LMFDB - Embedded newform 45.3.h.a.14.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [45,3,Mod(14,45)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(45, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 3])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("45.14"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 45 = 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	45.h (of order $6$, degree $2$, 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:	$1.22616118962$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 3 x^{18} - 19 x^{16} + 66 x^{14} + 109 x^{12} - 813 x^{10} + 981 x^{8} + 5346 x^{6} + \cdots + 59049 $ x^20 - 3x^18 - 19x^16 + 66x^14 + 109x^12 - 813x^10 + 981x^8 + 5346x^6 - 13851x^4 - 19683*x^2 + 59049
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{10} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			14.8
Root			$1.72886 + 0.105167i$ of defining polynomial
Character	$\chi$	$=$	45.14
Dual form			45.3.h.a.29.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.14670 + 1.98614i) q^{2} +(-0.182154 + 2.99446i) q^{3} +(-0.629835 + 1.09091i) q^{4} +(0.662169 - 4.95596i) q^{5} +(-6.15630 + 3.07197i) q^{6} +(-6.04559 + 3.49042i) q^{7} +6.28466 q^{8} +(-8.93364 - 1.09091i) q^{9} +(10.6025 - 4.36783i) q^{10} +(15.8064 - 9.12584i) q^{11} +(-3.15195 - 2.08473i) q^{12} +(-3.66955 - 2.11862i) q^{13} +(-13.8649 - 8.00492i) q^{14} +(14.7198 + 2.88559i) q^{15} +(9.72596 + 16.8458i) q^{16} -17.3066 q^{17} +(-8.07750 - 18.9944i) q^{18} -3.96601 q^{19} +(4.98943 + 3.84380i) q^{20} +(-9.35072 - 18.7391i) q^{21} +(36.2504 + 20.9292i) q^{22} +(0.287675 - 0.498269i) q^{23} +(-1.14478 + 18.8192i) q^{24} +(-24.1231 - 6.56337i) q^{25} -9.71765i q^{26} +(4.89398 - 26.5528i) q^{27} -8.79356i q^{28} +(-18.1762 + 10.4940i) q^{29} +(11.1480 + 32.5445i) q^{30} +(-16.7326 + 28.9818i) q^{31} +(-9.73615 + 16.8635i) q^{32} +(24.4478 + 48.9941i) q^{33} +(-19.8455 - 34.3734i) q^{34} +(13.2952 + 32.2729i) q^{35} +(6.81680 - 9.05867i) q^{36} -21.4222i q^{37} +(-4.54782 - 7.87705i) q^{38} +(7.01254 - 10.6024i) q^{39} +(4.16151 - 31.1465i) q^{40} +(44.1003 + 25.4613i) q^{41} +(26.4960 - 40.0599i) q^{42} +(-7.15514 + 4.13102i) q^{43} +22.9911i q^{44} +(-11.3221 + 43.5524i) q^{45} +1.31951 q^{46} +(-7.57789 - 13.1253i) q^{47} +(-52.2159 + 26.0555i) q^{48} +(-0.133907 + 0.231934i) q^{49} +(-14.6261 - 55.4380i) q^{50} +(3.15247 - 51.8241i) q^{51} +(4.62242 - 2.66876i) q^{52} +24.5806 q^{53} +(58.3494 - 20.7279i) q^{54} +(-34.7608 - 84.3789i) q^{55} +(-37.9945 + 21.9361i) q^{56} +(0.722424 - 11.8761i) q^{57} +(-41.6853 - 24.0670i) q^{58} +(43.1589 + 24.9178i) q^{59} +(-12.4190 + 14.2405i) q^{60} +(-31.4674 - 54.5031i) q^{61} -76.7492 q^{62} +(57.8168 - 24.5870i) q^{63} +33.1499 q^{64} +(-12.9296 + 16.7833i) q^{65} +(-69.2749 + 104.738i) q^{66} +(103.545 + 59.7818i) q^{67} +(10.9003 - 18.8799i) q^{68} +(1.43965 + 0.952196i) q^{69} +(-48.8530 + 63.4134i) q^{70} -66.8256i q^{71} +(-56.1449 - 6.85598i) q^{72} +48.9419i q^{73} +(42.5475 - 24.5648i) q^{74} +(24.0479 - 71.0401i) q^{75} +(2.49793 - 4.32654i) q^{76} +(-63.7061 + 110.342i) q^{77} +(29.0992 + 1.77011i) q^{78} +(58.9661 + 102.132i) q^{79} +(89.9276 - 37.0466i) q^{80} +(78.6198 + 19.4915i) q^{81} +116.786i q^{82} +(3.66063 + 6.34040i) q^{83} +(26.3320 + 1.60178i) q^{84} +(-11.4599 + 85.7710i) q^{85} +(-16.4096 - 9.47408i) q^{86} +(-28.1132 - 56.3396i) q^{87} +(99.3381 - 57.3529i) q^{88} -100.624i q^{89} +(-99.4842 + 27.4543i) q^{90} +29.5794 q^{91} +(0.362376 + 0.627654i) q^{92} +(-83.7371 - 55.3845i) q^{93} +(17.3791 - 30.1015i) q^{94} +(-2.62617 + 19.6554i) q^{95} +(-48.7237 - 32.2263i) q^{96} +(-3.59238 + 2.07406i) q^{97} -0.614205 q^{98} +(-151.164 + 64.2837i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 18 q^{4} - 12 q^{5} + 12 q^{6} - 18 q^{9} + 4 q^{10} - 24 q^{11} + 30 q^{14} + 24 q^{15} - 26 q^{16} - 8 q^{19} + 144 q^{20} - 96 q^{21} - 102 q^{24} + 2 q^{25} - 114 q^{29} - 48 q^{30} + 28 q^{31}+ \cdots - 468 q^{99}+O(q^{100}) $ 20 * q - 18 * q^4 - 12 * q^5 + 12 * q^6 - 18 * q^9 + 4 * q^10 - 24 * q^11 + 30 * q^14 + 24 * q^15 - 26 * q^16 - 8 * q^19 + 144 * q^20 - 96 * q^21 - 102 * q^24 + 2 * q^25 - 114 * q^29 - 48 * q^30 + 28 * q^31 - 4 * q^34 + 432 * q^36 + 240 * q^39 - 34 * q^40 + 102 * q^41 - 162 * q^45 + 116 * q^46 - 40 * q^49 - 408 * q^50 - 156 * q^51 - 270 * q^54 + 36 * q^55 - 618 * q^56 + 120 * q^59 + 330 * q^60 - 50 * q^61 + 140 * q^64 + 492 * q^65 - 768 * q^66 + 162 * q^69 - 54 * q^70 + 504 * q^74 + 276 * q^75 - 96 * q^76 - 128 * q^79 + 846 * q^81 + 450 * q^84 - 74 * q^85 + 1488 * q^86 - 990 * q^90 - 288 * q^91 + 218 * q^94 - 762 * q^95 - 474 * q^96 - 468 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/45\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	1.14670	+	1.98614i	0.573349	+	0.993070i	0.996219	+	0.0868795i	$0.0276895\pi$
$2$	1.14670	+	1.98614i	0.573349	+	0.993070i	−0.422870	+	0.906191i	$0.638977\pi$
$3$	−0.182154	+	2.99446i	−0.0607179	+	0.998155i
$3$	−0.182154	+	2.99446i	−0.0607179	+	0.998155i
$4$	−0.629835	+	1.09091i	−0.157459	+	0.272727i
$5$	0.662169	−	4.95596i	0.132434	−	0.991192i
$5$	0.662169	−	4.95596i	0.132434	−	0.991192i
$6$	−6.15630	+	3.07197i	−1.02605	+	0.511994i
$7$	−6.04559	+	3.49042i	−0.863655	+	0.498632i	−0.865235	−	0.501367i	$-0.832831\pi$
$7$	−6.04559	+	3.49042i	−0.863655	+	0.498632i	0.00157923	+	0.999999i	$0.499497\pi$
$8$	6.28466			0.785583
$9$	−8.93364	−	1.09091i	−0.992627	−	0.121212i
$10$	10.6025	−	4.36783i	1.06025	−	0.436783i
$11$	15.8064	−	9.12584i	1.43695	−	0.829622i	0.439311	−	0.898335i	$-0.355222\pi$
$11$	15.8064	−	9.12584i	1.43695	−	0.829622i	0.997636	+	0.0687126i	$0.0218892\pi$
$12$	−3.15195	−	2.08473i	−0.262663	−	0.173728i
$13$	−3.66955	−	2.11862i	−0.282273	−	0.162970i	0.352179	−	0.935933i	$-0.385441\pi$
$13$	−3.66955	−	2.11862i	−0.282273	−	0.162970i	−0.634452	+	0.772962i	$0.718774\pi$
$14$	−13.8649	−	8.00492i	−0.990352	−	0.571780i
$15$	14.7198	+	2.88559i	0.981322	+	0.192373i
$16$	9.72596	+	16.8458i	0.607872	+	1.05287i
$17$	−17.3066			−1.01804			−0.509019	−	0.860756i	$-0.669992\pi$
$17$	−17.3066			−1.01804			−0.509019	+	0.860756i	$0.669992\pi$
$18$	−8.07750	−	18.9944i	−0.448750	−	1.05524i
$19$	−3.96601			−0.208737			−0.104369	−	0.994539i	$-0.533282\pi$
$19$	−3.96601			−0.208737			−0.104369	+	0.994539i	$0.533282\pi$
$20$	4.98943	+	3.84380i	0.249472	+	0.192190i
$21$	−9.35072	−	18.7391i	−0.445272	−	0.892338i
$22$	36.2504	+	20.9292i	1.64775	+	0.951327i
$23$	0.287675	−	0.498269i	0.0125076	−	0.0216639i	−0.859704	−	0.510793i	$-0.829352\pi$
$23$	0.287675	−	0.498269i	0.0125076	−	0.0216639i	0.872211	+	0.489129i	$0.162685\pi$
$24$	−1.14478	+	18.8192i	−0.0476990	+	0.784134i
$25$	−24.1231	−	6.56337i	−0.964923	−	0.262535i
$26$		−	9.71765i		−	0.373756i
$27$	4.89398	−	26.5528i	0.181258	−	0.983435i
$28$		−	8.79356i		−	0.314056i
$29$	−18.1762	+	10.4940i	−0.626766	+	0.361863i	−0.779498	−	0.626404i	$-0.784526\pi$
$29$	−18.1762	+	10.4940i	−0.626766	+	0.361863i	0.152733	+	0.988268i	$0.451193\pi$
$30$	11.1480	+	32.5445i	0.371601	+	1.08482i
$31$	−16.7326	+	28.9818i	−0.539763	+	0.934897i	0.459154	+	0.888357i	$0.348153\pi$
$31$	−16.7326	+	28.9818i	−0.539763	+	0.934897i	−0.998916	+	0.0465398i	$0.985181\pi$
$32$	−9.73615	+	16.8635i	−0.304255	+	0.526985i
$33$	24.4478	+	48.9941i	0.740843	+	1.48467i
$34$	−19.8455	−	34.3734i	−0.583691	−	1.01098i
$35$	13.2952	+	32.2729i	0.379863	+	0.922084i
$36$	6.81680	−	9.05867i	0.189355	−	0.251630i
$37$		−	21.4222i		−	0.578978i	−0.957181	−	0.289489i	$-0.906515\pi$
$37$		−	21.4222i		−	0.578978i	0.957181	−	0.289489i	$-0.0934854\pi$
$38$	−4.54782	−	7.87705i	−0.119679	−	0.207291i
$39$	7.01254	−	10.6024i	0.179809	−	0.271857i
$40$	4.16151	−	31.1465i	0.104038	−	0.778663i
$41$	44.1003	+	25.4613i	1.07562	+	0.621008i	0.929711	−	0.368290i	$-0.120057\pi$
$41$	44.1003	+	25.4613i	1.07562	+	0.621008i	0.145907	+	0.989298i	$0.453390\pi$
$42$	26.4960	−	40.0599i	0.630857	−	0.953808i
$43$	−7.15514	+	4.13102i	−0.166399	+	0.0960703i	−0.580887	−	0.813984i	$-0.697294\pi$
$43$	−7.15514	+	4.13102i	−0.166399	+	0.0960703i	0.414488	+	0.910055i	$0.363961\pi$
$44$			22.9911i			0.522525i
$45$	−11.3221	+	43.5524i	−0.251602	+	0.967831i
$46$	1.31951			0.0286850
$47$	−7.57789	−	13.1253i	−0.161232	−	0.279262i	0.774079	−	0.633089i	$-0.218213\pi$
$47$	−7.57789	−	13.1253i	−0.161232	−	0.279262i	−0.935311	+	0.353828i	$0.884880\pi$
$48$	−52.2159	+	26.0555i	−1.08783	+	0.542823i
$49$	−0.133907	+	0.231934i	−0.00273280	+	0.00473335i
$50$	−14.6261	−	55.4380i	−0.292522	−	1.10876i
$51$	3.15247	−	51.8241i	0.0618131	−	1.01616i
$52$	4.62242	−	2.66876i	0.0888927	−	0.0513222i
$53$	24.5806			0.463784			0.231892	−	0.972741i	$-0.425508\pi$
$53$	24.5806			0.463784			0.231892	+	0.972741i	$0.425508\pi$
$54$	58.3494	−	20.7279i	1.08054	−	0.383850i
$55$	−34.7608	−	84.3789i	−0.632014	−	1.53416i
$56$	−37.9945	+	21.9361i	−0.678473	+	0.391717i
$57$	0.722424	−	11.8761i	0.0126741	−	0.208352i
$58$	−41.6853	−	24.0670i	−0.718711	−	0.414948i
$59$	43.1589	+	24.9178i	0.731506	+	0.422335i	0.818973	−	0.573832i	$-0.194544\pi$
$59$	43.1589	+	24.9178i	0.731506	+	0.422335i	−0.0874668	+	0.996167i	$0.527877\pi$
$60$	−12.4190	+	14.2405i	−0.206983	+	0.237342i
