LMFDB - Embedded newform 273.2.bf.b.185.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(152,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5, 4]))

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

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

chi := DirichletCharacter("273.152");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.bf (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			185.20
Character	$\chi$	$=$	273.185
Dual form			273.2.bf.b.152.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.730177 + 0.421568i) q^{2} +(1.64300 - 0.548211i) q^{3} +(-0.644561 - 1.11641i) q^{4} +(1.06280 + 1.84082i) q^{5} +(1.43079 + 0.292347i) q^{6} +(-0.110845 - 2.64343i) q^{7} -2.77318i q^{8} +(2.39893 - 1.80143i) q^{9} +1.79216i q^{10} +0.987856i q^{11} +(-1.67105 - 1.48092i) q^{12} +(-3.08300 + 1.86952i) q^{13} +(1.03345 - 1.97690i) q^{14} +(2.75534 + 2.44184i) q^{15} +(-0.120042 + 0.207918i) q^{16} +(0.920525 + 1.59440i) q^{17} +(2.51107 - 0.304049i) q^{18} +7.15770i q^{19} +(1.37008 - 2.37304i) q^{20} +(-1.63128 - 4.28240i) q^{21} +(-0.416448 + 0.721310i) q^{22} +(1.40903 + 0.813502i) q^{23} +(-1.52029 - 4.55634i) q^{24} +(0.240923 - 0.417291i) q^{25} +(-3.03926 + 0.0653890i) q^{26} +(2.95389 - 4.27487i) q^{27} +(-2.87971 + 1.82760i) q^{28} +(-0.488355 + 0.281952i) q^{29} +(0.982484 + 2.94453i) q^{30} +(-4.23375 - 2.44435i) q^{31} +(-4.97858 + 2.87439i) q^{32} +(0.541554 + 1.62305i) q^{33} +1.55226i q^{34} +(4.74827 - 3.01347i) q^{35} +(-3.55739 - 1.51707i) q^{36} +(-1.64578 + 2.85058i) q^{37} +(-3.01745 + 5.22638i) q^{38} +(-4.04049 + 4.76177i) q^{39} +(5.10491 - 2.94732i) q^{40} +(-4.93559 - 8.54870i) q^{41} +(0.614202 - 3.81460i) q^{42} +(-0.214038 + 0.370726i) q^{43} +(1.10286 - 0.636734i) q^{44} +(5.86568 + 2.50144i) q^{45} +(0.685893 + 1.18800i) q^{46} +(6.40449 + 11.0929i) q^{47} +(-0.0832459 + 0.407419i) q^{48} +(-6.97543 + 0.586021i) q^{49} +(0.351833 - 0.203131i) q^{50} +(2.38649 + 2.11496i) q^{51} +(4.07434 + 2.23688i) q^{52} +(-6.59657 - 3.80853i) q^{53} +(3.95901 - 1.87615i) q^{54} +(-1.81847 + 1.04989i) q^{55} +(-7.33069 + 0.307392i) q^{56} +(3.92393 + 11.7601i) q^{57} -0.475447 q^{58} +(5.96320 + 10.3286i) q^{59} +(0.950114 - 4.65001i) q^{60} -2.21713i q^{61} +(-2.06092 - 3.56962i) q^{62} +(-5.02785 - 6.14172i) q^{63} -4.36683 q^{64} +(-6.71806 - 3.68832i) q^{65} +(-0.288797 + 1.41342i) q^{66} -2.45385 q^{67} +(1.18667 - 2.05537i) q^{68} +(2.76101 + 0.564144i) q^{69} +(4.73746 - 0.198652i) q^{70} +(-2.48976 - 1.43746i) q^{71} +(-4.99567 - 6.65265i) q^{72} +(-8.31343 - 4.79976i) q^{73} +(-2.40342 + 1.38762i) q^{74} +(0.167074 - 0.817688i) q^{75} +(7.99095 - 4.61358i) q^{76} +(2.61133 - 0.109499i) q^{77} +(-4.95768 + 1.77359i) q^{78} +(-7.27556 - 12.6016i) q^{79} -0.510320 q^{80} +(2.50972 - 8.64299i) q^{81} -8.32274i q^{82} +14.4620 q^{83} +(-3.72947 + 4.58145i) q^{84} +(-1.95666 + 3.38904i) q^{85} +(-0.312572 + 0.180463i) q^{86} +(-0.647800 + 0.730969i) q^{87} +2.73950 q^{88} +(2.59362 - 4.49228i) q^{89} +(3.22845 + 4.29927i) q^{90} +(5.28368 + 7.94246i) q^{91} -2.09741i q^{92} +(-8.29609 - 1.69510i) q^{93} +10.7997i q^{94} +(-13.1760 + 7.60718i) q^{95} +(-6.60407 + 7.45195i) q^{96} +(0.172790 + 0.0997601i) q^{97} +(-5.34034 - 2.51272i) q^{98} +(1.77955 + 2.36980i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 32 q^{4} - 12 q^{6} - 4 q^{7} + 8 q^{9} + 6 q^{12} - 12 q^{13} - 9 q^{15} - 16 q^{16} + 2 q^{18} + 10 q^{21} + 10 q^{22} - 24 q^{25} - 50 q^{28} - 16 q^{30} - 24 q^{31} - 33 q^{39} + 90 q^{40} - 48 q^{42}+ \cdots + 22 q^{99}+O(q^{100}) $ 64 * q + 32 * q^4 - 12 * q^6 - 4 * q^7 + 8 * q^9 + 6 * q^12 - 12 * q^13 - 9 * q^15 - 16 * q^16 + 2 * q^18 + 10 * q^21 + 10 * q^22 - 24 * q^25 - 50 * q^28 - 16 * q^30 - 24 * q^31 - 33 * q^39 + 90 * q^40 - 48 * q^42 - 20 * q^43 - 3 * q^45 + 6 * q^48 - 10 * q^51 + 30 * q^52 - 27 * q^54 + 18 * q^55 + 4 * q^57 - 60 * q^58 + 55 * q^60 - 74 * q^63 - 84 * q^64 + 75 * q^66 - 88 * q^67 - 33 * q^69 + 20 * q^70 - 34 * q^72 + 84 * q^73 + 33 * q^75 + 18 * q^76 - 71 * q^78 + 20 * q^79 - 32 * q^81 - 6 * q^84 - 2 * q^85 + 3 * q^87 + 92 * q^88 - 76 * q^91 + 28 * q^93 + 30 * q^96 + 24 * q^97 + 22 * q^99

Character values

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

$n$	$92$	$106$	$157$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.730177	+	0.421568i	0.516313	+	0.298093i	0.735425	−	0.677606i	$-0.236983\pi$
$2$	0.730177	+	0.421568i	0.516313	+	0.298093i	−0.219112	+	0.975700i	$0.570316\pi$
$3$	1.64300	−	0.548211i	0.948589	−	0.316510i
$3$	1.64300	−	0.548211i	0.948589	−	0.316510i
$4$	−0.644561	−	1.11641i	−0.322281	−	0.558207i
$5$	1.06280	+	1.84082i	0.475297	+	0.823239i	0.999600	−	0.0282929i	$-0.00900711\pi$
$5$	1.06280	+	1.84082i	0.475297	+	0.823239i	−0.524302	+	0.851532i	$0.675674\pi$
$6$	1.43079	+	0.292347i	0.584118	+	0.119350i
$7$	−0.110845	−	2.64343i	−0.0418954	−	0.999122i
$7$	−0.110845	−	2.64343i	−0.0418954	−	0.999122i
$8$		−	2.77318i		−	0.980466i
$9$	2.39893	−	1.80143i	0.799643	−	0.600476i
$10$			1.79216i			0.566732i
$11$			0.987856i			0.297850i	0.988849	+	0.148925i	$0.0475813\pi$
$11$			0.987856i			0.297850i	−0.988849	+	0.148925i	$0.952419\pi$
$12$	−1.67105	−	1.48092i	−0.482390	−	0.427504i
$13$	−3.08300	+	1.86952i	−0.855070	+	0.518512i
$13$	−3.08300	+	1.86952i	−0.855070	+	0.518512i
$14$	1.03345	−	1.97690i	0.276200	−	0.528348i
$15$	2.75534	+	2.44184i	0.711425	+	0.630480i
$16$	−0.120042	+	0.207918i	−0.0300104	+	0.0519796i
$17$	0.920525	+	1.59440i	0.223260	+	0.386698i	0.955796	−	0.294030i	$-0.0949967\pi$
$17$	0.920525	+	1.59440i	0.223260	+	0.386698i	−0.732536	+	0.680728i	$0.761663\pi$
$18$	2.51107	−	0.304049i	0.591864	−	0.0716650i
$19$			7.15770i			1.64209i	0.570864	+	0.821044i	$0.306608\pi$
$19$			7.15770i			1.64209i	−0.570864	+	0.821044i	$0.693392\pi$
$20$	1.37008	−	2.37304i	0.306358	−	0.530628i
$21$	−1.63128	−	4.28240i	−0.355974	−	0.934496i
$22$	−0.416448	+	0.721310i	−0.0887871	+	0.153784i
$23$	1.40903	+	0.813502i	0.293803	+	0.169627i	0.639655	−	0.768662i	$-0.279077\pi$
$23$	1.40903	+	0.813502i	0.293803	+	0.169627i	−0.345853	+	0.938289i	$0.612410\pi$
$24$	−1.52029	−	4.55634i	−0.310327	−	0.930059i
$25$	0.240923	−	0.417291i	0.0481846	−	0.0834582i
$26$	−3.03926	+	0.0653890i	−0.596049	+	0.0128238i
$27$	2.95389	−	4.27487i	0.568476	−	0.822700i
$28$	−2.87971	+	1.82760i	−0.544214	+	0.345384i
$29$	−0.488355	+	0.281952i	−0.0906852	+	0.0523571i	−0.544657	−	0.838659i	$-0.683340\pi$
$29$	−0.488355	+	0.281952i	−0.0906852	+	0.0523571i	0.453972	+	0.891016i	$0.350007\pi$
$30$	0.982484	+	2.94453i	0.179376	+	0.537596i
$31$	−4.23375	−	2.44435i	−0.760403	−	0.439019i	0.0690374	−	0.997614i	$-0.478007\pi$
$31$	−4.23375	−	2.44435i	−0.760403	−	0.439019i	−0.829440	+	0.558595i	$0.811341\pi$
$32$	−4.97858	+	2.87439i	−0.880098	+	0.508125i
$33$	0.541554	+	1.62305i	0.0942724	+	0.282537i
$34$			1.55226i			0.266210i
$35$	4.74827	−	3.01347i	0.802604	−	0.509370i
$36$	−3.55739	−	1.51707i	−0.592899	−	0.252844i
$37$	−1.64578	+	2.85058i	−0.270565	+	0.468633i	−0.969007	−	0.247035i	$-0.920544\pi$
$37$	−1.64578	+	2.85058i	−0.270565	+	0.468633i	0.698442	+	0.715667i	$0.253877\pi$
$38$	−3.01745	+	5.22638i	−0.489496	+	0.847831i
$39$	−4.04049	+	4.76177i	−0.646996	+	0.762493i
$40$	5.10491	−	2.94732i	0.807158	−	0.466013i
$41$	−4.93559	−	8.54870i	−0.770810	−	1.33508i	−0.937120	−	0.349008i	$-0.886518\pi$
$41$	−4.93559	−	8.54870i	−0.770810	−	1.33508i	0.166310	−	0.986074i	$-0.446815\pi$
$42$	0.614202	−	3.81460i	0.0947734	−	0.588606i
$43$	−0.214038	+	0.370726i	−0.0326406	+	0.0565351i	−0.881884	−	0.471466i	$-0.843725\pi$
$43$	−0.214038	+	0.370726i	−0.0326406	+	0.0565351i	0.849244	+	0.528001i	$0.177058\pi$
$44$	1.10286	−	0.636734i	0.166262	−	0.0959913i
$45$	5.86568	+	2.50144i	0.874404	+	0.372893i
$46$	0.685893	+	1.18800i	0.101129	+	0.175161i
$47$	6.40449	+	11.0929i	0.934190	+	1.61807i	0.776071	+	0.630645i	$0.217210\pi$
$47$	6.40449	+	11.0929i	0.934190	+	1.61807i	0.158119	+	0.987420i	$0.449457\pi$
$48$	−0.0832459	+	0.407419i	−0.0120155	+	0.0588059i
$49$	−6.97543	+	0.586021i	−0.996490	+	0.0837173i
$50$	0.351833	−	0.203131i	0.0497567	−	0.0287270i
$51$	2.38649	+	2.11496i	0.334176	+	0.296154i
$52$	4.07434	+	2.23688i	0.565010	+	0.310199i
$53$	−6.59657	−	3.80853i	−0.906109	−	0.523142i	−0.0269320	−	0.999637i	$-0.508574\pi$
$53$	−6.59657	−	3.80853i	−0.906109	−	0.523142i	−0.879177	+	0.476495i	$0.841907\pi$
$54$	3.95901	−	1.87615i	0.538753	−	0.255311i
$55$	−1.81847	+	1.04989i	−0.245202	+	0.141567i
$56$	−7.33069	+	0.307392i	−0.979605	+	0.0410770i
$57$	3.92393	+	11.7601i	0.519737	+	1.55767i
$58$	−0.475447			−0.0624292
$59$	5.96320	+	10.3286i	0.776342	+	1.34466i	0.934037	+	0.357176i	$0.116260\pi$
$59$	5.96320	+	10.3286i	0.776342	+	1.34466i	−0.157695	+	0.987488i	$0.550406\pi$
$60$	0.950114	−	4.65001i	0.122659	−	0.600314i
$61$		−	2.21713i		−	0.283875i	−0.989876	−	0.141937i	$-0.954667\pi$
$61$		−	2.21713i		−	0.283875i	0.989876	−	0.141937i	$-0.0453332\pi$
$62$	−2.06092	−	3.56962i	−0.261737	−	0.453342i
$63$	−5.02785	−	6.14172i	−0.633450	−	0.773784i
$64$	−4.36683			−0.545853
