LMFDB - Embedded newform 441.3.t.a.178.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [441,3,Mod(166,441)] 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("441.166"); 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([2, 5])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	441.t (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [28,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == 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			178.11
Character	$\chi$	$=$	441.178
Dual form			441.3.t.a.166.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.24050 q^{2} +(-2.95463 - 0.519775i) q^{3} +1.01982 q^{4} +(1.67528 + 0.967222i) q^{5} +(-6.61983 - 1.16455i) q^{6} -6.67708 q^{8} +(8.45967 + 3.07148i) q^{9} +(3.75345 + 2.16706i) q^{10} +(0.186168 + 0.322453i) q^{11} +(-3.01319 - 0.530076i) q^{12} +(-5.01827 + 2.89730i) q^{13} +(-4.44709 - 3.72855i) q^{15} -19.0392 q^{16} +(-9.96576 - 5.75374i) q^{17} +(18.9538 + 6.88165i) q^{18} +(-18.2323 + 10.5264i) q^{19} +(1.70848 + 0.986391i) q^{20} +(0.417109 + 0.722455i) q^{22} +(-13.6417 + 23.6282i) q^{23} +(19.7283 + 3.47058i) q^{24} +(-10.6290 - 18.4099i) q^{25} +(-11.2434 + 6.49139i) q^{26} +(-23.3987 - 13.4722i) q^{27} +(-20.1404 + 34.8842i) q^{29} +(-9.96367 - 8.35380i) q^{30} +48.8145i q^{31} -15.9490 q^{32} +(-0.382456 - 1.04950i) q^{33} +(-22.3282 - 12.8912i) q^{34} +(8.62732 + 3.13236i) q^{36} +(14.7691 + 25.5809i) q^{37} +(-40.8493 + 23.5844i) q^{38} +(16.3331 - 5.95208i) q^{39} +(-11.1860 - 6.45822i) q^{40} +(-19.6397 + 11.3390i) q^{41} +(10.7407 - 18.6035i) q^{43} +(0.189858 + 0.328844i) q^{44} +(11.2015 + 13.3280i) q^{45} +(-30.5642 + 52.9388i) q^{46} -53.3035i q^{47} +(56.2539 + 9.89612i) q^{48} +(-23.8141 - 41.2473i) q^{50} +(26.4545 + 22.1801i) q^{51} +(-5.11773 + 2.95472i) q^{52} +(43.7300 - 75.7426i) q^{53} +(-52.4247 - 30.1844i) q^{54} +0.720265i q^{55} +(59.3409 - 21.6249i) q^{57} +(-45.1245 + 78.1579i) q^{58} +9.23111i q^{59} +(-4.53522 - 3.80244i) q^{60} -70.5346i q^{61} +109.369i q^{62} +40.4233 q^{64} -11.2093 q^{65} +(-0.856890 - 2.35139i) q^{66} -75.5440 q^{67} +(-10.1633 - 5.86777i) q^{68} +(52.5876 - 62.7219i) q^{69} -97.4729 q^{71} +(-56.4859 - 20.5086i) q^{72} +(75.3269 + 43.4900i) q^{73} +(33.0902 + 57.3139i) q^{74} +(21.8356 + 59.9191i) q^{75} +(-18.5936 + 10.7350i) q^{76} +(36.5942 - 13.3356i) q^{78} -47.1994 q^{79} +(-31.8960 - 18.4152i) q^{80} +(62.1320 + 51.9675i) q^{81} +(-44.0025 + 25.4049i) q^{82} +(81.1770 + 46.8676i) q^{83} +(-11.1303 - 19.2782i) q^{85} +(24.0646 - 41.6810i) q^{86} +(77.6394 - 92.6014i) q^{87} +(-1.24306 - 2.15305i) q^{88} +(25.6803 - 14.8266i) q^{89} +(25.0969 + 29.8612i) q^{90} +(-13.9121 + 24.0965i) q^{92} +(25.3726 - 144.229i) q^{93} -119.426i q^{94} -40.7255 q^{95} +(47.1234 + 8.28989i) q^{96} +(-122.538 - 70.7471i) q^{97} +(0.584513 + 3.29966i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 2 q^{2} + 3 q^{3} + 46 q^{4} + 3 q^{5} + 12 q^{6} - 16 q^{8} - 15 q^{9} + 6 q^{10} + 7 q^{11} + 30 q^{12} + 15 q^{13} - 18 q^{15} + 54 q^{16} + 33 q^{17} - 42 q^{18} + 6 q^{19} + 108 q^{20} - 10 q^{22}+ \cdots - 162 q^{99}+O(q^{100}) $ 28 * q - 2 * q^2 + 3 * q^3 + 46 * q^4 + 3 * q^5 + 12 * q^6 - 16 * q^8 - 15 * q^9 + 6 * q^10 + 7 * q^11 + 30 * q^12 + 15 * q^13 - 18 * q^15 + 54 * q^16 + 33 * q^17 - 42 * q^18 + 6 * q^19 + 108 * q^20 - 10 * q^22 + 34 * q^23 + 78 * q^24 + 31 * q^25 - 54 * q^26 - 81 * q^27 + 70 * q^29 - 27 * q^30 - 306 * q^32 + 3 * q^33 + 12 * q^34 - 174 * q^36 + 9 * q^37 - 87 * q^38 + 129 * q^39 + 102 * q^40 - 234 * q^41 + 30 * q^43 + 51 * q^44 - 273 * q^45 - 22 * q^46 + 147 * q^48 + 241 * q^50 + 12 * q^51 + 219 * q^52 + 148 * q^53 - 171 * q^54 + 189 * q^57 + 17 * q^58 + 33 * q^60 - 48 * q^64 - 228 * q^65 - 258 * q^66 + 68 * q^67 + 18 * q^68 + 78 * q^69 - 350 * q^71 + 162 * q^72 + 6 * q^73 + 359 * q^74 + 510 * q^75 + 72 * q^76 - 375 * q^78 + 164 * q^79 + 609 * q^80 - 435 * q^81 + 18 * q^82 + 738 * q^83 + 3 * q^85 + 17 * q^86 + 561 * q^87 + 25 * q^88 - 21 * q^89 - 543 * q^90 + 288 * q^92 - 222 * q^93 - 1014 * q^95 - 231 * q^96 - 57 * q^97 - 162 * q^99

Character values

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

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	2.24050			1.12025			0.560124	−	0.828409i	$-0.310754\pi$
$2$	2.24050			1.12025			0.560124	+	0.828409i	$0.310754\pi$
$3$	−2.95463	−	0.519775i	−0.984876	−	0.173258i
$3$	−2.95463	−	0.519775i	−0.984876	−	0.173258i
$4$	1.01982			0.254955
$5$	1.67528	+	0.967222i	0.335055	+	0.193444i	0.658083	−	0.752945i	$-0.271367\pi$
$5$	1.67528	+	0.967222i	0.335055	+	0.193444i	−0.323028	+	0.946389i	$0.604701\pi$
$6$	−6.61983	−	1.16455i	−1.10331	−	0.194092i
$7$		0			0
$7$		0			0
$8$	−6.67708			−0.834635
$9$	8.45967	+	3.07148i	0.939963	+	0.341276i
$10$	3.75345	+	2.16706i	0.375345	+	0.216706i
$11$	0.186168	+	0.322453i	0.0169244	+	0.0293139i	0.874364	−	0.485271i	$-0.161279\pi$
$11$	0.186168	+	0.322453i	0.0169244	+	0.0293139i	−0.857439	+	0.514585i	$0.827946\pi$
$12$	−3.01319	−	0.530076i	−0.251099	−	0.0441730i
$13$	−5.01827	+	2.89730i	−0.386021	+	0.222869i	−0.680435	−	0.732809i	$-0.738209\pi$
$13$	−5.01827	+	2.89730i	−0.386021	+	0.222869i	0.294414	+	0.955678i	$0.404876\pi$
$14$		0			0
$15$	−4.44709	−	3.72855i	−0.296472	−	0.248570i
$16$	−19.0392			−1.18995
$17$	−9.96576	−	5.75374i	−0.586221	−	0.338455i	0.177381	−	0.984142i	$-0.443238\pi$
$17$	−9.96576	−	5.75374i	−0.586221	−	0.338455i	−0.763602	+	0.645687i	$0.776571\pi$
$18$	18.9538	+	6.88165i	1.05299	+	0.382314i
$19$	−18.2323	+	10.5264i	−0.959593	+	0.554021i	−0.896048	−	0.443958i	$-0.853574\pi$
$19$	−18.2323	+	10.5264i	−0.959593	+	0.554021i	−0.0635451	+	0.997979i	$0.520241\pi$
$20$	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	0.400690	+	0.916214i	$0.368770\pi$
$23$	−13.6417	+	23.6282i	−0.593119	+	1.02731i	−0.993809	+	0.111099i	$0.964563\pi$
$24$	19.7283	+	3.47058i	0.822013	+	0.144608i
$25$	−10.6290	−	18.4099i	−0.425159	−	0.736396i
$26$	−11.2434	+	6.49139i	−0.432439	+	0.249669i
$27$	−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	$0.922294\pi$
$30$	−9.96367	−	8.35380i	−0.332122	−	0.278460i
$31$			48.8145i			1.57466i	0.616530	+	0.787331i	$0.288538\pi$
$31$			48.8145i			1.57466i	−0.616530	+	0.787331i	$0.711462\pi$
$32$	−15.9490			−0.498406
$33$	−0.382456	−	1.04950i	−0.0115896	−	0.0318029i
$34$	−22.3282	−	12.8912i	−0.656713	−	0.379154i
$35$		0			0
$36$	8.62732	+	3.13236i	0.239648	+	0.0870099i
$37$	14.7691	+	25.5809i	0.399166	+	0.691376i	0.993623	−	0.112751i	$-0.0359663\pi$
$37$	14.7691	+	25.5809i	0.399166	+	0.691376i	−0.594457	+	0.804127i	$0.702633\pi$
$38$	−40.8493	+	23.5844i	−1.07498	+	0.620641i
$39$	16.3331	−	5.95208i	0.418797	−	0.152617i
$40$	−11.1860	−	6.45822i	−0.279649	−	0.161455i
$41$	−19.6397	+	11.3390i	−0.479016	+	0.276560i	−0.720006	−	0.693968i	$-0.755861\pi$
$41$	−19.6397	+	11.3390i	−0.479016	+	0.276560i	0.240990	+	0.970528i	$0.422528\pi$
$42$		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	$0.0863069\pi$
$44$	0.189858	+	0.328844i	0.00431495	+	0.00747372i
$45$	11.2015	+	13.3280i	0.248922	+	0.296177i
$46$	−30.5642	+	52.9388i	−0.664440	+	1.15084i
$47$		−	53.3035i		−	1.13412i	−0.823677	−	0.567059i	$-0.808081\pi$
$47$		−	53.3035i		−	1.13412i	0.823677	−	0.567059i	$-0.191919\pi$
$48$	56.2539	+	9.89612i	1.17196	+	0.206169i
$49$		0			0
$50$	−23.8141	−	41.2473i	−0.476283	−	0.824946i
$51$	26.4545	+	22.1801i	0.518716	+	0.434904i
$52$	−5.11773	+	2.95472i	−0.0984178	+	0.0568216i
$53$	43.7300	−	75.7426i	0.825094	−	1.42911i	−0.0767530	−	0.997050i	$-0.524455\pi$
