LMFDB - Embedded newform 185.2.v.a.104.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [185,2,Mod(4,185)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("185.4"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(185, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 185 = 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	185.v (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$1.47723243739$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$16$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			104.5
Character	$\chi$	$=$	185.104
Dual form			185.2.v.a.169.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.24932 + 0.454714i) q^{2} +(-0.712514 + 1.95762i) q^{3} +(-0.178063 + 0.149413i) q^{4} +(-0.804785 + 2.08622i) q^{5} -2.76967i q^{6} +(-2.05749 + 0.362791i) q^{7} +(1.48401 - 2.57038i) q^{8} +(-1.02645 - 0.861296i) q^{9} +(0.0567971 - 2.97230i) q^{10} +(1.09872 - 1.90303i) q^{11} +(-0.165620 - 0.455038i) q^{12} +(0.109278 - 0.0916955i) q^{13} +(2.40549 - 1.38881i) q^{14} +(-3.51060 - 3.06192i) q^{15} +(-0.604483 + 3.42819i) q^{16} +(-1.68858 - 1.41689i) q^{17} +(1.67401 + 0.609289i) q^{18} +(-1.39535 + 3.83370i) q^{19} +(-0.168405 - 0.491724i) q^{20} +(0.755786 - 4.28627i) q^{21} +(-0.507309 + 2.87709i) q^{22} +(-1.39578 - 2.41756i) q^{23} +(3.97445 + 4.73656i) q^{24} +(-3.70464 - 3.35792i) q^{25} +(-0.0948281 + 0.164247i) q^{26} +(-2.99500 + 1.72916i) q^{27} +(0.312158 - 0.372015i) q^{28} +(-2.08912 - 1.20615i) q^{29} +(5.77815 + 2.22899i) q^{30} +7.10743i q^{31} +(0.227127 + 1.28810i) q^{32} +(2.94256 + 3.50681i) q^{33} +(2.75385 + 1.00232i) q^{34} +(0.898976 - 4.58435i) q^{35} +0.311462 q^{36} +(1.92013 + 5.77175i) q^{37} -5.42399i q^{38} +(0.101642 + 0.279260i) q^{39} +(4.16808 + 5.16458i) q^{40} +(3.30254 - 2.77116i) q^{41} +(1.00481 + 5.69858i) q^{42} -0.637427 q^{43} +(0.0886964 + 0.503022i) q^{44} +(2.62293 - 1.44825i) q^{45} +(2.84307 + 2.38562i) q^{46} +(-4.36233 + 2.51859i) q^{47} +(-6.28039 - 3.62598i) q^{48} +(-2.47619 + 0.901260i) q^{49} +(6.15516 + 2.51055i) q^{50} +(3.97686 - 2.29604i) q^{51} +(-0.00575799 + 0.0326552i) q^{52} +(12.0033 + 2.11651i) q^{53} +(2.95542 - 3.52214i) q^{54} +(3.08592 + 3.82370i) q^{55} +(-2.12083 + 5.82693i) q^{56} +(-6.51071 - 5.46313i) q^{57} +(3.15842 + 0.556915i) q^{58} +(-13.3122 - 2.34730i) q^{59} +(1.08260 + 0.0206872i) q^{60} +(6.93152 + 8.26066i) q^{61} +(-3.23185 - 8.87943i) q^{62} +(2.42439 + 1.39972i) q^{63} +(-4.35055 - 7.53537i) q^{64} +(0.103351 + 0.301774i) q^{65} +(-5.27078 - 3.04309i) q^{66} +(3.15297 - 0.555953i) q^{67} +0.512375 q^{68} +(5.72717 - 1.00985i) q^{69} +(0.961464 + 6.13608i) q^{70} +(-7.56215 - 2.75240i) q^{71} +(-3.73713 + 1.36020i) q^{72} +1.78846i q^{73} +(-5.02334 - 6.33763i) q^{74} +(9.21313 - 4.85970i) q^{75} +(-0.324343 - 0.891124i) q^{76} +(-1.57020 + 4.31408i) q^{77} +(-0.253966 - 0.302665i) q^{78} +(-15.4992 + 2.73292i) q^{79} +(-6.66549 - 4.02005i) q^{80} +(-1.94909 - 11.0539i) q^{81} +(-2.86583 + 4.96377i) q^{82} +(-2.13561 + 2.54512i) q^{83} +(0.505846 + 0.876151i) q^{84} +(4.31488 - 2.38246i) q^{85} +(0.796348 - 0.289847i) q^{86} +(3.84971 - 3.23029i) q^{87} +(-3.26102 - 5.64825i) q^{88} +(18.4072 + 3.24569i) q^{89} +(-2.61833 + 3.00200i) q^{90} +(-0.191573 + 0.228308i) q^{91} +(0.609751 + 0.221931i) q^{92} +(-13.9136 - 5.06414i) q^{93} +(4.30469 - 5.13013i) q^{94} +(-6.87499 - 5.99632i) q^{95} +(-2.68343 - 0.473162i) q^{96} +(-4.78516 - 8.28814i) q^{97} +(2.68373 - 2.25192i) q^{98} +(-2.76686 + 1.00705i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 12 q^{4} - 12 q^{5} - 6 q^{9} - 3 q^{10} - 30 q^{11} - 36 q^{14} - 21 q^{15} - 18 q^{19} - 39 q^{20} - 24 q^{21} + 96 q^{24} + 36 q^{25} + 48 q^{26} - 18 q^{29} - 30 q^{30} - 54 q^{34} + 6 q^{35}+ \cdots - 24 q^{99}+O(q^{100}) $ 96 * q - 12 * q^4 - 12 * q^5 - 6 * q^9 - 3 * q^10 - 30 * q^11 - 36 * q^14 - 21 * q^15 - 18 * q^19 - 39 * q^20 - 24 * q^21 + 96 * q^24 + 36 * q^25 + 48 * q^26 - 18 * q^29 - 30 * q^30 - 54 * q^34 + 6 * q^35 + 24 * q^36 - 36 * q^39 - 63 * q^40 + 72 * q^41 - 84 * q^44 - 36 * q^45 - 18 * q^46 - 6 * q^49 - 27 * q^50 - 18 * q^51 + 24 * q^54 + 6 * q^55 + 90 * q^56 + 18 * q^59 + 108 * q^60 - 144 * q^61 + 66 * q^64 + 27 * q^65 - 36 * q^66 - 6 * q^69 - 66 * q^70 - 30 * q^71 - 6 * q^74 + 96 * q^75 - 54 * q^76 + 60 * q^79 - 18 * q^81 + 48 * q^84 + 21 * q^85 - 72 * q^86 + 108 * q^89 + 165 * q^90 - 54 * q^91 + 6 * q^94 + 57 * q^95 + 24 * q^96 - 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/185\mathbb{Z}\right)^\times$.

$n$	$76$	$112$
$\chi(n)$	$e\left(\frac{7}{18}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	−1.24932	+	0.454714i	−0.883400	+	0.321531i	−0.743581	−	0.668646i	$-0.766874\pi$
$2$	−1.24932	+	0.454714i	−0.883400	+	0.321531i	−0.139819	+	0.990177i	$0.544652\pi$
$3$	−0.712514	+	1.95762i	−0.411370	+	1.13023i	0.545092	+	0.838376i	$0.316495\pi$
$3$	−0.712514	+	1.95762i	−0.411370	+	1.13023i	−0.956463	+	0.291855i	$0.905728\pi$
$4$	−0.178063	+	0.149413i	−0.0890315	+	0.0747063i
$5$	−0.804785	+	2.08622i	−0.359911	+	0.932987i
$5$	−0.804785	+	2.08622i	−0.359911	+	0.932987i
$6$		−	2.76967i		−	1.13071i
$7$	−2.05749	+	0.362791i	−0.777659	+	0.137122i	−0.548370	−	0.836236i	$-0.684751\pi$
$7$	−2.05749	+	0.362791i	−0.777659	+	0.137122i	−0.229289	+	0.973358i	$0.573640\pi$
$8$	1.48401	−	2.57038i	0.524677	−	0.908768i
$9$	−1.02645	−	0.861296i	−0.342151	−	0.287099i
$10$	0.0567971	−	2.97230i	0.0179608	−	0.939923i
$11$	1.09872	−	1.90303i	0.331276	−	0.573786i	−0.651487	−	0.758660i	$-0.725854\pi$
$11$	1.09872	−	1.90303i	0.331276	−	0.573786i	0.982762	+	0.184874i	$0.0591876\pi$
$12$	−0.165620	−	0.455038i	−0.0478104	−	0.131358i
$13$	0.109278	−	0.0916955i	0.0303084	−	0.0254318i	−0.627508	−	0.778610i	$-0.715925\pi$
$13$	0.109278	−	0.0916955i	0.0303084	−	0.0254318i	0.657816	+	0.753179i	$0.271480\pi$
$14$	2.40549	−	1.38881i	0.642895	−	0.371175i
$15$	−3.51060	−	3.06192i	−0.906433	−	0.790585i
$16$	−0.604483	+	3.42819i	−0.151121	+	0.857049i
$17$	−1.68858	−	1.41689i	−0.409541	−	0.343645i	0.414627	−	0.909992i	$-0.363912\pi$
$17$	−1.68858	−	1.41689i	−0.409541	−	0.343645i	−0.824168	+	0.566346i	$0.808357\pi$
$18$	1.67401	+	0.609289i	0.394567	+	0.143611i
$19$	−1.39535	+	3.83370i	−0.320116	+	0.879511i	0.670386	+	0.742013i	$0.266129\pi$
$19$	−1.39535	+	3.83370i	−0.320116	+	0.879511i	−0.990502	+	0.137499i	$0.956094\pi$
$20$	−0.168405	−	0.491724i	−0.0376566	−	0.109953i
$21$	0.755786	−	4.28627i	0.164926	−	0.935342i
$22$	−0.507309	+	2.87709i	−0.108159	+	0.613398i
$23$	−1.39578	−	2.41756i	−0.291040	−	0.504096i	0.683016	−	0.730404i	$-0.260668\pi$
$23$	−1.39578	−	2.41756i	−0.291040	−	0.504096i	−0.974056	+	0.226307i	$0.927335\pi$
$24$	3.97445	+	4.73656i	0.811280	+	0.966846i
$25$	−3.70464	−	3.35792i	−0.740928	−	0.671584i
$26$	−0.0948281	+	0.164247i	−0.0185973	+	0.0322115i
$27$	−2.99500	+	1.72916i	−0.576388	+	0.332778i
$28$	0.312158	−	0.372015i	0.0589923	−	0.0703043i
$29$	−2.08912	−	1.20615i	−0.387940	−	0.223977i	0.293327	−	0.956012i	$-0.405237\pi$
$29$	−2.08912	−	1.20615i	−0.387940	−	0.223977i	−0.681267	+	0.732035i	$0.738571\pi$
$30$	5.77815	+	2.22899i	1.05494	+	0.406956i
$31$			7.10743i			1.27653i	0.769816	+	0.638266i	$0.220348\pi$
$31$			7.10743i			1.27653i	−0.769816	+	0.638266i	$0.779652\pi$
$32$	0.227127	+	1.28810i	0.0401507	+	0.227706i
$33$	2.94256	+	3.50681i	0.512234	+	0.610457i
$34$	2.75385	+	1.00232i	0.472281	+	0.171896i
$35$	0.898976	−	4.58435i	0.151955	−	0.774897i
$36$	0.311462			0.0519103
$37$	1.92013	+	5.77175i	0.315667	+	0.948870i
$37$	1.92013	+	5.77175i	0.315667	+	0.948870i
$38$		−	5.42399i		−	0.879888i
$39$	0.101642	+	0.279260i	0.0162758	+	0.0447173i
$40$	4.16808	+	5.16458i	0.659031	+	0.816592i
$41$	3.30254	−	2.77116i	0.515770	−	0.432783i	−0.347384	−	0.937723i	$-0.612930\pi$
$41$	3.30254	−	2.77116i	0.515770	−	0.432783i	0.863154	+	0.504940i	$0.168486\pi$
$42$	1.00481	+	5.69858i	0.155046	+	0.879310i
$43$	−0.637427			−0.0972067			−0.0486034	−	0.998818i	$-0.515477\pi$
$43$	−0.637427			−0.0972067			−0.0486034	+	0.998818i	$0.515477\pi$
$44$	0.0886964	+	0.503022i	0.0133715	+	0.0758335i
$45$	2.62293	−	1.44825i	0.391003	−	0.215892i
$46$	2.84307	+	2.38562i	0.419187	+	0.351740i
$47$	−4.36233	+	2.51859i	−0.636311	+	0.367374i	−0.783192	−	0.621780i	$-0.786410\pi$
$47$	−4.36233	+	2.51859i	−0.636311	+	0.367374i	0.146881	+	0.989154i	$0.453077\pi$
$48$	−6.28039	−	3.62598i	−0.906496	−	0.523366i
$49$	−2.47619	+	0.901260i	−0.353742	+	0.128751i
$50$	6.15516	+	2.51055i	0.870471	+	0.355046i
$51$	3.97686	−	2.29604i	0.556871	−	0.321510i
$52$	−0.00575799	+	0.0326552i	−0.000798489	+	0.00452846i
$53$	12.0033	+	2.11651i	1.64879	+	0.290725i	0.919384	−	0.393360i	$-0.128688\pi$
$53$	12.0033	+	2.11651i	1.64879	+	0.290725i	0.729401	+	0.684086i	$0.239799\pi$
$54$	2.95542	−	3.52214i	0.402182	−	0.479302i
$55$	3.08592	+	3.82370i	0.416105	+	0.515588i
$56$	−2.12083	+	5.82693i	−0.283408	+	0.778656i
$57$	−6.51071	−	5.46313i	−0.862364	−	0.723610i
$58$	3.15842	+	0.556915i	0.414721	+	0.0731266i
$59$	−13.3122	−	2.34730i	−1.73310	−	0.305592i	−0.784046	−	0.620703i	$-0.786847\pi$
$59$	−13.3122	−	2.34730i	−1.73310	−	0.305592i	−0.949055	+	0.315111i	$0.897958\pi$
$60$	1.08260	+	0.0206872i	0.139763	+	0.00267071i
$61$	6.93152	+	8.26066i	0.887490	+	1.05767i	0.997963	+	0.0637899i	$0.0203188\pi$
$61$	6.93152	+	8.26066i	0.887490	+	1.05767i	−0.110474	+	0.993879i	$0.535237\pi$
$62$	−3.23185	−	8.87943i	−0.410445	−	1.12769i
$63$	2.42439	+	1.39972i	0.305444	+	0.176348i