$65$	−6.71806	−	3.68832i	−0.833272	−	0.457480i
$66$	−0.288797	+	1.41342i	−0.0355484	+	0.173980i
$67$	−2.45385			−0.299785			−0.149892	−	0.988702i	$-0.547893\pi$
$67$	−2.45385			−0.299785			−0.149892	+	0.988702i	$0.547893\pi$
$68$	1.18667	−	2.05537i	0.143905	−	0.249251i
$69$	2.76101	+	0.564144i	0.332387	+	0.0679149i
$70$	4.73746	−	0.198652i	0.566234	−	0.0237435i
$71$	−2.48976	−	1.43746i	−0.295480	−	0.170596i	0.344930	−	0.938628i	$-0.387903\pi$
$71$	−2.48976	−	1.43746i	−0.295480	−	0.170596i	−0.640411	+	0.768033i	$0.721236\pi$
$72$	−4.99567	−	6.65265i	−0.588746	−	0.784023i
$73$	−8.31343	−	4.79976i	−0.973013	−	0.561769i	−0.0728598	−	0.997342i	$-0.523213\pi$
$73$	−8.31343	−	4.79976i	−0.973013	−	0.561769i	−0.900154	+	0.435573i	$0.856546\pi$
$74$	−2.40342	+	1.38762i	−0.279392	+	0.161307i
$75$	0.167074	−	0.817688i	0.0192921	−	0.0944185i
$76$	7.99095	−	4.61358i	0.916625	−	0.529214i
$77$	2.61133	−	0.109499i	0.297588	−	0.0124785i
$78$	−4.95768	+	1.77359i	−0.561347	+	0.200820i
$79$	−7.27556	−	12.6016i	−0.818565	−	1.41780i	−0.906740	−	0.421691i	$-0.861437\pi$
$79$	−7.27556	−	12.6016i	−0.818565	−	1.41780i	0.0881750	−	0.996105i	$-0.471897\pi$
$80$	−0.510320			−0.0570555
$81$	2.50972	−	8.64299i	0.278858	−	0.960332i
$82$		−	8.32274i		−	0.919093i
$83$	14.4620			1.58741			0.793707	−	0.608301i	$-0.208149\pi$
$83$	14.4620			1.58741			0.793707	+	0.608301i	$0.208149\pi$
$84$	−3.72947	+	4.58145i	−0.406918	+	0.499877i
$85$	−1.95666	+	3.38904i	−0.212230	+	0.367593i
$86$	−0.312572	+	0.180463i	−0.0337055	+	0.0194599i
$87$	−0.647800	+	0.730969i	−0.0694514	+	0.0783681i
$88$	2.73950			0.292032
$89$	2.59362	−	4.49228i	0.274923	−	0.476181i	−0.695193	−	0.718824i	$-0.744681\pi$
$89$	2.59362	−	4.49228i	0.274923	−	0.476181i	0.970116	+	0.242643i	$0.0780142\pi$
$90$	3.22845	+	4.29927i	0.340309	+	0.453183i
$91$	5.28368	+	7.94246i	0.553881	+	0.832596i
$92$		−	2.09741i		−	0.218670i
$93$	−8.29609	−	1.69510i	−0.860264	−	0.175774i
$94$			10.7997i			1.11390i
$95$	−13.1760	+	7.60718i	−1.35183	+	0.780481i
$96$	−6.60407	+	7.45195i	−0.674025	+	0.760561i
$97$	0.172790	+	0.0997601i	0.0175441	+	0.0101291i	0.508746	−	0.860916i	$-0.330109\pi$
$97$	0.172790	+	0.0997601i	0.0175441	+	0.0101291i	−0.491202	+	0.871046i	$0.663442\pi$
$98$	−5.34034	−	2.51272i	−0.539456	−	0.253823i
$99$	1.77955	+	2.36980i	0.178852	+	0.238174i
$100$	−0.621159			−0.0621159
$101$	6.01356			0.598372			0.299186	−	0.954195i	$-0.403285\pi$
$101$	6.01356			0.598372			0.299186	+	0.954195i	$0.403285\pi$
$102$	0.850964	+	2.55036i	0.0842579	+	0.252524i
$103$	8.42274	−	4.86287i	0.829917	−	0.479153i	−0.0239072	−	0.999714i	$-0.507611\pi$
$103$	8.42274	−	4.86287i	0.829917	−	0.479153i	0.853824	+	0.520561i	$0.174277\pi$
$104$	5.18451	+	8.54970i	0.508384	+	0.838367i
$105$	6.14941	−	7.55421i	0.600121	−	0.737215i
$106$	−3.21111	−	5.56181i	−0.311891	−	0.540210i
$107$	−0.532349	−	0.307352i	−0.0514642	−	0.0297128i	0.474047	−	0.880499i	$-0.342793\pi$
$107$	−0.532349	−	0.307352i	−0.0514642	−	0.0297128i	−0.525511	+	0.850787i	$0.676126\pi$
$108$	−6.67649	−	0.542343i	−0.642445	−	0.0521870i
$109$	−5.78829	+	10.0256i	−0.554418	+	0.960280i	0.443531	+	0.896259i	$0.353726\pi$
$109$	−5.78829	+	10.0256i	−0.554418	+	0.960280i	−0.997949	+	0.0640208i	$0.979608\pi$
$110$	−1.77040			−0.168801
$111$	−1.14131	+	5.58575i	−0.108328	+	0.530176i
$112$	0.562923	+	0.294275i	0.0531912	+	0.0278064i
$113$	6.10760	+	3.52622i	0.574554	+	0.331719i	0.758966	−	0.651130i	$-0.225705\pi$
$113$	6.10760	+	3.52622i	0.574554	+	0.331719i	−0.184412	+	0.982849i	$0.559038\pi$
$114$	−2.09253	+	10.2412i	−0.195983	+	0.959174i
$115$			3.45835i			0.322493i
$116$	0.629549	+	0.363470i	0.0584522	+	0.0337474i
$117$	−4.02809	+	10.0387i	−0.372397	+	0.928074i
$118$			10.0556i			0.925690i
$119$	4.11264	−	2.61007i	0.377005	−	0.239265i
$120$	6.77164	−	7.64104i	0.618164	−	0.697528i
$121$	10.0241			0.911285
$122$	0.934672	−	1.61890i	0.0846212	−	0.146568i
$123$	−12.7957	−	11.3398i	−1.15375	−	1.02248i
$124$			6.30215i			0.565949i
$125$	11.6522			1.04220
$126$	−1.08207	−	6.60412i	−0.0963985	−	0.588342i
$127$	−5.43519	−	9.41402i	−0.482295	−	0.835359i	0.517499	−	0.855684i	$-0.326863\pi$
$127$	−5.43519	−	9.41402i	−0.482295	−	0.835359i	−0.999793	+	0.0203250i	$0.993530\pi$
$128$	6.76861	+	3.90786i	0.598267	+	0.345409i
$129$	−0.148430	+	0.726442i	−0.0130686	+	0.0639597i
$130$	−3.35049	−	5.52524i	−0.293858	−	0.484596i
$131$	−8.66948	−	15.0160i	−0.757456	−	1.31195i	−0.944144	−	0.329533i	$-0.893109\pi$
$131$	−8.66948	−	15.0160i	−0.757456	−	1.31195i	0.186688	−	0.982419i	$-0.440225\pi$
$132$	1.46293	−	1.65076i	0.127332	−	0.143680i
$133$	18.9209	−	0.793394i	1.64065	−	0.0687960i
$134$	−1.79174	−	1.03446i	−0.154783	−	0.0893639i
$135$	11.0087	+	0.894252i	0.947474	+	0.0769650i
$136$	4.42154	−	2.55278i	0.379144	−	0.218899i
$137$	11.0502	−	6.37986i	0.944086	−	0.545068i	0.0528469	−	0.998603i	$-0.483170\pi$
$137$	11.0502	−	6.37986i	0.944086	−	0.545068i	0.891239	+	0.453535i	$0.149837\pi$
$138$	1.77820	+	1.57588i	0.151370	+	0.134148i
$139$	13.6009	+	7.85246i	1.15361	+	0.666037i	0.949764	−	0.312966i	$-0.101322\pi$
$139$	13.6009	+	7.85246i	1.15361	+	0.666037i	0.203846	+	0.979003i	$0.434656\pi$
$140$	−6.42483	−	3.35866i	−0.542997	−	0.283859i
$141$	16.6039	+	14.7147i	1.39830	+	1.23920i
$142$	−1.21198	−	2.09921i	−0.101707	−	0.176161i
$143$	−1.84682	−	3.04556i	−0.154439	−	0.254683i
$144$	0.0865782	+	0.715028i	0.00721485	+	0.0595856i
$145$	−1.03804	−	0.599315i	−0.0862049	−	0.0497704i
$146$	−4.04685	−	7.00935i	−0.334920	−	0.580098i
$147$	−11.1394	+	4.78684i	−0.918762	+	0.394812i
$148$	4.24323			0.348792
$149$		−	7.52267i		−	0.616281i	−0.951341	−	0.308141i	$-0.900293\pi$
$149$		−	7.52267i		−	0.616281i	0.951341	−	0.308141i	$-0.0997068\pi$
$150$	0.466704	−	0.526623i	0.0381063	−	0.0429986i
$151$	1.77190	−	3.06902i	0.144195	−	0.249753i	−0.784877	−	0.619651i	$-0.787274\pi$
$151$	1.77190	−	3.06902i	0.144195	−	0.249753i	0.929072	+	0.369898i	$0.120607\pi$
$152$	19.8496			1.61001
$153$	5.08047	+	2.16659i	0.410731	+	0.175158i
$154$	1.95289	+	1.02090i	0.157368	+	0.0822663i
$155$		−	10.3914i		−	0.834658i
$156$	7.92045	+	1.44160i	0.634143	+	0.115421i
$157$	−12.7221	−	7.34511i	−1.01533	−	0.586204i	−0.102585	−	0.994724i	$-0.532711\pi$
$157$	−12.7221	−	7.34511i	−1.01533	−	0.586204i	−0.912749	+	0.408521i	$0.866045\pi$
$158$		−	12.2686i		−	0.976035i
$159$	−12.9261	−	2.64112i	−1.02511	−	0.209455i
$160$	−10.5825	−	6.10978i	−0.836616	−	0.483021i
$161$	1.99425	−	3.81484i	0.157169	−	0.300651i
$162$	5.47615	−	5.25289i	0.430247	−	0.412706i
$163$	0.893571			0.0699899			0.0349949	−	0.999387i	$-0.488858\pi$
$163$	0.893571			0.0699899			0.0349949	+	0.999387i	$0.488858\pi$
$164$	−6.36258	+	11.0203i	−0.496834	+	0.860542i
$165$	−2.41218	+	2.72188i	−0.187788	+	0.211898i
$166$	10.5598	+	6.09672i	0.819602	+	0.473197i
$167$	2.80871	+	4.86483i	0.217345	+	0.376452i	0.953995	−	0.299821i	$-0.0969271\pi$
$167$	2.80871	+	4.86483i	0.217345	+	0.376452i	−0.736651	+	0.676274i	$0.763594\pi$
$168$	−11.8758	+	4.52381i	−0.916241	+	0.349020i
$169$	6.00977	−	11.5275i	0.462290	−	0.886729i
$170$	−2.85742	+	1.64973i	−0.219154	+	0.126529i
$171$	12.8941	+	17.1708i	0.986034	+	1.31308i
$172$	0.551844			0.0420777
$173$	−14.4173			−1.09613			−0.548064	−	0.836437i	$-0.684635\pi$
$173$	−14.4173			−1.09613			−0.548064	+	0.836437i	$0.684635\pi$
$174$	−0.781161	+	0.260645i	−0.0592197	+	0.0197595i
$175$	−1.12978	−	0.590608i	−0.0854036	−	0.0446458i
$176$	−0.205393	−	0.118584i	−0.0154821	−	0.00893860i
$177$	15.4598	+	13.7008i	1.16203	+	1.02981i
$178$	3.78760	−	2.18677i	0.283893	−	0.163906i
$179$			22.2997i			1.66676i	0.552700	+	0.833380i	$0.313598\pi$
$179$			22.2997i			1.66676i	−0.552700	+	0.833380i	$0.686402\pi$
$180$	−0.988146	−	8.16085i	−0.0736520	−	0.608274i
$181$		−	6.26949i		−	0.466007i	−0.972476	−	0.233004i	$-0.925145\pi$
$181$		−	6.26949i		−	0.466007i	0.972476	−	0.233004i	$-0.0748554\pi$
$182$	0.509738	+	8.02683i	0.0377843	+	0.594988i
$183$	−1.21546	−	3.64276i	−0.0898492	−	0.269281i
$184$	2.25599	−	3.90748i	0.166313	−	0.288063i
$185$	−6.99654			−0.514396
$186$	−5.34301	−	4.73508i	−0.391768	−	0.347193i
$187$	−1.57504	+	0.909347i	−0.115178	+	0.0664980i
$188$	8.25617	−	14.3001i	0.602143	−	1.04294i
$189$	−11.6277	−	7.33455i	−0.845794	−	0.533510i
$190$	−12.8278			−0.930624
$191$			4.93340i			0.356968i	0.983943	+	0.178484i	$0.0571193\pi$
$191$			4.93340i			0.356968i	−0.983943	+	0.178484i	$0.942881\pi$
$192$	−7.17472	+	2.39394i	−0.517791	+	0.172768i
$193$	−5.38159			−0.387376			−0.193688	−	0.981063i	$-0.562045\pi$
$193$	−5.38159			−0.387376			−0.193688	+	0.981063i	$0.562045\pi$
$194$	0.0841113	+	0.145685i	0.00603884	+	0.0104596i
$195$	−13.0598	−	2.37701i	−0.935230	−	0.170221i
$196$	5.15033	+	7.40973i	0.367881	+	0.529267i
$197$	−1.73936	+	1.00422i	−0.123924	+	0.0715477i	−0.560681	−	0.828032i	$-0.689460\pi$
$197$	−1.73936	+	1.00422i	−0.123924	+	0.0715477i	0.436756	+	0.899580i	$0.356127\pi$
$198$	0.300357	+	2.48057i	0.0213454	+	0.176287i
$199$	−1.63133	+	0.941849i	−0.115642	+	0.0667659i	−0.556705	−	0.830710i	$-0.687935\pi$
