LMFDB - Embedded newform 225.3.o.b.157.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [225,3,Mod(7,225)] 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("225.7"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(225, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([8, 3])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	225.o (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [40] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$6.13080594811$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			157.5
Character	$\chi$	$=$	225.157
Dual form			225.3.o.b.43.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.194442 + 0.725667i) q^{2} +(1.34163 + 2.68329i) q^{3} +(2.97532 + 1.71780i) q^{4} +(-2.20804 + 0.451834i) q^{6} +(-0.481578 + 1.79727i) q^{7} +(-3.94998 + 3.94998i) q^{8} +(-5.40005 + 7.19996i) q^{9} +(5.82294 + 10.0856i) q^{11} +(-0.617573 + 10.2883i) q^{12} +(-5.30726 - 19.8070i) q^{13} +(-1.21058 - 0.698930i) q^{14} +(4.77288 + 8.26686i) q^{16} +(10.0254 + 10.0254i) q^{17} +(-4.17477 - 5.31861i) q^{18} -10.8032i q^{19} +(-5.46870 + 1.11907i) q^{21} +(-8.45102 + 2.26444i) q^{22} +(-0.360576 - 1.34569i) q^{23} +(-15.8983 - 5.29951i) q^{24} +15.4052 q^{26} +(-26.5644 - 4.83020i) q^{27} +(-4.52021 + 4.52021i) q^{28} +(-20.7968 + 12.0070i) q^{29} +(21.6233 - 37.4526i) q^{31} +(-28.5101 + 7.63926i) q^{32} +(-19.2504 + 29.1558i) q^{33} +(-9.22442 + 5.32572i) q^{34} +(-28.4350 + 12.1460i) q^{36} +(32.5443 + 32.5443i) q^{37} +(7.83949 + 2.10058i) q^{38} +(46.0274 - 40.8145i) q^{39} +(-20.5409 + 35.5778i) q^{41} +(0.251275 - 4.18605i) q^{42} +(8.01349 + 2.14721i) q^{43} +40.0106i q^{44} +1.04663 q^{46} +(4.62418 - 17.2577i) q^{47} +(-15.7789 + 23.8981i) q^{48} +(39.4370 + 22.7689i) q^{49} +(-13.4506 + 40.3513i) q^{51} +(18.2336 - 68.0488i) q^{52} +(51.3281 - 51.3281i) q^{53} +(8.67035 - 18.3377i) q^{54} +(-5.19697 - 9.00141i) q^{56} +(28.9880 - 14.4938i) q^{57} +(-4.66933 - 17.4262i) q^{58} +(-24.3449 - 14.0555i) q^{59} +(-41.1002 - 71.1876i) q^{61} +(22.9736 + 22.9736i) q^{62} +(-10.3398 - 13.1727i) q^{63} +16.0088i q^{64} +(-17.4143 - 19.6385i) q^{66} +(32.3105 - 8.65757i) q^{67} +(12.6071 + 47.0502i) q^{68} +(3.12710 - 2.77294i) q^{69} +99.6917 q^{71} +(-7.10958 - 49.7697i) q^{72} +(22.3583 - 22.3583i) q^{73} +(-29.9443 + 17.2883i) q^{74} +(18.5577 - 32.1428i) q^{76} +(-20.9308 + 5.60840i) q^{77} +(20.6681 + 41.3366i) q^{78} +(52.9926 - 30.5953i) q^{79} +(-22.6788 - 77.7603i) q^{81} +(-21.8237 - 21.8237i) q^{82} +(49.9199 + 13.3760i) q^{83} +(-18.1935 - 6.06456i) q^{84} +(-3.11631 + 5.39761i) q^{86} +(-60.1198 - 39.6947i) q^{87} +(-62.8384 - 16.8375i) q^{88} -113.914i q^{89} +38.1544 q^{91} +(1.23879 - 4.62324i) q^{92} +(129.506 + 7.77386i) q^{93} +(11.6242 + 6.71123i) q^{94} +(-58.7483 - 66.2517i) q^{96} +(-7.92297 + 29.5689i) 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} - 24 q^{6} + 2 q^{7} + 24 q^{8} + 8 q^{11} + 30 q^{12} + 2 q^{13} + 28 q^{16} - 28 q^{17} - 48 q^{18} + 12 q^{21} - 14 q^{22} - 82 q^{23} - 112 q^{26} + 198 q^{27} + 88 q^{28} - 4 q^{31}+ \cdots + 1876 q^{98}+O(q^{100}) $ 40 * q + 2 * q^2 + 6 * q^3 - 24 * q^6 + 2 * q^7 + 24 * q^8 + 8 * q^11 + 30 * q^12 + 2 * q^13 + 28 * q^16 - 28 * q^17 - 48 * q^18 + 12 * q^21 - 14 * q^22 - 82 * q^23 - 112 * q^26 + 198 * q^27 + 88 * q^28 - 4 * q^31 + 14 * q^32 - 96 * q^33 + 264 * q^36 + 92 * q^37 - 330 * q^38 - 28 * q^41 - 498 * q^42 + 2 * q^43 - 136 * q^46 - 64 * q^47 + 510 * q^48 - 396 * q^51 + 74 * q^52 + 608 * q^53 - 192 * q^56 + 114 * q^57 - 30 * q^58 + 92 * q^61 + 100 * q^62 - 24 * q^63 + 588 * q^66 + 80 * q^67 - 626 * q^68 + 248 * q^71 + 162 * q^72 + 8 * q^73 - 96 * q^76 - 338 * q^77 - 1062 * q^78 + 204 * q^81 - 104 * q^82 - 370 * q^83 - 328 * q^86 - 534 * q^87 + 210 * q^88 + 152 * q^91 - 388 * q^92 + 1062 * q^93 - 876 * q^96 - 292 * q^97 + 1876 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−0.194442	+	0.725667i	−0.0972209	+	0.362833i	−0.997347	−	0.0727965i	$-0.976808\pi$
$2$	−0.194442	+	0.725667i	−0.0972209	+	0.362833i	0.900126	+	0.435630i	$0.143474\pi$
$3$	1.34163	+	2.68329i	0.447210	+	0.894429i
$3$	1.34163	+	2.68329i	0.447210	+	0.894429i
$4$	2.97532	+	1.71780i	0.743829	+	0.429450i
$5$		0			0
$5$		0			0
$6$	−2.20804	+	0.451834i	−0.368007	+	0.0753056i
$7$	−0.481578	+	1.79727i	−0.0687969	+	0.256753i	−0.991755	−	0.128146i	$-0.959097\pi$
$7$	−0.481578	+	1.79727i	−0.0687969	+	0.256753i	0.922958	+	0.384900i	$0.125764\pi$
$8$	−3.94998	+	3.94998i	−0.493747	+	0.493747i
$9$	−5.40005	+	7.19996i	−0.600006	+	0.799996i
$10$		0			0
$11$	5.82294	+	10.0856i	0.529358	+	0.916875i	0.999414	+	0.0342381i	$0.0109005\pi$
$11$	5.82294	+	10.0856i	0.529358	+	0.916875i	−0.470056	+	0.882637i	$0.655766\pi$
$12$	−0.617573	+	10.2883i	−0.0514644	+	0.857357i
$13$	−5.30726	−	19.8070i	−0.408251	−	1.52361i	−0.797980	−	0.602684i	$-0.794098\pi$
$13$	−5.30726	−	19.8070i	−0.408251	−	1.52361i	0.389729	−	0.920930i	$-0.372569\pi$
$14$	−1.21058	−	0.698930i	−0.0864702	−	0.0499236i
$15$		0			0
$16$	4.77288	+	8.26686i	0.298305	+	0.516679i
$17$	10.0254	+	10.0254i	0.589728	+	0.589728i	0.937558	−	0.347830i	$-0.113081\pi$
$17$	10.0254	+	10.0254i	0.589728	+	0.589728i	−0.347830	+	0.937558i	$0.613081\pi$
$18$	−4.17477	−	5.31861i	−0.231932	−	0.295478i
$19$		−	10.8032i		−	0.568587i	−0.958737	−	0.284294i	$-0.908241\pi$
$19$		−	10.8032i		−	0.568587i	0.958737	−	0.284294i	$-0.0917590\pi$
$20$		0			0
$21$	−5.46870	+	1.11907i	−0.260414	+	0.0532889i
$22$	−8.45102	+	2.26444i	−0.384137	+	0.102929i
$23$	−0.360576	−	1.34569i	−0.0156772	−	0.0585081i	0.957644	−	0.287954i	$-0.0929751\pi$
$23$	−0.360576	−	1.34569i	−0.0156772	−	0.0585081i	−0.973321	+	0.229446i	$0.926308\pi$
$24$	−15.8983	−	5.29951i	−0.662430	−	0.220813i
$25$		0			0
$26$	15.4052			0.592508
$27$	−26.5644	−	4.83020i	−0.983868	−	0.178896i
$28$	−4.52021	+	4.52021i	−0.161436	+	0.161436i
$29$	−20.7968	+	12.0070i	−0.717130	+	0.414035i	−0.813695	−	0.581292i	$-0.802548\pi$
$29$	−20.7968	+	12.0070i	−0.717130	+	0.414035i	0.0965656	+	0.995327i	$0.469214\pi$
$30$		0			0
$31$	21.6233	−	37.4526i	0.697524	−	1.20815i	−0.271798	−	0.962354i	$-0.587618\pi$
$31$	21.6233	−	37.4526i	0.697524	−	1.20815i	0.969322	−	0.245793i	$-0.0790484\pi$
$32$	−28.5101	+	7.63926i	−0.890941	+	0.238727i
$33$	−19.2504	+	29.1558i	−0.583345	+	0.883509i
$34$	−9.22442	+	5.32572i	−0.271307	+	0.156639i
$35$		0			0
$36$	−28.4350	+	12.1460i	−0.789860	+	0.337388i
$37$	32.5443	+	32.5443i	0.879576	+	0.879576i	0.993491	−	0.113915i	$-0.0363391\pi$
$37$	32.5443	+	32.5443i	0.879576	+	0.879576i	−0.113915	+	0.993491i	$0.536339\pi$
$38$	7.83949	+	2.10058i	0.206302	+	0.0552785i
$39$	46.0274	−	40.8145i	1.18019	−	1.04653i
$40$		0			0
$41$	−20.5409	+	35.5778i	−0.500997	+	0.867752i	0.499002	+	0.866601i	$0.333700\pi$
$41$	−20.5409	+	35.5778i	−0.500997	+	0.867752i	−0.999999	+	0.00115173i	$0.999633\pi$
$42$	0.251275	−	4.18605i	0.00598274	−	0.0996678i
$43$	8.01349	+	2.14721i	0.186360	+	0.0499351i	0.350792	−	0.936453i	$-0.385912\pi$
$43$	8.01349	+	2.14721i	0.186360	+	0.0499351i	−0.164432	+	0.986388i	$0.552579\pi$
$44$			40.0106i			0.909331i
$45$		0			0
$46$	1.04663			0.0227528
$47$	4.62418	−	17.2577i	0.0983868	−	0.367185i	−0.899124	−	0.437693i	$-0.855796\pi$
$47$	4.62418	−	17.2577i	0.0983868	−	0.367185i	0.997511	+	0.0705087i	$0.0224622\pi$
$48$	−15.7789	+	23.8981i	−0.328728	+	0.497876i
$49$	39.4370	+	22.7689i	0.804836	+	0.464672i
$50$		0			0
$51$	−13.4506	+	40.3513i	−0.263737	+	0.791202i
$52$	18.2336	−	68.0488i	0.350647	−	1.30863i
$53$	51.3281	−	51.3281i	0.968455	−	0.968455i	−0.0310621	−	0.999517i	$-0.509889\pi$
$53$	51.3281	−	51.3281i	0.968455	−	0.968455i	0.999517	+	0.0310621i	$0.00988897\pi$
$54$	8.67035	−	18.3377i	0.160562	−	0.339588i
$55$		0			0
$56$	−5.19697	−	9.00141i	−0.0928030	−	0.160739i
$57$	28.9880	−	14.4938i	0.508561	−	0.254278i
$58$	−4.66933	−	17.4262i	−0.0805057	−	0.300451i
$59$	−24.3449	−	14.0555i	−0.412625	−	0.238229i	0.279292	−	0.960206i	$-0.409900\pi$
$59$	−24.3449	−	14.0555i	−0.412625	−	0.238229i	−0.691917	+	0.721977i	$0.743234\pi$
$60$		0			0
$61$	−41.1002	−	71.1876i	−0.673774	−	1.16701i	−0.976826	−	0.214036i	$-0.931339\pi$
$61$	−41.1002	−	71.1876i	−0.673774	−	1.16701i	0.303052	−	0.952974i	$-0.401994\pi$
$62$	22.9736	+	22.9736i	0.370542	+	0.370542i
$63$	−10.3398	−	13.1727i	−0.164123	−	0.209091i
$64$			16.0088i			0.250137i
$65$		0			0
$66$	−17.4143	−	19.6385i	−0.263853	−	0.297552i
