LMFDB - Embedded newform 45.3.k.a.13.2

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			13.2
Character	$\chi$	$=$	45.13
Dual form			45.3.k.a.7.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3.22423 - 0.863931i) q^{2} +(1.08621 - 2.79645i) q^{3} +(6.18520 + 3.57103i) q^{4} +(-4.88999 - 1.04305i) q^{5} +(-5.91814 + 8.07800i) q^{6} +(-8.79970 - 2.35787i) 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} +(16.7046 - 13.4177i) q^{12} +(4.18269 - 1.12075i) q^{13} +(26.3352 + 15.2047i) q^{14} +(-8.22842 + 12.5417i) q^{15} +(3.22036 + 5.57783i) q^{16} +(17.1585 - 17.1585i) q^{17} +(16.1614 + 25.3242i) q^{18} -18.6363i q^{19} +(-26.5208 - 23.9138i) q^{20} +(-16.1520 + 22.0468i) q^{21} +(-1.76882 - 6.60133i) q^{22} +(-11.5078 + 3.08350i) q^{23} +(-28.7946 + 12.6835i) q^{24} +(22.8241 + 10.2010i) q^{25} -14.4542 q^{26} +(-24.2014 + 11.9704i) q^{27} +(-46.0079 - 46.0079i) q^{28} +(19.4918 - 11.2536i) q^{29} +(37.3655 - 33.3284i) q^{30} +(11.9368 - 20.6752i) q^{31} +(5.29373 + 19.7565i) q^{32} +(6.07038 - 0.936770i) 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} +(-16.1005 + 60.0877i) q^{38} +(1.40917 - 12.9141i) q^{39} +(28.5297 + 44.0007i) q^{40} +(2.15756 - 3.73700i) q^{41} +(71.1247 - 57.1297i) q^{42} +(8.15051 - 30.4181i) q^{43} +14.6227i q^{44} +(26.1343 + 36.6333i) q^{45} +39.7677 q^{46} +(-0.838990 - 0.224807i) q^{47} +(19.0961 - 2.94688i) q^{48} +(29.4398 + 16.9971i) q^{49} +(-64.7772 - 52.6090i) q^{50} +(-29.3451 - 66.6207i) q^{51} +(29.8730 + 8.00445i) 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} +(-52.1155 - 20.2430i) q^{57} +(-72.5684 + 19.4446i) q^{58} +(-66.3254 - 38.2930i) q^{59} +(-95.6810 + 48.1888i) q^{60} +(35.3623 + 61.2493i) q^{61} +(-56.3490 + 56.3490i) q^{62} +(44.1082 + 69.1158i) q^{63} -94.0358i q^{64} +(-21.6223 + 1.11769i) q^{65} +(-20.3816 - 2.22403i) q^{66} +(5.59919 + 20.8965i) q^{67} +(167.402 - 44.8553i) q^{68} +(-3.87703 + 35.5302i) q^{69} +(-112.920 - 101.820i) q^{70} -28.6105 q^{71} +(4.19166 + 94.2997i) q^{72} +(48.1316 + 48.1316i) q^{73} +(136.071 - 78.5604i) q^{74} +(53.3185 - 52.7460i) q^{75} +(66.5507 - 115.269i) q^{76} +(-4.82753 - 18.0166i) q^{77} +(-15.7004 + 40.4205i) 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} +(41.1240 - 153.477i) q^{83} +(-178.633 + 78.6845i) q^{84} +(-101.802 + 66.0077i) q^{85} +(-52.5583 + 91.0337i) q^{86} +(-10.2979 - 66.7316i) q^{87} +(5.55774 - 20.7418i) q^{88} +103.385i q^{89} +(-52.6145 - 140.692i) q^{90} -39.4490 q^{91} +(-82.1891 - 22.0225i) q^{92} +(-44.8512 - 55.8384i) q^{93} +(2.51088 + 1.44966i) q^{94} +(-19.4386 + 91.1313i) q^{95} +(60.9981 + 6.65606i) q^{96} +(69.7287 + 18.6837i) 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 $\left(\mathbb{Z}/45\mathbb{Z}\right)^\times$.

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

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 $

$2$	−3.22423	−	0.863931i	−1.61212	−	0.431965i	−0.663444	−	0.748226i	$-0.730906\pi$
$2$	−3.22423	−	0.863931i	−1.61212	−	0.431965i	−0.948672	+	0.316261i	$0.897573\pi$
$3$	1.08621	−	2.79645i	0.362071	−	0.932151i
$3$	1.08621	−	2.79645i	0.362071	−	0.932151i
$4$	6.18520	+	3.57103i	1.54630	+	0.892757i
$5$	−4.88999	−	1.04305i	−0.977999	−	0.208610i
$5$	−4.88999	−	1.04305i	−0.977999	−	0.208610i
$6$	−5.91814	+	8.07800i	−0.986357	+	1.34633i
$7$	−8.79970	−	2.35787i	−1.25710	−	0.336839i	−0.432024	−	0.901862i	$-0.642201\pi$
$7$	−8.79970	−	2.35787i	−1.25710	−	0.336839i	−0.825075	+	0.565023i	$0.808867\pi$
$8$	−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	$0.803667\pi$
$12$	16.7046	−	13.4177i	1.39205	−	1.11814i
$13$	4.18269	−	1.12075i	0.321746	−	0.0862115i	−0.0943314	−	0.995541i	$-0.530071\pi$
$13$	4.18269	−	1.12075i	0.321746	−	0.0862115i	0.416077	+	0.909329i	$0.363405\pi$
$14$	26.3352	+	15.2047i	1.88109	+	1.08605i
$15$	−8.22842	+	12.5417i	−0.548561	+	0.836110i
$16$	3.22036	+	5.57783i	0.201273	+	0.348615i
$17$	17.1585	−	17.1585i	1.00932	−	1.00932i	0.00936716	−	0.999956i	$-0.497018\pi$
$17$	17.1585	−	17.1585i	1.00932	−	1.00932i	0.999956	−	0.00936716i	$-0.00298170\pi$
$18$	16.1614	+	25.3242i	0.897854	+	1.40690i
$19$		−	18.6363i		−	0.980857i	−0.871481	−	0.490428i	$-0.836840\pi$
$19$		−	18.6363i		−	0.980857i	0.871481	−	0.490428i	$-0.163160\pi$
$20$	−26.5208	−	23.9138i	−1.32604	−	1.19569i
$21$	−16.1520	+	22.0468i	−0.769143	+	1.04985i
$22$	−1.76882	−	6.60133i	−0.0804010	−	0.300061i
$23$	−11.5078	+	3.08350i	−0.500338	+	0.134065i	−0.500157	−	0.865935i	$-0.666724\pi$
$23$	−11.5078	+	3.08350i	−0.500338	+	0.134065i	−0.000180980		1.00000i	$0.500058\pi$
$24$	−28.7946	+	12.6835i	−1.19978	+	0.528478i
$25$	22.8241	+	10.2010i	0.912963	+	0.408042i
$26$	−14.4542			−0.555932
$27$	−24.2014	+	11.9704i	−0.896349	+	0.443348i
$28$	−46.0079	−	46.0079i	−1.64314	−	1.64314i
$29$	19.4918	−	11.2536i	0.672131	−	0.388055i	−0.124753	−	0.992188i	$-0.539814\pi$
$29$	19.4918	−	11.2536i	0.672131	−	0.388055i	0.796883	+	0.604133i	$0.206480\pi$
$30$	37.3655	−	33.3284i	1.24552	−	1.11095i
$31$	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	$0.0408478\pi$
$32$	5.29373	+	19.7565i	0.165429	+	0.617389i
$33$	6.07038	−	0.936770i	0.183951	−	0.0283870i
$34$	−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	−0.995398	−	0.0958294i	$-0.969450\pi$
$37$	−33.2840	+	33.2840i	−0.899568	+	0.899568i	0.0958294	+	0.995398i	$0.469450\pi$
$38$	−16.1005	+	60.0877i	−0.423696	+	1.58126i
$39$	1.40917	−	12.9141i	0.0361326	−	0.331130i
$40$	28.5297	+	44.0007i	0.713242	+	1.10002i
$41$	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	$0.149908\pi$
$42$	71.1247	−	57.1297i	1.69345	−	1.36023i
$43$	8.15051	−	30.4181i	0.189547	−	0.707398i	−0.804065	−	0.594542i	$-0.797333\pi$
$43$	8.15051	−	30.4181i	0.189547	−	0.707398i	0.993611	−	0.112856i	$-0.0360000\pi$
$44$			14.6227i			0.332335i
$45$	26.1343	+	36.6333i	0.580763	+	0.814073i
$46$	39.7677			0.864514
$47$	−0.838990	−	0.224807i	−0.0178509	−	0.00478312i	0.249883	−	0.968276i	$-0.419608\pi$
$47$	−0.838990	−	0.224807i	−0.0178509	−	0.00478312i	−0.267733	+	0.963493i	$0.586275\pi$
$48$	19.0961	−	2.94688i	0.397836	−	0.0613933i
$49$	29.4398	+	16.9971i	0.600813	+	0.346880i
$50$	−64.7772	−	52.6090i	−1.29554	−	1.05218i
$51$	−29.3451	−	66.6207i	−0.575395	−	1.30629i
$52$	29.8730	+	8.00445i	0.574481	+	0.153932i
$53$	−3.33316	−	3.33316i	−0.0628899	−	0.0628899i	0.674962	−	0.737852i	$-0.264160\pi$
$53$	−3.33316	−	3.33316i	−0.0628899	−	0.0628899i	−0.737852	+	0.674962i	$0.764160\pi$
$54$	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
$57$	−52.1155	−	20.2430i	−0.914306	−	0.355140i
$58$	−72.5684	+	19.4446i	−1.25118	+	0.335252i
$59$	−66.3254	−	38.2930i	−1.12416	−	0.649033i	−0.181699	−	0.983354i	$-0.558160\pi$
$59$	−66.3254	−	38.2930i	−1.12416	−	0.649033i	−0.942459	+	0.334321i	$0.891493\pi$
$60$	−95.6810	+	48.1888i	−1.59468	+	0.803146i
$61$	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
$63$	44.1082	+	69.1158i	0.700131	+	1.09708i
$64$		−	94.0358i		−	1.46931i
$65$	−21.6223	+	1.11769i	−0.332651	+	0.0171952i
$66$	−20.3816	−	2.22403i	−0.308813	−	0.0336974i
$67$	5.59919	+	20.8965i	0.0835700	+	0.311888i	0.995040	−	0.0994800i	$-0.0317179\pi$
$67$	5.59919	+	20.8965i	0.0835700	+	0.311888i	−0.911470	+	0.411368i	$0.865051\pi$
$68$	167.402	−	44.8553i	2.46180	−	0.659637i
$69$	−3.87703	+	35.5302i	−0.0561888	+	0.514931i
$70$	−112.920	−	101.820i	−1.61314	−	1.45457i
$71$	−28.6105			−0.402965			−0.201483	−	0.979492i	$-0.564576\pi$
$71$	−28.6105			−0.402965			−0.201483	+	0.979492i	$0.564576\pi$
$72$	4.19166	+	94.2997i	0.0582175	+	1.30972i
$73$	48.1316	+	48.1316i	0.659336	+	0.659336i	0.955223	−	0.295887i	$-0.0956151\pi$
$73$	48.1316	+	48.1316i	0.659336	+	0.659336i	−0.295887	+	0.955223i	$0.595615\pi$
$74$	136.071	−	78.5604i	1.83879	−	1.06163i
$75$	53.3185	−	52.7460i	0.710914	−	0.703279i
$76$	66.5507	−	115.269i	0.875667	−	1.51670i
$77$	−4.82753	−	18.0166i	−0.0626953	−	0.233982i
$78$	−15.7004	+	40.4205i	−0.201287	+	0.518212i
$79$	−0.201686	+	0.116444i	−0.00255299	+	0.00147397i	−0.501276	−	0.865287i	$-0.667136\pi$
