LMFDB - Embedded newform 45.3.k.a.22.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [45,3,Mod(7,45)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(45, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([8, 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("45.7"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 45 = 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	45.k (of order $12$, degree $4$, 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:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			22.9
Character	$\chi$	$=$	45.22
Dual form			45.3.k.a.43.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.863931 - 3.22423i) q^{2} +(-2.79645 - 1.08621i) q^{3} +(-6.18520 - 3.57103i) q^{4} +(3.34831 + 3.71333i) q^{5} +(-5.91814 + 8.07800i) q^{6} +(2.35787 - 8.79970i) q^{7} +(-7.41620 + 7.41620i) q^{8} +(6.64028 + 6.07508i) q^{9} +(14.8654 - 7.58766i) q^{10} +(1.02371 + 1.77311i) q^{11} +(13.4177 + 16.7046i) q^{12} +(-1.12075 - 4.18269i) q^{13} +(-26.3352 - 15.2047i) q^{14} +(-5.32991 - 14.0211i) q^{15} +(3.22036 + 5.57783i) q^{16} +(17.1585 + 17.1585i) q^{17} +(25.3242 - 16.1614i) q^{18} +18.6363i q^{19} +(-7.44954 - 34.9246i) q^{20} +(-16.1520 + 22.0468i) q^{21} +(6.60133 - 1.76882i) q^{22} +(3.08350 + 11.5078i) q^{23} +(28.7946 - 12.6835i) q^{24} +(-2.57768 + 24.8668i) q^{25} -14.4542 q^{26} +(-11.9704 - 24.2014i) q^{27} +(-46.0079 + 46.0079i) q^{28} +(-19.4918 + 11.2536i) q^{29} +(-49.8121 + 5.07159i) q^{30} +(11.9368 - 20.6752i) q^{31} +(-19.7565 + 5.29373i) q^{32} +(-0.936770 - 6.07038i) q^{33} +(70.1467 - 40.4992i) q^{34} +(40.5711 - 20.7085i) q^{35} +(-19.3772 - 61.2882i) q^{36} +(-33.2840 - 33.2840i) q^{37} +(60.0877 + 16.1005i) q^{38} +(-1.40917 + 12.9141i) q^{39} +(-52.3705 - 2.70711i) q^{40} +(2.15756 - 3.73700i) q^{41} +(57.1297 + 71.1247i) q^{42} +(-30.4181 - 8.15051i) q^{43} -14.6227i q^{44} +(-0.325090 + 44.9988i) q^{45} +39.7677 q^{46} +(0.224807 - 0.838990i) q^{47} +(-2.94688 - 19.0961i) q^{48} +(-29.4398 - 16.9971i) q^{49} +(77.9493 + 29.7942i) q^{50} +(-29.3451 - 66.6207i) q^{51} +(-8.00445 + 29.8730i) q^{52} +(-3.33316 + 3.33316i) q^{53} +(-88.3727 + 17.6870i) q^{54} +(-3.15647 + 9.73828i) q^{55} +(47.7739 + 82.7467i) q^{56} +(20.2430 - 52.1155i) q^{57} +(19.4446 + 72.5684i) q^{58} +(66.3254 + 38.2930i) q^{59} +(-17.1033 + 105.757i) q^{60} +(35.3623 + 61.2493i) q^{61} +(-56.3490 - 56.3490i) q^{62} +(69.1158 - 44.1082i) q^{63} +94.0358i q^{64} +(11.7791 - 18.1667i) q^{65} +(-20.3816 - 2.22403i) q^{66} +(-20.8965 + 5.59919i) q^{67} +(-44.8553 - 167.402i) q^{68} +(3.87703 - 35.5302i) q^{69} +(-31.7185 - 148.701i) q^{70} -28.6105 q^{71} +(-94.2997 + 4.19166i) q^{72} +(48.1316 - 48.1316i) q^{73} +(-136.071 + 78.5604i) q^{74} +(34.2189 - 66.7388i) q^{75} +(66.5507 - 115.269i) q^{76} +(18.0166 - 4.82753i) q^{77} +(40.4205 + 15.7004i) q^{78} +(0.201686 - 0.116444i) q^{79} +(-9.92959 + 30.6346i) q^{80} +(7.18677 + 80.6805i) q^{81} +(-10.1850 - 10.1850i) q^{82} +(-153.477 - 41.1240i) q^{83} +(178.633 - 78.6845i) q^{84} +(-6.26330 + 121.167i) q^{85} +(-52.5583 + 91.0337i) q^{86} +(66.7316 - 10.2979i) q^{87} +(-20.7418 - 5.55774i) q^{88} -103.385i q^{89} +(144.806 + 39.9240i) q^{90} -39.4490 q^{91} +(22.0225 - 82.1891i) q^{92} +(-55.8384 + 44.8512i) q^{93} +(-2.51088 - 1.44966i) q^{94} +(-69.2027 + 62.4000i) q^{95} +(60.9981 + 6.65606i) q^{96} +(-18.6837 + 69.7287i) q^{97} +(-80.2366 + 80.2366i) q^{98} +(-3.97409 + 17.9931i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 2 q^{2} - 6 q^{3} - 2 q^{5} - 24 q^{6} - 2 q^{7} - 24 q^{8} - 8 q^{10} + 8 q^{11} - 30 q^{12} - 2 q^{13} - 30 q^{15} + 28 q^{16} + 28 q^{17} + 48 q^{18} - 114 q^{20} + 12 q^{21} + 14 q^{22} + 82 q^{23}+ \cdots - 1876 q^{98}+O(q^{100}) $ 40 * q - 2 * q^2 - 6 * q^3 - 2 * q^5 - 24 * q^6 - 2 * q^7 - 24 * q^8 - 8 * q^10 + 8 * q^11 - 30 * q^12 - 2 * q^13 - 30 * q^15 + 28 * q^16 + 28 * q^17 + 48 * q^18 - 114 * q^20 + 12 * q^21 + 14 * q^22 + 82 * q^23 - 8 * q^25 - 112 * q^26 - 198 * q^27 - 88 * q^28 + 162 * q^30 - 4 * q^31 - 14 * q^32 + 96 * q^33 + 352 * q^35 + 264 * q^36 - 92 * q^37 + 330 * q^38 + 30 * q^40 - 28 * q^41 + 498 * q^42 - 2 * q^43 - 72 * q^45 - 136 * q^46 + 64 * q^47 - 510 * q^48 - 458 * q^50 - 396 * q^51 - 74 * q^52 - 608 * q^53 + 224 * q^55 - 192 * q^56 - 114 * q^57 + 30 * q^58 - 798 * q^60 + 92 * q^61 - 100 * q^62 + 24 * q^63 - 326 * q^65 + 588 * q^66 - 80 * q^67 + 626 * q^68 - 102 * q^70 + 248 * q^71 - 162 * q^72 - 8 * q^73 + 810 * q^75 - 96 * q^76 + 338 * q^77 + 1062 * q^78 + 1444 * q^80 + 204 * q^81 + 104 * q^82 + 370 * q^83 - 98 * q^85 - 328 * q^86 + 534 * q^87 - 210 * q^88 + 462 * q^90 + 152 * q^91 + 388 * q^92 - 1062 * q^93 - 360 * q^95 - 876 * q^96 + 292 * q^97 - 1876 * q^98

Character values

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

$n$	$11$	$37$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	0.863931	−	3.22423i	0.431965	−	1.61212i	−0.316261	−	0.948672i	$-0.602427\pi$
$2$	0.863931	−	3.22423i	0.431965	−	1.61212i	0.748226	−	0.663444i	$-0.230906\pi$
$3$	−2.79645	−	1.08621i	−0.932151	−	0.362071i
$3$	−2.79645	−	1.08621i	−0.932151	−	0.362071i
$4$	−6.18520	−	3.57103i	−1.54630	−	0.892757i
$5$	3.34831	+	3.71333i	0.669661	+	0.742667i
$5$	3.34831	+	3.71333i	0.669661	+	0.742667i
$6$	−5.91814	+	8.07800i	−0.986357	+	1.34633i
$7$	2.35787	−	8.79970i	0.336839	−	1.25710i	−0.565023	−	0.825075i	$-0.691133\pi$
$7$	2.35787	−	8.79970i	0.336839	−	1.25710i	0.901862	−	0.432024i	$-0.142201\pi$
$8$	−7.41620	+	7.41620i	−0.927025	+	0.927025i
$9$	6.64028	+	6.07508i	0.737809	+	0.675009i
$10$	14.8654	−	7.58766i	1.48654	−	0.758766i
$11$	1.02371	+	1.77311i	0.0930642	+	0.161192i	0.908799	−	0.417234i	$-0.137000\pi$
$11$	1.02371	+	1.77311i	0.0930642	+	0.161192i	−0.815735	+	0.578426i	$0.803667\pi$
$12$	13.4177	+	16.7046i	1.11814	+	1.39205i
$13$	−1.12075	−	4.18269i	−0.0862115	−	0.321746i	0.909329	−	0.416077i	$-0.136595\pi$
$13$	−1.12075	−	4.18269i	−0.0862115	−	0.321746i	−0.995541	+	0.0943314i	$0.969929\pi$
$14$	−26.3352	−	15.2047i	−1.88109	−	1.08605i
$15$	−5.32991	−	14.0211i	−0.355327	−	0.934742i
$16$	3.22036	+	5.57783i	0.201273	+	0.348615i
$17$	17.1585	+	17.1585i	1.00932	+	1.00932i	0.999956	+	0.00936716i	$0.00298170\pi$
$17$	17.1585	+	17.1585i	1.00932	+	1.00932i	0.00936716	+	0.999956i	$0.497018\pi$
$18$	25.3242	−	16.1614i	1.40690	−	0.897854i
$19$			18.6363i			0.980857i	0.871481	+	0.490428i	$0.163160\pi$
$19$			18.6363i			0.980857i	−0.871481	+	0.490428i	$0.836840\pi$
$20$	−7.44954	−	34.9246i	−0.372477	−	1.74623i
$21$	−16.1520	+	22.0468i	−0.769143	+	1.04985i
$22$	6.60133	−	1.76882i	0.300061	−	0.0804010i
$23$	3.08350	+	11.5078i	0.134065	+	0.500338i	1.00000		0.000180980i	$5.76078e-5\pi$
$23$	3.08350	+	11.5078i	0.134065	+	0.500338i	−0.865935	+	0.500157i	$0.833276\pi$
$24$	28.7946	−	12.6835i	1.19978	−	0.528478i
$25$	−2.57768	+	24.8668i	−0.103107	+	0.994670i
$26$	−14.4542			−0.555932
$27$	−11.9704	−	24.2014i	−0.443348	−	0.896349i
$28$	−46.0079	+	46.0079i	−1.64314	+	1.64314i
$29$	−19.4918	+	11.2536i	−0.672131	+	0.388055i	−0.796883	−	0.604133i	$-0.793520\pi$
$29$	−19.4918	+	11.2536i	−0.672131	+	0.388055i	0.124753	+	0.992188i	$0.460186\pi$
$30$	−49.8121	+	5.07159i	−1.66040	+	0.169053i
$31$	11.9368	−	20.6752i	0.385059	−	0.666941i	−0.606719	−	0.794917i	$-0.707514\pi$
$31$	11.9368	−	20.6752i	0.385059	−	0.666941i	0.991777	+	0.127975i	$0.0408478\pi$
$32$	−19.7565	+	5.29373i	−0.617389	+	0.165429i
$33$	−0.936770	−	6.07038i	−0.0283870	−	0.183951i
$34$	70.1467	−	40.4992i	2.06314	−	1.19115i
$35$	40.5711	−	20.7085i	1.15917	−	0.591672i
$36$	−19.3772	−	61.2882i	−0.538256	−	1.70245i
$37$	−33.2840	−	33.2840i	−0.899568	−	0.899568i	0.0958294	−	0.995398i	$-0.469450\pi$
$37$	−33.2840	−	33.2840i	−0.899568	−	0.899568i	−0.995398	+	0.0958294i	$0.969450\pi$
$38$	60.0877	+	16.1005i	1.58126	+	0.423696i
$39$	−1.40917	+	12.9141i	−0.0361326	+	0.331130i
$40$	−52.3705	−	2.70711i	−1.30926	−	0.0676777i
$41$	2.15756	−	3.73700i	0.0526234	−	0.0911464i	−0.838514	−	0.544880i	$-0.816575\pi$
$41$	2.15756	−	3.73700i	0.0526234	−	0.0911464i	0.891137	+	0.453734i	$0.149908\pi$
$42$	57.1297	+	71.1247i	1.36023	+	1.69345i
$43$	−30.4181	−	8.15051i	−0.707398	−	0.189547i	−0.112856	−	0.993611i	$-0.536000\pi$
$43$	−30.4181	−	8.15051i	−0.707398	−	0.189547i	−0.594542	+	0.804065i	$0.702667\pi$
$44$		−	14.6227i		−	0.332335i
$45$	−0.325090	+	44.9988i	−0.00722421	+	0.999974i
$46$	39.7677			0.864514
$47$	0.224807	−	0.838990i	0.00478312	−	0.0178509i	−0.963493	−	0.267733i	$-0.913725\pi$
$47$	0.224807	−	0.838990i	0.00478312	−	0.0178509i	0.968276	+	0.249883i	$0.0803920\pi$
$48$	−2.94688	−	19.0961i	−0.0613933	−	0.397836i
$49$	−29.4398	−	16.9971i	−0.600813	−	0.346880i
$50$	77.9493	+	29.7942i	1.55899	+	0.595884i
$51$	−29.3451	−	66.6207i	−0.575395	−	1.30629i
$52$	−8.00445	+	29.8730i	−0.153932	+	0.574481i
$53$	−3.33316	+	3.33316i	−0.0628899	+	0.0628899i	−0.737852	−	0.674962i	$-0.764160\pi$
$53$	−3.33316	+	3.33316i	−0.0628899	+	0.0628899i	0.674962	+	0.737852i	$0.264160\pi$
$54$	−88.3727	+	17.6870i	−1.63653	+	0.327537i
$55$	−3.15647	+	9.73828i	−0.0573904	+	0.177060i
$56$	47.7739	+	82.7467i	0.853105	+	1.47762i
$57$	20.2430	−	52.1155i	0.355140	−	0.914306i
$58$	19.4446	+	72.5684i	0.335252	+	1.25118i
$59$	66.3254	+	38.2930i	1.12416	+	0.649033i	0.942459	−	0.334321i	$-0.108507\pi$
$59$	66.3254	+	38.2930i	1.12416	+	0.649033i	0.181699	+	0.983354i	$0.441840\pi$
$60$	−17.1033	+	105.757i	−0.285055	+	1.76261i
