0.0266921i	$-0.00849737\pi$
$660$	−0.233593	−	0.819508i	−0.00909258	−	0.0318993i
$661$	−1.79532	+	13.6368i	−0.0698298	+	0.530410i	0.920401	+	0.390975i	$0.127862\pi$
$661$	−1.79532	+	13.6368i	−0.0698298	+	0.530410i	−0.990231	+	0.139435i	$0.955471\pi$
$662$	9.87699	−	20.4359i	0.383880	−	0.794265i
$663$	2.34295	−	8.74402i	0.0909928	−	0.339590i
$664$	3.35981	+	15.0131i	0.130386	+	0.582620i
$665$	50.5027	+	53.1829i	1.95841	+	2.06234i
$666$	−29.3037	−	25.2899i	−1.13549	−	0.979965i
$667$	1.10947	−	1.44590i	0.0429590	−	0.0559853i
$668$	8.84895	−	22.3609i	0.342376	−	0.865170i
$669$	0.793720	+	1.03440i	0.0306870	+	0.0399920i
$670$	−61.1496	+	12.6688i	−2.36241	+	0.489440i
$671$	−1.24012			−0.0478743
$672$	1.60766	−	8.71097i	0.0620166	−	0.336033i
$673$	28.1723			1.08596			0.542982	−	0.839744i	$-0.317295\pi$
$673$	28.1723			1.08596			0.542982	+	0.839744i	$0.317295\pi$
$674$	−35.9996	+	7.45832i	−1.38665	+	0.287284i
$675$	17.4722	+	22.7703i	0.672507	+	0.876428i
$676$	16.7603	+	6.63261i	0.644628	+	0.255100i
$677$	−5.06366	+	6.59909i	−0.194612	+	0.253624i	−0.880459	−	0.474122i	$-0.842765\pi$
$677$	−5.06366	+	6.59909i	−0.194612	+	0.253624i	0.685847	+	0.727746i	$0.259432\pi$
$678$	0.804964	+	0.694708i	0.0309145	+	0.0266801i
$679$	−7.05460	+	23.8454i	−0.270731	+	0.915101i
$680$	−18.2019	+	28.6977i	−0.698013	+	1.10051i
$681$	0.874306	−	3.26295i	0.0335035	−	0.125037i
$682$	0.445033	−	0.920794i	0.0170412	−	0.0352590i
$683$	2.02274	−	15.3642i	0.0773980	−	0.587896i	−0.908168	−	0.418606i	$-0.862519\pi$
$683$	2.02274	−	15.3642i	0.0773980	−	0.587896i	0.985566	−	0.169291i	$-0.0541477\pi$
$684$	−38.3319	+	10.9261i	−1.46566	+	0.417770i
$685$	30.8882	−	74.5707i	1.18018	−	2.84920i
$686$	−16.0304	+	20.7130i	−0.612043	+	0.790824i
$687$	−14.3298			−0.546716
$688$	−3.48861	+	9.24177i	−0.133002	+	0.352339i
$689$	−21.1522	+	36.6366i	−0.805833	+	1.39574i
$690$	−0.155943	+	2.70851i	−0.00593663	+	0.103111i
$691$	−1.59354	−	12.1041i	−0.0606211	−	0.460463i	−0.994653	−	0.103273i	$-0.967068\pi$
$691$	−1.59354	−	12.1041i	−0.0606211	−	0.460463i	0.934032	−	0.357189i	$-0.116265\pi$
$692$	−12.4733	+	7.46798i	−0.474164	+	0.283890i
$693$	−1.06447	−	0.861399i	−0.0404359	−	0.0327218i
$694$	−2.69477	−	36.6534i	−0.102292	−	1.39135i
$695$	67.4643	+	18.0770i	2.55907	+	0.685700i
$696$	−2.66194	−	2.22458i	−0.100900	−	0.0843225i
$697$	4.55319	+	16.9927i	0.172464	+	0.643646i
$698$	−2.85967	+	14.9978i	−0.108240	+	0.567675i
$699$	9.70505	−	4.01996i	0.367079	−	0.152049i
$700$	16.9621	+	42.1330i	0.641106	+	1.59248i
$701$	−10.0224	+	24.1963i	−0.378542	+	0.913881i	0.613698	+	0.789541i	$0.289681\pi$
$701$	−10.0224	+	24.1963i	−0.378542	+	0.913881i	−0.992240	+	0.124340i	$0.960319\pi$
$702$	21.7253	−	4.50100i	0.819968	−	0.169879i
$703$	38.8463	−	67.2837i	1.46512	−	2.53765i
$704$	1.38894	+	0.715996i	0.0523477	+	0.0269851i
$705$	3.45006	−	1.99189i	0.129937	−	0.0750189i