$79$	−0.201686	+	0.116444i	−0.00255299	+	0.00147397i	0.498723	+	0.866761i	$0.333803\pi$
$80$	−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
$83$	41.1240	−	153.477i	0.495470	−	1.84912i	−0.0319094	−	0.999491i	$-0.510159\pi$
$83$	41.1240	−	153.477i	0.495470	−	1.84912i	0.527380	−	0.849630i	$-0.323175\pi$
$84$	−178.633	+	78.6845i	−2.12658	+	0.936720i
$85$	−101.802	+	66.0077i	−1.19767	+	0.776562i
$86$	−52.5583	+	91.0337i	−0.611143	+	1.05853i
$87$	−10.2979	−	66.7316i	−0.118367	−	0.767030i
$88$	5.55774	−	20.7418i	0.0631561	−	0.235702i
$89$			103.385i			1.16163i	0.814035	+	0.580816i	$0.197266\pi$
$89$			103.385i			1.16163i	−0.814035	+	0.580816i	$0.802734\pi$
$90$	−52.6145	−	140.692i	−0.584606	−	1.56325i
$91$	−39.4490			−0.433506
$92$	−82.1891	−	22.0225i	−0.893360	−	0.239375i
$93$	−44.8512	−	55.8384i	−0.482271	−	0.600413i
$94$	2.51088	+	1.44966i	0.0267115	+	0.0154219i
$95$	−19.4386	+	91.1313i	−0.204617	+	0.959277i
$96$	60.9981	+	6.65606i	0.635397	+	0.0693340i
$97$	69.7287	+	18.6837i	0.718852	+	0.192616i	0.599660	−	0.800255i	$-0.295303\pi$
$97$	69.7287	+	18.6837i	0.718852	+	0.192616i	0.119193	+	0.992871i	$0.461969\pi$
$98$	−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	$0.932664\pi$
$102$	37.0599	+	240.153i	0.363332	+	2.35444i
$103$	51.0537	−	13.6798i	0.495667	−	0.132813i	−0.00232157	−	0.999997i	$-0.500739\pi$
$103$	51.0537	−	13.6798i	0.495667	−	0.132813i	0.497988	+	0.867184i	$0.334072\pi$
$104$	−39.3314	−	22.7080i	−0.378186	−	0.218346i
$105$	101.979	−	90.9612i	0.971230	−	0.866297i
$106$	7.86727	+	13.6265i	0.0742195	+	0.128552i
$107$	84.3909	−	84.3909i	0.788700	−	0.788700i	−0.192581	−	0.981281i	$-0.561686\pi$
$107$	84.3909	−	84.3909i	0.788700	−	0.788700i	0.981281	+	0.192581i	$0.0616859\pi$
$108$	−192.437	−	12.3846i	−1.78183	−	0.114672i
$109$		−	102.481i		−	0.940190i	−0.882616	−	0.470095i	$-0.844220\pi$
$109$		−	102.481i		−	0.940190i	0.882616	−	0.470095i	$-0.155780\pi$
$110$	1.76399	+	34.1255i	0.0160363	+	0.310231i
$111$	56.9237	+	129.231i	0.512826	+	1.16424i
$112$	−15.1864	−	56.6764i	−0.135593	−	0.506040i
$113$	39.2529	−	10.5178i	0.347371	−	0.0930777i	−0.0809152	−	0.996721i	$-0.525784\pi$
$113$	39.2529	−	10.5178i	0.347371	−	0.0930777i	0.428286	+	0.903643i	$0.359118\pi$
$114$	150.544	+	110.292i	1.32056	+	0.967475i
$115$	59.4892	−	3.07508i	0.517297	−	0.0267398i
$116$	160.747			1.38575
$117$	−34.5829	−	17.9681i	−0.295580	−	0.153574i
$118$	180.766	+	180.766i	1.53192	+	1.53192i
$119$	−191.447	+	110.532i	−1.60880	+	0.928840i
$120$	154.035	−	31.9878i	1.28363	−	0.266565i
$121$	58.4041	−	101.159i	0.482678	−	0.836023i
$122$	−61.1012	−	228.033i	−0.500829	−	1.86912i
$123$	−8.10678	−	10.0927i	−0.0659088	−	0.0820544i
$124$	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	−0.950696	−	0.310124i	$-0.899630\pi$
$127$	−81.3527	+	81.3527i	−0.640572	+	0.640572i	0.310124	+	0.950696i	$0.399630\pi$
$128$	−60.0655	+	224.167i	−0.469261	+	1.75131i
$129$	−76.2096	−	55.8331i	−0.590772	−	0.432814i
$130$	70.6811	+	15.0765i	0.543701	+	0.115973i
$131$	−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	$0.268868\pi$
$132$	40.8918	+	15.8834i	0.309786	+	0.120329i
$133$	−43.9420	+	163.994i	−0.330391	+	1.23303i
$134$		−	72.2124i		−	0.538899i
$135$	130.831	−	33.2919i	0.969116	−	0.246606i
$136$	−254.502			−1.87134
$137$	150.637	+	40.3630i	1.09954	+	0.294621i	0.762577	−	0.646898i	$-0.223934\pi$
$137$	150.637	+	40.3630i	1.09954	+	0.294621i	0.336962	+	0.941518i	$0.390601\pi$
$138$	43.1961	−	111.208i	0.313015	−	0.805857i
$139$	1.35272	+	0.780993i	0.00973180	+	0.00561866i	0.504858	−	0.863202i	$-0.331545\pi$
$139$	1.35272	+	0.780993i	0.00973180	+	0.00561866i	−0.495126	+	0.868821i	$0.664878\pi$
$140$	176.990	+	272.967i	1.26421	+	1.94976i
$141$	−1.53998	+	2.10201i	−0.0109219	+	0.0149079i
$142$	92.2470	+	24.7175i	0.649627	+	0.174067i
$143$	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
$147$	79.5095	−	63.8646i	0.540881	−	0.434453i
$148$	−324.727	+	87.0102i	−2.19410	+	0.587907i
$149$	87.4092	+	50.4657i	0.586639	+	0.338696i	0.763767	−	0.645492i	$-0.223347\pi$
$149$	87.4092	+	50.4657i	0.586639	+	0.338696i	−0.177128	+	0.984188i	$0.556681\pi$
$150$	−217.480	+	124.002i	−1.44987	+	0.826678i
$151$	−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
$153$	−218.177	+	9.69804i	−1.42599	+	0.0633859i
$154$			62.2604i			0.404288i
$155$	−79.9363	+	88.6508i	−0.515718	+	0.571941i
$156$	54.8325	−	74.8439i	0.351490	−	0.479769i
$157$	−68.7136	−	256.443i	−0.437666	−	1.63339i	−0.734604	−	0.678496i	$-0.762632\pi$
$157$	−68.7136	−	256.443i	−0.437666	−	1.63339i	0.296937	−	0.954897i	$-0.404035\pi$
$158$	0.750883	−	0.201198i	0.00475242	−	0.00127341i
$159$	−12.9416	+	5.70051i	−0.0813934	+	0.0358522i
$160$	−5.27928	−	102.131i	−0.0329955	−	0.638316i
$161$	108.535			0.674133
$162$	46.5306	−	266.342i	0.287226	−	1.64408i
$163$	−161.076	−	161.076i	−0.988199	−	0.988199i	0.0117324	−	0.999931i	$-0.496265\pi$
$163$	−161.076	−	161.076i	−0.988199	−	0.988199i	−0.999931	+	0.0117324i	$0.996265\pi$
$164$	26.6899	−	15.4094i	0.162743	−	0.0939598i
$165$	−30.6612	−	1.75093i	−0.185826	−	0.0106117i
$166$	−265.187	+	459.317i	−1.59751	+	2.76697i
$167$	15.4399	+	57.6223i	0.0924542	+	0.345044i	0.996621	−	0.0821354i	$-0.0261740\pi$
$167$	15.4399	+	57.6223i	0.0924542	+	0.345044i	−0.904167	+	0.427179i	$0.859507\pi$
$168$	283.290	−	43.7167i	1.68625	−	0.260219i
$169$	−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
$173$	25.0902	−	93.6378i	0.145030	−	0.541259i	−0.854724	−	0.519083i	$-0.826274\pi$
$173$	25.0902	−	93.6378i	0.145030	−	0.541259i	0.999754	−	0.0221766i	$-0.00705962\pi$
$174$	−24.4487	+	224.055i	−0.140510	+	1.28767i
$175$	−176.792	−	143.582i	−1.01024	−	0.820470i
$176$	−6.59341	+	11.4201i	−0.0374626	+	0.0648871i
$177$	−179.128	+	143.881i	−1.01202	+	0.812889i
$178$	89.3176	−	333.338i	0.501784	−	1.87269i
$179$			89.4315i			0.499617i	0.968295	+	0.249809i	$0.0803677\pi$
$179$			89.4315i			0.499617i	−0.968295	+	0.249809i	$0.919632\pi$
$180$	30.8276	+	319.911i	0.171265	+	1.77728i
$181$	307.336			1.69799			0.848995	−	0.528401i	$-0.177208\pi$
$181$	307.336			1.69799			0.848995	+	0.528401i	$0.177208\pi$
$182$	127.193	+	34.0812i	0.698861	+	0.187259i
$183$	209.692	−	32.3592i	1.14586	−	0.176826i
$184$	108.212	+	62.4761i	0.588107	+	0.339544i
$185$	197.476	−	128.042i	1.06744	−	0.692117i
$186$	96.3703	+	218.784i	0.518120	+	1.17626i
$187$	47.9892	+	12.8587i	0.256627	+	0.0687629i
$188$	−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	$0.692458\pi$
$192$	−262.966	−	102.143i	−1.36962	−	0.531994i
$193$	245.520	−	65.7869i	1.27212	−	0.340865i	0.441280	−	0.897369i	$-0.354524\pi$
$193$	245.520	−	65.7869i	1.27212	−	0.340865i	0.830845	+	0.556504i	$0.187858\pi$
$194$	−208.680	−	120.481i	−1.07567	−	0.621039i
$195$	−20.3609	+	61.6799i	−0.104415	+	0.316307i
$196$	121.394	+	210.261i	0.619358	+	1.07276i
$197$	−83.9878	+	83.9878i	−0.426334	+	0.426334i	−0.887377	−	0.461044i	$-0.847475\pi$
$197$	−83.9878	+	83.9878i	−0.426334	+	0.426334i	0.461044	+	0.887377i	$0.347475\pi$
$198$	−28.3582	+	54.5805i	−0.143223	+	0.275659i
$199$			165.065i			0.829471i	0.909942	+	0.414736i	$0.136126\pi$
$199$			165.065i			0.829471i	−0.909942	+	0.414736i	$0.863874\pi$
$200$	−93.6150	−	244.921i	−0.468075	−	1.22460i
$201$	64.5179	+	7.04014i	0.320985	+	0.0350256i
$202$	53.5786	+	199.958i	0.265240	+	0.989891i
$203$	−198.056	+	53.0690i	−0.975647	+	0.261424i
$204$	56.3987	−	516.855i	0.276464	−	2.53360i
$205$	−14.4483	+	16.0235i	−0.0704797	+	0.0781633i
$206$	−176.427			−0.856443
$207$	95.1473	+	49.4353i	0.459649	+	0.238818i
$208$	19.7211	+	19.7211i	0.0948132	+	0.0948132i
$209$	33.0442	−	19.0781i	0.158106	−	0.0912827i
$210$	−407.389	+	205.177i	−1.93995	+	0.977034i
$211$	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	$0.157806\pi$
$212$	−8.71347	−	32.5191i	−0.0411013	−	0.153392i
$213$	−31.0771	+	80.0080i	−0.145902	+	0.375624i
$214$	−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
$218$	−88.5362	+	330.422i	−0.406129	+	1.51570i