$61$	−31.4674	−	54.5031i	−0.515858	−	0.893493i	−0.999831	−	0.0184097i	$-0.994140\pi$
$61$	−31.4674	−	54.5031i	−0.515858	−	0.893493i	0.483972	−	0.875083i	$-0.339194\pi$
$62$	−76.7492			−1.23789
$63$	57.8168	−	24.5870i	0.917728	−	0.390270i
$64$	33.1499			0.517968
$65$	−12.9296	+	16.7833i	−0.198917	+	0.258204i
$66$	−69.2749	+	104.738i	−1.04962	+	1.58694i
$67$	103.545	+	59.7818i	1.54545	+	0.892266i	0.998480	+	0.0551129i	$0.0175519\pi$
$67$	103.545	+	59.7818i	1.54545	+	0.892266i	0.546969	+	0.837153i	$0.315781\pi$
$68$	10.9003	−	18.8799i	0.160299	−	0.277646i
$69$	1.43965	+	0.952196i	0.0208644	+	0.0137999i
$70$	−48.8530	+	63.4134i	−0.697900	+	0.905906i
$71$		−	66.8256i		−	0.941205i	−0.882345	−	0.470603i	$-0.844037\pi$
$71$		−	66.8256i		−	0.941205i	0.882345	−	0.470603i	$-0.155963\pi$
$72$	−56.1449	−	6.85598i	−0.779791	−	0.0952220i
$73$			48.9419i			0.670437i	0.942140	+	0.335218i	$0.108810\pi$
$73$			48.9419i			0.670437i	−0.942140	+	0.335218i	$0.891190\pi$
$74$	42.5475	−	24.5648i	0.574966	−	0.331957i
$75$	24.0479	−	71.0401i	0.320638	−	0.947202i
$76$	2.49793	−	4.32654i	0.0328675	−	0.0569282i
$77$	−63.7061	+	110.342i	−0.827352	+	1.43302i
$78$	29.0992	+	1.77011i	0.373066	+	0.0226937i
$79$	58.9661	+	102.132i	0.746407	+	1.29281i	0.949535	+	0.313662i	$0.101556\pi$
$79$	58.9661	+	102.132i	0.746407	+	1.29281i	−0.203128	+	0.979152i	$0.565111\pi$
$80$	89.9276	−	37.0466i	1.12409	−	0.463083i
$81$	78.6198	+	19.4915i	0.970615	+	0.240636i
$82$			116.786i			1.42422i
$83$	3.66063	+	6.34040i	0.0441040	+	0.0763904i	0.887235	−	0.461318i	$-0.152623\pi$
$83$	3.66063	+	6.34040i	0.0441040	+	0.0763904i	−0.843131	+	0.537709i	$0.819290\pi$
$84$	26.3320	+	1.60178i	0.313476	+	0.0190688i
$85$	−11.4599	+	85.7710i	−0.134823	+	1.00907i
$86$	−16.4096	−	9.47408i	−0.190809	−	0.110164i
$87$	−28.1132	−	56.3396i	−0.323140	−	0.647581i
$88$	99.3381	−	57.3529i	1.12884	−	0.651737i
$89$		−	100.624i		−	1.13060i	−0.824884	−	0.565302i	$-0.808759\pi$
$89$		−	100.624i		−	1.13060i	0.824884	−	0.565302i	$-0.191241\pi$
$90$	−99.4842	+	27.4543i	−1.10538	+	0.305047i
$91$	29.5794			0.325049
$92$	0.362376	+	0.627654i	0.00393887	+	0.00682233i
$93$	−83.7371	−	55.3845i	−0.900399	−	0.595532i
$94$	17.3791	−	30.1015i	0.184884	−	0.320229i
$95$	−2.62617	+	19.6554i	−0.0276439	+	0.206899i
$96$	−48.7237	−	32.2263i	−0.507539	−	0.335691i
$97$	−3.59238	+	2.07406i	−0.0370349	+	0.0213821i	−0.518403	−	0.855136i	$-0.673473\pi$
$97$	−3.59238	+	2.07406i	−0.0370349	+	0.0213821i	0.481368	+	0.876518i	$0.340140\pi$
$98$	−0.614205			−0.00626740
$99$	−151.164	+	64.2837i	−1.52691	+	0.649330i
$100$	22.3536	−	22.1822i	0.223536	−	0.221822i
$101$	−140.266	+	80.9826i	−1.38877	+	0.801808i	−0.993177	−	0.116617i	$-0.962795\pi$
$101$	−140.266	+	80.9826i	−1.38877	+	0.801808i	−0.395595	+	0.918425i	$0.629462\pi$
$102$	106.545	−	53.1654i	1.04456	−	0.521229i
$103$	−142.152	−	82.0717i	−1.38012	−	0.796813i	−0.387947	−	0.921682i	$-0.626816\pi$
$103$	−142.152	−	82.0717i	−1.38012	−	0.796813i	−0.992173	+	0.124869i	$0.960149\pi$
$104$	−23.0619	−	13.3148i	−0.221749	−	0.128027i
$105$	−99.0620	+	33.9333i	−0.943447	+	0.323175i
$106$	28.1865	+	48.8205i	0.265910	+	0.460570i
$107$	48.4086			0.452416			0.226208	−	0.974079i	$-0.427367\pi$
$107$	48.4086			0.452416			0.226208	+	0.974079i	$0.427367\pi$
$108$	25.8842	+	22.0627i	0.239668	+	0.204285i
$109$	23.7458			0.217851			0.108925	−	0.994050i	$-0.465259\pi$
$109$	23.7458			0.217851			0.108925	+	0.994050i	$0.465259\pi$
$110$	127.728	−	165.797i	1.16116	−	1.50724i
$111$	64.1480	+	3.90213i	0.577910	+	0.0351544i
$112$	−117.598	−	67.8954i	−1.04998	−	0.606209i
$113$	56.3972	−	97.6828i	0.499090	−	0.864449i	−0.500909	−	0.865500i	$-0.667001\pi$
$113$	56.3972	−	97.6828i	0.499090	−	0.864449i	0.999999	+	0.00105049i	$0.000334381\pi$
$114$	24.4160	−	12.1834i	0.214175	−	0.106872i
$115$	−2.27891	−	1.75565i	−0.0198166	−	0.0152665i
$116$		−	26.4381i		−	0.227914i
$117$	30.4712	+	22.9301i	0.260438	+	0.195984i
$118$			114.293i			0.968582i
$119$	104.629	−	60.4074i	0.879233	−	0.507626i
$120$	92.5092	+	18.1350i	0.770910	+	0.151125i
$121$	106.062	−	183.705i	0.876546	−	1.51822i
$122$	72.1672	−	124.997i	0.591534	−	1.02457i
$123$	−84.2761	+	127.419i	−0.685171	+	1.03593i
$124$	−21.0776	−	36.5075i	−0.169981	−	0.294415i
$125$	−48.5013	+	115.207i	−0.388011	+	0.921655i
$126$	115.132	+	86.6385i	0.913744	+	0.687607i
$127$		−	97.5047i		−	0.767754i	−0.923384	−	0.383877i	$-0.874589\pi$
$127$		−	97.5047i		−	0.767754i	0.923384	−	0.383877i	$-0.125411\pi$
$128$	76.9576	+	133.294i	0.601231	+	1.04136i
$129$	−11.0669	−	22.1783i	−0.0857897	−	0.171925i
$130$	−48.1603	−	6.43473i	−0.370464	−	0.0494979i
$131$	17.7898	+	10.2709i	0.135800	+	0.0784041i	0.566361	−	0.824157i	$-0.308351\pi$
$131$	17.7898	+	10.2709i	0.135800	+	0.0784041i	−0.430561	+	0.902562i	$0.641684\pi$
$132$	−68.8461	−	4.18792i	−0.521561	−	0.0317267i
$133$	23.9769	−	13.8430i	0.180277	−	0.104083i
$134$			274.207i			2.04632i
$135$	−128.354	−	41.8368i	−0.950769	−	0.309902i
$136$	−108.766			−0.799753
$137$	−9.83571	−	17.0360i	−0.0717935	−	0.124350i	0.827894	−	0.560885i	$-0.189539\pi$
$137$	−9.83571	−	17.0360i	−0.0717935	−	0.124350i	−0.899687	+	0.436535i	$0.856206\pi$
$138$	−0.240353	+	3.95122i	−0.00174169	+	0.0286320i
$139$	−54.0215	+	93.5679i	−0.388644	+	0.673150i	−0.992267	−	0.124119i	$-0.960390\pi$
$139$	−54.0215	+	93.5679i	−0.388644	+	0.673150i	0.603624	+	0.797269i	$0.293723\pi$
$140$	−43.5805	−	5.82282i	−0.311290	−	0.0415916i
$141$	40.6836	−	20.3009i	0.288536	−	0.143978i
$142$	132.725	−	76.6288i	0.934683	−	0.539639i
$143$	−77.3366			−0.540816
$144$	−68.5109	−	161.105i	−0.475770	−	1.11878i
$145$	39.9723	+	97.0294i	0.275671	+	0.669168i
$146$	−97.2054	+	56.1216i	−0.665791	+	0.384394i
$147$	−0.670127	−	0.443228i	−0.00455869	−	0.00301516i
$148$	23.3696	+	13.4925i	0.157903	+	0.0911652i
$149$	−196.553	−	113.480i	−1.31915	−	0.761612i	−0.335558	−	0.942019i	$-0.608925\pi$
$149$	−196.553	−	113.480i	−1.31915	−	0.761612i	−0.983592	+	0.180408i	$0.942258\pi$
$150$	168.671	−	33.6992i	1.12448	−	0.224661i
$151$	−27.9141	−	48.3486i	−0.184862	−	0.320190i	0.758668	−	0.651477i	$-0.225850\pi$
$151$	−27.9141	−	48.3486i	−0.184862	−	0.320190i	−0.943530	+	0.331288i	$0.892517\pi$
$152$	−24.9250			−0.163980
$153$	154.611	+	18.8799i	1.01053	+	0.123398i
$154$	−292.207			−1.89745
$155$	132.553	+	102.117i	0.855179	+	0.658821i
$156$	7.14951	+	14.3278i	0.0458302	+	0.0918449i
$157$	59.2359	+	34.1999i	0.377299	+	0.217833i	0.676642	−	0.736312i	$-0.263434\pi$
$157$	59.2359	+	34.1999i	0.377299	+	0.217833i	−0.299344	+	0.954145i	$0.596768\pi$
$158$	−135.233	+	234.230i	−0.855904	+	1.48247i
$159$	−4.47744	+	73.6057i	−0.0281600	+	0.462929i
$160$	77.1279	+	59.4185i	0.482049	+	0.371365i
$161$			4.01644i			0.0249468i
$162$	51.4404	+	178.501i	0.317533	+	1.10186i
$163$			80.5043i			0.493892i	0.969029	+	0.246946i	$0.0794269\pi$
$163$			80.5043i			0.493892i	−0.969029	+	0.246946i	$0.920573\pi$
$164$	−55.5519	+	32.0729i	−0.338731	+	0.195566i
$165$	259.001	−	88.7200i	1.56971	−	0.537697i
$166$	−8.39529	+	14.5411i	−0.0505740	+	0.0875968i
$167$	37.4114	−	64.7985i	0.224020	−	0.388015i	−0.732005	−	0.681300i	$-0.761415\pi$
$167$	37.4114	−	64.7985i	0.224020	−	0.388015i	0.956025	+	0.293285i	$0.0947484\pi$
$168$	−58.7661	−	117.769i	−0.349798	−	0.701006i
$169$	−75.5229	−	130.810i	−0.446881	−	0.774021i
$170$	−183.494	+	75.5924i	−1.07938	+	0.444661i
$171$	35.4309	+	4.32654i	0.207198	+	0.0253014i
$172$		−	10.4075i		−	0.0605085i
$173$	−159.212	−	275.763i	−0.920301	−	1.59401i	−0.798950	−	0.601398i	$-0.794611\pi$
$173$	−159.212	−	275.763i	−0.920301	−	1.59401i	−0.121351	−	0.992610i	$-0.538723\pi$
$174$	79.6609	−	120.441i	0.457821	−	0.692191i
$175$	168.747	−	44.5203i	0.964269	−	0.254402i
$176$	307.465	+	177.515i	1.74696	+	1.00861i
$177$	−82.4770	+	124.699i	−0.465972	+	0.704513i
$178$	199.853	−	115.385i	1.12277	−	0.648232i
$179$			3.14738i			0.0175831i	0.999961	+	0.00879155i	$0.00279847\pi$
$179$			3.14738i			0.0175831i	−0.999961	+	0.00879155i	$0.997202\pi$
$180$	−40.3805	−	39.7821i	−0.224336	−	0.221012i
$181$	−0.833264			−0.00460367			−0.00230183	−	0.999997i	$-0.500733\pi$
$181$	−0.833264			−0.00460367			−0.00230183	+	0.999997i	$0.500733\pi$
$182$	33.9187	+	58.7489i	0.186367	+	0.322796i
$183$	168.939	−	84.3000i	0.923166	−	0.460656i
$184$	1.80794	−	3.13145i	0.00982578	−	0.0170188i
$185$	−106.168	−	14.1851i	−0.573878	−	0.0766763i
$186$	13.9802	−	229.823i	0.0751622	−	1.23561i
$187$	−273.556	+	157.938i	−1.46287	+	0.844586i
$188$	19.0913			0.101549
$189$	63.0934	+	177.609i	0.333827	+	0.939731i
$190$	−42.0498	+	17.3229i	−0.221315	+	0.0911729i
$191$	49.8127	−	28.7594i	0.260799	−	0.150573i	−0.363900	−	0.931438i	$-0.618555\pi$
$191$	49.8127	−	28.7594i	0.260799	−	0.150573i	0.624699	+	0.780866i	$0.285222\pi$
$192$	−6.03839	+	99.2663i	−0.0314499	+	0.517012i
$193$	31.4897	+	18.1806i	0.163159	+	0.0941999i	0.579356	−	0.815075i	$-0.303304\pi$
$193$	31.4897	+	18.1806i	0.163159	+	0.0941999i	−0.416197	+	0.909274i	$0.636637\pi$
$194$	−8.23876	−	4.75665i	−0.0424678	−	0.0245188i
$195$	−47.9017	−	41.7745i	−0.245650	−	0.214228i
$196$	−0.168679	−	0.292161i	−0.000860607	−	0.00149062i
$197$	151.285			0.767943			0.383972	−	0.923345i	$-0.374556\pi$