$53$	43.7300	−	75.7426i	0.825094	−	1.42911i	0.901847	−	0.432055i	$-0.142211\pi$
$54$	−52.4247	−	30.1844i	−0.970827	−	0.558971i
$55$			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
$59$			9.23111i			0.156460i	0.996935	+	0.0782298i	$0.0249268\pi$
$59$			9.23111i			0.156460i	−0.996935	+	0.0782298i	$0.975073\pi$
$60$	−4.53522	−	3.80244i	−0.0755870	−	0.0633740i
$61$		−	70.5346i		−	1.15631i	−0.815929	−	0.578153i	$-0.803774\pi$
$61$		−	70.5346i		−	1.15631i	0.815929	−	0.578153i	$-0.196226\pi$
$62$			109.369i			1.76401i
$63$		0			0
$64$	40.4233			0.631614
$65$	−11.2093			−0.172451
$66$	−0.856890	−	2.35139i	−0.0129832	−	0.0356271i
$67$	−75.5440			−1.12752			−0.563761	−	0.825938i	$-0.690646\pi$
$67$	−75.5440			−1.12752			−0.563761	+	0.825938i	$0.690646\pi$
$68$	−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	$0.740823\pi$
$72$	−56.4859	−	20.5086i	−0.784526	−	0.284841i
$73$	75.3269	+	43.4900i	1.03188	+	0.595754i	0.917521	−	0.397687i	$-0.130187\pi$
$73$	75.3269	+	43.4900i	1.03188	+	0.595754i	0.114354	+	0.993440i	$0.463520\pi$
$74$	33.0902	+	57.3139i	0.447165	+	0.774512i
$75$	21.8356	+	59.9191i	0.291142	+	0.798922i
$76$	−18.5936	+	10.7350i	−0.244653	+	0.141250i
$77$		0			0
$78$	36.5942	−	13.3356i	0.469156	−	0.170969i
$79$	−47.1994			−0.597461			−0.298730	−	0.954338i	$-0.596563\pi$
$79$	−47.1994			−0.597461			−0.298730	+	0.954338i	$0.596563\pi$
$80$	−31.8960	−	18.4152i	−0.398700	−	0.230190i
$81$	62.1320	+	51.9675i	0.767061	+	0.641574i
$82$	−44.0025	+	25.4049i	−0.536616	+	0.309816i
$83$	81.1770	+	46.8676i	0.978036	+	0.564669i	0.901677	−	0.432411i	$-0.142337\pi$
$83$	81.1770	+	46.8676i	0.978036	+	0.564669i	0.0763594	+	0.997080i	$0.475670\pi$
$84$		0			0
$85$	−11.1303	−	19.2782i	−0.130944	−	0.226802i
$86$	24.0646	−	41.6810i	0.279821	−	0.484663i
$87$	77.6394	−	92.6014i	0.892407	−	1.06438i
$88$	−1.24306	−	2.15305i	−0.0141257	−	0.0244664i
$89$	25.6803	−	14.8266i	0.288543	−	0.166590i	−0.348742	−	0.937219i	$-0.613391\pi$
$89$	25.6803	−	14.8266i	0.288543	−	0.166590i	0.637285	+	0.770628i	$0.280058\pi$
$90$	25.0969	+	29.8612i	0.278854	+	0.331792i
$91$		0			0
$92$	−13.9121	+	24.0965i	−0.151218	+	0.261918i
$93$	25.3726	−	144.229i	0.272823	−	1.55085i
$94$		−	119.426i		−	1.27049i
$95$	−40.7255			−0.428689
$96$	47.1234	+	8.28989i	0.490869	+	0.0863531i
$97$	−122.538	−	70.7471i	−1.26327	−	0.729351i	−0.289567	−	0.957158i	$-0.593511\pi$
$97$	−122.538	−	70.7471i	−1.26327	−	0.729351i	−0.973706	+	0.227806i	$0.926845\pi$
$98$		0			0
$99$	0.584513	+	3.29966i	0.00590417	+	0.0333299i
$100$	−10.8396	−	18.7748i	−0.108396	−	0.187748i
$101$	−40.6345	+	23.4603i	−0.402321	+	0.232280i	−0.687485	−	0.726198i	$-0.741285\pi$
$101$	−40.6345	+	23.4603i	−0.402321	+	0.232280i	0.285164	+	0.958479i	$0.407952\pi$
$102$	59.2712	+	49.6944i	0.581090	+	0.487200i
$103$	113.923	+	65.7733i	1.10605	+	0.638576i	0.937802	−	0.347169i	$-0.112857\pi$
$103$	113.923	+	65.7733i	1.10605	+	0.638576i	0.168244	+	0.985745i	$0.446190\pi$
$104$	33.5074	−	19.3455i	0.322187	−	0.186015i
$105$		0			0
$106$	97.9768	−	169.701i	0.924310	−	1.60095i
$107$	69.9586	+	121.172i	0.653819	+	1.13245i	0.982188	+	0.187899i	$0.0601676\pi$
$107$	69.9586	+	121.172i	0.653819	+	1.13245i	−0.328369	+	0.944549i	$0.606499\pi$
$108$	−23.8624	−	13.7392i	−0.220948	−	0.127215i
$109$	55.5420	−	96.2016i	0.509560	−	0.882583i	−0.490379	−	0.871509i	$-0.663142\pi$
$109$	55.5420	−	96.2016i	0.509560	−	0.882583i	0.999939	−	0.0110739i	$-0.00352500\pi$
$110$			1.61375i			0.0146704i
$111$	−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	$0.685030\pi$
$114$	132.953	−	48.4506i	1.16626	−	0.425005i
$115$	−45.7074	+	26.3892i	−0.397456	+	0.229471i
$116$	−20.5396	+	35.5756i	−0.177065	+	0.306686i
$117$	−51.3519	+	9.09666i	−0.438906	+	0.0777492i
$118$			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
$122$		−	158.032i		−	1.29535i
$123$	63.9216	−	23.2942i	0.519688	−	0.189384i
$124$			49.7820i			0.401468i
$125$		−	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	$0.561923\pi$
$128$	154.364			1.20597
$129$	−41.4045	+	49.3837i	−0.320965	+	0.382819i
$130$	−25.1145			−0.193188
$131$	107.596	+	62.1204i	0.821341	+	0.474202i	0.850879	−	0.525362i	$-0.176070\pi$
$131$	107.596	+	62.1204i	0.821341	+	0.474202i	−0.0295376	+	0.999564i	$0.509403\pi$
$132$	−0.390035	−	1.07029i	−0.00295481	−	0.00810829i
$133$		0			0
$134$	−169.256			−1.26310
$135$	−26.1687	−	45.2014i	−0.193842	−	0.334826i
$136$	66.5422	+	38.4182i	0.489281	+	0.282487i
$137$	−2.31536	−	4.01032i	−0.0169004	−	0.0292724i	0.857452	−	0.514565i	$-0.172046\pi$
$137$	−2.31536	−	4.01032i	−0.0169004	−	0.0292724i	−0.874352	+	0.485292i	$0.838713\pi$
$138$	117.822	−	140.528i	0.853785	−	1.01832i
$139$	−37.7043	+	21.7686i	−0.271254	+	0.156608i	−0.629457	−	0.777035i	$-0.716723\pi$
$139$	−37.7043	+	21.7686i	−0.271254	+	0.156608i	0.358204	+	0.933644i	$0.383389\pi$
$140$		0			0
$141$	−27.7058	+	157.492i	−0.196495	+	1.11697i
$142$	−218.387			−1.53794
$143$	−1.86849	−	1.07877i	−0.0130664	−	0.00754386i
$144$	−161.066	−	58.4787i	−1.11851	−	0.406102i
$145$	−67.4815	+	38.9605i	−0.465390	+	0.268693i
$146$	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	−0.818595	−	0.574372i	$-0.805246\pi$
$149$	13.1304	−	22.7425i	0.0881232	−	0.152634i	0.906718	+	0.421738i	$0.138580\pi$
$150$	48.9226	+	134.248i	0.326151	+	0.894990i
$151$	−59.9365	−	103.813i	−0.396931	−	0.687504i	0.596415	−	0.802676i	$-0.296591\pi$
$151$	−59.9365	−	103.813i	−0.396931	−	0.687504i	−0.993346	+	0.115172i	$0.963258\pi$
$152$	121.738	−	70.2857i	0.800910	−	0.462406i
$153$	−66.6345	−	79.2844i	−0.435520	−	0.518199i
$154$		0			0
$155$	−47.2145	+	81.7779i	−0.304610	+	0.527599i
$156$	16.6568	−	6.07004i	0.106774	−	0.0389105i
$157$		−	195.955i		−	1.24812i	−0.781377	−	0.624059i	$-0.785482\pi$
$157$		−	195.955i		−	1.24812i	0.781377	−	0.624059i	$-0.214518\pi$
$158$	−105.750			−0.669304
$159$	−168.575	+	201.061i	−1.06022	+	1.26454i
$160$	−26.7190	−	15.4262i	−0.166994	−	0.0964139i
$161$		0			0
$162$	139.206	+	116.433i	0.859299	+	0.718722i
$163$	41.8418	+	72.4721i	0.256698	+	0.444614i	0.965355	−	0.260939i	$-0.0840321\pi$
$163$	41.8418	+	72.4721i	0.256698	+	0.444614i	−0.708657	+	0.705553i	$0.750699\pi$
$164$	−20.0289	+	11.5637i	−0.122127	+	0.0705102i
$165$	0.374376	−	2.12811i	0.00226894	−	0.0128977i
$166$	181.877	+	105.007i	1.09564	+	0.632569i
$167$	−215.835	+	124.612i	−1.29242	+	0.746181i	−0.979083	−	0.203460i	$-0.934781\pi$
$167$	−215.835	+	124.612i	−1.29242	+	0.746181i	−0.313340	+	0.949641i	$0.601448\pi$
$168$		0			0
$169$	−67.7113	+	117.279i	−0.400659	+	0.693961i
$170$	−24.9373	−	43.1927i	−0.146690	−	0.254075i
$171$	−186.571	+	33.0497i	−1.09106	+	0.193273i
$172$	10.9536	−	18.9722i	0.0636837	−	0.110303i
$173$			278.453i			1.60956i	0.593575	+	0.804779i	$0.297716\pi$
$173$			278.453i			1.60956i	−0.593575	+	0.804779i	$0.702284\pi$
$174$	173.951	−	207.473i	0.999716	−	1.19237i
$175$		0			0
$176$	−3.54451	−	6.13926i	−0.0201392	−	0.0348822i
$177$	4.79810	−	27.2745i	0.0271079	−	0.154093i
$178$	57.5367	−	33.2188i	0.323240	−	0.186623i
$179$	−128.758	+	223.015i	−0.719317	+	1.24589i	0.241954	+	0.970288i	$0.422212\pi$
$179$	−128.758	+	223.015i	−0.719317	+	1.24589i	−0.961271	+	0.275605i	$0.911122\pi$
$180$	11.4235	+	13.5921i	0.0634638	+	0.0755117i
$181$		−	29.2542i		−	0.161625i	−0.996729	−	0.0808126i	$-0.974248\pi$
$181$		−	29.2542i		−	0.161625i	0.996729	−	0.0808126i	$-0.0257515\pi$
$182$		0			0
$183$	−36.6621	+	208.404i	−0.200340	+	1.13882i
$184$	91.0870	−	157.767i	0.495038	−	0.857431i
$185$			57.1402i			0.308866i
$186$	56.8471	−	323.144i	0.305630	−	1.73733i
$187$		−	4.28466i		−	0.0229126i