$67$	32.3105	−	8.65757i	0.482246	−	0.129217i	−0.00950210	−	0.999955i	$-0.503025\pi$
$67$	32.3105	−	8.65757i	0.482246	−	0.129217i	0.491748	+	0.870737i	$0.336358\pi$
$68$	12.6071	+	47.0502i	0.185398	+	0.691915i
$69$	3.12710	−	2.77294i	0.0453203	−	0.0401876i
$70$		0			0
$71$	99.6917			1.40411			0.702054	−	0.712123i	$-0.252266\pi$
$71$	99.6917			1.40411			0.702054	+	0.712123i	$0.252266\pi$
$72$	−7.10958	−	49.7697i	−0.0987442	−	0.691246i
$73$	22.3583	−	22.3583i	0.306278	−	0.306278i	−0.537186	−	0.843464i	$-0.680513\pi$
$73$	22.3583	−	22.3583i	0.306278	−	0.306278i	0.843464	+	0.537186i	$0.180513\pi$
$74$	−29.9443	+	17.2883i	−0.404653	+	0.233626i
$75$		0			0
$76$	18.5577	−	32.1428i	0.244180	−	0.422932i
$77$	−20.9308	+	5.60840i	−0.271829	+	0.0728363i
$78$	20.6681	+	41.3366i	0.264976	+	0.529956i
$79$	52.9926	−	30.5953i	0.670793	−	0.387282i	−0.125584	−	0.992083i	$-0.540081\pi$
$79$	52.9926	−	30.5953i	0.670793	−	0.387282i	0.796377	+	0.604801i	$0.206747\pi$
$80$		0			0
$81$	−22.6788	−	77.7603i	−0.279986	−	0.960004i
$82$	−21.8237	−	21.8237i	−0.266142	−	0.266142i
$83$	49.9199	+	13.3760i	0.601444	+	0.161157i	0.546678	−	0.837343i	$-0.315892\pi$
$83$	49.9199	+	13.3760i	0.601444	+	0.161157i	0.0547660	+	0.998499i	$0.482559\pi$
$84$	−18.1935	−	6.06456i	−0.216589	−	0.0721971i
$85$		0			0
$86$	−3.11631	+	5.39761i	−0.0362362	+	0.0627630i
$87$	−60.1198	−	39.6947i	−0.691033	−	0.456261i
$88$	−62.8384	−	16.8375i	−0.714073	−	0.191335i
$89$		−	113.914i		−	1.27993i	−0.768402	−	0.639967i	$-0.778948\pi$
$89$		−	113.914i		−	1.27993i	0.768402	−	0.639967i	$-0.221052\pi$
$90$		0			0
$91$	38.1544			0.419279
$92$	1.23879	−	4.62324i	0.0134651	−	0.0502526i
$93$	129.506	+	7.77386i	1.39254	+	0.0835899i
$94$	11.6242	+	6.71123i	0.123662	+	0.0713960i
$95$		0			0
$96$	−58.7483	−	66.2517i	−0.611962	−	0.690122i
$97$	−7.92297	+	29.5689i	−0.0816801	+	0.304834i	−0.994665	−	0.103160i	$-0.967105\pi$
$97$	−7.92297	+	29.5689i	−0.0816801	+	0.304834i	0.912985	+	0.407994i	$0.133771\pi$
$98$	−24.1909	+	24.1909i	−0.246845	+	0.246845i
$99$	−104.060	−	12.5380i	−1.05111	−	0.126646i
$100$		0			0
$101$	29.8920	+	51.7745i	0.295961	+	0.512619i	0.975208	−	0.221291i	$-0.0710270\pi$
$101$	29.8920	+	51.7745i	0.295961	+	0.512619i	−0.679247	+	0.733909i	$0.737694\pi$
$102$	−26.6662	−	17.6066i	−0.261433	−	0.172614i
$103$	−13.1011	−	48.8939i	−0.127195	−	0.474698i	0.872713	−	0.488233i	$-0.162358\pi$
$103$	−13.1011	−	48.8939i	−0.127195	−	0.474698i	−0.999908	+	0.0135348i	$0.995692\pi$
$104$	99.2006	+	57.2735i	0.953852	+	0.550707i
$105$		0			0
$106$	27.2668	+	47.2274i	0.257234	+	0.445542i
$107$	14.8359	+	14.8359i	0.138653	+	0.138653i	0.773027	−	0.634374i	$-0.218742\pi$
$107$	14.8359	+	14.8359i	0.138653	+	0.138653i	−0.634374	+	0.773027i	$0.718742\pi$
$108$	−70.7403	−	60.0038i	−0.655003	−	0.555591i
$109$			115.290i			1.05770i	0.848714	+	0.528852i	$0.177377\pi$
$109$			115.290i			1.05770i	−0.848714	+	0.528852i	$0.822623\pi$
$110$		0			0
$111$	−43.6633	+	130.988i	−0.393363	+	1.18007i
$112$	−17.1563	+	4.59703i	−0.153182	+	0.0410449i
$113$	27.1198	+	101.212i	0.239998	+	0.895686i	0.975832	+	0.218523i	$0.0701239\pi$
$113$	27.1198	+	101.212i	0.239998	+	0.895686i	−0.735833	+	0.677163i	$0.763209\pi$
$114$	4.88123	+	23.8538i	0.0428178	+	0.209244i
$115$		0			0
$116$	−82.5026			−0.711229
$117$	171.269	+	68.7466i	1.46384	+	0.587578i
$118$	14.9333	−	14.9333i	0.126553	−	0.126553i
$119$	−22.8463	+	13.1903i	−0.191986	+	0.110843i
$120$		0			0
$121$	−7.31319	+	12.6668i	−0.0604396	+	0.104684i
$122$	59.6501	−	15.9832i	0.488935	−	0.131010i
$123$	−123.024	−	7.38473i	−1.00019	−	0.0600385i
$124$	128.672	−	74.2889i	1.03768	−	0.599104i
$125$		0			0
$126$	11.5695	−	4.94189i	0.0918213	−	0.0392213i
$127$	−56.0831	−	56.0831i	−0.441599	−	0.441599i	0.450950	−	0.892549i	$-0.351085\pi$
$127$	−56.0831	−	56.0831i	−0.441599	−	0.441599i	−0.892549	+	0.450950i	$0.851085\pi$
$128$	−125.657	−	33.6698i	−0.981699	−	0.263045i
$129$	4.98957	+	24.3832i	0.0386788	+	0.189017i
$130$		0			0
$131$	−2.31731	+	4.01371i	−0.0176894	+	0.0306390i	−0.874735	−	0.484602i	$-0.838964\pi$
$131$	−2.31731	+	4.01371i	−0.0176894	+	0.0306390i	0.857045	+	0.515241i	$0.172298\pi$
$132$	−107.360	+	53.6794i	−0.813332	+	0.406662i
$133$	19.4162	+	5.20256i	0.145987	+	0.0391170i
$134$			25.1300i			0.187538i
$135$		0			0
$136$	−79.1999			−0.582352
$137$	0.615617	−	2.29751i	0.00449355	−	0.0167702i	−0.963643	−	0.267194i	$-0.913903\pi$
$137$	0.615617	−	2.29751i	0.00449355	−	0.0167702i	0.968136	+	0.250424i	$0.0805701\pi$
$138$	1.40419	+	2.80841i	0.0101753	+	0.0203508i
$139$	−221.925	−	128.128i	−1.59658	−	0.921786i	−0.992140	−	0.125136i	$-0.960063\pi$
$139$	−221.925	−	128.128i	−1.59658	−	0.921786i	−0.604441	−	0.796650i	$-0.706603\pi$
$140$		0			0
$141$	52.5112	−	10.7454i	0.372420	−	0.0762087i
$142$	−19.3842	+	72.3429i	−0.136509	+	0.509457i
$143$	168.862	−	168.862i	1.18085	−	1.18085i
$144$	−85.2949	−	10.2770i	−0.592325	−	0.0713680i
$145$		0			0
$146$	11.8773	+	20.5721i	0.0813513	+	0.140905i
$147$	−8.18575	+	136.368i	−0.0556854	+	0.927675i
$148$	40.9250	+	152.734i	0.276520	+	1.03199i
$149$	81.5954	+	47.1091i	0.547620	+	0.316168i	0.748161	−	0.663517i	$-0.230937\pi$
$149$	81.5954	+	47.1091i	0.547620	+	0.316168i	−0.200542	+	0.979685i	$0.564270\pi$
$150$		0			0
$151$	14.0475	+	24.3310i	0.0930299	+	0.161133i	0.908785	−	0.417265i	$-0.137011\pi$
$151$	14.0475	+	24.3310i	0.0930299	+	0.161133i	−0.815755	+	0.578398i	$0.803678\pi$
$152$	42.6722	+	42.6722i	0.280738	+	0.280738i
$153$	−126.320	+	18.0447i	−0.825619	+	0.117939i
$154$		−	16.2793i		−	0.105710i
$155$		0			0
$156$	207.057	−	42.3704i	1.32729	−	0.271605i
$157$	37.2690	−	9.98621i	0.237382	−	0.0636064i	−0.138166	−	0.990409i	$-0.544121\pi$
$157$	37.2690	−	9.98621i	0.237382	−	0.0636064i	0.375549	+	0.926803i	$0.377454\pi$
$158$	11.8980	+	44.4040i	0.0753039	+	0.281038i
$159$	206.591	+	68.8647i	1.29932	+	0.433111i
$160$		0			0
$161$	2.59221			0.0161007
$162$	60.8378	−	1.33742i	0.375542	−	0.00825566i
$163$	−140.797	+	140.797i	−0.863787	+	0.863787i	−0.991776	−	0.127989i	$-0.959148\pi$
$163$	−140.797	+	140.797i	−0.863787	+	0.863787i	0.127989	+	0.991776i	$0.459148\pi$
$164$	−122.231	+	70.5703i	−0.745313	+	0.430306i
$165$		0			0
$166$	−19.4130	+	33.6243i	−0.116946	+	0.202556i
$167$	−273.273	+	73.2232i	−1.63636	+	0.438462i	−0.955750	−	0.294180i	$-0.904953\pi$
$167$	−273.273	+	73.2232i	−1.63636	+	0.438462i	−0.680614	+	0.732642i	$0.738287\pi$
$168$	17.1810	−	26.0215i	0.102268	−	0.154890i
$169$	−217.791	+	125.742i	−1.28870	+	0.744033i
$170$		0			0
$171$	77.7823	+	58.3376i	0.454867	+	0.341156i
$172$	20.1542	+	20.1542i	0.117176	+	0.117176i
$173$	−299.418	−	80.2289i	−1.73074	−	0.463751i	−0.750387	−	0.660998i	$-0.770133\pi$
$173$	−299.418	−	80.2289i	−1.73074	−	0.463751i	−0.980354	+	0.197248i	$0.936800\pi$
$174$	40.4949	−	35.9087i	0.232729	−	0.206372i
$175$		0			0
$176$	−55.5843	+	96.2748i	−0.315820	+	0.547016i
$177$	5.05315	−	84.1816i	0.0285489	−	0.475602i
$178$	82.6637	+	22.1497i	0.464403	+	0.124436i
$179$		−	151.884i		−	0.848512i	−0.905542	−	0.424256i	$-0.860536\pi$
$179$		−	151.884i		−	0.848512i	0.905542	−	0.424256i	$-0.139464\pi$
$180$		0			0
$181$	48.0978			0.265734			0.132867	−	0.991134i	$-0.457582\pi$
$181$	48.0978			0.265734			0.132867	+	0.991134i	$0.457582\pi$
$182$	−7.41881	+	27.6874i	−0.0407627	+	0.152128i
$183$	135.876	−	205.791i	0.742489	−	1.12454i
$184$	6.73969	+	3.89116i	0.0366288	+	0.0211476i
$185$		0			0
$186$	−30.8227	+	92.4669i	−0.165713	+	0.497134i
$187$	−42.7350	+	159.489i	−0.228529	+	0.852883i
$188$	43.4036	−	43.4036i	0.230870	−	0.230870i
$189$	21.4741	−	45.4174i	0.113619	−	0.240304i
$190$		0			0
$191$	−181.698	−	314.711i	−0.951300	−	1.64770i	−0.742617	−	0.669717i	$-0.766416\pi$
$191$	−181.698	−	314.711i	−0.951300	−	1.64770i	−0.208683	−	0.977983i	$-0.566918\pi$
$192$	−42.9562	+	21.4779i	−0.223730	+	0.111864i
$193$	3.09769	+	11.5607i	0.0160502	+	0.0599001i	0.973486	−	0.228745i	$-0.0734620\pi$
$193$	3.09769	+	11.5607i	0.0160502	+	0.0599001i	−0.957436	+	0.288645i	$0.906795\pi$
$194$	−19.9166	−	11.4989i	−0.102663	−	0.0592725i
$195$		0			0
$196$	78.2250	+	135.490i	0.399107	+	0.691274i
$197$	−45.3414	−	45.3414i	−0.230159	−	0.230159i	0.582600	−	0.812759i	$-0.302036\pi$
$197$	−45.3414	−	45.3414i	−0.230159	−	0.230159i	−0.812759	+	0.582600i	$0.802036\pi$
$198$	29.3321	−	73.0751i	0.148142	−	0.369066i
$199$		−	17.0082i		−	0.0854685i	−0.999086	−	0.0427343i	$-0.986393\pi$
$199$		−	17.0082i		−	0.0854685i	0.999086	−	0.0427343i	$-0.0136069\pi$