$219$	186.879	−	82.3165i	0.853327	−	0.375874i
$220$	15.2523	−	71.5051i	0.0693285	−	0.325023i
$221$	52.5383	−	90.9991i	0.237730	−	0.411761i
$222$	−71.8888	−	465.848i	−0.323823	−	2.09841i
$223$	−3.31460	+	12.3702i	−0.0148637	+	0.0554720i	−0.972959	−	0.230976i	$-0.925808\pi$
$223$	−3.31460	+	12.3702i	−0.0148637	+	0.0554720i	0.958096	+	0.286448i	$0.0924747\pi$
$224$		−	186.333i		−	0.831843i
$225$	−89.5863	−	206.396i	−0.398161	−	0.917315i
$226$	−135.647			−0.600208
$227$	427.557	+	114.563i	1.88351	+	0.504685i	0.999293	+	0.0376093i	$0.0119742\pi$
$227$	427.557	+	114.563i	1.88351	+	0.504685i	0.884217	+	0.467076i	$0.154692\pi$
$228$	−250.056	−	311.313i	−1.09674	−	1.36541i
$229$	164.262	+	94.8369i	0.717303	+	0.414135i	0.813759	−	0.581202i	$-0.197417\pi$
$229$	164.262	+	94.8369i	0.717303	+	0.414135i	−0.0964562	+	0.995337i	$0.530751\pi$
$230$	−194.464	−	41.4797i	−0.845494	−	0.180347i
$231$	−55.6263	−	6.06989i	−0.240806	−	0.0262766i
$232$	−228.014	−	61.0961i	−0.982818	−	0.263345i
$233$	−62.7917	−	62.7917i	−0.269492	−	0.269492i	0.559403	−	0.828896i	$-0.311030\pi$
$233$	−62.7917	−	62.7917i	−0.269492	−	0.269492i	−0.828896	+	0.559403i	$0.811030\pi$
$234$	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
$237$	0.106555	+	0.690489i	0.000449599	+	0.00291345i
$238$	712.762	−	190.984i	2.99480	−	0.802454i
$239$	57.9140	+	33.4367i	0.242318	+	0.139902i	0.616242	−	0.787557i	$-0.288654\pi$
$239$	57.9140	+	33.4367i	0.242318	+	0.139902i	−0.373924	+	0.927460i	$0.621988\pi$
$240$	−96.4538	−	5.50805i	−0.401891	−	0.0229502i
$241$	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
$243$	233.426	+	67.5388i	0.960599	+	0.277937i
$244$			505.119i			2.07016i
$245$	−126.232	−	113.823i	−0.515232	−	0.464584i
$246$	17.4188	+	39.5449i	0.0708080	+	0.160751i
$247$	−20.8866	−	77.9498i	−0.0845611	−	0.315586i
$248$	−241.857	+	64.8054i	−0.975230	+	0.261312i
$249$	−384.522	−	281.710i	−1.54426	−	1.13137i
$250$	261.886	+	324.823i	1.04754	+	1.29929i
$251$	−88.5781			−0.352901			−0.176450	−	0.984310i	$-0.556461\pi$
$251$	−88.5781			−0.352901			−0.176450	+	0.984310i	$0.556461\pi$
$252$	26.0038	+	585.007i	0.103190	+	2.32146i
$253$	−17.2480	−	17.2480i	−0.0681737	−	0.0681737i
$254$	332.583	−	192.017i	1.30938	−	0.755972i
$255$	74.0087	+	356.383i	0.290230	+	1.39758i
$256$	199.259	−	345.126i	0.778354	−	1.34815i
$257$	−40.6797	−	151.819i	−0.158287	−	0.590734i	−0.998801	−	0.0489452i	$-0.984414\pi$
$257$	−40.6797	−	151.819i	−0.158287	−	0.590734i	0.840515	−	0.541789i	$-0.182253\pi$
$258$	197.482	+	245.859i	0.765433	+	0.952940i
$259$	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
$263$	−90.8401	+	339.020i	−0.345400	+	1.28905i	0.546745	+	0.837299i	$0.315867\pi$
$263$	−90.8401	+	339.020i	−0.345400	+	1.28905i	−0.892145	+	0.451750i	$0.850800\pi$
$264$	−51.9664	−	38.0719i	−0.196843	−	0.144212i
$265$	12.8225	+	19.7758i	0.0483867	+	0.0746257i
$266$	283.358	−	490.791i	1.06526	−	1.84508i
$267$	289.112	+	112.298i	1.08282	+	0.420593i
$268$	−39.9897	+	149.244i	−0.149215	+	0.556880i
$269$			81.1798i			0.301784i	0.988550	+	0.150892i	$0.0482145\pi$
$269$			81.1798i			0.301784i	−0.988550	+	0.150892i	$0.951785\pi$
$270$	−450.590	−	5.68787i	−1.66885	−	0.0210662i
$271$	−96.4105			−0.355758			−0.177879	−	0.984052i	$-0.556924\pi$
$271$	−96.4105			−0.355758			−0.177879	+	0.984052i	$0.556924\pi$
$272$	150.964	+	40.4506i	0.555014	+	0.148716i
$273$	−42.8500	+	110.317i	−0.156960	+	0.404092i
$274$	−450.817	−	260.280i	−1.64532	−	0.949925i
$275$	5.27758	+	50.9125i	0.0191912	+	0.185136i
$276$	−150.860	+	205.917i	−0.546593	+	0.746075i
$277$	−423.206	−	113.398i	−1.52782	−	0.409378i	−0.605512	−	0.795836i	$-0.707032\pi$
$277$	−423.206	−	113.398i	−1.52782	−	0.409378i	−0.922307	+	0.386458i	$0.873698\pi$
$278$	−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	$0.943776\pi$
$282$	6.78125	−	5.44693i	0.0240470	−	0.0193153i
$283$	−334.424	+	89.6088i	−1.18171	+	0.316639i	−0.795605	−	0.605815i	$-0.792847\pi$
$283$	−334.424	+	89.6088i	−1.18171	+	0.316639i	−0.386107	+	0.922454i	$0.626180\pi$
$284$	−176.962	−	102.169i	−0.623105	−	0.359750i
$285$	233.730	+	153.347i	0.820105	+	0.538060i
$286$	−14.7969	−	25.6289i	−0.0517373	−	0.0896117i
$287$	−27.7972	+	27.7972i	−0.0968545	+	0.0968545i
$288$	84.8702	−	163.348i	0.294688	−	0.567182i
$289$		−	299.828i		−	1.03747i
$290$	375.141	−	19.3916i	1.29359	−	0.0668674i
$291$	127.988	−	174.698i	0.439822	−	0.600338i
$292$	125.824	+	469.582i	0.430905	+	1.60816i
$293$	289.453	−	77.5588i	0.987895	−	0.264706i	0.271529	−	0.962430i	$-0.412471\pi$
$293$	289.453	−	77.5588i	0.987895	−	0.264706i	0.716366	+	0.697725i	$0.245804\pi$
$294$	−311.532	+	137.224i	−1.05963	+	0.466748i
$295$	284.389	+	256.433i	0.964031	+	0.869265i
$296$	493.682			1.66784
$297$	−46.0000	−	30.6576i	−0.154882	−	0.103224i
$298$	−238.229	−	238.229i	−0.799426	−	0.799426i
$299$	−44.6776	+	25.7946i	−0.149423	+	0.0862697i
$300$	518.143	−	135.842i	1.72714	−	0.452808i
$301$	−143.444	+	248.452i	−0.476558	+	0.825423i
$302$	188.499	+	703.489i	0.624170	+	2.32944i
$303$	−183.875	+	28.3753i	−0.606849	+	0.0936477i
$304$	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	−0.444817	−	0.895622i	$-0.646731\pi$
$307$	138.397	−	138.397i	0.450805	−	0.450805i	0.895622	+	0.444817i	$0.146731\pi$
$308$	34.4785	−	128.676i	0.111943	−	0.417778i
$309$	17.2003	−	157.628i	0.0556643	−	0.510124i
$310$	334.321	−	216.771i	1.07846	−	0.699263i
$311$	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	$0.111493\pi$
$312$	−106.224	+	85.3226i	−0.340462	+	0.273470i
$313$	−141.559	+	528.306i	−0.452266	+	1.68788i	0.243738	+	0.969841i	$0.421626\pi$
$313$	−141.559	+	528.306i	−0.452266	+	1.68788i	−0.696004	+	0.718038i	$0.745040\pi$
$314$			886.195i			2.82228i
$315$	−143.598	−	383.983i	−0.455865	−	1.21899i
$316$	−1.66329			−0.00526359
$317$	−421.463	−	112.931i	−1.32954	−	0.356248i	−0.476994	−	0.878906i	$-0.658274\pi$
$317$	−421.463	−	112.931i	−1.32954	−	0.356248i	−0.852542	+	0.522658i	$0.824941\pi$
$318$	46.6514	−	7.19916i	0.146703	−	0.0226389i
$319$	39.9077	+	23.0407i	0.125103	+	0.0722280i
$320$	−98.0842	+	459.834i	−0.306513	+	1.43698i
$321$	−144.329	−	327.661i	−0.449622	−	1.02075i
$322$	−349.943	−	93.7670i	−1.08678	−	0.291202i
$323$	−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
$327$	−286.582	−	111.316i	−0.876398	−	0.340415i
$328$	−43.7152	+	11.7135i	−0.133278	+	0.0357118i
$329$	6.85279	+	3.95646i	0.0208292	+	0.0120257i
$330$	97.3463	+	32.1346i	0.294989	+	0.0973775i
$331$	−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
$333$	423.219	−	18.8122i	1.27093	−	0.0564932i
$334$		−	199.127i		−	0.596188i
$335$	−5.58391	−	108.024i	−0.0166684	−	0.322459i
$336$	−174.989	−	19.0946i	−0.520799	−	0.0568292i
$337$	123.174	+	459.691i	0.365501	+	1.36407i	0.866740	+	0.498760i	$0.166211\pi$
$337$	123.174	+	459.691i	0.365501	+	1.36407i	−0.501239	+	0.865309i	$0.667122\pi$
$338$	484.438	−	129.805i	1.43325	−	0.384038i
$339$	13.2245	−	121.193i	0.0390104	−	0.357502i
$340$	−865.382	+	44.7328i	−2.54524	+	0.131567i
$341$	48.8792			0.143341
$342$	471.949	−	301.188i	1.37997	−	0.880667i
$343$	96.6647	+	96.6647i	0.281821	+	0.281821i
$344$	−286.033	+	165.141i	−0.831490	+	0.480061i
$345$	56.0186	−	169.699i	0.162373	−	0.491880i
$346$	−161.793	+	280.234i	−0.467610	+	0.809925i
$347$	−45.4544	−	169.638i	−0.130992	−	0.488870i	0.868990	−	0.494830i	$-0.164770\pi$
$347$	−45.4544	−	169.638i	−0.130992	−	0.488870i	−0.999982	+	0.00595969i	$0.998103\pi$
$348$	174.606	−	449.523i	0.501741	−	1.29173i
$349$	298.148	−	172.136i	0.854292	−	0.493226i	−0.00780468	−	0.999970i	$-0.502484\pi$
$349$	298.148	−	172.136i	0.854292	−	0.493226i	0.862097	+	0.506744i	$0.169151\pi$
$350$	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
$353$	−69.7848	+	260.440i	−0.197691	+	0.737792i	0.793863	+	0.608096i	$0.208067\pi$
$353$	−69.7848	+	260.440i	−0.197691	+	0.737792i	−0.991554	+	0.129695i	$0.958600\pi$
$354$	701.854	−	309.153i	1.98264	−	0.873314i
$355$	139.905	+	29.8423i	0.394100	+	0.0840628i
$356$	−369.191	+	639.458i	−1.03705	+	1.79623i