$188$		−	54.3599i		−	0.289149i
$189$		0			0
$190$	−91.2452			−0.480238
$191$	−60.7704			−0.318170			−0.159085	−	0.987265i	$-0.550854\pi$
$191$	−60.7704			−0.318170			−0.159085	+	0.987265i	$0.550854\pi$
$192$	−119.436	−	21.0110i	−0.622062	−	0.109432i
$193$	24.8767			0.128895			0.0644474	−	0.997921i	$-0.479472\pi$
$193$	24.8767			0.128895			0.0644474	+	0.997921i	$0.479472\pi$
$194$	−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	$0.354114\pi$
$198$	1.30960	+	7.39287i	0.00661413	+	0.0373377i
$199$	−250.227	−	144.468i	−1.25742	−	0.725972i	−0.284848	−	0.958573i	$-0.591943\pi$
$199$	−250.227	−	144.468i	−1.25742	−	0.725972i	−0.972572	+	0.232600i	$0.925277\pi$
$200$	70.9705	+	122.924i	0.354852	+	0.614622i
$201$	223.204	+	39.2659i	1.11047	+	0.195353i
$202$	−91.0413	+	52.5627i	−0.450699	+	0.260211i
$203$		0			0
$204$	26.9788	+	22.6197i	0.132249	+	0.110881i
$205$	−43.8692			−0.213996
$206$	255.243	+	147.365i	1.23905	+	0.715363i
$207$	−187.978	+	157.986i	−0.908107	+	0.763218i
$208$	95.5441	−	55.1624i	0.459347	−	0.265204i
$209$	−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
$213$	287.996	+	50.6640i	1.35209	+	0.237859i
$214$	156.742	+	271.485i	0.732439	+	1.26862i
$215$	35.9874	−	20.7773i	0.167383	−	0.0966388i
$216$	156.235	+	89.9551i	0.723310	+	0.416459i
$217$		0			0
$218$	124.442	−	215.539i	0.570833	−	0.988712i
$219$	−199.958	−	167.650i	−0.913050	−	0.765525i
$220$			0.734539i			0.00333881i
$221$	66.6812			0.301725
$222$	−67.9789	−	186.541i	−0.306211	−	0.840274i
$223$	−14.0772	−	8.12745i	−0.0631263	−	0.0364460i	0.468105	−	0.883673i	$-0.344937\pi$
$223$	−14.0772	−	8.12745i	−0.0631263	−	0.0364460i	−0.531231	+	0.847227i	$0.678270\pi$
$224$		0			0
$225$	−33.3718	−	188.388i	−0.148319	−	0.837282i
$226$	113.736	+	196.996i	0.503255	+	0.871664i
$227$	26.4526	−	15.2724i	0.116531	−	0.0672793i	−0.440602	−	0.897703i	$-0.645235\pi$
$227$	26.4526	−	15.2724i	0.116531	−	0.0672793i	0.557133	+	0.830423i	$0.311901\pi$
$228$	60.5170	−	22.0535i	0.265425	−	0.0967259i
$229$	−158.134	−	91.2986i	−0.690541	−	0.398684i	0.113274	−	0.993564i	$-0.463866\pi$
$229$	−158.134	−	91.2986i	−0.690541	−	0.398684i	−0.803815	+	0.594880i	$0.797200\pi$
$230$	−102.407	+	59.1248i	−0.445249	+	0.257064i
$231$		0			0
$232$	134.479	−	232.925i	0.579652	−	1.00399i
$233$	174.898	+	302.932i	0.750635	+	1.30014i	0.947515	+	0.319710i	$0.103586\pi$
$233$	174.898	+	302.932i	0.750635	+	1.30014i	−0.196880	+	0.980428i	$0.563081\pi$
$234$	−115.054	+	20.3810i	−0.491683	+	0.0870984i
$235$	51.5563	−	89.2982i	0.219389	−	0.379992i
$236$			9.41406i			0.0398901i
$237$	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	$0.766769\pi$
$240$	84.6692	+	70.9888i	0.352788	+	0.295786i
$241$	−243.343	+	140.494i	−1.00972	+	0.582964i	−0.911110	−	0.412162i	$-0.864774\pi$
$241$	−243.343	+	140.494i	−1.00972	+	0.582964i	−0.0986123	+	0.995126i	$0.531440\pi$
$242$	135.395	−	234.510i	0.559482	−	0.969051i
$243$	−156.566	−	185.839i	−0.644303	−	0.764771i
$244$		−	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
$248$		−	325.939i		−	1.31427i
$249$	−215.487	−	180.670i	−0.865411	−	0.725582i
$250$		−	200.487i		−	0.801948i
$251$			16.5983i			0.0661286i	0.999453	+	0.0330643i	$0.0105266\pi$
$251$			16.5983i			0.0661286i	−0.999453	+	0.0330643i	$0.989473\pi$
$252$		0			0
$253$	−10.1586			−0.0401527
$254$	−110.011			−0.433116
$255$	22.8655	+	62.7452i	0.0896687	+	0.246060i
$256$	184.159			0.719371
$257$	−73.7864	−	42.6006i	−0.287106	−	0.165761i	0.349530	−	0.936925i	$-0.386341\pi$
$257$	−73.7864	−	42.6006i	−0.287106	−	0.165761i	−0.636636	+	0.771164i	$0.719675\pi$
$258$	−92.7666	+	110.644i	−0.359561	+	0.428852i
$259$		0			0
$260$	−11.4315			−0.0439672
$261$	−277.527	+	233.248i	−1.06332	+	0.893670i
$262$	241.068	+	139.180i	0.920105	+	0.531223i
$263$	178.327	+	308.872i	0.678050	+	1.17442i	0.975567	+	0.219701i	$0.0705082\pi$
$263$	178.327	+	308.872i	0.678050	+	1.17442i	−0.297517	+	0.954717i	$0.596158\pi$
$264$	2.55369	+	7.00757i	0.00967306	+	0.0265438i
$265$	146.520	−	84.5932i	0.552905	−	0.319220i
$266$		0			0
$267$	−83.5824	+	30.4590i	−0.313043	+	0.114079i
$268$	−77.0412			−0.287467
$269$	333.500	+	192.546i	1.23978	+	0.715785i	0.969048	−	0.246871i	$-0.0794025\pi$
$269$	333.500	+	192.546i	1.23978	+	0.715785i	0.270727	+	0.962656i	$0.412736\pi$
$270$	−58.6308	−	101.274i	−0.217151	−	0.375087i
$271$	−53.9536	+	31.1502i	−0.199091	+	0.114945i	−0.596231	−	0.802813i	$-0.703336\pi$
$271$	−53.9536	+	31.1502i	−0.199091	+	0.114945i	0.397140	+	0.917758i	$0.370003\pi$
$272$	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
$276$	53.6298	−	63.9649i	0.194311	−	0.231757i
$277$	−42.5057	−	73.6221i	−0.153450	−	0.265784i	0.779043	−	0.626970i	$-0.215705\pi$
$277$	−42.5057	−	73.6221i	−0.153450	−	0.265784i	−0.932494	+	0.361186i	$0.882372\pi$
$278$	−84.4762	+	48.7724i	−0.303871	+	0.175440i
$279$	−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	$0.0819781\pi$
$282$	−62.0748	+	352.861i	−0.220123	+	1.25128i
$283$		−	350.815i		−	1.23963i	−0.784748	−	0.619815i	$-0.787208\pi$
$283$		−	350.815i		−	1.23963i	0.784748	−	0.619815i	$-0.212792\pi$
$284$	−99.4046			−0.350016
$285$	120.329	+	21.1681i	0.422206	+	0.0742740i
$286$	−4.18634	−	2.41698i	−0.0146375	−	0.00845099i
$287$		0			0
$288$	−134.923	−	48.9871i	−0.468484	−	0.170094i
$289$	−78.2890	−	135.601i	−0.270896	−	0.469206i
$290$	−151.192	+	87.2908i	−0.521352	+	0.301003i
$291$	325.280	+	272.723i	1.11780	+	0.937194i
$292$	76.8198	+	44.3519i	0.263081	+	0.151890i
$293$	42.7689	−	24.6927i	0.145969	−	0.0842753i	−0.425237	−	0.905082i	$-0.639809\pi$
$293$	42.7689	−	24.6927i	0.145969	−	0.0842753i	0.571206	+	0.820807i	$0.306476\pi$
$294$		0			0
$295$	−8.92853	+	15.4647i	−0.0302662	+	0.0524226i
$296$	−98.6148	−	170.806i	−0.333158	−	0.577047i
$297$	−0.0119384	−	10.0531i	−4.01967e−5	−	0.0338488i
$298$	29.4185	−	50.9544i	0.0987198	−	0.170988i
$299$		−	158.097i		−	0.528752i
$300$	22.2684	+	61.1066i	0.0742280	+	0.203689i
$301$		0			0
$302$	−134.288	−	232.593i	−0.444661	−	0.770175i
$303$	132.254	−	48.1958i	0.436481	−	0.159062i
$304$	347.129	−	200.415i	1.14187	−	0.659259i
$305$	68.2226	−	118.165i	0.223681	−	0.387426i
$306$	−149.294	−	177.636i	−0.487890	−	0.580511i
$307$			432.680i			1.40938i	0.709515	+	0.704691i	$0.248914\pi$
$307$			432.680i			1.40938i	−0.709515	+	0.704691i	$0.751086\pi$
$308$		0			0
$309$	−302.412	−	253.550i	−0.978680	−	0.820550i
$310$	−105.784	+	183.223i	−0.341238	+	0.591042i
$311$			167.189i			0.537586i	0.963198	+	0.268793i	$0.0866248\pi$
$311$			167.189i			0.537586i	−0.963198	+	0.268793i	$0.913375\pi$
$312$	−109.057	+	39.7425i	−0.349543	+	0.127380i
$313$		−	258.585i		−	0.826151i	−0.910697	−	0.413075i	$-0.864455\pi$
$313$		−	258.585i		−	0.826151i	0.910697	−	0.413075i	$-0.135545\pi$
$314$		−	439.035i		−	1.39820i
$315$		0			0
$316$	−48.1348			−0.152325
$317$	−202.513			−0.638844			−0.319422	−	0.947613i	$-0.603489\pi$
$317$	−202.513			−0.638844			−0.319422	+	0.947613i	$0.603489\pi$
$318$	−377.691	+	450.477i	−1.18771	+	1.41660i
$319$	−14.9980			−0.0470158
$320$	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
$324$	63.3633	+	52.9974i	0.195566	+	0.163572i
$325$	106.678	+	61.5906i	0.328240	+	0.189510i
$326$	93.7463	+	162.373i	0.287565	+	0.498078i
$327$	−214.109	+	255.371i	−0.654768	+	0.780950i
$328$	131.136	−	75.7112i	0.399804	−	0.230827i
$329$		0			0
$330$	0.838787	−	4.76803i	0.00254178	−	0.0144486i
$331$	34.1563			0.103191			0.0515956	−	0.998668i	$-0.483569\pi$
$331$	34.1563			0.103191			0.0515956	+	0.998668i	$0.483569\pi$
$332$	82.7858	+	47.7964i	0.249355	+	0.143965i
