LMFDB - Embedded newform 45.3.k.a.7.5

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)

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);

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")

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			7.5
Character	$\chi$	$=$	45.7
Dual form			45.3.k.a.13.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.725667 + 0.194442i) q^{2} +(2.68329 + 1.34163i) q^{3} +(-2.97532 + 1.71780i) q^{4} +(4.81907 + 1.33289i) q^{5} +(-2.20804 - 0.451834i) q^{6} +(-1.79727 + 0.481578i) q^{7} +(3.94998 - 3.94998i) q^{8} +(5.40005 + 7.19996i) q^{9} +(-3.75621 - 0.0302083i) q^{10} +(5.82294 - 10.0856i) q^{11} +(-10.2883 + 0.617573i) q^{12} +(-19.8070 - 5.30726i) q^{13} +(1.21058 - 0.698930i) q^{14} +(11.1427 + 10.0419i) q^{15} +(4.77288 - 8.26686i) q^{16} +(-10.0254 - 10.0254i) q^{17} +(-5.31861 - 4.17477i) q^{18} -10.8032i q^{19} +(-16.6279 + 4.31241i) q^{20} +(-5.46870 - 1.11907i) q^{21} +(-2.26444 + 8.45102i) q^{22} +(-1.34569 - 0.360576i) q^{23} +(15.8983 - 5.29951i) q^{24} +(21.4468 + 12.8466i) q^{25} +15.4052 q^{26} +(4.83020 + 26.5644i) q^{27} +(4.52021 - 4.52021i) q^{28} +(20.7968 + 12.0070i) q^{29} +(-10.0384 - 5.12050i) q^{30} +(21.6233 + 37.4526i) q^{31} +(-7.63926 + 28.5101i) q^{32} +(29.1558 - 19.2504i) q^{33} +(9.22442 + 5.32572i) q^{34} +(-9.30307 - 0.0748176i) q^{35} +(-28.4350 - 12.1460i) q^{36} +(-32.5443 - 32.5443i) q^{37} +(2.10058 + 7.83949i) q^{38} +(-46.0274 - 40.8145i) q^{39} +(24.3001 - 13.7703i) q^{40} +(-20.5409 - 35.5778i) q^{41} +(4.18605 - 0.251275i) q^{42} +(2.14721 + 8.01349i) q^{43} +40.0106i q^{44} +(16.4264 + 41.8948i) q^{45} +1.04663 q^{46} +(17.2577 - 4.62418i) q^{47} +(23.8981 - 15.7789i) q^{48} +(-39.4370 + 22.7689i) q^{49} +(-18.0611 - 5.15220i) q^{50} +(-13.4506 - 40.3513i) q^{51} +(68.0488 - 18.2336i) q^{52} +(-51.3281 + 51.3281i) q^{53} +(-8.67035 - 18.3377i) q^{54} +(41.5042 - 40.8419i) q^{55} +(-5.19697 + 9.00141i) q^{56} +(14.4938 - 28.9880i) q^{57} +(-17.4262 - 4.66933i) q^{58} +(24.3449 - 14.0555i) q^{59} +(-50.4031 - 10.7371i) q^{60} +(-41.1002 + 71.1876i) q^{61} +(-22.9736 - 22.9736i) q^{62} +(-13.1727 - 10.3398i) q^{63} +16.0088i q^{64} +(-88.3771 - 51.9766i) q^{65} +(-17.4143 + 19.6385i) q^{66} +(8.65757 - 32.3105i) q^{67} +(47.0502 + 12.6071i) q^{68} +(-3.12710 - 2.77294i) q^{69} +(6.76548 - 1.75461i) q^{70} +99.6917 q^{71} +(49.7697 + 7.10958i) q^{72} +(-22.3583 + 22.3583i) q^{73} +(29.9443 + 17.2883i) q^{74} +(40.3125 + 63.2448i) q^{75} +(18.5577 + 32.1428i) q^{76} +(-5.60840 + 20.9308i) q^{77} +(41.3366 + 20.6681i) q^{78} +(-52.9926 - 30.5953i) q^{79} +(34.0196 - 33.4768i) q^{80} +(-22.6788 + 77.7603i) q^{81} +(21.8237 + 21.8237i) q^{82} +(13.3760 + 49.9199i) q^{83} +(18.1935 - 6.06456i) q^{84} +(-34.9502 - 61.6757i) q^{85} +(-3.11631 - 5.39761i) q^{86} +(39.6947 + 60.1198i) q^{87} +(-16.8375 - 62.8384i) q^{88} -113.914i q^{89} +(-20.0662 - 27.2077i) q^{90} +38.1544 q^{91} +(4.62324 - 1.23879i) q^{92} +(7.77386 + 129.506i) q^{93} +(-11.6242 + 6.71123i) q^{94} +(14.3995 - 52.0611i) q^{95} +(-58.7483 + 66.2517i) q^{96} +(-29.5689 + 7.92297i) q^{97} +(24.1909 - 24.1909i) q^{98} +(104.060 - 12.5380i) 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 $\left(\mathbb{Z}/45\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.725667	+	0.194442i	−0.362833	+	0.0972209i	−0.435630	−	0.900126i	$-0.643474\pi$
$2$	−0.725667	+	0.194442i	−0.362833	+	0.0972209i	0.0727965	+	0.997347i	$0.476808\pi$
$3$	2.68329	+	1.34163i	0.894429	+	0.447210i
$3$	2.68329	+	1.34163i	0.894429	+	0.447210i
$4$	−2.97532	+	1.71780i	−0.743829	+	0.429450i
$5$	4.81907	+	1.33289i	0.963813	+	0.266579i
$5$	4.81907	+	1.33289i	0.963813	+	0.266579i
$6$	−2.20804	−	0.451834i	−0.368007	−	0.0753056i
$7$	−1.79727	+	0.481578i	−0.256753	+	0.0687969i	−0.384900	−	0.922958i	$-0.625764\pi$
$7$	−1.79727	+	0.481578i	−0.256753	+	0.0687969i	0.128146	+	0.991755i	$0.459097\pi$
$8$	3.94998	−	3.94998i	0.493747	−	0.493747i
$9$	5.40005	+	7.19996i	0.600006	+	0.799996i
$10$	−3.75621	−	0.0302083i	−0.375621	−	0.00302083i
$11$	5.82294	−	10.0856i	0.529358	−	0.916875i	−0.470056	−	0.882637i	$-0.655766\pi$
$11$	5.82294	−	10.0856i	0.529358	−	0.916875i	0.999414	−	0.0342381i	$-0.0109005\pi$
$12$	−10.2883	+	0.617573i	−0.857357	+	0.0514644i
$13$	−19.8070	−	5.30726i	−1.52361	−	0.408251i	−0.602684	−	0.797980i	$-0.705902\pi$
$13$	−19.8070	−	5.30726i	−1.52361	−	0.408251i	−0.920930	+	0.389729i	$0.872569\pi$
$14$	1.21058	−	0.698930i	0.0864702	−	0.0499236i
$15$	11.1427	+	10.0419i	0.742846	+	0.669463i
$16$	4.77288	−	8.26686i	0.298305	−	0.516679i
$17$	−10.0254	−	10.0254i	−0.589728	−	0.589728i	0.347830	−	0.937558i	$-0.386919\pi$
$17$	−10.0254	−	10.0254i	−0.589728	−	0.589728i	−0.937558	+	0.347830i	$0.886919\pi$
$18$	−5.31861	−	4.17477i	−0.295478	−	0.231932i
$19$		−	10.8032i		−	0.568587i	−0.958737	−	0.284294i	$-0.908241\pi$
$19$		−	10.8032i		−	0.568587i	0.958737	−	0.284294i	$-0.0917590\pi$
$20$	−16.6279	+	4.31241i	−0.831395	+	0.215621i
$21$	−5.46870	−	1.11907i	−0.260414	−	0.0532889i
$22$	−2.26444	+	8.45102i	−0.102929	+	0.384137i
$23$	−1.34569	−	0.360576i	−0.0585081	−	0.0156772i	0.229446	−	0.973321i	$-0.426308\pi$
$23$	−1.34569	−	0.360576i	−0.0585081	−	0.0156772i	−0.287954	+	0.957644i	$0.592975\pi$
$24$	15.8983	−	5.29951i	0.662430	−	0.220813i
$25$	21.4468	+	12.8466i	0.857872	+	0.513864i
$26$	15.4052			0.592508
$27$	4.83020	+	26.5644i	0.178896	+	0.983868i
$28$	4.52021	−	4.52021i	0.161436	−	0.161436i
$29$	20.7968	+	12.0070i	0.717130	+	0.414035i	0.813695	−	0.581292i	$-0.197452\pi$
$29$	20.7968	+	12.0070i	0.717130	+	0.414035i	−0.0965656	+	0.995327i	$0.530786\pi$
$30$	−10.0384	−	5.12050i	−0.334615	−	0.170683i
$31$	21.6233	+	37.4526i	0.697524	+	1.20815i	0.969322	+	0.245793i	$0.0790484\pi$
$31$	21.6233	+	37.4526i	0.697524	+	1.20815i	−0.271798	+	0.962354i	$0.587618\pi$
$32$	−7.63926	+	28.5101i	−0.238727	+	0.890941i
$33$	29.1558	−	19.2504i	0.883509	−	0.583345i
$34$	9.22442	+	5.32572i	0.271307	+	0.156639i
$35$	−9.30307	−	0.0748176i	−0.265802	−	0.00213765i
$36$	−28.4350	−	12.1460i	−0.789860	−	0.337388i
$37$	−32.5443	−	32.5443i	−0.879576	−	0.879576i	0.113915	−	0.993491i	$-0.463661\pi$
$37$	−32.5443	−	32.5443i	−0.879576	−	0.879576i	−0.993491	+	0.113915i	$0.963661\pi$
$38$	2.10058	+	7.83949i	0.0552785	+	0.206302i
$39$	−46.0274	−	40.8145i	−1.18019	−	1.04653i
$40$	24.3001	−	13.7703i	0.607502	−	0.344257i
$41$	−20.5409	−	35.5778i	−0.500997	−	0.867752i	−0.999999	−	0.00115173i	$-0.999633\pi$
$41$	−20.5409	−	35.5778i	−0.500997	−	0.867752i	0.499002	−	0.866601i	$-0.333700\pi$
$42$	4.18605	−	0.251275i	0.0996678	−	0.00598274i
$43$	2.14721	+	8.01349i	0.0499351	+	0.186360i	0.986388	−	0.164432i	$-0.0525791\pi$
$43$	2.14721	+	8.01349i	0.0499351	+	0.186360i	−0.936453	+	0.350792i	$0.885912\pi$
$44$			40.0106i			0.909331i
$45$	16.4264	+	41.8948i	0.365032	+	0.930995i
$46$	1.04663			0.0227528
$47$	17.2577	−	4.62418i	0.367185	−	0.0983868i	−0.0705087	−	0.997511i	$-0.522462\pi$
$47$	17.2577	−	4.62418i	0.367185	−	0.0983868i	0.437693	+	0.899124i	$0.355796\pi$
$48$	23.8981	−	15.7789i	0.497876	−	0.328728i
$49$	−39.4370	+	22.7689i	−0.804836	+	0.464672i
$50$	−18.0611	−	5.15220i	−0.361223	−	0.103044i
$51$	−13.4506	−	40.3513i	−0.263737	−	0.791202i
$52$	68.0488	−	18.2336i	1.30863	−	0.350647i
$53$	−51.3281	+	51.3281i	−0.968455	+	0.968455i	−0.999517	−	0.0310621i	$-0.990111\pi$
$53$	−51.3281	+	51.3281i	−0.968455	+	0.968455i	0.0310621	+	0.999517i	$0.490111\pi$
$54$	−8.67035	−	18.3377i	−0.160562	−	0.339588i
$55$	41.5042	−	40.8419i	0.754621	−	0.742580i
$56$	−5.19697	+	9.00141i	−0.0928030	+	0.160739i
$57$	14.4938	−	28.9880i	0.254278	−	0.508561i
$58$	−17.4262	−	4.66933i	−0.300451	−	0.0805057i
$59$	24.3449	−	14.0555i	0.412625	−	0.238229i	−0.279292	−	0.960206i	$-0.590100\pi$
$59$	24.3449	−	14.0555i	0.412625	−	0.238229i	0.691917	+	0.721977i	$0.256766\pi$
$60$	−50.4031	−	10.7371i	−0.840051	−	0.178951i
$61$	−41.1002	+	71.1876i	−0.673774	+	1.16701i	0.303052	+	0.952974i	$0.401994\pi$
$61$	−41.1002	+	71.1876i	−0.673774	+	1.16701i	−0.976826	+	0.214036i	$0.931339\pi$
$62$	−22.9736	−	22.9736i	−0.370542	−	0.370542i
$63$	−13.1727	−	10.3398i	−0.209091	−	0.164123i
$64$			16.0088i			0.250137i
$65$	−88.3771	−	51.9766i	−1.35965	−	0.799640i
$66$	−17.4143	+	19.6385i	−0.263853	+	0.297552i
$67$	8.65757	−	32.3105i	0.129217	−	0.482246i	−0.870737	−	0.491748i	$-0.836358\pi$
$67$	8.65757	−	32.3105i	0.129217	−	0.482246i	0.999955	+	0.00950210i	$0.00302466\pi$
$68$	47.0502	+	12.6071i	0.691915	+	0.185398i
$69$	−3.12710	−	2.77294i	−0.0453203	−	0.0401876i
$70$	6.76548	−	1.75461i	0.0966497	−	0.0250659i
$71$	99.6917			1.40411			0.702054	−	0.712123i	$-0.252266\pi$
$71$	99.6917			1.40411			0.702054	+	0.712123i	$0.252266\pi$
$72$	49.7697	+	7.10958i	0.691246	+	0.0987442i
$73$	−22.3583	+	22.3583i	−0.306278	+	0.306278i	−0.843464	−	0.537186i	$-0.819487\pi$
$73$	−22.3583	+	22.3583i	−0.306278	+	0.306278i	0.537186	+	0.843464i	$0.319487\pi$
$74$	29.9443	+	17.2883i	0.404653	+	0.233626i
$75$	40.3125	+	63.2448i	0.537500	+	0.843264i
$76$	18.5577	+	32.1428i	0.244180	+	0.422932i
$77$	−5.60840	+	20.9308i	−0.0728363	+	0.271829i
$78$	41.3366	+	20.6681i	0.529956	+	0.264976i
