LMFDB - Embedded newform 273.2.bf.b.185.13

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			185.13
Character	$\chi$	$=$	273.185
Dual form			273.2.bf.b.152.13

$q$-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} +(0.968576 + 1.09293i) 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} +(0.446987 + 2.18763i) q^{12} +(-3.08300 + 1.86952i) q^{13} +(-1.03345 + 1.97690i) q^{14} +(0.737024 + 3.60711i) q^{15} +(-0.120042 + 0.207918i) q^{16} +(-0.920525 - 1.59440i) q^{17} +(-0.992218 - 2.32667i) q^{18} +7.15770i q^{19} +(-1.37008 + 2.37304i) q^{20} +(-1.26704 + 4.40393i) 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} +(0.464880 - 3.83933i) q^{36} +(-1.64578 + 2.85058i) q^{37} +(3.01745 - 5.22638i) q^{38} +(6.09028 - 1.38150i) q^{39} +(5.10491 - 2.94732i) q^{40} +(4.93559 + 8.54870i) q^{41} +(2.78172 - 2.68151i) q^{42} +(-0.214038 + 0.370726i) q^{43} +(-1.10286 + 0.636734i) q^{44} +(0.766526 - 6.33055i) q^{45} +(0.685893 + 1.18800i) q^{46} +(-6.40449 - 11.0929i) q^{47} +(0.311212 - 0.275803i) q^{48} +(-6.97543 + 0.586021i) q^{49} +(-0.351833 + 0.203131i) q^{50} +(0.638362 + 3.12424i) q^{51} +(4.07434 + 2.23688i) q^{52} +(6.59657 + 3.80853i) q^{53} +(0.354713 + 4.36668i) 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} +(3.55197 - 3.14783i) q^{60} -2.21713i q^{61} +(2.06092 + 3.56962i) q^{62} +(4.49603 - 6.54108i) q^{63} -4.36683 q^{64} +(6.71806 + 3.68832i) q^{65} +(1.07966 - 0.956814i) q^{66} -2.45385 q^{67} +(-1.18667 + 2.05537i) q^{68} +(1.86907 + 2.10903i) 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} +(-0.624601 + 0.553534i) q^{75} +(7.99095 - 4.61358i) q^{76} +(-2.61133 + 0.109499i) q^{77} +(-5.02937 - 1.55872i) 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} +(5.73329 - 1.42407i) q^{84} +(-1.95666 + 3.38904i) q^{85} +(0.312572 - 0.180463i) q^{86} +(-0.956938 + 0.195526i) 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} +(5.61604 + 6.33707i) q^{93} +10.7997i q^{94} +(13.1760 - 7.60718i) q^{95} +(-9.75561 + 1.99332i) 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	0.219112	−	0.975700i	$-0.429684\pi$
$2$	−0.730177	−	0.421568i	−0.516313	−	0.298093i	−0.735425	+	0.677606i	$0.763017\pi$
$3$	−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	0.524302	−	0.851532i	$-0.324326\pi$
$5$	−1.06280	−	1.84082i	−0.475297	−	0.823239i	−0.999600	+	0.0282929i	$0.990993\pi$
$6$	0.968576	+	1.09293i	0.395419	+	0.446186i
$7$	−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	$-0.952419\pi$
$11$		−	0.987856i		−	0.297850i	0.988849	−	0.148925i	$-0.0475813\pi$
$12$	0.446987	+	2.18763i	0.129034	+	0.631514i
$13$	−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
$15$	0.737024	+	3.60711i	0.190299	+	0.931352i
$16$	−0.120042	+	0.207918i	−0.0300104	+	0.0519796i
$17$	−0.920525	−	1.59440i	−0.223260	−	0.386698i	0.732536	−	0.680728i	$-0.238337\pi$
$17$	−0.920525	−	1.59440i	−0.223260	−	0.386698i	−0.955796	+	0.294030i	$0.905003\pi$
$18$	−0.992218	−	2.32667i	−0.233868	−	0.548402i
$19$			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
$21$	−1.26704	+	4.40393i	−0.276490	+	0.961017i
$22$	−0.416448	+	0.721310i	−0.0887871	+	0.153784i
$23$	−1.40903	−	0.813502i	−0.293803	−	0.169627i	0.345853	−	0.938289i	$-0.387590\pi$
$23$	−1.40903	−	0.813502i	−0.293803	−	0.169627i	−0.639655	+	0.768662i	$0.720923\pi$
$24$	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	−0.453972	−	0.891016i	$-0.649993\pi$
$29$	0.488355	−	0.281952i	0.0906852	−	0.0523571i	0.544657	+	0.838659i	$0.316660\pi$
$30$	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
$36$	0.464880	−	3.83933i	0.0774799	−	0.639888i
$37$	−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
$39$	6.09028	−	1.38150i	0.975225	−	0.221217i
$40$	5.10491	−	2.94732i	0.807158	−	0.466013i
$41$	4.93559	+	8.54870i	0.770810	+	1.33508i	0.937120	+	0.349008i	$0.113482\pi$
$41$	4.93559	+	8.54870i	0.770810	+	1.33508i	−0.166310	+	0.986074i	$0.553185\pi$
$42$	2.78172	−	2.68151i	0.429228	−	0.413765i
$43$	−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
$45$	0.766526	−	6.33055i	0.114267	−	0.943702i
$46$	0.685893	+	1.18800i	0.101129	+	0.175161i
$47$	−6.40449	−	11.0929i	−0.934190	−	1.61807i	−0.776071	−	0.630645i	$-0.782790\pi$
$47$	−6.40449	−	11.0929i	−0.934190	−	1.61807i	−0.158119	−	0.987420i	$-0.550543\pi$
$48$	0.311212	−	0.275803i	0.0449196	−	0.0398087i
$49$	−6.97543	+	0.586021i	−0.996490	+	0.0837173i
$50$	−0.351833	+	0.203131i	−0.0497567	+	0.0287270i
$51$	0.638362	+	3.12424i	0.0893885	+	0.437482i
$52$	4.07434	+	2.23688i	0.565010	+	0.310199i
$53$	6.59657	+	3.80853i	0.906109	+	0.523142i	0.879177	−	0.476495i	$-0.158093\pi$
$53$	6.59657	+	3.80853i	0.906109	+	0.523142i	0.0269320	+	0.999637i	$0.491426\pi$
$54$	0.354713	+	4.36668i	0.0482703	+	0.594229i
$55$	−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	$-0.883740\pi$
$59$	−5.96320	−	10.3286i	−0.776342	−	1.34466i	0.157695	−	0.987488i	$-0.449594\pi$
$60$	3.55197	−	3.14783i	0.458557	−	0.406383i
$61$		−	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
$63$	4.49603	−	6.54108i	0.566447	−	0.824098i
$64$	−4.36683			−0.545853
$65$	6.71806	+	3.68832i	0.833272	+	0.457480i
$66$	1.07966	−	0.956814i	0.132897	−	0.117776i
$67$	−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
$69$	1.86907	+	2.10903i	0.225009	+	0.253898i
$70$	4.73746	−	0.198652i	0.566234	−	0.0237435i
$71$	2.48976	+	1.43746i	0.295480	+	0.170596i	0.640411	−	0.768033i	$-0.278764\pi$
$71$	2.48976	+	1.43746i	0.295480	+	0.170596i	−0.344930	+	0.938628i	$0.612097\pi$
$72$	−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
$75$	−0.624601	+	0.553534i	−0.0721227	+	0.0639166i
$76$	7.99095	−	4.61358i	0.916625	−	0.529214i
$77$	−2.61133	+	0.109499i	−0.297588	+	0.0124785i
$78$	−5.02937	−	1.55872i	−0.569464	−	0.176491i
$79$	−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	$-0.791851\pi$
$83$	−14.4620			−1.58741			−0.793707	+	0.608301i	$0.791851\pi$
