LMFDB - Embedded newform 63.4.s.a.47.16

Newspace parameters

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	63.s (of order $6$, degree $2$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$3.71712033036$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			47.16
Character	$\chi$	$=$	63.47
Dual form			63.4.s.a.59.16

$q$-expansion

$f(q)$	$=$	$q+(2.09278 - 1.20827i) q^{2} +(-5.12336 + 0.866692i) q^{3} +(-1.08019 + 1.87094i) q^{4} -10.7193 q^{5} +(-9.67487 + 8.00418i) q^{6} +(-17.6173 + 5.71220i) q^{7} +24.5529i q^{8} +(25.4977 - 8.88075i) q^{9} +O(q^{10})$	\(q+(2.09278 - 1.20827i) q^{2} +(-5.12336 + 0.866692i) q^{3} +(-1.08019 + 1.87094i) q^{4} -10.7193 q^{5} +(-9.67487 + 8.00418i) q^{6} +(-17.6173 + 5.71220i) q^{7} +24.5529i q^{8} +(25.4977 - 8.88075i) q^{9} +(-22.4331 + 12.9518i) q^{10} -26.1223i q^{11} +(3.91266 - 10.5217i) q^{12} +(-29.8910 + 17.2576i) q^{13} +(-29.9673 + 33.2408i) q^{14} +(54.9189 - 9.29033i) q^{15} +(21.0249 + 36.4162i) q^{16} +(2.29830 + 3.98078i) q^{17} +(42.6307 - 49.3934i) q^{18} +(6.74409 + 3.89370i) q^{19} +(11.5788 - 20.0551i) q^{20} +(85.3093 - 44.5345i) q^{21} +(-31.5627 - 54.6682i) q^{22} +39.1615i q^{23} +(-21.2798 - 125.793i) q^{24} -10.0965 q^{25} +(-41.7035 + 72.2327i) q^{26} +(-122.937 + 67.5979i) q^{27} +(8.34283 - 39.1311i) q^{28} +(210.884 + 121.754i) q^{29} +(103.708 - 85.7993i) q^{30} +(-269.441 - 155.562i) q^{31} +(-82.1062 - 47.4041i) q^{32} +(22.6400 + 133.834i) q^{33} +(9.61969 + 5.55393i) q^{34} +(188.846 - 61.2308i) q^{35} +(-10.9269 + 57.2974i) q^{36} +(-28.3008 + 49.0184i) q^{37} +18.8185 q^{38} +(138.186 - 114.323i) q^{39} -263.190i q^{40} +(148.047 + 256.425i) q^{41} +(124.724 - 196.277i) q^{42} +(-60.7001 + 105.136i) q^{43} +(48.8731 + 28.2169i) q^{44} +(-273.318 + 95.1955i) q^{45} +(47.3176 + 81.9564i) q^{46} +(112.910 + 195.566i) q^{47} +(-139.280 - 168.351i) q^{48} +(277.742 - 201.268i) q^{49} +(-21.1297 + 12.1992i) q^{50} +(-15.2252 - 18.4031i) q^{51} -74.5656i q^{52} +(-307.128 + 177.321i) q^{53} +(-175.604 + 290.008i) q^{54} +280.013i q^{55} +(-140.251 - 432.556i) q^{56} +(-37.9271 - 14.1038i) q^{57} +588.443 q^{58} +(-135.574 + 234.821i) q^{59} +(-41.9410 + 112.785i) q^{60} +(-649.461 + 374.967i) q^{61} -751.841 q^{62} +(-398.473 + 302.103i) q^{63} -565.506 q^{64} +(320.411 - 184.989i) q^{65} +(209.088 + 252.730i) q^{66} +(-497.425 + 861.565i) q^{67} -9.93038 q^{68} +(-33.9410 - 200.639i) q^{69} +(321.229 - 356.318i) q^{70} -1139.11i q^{71} +(218.048 + 626.041i) q^{72} +(1074.95 - 620.624i) q^{73} +136.780i q^{74} +(51.7280 - 8.75054i) q^{75} +(-14.5697 + 8.41184i) q^{76} +(149.216 + 460.205i) q^{77} +(151.059 - 406.218i) q^{78} +(-216.802 - 375.512i) q^{79} +(-225.373 - 390.357i) q^{80} +(571.265 - 452.877i) q^{81} +(619.659 + 357.760i) q^{82} +(492.785 - 853.528i) q^{83} +(-8.82872 + 207.714i) q^{84} +(-24.6362 - 42.6712i) q^{85} +293.367i q^{86} +(-1185.96 - 441.017i) q^{87} +641.377 q^{88} +(75.6350 - 131.004i) q^{89} +(-456.972 + 529.463i) q^{90} +(428.022 - 474.777i) q^{91} +(-73.2687 - 42.3017i) q^{92} +(1515.27 + 563.478i) q^{93} +(472.591 + 272.851i) q^{94} +(-72.2920 - 41.7378i) q^{95} +(461.745 + 171.707i) q^{96} +(781.452 + 451.172i) q^{97} +(338.067 - 756.794i) q^{98} +(-231.986 - 666.058i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44q - 3q^{2} - 3q^{3} + 81q^{4} - 6q^{5} - 24q^{6} + 5q^{7} - 3q^{9} + O(q^{10}) $	\( 44q - 3q^{2} - 3q^{3} + 81q^{4} - 6q^{5} - 24q^{6} + 5q^{7} - 3q^{9} - 6q^{10} - 3q^{12} + 36q^{13} + 129q^{14} - 141q^{15} - 263q^{16} + 72q^{17} - 15q^{18} - 6q^{19} - 24q^{20} - 306q^{21} + 14q^{22} - 66q^{24} + 698q^{25} + 96q^{26} - 432q^{27} - 156q^{28} - 132q^{29} + 852q^{30} + 177q^{31} - 501q^{32} + 849q^{33} - 24q^{34} - 765q^{35} + 1122q^{36} + 82q^{37} - 1746q^{38} - 645q^{39} - 618q^{41} - 963q^{42} + 82q^{43} - 603q^{44} + 303q^{45} + 266q^{46} - 201q^{47} + 1569q^{48} + 515q^{49} - 1845q^{50} + 417q^{51} - 564q^{53} - 684q^{54} + 3600q^{56} + 1170q^{57} - 538q^{58} + 747q^{59} - 516q^{60} - 1209q^{61} + 2904q^{62} + 1557q^{63} - 1144q^{64} - 831q^{65} + 1029q^{66} + 295q^{67} + 7008q^{68} + 1005q^{69} - 390q^{70} - 1119q^{72} - 6q^{73} - 1788q^{75} + 144q^{76} - 1203q^{77} - 5985q^{78} - 551q^{79} + 4239q^{80} + 3741q^{81} + 18q^{82} - 1830q^{83} - 7725q^{84} - 237q^{85} - 2130q^{87} + 1246q^{88} - 4266q^{89} - 9993q^{90} - 1140q^{91} + 7896q^{92} - 1479q^{93} - 3q^{94} - 1053q^{95} + 5034q^{96} + 792q^{97} - 5667q^{98} + 4335q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

$n$	$10$	$29$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	2.09278	−	1.20827i	0.739909	−	0.427187i	−0.0821272	−	0.996622i	$-0.526171\pi$
$2$	2.09278	−	1.20827i	0.739909	−	0.427187i	0.822036	+	0.569435i	$0.192838\pi$
$3$	−5.12336	+	0.866692i	−0.985992	+	0.166795i
$3$	−5.12336	+	0.866692i	−0.985992	+	0.166795i
$4$	−1.08019	+	1.87094i	−0.135023	+	0.233867i
$5$	−10.7193			−0.958764			−0.479382	−	0.877606i	$-0.659139\pi$
$5$	−10.7193			−0.958764			−0.479382	+	0.877606i	$0.659139\pi$
$6$	−9.67487	+	8.00418i	−0.658292	+	0.544615i
$7$	−17.6173	+	5.71220i	−0.951247	+	0.308430i
$7$	−17.6173	+	5.71220i	−0.951247	+	0.308430i
$8$			24.5529i			1.08509i
$9$	25.4977	−	8.88075i	0.944359	−	0.328917i
$10$	−22.4331	+	12.9518i	−0.709398	+	0.409571i
$11$		−	26.1223i		−	0.716015i	−0.933719	−	0.358008i	$-0.883456\pi$
$11$		−	26.1223i		−	0.716015i	0.933719	−	0.358008i	$-0.116544\pi$
$12$	3.91266	−	10.5217i	0.0941239	−	0.253112i
$13$	−29.8910	+	17.2576i	−0.637714	+	0.368184i	−0.783733	−	0.621097i	$-0.786687\pi$
$13$	−29.8910	+	17.2576i	−0.637714	+	0.368184i	0.146019	+	0.989282i	$0.453354\pi$
$14$	−29.9673	+	33.2408i	−0.572079	+	0.634570i
$15$	54.9189	−	9.29033i	0.945333	−	0.159917i
$16$	21.0249	+	36.4162i	0.328514	+	0.569004i
$17$	2.29830	+	3.98078i	0.0327895	+	0.0567930i	0.881954	−	0.471335i	$-0.156228\pi$
$17$	2.29830	+	3.98078i	0.0327895	+	0.0567930i	−0.849165	+	0.528128i	$0.822894\pi$
$18$	42.6307	−	49.3934i	0.558231	−	0.646786i
$19$	6.74409	+	3.89370i	0.0814316	+	0.0470146i	0.540163	−	0.841560i	$-0.318363\pi$
$19$	6.74409	+	3.89370i	0.0814316	+	0.0470146i	−0.458731	+	0.888575i	$0.651696\pi$
$20$	11.5788	−	20.0551i	0.129455	−	0.224223i
$21$	85.3093	−	44.5345i	0.886477	−	0.462772i
$22$	−31.5627	−	54.6682i	−0.305872	−	0.529786i
$23$			39.1615i			0.355032i	0.984118	+	0.177516i	$0.0568062\pi$
$23$			39.1615i			0.355032i	−0.984118	+	0.177516i	$0.943194\pi$
$24$	−21.2798	−	125.793i	−0.180988	−	1.06989i
$25$	−10.0965			−0.0807719
$26$	−41.7035	+	72.2327i	−0.314567	+	0.544846i
$27$	−122.937	+	67.5979i	−0.876268	+	0.481823i
$28$	8.34283	−	39.1311i	0.0563088	−	0.264110i
$29$	210.884	+	121.754i	1.35035	+	0.779624i	0.988298	−	0.152535i	$-0.0487437\pi$
$29$	210.884	+	121.754i	1.35035	+	0.779624i	0.362050	+	0.932159i	$0.382077\pi$
$30$	103.708	−	85.7993i	0.631146	−	0.522158i
$31$	−269.441	−	155.562i	−1.56107	−	0.901282i	−0.997149	−	0.0754513i	$-0.975960\pi$
$31$	−269.441	−	155.562i	−1.56107	−	0.901282i	−0.563917	−	0.825831i	$-0.690706\pi$
$32$	−82.1062	−	47.4041i	−0.453577	−	0.261873i
$33$	22.6400	+	133.834i	0.119428	+	0.705985i
$34$	9.61969	+	5.55393i	0.0485224	+	0.0280144i
$35$	188.846	−	61.2308i	0.912021	−	0.295711i
$36$	−10.9269	+	57.2974i	−0.0505876	+	0.265266i
$37$	−28.3008	+	49.0184i	−0.125747	+	0.217799i	−0.922024	−	0.387132i	$-0.873466\pi$