$79$	−52.9926	−	30.5953i	−0.670793	−	0.387282i	0.125584	−	0.992083i	$-0.459919\pi$
$79$	−52.9926	−	30.5953i	−0.670793	−	0.387282i	−0.796377	+	0.604801i	$0.793253\pi$
$80$	34.0196	−	33.4768i	0.425246	−	0.418460i
$81$	−22.6788	+	77.7603i	−0.279986	+	0.960004i
$82$	21.8237	+	21.8237i	0.266142	+	0.266142i
$83$	13.3760	+	49.9199i	0.161157	+	0.601444i	0.998499	+	0.0547660i	$0.0174413\pi$
$83$	13.3760	+	49.9199i	0.161157	+	0.601444i	−0.837343	+	0.546678i	$0.815892\pi$
$84$	18.1935	−	6.06456i	0.216589	−	0.0721971i
$85$	−34.9502	−	61.6757i	−0.411178	−	0.725596i
$86$	−3.11631	−	5.39761i	−0.0362362	−	0.0627630i
$87$	39.6947	+	60.1198i	0.456261	+	0.691033i
$88$	−16.8375	−	62.8384i	−0.191335	−	0.714073i
$89$		−	113.914i		−	1.27993i	−0.768402	−	0.639967i	$-0.778948\pi$
$89$		−	113.914i		−	1.27993i	0.768402	−	0.639967i	$-0.221052\pi$
$90$	−20.0662	−	27.2077i	−0.222958	−	0.302307i
$91$	38.1544			0.419279
$92$	4.62324	−	1.23879i	0.0502526	−	0.0134651i
$93$	7.77386	+	129.506i	0.0835899	+	1.39254i
$94$	−11.6242	+	6.71123i	−0.123662	+	0.0713960i
$95$	14.3995	−	52.0611i	0.151573	−	0.548012i
$96$	−58.7483	+	66.2517i	−0.611962	+	0.690122i
$97$	−29.5689	+	7.92297i	−0.304834	+	0.0816801i	−0.407994	−	0.912985i	$-0.633771\pi$
$97$	−29.5689	+	7.92297i	−0.304834	+	0.0816801i	0.103160	+	0.994665i	$0.467105\pi$
$98$	24.1909	−	24.1909i	0.246845	−	0.246845i
$99$	104.060	−	12.5380i	1.05111	−	0.126646i
$100$	−85.8789	−	1.38141i	−0.858789	−	0.0138141i
$101$	29.8920	−	51.7745i	0.295961	−	0.512619i	−0.679247	−	0.733909i	$-0.737694\pi$
$101$	29.8920	−	51.7745i	0.295961	−	0.512619i	0.975208	+	0.221291i	$0.0710270\pi$
$102$	17.6066	+	26.6662i	0.172614	+	0.261433i
$103$	−48.8939	−	13.1011i	−0.474698	−	0.127195i	0.0135348	−	0.999908i	$-0.495692\pi$
$103$	−48.8939	−	13.1011i	−0.474698	−	0.127195i	−0.488233	+	0.872713i	$0.662358\pi$
$104$	−99.2006	+	57.2735i	−0.953852	+	0.550707i
$105$	−24.8624	−	12.6820i	−0.236785	−	0.120781i
$106$	27.2668	−	47.2274i	0.257234	−	0.445542i
$107$	−14.8359	−	14.8359i	−0.138653	−	0.138653i	0.634374	−	0.773027i	$-0.281258\pi$
$107$	−14.8359	−	14.8359i	−0.138653	−	0.138653i	−0.773027	+	0.634374i	$0.781258\pi$
$108$	−60.0038	−	70.7403i	−0.555591	−	0.655003i
$109$			115.290i			1.05770i	0.848714	+	0.528852i	$0.177377\pi$
$109$			115.290i			1.05770i	−0.848714	+	0.528852i	$0.822623\pi$
$110$	−22.1768	+	37.7078i	−0.201607	+	0.342798i
$111$	−43.6633	−	130.988i	−0.393363	−	1.18007i
$112$	−4.59703	+	17.1563i	−0.0410449	+	0.153182i
$113$	101.212	+	27.1198i	0.895686	+	0.239998i	0.677163	−	0.735833i	$-0.263209\pi$
$113$	101.212	+	27.1198i	0.895686	+	0.239998i	0.218523	+	0.975832i	$0.429876\pi$
$114$	−4.88123	+	23.8538i	−0.0428178	+	0.209244i
$115$	−6.00434	−	3.53129i	−0.0522117	−	0.0307069i
$116$	−82.5026			−0.711229
$117$	−68.7466	−	171.269i	−0.587578	−	1.46384i
$118$	−14.9333	+	14.9333i	−0.126553	+	0.126553i
$119$	22.8463	+	13.1903i	0.191986	+	0.110843i
$120$	83.6788	−	4.34791i	0.697323	−	0.0362326i
$121$	−7.31319	−	12.6668i	−0.0604396	−	0.104684i
$122$	15.9832	−	59.6501i	0.131010	−	0.488935i
$123$	−7.38473	−	123.024i	−0.0600385	−	1.00019i
$124$	−128.672	−	74.2889i	−1.03768	−	0.599104i
$125$	86.2304	+	90.4949i	0.689843	+	0.723959i
$126$	11.5695	+	4.94189i	0.0918213	+	0.0392213i
$127$	56.0831	+	56.0831i	0.441599	+	0.441599i	0.892549	−	0.450950i	$-0.148915\pi$
$127$	56.0831	+	56.0831i	0.441599	+	0.441599i	−0.450950	+	0.892549i	$0.648915\pi$
$128$	−33.6698	−	125.657i	−0.263045	−	0.981699i
$129$	−4.98957	+	24.3832i	−0.0386788	+	0.189017i
$130$	74.2387	+	20.5335i	0.571067	+	0.157950i
$131$	−2.31731	−	4.01371i	−0.0176894	−	0.0306390i	0.857045	−	0.515241i	$-0.172298\pi$
$131$	−2.31731	−	4.01371i	−0.0176894	−	0.0306390i	−0.874735	+	0.484602i	$0.838964\pi$
$132$	−53.6794	+	107.360i	−0.406662	+	0.813332i
$133$	5.20256	+	19.4162i	0.0391170	+	0.145987i
$134$			25.1300i			0.187538i
$135$	−12.1305	+	134.454i	−0.0898554	+	0.995955i
$136$	−79.1999			−0.582352
$137$	2.29751	−	0.615617i	0.0167702	−	0.00449355i	−0.250424	−	0.968136i	$-0.580570\pi$
$137$	2.29751	−	0.615617i	0.0167702	−	0.00449355i	0.267194	+	0.963643i	$0.413903\pi$
$138$	2.80841	+	1.40419i	0.0203508	+	0.0101753i
$139$	221.925	−	128.128i	1.59658	−	0.921786i	0.604441	−	0.796650i	$-0.293397\pi$
$139$	221.925	−	128.128i	1.59658	−	0.921786i	0.992140	−	0.125136i	$-0.0399367\pi$
$140$	27.8081	−	15.7582i	0.198629	−	0.112559i
$141$	52.5112	+	10.7454i	0.372420	+	0.0762087i
$142$	−72.3429	+	19.3842i	−0.509457	+	0.136509i
$143$	−168.862	+	168.862i	−1.18085	+	1.18085i
$144$	85.2949	−	10.2770i	0.592325	−	0.0713680i
$145$	84.2169	+	85.5825i	0.580806	+	0.590224i
$146$	11.8773	−	20.5721i	0.0813513	−	0.140905i
$147$	−136.368	+	8.18575i	−0.927675	+	0.0556854i
$148$	152.734	+	40.9250i	1.03199	+	0.276520i
$149$	−81.5954	+	47.1091i	−0.547620	+	0.316168i	−0.748161	−	0.663517i	$-0.769063\pi$
$149$	−81.5954	+	47.1091i	−0.547620	+	0.316168i	0.200542	+	0.979685i	$0.435730\pi$
$150$	−41.5509	−	38.0562i	−0.277006	−	0.253708i
$151$	14.0475	−	24.3310i	0.0930299	−	0.161133i	−0.815755	−	0.578398i	$-0.803678\pi$
$151$	14.0475	−	24.3310i	0.0930299	−	0.161133i	0.908785	+	0.417265i	$0.137011\pi$
$152$	−42.6722	−	42.6722i	−0.280738	−	0.280738i
$153$	18.0447	−	126.320i	0.117939	−	0.825619i
$154$		−	16.2793i		−	0.105710i
$155$	54.2836	+	209.308i	0.350217	+	1.35037i
$156$	207.057	+	42.3704i	1.32729	+	0.271605i
$157$	9.98621	−	37.2690i	0.0636064	−	0.237382i	−0.926803	−	0.375549i	$-0.877454\pi$
$157$	9.98621	−	37.2690i	0.0636064	−	0.237382i	0.990409	+	0.138166i	$0.0441209\pi$
$158$	44.4040	+	11.8980i	0.281038	+	0.0753039i
$159$	−206.591	+	68.8647i	−1.29932	+	0.433111i
$160$	−74.8150	+	127.210i	−0.467594	+	0.795061i
$161$	2.59221			0.0161007
$162$	1.33742	−	60.8378i	0.00825566	−	0.375542i
$163$	140.797	−	140.797i	0.863787	−	0.863787i	−0.127989	−	0.991776i	$-0.540852\pi$
$163$	140.797	−	140.797i	0.863787	−	0.863787i	0.991776	+	0.127989i	$0.0408522\pi$
$164$	122.231	+	70.5703i	0.745313	+	0.430306i
$165$	166.162	−	53.9073i	1.00704	−	0.326711i
$166$	−19.4130	−	33.6243i	−0.116946	−	0.202556i
$167$	−73.2232	+	273.273i	−0.438462	+	1.63636i	0.294180	+	0.955750i	$0.404953\pi$
$167$	−73.2232	+	273.273i	−0.438462	+	1.63636i	−0.732642	+	0.680614i	$0.761713\pi$
$168$	−26.0215	+	17.1810i	−0.154890	+	0.102268i
$169$	217.791	+	125.742i	1.28870	+	0.744033i
$170$	37.3545	+	37.9602i	0.219732	+	0.223295i
$171$	77.7823	−	58.3376i	0.454867	−	0.341156i
$172$	−20.1542	−	20.1542i	−0.117176	−	0.117176i
$173$	−80.2289	−	299.418i	−0.463751	−	1.73074i	−0.660998	−	0.750387i	$-0.729867\pi$
$173$	−80.2289	−	299.418i	−0.463751	−	1.73074i	0.197248	−	0.980354i	$-0.436800\pi$
$174$	−40.4949	−	35.9087i	−0.232729	−	0.206372i
$175$	−44.7324	−	12.7606i	−0.255614	−	0.0729175i
$176$	−55.5843	−	96.2748i	−0.315820	−	0.547016i
$177$	84.1816	−	5.05315i	0.475602	−	0.0285489i
$178$	22.1497	+	82.6637i	0.124436	+	0.464403i
$179$		−	151.884i		−	0.848512i	−0.905542	−	0.424256i	$-0.860536\pi$
$179$		−	151.884i		−	0.848512i	0.905542	−	0.424256i	$-0.139464\pi$
$180$	−120.841	−	96.4329i	−0.671337	−	0.535738i
$181$	48.0978			0.265734			0.132867	−	0.991134i	$-0.457582\pi$
$181$	48.0978			0.265734			0.132867	+	0.991134i	$0.457582\pi$
$182$	−27.6874	+	7.41881i	−0.152128	+	0.0407627i
$183$	−205.791	+	135.876i	−1.12454	+	0.742489i
$184$	−6.73969	+	3.89116i	−0.0366288	+	0.0211476i
$185$	−113.455	−	200.211i	−0.613271	−	1.08222i
$186$	−30.8227	−	92.4669i	−0.165713	−	0.497134i
$187$	−159.489	+	42.7350i	−0.852883	+	0.228529i
$188$	−43.4036	+	43.4036i	−0.230870	+	0.230870i
$189$	−21.4741	−	45.4174i	−0.113619	−	0.240304i
$190$	−0.326345	+	40.5789i	−0.00171761	+	0.213573i
$191$	−181.698	+	314.711i	−0.951300	+	1.64770i	−0.208683	+	0.977983i	$0.566918\pi$
$191$	−181.698	+	314.711i	−0.951300	+	1.64770i	−0.742617	+	0.669717i	$0.766416\pi$
$192$	−21.4779	+	42.9562i	−0.111864	+	0.223730i
$193$	11.5607	+	3.09769i	0.0599001	+	0.0160502i	0.288645	−	0.957436i	$-0.406795\pi$
$193$	11.5607	+	3.09769i	0.0599001	+	0.0160502i	−0.228745	+	0.973486i	$0.573462\pi$
$194$	19.9166	−	11.4989i	0.102663	−	0.0592725i
$195$	−167.408	−	258.038i	−0.858501	−	1.32327i
$196$	78.2250	−	135.490i	0.399107	−	0.691274i
$197$	45.3414	+	45.3414i	0.230159	+	0.230159i	0.812759	−	0.582600i	$-0.197964\pi$
$197$	45.3414	+	45.3414i	0.230159	+	0.230159i	−0.582600	+	0.812759i	$0.697964\pi$
$198$	−73.0751	+	29.3321i	−0.369066	+	0.148142i
$199$		−	17.0082i		−	0.0854685i	−0.999086	−	0.0427343i	$-0.986393\pi$
$199$		−	17.0082i		−	0.0854685i	0.999086	−	0.0427343i	$-0.0136069\pi$
$200$	135.458	−	33.9705i	0.677290	−	0.169853i
$201$	66.5795	−	75.0831i	0.331241	−	0.373548i
$202$	−11.6245	+	43.3833i	−0.0575471	+	0.214769i
$203$	−43.1598	−	11.5646i	−0.212610	−	0.0569686i
$204$	109.335	+	96.9524i	0.535957	+	0.475257i
$205$	−51.5664	−	198.831i	−0.251543	−	0.969906i
$206$	38.0281			0.184602
$207$	−4.67065	−	11.6360i	−0.0225635	−	0.0562126i
$208$	−138.411	+	138.411i	−0.665436	+	0.665436i
$209$	−108.957	−	62.9061i	−0.521323	−	0.300986i
$210$	20.5078	+	4.36864i	0.0976560	+	0.0208031i
$211$	−148.887	−	257.879i	−0.705624	−	1.22218i	−0.966466	−	0.256795i	$-0.917333\pi$
$211$	−148.887	−	257.879i	−0.705624	−	1.22218i	0.260842	−	0.965382i	$-0.416000\pi$