$200$		0			0
$201$	66.5795	+	75.0831i	0.331241	+	0.373548i
$202$	−43.3833	+	11.6245i	−0.214769	+	0.0575471i
$203$	−11.5646	−	43.1598i	−0.0569686	−	0.212610i
$204$	−109.335	+	96.9524i	−0.535957	+	0.475257i
$205$		0			0
$206$	38.0281			0.184602
$207$	11.6360	+	4.67065i	0.0562126	+	0.0225635i
$208$	138.411	−	138.411i	0.665436	−	0.665436i
$209$	108.957	−	62.9061i	0.521323	−	0.300986i
$210$		0			0
$211$	−148.887	+	257.879i	−0.705624	+	1.22218i	0.260842	+	0.965382i	$0.416000\pi$
$211$	−148.887	+	257.879i	−0.705624	+	1.22218i	−0.966466	+	0.256795i	$0.917333\pi$
$212$	240.889	−	64.5460i	1.13627	−	0.304462i
$213$	133.749	+	267.501i	0.627932	+	1.25588i
$214$	−13.6506	+	7.88119i	−0.0637879	+	0.0368280i
$215$		0			0
$216$	124.008	−	85.8497i	0.574111	−	0.397452i
$217$	56.8993	+	56.8993i	0.262209	+	0.262209i
$218$	−83.6620	−	22.4172i	−0.383771	−	0.102831i
$219$	89.9903	+	29.9971i	0.410915	+	0.136973i
$220$		0			0
$221$	145.365	−	251.779i	0.657760	−	1.13927i
$222$	−86.5638	−	57.1545i	−0.389927	−	0.257453i
$223$	−30.8773	−	8.27356i	−0.138463	−	0.0371012i	0.188922	−	0.981992i	$-0.439501\pi$
$223$	−30.8773	−	8.27356i	−0.138463	−	0.0371012i	−0.327385	+	0.944891i	$0.606167\pi$
$224$		−	54.9194i		−	0.245176i
$225$		0			0
$226$	−78.7197			−0.348317
$227$	101.241	−	377.838i	0.445997	−	1.66449i	−0.267292	−	0.963616i	$-0.586129\pi$
$227$	101.241	−	377.838i	0.445997	−	1.66449i	0.713289	−	0.700870i	$-0.247205\pi$
$228$	111.146	+	6.67174i	0.487482	+	0.0292620i
$229$	217.228	+	125.417i	0.948594	+	0.547671i	0.892644	−	0.450762i	$-0.148848\pi$
$229$	217.228	+	125.417i	0.948594	+	0.547671i	0.0559502	+	0.998434i	$0.482181\pi$
$230$		0			0
$231$	−43.1304	−	48.6390i	−0.186712	−	0.210558i
$232$	34.7193	−	129.574i	0.149652	−	0.558509i
$233$	−239.086	+	239.086i	−1.02612	+	1.02612i	−0.0264709	+	0.999650i	$0.508427\pi$
$233$	−239.086	+	239.086i	−1.02612	+	1.02612i	−0.999650	+	0.0264709i	$0.991573\pi$
$234$	−83.1890	+	110.917i	−0.355508	+	0.474004i
$235$		0			0
$236$	−48.2891	−	83.6392i	−0.204615	−	0.354404i
$237$	153.193	+	101.147i	0.646382	+	0.426780i
$238$	−5.12950	−	19.1436i	−0.0215525	−	0.0804352i
$239$	−33.8483	−	19.5423i	−0.141625	−	0.0817672i	0.427513	−	0.904009i	$-0.359390\pi$
$239$	−33.8483	−	19.5423i	−0.141625	−	0.0817672i	−0.569138	+	0.822242i	$0.692723\pi$
$240$		0			0
$241$	−41.8525	−	72.4907i	−0.173662	−	0.300791i	0.766036	−	0.642798i	$-0.222227\pi$
$241$	−41.8525	−	72.4907i	−0.173662	−	0.300791i	−0.939697	+	0.342007i	$0.888893\pi$
$242$	−7.76989	−	7.76989i	−0.0321070	−	0.0321070i
$243$	178.227	−	165.179i	0.733443	−	0.679751i
$244$		−	282.408i		−	1.15741i
$245$		0			0
$246$	29.2798	−	87.8384i	0.119024	−	0.357067i
$247$	−213.978	+	57.3352i	−0.866307	+	0.232126i
$248$	62.5254	+	233.348i	0.252119	+	0.940920i
$249$	31.0824	+	151.895i	0.124829	+	0.610020i
$250$		0			0
$251$	−116.674			−0.464837			−0.232418	−	0.972616i	$-0.574664\pi$
$251$	−116.674			−0.464837			−0.232418	+	0.972616i	$0.574664\pi$
$252$	−8.13594	−	56.9546i	−0.0322855	−	0.226011i
$253$	11.4725	−	11.4725i	0.0453458	−	0.0453458i
$254$	51.6025	−	29.7927i	0.203159	−	0.117294i
$255$		0			0
$256$	16.8485	−	29.1825i	0.0658146	−	0.113994i
$257$	−4.62189	+	1.23843i	−0.0179840	+	0.00481880i	−0.267800	−	0.963475i	$-0.586297\pi$
$257$	−4.62189	+	1.23843i	−0.0179840	+	0.00481880i	0.249816	+	0.968293i	$0.419630\pi$
$258$	−18.6643	−	1.12036i	−0.0723422	−	0.00434247i
$259$	−74.1637	+	42.8184i	−0.286346	+	0.165322i
$260$		0			0
$261$	25.8536	−	214.574i	0.0990559	−	0.822124i
$262$	−2.46203	−	2.46203i	−0.00939706	−	0.00939706i
$263$	−94.4750	−	25.3145i	−0.359221	−	0.0962529i	0.0746949	−	0.997206i	$-0.476202\pi$
$263$	−94.4750	−	25.3145i	−0.359221	−	0.0962529i	−0.433916	+	0.900954i	$0.642868\pi$
$264$	−39.1261	−	191.203i	−0.148205	−	0.724255i
$265$		0			0
$266$	−7.55065	+	13.0781i	−0.0283859	+	0.0491658i
$267$	305.664	−	152.831i	1.14481	−	0.572400i
$268$	111.006	+	29.7440i	0.414201	+	0.110985i
$269$		−	212.871i		−	0.791340i	−0.918393	−	0.395670i	$-0.870512\pi$
$269$		−	212.871i		−	0.791340i	0.918393	−	0.395670i	$-0.129488\pi$
$270$		0			0
$271$	−180.243			−0.665102			−0.332551	−	0.943085i	$-0.607909\pi$
$271$	−180.243			−0.665102			−0.332551	+	0.943085i	$0.607909\pi$
$272$	−35.0285	+	130.728i	−0.128781	+	0.480618i
$273$	51.1891	+	102.379i	0.187506	+	0.375016i
$274$	1.54753	+	0.893465i	0.00564791	+	0.00326082i
$275$		0			0
$276$	14.0675	−	2.87864i	0.0509691	−	0.0104299i
$277$	84.7048	−	316.123i	0.305794	−	1.14124i	−0.626467	−	0.779448i	$-0.715499\pi$
$277$	84.7048	−	316.123i	0.305794	−	1.14124i	0.932260	−	0.361789i	$-0.117834\pi$
$278$	136.130	−	136.130i	0.489676	−	0.489676i
$279$	152.890	+	357.932i	0.547994	+	1.28291i
$280$		0			0
$281$	−15.6356	−	27.0816i	−0.0556426	−	0.0963758i	0.836862	−	0.547413i	$-0.184387\pi$
$281$	−15.6356	−	27.0816i	−0.0556426	−	0.0963758i	−0.892505	+	0.451037i	$0.851054\pi$
$282$	−2.41278	+	40.1950i	−0.00855596	+	0.142535i
$283$	52.4715	+	195.826i	0.185412	+	0.691966i	0.994542	+	0.104337i	$0.0332719\pi$
$283$	52.4715	+	195.826i	0.185412	+	0.691966i	−0.809130	+	0.587629i	$0.800061\pi$
$284$	296.614	+	171.250i	1.04442	+	0.602995i
$285$		0			0
$286$	89.7036	+	155.371i	0.313649	+	0.543256i
$287$	−54.0511	−	54.0511i	−0.188331	−	0.188331i
$288$	98.9537	−	246.524i	0.343589	−	0.855986i
$289$		−	87.9840i		−	0.304443i
$290$		0			0
$291$	−89.9715	+	18.4110i	−0.309181	+	0.0632679i
$292$	104.930	−	28.1159i	0.359350	−	0.0962875i
$293$	−10.0935	−	37.6696i	−0.0344490	−	0.128565i	0.946560	−	0.322528i	$-0.104533\pi$
$293$	−10.0935	−	37.6696i	−0.0344490	−	0.128565i	−0.981009	+	0.193963i	$0.937866\pi$
$294$	−97.3662	−	32.4558i	−0.331178	−	0.110394i
$295$		0			0
$296$	−257.098			−0.868576
$297$	−105.967	−	296.045i	−0.356793	−	0.996784i
$298$	−50.0510	+	50.0510i	−0.167957	+	0.167957i
$299$	−24.7403	+	14.2838i	−0.0827435	+	0.0477720i
$300$		0			0
$301$	−7.71824	+	13.3684i	−0.0256420	+	0.0444132i
$302$	−20.3876	+	5.46285i	−0.0675087	+	0.0180889i
$303$	−98.8217	+	149.671i	−0.326144	+	0.493964i
$304$	89.3082	−	51.5621i	0.293777	−	0.169612i
$305$		0			0
$306$	11.4674	−	95.1747i	0.0374751	−	0.311028i
$307$	28.4359	+	28.4359i	0.0926251	+	0.0926251i	0.751901	−	0.659276i	$-0.229137\pi$
$307$	28.4359	+	28.4359i	0.0926251	+	0.0926251i	−0.659276	+	0.751901i	$0.729137\pi$
$308$	−71.9100	−	19.2682i	−0.233474	−	0.0625591i
$309$	113.619	−	100.751i	0.367701	−	0.326057i
$310$		0			0
$311$	−215.953	+	374.041i	−0.694381	+	1.20270i	0.276007	+	0.961156i	$0.410989\pi$
$311$	−215.953	+	374.041i	−0.694381	+	1.20270i	−0.970389	+	0.241548i	$0.922345\pi$
$312$	−20.5906	+	343.024i	−0.0659956	+	1.09943i
$313$	200.386	+	53.6933i	0.640211	+	0.171544i	0.564299	−	0.825571i	$-0.309147\pi$
$313$	200.386	+	53.6933i	0.640211	+	0.171544i	0.0759119	+	0.997115i	$0.475813\pi$
$314$			28.9866i			0.0923141i
$315$		0			0
$316$	210.226			0.665274
$317$	91.9060	−	342.998i	0.289924	−	1.08201i	−0.655241	−	0.755420i	$-0.727433\pi$
$317$	91.9060	−	342.998i	0.289924	−	1.08201i	0.945165	−	0.326593i	$-0.105900\pi$
$318$	−90.1428	+	136.526i	−0.283468	+	0.429328i
$319$	−242.196	−	139.832i	−0.759237	−	0.438345i
$320$		0			0
$321$	−19.9046	+	59.7132i	−0.0620082	+	0.186022i
$322$	−0.504034	+	1.88108i	−0.00156532	+	0.00584187i
$323$	108.306	−	108.306i	0.335311	−	0.335311i
$324$	66.1000	−	270.319i	0.204012	−	0.834319i
$325$		0			0
$326$	−74.7950	−	129.549i	−0.229432	−	0.397389i
$327$	−309.356	+	154.676i	−0.946042	+	0.473016i
$328$	−59.3957	−	221.668i	−0.181084	−	0.675816i
$329$	28.7899	+	16.6218i	0.0875072	+	0.0505223i
$330$		0			0
$331$	−187.451	−	324.675i	−0.566318	−	0.980891i	−0.996926	−	0.0783519i	$-0.975034\pi$
$331$	−187.451	−	324.675i	−0.566318	−	0.980891i	0.430608	−	0.902539i	$-0.358299\pi$
$332$	125.550	+	125.550i	0.378163	+	0.378163i
$333$	−410.059	+	58.5767i	−1.23141	+	0.175906i
$334$		−	212.543i		−	0.636355i
$335$		0			0
$336$	−35.3526	−	39.8678i	−0.105216	−	0.118654i
$337$	−143.584	+	38.4732i	−0.426065	+	0.114164i	−0.465478	−	0.885059i	$-0.654118\pi$
$337$	−143.584	+	38.4732i	−0.426065	+	0.114164i	0.0394135	+	0.999223i	$0.487451\pi$
$338$	−48.8988	−	182.493i	−0.144671	−	0.539920i
$339$	−235.197	+	208.560i	−0.693797	+	0.615221i
$340$		0			0
$341$	503.643			1.47696
$342$	−57.4578	+	45.1007i	−0.168005	+	0.131873i
$343$	−124.383	+	124.383i	−0.362633	+	0.362633i
$344$	−40.1345	+	23.1717i	−0.116670	+	0.0673595i
$345$		0			0
$346$	116.439	−	201.678i	0.336528	−	0.582884i