$84$	5.73329	−	1.42407i	0.625553	−	0.155378i
$85$	−1.95666	+	3.38904i	−0.212230	+	0.367593i
$86$	0.312572	−	0.180463i	0.0337055	−	0.0194599i
$87$	−0.956938	+	0.195526i	−0.102595	+	0.0209626i
$88$	2.73950			0.292032
$89$	−2.59362	+	4.49228i	−0.274923	+	0.476181i	−0.970116	−	0.242643i	$-0.921986\pi$
$89$	−2.59362	+	4.49228i	−0.274923	+	0.476181i	0.695193	+	0.718824i	$0.255319\pi$
$90$	−3.22845	+	4.29927i	−0.340309	+	0.453183i
$91$	5.28368	+	7.94246i	0.553881	+	0.832596i
$92$			2.09741i			0.218670i
$93$	5.61604	+	6.33707i	0.582356	+	0.657124i
$94$			10.7997i			1.11390i
$95$	13.1760	−	7.60718i	1.35183	−	0.780481i
$96$	−9.75561	+	1.99332i	−0.995678	+	0.203442i
$97$	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	$-0.596715\pi$
$101$	−6.01356			−0.598372			−0.299186	+	0.954195i	$0.596715\pi$
$102$	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
$105$	9.45345	−	2.34810i	0.922562	−	0.229151i
$106$	−3.21111	−	5.56181i	−0.311891	−	0.540210i
$107$	0.532349	+	0.307352i	0.0514642	+	0.0297128i	0.525511	−	0.850787i	$-0.323874\pi$
$107$	0.532349	+	0.307352i	0.0514642	+	0.0297128i	−0.474047	+	0.880499i	$0.657207\pi$
$108$	−2.86856	+	6.05318i	−0.276027	+	0.582467i
$109$	−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
$111$	4.26675	−	3.78128i	0.404982	−	0.358903i
$112$	0.562923	+	0.294275i	0.0531912	+	0.0278064i
$113$	−6.10760	−	3.52622i	−0.574554	−	0.331719i	0.184412	−	0.982849i	$-0.440962\pi$
$113$	−6.10760	−	3.52622i	−0.574554	−	0.331719i	−0.758966	+	0.651130i	$0.774295\pi$
$114$	−7.82285	+	6.93277i	−0.732677	+	0.649314i
$115$			3.45835i			0.322493i
$116$	−0.629549	−	0.363470i	−0.0584522	−	0.0337474i
$117$	−10.7637	−	1.06895i	−0.995105	−	0.0988241i
$118$			10.0556i			0.925690i
$119$	−4.11264	+	2.61007i	−0.377005	+	0.239265i
$120$	−10.0032	+	2.04390i	−0.913159	+	0.186581i
$121$	10.0241			0.911285
$122$	−0.934672	+	1.61890i	−0.0846212	+	0.146568i
$123$	−3.42271	−	16.7513i	−0.308615	−	1.51041i
$124$			6.30215i			0.565949i
$125$	−11.6522			−1.04220
$126$	−6.04041	+	2.88076i	−0.538122	+	0.256638i
$127$	−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
$129$	0.554902	−	0.491766i	0.0488564	−	0.0432975i
$130$	−3.35049	−	5.52524i	−0.293858	−	0.484596i
$131$	8.66948	+	15.0160i	0.757456	+	1.31195i	0.944144	+	0.329533i	$0.106891\pi$
$131$	8.66948	+	15.0160i	0.757456	+	1.31195i	−0.186688	+	0.982419i	$0.559775\pi$
$132$	2.16106	−	0.441559i	0.188096	−	0.0384328i
$133$	18.9209	−	0.793394i	1.64065	−	0.0687960i
$134$	1.79174	+	1.03446i	0.154783	+	0.0893639i
$135$	−4.72988	+	9.98090i	−0.407083	+	0.859019i
$136$	4.42154	−	2.55278i	0.379144	−	0.218899i
$137$	−11.0502	+	6.37986i	−0.944086	+	0.545068i	−0.891239	−	0.453535i	$-0.850163\pi$
$137$	−11.0502	+	6.37986i	−0.944086	+	0.545068i	−0.0528469	+	0.998603i	$0.516830\pi$
$138$	−0.475650	−	2.32791i	−0.0404900	−	0.198164i
$139$	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
$141$	4.44135	+	21.7367i	0.374029	+	1.83056i
$142$	−1.21198	−	2.09921i	−0.101707	−	0.176161i
$143$	1.84682	+	3.04556i	0.154439	+	0.254683i
$144$	−0.662521	+	0.282535i	−0.0552101	+	0.0235446i
$145$	−1.03804	−	0.599315i	−0.0862049	−	0.0497704i
$146$	4.04685	+	7.00935i	0.334920	+	0.580098i
$147$	11.7819	+	2.86117i	0.971757	+	0.235985i
$148$	4.24323			0.348792
$149$			7.52267i			0.616281i	0.951341	+	0.308141i	$0.0997068\pi$
$149$			7.52267i			0.616281i	−0.951341	+	0.308141i	$0.900293\pi$
$150$	0.689421	−	0.140866i	0.0562910	−	0.0115017i
$151$	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
$153$	0.663914	−	5.48310i	0.0536743	−	0.443283i
$154$	1.95289	+	1.02090i	0.157368	+	0.0822663i
$155$			10.3914i			0.834658i
$156$	−5.46788	−	5.90880i	−0.437781	−	0.473083i
$157$	−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
$159$	−8.75032	−	9.87376i	−0.693946	−	0.783040i
$160$	−10.5825	−	6.10978i	−0.836616	−	0.483021i
$161$	−1.99425	+	3.81484i	−0.157169	+	0.300651i
$162$	1.81107	−	7.36893i	0.142291	−	0.578958i
$163$	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
$165$	3.56331	−	0.728074i	0.277403	−	0.0566804i
$166$	10.5598	+	6.09672i	0.819602	+	0.473197i
$167$	−2.80871	−	4.86483i	−0.217345	−	0.376452i	0.736651	−	0.676274i	$-0.236406\pi$
$167$	−2.80871	−	4.86483i	−0.217345	−	0.376452i	−0.953995	+	0.299821i	$0.903073\pi$
$168$	−12.2129	−	3.51372i	−0.942244	−	0.271089i
$169$	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	$-0.315365\pi$
$173$	14.4173			1.09613			0.548064	+	0.836437i	$0.315365\pi$
$174$	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
$177$	4.13533	+	20.2390i	0.310830	+	1.52125i
$178$	3.78760	−	2.18677i	0.283893	−	0.163906i
$179$		−	22.2997i		−	1.66676i	−0.552700	−	0.833380i	$-0.686402\pi$
$179$		−	22.2997i		−	1.66676i	0.552700	−	0.833380i	$-0.313598\pi$
$180$	−7.56158	+	3.22467i	−0.563607	+	0.240352i
$181$		−	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
$186$	−1.42920	−	6.99472i	−0.104794	−	0.512878i
$187$	−1.57504	+	0.909347i	−0.115178	+	0.0664980i
$188$	−8.25617	+	14.3001i	−0.602143	+	1.04294i
$189$	−10.9729	+	8.28224i	−0.798161	+	0.602445i
$190$	−12.8278			−0.930624
$191$		−	4.93340i		−	0.356968i	−0.983943	−	0.178484i	$-0.942881\pi$
$191$		−	4.93340i		−	0.356968i	0.983943	−	0.178484i	$-0.0571193\pi$
$192$	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
$195$	−9.01582	−	9.74284i	−0.645636	−	0.697699i
$196$	5.15033	+	7.40973i	0.367881	+	0.529267i
$197$	1.73936	−	1.00422i	0.123924	−	0.0715477i	−0.436756	−	0.899580i	$-0.643873\pi$
$197$	1.73936	−	1.00422i	0.123924	−	0.0715477i	0.560681	+	0.828032i	$0.310540\pi$
$198$	−2.29842	+	0.980169i	−0.163341	+	0.0696576i
$199$	−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
$204$	3.07648	−	2.72644i	0.215397	−	0.190889i
$205$	10.4911	−	18.1711i	0.732728	−	1.26912i
$206$	−8.20012			−0.571329
$207$	−1.91469	−	4.48980i	−0.133080	−	0.312062i
$208$	−0.0186196	−	0.865433i	−0.00129103	−	0.0600070i