$212$	64.5460	−	240.889i	0.304462	−	1.13627i
$213$	267.501	+	133.749i	1.25588	+	0.627932i
$214$	13.6506	+	7.88119i	0.0637879	+	0.0368280i
$215$	−0.333589	+	41.4795i	−0.00155157	+	0.192928i
$216$	124.008	+	85.8497i	0.574111	+	0.397452i
$217$	−56.8993	−	56.8993i	−0.262209	−	0.262209i
$218$	−22.4172	−	83.6620i	−0.102831	−	0.383771i
$219$	−89.9903	+	29.9971i	−0.410915	+	0.136973i
$220$	−53.3298	+	192.814i	−0.242408	+	0.876425i
$221$	145.365	+	251.779i	0.657760	+	1.13927i
$222$	57.1545	+	86.5638i	0.257453	+	0.389927i
$223$	−8.27356	−	30.8773i	−0.0371012	−	0.138463i	0.944891	−	0.327385i	$-0.106167\pi$
$223$	−8.27356	−	30.8773i	−0.0371012	−	0.138463i	−0.981992	+	0.188922i	$0.939501\pi$
$224$		−	54.9194i		−	0.245176i
$225$	23.3188	+	223.788i	0.103639	+	0.994615i
$226$	−78.7197			−0.348317
$227$	377.838	−	101.241i	1.66449	−	0.445997i	0.700870	−	0.713289i	$-0.252795\pi$
$227$	377.838	−	101.241i	1.66449	−	0.445997i	0.963616	+	0.267292i	$0.0861288\pi$
$228$	6.67174	+	111.146i	0.0292620	+	0.487482i
$229$	−217.228	+	125.417i	−0.948594	+	0.547671i	−0.892644	−	0.450762i	$-0.851152\pi$
$229$	−217.228	+	125.417i	−0.948594	+	0.547671i	−0.0559502	+	0.998434i	$0.517819\pi$
$230$	5.04378	+	1.39505i	0.0219295	+	0.00606542i
$231$	−43.1304	+	48.6390i	−0.186712	+	0.210558i
$232$	129.574	−	34.7193i	0.558509	−	0.149652i
$233$	239.086	−	239.086i	1.02612	−	1.02612i	0.0264709	−	0.999650i	$-0.491573\pi$
$233$	239.086	−	239.086i	1.02612	−	1.02612i	0.999650	−	0.0264709i	$-0.00842693\pi$
$234$	83.1890	+	110.917i	0.355508	+	0.474004i
$235$	89.3294	+	0.718409i	0.380125	+	0.00305706i
$236$	−48.2891	+	83.6392i	−0.204615	+	0.354404i
$237$	−101.147	−	153.193i	−0.426780	−	0.646382i
$238$	−19.1436	−	5.12950i	−0.0804352	−	0.0215525i
$239$	33.8483	−	19.5423i	0.141625	−	0.0817672i	−0.427513	−	0.904009i	$-0.640610\pi$
$239$	33.8483	−	19.5423i	0.141625	−	0.0817672i	0.569138	+	0.822242i	$0.307277\pi$
$240$	136.198	−	44.1861i	0.567492	−	0.184109i
$241$	−41.8525	+	72.4907i	−0.173662	+	0.300791i	−0.939697	−	0.342007i	$-0.888893\pi$
$241$	−41.8525	+	72.4907i	−0.173662	+	0.300791i	0.766036	+	0.642798i	$0.222227\pi$
$242$	7.76989	+	7.76989i	0.0321070	+	0.0321070i
$243$	−165.179	+	178.227i	−0.679751	+	0.733443i
$244$		−	282.408i		−	1.15741i
$245$	−220.398	+	57.1598i	−0.899583	+	0.233305i
$246$	29.2798	+	87.8384i	0.119024	+	0.357067i
$247$	−57.3352	+	213.978i	−0.232126	+	0.866307i
$248$	233.348	+	62.5254i	0.940920	+	0.252119i
$249$	−31.0824	+	151.895i	−0.124829	+	0.610020i
$250$	−80.1705	−	48.9023i	−0.320682	−	0.195609i
$251$	−116.674			−0.464837			−0.232418	−	0.972616i	$-0.574664\pi$
$251$	−116.674			−0.464837			−0.232418	+	0.972616i	$0.574664\pi$
$252$	56.9546	+	8.13594i	0.226011	+	0.0322855i
$253$	−11.4725	+	11.4725i	−0.0453458	+	0.0453458i
$254$	−51.6025	−	29.7927i	−0.203159	−	0.117294i
$255$	−11.0354	−	212.384i	−0.0432759	−	0.832877i
$256$	16.8485	+	29.1825i	0.0658146	+	0.113994i
$257$	−1.23843	+	4.62189i	−0.00481880	+	0.0179840i	−0.968293	−	0.249816i	$-0.919630\pi$
$257$	−1.23843	+	4.62189i	−0.00481880	+	0.0179840i	0.963475	+	0.267800i	$0.0862966\pi$
$258$	−1.12036	−	18.6643i	−0.00434247	−	0.0723422i
$259$	74.1637	+	42.8184i	0.286346	+	0.165322i
$260$	352.235	+	2.83276i	1.35475	+	0.0108952i
$261$	25.8536	+	214.574i	0.0990559	+	0.822124i
$262$	2.46203	+	2.46203i	0.00939706	+	0.00939706i
$263$	−25.3145	−	94.4750i	−0.0962529	−	0.359221i	0.900954	−	0.433916i	$-0.142868\pi$
$263$	−25.3145	−	94.4750i	−0.0962529	−	0.359221i	−0.997206	+	0.0746949i	$0.976202\pi$
$264$	39.1261	−	191.203i	0.148205	−	0.724255i
$265$	−315.769	+	178.939i	−1.19158	+	0.675241i
$266$	−7.55065	−	13.0781i	−0.0283859	−	0.0491658i
$267$	152.831	−	305.664i	0.572400	−	1.14481i
$268$	29.7440	+	111.006i	0.110985	+	0.414201i
$269$		−	212.871i		−	0.791340i	−0.918393	−	0.395670i	$-0.870512\pi$
$269$		−	212.871i		−	0.791340i	0.918393	−	0.395670i	$-0.129488\pi$
$270$	−17.3408	−	99.9274i	−0.0642251	−	0.370101i
$271$	−180.243			−0.665102			−0.332551	−	0.943085i	$-0.607909\pi$
$271$	−180.243			−0.665102			−0.332551	+	0.943085i	$0.607909\pi$
$272$	−130.728	+	35.0285i	−0.480618	+	0.128781i
$273$	102.379	+	51.1891i	0.375016	+	0.187506i
$274$	−1.54753	+	0.893465i	−0.00564791	+	0.00326082i
$275$	254.449	−	141.499i	0.925270	−	0.514543i
$276$	14.0675	+	2.87864i	0.0509691	+	0.0104299i
$277$	316.123	−	84.7048i	1.14124	−	0.305794i	0.361789	−	0.932260i	$-0.382166\pi$
$277$	316.123	−	84.7048i	1.14124	−	0.305794i	0.779448	+	0.626467i	$0.215499\pi$
$278$	−136.130	+	136.130i	−0.489676	+	0.489676i
$279$	−152.890	+	357.932i	−0.547994	+	1.28291i
$280$	−37.0424	+	36.4514i	−0.132294	+	0.130184i
$281$	−15.6356	+	27.0816i	−0.0556426	+	0.0963758i	−0.892505	−	0.451037i	$-0.851054\pi$
$281$	−15.6356	+	27.0816i	−0.0556426	+	0.0963758i	0.836862	+	0.547413i	$0.184387\pi$
$282$	−40.1950	+	2.41278i	−0.142535	+	0.00855596i
$283$	195.826	+	52.4715i	0.691966	+	0.185412i	0.587629	−	0.809130i	$-0.300061\pi$
$283$	195.826	+	52.4715i	0.691966	+	0.185412i	0.104337	+	0.994542i	$0.466728\pi$
$284$	−296.614	+	171.250i	−1.04442	+	0.602995i
$285$	108.485	−	120.376i	0.380648	−	0.422372i
$286$	89.7036	−	155.371i	0.313649	−	0.543256i
$287$	54.0511	+	54.0511i	0.188331	+	0.188331i
$288$	−246.524	+	98.9537i	−0.855986	+	0.343589i
$289$		−	87.9840i		−	0.304443i
$290$	−77.7542	−	45.7291i	−0.268118	−	0.157686i
$291$	−89.9715	−	18.4110i	−0.309181	−	0.0632679i
$292$	28.1159	−	104.930i	0.0962875	−	0.359350i
$293$	−37.6696	−	10.0935i	−0.128565	−	0.0344490i	0.193963	−	0.981009i	$-0.437866\pi$
$293$	−37.6696	−	10.0935i	−0.128565	−	0.0344490i	−0.322528	+	0.946560i	$0.604533\pi$
$294$	97.3662	−	32.4558i	0.331178	−	0.110394i
$295$	136.054	−	35.2854i	0.461200	−	0.119611i
$296$	−257.098			−0.868576
$297$	296.045	+	105.967i	0.996784	+	0.356793i
$298$	50.0510	−	50.0510i	0.167957	−	0.167957i
$299$	24.7403	+	14.2838i	0.0827435	+	0.0477720i
$300$	−228.584	−	118.924i	−0.761948	−	0.396415i
$301$	−7.71824	−	13.3684i	−0.0256420	−	0.0444132i
$302$	−5.46285	+	20.3876i	−0.0180889	+	0.0675087i
$303$	149.671	−	98.8217i	0.493964	−	0.326144i
$304$	−89.3082	−	51.5621i	−0.293777	−	0.169612i
$305$	−292.950	+	288.276i	−0.960492	+	0.945166i
$306$	11.4674	+	95.1747i	0.0374751	+	0.311028i
$307$	−28.4359	−	28.4359i	−0.0926251	−	0.0926251i	0.659276	−	0.751901i	$-0.270863\pi$
$307$	−28.4359	−	28.4359i	−0.0926251	−	0.0926251i	−0.751901	+	0.659276i	$0.770863\pi$
$308$	−19.2682	−	71.9100i	−0.0625591	−	0.233474i
$309$	−113.619	−	100.751i	−0.367701	−	0.326057i
$310$	−80.0900	−	141.333i	−0.258355	−	0.455912i
$311$	−215.953	−	374.041i	−0.694381	−	1.20270i	−0.970389	−	0.241548i	$-0.922345\pi$
$311$	−215.953	−	374.041i	−0.694381	−	1.20270i	0.276007	−	0.961156i	$-0.410989\pi$
$312$	−343.024	+	20.5906i	−1.09943	+	0.0659956i
$313$	53.6933	+	200.386i	0.171544	+	0.640211i	0.997115	+	0.0759119i	$0.0241868\pi$
$313$	53.6933	+	200.386i	0.171544	+	0.640211i	−0.825571	+	0.564299i	$0.809147\pi$
$314$			28.9866i			0.0923141i
$315$	−49.6984	−	67.3858i	−0.157773	−	0.213923i
$316$	210.226			0.665274
$317$	342.998	−	91.9060i	1.08201	−	0.289924i	0.326593	−	0.945165i	$-0.394100\pi$
$317$	342.998	−	91.9060i	1.08201	−	0.289924i	0.755420	+	0.655241i	$0.227433\pi$
$318$	136.526	−	90.1428i	0.429328	−	0.283468i
$319$	242.196	−	139.832i	0.759237	−	0.438345i
$320$	−21.3380	+	77.1474i	−0.0666813	+	0.241086i
$321$	−19.9046	−	59.7132i	−0.0620082	−	0.186022i
$322$	−1.88108	+	0.504034i	−0.00584187	+	0.00156532i
$323$	−108.306	+	108.306i	−0.335311	+	0.335311i
$324$	−66.1000	−	270.319i	−0.204012	−	0.834319i
$325$	−356.616	−	368.276i	−1.09728	−	1.13316i
$326$	−74.7950	+	129.549i	−0.229432	+	0.397389i
$327$	−154.676	+	309.356i	−0.473016	+	0.946042i
$328$	−221.668	−	59.3957i	−0.675816	−	0.181084i
$329$	−28.7899	+	16.6218i	−0.0875072	+	0.0505223i
$330$	−110.097	+	71.4276i	−0.333626	+	0.216447i
$331$	−187.451	+	324.675i	−0.566318	+	0.980891i	0.430608	+	0.902539i	$0.358299\pi$
$331$	−187.451	+	324.675i	−0.566318	+	0.980891i	−0.996926	+	0.0783519i	$0.975034\pi$
$332$	−125.550	−	125.550i	−0.378163	−	0.378163i
$333$	58.5767	−	410.059i	0.175906	−	1.23141i
$334$		−	212.543i		−	0.636355i
$335$	84.7879	−	144.167i	0.253098	−	0.430349i
$336$	−35.3526	+	39.8678i	−0.105216	+	0.118654i
$337$	−38.4732	+	143.584i	−0.114164	+	0.426065i	−0.999223	−	0.0394135i	$-0.987451\pi$
$337$	−38.4732	+	143.584i	−0.114164	+	0.426065i	0.885059	+	0.465478i	$0.154118\pi$
$338$	−182.493	−	48.8988i	−0.539920	−	0.144671i
$339$	235.197	+	208.560i	0.693797	+	0.615221i
$340$	209.934	+	123.467i	0.617454	+	0.363139i
$341$	503.643			1.47696
$342$	−45.1007	+	57.4578i	−0.131873	+	0.168005i
$343$	124.383	−	124.383i	0.362633	−	0.362633i
$344$	40.1345	+	23.1717i	0.116670	+	0.0673595i
$345$	−11.3737	−	17.5311i	−0.0329672	−	0.0508147i
$346$	116.439	+	201.678i	0.336528	+	0.582884i
$347$	−62.5014	+	233.258i	−0.180119	+	0.672214i	0.815504	+	0.578752i	$0.196460\pi$
$347$	−62.5014	+	233.258i	−0.180119	+	0.672214i	−0.995623	+	0.0934622i	$0.970207\pi$
$348$	−221.378	−	110.688i	−0.636144	−	0.318069i
$349$	331.191	+	191.213i	0.948971	+	0.547889i	0.892761	−	0.450530i	$-0.148765\pi$
$349$	331.191	+	191.213i	0.948971	+	0.547889i	0.0562101	+	0.998419i	$0.482098\pi$