$64$	−4.35055	−	7.53537i	−0.543819	−	0.941921i
$65$	0.103351	+	0.301774i	0.0128192	+	0.0374305i
$66$	−5.27078	−	3.04309i	−0.648788	−	0.374578i
$67$	3.15297	−	0.555953i	0.385196	−	0.0679205i	0.0223030	−	0.999751i	$-0.492900\pi$
$67$	3.15297	−	0.555953i	0.385196	−	0.0679205i	0.362893	+	0.931831i	$0.381789\pi$
$68$	0.512375			0.0621345
$69$	5.72717	−	1.00985i	0.689470	−	0.121572i
$70$	0.961464	+	6.13608i	0.114917	+	0.733402i
$71$	−7.56215	−	2.75240i	−0.897462	−	0.326649i	−0.148227	−	0.988953i	$-0.547357\pi$
$71$	−7.56215	−	2.75240i	−0.897462	−	0.326649i	−0.749235	+	0.662304i	$0.769579\pi$
$72$	−3.73713	+	1.36020i	−0.440425	+	0.160302i
$73$			1.78846i			0.209323i	0.994508	+	0.104662i	$0.0333760\pi$
$73$			1.78846i			0.209323i	−0.994508	+	0.104662i	$0.966624\pi$
$74$	−5.02334	−	6.33763i	−0.583951	−	0.736735i
$75$	9.21313	−	4.85970i	1.06384	−	0.561150i
$76$	−0.324343	−	0.891124i	−0.0372047	−	0.102219i
$77$	−1.57020	+	4.31408i	−0.178941	+	0.491635i
$78$	−0.253966	−	0.302665i	−0.0287560	−	0.0342701i
$79$	−15.4992	+	2.73292i	−1.74379	+	0.307478i	−0.952631	−	0.304129i	$-0.901635\pi$
$79$	−15.4992	+	2.73292i	−1.74379	+	0.307478i	−0.791162	+	0.611606i	$0.790524\pi$
$80$	−6.66549	−	4.02005i	−0.745225	−	0.449455i
$81$	−1.94909	−	11.0539i	−0.216566	−	1.22821i
$82$	−2.86583	+	4.96377i	−0.316478	+	0.548156i
$83$	−2.13561	+	2.54512i	−0.234413	+	0.279363i	−0.870409	−	0.492330i	$-0.836145\pi$
$83$	−2.13561	+	2.54512i	−0.234413	+	0.279363i	0.635995	+	0.771693i	$0.280590\pi$
$84$	0.505846	+	0.876151i	0.0551923	+	0.0955959i
$85$	4.31488	−	2.38246i	0.468015	−	0.258414i
$86$	0.796348	−	0.289847i	0.0858724	−	0.0312550i
$87$	3.84971	−	3.23029i	0.412732	−	0.346324i
$88$	−3.26102	−	5.64825i	−0.347626	−	0.602105i
$89$	18.4072	+	3.24569i	1.95116	+	0.344043i	0.999295	+	0.0375378i	$0.0119515\pi$
$89$	18.4072	+	3.24569i	1.95116	+	0.344043i	0.951869	+	0.306505i	$0.0991597\pi$
$90$	−2.61833	+	3.00200i	−0.275996	+	0.316439i
$91$	−0.191573	+	0.228308i	−0.0200823	+	0.0239332i
$92$	0.609751	+	0.221931i	0.0635709	+	0.0231379i
$93$	−13.9136	−	5.06414i	−1.44278	−	0.525127i
$94$	4.30469	−	5.13013i	0.443995	−	0.529132i
$95$	−6.87499	−	5.99632i	−0.705359	−	0.615210i
$96$	−2.68343	−	0.473162i	−0.273877	−	0.0482919i
$97$	−4.78516	−	8.28814i	−0.485859	−	0.841533i	0.514009	−	0.857785i	$-0.328160\pi$
$97$	−4.78516	−	8.28814i	−0.485859	−	0.841533i	−0.999868	+	0.0162519i	$0.994827\pi$
$98$	2.68373	−	2.25192i	0.271098	−	0.227478i
$99$	−2.76686	+	1.00705i	−0.278080	+	0.101213i
$100$	1.16138	+	0.0444013i	0.116138	+	0.00444013i
$101$	0.914760	+	1.58441i	0.0910220	+	0.157655i	0.907941	−	0.419097i	$-0.137653\pi$
$101$	0.914760	+	1.58441i	0.0910220	+	0.157655i	−0.816919	+	0.576752i	$0.804320\pi$
$102$	−3.92431	+	4.67681i	−0.388565	+	0.463073i
$103$	−6.40012	+	11.0853i	−0.630623	+	1.09227i	0.356802	+	0.934180i	$0.383867\pi$
$103$	−6.40012	+	11.0853i	−0.630623	+	1.09227i	−0.987425	+	0.158090i	$0.949466\pi$
$104$	−0.0735221	−	0.416965i	−0.00720944	−	0.0408868i
$105$	8.33387	+	5.02627i	0.813303	+	0.490513i
$106$	−15.9584	+	2.81389i	−1.55001	+	0.273309i
$107$	4.76553	+	5.67934i	0.460701	+	0.549042i	0.945517	−	0.325574i	$-0.105558\pi$
$107$	4.76553	+	5.67934i	0.460701	+	0.549042i	−0.484815	+	0.874617i	$0.661113\pi$
$108$	0.274940	−	0.755391i	0.0264561	−	0.0726875i
$109$	−2.87069	−	7.88717i	−0.274963	−	0.755454i	−0.997914	−	0.0645550i	$-0.979437\pi$
$109$	−2.87069	−	7.88717i	−0.274963	−	0.755454i	0.722951	−	0.690899i	$-0.242785\pi$
$110$	−5.59398	−	3.37380i	−0.533365	−	0.321679i
$111$	−12.6670	−	0.353584i	−1.20230	−	0.0335607i
$112$		−	7.27278i		−	0.687213i
$113$	−11.6809	+	4.25150i	−1.09885	+	0.399947i	−0.826891	−	0.562363i	$-0.809893\pi$
$113$	−11.6809	+	4.25150i	−1.09885	+	0.399947i	−0.271955	+	0.962310i	$0.587670\pi$
$114$	10.6181	+	3.86467i	0.994476	+	0.361960i
$115$	6.16687	−	0.966288i	0.575064	−	0.0901068i
$116$	0.552209	−	0.0973694i	0.0512714	−	0.00904052i
$117$	−0.191146			−0.0176715
$118$	17.6985	−	3.12072i	1.62928	−	0.287286i
$119$	3.98827	+	2.30263i	0.365604	+	0.211082i
$120$	−13.0801	+	4.47966i	−1.19404	+	0.408935i
$121$	3.08564	+	5.34449i	0.280513	+	0.485862i
$122$	−12.4159	−	7.16832i	−1.12408	−	0.648989i
$123$	3.07176	+	8.43960i	0.276972	+	0.760973i
$124$	−1.06194	−	1.26557i	−0.0953650	−	0.113652i
$125$	9.98681	−	5.02630i	0.893247	−	0.449566i
$126$	−3.66530	−	0.646291i	−0.326531	−	0.0575762i
$127$	20.2981	+	3.57911i	1.80117	+	0.317594i	0.970848	−	0.239695i	$-0.0770474\pi$
$127$	20.2981	+	3.57911i	1.80117	+	0.317594i	0.830318	+	0.557289i	$0.188159\pi$
$128$	6.85772	+	5.75431i	0.606143	+	0.508614i
$129$	0.454176	−	1.24784i	0.0399879	−	0.109866i
$130$	−0.266340	−	0.330016i	−0.0233595	−	0.0289443i
$131$	0.580925	−	0.692320i	0.0507557	−	0.0604883i	−0.740069	−	0.672531i	$-0.765207\pi$
$131$	0.580925	−	0.692320i	0.0507557	−	0.0604883i	0.790825	+	0.612042i	$0.209652\pi$
$132$	−1.04792	−	0.184777i	−0.0912099	−	0.0160828i
$133$	1.48009	−	8.39403i	0.128340	−	0.727855i
$134$	−3.68625	+	2.12826i	−0.318444	+	0.183853i
$135$	−1.19709	−	7.63983i	−0.103029	−	0.657532i
$136$	−6.14781	+	2.23762i	−0.527171	+	0.191874i
$137$	2.24956	+	1.29879i	0.192193	+	0.110963i	0.593009	−	0.805196i	$-0.297940\pi$
$137$	2.24956	+	1.29879i	0.192193	+	0.110963i	−0.400816	+	0.916159i	$0.631273\pi$
$138$	−6.69585	+	3.86585i	−0.569989	+	0.329083i
$139$	12.1476	+	10.1930i	1.03035	+	0.864563i	0.990892	−	0.134658i	$-0.0429936\pi$
$139$	12.1476	+	10.1930i	1.03035	+	0.864563i	0.0394541	+	0.999221i	$0.487438\pi$
$140$	0.524886	+	0.950623i	0.0443610	+	0.0803423i
$141$	−1.82222	−	10.3343i	−0.153458	−	0.870305i
$142$	10.6991			0.897846
$143$	−0.0544336	−	0.308708i	−0.00455196	−	0.0258155i
$144$	3.57316	−	2.99824i	0.297764	−	0.249853i
$145$	4.19759	−	3.38767i	0.348591	−	0.281331i
$146$	−0.813238	−	2.23435i	−0.0673040	−	0.184916i
$147$		−	5.48960i		−	0.452774i
$148$	−1.20428	−	0.740845i	−0.0989909	−	0.0608971i
$149$	19.1935			1.57240			0.786198	−	0.617975i	$-0.212047\pi$
$149$	19.1935			1.57240			0.786198	+	0.617975i	$0.212047\pi$
$150$	−9.30034	+	10.2606i	−0.759369	+	0.837778i
$151$	11.2417	+	4.09164i	0.914836	+	0.332973i	0.756182	−	0.654361i	$-0.227062\pi$
$151$	11.2417	+	4.09164i	0.914836	+	0.332973i	0.158654	+	0.987334i	$0.449285\pi$
$152$	7.78336	+	9.27585i	0.631314	+	0.752371i
$153$	0.512888	+	2.90873i	0.0414646	+	0.235157i
$154$		−	6.10364i		−	0.491846i
$155$	−14.8277	−	5.71995i	−1.19099	−	0.459438i
$156$	−0.0598237	−	0.0345392i	−0.00478973	−	0.00276535i
$157$	−0.0530778	+	0.0632556i	−0.00423607	+	0.00504835i	−0.768158	−	0.640260i	$-0.778827\pi$
$157$	−0.0530778	+	0.0632556i	−0.00423607	+	0.00504835i	0.763922	+	0.645308i	$0.223271\pi$
$158$	18.1207	−	10.4620i	1.44160	−	0.832310i
$159$	−12.6959	+	21.9899i	−1.00685	+	1.74391i
$160$	−2.87005	−	0.562806i	−0.226897	−	0.0444938i
$161$	3.74887	+	4.46774i	0.295453	+	0.352107i
$162$	7.46137	+	12.9235i	0.586221	+	1.01536i
$163$	3.92185	−	22.2419i	0.307183	−	1.74212i	−0.305864	−	0.952075i	$-0.598945\pi$
$163$	3.92185	−	22.2419i	0.307183	−	1.74212i	0.613047	−	0.790046i	$-0.289943\pi$
$164$	−0.174014	+	0.986883i	−0.0135882	+	0.0770626i
$165$	−9.68410	+	3.31661i	−0.753906	+	0.258197i
$166$	1.51075	−	4.15075i	0.117257	−	0.322160i
$167$	8.88421	+	3.23359i	0.687481	+	0.250223i	0.662056	−	0.749454i	$-0.269684\pi$
$167$	8.88421	+	3.23359i	0.687481	+	0.250223i	0.0254245	+	0.999677i	$0.491906\pi$
$168$	−9.89577	−	8.30354i	−0.763475	−	0.640632i
$169$	−2.25389	+	12.7825i	−0.173376	+	0.983266i
$170$	−4.30731	+	4.93849i	−0.330356	+	0.378765i
$171$	4.73422	−	2.73330i	0.362035	−	0.209021i
$172$	0.113502	−	0.0952397i	0.00865446	−	0.00726196i
$173$	7.27472	+	19.9871i	0.553086	+	1.51959i	0.829474	+	0.558546i	$0.188641\pi$
$173$	7.27472	+	19.9871i	0.553086	+	1.51959i	−0.276387	+	0.961046i	$0.589137\pi$
$174$	−3.34065	+	5.78617i	−0.253254	+	0.438649i
$175$	8.84050	+	5.56488i	0.668279	+	0.420666i
$176$	5.85981	+	4.91697i	0.441700	+	0.370630i
$177$	14.0802	−	24.3877i	1.05834	−	1.83309i
$178$	−24.4723	+	4.31513i	−1.83428	+	0.323433i
$179$		−	9.99260i		−	0.746882i	−0.927654	−	0.373441i	$-0.878178\pi$
$179$		−	9.99260i		−	0.746882i	0.927654	−	0.373441i	$-0.121822\pi$
$180$	−0.250660	+	0.649779i	−0.0186831	+	0.0484316i
$181$	−9.05557	+	7.59852i	−0.673095	+	0.564794i	−0.913980	−	0.405760i	$-0.867007\pi$
$181$	−9.05557	+	7.59852i	−0.673095	+	0.564794i	0.240885	+	0.970554i	$0.422562\pi$
$182$	0.135521	−	0.372340i	0.0100455	−	0.0275997i
$183$	−21.1100	+	7.68341i	−1.56050	+	0.567974i
$184$	−8.28541			−0.610809
$185$	−13.5864	−	0.639211i	−0.998895	−	0.0469957i
$186$	19.6852			1.44339
$187$	−4.55166	+	1.65667i	−0.332850	+	0.121148i
$188$	0.400460	−	1.10026i	0.0292066	−	0.0802444i
$189$	5.53486	−	4.64430i	0.402602	−	0.337823i
$190$	11.3156	+	4.36515i	0.820923	+	0.316681i
$191$			18.9524i			1.37135i	0.727909	+	0.685674i	$0.240493\pi$
$191$			18.9524i			1.37135i	−0.727909	+	0.685674i	$0.759507\pi$
$192$	17.8512	−	3.14765i	1.28830	−	0.227162i
$193$	−7.04176	+	12.1967i	−0.506877	+	0.877937i	0.493091	+	0.869978i	$0.335867\pi$
$193$	−7.04176	+	12.1967i	−0.506877	+	0.877937i	−0.999968	+	0.00795950i	$0.997466\pi$
$194$	9.74691	+	8.17863i	0.699787	+	0.587191i
$195$	−0.664398	−	0.0126959i	−0.0475785	−	0.000909170i
$196$	0.306259	−	0.530456i	0.0218756	−	0.0378897i
$197$	−4.84371	−	13.3080i	−0.345100	−	0.948154i	−0.983890	−	0.178773i	$-0.942787\pi$
$197$	−4.84371	−	13.3080i	−0.345100	−	0.948154i	0.638790	−	0.769381i	$-0.279435\pi$
$198$	2.99876	−	2.51626i	0.213112	−	0.178823i