$706$	4.55999	−	13.7921i	0.171618	−	0.519071i
$707$	3.33084	+	1.48164i	0.125269	+	0.0557229i
$708$	−6.01521	+	8.10235i	−0.226066	+	0.304505i
$709$	−26.5977	−	20.4091i	−0.998898	−	0.766482i	−0.0264620	−	0.999650i	$-0.508424\pi$
$709$	−26.5977	−	20.4091i	−0.998898	−	0.766482i	−0.972436	+	0.233168i	$0.925091\pi$
$710$	−12.0241	−	34.5191i	−0.451256	−	1.29548i
$711$	12.2489	−	3.28207i	0.459368	−	0.123087i
$712$	−0.266363	+	0.0975515i	−0.00998238	+	0.00365590i
$713$	−2.30233	+	2.30233i	−0.0862228	+	0.0862228i
$714$	−0.343110	−	7.21117i	−0.0128406	−	0.269871i
$715$	3.12047	−	1.29254i	0.116699	−	0.0483383i
$716$	29.3894	+	16.3515i	1.09833	+	0.611083i
$717$	−4.56519	−	5.94948i	−0.170490	−	0.222187i
$718$	46.3659	+	2.66952i	1.73036	+	0.0996255i
$719$	22.7929	−	13.1595i	0.850031	−	0.490766i	−0.0106300	−	0.999943i	$-0.503384\pi$
$719$	22.7929	−	13.1595i	0.850031	−	0.490766i	0.860661	+	0.509178i	$0.170050\pi$
$720$	−38.8709	−	3.86658i	−1.44863	−	0.144099i
$721$	−26.0510	−	15.9520i	−0.970189	−	0.594084i
$722$	−23.8775	−	47.4652i	−0.888629	−	1.76647i
$723$	−5.09013	+	0.670129i	−0.189304	+	0.0249224i
$724$	2.22973	−	2.30167i	0.0828671	−	0.0855411i
$725$	17.6354	+	2.32174i	0.654961	+	0.0862273i
$726$	7.58818	−	5.15785i	0.281624	−	0.191426i
$727$	32.3640	+	32.3640i	1.20031	+	1.20031i	0.974071	+	0.226244i	$0.0726447\pi$
$727$	32.3640	+	32.3640i	1.20031	+	1.20031i	0.226244	+	0.974071i	$0.427355\pi$
$728$	35.0299	+	2.36736i	1.29830	+	0.0877403i
$729$	−6.98747	+	6.98747i	−0.258795	+	0.258795i
$730$	−7.68413	+	40.3001i	−0.284402	+	1.49157i
$731$	−1.05084	+	7.98192i	−0.0388667	+	0.295222i
$732$	2.76537	−	6.98798i	0.102211	−	0.258283i
$733$	5.72060	+	43.4522i	0.211295	+	1.60495i	0.687885	+	0.725820i	$0.258539\pi$
$733$	5.72060	+	43.4522i	0.211295	+	1.60495i	−0.476590	+	0.879126i	$0.658127\pi$
$734$	2.52854	−	7.64776i	0.0933300	−	0.282284i
$735$	−12.8115	−	8.30763i	−0.472558	−	0.306431i
$736$	−3.42606	−	3.60726i	−0.126286	−	0.132965i
$737$	1.17013	+	2.02673i	0.0431025	+	0.0746557i
$738$	−15.0971	+	13.4533i	−0.555731	+	0.495222i
$739$	15.5293	−	11.9160i	0.571253	−	0.438338i	−0.282313	−	0.959322i	$-0.591102\pi$
$739$	15.5293	−	11.9160i	0.571253	−	0.438338i	0.853566	+	0.520984i	$0.174435\pi$
$740$	59.6633	−	47.3049i	2.19327	−	1.73896i
$741$	7.99254	+	19.2957i	0.293613	+	0.708845i
$742$	−7.17327	+	32.9662i	−0.263339	+	1.21023i
$743$	6.32677	+	6.32677i	0.232107	+	0.232107i	0.813572	−	0.581465i	$-0.197520\pi$
$743$	6.32677	+	6.32677i	0.232107	+	0.232107i	−0.581465	+	0.813572i	$0.697520\pi$
$744$	4.19621	+	4.56102i	0.153840	+	0.167215i
$745$	−7.01380	−	26.1759i	−0.256966	−	0.959009i
$746$	−3.26158	−	1.57637i	−0.119415	−	0.0577149i
$747$	−8.77366	+	11.4341i	−0.321012	+	0.418350i
$748$	1.23522	+	0.310045i	0.0451643	+	0.0113364i
$749$	−10.0066	−	13.7632i	−0.365633	−	0.502896i