$350$	34.9420	+	0.562061i	0.0998343	+	0.00160589i
$351$	45.3127	−	551.796i	0.129096	−	1.57207i
$352$	243.059	+	243.059i	0.690509	+	0.690509i
$353$	134.782	+	503.013i	0.381819	+	1.42497i	0.843121	+	0.537724i	$0.180716\pi$
$353$	134.782	+	503.013i	0.381819	+	1.42497i	−0.461302	+	0.887243i	$0.652618\pi$
$354$	−60.1052	+	20.0353i	−0.169789	+	0.0565969i
$355$	480.421	+	132.878i	1.35330	+	0.374305i
$356$	195.682	+	338.931i	0.549668	+	0.952052i
$357$	43.6067	+	66.0448i	0.122148	+	0.184999i
$358$	29.5325	+	110.217i	0.0824931	+	0.307868i
$359$			326.956i			0.910741i	0.890302	+	0.455370i	$0.150493\pi$
$359$			326.956i			0.910741i	−0.890302	+	0.455370i	$0.849507\pi$
$360$	230.367	+	100.599i	0.639909	+	0.279443i
$361$	244.292			0.676709
$362$	−34.9030	+	9.35222i	−0.0964170	+	0.0258349i
$363$	−2.62919	−	43.8003i	−0.00724296	−	0.120662i
$364$	−113.521	+	65.5417i	−0.311872	+	0.180060i
$365$	−137.547	+	77.9449i	−0.376842	+	0.213548i
$366$	122.916	−	138.615i	0.335836	−	0.378729i
$367$	−505.039	+	135.325i	−1.37613	+	0.368733i	−0.869713	−	0.493557i	$-0.835696\pi$
$367$	−505.039	+	135.325i	−1.37613	+	0.368733i	−0.506415	+	0.862290i	$0.669030\pi$
$368$	−9.40362	+	9.40362i	−0.0255533	+	0.0255533i
$369$	145.237	−	340.016i	0.393597	−	0.921452i
$370$	121.260	+	123.226i	0.327730	+	0.333044i
$371$	67.5322	−	116.969i	0.182028	−	0.315281i
$372$	−245.596	−	371.969i	−0.660204	−	0.999916i
$373$	−23.4631	−	6.28693i	−0.0629039	−	0.0168550i	0.227230	−	0.973841i	$-0.427033\pi$
$373$	−23.4631	−	6.28693i	−0.0629039	−	0.0168550i	−0.290134	+	0.956986i	$0.593700\pi$
$374$	107.426	−	62.0227i	0.287237	−	0.165836i
$375$	109.970	+	358.513i	0.293253	+	0.956035i
$376$	49.9020	−	86.4328i	0.132718	−	0.229874i
$377$	−348.197	−	348.197i	−0.923598	−	0.923598i
$378$	24.4141	+	28.7825i	0.0645874	+	0.0761441i
$379$			364.939i			0.962900i	0.876474	+	0.481450i	$0.159890\pi$
$379$			364.939i			0.962900i	−0.876474	+	0.481450i	$0.840110\pi$
$380$	46.5877	+	179.634i	0.122599	+	0.472720i
$381$	75.2442	+	225.730i	0.197491	+	0.592466i
$382$	70.6595	−	263.705i	0.184972	−	0.690327i
$383$	3.24720	+	0.870084i	0.00847832	+	0.00227176i	0.263056	−	0.964781i	$-0.415270\pi$
$383$	3.24720	+	0.870084i	0.00847832	+	0.00227176i	−0.254577	+	0.967052i	$0.581936\pi$
$384$	78.2401	−	382.347i	0.203750	−	0.995696i
$385$	−54.9258	+	93.3916i	−0.142664	+	0.242576i
$386$	−8.99155			−0.0232942
$387$	−46.1018	+	58.7331i	−0.119126	+	0.151765i
$388$	74.3668	−	74.3668i	0.191667	−	0.191667i
$389$	131.808	+	76.0995i	0.338838	+	0.195628i	0.659758	−	0.751478i	$-0.270659\pi$
$389$	131.808	+	76.0995i	0.338838	+	0.195628i	−0.320920	+	0.947106i	$0.603992\pi$
$390$	171.655	+	154.698i	0.440142	+	0.396662i
$391$	9.87610	+	17.1059i	0.0252586	+	0.0437491i
$392$	−65.8383	+	245.712i	−0.167955	+	0.626816i
$393$	−0.833107	−	13.8789i	−0.00211986	−	0.0353153i
$394$	−41.7190	−	24.0865i	−0.105886	−	0.0611332i
$395$	−214.595	−	218.074i	−0.543278	−	0.552087i
$396$	−288.074	+	216.059i	−0.727461	+	0.545604i
$397$	−275.868	−	275.868i	−0.694882	−	0.694882i	0.268420	−	0.963302i	$-0.413498\pi$
$397$	−275.868	−	275.868i	−0.694882	−	0.694882i	−0.963302	+	0.268420i	$0.913498\pi$
$398$	3.30711	+	12.3423i	0.00830933	+	0.0310108i
$399$	−12.0894	+	59.0792i	−0.0302994	+	0.148068i
$400$	208.564	−	115.982i	0.521410	−	0.289956i
$401$	−337.489	−	584.548i	−0.841618	−	1.45773i	−0.888526	−	0.458826i	$-0.848270\pi$
$401$	−337.489	−	584.548i	−0.841618	−	1.45773i	0.0469080	−	0.998899i	$-0.485063\pi$
$402$	−33.7152	+	67.4311i	−0.0838688	+	0.167739i
$403$	−229.521	−	856.582i	−0.569530	−	2.12551i
$404$			205.394i			0.508401i
$405$	−212.937	+	344.504i	−0.525770	+	0.850626i
$406$	33.5683			0.0826805
$407$	−517.733	+	138.726i	−1.27207	+	0.340850i
$408$	−212.516	−	106.257i	−0.520873	−	0.260434i
$409$	−375.213	+	216.629i	−0.917390	+	0.529655i	−0.882802	−	0.469746i	$-0.844345\pi$
$409$	−375.213	+	216.629i	−0.917390	+	0.529655i	−0.0345887	+	0.999402i	$0.511012\pi$
$410$	76.0810	+	134.258i	0.185563	+	0.327459i
$411$	6.99082	+	1.43054i	0.0170093	+	0.00348063i
$412$	167.980	−	45.0101i	0.407718	−	0.109248i
$413$	−36.9856	+	36.9856i	−0.0895534	+	0.0895534i
$414$	5.65186	+	7.53570i	0.0136518	+	0.0182022i
$415$	−2.07808	+	258.396i	−0.00500743	+	0.622641i
$416$	302.621	−	524.155i	0.727455	−	1.25999i
$417$	767.388	−	46.0639i	1.84026	−	0.110465i
$418$	91.2977	+	24.4631i	0.218416	+	0.0585243i
$419$	432.869	−	249.917i	1.03310	−	0.596461i	0.115229	−	0.993339i	$-0.463240\pi$
$419$	432.869	−	249.917i	1.03310	−	0.596461i	0.917871	+	0.396878i	$0.129907\pi$
$420$	95.7589	−	4.97558i	0.227997	−	0.0118466i
$421$	15.0425	−	26.0544i	0.0357304	−	0.0618869i	−0.847607	−	0.530624i	$-0.821958\pi$
$421$	15.0425	−	26.0544i	0.0357304	−	0.0618869i	0.883338	+	0.468737i	$0.155291\pi$
$422$	158.185	+	158.185i	0.374845	+	0.374845i
$423$	126.486	+	99.2837i	0.299022	+	0.234713i
$424$			405.490i			0.956344i
$425$	−86.2201	−	343.804i	−0.202871	−	0.808950i
$426$	−220.123	−	45.0441i	−0.516721	−	0.105737i
$427$	39.5859	−	147.737i	0.0927071	−	0.345987i
$428$	69.6265	+	18.6564i	0.162679	+	0.0435896i
$429$	−679.655	+	226.554i	−1.58428	+	0.528099i
$430$	−7.82328	−	30.1652i	−0.0181937	−	0.0701516i
$431$	515.749			1.19663			0.598316	−	0.801260i	$-0.295837\pi$
$431$	515.749			1.19663			0.598316	+	0.801260i	$0.295837\pi$
$432$	242.659	+	86.8581i	0.561710	+	0.201060i
$433$	−305.797	+	305.797i	−0.706229	+	0.706229i	−0.965740	−	0.259511i	$-0.916439\pi$
$433$	−305.797	+	305.797i	−0.706229	+	0.706229i	0.259511	+	0.965740i	$0.416439\pi$
$434$	52.3535	+	30.2263i	0.120630	+	0.0696458i
$435$	111.158	+	342.630i	0.255536	+	0.787656i
$436$	−198.045	−	343.024i	−0.454231	−	0.786752i
$437$	−3.89535	+	14.5377i	−0.00891385	+	0.0332669i
$438$	59.4703	−	39.2658i	0.135777	−	0.0896480i
$439$	−437.591	−	252.643i	−0.996790	−	0.575497i	−0.0894929	−	0.995987i	$-0.528525\pi$
$439$	−437.591	−	252.643i	−0.996790	−	0.575497i	−0.907297	+	0.420491i	$0.861858\pi$
$440$	2.61586	−	325.265i	0.00594514	−	0.739239i
$441$	−376.897	−	160.991i	−0.854642	−	0.365059i
$442$	−154.443	−	154.443i	−0.349418	−	0.349418i
$443$	−52.3076	−	195.215i	−0.118076	−	0.440665i	0.881423	−	0.472328i	$-0.156586\pi$
$443$	−52.3076	−	195.215i	−0.118076	−	0.440665i	−0.999499	+	0.0316632i	$0.989920\pi$
$444$	354.923	+	314.726i	0.799377	+	0.708843i
$445$	151.835	−	548.960i	0.341203	−	1.23362i
$446$	12.0077	+	20.7979i	0.0269231	+	0.0466321i
$447$	−282.147	+	16.9364i	−0.631201	+	0.0378890i
$448$	−7.70948	−	28.7722i	−0.0172087	−	0.0642236i
$449$		−	145.089i		−	0.323138i	−0.986861	−	0.161569i	$-0.948345\pi$
$449$		−	145.089i		−	0.323138i	0.986861	−	0.161569i	$-0.0516554\pi$
$450$	−60.4355	−	157.862i	−0.134301	−	0.350804i
$451$	−478.433			−1.06083
$452$	−347.726	+	93.1728i	−0.769305	+	0.206135i
$453$	70.3367	−	46.4405i	0.155269	−	0.102518i
$454$	−254.499	+	146.935i	−0.560570	+	0.323645i
$455$	183.869	+	50.8558i	0.404107	+	0.111771i
$456$	−57.2514	−	171.752i	−0.125551	−	0.376649i
$457$	−286.527	+	76.7746i	−0.626973	+	0.167997i	−0.558296	−	0.829642i	$-0.688545\pi$
$457$	−286.527	+	76.7746i	−0.626973	+	0.167997i	−0.0686775	+	0.997639i	$0.521878\pi$
$458$	133.249	−	133.249i	0.290936	−	0.290936i
$459$	217.894	−	314.743i	0.474714	−	0.685714i
$460$	23.9309	+	0.192458i	0.0520236	+	0.000418387i
$461$	143.044	−	247.759i	0.310291	−	0.537439i	−0.668135	−	0.744040i	$-0.732907\pi$
$461$	143.044	−	247.759i	0.310291	−	0.537439i	0.978425	+	0.206601i	$0.0662403\pi$
$462$	21.8408	−	43.6821i	0.0472745	−	0.0945499i
$463$	−241.707	−	64.7653i	−0.522046	−	0.139882i	−0.0118333	−	0.999930i	$-0.503767\pi$
$463$	−241.707	−	64.7653i	−0.522046	−	0.139882i	−0.510213	+	0.860048i	$0.670433\pi$
$464$	198.521	−	114.616i	0.427846	−	0.247017i
$465$	−135.155	+	634.462i	−0.290657	+	1.36443i
$466$	−127.008	+	219.985i	−0.272550	+	0.472071i
$467$	−71.3291	−	71.3291i	−0.152739	−	0.152739i	0.626601	−	0.779340i	$-0.284446\pi$
$467$	−71.3291	−	71.3291i	−0.152739	−	0.152739i	−0.779340	+	0.626601i	$0.784446\pi$
$468$	498.749	+	391.486i	1.06570	+	0.836509i
$469$			62.2401i			0.132708i
$470$	−64.9631	+	16.8480i	−0.138219	+	0.0358469i
$471$	76.7972	−	86.6057i	0.163051	−	0.183876i
$472$	40.6427	−	151.681i	0.0861074	−	0.321357i
$473$	93.3241	+	25.0061i	0.197302	+	0.0528670i
$474$	103.186	+	91.4995i	0.217692	+	0.193037i
$475$	138.784	−	231.693i	0.292176	−	0.487775i
$476$	−90.6334			−0.190406
$477$	−646.735	−	92.3858i	−1.35584	−	0.193681i
$478$	−20.7628	+	20.7628i	−0.0434367	+	0.0434367i
$479$	−169.803	−	98.0357i	−0.354494	−	0.204667i	0.312169	−	0.950027i	$-0.398945\pi$
$479$	−169.803	−	98.0357i	−0.354494	−	0.204667i	−0.666663	+	0.745359i	$0.732278\pi$
$480$	−371.419	+	240.966i	−0.773789	+	0.502013i
$481$	471.883	+	817.325i	0.981046	+	1.69922i
$482$	16.2758	−	60.7419i	0.0337671	−	0.126021i
$483$	6.95565	+	3.47779i	0.0144009	+	0.00720040i
$484$	43.5181	+	25.1252i	0.0899135	+	0.0519116i
$485$	−153.055	−	1.23091i	−0.315577	−	0.00253795i
$486$	85.2105	−	161.451i	0.175330	−	0.332204i
$487$	660.124	+	660.124i	1.35549	+	1.35549i	0.879391	+	0.476100i	$0.157950\pi$
$487$	660.124	+	660.124i	1.35549	+	1.35549i	0.476100	+	0.879391i	$0.342050\pi$
$488$	118.845	+	443.534i	0.243534	+	0.908882i