$357$	101.145	+	655.434i	0.283320	+	1.83595i
$358$	77.2626	−	288.348i	0.215817	−	0.805441i
$359$		−	411.438i		−	1.14607i	−0.819532	−	0.573033i	$-0.805767\pi$
$359$		−	411.438i		−	1.14607i	0.819532	−	0.573033i	$-0.194233\pi$
$360$	77.8623	−	465.497i	0.216284	−	1.29305i
$361$	13.6890			0.0379198
$362$	−990.923	−	265.517i	−2.73736	−	0.733473i
$363$	−219.446	−	273.204i	−0.604536	−	0.752628i
$364$	−244.000	−	140.873i	−0.670330	−	0.387015i
$365$	−185.159	−	285.567i	−0.507286	−	0.782375i
$366$	−704.051	−	76.8255i	−1.92364	−	0.209906i
$367$	626.938	+	167.988i	1.70828	+	0.457732i	0.975001	−	0.222199i	$-0.0713234\pi$
$367$	626.938	+	167.988i	1.70828	+	0.457732i	0.733277	+	0.679930i	$0.237990\pi$
$368$	−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
$372$	−78.0134	−	505.537i	−0.209714	−	1.35897i
$373$	−107.220	+	28.7295i	−0.287453	+	0.0770229i	−0.399664	−	0.916662i	$-0.630873\pi$
$373$	−107.220	+	28.7295i	−0.287453	+	0.0770229i	0.112211	+	0.993684i	$0.464207\pi$
$374$	−143.619	−	82.9186i	−0.384009	−	0.221708i
$375$	−315.744	+	202.313i	−0.841984	+	0.539502i
$376$	4.55491	+	7.88933i	0.0121141	+	0.0209823i
$377$	68.9157	−	68.9157i	0.182800	−	0.182800i
$378$	−819.356	−	52.7309i	−2.16761	−	0.139500i
$379$			317.077i			0.836614i	0.908306	+	0.418307i	$0.137376\pi$
$379$			317.077i			0.836614i	−0.908306	+	0.418307i	$0.862624\pi$
$380$	−445.664	+	494.250i	−1.17280	+	1.30066i
$381$	139.133	+	315.865i	0.365177	+	0.829043i
$382$	−141.337	−	527.478i	−0.369993	−	1.38083i
$383$	−86.0774	+	23.0644i	−0.224745	+	0.0602203i	−0.369434	−	0.929257i	$-0.620448\pi$
$383$	−86.0774	+	23.0644i	−0.224745	+	0.0602203i	0.144689	+	0.989477i	$0.453782\pi$
$384$	561.629	+	411.464i	1.46258	+	1.07152i
$385$	4.81436	+	93.1365i	0.0125048	+	0.241913i
$386$	−848.449			−2.19806
$387$	−238.914	+	152.470i	−0.617350	+	0.393979i
$388$	364.566	+	364.566i	0.939602	+	0.939602i
$389$	−64.0677	+	36.9895i	−0.164698	+	0.0950887i	−0.580084	−	0.814557i	$-0.696980\pi$
$389$	−64.0677	+	36.9895i	−0.164698	+	0.0950887i	0.415385	+	0.909646i	$0.363647\pi$
$390$	118.935	−	181.280i	0.304963	−	0.464820i
$391$	−144.548	+	250.364i	−0.369687	+	0.640318i
$392$	−92.2778	−	344.386i	−0.235403	−	0.878535i
$393$	155.338	+	193.391i	0.395261	+	0.492088i
$394$	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	−0.152830	−	0.988252i	$-0.548839\pi$
$397$	331.663	−	331.663i	0.835422	−	0.835422i	0.988252	+	0.152830i	$0.0488387\pi$
$398$	142.605	−	532.207i	0.358303	−	1.33720i
$399$	410.870	+	301.013i	1.02975	+	0.754420i
$400$	16.6022	+	160.160i	0.0415054	+	0.400400i
$401$	−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	$0.866742\pi$
$402$	−201.939	−	78.4380i	−0.502335	−	0.195119i
$403$	26.7564	−	99.8561i	0.0663930	−	0.247782i
$404$		−	442.930i		−	1.09636i
$405$	49.0108	−	402.024i	0.121014	−	0.992651i
$406$	684.428			1.68578
$407$	−93.0893	−	24.9432i	−0.228721	−	0.0612855i
$408$	−276.443	+	711.702i	−0.677556	+	1.74437i
$409$	545.487	+	314.937i	1.33371	+	0.770017i	0.985866	−	0.167536i	$-0.0535812\pi$
$409$	545.487	+	314.937i	1.33371	+	0.770017i	0.347842	+	0.937553i	$0.386914\pi$
$410$	60.4280	−	39.1810i	0.147385	−	0.0955635i
$411$	276.497	−	377.406i	0.672742	−	0.918262i
$412$	364.628	+	97.7018i	0.885019	+	0.237140i
$413$	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
$417$	3.65335	−	2.93449i	0.00876103	−	0.00703715i
$418$	−123.024	+	32.9643i	−0.294317	+	0.0788619i
$419$	153.113	+	88.3997i	0.365424	+	0.210978i	0.671457	−	0.741043i	$-0.265669\pi$
$419$	153.113	+	88.3997i	0.365424	+	0.210978i	−0.306033	+	0.952021i	$0.599002\pi$
$420$	955.587	−	198.443i	2.27521	−	0.472483i
$421$	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
$423$	4.20542	+	6.58972i	0.00994188	+	0.0155785i
$424$			49.4388i			0.116601i
$425$	566.661	−	216.592i	1.33332	−	0.509629i
$426$	169.321	−	231.116i	0.397468	−	0.542526i
$427$	−166.760	−	622.355i	−0.390538	−	1.45751i
$428$	823.337	−	220.612i	1.92368	−	0.515449i
$429$	24.3407	−	10.7216i	0.0567381	−	0.0249921i
$430$	351.963	−	390.333i	0.818518	−	0.907751i
$431$	648.364			1.50433			0.752163	−	0.658977i	$-0.229011\pi$
$431$	648.364			1.50433			0.752163	+	0.658977i	$0.229011\pi$
$432$	−144.706	−	96.4425i	−0.334968	−	0.223247i
$433$	−481.270	−	481.270i	−1.11148	−	1.11148i	−0.992951	−	0.118526i	$-0.962183\pi$
$433$	−481.270	−	481.270i	−1.11148	−	1.11148i	−0.118526	−	0.992951i	$-0.537817\pi$
$434$	628.718	−	362.991i	1.44866	−	0.836384i
$435$	−19.2479	+	337.059i	−0.0442481	+	0.774847i
$436$	365.961	−	633.864i	0.839361	−	1.45382i
$437$	57.4649	+	214.462i	0.131499	+	0.490760i
$438$	−673.656	+	103.957i	−1.53803	+	0.237345i
$439$	−543.519	+	313.801i	−1.23808	+	0.714809i	−0.968702	−	0.248225i	$-0.920153\pi$
$439$	−543.519	+	313.801i	−1.23808	+	0.714809i	−0.269382	+	0.963033i	$0.586820\pi$
$440$	−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
$443$	139.184	−	519.441i	0.314185	−	1.17255i	−0.610562	−	0.791969i	$-0.709056\pi$
$443$	139.184	−	519.441i	0.314185	−	1.17255i	0.924746	−	0.380584i	$-0.124277\pi$
$444$	−109.402	+	1002.59i	−0.246401	+	2.25809i
$445$	107.836	−	505.553i	0.242328	−	1.13607i
$446$	21.3741	−	37.0210i	0.0479239	−	0.0830067i
$447$	236.070	−	189.619i	0.528121	−	0.424204i
$448$	−221.724	+	827.486i	−0.494920	+	1.84707i
$449$		−	252.073i		−	0.561410i	−0.959794	−	0.280705i	$-0.909432\pi$
$449$		−	252.073i		−	0.561410i	0.959794	−	0.280705i	$-0.0905683\pi$
$450$	110.535	+	742.865i	0.245634	+	1.65081i
$451$	8.83482			0.0195894
$452$	280.346	+	75.1186i	0.620235	+	0.166191i
$453$	−646.907	+	99.8294i	−1.42805	+	0.220374i
$454$	−1279.57	−	738.759i	−2.81843	−	1.62722i
$455$	192.905	+	41.1474i	0.423968	+	0.0904338i
$456$	236.373	+	536.624i	0.518361	+	1.17681i
$457$	−285.126	−	76.3993i	−0.623908	−	0.167176i	−0.0670042	−	0.997753i	$-0.521344\pi$
$457$	−285.126	−	76.3993i	−0.623908	−	0.167176i	−0.556904	+	0.830577i	$0.688011\pi$
$458$	−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	$0.646859\pi$
$462$	174.108	+	67.6280i	0.376858	+	0.146381i
$463$	285.192	−	76.4168i	0.615964	−	0.165047i	0.0626719	−	0.998034i	$-0.480038\pi$
$463$	285.192	−	76.4168i	0.615964	−	0.165047i	0.553293	+	0.832987i	$0.313371\pi$
$464$	125.541	+	72.4813i	0.270563	+	0.156210i
$465$	161.080	+	319.832i	0.346408	+	0.687810i
$466$	148.208	+	256.703i	0.318042	+	0.550865i
$467$	−375.745	+	375.745i	−0.804593	+	0.804593i	−0.983810	−	0.179217i	$-0.942644\pi$
$467$	−375.745	+	375.745i	−0.804593	+	0.804593i	0.179217	+	0.983810i	$0.442644\pi$
$468$	−149.738	−	234.633i	−0.319952	−	0.501352i
$469$		−	197.085i		−	0.420223i
$470$	−10.7661	−	9.70781i	−0.0229067	−	0.0206549i
$471$	−791.767	−	86.3970i	−1.68103	−	0.183433i
$472$	207.894	+	775.871i	0.440453	+	1.64379i
$473$	62.2784	−	16.6875i	0.131667	−	0.0352800i
$474$	0.252977	−	2.31835i	0.000533706	−	0.00489104i
$475$	190.109	−	425.356i	0.400230	−	0.895486i
$476$	−1578.85			−3.31691
$477$	1.88391	+	42.3824i	0.00394951	+	0.0888520i
$478$	−157.841	−	157.841i	−0.330212	−	0.330212i
$479$	−375.237	+	216.643i	−0.783376	+	0.452282i	−0.837625	−	0.546245i	$-0.816057\pi$
$479$	−375.237	+	216.643i	−0.783376	+	0.452282i	0.0542492	+	0.998527i	$0.482723\pi$
$480$	−291.338	−	96.1723i	−0.606954	−	0.200359i
$481$	−101.914	+	176.520i	−0.211879	+	0.366985i
$482$	−51.2656	−	191.326i	−0.106360	−	0.396942i
$483$	117.892	−	303.514i	0.244084	−	0.628393i
$484$	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	−0.133345	−	0.991070i	$-0.542572\pi$
$487$	417.712	−	417.712i	0.857725	−	0.857725i	0.991070	+	0.133345i	$0.0425719\pi$
$488$	191.983	−	716.491i	0.393408	−	1.46822i
$489$	−625.406	+	275.479i	−1.27895	+	0.563352i
$490$	308.665	+	476.047i	0.629930	+	0.971525i
$491$	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	$-0.120219\pi$
$492$	−14.1008	−	91.3748i	−0.0286601	−	0.185721i
$493$	141.355	−	527.544i	0.286724	−	1.07007i
$494$			269.373i			0.545289i
$495$	−38.2010	+	83.8408i	−0.0771737	+	0.169375i
$496$	153.764			0.310007
$497$	251.764	+	67.4600i	0.506567	+	0.135734i