$197$	151.285			0.767943			0.383972	+	0.923345i	$0.374556\pi$
$198$	−301.016	−	226.520i	−1.52028	−	1.14404i
$199$	268.742			1.35046			0.675232	−	0.737605i	$-0.264043\pi$
$199$	268.742			1.35046			0.675232	+	0.737605i	$0.264043\pi$
$200$	−151.605	−	41.2485i	−0.758027	−	0.206243i
$201$	−197.876	+	299.173i	−0.984456	+	1.48842i
$202$	−321.686	−	185.725i	−1.59250	−	0.919432i
$203$	73.2573	−	126.885i	0.360873	−	0.625051i
$204$	54.5497	+	36.0797i	0.267401	+	0.176861i
$205$	155.387	−	201.700i	0.757986	−	0.983901i
$206$		−	376.446i		−	1.82741i
$207$	−3.11355	+	4.13752i	−0.0150413	+	0.0199880i
$208$		−	82.4222i		−	0.396261i
$209$	−62.6884	+	36.1932i	−0.299945	+	0.173173i
$210$	−180.991	−	157.840i	−0.861860	−	0.751617i
$211$	−178.833	+	309.747i	−0.847548	+	1.46800i	0.0358410	+	0.999358i	$0.488589\pi$
$211$	−178.833	+	309.747i	−0.847548	+	1.46800i	−0.883389	+	0.468640i	$0.844744\pi$
$212$	−15.4817	+	26.8151i	−0.0730269	+	0.126486i
$213$	200.107	+	12.1725i	0.939469	+	0.0571480i
$214$	55.5100	+	96.1462i	0.259393	+	0.449281i
$215$	15.7353	+	38.1960i	0.0731873	+	0.177656i
$216$	30.7570	−	166.875i	0.142394	−	0.772570i
$217$		−	233.616i		−	1.07657i
$218$	27.2292	+	47.1624i	0.124905	+	0.216341i
$219$	−146.555	−	8.91495i	−0.669200	−	0.0407075i
$220$	113.943	+	15.2240i	0.517923	+	0.0692000i
$221$	63.5075	+	36.6661i	0.287364	+	0.165910i
$222$	65.8082	+	131.882i	0.296434	+	0.594061i
$223$	−309.408	+	178.637i	−1.38748	+	0.801062i	−0.993031	−	0.117856i	$-0.962398\pi$
$223$	−309.408	+	178.637i	−1.38748	+	0.801062i	−0.394449	+	0.918918i	$0.629064\pi$
$224$		−	135.933i		−	0.606844i
$225$	208.347	+	84.9507i	0.925986	+	0.377559i
$226$	258.682			1.14461
$227$	64.4002	+	111.544i	0.283701	+	0.491385i	0.972293	−	0.233764i	$-0.0751042\pi$
$227$	64.4002	+	111.544i	0.283701	+	0.491385i	−0.688592	+	0.725149i	$0.741771\pi$
$228$	12.5007	+	8.26807i	0.0548275	+	0.0362634i
$229$	126.552	−	219.195i	0.552631	−	0.957184i	−0.445453	−	0.895305i	$-0.646957\pi$
$229$	126.552	−	219.195i	0.552631	−	0.957184i	0.998084	−	0.0618791i	$-0.0197093\pi$
$230$	0.873737	−	6.53943i	0.00379886	−	0.0284323i
$231$	−318.812	−	210.865i	−1.38014	−	0.912835i
$232$	−114.231	+	65.9515i	−0.492377	+	0.284274i
$233$	96.3566			0.413548			0.206774	−	0.978389i	$-0.433704\pi$
$233$	96.3566			0.413548			0.206774	+	0.978389i	$0.433704\pi$
$234$	−10.6010	+	86.8140i	−0.0453036	+	0.371000i
$235$	−70.0663	+	28.8646i	−0.298154	+	0.122828i
$236$	−54.3659	+	31.3882i	−0.230364	+	0.133001i
$237$	−316.573	+	157.968i	−1.33575	+	0.666533i
$238$	239.955	+	138.538i	1.00822	+	0.582094i
$239$	94.7361	+	54.6959i	0.396385	+	0.228853i	0.684923	−	0.728615i	$-0.259836\pi$
$239$	94.7361	+	54.6959i	0.396385	+	0.228853i	−0.288538	+	0.957469i	$0.593169\pi$
$240$	94.5542	+	276.033i	0.393976	+	1.15014i
$241$	156.812	+	271.606i	0.650672	+	1.12700i	0.982960	+	0.183819i	$0.0588460\pi$
$241$	156.812	+	271.606i	0.650672	+	1.12700i	−0.332288	+	0.943178i	$0.607821\pi$
$242$	486.485			2.01027
$243$	−72.6876	+	231.874i	−0.299126	+	0.954214i
$244$	79.2770			0.324906
$245$	1.06079	+	0.817219i	0.00432974	+	0.00333559i
$246$	−349.711	−	21.2730i	−1.42159	−	0.0864756i
$247$	14.5535	+	8.40245i	0.0589209	+	0.0340180i
$248$	−105.159	+	182.141i	−0.424029	+	0.734439i
$249$	−19.6529	+	9.80671i	−0.0789274	+	0.0393844i
$250$	−284.433	+	35.7771i	−1.13773	+	0.143109i
$251$		−	192.888i		−	0.768478i	−0.923234	−	0.384239i	$-0.874464\pi$
$251$		−	192.888i		−	0.768478i	0.923234	−	0.384239i	$-0.125536\pi$
$252$	−9.59295	+	78.5585i	−0.0380673	+	0.311740i
$253$		−	10.5011i		−	0.0415064i
$254$	193.658	−	111.809i	0.762433	−	0.440191i
$255$	−254.751	−	49.9398i	−0.999022	−	0.195842i
$256$	−110.194	+	190.862i	−0.430447	+	0.745556i
$257$	186.757	−	323.472i	0.726680	−	1.25865i	−0.231599	−	0.972811i	$-0.574396\pi$
$257$	186.757	−	323.472i	0.726680	−	1.25865i	0.958279	−	0.285835i	$-0.0922710\pi$
$258$	31.3589	−	47.4122i	0.121546	−	0.183768i
$259$	74.7725	+	129.510i	0.288697	+	0.500038i
$260$	−10.1654	−	24.6757i	−0.0390978	−	0.0949066i
$261$	173.828	−	73.9214i	0.666007	−	0.283224i
$262$			47.1107i			0.179812i
$263$	100.790	+	174.573i	0.383230	+	0.663774i	0.991522	−	0.129939i	$-0.0414783\pi$
$263$	100.790	+	174.573i	0.383230	+	0.663774i	−0.608292	+	0.793713i	$0.708145\pi$
$264$	153.646	+	307.911i	0.581994	+	1.16633i
$265$	16.2765	−	121.820i	0.0614207	−	0.459699i
$266$	54.9885	+	31.7476i	0.206724	+	0.119352i
$267$	301.315	+	18.3290i	1.12852	+	0.0686480i
$268$	−130.433	+	75.3054i	−0.486689	+	0.280990i
$269$			7.31695i			0.0272006i	0.999908	+	0.0136003i	$0.00432924\pi$
$269$			7.31695i			0.0272006i	−0.999908	+	0.0136003i	$0.995671\pi$
$270$	−64.0894	−	302.903i	−0.237368	−	1.12186i
$271$	−93.8451			−0.346292			−0.173146	−	0.984896i	$-0.555393\pi$
$271$	−93.8451			−0.346292			−0.173146	+	0.984896i	$0.555393\pi$
$272$	−168.324	−	291.545i	−0.618837	−	1.07186i
$273$	−5.38801	+	88.5746i	−0.0197363	+	0.324449i
$274$	22.5572	−	39.0702i	0.0823255	−	0.142592i
$275$	−441.196	+	116.400i	−1.60435	+	0.423273i
$276$	−1.94550	+	0.970793i	−0.00704890	+	0.00351737i
$277$	231.116	−	133.435i	0.834353	−	0.481714i	−0.0209878	−	0.999780i	$-0.506681\pi$
$277$	231.116	−	133.435i	0.834353	−	0.481714i	0.855341	+	0.518066i	$0.173348\pi$
$278$	−247.785			−0.891314
$279$	181.100	−	240.659i	0.649104	−	0.862578i
$280$	83.5558	+	202.825i	0.298414	+	0.724374i
$281$	5.46813	−	3.15703i	0.0194595	−	0.0112350i	−0.490239	−	0.871588i	$-0.663090\pi$
$281$	5.46813	−	3.15703i	0.0194595	−	0.0112350i	0.509698	+	0.860353i	$0.329757\pi$
$282$	86.9722	+	57.5243i	0.308412	+	0.203987i
$283$	300.060	+	173.240i	1.06028	+	0.612155i	0.925511	−	0.378722i	$-0.123636\pi$
$283$	300.060	+	173.240i	1.06028	+	0.612155i	0.134773	+	0.990877i	$0.456970\pi$
$284$	72.9004	+	42.0891i	0.256692	+	0.148201i
$285$	−58.3790	−	11.4443i	−0.204839	−	0.0401553i
$286$	−88.6818	−	153.601i	−0.310076	−	0.537068i
$287$	−355.483			−1.23862
$288$	105.376	−	140.031i	0.365888	−	0.486220i
$289$	10.5195			0.0363996
$290$	−146.878	+	190.654i	−0.506475	+	0.657428i
$291$	−5.55634	−	11.1351i	−0.0190940	−	0.0382648i
$292$	−53.3910	−	30.8253i	−0.182846	−	0.105566i
$293$	−53.3460	+	92.3980i	−0.182068	+	0.315352i	−0.942585	−	0.333967i	$-0.891613\pi$
$293$	−53.3460	+	92.3980i	−0.182068	+	0.315352i	0.760516	+	0.649319i	$0.224946\pi$
$294$	0.111880	−	1.83922i	0.000380544	−	0.00625583i
$295$	152.070	−	197.394i	0.515491	−	0.669131i
$296$		−	134.631i		−	0.454835i
$297$	−164.960	−	464.366i	−0.555421	−	1.56352i
$298$		−	520.510i		−	1.74668i
$299$	−2.11128	+	1.21895i	−0.00706113	+	0.00407675i
$300$	62.3519	+	70.9776i	0.207840	+	0.236592i
$301$	28.8380	−	49.9489i	0.0958074	−	0.165943i
$302$	64.0181	−	110.883i	0.211980	−	0.367161i
$303$	−216.950	−	434.773i	−0.716005	−	1.43489i
$304$	−38.5732	−	66.8108i	−0.126886	−	0.219772i
$305$	−290.952	+	119.861i	−0.953940	+	0.392986i
$306$	139.794	+	328.729i	0.456844	+	1.07428i
$307$		−	161.083i		−	0.524702i	−0.964973	−	0.262351i	$-0.915502\pi$
$307$		−	161.083i		−	0.524702i	0.964973	−	0.262351i	$-0.0844978\pi$
$308$	−80.2487	−	138.995i	−0.260548	−	0.451282i
$309$	271.655	−	410.721i	0.879141	−	1.32919i
$310$	−50.8210	+	380.366i	−0.163939	+	1.22699i
$311$	15.0468	+	8.68727i	0.0483820	+	0.0279333i	0.523996	−	0.851721i	$-0.324441\pi$
$311$	15.0468	+	8.68727i	0.0483820	+	0.0279333i	−0.475614	+	0.879654i	$0.657774\pi$
$312$	44.0715	−	66.6327i	0.141255	−	0.213566i
$313$	−301.788	+	174.238i	−0.964180	+	0.556670i	−0.897457	−	0.441102i	$-0.854588\pi$
$313$	−301.788	+	174.238i	−0.964180	+	0.556670i	−0.0667232	+	0.997772i	$0.521254\pi$
$314$			156.868i			0.499579i
$315$	−83.5677	−	302.819i	−0.265294	−	0.961329i
$316$	−148.556			−0.470113
$317$	148.425	+	257.080i	0.468218	+	0.810978i	0.999340	−	0.0363175i	$-0.0115628\pi$
$317$	148.425	+	257.080i	0.468218	+	0.810978i	−0.531122	+	0.847295i	$0.678229\pi$
$318$	−151.325	+	75.5107i	−0.475866	+	0.237455i
$319$	−191.534	+	331.747i	−0.600420	+	1.03996i
$320$	21.9509	−	164.290i	0.0685964	−	0.513405i
$321$	−8.81780	+	144.958i	−0.0274698	+	0.451582i
$322$	−7.97720	+	4.60564i	−0.0247739	+	0.0143032i
$323$	68.6383			0.212502
$324$	−70.7810	+	73.4904i	−0.218460	+	0.226822i
$325$	74.6155	+	75.1921i	0.229586	+	0.231360i
$326$	−159.893	+	92.3142i	−0.490469	+	0.283172i
$327$	−4.32538	+	71.1058i	−0.0132275	+	0.217449i
$328$	277.156	+	160.016i	0.844987	+	0.487853i
$329$	91.6256	+	52.9001i	0.278497	+	0.160791i
$330$	473.207	+	412.678i	1.43396	+	1.25054i
$331$	−101.347	−	175.538i	−0.306184	−	0.530326i	0.671341	−	0.741149i	$-0.265719\pi$
$331$	−101.347	−	175.538i	−0.306184	−	0.530326i	−0.977524	+	0.210823i	$0.932385\pi$
$332$	−9.22238			−0.0277783
$333$	−23.3696	+	191.378i	−0.0701790	+	0.574709i
$334$	171.598			0.513768
$335$	364.841	−	473.580i	1.08908	−	1.41367i
$336$	224.731	−	339.776i	0.668843	−	1.01124i
$337$	−28.3716	−	16.3804i	−0.0841888	−	0.0486064i	0.457315	−	0.889305i	$-0.348811\pi$
$337$	−28.3716	−	16.3804i	−0.0841888	−	0.0486064i	−0.541503	+	0.840699i	$0.682145\pi$
$338$	173.204	−	299.998i	0.512438	−	0.887569i
$339$	282.235	+	186.673i	0.832551	+	0.550657i
$340$	−86.3502	−	66.5233i	−0.253971	−	0.195657i
$341$			610.798i			1.79120i
$342$	32.0354	+	75.3320i	0.0936709	+	0.220269i
$343$		−	343.931i		−	1.00271i