$489$	566.697	−	188.901i	1.15889	−	0.386301i
$490$	148.821	−	84.3335i	0.303717	−	0.172109i
$491$	393.999	+	682.426i	0.802442	+	1.38987i	0.918004	+	0.396570i	$0.129800\pi$
$491$	393.999	+	682.426i	0.802442	+	1.38987i	−0.115562	+	0.993300i	$0.536867\pi$
$492$	233.302	+	353.349i	0.474192	+	0.718190i
$493$	−88.1204	−	328.870i	−0.178743	−	0.667079i
$494$		−	166.425i		−	0.336892i
$495$	518.185	+	78.2798i	1.04684	+	0.158141i
$496$	412.820			0.832299
$497$	−179.173	+	48.0093i	−0.360510	+	0.0965983i
$498$	−6.97925	−	116.269i	−0.0140146	−	0.233472i
$499$	144.756	−	83.5751i	0.290093	−	0.167485i	−0.347891	−	0.937535i	$-0.613102\pi$
$499$	144.756	−	83.5751i	0.290093	−	0.167485i	0.637984	+	0.770050i	$0.279769\pi$
$500$	−412.015	−	121.124i	−0.824030	−	0.242249i
$501$	−563.110	+	635.031i	−1.12397	+	1.26753i
$502$	84.6664	−	22.6863i	0.168658	−	0.0451918i
$503$	249.990	−	249.990i	0.496998	−	0.496998i	−0.413504	−	0.910502i	$-0.635695\pi$
$503$	249.990	−	249.990i	0.496998	−	0.496998i	0.910502	+	0.413504i	$0.135695\pi$
$504$	−92.8737	+	11.1901i	−0.184273	+	0.0222027i
$505$	213.061	−	209.662i	0.421904	−	0.415172i
$506$	6.09446	−	10.5559i	0.0120444	−	0.0208615i
$507$	415.696	+	629.596i	0.819914	+	1.24181i
$508$	−263.204	−	70.5254i	−0.518119	−	0.138830i
$509$	95.6645	−	55.2319i	0.187946	−	0.108511i	−0.403075	−	0.915167i	$-0.632059\pi$
$509$	95.6645	−	55.2319i	0.187946	−	0.108511i	0.591021	+	0.806656i	$0.298725\pi$
$510$	49.3042	+	151.974i	0.0966750	+	0.297988i
$511$	29.4167	−	50.9513i	0.0575670	−	0.0997089i
$512$	350.050	+	350.050i	0.683691	+	0.683691i
$513$	286.980	−	52.1814i	0.559415	−	0.101718i
$514$		−	3.59475i		−	0.00699368i
$515$	−218.160	−	128.305i	−0.423613	−	0.249136i
$516$	−27.0400	−	81.1190i	−0.0524031	−	0.157207i
$517$	53.8526	−	200.981i	0.104164	−	0.388744i
$518$	−62.1438	−	16.6514i	−0.119969	−	0.0321455i
$519$	186.432	−	911.062i	0.359213	−	1.75542i
$520$	−554.394	+	143.781i	−1.06614	+	0.276502i
$521$	−415.088			−0.796715			−0.398357	−	0.917230i	$-0.630420\pi$
$521$	−415.088			−0.796715			−0.398357	+	0.917230i	$0.630420\pi$
$522$	−60.4833	−	150.682i	−0.115868	−	0.288664i
$523$	−384.585	+	384.585i	−0.735344	+	0.735344i	−0.971673	−	0.236329i	$-0.924056\pi$
$523$	−384.585	+	384.585i	−0.735344	+	0.735344i	0.236329	+	0.971673i	$0.424056\pi$
$524$	13.7895	+	7.96136i	0.0263158	+	0.0151934i
$525$	−102.910	−	94.2546i	−0.196019	−	0.179533i
$526$	36.7398	+	63.6352i	0.0698475	+	0.120979i
$527$	158.695	−	592.257i	0.301129	−	1.12383i
$528$	−19.9833	−	332.907i	−0.0378472	−	0.630505i
$529$	−456.447	−	263.530i	−0.862848	−	0.498166i
$530$	194.350	−	191.248i	0.366697	−	0.360846i
$531$	232.663	+	99.3815i	0.438160	+	0.187159i
$532$	−48.8325	−	48.8325i	−0.0917904	−	0.0917904i
$533$	218.032	+	813.705i	0.409065	+	1.52665i
$534$	−51.4702	+	251.527i	−0.0963862	+	0.471024i
$535$	−51.7204	−	91.2697i	−0.0966737	−	0.170598i
$536$	−93.4285	−	161.823i	−0.174307	−	0.301908i
$537$	203.772	−	407.547i	0.379463	−	0.758933i
$538$	41.3909	+	154.473i	0.0769348	+	0.287125i
$539$			530.329i			0.983912i
$540$	−194.873	−	420.881i	−0.360876	−	0.779409i
$541$	251.489			0.464859			0.232430	−	0.972613i	$-0.425332\pi$
$541$	251.489			0.464859			0.232430	+	0.972613i	$0.425332\pi$
$542$	130.796	−	35.0467i	0.241321	−	0.0646618i
$543$	129.060	+	64.5295i	0.237680	+	0.118839i
$544$	362.411	−	209.238i	0.666196	−	0.384628i
$545$	−153.669	+	555.589i	−0.281961	+	1.01943i
$546$	−84.2465	−	17.2394i	−0.154298	−	0.0315741i
$547$	539.479	−	144.553i	0.986251	−	0.264265i	0.270576	−	0.962699i	$-0.412786\pi$
$547$	539.479	−	144.553i	0.986251	−	0.264265i	0.715675	+	0.698433i	$0.246119\pi$
$548$	−5.77833	+	5.77833i	−0.0105444	+	0.0105444i
$549$	−734.491	+	88.4973i	−1.33787	+	0.161197i
$550$	−157.132	+	152.157i	−0.285694	+	0.276649i
$551$	129.714	−	224.671i	0.235415	−	0.407751i
$552$	−23.3050	+	1.39893i	−0.0422193	+	0.00253429i
$553$	109.976	+	29.4681i	0.198872	+	0.0532876i
$554$	−212.930	+	122.935i	−0.384349	+	0.221904i
$555$	−35.8229	−	689.439i	−0.0645458	−	1.24223i
$556$	−440.197	+	762.444i	−0.791722	+	1.37130i
$557$	302.419	+	302.419i	0.542943	+	0.542943i	0.924391	−	0.381447i	$-0.124574\pi$
$557$	302.419	+	302.419i	0.542943	+	0.542943i	−0.381447	+	0.924391i	$0.624574\pi$
$558$	41.3504	−	289.468i	0.0741046	−	0.518760i
$559$		−	170.119i		−	0.304327i
$560$	−45.0209	+	76.5501i	−0.0803945	+	0.136697i
$561$	−485.290	−	99.3053i	−0.865044	−	0.177015i
$562$	6.08041	−	22.6924i	0.0108192	−	0.0403780i
$563$	−874.123	−	234.221i	−1.55262	−	0.416022i	−0.622300	−	0.782779i	$-0.713802\pi$
$563$	−874.123	−	234.221i	−1.55262	−	0.416022i	−0.930317	+	0.366756i	$0.880468\pi$
$564$	−174.696	+	58.2327i	−0.309745	+	0.103250i
$565$	451.602	+	265.598i	0.799295	+	0.470084i
$566$	−152.307			−0.269094
$567$	3.31241	−	150.678i	0.00584199	−	0.265747i
$568$	393.780	−	393.780i	0.693274	−	0.693274i
$569$	194.081	+	112.053i	0.341092	+	0.196929i	0.660755	−	0.750602i	$-0.270236\pi$
$569$	194.081	+	112.053i	0.341092	+	0.196929i	−0.319663	+	0.947531i	$0.603570\pi$
$570$	−55.3175	+	108.447i	−0.0970483	+	0.190258i
$571$	−28.3061	−	49.0275i	−0.0495728	−	0.0858626i	0.840174	−	0.542317i	$-0.182453\pi$
$571$	−28.3061	−	49.0275i	−0.0495728	−	0.0858626i	−0.889747	+	0.456454i	$0.849119\pi$
$572$	212.347	−	792.488i	0.371235	−	1.38547i
$573$	−909.774	+	600.687i	−1.58774	+	1.04832i
$574$	−49.7329	−	28.7133i	−0.0866426	−	0.0500232i
$575$	−24.2285	−	25.0207i	−0.0421365	−	0.0435142i
$576$	−115.263	+	86.4483i	−0.200109	+	0.150084i
$577$	−450.543	−	450.543i	−0.780838	−	0.780838i	0.199135	−	0.979972i	$-0.436187\pi$
$577$	−450.543	−	450.543i	−0.780838	−	0.780838i	−0.979972	+	0.199135i	$0.936187\pi$
$578$	17.1078	+	63.8471i	0.0295982	+	0.110462i
$579$	26.8648	+	23.8222i	0.0463986	+	0.0411437i
$580$	−397.586	−	109.967i	−0.685492	−	0.189599i
$581$	−48.0806	−	83.2781i	−0.0827550	−	0.143336i
$582$	68.8692	−	4.13400i	0.118332	−	0.00710309i
$583$	218.796	+	816.557i	0.375293	+	1.40061i
$584$			176.630i			0.302448i
$585$	−103.011	−	916.988i	−0.176088	−	1.56750i
$586$	29.2982			0.0499969
$587$	335.371	−	89.8623i	0.571330	−	0.153087i	0.0384234	−	0.999262i	$-0.487766\pi$
$587$	335.371	−	89.8623i	0.571330	−	0.153087i	0.532906	+	0.846174i	$0.321100\pi$
$588$	391.677	−	258.609i	0.666118	−	0.439810i
$589$	404.606	−	233.599i	0.686937	−	0.396603i
$590$	−91.8689	+	52.0600i	−0.155710	+	0.0882373i
$591$	60.8326	+	182.495i	0.102932	+	0.308791i
$592$	−424.369	+	113.709i	−0.716840	+	0.192077i
$593$	−235.628	+	235.628i	−0.397350	+	0.397350i	−0.877297	−	0.479948i	$-0.840656\pi$
$593$	−235.628	+	235.628i	−0.397350	+	0.397350i	0.479948	+	0.877297i	$0.340656\pi$
$594$	−235.434	−	19.3335i	−0.396354	−	0.0325480i
$595$	92.5167	+	94.0168i	0.155490	+	0.158011i
$596$	161.848	−	280.329i	0.271557	−	0.470351i
$597$	22.8188	−	45.6380i	0.0382224	−	0.0764455i
$598$	−20.7306	−	5.55474i	−0.0346665	−	0.00928887i
$599$	−513.829	+	296.659i	−0.857811	+	0.495258i	−0.863279	−	0.504727i	$-0.831593\pi$
$599$	−513.829	+	296.659i	−0.857811	+	0.495258i	0.00546746	+	0.999985i	$0.498260\pi$
$600$	409.049	+	90.5820i	0.681748	+	0.150970i
$601$	269.249	−	466.354i	0.448002	−	0.775963i	−0.550254	−	0.834998i	$-0.685469\pi$
$601$	269.249	−	466.354i	0.448002	−	0.775963i	0.998256	+	0.0590349i	$0.0188023\pi$
$602$	8.20024	+	8.20024i	0.0136217	+	0.0136217i
$603$	279.386	−	112.144i	0.463326	−	0.185977i
$604$			96.5233i			0.159807i
$605$	−18.3592	−	70.7899i	−0.0303458	−	0.117008i
$606$	−89.3962	+	100.814i	−0.147519	+	0.166360i
$607$	105.915	−	395.280i	0.174489	−	0.651203i	−0.822149	−	0.569273i	$-0.807225\pi$
$607$	105.915	−	395.280i	0.174489	−	0.651203i	0.996638	−	0.0819303i	$-0.0261085\pi$
$608$	307.999	+	82.5281i	0.506577	+	0.135737i
$609$	−100.295	−	88.9357i	−0.164687	−	0.146036i
$610$	156.531	−	266.154i	0.256609	−	0.436318i
$611$	−366.364			−0.599614
$612$	163.303	+	406.839i	0.266836	+	0.664769i
$613$	−10.5026	+	10.5026i	−0.0171331	+	0.0171331i	−0.715621	−	0.698488i	$-0.753856\pi$
$613$	−10.5026	+	10.5026i	−0.0171331	+	0.0171331i	0.698488	+	0.715621i	$0.253856\pi$
$614$	26.1641	+	15.1059i	0.0426126	+	0.0246024i
$615$	128.390	−	602.703i	0.208764	−	0.980005i
$616$	60.5232	+	104.829i	0.0982520	+	0.170177i
$617$	−113.048	+	421.900i	−0.183222	+	0.683793i	0.811782	+	0.583960i	$0.198498\pi$
$617$	−113.048	+	421.900i	−0.183222	+	0.683793i	−0.995004	+	0.0998331i	$0.968169\pi$
$618$	102.040	+	51.0196i	0.165114	+	0.0825560i
$619$	−8.91186	−	5.14527i	−0.0143972	−	0.00831222i	0.492784	−	0.870152i	$-0.335979\pi$
$619$	−8.91186	−	5.14527i	−0.0143972	−	0.00831222i	−0.507181	+	0.861839i	$0.669313\pi$
$620$	−521.060	−	529.509i	−0.840420	−	0.854047i
$621$	3.07855	−	37.4890i	0.00495740	−	0.0603688i
$622$	229.439	+	229.439i	0.368873	+	0.368873i
$623$	54.8585	+	204.735i	0.0880554	+	0.328627i
$624$	−557.091	+	185.699i	−0.892775	+	0.297595i
$625$	294.930	+	551.037i	0.471888	+	0.881659i
$626$	−77.9268	−	134.973i	−0.124484	−	0.215612i
$627$	−207.965	−	314.975i	−0.331682	−	0.502352i
$628$	34.3086	+	128.042i	0.0546316	+	0.203888i
$629$			652.537i			1.03742i
$630$	49.1671	+	39.2362i	0.0780430	+	0.0622796i
$631$	154.559			0.244943			0.122472	−	0.992472i	$-0.460918\pi$
