LMFDB - Embedded newform 441.3.l.b.97.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [441,3,Mod(97,441)] 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("441.97"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(441, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4, 3])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	441.l (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [28,1,0,-23,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$12.0163796583$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			97.4
Character	$\chi$	$=$	441.97
Dual form			441.3.l.b.391.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.12025 + 1.94033i) q^{2} +(-1.02718 - 2.81867i) q^{3} +(-0.509909 - 0.883189i) q^{4} +(1.67528 - 0.967222i) q^{5} +(6.61983 + 1.16455i) q^{6} -6.67708 q^{8} +(-6.88982 + 5.79054i) q^{9} +4.33411i q^{10} +(0.186168 - 0.322453i) q^{11} +(-1.96565 + 2.34446i) q^{12} +(5.01827 - 2.89730i) q^{13} +(-4.44709 - 3.72855i) q^{15} +(9.51962 - 16.4885i) q^{16} -11.5075i q^{17} +(-3.51724 - 19.8553i) q^{18} +21.0528i q^{19} +(-1.70848 - 0.986391i) q^{20} +(0.417109 + 0.722455i) q^{22} +(-13.6417 - 23.6282i) q^{23} +(6.85854 + 18.8205i) q^{24} +(-10.6290 + 18.4099i) q^{25} +12.9828i q^{26} +(23.3987 + 13.4722i) q^{27} +(-20.1404 + 34.8842i) q^{29} +(12.2164 - 4.45190i) q^{30} +(-42.2746 + 24.4073i) q^{31} +(7.97450 + 13.8122i) q^{32} +(-1.10012 - 0.193531i) q^{33} +(22.3282 + 12.8912i) q^{34} +(8.62732 + 3.13236i) q^{36} -29.5383 q^{37} +(-40.8493 - 23.5844i) q^{38} +(-13.3212 - 11.1688i) q^{39} +(-11.1860 + 6.45822i) q^{40} +(19.6397 - 11.3390i) q^{41} +(10.7407 - 18.6035i) q^{43} -0.379716 q^{44} +(-5.94161 + 16.3648i) q^{45} +61.1285 q^{46} +(-46.1622 - 26.6518i) q^{47} +(-56.2539 - 9.89612i) q^{48} +(-23.8141 - 41.2473i) q^{50} +(-32.4358 + 11.8202i) q^{51} +(-5.11773 - 2.95472i) q^{52} -87.4600 q^{53} +(-52.3528 + 30.3089i) q^{54} -0.720265i q^{55} +(59.3409 - 21.6249i) q^{57} +(-45.1245 - 78.1579i) q^{58} +(-7.99438 + 4.61556i) q^{59} +(-1.02540 + 5.82884i) q^{60} +(-61.0848 - 35.2673i) q^{61} -109.369i q^{62} +40.4233 q^{64} +(5.60467 - 9.70757i) q^{65} +(1.60792 - 1.91778i) q^{66} +(37.7720 + 65.4230i) q^{67} +(-10.1633 + 5.86777i) q^{68} +(-52.5876 + 62.7219i) q^{69} -97.4729 q^{71} +(46.0039 - 38.6639i) q^{72} +86.9800i q^{73} +(33.0902 - 57.3139i) q^{74} +(62.8093 + 11.0493i) q^{75} +(18.5936 - 10.7350i) q^{76} +(36.5942 - 13.3356i) q^{78} +(23.5997 - 40.8759i) q^{79} -36.8303i q^{80} +(13.9392 - 79.7916i) q^{81} +50.8098i q^{82} +(-81.1770 - 46.8676i) q^{83} +(-11.1303 - 19.2782i) q^{85} +(24.0646 + 41.6810i) q^{86} +(119.015 + 20.9370i) q^{87} +(-1.24306 + 2.15305i) q^{88} -29.6531i q^{89} +(-25.0969 - 29.8612i) q^{90} +(-13.9121 + 24.0965i) q^{92} +(112.220 + 94.0877i) q^{93} +(103.426 - 59.7132i) q^{94} +(20.3627 + 35.2693i) q^{95} +(30.7410 - 36.6651i) q^{96} +(122.538 + 70.7471i) q^{97} +(0.584513 + 3.29966i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + q^{2} - 23 q^{4} + 3 q^{5} - 12 q^{6} - 16 q^{8} + 6 q^{9} + 7 q^{11} + 27 q^{12} - 15 q^{13} - 18 q^{15} - 27 q^{16} + 9 q^{18} - 108 q^{20} - 10 q^{22} + 34 q^{23} + 120 q^{24} + 31 q^{25} + 81 q^{27}+ \cdots - 162 q^{99}+O(q^{100}) $ 28 * q + q^2 - 23 * q^4 + 3 * q^5 - 12 * q^6 - 16 * q^8 + 6 * q^9 + 7 * q^11 + 27 * q^12 - 15 * q^13 - 18 * q^15 - 27 * q^16 + 9 * q^18 - 108 * q^20 - 10 * q^22 + 34 * q^23 + 120 * q^24 + 31 * q^25 + 81 * q^27 + 70 * q^29 + 33 * q^30 + 45 * q^31 + 153 * q^32 - 111 * q^33 - 12 * q^34 - 174 * q^36 - 18 * q^37 - 87 * q^38 - 9 * q^39 + 102 * q^40 + 234 * q^41 + 30 * q^43 - 102 * q^44 + 3 * q^45 + 44 * q^46 - 111 * q^47 - 147 * q^48 + 241 * q^50 - 6 * q^51 + 219 * q^52 - 296 * q^53 + 207 * q^54 + 189 * q^57 + 17 * q^58 + 42 * q^59 - 489 * q^60 + 120 * q^61 - 48 * q^64 + 114 * q^65 - 705 * q^66 - 34 * q^67 + 18 * q^68 - 78 * q^69 - 350 * q^71 + 177 * q^72 + 359 * q^74 + 387 * q^75 - 72 * q^76 - 375 * q^78 - 82 * q^79 + 438 * q^81 - 738 * q^83 + 3 * q^85 + 17 * q^86 + 564 * q^87 + 25 * q^88 + 543 * q^90 + 288 * q^92 - 30 * q^93 - 3 * q^94 + 507 * q^95 - 813 * q^96 + 57 * q^97 - 162 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.12025	+	1.94033i	−0.560124	+	0.970163i	0.437361	+	0.899286i	$0.355913\pi$
$2$	−1.12025	+	1.94033i	−0.560124	+	0.970163i	−0.997485	+	0.0708770i	$0.977420\pi$
$3$	−1.02718	−	2.81867i	−0.342392	−	0.939557i
$3$	−1.02718	−	2.81867i	−0.342392	−	0.939557i
$4$	−0.509909	−	0.883189i	−0.127477	−	0.220797i
$5$	1.67528	−	0.967222i	0.335055	−	0.193444i	−0.323028	−	0.946389i	$-0.604701\pi$
$5$	1.67528	−	0.967222i	0.335055	−	0.193444i	0.658083	+	0.752945i	$0.271367\pi$
$6$	6.61983	+	1.16455i	1.10331	+	0.194092i
$7$		0			0
$7$		0			0
$8$	−6.67708			−0.834635
$9$	−6.88982	+	5.79054i	−0.765535	+	0.643394i
$10$			4.33411i			0.433411i
$11$	0.186168	−	0.322453i	0.0169244	−	0.0293139i	−0.857439	−	0.514585i	$-0.827946\pi$
$11$	0.186168	−	0.322453i	0.0169244	−	0.0293139i	0.874364	+	0.485271i	$0.161279\pi$
$12$	−1.96565	+	2.34446i	−0.163804	+	0.195371i
$13$	5.01827	−	2.89730i	0.386021	−	0.222869i	−0.294414	−	0.955678i	$-0.595124\pi$
$13$	5.01827	−	2.89730i	0.386021	−	0.222869i	0.680435	+	0.732809i	$0.261791\pi$
$14$		0			0
$15$	−4.44709	−	3.72855i	−0.296472	−	0.248570i
$16$	9.51962	−	16.4885i	0.594976	−	1.03053i
$17$		−	11.5075i		−	0.676910i	−0.940983	−	0.338455i	$-0.890096\pi$
$17$		−	11.5075i		−	0.676910i	0.940983	−	0.338455i	$-0.109904\pi$
$18$	−3.51724	−	19.8553i	−0.195402	−	1.10307i
$19$			21.0528i			1.10804i	0.832503	+	0.554021i	$0.186907\pi$
$19$			21.0528i			1.10804i	−0.832503	+	0.554021i	$0.813093\pi$
$20$	−1.70848	−	0.986391i	−0.0854239	−	0.0493195i
$21$		0			0
$22$	0.417109	+	0.722455i	0.0189595	+	0.0328389i
$23$	−13.6417	−	23.6282i	−0.593119	−	1.02731i	−0.993809	−	0.111099i	$-0.964563\pi$
$23$	−13.6417	−	23.6282i	−0.593119	−	1.02731i	0.400690	−	0.916214i	$-0.368770\pi$
$24$	6.85854	+	18.8205i	0.285773	+	0.784188i
$25$	−10.6290	+	18.4099i	−0.425159	+	0.736396i
$26$			12.9828i			0.499338i
$27$	23.3987	+	13.4722i	0.866619	+	0.498971i
$28$		0			0
$29$	−20.1404	+	34.8842i	−0.694497	+	1.20290i	0.275853	+	0.961200i	$0.411040\pi$
$29$	−20.1404	+	34.8842i	−0.694497	+	1.20290i	−0.970350	+	0.241704i	$0.922294\pi$
$30$	12.2164	−	4.45190i	0.407215	−	0.148397i
$31$	−42.2746	+	24.4073i	−1.36370	+	0.787331i	−0.990114	−	0.140265i	$-0.955205\pi$
$31$	−42.2746	+	24.4073i	−1.36370	+	0.787331i	−0.373584	+	0.927596i	$0.621871\pi$
$32$	7.97450	+	13.8122i	0.249203	+	0.431633i
$33$	−1.10012	−	0.193531i	−0.0333369	−	0.00586459i
$34$	22.3282	+	12.8912i	0.656713	+	0.379154i
$35$		0			0
$36$	8.62732	+	3.13236i	0.239648	+	0.0870099i
$37$	−29.5383			−0.798332			−0.399166	−	0.916879i	$-0.630700\pi$
$37$	−29.5383			−0.798332			−0.399166	+	0.916879i	$0.630700\pi$
$38$	−40.8493	−	23.5844i	−1.07498	−	0.620641i
$39$	−13.3212	−	11.1688i	−0.341569	−	0.286380i
$40$	−11.1860	+	6.45822i	−0.279649	+	0.161455i
$41$	19.6397	−	11.3390i	0.479016	−	0.276560i	−0.240990	−	0.970528i	$-0.577472\pi$
$41$	19.6397	−	11.3390i	0.479016	−	0.276560i	0.720006	+	0.693968i	$0.244139\pi$
$42$		0			0
$43$	10.7407	−	18.6035i	0.249785	−	0.432639i	−0.713681	−	0.700470i	$-0.752974\pi$
$43$	10.7407	−	18.6035i	0.249785	−	0.432639i	0.963466	+	0.267831i	$0.0863069\pi$
$44$	−0.379716			−0.00862991
$45$	−5.94161	+	16.3648i	−0.132036	+	0.363661i
$46$	61.1285			1.32888
$47$	−46.1622	−	26.6518i	−0.982175	−	0.567059i	−0.0792489	−	0.996855i	$-0.525252\pi$
$47$	−46.1622	−	26.6518i	−0.982175	−	0.567059i	−0.902926	+	0.429796i	$0.858586\pi$
$48$	−56.2539	−	9.89612i	−1.17196	−	0.206169i
$49$		0			0
$50$	−23.8141	−	41.2473i	−0.476283	−	0.824946i
$51$	−32.4358	+	11.8202i	−0.635996	+	0.231769i
$52$	−5.11773	−	2.95472i	−0.0984178	−	0.0568216i
$53$	−87.4600			−1.65019			−0.825094	−	0.564995i	$-0.808878\pi$
$53$	−87.4600			−1.65019			−0.825094	+	0.564995i	$0.808878\pi$
$54$	−52.3528	+	30.3089i	−0.969497	+	0.561275i
$55$		−	0.720265i		−	0.0130957i
$56$		0			0
$57$	59.3409	−	21.6249i	1.04107	−	0.379385i
$58$	−45.1245	−	78.1579i	−0.778008	−	1.34755i
$59$	−7.99438	+	4.61556i	−0.135498	+	0.0782298i	−0.566217	−	0.824256i	$-0.691593\pi$
$59$	−7.99438	+	4.61556i	−0.135498	+	0.0782298i	0.430719	+	0.902486i	$0.358260\pi$
$60$	−1.02540	+	5.82884i	−0.0170900	+	0.0971473i
$61$	−61.0848	−	35.2673i	−1.00139	−	0.578153i	−0.0927306	−	0.995691i	$-0.529560\pi$
$61$	−61.0848	−	35.2673i	−1.00139	−	0.578153i	−0.908659	+	0.417539i	$0.862893\pi$