$199$	−8.71697	+	5.03275i	−0.617930	+	0.356762i	−0.776063	−	0.630656i	$-0.782786\pi$
$199$	−8.71697	+	5.03275i	−0.617930	+	0.356762i	0.158133	+	0.987418i	$0.449453\pi$
$200$	−14.1289	+	4.53916i	−0.999062	+	0.320967i
$201$	−1.15819	+	6.56842i	−0.0816924	+	0.463301i
$202$	−1.86328	−	1.56348i	−0.131100	−	0.110006i
$203$	4.73593	+	1.72374i	0.332397	+	0.120983i
$204$	−0.365074	+	1.00303i	−0.0255603	+	0.0702264i
$205$	3.12342	+	9.12002i	0.218149	+	0.636970i
$206$	2.95512	−	16.7593i	0.205893	−	1.16768i
$207$	−0.649534	+	3.68369i	−0.0451457	+	0.256034i
$208$	0.248293	+	0.430056i	0.0172160	+	0.0298190i
$209$	5.76257	+	6.86756i	0.398605	+	0.475039i
$210$	−12.6972	−	2.48987i	−0.876187	−	0.171817i
$211$	6.02963	−	10.4436i	0.415097	−	0.718969i	−0.580342	−	0.814373i	$-0.697081\pi$
$211$	6.02963	−	10.4436i	0.415097	−	0.718969i	0.995439	+	0.0954044i	$0.0304144\pi$
$212$	−2.45359	+	1.41658i	−0.168513	+	0.0972910i
$213$	10.7763	−	12.8427i	0.738378	−	0.879965i
$214$	−8.53613	−	4.92834i	−0.583518	−	0.336894i
$215$	0.512992	−	1.32981i	0.0349857	−	0.0906926i
$216$			10.2644i			0.698403i
$217$	−2.57851	−	14.6235i	−0.175041	−	0.992706i
$218$	7.17281	+	8.54822i	0.485804	+	0.578959i
$219$	−3.50112	−	1.27430i	−0.236584	−	0.0861094i
$220$	−1.12080	−	0.219785i	−0.0755642	−	0.0148179i
$221$	−0.314448			−0.0211520
$222$	15.9859	−	5.31812i	1.07290	−	0.356929i
$223$		−	1.11069i		−	0.0743776i	−0.999308	−	0.0371888i	$-0.988160\pi$
$223$		−	1.11069i		−	0.0743776i	0.999308	−	0.0371888i	$-0.0118403\pi$
$224$	−0.934622	−	2.56785i	−0.0624471	−	0.171572i
$225$	0.910476	+	6.63754i	0.0606984	+	0.442503i
$226$	12.6599	−	10.6229i	0.842125	−	0.706627i
$227$	−1.68977	−	9.58318i	−0.112154	−	0.636058i	−0.988120	−	0.153685i	$-0.950886\pi$
$227$	−1.68977	−	9.58318i	−0.112154	−	0.636058i	0.875966	−	0.482373i	$-0.160225\pi$
$228$	1.97558			0.130836
$229$	−2.60606	−	14.7797i	−0.172213	−	0.976669i	−0.941312	−	0.337539i	$-0.890406\pi$
$229$	−2.60606	−	14.7797i	−0.172213	−	0.976669i	0.769098	−	0.639130i	$-0.220706\pi$
$230$	−7.26498	+	4.01136i	−0.479039	+	0.264501i
$231$	−7.32653	−	6.14769i	−0.482050	−	0.404488i
$232$	−6.20055	+	3.57989i	−0.407086	+	0.235031i
$233$	−19.2509	−	11.1145i	−1.26117	−	0.728134i	−0.287866	−	0.957671i	$-0.592946\pi$
$233$	−19.2509	−	11.1145i	−1.26117	−	0.728134i	−0.973300	+	0.229537i	$0.926279\pi$
$234$	0.238802	−	0.0869168i	0.0156110	−	0.00568193i
$235$	−1.74360	−	11.1277i	−0.113740	−	0.725892i
$236$	2.72113	−	1.57104i	0.177130	−	0.102266i
$237$	5.69337	−	32.2887i	0.369824	−	2.09738i
$238$	−6.02965	−	1.06319i	−0.390844	−	0.0689164i
$239$	3.56934	−	4.25378i	0.230882	−	0.275154i	−0.638148	−	0.769913i	$-0.720299\pi$
$239$	3.56934	−	4.25378i	0.230882	−	0.275154i	0.869030	+	0.494759i	$0.164744\pi$
$240$	12.6190	−	10.1841i	0.814551	−	0.657384i
$241$	4.93122	−	13.5484i	0.317648	−	0.872731i	−0.673406	−	0.739272i	$-0.735170\pi$
$241$	4.93122	−	13.5484i	0.317648	−	0.872731i	0.991054	−	0.133458i	$-0.0426082\pi$
$242$	−6.28515	−	5.27387i	−0.404025	−	0.339017i
$243$	12.8106	+	2.25886i	0.821801	+	0.144906i
$244$	−2.46849	−	0.435262i	−0.158029	−	0.0278648i
$245$	0.112574	−	5.89121i	0.00719210	−	0.376375i
$246$	−7.67520	−	9.14695i	−0.489353	−	0.583188i
$247$	0.199051	+	0.546889i	0.0126653	+	0.0347977i
$248$	18.2688	+	10.5475i	1.16007	+	0.669767i
$249$	−3.46071	−	5.99413i	−0.219314	−	0.379863i
$250$	−10.1912	+	10.8206i	−0.644545	+	0.684353i
$251$	−0.243065	−	0.140333i	−0.0153421	−	0.00885777i	0.492309	−	0.870420i	$-0.336153\pi$
$251$	−0.243065	−	0.140333i	−0.0153421	−	0.00885777i	−0.507651	+	0.861563i	$0.669486\pi$
$252$	−0.640830	+	0.112996i	−0.0403685	+	0.00711806i
$253$	−6.13427			−0.385658
$254$	−26.9862	+	4.75840i	−1.69327	+	0.298569i
$255$	1.58953	+	10.1444i	0.0995404	+	0.635269i
$256$	5.16869	+	1.88125i	0.323043	+	0.117578i
$257$	−6.01727	+	2.19011i	−0.375347	+	0.136615i	−0.522803	−	0.852454i	$-0.675114\pi$
$257$	−6.01727	+	2.19011i	−0.375347	+	0.136615i	0.147456	+	0.989069i	$0.452891\pi$
$258$			1.76546i			0.109913i
$259$	−6.04459	−	11.1787i	−0.375592	−	0.694612i
$260$	−0.0634920	−	0.0382928i	−0.00393761	−	0.00237482i
$261$	1.10553	+	3.03741i	0.0684304	+	0.188011i
$262$	−0.410952	+	1.12908i	−0.0253887	+	0.0697548i
$263$	14.6255	+	17.4300i	0.901850	+	1.07478i	0.996850	+	0.0793057i	$0.0252703\pi$
$263$	14.6255	+	17.4300i	0.901850	+	1.07478i	−0.0950004	+	0.995477i	$0.530285\pi$
$264$	13.3806	−	2.35937i	0.823521	−	0.145209i
$265$	−14.0756	+	23.3383i	−0.864659	+	1.43366i
$266$	1.96778	+	11.1598i	0.120652	+	0.684252i
$267$	−19.4692	+	33.7217i	−1.19150	+	2.06374i
$268$	−0.478360	+	0.570088i	−0.0292205	+	0.0348237i
$269$	6.24891	+	10.8234i	0.381003	+	0.659916i	0.991206	−	0.132329i	$-0.0422456\pi$
$269$	6.24891	+	10.8234i	0.381003	+	0.659916i	−0.610203	+	0.792245i	$0.708912\pi$
$270$	4.96948	+	9.00024i	0.302433	+	0.547737i
$271$	9.15858	−	3.33345i	0.556344	−	0.202493i	−0.0485187	−	0.998822i	$-0.515450\pi$
$271$	9.15858	−	3.33345i	0.556344	−	0.202493i	0.604863	+	0.796329i	$0.293228\pi$
$272$	5.87808	−	4.93230i	0.356411	−	0.299064i
$273$	−0.310441	−	0.537700i	−0.0187887	−	0.0325431i
$274$	−3.40099	−	0.599687i	−0.205462	−	0.0362284i
$275$	−10.4606	+	3.36065i	−0.630797	+	0.202655i
$276$	−0.868912	+	1.03553i	−0.0523024	+	0.0623316i
$277$	20.5310	+	7.47266i	1.23359	+	0.448988i	0.874824	−	0.484441i	$-0.160977\pi$
$277$	20.5310	+	7.47266i	1.23359	+	0.448988i	0.358761	+	0.933429i	$0.383199\pi$
$278$	−19.8111	−	7.21066i	−1.18819	−	0.432466i
$279$	6.12160	−	7.29544i	0.366491	−	0.436767i
$280$	−10.4495	−	9.11395i	−0.624474	−	0.544662i
$281$	−19.9371	−	3.51546i	−1.18935	−	0.209715i	−0.456260	−	0.889846i	$-0.650811\pi$
$281$	−19.9371	−	3.51546i	−1.18935	−	0.209715i	−0.733090	+	0.680132i	$0.761923\pi$
$282$	6.97567	+	12.0822i	0.415395	+	0.719485i
$283$	−19.3047	+	16.1985i	−1.14754	+	0.962903i	−0.999659	−	0.0261013i	$-0.991691\pi$
$283$	−19.3047	+	16.1985i	−1.14754	+	0.962903i	−0.147884	+	0.989005i	$0.547246\pi$
$284$	1.75778	−	0.639781i	0.104305	−	0.0379640i
$285$	16.6370	−	9.18613i	0.985492	−	0.544140i
$286$	0.208379	+	0.360922i	0.0123217	+	0.0213418i
$287$	−5.78960	+	6.89977i	−0.341749	+	0.407281i
$288$	0.876300	−	1.51780i	0.0516365	−	0.0894370i
$289$	−2.10829	−	11.9567i	−0.124017	−	0.703334i
$290$	−3.70370	+	6.14097i	−0.217489	+	0.360610i
$291$	19.6345	−	3.46209i	1.15099	−	0.202951i
$292$	−0.267219	−	0.318459i	−0.0156378	−	0.0186364i
$293$	−2.71705	+	7.46503i	−0.158732	+	0.436112i	−0.993408	−	0.114628i	$-0.963432\pi$
$293$	−2.71705	+	7.46503i	−0.158732	+	0.436112i	0.834677	+	0.550740i	$0.185654\pi$
$294$	2.49620	+	6.85824i	0.145581	+	0.399981i
$295$	15.6104	−	25.8831i	0.908875	−	1.50697i
$296$	17.6851	+	3.62989i	1.02793	+	0.210983i
$297$			7.59944i			0.440965i
$298$	−23.9788	+	8.72757i	−1.38905	+	0.505574i
$299$	−0.374208	−	0.136201i	−0.0216410	−	0.00787669i
$300$	−0.914417	+	2.24189i	−0.0527939	+	0.129436i
$301$	1.31150	−	0.231253i	0.0755937	−	0.0133292i
$302$	−15.9050			−0.915228
$303$	−3.75345	+	0.661834i	−0.215630	+	0.0380214i
$304$	−12.2992	−	7.10095i	−0.705408	−	0.407267i
$305$	−22.8119	+	7.81262i	−1.30621	+	0.447349i
$306$	−1.96340	−	3.40071i	−0.112240	−	0.194406i
$307$	14.3001	+	8.25618i	0.816151	+	0.471205i	0.849087	−	0.528252i	$-0.177152\pi$
$307$	14.3001	+	8.25618i	0.816151	+	0.471205i	−0.0329361	+	0.999457i	$0.510486\pi$
$308$	−0.364984	−	1.00279i	−0.0207969	−	0.0571391i
$309$	−17.1407	−	20.4274i	−0.975098	−	1.16208i
$310$	21.1254	+	0.403682i	1.19984	+	0.0229276i
$311$	−21.6718	−	3.82132i	−1.22889	−	0.216687i	−0.478743	−	0.877955i	$-0.658907\pi$
$311$	−21.6718	−	3.82132i	−1.22889	−	0.216687i	−0.750150	+	0.661268i	$0.770019\pi$
$312$	0.868643	+	0.153165i	0.0491772	+	0.00867127i
$313$	3.98487	+	3.34370i	0.225238	+	0.188997i	0.748422	−	0.663222i	$-0.230812\pi$
$313$	3.98487	+	3.34370i	0.225238	+	0.188997i	−0.523184	+	0.852220i	$0.675256\pi$
$314$	0.0375477	−	0.103161i	0.00211894	−	0.00582174i
$315$	−4.87124	+	3.93134i	−0.274463	+	0.221506i
$316$	2.35150	−	2.80241i	0.132282	−	0.157648i
$317$	−5.31370	−	0.936949i	−0.298447	−	0.0526243i	0.0224194	−	0.999749i	$-0.492863\pi$
$317$	−5.31370	−	0.936949i	−0.298447	−	0.0526243i	−0.320867	+	0.947124i	$0.603974\pi$
$318$	5.86205	−	33.2453i	0.328727	−	1.86430i
$319$	−4.59070	+	2.65044i	−0.257030	+	0.148396i
$320$	19.2217	−	3.01185i	1.07453	−	0.168368i
$321$	−14.5135	+	5.28247i	−0.810063	+	0.294839i
$322$	−6.71507	−	3.87695i	−0.374216	−	0.216054i
$323$	7.78809	−	4.49645i	0.433341	−	0.250189i
$324$	1.99865	+	1.67706i	0.111036	+	0.0931703i
$325$	−0.712744	−	0.0272494i	−0.0395359	−	0.00151152i
$326$	5.21408	+	29.5705i	0.288781	+	1.63776i
$327$	17.4855			0.966948
$328$	−2.22194	−	12.6012i	−0.122686	−	0.695786i
$329$	8.06173	−	6.76460i	0.444458	−	0.372944i
$330$	10.5904	−	8.54698i	0.582982	−	0.470496i
$331$	−0.834469	−	2.29269i	−0.0458666	−	0.126017i	0.914645	−	0.404259i	$-0.132471\pi$
$331$	−0.834469	−	2.29269i	−0.0458666	−	0.126017i	−0.960511	+	0.278242i	$0.910248\pi$
$332$		−	0.772279i		−	0.0423843i
$333$	3.00027	−	7.57823i	0.164414	−	0.415284i
$334$	−12.5695			−0.687775
$335$	−1.37762	+	7.02521i	−0.0752674	+	0.383828i
$336$	14.2373	+	5.18196i	0.776710	+	0.282699i
$337$	−11.4063	−	13.5936i	−0.621343	−	0.740488i	0.359958	−	0.932969i	$-0.382791\pi$
$337$	−11.4063	−	13.5936i	−0.621343	−	0.740488i	−0.981301	+	0.192481i	$0.938347\pi$
$338$	−2.99654	−	16.9942i	−0.162990	−	0.924363i
$339$		−	25.8960i		−	1.40648i
$340$	−0.412351	+	1.06893i	−0.0223629	+	0.0579707i
$341$	13.5257	+	7.80906i	0.732457	+	0.422884i