$209$	7.07078			0.489096
$210$	−7.89257	−	2.27074i	−0.544639	−	0.156696i
$211$	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
$213$	−3.30266	−	3.72668i	−0.226294	−	0.255348i
$214$	−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
$219$	11.0277	+	12.4435i	0.745184	+	0.840857i
$220$	2.34422	+	1.35344i	0.158048	+	0.0912488i
$221$	5.81874	+	3.19458i	0.391411	+	0.214891i
$222$	−4.70955	+	0.962279i	−0.316084	+	0.0645839i
$223$	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
$225$	1.32968	−	0.567046i	0.0886451	−	0.0378031i
$226$	2.97308	+	5.14953i	0.197767	+	0.342542i
$227$	−1.49119	−	2.58281i	−0.0989736	−	0.171427i	0.812286	−	0.583259i	$-0.198223\pi$
$227$	−1.49119	−	2.58281i	−0.0989736	−	0.171427i	−0.911260	+	0.411831i	$0.864889\pi$
$228$	−15.6584	+	3.19940i	−1.03700	+	0.211885i
$229$	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
$231$	4.35045	+	1.25165i	0.286239	+	0.0823526i
$232$	0.781902	+	1.35429i	0.0513343	+	0.0889137i
$233$	14.3523	−	8.28630i	0.940250	−	0.542854i	0.0502115	−	0.998739i	$-0.484010\pi$
$233$	14.3523	−	8.28630i	0.940250	−	0.542854i	0.890039	+	0.455885i	$0.150677\pi$
$234$	7.40877	+	5.31815i	0.484327	+	0.347658i
$235$	−13.6133	+	23.5790i	−0.888037	+	1.53812i
$236$	−7.68729	+	13.3148i	−0.500400	+	0.866718i
$237$	5.04542	+	24.6931i	0.327735	+	1.60399i
$238$	4.10328	−	0.172060i	0.265976	−	0.0111530i
$239$		−	29.6350i		−	1.91693i	−0.285211	−	0.958465i	$-0.592064\pi$
$239$		−	29.6350i		−	1.91693i	0.285211	−	0.958465i	$-0.407936\pi$
$240$	−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	−0.720863	−	0.693077i	$-0.756254\pi$
$251$	3.79901	−	6.58007i	0.239791	−	0.415330i	0.960654	+	0.277747i	$0.0895877\pi$
$252$	−10.2005	−	0.803307i	−0.642572	−	0.0506036i
$253$	−0.803624	+	1.39192i	−0.0505234	+	0.0875091i
$254$			9.16519i			0.575075i
$255$	5.07272	−	4.49555i	0.317666	−	0.281522i
$256$	7.66168	+	13.2704i	0.478855	+	0.829402i
$257$	11.8505	−	20.5256i	0.739212	−	1.28035i	−0.213638	−	0.976913i	$-0.568531\pi$
$257$	11.8505	−	20.5256i	0.739212	−	1.28035i	0.952851	−	0.303440i	$-0.0981352\pi$
$258$	−0.612489	+	0.125147i	−0.0381319	+	0.00779131i
$259$	7.71773	+	4.03454i	0.479556	+	0.250694i
$260$	−0.212511	−	9.87748i	−0.0131794	−	0.612575i
$261$	1.67944	+	0.203353i	0.103955	+	0.0125872i
$262$		−	14.6191i		−	0.903170i
$263$			17.5614i			1.08288i	0.840740	+	0.541440i	$0.182121\pi$
$263$			17.5614i			1.08288i	−0.840740	+	0.541440i	$0.817879\pi$
$264$	−4.50101	−	1.50182i	−0.277018	−	0.0924309i
$265$		−	16.1908i		−	0.994593i
$266$	−14.1500	−	7.39711i	−0.867595	−	0.453546i
$267$	6.72405	−	5.95899i	0.411505	−	0.364684i
$268$	1.58165	+	2.73951i	0.0966149	+	0.167342i
$269$	11.8706	+	20.5606i	0.723766	+	1.25360i	0.959480	+	0.281777i	$0.0909240\pi$
$269$	11.8706	+	20.5606i	0.723766	+	1.25360i	−0.235714	+	0.971823i	$0.575743\pi$
$270$	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
$273$	−4.32697	−	15.9461i	−0.261880	−	0.965100i
$274$	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
$279$	−5.75313	−	13.4906i	−0.344431	−	0.807662i
$280$	−8.35689	−	13.1678i	−0.499420	−	0.786925i
$281$			27.1501i			1.61964i	0.586680	+	0.809819i	$0.300435\pi$
$281$			27.1501i			1.61964i	−0.586680	+	0.809819i	$0.699565\pi$
$282$	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
$285$	−25.8186	+	5.27539i	−1.52936	+	0.312487i
$286$	−0.0645949	−	3.00236i	−0.00381958	−	0.177533i
$287$	22.0508	−	13.9945i	1.30162	−	0.826067i
$288$	17.1213	+	2.07311i	1.00888	+	0.122159i
$289$	6.80527	−	11.7871i	0.400310	−	0.693357i
$290$	0.505304	+	0.875212i	0.0296725	+	0.0513942i
$291$	−0.229204	−	0.258631i	−0.0134362	−	0.0151612i
$292$			12.3750i			0.724190i
$293$	11.3968	−	19.7398i	0.665805	−	1.15321i	−0.313261	−	0.949667i	$-0.601421\pi$
$293$	11.3968	−	19.7398i	0.665805	−	1.15321i	0.979066	−	0.203542i	$-0.0652452\pi$
$294$	−7.39671	−	7.05604i	−0.431385	−	0.411516i
$295$	−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
$309$	−16.5045	+	3.37228i	−0.938907	+	0.191842i
$310$	4.38068	−	7.58757i	0.248806	−	0.430945i
$311$	−9.00463	+	15.5965i	−0.510606	+	0.884395i	0.489319	+	0.872105i	$0.337246\pi$
$311$	−9.00463	+	15.5965i	−0.510606	+	0.884395i	−0.999924	+	0.0122902i	$0.996088\pi$
$312$	3.83114	+	16.8894i	0.216896	+	0.956174i
$313$	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
$315$	−16.8193	−	1.32455i	−0.947661	−	0.0746298i
$316$	−9.37909	+	16.2451i	−0.527615	+	0.913856i
$317$	8.12697	−	4.69211i	0.456456	−	0.263535i	−0.254097	−	0.967179i	$-0.581778\pi$
$317$	8.12697	−	4.69211i	0.456456	−	0.263535i	0.710553	+	0.703644i	$0.248445\pi$
$318$	2.22682	+	10.8984i	0.124874	+	0.611154i
$319$	−0.278528	−	0.482424i	−0.0155946	−	0.0270106i
$320$	4.64105	+	8.03854i	0.259443	+	0.449368i
$321$	−0.706159	−	0.796821i	−0.0394139	−	0.0444742i
$322$	3.06437	−	1.94479i	0.170771	−	0.108379i
$323$	11.4122	−	6.58884i	0.634993	−	0.366613i
$324$	8.03148	−	8.37282i	0.446193	−	0.465157i
$325$	0.0373693	+	1.73692i	0.00207288	+	0.0963469i
$326$	−0.652465	−	0.376701i	−0.0361367	−	0.0208635i
$327$	15.0063	−	13.2989i	0.829853	−	0.735433i
$328$	−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
$333$	−9.08323	+	3.87358i	−0.497758	+	0.212271i
$334$			4.73625i			0.259156i
$335$	2.60794	+	4.51709i	0.142487	+	0.246795i
$336$	−0.763561	−	0.792096i	−0.0416556	−	0.0432124i
$337$	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
$339$	8.10170	+	9.14185i	0.440024	+	0.496517i
$340$	5.04476			0.273591
$341$	−2.41467	+	4.18233i	−0.130762	+	0.226486i
$342$	16.6536	−	7.10200i	0.900524	−	0.384032i
$343$	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	−0.559886	−	0.828570i	$-0.689155\pi$
$347$	−2.27756	+	1.31495i	−0.122266	+	0.0705902i	0.437620	+	0.899160i	$0.355822\pi$
$348$	0.835094	+	0.942309i	0.0447657	+	0.0505131i
$349$	−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