$344$	−44.9677	+	25.9621i	−0.130720	+	0.0754712i
$345$	5.67233	−	6.50431i	0.0164415	−	0.0188531i
$346$	365.136	−	632.435i	1.05531	−	1.82785i
$347$	−334.696	+	579.710i	−0.964540	+	1.67063i	−0.253696	+	0.967284i	$0.581646\pi$
$347$	−334.696	+	579.710i	−0.964540	+	1.67063i	−0.710845	+	0.703349i	$0.751687\pi$
$348$	79.1678	+	4.81579i	0.227494	+	0.0138385i
$349$	−274.137	−	474.819i	−0.785492	−	1.36051i	−0.928705	−	0.370821i	$-0.879076\pi$
$349$	−274.137	−	474.819i	−0.785492	−	1.36051i	0.143212	−	0.989692i	$-0.454257\pi$
$350$	281.925	+	284.104i	0.805501	+	0.811726i
$351$	−74.2138	+	87.0682i	−0.211435	+	0.248058i
$352$			355.402i			1.00967i
$353$	−10.0056	−	17.3302i	−0.0283444	−	0.0490939i	0.851505	−	0.524346i	$-0.175690\pi$
$353$	−10.0056	−	17.3302i	−0.0283444	−	0.0490939i	−0.879850	+	0.475252i	$0.842357\pi$
$354$	−342.246	−	20.8189i	−0.966795	−	0.0588103i
$355$	−331.185	−	44.2498i	−0.932915	−	0.124647i
$356$	109.771	+	63.3764i	0.308346	+	0.178024i
$357$	161.829	+	324.311i	0.453304	+	0.908433i
$358$	−6.25113	+	3.60909i	−0.0174613	+	0.0100813i
$359$			224.934i			0.626556i	0.949661	+	0.313278i	$0.101427\pi$
$359$			224.934i			0.626556i	−0.949661	+	0.313278i	$0.898573\pi$
$360$	−71.1554	+	273.712i	−0.197654	+	0.760312i
$361$	−345.271			−0.956429
$362$	−0.955502	−	1.65498i	−0.00263951	−	0.00457176i
$363$	530.778	+	351.062i	1.46220	+	0.967112i
$364$	−18.6302	+	32.2684i	−0.0511818	+	0.0886495i
$365$	242.554	+	32.4078i	0.664531	+	0.0887885i
$366$	361.154	+	238.871i	0.986760	+	0.652652i
$367$	−43.7972	+	25.2863i	−0.119338	+	0.0689000i	−0.558481	−	0.829517i	$-0.688616\pi$
$367$	−43.7972	+	25.2863i	−0.119338	+	0.0689000i	0.439143	+	0.898417i	$0.355282\pi$
$368$	11.1917			0.0304122
$369$	−366.200	−	275.572i	−0.992413	−	0.746807i
$370$	−93.5685	−	227.130i	−0.252888	−	0.613864i
$371$	−148.604	+	85.7966i	−0.400550	+	0.231258i
$372$	113.160	−	56.4662i	0.304193	−	0.151791i
$373$	−244.861	−	141.371i	−0.656464	−	0.379010i	0.134464	−	0.990918i	$-0.457069\pi$
$373$	−244.861	−	141.371i	−0.656464	−	0.379010i	−0.790928	+	0.611909i	$0.790402\pi$
$374$	−627.373	−	362.214i	−1.67747	−	0.968486i
$375$	−336.148	−	166.221i	−0.896395	−	0.443256i
$376$	−47.6245	−	82.4881i	−0.126661	−	0.219383i
$377$	88.9313			0.235892
$378$	−280.407	+	328.976i	−0.741819	+	0.870308i
$379$	−435.602			−1.14935			−0.574673	−	0.818383i	$-0.694871\pi$
$379$	−435.602			−1.14935			−0.574673	+	0.818383i	$0.694871\pi$
$380$	−19.7881	−	15.2446i	−0.0520740	−	0.0401172i
$381$	291.974	+	17.7609i	0.766337	+	0.0466164i
$382$	114.240	+	65.9566i	0.299058	+	0.172661i
$383$	156.225	−	270.589i	0.407897	−	0.706499i	−0.586757	−	0.809763i	$-0.699595\pi$
$383$	156.225	−	270.589i	0.407897	−	0.706499i	0.994654	+	0.103265i	$0.0329288\pi$
$384$	−413.164	+	206.167i	−1.07595	+	0.536892i
$385$	504.667	+	388.790i	1.31082	+	1.00984i
$386$			83.3905i			0.216038i
$387$	68.4280	−	29.0995i	0.176817	−	0.0751925i
$388$		−	5.22527i		−	0.0134672i
$389$	−217.725	+	125.703i	−0.559704	+	0.323145i	−0.753027	−	0.657990i	$-0.771407\pi$
$389$	−217.725	+	125.703i	−0.559704	+	0.323145i	0.193323	+	0.981135i	$0.438074\pi$
$390$	28.0411	−	143.042i	0.0719004	−	0.366775i
$391$	−4.97869	+	8.62335i	−0.0127332	+	0.0220546i
$392$	−0.841562	+	1.45763i	−0.00214684	+	0.00371844i
$393$	−33.9965	+	51.4000i	−0.0865050	+	0.130789i
$394$	173.478	+	300.473i	0.440300	+	0.762622i
$395$	545.209	−	224.605i	1.38028	−	0.568620i
$396$	25.0812	−	205.394i	0.0633362	−	0.518672i
$397$			237.163i			0.597388i	0.954349	+	0.298694i	$0.0965510\pi$
$397$			237.163i			0.597388i	−0.954349	+	0.298694i	$0.903449\pi$
$398$	308.167	+	533.760i	0.774288	+	1.34111i
$399$	37.0850	+	74.3194i	0.0929450	+	0.186264i
$400$	−124.054	−	470.209i	−0.310136	−	1.17552i
$401$	−464.967	−	268.449i	−1.15952	−	0.669448i	−0.208330	−	0.978059i	$-0.566803\pi$
$401$	−464.967	−	268.449i	−1.15952	−	0.669448i	−0.951188	+	0.308611i	$0.900136\pi$
$402$	−821.103	−	49.9478i	−2.04254	−	0.124248i
$403$	122.803	−	70.9001i	0.304721	−	0.175931i
$404$		−	204.023i		−	0.505007i
$405$	148.659	−	376.730i	0.367059	−	0.930198i
$406$	336.016			0.827626
$407$	−195.496	−	338.608i	−0.480333	−	0.831962i
$408$	19.8122	−	325.697i	0.0485593	−	0.798277i
$409$	20.7517	−	35.9430i	0.0507376	−	0.0878801i	−0.839541	−	0.543296i	$-0.817176\pi$
$409$	20.7517	−	35.9430i	0.0507376	−	0.0878801i	0.890279	+	0.455416i	$0.150509\pi$
$410$	578.786	+	77.3320i	1.41167	+	0.188615i
$411$	52.8052	−	26.3495i	0.128480	−	0.0641108i
$412$	179.065	−	103.383i	0.434624	−	0.250930i
$413$	−347.894			−0.842359
$414$	−11.7880	−	1.43946i	−0.0284735	−	0.00347696i
$415$	33.8467	−	13.9435i	0.0815584	−	0.0335989i
$416$	71.4546	−	41.2543i	0.171766	−	0.0991690i
$417$	−270.346	−	178.809i	−0.648311	−	0.428799i
$418$	−143.769	−	83.0053i	−0.343946	−	0.198577i
$419$	636.413	+	367.433i	1.51889	+	0.876929i	0.999753	+	0.0222364i	$0.00707866\pi$
$419$	636.413	+	367.433i	1.51889	+	0.876929i	0.519134	+	0.854693i	$0.326255\pi$
$420$	25.3746	−	129.440i	0.0604157	−	0.308190i
$421$	7.65881	+	13.2655i	0.0181920	+	0.0315094i	0.874978	−	0.484163i	$-0.160876\pi$
$421$	7.65881	+	13.2655i	0.0181920	+	0.0315094i	−0.856786	+	0.515672i	$0.827542\pi$
$422$	−820.269			−1.94377
$423$	53.3797	+	125.523i	0.126193	+	0.296746i
$424$	154.481			0.364341
$425$	417.489	+	113.590i	0.982327	+	0.267270i
$426$	205.286	+	411.398i	0.481892	+	0.965724i
$427$	380.478	+	219.669i	0.891048	+	0.514447i
$428$	−30.4894	+	52.8092i	−0.0712369	+	0.123386i
$429$	14.0872	−	231.582i	0.0328372	−	0.539818i
$430$	−57.8191	+	75.0518i	−0.134463	+	0.174539i
$431$			98.8622i			0.229379i	0.993401	+	0.114689i	$0.0365872\pi$
$431$			98.8622i			0.229379i	−0.993401	+	0.114689i	$0.963413\pi$
$432$	494.902	−	175.808i	1.14561	−	0.406962i
$433$			573.821i			1.32522i	0.748964	+	0.662610i	$0.230551\pi$
$433$			573.821i			1.32522i	−0.748964	+	0.662610i	$0.769449\pi$
$434$	463.994	−	267.887i	1.06911	−	0.617252i
$435$	−297.832	+	102.021i	−0.684672	+	0.234532i
$436$	−14.9559	+	25.9044i	−0.0343025	+	0.0594137i
$437$	−1.14092	+	1.97614i	−0.00261081	+	0.00452205i
$438$	−150.348	−	301.301i	−0.343260	−	0.687902i
$439$	119.927	+	207.719i	0.273182	+	0.473165i	0.969675	−	0.244399i	$-0.0785906\pi$
$439$	119.927	+	207.719i	0.273182	+	0.473165i	−0.696493	+	0.717564i	$0.745257\pi$
$440$	−218.460	−	530.293i	−0.496500	−	1.20521i
$441$	1.44930	−	1.92594i	0.00328639	−	0.00436720i
$442$			168.180i			0.380497i
$443$	−183.257	−	317.411i	−0.413673	−	0.716503i	0.581615	−	0.813464i	$-0.302421\pi$
$443$	−183.257	−	317.411i	−0.413673	−	0.716503i	−0.995288	+	0.0969610i	$0.969088\pi$
$444$	−44.6595	+	67.5218i	−0.100585	+	0.152076i
$445$	−498.688	−	66.6300i	−1.12065	−	0.149730i
$446$	−709.595	−	409.685i	−1.59102	−	0.918576i
$447$	375.615	−	567.901i	0.840303	−	1.27047i
$448$	−200.411	+	115.707i	−0.447346	+	0.258275i
$449$		−	623.682i		−	1.38905i	−0.719470	−	0.694523i	$-0.755615\pi$
$449$		−	623.682i		−	1.38905i	0.719470	−	0.694523i	$-0.244385\pi$
$450$	70.1868	+	511.219i	0.155971	+	1.13604i
$451$	929.424			2.06081
$452$	71.0418	+	123.048i	0.157172	+	0.272230i
$453$	149.863	−	74.7809i	0.330823	−	0.165079i
$454$	−147.695	+	255.816i	−0.325320	+	0.563471i
$455$	19.5866	−	146.595i	0.0430475	−	0.322186i
$456$	4.54019	−	74.6371i	0.00995656	−	0.163678i
$457$	336.409	−	194.226i	0.736126	−	0.425002i	−0.0845333	−	0.996421i	$-0.526940\pi$
$457$	336.409	−	194.226i	0.736126	−	0.425002i	0.820659	+	0.571418i	$0.193607\pi$
$458$	580.470			1.26740
$459$	−84.6983	+	459.539i	−0.184528	+	1.00117i
$460$	3.35058	−	1.38031i	0.00728387	−	0.00300067i
$461$	328.964	−	189.927i	0.713588	−	0.411990i	−0.0988003	−	0.995107i	$-0.531501\pi$
$461$	328.964	−	189.927i	0.713588	−	0.411990i	0.812388	+	0.583117i	$0.198167\pi$
$462$	53.2266	−	875.003i	0.115209	−	1.89395i
$463$	−331.040	−	191.126i	−0.714990	−	0.412800i	0.0979160	−	0.995195i	$-0.468782\pi$
$463$	−331.040	−	191.126i	−0.714990	−	0.412800i	−0.812906	+	0.582395i	$0.802116\pi$
$464$	−353.562	−	204.129i	−0.761987	−	0.439933i
$465$	−329.931	+	378.324i	−0.709530	+	0.813599i
$466$	110.492	+	191.378i	0.237107	+	0.410682i
$467$	35.3515			0.0756992			0.0378496	−	0.999283i	$-0.487949\pi$
$467$	35.3515			0.0756992			0.0378496	+	0.999283i	$0.487949\pi$
$468$	−44.2064	+	18.7991i	−0.0944582	+	0.0401690i
$469$	−834.655			−1.77965
$470$	−137.674	−	106.062i	−0.292923	−	0.225665i
$471$	−113.200	+	171.150i	−0.240340	+	0.363376i
$472$	271.239	+	156.600i	0.574659	+	0.331779i
$473$	−75.3982	+	130.593i	−0.159404	+	0.276096i
$474$	−676.760	−	447.616i	−1.42776	−	0.944337i
$475$	95.6723	+	26.0304i	0.201415	+	0.0548008i
$476$			152.187i			0.319720i
$477$	−219.594	−	26.8151i	−0.460365	−	0.0562161i
$478$			250.879i			0.524851i
$479$	−501.226	+	289.383i	−1.04640	+	0.604139i	−0.921639	−	0.388047i	$-0.873150\pi$
$479$	−501.226	+	289.383i	−1.04640	+	0.604139i	−0.124761	+	0.992187i	$0.539816\pi$
$480$	−191.976	+	220.133i	−0.399949	+	0.458611i
$481$	−45.3854	+	78.6098i	−0.0943563	+	0.163430i
$482$	−359.632	+	622.901i	−0.746124	+	1.29233i
$483$	−12.0271	−	0.731609i	−0.0249008	−	0.00151472i
$484$	133.603	+	231.408i	0.276040	+	0.478115i
$485$	7.90020	+	19.1771i	0.0162891	+	0.0395404i
$486$	−543.885	+	121.522i	−1.11910	+	0.250045i
$487$			424.778i			0.872235i	0.899890	+	0.436117i	$0.143647\pi$