$333$	46.3707	+	261.769i	0.139251	+	0.786094i
$334$	−483.576	+	279.193i	−1.44783	+	0.835907i
$335$	−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
$339$	−104.286	−	286.172i	−0.307629	−	0.844165i
$340$	−11.3509	−	19.6603i	−0.0333849	−	0.0578243i
$341$	−15.7404	+	9.08773i	−0.0461595	+	0.0266502i
$342$	−418.010	+	74.0478i	−1.22225	+	0.216514i
$343$		0			0
$344$	−71.7168	+	124.217i	−0.208479	+	0.361096i
$345$	148.765	−	54.2127i	0.431202	−	0.157138i
$346$			623.874i			1.80310i
$347$	−597.488			−1.72187			−0.860933	−	0.508718i	$-0.830119\pi$
$347$	−597.488			−1.72187			−0.860933	+	0.508718i	$0.830119\pi$
$348$	79.1781	−	94.4366i	0.227523	−	0.271370i
$349$	72.8266	+	42.0465i	0.208672	+	0.120477i	0.600694	−	0.799479i	$-0.294891\pi$
$349$	72.8266	+	42.0465i	0.208672	+	0.120477i	−0.392022	+	0.919956i	$0.628224\pi$
$350$		0			0
$351$	156.454	−	0.185795i	0.445738	−	0.000529331i
$352$	−2.96920	−	5.14281i	−0.00843523	−	0.0146102i
$353$	−397.017	+	229.218i	−1.12469	+	0.649343i	−0.942595	−	0.333937i	$-0.891623\pi$
$353$	−397.017	+	229.218i	−1.12469	+	0.649343i	−0.182099	+	0.983280i	$0.558289\pi$
$354$	10.7501	−	61.1084i	0.0303676	−	0.172623i
$355$	−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
$359$	6.42758	+	11.1329i	0.0179041	+	0.0310109i	0.874839	−	0.484414i	$-0.160967\pi$
$359$	6.42758	+	11.1329i	0.0179041	+	0.0310109i	−0.856935	+	0.515425i	$0.827634\pi$
$360$	−74.7932	−	88.9919i	−0.207759	−	0.247200i
$361$	41.1103	−	71.2051i	0.113879	−	0.197244i
$362$		−	65.5438i		−	0.181060i
$363$	−232.955	+	277.848i	−0.641748	+	0.765421i
$364$		0			0
$365$	84.1290	+	145.716i	0.230490	+	0.399221i
$366$	−82.1413	+	466.927i	−0.224430	+	1.27576i
$367$	−535.505	+	309.174i	−1.45914	+	0.842436i	−0.998969	−	0.0453934i	$-0.985546\pi$
$367$	−535.505	+	309.174i	−1.45914	+	0.842436i	−0.460173	+	0.887829i	$0.652213\pi$
$368$	259.728	−	449.863i	0.705784	−	1.22245i
$369$	−200.972	+	35.6009i	−0.544641	+	0.0964795i
$370$			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	−0.866413	−	0.499327i	$-0.833580\pi$
$373$	−0.289633	+	0.501659i	−0.000776495	+	0.00134493i	0.865637	+	0.500672i	$0.166914\pi$
$374$		−	9.59975i		−	0.0256678i
$375$	−46.5112	+	264.390i	−0.124030	+	0.705040i
$376$			355.912i			0.946575i
$377$		−	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	$0.492230\pi$
$380$	−41.5326			−0.109296
$381$	145.076	+	25.5217i	0.380778	+	0.0669860i
$382$	−136.156			−0.356429
$383$	−49.0332	−	28.3093i	−0.128024	−	0.0739147i	0.434620	−	0.900614i	$-0.356883\pi$
$383$	−49.0332	−	28.3093i	−0.128024	−	0.0739147i	−0.562644	+	0.826699i	$0.690216\pi$
$384$	−456.089	−	80.2347i	−1.18773	−	0.208944i
$385$		0			0
$386$	55.7361			0.144394
$387$	148.003	−	124.389i	0.382438	−	0.321420i
$388$	−124.966	−	72.1492i	−0.322077	−	0.185951i
$389$	−206.783	−	358.158i	−0.531575	−	0.920715i	−0.999321	−	0.0368521i	$-0.988267\pi$
$389$	−206.783	−	358.158i	−0.531575	−	0.920715i	0.467746	−	0.883863i	$-0.345066\pi$
$390$	74.2039	+	13.0539i	0.190266	+	0.0334715i
$391$	271.901	−	156.982i	0.695398	−	0.401488i
$392$		0			0
$393$	−285.617	−	239.468i	−0.726760	−	0.609334i
$394$	390.563			0.991277
$395$	−79.0721	−	45.6523i	−0.200182	−	0.115575i
$396$	0.596097	+	3.36505i	0.00150530	+	0.00849761i
$397$	540.503	−	312.059i	1.36147	−	0.786044i	0.371648	−	0.928374i	$-0.378793\pi$
$397$	540.503	−	312.059i	1.36147	−	0.786044i	0.989819	+	0.142330i	$0.0454594\pi$
$398$	−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	−0.934219	−	0.356701i	$-0.883902\pi$
$401$	−63.4372	+	109.876i	−0.158198	+	0.274006i	0.776021	+	0.630707i	$0.217235\pi$
$402$	500.089	+	87.9750i	1.24400	+	0.218843i
$403$	−141.430	−	244.965i	−0.350944	−	0.607853i
$404$	−41.4398	+	23.9253i	−0.102574	+	0.0592209i
$405$	53.8242	+	147.155i	0.132899	+	0.363347i
$406$		0			0
$407$	−5.49910	+	9.52472i	−0.0135113	+	0.0234023i
$408$	−176.639	−	148.098i	−0.432938	−	0.362986i
$409$			432.530i			1.05753i	0.848768	+	0.528765i	$0.177345\pi$
$409$			432.530i			1.05753i	−0.848768	+	0.528765i	$0.822655\pi$
$410$	−98.2886			−0.239728
$411$	4.75656	+	13.0525i	0.0115731	+	0.0317578i
$412$	116.181	+	67.0769i	0.281992	+	0.162808i
$413$		0			0
$414$	−421.164	+	353.967i	−1.01730	+	0.854993i
$415$	90.6626	+	157.032i	0.218464	+	0.378391i
$416$	80.0365	−	46.2091i	0.192395	−	0.111080i
$417$	122.717	−	44.7203i	0.294285	−	0.107243i
$418$	−15.2097	−	8.78132i	−0.0363868	−	0.0210080i
$419$	150.801	−	87.0648i	0.359906	−	0.207792i	−0.309134	−	0.951019i	$-0.600039\pi$
$419$	150.801	−	87.0648i	0.359906	−	0.207792i	0.669040	+	0.743227i	$0.266706\pi$
$420$		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	$0.303513\pi$
$422$	−335.180	−	580.549i	−0.794265	−	1.37571i
$423$	163.721	−	450.930i	0.387047	−	1.06603i
$424$	−291.989	+	505.739i	−0.688653	+	1.19278i
$425$			244.625i			0.575588i
$426$	645.254	+	113.512i	1.51468	+	0.266461i
$427$		0			0
$428$	71.3451	+	123.573i	0.166694	+	0.288723i
$429$	4.95997	+	4.15856i	0.0115617	+	0.00969362i
$430$	80.6296	−	46.5515i	0.187511	−	0.108259i
$431$	367.837	−	637.113i	0.853451	−	1.47822i	−0.0246236	−	0.999697i	$-0.507839\pi$
$431$	367.837	−	637.113i	0.853451	−	1.47822i	0.878075	−	0.478524i	$-0.158828\pi$
$432$	445.494	+	256.501i	1.03124	+	0.593752i
$433$		−	134.778i		−	0.311266i	−0.987815	−	0.155633i	$-0.950258\pi$
$433$		−	134.778i		−	0.311266i	0.987815	−	0.155633i	$-0.0497417\pi$
$434$		0			0
$435$	219.634	−	80.0386i	0.504905	−	0.183997i
$436$	56.6427	−	98.1081i	0.129915	−	0.225019i
$437$		−	574.394i		−	1.31440i
$438$	−448.005	−	375.619i	−1.02284	−	0.857577i
$439$			5.84694i			0.0133188i	0.999978	+	0.00665939i	$0.00211977\pi$
$439$			5.84694i			0.0133188i	−0.999978	+	0.00665939i	$0.997880\pi$
$440$		−	4.80927i		−	0.0109302i
$441$		0			0
$442$	149.399			0.338007
$443$	−160.318			−0.361892			−0.180946	−	0.983493i	$-0.557916\pi$
$443$	−160.318			−0.361892			−0.180946	+	0.983493i	$0.557916\pi$
$444$	−30.9423	−	84.9088i	−0.0696900	−	0.191236i
$445$	57.3623			0.128904
$446$	−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	$0.483407\pi$
$450$	−74.7693	−	422.083i	−0.166154	−	0.937963i
$451$	−7.31257	−	4.22191i	−0.0162141	−	0.00936122i
$452$	51.7697	+	89.6677i	0.114535	+	0.198380i
$453$	123.131	+	337.883i	0.271812	+	0.745878i
$454$	59.2669	−	34.2177i	0.130544	−	0.0753695i
$455$		0			0
$456$	−396.224	+	144.392i	−0.868913	+	0.316648i
$457$	554.340			1.21300			0.606499	−	0.795084i	$-0.292573\pi$
$457$	554.340			1.21300			0.606499	+	0.795084i	$0.292573\pi$
$458$	−354.298	−	204.554i	−0.773577	−	0.446625i
$459$	155.670	+	268.891i	0.339151	+	0.585819i
$460$	−46.6132	+	26.9122i	−0.101333	+	0.0585047i
$461$	117.654	+	67.9273i	0.255214	+	0.147348i	0.622149	−	0.782899i	$-0.286260\pi$
$461$	117.654	+	67.9273i	0.255214	+	0.147348i	−0.366935	+	0.930246i	$0.619593\pi$
$462$		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
$465$	182.007	−	217.082i	0.391414	−	0.466844i
$466$	391.858	+	678.718i	0.840897	+	1.45648i
$467$	89.3271	−	51.5730i	0.191278	−	0.110435i	−0.401302	−	0.915946i	$-0.631442\pi$
$467$	89.3271	−	51.5730i	0.191278	−	0.110435i	0.592581	+	0.805511i	$0.298109\pi$
$468$	−52.3697	+	9.27694i	−0.111901	+	0.0198225i
$469$		0			0
$470$	115.512	−	200.072i	0.245770	−	0.425686i
$471$	−101.852	+	578.973i	−0.216247	+	1.22924i
$472$		−	61.6369i		−	0.130587i
$473$	7.99834			0.0169098
$474$	312.452	+	54.9662i	0.659182	+	0.115962i
$475$	387.580	+	223.769i	0.815958	+	0.471094i
$476$		0			0
$477$	602.583	−	506.441i	1.26328	−	1.06172i
$478$	111.163	+	192.540i	0.232559	+	0.402804i
$479$	−165.785	+	95.7160i	−0.346106	+	0.199825i	−0.662969	−	0.748647i	$-0.730704\pi$