$62$		−	109.369i		−	1.76401i
$63$		0			0
$64$	40.4233			0.631614
$65$	5.60467	−	9.70757i	0.0862256	−	0.149347i
$66$	1.60792	−	1.91778i	0.0243624	−	0.0290573i
$67$	37.7720	+	65.4230i	0.563761	+	0.976463i	0.997164	+	0.0752625i	$0.0239795\pi$
$67$	37.7720	+	65.4230i	0.563761	+	0.976463i	−0.433403	+	0.901200i	$0.642687\pi$
$68$	−10.1633	+	5.86777i	−0.149460	+	0.0862907i
$69$	−52.5876	+	62.7219i	−0.762139	+	0.909013i
$70$		0			0
$71$	−97.4729			−1.37286			−0.686429	−	0.727197i	$-0.740823\pi$
$71$	−97.4729			−1.37286			−0.686429	+	0.727197i	$0.740823\pi$
$72$	46.0039	−	38.6639i	0.638943	−	0.536999i
$73$			86.9800i			1.19151i	0.803167	+	0.595754i	$0.203146\pi$
$73$			86.9800i			1.19151i	−0.803167	+	0.595754i	$0.796854\pi$
$74$	33.0902	−	57.3139i	0.447165	−	0.774512i
$75$	62.8093	+	11.0493i	0.837457	+	0.147325i
$76$	18.5936	−	10.7350i	0.244653	−	0.141250i
$77$		0			0
$78$	36.5942	−	13.3356i	0.469156	−	0.170969i
$79$	23.5997	−	40.8759i	0.298730	−	0.517416i	−0.677115	−	0.735877i	$-0.736770\pi$
$79$	23.5997	−	40.8759i	0.298730	−	0.517416i	0.975846	+	0.218461i	$0.0701036\pi$
$80$		−	36.8303i		−	0.460379i
$81$	13.9392	−	79.7916i	0.172089	−	0.985081i
$82$			50.8098i			0.619631i
$83$	−81.1770	−	46.8676i	−0.978036	−	0.564669i	−0.0763594	−	0.997080i	$-0.524330\pi$
$83$	−81.1770	−	46.8676i	−0.978036	−	0.564669i	−0.901677	+	0.432411i	$0.857663\pi$
$84$		0			0
$85$	−11.1303	−	19.2782i	−0.130944	−	0.226802i
$86$	24.0646	+	41.6810i	0.279821	+	0.484663i
$87$	119.015	+	20.9370i	1.36799	+	0.240655i
$88$	−1.24306	+	2.15305i	−0.0141257	+	0.0244664i
$89$		−	29.6531i		−	0.333181i	−0.986026	−	0.166590i	$-0.946724\pi$
$89$		−	29.6531i		−	0.333181i	0.986026	−	0.166590i	$-0.0532758\pi$
$90$	−25.0969	−	29.8612i	−0.278854	−	0.331792i
$91$		0			0
$92$	−13.9121	+	24.0965i	−0.151218	+	0.261918i
$93$	112.220	+	94.0877i	1.20666	+	1.01170i
$94$	103.426	−	59.7132i	1.10028	−	0.635246i
$95$	20.3627	+	35.2693i	0.214345	+	0.371256i
$96$	30.7410	−	36.6651i	0.320218	−	0.381928i
$97$	122.538	+	70.7471i	1.26327	+	0.729351i	0.973706	−	0.227806i	$-0.0731553\pi$
$97$	122.538	+	70.7471i	1.26327	+	0.729351i	0.289567	+	0.957158i	$0.406489\pi$
$98$		0			0
$99$	0.584513	+	3.29966i	0.00590417	+	0.0333299i
$100$	21.6792			0.216792
$101$	−40.6345	−	23.4603i	−0.402321	−	0.232280i	0.285164	−	0.958479i	$-0.407952\pi$
$101$	−40.6345	−	23.4603i	−0.402321	−	0.232280i	−0.687485	+	0.726198i	$0.741285\pi$
$102$	13.4011	−	76.1775i	0.131383	−	0.746839i
$103$	113.923	−	65.7733i	1.10605	−	0.638576i	0.168244	−	0.985745i	$-0.446190\pi$
$103$	113.923	−	65.7733i	1.10605	−	0.638576i	0.937802	+	0.347169i	$0.112857\pi$
$104$	−33.5074	+	19.3455i	−0.322187	+	0.186015i
$105$		0			0
$106$	97.9768	−	169.701i	0.924310	−	1.60095i
$107$	−139.917			−1.30764			−0.653819	−	0.756651i	$-0.726834\pi$
$107$	−139.917			−1.30764			−0.653819	+	0.756651i	$0.726834\pi$
$108$	−0.0326989	−	27.5351i	−0.000302768	−	0.254954i
$109$	−111.084			−1.01912			−0.509560	−	0.860435i	$-0.670192\pi$
$109$	−111.084			−1.01912			−0.509560	+	0.860435i	$0.670192\pi$
$110$	1.39755	+	0.806875i	0.0127050	+	0.00733522i
$111$	30.3410	+	83.2587i	0.273343	+	0.750079i
$112$		0			0
$113$	50.7636	+	87.9252i	0.449236	+	0.778099i	0.998336	−	0.0576571i	$-0.0183630\pi$
$113$	50.7636	+	87.9252i	0.449236	+	0.778099i	−0.549101	+	0.835756i	$0.685030\pi$
$114$	−24.5171	+	139.366i	−0.215062	+	1.22251i
$115$	−45.7074	−	26.3892i	−0.397456	−	0.229471i
$116$	41.0791			0.354130
$117$	−17.7980	+	49.0204i	−0.152120	+	0.418978i
$118$		−	20.6823i		−	0.175273i
$119$		0			0
$120$	29.6936	+	24.8958i	0.247446	+	0.207465i
$121$	60.4307	+	104.669i	0.499427	+	0.865033i
$122$	136.860	−	79.0162i	1.12180	−	0.647674i
$123$	−52.1342	−	43.7106i	−0.423855	−	0.355371i
$124$	43.1125	+	24.8910i	0.347681	+	0.200734i
$125$			89.4834i			0.715867i
$126$		0			0
$127$	−49.1014			−0.386625			−0.193312	−	0.981137i	$-0.561923\pi$
$127$	−49.1014			−0.386625			−0.193312	+	0.981137i	$0.561923\pi$
$128$	−77.1821	+	133.683i	−0.602985	+	1.04440i
$129$	−63.4698	−	11.1655i	−0.492014	−	0.0865545i
$130$	12.5572	+	21.7498i	0.0965941	+	0.167306i
$131$	107.596	−	62.1204i	0.821341	−	0.474202i	−0.0295376	−	0.999564i	$-0.509403\pi$
$131$	107.596	−	62.1204i	0.821341	−	0.474202i	0.850879	+	0.525362i	$0.176070\pi$
$132$	0.390035	+	1.07029i	0.00295481	+	0.00810829i
$133$		0			0
$134$	−169.256			−1.26310
$135$	52.2299	−	0.0620250i	0.386888	−	0.000459444i
$136$			76.8364i			0.564973i
$137$	−2.31536	+	4.01032i	−0.0169004	+	0.0292724i	−0.874352	−	0.485292i	$-0.838713\pi$
$137$	−2.31536	+	4.01032i	−0.0169004	+	0.0292724i	0.857452	+	0.514565i	$0.172046\pi$
$138$	−62.7897	−	172.301i	−0.454998	−	1.24856i
$139$	37.7043	−	21.7686i	0.271254	−	0.156608i	−0.358204	−	0.933644i	$-0.616611\pi$
$139$	37.7043	−	21.7686i	0.271254	−	0.156608i	0.629457	+	0.777035i	$0.283277\pi$
$140$		0			0
$141$	−27.7058	+	157.492i	−0.196495	+	1.11697i
$142$	109.194	−	189.129i	0.768970	−	1.33190i
$143$		−	2.15754i		−	0.0150877i
$144$	29.8888	+	168.726i	0.207561	+	1.17171i
$145$			77.9210i			0.537386i
$146$	−168.770	−	97.4391i	−1.15596	−	0.667391i
$147$		0			0
$148$	15.0618	+	26.0879i	0.101769	+	0.176269i
$149$	13.1304	+	22.7425i	0.0881232	+	0.152634i	0.906718	−	0.421738i	$-0.138580\pi$
$149$	13.1304	+	22.7425i	0.0881232	+	0.152634i	−0.818595	+	0.574372i	$0.805246\pi$
$150$	−91.8013	+	109.492i	−0.612009	+	0.729950i
$151$	−59.9365	+	103.813i	−0.396931	+	0.687504i	−0.993346	−	0.115172i	$-0.963258\pi$
$151$	−59.9365	+	103.813i	−0.396931	+	0.687504i	0.596415	+	0.802676i	$0.296591\pi$
$152$		−	140.571i		−	0.924811i
$153$	66.6345	+	79.2844i	0.435520	+	0.518199i
$154$		0			0
$155$	−47.2145	+	81.7779i	−0.304610	+	0.527599i
$156$	−3.07158	+	17.4602i	−0.0196896	+	0.111924i
$157$	169.702	−	97.9773i	1.08090	−	0.624059i	0.149763	−	0.988722i	$-0.452149\pi$
$157$	169.702	−	97.9773i	1.08090	−	0.624059i	0.931140	+	0.364663i	$0.118816\pi$
$158$	52.8750	+	91.5822i	0.334652	+	0.579634i
$159$	89.8368	+	246.521i	0.565011	+	1.55045i
$160$	26.7190	+	15.4262i	0.166994	+	0.0964139i
$161$		0			0
$162$	139.206	+	116.433i	0.859299	+	0.718722i
$163$	−83.6836			−0.513396			−0.256698	−	0.966492i	$-0.582635\pi$
$163$	−83.6836			−0.513396			−0.256698	+	0.966492i	$0.582635\pi$
$164$	−20.0289	−	11.5637i	−0.122127	−	0.0705102i
$165$	−2.03019	+	0.739839i	−0.0123042	+	0.00448387i
$166$	181.877	−	105.007i	1.09564	−	0.632569i
$167$	215.835	−	124.612i	1.29242	−	0.746181i	0.313340	−	0.949641i	$-0.398552\pi$
$167$	215.835	−	124.612i	1.29242	−	0.746181i	0.979083	+	0.203460i	$0.0652188\pi$
$168$		0			0
$169$	−67.7113	+	117.279i	−0.400659	+	0.693961i
$170$	49.8747			0.293380
$171$	−121.907	−	145.050i	−0.712908	−	0.848246i
$172$	−21.9072			−0.127367
$173$	241.148	+	139.227i	1.39392	+	0.804779i	0.993746	−	0.111661i	$-0.0356172\pi$
$173$	241.148	+	139.227i	1.39392	+	0.804779i	0.400171	+	0.916440i	$0.368951\pi$
$174$	−173.951	+	207.473i	−0.999716	+	1.19237i
$175$		0			0
$176$	−3.54451	−	6.13926i	−0.0201392	−	0.0348822i
$177$	21.2214	+	17.7925i	0.119895	+	0.100523i
$178$	57.5367	+	33.2188i	0.323240	+	0.186623i
$179$	257.515			1.43863			0.719317	−	0.694682i	$-0.244455\pi$
$179$	257.515			1.43863			0.719317	+	0.694682i	$0.244455\pi$
$180$	17.4828	−	3.09697i	0.0971269	−	0.0172054i
$181$			29.2542i			0.161625i	0.996729	+	0.0808126i	$0.0257515\pi$
$181$			29.2542i			0.161625i	−0.996729	+	0.0808126i	$0.974248\pi$
$182$		0			0
$183$	−36.6621	+	208.404i	−0.200340	+	1.13882i
$184$	91.0870	+	157.767i	0.495038	+	0.857431i
$185$	−49.4848	+	28.5701i	−0.267486	+	0.154433i
$186$	−308.275	+	112.341i	−1.65739	+	0.603984i
$187$	−3.71062	−	2.14233i	−0.0198429	−	0.0114563i
$188$			54.3599i			0.289149i
$189$		0			0
$190$	−91.2452			−0.480238
$191$	30.3852	−	52.6287i	0.159085	−	0.275543i	−0.775454	−	0.631404i	$-0.782479\pi$
$191$	30.3852	−	52.6287i	0.159085	−	0.275543i	0.934539	+	0.355861i	$0.115812\pi$
$192$	−41.5219	−	113.940i	−0.216260	−	0.593438i
$193$	−12.4384	−	21.5439i	−0.0644474	−	0.111626i	0.832001	−	0.554774i	$-0.187195\pi$
$193$	−12.4384	−	21.5439i	−0.0644474	−	0.111626i	−0.896449	+	0.443147i	$0.853862\pi$
$194$	−274.545	+	158.508i	−1.41518	+	0.817054i
$195$	−33.1194	−	5.82633i	−0.169843	−	0.0298786i
$196$		0			0
$197$	174.320			0.884873			0.442437	−	0.896800i	$-0.354114\pi$
$197$	174.320			0.884873			0.442437	+	0.896800i	$0.354114\pi$
$198$	−7.05721	−	2.56229i	−0.0356425	−	0.0129409i