$631$	154.559			0.244943			0.122472	+	0.992472i	$0.460918\pi$
$632$	−330.170	+	88.4689i	−0.522421	+	0.139982i
$633$	−53.5268	−	891.715i	−0.0845606	−	1.40871i
$634$	−231.032	+	133.386i	−0.364403	+	0.210388i
$635$	195.515	+	345.021i	0.307898	+	0.543340i
$636$	496.379	−	559.777i	0.780471	−	0.880153i
$637$	901.968	−	241.682i	1.41596	−	0.379406i
$638$	−148.565	+	148.565i	−0.232860	+	0.232860i
$639$	538.341	+	717.776i	0.842474	+	1.12328i
$640$	5.23092	−	650.430i	0.00817331	−	1.01630i
$641$	−302.816	+	524.493i	−0.472412	+	0.818242i	−0.999502	−	0.0315680i	$-0.989950\pi$
$641$	−302.816	+	524.493i	−0.472412	+	0.818242i	0.527089	+	0.849810i	$0.323283\pi$
$642$	26.0549	+	39.4616i	0.0405839	+	0.0614666i
$643$	450.687	+	120.761i	0.700912	+	0.187809i	0.591639	−	0.806203i	$-0.298481\pi$
$643$	450.687	+	120.761i	0.700912	+	0.187809i	0.109273	+	0.994012i	$0.465148\pi$
$644$	−7.71265	+	4.45290i	−0.0119762	+	0.00691444i
$645$	−56.5453	+	110.854i	−0.0876672	+	0.171867i
$646$	57.5346	−	99.6529i	0.0890629	−	0.154261i
$647$	−117.084	−	117.084i	−0.180965	−	0.180965i	0.610811	−	0.791776i	$-0.290843\pi$
$647$	−117.084	−	117.084i	−0.180965	−	0.180965i	−0.791776	+	0.610811i	$0.790843\pi$
$648$	217.571	+	396.732i	0.335757	+	0.612241i
$649$		−	327.378i		−	0.504434i
$650$	330.392	+	197.905i	0.508296	+	0.304469i
$651$	−76.3392	−	229.015i	−0.117265	−	0.351789i
$652$	−177.055	+	660.778i	−0.271557	+	1.01346i
$653$	322.638	+	86.4506i	0.494086	+	0.132390i	0.497254	−	0.867605i	$-0.334342\pi$
$653$	322.638	+	86.4506i	0.494086	+	0.132390i	−0.00316798	+	0.999995i	$0.501008\pi$
$654$	52.0918	−	254.565i	0.0796511	−	0.389242i
$655$	−5.81745	−	22.4310i	−0.00888160	−	0.0342459i
$656$	−392.156			−0.597799
$657$	−281.715	−	40.2428i	−0.428790	−	0.0612524i
$658$	17.6599	−	17.6599i	0.0268387	−	0.0268387i
$659$	−1062.27	−	613.303i	−1.61195	−	0.930657i	−0.988919	−	0.148457i	$-0.952569\pi$
$659$	−1062.27	−	613.303i	−1.61195	−	0.930657i	−0.623027	−	0.782200i	$-0.714097\pi$
$660$	−401.784	+	445.825i	−0.608763	+	0.675493i
$661$	79.8777	+	138.352i	0.120844	+	0.209307i	0.920101	−	0.391682i	$-0.128107\pi$
$661$	79.8777	+	138.352i	0.120844	+	0.209307i	−0.799257	+	0.600989i	$0.794773\pi$
$662$	72.8967	−	272.054i	0.110116	−	0.410958i
$663$	52.2607	+	870.622i	0.0788246	+	1.31316i
$664$	250.017	+	144.347i	0.376532	+	0.217391i
$665$	−0.808266	+	100.503i	−0.00121544	+	0.151132i
$666$	37.2254	+	308.956i	0.0558940	+	0.463897i
$667$	−23.6565	−	23.6565i	−0.0354670	−	0.0354670i
$668$	−251.566	−	938.856i	−0.376595	−	1.40547i
$669$	19.2257	−	93.9528i	0.0287379	−	0.140438i
$670$	−33.4957	+	121.103i	−0.0499935	+	0.180751i
$671$	478.648	+	829.042i	0.713335	+	1.23553i
$672$	73.6815	−	147.364i	0.109645	−	0.219292i
$673$	12.3181	+	45.9717i	0.0183032	+	0.0683086i	0.974473	−	0.224503i	$-0.0720758\pi$
$673$	12.3181	+	45.9717i	0.0183032	+	0.0683086i	−0.956170	+	0.292811i	$0.905409\pi$
$674$		−	111.675i		−	0.165690i
$675$	−237.670	+	631.774i	−0.352104	+	0.935961i
$676$	−863.996			−1.27810
$677$	−141.633	+	37.9504i	−0.209206	+	0.0560567i	−0.361900	−	0.932217i	$-0.617872\pi$
$677$	−141.633	+	37.9504i	−0.209206	+	0.0560567i	0.152694	+	0.988274i	$0.451205\pi$
$678$	−211.228	−	105.613i	−0.311545	−	0.155771i
$679$	49.3279	−	28.4795i	0.0726479	−	0.0419433i
$680$	−381.670	−	105.565i	−0.561279	−	0.155243i
$681$	1149.68	+	235.260i	1.68822	+	0.345462i
$682$	−365.477	+	97.9293i	−0.535890	+	0.143591i
$683$	882.608	−	882.608i	1.29225	−	1.29225i	0.358860	−	0.933391i	$-0.383165\pi$
$683$	882.608	−	882.608i	1.29225	−	1.29225i	0.933391	−	0.358860i	$-0.116835\pi$
$684$	−131.215	+	307.187i	−0.191834	+	0.449104i
$685$	11.8924	+	0.0956418i	0.0173612	+	0.000139623i
$686$	−66.0754	+	114.446i	−0.0963198	+	0.166831i
$687$	−751.148	+	45.0890i	−1.09337	+	0.0656318i
$688$	76.4948	+	20.4967i	0.111184	+	0.0297917i
$689$	1289.07	−	744.243i	1.87092	−	1.08018i
$690$	11.6623	+	10.5102i	0.0169018	+	0.0152322i
$691$	253.832	−	439.650i	0.367340	−	0.636252i	−0.621808	−	0.783169i	$-0.713602\pi$
$691$	253.832	−	439.650i	0.367340	−	0.636252i	0.989149	+	0.146917i	$0.0469351\pi$
$692$	753.047	+	753.047i	1.08822	+	1.08822i
$693$	−180.987	+	72.6473i	−0.261164	+	0.104830i
$694$		−	181.421i		−	0.261413i
$695$	1240.25	−	321.657i	1.78453	−	0.462815i
$696$	394.265	+	80.6788i	0.566473	+	0.115918i
$697$	−150.751	+	562.611i	−0.216286	+	0.807189i
$698$	−277.514	−	74.3597i	−0.397585	−	0.106532i
$699$	962.302	−	320.771i	1.37668	−	0.458900i
$700$	155.013	−	38.8746i	0.221447	−	0.0555352i
$701$	194.042			0.276807			0.138403	−	0.990376i	$-0.455803\pi$
$701$	194.042			0.276807			0.138403	+	0.990376i	$0.455803\pi$
$702$	74.4103	+	409.231i	0.105998	+	0.582950i
$703$	−351.581	+	351.581i	−0.500115	+	0.500115i
$704$	161.459	+	93.2182i	0.229345	+	0.132412i
$705$	238.733	+	121.775i	0.338628	+	0.172730i
$706$	−195.614	−	338.813i	−0.277073	−	0.479905i
$707$	−28.7907	+	107.448i	−0.0407223	+	0.151978i
$708$	−241.787	+	159.642i	−0.341506	+	0.225483i
$709$	414.499	+	239.311i	0.584625	+	0.337534i	0.762969	−	0.646435i	$-0.223741\pi$
$709$	414.499	+	239.311i	0.584625	+	0.337534i	−0.178344	+	0.983968i	$0.557074\pi$
$710$	−374.463	−	3.01152i	−0.527412	−	0.00424158i
$711$	−65.8781	−	546.761i	−0.0926555	−	0.769003i
$712$	−449.958	−	449.958i	−0.631963	−	0.631963i
$713$	−15.5936	−	58.1962i	−0.0218705	−	0.0816216i
$714$	−44.4858	−	39.4475i	−0.0623050	−	0.0552486i
$715$	−1038.83	+	588.681i	−1.45291	+	0.823331i
$716$	260.906	+	451.902i	0.364393	+	0.631148i
$717$	117.043	−	7.02575i	0.163240	−	0.00979881i
$718$	−63.5739	−	237.261i	−0.0885430	−	0.330447i
$719$		−	443.536i		−	0.616879i	−0.951244	−	0.308439i	$-0.900193\pi$
$719$		−	443.536i		−	0.616879i	0.951244	−	0.308439i	$-0.0998067\pi$
$720$	424.740	+	64.1634i	0.589916	+	0.0891159i
$721$	94.1849			0.130631
$722$	−177.274	+	47.5005i	−0.245532	+	0.0657902i
$723$	−209.558	+	138.363i	−0.289845	+	0.191373i
$724$	−143.106	+	82.6224i	−0.197660	+	0.114119i
$725$	291.774	+	524.680i	0.402448	+	0.723696i
$726$	10.4245	+	31.2732i	0.0143588	+	0.0430760i
$727$	−280.010	+	75.0285i	−0.385158	+	0.103203i	−0.446202	−	0.894932i	$-0.647224\pi$
$727$	−280.010	+	75.0285i	−0.385158	+	0.103203i	0.0610438	+	0.998135i	$0.480557\pi$
$728$	150.709	−	150.709i	0.207018	−	0.207018i
$729$	−682.338	+	256.623i	−0.935992	+	0.352021i
$730$	84.6578	−	83.3070i	0.115970	−	0.114119i
$731$	58.8116	−	101.865i	0.0804536	−	0.139350i
$732$	378.887	−	757.781i	0.517605	−	1.03522i
$733$	−987.435	−	264.583i	−1.34712	−	0.360958i	−0.488046	−	0.872818i	$-0.662290\pi$
$733$	−987.435	−	264.583i	−1.34712	−	0.360958i	−0.859069	+	0.511859i	$0.828957\pi$
$734$	340.177	−	196.401i	0.463457	−	0.267577i
$735$	−668.078	−	142.317i	−0.908950	−	0.193628i
$736$	20.5601	−	35.6111i	0.0279349	−	0.0483847i
$737$	−275.459	−	275.459i	−0.373757	−	0.373757i
$738$	−39.2805	+	274.978i	−0.0532256	+	0.372599i
$739$			153.917i			0.208277i	0.994563	+	0.104138i	$0.0332085\pi$
$739$			153.917i			0.208277i	−0.994563	+	0.104138i	$0.966791\pi$
$740$	681.488	+	400.799i	0.920929	+	0.541620i
$741$	−440.926	+	497.241i	−0.595042	+	0.671041i
$742$	−26.2622	+	98.0117i	−0.0353938	+	0.132091i
$743$	−1261.02	−	337.889i	−1.69720	−	0.454763i	−0.724966	−	0.688784i	$-0.758145\pi$
$743$	−1261.02	−	337.889i	−1.69720	−	0.454763i	−0.972231	+	0.234021i	$0.924811\pi$
$744$	542.254	+	480.841i	0.728836	+	0.646291i
$745$	−456.005	+	118.264i	−0.612087	+	0.158744i
$746$	18.2489			0.0244623
$747$	−287.190	+	365.877i	−0.384458	+	0.489795i
$748$	401.121	−	401.121i	0.536258	−	0.536258i
$749$	33.8088	+	19.5195i	0.0451385	+	0.0260607i
$750$	−149.511	−	238.778i	−0.199349	−	0.318371i
$751$	−728.908	−	1262.51i	−0.970583	−	1.68110i	−0.693801	−	0.720167i	$-0.744065\pi$
$751$	−728.908	−	1262.51i	−0.970583	−	1.68110i	−0.276783	−	0.960933i	$-0.589268\pi$
$752$	44.1413	−	164.737i	0.0586985	−	0.219066i
$753$	−313.070	−	156.533i	−0.415763	−	0.207880i
$754$	320.379	+	184.971i	0.424905	+	0.245319i
$755$	100.127	−	98.5289i	0.132618	−	0.130502i
$756$	141.910	+	98.2432i	0.187712	+	0.129951i
$757$	−575.216	−	575.216i	−0.759863	−	0.759863i	0.216434	−	0.976297i	$-0.430557\pi$
$757$	−575.216	−	575.216i	−0.759863	−	0.759863i	−0.976297	+	0.216434i	$0.930557\pi$
$758$	−70.9594	−	264.824i	−0.0936140	−	0.349372i
$759$	−46.1758	+	15.3921i	−0.0608376	+	0.0202795i
$760$	−148.763	−	262.518i	−0.195740	−	0.345418i
$761$	−506.722	−	877.668i	−0.665863	−	1.15331i	−0.979051	−	0.203618i	$-0.934730\pi$
$761$	−506.722	−	877.668i	−0.665863	−	1.15331i	0.313187	−	0.949691i	$-0.398603\pi$
$762$	−98.4935	−	149.174i	−0.129257	−	0.195766i
$763$	−55.5211	−	207.207i	−0.0727668	−	0.271569i
$764$		−	1248.49i		−	1.63414i
$765$	255.329	−	584.692i	0.333764	−	0.764303i
$766$	−2.52556			−0.00329708
$767$	−556.794	+	149.193i	−0.725938	+	0.194515i
$768$	6.05728	+	100.910i	0.00788709	+	0.131393i
$769$	−486.081	+	280.639i	−0.632095	+	0.364940i	−0.781563	−	0.623827i	$-0.785577\pi$
$769$	−486.081	+	280.639i	−0.632095	+	0.364940i	0.149468	+	0.988767i	$0.452244\pi$
$770$	21.6986	−	78.4511i	0.0281800	−	0.101884i
$771$	−9.52393	+	10.7403i	−0.0123527	+	0.0139304i
$772$	−39.7180	+	10.6424i	−0.0514482	+	0.0137855i
$773$	445.834	−	445.834i	0.576758	−	0.576758i	−0.357251	−	0.934008i	$-0.616286\pi$