$479$	−165.785	+	95.7160i	−0.346106	+	0.199825i	0.316863	+	0.948471i	$0.397371\pi$
$480$	70.9266	+	59.4666i	0.147764	+	0.123889i
$481$	−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
$485$	−136.856	−	237.042i	−0.282178	−	0.488746i
$486$	−350.784	−	416.372i	−0.721778	−	0.856733i
$487$	−224.406	+	388.683i	−0.460794	+	0.798118i	−0.999001	−	0.0446948i	$-0.985768\pi$
$487$	−224.406	+	388.683i	−0.460794	+	0.798118i	0.538207	+	0.842813i	$0.319102\pi$
$488$			470.966i			0.965093i
$489$	−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	$0.859868\pi$
$492$	65.1884	−	23.7559i	0.132497	−	0.0482843i
$493$	401.429	−	231.765i	0.814258	−	0.470112i
$494$	136.662	−	236.705i	0.276644	−	0.479161i
$495$	−2.21228	+	6.09320i	−0.00446926	+	0.0123095i
$496$		−	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	−0.851896	−	0.523710i	$-0.824547\pi$
$499$	13.7715	−	23.8529i	0.0275982	−	0.0478014i	0.879495	+	0.475909i	$0.157881\pi$
$500$		−	91.2568i		−	0.182514i
$501$	702.482	−	255.997i	1.40216	−	0.510973i
$502$			37.1884i			0.0740805i
$503$			49.4903i			0.0983902i	0.998789	+	0.0491951i	$0.0156656\pi$
$503$			49.4903i			0.0983902i	−0.998789	+	0.0491951i	$0.984334\pi$
$504$		0			0
$505$	−90.7653			−0.179733
$506$	−22.7604			−0.0449810
$507$	261.021	−	311.322i	0.514834	−	0.614048i
$508$	−50.0745			−0.0985718
$509$	108.850	+	62.8447i	0.213851	+	0.123467i	0.603100	−	0.797666i	$-0.293932\pi$
$509$	108.850	+	62.8447i	0.213851	+	0.123467i	−0.389249	+	0.921133i	$0.627265\pi$
$510$	51.2301	+	140.580i	0.100451	+	0.275648i
$511$		0			0
$512$	−204.849			−0.400097
$513$	568.425	−	0.675026i	1.10804	−	0.00131584i
$514$	−165.318	−	95.4464i	−0.321630	−	0.185693i
$515$	127.235	+	220.377i	0.247058	+	0.427917i
$516$	−42.2251	+	50.3624i	−0.0818316	+	0.0976015i
$517$	17.1879	−	9.92344i	0.0332454	−	0.0191943i
$518$		0			0
$519$	144.733	−	822.727i	0.278869	−	1.58522i
$520$	74.8456			0.143934
$521$	606.831	+	350.354i	1.16474	+	0.672464i	0.952436	−	0.304739i	$-0.0985692\pi$
$521$	606.831	+	350.354i	1.16474	+	0.672464i	0.212306	+	0.977203i	$0.431903\pi$
$522$	−621.799	+	522.591i	−1.19119	+	1.00113i
$523$	302.754	−	174.795i	0.578879	−	0.334216i	−0.181809	−	0.983334i	$-0.558195\pi$
$523$	302.754	−	174.795i	0.578879	−	0.334216i	0.760688	+	0.649118i	$0.224862\pi$
$524$	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
$528$	7.28166	+	19.9816i	0.0137910	+	0.0378439i
$529$	−107.694	−	186.531i	−0.203580	−	0.352611i
$530$	328.277	−	189.531i	0.619390	−	0.357605i
$531$	−28.3532	+	78.0921i	−0.0533959	+	0.147066i
$532$		0			0
$533$	65.7048	−	113.804i	0.123273	−	0.213516i
$534$	−187.266	+	68.2432i	−0.350685	+	0.127796i
$535$			270.662i			0.505911i
$536$	504.413			0.941070
$537$	496.349	−	592.001i	0.924299	−	1.10242i
$538$	747.204	+	431.399i	1.38886	+	0.801856i
$539$		0			0
$540$	−26.6873	−	46.0973i	−0.0494209	−	0.0853653i
$541$	−350.723	−	607.469i	−0.648286	−	1.12286i	−0.983532	−	0.180734i	$-0.942153\pi$
$541$	−350.723	−	607.469i	−0.648286	−	1.12286i	0.335246	−	0.942131i	$-0.391180\pi$
$542$	−120.883	+	69.7918i	−0.223031	+	0.128767i
$543$	−15.2056	+	86.4352i	−0.0280029	+	0.159181i
$544$	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	$0.287459\pi$
$548$	−2.36124	−	4.08979i	−0.00430884	−	0.00746313i
$549$	216.646	−	596.700i	0.394619	−	1.08688i
$550$	8.86688	−	15.3579i	0.0161216	−	0.0279234i
$551$		−	848.024i		−	1.53906i
$552$	−351.132	+	418.799i	−0.636108	+	0.758694i
$553$		0			0
$554$	−95.2339	−	164.950i	−0.171902	−	0.297744i
$555$	29.7000	−	168.828i	0.0535136	−	0.304195i
$556$	−38.4515	+	22.2000i	−0.0691574	+	0.0399280i
$557$	−51.7943	+	89.7104i	−0.0929880	+	0.161060i	−0.908767	−	0.417304i	$-0.862975\pi$
$557$	−51.7943	+	89.7104i	−0.0929880	+	0.161060i	0.815779	+	0.578364i	$0.196308\pi$
$558$	−335.924	+	925.223i	−0.602015	+	1.65811i
$559$			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
$563$		−	130.812i		−	0.232348i	−0.993229	−	0.116174i	$-0.962937\pi$
$563$		−	130.812i		−	0.232348i	0.993229	−	0.116174i	$-0.0370630\pi$
$564$	−28.2549	+	160.613i	−0.0500974	+	0.284776i
$565$			196.399i			0.347608i
$566$		−	786.000i		−	1.38869i
$567$		0			0
$568$	650.834			1.14584
$569$	−635.580			−1.11701			−0.558506	−	0.829500i	$-0.688625\pi$
$569$	−635.580			−1.11701			−0.558506	+	0.829500i	$0.688625\pi$
$570$	269.596	+	47.4270i	0.472975	+	0.0832052i
$571$	172.059			0.301330			0.150665	−	0.988585i	$-0.451859\pi$
$571$	172.059			0.301330			0.150665	+	0.988585i	$0.451859\pi$
$572$	−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
$576$	341.968	+	124.160i	0.593694	+	0.215555i
$577$	−27.4829	−	15.8672i	−0.0476306	−	0.0274996i	0.475996	−	0.879448i	$-0.342088\pi$
$577$	−27.4829	−	15.8672i	−0.0476306	−	0.0274996i	−0.523626	+	0.851948i	$0.675421\pi$
$578$	−175.406	−	303.812i	−0.303471	−	0.525627i
$579$	−73.5014	−	12.9303i	−0.126946	−	0.0223321i
$580$	−68.8189	+	39.7326i	−0.118653	+	0.0685045i
$581$		0			0
$582$	728.789	+	611.035i	1.25222	+	1.04989i
$583$	32.5646			0.0558569
$584$	−502.964	−	290.386i	−0.861240	−	0.497237i
$585$	−94.8272	−	34.4293i	−0.162098	−	0.0588535i
$586$	95.8236	−	55.3238i	0.163521	−	0.0944092i
$587$	780.765	+	450.775i	1.33009	+	0.767929i	0.985314	−	0.170754i	$-0.0546204\pi$
$587$	780.765	+	450.775i	1.33009	+	0.767929i	0.344779	+	0.938684i	$0.387954\pi$
$588$		0			0
$589$	−513.842	−	890.000i	−0.872396	−	1.51104i
$590$	−20.0043	+	34.6485i	−0.0339056	+	0.0587263i
$591$	−515.051	−	90.6072i	−0.871491	−	0.153312i
$592$	−281.193	−	487.041i	−0.474989	−	0.822705i
$593$	92.1847	−	53.2228i	0.155455	−	0.0897518i	−0.420255	−	0.907406i	$-0.638059\pi$
$593$	92.1847	−	53.2228i	0.155455	−	0.0897518i	0.575709	+	0.817654i	$0.304726\pi$
$594$	−0.0267479	−	22.5239i	−4.50302e−5	−	0.0379190i
$595$		0			0
$596$	13.3906	−	23.1932i	0.0224674	−	0.0389147i
$597$	664.236	+	556.912i	1.11262	+	0.932852i
$598$		−	354.215i		−	0.592333i
$599$	−815.080			−1.36073			−0.680367	−	0.732871i	$-0.738180\pi$
$599$	−815.080			−1.36073			−0.680367	+	0.732871i	$0.738180\pi$
$600$	−145.798	−	400.085i	−0.242997	−	0.666808i
$601$	222.029	+	128.189i	0.369433	+	0.213292i	0.673211	−	0.739451i	$-0.264915\pi$
$601$	222.029	+	128.189i	0.369433	+	0.213292i	−0.303778	+	0.952743i	$0.598248\pi$
$602$		0			0
$603$	−639.077	−	232.032i	−1.05983	−	0.384796i
$604$	−61.1244	−	105.871i	−0.101199	−	0.175282i
$605$	202.476	−	116.900i	0.334672	−	0.193223i
$606$	296.314	−	107.982i	0.488967	−	0.178189i
$607$	−280.441	−	161.913i	−0.462012	−	0.266742i	0.250878	−	0.968019i	$-0.419281\pi$
$607$	−280.441	−	161.913i	−0.462012	−	0.266742i	−0.712890	+	0.701276i	$0.752614\pi$
$608$	290.786	−	167.886i	0.478267	−	0.276128i
$609$		0			0
$610$	152.852	−	264.748i	0.250578	−	0.434014i
$611$	154.436	+	267.492i	0.252760	+	0.437793i
$612$	−67.9551	−	80.8557i	−0.111038	−	0.132117i
$613$	310.620	−	538.010i	0.506721	−	0.877667i	−0.493248	−	0.869888i	$-0.664191\pi$
$613$	310.620	−	538.010i	0.506721	−	0.877667i	0.999970	−	0.00777855i	$-0.00247602\pi$
$614$			969.418i			1.57886i
$615$	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	$0.627110\pi$
$618$	−677.553	−	568.078i	−1.09636	−	0.919219i
$619$	159.035	−	91.8186i	0.256922	−	0.148334i	−0.366008	−	0.930612i	$-0.619276\pi$
$619$	159.035	−	91.8186i	0.256922	−	0.148334i	0.622930	+	0.782278i	$0.285942\pi$
$620$	−48.1502	+	83.3986i	−0.0776616	+	0.134514i
$621$	637.523	−	369.084i	1.02661	−	0.594339i
$622$			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
$626$		−	579.359i		−	0.925493i
$627$	18.0204	+	15.1088i	0.0287407	+	0.0240970i
$628$		−	199.838i		−	0.318214i