$347$	−233.258	+	62.5014i	−0.672214	+	0.180119i	−0.578752	−	0.815504i	$-0.696460\pi$
$347$	−233.258	+	62.5014i	−0.672214	+	0.180119i	−0.0934622	+	0.995623i	$0.529793\pi$
$348$	−110.688	−	221.378i	−0.318069	−	0.636144i
$349$	−331.191	+	191.213i	−0.948971	+	0.547889i	−0.892761	−	0.450530i	$-0.851235\pi$
$349$	−331.191	+	191.213i	−0.948971	+	0.547889i	−0.0562101	+	0.998419i	$0.517902\pi$
$350$		0			0
$351$	45.3127	+	551.796i	0.129096	+	1.57207i
$352$	−243.059	−	243.059i	−0.690509	−	0.690509i
$353$	503.013	+	134.782i	1.42497	+	0.381819i	0.887243	−	0.461302i	$-0.152618\pi$
$353$	503.013	+	134.782i	1.42497	+	0.381819i	0.537724	+	0.843121i	$0.319284\pi$
$354$	60.1052	+	20.0353i	0.169789	+	0.0565969i
$355$		0			0
$356$	195.682	−	338.931i	0.549668	−	0.952052i
$357$	−66.0448	−	43.6067i	−0.184999	−	0.122148i
$358$	110.217	+	29.5325i	0.307868	+	0.0824931i
$359$			326.956i			0.910741i	0.890302	+	0.455370i	$0.150493\pi$
$359$			326.956i			0.910741i	−0.890302	+	0.455370i	$0.849507\pi$
$360$		0			0
$361$	244.292			0.676709
$362$	−9.35222	+	34.9030i	−0.0258349	+	0.0964170i
$363$	−43.8003	−	2.62919i	−0.120662	−	0.00724296i
$364$	113.521	+	65.5417i	0.311872	+	0.180060i
$365$		0			0
$366$	122.916	+	138.615i	0.335836	+	0.378729i
$367$	−135.325	+	505.039i	−0.368733	+	1.37613i	0.493557	+	0.869713i	$0.335696\pi$
$367$	−135.325	+	505.039i	−0.368733	+	1.37613i	−0.862290	+	0.506415i	$0.830970\pi$
$368$	9.40362	−	9.40362i	0.0255533	−	0.0255533i
$369$	−145.237	−	340.016i	−0.393597	−	0.921452i
$370$		0			0
$371$	67.5322	+	116.969i	0.182028	+	0.315281i
$372$	371.969	+	245.596i	0.999916	+	0.660204i
$373$	−6.28693	−	23.4631i	−0.0168550	−	0.0629039i	0.956986	−	0.290134i	$-0.0936998\pi$
$373$	−6.28693	−	23.4631i	−0.0168550	−	0.0629039i	−0.973841	+	0.227230i	$0.927033\pi$
$374$	−107.426	−	62.0227i	−0.287237	−	0.165836i
$375$		0			0
$376$	49.9020	+	86.4328i	0.132718	+	0.229874i
$377$	348.197	+	348.197i	0.923598	+	0.923598i
$378$	28.7825	+	24.4141i	0.0761441	+	0.0645874i
$379$			364.939i			0.962900i	0.876474	+	0.481450i	$0.159890\pi$
$379$			364.939i			0.962900i	−0.876474	+	0.481450i	$0.840110\pi$
$380$		0			0
$381$	75.2442	−	225.730i	0.197491	−	0.592466i
$382$	263.705	−	70.6595i	0.690327	−	0.184972i
$383$	0.870084	+	3.24720i	0.00227176	+	0.00847832i	0.967052	−	0.254577i	$-0.0819364\pi$
$383$	0.870084	+	3.24720i	0.00227176	+	0.00847832i	−0.964781	+	0.263056i	$0.915270\pi$
$384$	−78.2401	−	382.347i	−0.203750	−	0.995696i
$385$		0			0
$386$	−8.99155			−0.0232942
$387$	−58.7331	+	46.1018i	−0.151765	+	0.119126i
$388$	−74.3668	+	74.3668i	−0.191667	+	0.191667i
$389$	−131.808	+	76.0995i	−0.338838	+	0.195628i	−0.659758	−	0.751478i	$-0.729341\pi$
$389$	−131.808	+	76.0995i	−0.338838	+	0.195628i	0.320920	+	0.947106i	$0.396008\pi$
$390$		0			0
$391$	9.87610	−	17.1059i	0.0252586	−	0.0437491i
$392$	−245.712	+	65.8383i	−0.626816	+	0.167955i
$393$	−13.8789	−	0.833107i	−0.0353153	−	0.00211986i
$394$	41.7190	−	24.0865i	0.105886	−	0.0611332i
$395$		0			0
$396$	−288.074	−	216.059i	−0.727461	−	0.545604i
$397$	275.868	+	275.868i	0.694882	+	0.694882i	0.963302	−	0.268420i	$-0.0865016\pi$
$397$	275.868	+	275.868i	0.694882	+	0.694882i	−0.268420	+	0.963302i	$0.586502\pi$
$398$	12.3423	+	3.30711i	0.0310108	+	0.00830933i
$399$	12.0894	+	59.0792i	0.0302994	+	0.148068i
$400$		0			0
$401$	−337.489	+	584.548i	−0.841618	+	1.45773i	0.0469080	+	0.998899i	$0.485063\pi$
$401$	−337.489	+	584.548i	−0.841618	+	1.45773i	−0.888526	+	0.458826i	$0.848270\pi$
$402$	−67.4311	+	33.7152i	−0.167739	+	0.0838688i
$403$	−856.582	−	229.521i	−2.12551	−	0.569530i
$404$			205.394i			0.508401i
$405$		0			0
$406$	33.5683			0.0826805
$407$	−138.726	+	517.733i	−0.340850	+	1.27207i
$408$	−106.257	−	212.516i	−0.260434	−	0.520873i
$409$	375.213	+	216.629i	0.917390	+	0.529655i	0.882802	−	0.469746i	$-0.155655\pi$
$409$	375.213	+	216.629i	0.917390	+	0.529655i	0.0345887	+	0.999402i	$0.488988\pi$
$410$		0			0
$411$	6.99082	−	1.43054i	0.0170093	−	0.00348063i
$412$	45.0101	−	167.980i	0.109248	−	0.407718i
$413$	36.9856	−	36.9856i	0.0895534	−	0.0895534i
$414$	−5.65186	+	7.53570i	−0.0136518	+	0.0182022i
$415$		0			0
$416$	302.621	+	524.155i	0.727455	+	1.25999i
$417$	46.0639	−	767.388i	0.110465	−	1.84026i
$418$	24.4631	+	91.2977i	0.0585243	+	0.218416i
$419$	−432.869	−	249.917i	−1.03310	−	0.596461i	−0.115229	−	0.993339i	$-0.536760\pi$
$419$	−432.869	−	249.917i	−1.03310	−	0.596461i	−0.917871	+	0.396878i	$0.870093\pi$
$420$		0			0
$421$	15.0425	+	26.0544i	0.0357304	+	0.0618869i	0.883338	−	0.468737i	$-0.155291\pi$
$421$	15.0425	+	26.0544i	0.0357304	+	0.0618869i	−0.847607	+	0.530624i	$0.821958\pi$
$422$	−158.185	−	158.185i	−0.374845	−	0.374845i
$423$	99.2837	+	126.486i	0.234713	+	0.299022i
$424$			405.490i			0.956344i
$425$		0			0
$426$	−220.123	+	45.0441i	−0.516721	+	0.105737i
$427$	147.737	−	39.5859i	0.345987	−	0.0927071i
$428$	18.6564	+	69.6265i	0.0435896	+	0.162679i
$429$	679.655	+	226.554i	1.58428	+	0.528099i
$430$		0			0
$431$	515.749			1.19663			0.598316	−	0.801260i	$-0.295837\pi$
$431$	515.749			1.19663			0.598316	+	0.801260i	$0.295837\pi$
$432$	−86.8581	−	242.659i	−0.201060	−	0.561710i
$433$	305.797	−	305.797i	0.706229	−	0.706229i	−0.259511	−	0.965740i	$-0.583561\pi$
$433$	305.797	−	305.797i	0.706229	−	0.706229i	0.965740	+	0.259511i	$0.0835613\pi$
$434$	−52.3535	+	30.2263i	−0.120630	+	0.0696458i
$435$		0			0
$436$	−198.045	+	343.024i	−0.454231	+	0.786752i
$437$	−14.5377	+	3.89535i	−0.0332669	+	0.00891385i
$438$	−39.2658	+	59.4703i	−0.0896480	+	0.135777i
$439$	437.591	−	252.643i	0.996790	−	0.575497i	0.0894929	−	0.995987i	$-0.471475\pi$
$439$	437.591	−	252.643i	0.996790	−	0.575497i	0.907297	+	0.420491i	$0.138142\pi$
$440$		0			0
$441$	−376.897	+	160.991i	−0.854642	+	0.365059i
$442$	154.443	+	154.443i	0.349418	+	0.349418i
$443$	−195.215	−	52.3076i	−0.440665	−	0.118076i	0.0316632	−	0.999499i	$-0.489920\pi$
$443$	−195.215	−	52.3076i	−0.440665	−	0.118076i	−0.472328	+	0.881423i	$0.656586\pi$
$444$	−354.923	+	314.726i	−0.799377	+	0.708843i
$445$		0			0
$446$	12.0077	−	20.7979i	0.0269231	−	0.0466321i
$447$	−16.9364	+	282.147i	−0.0378890	+	0.631201i
$448$	−28.7722	−	7.70948i	−0.0642236	−	0.0172087i
$449$		−	145.089i		−	0.323138i	−0.986861	−	0.161569i	$-0.948345\pi$
$449$		−	145.089i		−	0.323138i	0.986861	−	0.161569i	$-0.0516554\pi$
$450$		0			0
$451$	−478.433			−1.06083
$452$	−93.1728	+	347.726i	−0.206135	+	0.769305i
$453$	−46.4405	+	70.3367i	−0.102518	+	0.155269i
$454$	254.499	+	146.935i	0.560570	+	0.323645i
$455$		0			0
$456$	−57.2514	+	171.752i	−0.125551	+	0.376649i
$457$	−76.7746	+	286.527i	−0.167997	+	0.626973i	0.829642	+	0.558296i	$0.188545\pi$
$457$	−76.7746	+	286.527i	−0.167997	+	0.626973i	−0.997639	+	0.0686775i	$0.978122\pi$
$458$	−133.249	+	133.249i	−0.290936	+	0.290936i
$459$	−217.894	−	314.743i	−0.474714	−	0.685714i
$460$		0			0
$461$	143.044	+	247.759i	0.310291	+	0.537439i	0.978425	−	0.206601i	$-0.0662403\pi$
$461$	143.044	+	247.759i	0.310291	+	0.537439i	−0.668135	+	0.744040i	$0.732907\pi$
$462$	43.6821	−	21.8408i	0.0945499	−	0.0472745i
$463$	−64.7653	−	241.707i	−0.139882	−	0.522046i	−0.999930	−	0.0118333i	$-0.996233\pi$
$463$	−64.7653	−	241.707i	−0.139882	−	0.522046i	0.860048	−	0.510213i	$-0.170433\pi$
$464$	−198.521	−	114.616i	−0.427846	−	0.247017i
$465$		0			0
$466$	−127.008	−	219.985i	−0.272550	−	0.472071i
$467$	71.3291	+	71.3291i	0.152739	+	0.152739i	0.779340	−	0.626601i	$-0.215554\pi$
$467$	71.3291	+	71.3291i	0.152739	+	0.152739i	−0.626601	+	0.779340i	$0.715554\pi$
$468$	391.486	+	498.749i	0.836509	+	1.06570i
$469$			62.2401i			0.132708i
$470$		0			0
$471$	76.7972	+	86.6057i	0.163051	+	0.183876i
$472$	151.681	−	40.6427i	0.321357	−	0.0861074i
$473$	25.0061	+	93.3241i	0.0528670	+	0.197302i
$474$	−103.186	+	91.4995i	−0.217692	+	0.193037i
$475$		0			0
$476$	−90.6334			−0.190406
$477$	92.3858	+	646.735i	0.193681	+	1.35584i
$478$	20.7628	−	20.7628i	0.0434367	−	0.0434367i
$479$	169.803	−	98.0357i	0.354494	−	0.204667i	−0.312169	−	0.950027i	$-0.601055\pi$
$479$	169.803	−	98.0357i	0.354494	−	0.204667i	0.666663	+	0.745359i	$0.267722\pi$
$480$		0			0
$481$	471.883	−	817.325i	0.981046	−	1.69922i
$482$	60.7419	−	16.2758i	0.126021	−	0.0337671i
$483$	3.47779	+	6.95565i	0.00720040	+	0.0144009i
$484$	−43.5181	+	25.1252i	−0.0899135	+	0.0519116i
$485$		0			0
$486$	85.2105	+	161.451i	0.175330	+	0.332204i
$487$	−660.124	−	660.124i	−1.35549	−	1.35549i	−0.879391	−	0.476100i	$-0.842050\pi$