$342$	−4.67166	+	5.56747i	−0.252615	+	0.301054i
$343$	17.4331	−	10.0650i	0.941297	−	0.543458i
$344$	−0.945949	+	1.63843i	−0.0510021	+	0.0883383i
$345$	−2.50236	+	12.7609i	−0.134723	+	0.687022i
$346$	−18.1768	−	21.6623i	−0.977193	−	1.16457i
$347$	5.93991	+	10.2882i	0.318871	+	0.552301i	0.980253	−	0.197749i	$-0.0633630\pi$
$347$	5.93991	+	10.2882i	0.318871	+	0.552301i	−0.661382	+	0.750049i	$0.730030\pi$
$348$	−0.202845	+	1.15039i	−0.0108736	+	0.0616674i
$349$	4.87443	−	27.6443i	0.260922	−	1.47976i	−0.519479	−	0.854483i	$-0.673874\pi$
$349$	4.87443	−	27.6443i	0.260922	−	1.47976i	0.780401	−	0.625280i	$-0.215015\pi$
$350$	−13.5750	−	2.93240i	−0.725614	−	0.156743i
$351$	−0.168732	+	0.463588i	−0.00900626	+	0.0247445i
$352$	2.70084	+	0.983027i	0.143955	+	0.0523955i
$353$	16.5944	+	13.9243i	0.883228	+	0.741117i	0.966840	−	0.255382i	$-0.0822012\pi$
$353$	16.5944	+	13.9243i	0.883228	+	0.741117i	−0.0836120	+	0.996498i	$0.526646\pi$
$354$	−6.50125	+	36.8704i	−0.345537	+	1.95964i
$355$	11.8280	−	13.5612i	0.627766	−	0.719755i
$356$	−3.76260	+	2.17234i	−0.199417	+	0.115134i
$357$	−7.34937	+	6.16685i	−0.388970	+	0.326384i
$358$	4.54377	+	12.4839i	0.240146	+	0.659795i
$359$	−13.0696	+	22.6372i	−0.689786	+	1.19474i	0.282121	+	0.959379i	$0.408962\pi$
$359$	−13.0696	+	22.6372i	−0.689786	+	1.19474i	−0.971907	+	0.235366i	$0.924371\pi$
$360$	0.169899	−	8.89115i	0.00895449	−	0.468605i
$361$	1.80459	+	1.51423i	0.0949784	+	0.0796963i
$362$	7.85811	−	13.6106i	0.413013	−	0.715360i
$363$	−12.6610	+	2.23248i	−0.664531	+	0.117175i
$364$		−	0.0692767i		−	0.00363109i
$365$	−3.73112	−	1.43933i	−0.195296	−	0.0753378i
$366$	22.8793	−	19.1980i	1.19592	−	1.00350i
$367$	−3.85993	+	10.6051i	−0.201487	+	0.553580i	−0.998746	−	0.0500565i	$-0.984060\pi$
$367$	−3.85993	+	10.6051i	−0.201487	+	0.553580i	0.797260	+	0.603636i	$0.206282\pi$
$368$	9.13159	−	3.32363i	0.476017	−	0.173256i
$369$	−5.77669			−0.300723
$370$	17.2644	−	5.37937i	0.897534	−	0.279660i
$371$	−25.4646			−1.32206
$372$	3.23415	−	1.17713i	0.167683	−	0.0610316i
$373$	−3.73627	+	10.2653i	−0.193457	+	0.531519i	−0.998058	−	0.0622977i	$-0.980157\pi$
$373$	−3.73627	+	10.2653i	−0.193457	+	0.531519i	0.804601	+	0.593816i	$0.202379\pi$
$374$	4.93315	−	4.13940i	0.255087	−	0.214043i
$375$	2.72382	+	23.1316i	0.140658	+	1.19451i
$376$			14.9505i			0.771012i
$377$	−0.338894	+	0.0597562i	−0.0174540	+	0.00307760i
$378$	−4.80296	+	8.31897i	−0.247038	+	0.427882i
$379$	19.4059	+	16.2835i	0.996813	+	0.836425i	0.986540	−	0.163522i	$-0.0522855\pi$
$379$	19.4059	+	16.2835i	0.996813	+	0.836425i	0.0102730	+	0.999947i	$0.496730\pi$
$380$	2.12011	+	0.0405128i	0.108759	+	0.00207826i
$381$	−21.4692	+	37.1858i	−1.09990	+	1.90508i
$382$	−8.61792	−	23.6776i	−0.440931	−	1.21145i
$383$	13.1740	−	11.0543i	0.673162	−	0.564850i	−0.240837	−	0.970565i	$-0.577422\pi$
$383$	13.1740	−	11.0543i	0.673162	−	0.564850i	0.913999	+	0.405715i	$0.132978\pi$
$384$	−16.1510	+	9.32476i	−0.824200	+	0.475852i
$385$	−7.73646	−	6.74769i	−0.394287	−	0.343894i
$386$	3.25138	−	18.4395i	0.165491	−	0.938546i
$387$	0.654289	+	0.549013i	0.0332594	+	0.0279079i
$388$	2.09041	+	0.760848i	0.106125	+	0.0386262i
$389$	−5.33010	+	14.6443i	−0.270247	+	0.742497i	0.728124	+	0.685445i	$0.240392\pi$
$389$	−5.33010	+	14.6443i	−0.270247	+	0.742497i	−0.998371	+	0.0570519i	$0.981830\pi$
$390$	0.835816	−	0.286250i	0.0423232	−	0.0144948i
$391$	−1.06852	+	6.05991i	−0.0540376	+	0.306463i
$392$	−1.35811	+	7.70224i	−0.0685951	+	0.389022i
$393$	0.941379	+	1.63052i	0.0474863	+	0.0822487i
$394$	12.1026	+	14.4234i	0.609722	+	0.726639i
$395$	6.77202	−	34.5341i	0.340737	−	1.73760i
$396$	0.342209	−	0.592723i	0.0171966	−	0.0297854i
$397$	−1.90550	+	1.10014i	−0.0956341	+	0.0552144i	−0.547054	−	0.837097i	$-0.684251\pi$
$397$	−1.90550	+	1.10014i	−0.0956341	+	0.0552144i	0.451420	+	0.892311i	$0.350918\pi$
$398$	8.60179	−	10.2512i	0.431169	−	0.513847i
$399$	15.3777	+	8.87832i	0.769848	+	0.444472i
$400$	13.7510	−	10.6704i	0.687550	−	0.533521i
$401$		−	21.3109i		−	1.06422i	−0.846677	−	0.532108i	$-0.821400\pi$
$401$		−	21.3109i		−	1.06422i	0.846677	−	0.532108i	$-0.178600\pi$
$402$	−1.53981	−	8.73268i	−0.0767986	−	0.435546i
$403$	0.651719	+	0.776689i	0.0324645	+	0.0386896i
$404$	−0.399616	−	0.145448i	−0.0198816	−	0.00723632i
$405$	24.6294	+	4.82974i	1.22384	+	0.239992i
$406$	−6.70047			−0.332539
$407$	13.0935	+	2.68746i	0.649022	+	0.133212i
$408$		−	13.6294i		−	0.674756i
$409$	4.65509	+	12.7898i	0.230179	+	0.632413i	0.999983	−	0.00586827i	$-0.00186794\pi$
$409$	4.65509	+	12.7898i	0.230179	+	0.632413i	−0.769803	+	0.638281i	$0.779646\pi$
$410$	−8.04914	−	9.97353i	−0.397519	−	0.492557i
$411$	−4.14537	+	3.47838i	−0.204476	+	0.171576i
$412$	−0.516664	−	2.93015i	−0.0254542	−	0.144358i
$413$	28.2413			1.38966
$414$	−0.863552	−	4.89745i	−0.0424413	−	0.240696i
$415$	−3.59098	−	6.50362i	−0.176274	−	0.319250i
$416$	0.142933	+	0.119935i	0.00700786	+	0.00588030i
$417$	−28.6094	+	16.5177i	−1.40101	+	0.808873i
$418$	−10.3220	−	5.95943i	−0.504867	−	0.291485i
$419$	16.0684	−	5.84843i	0.784994	−	0.285714i	0.0817404	−	0.996654i	$-0.473952\pi$
$419$	16.0684	−	5.84843i	0.784994	−	0.285714i	0.703253	+	0.710939i	$0.251730\pi$
$420$	−2.23494	+	0.350194i	−0.109054	+	0.0170877i
$421$	8.59287	−	4.96110i	0.418791	−	0.241789i	−0.275769	−	0.961224i	$-0.588932\pi$
$421$	8.59287	−	4.96110i	0.418791	−	0.241789i	0.694560	+	0.719435i	$0.255599\pi$
$422$	−2.78405	+	15.7891i	−0.135525	+	0.768603i
$423$	6.64698	+	1.17204i	0.323187	+	0.0569866i
$424$	23.2533	−	27.7123i	1.12928	−	1.34583i
$425$	1.49779	+	10.9192i	0.0726535	+	0.529658i
$426$	−7.62324	+	20.9447i	−0.369347	+	1.01477i
$427$	−17.2584	−	14.4815i	−0.835194	−	0.700811i
$428$	−1.69713	−	0.299250i	−0.0820339	−	0.0144648i
$429$	0.643117	+	0.113399i	0.0310500	+	0.00547495i
$430$	−0.0362040	+	1.89462i	−0.00174591	+	0.0913668i
$431$	−5.07276	−	6.04548i	−0.244346	−	0.291201i	0.629907	−	0.776671i	$-0.283093\pi$
$431$	−5.07276	−	6.04548i	−0.244346	−	0.291201i	−0.874253	+	0.485470i	$0.838649\pi$
$432$	−4.11748	−	11.3127i	−0.198102	−	0.544282i
$433$	−3.53581	−	2.04140i	−0.169920	−	0.0981036i	0.412628	−	0.910900i	$-0.364611\pi$
$433$	−3.53581	−	2.04140i	−0.169920	−	0.0981036i	−0.582548	+	0.812796i	$0.697944\pi$
$434$	9.87088	+	17.0969i	0.473817	+	0.820676i
$435$	3.64091	+	10.6310i	0.174568	+	0.509719i
$436$	1.68961	+	0.975496i	0.0809175	+	0.0467178i
$437$	11.2158	−	1.97765i	0.536525	−	0.0946038i
$438$	4.95345			0.236685
$439$	22.3347	−	3.93820i	1.06598	−	0.187960i	0.386969	−	0.922093i	$-0.373522\pi$
$439$	22.3347	−	3.93820i	1.06598	−	0.187960i	0.679006	+	0.734132i	$0.262411\pi$
$440$	14.4079	−	2.25758i	0.686871	−	0.107626i
$441$	3.31795	+	1.20763i	0.157997	+	0.0575064i
$442$	0.392844	−	0.142984i	0.0186857	−	0.00680104i
$443$		−	4.29550i		−	0.204085i	−0.994780	−	0.102043i	$-0.967462\pi$
$443$		−	4.29550i		−	0.204085i	0.994780	−	0.102043i	$-0.0325378\pi$
$444$	2.30835	−	1.82965i	0.109550	−	0.0868313i
$445$	−21.5851	+	35.7895i	−1.02323	+	1.69659i
$446$	0.505048	+	1.38761i	0.0239147	+	0.0657051i
$447$	−13.6757	+	37.5736i	−0.646837	+	1.77717i
$448$	11.6850	+	13.9256i	0.552064	+	0.657924i
$449$	13.3603	−	2.35578i	0.630512	−	0.111176i	0.150746	−	0.988573i	$-0.451832\pi$
$449$	13.3603	−	2.35578i	0.630512	−	0.111176i	0.479767	+	0.877396i	$0.340721\pi$
$450$	−4.15565	−	7.87838i	−0.195899	−	0.371390i
$451$	−1.64505	−	9.32957i	−0.0774626	−	0.439312i
$452$	1.44471	−	2.50231i	0.0679534	−	0.117699i
$453$	−16.0197	+	19.0916i	−0.752673	+	0.897001i
$454$	6.46866	+	11.2041i	0.303589	+	0.525832i
$455$	−0.322126	−	0.583403i	−0.0151015	−	0.0273504i
$456$	−23.7043	+	8.62766i	−1.11006	+	0.404027i
$457$	−18.4071	+	15.4454i	−0.861047	+	0.722504i	−0.962193	−	0.272368i	$-0.912193\pi$
$457$	−18.4071	+	15.4454i	−0.861047	+	0.722504i	0.101147	+	0.994872i	$0.467749\pi$
$458$	9.97632	+	17.2795i	0.466163	+	0.807418i
$459$	7.50732	+	1.32374i	0.350412	+	0.0617870i
$460$	−0.953716	+	1.09347i	−0.0444672	+	0.0509832i
$461$	−10.2581	+	12.2251i	−0.477766	+	0.569379i	−0.950062	−	0.312061i	$-0.898981\pi$
$461$	−10.2581	+	12.2251i	−0.477766	+	0.569379i	0.472296	+	0.881440i	$0.343425\pi$
$462$	11.9486	+	4.34893i	0.555899	+	0.202331i
$463$	−29.4514	−	10.7194i	−1.36872	−	0.498175i	−0.449984	−	0.893037i	$-0.648570\pi$
$463$	−29.4514	−	10.7194i	−1.36872	−	0.498175i	−0.918741	+	0.394862i	$0.870793\pi$
$464$	5.39776	−	6.43280i	0.250585	−	0.298635i
$465$	21.7624	−	24.9514i	1.00921	−	1.15709i
$466$	29.1043	+	5.13188i	1.34823	+	0.237730i
$467$	−18.7962	−	32.5560i	−0.869786	−	1.50651i	−0.862215	−	0.506542i	$-0.830924\pi$
$467$	−18.7962	−	32.5560i	−0.869786	−	1.50651i	−0.00757047	−	0.999971i	$-0.502410\pi$
$468$	0.0340361	−	0.0285597i	0.00157332	−	0.00132017i
$469$	−6.28551	+	2.28774i	−0.290238	+	0.105638i
$470$	7.23823	+	13.1092i	0.333875	+	0.604682i
$471$	−0.0860116	−	0.148976i	−0.00396321	−	0.00686447i
$472$	−25.7889	+	30.7340i	−1.18703	+	1.41465i
$473$	−0.700352	+	1.21305i	−0.0322022	+	0.0557759i
$474$	7.56930	+	42.9276i	0.347669	+	1.97173i
$475$	18.0425	−	9.51700i	0.827849	−	0.436670i
$476$	−1.05421	+	0.185885i	−0.0483195	+	0.00852003i
$477$	−10.4979	−	12.5109i	−0.480667	−	0.572836i
$478$	−2.52499	+	6.93734i	−0.115490	+	0.317307i
$479$	−6.18829	−	17.0022i	−0.282750	−	0.776850i	−0.997032	−	0.0769916i	$-0.975469\pi$
$479$	−6.18829	−	17.0022i	−0.282750	−	0.776850i	0.714281	−	0.699859i	$-0.246754\pi$
$480$	3.14671	−	5.21745i	0.143627	−	0.238143i
$481$	0.739072	+	0.454661i	0.0336988	+	0.0207308i
$482$			19.1686i			0.873104i