$351$	17.0988	+	7.65707i	0.912667	+	0.408704i
$352$	−2.83948	−	4.91813i	−0.151345	−	0.262137i
$353$	−22.7672			−1.21178			−0.605888	−	0.795550i	$-0.707182\pi$
$353$	−22.7672			−1.21178			−0.605888	+	0.795550i	$0.707182\pi$
$354$	5.51257	−	16.5213i	0.292990	−	0.878099i
$355$		−	6.11093i		−	0.324335i
$356$	6.68699			0.354410
$357$	8.18796	−	2.03377i	0.433353	−	0.107638i
$358$	−9.40085	+	16.2827i	−0.496850	+	0.860570i
$359$	−5.83980	+	3.37161i	−0.308213	+	0.177947i	−0.646126	−	0.763230i	$-0.723612\pi$
$359$	−5.83980	+	3.37161i	−0.308213	+	0.177947i	0.337914	+	0.941177i	$0.390279\pi$
$360$	17.5557	+	2.12571i	0.925268	+	0.112035i
$361$	−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
$366$	2.42317	−	2.14746i	0.126661	−	0.112250i
$367$			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
$369$	−3.55972	+	29.3988i	−0.185311	+	1.53044i
$370$	−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
$378$	11.5037	−	1.42168i	0.591685	−	0.0731234i
$379$	−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
$381$	3.76917	+	18.4469i	0.193100	+	0.945064i
$382$	−2.07976	+	3.60225i	−0.106410	+	0.184307i
$383$	8.28720			0.423456			0.211728	−	0.977329i	$-0.432091\pi$
$383$	8.28720			0.423456			0.211728	+	0.977329i	$0.432091\pi$
$384$	8.97853	+	10.1313i	0.458184	+	0.517009i
$385$	2.97688	+	4.69061i	0.151716	+	0.239055i
$386$	3.92951	+	2.26871i	0.200007	+	0.115474i
$387$	−1.18130	+	0.503770i	−0.0600488	+	0.0256080i
$388$		−	0.257206i		−	0.0130577i
$389$	−23.2193	−	13.4057i	−1.17727	−	0.679695i	−0.221886	−	0.975073i	$-0.571221\pi$
$389$	−23.2193	−	13.4057i	−1.17727	−	0.679695i	−0.955381	+	0.295378i	$0.904555\pi$
$390$	2.47587	+	10.9148i	0.125371	+	0.552691i
$391$			2.99540i			0.151484i
$392$	−1.62514	−	19.3441i	−0.0820819	−	0.977024i
$393$	−6.01207	−	29.4240i	−0.303269	−	1.48425i
$394$	−1.69339			−0.0853116
$395$	−15.4649	+	26.7860i	−0.778124	+	1.34775i
$396$	−3.79270	−	0.459234i	−0.190591	−	0.0230774i
$397$			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
$399$	−31.5220	−	9.06908i	−1.57807	−	0.454022i
$400$	0.0578416	+	0.100185i	0.00289208	+	0.00500923i
$401$	3.59360	+	2.07476i	0.179456	+	0.103609i	0.587037	−	0.809560i	$-0.300294\pi$
$401$	3.59360	+	2.07476i	0.179456	+	0.103609i	−0.407581	+	0.913169i	$0.633628\pi$
$402$	−2.37673	−	2.68188i	−0.118541	−	0.133760i
$403$	17.6224	−	0.379141i	0.877835	−	0.0188864i
$404$	3.87611	+	6.71362i	0.192844	+	0.334015i
$405$	13.2429	−	13.8057i	0.658043	−	0.686010i
$406$	0.0527008	+	1.25681i	0.00261550	+	0.0623744i
$407$	2.81596	+	1.62580i	0.139582	+	0.0805878i
$408$	−8.66408	+	1.77029i	−0.428936	+	0.0876423i
$409$	−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
$411$	21.6531	−	4.42427i	1.06807	−	0.218233i
$412$	−10.8579	−	6.26884i	−0.534933	−	0.308843i
$413$	−26.6418	+	16.9082i	−1.31096	+	0.831996i
$414$	−0.494689	+	4.08552i	−0.0243126	+	0.200792i
$415$	15.3702	+	26.6220i	0.754493	+	1.30682i
$416$	−9.97524	+	18.1693i	−0.489076	+	0.890824i
$417$	−18.0415	−	20.3578i	−0.883495	−	0.996925i
$418$	−5.16292	−	2.98081i	−0.252527	−	0.145796i
$419$	−4.05247	−	7.01909i	−0.197976	−	0.342905i	0.749896	−	0.661556i	$-0.230104\pi$
$419$	−4.05247	−	7.01909i	−0.197976	−	0.342905i	−0.947872	+	0.318651i	$0.896770\pi$
$420$	−8.71478	−	9.04046i	−0.425238	−	0.441129i
$421$	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
$423$	4.61913	−	38.1483i	0.224590	−	1.85483i
$424$	−10.5617	+	18.2935i	−0.512923	+	0.888409i
$425$	−0.887103			−0.0430308
$426$	0.840476	+	4.11342i	0.0407212	+	0.199296i
$427$	−5.86083	+	0.245758i	−0.283626	+	0.0118931i
$428$		−	0.792429i		−	0.0383035i
$429$	−1.36472	−	6.01632i	−0.0658895	−	0.290471i
$430$	−0.664401	−	0.383592i	−0.0320403	−	0.0184985i
$431$			13.8352i			0.666416i	0.942853	+	0.333208i	$0.108131\pi$
$431$			13.8352i			0.666416i	−0.942853	+	0.333208i	$0.891869\pi$
$432$	1.24341	−	0.101005i	0.0598238	−	0.00485959i
$433$	−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
$435$	1.37696	+	1.55374i	0.0660202	+	0.0744964i
$436$	14.9236			0.714713
$437$	5.82281	−	10.0854i	0.278543	−	0.482450i
$438$	−2.80639	−	13.7349i	−0.134094	−	0.656280i
$439$	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
$441$	−17.7892	−	11.1599i	−0.847106	−	0.531424i
$442$	−2.90198	−	4.78560i	−0.138033	−	0.227628i
$443$	−23.7433	+	13.7082i	−1.12808	+	0.651298i	−0.943451	−	0.331511i	$-0.892442\pi$
$443$	−23.7433	+	13.7082i	−1.12808	+	0.651298i	−0.184629	+	0.982808i	$0.559108\pi$
$444$	−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	0.362726	−	0.931896i	$-0.381846\pi$
$449$	−5.57195	−	3.21697i	−0.262957	−	0.151818i	−0.625683	+	0.780078i	$0.715179\pi$
$450$	−1.20995	−	0.146505i	−0.0570375	−	0.00690630i
$451$	8.44488	−	4.87566i	0.397654	−	0.229586i
$452$			9.09147i			0.427627i
$453$	−4.59370	+	4.07103i	−0.215831	+	0.191274i
$454$			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
$459$	−4.09671	+	8.64480i	−0.191218	+	0.403505i
$460$	3.86095	−	2.22912i	0.180018	−	0.103933i
$461$	3.15743	−	5.46883i	0.147056	−	0.254709i	−0.783082	−	0.621918i	$-0.786354\pi$
$461$	3.15743	−	5.46883i	0.147056	−	0.254709i	0.930138	+	0.367210i	$0.119687\pi$
$462$	−2.64894	−	2.74794i	−0.123240	−	0.127846i
$463$	−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	0.909444	−	0.415826i	$-0.136508\pi$
$467$	2.04445	+	3.54109i	0.0946057	+	0.163862i	−0.814838	+	0.579688i	$0.803174\pi$
$468$	5.74448	+	12.7057i	0.265539	+	0.587323i
$469$	0.271996	+	6.48656i	0.0125596	+	0.299522i
$470$	19.8803	−	11.4779i	0.917009	−	0.529436i
$471$	16.8758	+	19.0425i	0.777596	+	0.877430i
$472$	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
$477$	8.96392	+	21.0197i	0.410430	+	0.962424i
$478$	−12.4932	+	21.6388i	−0.571424	+	0.989735i
$479$	30.3359			1.38608			0.693042	−	0.720897i	$-0.256270\pi$
$479$	30.3359			1.38608			0.693042	+	0.720897i	$0.256270\pi$
$480$	14.0376	+	15.8398i	0.640725	+	0.722986i