$487$			424.778i			0.872235i	−0.899890	+	0.436117i	$0.856353\pi$
$488$	−197.762	−	342.534i	−0.405250	−	0.701913i
$489$	−241.067	−	14.6642i	−0.492980	−	0.0299881i
$490$	−0.406708	+	3.04398i	−0.000830015	+	0.00621219i
$491$	337.754	+	195.002i	0.687890	+	0.397154i	0.802821	−	0.596220i	$-0.203331\pi$
$491$	337.754	+	195.002i	0.687890	+	0.397154i	−0.114931	+	0.993373i	$0.536665\pi$
$492$	−85.9221	−	172.190i	−0.174638	−	0.349980i
$493$	314.569	−	181.616i	0.638071	−	0.368390i
$494$			38.5403i			0.0780168i
$495$	218.491	+	791.731i	0.441396	+	1.59946i
$496$	−650.964			−1.31243
$497$	233.249	+	404.000i	0.469315	+	0.812877i
$498$	−42.0135	−	27.7881i	−0.0843644	−	0.0557994i
$499$	308.776	−	534.816i	0.618790	−	1.07178i	−0.370916	−	0.928666i	$-0.620956\pi$
$499$	308.776	−	534.816i	0.618790	−	1.07178i	0.989707	−	0.143110i	$-0.0457103\pi$
$500$	−95.1321	−	125.472i	−0.190264	−	0.250943i
$501$	187.222	+	123.830i	0.373697	+	0.247167i
$502$	383.102	−	221.184i	0.763152	−	0.440606i
$503$	551.752			1.09692			0.548461	−	0.836176i	$-0.315214\pi$
$503$	551.752			1.09692			0.548461	+	0.836176i	$0.315214\pi$
$504$	363.359	−	154.521i	0.720951	−	0.306589i
$505$	308.467	+	748.777i	0.610825	+	1.48273i
$506$	20.8567	−	12.0416i	0.0412188	−	0.0237977i
$507$	405.461	−	202.323i	0.799727	−	0.399060i
$508$	106.369	+	61.4119i	0.209387	+	0.120890i
$509$	383.782	+	221.577i	0.753992	+	0.435317i	0.827134	−	0.562004i	$-0.189970\pi$
$509$	383.782	+	221.577i	0.753992	+	0.435317i	−0.0731427	+	0.997321i	$0.523303\pi$
$510$	−192.935	−	563.236i	−0.378303	−	1.10439i
$511$	−170.828	−	295.882i	−0.334301	−	0.579026i
$512$	110.221			0.215276
$513$	−19.4096	+	105.308i	−0.0378354	+	0.205280i
$514$	856.615			1.66657
$515$	−500.873	+	650.156i	−0.972569	+	1.26244i
$516$	31.1648	+	1.89576i	0.0603968	+	0.00367395i
$517$	−239.559	−	138.309i	−0.463363	−	0.267523i
$518$	−171.483	+	297.017i	−0.331048	+	0.573393i
$519$	854.765	−	426.523i	1.64695	−	0.821818i
$520$	−81.2584	+	105.477i	−0.156266	+	0.202841i
$521$		−	716.733i		−	1.37569i	−0.725859	−	0.687843i	$-0.758558\pi$
$521$		−	716.733i		−	1.37569i	0.725859	−	0.687843i	$-0.241442\pi$
$522$	346.146	+	260.481i	0.663116	+	0.499005i
$523$		−	417.591i		−	0.798453i	−0.916852	−	0.399227i	$-0.869279\pi$
$523$		−	417.591i		−	0.798453i	0.916852	−	0.399227i	$-0.130721\pi$
$524$	−22.4093	+	12.9380i	−0.0427658	+	0.0246908i
$525$	102.576	+	513.417i	0.195384	+	0.977936i
$526$	−231.150	+	400.364i	−0.439449	+	0.761149i
$527$	289.586	−	501.577i	0.549499	−	0.951760i
$528$	−587.569	+	888.359i	−1.11282	+	1.68250i
$529$	264.334	+	457.841i	0.499687	+	0.865483i
$530$	260.616	−	107.364i	0.491729	−	0.202573i
$531$	−358.383	−	269.689i	−0.674920	−	0.507888i
$532$			34.8753i			0.0655552i
$533$	−107.886	−	186.863i	−0.202412	−	0.350588i
$534$	309.113	+	619.471i	0.578863	+	1.16006i
$535$	32.0546	−	239.911i	0.0599152	−	0.448431i
$536$	650.746	+	375.709i	1.21408	+	0.700949i
$537$	−9.42471	−	0.573307i	−0.0175507	−	0.00106761i
$538$	−14.5325	+	8.39034i	−0.0270121	+	0.0155954i
$539$			4.88807i			0.00906877i
$540$	126.482	−	113.672i	0.234225	−	0.210503i
$541$	−365.297			−0.675225			−0.337612	−	0.941285i	$-0.609619\pi$
$541$	−365.297			−0.675225			−0.337612	+	0.941285i	$0.609619\pi$
$542$	−107.612	−	186.389i	−0.198546	−	0.343892i
$543$	0.151782	−	2.49518i	0.000279525	−	0.00459517i
$544$	168.500	−	291.851i	0.309743	−	0.536490i
$545$	15.7237	−	117.683i	0.0288508	−	0.215932i
$546$	−182.100	+	90.8670i	−0.333517	+	0.166423i
$547$	−529.651	+	305.794i	−0.968283	+	0.559039i	−0.898712	−	0.438538i	$-0.855496\pi$
$547$	−529.651	+	305.794i	−0.968283	+	0.559039i	−0.0695708	+	0.997577i	$0.522163\pi$
$548$	24.7795			0.0452181
$549$	221.660	+	521.239i	0.403753	+	0.949433i
$550$	−737.105	−	742.801i	−1.34019	−	1.35055i
$551$	72.0870	−	41.6195i	0.130829	−	0.0755344i
$552$	9.04769	+	5.98423i	0.0163908	+	0.0108410i
$553$	−712.970	−	411.633i	−1.28928	−	0.744364i
$554$	530.040	+	306.019i	0.956751	+	0.552381i
$555$	61.8156	−	315.331i	0.111380	−	0.568164i
$556$	−68.0492	−	117.865i	−0.122391	−	0.211987i
$557$	−510.888			−0.917214			−0.458607	−	0.888639i	$-0.651651\pi$
$557$	−510.888			−0.917214			−0.458607	+	0.888639i	$0.651651\pi$
$558$	685.650	+	83.7262i	1.22876	+	0.150047i
$559$	35.0082			0.0626265
$560$	−414.357	+	537.854i	−0.739923	+	0.960453i
$561$	−423.109	−	847.923i	−0.754206	−	1.51145i
$562$	12.5406	+	7.24031i	0.0223142	+	0.0128831i
$563$	78.8759	−	136.617i	0.140099	−	0.242659i	−0.787435	−	0.616398i	$-0.788591\pi$
$563$	78.8759	−	136.617i	0.140099	−	0.242659i	0.927534	+	0.373739i	$0.121924\pi$
$564$	−3.47755	+	57.1682i	−0.00616587	+	0.101362i
$565$	−446.767	−	344.185i	−0.790739	−	0.609176i
$566$			794.615i			1.40391i
$567$	−543.337	+	156.579i	−0.958266	+	0.276153i
$568$		−	419.976i		−	0.739395i
$569$	−152.312	+	87.9374i	−0.267684	+	0.154547i	−0.627835	−	0.778347i	$-0.716059\pi$
$569$	−152.312	+	87.9374i	−0.267684	+	0.154547i	0.360151	+	0.932894i	$0.382725\pi$
$570$	−44.2132	−	129.072i	−0.0775669	−	0.226442i
$571$	294.258	−	509.670i	0.515338	−	0.892591i	−0.484504	−	0.874789i	$-0.661000\pi$
$571$	294.258	−	509.670i	0.515338	−	0.892591i	0.999842	−	0.0178020i	$-0.00566685\pi$
$572$	48.7093	−	84.3670i	0.0851562	−	0.147495i
$573$	77.0453	+	154.401i	0.134460	+	0.269461i
$574$	−407.632	−	706.039i	−0.710160	−	1.23003i
$575$	−10.2099	+	10.1316i	−0.0177564	+	0.0176203i
$576$	−296.150	−	36.1635i	−0.514148	−	0.0627838i
$577$		−	323.853i		−	0.561270i	−0.959815	−	0.280635i	$-0.909455\pi$
$577$		−	323.853i		−	0.561270i	0.959815	−	0.280635i	$-0.0905451\pi$
$578$	12.0627	+	20.8932i	0.0208697	+	0.0361474i
$579$	−60.1771	+	90.9831i	−0.103933	+	0.157138i
$580$	−131.026	−	17.5065i	−0.225907	−	0.0301836i
$581$	−44.2614	−	25.5543i	−0.0761814	−	0.0439833i
$582$	15.7443	−	23.8042i	0.0270521	−	0.0409007i
$583$	388.531	−	224.318i	0.666434	−	0.384766i
$584$			307.583i			0.526684i
$585$	133.818	−	135.831i	0.228748	−	0.232189i
$586$	−244.687			−0.417555
$587$	−515.537	−	892.937i	−0.878258	−	1.52119i	−0.853251	−	0.521500i	$-0.825373\pi$
$587$	−515.537	−	892.937i	−0.878258	−	1.52119i	−0.0250065	−	0.999687i	$-0.507961\pi$
$588$	0.905590	−	0.451885i	0.00154012	−	0.000768512i
$589$	66.3618	−	114.942i	0.112669	−	0.195148i
$590$	566.430	+	75.6811i	0.960051	+	0.128273i
$591$	−27.5571	+	453.017i	−0.0466279	+	0.766527i
$592$	360.875	−	208.351i	0.609586	−	0.351945i
$593$	193.131			0.325685			0.162842	−	0.986652i	$-0.447934\pi$
$593$	193.131			0.325685			0.162842	+	0.986652i	$0.447934\pi$
$594$	733.136	−	860.121i	1.23424	−	1.44802i
$595$	−230.095	−	558.536i	−0.386714	−	0.938716i
$596$	247.592	−	142.948i	0.415424	−	0.239845i
$597$	−48.9525	+	804.740i	−0.0819974	+	1.34797i
$598$	−4.84200	−	2.79553i	−0.00809699	−	0.00467480i
$599$	−354.438	−	204.635i	−0.591716	−	0.341627i	0.174060	−	0.984735i	$-0.444311\pi$
$599$	−354.438	−	204.635i	−0.591716	−	0.341627i	−0.765776	+	0.643108i	$0.777645\pi$
$600$	151.133	−	446.463i	0.251888	−	0.744106i
$601$	520.432	+	901.414i	0.865943	+	1.49986i	0.866108	+	0.499857i	$0.166614\pi$
$601$	520.432	+	901.414i	0.865943	+	1.49986i	−0.000165360		1.00000i	$0.500053\pi$
$602$	132.274			0.219724
$603$	−859.818	−	647.027i	−1.42590	−	1.07301i
$604$	70.3251			0.116432
$605$	−840.203	−	647.283i	−1.38877	−	1.06989i
$606$	614.744	−	929.446i	1.01443	−	1.53374i
$607$	589.637	+	340.427i	0.971396	+	0.560836i	0.899661	−	0.436588i	$-0.143813\pi$
$607$	589.637	+	340.427i	0.971396	+	0.560836i	0.0717342	+	0.997424i	$0.477147\pi$
$608$	38.6137	−	66.8808i	0.0635093	−	0.110001i
$609$	366.609	+	242.479i	0.601986	+	0.398159i
$610$	−571.694	−	440.427i	−0.937204	−	0.722011i
$611$			64.2185i			0.105104i
$612$	−117.976	+	156.775i	−0.192771	+	0.256169i
$613$			1024.19i			1.67079i	0.549651	+	0.835395i	$0.314761\pi$
$613$			1024.19i			1.67079i	−0.549651	+	0.835395i	$0.685239\pi$
$614$	319.934	−	184.714i	0.521066	−	0.300837i
$615$	575.678	+	502.042i	0.936062	+	0.816328i
$616$	−400.371	+	693.464i	−0.649954	+	1.12575i
$617$	−555.636	+	962.389i	−0.900544	+	1.55979i	−0.0737542	+	0.997276i	$0.523498\pi$
$617$	−555.636	+	962.389i	−0.900544	+	1.55979i	−0.826790	+	0.562511i	$0.809835\pi$
$618$	1127.25	+	68.5711i	1.82404	+	0.110956i
$619$	−400.940	−	694.448i	−0.647722	−	1.12189i	−0.983666	−	0.180005i	$-0.942389\pi$
$619$	−400.940	−	694.448i	−0.647722	−	1.12189i	0.335944	−	0.941882i	$-0.390945\pi$
$620$	−194.887	+	80.2857i	−0.314333	+	0.129493i
$621$	−11.8225	−	10.0771i	−0.0190379	−	0.0162272i
$622$			39.8467i			0.0640622i
$623$	351.220	+	608.330i	0.563755	+	0.976453i
$624$	246.810	+	15.0135i	0.395530	+	0.0240601i
$625$	538.844	+	316.657i	0.862151	+	0.506651i
$626$	−692.121	−	399.596i	−1.10562	−	0.638332i
$627$	−96.9603	−	194.311i	−0.154642	−	0.309906i
$628$	−74.6177	+	43.0805i	−0.118818	+	0.0685996i
$629$			370.746i			0.589421i
$630$	505.613	−	513.219i	0.802561	−	0.814633i
$631$	−564.192			−0.894124			−0.447062	−	0.894503i	$-0.647530\pi$
$631$	−564.192			−0.894124			−0.447062	+	0.894503i	$0.647530\pi$
$632$	370.582	+	641.868i	0.586365	+	1.01561i
$633$	−894.953	−	591.930i	−1.41383	−	0.935118i
$634$	−340.398	+	589.587i	−0.536905	+	0.929947i
$635$	−483.229	−	64.5646i	−0.760991	−	0.101677i