$629$		−	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	$0.416864\pi$
$632$	315.154			0.498662
$633$	307.333	+	843.351i	0.485518	+	1.33231i
$634$	−453.730			−0.715663
$635$	−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
$639$	−824.588	−	299.386i	−1.29044	−	0.468523i
$640$	258.603	+	149.304i	0.404067	+	0.233288i
$641$	89.3312	+	154.726i	0.139362	+	0.241383i	0.927255	−	0.374429i	$-0.122161\pi$
$641$	89.3312	+	154.726i	0.139362	+	0.241383i	−0.787893	+	0.615812i	$0.788828\pi$
$642$	−322.003	−	883.608i	−0.501563	−	1.37634i
$643$	60.1837	−	34.7471i	0.0935983	−	0.0540390i	−0.452470	−	0.891780i	$-0.649457\pi$
$643$	60.1837	−	34.7471i	0.0935983	−	0.0540390i	0.546069	+	0.837740i	$0.316124\pi$
$644$		0			0
$645$	−117.129	+	42.6840i	−0.181595	+	0.0661767i
$646$	542.793			0.840236
$647$	712.875	+	411.579i	1.10182	+	0.636134i	0.936697	−	0.350140i	$-0.113866\pi$
$647$	712.875	+	411.579i	1.10182	+	0.636134i	0.165119	+	0.986274i	$0.447199\pi$
$648$	−414.860	−	346.991i	−0.640216	−	0.535480i
$649$	−2.97660	+	1.71854i	−0.00458644	+	0.00264798i
$650$	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	0.393845	+	0.919177i	$0.371145\pi$
$653$	−391.218	+	677.609i	−0.599108	+	1.03769i	−0.992953	+	0.118509i	$0.962189\pi$
$654$	−479.711	+	572.157i	−0.733502	+	0.874857i
$655$	120.168	+	208.138i	0.183463	+	0.317768i
$656$	373.924	−	215.885i	0.570006	−	0.329093i
$657$	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	$0.122727\pi$
$660$	0.381795	−	2.17029i	0.000578477	−	0.00328832i
$661$			192.972i			0.291940i	0.989289	+	0.145970i	$0.0466303\pi$
$661$			192.972i			0.291940i	−0.989289	+	0.145970i	$0.953370\pi$
$662$	76.5270			0.115600
$663$	−197.018	−	34.6592i	−0.297162	−	0.0522764i
$664$	−542.025	−	312.939i	−0.816303	−	0.471293i
$665$		0			0
$666$	103.893	+	586.493i	0.155996	+	0.880620i
$667$	−549.500	−	951.762i	−0.823839	−	1.42693i
$668$	−220.112	+	127.082i	−0.329509	+	0.190242i
$669$	37.3683	+	31.3306i	0.0558570	+	0.0468319i
$670$	−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	$0.186518\pi$
$674$	461.215	+	798.849i	0.684296	+	1.18524i
$675$	0.681603	+	573.964i	0.00100978	+	0.850317i
$676$	−69.0532	+	119.604i	−0.102150	+	0.176929i
$677$		−	207.203i		−	0.306060i	−0.988222	−	0.153030i	$-0.951097\pi$
$677$		−	207.203i		−	0.306060i	0.988222	−	0.153030i	$-0.0489031\pi$
$678$	−233.653	−	641.167i	−0.344621	−	0.945674i
$679$		0			0
$680$	74.3178	+	128.722i	0.109291	+	0.189297i
$681$	−86.0958	+	31.3749i	−0.126425	+	0.0460718i
$682$	−35.2663	+	20.3610i	−0.0517101	+	0.0298549i
$683$	−639.939	+	1108.41i	−0.936953	+	1.62285i	−0.165841	+	0.986153i	$0.553034\pi$
$683$	−639.939	+	1108.41i	−0.936953	+	1.62285i	−0.771113	+	0.636698i	$0.780300\pi$
$684$	−190.268	+	33.7047i	−0.278170	+	0.0492759i
$685$		−	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
$689$			506.796i			0.735553i
$690$	333.307	−	121.463i	0.483053	−	0.176034i
$691$			1215.74i			1.75939i	0.475538	+	0.879695i	$0.342253\pi$
$691$			1215.74i			1.75939i	−0.475538	+	0.879695i	$0.657747\pi$
$692$			283.972i			0.410364i
$693$		0			0
$694$	−1338.67			−1.92892
$695$	−84.2201			−0.121180
$696$	−518.405	+	618.307i	−0.744834	+	0.888373i
$697$	260.966			0.374413
$698$	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	$0.814965\pi$
$702$	350.535	−	0.416273i	0.499337	−	0.000592981i
$703$	−538.550	−	310.932i	−0.766074	−	0.442293i
$704$	7.52554	+	13.0346i	0.0106897	+	0.0185151i
$705$	−198.745	+	237.045i	−0.281908	+	0.336235i
$706$	−889.515	+	513.562i	−1.25994	+	0.727425i
$707$		0			0
$708$	4.89319	−	27.8150i	0.00691129	−	0.0392868i
$709$	−111.673			−0.157508			−0.0787540	−	0.996894i	$-0.525094\pi$
$709$	−111.673			−0.157508			−0.0787540	+	0.996894i	$0.525094\pi$
$710$	−365.860	−	211.229i	−0.515295	−	0.297506i
$711$	−399.291	−	144.972i	−0.561591	−	0.203899i
$712$	−171.470	+	98.9981i	−0.240828	+	0.139042i
$713$	−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
$717$	−101.928	−	279.699i	−0.142158	−	0.390097i
$718$	14.4010	+	24.9432i	0.0200571	+	0.0347398i
$719$	−1204.35	+	695.331i	−1.67503	+	0.967081i	−0.710283	+	0.703917i	$0.751433\pi$
$719$	−1204.35	+	695.331i	−1.67503	+	0.967081i	−0.964751	+	0.263164i	$0.915234\pi$
$720$	−213.268	−	253.754i	−0.296205	−	0.352437i
$721$		0			0
$722$	92.1074	−	159.535i	0.127573	−	0.220962i
$723$	792.014	−	288.625i	1.09546	−	0.399204i
$724$		−	29.8339i		−	0.0412071i
$725$	856.287			1.18109
$726$	−521.934	+	622.517i	−0.718917	+	0.857461i
$727$	−570.198	−	329.204i	−0.784317	−	0.452826i	0.0536411	−	0.998560i	$-0.482917\pi$
$727$	−570.198	−	329.204i	−0.784317	−	0.452826i	−0.837958	+	0.545735i	$0.816251\pi$
$728$		0			0
$729$	365.998	+	630.465i	0.502055	+	0.864835i
$730$	188.491	+	326.475i	0.258206	+	0.447226i
$731$	−214.079	+	123.599i	−0.292858	+	0.169082i
$732$	−37.3887	+	212.534i	−0.0510775	+	0.290347i
$733$	−322.167	−	186.003i	−0.439518	−	0.253756i	0.263875	−	0.964557i	$-0.414999\pi$
$733$	−322.167	−	186.003i	−0.439518	−	0.253756i	−0.703393	+	0.710801i	$0.748333\pi$
$734$	−1199.80	+	692.703i	−1.63460	+	0.943737i
$735$		0			0
$736$	217.572	−	376.846i	0.295614	−	0.512019i
$737$	−14.0639	−	24.3594i	−0.0190826	−	0.0330521i
$738$	−450.278	+	79.7637i	−0.610132	+	0.108081i
$739$	470.172	−	814.362i	0.636227	−	1.10198i	−0.350026	−	0.936740i	$-0.613827\pi$
$739$	470.172	−	814.362i	0.636227	−	1.10198i	0.986254	−	0.165238i	$-0.0528393\pi$
$740$			58.2726i			0.0787467i
$741$	−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	$0.877792\pi$
$744$	−169.415	+	963.028i	−0.227708	+	1.29439i
$745$	43.9940	−	25.3999i	0.0590523	−	0.0340939i
$746$	−0.648921	+	1.12396i	−0.000869867	+	0.00150665i
$747$	542.777	+	645.818i	0.726610	+	0.864549i
$748$		−	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	−0.252641	+	0.967560i	$0.581299\pi$
$751$	−724.153	+	1254.27i	−0.964252	+	1.67013i	−0.711611	+	0.702574i	$0.752034\pi$
$752$			1014.86i			1.34955i
$753$	8.62738	−	49.0418i	0.0114573	−	0.0651285i
$754$		−	522.957i		−	0.693577i
$755$		−	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	$0.562847\pi$
$758$	41.4524			0.0546866
$759$	30.0150	+	5.28021i	0.0395455	+	0.00695680i
$760$	271.927			0.357799
$761$	−254.681	−	147.040i	−0.334666	−	0.193220i	0.323245	−	0.946315i	$-0.395226\pi$
$761$	−254.681	−	147.040i	−0.334666	−	0.193220i	−0.657911	+	0.753096i	$0.728560\pi$
$762$	325.043	+	57.1812i	0.426565	+	0.0750409i
$763$		0			0
$764$	−61.9748			−0.0811188
$765$	−34.9457	−	197.274i	−0.0456807	−	0.257874i
$766$	−109.859	−	63.4270i	−0.143419	−	0.0828028i
$767$	−26.7453	−	46.3242i	−0.0348700	−	0.0603967i
$768$	−544.122	−	95.7213i	−0.708492	−	0.124637i
$769$	−91.6783	+	52.9305i	−0.119218	+	0.0688303i	−0.558423	−	0.829556i	$-0.688593\pi$
$769$	−91.6783	+	52.9305i	−0.119218	+	0.0688303i	0.439205	+	0.898387i	$0.355260\pi$
$770$		0			0
$771$	195.869	+	164.221i	0.254045	+	0.212998i
$772$	25.3697			0.0328623
$773$	1070.93	+	618.299i	1.38541	+	0.799869i	0.992794	−	0.119832i	$-0.0382355\pi$
$773$	1070.93	+	618.299i	1.38541	+	0.799869i	0.392620	+	0.919701i	$0.371569\pi$
$774$	331.601	−	278.694i	0.428425	−	0.360070i
$775$	898.671	−	518.848i	1.15958	−	0.669481i
$776$	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
$780$	33.7758	+	5.94180i	0.0433023	+	0.00761769i
$781$	−18.1464	−	31.4304i	−0.0232348	−	0.0402438i
$782$	609.192	−	351.717i	0.779018	−	0.449766i
$783$	941.227	−	544.909i	1.20208	−	0.695925i
$784$		0			0
$785$	189.532	−	328.278i	0.241442	−	0.418189i
$786$	−639.923	−	536.528i	−0.814151	−	0.682605i
$787$		−	841.649i		−	1.06944i	−0.845029	−	0.534720i	$-0.820417\pi$
$787$		−	841.649i		−	1.06944i	0.845029	−	0.534720i	$-0.179583\pi$