$61$	35.3623	+	61.2493i	0.579710	+	1.00409i	0.995512	+	0.0946322i	$0.0301675\pi$
$61$	35.3623	+	61.2493i	0.579710	+	1.00409i	−0.415802	+	0.909455i	$0.636499\pi$
$62$	−56.3490	−	56.3490i	−0.908855	−	0.908855i
$63$	69.1158	−	44.1082i	1.09708	−	0.700131i
$64$			94.0358i			1.46931i
$65$	11.7791	−	18.1667i	0.181217	−	0.279487i
$66$	−20.3816	−	2.22403i	−0.308813	−	0.0336974i
$67$	−20.8965	+	5.59919i	−0.311888	+	0.0835700i	−0.411368	−	0.911470i	$-0.634949\pi$
$67$	−20.8965	+	5.59919i	−0.311888	+	0.0835700i	0.0994800	+	0.995040i	$0.468282\pi$
$68$	−44.8553	−	167.402i	−0.659637	−	2.46180i
$69$	3.87703	−	35.5302i	0.0561888	−	0.514931i
$70$	−31.7185	−	148.701i	−0.453121	−	2.12430i
$71$	−28.6105			−0.402965			−0.201483	−	0.979492i	$-0.564576\pi$
$71$	−28.6105			−0.402965			−0.201483	+	0.979492i	$0.564576\pi$
$72$	−94.2997	+	4.19166i	−1.30972	+	0.0582175i
$73$	48.1316	−	48.1316i	0.659336	−	0.659336i	−0.295887	−	0.955223i	$-0.595615\pi$
$73$	48.1316	−	48.1316i	0.659336	−	0.659336i	0.955223	+	0.295887i	$0.0956151\pi$
$74$	−136.071	+	78.5604i	−1.83879	+	1.06163i
$75$	34.2189	−	66.7388i	0.456253	−	0.889850i
$76$	66.5507	−	115.269i	0.875667	−	1.51670i
$77$	18.0166	−	4.82753i	0.233982	−	0.0626953i
$78$	40.4205	+	15.7004i	0.518212	+	0.201287i
$79$	0.201686	−	0.116444i	0.00255299	−	0.00147397i	−0.498723	−	0.866761i	$-0.666197\pi$
$79$	0.201686	−	0.116444i	0.00255299	−	0.00147397i	0.501276	+	0.865287i	$0.332864\pi$
$80$	−9.92959	+	30.6346i	−0.124120	+	0.382932i
$81$	7.18677	+	80.6805i	0.0887255	+	0.996056i
$82$	−10.1850	−	10.1850i	−0.124207	−	0.124207i
$83$	−153.477	−	41.1240i	−1.84912	−	0.495470i	−0.849630	−	0.527380i	$-0.823175\pi$
$83$	−153.477	−	41.1240i	−1.84912	−	0.495470i	−0.999491	+	0.0319094i	$0.989841\pi$
$84$	178.633	−	78.6845i	2.12658	−	0.936720i
$85$	−6.26330	+	121.167i	−0.0736859	+	1.42550i
$86$	−52.5583	+	91.0337i	−0.611143	+	1.05853i
$87$	66.7316	−	10.2979i	0.767030	−	0.118367i
$88$	−20.7418	−	5.55774i	−0.235702	−	0.0631561i
$89$		−	103.385i		−	1.16163i	−0.814035	−	0.580816i	$-0.802734\pi$
$89$		−	103.385i		−	1.16163i	0.814035	−	0.580816i	$-0.197266\pi$
$90$	144.806	+	39.9240i	1.60895	+	0.443600i
$91$	−39.4490			−0.433506
$92$	22.0225	−	82.1891i	0.239375	−	0.893360i
$93$	−55.8384	+	44.8512i	−0.600413	+	0.482271i
$94$	−2.51088	−	1.44966i	−0.0267115	−	0.0154219i
$95$	−69.2027	+	62.4000i	−0.728450	+	0.656842i
$96$	60.9981	+	6.65606i	0.635397	+	0.0693340i
$97$	−18.6837	+	69.7287i	−0.192616	+	0.718852i	0.800255	+	0.599660i	$0.204697\pi$
$97$	−18.6837	+	69.7287i	−0.192616	+	0.718852i	−0.992871	+	0.119193i	$0.961969\pi$
$98$	−80.2366	+	80.2366i	−0.818741	+	0.818741i
$99$	−3.97409	+	17.9931i	−0.0401424	+	0.181748i
$100$	104.743	−	144.601i	1.04743	−	1.44601i
$101$	−31.0086	−	53.7085i	−0.307016	−	0.531767i	0.670692	−	0.741736i	$-0.265997\pi$
$101$	−31.0086	−	53.7085i	−0.307016	−	0.531767i	−0.977708	+	0.209969i	$0.932664\pi$
$102$	−240.153	+	37.0599i	−2.35444	+	0.363332i
$103$	−13.6798	−	51.0537i	−0.132813	−	0.495667i	0.867184	−	0.497988i	$-0.165928\pi$
$103$	−13.6798	−	51.0537i	−0.132813	−	0.495667i	−0.999997	+	0.00232157i	$0.999261\pi$
$104$	39.3314	+	22.7080i	0.378186	+	0.218346i
$105$	−135.949	+	13.8416i	−1.29475	+	0.131824i
$106$	7.86727	+	13.6265i	0.0742195	+	0.128552i
$107$	84.3909	+	84.3909i	0.788700	+	0.788700i	0.981281	−	0.192581i	$-0.0616859\pi$
$107$	84.3909	+	84.3909i	0.788700	+	0.788700i	−0.192581	+	0.981281i	$0.561686\pi$
$108$	−12.3846	+	192.437i	−0.114672	+	1.78183i
$109$			102.481i			0.940190i	0.882616	+	0.470095i	$0.155780\pi$
$109$			102.481i			0.940190i	−0.882616	+	0.470095i	$0.844220\pi$
$110$	28.6715	+	18.5904i	0.260650	+	0.169004i
$111$	56.9237	+	129.231i	0.512826	+	1.16424i
$112$	56.6764	−	15.1864i	0.506040	−	0.135593i
$113$	−10.5178	−	39.2529i	−0.0930777	−	0.347371i	0.903643	−	0.428286i	$-0.140882\pi$
$113$	−10.5178	−	39.2529i	−0.0930777	−	0.347371i	−0.996721	+	0.0809152i	$0.974216\pi$
$114$	−150.544	−	110.292i	−1.32056	−	0.967475i
$115$	−32.4077	+	49.9816i	−0.281806	+	0.434622i
$116$	160.747			1.38575
$117$	17.9681	−	34.5829i	0.153574	−	0.295580i
$118$	180.766	−	180.766i	1.53192	−	1.53192i
$119$	191.447	−	110.532i	1.60880	−	0.928840i
$120$	143.511	+	64.4558i	1.19593	+	0.537132i
$121$	58.4041	−	101.159i	0.482678	−	0.836023i
$122$	228.033	−	61.1012i	1.86912	−	0.500829i
$123$	−10.0927	+	8.10678i	−0.0820544	+	0.0659088i
$124$	−147.663	+	85.2534i	−1.19083	+	0.687528i
$125$	−100.969	+	73.6897i	−0.807755	+	0.589518i
$126$	−82.5039	−	260.952i	−0.654793	−	2.07105i
$127$	−81.3527	−	81.3527i	−0.640572	−	0.640572i	0.310124	−	0.950696i	$-0.399630\pi$
$127$	−81.3527	−	81.3527i	−0.640572	−	0.640572i	−0.950696	+	0.310124i	$0.899630\pi$
$128$	224.167	+	60.0655i	1.75131	+	0.469261i
$129$	76.2096	+	55.8331i	0.590772	+	0.432814i
$130$	−48.3972	−	53.6734i	−0.372286	−	0.412872i
$131$	−41.3420	+	71.6064i	−0.315588	+	0.546614i	−0.979562	−	0.201141i	$-0.935535\pi$
$131$	−41.3420	+	71.6064i	−0.315588	+	0.546614i	0.663975	+	0.747755i	$0.268868\pi$
$132$	−15.8834	+	40.8918i	−0.120329	+	0.309786i
$133$	163.994	+	43.9420i	1.23303	+	0.330391i
$134$			72.2124i			0.538899i
$135$	49.7874	−	125.484i	0.368795	−	0.929511i
$136$	−254.502			−1.87134
$137$	−40.3630	+	150.637i	−0.294621	+	1.09954i	0.646898	+	0.762577i	$0.276066\pi$
$137$	−40.3630	+	150.637i	−0.294621	+	1.09954i	−0.941518	+	0.336962i	$0.890601\pi$
$138$	−111.208	−	43.1961i	−0.805857	−	0.313015i
$139$	−1.35272	−	0.780993i	−0.00973180	−	0.00561866i	0.495126	−	0.868821i	$-0.335122\pi$
$139$	−1.35272	−	0.780993i	−0.00973180	−	0.00561866i	−0.504858	+	0.863202i	$0.668455\pi$
$140$	−324.891	−	16.7941i	−2.32065	−	0.119958i
$141$	−1.53998	+	2.10201i	−0.0109219	+	0.0149079i
$142$	−24.7175	+	92.2470i	−0.174067	+	0.649627i
$143$	6.26906	−	6.26906i	0.0438396	−	0.0438396i
$144$	−12.5017	+	56.6024i	−0.0868171	+	0.393072i
$145$	−107.053	−	34.6990i	−0.738295	−	0.239304i
$146$	−113.605	−	196.770i	−0.778117	−	1.34774i
$147$	63.8646	+	79.5095i	0.434453	+	0.540881i
$148$	87.0102	+	324.727i	0.587907	+	2.19410i
$149$	−87.4092	−	50.4657i	−0.586639	−	0.338696i	0.177128	−	0.984188i	$-0.443319\pi$
$149$	−87.4092	−	50.4657i	−0.586639	−	0.338696i	−0.763767	+	0.645492i	$0.776653\pi$
$150$	−185.619	−	167.988i	−1.23746	−	1.11992i
$151$	−109.094	−	188.956i	−0.722477	−	1.25137i	−0.960004	−	0.279986i	$-0.909670\pi$
$151$	−109.094	−	188.956i	−0.722477	−	1.25137i	0.237527	−	0.971381i	$-0.423663\pi$
$152$	−138.210	−	138.210i	−0.909279	−	0.909279i
$153$	9.69804	+	218.177i	0.0633859	+	1.42599i
$154$		−	62.2604i		−	0.404288i
$155$	116.742	−	24.9015i	0.753174	−	0.160655i
$156$	54.8325	−	74.8439i	0.351490	−	0.479769i
$157$	256.443	−	68.7136i	1.63339	−	0.437666i	0.678496	−	0.734604i	$-0.262632\pi$
$157$	256.443	−	68.7136i	1.63339	−	0.437666i	0.954897	+	0.296937i	$0.0959653\pi$
$158$	−0.201198	−	0.750883i	−0.00127341	−	0.00475242i
$159$	12.9416	−	5.70051i	0.0813934	−	0.0358522i
$160$	−85.8081	−	55.6373i	−0.536300	−	0.347733i
$161$	108.535			0.674133
$162$	266.342	+	46.5306i	1.64408	+	0.287226i
$163$	−161.076	+	161.076i	−0.988199	+	0.988199i	−0.999931	−	0.0117324i	$-0.996265\pi$
$163$	−161.076	+	161.076i	−0.988199	+	0.988199i	0.0117324	+	0.999931i	$0.496265\pi$
$164$	−26.6899	+	15.4094i	−0.162743	+	0.0939598i
$165$	19.4048	−	23.8040i	0.117605	−	0.144267i
$166$	−265.187	+	459.317i	−1.59751	+	2.76697i
$167$	−57.6223	+	15.4399i	−0.345044	+	0.0924542i	−0.427179	−	0.904167i	$-0.640493\pi$
$167$	−57.6223	+	15.4399i	−0.345044	+	0.0924542i	0.0821354	+	0.996621i	$0.473826\pi$
$168$	−43.7167	−	283.290i	−0.260219	−	1.68625i
$169$	130.119	−	75.1245i	0.769938	−	0.444524i
$170$	385.260	+	124.874i	2.26624	+	0.734555i
$171$	−113.217	+	123.750i	−0.662087	+	0.723685i
$172$	159.037	+	159.037i	0.924631	+	0.924631i
$173$	−93.6378	−	25.0902i	−0.541259	−	0.145030i	−0.0221766	−	0.999754i	$-0.507060\pi$
$173$	−93.6378	−	25.0902i	−0.541259	−	0.145030i	−0.519083	+	0.854724i	$0.673726\pi$
$174$	24.4487	−	224.055i	0.140510	−	1.28767i
$175$	212.742	+	81.3154i	1.21567	+	0.464660i
$176$	−6.59341	+	11.4201i	−0.0374626	+	0.0648871i
$177$	−143.881	−	179.128i	−0.812889	−	1.01202i
$178$	−333.338	−	89.3176i	−1.87269	−	0.501784i
$179$		−	89.4315i		−	0.499617i	−0.968295	−	0.249809i	$-0.919632\pi$
$179$		−	89.4315i		−	0.499617i	0.968295	−	0.249809i	$-0.0803677\pi$
$180$	162.703	−	277.166i	0.903904	−	1.53981i
$181$	307.336			1.69799			0.848995	−	0.528401i	$-0.177208\pi$
$181$	307.336			1.69799			0.848995	+	0.528401i	$0.177208\pi$
$182$	−34.0812	+	127.193i	−0.187259	+	0.698861i
$183$	−32.3592	−	209.692i	−0.176826	−	1.14586i
$184$	−108.212	−	62.4761i	−0.588107	−	0.339544i
$185$	12.1495	−	235.040i	0.0656732	−	1.27049i
$186$	96.3703	+	218.784i	0.518120	+	1.17626i
$187$	−12.8587	+	47.9892i	−0.0687629	+	0.256627i
$188$	−4.38653	+	4.38653i	−0.0233326	+	0.0233326i
$189$	−241.190	+	48.2721i	−1.27614	+	0.255408i
$190$	141.406	+	277.035i	0.744241	+	1.45808i
$191$	81.7990	+	141.680i	0.428267	+	0.741780i	0.996719	−	0.0809360i	$-0.0257910\pi$
$191$	81.7990	+	141.680i	0.428267	+	0.741780i	−0.568452	+	0.822716i	$0.692458\pi$
$192$	102.143	−	262.966i	0.531994	−	1.36962i
$193$	−65.7869	−	245.520i	−0.340865	−	1.27212i	−0.897369	−	0.441280i	$-0.854524\pi$
$193$	−65.7869	−	245.520i	−0.340865	−	1.27212i	0.556504	−	0.830845i	$-0.312142\pi$
$194$	208.680	+	120.481i	1.07567	+	0.621039i
$195$	−52.6726	+	38.0075i	−0.270116	+	0.194910i
$196$	121.394	+	210.261i	0.619358	+	1.07276i
$197$	−83.9878	−	83.9878i	−0.426334	−	0.426334i	0.461044	−	0.887377i	$-0.347475\pi$