$498$	996.409	+	1240.50i	2.00082	+	2.49096i
$499$	84.7687	+	48.9412i	0.169877	+	0.0980786i	0.582528	−	0.812811i	$-0.302064\pi$
$499$	84.7687	+	48.9412i	0.169877	+	0.0980786i	−0.412651	+	0.910889i	$0.635397\pi$
$500$	−361.368	−	816.350i	−0.722736	−	1.63270i
$501$	177.909	+	19.4133i	0.355108	+	0.0387491i
$502$	285.596	+	76.5253i	0.568917	+	0.152441i
$503$	350.849	+	350.849i	0.697512	+	0.697512i	0.963873	−	0.266361i	$-0.0858213\pi$
$503$	350.849	+	350.849i	0.697512	+	0.697512i	−0.266361	+	0.963873i	$0.585821\pi$
$504$	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
$507$	68.7447	+	445.474i	0.135591	+	0.878647i
$508$	−793.696	+	212.670i	−1.56239	+	0.418642i
$509$	−389.842	−	225.075i	−0.765897	−	0.442191i	0.0655119	−	0.997852i	$-0.479132\pi$
$509$	−389.842	−	225.075i	−0.765897	−	0.442191i	−0.831409	+	0.555661i	$0.812465\pi$
$510$	69.2692	−	1213.00i	0.135822	−	2.37843i
$511$	−310.055	−	537.031i	−0.606761	−	1.05094i
$512$	−284.213	+	284.213i	−0.555104	+	0.555104i
$513$	223.084	+	451.025i	0.434861	+	0.879190i
$514$			524.643i			1.02071i
$515$	−263.921	+	13.6424i	−0.512468	+	0.0264902i
$516$	−271.991	−	617.485i	−0.527113	−	1.19668i
$517$	−0.460272	−	1.71776i	−0.000890275	−	0.00332255i
$518$	−1382.61	+	370.470i	−2.66914	+	0.715194i
$519$	−234.600	−	171.874i	−0.452024	−	0.331164i
$520$	168.645	+	152.067i	0.324317	+	0.292436i
$521$	749.947			1.43944			0.719718	−	0.694266i	$-0.244271\pi$
$521$	749.947			1.43944			0.719718	+	0.694266i	$0.244271\pi$
$522$	600.002	+	311.741i	1.14943	+	0.597205i
$523$	377.284	+	377.284i	0.721385	+	0.721385i	0.968887	−	0.247502i	$-0.0796098\pi$
$523$	377.284	+	377.284i	0.721385	+	0.721385i	−0.247502	+	0.968887i	$0.579610\pi$
$524$	−511.417	+	295.267i	−0.975986	+	0.563486i
$525$	−593.555	+	338.430i	−1.13058	+	0.644629i
$526$	585.779	−	1014.60i	1.11365	−	1.92890i
$527$	−149.937	−	559.573i	−0.284511	−	1.06181i
$528$	24.7740	+	30.8428i	0.0469204	+	0.0584145i
$529$	−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
$533$	4.83616	−	18.0488i	0.00907348	−	0.0338627i
$534$	−835.146	−	611.848i	−1.56394	−	1.14578i
$535$	−500.695	+	324.647i	−0.935878	+	0.606816i
$536$	113.448	−	196.497i	0.211656	−	0.366599i
$537$	250.091	+	97.1416i	0.465719	+	0.180897i
$538$	70.1337	−	261.743i	0.130360	−	0.486510i
$539$			69.6001i			0.129128i
$540$	928.100	+	261.283i	1.71870	+	0.483857i
$541$	861.919			1.59320			0.796598	−	0.604509i	$-0.206631\pi$
$541$	861.919			1.59320			0.796598	+	0.604509i	$0.206631\pi$
$542$	310.850	+	83.2920i	0.573524	+	0.153675i
$543$	333.832	−	859.451i	0.614793	−	1.58278i
$544$	429.824	+	248.159i	0.790117	+	0.456174i
$545$	−106.893	+	501.130i	−0.196133	+	0.919504i
$546$	233.465	−	318.669i	0.427591	−	0.583643i
$547$	−385.325	−	103.247i	−0.704433	−	0.188752i	−0.111218	−	0.993796i	$-0.535475\pi$
$547$	−385.325	−	103.247i	−0.704433	−	0.188752i	−0.593215	+	0.805044i	$0.702142\pi$
$548$	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
$552$	292.252	−	234.747i	0.529442	−	0.425266i
$553$	2.04934	−	0.549118i	0.00370585	−	0.000992981i
$554$	1266.55	+	731.241i	2.28619	+	1.31993i
$555$	−143.562	−	691.312i	−0.258670	−	1.24561i
$556$	5.57790	+	9.66120i	0.0100322	+	0.0173763i
$557$	−262.321	+	262.321i	−0.470954	+	0.470954i	−0.902223	−	0.431269i	$-0.858066\pi$
$557$	−262.321	+	262.321i	−0.470954	+	0.470954i	0.431269	+	0.902223i	$0.358066\pi$
$558$	716.499	−	31.8487i	1.28405	−	0.0570765i
$559$		−	136.364i		−	0.243943i
$560$	15.1450	+	292.988i	0.0270446	+	0.523192i
$561$	88.0851	−	120.232i	0.157014	−	0.214318i
$562$	165.102	+	616.171i	0.293777	+	1.09639i
$563$	−877.872	+	235.225i	−1.55928	+	0.417806i	−0.932434	−	0.361341i	$-0.882319\pi$
$563$	−877.872	+	235.225i	−1.55928	+	0.417806i	−0.626841	+	0.779147i	$0.715653\pi$
$564$	−17.0314	+	7.50202i	−0.0301976	+	0.0133015i
$565$	−202.917	+	10.4891i	−0.359145	+	0.0185647i
$566$	1155.68			2.04183
$567$	126.993	−	726.910i	0.223973	−	1.28203i
$568$	212.181	+	212.181i	0.373559	+	0.373559i
$569$	632.780	−	365.336i	1.11209	−	0.642066i	0.172721	−	0.984971i	$-0.444744\pi$
$569$	632.780	−	365.336i	1.11209	−	0.642066i	0.939370	+	0.342905i	$0.111411\pi$
$570$	−621.118	−	696.353i	−1.08968	−	1.22167i
$571$	−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	$0.957848\pi$
$572$	16.3884	+	61.1624i	0.0286511	+	0.106927i
$573$	485.052	−	74.8523i	0.846514	−	0.130632i
$574$	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	−0.996148	−	0.0876926i	$-0.972051\pi$
$577$	−524.179	+	524.179i	−0.908455	+	0.908455i	0.0876926	+	0.996148i	$0.472051\pi$
$578$	−259.031	+	966.715i	−0.448150	+	1.67252i
$579$	82.7171	−	758.044i	0.142862	−	1.30923i
$580$	−786.054	−	167.668i	−1.35527	−	0.289083i
$581$	−723.758	+	1253.59i	−1.24571	+	2.15763i
$582$	−563.591	+	452.695i	−0.968370	+	0.777827i
$583$	2.49789	−	9.32225i	0.00428454	−	0.0159901i
$584$		−	713.907i		−	1.22244i
$585$	150.369	+	123.936i	0.257040	+	0.211856i
$586$	−1000.27			−1.70695
$587$	527.677	+	141.391i	0.898938	+	0.240870i	0.678560	−	0.734545i	$-0.262604\pi$
$587$	527.677	+	141.391i	0.898938	+	0.240870i	0.220378	+	0.975415i	$0.429271\pi$
$588$	719.845	−	111.085i	1.22423	−	0.188920i
$589$	−385.309	−	222.458i	−0.654174	−	0.377688i
$590$	−695.396	−	1072.49i	−1.17864	−	1.81778i
$591$	143.639	+	326.096i	0.243044	+	0.551770i
$592$	−292.839	−	78.4661i	−0.494661	−	0.132544i
$593$	−61.2676	−	61.2676i	−0.103318	−	0.103318i	0.653558	−	0.756876i	$-0.273275\pi$
$593$	−61.2676	−	61.2676i	−0.103318	−	0.103318i	−0.756876	+	0.653558i	$0.773275\pi$
$594$	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
$597$	461.596	+	179.295i	0.773192	+	0.300327i
$598$	166.336	−	44.5696i	0.278154	−	0.0745310i
$599$	572.037	+	330.266i	0.954987	+	0.551362i	0.894626	−	0.446815i	$-0.147442\pi$
$599$	572.037	+	330.266i	0.954987	+	0.551362i	0.0603602	+	0.998177i	$0.480775\pi$
$600$	−786.595	−	4.24624i	−1.31099	−	0.00707706i
$601$	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
$603$	89.7675	−	172.774i	0.148868	−	0.286524i
$604$		−	1558.31i		−	2.57999i
$605$	−391.109	+	433.747i	−0.646462	+	0.716938i
$606$	617.371	+	67.3669i	1.01876	+	0.111167i
$607$	−84.0689	−	313.749i	−0.138499	−	0.516885i	−0.999959	−	0.00905986i	$-0.997116\pi$
$607$	−84.0689	−	313.749i	−0.138499	−	0.516885i	0.861460	−	0.507826i	$-0.169551\pi$
$608$	368.187	−	98.6554i	0.605571	−	0.162262i
$609$	−66.7263	+	611.499i	−0.109567	+	1.00410i
$610$	60.9344	+	1178.81i	0.0998924	+	1.93248i
$611$	−3.76119			−0.00615580
$612$	−1384.10	−	719.130i	−2.26160	−	1.17505i
$613$	−778.916	−	778.916i	−1.27066	−	1.27066i	−0.945741	−	0.324921i	$-0.894662\pi$
$613$	−778.916	−	778.916i	−1.27066	−	1.27066i	−0.324921	−	0.945741i	$-0.605338\pi$
$614$	−565.790	+	326.659i	−0.921482	+	0.532018i
$615$	29.1149	+	57.8090i	0.0473413	+	0.0939983i
$616$	−97.8128	+	169.417i	−0.158787	+	0.275027i
$617$	−88.7130	−	331.081i	−0.143781	−	0.536599i	−0.999807	−	0.0196651i	$-0.993740\pi$
$617$	−88.7130	−	331.081i	−0.143781	−	0.536599i	0.856025	−	0.516934i	$-0.172927\pi$
$618$	−191.637	+	493.370i	−0.310093	+	0.798334i
$619$	−448.805	+	259.118i	−0.725049	+	0.418607i	−0.816608	−	0.577192i	$-0.804148\pi$
$619$	−448.805	+	259.118i	−0.725049	+	0.418607i	0.0915591	+	0.995800i	$0.470815\pi$
$620$	−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
$623$	243.769	−	909.758i	0.391282	−	1.46029i
$624$	76.5706	−	33.7279i	0.122709	−	0.0540511i
$625$	416.878	+	465.659i	0.667004	+	0.745054i
$626$	912.840	−	1581.09i	1.45821	−	2.52569i
$627$	−17.4579	−	113.129i	−0.0278435	−	0.180430i
$628$	490.756	−	1831.53i	0.781459	−	2.91645i
$629$			1142.21i			1.81591i
$630$	131.257	+	1362.11i	0.208345	+	2.16208i
$631$	−48.4016			−0.0767062			−0.0383531	−	0.999264i	$-0.512211\pi$
$631$	−48.4016			−0.0767062			−0.0383531	+	0.999264i	$0.512211\pi$
$632$	2.35932	+	0.632177i	0.00373309	+	0.00100028i
$633$	−22.0662	−	27.4717i	−0.0348597	−	0.0433992i
$634$	1261.33	+	728.230i	1.98948	+	1.14863i
$635$	482.669	−	312.959i	0.760109	−	0.492849i
$636$	−100.403	−	10.9559i	−0.157866	−	0.0172262i