$483$	−11.4172	+	4.15553i	−0.519502	+	0.189083i
$484$	−1.34797	−	0.490622i	−0.0612715	−	0.0223010i
$485$	21.1419	−	3.31273i	0.960005	−	0.150423i
$486$	−17.0316	+	3.00314i	−0.772571	+	0.136225i
$487$	4.82913			0.218829			0.109414	−	0.993996i	$-0.465102\pi$
$487$	4.82913			0.218829			0.109414	+	0.993996i	$0.465102\pi$
$488$	31.5195	−	5.55774i	1.42682	−	0.251587i
$489$	40.7468	+	23.5252i	1.84263	+	1.06384i
$490$	2.53817	+	7.41117i	0.114663	+	0.334802i
$491$	−17.3191	−	29.9976i	−0.781601	−	1.35377i	−0.931009	−	0.364997i	$-0.881070\pi$
$491$	−17.3191	−	29.9976i	−0.781601	−	1.35377i	0.149408	−	0.988776i	$-0.452263\pi$
$492$	−1.80795	−	1.04382i	−0.0815087	−	0.0470591i
$493$	1.81866	+	4.99673i	0.0819084	+	0.225041i
$494$	−0.497356	−	0.592725i	−0.0223771	−	0.0266680i
$495$	0.125788	−	6.58274i	0.00565377	−	0.295872i
$496$	−24.3656	−	4.29632i	−1.09405	−	0.192911i
$497$	16.5576	+	2.91955i	0.742710	+	0.130960i
$498$	7.04914	+	5.91493i	0.315880	+	0.265054i
$499$	−6.97162	+	19.1544i	−0.312092	+	0.857467i	0.680141	+	0.733081i	$0.261918\pi$
$499$	−6.97162	+	19.1544i	−0.312092	+	0.857467i	−0.992234	+	0.124386i	$0.960304\pi$
$500$	−1.02729	+	2.38715i	−0.0459418	+	0.106757i
$501$	−12.6602	+	15.0879i	−0.565618	+	0.674078i
$502$	0.367476	+	0.0647959i	0.0164013	+	0.00289198i
$503$	1.09234	−	6.19494i	0.0487048	−	0.276219i	−0.950723	−	0.310042i	$-0.899657\pi$
$503$	1.09234	−	6.19494i	0.0487048	−	0.276219i	0.999428	+	0.0338227i	$0.0107681\pi$
$504$	7.19564	−	4.15441i	0.320519	−	0.185052i
$505$	−4.04162	+	0.633282i	−0.179850	+	0.0281807i
$506$	7.66364	−	2.78934i	0.340690	−	0.124001i
$507$	−23.4172	−	13.5199i	−1.04000	−	0.600442i
$508$	−4.14911	+	2.39549i	−0.184087	+	0.106283i
$509$	−20.1589	−	16.9153i	−0.893526	−	0.749757i	0.0753881	−	0.997154i	$-0.475980\pi$
$509$	−20.1589	−	16.9153i	−0.893526	−	0.749757i	−0.968914	+	0.247397i	$0.920425\pi$
$510$	−6.59864	−	11.9508i	−0.292193	−	0.529191i
$511$	−0.648838	−	3.67974i	−0.0287029	−	0.162782i
$512$	−25.2170			−1.11444
$513$	−2.45001	−	13.8947i	−0.108171	−	0.613467i
$514$	6.52159	−	5.47227i	0.287655	−	0.241371i
$515$	−17.9757	−	22.2734i	−0.792106	−	0.981483i
$516$	0.105571	+	0.290053i	0.00464750	+	0.0127689i
$517$			11.0689i			0.486809i
$518$	12.6347	+	11.2172i	0.555138	+	0.492856i
$519$	−44.3104			−1.94501
$520$	0.929050	+	0.182184i	0.0407416	+	0.00798928i
$521$	−10.5656	−	3.84556i	−0.462887	−	0.168477i	0.100040	−	0.994983i	$-0.468103\pi$
$521$	−10.5656	−	3.84556i	−0.462887	−	0.168477i	−0.562928	+	0.826506i	$0.690325\pi$
$522$	−2.76230	−	3.29198i	−0.120903	−	0.144086i
$523$	−3.96641	−	22.4946i	−0.173439	−	0.983621i	−0.939930	−	0.341367i	$-0.889110\pi$
$523$	−3.96641	−	22.4946i	−0.173439	−	0.983621i	0.766491	−	0.642255i	$-0.222001\pi$
$524$			0.210074i			0.00917713i
$525$	−17.1929	+	13.3412i	−0.750359	+	0.582260i
$526$	−26.1976	−	15.1252i	−1.14227	−	0.659490i
$527$	10.0704	−	12.0015i	0.438674	−	0.522792i
$528$	−13.8007	+	7.96786i	−0.600600	+	0.346757i
$529$	7.60360	−	13.1698i	0.330591	−	0.572601i
$530$	6.97266	−	35.5573i	0.302873	−	1.54451i
$531$	11.6426	+	13.8751i	0.505247	+	0.602130i
$532$	0.990625	+	1.71581i	0.0429490	+	0.0743899i
$533$	0.106794	−	0.605656i	0.00462574	−	0.0262339i
$534$	8.98951	−	50.9820i	0.389014	−	2.20621i
$535$	−15.6836	+	5.37131i	−0.678061	+	0.232222i
$536$	3.25002	−	8.92937i	0.140380	−	0.385690i
$537$	19.5617	+	7.11987i	0.844149	+	0.307245i
$538$	−12.7284	−	10.6804i	−0.548761	−	0.460465i
$539$	−1.00551	+	5.70251i	−0.0433102	+	0.245624i
$540$	1.35465	+	1.18151i	0.0582946	+	0.0508442i
$541$	−0.0544889	+	0.0314592i	−0.00234266	+	0.00135254i	−0.501171	−	0.865348i	$-0.667097\pi$
$541$	−0.0544889	+	0.0314592i	−0.00234266	+	0.00135254i	0.498828	+	0.866701i	$0.333764\pi$
$542$	−9.92620	+	8.32907i	−0.426367	+	0.357764i
$543$	−8.42277	−	23.1414i	−0.361456	−	0.993092i
$544$	1.44157	−	2.49687i	0.0618068	−	0.107052i
$545$	18.7647	+	0.358571i	0.803790	+	0.0153595i
$546$	0.632338	+	0.530595i	0.0270616	+	0.0227074i
$547$	1.60317	−	2.77677i	0.0685464	−	0.118726i	−0.829715	−	0.558187i	$-0.811497\pi$
$547$	1.60317	−	2.77677i	0.0685464	−	0.118726i	0.898262	+	0.439461i	$0.144831\pi$
$548$	−0.594620	+	0.104847i	−0.0254009	+	0.00447886i
$549$		−	14.4493i		−	0.616679i
$550$	11.5404	−	8.95510i	0.492086	−	0.381847i
$551$	7.53909	−	6.32605i	0.321176	−	0.269499i
$552$	5.90347	−	16.2197i	0.251268	−	0.690354i
$553$	30.8979	−	11.2459i	1.31391	−	0.478226i
$554$	−29.0476			−1.23411
$555$	10.9319	−	26.1416i	0.464032	−	1.10965i
$556$	−3.68601			−0.156322
$557$	−14.1122	+	5.13642i	−0.597953	+	0.217637i	−0.623224	−	0.782044i	$-0.714177\pi$
$557$	−14.1122	+	5.13642i	−0.597953	+	0.217637i	0.0252709	+	0.999681i	$0.491955\pi$
$558$	−4.33048	+	11.8979i	−0.183324	+	0.503678i
$559$	−0.0696570	+	0.0584492i	−0.00294618	+	0.00247214i
$560$	15.1726	+	5.85303i	0.641161	+	0.247336i
$561$		−	10.0908i		−	0.426034i
$562$	26.5063	−	4.67378i	1.11810	−	0.197151i
$563$	16.9565	−	29.3696i	0.714633	−	1.23778i	−0.248468	−	0.968640i	$-0.579927\pi$
$563$	16.9565	−	29.3696i	0.714633	−	1.23778i	0.963101	−	0.269141i	$-0.0867397\pi$
$564$	1.86854	+	1.56789i	0.0786799	+	0.0660203i
$565$	0.531044	−	27.7905i	0.0223412	−	1.16915i
$566$	16.7519	−	29.0152i	0.704136	−	1.21960i
$567$	8.02049	+	22.0361i	0.336829	+	0.925430i
$568$	−18.2970	+	15.3530i	−0.767726	+	0.644199i
$569$	−21.1609	+	12.2173i	−0.887111	+	0.512174i	−0.872997	−	0.487726i	$-0.837826\pi$
$569$	−21.1609	+	12.2173i	−0.887111	+	0.512174i	−0.0141148	+	0.999900i	$0.504493\pi$
$570$	−16.6078	+	19.0415i	−0.695626	+	0.797559i
$571$	−1.40560	+	7.97157i	−0.0588227	+	0.333600i	−0.999991	−	0.00433936i	$-0.998619\pi$
$571$	−1.40560	+	7.97157i	−0.0588227	+	0.333600i	0.941168	+	0.337939i	$0.109730\pi$
$572$	0.0558175	+	0.0468365i	0.00233385	+	0.00195833i
$573$	−37.1016	−	13.5039i	−1.54994	−	0.564132i
$574$	4.09561	−	11.2526i	0.170948	−	0.469675i
$575$	−2.94711	+	13.6431i	−0.122903	+	0.568957i
$576$	−2.02455	+	11.4818i	−0.0843564	+	0.478409i
$577$	−2.34435	+	13.2954i	−0.0975964	+	0.553497i	0.896324	+	0.443399i	$0.146228\pi$
$577$	−2.34435	+	13.2954i	−0.0975964	+	0.553497i	−0.993921	+	0.110098i	$0.964884\pi$
$578$	8.07078	+	13.9790i	0.335700	+	0.581450i
$579$	−18.8591	−	22.4754i	−0.783757	−	0.934045i
$580$	−0.241276	+	1.23039i	−0.0100184	+	0.0510893i
$581$	3.47065	−	6.01134i	0.143987	−	0.249392i
$582$	−22.9554	+	13.2533i	−0.951533	+	0.549368i
$583$	17.2161	−	20.5173i	0.713017	−	0.849741i
$584$	4.59703	+	2.65410i	0.190226	+	0.109827i
$585$	0.153832	−	0.398773i	0.00636015	−	0.0164872i
$586$		−	10.5617i		−	0.436298i
$587$	2.15400	+	12.2159i	0.0889050	+	0.504205i	0.996445	+	0.0842405i	$0.0268464\pi$
$587$	2.15400	+	12.2159i	0.0889050	+	0.504205i	−0.907540	+	0.419965i	$0.862042\pi$
$588$	0.820215	+	0.977495i	0.0338251	+	0.0403112i
$589$	−27.2478	−	9.91737i	−1.12272	−	0.408638i
$590$	−7.73297	+	39.4345i	−0.318361	+	1.62349i
$591$	29.5031			1.21360
$592$	−20.9474	+	3.09364i	−0.860932	+	0.127148i
$593$			7.59807i			0.312015i	0.987756	+	0.156008i	$0.0498624\pi$
$593$			7.59807i			0.312015i	−0.987756	+	0.156008i	$0.950138\pi$
$594$	−3.45557	−	9.49411i	−0.141784	−	0.389548i
$595$	−8.01350	+	6.46730i	−0.328522	+	0.265133i
$596$	−3.41766	+	2.86776i	−0.139993	+	0.117468i
$597$	−3.64122	−	20.6504i	−0.149025	−	0.845164i
$598$	0.529437			0.0216503
$599$	−0.841380	−	4.77171i	−0.0343779	−	0.194967i	0.962782	−	0.270279i	$-0.0871158\pi$
$599$	−0.841380	−	4.77171i	−0.0343779	−	0.194967i	−0.997160	+	0.0753120i	$0.976005\pi$
$600$	1.18109	−	30.8931i	0.0482180	−	1.26121i
$601$	1.41912	+	1.19078i	0.0578870	+	0.0485729i	0.671272	−	0.741211i	$-0.265748\pi$
$601$	1.41912	+	1.19078i	0.0578870	+	0.0485729i	−0.613385	+	0.789784i	$0.710193\pi$
$602$	−1.53333	+	0.885266i	−0.0624937	+	0.0360807i
$603$	−3.71521	−	2.14498i	−0.151295	−	0.0873502i
$604$	−2.61308	+	0.951082i	−0.106325	+	0.0386990i
$605$	−13.6331	+	2.13617i	−0.554263	+	0.0868475i
$606$	4.38830	−	2.53358i	0.178262	−	0.102920i
$607$	−0.330369	+	1.87362i	−0.0134093	+	0.0760478i	−0.990778	−	0.135495i	$-0.956738\pi$
$607$	−0.330369	+	1.87362i	−0.0134093	+	0.0760478i	0.977369	+	0.211543i	$0.0678487\pi$
$608$	−5.25511	−	0.926617i	−0.213123	−	0.0375793i
$609$	−6.74883	+	8.04294i	−0.273476	+	0.325916i
$610$	24.9468	−	20.1333i	1.01007	−	0.815175i
$611$	−0.245765	+	0.675234i	−0.00994259	+	0.0273170i
$612$	−0.525928	−	0.441306i	−0.0212594	−	0.0178387i
$613$	24.1651	+	4.26097i	0.976021	+	0.172099i	0.638839	−	0.769341i	$-0.279415\pi$
$613$	24.1651	+	4.26097i	0.976021	+	0.172099i	0.337182	+	0.941440i	$0.390526\pi$
$614$	−21.6196	−	3.81211i	−0.872495	−	0.153844i
$615$	−20.0790	−	0.383686i	−0.809663	−	0.0154717i
$616$	8.75865	+	10.4382i	0.352896	+	0.420565i
$617$	−9.75554	−	26.8031i	−0.392743	−	1.07905i	−0.965744	−	0.259498i	$-0.916443\pi$
$617$	−9.75554	−	26.8031i	−0.392743	−	1.07905i	0.573000	−	0.819555i	$-0.305779\pi$
$618$	30.7027	+	17.7262i	1.23505	+	0.713054i
$619$	9.57288	+	16.5807i	0.384767	+	0.666435i	0.991737	−	0.128289i	$-0.0409486\pi$
$619$	9.57288	+	16.5807i	0.384767	+	0.666435i	−0.606970	+	0.794725i	$0.707615\pi$
$620$	3.49489	−	1.19693i	0.140358	−	0.0480699i
$621$	8.36071	+	4.82706i	0.335504	+	0.193703i
$622$	28.8125	−	5.08042i	1.15528	−	0.203706i
$623$	−39.0503			−1.56452
$624$	−1.01880	+	0.179641i	−0.0407845	+	0.00719141i
$625$	2.44874	+	24.8798i	0.0979496	+	0.995191i
$626$	−6.49879	−	2.36537i	−0.259744	−	0.0945390i
$627$	−17.5500	+	6.38766i	−0.700878	+	0.255099i
$628$		−	0.0191940i		−	0.000765924i
$629$	4.93563	−	12.4667i	0.196797	−	0.497078i