$37$	−28.3008	+	49.0184i	−0.125747	+	0.217799i	0.796278	+	0.604931i	$0.206799\pi$
$38$	18.8185			0.0803360
$39$	138.186	−	114.323i	0.567369	−	0.469394i
$40$		−	263.190i		−	1.04035i
$41$	148.047	+	256.425i	0.563928	+	0.976752i	0.997149	+	0.0754640i	$0.0240438\pi$
$41$	148.047	+	256.425i	0.563928	+	0.976752i	−0.433221	+	0.901288i	$0.642623\pi$
$42$	124.724	−	196.277i	0.458222	−	0.721101i
$43$	−60.7001	+	105.136i	−0.215271	+	0.372861i	−0.953357	−	0.301847i	$-0.902397\pi$
$43$	−60.7001	+	105.136i	−0.215271	+	0.372861i	0.738085	+	0.674708i	$0.235730\pi$
$44$	48.8731	+	28.2169i	0.167452	+	0.0966786i
$45$	−273.318	+	95.1955i	−0.905417	+	0.315353i
$46$	47.3176	+	81.9564i	0.151665	+	0.262692i
$47$	112.910	+	195.566i	0.350417	+	0.606940i	0.986323	−	0.164827i	$-0.0527065\pi$
$47$	112.910	+	195.566i	0.350417	+	0.606940i	−0.635905	+	0.771767i	$0.719373\pi$
$48$	−139.280	−	168.351i	−0.418819	−	0.506238i
$49$	277.742	−	201.268i	0.809742	−	0.586786i
$50$	−21.1297	+	12.1992i	−0.0597638	+	0.0345047i
$51$	−15.2252	−	18.4031i	−0.0418029	−	0.0505283i
$52$		−	74.5656i		−	0.198854i
$53$	−307.128	+	177.321i	−0.795987	+	0.459563i	−0.842066	−	0.539375i	$-0.818661\pi$
$53$	−307.128	+	177.321i	−0.795987	+	0.459563i	0.0460792	+	0.998938i	$0.485327\pi$
$54$	−175.604	+	290.008i	−0.442530	+	0.730836i
$55$			280.013i			0.686490i
$56$	−140.251	−	432.556i	−0.334675	−	1.03219i
$57$	−37.9271	−	14.1038i	−0.0881327	−	0.0327736i
$58$	588.443			1.33218
$59$	−135.574	+	234.821i	−0.299157	+	0.518154i	−0.975943	−	0.218025i	$-0.930039\pi$
$59$	−135.574	+	234.821i	−0.299157	+	0.518154i	0.676787	+	0.736179i	$0.263372\pi$
$60$	−41.9410	+	112.785i	−0.0902426	+	0.242675i
$61$	−649.461	+	374.967i	−1.36320	+	0.787042i	−0.990048	−	0.140729i	$-0.955055\pi$
$61$	−649.461	+	374.967i	−1.36320	+	0.787042i	−0.373149	+	0.927771i	$0.621722\pi$
$62$	−751.841			−1.54006
$63$	−398.473	+	302.103i	−0.796871	+	0.604150i
$64$	−565.506			−1.10450
$65$	320.411	−	184.989i	0.611417	−	0.353002i
$66$	209.088	+	252.730i	0.389953	+	0.471347i
$67$	−497.425	+	861.565i	−0.907016	+	1.57100i	−0.0888281	+	0.996047i	$0.528312\pi$
$67$	−497.425	+	861.565i	−0.907016	+	1.57100i	−0.818188	+	0.574951i	$0.805021\pi$
$68$	−9.93038			−0.0177093
$69$	−33.9410	−	200.639i	−0.0592176	−	0.350059i
$70$	321.229	−	356.318i	0.548489	−	0.608403i
$71$		−	1139.11i		−	1.90405i	−0.306018	−	0.952026i	$-0.598997\pi$
$71$		−	1139.11i		−	1.90405i	0.306018	−	0.952026i	$-0.401003\pi$
$72$	218.048	+	626.041i	0.356905	+	1.02472i
$73$	1074.95	−	620.624i	1.72348	−	0.995049i	0.812045	−	0.583594i	$-0.198354\pi$
$73$	1074.95	−	620.624i	1.72348	−	0.995049i	0.911430	−	0.411455i	$-0.134979\pi$
$74$			136.780i			0.214869i
$75$	51.7280	−	8.75054i	0.0796404	−	0.0134723i
$76$	−14.5697	+	8.41184i	−0.0219903	+	0.0126961i
$77$	149.216	+	460.205i	0.220841	+	0.681108i
$78$	151.059	−	406.218i	0.219283	−	0.589681i
$79$	−216.802	−	375.512i	−0.308761	−	0.534789i	0.669331	−	0.742964i	$-0.266581\pi$
$79$	−216.802	−	375.512i	−0.308761	−	0.534789i	−0.978092	+	0.208175i	$0.933248\pi$
$80$	−225.373	−	390.357i	−0.314968	−	0.545540i
$81$	571.265	−	452.877i	0.783628	−	0.621231i
$82$	619.659	+	357.760i	0.834511	+	0.481805i
$83$	492.785	−	853.528i	0.651689	−	1.12876i	−0.331024	−	0.943622i	$-0.607394\pi$
$83$	492.785	−	853.528i	0.651689	−	1.12876i	0.982713	−	0.185136i	$-0.0592724\pi$
$84$	−8.82872	+	207.714i	−0.0114678	+	0.269803i
$85$	−24.6362	−	42.6712i	−0.0314373	−	0.0544511i
$86$			293.367i			0.367844i
$87$	−1185.96	−	441.017i	−1.46147	−	0.543471i
$88$	641.377			0.776944
$89$	75.6350	−	131.004i	0.0900819	−	0.156027i	−0.817463	−	0.575980i	$-0.804620\pi$
$89$	75.6350	−	131.004i	0.0900819	−	0.156027i	0.907545	+	0.419954i	$0.137954\pi$
$90$	−456.972	+	529.463i	−0.535212	+	0.620115i
$91$	428.022	−	474.777i	0.493064	−	0.546924i
$92$	−73.2687	−	42.3017i	−0.0830303	−	0.0479376i
$93$	1515.27	+	563.478i	1.68953	+	0.628279i
$94$	472.591	+	272.851i	0.518554	+	0.299387i
$95$	−72.2920	−	41.7378i	−0.0780737	−	0.0450759i
$96$	461.745	+	171.707i	0.490902	+	0.182550i
$97$	781.452	+	451.172i	0.817984	+	0.472263i	0.849721	−	0.527233i	$-0.176770\pi$
$97$	781.452	+	451.172i	0.817984	+	0.472263i	−0.0317367	+	0.999496i	$0.510104\pi$
$98$	338.067	−	756.794i	0.348468	−	0.780079i
$99$	−231.986	−	666.058i	−0.235509	−	0.676176i
$100$	10.9061	−	18.8899i	0.0109061	−	0.0188899i
$101$	−278.651			−0.274523			−0.137261	−	0.990535i	$-0.543830\pi$
$101$	−278.651			−0.274523			−0.137261	+	0.990535i	$0.543830\pi$
$102$	−54.0987	−	20.1175i	−0.0525154	−	0.0195287i
$103$			1288.26i			1.23238i	0.787596	+	0.616192i	$0.211326\pi$
$103$			1288.26i			1.23238i	−0.787596	+	0.616192i	$0.788674\pi$
$104$	−423.723	−	733.910i	−0.399514	−	0.691979i
$105$	−914.457	+	477.379i	−0.849922	+	0.443689i
$106$	−428.501	+	742.185i	−0.392638	+	0.680070i
$107$	−1405.87	−	811.679i	−1.27019	−	0.733346i	−0.295168	−	0.955445i	$-0.595376\pi$
$107$	−1405.87	−	811.679i	−1.27019	−	0.733346i	−0.975024	+	0.222100i	$0.928709\pi$
$108$	6.32340	−	303.026i	0.00563397	−	0.269987i
$109$	−426.818	−	739.271i	−0.375062	−	0.649627i	0.615274	−	0.788313i	$-0.289045\pi$
$109$	−426.818	−	739.271i	−0.375062	−	0.649627i	−0.990336	+	0.138686i	$0.955712\pi$
$110$	338.330	+	586.005i	0.293259	+	0.507940i
$111$	102.511	−	275.667i	0.0876572	−	0.235722i
$112$	−578.420	−	521.459i	−0.487996	−	0.439939i
$113$	1119.93	−	646.595i	0.932342	−	0.538288i	0.0447903	−	0.998996i	$-0.485738\pi$
$113$	1119.93	−	646.595i	0.932342	−	0.538288i	0.887551	+	0.460709i	$0.152405\pi$
$114$	−96.4141	+	16.3099i	−0.0792106	+	0.0133996i
$115$		−	419.784i		−	0.340392i
$116$	−455.586	+	263.033i	−0.364656	+	0.210534i
$117$	−608.892	+	705.484i	−0.481129	+	0.557453i
$118$			655.238i			0.511183i
$119$	−63.2290	−	57.0024i	−0.0487075	−	0.0439109i
$120$	228.104	+	1348.42i	0.173525	+	1.02577i
$121$	648.625			0.487322
$122$	−906.119	+	1569.44i	−0.672428	+	1.16468i
$123$	−980.739	−	1185.45i	−0.718945	−	0.869009i
$124$	582.093	−	336.071i	0.421560	−	0.243388i
$125$	1448.14			1.03621
$126$	−468.895	+	1113.70i	−0.331527	+	0.787428i
$127$	−2072.04			−1.44775			−0.723873	−	0.689933i	$-0.757640\pi$
$127$	−2072.04			−1.44775			−0.723873	+	0.689933i	$0.757640\pi$
$128$	−526.628	+	304.049i	−0.363655	+	0.209956i
$129$	219.868	−	591.256i	0.150065	−	0.403544i
$130$	447.033	−	774.284i	0.301595	−	0.522378i
$131$	17.7370			0.0118297			0.00591485	−	0.999983i	$-0.498117\pi$
$131$	17.7370			0.0118297			0.00591485	+	0.999983i	$0.498117\pi$
$132$	−274.850	−	102.208i	−0.181232	−	0.0673941i
$133$	−141.055	−	30.0731i	−0.0919623	−	0.0196065i
$134$			2404.09i			1.54986i
$135$	1317.80	−	724.603i	0.840134	−	0.461955i
$136$	−97.7396	+	56.4300i	−0.0616257	+	0.0355796i
$137$			2005.03i			1.25037i	0.780475	+	0.625187i	$0.214977\pi$
$137$			2005.03i			1.25037i	−0.780475	+	0.625187i	$0.785023\pi$
$138$	−313.456	−	378.883i	−0.193356	−	0.233715i
$139$	−618.188	+	356.911i	−0.377223	+	0.217790i	−0.676609	−	0.736342i	$-0.736551\pi$
$139$	−618.188	+	356.911i	−0.377223	+	0.217790i	0.299386	+	0.954132i	$0.403218\pi$
$140$	−89.4294	+	419.459i	−0.0539869	+	0.253219i
$141$	−747.974	−	904.096i	−0.446743	−	0.539990i
$142$	−1376.35	−	2383.91i	−0.813385	−	1.40882i
$143$	450.808	+	780.822i	0.263626	+	0.456613i
$144$	859.490	+	741.813i	0.497390	+	0.429290i