$197$	−83.9878	−	83.9878i	−0.426334	−	0.426334i	−0.887377	+	0.461044i	$0.847475\pi$
$198$	54.5805	+	28.3582i	0.275659	+	0.143223i
$199$		−	165.065i		−	0.829471i	−0.909942	−	0.414736i	$-0.863874\pi$
$199$		−	165.065i		−	0.829471i	0.909942	−	0.414736i	$-0.136126\pi$
$200$	−165.300	−	203.533i	−0.826501	−	1.01767i
$201$	64.5179	+	7.04014i	0.320985	+	0.0350256i
$202$	−199.958	+	53.5786i	−0.989891	+	0.265240i
$203$	53.0690	+	198.056i	0.261424	+	0.975647i
$204$	−56.3987	+	516.855i	−0.276464	+	2.53360i
$205$	21.1009	−	4.50089i	0.102931	−	0.0219556i
$206$	−176.427			−0.856443
$207$	−49.4353	+	95.1473i	−0.238818	+	0.459649i
$208$	19.7211	−	19.7211i	0.0948132	−	0.0948132i
$209$	−33.0442	+	19.0781i	−0.158106	+	0.0912827i
$210$	−72.8220	+	450.289i	−0.346771	+	2.14423i
$211$	5.87275	−	10.1719i	0.0278329	−	0.0482081i	−0.851773	−	0.523910i	$-0.824473\pi$
$211$	5.87275	−	10.1719i	0.0278329	−	0.0482081i	0.879606	+	0.475702i	$0.157806\pi$
$212$	32.5191	−	8.71347i	0.153392	−	0.0411013i
$213$	80.0080	+	31.0771i	0.375624	+	0.145902i
$214$	345.004	−	199.188i	1.61217	−	0.930785i
$215$	−71.5837	−	140.243i	−0.332947	−	0.652293i
$216$	268.258	+	90.7077i	1.24193	+	0.419943i
$217$	−153.790	−	153.790i	−0.708709	−	0.708709i
$218$	330.422	+	88.5362i	1.51570	+	0.406129i
$219$	−186.879	+	82.3165i	−0.853327	+	0.375874i
$220$	54.2991	−	48.9614i	0.246814	−	0.222552i
$221$	52.5383	−	90.9991i	0.237730	−	0.411761i
$222$	465.848	−	71.8888i	2.09841	−	0.323823i
$223$	12.3702	+	3.31460i	0.0554720	+	0.0148637i	0.286448	−	0.958096i	$-0.407525\pi$
$223$	12.3702	+	3.31460i	0.0554720	+	0.0148637i	−0.230976	+	0.972959i	$0.574192\pi$
$224$			186.333i			0.831843i
$225$	−168.184	+	149.463i	−0.747485	+	0.664279i
$226$	−135.647			−0.600208
$227$	−114.563	+	427.557i	−0.504685	+	1.88351i	−0.0376093	+	0.999293i	$0.511974\pi$
$227$	−114.563	+	427.557i	−0.504685	+	1.88351i	−0.467076	+	0.884217i	$0.654692\pi$
$228$	−311.313	+	250.056i	−1.36541	+	1.09674i
$229$	−164.262	−	94.8369i	−0.717303	−	0.414135i	0.0964562	−	0.995337i	$-0.469249\pi$
$229$	−164.262	−	94.8369i	−0.717303	−	0.414135i	−0.813759	+	0.581202i	$0.802583\pi$
$230$	133.154	+	147.671i	0.578932	+	0.642046i
$231$	−55.6263	−	6.06989i	−0.240806	−	0.0262766i
$232$	61.0961	−	228.014i	0.263345	−	0.982818i
$233$	−62.7917	+	62.7917i	−0.269492	+	0.269492i	−0.828896	−	0.559403i	$-0.811030\pi$
$233$	−62.7917	+	62.7917i	−0.269492	+	0.269492i	0.559403	+	0.828896i	$0.311030\pi$
$234$	−95.9802	−	87.8106i	−0.410172	−	0.375259i
$235$	3.86817	−	1.97441i	0.0164603	−	0.00840176i
$236$	−273.491	−	473.699i	−1.15886	−	2.00720i
$237$	−0.690489	+	0.106555i	−0.00291345	+	0.000449599i
$238$	−190.984	−	712.762i	−0.802454	−	2.99480i
$239$	−57.9140	−	33.4367i	−0.242318	−	0.139902i	0.373924	−	0.927460i	$-0.378012\pi$
$239$	−57.9140	−	33.4367i	−0.242318	−	0.139902i	−0.616242	+	0.787557i	$0.711346\pi$
$240$	61.0433	−	74.8825i	0.254347	−	0.312010i
$241$	29.6700	+	51.3900i	0.123112	+	0.213236i	0.920993	−	0.389578i	$-0.127379\pi$
$241$	29.6700	+	51.3900i	0.123112	+	0.213236i	−0.797881	+	0.602815i	$0.794046\pi$
$242$	−275.702	−	275.702i	−1.13927	−	1.13927i
$243$	67.5388	−	233.426i	0.277937	−	0.960599i
$244$		−	505.119i		−	2.07016i
$245$	−35.4577	−	166.231i	−0.144725	−	0.678496i
$246$	17.4188	+	39.5449i	0.0708080	+	0.160751i
$247$	77.9498	−	20.8866i	0.315586	−	0.0845611i
$248$	64.8054	+	241.857i	0.261312	+	0.975230i
$249$	384.522	+	281.710i	1.54426	+	1.13137i
$250$	150.362	+	389.212i	0.601449	+	1.55685i
$251$	−88.5781			−0.352901			−0.176450	−	0.984310i	$-0.556461\pi$
$251$	−88.5781			−0.352901			−0.176450	+	0.984310i	$0.556461\pi$
$252$	−585.007	+	26.0038i	−2.32146	+	0.103190i
$253$	−17.2480	+	17.2480i	−0.0681737	+	0.0681737i
$254$	−332.583	+	192.017i	−1.30938	+	0.755972i
$255$	149.128	−	332.035i	0.584817	−	1.30210i
$256$	199.259	−	345.126i	0.778354	−	1.34815i
$257$	151.819	−	40.6797i	0.590734	−	0.158287i	0.0489452	−	0.998801i	$-0.484414\pi$
$257$	151.819	−	40.6797i	0.590734	−	0.158287i	0.541789	+	0.840515i	$0.317747\pi$
$258$	245.859	−	197.482i	0.952940	−	0.765433i
$259$	−371.369	+	214.410i	−1.43386	+	0.827837i
$260$	−137.730	+	70.3008i	−0.529730	+	0.270388i
$261$	−197.797	−	43.6872i	−0.757845	−	0.167384i
$262$	195.159	+	195.159i	0.744882	+	0.744882i
$263$	339.020	+	90.8401i	1.28905	+	0.345400i	0.837299	−	0.546745i	$-0.184133\pi$
$263$	339.020	+	90.8401i	1.28905	+	0.345400i	0.451750	+	0.892145i	$0.350800\pi$
$264$	51.9664	+	38.0719i	0.196843	+	0.144212i
$265$	−23.5376	−	1.21669i	−0.0888211	−	0.00459129i
$266$	283.358	−	490.791i	1.06526	−	1.84508i
$267$	−112.298	+	289.112i	−0.420593	+	1.08282i
$268$	149.244	+	39.9897i	0.556880	+	0.149215i
$269$		−	81.1798i		−	0.301784i	−0.988550	−	0.150892i	$-0.951785\pi$
$269$		−	81.1798i		−	0.301784i	0.988550	−	0.150892i	$-0.0482145\pi$
$270$	−361.577	−	268.936i	−1.33917	−	0.996058i
$271$	−96.4105			−0.355758			−0.177879	−	0.984052i	$-0.556924\pi$
$271$	−96.4105			−0.355758			−0.177879	+	0.984052i	$0.556924\pi$
$272$	−40.4506	+	150.964i	−0.148716	+	0.555014i
$273$	110.317	+	42.8500i	0.404092	+	0.156960i
$274$	450.817	+	260.280i	1.64532	+	0.949925i
$275$	−46.7303	+	20.8857i	−0.169928	+	0.0759481i
$276$	−150.860	+	205.917i	−0.546593	+	0.746075i
$277$	113.398	−	423.206i	0.409378	−	1.52782i	−0.386458	−	0.922307i	$-0.626302\pi$
$277$	113.398	−	423.206i	0.409378	−	1.52782i	0.795836	−	0.605512i	$-0.207032\pi$
$278$	−3.68676	+	3.68676i	−0.0132617	+	0.0132617i
$279$	204.867	−	64.7719i	0.734292	−	0.232157i
$280$	−147.305	+	454.462i	−0.526088	+	1.62308i
$281$	−95.5531	−	165.503i	−0.340047	−	0.588978i	0.644394	−	0.764693i	$-0.277110\pi$
$281$	−95.5531	−	165.503i	−0.340047	−	0.588978i	−0.984441	+	0.175715i	$0.943776\pi$
$282$	5.44693	+	6.78125i	0.0193153	+	0.0240470i
$283$	89.6088	+	334.424i	0.316639	+	1.18171i	0.922454	+	0.386107i	$0.126180\pi$
$283$	89.6088	+	334.424i	0.316639	+	1.18171i	−0.605815	+	0.795605i	$0.707153\pi$
$284$	176.962	+	102.169i	0.623105	+	0.359750i
$285$	261.302	−	99.3297i	0.916848	−	0.348525i
$286$	−14.7969	−	25.6289i	−0.0517373	−	0.0896117i
$287$	−27.7972	−	27.7972i	−0.0968545	−	0.0968545i
$288$	−163.348	−	84.8702i	−0.567182	−	0.294688i
$289$			299.828i			1.03747i
$290$	−204.364	+	315.186i	−0.704703	+	1.08685i
$291$	127.988	−	174.698i	0.439822	−	0.600338i
$292$	−469.582	+	125.824i	−1.60816	+	0.430905i
$293$	−77.5588	−	289.453i	−0.264706	−	0.987895i	−0.962430	−	0.271529i	$-0.912471\pi$
$293$	−77.5588	−	289.453i	−0.264706	−	0.987895i	0.697725	−	0.716366i	$-0.254196\pi$
$294$	311.532	−	137.224i	1.05963	−	0.466748i
$295$	79.8831	+	374.505i	0.270790	+	1.26951i
$296$	493.682			1.66784
$297$	30.6576	−	46.0000i	0.103224	−	0.154882i
$298$	−238.229	+	238.229i	−0.799426	+	0.799426i
$299$	44.6776	−	25.7946i	0.149423	−	0.0862697i
$300$	−449.977	+	290.596i	−1.49992	+	0.968653i
$301$	−143.444	+	248.452i	−0.476558	+	0.825423i
$302$	−703.489	+	188.499i	−2.32944	+	0.624170i
$303$	28.3753	+	183.875i	0.0936477	+	0.606849i
$304$	−103.950	+	60.0156i	−0.341941	+	0.197420i
$305$	−109.035	+	336.394i	−0.357493	+	1.10293i
$306$	711.831	+	157.221i	2.32624	+	0.513793i
$307$	138.397	+	138.397i	0.450805	+	0.450805i	0.895622	−	0.444817i	$-0.146731\pi$
$307$	138.397	+	138.397i	0.450805	+	0.450805i	−0.444817	+	0.895622i	$0.646731\pi$
$308$	−128.676	−	34.4785i	−0.417778	−	0.111943i
$309$	−17.2003	+	157.628i	−0.0556643	+	0.510124i
$310$	20.5689	−	397.917i	0.0663512	−	1.28360i
$311$	53.6367	−	92.9015i	0.172465	−	0.298719i	−0.766816	−	0.641867i	$-0.778160\pi$
$311$	53.6367	−	92.9015i	0.172465	−	0.298719i	0.939281	+	0.343148i	$0.111493\pi$
$312$	−85.3226	−	106.224i	−0.273470	−	0.340462i
$313$	528.306	+	141.559i	1.68788	+	0.452266i	0.969841	−	0.243738i	$-0.0783736\pi$
$313$	528.306	+	141.559i	1.68788	+	0.452266i	0.718038	+	0.696004i	$0.245040\pi$
$314$		−	886.195i		−	2.82228i
$315$	395.209	+	108.962i	1.25463	+	0.345912i
$316$	−1.66329			−0.00526359
$317$	112.931	−	421.463i	0.356248	−	1.32954i	−0.522658	−	0.852542i	$-0.675059\pi$
$317$	112.931	−	421.463i	0.356248	−	1.32954i	0.878906	−	0.476994i	$-0.158274\pi$
$318$	−7.19916	−	46.6514i	−0.0226389	−	0.146703i
$319$	−39.9077	−	23.0407i	−0.125103	−	0.0722280i
$320$	−349.186	+	314.861i	−1.09121	+	0.983939i
$321$	−144.329	−	327.661i	−0.449622	−	1.02075i
$322$	93.7670	−	349.943i	0.291202	−	1.08678i
$323$	−319.771	+	319.771i	−0.990002	+	0.990002i
$324$	243.661	−	524.690i	0.752040	−	1.61941i
$325$	106.899	−	17.0877i	0.328920	−	0.0525777i
$326$	380.189	+	658.507i	1.16622	+	2.01996i
$327$	111.316	−	286.582i	0.340415	−	0.876398i
$328$	11.7135	+	43.7152i	0.0357118	+	0.133278i
$329$	−6.85279	−	3.95646i	−0.0208292	−	0.0120257i
$330$	−59.9854	−	83.1305i	−0.181774	−	0.251911i
$331$	−293.152	−	507.754i	−0.885655	−	1.53400i	−0.844961	−	0.534827i	$-0.820377\pi$
$331$	−293.152	−	507.754i	−0.885655	−	1.53400i	−0.0406933	−	0.999172i	$-0.512957\pi$
$332$	802.431	+	802.431i	2.41696	+	2.41696i
$333$	−18.8122	−	423.219i	−0.0564932	−	1.27093i
$334$			199.127i			0.596188i
$335$	−90.7595	−	58.8477i	−0.270924	−	0.175665i
$336$	−174.989	−	19.0946i	−0.520799	−	0.0568292i
$337$	−459.691	+	123.174i	−1.36407	+	0.365501i	−0.865309	−	0.501239i	$-0.832878\pi$
$337$	−459.691	+	123.174i	−1.36407	+	0.365501i	−0.498760	+	0.866740i	$0.666211\pi$
$338$	−129.805	−	484.438i	−0.384038	−	1.43325i
$339$	−13.2245	+	121.193i	−0.0390104	+	0.357502i
$340$	471.431	−	727.077i	1.38656	−	2.13846i
$341$	48.8792			0.143341
$342$	301.188	+	471.949i	0.880667	+	1.37997i
$343$	96.6647	−	96.6647i	0.281821	−	0.281821i