$199$		−	288.937i		−	1.45194i	−0.687724	−	0.725972i	$-0.741390\pi$
$199$		−	288.937i		−	1.45194i	0.687724	−	0.725972i	$-0.258610\pi$
$200$	70.9705	−	122.924i	0.354852	−	0.614622i
$201$	145.607	−	173.668i	0.724415	−	0.864019i
$202$	91.0413	−	52.5627i	0.450699	−	0.260211i
$203$		0			0
$204$	26.9788	+	22.6197i	0.132249	+	0.110881i
$205$	21.9346	−	37.9918i	0.106998	−	0.185326i
$206$			294.730i			1.43073i
$207$	230.809	+	83.8008i	1.11502	+	0.404835i
$208$		−	110.325i		−	0.530408i
$209$	6.78854	+	3.91937i	0.0324811	+	0.0187530i
$210$		0			0
$211$	−149.601	−	259.116i	−0.709009	−	1.22804i	−0.965225	−	0.261419i	$-0.915809\pi$
$211$	−149.601	−	259.116i	−0.709009	−	1.22804i	0.256217	−	0.966619i	$-0.417524\pi$
$212$	44.5967	+	77.2437i	0.210362	+	0.364357i
$213$	100.122	+	274.744i	0.470055	+	1.28988i
$214$	156.742	−	271.485i	0.732439	−	1.26862i
$215$		−	41.5547i		−	0.193278i
$216$	−156.235	−	89.9551i	−0.723310	−	0.416459i
$217$		0			0
$218$	124.442	−	215.539i	0.570833	−	0.988712i
$219$	245.168	−	89.3438i	1.11949	−	0.407963i
$220$	−0.636130	+	0.367270i	−0.00289150	+	0.00166941i
$221$	−33.3406	−	57.7477i	−0.150863	−	0.261302i
$222$	−195.539	−	34.3989i	−0.880804	−	0.154950i
$223$	14.0772	+	8.12745i	0.0631263	+	0.0364460i	0.531231	−	0.847227i	$-0.321730\pi$
$223$	14.0772	+	8.12745i	0.0631263	+	0.0364460i	−0.468105	+	0.883673i	$0.655063\pi$
$224$		0			0
$225$	−33.3718	−	188.388i	−0.148319	−	0.837282i
$226$	−227.471			−1.00651
$227$	26.4526	+	15.2724i	0.116531	+	0.0672793i	0.557133	−	0.830423i	$-0.311901\pi$
$227$	26.4526	+	15.2724i	0.116531	+	0.0672793i	−0.440602	+	0.897703i	$0.645235\pi$
$228$	−49.3574	−	41.3825i	−0.216480	−	0.181502i
$229$	−158.134	+	91.2986i	−0.690541	+	0.398684i	−0.803815	−	0.594880i	$-0.797200\pi$
$229$	−158.134	+	91.2986i	−0.690541	+	0.398684i	0.113274	+	0.993564i	$0.463866\pi$
$230$	102.407	−	59.1248i	0.445249	−	0.257064i
$231$		0			0
$232$	134.479	−	232.925i	0.579652	−	1.00399i
$233$	−349.796			−1.50127			−0.750635	−	0.660717i	$-0.770252\pi$
$233$	−349.796			−1.50127			−0.750635	+	0.660717i	$0.770252\pi$
$234$	−75.1774	−	89.4490i	−0.321271	−	0.382261i
$235$	−103.113			−0.438777
$236$	8.15281	+	4.70703i	0.0345458	+	0.0199450i
$237$	−139.457	−	24.5331i	−0.588425	−	0.103515i
$238$		0			0
$239$	49.6154	+	85.9365i	0.207596	+	0.359567i	0.950957	−	0.309324i	$-0.100103\pi$
$239$	49.6154	+	85.9365i	0.207596	+	0.359567i	−0.743361	+	0.668891i	$0.766769\pi$
$240$	−103.813	+	37.8313i	−0.432553	+	0.157630i
$241$	−243.343	−	140.494i	−1.00972	−	0.582964i	−0.0986123	−	0.995126i	$-0.531440\pi$
$241$	−243.343	−	140.494i	−1.00972	−	0.582964i	−0.911110	+	0.412162i	$0.864774\pi$
$242$	−270.789			−1.11896
$243$	−239.224	+	42.6701i	−0.984462	+	0.175597i
$244$			71.9325i			0.294805i
$245$		0			0
$246$	143.216	−	52.1906i	0.582179	−	0.212157i
$247$	60.9963	+	105.649i	0.246949	+	0.427728i
$248$	282.271	−	162.969i	1.13819	−	0.657135i
$249$	−48.7212	+	276.952i	−0.195667	+	1.11226i
$250$	−173.627	−	100.244i	−0.694507	−	0.400974i
$251$		−	16.5983i		−	0.0661286i	−0.999453	−	0.0330643i	$-0.989473\pi$
$251$		−	16.5983i		−	0.0661286i	0.999453	−	0.0330643i	$-0.0105266\pi$
$252$		0			0
$253$	−10.1586			−0.0401527
$254$	55.0057	−	95.2726i	0.216558	−	0.375089i
$255$	−42.9062	+	51.1747i	−0.168260	+	0.200685i
$256$	−92.0795	−	159.486i	−0.359686	−	0.622994i
$257$	−73.7864	+	42.6006i	−0.287106	+	0.165761i	−0.636636	−	0.771164i	$-0.719675\pi$
$257$	−73.7864	+	42.6006i	−0.287106	+	0.165761i	0.349530	+	0.936925i	$0.386341\pi$
$258$	92.7666	−	110.644i	0.359561	−	0.428852i
$259$		0			0
$260$	−11.4315			−0.0439672
$261$	−63.2348	−	356.970i	−0.242279	−	1.36770i
$262$			278.361i			1.06245i
$263$	178.327	−	308.872i	0.678050	−	1.17442i	−0.297517	−	0.954717i	$-0.596158\pi$
$263$	178.327	−	308.872i	0.678050	−	1.17442i	0.975567	−	0.219701i	$-0.0705082\pi$
$264$	7.34557	+	1.29222i	0.0278241	+	0.00489479i
$265$	−146.520	+	84.5932i	−0.552905	+	0.319220i
$266$		0			0
$267$	−83.5824	+	30.4590i	−0.313043	+	0.114079i
$268$	38.5206	−	66.7196i	0.143733	−	0.248954i
$269$			385.092i			1.43157i	0.698321	+	0.715785i	$0.253931\pi$
$269$			385.092i			1.43157i	−0.698321	+	0.715785i	$0.746069\pi$
$270$	−58.3901	+	101.413i	−0.216260	+	0.375602i
$271$			62.3003i			0.229890i	0.993372	+	0.114945i	$0.0366692\pi$
$271$			62.3003i			0.229890i	−0.993372	+	0.114945i	$0.963331\pi$
$272$	−189.741	−	109.547i	−0.697576	−	0.402746i
$273$		0			0
$274$	−5.18755	−	8.98509i	−0.0189327	−	0.0327923i
$275$	3.95755	+	6.85469i	0.0143911	+	0.0249261i
$276$	82.2102	+	14.4623i	0.297863	+	0.0523997i
$277$	−42.5057	+	73.6221i	−0.153450	+	0.265784i	−0.932494	−	0.361186i	$-0.882372\pi$
$277$	−42.5057	+	73.6221i	−0.153450	+	0.265784i	0.779043	+	0.626970i	$0.215705\pi$
$278$			97.5447i			0.350880i
$279$	149.933	−	412.955i	0.537395	−	1.48012i
$280$		0			0
$281$	73.8831	−	127.969i	0.262929	−	0.455407i	−0.704090	−	0.710111i	$-0.748645\pi$
$281$	73.8831	−	127.969i	0.262929	−	0.455407i	0.967019	+	0.254704i	$0.0819781\pi$
$282$	−274.549	−	230.189i	−0.973577	−	0.816272i
$283$	303.815	−	175.408i	1.07355	−	0.619815i	0.144402	−	0.989519i	$-0.453874\pi$
$283$	303.815	−	175.408i	1.07355	−	0.619815i	0.929150	+	0.369704i	$0.120541\pi$
$284$	49.7023	+	86.0869i	0.175008	+	0.303123i
$285$	78.4964	−	93.6236i	0.275426	−	0.328504i
$286$	4.18634	+	2.41698i	0.0146375	+	0.00845099i
$287$		0			0
$288$	−134.923	−	48.9871i	−0.468484	−	0.170094i
$289$	156.578			0.541793
$290$	−151.192	−	87.2908i	−0.521352	−	0.301003i
$291$	73.5451	−	418.063i	0.252732	−	1.43664i
$292$	76.8198	−	44.3519i	0.263081	−	0.151890i
$293$	−42.7689	+	24.6927i	−0.145969	+	0.0842753i	−0.571206	−	0.820807i	$-0.693524\pi$
$293$	−42.7689	+	24.6927i	−0.145969	+	0.0842753i	0.425237	+	0.905082i	$0.360191\pi$
$294$		0			0
$295$	−8.92853	+	15.4647i	−0.0302662	+	0.0524226i
$296$	197.230			0.666316
$297$	8.70026	−	5.03688i	0.0292938	−	0.0169592i
$298$	−58.8370			−0.197440
$299$	−136.916	−	79.0484i	−0.457913	−	0.264376i
$300$	−22.2684	−	61.1066i	−0.0742280	−	0.203689i
$301$		0			0
$302$	−134.288	−	232.593i	−0.444661	−	0.770175i
$303$	−24.3882	+	138.633i	−0.0804890	+	0.457535i
$304$	347.129	+	200.415i	1.14187	+	0.659259i
$305$	−136.445			−0.447362
$306$	−228.485	+	40.4746i	−0.746682	+	0.132270i
$307$		−	432.680i		−	1.40938i	−0.709515	−	0.704691i	$-0.751086\pi$
$307$		−	432.680i		−	1.40938i	0.709515	−	0.704691i	$-0.248914\pi$
$308$		0			0
$309$	−302.412	−	253.550i	−0.978680	−	0.820550i
$310$	−105.784	−	183.223i	−0.341238	−	0.591042i
$311$	−144.790	+	83.5947i	−0.465563	+	0.268793i	−0.714381	−	0.699757i	$-0.753291\pi$
$311$	−144.790	+	83.5947i	−0.465563	+	0.268793i	0.248817	+	0.968550i	$0.419958\pi$
$312$	88.9467	+	74.5752i	0.285086	+	0.239023i
$313$	−223.941	−	129.293i	−0.715467	−	0.413075i	0.0976148	−	0.995224i	$-0.468879\pi$
$313$	−223.941	−	129.293i	−0.715467	−	0.413075i	−0.813082	+	0.582149i	$0.802212\pi$
$314$			439.035i			1.39820i
$315$		0			0
$316$	−48.1348			−0.152325
$317$	101.257	−	175.382i	0.319422	−	0.553255i	−0.660946	−	0.750434i	$-0.729845\pi$
$317$	101.257	−	175.382i	0.319422	−	0.553255i	0.980368	+	0.197179i	$0.0631780\pi$
$318$	−578.970	−	101.852i	−1.82066	−	0.320289i
$319$	7.49902	+	12.9887i	0.0235079	+	0.0407169i
$320$	67.7203	−	39.0983i	0.211626	−	0.122182i
$321$	143.720	+	394.381i	0.447725	+	1.22860i
$322$		0			0
$323$	242.265			0.750045
$324$	−77.5787	+	28.3755i	−0.239441	+	0.0875788i
$325$			123.181i			0.379019i
$326$	93.7463	−	162.373i	0.287565	−	0.498078i
$327$	114.103	+	313.109i	0.348938	+	0.957521i
$328$	−131.136	+	75.7112i	−0.399804	+	0.230827i
$329$		0			0
$330$	0.838787	−	4.76803i	0.00254178	−	0.0144486i
$331$	−17.0781	+	29.5802i	−0.0515956	+	0.0893662i	−0.890670	−	0.454651i	$-0.849764\pi$
$331$	−17.0781	+	29.5802i	−0.0515956	+	0.0893662i	0.839074	+	0.544017i	$0.183097\pi$
$332$			95.5928i			0.287930i
$333$	203.513	−	171.043i	0.611152	−	0.513642i
$334$			558.386i			1.67181i
$335$	126.557	+	73.0678i	0.377783	+	0.218113i
$336$		0			0
$337$	205.854	+	356.550i	0.610844	+	1.05801i	0.991099	+	0.133130i	$0.0425029\pi$
$337$	205.854	+	356.550i	0.610844	+	1.05801i	−0.380255	+	0.924882i	$0.624164\pi$
$338$	−151.707	−	262.764i	−0.448837	−	0.777408i
$339$	195.689	−	233.401i	0.577254	−	0.688498i
$340$	−11.3509	+	19.6603i	−0.0333849	+	0.0578243i
$341$			18.1755i			0.0533005i
$342$	418.010	−	74.0478i	1.22225	−	0.216514i
$343$		0			0
$344$	−71.7168	+	124.217i	−0.208479	+	0.361096i
$345$	−27.4329	+	155.940i	−0.0795155	+	0.452001i