$487$	−660.124	−	660.124i	−1.35549	−	1.35549i	−0.476100	−	0.879391i	$-0.657950\pi$
$488$	443.534	+	118.845i	0.908882	+	0.243534i
$489$	−566.697	−	188.901i	−1.15889	−	0.386301i
$490$		0			0
$491$	393.999	−	682.426i	0.802442	−	1.38987i	−0.115562	−	0.993300i	$-0.536867\pi$
$491$	393.999	−	682.426i	0.802442	−	1.38987i	0.918004	−	0.396570i	$-0.129800\pi$
$492$	−353.349	−	233.302i	−0.718190	−	0.474192i
$493$	−328.870	−	88.1204i	−0.667079	−	0.178743i
$494$		−	166.425i		−	0.336892i
$495$		0			0
$496$	412.820			0.832299
$497$	−48.0093	+	179.173i	−0.0965983	+	0.360510i
$498$	−116.269	−	6.97925i	−0.233472	−	0.0140146i
$499$	−144.756	−	83.5751i	−0.290093	−	0.167485i	0.347891	−	0.937535i	$-0.386898\pi$
$499$	−144.756	−	83.5751i	−0.290093	−	0.167485i	−0.637984	+	0.770050i	$0.720231\pi$
$500$		0			0
$501$	−563.110	−	635.031i	−1.12397	−	1.26753i
$502$	22.6863	−	84.6664i	0.0451918	−	0.168658i
$503$	−249.990	+	249.990i	−0.496998	+	0.496998i	−0.910502	−	0.413504i	$-0.864305\pi$
$503$	−249.990	+	249.990i	−0.496998	+	0.496998i	0.413504	+	0.910502i	$0.364305\pi$
$504$	92.8737	+	11.1901i	0.184273	+	0.0222027i
$505$		0			0
$506$	6.09446	+	10.5559i	0.0120444	+	0.0208615i
$507$	−629.596	−	415.696i	−1.24181	−	0.819914i
$508$	−70.5254	−	263.204i	−0.138830	−	0.518119i
$509$	−95.6645	−	55.2319i	−0.187946	−	0.108511i	0.403075	−	0.915167i	$-0.367941\pi$
$509$	−95.6645	−	55.2319i	−0.187946	−	0.108511i	−0.591021	+	0.806656i	$0.701275\pi$
$510$		0			0
$511$	29.4167	+	50.9513i	0.0575670	+	0.0997089i
$512$	−350.050	−	350.050i	−0.683691	−	0.683691i
$513$	−52.1814	+	286.980i	−0.101718	+	0.559415i
$514$		−	3.59475i		−	0.00699368i
$515$		0			0
$516$	−27.0400	+	81.1190i	−0.0524031	+	0.157207i
$517$	200.981	−	53.8526i	0.388744	−	0.104164i
$518$	−16.6514	−	62.1438i	−0.0321455	−	0.119969i
$519$	−186.432	−	911.062i	−0.359213	−	1.75542i
$520$		0			0
$521$	−415.088			−0.796715			−0.398357	−	0.917230i	$-0.630420\pi$
$521$	−415.088			−0.796715			−0.398357	+	0.917230i	$0.630420\pi$
$522$	150.682	+	60.4833i	0.288664	+	0.115868i
$523$	384.585	−	384.585i	0.735344	−	0.735344i	−0.236329	−	0.971673i	$-0.575944\pi$
$523$	384.585	−	384.585i	0.735344	−	0.735344i	0.971673	+	0.236329i	$0.0759444\pi$
$524$	−13.7895	+	7.96136i	−0.0263158	+	0.0151934i
$525$		0			0
$526$	36.7398	−	63.6352i	0.0698475	−	0.120979i
$527$	592.257	−	158.695i	1.12383	−	0.301129i
$528$	−332.907	−	19.9833i	−0.630505	−	0.0378472i
$529$	456.447	−	263.530i	0.862848	−	0.498166i
$530$		0			0
$531$	232.663	−	99.3815i	0.438160	−	0.187159i
$532$	48.8325	+	48.8325i	0.0917904	+	0.0917904i
$533$	813.705	+	218.032i	1.52665	+	0.409065i
$534$	51.4702	+	251.527i	0.0963862	+	0.471024i
$535$		0			0
$536$	−93.4285	+	161.823i	−0.174307	+	0.301908i
$537$	407.547	−	203.772i	0.758933	−	0.379463i
$538$	154.473	+	41.3909i	0.287125	+	0.0769348i
$539$			530.329i			0.983912i
$540$		0			0
$541$	251.489			0.464859			0.232430	−	0.972613i	$-0.425332\pi$
$541$	251.489			0.464859			0.232430	+	0.972613i	$0.425332\pi$
$542$	35.0467	−	130.796i	0.0646618	−	0.241321i
$543$	64.5295	+	129.060i	0.118839	+	0.237680i
$544$	−362.411	−	209.238i	−0.666196	−	0.384628i
$545$		0			0
$546$	−84.2465	+	17.2394i	−0.154298	+	0.0315741i
$547$	144.553	−	539.479i	0.264265	−	0.986251i	−0.698433	−	0.715675i	$-0.746119\pi$
$547$	144.553	−	539.479i	0.264265	−	0.986251i	0.962699	−	0.270576i	$-0.0872142\pi$
$548$	5.77833	−	5.77833i	0.0105444	−	0.0105444i
$549$	734.491	+	88.4973i	1.33787	+	0.161197i
$550$		0			0
$551$	129.714	+	224.671i	0.235415	+	0.407751i
$552$	−1.39893	+	23.3050i	−0.00253429	+	0.0422193i
$553$	29.4681	+	109.976i	0.0532876	+	0.198872i
$554$	212.930	+	122.935i	0.384349	+	0.221904i
$555$		0			0
$556$	−440.197	−	762.444i	−0.791722	−	1.37130i
$557$	−302.419	−	302.419i	−0.542943	−	0.542943i	0.381447	−	0.924391i	$-0.375426\pi$
$557$	−302.419	−	302.419i	−0.542943	−	0.542943i	−0.924391	+	0.381447i	$0.875426\pi$
$558$	−289.468	+	41.3504i	−0.518760	+	0.0741046i
$559$		−	170.119i		−	0.304327i
$560$		0			0
$561$	−485.290	+	99.3053i	−0.865044	+	0.177015i
$562$	22.6924	−	6.08041i	0.0403780	−	0.0108192i
$563$	−234.221	−	874.123i	−0.416022	−	1.55262i	−0.782779	−	0.622300i	$-0.786198\pi$
$563$	−234.221	−	874.123i	−0.416022	−	1.55262i	0.366756	−	0.930317i	$-0.380468\pi$
$564$	174.696	+	58.2327i	0.309745	+	0.103250i
$565$		0			0
$566$	−152.307			−0.269094
$567$	150.678	−	3.31241i	0.265747	−	0.00584199i
$568$	−393.780	+	393.780i	−0.693274	+	0.693274i
$569$	−194.081	+	112.053i	−0.341092	+	0.196929i	−0.660755	−	0.750602i	$-0.729764\pi$
$569$	−194.081	+	112.053i	−0.341092	+	0.196929i	0.319663	+	0.947531i	$0.396430\pi$
$570$		0			0
$571$	−28.3061	+	49.0275i	−0.0495728	+	0.0858626i	−0.889747	−	0.456454i	$-0.849119\pi$
$571$	−28.3061	+	49.0275i	−0.0495728	+	0.0858626i	0.840174	+	0.542317i	$0.182453\pi$
$572$	792.488	−	212.347i	1.38547	−	0.371235i
$573$	600.687	−	909.774i	1.04832	−	1.58774i
$574$	49.7329	−	28.7133i	0.0866426	−	0.0500232i
$575$		0			0
$576$	−115.263	−	86.4483i	−0.200109	−	0.150084i
$577$	450.543	+	450.543i	0.780838	+	0.780838i	0.979972	−	0.199135i	$-0.0638131\pi$
$577$	450.543	+	450.543i	0.780838	+	0.780838i	−0.199135	+	0.979972i	$0.563813\pi$
$578$	63.8471	+	17.1078i	0.110462	+	0.0295982i
$579$	−26.8648	+	23.8222i	−0.0463986	+	0.0411437i
$580$		0			0
$581$	−48.0806	+	83.2781i	−0.0827550	+	0.143336i
$582$	4.13400	−	68.8692i	0.00710309	−	0.118332i
$583$	816.557	+	218.796i	1.40061	+	0.375293i
$584$			176.630i			0.302448i
$585$		0			0
$586$	29.2982			0.0499969
$587$	89.8623	−	335.371i	0.153087	−	0.571330i	−0.846174	−	0.532906i	$-0.821100\pi$
$587$	89.8623	−	335.371i	0.153087	−	0.571330i	0.999262	−	0.0384234i	$-0.0122336\pi$
$588$	−258.609	+	391.677i	−0.439810	+	0.666118i
$589$	−404.606	−	233.599i	−0.686937	−	0.396603i
$590$		0			0
$591$	60.8326	−	182.495i	0.102932	−	0.308791i
$592$	−113.709	+	424.369i	−0.192077	+	0.716840i
$593$	235.628	−	235.628i	0.397350	−	0.397350i	−0.479948	−	0.877297i	$-0.659344\pi$
$593$	235.628	−	235.628i	0.397350	−	0.397350i	0.877297	+	0.479948i	$0.159344\pi$
$594$	235.434	−	19.3335i	0.396354	−	0.0325480i
$595$		0			0
$596$	161.848	+	280.329i	0.271557	+	0.470351i
$597$	45.6380	−	22.8188i	0.0764455	−	0.0382224i
$598$	−5.55474	−	20.7306i	−0.00928887	−	0.0346665i
$599$	513.829	+	296.659i	0.857811	+	0.495258i	0.863279	−	0.504727i	$-0.168407\pi$
$599$	513.829	+	296.659i	0.857811	+	0.495258i	−0.00546746	+	0.999985i	$0.501740\pi$
$600$		0			0
$601$	269.249	+	466.354i	0.448002	+	0.775963i	0.998256	−	0.0590349i	$-0.0188023\pi$
$601$	269.249	+	466.354i	0.448002	+	0.775963i	−0.550254	+	0.834998i	$0.685469\pi$
$602$	−8.20024	−	8.20024i	−0.0136217	−	0.0136217i
$603$	−112.144	+	279.386i	−0.185977	+	0.463326i
$604$			96.5233i			0.159807i
$605$		0			0
$606$	−89.3962	−	100.814i	−0.147519	−	0.166360i
$607$	395.280	−	105.915i	0.651203	−	0.174489i	0.0819303	−	0.996638i	$-0.473892\pi$
$607$	395.280	−	105.915i	0.651203	−	0.174489i	0.569273	+	0.822149i	$0.307225\pi$
$608$	82.5281	+	307.999i	0.135737	+	0.506577i
$609$	100.295	−	88.9357i	0.164687	−	0.146036i
$610$		0			0
$611$	−366.364			−0.599614
$612$	−406.839	−	163.303i	−0.664769	−	0.266836i
$613$	10.5026	−	10.5026i	0.0171331	−	0.0171331i	−0.698488	−	0.715621i	$-0.746144\pi$
$613$	10.5026	−	10.5026i	0.0171331	−	0.0171331i	0.715621	+	0.698488i	$0.246144\pi$
$614$	−26.1641	+	15.1059i	−0.0426126	+	0.0246024i
$615$		0			0
$616$	60.5232	−	104.829i	0.0982520	−	0.170177i
$617$	−421.900	+	113.048i	−0.683793	+	0.183222i	−0.583960	−	0.811782i	$-0.698498\pi$
$617$	−421.900	+	113.048i	−0.683793	+	0.183222i	−0.0998331	+	0.995004i	$0.531831\pi$
$618$	51.0196	+	102.040i	0.0825560	+	0.165114i
$619$	8.91186	−	5.14527i	0.0143972	−	0.00831222i	−0.492784	−	0.870152i	$-0.664021\pi$
$619$	8.91186	−	5.14527i	0.0143972	−	0.00831222i	0.507181	+	0.861839i	$0.330687\pi$
$620$		0			0
$621$	3.07855	+	37.4890i	0.00495740	+	0.0603688i
$622$	−229.439	−	229.439i	−0.368873	−	0.368873i
$623$	204.735	+	54.8585i	0.328627	+	0.0880554i
$624$	557.091	+	185.699i	0.892775	+	0.297595i
$625$		0			0
$626$	−77.9268	+	134.973i	−0.124484	+	0.215612i
$627$	314.975	+	207.965i	0.502352	+	0.331682i
$628$	128.042	+	34.3086i	0.203888	+	0.0546316i
$629$			652.537i			1.03742i
$630$		0			0
$631$	154.559			0.244943			0.122472	−	0.992472i	$-0.460918\pi$
$631$	154.559			0.244943			0.122472	+	0.992472i	$0.460918\pi$
$632$	−88.4689	+	330.170i	−0.139982	+	0.522421i
$633$	−891.715	−	53.5268i	−1.40871	−	0.0845606i