$344$	286.033	−	165.141i	0.831490	−	0.480061i
$345$	144.917	−	104.569i	0.420050	−	0.303100i
$346$	−161.793	+	280.234i	−0.467610	+	0.809925i
$347$	169.638	−	45.4544i	0.488870	−	0.130992i	−0.00595969	−	0.999982i	$-0.501897\pi$
$347$	169.638	−	45.4544i	0.488870	−	0.130992i	0.494830	+	0.868990i	$0.335230\pi$
$348$	−449.523	−	174.606i	−1.29173	−	0.501741i
$349$	−298.148	+	172.136i	−0.854292	+	0.493226i	−0.862097	−	0.506744i	$-0.830849\pi$
$349$	−298.148	+	172.136i	−0.854292	+	0.493226i	0.00780468	+	0.999970i	$0.497516\pi$
$350$	445.974	−	615.679i	1.27421	−	1.75908i
$351$	−87.8113	+	77.1923i	−0.250175	+	0.219921i
$352$	−29.6112	−	29.6112i	−0.0841227	−	0.0841227i
$353$	260.440	+	69.7848i	0.737792	+	0.197691i	0.608096	−	0.793863i	$-0.291933\pi$
$353$	260.440	+	69.7848i	0.737792	+	0.197691i	0.129695	+	0.991554i	$0.458600\pi$
$354$	−701.854	+	309.153i	−1.98264	+	0.873314i
$355$	−95.7968	−	106.240i	−0.269850	−	0.299269i
$356$	−369.191	+	639.458i	−1.03705	+	1.79623i
$357$	−655.434	+	101.145i	−1.83595	+	0.283320i
$358$	−288.348	−	77.2626i	−0.805441	−	0.215817i
$359$			411.438i			1.14607i	0.819532	+	0.573033i	$0.194233\pi$
$359$			411.438i			1.14607i	−0.819532	+	0.573033i	$0.805767\pi$
$360$	−331.309	−	336.131i	−0.920304	−	0.933698i
$361$	13.6890			0.0379198
$362$	265.517	−	990.923i	0.733473	−	2.73736i
$363$	−273.204	+	219.446i	−0.752628	+	0.604536i
$364$	244.000	+	140.873i	0.670330	+	0.387015i
$365$	339.888	+	17.5693i	0.931199	+	0.0481350i
$366$	−704.051	−	76.8255i	−1.92364	−	0.209906i
$367$	−167.988	+	626.938i	−0.457732	+	1.70828i	0.222199	+	0.975001i	$0.428677\pi$
$367$	−167.988	+	626.938i	−0.457732	+	1.70828i	−0.679930	+	0.733277i	$0.737990\pi$
$368$	−54.2584	+	54.2584i	−0.147441	+	0.147441i
$369$	37.0294	−	11.7074i	0.100351	−	0.0317274i
$370$	−747.327	−	242.231i	−2.01980	−	0.654679i
$371$	21.4716	+	37.1900i	0.0578751	+	0.100243i
$372$	505.537	−	78.0134i	1.35897	−	0.209714i
$373$	28.7295	+	107.220i	0.0770229	+	0.287453i	0.993684	−	0.112211i	$-0.0357933\pi$
$373$	28.7295	+	107.220i	0.0770229	+	0.287453i	−0.916662	+	0.399664i	$0.869127\pi$
$374$	143.619	+	82.9186i	0.384009	+	0.221708i
$375$	362.399	−	96.3955i	0.966397	−	0.257055i
$376$	4.55491	+	7.88933i	0.0121141	+	0.0209823i
$377$	68.9157	+	68.9157i	0.182800	+	0.182800i
$378$	−52.7309	+	819.356i	−0.139500	+	2.16761i
$379$		−	317.077i		−	0.836614i	−0.908306	−	0.418307i	$-0.862624\pi$
$379$		−	317.077i		−	0.836614i	0.908306	−	0.418307i	$-0.137376\pi$
$380$	650.865	−	138.832i	1.71280	−	0.365346i
$381$	139.133	+	315.865i	0.365177	+	0.829043i
$382$	527.478	−	141.337i	1.38083	−	0.369993i
$383$	23.0644	+	86.0774i	0.0602203	+	0.224745i	0.989477	−	0.144689i	$-0.0462182\pi$
$383$	23.0644	+	86.0774i	0.0602203	+	0.224745i	−0.929257	+	0.369434i	$0.879552\pi$
$384$	−561.629	−	411.464i	−1.46258	−	1.07152i
$385$	78.2514	+	50.7376i	0.203250	+	0.131786i
$386$	−848.449			−2.19806
$387$	−152.470	−	238.914i	−0.393979	−	0.617350i
$388$	364.566	−	364.566i	0.939602	−	0.939602i
$389$	64.0677	−	36.9895i	0.164698	−	0.0950887i	−0.415385	−	0.909646i	$-0.636353\pi$
$389$	64.0677	−	36.9895i	0.164698	−	0.0950887i	0.580084	+	0.814557i	$0.303020\pi$
$390$	77.0397	+	202.665i	0.197538	+	0.519653i
$391$	−144.548	+	250.364i	−0.369687	+	0.640318i
$392$	344.386	−	92.2778i	0.878535	−	0.235403i
$393$	193.391	−	155.338i	0.492088	−	0.395261i
$394$	−343.356	+	198.237i	−0.871461	+	0.503138i
$395$	1.10770	+	0.359039i	0.00280431	+	0.000908961i
$396$	88.8343	−	97.0991i	0.224329	−	0.245200i
$397$	331.663	+	331.663i	0.835422	+	0.835422i	0.988252	−	0.152830i	$-0.0488387\pi$
$397$	331.663	+	331.663i	0.835422	+	0.835422i	−0.152830	+	0.988252i	$0.548839\pi$
$398$	−532.207	−	142.605i	−1.33720	−	0.358303i
$399$	−410.870	−	301.013i	−1.02975	−	0.754420i
$400$	−147.004	+	65.7021i	−0.367509	+	0.164255i
$401$	−324.360	+	561.808i	−0.808877	+	1.40102i	0.104765	+	0.994497i	$0.466591\pi$
$401$	−324.360	+	561.808i	−0.808877	+	1.40102i	−0.913642	+	0.406520i	$0.866742\pi$
$402$	78.4380	−	201.939i	0.195119	−	0.502335i
$403$	−99.8561	−	26.7564i	−0.247782	−	0.0663930i
$404$			442.930i			1.09636i
$405$	−275.530	+	296.830i	−0.680322	+	0.732914i
$406$	684.428			1.68578
$407$	24.9432	−	93.0893i	0.0612855	−	0.228721i
$408$	711.702	+	276.443i	1.74437	+	0.677556i
$409$	−545.487	−	314.937i	−1.33371	−	0.770017i	−0.347842	−	0.937553i	$-0.613086\pi$
$409$	−545.487	−	314.937i	−1.33371	−	0.770017i	−0.985866	+	0.167536i	$0.946419\pi$
$410$	3.71779	−	71.9227i	0.00906777	−	0.175421i
$411$	276.497	−	377.406i	0.672742	−	0.918262i
$412$	−97.7018	+	364.628i	−0.237140	+	0.885019i
$413$	493.353	−	493.353i	1.19456	−	1.19456i
$414$	264.069	+	241.592i	0.637847	+	0.583555i
$415$	−361.181	−	707.607i	−0.870315	−	1.70508i
$416$	44.2841	+	76.7023i	0.106452	+	0.184380i
$417$	2.93449	+	3.65335i	0.00703715	+	0.00876103i
$418$	32.9643	+	123.024i	0.0788619	+	0.294317i
$419$	−153.113	−	88.3997i	−0.365424	−	0.210978i	0.306033	−	0.952021i	$-0.400998\pi$
$419$	−153.113	−	88.3997i	−0.365424	−	0.210978i	−0.671457	+	0.741043i	$0.734331\pi$
$420$	890.300	+	399.864i	2.11976	+	0.952058i
$421$	44.6779	+	77.3843i	0.106123	+	0.183811i	0.914197	−	0.405271i	$-0.132823\pi$
$421$	44.6779	+	77.3843i	0.106123	+	0.183811i	−0.808073	+	0.589082i	$0.799490\pi$
$422$	−27.7229	−	27.7229i	−0.0656941	−	0.0656941i
$423$	6.58972	−	4.20542i	0.0155785	−	0.00994188i
$424$		−	49.4388i		−	0.116601i
$425$	−470.905	+	382.447i	−1.10801	+	0.899875i
$426$	169.321	−	231.116i	0.397468	−	0.542526i
$427$	622.355	−	166.760i	1.45751	−	0.390538i
$428$	−220.612	−	823.337i	−0.515449	−	1.92368i
$429$	−24.3407	+	10.7216i	−0.0567381	+	0.0249921i
$430$	−514.020	+	109.642i	−1.19539	+	0.254982i
$431$	648.364			1.50433			0.752163	−	0.658977i	$-0.229011\pi$
$431$	648.364			1.50433			0.752163	+	0.658977i	$0.229011\pi$
$432$	96.4425	−	144.706i	0.223247	−	0.334968i
$433$	−481.270	+	481.270i	−1.11148	+	1.11148i	−0.118526	+	0.992951i	$0.537817\pi$
$433$	−481.270	+	481.270i	−1.11148	+	1.11148i	−0.992951	+	0.118526i	$0.962183\pi$
$434$	−628.718	+	362.991i	−1.44866	+	0.836384i
$435$	261.677	+	213.316i	0.601557	+	0.490382i
$436$	365.961	−	633.864i	0.839361	−	1.45382i
$437$	−214.462	+	57.4649i	−0.490760	+	0.131499i
$438$	103.957	+	673.656i	0.237345	+	1.53803i
$439$	543.519	−	313.801i	1.23808	−	0.714809i	0.269382	−	0.963033i	$-0.413180\pi$
$439$	543.519	−	313.801i	1.23808	−	0.714809i	0.968702	+	0.248225i	$0.0798471\pi$
$440$	−48.8120	−	95.6301i	−0.110936	−	0.217341i
$441$	−92.2302	−	291.715i	−0.209139	−	0.661485i
$442$	−248.013	−	248.013i	−0.561115	−	0.561115i
$443$	−519.441	−	139.184i	−1.17255	−	0.314185i	−0.380584	−	0.924746i	$-0.624277\pi$
$443$	−519.441	−	139.184i	−1.17255	−	0.314185i	−0.791969	+	0.610562i	$0.790944\pi$
$444$	109.402	−	1002.59i	0.246401	−	2.25809i
$445$	383.904	−	346.165i	0.862705	−	0.777900i
$446$	21.3741	−	37.0210i	0.0479239	−	0.0830067i
$447$	189.619	+	236.070i	0.424204	+	0.528121i
$448$	827.486	+	221.724i	1.84707	+	0.494920i
$449$			252.073i			0.561410i	0.959794	+	0.280705i	$0.0905683\pi$
$449$			252.073i			0.561410i	−0.959794	+	0.280705i	$0.909432\pi$
$450$	336.603	+	671.390i	0.748007	+	1.49198i
$451$	8.83482			0.0195894
$452$	−75.1186	+	280.346i	−0.166191	+	0.620235i
$453$	99.8294	+	646.907i	0.220374	+	1.42805i
$454$	1279.57	+	738.759i	2.81843	+	1.62722i
$455$	−132.087	−	146.487i	−0.290302	−	0.321950i
$456$	236.373	+	536.624i	0.518361	+	1.17681i
$457$	76.3993	−	285.126i	0.167176	−	0.623908i	−0.830577	−	0.556904i	$-0.811989\pi$
$457$	76.3993	−	285.126i	0.167176	−	0.623908i	0.997753	−	0.0670042i	$-0.0213441\pi$
$458$	−447.688	+	447.688i	−0.977484	+	0.977484i
$459$	209.866	−	620.654i	0.457224	−	1.35219i
$460$	378.934	−	193.417i	0.823769	−	0.420473i
$461$	254.881	+	441.467i	0.552887	+	0.957629i	0.998065	+	0.0621865i	$0.0198074\pi$
$461$	254.881	+	441.467i	0.552887	+	0.957629i	−0.445177	+	0.895443i	$0.646859\pi$
$462$	−67.6280	+	174.108i	−0.146381	+	0.376858i
$463$	−76.4168	−	285.192i	−0.165047	−	0.615964i	−0.998034	−	0.0626719i	$-0.980038\pi$
$463$	−76.4168	−	285.192i	−0.165047	−	0.615964i	0.832987	−	0.553293i	$-0.186629\pi$
$464$	−125.541	−	72.4813i	−0.270563	−	0.156210i
$465$	−353.512	−	57.1709i	−0.760240	−	0.122948i
$466$	148.208	+	256.703i	0.318042	+	0.550865i
$467$	−375.745	−	375.745i	−0.804593	−	0.804593i	0.179217	−	0.983810i	$-0.442644\pi$
$467$	−375.745	−	375.745i	−0.804593	−	0.804593i	−0.983810	+	0.179217i	$0.942644\pi$
$468$	−234.633	+	149.738i	−0.501352	+	0.319952i
$469$			197.085i			0.420223i
$470$	−3.02414	−	14.1776i	−0.00643434	−	0.0301652i
$471$	−791.767	−	86.3970i	−1.68103	−	0.183433i
$472$	−775.871	+	207.894i	−1.64379	+	0.440453i
$473$	−16.6875	−	62.2784i	−0.0352800	−	0.131667i
$474$	−0.252977	+	2.31835i	−0.000533706	+	0.00489104i
$475$	−463.424	−	48.0384i	−0.975629	−	0.101134i
$476$	−1578.85			−3.31691
$477$	−42.3824	+	1.88391i	−0.0888520	+	0.00394951i
$478$	−157.841	+	157.841i	−0.330212	+	0.330212i
$479$	375.237	−	216.643i	0.783376	−	0.452282i	−0.0542492	−	0.998527i	$-0.517277\pi$
$479$	375.237	−	216.643i	0.783376	−	0.452282i	0.837625	+	0.546245i	$0.183943\pi$
$480$	179.524	+	248.793i	0.374009	+	0.518318i
$481$	−101.914	+	176.520i	−0.211879	+	0.366985i
$482$	191.326	−	51.2656i	0.396942	−	0.106360i
$483$	−303.514	−	117.892i	−0.628393	−	0.244084i
$484$	−722.482	+	417.125i	−1.49273	+	0.861828i
$485$	−321.485	+	164.094i	−0.662855	+	0.338338i
$486$	−694.270	−	419.424i	−1.42854	−	0.863013i
$487$	417.712	+	417.712i	0.857725	+	0.857725i	0.991070	−	0.133345i	$-0.0425719\pi$