$145$	−2260.53	−	1305.11i	−1.29466	−	0.747475i
$146$	1499.76	−	2597.66i	0.850143	−	1.47249i
$147$	−1248.53	+	1271.88i	−0.700526	+	0.713627i
$148$	−61.1402	−	105.898i	−0.0339574	−	0.0588159i
$149$			1605.04i			0.882485i	0.897388	+	0.441243i	$0.145462\pi$
$149$			1605.04i			0.882485i	−0.897388	+	0.441243i	$0.854538\pi$
$150$	97.6822	−	80.8141i	0.0531715	−	0.0439896i
$151$	1112.79			0.599717			0.299859	−	0.953984i	$-0.403060\pi$
$151$	1112.79			0.599717			0.299859	+	0.953984i	$0.403060\pi$
$152$	−95.6016	+	165.587i	−0.0510152	+	0.0883609i
$153$	93.9538	+	81.0900i	0.0496452	+	0.0428480i
$154$	868.326	+	782.816i	0.454362	+	0.409617i
$155$	2888.22	+	1667.52i	1.49669	+	0.864117i
$156$	64.6254	+	382.027i	0.0331678	+	0.196068i
$157$	149.815	+	86.4957i	0.0761563	+	0.0439688i	0.537595	−	0.843203i	$-0.319333\pi$
$157$	149.815	+	86.4957i	0.0761563	+	0.0439688i	−0.461438	+	0.887172i	$0.652666\pi$
$158$	−907.436	−	523.908i	−0.456910	−	0.263797i
$159$	1419.85	−	1174.66i	0.708183	−	0.585892i
$160$	880.122	+	508.139i	0.434873	+	0.251074i
$161$	−223.699	−	689.922i	−0.109503	−	0.337723i
$162$	648.334	−	1638.01i	0.314432	−	0.794410i
$163$	−1100.08	+	1905.39i	−0.528617	+	0.915591i	0.470826	+	0.882226i	$0.343956\pi$
$163$	−1100.08	+	1905.39i	−0.528617	+	0.915591i	−0.999443	+	0.0333655i	$0.989377\pi$
$164$	−639.672			−0.304573
$165$	−242.685	−	1434.61i	−0.114503	−	0.676873i
$166$		−	2381.66i		−	1.11357i
$167$	68.4457	+	118.551i	0.0317155	+	0.0549328i	0.881447	−	0.472282i	$-0.156570\pi$
$167$	68.4457	+	118.551i	0.0317155	+	0.0549328i	−0.849732	+	0.527215i	$0.823236\pi$
$168$	1093.45	+	2094.59i	0.502151	+	0.961911i
$169$	−502.851	+	870.963i	−0.228881	+	0.396433i
$170$	−103.116	−	59.5343i	−0.0465216	−	0.0268592i
$171$	206.538	+	39.3878i	0.0923645	+	0.0176144i
$172$	−131.135	−	227.132i	−0.0581332	−	0.100690i
$173$	−745.967	−	1292.05i	−0.327831	−	0.567821i	0.654250	−	0.756278i	$-0.272984\pi$
$173$	−745.967	−	1292.05i	−0.327831	−	0.567821i	−0.982081	+	0.188458i	$0.939651\pi$
$174$	−3014.81	+	509.999i	−1.31352	+	0.222201i
$175$	177.873	−	57.6732i	0.0768340	−	0.0249125i
$176$	951.276	−	549.219i	0.407415	−	0.235221i
$177$	491.077	−	1320.57i	0.208540	−	0.560794i
$178$		−	365.549i		−	0.153927i
$179$	589.130	−	340.135i	0.245998	−	0.142027i	−0.371932	−	0.928260i	$-0.621305\pi$
$179$	589.130	−	340.135i	0.245998	−	0.142027i	0.617930	+	0.786233i	$0.287971\pi$
$180$	117.129	−	614.188i	0.0485015	−	0.254327i
$181$			2275.25i			0.934355i	0.884164	+	0.467177i	$0.154729\pi$
$181$			2275.25i			0.934355i	−0.884164	+	0.467177i	$0.845271\pi$
$182$	322.098	−	1510.77i	0.131184	−	0.615305i
$183$	3002.45	−	2483.97i	1.21283	−	1.00339i
$184$	−961.528			−0.385243
$185$	303.365	−	525.443i	0.120561	−	0.208818i
$186$	3851.96	−	651.614i	1.51849	−	0.256875i
$187$	103.987	−	60.0370i	0.0406647	−	0.0234778i
$188$	−487.854			−0.189258
$189$	1779.69	−	1893.14i	0.684939	−	0.728600i
$190$	−201.721			−0.0770232
$191$	−2899.43	+	1673.99i	−1.09840	+	0.634164i	−0.935802	−	0.352527i	$-0.885322\pi$
$191$	−2899.43	+	1673.99i	−1.09840	+	0.634164i	−0.162603	+	0.986692i	$0.551989\pi$
$192$	2897.29	−	490.119i	1.08903	−	0.184225i
$193$	−1032.44	+	1788.24i	−0.385060	+	0.666944i	−0.991778	−	0.127974i	$-0.959153\pi$
$193$	−1032.44	+	1788.24i	−0.385060	+	0.666944i	0.606717	+	0.794918i	$0.292486\pi$
$194$	2180.54			0.806978
$195$	−1481.25	+	1225.47i	−0.543973	+	0.450038i
$196$	76.5464	+	737.043i	0.0278959	+	0.268602i
$197$			2890.54i			1.04539i	0.852519	+	0.522696i	$0.175074\pi$
$197$			2890.54i			1.04539i	−0.852519	+	0.522696i	$0.824926\pi$
$198$	−1290.27	−	1113.61i	−0.463109	−	0.399702i
$199$	1007.22	−	581.519i	0.358794	−	0.207150i	−0.309758	−	0.950816i	$-0.600248\pi$
$199$	1007.22	−	581.519i	0.358794	−	0.207150i	0.668552	+	0.743666i	$0.266915\pi$
$200$		−	247.898i		−	0.0876451i
$201$	1801.78	−	4845.22i	0.632276	−	1.70028i
$202$	−583.154	+	336.684i	−0.203122	+	0.117272i
$203$	−4410.69	−	940.367i	−1.52497	−	0.325127i
$204$	50.8769	−	8.60657i	0.0174613	−	0.00295383i
$205$	−1586.96	−	2748.70i	−0.540674	−	0.936474i
$206$	1556.56	+	2696.03i	0.526458	+	0.911853i
$207$	347.784	+	998.529i	0.116776	+	0.335278i
$208$	−1256.91	−	725.679i	−0.418996	−	0.241908i
$209$	101.712	−	176.171i	0.0336632	−	0.0583063i
$210$	−1336.95	+	2103.96i	−0.439327	+	0.691365i
$211$	−540.323	−	935.867i	−0.176291	−	0.305345i	0.764316	−	0.644841i	$-0.223077\pi$
$211$	−540.323	−	935.867i	−0.176291	−	0.305345i	−0.940607	+	0.339497i	$0.889743\pi$
$212$		−	766.156i		−	0.248207i
$213$	987.258	+	5836.08i	0.317586	+	1.87738i
$214$	−3922.90			−1.25310
$215$	650.662	−	1126.98i	0.206394	−	0.357486i
$216$	−1659.72	−	3018.46i	−0.522823	−	0.950833i
$217$	5635.44	+	1201.49i	1.76294	+	0.375863i
$218$	−1786.47	−	1031.42i	−0.555024	−	0.320443i
$219$	−4969.48	+	4111.34i	−1.53336	+	1.26858i
$220$	−523.886	−	302.466i	−0.160547	−	0.0926920i
$221$	−137.397	−	79.3264i	−0.0418206	−	0.0241451i
$222$	−118.546	−	700.771i	−0.0358390	−	0.211859i
$223$	5362.37	+	3095.96i	1.61027	+	0.929691i	0.989306	+	0.145854i	$0.0465928\pi$
$223$	5362.37	+	3095.96i	1.61027	+	0.929691i	0.620966	+	0.783838i	$0.286741\pi$
$224$	1717.28	+	366.126i	0.512233	+	0.109209i
$225$	−257.437	+	89.6644i	−0.0762777	+	0.0265672i
$226$	1562.52	−	2706.36i	0.459899	−	0.796568i
$227$	−55.0293			−0.0160900			−0.00804499	−	0.999968i	$-0.502561\pi$
$227$	−55.0293			−0.0160900			−0.00804499	+	0.999968i	$0.502561\pi$
$228$	67.3556	−	55.7244i	0.0195646	−	0.0161861i
$229$			1447.92i			0.417822i	0.977935	+	0.208911i	$0.0669918\pi$
$229$			1447.92i			0.417822i	−0.977935	+	0.208911i	$0.933008\pi$
$230$	−507.211	−	878.516i	−0.145411	−	0.251859i
$231$	−1163.34	−	2228.48i	−0.331352	−	0.634731i
$232$	−2989.40	+	5177.80i	−0.845965	+	1.46525i
$233$	−1409.38	−	813.703i	−0.396271	−	0.228787i	0.288602	−	0.957449i	$-0.406809\pi$
$233$	−1409.38	−	813.703i	−0.396271	−	0.228787i	−0.684874	+	0.728662i	$0.740143\pi$
$234$	−421.864	+	2212.12i	−0.117855	+	0.617996i
$235$	−1210.32	−	2096.33i	−0.335967	−	0.581912i
$236$	−292.890	−	507.300i	−0.0807861	−	0.139926i
$237$	1436.21	+	1735.98i	0.393636	+	0.475798i
$238$	−201.198	−	42.8959i	−0.0547973	−	0.0116829i
$239$	1829.22	−	1056.10i	0.495073	−	0.285830i	−0.231604	−	0.972810i	$-0.574397\pi$
$239$	1829.22	−	1056.10i	0.495073	−	0.285830i	0.726676	+	0.686980i	$0.241064\pi$
$240$	1492.98	+	1804.61i	0.401549	+	0.485363i
$241$			2195.88i			0.586926i	0.955970	+	0.293463i	$0.0948077\pi$
$241$			2195.88i			0.586926i	−0.955970	+	0.293463i	$0.905192\pi$
$242$	1357.43	−	783.712i	0.360574	−	0.208177i
$243$	−2534.29	+	2815.36i	−0.669032	+	0.743233i
$244$		−	1620.13i		−	0.425076i
$245$	−2977.20	+	2157.45i	−0.776351	+	0.562589i
$246$	−3484.81	−	1295.88i	−0.903183	−	0.335864i
$247$	−268.784			−0.0692401
$248$	3819.49	−	6615.55i	0.977976	−	1.69390i
$249$	−1784.97	+	4800.03i	−0.454289	+	1.22164i
$250$	3030.64	−	1749.74i	0.766697	−	0.442653i
$251$	3257.57			0.819188			0.409594	−	0.912268i	$-0.365670\pi$
$251$	3257.57			0.819188			0.409594	+	0.912268i	$0.365670\pi$
$252$	−134.791	−	1071.84i	−0.0336946	−	0.267936i
$253$	1022.99			0.254209
$254$	−4336.32	+	2503.57i	−1.07120	+	0.618458i
$255$	163.203	+	197.268i	0.0400791	+	0.0484447i
$256$	1527.28	−	2645.32i	0.372871	−	0.645831i
$257$	−2087.45			−0.506661			−0.253330	−	0.967380i	$-0.581526\pi$
$257$	−2087.45			−0.506661			−0.253330	+	0.967380i	$0.581526\pi$