$199$	−1.63133	+	0.941849i	−0.115642	+	0.0667659i	0.441063	+	0.897476i	$0.354601\pi$
$200$	−1.15722	−	0.668122i	−0.0818279	−	0.0472434i
$201$	−4.03168	+	1.34523i	−0.284373	+	0.0948849i
$202$	4.39096	+	2.53512i	0.308947	+	0.178371i
$203$	0.799451	+	1.25968i	0.0561104	+	0.0884120i
$204$	0.822926	−	4.02753i	0.0576164	−	0.281984i
$205$	10.4911	−	18.1711i	0.732728	−	1.26912i
$206$	8.20012			0.571329
$207$	4.84562	−	0.586726i	0.336794	−	0.0407803i
$208$	−0.0186196	−	0.865433i	−0.00129103	−	0.0600070i
$209$	−7.07078			−0.489096
$210$	7.67476	−	2.92351i	0.529609	−	0.201742i
$211$	3.68771	+	6.38731i	0.253873	+	0.439720i	0.964589	−	0.263759i	$-0.0849623\pi$
$211$	3.68771	+	6.38731i	0.253873	+	0.439720i	−0.710716	+	0.703479i	$0.751629\pi$
$212$			9.81934i			0.674395i
$213$	−4.87872	−	0.996846i	−0.334285	−	0.0683027i
$214$	−0.259139	−	0.448843i	−0.0177144	−	0.0306822i
$215$	−0.909918			−0.0620559
$216$	−11.8550	−	8.19165i	−0.806629	−	0.557371i
$217$	−5.99219	+	11.4625i	−0.406776	+	0.778128i
$218$	−8.45295	+	4.88031i	−0.572506	+	0.330537i
$219$	−16.2903	−	3.32851i	−1.10080	−	0.224920i
$220$	2.34422	+	1.35344i	0.158048	+	0.0912488i
$221$	−5.81874	−	3.19458i	−0.391411	−	0.214891i
$222$	−3.18813	+	3.59745i	−0.213973	+	0.241445i
$223$	1.19481	−	0.689825i	0.0800106	−	0.0461941i	−0.459461	−	0.888198i	$-0.651957\pi$
$223$	1.19481	−	0.689825i	0.0800106	−	0.0461941i	0.539472	+	0.842004i	$0.318624\pi$
$224$	8.15009	+	12.8419i	0.544551	+	0.858037i
$225$	−0.173762	−	1.43506i	−0.0115841	−	0.0956705i
$226$	2.97308	+	5.14953i	0.197767	+	0.342542i
$227$	1.49119	+	2.58281i	0.0989736	+	0.171427i	0.911260	−	0.411831i	$-0.135111\pi$
$227$	1.49119	+	2.58281i	0.0989736	+	0.171427i	−0.812286	+	0.583259i	$0.801777\pi$
$228$	10.6000	−	11.9609i	0.701999	−	0.792127i
$229$	10.3410	−	5.97040i	0.683355	−	0.394535i	−0.117763	−	0.993042i	$-0.537572\pi$
$229$	10.3410	−	5.97040i	0.683355	−	0.394535i	0.801118	+	0.598506i	$0.204239\pi$
$230$	−1.45793	+	2.52521i	−0.0961331	+	0.166507i
$231$	4.23040	−	1.61147i	0.278340	−	0.106027i
$232$	0.781902	+	1.35429i	0.0513343	+	0.0889137i
$233$	−14.3523	+	8.28630i	−0.940250	+	0.542854i	−0.890039	−	0.455885i	$-0.849323\pi$
$233$	−14.3523	+	8.28630i	−0.940250	+	0.542854i	−0.0502115	+	0.998739i	$0.515990\pi$
$234$	−7.17319	+	5.63188i	−0.468926	+	0.368167i
$235$	−13.6133	+	23.5790i	−0.888037	+	1.53812i
$236$	7.68729	−	13.3148i	0.500400	−	0.866718i
$237$	−18.8621	−	16.7160i	−1.22523	−	1.08582i
$238$	4.10328	−	0.172060i	0.265976	−	0.0111530i
$239$			29.6350i			1.91693i	0.285211	+	0.958465i	$0.407936\pi$
$239$			29.6350i			1.91693i	−0.285211	+	0.958465i	$0.592064\pi$
$240$	−0.838458	+	0.279763i	−0.0541222	+	0.0180586i
$241$	15.6963	−	9.06224i	1.01108	−	0.583750i	0.0995756	−	0.995030i	$-0.468251\pi$
$241$	15.6963	−	9.06224i	1.01108	−	0.583750i	0.911509	+	0.411280i	$0.134918\pi$
$242$	7.31939	+	4.22585i	0.470508	+	0.271648i
$243$	−0.614701	−	15.5763i	−0.0394331	−	0.999222i
$244$	−2.47524	+	1.42908i	−0.158461	+	0.0914874i
$245$	−8.49222	−	12.2177i	−0.542548	−	0.780559i
$246$	−4.56262	−	13.6743i	−0.290902	−	0.871842i
$247$	−13.3815	−	22.0672i	−0.851443	−	1.40410i
$248$	−6.77862	+	11.7409i	−0.430443	+	0.745549i
$249$	23.7612	−	7.92824i	1.50580	−	0.502432i
$250$	8.50815	+	4.91218i	0.538103	+	0.310674i
$251$	−3.79901	+	6.58007i	−0.239791	+	0.415330i	−0.960654	−	0.277747i	$-0.910412\pi$
$251$	−3.79901	+	6.58007i	−0.239791	+	0.415330i	0.720863	+	0.693077i	$0.243746\pi$
$252$	−3.61594	+	9.57187i	−0.227783	+	0.602971i
$253$	−0.803624	+	1.39192i	−0.0505234	+	0.0875091i
$254$		−	9.16519i		−	0.575075i
$255$	−1.35690	+	6.64088i	−0.0849723	+	0.415868i
$256$	7.66168	+	13.2704i	0.478855	+	0.829402i
$257$	−11.8505	+	20.5256i	−0.739212	+	1.28035i	0.213638	+	0.976913i	$0.431469\pi$
$257$	−11.8505	+	20.5256i	−0.739212	+	1.28035i	−0.952851	+	0.303440i	$0.901865\pi$
$258$	−0.414625	+	0.467858i	−0.0258134	+	0.0291275i
$259$	7.71773	+	4.03454i	0.479556	+	0.250694i
$260$	0.212511	+	9.87748i	0.0131794	+	0.612575i
$261$	−0.663613	+	1.55612i	−0.0410766	+	0.0963212i
$262$		−	14.6191i		−	0.903170i
$263$		−	17.5614i		−	1.08288i	−0.840740	−	0.541440i	$-0.817879\pi$
$263$		−	17.5614i		−	1.08288i	0.840740	−	0.541440i	$-0.182121\pi$
$264$	4.50101	−	1.50182i	0.277018	−	0.0924309i
$265$		−	16.1908i		−	0.994593i
$266$	14.1500	+	7.39711i	0.867595	+	0.453546i
$267$	1.79861	−	8.80269i	0.110073	−	0.538716i
$268$	1.58165	+	2.73951i	0.0966149	+	0.167342i
$269$	−11.8706	−	20.5606i	−0.723766	−	1.25360i	−0.959480	−	0.281777i	$-0.909076\pi$
$269$	−11.8706	−	20.5606i	−0.723766	−	1.25360i	0.235714	−	0.971823i	$-0.424257\pi$
$270$	7.66127	+	5.29385i	0.466250	+	0.322174i
$271$	−26.2482	−	15.1544i	−1.59446	−	0.920565i	−0.992528	−	0.122021i	$-0.961062\pi$
$271$	−26.2482	−	15.1544i	−1.59446	−	0.920565i	−0.601937	−	0.798543i	$-0.705604\pi$
$272$	−0.442006			−0.0268005
$273$	13.0353	+	10.1529i	0.788930	+	0.614483i
$274$	10.7582			0.649925
$275$	0.412224	+	0.237997i	0.0248580	+	0.0143518i
$276$	−1.14982	−	3.44605i	−0.0692112	−	0.207428i
$277$	−8.79054	−	15.2257i	−0.528172	−	0.914821i	−0.999461	−	0.0328418i	$-0.989544\pi$
$277$	−8.79054	−	15.2257i	−0.528172	−	0.914821i	0.471288	−	0.881979i	$-0.343789\pi$
$278$	6.62069	+	11.4674i	0.397083	+	0.687767i
$279$	−14.5598	+	1.76295i	−0.871671	+	0.105545i
$280$	−8.35689	−	13.1678i	−0.499420	−	0.786925i
$281$		−	27.1501i		−	1.61964i	−0.586680	−	0.809819i	$-0.699565\pi$
$281$		−	27.1501i		−	1.61964i	0.586680	−	0.809819i	$-0.300435\pi$
$282$	5.92051	+	17.7440i	0.352562	+	1.05664i
$283$			7.16342i			0.425821i	0.977072	+	0.212910i	$0.0682943\pi$
$283$			7.16342i			0.425821i	−0.977072	+	0.212910i	$0.931706\pi$
$284$			3.70614i			0.219919i
$285$	−17.4779	+	19.7219i	−1.03530	+	1.16822i
$286$	−0.0645949	−	3.00236i	−0.00381958	−	0.177533i
$287$	−22.0508	+	13.9945i	−1.30162	+	0.826067i
$288$	−6.76527	+	15.8640i	−0.398647	+	0.934796i
$289$	6.80527	−	11.7871i	0.400310	−	0.693357i
$290$	−0.505304	−	0.875212i	−0.0296725	−	0.0513942i
$291$	0.338584	+	0.0691812i	0.0198481	+	0.00405547i
$292$			12.3750i			0.724190i
$293$	−11.3968	+	19.7398i	−0.665805	+	1.15321i	0.313261	+	0.949667i	$0.398579\pi$
$293$	−11.3968	+	19.7398i	−0.665805	+	1.15321i	−0.979066	+	0.203542i	$0.934755\pi$
$294$	−10.1517	−	1.20077i	−0.592059	−	0.0700303i
$295$	−12.6753	+	21.9543i	−0.737987	+	1.27823i
$296$	7.90516	+	4.56405i	0.459478	+	0.265280i
$297$	4.22296	+	2.91802i	0.245041	+	0.169321i
$298$	3.17132	−	5.49288i	0.183709	−	0.318194i
$299$	−5.86489	+	0.126182i	−0.339175	+	0.00729727i
$300$	−1.02057	+	0.340526i	−0.0589225	+	0.0196603i
$301$	1.00371	+	0.524702i	0.0578530	+	0.0302433i
$302$	2.58760	−	1.49395i	0.148899	−	0.0859671i
$303$	9.88031	−	3.29670i	0.567609	−	0.189391i
$304$	−1.48822	−	0.859222i	−0.0853551	−	0.0492798i
$305$	4.08134	−	2.35636i	0.233697	−	0.134925i
$306$	2.79627	+	3.72375i	0.159852	+	0.212873i
$307$			24.9738i			1.42533i	0.701504	+	0.712665i	$0.252512\pi$
$307$			24.9738i			1.42533i	−0.701504	+	0.712665i	$0.747488\pi$
$308$	−1.80541	−	2.84474i	−0.102873	−	0.162094i
$309$	11.1727	−	12.6072i	0.635594	−	0.717196i
$310$	4.38068	−	7.58757i	0.248806	−	0.430945i
$311$	9.00463	−	15.5965i	0.510606	−	0.884395i	−0.489319	−	0.872105i	$-0.662754\pi$
$311$	9.00463	−	15.5965i	0.510606	−	0.884395i	0.999924	−	0.0122902i	$-0.00391219\pi$
$312$	13.2052	+	11.2050i	0.747599	+	0.634357i
$313$	17.5542	−	10.1349i	0.992223	−	0.572860i	0.0862849	−	0.996271i	$-0.472500\pi$
$313$	17.5542	−	10.1349i	0.992223	−	0.572860i	0.905938	+	0.423410i	$0.139167\pi$
$314$	−6.19292	−	10.7265i	−0.349487	−	0.605329i
$315$	5.96220	−	15.7828i	0.335932	−	0.889258i
$316$	−9.37909	+	16.2451i	−0.527615	+	0.913856i
$317$	−8.12697	+	4.69211i	−0.456456	+	0.263535i	−0.710553	−	0.703644i	$-0.751555\pi$
$317$	−8.12697	+	4.69211i	−0.456456	+	0.263535i	0.254097	+	0.967179i	$0.418222\pi$
$318$	−8.32491	−	7.37771i	−0.466838	−	0.413721i
$319$	−0.278528	−	0.482424i	−0.0155946	−	0.0270106i
$320$	−4.64105	−	8.03854i	−0.259443	−	0.449368i
$321$	−1.04315	−	0.213141i	−0.0582228	−	0.0118964i
$322$	3.06437	−	1.94479i	0.170771	−	0.108379i
$323$	−11.4122	+	6.58884i	−0.634993	+	0.366613i
$324$	−11.2668	+	2.76905i	−0.625934	+	0.153836i
$325$	0.0373693	+	1.73692i	0.00207288	+	0.0963469i
$326$	0.652465	+	0.376701i	0.0361367	+	0.0208635i
$327$	−4.01404	+	19.6453i	−0.221977	+	1.08639i
$328$	−23.7070	+	13.6873i	−1.30900	+	0.755753i
$329$	28.6134	−	18.1594i	1.57751	−	1.00116i
$330$	−2.90878	+	0.970553i	−0.160123	+	0.0534272i
$331$	−18.8085			−1.03381			−0.516905	−	0.856043i	$-0.672916\pi$
$331$	−18.8085			−1.03381			−0.516905	+	0.856043i	$0.672916\pi$
$332$	−9.32166	−	16.1456i	−0.511593	−	0.886104i
$333$	1.18700	+	9.80310i	0.0650469	+	0.537206i
$334$			4.73625i			0.259156i
$335$	−2.60794	−	4.51709i	−0.142487	−	0.246795i
$336$	1.08621	+	0.174894i	0.0592576	+	0.00954127i
$337$	20.7828			1.13211			0.566056	−	0.824367i	$-0.308469\pi$
$337$	20.7828			1.13211			0.566056	+	0.824367i	$0.308469\pi$
$338$	9.24780	−	5.88357i	0.503014	−	0.320024i
$339$	11.9679	+	2.44535i	0.650008	+	0.132813i
$340$	5.04476			0.273591
$341$	2.41467	−	4.18233i	0.130762	−	0.226486i