$487$	417.712	+	417.712i	0.857725	+	0.857725i	−0.133345	+	0.991070i	$0.542572\pi$
$488$	−716.491	−	191.983i	−1.46822	−	0.393408i
$489$	625.406	−	275.479i	1.27895	−	0.563352i
$490$	−566.602	−	29.2885i	−1.15633	−	0.0597724i
$491$	385.003	−	666.845i	0.784121	−	1.35814i	−0.145402	−	0.989373i	$-0.546447\pi$
$491$	385.003	−	666.845i	0.784121	−	1.35814i	0.929523	−	0.368765i	$-0.120219\pi$
$492$	91.3748	−	14.1008i	0.185721	−	0.0286601i
$493$	−527.544	−	141.355i	−1.07007	−	0.286724i
$494$		−	269.373i		−	0.545289i
$495$	−80.1207	+	45.4892i	−0.161860	+	0.0918973i
$496$	153.764			0.310007
$497$	−67.4600	+	251.764i	−0.135734	+	0.506567i
$498$	1240.50	−	996.409i	2.49096	−	2.00082i
$499$	−84.7687	−	48.9412i	−0.169877	−	0.0980786i	0.412651	−	0.910889i	$-0.364603\pi$
$499$	−84.7687	−	48.9412i	−0.169877	−	0.0980786i	−0.582528	+	0.812811i	$0.697936\pi$
$500$	887.664	−	95.2212i	1.77533	−	0.190442i
$501$	177.909	+	19.4133i	0.355108	+	0.0387491i
$502$	−76.5253	+	285.596i	−0.152441	+	0.568917i
$503$	350.849	−	350.849i	0.697512	−	0.697512i	−0.266361	−	0.963873i	$-0.585821\pi$
$503$	350.849	−	350.849i	0.697512	−	0.697512i	0.963873	+	0.266361i	$0.0858213\pi$
$504$	−185.461	+	839.692i	−0.367979	+	1.66606i
$505$	95.6112	−	294.978i	0.189329	−	0.584114i
$506$	40.7104	+	70.5125i	0.0804553	+	0.139353i
$507$	−445.474	+	68.7447i	−0.878647	+	0.135591i
$508$	212.670	+	793.696i	0.418642	+	1.56239i
$509$	389.842	+	225.075i	0.765897	+	0.442191i	0.831409	−	0.555661i	$-0.187535\pi$
$509$	389.842	+	225.075i	0.765897	+	0.442191i	−0.0655119	+	0.997852i	$0.520868\pi$
$510$	−941.721	−	767.679i	−1.84651	−	1.50525i
$511$	−310.055	−	537.031i	−0.606761	−	1.05094i
$512$	−284.213	−	284.213i	−0.555104	−	0.555104i
$513$	451.025	−	223.084i	0.879190	−	0.434861i
$514$		−	524.643i		−	1.02071i
$515$	143.775	−	221.741i	0.279175	−	0.430565i
$516$	−271.991	−	617.485i	−0.527113	−	1.19668i
$517$	1.71776	−	0.460272i	0.00332255	−	0.000890275i
$518$	370.470	+	1382.61i	0.715194	+	2.66914i
$519$	234.600	+	171.874i	0.452024	+	0.331164i
$520$	47.3712	+	222.084i	0.0910985	+	0.427084i
$521$	749.947			1.43944			0.719718	−	0.694266i	$-0.244271\pi$
$521$	749.947			1.43944			0.719718	+	0.694266i	$0.244271\pi$
$522$	−311.741	+	600.002i	−0.597205	+	1.14943i
$523$	377.284	−	377.284i	0.721385	−	0.721385i	−0.247502	−	0.968887i	$-0.579610\pi$
$523$	377.284	−	377.284i	0.721385	−	0.721385i	0.968887	+	0.247502i	$0.0796098\pi$
$524$	511.417	−	295.267i	0.975986	−	0.563486i
$525$	−506.597	−	458.478i	−0.964947	−	0.873291i
$526$	585.779	−	1014.60i	1.11365	−	1.92890i
$527$	559.573	−	149.937i	1.06181	−	0.284511i
$528$	30.8428	−	24.7740i	0.0584145	−	0.0469204i
$529$	335.207	−	193.532i	0.633661	−	0.365844i
$530$	−24.2577	+	74.8395i	−0.0457693	+	0.141207i
$531$	207.786	+	657.208i	0.391312	+	1.23768i
$532$	−857.415	−	857.415i	−1.61168	−	1.61168i
$533$	−18.0488	−	4.83616i	−0.0338627	−	0.00907348i
$534$	835.146	+	611.848i	1.56394	+	1.14578i
$535$	−30.8049	+	595.938i	−0.0575792	+	1.11390i
$536$	113.448	−	196.497i	0.211656	−	0.366599i
$537$	−97.1416	+	250.091i	−0.180897	+	0.465719i
$538$	−261.743	−	70.1337i	−0.486510	−	0.130360i
$539$		−	69.6001i		−	0.129128i
$540$	−756.052	+	598.351i	−1.40010	+	1.10806i
$541$	861.919			1.59320			0.796598	−	0.604509i	$-0.206631\pi$
$541$	861.919			1.59320			0.796598	+	0.604509i	$0.206631\pi$
$542$	−83.2920	+	310.850i	−0.153675	+	0.573524i
$543$	−859.451	−	333.832i	−1.58278	−	0.614793i
$544$	−429.824	−	248.159i	−0.790117	−	0.456174i
$545$	−380.545	+	343.137i	−0.698248	+	0.629609i
$546$	233.465	−	318.669i	0.427591	−	0.583643i
$547$	103.247	−	385.325i	0.188752	−	0.704433i	−0.805044	−	0.593215i	$-0.797858\pi$
$547$	103.247	−	385.325i	0.188752	−	0.704433i	0.993796	−	0.111218i	$-0.0354750\pi$
$548$	787.582	−	787.582i	1.43719	−	1.43719i
$549$	−137.279	+	621.542i	−0.250052	+	1.13213i
$550$	26.9687	+	168.713i	0.0490340	+	0.306751i
$551$	−209.725	−	363.254i	−0.380626	−	0.659264i
$552$	234.747	+	292.252i	0.425266	+	0.529442i
$553$	−0.549118	−	2.04934i	−0.000992981	−	0.00370585i
$554$	−1266.55	−	731.241i	−2.28619	−	1.31993i
$555$	−289.279	+	644.081i	−0.521223	+	1.16051i
$556$	5.57790	+	9.66120i	0.0100322	+	0.0173763i
$557$	−262.321	−	262.321i	−0.470954	−	0.470954i	0.431269	−	0.902223i	$-0.358066\pi$
$557$	−262.321	−	262.321i	−0.470954	−	0.470954i	−0.902223	+	0.431269i	$0.858066\pi$
$558$	−31.8487	−	716.499i	−0.0570765	−	1.28405i
$559$			136.364i			0.243943i
$560$	246.162	+	159.610i	0.439576	+	0.285017i
$561$	88.0851	−	120.232i	0.157014	−	0.214318i
$562$	−616.171	+	165.102i	−1.09639	+	0.293777i
$563$	235.225	+	877.872i	0.417806	+	1.55928i	0.779147	+	0.626841i	$0.215653\pi$
$563$	235.225	+	877.872i	0.417806	+	1.55928i	−0.361341	+	0.932434i	$0.617681\pi$
$564$	17.0314	−	7.50202i	0.0301976	−	0.0133015i
$565$	110.542	−	170.487i	0.195650	−	0.301746i
$566$	1155.68			2.04183
$567$	726.910	+	126.993i	1.28203	+	0.223973i
$568$	212.181	−	212.181i	0.373559	−	0.373559i
$569$	−632.780	+	365.336i	−1.11209	+	0.642066i	−0.939370	−	0.342905i	$-0.888589\pi$
$569$	−632.780	+	365.336i	−1.11209	+	0.642066i	−0.172721	+	0.984971i	$0.555256\pi$
$570$	−94.5155	−	928.312i	−0.165817	−	1.62862i
$571$	−348.293	+	603.262i	−0.609971	+	1.05650i	0.381273	+	0.924462i	$0.375486\pi$
$571$	−348.293	+	603.262i	−0.609971	+	1.05650i	−0.991245	+	0.132039i	$0.957848\pi$
$572$	−61.1624	+	16.3884i	−0.106927	+	0.0286511i
$573$	−74.8523	−	485.052i	−0.130632	−	0.846514i
$574$	−113.640	+	65.6099i	−0.197978	+	0.114303i
$575$	−294.109	+	47.0132i	−0.511494	+	0.0817621i
$576$	−571.275	+	624.424i	−0.991797	+	1.08407i
$577$	−524.179	−	524.179i	−0.908455	−	0.908455i	0.0876926	−	0.996148i	$-0.472051\pi$
$577$	−524.179	−	524.179i	−0.908455	−	0.908455i	−0.996148	+	0.0876926i	$0.972051\pi$
$578$	966.715	+	259.031i	1.67252	+	0.448150i
$579$	−82.7171	+	758.044i	−0.142862	+	1.30923i
$580$	538.232	+	596.909i	0.927986	+	1.02915i
$581$	−723.758	+	1253.59i	−1.24571	+	2.15763i
$582$	−452.695	−	563.591i	−0.777827	−	0.968370i
$583$	−9.32225	−	2.49789i	−0.0159901	−	0.00428454i
$584$			713.907i			1.22244i
$585$	188.581	−	49.0726i	0.322360	−	0.0838849i
$586$	−1000.27			−1.70695
$587$	−141.391	+	527.677i	−0.240870	+	0.898938i	0.734545	+	0.678560i	$0.237396\pi$
$587$	−141.391	+	527.677i	−0.240870	+	0.898938i	−0.975415	+	0.220378i	$0.929271\pi$
$588$	−111.085	−	719.845i	−0.188920	−	1.22423i
$589$	385.309	+	222.458i	0.654174	+	0.377688i
$590$	1276.50	+	65.9843i	2.16357	+	0.111838i
$591$	143.639	+	326.096i	0.243044	+	0.551770i
$592$	78.4661	−	292.839i	0.132544	−	0.494661i
$593$	−61.2676	+	61.2676i	−0.103318	+	0.103318i	−0.756876	−	0.653558i	$-0.773275\pi$
$593$	−61.2676	+	61.2676i	−0.103318	+	0.103318i	0.653558	+	0.756876i	$0.273275\pi$
$594$	−121.829	−	138.588i	−0.205099	−	0.233314i
$595$	1051.47	+	340.812i	1.76717	+	0.572793i
$596$	360.429	+	624.282i	0.604747	+	1.04745i
$597$	−179.295	+	461.596i	−0.300327	+	0.773192i
$598$	−44.5696	−	166.336i	−0.0745310	−	0.278154i
$599$	−572.037	−	330.266i	−0.954987	−	0.551362i	−0.0603602	−	0.998177i	$-0.519225\pi$
$599$	−572.037	−	330.266i	−0.954987	−	0.551362i	−0.894626	+	0.446815i	$0.852558\pi$
$600$	241.174	+	748.723i	0.401956	+	1.24787i
$601$	65.1748	+	112.886i	0.108444	+	0.187830i	0.915140	−	0.403136i	$-0.132080\pi$
$601$	65.1748	+	112.886i	0.108444	+	0.187830i	−0.806696	+	0.590966i	$0.798747\pi$
$602$	677.143	+	677.143i	1.12482	+	1.12482i
$603$	−172.774	−	89.7675i	−0.286524	−	0.148868i
$604$			1558.31i			2.57999i
$605$	571.191	−	121.837i	0.944117	−	0.201383i
$606$	617.371	+	67.3669i	1.01876	+	0.111167i
$607$	313.749	−	84.0689i	0.516885	−	0.138499i	0.00905986	−	0.999959i	$-0.497116\pi$
$607$	313.749	−	84.0689i	0.516885	−	0.138499i	0.507826	+	0.861460i	$0.330449\pi$
$608$	−98.6554	−	368.187i	−0.162262	−	0.605571i
$609$	66.7263	−	611.499i	0.109567	−	1.00410i
$610$	990.412	+	642.176i	1.62363	+	1.05275i
$611$	−3.76119			−0.00615580
$612$	719.130	−	1384.10i	1.17505	−	2.26160i
$613$	−778.916	+	778.916i	−1.27066	+	1.27066i	−0.324921	+	0.945741i	$0.605338\pi$
$613$	−778.916	+	778.916i	−1.27066	+	1.27066i	−0.945741	+	0.324921i	$0.894662\pi$
$614$	565.790	−	326.659i	0.921482	−	0.532018i
$615$	−63.8966	−	10.3335i	−0.103897	−	0.0168025i
$616$	−97.8128	+	169.417i	−0.158787	+	0.275027i
$617$	331.081	−	88.7130i	0.536599	−	0.143781i	0.0196651	−	0.999807i	$-0.493740\pi$
$617$	331.081	−	88.7130i	0.536599	−	0.143781i	0.516934	+	0.856025i	$0.327073\pi$
$618$	493.370	+	191.637i	0.798334	+	0.310093i
$619$	448.805	−	259.118i	0.725049	−	0.418607i	−0.0915591	−	0.995800i	$-0.529185\pi$
$619$	448.805	−	259.118i	0.725049	−	0.418607i	0.816608	+	0.577192i	$0.195852\pi$
$620$	−810.996	−	262.868i	−1.30806	−	0.423981i
$621$	241.594	−	212.378i	0.389040	−	0.341993i
$622$	−253.198	−	253.198i	−0.407070	−	0.407070i
$623$	−909.758	−	243.769i	−1.46029	−	0.391282i
$624$	−76.5706	+	33.7279i	−0.122709	+	0.0540511i
$625$	−611.711	−	128.197i	−0.978738	−	0.205116i
$626$	912.840	−	1581.09i	1.45821	−	2.52569i
$627$	113.129	−	17.4579i	0.180430	−	0.0278435i
$628$	−1831.53	−	490.756i	−2.91645	−	0.781459i
$629$		−	1142.21i		−	1.81591i
$630$	692.753	−	1180.11i	1.09961	−	1.87319i
$631$	−48.4016			−0.0767062			−0.0383531	−	0.999264i	$-0.512211\pi$
$631$	−48.4016			−0.0767062			−0.0383531	+	0.999264i	$0.512211\pi$
$632$	−0.632177	+	2.35932i	−0.00100028	+	0.00373309i
$633$	−27.4717	+	22.0662i	−0.0433992	+	0.0348597i
$634$	−1261.33	−	728.230i	−1.98948	−	1.14863i
$635$	29.6959	−	574.483i	0.0467651	−	0.904698i