$750$	−9.87519	+	4.96775i	−0.360591	+	0.181396i
$751$	20.1360	+	34.8765i	0.734772	+	1.27266i	0.954823	+	0.297174i	$0.0960441\pi$
$751$	20.1360	+	34.8765i	0.734772	+	1.27266i	−0.220051	+	0.975488i	$0.570623\pi$
$752$	−1.66576	+	7.11280i	−0.0607441	+	0.259377i
$753$	−2.34345	−	1.35299i	−0.0853999	−	0.0493057i
$754$	7.54815	−	11.4931i	0.274887	−	0.418553i
$755$	−72.2070	−	29.9091i	−2.62788	−	1.08850i
$756$	15.4107	−	8.69373i	0.560481	−	0.316188i
$757$	−12.9976	−	31.3791i	−0.472408	−	1.14049i	−0.963096	−	0.269158i	$-0.913255\pi$
$757$	−12.9976	−	31.3791i	−0.472408	−	1.14049i	0.490688	−	0.871335i	$-0.336745\pi$
$758$	−22.8202	+	15.5114i	−0.828865	+	0.563398i
$759$	0.0982064	−	0.0263143i	0.00356466	−	0.000955149i
$760$	−6.98953	−	78.0929i	−0.253537	−	2.83273i
$761$	−1.20598	+	4.50078i	−0.0437167	+	0.163153i	−0.984333	−	0.176318i	$-0.943581\pi$
$761$	−1.20598	+	4.50078i	−0.0437167	+	0.163153i	0.940617	+	0.339471i	$0.110248\pi$
$762$	−3.98908	−	3.44270i	−0.144509	−	0.124716i
$763$	−17.3273	+	6.65802i	−0.627291	+	0.241036i
$764$	−9.69796	+	13.0629i	−0.350860	+	0.472600i
$765$	−31.5637	+	4.15544i	−1.14119	+	0.150240i
$766$	−19.6335	+	17.4958i	−0.709389	+	0.632150i
$767$	−34.6385	−	19.9986i	−1.25072	−	0.722106i
$768$	−7.13181	+	6.22995i	−0.257347	+	0.224804i
$769$			17.4876i			0.630619i	0.948989	+	0.315310i	$0.102108\pi$
$769$			17.4876i			0.630619i	−0.948989	+	0.315310i	$0.897892\pi$
$770$	2.05664	−	1.73947i	0.0741160	−	0.0626863i
$771$	0.0280843	+	0.0116329i	0.00101143	+	0.000418949i
$772$	−0.733146	+	6.34577i	−0.0263865	+	0.228389i
$773$	−28.5620	−	3.76026i	−1.02730	−	0.135247i	−0.402008	−	0.915636i	$-0.631688\pi$
$773$	−28.5620	−	3.76026i	−1.02730	−	0.135247i	−0.625294	+	0.780389i	$0.715021\pi$
$774$	−8.73911	+	3.04411i	−0.314121	+	0.109418i
$775$	−30.6953	−	8.22477i	−1.10261	−	0.295442i
$776$	21.7458	−	15.2914i	0.780629	−	0.548930i
$777$	−4.58879	+	15.5106i	−0.164622	+	0.556441i
$778$	5.08104	−	0.373560i	0.182164	−	0.0133928i
$779$	−32.2006	−	24.7084i	−1.15371	−	0.885270i
$780$	0.324957	+	20.4659i	0.0116353	+	0.732795i
$781$	−1.08678	+	0.833914i	−0.0388880	+	0.0298398i
$782$	−3.38904	−	2.22577i	−0.121192	−	0.0795935i
$783$		−	6.92943i		−	0.247638i
$784$	27.1850	−	6.70639i	0.970893	−	0.239514i
$785$			13.6350i			0.486654i
$786$	9.35003	−	14.2367i	0.333505	−	0.507806i
$787$	−32.1084	+	24.6377i	−1.14454	+	0.878237i	−0.993893	−	0.110350i	$-0.964803\pi$
$787$	−32.1084	+	24.6377i	−1.14454	+	0.878237i	−0.150649	+	0.988587i	$0.548136\pi$
$788$	34.2977	−	35.4044i	1.22180	−	1.26123i
$789$	−0.806460	−	0.618819i	−0.0287107	−	0.0220305i
$790$	1.82898	+	24.8773i	0.0650723	+	0.885095i
$791$	−0.953496	+	3.22293i	−0.0339024	+	0.114594i
$792$	0.319699	+	1.42855i	0.0113600	+	0.0507615i
$793$	28.7724	+	7.70955i	1.02174	+	0.273774i
$794$	−6.55689	−	18.8237i	−0.232695	−	0.668029i
$795$	−19.5002	−	2.56725i	−0.691600	−	0.0910509i