$342$	2.17629	+	17.9734i	0.117680	+	0.971893i
$343$	2.32229	+	18.3741i	0.125392	+	0.992107i
$344$	1.02809	+	0.593566i	0.0554307	+	0.0320030i
$345$	1.89591	+	5.68209i	0.102072	+	0.305913i
$346$	−10.5272	−	6.07787i	−0.565945	−	0.326748i
$347$	2.27756	−	1.31495i	0.122266	−	0.0705902i	−0.437620	−	0.899160i	$-0.644178\pi$
$347$	2.27756	−	1.31495i	0.122266	−	0.0705902i	0.559886	+	0.828570i	$0.310845\pi$
$348$	1.23361	+	0.252058i	0.0661285	+	0.0135117i
$349$	−2.04081	+	1.17826i	−0.109242	+	0.0630710i	−0.553626	−	0.832766i	$-0.686756\pi$
$349$	−2.04081	+	1.17826i	−0.109242	+	0.0630710i	0.444383	+	0.895837i	$0.353423\pi$
$350$	−0.575960	−	0.907529i	−0.0307864	−	0.0485095i
$351$	−1.11487	+	18.7018i	−0.0595072	+	0.998228i
$352$	−2.83948	−	4.91813i	−0.151345	−	0.262137i
$353$	22.7672			1.21178			0.605888	−	0.795550i	$-0.292818\pi$
$353$	22.7672			1.21178			0.605888	+	0.795550i	$0.292818\pi$
$354$	5.51257	+	16.5213i	0.292990	+	0.878099i
$355$		−	6.11093i		−	0.324335i
$356$	−6.68699			−0.354410
$357$	5.32621	−	6.54296i	0.281893	−	0.346290i
$358$	−9.40085	+	16.2827i	−0.496850	+	0.860570i
$359$	5.83980	−	3.37161i	0.308213	−	0.177947i	−0.337914	−	0.941177i	$-0.609721\pi$
$359$	5.83980	−	3.37161i	0.308213	−	0.177947i	0.646126	+	0.763230i	$0.276388\pi$
$360$	6.93694	−	16.2666i	0.365609	−	0.857323i
$361$	−32.2327			−1.69646
$362$	2.64301	−	4.57783i	0.138914	−	0.240605i
$363$	16.4697	−	5.49535i	0.864436	−	0.288431i
$364$	5.46141	−	11.0182i	0.286256	−	0.577509i
$365$		−	20.4047i		−	1.06803i
$366$	0.648172	−	3.17226i	0.0338805	−	0.165816i
$367$			12.7761i			0.666907i	0.942766	+	0.333454i	$0.108214\pi$
$367$			12.7761i			0.666907i	−0.942766	+	0.333454i	$0.891786\pi$
$368$	−0.338284	+	0.195308i	−0.0176343	+	0.0101812i
$369$	−27.2400	−	11.6166i	−1.41806	−	0.604736i
$370$	−5.10871	−	2.94951i	−0.265589	−	0.153338i
$371$	−9.33639	+	17.8597i	−0.484721	+	0.927231i
$372$	3.45491	+	10.3545i	0.179129	+	0.536853i
$373$	−25.7056			−1.33099			−0.665493	−	0.746404i	$-0.731779\pi$
$373$	−25.7056			−1.33099			−0.665493	+	0.746404i	$0.731779\pi$
$374$	−1.53341			−0.0792905
$375$	19.1446	−	6.38786i	0.988623	−	0.329868i
$376$	30.7625	−	17.7608i	1.58646	−	0.915942i
$377$	0.978482	−	1.78225i	0.0503944	−	0.0917904i
$378$	−5.39830	−	10.2574i	−0.277659	−	0.527583i
$379$	−15.2609	−	26.4326i	−0.783898	−	1.35775i	−0.929655	−	0.368431i	$-0.879895\pi$
$379$	−15.2609	−	26.4326i	−0.783898	−	1.35775i	0.145757	−	0.989320i	$-0.453438\pi$
$380$	16.9855	+	9.80660i	0.871339	+	0.503068i
$381$	−14.0909	−	12.4876i	−0.721899	−	0.639762i
$382$	−2.07976	+	3.60225i	−0.106410	+	0.184307i
$383$	−8.28720			−0.423456			−0.211728	−	0.977329i	$-0.567909\pi$
$383$	−8.28720			−0.423456			−0.211728	+	0.977329i	$0.567909\pi$
$384$	13.2632	+	2.71000i	0.676835	+	0.138294i
$385$	2.97688	+	4.69061i	0.151716	+	0.239055i
$386$	−3.92951	−	2.26871i	−0.200007	−	0.115474i
$387$	0.154372	+	1.27492i	0.00784716	+	0.0648078i
$388$		−	0.257206i		−	0.0130577i
$389$	23.2193	+	13.4057i	1.17727	+	0.679695i	0.955381	−	0.295378i	$-0.0954454\pi$
$389$	23.2193	+	13.4057i	1.17727	+	0.679695i	0.221886	+	0.975073i	$0.428779\pi$
$390$	−8.53387	−	7.24122i	−0.432129	−	0.366673i
$391$			2.99540i			0.151484i
$392$	1.62514	+	19.3441i	0.0820819	+	0.977024i
$393$	−22.4759	−	19.9186i	−1.13376	−	1.00476i
$394$	−1.69339			−0.0853116
$395$	15.4649	−	26.7860i	0.778124	−	1.34775i
$396$	1.49864	−	3.51419i	0.0753096	−	0.176595i
$397$			5.84724i			0.293464i	0.989176	+	0.146732i	$0.0468756\pi$
$397$			5.84724i			0.293464i	−0.989176	+	0.146732i	$0.953124\pi$
$398$	−1.58821			−0.0796099
$399$	30.6521	−	11.6762i	1.53453	−	0.584540i
$400$	0.0578416	+	0.100185i	0.00289208	+	0.00500923i
$401$	−3.59360	−	2.07476i	−0.179456	−	0.103609i	0.407581	−	0.913169i	$-0.366372\pi$
$401$	−3.59360	−	2.07476i	−0.179456	−	0.103609i	−0.587037	+	0.809560i	$0.699706\pi$
$402$	−3.51094	−	0.717374i	−0.175110	−	0.0357793i
$403$	17.6224	−	0.379141i	0.877835	−	0.0188864i
$404$	−3.87611	−	6.71362i	−0.192844	−	0.334015i
$405$	18.5775	−	4.56581i	0.923124	−	0.226877i
$406$	0.0527008	+	1.25681i	0.00261550	+	0.0623744i
$407$	−2.81596	−	1.62580i	−0.139582	−	0.0805878i
$408$	5.86515	−	6.61817i	0.290368	−	0.327648i
$409$	−9.22250	+	5.32461i	−0.456023	+	0.263285i	−0.710371	−	0.703828i	$-0.751473\pi$
$409$	−9.22250	+	5.32461i	−0.456023	+	0.263285i	0.254347	+	0.967113i	$0.418139\pi$
$410$	15.3207	−	8.84539i	0.756634	−	0.436843i
$411$	14.6581	−	16.5400i	0.723030	−	0.815858i
$412$	−10.8579	−	6.26884i	−0.534933	−	0.308843i
$413$	26.6418	−	16.9082i	1.31096	−	0.831996i
$414$	3.78550	+	1.61434i	0.186047	+	0.0793407i
$415$	15.3702	+	26.6220i	0.754493	+	1.30682i
$416$	9.97524	−	18.1693i	0.489076	−	0.890824i
$417$	26.6511	+	5.44549i	1.30511	+	0.266667i
$418$	−5.16292	−	2.98081i	−0.252527	−	0.145796i
$419$	4.05247	+	7.01909i	0.197976	+	0.342905i	0.947872	−	0.318651i	$-0.103230\pi$
$419$	4.05247	+	7.01909i	0.197976	+	0.342905i	−0.749896	+	0.661556i	$0.769896\pi$
$420$	−12.3973	−	1.99613i	−0.604926	−	0.0974011i
$421$	16.7895			0.818270			0.409135	−	0.912474i	$-0.365830\pi$
$421$	16.7895			0.818270			0.409135	+	0.912474i	$0.365830\pi$
$422$			6.21848i			0.302711i
$423$	35.3470	+	15.0739i	1.71863	+	0.732916i
$424$	−10.5617	+	18.2935i	−0.512923	+	0.888409i
$425$	0.887103			0.0430308
$426$	−3.14209	−	2.78459i	−0.152235	−	0.134914i
$427$	−5.86083	+	0.245758i	−0.283626	+	0.0118931i
$428$			0.792429i			0.0383035i
$429$	−4.70394	−	3.99142i	−0.227109	−	0.192708i
$430$	−0.664401	−	0.383592i	−0.0320403	−	0.0184985i
$431$		−	13.8352i		−	0.666416i	−0.942853	−	0.333208i	$-0.891869\pi$
$431$		−	13.8352i		−	0.666416i	0.942853	−	0.333208i	$-0.108131\pi$
$432$	0.534234	+	1.12733i	0.0257034	+	0.0542387i
$433$	−10.1569	−	5.86410i	−0.488111	−	0.281811i	0.235680	−	0.971831i	$-0.424268\pi$
$433$	−10.1569	−	5.86410i	−0.488111	−	0.281811i	−0.723790	+	0.690020i	$0.757602\pi$
$434$	−9.20759	+	5.84357i	−0.441979	+	0.280500i
$435$	−2.03406	−	0.415610i	−0.0975258	−	0.0199270i
$436$	14.9236			0.714713
$437$	−5.82281	+	10.0854i	−0.278543	+	0.482450i
$438$	−10.4916	−	9.29786i	−0.501308	−	0.444269i
$439$	23.7717	+	13.7246i	1.13456	+	0.655039i	0.945078	−	0.326845i	$-0.105985\pi$
$439$	23.7717	+	13.7246i	1.13456	+	0.655039i	0.189483	+	0.981884i	$0.439319\pi$
$440$	2.91153	+	5.04292i	0.138802	+	0.240412i
$441$	−15.6779	+	13.9715i	−0.746566	+	0.665312i
$442$	−2.90198	−	4.78560i	−0.138033	−	0.227628i
$443$	23.7433	−	13.7082i	1.12808	−	0.651298i	0.184629	−	0.982808i	$-0.440892\pi$
$443$	23.7433	−	13.7082i	1.12808	−	0.651298i	0.943451	+	0.331511i	$0.107558\pi$
$444$	6.97165	−	2.32619i	0.330860	−	0.110396i
$445$	11.0260			0.522681
$446$	1.16323			0.0550806
$447$	−4.12401	−	12.3598i	−0.195059	−	0.584598i
$448$	0.484040	+	11.5434i	0.0228688	+	0.545374i
$449$	5.57195	+	3.21697i	0.262957	+	0.151818i	0.625683	−	0.780078i	$-0.284821\pi$
$449$	5.57195	+	3.21697i	0.262957	+	0.151818i	−0.362726	+	0.931896i	$0.618154\pi$
$450$	0.478097	−	1.12110i	0.0225377	−	0.0528490i
$451$	8.44488	−	4.87566i	0.397654	−	0.229586i
$452$		−	9.09147i		−	0.427627i
$453$	1.22877	−	6.01378i	0.0577325	−	0.282552i
$454$			2.51455i			0.118013i
$455$	−9.00515	+	18.1675i	−0.422168	+	0.851707i
$456$	32.6129	−	10.8817i	1.52724	−	0.509585i
$457$	−11.9978	+	20.7809i	−0.561235	+	0.972088i	0.436154	+	0.899872i	$0.356340\pi$
$457$	−11.9978	+	20.7809i	−0.561235	+	0.972088i	−0.997389	+	0.0722160i	$0.976993\pi$
$458$	10.0677			0.470433
$459$	9.53497	+	0.774543i	0.445054	+	0.0361526i
$460$	3.86095	−	2.22912i	0.180018	−	0.103933i
$461$	−3.15743	+	5.46883i	−0.147056	+	0.254709i	−0.930138	−	0.367210i	$-0.880313\pi$
$461$	−3.15743	+	5.46883i	−0.147056	+	0.254709i	0.783082	+	0.621918i	$0.213646\pi$
$462$	3.76828	+	0.606743i	0.175316	+	0.0282282i
$463$	−4.43562			−0.206141			−0.103070	−	0.994674i	$-0.532867\pi$
$463$	−4.43562			−0.206141			−0.103070	+	0.994674i	$0.532867\pi$
$464$		−	0.135384i		−	0.00628504i
$465$	−5.69669	−	17.0731i	−0.264178	−	0.791748i
$466$	−13.9729			−0.647284
$467$	−2.04445	−	3.54109i	−0.0946057	−	0.163862i	0.814838	−	0.579688i	$-0.196826\pi$
$467$	−2.04445	−	3.54109i	−0.0946057	−	0.163862i	−0.909444	+	0.415826i	$0.863492\pi$
$468$	13.8036	−	1.97352i	0.638073	−	0.0912259i
$469$	0.271996	+	6.48656i	0.0125596	+	0.299522i
$470$	−19.8803	+	11.4779i	−0.917009	+	0.529436i
$471$	−24.9291	−	5.09365i	−1.14867	−	0.234703i
$472$	28.6429	−	16.5370i	1.31840	−	0.761177i
$473$	−0.366224	−	0.211439i	−0.0168390	−	0.00972199i
$474$	−6.72577	−	20.1573i	−0.308925	−	0.925856i
$475$	2.98684	+	1.72445i	0.137046	+	0.0791234i
$476$	−5.56477	−	2.90905i	−0.255061	−	0.133336i
$477$	−22.6855	+	2.74684i	−1.03870	+	0.125769i
$478$	−12.4932	+	21.6388i	−0.571424	+	0.989735i
$479$	−30.3359			−1.38608			−0.693042	−	0.720897i	$-0.743730\pi$
$479$	−30.3359			−1.38608			−0.693042	+	0.720897i	$0.743730\pi$
$480$	−20.7365	−	4.23698i	−0.946486	−	0.193391i
$481$	−0.255276	−	11.8652i	−0.0116396	−	0.541005i
$482$	15.2814			0.696048
$483$	1.18523	−	7.36106i	0.0539298	−	0.334940i
$484$	−6.46117	−	11.1911i	−0.293690	−	0.508686i
$485$			0.424099i			0.0192573i