$481$	−0.255276	−	11.8652i	−0.0116396	−	0.541005i
$482$	−15.2814			−0.696048
$483$	5.36790	−	5.17452i	0.244248	−	0.235449i
$484$	−6.46117	−	11.1911i	−0.293690	−	0.508686i
$485$		−	0.424099i		−	0.0192573i
$486$	−7.01532	+	11.1143i	−0.318221	+	0.504157i
$487$	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	−0.901628	−	0.432512i	$-0.857627\pi$
$491$	−21.6683	+	12.5102i	−0.977875	+	0.564577i	−0.0762474	+	0.997089i	$0.524294\pi$
$492$	−16.4952	+	14.6184i	−0.743662	+	0.659048i
$493$	−0.899086	−	0.519087i	−0.0404928	−	0.0233785i
$494$	0.468034	+	21.7541i	0.0210579	+	0.978765i
$495$	−6.25367	−	0.757217i	−0.281082	−	0.0340344i
$496$	1.01645	−	0.586849i	0.0456400	−	0.0263503i
$497$	3.52386	−	6.74084i	0.158067	−	0.302368i
$498$	−14.0076	−	15.8060i	−0.627694	−	0.708282i
$499$	−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
$501$	1.94777	+	9.53271i	0.0870201	+	0.425890i
$502$	−5.54789	+	3.20308i	−0.247614	+	0.142960i
$503$	19.4463	−	33.6820i	0.867069	−	1.50181i	0.00209081	−	0.999998i	$-0.499334\pi$
$503$	19.4463	−	33.6820i	0.867069	−	1.50181i	0.864978	−	0.501810i	$-0.167332\pi$
$504$	18.1396	+	12.4683i	0.808000	+	0.555382i
$505$	6.39120	+	11.0699i	0.284405	+	0.492603i
$506$	1.17357	−	0.677563i	0.0521717	−	0.0301214i
$507$	−16.1936	+	15.6451i	−0.719182	+	0.694822i
$508$	−7.00662	+	12.1358i	−0.310869	+	0.538440i
$509$	15.0919	−	26.1400i	0.668939	−	1.15864i	−0.309262	−	0.950977i	$-0.600082\pi$
$509$	15.0919	−	26.1400i	0.668939	−	1.15864i	0.978201	−	0.207659i	$-0.0665845\pi$
$510$	−5.59916	+	1.14405i	−0.247935	+	0.0506593i
$511$	−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	$-0.573909\pi$
$521$	16.6107	−	28.7706i	0.727729	−	1.26046i	0.957841	−	0.287299i	$-0.0927573\pi$
$522$	−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
$525$	1.53246	+	1.58973i	0.0668821	+	0.0693816i
$526$	7.40330	−	12.8229i	0.322799	−	0.559104i
$527$			9.00036i			0.392062i
$528$	−0.272453	−	0.307433i	−0.0118570	−	0.0133793i
$529$	−10.1764	−	17.6261i	−0.442453	−	0.766352i
$530$	−6.82552	+	11.8221i	−0.296482	+	0.513521i
$531$	4.30086	−	35.5197i	0.186641	−	1.54143i
$532$	−13.0814	−	20.6121i	−0.567151	−	0.893648i
$533$	−31.1984	−	17.1284i	−1.35135	−	0.741914i
$534$	−7.42186	+	1.51647i	−0.321175	+	0.0656242i
$535$		−	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
$540$	14.1915	−	1.15280i	0.610705	−	0.0496087i
$541$	−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
$546$	−3.56290	+	13.4676i	−0.152478	+	0.576358i
$547$	−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
$552$	−5.84872	+	5.18325i	−0.248938	+	0.220614i
$553$	−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	$-0.806542\pi$
$557$		−	26.9538i		−	1.14207i	0.820926	−	0.571034i	$-0.193458\pi$
$558$	−1.48641	+	12.2759i	−0.0629246	+	0.519679i
$559$	−0.0331993	−	1.54310i	−0.00140418	−	0.0652660i
$560$	−0.0565664	−	1.34899i	−0.00239037	−	0.0570054i
$561$	3.08630	−	0.630610i	0.130304	−	0.0266244i
$562$	11.4456	−	19.8244i	0.482803	−	0.836240i
$563$	3.82050	+	6.61729i	0.161015	+	0.278886i	0.935233	−	0.354033i	$-0.115190\pi$
$563$	3.82050	+	6.61729i	0.161015	+	0.278886i	−0.774218	+	0.632919i	$0.781857\pi$
$564$	21.4044	−	18.9690i	0.901288	−	0.798740i
$565$			14.9906i			0.630661i
$566$	3.01986	−	5.23056i	0.126934	−	0.219857i
$567$	22.5689	−	7.59230i	0.947806	−	0.318847i
$568$	−3.98634	+	6.90454i	−0.167263	+	0.289708i
$569$	3.23724	+	1.86902i	0.135712	+	0.0783534i	0.566319	−	0.824186i	$-0.308367\pi$
$569$	3.23724	+	1.86902i	0.135712	+	0.0783534i	−0.430607	+	0.902540i	$0.641700\pi$
$570$	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
$582$	0.0583291	+	0.285472i	0.00241782	+	0.0118332i
$583$	3.76228	−	6.51647i	0.155818	−	0.269885i
$584$	13.3106	−	23.0546i	0.550796	−	0.954006i
$585$	9.47190	+	20.9501i	0.391615	+	0.866180i
$586$	−16.6433	+	9.60900i	−0.687528	+	0.396944i
$587$	−2.83282	−	4.90659i	−0.116923	−	0.202516i	0.801624	−	0.597829i	$-0.203970\pi$
$587$	−2.83282	−	4.90659i	−0.116923	−	0.202516i	−0.918547	+	0.395312i	$0.870636\pi$
$588$	−4.39992	−	14.9977i	−0.181450	−	0.618494i
$589$	17.4959	−	30.3039i	0.720908	−	1.24865i
$590$	18.5105	−	10.6870i	0.762064	−	0.439978i
$591$	−3.40830	+	0.696401i	−0.140199	+	0.0286461i
$592$	−0.395125	−	0.684377i	−0.0162395	−	0.0281277i
$593$	−1.76064	−	3.04952i	−0.0723010	−	0.125229i	0.827608	−	0.561306i	$-0.189701\pi$
$593$	−1.76064	−	3.04952i	−0.0723010	−	0.125229i	−0.899909	+	0.436077i	$0.856368\pi$
$594$	4.31365	−	0.350405i	0.176991	−	0.0143773i
$595$	9.17558	+	4.79664i	0.376162	+	0.196643i
$596$	8.39841	−	4.84883i	0.344012	−	0.198616i
$597$	3.19661	−	0.653149i	0.130829	−	0.0267316i
$598$	−4.33560	−	2.38031i	−0.177296	−	0.0973383i
$599$	−22.9515	−	13.2511i	−0.937774	−	0.541424i	−0.0485125	−	0.998823i	$-0.515448\pi$
$599$	−22.9515	−	13.2511i	−0.937774	−	0.541424i	−0.889262	+	0.457398i	$0.848781\pi$
$600$	−1.53505	−	1.73213i	−0.0626681	−	0.0707139i
$601$	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
$606$	−5.82459	−	6.57240i	−0.236608	−	0.266985i
$607$		−	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
$609$	0.622932	+	2.50792i	0.0252425	+	0.101626i
$610$	3.97347			0.160881
$611$	40.4834	+	22.2261i	1.63779	+	0.899170i
$612$	−6.54934	+	2.79299i	−0.264742	+	0.112900i
$613$	−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
$615$	−27.1985	+	24.1038i	−1.09675	+	0.971960i
$616$	−0.303659	−	7.24167i	−0.0122348	−	0.291775i
$617$	−10.0946	−	5.82812i	−0.406393	−	0.234631i	0.282846	−	0.959165i	$-0.408722\pi$
$617$	−10.0946	−	5.82812i	−0.406393	−	0.234631i	−0.689239	+	0.724534i	$0.742055\pi$
$618$	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
$621$	0.684492	+	8.42641i	0.0274677	+	0.338140i
$622$	13.1499	−	7.59212i	0.527265	−	0.304416i
$623$	12.1625	+	6.35810i	0.487281	+	0.254732i
$624$	−0.443848	+	1.43212i	−0.0177681	+	0.0573306i
$625$	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