$634$	231.032	+	133.386i	0.364403	+	0.210388i
$635$		0			0
$636$	496.379	+	559.777i	0.780471	+	0.880153i
$637$	241.682	−	901.968i	0.379406	−	1.41596i
$638$	148.565	−	148.565i	0.232860	−	0.232860i
$639$	−538.341	+	717.776i	−0.842474	+	1.12328i
$640$		0			0
$641$	−302.816	−	524.493i	−0.472412	−	0.818242i	0.527089	−	0.849810i	$-0.323283\pi$
$641$	−302.816	−	524.493i	−0.472412	−	0.818242i	−0.999502	+	0.0315680i	$0.989950\pi$
$642$	−39.4616	−	26.0549i	−0.0614666	−	0.0405839i
$643$	120.761	+	450.687i	0.187809	+	0.700912i	0.994012	+	0.109273i	$0.0348523\pi$
$643$	120.761	+	450.687i	0.187809	+	0.700912i	−0.806203	+	0.591639i	$0.798481\pi$
$644$	7.71265	+	4.45290i	0.0119762	+	0.00691444i
$645$		0			0
$646$	57.5346	+	99.6529i	0.0890629	+	0.154261i
$647$	117.084	+	117.084i	0.180965	+	0.180965i	0.791776	−	0.610811i	$-0.209157\pi$
$647$	117.084	+	117.084i	0.180965	+	0.180965i	−0.610811	+	0.791776i	$0.709157\pi$
$648$	396.732	+	217.571i	0.612241	+	0.335757i
$649$		−	327.378i		−	0.504434i
$650$		0			0
$651$	−76.3392	+	229.015i	−0.117265	+	0.351789i
$652$	−660.778	+	177.055i	−1.01346	+	0.271557i
$653$	86.4506	+	322.638i	0.132390	+	0.494086i	0.999995	−	0.00316798i	$-0.00100840\pi$
$653$	86.4506	+	322.638i	0.132390	+	0.494086i	−0.867605	+	0.497254i	$0.834342\pi$
$654$	−52.0918	−	254.565i	−0.0796511	−	0.389242i
$655$		0			0
$656$	−392.156			−0.597799
$657$	40.2428	+	281.715i	0.0612524	+	0.428790i
$658$	−17.6599	+	17.6599i	−0.0268387	+	0.0268387i
$659$	1062.27	−	613.303i	1.61195	−	0.930657i	0.623027	−	0.782200i	$-0.285903\pi$
$659$	1062.27	−	613.303i	1.61195	−	0.930657i	0.988919	−	0.148457i	$-0.0474308\pi$
$660$		0			0
$661$	79.8777	−	138.352i	0.120844	−	0.209307i	−0.799257	−	0.600989i	$-0.794773\pi$
$661$	79.8777	−	138.352i	0.120844	−	0.209307i	0.920101	+	0.391682i	$0.128107\pi$
$662$	272.054	−	72.8967i	0.410958	−	0.110116i
$663$	870.622	+	52.2607i	1.31316	+	0.0788246i
$664$	−250.017	+	144.347i	−0.376532	+	0.217391i
$665$		0			0
$666$	37.2254	−	308.956i	0.0558940	−	0.463897i
$667$	23.6565	+	23.6565i	0.0354670	+	0.0354670i
$668$	−938.856	−	251.566i	−1.40547	−	0.376595i
$669$	−19.2257	−	93.9528i	−0.0287379	−	0.140438i
$670$		0			0
$671$	478.648	−	829.042i	0.713335	−	1.23553i
$672$	147.364	−	73.6815i	0.219292	−	0.109645i
$673$	45.9717	+	12.3181i	0.0683086	+	0.0183032i	0.292811	−	0.956170i	$-0.405409\pi$
$673$	45.9717	+	12.3181i	0.0683086	+	0.0183032i	−0.224503	+	0.974473i	$0.572076\pi$
$674$		−	111.675i		−	0.165690i
$675$		0			0
$676$	−863.996			−1.27810
$677$	−37.9504	+	141.633i	−0.0560567	+	0.209206i	−0.988274	−	0.152694i	$-0.951205\pi$
$677$	−37.9504	+	141.633i	−0.0560567	+	0.209206i	0.932217	+	0.361900i	$0.117872\pi$
$678$	−105.613	−	211.228i	−0.155771	−	0.311545i
$679$	−49.3279	−	28.4795i	−0.0726479	−	0.0419433i
$680$		0			0
$681$	1149.68	−	235.260i	1.68822	−	0.345462i
$682$	−97.9293	+	365.477i	−0.143591	+	0.535890i
$683$	−882.608	+	882.608i	−1.29225	+	1.29225i	−0.358860	+	0.933391i	$0.616835\pi$
$683$	−882.608	+	882.608i	−1.29225	+	1.29225i	−0.933391	+	0.358860i	$0.883165\pi$
$684$	131.215	+	307.187i	0.191834	+	0.449104i
$685$		0			0
$686$	−66.0754	−	114.446i	−0.0963198	−	0.166831i
$687$	−45.0890	+	751.148i	−0.0656318	+	1.09337i
$688$	20.4967	+	76.4948i	0.0297917	+	0.111184i
$689$	−1289.07	−	744.243i	−1.87092	−	1.08018i
$690$		0			0
$691$	253.832	+	439.650i	0.367340	+	0.636252i	0.989149	−	0.146917i	$-0.0469351\pi$
$691$	253.832	+	439.650i	0.367340	+	0.636252i	−0.621808	+	0.783169i	$0.713602\pi$
$692$	−753.047	−	753.047i	−1.08822	−	1.08822i
$693$	72.6473	−	180.987i	0.104830	−	0.261164i
$694$		−	181.421i		−	0.261413i
$695$		0			0
$696$	394.265	−	80.6788i	0.566473	−	0.115918i
$697$	−562.611	+	150.751i	−0.807189	+	0.216286i
$698$	−74.3597	−	277.514i	−0.106532	−	0.397585i
$699$	−962.302	−	320.771i	−1.37668	−	0.458900i
$700$		0			0
$701$	194.042			0.276807			0.138403	−	0.990376i	$-0.455803\pi$
$701$	194.042			0.276807			0.138403	+	0.990376i	$0.455803\pi$
$702$	−409.231	−	74.4103i	−0.582950	−	0.105998i
$703$	351.581	−	351.581i	0.500115	−	0.500115i
$704$	−161.459	+	93.2182i	−0.229345	+	0.132412i
$705$		0			0
$706$	−195.614	+	338.813i	−0.277073	+	0.479905i
$707$	−107.448	+	28.7907i	−0.151978	+	0.0407223i
$708$	159.642	−	241.787i	0.225483	−	0.341506i
$709$	−414.499	+	239.311i	−0.584625	+	0.337534i	−0.762969	−	0.646435i	$-0.776259\pi$
$709$	−414.499	+	239.311i	−0.584625	+	0.337534i	0.178344	+	0.983968i	$0.442926\pi$
$710$		0			0
$711$	−65.8781	+	546.761i	−0.0926555	+	0.769003i
$712$	449.958	+	449.958i	0.631963	+	0.631963i
$713$	−58.1962	−	15.5936i	−0.0816216	−	0.0218705i
$714$	44.4858	−	39.4475i	0.0623050	−	0.0552486i
$715$		0			0
$716$	260.906	−	451.902i	0.364393	−	0.631148i
$717$	7.02575	−	117.043i	0.00979881	−	0.163240i
$718$	−237.261	−	63.5739i	−0.330447	−	0.0885430i
$719$		−	443.536i		−	0.616879i	−0.951244	−	0.308439i	$-0.900193\pi$
$719$		−	443.536i		−	0.616879i	0.951244	−	0.308439i	$-0.0998067\pi$
$720$		0			0
$721$	94.1849			0.130631
$722$	−47.5005	+	177.274i	−0.0657902	+	0.245532i
$723$	138.363	−	209.558i	0.191373	−	0.289845i
$724$	143.106	+	82.6224i	0.197660	+	0.114119i
$725$		0			0
$726$	10.4245	−	31.2732i	0.0143588	−	0.0430760i
$727$	−75.0285	+	280.010i	−0.103203	+	0.385158i	−0.998135	−	0.0610438i	$-0.980557\pi$
$727$	−75.0285	+	280.010i	−0.103203	+	0.385158i	0.894932	+	0.446202i	$0.147224\pi$
$728$	−150.709	+	150.709i	−0.207018	+	0.207018i
$729$	682.338	+	256.623i	0.935992	+	0.352021i
$730$		0			0
$731$	58.8116	+	101.865i	0.0804536	+	0.139350i
$732$	757.781	−	378.887i	1.03522	−	0.517605i
$733$	−264.583	−	987.435i	−0.360958	−	1.34712i	−0.872818	−	0.488046i	$-0.837710\pi$
$733$	−264.583	−	987.435i	−0.360958	−	1.34712i	0.511859	−	0.859069i	$-0.328957\pi$
$734$	−340.177	−	196.401i	−0.463457	−	0.267577i
$735$		0			0
$736$	20.5601	+	35.6111i	0.0279349	+	0.0483847i
$737$	275.459	+	275.459i	0.373757	+	0.373757i
$738$	274.978	−	39.2805i	0.372599	−	0.0532256i
$739$			153.917i			0.208277i	0.994563	+	0.104138i	$0.0332085\pi$
$739$			153.917i			0.208277i	−0.994563	+	0.104138i	$0.966791\pi$
$740$		0			0
$741$	−440.926	−	497.241i	−0.595042	−	0.671041i
$742$	−98.0117	+	26.2622i	−0.132091	+	0.0353938i
$743$	−337.889	−	1261.02i	−0.454763	−	1.69720i	−0.688784	−	0.724966i	$-0.741855\pi$
$743$	−337.889	−	1261.02i	−0.454763	−	1.69720i	0.234021	−	0.972231i	$-0.424811\pi$
$744$	−542.254	+	480.841i	−0.728836	+	0.646291i
$745$		0			0
$746$	18.2489			0.0244623
$747$	−365.877	+	287.190i	−0.489795	+	0.384458i
$748$	−401.121	+	401.121i	−0.536258	+	0.536258i
$749$	−33.8088	+	19.5195i	−0.0451385	+	0.0260607i
$750$		0			0
$751$	−728.908	+	1262.51i	−0.970583	+	1.68110i	−0.276783	+	0.960933i	$0.589268\pi$
$751$	−728.908	+	1262.51i	−0.970583	+	1.68110i	−0.693801	+	0.720167i	$0.744065\pi$
$752$	164.737	−	44.1413i	0.219066	−	0.0586985i
$753$	−156.533	−	313.070i	−0.207880	−	0.415763i
$754$	−320.379	+	184.971i	−0.424905	+	0.245319i
$755$		0			0
$756$	141.910	−	98.2432i	0.187712	−	0.129951i
$757$	575.216	+	575.216i	0.759863	+	0.759863i	0.976297	−	0.216434i	$-0.0694426\pi$
$757$	575.216	+	575.216i	0.759863	+	0.759863i	−0.216434	+	0.976297i	$0.569443\pi$
$758$	−264.824	−	70.9594i	−0.349372	−	0.0936140i
$759$	46.1758	+	15.3921i	0.0608376	+	0.0202795i
$760$		0			0
$761$	−506.722	+	877.668i	−0.665863	+	1.15331i	0.313187	+	0.949691i	$0.398603\pi$
$761$	−506.722	+	877.668i	−0.665863	+	1.15331i	−0.979051	+	0.203618i	$0.934730\pi$
$762$	149.174	+	98.4935i	0.195766	+	0.129257i
$763$	−207.207	−	55.5211i	−0.271569	−	0.0727668i
$764$		−	1248.49i		−	1.63414i
$765$		0			0
$766$	−2.52556			−0.00329708
$767$	−149.193	+	556.794i	−0.194515	+	0.725938i
$768$	100.910	+	6.05728i	0.131393	+	0.00788709i
$769$	486.081	+	280.639i	0.632095	+	0.364940i	0.781563	−	0.623827i	$-0.214423\pi$
$769$	486.081	+	280.639i	0.632095	+	0.364940i	−0.149468	+	0.988767i	$0.547756\pi$
$770$		0			0
$771$	−9.52393	−	10.7403i	−0.0123527	−	0.0139304i
$772$	−10.6424	+	39.7180i	−0.0137855	+	0.0514482i
$773$	−445.834	+	445.834i	−0.576758	+	0.576758i	−0.934008	−	0.357251i	$-0.883714\pi$
$773$	−445.834	+	445.834i	−0.576758	+	0.576758i	0.357251	+	0.934008i	$0.383714\pi$
$774$	−22.0343	−	51.5847i	−0.0284681	−	0.0666469i
$775$		0			0
$776$	−85.5009	−	148.092i	−0.110182	−	0.190840i
$777$	−214.394	−	141.556i	−0.275926	−	0.182183i
$778$	−29.5938	−	110.446i	−0.0380383	−	0.141961i
$779$	384.353	+	221.906i	0.493393	+	0.284860i
$780$		0			0
$781$	580.499	+	1005.45i	0.743276	+	1.28739i