$788$	177.775			0.225602
$789$	−366.347	−	1005.29i	−0.464318	−	1.27413i
$790$	−177.161	−	102.284i	−0.224254	−	0.129473i
$791$		0			0
$792$	−3.90284	−	22.0321i	−0.00492783	−	0.0278183i
$793$	204.360	+	353.962i	0.257705	+	0.446358i
$794$	1210.99	−	699.167i	1.52518	−	0.880564i
$795$	−476.881	+	173.784i	−0.599850	+	0.218597i
$796$	−255.186	−	147.332i	−0.320585	−	0.185090i
$797$	−138.377	+	79.8921i	−0.173622	+	0.100241i	−0.584293	−	0.811543i	$-0.698628\pi$
$797$	−138.377	+	79.8921i	−0.173622	+	0.100241i	0.410670	+	0.911784i	$0.365295\pi$
$798$		0			0
$799$	−306.695	+	531.211i	−0.383848	+	0.664844i
$800$	169.521	+	293.620i	0.211902	+	0.367025i
$801$	262.787	−	46.5509i	0.328073	−	0.0581160i
$802$	−142.131	+	246.178i	−0.177220	+	0.306955i
$803$			32.3859i			0.0403311i
$804$	227.628	+	40.0441i	0.283119	+	0.0498061i
$805$		0			0
$806$	−316.874	−	548.842i	−0.393144	−	0.680946i
$807$	−885.287	−	742.247i	−1.09701	−	0.919761i
$808$	271.320	−	156.646i	0.335792	−	0.193869i
$809$	−17.7511	+	30.7458i	−0.0219420	+	0.0380046i	−0.876788	−	0.480877i	$-0.840318\pi$
$809$	−17.7511	+	30.7458i	−0.0219420	+	0.0380046i	0.854846	+	0.518882i	$0.173652\pi$
$810$	120.593	+	329.701i	0.148880	+	0.407038i
$811$			264.939i			0.326682i	0.986570	+	0.163341i	$0.0522271\pi$
$811$			264.939i			0.326682i	−0.986570	+	0.163341i	$0.947773\pi$
$812$		0			0
$813$	175.604	−	63.9934i	0.215995	−	0.0787127i
$814$	−12.3207	+	21.3401i	−0.0151360	+	0.0262163i
$815$			161.881i			0.198627i
$816$	−503.674	−	422.293i	−0.617247	−	0.517515i
$817$			452.245i			0.553544i
$818$			969.081i			1.18470i
$819$		0			0
$820$	−44.7386			−0.0545592
$821$	1507.56			1.83625			0.918126	−	0.396289i	$-0.129702\pi$
$821$	1507.56			1.83625			0.918126	+	0.396289i	$0.129702\pi$
$822$	10.6570	+	29.2440i	0.0129648	+	0.0355766i
$823$	1234.84			1.50041			0.750207	−	0.661203i	$-0.229954\pi$
$823$	1234.84			1.50041			0.750207	+	0.661203i	$0.229954\pi$
$824$	−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	$0.372953\pi$
$828$	−191.704	+	161.117i	−0.231526	+	0.194586i
$829$	−831.340	−	479.974i	−1.00282	−	0.578980i	−0.0937403	−	0.995597i	$-0.529882\pi$
$829$	−831.340	−	479.974i	−1.00282	−	0.578980i	−0.909082	+	0.416617i	$0.863216\pi$
$830$	203.129	+	351.830i	0.244734	+	0.423892i
$831$	87.3218	+	239.619i	0.105080	+	0.288351i
$832$	−202.855	+	117.119i	−0.243816	+	0.140767i
$833$		0			0
$834$	274.947	−	100.196i	0.329672	−	0.120139i
$835$	−482.110			−0.577378
$836$	−6.92308	−	3.99704i	−0.00828120	−	0.00478115i
$837$	657.640	−	1142.20i	0.785711	−	1.36463i
$838$	337.868	−	195.068i	0.403184	−	0.232778i
$839$	409.757	+	236.574i	0.488388	+	0.281971i	0.723905	−	0.689899i	$-0.242345\pi$
$839$	409.757	+	236.574i	0.488388	+	0.281971i	−0.235518	+	0.971870i	$0.575679\pi$
$840$		0			0
$841$	−390.772	−	676.837i	−0.464652	−	0.804800i
$842$	−393.140	+	680.938i	−0.466912	+	0.808715i
$843$	−284.812	+	339.699i	−0.337856	+	0.402965i
$844$	−152.566	−	264.251i	−0.180765	−	0.313094i
$845$	−226.870	+	130.984i	−0.268486	+	0.155010i
$846$	366.816	−	1010.31i	0.433589	−	1.19422i
$847$		0			0
$848$	−832.586	+	1442.08i	−0.981823	+	1.70057i
$849$	−182.345	+	1036.53i	−0.214776	+	1.22088i
$850$			548.081i			0.644801i
$851$	−805.907			−0.947012
$852$	293.704	+	51.6680i	0.344723	+	0.0606432i
$853$	−1068.57	−	616.937i	−1.25271	−	0.723255i	−0.281067	−	0.959688i	$-0.590688\pi$
$853$	−1068.57	−	616.937i	−1.25271	−	0.723255i	−0.971648	+	0.236433i	$0.924022\pi$
$854$		0			0
$855$	−344.524	−	125.088i	−0.402952	−	0.146301i
$856$	−467.120	−	809.075i	−0.545701	−	0.945181i
$857$	−344.080	+	198.655i	−0.401493	+	0.231802i	−0.687128	−	0.726536i	$-0.741129\pi$
$857$	−344.080	+	198.655i	−0.401493	+	0.231802i	0.285635	+	0.958339i	$0.407796\pi$
$858$	11.1128	+	9.31724i	0.0129520	+	0.0108593i
$859$	473.197	+	273.200i	0.550870	+	0.318045i	0.749473	−	0.662035i	$-0.230307\pi$
$859$	473.197	+	273.200i	0.550870	+	0.318045i	−0.198603	+	0.980080i	$0.563640\pi$
$860$	36.7006	−	21.1891i	0.0426752	−	0.0246385i
$861$		0			0
$862$	824.138	−	1427.45i	0.956076	−	1.65597i
$863$	−7.86960	−	13.6305i	−0.00911888	−	0.0157944i	0.861430	−	0.507876i	$-0.169569\pi$
$863$	−7.86960	−	13.6305i	−0.00911888	−	0.0157944i	−0.870549	+	0.492082i	$0.836236\pi$
$864$	373.186	+	214.869i	0.431928	+	0.248690i
$865$	−269.326	+	466.487i	−0.311360	+	0.539291i
$866$		−	301.969i		−	0.348695i
$867$	160.833	+	441.342i	0.185505	+	0.509045i
$868$		0			0
$869$	−8.78704	−	15.2196i	−0.0101117	−	0.0175139i
$870$	492.088	−	179.326i	0.565618	−	0.206122i
$871$	379.100	−	218.874i	0.435247	−	0.251290i
$872$	−370.858	+	642.346i	−0.425296	+	0.736635i
$873$	−819.328	−	974.869i	−0.938520	−	1.11669i
$874$		−	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	−0.812331	−	0.583197i	$-0.801801\pi$
$877$	86.7339	−	150.227i	0.0988984	−	0.171297i	0.911229	+	0.411900i	$0.135135\pi$
$878$			13.1000i			0.0149203i
$879$	−139.201	+	50.7274i	−0.158363	+	0.0577104i
$880$		−	13.7133i		−	0.0155833i
$881$			1381.76i			1.56840i	0.620507	+	0.784201i	$0.286927\pi$
$881$			1381.76i			1.56840i	−0.620507	+	0.784201i	$0.713073\pi$
$882$		0			0
$883$	1346.90			1.52537			0.762685	−	0.646771i	$-0.223881\pi$
$883$	1346.90			1.52537			0.762685	+	0.646771i	$0.223881\pi$
$884$	68.0028			0.0769262
$885$	34.4187	−	41.0515i	0.0388911	−	0.0463859i
$886$	−359.192			−0.405408
$887$	−532.683	−	307.545i	−0.600544	−	0.346724i	0.168711	−	0.985665i	$-0.446039\pi$
$887$	−532.683	−	307.545i	−0.600544	−	0.346724i	−0.769256	+	0.638941i	$0.779373\pi$
$888$	202.590	+	555.926i	0.228141	+	0.626042i
$889$		0			0
$890$	128.520			0.144404
$891$	−5.19007	+	29.7094i	−0.00582499	+	0.0333438i
$892$	−14.3561	−	8.28852i	−0.0160943	−	0.00929206i
$893$	561.095	+	971.844i	0.628325	+	1.08829i
$894$	−113.406	+	135.260i	−0.126852	+	0.151298i
$895$	−431.410	+	249.074i	−0.482022	+	0.278295i
$896$		0			0
$897$	−82.1748	+	467.118i	−0.0916107	+	0.520756i
$898$	104.833			0.116740
$899$	−1702.86	−	983.145i	−1.89417	−	1.09360i
$900$	−34.0331	−	192.122i	−0.0378146	−	0.213469i
$901$	−871.606	+	503.222i	−0.967376	+	0.558515i
$902$	−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
$906$	275.874	+	757.025i	0.304497	+	0.835568i
$907$	249.391	+	431.958i	0.274962	+	0.476249i	0.970126	−	0.242603i	$-0.0780012\pi$
$907$	249.391	+	431.958i	0.274962	+	0.476249i	−0.695163	+	0.718852i	$0.744668\pi$
$908$	26.9768	−	15.5751i	0.0297102	−	0.0171532i
$909$	−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	$-0.00293622\pi$
$912$	−1129.81	+	411.723i	−1.23882	+	0.451450i
$913$			34.9010i			0.0382268i
$914$	1242.00			1.35886
$915$	−262.992	+	313.674i	−0.287423	+	0.342813i
$916$	−161.268	−	93.1080i	−0.176057	−	0.101646i
$917$		0			0
$918$	348.779	+	602.449i	0.379933	+	0.656262i
$919$	544.947	+	943.877i	0.592979	+	1.02707i	0.993829	+	0.110925i	$0.0353815\pi$
$919$	544.947	+	943.877i	0.592979	+	1.02707i	−0.400850	+	0.916144i	$0.631285\pi$
$920$	305.192	−	176.203i	0.331730	−	0.191525i
$921$	224.896	−	1278.41i	0.244187	−	1.38807i
$922$	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
$926$	2.13331	+	3.69500i	0.00230379	+	0.00399028i
$927$	761.727	+	906.333i	0.821712	+	0.977705i
$928$	321.219	−	556.368i	0.346142	−	0.599535i
$929$		−	537.759i		−	0.578858i	−0.957199	−	0.289429i	$-0.906535\pi$
$929$		−	537.759i		−	0.578858i	0.957199	−	0.289429i	$-0.0934654\pi$
$930$	407.787	−	486.372i	0.438480	−	0.522981i
$931$		0			0
$932$	178.364	+	308.936i	0.191378	+	0.331476i
$933$	86.9008	−	493.982i	0.0931413	−	0.529456i
$934$	200.137	−	115.549i	0.214279	−	0.123714i
$935$	4.14421	−	7.17799i	0.00443231	−	0.00767699i