$630$	11.7227	+	8.05763i	0.467043	+	0.321024i
$631$	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
$633$	−2.55734	−	12.5160i	−0.101645	−	0.497467i
$634$	−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
$639$	3.38327	+	7.93350i	0.133840	+	0.313844i
$640$			16.6131i			0.656689i
$641$	−29.6869	+	17.1398i	−1.17256	+	0.676980i	−0.954282	−	0.298906i	$-0.903378\pi$
$641$	−29.6869	+	17.1398i	−1.17256	+	0.676980i	−0.218281	+	0.975886i	$0.570045\pi$
$642$	0.179707	+	0.879514i	0.00709246	+	0.0347116i
$643$	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	$-0.367237\pi$
$647$	20.6083			0.810197			0.405098	+	0.914273i	$0.367237\pi$
$648$	−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
$651$	16.1291	−	15.5480i	0.632149	−	0.609376i
$652$	−0.575962	−	0.997595i	−0.0225564	−	0.0390688i
$653$	23.8267	+	13.7563i	0.932410	+	0.538327i	0.887573	−	0.460667i	$-0.152390\pi$
$653$	23.8267	+	13.7563i	0.932410	+	0.538327i	0.0448370	+	0.998994i	$0.485723\pi$
$654$	−16.5637	+	3.38438i	−0.647691	+	0.132340i
$655$	18.4278	−	31.9179i	0.720034	−	1.24713i
$656$	−2.36991			−0.0925293
$657$	−11.2969	−	26.4903i	−0.440734	−	1.03349i
$658$	28.5482	−	1.19709i	1.11293	−	0.0466675i
$659$	−33.0777	−	19.0974i	−1.28852	−	0.743929i	−0.310132	−	0.950693i	$-0.600373\pi$
$659$	−33.0777	−	19.0974i	−1.28852	−	0.743929i	−0.978391	+	0.206764i	$0.933707\pi$
$660$	−3.10960	−	3.50884i	−0.121041	−	0.136581i
$661$		−	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
$663$	−7.80891	−	8.43861i	−0.303273	−	0.327728i
$664$		−	40.1057i		−	1.55640i
$665$	−21.5695	−	33.9867i	−0.836431	−	1.31795i
$666$	8.26534	+	1.00080i	0.320275	+	0.0387801i
$667$	−0.917474			−0.0355247
$668$	−3.62078	+	6.27137i	−0.140092	+	0.242646i
$669$	−2.34125	+	0.478377i	−0.0905180	+	0.0184951i
$670$		−	4.39769i		−	0.169898i
$671$	−2.19021			−0.0845521
$672$	6.35055	+	25.5673i	0.244978	+	0.986280i
$673$	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
$675$	−2.49553	+	0.202716i	−0.0960528	+	0.00780254i
$676$	−16.7431	+	0.720780i	−0.643965	+	0.0277223i
$677$	−14.9397	−	25.8763i	−0.574178	−	0.994506i	−0.996130	−	0.0878879i	$-0.971988\pi$
$677$	−14.9397	−	25.8763i	−0.574178	−	0.994506i	0.421952	−	0.906618i	$-0.361345\pi$
$678$	−2.06176	−	10.0906i	−0.0791814	−	0.387526i
$679$	0.244556	−	0.467815i	0.00938519	−	0.0179531i
$680$	−9.39841	−	5.42617i	−0.360413	−	0.208084i
$681$	1.03410	+	5.06106i	0.0396269	+	0.193940i
$682$	3.52627	−	2.03589i	0.135028	−	0.0779584i
$683$	3.29835	−	1.90431i	0.126208	−	0.0728662i	−0.435567	−	0.900156i	$-0.643452\pi$
$683$	3.29835	−	1.90431i	0.126208	−	0.0728662i	0.561775	+	0.827290i	$0.310119\pi$
$684$	27.4807	+	3.32747i	1.05075	+	0.127229i
$685$	23.4883	+	13.5610i	0.897443	+	0.518139i
$686$	6.05023	−	14.3953i	0.230999	−	0.549616i
$687$	−20.2634	+	4.14033i	−0.773098	+	0.157963i
$688$	−0.0513871	−	0.0890050i	−0.00195911	−	0.00339329i
$689$	−27.4574	+	0.590738i	−1.04604	+	0.0225053i
$690$	−3.77973	+	3.34968i	−0.143892	+	0.127520i
$691$	−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
$693$	−6.46164	−	4.44144i	−0.245458	−	0.168716i
$694$	2.21736			0.0841699
$695$		−	33.3823i		−	1.26626i
$696$	−0.542229	−	2.65376i	−0.0205531	−	0.100590i
$697$	9.08668	−	15.7386i	0.344182	−	0.596141i
$698$	1.98687			0.0752041
$699$	−28.1235	+	5.74635i	−1.06373	+	0.217347i
$700$	0.0688523	+	1.64199i	0.00260237	+	0.0620613i
$701$			8.39232i			0.316974i	0.987361	+	0.158487i	$0.0506616\pi$
$701$			8.39232i			0.316974i	−0.987361	+	0.158487i	$0.949338\pi$
$702$	−9.25718	−	12.7993i	−0.349390	−	0.483079i
$703$	−20.4036	−	11.7800i	−0.769536	−	0.444292i
$704$			4.31380i			0.162582i
$705$	35.2931	−	31.2774i	1.32921	−	1.17798i
$706$	16.6241	+	9.59791i	0.625655	+	0.361222i
$707$	0.666573	+	15.8964i	0.0250690	+	0.597847i
$708$	19.9296	−	17.6620i	0.748999	−	0.663778i
$709$	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
$711$	5.24738	−	43.3368i	0.196792	−	1.62526i
$712$	−12.4579	−	7.19256i	−0.466879	−	0.269553i
$713$	3.97698	+	6.88832i	0.148939	+	0.257970i
$714$	−6.83603	−	1.96677i	−0.255832	−	0.0736044i
$715$	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	$-0.684765\pi$
$719$	−29.4101			−1.09681			−0.548405	+	0.836213i	$0.684765\pi$
$720$	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
$723$	−30.7570	+	6.28444i	−1.14387	+	0.233721i
$724$	−6.99934	+	4.04107i	−0.260128	+	0.150185i
$725$		−	0.271715i		−	0.0100912i
$726$	9.70914	+	10.9557i	0.360340	+	0.406603i
$727$			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
$732$	4.85026	−	0.991031i	0.179271	−	0.0366295i
$733$	−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
$735$	−7.25490	−	24.7292i	−0.267601	−	0.912152i
$736$	−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
$741$	9.88836	+	43.5924i	0.363258	+	1.60141i
$742$	−14.3463	+	9.10484i	−0.526669	+	0.334249i
$743$	41.4254	−	23.9170i	1.51975	−	0.877428i	0.520022	−	0.854153i	$-0.325924\pi$
$743$	41.4254	−	23.9170i	1.51975	−	0.877428i	0.999729	−	0.0232753i	$-0.00740942\pi$
$744$	−17.5738	+	15.5743i	−0.644287	+	0.570980i
$745$	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
$750$	−11.2860	−	12.7350i	−0.412107	−	0.465017i
$751$	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
$753$	−9.84905	+	8.72843i	−0.358919	+	0.318082i
$754$	1.46580	−	0.888859i	0.0533814	−	0.0323703i
$755$	−7.53267			−0.274142
$756$	16.3191	+	6.91187i	0.593520	+	0.251382i
$757$	−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
$759$	2.08342	−	1.84637i	0.0756234	−	0.0670190i
$760$	21.0961	+	36.5394i	0.765234	+	1.32542i
$761$	22.7887			0.826090			0.413045	−	0.910711i	$-0.364465\pi$
$761$	22.7887			0.826090			0.413045	+	0.910711i	$0.364465\pi$
$762$	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
$765$	−10.7990	+	4.60528i	−0.390439	+	0.166504i
$766$	−6.05112	−	3.49362i	−0.218636	−	0.126230i
$767$	37.6940	+	20.6946i	1.36105	+	0.747239i
$768$	−5.31319	−	26.0036i	−0.191723	−	0.938324i