$782$	10.4929	+	10.4929i	0.0134180	+	0.0134180i
$783$	610.451	−	218.507i	0.779630	−	0.279064i
$784$			434.693i			0.554456i
$785$		0			0
$786$	3.30320	−	9.90946i	0.00420254	−	0.0126075i
$787$	−1353.23	+	362.598i	−1.71948	+	0.460734i	−0.977717	−	0.209925i	$-0.932678\pi$
$787$	−1353.23	+	362.598i	−1.71948	+	0.460734i	−0.741766	+	0.670659i	$0.766011\pi$
$788$	−57.0176	−	212.793i	−0.0723573	−	0.270041i
$789$	−58.8245	−	287.466i	−0.0745558	−	0.364343i
$790$		0			0
$791$	−194.967			−0.246482
$792$	460.560	−	361.511i	0.581515	−	0.456453i
$793$	−1191.88	+	1191.88i	−1.50300	+	1.50300i
$794$	−253.828	+	146.548i	−0.319683	+	0.184569i
$795$		0			0
$796$	29.2167	−	50.6049i	0.0367045	−	0.0635740i
$797$	−458.403	+	122.829i	−0.575160	+	0.154114i	−0.534662	−	0.845066i	$-0.679561\pi$
$797$	−458.403	+	122.829i	−0.575160	+	0.154114i	−0.0404981	+	0.999180i	$0.512894\pi$
$798$	−45.2225	−	2.71456i	−0.0566698	−	0.00340171i
$799$	219.374	−	126.655i	0.274560	−	0.158517i
$800$		0			0
$801$	820.177	+	615.142i	1.02394	+	0.767968i
$802$	−358.565	−	358.565i	−0.447088	−	0.447088i
$803$	355.688	+	95.3064i	0.442949	+	0.118688i
$804$	69.1175	+	337.766i	0.0859670	+	0.420107i
$805$		0			0
$806$	333.111	−	576.965i	0.413289	−	0.715837i
$807$	571.193	−	285.594i	0.707798	−	0.353895i
$808$	−322.581	−	86.4352i	−0.399234	−	0.106974i
$809$			806.321i			0.996689i	0.866979	+	0.498344i	$0.166059\pi$
$809$			806.321i			0.996689i	−0.866979	+	0.498344i	$0.833941\pi$
$810$		0			0
$811$	−928.637			−1.14505			−0.572526	−	0.819887i	$-0.694036\pi$
$811$	−928.637			−1.14505			−0.572526	+	0.819887i	$0.694036\pi$
$812$	39.7315	−	148.280i	0.0489304	−	0.182611i
$813$	−241.819	−	483.642i	−0.297440	−	0.594886i
$814$	−348.727	−	201.338i	−0.428412	−	0.247344i
$815$		0			0
$816$	−397.776	+	81.3974i	−0.487471	+	0.0997517i
$817$	23.1966	−	86.5709i	0.0283924	−	0.105962i
$818$	−230.158	+	230.158i	−0.281366	+	0.281366i
$819$	−206.036	+	274.710i	−0.251570	+	0.335422i
$820$		0			0
$821$	−259.589	−	449.622i	−0.316187	−	0.547652i	0.663502	−	0.748174i	$-0.269069\pi$
$821$	−259.589	−	449.622i	−0.316187	−	0.547652i	−0.979689	+	0.200523i	$0.935736\pi$
$822$	−0.321213	+	5.35116i	−0.000390770	+	0.00650993i
$823$	333.724	+	1245.48i	0.405497	+	1.51334i	0.803136	+	0.595795i	$0.203163\pi$
$823$	333.724	+	1245.48i	0.405497	+	1.51334i	−0.397639	+	0.917542i	$0.630170\pi$
$824$	244.879	+	141.381i	0.297183	+	0.171579i
$825$		0			0
$826$	19.6477	+	34.0307i	0.0237865	+	0.0411994i
$827$	380.149	+	380.149i	0.459672	+	0.459672i	0.898548	−	0.438876i	$-0.144623\pi$
$827$	380.149	+	380.149i	0.459672	+	0.459672i	−0.438876	+	0.898548i	$0.644623\pi$
$828$	26.5976	+	33.8850i	0.0321227	+	0.0409239i
$829$		−	511.167i		−	0.616606i	−0.951288	−	0.308303i	$-0.900239\pi$
$829$		−	511.167i		−	0.616606i	0.951288	−	0.308303i	$-0.0997611\pi$
$830$		0			0
$831$	961.890	−	196.833i	1.15751	−	0.236862i
$832$	317.086	−	84.9628i	0.381113	−	0.102119i
$833$	167.103	+	623.637i	0.200604	+	0.748664i
$834$	547.911	+	182.639i	0.656968	+	0.218992i
$835$		0			0
$836$	432.240			0.517034
$837$	−755.313	+	890.462i	−0.902405	+	1.06387i
$838$	265.524	−	265.524i	0.316855	−	0.316855i
$839$	889.044	−	513.290i	1.05965	−	0.611788i	0.134313	−	0.990939i	$-0.457117\pi$
$839$	889.044	−	513.290i	1.05965	−	0.611788i	0.925335	+	0.379151i	$0.123784\pi$
$840$		0			0
$841$	−132.163	+	228.913i	−0.157150	+	0.272192i
$842$	−21.8317	+	5.84978i	−0.0259284	+	0.00694749i
$843$	51.6905	−	78.2882i	0.0613173	−	0.0928686i
$844$	−885.970	+	511.515i	−1.04973	+	0.606061i
$845$		0			0
$846$	−111.092	+	47.4527i	−0.131314	+	0.0560906i
$847$	−19.2439	−	19.2439i	−0.0227200	−	0.0227200i
$848$	669.305	+	179.340i	0.789275	+	0.211486i
$849$	−455.061	+	403.523i	−0.535996	+	0.475292i
$850$		0			0
$851$	32.0597	−	55.5291i	0.0376730	−	0.0652516i
$852$	−61.5669	+	1025.66i	−0.0722616	+	1.20382i
$853$	1345.32	+	360.478i	1.57717	+	0.422600i	0.938047	−	0.346508i	$-0.112633\pi$
$853$	1345.32	+	360.478i	1.57717	+	0.422600i	0.639119	+	0.769108i	$0.279299\pi$
$854$			114.905i			0.134549i
$855$		0			0
$856$	−117.203			−0.136919
$857$	85.4914	−	319.058i	0.0997566	−	0.372297i	−0.897941	−	0.440116i	$-0.854937\pi$
$857$	85.4914	−	319.058i	0.0997566	−	0.372297i	0.997698	+	0.0678191i	$0.0216041\pi$
$858$	−296.556	+	449.151i	−0.345637	+	0.523486i
$859$	−264.795	−	152.879i	−0.308259	−	0.177974i	0.337888	−	0.941186i	$-0.390287\pi$
$859$	−264.795	−	152.879i	−0.308259	−	0.177974i	−0.646147	+	0.763213i	$0.723621\pi$
$860$		0			0
$861$	72.5180	−	217.551i	0.0842253	−	0.252673i
$862$	−100.283	+	374.262i	−0.116338	+	0.434178i
$863$	−386.017	+	386.017i	−0.447297	+	0.447297i	−0.894455	−	0.447158i	$-0.852436\pi$
$863$	−386.017	+	386.017i	−0.447297	+	0.447297i	0.447158	+	0.894455i	$0.352436\pi$
$864$	794.254	−	65.2230i	0.919275	−	0.0754895i
$865$		0			0
$866$	162.447	+	281.367i	0.187583	+	0.324904i
$867$	236.086	−	118.042i	0.272303	−	0.136150i
$868$	71.5518	+	267.035i	0.0824329	+	0.307644i
$869$	617.145	+	356.309i	0.710179	+	0.410022i
$870$		0			0
$871$	−342.961	−	594.025i	−0.393755	−	0.682004i
$872$	−455.392	−	455.392i	−0.522238	−	0.522238i
$873$	−170.111	−	216.719i	−0.194857	−	0.248246i
$874$		−	11.3069i		−	0.0129370i
$875$		0			0
$876$	216.221	+	243.836i	0.246827	+	0.278352i
$877$	403.592	−	108.142i	0.460196	−	0.123309i	−0.0212701	−	0.999774i	$-0.506771\pi$
$877$	403.592	−	108.142i	0.460196	−	0.123309i	0.481466	+	0.876465i	$0.340104\pi$
$878$	98.2488	+	366.669i	0.111901	+	0.417619i
$879$	87.5366	−	77.6226i	0.0995865	−	0.0883078i
$880$		0			0
$881$	−1495.93			−1.69799			−0.848993	−	0.528403i	$-0.822791\pi$
$881$	−1495.93			−1.69799			−0.848993	+	0.528403i	$0.822791\pi$
$882$	−43.5413	−	304.805i	−0.0493665	−	0.345584i
$883$	158.383	−	158.383i	0.179369	−	0.179369i	−0.611712	−	0.791081i	$-0.709519\pi$
$883$	158.383	−	158.383i	0.179369	−	0.179369i	0.791081	+	0.611712i	$0.209519\pi$
$884$	865.014	−	499.416i	0.978522	−	0.564950i
$885$		0			0
$886$	75.9157	−	131.490i	0.0856837	−	0.148408i
$887$	1325.65	−	355.206i	1.49453	−	0.400458i	0.583266	−	0.812281i	$-0.301775\pi$
$887$	1325.65	−	355.206i	1.49453	−	0.400458i	0.911264	+	0.411823i	$0.135108\pi$
$888$	−344.931	−	689.869i	−0.388436	−	0.776879i
$889$	127.805	−	73.7883i	0.143763	−	0.0830014i
$890$		0			0
$891$	652.204	−	681.524i	0.731991	−	0.764898i
$892$	−77.6576	−	77.6576i	−0.0870601	−	0.0870601i
$893$	−186.437	−	49.9557i	−0.208776	−	0.0559415i
$894$	−201.451	−	67.1513i	−0.225337	−	0.0751133i
$895$		0			0
$896$	121.028	−	209.626i	0.135076	−	0.233958i
$897$	−71.5199	−	47.2217i	−0.0797324	−	0.0526440i
$898$	105.286	+	28.2113i	0.117245	+	0.0314157i
$899$			1038.52i			1.15520i
$900$		0			0
$901$	1029.17			1.14225
$902$	93.0274	−	347.183i	0.103135	−	0.384903i
$903$	−46.2262	−	2.77482i	−0.0511918	−	0.00307288i
$904$	−506.909	−	292.664i	−0.560741	−	0.323744i
$905$		0			0
$906$	−42.0111	−	47.3767i	−0.0463698	−	0.0522922i
$907$	143.552	−	535.743i	0.158271	−	0.590676i	−0.840532	−	0.541762i	$-0.817757\pi$
$907$	143.552	−	535.743i	0.158271	−	0.590676i	0.998803	−	0.0489140i	$-0.0155760\pi$
$908$	950.276	−	950.276i	1.04656	−	1.04656i
$909$	−534.193	−	64.3637i	−0.587671	−	0.0708072i
$910$		0			0
$911$	−484.409	−	839.021i	−0.531733	−	0.920989i	−0.999314	−	0.0370382i	$-0.988208\pi$
$911$	−484.409	−	839.021i	−0.531733	−	0.920989i	0.467581	−	0.883950i	$-0.345126\pi$
$912$	258.175	+	170.462i	0.283086	+	0.186910i
$913$	155.775	+	581.361i	0.170619	+	0.636759i
$914$	−192.995	−	111.426i	−0.211154	−	0.121910i
$915$		0			0
$916$	430.882	+	746.309i	0.470395	+	0.814748i
$917$	−6.09776	−	6.09776i	−0.00664968	−	0.00664968i
$918$	270.766	−	96.9190i	0.294952	−	0.105576i
$919$		−	600.903i		−	0.653866i	−0.945048	−	0.326933i	$-0.893985\pi$
$919$		−	600.903i		−	0.653866i	0.945048	−	0.326933i	$-0.106015\pi$
$920$		0			0
$921$	−38.1512	+	114.452i	−0.0414237	+	0.124270i
$922$	−207.604	+	55.6275i	−0.225168	+	0.0603335i
$923$	−529.090	−	1974.59i	−0.573229	−	2.13932i
$924$	−44.7745	−	218.806i	−0.0484572	−	0.236803i
$925$		0			0
$926$	187.992			0.203015
$927$	422.780	+	169.702i	0.456074	+	0.183066i
$928$	501.193	−	501.193i	0.540079	−	0.540079i
$929$	−435.996	+	251.722i	−0.469318	+	0.270961i	−0.715954	−	0.698147i	$-0.754008\pi$
$929$	−435.996	+	251.722i	−0.469318	+	0.270961i	0.246636	+	0.969108i	$0.420675\pi$
$930$		0			0
$931$	245.976	−	426.044i	0.264207	−	0.457619i
$932$	−1122.06	+	300.655i	−1.20393	+	0.322591i
$933$	−1293.39	−	77.6380i	−1.38627	−	0.0832133i