$796$	17.9779	+	22.6746i	0.637208	+	0.803678i
$797$	30.2358	+	12.5241i	1.07101	+	0.443625i	0.847345	−	0.531042i	$-0.178199\pi$
$797$	30.2358	+	12.5241i	1.07101	+	0.443625i	0.223660	+	0.974667i	$0.428199\pi$
$798$	10.7562	+	12.7174i	0.380765	+	0.450190i
$799$			5.95378i			0.210629i
$800$	13.7708	−	46.5614i	0.486870	−	1.64619i
$801$	−0.230138	−	0.132870i	−0.00813153	−	0.00469474i
$802$	10.8289	+	12.1520i	0.382380	+	0.429101i
$803$	1.52432	−	0.200680i	0.0537920	−	0.00708185i
$804$	−14.0298	+	2.07416i	−0.494792	+	0.0731498i
$805$	−8.00504	+	3.07593i	−0.282140	+	0.108412i
$806$	−16.0497	+	18.5970i	−0.565327	+	0.655050i
$807$	−0.336991	+	1.25767i	−0.0118626	+	0.0442720i
$808$	−1.80644	−	3.45327i	−0.0635503	−	0.121486i
$809$	−21.7114	+	5.81756i	−0.763333	+	0.204535i	−0.619424	−	0.785056i	$-0.712634\pi$
$809$	−21.7114	+	5.81756i	−0.763333	+	0.204535i	−0.143909	+	0.989591i	$0.545967\pi$
$810$	−17.4926	−	25.7348i	−0.614626	−	0.904230i
$811$	0.866622	+	2.09221i	0.0304312	+	0.0734675i	0.938365	−	0.345647i	$-0.112341\pi$
$811$	0.866622	+	2.09221i	0.0304312	+	0.0734675i	−0.907933	+	0.419115i	$0.862341\pi$
$812$	2.94355	−	10.5632i	0.103298	−	0.370696i
$813$	2.51800	+	1.04299i	0.0883100	+	0.0365792i
$814$	−2.38504	−	1.56639i	−0.0835956	−	0.0549020i
$815$	−46.1044	−	26.6184i	−1.61497	−	0.932402i
$816$	−4.50153	+	6.26901i	−0.157585	+	0.219459i
$817$	−9.28724	−	16.0860i	−0.324919	−	0.562777i
$818$	−6.89662	−	13.7095i	−0.241135	−	0.479342i
$819$	19.3420	+	26.6031i	0.675864	+	0.929589i
$820$	−20.4331	−	34.1282i	−0.713555	−	1.19181i
$821$	−26.6553	+	34.7378i	−0.930276	+	1.21236i	0.0466784	+	0.998910i	$0.485136\pi$
$821$	−26.6553	+	34.7378i	−0.930276	+	1.21236i	−0.976954	+	0.213449i	$0.931530\pi$
$822$	7.97670	−	16.5041i	0.278219	−	0.575648i
$823$	9.34890	+	34.8906i	0.325882	+	1.21621i	0.913422	+	0.407014i	$0.133430\pi$
$823$	9.34890	+	34.8906i	0.325882	+	1.21621i	−0.587540	+	0.809195i	$0.699903\pi$
$824$	11.2304	+	30.6643i	0.391228	+	1.06824i
$825$	0.701660	+	0.701660i	0.0244287	+	0.0244287i
$826$	−31.1683	−	6.78205i	−1.08448	−	0.235978i
$827$	8.76859	+	21.1692i	0.304914	+	0.736127i	0.999854	+	0.0170597i	$0.00543055\pi$
$827$	8.76859	+	21.1692i	0.304914	+	0.736127i	−0.694941	+	0.719067i	$0.744569\pi$
$828$	0.534895	−	4.62981i	0.0185889	−	0.160897i
$829$	34.7510	−	26.6654i	1.20695	−	0.926126i	0.208301	−	0.978065i	$-0.433207\pi$
$829$	34.7510	−	26.6654i	1.20695	−	0.926126i	0.998650	+	0.0519385i	$0.0165400\pi$
$830$	−18.8612	−	21.1657i	−0.654681	−	0.734673i
$831$	−1.56411	−	2.70912i	−0.0542585	−	0.0939785i
$832$	−27.7741	−	25.2468i	−0.962893	−	0.875275i
$833$	20.3258	−	10.3737i	0.704246	−	0.359428i
$834$	15.0602	+	4.97927i	0.521491	+	0.172418i
$835$	5.78434	+	43.9364i	0.200175	+	1.52048i
$836$	−2.69641	+	1.16738i	−0.0932572	+	0.0403747i
$837$	−1.61587	+	12.2738i	−0.0558527	+	0.424243i