$486$	6.11764	−	11.6326i	0.277502	−	0.527666i
$487$	18.2717	+	31.6476i	0.827971	+	1.43409i	0.899627	+	0.436659i	$0.143838\pi$
$487$	18.2717	+	31.6476i	0.827971	+	1.43409i	−0.0716562	+	0.997429i	$0.522828\pi$
$488$	−6.14850			−0.278330
$489$	1.46814	−	0.489866i	0.0663917	−	0.0221525i
$490$	−1.05025	−	12.5011i	−0.0474453	−	0.564743i
$491$	21.6683	−	12.5102i	0.977875	−	0.564577i	0.0762474	−	0.997089i	$-0.475706\pi$
$491$	21.6683	−	12.5102i	0.977875	−	0.564577i	0.901628	+	0.432512i	$0.142373\pi$
$492$	−4.41229	+	21.5945i	−0.198922	+	0.973554i
$493$	−0.899086	−	0.519087i	−0.0404928	−	0.0233785i
$494$	−0.468034	−	21.7541i	−0.0210579	−	0.978765i
$495$	−2.47107	+	5.79445i	−0.111066	+	0.260441i
$496$	1.01645	−	0.586849i	0.0456400	−	0.0263503i
$497$	−3.52386	+	6.74084i	−0.158067	+	0.302368i
$498$	20.6921	+	4.22792i	0.927237	+	0.189458i
$499$	−8.03279	−	13.9132i	−0.359597	−	0.622841i	0.628296	−	0.777974i	$-0.283753\pi$
$499$	−8.03279	−	13.9132i	−0.359597	−	0.622841i	−0.987894	+	0.155133i	$0.950419\pi$
$500$	−7.51055	−	13.0087i	−0.335882	−	0.581765i
$501$	7.28168	+	6.45318i	0.325322	+	0.288307i
$502$	−5.54789	+	3.20308i	−0.247614	+	0.142960i
$503$	−19.4463	+	33.6820i	−0.867069	+	1.50181i	−0.00209081	+	0.999998i	$0.500666\pi$
$503$	−19.4463	+	33.6820i	−0.867069	+	1.50181i	−0.864978	+	0.501810i	$0.832668\pi$
$504$	−17.0321	+	13.9431i	−0.758668	+	0.621076i
$505$	6.39120	+	11.0699i	0.284405	+	0.492603i
$506$	−1.17357	+	0.677563i	−0.0521717	+	0.0301214i
$507$	3.55459	−	22.2343i	0.157865	−	0.987461i
$508$	−7.00662	+	12.1358i	−0.310869	+	0.538440i
$509$	−15.0919	+	26.1400i	−0.668939	+	1.15864i	0.309262	+	0.950977i	$0.399918\pi$
$509$	−15.0919	+	26.1400i	−0.668939	+	1.15864i	−0.978201	+	0.207659i	$0.933415\pi$
$510$	−3.79035	+	4.27699i	−0.167840	+	0.189388i
$511$	−11.7663	+	22.5080i	−0.520511	+	0.995695i
$512$		−	2.71177i		−	0.119845i
$513$	30.5983	+	21.1431i	1.35095	+	0.933489i
$514$	−17.3059	+	9.99155i	−0.763329	+	0.440708i
$515$	17.9033	+	10.3365i	0.788915	+	0.455480i
$516$	0.906682	−	0.302527i	0.0399144	−	0.0133180i
$517$	−10.9582	+	6.32671i	−0.481941	+	0.278249i
$518$	3.93448	+	6.19947i	0.172871	+	0.272389i
$519$	−23.6877	+	7.90373i	−1.03977	+	0.346935i
$520$	−10.2284	+	18.6304i	−0.448543	+	0.816995i
$521$	−16.6107	+	28.7706i	−0.727729	+	1.26046i	0.230112	+	0.973164i	$0.426091\pi$
$521$	−16.6107	+	28.7706i	−0.727729	+	1.26046i	−0.957841	+	0.287299i	$0.907243\pi$
$522$	−1.14056	+	0.856483i	−0.0499211	+	0.0374872i
$523$	16.7501	+	9.67070i	0.732432	+	0.422870i	0.819311	−	0.573349i	$-0.194356\pi$
$523$	16.7501	+	9.67070i	0.732432	+	0.422870i	−0.0868789	+	0.996219i	$0.527689\pi$
$524$	−11.1760	+	19.3574i	−0.488227	+	0.845634i
$525$	−2.18002	−	0.351012i	−0.0951438	−	0.0153194i
$526$	7.40330	−	12.8229i	0.322799	−	0.559104i
$527$		−	9.00036i		−	0.392062i
$528$	−0.402471	−	0.0822350i	−0.0175153	−	0.00357882i
$529$	−10.1764	−	17.6261i	−0.442453	−	0.766352i
$530$	6.82552	−	11.8221i	0.296482	−	0.513521i
$531$	32.9114	+	14.0352i	1.42823	+	0.609077i
$532$	−13.0814	−	20.6121i	−0.567151	−	0.893648i
$533$	31.1984	+	17.1284i	1.35135	+	0.741914i
$534$	5.02423	−	5.66928i	0.217420	−	0.245334i
$535$		−	1.30661i		−	0.0564898i
$536$			6.80494i			0.293929i
$537$	12.2250	+	36.6386i	0.527546	+	1.58107i
$538$		−	20.0171i		−	0.863000i
$539$	−0.578905	−	6.89072i	−0.0249352	−	0.296804i
$540$	−6.09740	−	12.8666i	−0.262390	−	0.553691i
$541$	−13.4353	−	23.2706i	−0.577629	−	1.00048i	−0.995751	−	0.0920914i	$-0.970645\pi$
$541$	−13.4353	−	23.2706i	−0.577629	−	1.00048i	0.418122	−	0.908391i	$-0.362689\pi$
$542$	−12.7772	−	22.1308i	−0.548828	−	0.950599i
$543$	−3.43700	−	10.3008i	−0.147496	−	0.442049i
$544$	−9.16583	−	5.29189i	−0.392982	−	0.226888i
$545$	−24.6071			−1.05405
$546$	5.23790	+	12.9087i	0.224161	+	0.552440i
$547$	−30.2508			−1.29343			−0.646716	−	0.762731i	$-0.723858\pi$
$547$	−30.2508			−1.29343			−0.646716	+	0.762731i	$0.723858\pi$
$548$	−14.2451	−	8.22442i	−0.608521	−	0.351330i
$549$	−3.99400	−	5.31875i	−0.170460	−	0.226999i
$550$	0.200664	+	0.347560i	0.00855634	+	0.0148200i
$551$	−2.01813	−	3.49550i	−0.0859750	−	0.148913i
$552$	1.56447	−	7.65677i	0.0665883	−	0.325894i
$553$	−32.5051	+	20.6293i	−1.38226	+	0.877245i
$554$		−	14.8232i		−	0.629778i
$555$	−11.4953	+	3.83558i	−0.487950	+	0.162811i
$556$		−	20.2456i		−	0.858604i
$557$			26.9538i			1.14207i	0.820926	+	0.571034i	$0.193458\pi$
$557$			26.9538i			1.14207i	−0.820926	+	0.571034i	$0.806542\pi$
$558$	−11.3744	−	4.85067i	−0.481517	−	0.205345i
$559$	−0.0331993	−	1.54310i	−0.00140418	−	0.0652660i
$560$	0.0565664	+	1.34899i	0.00239037	+	0.0570054i
$561$	−2.08928	+	2.35751i	−0.0882093	+	0.0995343i
$562$	11.4456	−	19.8244i	0.482803	−	0.836240i
$563$	−3.82050	−	6.61729i	−0.161015	−	0.278886i	0.774218	−	0.632919i	$-0.218143\pi$
$563$	−3.82050	−	6.61729i	−0.161015	−	0.278886i	−0.935233	+	0.354033i	$0.884810\pi$
$564$	5.72545	−	28.0213i	0.241085	−	1.17991i
$565$			14.9906i			0.630661i
$566$	−3.01986	+	5.23056i	−0.126934	+	0.219857i
$567$	−23.1253	−	5.67624i	−0.971172	−	0.238380i
$568$	−3.98634	+	6.90454i	−0.167263	+	0.289708i
$569$	−3.23724	−	1.86902i	−0.135712	−	0.0783534i	0.430607	−	0.902540i	$-0.358300\pi$
$569$	−3.23724	−	1.86902i	−0.135712	−	0.0783534i	−0.566319	+	0.824186i	$0.691633\pi$
$570$	−21.0761	+	7.03233i	−0.882780	+	0.294552i
$571$	7.51056	−	13.0087i	0.314307	−	0.544396i	−0.664983	−	0.746859i	$-0.731561\pi$
$571$	7.51056	−	13.0087i	0.314307	−	0.544396i	0.979290	+	0.202463i	$0.0648945\pi$
$572$	−2.20971	+	4.02487i	−0.0923928	+	0.168288i
$573$	2.70454	+	8.10559i	0.112984	+	0.338616i
$574$	−22.0006	+	0.922534i	−0.918286	+	0.0385058i
$575$	0.678935	−	0.391983i	0.0283135	−	0.0163468i
$576$	−10.4757	+	7.86652i	−0.436488	+	0.327772i
$577$	15.7668	+	9.10299i	0.656382	+	0.378963i	0.790897	−	0.611949i	$-0.209614\pi$
$577$	15.7668	+	9.10299i	0.656382	+	0.378963i	−0.134515	+	0.990912i	$0.542948\pi$
$578$	9.93809	−	5.73776i	0.413370	−	0.238659i
$579$	−8.84198	+	2.95025i	−0.367460	+	0.122608i
$580$			1.54518i			0.0641602i
$581$	−1.60304	−	38.2293i	−0.0665053	−	1.58602i
$582$	0.218061	+	0.193250i	0.00903893	+	0.00801049i
$583$	3.76228	−	6.51647i	0.155818	−	0.269885i
$584$	−13.3106	+	23.0546i	−0.550796	+	0.954006i
$585$	−22.7604	+	3.25407i	−0.941026	+	0.134539i
$586$	−16.6433	+	9.60900i	−0.687528	+	0.396944i
$587$	2.83282	+	4.90659i	0.116923	+	0.202516i	0.918547	−	0.395312i	$-0.129364\pi$
$587$	2.83282	+	4.90659i	0.116923	+	0.202516i	−0.801624	+	0.597829i	$0.796030\pi$
$588$	12.5241	+	9.35075i	0.516486	+	0.385619i
$589$	17.4959	−	30.3039i	0.720908	−	1.24865i
$590$	−18.5105	+	10.6870i	−0.762064	+	0.439978i
$591$	−2.30725	+	2.60347i	−0.0949077	+	0.107093i
$592$	−0.395125	−	0.684377i	−0.0162395	−	0.0281277i
$593$	1.76064	+	3.04952i	0.0723010	+	0.125229i	0.899909	−	0.436077i	$-0.143632\pi$
$593$	1.76064	+	3.04952i	0.0723010	+	0.125229i	−0.827608	+	0.561306i	$0.810299\pi$
$594$	1.85336	+	3.91093i	0.0760445	+	0.160468i
$595$	9.17558	+	4.79664i	0.376162	+	0.196643i
$596$	−8.39841	+	4.84883i	−0.344012	+	0.198616i
$597$	−2.16395	+	2.44178i	−0.0885646	+	0.0999352i
$598$	−4.33560	−	2.38031i	−0.177296	−	0.0973383i
$599$	22.9515	+	13.2511i	0.937774	+	0.541424i	0.889262	−	0.457398i	$-0.151219\pi$
$599$	22.9515	+	13.2511i	0.937774	+	0.541424i	0.0485125	+	0.998823i	$0.484552\pi$
$600$	−2.26759	−	0.463326i	−0.0925741	−	0.0189152i
$601$	24.6360	−	14.2236i	1.00492	−	0.580194i	0.0952232	−	0.995456i	$-0.469644\pi$
$601$	24.6360	−	14.2236i	1.00492	−	0.580194i	0.909702	+	0.415262i	$0.136310\pi$
$602$	0.511689	+	0.806258i	0.0208549	+	0.0328606i
$603$	−5.88660	+	4.42042i	−0.239721	+	0.180014i
$604$	−4.56839			−0.185885
$605$	10.6536	+	18.4526i	0.433132	+	0.750206i
$606$	8.60416	+	1.75805i	0.349520	+	0.0714157i
$607$		−	9.70112i		−	0.393756i	−0.980428	−	0.196878i	$-0.936920\pi$
$607$		−	9.70112i		−	0.393756i	0.980428	−	0.196878i	$-0.0630803\pi$
$608$	−20.5740	−	35.6352i	−0.834386	−	1.44520i
$609$	2.00407	+	1.63139i	0.0812090	+	0.0661072i
$610$	3.97347			0.160881
$611$	−40.4834	−	22.2261i	−1.63779	−	0.899170i
$612$	−0.855867	−	7.06840i	−0.0345964	−	0.285723i
$613$	−8.46434			−0.341871			−0.170936	−	0.985282i	$-0.554679\pi$
$613$	−8.46434			−0.341871			−0.170936	+	0.985282i	$0.554679\pi$
$614$	−10.5281	+	18.2353i	−0.424882	+	0.735916i
$615$	7.27530	−	35.6065i	0.293368	−	1.43579i
$616$	−0.303659	−	7.24167i	−0.0122348	−	0.291775i
$617$	10.0946	+	5.82812i	0.406393	+	0.234631i	0.689239	−	0.724534i	$-0.257945\pi$
$617$	10.0946	+	5.82812i	0.406393	+	0.234631i	−0.282846	+	0.959165i	$0.591278\pi$
$618$	13.4728	−	4.49539i	0.541957	−	0.180831i
$619$	25.2951	+	14.6041i	1.01669	+	0.586989i	0.913145	−	0.407635i	$-0.133646\pi$
$619$	25.2951	+	14.6041i	1.01669	+	0.586989i	0.103550	+	0.994624i	$0.466980\pi$
$620$	−11.6011	+	6.69790i	−0.465912	+	0.268994i
$621$	7.63973	−	3.62042i	0.306572	−	0.145282i
$622$	13.1499	−	7.59212i	0.527265	−	0.304416i
$623$	−12.1625	−	6.35810i	−0.487281	−	0.254732i
$624$	−0.505032	−	1.41170i	−0.0202175	−	0.0565133i
$625$	11.1793	+	19.3631i	0.447172	+	0.774524i
$626$	17.0902			0.683063
$627$	−11.6173	+	3.87628i	−0.463951	+	0.154804i