$934$	−65.6305	+	37.8918i	−0.0702682	+	0.0405694i
$935$		0			0
$936$	−948.056	+	404.960i	−1.01288	+	0.432650i
$937$	−1181.10	−	1181.10i	−1.26051	−	1.26051i	−0.950847	−	0.309660i	$-0.899785\pi$
$937$	−1181.10	−	1181.10i	−1.26051	−	1.26051i	−0.309660	−	0.950847i	$-0.600215\pi$
$938$	−45.1656	−	12.1021i	−0.0481509	−	0.0129020i
$939$	124.770	+	609.730i	0.132875	+	0.649339i
$940$		0			0
$941$	−576.616	+	998.729i	−0.612770	+	1.06135i	0.378002	+	0.925805i	$0.376611\pi$
$941$	−576.616	+	998.729i	−0.612770	+	1.06135i	−0.990771	+	0.135543i	$0.956722\pi$
$942$	−77.7795	+	38.8894i	−0.0825684	+	0.0412838i
$943$	55.2832	+	14.8131i	0.0586248	+	0.0157085i
$944$		−	268.341i		−	0.284259i
$945$		0			0
$946$	−72.5844			−0.0767277
$947$	354.616	−	1323.45i	0.374463	−	1.39751i	−0.479665	−	0.877451i	$-0.659242\pi$
$947$	354.616	−	1323.45i	0.374463	−	1.39751i	0.854128	−	0.520063i	$-0.174091\pi$
$948$	282.046	+	564.098i	0.297517	+	0.595040i
$949$	−561.512	−	324.189i	−0.591688	−	0.341611i
$950$		0			0
$951$	1043.67	−	213.566i	1.09744	−	0.224570i
$952$	38.1409	−	142.344i	0.0400640	−	0.149521i
$953$	−77.4456	+	77.4456i	−0.0812650	+	0.0812650i	−0.746571	−	0.665306i	$-0.768301\pi$
$953$	−77.4456	+	77.4456i	−0.0812650	+	0.0812650i	0.665306	+	0.746571i	$0.268301\pi$
$954$	−487.278	−	58.7110i	−0.510773	−	0.0615420i
$955$		0			0
$956$	−67.1397	−	116.289i	−0.0702298	−	0.121642i
$957$	50.2716	−	837.486i	0.0525304	−	0.875116i
$958$	38.1245	+	142.282i	0.0397959	+	0.148520i
$959$	3.83279	+	2.21286i	0.00399666	+	0.00230747i
$960$		0			0
$961$	−454.630	−	787.443i	−0.473080	−	0.819399i
$962$	501.352	+	501.352i	0.521156	+	0.521156i
$963$	−186.932	+	26.7032i	−0.194114	+	0.0277292i
$964$		−	287.577i		−	0.298316i
$965$		0			0
$966$	−5.72371	+	1.17125i	−0.00592517	+	0.00121247i
$967$	1559.00	−	417.733i	1.61220	−	0.431989i	0.663505	−	0.748172i	$-0.269068\pi$
$967$	1559.00	−	417.733i	1.61220	−	0.431989i	0.948698	+	0.316183i	$0.102401\pi$
$968$	−21.1467	−	78.9205i	−0.0218458	−	0.0815295i
$969$	435.921	+	145.309i	0.449867	+	0.149958i
$970$		0			0
$971$	158.612			0.163349			0.0816745	−	0.996659i	$-0.473973\pi$
$971$	158.612			0.163349			0.0816745	+	0.996659i	$0.473973\pi$
$972$	814.026	−	185.304i	0.837475	−	0.190642i
$973$	337.156	−	337.156i	0.346511	−	0.346511i
$974$	607.386	−	350.674i	0.623599	−	0.360035i
$975$		0			0
$976$	392.332	−	679.539i	0.401980	−	0.696249i
$977$	10.6944	−	2.86555i	0.0109461	−	0.00293301i	−0.253342	−	0.967377i	$-0.581530\pi$
$977$	10.6944	−	2.86555i	0.0109461	−	0.00293301i	0.264288	+	0.964444i	$0.414863\pi$
$978$	247.269	−	374.503i	0.252831	−	0.382927i
$979$	1148.89	−	663.315i	1.17354	−	0.677543i
$980$		0			0
$981$	−830.082	−	622.571i	−0.846159	−	0.634629i
$982$	418.604	+	418.604i	0.426277	+	0.426277i
$983$	1101.63	+	295.182i	1.12069	+	0.300287i	0.771161	−	0.636640i	$-0.219676\pi$
$983$	1101.63	+	295.182i	1.12069	+	0.300287i	0.349525	+	0.936927i	$0.386343\pi$
$984$	515.111	−	456.772i	0.523486	−	0.464199i
$985$		0			0
$986$	127.892	−	221.516i	0.129708	−	0.224661i
$987$	−5.97578	+	99.5518i	−0.00605449	+	0.100863i
$988$	−735.142	−	196.981i	−0.744071	−	0.199373i
$989$		−	11.5579i		−	0.0116864i
$990$		0			0
$991$	−95.8581			−0.0967287			−0.0483643	−	0.998830i	$-0.515401\pi$
$991$	−95.8581			−0.0967287			−0.0483643	+	0.998830i	$0.515401\pi$
$992$	−330.371	+	1232.96i	−0.333036	+	1.24291i
$993$	619.706	−	938.579i	0.624074	−	0.945195i
$994$	−120.685	−	69.6776i	−0.121414	−	0.0700982i
$995$		0			0
$996$	−168.445	+	505.329i	−0.169122	+	0.507359i
$997$	−227.782	+	850.093i	−0.228467	+	0.852651i	0.752518	+	0.658571i	$0.228839\pi$
$997$	−227.782	+	850.093i	−0.228467	+	0.852651i	−0.980986	+	0.194080i	$0.937828\pi$
$998$	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	225.3.o.b.157.5		40
5.2	odd	4		45.3.k.a.13.5	yes	40
5.3	odd	4	inner	225.3.o.b.193.6		40
5.4	even	2		45.3.k.a.22.6	yes	40
9.7	even	3	inner	225.3.o.b.7.6		40
15.2	even	4		135.3.l.a.118.6		40
15.14	odd	2		135.3.l.a.37.5		40
45.2	even	12		135.3.l.a.73.5		40
45.4	even	6		405.3.g.h.82.6		20
45.7	odd	12		45.3.k.a.43.6	yes	40
45.14	odd	6		405.3.g.g.82.5		20
45.22	odd	12		405.3.g.h.163.6		20
45.29	odd	6		135.3.l.a.127.6		40
45.32	even	12		405.3.g.g.163.5		20
45.34	even	6		45.3.k.a.7.5	✓	40
45.43	odd	12	inner	225.3.o.b.43.5		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.3.k.a.7.5	✓	40	45.34	even	6
45.3.k.a.13.5	yes	40	5.2	odd	4
45.3.k.a.22.6	yes	40	5.4	even	2
45.3.k.a.43.6	yes	40	45.7	odd	12
135.3.l.a.37.5		40	15.14	odd	2
135.3.l.a.73.5		40	45.2	even	12
135.3.l.a.118.6		40	15.2	even	4
135.3.l.a.127.6		40	45.29	odd	6
225.3.o.b.7.6		40	9.7	even	3	inner
225.3.o.b.43.5		40	45.43	odd	12	inner
225.3.o.b.157.5		40	1.1	even	1	trivial
225.3.o.b.193.6		40	5.3	odd	4	inner
405.3.g.g.82.5		20	45.14	odd	6
405.3.g.g.163.5		20	45.32	even	12
405.3.g.h.82.6		20	45.4	even	6
405.3.g.h.163.6		20	45.22	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:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	225.o (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.194442 + 0.725667i) q^{2} +(1.34163 + 2.68329i) q^{3} +(2.97532 + 1.71780i) q^{4} +(-2.20804 + 0.451834i) q^{6} +(-0.481578 + 1.79727i) q^{7} +(-3.94998 + 3.94998i) q^{8} +(-5.40005 + 7.19996i) q^{9} +(5.82294 + 10.0856i) q^{11} +(-0.617573 + 10.2883i) q^{12} +(-5.30726 - 19.8070i) q^{13} +(-1.21058 - 0.698930i) q^{14} +(4.77288 + 8.26686i) q^{16} +(10.0254 + 10.0254i) q^{17} +(-4.17477 - 5.31861i) q^{18} -10.8032i q^{19} +(-5.46870 + 1.11907i) q^{21} +(-8.45102 + 2.26444i) q^{22} +(-0.360576 - 1.34569i) q^{23} +(-15.8983 - 5.29951i) q^{24} +15.4052 q^{26} +(-26.5644 - 4.83020i) q^{27} +(-4.52021 + 4.52021i) q^{28} +(-20.7968 + 12.0070i) q^{29} +(21.6233 - 37.4526i) q^{31} +(-28.5101 + 7.63926i) q^{32} +(-19.2504 + 29.1558i) q^{33} +(-9.22442 + 5.32572i) q^{34} +(-28.4350 + 12.1460i) q^{36} +(32.5443 + 32.5443i) q^{37} +(7.83949 + 2.10058i) q^{38} +(46.0274 - 40.8145i) q^{39} +(-20.5409 + 35.5778i) q^{41} +(0.251275 - 4.18605i) q^{42} +(8.01349 + 2.14721i) q^{43} +40.0106i q^{44} +1.04663 q^{46} +(4.62418 - 17.2577i) q^{47} +(-15.7789 + 23.8981i) q^{48} +(39.4370 + 22.7689i) q^{49} +(-13.4506 + 40.3513i) q^{51} +(18.2336 - 68.0488i) q^{52} +(51.3281 - 51.3281i) q^{53} +(8.67035 - 18.3377i) q^{54} +(-5.19697 - 9.00141i) q^{56} +(28.9880 - 14.4938i) q^{57} +(-4.66933 - 17.4262i) q^{58} +(-24.3449 - 14.0555i) q^{59} +(-41.1002 - 71.1876i) q^{61} +(22.9736 + 22.9736i) q^{62} +(-10.3398 - 13.1727i) q^{63} +16.0088i q^{64} +(-17.4143 - 19.6385i) q^{66} +(32.3105 - 8.65757i) q^{67} +(12.6071 + 47.0502i) q^{68} +(3.12710 - 2.77294i) q^{69} +99.6917 q^{71} +(-7.10958 - 49.7697i) q^{72} +(22.3583 - 22.3583i) q^{73} +(-29.9443 + 17.2883i) q^{74} +(18.5577 - 32.1428i) q^{76} +(-20.9308 + 5.60840i) q^{77} +(20.6681 + 41.3366i) q^{78} +(52.9926 - 30.5953i) q^{79} +(-22.6788 - 77.7603i) q^{81} +(-21.8237 - 21.8237i) q^{82} +(49.9199 + 13.3760i) q^{83} +(-18.1935 - 6.06456i) q^{84} +(-3.11631 + 5.39761i) q^{86} +(-60.1198 - 39.6947i) q^{87} +(-62.8384 - 16.8375i) q^{88} -113.914i q^{89} +38.1544 q^{91} +(1.23879 - 4.62324i) q^{92} +(129.506 + 7.77386i) q^{93} +(11.6242 + 6.71123i) q^{94} +(-58.7483 - 66.2517i) q^{96} +(-7.92297 + 29.5689i) q^{97} +(-24.1909 + 24.1909i) q^{98} +(-104.060 - 12.5380i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 2 q^{2} + 6 q^{3} - 24 q^{6} + 2 q^{7} + 24 q^{8} + 8 q^{11} + 30 q^{12} + 2 q^{13} + 28 q^{16} - 28 q^{17} - 48 q^{18} + 12 q^{21} - 14 q^{22} - 82 q^{23} - 112 q^{26} + 198 q^{27} + 88 q^{28} - 4 q^{31}+ \cdots + 1876 q^{98}+O(q^{100}) \) 40 * q + 2 * q^2 + 6 * q^3 - 24 * q^6 + 2 * q^7 + 24 * q^8 + 8 * q^11 + 30 * q^12 + 2 * q^13 + 28 * q^16 - 28 * q^17 - 48 * q^18 + 12 * q^21 - 14 * q^22 - 82 * q^23 - 112 * q^26 + 198 * q^27 + 88 * q^28 - 4 * q^31 + 14 * q^32 - 96 * q^33 + 264 * q^36 + 92 * q^37 - 330 * q^38 - 28 * q^41 - 498 * q^42 + 2 * q^43 - 136 * q^46 - 64 * q^47 + 510 * q^48 - 396 * q^51 + 74 * q^52 + 608 * q^53 - 192 * q^56 + 114 * q^57 - 30 * q^58 + 92 * q^61 + 100 * q^62 - 24 * q^63 + 588 * q^66 + 80 * q^67 - 626 * q^68 + 248 * q^71 + 162 * q^72 + 8 * q^73 - 96 * q^76 - 338 * q^77 - 1062 * q^78 + 204 * q^81 - 104 * q^82 - 370 * q^83 - 328 * q^86 - 534 * q^87 + 210 * q^88 + 152 * q^91 - 388 * q^92 + 1062 * q^93 - 876 * q^96 - 292 * q^97 + 1876 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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