$636$	−100.403	−	10.9559i	−0.157866	−	0.0172262i
$637$	−38.0990	+	142.187i	−0.0598100	+	0.223214i
$638$	−108.766	+	108.766i	−0.170480	+	0.170480i
$639$	−189.982	−	173.811i	−0.297312	−	0.272005i
$640$	527.538	+	1033.53i	0.824278	+	1.61488i
$641$	−313.217	−	542.507i	−0.488637	−	0.846345i	0.511277	−	0.859416i	$-0.329173\pi$
$641$	−313.217	−	542.507i	−0.488637	−	0.846345i	−0.999915	+	0.0130711i	$0.995839\pi$
$642$	−1181.15	+	182.272i	−1.83979	+	0.283913i
$643$	125.261	+	467.479i	0.194807	+	0.727028i	0.992317	+	0.123723i	$0.0394833\pi$
$643$	125.261	+	467.479i	0.194807	+	0.727028i	−0.797510	+	0.603305i	$0.793850\pi$
$644$	−671.313	−	387.583i	−1.04241	−	0.601836i
$645$	47.8465	+	469.938i	0.0741806	+	0.728586i
$646$	754.755	+	1307.27i	1.16835	+	2.02364i
$647$	−388.357	−	388.357i	−0.600242	−	0.600242i	0.340135	−	0.940377i	$-0.389527\pi$
$647$	−388.357	−	388.357i	−0.600242	−	0.600242i	−0.940377	+	0.340135i	$0.889527\pi$
$648$	−651.642	−	545.045i	−1.00562	−	0.841118i
$649$			156.803i			0.241607i
$650$	37.2584	−	359.430i	0.0573206	−	0.552969i
$651$	263.017	+	597.114i	0.404021	+	0.917226i
$652$	1571.50	−	421.082i	2.41027	−	0.645831i
$653$	51.2298	+	191.192i	0.0784530	+	0.292791i	0.993994	−	0.109434i	$-0.0349038\pi$
$653$	51.2298	+	191.192i	0.0784530	+	0.292791i	−0.915541	+	0.402225i	$0.868237\pi$
$654$	−827.839	−	606.495i	−1.26581	−	0.927363i
$655$	−404.324	+	86.2437i	−0.617289	+	0.131670i
$656$	27.7925			0.0423666
$657$	612.010	−	27.2041i	0.931523	−	0.0414066i
$658$	−18.6769	+	18.6769i	−0.0283843	+	0.0283843i
$659$	−97.2838	+	56.1668i	−0.147623	+	0.0852304i	−0.571992	−	0.820259i	$-0.693829\pi$
$659$	−97.2838	+	56.1668i	−0.147623	+	0.0852304i	0.424369	+	0.905489i	$0.360496\pi$
$660$	−205.027	+	77.9378i	−0.310647	+	0.118088i
$661$	55.4873	−	96.1067i	0.0839444	−	0.145396i	−0.820997	−	0.570933i	$-0.806582\pi$
$661$	55.4873	−	96.1067i	0.0839444	−	0.145396i	0.904941	+	0.425537i	$0.139915\pi$
$662$	−1890.38	+	506.525i	−2.85556	+	0.765144i
$663$	−245.765	+	197.407i	−0.370687	+	0.297748i
$664$	1443.20	−	833.232i	2.17349	−	1.25487i
$665$	385.930	+	756.094i	0.580346	+	1.13698i
$666$	−1380.81	−	304.976i	−2.07329	−	0.457923i
$667$	−189.607	−	189.607i	−0.284268	−	0.284268i
$668$	411.542	+	110.272i	0.616081	+	0.165078i
$669$	−30.9924	−	22.7058i	−0.0463265	−	0.0339400i
$670$	−268.149	+	241.789i	−0.400222	+	0.360880i
$671$	−72.4012	+	125.403i	−0.107900	+	0.186889i
$672$	202.397	−	521.071i	0.301186	−	0.775403i
$673$	−202.929	−	54.3747i	−0.301529	−	0.0807945i	0.104882	−	0.994485i	$-0.466553\pi$
$673$	−202.929	−	54.3747i	−0.301529	−	0.0807945i	−0.406412	+	0.913690i	$0.633220\pi$
$674$			1588.56i			2.35692i
$675$	632.667	−	235.282i	0.937285	−	0.348565i
$676$	−1073.09			−1.58741
$677$	193.957	−	723.857i	0.286495	−	1.06921i	−0.661246	−	0.750169i	$-0.729972\pi$
$677$	193.957	−	723.857i	0.286495	−	1.06921i	0.947740	−	0.319043i	$-0.103361\pi$
$678$	379.331	+	147.342i	0.559485	+	0.217318i
$679$	569.537	+	328.822i	0.838788	+	0.484275i
$680$	−852.150	−	945.049i	−1.25316	−	1.38978i
$681$	784.789	−	1071.20i	1.15241	−	1.57298i
$682$	42.2282	−	157.598i	0.0619182	−	0.231082i
$683$	441.268	−	441.268i	0.646074	−	0.646074i	−0.305968	−	0.952042i	$-0.598980\pi$
$683$	441.268	−	441.268i	0.646074	−	0.646074i	0.952042	+	0.305968i	$0.0989800\pi$
$684$	1142.18	−	361.119i	1.66986	−	0.527952i
$685$	−694.513	+	354.497i	−1.01389	+	0.517514i
$686$	−228.158	−	395.181i	−0.332592	−	0.576066i
$687$	356.339	+	443.631i	0.518688	+	0.645751i
$688$	−52.4952	−	195.915i	−0.0763012	−	0.284760i
$689$	17.6772	+	10.2060i	0.0256564	+	0.0148127i
$690$	−211.958	−	557.587i	−0.307185	−	0.808098i
$691$	396.083	+	686.036i	0.573202	+	0.992816i	0.996234	+	0.0867010i	$0.0276325\pi$
$691$	396.083	+	686.036i	0.573202	+	0.992816i	−0.423032	+	0.906115i	$0.639034\pi$
$692$	489.571	+	489.571i	0.707473	+	0.707473i
$693$	148.963	+	77.3961i	0.214954	+	0.111683i
$694$		−	586.222i		−	0.844700i
$695$	−1.62923	−	7.63810i	−0.00234422	−	0.0109901i
$696$	−418.524	+	571.266i	−0.601327	+	0.820785i
$697$	101.142	−	27.1009i	0.145110	−	0.0388822i
$698$	297.427	+	1110.01i	0.426113	+	1.59027i
$699$	243.799	−	107.389i	0.348783	−	0.153632i
$700$	−1025.47	−	1262.66i	−1.46496	−	1.80380i
$701$	−1185.25			−1.69080			−0.845401	−	0.534133i	$-0.820638\pi$
$701$	−1185.25			−1.69080			−0.845401	+	0.534133i	$0.820638\pi$
$702$	173.023	+	349.813i	0.246471	+	0.498309i
$703$	620.290	−	620.290i	0.882348	−	0.882348i
$704$	−166.736	+	96.2650i	−0.236841	+	0.136740i
$705$	−12.9618	+	1.31970i	−0.0183855	+	0.00187191i
$706$	450.005	−	779.431i	0.637401	−	1.10401i
$707$	−545.733	+	146.229i	−0.771899	+	0.206830i
$708$	250.265	+	1621.75i	0.353481	+	2.29060i
$709$	237.674	−	137.221i	0.335224	−	0.193542i	−0.322934	−	0.946421i	$-0.604669\pi$
$709$	237.674	−	137.221i	0.335224	−	0.193542i	0.658158	+	0.752880i	$0.271336\pi$
$710$	−425.306	+	217.087i	−0.599022	+	0.305756i
$711$	2.04666	+	0.452042i	0.00287856	+	0.000635783i
$712$	766.725	+	766.725i	1.07686	+	1.07686i
$713$	274.732	+	73.6143i	0.385319	+	0.103246i
$714$	−240.133	+	2200.65i	−0.336321	+	3.08215i
$715$	44.2698	+	2.28837i	0.0619159	+	0.00320052i
$716$	−319.362	+	553.152i	−0.446037	+	0.772558i
$717$	125.634	+	156.411i	0.175222	+	0.218146i
$718$	1326.57	+	355.454i	1.84759	+	0.495061i
$719$			1409.12i			1.95983i	0.199416	+	0.979915i	$0.436096\pi$
$719$			1409.12i			1.95983i	−0.199416	+	0.979915i	$0.563904\pi$
$720$	−252.043	+	143.099i	−0.350060	+	0.198749i
$721$	−481.512			−0.667839
$722$	11.8264	−	44.1367i	0.0163800	−	0.0611311i
$723$	−27.1503	−	175.937i	−0.0375523	−	0.243344i
$724$	−1900.94	−	1097.51i	−2.62560	−	1.51589i
$725$	−229.597	−	513.706i	−0.316685	−	0.708560i
$726$	471.517	+	1070.46i	0.649473	+	1.47446i
$727$	−184.607	+	688.962i	−0.253930	+	0.947678i	0.714753	+	0.699377i	$0.246539\pi$
$727$	−184.607	+	688.962i	−0.253930	+	0.947678i	−0.968683	+	0.248302i	$0.920128\pi$
$728$	292.562	−	292.562i	0.401870	−	0.401870i
$729$	−442.419	+	579.402i	−0.606884	+	0.794790i
$730$	350.287	−	1080.70i	0.479845	−	1.48041i
$731$	−382.079	−	661.780i	−0.522680	−	0.905308i
$732$	−548.667	+	1412.54i	−0.749545	+	1.92970i
$733$	−230.005	−	858.390i	−0.313786	−	1.17106i	−0.925115	−	0.379688i	$-0.876031\pi$
$733$	−230.005	−	858.390i	−0.313786	−	1.17106i	0.611329	−	0.791377i	$-0.290635\pi$
$734$	1876.26	+	1083.26i	2.55622	+	1.47583i
$735$	−81.4068	+	503.373i	−0.110758	+	0.684861i
$736$	−121.838	−	211.030i	−0.165541	−	0.286725i
$737$	−31.3198	−	31.3198i	−0.0424964	−	0.0424964i
$738$	−5.75659	−	129.506i	−0.00780025	−	0.175482i
$739$		−	719.160i		−	0.973153i	−0.873638	−	0.486577i	$-0.838245\pi$
$739$		−	719.160i		−	0.973153i	0.873638	−	0.486577i	$-0.161755\pi$
$740$	−914.481	+	1410.38i	−1.23579	+	1.90592i
$741$	−240.670	−	26.2617i	−0.324791	−	0.0354409i
$742$	138.459	−	37.1000i	0.186603	−	0.0500000i
$743$	−43.1096	−	160.887i	−0.0580210	−	0.216537i	0.930828	−	0.365457i	$-0.119087\pi$
$743$	−43.1096	−	160.887i	−0.0580210	−	0.216537i	−0.988849	+	0.148919i	$0.952421\pi$
$744$	81.4830	−	746.734i	0.109520	−	1.00368i
$745$	−105.277	−	493.554i	−0.141311	−	0.662489i
$746$	370.523			0.496679
$747$	−769.299	−	1205.46i	−1.02985	−	1.61374i
$748$	250.904	−	250.904i	0.335433	−	0.335433i
$749$	941.597	−	543.631i	1.25714	−	0.725809i
$750$	2.28577	−	1251.74i	0.00304770	−	1.66898i
$751$	241.781	−	418.776i	0.321945	−	0.557625i	−0.658945	−	0.752192i	$-0.728997\pi$
$751$	241.781	−	418.776i	0.321945	−	0.557625i	0.980889	+	0.194567i	$0.0623301\pi$
$752$	5.40371	−	1.44792i	0.00718578	−	0.00192542i
$753$	247.704	+	96.2146i	0.328957	+	0.127775i
$754$	281.739	−	162.662i	0.373659	−	0.215732i
$755$	336.378	−	1037.79i	0.445534	−	1.37455i
$756$	1664.19	+	562.723i	2.20131	+	0.744343i
$757$	144.792	+	144.792i	0.191270	+	0.191270i	0.796245	−	0.604974i	$-0.206817\pi$
$757$	144.792	+	144.792i	0.191270	+	0.191270i	−0.604974	+	0.796245i	$0.706817\pi$
$758$	−1022.33	−	273.932i	−1.34872	−	0.361388i
$759$	66.9680	−	29.4981i	0.0882319	−	0.0388645i
$760$	50.4504	−	975.992i	0.0663821	−	1.28420i
$761$	149.929	−	259.685i	0.197016	−	0.341241i	−0.750544	−	0.660821i	$-0.770208\pi$
$761$	149.929	−	259.685i	0.197016	−	0.341241i	0.947559	+	0.319580i	$0.103542\pi$
$762$	1138.62	−	175.710i	1.49426	−	0.230591i
$763$	901.799	+	241.636i	1.18191	+	0.316692i
$764$		−	1168.43i		−	1.52935i
$765$	−777.690	+	766.534i	−1.01659	+	1.00201i
$766$	297.459			0.388328
$767$	85.8336	−	320.335i	0.111908	−	0.417647i
$768$	−932.097	+	748.691i	−1.21367	+	0.974858i
$769$	−96.6554	−	55.8040i	−0.125690	−	0.0725670i	0.435837	−	0.900026i	$-0.356452\pi$
$769$	−96.6554	−	55.8040i	−0.125690	−	0.0725670i	−0.561527	+	0.827459i	$0.689786\pi$
$770$	231.194	−	208.467i	0.300251	−	0.270736i
$771$	−468.740	−	51.1485i	−0.607964	−	0.0663405i
$772$	−469.854	+	1753.52i	−0.608619	+	2.27140i
$773$	−43.6287	+	43.6287i	−0.0564408	+	0.0564408i	−0.734764	−	0.678323i	$-0.762707\pi$
$773$	−43.6287	+	43.6287i	−0.0564408	+	0.0564408i	0.678323	+	0.734764i	$0.262707\pi$
$774$	−902.039	+	285.193i	−1.16543	+	0.368467i
$775$	483.355	+	350.124i	0.623684	+	0.451773i
$776$	−378.559	−	655.684i	−0.487834	−	0.844954i
$777$	1271.41	−	196.201i	1.63631	−	0.252512i
$778$	−63.9127	−	238.526i	−0.0821500	−	0.306588i
$779$	69.6438	+	40.2089i	0.0894015	+	0.0516160i
$780$	461.516	−	46.9891i	0.591688	−	0.0602424i
$781$	−29.2888	−	50.7297i	−0.0375016	−	0.0649547i
$782$	682.353	+	682.353i	0.872574	+	0.872574i
$783$	505.678	+	337.019i	0.645821	+	0.430420i
$784$		−	218.947i		−	0.279270i