$628$			18.9375i			0.755688i
$629$	−6.05994			−0.241626
$630$	11.0070	−	9.01074i	0.438528	−	0.358996i
$631$	12.7791	−	22.1340i	0.508727	−	0.881141i	−0.491222	−	0.871034i	$-0.663450\pi$
$631$	12.7791	−	22.1340i	0.508727	−	0.881141i	0.999949	−	0.0101065i	$-0.00321706\pi$
$632$	−34.9466	+	20.1764i	−1.39010	+	0.802575i
$633$	9.56052	+	8.47273i	0.379997	+	0.336761i
$634$	−7.91217			−0.314232
$635$	11.5530	−	20.0104i	0.458467	−	0.794088i
$636$	5.38307	+	16.1332i	0.213453	+	0.639724i
$637$	20.4097	−	14.8474i	0.808660	−	0.588276i
$638$		−	0.469673i		−	0.0185945i
$639$	−8.56225	+	1.03675i	−0.338717	+	0.0410131i
$640$			16.6131i			0.656689i
$641$	29.6869	−	17.1398i	1.17256	−	0.676980i	0.218281	−	0.975886i	$-0.429955\pi$
$641$	29.6869	−	17.1398i	1.17256	−	0.676980i	0.954282	+	0.298906i	$0.0966218\pi$
$642$	−0.671828	−	0.595387i	−0.0265149	−	0.0234981i
$643$	19.3892	+	11.1943i	0.764634	+	0.441462i	0.830957	−	0.556336i	$-0.187793\pi$
$643$	19.3892	+	11.1943i	0.764634	+	0.441462i	−0.0663229	+	0.997798i	$0.521127\pi$
$644$	−5.54435	+	0.232487i	−0.218478	+	0.00916127i
$645$	−1.49500	+	0.498827i	−0.0588656	+	0.0196413i
$646$	−11.1106			−0.437140
$647$	−20.6083			−0.810197			−0.405098	−	0.914273i	$-0.632763\pi$
$647$	−20.6083			−0.810197			−0.405098	+	0.914273i	$0.632763\pi$
$648$	−23.9685	−	6.95990i	−0.941573	−	0.273411i
$649$	−10.2031	+	5.89078i	−0.400508	+	0.231233i
$650$	−0.704943	+	1.28401i	−0.0276501	+	0.0503631i
$651$	−3.56129	+	22.1180i	−0.139578	+	0.866873i
$652$	−0.575962	−	0.997595i	−0.0225564	−	0.0390688i
$653$	−23.8267	−	13.7563i	−0.932410	−	0.538327i	−0.0448370	−	0.998994i	$-0.514277\pi$
$653$	−23.8267	−	13.7563i	−0.932410	−	0.538327i	−0.887573	+	0.460667i	$0.847610\pi$
$654$	−11.2128	+	12.6524i	−0.438455	+	0.494747i
$655$	18.4278	−	31.9179i	0.720034	−	1.24713i
$656$	2.36991			0.0925293
$657$	−28.5897	+	3.46175i	−1.11539	+	0.135056i
$658$	28.5482	−	1.19709i	1.11293	−	0.0466675i
$659$	33.0777	+	19.0974i	1.28852	+	0.743929i	0.978391	−	0.206764i	$-0.0662933\pi$
$659$	33.0777	+	19.0974i	1.28852	+	0.743929i	0.310132	+	0.950693i	$0.399627\pi$
$660$	4.59354	+	0.938576i	0.178803	+	0.0365340i
$661$		−	6.67645i		−	0.259684i	−0.991535	−	0.129842i	$-0.958553\pi$
$661$		−	6.67645i		−	0.259684i	0.991535	−	0.129842i	$-0.0414470\pi$
$662$	−13.7335	−	7.92907i	−0.533770	−	0.308172i
$663$	−11.3115	−	2.05881i	−0.439303	−	0.0799577i
$664$		−	40.1057i		−	1.55640i
$665$	21.5695	+	33.9867i	0.836431	+	1.31795i
$666$	−3.26595	+	7.65839i	−0.126553	+	0.296757i
$667$	−0.917474			−0.0355247
$668$	3.62078	−	6.27137i	0.140092	−	0.242646i
$669$	1.58491	−	1.78840i	0.0612763	−	0.0691434i
$670$		−	4.39769i		−	0.169898i
$671$	2.19021			0.0845521
$672$	20.4307	+	16.6314i	0.788132	+	0.641569i
$673$	5.54228	+	9.59951i	0.213639	+	0.370034i	0.952851	−	0.303439i	$-0.0981350\pi$
$673$	5.54228	+	9.59951i	0.213639	+	0.370034i	−0.739212	+	0.673473i	$0.764802\pi$
$674$	15.1751	+	8.76136i	0.584524	+	0.337475i
$675$	−1.07221	−	2.26255i	−0.0412692	−	0.0870855i
$676$	−16.7431	+	0.720780i	−0.643965	+	0.0277223i
$677$	14.9397	+	25.8763i	0.574178	+	0.994506i	0.996130	+	0.0878879i	$0.0280117\pi$
$677$	14.9397	+	25.8763i	0.574178	+	0.994506i	−0.421952	+	0.906618i	$0.638655\pi$
$678$	7.70782	+	6.83083i	0.296017	+	0.262336i
$679$	0.244556	−	0.467815i	0.00938519	−	0.0179531i
$680$	9.39841	+	5.42617i	0.360413	+	0.208084i
$681$	3.86595	+	3.42609i	0.148144	+	0.131288i
$682$	3.52627	−	2.03589i	0.135028	−	0.0779584i
$683$	−3.29835	+	1.90431i	−0.126208	+	0.0728662i	−0.561775	−	0.827290i	$-0.689881\pi$
$683$	−3.29835	+	1.90431i	−0.126208	+	0.0728662i	0.435567	+	0.900156i	$0.356548\pi$
$684$	10.8587	−	25.4628i	0.415193	−	0.973593i
$685$	23.4883	+	13.5610i	0.897443	+	0.518139i
$686$	−6.05023	+	14.3953i	−0.230999	+	0.549616i
$687$	13.7173	−	15.4785i	0.523349	−	0.590541i
$688$	−0.0513871	−	0.0890050i	−0.00195911	−	0.00339329i
$689$	27.4574	−	0.590738i	1.04604	−	0.0225053i
$690$	−1.01104	+	4.94818i	−0.0384896	+	0.188374i
$691$	−28.0069	−	16.1698i	−1.06543	−	0.615127i	−0.138501	−	0.990362i	$-0.544229\pi$
$691$	−28.0069	−	16.1698i	−1.06543	−	0.615127i	−0.926930	+	0.375235i	$0.877562\pi$
$692$	9.29284	+	16.0957i	0.353261	+	0.611866i
$693$	6.06714	−	4.96680i	0.230471	−	0.188673i
$694$	2.21736			0.0841699
$695$			33.3823i			1.26626i
$696$	2.02711	+	1.79646i	0.0768373	+	0.0680948i
$697$	9.08668	−	15.7386i	0.344182	−	0.596141i
$698$	−1.98687			−0.0752041
$699$	−19.0382	+	21.4825i	−0.720093	+	0.812544i
$700$	0.0688523	+	1.64199i	0.00260237	+	0.0620613i
$701$		−	8.39232i		−	0.316974i	−0.987361	−	0.158487i	$-0.949338\pi$
$701$		−	8.39232i		−	0.316974i	0.987361	−	0.158487i	$-0.0506616\pi$
$702$	−8.69812	+	13.1856i	−0.328289	+	0.497659i
$703$	−20.4036	−	11.7800i	−0.769536	−	0.444292i
$704$		−	4.31380i		−	0.162582i
$705$	−9.44052	+	46.2034i	−0.355550	+	1.74012i
$706$	16.6241	+	9.59791i	0.625655	+	0.361222i
$707$	−0.666573	−	15.8964i	−0.0250690	−	0.597847i
$708$	5.33095	−	26.0905i	0.200349	−	0.980541i
$709$	27.1958			1.02136			0.510679	−	0.859771i	$-0.329394\pi$
$709$	27.1958			1.02136			0.510679	+	0.859771i	$0.329394\pi$
$710$	2.57617	−	4.46206i	0.0966820	−	0.167458i
$711$	−40.1545	−	17.1241i	−1.50591	−	0.642202i
$712$	−12.4579	−	7.19256i	−0.466879	−	0.269553i
$713$	−3.97698	−	6.88832i	−0.148939	−	0.257970i
$714$	6.64738	−	2.53216i	0.248772	−	0.0947635i
$715$	3.64353	−	6.63648i	0.136260	−	0.248190i
$716$	24.8957	−	14.3735i	0.930397	−	0.537165i
$717$	16.2462	+	48.6905i	0.606727	+	1.81838i
$718$	5.68544			0.212179
$719$	29.4101			1.09681			0.548405	−	0.836213i	$-0.315235\pi$
$719$	29.4101			1.09681			0.548405	+	0.836213i	$0.315235\pi$
$720$	−1.22422	+	0.919304i	−0.0456240	+	0.0342604i
$721$	−13.7883	−	21.7259i	−0.513502	−	0.809114i
$722$	−23.5355	−	13.5882i	−0.875902	−	0.505702i
$723$	20.8210	−	23.4942i	0.774341	−	0.873757i
$724$	−6.99934	+	4.04107i	−0.260128	+	0.150185i
$725$			0.271715i			0.0100912i
$726$	14.3425	+	2.93052i	0.532298	+	0.108762i
$727$			31.8635i			1.18175i	0.806763	+	0.590876i	$0.201218\pi$
$727$			31.8635i			1.18175i	−0.806763	+	0.590876i	$0.798782\pi$
$728$	22.0258	−	14.6526i	0.816332	−	0.543061i
$729$	−9.54908	−	25.2550i	−0.353669	−	0.935370i
$730$	8.60196	−	14.8990i	0.318373	−	0.551438i
$731$	−0.788112			−0.0291494
$732$	−3.28339	+	3.70494i	−0.121358	+	0.136938i
$733$	−8.03692	+	4.64012i	−0.296850	+	0.171387i	−0.641027	−	0.767518i	$-0.721491\pi$
$733$	−8.03692	+	4.64012i	−0.296850	+	0.171387i	0.344177	+	0.938905i	$0.388158\pi$
$734$	−5.38599	+	9.32881i	−0.198801	+	0.344333i
$735$	−20.6506	−	15.4182i	−0.761710	−	0.568708i
$736$	−9.35328			−0.344767
$737$		−	2.42405i		−	0.0892909i
$738$	−14.9928	−	19.9657i	−0.551893	−	0.734947i
$739$	38.3327			1.41009			0.705046	−	0.709162i	$-0.250926\pi$
$739$	38.3327			1.41009			0.705046	+	0.709162i	$0.250926\pi$
$740$	4.50970	+	7.81103i	0.165780	+	0.287139i
$741$	−34.0833	−	28.9206i	−1.25208	−	1.06242i
$742$	−14.3463	+	9.10484i	−0.526669	+	0.334249i
$743$	−41.4254	+	23.9170i	−1.51975	+	0.877428i	−0.520022	+	0.854153i	$0.674076\pi$
$743$	−41.4254	+	23.9170i	−1.51975	+	0.877428i	−0.999729	+	0.0232753i	$0.992591\pi$
$744$	−4.70081	+	23.0065i	−0.172340	+	0.843459i
$745$	13.8479	−	7.99508i	0.507347	−	0.292917i
$746$	−18.7696	−	10.8367i	−0.687205	−	0.396758i
$747$	34.6934	−	26.0523i	1.26936	−	0.953203i
$748$	2.03041	+	1.17226i	0.0742393	+	0.0428621i
$749$	−0.753455	+	1.44130i	−0.0275306	+	0.0526638i
$750$	16.6718	+	3.40648i	0.608770	+	0.124387i
$751$	9.80592	−	16.9844i	0.357823	−	0.619768i	−0.629774	−	0.776779i	$-0.716852\pi$
$751$	9.80592	−	16.9844i	0.357823	−	0.619768i	0.987597	+	0.157011i	$0.0501857\pi$
$752$	−3.07522			−0.112142
$753$	−2.63452	+	12.8937i	−0.0960071	+	0.469874i
$754$	1.46580	−	0.888859i	0.0533814	−	0.0323703i
$755$	7.53267			0.274142
$756$	−0.693590	+	17.7089i	−0.0252256	+	0.644068i
$757$	−6.86398	−	11.8888i	−0.249476	−	0.432105i	0.713905	−	0.700243i	$-0.246925\pi$
$757$	−6.86398	−	11.8888i	−0.249476	−	0.432105i	−0.963380	+	0.268138i	$0.913592\pi$
$758$		−	25.7339i		−	0.934699i
$759$	−0.557293	+	2.72748i	−0.0202285	+	0.0990013i
$760$	21.0961	+	36.5394i	0.765234	+	1.32542i
$761$	−22.7887			−0.826090			−0.413045	−	0.910711i	$-0.635535\pi$
$761$	−22.7887			−0.826090			−0.413045	+	0.910711i	$0.635535\pi$
$762$	−5.02446	−	15.0585i	−0.182017	−	0.545510i
$763$	27.1436	+	14.1896i	0.982664	+	0.513700i
$764$	5.50771	−	3.17988i	0.199262	−	0.115044i
$765$	1.41121	+	11.6549i	0.0510225	+	0.421382i
$766$	−6.05112	−	3.49362i	−0.218636	−	0.126230i
$767$	−37.6940	−	20.6946i	−1.36105	−	0.747239i
$768$	19.8632	+	17.6031i	0.716751	+	0.635199i
$769$	−20.0316	+	11.5653i	−0.722359	+	0.417054i	−0.815620	−	0.578588i	$-0.803604\pi$
$769$	−20.0316	+	11.5653i	−0.722359	+	0.417054i	0.0932614	+	0.995642i	$0.470271\pi$
$770$	0.196240	+	4.67993i	0.00707199	+	0.168653i
$771$	−8.21801	+	40.2202i	−0.295964	+	1.44850i
$772$	3.46877	+	6.00808i	0.124844	+	0.216236i
$773$	−0.639209	−	1.10714i	−0.0229908	−	0.0398211i	0.854301	−	0.519778i	$-0.173985\pi$
$773$	−0.639209	−	1.10714i	−0.0229908	−	0.0398211i	−0.877292	+	0.479957i	$0.840652\pi$