$773$	445.834	−	445.834i	0.576758	−	0.576758i	0.934008	+	0.357251i	$0.116286\pi$
$774$	22.0343	−	51.5847i	0.0284681	−	0.0666469i
$775$	−17.3888	+	1081.02i	−0.0224372	+	1.39487i
$776$	−85.5009	+	148.092i	−0.110182	+	0.190840i
$777$	141.556	+	214.394i	0.182183	+	0.275926i
$778$	−110.446	−	29.5938i	−0.141961	−	0.0380383i
$779$	−384.353	+	221.906i	−0.493393	+	0.284860i
$780$	941.348	+	480.171i	1.20686	+	0.615604i
$781$	580.499	−	1005.45i	0.743276	−	1.28739i
$782$	−10.4929	−	10.4929i	−0.0134180	−	0.0134180i
$783$	−218.507	+	610.451i	−0.279064	+	0.779630i
$784$			434.693i			0.554456i
$785$	97.7999	−	166.291i	0.124586	−	0.211836i
$786$	3.30320	+	9.90946i	0.00420254	+	0.0126075i
$787$	−362.598	+	1353.23i	−0.460734	+	1.71948i	0.209925	+	0.977717i	$0.432678\pi$
$787$	−362.598	+	1353.23i	−0.460734	+	1.71948i	−0.670659	+	0.741766i	$0.733989\pi$
$788$	−212.793	−	57.0176i	−0.270041	−	0.0723573i
$789$	58.8245	−	287.466i	0.0745558	−	0.364343i
$790$	198.127	+	116.523i	0.250794	+	0.147498i
$791$	−194.967			−0.246482
$792$	361.511	−	460.560i	0.456453	−	0.581515i
$793$	1191.88	−	1191.88i	1.50300	−	1.50300i
$794$	253.828	+	146.548i	0.319683	+	0.184569i
$795$	−1087.37	+	56.4991i	−1.36776	+	0.0710680i
$796$	29.2167	+	50.6049i	0.0367045	+	0.0635740i
$797$	−122.829	+	458.403i	−0.154114	+	0.575160i	0.845066	+	0.534662i	$0.179561\pi$
$797$	−122.829	+	458.403i	−0.154114	+	0.575160i	−0.999180	+	0.0404981i	$0.987106\pi$
$798$	−2.71456	−	45.2225i	−0.00340171	−	0.0566698i
$799$	−219.374	−	126.655i	−0.274560	−	0.158517i
$800$	−530.095	+	513.312i	−0.662619	+	0.641640i
$801$	820.177	−	615.142i	1.02394	−	0.767968i
$802$	358.565	+	358.565i	0.447088	+	0.447088i
$803$	95.3064	+	355.688i	0.118688	+	0.442949i
$804$	−69.1175	+	337.766i	−0.0859670	+	0.420107i
$805$	12.4920	+	3.45514i	0.0155181	+	0.00429210i
$806$	333.111	+	576.965i	0.413289	+	0.715837i
$807$	285.594	−	571.193i	0.353895	−	0.707798i
$808$	−86.4352	−	322.581i	−0.106974	−	0.399234i
$809$			806.321i			0.996689i	0.866979	+	0.498344i	$0.166059\pi$
$809$			806.321i			0.996689i	−0.866979	+	0.498344i	$0.833941\pi$
$810$	87.5354	−	291.399i	0.108068	−	0.359751i
$811$	−928.637			−1.14505			−0.572526	−	0.819887i	$-0.694036\pi$
$811$	−928.637			−1.14505			−0.572526	+	0.819887i	$0.694036\pi$
$812$	148.280	−	39.7315i	0.182611	−	0.0489304i
$813$	−483.642	−	241.819i	−0.594886	−	0.297440i
$814$	348.727	−	201.338i	0.428412	−	0.247344i
$815$	866.179	−	490.843i	1.06280	−	0.602262i
$816$	−397.776	−	81.3974i	−0.487471	−	0.0997517i
$817$	86.5709	−	23.1966i	0.105962	−	0.0283924i
$818$	230.158	−	230.158i	0.281366	−	0.281366i
$819$	206.036	+	274.710i	0.251570	+	0.335422i
$820$	494.978	+	503.004i	0.603632	+	0.613419i
$821$	−259.589	+	449.622i	−0.316187	+	0.547652i	−0.979689	−	0.200523i	$-0.935736\pi$
$821$	−259.589	+	449.622i	−0.316187	+	0.547652i	0.663502	+	0.748174i	$0.269069\pi$
$822$	−5.35116	+	0.321213i	−0.00650993	+	0.000390770i
$823$	1245.48	+	333.724i	1.51334	+	0.405497i	0.917542	−	0.397639i	$-0.130170\pi$
$823$	1245.48	+	333.724i	1.51334	+	0.405497i	0.595795	+	0.803136i	$0.296837\pi$
$824$	−244.879	+	141.381i	−0.297183	+	0.171579i
$825$	872.600	−	38.3062i	1.05770	−	0.0464318i
$826$	19.6477	−	34.0307i	0.0237865	−	0.0411994i
$827$	−380.149	−	380.149i	−0.459672	−	0.459672i	0.438876	−	0.898548i	$-0.355377\pi$
$827$	−380.149	−	380.149i	−0.459672	−	0.459672i	−0.898548	+	0.438876i	$0.855377\pi$
$828$	33.8850	+	26.5976i	0.0409239	+	0.0321227i
$829$		−	511.167i		−	0.616606i	−0.951288	−	0.308303i	$-0.900239\pi$
$829$		−	511.167i		−	0.616606i	0.951288	−	0.308303i	$-0.0997611\pi$
$830$	−48.7350	−	187.913i	−0.0587168	−	0.226402i
$831$	961.890	+	196.833i	1.15751	+	0.236862i
$832$	84.9628	−	317.086i	0.102119	−	0.381113i
$833$	623.637	+	167.103i	0.748664	+	0.200604i
$834$	−547.911	+	182.639i	−0.656968	+	0.218992i
$835$	−717.111	+	1219.32i	−0.858815	+	1.46026i
$836$	432.240			0.517034
$837$	−890.462	+	755.313i	−1.06387	+	0.902405i
$838$	−265.524	+	265.524i	−0.316855	+	0.316855i
$839$	−889.044	−	513.290i	−1.05965	−	0.611788i	−0.134313	−	0.990939i	$-0.542883\pi$
$839$	−889.044	−	513.290i	−1.05965	−	0.611788i	−0.925335	+	0.379151i	$0.876216\pi$
$840$	−148.300	+	48.1122i	−0.176547	+	0.0572765i
$841$	−132.163	−	228.913i	−0.157150	−	0.272192i
$842$	−5.84978	+	21.8317i	−0.00694749	+	0.0259284i
$843$	−78.2882	+	51.6905i	−0.0928686	+	0.0613173i
$844$	885.970	+	511.515i	1.04973	+	0.606061i
$845$	881.948	+	896.249i	1.04373	+	1.06065i
$846$	−111.092	−	47.4527i	−0.131314	−	0.0560906i
$847$	19.2439	+	19.2439i	0.0227200	+	0.0227200i
$848$	179.340	+	669.305i	0.211486	+	0.789275i
$849$	455.061	+	403.523i	0.535996	+	0.475292i
$850$	129.417	+	232.722i	0.152255	+	0.273791i
$851$	32.0597	+	55.5291i	0.0376730	+	0.0652516i
$852$	−1025.66	+	61.5669i	−1.20382	+	0.0722616i
$853$	360.478	+	1345.32i	0.422600	+	1.57717i	0.769108	+	0.639119i	$0.220701\pi$
$853$	360.478	+	1345.32i	0.422600	+	1.57717i	−0.346508	+	0.938047i	$0.612633\pi$
$854$			114.905i			0.134549i
$855$	452.596	−	177.457i	0.529352	−	0.207552i
$856$	−117.203			−0.136919
$857$	319.058	−	85.4914i	0.372297	−	0.0997566i	−0.0678191	−	0.997698i	$-0.521604\pi$
$857$	319.058	−	85.4914i	0.372297	−	0.0997566i	0.440116	+	0.897941i	$0.354937\pi$
$858$	449.151	−	296.556i	0.523486	−	0.345637i
$859$	264.795	−	152.879i	0.308259	−	0.177974i	−0.337888	−	0.941186i	$-0.609713\pi$
$859$	264.795	−	152.879i	0.308259	−	0.177974i	0.646147	+	0.763213i	$0.276379\pi$
$860$	−70.2610	−	123.988i	−0.0816988	−	0.144172i
$861$	72.5180	+	217.551i	0.0842253	+	0.252673i
$862$	−374.262	+	100.283i	−0.434178	+	0.116338i
$863$	386.017	−	386.017i	0.447297	−	0.447297i	−0.447158	−	0.894455i	$-0.647564\pi$
$863$	386.017	−	386.017i	0.447297	−	0.447297i	0.894455	+	0.447158i	$0.147564\pi$
$864$	−794.254	−	65.2230i	−0.919275	−	0.0754895i
$865$	12.4643	−	1549.85i	0.0144096	−	1.79174i
$866$	162.447	−	281.367i	0.187583	−	0.324904i
$867$	118.042	−	236.086i	0.136150	−	0.272303i
$868$	267.035	+	71.5518i	0.307644	+	0.0824329i
$869$	−617.145	+	356.309i	−0.710179	+	0.410022i
$870$	−147.285	−	227.022i	−0.169293	−	0.260944i
$871$	−342.961	+	594.025i	−0.393755	+	0.682004i
$872$	455.392	+	455.392i	0.522238	+	0.522238i
$873$	−216.719	−	170.111i	−0.248246	−	0.194857i
$874$		−	11.3069i		−	0.0129370i
$875$	−198.560	−	121.117i	−0.226926	−	0.138420i
$876$	216.221	−	243.836i	0.246827	−	0.278352i
$877$	108.142	−	403.592i	0.123309	−	0.460196i	−0.876465	−	0.481466i	$-0.840104\pi$
$877$	108.142	−	403.592i	0.123309	−	0.460196i	0.999774	+	0.0212701i	$0.00677100\pi$
$878$	366.669	+	98.2488i	0.417619	+	0.111901i
$879$	−87.5366	−	77.6226i	−0.0995865	−	0.0883078i
$880$	−139.540	−	538.043i	−0.158569	−	0.611412i
$881$	−1495.93			−1.69799			−0.848993	−	0.528403i	$-0.822791\pi$
$881$	−1495.93			−1.69799			−0.848993	+	0.528403i	$0.822791\pi$
$882$	304.805	+	43.5413i	0.345584	+	0.0493665i
$883$	−158.383	+	158.383i	−0.179369	+	0.179369i	−0.791081	−	0.611712i	$-0.790481\pi$
$883$	−158.383	+	158.383i	−0.179369	+	0.179369i	0.611712	+	0.791081i	$0.290481\pi$
$884$	−865.014	−	499.416i	−0.978522	−	0.564950i
$885$	412.412	+	87.8536i	0.466002	+	0.0992696i
$886$	75.9157	+	131.490i	0.0856837	+	0.148408i
$887$	355.206	−	1325.65i	0.400458	−	1.49453i	−0.411823	−	0.911264i	$-0.635108\pi$
$887$	355.206	−	1325.65i	0.400458	−	1.49453i	0.812281	−	0.583266i	$-0.198225\pi$
$888$	−689.869	−	344.931i	−0.776879	−	0.388436i
$889$	−127.805	−	73.7883i	−0.143763	−	0.0830014i
$890$	−3.44115	+	427.885i	−0.00386647	+	0.480769i
$891$	652.204	+	681.524i	0.731991	+	0.764898i
$892$	77.6576	+	77.6576i	0.0870601	+	0.0870601i
$893$	−49.9557	−	186.437i	−0.0559415	−	0.208776i
$894$	201.451	−	67.1513i	0.225337	−	0.0751133i
$895$	202.445	−	731.937i	0.226195	−	0.817807i
$896$	121.028	+	209.626i	0.135076	+	0.233958i
$897$	47.2217	+	71.5199i	0.0526440	+	0.0797324i
$898$	28.2113	+	105.286i	0.0314157	+	0.117245i
$899$			1038.52i			1.15520i
$900$	−453.805	−	625.784i	−0.504227	−	0.695316i
$901$	1029.17			1.14225
$902$	347.183	−	93.0274i	0.384903	−	0.103135i
$903$	−2.77482	−	46.2262i	−0.00307288	−	0.0511918i
$904$	506.909	−	292.664i	0.560741	−	0.323744i
$905$	231.786	+	64.1092i	0.256118	+	0.0708389i
$906$	−42.0111	+	47.3767i	−0.0463698	+	0.0522922i
$907$	535.743	−	143.552i	0.590676	−	0.158271i	0.0489140	−	0.998803i	$-0.484424\pi$
$907$	535.743	−	143.552i	0.590676	−	0.158271i	0.541762	+	0.840532i	$0.317757\pi$
$908$	−950.276	+	950.276i	−1.04656	+	1.04656i
$909$	534.193	−	64.3637i	0.587671	−	0.0708072i
$910$	−143.316	−	1.15258i	−0.157490	−	0.00126657i
$911$	−484.409	+	839.021i	−0.531733	+	0.920989i	0.467581	+	0.883950i	$0.345126\pi$
$911$	−484.409	+	839.021i	−0.531733	+	0.920989i	−0.999314	+	0.0370382i	$0.988208\pi$
$912$	−170.462	−	258.175i	−0.186910	−	0.283086i
$913$	581.361	+	155.775i	0.636759	+	0.170619i
$914$	192.995	−	111.426i	0.211154	−	0.121910i
$915$	−1172.83	+	380.496i	−1.28178	+	0.415842i
$916$	430.882	−	746.309i	0.470395	−	0.814748i
$917$	6.09776	+	6.09776i	0.00664968	+	0.00664968i
$918$	−96.9190	+	270.766i	−0.105576	+	0.294952i
$919$		−	600.903i		−	0.653866i	−0.945048	−	0.326933i	$-0.893985\pi$
$919$		−	600.903i		−	0.653866i	0.945048	−	0.326933i	$-0.106015\pi$