$346$	−540.290	+	311.937i	−1.56153	+	0.901551i
$347$	298.744	+	517.439i	0.860933	+	1.49118i	0.871029	+	0.491231i	$0.163453\pi$
$347$	298.744	+	517.439i	0.860933	+	1.49118i	−0.0100965	+	0.999949i	$0.503214\pi$
$348$	−42.1955	−	115.789i	−0.121251	−	0.332726i
$349$	−72.8266	−	42.0465i	−0.208672	−	0.120477i	0.392022	−	0.919956i	$-0.371776\pi$
$349$	−72.8266	−	42.0465i	−0.208672	−	0.120477i	−0.600694	+	0.799479i	$0.705109\pi$
$350$		0			0
$351$	156.454	−	0.185795i	0.445738	−	0.000529331i
$352$	5.93840			0.0168705
$353$	−397.017	−	229.218i	−1.12469	−	0.649343i	−0.182099	−	0.983280i	$-0.558289\pi$
$353$	−397.017	−	229.218i	−1.12469	−	0.649343i	−0.942595	+	0.333937i	$0.891623\pi$
$354$	−58.2965	+	21.2443i	−0.164679	+	0.0600122i
$355$	−163.294	+	94.2779i	−0.459983	+	0.265572i
$356$	−26.1893	+	15.1204i	−0.0735654	+	0.0424730i
$357$		0			0
$358$	−288.481	+	499.664i	−0.805813	+	1.39571i
$359$	−12.8552			−0.0358083			−0.0179041	−	0.999840i	$-0.505699\pi$
$359$	−12.8552			−0.0358083			−0.0179041	+	0.999840i	$0.505699\pi$
$360$	39.6726	−	109.269i	0.110202	−	0.303524i
$361$	−82.2206			−0.227758
$362$	−56.7626	−	32.7719i	−0.156803	−	0.0905302i
$363$	232.955	−	277.848i	0.641748	−	0.765421i
$364$		0			0
$365$	84.1290	+	145.716i	0.230490	+	0.399221i
$366$	−363.300	−	304.600i	−0.992624	−	0.832241i
$367$	−535.505	−	309.174i	−1.45914	−	0.842436i	−0.460173	−	0.887829i	$-0.652213\pi$
$367$	−535.505	−	309.174i	−1.45914	−	0.842436i	−0.998969	+	0.0453934i	$0.985546\pi$
$368$	−519.457			−1.41157
$369$	−69.6549	+	191.848i	−0.188767	+	0.519912i
$370$		−	128.022i		−	0.346006i
$371$		0			0
$372$	25.8754	−	147.087i	0.0695576	−	0.395396i
$373$	−0.289633	−	0.501659i	−0.000776495	−	0.00134493i	0.865637	−	0.500672i	$-0.166914\pi$
$373$	−0.289633	−	0.501659i	−0.000776495	−	0.00134493i	−0.866413	+	0.499327i	$0.833580\pi$
$374$	8.31363	−	4.79988i	0.0222290	−	0.0128339i
$375$	252.224	−	91.9152i	0.672598	−	0.245107i
$376$	308.229	+	177.956i	0.819758	+	0.473287i
$377$			233.411i			0.619128i
$378$		0			0
$379$	18.5015			0.0488165			0.0244083	−	0.999702i	$-0.492230\pi$
$379$	18.5015			0.0488165			0.0244083	+	0.999702i	$0.492230\pi$
$380$	20.7663	−	35.9683i	0.0546481	−	0.0946533i
$381$	50.4358	+	138.401i	0.132377	+	0.363256i
$382$	68.0779	+	117.914i	0.178214	+	0.308676i
$383$	−49.0332	+	28.3093i	−0.128024	+	0.0739147i	−0.562644	−	0.826699i	$-0.690216\pi$
$383$	−49.0332	+	28.3093i	−0.128024	+	0.0739147i	0.434620	+	0.900614i	$0.356883\pi$
$384$	456.089	+	80.2347i	1.18773	+	0.208944i
$385$		0			0
$386$	55.7361			0.144394
$387$	33.7227	+	190.369i	0.0871387	+	0.491911i
$388$		−	144.298i		−	0.371903i
$389$	−206.783	+	358.158i	−0.531575	+	0.920715i	0.467746	+	0.883863i	$0.345066\pi$
$389$	−206.783	+	358.158i	−0.531575	+	0.920715i	−0.999321	+	0.0368521i	$0.988267\pi$
$390$	48.4069	−	57.7355i	0.124120	−	0.148040i
$391$	−271.901	+	156.982i	−0.695398	+	0.401488i
$392$		0			0
$393$	−285.617	−	239.468i	−0.726760	−	0.609334i
$394$	−195.282	+	338.238i	−0.495639	+	0.858471i
$395$		−	91.3046i		−	0.231151i
$396$	2.61617	−	2.19876i	0.00660650	−	0.00555243i
$397$		−	624.119i		−	1.57209i	−0.618171	−	0.786044i	$-0.712126\pi$
$397$		−	624.119i		−	1.57209i	0.618171	−	0.786044i	$-0.287874\pi$
$398$	560.632	+	323.681i	1.40862	+	0.813269i
$399$		0			0
$400$	202.367	+	350.511i	0.505919	+	0.876277i
$401$	−63.4372	−	109.876i	−0.158198	−	0.274006i	0.776021	−	0.630707i	$-0.217235\pi$
$401$	−63.4372	−	109.876i	−0.158198	−	0.274006i	−0.934219	+	0.356701i	$0.883902\pi$
$402$	173.856	+	477.077i	0.432477	+	1.18676i
$403$	−141.430	+	244.965i	−0.350944	+	0.607853i
$404$			47.8505i			0.118442i
$405$	−53.8242	−	147.155i	−0.132899	−	0.363347i
$406$		0			0
$407$	−5.49910	+	9.52472i	−0.0135113	+	0.0234023i
$408$	216.576	−	78.9245i	0.530825	−	0.193442i
$409$	−374.582	+	216.265i	−0.915848	+	0.528765i	−0.882308	−	0.470672i	$-0.844011\pi$
$409$	−374.582	+	216.265i	−0.915848	+	0.528765i	−0.0335397	+	0.999437i	$0.510678\pi$
$410$	49.1443	+	85.1205i	0.119864	+	0.207611i
$411$	13.6820	+	2.40693i	0.0332896	+	0.00585628i
$412$	−116.181	−	67.0769i	−0.281992	−	0.162808i
$413$		0			0
$414$	−421.164	+	353.967i	−1.01730	+	0.854993i
$415$	−181.325			−0.436928
$416$	80.0365	+	46.2091i	0.192395	+	0.111080i
$417$	−100.087	−	83.9158i	−0.240018	−	0.201237i
$418$	−15.2097	+	8.78132i	−0.0363868	+	0.0210080i
$419$	−150.801	+	87.0648i	−0.359906	+	0.207792i	−0.669040	−	0.743227i	$-0.733294\pi$
$419$	−150.801	+	87.0648i	−0.359906	+	0.207792i	0.309134	+	0.951019i	$0.399961\pi$
$420$		0			0
$421$	−175.470	+	303.923i	−0.416793	+	0.721907i	−0.995615	−	0.0935470i	$-0.970179\pi$
$421$	−175.470	+	303.923i	−0.416793	+	0.721907i	0.578822	+	0.815454i	$0.303513\pi$
$422$	670.360			1.58853
$423$	472.378	−	83.6786i	1.11673	−	0.197822i
$424$	583.978			1.37731
$425$	211.852	+	122.313i	0.498474	+	0.287794i
$426$	−645.254	−	113.512i	−1.51468	−	0.266461i
$427$		0			0
$428$	71.3451	+	123.573i	0.166694	+	0.288723i
$429$	−6.08141	+	2.21618i	−0.0141758	+	0.00516592i
$430$	80.6296	+	46.5515i	0.187511	+	0.108259i
$431$	−735.675			−1.70690			−0.853451	−	0.521173i	$-0.825495\pi$
$431$	−735.675			−1.70690			−0.853451	+	0.521173i	$0.825495\pi$
$432$	444.883	−	257.558i	1.02982	−	0.596200i
$433$			134.778i			0.311266i	0.987815	+	0.155633i	$0.0497417\pi$
$433$			134.778i			0.311266i	−0.987815	+	0.155633i	$0.950258\pi$
$434$		0			0
$435$	219.634	−	80.0386i	0.504905	−	0.183997i
$436$	56.6427	+	98.1081i	0.129915	+	0.225019i
$437$	497.439	−	287.197i	1.13831	−	0.657201i
$438$	−101.293	+	575.793i	−0.231262	+	1.31460i
$439$	5.06360	+	2.92347i	0.0115344	+	0.00665939i	0.505756	−	0.862677i	$-0.331214\pi$
$439$	5.06360	+	2.92347i	0.0115344	+	0.00665939i	−0.494222	+	0.869336i	$0.664547\pi$
$440$			4.80927i			0.0109302i
$441$		0			0
$442$	149.399			0.338007
$443$	80.1590	−	138.839i	0.180946	−	0.313407i	−0.761257	−	0.648450i	$-0.775417\pi$
$443$	80.1590	−	138.839i	0.180946	−	0.313407i	0.942203	+	0.335043i	$0.108751\pi$
$444$	58.0620	−	69.2513i	0.130770	−	0.155971i
$445$	−28.6811	−	49.6772i	−0.0644520	−	0.111634i
$446$	−31.5398	+	18.2095i	−0.0707170	+	0.0408285i
$447$	50.6163	−	60.3707i	0.113236	−	0.135057i
$448$		0			0
$449$	46.7901			0.104209			0.0521047	−	0.998642i	$-0.483407\pi$
$449$	46.7901			0.104209			0.0521047	+	0.998642i	$0.483407\pi$
$450$	402.919	+	146.290i	0.895377	+	0.325088i
$451$		−	8.44382i		−	0.0187224i
$452$	51.7697	−	89.6677i	0.114535	−	0.198380i
$453$	354.181	+	62.3070i	0.781855	+	0.137543i
$454$	−59.2669	+	34.2177i	−0.130544	+	0.0753695i
$455$		0			0
$456$	−396.224	+	144.392i	−0.868913	+	0.316648i
$457$	−277.170	+	480.073i	−0.606499	+	1.05049i	0.385314	+	0.922786i	$0.374093\pi$
$457$	−277.170	+	480.073i	−0.606499	+	1.05049i	−0.991813	+	0.127702i	$0.959240\pi$
$458$		−	409.108i		−	0.893250i
$459$	155.031	−	269.260i	0.337759	−	0.586623i
$460$			53.8243i			0.117009i
$461$	−117.654	−	67.9273i	−0.255214	−	0.147348i	0.366935	−	0.930246i	$-0.380407\pi$
$461$	−117.654	−	67.9273i	−0.255214	−	0.147348i	−0.622149	+	0.782899i	$0.713740\pi$
$462$		0			0
$463$	0.952160	+	1.64919i	0.00205650	+	0.00356196i	0.867052	−	0.498218i	$-0.166012\pi$
$463$	0.952160	+	1.64919i	0.00205650	+	0.00356196i	−0.864995	+	0.501780i	$0.832679\pi$
$464$	383.458	+	664.169i	0.826418	+	1.43140i
$465$	279.003	+	49.0818i	0.600006	+	0.105552i
$466$	391.858	−	678.718i	0.840897	−	1.45648i
$467$		−	103.146i		−	0.220869i	−0.993883	−	0.110435i	$-0.964776\pi$
$467$		−	103.146i		−	0.220869i	0.993883	−	0.110435i	$-0.0352243\pi$
$468$	52.3697	−	9.27694i	0.111901	−	0.0198225i
$469$		0			0
$470$	115.512	−	200.072i	0.245770	−	0.425686i
$471$	−450.479	−	377.693i	−0.956432	−	0.801897i
$472$	53.3791	−	30.8184i	0.113091	−	0.0652933i
$473$	−3.99917	−	6.92677i	−0.00845491	−	0.0146443i
$474$	203.828	−	243.108i	0.430017	−	0.512887i
$475$	−387.580	−	223.769i	−0.815958	−	0.471094i
$476$		0			0
$477$	602.583	−	506.441i	1.26328	−	1.06172i
$478$	−222.326			−0.465118
$479$	−165.785	−	95.7160i	−0.346106	−	0.199825i	0.316863	−	0.948471i	$-0.397371\pi$
$479$	−165.785	−	95.7160i	−0.346106	−	0.199825i	−0.662969	+	0.748647i	$0.730704\pi$
$480$	16.0363	−	91.1575i	0.0334090	−	0.189912i
$481$	−148.231	+	85.5813i	−0.308173	+	0.177924i
$482$	545.209	−	314.777i	1.13114	−	0.653064i
$483$		0			0
$484$	61.6283	−	106.743i	0.127331	−	0.220544i
$485$	273.712			0.564356
$486$	185.197	−	511.974i	0.381063	−	1.05344i
$487$	448.813			0.921587			0.460794	−	0.887507i	$-0.347565\pi$