$636$	−77.4768	−	51.2439i	−0.121819	−	0.0805722i
$637$	0.982759	−	0.567396i	0.00154279	−	0.000890731i
$638$	−878.527			−1.37700
$639$	−72.9004	+	596.996i	−0.114085	+	0.934265i
$640$	711.561	−	293.135i	1.11181	−	0.458024i
$641$	1043.99	−	602.749i	1.62869	−	0.940327i	0.644210	−	0.764848i	$-0.277186\pi$
$641$	1043.99	−	602.749i	1.62869	−	0.940327i	0.984483	−	0.175478i	$-0.0561472\pi$
$642$	−298.018	+	148.709i	−0.464202	+	0.231635i
$643$	402.110	+	232.158i	0.625365	+	0.361055i	0.778955	−	0.627080i	$-0.215750\pi$
$643$	402.110	+	232.158i	0.625365	+	0.361055i	−0.153590	+	0.988135i	$0.549083\pi$
$644$	−4.38156	−	2.52969i	−0.00680366	−	0.00392809i
$645$	−117.243	+	40.1612i	−0.181772	+	0.0622654i
$646$	78.7074	+	136.325i	0.121838	+	0.211030i
$647$	−372.702			−0.576046			−0.288023	−	0.957624i	$-0.592998\pi$
$647$	−372.702			−0.576046			−0.288023	+	0.957624i	$0.592998\pi$
$648$	494.099	+	122.498i	0.762499	+	0.189040i
$649$	909.583			1.40151
$650$	−63.7805	+	234.420i	−0.0981239	+	0.360645i
$651$	699.555	+	42.5541i	1.07459	+	0.0653672i
$652$	−87.8227	−	50.7044i	−0.134697	−	0.0777676i
$653$	−110.705	+	191.747i	−0.169533	+	0.293639i	−0.938256	−	0.345943i	$-0.887559\pi$
$653$	−110.705	+	191.747i	−0.169533	+	0.293639i	0.768723	+	0.639582i	$0.220893\pi$
$654$	−146.186	+	72.9461i	−0.223526	+	0.111538i
$655$	62.6822	−	81.3644i	0.0956980	−	0.124220i
$656$			990.543i			1.50997i
$657$	53.3910	−	437.229i	0.0812649	−	0.665493i
$658$			242.642i			0.368757i
$659$	−541.098	+	312.403i	−0.821090	+	0.474057i	−0.850792	−	0.525502i	$-0.823877\pi$
$659$	−541.098	+	312.403i	−0.821090	+	0.474057i	0.0297021	+	0.999559i	$0.490544\pi$
$660$	−66.3429	+	338.425i	−0.100520	+	0.512765i
$661$	−167.257	+	289.698i	−0.253037	+	0.438273i	−0.964360	−	0.264592i	$-0.914763\pi$
$661$	−167.257	+	289.698i	−0.253037	+	0.438273i	0.711324	+	0.702865i	$0.248096\pi$
$662$	232.428	−	402.578i	0.351100	−	0.608124i
$663$	−121.363	+	183.492i	−0.183052	+	0.276761i
$664$	23.0059	+	39.8473i	0.0346474	+	0.0600110i
$665$	−52.7288	−	127.995i	−0.0792915	−	0.192473i
$666$	−406.902	+	173.038i	−0.610964	+	0.259816i
$667$			12.0755i			0.0181042i
$668$	47.1260	+	81.6247i	0.0705480	+	0.122193i
$669$	−478.562	−	959.050i	−0.715339	−	1.43356i
$670$	1358.96	+	181.571i	2.02830	+	0.271002i
$671$	−994.773	−	574.333i	−1.48252	−	0.855935i
$672$	407.047	+	24.7607i	0.605725	+	0.0368463i
$673$	820.344	−	473.626i	1.21894	−	0.703753i	0.254245	−	0.967140i	$-0.418173\pi$
$673$	820.344	−	473.626i	1.21894	−	0.703753i	0.964690	+	0.263387i	$0.0848396\pi$
$674$		−	75.1334i		−	0.111474i
$675$	−292.333	+	608.413i	−0.433086	+	0.901353i
$676$	190.268			0.281462
$677$	504.620	+	874.028i	0.745377	+	1.29103i	0.950018	+	0.312194i	$0.101064\pi$
$677$	504.620	+	874.028i	0.745377	+	1.29103i	−0.204641	+	0.978837i	$0.565603\pi$
$678$	−47.1200	+	774.615i	−0.0694985	+	1.14250i
$679$	14.4787	−	25.0778i	0.0213236	−	0.0369335i
$680$	−72.0217	+	539.042i	−0.105914	+	0.792708i
$681$	−345.747	+	172.526i	−0.507705	+	0.253342i
$682$	−1213.13	+	700.401i	−1.77878	+	1.02698i
$683$	−697.555			−1.02131			−0.510655	−	0.859786i	$-0.670597\pi$
$683$	−697.555			−1.02131			−0.510655	+	0.859786i	$0.670597\pi$
$684$	−27.0355	+	35.9268i	−0.0395256	+	0.0525245i
$685$	−90.9424	+	37.4647i	−0.132763	+	0.0546930i
$686$	683.095	−	394.385i	0.995765	−	0.574905i
$687$	633.320	+	418.884i	0.921864	+	0.609729i
$688$	−139.181	−	80.3563i	−0.202298	−	0.116797i
$689$	−90.1996	−	52.0768i	−0.130914	−	0.0755831i
$690$	19.4229	+	3.80756i	0.0281492	+	0.00551820i
$691$	89.5928	+	155.179i	0.129657	+	0.224572i	0.923544	−	0.383493i	$-0.125279\pi$
$691$	89.5928	+	155.179i	0.129657	+	0.224572i	−0.793887	+	0.608066i	$0.791946\pi$
$692$	401.109			0.579638
$693$	689.500	−	916.260i	0.994950	−	1.32216i
$694$	−1535.18			−2.21207
$695$	427.947	+	329.686i	0.615752	+	0.474368i
$696$	−176.682	−	354.075i	−0.253853	−	0.508729i
$697$	−763.228	−	440.650i	−1.09502	−	0.632209i
$698$	628.705	−	1088.95i	0.900723	−	1.56010i
$699$	−17.5517	+	288.536i	−0.0251098	+	0.412785i
$700$	−57.7154	+	212.128i	−0.0824505	+	0.303040i
$701$			211.499i			0.301710i	0.988556	+	0.150855i	$0.0482026\pi$
$701$			211.499i			0.301710i	−0.988556	+	0.150855i	$0.951797\pi$
$702$	−258.030	−	47.5580i	−0.367565	−	0.0677464i
$703$			84.9606i			0.120854i
$704$	523.982	−	302.521i	0.744292	−	0.429717i
$705$	−73.6711	−	215.069i	−0.104498	−	0.305062i
$706$	22.9468	−	39.7449i	0.0325025	−	0.0562960i
$707$	565.327	−	979.175i	0.799614	−	1.38497i
$708$	−84.0879	−	168.514i	−0.118768	−	0.238015i
$709$	216.625	+	375.205i	0.305536	+	0.529203i	0.977380	−	0.211489i	$-0.0678312\pi$
$709$	216.625	+	375.205i	0.305536	+	0.529203i	−0.671845	+	0.740692i	$0.734498\pi$
$710$	−291.883	−	708.521i	−0.411103	−	0.997916i
$711$	−415.365	−	976.740i	−0.584199	−	1.37376i
$712$		−	632.387i		−	0.888184i
$713$	9.62715	+	16.6747i	0.0135023	+	0.0233867i
$714$	−458.557	+	693.303i	−0.642236	+	0.971012i
$715$	−51.2099	+	383.277i	−0.0716223	+	0.536052i
$716$	−3.43349	−	1.98233i	−0.00479538	−	0.00276861i
$717$	−181.042	+	273.721i	−0.252499	+	0.381758i
$718$	−446.750	+	257.931i	−0.622214	+	0.359236i
$719$		−	588.734i		−	0.818824i	−0.912350	−	0.409412i	$-0.865734\pi$
$719$		−	588.734i		−	0.818824i	0.912350	−	0.409412i	$-0.134266\pi$
$720$	−843.795	+	232.859i	−1.17194	+	0.323415i
$721$	1145.86			1.58927
$722$	−395.921	−	685.756i	−0.548368	−	0.949801i
$723$	−841.879	+	420.094i	−1.16442	+	0.581042i
$724$	0.524819	−	0.909013i	0.000724888	−	0.00125554i
$725$	507.342	−	133.851i	0.699782	−	0.184622i
$726$	−88.6151	+	1456.76i	−0.122059	+	2.00656i
$727$	−218.273	+	126.020i	−0.300238	+	0.173343i	−0.642550	−	0.766244i	$-0.722124\pi$
$727$	−218.273	+	126.020i	−0.300238	+	0.173343i	0.342312	+	0.939587i	$0.388790\pi$
$728$	185.897			0.255353
$729$	−681.098	−	259.897i	−0.934291	−	0.356512i
$730$	213.770	+	518.908i	0.292835	+	0.710833i
$731$	123.831	−	71.4941i	0.169400	−	0.0978031i
$732$	−14.4406	+	237.392i	−0.0197276	+	0.324306i
$733$	166.687	+	96.2366i	0.227403	+	0.131291i	0.609374	−	0.792883i	$-0.291421\pi$
$733$	166.687	+	96.2366i	0.227403	+	0.131291i	−0.381970	+	0.924175i	$0.624754\pi$
$734$	−100.444	−	57.9916i	−0.136845	−	0.0790076i
$735$	−2.64036	+	3.02763i	−0.00359232	+	0.00411922i
$736$	5.60170	+	9.70244i	0.00761101	+	0.0131827i
$737$	2182.24			2.96097
$738$	127.402	−	1043.32i	0.172632	−	1.41372i
$739$	811.337			1.09788			0.548942	−	0.835860i	$-0.315031\pi$
$739$	811.337			1.09788			0.548942	+	0.835860i	$0.315031\pi$
$740$	82.3427	−	106.885i	0.111274	−	0.144439i
$741$	−27.8118	+	42.0493i	−0.0375328	+	0.0567467i
$742$	−340.808	−	196.766i	−0.459310	−	0.265183i
$743$	−510.716	+	884.586i	−0.687370	+	1.19056i	0.285315	+	0.958434i	$0.407902\pi$
$743$	−510.716	+	884.586i	−0.687370	+	1.19056i	−0.972686	+	0.232126i	$0.925432\pi$
$744$	−526.259	−	348.073i	−0.707338	−	0.467840i
$745$	−692.555	+	898.968i	−0.929604	+	1.20667i
$746$		−	648.438i		−	0.869219i
$747$	−25.7860	−	60.6363i	−0.0345194	−	0.0811731i
$748$		−	397.899i		−	0.531950i
$749$	−292.658	+	168.966i	−0.390732	+	0.225589i
$750$	−55.3227	−	858.243i	−0.0737637	−	1.14432i
$751$	477.189	−	826.515i	0.635404	−	1.10055i	−0.351025	−	0.936366i	$-0.614167\pi$
$751$	477.189	−	826.515i	0.635404	−	1.10055i	0.986429	−	0.164186i	$-0.0524999\pi$
$752$	147.404	−	255.312i	0.196017	−	0.339511i
$753$	577.596	+	35.1353i	0.767060	+	0.0466604i
$754$	101.977	+	176.630i	0.135249	+	0.234257i
$755$	−258.098	+	106.326i	−0.341851	+	0.140829i
$756$	−233.493	−	43.0355i	−0.308854	−	0.0569253i
$757$		−	1462.32i		−	1.93173i	−0.259040	−	0.965866i	$-0.583406\pi$
$757$		−	1462.32i		−	1.93173i	0.259040	−	0.965866i	$-0.416594\pi$
$758$	−499.504	−	865.166i	−0.658976	−	1.14138i
$759$	31.4453	+	1.91282i	0.0414299	+	0.00252019i
$760$	−16.5046	+	123.527i	−0.0217166	+	0.162536i
$761$	−33.0469	−	19.0796i	−0.0434256	−	0.0250718i	0.478130	−	0.878289i	$-0.341315\pi$
$761$	−33.0469	−	19.0796i	−0.0434256	−	0.0250718i	−0.521556	+	0.853217i	$0.674648\pi$
$762$	299.531	+	600.269i	0.393086	+	0.787754i
$763$	−143.557	+	82.8827i	−0.188148	+	0.108627i
$764$			72.4546i			0.0948359i
$765$	195.947	−	753.745i	0.256140	−	0.985288i
$766$	716.570			0.935470
$767$	−105.582	−	182.874i	−0.137656	−	0.238428i
$768$	−551.458	−	364.740i	−0.718045	−	0.474921i
$769$	−301.249	+	521.778i	−0.391741	+	0.678515i	−0.992679	−	0.120781i	$-0.961460\pi$
$769$	−301.249	+	521.778i	−0.391741	+	0.678515i	0.600939	+	0.799295i	$0.294794\pi$
$770$	−193.490	+	1448.16i	−0.251286	+	1.88073i
$771$	934.608	+	618.158i	1.21220	+	0.801762i
$772$	−39.6666	+	22.9015i	−0.0513816	+	0.0296652i
$773$	394.816			0.510758			0.255379	−	0.966841i	$-0.417800\pi$
$773$	394.816			0.510758			0.255379	+	0.966841i	$0.417800\pi$
$774$	136.262	+	102.539i	0.176049	+	0.132480i
$775$	593.861	−	589.307i	0.766272	−	0.760397i
$776$	−22.5769	+	13.0348i	−0.0290940	+	0.0167974i
$777$	−401.433	+	200.313i	−0.516644	+	0.257803i
$778$	−499.329	−	288.288i	−0.641811	−	0.370550i
$779$	−174.902	−	100.980i	−0.224521	−	0.129628i
$780$	75.7422	−	25.9452i	0.0971054	−	0.0332631i
$781$	−609.840	−	1056.27i	−0.780845	−	1.35246i
$782$	−22.8362			−0.0292024
$783$	189.692	+	533.986i	0.242263	+	0.681975i
$784$	−5.20950			−0.00664478
$785$	208.717	−	270.925i	0.265882	−	0.345127i