$838$	−4.16949	−	0.795009i	−0.144033	−	0.0274631i
$839$	37.8886	−	37.8886i	1.30806	−	1.30806i	0.385248	−	0.922813i	$-0.374116\pi$
$839$	37.8886	−	37.8886i	1.30806	−	1.30806i	0.922813	−	0.385248i	$-0.125884\pi$
$840$	5.21566	+	15.4679i	0.179957	+	0.533692i
$841$	17.4694	+	17.4694i	0.602394	+	0.602394i
$842$	16.0068	+	23.5490i	0.551631	+	0.811554i
$843$	−5.40698	−	0.711842i	−0.186226	−	0.0245172i
$844$	0.568328	+	35.7934i	0.0195627	+	1.23206i
$845$	−32.9320	+	4.33558i	−1.13289	+	0.149148i
$846$	−6.11367	+	3.07550i	−0.210192	+	0.105738i
$847$	24.7336	+	15.1454i	0.849858	+	0.520401i
$848$	27.9024	−	22.8536i	0.958172	−	0.784794i
$849$	6.27254	−	3.62145i	0.215273	−	0.124288i
$850$	2.27461	−	39.5069i	0.0780186	−	1.35508i
$851$	5.53027	+	7.20718i	0.189575	+	0.247059i
$852$	−2.27561	−	7.98346i	−0.0779609	−	0.273509i
$853$	−18.0841	+	7.49066i	−0.619186	+	0.256475i	−0.670151	−	0.742225i	$-0.733770\pi$
$853$	−18.0841	+	7.49066i	−0.619186	+	0.256475i	0.0509644	+	0.998700i	$0.483770\pi$
$854$	23.7285	−	1.12901i	0.811974	−	0.0386340i
$855$	51.9376	−	51.9376i	1.77623	−	1.77623i
$856$	−0.757172	+	18.1755i	−0.0258796	+	0.621226i
$857$	22.2379	−	5.95862i	0.759631	−	0.203543i	0.141845	−	0.989889i	$-0.454696\pi$
$857$	22.2379	−	5.95862i	0.759631	−	0.203543i	0.617786	+	0.786346i	$0.288030\pi$
$858$	0.724375	−	0.252323i	0.0247298	−	0.00861415i
$859$	0.714878	+	0.548545i	0.0243913	+	0.0187161i	0.620885	−	0.783902i	$-0.286773\pi$
$859$	0.714878	+	0.548545i	0.0243913	+	0.0187161i	−0.596494	+	0.802618i	$0.703440\pi$
$860$	−2.66227	−	18.0078i	−0.0907826	−	0.614062i
$861$	7.72080	+	3.43441i	0.263124	+	0.117044i
$862$	−1.10169	−	0.364245i	−0.0375236	−	0.0124062i
$863$	26.9099	−	15.5365i	0.916024	−	0.528867i	0.0336599	−	0.999433i	$-0.489284\pi$
$863$	26.9099	−	15.5365i	0.916024	−	0.528867i	0.882365	+	0.470566i	$0.155950\pi$
$864$	−18.6838	−	2.95115i	−0.635636	−	0.100400i
$865$	13.3952	−	23.2012i	0.455451	−	0.788865i
$866$	5.50525	+	26.5726i	0.187076	+	0.902973i
$867$	1.44331	−	3.48446i	0.0490174	−	0.118339i
$868$	−7.67700	+	18.0237i	−0.260574	+	0.611764i
$869$	0.863646	−	0.357734i	0.0292972	−	0.0121353i
$870$	6.27967	+	1.19736i	0.212901	+	0.0405944i
$871$	−14.5489	−	54.2973i	−0.492972	−	1.83979i
$872$	18.9376	+	5.92941i	0.641306	+	0.200795i
$873$	24.0556	+	6.44568i	0.814159	+	0.218153i
$874$	9.32940	−	0.685899i	0.315572	−	0.0232009i
$875$	−27.1626	−	21.9807i	−0.918262	−	0.743083i
$876$	−2.26829	+	9.03691i	−0.0766385	+	0.305329i
$877$	−4.47664	−	34.0035i	−0.151165	−	1.14822i	−0.883892	−	0.467692i	$-0.845086\pi$
$877$	−4.47664	−	34.0035i	−0.151165	−	1.14822i	0.732726	−	0.680524i	$-0.238248\pi$
$878$	−43.8104	−	2.52238i	−1.47853	−	0.0851263i
$879$	−7.49211	+	12.9767i	−0.252702	+	0.437694i
$880$	−2.87814	+	0.0914212i	−0.0970219	+	0.00308181i
$881$	−8.67844			−0.292384			−0.146192	−	0.989256i	$-0.546702\pi$