$258$	−254.259	−	1503.03i	−0.0613545	−	0.362691i
$259$	218.582	−	1025.23i	0.0524402	−	0.245965i
$260$			799.291i			0.190654i
$261$	6458.31	+	1231.63i	1.53164	+	0.292093i
$262$	37.1197	−	21.4310i	0.00875290	−	0.00505349i
$263$			1779.81i			0.417293i	0.977991	+	0.208646i	$0.0669058\pi$
$263$			1779.81i			0.417293i	−0.977991	+	0.208646i	$0.933094\pi$
$264$	−3286.01	+	555.876i	−0.766060	+	0.129590i
$265$	3292.20	−	1900.75i	0.763163	−	0.440613i
$266$	−331.532	+	107.495i	−0.0764194	+	0.0247780i
$267$	−273.966	+	736.731i	−0.0627956	+	0.168866i
$268$	−1074.62	−	1861.30i	−0.244936	−	0.424242i
$269$	−1531.88	−	2653.29i	−0.347213	−	0.601390i	0.638540	−	0.769588i	$-0.279538\pi$
$269$	−1531.88	−	2653.29i	−0.347213	−	0.601390i	−0.985753	+	0.168198i	$0.946205\pi$
$270$	1882.35	−	3108.69i	0.424282	−	0.700699i
$271$	110.943	+	64.0531i	0.0248683	+	0.0143577i	0.512383	−	0.858757i	$-0.328763\pi$
$271$	110.943	+	64.0531i	0.0248683	+	0.0143577i	−0.487514	+	0.873115i	$0.662096\pi$
$272$	−96.6433	+	167.391i	−0.0215436	+	0.0373146i
$273$	−1781.43	+	2803.42i	−0.394933	+	0.621503i
$274$	2422.61	+	4196.08i	0.534143	+	0.925163i
$275$			263.743i			0.0578339i
$276$	412.045	+	153.226i	0.0898629	+	0.0334170i
$277$	−4962.44			−1.07640			−0.538202	−	0.842816i	$-0.680896\pi$
$277$	−4962.44			−1.07640			−0.538202	+	0.842816i	$0.680896\pi$
$278$	−862.487	+	1493.87i	−0.186074	+	0.322290i
$279$	−8251.64	−	1573.63i	−1.77065	−	0.337673i
$280$	1503.39	+	4636.70i	0.320875	+	0.989629i
$281$	3651.52	+	2108.21i	0.775201	+	0.447563i	0.834727	−	0.550664i	$-0.185626\pi$
$281$	3651.52	+	2108.21i	0.775201	+	0.447563i	−0.0595257	+	0.998227i	$0.518959\pi$
$282$	−2657.73	−	988.322i	−0.561226	−	0.208701i
$283$	−2513.50	−	1451.17i	−0.527958	−	0.304817i	0.212227	−	0.977220i	$-0.431929\pi$
$283$	−2513.50	−	1451.17i	−0.527958	−	0.304817i	−0.740184	+	0.672404i	$0.765262\pi$
$284$	2131.20	+	1230.45i	0.445295	+	0.257091i
$285$	406.552	+	151.183i	0.0844984	+	0.0314221i
$286$	1886.88	+	1089.39i	0.390118	+	0.225235i
$287$	−4072.94	−	3671.85i	−0.837694	−	0.755200i
$288$	−2514.50	−	479.529i	−0.514474	−	0.0981129i
$289$	2445.94	−	4236.48i	0.497850	−	0.862301i
$290$	−6307.70			−1.27725
$291$	−4394.69	−	1634.24i	−0.885297	−	0.329212i
$292$			2681.56i			0.537419i
$293$	184.087	+	318.848i	0.0367047	+	0.0635744i	0.883794	−	0.467876i	$-0.154981\pi$
$293$	184.087	+	318.848i	0.0367047	+	0.0635744i	−0.847089	+	0.531450i	$0.821647\pi$
$294$	−1076.13	+	4170.33i	−0.213474	+	0.827274i
$295$	1453.26	−	2517.12i	0.286820	−	0.496788i
$296$	−1203.54	−	694.865i	−0.236333	−	0.136447i
$297$	1765.81	+	3211.40i	0.344993	+	0.627422i
$298$	1939.32	+	3359.00i	0.376986	+	0.652959i
$299$	−675.834	−	1170.58i	−0.130717	−	0.226409i
$300$	−39.5041	+	106.232i	−0.00760256	+	0.0204443i
$301$	468.818	−	2198.94i	0.0897748	−	0.421079i
$302$	2328.82	−	1344.54i	0.443736	−	0.256191i
$303$	1427.63	−	241.504i	0.270677	−	0.0457889i
$304$			327.459i			0.0617798i
$305$	6961.78	−	4019.38i	1.30698	−	0.754588i
$306$	294.603	+	56.1823i	0.0550370	+	0.0104958i
$307$		−	860.553i		−	0.159982i	−0.996796	−	0.0799908i	$-0.974511\pi$
$307$		−	860.553i		−	0.159982i	0.996796	−	0.0799908i	$-0.0254891\pi$
$308$	−1022.20	−	217.934i	−0.189107	−	0.0403180i
$309$	−1116.52	−	6600.20i	−0.205555	−	1.21512i
$310$	8059.22			1.47656
$311$	2325.27	−	4027.49i	0.423968	−	0.734334i	−0.572356	−	0.820006i	$-0.693970\pi$
$311$	2325.27	−	4027.49i	0.423968	−	0.734334i	0.996323	+	0.0856717i	$0.0273036\pi$
$312$	2806.96	+	3392.85i	0.509336	+	0.615649i
$313$	3556.44	−	2053.31i	0.642243	−	0.370799i	−0.143235	−	0.989689i	$-0.545750\pi$
$313$	3556.44	−	2053.31i	0.642243	−	0.370799i	0.785478	+	0.618889i	$0.212417\pi$
$314$	418.039			0.0751316
$315$	4271.35	−	3238.34i	0.764011	−	0.579237i
$316$	936.744			0.166759
$317$	4092.06	−	2362.55i	0.725025	−	0.418593i	−0.0915746	−	0.995798i	$-0.529190\pi$
$317$	4092.06	−	2362.55i	0.725025	−	0.418593i	0.816599	+	0.577205i	$0.195857\pi$
$318$	1552.12	−	4173.86i	0.273706	−	0.736033i
$319$	3180.49	−	5508.76i	0.558223	−	0.966870i
$320$	6061.83			1.05896
$321$	7906.26	+	2940.07i	1.37472	+	0.511211i
$322$	−1301.76	−	1173.57i	−0.225293	−	0.203107i
$323$			35.7957i			0.00616633i
$324$	230.233	+	1557.99i	0.0394775	+	0.267145i
$325$	301.794	−	174.241i	0.0515094	−	0.0297389i
$326$			5316.74i			0.903272i
$327$	2827.47	+	3417.63i	0.478163	+	0.577968i
$328$	−6295.96	+	3634.98i	−1.05987	+	0.611915i
$329$	−3106.28	−	2800.38i	−0.520532	−	0.469271i
$330$	−2241.27	−	2709.09i	−0.373873	−	0.451910i
$331$	592.724	+	1026.63i	0.0984262	+	0.170479i	0.911033	−	0.412333i	$-0.135286\pi$
$331$	592.724	+	1026.63i	0.0984262	+	0.170479i	−0.812607	+	0.582812i	$0.801952\pi$
$332$	1064.60	+	1843.94i	0.175986	+	0.304817i
$333$	−286.285	+	1501.19i	−0.0471120	+	0.247041i
$334$	286.483	+	165.401i	0.0469332	+	0.0270969i
$335$	5332.05	−	9235.37i	0.869614	−	1.50622i
$336$	3415.40	+	2170.31i	0.554540	+	0.352381i
$337$	−3299.99	−	5715.76i	−0.533419	−	0.923908i	−0.999238	−	0.0390284i	$-0.987574\pi$
$337$	−3299.99	−	5715.76i	−0.533419	−	0.923908i	0.465819	−	0.884880i	$-0.345760\pi$
$338$			2430.31i			0.391099i
$339$	−5177.43	+	4283.38i	−0.829498	+	0.686257i
$340$	106.447			0.0169791
$341$	−4063.64	+	7038.42i	−0.645332	+	1.11775i
$342$	479.829	−	167.123i	0.0758660	−	0.0264238i
$343$	−3743.39	+	5132.32i	−0.589282	+	0.807927i
$344$	−2581.38	−	1490.36i	−0.404589	−	0.233590i
$345$	363.824	+	2150.71i	0.0567757	+	0.335624i
$346$	−3122.29	−	1802.65i	−0.485131	−	0.280090i
$347$	−2271.12	−	1311.23i	−0.351355	−	0.202855i	0.313927	−	0.949447i	$-0.398355\pi$
$347$	−2271.12	−	1311.23i	−0.351355	−	0.202855i	−0.665282	+	0.746592i	$0.731689\pi$
$348$	2106.17	−	1742.47i	0.324432	−	0.268408i
$349$	−6093.48	−	3518.07i	−0.934603	−	0.539593i	−0.0463383	−	0.998926i	$-0.514755\pi$
$349$	−6093.48	−	3518.07i	−0.934603	−	0.539593i	−0.888264	+	0.459333i	$0.848089\pi$
$350$	302.565	−	335.615i	0.0462079	−	0.0512554i
$351$	2508.14	−	4142.17i	0.381409	−	0.629894i
$352$	−1238.30	+	2144.80i	−0.187505	+	0.324768i
$353$	−10451.4			−1.57585			−0.787923	−	0.615774i	$-0.788844\pi$
$353$	−10451.4			−1.57585			−0.787923	+	0.615774i	$0.788844\pi$
$354$	−567.889	−	3357.02i	−0.0852626	−	0.504022i
$355$			12210.5i			1.82554i
$356$	163.400	+	283.016i	0.0243263	+	0.0421344i
$357$	373.349	+	237.244i	0.0553493	+	0.0351716i
$358$	821.946	−	1423.65i	0.121344	−	0.210174i
$359$	9887.03	+	5708.28i	1.45353	+	0.839197i	0.998680	−	0.0513705i	$-0.0163589\pi$
$359$	9887.03	+	5708.28i	1.45353	+	0.839197i	0.454852	+	0.890567i	$0.349692\pi$
$360$	−2337.32	−	6710.73i	−0.342188	−	0.982462i
$361$	−3399.18	−	5887.55i	−0.495579	−	0.858368i
$362$	2749.11	+	4761.60i	0.399144	+	0.691338i
$363$	−3323.14	+	562.158i	−0.480495	+	0.0812828i
$364$	425.934	+	1313.65i	0.0613324	+	0.189159i
$365$	−11522.7	+	6652.66i	−1.65241	+	0.954017i
$366$	3282.15	−	8826.16i	0.468746	−	1.26052i
$367$			7586.82i			1.07910i	0.841954	+	0.539549i	$0.181405\pi$
$367$			7586.82i			1.07910i	−0.841954	+	0.539549i	$0.818595\pi$
$368$	−1426.12	+	823.368i	−0.202015	+	0.116633i
$369$	6052.10	+	5223.47i	0.853820	+	0.736919i
$370$		−	1466.18i		−	0.206009i
$371$	4397.89	−	4878.29i	0.615437	−	0.682664i
$372$	−2691.00	+	2226.31i	−0.375059	+	0.310293i
$373$	−2144.93			−0.297749			−0.148874	−	0.988856i	$-0.547565\pi$