$920$	−37.6655	+	9.76848i	−0.0409408	+	0.0106179i
$921$	−38.1512	−	114.452i	−0.0414237	−	0.124270i
$922$	−55.6275	+	207.604i	−0.0603335	+	0.225168i
$923$	−1974.59	−	529.090i	−2.13932	−	0.573229i
$924$	44.7745	−	218.806i	0.0484572	−	0.236803i
$925$	−279.887	−	1116.05i	−0.302581	−	1.20655i
$926$	187.992			0.203015
$927$	−169.702	−	422.780i	−0.183066	−	0.456074i
$928$	−501.193	+	501.193i	−0.540079	+	0.540079i
$929$	435.996	+	251.722i	0.469318	+	0.270961i	0.715954	−	0.698147i	$-0.245992\pi$
$929$	435.996	+	251.722i	0.469318	+	0.270961i	−0.246636	+	0.969108i	$0.579325\pi$
$930$	−25.2880	−	486.688i	−0.0271914	−	0.523320i
$931$	245.976	+	426.044i	0.264207	+	0.457619i
$932$	−300.655	+	1122.06i	−0.322591	+	1.20393i
$933$	−77.6380	−	1293.39i	−0.0832133	−	1.38627i
$934$	65.6305	+	37.8918i	0.0702682	+	0.0405694i
$935$	−825.550	−	6.63928i	−0.882941	−	0.00710083i
$936$	−948.056	−	404.960i	−1.01288	−	0.432650i
$937$	1181.10	+	1181.10i	1.26051	+	1.26051i	0.950847	+	0.309660i	$0.100215\pi$
$937$	1181.10	+	1181.10i	1.26051	+	1.26051i	0.309660	+	0.950847i	$0.399785\pi$
$938$	−12.1021	−	45.1656i	−0.0129020	−	0.0481509i
$939$	−124.770	+	609.730i	−0.132875	+	0.649339i
$940$	−267.017	+	151.313i	−0.284061	+	0.160971i
$941$	−576.616	−	998.729i	−0.612770	−	1.06135i	−0.990771	−	0.135543i	$-0.956722\pi$
$941$	−576.616	−	998.729i	−0.612770	−	1.06135i	0.378002	−	0.925805i	$-0.376611\pi$
$942$	−38.8894	+	77.7795i	−0.0412838	+	0.0825684i
$943$	14.8131	+	55.2832i	0.0157085	+	0.0586248i
$944$		−	268.341i		−	0.284259i
$945$	−42.9483	−	247.492i	−0.0454479	−	0.261897i
$946$	−72.5844			−0.0767277
$947$	1323.45	−	354.616i	1.39751	−	0.374463i	0.520063	−	0.854128i	$-0.325909\pi$
$947$	1323.45	−	354.616i	1.39751	−	0.374463i	0.877451	+	0.479665i	$0.159242\pi$
$948$	564.098	+	282.046i	0.595040	+	0.297517i
$949$	561.512	−	324.189i	0.591688	−	0.341611i
$950$	−55.6600	+	195.117i	−0.0585894	+	0.205387i
$951$	1043.67	+	213.566i	1.09744	+	0.224570i
$952$	142.344	−	38.1409i	0.149521	−	0.0400640i
$953$	77.4456	−	77.4456i	0.0812650	−	0.0812650i	−0.665306	−	0.746571i	$-0.731699\pi$
$953$	77.4456	−	77.4456i	0.0812650	−	0.0812650i	0.746571	+	0.665306i	$0.231699\pi$
$954$	487.278	−	58.7110i	0.510773	−	0.0615420i
$955$	−1295.09	+	1274.43i	−1.35612	+	1.33448i
$956$	−67.1397	+	116.289i	−0.0702298	+	0.121642i
$957$	837.486	−	50.2716i	0.875116	−	0.0525304i
$958$	142.282	+	38.1245i	0.148520	+	0.0397959i
$959$	−3.83279	+	2.21286i	−0.00399666	+	0.00230747i
$960$	−160.759	+	178.381i	−0.167458	+	0.185813i
$961$	−454.630	+	787.443i	−0.473080	+	0.819399i
$962$	−501.352	−	501.352i	−0.521156	−	0.521156i
$963$	26.7032	−	186.932i	0.0277292	−	0.194114i
$964$		−	287.577i		−	0.298316i
$965$	51.5830	+	30.3372i	0.0534539	+	0.0314375i
$966$	−5.72371	−	1.17125i	−0.00592517	−	0.00121247i
$967$	417.733	−	1559.00i	0.431989	−	1.61220i	−0.316183	−	0.948698i	$-0.602401\pi$
$967$	417.733	−	1559.00i	0.431989	−	1.61220i	0.748172	−	0.663505i	$-0.230932\pi$
$968$	−78.9205	−	21.1467i	−0.0815295	−	0.0218458i
$969$	−435.921	+	145.309i	−0.449867	+	0.149958i
$970$	111.306	−	28.8671i	0.114749	−	0.0297599i
$971$	158.612			0.163349			0.0816745	−	0.996659i	$-0.473973\pi$
$971$	158.612			0.163349			0.0816745	+	0.996659i	$0.473973\pi$
$972$	185.304	−	814.026i	0.190642	−	0.837475i
$973$	−337.156	+	337.156i	−0.346511	+	0.346511i
$974$	−607.386	−	350.674i	−0.623599	−	0.360035i
$975$	−462.812	−	1466.64i	−0.474679	−	1.50424i
$976$	392.332	+	679.539i	0.401980	+	0.696249i
$977$	2.86555	−	10.6944i	0.00293301	−	0.0109461i	−0.964444	−	0.264288i	$-0.914863\pi$
$977$	2.86555	−	10.6944i	0.00293301	−	0.0109461i	0.967377	+	0.253342i	$0.0815297\pi$
$978$	−374.503	+	247.269i	−0.382927	+	0.252831i
$979$	−1148.89	−	663.315i	−1.17354	−	0.677543i
$980$	557.565	−	548.668i	0.568944	−	0.559865i
$981$	−830.082	+	622.571i	−0.846159	+	0.634629i
$982$	−418.604	−	418.604i	−0.426277	−	0.426277i
$983$	295.182	+	1101.63i	0.300287	+	1.12069i	0.936927	+	0.349525i	$0.113657\pi$
$983$	295.182	+	1101.63i	0.300287	+	1.12069i	−0.636640	+	0.771161i	$0.719676\pi$
$984$	−515.111	−	456.772i	−0.523486	−	0.464199i
$985$	158.068	+	278.938i	0.160475	+	0.283186i
$986$	127.892	+	221.516i	0.129708	+	0.224661i
$987$	−99.5518	+	5.97578i	−0.100863	+	0.00605449i
$988$	−196.981	−	735.142i	−0.199373	−	0.744071i
$989$		−	11.5579i		−	0.0116864i
$990$	−391.250	+	43.9518i	−0.395202	+	0.0443957i
$991$	−95.8581			−0.0967287			−0.0483643	−	0.998830i	$-0.515401\pi$
$991$	−95.8581			−0.0967287			−0.0483643	+	0.998830i	$0.515401\pi$
$992$	−1232.96	+	330.371i	−1.24291	+	0.333036i
$993$	−938.579	+	619.706i	−0.945195	+	0.624074i
$994$	120.685	−	69.6776i	0.121414	−	0.0700982i
$995$	22.6702	−	81.9638i	0.0227841	−	0.0823757i
$996$	−168.445	−	505.329i	−0.169122	−	0.507359i
$997$	−850.093	+	227.782i	−0.852651	+	0.228467i	−0.658571	−	0.752518i	$-0.728839\pi$
$997$	−850.093	+	227.782i	−0.852651	+	0.228467i	−0.194080	+	0.980986i	$0.562172\pi$
$998$	−88.7943	+	88.7943i	−0.0889723	+	0.0889723i
$999$	707.325	−	1021.72i	0.708033	−	1.02274i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.3.k.a.7.5	✓	40
3.2	odd	2		135.3.l.a.127.6		40
5.2	odd	4		225.3.o.b.43.5		40
5.3	odd	4	inner	45.3.k.a.43.6	yes	40
5.4	even	2		225.3.o.b.7.6		40
9.2	odd	6		405.3.g.g.82.5		20
9.4	even	3	inner	45.3.k.a.22.6	yes	40
9.5	odd	6		135.3.l.a.37.5		40
9.7	even	3		405.3.g.h.82.6		20
15.8	even	4		135.3.l.a.73.5		40
45.4	even	6		225.3.o.b.157.5		40
45.13	odd	12	inner	45.3.k.a.13.5	yes	40
45.22	odd	12		225.3.o.b.193.6		40
45.23	even	12		135.3.l.a.118.6		40
45.38	even	12		405.3.g.g.163.5		20
45.43	odd	12		405.3.g.h.163.6		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.3.k.a.7.5	✓	40	1.1	even	1	trivial
45.3.k.a.13.5	yes	40	45.13	odd	12	inner
45.3.k.a.22.6	yes	40	9.4	even	3	inner
45.3.k.a.43.6	yes	40	5.3	odd	4	inner
135.3.l.a.37.5		40	9.5	odd	6
135.3.l.a.73.5		40	15.8	even	4
135.3.l.a.118.6		40	45.23	even	12
135.3.l.a.127.6		40	3.2	odd	2
225.3.o.b.7.6		40	5.4	even	2
225.3.o.b.43.5		40	5.2	odd	4
225.3.o.b.157.5		40	45.4	even	6
225.3.o.b.193.6		40	45.22	odd	12
405.3.g.g.82.5		20	9.2	odd	6
405.3.g.g.163.5		20	45.38	even	12
405.3.g.h.82.6		20	9.7	even	3
405.3.g.h.163.6		20	45.43	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+(-0.725667 + 0.194442i) q^{2} +(2.68329 + 1.34163i) q^{3} +(-2.97532 + 1.71780i) q^{4} +(4.81907 + 1.33289i) q^{5} +(-2.20804 - 0.451834i) q^{6} +(-1.79727 + 0.481578i) q^{7} +(3.94998 - 3.94998i) q^{8} +(5.40005 + 7.19996i) q^{9} +(-3.75621 - 0.0302083i) q^{10} +(5.82294 - 10.0856i) q^{11} +(-10.2883 + 0.617573i) q^{12} +(-19.8070 - 5.30726i) q^{13} +(1.21058 - 0.698930i) q^{14} +(11.1427 + 10.0419i) q^{15} +(4.77288 - 8.26686i) q^{16} +(-10.0254 - 10.0254i) q^{17} +(-5.31861 - 4.17477i) q^{18} -10.8032i q^{19} +(-16.6279 + 4.31241i) q^{20} +(-5.46870 - 1.11907i) q^{21} +(-2.26444 + 8.45102i) q^{22} +(-1.34569 - 0.360576i) q^{23} +(15.8983 - 5.29951i) q^{24} +(21.4468 + 12.8466i) q^{25} +15.4052 q^{26} +(4.83020 + 26.5644i) q^{27} +(4.52021 - 4.52021i) q^{28} +(20.7968 + 12.0070i) q^{29} +(-10.0384 - 5.12050i) q^{30} +(21.6233 + 37.4526i) q^{31} +(-7.63926 + 28.5101i) q^{32} +(29.1558 - 19.2504i) q^{33} +(9.22442 + 5.32572i) q^{34} +(-9.30307 - 0.0748176i) q^{35} +(-28.4350 - 12.1460i) q^{36} +(-32.5443 - 32.5443i) q^{37} +(2.10058 + 7.83949i) q^{38} +(-46.0274 - 40.8145i) q^{39} +(24.3001 - 13.7703i) q^{40} +(-20.5409 - 35.5778i) q^{41} +(4.18605 - 0.251275i) q^{42} +(2.14721 + 8.01349i) q^{43} +40.0106i q^{44} +(16.4264 + 41.8948i) q^{45} +1.04663 q^{46} +(17.2577 - 4.62418i) q^{47} +(23.8981 - 15.7789i) q^{48} +(-39.4370 + 22.7689i) q^{49} +(-18.0611 - 5.15220i) q^{50} +(-13.4506 - 40.3513i) q^{51} +(68.0488 - 18.2336i) q^{52} +(-51.3281 + 51.3281i) q^{53} +(-8.67035 - 18.3377i) q^{54} +(41.5042 - 40.8419i) q^{55} +(-5.19697 + 9.00141i) q^{56} +(14.4938 - 28.9880i) q^{57} +(-17.4262 - 4.66933i) q^{58} +(24.3449 - 14.0555i) q^{59} +(-50.4031 - 10.7371i) q^{60} +(-41.1002 + 71.1876i) q^{61} +(-22.9736 - 22.9736i) q^{62} +(-13.1727 - 10.3398i) q^{63} +16.0088i q^{64} +(-88.3771 - 51.9766i) q^{65} +(-17.4143 + 19.6385i) q^{66} +(8.65757 - 32.3105i) q^{67} +(47.0502 + 12.6071i) q^{68} +(-3.12710 - 2.77294i) q^{69} +(6.76548 - 1.75461i) q^{70} +99.6917 q^{71} +(49.7697 + 7.10958i) q^{72} +(-22.3583 + 22.3583i) q^{73} +(29.9443 + 17.2883i) q^{74} +(40.3125 + 63.2448i) q^{75} +(18.5577 + 32.1428i) q^{76} +(-5.60840 + 20.9308i) q^{77} +(41.3366 + 20.6681i) q^{78} +(-52.9926 - 30.5953i) q^{79} +(34.0196 - 33.4768i) q^{80} +(-22.6788 + 77.7603i) q^{81} +(21.8237 + 21.8237i) q^{82} +(13.3760 + 49.9199i) q^{83} +(18.1935 - 6.06456i) q^{84} +(-34.9502 - 61.6757i) q^{85} +(-3.11631 - 5.39761i) q^{86} +(39.6947 + 60.1198i) q^{87} +(-16.8375 - 62.8384i) q^{88} -113.914i q^{89} +(-20.0662 - 27.2077i) q^{90} +38.1544 q^{91} +(4.62324 - 1.23879i) q^{92} +(7.77386 + 129.506i) q^{93} +(-11.6242 + 6.71123i) q^{94} +(14.3995 - 52.0611i) q^{95} +(-58.7483 + 66.2517i) q^{96} +(-29.5689 + 7.92297i) q^{97} +(24.1909 - 24.1909i) q^{98} +(104.060 - 12.5380i) 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

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