$487$	448.813			0.921587			0.460794	+	0.887507i	$0.347565\pi$
$488$	407.868	+	235.483i	0.835795	+	0.482547i
$489$	85.9578	+	235.876i	0.175783	+	0.482365i
$490$		0			0
$491$	−40.8828	−	70.8111i	−0.0832644	−	0.144218i	0.821386	−	0.570373i	$-0.193201\pi$
$491$	−40.8828	−	70.8111i	−0.0832644	−	0.144218i	−0.904650	+	0.426155i	$0.859868\pi$
$492$	−12.0210	+	68.3328i	−0.0244330	+	0.138888i
$493$	401.429	+	231.765i	0.814258	+	0.470112i
$494$	−273.324			−0.553287
$495$	4.17072	+	4.96249i	0.00842571	+	0.0100252i
$496$			929.392i			1.87377i
$497$		0			0
$498$	−482.798	−	404.790i	−0.969474	−	0.812832i
$499$	13.7715	+	23.8529i	0.0275982	+	0.0478014i	0.879495	−	0.475909i	$-0.157881\pi$
$499$	13.7715	+	23.8529i	0.0275982	+	0.0478014i	−0.851896	+	0.523710i	$0.824547\pi$
$500$	79.0307	−	45.6284i	0.158061	−	0.0912568i
$501$	−572.941	−	480.368i	−1.14359	−	0.958819i
$502$	32.2061	+	18.5942i	0.0641556	+	0.0370402i
$503$		−	49.4903i		−	0.0983902i	−0.998789	−	0.0491951i	$-0.984334\pi$
$503$		−	49.4903i		−	0.0983902i	0.998789	−	0.0491951i	$-0.0156656\pi$
$504$		0			0
$505$	−90.7653			−0.179733
$506$	11.3802	−	19.7111i	0.0224905	−	0.0389547i
$507$	400.124	+	70.3893i	0.789198	+	0.138835i
$508$	25.0372	+	43.3658i	0.0492859	+	0.0853657i
$509$	108.850	−	62.8447i	0.213851	−	0.123467i	−0.389249	−	0.921133i	$-0.627265\pi$
$509$	108.850	−	62.8447i	0.213851	−	0.123467i	0.603100	+	0.797666i	$0.293932\pi$
$510$	−51.2301	−	140.580i	−0.100451	−	0.275648i
$511$		0			0
$512$	−204.849			−0.400097
$513$	−283.628	+	492.608i	−0.552881	+	0.960250i
$514$		−	190.893i		−	0.371387i
$515$	127.235	−	220.377i	0.247058	−	0.427917i
$516$	22.5026	+	61.7492i	0.0436096	+	0.119669i
$517$	−17.1879	+	9.92344i	−0.0332454	+	0.0191943i
$518$		0			0
$519$	144.733	−	822.727i	0.278869	−	1.58522i
$520$	−37.4228	+	64.8182i	−0.0719670	+	0.124650i
$521$			700.708i			1.34493i	0.740130	+	0.672464i	$0.234764\pi$
$521$			700.708i			1.34493i	−0.740130	+	0.672464i	$0.765236\pi$
$522$	763.476	+	277.198i	1.46260	+	0.531031i
$523$		−	349.590i		−	0.668432i	−0.942496	−	0.334216i	$-0.891528\pi$
$523$		−	349.590i		−	0.668432i	0.942496	−	0.334216i	$-0.108472\pi$
$524$	−109.728	−	63.3515i	−0.209405	−	0.120900i
$525$		0			0
$526$	399.541	+	692.026i	0.759584	+	1.31564i
$527$	280.866	+	486.474i	0.532953	+	0.923101i
$528$	−13.6637	+	16.2969i	−0.0258783	+	0.0308653i
$529$	−107.694	+	186.531i	−0.203580	+	0.352611i
$530$		−	379.061i		−	0.715210i
$531$	28.3532	−	78.0921i	0.0533959	−	0.147066i
$532$		0			0
$533$	65.7048	−	113.804i	0.123273	−	0.213516i
$534$	34.5326	−	196.299i	0.0646678	−	0.367600i
$535$	−234.400	+	135.331i	−0.438131	+	0.252955i
$536$	−252.207	−	436.835i	−0.470535	−	0.814990i
$537$	−264.514	−	725.851i	−0.492577	−	1.35168i
$538$	−747.204	−	431.399i	−1.38886	−	0.801856i
$539$		0			0
$540$	−26.6873	−	46.0973i	−0.0494209	−	0.0853653i
$541$	701.445			1.29657			0.648286	−	0.761397i	$-0.275486\pi$
$541$	701.445			1.29657			0.648286	+	0.761397i	$0.275486\pi$
$542$	−120.883	−	69.7918i	−0.223031	−	0.128767i
$543$	82.4579	−	30.0492i	0.151856	−	0.0553392i
$544$	158.944	−	91.7664i	0.292177	−	0.168688i
$545$	−186.096	+	107.443i	−0.341461	+	0.197143i
$546$		0			0
$547$	−202.629	+	350.964i	−0.370437	+	0.641616i	−0.989633	−	0.143620i	$-0.954126\pi$
$547$	−202.629	+	350.964i	−0.370437	+	0.641616i	0.619195	+	0.785237i	$0.287459\pi$
$548$	4.72249			0.00861768
$549$	625.080	−	110.729i	1.13858	−	0.201692i
$550$	−17.7338			−0.0322432
$551$	−734.410	−	424.012i	−1.33287	−	0.769532i
$552$	351.132	−	418.799i	0.636108	−	0.758694i
$553$		0			0
$554$	−95.2339	−	164.950i	−0.171902	−	0.297744i
$555$	131.359	+	110.135i	0.236683	+	0.198441i
$556$	−38.4515	−	22.2000i	−0.0691574	−	0.0399280i
$557$	103.589			0.185976			0.0929880	−	0.995667i	$-0.470358\pi$
$557$	103.589			0.185976			0.0929880	+	0.995667i	$0.470358\pi$
$558$	633.305	+	753.531i	1.13495	+	1.35041i
$559$		−	124.477i		−	0.222677i
$560$		0			0
$561$	−2.22706	+	12.6596i	−0.00396980	+	0.0225661i
$562$	165.535	+	286.715i	0.294546	+	0.510168i
$563$	113.286	−	65.4059i	0.201219	−	0.116174i	−0.396005	−	0.918248i	$-0.629604\pi$
$563$	113.286	−	65.4059i	0.201219	−	0.116174i	0.597224	+	0.802074i	$0.296270\pi$
$564$	153.223	−	55.8372i	0.271672	−	0.0990022i
$565$	170.086	+	98.1994i	0.301038	+	0.173804i
$566$			786.000i			1.38869i
$567$		0			0
$568$	650.834			1.14584
$569$	317.790	−	550.428i	0.558506	−	0.967361i	−0.439115	−	0.898431i	$-0.644708\pi$
$569$	317.790	−	550.428i	0.558506	−	0.967361i	0.997621	−	0.0689303i	$-0.0219586\pi$
$570$	93.7249	+	257.190i	0.164430	+	0.451211i
$571$	−86.0297	−	149.008i	−0.150665	−	0.260959i	0.780807	−	0.624772i	$-0.214808\pi$
$571$	−86.0297	−	149.008i	−0.150665	−	0.260959i	−0.931472	+	0.363813i	$0.881475\pi$
$572$	−1.90552	+	1.10015i	−0.00333133	+	0.00192334i
$573$	−179.554	−	31.5869i	−0.313358	−	0.0551255i
$574$		0			0
$575$	579.990			1.00868
$576$	−278.509	+	234.073i	−0.483523	+	0.406377i
$577$		−	31.7345i		−	0.0549991i	−0.999622	−	0.0274996i	$-0.991246\pi$
$577$		−	31.7345i		−	0.0549991i	0.999622	−	0.0274996i	$-0.00875448\pi$
$578$	−175.406	+	303.812i	−0.303471	+	0.525627i
$579$	−47.9487	+	57.1890i	−0.0828129	+	0.0987720i
$580$	68.8189	−	39.7326i	0.118653	−	0.0685045i
$581$		0			0
$582$	728.789	+	611.035i	1.25222	+	1.04989i
$583$	−16.2823	+	28.2017i	−0.0279285	+	0.0483735i
$584$		−	580.773i		−	0.994474i
$585$	17.5970	+	99.3374i	0.0300803	+	0.169808i
$586$		−	110.648i		−	0.188818i
$587$	−780.765	−	450.775i	−1.33009	−	0.767929i	−0.344779	−	0.938684i	$-0.612046\pi$
$587$	−780.765	−	450.775i	−1.33009	−	0.767929i	−0.985314	+	0.170754i	$0.945380\pi$
$588$		0			0
$589$	−513.842	−	890.000i	−0.872396	−	1.51104i
$590$	−20.0043	−	34.6485i	−0.0339056	−	0.0587263i
$591$	−179.057	−	491.351i	−0.302974	−	0.831389i
$592$	−281.193	+	487.041i	−0.474989	+	0.822705i
$593$		−	106.446i		−	0.179504i	−0.995964	−	0.0897518i	$-0.971393\pi$
$593$		−	106.446i		−	0.179504i	0.995964	−	0.0897518i	$-0.0286074\pi$
$594$	0.0267479	+	22.5239i	4.50302e−5	+	0.0379190i
$595$		0			0
$596$	13.3906	−	23.1932i	0.0224674	−	0.0389147i
$597$	−814.418	+	296.789i	−1.36418	+	0.497134i
$598$	306.759	−	177.108i	0.512976	−	0.296167i
$599$	407.540	+	705.880i	0.680367	+	1.17843i	0.974869	+	0.222780i	$0.0715131\pi$
$599$	407.540	+	705.880i	0.680367	+	1.17843i	−0.294501	+	0.955651i	$0.595154\pi$
$600$	−419.383	−	73.7773i	−0.698971	−	0.122962i
$601$	−222.029	−	128.189i	−0.369433	−	0.213292i	0.303778	−	0.952743i	$-0.401752\pi$
$601$	−222.029	−	128.189i	−0.369433	−	0.213292i	−0.673211	+	0.739451i	$0.735085\pi$
$602$		0			0
$603$	−639.077	−	232.032i	−1.05983	−	0.384796i
$604$	122.249			0.202399
$605$	202.476	+	116.900i	0.334672	+	0.193223i
$606$	−241.672	−	202.624i	−0.398799	−	0.334364i
$607$	−280.441	+	161.913i	−0.462012	+	0.266742i	−0.712890	−	0.701276i	$-0.752614\pi$
$607$	−280.441	+	161.913i	−0.462012	+	0.266742i	0.250878	+	0.968019i	$0.419281\pi$
$608$	−290.786	+	167.886i	−0.478267	+	0.276128i
$609$		0			0
$610$	152.852	−	264.748i	0.250578	−	0.434014i
$611$	−308.873			−0.505520
$612$	36.0455	−	99.2787i	0.0588979	−	0.162220i
$613$	−621.240			−1.01344			−0.506721	−	0.862110i	$-0.669143\pi$
$613$	−621.240			−1.01344			−0.506721	+	0.862110i	$0.669143\pi$
$614$	839.540	+	484.709i	1.36733	+	0.789428i
$615$	−129.617	−	22.8021i	−0.210759	−	0.0370766i
$616$		0			0
$617$	372.353	+	644.935i	0.603490	+	1.04527i	0.992288	+	0.123952i	$0.0395569\pi$
$617$	372.353	+	644.935i	0.603490	+	1.04527i	−0.388799	+	0.921323i	$0.627110\pi$
$618$	830.746	−	302.739i	1.34425	−	0.489870i
$619$	159.035	+	91.8186i	0.256922	+	0.148334i	0.622930	−	0.782278i	$-0.285942\pi$
$619$	159.035	+	91.8186i	0.256922	+	0.148334i	−0.366008	+	0.930612i	$0.619276\pi$
$620$	96.3004			0.155323
$621$	−0.874803	−	736.653i	−0.00140870	−	1.18624i
$622$		−	374.587i		−	0.602230i
$623$		0			0
$624$	−310.970	+	113.323i	−0.498349	+	0.181607i
$625$	−179.174	−	310.338i	−0.286678	−	0.496541i
$626$	501.739	−	289.679i	0.801501	−	0.462747i
$627$	4.07438	−	23.1606i	0.00649821	−	0.0369387i
$628$	−173.065	−	99.9191i	−0.275581	−	0.159107i
$629$			339.911i			0.540399i
$630$		0			0
$631$	325.873			0.516439			0.258220	−	0.966086i	$-0.416864\pi$
$631$	325.873			0.516439			0.258220	+	0.966086i	$0.416864\pi$
$632$	−157.577	+	272.932i	−0.249331	+	0.431854i
$633$	−576.697	+	687.834i	−0.911054	+	1.08662i
$634$	226.865	+	392.942i	0.357831	+	0.619782i
$635$	−82.2584	+	47.4919i	−0.129541	+	0.0747904i