$373$	−2144.93			−0.297749			−0.148874	+	0.988856i	$0.547565\pi$
$374$	145.081	−	251.288i	0.0200588	−	0.0347428i
$375$	−7419.35	+	1255.09i	−1.02169	+	0.172834i
$376$	−4801.70	+	2772.26i	−0.658587	+	0.380235i
$377$	−8404.70			−1.14818
$378$	1437.09	−	6112.26i	0.195544	−	0.831695i
$379$	1473.32			0.199682			0.0998408	−	0.995003i	$-0.468167\pi$
$379$	1473.32			0.199682			0.0998408	+	0.995003i	$0.468167\pi$
$380$	156.177	−	90.1691i	0.0210835	−	0.0121726i
$381$	10615.8	−	1795.82i	1.42747	−	0.241477i
$382$	−4045.24	+	7006.56i	−0.541813	+	0.938448i
$383$	−12643.8			−1.68686			−0.843431	−	0.537238i	$-0.819468\pi$
$383$	−12643.8			−1.68686			−0.843431	+	0.537238i	$0.819468\pi$
$384$	2434.59	−	2014.18i	0.323541	−	0.267671i
$385$	−1599.49	−	4933.08i	−0.211734	−	0.653021i
$386$			4989.85i			0.657971i
$387$	−614.028	+	3219.78i	−0.0806533	+	0.422921i
$388$	−1688.23	+	974.698i	−0.220894	+	0.127533i
$389$			8455.52i			1.10209i	0.834476	+	0.551044i	$0.185770\pi$
$389$			8455.52i			1.10209i	−0.834476	+	0.551044i	$0.814230\pi$
$390$	−1619.25	+	4354.38i	−0.210240	+	0.565365i
$391$	−155.893	+	90.0051i	−0.0201634	+	0.0116413i
$392$	4941.70	+	6819.35i	0.636718	+	0.878646i
$393$	−90.8732	+	15.3725i	−0.0116640	+	0.00197313i
$394$	3492.54	+	6049.25i	0.446577	+	0.773495i
$395$	2323.96	+	4025.22i	0.296029	+	0.512737i
$396$	1496.74	+	285.436i	0.189934	+	0.0362215i
$397$	−8524.29	−	4921.50i	−1.07764	−	0.622174i	−0.147379	−	0.989080i	$-0.547084\pi$
$397$	−8524.29	−	4921.50i	−1.07764	−	0.622174i	−0.930258	+	0.366906i	$0.880417\pi$
$398$	1405.26	−	2433.98i	0.176983	−	0.306544i
$399$	748.738	+	31.8246i	0.0939443	+	0.00399304i
$400$	−212.278	−	367.676i	−0.0265347	−	0.0459595i
$401$		−	2361.32i		−	0.294061i	−0.989132	−	0.147031i	$-0.953028\pi$
$401$		−	2361.32i		−	0.294061i	0.989132	−	0.147031i	$-0.0469716\pi$
$402$	−2083.60	−	12317.0i	−0.258509	−	1.52815i
$403$	10738.5			1.32735
$404$	300.994	−	521.337i	0.0370669	−	0.0642017i
$405$	−6123.56	+	4854.53i	−0.751314	+	0.595614i
$406$	−10366.8	+	3361.31i	−1.26723	+	0.410884i
$407$	1280.47	+	739.282i	0.155948	+	0.0900364i
$408$	451.848	−	373.821i	0.0548280	−	0.0453601i
$409$	−4248.01	−	2452.59i	−0.513572	−	0.296511i	0.220729	−	0.975335i	$-0.429156\pi$
$409$	−4248.01	−	2452.59i	−0.513572	−	0.296511i	−0.734301	+	0.678825i	$0.762490\pi$
$410$	−6642.31	−	3834.94i	−0.800099	−	0.461937i
$411$	−1737.74	−	10272.5i	−0.208556	−	1.23286i
$412$	−2410.24	−	1391.56i	−0.288214	−	0.166400i
$413$	1047.11	−	4911.35i	0.124758	−	0.585162i
$414$	1934.32	+	1669.48i	0.229630	+	0.198190i
$415$	−5282.31	+	9149.23i	−0.624815	+	1.08221i
$416$	3272.32			0.385670
$417$	2857.87	−	2364.36i	0.335613	−	0.277658i
$418$		−	491.583i		−	0.0575218i
$419$	5174.25	+	8962.06i	0.603290	+	1.04493i	0.992319	+	0.123704i	$0.0394772\pi$
$419$	5174.25	+	8962.06i	0.603290	+	1.04493i	−0.389029	+	0.921225i	$0.627189\pi$
$420$	94.6378	−	2226.55i	0.0109949	−	0.258677i
$421$	1438.21	−	2491.05i	0.166494	−	0.288376i	−0.770691	−	0.637209i	$-0.780089\pi$
$421$	1438.21	−	2491.05i	0.166494	−	0.288376i	0.937185	+	0.348833i	$0.113422\pi$
$422$	−2261.55	−	1305.71i	−0.260878	−	0.150618i
$423$	4615.71	+	3983.75i	0.530552	+	0.457911i
$424$	−4353.73	−	7540.88i	−0.498669	−	0.863720i
$425$	−23.2048	−	40.1919i	−0.00264847	−	0.00458728i
$426$	9117.65	+	11020.8i	1.03698	+	1.25342i
$427$	9299.90	−	10315.8i	1.05399	−	1.16912i
$428$	3037.20	−	1753.53i	0.343011	−	0.198037i
$429$	−2986.39	−	3609.73i	−0.336093	−	0.406245i
$430$		−	3144.69i		−	0.352676i
$431$	5858.22	−	3382.24i	0.654711	−	0.377998i	−0.135548	−	0.990771i	$-0.543279\pi$
$431$	5858.22	−	3382.24i	0.654711	−	0.377998i	0.790259	+	0.612773i	$0.209946\pi$
$432$	−5046.40	−	3055.66i	−0.562026	−	0.340314i
$433$			10320.4i			1.14542i	0.819756	+	0.572712i	$0.194109\pi$
$433$			10320.4i			1.14542i	−0.819756	+	0.572712i	$0.805891\pi$
$434$	13245.4	−	4294.67i	1.46498	−	0.475001i
$435$	12712.6	+	4727.40i	1.40120	+	0.521061i
$436$	1844.17			0.202568
$437$	−152.483	+	264.109i	−0.0166917	+	0.0289109i
$438$	−5432.44	+	14608.6i	−0.592630	+	1.59366i
$439$	5671.87	−	3274.65i	0.616637	−	0.356015i	−0.158922	−	0.987291i	$-0.550802\pi$
$439$	5671.87	−	3274.65i	0.616637	−	0.356015i	0.775558	+	0.631276i	$0.217468\pi$
$440$	−6875.12			−0.744906
$441$	5294.36	−	7598.41i	0.571683	−	0.820474i
$442$	−383.390			−0.0412579
$443$	15074.9	−	8703.51i	1.61677	−	0.933445i	0.629027	−	0.777383i	$-0.283453\pi$
$443$	15074.9	−	8703.51i	1.61677	−	0.933445i	0.987747	−	0.156062i	$-0.0498800\pi$
$444$	405.024	+	489.564i	0.0432919	+	0.0523281i
$445$	−810.755	+	1404.27i	−0.0863673	+	0.149593i
$446$	14963.0			1.58861
$447$	−1391.08	−	8223.22i	−0.147194	−	0.870123i
$448$	9962.71	−	3230.28i	1.05066	−	0.340662i
$449$		−	8031.38i		−	0.844152i	−0.906560	−	0.422076i	$-0.861301\pi$
$449$		−	8031.38i		−	0.844152i	0.906560	−	0.422076i	$-0.138699\pi$
$450$	−430.420	+	498.700i	−0.0450894	+	0.0522421i
$451$	6698.41	−	3867.33i	0.699369	−	0.403781i
$452$			2793.77i			0.290725i
$453$	−5701.21	+	964.443i	−0.591316	+	0.100030i
$454$	−115.164	+	66.4901i	−0.0119051	+	0.00687342i
$455$	−4588.10	+	5089.27i	−0.472732	+	0.524371i
$456$	346.289	−	931.218i	0.0355624	−	0.0956322i
$457$	−5105.37	−	8842.75i	−0.522580	−	0.905135i	−0.999655	−	0.0262722i	$-0.991636\pi$
$457$	−5105.37	−	8842.75i	−0.522580	−	0.905135i	0.477075	−	0.878863i	$-0.341697\pi$
$458$	1749.47	+	3030.17i	0.178488	+	0.309150i
$459$	−551.639	−	334.025i	−0.0560966	−	0.0339672i
$460$	785.390	+	453.445i	0.0796065	+	0.0459608i
$461$	−8240.35	+	14272.7i	−0.832519	+	1.44197i	0.0635154	+	0.997981i	$0.479769\pi$
$461$	−8240.35	+	14272.7i	−0.832519	+	1.44197i	−0.896034	+	0.443984i	$0.853565\pi$
$462$	−5127.21	−	3258.08i	−0.516319	−	0.328094i
$463$	−1041.49	−	1803.91i	−0.104540	−	0.181069i	0.809010	−	0.587795i	$-0.200004\pi$
$463$	−1041.49	−	1803.91i	−0.104540	−	0.181069i	−0.913550	+	0.406726i	$0.866670\pi$
$464$			10239.4i			1.02447i
$465$	−16242.6	−	6040.09i	−1.61986	−	0.602371i
$466$	−3932.68			−0.390940
$467$	−3810.55	+	6600.06i	−0.377583	+	0.653993i	−0.990710	−	0.135992i	$-0.956578\pi$
$467$	−3810.55	+	6600.06i	−0.377583	+	0.653993i	0.613127	+	0.789984i	$0.289911\pi$
$468$	−662.198	−	1901.25i	−0.0654063	−	0.187789i
$469$	3841.87	−	18019.9i	0.378254	−	1.77416i
$470$	−5065.85	−	2924.77i	−0.497170	−	0.287041i
$471$	−842.522	−	313.306i	−0.0824232	−	0.0306504i
$472$	−5765.53	−	3328.73i	−0.562246	−	0.324613i
$473$	2746.38	+	1585.62i	0.266974	+	0.154138i
$474$	5103.19	+	1897.71i	0.494509	+	0.183891i
$475$	−68.0916	−	39.3127i	−0.00657739	−	0.00379746i
$476$	174.947	−	56.7243i	0.0168460	−	0.00546209i
$477$	−6256.32	+	7248.79i	−0.600539	+	0.695806i
$478$	2552.10	−	4420.37i	0.244206	−	0.422977i
$479$	6836.50			0.652124			0.326062	−	0.945348i	$-0.394278\pi$
$479$	6836.50			0.652124			0.326062	+	0.945348i	$0.394278\pi$
$480$	−4949.58	−	1840.58i	−0.470659	−	0.175022i
$481$		−	1953.61i		−	0.185192i
$482$	2653.21	+	4595.49i	0.250727	+	0.434272i
$483$	1744.04	+	3340.84i	0.164299	+	0.314728i
$484$	−700.636	+	1213.54i	−0.0657997	+	0.113968i
$485$	−8376.63	−	4836.25i	−0.784254	−	0.452789i
$486$	−1902.00	+	8954.03i	−0.177524	+	0.835727i
$487$	9331.03	+	16161.8i	0.868233	+	1.50382i	0.863801	+	0.503833i	$0.168077\pi$
$487$	9331.03	+	16161.8i	0.868233	+	1.50382i	0.00443162	+	0.999990i	$0.498589\pi$
$488$	−9206.51	−	15946.1i	−0.854014	−	1.47920i