$769$	−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
$771$	−30.7228	+	27.2271i	−1.10645	+	0.980561i
$772$	3.46877	+	6.00808i	0.124844	+	0.216236i
$773$	0.639209	+	1.10714i	0.0229908	+	0.0398211i	0.877292	−	0.479957i	$-0.159348\pi$
$773$	0.639209	+	1.10714i	0.0229908	+	0.0398211i	−0.854301	+	0.519778i	$0.826015\pi$
$774$	1.07493	+	0.130156i	0.0386375	+	0.00467837i
$775$	−2.04001	+	1.17780i	−0.0732795	+	0.0423079i
$776$	−0.276652	+	0.479176i	−0.00993124	+	0.0172014i
$777$	−10.4685	−	10.8597i	−0.375555	−	0.389590i
$778$	11.3028	+	19.5770i	0.405225	+	0.701871i
$779$	−61.1890	+	35.3275i	−2.19232	+	1.26574i
$780$	−5.06579	+	16.3452i	−0.181384	+	0.585254i
$781$	1.42001	−	2.45953i	0.0508119	−	0.0880088i
$782$	1.26276	−	2.18717i	0.0451563	−	0.0782130i
$783$	−2.64785	−	1.25480i	−0.0946265	−	0.0448429i
$784$	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	−0.998302	−	0.0582448i	$-0.981450\pi$
$797$	−12.6676	+	21.9409i	−0.448710	+	0.777188i	0.549593	+	0.835433i	$0.314783\pi$
$798$	19.1934	+	19.9107i	0.679439	+	0.704831i
$799$	−11.7910	+	20.4226i	−0.417135	+	0.722499i
$800$		−	2.77002i		−	0.0979352i
$801$	−14.3144	+	6.10445i	−0.505775	+	0.215690i
$802$	−1.74931	−	3.02989i	−0.0617702	−	0.106989i
$803$	−4.74147	+	8.21247i	−0.167323	+	0.289812i
$804$	−1.09684	−	5.36810i	−0.0386825	−	0.189318i
$805$	9.14191	−	0.383341i	0.322210	−	0.0135110i
$806$	−13.0273	−	7.15220i	−0.458867	−	0.251925i
$807$	−8.23200	−	40.2887i	−0.289780	−	1.41823i
$808$		−	16.6767i		−	0.586683i
$809$		−	24.9292i		−	0.876462i	−0.898862	−	0.438231i	$-0.855605\pi$
$809$		−	24.9292i		−	0.876462i	0.898862	−	0.438231i	$-0.144395\pi$
$810$	−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
$813$	34.8181	+	39.2883i	1.22112	+	1.37790i
$814$	−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
$819$	−1.63258	+	28.5716i	−0.0570470	+	0.998371i
$820$	−27.0486			−0.944577
$821$	−21.6417	−	12.4948i	−0.755299	−	0.436072i	0.0723065	−	0.997382i	$-0.476964\pi$
$821$	−21.6417	−	12.4948i	−0.755299	−	0.436072i	−0.827605	+	0.561310i	$0.810297\pi$
$822$	−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
$825$	0.546812	+	0.617016i	0.0190376	+	0.0214818i
$826$	26.5812	−	1.11461i	0.924877	−	0.0387822i
$827$			32.2623i			1.12187i	0.827860	+	0.560934i	$0.189558\pi$
$827$			32.2623i			1.12187i	−0.827860	+	0.560934i	$0.810442\pi$
$828$	−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
$831$	6.09602	+	29.8349i	0.211469	+	1.03496i
$832$	13.4629	−	8.16388i	0.466743	−	0.283032i
$833$	7.35541	+	10.5822i	0.254850	+	0.366650i
$834$	4.59128	+	22.4705i	0.158983	+	0.778089i
$835$	−5.97019	+	10.3407i	−0.206607	+	0.357853i
$836$	−4.55755	−	7.89391i	−0.157626	−	0.273017i
$837$	2.05671	+	25.3191i	0.0710904	+	0.875155i
$838$			6.83356i			0.236062i
$839$	−22.8424	+	39.5642i	−0.788608	+	1.36591i	0.138211	+	0.990403i	$0.455865\pi$
$839$	−22.8424	+	39.5642i	−0.788608	+	1.36591i	−0.926820	+	0.375507i	$0.877469\pi$
$840$	6.51169	+	26.2161i	0.224675	+	0.904540i
$841$	−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
$855$	45.3121	+	5.48656i	1.54964	+	0.187636i
$856$	−0.852341	+	1.47630i	−0.0291324	+	0.0504588i
$857$	0.325260	−	0.563367i	0.0111107	−	0.0192443i	−0.860417	−	0.509591i	$-0.829797\pi$
$857$	0.325260	−	0.563367i	0.0111107	−	0.0192443i	0.871527	+	0.490347i	$0.163130\pi$
$858$	−1.53980	+	4.96830i	−0.0525678	+	0.169615i
$859$	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
$861$	−43.9015	+	10.9045i	−1.49616	+	0.371624i
$862$	5.83246	−	10.1021i	0.198654	−	0.344079i
$863$	7.67159	−	4.42919i	0.261144	−	0.150771i	−0.363712	−	0.931511i	$-0.618491\pi$
$863$	7.67159	−	4.42919i	0.261144	−	0.150771i	0.624856	+	0.780740i	$0.285158\pi$
$864$	−26.9938	−	12.7922i	−0.918349	−	0.435199i
$865$	−15.3227	−	26.5397i	−0.520987	−	0.902375i
$866$	4.94423	+	8.56366i	0.168012	+	0.291005i
$867$	−17.6429	+	15.6355i	−0.599184	+	0.531009i
$868$	16.6593	−	0.698560i	0.565452	−	0.0237107i
$869$	−12.4486	+	7.18721i	−0.422290	+	0.243809i
$870$	−0.350416	−	1.71499i	−0.0118802	−	0.0581436i
$871$	7.56520	−	4.58752i	0.256337	−	0.155442i
$872$	−27.8028	−	16.0520i	−0.941522	−	0.543588i
$873$	0.234799	+	0.550585i	0.00794675	+	0.0186345i
$874$	−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
$879$	−29.5465	+	26.1847i	−0.996578	+	0.883187i
$880$		−	0.504123i		−	0.0169940i
$881$	−9.25255	−	16.0259i	−0.311726	−	0.539926i	0.667010	−	0.745049i	$-0.267574\pi$
$881$	−9.25255	−	16.0259i	−0.311726	−	0.539926i	−0.978736	+	0.205123i	$0.934240\pi$
$882$	8.28463	+	15.6481i	0.278958	+	0.526898i
$883$	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
$885$	32.8613	−	29.1223i	1.10462	−	0.978936i
$886$	23.1158			0.776590
$887$	−14.9001	+	25.8078i	−0.500298	+	0.866542i	0.499702	+	0.866197i	$0.333443\pi$
$887$	−14.9001	+	25.8078i	−0.500298	+	0.866542i	−1.00000		0.000344167i	$0.999890\pi$
$888$	10.4862	+	11.8324i	0.351892	+	0.397071i
$889$	−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
$894$	−8.22174	+	7.28628i	−0.274976	+	0.243690i
$895$	−41.0498	+	23.7001i	−1.37214	+	0.792207i
$896$	−9.57988	+	18.3255i	−0.320041	+	0.612212i
$897$	−9.70522	−	3.00788i	−0.324048	−	0.100430i
$898$	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
$903$	−1.36146	−	1.41233i	−0.0453064	−	0.0469995i
$904$	9.77884	−	16.9374i	0.325239	−	0.563331i
$905$	−11.5410	+	6.66319i	−0.383635	+	0.221492i
$906$	5.07043	−	1.03602i	0.168454	−	0.0344193i
$907$	−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	$-0.837418\pi$
$911$		−	29.5095i		−	0.977692i	0.872370	−	0.488846i	$-0.162582\pi$
$912$	1.97411	+	2.22756i	0.0653694	+	0.0737620i
$913$			14.2864i			0.472811i
$914$	17.5211	−	10.1158i	0.579546	−	0.334601i
$915$	7.99745	−	1.63408i	0.264388	−	0.0540210i
$916$	−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
$924$	−1.40677	−	5.66367i	−0.0462794	−	0.186321i
$925$	0.793014	+	1.37354i	0.0260742	+	0.0451618i