$637$	142.187	+	38.0990i	0.223214	+	0.0598100i
$638$	−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	$0.995839\pi$
$642$	182.272	+	1181.15i	0.283913	+	1.83979i
$643$	−467.479	+	125.261i	−0.727028	+	0.194807i	−0.603305	−	0.797510i	$-0.706150\pi$
$643$	−467.479	+	125.261i	−0.727028	+	0.194807i	−0.123723	+	0.992317i	$0.539483\pi$
$644$	671.313	+	387.583i	1.04241	+	0.601836i
$645$	314.428	+	352.514i	0.487485	+	0.546533i
$646$	754.755	+	1307.27i	1.16835	+	2.02364i
$647$	−388.357	+	388.357i	−0.600242	+	0.600242i	−0.940377	−	0.340135i	$-0.889527\pi$
$647$	−388.357	+	388.357i	−0.600242	+	0.600242i	0.340135	+	0.940377i	$0.389527\pi$
$648$	545.045	−	651.642i	0.841118	−	1.00562i
$649$		−	156.803i		−	0.241607i
$650$	−329.904	−	147.448i	−0.507545	−	0.226843i
$651$	263.017	+	597.114i	0.404021	+	0.917226i
$652$	−421.082	−	1571.50i	−0.645831	−	2.41027i
$653$	−191.192	+	51.2298i	−0.292791	+	0.0784530i	−0.402225	−	0.915541i	$-0.631763\pi$
$653$	−191.192	+	51.2298i	−0.292791	+	0.0784530i	0.109434	+	0.993994i	$0.465096\pi$
$654$	827.839	+	606.495i	1.26581	+	0.927363i
$655$	276.851	−	307.033i	0.422674	−	0.468753i
$656$	27.7925			0.0423666
$657$	−27.2041	−	612.010i	−0.0414066	−	0.931523i
$658$	−18.6769	−	18.6769i	−0.0283843	−	0.0283843i
$659$	97.2838	−	56.1668i	0.147623	−	0.0852304i	−0.424369	−	0.905489i	$-0.639504\pi$
$659$	97.2838	−	56.1668i	0.147623	−	0.0852304i	0.571992	+	0.820259i	$0.306171\pi$
$660$	−183.393	−	120.322i	−0.277869	−	0.182306i
$661$	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	$0.139915\pi$
$662$	506.525	+	1890.38i	0.765144	+	2.85556i
$663$	−197.407	−	245.765i	−0.297748	−	0.370687i
$664$	−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
$668$	−110.272	+	411.542i	−0.165078	+	0.616081i
$669$	30.9924	+	22.7058i	0.0463265	+	0.0339400i
$670$	−75.3213	+	353.118i	−0.112420	+	0.527042i
$671$	−72.4012	+	125.403i	−0.107900	+	0.186889i
$672$	−521.071	−	202.397i	−0.775403	−	0.301186i
$673$	54.3747	−	202.929i	0.0807945	−	0.301529i	−0.913690	−	0.406412i	$-0.866780\pi$
$673$	54.3747	−	202.929i	0.0807945	−	0.301529i	0.994485	+	0.104882i	$0.0334466\pi$
$674$		−	1588.56i		−	2.35692i
$675$	−674.486	+	26.3338i	−0.999239	+	0.0390131i
$676$	−1073.09			−1.58741
$677$	−723.857	−	193.957i	−1.06921	−	0.286495i	−0.319043	−	0.947740i	$-0.603361\pi$
$677$	−723.857	−	193.957i	−1.06921	−	0.286495i	−0.750169	+	0.661246i	$0.770028\pi$
$678$	−147.342	+	379.331i	−0.217318	+	0.559485i
$679$	−569.537	−	328.822i	−0.838788	−	0.484275i
$680$	1244.51	+	265.459i	1.83016	+	0.390380i
$681$	784.789	−	1071.20i	1.15241	−	1.57298i
$682$	−157.598	−	42.2282i	−0.231082	−	0.0619182i
$683$	441.268	+	441.268i	0.646074	+	0.646074i	0.952042	−	0.305968i	$-0.0989800\pi$
$683$	441.268	+	441.268i	0.646074	+	0.646074i	−0.305968	+	0.952042i	$0.598980\pi$
$684$	−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
$687$	443.631	−	356.339i	0.645751	−	0.518688i
$688$	195.915	−	52.4952i	0.284760	−	0.0763012i
$689$	−17.6772	−	10.2060i	−0.0256564	−	0.0148127i
$690$	−327.225	+	498.752i	−0.474239	+	0.722829i
$691$	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
$693$	−77.3961	+	148.963i	−0.111683	+	0.214954i
$694$			586.222i			0.844700i
$695$	−5.80018	−	5.23001i	−0.00834558	−	0.00752519i
$696$	−418.524	+	571.266i	−0.601327	+	0.820785i
$697$	−27.1009	−	101.142i	−0.0388822	−	0.145110i
$698$	−1110.01	+	297.427i	−1.59027	+	0.426113i
$699$	−243.799	+	107.389i	−0.348783	+	0.153632i
$700$	−580.759	−	1519.42i	−0.829656	−	2.17059i
$701$	−1185.25			−1.69080			−0.845401	−	0.534133i	$-0.820638\pi$
$701$	−1185.25			−1.69080			−0.845401	+	0.534133i	$0.820638\pi$
$702$	349.813	−	173.023i	0.498309	−	0.246471i
$703$	620.290	+	620.290i	0.882348	+	0.882348i
$704$	166.736	−	96.2650i	0.236841	−	0.136740i
$705$	9.72301	−	8.67252i	0.0137915	−	0.0123015i
$706$	450.005	−	779.431i	0.637401	−	1.10401i
$707$	146.229	+	545.733i	0.206830	+	0.771899i
$708$	−1621.75	+	250.265i	−2.29060	+	0.353481i
$709$	−237.674	+	137.221i	−0.335224	+	0.193542i	−0.658158	−	0.752880i	$-0.728664\pi$
$709$	−237.674	+	137.221i	−0.335224	+	0.193542i	0.322934	+	0.946421i	$0.395331\pi$
$710$	−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
$713$	−73.6143	+	274.732i	−0.103246	+	0.385319i
$714$	240.133	−	2200.65i	0.336321	−	3.08215i
$715$	−24.1167	−	37.1946i	−0.0337297	−	0.0520205i
$716$	−319.362	+	553.152i	−0.446037	+	0.772558i
$717$	156.411	−	125.634i	0.218146	−	0.175222i
$718$	−355.454	+	1326.57i	−0.495061	+	1.84759i
$719$		−	1409.12i		−	1.95983i	−0.199416	−	0.979915i	$-0.563904\pi$
$719$		−	1409.12i		−	1.95983i	0.199416	−	0.979915i	$-0.436096\pi$
$720$	−120.172	+	263.745i	−0.166906	+	0.366313i
$721$	−481.512			−0.667839
$722$	−44.1367	−	11.8264i	−0.0611311	−	0.0163800i
$723$	175.937	−	27.1503i	0.243344	−	0.0375523i
$724$	1900.94	+	1097.51i	2.62560	+	1.51589i
$725$	559.680	−	58.0164i	0.771973	−	0.0800226i
$726$	471.517	+	1070.46i	0.649473	+	1.47446i
$727$	688.962	+	184.607i	0.947678	+	0.253930i	0.699377	−	0.714753i	$-0.253461\pi$
$727$	688.962	+	184.607i	0.947678	+	0.253930i	0.248302	+	0.968683i	$0.420128\pi$
$728$	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
$732$	1412.54	+	548.667i	1.92970	+	0.749545i
$733$	858.390	−	230.005i	1.17106	−	0.313786i	0.379688	−	0.925115i	$-0.376031\pi$
$733$	858.390	−	230.005i	1.17106	−	0.313786i	0.791377	+	0.611329i	$0.209365\pi$
$734$	−1876.26	−	1083.26i	−2.55622	−	1.47583i
$735$	−455.415	+	229.365i	−0.619612	+	0.312061i
$736$	−121.838	−	211.030i	−0.165541	−	0.286725i
$737$	−31.3198	+	31.3198i	−0.0424964	+	0.0424964i
$738$	129.506	−	5.75659i	0.175482	−	0.00780025i
$739$			719.160i			0.973153i	0.873638	+	0.486577i	$0.161755\pi$
$739$			719.160i			0.973153i	−0.873638	+	0.486577i	$0.838245\pi$
$740$	1678.67	−	86.7727i	2.26847	−	0.117260i
$741$	−240.670	−	26.2617i	−0.324791	−	0.0354409i
$742$	−37.1000	−	138.459i	−0.0500000	−	0.186603i
$743$	160.887	−	43.1096i	0.216537	−	0.0580210i	−0.148919	−	0.988849i	$-0.547579\pi$
$743$	160.887	−	43.1096i	0.216537	−	0.0580210i	0.365457	+	0.930828i	$0.380913\pi$
$744$	−81.4830	+	746.734i	−0.109520	+	1.00368i
$745$	−374.792	−	337.950i	−0.503077	−	0.453624i
$746$	370.523			0.496679
$747$	−1205.46	+	769.299i	−1.61374	+	1.02985i
$748$	250.904	+	250.904i	0.335433	+	0.335433i
$749$	−941.597	+	543.631i	−1.25714	+	0.725809i
$750$	1192.82	−	379.525i	1.59042	−	0.506033i
$751$	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	$0.0623301\pi$
$752$	−1.44792	−	5.40371i	−0.00192542	−	0.00718578i
$753$	−96.2146	+	247.704i	−0.127775	+	0.328957i
$754$	−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	−0.604974	−	0.796245i	$-0.706817\pi$
$757$	144.792	−	144.792i	0.191270	−	0.191270i	0.796245	+	0.604974i	$0.206817\pi$
$758$	273.932	−	1022.33i	0.361388	−	1.34872i
$759$	−66.9680	+	29.4981i	−0.0882319	+	0.0388645i
$760$	820.009	−	531.687i	1.07896	−	0.699589i
$761$	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	$0.103542\pi$
$762$	−175.710	−	1138.62i	−0.230591	−	1.49426i
$763$	−241.636	+	901.799i	−0.316692	+	1.18191i
$764$			1168.43i			1.52935i
$765$	1077.00	+	180.146i	1.40784	+	0.235485i
$766$	297.459			0.388328
$767$	−320.335	−	85.8336i	−0.417647	−	0.111908i
$768$	−748.691	−	932.097i	−0.974858	−	1.21367i
$769$	96.6554	+	55.8040i	0.125690	+	0.0725670i	0.561527	−	0.827459i	$-0.310214\pi$
$769$	96.6554	+	55.8040i	0.125690	+	0.0725670i	−0.435837	+	0.900026i	$0.643548\pi$
$770$	64.9408	−	304.453i	0.0843388	−	0.395393i
$771$	−468.740	−	51.1485i	−0.607964	−	0.0663405i
$772$	1753.52	+	469.854i	2.27140	+	0.608619i
$773$	−43.6287	−	43.6287i	−0.0564408	−	0.0564408i	0.678323	−	0.734764i	$-0.262707\pi$
$773$	−43.6287	−	43.6287i	−0.0564408	−	0.0564408i	−0.734764	+	0.678323i	$0.762707\pi$
$774$	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
$777$	−196.201	−	1271.41i	−0.252512	−	1.63631i
$778$	238.526	−	63.9127i	0.306588	−	0.0821500i
$779$	−69.6438	−	40.2089i	−0.0894015	−	0.0516160i
$780$	−346.197	+	308.793i	−0.443842	+	0.395889i
$781$	−29.2888	−	50.7297i	−0.0375016	−	0.0649547i