$489$	3984.70	−	10715.4i	0.368496	−	0.990936i
$490$	−3623.84	+	8112.31i	−0.334099	+	0.747912i
$491$	8389.01	−	4843.40i	0.771061	−	0.445172i	−0.0621920	−	0.998064i	$-0.519809\pi$
$491$	8389.01	−	4843.40i	0.771061	−	0.445172i	0.833253	+	0.552892i	$0.186476\pi$
$492$	3277.27	−	554.399i	0.300307	−	0.0508013i
$493$			1119.31i			0.102254i
$494$	−562.505	+	324.762i	−0.0512314	+	0.0295784i
$495$	2486.72	+	7139.68i	0.225798	+	0.648293i
$496$		−	13082.7i		−	1.18434i
$497$	6506.83	+	20068.1i	0.587266	+	1.81122i
$498$	2064.17	+	12202.1i	0.185738	+	1.09797i
$499$	−4149.59			−0.372267			−0.186134	−	0.982524i	$-0.559596\pi$
$499$	−4149.59			−0.372267			−0.186134	+	0.982524i	$0.559596\pi$
$500$	−1564.26	+	2709.38i	−0.139912	+	0.242334i
$501$	−453.420	−	548.061i	−0.0404337	−	0.0488733i
$502$	6817.38	−	3936.01i	0.606124	−	0.349946i
$503$	−11384.6			−1.00917			−0.504586	−	0.863362i	$-0.668355\pi$
$503$	−11384.6			−1.00917			−0.504586	+	0.863362i	$0.668355\pi$
$504$	−7417.50	−	9783.65i	−0.655559	−	0.864680i
$505$	2986.94			0.263202
$506$	2140.89	−	1236.04i	0.188091	−	0.108595i
$507$	1821.43	−	4898.08i	0.159551	−	0.429056i
$508$	2238.19	−	3876.65i	0.195479	−	0.338580i
$509$	2020.20			0.175921			0.0879605	−	0.996124i	$-0.471965\pi$
$509$	2020.20			0.175921			0.0879605	+	0.996124i	$0.471965\pi$
$510$	579.900	+	215.646i	0.0503498	+	0.0187234i
$511$	−15392.7	+	17074.1i	−1.33255	+	1.47811i
$512$		−	12246.2i		−	1.05705i
$513$	−1092.31	−	22.7937i	−0.0940087	−	0.00196173i
$514$	−4368.58	+	2522.20i	−0.374883	+	0.216439i
$515$		−	13809.2i		−	1.18157i
$516$	868.703	+	1050.03i	0.0741134	+	0.0895829i
$517$	5108.63	−	2949.47i	0.434579	−	0.250904i
$518$	−781.312	−	2409.69i	−0.0662720	−	0.204393i
$519$	4941.67	+	5973.13i	0.417949	+	0.505186i
$520$	4542.02	+	7867.01i	0.383040	+	0.663445i
$521$	−5932.30	−	10275.0i	−0.498846	−	0.864027i	0.501153	−	0.865359i	$-0.332909\pi$
$521$	−5932.30	−	10275.0i	−0.498846	−	0.864027i	−0.999999	+	0.00133177i	$0.999576\pi$
$522$	15003.9	−	5225.82i	1.25806	−	0.438176i
$523$	5064.90	+	2924.22i	0.423466	+	0.244488i	0.696559	−	0.717499i	$-0.254713\pi$
$523$	5064.90	+	2924.22i	0.423466	+	0.244488i	−0.273093	+	0.961988i	$0.588047\pi$
$524$	−19.1593	+	33.1848i	−0.00159728	+	0.00276658i
$525$	−861.324	+	449.642i	−0.0716024	+	0.0373790i
$526$	2150.49	+	3724.76i	0.178262	+	0.308759i
$527$		−	1430.12i		−	0.118210i
$528$	−4397.73	+	3638.31i	−0.362474	+	0.299881i
$529$	10633.4			0.873952
$530$	4593.23	−	7955.71i	0.376448	−	0.652026i
$531$	−1371.44	+	7191.39i	−0.112082	+	0.587721i
$532$	208.630	−	231.420i	0.0170024	−	0.0188596i
$533$	−8850.55	−	5109.87i	−0.719249	−	0.415259i
$534$	316.818	+	1872.84i	0.0256743	+	0.151771i
$535$	15069.9	+	8700.64i	1.21781	+	0.703105i
$536$	−21153.9	−	12213.2i	−1.70468	−	0.984197i
$537$	−2723.54	+	2253.23i	−0.218863	+	0.181069i
$538$	−6411.76	−	3701.83i	−0.513812	−	0.296649i
$539$	−5257.57	−	7255.25i	−0.420148	−	0.579788i
$540$	−67.7824	+	3248.22i	−0.00540165	+	0.258854i
$541$	−5802.24	+	10049.8i	−0.461105	+	0.798657i	−0.999016	−	0.0443443i	$-0.985880\pi$
$541$	−5802.24	+	10049.8i	−0.461105	+	0.798657i	0.537911	+	0.843001i	$0.319213\pi$
$542$	309.573			0.0245337
$543$	−1971.94	−	11656.9i	−0.155846	−	0.921266i
$544$		−	435.796i		−	0.0343467i
$545$	4575.20	+	7924.47i	0.359596	+	0.622839i
$546$	−340.857	+	8019.36i	−0.0267168	+	0.628566i
$547$	−2895.79	+	5015.65i	−0.226353	+	0.392055i	−0.956724	−	0.290995i	$-0.906014\pi$
$547$	−2895.79	+	5015.65i	−0.226353	+	0.392055i	0.730372	+	0.683050i	$0.239347\pi$
$548$	−3751.28	−	2165.80i	−0.292421	−	0.168829i
$549$	−13229.8	+	15328.5i	−1.02848	+	1.19163i
$550$	318.672	+	551.957i	0.0247059	+	0.0427918i
$551$	948.145	+	1642.24i	0.0733073	+	0.126972i
$552$	4926.26	−	833.348i	0.379847	−	0.0642566i
$553$	5964.47	+	5377.10i	0.458653	+	0.413486i
$554$	−10385.3	+	5995.95i	−0.796441	+	0.459826i
$555$	−1098.85	+	2954.96i	−0.0840425	+	0.226002i
$556$		−	1542.12i		−	0.117627i
$557$	5630.99	−	3251.06i	0.428353	−	0.247310i	−0.270292	−	0.962779i	$-0.587120\pi$
$557$	5630.99	−	3251.06i	0.428353	−	0.247310i	0.698645	+	0.715469i	$0.253787\pi$
$558$	−19170.2	+	6676.91i	−1.45437	+	0.506552i
$559$		−	4190.15i		−	0.317038i
$560$	6200.26	+	5589.67i	0.467873	+	0.421798i
$561$	−480.730	+	397.716i	−0.0361791	+	0.0299315i
$562$	10189.1			0.764771
$563$	2513.57	−	4353.63i	0.188160	−	0.325903i	−0.756477	−	0.654021i	$-0.773081\pi$
$563$	2513.57	−	4353.63i	0.188160	−	0.325903i	0.944637	+	0.328117i	$0.106414\pi$
$564$	2499.46	−	422.819i	0.186606	−	0.0315672i
$565$	−12004.9	+	6931.05i	−0.893896	+	0.516091i
$566$	−7013.60			−0.520854
$567$	−7477.24	+	11241.7i	−0.553817	+	0.832638i
$568$	27968.4			2.06607
$569$	−772.957	+	446.267i	−0.0569491	+	0.0328796i	−0.528204	−	0.849117i	$-0.677134\pi$
$569$	−772.957	+	446.267i	−0.0569491	+	0.0328796i	0.471255	+	0.881997i	$0.343801\pi$
$570$	1033.49	−	174.830i	0.0759443	−	0.0128471i
$571$	−8709.40	+	15085.1i	−0.638313	+	1.10559i	0.347489	+	0.937684i	$0.387034\pi$
$571$	−8709.40	+	15085.1i	−0.638313	+	1.10559i	−0.985803	+	0.167907i	$0.946299\pi$
$572$	−1947.82			−0.142382
$573$	13404.0	−	11089.3i	0.977242	−	0.808489i
$574$	−12960.3	−	2763.17i	−0.942429	−	0.200928i
$575$		−	395.394i		−	0.0286766i
$576$	−14419.1	+	5022.11i	−1.04305	+	0.363290i
$577$	5638.05	−	3255.13i	0.406785	−	0.234858i	−0.282622	−	0.959231i	$-0.591204\pi$
$577$	5638.05	−	3255.13i	0.406785	−	0.234858i	0.689407	+	0.724374i	$0.257871\pi$
$578$		−	11821.4i		−	0.850699i
$579$	3739.71	−	10056.6i	0.268423	−	0.721827i
$580$	4883.57	−	2819.53i	0.349619	−	0.201853i
$581$	−3806.03	+	17851.8i	−0.271774	+	1.27473i
$582$	−11171.7	+	1889.86i	−0.795674	+	0.134600i
$583$	4632.02	+	8022.89i	0.329054	+	0.569939i
$584$	15238.1	+	26393.2i	1.07972	+	1.87013i
$585$	6526.90	−	7562.29i	0.461289	−	0.534466i
$586$	770.507	+	444.852i	0.0543163	+	0.0313595i
$587$	2173.87	−	3765.25i	0.152854	−	0.264750i	−0.779422	−	0.626500i	$-0.784487\pi$
$587$	2173.87	−	3765.25i	0.152854	−	0.264750i	0.932275	+	0.361749i	$0.117820\pi$
$588$	−1030.96	−	3709.79i	−0.0723065	−	0.260186i
$589$	−1211.42	−	2098.25i	−0.0847468	−	0.146786i
$590$		−	7023.70i		−	0.490103i
$591$	−2505.20	−	14809.3i	−0.174366	−	1.03075i
$592$	−2380.09			−0.165238
$593$	7744.80	−	13414.4i	0.536325	−	0.928942i	−0.462773	−	0.886477i	$-0.653145\pi$
$593$	7744.80	−	13414.4i	0.536325	−	0.928942i	0.999098	−	0.0424652i	$-0.0135212\pi$
$594$	7575.68	+	4587.17i	0.523290	+	0.316859i
$595$	677.771	+	611.026i	0.0466990	+	0.0421002i
$596$	−3002.93	−	1733.74i	−0.206384	−	0.119156i
$597$	−4656.36	+	3852.28i	−0.319216	+	0.264093i
$598$	−2828.74	−	1633.17i	−0.193438	−	0.111681i
$599$	−11074.4	−	6393.82i	−0.755406	−	0.436134i	0.0722376	−	0.997387i	$-0.476986\pi$
$599$	−11074.4	−	6393.82i	−0.755406	−	0.436134i	−0.827644	+	0.561253i	$0.810319\pi$
$600$	214.851	+	1270.07i	0.0146187	+	0.0864173i
$601$	−14961.0	−	8637.74i	−1.01543	−	0.586258i	−0.102652	−	0.994717i	$-0.532733\pi$
$601$	−14961.0	−	8637.74i	−1.01543	−	0.586258i	−0.912776	+	0.408460i	$0.866066\pi$
$602$	−1675.77	−	5168.35i	−0.113454	−	0.349911i
$603$	−5031.84	+	26385.4i	−0.339821	+	1.78192i
$604$	−1202.02	+	2081.95i	−0.0809757	+	0.140254i
$605$	−6952.81			−0.467227
$606$	2695.91	−	2230.37i	0.180716	−	0.149509i
$607$		−	10285.3i		−	0.687755i	−0.939014	−	0.343878i	$-0.888259\pi$