$785$	1113.81	+	722.183i	1.41886	+	0.919978i
$786$	−333.769	−	757.737i	−0.424642	−	0.964042i
$787$	−1190.57	+	319.011i	−1.51279	+	0.405351i	−0.917361	−	0.398056i	$-0.869685\pi$
$787$	−1190.57	+	319.011i	−1.51279	+	0.405351i	−0.595430	+	0.803407i	$0.703018\pi$
$788$	219.559	+	819.404i	0.278628	+	1.03985i
$789$	−849.381	−	622.277i	−1.07653	−	0.788691i
$790$	2.11460	−	3.26130i	0.00267671	−	0.00412823i
$791$	−370.213			−0.468032
$792$	−103.967	−	162.913i	−0.131272	−	0.205698i
$793$	216.555	−	216.555i	0.273083	−	0.273083i
$794$	1355.89	−	782.824i	1.70767	−	0.985925i
$795$	64.5002	+	28.9692i	0.0811323	+	0.0364393i
$796$	−589.451	+	1020.96i	−0.740516	+	1.28261i
$797$	735.470	−	197.069i	0.922799	−	0.247263i	0.234017	−	0.972232i	$-0.424813\pi$
$797$	735.470	−	197.069i	0.922799	−	0.247263i	0.688781	+	0.724969i	$0.258146\pi$
$798$	−1325.50	+	1064.69i	−1.66103	+	1.33419i
$799$	18.2532	−	10.5385i	0.0228450	−	0.0131896i
$800$	−80.7119	−	504.925i	−0.100890	−	0.631156i
$801$	628.073	−	686.507i	0.784112	−	0.857063i
$802$	1531.17	+	1531.17i	1.90920	+	1.90920i
$803$	134.615	+	36.0700i	0.167640	+	0.0449191i
$804$	−373.916	−	273.940i	−0.465069	−	0.340721i
$805$	363.410	+	403.028i	0.451441	+	0.500656i
$806$	−172.538	+	298.844i	−0.214066	+	0.370774i
$807$	−88.1785	+	227.015i	−0.109267	+	0.281308i
$808$	628.279	+	168.347i	0.777573	+	0.208350i
$809$			225.758i			0.279058i	0.990218	+	0.139529i	$0.0445589\pi$
$809$			225.758i			0.279058i	−0.990218	+	0.139529i	$0.955441\pi$
$810$	719.010	+	1144.81i	0.887667	+	1.41335i
$811$	−149.469			−0.184303			−0.0921513	−	0.995745i	$-0.529374\pi$
$811$	−149.469			−0.184303			−0.0921513	+	0.995745i	$0.529374\pi$
$812$	379.022	−	1414.53i	0.466776	−	1.74203i
$813$	269.607	+	104.722i	0.331620	+	0.128810i
$814$	−278.593	−	160.845i	−0.342251	−	0.197599i
$815$	−1137.46	−	58.7971i	−1.39566	−	0.0721437i
$816$	277.097	−	378.225i	0.339580	−	0.463511i
$817$	151.895	−	566.881i	0.185918	−	0.693856i
$818$	−1486.69	+	1486.69i	−1.81747	+	1.81747i
$819$	−261.953	−	239.656i	−0.319844	−	0.292620i
$820$	−146.586	−	47.5130i	−0.178764	−	0.0579426i
$821$	2.78890	+	4.83052i	0.00339696	+	0.00588370i	0.867719	−	0.497055i	$-0.165585\pi$
$821$	2.78890	+	4.83052i	0.00339696	+	0.00588370i	−0.864322	+	0.502939i	$0.832252\pi$
$822$	−977.970	−	1217.54i	−1.18974	−	1.48120i
$823$	−167.604	−	625.506i	−0.203650	−	0.760032i	−0.989857	−	0.142069i	$-0.954625\pi$
$823$	−167.604	−	625.506i	−0.203650	−	0.760032i	0.786207	−	0.617963i	$-0.212042\pi$
$824$	480.076	+	277.172i	0.582617	+	0.336374i
$825$	153.365	−	7.64690i	0.185897	−	0.00926897i
$826$	−1164.46	−	2016.91i	−1.40976	−	2.44178i
$827$	230.120	+	230.120i	0.278258	+	0.278258i	0.832413	−	0.554155i	$-0.186959\pi$
$827$	230.120	+	230.120i	0.278258	+	0.278258i	−0.554155	+	0.832413i	$0.686959\pi$
$828$	645.541	−	411.971i	0.779639	−	0.497549i
$829$			1504.68i			1.81505i	0.419994	+	0.907527i	$0.362032\pi$
$829$			1504.68i			1.81505i	−0.419994	+	0.907527i	$0.637968\pi$
$830$	−2593.53	+	553.208i	−3.12473	+	0.666515i
$831$	−776.803	+	1060.30i	−0.934781	+	1.27593i
$832$	393.323	−	105.390i	0.472744	−	0.126671i
$833$	−213.499	−	796.788i	−0.256301	−	0.956528i
$834$	14.3145	−	6.30524i	0.0171636	−	0.00756024i
$835$	−250.271	−	162.274i	−0.299725	−	0.194340i
$836$	272.513			0.325973
$837$	−643.258	−	41.3979i	−0.768528	−	0.0494598i
$838$	−417.300	+	417.300i	−0.497971	+	0.497971i
$839$	−915.370	+	528.489i	−1.09103	+	0.629904i	−0.933849	−	0.357667i	$-0.883572\pi$
$839$	−915.370	+	528.489i	−1.09103	+	0.629904i	−0.157176	+	0.987571i	$0.550239\pi$
$840$	905.572	−	1110.88i	1.07806	−	1.32247i
$841$	−167.214	+	289.622i	−0.198827	+	0.344378i
$842$	288.104	−	77.1972i	0.342166	−	0.0916831i
$843$	87.4384	+	566.612i	0.103723	+	0.672137i
$844$	−72.6483	+	41.9435i	−0.0860762	+	0.0496961i
$845$	714.642	+	231.637i	0.845730	+	0.274127i
$846$	−7.86618	−	24.8800i	−0.00929809	−	0.0294089i
$847$	−752.457	−	752.457i	−0.888379	−	0.888379i
$848$	−29.3258	−	7.85783i	−0.0345823	−	0.00926631i
$849$	112.669	−	1032.54i	0.132708	−	1.21618i
$850$	826.269	+	1848.72i	0.972081	+	2.17496i
$851$	280.394	−	485.656i	0.329487	−	0.570689i
$852$	−383.888	−	477.929i	−0.450573	−	0.560949i
$853$	−715.340	−	191.675i	−0.838617	−	0.224707i	−0.186148	−	0.982522i	$-0.559600\pi$
$853$	−715.340	−	191.675i	−0.838617	−	0.224707i	−0.652469	+	0.757815i	$0.726267\pi$
$854$		−	2150.69i		−	2.51837i
$855$	−838.611	−	6.05846i	−0.980831	−	0.00708592i
$856$	−1251.72			−1.46229
$857$	−326.446	+	1218.31i	−0.380918	+	1.42160i	0.463585	+	0.886052i	$0.346563\pi$
$857$	−326.446	+	1218.31i	−0.380918	+	1.42160i	−0.844503	+	0.535551i	$0.820104\pi$
$858$	13.5403	+	87.7427i	0.0157812	+	0.102264i
$859$	37.7603	+	21.8009i	0.0439584	+	0.0253794i	0.521818	−	0.853057i	$-0.325254\pi$
$859$	37.7603	+	21.8009i	0.0439584	+	0.0253794i	−0.477860	+	0.878436i	$0.658587\pi$
$860$	−58.0525	+	1123.06i	−0.0675029	+	1.30588i
$861$	47.5399	+	107.927i	0.0552148	+	0.125351i
$862$	560.142	−	2090.48i	0.649817	−	2.42515i
$863$	−274.423	+	274.423i	−0.317988	+	0.317988i	−0.847994	−	0.530006i	$-0.822190\pi$
$863$	−274.423	+	274.423i	−0.317988	+	0.317988i	0.530006	+	0.847994i	$0.322190\pi$
$864$	364.609	+	414.767i	0.422001	+	0.480054i
$865$	−220.360	−	431.718i	−0.254751	−	0.499096i
$866$	1135.94	+	1967.51i	1.31171	+	2.27195i
$867$	325.677	−	838.454i	0.375637	−	0.967075i
$868$	402.033	+	1500.41i	0.463172	+	1.72858i
$869$	0.412935	+	0.238408i	0.000475184	+	0.000274348i
$870$	913.852	−	659.419i	1.05041	−	0.757953i
$871$	46.8394	+	81.1282i	0.0537766	+	0.0931438i
$872$	−760.017	−	760.017i	−0.871579	−	0.871579i
$873$	−547.673	+	349.513i	−0.627346	+	0.400359i
$874$			741.121i			0.847965i
$875$	410.374	+	1062.25i	0.468999	+	1.21400i
$876$	1449.84	+	158.205i	1.65506	+	0.180599i
$877$	171.710	−	46.0094i	0.195792	−	0.0524623i	−0.159590	−	0.987183i	$-0.551017\pi$
$877$	171.710	−	46.0094i	0.195792	−	0.0524623i	0.355382	+	0.934721i	$0.384351\pi$
$878$	−542.205	−	2023.53i	−0.617545	−	2.30471i
$879$	−97.5184	+	893.687i	−0.110942	+	1.01671i
$880$	−64.4835	+	13.7545i	−0.0732767	+	0.0156302i
$881$	−1000.82			−1.13600			−0.568000	−	0.823029i	$-0.692282\pi$
$881$	−1000.82			−1.13600			−0.568000	+	0.823029i	$0.692282\pi$
$882$	−1020.24	+	45.3500i	−1.15673	+	0.0514172i
$883$	766.494	−	766.494i	0.868057	−	0.868057i	−0.124201	−	0.992257i	$-0.539637\pi$
$883$	766.494	−	766.494i	0.868057	−	0.868057i	0.992257	+	0.124201i	$0.0396366\pi$
$884$	−649.920	+	375.232i	−0.735204	+	0.424470i
$885$	183.402	−	1134.05i	0.207234	−	1.28142i
$886$	−897.522	+	1554.55i	−1.01300	+	1.75457i
$887$	−621.429	+	166.511i	−0.700596	+	0.187724i	−0.591498	−	0.806307i	$-0.701463\pi$
$887$	−621.429	+	166.511i	−0.700596	+	0.187724i	−0.109099	+	0.994031i	$0.534796\pi$
$888$	−1380.56	−	536.244i	−1.55468	−	0.603878i
$889$	−907.698	+	524.060i	−1.02103	+	0.589494i
$890$	−784.452	−	1536.86i	−0.881406	−	1.72681i
$891$	−135.698	+	95.3361i	−0.152299	+	0.106999i
$892$	−64.6759	−	64.6759i	−0.0725067	−	0.0725067i
$893$	15.6357	+	4.18956i	0.0175091	+	0.00469156i
$894$	924.963	−	407.428i	1.03463	−	0.455736i
$895$	332.089	−	299.444i	0.371049	−	0.334574i
$896$	1057.12	−	1830.98i	1.17982	−	2.04350i
$897$	−152.957	+	23.6041i	−0.170521	+	0.0263145i
$898$	812.743	+	217.774i	0.905058	+	0.242510i
$899$			537.328i			0.597696i
$900$	1573.99	−	323.867i	1.74888	−	0.359852i
$901$	−114.384			−0.126952
$902$	7.63268	−	28.4855i	0.00846195	−	0.0315804i
$903$	671.006	−	538.974i	0.743086	−	0.596871i
$904$	369.109	+	213.105i	0.408307	+	0.235736i
$905$	1029.06	+	1141.24i	1.13708	+	1.26104i
$906$	2172.02	+	237.009i	2.39738	+	0.261600i
$907$	−170.993	+	638.156i	−0.188526	+	0.703589i	0.805322	+	0.592838i	$0.201992\pi$
$907$	−170.993	+	638.156i	−0.188526	+	0.703589i	−0.993848	+	0.110752i	$0.964674\pi$
$908$	2235.42	−	2235.42i	2.46191	−	2.46191i
$909$	120.377	−	545.019i	0.132428	−	0.599581i
$910$	−586.423	+	299.326i	−0.644421	+	0.328929i
$911$	536.476	+	929.204i	0.588887	+	1.01998i	0.994379	+	0.105884i	$0.0337671\pi$
$911$	536.476	+	929.204i	0.588887	+	1.01998i	−0.405491	+	0.914099i	$0.632900\pi$
$912$	355.881	−	54.9189i	0.390221	−	0.0602181i
$913$	−84.1979	−	314.231i	−0.0922211	−	0.344174i
$914$	−853.309	−	492.658i	−0.933598	−	0.539013i
$915$	670.307	−	822.273i	0.732576	−	0.898659i
$916$	677.331	+	1173.17i	0.739444	+	1.28075i
$917$	532.635	+	532.635i	0.580846	+	0.580846i
$918$	−1819.82	−	1212.86i	−1.98238	−	1.32120i
$919$			728.665i			0.792889i	0.918059	+	0.396444i	$0.129756\pi$
$919$			728.665i			0.792889i	−0.918059	+	0.396444i	$0.870244\pi$
$920$	−130.332	−	611.015i	−0.141665	−	0.664147i
$921$	−236.692	−	537.349i	−0.256995	−	0.583441i
$922$	1643.59	−	440.399i	1.78264	−	0.477656i
$923$	32.0652	+	119.669i	0.0347402	+	0.129652i
$924$	322.384	+	236.187i	0.348901	+	0.255613i
$925$	913.461	−	741.870i	0.987526	−	0.802022i
$926$	−985.543			−1.06430
$927$	219.317	−	422.117i	0.236588	−	0.455358i
$928$	325.515	−	325.515i	0.350771	−	0.350771i
$929$	−844.876	+	487.790i	−0.909447	+	0.525070i	−0.880253	−	0.474504i	$-0.842627\pi$
$929$	−844.876	+	487.790i	−0.909447	+	0.525070i	−0.0291940	+	0.999574i	$0.509294\pi$
$930$	−489.742	+	1090.41i	−0.526604	+	1.17249i
$931$	316.763	−	548.649i	0.340239	−	0.589312i
$932$	612.611	−	164.149i	0.657308	−	0.176125i
$933$	−250.903	+	201.534i	−0.268921	+	0.216006i
$934$	−1536.11	+	886.871i	−1.64465	+	0.949541i
$935$	−221.255	+	112.934i	−0.236636	+	0.120785i
$936$	123.219	+	389.729i	0.131644	+	0.416377i