$926$	3.23879	+	1.86992i	0.106433	+	0.0614492i
$927$	28.9657	+	3.50727i	0.951357	+	0.115194i
$928$	1.62088	−	2.80744i	0.0532079	−	0.0921587i
$929$	30.2792			0.993429			0.496714	−	0.867914i	$-0.334540\pi$
$929$	30.2792			0.993429			0.496714	+	0.867914i	$0.334540\pi$
$930$	−11.3571	+	10.0649i	−0.372413	+	0.330040i
$931$	−4.19456	−	49.9280i	−0.137471	−	1.63632i
$932$	−18.5019	−	10.6821i	−0.606049	−	0.349903i
$933$	23.3448	−	20.6887i	0.764275	−	0.677316i
$934$		−	3.44749i		−	0.112805i
$935$	3.34789	+	1.93290i	0.109488	+	0.0632127i
$936$	2.96437	−	29.8496i	0.0968936	−	0.975666i
$937$		−	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
$939$	−34.3977	+	7.02832i	−1.12253	+	0.229361i
$940$	35.0985			1.14479
$941$	8.91584	−	15.4427i	0.290648	−	0.503417i	−0.683315	−	0.730124i	$-0.739462\pi$
$941$	8.91584	−	15.4427i	0.290648	−	0.503417i	0.973963	+	0.226706i	$0.0727958\pi$
$942$	−4.29464	−	21.0186i	−0.139927	−	0.684824i
$943$		−	16.0605i		−	0.523001i
$944$	2.86333			0.0931934
$945$	26.9081	+	11.3968i	0.875320	+	0.370737i
$946$	−0.178272	−	0.308776i	−0.00579612	−	0.0100392i
$947$	−12.8477	−	7.41765i	−0.417496	−	0.241041i	0.276510	−	0.961011i	$-0.410822\pi$
$947$	−12.8477	−	7.41765i	−0.417496	−	0.241041i	−0.694005	+	0.719970i	$0.744156\pi$
$948$	24.3156	−	21.5490i	0.789735	−	0.699879i
$949$	34.6036	−	0.744486i	1.12328	−	0.0241670i
$950$	−1.45395	−	2.51831i	−0.0471723	−	0.0817049i
$951$	−15.9249	+	3.25386i	−0.516401	+	0.105514i
$952$	−7.23819	−	11.4051i	−0.234591	−	0.369640i
$953$	−2.58732	−	1.49379i	−0.0838116	−	0.0483887i	0.457508	−	0.889205i	$-0.348742\pi$
$953$	−2.58732	−	1.49379i	−0.0838116	−	0.0483887i	−0.541320	+	0.840817i	$0.682075\pi$
$954$	2.31596	−	19.1270i	0.0749820	−	0.619258i
$955$	−9.08149	+	5.24320i	−0.293870	+	0.169666i
$956$	−33.0849	+	19.1016i	−1.07004	+	0.617789i
$957$	0.193152	+	0.945317i	0.00624372	+	0.0305578i
$958$	−22.1506	−	12.7887i	−0.715653	−	0.413183i
$959$	18.0896	+	28.5033i	0.584142	+	0.920421i
$960$	−3.21846	−	15.7516i	−0.103875	−	0.508382i
$961$	−3.55027	−	6.14924i	−0.114525	−	0.198363i
$962$	−4.81557	+	8.77128i	−0.155260	+	0.282798i
$963$	0.723396	+	1.69630i	0.0233111	+	0.0546626i
$964$	−20.2344	−	11.6823i	−0.651706	−	0.376263i
$965$	5.71954	+	9.90654i	0.184119	+	0.318903i
$966$	−6.10093	+	1.51538i	−0.196294	+	0.0487566i
$967$	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
$969$	−22.3624	+	4.56920i	−0.718384	+	0.146784i
$970$	−0.178786	+	0.309667i	−0.00574049	+	0.00994282i
$971$	−33.8092			−1.08499			−0.542495	−	0.840059i	$-0.682520\pi$
$971$	−33.8092			−1.08499			−0.542495	+	0.840059i	$0.682520\pi$
$972$	−17.7858	+	9.35364i	−0.570481	+	0.300018i
$973$	19.2498	−	36.8233i	0.617122	−	1.18050i
$974$		−	30.8111i		−	0.987251i
$975$	0.890800	−	2.87425i	0.0285284	−	0.0920497i
$976$	0.460983	+	0.266148i	0.0147557	+	0.00851921i
$977$			27.3800i			0.875964i	0.898984	+	0.437982i	$0.144307\pi$
$977$			27.3800i			0.875964i	−0.898984	+	0.437982i	$0.855693\pi$
$978$	0.865491	+	0.976610i	0.0276754	+	0.0312285i
$979$	4.43773	+	2.56212i	0.141830	+	0.0818858i
$980$	8.16622	−	17.3559i	0.260860	−	0.554413i
$981$	−31.9461	+	13.6236i	−1.01996	+	0.434967i
$982$	21.0956			0.673186
$983$	16.3929	−	28.3933i	0.522851	−	0.905605i	−0.476795	−	0.879014i	$-0.658202\pi$
$983$	16.3929	−	28.3933i	0.522851	−	0.905605i	0.999646	−	0.0265906i	$-0.00846504\pi$
$984$	46.4543	−	9.49178i	1.48091	−	0.302587i
$985$	−3.69717	−	2.13456i	−0.117802	−	0.0680129i
$986$	0.437661	+	0.758051i	0.0139380	+	0.0241413i
$987$	56.9671	−	14.1498i	1.81328	−	0.450393i
$988$	−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
$996$	−6.46434	−	31.6375i	−0.204830	−	1.00247i
$997$	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
$999$	17.0473	−	1.38478i	0.539354	−	0.0438126i

Twists

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

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

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} +(0.968576 + 1.09293i) 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} +(0.446987 + 2.18763i) q^{12} +(-3.08300 + 1.86952i) q^{13} +(-1.03345 + 1.97690i) q^{14} +(0.737024 + 3.60711i) q^{15} +(-0.120042 + 0.207918i) q^{16} +(-0.920525 - 1.59440i) q^{17} +(-0.992218 - 2.32667i) q^{18} +7.15770i q^{19} +(-1.37008 + 2.37304i) q^{20} +(-1.26704 + 4.40393i) 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} +(0.464880 - 3.83933i) q^{36} +(-1.64578 + 2.85058i) q^{37} +(3.01745 - 5.22638i) q^{38} +(6.09028 - 1.38150i) q^{39} +(5.10491 - 2.94732i) q^{40} +(4.93559 + 8.54870i) q^{41} +(2.78172 - 2.68151i) q^{42} +(-0.214038 + 0.370726i) q^{43} +(-1.10286 + 0.636734i) q^{44} +(0.766526 - 6.33055i) q^{45} +(0.685893 + 1.18800i) q^{46} +(-6.40449 - 11.0929i) q^{47} +(0.311212 - 0.275803i) q^{48} +(-6.97543 + 0.586021i) q^{49} +(-0.351833 + 0.203131i) q^{50} +(0.638362 + 3.12424i) q^{51} +(4.07434 + 2.23688i) q^{52} +(6.59657 + 3.80853i) q^{53} +(0.354713 + 4.36668i) 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} +(3.55197 - 3.14783i) q^{60} -2.21713i q^{61} +(2.06092 + 3.56962i) q^{62} +(4.49603 - 6.54108i) q^{63} -4.36683 q^{64} +(6.71806 + 3.68832i) q^{65} +(1.07966 - 0.956814i) q^{66} -2.45385 q^{67} +(-1.18667 + 2.05537i) q^{68} +(1.86907 + 2.10903i) 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} +(-0.624601 + 0.553534i) q^{75} +(7.99095 - 4.61358i) q^{76} +(-2.61133 + 0.109499i) q^{77} +(-5.02937 - 1.55872i) 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} +(5.73329 - 1.42407i) q^{84} +(-1.95666 + 3.38904i) q^{85} +(0.312572 - 0.180463i) q^{86} +(-0.956938 + 0.195526i) 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} +(5.61604 + 6.33707i) q^{93} +10.7997i q^{94} +(13.1760 - 7.60718i) q^{95} +(-9.75561 + 1.99332i) 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

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