$607$		−	10285.3i		−	0.687755i	0.939014	−	0.343878i	$-0.111741\pi$
$608$	−369.155	−	639.395i	−0.0246237	−	0.0426495i
$609$	23412.6	+	995.135i	1.55784	+	0.0662149i
$610$	9712.97	−	16823.4i	0.644699	−	1.11665i
$611$	−6749.99	−	3897.11i	−0.446932	−	0.258036i
$612$	−253.202	+	88.1892i	−0.0167240	+	0.00582490i
$613$	12096.2	+	20951.3i	0.797002	+	1.38045i	0.921560	+	0.388236i	$0.126916\pi$
$613$	12096.2	+	20951.3i	0.797002	+	1.38045i	−0.124558	+	0.992212i	$0.539751\pi$
$614$	−1039.78	−	1800.95i	−0.0683420	−	0.118372i
$615$	10512.8	+	12707.2i	0.689299	+	0.833174i
$616$	−11299.4	+	3663.68i	−0.739065	+	0.239633i
$617$	2592.10	−	1496.55i	0.169132	−	0.0976481i	−0.413045	−	0.910711i	$-0.635535\pi$
$617$	2592.10	−	1496.55i	0.169132	−	0.0976481i	0.582176	+	0.813063i	$0.302201\pi$
$618$	−10311.4	−	12463.7i	−0.671176	−	0.811269i
$619$		−	6609.48i		−	0.429172i	−0.976705	−	0.214586i	$-0.931160\pi$
$619$		−	6609.48i		−	0.429172i	0.976705	−	0.214586i	$-0.0688402\pi$
$620$	−6239.63	+	3602.45i	−0.404177	+	0.233352i
$621$	−2647.24	−	4814.40i	−0.171063	−	0.311104i
$622$		−	11238.2i		−	0.724454i
$623$	−584.168	+	2739.98i	−0.0375670	+	0.176204i
$624$	7068.56	+	2628.56i	0.453476	+	0.168632i
$625$	−14261.0			−0.912704
$626$	4961.90	−	8594.26i	0.316801	−	0.548715i
$627$	−368.424	+	990.742i	−0.0234664	+	0.0631044i
$628$	−323.656	+	186.863i	−0.0205657	+	0.0118736i
$629$	−260.175			−0.0164926
$630$	5026.22	−	11938.1i	0.317856	−	0.754958i
$631$	−17308.9			−1.09201			−0.546005	−	0.837782i	$-0.683852\pi$
$631$	−17308.9			−1.09201			−0.546005	+	0.837782i	$0.683852\pi$
$632$	9219.88	−	5323.10i	0.580296	−	0.335034i
$633$	3579.38	+	4326.49i	0.224751	+	0.271663i
$634$	5709.18	−	9888.59i	0.357635	−	0.619442i
$635$	22210.8			1.38805
$636$	664.021	+	3925.29i	0.0413996	+	0.244730i
$637$	−4828.59	+	10809.2i	−0.300338	+	0.672336i
$638$		−	15371.5i		−	0.953861i
$639$	−10116.2	−	29044.7i	−0.626274	−	1.79811i
$640$	5645.09	−	3259.19i	0.348659	−	0.201298i
$641$			25361.0i			1.56271i	0.624084	+	0.781357i	$0.285472\pi$
$641$			25361.0i			1.56271i	−0.624084	+	0.781357i	$0.714528\pi$
$642$	20098.4	−	3399.94i	1.23555	−	0.209011i
$643$	10112.2	−	5838.27i	0.620195	−	0.358070i	−0.156750	−	0.987638i	$-0.550102\pi$
$643$	10112.2	−	5838.27i	0.620195	−	0.358070i	0.776945	+	0.629568i	$0.216768\pi$
$644$	1532.44	+	326.718i	0.0937677	+	0.0199915i
$645$	−2356.84	+	6337.85i	−0.143876	+	0.386903i
$646$	43.2507	+	74.9124i	0.00263417	+	0.00456252i
$647$	5873.10	+	10172.5i	0.356871	+	0.618118i	0.987436	−	0.158018i	$-0.0505103\pi$
$647$	5873.10	+	10172.5i	0.356871	+	0.618118i	−0.630566	+	0.776136i	$0.717177\pi$
$648$	11119.4	+	14026.2i	0.674094	+	0.850309i
$649$	6134.07	+	3541.51i	0.371006	+	0.214201i
$650$	421.059	−	729.296i	0.0254082	−	0.0440082i
$651$	−29913.7	−	1271.46i	−1.80094	−	0.0765476i
$652$	−2376.57	−	4116.34i	−0.142751	−	0.247252i
$653$		−	6900.05i		−	0.413507i	−0.978393	−	0.206753i	$-0.933710\pi$
$653$		−	6900.05i		−	0.413507i	0.978393	−	0.206753i	$-0.0662898\pi$
$654$	10046.7	+	3736.02i	0.600697	+	0.223379i
$655$	−190.129			−0.0113419
$656$	−6225.35	+	10782.6i	−0.370517	+	0.641754i
$657$	21897.2	−	25370.9i	1.30029	−	1.50656i
$658$	−9884.37	−	2107.37i	−0.585612	−	0.124854i
$659$	−4602.35	−	2657.17i	−0.272052	−	0.157069i	0.357768	−	0.933811i	$-0.383538\pi$
$659$	−4602.35	−	2657.17i	−0.272052	−	0.157069i	−0.629820	+	0.776741i	$0.716871\pi$
$660$	2946.20	+	1095.59i	0.173759	+	0.0646151i
$661$	16093.7	+	9291.68i	0.947006	+	0.546754i	0.892150	−	0.451740i	$-0.149197\pi$
$661$	16093.7	+	9291.68i	0.947006	+	0.546754i	0.0548563	+	0.998494i	$0.482530\pi$
$662$	2480.88	+	1432.34i	0.145653	+	0.0840927i
$663$	772.688	+	287.337i	0.0452620	+	0.0168314i
$664$	20956.6	+	12099.3i	1.22481	+	0.707143i
$665$	1512.01	+	322.363i	0.0881701	+	0.0187980i
$666$	1214.70	+	3487.56i	0.0706740	+	0.202913i
$667$	−4768.06	+	8258.52i	−0.276792	+	0.479417i
$668$	−295.736			−0.0171293
$669$	−30156.6	−	11214.2i	−1.74278	−	0.648082i
$670$		−	25770.1i		−	1.48595i
$671$	9794.99	+	16965.4i	0.563534	+	0.976070i
$672$	−9115.54	−	387.450i	−0.523273	−	0.0222414i
$673$	5147.44	−	8915.63i	0.294828	−	0.510657i	−0.680117	−	0.733104i	$-0.738071\pi$
$673$	5147.44	−	8915.63i	0.294828	−	0.510657i	0.974945	+	0.222447i	$0.0714043\pi$
$674$	−13812.3	−	7974.54i	−0.789363	−	0.455739i
$675$	1241.23	−	682.502i	0.0707779	−	0.0389178i
$676$	−1086.34	−	1881.60i	−0.0618084	−	0.107055i
$677$	−2634.11	−	4562.41i	−0.149538	−	0.259007i	0.781519	−	0.623881i	$-0.214445\pi$
$677$	−2634.11	−	4562.41i	−0.149538	−	0.259007i	−0.931057	+	0.364875i	$0.881112\pi$
$678$	−5659.76	+	15219.9i	−0.320593	+	0.862118i
$679$	−16344.3	−	3484.63i	−0.923765	−	0.196948i
$680$	1047.70	−	604.890i	0.0590845	−	0.0341125i
$681$	281.935	−	47.6935i	0.0158646	−	0.00268373i
$682$			19639.8i			1.10271i
$683$	15591.8	−	9001.90i	0.873502	−	0.504317i	0.00499159	−	0.999988i	$-0.498411\pi$
$683$	15591.8	−	9001.90i	0.873502	−	0.504317i	0.868510	+	0.495671i	$0.165078\pi$
$684$	−296.791	+	343.873i	−0.0165908	+	0.0192227i
$685$		−	21492.5i		−	1.19881i
$686$	−1632.88	+	15263.8i	−0.0908797	+	0.849526i
$687$	−1254.90	−	7418.21i	−0.0696905	−	0.411969i
$688$	−5104.85			−0.282879
$689$	6120.25	−	10600.6i	0.338408	−	0.586140i
$690$	3360.03	+	4061.36i	0.185383	+	0.224077i
$691$	8943.10	−	5163.30i	0.492347	−	0.284257i	−0.233201	−	0.972429i	$-0.574920\pi$
$691$	8943.10	−	5163.30i	0.492347	−	0.284257i	0.725548	+	0.688172i	$0.241587\pi$
$692$	3223.13			0.177059
$693$	7891.63	+	10409.0i	0.432580	+	0.570572i
$694$	−6337.26			−0.346627
$695$	6626.55	−	3825.84i	0.361668	−	0.208809i
$696$	10828.2	−	29118.6i	0.589717	−	1.58583i
$697$	−680.514	+	1178.68i	−0.0369818	+	0.0640543i
$698$	−17003.1			−0.922028
$699$	7925.97	+	2947.40i	0.428881	+	0.159486i
$700$	−84.2333	+	395.087i	−0.00454817	+	0.0213327i
$701$			26276.7i			1.41577i	0.706326	+	0.707887i	$0.250351\pi$
$701$			26276.7i			1.41577i	−0.706326	+	0.707887i	$0.749649\pi$
$702$	244.132	−	11699.1i	0.0131256	−	0.628997i
$703$	−381.726	+	220.390i	−0.0204795	+	0.0118238i
$704$			14772.3i			0.790841i
$705$	8017.76	+	9691.28i	0.428321	+	0.517723i
$706$	−21872.5	+	12628.1i	−1.16598	+	0.673181i
$707$	4909.08	−	1591.71i	0.261139	−	0.0846709i
$708$	1940.26	+	2345.24i	0.102993	+	0.124491i
$709$	6475.59	+	11216.0i	0.343012	+	0.594115i	0.984991	−	0.172608i	$-0.0552194\pi$
$709$	6475.59	+	11216.0i	0.343012	+	0.594115i	−0.641978	+	0.766723i	$0.721886\pi$
$710$	14753.5	+	25553.8i	0.779844	+	1.35073i
$711$	−8862.77	−	7649.32i	−0.467482	−	0.403476i
$712$	3216.52	+	1857.06i	0.169303	+	0.0977473i
$713$	6092.05	−	10551.7i	0.319984	−	0.554229i
$714$	1067.99	+	45.3942i	0.0559783	+	0.00237932i
$715$	−4832.35	−	8369.87i	−0.252755	−	0.437784i
$716$			1469.63i			0.0767078i
$717$	−8456.44	+	6996.15i	−0.440462	+	0.364402i
$718$	27588.5			1.43397
$719$	−6027.33	+	10439.6i	−0.312631	+	0.541492i	−0.978931	−	0.204191i	$-0.934544\pi$
$719$	−6027.33	+	10439.6i	−0.312631	+	0.541492i	0.666300	+	0.745684i	$0.267877\pi$
$720$	−9213.14	−	7951.72i	−0.476880	−	0.411588i
$721$	−7358.78	−	22695.7i	−0.380104	−	1.17230i
$722$	−14227.5	−	8214.22i	−0.733367	−	0.423410i
$723$	−1903.15	−	11250.3i	−0.0978962	−	0.578704i
$724$	−4256.85	−	2457.69i	−0.218515	−	0.126160i
$725$	−2129.18	−	1229.28i	−0.109070	−	0.0629717i
$726$	−6275.37	+	5191.72i	−0.320800	+	0.265403i