$782$	682.353	−	682.353i	0.872574	−	0.872574i
$783$	−337.019	+	505.678i	−0.430420	+	0.645821i
$784$			218.947i			0.279270i
$785$	68.5260	+	1325.68i	0.0872943	+	1.68876i
$786$	−333.769	−	757.737i	−0.424642	−	0.964042i
$787$	319.011	+	1190.57i	0.405351	+	1.51279i	0.803407	+	0.595430i	$0.203018\pi$
$787$	319.011	+	1190.57i	0.405351	+	1.51279i	−0.398056	+	0.917361i	$0.630315\pi$
$788$	−819.404	+	219.559i	−1.03985	+	0.278628i
$789$	849.381	+	622.277i	1.07653	+	0.788691i
$790$	−3.88167	+	0.200649i	−0.00491351	+	0.000253986i
$791$	−370.213			−0.468032
$792$	−162.913	+	103.967i	−0.205698	+	0.131272i
$793$	216.555	+	216.555i	0.273083	+	0.273083i
$794$	−1355.89	+	782.824i	−1.70767	+	0.985925i
$795$	69.2300	−	14.3767i	0.0870818	−	0.0180839i
$796$	−589.451	+	1020.96i	−0.740516	+	1.28261i
$797$	−197.069	−	735.470i	−0.247263	−	0.922799i	−0.972232	−	0.234017i	$-0.924813\pi$
$797$	−197.069	−	735.470i	−0.247263	−	0.922799i	0.724969	−	0.688781i	$-0.241854\pi$
$798$	−1064.69	−	1325.50i	−1.33419	−	1.66103i
$799$	−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
$803$	−36.0700	+	134.615i	−0.0449191	+	0.167640i
$804$	373.916	+	273.940i	0.465069	+	0.340721i
$805$	−530.737	−	113.208i	−0.659301	−	0.140631i
$806$	−172.538	+	298.844i	−0.214066	+	0.370774i
$807$	227.015	+	88.1785i	0.281308	+	0.109267i
$808$	−168.347	+	628.279i	−0.208350	+	0.777573i
$809$		−	225.758i		−	0.279058i	−0.990218	−	0.139529i	$-0.955441\pi$
$809$		−	225.758i		−	0.279058i	0.990218	−	0.139529i	$-0.0445589\pi$
$810$	−505.343	+	1253.88i	−0.623880	+	1.54799i
$811$	−149.469			−0.184303			−0.0921513	−	0.995745i	$-0.529374\pi$
$811$	−149.469			−0.184303			−0.0921513	+	0.995745i	$0.529374\pi$
$812$	−1414.53	−	379.022i	−1.74203	−	0.466776i
$813$	−104.722	+	269.607i	−0.128810	+	0.331620i
$814$	278.593	+	160.845i	0.342251	+	0.197599i
$815$	619.652	+	955.674i	0.760309	+	1.17261i
$816$	277.097	−	378.225i	0.339580	−	0.463511i
$817$	−566.881	−	151.895i	−0.693856	−	0.185918i
$818$	−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	$0.832252\pi$
$822$	−1217.54	+	977.970i	−1.48120	+	1.18974i
$823$	625.506	−	167.604i	0.760032	−	0.203650i	0.142069	−	0.989857i	$-0.454625\pi$
$823$	625.506	−	167.604i	0.760032	−	0.203650i	0.617963	+	0.786207i	$0.287958\pi$
$824$	−480.076	−	277.172i	−0.582617	−	0.336374i
$825$	148.107	+	40.5433i	0.179524	+	0.0491434i
$826$	−1164.46	−	2016.91i	−1.40976	−	2.44178i
$827$	230.120	−	230.120i	0.278258	−	0.278258i	−0.554155	−	0.832413i	$-0.686959\pi$
$827$	230.120	−	230.120i	0.278258	−	0.278258i	0.832413	+	0.554155i	$0.186959\pi$
$828$	411.971	+	645.541i	0.497549	+	0.779639i
$829$		−	1504.68i		−	1.81505i	−0.419994	−	0.907527i	$-0.637968\pi$
$829$		−	1504.68i		−	1.81505i	0.419994	−	0.907527i	$-0.362032\pi$
$830$	1775.85	−	1969.45i	2.13958	−	2.37284i
$831$	−776.803	+	1060.30i	−0.934781	+	1.27593i
$832$	−105.390	−	393.323i	−0.126671	−	0.472744i
$833$	796.788	−	213.499i	0.956528	−	0.256301i
$834$	−14.3145	+	6.30524i	−0.0171636	+	0.00756024i
$835$	−15.3977	−	297.877i	−0.0184404	−	0.356739i
$836$	272.513			0.325973
$837$	−41.3979	+	643.258i	−0.0494598	+	0.768528i
$838$	−417.300	−	417.300i	−0.497971	−	0.497971i
$839$	915.370	−	528.489i	1.09103	−	0.629904i	0.157176	−	0.987571i	$-0.449761\pi$
$839$	915.370	−	528.489i	1.09103	−	0.629904i	0.933849	+	0.357667i	$0.116428\pi$
$840$	−1430.88	−	81.7115i	−1.70343	−	0.0972756i
$841$	−167.214	+	289.622i	−0.198827	+	0.344378i
$842$	−77.1972	−	288.104i	−0.0916831	−	0.342166i
$843$	−566.612	+	87.4384i	−0.672137	+	0.103723i
$844$	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
$848$	7.85783	−	29.3258i	0.00926631	−	0.0345823i
$849$	−112.669	+	1032.54i	−0.132708	+	1.21618i
$850$	−2014.17	+	208.788i	−2.36961	+	0.245633i
$851$	280.394	−	485.656i	0.329487	−	0.570689i
$852$	−477.929	+	383.888i	−0.560949	+	0.450573i
$853$	191.675	−	715.340i	0.224707	−	0.838617i	−0.757815	−	0.652469i	$-0.773733\pi$
$853$	191.675	−	715.340i	0.224707	−	0.838617i	0.982522	−	0.186148i	$-0.0596003\pi$
$854$			2150.69i			2.51837i
$855$	682.708	−	487.047i	0.798489	−	0.569645i
$856$	−1251.72			−1.46229
$857$	1218.31	+	326.446i	1.42160	+	0.380918i	0.886052	−	0.463585i	$-0.153437\pi$
$857$	1218.31	+	326.446i	1.42160	+	0.380918i	0.535551	+	0.844503i	$0.320104\pi$
$858$	−87.7427	+	13.5403i	−0.102264	+	0.0157812i
$859$	−37.7603	−	21.8009i	−0.0439584	−	0.0253794i	0.477860	−	0.878436i	$-0.341413\pi$
$859$	−37.7603	−	21.8009i	−0.0439584	−	0.0253794i	−0.521818	+	0.853057i	$0.674746\pi$
$860$	−943.571	+	611.804i	−1.09718	+	0.711400i
$861$	47.5399	+	107.927i	0.0552148	+	0.125351i
$862$	−2090.48	−	560.142i	−2.42515	−	0.649817i
$863$	−274.423	−	274.423i	−0.317988	−	0.317988i	0.530006	−	0.847994i	$-0.322190\pi$
$863$	−274.423	−	274.423i	−0.317988	−	0.317988i	−0.847994	+	0.530006i	$0.822190\pi$
$864$	−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
$867$	−838.454	−	325.677i	−0.967075	−	0.375637i
$868$	−1500.41	+	402.033i	−1.72858	+	0.463172i
$869$	−0.412935	−	0.238408i	−0.000475184	−	0.000274348i
$870$	353.255	−	1070.13i	0.406040	−	1.23003i
$871$	46.8394	+	81.1282i	0.0537766	+	0.0931438i
$872$	−760.017	+	760.017i	−0.871579	+	0.871579i
$873$	−349.513	−	547.673i	−0.400359	−	0.627346i
$874$		−	741.121i		−	0.847965i
$875$	714.749	+	886.520i	0.816856	+	1.01317i
$876$	1449.84	+	158.205i	1.65506	+	0.180599i
$877$	−46.0094	−	171.710i	−0.0524623	−	0.195792i	0.934721	−	0.355382i	$-0.115649\pi$
$877$	−46.0094	−	171.710i	−0.0524623	−	0.195792i	−0.987183	+	0.159590i	$0.948983\pi$
$878$	2023.53	−	542.205i	2.30471	−	0.617545i
$879$	97.5184	−	893.687i	0.110942	−	1.01671i
$880$	44.1535	−	48.9671i	0.0501745	−	0.0556444i
$881$	−1000.82			−1.13600			−0.568000	−	0.823029i	$-0.692282\pi$
$881$	−1000.82			−1.13600			−0.568000	+	0.823029i	$0.692282\pi$
$882$	45.3500	+	1020.24i	0.0514172	+	1.15673i
$883$	766.494	+	766.494i	0.868057	+	0.868057i	0.992257	−	0.124201i	$-0.0396366\pi$
$883$	766.494	+	766.494i	0.868057	+	0.868057i	−0.124201	+	0.992257i	$0.539637\pi$
$884$	649.920	−	375.232i	0.735204	−	0.424470i
$885$	1026.01	−	516.739i	1.15933	−	0.583886i
$886$	−897.522	+	1554.55i	−1.01300	+	1.75457i
$887$	166.511	+	621.429i	0.187724	+	0.700596i	0.994031	+	0.109099i	$0.0347964\pi$
$887$	166.511	+	621.429i	0.187724	+	0.700596i	−0.806307	+	0.591498i	$0.798537\pi$
$888$	536.244	−	1380.56i	0.603878	−	1.55468i
$889$	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
$893$	−4.18956	+	15.6357i	−0.00469156	+	0.0175091i
$894$	−924.963	+	407.428i	−1.03463	+	0.455736i
$895$	93.2817	−	437.319i	0.104225	−	0.488625i
$896$	1057.12	−	1830.98i	1.17982	−	2.04350i
$897$	23.6041	+	152.957i	0.0263145	+	0.170521i
$898$	−217.774	+	812.743i	−0.242510	+	0.905058i
$899$		−	537.328i		−	0.597696i
$900$	182.937	−	1596.52i	0.203263	−	1.77391i
$901$	−114.384			−0.126952
$902$	−28.4855	−	7.63268i	−0.0315804	−	0.00846195i
$903$	538.974	+	671.006i	0.596871	+	0.743086i
$904$	−369.109	−	213.105i	−0.408307	−	0.235736i
$905$	−1502.87	−	320.568i	−1.66063	−	0.354218i
$906$	2172.02	+	237.009i	2.39738	+	0.261600i
$907$	638.156	+	170.993i	0.703589	+	0.188526i	0.592838	−	0.805322i	$-0.298008\pi$
$907$	638.156	+	170.993i	0.703589	+	0.188526i	0.110752	+	0.993848i	$0.464674\pi$
$908$	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	$0.632900\pi$
$912$	−54.9189	−	355.881i	−0.0602181	−	0.390221i
$913$	314.231	−	84.1979i	0.344174	−	0.0922211i
$914$	853.309	+	492.658i	0.933598	+	0.539013i
$915$	−1059.14	−	60.4830i	−1.15753	−	0.0661017i
$916$	677.331	+	1173.17i	0.739444	+	1.28075i
$917$	532.635	−	532.635i	0.580846	−	0.580846i
$918$	1212.86	−	1819.82i	1.32120	−	1.98238i
$919$		−	728.665i		−	0.792889i	−0.918059	−	0.396444i	$-0.870244\pi$
$919$		−	728.665i		−	0.792889i	0.918059	−	0.396444i	$-0.129756\pi$
$920$	−463.989	−	418.378i	−0.504336	−	0.454759i
$921$	−236.692	−	537.349i	−0.256995	−	0.583441i
$922$	−440.399	−	1643.59i	−0.477656	−	1.78264i
$923$	−119.669	+	32.0652i	−0.129652	+	0.0347402i
$924$	−322.384	−	236.187i	−0.348901	−	0.255613i