$881$	−8.67844			−0.292384			−0.146192	+	0.989256i	$0.546702\pi$
$882$	21.1519	+	15.5130i	0.712220	+	0.522348i
$883$	−3.72606	+	8.99549i	−0.125392	+	0.302722i	−0.974092	−	0.226151i	$-0.927386\pi$
$883$	−3.72606	+	8.99549i	−0.125392	+	0.302722i	0.848700	+	0.528874i	$0.177386\pi$
$884$	−26.7313	−	14.8726i	−0.899072	−	0.500219i
$885$	2.42723	−	18.4367i	0.0815906	−	0.619742i
$886$	8.46459	+	4.09106i	0.284373	+	0.137442i
$887$	5.31881	−	19.8501i	0.178588	−	0.666501i	−0.817324	−	0.576178i	$-0.804544\pi$
$887$	5.31881	−	19.8501i	0.178588	−	0.666501i	0.995913	−	0.0903226i	$-0.0287898\pi$
$888$	14.1449	−	9.94657i	0.474673	−	0.333785i
$889$	4.72515	−	15.9715i	0.158476	−	0.535668i
$890$	0.341531	−	0.395735i	0.0114481	−	0.0132651i
$891$	−0.709892	+	0.925149i	−0.0237823	+	0.0309937i
$892$	4.04324	−	1.75047i	0.135378	−	0.0586102i
$893$	−8.36214	−	10.8977i	−0.279828	−	0.364679i
$894$	−1.24854	−	6.02639i	−0.0417573	−	0.201553i
$895$	−61.9765			−2.07164
$896$	−27.2279	−	12.4354i	−0.909621	−	0.415438i
$897$	−2.44211			−0.0815396
$898$	−6.27864	−	30.3055i	−0.209521	−	1.01131i
$899$	4.67058	+	6.08682i	0.155773	+	0.203007i
$900$	41.7429	−	18.0721i	1.39143	−	0.602404i
$901$	17.8943	−	23.3203i	0.596145	−	0.776911i
$902$	−0.973943	+	1.12852i	−0.0324288	+	0.0375755i
$903$	2.66289	+	2.80421i	0.0886153	+	0.0933182i
$904$	2.93915	−	2.06678i	0.0977547	−	0.0687401i
$905$	−1.52842	+	5.70414i	−0.0508064	+	0.189612i
$906$	−15.9810	−	7.72386i	−0.530934	−	0.256608i
$907$	1.82736	−	13.8802i	0.0606765	−	0.460884i	−0.933954	−	0.357393i	$-0.883666\pi$
$907$	1.82736	−	13.8802i	0.0606765	−	0.460884i	0.994630	−	0.103491i	$-0.0330011\pi$
$908$	−9.97517	−	5.54991i	−0.331038	−	0.184180i
$909$	1.39716	−	3.37305i	0.0463410	−	0.111877i
$910$	−58.5306	+	27.5725i	−1.94027	+	0.914018i
$911$	−29.8181			−0.987917			−0.493958	−	0.869486i	$-0.664450\pi$
$911$	−29.8181			−0.987917			−0.493958	+	0.869486i	$0.664450\pi$
$912$	−0.565311	−	17.7972i	−0.0187193	−	0.589324i
$913$	−0.531217	+	0.920094i	−0.0175807	+	0.0304507i
$914$	27.5343	+	1.58529i	0.910755	+	0.0524367i
$915$	1.80766	+	13.7305i	0.0597593	+	0.453917i
$916$	−11.7887	+	46.9664i	−0.389510	+	1.55181i
$917$	53.1790	+	8.40439i	1.75612	+	0.277538i
$918$	−15.3746	+	1.13034i	−0.507437	+	0.0373069i
$919$	−17.5490	−	4.70223i	−0.578887	−	0.155112i	−0.0425176	−	0.999096i	$-0.513538\pi$
$919$	−17.5490	−	4.70223i	−0.578887	−	0.155112i	−0.536369	+	0.843983i	$0.680205\pi$
$920$	8.74895	+	2.73932i	0.288444	+	0.0903128i
$921$	0.230556	+	0.860446i	0.00759708	+	0.0283527i
$922$	18.1775	+	3.46595i	0.598642	+	0.114145i
$923$	30.3989	−	12.5916i	1.00059	−	0.414459i
$924$	0.489006	−	0.367543i	0.0160871	−	0.0120913i
$925$	−33.9300	+	81.9143i	−1.11561	+	2.69333i
$926$	−10.7599	−	51.9353i	−0.353591	−	1.70670i
$927$	−15.2963	+	26.4940i	−0.502398	+	0.870178i
$928$	−9.48103	+	6.89448i	−0.311230	+	0.226323i