$630$	4.29809	−	7.12650i	0.171240	−	0.283927i
$631$	5.02154	+	13.7966i	0.199905	+	0.549233i	0.998622	−	0.0524726i	$-0.0167102\pi$
$631$	5.02154	+	13.7966i	0.199905	+	0.549233i	−0.798718	+	0.601706i	$0.794488\pi$
$632$	−15.9763	+	43.8945i	−0.635503	+	1.74603i
$633$	16.1484	+	19.2449i	0.641842	+	0.764917i
$634$	7.06454	−	1.24567i	0.280569	−	0.0494718i
$635$	−23.8024	+	39.4660i	−0.944571	+	1.56616i
$636$	−1.02490	−	5.81251i	−0.0406400	−	0.230481i
$637$	−0.187953	+	0.325544i	−0.00744697	+	0.0128985i
$638$	4.53004	−	5.39870i	0.179346	−	0.213736i
$639$	5.39156	+	9.33846i	0.213287	+	0.369424i
$640$	−17.5238	+	9.67574i	−0.692688	+	0.382467i
$641$	24.9108	−	9.06678i	0.983916	−	0.358116i	0.200555	−	0.979683i	$-0.435726\pi$
$641$	24.9108	−	9.06678i	0.983916	−	0.358116i	0.783361	+	0.621566i	$0.213503\pi$
$642$	15.7299	−	13.1990i	0.620810	−	0.520921i
$643$	−6.64999	−	11.5181i	−0.262250	−	0.454230i	0.704590	−	0.709615i	$-0.251131\pi$
$643$	−6.64999	−	11.5181i	−0.262250	−	0.454230i	−0.966839	+	0.255385i	$0.917798\pi$
$644$	−1.33507	−	0.235409i	−0.0526092	−	0.00927643i
$645$	2.23775	+	1.95175i	0.0881114	+	0.0768502i
$646$	−7.68518	+	9.15884i	−0.302369	+	0.360350i
$647$	27.8545	+	10.1382i	1.09507	+	0.398574i	0.825498	−	0.564405i	$-0.190894\pi$
$647$	27.8545	+	10.1382i	1.09507	+	0.398574i	0.269576	+	0.962979i	$0.413116\pi$
$648$	−31.3051	−	11.3941i	−1.22978	−	0.447604i
$649$	−19.0933	+	22.7545i	−0.749479	+	0.893194i
$650$	0.902833	−	0.290051i	0.0354120	−	0.0113768i
$651$	30.4644	+	5.37169i	1.19399	+	0.210533i
$652$	2.62489	+	4.54644i	0.102799	+	0.178052i
$653$	−15.9960	+	13.4223i	−0.625972	+	0.525253i	−0.899675	−	0.436561i	$-0.856196\pi$
$653$	−15.9960	+	13.4223i	−0.625972	+	0.525253i	0.273702	+	0.961815i	$0.411752\pi$
$654$	−21.8449	+	7.95088i	−0.854202	+	0.310904i
$655$	0.976812	+	1.76911i	0.0381672	+	0.0691247i
$656$	7.50375	+	12.9969i	0.292972	+	0.507443i
$657$	1.54039	−	1.83577i	0.0600965	−	0.0716202i
$658$	−6.99569	+	12.1169i	−0.272721	+	0.472366i
$659$	−3.22331	−	18.2803i	−0.125562	−	0.712099i	−0.980972	−	0.194148i	$-0.937806\pi$
$659$	−3.22331	−	18.2803i	−0.125562	−	0.712099i	0.855410	−	0.517952i	$-0.173305\pi$
$660$	1.22884	−	2.03749i	0.0478325	−	0.0793093i
$661$	19.6481	−	3.46449i	0.764222	−	0.134753i	0.222067	−	0.975031i	$-0.428720\pi$
$661$	19.6481	−	3.46449i	0.764222	−	0.134753i	0.542155	+	0.840278i	$0.317608\pi$
$662$	2.08503	+	2.48484i	0.0810371	+	0.0965762i
$663$	0.224048	−	0.615568i	0.00870132	−	0.0239067i
$664$	3.37266	+	9.26631i	0.130885	+	0.359603i
$665$	16.3207	+	9.84320i	0.632888	+	0.381703i
$666$	−0.302358	+	10.8319i	−0.0117162	+	0.419726i
$667$			6.73409i			0.260745i
$668$	−2.06509	+	0.751631i	−0.0799007	+	0.0290815i
$669$	2.17431	+	0.791385i	0.0840638	+	0.0305967i
$670$	−1.47338	−	9.40313i	−0.0569216	−	0.363274i
$671$	23.3361	−	4.11478i	0.900880	−	0.158849i
$672$	5.69280			0.219605
$673$	5.18426	−	0.914124i	0.199838	−	0.0352369i	−0.0728329	−	0.997344i	$-0.523204\pi$
$673$	5.18426	−	0.914124i	0.199838	−	0.0352369i	0.272671	+	0.962107i	$0.412093\pi$
$674$	20.4313	+	11.7960i	0.786984	+	0.454366i
$675$	16.9018	+	3.65104i	0.650550	+	0.140528i
$676$	−1.50853	−	2.61284i	−0.0580202	−	0.100494i
$677$	−15.8923	−	9.17542i	−0.610791	−	0.352640i	0.162484	−	0.986711i	$-0.448049\pi$
$677$	−15.8923	−	9.17542i	−0.610791	−	0.352640i	−0.773275	+	0.634071i	$0.781383\pi$
$678$	11.7753	+	32.3522i	0.452226	+	1.24248i
$679$	12.8523	+	15.3168i	0.493226	+	0.587804i
$680$	0.279495	−	14.6265i	0.0107182	−	0.560901i
$681$	19.9642	+	3.52022i	0.765029	+	0.134895i
$682$	−20.4487	−	3.60566i	−0.783023	−	0.138068i
$683$	1.67762	+	1.40769i	0.0641922	+	0.0538636i	0.674319	−	0.738440i	$-0.264437\pi$
$683$	1.67762	+	1.40769i	0.0641922	+	0.0538636i	−0.610127	+	0.792304i	$0.708882\pi$
$684$	−0.434599	+	1.19405i	−0.0166173	+	0.0456557i
$685$	−4.51997	+	3.64785i	−0.172699	+	0.139377i
$686$	−17.2027	+	20.5014i	−0.656803	+	0.782748i
$687$	30.7898	+	5.42907i	1.17470	+	0.207132i
$688$	0.385314	−	2.18522i	0.0146900	−	0.0833109i
$689$	1.50578	−	0.869363i	0.0573657	−	0.0331201i
$690$	−2.67630	−	17.0802i	−0.101885	−	0.650232i
$691$	21.0301	−	7.65434i	0.800023	−	0.291185i	0.0905272	−	0.995894i	$-0.471145\pi$
$691$	21.0301	−	7.65434i	0.800023	−	0.291185i	0.709496	+	0.704709i	$0.248923\pi$
$692$	−4.28169	−	2.47203i	−0.162765	−	0.0939726i
$693$	5.32744	−	3.07580i	0.202373	−	0.116840i
$694$	−12.0990	−	10.1523i	−0.459272	−	0.385375i
$695$	−31.0412	+	17.1394i	−1.17746	+	0.650134i
$696$	−2.59007	−	14.6890i	−0.0981764	−	0.556786i
$697$	−9.50302			−0.359953
$698$	6.48052	+	36.7529i	0.245291	+	1.39112i
$699$	35.4744	−	29.7666i	1.34177	−	1.12587i
$700$	−2.40563	+	0.329982i	−0.0909243	+	0.0124721i
$701$	16.5034	+	45.3428i	0.623326	+	1.71257i	0.698695	+	0.715419i	$0.253764\pi$
$701$	16.5034	+	45.3428i	0.623326	+	1.71257i	−0.0753692	+	0.997156i	$0.524014\pi$
$702$		−	0.655893i		−	0.0247551i
$703$	−24.8064	−	0.692441i	−0.935592	−	0.0261159i
$704$	−19.1201			−0.720616
$705$	23.0261	+	4.51534i	0.867214	+	0.170058i
$706$	−27.0632	−	9.85019i	−1.01854	−	0.370717i
$707$	−2.45692	−	2.92804i	−0.0924020	−	0.110120i
$708$	1.13666	+	6.44631i	0.0427183	+	0.242267i
$709$			35.8242i			1.34540i	0.739913	+	0.672702i	$0.234867\pi$
$709$			35.8242i			1.34540i	−0.739913	+	0.672702i	$0.765133\pi$
$710$	−8.61045	+	22.3206i	−0.323144	+	0.837678i
$711$	18.2630	+	10.5442i	0.684917	+	0.395437i
$712$	35.6592	−	42.4970i	1.33639	−	1.59264i
$713$	17.1826	−	9.92040i	0.643495	−	0.371522i
$714$	6.37753	−	11.0462i	0.238673	−	0.413394i
$715$	0.687841	+	0.134883i	0.0257238	+	0.00504435i
$716$	1.49302	+	1.77931i	0.0557968	+	0.0664961i
$717$	5.78406	+	10.0183i	0.216010	+	0.374140i
$718$	6.03460	−	34.2239i	0.225209	−	1.27722i
$719$	−0.902323	+	5.11733i	−0.0336510	+	0.190844i	−0.996999	−	0.0774090i	$-0.975335\pi$
$719$	−0.902323	+	5.11733i	−0.0336510	+	0.190844i	0.963348	+	0.268253i	$0.0864464\pi$
$720$	3.37936	+	9.86735i	0.125941	+	0.367734i
$721$	9.14653	−	25.1299i	0.340635	−	0.935886i
$722$	−2.94304	−	1.07118i	−0.109529	−	0.0398652i
$723$	23.0090	+	19.3069i	0.855716	+	0.718031i
$724$	0.477147	−	2.70603i	0.0177330	−	0.100569i
$725$	3.68927	+	11.4835i	0.137016	+	0.426485i
$726$	14.8025	−	8.54621i	0.549371	−	0.317180i
$727$	12.8308	−	10.7663i	0.475869	−	0.399302i	−0.373061	−	0.927807i	$-0.621692\pi$
$727$	12.8308	−	10.7663i	0.475869	−	0.399302i	0.848930	+	0.528505i	$0.177247\pi$
$728$	0.302542	+	0.831228i	0.0112130	+	0.0308074i
$729$	3.28685	−	5.69300i	0.121735	−	0.210852i
$730$	5.31583	+	0.101579i	0.196748	+	0.00375962i
$731$	1.07635	+	0.903162i	0.0398101	+	0.0334046i
$732$	2.61091	−	4.52223i	0.0965021	−	0.167147i
$733$	21.3058	−	3.75680i	0.786949	−	0.138760i	0.234289	−	0.972167i	$-0.424724\pi$
$733$	21.3058	−	3.75680i	0.786949	−	0.138760i	0.552660	+	0.833407i	$0.313613\pi$
$734$		−	15.0042i		−	0.553817i
$735$	11.4525	+	4.41795i	0.422432	+	0.162958i
$736$	2.79704	−	2.34699i	0.103100	−	0.0865113i
$737$	2.40622	−	6.61104i	0.0886343	−	0.243521i
$738$	7.21691	−	2.62674i	0.265658	−	0.0966917i
$739$	1.79050			0.0658646			0.0329323	−	0.999458i	$-0.489515\pi$
$739$	1.79050			0.0658646			0.0329323	+	0.999458i	$0.489515\pi$
$740$	2.51475	−	1.91617i	0.0924441	−	0.0704397i
$741$	−1.21243			−0.0445395
$742$	31.8134	−	11.5791i	1.16791	−	0.425083i
$743$	11.8038	−	32.4307i	0.433040	−	1.18977i	−0.510897	−	0.859642i	$-0.670687\pi$
$743$	11.8038	−	32.4307i	0.433040	−	1.18977i	0.943937	−	0.330126i	$-0.107091\pi$
$744$	−33.6648	+	28.2481i	−1.23421	+	1.03563i
$745$	−15.4467	+	40.0420i	−0.565922	+	1.46702i
$746$		−	14.5236i		−	0.531746i
$747$	4.38420	−	0.773053i	0.160410	−	0.0282845i
$748$	0.562955	−	0.975066i	0.0205837	−	0.0356520i
$749$	−11.8655	−	9.95630i	−0.433554	−	0.363795i
$750$	−13.9212	−	27.6602i	−0.508330	−	1.01001i
$751$	−5.48231	+	9.49563i	−0.200052	+	0.346501i	−0.948545	−	0.316642i	$-0.897444\pi$
$751$	−5.48231	+	9.49563i	−0.200052	+	0.346501i	0.748493	+	0.663143i	$0.230778\pi$
$752$	−5.99727	−	16.4774i	−0.218698	−	0.600867i
$753$	0.447906	−	0.375838i	0.0163226	−	0.0136963i
$754$	0.396214	−	0.228754i	0.0144293	−	0.00833075i
$755$	−17.5832	+	20.1598i	−0.639919	+	0.733690i
$756$	−0.291637	+	1.65396i	−0.0106067	+	0.0601538i
$757$	23.6190	+	19.8187i	0.858447	+	0.720323i	0.961633	−	0.274339i	$-0.0884592\pi$
$757$	23.6190	+	19.8187i	0.858447	+	0.720323i	−0.103186	+	0.994662i	$0.532904\pi$
$758$	−31.6484	−	11.5191i	−1.14952	−	0.418391i
$759$	4.37075	−	12.0085i	0.158648	−	0.435883i
$760$	−25.6154	+	8.77275i	−0.929169	+	0.318221i
$761$	2.55661	−	14.4993i	0.0926772	−	0.525598i	−0.902757	−	0.430150i	$-0.858461\pi$
$761$	2.55661	−	14.4993i	0.0926772	−	0.525598i	0.995434	−	0.0954479i	$-0.0304283\pi$
$762$	9.91295	−	56.2191i	0.359108	−	2.03660i
$763$	8.76783	+	15.1863i	0.317417	+	0.549782i
$764$	−2.83173	−	3.37473i	−0.102448	−	0.122093i
$765$	−6.48103	−	1.27091i	−0.234322	−	0.0459498i
$766$	−11.4320	+	19.8008i	−0.413054	+	0.715431i
$767$	−1.66997	+	0.964160i	−0.0602992	+	0.0348138i
$768$	−7.36553	+	8.77789i	−0.265781	+	0.316745i
$769$	23.3973	+	13.5084i	0.843728	+	0.487127i	0.858530	−	0.512764i	$-0.171378\pi$
$769$	23.3973	+	13.5084i	0.843728	+	0.487127i	−0.0148015	+	0.999890i	$0.504712\pi$
$770$	12.7336	+	4.91212i	0.458885	+	0.177021i
$771$		−	13.3400i		−	0.480428i
$772$	−0.568462	−	3.22391i	−0.0204594	−	0.116031i
$773$	−13.7563	−	16.3941i	−0.494778	−	0.589654i	0.459648	−	0.888101i	$-0.347976\pi$
$773$	−13.7563	−	16.3941i	−0.494778	−	0.589654i	−0.954426	+	0.298447i	$0.903531\pi$