$727$	−24377.4	−	14074.3i	−1.24361	−	0.718000i	−0.273785	−	0.961791i	$-0.588276\pi$
$727$	−24377.4	−	14074.3i	−1.24361	−	0.718000i	−0.969828	+	0.243791i	$0.921609\pi$
$728$	11657.1	+	10509.2i	0.593464	+	0.535021i
$729$	10544.0	−	16620.6i	0.535693	−	0.844413i
$730$	−16076.4	+	27845.1i	−0.815087	+	1.41177i
$731$	−558.029			−0.0282345
$732$	1404.16	+	8300.53i	0.0709004	+	0.419121i
$733$		−	6108.23i		−	0.307794i	−0.988087	−	0.153897i	$-0.950818\pi$
$733$		−	6108.23i		−	0.307794i	0.988087	−	0.153897i	$-0.0491824\pi$
$734$	9166.90	+	15877.5i	0.460976	+	0.798434i
$735$	13383.4	−	13633.7i	0.671639	−	0.684200i
$736$	1856.42	−	3215.41i	0.0929733	−	0.161035i
$737$	22506.0	+	12993.9i	1.12486	+	0.649437i
$738$	18977.1	+	3619.02i	0.946551	+	0.180512i
$739$	−8878.08	−	15377.3i	−0.441929	−	0.765443i	0.555904	−	0.831247i	$-0.312372\pi$
$739$	−8878.08	−	15377.3i	−0.441929	−	0.765443i	−0.997833	+	0.0658036i	$0.979039\pi$
$740$	655.380	+	1135.15i	0.0325571	+	0.0563906i
$741$	1377.08	−	232.953i	0.0682702	−	0.0115489i
$742$	3309.53	−	15523.0i	0.163742	−	0.768016i
$743$	−8335.34	+	4812.41i	−0.411567	+	0.237618i	−0.691463	−	0.722412i	$-0.743033\pi$
$743$	−8335.34	+	4812.41i	−0.411567	+	0.237618i	0.279896	+	0.960030i	$0.409700\pi$
$744$	−13835.0	+	37204.2i	−0.681742	+	1.83330i
$745$		−	17205.0i		−	0.846095i
$746$	−4488.87	+	2591.65i	−0.220307	+	0.127194i
$747$	4984.90	−	26139.3i	0.244161	−	1.28030i
$748$			259.404i			0.0126802i
$749$	29404.2	+	6269.02i	1.43445	+	0.305828i
$750$	−14010.6	+	11591.2i	−0.682125	+	0.564333i
$751$	−16189.7			−0.786643			−0.393322	−	0.919401i	$-0.628674\pi$
$751$	−16189.7			−0.786643			−0.393322	+	0.919401i	$0.628674\pi$
$752$	−4747.84	+	8223.51i	−0.230234	+	0.398777i
$753$	−16689.7	+	2823.31i	−0.807712	+	0.136636i
$754$	−17589.2	+	10155.1i	−0.849549	+	0.490488i
$755$	−11928.3			−0.574987
$756$	1619.54	+	5374.63i	0.0779129	+	0.258562i
$757$	−16960.5			−0.814318			−0.407159	−	0.913357i	$-0.633481\pi$
$757$	−16960.5			−0.814318			−0.407159	+	0.913357i	$0.633481\pi$
$758$	3083.33	−	1780.16i	0.147746	−	0.0853013i
$759$	−5241.14	+	886.616i	−0.250648	+	0.0424007i
$760$	1024.78	−	1774.98i	0.0489115	−	0.0847173i
$761$	−1386.80			−0.0660597			−0.0330299	−	0.999454i	$-0.510516\pi$
$761$	−1386.80			−0.0660597			−0.0330299	+	0.999454i	$0.510516\pi$
$762$	20046.7	−	16585.0i	0.953039	−	0.788465i
$763$	11742.3	+	10585.9i	0.557141	+	0.502275i
$764$		−	7232.86i		−	0.342507i
$765$	−1007.12	−	869.229i	−0.0475980	−	0.0410811i
$766$	−26460.7	+	15277.1i	−1.24812	+	0.720605i
$767$		−	9358.73i		−	0.440579i
$768$	−5532.12	+	14876.6i	−0.259926	+	0.698977i
$769$	−18569.7	+	10721.2i	−0.870795	+	0.502754i	−0.867612	−	0.497241i	$-0.834346\pi$
$769$	−18569.7	+	10721.2i	−0.870795	+	0.502754i	−0.00318241	+	0.999995i	$0.501013\pi$
$770$	−9307.86	−	8391.24i	−0.435626	−	0.392726i
$771$	10694.8	−	1809.18i	0.499563	−	0.0845084i
$772$	−2230.45	−	3863.26i	−0.103984	−	0.180106i
$773$	6650.89	+	11519.7i

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	63.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.09278 - 1.20827i) q^{2} +(-5.12336 + 0.866692i) q^{3} +(-1.08019 + 1.87094i) q^{4} -10.7193 q^{5} +(-9.67487 + 8.00418i) q^{6} +(-17.6173 + 5.71220i) q^{7} +24.5529i q^{8} +(25.4977 - 8.88075i) q^{9} +O(q^{10})\)	\(q+(2.09278 - 1.20827i) q^{2} +(-5.12336 + 0.866692i) q^{3} +(-1.08019 + 1.87094i) q^{4} -10.7193 q^{5} +(-9.67487 + 8.00418i) q^{6} +(-17.6173 + 5.71220i) q^{7} +24.5529i q^{8} +(25.4977 - 8.88075i) q^{9} +(-22.4331 + 12.9518i) q^{10} -26.1223i q^{11} +(3.91266 - 10.5217i) q^{12} +(-29.8910 + 17.2576i) q^{13} +(-29.9673 + 33.2408i) q^{14} +(54.9189 - 9.29033i) q^{15} +(21.0249 + 36.4162i) q^{16} +(2.29830 + 3.98078i) q^{17} +(42.6307 - 49.3934i) q^{18} +(6.74409 + 3.89370i) q^{19} +(11.5788 - 20.0551i) q^{20} +(85.3093 - 44.5345i) q^{21} +(-31.5627 - 54.6682i) q^{22} +39.1615i q^{23} +(-21.2798 - 125.793i) q^{24} -10.0965 q^{25} +(-41.7035 + 72.2327i) q^{26} +(-122.937 + 67.5979i) q^{27} +(8.34283 - 39.1311i) q^{28} +(210.884 + 121.754i) q^{29} +(103.708 - 85.7993i) q^{30} +(-269.441 - 155.562i) q^{31} +(-82.1062 - 47.4041i) q^{32} +(22.6400 + 133.834i) q^{33} +(9.61969 + 5.55393i) q^{34} +(188.846 - 61.2308i) q^{35} +(-10.9269 + 57.2974i) q^{36} +(-28.3008 + 49.0184i) q^{37} +18.8185 q^{38} +(138.186 - 114.323i) q^{39} -263.190i q^{40} +(148.047 + 256.425i) q^{41} +(124.724 - 196.277i) q^{42} +(-60.7001 + 105.136i) q^{43} +(48.8731 + 28.2169i) q^{44} +(-273.318 + 95.1955i) q^{45} +(47.3176 + 81.9564i) q^{46} +(112.910 + 195.566i) q^{47} +(-139.280 - 168.351i) q^{48} +(277.742 - 201.268i) q^{49} +(-21.1297 + 12.1992i) q^{50} +(-15.2252 - 18.4031i) q^{51} -74.5656i q^{52} +(-307.128 + 177.321i) q^{53} +(-175.604 + 290.008i) q^{54} +280.013i q^{55} +(-140.251 - 432.556i) q^{56} +(-37.9271 - 14.1038i) q^{57} +588.443 q^{58} +(-135.574 + 234.821i) q^{59} +(-41.9410 + 112.785i) q^{60} +(-649.461 + 374.967i) q^{61} -751.841 q^{62} +(-398.473 + 302.103i) q^{63} -565.506 q^{64} +(320.411 - 184.989i) q^{65} +(209.088 + 252.730i) q^{66} +(-497.425 + 861.565i) q^{67} -9.93038 q^{68} +(-33.9410 - 200.639i) q^{69} +(321.229 - 356.318i) q^{70} -1139.11i q^{71} +(218.048 + 626.041i) q^{72} +(1074.95 - 620.624i) q^{73} +136.780i q^{74} +(51.7280 - 8.75054i) q^{75} +(-14.5697 + 8.41184i) q^{76} +(149.216 + 460.205i) q^{77} +(151.059 - 406.218i) q^{78} +(-216.802 - 375.512i) q^{79} +(-225.373 - 390.357i) q^{80} +(571.265 - 452.877i) q^{81} +(619.659 + 357.760i) q^{82} +(492.785 - 853.528i) q^{83} +(-8.82872 + 207.714i) q^{84} +(-24.6362 - 42.6712i) q^{85} +293.367i q^{86} +(-1185.96 - 441.017i) q^{87} +641.377 q^{88} +(75.6350 - 131.004i) q^{89} +(-456.972 + 529.463i) q^{90} +(428.022 - 474.777i) q^{91} +(-73.2687 - 42.3017i) q^{92} +(1515.27 + 563.478i) q^{93} +(472.591 + 272.851i) q^{94} +(-72.2920 - 41.7378i) q^{95} +(461.745 + 171.707i) q^{96} +(781.452 + 451.172i) q^{97} +(338.067 - 756.794i) q^{98} +(-231.986 - 666.058i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44q - 3q^{2} - 3q^{3} + 81q^{4} - 6q^{5} - 24q^{6} + 5q^{7} - 3q^{9} + O(q^{10}) \)	\( 44q - 3q^{2} - 3q^{3} + 81q^{4} - 6q^{5} - 24q^{6} + 5q^{7} - 3q^{9} - 6q^{10} - 3q^{12} + 36q^{13} + 129q^{14} - 141q^{15} - 263q^{16} + 72q^{17} - 15q^{18} - 6q^{19} - 24q^{20} - 306q^{21} + 14q^{22} - 66q^{24} + 698q^{25} + 96q^{26} - 432q^{27} - 156q^{28} - 132q^{29} + 852q^{30} + 177q^{31} - 501q^{32} + 849q^{33} - 24q^{34} - 765q^{35} + 1122q^{36} + 82q^{37} - 1746q^{38} - 645q^{39} - 618q^{41} - 963q^{42} + 82q^{43} - 603q^{44} + 303q^{45} + 266q^{46} - 201q^{47} + 1569q^{48} + 515q^{49} - 1845q^{50} + 417q^{51} - 564q^{53} - 684q^{54} + 3600q^{56} + 1170q^{57} - 538q^{58} + 747q^{59} - 516q^{60} - 1209q^{61} + 2904q^{62} + 1557q^{63} - 1144q^{64} - 831q^{65} + 1029q^{66} + 295q^{67} + 7008q^{68} + 1005q^{69} - 390q^{70} - 1119q^{72} - 6q^{73} - 1788q^{75} + 144q^{76} - 1203q^{77} - 5985q^{78} - 551q^{79} + 4239q^{80} + 3741q^{81} + 18q^{82} - 1830q^{83} - 7725q^{84} - 237q^{85} - 2130q^{87} + 1246q^{88} - 4266q^{89} - 9993q^{90} - 1140q^{91} + 7896q^{92} - 1479q^{93} - 3q^{94} - 1053q^{95} + 5034q^{96} + 792q^{97} - 5667q^{98} + 4335q^{99} + O(q^{100}) \)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Properties

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