$929$	−44.1260	+	25.4762i	−1.44773	+	0.835846i	−0.998346	−	0.0574938i	$-0.981689\pi$
$929$	−44.1260	+	25.4762i	−1.44773	+	0.835846i	−0.449382	+	0.893340i	$0.648356\pi$
$930$	−10.8437	−	3.58518i	−0.355578	−	0.117563i
$931$	−22.6342	+	47.5357i	−0.741805	+	1.55792i
$932$	−5.19149	−	35.1157i	−0.170053	−	1.15025i
$933$	−14.2140	−	10.9068i	−0.465345	−	0.357072i
$934$	−25.2048	+	8.77962i	−0.824726	+	0.287278i
$935$	−2.26689	+	0.607412i	−0.0741354	+	0.0198645i
$936$	1.46355	−	35.1318i	0.0478378	−	1.14832i
$937$	−21.8870	+	21.8870i	−0.715016	+	0.715016i	−0.967580	−	0.252564i	$-0.918726\pi$
$937$	−21.8870	+	21.8870i	−0.715016	+	0.715016i	0.252564	+	0.967580i	$0.418726\pi$
$938$	−24.2346	−	37.7143i	−0.791287	−	1.23142i
$939$	−1.56467	+	0.648109i	−0.0510612	+	0.0211503i
$940$	−3.69022	−	12.9463i	−0.120362	−	0.422263i
$941$	−15.5346	−	20.2450i	−0.506412	−	0.659969i	0.468265	−	0.883588i	$-0.344879\pi$
$941$	−15.5346	−	20.2450i	−0.506412	−	0.659969i	−0.974677	+	0.223619i	$0.928213\pi$
$942$	−0.177991	+	3.09146i	−0.00579925	+	0.100725i
$943$	4.11005	−	2.37294i	0.133842	−	0.0772735i
$944$	21.6072	+	26.3806i	0.703253	+	0.858617i
$945$	−17.0271	+	27.8068i	−0.553893	+	0.904554i
$946$	−0.609420	+	0.306571i	−0.0198139	+	0.00996747i
$947$	15.5424	−	2.04619i	0.505060	−	0.0664924i	0.126309	−	0.991991i	$-0.459687\pi$
$947$	15.5424	−	2.04619i	0.505060	−	0.0664924i	0.378751	+	0.925499i	$0.376354\pi$
$948$	0.0899376	+	5.66429i	0.00292104	+	0.183968i
$949$	−36.6138	−	4.82029i	−1.18853	−	0.156473i
$950$	51.3245	+	75.5079i	1.66519	+	2.44980i
$951$	−2.23299	−	2.23299i	−0.0724095	−	0.0724095i
$952$	−23.9171	−	4.80787i	−0.775158	−	0.155824i
$953$	35.1047	−	35.1047i	1.13715	−	1.13715i	0.148196	−	0.988958i	$-0.452653\pi$
$953$	35.1047	−	35.1047i	1.13715	−	1.13715i	0.988958	−	0.148196i	$-0.0473467\pi$
$954$	33.1901	+	6.32844i	1.07457	+	0.204891i
$955$	3.91328	−	29.7243i	0.126631	−	0.961856i
$956$	−23.2553	+	10.0681i	−0.752129	+	0.325626i
$957$	−0.0312705	−	0.237523i	−0.00101083	−	0.00767804i
$958$	−24.8901	−	8.22929i	−0.804163	−	0.265876i
$959$	57.9232	+	1.49729i	1.87044	+	0.0483499i
$960$	5.90287	−	16.4219i	0.190514	−	0.530015i
$961$	8.64661	+	14.9764i	0.278923	+	0.483109i
$962$	45.5982	+	51.1696i	1.47014	+	1.64977i
$963$	−13.5202	+	10.3744i	−0.435682	+	0.334311i
$964$	−1.99114	+	17.2344i	−0.0641303	+	0.555082i
$965$	−4.50482	−	10.8756i	−0.145015	−	0.350098i
$966$	−1.85513	+	0.592907i	−0.0596878	+	0.0190765i
$967$	4.13197	+	4.13197i	0.132875	+	0.132875i	0.770416	−	0.637541i	$-0.220048\pi$
$967$	4.13197	+	4.13197i	0.132875	+	0.132875i	−0.637541	+	0.770416i	$0.720048\pi$
$968$	−10.6625	−	29.1137i	−0.342705	−	0.935750i
$969$	−3.75599	−	14.0175i	−0.120660	−	0.450308i
$970$	−21.3176	+	44.1071i	−0.684467	+	1.41619i
$971$	23.8366	−	31.0644i	0.764952	−	0.996905i	−0.234739	−	0.972058i	$-0.575424\pi$