$937$	−141.251	−	141.251i	−0.150749	−	0.150749i	0.627704	−	0.778452i	$-0.283995\pi$
$937$	−141.251	−	141.251i	−0.150749	−	0.150749i	−0.778452	+	0.627704i	$0.783995\pi$
$938$	635.447	+	170.268i	0.677449	+	0.181522i
$939$	−1323.62	−	969.716i	−1.40961	−	1.03271i
$940$	−30.9761	−	1.60120i	−0.0329533	−	0.00170340i
$941$	557.909	−	966.326i	0.592889	−	1.02691i	−0.400952	−	0.916099i	$-0.631321\pi$
$941$	557.909	−	966.326i	0.592889	−	1.02691i	0.993841	−	0.110815i	$-0.0353461\pi$
$942$	−962.596	+	2478.20i	−1.02186	+	2.63079i
$943$	49.6574	+	13.3057i	0.0526589	+	0.0141099i
$944$			493.269i			0.522531i
$945$	−986.828	−	733.989i	−1.04426	−	0.776708i
$946$	−215.217			−0.227502
$947$	205.274	−	766.094i	0.216763	−	0.808969i	−0.768776	−	0.639518i	$-0.779134\pi$
$947$	205.274	−	766.094i	0.216763	−	0.808969i	0.985539	−	0.169451i	$-0.0541994\pi$
$948$	4.65132	+	1.80669i	0.00490646	+	0.00190579i
$949$	−255.263	−	147.376i	−0.268981	−	0.155296i
$950$	−555.253	+	1452.68i	−0.584477	+	1.52914i
$951$	−773.604	+	1055.93i	−0.813464	+	1.11034i
$952$	−600.082	+	2239.54i	−0.630338	+	2.35245i
$953$	−80.4623	+	80.4623i	−0.0844305	+	0.0844305i	−0.748061	−	0.663630i	$-0.769015\pi$
$953$	−80.4623	+	80.4623i	−0.0844305	+	0.0844305i	0.663630	+	0.748061i	$0.269015\pi$
$954$	−30.5413	+	138.278i	−0.0320139	+	0.144946i
$955$	−252.217	+	778.135i	−0.264102	+	0.814801i
$956$	238.807	+	413.625i	0.249798	+	0.432662i
$957$	86.5729	+	107.781i	0.0904628	+	0.112623i
$958$	−374.330	−	1397.02i	−0.390741	−	1.45826i
$959$	1230.39	+	710.365i	1.28299	+	0.740735i
$960$	1318.49	−	501.202i	1.37342	−	0.522086i
$961$	195.525	+	338.658i	0.203459	+	0.352402i
$962$	481.095	+	481.095i	0.500099	+	0.500099i
$963$	47.6980	+	1073.06i	0.0495306	+	1.11429i
$964$		−	423.810i		−	0.439636i
$965$	691.423	−	1066.37i	0.716501	−	1.10504i
$966$	−642.328	+	876.748i	−0.664935	+	0.907607i
$967$	−328.164	+	87.9314i	−0.339363	+	0.0909322i	−0.424476	−	0.905439i	$-0.639542\pi$
$967$	−328.164	+	87.9314i	−0.339363	+	0.0909322i	0.0851126	+	0.996371i	$0.472875\pi$
$968$	317.078	+	1183.35i	0.327560	+	1.22247i
$969$	1241.56	−	546.884i	1.28128	−	0.564380i
$970$	251.337	+	1178.31i	0.259110	+	1.21475i
$971$	1786.19			1.83954			0.919769	−	0.392460i	$-0.128376\pi$
$971$	1786.19			1.83954			0.919769	+	0.392460i	$0.128376\pi$
$972$	−1251.31	+	1202.60i	−1.28736	+	1.23724i
$973$	−10.0620	+	10.0620i	−0.0103413	+	0.0103413i
$974$	1707.67	−	985.926i	1.75326	−	1.01224i
$975$	−317.499	−	68.3299i	−0.325640	−	0.0700820i
$976$	−227.759	+	394.490i	−0.233360	+	0.404191i
$977$	743.412	−	199.197i	0.760913	−	0.203886i	0.142560	−	0.989786i	$-0.454467\pi$
$977$	743.412	−	199.197i	0.760913	−	0.203886i	0.618353	+	0.785900i	$0.287800\pi$
$978$	−347.902	−	2254.45i	−0.355728	−	2.30516i
$979$	183.313	−	105.836i	0.187246	−	0.108106i
$980$	−374.304	+	1154.80i	−0.381943	+	1.17836i
$981$	−622.578	+	680.501i	−0.634637	+	0.693681i
$982$	−1817.45	−	1817.45i	−1.85076	−	1.85076i
$983$	79.2948	+	21.2470i	0.0806661	+	0.0216144i	0.298926	−	0.954276i	$-0.403371\pi$
$983$	79.2948	+	21.2470i	0.0806661	+	0.0216144i	−0.218260	+	0.975891i	$0.570038\pi$
$984$	14.7279	−	134.971i	0.0149674	−	0.137166i
$985$	30.6577	−	593.091i	0.0311246	−	0.602123i
$986$	−911.523	+	1578.80i	−0.924466	+	1.60122i
$987$	14.8660	+	18.5076i	0.0150618	+	0.0187514i
$988$	−556.722	−	149.173i	−0.563484	−	0.150985i
$989$		−	375.177i		−	0.379350i
$990$	77.4489	+	297.627i	0.0782312	+	0.300634i
$991$	−515.156			−0.519835			−0.259917	−	0.965631i	$-0.583695\pi$
$991$	−515.156			−0.519835			−0.259917	+	0.965631i	$0.583695\pi$
$992$	−126.381	+	471.659i	−0.127400	+	0.475462i
$993$	268.256	+	1738.33i	0.270147	+	1.75059i
$994$	753.465	+	435.013i	0.758013	+	0.437639i
$995$	612.940	−	552.687i	0.616021	−	0.555465i
$996$	−1372.35	−	3115.57i	−1.37786	−	3.12808i
$997$	−96.0965	+	358.637i	−0.0963856	+	0.359716i	−0.997226	−	0.0744346i	$-0.976285\pi$
$997$	−96.0965	+	358.637i	−0.0963856	+	0.359716i	0.900840	+	0.434151i	$0.142951\pi$
$998$	−231.032	+	231.032i	−0.231495	+	0.231495i
$999$	−407.098	+	1203.94i	−0.407505	+	1.20515i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.3.k.a.22.9	yes	40
3.2	odd	2		135.3.l.a.37.2		40
5.2	odd	4		225.3.o.b.193.9		40
5.3	odd	4	inner	45.3.k.a.13.2	yes	40
5.4	even	2		225.3.o.b.157.2		40
9.2	odd	6		135.3.l.a.127.9		40
9.4	even	3		405.3.g.h.82.9		20
9.5	odd	6		405.3.g.g.82.2		20
9.7	even	3	inner	45.3.k.a.7.2	✓	40
15.8	even	4		135.3.l.a.118.9		40
45.7	odd	12		225.3.o.b.43.2		40
45.13	odd	12		405.3.g.h.163.9		20
45.23	even	12		405.3.g.g.163.2		20
45.34	even	6		225.3.o.b.7.9		40
45.38	even	12		135.3.l.a.73.2		40
45.43	odd	12	inner	45.3.k.a.43.9	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.3.k.a.7.2	✓	40	9.7	even	3	inner
45.3.k.a.13.2	yes	40	5.3	odd	4	inner
45.3.k.a.22.9	yes	40	1.1	even	1	trivial
45.3.k.a.43.9	yes	40	45.43	odd	12	inner
135.3.l.a.37.2		40	3.2	odd	2
135.3.l.a.73.2		40	45.38	even	12
135.3.l.a.118.9		40	15.8	even	4
135.3.l.a.127.9		40	9.2	odd	6
225.3.o.b.7.9		40	45.34	even	6
225.3.o.b.43.2		40	45.7	odd	12
225.3.o.b.157.2		40	5.4	even	2
225.3.o.b.193.9		40	5.2	odd	4
405.3.g.g.82.2		20	9.5	odd	6
405.3.g.g.163.2		20	45.23	even	12
405.3.g.h.82.9		20	9.4	even	3
405.3.g.h.163.9		20	45.13	odd	12

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.k (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.863931 - 3.22423i) q^{2} +(-2.79645 - 1.08621i) q^{3} +(-6.18520 - 3.57103i) q^{4} +(3.34831 + 3.71333i) q^{5} +(-5.91814 + 8.07800i) q^{6} +(2.35787 - 8.79970i) q^{7} +(-7.41620 + 7.41620i) q^{8} +(6.64028 + 6.07508i) q^{9} +(14.8654 - 7.58766i) q^{10} +(1.02371 + 1.77311i) q^{11} +(13.4177 + 16.7046i) q^{12} +(-1.12075 - 4.18269i) q^{13} +(-26.3352 - 15.2047i) q^{14} +(-5.32991 - 14.0211i) q^{15} +(3.22036 + 5.57783i) q^{16} +(17.1585 + 17.1585i) q^{17} +(25.3242 - 16.1614i) q^{18} +18.6363i q^{19} +(-7.44954 - 34.9246i) q^{20} +(-16.1520 + 22.0468i) q^{21} +(6.60133 - 1.76882i) q^{22} +(3.08350 + 11.5078i) q^{23} +(28.7946 - 12.6835i) q^{24} +(-2.57768 + 24.8668i) q^{25} -14.4542 q^{26} +(-11.9704 - 24.2014i) q^{27} +(-46.0079 + 46.0079i) q^{28} +(-19.4918 + 11.2536i) q^{29} +(-49.8121 + 5.07159i) q^{30} +(11.9368 - 20.6752i) q^{31} +(-19.7565 + 5.29373i) q^{32} +(-0.936770 - 6.07038i) q^{33} +(70.1467 - 40.4992i) q^{34} +(40.5711 - 20.7085i) q^{35} +(-19.3772 - 61.2882i) q^{36} +(-33.2840 - 33.2840i) q^{37} +(60.0877 + 16.1005i) q^{38} +(-1.40917 + 12.9141i) q^{39} +(-52.3705 - 2.70711i) q^{40} +(2.15756 - 3.73700i) q^{41} +(57.1297 + 71.1247i) q^{42} +(-30.4181 - 8.15051i) q^{43} -14.6227i q^{44} +(-0.325090 + 44.9988i) q^{45} +39.7677 q^{46} +(0.224807 - 0.838990i) q^{47} +(-2.94688 - 19.0961i) q^{48} +(-29.4398 - 16.9971i) q^{49} +(77.9493 + 29.7942i) q^{50} +(-29.3451 - 66.6207i) q^{51} +(-8.00445 + 29.8730i) q^{52} +(-3.33316 + 3.33316i) q^{53} +(-88.3727 + 17.6870i) q^{54} +(-3.15647 + 9.73828i) q^{55} +(47.7739 + 82.7467i) q^{56} +(20.2430 - 52.1155i) q^{57} +(19.4446 + 72.5684i) q^{58} +(66.3254 + 38.2930i) q^{59} +(-17.1033 + 105.757i) q^{60} +(35.3623 + 61.2493i) q^{61} +(-56.3490 - 56.3490i) q^{62} +(69.1158 - 44.1082i) q^{63} +94.0358i q^{64} +(11.7791 - 18.1667i) q^{65} +(-20.3816 - 2.22403i) q^{66} +(-20.8965 + 5.59919i) q^{67} +(-44.8553 - 167.402i) q^{68} +(3.87703 - 35.5302i) q^{69} +(-31.7185 - 148.701i) q^{70} -28.6105 q^{71} +(-94.2997 + 4.19166i) q^{72} +(48.1316 - 48.1316i) q^{73} +(-136.071 + 78.5604i) q^{74} +(34.2189 - 66.7388i) q^{75} +(66.5507 - 115.269i) q^{76} +(18.0166 - 4.82753i) q^{77} +(40.4205 + 15.7004i) q^{78} +(0.201686 - 0.116444i) q^{79} +(-9.92959 + 30.6346i) q^{80} +(7.18677 + 80.6805i) q^{81} +(-10.1850 - 10.1850i) q^{82} +(-153.477 - 41.1240i) q^{83} +(178.633 - 78.6845i) q^{84} +(-6.26330 + 121.167i) q^{85} +(-52.5583 + 91.0337i) q^{86} +(66.7316 - 10.2979i) q^{87} +(-20.7418 - 5.55774i) q^{88} -103.385i q^{89} +(144.806 + 39.9240i) q^{90} -39.4490 q^{91} +(22.0225 - 82.1891i) q^{92} +(-55.8384 + 44.8512i) q^{93} +(-2.51088 - 1.44966i) q^{94} +(-69.2027 + 62.4000i) q^{95} +(60.9981 + 6.65606i) q^{96} +(-18.6837 + 69.7287i) q^{97} +(-80.2366 + 80.2366i) q^{98} +(-3.97409 + 17.9931i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 2 q^{2} - 6 q^{3} - 2 q^{5} - 24 q^{6} - 2 q^{7} - 24 q^{8} - 8 q^{10} + 8 q^{11} - 30 q^{12} - 2 q^{13} - 30 q^{15} + 28 q^{16} + 28 q^{17} + 48 q^{18} - 114 q^{20} + 12 q^{21} + 14 q^{22} + 82 q^{23}+ \cdots - 1876 q^{98}+O(q^{100}) \) 40 * q - 2 * q^2 - 6 * q^3 - 2 * q^5 - 24 * q^6 - 2 * q^7 - 24 * q^8 - 8 * q^10 + 8 * q^11 - 30 * q^12 - 2 * q^13 - 30 * q^15 + 28 * q^16 + 28 * q^17 + 48 * q^18 - 114 * q^20 + 12 * q^21 + 14 * q^22 + 82 * q^23 - 8 * q^25 - 112 * q^26 - 198 * q^27 - 88 * q^28 + 162 * q^30 - 4 * q^31 - 14 * q^32 + 96 * q^33 + 352 * q^35 + 264 * q^36 - 92 * q^37 + 330 * q^38 + 30 * q^40 - 28 * q^41 + 498 * q^42 - 2 * q^43 - 72 * q^45 - 136 * q^46 + 64 * q^47 - 510 * q^48 - 458 * q^50 - 396 * q^51 - 74 * q^52 - 608 * q^53 + 224 * q^55 - 192 * q^56 - 114 * q^57 + 30 * q^58 - 798 * q^60 + 92 * q^61 - 100 * q^62 + 24 * q^63 - 326 * q^65 + 588 * q^66 - 80 * q^67 + 626 * q^68 - 102 * q^70 + 248 * q^71 - 162 * q^72 - 8 * q^73 + 810 * q^75 - 96 * q^76 + 338 * q^77 + 1062 * q^78 + 1444 * q^80 + 204 * q^81 + 104 * q^82 + 370 * q^83 - 98 * q^85 - 328 * q^86 + 534 * q^87 - 210 * q^88 + 462 * q^90 + 152 * q^91 + 388 * q^92 - 1062 * q^93 - 360 * q^95 - 876 * q^96 + 292 * q^97 - 1876 * q^98

Introduction

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