$786$	−141.071	−	8.58139i	−0.179480	−	0.0109178i
$787$	713.353	+	411.855i	0.906421	+	0.523322i	0.879278	−	0.476309i	$-0.158026\pi$
$787$	713.353	+	411.855i	0.906421	+	0.523322i	0.0271429	+	0.999632i	$0.491359\pi$
$788$	−95.2845	+	165.038i	−0.120919	+	0.209439i
$789$	−541.111	+	270.012i	−0.685818	+	0.342220i
$790$	1071.29	+	825.308i	1.35606	+	1.04469i
$791$			787.400i			0.995448i
$792$	−950.017	+	404.001i	−1.19952	+	0.510103i
$793$			266.669i			0.336279i
$794$	−471.039	+	271.955i	−0.593248	+	0.342512i
$795$	361.822	+	70.9294i	0.455122	+	0.0892194i
$796$	−169.263	+	293.173i	−0.212642	+	0.368308i
$797$	459.750	−	796.310i	0.576850	−	0.999134i	−0.418988	−	0.907992i	$-0.637615\pi$
$797$	459.750	−	796.310i	0.576850	−	0.999134i	0.995838	−	0.0911420i	$-0.0290517\pi$
$798$	−105.083	+	158.878i	−0.131683	+	0.199095i
$799$	131.148	+	227.155i	0.164140	+	0.284299i
$800$	345.547	−	342.898i	0.431934	−	0.428622i
$801$	−109.771	+	898.937i	−0.137043	+	1.12227i
$802$		−	1231.32i		−	1.53531i
$803$	446.636	+	773.596i	0.556209	+	0.963383i
$804$	−201.740	−	404.293i	−0.250921	−	0.502852i
$805$	19.9053	+	2.65956i	0.0247271	+	0.00330380i
$806$	281.635	+	162.602i	0.349423	+	0.201740i
$807$	−21.9104	−	1.33281i	−0.0271504	−	0.00165156i
$808$	−881.525	+	508.948i	−1.09100	+	0.629887i
$809$		−	1432.18i		−	1.77031i	−0.465300	−	0.885153i	$-0.654054\pi$
$809$		−	1432.18i		−	1.77031i	0.465300	−	0.885153i	$-0.345946\pi$
$810$	918.706	−	136.738i	1.13420	−	0.168813i
$811$	−422.921			−0.521481			−0.260740	−	0.965409i	$-0.583967\pi$
$811$	−422.921			−0.521481			−0.260740	+	0.965409i	$0.583967\pi$
$812$	92.2800	+	159.834i	0.113645	+	0.196839i
$813$	17.0942	−	281.016i	0.0210261	−	0.345653i
$814$	448.349	−	776.563i	0.550797	−	0.954009i
$815$	398.976	+	53.3075i	0.489541	+	0.0654079i
$816$	903.682	−	450.933i	1.10745	−	0.552614i
$817$	28.3774	−	16.3837i	0.0347336	−	0.0200535i
$818$	95.1837			0.116362
$819$	−264.252	−	32.2684i	−0.322652	−	0.0393998i
$820$	122.167	+	296.550i	0.148984	+	0.361647i
$821$	−151.022	+	87.1926i	−0.183949	+	0.106203i	−0.589147	−	0.808026i	$-0.700536\pi$
$821$	−151.022	+	87.1926i	−0.183949	+	0.106203i	0.405198	+	0.914229i	$0.367203\pi$
$822$	112.886	+	74.6635i	0.137330	+	0.0908315i
$823$	777.136	+	448.680i	0.944272	+	0.545176i	0.891297	−	0.453420i	$-0.149796\pi$
$823$	777.136	+	448.680i	0.944272	+	0.545176i	0.0529754	+	0.998596i	$0.483130\pi$
$824$	−893.380	−	515.793i	−1.08420	−	0.625963i
$825$	−268.190	−	1342.35i	−0.325079	−	1.62709i
$826$	−398.930	−	690.967i	−0.482966	−	0.836522i
$827$	−233.440			−0.282273			−0.141137	−	0.989990i	$-0.545076\pi$
$827$	−233.440			−0.282273			−0.141137	+	0.989990i	$0.545076\pi$
$828$	−2.55263	−	6.00255i	−0.00308288	−	0.00724946i
$829$	−990.934			−1.19534			−0.597668	−	0.801744i	$-0.703906\pi$
$829$	−990.934			−1.19534			−0.597668	+	0.801744i	$0.703906\pi$
$830$	66.5058	+	51.2353i	0.0801275	+	0.0617293i
$831$	357.467	+	716.374i	0.430165	+	0.862062i
$832$	−121.645	−	70.2319i	−0.146208	−	0.0844134i
$833$	2.31748	−	4.01400i	0.00278209	−	0.00481873i
$834$	45.1350	−	741.984i	0.0541187	−	0.889669i
$835$	−296.366	−	228.317i	−0.354929	−	0.273433i
$836$		−	91.1829i		−	0.109071i
$837$	687.658	+	586.134i	0.821574	+	0.700280i
$838$			1685.34i			2.01115i
$839$	−301.025	+	173.797i	−0.358790	+	0.207148i	−0.668550	−	0.743667i	$-0.733085\pi$
$839$	−301.025	+	173.797i	−0.358790	+	0.207148i	0.309760	+	0.950815i	$0.399751\pi$
$840$	−622.571	+	213.260i	−0.741156	+	0.253881i
$841$	−200.250	+	346.844i	−0.238110	+	0.412418i
$842$	−17.5647	+	30.4229i	−0.0208607	+	0.0361318i
$843$	8.45756	+	16.9492i	0.0100327	+	0.0201058i
$844$	−225.270	−	390.180i	−0.266908	−	0.462298i
$845$	−698.296	+	287.671i	−0.826386	+	0.340439i
$846$	−188.097	+	249.957i	−0.222337	+	0.295458i
$847$			1480.81i			1.74829i
$848$	239.070	+	414.081i	0.281922	+	0.488303i
$849$	−573.418	+	866.963i	−0.675404	+	1.02116i
$850$	253.129	+	959.445i	0.297799	+	1.12876i
$851$	−10.6740	−	6.16264i	−0.0125429	−	0.00724165i
$852$	−139.313	+	210.631i	−0.163513	+	0.247220i
$853$	1070.74	−	618.192i	1.25526	−	0.724727i	0.283114	−	0.959086i	$-0.408632\pi$
$853$	1070.74	−	618.192i	1.25526	−	0.724727i	0.972150	+	0.234359i	$0.0752991\pi$
$854$			1007.58i			1.17983i
$855$	44.9034	−	172.729i	0.0525186	−	0.202022i
$856$	304.231			0.355411
$857$	−457.353	−	792.158i	−0.533667	−	0.924338i	−0.999227	−	0.0393219i	$-0.987480\pi$
$857$	−457.353	−	792.158i	−0.533667	−	0.924338i	0.465560	−	0.885017i	$-0.345853\pi$
$858$	476.108	−	237.575i	0.554904	−	0.276894i
$859$	−571.510	+	989.884i	−0.665320	+	1.15237i	0.313879	+	0.949463i	$0.398371\pi$
$859$	−571.510	+	989.884i	−0.665320	+	1.15237i	−0.979199	+	0.202905i	$0.934962\pi$
$860$	−51.5789	−	6.89149i	−0.0599755	−	0.00801337i
$861$	64.7526	−	1064.48i	0.0752063	−	1.23633i
$862$	−196.354	+	113.365i	−0.227789	+	0.131514i
$863$	−1228.14			−1.42311			−0.711554	−	0.702632i	$-0.752008\pi$
$863$	−1228.14			−1.42311			−0.711554	+	0.702632i	$0.752008\pi$
$864$	400.124	+	341.051i	0.463107	+	0.394735i
$865$	−1472.10	+	606.446i	−1.70185	+	0.701094i
$866$	−1139.69	+	657.999i	−1.31604	+	0.759814i
$867$	−1.91617	+	31.5003i	−0.00221011	+	0.0363325i
$868$	254.853	+	147.140i	0.293610	+	0.169516i
$869$	1864.09	+	1076.23i	2.14510	+	1.23847i
$870$	−544.153	−	474.549i	−0.625463	−	0.545458i
$871$	−253.309	−	438.745i	−0.290826	−	0.503725i
$872$	149.234			0.171140
$873$	34.3556	−	14.6100i	0.0393535	−	0.0167354i
$874$	−5.23318			−0.00598762
$875$	−108.902	−	865.783i	−0.124459	−	0.989467i
$876$	102.031	−	154.263i	0.116473	−	0.176099i
$877$	−1193.15	−	688.864i	−1.36049	−	0.785478i	−0.370799	−	0.928713i	$-0.620916\pi$
$877$	−1193.15	−	688.864i	−1.36049	−	0.785478i	−0.989689	+	0.143235i	$0.954250\pi$
$878$	−275.040	+	476.383i	−0.313257	+	0.542578i
$879$	−266.965	−	176.573i	−0.303715	−	0.200880i
$880$	1083.35	−	1406.24i	1.23108	−	1.59800i
$881$			1087.45i			1.23434i	0.786831	+	0.617168i	$0.211720\pi$
$881$			1087.45i			1.23434i	−0.786831	+	0.617168i	$0.788280\pi$
$882$	5.48709	+	0.670040i	0.00622119	+	0.000759683i
$883$		−	922.151i		−	1.04434i	−0.852842	−	0.522170i	$-0.825123\pi$
$883$		−	922.151i		−	1.04434i	0.852842	−	0.522170i	$-0.174877\pi$
$884$	−79.9986	+	46.1872i	−0.0904961	+	0.0522480i
$885$	563.389	+	491.324i	0.636597	+	0.555169i
$886$	420.282	−	727.949i	0.474359	−	0.821613i
$887$	−530.496	+	918.846i	−0.598079	+	1.03590i	0.395026	+	0.918670i	$0.370736\pi$
$887$	−530.496	+	918.846i	−0.598079	+	1.03590i	−0.993104	+	0.117233i	$0.962598\pi$
$888$	403.149	+	24.5236i	0.453996	+	0.0276167i
$889$	340.333	+	589.473i	0.382826	+	0.663075i
$890$	−439.508	−	1066.87i	−0.493829	−	1.19873i
$891$	1420.58	−	409.381i	1.59436	−	0.459462i
$892$		−	450.047i		−	0.504537i
$893$	30.0540	+	52.0550i	0.0336551	+	0.0582923i
$894$	1558.65	+	94.8129i	1.74346	+	0.106055i
$895$	15.5983	+	2.08409i	0.0174282	+	0.00232860i
$896$	−930.508	−	537.229i	−1.03851	−	0.599586i
$897$	−3.26552	−	6.54419i	−0.00364049	−	0.00729564i
$898$	1238.72	−	715.175i	1.37942	−	0.796409i
$899$		−	702.372i		−	0.781282i
$900$	−223.897	+	173.782i	−0.248775	+	0.193091i
$901$	−425.407			−0.472150
$902$	1065.77	+	1845.97i	1.18156	+	2.04653i
$903$	144.317	+	95.4529i	0.159820	+	0.105706i
$904$	354.437	−	613.903i	0.392077	−	0.679097i
$905$	−0.551761	+	4.12962i	−0.000609681	+	0.00456312i
$906$	320.373	+	211.898i	0.353612	+	0.233883i
$907$	−1208.95	+	697.990i	−1.33292	+	0.769559i	−0.985745	−	0.168243i	$-0.946191\pi$
$907$	−1208.95	+	697.990i	−1.33292	+	0.769559i	−0.347170	+	0.937802i	$0.612857\pi$
$908$	−162.246			−0.178685
$909$	1341.43	−	570.452i	1.47572	−	0.627560i
$910$	313.617	−	129.198i	0.344634	−	0.141976i
$911$	−1100.06	+	635.123i	−1.20754	+	0.697171i	−0.962220	−	0.272272i	$-0.912225\pi$
$911$	−1100.06	+	635.123i	−1.20754	+	0.697171i	−0.245315	+	0.969443i	$0.578891\pi$
$912$	207.089	−	103.336i	0.227071	−	0.113307i
$913$	115.723	+	66.8128i	0.126750	+	0.0731794i
$914$	771.520	+	445.438i	0.844114	+	0.487350i
$915$	−305.921	−	893.078i	−0.334340	−	0.976041i
$916$	159.414	+	276.114i	0.174033	+	0.301434i
$917$	−143.400			−0.156379
$918$	−1009.83	+	358.730i	−1.10003	+	0.390773i
$919$	269.489			0.293242			0.146621	−	0.989193i	$-0.453160\pi$
$919$	269.489			0.293242			0.146621	+	0.989193i	$0.453160\pi$
$920$	−14.3222	−	11.0336i	−0.0155676	−	0.0119931i
$921$	482.359	+	29.3420i	0.523734	+	0.0318588i
$922$	754.445	+	435.579i	0.818270	+	0.472428i
$923$	−141.578	+	245.220i	−0.153389	+	0.265677i
$924$	430.833	−	214.983i	0.466269	−	0.232666i
$925$	−140.602	+	516.769i	−0.152002	+	0.558669i
$926$		−	876.657i		−	0.946713i
$927$	1180.41	+	888.274i	1.27336	+	0.958225i
$928$		−	408.686i		−	0.440395i
$929$	958.120	−	553.171i	1.03135	−	0.595447i	0.113976	−	0.993484i	$-0.463641\pi$
$929$	958.120	−	553.171i	1.03135	−	0.595447i	0.917370	+	0.398036i	$0.130308\pi$
$930$	−1129.74	−	221.467i	−1.21477	−	0.238136i
$931$	0.531077	−	0.919853i	0.000570438	−	0.000988027i
$932$	−60.6888	+	105.116i	−0.0651167	+	0.112785i
$933$	−28.7545	+	43.4747i	−0.0308194	+	0.0465966i
$934$	40.5375	+	70.2131i	0.0434021	+	0.0751746i
$935$	601.592	+	1460.31i	0.643414	+	1.56183i
$936$	191.501	+	144.108i	0.204596	+	0.153961i
$937$			130.956i			0.139761i	0.997555	+	0.0698805i	$0.0222618\pi$