$774$	−1.06706	−	0.388377i	−0.0383546	−	0.0139599i
$775$	23.8662	−	26.3305i	0.857299	−	0.945819i
$776$	−28.4049			−1.01968
$777$	26.1905	−	3.86798i	0.939579	−	0.138763i
$778$		−	20.7191i		−	0.742814i
$779$	6.01559	+	16.5277i	0.215531	+	0.592166i
$780$	0.120202	−	0.0970088i	0.00430391	−	0.00347347i
$781$	−13.5466	+	11.3669i	−0.484734	+	0.406740i
$782$	−1.42060	−	8.05661i	−0.0508005	−	0.288104i
$783$	8.34254			0.298138
$784$	−1.59288	−	9.03367i	−0.0568885	−	0.322631i
$785$	−0.0892491	−	0.161639i	−0.00318544	−	0.00576915i
$786$	−1.91750	−	1.60897i	−0.0683949	−	0.0573901i
$787$	−9.63758	+	5.56426i	−0.343543	+	0.198344i	−0.661838	−	0.749647i	$-0.730223\pi$
$787$	−9.63758	+	5.56426i	−0.343543	+	0.198344i	0.318295	+	0.947992i	$0.396890\pi$
$788$	2.85087	+	1.64595i	0.101558	+	0.0586345i
$789$	−44.5423	+	16.2121i	−1.58575	+	0.577165i
$790$	7.24275	+	46.2234i	0.257685	+	1.64455i
$791$	22.4909	−	12.9852i	0.799686	−	0.461699i
$792$	−1.51753	+	8.60636i	−0.0539232	+	0.305814i
$793$	1.51493	+	0.267123i	0.0537968	+	0.00948582i
$794$	1.88032	−	2.24088i	0.0667300	−	0.0795257i
$795$	−35.6583	−	44.1835i	−1.26467	−	1.56703i
$796$	0.800215	−	2.19857i	0.0283629	−	0.0779263i
$797$	−17.0974	−	14.3465i	−0.605622	−	0.508177i	0.287625	−	0.957743i	$-0.407134\pi$
$797$	−17.0974	−	14.3465i	−0.605622	−	0.508177i	−0.893247	+	0.449566i	$0.851579\pi$
$798$	−23.2487	−	4.09938i	−0.822995	−	0.145116i
$799$	10.9347	+	1.92808i	0.386842	+	0.0682106i
$800$	3.48391	−	5.53462i	0.123175	−	0.195678i
$801$	−16.0987	−	19.1856i	−0.568818	−	0.677891i
$802$	9.69036	+	26.6240i	0.342178	+	0.940127i
$803$	3.40350	+	1.96501i	0.120107	+	0.0693438i
$804$	−0.775175	−	1.34264i	−0.0273383	−	0.0473513i
$805$	−12.3377	+	4.22542i	−0.434848	+	0.148926i
$806$	−1.16737	−	0.673984i	−0.0411190	−	0.0237401i
$807$	−25.6405	+	4.52112i	−0.902590	+	0.159151i
$808$	5.43005			0.191029
$809$	−45.1641	+	7.96366i	−1.58789	+	0.279987i	−0.896683	−	0.442673i	$-0.854030\pi$
$809$	−45.1641	+	7.96366i	−1.58789	+	0.279987i	−0.691203	+	0.722660i	$0.742919\pi$
$810$	−32.9660	+	5.16546i	−1.15831	+	0.181496i
$811$	19.3106	+	7.02847i	0.678086	+	0.246803i	0.658025	−	0.752996i	$-0.271392\pi$
$811$	19.3106	+	7.02847i	0.678086	+	0.246803i	0.0200603	+	0.999799i	$0.493614\pi$
$812$	−1.10084	+	0.400674i	−0.0386320	+	0.0140609i
$813$			20.3041i			0.712097i
$814$	−17.5800	+	2.59632i	−0.616177	+	0.0910009i
$815$	43.2453	+	26.0818i	1.51482	+	0.913606i
$816$	5.46733	+	15.0214i	0.191395	+	0.525853i
$817$	0.889436	−	2.44370i	0.0311174	−	0.0854944i
$818$	−11.6314	−	13.8617i	−0.406681	−	0.484664i
$819$	0.393282	−	0.0693462i	0.0137424	−	0.00242315i
$820$	−1.91881	−	1.15726i	−0.0670078	−	0.0404133i
$821$	7.67867	+	43.5479i	0.267987	+	1.51983i	0.760392	+	0.649465i	$0.225007\pi$
$821$	7.67867	+	43.5479i	0.267987	+	1.51983i	−0.492404	+	0.870367i	$0.663882\pi$
$822$	3.59721	−	6.23056i	0.125467	−	0.217316i
$823$	8.50996	−	10.1418i	0.296639	−	0.353520i	−0.597053	−	0.802202i	$-0.703662\pi$
$823$	8.50996	−	10.1418i	0.296639	−	0.353520i	0.893692	+	0.448682i	$0.148106\pi$
$824$	18.9957	+	32.9015i	0.661747	+	1.14618i
$825$	0.874447	−	22.8723i	0.0304443	−	0.796313i
$826$	−35.2823	+	12.8417i	−1.22763	+	0.446821i
$827$	41.4837	−	34.8089i	1.44253	−	1.21042i	0.504714	−	0.863287i	$-0.331598\pi$
$827$	41.4837	−	34.8089i	1.44253	−	1.21042i	0.937814	−	0.347138i	$-0.112847\pi$
$828$	−0.434732	−	0.752978i	−0.0151080	−	0.0261678i
$829$	47.4160	+	8.36072i	1.64683	+	0.290380i	0.918668	−	0.395031i	$-0.129266\pi$
$829$	47.4160	+	8.36072i	1.64683	+	0.290380i	0.728157	+	0.685410i	$0.240377\pi$
$830$	7.44355	+	6.49222i	0.258369	+	0.225348i
$831$	−29.2572	+	34.8674i	−1.01492	+	1.20954i
$832$	−1.16638	−	0.424528i	−0.0404370	−	0.0147179i
$833$	5.45823	+	1.98663i	0.189117	+	0.0688328i
$834$	28.2314	−	33.6449i	0.977573	−	1.16503i
$835$	−13.8959	+	15.9321i	−0.480886	+	0.551353i
$836$	−2.05220	−	0.361858i	−0.0709768	−	0.0125151i
$837$	−12.2899	−	21.2867i	−0.424801	−	0.735777i
$838$	−17.4152	+	14.6131i	−0.601597	+	0.504800i
$839$	44.9348	−	16.3549i	1.55132	−	0.564635i	0.582595	−	0.812762i	$-0.302037\pi$
$839$	44.9348	−	16.3549i	1.55132	−	0.564635i	0.968728	+	0.248127i	$0.0798150\pi$
$840$	25.2870	−	13.9622i	0.872484	−	0.481742i
$841$	−11.5904	−	20.0751i	−0.399669	−	0.692246i
$842$	−8.47933	+	10.1053i	−0.292217	+	0.348251i
$843$	21.0874	−	36.5245i	0.726289	−	1.25797i
$844$	0.486755	+	2.76053i	0.0167548	+	0.0950212i
$845$	−24.8531	−	14.9893i	−0.854974	−	0.515646i
$846$	−8.83712	+	1.55822i	−0.303826	+	0.0535728i
$847$	−8.28761	−	9.87679i	−0.284766	−	0.339371i
$848$	−14.5116	+	39.8704i	−0.498332	+	1.36915i
$849$	−17.9557	−	49.3328i	−0.616237	−	1.69310i
$850$	−6.83631	−	12.9604i	−0.234484	−	0.444539i
$851$	11.2735	−	12.6981i	0.386450	−	0.435286i
$852$			3.89692i			0.133506i
$853$	−38.5181	+	14.0194i	−1.31883	+	0.480016i	−0.903084	−	0.429464i	$-0.858703\pi$
$853$	−38.5181	+	14.0194i	−1.31883	+	0.480016i	−0.415749	+	0.909479i	$0.636480\pi$
$854$	28.1462	+	10.2444i	0.963143	+	0.350555i
$855$	1.89224	+	12.0763i	0.0647134	+	0.413002i
$856$	21.6702	−	3.82104i	0.740672	−	0.130600i
$857$	25.8675			0.883618			0.441809	−	0.897109i	$-0.354337\pi$
$857$	25.8675			0.883618			0.441809	+	0.897109i	$0.354337\pi$
$858$	−0.855020	+	0.150763i	−0.0291899	+	0.00514697i
$859$	22.6747	+	13.0913i	0.773652	+	0.446668i	0.834176	−	0.551499i	$-0.185944\pi$
$859$	22.6747	+	13.0913i	0.773652	+	0.446668i	−0.0605241	+	0.998167i	$0.519277\pi$
$860$	0.107346	+	0.313438i	0.00366047	+	0.0106882i
$861$	−9.38194	−	16.2500i	−0.319736	−	0.553798i
$862$	9.08645	+	5.24606i	0.309486	+	0.178682i
$863$	0.623881	+	1.71410i	0.0212371	+	0.0583486i	0.949858	−	0.312681i	$-0.101227\pi$
$863$	0.623881	+	1.71410i	0.0212371	+	0.0583486i	−0.928621	+	0.371030i	$0.879005\pi$
$864$	−2.90758	−	3.46511i	−0.0989178	−	0.117886i
$865$	−47.5521	−	0.908666i	−1.61682	−	0.0308956i
$866$	5.34560	+	0.942574i	0.181651	+	0.0320300i
$867$	24.9088	+	4.39209i	0.845946	+	0.149163i
$868$	2.64407	+	2.21864i	0.0897456	+	0.0753055i
$869$	−11.8284	+	32.4982i	−0.401250	+	1.10242i
$870$	−9.38273	−	11.6260i	−0.318104	−	0.394157i
$871$	0.293573	−	0.349867i	0.00994734	−	0.0118548i
$872$	−24.5332	−	4.32586i	−0.830799	−	0.146492i
$873$	−2.22680	+	12.6288i	−0.0753658	+	0.427421i
$874$	−13.1128	+	7.57069i	−0.443548	+	0.256083i
$875$	−18.7243	+	13.9647i	−0.632996	+	0.472093i
$876$	0.813817	−	0.296205i	0.0274963	−	0.0100078i
$877$	−48.9945	−	28.2870i	−1.65443	−	0.955184i	−0.975220	−	0.221239i	$-0.928990\pi$
$877$	−48.9945	−	28.2870i	−1.65443	−	0.955184i	−0.679208	−	0.733946i	$-0.737677\pi$
$878$	−26.1123	+	15.0759i	−0.881248	+	0.508789i
$879$	−12.6777	−	10.6379i	−0.427609	−	0.358807i
$880$	−14.9738	+	8.26777i	−0.504766	+	0.278706i
$881$	−7.41720	−	42.0650i	−0.249892	−	1.41721i	−0.808852	−	0.588013i	$-0.799911\pi$
$881$	−7.41720	−	42.0650i	−0.249892	−	1.41721i	0.558960	−	0.829195i	$-0.311201\pi$
$882$	−4.69429			−0.158065
$883$	4.36976	+	24.7822i	0.147054	+	0.833986i	0.965695	+	0.259680i	$0.0836170\pi$
$883$	4.36976	+	24.7822i	0.147054	+	0.833986i	−0.818641	+	0.574306i	$0.805272\pi$
$884$	0.0559915	−	0.0469825i	0.00188320	−	0.00158019i
$885$	39.5466	+	49.0014i	1.32934	+	1.64716i
$886$	1.95322	+	5.36643i	0.0656198	+	0.180289i
$887$			39.2137i			1.31667i	0.752727	+	0.658333i	$0.228738\pi$
$887$			39.2137i			1.31667i	−0.752727	+	0.658333i	$0.771262\pi$
$888$	−19.7068	+	32.0343i	−0.661317	+	1.07500i
$889$	−43.0617			−1.44424
$890$	10.6926	−	54.5275i	0.358418	−	1.82776i
$891$	−23.1774	−	8.43587i	−0.776471	−	0.282612i
$892$	0.165952	+	0.197774i	0.00555648	+	0.00662195i
$893$	−3.56854	−	20.2382i	−0.119417	−	0.677245i
$894$		−	53.1598i		−	1.77793i
$895$	20.8468	+	8.04190i	0.696831	+	0.268811i
$896$	−16.1973	−	9.35153i	−0.541115	−	0.312413i
$897$	0.533257	−	0.635511i	0.0178049	−	0.0212191i
$898$	−15.6201	+	9.01824i	−0.521248	+	0.300943i
$899$	8.57265	−	14.8483i	0.285914	−	0.495217i
$900$	−1.15385	−	1.04586i	−0.0384618	−	0.0348621i
$901$	−17.2697	−	20.5813i	−0.575339	−	0.685662i
$902$	6.29748	+	10.9076i	0.209683	+	0.363182i
$903$	−0.481758	+	2.73219i	−0.0160319	+	0.0909215i
$904$	−6.40660	+	36.3336i	−0.213080	+	1.20844i
$905$	−8.56442	−	25.0071i	−0.284691	−	0.831264i
$906$	11.3325	−	31.1358i	0.376497	−	1.03442i
$907$	38.8394	+	14.1364i	1.28964	+	0.469391i	0.893609	−	0.448847i	$-0.148165\pi$
$907$	38.8394	+	14.1364i	1.28964	+	0.469391i	0.396031	+	0.918237i	$0.370387\pi$
$908$	1.73273	+	1.45394i	0.0575028	+	0.0482506i
$909$	0.425689	−	2.41420i	0.0141192	−	0.0800740i
$910$	0.667719	+	0.582380i	0.0221347	+	0.0193057i
$911$	−37.9514	+	21.9112i	−1.25739	+	0.725952i	−0.972565	−	0.232629i	$-0.925267\pi$
$911$	−37.9514	+	21.9112i	−1.25739	+	0.725952i	−0.284820	+	0.958581i	$0.591934\pi$
$912$	22.6643	−	19.0176i	0.750490	−	0.629736i
$913$	2.49702	+	6.86050i	0.0826392	+	0.227049i
$914$	15.9730	−	27.6661i	0.528341	−	0.915113i
$915$	0.959715	−	50.2236i	0.0317272	−	1.66034i
$916$	2.67232	+	2.24234i	0.0882958	+	0.0740890i
$917$	−0.944081	+	1.63520i	−0.0311763	+	0.0539990i
$918$	−9.98094	+	1.75991i	−0.329420	+	0.0580857i
$919$			6.58051i			0.217071i	0.994093	+	0.108535i	$0.0346161\pi$
$919$			6.58051i			0.217071i	−0.994093	+	0.108535i	$0.965384\pi$
$920$	6.66797	−	17.2852i	0.219837	−	0.569876i
$921$	−26.3515	+	22.1115i	−0.868311	+	0.728599i
$922$	7.25665	−	19.9375i	0.238985	−	0.656606i
$923$	−1.07876	+	0.392638i	−0.0355079	+	0.0129238i
$924$	2.22313			0.0731355
$925$	12.2677	−	27.8299i	0.403360	−	0.915042i
$926$	41.6684			1.36931
$927$	16.1172	−	5.86617i	0.529358	−	0.192670i