$936$	342.881	−	60.7391i	0.366326	−	0.0648922i
$937$			647.389i			0.690917i	0.938434	+	0.345459i	$0.112277\pi$
$937$			647.389i			0.690917i	−0.938434	+	0.345459i	$0.887723\pi$
$938$		0			0
$939$	−134.406	+	764.023i	−0.143137	+	0.813656i
$940$	52.5781	−	91.0680i	0.0559342	−	0.0968808i
$941$			131.133i			0.139355i	0.997570	+	0.0696777i	$0.0221971\pi$
$941$			131.133i			0.139355i	−0.997570	+	0.0696777i	$0.977803\pi$
$942$	−228.200	+	1297.19i	−0.242250	+	1.37706i
$943$		−	618.732i		−	0.656132i
$944$		−	175.753i		−	0.186179i
$945$		0			0
$946$	17.9202			0.0189432
$947$	418.984			0.442433			0.221217	−	0.975225i	$-0.428997\pi$
$947$	418.984			0.442433			0.221217	+	0.975225i	$0.428997\pi$
$948$	142.221	+	25.0193i	0.150022	+	0.0263916i
$949$	−504.015			−0.531101
$950$	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	$0.702262\pi$
$954$	1350.09	−	1134.68i	1.41518	−	1.18939i
$955$	−101.807	−	58.7785i	−0.106604	−	0.0615481i
$956$	50.5987	+	87.6396i	0.0529275	+	0.0916732i
$957$	44.3136	+	7.79560i	0.0463047	+	0.00814587i
$958$	−371.440	+	214.451i	−0.387725	+	0.223853i
$959$		0			0
$960$	−179.766	−	150.720i	−0.187256	−	0.157000i
$961$	−1421.86			−1.47956
$962$	−332.111	−	191.745i	−0.345230	−	0.199319i
$963$	219.649	+	1239.95i	0.228088	+	1.28759i
$964$	−248.166	+	143.279i	−0.257433	+	0.148629i
$965$	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
$969$	−715.802	−	125.923i	−0.738702	−	0.129952i
$970$	−306.626	−	531.091i	−0.316109	−	0.547517i
$971$	−402.557	+	232.416i	−0.414579	+	0.239358i	−0.692755	−	0.721173i	$-0.743603\pi$
$971$	−402.557	+	232.416i	−0.414579	+	0.239358i	0.278176	+	0.960530i	$0.410270\pi$
$972$	−159.668	−	189.522i	−0.164268	−	0.194982i
$973$		0			0
$974$	−502.782	+	870.843i	−0.516203	+	0.894089i
$975$	−283.181	−	237.426i	−0.290442	−	0.243514i
$976$			1342.93i			1.37595i
$977$	−1778.98			−1.82086			−0.910429	−	0.413666i	$-0.864248\pi$
$977$	−1778.98			−1.82086			−0.910429	+	0.413666i	$0.864248\pi$
$978$	−192.588	−	528.480i	−0.196920	−	0.540368i
$979$	9.56174	+	5.52047i	0.00976684	+	0.00563889i
$980$		0			0
$981$	765.348	−	643.237i	0.780172	−	0.655695i
$982$	−91.5977	−	158.652i	−0.0932767	−	0.161560i
$983$	−199.156	+	114.983i	−0.202601	+	0.116972i	−0.597868	−	0.801595i	$-0.703985\pi$
$983$	−199.156	+	114.983i	−0.202601	+	0.116972i	0.395267	+	0.918566i	$0.370652\pi$
$984$	−426.810	+	155.537i	−0.433750	+	0.158066i
$985$	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
$989$	293.045	+	507.568i	0.296304	+	0.513213i
$990$	−4.95661	+	13.6518i	−0.00500667	+	0.0137897i
$991$	−561.974	+	973.368i	−0.567078	+	0.982208i	0.429775	+	0.902936i	$0.358593\pi$
$991$	−561.974	+	973.368i	−0.567078	+	0.982208i	−0.996853	+	0.0792720i	$0.974740\pi$
$992$		−	778.543i		−	0.784822i
$993$	−100.919	−	17.7536i	−0.101631	−	0.0178787i
$994$		0			0
$995$	−279.466	−	484.050i	−0.280870	−	0.486482i
$996$	−219.758	−	184.251i	−0.220640	−	0.184991i
$997$	554.198	−	319.966i	0.555866	−	0.320929i	−0.195619	−	0.980680i	$-0.562672\pi$
$997$	554.198	−	319.966i	0.555866	−	0.320929i	0.751484	+	0.659751i	$0.229338\pi$
$998$	30.8550	−	53.4424i	0.0309168	−	0.0535495i
$999$	−0.947100	−	797.533i	−0.000948048	−	0.798332i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.3.k.a.31.4	✓	28	63.13	odd	6
63.3.k.a.61.4	yes	28	7.2	even	3
63.3.t.a.40.11	yes	28	63.58	even	3
63.3.t.a.52.11	yes	28	7.6	odd	2
189.3.k.a.10.11		28	63.41	even	6
189.3.k.a.19.11		28	21.2	odd	6
189.3.t.a.73.4		28	21.20	even	2
189.3.t.a.145.4		28	63.23	odd	6
441.3.k.b.31.4		28	9.4	even	3
441.3.k.b.313.4		28	7.5	odd	6
441.3.l.a.97.4		28	7.4	even	3
441.3.l.a.391.4		28	63.31	odd	6
441.3.l.b.97.4		28	7.3	odd	6
441.3.l.b.391.4		28	63.4	even	3
441.3.t.a.166.11		28	63.40	odd	6	inner
441.3.t.a.178.11		28	1.1	even	1	trivial

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.t (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+2.24050 q^{2} +(-2.95463 - 0.519775i) q^{3} +1.01982 q^{4} +(1.67528 + 0.967222i) q^{5} +(-6.61983 - 1.16455i) q^{6} -6.67708 q^{8} +(8.45967 + 3.07148i) q^{9} +(3.75345 + 2.16706i) q^{10} +(0.186168 + 0.322453i) q^{11} +(-3.01319 - 0.530076i) q^{12} +(-5.01827 + 2.89730i) q^{13} +(-4.44709 - 3.72855i) q^{15} -19.0392 q^{16} +(-9.96576 - 5.75374i) q^{17} +(18.9538 + 6.88165i) q^{18} +(-18.2323 + 10.5264i) q^{19} +(1.70848 + 0.986391i) q^{20} +(0.417109 + 0.722455i) q^{22} +(-13.6417 + 23.6282i) q^{23} +(19.7283 + 3.47058i) q^{24} +(-10.6290 - 18.4099i) q^{25} +(-11.2434 + 6.49139i) q^{26} +(-23.3987 - 13.4722i) q^{27} +(-20.1404 + 34.8842i) q^{29} +(-9.96367 - 8.35380i) q^{30} +48.8145i q^{31} -15.9490 q^{32} +(-0.382456 - 1.04950i) q^{33} +(-22.3282 - 12.8912i) q^{34} +(8.62732 + 3.13236i) q^{36} +(14.7691 + 25.5809i) q^{37} +(-40.8493 + 23.5844i) q^{38} +(16.3331 - 5.95208i) q^{39} +(-11.1860 - 6.45822i) q^{40} +(-19.6397 + 11.3390i) q^{41} +(10.7407 - 18.6035i) q^{43} +(0.189858 + 0.328844i) q^{44} +(11.2015 + 13.3280i) q^{45} +(-30.5642 + 52.9388i) q^{46} -53.3035i q^{47} +(56.2539 + 9.89612i) q^{48} +(-23.8141 - 41.2473i) q^{50} +(26.4545 + 22.1801i) q^{51} +(-5.11773 + 2.95472i) q^{52} +(43.7300 - 75.7426i) q^{53} +(-52.4247 - 30.1844i) q^{54} +0.720265i q^{55} +(59.3409 - 21.6249i) q^{57} +(-45.1245 + 78.1579i) q^{58} +9.23111i q^{59} +(-4.53522 - 3.80244i) q^{60} -70.5346i q^{61} +109.369i q^{62} +40.4233 q^{64} -11.2093 q^{65} +(-0.856890 - 2.35139i) q^{66} -75.5440 q^{67} +(-10.1633 - 5.86777i) q^{68} +(52.5876 - 62.7219i) q^{69} -97.4729 q^{71} +(-56.4859 - 20.5086i) q^{72} +(75.3269 + 43.4900i) q^{73} +(33.0902 + 57.3139i) q^{74} +(21.8356 + 59.9191i) q^{75} +(-18.5936 + 10.7350i) q^{76} +(36.5942 - 13.3356i) q^{78} -47.1994 q^{79} +(-31.8960 - 18.4152i) q^{80} +(62.1320 + 51.9675i) q^{81} +(-44.0025 + 25.4049i) q^{82} +(81.1770 + 46.8676i) q^{83} +(-11.1303 - 19.2782i) q^{85} +(24.0646 - 41.6810i) q^{86} +(77.6394 - 92.6014i) q^{87} +(-1.24306 - 2.15305i) q^{88} +(25.6803 - 14.8266i) q^{89} +(25.0969 + 29.8612i) q^{90} +(-13.9121 + 24.0965i) q^{92} +(25.3726 - 144.229i) q^{93} -119.426i q^{94} -40.7255 q^{95} +(47.1234 + 8.28989i) q^{96} +(-122.538 - 70.7471i) q^{97} +(0.584513 + 3.29966i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 2 q^{2} + 3 q^{3} + 46 q^{4} + 3 q^{5} + 12 q^{6} - 16 q^{8} - 15 q^{9} + 6 q^{10} + 7 q^{11} + 30 q^{12} + 15 q^{13} - 18 q^{15} + 54 q^{16} + 33 q^{17} - 42 q^{18} + 6 q^{19} + 108 q^{20} - 10 q^{22}+ \cdots - 162 q^{99}+O(q^{100}) \) 28 * q - 2 * q^2 + 3 * q^3 + 46 * q^4 + 3 * q^5 + 12 * q^6 - 16 * q^8 - 15 * q^9 + 6 * q^10 + 7 * q^11 + 30 * q^12 + 15 * q^13 - 18 * q^15 + 54 * q^16 + 33 * q^17 - 42 * q^18 + 6 * q^19 + 108 * q^20 - 10 * q^22 + 34 * q^23 + 78 * q^24 + 31 * q^25 - 54 * q^26 - 81 * q^27 + 70 * q^29 - 27 * q^30 - 306 * q^32 + 3 * q^33 + 12 * q^34 - 174 * q^36 + 9 * q^37 - 87 * q^38 + 129 * q^39 + 102 * q^40 - 234 * q^41 + 30 * q^43 + 51 * q^44 - 273 * q^45 - 22 * q^46 + 147 * q^48 + 241 * q^50 + 12 * q^51 + 219 * q^52 + 148 * q^53 - 171 * q^54 + 189 * q^57 + 17 * q^58 + 33 * q^60 - 48 * q^64 - 228 * q^65 - 258 * q^66 + 68 * q^67 + 18 * q^68 + 78 * q^69 - 350 * q^71 + 162 * q^72 + 6 * q^73 + 359 * q^74 + 510 * q^75 + 72 * q^76 - 375 * q^78 + 164 * q^79 + 609 * q^80 - 435 * q^81 + 18 * q^82 + 738 * q^83 + 3 * q^85 + 17 * q^86 + 561 * q^87 + 25 * q^88 - 21 * q^89 - 543 * q^90 + 288 * q^92 - 222 * q^93 - 1014 * q^95 - 231 * q^96 - 57 * q^97 - 162 * q^99

Introduction

L-functions

Modular forms

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Database

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