$937$			130.956i			0.139761i	−0.997555	+	0.0698805i	$0.977738\pi$
$938$	−957.097	−	1657.74i	−1.02036	−	1.76731i
$939$	−466.777	−	935.433i	−0.497100	−	0.996201i
$940$	12.6417	−	94.6157i	0.0134486	−	0.100655i
$941$	−308.082	−	177.871i	−0.327398	−	0.189023i	0.327287	−	0.944925i	$-0.393866\pi$
$941$	−308.082	−	177.871i	−0.327398	−	0.189023i	−0.654685	+	0.755901i	$0.727199\pi$
$942$	−469.735	−	28.5740i	−0.498657	−	0.0303334i
$943$	25.3732	−	14.6492i	0.0269068	−	0.0155347i
$944$			969.397i			1.02690i
$945$	922.002	−	195.081i	0.975663	−	0.206435i
$946$	−345.836			−0.365577
$947$	−511.335	−	885.658i	−0.539953	−	0.935225i	−0.998906	−	0.0467648i	$-0.985109\pi$
$947$	−511.335	−	885.658i	−0.539953	−	0.935225i	0.458953	−	0.888460i	$-0.348224\pi$
$948$	27.0600	−	444.845i	0.0285443	−	0.469246i
$949$	103.689	−	179.595i	0.109261	−	0.189246i
$950$	58.0073	+	219.868i	0.0610603	+	0.231440i
$951$	−796.853	+	397.626i	−0.837911	+	0.418114i
$952$	657.557	−	379.641i	0.690711	−	0.398782i
$953$	475.336			0.498778			0.249389	−	0.968403i	$-0.419770\pi$
$953$	475.336			0.498778			0.249389	+	0.968403i	$0.419770\pi$
$954$	−198.550	−	466.893i	−0.208123	−	0.489406i
$955$	−109.546	−	265.913i	−0.114708	−	0.278443i
$956$	−119.336	+	68.8988i	−0.124829	+	0.0720699i
$957$	−958.515	−	633.971i	−1.00158	−	0.662456i
$958$	−1149.51	−	663.670i	−1.19991	−	0.692766i
$959$	118.925	+	68.6616i	0.124010	+	0.0715971i
$960$	487.961	+	95.6571i	0.508293	+	0.0996428i
$961$	−79.4631	−	137.634i	−0.0826880	−	0.143220i
$962$	−208.173			−0.216397
$963$	−432.465	−	52.8092i	−0.449081	−	0.0548382i
$964$	−395.063			−0.409816
$965$	110.954	−	144.023i	0.114978	−	0.149247i
$966$	−12.3384	−	24.7264i	−0.0127726	−	0.0255967i
$967$	−1084.58	−	626.185i	−1.12160	−	0.647554i	−0.179788	−	0.983705i	$-0.557541\pi$
$967$	−1084.58	−	626.185i	−1.12160	−	0.647554i	−0.941808	+	0.336151i	$0.890875\pi$
$968$	666.565	−	1154.52i	0.688600	−	1.19269i
$969$	−12.5027	+	205.535i	−0.0129027	+	0.212110i
$970$	−29.0292	+	37.6812i	−0.0299270	+	0.0388466i
$971$			280.624i			0.289005i	0.989504	+	0.144502i	$0.0461581\pi$
$971$			280.624i			0.289005i	−0.989504	+	0.144502i	$0.953842\pi$
$972$	−207.172	−	225.338i	−0.213139	−	0.231829i
$973$		−	754.231i		−	0.775160i
$974$	−843.669	+	487.093i	−0.866190	+	0.500095i
$975$	−238.752	+	209.737i	−0.244873	+	0.215115i
$976$	612.100	−	1060.19i	0.627152	−	1.08626i
$977$	165.797	−	287.169i	0.169700	−	0.293929i	−0.768614	−	0.639712i	$-0.779053\pi$
$977$	165.797	−	287.169i	0.169700	−	0.293929i	0.938314	+	0.345783i	$0.112387\pi$
$978$	−247.306	−	495.609i	−0.252870	−	0.506758i
$979$	−918.278	−	1590.50i	−0.937975	−	1.62462i
$980$	−1.55963	+	0.642507i	−0.00159146	+	0.000655619i
$981$	−212.136	−	25.9044i	−0.216245	−	0.0264061i
$982$			894.436i			0.910831i
$983$	6.49145	+	11.2435i	0.00660372	+	0.0114380i	0.869308	−	0.494270i	$-0.164565\pi$
$983$	6.49145	+	11.2435i	0.00660372	+	0.0114380i	−0.862705	+	0.505708i	$0.831231\pi$
$984$	−529.647	+	800.785i	−0.538259	+	0.813806i
$985$	100.176	−	749.762i	0.101702	−	0.761179i
$986$	721.432	+	416.519i	0.731675	+	0.422433i
$987$	−175.097	+	264.734i	−0.177404	+	0.268221i
$988$	−18.3326	+	10.5843i	−0.0185552	+	0.0107129i
$989$			4.75358i			0.00480645i
$990$	−1321.95	+	1341.83i	−1.33530	+	1.35538i
$991$	−1366.83			−1.37924			−0.689619	−	0.724172i	$-0.742222\pi$
$991$	−1366.83			−1.37924			−0.689619	+	0.724172i	$0.742222\pi$
$992$	−325.823	−	564.342i	−0.328451	−	0.568893i
$993$	544.102	−	271.505i	0.547938	−	0.273418i
$994$	−534.934	+	926.532i	−0.538163	+	0.932125i
$995$	177.953	−	1331.88i	0.178847	−	1.33857i
$996$	1.67989	−	27.6161i	0.00168664	−	0.0277270i
$997$	890.111	−	513.906i	0.892789	−	0.515452i	0.0179352	−	0.999839i	$-0.494291\pi$
$997$	890.111	−	513.906i	0.892789	−	0.515452i	0.874854	+	0.484387i	$0.160957\pi$
$998$	1416.29			1.41913
$999$	−568.818	−	104.840i	−0.569388	−	0.104945i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.3.h.a.14.8	yes	20
3.2	odd	2		135.3.h.a.44.3		20
5.2	odd	4		225.3.j.e.176.3		20
5.3	odd	4		225.3.j.e.176.8		20
5.4	even	2	inner	45.3.h.a.14.3	✓	20
9.2	odd	6	inner	45.3.h.a.29.3	yes	20
9.4	even	3		405.3.d.a.404.6		20
9.5	odd	6		405.3.d.a.404.15		20
9.7	even	3		135.3.h.a.89.8		20
15.2	even	4		675.3.j.e.476.8		20
15.8	even	4		675.3.j.e.476.3		20
15.14	odd	2		135.3.h.a.44.8		20
45.2	even	12		225.3.j.e.101.3		20
45.4	even	6		405.3.d.a.404.16		20
45.7	odd	12		675.3.j.e.251.8		20
45.14	odd	6		405.3.d.a.404.5		20
45.29	odd	6	inner	45.3.h.a.29.8	yes	20
45.34	even	6		135.3.h.a.89.3		20
45.38	even	12		225.3.j.e.101.8		20
45.43	odd	12		675.3.j.e.251.3		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.3.h.a.14.3	✓	20	5.4	even	2	inner
45.3.h.a.14.8	yes	20	1.1	even	1	trivial
45.3.h.a.29.3	yes	20	9.2	odd	6	inner
45.3.h.a.29.8	yes	20	45.29	odd	6	inner
135.3.h.a.44.3		20	3.2	odd	2
135.3.h.a.44.8		20	15.14	odd	2
135.3.h.a.89.3		20	45.34	even	6
135.3.h.a.89.8		20	9.7	even	3
225.3.j.e.101.3		20	45.2	even	12
225.3.j.e.101.8		20	45.38	even	12
225.3.j.e.176.3		20	5.2	odd	4
225.3.j.e.176.8		20	5.3	odd	4
405.3.d.a.404.5		20	45.14	odd	6
405.3.d.a.404.6		20	9.4	even	3
405.3.d.a.404.15		20	9.5	odd	6
405.3.d.a.404.16		20	45.4	even	6
675.3.j.e.251.3		20	45.43	odd	12
675.3.j.e.251.8		20	45.7	odd	12
675.3.j.e.476.3		20	15.8	even	4
675.3.j.e.476.8		20	15.2	even	4

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:	\( N \)	\(=\)	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	45.h (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.14670 + 1.98614i) q^{2} +(-0.182154 + 2.99446i) q^{3} +(-0.629835 + 1.09091i) q^{4} +(0.662169 - 4.95596i) q^{5} +(-6.15630 + 3.07197i) q^{6} +(-6.04559 + 3.49042i) q^{7} +6.28466 q^{8} +(-8.93364 - 1.09091i) q^{9} +(10.6025 - 4.36783i) q^{10} +(15.8064 - 9.12584i) q^{11} +(-3.15195 - 2.08473i) q^{12} +(-3.66955 - 2.11862i) q^{13} +(-13.8649 - 8.00492i) q^{14} +(14.7198 + 2.88559i) q^{15} +(9.72596 + 16.8458i) q^{16} -17.3066 q^{17} +(-8.07750 - 18.9944i) q^{18} -3.96601 q^{19} +(4.98943 + 3.84380i) q^{20} +(-9.35072 - 18.7391i) q^{21} +(36.2504 + 20.9292i) q^{22} +(0.287675 - 0.498269i) q^{23} +(-1.14478 + 18.8192i) q^{24} +(-24.1231 - 6.56337i) q^{25} -9.71765i q^{26} +(4.89398 - 26.5528i) q^{27} -8.79356i q^{28} +(-18.1762 + 10.4940i) q^{29} +(11.1480 + 32.5445i) q^{30} +(-16.7326 + 28.9818i) q^{31} +(-9.73615 + 16.8635i) q^{32} +(24.4478 + 48.9941i) q^{33} +(-19.8455 - 34.3734i) q^{34} +(13.2952 + 32.2729i) q^{35} +(6.81680 - 9.05867i) q^{36} -21.4222i q^{37} +(-4.54782 - 7.87705i) q^{38} +(7.01254 - 10.6024i) q^{39} +(4.16151 - 31.1465i) q^{40} +(44.1003 + 25.4613i) q^{41} +(26.4960 - 40.0599i) q^{42} +(-7.15514 + 4.13102i) q^{43} +22.9911i q^{44} +(-11.3221 + 43.5524i) q^{45} +1.31951 q^{46} +(-7.57789 - 13.1253i) q^{47} +(-52.2159 + 26.0555i) q^{48} +(-0.133907 + 0.231934i) q^{49} +(-14.6261 - 55.4380i) q^{50} +(3.15247 - 51.8241i) q^{51} +(4.62242 - 2.66876i) q^{52} +24.5806 q^{53} +(58.3494 - 20.7279i) q^{54} +(-34.7608 - 84.3789i) q^{55} +(-37.9945 + 21.9361i) q^{56} +(0.722424 - 11.8761i) q^{57} +(-41.6853 - 24.0670i) q^{58} +(43.1589 + 24.9178i) q^{59} +(-12.4190 + 14.2405i) q^{60} +(-31.4674 - 54.5031i) q^{61} -76.7492 q^{62} +(57.8168 - 24.5870i) q^{63} +33.1499 q^{64} +(-12.9296 + 16.7833i) q^{65} +(-69.2749 + 104.738i) q^{66} +(103.545 + 59.7818i) q^{67} +(10.9003 - 18.8799i) q^{68} +(1.43965 + 0.952196i) q^{69} +(-48.8530 + 63.4134i) q^{70} -66.8256i q^{71} +(-56.1449 - 6.85598i) q^{72} +48.9419i q^{73} +(42.5475 - 24.5648i) q^{74} +(24.0479 - 71.0401i) q^{75} +(2.49793 - 4.32654i) q^{76} +(-63.7061 + 110.342i) q^{77} +(29.0992 + 1.77011i) q^{78} +(58.9661 + 102.132i) q^{79} +(89.9276 - 37.0466i) q^{80} +(78.6198 + 19.4915i) q^{81} +116.786i q^{82} +(3.66063 + 6.34040i) q^{83} +(26.3320 + 1.60178i) q^{84} +(-11.4599 + 85.7710i) q^{85} +(-16.4096 - 9.47408i) q^{86} +(-28.1132 - 56.3396i) q^{87} +(99.3381 - 57.3529i) q^{88} -100.624i q^{89} +(-99.4842 + 27.4543i) q^{90} +29.5794 q^{91} +(0.362376 + 0.627654i) q^{92} +(-83.7371 - 55.3845i) q^{93} +(17.3791 - 30.1015i) q^{94} +(-2.62617 + 19.6554i) q^{95} +(-48.7237 - 32.2263i) q^{96} +(-3.59238 + 2.07406i) q^{97} -0.614205 q^{98} +(-151.164 + 64.2837i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 18 q^{4} - 12 q^{5} + 12 q^{6} - 18 q^{9} + 4 q^{10} - 24 q^{11} + 30 q^{14} + 24 q^{15} - 26 q^{16} - 8 q^{19} + 144 q^{20} - 96 q^{21} - 102 q^{24} + 2 q^{25} - 114 q^{29} - 48 q^{30} + 28 q^{31}+ \cdots - 468 q^{99}+O(q^{100}) \) 20 * q - 18 * q^4 - 12 * q^5 + 12 * q^6 - 18 * q^9 + 4 * q^10 - 24 * q^11 + 30 * q^14 + 24 * q^15 - 26 * q^16 - 8 * q^19 + 144 * q^20 - 96 * q^21 - 102 * q^24 + 2 * q^25 - 114 * q^29 - 48 * q^30 + 28 * q^31 - 4 * q^34 + 432 * q^36 + 240 * q^39 - 34 * q^40 + 102 * q^41 - 162 * q^45 + 116 * q^46 - 40 * q^49 - 408 * q^50 - 156 * q^51 - 270 * q^54 + 36 * q^55 - 618 * q^56 + 120 * q^59 + 330 * q^60 - 50 * q^61 + 140 * q^64 + 492 * q^65 - 768 * q^66 + 162 * q^69 - 54 * q^70 + 504 * q^74 + 276 * q^75 - 96 * q^76 - 128 * q^79 + 846 * q^81 + 450 * q^84 - 74 * q^85 + 1488 * q^86 - 990 * q^90 - 288 * q^91 + 218 * q^94 - 762 * q^95 - 474 * q^96 - 468 * q^99

Introduction

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