$928$	1.07915	−	2.96494i	0.0354248	−	0.0973289i
$929$	−29.3245	+	24.6062i	−0.962106	+	0.807303i	−0.981294	−	0.192513i	$-0.938336\pi$
$929$	−29.3245	+	24.6062i	−0.962106	+	0.807303i	0.0191883	+	0.999816i	$0.493892\pi$
$930$	−15.8424	+	41.0678i	−0.519493	+	1.34667i
$931$		−	10.7506i		−	0.352335i
$932$	5.08851	−	0.897242i	0.166680	−	0.0293901i
$933$	22.9221	−	39.7023i	0.750436	−	1.29979i
$934$	38.2861	+	32.1259i	1.25276	+	1.05119i
$935$	0.206930	−	10.8290i	0.00676733	−	0.354147i
$936$	−0.283663	+	0.491319i	−0.00927182	+	0.0160593i
$937$	9.64352	+	26.4954i	0.315040	+	0.865565i	0.991619	+	0.129195i	$0.0412395\pi$
$937$	9.64352	+	26.4954i	0.315040	+	0.865565i	−0.676579	+	0.736370i	$0.736538\pi$
$938$	6.81232	−	5.71621i	0.222430	−	0.186641i
$939$	−9.38496	+	5.41841i	−0.306267	+	0.176823i
$940$	1.97309	+	1.72092i	0.0643552	+	0.0561301i
$941$	4.01276	−	22.7575i	0.130812	−	0.741873i	−0.846873	−	0.531796i	$-0.821517\pi$
$941$	4.01276	−	22.7575i	0.130812	−	0.741873i	0.977685	−	0.210077i	$-0.0673715\pi$
$942$	0.175197	+	0.147008i	0.00570824	+	0.00478978i
$943$	−11.3091	−	4.11616i	−0.368274	−	0.134041i
$944$	16.0940	−	44.2179i	0.523815	−	1.43917i
$945$	5.23466	+	15.2846i	0.170284	+	0.497208i
$946$	0.323373	−	1.83394i	0.0105137	−	0.0596264i
$947$	−6.28019	+	35.6167i	−0.204079	+	1.15739i	0.694804	+	0.719199i	$0.255491\pi$
$947$	−6.28019	+	35.6167i	−0.204079	+	1.15739i	−0.898883	+	0.438189i	$0.855620\pi$
$948$	3.81056	+	6.60008i	0.123761	+	0.214361i
$949$	0.163994	+	0.195440i	0.00532346	+	0.00634426i
$950$	−18.2133	+	20.0939i	−0.590918	+	0.651934i
$951$	5.62028	−	9.73460i	0.182250	−	0.315666i
$952$	11.8373	−	6.83426i	0.383649	−	0.221500i
$953$	−2.13889	+	2.54903i	−0.0692855	+	0.0825712i	−0.799574	−	0.600568i	$-0.794941\pi$
$953$	−2.13889	+	2.54903i	−0.0692855	+	0.0825712i	0.730288	+	0.683139i	$0.239386\pi$
$954$	18.8041	+	10.8566i	0.608806	+	0.351494i
$955$	−39.5389	−	15.2526i	−1.27945	−	0.493563i
$956$			1.29075i			0.0417457i
$957$	−1.91761	−	10.8753i	−0.0619875	−	0.351549i
$958$	15.4623	+	18.4272i	0.499563	+	0.595356i
$959$	−5.09965	−	1.85612i	−0.164676	−	0.0599373i
$960$	−7.79969	+	39.7747i	−0.251734	+	1.28372i
$961$	−19.5156			−0.629534
$962$	−1.13008	−	0.231949i	−0.0364351	−	0.00747834i
$963$		−	9.93411i		−	0.320122i
$964$	1.14624	+	3.14926i	0.0369178	+	0.101431i
$965$	−19.7779	−	24.5064i	−0.636673	−	0.788889i
$966$	12.3742	−	10.3832i	0.398132	−	0.334072i
$967$	−1.53018	−	8.67808i	−0.0492073	−	0.279068i	0.950269	−	0.311430i	$-0.100808\pi$
$967$	−1.53018	−	8.67808i	−0.0492073	−	0.279068i	−0.999476	+	0.0323622i	$0.989697\pi$
$968$	18.3165			0.588715
$969$	3.25321	+	18.4499i	0.104508	+	0.592695i
$970$	−24.9066	+	13.7522i	−0.799703	+	0.441556i
$971$	19.8224	+	16.6330i	0.636132	+	0.533778i	0.902828	−	0.430003i	$-0.141487\pi$
$971$	19.8224	+	16.6330i	0.636132	+	0.533778i	−0.266695	+	0.963781i	$0.585932\pi$
$972$	−2.61860	+	1.51185i	−0.0839916	+	0.0484926i
$973$	−28.6915	−	16.5651i	−0.919809	−	0.531052i
$974$	−6.03311	+	2.19587i	−0.193313	+	0.0703603i
$975$	0.561184	−	1.37586i	0.0179723	−	0.0440629i
$976$	−32.5091	+	18.7692i	−1.04059	+	0.600786i
$977$	5.01628	−	28.4487i	0.160485	−	0.910156i	−0.793113	−	0.609074i	$-0.791541\pi$
$977$	5.01628	−	28.4487i	0.160485	−	0.910156i	0.953598	−	0.301082i	$-0.0973477\pi$
$978$	−61.6028	−	10.8622i	−1.96984	−	0.347336i
$979$	26.4010	−	31.4635i	0.843780	−	1.00558i
$980$	0.860176	+	1.06583i	0.0274773	+	0.0340466i
$981$	−3.84656	+	10.5683i	−0.122811	+	0.337421i
$982$	35.2774	+	29.6012i	1.12575	+	0.944613i
$983$	−20.8800	−	3.68171i	−0.665969	−	0.117428i	−0.169564	−	0.985519i	$-0.554236\pi$
$983$	−20.8800	−	3.68171i	−0.665969	−	0.117428i	−0.496405	+	0.868091i	$0.665347\pi$
$984$	26.2515	+	4.62885i	0.836868	+	0.147562i
$985$	31.6615	+	0.605015i	1.00882	+	0.0192774i
$986$	−4.54416	−	5.41552i	−0.144716	−	0.172465i
$987$	7.49839	+	20.6016i	0.238676	+	0.655758i
$988$	−0.117156	−	0.0676399i	−0.00372722	−	0.00215191i
$989$	0.889707	+	1.54102i	0.0282910	+	0.0490015i
$990$	2.83611	+	8.28112i	0.0901376	+	0.263191i
$991$	−32.8374	−	18.9587i	−1.04311	−	0.602242i	−0.122401	−	0.992481i	$-0.539059\pi$
$991$	−32.8374	−	18.9587i	−1.04311	−	0.602242i	−0.920714	+	0.390238i	$0.872393\pi$
$992$	−9.15507	+	1.61429i	−0.290674	+	0.0512536i
$993$	5.08277			0.161297
$994$	−22.0132	+	3.88153i	−0.698218	+	0.123115i
$995$	−3.48413	−	22.2358i	−0.110454	−	0.704923i
$996$	1.51183	+	0.550259i	0.0479040	+	0.0174356i
$997$	9.80869	−	3.57007i	0.310644	−	0.113065i	−0.181993	−	0.983300i	$-0.558255\pi$
$997$	9.80869	−	3.57007i	0.310644	−	0.113065i	0.492638	+	0.870234i	$0.336033\pi$
$998$		−	27.0999i		−	0.857834i
$999$	−15.7311	−	13.9662i	−0.497709	−	0.441870i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	185.2.v.a.104.5	✓	96
5.2	odd	4		925.2.bb.e.326.5		96
5.3	odd	4		925.2.bb.e.326.12		96
5.4	even	2	inner	185.2.v.a.104.12	yes	96
37.21	even	18	inner	185.2.v.a.169.12	yes	96
185.58	odd	36		925.2.bb.e.576.12		96
185.132	odd	36		925.2.bb.e.576.5		96
185.169	even	18	inner	185.2.v.a.169.5	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
185.2.v.a.104.5	✓	96	1.1	even	1	trivial
185.2.v.a.104.12	yes	96	5.4	even	2	inner
185.2.v.a.169.5	yes	96	185.169	even	18	inner
185.2.v.a.169.12	yes	96	37.21	even	18	inner
925.2.bb.e.326.5		96	5.2	odd	4
925.2.bb.e.326.12		96	5.3	odd	4
925.2.bb.e.576.5		96	185.132	odd	36
925.2.bb.e.576.12		96	185.58	odd	36

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 185 = 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	185.v (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.24932 + 0.454714i) q^{2} +(-0.712514 + 1.95762i) q^{3} +(-0.178063 + 0.149413i) q^{4} +(-0.804785 + 2.08622i) q^{5} -2.76967i q^{6} +(-2.05749 + 0.362791i) q^{7} +(1.48401 - 2.57038i) q^{8} +(-1.02645 - 0.861296i) q^{9} +(0.0567971 - 2.97230i) q^{10} +(1.09872 - 1.90303i) q^{11} +(-0.165620 - 0.455038i) q^{12} +(0.109278 - 0.0916955i) q^{13} +(2.40549 - 1.38881i) q^{14} +(-3.51060 - 3.06192i) q^{15} +(-0.604483 + 3.42819i) q^{16} +(-1.68858 - 1.41689i) q^{17} +(1.67401 + 0.609289i) q^{18} +(-1.39535 + 3.83370i) q^{19} +(-0.168405 - 0.491724i) q^{20} +(0.755786 - 4.28627i) q^{21} +(-0.507309 + 2.87709i) q^{22} +(-1.39578 - 2.41756i) q^{23} +(3.97445 + 4.73656i) q^{24} +(-3.70464 - 3.35792i) q^{25} +(-0.0948281 + 0.164247i) q^{26} +(-2.99500 + 1.72916i) q^{27} +(0.312158 - 0.372015i) q^{28} +(-2.08912 - 1.20615i) q^{29} +(5.77815 + 2.22899i) q^{30} +7.10743i q^{31} +(0.227127 + 1.28810i) q^{32} +(2.94256 + 3.50681i) q^{33} +(2.75385 + 1.00232i) q^{34} +(0.898976 - 4.58435i) q^{35} +0.311462 q^{36} +(1.92013 + 5.77175i) q^{37} -5.42399i q^{38} +(0.101642 + 0.279260i) q^{39} +(4.16808 + 5.16458i) q^{40} +(3.30254 - 2.77116i) q^{41} +(1.00481 + 5.69858i) q^{42} -0.637427 q^{43} +(0.0886964 + 0.503022i) q^{44} +(2.62293 - 1.44825i) q^{45} +(2.84307 + 2.38562i) q^{46} +(-4.36233 + 2.51859i) q^{47} +(-6.28039 - 3.62598i) q^{48} +(-2.47619 + 0.901260i) q^{49} +(6.15516 + 2.51055i) q^{50} +(3.97686 - 2.29604i) q^{51} +(-0.00575799 + 0.0326552i) q^{52} +(12.0033 + 2.11651i) q^{53} +(2.95542 - 3.52214i) q^{54} +(3.08592 + 3.82370i) q^{55} +(-2.12083 + 5.82693i) q^{56} +(-6.51071 - 5.46313i) q^{57} +(3.15842 + 0.556915i) q^{58} +(-13.3122 - 2.34730i) q^{59} +(1.08260 + 0.0206872i) q^{60} +(6.93152 + 8.26066i) q^{61} +(-3.23185 - 8.87943i) q^{62} +(2.42439 + 1.39972i) q^{63} +(-4.35055 - 7.53537i) q^{64} +(0.103351 + 0.301774i) q^{65} +(-5.27078 - 3.04309i) q^{66} +(3.15297 - 0.555953i) q^{67} +0.512375 q^{68} +(5.72717 - 1.00985i) q^{69} +(0.961464 + 6.13608i) q^{70} +(-7.56215 - 2.75240i) q^{71} +(-3.73713 + 1.36020i) q^{72} +1.78846i q^{73} +(-5.02334 - 6.33763i) q^{74} +(9.21313 - 4.85970i) q^{75} +(-0.324343 - 0.891124i) q^{76} +(-1.57020 + 4.31408i) q^{77} +(-0.253966 - 0.302665i) q^{78} +(-15.4992 + 2.73292i) q^{79} +(-6.66549 - 4.02005i) q^{80} +(-1.94909 - 11.0539i) q^{81} +(-2.86583 + 4.96377i) q^{82} +(-2.13561 + 2.54512i) q^{83} +(0.505846 + 0.876151i) q^{84} +(4.31488 - 2.38246i) q^{85} +(0.796348 - 0.289847i) q^{86} +(3.84971 - 3.23029i) q^{87} +(-3.26102 - 5.64825i) q^{88} +(18.4072 + 3.24569i) q^{89} +(-2.61833 + 3.00200i) q^{90} +(-0.191573 + 0.228308i) q^{91} +(0.609751 + 0.221931i) q^{92} +(-13.9136 - 5.06414i) q^{93} +(4.30469 - 5.13013i) q^{94} +(-6.87499 - 5.99632i) q^{95} +(-2.68343 - 0.473162i) q^{96} +(-4.78516 - 8.28814i) q^{97} +(2.68373 - 2.25192i) q^{98} +(-2.76686 + 1.00705i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 12 q^{4} - 12 q^{5} - 6 q^{9} - 3 q^{10} - 30 q^{11} - 36 q^{14} - 21 q^{15} - 18 q^{19} - 39 q^{20} - 24 q^{21} + 96 q^{24} + 36 q^{25} + 48 q^{26} - 18 q^{29} - 30 q^{30} - 54 q^{34} + 6 q^{35}+ \cdots - 24 q^{99}+O(q^{100}) \) 96 * q - 12 * q^4 - 12 * q^5 - 6 * q^9 - 3 * q^10 - 30 * q^11 - 36 * q^14 - 21 * q^15 - 18 * q^19 - 39 * q^20 - 24 * q^21 + 96 * q^24 + 36 * q^25 + 48 * q^26 - 18 * q^29 - 30 * q^30 - 54 * q^34 + 6 * q^35 + 24 * q^36 - 36 * q^39 - 63 * q^40 + 72 * q^41 - 84 * q^44 - 36 * q^45 - 18 * q^46 - 6 * q^49 - 27 * q^50 - 18 * q^51 + 24 * q^54 + 6 * q^55 + 90 * q^56 + 18 * q^59 + 108 * q^60 - 144 * q^61 + 66 * q^64 + 27 * q^65 - 36 * q^66 - 6 * q^69 - 66 * q^70 - 30 * q^71 - 6 * q^74 + 96 * q^75 - 54 * q^76 + 60 * q^79 - 18 * q^81 + 48 * q^84 + 21 * q^85 - 72 * q^86 + 108 * q^89 + 165 * q^90 - 54 * q^91 + 6 * q^94 + 57 * q^95 + 24 * q^96 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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