$774$	−0.424746	+	0.995994i	−0.0152672	+	0.0358003i
$775$	−2.04001	+	1.17780i	−0.0732795	+	0.0423079i
$776$	0.276652	−	0.479176i	0.00993124	−	0.0172014i
$777$	14.8920	+	2.39782i	0.534249	+	0.0860213i
$778$	11.3028	+	19.5770i	0.405225	+	0.701871i
$779$	61.1890	−	35.3275i	2.19232	−	1.26574i
$780$	5.76410	+	16.1122i	0.206388	+	0.576911i
$781$	1.42001	−	2.45953i	0.0508119	−	0.0880088i
$782$	−1.26276	+	2.18717i	−0.0451563	+	0.0782130i
$783$	−0.237238	+	2.92051i	−0.00847819	+	0.104370i
$784$	0.715498	−	1.52067i	0.0255535	−	0.0543095i
$785$		−	31.2255i		−	1.11448i
$786$	−8.01435	−	24.0192i	−0.285862	−	0.856737i
$787$	−47.7112	+	27.5461i	−1.70072	+	0.981911i	−0.755690	+	0.654930i	$0.772698\pi$
$787$	−47.7112	+	27.5461i	−1.70072	+	0.981911i	−0.945031	+	0.326982i	$0.893968\pi$
$788$	2.24225	+	1.29456i	0.0798768	+	0.0461169i
$789$	−9.62733	−	28.8534i	−0.342742	−	1.02721i
$790$	22.5842	−	13.0390i	0.803510	−	0.463907i
$791$	8.64432	−	16.5359i	0.307357	−	0.587947i
$792$	6.57186	−	4.93501i	0.233521	−	0.175358i
$793$	4.14498	+	6.83542i	0.147193	+	0.242733i
$794$	−2.46501	+	4.26952i	−0.0874798	+	0.151519i
$795$	−8.87598	−	26.6016i	−0.314799	−	0.943460i
$796$	2.10298	+	1.21416i	0.0745383	+	0.0430347i
$797$	12.6676	−	21.9409i	0.448710	−	0.777188i	−0.549593	−	0.835433i	$-0.685217\pi$
$797$	12.6676	−	21.9409i	0.448710	−	0.777188i	0.998302	+	0.0582448i	$0.0185504\pi$
$798$	27.3038	+	4.39627i	0.966543	+	0.155626i
$799$	−11.7910	+	20.4226i	−0.417135	+	0.722499i
$800$			2.77002i			0.0979352i
$801$	−1.87061	−	15.4489i	−0.0660947	−	0.545859i
$802$	−1.74931	−	3.02989i	−0.0617702	−	0.106989i
$803$	4.74147	−	8.21247i	0.167323	−	0.289812i
$804$	4.10049	+	3.63394i	0.144613	+	0.128159i
$805$	9.14191	−	0.383341i	0.322210	−	0.0135110i
$806$	13.0273	+	7.15220i	0.458867	+	0.251925i
$807$	−30.7751	−	27.2735i	−1.08333	−	0.960072i
$808$		−	16.6767i		−	0.586683i
$809$			24.9292i			0.876462i	0.898862	+	0.438231i	$0.144395\pi$
$809$			24.9292i			0.876462i	−0.898862	+	0.438231i	$0.855605\pi$
$810$	15.4897	+	4.49783i	0.544251	+	0.158038i
$811$		−	13.2404i		−	0.464932i	−0.972605	−	0.232466i	$-0.925321\pi$
$811$		−	13.2404i		−	0.464932i	0.972605	−	0.232466i	$-0.0746794\pi$
$812$	0.891026	−	1.70446i	0.0312689	−	0.0598147i
$813$	−51.4337	−	10.5092i	−1.80386	−	0.368574i
$814$	−1.37077	−	2.37424i	−0.0480454	−	0.0832170i
$815$	0.949685	+	1.64490i	0.0332660	+	0.0576184i
$816$	−0.726218	+	0.242312i	−0.0254227	+	0.00848263i
$817$	−2.65354	−	1.53202i	−0.0928357	−	0.0535987i
$818$	−8.97874			−0.313934
$819$	26.9829	+	9.53523i	0.942860	+	0.333188i
$820$	−27.0486			−0.944577
$821$	21.6417	+	12.4948i	0.755299	+	0.436072i	0.827605	−	0.561310i	$-0.189703\pi$
$821$	21.6417	+	12.4948i	0.755299	+	0.436072i	−0.0723065	+	0.997382i	$0.523036\pi$
$822$	17.6757	−	5.89775i	0.616512	−	0.205708i
$823$	11.7636	+	20.3752i	0.410054	+	0.710234i	0.994895	−	0.100914i	$-0.0321766\pi$
$823$	11.7636	+	20.3752i	0.410054	+	0.710234i	−0.584841	+	0.811148i	$0.698843\pi$
$824$	−13.4856	−	23.3577i	−0.469793	−	0.813705i
$825$	0.807758	+	0.165045i	0.0281225	+	0.00574614i
$826$	26.5812	−	1.11461i	0.924877	−	0.0387822i
$827$		−	32.2623i		−	1.12187i	−0.827860	−	0.560934i	$-0.810442\pi$
$827$		−	32.2623i		−	1.12187i	0.827860	−	0.560934i	$-0.189558\pi$
$828$	−3.77833	−	5.03154i	−0.131306	−	0.174858i
$829$			31.1536i			1.08201i	0.841019	+	0.541005i	$0.181956\pi$
$829$			31.1536i			1.08201i	−0.841019	+	0.541005i	$0.818044\pi$
$830$			25.9183i			0.899638i
$831$	−22.7898	−	20.1968i	−0.790568	−	0.700618i
$832$	13.4629	−	8.16388i	0.466743	−	0.283032i
$833$	−7.35541	−	10.5822i	−0.254850	−	0.366650i
$834$	17.1644	+	15.2114i	0.594353	+	0.526728i
$835$	−5.97019	+	10.3407i	−0.206607	+	0.357853i
$836$	4.55755	+	7.89391i	0.157626	+	0.273017i
$837$	−22.9553	+	10.8784i	−0.793452	+	0.376012i
$838$			6.83356i			0.236062i
$839$	22.8424	−	39.5642i	0.788608	−	1.36591i	−0.138211	−	0.990403i	$-0.544135\pi$
$839$	22.8424	−	39.5642i	0.788608	−	1.36591i	0.926820	−	0.375507i	$-0.122531\pi$
$840$	−20.9491	−	17.0534i	−0.722814	−	0.588398i
$841$	−14.3410	+	24.8394i	−0.494517	+	0.856529i
$842$	12.2593	+	7.07791i	0.422483	+	0.243921i
$843$	−14.8840	−	44.6077i	−0.512632	−	1.53637i
$844$	4.75391	−	8.23402i	0.163636	−	0.283427i
$845$	27.6072	−	1.18847i	0.949715	−	0.0408847i
$846$	19.4549	+	25.9077i	0.668872	+	0.890725i
$847$	−1.11112	−	26.4981i	−0.0381787	−	0.910485i
$848$	1.58373	−	0.914366i	0.0543854	−	0.0313995i
$849$	3.92706	+	11.7695i	0.134777	+	0.403929i
$850$	0.647742	+	0.373974i	0.0222174	+	0.0128272i
$851$	−4.63791	+	2.67770i	−0.158985	+	0.0917903i
$852$	2.03175	+	6.08920i	0.0696064	+	0.208613i
$853$			15.6593i			0.536165i	0.963396	+	0.268082i	$0.0863900\pi$
$853$			15.6593i			0.536165i	−0.963396	+	0.268082i	$0.913610\pi$
$854$	−4.38305	−	2.29129i	−0.149985	−	0.0784064i
$855$	−17.9046	+	41.9848i	−0.612323	+	1.43585i
$856$	−0.852341	+	1.47630i	−0.0291324	+	0.0504588i
$857$	−0.325260	+	0.563367i	−0.0111107	+	0.0192443i	−0.871527	−	0.490347i	$-0.836870\pi$
$857$	−0.325260	+	0.563367i	−0.0111107	+	0.0192443i	0.860417	+	0.509591i	$0.170203\pi$
$858$	−1.75206	−	4.89747i	−0.0598142	−	0.167197i
$859$	20.5321	−	11.8542i	0.700547	−	0.404461i	−0.107004	−	0.994259i	$-0.534126\pi$
$859$	20.5321	−	11.8542i	0.700547	−	0.404461i	0.807551	+	0.589798i	$0.200792\pi$
$860$	0.586498	+	1.01584i	0.0199994	+	0.0346400i
$861$	−28.5576	+	35.0815i	−0.973241	+	1.19557i
$862$	5.83246	−	10.1021i	0.198654	−	0.344079i
$863$	−7.67159	+	4.42919i	−0.261144	+	0.150771i	−0.624856	−	0.780740i	$-0.714842\pi$
$863$	−7.67159	+	4.42919i	−0.261144	+	0.150771i	0.363712	+	0.931511i	$0.381509\pi$
$864$	−2.41855	+	29.7734i	−0.0822807	+	1.01291i
$865$	−15.3227	−	26.5397i	−0.520987	−	0.902375i
$866$	−4.94423	−	8.56366i	−0.168012	−	0.291005i
$867$	4.71928	−	23.0969i	0.160275	−	0.784413i
$868$	16.6593	−	0.698560i	0.565452	−	0.0237107i
$869$	12.4486	−	7.18721i	0.422290	−	0.243809i
$870$	−1.31002	−	1.16096i	−0.0444137	−	0.0393604i
$871$	7.56520	−	4.58752i	0.256337	−	0.155442i
$872$	27.8028	+	16.0520i	0.941522	+	0.543588i
$873$	0.594220	−	0.0719504i	0.0201113	−	0.00243515i
$874$	−8.50335	+	4.90941i	−0.287630	+	0.166063i
$875$	−1.29158	−	30.8017i	−0.0436635	−	1.04129i
$876$	6.78409	+	20.3321i	0.229213	+	0.686959i
$877$	−9.22225			−0.311413			−0.155707	−	0.987803i	$-0.549765\pi$
$877$	−9.22225			−0.311413			−0.155707	+	0.987803i	$0.549765\pi$
$878$	11.5717	+	20.0428i	0.390526	+	0.676410i
$879$	−7.90336	+	38.6803i	−0.266574	+	1.30466i
$880$		−	0.504123i		−	0.0169940i
$881$	9.25255	+	16.0259i	0.311726	+	0.539926i	0.978736	−	0.205123i	$-0.0657595\pi$
$881$	9.25255	+	16.0259i	0.311726	+	0.539926i	−0.667010	+	0.745049i	$0.732426\pi$
$882$	−17.3376	+	3.59241i	−0.583786	+	0.120963i
$883$	38.1017			1.28223			0.641113	−	0.767447i	$-0.278473\pi$
$883$	38.1017			1.28223			0.641113	+	0.767447i	$0.278473\pi$
$884$	0.184063	+	8.55522i	0.00619072	+	0.287743i
$885$	−8.79003	+	43.0198i	−0.295474	+	1.44610i
$886$	23.1158			0.776590
$887$	14.9001	−	25.8078i	0.500298	−	0.866542i	−0.499702	−	0.866197i	$-0.666557\pi$
$887$	14.9001	−	25.8078i	0.500298	−	0.866542i	1.00000		0.000344167i	$-0.000109552\pi$
$888$	15.4903	+	3.16505i	0.519820	+	0.106212i
$889$	−24.2828	+	15.4110i	−0.814420	+	0.516869i
$890$	8.05091	+	4.64819i	0.269867	+	0.155808i
$891$	8.53803	+	2.47924i	0.286035	+	0.0830578i
$892$	−1.54026	−	0.889269i	−0.0515717	−	0.0297749i
$893$	−79.3996	+	45.8414i	−2.65701	+	1.53402i
$894$	2.19923	−	10.7634i	0.0735532	−	0.359981i
$895$	−41.0498	+	23.7001i	−1.37214	+	0.792207i
$896$	9.57988	−	18.3255i	0.320041	−	0.612212i
$897$	−9.56687	+	3.42252i	−0.319429	+	0.114274i
$898$	2.71234	+	4.69791i	0.0905120	+	0.156771i
$899$	2.75676			0.0919431
$900$	−1.49012	+	1.11897i	−0.0496705	+	0.0372991i
$901$		−	14.0234i		−	0.467188i
$902$	8.22168			0.273752
$903$	1.93675	+	0.311843i	0.0644510	+	0.0103775i
$904$	9.77884	−	16.9374i	0.325239	−	0.563331i
$905$	11.5410	−	6.66319i	0.383635	−	0.221492i
$906$	3.43243	−	3.87311i	0.114035	−	0.128676i
$907$	−25.1971			−0.836657			−0.418329	−	0.908296i	$-0.637384\pi$
$907$	−25.1971			−0.836657			−0.418329	+	0.908296i	$0.637384\pi$
$908$	1.92232	−	3.32956i	0.0637946	−	0.110495i
$909$	14.4261	−	10.8330i	0.478484	−	0.359308i
$910$	−14.2342	+	9.46923i	−0.471859	+	0.313902i
$911$			29.5095i			0.977692i	0.872370	+	0.488846i	$0.162582\pi$
$911$			29.5095i			0.977692i	−0.872370	+	0.488846i	$0.837418\pi$
$912$	−2.91618	−	0.595849i	−0.0965644	−	0.0197305i
$913$			14.2864i			0.472811i
$914$	−17.5211	+	10.1158i	−0.579546	+	0.334601i
$915$	5.41388	−	6.10895i	0.178977	−	0.201956i
$916$	−13.3309	−	7.69658i	−0.440464	−	0.254302i
$917$	−38.7327	+	24.5816i	−1.27907	+	0.811756i
$918$	6.63569	+	4.58519i	0.219011	+	0.151334i
$919$	42.3593			1.39730			0.698652	−	0.715461i	$-0.253784\pi$
$919$	42.3593			1.39730			0.698652	+	0.715461i	$0.253784\pi$
$920$	9.59062			0.316193
$921$	13.6909	+	41.0321i	0.451131	+	1.35205i
$922$	−4.61096	+	2.66214i	−0.151854	+	0.0876729i
$923$	10.3633	−	0.222964i	0.341112	−	0.00733894i
$924$	−4.52581	−	3.68418i	−0.148888	−	0.121201i