$971$	23.8366	−	31.0644i	0.764952	−	0.996905i	0.999691	−	0.0248466i	$-0.00790973\pi$
$972$	−13.9361	−	23.2767i	−0.447002	−	0.746600i
$973$	5.25771	+	49.8625i	0.168554	+	1.59852i
$974$	−3.58560	−	7.12767i	−0.114890	−	0.228385i
$975$	−11.9174	−	20.6415i	−0.381661	−	0.661057i
$976$	−20.6283	−	14.8124i	−0.660297	−	0.474134i
$977$	26.3775	+	15.2291i	0.843892	+	0.487221i	0.858585	−	0.512671i	$-0.171344\pi$
$977$	26.3775	+	15.2291i	0.843892	+	0.487221i	−0.0146935	+	0.999892i	$0.504677\pi$
$978$	−10.1057	−	6.63701i	−0.323146	−	0.212228i
$979$	−0.0180984	−	0.00749662i	−0.000578429	−	0.000239593i
$980$	−37.7682	+	35.1556i	−1.20646	+	1.12300i
$981$	7.11417	+	17.1751i	0.227138	+	0.548359i
$982$	−23.4713	−	34.5307i	−0.748999	−	1.10192i
$983$	−32.2311	+	8.63630i	−1.02801	+	0.275455i	−0.733138	−	0.680080i	$-0.761945\pi$
$983$	−32.2311	+	8.63630i	−1.02801	+	0.275455i	−0.294875	+	0.955536i	$0.595278\pi$
$984$	−4.18728	−	8.00459i	−0.133486	−	0.255177i
$985$	−23.5102	+	87.7413i	−0.749097	+	2.79567i
$986$	−6.24221	+	7.23291i	−0.198793	+	0.230343i
$987$	2.22311	+	1.79900i	0.0707624	+	0.0572628i
$988$	69.8175	−	10.3218i	2.22119	−	0.328380i
$989$	2.15330	−	0.283487i	0.0684710	−	0.00901438i
$990$	−1.79472	−	2.01401i	−0.0570399	−	0.0640093i
$991$	−14.8667	−	8.58331i	−0.472257	−	0.272658i	0.244927	−	0.969542i	$-0.421236\pi$
$991$	−14.8667	−	8.58331i	−0.472257	−	0.272658i	−0.717184	+	0.696884i	$0.754569\pi$
$992$	18.4010	−	10.0010i	0.584233	−	0.317532i
$993$			9.49907i			0.301444i
$994$	20.0353	−	16.9456i	0.635480	−	0.537481i
$995$	−49.2652	−	20.4063i	−1.56181	−	0.646924i
$996$	−4.00008	−	5.04510i	−0.126747	−	0.159860i
$997$	11.9613	+	1.57473i	0.378817	+	0.0498723i	0.317531	−	0.948248i	$-0.397146\pi$
$997$	11.9613	+	1.57473i	0.378817	+	0.0498723i	0.0612866	+	0.998120i	$0.480480\pi$
$998$	−5.26054	−	15.1021i	−0.166519	−	0.478049i
$999$	33.3634	+	8.93969i	1.05557	+	0.282839i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	224.2.be.a.115.17	yes	240
4.3	odd	2		896.2.bi.a.367.18		240
7.5	odd	6	inner	224.2.be.a.19.24	✓	240
28.19	even	6		896.2.bi.a.495.18		240
32.5	even	8		896.2.bi.a.143.18		240
32.27	odd	8	inner	224.2.be.a.59.24	yes	240
224.5	odd	24		896.2.bi.a.271.18		240
224.187	even	24	inner	224.2.be.a.187.17	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.2.be.a.19.24	✓	240	7.5	odd	6	inner
224.2.be.a.59.24	yes	240	32.27	odd	8	inner
224.2.be.a.115.17	yes	240	1.1	even	1	trivial
224.2.be.a.187.17	yes	240	224.187	even	24	inner
896.2.bi.a.143.18		240	32.5	even	8
896.2.bi.a.271.18		240	224.5	odd	24
896.2.bi.a.367.18		240	4.3	odd	2
896.2.bi.a.495.18		240	28.19	even	6

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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	224.2.be.a.115.17

Level	$224$
Weight	$2$
Character	224.115
Analytic conductor	$1.789$
Analytic rank	$0$
Dimension	$240$
Inner twists	$4$