$636$	171.916	−	205.046i	0.270308	−	0.322400i
$637$		0			0
$638$	−33.6030			−0.0526693
$639$	671.570	−	564.421i	1.05097	−	0.883288i
$640$			298.609i			0.466576i
$641$	89.3312	−	154.726i	0.139362	−	0.241383i	−0.787893	−	0.615812i	$-0.788828\pi$
$641$	89.3312	−	154.726i	0.139362	−	0.241383i	0.927255	+	0.374429i	$0.122161\pi$
$642$	−926.229	−	162.941i	−1.44272	−	0.253802i
$643$	−60.1837	+	34.7471i	−0.0935983	+	0.0540390i	−0.546069	−	0.837740i	$-0.683876\pi$
$643$	−60.1837	+	34.7471i	−0.0935983	+	0.0540390i	0.452470	+	0.891780i	$0.350543\pi$
$644$		0			0
$645$	−117.129	+	42.6840i	−0.181595	+	0.0661767i
$646$	−271.396	+	470.072i	−0.420118	+	0.727666i
$647$			823.157i			1.27227i	0.771579	+	0.636134i	$0.219467\pi$
$647$			823.157i			1.27227i	−0.771579	+	0.636134i	$0.780533\pi$
$648$	−93.0730	+	532.775i	−0.143631	+	0.822184i
$649$			3.43708i			0.00529597i
$650$	−239.012	−	137.993i	−0.367710	−	0.212298i
$651$		0			0
$652$	42.6710	+	73.9084i	0.0654463	+	0.113356i
$653$	−391.218	−	677.609i	−0.599108	−	1.03769i	−0.992953	−	0.118509i	$-0.962189\pi$
$653$	−391.218	−	677.609i	−0.599108	−	1.03769i	0.393845	−	0.919177i	$-0.371145\pi$
$654$	−735.357	−	129.363i	−1.12440	−	0.197803i
$655$	120.168	−	208.138i	0.183463	−	0.317768i
$656$		−	431.770i		−	0.658187i
$657$	−503.662	−	599.276i	−0.766608	−	0.912141i
$658$		0			0
$659$	90.6800	−	157.062i	0.137602	−	0.238334i	−0.788986	−	0.614411i	$-0.789394\pi$
$659$	90.6800	−	157.062i	0.137602	−	0.238334i	0.926589	+	0.376077i	$0.122727\pi$
$660$	1.68863	+	1.41579i	0.00255853	+	0.00214514i
$661$	−167.119	+	96.4862i	−0.252827	+	0.145970i	−0.621058	−	0.783764i	$-0.713297\pi$
$661$	−167.119	+	96.4862i	−0.252827	+	0.145970i	0.368231	+	0.929734i	$0.379964\pi$
$662$	−38.2635	−	66.2743i	−0.0577999	−	0.100112i
$663$	−128.525	+	153.293i	−0.193854	+	0.231212i
$664$	542.025	+	312.939i	0.816303	+	0.471293i
$665$		0			0
$666$	103.893	+	586.493i	0.155996	+	0.880620i
$667$	1099.00			1.64768
$668$	−220.112	−	127.082i	−0.329509	−	0.190242i
$669$	8.44889	−	48.0272i	0.0126291	−	0.0717895i
$670$	−283.551	+	163.708i	−0.423210	+	0.244340i
$671$	−22.7441	+	13.1313i	−0.0338958	+	0.0195698i
$672$		0			0
$673$	−41.9447	+	72.6503i	−0.0623249	+	0.107950i	−0.895504	−	0.445053i	$-0.853185\pi$
$673$	−41.9447	+	72.6503i	−0.0623249	+	0.107950i	0.833179	+	0.553003i	$0.186518\pi$
$674$	−922.431			−1.36859
$675$	−496.726	+	287.572i	−0.735891	+	0.426033i
$676$	138.106			0.204299
$677$	−179.443	−	103.601i	−0.265056	−	0.153030i	0.361583	−	0.932340i	$-0.382236\pi$
$677$	−179.443	−	103.601i	−0.265056	−	0.153030i	−0.626639	+	0.779310i	$0.715570\pi$
$678$	233.653	+	641.167i	0.344621	+	0.945674i
$679$		0			0
$680$	74.3178	+	128.722i	0.109291	+	0.189297i
$681$	15.8764	−	90.2486i	0.0233134	−	0.132524i
$682$	−35.2663	−	20.3610i	−0.0517101	−	0.0298549i
$683$	1279.88			1.87391			0.936953	−	0.349454i	$-0.113633\pi$
$683$	1279.88			1.87391			0.936953	+	0.349454i	$0.113633\pi$
$684$	−65.9449	+	181.629i	−0.0964107	+	0.265540i
$685$			8.95786i			0.0130772i
$686$		0			0
$687$	419.772	+	351.948i	0.611022	+	0.512296i
$688$	−204.495	−	354.197i	−0.297232	−	0.514821i
$689$	−438.898	+	253.398i	−0.637007	+	0.367776i
$690$	−271.844	−	227.921i	−0.393976	−	0.330320i
$691$	1052.86	+	607.869i	1.52368	+	0.879695i	0.999607	+	0.0280193i	$0.00892000\pi$
$691$	1052.86	+	607.869i	1.52368	+	0.879695i	0.524069	+	0.851676i	$0.324413\pi$
$692$		−	283.972i		−	0.410364i
$693$		0			0
$694$	−1338.67			−1.92892
$695$	42.1101	−	72.9368i	0.0605900	−	0.104945i
$696$	−794.672	−	139.798i	−1.14177	−	0.200859i
$697$	−130.483	−	226.003i	−0.187206	−	0.324251i
$698$	163.168	−	94.2049i	0.233765	−	0.134964i
$699$	359.302	+	985.960i	0.514023	+	1.41053i
$700$		0			0
$701$	−1171.72			−1.67149			−0.835747	−	0.549114i	$-0.814965\pi$
$701$	−1171.72			−1.67149			−0.835747	+	0.549114i	$0.814965\pi$
$702$	−174.907	+	303.780i	−0.249155	+	0.432735i
$703$		−	621.864i		−	0.884586i
$704$	7.52554	−	13.0346i	0.0106897	−	0.0185151i
$705$	105.915	+	290.641i	0.150234	+	0.412256i
$706$	889.515	−	513.562i	1.25994	−	0.727425i
$707$		0			0
$708$	4.89319	−	27.8150i	0.00691129	−	0.0392868i
$709$	55.8366	−	96.7119i	0.0787540	−	0.136406i	−0.823959	−	0.566650i	$-0.808239\pi$
$709$	55.8366	−	96.7119i	0.0787540	−	0.136406i	0.902713	+	0.430244i	$0.141572\pi$
$710$		−	422.458i		−	0.595012i
$711$	74.0960	+	418.282i	0.104214	+	0.588302i
$712$			197.996i			0.278085i
$713$	1153.40	+	665.915i	1.61767	+	0.933962i
$714$		0			0
$715$	−2.08682	−	3.61448i	−0.00291863	−	0.00505522i
$716$	−131.309	−	227.435i	−0.183393	−	0.317646i
$717$	191.263	−	228.121i	0.266754	−	0.318161i
$718$	14.4010	−	24.9432i	0.0200571	−	0.0347398i
$719$			1390.66i			1.93416i	0.254468	+	0.967081i	$0.418100\pi$
$719$			1390.66i			1.93416i	−0.254468	+	0.967081i	$0.581900\pi$
$720$	213.268	+	253.754i	0.296205	+	0.352437i
$721$		0			0
$722$	92.1074	−	159.535i	0.127573	−	0.220962i
$723$	−146.051	+	830.217i	−0.202007	+	1.14829i
$724$	25.8370	−	14.9170i	0.0356864	−	0.0206036i
$725$	−428.143	−	741.566i	−0.590543	−	1.02285i
$726$	278.148	+	763.266i	0.383124	+	1.05133i
$727$	570.198	+	329.204i	0.784317	+	0.452826i	0.837958	−	0.545735i	$-0.183749\pi$
$727$	570.198	+	329.204i	0.784317	+	0.452826i	−0.0536411	+	0.998560i	$0.517083\pi$
$728$		0			0
$729$	365.998	+	630.465i	0.502055	+	0.864835i
$730$	−376.981			−0.516412
$731$	−214.079	−	123.599i	−0.292858	−	0.169082i
$732$	202.754	−	73.8874i	0.276987	−	0.100939i
$733$	−322.167	+	186.003i	−0.439518	+	0.253756i	−0.703393	−	0.710801i	$-0.748333\pi$
$733$	−322.167	+	186.003i	−0.439518	+	0.253756i	0.263875	+	0.964557i	$0.414999\pi$
$734$	1199.80	−	692.703i	1.63460	−	0.943737i
$735$		0			0
$736$	217.572	−	376.846i	0.295614	−	0.512019i
$737$	28.1278			0.0381653
$738$	−294.216	−	350.070i	−0.398667	−	0.474350i
$739$	−940.344			−1.27245			−0.636227	−	0.771502i	$-0.719506\pi$
$739$	−940.344			−1.27245			−0.636227	+	0.771502i	$0.719506\pi$
$740$	50.4655	+	29.1363i	0.0681967	+	0.0393734i
$741$	235.135	−	280.448i	0.317321	−	0.378473i
$742$		0			0
$743$	−103.438	−	179.161i	−0.139217	−	0.241131i	0.787983	−	0.615697i	$-0.211125\pi$
$743$	−103.438	−	179.161i	−0.139217	−	0.241131i	−0.927201	+	0.374565i	$0.877792\pi$
$744$	−749.299	−	628.232i	−1.00712	−	0.844397i
$745$	43.9940	+	25.3999i	0.0590523	+	0.0340939i
$746$	1.29784			0.00173973
$747$	830.683	−	147.150i	1.11203	−	0.196988i
$748$			4.36957i			0.00584167i
$749$		0			0
$750$	−104.208	+	592.365i	−0.138944	+	0.789820i
$751$	−724.153	−	1254.27i	−0.964252	−	1.67013i	−0.711611	−	0.702574i	$-0.752034\pi$
$751$	−724.153	−	1254.27i	−0.964252	−	1.67013i	−0.252641	−	0.967560i	$-0.581299\pi$
$752$	−878.894	+	507.430i	−1.16874	+	0.674773i
$753$	−46.7851	+	17.0494i	−0.0621316	+	0.0226419i
$754$	−452.894	−	261.478i	−0.600655	−	0.346788i
$755$			231.888i			0.307136i
$756$		0			0
$757$	−296.987			−0.392321			−0.196161	−	0.980572i	$-0.562847\pi$
$757$	−296.987			−0.392321			−0.196161	+	0.980572i	$0.562847\pi$
$758$	−20.7262	+	35.8989i	−0.0273433	+	0.0473600i
$759$	10.4347	+	28.6339i	0.0137480	+	0.0377258i
$760$	−135.964	−	235.496i	−0.178900	−	0.309863i
$761$	−254.681	+	147.040i	−0.334666	+	0.193220i	−0.657911	−	0.753096i	$-0.728560\pi$
$761$	−254.681	+	147.040i	−0.334666	+	0.193220i	0.323245	+	0.946315i	$0.395226\pi$
$762$	−325.043	−	57.1812i	−0.426565	−	0.0750409i
$763$		0			0
$764$	−61.9748			−0.0811188
$765$	188.317	+	68.3730i	0.246166	+	0.0893764i
$766$		−	126.854i		−	0.165606i
$767$	−26.7453	+	46.3242i	−0.0348700	+	0.0603967i
$768$	−354.958	+	423.363i	−0.462185	+	0.551254i
$769$	91.6783	−	52.9305i	0.119218	−	0.0688303i	−0.439205	−	0.898387i	$-0.644740\pi$
$769$	91.6783	−	52.9305i	0.119218	−	0.0688303i	0.558423	+	0.829556i	$0.311407\pi$
$770$		0			0
$771$	195.869	+	164.221i	0.254045	+	0.212998i
$772$	−12.6849	+	21.9708i	−0.0164312	+	0.0284596i
$773$			1236.60i			1.59974i	0.600174	+	0.799869i	$0.295098\pi$
$773$			1236.60i			1.59974i	−0.600174	+	0.799869i	$0.704902\pi$
$774$	−407.156	−	147.828i	−0.526042	−	0.190992i
$775$		−	1037.70i		−	1.33896i
$776$	−818.193	−	472.384i	−1.05437	−	0.608742i
$777$		0			0
$778$	−463.296	−	802.452i	−0.595496	−	1.03143i
$779$	238.717	+	413.470i	0.306440	+	0.530770i
$780$	11.7421	+	32.2216i	0.0150540	+	0.0413097i
$781$	−18.1464	+	31.4304i	−0.0232348	+	0.0402438i
$782$		−	703.434i		−	0.899533i
$783$	−941.227	+	544.909i	−1.20208	+	0.695925i
$784$		0			0
$785$	189.532	−	328.278i	0.241442	−	0.418189i