$925$	0.793014	+	1.37354i	0.0260742	+	0.0451618i
$926$	−3.23879	−	1.86992i	−0.106433	−	0.0614492i
$927$	11.4454	−	26.8386i	0.375918	−	0.881496i
$928$	1.62088	−	2.80744i	0.0532079	−	0.0921587i
$929$	−30.2792			−0.993429			−0.496714	−	0.867914i	$-0.665460\pi$
$929$	−30.2792			−0.993429			−0.496714	+	0.867914i	$0.665460\pi$
$930$	3.03790	−	14.8679i	0.0996165	−	0.487539i
$931$	−4.19456	−	49.9280i	−0.137471	−	1.63632i
$932$	18.5019	+	10.6821i	0.606049	+	0.349903i
$933$	6.24449	−	30.5615i	0.204435	−	1.00054i
$934$		−	3.44749i		−	0.112805i
$935$	−3.34789	−	1.93290i	−0.109488	−	0.0632127i
$936$	27.8389	+	11.1706i	0.909944	+	0.365122i
$937$		−	1.23501i		−	0.0403459i	−0.999797	−	0.0201730i	$-0.993578\pi$
$937$		−	1.23501i		−	0.0403459i	0.999797	−	0.0201730i	$-0.00642169\pi$
$938$	−2.53592	+	4.85100i	−0.0828007	+	0.158391i
$939$	23.2856	−	26.2752i	0.759896	−	0.857457i
$940$	35.0985			1.14479
$941$	−8.91584	+	15.4427i	−0.290648	+	0.503417i	−0.973963	−	0.226706i	$-0.927204\pi$
$941$	−8.91584	+	15.4427i	−0.290648	+	0.503417i	0.683315	+	0.730124i	$0.260538\pi$
$942$	−16.0554	−	14.2286i	−0.523112	−	0.463592i
$943$		−	16.0605i		−	0.523001i
$944$	−2.86333			−0.0931934
$945$	1.14364	−	29.1997i	0.0372026	−	0.949867i
$946$	−0.178272	−	0.308776i	−0.00579612	−	0.0100392i
$947$	12.8477	+	7.41765i	0.417496	+	0.241041i	0.694005	−	0.719970i	$-0.255844\pi$
$947$	12.8477	+	7.41765i	0.417496	+	0.241041i	−0.276510	+	0.961011i	$0.589178\pi$
$948$	−6.50417	+	31.8324i	−0.211246	+	1.03387i
$949$	34.6036	−	0.744486i	1.12328	−	0.0241670i
$950$	1.45395	+	2.51831i	0.0471723	+	0.0817049i
$951$	−10.7804	+	12.1645i	−0.349578	+	0.394460i
$952$	−7.23819	−	11.4051i	−0.234591	−	0.369640i
$953$	2.58732	+	1.49379i	0.0838116	+	0.0483887i	0.541320	−	0.840817i	$-0.317925\pi$
$953$	2.58732	+	1.49379i	0.0838116	+	0.0483887i	−0.457508	+	0.889205i	$0.651258\pi$
$954$	−17.7224	−	7.55780i	−0.573784	−	0.244693i
$955$	−9.08149	+	5.24320i	−0.293870	+	0.169666i
$956$	33.0849	−	19.1016i	1.07004	−	0.617789i
$957$	−0.722093	−	0.639933i	−0.0233419	−	0.0206861i
$958$	−22.1506	−	12.7887i	−0.715653	−	0.413183i
$959$	−18.0896	−	28.5033i	−0.584142	−	0.920421i
$960$	−12.0321	−	10.6631i	−0.388334	−	0.344149i
$961$	−3.55027	−	6.14924i	−0.114525	−	0.198363i
$962$	4.81557	−	8.77128i	0.155260	−	0.282798i
$963$	−1.83074	+	0.221673i	−0.0589948	+	0.00714331i
$964$	−20.2344	−	11.6823i	−0.651706	−	0.376263i
$965$	−5.71954	−	9.90654i	−0.184119	−	0.318903i
$966$	3.96861	−	4.87522i	0.127688	−	0.156858i
$967$	13.1157			0.421773			0.210887	−	0.977511i	$-0.432365\pi$
$967$	13.1157			0.421773			0.210887	+	0.977511i	$0.432365\pi$
$968$		−	27.7987i		−	0.893484i
$969$	−15.1382	+	17.0818i	−0.486310	+	0.548747i
$970$	−0.178786	+	0.309667i	−0.00574049	+	0.00994282i
$971$	33.8092			1.08499			0.542495	−	0.840059i	$-0.317480\pi$
$971$	33.8092			1.08499			0.542495	+	0.840059i	$0.317480\pi$
$972$	−16.9934	+	10.7262i	−0.545064	+	0.344042i
$973$	19.2498	−	36.8233i	0.617122	−	1.18050i
$974$			30.8111i			0.987251i
$975$	1.01360	+	2.83328i	0.0324611	+	0.0907376i
$976$	0.460983	+	0.266148i	0.0147557	+	0.00851921i
$977$		−	27.3800i		−	0.875964i	−0.898984	−	0.437982i	$-0.855693\pi$
$977$		−	27.3800i		−	0.875964i	0.898984	−	0.437982i	$-0.144307\pi$
$978$	1.27851	+	0.261233i	0.0408824	+	0.00835330i
$979$	4.43773	+	2.56212i	0.141830	+	0.0818858i
$980$	−8.16622	+	17.3559i	−0.260860	+	0.554413i
$981$	4.17471	+	34.4779i	0.133288	+	1.10080i
$982$	21.0956			0.673186
$983$	−16.3929	+	28.3933i	−0.522851	+	0.905605i	0.476795	+	0.879014i	$0.341798\pi$
$983$	−16.3929	+	28.3933i	−0.522851	+	0.905605i	−0.999646	+	0.0265906i	$0.991535\pi$
$984$	−31.4473	+	35.4847i	−1.00250	+	1.13121i
$985$	−3.69717	−	2.13456i	−0.117802	−	0.0680129i
$986$	−0.437661	−	0.758051i	−0.0139380	−	0.0241413i
$987$	37.0567	−	45.5221i	1.17953	−	1.44899i
$988$	−16.0109	+	29.1629i	−0.509375	+	0.927796i
$989$	−0.603172	+	0.348242i	−0.0191798	+	0.0110734i
$990$	−4.24707	+	3.18925i	−0.134981	+	0.101361i
$991$	−14.0416			−0.446047			−0.223023	−	0.974813i	$-0.571593\pi$
$991$	−14.0416			−0.446047			−0.223023	+	0.974813i	$0.571593\pi$
$992$	28.1041			0.892305
$993$	−30.9025	+	10.3110i	−0.980661	+	0.327211i
$994$	−5.41476	+	3.43646i	−0.171746	+	0.108998i
$995$	−3.46755	−	2.00199i	−0.109929	−	0.0634673i
$996$	−24.1667	−	21.4170i	−0.765752	−	0.678625i
$997$	37.1287	−	21.4363i	1.17588	−	0.678893i	0.220820	−	0.975315i	$-0.429127\pi$
$997$	37.1287	−	21.4363i	1.17588	−	0.678893i	0.955057	+	0.296422i	$0.0957934\pi$
$998$		−	13.5455i		−	0.428774i
$999$	7.32441	+	15.4558i	0.231734	+	0.489000i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.bf.b.185.20	yes	64
3.2	odd	2	inner	273.2.bf.b.185.13	yes	64
7.5	odd	6		273.2.r.b.68.13	✓	64
13.9	even	3		273.2.r.b.269.13	yes	64
21.5	even	6		273.2.r.b.68.20	yes	64
39.35	odd	6		273.2.r.b.269.20	yes	64
91.61	odd	6	inner	273.2.bf.b.152.13	yes	64
273.152	even	6	inner	273.2.bf.b.152.20	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.r.b.68.13	✓	64	7.5	odd	6
273.2.r.b.68.20	yes	64	21.5	even	6
273.2.r.b.269.13	yes	64	13.9	even	3
273.2.r.b.269.20	yes	64	39.35	odd	6
273.2.bf.b.152.13	yes	64	91.61	odd	6	inner
273.2.bf.b.152.20	yes	64	273.152	even	6	inner
273.2.bf.b.185.13	yes	64	3.2	odd	2	inner
273.2.bf.b.185.20	yes	64	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.bf (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.730177 + 0.421568i) q^{2} +(1.64300 - 0.548211i) q^{3} +(-0.644561 - 1.11641i) q^{4} +(1.06280 + 1.84082i) q^{5} +(1.43079 + 0.292347i) q^{6} +(-0.110845 - 2.64343i) q^{7} -2.77318i q^{8} +(2.39893 - 1.80143i) q^{9} +1.79216i q^{10} +0.987856i q^{11} +(-1.67105 - 1.48092i) q^{12} +(-3.08300 + 1.86952i) q^{13} +(1.03345 - 1.97690i) q^{14} +(2.75534 + 2.44184i) q^{15} +(-0.120042 + 0.207918i) q^{16} +(0.920525 + 1.59440i) q^{17} +(2.51107 - 0.304049i) q^{18} +7.15770i q^{19} +(1.37008 - 2.37304i) q^{20} +(-1.63128 - 4.28240i) q^{21} +(-0.416448 + 0.721310i) q^{22} +(1.40903 + 0.813502i) q^{23} +(-1.52029 - 4.55634i) q^{24} +(0.240923 - 0.417291i) q^{25} +(-3.03926 + 0.0653890i) q^{26} +(2.95389 - 4.27487i) q^{27} +(-2.87971 + 1.82760i) q^{28} +(-0.488355 + 0.281952i) q^{29} +(0.982484 + 2.94453i) q^{30} +(-4.23375 - 2.44435i) q^{31} +(-4.97858 + 2.87439i) q^{32} +(0.541554 + 1.62305i) q^{33} +1.55226i q^{34} +(4.74827 - 3.01347i) q^{35} +(-3.55739 - 1.51707i) q^{36} +(-1.64578 + 2.85058i) q^{37} +(-3.01745 + 5.22638i) q^{38} +(-4.04049 + 4.76177i) q^{39} +(5.10491 - 2.94732i) q^{40} +(-4.93559 - 8.54870i) q^{41} +(0.614202 - 3.81460i) q^{42} +(-0.214038 + 0.370726i) q^{43} +(1.10286 - 0.636734i) q^{44} +(5.86568 + 2.50144i) q^{45} +(0.685893 + 1.18800i) q^{46} +(6.40449 + 11.0929i) q^{47} +(-0.0832459 + 0.407419i) q^{48} +(-6.97543 + 0.586021i) q^{49} +(0.351833 - 0.203131i) q^{50} +(2.38649 + 2.11496i) q^{51} +(4.07434 + 2.23688i) q^{52} +(-6.59657 - 3.80853i) q^{53} +(3.95901 - 1.87615i) q^{54} +(-1.81847 + 1.04989i) q^{55} +(-7.33069 + 0.307392i) q^{56} +(3.92393 + 11.7601i) q^{57} -0.475447 q^{58} +(5.96320 + 10.3286i) q^{59} +(0.950114 - 4.65001i) q^{60} -2.21713i q^{61} +(-2.06092 - 3.56962i) q^{62} +(-5.02785 - 6.14172i) q^{63} -4.36683 q^{64} +(-6.71806 - 3.68832i) q^{65} +(-0.288797 + 1.41342i) q^{66} -2.45385 q^{67} +(1.18667 - 2.05537i) q^{68} +(2.76101 + 0.564144i) q^{69} +(4.73746 - 0.198652i) q^{70} +(-2.48976 - 1.43746i) q^{71} +(-4.99567 - 6.65265i) q^{72} +(-8.31343 - 4.79976i) q^{73} +(-2.40342 + 1.38762i) q^{74} +(0.167074 - 0.817688i) q^{75} +(7.99095 - 4.61358i) q^{76} +(2.61133 - 0.109499i) q^{77} +(-4.95768 + 1.77359i) q^{78} +(-7.27556 - 12.6016i) q^{79} -0.510320 q^{80} +(2.50972 - 8.64299i) q^{81} -8.32274i q^{82} +14.4620 q^{83} +(-3.72947 + 4.58145i) q^{84} +(-1.95666 + 3.38904i) q^{85} +(-0.312572 + 0.180463i) q^{86} +(-0.647800 + 0.730969i) q^{87} +2.73950 q^{88} +(2.59362 - 4.49228i) q^{89} +(3.22845 + 4.29927i) q^{90} +(5.28368 + 7.94246i) q^{91} -2.09741i q^{92} +(-8.29609 - 1.69510i) q^{93} +10.7997i q^{94} +(-13.1760 + 7.60718i) q^{95} +(-6.60407 + 7.45195i) q^{96} +(0.172790 + 0.0997601i) q^{97} +(-5.34034 - 2.51272i) q^{98} +(1.77955 + 2.36980i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 32 q^{4} - 12 q^{6} - 4 q^{7} + 8 q^{9} + 6 q^{12} - 12 q^{13} - 9 q^{15} - 16 q^{16} + 2 q^{18} + 10 q^{21} + 10 q^{22} - 24 q^{25} - 50 q^{28} - 16 q^{30} - 24 q^{31} - 33 q^{39} + 90 q^{40} - 48 q^{42}+ \cdots + 22 q^{99}+O(q^{100}) \) 64 * q + 32 * q^4 - 12 * q^6 - 4 * q^7 + 8 * q^9 + 6 * q^12 - 12 * q^13 - 9 * q^15 - 16 * q^16 + 2 * q^18 + 10 * q^21 + 10 * q^22 - 24 * q^25 - 50 * q^28 - 16 * q^30 - 24 * q^31 - 33 * q^39 + 90 * q^40 - 48 * q^42 - 20 * q^43 - 3 * q^45 + 6 * q^48 - 10 * q^51 + 30 * q^52 - 27 * q^54 + 18 * q^55 + 4 * q^57 - 60 * q^58 + 55 * q^60 - 74 * q^63 - 84 * q^64 + 75 * q^66 - 88 * q^67 - 33 * q^69 + 20 * q^70 - 34 * q^72 + 84 * q^73 + 33 * q^75 + 18 * q^76 - 71 * q^78 + 20 * q^79 - 32 * q^81 - 6 * q^84 - 2 * q^85 + 3 * q^87 + 92 * q^88 - 76 * q^91 + 28 * q^93 + 30 * q^96 + 24 * q^97 + 22 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more