$925$	−1099.21	+	420.146i	−1.18833	+	0.454212i
$926$	−985.543			−1.06430
$927$	−422.117	−	219.317i	−0.455358	−	0.236588i
$928$	325.515	+	325.515i	0.350771	+	0.350771i
$929$	844.876	−	487.790i	0.909447	−	0.525070i	0.0291940	−	0.999574i	$-0.490706\pi$
$929$	844.876	−	487.790i	0.909447	−	0.525070i	0.880253	+	0.474504i	$0.157373\pi$
$930$	−243.047	−	1170.37i	−0.261341	−	1.25847i
$931$	316.763	−	548.649i	0.340239	−	0.589312i
$932$	−164.149	−	612.611i	−0.176125	−	0.657308i
$933$	−201.534	−	250.903i	−0.216006	−	0.268921i
$934$	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	−0.778452	−	0.627704i	$-0.783995\pi$
$937$	−141.251	+	141.251i	−0.150749	+	0.150749i	0.627704	+	0.778452i	$0.283995\pi$
$938$	−170.268	+	635.447i	−0.181522	+	0.677449i
$939$	1323.62	+	969.716i	1.40961	+	1.03271i
$940$	16.8747	+	26.0255i	0.0179518	+	0.0276867i
$941$	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	$-0.0353461\pi$
$942$	2478.20	+	962.596i	2.63079	+	1.02186i
$943$	−13.3057	+	49.6574i	−0.0141099	+	0.0526589i
$944$		−	493.269i		−	0.522531i
$945$	−1229.77	−	15.5235i	−1.30134	−	0.0164270i
$946$	−215.217			−0.227502
$947$	−766.094	−	205.274i	−0.808969	−	0.216763i	−0.169451	−	0.985539i	$-0.554199\pi$
$947$	−766.094	−	205.274i	−0.808969	−	0.216763i	−0.639518	+	0.768776i	$0.720866\pi$
$948$	−1.80669	+	4.65132i	−0.00190579	+	0.00490646i
$949$	255.263	+	147.376i	0.268981	+	0.155296i
$950$	−980.435	+	1207.21i	−1.03204	+	1.27074i
$951$	−773.604	+	1055.93i	−0.813464	+	1.11034i
$952$	2239.54	+	600.082i	2.35245	+	0.630338i
$953$	−80.4623	−	80.4623i	−0.0844305	−	0.0844305i	0.663630	−	0.748061i	$-0.269015\pi$
$953$	−80.4623	−	80.4623i	−0.0844305	−	0.0844305i	−0.748061	+	0.663630i	$0.769015\pi$
$954$	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
$957$	107.781	−	86.5729i	0.112623	−	0.0904628i
$958$	1397.02	−	374.330i	1.45826	−	0.390741i
$959$	−1230.39	−	710.365i	−1.28299	−	0.740735i
$960$	1179.36	+	773.765i	1.22850	+	0.806006i
$961$	195.525	+	338.658i	0.203459	+	0.352402i
$962$	481.095	−	481.095i	0.500099	−	0.500099i
$963$	−1073.06	+	47.6980i	−1.11429	+	0.0495306i
$964$			423.810i			0.439636i
$965$	−1269.21	+	65.6073i	−1.31524	+	0.0679869i
$966$	−642.328	+	876.748i	−0.664935	+	0.907607i
$967$	87.9314	+	328.164i	0.0909322	+	0.339363i	0.996371	−	0.0851126i	$-0.0271250\pi$
$967$	87.9314	+	328.164i	0.0909322	+	0.339363i	−0.905439	+	0.424476i	$0.860458\pi$
$968$	−1183.35	+	317.078i	−1.22247	+	0.327560i
$969$	−1241.56	+	546.884i	−1.28128	+	0.564380i
$970$	894.776	+	806.818i	0.922449	+	0.831771i
$971$	1786.19			1.83954			0.919769	−	0.392460i	$-0.128376\pi$
$971$	1786.19			1.83954			0.919769	+	0.392460i	$0.128376\pi$
$972$	1202.60	+	1251.31i	1.23724	+	1.28736i
$973$	−10.0620	−	10.0620i	−0.0103413	−	0.0103413i
$974$	−1707.67	+	985.926i	−1.75326	+	1.01224i
$975$	163.900	−	280.377i	0.168103	−	0.287566i
$976$	−227.759	+	394.490i	−0.233360	+	0.404191i
$977$	−199.197	−	743.412i	−0.203886	−	0.760913i	−0.989786	−	0.142560i	$-0.954467\pi$
$977$	−199.197	−	743.412i	−0.203886	−	0.760913i	0.785900	−	0.618353i	$-0.212200\pi$
$978$	2254.45	−	347.902i	2.30516	−	0.355728i
$979$	−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
$983$	−21.2470	+	79.2948i	−0.0216144	+	0.0806661i	−0.975891	−	0.218260i	$-0.929962\pi$
$983$	−21.2470	+	79.2948i	−0.0216144	+	0.0806661i	0.954276	+	0.298926i	$0.0966285\pi$
$984$	−14.7279	+	134.971i	−0.0149674	+	0.137166i
$985$	498.303	−	323.096i	0.505892	−	0.328016i
$986$	−911.523	+	1578.80i	−0.924466	+	1.60122i
$987$	18.5076	−	14.8660i	0.0187514	−	0.0150618i
$988$	149.173	−	556.722i	0.150985	−	0.563484i
$989$			375.177i			0.379350i
$990$	195.602	−	237.319i	0.197577	−	0.239716i
$991$	−515.156			−0.519835			−0.259917	−	0.965631i	$-0.583695\pi$
$991$	−515.156			−0.519835			−0.259917	+	0.965631i	$0.583695\pi$
$992$	471.659	+	126.381i	0.475462	+	0.127400i
$993$	−1738.33	+	268.256i	−1.75059	+	0.270147i
$994$	−753.465	−	435.013i	−0.758013	−	0.437639i
$995$	172.171	−	807.166i	0.173036	−	0.811222i
$996$	−1372.35	−	3115.57i	−1.37786	−	3.12808i
$997$	358.637	+	96.0965i	0.359716	+	0.0963856i	0.434151	−	0.900840i	$-0.357049\pi$
$997$	358.637	+	96.0965i	0.359716	+	0.0963856i	−0.0744346	+	0.997226i	$0.523715\pi$
$998$	−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.13.2	yes	40
3.2	odd	2		135.3.l.a.118.9		40
5.2	odd	4	inner	45.3.k.a.22.9	yes	40
5.3	odd	4		225.3.o.b.157.2		40
5.4	even	2		225.3.o.b.193.9		40
9.2	odd	6		135.3.l.a.73.2		40
9.4	even	3		405.3.g.h.163.9		20
9.5	odd	6		405.3.g.g.163.2		20
9.7	even	3	inner	45.3.k.a.43.9	yes	40
15.2	even	4		135.3.l.a.37.2		40
45.2	even	12		135.3.l.a.127.9		40
45.7	odd	12	inner	45.3.k.a.7.2	✓	40
45.22	odd	12		405.3.g.h.82.9		20
45.32	even	12		405.3.g.g.82.2		20
45.34	even	6		225.3.o.b.43.2		40
45.43	odd	12		225.3.o.b.7.9		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.3.k.a.7.2	✓	40	45.7	odd	12	inner
45.3.k.a.13.2	yes	40	1.1	even	1	trivial
45.3.k.a.22.9	yes	40	5.2	odd	4	inner
45.3.k.a.43.9	yes	40	9.7	even	3	inner
135.3.l.a.37.2		40	15.2	even	4
135.3.l.a.73.2		40	9.2	odd	6
135.3.l.a.118.9		40	3.2	odd	2
135.3.l.a.127.9		40	45.2	even	12
225.3.o.b.7.9		40	45.43	odd	12
225.3.o.b.43.2		40	45.34	even	6
225.3.o.b.157.2		40	5.3	odd	4
225.3.o.b.193.9		40	5.4	even	2
405.3.g.g.82.2		20	45.32	even	12
405.3.g.g.163.2		20	9.5	odd	6
405.3.g.h.82.9		20	45.22	odd	12
405.3.g.h.163.9		20	9.4	even	3

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+(-3.22423 - 0.863931i) q^{2} +(1.08621 - 2.79645i) q^{3} +(6.18520 + 3.57103i) q^{4} +(-4.88999 - 1.04305i) q^{5} +(-5.91814 + 8.07800i) q^{6} +(-8.79970 - 2.35787i) 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} +(16.7046 - 13.4177i) q^{12} +(4.18269 - 1.12075i) q^{13} +(26.3352 + 15.2047i) q^{14} +(-8.22842 + 12.5417i) q^{15} +(3.22036 + 5.57783i) q^{16} +(17.1585 - 17.1585i) q^{17} +(16.1614 + 25.3242i) q^{18} -18.6363i q^{19} +(-26.5208 - 23.9138i) q^{20} +(-16.1520 + 22.0468i) q^{21} +(-1.76882 - 6.60133i) q^{22} +(-11.5078 + 3.08350i) q^{23} +(-28.7946 + 12.6835i) q^{24} +(22.8241 + 10.2010i) q^{25} -14.4542 q^{26} +(-24.2014 + 11.9704i) q^{27} +(-46.0079 - 46.0079i) q^{28} +(19.4918 - 11.2536i) q^{29} +(37.3655 - 33.3284i) q^{30} +(11.9368 - 20.6752i) q^{31} +(5.29373 + 19.7565i) q^{32} +(6.07038 - 0.936770i) 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} +(-16.1005 + 60.0877i) q^{38} +(1.40917 - 12.9141i) q^{39} +(28.5297 + 44.0007i) q^{40} +(2.15756 - 3.73700i) q^{41} +(71.1247 - 57.1297i) q^{42} +(8.15051 - 30.4181i) q^{43} +14.6227i q^{44} +(26.1343 + 36.6333i) q^{45} +39.7677 q^{46} +(-0.838990 - 0.224807i) q^{47} +(19.0961 - 2.94688i) q^{48} +(29.4398 + 16.9971i) q^{49} +(-64.7772 - 52.6090i) q^{50} +(-29.3451 - 66.6207i) q^{51} +(29.8730 + 8.00445i) 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} +(-52.1155 - 20.2430i) q^{57} +(-72.5684 + 19.4446i) q^{58} +(-66.3254 - 38.2930i) q^{59} +(-95.6810 + 48.1888i) q^{60} +(35.3623 + 61.2493i) q^{61} +(-56.3490 + 56.3490i) q^{62} +(44.1082 + 69.1158i) q^{63} -94.0358i q^{64} +(-21.6223 + 1.11769i) q^{65} +(-20.3816 - 2.22403i) q^{66} +(5.59919 + 20.8965i) q^{67} +(167.402 - 44.8553i) q^{68} +(-3.87703 + 35.5302i) q^{69} +(-112.920 - 101.820i) q^{70} -28.6105 q^{71} +(4.19166 + 94.2997i) q^{72} +(48.1316 + 48.1316i) q^{73} +(136.071 - 78.5604i) q^{74} +(53.3185 - 52.7460i) q^{75} +(66.5507 - 115.269i) q^{76} +(-4.82753 - 18.0166i) q^{77} +(-15.7004 + 40.4205i) 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} +(41.1240 - 153.477i) q^{83} +(-178.633 + 78.6845i) q^{84} +(-101.802 + 66.0077i) q^{85} +(-52.5583 + 91.0337i) q^{86} +(-10.2979 - 66.7316i) q^{87} +(5.55774 - 20.7418i) q^{88} +103.385i q^{89} +(-52.6145 - 140.692i) q^{90} -39.4490 q^{91} +(-82.1891 - 22.0225i) q^{92} +(-44.8512 - 55.8384i) q^{93} +(2.51088 + 1.44966i) q^{94} +(-19.4386 + 91.1313i) q^{95} +(60.9981 + 6.65606i) q^{96} +(69.7287 + 18.6837i) 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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