$786$	784.608	−	285.926i	0.998229	−	0.363773i
$787$	728.889	−	420.825i	0.926162	−	0.534720i	0.0405663	−	0.999177i	$-0.487084\pi$
$787$	728.889	−	420.825i	0.926162	−	0.534720i	0.885596	+	0.464457i	$0.153750\pi$
$788$	−88.8874	−	153.957i	−0.112801	−	0.195377i
$789$	−1053.78	−	185.380i	−1.33559	−	0.234956i
$790$	177.161	+	102.284i	0.224254	+	0.129473i
$791$		0			0
$792$	−3.90284	−	22.0321i	−0.00492783	−	0.0278183i
$793$	−408.720			−0.515410
$794$	1210.99	+	699.167i	1.52518	+	0.880564i
$795$	388.942	+	326.099i	0.489235	+	0.410187i
$796$	−255.186	+	147.332i	−0.320585	+	0.185090i
$797$	138.377	−	79.8921i	0.173622	−	0.100241i	−0.410670	−	0.911784i	$-0.634705\pi$
$797$	138.377	−	79.8921i	0.173622	−	0.100241i	0.584293	+	0.811543i	$0.301372\pi$
$798$		0			0
$799$	−306.695	+	531.211i	−0.383848	+	0.664844i
$800$	−339.043			−0.423803
$801$	171.708	+	204.304i	0.214367	+	0.255062i
$802$	284.261			0.354441
$803$	28.0470	+	16.1929i	0.0349277	+	0.0201655i
$804$	−227.628	−	40.0441i	−0.283119	−	0.0498061i
$805$		0			0
$806$	−316.874	−	548.842i	−0.393144	−	0.680946i
$807$	1085.45	−	395.558i	1.34504	−	0.490158i
$808$	271.320	+	156.646i	0.335792	+	0.193869i
$809$	35.5021			0.0438840			0.0219420	−	0.999759i	$-0.493015\pi$
$809$	35.5021			0.0438840			0.0219420	+	0.999759i	$0.493015\pi$
$810$	345.826	+	60.4140i	0.426945	+	0.0745851i
$811$		−	264.939i		−	0.326682i	−0.986570	−	0.163341i	$-0.947773\pi$
$811$		−	264.939i		−	0.326682i	0.986570	−	0.163341i	$-0.0522271\pi$
$812$		0			0
$813$	175.604	−	63.9934i	0.215995	−	0.0787127i
$814$	−12.3207	−	21.3401i	−0.0151360	−	0.0262163i
$815$	−140.193	+	80.9406i	−0.172016	+	0.0993136i
$816$	−113.879	+	647.340i	−0.139558	+	0.793309i
$817$	391.656	+	226.123i	0.479383	+	0.276772i
$818$		−	969.081i		−	1.18470i
$819$		0			0
$820$	−44.7386			−0.0545592
$821$	−753.781	+	1305.59i	−0.918126	+	1.59024i	−0.115866	+	0.993265i	$0.536964\pi$
$821$	−753.781	+	1305.59i	−0.918126	+	1.59024i	−0.802260	+	0.596975i	$0.796369\pi$
$822$	−19.9975	+	23.8513i	−0.0243279	+	0.0290161i
$823$	−617.420	−	1069.40i	−0.750207	−	1.29940i	−0.947722	−	0.319097i	$-0.896621\pi$
$823$	−617.420	−	1069.40i	−0.750207	−	1.29940i	0.197515	−	0.980300i	$-0.436713\pi$
$824$	−760.672	+	439.174i	−0.923145	+	0.532978i
$825$	15.2560	−	18.1960i	0.0184921	−	0.0220558i
$826$		0			0
$827$	642.770			0.777231			0.388616	−	0.921400i	$-0.372953\pi$
$827$	642.770			0.777231			0.388616	+	0.921400i	$0.372953\pi$
$828$	−43.6798	−	246.579i	−0.0527534	−	0.297800i
$829$		−	959.949i		−	1.15796i	−0.815342	−	0.578980i	$-0.803451\pi$
$829$		−	959.949i		−	1.15796i	0.815342	−	0.578980i	$-0.196549\pi$
$830$	203.129	−	351.830i	0.244734	−	0.423892i
$831$	251.177	+	44.1868i	0.302259	+	0.0531731i
$832$	202.855	−	117.119i	0.243816	−	0.140767i
$833$		0			0
$834$	274.947	−	100.196i	0.329672	−	0.120139i
$835$	241.055	−	417.520i	0.288689	−	0.500024i
$836$		−	7.99409i		−	0.00956230i
$837$	−1317.99	+	1.56516i	−1.57466	+	0.00186997i
$838$		−	390.136i		−	0.465557i
$839$	−409.757	−	236.574i	−0.488388	−	0.281971i	0.235518	−	0.971870i	$-0.424321\pi$
$839$	−409.757	−	236.574i	−0.488388	−	0.281971i	−0.723905	+	0.689899i	$0.757655\pi$
$840$		0			0
$841$	−390.772	−	676.837i	−0.464652	−	0.804800i
$842$	−393.140	−	680.938i	−0.466912	−	0.808715i
$843$	−436.594	−	76.8052i	−0.517906	−	0.0911094i
$844$	−152.566	+	264.251i	−0.180765	+	0.313094i
$845$			261.967i			0.310021i
$846$	−366.816	+	1010.31i	−0.433589	+	1.19422i
$847$		0			0
$848$	−832.586	+	1442.08i	−0.981823	+	1.70057i
$849$	−806.488	−	676.180i	−0.949927	−	0.796443i
$850$	−474.652	+	274.041i	−0.558414	+	0.322401i
$851$	402.954	+	697.936i	0.473506	+	0.820136i
$852$	191.598	−	228.521i	0.224880	−	0.268217i
$853$	1068.57	+	616.937i	1.25271	+	0.723255i	0.971648	−	0.236433i	$-0.0759783\pi$
$853$	1068.57	+	616.937i	1.25271	+	0.723255i	0.281067	+	0.959688i	$0.409312\pi$
$854$		0			0
$855$	−344.524	−	125.088i	−0.402952	−	0.146301i
$856$	934.239			1.09140
$857$	−344.080	−	198.655i	−0.401493	−	0.231802i	0.285635	−	0.958339i	$-0.407796\pi$
$857$	−344.080	−	198.655i	−0.401493	−	0.231802i	−0.687128	+	0.726536i	$0.741129\pi$
$858$	2.51258	−	14.2826i	0.00292841	−	0.0166464i
$859$	473.197	−	273.200i	0.550870	−	0.318045i	−0.198603	−	0.980080i	$-0.563640\pi$
$859$	473.197	−	273.200i	0.550870	−	0.318045i	0.749473	+	0.662035i	$0.230307\pi$
$860$	−36.7006	+	21.1891i	−0.0426752	+	0.0246385i
$861$		0			0
$862$	824.138	−	1427.45i	0.956076	−	1.65597i
$863$	15.7392			0.0182378			0.00911888	−	0.999958i	$-0.497097\pi$
$863$	15.7392			0.0182378			0.00911888	+	0.999958i	$0.497097\pi$
$864$	0.511380	+	430.623i	0.000591875	+	0.498406i
$865$	538.653			0.622720
$866$	−261.513	−	150.985i	−0.301978	−	0.174347i
$867$	−160.833	−	441.342i	−0.185505	−	0.509045i
$868$		0			0
$869$	−8.78704	−	15.2196i	−0.0101117	−	0.0175139i
$870$	−90.7431	+	515.824i	−0.104302	+	0.592901i
$871$	379.100	+	218.874i	0.435247	+	0.251290i
$872$	741.717			0.850593
$873$	−1253.93	+	222.125i	−1.43634	+	0.254438i
$874$			1286.93i			1.47246i
$875$		0			0
$876$	−203.921	−	170.972i	−0.232786	−	0.195174i
$877$	86.7339	+	150.227i	0.0988984	+	0.171297i	0.911229	−	0.411900i	$-0.135135\pi$
$877$	86.7339	+	150.227i	0.0988984	+	0.171297i	−0.812331	+	0.583197i	$0.801801\pi$
$878$	−11.3450	+	6.55002i	−0.0129214	+	0.00746017i
$879$	113.532	+	95.1879i	0.129160	+	0.108291i
$880$	−11.8761	−	6.85665i	−0.0134955	−	0.00779164i
$881$		−	1381.76i		−	1.56840i	−0.620507	−	0.784201i	$-0.713073\pi$
$881$		−	1381.76i		−	1.56840i	0.620507	−	0.784201i	$-0.286927\pi$
$882$		0			0
$883$	1346.90			1.52537			0.762685	−	0.646771i	$-0.223881\pi$
$883$	1346.90			1.52537			0.762685	+	0.646771i	$0.223881\pi$
$884$	−34.0014	+	58.8921i	−0.0384631	+	0.0666200i
$885$	52.7610	+	9.28166i	0.0596170	+	0.0104877i
$886$	179.596	+	311.069i	0.202704	+	0.351094i
$887$	−532.683	+	307.545i	−0.600544	+	0.346724i	−0.769256	−	0.638941i	$-0.779373\pi$
$887$	−532.683	+	307.545i	−0.600544	+	0.346724i	0.168711	+	0.985665i	$0.446039\pi$
$888$	−202.590	−	555.926i	−0.228141	−	0.626042i
$889$		0			0
$890$	128.520			0.144404
$891$	−23.1340	−	19.3494i	−0.0259641	−	0.0217165i
$892$		−	16.5770i		−	0.0185841i
$893$	561.095	−	971.844i	0.628325	−	1.08829i
$894$	60.4360	+	165.842i	0.0676018	+	0.185506i
$895$	431.410	−	249.074i	0.482022	−	0.278295i
$896$		0			0
$897$	−82.1748	+	467.118i	−0.0916107	+	0.520756i
$898$	−52.4164	+	90.7880i	−0.0583702	+	0.101100i
$899$		−	1966.29i		−	2.18720i
$900$	−149.366	+	125.535i	−0.165962	+	0.139483i
$901$			1006.44i			1.11703i
$902$	16.3838	+	9.45917i	0.0181638	+	0.0104869i
$903$		0			0
$904$	−338.953	−	587.084i	−0.374948	−	0.649429i
$905$	28.2953	+	49.0089i	0.0312655	+	0.0541534i
$906$	−517.666	+	617.426i	−0.571375	+	0.681486i
$907$	249.391	−	431.958i	0.274962	−	0.476249i	−0.695163	−	0.718852i	$-0.744668\pi$
$907$	249.391	−	431.958i	0.274962	−	0.476249i	0.970126	+	0.242603i	$0.0780012\pi$
$908$		−	31.1501i		−	0.0343063i
$909$	415.812	−	73.6583i	0.457439	−	0.0810323i
$910$		0			0
$911$	462.758	−	801.521i	0.507967	−	0.879825i	−0.491990	−	0.870601i	$-0.663730\pi$
$911$	462.758	−	801.521i	0.507967	−	0.879825i	0.999957	−	0.00922428i	$-0.00293622\pi$
$912$	208.341	−	1184.30i	0.228444	−	1.29858i
$913$	−30.2252	+	17.4505i	−0.0331053	+	0.0191134i
$914$	−620.998	−	1075.60i	−0.679429	−	1.17681i
$915$	140.153	+	384.594i	0.153173	+	0.420322i
$916$	161.268	+	93.1080i	0.176057	+	0.101646i
$917$		0			0
$918$	348.779	+	602.449i	0.379933	+	0.656262i
$919$	−1089.89			−1.18596			−0.592979	−	0.805218i	$-0.702048\pi$
$919$	−1089.89			−1.18596			−0.592979	+	0.805218i	$0.702048\pi$
$920$	305.192	+	176.203i	0.331730	+	0.191525i
$921$	−1219.58	+	444.439i	−1.32419	+	0.482561i
$922$	263.602	−	152.191i	0.285903	−	0.165066i
$923$	−489.146	+	282.408i	−0.529952	+	0.305968i
$924$		0			0
$925$	313.961	−	543.797i	0.339418	−	0.587889i
$926$	−4.26662			−0.00460758
$927$	−404.044	+	1112.84i	−0.435862	+	1.20048i
$928$	−642.439			−0.692283
$929$	−465.713	−	268.879i	−0.501306	−	0.289429i	0.227947	−	0.973674i	$-0.426799\pi$
$929$	−465.713	−	268.879i	−0.501306	−	0.289429i	−0.729253	+	0.684245i	$0.760132\pi$
$930$	−407.787	+	486.372i	−0.438480	+	0.522981i
$931$		0			0
$932$	178.364	+	308.936i	0.191378	+	0.331476i
$933$	384.351	+	322.250i	0.411952	+	0.345391i
$934$	200.137	+	115.549i	0.214279	+	0.123714i
$935$	−8.28843			−0.00886463
$936$	118.839	−	327.313i	0.126965	−	0.349694i
$937$		−	647.389i		−	0.690917i	−0.938434	−	0.345459i	$-0.887723\pi$
$937$		−	647.389i		−	0.690917i	0.938434	−	0.345459i	$-0.112277\pi$
$938$		0			0
$939$	−134.406	+	764.023i	−0.143137	+	0.813656i
$940$	52.5781	+	91.0680i	0.0559342	+	0.0968808i
$941$	−113.565	+	65.5667i	−0.120685	+	0.0696777i	−0.559127	−	0.829082i	$-0.688864\pi$
$941$	−113.565	+	65.5667i	−0.120685	+	0.0696777i	0.438442	+	0.898759i	$0.355530\pi$
$942$	1237.50	−	450.967i	1.31369	−	0.478733i
$943$	−535.838	−	309.366i	−0.568227	−	0.328066i
$944$			175.753i			0.186179i
$945$		0			0
$946$	17.9202			0.0189432
$947$	−209.492	+	362.851i	−0.221217	+	0.383159i	−0.955178	−	0.296033i	$-0.904336\pi$
$947$	−209.492	+	362.851i	−0.221217	+	0.383159i	0.733961	+	0.679192i	$0.237669\pi$
$948$	49.4429	+	135.676i	0.0521550	+	0.143118i
$949$	252.007	+	436.489i	0.265550	+	0.459947i
$950$	868.371	−	501.354i	0.914075	−	0.527742i
$951$	−598.352	−	105.261i	−0.629182	−	0.110685i
$952$		0			0
$953$	−1131.25			−1.18704			−0.593520	−	0.804819i	$-0.702262\pi$
$953$	−1131.25			−1.18704			−0.593520	+	0.804819i	$0.702262\pi$
$954$	307.618	+	1736.55i	0.322451	+	1.82028i
$955$		−	117.557i		−	0.123096i
$956$	50.5987	−	87.6396i	0.0529275	−	0.0916732i
$957$	28.9080	−	34.4789i	0.0302069	−	0.0360281i
$958$	371.440	−	214.451i	0.387725	−	0.223853i
$959$		0			0
$960$	−179.766	−	150.720i	−0.187256	−	0.157000i
$961$	710.930	−	1231.37i	0.739781	−	1.28134i
$962$		−	383.489i		−	0.398637i
$963$	964.005	−	810.197i	1.00104	−	0.841326i
$964$			286.557i			0.297259i
$965$	−41.6754	−	24.0613i	−0.0431869	−	0.0249340i
$966$		0			0
$967$	−115.840	−	200.640i	−0.119793	−	0.207488i	0.799893	−	0.600143i	$-0.204890\pi$
$967$	−115.840	−	200.640i	−0.119793	−	0.207488i	−0.919686	+	0.392656i	$0.871556\pi$
$968$	−403.501	−	698.884i	−0.416840	−	0.721987i
$969$	−248.848	−	682.864i	−0.256810	−	0.704710i
$970$	−306.626	+	531.091i	−0.316109	+	0.547517i
$971$			464.832i			0.478715i	0.970932	+	0.239358i	$0.0769368\pi$
$971$			464.832i			0.478715i	−0.970932	+	0.239358i	$0.923063\pi$
$972$	159.668	+	189.522i	0.164268	+	0.194982i
$973$		0			0
$974$	−502.782	+	870.843i	−0.516203	+	0.894089i
$975$	347.207	−	126.529i	0.356110	−	0.129773i
$976$	−1163.01	+	671.463i	−1.19161	+	0.687974i
$977$	889.489	+	1540.64i	0.910429	+	1.57691i	0.813459	+	0.581622i	$0.197582\pi$
$977$	889.489	+	1540.64i	0.910429	+	1.57691i	0.0969695	+	0.995287i	$0.469085\pi$
$978$	−553.971	−	97.4540i	−0.566433	−	0.0996462i
$979$	−9.56174	−	5.52047i	−0.00976684	−	0.00563889i
$980$		0			0
$981$	765.348	−	643.237i	0.780172	−	0.655695i
$982$	183.195			0.186553
$983$	−199.156	−	114.983i	−0.202601	−	0.116972i	0.395267	−	0.918566i	$-0.370652\pi$
$983$	−199.156	−	114.983i	−0.202601	−	0.116972i	−0.597868	+	0.801595i	$0.703985\pi$
$984$	348.104	+	291.859i	0.353764	+	0.296605i
$985$	292.034	−	168.606i	0.296482	−	0.171174i
$986$	−899.400	+	519.269i	−0.912170	+	0.526642i
$987$		0			0
$988$	62.2052	−	107.743i	0.0629607	−	0.109051i
$989$	−586.089			−0.592608
$990$	−14.3011	+	2.53334i	−0.0144456	+	0.00255893i
$991$	1123.95			1.13416			0.567078	−	0.823664i	$-0.308074\pi$
$991$	1123.95			1.13416			0.567078	+	0.823664i	$0.308074\pi$
$992$	−674.238	−	389.272i	−0.679676	−	0.392411i
$993$	100.919	+	17.7536i	0.101631	+	0.0178787i
$994$		0			0
$995$	−279.466	−	484.050i	−0.280870	−	0.486482i
$996$	269.445	−	98.1906i	0.270527	−	0.0985850i
$997$	554.198	+	319.966i	0.555866	+	0.320929i	0.751484	−	0.659751i	$-0.229338\pi$
$997$	554.198	+	319.966i	0.555866	+	0.320929i	−0.195619	+	0.980680i	$0.562672\pi$
$998$	−61.7099			−0.0618336
$999$	−691.158	−	397.946i	−0.691850	−	0.398345i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.3.l.b.97.4		28
7.2	even	3		63.3.t.a.52.11	yes	28
7.3	odd	6		63.3.k.a.61.4	yes	28
7.4	even	3		441.3.k.b.313.4		28
7.5	odd	6		441.3.t.a.178.11		28
7.6	odd	2		441.3.l.a.97.4		28
9.4	even	3		441.3.l.a.391.4		28
21.2	odd	6		189.3.t.a.73.4		28
21.17	even	6		189.3.k.a.19.11		28
63.4	even	3		441.3.t.a.166.11		28
63.13	odd	6	inner	441.3.l.b.391.4		28
63.23	odd	6		189.3.k.a.10.11		28
63.31	odd	6		63.3.t.a.40.11	yes	28
63.40	odd	6		441.3.k.b.31.4		28
63.58	even	3		63.3.k.a.31.4	✓	28
63.59	even	6		189.3.t.a.145.4		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.3.k.a.31.4	✓	28	63.58	even	3
63.3.k.a.61.4	yes	28	7.3	odd	6
63.3.t.a.40.11	yes	28	63.31	odd	6
63.3.t.a.52.11	yes	28	7.2	even	3
189.3.k.a.10.11		28	63.23	odd	6
189.3.k.a.19.11		28	21.17	even	6
189.3.t.a.73.4		28	21.2	odd	6
189.3.t.a.145.4		28	63.59	even	6
441.3.k.b.31.4		28	63.40	odd	6
441.3.k.b.313.4		28	7.4	even	3
441.3.l.a.97.4		28	7.6	odd	2
441.3.l.a.391.4		28	9.4	even	3
441.3.l.b.97.4		28	1.1	even	1	trivial
441.3.l.b.391.4		28	63.13	odd	6	inner
441.3.t.a.166.11		28	63.4	even	3
441.3.t.a.178.11		28	7.5	odd	6

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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	441.l (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.12025 + 1.94033i) q^{2} +(-1.02718 - 2.81867i) q^{3} +(-0.509909 - 0.883189i) q^{4} +(1.67528 - 0.967222i) q^{5} +(6.61983 + 1.16455i) q^{6} -6.67708 q^{8} +(-6.88982 + 5.79054i) q^{9} +4.33411i q^{10} +(0.186168 - 0.322453i) q^{11} +(-1.96565 + 2.34446i) q^{12} +(5.01827 - 2.89730i) q^{13} +(-4.44709 - 3.72855i) q^{15} +(9.51962 - 16.4885i) q^{16} -11.5075i q^{17} +(-3.51724 - 19.8553i) q^{18} +21.0528i q^{19} +(-1.70848 - 0.986391i) q^{20} +(0.417109 + 0.722455i) q^{22} +(-13.6417 - 23.6282i) q^{23} +(6.85854 + 18.8205i) q^{24} +(-10.6290 + 18.4099i) q^{25} +12.9828i q^{26} +(23.3987 + 13.4722i) q^{27} +(-20.1404 + 34.8842i) q^{29} +(12.2164 - 4.45190i) q^{30} +(-42.2746 + 24.4073i) q^{31} +(7.97450 + 13.8122i) q^{32} +(-1.10012 - 0.193531i) q^{33} +(22.3282 + 12.8912i) q^{34} +(8.62732 + 3.13236i) q^{36} -29.5383 q^{37} +(-40.8493 - 23.5844i) q^{38} +(-13.3212 - 11.1688i) q^{39} +(-11.1860 + 6.45822i) q^{40} +(19.6397 - 11.3390i) q^{41} +(10.7407 - 18.6035i) q^{43} -0.379716 q^{44} +(-5.94161 + 16.3648i) q^{45} +61.1285 q^{46} +(-46.1622 - 26.6518i) q^{47} +(-56.2539 - 9.89612i) q^{48} +(-23.8141 - 41.2473i) q^{50} +(-32.4358 + 11.8202i) q^{51} +(-5.11773 - 2.95472i) q^{52} -87.4600 q^{53} +(-52.3528 + 30.3089i) q^{54} -0.720265i q^{55} +(59.3409 - 21.6249i) q^{57} +(-45.1245 - 78.1579i) q^{58} +(-7.99438 + 4.61556i) q^{59} +(-1.02540 + 5.82884i) q^{60} +(-61.0848 - 35.2673i) q^{61} -109.369i q^{62} +40.4233 q^{64} +(5.60467 - 9.70757i) q^{65} +(1.60792 - 1.91778i) q^{66} +(37.7720 + 65.4230i) q^{67} +(-10.1633 + 5.86777i) q^{68} +(-52.5876 + 62.7219i) q^{69} -97.4729 q^{71} +(46.0039 - 38.6639i) q^{72} +86.9800i q^{73} +(33.0902 - 57.3139i) q^{74} +(62.8093 + 11.0493i) q^{75} +(18.5936 - 10.7350i) q^{76} +(36.5942 - 13.3356i) q^{78} +(23.5997 - 40.8759i) q^{79} -36.8303i q^{80} +(13.9392 - 79.7916i) q^{81} +50.8098i q^{82} +(-81.1770 - 46.8676i) q^{83} +(-11.1303 - 19.2782i) q^{85} +(24.0646 + 41.6810i) q^{86} +(119.015 + 20.9370i) q^{87} +(-1.24306 + 2.15305i) q^{88} -29.6531i q^{89} +(-25.0969 - 29.8612i) q^{90} +(-13.9121 + 24.0965i) q^{92} +(112.220 + 94.0877i) q^{93} +(103.426 - 59.7132i) q^{94} +(20.3627 + 35.2693i) q^{95} +(30.7410 - 36.6651i) q^{96} +(122.538 + 70.7471i) q^{97} +(0.584513 + 3.29966i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + q^{2} - 23 q^{4} + 3 q^{5} - 12 q^{6} - 16 q^{8} + 6 q^{9} + 7 q^{11} + 27 q^{12} - 15 q^{13} - 18 q^{15} - 27 q^{16} + 9 q^{18} - 108 q^{20} - 10 q^{22} + 34 q^{23} + 120 q^{24} + 31 q^{25} + 81 q^{27}+ \cdots - 162 q^{99}+O(q^{100}) \) 28 * q + q^2 - 23 * q^4 + 3 * q^5 - 12 * q^6 - 16 * q^8 + 6 * q^9 + 7 * q^11 + 27 * q^12 - 15 * q^13 - 18 * q^15 - 27 * q^16 + 9 * q^18 - 108 * q^20 - 10 * q^22 + 34 * q^23 + 120 * q^24 + 31 * q^25 + 81 * q^27 + 70 * q^29 + 33 * q^30 + 45 * q^31 + 153 * q^32 - 111 * q^33 - 12 * q^34 - 174 * q^36 - 18 * q^37 - 87 * q^38 - 9 * q^39 + 102 * q^40 + 234 * q^41 + 30 * q^43 - 102 * q^44 + 3 * q^45 + 44 * q^46 - 111 * q^47 - 147 * q^48 + 241 * q^50 - 6 * q^51 + 219 * q^52 - 296 * q^53 + 207 * q^54 + 189 * q^57 + 17 * q^58 + 42 * q^59 - 489 * q^60 + 120 * q^61 - 48 * q^64 + 114 * q^65 - 705 * q^66 - 34 * q^67 + 18 * q^68 - 78 * q^69 - 350 * q^71 + 177 * q^72 + 359 * q^74 + 387 * q^75 - 72 * q^76 - 375 * q^78 - 82 * q^79 + 438 * q^81 - 738 * q^83 + 3 * q^85 + 17 * q^86 + 564 * q^87 + 25 * q^88 + 543 * q^90 + 288 * q^92 - 30 * q^93 - 3 * q^94 + 507 * q^95 - 813 * q^96 + 57 * q^97 - 162 * q^99

Introduction

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